# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/displaystyleT;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2087.png"
 ALT="$\displaystyle T$">|; 

$key = q/(A)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3600.png"
 ALT="$ (A)^2$">|; 

$key = q/displaystyle=frac{nablarho}{epsilon_0}+mu_0,frac{partial{bfj}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2751.png"
 ALT="$\displaystyle = \frac{\nabla \rho}{\epsilon_0} + \mu_0 \frac{\partial {\bf j}}{\partial t},$">|; 

$key = q/displaystylealpha_{0,0}(r',theta',varphi')=frac{Y_{0,0}^ast(theta',varphi')}{a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="$\displaystyle \alpha_{0,0}(r',\theta',\varphi') = \frac{Y_{0,0}^\ast(\theta',\varphi')}{a}.$">|; 

$key = q/displaystyledx^{,2}+dy^{,2}+dz^{,2}-c^{,2},dt^{,2}=d{x'}^{,2}+d{y'}^{,2}+d{z'}^{,2}-c^{,2},d{t'}^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3611.png"
 ALT="$\displaystyle dx^{ 2} + dy^{ 2} + dz^{ 2} - c^{ 2} dt^{ 2} = d{x'}^{ 2} + d{y'}^{ 2}+d{z'}^{ 2} -c^{ 2} d{t'}^{ 2}.$">|; 

$key = q/displaystyleW=frac{1}{2}frac{1}{4pi,epsilon_0}sum_{i=1,N}sum_{j=1,N}^{jneqi}frac{q_i,q_j}{|{bfr}_i-{bfr}_j|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="$\displaystyle W =\frac{1}{2} \frac{1}{4\pi \epsilon_0} \sum_{i=1,N} \sum_{j=1,N}^{j\neq i} \frac{q_i  q_j}{\vert{\bf r}_i-{\bf r}_j\vert}.$">|; 

$key = q/displaystyleP_2^{,-1}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="$\displaystyle P_2^{ -1}(x)$">|; 

$key = q/|a_E|^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3160.png"
 ALT="$ \vert a_E\vert^{ 2}$">|; 

$key = q/{bfj}_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1432.png"
 ALT="$ {\bf j}_m$">|; 

$key = q/{bfu}'=d{bfr}'slashdt';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4173.png"
 ALT="$ {\bf u}'=d{\bf r}'/dt'$">|; 

$key = q/displaystyle{bfP}({bfr})=sum_iN_i,langle{bfp}_irangle,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1061.png"
 ALT="$\displaystyle {\bf P}({\bf r}) = \sum_i N_i  \langle {\bf p}_i\rangle,$">|; 

$key = q/theta_c<45^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2181.png"
 ALT="$ \theta_c&lt;45^\circ$">|; 

$key = q/omega<omega_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1705.png"
 ALT="$ \omega &lt; \omega_p$">|; 

$key = q/k_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2844.png"
 ALT="$ k_s$">|; 

$key = q/displaystylek_{i,y}=k_{r,y}=k_{t,y}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2026.png"
 ALT="$\displaystyle k_{i y} = k_{r y} = k_{t y}.$">|; 

$key = q/displaystyleY_{l,m}(theta,varphi)=left[frac{(2,l+1),(l-m)!}{4pi,(l+m)!}right]^{1slash2},P_l^{,m}(costheta),{rme}^{,{rmi},m,varphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="$\displaystyle Y_{l,m}(\theta,\varphi)= \left[\frac{(2 l+1) (l-m)!}{4\pi (l+m)!}\right]^{1/2} P_l^{ m}(\cos\theta) {\rm e}^{ {\rm i} m \varphi}.$">|; 

$key = q/displaystyleP_{rmload}=P_{rmrad}=frac{V_0^{,2}}{8,R_{rmrad}}=frac{P_{rmin}}{2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2665.png"
 ALT="$\displaystyle P_{\rm load} = P_{\rm rad} = \frac{V_0^{ 2}}{8  R_{\rm rad}} = \frac{P_{\rm in}}{2}.$">|; 

$key = q/displaystyleW=frac{1}{2}sum_{i=1,N}q_i,phi_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="$\displaystyle W = \frac{1}{2} \sum_{i=1,N} q_i  \phi_i,$">|; 

$key = q/{bfE}times{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4190.png"
 ALT="$ {\bf E}\times {\bf B}$">|; 

$key = q/omega_p^{,2}(z_0)=omega^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2357.png"
 ALT="$ \omega_p^{ 2}(z_0) = \omega^{ 2}$">|; 

$key = q/delta_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3373.png"
 ALT="$ \delta_l$">|; 

$key = q/displaystyle=left[frac{(2,l+1)}{4pi,l,(l+1)}right]^{1slash2},P_l^{,1}(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1340.png"
 ALT="$\displaystyle = \left[\frac{(2 l+1)}{4\pi l (l+1)}\right]^{1/2} P_l^{ 1}(\cos\theta),$">|; 

$key = q/displaystyleepsilon^{,ijk}partial_jE_k=epsilon^{,ijk}partial_j(1slash2,epsilon_{kab}E^{,ab})=partial_jE^{,ij}=-partial_4,(c,B^{,i}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3844.png"
 ALT="$\displaystyle \epsilon^{ ijk}\partial_j E_k = \epsilon^{ ijk}\partial_j (1/2 \epsilon_{kab} E^{ ab}) = \partial_j E^{ ij} = -\partial_4  (c B^{ i}),$">|; 

$key = q/(x^{,1'},x^{,2'},cdots,x^{,n'});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3534.png"
 ALT="$ (x^{ 1'}, x^{ 2'}, \cdots, x^{ n'})$">|; 

$key = q/displaystylesimeq-frac{2,{rmi},(k,a)^{2,l+1}}{(2,l+1),[(2,l-1)!!]^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3380.png"
 ALT="$\displaystyle \simeq -\frac{2 {\rm i} (k a)^{2 l+1}} {(2 l+1) [(2 l-1)!!]^{ 2}},$">|; 

$key = q/displaystyle={bfe}_ztimes{bfE}=mp,{rmi},{bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3303.png"
 ALT="$\displaystyle = {\bf e}_z\times{\bf E} = \mp {\rm i}  {\bf E}.$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi,r}sum_{l=0,infty}left(frac{r'}{r}right)^lP_l(cosgamma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\frac{1}{4\pi r}\sum_{l=0,\infty}\left(\frac{r'}{r}\right)^lP_l(\cos\gamma)$">|; 

$key = q/displaystyle=-frac{mu_0,I}{2,a}sum_{l=1,3,5,cdots}P_l^1(0)left(frac{r}{a}right)^{l-1}P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1355.png"
 ALT="$\displaystyle = -\frac{\mu_0 I}{2 a}\sum_{l=1,3,5,\cdots}P_l^1(0)\left(\frac{r}{a}\right)^{l-1}P_l(\cos\theta),$">|; 

$key = q/{rmi},k,n_n,sintheta_n={rmi},k,sintheta_I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2293.png"
 ALT="$ {\rm i} k n_n \sin\theta_n = {\rm i}  k \sin\theta_I$">|; 

$key = q/partialphi({bfr})slashpartialn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$ \partial\phi({\bf r})/\partial n$">|; 

$key = q/r+dr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="$ r+dr$">|; 

$key = q/q(x)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2559.png"
 ALT="$ q(x)=1$">|; 

$key = q/displaystyleg_l(r,r')=A,j_l(k,r_<),h_l^{(1)}(k,r_>),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3183.png"
 ALT="$\displaystyle g_l(r, r') = A  j_l(k r_&lt;)  h_l^{(1)}(k  r_&gt;),$">|; 

$key = q/displaystyleleft(frac{dsigma}{d{mitOmega}}right)_{rmunpolarized}=left(frac{q^{,2}}{4pi,epsilon_0,m,c^{,2}}right)^2left(frac{1+cos^2varphi}{2}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2737.png"
 ALT="$\displaystyle \left(\frac{d\sigma}{d {\mit \Omega}}\right)_{\rm unpolarized} = ...
...4\pi \epsilon_0  m c^{ 2}}\right)^2\left( \frac{1+\cos^2\varphi}{2}\right).$">|; 

$key = q/displaystyle=psi_t,{rme}^{-n_2,k_0,sinhtheta_t,z},cos(omega,t-n_1,k_0,sintheta_i,x+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2141.png"
 ALT="$\displaystyle = \psi_t {\rm e}^{-n_2 k_0 \sinh\theta_t z} \cos(\omega t-n_1 k_0 \sin\theta_i x+\phi_t),$">|; 

$key = q/displaystylefrac{d}{dx}!left[(1-x^{,2}),frac{dP_l^{,m}}{dx}right]+left[l,(l+1)-frac{m^{,2}}{1-x^{,2}}right]P_l^{,m}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="$\displaystyle \frac{d}{dx}\!\left[(1-x^{ 2}) \frac{dP_l^{ m}}{dx}\right]+\left[l (l+1)-\frac{m^{ 2}}{1-x^{ 2}}\right]P_l^{ m} = 0,$">|; 

$key = q/|z|<dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2622.png"
 ALT="$ \vert z\vert&lt;d/2$">|; 

$key = q/displaystylen^{,2}_pm(omega)=1+frac{(N,e^{,2}slashepsilon_0,m)}{omega_0^{,2}-omega^{,2}mpomega,{mitOmega}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1735.png"
 ALT="$\displaystyle n^{ 2}_\pm(\omega) = 1 + \frac{(N e^{ 2}/\epsilon_0  m)} {\omega_0^{ 2} -\omega^{ 2} \mp \omega  {\mit\Omega}}.$">|; 

$key = q/displaystyletanphi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2153.png"
 ALT="$\displaystyle \tan\phi_r$">|; 

$key = q/x_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1598.png"
 ALT="$ x_0$">|; 

$key = q/zgg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1877.png"
 ALT="$ z\gg 1$">|; 

$key = q/h_l^{(1)}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3024.png"
 ALT="$ h_l^{(1)}(r)$">|; 

$key = q/displaystylex=Sint_0^zfrac{dz'}{sqrt{n^{,2}(z)-S^{,2}}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2395.png"
 ALT="$\displaystyle x = S \int_0^z \frac{dz'}{\sqrt{n^{ 2}(z)-S^{ 2}}},$">|; 

$key = q/j_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="$ j_{mn}$">|; 

$key = q/displaystylef^{,mu}=left(rho,{bfE}+{bfj}times{bfB},,frac{{bfE}cdot{bfj}}{c}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3945.png"
 ALT="$\displaystyle f^{ \mu} = \left( \rho {\bf E} + {\bf j}\times{\bf B},  \frac{{\bf E}\cdot {\bf j}}{c}\right).$">|; 

$key = q/sqrt{xislashs};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1867.png"
 ALT="$ \sqrt{\xi/s}$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06slashfig20.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="367" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img2568.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06/fig20.eps}}
\end{figure}">|; 

$key = q/displaystyle{bfE}={bfE}_0+frac{bfP}{3,epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1249.png"
 ALT="$\displaystyle {\bf E} = {\bf E}_0 + \frac{\bf P}{3 \epsilon_0},$">|; 

$key = q/{rmRe}(z)>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2442.png"
 ALT="$ {\rm Re}(z) &gt; 0$">|; 

$key = q/displaystylecdot{bfE}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4202.png"
 ALT="$\displaystyle \cdot{\bf E}) $">|; 

$key = q/dV'slashr'=dVslashr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3755.png"
 ALT="$ dV'/r' = dV/r$">|; 

$key = q/r_<=r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3292.png"
 ALT="$ r_&lt;= r$">|; 

$key = q/{bfp};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$ {\bf p}$">|; 

$key = q/{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ {\bf E}$">|; 

$key = q/K=pm1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3439.png"
 ALT="$ K=\pm 1$">|; 

$key = q/displaystyle,cdot{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1080.png"
 ALT="$\displaystyle  \cdot{\bf E},$">|; 

$key = q/displaystyleZ_n=frac{2}{L}int_0^LZ(z),sin(k_n,z),dz,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1001.png"
 ALT="$\displaystyle Z_n = \frac{2}{L}\int_0^L Z(z) \sin(k_n z) dz,$">|; 

$key = q/w=u_1-u_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$ w=u_1-u_2$">|; 

$key = q/displaystylelangleIrangle=frac{E^{,2}}{sqrt{8},Z},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1985.png"
 ALT="$\displaystyle \langle I\rangle = \frac{E^{ 2}}{\sqrt{8} Z},
$">|; 

$key = q/H_theta(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2988.png"
 ALT="$ H_\theta(r)$">|; 

$key = q/displaystylenabla^{,2}{bfB}-frac{1}{c^{,2}},frac{partial^{,2}{bfB}}{partialt^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2752.png"
 ALT="$\displaystyle \nabla^{ 2}{\bf B} - \frac{1}{c^{ 2}} \frac{\partial^{ 2} {\bf B}}{\partial t^{ 2}}$">|; 

$key = q/displaystylefrac{partialrho}{partialt}+nablacdot{bfj}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle \frac{\partial \rho}{\partial t} + \nabla\cdot{\bf j} = 0.$">|; 

$key = q/displaystyle{mitDelta}chi_e=epsilon_1-epsilon_2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1124.png"
 ALT="$\displaystyle {\mit\Delta}\chi_e = \epsilon_1-\epsilon_2.$">|; 

$key = q/{rmi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2524.png"
 ALT="$ {\rm i}$">|; 

$key = q/displaystyleE^{,i}=frac{1}{2},epsilon^{,ijk},E_{jk}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3815.png"
 ALT="$\displaystyle E^{ i} =\frac{1}{2} \epsilon^{ ijk}  E_{jk}.$">|; 

$key = q/displaystylenablatimesf(r),{bfX}_{lm}=frac{{rmi},sqrt{l,(l+1)}}{r},f(r),Y_{lm},{bfn}+frac{1}{r}frac{d[r,f(r)]}{dr},{bfn}times{bfX}_{lm}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3343.png"
 ALT="$\displaystyle \nabla\times f(r)  {\bf X}_{lm} =\frac{{\rm i} \sqrt{l (l+1)}}...
..._{lm}  {\bf n}+ \frac{1}{r}\frac{d[r  f(r)]}{dr} {\bf n}\times {\bf X}_{lm}.$">|; 

$key = q/displaystyle=-left[frac{9,mu,mu_0}{(2,mu+mu_0),(mu+2,mu_0)-2,(a^{,3}slashb^{,3}),(mu-mu_0)^{,2}}right]B_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1572.png"
 ALT="$\displaystyle = -\left[ \frac{9 \mu \mu_0}{(2 \mu+\mu_0) (\mu+2 \mu_0) - 2 (a^{ 3}/b^{ 3}) (\mu-\mu_0)^{ 2}}\right] B_0.$">|; 

$key = q/{bfD}({bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="$ {\bf D}({\bf r}')$">|; 

$key = q/displaystyle{mitOmega}=frac{e,B}{gamma,m}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4179.png"
 ALT="$\displaystyle {\mit\Omega} = \frac{e B}{\gamma m}.
$">|; 

$key = q/theta_n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2286.png"
 ALT="$ \theta_n$">|; 

$key = q/f(z)slashphi(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2405.png"
 ALT="$ f(z)/\phi(z)$">|; 

$key = q/PQ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3750.png"
 ALT="$ PQ$">|; 

$key = q/displaystylec,t';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4160.png"
 ALT="$\displaystyle c t'$">|; 

$key = q/displaystylerho=epsilon_0,nablacdot{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="$\displaystyle \rho = \epsilon_0  \nabla \cdot {\bf E},$">|; 

$key = q/partialslashpartialtheta=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2928.png"
 ALT="$ \partial/\partial\theta = 0$">|; 

$key = q/{multline}H_y(x,z,t)=psi_i,cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z.5ex]+psi_r,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z){multline};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="539" HEIGHT="62" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2053.png"
 ALT="\begin{multline}
H_y(x,z,t) = \psi_i \cos(\omega t-n_1 k_0 \sin\theta_i x-n...
...os(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z)
\end{multline}">|; 

$key = q/displaystylefrac{E}{B}=c,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$\displaystyle \frac{E}{B} = c,$">|; 

$key = q/displaystyle{mitDelta}U=intoint{bfH}cdotd{bfB},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1594.png"
 ALT="$\displaystyle {\mit\Delta} U = \int \oint {\bf H}\cdot d{\bf B}  dV.$">|; 

$key = q/displaystylew(x,h)=A,(x,0)+{rmi},A,(0,x).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2558.png"
 ALT="$\displaystyle w(x,h) = A (x,0) + {\rm i} A (0,x).$">|; 

$key = q/displaystylesimeqc,{bfB}times{bfn},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3274.png"
 ALT="$\displaystyle \simeq c {\bf B}\times{\bf n},$">|; 

$key = q/displaystylephi({bfr})rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$\displaystyle \phi({\bf r}) \rightarrow 0$">|; 

$key = q/displaystylephi(z)={rmsgn}(z),Vleft[1-frac{z^{,2}-a^{,2}}{|z|,(z^{,2}+a^{,2})^{1slash2}}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="$\displaystyle \phi(z) = {\rm sgn}(z) V\left[1-\frac{z^{ 2}-a^{ 2}}{\vert z\vert (z^{ 2}+a^{ 2})^{1/2}}\right]$">|; 

$key = q/A_mu,U^{,mu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3939.png"
 ALT="$ A_\mu  U^{ \mu} =0$">|; 

$key = q/displaystylefrac{1}{4},G_{munu},F^{,munu}=c,{bfE}cdot{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3860.png"
 ALT="$\displaystyle \frac{1}{4}  G_{\mu\nu}  F^{ \mu\nu} = c {\bf E} \cdot {\bf B}.$">|; 

$key = q/displaystyle{bfm}=I,A,{bfn}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1373.png"
 ALT="$\displaystyle {\bf m}= I A {\bf n}.$">|; 

$key = q/displaystyleW_3=frac{1}{4pi,epsilon_0}left(frac{q_3,q_1}{|{bfr}_3-{bfr}_1|}+frac{q_3,q_2}{|{bfr}_3-{bfr}_2|}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$\displaystyle W_3 = \frac{1}{4\pi \epsilon_0} \left( \frac{q_3  q_1}{\vert{\b...
...3 - {\bf r}_1\vert} + \frac{q_3  q_2}{\vert{\bf r}_3 - {\bf r}_2\vert}\right).$">|; 

$key = q/A+B=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$ A+B=1$">|; 

$key = q/displaystyle[H_y]_{z=0_-}^{z=0_+}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2065.png"
 ALT="$\displaystyle [H_y]_{z=0_-}^{z=0_+}=0,$">|; 

$key = q/displaystyleu=frac{epsilon_0}{4},({bfE}cdot{bfE}^{,ast}+c,{bfB}cdotc,{bfB}^{,ast}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3156.png"
 ALT="$\displaystyle u = \frac{\epsilon_0}{4} ({\bf E}\cdot{\bf E}^{ \ast} + c {\bf B}\cdot c {\bf B}^{ \ast}).$">|; 

$key = q/B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$ B$">|; 

$key = q/|f_1|ll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1881.png"
 ALT="$ \vert f_1\vert\ll 1$">|; 

$key = q/F(a,c,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2427.png"
 ALT="$ F(a,c,z)$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}intfrac{rho({bfr'},t-|{bfr}-{bfr'}|slashc)}{|{bfr}-{bfr}'|},dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle = \frac{1}{4\pi \epsilon_0} \int \frac{\rho({\bf r'}, t- \vert{\bf r} -{\bf r '}\vert/c)}{\vert{\bf r} - {\bf r}'\vert}  dV'$">|; 

$key = q/h_l^{(2)}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3025.png"
 ALT="$ h_l^{(2)}(r)$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-sum_{l=0,infty}sum_{m=-l,+l}frac{1}{2,l+1}left(frac}^{,l+1}}right)Y^{,ast}_{l,m}(theta',varphi'),Y_{l,m}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\sum_{l=0,\infty}\sum_{m=-l,+l}\frac{1}{2\...
...{&gt;}^{ l+1}}\right)Y^{ \ast}_{l,m}(\theta',\varphi') Y_{l,m}(\theta,\varphi),$">|; 

$key = q/m>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2995.png"
 ALT="$ m&gt;0$">|; 

$key = q/displaystylefrac{partialD_x}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2045.png"
 ALT="$\displaystyle \frac{\partial D_x}{\partial t}$">|; 

$key = q/z=z_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1049.png"
 ALT="$ z=z_0$">|; 

$key = q/displaystylea_M(l,m),g_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3122.png"
 ALT="$\displaystyle a_M(l,m)  g_l(k r)$">|; 

$key = q/displaystylef_1(xi,t)=frac{{rmi}}{tau}sqrt{frac{s}{xi}}int_0^{2pi}expleft(-2,{rmi},sqrt{xis},cosuright),{rme}^{-{rmi},u},du.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1866.png"
 ALT="$\displaystyle f_1(\xi, t) = \frac{{\rm i}}{\tau} \sqrt{\frac{s}{\xi}}\int_0^{2\...
...xp\left(-2 {\rm i}  \sqrt{\xi s}  \cos u\right) {\rm e}^{-{\rm i} u}  du.$">|; 

$key = q/cosphi=costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4128.png"
 ALT="$ \cos\phi=\cos\theta$">|; 

$key = q/displaystylep_2-p_1=left[frac{epsilon_0,E^{,2}}{2}frac{(epsilon-1),(epsilon+2)}{3}right]_{1}^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1259.png"
 ALT="$\displaystyle p_2 - p_1 = \left[ \frac{\epsilon_0  E^{ 2}}{2} \frac{(\epsilon-1) (\epsilon+2)}{3} \right]_{1}^2.$">|; 

$key = q/muslashmu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1578.png"
 ALT="$ \mu/\mu_0$">|; 

$key = q/displaystyley'=A,y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3455.png"
 ALT="$\displaystyle y' = A y,$">|; 

$key = q/displaystyle=pmk,q,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2322.png"
 ALT="$\displaystyle = \pm k q,$">|; 

$key = q/displaystyle=hat{alpha},beta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2176.png"
 ALT="$\displaystyle = \hat{\alpha} \beta,$">|; 

$key = q/{bfu}=d{bfr}slashdt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4172.png"
 ALT="$ {\bf u} =d{\bf r}/dt$">|; 

$key = q/displaystyle{bfr}cdot{bfE}=-frac{1}{k}sum_{l,m}a_E(l,m),f_l(k,r),{bfL},{bfX}_{lm}=-frac{1}{k}sum_{l,m}a_E(l,m),f_l(k,r)sqrt{l,(l+1)},Y_{lm},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3121.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf E} = -\frac{1}{k} \sum_{l,m}a_E(l,m)  f_l(k r)...
..._{lm} = - \frac{1}{k} \sum_{l,m} a_E(l,m)  f_l(k r)\sqrt{l (l+1)}   Y_{lm},$">|; 

$key = q/g_{munu},R^{,mu},Q^{,nu}=R_mu,Q^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3657.png"
 ALT="$ g_{\mu\nu} R^{ \mu}  Q^{ \nu} = R_\mu  Q^{ \mu}$">|; 

$key = q/displaystylek_-=n_-,frac{omega}{c}simeqfrac{omega_p}{c}sqrt{frac{omega}{mitOmega}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1767.png"
 ALT="$\displaystyle k_- = n_- \frac{\omega}{c} \simeq\frac{\omega_p}{c} \sqrt{\frac{\omega}{\mit \Omega}}.$">|; 

$key = q/displaystyle=y(x=g_i)=frac{n_i^{,2}}{a^{,2}}-frac{1}{2,g_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1661.png"
 ALT="$\displaystyle = y(x=g_i) = \frac{n_i^{ 2}}{a^{ 2}} -\frac{1}{2 g_i},$">|; 

$key = q/displaystyle=gamma,({bfE}_perp+{bfv}times{bfB}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3856.png"
 ALT="$\displaystyle = \gamma ({\bf E}_\perp +{\bf v}\times{\bf B}),$">|; 

$key = q/B_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3577.png"
 ALT="$ B_i$">|; 

$key = q/p_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="$ p_{ij}$">|; 

$key = q/rneqr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img960.png"
 ALT="$ r\neq r'$">|; 

$key = q/displaystyleoverline{N_z}=sqrt{frac{mu_0}{epsilon_0}},sqrt{1-omega_c^{,2}slashomega^{,2}},frac{H_{s,0}^{,2}}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2897.png"
 ALT="$\displaystyle \overline{N_z} = \sqrt{\frac{\mu_0}{\epsilon_0}}  \sqrt{1-\omega_c^{ 2}/\omega^{ 2}} \frac{H_{s 0}^{ 2}}{2}$">|; 

$key = q/x_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$ x_3$">|; 

$key = q/displaystyle0=1+u,t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2518.png"
 ALT="$\displaystyle 0 = 1 + u  t.$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{1}{2,mu_0,c,k^{,2}}left|sum_{l,m}(-{rmi})[a_E(l,m),{bfX}_{lm}+a_M(l,m),{bfn}times{bfX}_{lm}right]right|^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3276.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} = \frac{1}{2 \mu_0  c   k^{ 2}}\lef...
...,m) {\bf X}_{lm} +a_M(l,m) {\bf n}\times{\bf X}_{lm}\right]\right\vert^{ 2}.$">|; 

$key = q/{bfA}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$ {\bf A}({\bf r},t)$">|; 

$key = q/(1slash2),{bfr}timesd{bfr}=d{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1409.png"
 ALT="$ (1/2) {\bf r}\times d{\bf r}=d{\bf A}$">|; 

$key = q/displaystyle=frac{2}{L}int_0^L{mitPhi}_m(z'),sin(k_n,z'),dz',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1026.png"
 ALT="$\displaystyle = \frac{2}{L}\int_0^L {\mit\Phi}_m(z') \sin(k_n z') dz',$">|; 

$key = q/displaystyle=2,E_0cos[(omegaslashc),(n,z-c,t)],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1746.png"
 ALT="$\displaystyle = 2  E_0 \cos[(\omega/c) (n  z -c  t)],$">|; 

$key = q/displaystyleg_l(k,r)=A_l^{(1)},h_l^{(1)}(k,r)+A_l^{(2)},h_l^{(2)}(k,r).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3087.png"
 ALT="$\displaystyle g_l(k r) = A_l^{(1)}  h_l^{(1)} (k r) + A_l^{(2)}  h_l^{(2)}(k r).$">|; 

$key = q/displaystylefrac{dP_{rmsc}}{d{mitOmega}}=frac{a^{,2}}{2,mu_0},{rmRe},[{bfn}cdot{2,mu_0},{rmRe},[{bfE}_{rmsc}cdot({bfn}times{bfB}_{rmsc}^ast)]_{r=a},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="418" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3339.png"
 ALT="$\displaystyle \frac{d P_{\rm sc}}{d{\mit \Omega}} = \frac{a^{ 2}}{2 \mu_0}  ...
..., {\rm Re} [{\bf E}_{\rm sc}\cdot ({\bf n}\times{\bf B}_{\rm sc}^\ast)]_{r=a},$">|; 

$key = q/rho_0=e,n_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3714.png"
 ALT="$ \rho_0=e n_0$">|; 

$key = q/displaystylec=frac{1}{sqrt{epsilon_0,mu_0}}=2.99729times10^8,,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3390.png"
 ALT="$\displaystyle c = \frac{1}{\sqrt{\epsilon_0  \mu_0}}=2.99729\times 10^8  $">|; 

$key = q/displaystylelanglePrangle_{rmheat}=langleI^{,2}rangle,R=frac{I_0^{,2},R}{2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2636.png"
 ALT="$\displaystyle \langle P\rangle_{\rm heat} =\langle I^{ 2}\rangle  R = \frac{I_0^{ 2} R}{2},$">|; 

$key = q/displaystyle=-frac{h^{(2)}_l(k,a)}{h^{(1)}_l(k,a)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3363.png"
 ALT="$\displaystyle = -\frac{h^{(2)}_l(k a)}{h^{(1)}_l(k a)},$">|; 

$key = q/displaystyleY_{l,1}^{,ast}(pislash2,varphi'),{rme}^{,{rmi},varphi'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1341.png"
 ALT="$\displaystyle Y_{l,1}^{ \ast}(\pi/2,\varphi') {\rm e}^{ {\rm i} \varphi'}$">|; 

$key = q/displaystyle=nabla_stimes{bfH}_z+nabla_ztimes{bfH}_s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2824.png"
 ALT="$\displaystyle = \nabla_s\times{\bf H}_z + \nabla_z\times{\bf H}_s.$">|; 

$key = q/displaystylenablacdot{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle \nabla\cdot {\bf E}$">|; 

$key = q/displaystyle={rmi},k,c,{bfB},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2226.png"
 ALT="$\displaystyle = {\rm i} k c {\bf B},$">|; 

$key = q/phi({bfr}')=G_3({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="$ \phi({\bf r}')=G_3({\bf r},{\bf r}')$">|; 

$key = q/(0,pm1,0,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3428.png"
 ALT="$ (0,\pm 1, 0, 1)$">|; 

$key = q/displaystylephi(r,theta)rightarrowfrac{Q,(pi-alpha)^{,2}}{16pi,epsilon_0,R}sum_{l=0,infty}(-1)^l,frac{r^{,l}}{R^{,l}},P_l(costheta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1044.png"
 ALT="$\displaystyle \phi(r,\theta) \rightarrow\frac{Q (\pi-\alpha)^{ 2}}{16\pi \epsilon_0 R}\sum_{l=0,\infty}(-1)^l \frac{r^{ l}}{R^{ l}} P_l(\cos\theta).
$">|; 

$key = q/displaystyle=q^{-1slash4}(x),expleft(,{rmi},hint_a^xq^{,1slash2}(x'),dx'right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2561.png"
 ALT="$\displaystyle = q^{-1/4}(x) \exp\left( {\rm i} h\int_a^x q^{ 1/2}(x') dx'\right)$">|; 

$key = q/displaystyleu_1';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3491.png"
 ALT="$\displaystyle u_1'$">|; 

$key = q/displaystyleA^{,mu}=gammaleft(frac{dgamma}{dt},{bfu}+gamma,{bfa},,c,frac{dgamma}{dt}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3908.png"
 ALT="$\displaystyle A^{ \mu} = \gamma\left(\frac{d\gamma}{dt} {\bf u} + \gamma  {\bf a},  c \frac{d\gamma}{dt}\right).$">|; 

$key = q/i,j,k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3633.png"
 ALT="$ i,j,k$">|; 

$key = q/g^{,ij}=g^{,ji};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3593.png"
 ALT="$ g^{ ij} = g^{ ji}$">|; 

$key = q/displaystylea_M(l,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3221.png"
 ALT="$\displaystyle a_M(l,m)$">|; 

$key = q/displaystyleF_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3795.png"
 ALT="$\displaystyle F_{ij}$">|; 

$key = q/displaystyle=sum_{l,m}left[a_pm(l,m),j_l(k,r),{bfX}_{lm}+frac{rmi}{k},b_pm(l,m),nablatimesj_l(k,r){bfX}_{lm}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3305.png"
 ALT="$\displaystyle = \sum_{l,m}\left[ a_\pm(l,m) j_l(k r)  {\bf X}_{lm} +\frac{\rm i}{k} b_\pm(l,m) \nabla\times j_l(k r) {\bf X}_{lm} \right],$">|; 

$key = q/displaystyleU=frac{epsilon_0}{2},E^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$\displaystyle U = \frac{\epsilon_0}{2}  E^{ 2}.$">|; 

$key = q/displaystylefrac{partial{bfL}}{partialt}+nablacdot{bfM}=-{bfr}times(rho,{bfE}+{bfj}times{bfB}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$\displaystyle \frac{\partial {\bf L}}{\partial t} + \nabla\cdot{\bf M} = - {\bf r}\times (\rho {\bf E} + {\bf j}\times {\bf B}),
$">|; 

$key = q/displaystyle{calF}_mu,U^{,mu}=frac{e}{c},F_{munu},U^{,mu},U^{,nu}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3936.png"
 ALT="$\displaystyle {\cal F}_\mu  U^{ \mu} = \frac{e}{c}  F_{\mu\nu}  U^{ \mu}  U^{ \nu} = 0.$">|; 

$key = q/zgeq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="$ z\geq 0$">|; 

$key = q/displaystyle=({bfe}_xpm{rmi},{bfe}_y),{rme}^{,{rmi},k,z},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3301.png"
 ALT="$\displaystyle = ({\bf e}_x \pm {\rm i} {\bf e}_y)  {\rm e}^{ {\rm i} k z},$">|; 

$key = q/displaystyle{bfB}=frac{{bfr}times{bfE}}{r,c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4015.png"
 ALT="$\displaystyle {\bf B} = \frac{{\bf r}\times{\bf E}}{r c}.$">|; 

$key = q/displaystyleint_Vdelta({bfr}-{bfr}'),dV=1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle \int_V \delta({\bf r}-{\bf r}')  dV = 1.$">|; 

$key = q/nabla^{,2}phi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3135.png"
 ALT="$ \nabla^{ 2}\phi = 0$">|; 

$key = q/displaystylephi(r,theta)rightarrowfrac{Q}{4pi,epsilon_0,R}-frac{Q,alpha^{,2}}{16pi,epsilon_0,R}sum_{l=0,infty}frac{r^{,l}}{R^{,l}},P_l(costheta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1042.png"
 ALT="$\displaystyle \phi(r,\theta) \rightarrow \frac{Q}{4\pi \epsilon_0 R}-\frac{Q\...
...6\pi \epsilon_0 R}\sum_{l=0,\infty}\frac{r^{ l}}{R^{ l}} P_l(\cos\theta).
$">|; 

$key = q/k,rll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3126.png"
 ALT="$ k r\ll 1$">|; 

$key = q/displaystyle=(1slash2),(3,x^{,2}-1),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="$\displaystyle =(1/2) (3 x^{ 2}-1),$">|; 

$key = q/displaystylek_n=n,frac{pi}{L}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img934.png"
 ALT="$\displaystyle k_n = n \frac{\pi}{L}.$">|; 

$key = q/B_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1541.png"
 ALT="$ B_s$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{epsilon_0}int_VG_D({bfr},{bfr}'),rho({bfr}'),dV'+int_Sphi({bfr}'),frac{partialG_D({bfr},{bfr}')}{partialn'},dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="$\displaystyle \phi({\bf r})=-\frac{1}{\epsilon_0} \int_V G_D({\bf r},{\bf r}')\...
...nt_S \phi({\bf r}') \frac{\partial G_D({\bf r},{\bf r}')}{\partial n'}  d S'.$">|; 

$key = q/displaystyle={rmi},{bfL},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3067.png"
 ALT="$\displaystyle = {\rm i} {\bf L},$">|; 

$key = q/displaystyle=-{rmi},k,n^{,2},E_y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2235.png"
 ALT="$\displaystyle = -{\rm i} k n^{ 2}  E_y,$">|; 

$key = q/displaystyleI=A_mu,B^{,mu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4056.png"
 ALT="$\displaystyle I = A_\mu  B^{ \mu},$">|; 

$key = q/displaystyle=beta^{,-1},cosphi_t,psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2171.png"
 ALT="$\displaystyle = \beta^{ -1} \cos\phi_t \psi_t $">|; 

$key = q/{rmi},varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4163.png"
 ALT="$ {\rm i} \varphi$">|; 

$key = q/displaystyleU_mu,A^{,mu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3708.png"
 ALT="$\displaystyle U_\mu  A^{ \mu} = 0$">|; 

$key = q/x';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3394.png"
 ALT="$ x'$">|; 

$key = q/pi^2slash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3286.png"
 ALT="$ \pi^2/4$">|; 

$key = q/(x^{,1},x^{,2},cdots,x^{,n});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3532.png"
 ALT="$ (x^{ 1}, x^{ 2}, \cdots, x^{ n})$">|; 

$key = q/displaystyle=-{rmi},k,{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3071.png"
 ALT="$\displaystyle =-{\rm i} k  {\bf E},$">|; 

$key = q/displaystyleoverline{bfN}=overline{K^{,2}},R_s,{bfn}=frac{1}{2},K_0^{,2},R_s,{bfn},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2798.png"
 ALT="$\displaystyle \overline{\bf N} = \overline{K^{ 2}}  R_s {\bf n}= \frac{1}{2} K_0^{ 2} R_s {\bf n},$">|; 

$key = q/R=(E^{,2}+c^{,2},B^{,2})slash|{bfE}timesc{bfB}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4195.png"
 ALT="$ R = (E^{ 2}+c^{ 2} B^{ 2})/\vert{\bf E}\times c{\bf B}\vert$">|; 

$key = q/displaystyledeltaU=frac{1}{2,epsilon_0}int_Vleft[D^{,2},delta(1slashepsilon)+2,{bfD}cdotdelta{bfD}slashepsilonright]dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1211.png"
 ALT="$\displaystyle \delta U = \frac{1}{2 \epsilon_0}\int_V \left[D^{ 2} \delta(1/\epsilon) + 2  {\bf D} \cdot \delta {\bf D}/\epsilon\right]dV,$">|; 

$key = q/displaystyle{bfE}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3140.png"
 ALT="$\displaystyle {\bf E}^{(E)}$">|; 

$key = q/displaystylev_z(omega,z)=frac{c}{n(omega,z)}=c,left(1-frac{omega_p^{~2}(z)}{omega^{,2}}right)^{-1slash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2345.png"
 ALT="$\displaystyle v_z(\omega,z) = \frac{c}{n(\omega,z)} = c \left(1-\frac{\omega_p^{&nbsp;2}(z)}{\omega^{ 2}}\right)^{-1/2}.$">|; 

$key = q/displaystyle=-psi_t,costheta_t,cos(omega,t-n_1,k_0,sintheta_i,x-n_2,k_0,costheta_t,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2111.png"
 ALT="$\displaystyle =-\psi_t \cos\theta_t \cos(\omega t-n_1 k_0 \sin\theta_i x-n_2 k_0 \cos\theta_t z),$">|; 

$key = q/displaystyleE_x(x,y,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2778.png"
 ALT="$\displaystyle E_x(x,y,z,t)$">|; 

$key = q/omega>omega_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2884.png"
 ALT="$ \omega&gt;\omega_c$">|; 

$key = q/G_1({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="$ G_1({\bf r},{\bf r}')$">|; 

$key = q/displaystyle{bfA}(x^{,i},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3989.png"
 ALT="$\displaystyle {\bf A}(x^{ i}, t)$">|; 

$key = q/displaystyle={bf0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2757.png"
 ALT="$\displaystyle ={\bf0},$">|; 

$key = q/displaystyle{bfB}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$\displaystyle {\bf B} ({\bf r},t)$">|; 

$key = q/displaystylex'=B,(x-v,t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3462.png"
 ALT="$\displaystyle x' = B  (x-v t),$">|; 

$key = q/v_g(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1918.png"
 ALT="$ v_g(\omega)$">|; 

$key = q/displaystyle{calF}^{,mu}=frac{dP^{,mu}}{dtau}=m_0,A^{,mu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3924.png"
 ALT="$\displaystyle {\cal F}^{ \mu} = \frac{dP^{ \mu}}{d\tau} = m_0  A^{ \mu},$">|; 

$key = q/displaystyle=frac{1}{r,sintheta},frac{partial}{partialtheta},(sintheta,A_varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1348.png"
 ALT="$\displaystyle = \frac{1}{r \sin\theta} \frac{\partial}{\partial\theta} (\sin\theta A_\varphi),$">|; 

$key = q/i=1,N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$ i=1, N$">|; 

$key = q/displaystyleP_{1}^{,-1}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="$\displaystyle P_{1}^{ -1}(x)$">|; 

$key = q/displaystyle=-frac{mu_0,c,k^{,2}}{sqrt{l,(l+1)}}intj_l(k,r),Y_{lm}^{,ast},{bfL}cdot({bfj}+nablatimes{bfM}),dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3222.png"
 ALT="$\displaystyle = -\frac{\mu_0  c k^{ 2}}{\sqrt{l (l+1)}}\int j_l(k r) Y_{lm}^{ \ast}  {\bf L}\cdot({\bf j} +\nabla\times{\bf M})  dV.$">|; 

$key = q/displaystyle-{bfE}cdot{bfj}=nablacdotleft(frac{{bfE}times{bfB}}{mu_0}right)-frac{mu_0}+frac{partial}{partialt}!left(frac{epsilon_0,E^{,2}}{2}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$\displaystyle - {\bf E} \cdot {\bf j} = \nabla \cdot \left(\frac{{\bf E}\times{...
..._0} + \frac{\partial}{\partial t}\!\left(\frac{\epsilon_0  E^{ 2}}{2}\right).$">|; 

$key = q/displaystylenablacdot{bfP}=epsilon_0,chi_e,nablacdot{bfE}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1123.png"
 ALT="$\displaystyle \nabla \cdot{\bf P} = \epsilon_0 \chi_e  \nabla \cdot {\bf E} = 0,$">|; 

$key = q/K;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3426.png"
 ALT="$ K$">|; 

$key = q/displaystyle=x-v,t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3398.png"
 ALT="$\displaystyle = x - v t,$">|; 

$key = q/displaystyleE_x(z=0_+);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1099.png"
 ALT="$\displaystyle E_x (z=0_+)$">|; 

$key = q/displaystyleW=frac{r^{,2},({bfp}_1cdot{bfp}_2)-3,({bfp}_1cdot{bfr}),({bfp}_2cdot{bfr})}{4pi,epsilon_0,r^{,5}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="$\displaystyle W = \frac{r^{ 2} ({\bf p}_1\cdot{\bf p}_2) - 3 ({\bf p}_1\cdot{\bf r}) ({\bf p}_2\cdot{\bf r})}{4\pi \epsilon_0 r^{ 5}},
$">|; 

$key = q/(R,theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$ (R, \theta, \varphi)$">|; 

$key = q/displaystylefrac{1}{2},partial_j(c,B^{,ij}-c,B^{,ji})+partial_4F^{,4i}=partial_jF^{,ji}+partial_4F^{,4i}=frac{J^{,i}}{c,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3811.png"
 ALT="$\displaystyle \frac{1}{2} \partial_j(c  B^{ ij} - c  B^{ ji}) +\partial_4 ...
...,4i} = \partial_j F^{ ji} +\partial_4 F^{ 4i} =\frac{J^{ i}}{c \epsilon_0}.$">|; 

$key = q/displaystylet_1=frac{n(0),x}{c}>t_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1943.png"
 ALT="$\displaystyle t_1 = \frac{n(0)  x}{c}&gt;t_0$">|; 

$key = q/displaystylephantom{=}+frac{1}{mu_0}left[nabla(B^{,2}slash2)-(nablacdot{bfB}),{bfB}-({bfB}cdotnabla),{bfB}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$\displaystyle \phantom{=} +\frac{1}{\mu_0}\left[\nabla(B^{ 2}/2) - (\nabla\cdot {\bf B}) {\bf B} - ({\bf B}\cdot\nabla) {\bf B}\right]$">|; 

$key = q/A=A(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$ A=A(\omega)$">|; 

$key = q/displaystyle=frac{epsilon_0,c}{4,k^{,3}},{rmRe}!sum_mleft[sqrt{(l-m),(l+m+1)},a_E^{,ast}(l,m+1)right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3168.png"
 ALT="$\displaystyle =\frac{\epsilon_0  c}{4  k^{ 3}}  {\rm Re}\!\sum_m\left[\sqrt{(l-m) (l+m+1)}  a_E^{ \ast}(l, m+1)\right.$">|; 

$key = q/phi_1({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$ \phi_1({\bf r})$">|; 

$key = q/A_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3562.png"
 ALT="$ A_{ij}$">|; 

$key = q/displaystylez=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1651.png"
 ALT="$\displaystyle z=$">|; 

$key = q/displaystylebeta(r')=frac{I_m(k_n,r')}{I_m(k_n,a)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1011.png"
 ALT="$\displaystyle \beta(r') = \frac{I_m(k_n r')}{I_m(k_n a)},$">|; 

$key = q/P_1,P_2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3583.png"
 ALT="$ P_1, P_2,$">|; 

$key = q/displaystylenablatimes{bfE}-{rmi},k,c,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3191.png"
 ALT="$\displaystyle \nabla\times{\bf E} -{\rm i} k  c {\bf B}$">|; 

$key = q/47.6^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2184.png"
 ALT="$ 47.6^\circ$">|; 

$key = q/displaystyle+sum_{l=0,infty}sum_{m=-l,+l}left[alpha_{l,m}(r',theta',varphi'),r^{beta_{l,m}(r',theta',varphi')}{r^{,l+1}}right]Y_{l,m}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="$\displaystyle + \sum_{l=0,\infty}\sum_{m=-l,+l}\left[\alpha_{l,m}(r',\theta',\v...
...rac{\beta_{l,m}(r',\theta',\varphi')}{r^{ l+1}}\right]Y_{l,m}(\theta,\varphi),$">|; 

$key = q/displaystylef(x,y),{rme}^{,{rmi},(k_g,z-omega,t)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2877.png"
 ALT="$\displaystyle f(x,y)  {\rm e}^{ {\rm i} (k_g  z-\omega  t)}.$">|; 

$key = q/R=|{bfr}-{bfr}'|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$ R=\vert{\bf r}-{\bf r}'\vert$">|; 

$key = q/10^5,mu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1462.png"
 ALT="$ 10^5 \mu_0$">|; 

$key = q/displaystyleF^{,i4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3801.png"
 ALT="$\displaystyle F^{ i4}$">|; 

$key = q/R>2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4196.png"
 ALT="$ R&gt;2$">|; 

$key = q/displaystyley_{rmmax};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1662.png"
 ALT="$\displaystyle y_{\rm max}$">|; 

$key = q/I(dslash2)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3248.png"
 ALT="$ I(d/2)=0$">|; 

$key = q/displaystyleg_{m,n}(r=r'_{+},r')=g_{m,n}(r=r_{-}',r').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1009.png"
 ALT="$\displaystyle g_{m,n}(r=r'_{+},r')= g_{m,n}(r=r_{-}',r').$">|; 

$key = q/displaystyle=sum_{n=0,infty}phi_{m,n}(r),sin(k_n,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1017.png"
 ALT="$\displaystyle = \sum_{n=0,\infty}\phi_{m,n}(r) \sin(k_n z),$">|; 

$key = q/displaystylefrac{rmi}{h},phi''-(phi')^{,2}+q=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2465.png"
 ALT="$\displaystyle \frac{\rm i}{h}  \phi'' - (\phi')^{ 2} + q = 0.$">|; 

$key = q/displaystylenabla^{,2},u_omega=-v_omega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle \nabla^{ 2} u_\omega = -v_\omega,$">|; 

$key = q/{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1311.png"
 ALT="$ {\bf A}$">|; 

$key = q/displaystyle{bfB}=mu(B),{bfH},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1530.png"
 ALT="$\displaystyle {\bf B} = \mu(B)  {\bf H},$">|; 

$key = q/{figure}{epsfysize{=2.75in{centerline{epsffile{Chapter06bslashfig10.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="489" HEIGHT="310" BORDER="0"
 SRC="|."$dir".q|img2178.png"
 ALT="\begin{figure}
\epsfysize =2.75in
\centerline{\epsffile{Chapter06b/fig10.eps}}
\end{figure}">|; 

$key = q/gamma^{,6};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4138.png"
 ALT="$ \gamma^{ 6}$">|; 

$key = q/Y_{l,m+1}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3098.png"
 ALT="$ Y_{l,m+1}(\theta,\varphi)$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter05slashhst1.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="341" BORDER="0"
 SRC="|."$dir".q|img1465.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter05/hst1.eps}}
\end{figure}">|; 

$key = q/displaystyled{bfM}=frac{epsilon_0,c,dr}{2,k^{,3}},{rmRe}!sum_{m,m'}a_E^ast(l,m'),a_E(l,m)oint({bfL}cdot{bfX}_{lm'})^{,ast},{bfX}_{lm},d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3164.png"
 ALT="$\displaystyle d{\bf M} = \frac{\epsilon_0  c  dr} {2 k^{ 3}}  {\rm Re} \!\...
...l,m) \oint ({\bf L}\cdot{\bf X}_{lm'})^{ \ast}  {\bf X}_{lm}  d{\mit\Omega}.$">|; 

$key = q/psi_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2022.png"
 ALT="$ \psi_t$">|; 

$key = q/E(z)rightarrowE_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1144.png"
 ALT="$ E(z)\rightarrow E_0$">|; 

$key = q/displaystyleW=frac{1}{2}sum_{i,j=1,N}p_{ij},Q_i,Q_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="$\displaystyle W = \frac{1}{2}\sum_{i,j=1,N}p_{ij} Q_i Q_j.
$">|; 

$key = q/displaystylenabla^{,2}phi_m=-rho_m,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1477.png"
 ALT="$\displaystyle \nabla^{ 2}\phi_m =- \rho_m,$">|; 

$key = q/displaystyleB_varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1351.png"
 ALT="$\displaystyle B_\varphi$">|; 

$key = q/displaystylephi({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle \phi({\bf r},t)$">|; 

$key = q/displaystyle=gamma^{,3},a,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3910.png"
 ALT="$\displaystyle = \gamma^{ 3}  a,$">|; 

$key = q/displaystyle(n,m)=frac{(4,n^{,2}-1),(4,n^{,2}-9)cdots(4,n^{,2}-{2,m-1}^2)}{2^{,2,m},m!};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\displaystyle (n,m) = \frac{(4 n^{ 2}-1) (4 n^{ 2}-9)\cdots (4 n^{ 2}-\{2 m -1\}^2)}{2^{ 2 m}  m!}$">|; 

$key = q/displaystylephi=left{{array}{rll}-(sigmaslash2,epsilon_0),x&mbox{hspace{0.5cm}}&x>0[0.5ex](sigmaslash2,epsilon_0),x&&x<0{array}right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="$\displaystyle \phi = \left\{ \begin{array}{rll} -(\sigma/2 \epsilon_0) x&amp;\mbo...
...space{0.5cm}}&amp; x&gt;0\ [0.5ex] (\sigma/2 \epsilon_0) x&amp;&amp;x&lt;0 \end{array}\right..$">|; 

$key = q/displaystyleB_4=frac{1}{2pi},{rmRe},oint_{B_4}{rme}^{,{rmi},(k,x-omega,t)}frac{domega}{omega-2pislashtau},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1832.png"
 ALT="$\displaystyle B_4 = \frac{1}{2\pi} {\rm Re}  \oint_{B_4} {\rm e}^{ {\rm i} (k  x- \omega  t)} \frac{d\omega}{\omega -2\pi/\tau},$">|; 

$key = q/displaystyle=frac{C_{mn}}{I_m(k_n,a)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img945.png"
 ALT="$\displaystyle = \frac{C_{mn}}{I_m(k_n a)},$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),u_omega=-v_omega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2}) u_\omega = - v_\omega,$">|; 

$key = q/displaystyle=E_x(z=0_-),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1100.png"
 ALT="$\displaystyle = E_x (z=0_-),$">|; 

$key = q/displaystyle=frac{partial}{partialx_j}!left(epsilon_0,E^{,2},delta_{ij}slash2-epsilon_0,E_i,E_j+B^{,2},delta_{ij}slash2,mu_0-B_i,B_jslashmu_0right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$\displaystyle = \frac{\partial}{\partial x_j}\!\left(\epsilon_0 E^{ 2} \delt...
...2 - \epsilon_0 E_i E_j+ B^{ 2} \delta_{ij}/2 \mu_0 - B_i B_j/\mu_0\right)$">|; 

$key = q/t=T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1777.png"
 ALT="$ t=T$">|; 

$key = q/displaystyle=int_0^inftyk,r,J_m(k,r),C_m(r),dr,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img925.png"
 ALT="$\displaystyle = \int_0^\infty k r J_m(k r) C_m(r) dr,$">|; 

$key = q/displaystylenabla^{,2}left(frac{1}{|{bfr}-{bfr}'|}right)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle \nabla^{ 2}\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)=0$">|; 

$key = q/displaystyleR_{m,n}(r');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1022.png"
 ALT="$\displaystyle R_{m,n}(r')$">|; 

$key = q/displaystylec,{bfB}_{lm}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3103.png"
 ALT="$\displaystyle c {\bf B}_{lm}^{(E)}$">|; 

$key = q/s>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1810.png"
 ALT="$ s&gt;0$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}},d{mitOmega}=-frac{dE(theta,varphi)}{dt'},d{mitOmega}=epsilon_0,c,E_{rmrad}^{,2},frac{s}{r},r^{,2},d{mitOmega},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="444" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4096.png"
 ALT="$\displaystyle \frac{dP(t')}{d{\mit\Omega}}  d{\mit\Omega} = -\frac{dE(\theta,\...
... = \epsilon_0  c  E_{\rm rad}^{ 2}  \frac{s}{r}  r^{ 2}  d{\mit \Omega},$">|; 

$key = q/displaystyleh(omega)=int_0^{z_0(omega)}frac{omega}{[omega^{,2}-omega_p^{,2}(z)]^{1slash2}},dz,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2356.png"
 ALT="$\displaystyle h(\omega) = \int_0^{z_0(\omega)} \frac{\omega}{[\omega^{ 2}-\omega_p^{ 2}(z)]^{1/2}}  dz,$">|; 

$key = q/E_irightarrow-c,B_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3840.png"
 ALT="$ E_i\rightarrow -c B_i$">|; 

$key = q/displaystylepartial_muF_{nusigma}+partial_nuF_{sigmamu}+partial_sigmaF_{munu}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3947.png"
 ALT="$\displaystyle \partial_\mu F_{\nu\sigma} + \partial_\nu F_{\sigma\mu} + \partial_\sigma F_{\mu\nu} = 0.$">|; 

$key = q/(l,m,n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3447.png"
 ALT="$ (l, m, n)$">|; 

$key = q/{mitOmega}=e,B_0slashm_e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2010.png"
 ALT="$ {\mit\Omega}=e B_0/m_e$">|; 

$key = q/displaystylembox{hspace{4.2cm}as{prightarrow0{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="$\displaystyle \mbox{\hspace{4.2cm}as $p\rightarrow 0$}$">|; 

$key = q/tanxi=dxslashdz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2399.png"
 ALT="$ \tan\xi = dx/dz$">|; 

$key = q/d{bfp};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4065.png"
 ALT="$ d{\bf p}$">|; 

$key = q/displaystyle=E_i,Z_0^{,-1},cos[k_0,(c,t-z)]-E_r,Z_0^{,-1},cos[k_0,(c,t+z)+phi_r],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2191.png"
 ALT="$\displaystyle = E_i Z_0^{ -1} \cos[k_0 (c t-z)] - E_r Z_0^{ -1} \cos[k_0 (c t+z)+\phi_r],$">|; 

$key = q/l=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="$ l=2$">|; 

$key = q/-0.21times10^{-8};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1451.png"
 ALT="$ -0.21\times 10^{-8}$">|; 

$key = q/displaystyleA_varphi(r,theta)=frac{1}{2},mu_0,Isum_{l=1,3,5,cdots}frac{P_l^1(0)}{l,(l+1)}left(frac{a}{r}right)^{l+1}P_l^1(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1346.png"
 ALT="$\displaystyle A_\varphi(r,\theta) = \frac{1}{2} \mu_0 I\sum_{l=1,3,5,\cdots}\frac{P_l^1(0)}{l (l+1)}\left(\frac{a}{r}\right)^{l+1}P_l^1(\cos\theta)$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=sum_{m=0,infty}left[C_m(r),cos(m,theta)+S_m(r),sin(m,theta)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) =\sum_{m=0,\infty}\left[C_m(r) \cos(m \theta)+S_m(r) \sin(m \theta)\right].$">|; 

$key = q/C;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1321.png"
 ALT="$ C$">|; 

$key = q/displaystyleq_{l,m}^{,ast}=(-1)^m,q_{l,-m}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="$\displaystyle q_{l,m}^{ \ast} = (-1)^m q_{l,-m}.$">|; 

$key = q/displaystyle{bfn}cdot{bfD};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2767.png"
 ALT="$\displaystyle {\bf n}\cdot{\bf D}$">|; 

$key = q/displaystylenablatimes{bfE}={bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1096.png"
 ALT="$\displaystyle \nabla\times{\bf E} = {\bf0}$">|; 

$key = q/displaystyle=E_1,cos(k_1,x)sin(k_2,y)sin(k_3,z),{rme}^{-{rmi},omega,t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2779.png"
 ALT="$\displaystyle = E_1  \cos(k_1  x)\sin(k_2  y) \sin(k_3  z)  {\rm e}^{-{\rm i} \omega  t},$">|; 

$key = q/k=omegaslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$ k=\omega/c$">|; 

$key = q/f(x,y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2836.png"
 ALT="$ f(x,y)$">|; 

$key = q/displaystylecostheta={bfe}cdot{bfn}=cospsi,sinvarphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2733.png"
 ALT="$\displaystyle \cos\theta ={\bf e}\cdot{\bf n}= \cos\psi  \sin\varphi,$">|; 

$key = q/displaystylek_t^{,2}+k_s^{,2}=(epsilon_1-1),frac{omega^{,2}}{c^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2960.png"
 ALT="$\displaystyle k_t^{ 2} + k_s^{ 2} = (\epsilon_1 -1) \frac{\omega^{ 2}}{c^{ 2}}.$">|; 

$key = q/displaystyletantheta_1=-2,tantheta_2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1424.png"
 ALT="$\displaystyle \tan\theta_1 = - 2 \tan\theta_2,
$">|; 

$key = q/t=t_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1933.png"
 ALT="$ t=t_0$">|; 

$key = q/displaystyleint{bfE}'cdot(nablatimes{bfH}),dV=intfrac{(nablatimes{bfH})^2}{sigma},dV-int{bfE}cdot(nablatimes{bfH}),dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1584.png"
 ALT="$\displaystyle \int {\bf E}'\cdot(\nabla\times{\bf H}) dV = \int\frac{(\nabla\times{\bf H})^2}{\sigma}  dV - \int {\bf E}\cdot(\nabla\times{\bf H})  dV.$">|; 

$key = q/displaystylenabla^{,2}phi({bfr})=v({bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$\displaystyle \nabla^{ 2}\phi({\bf r}) = v({\bf r}).$">|; 

$key = q/displaystylef_{lm}(r)=frac{u_{lm}(r)}{r^{,1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3009.png"
 ALT="$\displaystyle f_{lm}(r) = \frac{u_{lm}(r)}{r^{ 1/2}},$">|; 

$key = q/displaystyleomega_c=k_c,cequivk_s,c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2883.png"
 ALT="$\displaystyle \omega_c = k_c c\equiv k_s c$">|; 

$key = q/displaystylerightarrow{bfE}^{(M)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3143.png"
 ALT="$\displaystyle \rightarrow {\bf E}^{(M)}.$">|; 

$key = q/displaystyleint_Vrho,phi',dV+int_Ssigma,phi',dS=int_Vrho',phi,dV+int_S,sigma',phi,dS.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="337" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="$\displaystyle \int_V \rho \phi' dV + \int_S \sigma \phi' dS = \int_V \rho' \phi dV+\int_S \sigma' \phi dS.
$">|; 

$key = q/j_{ml};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2870.png"
 ALT="$ j_{ml}$">|; 

$key = q/{rme}^{,{rmi},(k,x-omega,t)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1806.png"
 ALT="$ {\rm e}^{ {\rm i} (k x-\omega  t)}$">|; 

$key = q/J_0(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2912.png"
 ALT="$ J_0(k_s  r)$">|; 

$key = q/epsilon_1neqepsilon_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1290.png"
 ALT="$ \epsilon_1\neq \epsilon_2$">|; 

$key = q/alpha_pm(l)+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3367.png"
 ALT="$ \alpha_\pm(l) + 1$">|; 

$key = q/r^{,l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1160.png"
 ALT="$ r^{ l}$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=left[frac{mu_0,c,I^{,2}}{8pi^2}frac{cos^2(pi,ceta}right]left[frac{sin^2(N,alphaslash2)}{sin^2(alphaslash2)}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2697.png"
 ALT="$\displaystyle \frac{d P}{d{\mit \Omega}}=\left[\frac{\mu_0 c I^{ 2}}{8\pi^2}...
...in^2\theta} \right] \left[\frac{\sin^2(N \alpha/2)}{\sin^2(\alpha /2)}\right].$">|; 

$key = q/displaystyle={rmi},k,c,B_x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2233.png"
 ALT="$\displaystyle = {\rm i} k c  B_x,$">|; 

$key = q/d{bfS}_1=-d{bfS}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1085.png"
 ALT="$ d{\bf S}_1= - d{\bf S}_2$">|; 

$key = q/n(z_0)=S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2397.png"
 ALT="$ n(z_0) = S$">|; 

$key = q/displaystyle=-left(frac{3}{8pi}right)^{1slash2},(x+{rmi},y).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="$\displaystyle = -\left(\frac{3}{8\pi}\right)^{1/2} (x+{\rm i} y).$">|; 

$key = q/(A_1,A_2,cdots,A_n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3525.png"
 ALT="$ (A_1, A_2, \cdots, A_n)$">|; 

$key = q/p_{mu}^{,nu'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3687.png"
 ALT="$ p_{\mu}^{ \nu'}$">|; 

$key = q/int_Swidetilde{G}_N({bfr},{bfr}'),dS'leftslashint_SdS'right.=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="$ \int_S \widetilde{G}_N({\bf r},{\bf r}') dS'\left/\int_S dS'\right.=0$">|; 

$key = q/displaystylepartial_muF^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3847.png"
 ALT="$\displaystyle \partial_\mu F^{ \mu\nu}$">|; 

$key = q/displaystyle{bfn}cdot({bfD}_1-{bfD}_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2754.png"
 ALT="$\displaystyle {\bf n}\cdot ({\bf D}_1 - {\bf D}_2)$">|; 

$key = q/displaystyle{bfj}_t=sigma,({bfE}+{bfE}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1581.png"
 ALT="$\displaystyle {\bf j}_t = \sigma  ({\bf E} + {\bf E}'),$">|; 

$key = q/|R|=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2566.png"
 ALT="$ \vert R\vert=1$">|; 

$key = q/displaystylef=m_0,gamma^{,3},frac{du}{dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3913.png"
 ALT="$\displaystyle f = m_0 \gamma^{ 3} \frac{du}{dt},$">|; 

$key = q/{rmi},c,t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4164.png"
 ALT="$ {\rm i} c t$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi,|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = - \frac{1}{4\pi \vert{\bf r}-{\bf r}'\vert}.$">|; 

$key = q/displaystylephi_i=frac{partialphi}{partialx^{,i}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3559.png"
 ALT="$\displaystyle \phi_i = \frac{\partial\phi}{\partial x^{ i}},$">|; 

$key = q/displaystyle=-frac{1}{L,pi}sum_{m=-infty,infty}sum_{n=1,infty}sin(k_n,z),sin(k_n,z'),{rme}^{,{rmi},m,(theta-theta')};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1014.png"
 ALT="$\displaystyle = -\frac{1}{L \pi}\sum_{m=-\infty,\infty}\sum_{n=1,\infty}\sin(k_n z) \sin(k_n z') {\rm e}^{ {\rm i} m (\theta-\theta')}$">|; 

$key = q/phi({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$ \phi({\bf r},t)$">|; 

$key = q/-{bfF};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$ -{\bf F}$">|; 

$key = q/displaystyle=frac{e}{4pi,epsilon_0}frac{1}{s},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3992.png"
 ALT="$\displaystyle = \frac{e}{4\pi \epsilon_0} \frac{1}{s},$">|; 

$key = q/displaystyleds^{,2}=c^{,2},dtau^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3688.png"
 ALT="$\displaystyle ds^{ 2} = c^{ 2}  d\tau^{ 2}.$">|; 

$key = q/v_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4165.png"
 ALT="$ v_1$">|; 

$key = q/displaystyle=frac{1}{k_s^{,2}},nabla_s!frac{partialE_z}{partialz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2846.png"
 ALT="$\displaystyle = \frac{1}{k_s^{ 2}}  \nabla_s \!\frac{\partial E_z}{\partial z},$">|; 

$key = q/displaystyleepsilon^{,ijk},epsilon_{ijb};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3766.png"
 ALT="$\displaystyle \epsilon^{ ijk} \epsilon_{ijb}$">|; 

$key = q/displaystyle=frac{63}{16pi},sin^2theta,(5cos^2theta-1)^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3281.png"
 ALT="$\displaystyle = \frac{63}{16\pi} \sin^2\theta  (5\cos^2\theta -1)^2,$">|; 

$key = q/displaystyle=frac{v_1}{v_2}=frac{n_2}{n_1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2073.png"
 ALT="$\displaystyle =\frac{v_1}{v_2}=\frac{n_2}{n_1}.$">|; 

$key = q/displaystylef(t)=frac{1}{2pi}int_{-infty}^{infty}domegaint_{-infty}^{infty}f(t'),{rme}^{-{rmi},omega,(t-t')},dt'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1778.png"
 ALT="$\displaystyle f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} d\omega \int_{-\infty}^{\infty} f(t') {\rm e}^{-{\rm i} \omega (t-t')} dt'.$">|; 

$key = q/displaystylenablatimes{bfB}=mu_0,{bfj}+mu_0,epsilon_0,frac{partial{bfE}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1438.png"
 ALT="$\displaystyle \nabla\times{\bf B} = \mu_0 {\bf j} + \mu_0 \epsilon_0 \frac{\partial {\bf E}} {\partial t},$">|; 

$key = q/varphi=pmpislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2708.png"
 ALT="$ \varphi=\pm \pi/2$">|; 

$key = q/displaystyle=psi_i,sintheta_i,cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2108.png"
 ALT="$\displaystyle = \psi_i \sin\theta_i \cos(\omega t-n_1 k_0 \sin\theta_i x-n_1 k_0 \cos\theta_i z)$">|; 

$key = q/{bfB}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1305.png"
 ALT="$ {\bf B}({\bf r})$">|; 

$key = q/d{bfS}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1083.png"
 ALT="$ d{\bf S}_1$">|; 

$key = q/f(0,2pi,cdots)rightarrowN^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2703.png"
 ALT="$ f(0, 2\pi, \cdots)\rightarrow
N^{ 2}$">|; 

$key = q/displaystyleint_Vdelta({bfr}-{bfr}'),dV=int_Vdelta({bfr}-{bfr}'),r,dr,dtheta,dz=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img952.png"
 ALT="$\displaystyle \int_V \delta({\bf r}-{\bf r}') dV = \int_V\delta({\bf r}-{\bf r}') r dr d\theta dz = 1$">|; 

$key = q/ds^{,2}=(dx^{,1})^2+(dx^{,2})^2+cdots+(dx^{,n})^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3589.png"
 ALT="$ ds^{ 2} = (dx^{ 1})^2 +(dx^{ 2})^2 + \cdots + (dx^{ n})^2$">|; 

$key = q/displaystylepsi_i+psi_r=psi_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2066.png"
 ALT="$\displaystyle \psi_i+\psi_r=\psi_t$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}int_S{bfD}({bfr'})cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right)dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int_S {\bf D}({\bf r'})\cdot\nabla'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right) dS'.$">|; 

$key = q/{bfG};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$ {\bf G}$">|; 

$key = q/theta_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1425.png"
 ALT="$ \theta_1$">|; 

$key = q/u_r={bfu}cdot{bfr}_0slashr_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4021.png"
 ALT="$ u_r={\bf u}\cdot{\bf r}_0/r_0$">|; 

$key = q/displaystyleleft(-nabla^{,2}+frac{1}{c^{,2}}frac{partial^{,2}}{partialt^{,2}}right){bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3724.png"
 ALT="$\displaystyle \left(-\nabla^{ 2}+\frac{1}{c^{ 2}} \frac{\partial^{ 2}}{\partial t^{ 2}}\right){\bf A}$">|; 

$key = q/{bfE}rightarrowalpha,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$ {\bf E}\rightarrow \alpha  {\bf E}$">|; 

$key = q/f_n(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$ f_n(\theta,\varphi)$">|; 

$key = q/ds^{,2}=g_{ij},dx^{,i},dx^{,j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3620.png"
 ALT="$ ds^{ 2} = g_{ij} dx^{ i}  dx^{ j}$">|; 

$key = q/P_l^0(x)=P_l(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="$ P_l^0(x)=P_l(x)$">|; 

$key = q/0<theta<pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4131.png"
 ALT="$ 0&lt;\theta&lt;\pi/2$">|; 

$key = q/displaystyles_pm=s_xpm{rmi},s_y.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1723.png"
 ALT="$\displaystyle s_\pm = s_x \pm {\rm i}  s_y.$">|; 

$key = q/f_l(z)={rmi}^{,l},h_l^{(1)}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3350.png"
 ALT="$ f_l(z) = {\rm i}^{ l} h_l^{(1)}(z)$">|; 

$key = q/displaystylefrac{partialrho_f}{partialt}+nablacdot(rho_f,{bfu})=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1224.png"
 ALT="$\displaystyle \frac{\partial \rho_f}{\partial t} + \nabla\cdot(\rho_f  {\bf u}) = 0.$">|; 

$key = q/omega_{0-};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1823.png"
 ALT="$ \omega_{0-}$">|; 

$key = q/displaystyle=frac{e}{4pi,epsilon_0}frac{1}{[r+{bfr}cdot{bfu}slashc]},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3882.png"
 ALT="$\displaystyle = \frac{e}{4\pi \epsilon_0} \frac{1}{[r+ {\bf r}\cdot{\bf u}/c]},$">|; 

$key = q/displaystyleintj_i({bfr}'),dV'=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1395.png"
 ALT="$\displaystyle \int j_i({\bf r}') dV'= 0.$">|; 

$key = q/displaystylenablar=-c,nablat'=nabla'r+frac{partialr}{partialt'},nablat'=frac{{bfr}}{r}-frac{{bfr}cdot{bfu}}{r},nablat',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4003.png"
 ALT="$\displaystyle \nabla r = - c  \nabla t' = \nabla'r + \frac{\partial r}{ \partial t'} \nabla t' = \frac{{\bf r}}{r} - \frac{{\bf r}\cdot{\bf u}}{r}  \nabla t',$">|; 

$key = q/displaystylephi=frac{q}{4pi,epsilon_0,r},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="$\displaystyle \phi = \frac{q}{4\pi \epsilon_0 r},$">|; 

$key = q/lambdabarequiv1slashk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2776.png"
 ALT="$ \lambdabar\equiv
1/k$">|; 

$key = q/displaystyle[{bfr}times({bfr}_utimesdot{bfu})]^{,2}=dot{u}^{,2},r^{,4}left[left(right)^2-left(1-frac{u^{,2}}{c^{,2}}right)tan^2phi,cos^2thetaright].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4124.png"
 ALT="$\displaystyle [{\bf r}\times({\bf r}_u\times \dot{\bf u})]^{ 2} = \dot{u}^{ 2...
...^2 - \left( 1-\frac{u^{ 2}}{c^{ 2}}\right) \tan^2 \phi  \cos^2\theta\right].$">|; 

$key = q/displaystylef(x,t)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1814.png"
 ALT="$\displaystyle f(x,t) = 0$">|; 

$key = q/displaystylesimeqc,{bfB}times{bfn}={rmi},c,k,({bfn}times{bfA})times{bfn}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2618.png"
 ALT="$\displaystyle \simeq c {\bf B}\times{\bf n} = {\rm i} c k ({\bf n} \times{\bf A})\times{\bf n}.$">|; 

$key = q/{bfr}_usimeq{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4028.png"
 ALT="$ {\bf r}_u \simeq{\bf r}$">|; 

$key = q/{bfv}=(v,0,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3509.png"
 ALT="$ {\bf v} = (v, 0, 0)$">|; 

$key = q/c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1292.png"
 ALT="$ c$">|; 

$key = q/omega_p^{,2}(z)=u(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2361.png"
 ALT="$ \omega_p^{ 2}(z) = u(z)$">|; 

$key = q/displaystyleB_theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1349.png"
 ALT="$\displaystyle B_\theta$">|; 

$key = q/displaystyle=-frac{1}{r},frac{partial}{partialr},(r,A_varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1350.png"
 ALT="$\displaystyle = -\frac{1}{r} \frac{\partial}{\partial r} (r A_\varphi),$">|; 

$key = q/displaystyledx^{,2}+dy^{,2}+dz^{,2}-c^{,2},dt^{,2}=Kleft(dx'^{,2}+dy'^{,2}+dz'^{,2}-c^{,2},dt'^{,2}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3438.png"
 ALT="$\displaystyle dx^{ 2} + dy^{ 2} + dz^{ 2} -c^{ 2}  dt^{ 2} = K\left(dx'^{ 2} + dy'^{ 2} + dz'^{ 2} -c^{ 2}  dt'^{ 2}\right),$">|; 

$key = q/displaystylefrac{J_1(k_s,a)}{k_s,J_0(k_s,a)}+frac{K_1(k_t,a)}{k_t,K_0(k_t,a)}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2959.png"
 ALT="$\displaystyle \frac{J_1(k_s  a)}{k_s J_0(k_s  a)} + \frac{K_1(k_t  a)}{k_t K_0(k_t  a)}= 0,$">|; 

$key = q/skew{3}bar{V};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="$ \skew{3}\bar{V}$">|; 

$key = q/epsilonrightarrow1slashepsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1188.png"
 ALT="$ \epsilon\rightarrow 1/\epsilon$">|; 

$key = q/R_{rmload}neqR_{rmres};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2666.png"
 ALT="$ R_{\rm load}\neq R_{\rm res}$">|; 

$key = q/{bfk}_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2016.png"
 ALT="$ {\bf k}_t$">|; 

$key = q/G^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3980.png"
 ALT="$ G^{ ij}$">|; 

$key = q/E_x(z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1992.png"
 ALT="$ E_x(z,t)$">|; 

$key = q/A={rmi},k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3184.png"
 ALT="$ A = {\rm i} k$">|; 

$key = q/displaystyle=left(frac{pi}{2,z}right)^{1slash2}Y_{l+1slash2}(z).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3023.png"
 ALT="$\displaystyle = \left(\frac{\pi}{2  z}\right)^{1/2} Y_{l+1/2}(z).$">|; 

$key = q/displaystyleleft(frac{partialphi}{partialS}right)_{S=S_0}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2392.png"
 ALT="$\displaystyle \left(\frac{\partial\phi}{\partial S}\right)_{S=S_0} = 0,$">|; 

$key = q/displaystylefrac{partialrho_m}{partialt}+nablacdot(rho_m,{bfu})=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1221.png"
 ALT="$\displaystyle \frac{\partial \rho_m}{\partial t} + \nabla\cdot(\rho_m  {\bf u}) = 0,$">|; 

$key = q/I_0=I,k,dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2633.png"
 ALT="$ I_0 = I k d/2$">|; 

$key = q/musimeqmu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1547.png"
 ALT="$ \mu\simeq \mu_0$">|; 

$key = q/displaystyle=-frac{partial{bfB}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle = -\frac{\partial{\bf B}}{\partial t},$">|; 

$key = q/B^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4059.png"
 ALT="$ B^{ \mu}$">|; 

$key = q/displaystylefrac{domega}{omega}={rmi},du,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1863.png"
 ALT="$\displaystyle \frac{d\omega}{\omega} = {\rm i}  du,$">|; 

$key = q/displaystyleint_V(psi,nabla^{,2}phi-phi,nabla^{,2}psi),dV=int_S(psi,nablaphi-phi,nablapsi)cdotd{bfS}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="$\displaystyle \int_V (\psi \nabla^{ 2}\phi-\phi \nabla^{ 2}\psi) dV = \int_S (\psi \nabla\phi-\phi \nabla\psi)\cdot d{\bf S}.$">|; 

$key = q/displaystylephi_m({bfr})=frac{1}{4pi}int{bfM}({bfr}')cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right),dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1481.png"
 ALT="$\displaystyle \phi_m({\bf r}) =\frac{1}{4\pi}\int {\bf M}({\bf r}')\cdot \nabla'\left(\frac{1}{\vert{\bf r} - {\bf r}'\vert}\right) dV'.$">|; 

$key = q/displaystyleA_i({bfr})=frac{mu_0}{4pi},frac{{bfr}}{|{bfr}|^{,3}}cdotintj_i({bfr}'),{bfr}',dV'+cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1399.png"
 ALT="$\displaystyle A_i({\bf r})= \frac{\mu_0}{4\pi} \frac{{\bf r}}{\vert{\bf r}\vert^{ 3}}\cdot\int j_i({\bf r}') {\bf r}' dV'+\cdots.$">|; 

$key = q/displaystylembox{boldmath{{epsilon{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1079.png"
 ALT="$\displaystyle \mbox{\boldmath$\epsilon$}$">|; 

$key = q/displaystyleI=intT^{,4},d^{,3}x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4040.png"
 ALT="$\displaystyle I = \int T^{ 4} d^{ 3} x,$">|; 

$key = q/{bfj}_m=nablatimes{bfM};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1494.png"
 ALT="$ {\bf j}_m = \nabla\times{\bf M}$">|; 

$key = q/displaystyle{bfE}=left{{array}{rll}(sigmaslash2,epsilon_0),{bfe}_x&mbox{hspace{0.5cm}}&x>0[0.5ex]-(sigmaslash2,epsilon_0),{bfe}_x&&x<0{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="$\displaystyle {\bf E} = \left\{ \begin{array}{rll} (\sigma/2 \epsilon_0) {\bf...
...m}}&amp; x&gt;0\ [0.5ex] - (\sigma/2 \epsilon_0) {\bf e}_x&amp;&amp;x&lt;0 \end{array}\right.,$">|; 

$key = q/U^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3923.png"
 ALT="$ U^{ \mu}$">|; 

$key = q/displaystyle=-{rmi},omega,epsilon_0,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2820.png"
 ALT="$\displaystyle = -{\rm i} \omega  \epsilon_0  {\bf E}$">|; 

$key = q/t=t'=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3393.png"
 ALT="$ t=t'=0$">|; 

$key = q/displaystylephi(r,theta)=-E_0,r,costheta+left(frac{epsilon-1}{epsilon+2}right),E_0,frac{a^{,3}}{r^{,2}}costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1180.png"
 ALT="$\displaystyle \phi(r,\theta) = - E_0  r \cos\theta + \left(\frac{\epsilon-1}{\epsilon+2}\right)  E_0 \frac{a^{ 3}}{r^{ 2}}\cos\theta$">|; 

$key = q/displaystyleequiv{rmi},k,S,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2296.png"
 ALT="$\displaystyle \equiv {\rm i} k S,$">|; 

$key = q/displaystyle=frac{M_0,a^{,3}}{3}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1512.png"
 ALT="$\displaystyle = \frac{M_0  a^{ 3}}{3}.$">|; 

$key = q/v=w,sin^{,2}alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2375.png"
 ALT="$ v=w \sin^{ 2}\alpha$">|; 

$key = q/{mitDelta}=lambdaslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2713.png"
 ALT="$ {\mit\Delta}=\lambda/2$">|; 

$key = q/displaystyleA_{rmeff}=frac{d^{,2}}{16,epsilon_0,c,R_{rmrad}}=frac{3}{8pi},lambda^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2673.png"
 ALT="$\displaystyle A_{\rm eff} = \frac{d^{ 2}}{16 \epsilon_0  c  R_{\rm rad}} = \frac{3}{8\pi} \lambda^{ 2}.$">|; 

$key = q/displaystyleG_N({bfr},{bfr}')=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="$\displaystyle G_N({\bf r},{\bf r}') =$">|; 

$key = q/displaystyleB^i=frac{1}{2},epsilon^{,ijk},B_{jk}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3777.png"
 ALT="$\displaystyle B^i = \frac{1}{2}  \epsilon^{ ijk}  B_{jk}.$">|; 

$key = q/displaystyleL=frac{mu_0}{4pi},e,g.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$\displaystyle L= \frac{\mu_0}{4\pi} e g.
$">|; 

$key = q/muslashmu_0gg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1457.png"
 ALT="$ \mu/\mu_0\gg 1$">|; 

$key = q/A^{,mu}=(c,{bfA},,phi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3868.png"
 ALT="$ A^{ \mu}= (c {\bf A},  \phi)$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}intfrac{[{bfj}]}{R},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} \int \frac{[{\bf j}]}{R}  dV'.$">|; 

$key = q/A_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3013.png"
 ALT="$ A_{lm}$">|; 

$key = q/G^{,ij}=T^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3976.png"
 ALT="$ G^{ ij} = T^{ ij}$">|; 

$key = q/displaystyleint_V(w,nabla^{,2}w^ast-w^ast,nabla^{,2}w),dV=left(int_{Sigma_0}+intrac{partialw^ast}{partialn}-w^ast,frac{partialw}{partialn}right),dS,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle \int_V (w  \nabla^{ 2} w^\ast- w^\ast  \nabla^{ 2} w) dV = \...
...partial w^\ast}{\partial n} -w^\ast  \frac{\partial w}{\partial n}\right) dS,$">|; 

$key = q/displaystyle{bfF}=q,{bfE}({bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$\displaystyle {\bf F} = q {\bf E}({\bf r}).$">|; 

$key = q/displaystyleG^{,4i}=frac{1}{2},epsilon^{,4ijk},F_{jk}=-frac{1}{2},epsilon^{,ijk4},F_{jk}=frac{1}{2},epsilon^{,ijk},c,B_{jk}=c,B^{,i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3819.png"
 ALT="$\displaystyle G^{ 4i} = \frac{1}{2} \epsilon^{ 4ijk}  F_{jk} = -\frac{1}{2}...
...ilon^{ ijk4} F_{jk} = \frac{1}{2} \epsilon^{ ijk}  c B_{jk} = c B^{ i},$">|; 

$key = q/i=j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$ i=j$">|; 

$key = q/displaystyle{bfE}({bfr})=-frac{1}{4pi,epsilon_0}intrho({bfr'}),nablaleft(frac{1}{|{bfr}-{bfr}'|}right)dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = -\frac{1}{4\pi \epsilon_0}\int \rho({\bf r'}) \nabla\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dV'.$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{Chapter06slashanom.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="399" BORDER="0"
 SRC="|."$dir".q|img1667.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{Chapter06/anom.eps}}
\end{figure}">|; 

$key = q/displaystyle{mitPhi}_m(r,k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img987.png"
 ALT="$\displaystyle {\mit\Phi}_m(r,k)$">|; 

$key = q/displaystylephi(r,theta,z)=sum_{m=0,infty}sum_{n=1,infty}sinh(j_{mn},zslasha),J_m(j_{mn},rslasha)left[A_{mn},cos(m,theta)+B_{mn},sin(m,theta)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="$\displaystyle \phi(r,\theta,z) = \sum_{m=0,\infty}\sum_{n=1,\infty} \sinh(j_{mn...
... J_m(j_{mn} r/a)\left[A_{mn} \cos(m \theta)+B_{mn} \sin(m \theta)\right].$">|; 

$key = q/x,y,zrightarrow-x,-y,-z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3610.png"
 ALT="$ x,y,z\rightarrow -x,-y,-z$">|; 

$key = q/dt=dtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3693.png"
 ALT="$ dt=d\tau$">|; 

$key = q/displaystyleoverline{sin^2theta}=1-overline{cos^2psi},sin^2varphi=1-(sin^2varphi)slash2=frac{1+cos^2varphi}{2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="363" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2735.png"
 ALT="$\displaystyle \overline{\sin^2\theta} = 1 -\overline{\cos^2\psi}  \sin^2\varphi = 1 - (\sin^2\varphi)/2 = \frac{1+\cos^2\varphi}{2}.$">|; 

$key = q/displaystyledelta_j^{,i},p_i^{,i'},p_{j'}^{,j}=p_{j}^{,i'},p_{j'}^{,j}=delta_{j'}^{,i'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3561.png"
 ALT="$\displaystyle \delta_j^{ i}  p_i^{ i'} p_{j'}^{ j} = p_{j}^{ i'}  p_{j'}^{ j} = \delta_{j'}^{ i'}.$">|; 

$key = q/displaystyle=gamma,({bfB}_perp-{bfv}times{bfE}slashc^2),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3858.png"
 ALT="$\displaystyle = \gamma ({\bf B}_\perp-{\bf v}\times{\bf E}/c^2),$">|; 

$key = q/displaystyle{calF}_mu=frac{e}{c},F_{munu},U^{,nu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3935.png"
 ALT="$\displaystyle {\cal F}_\mu = \frac{e}{c}  F_{\mu\nu}  U^{ \nu}.$">|; 

$key = q/displaystylef(t)=frac{1}{pi}int_0^{infty}domegaint_0^Tsin!left(frac{2pi,t'}{tau}right),cos[omega,(t-t')],dt',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1781.png"
 ALT="$\displaystyle f(t) = \frac{1}{\pi}\int_0^{\infty} d\omega \int_0^T \sin\!\left(\frac{2\pi  t'}{\tau}\right)  \cos[\omega (t-t')] dt',$">|; 

$key = q/A_{ijkl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3528.png"
 ALT="$ A_{ijkl}$">|; 

$key = q/displaystyleint(f,{bfj}cdotnabla'g+g,{bfj}cdotnabla'f),dV'=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1391.png"
 ALT="$\displaystyle \int (f {\bf j}\cdot \nabla' g+g {\bf j}\cdot\nabla' f) dV'=0.$">|; 

$key = q/p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="$ p$">|; 

$key = q/displaystyleoint_C{bfB}cdotd{bfr}=mu_0int_S{bfj}cdotd{bfS}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1320.png"
 ALT="$\displaystyle \oint_C {\bf B}\cdot d {\bf r} = \mu_0\int_S {\bf j}\cdot d{\bf S}.$">|; 

$key = q/|{bfr}-{bfr}'|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2611.png"
 ALT="$ \vert{\bf r}-{\bf r}'\vert$">|; 

$key = q/Pneq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4193.png"
 ALT="$ P\neq 0$">|; 

$key = q/dVslashr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3744.png"
 ALT="$ dV/r$">|; 

$key = q/E;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1281.png"
 ALT="$ E$">|; 

$key = q/displaystyleJ_n(z)=frac{1}{2pi,{rmi}^{,n}}int_0^{2pi}{rme}^{,{rmi},z,costheta},cos(n,theta),dtheta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1870.png"
 ALT="$\displaystyle J_n(z) = \frac{1}{2\pi {\rm i}^{ n}}\int_0^{2\pi} {\rm e}^{ {\rm i} z \cos\theta}  \cos(n \theta) d\theta,$">|; 

$key = q/displaystyled{bfF}_{21}=I_2,d{bfr}_2times{bfB}({bfr}_2).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1302.png"
 ALT="$\displaystyle d{\bf F}_{21} = I_2 d{\bf r}_2\times {\bf B}({\bf r}_2).$">|; 

$key = q/pislash2<thetaleqpi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="$ \pi/2&lt;\theta\leq \pi$">|; 

$key = q/v_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1850.png"
 ALT="$ v_p$">|; 

$key = q/displaystyleG_3({bfr},{bfr}')rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$\displaystyle G_3({\bf r}, {\bf r}') \rightarrow 0$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}intfrac{[{bfj}({bfr}')]}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3741.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} \int \frac{[{\bf j}({\bf r}')]}{\vert{\bf r}- {\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle=hat{alpha},sinphi_t,psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2173.png"
 ALT="$\displaystyle = \hat{\alpha} \sin\phi_t \psi_t,$">|; 

$key = q/Q_{lm}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3238.png"
 ALT="$ Q_{lm}'$">|; 

$key = q/RllR_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$ R\ll R_0$">|; 

$key = q/displaystyleB_5=frac{1}{2pi},{rmRe},oint_{B_5}{rme}^{,{rmi},(k,x-omega,t)}frac{domega}{omega-2pislashtau},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1833.png"
 ALT="$\displaystyle B_5 = \frac{1}{2\pi} {\rm Re}  \oint_{B_5} {\rm e}^{ {\rm i} (k  x- \omega  t)} \frac{d\omega}{\omega -2\pi/\tau},$">|; 

$key = q/displaystyle{bfE}cdot{bfn}=-{bfn}cdotnablaphi=-frac{1}{4pi,epsilon_0}int_Ssigma(sigma({bfr}'),{bfn}cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right),dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="587" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="$\displaystyle {\bf E}\cdot{\bf n} = -{\bf n}\cdot\nabla\phi = -\frac{1}{4\pi \...
...}') {\bf n}\cdot\nabla'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right) dS'.$">|; 

$key = q/displaystylef_ssimeq-F(omega_s),{rme}^{,{rmi},phi_s}sqrt{frac{4pi}{phi_s''}}int_^inftyleft[cos(pi,t^{,2}slash2)+{rmi},sin(pi,t^{,2}slash2)right],dt,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1908.png"
 ALT="$\displaystyle f_s\simeq -F(\omega_s)  {\rm e}^{ {\rm i} \phi_s} \sqrt{\frac{...
...^\infty \left[ \cos(\pi  t^{ 2}/2)+{\rm i} \sin(\pi  t^{ 2}/2)\right] dt,$">|; 

$key = q/displaystylephantom{=}+frac{I_m(k_n,r)}{I_m(k_n,a)},{mitPhi}_{m,n},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1021.png"
 ALT="$\displaystyle \phantom{=}+ \frac{I_m(k_n r)}{I_m(k_n a)} {\mit\Phi}_{m,n},$">|; 

$key = q/displaystylesimeqZ_0^{,-1},E_0,cos[k,(c,t-z)-1slash(k,delta)],{rme}^{-zslashdelta},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2004.png"
 ALT="$\displaystyle \simeq Z_0^{ -1} E_0 \cos[k (c t-z)-1/(k \delta)] {\rm e}^{-z/\delta},$">|; 

$key = q/displaystylefrac{d{bfM}}{dr}=frac{epsilon_0,c}{2,k^{,3}},{rmRe}!sum_{m,m'}a_E^ast(l,m'),a_E(l,m)ointY_{lm'}^{,ast},{bfL},Y_{lm},d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3165.png"
 ALT="$\displaystyle \frac{d{\bf M}}{dr} = \frac{\epsilon_0  c}{2 k^{ 3}}  {\rm Re...
..._E^\ast(l,m') a_E(l,m) \oint Y_{lm'}^{ \ast} {\bf L} Y_{lm} d{\mit\Omega}.$">|; 

$key = q/displaystyleleft(frac{1}{c^{,2}},frac{partial^{,2}}{partialt^{,2}}-nabla^{,2}right)phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle \left(\frac{1}{c^{ 2}} \frac{\partial^{ 2}}{\partial t^{ 2}}-\nabla^{ 2}\right) \phi$">|; 

$key = q/displaystylex=Sint_0^{z_0(S)}frac{dz}{sqrt{n^{,2}(z)-S^{,2}}}+Sint_z^{z_0(S)}frac{dz}{sqrt{n^{,2}(z)-S^{,2}}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2396.png"
 ALT="$\displaystyle x = S\int_0^{z_0(S)} \frac{dz}{\sqrt{n^{ 2}(z)-S^{ 2}} } + S\int_z^{z_0(S)} \frac{dz}{\sqrt{n^{ 2}(z)-S^{ 2}}},$">|; 

$key = q/u_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2887.png"
 ALT="$ u_g$">|; 

$key = q/omega_p^{,2}(z)proptoN(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2359.png"
 ALT="$ \omega_p^{ 2}(z)\propto
N(z)$">|; 

$key = q/k,deltall1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2007.png"
 ALT="$ k \delta \ll 1$">|; 

$key = q/-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3769.png"
 ALT="$ -1$">|; 

$key = q/displaystyle=frac{V}{2}left[frac{a^{,l+1}-(-1)^l,b^{,l+1}}{a^{,2,l+1}-b^{,2,l+1}}right]left[P_{l-1}(0)-P_{l+1}(0)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1032.png"
 ALT="$\displaystyle = \frac{V}{2}\left[\frac{a^{ l+1}-(-1)^l b^{ l+1}}{a^{ 2 l+1}-b^{ 2 l+1}}\right]\left[P_{l-1}(0)-P_{l+1}(0)\right],$">|; 

$key = q/langlecdotsrangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2720.png"
 ALT="$ \langle\cdots\rangle$">|; 

$key = q/2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="$ 2$">|; 

$key = q/displaystyle{bfr}=r,(0,,sinalpha,,cosalpha),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4120.png"
 ALT="$\displaystyle {\bf r} = r (0,  \sin\alpha,  \cos\alpha),$">|; 

$key = q/displaystylephi_1=phi_2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="$\displaystyle \phi_1 = \phi_2.
$">|; 

$key = q/i=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$ i=1$">|; 

$key = q/G_D({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="$ G_D({\bf r},{\bf r}')=0$">|; 

$key = q/r<a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="$ r&lt;a$">|; 

$key = q/displaystyleoverline{bfN}=frac{1}{2},{rmRe},({bfE}_paralleltimes{bfH}_parallel)=_{parallel,0}^{,2},{bfn}=frac{H_{parallel,0}^{,2}}{2,sigma,d},{bfn},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2795.png"
 ALT="$\displaystyle \overline{\bf N} = \frac{1}{2}   {\rm Re} ({\bf E}_\parallel\ti...
...  0}^{ 2} {\bf n} = \frac{H_{\parallel  0}^{ 2}}{2 \sigma  d}  {\bf n},$">|; 

$key = q/{bfM}=N,{bfm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1428.png"
 ALT="$ {\bf M} = N  {\bf m}$">|; 

$key = q/displaystyle~~~~+psi_r,costheta_i,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z+phi_r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2166.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\psi_r \cos\theta_i \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z+\phi_r),$">|; 

$key = q/displaystyle=frac{u'_2}{gamma,(1+u'_1,vslashc^{,2})},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3506.png"
 ALT="$\displaystyle = \frac{u'_2}{\gamma (1+u'_1  v/c^{ 2})},$">|; 

$key = q/omega_{1+};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1822.png"
 ALT="$ \omega_{1+}$">|; 

$key = q/dt'=gamma,dt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4069.png"
 ALT="$ dt'=\gamma  dt$">|; 

$key = q/displaystyleP_{rmout}=langleurangle,G_r,A_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2683.png"
 ALT="$\displaystyle P_{\rm out} = \langle u\rangle  G_r  A_0.$">|; 

$key = q/displaystylefrac{c}{2}left(B_{ab}-B_{ba}right)=-partial_a{mitPhi}_b+partial_b{mitPhi}_a,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3786.png"
 ALT="$\displaystyle \frac{c}{2} \left(B_{ab} - B_{ba}\right) = - \partial_a {\mit \Phi}_b +\partial_b{\mit \Phi}_a,$">|; 

$key = q/displaystyleK=frac{1}{2,sigma,d}intleft(H_s^{,2}+H_z^{,2}right),dSleftslashintoverline{N_z},dSright.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2900.png"
 ALT="$\displaystyle K = \frac{1}{2 \sigma  d} \int \left(H_s^{ 2} + H_z^{ 2}\right) dS\left/ \int\overline{N_z} dS\right.,$">|; 

$key = q/displaystyle{bfn}cdot{bfj}=frac{partialtau}{partialt}=-{rmi},omega,tau.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2764.png"
 ALT="$\displaystyle {\bf n}\cdot{\bf j} = \frac{\partial\tau}{\partial t} = -{\rm i}  \omega \tau.$">|; 

$key = q/hat{z}=x+{rmi},y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2526.png"
 ALT="$ \hat{z} = x + {\rm i} y$">|; 

$key = q/Z(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img999.png"
 ALT="$ Z(z)$">|; 

$key = q/{bfj}_t={bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1472.png"
 ALT="$ {\bf j}_t = {\bf0}$">|; 

$key = q/displaystylek_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2788.png"
 ALT="$\displaystyle k_3$">|; 

$key = q/displaystyle{bfE}cdot{bfB}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\displaystyle {\bf E} \cdot {\bf B} = 0.$">|; 

$key = q/displaystyle{bfB}_perp';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3857.png"
 ALT="$\displaystyle {\bf B}_\perp'$">|; 

$key = q/displaystylealphaleft[E_i,cos(omega,t)-E_r,cos(omega,t+phi_r)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2201.png"
 ALT="$\displaystyle \alpha\left[E_i \cos(\omega t) - E_r \cos(\omega t+\phi_r)\right]$">|; 

$key = q/A_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1158.png"
 ALT="$ A_l$">|; 

$key = q/displaystylephi_3({bfr})=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="$\displaystyle \phi_3({\bf r}) = 0$">|; 

$key = q/displaystyle{calI}_z=E_x,H_y.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2078.png"
 ALT="$\displaystyle {\cal I}_z = E_x H_y.$">|; 

$key = q/phantom{phi}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1906.png"
 ALT="$ \phantom{\phi}'$">|; 

$key = q/displaystylew(2)=(A+t,B),(0,hat{z})_s+B,(hat{z},0)_d.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2500.png"
 ALT="$\displaystyle w(2) =( A+t B) (0,\hat{z})_s + B (\hat{z},0)_d.$">|; 

$key = q/{bfu}timesdot{bfu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4110.png"
 ALT="$ {\bf u}\times\dot{\bf u}
= 0$">|; 

$key = q/displaystyletheta_c=sin^{-1}(n_2slashn_1).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2135.png"
 ALT="$\displaystyle \theta_c = \sin^{-1}(n_2/n_1).$">|; 

$key = q/displaystyle=frac{dx'}{dt'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3492.png"
 ALT="$\displaystyle = \frac{dx'}{dt'},$">|; 

$key = q/displaystyledelta({bfr}-{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle \delta({\bf r}-{\bf r}') =0$">|; 

$key = q/displaystyle{bfE}=E_0,cos(omega,t-k,z),{bfe}_y.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1708.png"
 ALT="$\displaystyle {\bf E} = E_0 \cos(\omega t-k z) {\bf e}_y.$">|; 

$key = q/deltarho_f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1192.png"
 ALT="$ \delta\rho_f$">|; 

$key = q/displaystyleG({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img995.png"
 ALT="$\displaystyle G({\bf r},{\bf r}')=0$">|; 

$key = q/displaystyle{bfr}cdotintj_i,{bfr}',dV'=-frac{1}{2}intleft[({bfr}cdot{bfj}),{bfr}t]_idV'=-frac{1}{2}left[{bfr}timesint({bfr}'times{bfj}),dV'right]_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1401.png"
 ALT="$\displaystyle {\bf r}\cdot\int j_i {\bf r}' dV' = -\frac{1}{2}\int \left[({\b...
... = -\frac{1}{2}\left[{\bf r}\times \int ({\bf r}'\times {\bf j}) dV'\right]_i.$">|; 

$key = q/displaystyleK=int(f,{bfj}cdotnabla'g+g,{bfj}cdotnabla'f),dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1382.png"
 ALT="$\displaystyle K = \int (f {\bf j}\cdot \nabla' g+g {\bf j}\cdot\nabla' f) dV',$">|; 

$key = q/k,d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2630.png"
 ALT="$ k d$">|; 

$key = q/displaystyleW=frac{1}{4pi,epsilon_0}left(frac{q_2,q_1}{|{bfr}_2-{bfr}_1|}+frac{q_3,q_1}{|{bfr}_3-{bfr}_1|}+frac{q_3,q_2}{|{bfr}_3-{bfr}_2|}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="$\displaystyle W = \frac{1}{4\pi \epsilon_0}\left( \frac{q_2  q_1}{\vert{\bf r...
...3 - {\bf r}_1\vert} + \frac{q_3  q_2}{\vert{\bf r}_3 - {\bf r}_2\vert}\right).$">|; 

$key = q/displaystyleP(t')=-frac{dE}{dt'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4093.png"
 ALT="$\displaystyle P(t') = - \frac{dE}{dt'},$">|; 

$key = q/displaystyle{bfB}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3884.png"
 ALT="$\displaystyle {\bf B}'$">|; 

$key = q/A=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$ A=1$">|; 

$key = q/dy'=dy;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3498.png"
 ALT="$ dy'=dy$">|; 

$key = q/displaystyle=frac{1}{pm(1-v^{,2}slashc^{,2})^{1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3468.png"
 ALT="$\displaystyle = \frac{1}{\pm (1-v^{ 2}/c^{ 2})^{1/2}},$">|; 

$key = q/displaystyle=int_0^rint_0^pir'^{,l},rho(r',theta),P_l(costheta),2pi,r'^{,2},sintheta,dtheta,dr'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="$\displaystyle = \int_0^r \int_0^\pi r'^{ l}  \rho(r',\theta) P_l(\cos\theta) 2\pi r'^{ 2} \sin\theta d\theta dr'.$">|; 

$key = q/displaystyle{bfr}cdotc,{bfB}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3210.png"
 ALT="$\displaystyle {\bf r}\cdot c {\bf B}({\bf r})$">|; 

$key = q/displaystylefrac{partial^{,2}E_y}{partialz^{,2}}+k^{,2}q^{,2},E_y=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2308.png"
 ALT="$\displaystyle \frac{\partial^{ 2} E_y}{\partial z^{ 2}} + k^{ 2} q^{ 2}  E_y = 0.$">|; 

$key = q/displaystyleW=frac{mu_0}{8pi}intintfrac{{bfj}({bfr})cdot{bfj}({bfr}')}{|{bfr}-{bfr}'|},dV,dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$\displaystyle W = \frac{\mu_0}{8\pi}\int\int \frac{{\bf j}({\bf r})\cdot{\bf j}({\bf r}')}{\vert{\bf r} - {\bf r}'\vert} dV dV'.
$">|; 

$key = q/alpha=pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4127.png"
 ALT="$ \alpha=\pi/2$">|; 

$key = q/widetilde{G}_N({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="$ \widetilde{G}_N({\bf r},{\bf r}')$">|; 

$key = q/displaystylerho({bfr}'),dV'rightarrowq,delta(r'-b),delta(theta'),delta(varphi'),dr',dtheta',dvarphi'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="$\displaystyle \rho({\bf r}') dV' \rightarrow q \delta(r'-b) \delta(\theta') \delta(\varphi') dr' d\theta' d\varphi'.$">|; 

$key = q/displaystyleintleft(x_i',j_j+x_j',j_iright),dV'=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1398.png"
 ALT="$\displaystyle \int \left(x_i' j_j + x_j' j_i\right) dV' = 0.$">|; 

$key = q/g_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1633.png"
 ALT="$ g_i$">|; 

$key = q/displaystyleF=frac{9}{4},pi,epsilon_0,a^{,2},E^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1055.png"
 ALT="$\displaystyle F = \frac{9}{4} \pi \epsilon_0 a^{ 2} E^{ 2}.
$">|; 

$key = q/f=m_0,a_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3914.png"
 ALT="$ f=m_0  a_0$">|; 

$key = q/beta_pm(l);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3335.png"
 ALT="$ \beta_\pm(l)$">|; 

$key = q/displaystyleF_{munu}=partial_mu{mitPhi}_nu-partial_nu{mitPhi}_mu.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3789.png"
 ALT="$\displaystyle F_{\mu\nu} = \partial_\mu {\mit \Phi}_\nu -\partial_\nu {\mit \Phi}_\mu.$">|; 

$key = q/displaystylemu_0,frac{partialphi_m(r=a-,theta)}{partialr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1551.png"
 ALT="$\displaystyle \mu_0 \frac{\partial\phi_m(r=a-,\theta)}{\partial r}$">|; 

$key = q/displaystylephi_{m,n}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1018.png"
 ALT="$\displaystyle \phi_{m,n}(r)$">|; 

$key = q/lambda=2pislashk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2609.png"
 ALT="$ \lambda = 2\pi/k$">|; 

$key = q/nablatimes{bfH}={bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1596.png"
 ALT="$ \nabla\times {\bf H}={\bf0}$">|; 

$key = q/K_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2797.png"
 ALT="$ K_0$">|; 

$key = q/{rmRe}(z)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2445.png"
 ALT="$ {\rm Re}(z)= 0$">|; 

$key = q/displaystyle{bfm}=frac{epsilon_0}{2},{rmRe},[{bfr}times({bfE}times{bfB}^{,ast})].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3162.png"
 ALT="$\displaystyle {\bf m} = \frac{\epsilon_0}{2}  {\rm Re}  [{\bf r}\times({\bf E}\times {\bf B}^{ \ast})].$">|; 

$key = q/z_0(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2352.png"
 ALT="$ z_0(\omega)$">|; 

$key = q/u_r=u,xslashr={bfr}cdot{bfu}slashr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3880.png"
 ALT="$ u_r = u x/r = {\bf r}\cdot{\bf u}/r$">|; 

$key = q/displaystylew(hat{z},h)=expleft[,{rmi},h,phi(hat{z},h)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2464.png"
 ALT="$\displaystyle w(\hat{z}, h) = \exp\left[ {\rm i} h \phi(\hat{z}, h)\right].$">|; 

$key = q/varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1154.png"
 ALT="$ \varphi)$">|; 

$key = q/Z(0)=Z(L)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img932.png"
 ALT="$ Z(0)=Z(L)=0$">|; 

$key = q/m=pm1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3336.png"
 ALT="$ m=\pm 1$">|; 

$key = q/sll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1868.png"
 ALT="$ s\ll 1$">|; 

$key = q/displaystyleY_{1,-1}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="$\displaystyle Y_{1,-1}(\theta,\varphi)$">|; 

$key = q/displaystyle=frac{e}{4pi,epsilon_0,r'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3866.png"
 ALT="$\displaystyle = \frac{e}{4\pi \epsilon_0 r'},$">|; 

$key = q/l,d_1+m,d_2+n,d_3=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3446.png"
 ALT="$ l d_1 +m  d_2 + n d_3=0$">|; 

$key = q/{mitDelta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2690.png"
 ALT="$ {\mit\Delta}$">|; 

$key = q/displaystyle=frac{bfj}{c,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3728.png"
 ALT="$\displaystyle = \frac{\bf j} {c \epsilon_0}.$">|; 

$key = q/displaystyleu_2';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3493.png"
 ALT="$\displaystyle u_2'$">|; 

$key = q/displaystyle=-mu_0,nablatimes{bfj}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2753.png"
 ALT="$\displaystyle = - \mu_0 \nabla\times{\bf j}.$">|; 

$key = q/cslashv_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1922.png"
 ALT="$ c/v_g$">|; 

$key = q/depsilonslashdrho_m=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1266.png"
 ALT="$ d\epsilon/d\rho_m=0$">|; 

$key = q/displaystylenablatimes{bfB}=mu_0left({bfj}_t+frac{partial{bfD}}{partialt}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1678.png"
 ALT="$\displaystyle \nabla\times{\bf B} =\mu_0\left({\bf j}_t + \frac{\partial {\bf D}} {\partial t}\right).$">|; 

$key = q/displaystyle[{bfr}times({bfr}_utimesdot{bfu})]^{,2}=-({bfr}cdotdot{bfu})^{,2},r^{,2}slashc^{,2})+dot{u}^{,2},r^{,4},(1-{bfr}cdot{bfu}slashr,c)^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="418" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4123.png"
 ALT="$\displaystyle [{\bf r}\times({\bf r}_u\times \dot{\bf u})]^{ 2} = -({\bf r}\cd...
...u^{ 2}/c^{ 2}) +\dot{u}^{ 2}  r^{ 4}  (1-{\bf r}\cdot{\bf u}/r c)^{ 2},$">|; 

$key = q/displaystyleB_3=frac{1}{2pi},{rmRe}left(2pi,{rmi},{rme}^{{rmi},[k_tau,x-2pi,tslashtau]}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1827.png"
 ALT="$\displaystyle B_3 = \frac{1}{2\pi}  {\rm Re} \left(2\pi {\rm i} {\rm e}^{{\rm i} [k_\tau  x- 2\pi  t/\tau]}\right).$">|; 

$key = q/displaystyledW=frac{4pi}{3,epsilon_0},rho^{,2},r^{,4},dr.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="$\displaystyle dW = \frac{4\pi}{3 \epsilon_0}  \rho^{ 2}  r^{ 4} dr.$">|; 

$key = q/displaystylek_1,E_1+k_2,E_2+k_3,E_3=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2792.png"
 ALT="$\displaystyle k_1 E_1 + k_2  E_2 + k_3  E_3 = 0.$">|; 

$key = q/omega_0slashQ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2809.png"
 ALT="$ \omega_0/Q$">|; 

$key = q/r=infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="$ r=\infty$">|; 

$key = q/x_2=y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="$ x_2=y$">|; 

$key = q/displaystyle~~~+frac{1}{2,l+1}int_r^afrac{rho_{l,m}(r')}{epsilon_0}left(frac{r^{.r,frac{dphi_{l,m}}{dr}right|_{r=a}frac{1}{l}left(frac{r}{a}right)^l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;+ \frac{1}{2 l+1}\int_r^a \frac{\rho_{l,m}(r')}{\epsilon_0}\l...
... \frac{d\phi_{l,m}}{dr}\right\vert _{r=a}\frac{1}{l}\left(\frac{r}{a}\right)^l$">|; 

$key = q/hat{z}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2531.png"
 ALT="$ \hat{z}=0$">|; 

$key = q/{bfF};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="$ {\bf F}$">|; 

$key = q/Z=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1000.png"
 ALT="$ Z=0$">|; 

$key = q/l=3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3262.png"
 ALT="$ l= 3$">|; 

$key = q/displaystyle({bfB}_2-{bfB}_1)cdot{bfn}_{21}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1468.png"
 ALT="$\displaystyle ({\bf B}_2 - {\bf B}_1)\cdot{\bf n}_{21} = 0,$">|; 

$key = q/displaystylec,{bfB}_{lm}^{(M)}=-frac{rmi}{k},nablatimes{bfE}_{lm}^{(M)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3099.png"
 ALT="$\displaystyle c {\bf B}_{lm}^{(M)} = -\frac{\rm i}{k}  \nabla\times{\bf E}_{lm}^{(M)},$">|; 

$key = q/{bfn}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="$ {\bf n}'$">|; 

$key = q/I,pi,a^{,2}rightarrowm;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1375.png"
 ALT="$ I \pi a^{ 2}\rightarrow m$">|; 

$key = q/E=c,B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4183.png"
 ALT="$ E=c B$">|; 

$key = q/displaystyleA^{i'j'cdotsk'}=A^{ijcdotsk}p_i^{,i'},p_j^{,j'}cdotsp_k^{,k'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3550.png"
 ALT="$\displaystyle A^{i'j'\cdots k'} = A^{ij\cdots k} p_i^{ i'}  p_j^{ j'} \cdots p_k^{ k'}.$">|; 

$key = q/displaystyle=E_t,Z_0^{,-1},alpha^{-1},{rme}^{-zslashd},cos(omega,t-zslashd-pislash4+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2195.png"
 ALT="$\displaystyle = E_t Z_0^{ -1} \alpha^{-1} {\rm e}^{-z/d} \cos(\omega t-z/d-\pi/4+\phi_t),$">|; 

$key = q/partialG_N({bfr},{bfr}')slashpartialn'=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="$ \partial G_N({\bf r},{\bf r}')/\partial n'=0$">|; 

$key = q/T^{,mu}=A_nu,Q^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4054.png"
 ALT="$ T^{ \mu} = A_\nu  Q^{ \mu\nu}$">|; 

$key = q/k_t=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2966.png"
 ALT="$ k_t=0$">|; 

$key = q/displaystyleh(omega)=h_0+deltaleft(frac{omega}{omega_0}right)^p,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2580.png"
 ALT="$\displaystyle h(\omega)= h_0 + \delta\left(\frac{\omega}{\omega_0}\right)^p,
$">|; 

$key = q/displaystyle=frac{S(z-u,t)}{u},{bfe}_x+frac{T(z-u,t)}{u},{bfe}_y+frac{U(z-u,t)}{u},{bfe}_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1977.png"
 ALT="$\displaystyle = \frac{S(z-u t)}{u} {\bf e}_x + \frac{T(z-u t)}{u} {\bf e}_y+ \frac{U(z-u t)}{u} {\bf e}_z,$">|; 

$key = q/displaystyle{bfp}=intrho({bfr}),{bfr},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$\displaystyle {\bf p} = \int \rho({\bf r}) {\bf r} dV.$">|; 

$key = q/theta_0rightarrowpm1slashgamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4135.png"
 ALT="$ \theta_0 \rightarrow \pm 1/\gamma$">|; 

$key = q/rho_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3716.png"
 ALT="$ \rho_0$">|; 

$key = q/displaystylephi_m({bfr})simeq-nablaleft(frac{1}{4pi,r}right)cdotint{bfM}({bfr}'),dV'simeqfrac{{bfm}cdot{bfr}}{4pi,r^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1484.png"
 ALT="$\displaystyle \phi_m({\bf r}) \simeq -\nabla\left(\frac{1}{4\pi  r}\right)\cdot \int {\bf M}({\bf r}') dV'\simeq \frac{{\bf m}\cdot{\bf r}} {4\pi  r^{ 3}},$">|; 

$key = q/displaystyle=T^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3641.png"
 ALT="$\displaystyle = T^{ 2},$">|; 

$key = q/displaystyle=sum_{l,m}left[frac{rmi}{k},a_E(l,m),nablatimesf_l(k,r),{bfX}_{lm}+a_M(l,m),g_l(k,r),{bfX}_{lm}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3117.png"
 ALT="$\displaystyle = \sum_{l,m}\left[ \frac{\rm i}{k} a_E(l,m)  \nabla \times f_l(k r)  {\bf X}_{lm} + a_M(l,m)  g_l(k r)  {\bf X}_{lm}\right],$">|; 

$key = q/displaystyleH_x(x,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2104.png"
 ALT="$\displaystyle H_x(x,z,t)$">|; 

$key = q/r'=-c,t';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3877.png"
 ALT="$ r'= -c t'$">|; 

$key = q/epsilon,E_perp;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1271.png"
 ALT="$ \epsilon E_\perp$">|; 

$key = q/displaystylefrac{2,{rmRe}(n),{rmIm}(n)}{a^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1652.png"
 ALT="$\displaystyle \frac{2 {\rm Re}(n) {\rm Im}(n)}{a^{ 2}},$">|; 

$key = q/displaystylepartial_jG^{,ji}+partial_4G^{,4i}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3845.png"
 ALT="$\displaystyle \partial_j G^{ ji} + \partial_4 G^{ 4i} = 0.$">|; 

$key = q/displaystyle{bfj}_m=nablatimes{bfM}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1433.png"
 ALT="$\displaystyle {\bf j}_m = \nabla\times{\bf M}.$">|; 

$key = q/-v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3482.png"
 ALT="$ -v$">|; 

$key = q/B_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1524.png"
 ALT="$ B_R$">|; 

$key = q/deltaepsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1210.png"
 ALT="$ \delta\epsilon$">|; 

$key = q/k_s,a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2969.png"
 ALT="$ k_s  a$">|; 

$key = q/displaystyle={bfE}_0,expleft[,{rmi},({bfk}cdot{bfr}-omega,t)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1606.png"
 ALT="$\displaystyle = {\bf E}_0  \exp\left[ {\rm i} ({\bf k}\cdot{\bf r}-\omega  t)\right],$">|; 

$key = q/displaystylenablatimes{bfE}=-frac{partial{bfB}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle \nabla\times{\bf E} = - \frac{\partial {\bf B}}{\partial t},$">|; 

$key = q/I_m(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img962.png"
 ALT="$ I_m(k r)$">|; 

$key = q/displaystyleoverline{N_z}=frac{1}{2},|{bfE}_stimes{bfH}_s^{,ast}|.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2895.png"
 ALT="$\displaystyle \overline{N_z} =\frac{1}{2}  \vert{\bf E}_s\times{\bf H}_s^{ \ast}\vert.$">|; 

$key = q/{rmi},(k,x-omega,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1811.png"
 ALT="$ {\rm i} (k x -\omega  t)$">|; 

$key = q/displaystyle={bfr}+left[frac{(gamma-1),{bfr}cdot{bfv}}{v^{,2}}-gamma,tright]{bfv},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4169.png"
 ALT="$\displaystyle = {\bf r} + \left[\frac{(\gamma-1) {\bf r}\cdot{\bf v}}{v^{ 2}} - \gamma t\right]{\bf v},$">|; 

$key = q/d{bfp}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4067.png"
 ALT="$ d{\bf p} = 0$">|; 

$key = q/displaystyles=r_0,sqrt{1-u^{,2}slashc^{,2}+u_r^{,2}slashc^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4023.png"
 ALT="$\displaystyle s = r_0 \sqrt{1-u^{ 2}/c^{ 2} + u_r^{ 2}/c^{ 2}}$">|; 

$key = q/displaystyley=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1649.png"
 ALT="$\displaystyle y=$">|; 

$key = q/displaystyleI(z)=I,sin(k,dslash2-k,|z|),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3259.png"
 ALT="$\displaystyle I(z) = I \sin(k d/2 - k \vert z\vert),$">|; 

$key = q/displaystyle=frac{mu_0}{4pi},m,frac{sintheta}{r^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1371.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} m \frac{\sin\theta}{r^{ 3}},$">|; 

$key = q/displaystylepmalpha=frac{2pi}{N},frac{4pi}{N},cdotsfrac{(N-1),2pi}{N},frac{(N+1),2pi}{N}cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2701.png"
 ALT="$\displaystyle \pm\alpha = \frac{2\pi}{N}, \frac{4\pi}{N}, \cdots \frac{(N-1) 2\pi}{N}, \frac{(N+1) 2\pi}{N}\cdots.$">|; 

$key = q/displaystyle=-left(frac{epsilon_2-epsilon_1}{epsilon_2+epsilon_1}right)q,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1119.png"
 ALT="$\displaystyle = -\left(\frac{\epsilon_2-\epsilon_1}{\epsilon_2 + \epsilon_1} \right) q,$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06bslashabel.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="335" BORDER="0"
 SRC="|."$dir".q|img2383.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06b/abel.eps}}
\end{figure}">|; 

$key = q/displaystyle=-{rmi},k,n^{,2},{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2228.png"
 ALT="$\displaystyle = -{\rm i}  k n^{ 2} {\bf E},$">|; 

$key = q/displaystylerightarrowfrac{{rme}^{,p}}{sqrt{2pi,p}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img940.png"
 ALT="$\displaystyle \rightarrow \frac{{\rm e}^{ p}}{\sqrt{2\pi p}}$">|; 

$key = q/displaystylek,{bfr}cdotc,{bfB}=-{rmi},{bfr}cdot(nablatimes{bfE})=-{rmi},({bfr}timesnabla)cdot{bfE}={bfL}cdot{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3089.png"
 ALT="$\displaystyle k {\bf r}\cdot c {\bf B} = -{\rm i} {\bf r}\cdot (\nabla\times{\bf E}) = -{\rm i}  ({\bf r}\times\nabla)\cdot {\bf E} = {\bf L}\cdot{\bf E},$">|; 

$key = q/displaystyleB_theta(r,theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1356.png"
 ALT="$\displaystyle B_\theta(r,\theta)$">|; 

$key = q/dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2606.png"
 ALT="$ d/2$">|; 

$key = q/displaystyle{bfF}_{21}=-frac{mu_0,I_1,I_2}{4pi}oint_1oint_2frac{(d{bfr}_1cdotd{bfr}_2),{bfr}_{12}}{|{bfr}_{12}|^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1413.png"
 ALT="$\displaystyle {\bf F}_{21} =- \frac{\mu_0 I_1 I_2}{4\pi}\oint_1\oint_2\frac{(d{\bf r}_1\cdot d{\bf r}_2) {\bf r}_{12}}{\vert{\bf r}_{12}\vert^{ 3}}.
$">|; 

$key = q/displaystyledx'^{,2}+dy'^{,2}+dz'^{,2}-c^{,2},dt'^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3421.png"
 ALT="$\displaystyle dx'^{ 2} + dy'^{ 2} + dz'^{ 2} -c^{ 2}  dt'^{ 2}$">|; 

$key = q/alpha_pm(l);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3334.png"
 ALT="$ \alpha_\pm(l)$">|; 

$key = q/sin^2theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2644.png"
 ALT="$ \sin^2\theta$">|; 

$key = q/displaystylechi=frac{omega}{2,c},(n_+-n_-),z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1752.png"
 ALT="$\displaystyle \chi = \frac{\omega}{2 c}  (n_+ - n_-)  z,$">|; 

$key = q/displaystyle=-frac{partialH_y}{partialz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2046.png"
 ALT="$\displaystyle =-\frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystylealpha=beta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2124.png"
 ALT="$\displaystyle \alpha=\beta,$">|; 

$key = q/g_{ij}=g_{ji};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3588.png"
 ALT="$ g_{ij} = g_{ji}$">|; 

$key = q/displaystylepsi(r)=J_0(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2925.png"
 ALT="$\displaystyle \psi(r) = J_0(k_s  r)$">|; 

$key = q/displaystyleP_2^{,0}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="$\displaystyle P_2^{ 0}(x)$">|; 

$key = q/G_{munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3838.png"
 ALT="$ G_{\mu\nu}$">|; 

$key = q/-k^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3228.png"
 ALT="$ -k^{ 2}$">|; 

$key = q/displaystyle=left.frac{partialphi}{partialr}right|_{r=a_{+}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1149.png"
 ALT="$\displaystyle = \left. \frac{\partial\phi}{\partial r}\right\vert _{r=a_{+}},$">|; 

$key = q/displaystylen^{,2}(omega)=1-frac{omega_p^{,2}}{omega^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1701.png"
 ALT="$\displaystyle n^{ 2}(\omega) = 1 - \frac{\omega_p^{ 2}}{\omega^{ 2}},$">|; 

$key = q/P_l^1(0)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1344.png"
 ALT="$ P_l^1(0)=0$">|; 

$key = q/e^{,2}slash(6pi,epsilon_0,m_e,c^{,2})=1.28times10^{-15};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4083.png"
 ALT="$ e^{ 2}/(6\pi \epsilon_0 m_e  c^{ 2})
= 1.28\times 10^{-15}$">|; 

$key = q/displaystylenablaphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\displaystyle \nabla\phi$">|; 

$key = q/displaystyle]+rho,{bfv};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4203.png"
 ALT="$\displaystyle ] +\rho  {\bf v}
$">|; 

$key = q/displaystylex'=F(x,y,z,t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3418.png"
 ALT="$\displaystyle x' = F(x, y, z, t),$">|; 

$key = q/-pi<{rmarg}(z)<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2432.png"
 ALT="$ -\pi &lt; {\rm arg}(z) &lt; 0$">|; 

$key = q/deltaE_{rmmax}sim1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4091.png"
 ALT="$ \delta E_{\rm max}\sim 1$">|; 

$key = q/displaystyleleft[frac{d^{,2}}{dr^{,2}}+frac{1}{r}frac{d}{dr}+k^{,2}-frac{(l+1slash2)^{,2}}{r^{,2}}right]u_{lm}(r)=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3010.png"
 ALT="$\displaystyle \left[\frac{d^{ 2}}{dr^{ 2}} + \frac{1}{r}\frac{d}{dr} +k^{ 2} - \frac{(l+1/2)^{ 2}}{r^{ 2}}\right] u_{lm}(r) =0,$">|; 

$key = q/theta<pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4099.png"
 ALT="$ \theta &lt;\pi/2$">|; 

$key = q/displaystyleE_x(z)=pmA,n^{-1}(z),q^{,1slash2}(z),expleft(pm{rmi},kint^z!q(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2328.png"
 ALT="$\displaystyle E_x(z) = \pm A  n^{-1}(z) q^{ 1/2}(z)  \exp\left(\pm {\rm i}  k \int^z\!q(z') dz'\right).$">|; 

$key = q/{bfj}=rho,{bfu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3719.png"
 ALT="$ {\bf j} =\rho  {\bf u}$">|; 

$key = q/sigma({bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="$ \sigma({\bf r}')$">|; 

$key = q/displaystyle|{bfr}-{bfr}'|=rleft[1-frac{2,{bfn}cdot{bfr}'}{r}+frac{{r'}^{,2}}{r^{,2}}right]^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2601.png"
 ALT="$\displaystyle \vert{\bf r} - {\bf r}'\vert = r\left[1- \frac{2 {\bf n}\cdot{\bf r}'}{r}+ \frac{{r'}^{ 2}}{r^{ 2}}\right]^{1/2},$">|; 

$key = q/displaystyleH_y(x,z,t)=psi_t,cos(omega,t-n_1,k_0,sintheta_i,x-n_2,k_0,costheta_t,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2054.png"
 ALT="$\displaystyle H_y(x,z,t)= \psi_t \cos(\omega t-n_1 k_0 \sin\theta_i x-n_2 k_0 \cos\theta_t z)$">|; 

$key = q/f({bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1384.png"
 ALT="$ f({\bf r}')$">|; 

$key = q/n_+^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1763.png"
 ALT="$ n_+^{ 2}$">|; 

$key = q/displaystyle{bfE}=frac{q}{4pi,epsilon_0,r^{,2}},{bfe}_r,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="$\displaystyle {\bf E} = \frac{q}{4\pi \epsilon_0 r^{ 2}} {\bf e}_r,$">|; 

$key = q/rho_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1217.png"
 ALT="$ \rho_m$">|; 

$key = q/displaystyle{mitGamma}(z)=int_0^inftyt^{,z-1},{rme}^{-t},dt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2439.png"
 ALT="$\displaystyle {\mit\Gamma}(z)= \int_0^\infty t^{ z-1} {\rm e}^{-t} dt$">|; 

$key = q/displaystyle{bfH}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2827.png"
 ALT="$\displaystyle {\bf H}_s$">|; 

$key = q/N_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1600.png"
 ALT="$ N_2$">|; 

$key = q/nabla^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$ \nabla^{ 2}$">|; 

$key = q/displaystylefrac{dE}{dt}=frac{d(m,c^{,2})}{dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3918.png"
 ALT="$\displaystyle \frac{dE}{dt} = \frac{d (m c^{ 2})}{dt},$">|; 

$key = q/exp(-xslashd);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1698.png"
 ALT="$ \exp(-x/d)$">|; 

$key = q/displaystyledeltaE=frac{2pi,rho}{u},P=frac{e^{,2}}{3,epsilon_0,c^3}frac{gamma^{,4},u^{,3}}{rho}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4087.png"
 ALT="$\displaystyle \delta E = \frac{2\pi  \rho}{u}  P = \frac{e^{ 2}}{3 \epsilon_0  c^3} \frac{\gamma^{ 4}  u^{ 3}}{\rho}.$">|; 

$key = q/displaystyle{bfF}_{21}=frac{mu_0,I_1,I_2}{4pi}oint_1oint_2frac{d{bfr}_2times(d{bfr}_1times{bfr}_{12})}{|{bfr}_{12}|^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1303.png"
 ALT="$\displaystyle {\bf F}_{21} = \frac{\mu_0 I_1 I_2}{4\pi}\oint_1\oint_2\frac{d{\bf r}_2\times (d{\bf r}_1\times {\bf r}_{12})}{\vert{\bf r}_{12}\vert^{ 3}},$">|; 

$key = q/A_{ijcdotsk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3544.png"
 ALT="$ A_{ij\cdots k}$">|; 

$key = q/displaystyle=-frac{mu_0,I}{2,a},sintheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1363.png"
 ALT="$\displaystyle = -\frac{\mu_0 I}{2 a} \sin\theta.$">|; 

$key = q/displaystyle=-frac{mu_0,I}{2,a}sum_{l=1,3,5,cdots}frac{P_l^1(0)}{l}left(frac{r}{a}right)^{l-1}P_l^1(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1357.png"
 ALT="$\displaystyle = -\frac{\mu_0 I}{2 a}\sum_{l=1,3,5,\cdots}\frac{P_l^1(0)}{l}\left(\frac{r}{a}\right)^{l-1}P_l^1(\cos\theta)$">|; 

$key = q/displaystylephantom{=}+g,dx,dt+h,dy,dt+k,dz,dt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3423.png"
 ALT="$\displaystyle \phantom{=}+ g  dx  dt + h  dy  dt + k  dz  dt$">|; 

$key = q/|R|leq1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2571.png"
 ALT="$ \vert R\vert\leq 1$">|; 

$key = q/P={bfE}cdot{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4180.png"
 ALT="$ P={\bf E}\cdot{\bf B}$">|; 

$key = q/displaystyle={bfE}_{rminc}+{bfE}_{sc},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3326.png"
 ALT="$\displaystyle = {\bf E}_{\rm inc} + {\bf E}_{sc},$">|; 

$key = q/displaystylek,rgg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2614.png"
 ALT="$\displaystyle k r\gg 1$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=G_D({bfr}',{bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}')= G_D({\bf r}',{\bf r}).$">|; 

$key = q/displaystylephi'(r,theta)=-frac{q}{4pi,epsilon_0}frac{1}{(r^{,2},b^{,2}slasha^{,2}-2,r,b,costheta+a^{,2})^{1slash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="$\displaystyle \phi'(r,\theta) = -\frac{q}{4\pi \epsilon_0} \frac{1}{(r^{ 2} b^{ 2}/a^{ 2}-2 r b \cos\theta+a^{ 2})^{1/2}}$">|; 

$key = q/displaystyleboxemptyequivpartial_mu,partial^{,mu}=-nabla^{,2}+frac{1}{c^{,2}}frac{partial^{,2}}{partialt^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3671.png"
 ALT="$\displaystyle \boxempty \equiv \partial_\mu  \partial^{ \mu} = -\nabla^{ 2} + \frac{1}{c^{ 2}} \frac {\partial^{ 2}}{\partial t^{ 2}}.$">|; 

$key = q/{bfr}cdotc,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3090.png"
 ALT="$ {\bf r}\cdot c {\bf B}$">|; 

$key = q/{bfE}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$ {\bf E}({\bf r},t)$">|; 

$key = q/E=c,Bproptor^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2619.png"
 ALT="$ E=c B\propto r^{-1}$">|; 

$key = q/displaystylefrac{q+q'}{epsilon_1}=frac{q''}{epsilon_2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1115.png"
 ALT="$\displaystyle \frac{q+q'}{\epsilon_1} = \frac{q''}{\epsilon_2},$">|; 

$key = q/displaystyle{bfE}({bfr})=frac{3,({bfp}cdot{bfr}),{bfr}-r^{,2},{bfp}}{4pi,epsilon_0,r^{,5}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = \frac{3 ({\bf p}\cdot{\bf r}) {\bf r}-r^{ 2} {\bf p}}{4\pi \epsilon_0 r^{ 5}},
$">|; 

$key = q/displaystyle=gamma,{bfE}+frac{1-gamma}{v^{,2}},({bfv}cdot{bfE}),{bfv}+gamma,({bfv}times{bfB}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4177.png"
 ALT="$\displaystyle = \gamma {\bf E} + \frac{1-\gamma}{v^{ 2}} ({\bf v}\cdot{\bf E}) {\bf v} + \gamma ({\bf v}\times {\bf B}),$">|; 

$key = q/{figure}{epsfysize{=3.75in{centerline{epsffile{Chapter06slashsom.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="428" BORDER="0"
 SRC="|."$dir".q|img1887.png"
 ALT="\begin{figure}
\epsfysize =3.75in
\centerline{\epsffile{Chapter06/som.eps}}
\end{figure}">|; 

$key = q/displaystylefrac{partialepsilon}{partialt}=-frac{depsilon}{drho_m},rho_m,nablacdot{bfu}-{bfu}cdotnablaepsilon.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1223.png"
 ALT="$\displaystyle \frac{\partial \epsilon}{\partial t} = - \frac{d\epsilon}{d\rho_m}  \rho_m  \nabla\cdot{\bf u} - {\bf u} \cdot\nabla\epsilon.$">|; 

$key = q/displaystyleint_0^inftycos(pi,t^{,2}slash2),dt=int_0^inftysin(pi,t^{,2}slash2),dt=frac{1}{2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1910.png"
 ALT="$\displaystyle \int_0^\infty\cos(\pi  t^{ 2}/2) dt = \int_0^\infty\sin(\pi  t^{ 2}/2) dt =\frac{1}{2}.$">|; 

$key = q/{bfE}times{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1587.png"
 ALT="$ {\bf E}\times{\bf H}$">|; 

$key = q/displaystylefrac{partial,c,B_x}{partialz}=-{rmi},k,q^{,2},E_y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2306.png"
 ALT="$\displaystyle \frac{\partial c  B_x}{\partial z} = -{\rm i} k q^{ 2} E_y,$">|; 

$key = q/A_varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1331.png"
 ALT="$ A_\varphi$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}=frac{e^{,2},dot{u}^{,2}}{16pi^2,epsilon_0,c^{,3}}frac{[(uslashc)-costheta]^{,2}}{[1-(uslashc),costheta]^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4129.png"
 ALT="$\displaystyle \frac{d P(t')}{d{\mit\Omega}} = \frac{e^{ 2}  \dot{u}^{ 2}}{16...
...on_0  c^{ 3}} \frac{[(u/c) - \cos\theta]^{ 2}}{[1-(u/c) \cos\theta]^{ 5}}.$">|; 

$key = q/phi_S=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="$ \phi_S=0$">|; 

$key = q/{bfe};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2715.png"
 ALT="$ {\bf e}$">|; 

$key = q/displaystyleu_p,u_g=c^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2888.png"
 ALT="$\displaystyle u_p  u_g = c^{ 2}.$">|; 

$key = q/displaystyleP=frac{e^{,2}}{6pi,epsilon_0,c^{,3}},dot{u}^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4038.png"
 ALT="$\displaystyle P = \frac{e^{ 2}}{6\pi \epsilon_0  c^{ 3}}  \dot{u}^{ 2}.$">|; 

$key = q/displaystyleS_m(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="$\displaystyle S_m(r)$">|; 

$key = q/omega_p(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2382.png"
 ALT="$ \omega_p(z)$">|; 

$key = q/A^{,mu}=({bfa},,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3707.png"
 ALT="$ A^{ \mu} = ({\bf a}, 0)$">|; 

$key = q/displaystyle=mu_0,{bfj}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle = \mu_0  {\bf j}.$">|; 

$key = q/q_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="$ q_i$">|; 

$key = q/{bfD}({bfr}'),dS';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="$ {\bf D}({\bf r}') dS'$">|; 

$key = q/displaystyle=j_l(z)+{rmi},y_l(z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3027.png"
 ALT="$\displaystyle = j_l(z)+ {\rm i} y_l(z),$">|; 

$key = q/displaystyleW_2=frac{1}{4pi,epsilon_0}frac{q_2,q_1}{|{bfr}_2-{bfr}_1|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$\displaystyle W_2 = \frac{1}{4\pi \epsilon_0} \frac{q_2  q_1}{\vert{\bf r}_2 - {\bf r}_1\vert}.$">|; 

$key = q/displaystyleRsimeqleft(frac{E_r}{E_i}right)^2simeq1-2sqrt{2},alpha=1-left(frac{8,epsilon_0,omega}{sigma}right)^{1slash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2212.png"
 ALT="$\displaystyle R \simeq\left(\frac{E_r}{E_i}\right)^2\simeq 1-2\sqrt{2} \alpha =1- \left(\frac{8 \epsilon_0 \omega}{\sigma}\right)^{1/2}.$">|; 

$key = q/U_mu,U^{,mu}=c^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3938.png"
 ALT="$ U_\mu  U^{ \mu} = c^{ 2}$">|; 

$key = q/rho_b=-nablacdot{bfP};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1121.png"
 ALT="$ \rho_b = - \nabla \cdot
{\bf P}$">|; 

$key = q/displaystyleE_parallel';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3851.png"
 ALT="$\displaystyle E_\parallel'$">|; 

$key = q/n^r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3524.png"
 ALT="$ n^r$">|; 

$key = q/displaystyleK=frac{mbox{powerlossperunitlengthofguide}}{mbox{powertransmittedthroughguide}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2899.png"
 ALT="$\displaystyle K = \frac{\mbox{power loss per unit length of guide}} {\mbox{ power transmitted through guide}}.$">|; 

$key = q/z(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1664.png"
 ALT="$ z(x)$">|; 

$key = q/alpha_{l,m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="$ \alpha_{l,m}$">|; 

$key = q/f(r,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2854.png"
 ALT="$ f(r,\varphi)$">|; 

$key = q/displaystylelangleddot{s}^{,2}rangle=frac{q^{,2}}{m^{,2}}langleE^{,2}rangle=frac{q^{,2},E_0^{,2}}{2,m^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2721.png"
 ALT="$\displaystyle \langle \ddot{s}^{ 2}\rangle = \frac{q^{ 2}}{m^{ 2}} \langle E^{ 2}\rangle = \frac{q^{ 2}  E_0^{ 2}}{2 m^{ 2}}.$">|; 

$key = q/a_E(1,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3264.png"
 ALT="$ a_E(1,0)$">|; 

$key = q/displaystyle{bfB}({bf0})=frac{mu_0,I}{2,a},{bfe}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1364.png"
 ALT="$\displaystyle {\bf B}({\bf0}) = \frac{\mu_0 I}{2 a} {\bf e}_z.$">|; 

$key = q/A^j=C^{,ij},B_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3575.png"
 ALT="$ A^j = C^{ ij}  B_i$">|; 

$key = q/R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$ R$">|; 

$key = q/displaystyletau=2int_0^{z_0(omega)}frac{dz}{u_z(omega,z)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2353.png"
 ALT="$\displaystyle \tau = 2\int_0^{z_0(\omega)} \frac{dz}{u_z(\omega,z)}.$">|; 

$key = q/displaystylez(x=pmg_i)=frac{1}{2,g_i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1666.png"
 ALT="$\displaystyle z(x=\pm g_i) = \frac{1}{2 g_i}.$">|; 

$key = q/displaystylerightarrowfrac{z^{,l}}{(2,l+1)!!}left[1+{calO}(z^2)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3034.png"
 ALT="$\displaystyle \rightarrow \frac{z^{ l}}{(2 l+1)!!}\left[1+ {\cal O}(z^2)\right],$">|; 

$key = q/displaystyleepsilon_1,E_z(z=0_+);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1097.png"
 ALT="$\displaystyle \epsilon_1  E_z(z=0_+)$">|; 

$key = q/displaystyle=left(frac{5}{24pi}right)^{1slash2},(Q_{13}+{rmi},Q_{23}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="$\displaystyle =\left(\frac{5}{24\pi}\right)^{1/2} (Q_{13}+{\rm i} Q_{23}),$">|; 

$key = q/x^{,i}rightarrowx^{,i'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3549.png"
 ALT="$ x^{ i}\rightarrow x^{ i'}$">|; 

$key = q/displaystylepsi(x,y,z,t)=psi_i,cos(omega,t-{bfk}_icdot{bfr})+psi_r,cos(omega,t-{bfk}_rcdot{bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2017.png"
 ALT="$\displaystyle \psi(x,y,z,t)= \psi_i  \cos(\omega t-{\bf k}_i\cdot{\bf r}) + \psi_r \cos(\omega t-{\bf k}_r\cdot{\bf r})$">|; 

$key = q/displaystylek_{i,x}=k_{r,x}=k_{t,x},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2025.png"
 ALT="$\displaystyle k_{i x} = k_{r x} = k_{t x},$">|; 

$key = q/displaystylephi_m(r,theta)=frac{M_0,a^{,2}}{3}frac{r}{a^{,2}}costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1513.png"
 ALT="$\displaystyle \phi_m(r,\theta) = \frac{M_0  a^{ 2}}{3} \frac{r}{a^{ 2}} \cos\theta$">|; 

$key = q/displaystylek_{mn}=frac{j_{mn}}{a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="$\displaystyle k_{mn} = \frac{j_{mn}}{a}.$">|; 

$key = q/(0,hat{z})_d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2514.png"
 ALT="$ (0,\hat{z})_d$">|; 

$key = q/s_0=1slash(4,xi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1889.png"
 ALT="$ s_0 = 1/(4 \xi)$">|; 

$key = q/displaystylew(1)=A,(0,hat{z})_s+B,(hat{z},0)_d.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2499.png"
 ALT="$\displaystyle w(1) = A (0,\hat{z})_s + B (\hat{z},0)_d.$">|; 

$key = q/displaystyle{bfP}=frac{(N,e^{,2}slashm),{bfE}}{omega_0^{,2}-omega^{,2}-{rmi},g,omega,omega_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1624.png"
 ALT="$\displaystyle {\bf P} = \frac{(N e^{ 2}/m)  {\bf E}}{\omega_0^{ 2} -\omega^{ 2}- {\rm i} g \omega \omega_0}.$">|; 

$key = q/displaystyleG_D({bfr},{bfr}'')=G_D({bfr}'',{bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}'')=G_D({\bf r}'',{\bf r}).$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{{rmRe},({bfn}cdot{bfE}times{bfB}^{,ast}),r^{,2}}{2,mu_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3275.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} = \frac{{\rm Re} ( {\bf n}\cdot{\bf E}\times{\bf B}^{ \ast}) r^{ 2}} {2 \mu_0},$">|; 

$key = q/displaystylew''+h^{,2},q(hat{z}),w=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2551.png"
 ALT="$\displaystyle w'' + h^{ 2} q(\hat{z}) w = 0,$">|; 

$key = q/-sigma,[aslash(a-dslash2)]^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="$ -\sigma [a/(a-d/2)]^{ 2}$">|; 

$key = q/displaystylefrac{4pi,epsilon_0}{e},{bfE}=frac{1}{s^{,2},r}left({bfr}-frac{r,{bfuc}+frac{{bfr}cdotdot{bfu}}{c}right)-frac{r}{s^{,2},c^{,2}},dot{bfu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4010.png"
 ALT="$\displaystyle \frac{4\pi \epsilon_0}{e}  {\bf E} = \frac{1}{s^{ 2}  r} \lef...
...\bf r} \cdot\dot{\bf u}}{c}\right) - \frac{r}{s^{ 2}  c^{ 2}}  \dot{\bf u},$">|; 

$key = q/(x^1,,x^2,,x^3,,x^4);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3631.png"
 ALT="$ (x^1,  x^2,  x^3,  x^4)$">|; 

$key = q/displaystyleA_{kcdotsl,mn}^{icdotsj}=frac{partialA_{kcdotsl}^{icdotsj}}{partialx^{,m}partialx^{,n}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3585.png"
 ALT="$\displaystyle A_{k\cdots l,mn}^{i\cdots j} =\frac{\partial A_{k\cdots l}^{i\cdots j} } {\partial x^{ m} \partial x^{ n}}$">|; 

$key = q/displaystyleI(z,t)=I(|z|),{rme}^{-{rmi},omega,t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3247.png"
 ALT="$\displaystyle I(z, t) = I(\vert z\vert)  {\rm e}^{-{\rm i} \omega t},$">|; 

$key = q/displaystyle{bfE}=frac{rmi}{k},nablatimesc,{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3073.png"
 ALT="$\displaystyle {\bf E} = \frac{\rm i}{k} \nabla\times c {\bf B}.$">|; 

$key = q/{rmTE}_{,0l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2976.png"
 ALT="$ {\rm TE}_{ 0l}$">|; 

$key = q/displaystyle{bfE}_{rmsc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3330.png"
 ALT="$\displaystyle {\bf E}_{\rm sc}$">|; 

$key = q/displaystyleA=-{rmi},expleft(,{rmi},hint_a^0q^{,1slash2}(x'),dx'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2564.png"
 ALT="$\displaystyle A = -{\rm i} \exp\left( {\rm i} h\int_a^0 q^{ 1/2}(x') dx' \right).$">|; 

$key = q/{bfB}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4176.png"
 ALT="$ {\bf B}'$">|; 

$key = q/theta=sin^{-1}(vslashc);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4175.png"
 ALT="$ \theta =\sin^{-1}(v/c)$">|; 

$key = q/Q>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4188.png"
 ALT="$ Q&gt;0$">|; 

$key = q/displaystyle=gamma,(T^{,1}-beta,T^{,4}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3639.png"
 ALT="$\displaystyle = \gamma (T^{ 1}-\beta  T^{ 4}),$">|; 

$key = q/displaystylefrac{depsilon}{drho_m}=frac{(epsilon-1),(epsilon+2)}{3,rho_m}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1252.png"
 ALT="$\displaystyle \frac{d\epsilon}{d\rho_m} = \frac{(\epsilon-1) (\epsilon+2)}{3 \rho_m}.$">|; 

$key = q/displaystyleu({bfr},t)=intfrac{[v({bfr}')]}{4pi,|{bfr}-{bfr}'|},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle u({\bf r}, t) = \int \frac{ [v({\bf r}')]} {4\pi \vert{\bf r} - {\bf r}'\vert} dV',$">|; 

$key = q/partialslashpartialn'=-partialslashpartialr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="$ \partial/\partial n'=-\partial/\partial r'$">|; 

$key = q/displaystyle=-F_{ji}=-c,B_{ij}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3796.png"
 ALT="$\displaystyle = -F_{ji} = -c B_{ij}.$">|; 

$key = q/f(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2403.png"
 ALT="$ f(z)$">|; 

$key = q/m_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3907.png"
 ALT="$ m_0$">|; 

$key = q/d({A^{icdotsj}}_{kcdotsl})slashds;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3608.png"
 ALT="$ d({A^{i\cdots j}}_{k\cdots l})/ds$">|; 

$key = q/C_{,kl}^j=A^{ij},B_{ikl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3567.png"
 ALT="$ C_{ kl}^j = A^{ij}  B_{ikl}$">|; 

$key = q/displaystylew(x,h)=A,(x,0)_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2549.png"
 ALT="$\displaystyle w(x,h) =A  (x,0)_s,$">|; 

$key = q/displaystylechi=tan^{-1}(E_yslashE_x),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1751.png"
 ALT="$\displaystyle \chi = \tan^{-1}(E_y/E_x),$">|; 

$key = q/m_e,c^{,2}=0.511;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4082.png"
 ALT="$ m_e  c^{ 2} = 0.511$">|; 

$key = q/(x',y',z',t');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3451.png"
 ALT="$ (x', y', z', t')$">|; 

$key = q/displaystylenablacdot{bfA}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1313.png"
 ALT="$\displaystyle \nabla\cdot{\bf A}({\bf r})$">|; 

$key = q/Sigma_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$ \Sigma_0$">|; 

$key = q/displaystyle{bfM}({bfr})=sum_iN_i,langle{bfm}_irangle,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1429.png"
 ALT="$\displaystyle {\bf M} ({\bf r}) = \sum_i N_i  \langle {\bf m}_i\rangle,$">|; 

$key = q/dx^{,mu}slashds;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3699.png"
 ALT="$ dx^{ \mu}/ds$">|; 

$key = q/displaystyle{bfE}_{lm}^{(E)}=c,{bfB}_{lm}^{(E)}times{bfn},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3149.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(E)} = c {\bf B}_{lm}^{(E)}\times{\bf n},$">|; 

$key = q/g^{(i)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$ g^{(i)}$">|; 

$key = q/displaystyleu_z(omega_0,z)=cleftslashleft{frac{partial[omega,n(omega,z)]}{partialomega}right}_{omega=omega_0}right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2342.png"
 ALT="$\displaystyle u_z(\omega_0,z) = c\left/ \left\{\frac{\partial[\omega  n(\omega,z)]}{\partial\omega} \right\}_{\omega=\omega_0}\right..$">|; 

$key = q/displaystyleA,{rmexp}left[,{rmi},k,n_n(pmzcostheta_n+xsintheta_n)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2290.png"
 ALT="$\displaystyle A {\rm\exp}\left[ {\rm i} k  n_n(\pm z\cos\theta_n + x\sin\theta_n)\right],$">|; 

$key = q/displaystylefrac{omega^{,2}}{k^{,2}}=frac{c^{,2}}{epsilon},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1608.png"
 ALT="$\displaystyle \frac{\omega^{ 2}}{k^{ 2}} = \frac{c^{ 2}}{\epsilon},$">|; 

$key = q/|{bfE}|=c,|{bfB}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3151.png"
 ALT="$ \vert{\bf E}\vert=c \vert{\bf B}\vert$">|; 

$key = q/displaystyleG_omega=frac{{rme}^{-{rmi},k,R}}{4pi,R};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle G_\omega = \frac{{\rm e}^{-{\rm i} k R}}{4\pi  R}$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06bslashfig12.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img2189.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06b/fig12.eps}}
\end{figure}">|; 

$key = q/B_0>B_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1544.png"
 ALT="$ B_0 &gt; B_s$">|; 

$key = q/displaystyle{bfn}times({bfE}_1-{bfE}_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2756.png"
 ALT="$\displaystyle {\bf n}\times ({\bf E}_1-{\bf E}_2)$">|; 

$key = q/displaystylemu_0,delta=muleft(beta-frac{2,gamma}{a^{,3}}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1563.png"
 ALT="$\displaystyle \mu_0  \delta = \mu\left(\beta - \frac{2 \gamma}{a^{ 3}}\right),$">|; 

$key = q/displaystyleA_{,i'j'cdotsk'}=A_{ijcdotsk},p_{i'}^{,i},p_{j'}^{,j}cdotsp_{k'}^{,k}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3547.png"
 ALT="$\displaystyle A_{ i'j'\cdots k'} = A_{ij\cdots k}  p_{i'}^{ i}  p_{j'}^{ j} \cdots p_{k'}^{ k}.$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0}{4pi}int_Vfrac{nabla'times{bfM}({bfr}')}{|{bffrac{mu_0}{4pi}int_Sfrac{{bfM}({bfr}')timesd{bfS}'}{|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1497.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = \frac{\mu_0}{4\pi}\int_V \frac{\nabla'\times {...
...}\int_S \frac{ {\bf M}({\bf r}')\times d{\bf S}'}{\vert{\bf r}- {\bf r}'\vert}.$">|; 

$key = q/x^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3664.png"
 ALT="$ x^{ \mu}$">|; 

$key = q/E^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3829.png"
 ALT="$ E^{ ij}$">|; 

$key = q/{calO}(1slashz);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2444.png"
 ALT="$ {\cal O}(1/z)$">|; 

$key = q/J_0(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2874.png"
 ALT="$ J_0(z)$">|; 

$key = q/displaystylef_s=frac{sigma^{,2}}{2,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1278.png"
 ALT="$\displaystyle f_s = \frac{\sigma^{ 2}}{2 \epsilon_0}.$">|; 

$key = q/B,(0,hat{z})_d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2517.png"
 ALT="$ B (0,\hat{z})_d$">|; 

$key = q/displaystyleomega_p(z)=left[frac{pi,{mitGamma}(1+p)}{{mitGamma}(1slash2+pslash2)ht]^{1slashp}frac{omega_0}{2}left(frac{z-h_0}{delta}right)^{1slashp};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2585.png"
 ALT="$\displaystyle \omega_p(z) =\left[\frac{\pi {\mit\Gamma}(1+p)}{{\mit\Gamma}(1/2...
...2+p/2)}\right]^{1/p} \frac{\omega_0}{2}\left(\frac{z-h_0}{\delta}\right)^{1/p}
$">|; 

$key = q/displaystyle(0,x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2535.png"
 ALT="$\displaystyle (0, x)$">|; 

$key = q/E_theta(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2954.png"
 ALT="$ E_\theta(r)$">|; 

$key = q/m=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$ m=0$">|; 

$key = q/displaystylenabla^{,2}psi=nabla'^{,2}psi=-delta({bfr}-{bfr}').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="$\displaystyle \nabla^{ 2}\psi=\nabla'^{ 2}\psi = -\delta({\bf r}-{\bf r}').$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}=frac{e^{,2},dot{u}^{,2}}{16pi^2,epsilon_0,uslashc)-sinalpha,cosphi]^{,2}}{[1-(uslashc),sinalpha,cosphi]^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4126.png"
 ALT="$\displaystyle \frac{d P(t')}{d{\mit\Omega}} = \frac{e^{ 2}  \dot{u}^{ 2}}{16...
...ha+[(u/c)-\sin\alpha \cos\phi]^{ 2}} {[1-(u/c) \sin\alpha \cos\phi]^{ 5}}.$">|; 

$key = q/g_l(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3181.png"
 ALT="$ g_l(r)$">|; 

$key = q/displaystylesimeqfrac{mu_0}{4pi}intleft(frac{{bfj}times{bfR}}{R^{,3}}-frac{1}{2}al^{,2}{bfj}slashpartialt^{,2})times{bfR}}{c^{,2},R}+cdotsright)dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$\displaystyle \simeq \frac{\mu_0}{4\pi} \int \left(\frac{{\bf j}\times{\bf R}}{...
... 2} {\bf j}/ \partial t^{ 2})\times{\bf R}}{c^{ 2}  R} +\cdots \right) dV'.$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}int_a^inftyint_0^piint_0^{2pi}frac{rho(r',thea',dr',dtheta',dvarphi'}{(r^{,2}-2,r,r',cosgamma+r'^{,2})^{1slash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="$\displaystyle =\frac{1}{4\pi \epsilon_0}\int_a^\infty\int_0^\pi\int_0^{2\pi}\f...
...heta' dr' d\theta' d\varphi'}{(r^{ 2}-2 r r' \cos\gamma+r'^{ 2})^{1/2}}$">|; 

$key = q/psi(x,y,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2019.png"
 ALT="$ \psi(x,y,z,t)$">|; 

$key = q/displaystylefrac{dsigma}{d{mitOmega}}=left(frac{q^{,2}}{4pi,epsilon_0,m,c^{,2}}right)^2sin^2theta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2726.png"
 ALT="$\displaystyle \frac{d\sigma}{d {\mit \Omega}} = \left( \frac{q^{ 2}}{4\pi \epsilon_0  m  c^{ 2}}\right)^2 \sin^2\theta.$">|; 

$key = q/k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="$ k$">|; 

$key = q/{bfe}cdot{bfk}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2716.png"
 ALT="$ {\bf e}\cdot
{\bf k}=0$">|; 

$key = q/j_{02}=5.520;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="$ j_{02}=5.520$">|; 

$key = q/displaystyle{bfu}=frac{{bfE}times{bfB}}{mu_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3974.png"
 ALT="$\displaystyle {\bf u} = \frac{{\bf E}\times{\bf B}}{\mu_0}.$">|; 

$key = q/displaystylerightarrow-{rmi},(0,hat{z}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2510.png"
 ALT="$\displaystyle \rightarrow -{\rm i} (0,\hat{z}).$">|; 

$key = q/displaystyle=-frac{1}{pi,L}sum_{n=1,infty}sum_{m=-infty,infty}sinleft(frac{n,pi}ight),sinleft(frac{n,pi}{L},z'right),{rme}^{,{rmi},m,(theta-theta')};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1045.png"
 ALT="$\displaystyle =-\frac{1}{\pi L}\sum_{n=1,\infty}\sum_{m=-\infty,\infty}\sin\le...
...\sin\left(\frac{n \pi}{L} z'\right) {\rm e}^{ {\rm i} m (\theta-\theta')}$">|; 

$key = q/J_1'(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2876.png"
 ALT="$ J_1'(z)$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{mu_0,c,I^{,2}}{8pi^2}left|frac{cos(k,d,costhetaslash2)-cos(k,dslash2)}{sintheta}right|^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2629.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} =\frac{\mu_0  c I^{ 2}}{8\pi^2} \left\vert\frac{\cos(k d  \cos\theta/2) -\cos(k d/2)}{\sin\theta}\right\vert^{ 2}.$">|; 

$key = q/H_z=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2835.png"
 ALT="$ H_z=0$">|; 

$key = q/displaystylefrac{partialP_{rmload}}{partialR_{rmload}}=frac{V_0^{,2}}{2}left[frac{R_{rmload}-R_{rmrad}}{(R_{rmrad}+R_{rmload})^{,3}}right]=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2663.png"
 ALT="$\displaystyle \frac{\partial P_{\rm load}}{\partial R_{\rm load}} = \frac{V_0^{...
...rac{R_{\rm load} - R_{\rm rad}}{(R_{\rm rad} + R_{\rm load})^{ 3}}\right] = 0.$">|; 

$key = q/displaystylesimeq{rmi},k,{bfn}times{bfA}={rmi},k,frac{mu_0}{4pi}frac{{rme}^{,{rm}{r}int{bfn}times{bfj}({bfr}'),{rme}^{-{rmi},k,{bfn}cdot{bfr}'},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2616.png"
 ALT="$\displaystyle \simeq {\rm i} k {\bf n}\times{\bf A} = {\rm i} k \frac{\mu_0...
... n}\times{\bf j}({\bf r}') {\rm e}^{-{\rm i} k {\bf n} \cdot {\bf r}'} dV',$">|; 

$key = q/displaystylenablatimesc,{bfB}+{rmi},k,{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3199.png"
 ALT="$\displaystyle \nabla\times c {\bf B} + {\rm i} k  {\bf E}'$">|; 

$key = q/displaystyle({bfH}_2-{bfH}_1)times{bfn}_{21}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1469.png"
 ALT="$\displaystyle ({\bf H}_2 - {\bf H}_1)\times {\bf n}_{21} = 0,$">|; 

$key = q/displaystyle=-(1-x^{,2})^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="$\displaystyle = -(1-x^{ 2})^{1/2},$">|; 

$key = q/1.2188;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2647.png"
 ALT="$ 1.2188$">|; 

$key = q/+l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="$ +l$">|; 

$key = q/displaystylepartial_muequivfrac{partial}{partialx^{,mu}}=left(nabla,frac{1}{c}frac{partial}{partialt}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3665.png"
 ALT="$\displaystyle \partial_\mu \equiv \frac{\partial}{\partial x^{ \mu}} = \left(\nabla, \frac{1}{c}\frac{\partial}{\partial t}\right),$">|; 

$key = q/nablacdot{bfu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1262.png"
 ALT="$ \nabla\cdot{\bf u} =0$">|; 

$key = q/gamma(u),V;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3711.png"
 ALT="$ \gamma(u)  V$">|; 

$key = q/displaystyle{calF}_mu=frac{d(m_0,U_mu)}{dtau}=m_0,A_mu+frac{dm_0}{dtau},U_mu,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3937.png"
 ALT="$\displaystyle {\cal F}_\mu =\frac{d(m_0  U_\mu)}{d\tau} = m_0  A_\mu + \frac{dm_0}{d\tau}  U_\mu,$">|; 

$key = q/displaystylep_{mu'}^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3649.png"
 ALT="$\displaystyle p_{\mu'}^{ \mu}$">|; 

$key = q/displaystyle=psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2158.png"
 ALT="$\displaystyle = \psi_t,$">|; 

$key = q/displaystyle~~~~+frac{1}{4pi,epsilon_0}int_SD({bfr}'),frac{partial}{partialn'}!left(frac{1}{|{bfr}-{bfr}'|}right)dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\frac{1}{4\pi \epsilon_0}\int_S D({\bf r}') \frac{\partial}{\partial n'}\!\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dS',$">|; 

$key = q/displaystyleU=frac{1}{2}int_V{bfE}cdot{bfD},dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1295.png"
 ALT="$\displaystyle U = \frac{1}{2} \int_V {\bf E}\cdot{\bf D} dV
$">|; 

$key = q/displaystyle-{bfE}cdot{bfj}=nablacdotleft(frac{{bfE}times{bfB}}{mu_0}right)+fracpartialt}!left(frac{epsilon_0,E^{,2}}{2}+frac{B^{,2}}{2,mu_0}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$\displaystyle - {\bf E} \cdot {\bf j} = \nabla \cdot \left(\frac{{\bf E}\times{...
...ial t}\!\left( \frac{\epsilon_0 E^{ 2}}{2} +\frac{B^{ 2}}{2 \mu_0} \right).$">|; 

$key = q/displaystyle{A^i}_j=g^{,ip}A_{pj}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3599.png"
 ALT="$\displaystyle {A^i}_j = g^{ ip} A_{pj}.$">|; 

$key = q/omegarightarrow2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1829.png"
 ALT="$ \omega\rightarrow 2\pi/\tau$">|; 

$key = q/{mitDelta}x>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3521.png"
 ALT="$ {\mit\Delta} x&gt;0$">|; 

$key = q/displaystyleint_Vnabla^{,2}left(frac{1}{|{bfr}-{bfr}'|}right)dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \int_V \nabla^{ 2}\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dV$">|; 

$key = q/displaystyle{calI}_z=-E_y,H_x.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2120.png"
 ALT="$\displaystyle {\cal I}_z = -E_y H_x.$">|; 

$key = q/displaystylephi';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3865.png"
 ALT="$\displaystyle \phi'$">|; 

$key = q/displaystyleP(t')=frac{e^{,2}}{6pi,epsilon_0,c^{,3}},gamma^{,4},dot{u}^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4140.png"
 ALT="$\displaystyle P(t') = \frac{e^{ 2}}{6\pi \epsilon_0  c^{ 3}} \gamma^{ 4} \dot{u}^{ 2},$">|; 

$key = q/Q^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4051.png"
 ALT="$ Q^{ \mu\nu}$">|; 

$key = q/mu=BslashH;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1461.png"
 ALT="$ \mu = B/H$">|; 

$key = q/displaystylez_{rmmax}=frac{1}{g_i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1665.png"
 ALT="$\displaystyle z_{\rm max} = \frac{1}{g_i}.$">|; 

$key = q/{bfu}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3490.png"
 ALT="$ {\bf u}'$">|; 

$key = q/displaystylephi_1({bfr})=frac{1}{4pi,epsilon_0},frac{p_x,x+p_y,y+p_z,z}{r^{,3}}=frac{1}{4pi,epsilon_0},frac{{bfp}cdot{bfr}}{r^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="$\displaystyle \phi_1({\bf r})= \frac{1}{4\pi \epsilon_0} \frac{p_x x+p_y y+p_z z}{r^{ 3}}= \frac{1}{4\pi \epsilon_0} \frac{{\bf p}\cdot{\bf r}}{r^{ 3}},$">|; 

$key = q/displaystylef(t)=frac{1}{tau}int_{-infty}^{infty}frac{domega}{omega^{,2}-(2pislashtau)^{,2}}left(cos[omega,(t-T),]-cos[omega,t]right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1785.png"
 ALT="$\displaystyle f(t) = \frac{1}{\tau} \int_{-\infty}^{\infty} \frac{d\omega}{\omega^{ 2} -(2\pi/\tau)^{ 2}} \left(\cos[\omega (t-T) ] -\cos[\omega  t]\right),$">|; 

$key = q/[nablacdot{bfj}]simeq-[partial{bfj}slashpartialt]cdot{bfR}slash(c,R);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$ [\nabla\cdot {\bf j} ] \simeq -[\partial {\bf j}/\partial t]\cdot {\bf R}/(c  R)$">|; 

$key = q/displaystyleP=frac{e^{,2}}{6pi,epsilon_0,c^{,3}},gamma^{,4},dot{u}^{,2}=frac{e^{,2}}{6pi,epsilon_0,c^{,3}}frac{gamma^{,4},u^{,4}}{rho^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4085.png"
 ALT="$\displaystyle P = \frac{e^{ 2}}{6\pi \epsilon_0  c^{ 3}}   \gamma^{ 4}  ...
...e^{ 2}}{6\pi \epsilon_0  c^{ 3}} \frac{\gamma^{ 4}  u^{ 4}}{\rho^{ 2}},$">|; 

$key = q/displaystyle=-G^{ji}=-E^{ij},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3826.png"
 ALT="$\displaystyle = -G^{ji} = -E^{ij},$">|; 

$key = q/p_{sigma'}^{,nu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3683.png"
 ALT="$ p_{\sigma'}^{ \nu}$">|; 

$key = q/displaystylefrac{1}{r}frac{d}{dr}!left(r,frac{dg}{dr}right)+left(k_s^{,2}-frac{m^{,2}}{r^{,2}}right)g=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2857.png"
 ALT="$\displaystyle \frac{1}{r} \frac{d}{d r} \!\left(r \frac{d g} {d r}\right) + \left(k_s^{ 2}-\frac{m^{ 2}}{r^{ 2}}\right) g = 0,$">|; 

$key = q/displaystyle{bfE}=-frac{1}{4pi,epsilon_0}left[frac{bfp}{r^{,3}}-frac{3,({bfp}cdot{bfr}),{bfr}}{r^{,5}}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1245.png"
 ALT="$\displaystyle {\bf E} = -\frac{1}{4\pi \epsilon_0}\left[\frac{\bf p}{r^{ 3}} - \frac{3 ({\bf p}\cdot{\bf r}) {\bf r}}{r^{ 5}}\right].$">|; 

$key = q/displaystylembox{hspace{1cm}as{prightarrowinfty{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="$\displaystyle \mbox{\hspace{1cm}as $p\rightarrow \infty$}$">|; 

$key = q/{rmIm}(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1691.png"
 ALT="$ {\rm Im}(k)$">|; 

$key = q/displaystylef(x,t)=frac{1}{tau}int_C{rme}^{,{rmi},(k,x-omega,t)},frac{domega}{omega^{,2}-(2pislashtau)^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1840.png"
 ALT="$\displaystyle f(x,t) = \frac{1}{\tau} \int _C{\rm e}^{ {\rm i} (k x-\omega  t)}   \frac{d\omega}{\omega^{ 2}-(2\pi/\tau)^{ 2}}.$">|; 

$key = q/q(hat{z})equivn^{,2}(L,hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2456.png"
 ALT="$ q(\hat{z}) \equiv n^{ 2}(L  \hat{z})$">|; 

$key = q/n_1<n_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2132.png"
 ALT="$ n_1&lt; n_2$">|; 

$key = q/{bfr}_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="$ {\bf r}_i$">|; 

$key = q/displaystyleq_{l,m}^{,ast}=intr^{,l},rho(r,theta,varphi),Y_{l,m}(theta,varphi),dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="$\displaystyle q_{l,m}^{ \ast}= \int r^{ l} \rho(r,\theta,\varphi) Y_{l,m}(\theta,\varphi) dV$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter04slashplane.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="590" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1103.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter04/plane.eps}}
\end{figure}">|; 

$key = q/lambdabar;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2677.png"
 ALT="$ \lambdabar$">|; 

$key = q/displaystyle{bfP}=frac{N_A,rho_m,alpha}{M},epsilon_0,{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1233.png"
 ALT="$\displaystyle {\bf P} = \frac{N_A  \rho_m  \alpha}{M}  \epsilon_0  {\bf E},$">|; 

$key = q/K_m(p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img979.png"
 ALT="$ K_m(p)$">|; 

$key = q/A_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2687.png"
 ALT="$ A_t$">|; 

$key = q/displaystyleY_{0,0}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="$\displaystyle Y_{0,0}(\theta,\varphi)$">|; 

$key = q/C_k=A^{ij},B_{ijk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3568.png"
 ALT="$ C_k = A^{ij}  B_{ijk}$">|; 

$key = q/{bfu}=(u_1,u_2,u_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3508.png"
 ALT="$ {\bf u}
=(u_1, u_2, u_3)$">|; 

$key = q/displaystylepsi({bfr},t)=int_{-infty}^{infty}psi({bfr},omega),{rme}^{-{rmi},omega,t},domega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2997.png"
 ALT="$\displaystyle \psi({\bf r}, t) = \int_{-\infty}^{\infty} \psi({\bf r}, \omega)  {\rm e}^{-{\rm i} \omega  t}  d\omega,$">|; 

$key = q/displaystylefrac{d^{,2}phi}{dz^{,2}}simeqpmk,frac{dn}{dz}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2251.png"
 ALT="$\displaystyle \frac{d^{ 2} \phi}{dz^{ 2}} \simeq \pm k \frac{dn}{dz}.$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{mu_0,c,I^{,2}}{2pi^2}frac{cos^4(pi,costhetaslash2)}{sin^2theta}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2643.png"
 ALT="$\displaystyle \frac{d P}{d{\mit\Omega}} =\frac{\mu_0  c I^{ 2}}{2\pi^2} \frac{\cos^4(\pi \cos\theta/2)}{\sin^2\theta}.$">|; 

$key = q/{bfB}=mu_0,({bfH}+{bfM});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1520.png"
 ALT="$ {\bf B}
=\mu_0 ({\bf H} + {\bf M})$">|; 

$key = q/rho_f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1066.png"
 ALT="$ \rho_f$">|; 

$key = q/displaystyleint_V|nabla'G_3({bfr},{bfr}')|^{,2},dV'=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="$\displaystyle \int_V\vert\nabla' G_3({\bf r},{\bf r}')\vert^{ 2} dV'=0,$">|; 

$key = q/displaystylenablacdotc,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2225.png"
 ALT="$\displaystyle \nabla \cdot c {\bf B}$">|; 

$key = q/displaystylefrac{4pi}{mu_0,e},{bfB}=nablatimesfrac{bfu}{s}=-frac{nabla'stimes{bfrac{dot{bfu}}{s}-frac{{bfu}}{s^{,2}}frac{partials}{partialt'}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4012.png"
 ALT="$\displaystyle \frac{4\pi}{\mu_0 e}  {\bf B} = \nabla\times\frac{\bf u}{s} = -...
...ot{\bf u}}{s} - \frac{{\bf u}}{s^{ 2}} \frac{\partial s}{\partial t'} \right),$">|; 

$key = q/displaystyledx'=gammaleft(1+frac{v}{c},costhetaright)dx,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3753.png"
 ALT="$\displaystyle dx' = \gamma\left(1+\frac{v}{c}  \cos\theta\right) dx,$">|; 

$key = q/displaystylesigma_m={bfn}cdot{bfM},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1486.png"
 ALT="$\displaystyle \sigma_m = {\bf n}\cdot{\bf M},$">|; 

$key = q/displaystyleepsilon,A_1=-E_0-2,frac{C_1}{a^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1172.png"
 ALT="$\displaystyle \epsilon  A_1 = - E_0 -2 \frac{C_1}{a^{ 3}},$">|; 

$key = q/displaystyle=2,E_0cos[(omegaslashc),(n,z-c,t)]sin[(omegaslash2,c),(n_+-n_-),z],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1749.png"
 ALT="$\displaystyle =2 E_0 \cos[(\omega/c) (n z-c t)]\sin [(\omega/2 c) (n_+-n_-)  z],$">|; 

$key = q/displaystyleQ(theta)=sum_{m=0,infty}left[A_m,cos(m,theta)+B_m,sin(m,theta)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="$\displaystyle Q(\theta) = \sum_{m=0,\infty}\left[A_m \cos (m \theta) + B_m \sin(m \theta)\right].$">|; 

$key = q/displaystyle{mitOmega}=frac{e,B}{m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1721.png"
 ALT="$\displaystyle {\mit\Omega} = \frac{e  B}{m}$">|; 

$key = q/(omega_i^{,2}-omega^{,2})^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1636.png"
 ALT="$ (\omega_i^{ 2}-\omega^{ 2})^{-1}$">|; 

$key = q/displaystylepartial_muJ^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4206.png"
 ALT="$\displaystyle \partial_\mu J^{ \mu}$">|; 

$key = q/displaystyleint_S{bfE}cdotd{bfS}=frac{1}{epsilon_0}int_Vrho({bfr}),dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$\displaystyle \int_S {\bf E}\cdot d{\bf S} = \frac{1}{\epsilon_0}\int_V\rho({\bf r}) dV,$">|; 

$key = q/C_{kl}^{,j}=A_{ikl}^{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3570.png"
 ALT="$ C_{kl}^{ j} = A_{ikl}^{ij}$">|; 

$key = q/displaystylepsi_i,cos(omega,t-k_{i,x},x-k_{i,y},y)[0.5ex]+psi_r,cos(omega,t-k_{r,x},x-k_{r,y},y)=psi_t,cos(omega,t-k_{t,x},x-k_{t,y},y).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2024.png"
 ALT="$\displaystyle \psi_i \cos(\omega t-k_{i x} x-k_{i y} y)\ [0.5ex] + \psi_...
...ga t-k_{r x} x-k_{r y} y)=\psi_t \cos(\omega t-k_{t x} x-k_{t y} y).$">|; 

$key = q/displaystyleG_N({bfr},{bfr}')=-frac{1}{4pi,|{bfr}-{bfr}'|}+F({bfr},{bfr'}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="$\displaystyle G_N({\bf r},{\bf r}') = - \frac{1}{4\pi \vert{\bf r}-{\bf r}'\vert} + F({\bf r},{\bf r'}).$">|; 

$key = q/displaystyle{bfB}=-frac{mu_0,e,gamma}{4pi,{r'}^{,3}},{bfu}times{bfr}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3895.png"
 ALT="$\displaystyle {\bf B} = -\frac{\mu_0 e \gamma}{4\pi {r'}^{ 3}}  {\bf u}\times{\bf r}.$">|; 

$key = q/displaystyleJ_m(p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="$\displaystyle J_m(p)$">|; 

$key = q/displaystyle=frac{u'_3}{gamma,(1+u'_1,vslashc^{,2})}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3507.png"
 ALT="$\displaystyle = \frac{u'_3}{\gamma (1+u'_1  v/c^{ 2})}.$">|; 

$key = q/lambda(z)=2pislashk,n(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2264.png"
 ALT="$ \lambda(z)= 2\pi/ k n(z)$">|; 

$key = q/T=P;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1984.png"
 ALT="$ T=P$">|; 

$key = q/{bfE}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="$ {\bf E}({\bf r})$">|; 

$key = q/displaystylenabla^{,2}G({bfr},{bfr}')=-delta({bfr}-{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \nabla^{ 2} G({\bf r}, {\bf r}') = -\delta({\bf r}-{\bf r}'),$">|; 

$key = q/displaystyle=epsilon_0,E^{,i},E_j+frac{B^{,i},B_j}{mu_0}-delta_j^i,frac{1}{2}left(epsilon_0,E^{,k},E_k+frac{B^{,k},B_k}{mu_0}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3957.png"
 ALT="$\displaystyle = \epsilon_0  E^{ i}  E_j + \frac{B^{ i}  B_j}{\mu_0} - \del...
...frac{1}{2} \left(\epsilon_0 E^{ k}  E_k +\frac{B^{ k}  B_k}{\mu_0}\right),$">|; 

$key = q/B_parallel;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1757.png"
 ALT="$ B_\parallel$">|; 

$key = q/displaystyleP_1^{,+1}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="$\displaystyle P_1^{ +1}(x)$">|; 

$key = q/n+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$ n+1$">|; 

$key = q/x=k,a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3361.png"
 ALT="$ x=k a$">|; 

$key = q/n=gamma(u),n_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3712.png"
 ALT="$ n=\gamma(u)  n_0$">|; 

$key = q/p^{,mu'}_{mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3697.png"
 ALT="$ p^{ \mu'}_{\mu}$">|; 

$key = q/(x',,y',,z');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3863.png"
 ALT="$ (x',  y',  z')$">|; 

$key = q/B_4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1831.png"
 ALT="$ B_4$">|; 

$key = q/displaystylephi_ssimeq-2sqrt{xi,(t-t_0)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1937.png"
 ALT="$\displaystyle \phi_s \simeq -2\sqrt{\xi (t-t_0)},$">|; 

$key = q/displaystylek_n=n,frac{pi}{L},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img998.png"
 ALT="$\displaystyle k_n = n \frac{\pi}{L},$">|; 

$key = q/A^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3925.png"
 ALT="$ A^{ \mu}$">|; 

$key = q/displaystyle{calM}_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3240.png"
 ALT="$\displaystyle {\cal M}_{lm}$">|; 

$key = q/RslashR_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$ R/R_0$">|; 

$key = q/psi({bfr}')=G({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="$ \psi({\bf r}')=G({\bf r},{\bf r}')$">|; 

$key = q/displaystyle~~~~+psi_r,sintheta_i,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z+phi_r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2167.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\psi_r \sin\theta_i \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z+\phi_r)$">|; 

$key = q/q=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$ q=0$">|; 

$key = q/displaystyledE^{'}=gamma(u)left(dE+u,dp^1right)=gamma,dE.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4068.png"
 ALT="$\displaystyle dE^{'} = \gamma(u) \left(dE + u dp^1\right) = \gamma  dE.$">|; 

$key = q/C_{l,m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$ C_{l,m}$">|; 

$key = q/displaystyleE(t)=frac{1}{sqrt{2pi}}int_{-infty}^{infty}E(omega),{rme}^{-{rmi},omega,t},domega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2806.png"
 ALT="$\displaystyle E(t)= \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} E(\omega)  {\rm e}^{-{\rm i} \omega  t} d\omega,$">|; 

$key = q/displaystyle{T^{,i}}_4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3958.png"
 ALT="$\displaystyle {T^{ i}}_4$">|; 

$key = q/phirightarrowphi+partialpsislashpartialt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$ \phi\rightarrow \phi+\partial\psi/\partial t$">|; 

$key = q/displaystylec,A_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3873.png"
 ALT="$\displaystyle c A_3$">|; 

$key = q/displaystylecosgamma=costheta,costheta'+sintheta,sintheta',cos(varphi-varphi').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="$\displaystyle \cos\gamma = \cos\theta \cos\theta'+\sin\theta \sin\theta' \cos(\varphi-\varphi').$">|; 

$key = q/r_0=e^{,2}slash(4pi,epsilon_0,m_0,c^{,2})=2.82times10^{-15};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4143.png"
 ALT="$ r_0 = e^{ 2}/(4\pi \epsilon_0  m_0  c^{ 2}) = 2.82\times 10^{-15}$">|; 

$key = q/displaystyleA_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1325.png"
 ALT="$\displaystyle A_y$">|; 

$key = q/displaystyleF^{,musigma},partial_muF_{nusigma}=-frac{1}{2},F^{,musigma},partial_nuF_{sigmamu}=frac{1}{4},partial_nu(F^{,musigma},F_{musigma}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3951.png"
 ALT="$\displaystyle F^{ \mu\sigma}  \partial_\mu F_{\nu\sigma} = - \frac{1}{2}  F^...
...u F_{\sigma\mu} = \frac{1}{4}  \partial_\nu (F^{ \mu\sigma}  F_{\mu\sigma}).$">|; 

$key = q/displaystyle-frac{partialE_y}{partialz};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2232.png"
 ALT="$\displaystyle -\frac{\partial E_y}{\partial z}$">|; 

$key = q/{bfN};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2894.png"
 ALT="$ {\bf N}$">|; 

$key = q/displaystyle=hat{alpha},cosphi_t,psi_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2174.png"
 ALT="$\displaystyle =\hat{\alpha} \cos\phi_t \psi_t.$">|; 

$key = q/(0,hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2487.png"
 ALT="$ (0,\hat{z})$">|; 

$key = q/u=cslashsqrt{epsilon};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1981.png"
 ALT="$ u = c/\sqrt{\epsilon}$">|; 

$key = q/displaystylep_A-p_B=-int_A^B{bff}cdotd{bfr}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1265.png"
 ALT="$\displaystyle p_A - p_B = -\int_A^B {\bf f}\cdot d{\bf r}.$">|; 

$key = q/displaystyley_{rmmin};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1660.png"
 ALT="$\displaystyle y_{\rm min}$">|; 

$key = q/u_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$ u_1$">|; 

$key = q/j_{1l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$ j_{1l}$">|; 

$key = q/displaystyle[H_x]_{z=0_+}^{z=0_-};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2114.png"
 ALT="$\displaystyle [H_x]_{z=0_+}^{z=0_-}$">|; 

$key = q/{rme}^{-{rmi},omegas}slashomega^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1841.png"
 ALT="$ {\rm e}^{-{\rm i} \omega s}/\omega^{ 2}$">|; 

$key = q/mu_0,H;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1526.png"
 ALT="$ \mu_0  H$">|; 

$key = q/displaystylefrac{d^{,2}Z}{dz^{,2}}-k^{,2},Z=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$\displaystyle \frac{d^{ 2} Z}{dz^{ 2}} - k^{ 2}  Z = 0,$">|; 

$key = q/displaystyleint_Sphi({bfr}'),frac{partialphi}{partialn'},dS'=int_Vleft[phi({bfr}'),nabla'^{,2}phi+nabla'phicdotnabla'phiright]dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="$\displaystyle \int_S \phi({\bf r}') \frac{\partial\phi}{\partial n'} dS' = \int_V\left[\phi({\bf r}') \nabla'^{ 2}\phi+\nabla'\phi\cdot\nabla'\phi\right]dV'.$">|; 

$key = q/displaystylefrac{partialG_3({bfr},{bfr}')}{partialn'}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="$\displaystyle \frac{\partial G_3({\bf r},{\bf r}')}{\partial n'}=0$">|; 

$key = q/v=cslashn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2051.png"
 ALT="$ v=c/n$">|; 

$key = q/displaystyle=v^{,2}left(frac{partialD_z}{partialx}-frac{partialD_x}{partialz}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2049.png"
 ALT="$\displaystyle =v^{ 2}\left(\frac{\partial D_z}{\partial x}- \frac{\partial D_x}{\partial z}\right),$">|; 

$key = q/displaystyle{rme}^{-{rmIm}(k_tau),x}sin!left[2pi,frac{t}{tau}-{rmRe}(k_tau),xrigIm}(k_tau),x}sin!left(frac{2pi}{tau}left[t-frac{x}{v_p}right]right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1848.png"
 ALT="$\displaystyle {\rm e}^{-{\rm Im}(k_\tau)  x} \sin\!\left[2\pi \frac{t}{\tau} ...
...\tau)  x} \sin\!\left( \frac{2\pi}{\tau}\left[t - \frac{x}{v_p}\right]\right),$">|; 

$key = q/{bff};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1207.png"
 ALT="$ {\bf f}$">|; 

$key = q/displaystylegamma=(1-v^{,2}slashc^{,2})^{-1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3501.png"
 ALT="$\displaystyle \gamma = (1-v^{ 2}/c^{ 2})^{-1/2}$">|; 

$key = q/displaystylefrac{{mitGamma}(a),{mitGamma}(c-a)}{{mitGamma}(c)},F(a,c,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2435.png"
 ALT="$\displaystyle \frac{{\mit\Gamma}(a) {\mit\Gamma}(c-a)}{{\mit\Gamma}(c)}  F(a,c,z)$">|; 

$key = q/displaystyleomega_0^{,2}=frac{f}{m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1621.png"
 ALT="$\displaystyle \omega_0^{ 2} = \frac{f}{m}$">|; 

$key = q/displaystylenablat'=-frac{{bfr}}{s,c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4004.png"
 ALT="$\displaystyle \nabla t' = - \frac{{\bf r}}{s c},$">|; 

$key = q/dt'>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3417.png"
 ALT="$ dt'&gt;0$">|; 

$key = q/{bfB}_0=B_0,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1532.png"
 ALT="$ {\bf B}_0 = B_0  {\bf e}_z$">|; 

$key = q/B_1=-E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1165.png"
 ALT="$ B_1=-E_0$">|; 

$key = q/displaystyle|{bfn}times{bfX}_{1,pm1}|^{,2}=|{bfX}_{1,pm1}|^{,2}=frac{3}{16pi},(1+cos^2theta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3385.png"
 ALT="$\displaystyle \vert{\bf n}\times{\bf X}_{1,\pm 1}\vert^{ 2} = \vert{\bf X}_{1,\pm 1}\vert^{ 2} =\frac{3}{16\pi}  (1+\cos^2\theta),$">|; 

$key = q/t<t_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1955.png"
 ALT="$ t&lt;t_1$">|; 

$key = q/displaystylefrac{1}{4pi,|{bfr}-{bfr}'|}=sum_{l=0,infty}sum_{m=-l,+l}frac{1}{2,l+>^{,l+1}}right)Y_{l,m}^{,ast}(theta',varphi'),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="381" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1335.png"
 ALT="$\displaystyle \frac{1}{4\pi \vert{\bf r}-{\bf r}'\vert }= \sum_{l=0,\infty}\su...
...r_&gt;^{ l+1}}\right)Y_{l,m}^{ \ast}(\theta',\varphi') Y_{l,m}(\theta,\varphi).$">|; 

$key = q/J_m(p)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="$ J_m(p)=0$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),({bfr}cdot{bfE});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3081.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2}) ({\bf r}\cdot{\bf E})$">|; 

$key = q/k>k_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2839.png"
 ALT="$ k&gt;k_3$">|; 

$key = q/epsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1077.png"
 ALT="$ \epsilon$">|; 

$key = q/phi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2182.png"
 ALT="$ \phi_r$">|; 

$key = q/E_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2193.png"
 ALT="$ E_r$">|; 

$key = q/displaystylec,B^{,i}=frac{1}{2},epsilon^{,ijk},c,B_{jk}=-epsilon^{,ijk},partial_j{mitPhi}_k.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3783.png"
 ALT="$\displaystyle c B^{ i} = \frac{1}{2} \epsilon^{ ijk}  c B_{jk} = -\epsilon^{ ijk} \partial_j {\mit \Phi}_k.$">|; 

$key = q/d^{,2}phislashdz^{,2}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2249.png"
 ALT="$ d^{ 2}\phi/dz^{ 2}=0$">|; 

$key = q/displaystyle{calF}_mu=gammaleft(-{bff},,frac{{bff}cdot{bfu}}{c}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3934.png"
 ALT="$\displaystyle {\cal F}_\mu = \gamma\left(-{\bf f},  \frac{{\bf f}\cdot{\bf u}}{c} \right),$">|; 

$key = q/displaystylembox{hspace{0.5cm}forhspace{0.5cm}{{{bf{r}neq{{bf{r}'{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle \mbox{\hspace{0.5cm}for\hspace{0.5cm}${\bf r}\neq {\bf r}'$}$">|; 

$key = q/Y_{l+1slash2}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3016.png"
 ALT="$ Y_{l+1/2}(z)$">|; 

$key = q/displaystylephi({bfr})=intv({bfr}'),G({bfr},{bfr}'),dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="$\displaystyle \phi({\bf r}) = \int v({\bf r}') G({\bf r},{\bf r}') dV',$">|; 

$key = q/displaystyle({mitDelta}t_0,omega_p)_{rmsommerfeld}simleft(frac{omega_p}{xi}right)ll1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1966.png"
 ALT="$\displaystyle ({\mit\Delta} t_0  \omega_p)_{\rm sommerfeld} \sim \left(\frac{\omega_p} {\xi}\right) \ll 1.$">|; 

$key = q/displaystyle{bfB}=left(frac{3,mu}{mu+2,mu_0}right){bfB}_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1538.png"
 ALT="$\displaystyle {\bf B} = \left(\frac{3 \mu}{\mu+2 \mu_0}\right) {\bf B}_0,$">|; 

$key = q/displaystylephantom{=}-epsilon_0,(nablacdot{bfE}),{bfE}-frac{1}{mu_0},(nablacdot{bfB}),{bfB}+rho,{bfE}+{bfj}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$\displaystyle \phantom{=} - \epsilon_0 (\nabla\cdot {\bf E})  {\bf E} - \frac{1}{\mu_0} (\nabla\cdot {\bf B})  {\bf B}+ \rho {\bf E}+{\bf j}\times {\bf B}.$">|; 

$key = q/displaystyle=left(frac{beta-alpha}{beta+alpha}right)psi_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2075.png"
 ALT="$\displaystyle =\left(\frac{\beta-\alpha}{\beta+\alpha}\right)\psi_i,$">|; 

$key = q/0.0463;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3288.png"
 ALT="$ 0.0463$">|; 

$key = q/dot{~};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="8" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1619.png"
 ALT="$ \dot{&nbsp;}$">|; 

$key = q/RggR_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$ R\gg R_0$">|; 

$key = q/displaystyle{bfL}times{bfL};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3066.png"
 ALT="$\displaystyle {\bf L}\times{\bf L}$">|; 

$key = q/I_2,d{bfr}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1301.png"
 ALT="$ I_2 d{\bf r}_2$">|; 

$key = q/displaystyle=-E_0sin[(omegaslashc),(n_-z-c,t)].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1742.png"
 ALT="$\displaystyle =- E_0 \sin[(\omega/c) (n_- z-c t)].$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{mu_0,c,I^{,2}}{8pi^2}frac{cos^2(pi,costhetaslash2)}{sin^2theta}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2642.png"
 ALT="$\displaystyle \frac{d P}{d{\mit\Omega}} =\frac{\mu_0  c I^{ 2}}{8\pi^2} \frac{\cos^2(\pi \cos\theta/2)}{\sin^2\theta}.$">|; 

$key = q/n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$ n$">|; 

$key = q/theta_{rmmax};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4102.png"
 ALT="$ \theta_{\rm max}$">|; 

$key = q/{r'}^{,3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3898.png"
 ALT="$ {r'}^{ 3}$">|; 

$key = q/S=S_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2386.png"
 ALT="$ S=S_0$">|; 

$key = q/displaystyle=delta_a^{,j},delta_b^{,k}-delta_b^{,j},delta_a^{,k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3765.png"
 ALT="$\displaystyle = \delta_a^{ j}  \delta_b^{ k} - \delta_b^{ j} \delta_a^{ k},$">|; 

$key = q/F({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="$ F({\bf r},{\bf r}')$">|; 

$key = q/displaystyleW=int_P^Q(-{bfF})cdotd{bfr}=-qint_P^Q{bfE}cdotd{bfr}=qint_P^Qnablaphicdotd{bfr}=qleft[phi(Q)-phi(P)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$\displaystyle W = \int_P^Q (-{\bf F}) \cdot d{\bf r} =- q \int_P^Q {\bf E} \cdo...
...bf r} =q\int_P^Q \nabla\phi \cdot d{\bf r} = q \left[ \phi(Q) - \phi(P)\right],$">|; 

$key = q/g_m(r,r');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img971.png"
 ALT="$ g_m(r,r')$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0,I}{4pi}frac{2,{rme}^{,{rmi},k,r}}{k,r}left[frac{cos(k,d,costhetaslash2)-cos(k,dslash2)}{sin^2theta}right]{bfe}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2627.png"
 ALT="$\displaystyle {\bf A}({\bf r}) =\frac{\mu_0  I}{4\pi} \frac{2 {\rm e}^{ {\rm...
...t[\frac{\cos(k d  \cos\theta/2) -\cos(k d/2)}{\sin^2\theta}\right]{\bf e}_z.$">|; 

$key = q/{bfr}_u;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4017.png"
 ALT="$ {\bf r}_u$">|; 

$key = q/displaystyle{rmIm}left({rmi}!int_0^{hat{z}}q^{1slash2}(hat{z}'),dhat{z}'right)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2493.png"
 ALT="$\displaystyle {\rm Im} \left( {\rm i}\! \int_0^{\hat{z}} q^{1/2}(\hat{z}')  d\hat{z}' \right) = 0.$">|; 

$key = q/displaystyleG_omega({bfr},{bfr}')=frac{{rme}^{,{rmi},k,|{bfr}-bf{r}'|}}{4pi,|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3175.png"
 ALT="$\displaystyle G_\omega ({\bf r}, {\bf r}') =\frac{{\rm e}^{ {\rm i} k \vert{\bf r} -\bf {r}'\vert}} {4\pi  \vert{\bf r}-{\bf r}'\vert}.$">|; 

$key = q/displaystyleepsilon_1,frac{partialphi(z=0_+)}{partialz}=epsilon_2,frac{partialphi(z=0_-)}{partialz}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1114.png"
 ALT="$\displaystyle \epsilon_1  \frac{\partial\phi(z=0_+)}{\partial z} = \epsilon_2  \frac{\partial \phi(z=0_-)}{\partial z}.$">|; 

$key = q/a_E(3,0)slasha_E(1,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3265.png"
 ALT="$ a_E(3,0)/a_E(1,0)$">|; 

$key = q/E<c,B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4184.png"
 ALT="$ E&lt;c B$">|; 

$key = q/(x^{,i'},,t');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3982.png"
 ALT="$ (x^{ i'},  t')$">|; 

$key = q/n_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1641.png"
 ALT="$ n_i$">|; 

$key = q/{rmTE}_{,01};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2974.png"
 ALT="$ {\rm TE}_{ 01}$">|; 

$key = q/displaystyle=frac{hat{alpha}}{beta},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2156.png"
 ALT="$\displaystyle = \frac{\hat{\alpha}}{\beta},$">|; 

$key = q/displaystylev=frac{c}{{rmRe}(n)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1644.png"
 ALT="$\displaystyle v = \frac{c}{{\rm Re}(n)}.$">|; 

$key = q/n=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2288.png"
 ALT="$ n=1$">|; 

$key = q/displaystylefrac{partialH_x}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2091.png"
 ALT="$\displaystyle \frac{\partial H_x}{\partial t}$">|; 

$key = q/displaystyleZ(k)=sin(k_n,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img933.png"
 ALT="$\displaystyle Z(k) = \sin(k_n z),$">|; 

$key = q/displaystylet=u=v={rmi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2523.png"
 ALT="$\displaystyle t = u = v = {\rm i}.$">|; 

$key = q/displaystylefrac{partialH_y}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1988.png"
 ALT="$\displaystyle \frac{\partial H_y}{\partial t}$">|; 

$key = q/J_1(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ J_1(z)$">|; 

$key = q/displaystylep=-4pi,epsilon_0left(frac{epsilon-1}{2,epsilon+1}right)a^{,3},E_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1191.png"
 ALT="$\displaystyle p = - 4\pi \epsilon_0 \left(\frac{\epsilon -1}{2 \epsilon +1}\right)a^{ 3}  E_0.$">|; 

$key = q/{bfr}=(x,,y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="$ {\bf r}= (x, y)$">|; 

$key = q/displaystyle=frac{1}{2}left(epsilon_0,E^{,k},E_k+frac{B^{,k},B_k}{mu_0}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3961.png"
 ALT="$\displaystyle = \frac{1}{2} \left(\epsilon_0  E^{ k}  E_k +\frac{B^{ k}  B_k}{\mu_0}\right).$">|; 

$key = q/nabla^{,2}phi_m=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1549.png"
 ALT="$ \nabla^{ 2}\phi_m=0$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=-frac{1}{4pi,(r^{,2}-2,r,r',cosgamma+r'^{,2})^{1sl}{4pi,(r^{,2},r'^{,2}slasha^{,2}-2,r,r',cosgamma+a^{,2})^{1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}') = -\frac{1}{4\pi (r^{ 2}-2 r r' \cos\g...
...\frac{1}{4\pi (r^{ 2} r'^{ 2}/a^{ 2}-2 r r' \cos\gamma+a^{ 2})^{1/2}},$">|; 

$key = q/displaystyle{bfg}=frac{bfu}{c^{,2}}=epsilon_0,{bfE}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3979.png"
 ALT="$\displaystyle {\bf g} = \frac{\bf u}{c^{ 2}} = \epsilon_0  {\bf E}\times{\bf B}.$">|; 

$key = q/displaystyleleft(frac{1}{r^{,2}}frac{partial}{partialr},r^{,2}frac{partial}{partsin^2theta}frac{partial^{,2}}{partialvarphi^{,2}}+k^{,2}right)psi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="410" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3000.png"
 ALT="$\displaystyle \left(\frac{1}{r^{ 2}}\frac{\partial}{\partial r} r^{ 2} \frac...
...^2\theta}\frac{\partial^{ 2} }{\partial \varphi^{ 2}}+k^{ 2}\right)\psi = 0.$">|; 

$key = q/displaystyle=-frac{e}{m},E_x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1717.png"
 ALT="$\displaystyle = -\frac{e}{m}  E_x,$">|; 

$key = q/displaystyleG_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3835.png"
 ALT="$\displaystyle G_{ij}$">|; 

$key = q/displaystyle=-left(frac{3}{8pi}right)^{1slash2}intrho({bfr}),r,sintheta,{rme}^{-{rmi},varphi},dV=-left(frac{3}{8pi}right)^{1slash2},(p_x-{rmi},p_y),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="$\displaystyle =-\left(\frac{3}{8\pi}\right)^{1/2}\int \rho({\bf r}) r \sin\th...
...{\rm i} \varphi} dV = -\left(\frac{3}{8\pi}\right)^{1/2} (p_x-{\rm i} p_y),$">|; 

$key = q/displaystylefrac{c}{v_g}simeqn(omega)left(1+frac{omega^{,2}}{omega_0^{,2}-omega^{,2}}+frac{omega^{,2}}{omega^{,2}-omega_0^{,2}-omega_p^{,2}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1919.png"
 ALT="$\displaystyle \frac{c}{v_g} \simeq n(\omega) \left(1 +\frac{\omega^{ 2}}{\omeg...
...{ 2}} +\frac{\omega^{ 2}} {\omega^{ 2}-\omega_0^{ 2}-\omega_p^{ 2}}\right)$">|; 

$key = q/f(x,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1843.png"
 ALT="$ f(x,t)$">|; 

$key = q/x^{,sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3676.png"
 ALT="$ x^{ \sigma}$">|; 

$key = q/displaystyle-{bfE}cdot{bfj}=-frac{{bfE}cdotnablatimes{bfB}}{mu_0}+frac{partial}{partialt}!left(frac{epsilon_0,E^{,2}}{2}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle - {\bf E} \cdot {\bf j} = - \frac{ {\bf E}\cdot \nabla\times{\bf ...
...u_0} +\frac{\partial}{\partial t}\!\left(\frac{\epsilon_0  E^{ 2}}{2}\right).$">|; 

$key = q/displaystyle{rmi},(k,x-omega,t)=-{rmi},omega,(t-xslashc)=-{rmi},omega,s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1813.png"
 ALT="$\displaystyle {\rm i} (k x -\omega  t) = -{\rm i} \omega  (t-x/c) = -{\rm i} \omega  s.$">|; 

$key = q/f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2842.png"
 ALT="$ f$">|; 

$key = q/F_{munu}=-F_{numu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3821.png"
 ALT="$ F_{\mu\nu}=-F_{\nu\mu}$">|; 

$key = q/displaystyleomega_c=gamma^{,3},{mitOmega},cosalpha.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4219.png"
 ALT="$\displaystyle \omega_c = \gamma^{ 3}  {\mit\Omega}  \cos\alpha.
$">|; 

$key = q/omega=pmomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2333.png"
 ALT="$ \omega=\pm
\omega_0$">|; 

$key = q/displaystylepartial_muQ^{,munu}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4052.png"
 ALT="$\displaystyle \partial_\mu Q^{ \mu\nu}=0,$">|; 

$key = q/displaystylephi(r,theta)=sum_{l=0,infty}A_l,r^{,l},P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1163.png"
 ALT="$\displaystyle \phi(r,\theta) = \sum_{l=0,\infty} A_l r^{ l} P_l(\cos\theta),$">|; 

$key = q/displaystylefrac{partial^{,2}(R,w)}{partialR^{,2}}+frac{D,(R,w)}{R^{,2}}+k^{,2},R,w=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle \frac{\partial^{ 2}(R w)}{\partial R^{ 2}} + \frac{D (R w)}{R^{ 2}} + k^{ 2} R w=0,$">|; 

$key = q/displaystylew(x,h)=expleft(,{rmi},hint_a^0q^{,1slash2}(x'),dx'right),,{rme}^{-{rsh4},|q(x)|^{-1slash4},expleft(-hint_0^x|q(x')|^{,1slash2},dx'right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="497" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2563.png"
 ALT="$\displaystyle w(x,h) = \exp\left( {\rm i} h\int_a^0 q^{ 1/2}(x') dx'\right)...
...rt q(x)\vert^{-1/4}  \exp\left(-h\int_0^x \vert q(x')\vert^{ 1/2} dx'\right)$">|; 

$key = q/displaystyle=pmA,{rme}^{-{rmi},pislash4},|n(z)|^{1slash2}expleft(pmkint^z!|n(z')|,dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2276.png"
 ALT="$\displaystyle = \pm A  {\rm e}^{-{\rm i} \pi/4}  \vert n(z)\vert^{1/2} \exp\left(\pm k\int^z \!\vert n(z')\vert dz'\right),$">|; 

$key = q/{bfB}_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1533.png"
 ALT="$ {\bf B}_0$">|; 

$key = q/displaystyledq=4pi,r^{,2},rho,dr.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="$\displaystyle dq = 4\pi  r^{ 2}  \rho dr.$">|; 

$key = q/displaystylephi({bfr})=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$\displaystyle \phi({\bf r})= 0,$">|; 

$key = q/2.3times10^{-5};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1447.png"
 ALT="$ 2.3\times 10^{-5}$">|; 

$key = q/f_{lm}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3007.png"
 ALT="$ f_{lm}(r)$">|; 

$key = q/I_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1300.png"
 ALT="$ I_2$">|; 

$key = q/displaystylepartial_muJ^{,mu}=nablacdot{bfj}+frac{partialrho}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3721.png"
 ALT="$\displaystyle \partial_\mu J^{ \mu} = \nabla\cdot{\bf j} + \frac{\partial\rho}{\partial t}.$">|; 

$key = q/displaystylea_{mn}=frac{2}{J_{m+1}^{,2}(j_{mn})}int_0^1p,f(p),J_m(j_{mn},p),dp.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="$\displaystyle a_{mn} = \frac{2}{J_{m+1}^{ 2}(j_{mn})}\int_0^1 p f(p) J_m(j_{mn} p) dp.$">|; 

$key = q/displaystylef_ssimeqF(omega_s),{rme}^{,{rmi},phi_s}int_{infty}^{-infty}expleft[frac{rmi}{2},phi_s',(omega-omega_s)^{,2}right]domega.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1907.png"
 ALT="$\displaystyle f_s \simeq F(\omega_s)  {\rm e}^{ {\rm i} \phi_s} \int_{\infty...
...ty} \exp\left[\frac{\rm i}{2} \phi_s' (\omega-\omega_s)^{ 2}\right] d\omega.$">|; 

$key = q/omega=2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1790.png"
 ALT="$ \omega=2\pi/\tau$">|; 

$key = q/D_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2163.png"
 ALT="$ D_x$">|; 

$key = q/rho_b({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1064.png"
 ALT="$ \rho_b({\bf r})$">|; 

$key = q/displaystylef(x,t)=int_C{rme}^{,{rmi},phi(omega)}F(omega),domega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1897.png"
 ALT="$\displaystyle f(x,t) = \int_C {\rm e}^{ {\rm i}  \phi(\omega)} F(\omega)  d\omega$">|; 

$key = q/h;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1275.png"
 ALT="$ h$">|; 

$key = q/r=b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1550.png"
 ALT="$ r=b$">|; 

$key = q/displaystyle=frac{epsilon_0,c}{2,k^{,3}}sum_mm,|a_E(l,m)|^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3174.png"
 ALT="$\displaystyle = \frac{\epsilon_0  c}{2  k^{ 3}} \sum_m m \vert a_E(l,m)\vert^{ 2}.$">|; 

$key = q/{bfr'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$ {\bf r'}$">|; 

$key = q/displaystylerho(r,theta),2pi,r^{,2},sintheta,dtheta,drrightarrowq,delta(r-a),delta(theta-pislash2),dtheta,dr.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="$\displaystyle \rho(r,\theta) 2\pi r^{ 2} \sin\theta d\theta dr \rightarrow q \delta(r-a) \delta(\theta-\pi/2) d\theta dr.$">|; 

$key = q/displaystylenablatimes{bfE}=-frac{partial{bfB}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1605.png"
 ALT="$\displaystyle \nabla\times{\bf E} = -\frac{\partial{\bf B}}{\partial t}.$">|; 

$key = q/displaystyle={rmi},A,frac{omega,epsilon_0}{k_t},K_1(k_t,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2985.png"
 ALT="$\displaystyle ={\rm i} A \frac{\omega \epsilon_0}{k_t}  K_1(k_t  r),$">|; 

$key = q/displaystyleint_{Sigma_infty}left(w,frac{partialw^ast}{partialn}-w^ast,frac{partialw}{partialn}right),dS=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle \int_{\Sigma_\infty} \left( w \frac{\partial w^\ast}{\partial n} -w^\ast  \frac{\partial w}{\partial n}\right) dS =0.$">|; 

$key = q/displaystyleB_parallel';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3853.png"
 ALT="$\displaystyle B_\parallel'$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),{bfE}'=-{rmi},k,mu_0,c,nablatimesleft({bfM}+frac{nablatimes{bfj}}{k^{,2}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3202.png"
 ALT="$\displaystyle (\nabla^{ 2}+k^{ 2}) {\bf E}' = -{\rm i} k \mu_0  c \nabla\times\left( {\bf M} + \frac{\nabla\times{\bf j}}{k^{ 2}}\right).$">|; 

$key = q/g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$ g$">|; 

$key = q/displaystylenabla^{,2}({bfr}cdot{bfA})={bfr}cdot(nabla^{,2}{bfA})+2,nablacdot{bfA}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3078.png"
 ALT="$\displaystyle \nabla^{ 2}({\bf r}\cdot{\bf A}) = {\bf r}\cdot(\nabla^{ 2}{\bf A}) + 2  \nabla\cdot{\bf A}.$">|; 

$key = q/displaystyle{calF}_mu,U^{,mu}=c^{,2},frac{dm_0}{dtau}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3940.png"
 ALT="$\displaystyle {\cal F}_\mu  U^{ \mu} = c^{ 2}  \frac{dm_0}{d\tau}.$">|; 

$key = q/omega_s=2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1972.png"
 ALT="$ \omega_s=2\pi/\tau$">|; 

$key = q/displaystyleE_i=-partial_i{mitPhi}_4+partial_4{mitPhi}_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3782.png"
 ALT="$\displaystyle E_i = -\partial_i {\mit \Phi}_4 +\partial_4 {\mit \Phi}_i.$">|; 

$key = q/2pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2504.png"
 ALT="$ 2\pi$">|; 

$key = q/displaystylephi_m({bfr})=-frac{1}{4pi}intfrac{nabla'cdot{bfM}({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1480.png"
 ALT="$\displaystyle \phi_m({\bf r}) =-\frac{1}{4\pi}\int \frac{\nabla'\cdot {\bf M}({\bf r}')}{\vert{\bf r} - {\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle{bfr}_0={bfr}-frac{r}{c},{bfu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4022.png"
 ALT="$\displaystyle {\bf r}_0 = {\bf r} - \frac{r}{c} {\bf u}.$">|; 

$key = q/displaystyle(A)^2=g_{ij},A^i,A^j=A_i,A^i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3602.png"
 ALT="$\displaystyle (A)^2 = g_{ij}  A^i  A^j = A_i  A^i.$">|; 

$key = q/phantom{K}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img977.png"
 ALT="$ \phantom{K}'$">|; 

$key = q/displaystyleleft.+sqrt{(l+m),(l-m+1)},a_E^{,ast}(l,m-1)right]a_E(l,m),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3169.png"
 ALT="$\displaystyle \left.+ \sqrt{(l+m) (l-m+1)}  a_E^{ \ast}(l,m-1)\right]a_E(l,m),$">|; 

$key = q/displaystyle={mitPhi}(theta,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img928.png"
 ALT="$\displaystyle = {\mit\Phi}(\theta,z),$">|; 

$key = q/f_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3107.png"
 ALT="$ f_l(k r)$">|; 

$key = q/displaystyleE_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1726.png"
 ALT="$\displaystyle E_y$">|; 

$key = q/displaystyle=gamma,(T^{,4}-beta,T^{,1}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3645.png"
 ALT="$\displaystyle = \gamma (T^{ 4} - \beta  T^{ 1}),$">|; 

$key = q/{bfr}'-{bfd};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="$ {\bf r}'-{\bf d}$">|; 

$key = q/displaystyleepsilonleft.frac{partialphi}{partialr}right|_{r=a_{-}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1148.png"
 ALT="$\displaystyle \epsilon\left. \frac{\partial\phi}{\partial r}\right\vert _{r=a_{-}}$">|; 

$key = q/displaystyle=left(frac{2,beta}{1+alpha,beta}right)psi_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2119.png"
 ALT="$\displaystyle =\left(\frac{2 \beta}{1+\alpha \beta}\right)\psi_i.$">|; 

$key = q/f=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1392.png"
 ALT="$ f=1$">|; 

$key = q/displaystyle={rmi},nabla^{,2}({bfr}cdot{bfA})-{rmi},frac{1}{r}frac{partial(r^{,2},nablacdot{bfA})}{partialr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3226.png"
 ALT="$\displaystyle = {\rm i} \nabla^{ 2}({\bf r} \cdot{\bf A}) -{\rm i} \frac{1}{r}\frac{\partial (r^{ 2}  \nabla\cdot {\bf A})}{\partial r}$">|; 

$key = q/k,{mitDelta}=2pi,{mitDelta}slashlambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2706.png"
 ALT="$ k {\mit\Delta}= 2\pi 
{\mit\Delta}/\lambda$">|; 

$key = q/{rmarg}(z)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2449.png"
 ALT="$ {\rm arg}(z)=0$">|; 

$key = q/brightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="$ b\rightarrow 0$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}') =$">|; 

$key = q/displaystyle|f|simfrac{tau}{(x,k_0''')^{1slash3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1963.png"
 ALT="$\displaystyle \vert f\vert \sim \frac{\tau}{ (x  k_0''')^{1/3}}.$">|; 

$key = q/displaystylelangle{calI}_zrangle_t=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2161.png"
 ALT="$\displaystyle \langle{\cal I}_z\rangle_t= 0.$">|; 

$key = q/displaystyle=frac{2,hat{alpha},beta}{beta^{,2}-hat{alpha}^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2154.png"
 ALT="$\displaystyle =\frac{2 \hat{\alpha} \beta}{\beta^{ 2}-\hat{\alpha}^{ 2}},$">|; 

$key = q/displaystyleq';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1118.png"
 ALT="$\displaystyle q'$">|; 

$key = q/displaystyle=-3,x,(1-x^{,2})^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="$\displaystyle =-3 x (1-x^{ 2})^{1/2},$">|; 

$key = q/displaystyle={bfB}_{rminc}+{bfB}_{sc},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3327.png"
 ALT="$\displaystyle ={\bf B}_{\rm inc} + {\bf B}_{sc},$">|; 

$key = q/displaystyleq_{2,+2}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="$\displaystyle q_{2,+2}^{ \ast}$">|; 

$key = q/displaystyle{bfr}cdot{bfE}_{lm}^{(M)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3086.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf E}_{lm}^{(M)}$">|; 

$key = q/displaystylez=frac{2sqrt{2},|t-t_1|^{,3slash2}}{3sqrt{x,k_0'''}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1954.png"
 ALT="$\displaystyle z = \frac{2\sqrt{2}  \vert t-t_1\vert^{ 3/2}}{3 \sqrt{x  k_0'''}}.$">|; 

$key = q/{bfP}=P,{bfe}_z=epsilon_0,(epsilon-1),E_0,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1238.png"
 ALT="$ {\bf P} = P {\bf e}_z = \epsilon_0 (\epsilon-1) 
E_0 {\bf e}_z$">|; 

$key = q/displaystyleh_l^{(2)}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3028.png"
 ALT="$\displaystyle h_l^{(2)} (z)$">|; 

$key = q/displaystyleomega_{0l}=frac{j_{0l},c}{sqrt{epsilon_1-1},a},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2977.png"
 ALT="$\displaystyle \omega_{0l} = \frac{j_{0l} c}{\sqrt{\epsilon_1 -1}  a},$">|; 

$key = q/displaystyle={bfB}_0+frac{2}{3},mu_0,{bfM}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1536.png"
 ALT="$\displaystyle = {\bf B}_0 + \frac{2}{3}  \mu_0  {\bf M}.$">|; 

$key = q/K_m(z)rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2922.png"
 ALT="$ K_m(z)\rightarrow 0$">|; 

$key = q/displaystylef_ssimeqsqrt{frac{pi,xi^{,1slash2}}{(t-t_0)^{,3slash2}}},frac{t-t_0}{tau,xi},{rme}^{-2,{rmi}sqrt{xi,(t-t_0)}+3pi,{rmi}slash4}+{rmc.c.},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1940.png"
 ALT="$\displaystyle f_s \simeq \sqrt{\frac{\pi  \xi^{ 1/2} } {(t-t_0)^{ 3/2}}}  \...
...\xi}  {\rm e}^{-2 {\rm i} \sqrt{\xi (t-t_0)} +3\pi  {\rm i}/4} +{\rm c.c.},$">|; 

$key = q/displaystyleboxempty,phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3725.png"
 ALT="$\displaystyle \boxempty  \phi$">|; 

$key = q/trightarrow-t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$ t\rightarrow -t$">|; 

$key = q/displaystyleF^{,jk}=-c,B^{,jk}=frac{e}{4pi,epsilon_0,c,{r'}^{,3}},gamma(u),(u^{,j},r^{,k}-u^{,k},r^{,j}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3893.png"
 ALT="$\displaystyle F^{ jk} = -c B^{ jk}= \frac{e}{4\pi \epsilon_0 c {r'}^{ 3}} \gamma(u) (u^{ j}  r^{ k}-u^{ k}  r^{ j}),$">|; 

$key = q/displaystylephi(z)=frac{1}{4pi}int_0^piint_0^{2pi}frac{phi_S(theta',varphi'),(z^ntheta',dtheta',dvarphi'}{(z^{,2}-2,z,a,costheta'+a^{,2})^{3slash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="$\displaystyle \phi(z) = \frac{1}{4\pi}\int_0^\pi\int_0^{2\pi}\frac{\phi_S(\thet...
...\sin\theta' d\theta' d\varphi'}{(z^{ 2}-2 z a \cos\theta'+a^{ 2})^{3/2}}$">|; 

$key = q/displaystylesimeqmpA,n^{,1slash2}(z),expleft(pm{rmi},kint^z!n(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2263.png"
 ALT="$\displaystyle \simeq \mp A  n^{ 1/2}(z) \exp\left(\pm {\rm i} k \int^z\! n(z') dz'\right),$">|; 

$key = q/omega=omega_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2378.png"
 ALT="$ \omega=\omega_p$">|; 

$key = q/displaystylesimeqfrac{e}{4pi,epsilon_0,c^{,3}}frac{sintheta}{r},dot{u}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4036.png"
 ALT="$\displaystyle \simeq \frac{e}{4\pi \epsilon_0  c^{ 3}} \frac{\sin\theta}{r}  \dot{u}.$">|; 

$key = q/displaystylemu=mu_0,(1+chi_m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1455.png"
 ALT="$\displaystyle \mu = \mu_0 (1+ \chi_m)$">|; 

$key = q/displaystyleequiv-K_1(z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2951.png"
 ALT="$\displaystyle \equiv -K_1(z),$">|; 

$key = q/D>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="$ D&gt;0$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}int{bfj}({bfr}')cdotnablaleft(frac{1}{|{bfr}-{bfr}'|{4pi}int{bfj}({bfr}')cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right)dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1314.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi}\int {\bf j}({\bf r}')\cdot\nabla\left(\frac{...
...bf j}({\bf r}')\cdot\nabla'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dV'$">|; 

$key = q/displaystyle-sum_{l=1,infty}sum_{m=-l,+l}frac{1}{2,l+1}left(frac{r_<^{,l}}{r_>^{{a^{,2,l+1}}right)Y_{l,m}^ast(theta',varphi'),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="$\displaystyle -\sum_{l=1,\infty}\sum_{m=-l,+l}\frac{1}{2 l+1}\left(\frac{r_&lt;^{...
...}{a^{ 2 l+1}}\right) Y_{l,m}^\ast(\theta',\varphi') Y_{l,m}(\theta,\varphi).$">|; 

$key = q/F({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="$ F({\bf r})$">|; 

$key = q/I_m(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2919.png"
 ALT="$ I_m(z)$">|; 

$key = q/displaystyle=oint{bfX}_{lm}^{,ast}cdotc{bfB},d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3317.png"
 ALT="$\displaystyle = \oint {\bf X}_{lm}^{ \ast}\cdot\c{\bf B} d {\mit \Omega}.$">|; 

$key = q/displaystylex';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3397.png"
 ALT="$\displaystyle x'$">|; 

$key = q/|omega|=sqrt{xislashs}gg2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1879.png"
 ALT="$ \vert\omega\vert=\sqrt{\xi/s}\gg 2\pi/\tau$">|; 

$key = q/displaystylerggd.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2612.png"
 ALT="$\displaystyle r \gg d.$">|; 

$key = q/{bfu}'=(u'_1,u'_2,u'_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3510.png"
 ALT="$ {\bf u}' = (u'_1, u'_2, u'_3)$">|; 

$key = q/sin(n,pi,zslashL);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2850.png"
 ALT="$ \sin( n \pi  z/L)$">|; 

$key = q/{rme}^{-K,z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2898.png"
 ALT="$ {\rm e}^{-K z}$">|; 

$key = q/-f,{bfs};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1618.png"
 ALT="$ -f  {\bf s}$">|; 

$key = q/displaystylephi_i=sum_{j=1,N}p_{ij},Q_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="$\displaystyle \phi_i = \sum_{j=1,N} p_{ij} Q_j.
$">|; 

$key = q/nablatimes{bfH}={bfj}_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1583.png"
 ALT="$ \nabla\times{\bf H}
= {\bf j}_t$">|; 

$key = q/displaystylealpha=k,{mitDelta},sintheta,cosvarphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2699.png"
 ALT="$\displaystyle \alpha = k {\mit \Delta}  \sin\theta \cos\varphi.$">|; 

$key = q/displaystyle=E_0,n^{-1slash2}(z)expleft(,{rmi},kint_0^z!n(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2272.png"
 ALT="$\displaystyle = E_0 n^{-1/2}(z) \exp\left( {\rm i} k \int_0^z\! n(z') dz'\right),$">|; 

$key = q/P_l^{,m}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="$ P_l^{ m}(x)$">|; 

$key = q/displaystyletheta_{rmmax}=cos^{-1}left[frac{1}{3,uslashc}left(sqrt{1+15,u^{,2}slashc^{,2}}-1right)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4103.png"
 ALT="$\displaystyle \theta_{\rm max} = \cos^{-1} \left[ \frac{1}{3  u/c}\left(\sqrt{1+ 15  u^{ 2}/c^{ 2}} - 1\right)\right].$">|; 

$key = q/displaystyle=frac{rho,c}{c,epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3726.png"
 ALT="$\displaystyle = \frac{\rho  c}{c \epsilon_0},$">|; 

$key = q/displaystylef(t)=frac{1}{2pi},{rmRe}int_C{rme}^{-{rmi},omega,t}frac{domega}{omega-2pislashtau}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1795.png"
 ALT="$\displaystyle f(t) = \frac{1}{2\pi} {\rm Re}\int_C {\rm e}^{-{\rm i} \omega  t} \frac{d\omega}{\omega -2\pi/\tau}.$">|; 

$key = q/epsilon_2ggepsilon_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1128.png"
 ALT="$ \epsilon_2\gg \epsilon_1$">|; 

$key = q/v({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$ v({\bf r}, t)$">|; 

$key = q/{bfD}=epsilon_0,{bfE}+{bfP};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1440.png"
 ALT="$ {\bf D} = \epsilon_0 {\bf E} +
{\bf P}$">|; 

$key = q/uslashcrightarrow1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4101.png"
 ALT="$ u/c\rightarrow 1$">|; 

$key = q/displaystylef(t)=frac{1}{2pi},{rmRe}!int_{-infty}^{infty}frac{domega}{omega-2pisashtau}left[{rme}^{-{rmi},omega,(t-T)}-{rme}^{-{rmi},omega,t}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1786.png"
 ALT="$\displaystyle f(t) = \frac{1}{2\pi}  {\rm Re}\! \int_{-\infty}^{\infty} \frac{...
...left[ {\rm e}^{-{\rm i} \omega (t-T)} -{\rm e}^{-{\rm i} \omega  t}\right].$">|; 

$key = q/displaystyle={rmi},k,c,B_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2300.png"
 ALT="$\displaystyle = {\rm i} k c B_z,$">|; 

$key = q/d{mitOmega}=sintheta,dtheta,dvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="$ d{\mit\Omega}=\sin\theta d\theta d\varphi$">|; 

$key = q/phi(r=a_-)=phi(r=a_+);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1167.png"
 ALT="$ \phi(r=a_-)= \phi(r=a_+)$">|; 

$key = q/displaystyle=frac{mu_0,I}{2,a},costheta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1361.png"
 ALT="$\displaystyle = \frac{\mu_0 I}{2 a} \cos\theta,$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{mu_0,c,I_0^{,2}}{128pi^2},(k,d)^{,2},sin^2theta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2632.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} = \frac{\mu_0  c I_0^{ 2}}{128\pi^2}  (k d)^{ 2}  \sin^2\theta,$">|; 

$key = q/displaystyle{T^{,i}}_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3956.png"
 ALT="$\displaystyle {T^{ i}}_j$">|; 

$key = q/m=I,pi,a^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1372.png"
 ALT="$ m=I \pi a^{ 2}$">|; 

$key = q/displaystylefrac{dU}{dr}=frac{epsilon_0}{2,k^{,2}}sum_m|a_E(l,m)|^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3159.png"
 ALT="$\displaystyle \frac{dU}{dr} = \frac{\epsilon_0}{2 k^{ 2}} \sum_m \vert a_E(l,m)\vert^{ 2},$">|; 

$key = q/displaystylea_E(l,m)=frac{mu_0,c,k^{,2}}{{rmi},sqrt{l,(l+1)}}intY_{lm}^{,ast}lefbfj}),j_l(k,r)-{rmi},k,nablacdot({bfr}times{bfM}),j_l(k,r)right],dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="571" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3230.png"
 ALT="$\displaystyle a_E(l,m) = \frac{\mu_0  c k^{ 2}}{{\rm i} \sqrt{l (l+1)}} \i...
...,j_l(k r)-{\rm i} k \nabla\cdot({\bf r}\times{\bf M}) j_l(k r)\right] dV.$">|; 

$key = q/partialslashpartialz={rmi},k_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2891.png"
 ALT="$ \partial/\partial z = {\rm i} k_g$">|; 

$key = q/B_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1159.png"
 ALT="$ B_l$">|; 

$key = q/displaystyle{bfE}_{rmtan}=sum_l{rmi}^{,l}sqrt{4pi,(2,l+1)}left{left[j_l+frac{alpc{beta_pm(l)}{2},h^{(1)}_lright)right]{bfn}times{bfX}_{l,pm1}right},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3360.png"
 ALT="$\displaystyle {\bf E}_{\rm tan} = \sum_l {\rm i}^{ l} \sqrt{4\pi (2 l+1)} \l...
...a_\pm(l)}{2}  h^{(1)}_l \right)\right] {\bf n}\times{\bf X}_{l,\pm 1}\right\},$">|; 

$key = q/displaystylepsi_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2157.png"
 ALT="$\displaystyle \psi_i$">|; 

$key = q/displaystylephi_m({bfr})=frac{1}{4pi}intfrac{rho_m({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1479.png"
 ALT="$\displaystyle \phi_m({\bf r}) = \frac{1}{4\pi}\int \frac{\rho_m({\bf r}')}{ \vert{\bf r} - {\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle=frac{u,a_0}{c^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3912.png"
 ALT="$\displaystyle = \frac{u a_0}{c^{ 2}}.$">|; 

$key = q/n+1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$ n+1/2$">|; 

$key = q/displaystylew(2)=A,(hat{z},0)_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2555.png"
 ALT="$\displaystyle w(2) = A (\hat{z},0)_s,$">|; 

$key = q/displaystylemu_0,delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1571.png"
 ALT="$\displaystyle \mu_0 \delta$">|; 

$key = q/x=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="$ x=0$">|; 

$key = q/displaystyle={rmi},k,c,B_y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2237.png"
 ALT="$\displaystyle = {\rm i} k c  B_y,$">|; 

$key = q/displaystyle{bfm}=Iointfrac{1}{2},{bfr}timesd{bfr}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1408.png"
 ALT="$\displaystyle {\bf m} = I\oint\frac{1}{2} {\bf r}\times d{\bf r}.$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}intfrac{rho({bfr}')}{|{bfr}-{bfr}'|},dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho({\bf r}')} {\vert{\bf r} - {\bf r}'\vert} dV'$">|; 

$key = q/displaystylembox{boldmath{{rho{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4111.png"
 ALT="$\displaystyle \mbox{\boldmath$\rho$}$">|; 

$key = q/displaystyle=int_0^inftyJ_m(k,r),A_m(k),dk,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img921.png"
 ALT="$\displaystyle = \int_0^\infty J_m(k r) A_m(k) dk,$">|; 

$key = q/langlephirangle_S=int_Sphi({bfr}'),dS'leftslashint_SdS'right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="$ \langle\phi\rangle_S = \int_S \phi({\bf r}') dS'\left/\int_S dS'\right.$">|; 

$key = q/displaystyleP=-frac{e^{,2}}{6pi,epsilon_0,c^{,3}},A_mu,A^{,mu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4071.png"
 ALT="$\displaystyle P = -\frac{e^{ 2}}{6\pi \epsilon_0  c^{ 3}}  A_\mu  A^{ \mu},$">|; 

$key = q/A_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1329.png"
 ALT="$ A_x$">|; 

$key = q/displaystyle{bfE}_{lm}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3105.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(E)}$">|; 

$key = q/overline{sin^2theta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2736.png"
 ALT="$ \overline{\sin^2\theta}$">|; 

$key = q/u'<c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3514.png"
 ALT="$ u'&lt;c$">|; 

$key = q/psi_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2020.png"
 ALT="$ \psi_i$">|; 

$key = q/0.304;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3289.png"
 ALT="$ 0.304$">|; 

$key = q/displaystyle=m^{,2},Y_{lm},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3004.png"
 ALT="$\displaystyle = m^{ 2}  Y_{lm},$">|; 

$key = q/displaystylenablatimesc,{bfB}+{rmi},k,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3192.png"
 ALT="$\displaystyle \nabla\times c {\bf B} + {\rm i} k  {\bf E}$">|; 

$key = q/v({bfr},t)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$ v({\bf r}, t) =0$">|; 

$key = q/displaystyleU=frac{epsilon_0,E^{,2}}{2}+frac{B^{,2}}{2,mu_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3973.png"
 ALT="$\displaystyle U = \frac{\epsilon_0  E^{ 2}}{2} + \frac{B^{ 2}}{2 \mu_0},$">|; 

$key = q/gamma(u)gg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3903.png"
 ALT="$ \gamma(u)\gg 1$">|; 

$key = q/{mitDelta}omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2804.png"
 ALT="$ {\mit\Delta}\omega$">|; 

$key = q/displaystyle{bfE}({bfr})=-nablaleft(frac{q}{4pi,epsilon_0},frac{1}{|{bfr}-{bfr}'|}-frac{q}{4pi,epsilon_0},frac{1}{|{bfr}-{bfr}'+{bfd}|}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = -\nabla\left(\frac{q}{4\pi \epsilon_0} \frac...
...frac{q}{4\pi \epsilon_0} \frac{1}{\vert{\bf r}-{\bf r}'+{\bf d}\vert}\right).$">|; 

$key = q/S(x,y,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3391.png"
 ALT="$ S(x,y,z,t)$">|; 

$key = q/displaystylephantom{=}+rho,{bfE}+{bfj}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$\displaystyle \phantom{=}+ \rho {\bf E}+{\bf j}\times {\bf B}.$">|; 

$key = q/displaystylephi(omega)simeqomega,(t_1-t)+frac{x}{6},k_0''',omega^{,3},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1949.png"
 ALT="$\displaystyle \phi(\omega) \simeq \omega (t_1-t) + \frac{x}{6} k_0''' \omega^{ 3},$">|; 

$key = q/[F({bfr}',t)]equivF({bfr}',t_r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$ [F({\bf r}', t)]\equiv F({\bf r}', t_r)$">|; 

$key = q/(k^{,2}-k_3^{,2})=k_s^{,2}=k_1^{,2}+k_2^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2834.png"
 ALT="$ (k^{ 2}-k_3^{ 2})= k_s^{ 2} = k_1^{ 2} + k_2^{ 2}$">|; 

$key = q/displaystyle=x,coshvarphi-c,t,sinhvarphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4159.png"
 ALT="$\displaystyle = x \cosh\varphi - c t \sinh\varphi,$">|; 

$key = q/displaystyle=mu_0,{bfj}+epsilon_0,mu_0,frac{partial{bfE}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$\displaystyle = \mu_0 {\bf j} + \epsilon_0 \mu_0  \frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/displaystyleleft.r',frac{partialG({bfr},{bfr}')}{partialr'}right|_{r'=a}=frac{1}_n,z'),{rme}^{,{rmi},m,(theta-theta')},frac{I_m(k_n,r)}{I_m(k_n,a)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1016.png"
 ALT="$\displaystyle \left.r' \frac{\partial G({\bf r},{\bf r}')}{\partial r'}\right\...
...z') {\rm e}^{ {\rm i} m (\theta-\theta')} \frac{I_m(k_n r)}{I_m(k_n a)}.$">|; 

$key = q/displaystyle=frac{epsilon_0,c}{4,k^{,3}},{rmIm}!sum_mleft[sqrt{(l-m),(l+m+1)},a_E^{,ast}(l,m+1)right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3171.png"
 ALT="$\displaystyle = \frac{\epsilon_0  c}{4  k^{ 3}}  {\rm Im}\!\sum_m\left[\sqrt{(l-m) (l+m+1)}  a_E^{ \ast}(l, m+1)\right.$">|; 

$key = q/-infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1793.png"
 ALT="$ -\infty$">|; 

$key = q/displaystylesintheta_i=frac{beta}{sqrt{1+beta^{,2}}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2126.png"
 ALT="$\displaystyle \sin\theta_i = \frac{\beta}{\sqrt{1+\beta^{ 2}}},$">|; 

$key = q/displaystyleq_{1,-1}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="$\displaystyle q_{1,-1}^{ \ast}$">|; 

$key = q/sigmaslashepsilon_0,omegaggepsilon>1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1697.png"
 ALT="$ \sigma/\epsilon_0 \omega\gg \epsilon &gt; 1$">|; 

$key = q/sigma^{,-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2794.png"
 ALT="$ \sigma^{ -1}$">|; 

$key = q/4pi,a_0^{,3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1286.png"
 ALT="$ 4\pi a_0^{ 3}$">|; 

$key = q/D_r(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2989.png"
 ALT="$ D_r(r)$">|; 

$key = q/displaystyleR(r)=J_m(k,r).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="$\displaystyle R(r) = J_m(k r).$">|; 

$key = q/displaystylensimeq1+frac{(N,e^{,2}slashepsilon_0,m)}{omega_0^{,2}-omega^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1754.png"
 ALT="$\displaystyle n \simeq 1 + \frac{(N e^{ 2}/\epsilon_0  m)}{\omega_0^{ 2}-\omega^{ 2}},$">|; 

$key = q/displaystylen_-^{,2}simeqfrac{omega_p^{,2}}{omega,{mitOmega}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1766.png"
 ALT="$\displaystyle n_-^{ 2} \simeq \frac{\omega_p^{ 2}}{\omega {\mit \Omega}}.$">|; 

$key = q/beta=a,omega_0slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4215.png"
 ALT="$ \beta = a \omega_0/c$">|; 

$key = q/displaystylepsi({bfr},{bfr}')=frac{1}{4pi,|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="$\displaystyle \psi({\bf r},{\bf r}') = \frac{1}{4\pi \vert{\bf r}-{\bf r}'\vert}.$">|; 

$key = q/displaystyleomega_p=sqrt{frac{N,Z,e^{,2}}{epsilon_0,m}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1702.png"
 ALT="$\displaystyle \omega_p = \sqrt{\frac{N Z e^{ 2}}{\epsilon_0  m}}$">|; 

$key = q/F^{,4i}=-E^{,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3890.png"
 ALT="$ F^{ 4i} = -E^{ i}$">|; 

$key = q/displaystyle{bfA}=frac{mu_0}{4pi},frac{{bfm}times{bfr}}{r^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1377.png"
 ALT="$\displaystyle {\bf A} = \frac{\mu_0}{4\pi} \frac{{\bf m}\times {\bf r}}{r^{ 3}}.$">|; 

$key = q/nsimeq1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1759.png"
 ALT="$ n\simeq 1$">|; 

$key = q/displaystylef(t)=frac{1}{4pi}left(int_C{rme}^{-{rmi},omega,t}frac{domega}{omega-u}+int_C{rme}^{+{rmi},omega,t}frac{domega}{omega-2pislashtau}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1838.png"
 ALT="$\displaystyle f(t) = \frac{1}{4\pi}\left(\int_C {\rm e}^{-{\rm i} \omega  t} ...
... \int_C {\rm e}^{+{\rm i} \omega  t} \frac{d\omega}{\omega-2\pi/\tau}\right).$">|; 

$key = q/displaystyleskew{3}dot{u}^{,i}=frac{du^{,i'}}{dt'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3985.png"
 ALT="$\displaystyle \skew{3}\dot{u}^{ i} = \frac{du^{ i'}}{dt'},$">|; 

$key = q/displaystyle-frac{partial^{,2}Y_{lm}}{partialvarphi^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3003.png"
 ALT="$\displaystyle -\frac{\partial^{ 2} Y_{lm}}{\partial\varphi^{ 2}}$">|; 

$key = q/displaystyleoint{bfX}_{l'm'}^{,ast}cdot{bfX}_{lm},d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3110.png"
 ALT="$\displaystyle \oint {\bf X}_{l'm'}^{ \ast}\cdot{\bf X}_{lm} d{\mit\Omega}$">|; 

$key = q/displaystylenabla(E^{,2}slash2)equiv{bfE}times(nablatimes{bfE})+({bfE}cdot{nabla}),{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$\displaystyle \nabla (E^{ 2}/2) \equiv {\bf E}\times(\nabla\times {\bf E}) + ({\bf E}\cdot{\nabla}) {\bf E},$">|; 

$key = q/|t|<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="$ \vert t\vert&lt; 1$">|; 

$key = q/{bfr}_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4020.png"
 ALT="$ {\bf r}_0$">|; 

$key = q/displaystyleleft[nabla_s^{,2}+(k^{,2}-k_3^{,2})right]A_z=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2829.png"
 ALT="$\displaystyle \left[\nabla_s^{ 2} + (k^{ 2}-k_3^{ 2})\right] A_z = 0,$">|; 

$key = q/[partialrhoslashpartialt]=-[nablacdot{bfj}];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$ [\partial \rho/\partial t] = -[\nabla\cdot {\bf j}]$">|; 

$key = q/g_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3587.png"
 ALT="$ g_{ij}$">|; 

$key = q/displaystylepsi({bfr},omega)=sum_{l=0,infty}sum_{m=-l,+l}left[A_{lm},h_l^{(1)}(k,r)+B_{lm},h_l^{(2)}(k,r)right]Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3042.png"
 ALT="$\displaystyle \psi({\bf r},\omega) = \sum_{l=0,\infty}\sum_{m=-l,+l}\left[A_{lm} h_l^{(1)}(k r) + B_{lm} h_l^{(2)}(k r)\right]Y_{lm}(\theta,\varphi).$">|; 

$key = q/partialphislashpartialomega=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1914.png"
 ALT="$ \partial\phi/\partial\omega
=0$">|; 

$key = q/displaystyle{T^{,mu}}_sigma,{T^{,sigma}}_nu=frac{I^{,2}}{4},delta^{,mu}_nu,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4211.png"
 ALT="$\displaystyle {T^{ \mu}}_\sigma  {T^{ \sigma}}_\nu = \frac{I^{ 2}}{4}  \delta^{ \mu}_\nu,
$">|; 

$key = q/3slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2652.png"
 ALT="$ 3/2$">|; 

$key = q/g_{m,n}(a,r')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1007.png"
 ALT="$ g_{m,n}(a,r')=0$">|; 

$key = q/k_0=omegaslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2039.png"
 ALT="$ k_0=\omega/c$">|; 

$key = q/k^{,2}=omega^{,2}slashc^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2999.png"
 ALT="$ k^{ 2}=\omega^{ 2}/c^{ 2}$">|; 

$key = q/displaystylenablatimes{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle \nabla\times{\bf A}$">|; 

$key = q/A_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3594.png"
 ALT="$ A_i$">|; 

$key = q/[({bfE}cdotnabla),{bfE}]_iequivE_j,(partialE_islashpartialx_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$ [({\bf E}\cdot\nabla) {\bf E}]_i \equiv E_j (\partial E_i/\partial x_j)$">|; 

$key = q/displaystylenabla^{,2}G_D({bfr},{bfr}')=delta({bfr}-{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="$\displaystyle \nabla^{ 2}G_D({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}'),$">|; 

$key = q/displaystyle-dx^{,2}-dy^{,2}-dz^{,2}+c^{,2},dt^{,2}=ds^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3616.png"
 ALT="$\displaystyle -dx^{ 2} -dy^{ 2}-dz^{ 2} +c^{ 2}  dt^{ 2} =ds^{ 2},$">|; 

$key = q/omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$ \omega$">|; 

$key = q/{mitDelta}E;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4147.png"
 ALT="$ {\mit\Delta} E$">|; 

$key = q/displaystyledeltaU=int_Vphi,deltarho_f,dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1193.png"
 ALT="$\displaystyle \delta U = \int_V \phi  \delta\rho_f  dV,$">|; 

$key = q/displaystylelangle{calI}_zrangle_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2083.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle_t$">|; 

$key = q/displaystyler,Y_{1,-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="$\displaystyle r Y_{1,-1}$">|; 

$key = q/displaystylef(x,t)=frac{1}{2pi},{rmRe}int_C{rme}^{,{rmi},(k,x-omega,t)}frac{domega}{omega-2pislashtau}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1805.png"
 ALT="$\displaystyle f(x,t) = \frac{1}{2\pi} {\rm Re}\int_C {\rm e}^{ {\rm i} (k  x- \omega  t)} \frac{d\omega}{\omega -2\pi/\tau}.$">|; 

$key = q/phi(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1902.png"
 ALT="$ \phi(\omega)$">|; 

$key = q/l,m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3083.png"
 ALT="$ l, m$">|; 

$key = q/delta_l';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3374.png"
 ALT="$ \delta_l'$">|; 

$key = q/c=1slashsqrt{epsilon_0,mu_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1999.png"
 ALT="$ c=1/\sqrt{\epsilon_0 \mu_0}$">|; 

$key = q/displaystyleg_m(r,r')=left{{array}{ccc}alpha(r'),I_m(k,r)&mbox{hspace{1cm}}&r<r'[0.5ex]beta(r'),K_m(k,r)&&r>r'{array}right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img969.png"
 ALT="$\displaystyle g_m(r,r')=\left\{\begin{array}{ccc}\alpha(r') I_m(k r)&amp;\mbox{\hspace{1cm}}&amp; r&lt;r'\ [0.5ex] \beta(r') K_m(k r)&amp;&amp;r&gt;r'\end{array}\right..$">|; 

$key = q/displaystyle=-{rmi},frac{omega,epsilon_0,epsilon_1}{k_s},J_1(k_s,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2982.png"
 ALT="$\displaystyle =-{\rm i} \frac{\omega \epsilon_0 \epsilon_1}{k_s}  J_1(k_s  r),$">|; 

$key = q/displaystyle=-frac{omega,mu_0}{k_g},{bfe}_ztimes{bfH}_s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2893.png"
 ALT="$\displaystyle =- \frac{\omega \mu_0}{k_g}  {\bf e}_z\times {\bf H}_s.$">|; 

$key = q/displaystyleW=frac{Q^{,2}}{8pi,epsilon_0,a}left(frac{1}{5}+1right)=frac{3}{5}frac{Q^{,2}}{4pi,epsilon_0,a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="$\displaystyle W = \frac{Q^{ 2}}{8\pi \epsilon_0  a} \left( \frac{1}{5} + 1\right)= \frac{3}{5} \frac{Q^{ 2}}{4\pi \epsilon_0  a}.$">|; 

$key = q/rhosim1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4089.png"
 ALT="$ \rho \sim 1$">|; 

$key = q/x_3=z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="$ x_3=z$">|; 

$key = q/displaystyleG=frac{(dPslashd{mitOmega})_{rmmax}}{Pslash4pi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2651.png"
 ALT="$\displaystyle G = \frac{(dP/d {\mit \Omega})_{\rm max}}{P/4\pi}.$">|; 

$key = q/displaystyleW_i=frac{3}{5}frac{q_i^{,2}}{4pi,epsilon_0,b}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="$\displaystyle W_i = \frac{3}{5} \frac{q_i^{ 2}}{4\pi \epsilon_0  b}.$">|; 

$key = q/displaystylefrac{dh_l^{(1)}(z)}{dz},j_l(z)-h_l^{(1)}(z),frac{dj_l(z)}{dz}=frac{{rmi}}{z^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3185.png"
 ALT="$\displaystyle \frac{d h_l^{(1)}(z)}{dz}  j_l (z) - h_l^{(1)}(z)  \frac{d j_l(z)}{dz} = \frac{{\rm i}} {z^{ 2}}.$">|; 

$key = q/3.09times10^{-2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3272.png"
 ALT="$ 3.09\times
10^{-2}$">|; 

$key = q/pmsigma_b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1277.png"
 ALT="$ \pm\sigma_b$">|; 

$key = q/k=k_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="$ k=k_{mn}$">|; 

$key = q/A_{ijk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3527.png"
 ALT="$ A_{ijk}$">|; 

$key = q/q^{,1slash2}(hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2495.png"
 ALT="$ q^{ 1/2}(\hat{z})$">|; 

$key = q/displaystyleU^{,mu}=frac{dx^{,mu}}{dtau};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3701.png"
 ALT="$\displaystyle U^{ \mu} = \frac{dx^{ \mu}}{d\tau}$">|; 

$key = q/1slashhbar;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3049.png"
 ALT="$ 1/\hbar$">|; 

$key = q/mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1458.png"
 ALT="$ \mu$">|; 

$key = q/ssimeqr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4029.png"
 ALT="$ s\simeq r$">|; 

$key = q/displaystyle{bfn}timesc,{bfB}_{rmsc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3345.png"
 ALT="$\displaystyle {\bf n}\times c {\bf B}_{\rm sc}$">|; 

$key = q/displaystyleW=-{bfm}cdot{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1421.png"
 ALT="$\displaystyle W = - {\bf m}\cdot{\bf B}.
$">|; 

$key = q/displaystylephi(omega,z,t)=frac{omega}{c}int_0^{z}!n(omega,z'),dz'-omega,t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2335.png"
 ALT="$\displaystyle \phi(\omega, z,t) = \frac{\omega}{c} \int_0^{z} \!n(\omega, z') dz' - \omega  t.$">|; 

$key = q/displaystyle=left(frac{1}{4pi}right)^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="$\displaystyle = \left(\frac{1}{4\pi}\right)^{1/2},$">|; 

$key = q/delta({bfr}'-{bfr})=delta({bfr}-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="$ \delta({\bf r}'-{\bf r})=\delta({\bf r}-{\bf r}')$">|; 

$key = q/displaystylerho(r,theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="$\displaystyle \rho(r,\theta,\varphi)$">|; 

$key = q/displaystylephi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3731.png"
 ALT="$\displaystyle \phi$">|; 

$key = q/displaystylea_E(l,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3219.png"
 ALT="$\displaystyle a_E(l,m)$">|; 

$key = q/q^{,1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2570.png"
 ALT="$ q^{ 1/2}$">|; 

$key = q/n_1,sintheta_i=n_2,sintheta_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2056.png"
 ALT="$ n_1 \sin\theta_i=n_2 \sin\theta_t$">|; 

$key = q/J_0(k_s,a)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2965.png"
 ALT="$ J_0(k_s  a)=0$">|; 

$key = q/displaystylefrac{dphi}{dz}simeqpmk,nleft(1pmfrac{{rmi}}{k,n^{,2}}frac{dn}{dz}right)^{1slash2}simeqpmk,n+frac{rmi}{2,n}frac{dn}{dz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2254.png"
 ALT="$\displaystyle \frac{d\phi}{dz} \simeq \pm k n\left(1\pm \frac{{\rm i}}{k  n^{ 2}}\frac{dn}{dz} \right)^{1/2}\simeq \pm k n + \frac{\rm i}{2 n}\frac{dn}{dz},$">|; 

$key = q/displaystylenablatimes{bfB}({bfr})=-frac{mu_0}{4pi}int{bfj}({bfr}'),nabla^{,2}le)dV'=mu_0int{bfj}({bfr}'),delta({bfr}-{bfr}'),dV'=mu_0,{bfj}({bfr}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1318.png"
 ALT="$\displaystyle \nabla\times {\bf B}({\bf r})= -\frac{\mu_0}{4\pi}\int {\bf j}({\...
...int {\bf j}({\bf r}') \delta({\bf r}-{\bf r}') dV' = \mu_0 {\bf j}({\bf r}),$">|; 

$key = q/lneq1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1170.png"
 ALT="$ l\neq 1$">|; 

$key = q/displaystyle=m,Y_{lm}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3063.png"
 ALT="$\displaystyle = m Y_{lm}.$">|; 

$key = q/displaystyleA_{k'cdotsl',m'}^{i'cdotsj'}=A_{kcdotsl,m}^{icdotsj},p_i^{,i'}cdotsp_j^{,j'}p_{k'}^{,k}cdotsp_{l'}^{,l},p_{m'}^{,m}+P_1+P_2+cdots,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3582.png"
 ALT="$\displaystyle A_{k'\cdots l', m'}^{i'\cdots j'} = A_{k\cdots l,m}^{i\cdots j} ...
..._j^{ j'} p_{k'}^{ k} \cdots p_{l'}^{ l}  p_{m'}^{ m} + P_1 + P_2 + \cdots,$">|; 

$key = q/R^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3658.png"
 ALT="$ R^{ \mu}$">|; 

$key = q/displaystylek_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2786.png"
 ALT="$\displaystyle k_2$">|; 

$key = q/displaystyleint_Vf({bfr}),delta({bfr}-{bfr}'),dV=f({bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle \int_V f({\bf r}) \delta({\bf r}-{\bf r}') dV = f({\bf r}'),$">|; 

$key = q/omega_{01};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2973.png"
 ALT="$ \omega_{01}$">|; 

$key = q/q(x)equivn^{,2}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2567.png"
 ALT="$ q(x)\equiv n^{ 2}(x)$">|; 

$key = q/-(E_y,B_x^{,ast}+E_y^{,ast},B_x)slash(4,mu_0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2266.png"
 ALT="$ -(E_y  B_x^{ \ast}
+E_y^{ \ast}  B_x)/(4 \mu_0)$">|; 

$key = q/displaystylenablacdot(psi,nablaphi-phi,nablapsi)=psi,nabla^{,2}phi-phi,nabla^{,2}psi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="$\displaystyle \nabla\cdot(\psi \nabla\phi-\phi \nabla\psi) = \psi \nabla^{ 2}\phi - \phi \nabla^{ 2}\psi.$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{Chapter10slashfig1rel.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="283" BORDER="0"
 SRC="|."$dir".q|img4050.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{Chapter10/fig1rel.eps}}
\end{figure}">|; 

$key = q/displaystyle=sqrt{(l+m),(l-m+1)},Y_{l,m-1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3061.png"
 ALT="$\displaystyle =\sqrt{(l+m) (l-m+1)} Y_{l,m-1},$">|; 

$key = q/c^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2578.png"
 ALT="$ c^{ 2}$">|; 

$key = q/{rmRe}(k)gg{rmIm}(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1690.png"
 ALT="$ {\rm Re}(k) \gg {\rm Im}(k)$">|; 

$key = q/displaystyle=frac{1}{2}left(epsilon_0,E^{,2}+frac{B^{,2}}{mu_0}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3969.png"
 ALT="$\displaystyle = \frac{1}{2} \left(\epsilon_0  E^{ 2} +\frac{B^{ 2}}{\mu_0}\right).$">|; 

$key = q/displaystyle{bfE}_perp';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3855.png"
 ALT="$\displaystyle {\bf E}_\perp'$">|; 

$key = q/displaystyle=-(-z)^{,l}left(frac{1}{z}frac{d}{dz}right)^lleft(frac{cosz}{z}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3033.png"
 ALT="$\displaystyle = -(-z)^{ l} \left(\frac{1}{z}\frac{d}{dz}\right)^l \left(\frac{\cos z} {z}\right).$">|; 

$key = q/{bfn}'cdotnabla'phi({bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="$ {\bf n}'\cdot\nabla'\phi({\bf r}')$">|; 

$key = q/displaystyle=frac{n,pi}{c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2789.png"
 ALT="$\displaystyle = \frac{n \pi}{c}.$">|; 

$key = q/n,k_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2040.png"
 ALT="$ n k_0$">|; 

$key = q/displaystyleb_pm(l,m),j_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3316.png"
 ALT="$\displaystyle b_\pm(l,m) j_l(k r)$">|; 

$key = q/cslashn_-;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1743.png"
 ALT="$ c/n_-$">|; 

$key = q/{bfL},Y_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3108.png"
 ALT="$ {\bf L}  Y_{lm}$">|; 

$key = q/displaystylep_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="$\displaystyle p_x$">|; 

$key = q/t>T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1776.png"
 ALT="$ t&gt;T$">|; 

$key = q/u_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2343.png"
 ALT="$ u_z$">|; 

$key = q/f_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1673.png"
 ALT="$ f_0$">|; 

$key = q/displaystyle({bfE}_2-{bfE}_1)times{bfn}_{21}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1091.png"
 ALT="$\displaystyle ({\bf E}_2 - {\bf E}_1)\times {\bf n}_{21} = 0.$">|; 

$key = q/omega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1627.png"
 ALT="$ \omega_0$">|; 

$key = q/|omega|rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1812.png"
 ALT="$ \vert\omega\vert
\rightarrow\infty$">|; 

$key = q/n,vslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1714.png"
 ALT="$ n  v/c$">|; 

$key = q/F^{,44}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3809.png"
 ALT="$ F^{ 44}= 0$">|; 

$key = q/displaystyleG_{munu}=leftlgroup{array}{cccc}0&-E_z&+E_y&+c,B_x[0.5ex]+E_z&0&-E_xx]-E_y&+E_x&0&+c,B_z[0.5ex]-c,B_x&-c,B_y&-c,B_z&0{array}rightrgroup.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="105" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3837.png"
 ALT="$\displaystyle G_{\mu\nu} = \left\lgroup \begin{array}{cccc} 0 &amp; -E_z &amp; +E_y &amp; +...
...&amp; 0&amp; +c B_z\ [0.5ex] -c B_x &amp; -c B_y &amp;-c B_z &amp; 0\end{array}\right \rgroup.$">|; 

$key = q/x_i';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1394.png"
 ALT="$ x_i'$">|; 

$key = q/s<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1809.png"
 ALT="$ s&lt;0$">|; 

$key = q/{bfH}_s=(1slashZ_g),{bfe}_ztimes{bfE}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2905.png"
 ALT="$ {\bf H}_s = (1/Z_g)  {\bf e}_z\times
{\bf E}_s$">|; 

$key = q/(R)^2=R_mu,R^{,mu}=-r^{,2}+c^{,2},t^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3656.png"
 ALT="$ (R)^2 = R_\mu  R^{ \mu} = -r^{ 2} + c^{ 2}  t^{ 2}$">|; 

$key = q/displaystylefrac{partialE_x}{partialz};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2236.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial z}$">|; 

$key = q/displaystylelangle{calI}_zrangle_i=-langle{calI}_zrangle_r=frac{psi_i^{,2},costheta_i}{2,epsilon_0,c,n_1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2160.png"
 ALT="$\displaystyle \langle{\cal I}_z\rangle_i = -\langle{\cal I}_z\rangle_r =\frac{\psi_i^{ 2} \cos\theta_i}{2 \epsilon_0 c n_1},$">|; 

$key = q/displaystyle=frac{M_0}{3},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1510.png"
 ALT="$\displaystyle = \frac{M_0}{3},$">|; 

$key = q/displaystyletimesc,{bfB}-(;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4201.png"
 ALT="$\displaystyle \times c {\bf B}
-($">|; 

$key = q/displaystylenablatimes{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle \nabla\times {\bf E}$">|; 

$key = q/displaystyleF^{,musigma},partial_muF_{nusigma}=frac{1}{2},F^{,musigma}(partial_muF_{nusigma}+partial_sigmaF_{munu}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3950.png"
 ALT="$\displaystyle F^{ \mu\sigma}  \partial_\mu F_{\nu\sigma} = \frac{1}{2}  F^{ \mu\sigma} (\partial_\mu F_{\nu\sigma} + \partial_\sigma F_{\mu\nu}),$">|; 

$key = q/3.25times10^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3271.png"
 ALT="$ 3.25\times 10^{-1}$">|; 

$key = q/displaystyle=-nablaphi-frac{partial{bfA}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\displaystyle = - \nabla\phi - \frac{\partial {\bf A}}{\partial t},$">|; 

$key = q/displaystyleD_z(x,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2060.png"
 ALT="$\displaystyle D_z(x,z,t)$">|; 

$key = q/n=10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2422.png"
 ALT="$ n=10$">|; 

$key = q/displaystyle=frac{1}{2,l+1}int_a^rfrac{rho_{l,m}(r')}{epsilon_0}left(frac{r'^{,l}}{r^{,l+1}}-frac{a^{,2,l+1}}{r'^{,l+1},r^{,l+1}}right)r'^{,2},dr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="$\displaystyle =\frac{1}{2 l+1}\int_a^r \frac{\rho_{l,m}(r')}{\epsilon_0}\left(...
... l}}{r^{ l+1}}-\frac{a^{ 2 l+1}}{r'^{ l+1} r^{ l+1}}\right)r'^{ 2} dr'$">|; 

$key = q/displaystyleE_x(z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2001.png"
 ALT="$\displaystyle E_x(z,t)$">|; 

$key = q/gamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="$ \gamma$">|; 

$key = q/displaystylep_{l}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="$\displaystyle p_{l}(r)$">|; 

$key = q/displaystylec,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3115.png"
 ALT="$\displaystyle c {\bf B}$">|; 

$key = q/displaystylenablaR=frac{bfR}{R},~~~nablaleft(R^{,-1}right)=-frac{bfR}{R^{,3}},~~~nablat_r=-frac{bfR}{c,R}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle \nabla R = \frac{\bf R}{R},&nbsp;&nbsp;&nbsp;\nabla\left( R^{ -1}\right)= - \frac{\bf R}{R^{ 3}},&nbsp;&nbsp;&nbsp;\nabla t_r = - \frac{\bf R}{c R}.$">|; 

$key = q/displaystylev=frac{omega}{k}=frac{c}{n},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1610.png"
 ALT="$\displaystyle v = \frac{\omega}{k} = \frac{c}{n},$">|; 

$key = q/P=(0,,0,,0,,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3861.png"
 ALT="$ P=(0, 0, 0, 0)$">|; 

$key = q/displaystylep_A-p_B=frac{epsilon_0}{2}int_A^BE^{,2},nablaepsiloncdotd{bfr}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1268.png"
 ALT="$\displaystyle p_A - p_B = \frac{\epsilon_0}{2}\int_A^B E^{ 2}  \nabla\epsilon \cdot d{\bf r}.$">|; 

$key = q/gammagg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3905.png"
 ALT="$ \gamma\gg 1$">|; 

$key = q/displaystyledx^{,2}+dy^{,2}+dz^{,2}-c^{,2},dt^{,2}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3414.png"
 ALT="$\displaystyle dx^{ 2} + dy^{ 2} + dz^{ 2} -c^{ 2}  dt^{ 2} = 0$">|; 

$key = q/displaystyleB_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="$\displaystyle B_{mn}$">|; 

$key = q/displaystyle=sum_{l=1,infty}{rmi}^{,l}sqrt{4pi,(2,l+1)}left[frac{-{rmi}}{k},nablatimesj_l(k,r),{bfX}_{l,pm1}mp{rmi},j_l(k,r),{bfX}_{l,pm1}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="381" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3325.png"
 ALT="$\displaystyle = \sum_{l=1,\infty} {\rm i}^{ l}\sqrt{4\pi (2 l+1)}\left[\frac...
... j_l(k r) {\bf X}_{l,\pm 1}\mp {\rm i} j_l(k r)  {\bf X}_{l,\pm 1}\right].$">|; 

$key = q/displaystyle=frac{4,alpha,beta}{(beta+alpha)^2}=1-R.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2090.png"
 ALT="$\displaystyle =\frac{4 \alpha \beta}{(\beta+\alpha)^2} = 1-R.$">|; 

$key = q/L^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3046.png"
 ALT="$ L^2$">|; 

$key = q/j_{1l}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$ j_{1l}'$">|; 

$key = q/displaystyle=int_Vnablacdotnablaleft(frac{1}{|{bfr}-{bfr}'|}right)dV=int_Snablaleft(frac{1}{|{bfr}-{bfr}'|}right)cdotd{bfS};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle = \int_V \nabla\cdot\nabla\left(\frac{1}{\vert{\bf r}-{\bf r}'\ve...
... = \int_S \nabla\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)\cdot d{\bf S}$">|; 

$key = q/displaystyledelta(t-t')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\displaystyle \delta(t-t') =0$">|; 

$key = q/delta_{ij}=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$ \delta_{ij}=1$">|; 

$key = q/-0.50times10^{-8};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1453.png"
 ALT="$ -0.50\times 10^{-8}$">|; 

$key = q/alpha,h_0<2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2596.png"
 ALT="$ \alpha h_0&lt;2$">|; 

$key = q/displaystylefrac{{bfr}-{bfr}'}{|{bfr}-{bfr}'|^{,3}}=-nablaleft(frac{1}{|{bfr}-{bfr}'|}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1309.png"
 ALT="$\displaystyle \frac{{\bf r}-{\bf r}'}{\vert{\bf r}-{\bf r}'\vert^{ 3}} = -\nabla\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right),$">|; 

$key = q/displaystylefrac{partial}{partialx}=frac{partial}{partialy}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2230.png"
 ALT="$\displaystyle \frac{\partial}{\partial x}=\frac{\partial}{\partial y} = 0.$">|; 

$key = q/displaystyle=left(frac{3}{4pi}right)^{1slash2}z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="$\displaystyle = \left(\frac{3}{4\pi}\right)^{1/2}z,$">|; 

$key = q/displaystyle{calM}_{lm}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3242.png"
 ALT="$\displaystyle {\cal M}_{lm}'$">|; 

$key = q/displaystyle{bfj}={bfj}_t+nablatimes{bfM}+frac{partial{bfP}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1437.png"
 ALT="$\displaystyle {\bf j} = {\bf j}_t + \nabla\times{\bf M} + \frac{\partial{\bf P}}{\partial t}.$">|; 

$key = q/1slash3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1957.png"
 ALT="$ 1/3$">|; 

$key = q/displaystyleA_varphi(r,theta)=frac{1}{2},mu_0,Isum_{l=1,3,5,cdots}frac{P_l^1(0)}{l,(l+1)}left(frac{r}{a}right)^lP_l^1(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1345.png"
 ALT="$\displaystyle A_\varphi(r,\theta) = \frac{1}{2} \mu_0 I\sum_{l=1,3,5,\cdots}\frac{P_l^1(0)}{l (l+1)}\left(\frac{r}{a}\right)^lP_l^1(\cos\theta)$">|; 

$key = q/r=a-dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="$ r=a-d/2$">|; 

$key = q/omega^{,3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1948.png"
 ALT="$ \omega^{ 3}$">|; 

$key = q/displaystylefrac{1}{r},frac{d}{dr}!left(r,frac{dg_m}{dr}right)-left(k^{,2}+frac{m^{,2}}{r^{,2}}right)g_m=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img961.png"
 ALT="$\displaystyle \frac{1}{r} \frac{d}{dr}\!\left(r \frac{dg_m}{dr}\right)-\left(k^{ 2} + \frac{m^{ 2}}{r^{ 2}}\right) g_m= 0.$">|; 

$key = q/displaystyleleft(frac{partialphi}{partialomega}right)_{omega=omega_0}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2337.png"
 ALT="$\displaystyle \left(\frac{\partial\phi}{\partial\omega}\right)_{\omega=\omega_0} = 0,$">|; 

$key = q/displaystylephi=left{{array}{lll}-Dslashepsilon_0&mbox{hspace{0.5cm}}&r<a[0.5ex]0&&r>a{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="$\displaystyle \phi = \left\{ \begin{array}{lll} -D/\epsilon_0&amp;\mbox{\hspace{0.5cm}}&amp; r&lt;a\ [0.5ex] 0&amp;&amp;r&gt;a \end{array}\right.,$">|; 

$key = q/displaystyle{bfE}=left{{array}{rll}{bf0}&mbox{hspace{0.5cm}}&x>0[0.5ex]{bf0}&&x<0{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="$\displaystyle {\bf E} = \left\{ \begin{array}{rll} {\bf0}&amp;\mbox{\hspace{0.5cm}}&amp; x&gt;0\ [0.5ex] {\bf0}&amp;&amp;x&lt;0 \end{array}\right.,$">|; 

$key = q/a_1neq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2485.png"
 ALT="$ a_1\neq 0$">|; 

$key = q/displaystylefrac{1}{k^{,2}}left|frac{3}{4}left(frac{1}{q^{,2}},frac{dq}{dz}right)^{,2}-frac{1}{2,q^{,3}},frac{d^{,2}q}{dz^{,2}}right|ll1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2313.png"
 ALT="$\displaystyle \frac{1}{k^{ 2}}\left\vert \frac{3}{4}\left(\frac{1}{q^{ 2}}  ...
...ight)^{ 2} -\frac{1}{2 q^{ 3}} \frac{d^{ 2} q}{dz^{ 2}}\right\vert \ll 1.$">|; 

$key = q/displaystyle=frac{mu_0,e}{4pi}frac{bfu}{s},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3990.png"
 ALT="$\displaystyle = \frac{\mu_0 e}{4\pi} \frac{\bf u}{s},$">|; 

$key = q/n_+;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1736.png"
 ALT="$ n_+$">|; 

$key = q/dx^{,i}slashds;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3606.png"
 ALT="$ dx^{ i}/ds$">|; 

$key = q/displaystyleint_{Sigma_infty}left(w,frac{partialw^ast}{partialn}-w^ast,frac{partialw}{partialn}right),dS=-2,{rmi},kint|f_0|^{,2},d{mitOmega}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle \int_{\Sigma_\infty} \left(w \frac{\partial w^\ast}{\partial n} ...
... n}\right)  dS = -2 {\rm i}  k \int \vert f_0\vert^{ 2} d{\mit\Omega} = 0,$">|; 

$key = q/displaystyleE_r(r)=frac{Q}{4pi,epsilon_0,r^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="$\displaystyle E_r(r) = \frac{Q}{4\pi \epsilon_0 r^{ 2}}$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=-frac{1}{4pi,|{bfr}-{bfr}'|}+F({bfr},{bfr'}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}') = - \frac{1}{4\pi \vert{\bf r}-{\bf r}'\vert} + F({\bf r},{\bf r'}).$">|; 

$key = q/displaystylenablacdot{bfD}=rho_f,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1069.png"
 ALT="$\displaystyle \nabla \cdot {\bf D} = \rho_f,$">|; 

$key = q/r>b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1556.png"
 ALT="$ r&gt;b$">|; 

$key = q/{bfD}=epsilon_0,epsilon,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1199.png"
 ALT="$ {\bf D} =\epsilon_0  \epsilon  {\bf E}$">|; 

$key = q/displaystyle{bfj}=gamma,sigma,[{bfE}+;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4200.png"
 ALT="$\displaystyle {\bf j} = \gamma \sigma  [{\bf E} +$">|; 

$key = q/sintheta_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2134.png"
 ALT="$ \sin\theta_t$">|; 

$key = q/dy';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3411.png"
 ALT="$ dy'$">|; 

$key = q/displaystyle=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle =0,$">|; 

$key = q/displaystylefrac{dsigma}{d{mitOmega}}=frac{dPslashd{mitOmega}}{langleurangle}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2725.png"
 ALT="$\displaystyle \frac{d\sigma}{d {\mit \Omega}} = \frac{dP/d{\mit\Omega}}{\langle u \rangle}.$">|; 

$key = q/displaystyleR_{rmload}=R_{rmres}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2664.png"
 ALT="$\displaystyle R_{\rm load} = R_{\rm res}.$">|; 

$key = q/w^{,1slash2}=omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2376.png"
 ALT="$ w^{ 1/2}=\omega$">|; 

$key = q/jneqi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="$ j\neq i$">|; 

$key = q/E_z=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2849.png"
 ALT="$ E_z=0$">|; 

$key = q/displaystyleoint_C{bfH}cdotd{bfr}=int_S{bfj}_tcdotd{bfS}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1443.png"
 ALT="$\displaystyle \oint_C {\bf H}\cdot d{\bf r} = \int_S {\bf j}_t\cdot d{\bf S}.$">|; 

$key = q/displaystylef_1(xi,t)=frac{pi}{xi,tau},g(sslashs_0),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1888.png"
 ALT="$\displaystyle f_1(\xi, t) = \frac{\pi}{\xi \tau}  g(s/s_0),$">|; 

$key = q/{bfj}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$ {\bf j}({\bf r})$">|; 

$key = q/displaystylesum_{rmmols}x^{,2}=sum_{rmmols}y^{,2}=sum_{rmmols}z^{,2}=frac{1}{3}sum_{rmmols}r^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1247.png"
 ALT="$\displaystyle \sum_{\rm mols} x^{ 2}= \sum_{\rm mols} y^{ 2} = \sum_{\rm mols} z^{ 2} = \frac{1}{3} \sum_{\rm mols} r^{ 2}$">|; 

$key = q/45^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2188.png"
 ALT="$ 45^\circ$">|; 

$key = q/displaystyle{bfm}=frac{1}{2}int{bfr}times{bfj},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1427.png"
 ALT="$\displaystyle {\bf m} = \frac{1}{2}\int {\bf r}\times{\bf j} dV,$">|; 

$key = q/{bfE}=E_0,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1288.png"
 ALT="$ {\bf E} = E_0 {\bf e}_z$">|; 

$key = q/{mitDelta}varphisimeqlambdaslashN{mitDelta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2710.png"
 ALT="$ {\mit \Delta}\varphi\simeq \lambda/N
{\mit\Delta}$">|; 

$key = q/displaystyle=gammaleft(c,A_1'+frac{u}{c},phi'right)=frac{gamma,u,e}{4pi,epsilon_0,c,r'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3870.png"
 ALT="$\displaystyle = \gamma\left(c A_1' + \frac{u}{c}  \phi'\right)= \frac{\gamma  u e}{4\pi \epsilon_0  c  r'},$">|; 

$key = q/displaystyleP_{rmabs}=-frac{a^{,2}}{2,mu_0},{rmRe}!int[{bfn}cdot{bfE}times{bfB}^_0},{rmRe}!int[{bfE}cdot({bfn}times{bfB}^{,ast})]_{r=a},d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3355.png"
 ALT="$\displaystyle P_{\rm abs}= -\frac{a^{ 2}}{2 \mu_0}  {\rm Re}\!\int[ {\bf n}\...
... Re}\!\int[{\bf E}\cdot ({\bf n}\times{\bf B}^{ \ast})]_{r=a} d{\mit \Omega}.$">|; 

$key = q/displaystyleT^{,4}_4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3960.png"
 ALT="$\displaystyle T^{ 4}_4$">|; 

$key = q/displaystyle=-frac{mu_0,e}{4pi}frac{gamma}{r^{,3},(1+u_r^{,2},gamma^{,2}slashc^{,2})^{3slash2}},{bfu}times{bfr}=frac{1}{c^{,2}},{bfu}times{bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3901.png"
 ALT="$\displaystyle = - \frac{\mu_0 e}{4\pi} \frac{\gamma}{r^{ 3}  (1+u_r^{ 2}  ...
... 2})^{3/2}}  {\bf u}\times{\bf r} = \frac{1}{c^{ 2}}  {\bf u}\times{\bf E}.$">|; 

$key = q/displaystylec,{bfB}_{lm}^{(E)}rightarrow(-{rmi})^{,l+1}frac{{rme}^{,{rmi},k,r}}{k,r},{bfL},Y_{lm}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3145.png"
 ALT="$\displaystyle c {\bf B}_{lm}^{(E)} \rightarrow (-{\rm i})^{ l+1} \frac{{\rm e}^{ {\rm i} k r}} {k r}  {\bf L}  Y_{lm}.$">|; 

$key = q/displaystyle{bfp}=m,{bfu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3920.png"
 ALT="$\displaystyle {\bf p} = m  {\bf u},$">|; 

$key = q/[aslash(apmdslash2)]^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="$ [a/(a\pm d/2)]^{ 2}$">|; 

$key = q/displaystyle[D_z]_{z=0_-}^{z=0^+}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2067.png"
 ALT="$\displaystyle [D_z]_{z=0_-}^{z=0^+} = 0,$">|; 

$key = q/|{bfr}-{bfr}'|_{varphi=0}=[r^{,2}+r'^{,2}-2,r,r',(costheta,costheta'+sintheta,sintheta',cosvarphi')]^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1328.png"
 ALT="$ \vert{\bf r}-{\bf r}'\vert _{\varphi=0} = [r^{ 2} + r'^{ 2}-2 r r' (\cos\theta \cos\theta' + \sin\theta \sin\theta' \cos\varphi')]^{1/2}$">|; 

$key = q/a_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1284.png"
 ALT="$ a_0$">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}int_{skew{3}bar{V}}frac{rho({bfr}')}{|{bfr}-{br}'),frac{partial}{partialn'}!left(frac{1}{|{bfr}-{bfr}'|}right)dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="513" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="$\displaystyle \frac{1}{4\pi \epsilon_0}\int_{\skew{3}\bar{V}} \frac{\rho({\bf ...
...c{\partial}{\partial n'}\!\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dS'.$">|; 

$key = q/U^{,mu}=gamma(u),({bfu},,c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3888.png"
 ALT="$ U^{ \mu} =\gamma(u) ({\bf u},  c)$">|; 

$key = q/P_1(costheta)=costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1166.png"
 ALT="$ P_1(\cos\theta) = \cos\theta$">|; 

$key = q/gamma_0llomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2743.png"
 ALT="$ \gamma_0\ll \omega_0$">|; 

$key = q/t_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$ t_0$">|; 

$key = q/displaystyleint_0^inftyr,J_m(k,r),J_m(k',r),dr=frac{1}{k},delta(k-k').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img923.png"
 ALT="$\displaystyle \int_0^\infty r J_m(k r) J_m(k' r) dr = \frac{1}{k} \delta(k-k').$">|; 

$key = q/rho({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$ \rho({\bf r},t)$">|; 

$key = q/pi<{rmarg}(z)<2pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2438.png"
 ALT="$ \pi &lt; {\rm arg}(z) &lt; 2\pi$">|; 

$key = q/dslashall1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1574.png"
 ALT="$ d/a\ll1$">|; 

$key = q/displaystylep_2-p_1=frac{epsilon_0,rho_m}{2}left[E^{,2},frac{depsilon}{drho_m}right]_1^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1258.png"
 ALT="$\displaystyle p_2 - p_1 = \frac{\epsilon_0 \rho_m}{2} \left[E^{ 2} \frac{d\epsilon}{d\rho_m} \right]_1^2.$">|; 

$key = q/displaystylefrac{1}{r},frac{d}{dr}!left(r,frac{dg_m}{dr}right)-left(k^{,2}+frac{m^{,2}}{r^{,2}}right)g_m=frac{1}{r},delta(r-r').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img959.png"
 ALT="$\displaystyle \frac{1}{r} \frac{d}{dr}\!\left(r \frac{dg_m}{dr}\right)-\left(k^{ 2} + \frac{m^{ 2}}{r^{ 2}}\right) g_m= \frac{1}{r} \delta(r-r').$">|; 

$key = q/cos(n,pi,zslashL);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2845.png"
 ALT="$ \cos (n \pi  z/L)$">|; 

$key = q/displaystylesimeq2,alpha,E_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2209.png"
 ALT="$\displaystyle \simeq 2 \alpha E_i,$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=-sum_{l=0,infty}sum_{m=-l,+l}frac{1}{2,l+1}left(fr,r_>^{,l+1}}right)Y_{l,m}^ast(theta',varphi'),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}') =-\sum_{l=0,\infty}\sum_{m=-l,+l}\frac{1}{2...
...1} r_&gt;^{ l+1}}\right)Y_{l,m}^\ast(\theta',\varphi') Y_{l,m}(\theta,\varphi).$">|; 

$key = q/displaystyle{bfP}=epsilon_0,chi_e,{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1072.png"
 ALT="$\displaystyle {\bf P} = \epsilon_0 \chi_e  {\bf E},$">|; 

$key = q/displaystyleG^{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3825.png"
 ALT="$\displaystyle G^{ij}$">|; 

$key = q/displaystyle=frac{u_2}{gamma,(1-u_1,vslashc^{,2})},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3503.png"
 ALT="$\displaystyle = \frac{u_2}{\gamma (1-u_1  v/c^{ 2})},$">|; 

$key = q/a<R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$ a&lt;R$">|; 

$key = q/displaystylefrac{4pi}{mu_0,e},{bfB}=-frac{{bfr}times{bfu}}{s^{,2},r}-frac{{bfr}}dot{bfu}}{r}+frac{{bfr}cdotdot{bfu}}{c}-frac{u^{,2}}{c}right)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4013.png"
 ALT="$\displaystyle \frac{4\pi}{\mu_0 e}  {\bf B} = -\frac{{\bf r}\times{\bf u}}{s^...
...f u}}{r} + \frac{{\bf r}\cdot\dot{\bf u}}{c} - \frac{u^{ 2}}{c}\right)\right],$">|; 

$key = q/displaystyle={bfp}times{bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$\displaystyle = {\bf p}\times {\bf E}.
$">|; 

$key = q/A^{ijcdotsk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3548.png"
 ALT="$ A^{ij\cdots k}$">|; 

$key = q/{bfP}({bfr}'),dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="$ {\bf P}({\bf r}') dV'$">|; 

$key = q/displaystylepsi(x,y,z,t)=psi_t,cos(omega,t-{bfk}_tcdot{bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2018.png"
 ALT="$\displaystyle \psi(x,y,z,t)= \psi_t \cos(\omega t-{\bf k}_t\cdot{\bf r})$">|; 

$key = q/displaystyleomega_p=sqrt{frac{N,e^{,2}}{epsilon_0,m}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1819.png"
 ALT="$\displaystyle \omega_p=\sqrt{\frac{N e^{ 2}}{\epsilon_0  m}}$">|; 

$key = q/(dnslashdz)slash(k,n^{,2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2267.png"
 ALT="$ (dn/dz)/(k n^{ 2})$">|; 

$key = q/displaystylephi(omega)=k(omega),x-omega,t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1899.png"
 ALT="$\displaystyle \phi(\omega) = k(\omega)  x - \omega  t.$">|; 

$key = q/displaystyle{bfB}=mu_0,({bfH}+{bfM});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1463.png"
 ALT="$\displaystyle {\bf B} = \mu_0 ({\bf H} + {\bf M})$">|; 

$key = q/displaystyle=(1slash2),x,(1-x^{,2})^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="$\displaystyle =(1/2) x (1-x^{ 2})^{1/2},$">|; 

$key = q/displaystylecostheta=frac{{bfu}cdot{bfr}}{u,r}=sinalpha,cosphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4121.png"
 ALT="$\displaystyle \cos\theta = \frac{{\bf u}\cdot{\bf r}}{u  r} = \sin\alpha \cos\phi.$">|; 

$key = q/y'=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3454.png"
 ALT="$ y'=0$">|; 

$key = q/displaystylesigma_{rmsc}=frac{10pi}{3},a^{,2},(k,a)^4.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3388.png"
 ALT="$\displaystyle \sigma_{\rm sc} = \frac{10\pi}{3} a^{ 2} (k a)^4.$">|; 

$key = q/displaystylex=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1647.png"
 ALT="$\displaystyle x=$">|; 

$key = q/displaystyle{bfE}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2617.png"
 ALT="$\displaystyle {\bf E}({\bf r})$">|; 

$key = q/displaystyle=q^{-1slash4}(x),expleft(-{rmi},hint_0^{x}q^{,1slash2}(x'),dx'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2538.png"
 ALT="$\displaystyle = q^{-1/4}(x) \exp\left(-{\rm i} h\int_0^{x} q^{ 1/2}(x')  dx'\right).$">|; 

$key = q/N(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2381.png"
 ALT="$ N(z)$">|; 

$key = q/y';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3395.png"
 ALT="$ y'$">|; 

$key = q/displaystyle{bfB}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2615.png"
 ALT="$\displaystyle {\bf B}({\bf r})$">|; 

$key = q/displaystyleu({bfr},t)=frac{1}{4pi}int!intfrac{v_omega({bfr'})}{R}left[A,{rme}^{ga,(t-Rslashc)}+B,{rme}^{-{rmi},omega,(t+Rslashc)}right],domega,dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="401" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle u({\bf r}, t) = \frac{1}{4\pi} \int\! \int\frac{ v_\omega({\bf r'...
...mega (t-R/c)}+ B  {\rm e}^{-{\rm i}  \omega (t+R/c)} \right] d\omega dV'.$">|; 

$key = q/hat{bfk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2730.png"
 ALT="$ \hat{\bf k}$">|; 

$key = q/displaystyle{bfM}=chi_m,{bfH},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1445.png"
 ALT="$\displaystyle {\bf M} = \chi_m  {\bf H},$">|; 

$key = q/displaystylef,nabla_s^{,2}f=nabla_scdot(f,nabla_sf)-(nabla_sf)^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2840.png"
 ALT="$\displaystyle f \nabla_s^{ 2} f = \nabla_s\cdot(f \nabla_s f) - (\nabla_s f)^{ 2}.$">|; 

$key = q/{rmIm}(n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1669.png"
 ALT="$ {\rm Im}(n)$">|; 

$key = q/displaystyleG({bfr},{bfr}')=frac{1}{4pi^2}sum_{m=-infty,infty}int_{-infty}^infty{rme}^{,{rmi},k,(z-z')},{rme}^{,{rmi},m,(theta-theta')},g_m(r,r'),dk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img958.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = \frac{1}{4\pi^2}\sum_{m=-\infty,\infty}\int...
...{ {\rm i} k (z-z')} {\rm e}^{ {\rm i} m (\theta-\theta')} g_m(r,r') dk$">|; 

$key = q/kcdotsl;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3553.png"
 ALT="$ k\cdots l$">|; 

$key = q/Y_{l,m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$ Y_{l,m}$">|; 

$key = q/displaystyleddot{bfs}+gamma_0,dot{bfs}+omega_0^{,2},{bfs}=-frac{e}{m_e},{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2742.png"
 ALT="$\displaystyle \ddot{\bf s} + \gamma_0 \dot{\bf s} +\omega_0^{ 2} {\bf s} = -\frac{e}{m_e}  {\bf E},$">|; 

$key = q/displaystylefrac{partial}{partialx};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2295.png"
 ALT="$\displaystyle \frac{\partial}{\partial x}$">|; 

$key = q/displaystyle={bfB}_0,expleft[,{rmi},({bfk}cdot{bfr}-omega,t)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1607.png"
 ALT="$\displaystyle ={\bf B}_0  \exp\left[ {\rm i} ({\bf k}\cdot{\bf r}-\omega  t)\right],$">|; 

$key = q/displaystylew(R,theta,varphi)=frac{{rme}^{+{rmi},k,R}}{R}sum_{n=0,infty}frac{f_n(theta,varphi)}{R^{,n}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$\displaystyle w(R,\theta,\varphi) = \frac{{\rm e}^{+{\rm i} k R}}{R}\sum_{n=0,\infty} \frac{f_n(\theta,\varphi)}{R^{ n}},$">|; 

$key = q/{bfn}cdot{bfj}={bfn}cdotsigma,{bfE}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2765.png"
 ALT="$ {\bf n}\cdot{\bf j} = {\bf n}\cdot\sigma  {\bf E}_1$">|; 

$key = q/displaystyle=sqrt{frac{2}{pi,rho}},{rme}^{-{rmi},[rho-(n+1slash2),pislash2]}sum_{m=0,1,2,cdots}frac{(n,m)}{(+2,{rmi},rho)^{,m}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle = \sqrt{\frac{2}{\pi  \rho}}  {\rm e}^{-{\rm i} [\rho-(n+1/2) \pi/2]} \sum_{m=0, 1, 2, \cdots}\frac{(n,m)}{(+2 {\rm i} \rho)^{ m}},$">|; 

$key = q/displaystyle=int_r^inftyint_0^pifrac{1}{r'^{,l+1}},rho(r',theta),,P_l(costheta),2pi,r'^{,2},sintheta,dtheta,dr',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="$\displaystyle = \int_r^\infty \int_0^\pi \frac{1}{r'^{ l+1}}  \rho(r',\theta)  P_l(\cos\theta) 2\pi r'^{ 2} \sin\theta d\theta dr',$">|; 

$key = q/1slashr^{,5};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1588.png"
 ALT="$ 1/r^{ 5}$">|; 

$key = q/E_{rmmax}sim0.3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4090.png"
 ALT="$ E_{\rm max}\sim
0.3$">|; 

$key = q/R^{,-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$ R^{ -1}$">|; 

$key = q/E_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1239.png"
 ALT="$ E_z$">|; 

$key = q/displaystyle{bff}=e,({bfE}+{bfu}times{bfB}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3928.png"
 ALT="$\displaystyle {\bf f} = e ({\bf E} + {\bf u}\times {\bf B}).$">|; 

$key = q/{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ {\bf H}$">|; 

$key = q/E_perp;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1269.png"
 ALT="$ E_\perp$">|; 

$key = q/a_M(l,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3119.png"
 ALT="$ a_M(l,m)$">|; 

$key = q/displaystylef_nu=epsilon_0left[partial_mu(F^{,musigma},F_{nusigma})-frac{1}{4},partial_nu(F^{,musigma},F_{musigma})right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3952.png"
 ALT="$\displaystyle f_\nu =\epsilon_0 \left[\partial_\mu(F^{ \mu\sigma} F_{\nu\sigma}) -\frac{1}{4}  \partial_\nu (F^{ \mu\sigma} F_{\mu\sigma})\right].$">|; 

$key = q/displaystyle=left(frac{15}{32pi}right)^{1slash2}sin^2theta,{rme}^{-2,{rmi},varphi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="$\displaystyle =\left(\frac{15}{32\pi}\right)^{1/2}\sin^2\theta {\rm e}^{-2 {\rm i} \varphi},$">|; 

$key = q/displaystyleE_z(r,varphi,z,t)=A,J_m(k_l,r),{rme}^{,{rmi},m,varphi}cos(k_3,z),{rme}^{-{rmi},omega,t}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2864.png"
 ALT="$\displaystyle E_z(r,\varphi,z,t) = A  J_m(k_l  r)  {\rm e}^{ {\rm i} m \varphi} \cos(k_3  z)  {\rm e}^{-{\rm i} \omega  t}.$">|; 

$key = q/displaystyleq''&=left(frac{2,epsilon_2}{epsilon_2+epsilon_1}right)q.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1120.png"
 ALT="$\displaystyle q''&amp;= \left(\frac{2 \epsilon_2}{\epsilon_2+\epsilon_1}\right) q.$">|; 

$key = q/{bfn}_{21};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1089.png"
 ALT="$ {\bf n}_{21}$">|; 

$key = q/epsilonrightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1261.png"
 ALT="$ \epsilon\rightarrow \infty$">|; 

$key = q/exp(,-{rmi},omega,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1772.png"
 ALT="$ \exp( -{\rm i} \omega  t)$">|; 

$key = q/d{bfM}slashdr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3166.png"
 ALT="$ d{\bf M}/dr$">|; 

$key = q/displaystylefrac{4pi,epsilon_0}{e},{bfE}=frac{nabla's}{s^{,2}}-frac{{bfr}}{s^{,3,2}},dot{bfu}+frac{r,{bfu}}{s^{,3},c^{,2}}frac{partials}{partialt'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4007.png"
 ALT="$\displaystyle \frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{\nabla' s}{s^{ 2}}...
...t{\bf u} + \frac{r {\bf u}}{s^{ 3}  c^{ 2}} \frac{\partial s}{\partial t'}.$">|; 

$key = q/displaystylen^{,2}(omega)=1+frac{N,e^{,2}}{epsilon_0,m}sum_ifrac{f_i}{omega_i^{,2}-omega^{,2}-{rmi},g_i,omega,omega_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1634.png"
 ALT="$\displaystyle n^{ 2}(\omega) = 1 + \frac{N  e^{ 2}}{\epsilon_0  m}\sum_i \frac{f_i}{ \omega_i^{ 2} -\omega^{ 2} -{\rm i} g_i \omega \omega_i},$">|; 

$key = q/displaystyletanxi=pmfrac{S}{sqrt{n^{,2}(z)-S^{,2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2400.png"
 ALT="$\displaystyle \tan\xi =\pm \frac{S}{\sqrt{n^{ 2}(z)-S^{ 2}}}$">|; 

$key = q/theta_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2032.png"
 ALT="$ \theta_t$">|; 

$key = q/displaystyle=delta_{ll'},delta_{mm'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3353.png"
 ALT="$\displaystyle = \delta_{ll'} \delta_{mm'}.$">|; 

$key = q/{bfj}rightarrowalpha,{bfj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$ {\bf j} \rightarrow \alpha {\bf j}$">|; 

$key = q/displaystyleq-q'=q''.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1116.png"
 ALT="$\displaystyle q-q' = q''.$">|; 

$key = q/displaystyle=frac{1}{2pi}oint{mitPhi}(theta',z'),{rme}^{-{rmi},m,theta'}dtheta'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1028.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\oint {\mit\Phi}(\theta',z') {\rm e}^{-{\rm i} m \theta'}d\theta'.$">|; 

$key = q/B=B(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$ B=B(\omega)$">|; 

$key = q/h_l^{(1)}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3158.png"
 ALT="$ h_l^{(1)}(z)$">|; 

$key = q/sigmarightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2762.png"
 ALT="$ \sigma\rightarrow\infty$">|; 

$key = q/displaystyle=frac{-langle{calI}_zrangle_r}{langle{calI}_zrangle_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2086.png"
 ALT="$\displaystyle = \frac{-\langle {\cal I}_z\rangle_r}{\langle {\cal I}_z\rangle_i},$">|; 

$key = q/tantheta_i=beta=n_2slashn_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2127.png"
 ALT="$ \tan\theta_i = \beta = n_2/n_1$">|; 

$key = q/displaystyle|f|_{rmsommerfeld}simleft(frac{omega_p}{xi}right)ll|f|_{rmbrillouin}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1968.png"
 ALT="$\displaystyle \vert f\vert _{\rm sommerfeld} \sim \left(\frac{\omega_p}{\xi}\right) \ll \vert f\vert _{\rm brillouin}.$">|; 

$key = q/displaystylez;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1655.png"
 ALT="$\displaystyle z$">|; 

$key = q/displaystyleint_Vpartial_muT^{,mu},d^{,4}x=oint_ST^{,mu},dS_mu,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4041.png"
 ALT="$\displaystyle \int_V \partial_\mu T^{ \mu}  d^{ 4} x = \oint_S T^{ \mu} dS_\mu,$">|; 

$key = q/displaystylenabla_s^{,2}f=-k_s^{,2},f.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2837.png"
 ALT="$\displaystyle \nabla_s^{ 2} f = - k_s^{ 2}  f.$">|; 

$key = q/q^{,1slash2}rightarrow-q^{,1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2505.png"
 ALT="$ q^{ 1/2}\rightarrow -q^{ 1/2}$">|; 

$key = q/displaystyleP(t')=frac{e^{,2}}{6pi,epsilon_0,c^{,3}},gamma^{,6},dot{u}^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4109.png"
 ALT="$\displaystyle P(t') = \frac{e^{ 2}}{6\pi \epsilon_0  c^{ 3}} \gamma^{ 6} \dot{u}^{ 2},$">|; 

$key = q/nablatimes{bfE}={rmi},omega,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2791.png"
 ALT="$ \nabla\times{\bf E}={\rm i} \omega {\bf B}$">|; 

$key = q/displaystylefrac{dU}{dt}=int_Vleft[-rho_f,{bfE}+frac{epsilon_0}{2},E^{,2},nablaeblaleft(E^{,2},frac{depsilon}{drho_m},rho_mright)right]cdot{bfu},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1228.png"
 ALT="$\displaystyle \frac{dU}{dt} = \int_V\left[-\rho_f  {\bf E} +\frac{\epsilon_0}{...
...ft(E^{ 2} \frac{d\epsilon}{d\rho_m} \rho_m\right) \right]\cdot {\bf u}  dV.$">|; 

$key = q/epsilon(z)rightarrow1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1139.png"
 ALT="$ \epsilon(z)\rightarrow 1$">|; 

$key = q/displaystyley_l(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3022.png"
 ALT="$\displaystyle y_l(z)$">|; 

$key = q/displaystyle=frac{dy'}{dt'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3494.png"
 ALT="$\displaystyle = \frac{dy'}{dt'},$">|; 

$key = q/f{bf(r});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$ f{\bf (r})$">|; 

$key = q/omega^{,2}-(2pislashtau)^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1854.png"
 ALT="$ \omega^{ 2}-(2\pi/\tau)^{ 2}$">|; 

$key = q/yslashg_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ y/g_i$">|; 

$key = q/displaystyle{bfE}=frac{rmi}{k}nablatimesc,{bfB},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2600.png"
 ALT="$\displaystyle {\bf E} = \frac{\rm i}{k}\nabla\times c {\bf B},$">|; 

$key = q/xslasht;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1917.png"
 ALT="$ x/t$">|; 

$key = q/E_z=c,B_z=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2231.png"
 ALT="$ E_z=c B_z=0$">|; 

$key = q/1.02times10^{-3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3269.png"
 ALT="$ 1.02\times 10^{-3}$">|; 

$key = q/displaystylephantom{=}+l,dy,dz+m,dx,dz+n,dx,dy,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3424.png"
 ALT="$\displaystyle \phantom{=}+ l  dy  dz + m  dx  dz + n  dx  dy,$">|; 

$key = q/displaystylesum_{l=0,infty}sum_{m=-l,+l}left[frac{d}{dr}!left(r^{,2},frac{dphi_{l,m}}{dr}right)-l,(l+1),phi_{l,m}right]Y_{l,m}(theta,varphi)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="$\displaystyle \sum_{l=0,\infty}\sum_{m=-l,+l}\left[\frac{d}{dr}\!\left(r^{ 2}\...
...c{d\phi_{l,m}}{dr}\right)-l (l+1) \phi_{l,m}\right]Y_{l,m}(\theta,\varphi)=0.$">|; 

$key = q/displaystylefrac{d^{,2}Z}{dz^{,2}}+k^{,2},Z=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img930.png"
 ALT="$\displaystyle \frac{d^{ 2} Z}{dz^{ 2}} + k^{ 2}  Z = 0,$">|; 

$key = q/displaystyleu({bfr},t)=intfrac{v({bfr}',t-|{bfr}-{bfr}'|slashc)}{4pi,|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle u({\bf r}, t) = \int \frac{ v({\bf r}', t - \vert{\bf r} -{\bf r}'\vert/c)} {4\pi \vert{\bf r} - {\bf r}'\vert} dV'.$">|; 

$key = q/A_{rmeff};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2670.png"
 ALT="$ A_{\rm eff}$">|; 

$key = q/displaystyle=mpA,q^{,1slash2}(z)expleft(pm{rmi},kint^z!q(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2311.png"
 ALT="$\displaystyle = \mp A  q^{ 1/2}(z) \exp\left(\pm {\rm i} k\int^z\!q(z') dz'\right),$">|; 

$key = q/lgeq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="$ l\geq 0$">|; 

$key = q/omega=omega_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1904.png"
 ALT="$ \omega=\omega_s$">|; 

$key = q/B_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1577.png"
 ALT="$ B_0$">|; 

$key = q/{figure}{epsfysize{=3.25in{centerline{epsffile{Chapter06slashcont3.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="368" BORDER="0"
 SRC="|."$dir".q|img1825.png"
 ALT="\begin{figure}
\epsfysize =3.25in
\centerline{\epsffile{Chapter06/cont3.eps}}
\end{figure}">|; 

$key = q/f_l(k,r)=g_l(k,r)=h_l^{(1)}(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3215.png"
 ALT="$ f_l(k r) =g_l(k r) = h_l^{(1)}(k r)$">|; 

$key = q/displaystyleP_{rmload}=langleI^{,2},R_{rmload}rangle=frac{R_{rmload},V_0^{,2}}{2,(R_{rmrad}+R_{rmload})^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2660.png"
 ALT="$\displaystyle P_{\rm load} = \langle I^{ 2}  R_{\rm load}\rangle = \frac{R_{\rm load}  V_0^{ 2}} {2 (R_{\rm rad} + R_{\rm load})^{ 2}}.$">|; 

$key = q/displaystylefrac{dU}{dt}=-frac{omega_0}{Q},U,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2801.png"
 ALT="$\displaystyle \frac{dU}{dt} = -\frac{\omega_0}{Q} U,$">|; 

$key = q/displaystylea_E(l,m)simeqfrac{mu_0,c,k^{,l+2}}{{rmi},(2,l+1)!!},left(frac{l+1}{l}right)^{1slash2}(Q_{lm}+Q_{lm}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3232.png"
 ALT="$\displaystyle a_E(l,m) \simeq \frac{\mu_0  c  k^{ l+2}}{{\rm i}  (2 l+1)!!} \left(\frac{l+1}{l}\right)^{1/2} (Q_{lm}+Q_{lm}'),$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter05slashdemag1.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="340" BORDER="0"
 SRC="|."$dir".q|img1518.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter05/demag1.eps}}
\end{figure}">|; 

$key = q/displaystyle=frac{dz}{dt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3489.png"
 ALT="$\displaystyle = \frac{dz}{dt}.$">|; 

$key = q/sin(k_3,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2813.png"
 ALT="$ \sin( k_3  z)$">|; 

$key = q/displaystylerho_b=-nablacdot{bfP}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1065.png"
 ALT="$\displaystyle \rho_b = -\nabla \cdot {\bf P}.$">|; 

$key = q/Z(z)={rme}^{-k,z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img917.png"
 ALT="$ Z(z)={\rm e}^{-k z}$">|; 

$key = q/t_r=t-|{bfr}-{bfr'}|slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$ t_r = t - \vert{\bf r}-{\bf r'}\vert/c$">|; 

$key = q/4,h_0,(2slashalpha,h_0-1)^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2595.png"
 ALT="$ 4 h_0 (2/\alpha h_0-1)^{1/2}$">|; 

$key = q/Z_0=sqrt{mu_0slashepsilon_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2006.png"
 ALT="$ Z_0=\sqrt{\mu_0/\epsilon_0}$">|; 

$key = q/displaystylerightarrowphi+frac{partialpsi}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3732.png"
 ALT="$\displaystyle \rightarrow \phi + \frac{\partial\psi}{\partial t},$">|; 

$key = q/t_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1969.png"
 ALT="$ t_2$">|; 

$key = q/displaystyler(x^{,i},x^{,i'}(t'),)equivr(x^{,i},t')=c,(t-t'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3998.png"
 ALT="$\displaystyle r(x^{ i}, x^{ i'}(t') ) \equiv r(x^{ i}, t') = c (t-t'),$">|; 

$key = q/displaystyleU(t)=U(0),{rme}^{-omega_0,tslashQ}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2802.png"
 ALT="$\displaystyle U(t) = U(0)  {\rm e}^{-\omega_0  t/Q}.$">|; 

$key = q/displaystyleddot{bfs}+g,omega_0,dot{bfs}+omega_0^{,2},{bfs}=-frac{e}{m},{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1620.png"
 ALT="$\displaystyle \ddot{\bf s} + g  \omega_0  \dot{\bf s} + \omega_0^{ 2}  {\bf s} =-\frac{e}{m}  {\bf E},$">|; 

$key = q/displaystylea_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3909.png"
 ALT="$\displaystyle a_0$">|; 

$key = q/f(10);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2423.png"
 ALT="$ f(10)$">|; 

$key = q/displaystyle=frac{mu_0,c,{rmi},k^{,3}}{sqrt{l,(l+1)}}intj_l(k,r),Y^{,ast}_{lm},{bfL}cdotleft({bfM}+frac{nablatimes{bfj}}{k^{,2}}right),dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3220.png"
 ALT="$\displaystyle = \frac{\mu_0  c {\rm i} k^{ 3}}{\sqrt{l (l+1)}}\int j_l(k ...
...m} {\bf L}\cdot\left({\bf M} +\frac{\nabla\times {\bf j}}{k^{ 2}}\right) dV,$">|; 

$key = q/mu=mu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1456.png"
 ALT="$ \mu =\mu_0$">|; 

$key = q/displaystylefrac{{bfE}cdot{bfj}}{c}=-partial_iT^{,i4}-partial_4T^{,44}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3970.png"
 ALT="$\displaystyle \frac{{\bf E}\cdot {\bf j}}{c} = - \partial_i T^{ i4} - \partial_4 T^{ 44}.$">|; 

$key = q/displaystyle{bfr}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4168.png"
 ALT="$\displaystyle {\bf r}'$">|; 

$key = q/displaystyle=leftlgroup{array}{cccc}+gamma&0&0&-gamma,beta0&1&0&00&0&1&0-gamma,beta&0&0&+gamma{array}rightrgroup,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="94" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3648.png"
 ALT="$\displaystyle = \left\lgroup \begin{array}{cccc} +\gamma &amp; 0 &amp; 0 &amp; -\gamma \be...
... \ 0 &amp; 0 &amp; 1 &amp; 0 \ -\gamma \beta &amp; 0 &amp; 0 &amp; +\gamma \end{array}\right\rgroup,$">|; 

$key = q/displaystylenabla^{,2}phi({bfr})=intv({bfr}'),nabla^{,2}G({bfr},{bfr}'),dV'=intv({bfr}'),delta({bfr}-{bfr}'),dV'=v({bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="410" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$\displaystyle \nabla^{ 2}\phi({\bf r}) = \int v({\bf r}') \nabla^{ 2}G({\bf r},{\bf r}') dV' = \int v({\bf r}') \delta({\bf r}-{\bf r}') dV' = v({\bf r}).$">|; 

$key = q/displaystyle=-G_{ji}=-E_{ij},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3836.png"
 ALT="$\displaystyle = -G_{ji} = -E_{ij},$">|; 

$key = q/theta_0=pmpislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4134.png"
 ALT="$ \theta_0=\pm \pi/2$">|; 

$key = q/displaystylefrac{partial}{partialt}=frac{r}{s},frac{partial}{partialt'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4002.png"
 ALT="$\displaystyle \frac{\partial}{\partial t} = \frac{r}{s}  \frac{\partial}{\partial t'}.$">|; 

$key = q/displaystyle=a,dx^{,2}+b,dy^{,2}+c,dz^{,2}+d,dt^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3422.png"
 ALT="$\displaystyle =a  dx^{ 2} + b  dy^{ 2} + c  dz^{ 2} + d  dt^{ 2}$">|; 

$key = q/{bfE}_{rminc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3328.png"
 ALT="$ {\bf E}_{\rm inc}$">|; 

$key = q/c^{,2},BslashE;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4192.png"
 ALT="$ c^{ 2} B/E$">|; 

$key = q/r'<r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="$ r'&lt;r$">|; 

$key = q/displaystylefrac{Drho_m}{Dt}=-rho_mnablacdot{bfu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1222.png"
 ALT="$\displaystyle \frac{D\rho_m}{Dt} = - \rho_m \nabla\cdot{\bf u}.$">|; 

$key = q/displaystylepsi_i+psi_r=beta^{,-1},psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2115.png"
 ALT="$\displaystyle \psi_i+\psi_r = \beta^{ -1} \psi_t,$">|; 

$key = q/displaystyleH_z(x,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2107.png"
 ALT="$\displaystyle H_z(x,z,t)$">|; 

$key = q/|x|leq1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="$ \vert x\vert\leq 1$">|; 

$key = q/dS_mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4042.png"
 ALT="$ dS_\mu$">|; 

$key = q/x'rightarrowx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3471.png"
 ALT="$ x'\rightarrow x$">|; 

$key = q/c,{bfB}_{lm}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3150.png"
 ALT="$ c {\bf B}_{lm}^{(E)}$">|; 

$key = q/|m|leql;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="$ \vert m\vert\leq l$">|; 

$key = q/displaystylefrac{partialG_N({bfr},{bfr}')}{partialn'}=1leftslashint_SdS'right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="$\displaystyle \frac{\partial G_N({\bf r},{\bf r}')}{\partial n'} = 1\left/\int_S dS'\right.$">|; 

$key = q/displaystyleP'=frac{dE'}{dt'}=frac{dE}{dt}=P,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4070.png"
 ALT="$\displaystyle P' = \frac{dE'}{dt'} = \frac{dE}{dt} = P,$">|; 

$key = q/Y_{lm}slashr^{,l+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3132.png"
 ALT="$ Y_{lm}/r^{ l+1}$">|; 

$key = q/{bfr}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$ {\bf r}'$">|; 

$key = q/displaystylefrac{partialG_N({bfr},{bfr'})}{partialn'}=1leftslashint_SdS'right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="$\displaystyle \frac{\partial G_N({\bf r},{\bf r'})}{\partial n'} = 1\left/\int_S dS'\right.$">|; 

$key = q/zrightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img915.png"
 ALT="$ z\rightarrow \infty$">|; 

$key = q/displaystyle=sum_{l,m}left[frac{-{rmi}}{k},a_pm(l,m),nablatimesj_l(k,r),{bfX}_{lm}+b_pm(l,m),j_l(k,r),{bfX}_{lm}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3306.png"
 ALT="$\displaystyle =\sum_{l,m} \left[ \frac{-{\rm i}}{k} a_\pm(l,m) \nabla\times j_l(k r) {\bf X}_{lm} +b_\pm(l,m) j_l(k r) {\bf X}_{lm}\right].$">|; 

$key = q/displaystylechi_e=frac{(b^{,2}-a^{,2}),rho_m,g,h,ln(bslasha)}{epsilon_0,V^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1297.png"
 ALT="$\displaystyle \chi_e = \frac{(b^{ 2}-a^{ 2}) \rho_m g h \ln(b/a)}{\epsilon_0 V^{ 2}}
$">|; 

$key = q/displaystyle{bfE}={bfe},E_0,{rme}^{,{rmi},({bfk}cdot{bfr}-omega,t)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2714.png"
 ALT="$\displaystyle {\bf E} = {\bf e} E_0   {\rm e}^{ {\rm i} ({\bf k}\cdot{\bf r} -\omega  t )},$">|; 

$key = q/displaystyle{bfD}=epsilon,epsilon_0,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2050.png"
 ALT="$\displaystyle {\bf D} = \epsilon \epsilon_0 {\bf E}$">|; 

$key = q/t_r=t-Rslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$ t_r = t- R/c$">|; 

$key = q/displaystyle=E_0cos[(omegaslashc),(n_-z-c,t)],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1741.png"
 ALT="$\displaystyle = E_0 \cos[(\omega/c) (n_- z -c  t)],$">|; 

$key = q/displaystylefrac{{mitGamma}(a),{mitGamma}(c-a)}{{mitGamma}(c)},F(a,c,z)simeq{mit),z^{-a},{rme}^{,{rmi},pi,a}left[1+{calO}left(frac{1}{z}right)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="523" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2433.png"
 ALT="$\displaystyle \frac{{\mit\Gamma}(a) {\mit\Gamma}(c-a)}{{\mit\Gamma}(c)}  F(a,...
...}  {\rm e}^{ {\rm i} \pi  a}\left[1+{\cal O}\left(\frac{1}{z}\right)\right]$">|; 

$key = q/I=intT^{,4},d^{,3}x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4049.png"
 ALT="$ I = \int T^{ 4} d^{ 3} x$">|; 

$key = q/displaystylefrac{epsilon-1}{epsilon+2}=frac{N_A,rho_m,alpha}{3,M},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1251.png"
 ALT="$\displaystyle \frac{\epsilon -1}{\epsilon+2} = \frac{N_A \rho_m  \alpha}{3  M},$">|; 

$key = q/displaystyle{bff}=rho_f,{bfE}-frac{epsilon_0}{2},E^{,2},nablaepsilon+frac{epsilon_0}{2},nabla!left(E^{,2},frac{depsilon}{drho_m},rho_mright).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1229.png"
 ALT="$\displaystyle {\bf f} = \rho_f  {\bf E} - \frac{\epsilon_0}{2}  E^{ 2} \nab...
...ilon_0}{2}  \nabla\!\left(E^{ 2}  \frac{d\epsilon}{d\rho_m} \rho_m \right).$">|; 

$key = q/displaystylephi_s''simeq-2,frac{(t-t_0)^{,3slash2}}{xi^{,1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1938.png"
 ALT="$\displaystyle \phi_s'' \simeq -2 \frac{(t-t_0)^{ 3/2}}{\xi^{ 1/2}},$">|; 

$key = q/displaystylephi(r,theta,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img983.png"
 ALT="$\displaystyle \phi(r,\theta,z)$">|; 

$key = q/{bfP}=N,{bfp};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1060.png"
 ALT="$ {\bf P} = N  {\bf p}$">|; 

$key = q/displaystylesintheta_i=sintheta_r,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2042.png"
 ALT="$\displaystyle \sin\theta_i=\sin\theta_r,$">|; 

$key = q/displaystylealpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2070.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/q_{l,m}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="$ q_{l,m}^{ \ast}$">|; 

$key = q/displaystylepartial_muG^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3849.png"
 ALT="$\displaystyle \partial_\mu G^{ \mu\nu}$">|; 

$key = q/omega=4times10^{15},{rmrad.,s}^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2215.png"
 ALT="$ \omega = 4\times 10^{15} {\rm rad. s}^{-1}$">|; 

$key = q/x^{,4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3632.png"
 ALT="$ x^{ 4}$">|; 

$key = q/displaystyle=frac{l,(l+1)}{k},g_l(k,r),Y_{lm}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3085.png"
 ALT="$\displaystyle = \frac{l (l+1)}{k}  g_l(k r)  Y_{lm}(\theta, \varphi),$">|; 

$key = q/v({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="$ v({\bf r})$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{Chapter06bslashfig03.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="551" HEIGHT="398" BORDER="0"
 SRC="|."$dir".q|img2029.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{Chapter06b/fig03.eps}}
\end{figure}">|; 

$key = q/J_m(p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="$ J_m(p)$">|; 

$key = q/displaystyleomega>omega_{01}=frac{2.4048,c}{sqrt{epsilon_1-1},a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2972.png"
 ALT="$\displaystyle \omega &gt; \omega_{01} = \frac{2.4048 c}{\sqrt{\epsilon_1 -1}  a}.$">|; 

$key = q/displaystylephantom{==}I_mleft(frac{n,pi}{L},r_<right)K_mleft(frac{n,pi}{L},r_>right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1046.png"
 ALT="$\displaystyle \phantom{==}I_m\left(\frac{n \pi}{L} r_&lt;\right)K_m\left(\frac{n \pi}{L} r_&gt;\right).$">|; 

$key = q/hat{z}=a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2476.png"
 ALT="$ \hat{z}=a$">|; 

$key = q/displaystylenablatimes{bfE}={bf0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1090.png"
 ALT="$\displaystyle \nabla\times{\bf E} = {\bf0},$">|; 

$key = q/displaystyletandelta_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3375.png"
 ALT="$\displaystyle \tan\delta_l$">|; 

$key = q/displaystyleG({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1013.png"
 ALT="$\displaystyle G({\bf r},{\bf r}')$">|; 

$key = q/(0,x)_d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2547.png"
 ALT="$ (0,x)_d$">|; 

$key = q/beta(l);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3338.png"
 ALT="$ \beta(l)$">|; 

$key = q/displaystylea_E(l,0)=frac{mu_0,c,I}{pi,d}left[frac{4pi,(2,l+1)}{l,(l+1)}right]^{1slash2}left(frac{k,d}{2}right)^2,j_l(k,dslash2),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3261.png"
 ALT="$\displaystyle a_E(l, 0) = \frac{\mu_0  c  I}{\pi  d}\left[\frac{4\pi  (2 l+1)} {l (l+1)}\right]^{1/2} \left(\frac{k d}{2}\right)^2 j_l(k d/2),$">|; 

$key = q/displaystyle{bfE}_{lm}^{(E)}=-(-{rmi})^{,l+1}frac{{rme}^{,{rmi},k,r}}{k,r}left[{fn}times{bfL},Y_{lm}-frac{1}{k}({bfr},nabla^{,2}-nabla)Y_{lm}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3147.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(E)} = -(-{\rm i})^{ l+1} \frac{{\rm e}^{ {\rm i}...
...\times {\bf L} Y_{lm}-\frac{1}{k}({\bf r} \nabla^{ 2}-\nabla) Y_{lm}\right],$">|; 

$key = q/displaystyle=frac{n_i^{,2}}{a^{,2}}-frac{x}{x^{,2}+g_i^{,2},(1+x)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1654.png"
 ALT="$\displaystyle = \frac{n_i^{ 2}}{a^{ 2}} - \frac{x}{x^{ 2} + g_i^{ 2} (1+x)},$">|; 

$key = q/alpha,h_0<1slash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2591.png"
 ALT="$ \alpha h_0&lt;1/4$">|; 

$key = q/displaystyleU=int_{bf0}^{bfD}deltaU=int_{bf0}^{bfD}int_V{bfE}cdotdelta{bfD},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1201.png"
 ALT="$\displaystyle U = \int_{\bf0}^{\bf D} \delta U = \int_{\bf0}^{\bf D }\int_V {\bf E} \cdot \delta{\bf D} dV,$">|; 

$key = q/g_{munu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3629.png"
 ALT="$ g_{\mu\nu}=0$">|; 

$key = q/displaystylen=frac{1}{2},(n_++n_-);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1750.png"
 ALT="$\displaystyle n = \frac{1}{2}  (n_+ + n_-)$">|; 

$key = q/rho_m=-nablacdot{bfM};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1488.png"
 ALT="$ \rho_m = -\nabla\cdot{\bf M}$">|; 

$key = q/0leqtheta<pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$ 0\leq \theta&lt;\pi/2$">|; 

$key = q/A,(hat{z},0)_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2519.png"
 ALT="$ A  (\hat{z},0)_s$">|; 

$key = q/displaystylephi(r,theta,varphi)rightarrow-E_0,r,costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1152.png"
 ALT="$\displaystyle \phi(r,\theta,\varphi) \rightarrow - E_0  r \cos\theta$">|; 

$key = q/delta_{lk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="$ \delta_{lk}$">|; 

$key = q/dV'=gamma,dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3751.png"
 ALT="$ dV' = \gamma  dV$">|; 

$key = q/displaystyleu_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3488.png"
 ALT="$\displaystyle u_3$">|; 

$key = q/H_theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2938.png"
 ALT="$ H_\theta$">|; 

$key = q/+q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1057.png"
 ALT="$ +q$">|; 

$key = q/x_2^{,mu}-x_1^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3637.png"
 ALT="$ x_2^{ \mu}-x_1^{ \mu}$">|; 

$key = q/u'=({u'_1}^{2}+{u'_2}^{2}+{u'_3}^{2})^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3512.png"
 ALT="$ u'=({u'_1}^{2} + {u'_2}^{2}+ {u'_3}^{2})^{1/2}$">|; 

$key = q/displaystyle=n_2,k_0,(sintheta_t,,0,,costheta_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2038.png"
 ALT="$\displaystyle =n_2 k_0 (\sin\theta_t, 0, \cos\theta_t),$">|; 

$key = q/{bfE}_{lm}^{(M)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3094.png"
 ALT="$ {\bf E}_{lm}^{(M)}$">|; 

$key = q/r_>=r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3217.png"
 ALT="$ r_&gt;=r$">|; 

$key = q/A_{kcdotsl}^{icdotsj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3581.png"
 ALT="$ A_{k\cdots l}^{i\cdots j}$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{epsilon_0}int_VG_D({bfr},{bfr}'),rho({bfr}'),dV'+int_Sphi({bfr}'),frac{partialG_D({bfr},{bfr}')}{dn'},dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="$\displaystyle \phi({\bf r}) = -\frac{1}{\epsilon_0}\int_V G_D({\bf r},{\bf r}')...
... dV' + \int_S \phi({\bf r}') \frac{\partial G_D({\bf r},{\bf r}')}{dn'} dS',$">|; 

$key = q/omega=pm2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1901.png"
 ALT="$ \omega=\pm 2\pi/\tau$">|; 

$key = q/displaystyleJ^{,mu}=({bfj},,rho,c),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4204.png"
 ALT="$\displaystyle J^{ \mu} = ({\bf j}, \rho c),
$">|; 

$key = q/displaystyleleft(1+frac{{rmi},omega,epsilon_0,epsilon_1}{sigma}right){bfn}cdot{bfE}_1=frac{{rmi},omega,epsilon_0,epsilon_2}{sigma},{bfn}cdot{bfE}_2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2766.png"
 ALT="$\displaystyle \left(1+ \frac{{\rm i} \omega \epsilon_0 \epsilon_1}{\sigma} \...
...frac{{\rm i} \omega  \epsilon_0 \epsilon_2}{\sigma}  {\bf n}\cdot{\bf E}_2.$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}=frac{e^{,2},c,beta^{,4}}{16pi^2,epsilon_0,in^2theta,cos^2(omega_0,t')}{[1+beta,costheta,sin(omega_0,t')]^{,5}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4214.png"
 ALT="$\displaystyle \frac{dP(t')}{d{\mit\Omega}} = \frac{e^{ 2} c  \beta^{ 4}}{16...
...ta  \cos^2(\omega_0  t')}{[1+\beta \cos\theta  \sin(\omega_0  t')]^{ 5}}
$">|; 

$key = q/displaystyleq_{2,+1}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="$\displaystyle q_{2,+1}^{ \ast}$">|; 

$key = q/displaystyleepsilon(omega)equivn^{,2}(omega)=1+frac{(N,e^{,2}slashepsilon_0,m)}{omega_0^{,2}-omega^{,2}-{rmi},g,omega,omega_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1626.png"
 ALT="$\displaystyle \epsilon(\omega) \equiv n^{ 2}(\omega) = 1 + \frac{(N  e^{ 2}/\epsilon_0  m)} {\omega_0^{ 2} -\omega^{ 2}- {\rm i} g \omega \omega_0}.$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}int_Sfrac{sigma({bfr}')}{|{bfr}-{bfr}'|},dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img468.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int_S \frac{\sigma({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dS',$">|; 

$key = q/t-t_0gg1slashxi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1942.png"
 ALT="$ t-t_0 \gg 1/\xi$">|; 

$key = q/displaystylerightarrowfrac{sin(z-l,pislash2)}{z},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3037.png"
 ALT="$\displaystyle \rightarrow \frac{\sin(z-l \pi/2)}{z},$">|; 

$key = q/G^{(-)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$ G^{(-)}$">|; 

$key = q/displaystyle=-psi_t,sinhtheta_t,{rme}^{-n_2,k_0,sinhtheta_t,z},sin(omega,t-n_1,k_0,sintheta_i,x+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2169.png"
 ALT="$\displaystyle =-\psi_t \sinh\theta_t {\rm e}^{-n_2 k_0 \sinh\theta_t z} \sin(\omega t-n_1 k_0 \sin\theta_i x+\phi_t),$">|; 

$key = q/displaystylefrac{1}{k^{,2}}left|frac{3}{4}left(frac{1}{q^{,2}}frac{dq}{dz}right){,2}n}{dz^{,2}}-2left(frac{1}{n}frac{dn}{dz}right)^2right]right|ll1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2329.png"
 ALT="$\displaystyle \frac{1}{k^{ 2}}\left\vert \frac{3}{4}\left(\frac{1}{q^{ 2}} \f...
... z^{ 2}} -2 \left(\frac{1}{n} \frac{d n}{dz}\right)^2\right]\right\vert \ll 1.$">|; 

$key = q/displaystylem=gamma,m_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3916.png"
 ALT="$\displaystyle m = \gamma  m_0.$">|; 

$key = q/phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="$ \phi$">|; 

$key = q/displaystylef_nu=-partial_mu{T^{,mu}}_nu,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3953.png"
 ALT="$\displaystyle f_\nu = - \partial_\mu {T^{ \mu}}_\nu,$">|; 

$key = q/displaystyleF(omega_s)simeqfrac{t-t_0}{tau,xi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1939.png"
 ALT="$\displaystyle F(\omega_s) \simeq \frac{t-t_0}{\tau \xi}.$">|; 

$key = q/R(r),Q(theta),Z(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img996.png"
 ALT="$ R(r) Q(\theta) Z(z)$">|; 

$key = q/dS=2pi,a^2,sintheta,dtheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1241.png"
 ALT="$ dS = 2\pi  a^2 \sin\theta d\theta$">|; 

$key = q/theta_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1426.png"
 ALT="$ \theta_2$">|; 

$key = q/1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1412.png"
 ALT="$ 1$">|; 

$key = q/displaystylez^{,2},frac{d^{,2}g}{dz^{,2}}+z,frac{dg}{dz}+(z^{,2}-m^{,2}),g=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2858.png"
 ALT="$\displaystyle z^{ 2} \frac{d^{ 2} g}{dz^{ 2}} + z \frac{dg}{dz} + (z^{ 2} - m^{ 2})  g = 0,$">|; 

$key = q/displaystylenablatimes{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle \nabla\times {\bf B}$">|; 

$key = q/displaystyledelta({bfr}'-{bfr})=delta({bfr}-{bfr}').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle \delta({\bf r}'-{\bf r}) = \delta({\bf r}-{\bf r}').$">|; 

$key = q/C^{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3579.png"
 ALT="$ C^{ij}$">|; 

$key = q/{bfE}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="$ {\bf E}_1$">|; 

$key = q/displaystylenablatimes{bfE}'-{rmi},k,c,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3197.png"
 ALT="$\displaystyle \nabla\times{\bf E}' -{\rm i} k  c {\bf B}$">|; 

$key = q/displaystylew(5)=(A+t,B),(0,hat{z})_s+(B+u,[A+t,B]),(hat{z},0)_d.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2503.png"
 ALT="$\displaystyle w(5) =( A+t B) (0,\hat{z})_s + (B+ u [A+t B]) (\hat{z},0)_d.$">|; 

$key = q/displaystylefrac{domega}{omega^{,2}}={rmi},sqrt{frac{s}{xi}},{rme}^{-{rmi},u},du.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1864.png"
 ALT="$\displaystyle \frac{d\omega}{\omega^{ 2}} = {\rm i}  \sqrt{\frac{s}{\xi}}  {\rm e}^{-{\rm i}  u}  du.$">|; 

$key = q/displaystyle=sum_{l=0,infty}sum_{m=-l,+l}rho_{l,m}(r),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="$\displaystyle = \sum_{l=0,\infty}\sum_{m=-l,+l}\rho_{l,m}(r) Y_{l,m}(\theta,\varphi).$">|; 

$key = q/g=x_i';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1393.png"
 ALT="$ g=x_i'$">|; 

$key = q/ds^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3590.png"
 ALT="$ ds^{ 2}$">|; 

$key = q/displaystylefrac{partialr}{partialt}=cleft(1-frac{partialt'}{partialt}right)=fraialt'}{partialt}=-frac{{bfr}cdot{bfu}}{r},frac{partialt'}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4000.png"
 ALT="$\displaystyle \frac{\partial r}{\partial t} = c\left(1-\frac{\partial t'}{\part...
...{\partial t} = -\frac{{\bf r}\cdot{\bf u}}{r}  \frac{\partial t'}{\partial t},$">|; 

$key = q/rho({bfr}),{rme}^{-{rmi},omega,t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3188.png"
 ALT="$ \rho({\bf r})  {\rm e}^{-{\rm i} \omega  t}$">|; 

$key = q/displaystyleq_{2,-1}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="$\displaystyle q_{2,-1}^{ \ast}$">|; 

$key = q/displaystyleA_varphi(r,theta)=2pi,mu_0,I,a,,{rmRe}!sum_{l=0,infty}frac{Y_{l,1}(t,l+1}}right)Y_{l,1}^{,ast}(pislash2,varphi'),{rme}^{,{rmi},varphi'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1338.png"
 ALT="$\displaystyle A_\varphi(r,\theta)= 2\pi \mu_0 I a  {\rm Re}\!\sum_{l=0,\in...
...{ l+1}}\right)Y_{l,1}^{ \ast}(\pi/2,\varphi') {\rm e}^{ {\rm i} \varphi'}.$">|; 

$key = q/x^{,i'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3535.png"
 ALT="$ x^{ i'}$">|; 

$key = q/displaystyleA_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img907.png"
 ALT="$\displaystyle A_{mn}$">|; 

$key = q/{rmTM}_{,0l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2992.png"
 ALT="$ {\rm TM}_{ 0l}$">|; 

$key = q/p_l=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="$ p_l=0$">|; 

$key = q/displaystylerho=gamma(u),rho_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3715.png"
 ALT="$\displaystyle \rho = \gamma(u)  \rho_0.$">|; 

$key = q/{bfH}_{rmmax};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1466.png"
 ALT="$ {\bf H}_{\rm max}$">|; 

$key = q/displaystylephi_m({bfr})=-frac{1}{4pi}int_Vfrac{nabla'cdot{bfM}({bfr}')}{|{bfr}-dV'+frac{1}{4pi}int_Sfrac{{bfM}({bfr}')cdotd{bfS}'}{|{bfr}-{bfr}'|},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1487.png"
 ALT="$\displaystyle \phi_m({\bf r})= - \frac{1}{4\pi}\int_V\frac{\nabla'\cdot{\bf M}(...
...i}\int_S \frac{{\bf M}({\bf r}')\cdot d{\bf S}'}{\vert{\bf r} - {\bf r}'\vert},$">|; 

$key = q/displaystylephi_m({bfr})=-frac{1}{4pi}nablacdotintfrac{{bfM}({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1483.png"
 ALT="$\displaystyle \phi_m({\bf r})= - \frac{1}{4\pi}\nabla\cdot\int\frac{{\bf M}({\bf r}')} {\vert{\bf r} - {\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle1+beta+beta^{,2}+cdotsbeta^{,N-1}=frac{beta^{,N}-1}{beta-1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2695.png"
 ALT="$\displaystyle 1 + \beta + \beta^{ 2}+\cdots \beta^{ N-1} = \frac{\beta^{ N}-1}{\beta-1}.$">|; 

$key = q/f_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1631.png"
 ALT="$ f_i$">|; 

$key = q/displaystyleG^{,munu}=frac{1}{2},epsilon^{,munualphabeta},F_{alphabeta}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3818.png"
 ALT="$\displaystyle G^{ \mu\nu} = \frac{1}{2}  \epsilon^{ \mu\nu\alpha\beta}  F_{\alpha\beta}.$">|; 

$key = q/u=(u_1^{,2}+u_2^{,2}+u_3^{,2})^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3511.png"
 ALT="$ u=(u_1^{ 2} + u_2^{ 2}+ u_3^{ 2})^{1/2}$">|; 

$key = q/displaystyle=-dx^{,2}-dy^{,2}-dz^{,2}+c^{,2},dt^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3622.png"
 ALT="$\displaystyle = -dx^{ 2} -dy^{ 2} -dz^{ 2} +c^{ 2}  dt^{ 2}$">|; 

$key = q/displaystyleleft(frac{1}{c^{,2}}frac{partial^{,2}}{partialt^{,2}}-nabla^{,2}right)u=v,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle \left(\frac{1}{c^{ 2}}\frac{\partial^{ 2}}{\partial t^{ 2}}-\nabla^{ 2}\right)u = v,$">|; 

$key = q/displaystylesigmasimeqsigma_{rmThomson}left(frac{omega_0}{gamma_0}right)^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2747.png"
 ALT="$\displaystyle \sigma \simeq \sigma_{\rm Thomson}\left( \frac{\omega_0}{\gamma_0} \right)^{ 2},$">|; 

$key = q/J_n(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1871.png"
 ALT="$ J_n(z)$">|; 

$key = q/displaystyle=-frac{1}{mu_0},frac{partialE_x}{partialz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1989.png"
 ALT="$\displaystyle = - \frac{1}{\mu_0} \frac{\partial E_x}{\partial z},$">|; 

$key = q/T^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3963.png"
 ALT="$ T^{ \mu\nu}$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{2pi}sum_{m=-infty,infty}int_0^inftyfrac{sin]}{sinh(k,L)},J_m(k,r),J_m(k,r'),{rme}^{,{rmi},m,(theta-theta')},dk.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1047.png"
 ALT="$\displaystyle G({\bf r}, {\bf r}')=-\frac{1}{2\pi}\sum_{m=-\infty,\infty}\int_0...
...h(k L)} J_m(k r) J_m(k r') {\rm e}^{ {\rm i} m (\theta-\theta')} dk.
$">|; 

$key = q/displaystylefrac{1}{r},frac{partial}{partialr}left(r,frac{partialG}{partialr}rigrtialz^{,2}}=frac{1}{r},delta(r-r'),delta(theta-theta'),delta(z-z').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img953.png"
 ALT="$\displaystyle \frac{1}{r} \frac{\partial}{\partial r}\left(r \frac{\partial G...
...ial z^{ 2}} = \frac{1}{r} \delta(r-r') \delta(\theta-\theta') \delta(z-z').$">|; 

$key = q/displaystyler(x^{,i},x^{,i'})=left[(x^{,i}-x^{,i'}),(x_{,i}-x_{,i'})right]^{1slash2}=c,(t-t').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3988.png"
 ALT="$\displaystyle r(x^{ i}, x^{ i'}) = \left[ (x^{ i}-x^{ i'}) (x_{ i}-x_{ i'})\right]^{1/2} = c (t-t').$">|; 

$key = q/displaystylenablatimes{bfE}={bf0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$\displaystyle \nabla\times {\bf E} = {\bf0}.$">|; 

$key = q/-Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$ -Q$">|; 

$key = q/displaystyledeltaU=-int_V{bff}cdotdelta{bfr},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1208.png"
 ALT="$\displaystyle \delta U = - \int_V {\bf f}\cdot \delta {\bf r} dV.$">|; 

$key = q/displaystylen=sqrt{epsilon};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1611.png"
 ALT="$\displaystyle n = \sqrt{\epsilon}$">|; 

$key = q/{bfB}rightarrowalpha,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$ {\bf B}\rightarrow \alpha  {\bf B}$">|; 

$key = q/displaystyle{bfn}=sinvarphicospsi,{bfe}+sinvarphi,sinpsi,{bfe}timeshat{bfk}+cosvarphi,hat{bfk},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2732.png"
 ALT="$\displaystyle {\bf n} = \sin\varphi \cos\psi  {\bf e}+ \sin\varphi  \sin\psi  {\bf e}\times\hat{\bf k} + \cos\varphi  \hat{\bf k},$">|; 

$key = q/nabla';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="$ \nabla'$">|; 

$key = q/displaystyleK_m(p),I_m'(p)-K_m'(p),I_m(p)=frac{1}{p}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img980.png"
 ALT="$\displaystyle K_m(p) I_m'(p)-K_m'(p) I_m(p) = \frac{1}{p}.$">|; 

$key = q/displaystyle=ointrho(r,theta,varphi),Y_{l,m}^ast(theta,varphi),d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="$\displaystyle = \oint \rho(r,\theta,\varphi) Y_{l,m}^\ast(\theta,\varphi) d{\mit\Omega}.$">|; 

$key = q/displaystylef(t)=frac{2}{tau}int_{-infty}^{infty}domega,sin[omega,(t-Tslash2)],frac{sin(omega,Tslash2)}{omega^{,2}-(2pislashtau)^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1789.png"
 ALT="$\displaystyle f(t) = \frac{2}{\tau}\int_{-\infty}^{\infty}d\omega  \sin[\omega (t-T/2)]  \frac{\sin(\omega  T/2)}{\omega^{ 2} -(2\pi/\tau)^{ 2}}.$">|; 

$key = q/displaystyle{rme}^{+{rmi},k,R}sum_{n=0,infty}frac{-2,{rmi},k,(n+1),f_{n+1}+[n,(n+1)+D],f_n}{R^{,n+2}}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\displaystyle {\rm e}^{+{\rm i} k R} \sum_{n=0 \infty} \frac{-2 {\rm i} k  (n+1)  f_{n+1} + [n (n+1)+D] f_n }{R^{ n+2}} =0,$">|; 

$key = q/x^{,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3533.png"
 ALT="$ x^{ i}$">|; 

$key = q/displaystyleleft.-sqrt{(l+m),(l-m+1)},a_E^{,ast}(l,m-1)right]a_E(l,m),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3172.png"
 ALT="$\displaystyle \left. - \sqrt{(l+m) (l-m+1)}  a_E^{ \ast}(l,m-1)\right]a_E(l,m),$">|; 

$key = q/alpha,h_0=1slash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2592.png"
 ALT="$ \alpha h_0=1/4$">|; 

$key = q/displaystyleleft.frac{partialG_D}{partialr'}right|_{r'=a}=frac{a-r^{,2}slasha}{4pi,(r^{,2}-2,r,a,cosgamma+a^{,2})^{3slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="$\displaystyle \left.\frac{\partial G_D}{\partial r'}\right\vert _{r'=a}= \frac{a-r^{ 2}/a}{4\pi (r^{ 2}-2 r a \cos\gamma+a^{ 2})^{3/2}}.$">|; 

$key = q/Rrightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$ R\rightarrow 0$">|; 

$key = q/krightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$ k
\rightarrow 0$">|; 

$key = q/displaystyle=-tau,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2768.png"
 ALT="$\displaystyle = -\tau,$">|; 

$key = q/displaystyle{bfB}({bfr},t)simeqfrac{1}{4pi,epsilon_0}frac{left[intpartial{bfj}_perpslashpartialt,,dV'right]times{bfr}}{c^{,3},r^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle {\bf B}({\bf r},t) \simeq \frac{1}{4\pi \epsilon_0} \frac{ \left...
...ial {\bf j}_\perp /\partial t  dV'\right] \times{\bf r} }{c^{ 3}  r^{ 2}}.$">|; 

$key = q/dslashdx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3366.png"
 ALT="$ d/dx$">|; 

$key = q/omega_1=(omega_0^{~2}+omega_p^{~2})^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1929.png"
 ALT="$ \omega_1=(\omega_0^{&nbsp;2} + \omega_p^{&nbsp;2})^{1/2}$">|; 

$key = q/psi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3739.png"
 ALT="$ \psi=0$">|; 

$key = q/mitOmega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1753.png"
 ALT="$ \mit \Omega$">|; 

$key = q/displaystyleint_{-infty}^inftydelta(t-t'),dt'=1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \delta (t-t') dt' = 1.$">|; 

$key = q/n_2=1.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$ n_2=1.5$">|; 

$key = q/theta_{rmmax}rightarrow1slash(2,gamma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4105.png"
 ALT="$ \theta_{\rm max} \rightarrow 1/(2 \gamma)$">|; 

$key = q/sigma_b=-nablacdot{bfP};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1595.png"
 ALT="$ \sigma_b=-\nabla\cdot{\bf P}$">|; 

$key = q/{bfr}_u={bfr}_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4025.png"
 ALT="$ {\bf r}_u = {\bf r}_0$">|; 

$key = q/{mitDelta}t>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3520.png"
 ALT="$ {\mit\Delta} t&gt;0$">|; 

$key = q/displaystyletanphi_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2155.png"
 ALT="$\displaystyle \tan\phi_t$">|; 

$key = q/displaystylesimeqfrac{e}{4pi,epsilon_0,c^{,2}}frac{{bfr}times({bfr}timesdot{bfu})}{r^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4031.png"
 ALT="$\displaystyle \simeq \frac{e}{4\pi \epsilon_0  c^{ 2}} \frac{{\bf r}\times ({\bf r}\times\dot{\bf u})}{r^{ 3}},$">|; 

$key = q/displaystyleE_r(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2983.png"
 ALT="$\displaystyle E_r(r)$">|; 

$key = q/z=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="$ z=0$">|; 

$key = q/exp(-rho,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1852.png"
 ALT="$ \exp(-\rho  t)$">|; 

$key = q/j_l(k,r),Y_{lm}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3229.png"
 ALT="$ j_l(k r) Y_{lm}^{ \ast}$">|; 

$key = q/displaystyleT^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3964.png"
 ALT="$\displaystyle T^{ ij}$">|; 

$key = q/displaystyleg_{mu'nu'},p_{musigma}^{,mu'}p_{nu}^{,nu'}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3682.png"
 ALT="$\displaystyle g_{\mu'\nu'}  p_{\mu\sigma}^{ \mu'} p_{\nu}^{ \nu'} =0.$">|; 

$key = q/displaystyleY_{l,-m}=(-1)^{,m},Y_{l,m}^{,ast}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="$\displaystyle Y_{l,-m} = (-1)^{ m} Y_{l,m}^{ \ast}.$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{Chapter06slashbrill.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="485" HEIGHT="232" BORDER="0"
 SRC="|."$dir".q|img1960.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{Chapter06/brill.eps}}
\end{figure}">|; 

$key = q/p_l=q,P_l(0)slasha^{,l+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="$ p_l=q P_l(0)/a^{ l+1}$">|; 

$key = q/displaystylephi_m(r,theta)=sum_{l=0,infty}B_l,r^{-(l+1)}P_l(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1505.png"
 ALT="$\displaystyle \phi_m(r,\theta) =\sum_{l=0,\infty} B_l  r^{-(l+1)} P_l(\cos\theta)$">|; 

$key = q/P^{,mu}=(d{bfp},,dEslashc);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4064.png"
 ALT="$ P^{ \mu} = (d{\bf p},  dE/c)$">|; 

$key = q/H_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2162.png"
 ALT="$ H_y$">|; 

$key = q/-sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$ -\sigma$">|; 

$key = q/B,(hat{z},0)_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2521.png"
 ALT="$ B  (\hat{z},0)_s$">|; 

$key = q/displaystyle=x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$\displaystyle = x,$">|; 

$key = q/displaystyle(x,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2537.png"
 ALT="$\displaystyle (x, 0)$">|; 

$key = q/displaystyle=-{bfK}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2772.png"
 ALT="$\displaystyle = -{\bf K}.$">|; 

$key = q/{figure}{epsfysize{=2.75in{centerline{epsffile{Chapter06bslashfig09.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="708" HEIGHT="304" BORDER="0"
 SRC="|."$dir".q|img2164.png"
 ALT="\begin{figure}
\epsfysize =2.75in
\centerline{\epsffile{Chapter06b/fig09.eps}}
\end{figure}">|; 

$key = q/displaystyleH_z(r,varphi,z,t)=A,J_m(k_l,r),{rme}^{,{rmi},m,varphi}sin(k_3,z),{rme}^{-{rmi},omega,t}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2867.png"
 ALT="$\displaystyle H_z(r,\varphi,z,t) = A  J_m(k_l  r)  {\rm e}^{ {\rm i} m \varphi} \sin(k_3  z)  {\rm e}^{-{\rm i} \omega  t}.$">|; 

$key = q/E_y(t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2331.png"
 ALT="$ E_y(t)$">|; 

$key = q/displaystylepartial_muT^{,mu}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4039.png"
 ALT="$\displaystyle \partial_\mu T^{ \mu} = 0,$">|; 

$key = q/displaystylefrac{Ne^{,2},f_i}{epsilon_0,m,omega_i^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1646.png"
 ALT="$\displaystyle \frac{N e^{ 2}  f_i}{\epsilon_0  m \omega_i^{ 2}},$">|; 

$key = q/displaystyle{bfm}=frac{epsilon_0,c}{2,k},{rmRe},[{bfB}^{,ast}({bfL}cdot{bfB})].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3163.png"
 ALT="$\displaystyle {\bf m} = \frac{\epsilon_0  c}{2 k}  {\rm Re} [{\bf B}^{ \ast}({\bf L}\cdot {\bf B})].$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}=frac{e^{,2},dot{u}^{,2}}{16pi^2,epsilon_0,u^{,2}slashc^{,2})tan^2phi,cos^2theta}{[1-(uslashc),costheta]^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="433" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4125.png"
 ALT="$\displaystyle \frac{d P(t')}{d{\mit\Omega}} = \frac{e^{ 2}  \dot{u}^{ 2}}{16...
...2} -(1-u^{ 2}/c^{ 2})\tan^2\phi \cos^2\theta} {[1-(u/c) \cos\theta]^{ 5}}.$">|; 

$key = q/C^{,ij}_{klm}=A^{ij},B_{klm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3566.png"
 ALT="$ C^{ ij}_{klm} = A^{ij} 
B_{klm}$">|; 

$key = q/displaystyleu_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3484.png"
 ALT="$\displaystyle u_1$">|; 

$key = q/omega=omega_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1642.png"
 ALT="$ \omega=\omega_i$">|; 

$key = q/usimeqc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4081.png"
 ALT="$ u\simeq c$">|; 

$key = q/displaystyle=left(frac{3}{8pi}right)^{1slash2},(x-{rmi},y),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="$\displaystyle =\left(\frac{3}{8\pi}\right)^{1/2} (x-{\rm i} y),$">|; 

$key = q/displaystyle{bfB}=frac{2}{3},mu_0,{bfM}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1522.png"
 ALT="$\displaystyle {\bf B} = \frac{2}{3}  \mu_0  {\bf M}.$">|; 

$key = q/displaystyleE_y(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2260.png"
 ALT="$\displaystyle E_y(z)$">|; 

$key = q/displaystylep_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="$\displaystyle p_y$">|; 

$key = q/displaystylef_i=e,(E_i+epsilon_{ijk},u^{,j},B^{,k}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3929.png"
 ALT="$\displaystyle f_i = e (E_i + \epsilon_{ijk}  u^{ j}  B^{ k}),$">|; 

$key = q/g=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1923.png"
 ALT="$ g=0$">|; 

$key = q/V_0,cos(omega,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2654.png"
 ALT="$ V_0 \cos(\omega  t)$">|; 

$key = q/displaystyleA_l=frac{C_l}{a^{,2,l+1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1169.png"
 ALT="$\displaystyle A_l = \frac{C_l}{a^{ 2 l+1}}$">|; 

$key = q/displaystyle=-nablaleft(frac{nablaepsiloncdot{bfE}}{epsilon}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2573.png"
 ALT="$\displaystyle =- \nabla\left(\frac{\nabla\epsilon\cdot{\bf E}}{\epsilon}\right),$">|; 

$key = q/displaystylefrac{dphi}{dz}=pmleft[k^{,2}q^{,2}pm{rmi},kleft(frac{dq}{dz}-frac{2,q}{n}frac{dn}{dz}right)right]^{1slash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2325.png"
 ALT="$\displaystyle \frac{d\phi}{dz}=\pm \left[k^{ 2} q^{ 2} \pm {\rm i} k\left( \frac{dq}{dz} - \frac{2 q}{n} \frac{dn}{dz}\right)\right]^{1/2}.$">|; 

$key = q/displaystyle~~~~+frac{psi_r}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2103.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\frac{\psi_r}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z),$">|; 

$key = q/ssim1slashxi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1886.png"
 ALT="$ s\sim 1/\xi$">|; 

$key = q/n^{,1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2265.png"
 ALT="$ n^{ 1/2}$">|; 

$key = q/displaystyler^{,2},nabla^{,2}Y_{l,m}+l,(l+1),Y_{l,m}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="$\displaystyle r^{ 2} \nabla^{ 2} Y_{l,m} +l (l+1) Y_{l,m}=0,$">|; 

$key = q/displaystyleleft.frac{partialphi}{partialtheta}right|_{r=a_{-}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1150.png"
 ALT="$\displaystyle \left.\frac{\partial\phi}{\partial \theta}\right\vert _{r=a_{-}}$">|; 

$key = q/y_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3127.png"
 ALT="$ y_l(k r)$">|; 

$key = q/z=2.4048;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2971.png"
 ALT="$ z=2.4048$">|; 

$key = q/[(nablacdot{bfE}),{bfE}]_iequiv(partialE_jslashpartialx_j),E_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$ [(\nabla\cdot{\bf E}) {\bf E}]_i \equiv (\partial E_j/\partial x_j) E_i$">|; 

$key = q/displaystyledx'^{,2}+dy'^{,2}+dz'^{,2}-c^{,2},dt'^{,2}=Kleft(dx^{,2}+dy^{,2}+dz^{,2}-c^{,2},dt^{,2}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3425.png"
 ALT="$\displaystyle dx'^{ 2} + dy'^{ 2} + dz'^{ 2} -c^{ 2}  dt'^{ 2} = K\left(dx^{ 2} + dy^{ 2} + dz^{ 2} -c^{ 2}  dt^{ 2}\right),$">|; 

$key = q/displaystyledV'=gammaleft(1+frac{v}{c},costhetaright)dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3754.png"
 ALT="$\displaystyle dV' = \gamma \left(1+\frac{v}{c}  \cos\theta\right) dV.$">|; 

$key = q/displaystyledot{bfu}cdot{bfr}=-dot{u},r,sinalpha,sinphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4122.png"
 ALT="$\displaystyle \dot{\bf u}\cdot{\bf r} = -\dot{u}  r  \sin\alpha \sin\phi.$">|; 

$key = q/F^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3830.png"
 ALT="$ F^{ \mu\nu}$">|; 

$key = q/n_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2012.png"
 ALT="$ n_1$">|; 

$key = q/delta(t-t');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$ \delta(t-t')$">|; 

$key = q/displaystylefrac{partialg^{(i)}}{partialt}+nablacdot{bfG}^{(i)}=-(rho,{bfE}+{bfj}times{bfB})_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle \frac{\partial g^{(i)}}{\partial t} + \nabla\cdot{\bf G}^{(i)} = -(\rho {\bf E}+{\bf j}\times {\bf B})_i,$">|; 

$key = q/displaystyle{bfE}=frac{1}{4pi,epsilon_0}intleft([rho],frac{bfR}{R^{,3}}+left[frabfR}{c,R^{,2}}-frac{[partial{bfj}slashpartialt]}{c^{,2},R}right)dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle {\bf E} = \frac{1}{4\pi \epsilon_0} \int \left( [\rho]  \frac{\...
... R}{c R^{ 2}} - \frac{[\partial {\bf j}/\partial t]}{c^{ 2}  R} \right)dV',$">|; 

$key = q/displaystyleu^{,i}=frac{dx^{,i'}}{dt'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3984.png"
 ALT="$\displaystyle u^{ i} = \frac{dx^{ i'}}{dt'},$">|; 

$key = q/beta_pm(l)+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3368.png"
 ALT="$ \beta_\pm(l)+1$">|; 

$key = q/Q=c^{,2},B^{,2}-E^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4181.png"
 ALT="$ Q =c^{ 2} B^{ 2}-E^{ 2}$">|; 

$key = q/J_1(k_s,a)simeq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2994.png"
 ALT="$ J_1(k_s  a)\simeq 0$">|; 

$key = q/displaystyleG_omega=frac{{rme}^{+{rmi},k,R}}{4pi,R};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle G_\omega = \frac{{\rm e}^{+{\rm i} k R}}{4\pi  R}$">|; 

$key = q/displaystyledelta({bfr}-{bfr}')=frac{delta(r-r')}{r^{,2}}sum_{l=0,infty}sum_{m=-l,+l}Y^{,ast}_{lm}(theta',varphi'),Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3178.png"
 ALT="$\displaystyle \delta({\bf r}-{\bf r}') = \frac{\delta(r-r')}{r^{ 2}}\sum_{l=0,\infty}\sum_{m=-l,+l} Y^{ \ast}_{lm}(\theta',\varphi')  Y_{lm}(\theta,\varphi).$">|; 

$key = q/displaystyle[rho]simeqrho+frac{partialrho}{partialt},(t_r-t)+frac{1}{2}frac{partial^{,2}rho}{partialt^{,2}},(t_r-t)^2+cdots,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\displaystyle [\rho] \simeq \rho + \frac{\partial\rho}{\partial t}  (t_r-t) + \frac{1}{2} \frac{\partial^{ 2} \rho}{\partial t^{ 2}} (t_r -t )^2+\cdots,$">|; 

$key = q/displaystyleK=intleft[-g,{bfj}cdotnabla'f-g,f,nabla'cdot{bfj}+g,{bfj}cdotnabla'fright]dV'=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1389.png"
 ALT="$\displaystyle K = \int\left[-g {\bf j}\cdot\nabla' f -g f \nabla'\cdot{\bf j}+g {\bf j}\cdot\nabla' f\right]dV'=0,$">|; 

$key = q/d{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1410.png"
 ALT="$ d{\bf A}$">|; 

$key = q/h^{(2)}_l(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3030.png"
 ALT="$ h^{(2)}_l(z)$">|; 

$key = q/partial_mu=(nabla,,c^{-1}partialslashpartialt);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3781.png"
 ALT="$ \partial_\mu
=(\nabla,  c^{-1} \partial/\partial t)$">|; 

$key = q/displaystyleA_i=g_{ij},A^j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3595.png"
 ALT="$\displaystyle A_i = g_{ij}  A^j.$">|; 

$key = q/p=gamma,m_0,u;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4077.png"
 ALT="$ p= \gamma  m_0  u$">|; 

$key = q/displaystyle={rme}^{,2,{rmi},delta_l}-1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3370.png"
 ALT="$\displaystyle = {\rm e}^{ 2 {\rm i} \delta_l} -1,$">|; 

$key = q/cos(k_3,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2814.png"
 ALT="$ \cos(k_3  z)$">|; 

$key = q/psi(r)proptoK_0(k_t,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2924.png"
 ALT="$ \psi(r)\propto K_0(k_t  r)$">|; 

$key = q/displaystyleJ_1(z)=sqrt{frac{2}{pi,z}}cos(z-3pislash4)+{calO}(z^{-3slash2}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1878.png"
 ALT="$\displaystyle J_1(z) = \sqrt{\frac{2}{\pi  z}} \cos(z- 3\pi/4) + {\cal O}(z^{-3/2}).$">|; 

$key = q/displaystyle=gammaleft(t-frac{{bfr}cdot{bfv}}{c^{,2}}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4170.png"
 ALT="$\displaystyle = \gamma\left(t - \frac{{\bf r}\cdot{\bf v}}{c^{ 2}}\right),$">|; 

$key = q/displaystyleZ(z)=sinh(k,z).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="$\displaystyle Z(z)= \sinh(k z).$">|; 

$key = q/phi_3({bfr})=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$ \phi_3({\bf r})=0$">|; 

$key = q/displaystyle=frac{partialH_y}{partialx},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2048.png"
 ALT="$\displaystyle =\frac{\partial H_y}{\partial x},$">|; 

$key = q/R_mu,Q^{,mu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3662.png"
 ALT="$ R_\mu  Q^{ \mu} = 0$">|; 

$key = q/n_+>n_-;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1744.png"
 ALT="$ n_+ &gt; n_-$">|; 

$key = q/displaystylepartial^{,mu}A^{nusigma}equivg^{,mutau}{A^{nusigma}}_{,tau}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3668.png"
 ALT="$\displaystyle \partial^{ \mu} A^{\nu\sigma} \equiv g^{ \mu\tau} {A^{\nu\sigma}}_{,\tau}.$">|; 

$key = q/lambdabar=lambdaslash2pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2676.png"
 ALT="$ \lambdabar = \lambda/2\pi$">|; 

$key = q/{bfr}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="$ {\bf r}_1$">|; 

$key = q/displaystylephi_2({bfr})=frac{1}{5,epsilon_0}sum_{m=-2,+2}frac{q_{2,m}^{,ast},Y_}}=frac{1}{8pi,epsilon_0}sum_{i,j=1,3}frac{Q_{ij},,x_i,x_j}{r^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="$\displaystyle \phi_2({\bf r})= \frac{1}{5 \epsilon_0}\sum_{m=-2,+2} \frac{q_{2...
...3}}=\frac{1}{8\pi \epsilon_0}\sum_{i,j=1,3}\frac{Q_{ij}  x_i x_j}{r^{ 5}}.$">|; 

$key = q/displaystyle{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\displaystyle {\bf E}$">|; 

$key = q/Z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1630.png"
 ALT="$ Z$">|; 

$key = q/mathaccentV{hat}05E{z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$ \mathaccentV {hat}05E{z}$">|; 

$key = q/displaystylefrac{dx^{,i'}}{ds}=frac{partialx^{.i'}}{partialx^{,i}}frac{dx^{,i}}{ds}=frac{dx^{,i}}{ds},p_i^{,i'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3607.png"
 ALT="$\displaystyle \frac{dx^{ i'}}{ds} = \frac{\partial x^{\.i'}}{\partial x^{ i}} \frac{d x^{ i}}{ds} = \frac{dx^{ i}}{ds}  p_i^{ i'}.$">|; 

$key = q/displaystyleE_z=frac{P}{2,epsilon_0}int_0^picos^2theta,sintheta,dtheta=frac{P}{3,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1242.png"
 ALT="$\displaystyle E_z = \frac{P }{2 \epsilon_0} \int_0^\pi \cos^2\theta \sin\theta d\theta = \frac{P}{3 \epsilon_0}.$">|; 

$key = q/partialslashpartialx^{,i}|_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3995.png"
 ALT="$ \partial/\partial x^{ i}\vert _t$">|; 

$key = q/{bfu}cdotdot{bfu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4141.png"
 ALT="$ {\bf u}\cdot \dot{\bf u}=0$">|; 

$key = q/displaystyleY_{1,+1}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="$\displaystyle Y_{1,+1}(\theta,\varphi)$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}intfrac{[rho({bfr}')]}{|{bfr}-{bfr}'|},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3740.png"
 ALT="$\displaystyle = \frac{1}{4\pi \epsilon_0} \int \frac{[\rho({\bf r}')]}{\vert{\bf r}- {\bf r}'\vert} dV',$">|; 

$key = q/displaystyle=f_l^{,ast},g_l,delta_{ll'},delta_{mm'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3310.png"
 ALT="$\displaystyle = f_l^{ \ast}  g_l  \delta_{ll'} \delta_{mm'},$">|; 

$key = q/rho';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="$ \rho'$">|; 

$key = q/displaystylenablacdot{bfE}=-frac{1}{4pi,epsilon_0}intrho({bfr'}),nabla^{,2}left(}intrho({bfr}'),delta({bfr}-{bfr}'),dV'=frac{rho({bfr})}{epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="487" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="$\displaystyle \nabla\cdot{\bf E} = -\frac{1}{4\pi \epsilon_0}\int \rho({\bf r'...
...ho({\bf r}') \delta({\bf r}-{\bf r}') dV' = \frac{\rho({\bf r})}{\epsilon_0},$">|; 

$key = q/displaystyle{bfE}={bfE}_0,exp[,{rmi},(omegaslashc),({rmRe}(n),x-c,t)]exp[-(omegaslashc),{rmIm}(n),x].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1643.png"
 ALT="$\displaystyle {\bf E} = {\bf E}_0  \exp[ {\rm i} (\omega/c) ({\rm Re}(n) x-c  t)] \exp[-(\omega/c) {\rm Im}(n) x].$">|; 

$key = q/displaystyle(nablatimes{bfA})^i=epsilon^{,ijk},frac{partialA_k}{partialx^{,j}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3763.png"
 ALT="$\displaystyle (\nabla\times{\bf A})^i = \epsilon^{ ijk}  \frac{\partial A_k}{\partial x^{ j}}.$">|; 

$key = q/r_<=r';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3216.png"
 ALT="$ r_&lt; = r'$">|; 

$key = q/k,rrightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3128.png"
 ALT="$ k r\rightarrow 0$">|; 

$key = q/displaystylefrac{d^{,2}E_y}{dz^{,2}}+k^{,2}n^{,2}(z),E_y=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2451.png"
 ALT="$\displaystyle \frac{d^{ 2} E_y}{dz^{ 2}} + k^{ 2}n^{ 2}(z) E_y = 0$">|; 

$key = q/e,{bfv}times{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1444.png"
 ALT="$ e  {\bf v}\times {\bf B}$">|; 

$key = q/{bfD}({bfr})=D({bfr}),{bfn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="$ {\bf D}({\bf r}) = D({\bf r}) {\bf n}$">|; 

$key = q/rslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3743.png"
 ALT="$ r/c$">|; 

$key = q/displaystylefrac{1}{sintheta},frac{d}{dtheta}left[sintheta,P_l^1(costheta)right]=-l,(l+1),P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1353.png"
 ALT="$\displaystyle \frac{1}{\sin\theta} \frac{d}{d\theta}\left[\sin\theta P_l^1(\cos\theta)\right]=-l (l+1) P_l(\cos\theta),$">|; 

$key = q/eslash(4pi,epsilon_0,r'^{,3});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3887.png"
 ALT="$ e/(4\pi \epsilon_0 r'^{ 3})$">|; 

$key = q/displaystylenabla^{,2}G_D({bfr},{bfr}')=delta({bfr}-{bfr}')-frac{a}{r'},delta({bfr}-a^{,2},{bfr}'slashr'^{,2}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="$\displaystyle \nabla^{ 2} G_D({\bf r},{\bf r}') = \delta({\bf r}-{\bf r}')- \frac{a}{r'} \delta({\bf r}-a^{ 2} {\bf r}'/r'^{ 2}).$">|; 

$key = q/E_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1132.png"
 ALT="$ E_1$">|; 

$key = q/z_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2316.png"
 ALT="$ z_0$">|; 

$key = q/displaystylepartial^{,mu}A_mu=partial_mu,A^mu=nablacdot{bfA}+frac{1}{c}frac{partialA^0}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3670.png"
 ALT="$\displaystyle \partial^{ \mu} A_\mu = \partial_\mu  A^\mu = \nabla \cdot {\bf A} + \frac{1}{c}\frac{\partial A^0} {\partial t}.$">|; 

$key = q/{rmTE}_{,02};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2975.png"
 ALT="$ {\rm TE}_{ 02}$">|; 

$key = q/r^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$ r^{ 2}$">|; 

$key = q/displaystylesigma=int_0^pifrac{dsigma}{d{mitOmega}},2pi,sintheta,dtheta=frac{8pi}{3}left(frac{q^{,2}}{4piepsilon_0,m,c^{,2}}right)^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2727.png"
 ALT="$\displaystyle \sigma = \int_0^\pi \frac{d\sigma}{d {\mit \Omega}}  2\pi \sin\...
...a = \frac{8\pi}{3}\left( \frac{q^{ 2}}{4\pi\epsilon_0  m  c^{ 2}}\right)^2.$">|; 

$key = q/displaystyle|{bfL}Y_{1,0}|^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3278.png"
 ALT="$\displaystyle \vert{\bf L} Y_{1,0}\vert^{ 2}$">|; 

$key = q/displaystyle(a,hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2472.png"
 ALT="$\displaystyle (a, \hat{z})$">|; 

$key = q/h_l^{(2)}(k,R);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$ h_l^{(2)}(k R)$">|; 

$key = q/z=-dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$ z=-d/2$">|; 

$key = q/displaystyleg_{mu'nu'},p_{musigma}^{,mu'},p_{nu}^{,nu'}+g_{mu'nu'},p_{mu}^{,mu'},p_{nusigma}^{,nu'}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3677.png"
 ALT="$\displaystyle g_{\mu'\nu'} p_{\mu\sigma}^{ \mu'}  p_{\nu}^{ \nu'} + g_{\mu'\nu'}  p_{\mu}^{ \mu'} p_{\nu\sigma}^{ \nu'} = 0,$">|; 

$key = q/displaystyle(omega_0^{,2}-omega^{,2}+omega,{mitOmega}),s_-;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1730.png"
 ALT="$\displaystyle (\omega_0^{ 2} -\omega^{ 2} + \omega {\mit \Omega}) s_-$">|; 

$key = q/displaystylelim_{Rrightarrowinfty}Rleft(frac{partialG_omega}{partialR}-{rmi},k,G_omegaright)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle \lim_{R\rightarrow\infty} R \left(\frac{\partial G_\omega}{\partial R} -{\rm i} k  G_\omega \right) = 0.$">|; 

$key = q/(x_2,,y_2,,z_2,,t_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3615.png"
 ALT="$ (x_2,  y_2,  z_2,  t_2)$">|; 

$key = q/displaystylephi(r,theta,varphi)=sum_{l,m}frac{Y_{lm}(theta,varphi)}{r^{,l+1}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3137.png"
 ALT="$\displaystyle \phi(r,\theta,\varphi) = \sum_{l,m}\frac{Y_{lm}(\theta,\varphi)}{r^{ l+1}}.$">|; 

$key = q/(A)^2=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3603.png"
 ALT="$ (A)^2=0$">|; 

$key = q/displaystylefrac{d{bfr}}{dt'}=-{bfu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3987.png"
 ALT="$\displaystyle \frac{d{\bf r}}{dt'}= -{\bf u}.$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi,(r^{,2}-2,r,r',cosgamma+r'^{,2})^{1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\frac{1}{4\pi (r^{ 2}-2 r r' \cos\gamma+r'^{ 2})^{1/2}},$">|; 

$key = q/displaystyleU=frac{epsilon_0,E^{,2}}{2}+frac{B^{,2}}{2,mu_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$\displaystyle U = \frac{\epsilon_0 E^{ 2}}{2} + \frac{B^{ 2}}{2 \mu_0}$">|; 

$key = q/k_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2810.png"
 ALT="$ k_1$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}int_Vfrac{rho({bfr}')}{|{bfr}-{bfr}r}'),frac{partial}{partialn'}!left(frac{1}{|{bfr}-{bfr}'|}right)dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="556" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="$\displaystyle \phi({\bf r})= \frac{1}{4\pi \epsilon_0}\int_V \frac{\rho({\bf r...
...c{\partial}{\partial n'}\!\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dS'.$">|; 

$key = q/displaystylew(4)=(A+t,B),(0,hat{z})_d+(B+u,[A+t,B]),(hat{z},0)_s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2502.png"
 ALT="$\displaystyle w(4) =( A+t B) (0,\hat{z})_d + (B+ u [A+t B]) (\hat{z},0)_s.$">|; 

$key = q/displaystyley;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1653.png"
 ALT="$\displaystyle y$">|; 

$key = q/displaystyle=E_3,sin(k_1,x)sin(k_2,y)cos(k_3,z),{rme}^{-{rmi},omega,t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2783.png"
 ALT="$\displaystyle = E_3  \sin(k_1  x)\sin(k_2  y) \cos(k_3  z)  {\rm e}^{-{\rm i} \omega  t},$">|; 

$key = q/t-rslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$ t-r/c$">|; 

$key = q/{calE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1995.png"
 ALT="$ {\cal E}$">|; 

$key = q/A^i=C^{,ij},B_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3578.png"
 ALT="$ A^i = C^{ ij}  B_j$">|; 

$key = q/displaystyleJ^{,mu}-frac{1}{c^{,2}}(U_nu,J^{,nu}),U^{,mu}=frac{sigma}{c}F^{,munu}U_nu,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4198.png"
 ALT="$\displaystyle J^{ \mu} - \frac{1}{c^{ 2}}(U_\nu  J^{ \nu})  U^{ \mu}= \frac{\sigma}{c} F^{ \mu\nu} U_\nu,
$">|; 

$key = q/langlePrangle=langleQrangle=langleRrangle=langleSrangle=langleTrangle=langleUrangle=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1979.png"
 ALT="$ \langle P\rangle=\langle Q\rangle=\langle R\rangle=\langle S\rangle=\langle T\rangle=\langle U\rangle =0$">|; 

$key = q/displaystyleg^{,ij}g_{jk}=delta_k^{,i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3592.png"
 ALT="$\displaystyle g^{ ij} g_{jk} = \delta_k^{ i}.$">|; 

$key = q/displaystyletandelta_l';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3377.png"
 ALT="$\displaystyle \tan\delta_l'$">|; 

$key = q/displaystyle{bfA}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\displaystyle {\bf A}({\bf r}, t)$">|; 

$key = q/{bfu}=(u,,0,,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3862.png"
 ALT="$ {\bf u} = (u, 0, 0)$">|; 

$key = q/rggr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1379.png"
 ALT="$ r\gg r'$">|; 

$key = q/P=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4186.png"
 ALT="$ P=0$">|; 

$key = q/displaystyle=frac{k_g}{omega,epsilon_0,epsilon_1},H_theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2935.png"
 ALT="$\displaystyle = \frac{k_g}{\omega  \epsilon_0 \epsilon_1}  H_\theta$">|; 

$key = q/displaystyleP^{,mu}=m_0,U^{,mu}=gamma,m_0,({bfu},,c)=({bfp},,Eslashc),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3922.png"
 ALT="$\displaystyle P^{ \mu} = m_0  U^{ \mu} = \gamma  m_0  ({\bf u},  c) = ({\bf p},  E/c),$">|; 

$key = q/phirightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img914.png"
 ALT="$ \phi\rightarrow 0$">|; 

$key = q/displaystyle(x,0)_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2544.png"
 ALT="$\displaystyle (x, 0)_s$">|; 

$key = q/k_{r,y}=k_{t,y}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2028.png"
 ALT="$ k_{r y}=k_{t y}=0$">|; 

$key = q/displaystylefrac{{rme}^{,{rmi},k,|{bfr}-bf{r}'|}}{4pi,|{bfr}-{bfr}'|}={rmi},ksumr_>)sum_{m=-l,+l}Y_{lm}^{,ast}(theta',varphi'),Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3186.png"
 ALT="$\displaystyle \frac{{\rm e}^{ {\rm i} k \vert{\bf r} -\bf {r}'\vert}} {4\pi ...
...,r_&gt;)\sum_{m=-l,+l} Y_{lm}^{ \ast}(\theta',\varphi')  Y_{lm}(\theta,\varphi).$">|; 

$key = q/displaystyleG({bfr},{bfr}')=frac{ln|{bfr}-{bfr}'|}{2pi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="$\displaystyle G({\bf r}, {\bf r}') = \frac{\ln\vert{\bf r}-{\bf r}'\vert}{2\pi},
$">|; 

$key = q/displaystyle{bfE}({bfr})=frac{1}{4pi,epsilon_0}intfrac{rho({bfr'}),({bfr}-{bfr}')}{|{bfr}-{bfr}'|^{,3}},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho({\bf r'}) ({\bf r}-{\bf r}')}{\vert{\bf r}-{\bf r}'\vert^{ 3}} dV',$">|; 

$key = q/c,B^{,ij}rightarrowE^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3831.png"
 ALT="$ c B^{ ij} \rightarrow E^{ ij}$">|; 

$key = q/displaystyle=J_0(k_s,a),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2956.png"
 ALT="$\displaystyle =J_0(k_s  a),$">|; 

$key = q/displaystyleE_z=-frac{1}{4pi,epsilon_0}int_Sfrac{sigma_b(theta),costheta}{a^{,2}},dS,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1240.png"
 ALT="$\displaystyle E_z = -\frac{1}{4\pi \epsilon_0} \int_S \frac{\sigma_b(\theta)  \cos\theta}{a^{ 2}} dS,$">|; 

$key = q/{bfH}=-nablaphi_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1519.png"
 ALT="$ {\bf H} = -\nabla\phi_m$">|; 

$key = q/displaystyle=L_x+{rmi},L_y={rme}^{,{rmi},varphi}left(frac{partial}{partialtheta}+{rmi},cottheta,frac{partial}{partialvarphi}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3051.png"
 ALT="$\displaystyle =L_x + {\rm i} L_y = {\rm e}^{ {\rm i} \varphi} \left(\frac{\p...
...\partial\theta} +{\rm i} \cot\theta  \frac{\partial}{\partial\varphi}\right),$">|; 

$key = q/displaystyleT^{,4'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3644.png"
 ALT="$\displaystyle T^{ 4'}$">|; 

$key = q/displaystylen_pm^{,2}(omega)=1-frac{omega_p^{,2}}{omega,(omegamp{mitOmega})}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1762.png"
 ALT="$\displaystyle n_\pm^{ 2}(\omega) = 1 - \frac{\omega_p^{ 2}}{\omega (\omega\mp{\mit \Omega})}.$">|; 

$key = q/displaystylenablacdot{bfj}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1308.png"
 ALT="$\displaystyle \nabla\cdot{\bf j} = 0.$">|; 

$key = q/P_{rmin}=P_{rmload}+P_{rmrad};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2662.png"
 ALT="$ P_{\rm in} = P_{\rm load} + P_{\rm rad}$">|; 

$key = q/displaystyleQ_{ij}=intrho({bfr}),(3,x_i,x_j-r^{,2},delta_{ij}),dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="$\displaystyle Q_{ij} = \int \rho({\bf r}) (3 x_i x_j-r^{ 2} \delta_{ij}) dV,$">|; 

$key = q/displaystyle=frac{3}{4pi},sin^2theta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3279.png"
 ALT="$\displaystyle = \frac{3}{4\pi} \sin^2\theta,$">|; 

$key = q/(a,hat{z})_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2482.png"
 ALT="$ (a,\hat{z})_s$">|; 

$key = q/displaystyle=frac{nabla_s(partialH_zslashpartialz)}{k^{,2}-k_3^{,2}}-frac{{rmi},omega,epsilon_0}{k^{,2}-k_3^{,2}},nabla_stimes{bfE}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2828.png"
 ALT="$\displaystyle = \frac{\nabla_s(\partial H_z/\partial z)}{k^{ 2} - k_3^{ 2}} - \frac{{\rm i} \omega \epsilon_0}{k^{ 2}-k_3^{ 2}}  \nabla_s\times{\bf E}_z.$">|; 

$key = q/displaystyleG^{,ij}=-epsilon_0,E^{,i},E^{,j}-frac{B^{,i},B^{,j}}{mu_0}+delta^{,ij},frac{1}{2}left(epsilon_0,E^{,2}+frac{B^{,2}}{mu_0}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3978.png"
 ALT="$\displaystyle G^{ ij} = -\epsilon_0  E^{ i}  E^{ j} - \frac{B^{ i}  B^{\...
...a^{ ij} \frac{1}{2} \left(\epsilon_0  E^{ 2} +\frac{B^{ 2}}{\mu_0}\right),$">|; 

$key = q/displaystylefrac{partialA^{nusigma}}{partialx^{,mu}}={A^{nusigma}}_{,mu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3663.png"
 ALT="$\displaystyle \frac{\partial A^{\nu\sigma}}{\partial x^{ \mu}} = {A^{\nu\sigma}}_{,\mu}.$">|; 

$key = q/displaystyleq^{,2}=n^{,2}-S^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2394.png"
 ALT="$\displaystyle q^{ 2} = n^{ 2} - S^{ 2},$">|; 

$key = q/displaystyle=n_1,k_0,(sintheta_i,,0,,costheta_i),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2034.png"
 ALT="$\displaystyle = n_1 k_0 (\sin\theta_i, 0, \cos\theta_i),$">|; 

$key = q/E=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1264.png"
 ALT="$ E=0$">|; 

$key = q/displaystylefrac{A}{n^{,1slash2}}left[frac{3}{4}left(frac{1}{n}frac{dn}{dz}rightc{d^{,2}n}{dz^{,2}}right]{rmexp}left(pm{rmi},kint^z!n(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2258.png"
 ALT="$\displaystyle \frac{A}{n^{ 1/2}}\left[ \frac{3}{4}\left(\frac{1}{n} \frac{dn}{...
...2} n}{dz^{ 2}}\right] {\rm exp}\left( \pm {\rm i} k\int^z\!n(z') dz'\right),$">|; 

$key = q/displaystyle=-left[frac{3,(2,mu+mu_0),mu_0}{(2,mu+mu_0),(mu+2,mu_0)-2,(a^{,3}slashb^{,3}),(mu-mu_0)^{,2}}right]B_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1568.png"
 ALT="$\displaystyle =-\left[ \frac{3 (2 \mu+\mu_0) \mu_0} {(2 \mu+\mu_0) (\mu+2 \mu_0) - 2 (a^{ 3}/b^{ 3}) (\mu-\mu_0)^{ 2}}\right] B_0,$">|; 

$key = q/displaystyleG({bfr},{bfr}')=frac{1}{L,pi}sum_{m=-infty,infty}sum_{n=1,infty}sin(k_n,z),sin(k_n,z'),{rme}^{,{rmi},m,(theta-theta')},g_{m,n}(r,r'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1003.png"
 ALT="$\displaystyle G({\bf r}, {\bf r}') = \frac{1}{L \pi}\sum_{m=-\infty,\infty}\su...
..._n z) \sin(k_n z') {\rm e}^{ {\rm i} m (\theta-\theta')} g_{m,n}(r,r'),$">|; 

$key = q/r^{,2}=x^{,2}+y^{,2}+z^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3748.png"
 ALT="$ r^{ 2}=x^{ 2}+y^{ 2}+z^{ 2}$">|; 

$key = q/displaystyler,Y_{1,+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="$\displaystyle r Y_{1,+1}$">|; 

$key = q/displaystylerho=rho_f+rho_b.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1067.png"
 ALT="$\displaystyle \rho = \rho_f + \rho_b.$">|; 

$key = q/displaystyleleft(frac{dphi}{dz}right)^2=k^{,2},n^{,2}+{rmi},frac{d^{,2}phi}{dz^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2248.png"
 ALT="$\displaystyle \left(\frac{d\phi}{dz}\right)^2 = k^{ 2}  n^{ 2} +{\rm i} \frac{d^{ 2}\phi}{dz^{ 2}}.$">|; 

$key = q/(a,hat{z})_d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2481.png"
 ALT="$ (a,\hat{z})_d$">|; 

$key = q/n=S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2402.png"
 ALT="$ n=S$">|; 

$key = q/displaystyle=v^{,2},frac{partialD_y}{partialz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2092.png"
 ALT="$\displaystyle =v^{ 2} \frac{\partial D_y}{\partial z},$">|; 

$key = q/displaystyle{bfs}=-frac{(eslashm),{bfE}}{omega_0^{,2}-omega^{,2}-{rmi},g,omega,omega_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1623.png"
 ALT="$\displaystyle {\bf s} =- \frac{ (e/m) {\bf E}}{\omega_0^{ 2} -\omega^{ 2}- {\rm i} g \omega \omega_0}.$">|; 

$key = q/displaystyleA_0=frac{2}{3},A_{rmhd}=frac{lambda^{,2}}{4pi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2674.png"
 ALT="$\displaystyle A_0 = \frac{2}{3}  A_{\rm hd} = \frac{\lambda^{ 2}}{4\pi},$">|; 

$key = q/A^i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3576.png"
 ALT="$ A^i$">|; 

$key = q/displaystyle{bfj}({bfr})=frac{I(r)}{2pi,r^{,2}},left[delta(costheta-1)-delta(costheta+1)right]{bfe}_r,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3250.png"
 ALT="$\displaystyle {\bf j}({\bf r}) = \frac{I(r)}{2\pi  r^{ 2}}  \left[\delta(\cos\theta-1)-\delta(\cos\theta+1)\right]{\bf e}_r,$">|; 

$key = q/displaystyle=frac{costheta_t}{costheta_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2071.png"
 ALT="$\displaystyle =\frac{\cos\theta_t}{\cos\theta_i},$">|; 

$key = q/displaystylephi({bfr})=-intfrac{rho({bfr}')}{epsilon_0},G({bfr},{bfr}'),dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img948.png"
 ALT="$\displaystyle \phi({\bf r}) = -\int \frac{\rho({\bf r}')}{\epsilon_0} G({\bf r},{\bf r}') dV',$">|; 

$key = q/r_<;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="$ r_&lt;$">|; 

$key = q/displaystylew(R,theta,varphi)=sum_{l,m=0,infty}left[C_{l,m},h_l^{(1)}(k,R)+D_{l,m},h_l^{(2)}(k,R)right]Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle w(R,\theta,\varphi) =\sum_{l,m=0,\infty} \left[ C_{l,m}  h_l^{(1)}(k R) + D_{l,m}  h_l^{(2)}(k R) \right] Y_{l,m}(\theta,\varphi).$">|; 

$key = q/displaystyle{bfn}cdot{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2770.png"
 ALT="$\displaystyle {\bf n}\cdot{\bf B}$">|; 

$key = q/displaystyle=mu,frac{partialphi_m(r=a+,theta)}{partialr},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1552.png"
 ALT="$\displaystyle = \mu  \frac{\partial\phi_m(r=a+,\theta)}{\partial r},$">|; 

$key = q/dx';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3410.png"
 ALT="$ dx'$">|; 

$key = q/{figure}{epsfysize{=3.75in{centerline{epsffile{Chapter06bslashexp.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="429" HEIGHT="428" BORDER="0"
 SRC="|."$dir".q|img2424.png"
 ALT="\begin{figure}
\epsfysize =3.75in
\centerline{\epsffile{Chapter06b/exp.eps}}
\end{figure}">|; 

$key = q/{bfM}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1431.png"
 ALT="$ {\bf M}({\bf r})$">|; 

$key = q/displaystyleA_1=-E_0+frac{C_1}{a^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1168.png"
 ALT="$\displaystyle A_1 = - E_0 + \frac{C_1}{a^{ 3}},$">|; 

$key = q/displaystylef(t)=frac{1}{2pi}int_{-infty}^{infty}domegaint_0^Tf(t'),cos[omega,(t-t')],dt'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1779.png"
 ALT="$\displaystyle f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} d\omega \int_0^Tf(t') \cos[\omega (t-t')] dt'.$">|; 

$key = q/displaystyle-(x_2-x_1)^2-(y_2-y_1)^2-(z_2-z_1)^2+c^{,2},(t_2-t_1)^2=s^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3617.png"
 ALT="$\displaystyle -(x_2-x_1)^2- (y_2-y_1)^2 - (z_2-z_1)^2 +c^{ 2} (t_2-t_1)^2 = s^{ 2}.$">|; 

$key = q/displaystyle{bff}=q,{bfE}=m,ddot{bfs},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2717.png"
 ALT="$\displaystyle {\bf f} = q {\bf E} = m  \ddot{\bf s},$">|; 

$key = q/displaystylenablatimes{bfB}=mu_0,{bfj}_t+mu_0,nablatimes{bfM}+mu_0,frac{partial{bfD}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1439.png"
 ALT="$\displaystyle \nabla\times{\bf B} = \mu_0 {\bf j}_t +\mu_0 \nabla\times{\bf M} + \mu_0 \frac{\partial{\bf D}}{\partial t},$">|; 

$key = q/dt^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3435.png"
 ALT="$ dt^{ 2}$">|; 

$key = q/displaystyle=-frac{sigma}{epsilon_0},E_x-frac{1}{epsilon_0},frac{partialH_y}{partialz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1991.png"
 ALT="$\displaystyle =-\frac{\sigma}{\epsilon_0} E_x -\frac{1}{\epsilon_0} \frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyleu({bfr},t)=frac{A}{4pi}intfrac{v({bfr}',t-Rslashc)}{R},dV'+frac{B}{4pi}intfrac{v({bfr}',t+Rslashc)}{R},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle u({\bf r}, t) = \frac{A}{4\pi} \int \frac{v({\bf r}', t- R/c)}{R}  dV' + \frac{B}{4\pi} \int \frac{v({\bf r}', t+ R/c)}{R}  dV'.$">|; 

$key = q/displaystyleB_i=frac{1}{2},epsilon_{ijk}B^{,jk}=-frac{mu_0,e}{4pi,{r'}^{,3}},gamma(u),epsilon_{ijk},u^{,j},r^{,k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3894.png"
 ALT="$\displaystyle B_i = \frac{1}{2}  \epsilon_{ijk} B^{ jk} = -\frac{\mu_0 e}{4\pi {r'}^{ 3}}  \gamma(u) \epsilon_{ijk}  u^{ j}  r^{ k},$">|; 

$key = q/displaystyle=frac{2}{L}int_0^Lrho_m(r',z'),sin(k_n,z'),dz',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1023.png"
 ALT="$\displaystyle = \frac{2}{L}\int_0^L \rho_m(r',z') \sin(k_n z') dz',$">|; 

$key = q/displaystyleA_{k'cdotsl'}^{i'cdotsj'}=A_{kcdotsl}^{icdotsj},p_i^{,i'}cdotsp_j^{,j'},p^{,k}_{k'}cdotsp^{,l}_{l'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3554.png"
 ALT="$\displaystyle A_{k'\cdots l'}^{i'\cdots j'} = A_{k\cdots l}^{i\cdots j}  p_i^{ i'} \cdots p_j^{ j'}  p^{ k}_{k'}\cdots p^{ l}_{l'}.$">|; 

$key = q/-V;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="$ -V$">|; 

$key = q/{calI};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1996.png"
 ALT="$ {\cal I}$">|; 

$key = q/C_k=A_{kij}^{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3571.png"
 ALT="$ C_k = A_{kij}^{ij}$">|; 

$key = q/displaystyleH_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2929.png"
 ALT="$\displaystyle H_r$">|; 

$key = q/E_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2196.png"
 ALT="$ E_t$">|; 

$key = q/displaystyleY_{l0}(theta)=sqrt{frac{2,l+1}{4pi}},P_l(costheta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3300.png"
 ALT="$\displaystyle Y_{l0}(\theta) = \sqrt{\frac{2 l+1}{4\pi} }  P_l(\cos\theta).$">|; 

$key = q/displaystylefrac{partial,c,B_x}{partialz};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2234.png"
 ALT="$\displaystyle \frac{\partial  c  B_x}{\partial z}$">|; 

$key = q/q(mathaccentV{hat}05E{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$ q(\mathaccentV {hat}05E{z})$">|; 

$key = q/displaystylew(6)=-{rmi},(A+t,B),(hat{z},0)_s-{rmi},(B+u,[A+t,B]),(0,hat{z})_d.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="337" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2511.png"
 ALT="$\displaystyle w(6) =-{\rm i} ( A+t B) (\hat{z},0)_s -{\rm i} (B+ u [A+t B]) (0,\hat{z})_d.$">|; 

$key = q/arightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="$ a\rightarrow\infty$">|; 

$key = q/w=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$ w=0$">|; 

$key = q/displaystylesigma_m={bfe}_rcdot{bfM}=M_0costheta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1501.png"
 ALT="$\displaystyle \sigma_m = {\bf e}_r\cdot{\bf M} = M_0 \cos\theta,$">|; 

$key = q/varphi';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="$ \varphi'$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),psi=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2817.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2})  \psi = 0,$">|; 

$key = q/OA;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2541.png"
 ALT="$ OA$">|; 

$key = q/displaystyleint_Vfrac{epsilon_0}{2},E^{,2},frac{depsilon}{drho_m},rho_m,nablacdo2},nabla!left(E^{,2},frac{depsilon}{drho_m},rho_mright)cdot{bfu},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1227.png"
 ALT="$\displaystyle \int_V\frac{\epsilon_0}{2} E^{ 2} \frac{d\epsilon}{d\rho_m}  ...
...bla\!\left(E^{ 2}  \frac{d\epsilon}{d\rho_m} \rho_m\right)\cdot {\bf u} dV.$">|; 

$key = q/displaystyleds^{,2}=g_{ij},dx^{,i},dx^{,j},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3586.png"
 ALT="$\displaystyle ds^{ 2} = g_{ij}  dx^{ i}  dx^{ j},$">|; 

$key = q/k_g=sqrt{k^{,2}-k_s^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2881.png"
 ALT="$ k_g=\sqrt{k^{ 2}-k_s^{ 2}}$">|; 

$key = q/displaystylet_2=frac{x}{v_g(2pislashtau)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1973.png"
 ALT="$\displaystyle t_2 = \frac{x}{v_g(2\pi/\tau)},$">|; 

$key = q/displaystyle{rme}^{,{rmi},{bfk}cdot{bfr}}=sum_{l=0,infty}{rmi}^lsqrt{4pi,(2,l+1)},j_l(k,r),Y_{l0}(gamma),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3299.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} {\bf k}\cdot{\bf r}}=\sum_{l=0,\infty}{\rm i}^l \sqrt{4\pi (2 l+1)} j_l(k r) Y_{l0}(\gamma),$">|; 

$key = q/{bfH}={bfB}slashmu_0-{bfM};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1597.png"
 ALT="$ {\bf H}={\bf B}/\mu_0-{\bf M}$">|; 

$key = q/epsilon^{,alphabetagammadelta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3761.png"
 ALT="$ \epsilon^{ \alpha\beta\gamma\delta}$">|; 

$key = q/displaystyle{bfp}=q,{bfd},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="$\displaystyle {\bf p} = q {\bf d},$">|; 

$key = q/sigma({bfr}'),dS';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$ \sigma({\bf r}') dS'$">|; 

$key = q/RsimR_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$ R\sim R_0$">|; 

$key = q/y_l(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3019.png"
 ALT="$ y_l(r)$">|; 

$key = q/displaystyleR(r)=I_m(k_n,r).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img942.png"
 ALT="$\displaystyle R(r) = I_m(k_n r).$">|; 

$key = q/G_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2685.png"
 ALT="$ G_r$">|; 

$key = q/Q_{11}+Q_{22}+Q_{33}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="$ Q_{11}+Q_{22}+Q_{33}=0$">|; 

$key = q/displaystylefrac{4pi,epsilon_0}{e},{bfE}=frac{nablas}{s^{,2}}-frac{partial}{partialt}frac{bfu}{s,c^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4006.png"
 ALT="$\displaystyle \frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{\nabla s}{s^{ 2}} - \frac{\partial} {\partial t} \frac{\bf u}{s  c^{ 2}},$">|; 

$key = q/z<z_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2269.png"
 ALT="$ z&lt;z_0$">|; 

$key = q/displaystyleomega_0=frac{{mitOmega}}{cos^2alpha},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4217.png"
 ALT="$\displaystyle \omega_0 = \frac{{\mit\Omega}}{\cos^2\alpha},
$">|; 

$key = q/|p_mu^{,mu'}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3759.png"
 ALT="$ \vert p_\mu^{ \mu'}\vert$">|; 

$key = q/{bfj}({bfr}),{rme}^{-{rmi},omega,t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3189.png"
 ALT="$ {\bf j}({\bf r})  {\rm e}^{-{\rm i} \omega  t}$">|; 

$key = q/displaystylefrac{P}{dEslashdt}=frac{e^{,2}}{6pi,epsilon_0,m_0^{,2},c^{,3}}frac{1ac{e^{,2}}{6pi,epsilon_0,m_0,c^{,2}}frac{1}{m_0,c^{,2}}frac{dE}{dx},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="337" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4080.png"
 ALT="$\displaystyle \frac{P}{dE/dt} = \frac{e^{ 2}}{6\pi \epsilon_0  m_0^{ 2}  c...
...^{ 2}}{6\pi \epsilon_0  m_0  c^{ 2}}\frac{1}{m_0  c^{ 2}} \frac{dE}{dx},$">|; 

$key = q/displaystyle{bfu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4114.png"
 ALT="$\displaystyle {\bf u}$">|; 

$key = q/displaystyle(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2-c^2,(t_2-t_1)^2=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3612.png"
 ALT="$\displaystyle (x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2 -c^2 (t_2-t_1)^2 =$">|; 

$key = q/-2.2times10^{-5};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1449.png"
 ALT="$ -2.2\times 10^{-5}$">|; 

$key = q/displaystylefrac{dsigma_{rmsc}}{d{mitOmega}}=frac{pi}{2,k^{,2}}left|sum_lsqrt{2,_{l,pm1}pm{rmi},beta_pm(l),{bfn}times{bfX}_{l,pm1}right]right|^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3348.png"
 ALT="$\displaystyle \frac{d\sigma_{\rm sc}}{d{\mit \Omega}} =\frac{\pi}{2 k^{ 2}} \...
...rm i} \beta_\pm(l)  {\bf n}\times {\bf X}_{l,\pm 1}\right] \right\vert^{ 2}.$">|; 

$key = q/displaystyle=k,mu_0,c,{bfL}cdotleft({bfM}+frac{nablatimes{bfj}}{k^{,2}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3209.png"
 ALT="$\displaystyle =k \mu_0  c  {\bf L}\cdot\left({\bf M} + \frac{\nabla\times{\bf j}}{k^{ 2}}\right).$">|; 

$key = q/displaystylephi({bfr})=langlephirangle_S-frac{1}{epsilon_0}int_VG_N({bfr},{bfr}'),dV'-int_SG_N({bfr},{bfr}'),frac{partialphi({bfr}')}{partialn'}dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="$\displaystyle \phi({\bf r}) = \langle\phi\rangle_S -\frac{1}{\epsilon_0} \int_V...
... -\int_S G_N({\bf r},{\bf r}') \frac{\partial\phi({\bf r}')}{\partial n'}d S',$">|; 

$key = q/displaystyleA,kleft[K_m'(k,r'),I_m(k,r')-K_m(k,r'),I_m'(k,r')right]=frac{1}{r'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img976.png"
 ALT="$\displaystyle A k\left[K_m'(k r') I_m(k r')-K_m(k r') I_m'(k r')\right] = \frac{1}{r'},$">|; 

$key = q/displaystylelim_{xrightarrow0},x^{,n+1},{rme}^{,x},(-1)^{n+1},(n+1)!int_x^inftyfrac{{rme}^{-t}}{t^{,n+2}},dt=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2415.png"
 ALT="$\displaystyle \lim_{x\rightarrow 0} x^{ n+1} {\rm e}^{ x}  (-1)^{n+1} (n+1)!\int_x^\infty \frac{{\rm e}^{-t}}{t^{ n+2}}  dt = 0.$">|; 

$key = q/displaystylec=frac{1}{sqrt{epsilon_0,mu_0}}=2.988times10^8,{rmm,s^{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} = 2.988\times 10^8 {\rm m s^{-1}}$">|; 

$key = q/displaystyle={bfL},L^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3065.png"
 ALT="$\displaystyle = {\bf L}  L^2,$">|; 

$key = q/dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$ dV$">|; 

$key = q/displaystyleepsilon^{,ijk},epsilon_{iab};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3764.png"
 ALT="$\displaystyle \epsilon^{ ijk}  \epsilon_{iab}$">|; 

$key = q/r^{,-(l+1)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1161.png"
 ALT="$ r^{ -(l+1)}$">|; 

$key = q/displaystylef(x,t)={rme}^{-{rmIm}(k_tau),x}sinleft[2pi,frac{t}{tau}-{rmRe}(k_tau),xright]+B_4+B_5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1834.png"
 ALT="$\displaystyle f(x,t) = {\rm e}^{-{\rm Im}(k_\tau)  x} \sin\left[2\pi \frac{t}{\tau} -{\rm Re}(k_\tau) x\right]+ B_4 + B_5$">|; 

$key = q/r=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="$ r=0$">|; 

$key = q/displaystylesigma_{rmt}=-frac{pi}{k^{,2}}sum_l(2,l+1),{rmRe},[alpha_pm(l)+beta_pm(l)].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3359.png"
 ALT="$\displaystyle \sigma_{\rm t} = -\frac{\pi}{k^{ 2}} \sum_l (2 l+1)  {\rm Re} [\alpha_\pm(l) +\beta_\pm(l)].$">|; 

$key = q/r=-c,t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3878.png"
 ALT="$ r=-c t$">|; 

$key = q/displaystyleB=B_0+2,B_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1543.png"
 ALT="$\displaystyle B = B_0 + 2  B_s$">|; 

$key = q/displaystyle=J_0(k_sr),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2980.png"
 ALT="$\displaystyle = J_0(k_s r),$">|; 

$key = q/displaystylephi(a,theta,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$\displaystyle \phi(a,\theta,z)$">|; 

$key = q/displaystyle=int_r^inftyointfrac{1}{r'^{,l+1}},rho(r',theta,varphi),Y_{l,m}(theta,varphi),r'^{,2},d{mitOmega},dr',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$\displaystyle = \int_r^\infty \oint\frac{1}{r'^{ l+1}} \rho(r',\theta,\varphi) Y_{l,m}(\theta,\varphi) r'^{ 2} d{\mit\Omega} dr',$">|; 

$key = q/displaystyle=sqrt{frac{2}{pi,rho}},{rme}^{+{rmi},[rho-(n+1slash2),pislash2]}sum_{m=0,1,2,cdots}frac{(n,m)}{(-2,{rmi},rho)^{,m}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle = \sqrt{\frac{2}{\pi  \rho}}  {\rm e}^{+{\rm i} [\rho-(n+1/2) \pi/2]} \sum_{m=0, 1, 2, \cdots}\frac{(n,m)}{(-2 {\rm i} \rho)^{ m}},$">|; 

$key = q/displaystyle{bfk}_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2037.png"
 ALT="$\displaystyle {\bf k}_t$">|; 

$key = q/omegasimeqomega_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1639.png"
 ALT="$ \omega\simeq \omega_i$">|; 

$key = q/omega_{1-};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1824.png"
 ALT="$ \omega_{1-}$">|; 

$key = q/displaystyleA_l=B_l=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1509.png"
 ALT="$\displaystyle A_l = B_l = 0$">|; 

$key = q/phi({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$ \phi({\bf r})$">|; 

$key = q/Rrightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$ R\rightarrow\infty$">|; 

$key = q/displaystylealpha=left(frac{epsilon_0,omega}{sigma}right)^{1slash2}ll1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2198.png"
 ALT="$\displaystyle \alpha =\left(\frac{\epsilon_0 \omega}{\sigma}\right)^{1/2}\ll 1.$">|; 

$key = q/displaystyle=frac{1}{2pi}ointfrac{rho(r',theta',z')}{epsilon_0},{rme}^{-{rmi},m,theta'}dtheta',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1024.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\oint \frac{\rho(r',\theta',z')}{\epsilon_0} {\rm e}^{-{\rm i} m \theta'}d\theta',$">|; 

$key = q/displaystyle=c,A_3'=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3874.png"
 ALT="$\displaystyle = c A_3' = 0,$">|; 

$key = q/J_{l+1slash2}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3015.png"
 ALT="$ J_{l+1/2}(z)$">|; 

$key = q/displaystylephi=left{{array}{lll}qslash(4pi,epsilon_0,r)&mbox{hspace{0.5cm}}&r<a[0.5ex]0&&r>a{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="$\displaystyle \phi = \left\{ \begin{array}{lll} q/(4\pi \epsilon_0 r)&amp;\mbox{\hspace{0.5cm}}&amp; r&lt;a\ [0.5ex] 0&amp;&amp;r&gt;a \end{array}\right.,$">|; 

$key = q/{mitGamma}(n+1)=n!;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2440.png"
 ALT="$ {\mit\Gamma}(n+1)=n!$">|; 

$key = q/b>R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$ b&gt;R$">|; 

$key = q/displaystylesinphi_r,psi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2147.png"
 ALT="$\displaystyle \sin\phi_r \psi_r$">|; 

$key = q/displaystyle=A,K_0(k_t,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2945.png"
 ALT="$\displaystyle = A  K_0(k_t  r),$">|; 

$key = q/displaystyleB_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1347.png"
 ALT="$\displaystyle B_r$">|; 

$key = q/displaystyleK_m(p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img965.png"
 ALT="$\displaystyle K_m(p)$">|; 

$key = q/displaystyleB^{,i}=g^{,ij},B_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3597.png"
 ALT="$\displaystyle B^{ i} = g^{ ij}  B_j.$">|; 

$key = q/{calO}(1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2462.png"
 ALT="$ {\cal O}(1)$">|; 

$key = q/psi(r),{rme}^{,{rmi},k_g,z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2927.png"
 ALT="$ \psi(r)  
{\rm e}^{ {\rm i} k_g  z}$">|; 

$key = q/displaystylefrac{dM_x}{dr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3167.png"
 ALT="$\displaystyle \frac{d M_x}{dr}$">|; 

$key = q/ineqj;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3543.png"
 ALT="$ i\neq j$">|; 

$key = q/displaystyleE(omega)=frac{1}{sqrt{2pi}}int_0^inftyE_0,{rme}^{-omega_0,tslash2,Q},{rme}^{,{rmi},(omega-omega_0-{mitDelta}omega),t},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2807.png"
 ALT="$\displaystyle E(\omega) = \frac{1}{\sqrt{2\pi}}\int_0^\infty E_0  {\rm e}^{-\o...
...0  t/2 Q}  {\rm e}^{ {\rm i} (\omega-\omega_0-{\mit\Delta}\omega) t} dt.$">|; 

$key = q/displaystylea_E(l,0)=frac{mu_0,c,k}{2pi}left[frac{4pi,(2,l+1)}{l,(l+1)}right]^{1right]+rj_l(k,r)left(frac{d^{,2}I}{dr^{,2}}+k^{,2},Iright)right},dr.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="545" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3257.png"
 ALT="$\displaystyle a_E(l,0) =\frac{\mu_0  c k}{2\pi} \left[\frac{4\pi  (2 l+1)} ...
... +r j_l(k r) \left(\frac{d^{ 2} I}{dr^{ 2}} + k^{ 2} I\right)\right\} dr.$">|; 

$key = q/theta=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="$ \theta=0$">|; 

$key = q/y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ y$">|; 

$key = q/theta_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2030.png"
 ALT="$ \theta_i$">|; 

$key = q/displaystylenablacdot({bfE}times{bfB})equiv{bfB}cdotnablatimes{bfE}-{bfE}cdotnablatimes{bfB},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$\displaystyle \nabla\cdot({\bf E}\times{\bf B}) \equiv {\bf B}\cdot\nabla\times{\bf E} - {\bf E} \cdot \nabla\times{\bf B},$">|; 

$key = q/xi=pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2401.png"
 ALT="$ \xi=\pi/2$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftyrho_m(r',z'),{rme}^{-{rmi},k,z'},dz',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img990.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^\infty \rho_m(r',z') {\rm e}^{-{\rm i} k z'} dz',$">|; 

$key = q/displaystyleW=frac{4pi}{3,epsilon_0},rho^{,2}int_0^ar^{,4},dr=frac{4pi}{15,epsilon_0},rho^{,2},a^{,5}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="$\displaystyle W = \frac{4\pi}{3 \epsilon_0}  \rho^{ 2} \int_0^a r^{ 4} dr = \frac{4\pi}{15 \epsilon_0}  \rho^{ 2}  a^{ 5}.$">|; 

$key = q/displaystyleG_{i4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3833.png"
 ALT="$\displaystyle G_{i4}$">|; 

$key = q/rho({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="$ \rho({\bf r})$">|; 

$key = q/{bfr}_{12}={bfr}_2-{bfr}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1304.png"
 ALT="$ {\bf r}_{12} = {\bf r}_2-{\bf r}_1$">|; 

$key = q/displaystyle{bfj}({bfr}')=I,frac{delta(r'-a)}{a},delta(costheta'),{bfe}_{varphi'r'-a)}{a},delta(costheta'),(-sinvarphi',{bfe}_x+cosvarphi',{bfe}_y).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="489" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1322.png"
 ALT="$\displaystyle {\bf j}({\bf r}') = I \frac{\delta(r'-a)}{a} \delta(\cos\theta'...
...)}{a} \delta(\cos\theta') (-\sin\varphi' {\bf e}_x+\cos\varphi' {\bf e}_y).$">|; 

$key = q/epsilon(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1685.png"
 ALT="$ \epsilon(\omega)$">|; 

$key = q/sigma_b={bfP}cdot{bfe}_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1186.png"
 ALT="$ \sigma_b={\bf P} \cdot {\bf e}_r$">|; 

$key = q/{bfD}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1200.png"
 ALT="$ {\bf D}({\bf r})$">|; 

$key = q/{bfM}=M_0,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1499.png"
 ALT="$ {\bf M}= M_0  {\bf e}_z$">|; 

$key = q/beta=vslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3646.png"
 ALT="$ \beta = v/c$">|; 

$key = q/displaystyle=c,A_2'=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3872.png"
 ALT="$\displaystyle = c A_2' = 0,$">|; 

$key = q/displaystyleboxempty,c,{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3727.png"
 ALT="$\displaystyle \boxempty  c {\bf A}$">|; 

$key = q/dx'=gamma,(dx-v,dt);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3497.png"
 ALT="$ dx' = \gamma (dx-v dt)$">|; 

$key = q/displaystyle=a,(cosphi,,sinphi,,0),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4112.png"
 ALT="$\displaystyle = a (\cos\phi,  \sin\phi,  0),$">|; 

$key = q/-J_1(k_sslasha)slashk_s,J_0(k_s,a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2961.png"
 ALT="$ -J_1(k_s/a)/k_s  J_0(k_s  a)$">|; 

$key = q/displaystyletantheta=-frac{1}{2},tantheta';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="$\displaystyle \tan\theta=-\frac{1}{2} \tan\theta'
$">|; 

$key = q/{bfE}=-nablaphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1105.png"
 ALT="$ {\bf E} =-\nabla \phi$">|; 

$key = q/{rmi},(k,x-omega,t)=-{rmi},omega,s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1815.png"
 ALT="$ {\rm i} (k x -\omega  t) = -{\rm i} \omega  s$">|; 

$key = q/displaystylek_g=frac{sqrt{omega^{,2}-omega_c^{,2}}}{c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2882.png"
 ALT="$\displaystyle k_g = \frac{\sqrt{\omega^{ 2}-\omega_c^{ 2}}}{c},$">|; 

$key = q/displaystyle=frac{psi_t,sinhtheta_t}{v_2},{rme}^{-n_2,k_0,sinhtheta_t,z},sin(omega,t-n_1,k_0,sintheta_i,x+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2142.png"
 ALT="$\displaystyle =\frac{\psi_t \sinh\theta_t}{v_2} {\rm e}^{-n_2 k_0 \sinh\theta_t z} \sin(\omega t-n_1 k_0 \sin\theta_i x+\phi_t),$">|; 

$key = q/displaystyle=frac{mu_0}{4pi},m,frac{2,costheta}{r^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1370.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} m \frac{2 \cos\theta}{r^{ 3}},$">|; 

$key = q/displaystyle=beta^{,-1},sinphi_t,psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2172.png"
 ALT="$\displaystyle =\beta^{ -1} \sin\phi_t \psi_t,$">|; 

$key = q/displaystylef_nu=epsilon_0left[partial_mu(F^{,musigma},F_{nusigma})-F^{,musigma},partial_muF_{nusigma}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3949.png"
 ALT="$\displaystyle f_\nu = \epsilon_0 \left[\partial_\mu(F^{ \mu\sigma} F_{\nu\sigma}) -F^{ \mu\sigma}  \partial_\mu F_{\nu\sigma}\right].$">|; 

$key = q/displaystyle-frac{(l+1),B_l}{a^{,l+2}}-l,A_l,a^{,l-1}=-M_0,delta_{l1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1507.png"
 ALT="$\displaystyle - \frac{(l+1) B_l}{a^{ l+2}} - l  A_l  a^{ l-1} = - M_0  \delta_{l1}$">|; 

$key = q/dsproptodtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3700.png"
 ALT="$ ds\propto d\tau$">|; 

$key = q/displaystylesimeqfrac{e}{4pi,epsilon_0,c^{,3}}frac{dot{bfu}times{bfr}}{r^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4033.png"
 ALT="$\displaystyle \simeq \frac{e}{4\pi \epsilon_0  c^{ 3}} \frac{\dot{\bf u} \times{\bf r}}{r^{ 2}}.$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$ a$">|; 

$key = q/displaystyle({bfE}_2-{bfE}_1)cdot{bfn}=frac{sigma}{epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="$\displaystyle ({\bf E}_2-{\bf E}_1)\cdot {\bf n} = \frac{\sigma}{\epsilon_0},$">|; 

$key = q/{bfE}rightarrow-nablaphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3134.png"
 ALT="$ {\bf E}\rightarrow
-\nabla\phi$">|; 

$key = q/D_xrightarrowH_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2098.png"
 ALT="$ D_x\rightarrow H_x$">|; 

$key = q/delta{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1205.png"
 ALT="$ \delta{\bf r}$">|; 

$key = q/displaystyle=J_0(k_s,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2940.png"
 ALT="$\displaystyle = J_0(k_s  r),$">|; 

$key = q/P=Q=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4185.png"
 ALT="$ P=Q=0$">|; 

$key = q/displaystylefrac{dchi}{dl}=frac{kappa(omega),N,B_parallel}{n(omega)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1756.png"
 ALT="$\displaystyle \frac{d\chi}{dl} = \frac{\kappa(\omega) N  B_\parallel} {n(\omega)},$">|; 

$key = q/E_y(z_0)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2279.png"
 ALT="$ E_y(z_0)=0$">|; 

$key = q/N=N(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2221.png"
 ALT="$ N=N(z)$">|; 

$key = q/displaystylefrac{d^{,2}R}{dp^{,2}}+frac{1}{p},frac{dR}{dp}-left(1+frac{m^{,2}}{p^{,2}}right)R=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img936.png"
 ALT="$\displaystyle \frac{d^{ 2} R}{dp^{ 2}} + \frac{1}{p} \frac{dR}{dp}-\left(1+\frac{m^{ 2}}{p^{ 2}}\right) R = 0.$">|; 

$key = q/displaystyle-k_s^{,2}int_Vf^{,2},dV+int_V(nabla_sf)^{,2},dV=int_Sf,nablafcdotd{bfS},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2841.png"
 ALT="$\displaystyle -k_s^{ 2} \int_V f^{ 2}  dV + \int_V (\nabla_s f)^{ 2} dV = \int_S f \nabla f \cdot d{\bf S},$">|; 

$key = q/displaystylefrac{1}{r}frac{partial^{,2}(r,phi)}{partialr^{,2}}+frac{1}{r^{,2}sin{partialtheta}!left(sintheta,frac{partialphi}{partialtheta}right)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1156.png"
 ALT="$\displaystyle \frac{1}{r}\frac{\partial^{ 2} (r \phi)}{\partial r^{ 2}} +\fr...
...ial\theta}\!\left(\sin\theta  \frac{\partial\phi}{\partial\theta} \right) = 0.$">|; 

$key = q/displaystyle~~~~+frac{psi_r}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z+phi_r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2165.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\frac{\psi_r}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z+\phi_r),$">|; 

$key = q/mu_0,H_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1525.png"
 ALT="$ \mu_0  H_c$">|; 

$key = q/displaystyle=left(frac{3}{8pi}right)^{1slash2}intrho({bfr}),r,sintheta,{rme}^{+{rmi},varphi},dV=left(frac{3}{8pi}right)^{1slash2},(p_x+{rmi},p_y),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="$\displaystyle =\left(\frac{3}{8\pi}\right)^{1/2}\int \rho({\bf r}) r \sin\the...
...+{\rm i} \varphi} dV = \left(\frac{3}{8\pi}\right)^{1/2} (p_x+{\rm i} p_y),$">|; 

$key = q/displaystylesimeqfrac{{rme}^{,{rmi},(k,r-omega,t)}}{k,r}sum_{l,m}(-{rmi})^{,l+1}left[a_E(l,m),{bfX}_{lm}+a_M(l,m),{bfn}times{bfX}_{lm}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3273.png"
 ALT="$\displaystyle \simeq \frac{{\rm e}^{ {\rm i} (k r -\omega  t)}}{k r} \sum_...
...+1} \left[ a_E(l,m) {\bf X}_{lm}+ a_M(l,m)  {\bf n}\times{\bf X}_{lm}\right],$">|; 

$key = q/nabla'^{,2}G_D({bfr},{bfr}')=delta({bfr}-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="$ \nabla'^{ 2}G_D({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}')$">|; 

$key = q/G_2({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="$ G_2({\bf r},{\bf r}')$">|; 

$key = q/displaystyletheta_0=cos^{-1}(uslashc).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4133.png"
 ALT="$\displaystyle \theta_0 = \cos^{-1}(u/c).$">|; 

$key = q/displaystyleu_omega({bfr})=intv_omega({bfr}'),G_omega({bfr},{bfr}'),dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle u_\omega({\bf r}) = \int v_\omega({\bf r}') G_\omega ({\bf r}, {\bf r}') dV'.$">|; 

$key = q/phi_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2197.png"
 ALT="$ \phi_t$">|; 

$key = q/displaystylephi(z,r)=frac{q}{pi,epsilon_0,L}sum_{n=1,infty}sinleft(frac{n,pi}{L}_nright)sinleft(frac{n,pi}{L},zright),K_0left(frac{n,pi}{L},rright),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1048.png"
 ALT="$\displaystyle \phi(z,r)= \frac{q}{\pi \epsilon_0 L}\sum_{n=1,\infty}\sin\left...
...ght)\sin\left(\frac{n \pi}{L} z\right) K_0\left(\frac{n \pi}{L} r\right),
$">|; 

$key = q/z=b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1130.png"
 ALT="$ z=b$">|; 

$key = q/-{rmi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2525.png"
 ALT="$ -{\rm i}$">|; 

$key = q/-J_1(k_sslasha)slashk_stmspace+thinmuskip{.1667em}J_0(k_stmspace+thinmuskip{.1667em}a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$ -J_1(k_s/a)/k_s \tmspace +\thinmuskip {.1667em}J_0(k_s\tmspace +\thinmuskip {.1667em} a)$">|; 

$key = q/displaystyleT_{ij}=-G_{ij}=epsilon_0,(E_i,E_j-E^{,2},delta_{ij}slash2)+(B_i,B_j-B^{,2},delta_{ij}slash2)slashmu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$\displaystyle T_{ij} = - G_{ij} = \epsilon_0 (E_i E_j-E^{ 2} \delta_{ij}/2) + (B_i B_j-B^{ 2} \delta_{ij}/2)/ \mu_0$">|; 

$key = q/{bfj}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$ {\bf j}({\bf r},t)$">|; 

$key = q/displaystylefrac{1}{(1-2,x,t+t^{,2})^{1slash2}}=sum_{l=0,infty}P_l(x),t^{,l},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="$\displaystyle \frac{1}{(1-2 x t+t^{ 2})^{1/2}} = \sum_{l=0,\infty} P_l(x) t^{ l},$">|; 

$key = q/displaystyle|f|_{rmbrillouin}simleft(frac{omega_p}{xi}right)^{1slash3}ll1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1967.png"
 ALT="$\displaystyle \vert f\vert _{\rm brillouin} \sim \left(\frac{\omega_p}{\xi}\right)^{1/3} \ll 1,$">|; 

$key = q/|{bfd}|rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$ \vert{\bf d}\vert\rightarrow 0$">|; 

$key = q/displaystyle{mitPhi}_m(z');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1027.png"
 ALT="$\displaystyle {\mit\Phi}_m(z')$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{q^2,langleddot{s}^{,2}rangle}{16pi^2,epsilon_0,c^3},sin^2theta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2719.png"
 ALT="$\displaystyle \frac{d P}{d {\mit \Omega}}=\frac{q^2 \langle \ddot{s}^{ 2}\rangle} {16\pi^2  \epsilon_0  c^3} \sin^2\theta,$">|; 

$key = q/J_1(-z)=-J_1(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1873.png"
 ALT="$ J_1(-z) = - J_1(z)$">|; 

$key = q/displaystylelangleurangle=frac{epsilon_0,c,E_0^{,2}}{2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2723.png"
 ALT="$\displaystyle \langle u\rangle = \frac{\epsilon_0  c E_0^{ 2}}{2}.$">|; 

$key = q/displaystyleu_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3486.png"
 ALT="$\displaystyle u_2$">|; 

$key = q/displaystyle[H_z]_{z=0_+}^{z=0_-};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2113.png"
 ALT="$\displaystyle [H_z]_{z=0_+}^{z=0_-}$">|; 

$key = q/varphi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="$ \varphi=0$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3074.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2})  {\bf E}$">|; 

$key = q/displaystyleP=1.2188,frac{mu_0,c,I^{,2}}{4pi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2648.png"
 ALT="$\displaystyle P= 1.2188  \frac{\mu_0  c I^{ 2}}{4\pi}.$">|; 

$key = q/displaystyle-A_mu,A^{,mu}=gamma^{,2}left(frac{dgamma}{dt},{bfu}+gamma,dot{bfu}right)^2-gamma^{,2},c^{,2}left(frac{dgamma}{dt}right)^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4073.png"
 ALT="$\displaystyle -A_\mu  A^{ \mu} = \gamma^{ 2}\left(\frac{d\gamma}{dt} {\bf u...
...\dot{\bf u}\right)^2 - \gamma^{ 2}  c^{ 2}\left(\frac{d\gamma}{dt}\right)^2,$">|; 

$key = q/displaystyle=frac{3sqrt{21}}{8pi},sin^2theta,(5cos^2theta-1).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3283.png"
 ALT="$\displaystyle =\frac{3\sqrt{21}} {8\pi} \sin^2\theta (5\cos^2\theta-1).$">|; 

$key = q/displaystyle.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="8" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle .$">|; 

$key = q/B_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3014.png"
 ALT="$ B_{lm}$">|; 

$key = q/displaystyle(x_2'-x_1')^2+(y_2'-y_1')^2+(z_2'-z_1')^2-c^2,(t_2'-t_1')^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3613.png"
 ALT="$\displaystyle (x_2'-x_1')^2 + (y_2'-y_1')^2 + (z_2'-z_1')^2 -c^2 (t_2'-t_1')^2,$">|; 

$key = q/c,B_{ij}rightarrowE_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3839.png"
 ALT="$ c B_{ij} \rightarrow E_{ij}$">|; 

$key = q/E_rsimeq-E_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2213.png"
 ALT="$ E_r\simeq -E_i$">|; 

$key = q/G_D({bfr},{bfr}')=G_D({bfr}'',{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="$ G_D({\bf r},{\bf r}')=G_D({\bf r}'',{\bf r}')=0$">|; 

$key = q/u(z)<v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2364.png"
 ALT="$ u(z)&lt;v$">|; 

$key = q/sigma({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="$ \sigma({\bf r})$">|; 

$key = q/displaystyleu_3';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3495.png"
 ALT="$\displaystyle u_3'$">|; 

$key = q/drightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="$ d\rightarrow 0$">|; 

$key = q/displaystyler'=r,gamma,left(-frac{c,t}{r}+frac{v,x}{c,r}right)=r,gammaleft(1+frac{v}{c}costhetaright),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3749.png"
 ALT="$\displaystyle r' = r \gamma \left(-\frac{c t}{r} + \frac{v x}{c r}\right) = r \gamma \left(1 + \frac{v}{c} \cos\theta\right),$">|; 

$key = q/displaystylex;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3476.png"
 ALT="$\displaystyle x$">|; 

$key = q/displaystyleQ_{lm}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3235.png"
 ALT="$\displaystyle Q_{lm}'$">|; 

$key = q/{bfj}=e,n,{bfu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3941.png"
 ALT="$ {\bf j} = e  n  {\bf u}$">|; 

$key = q/v_g(2pislashtau);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1974.png"
 ALT="$ v_g(2\pi/\tau)$">|; 

$key = q/displaystyle=frac{rmi}{k}nablatimesc,{bfB}_{lm}^{(E)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3106.png"
 ALT="$\displaystyle = \frac{\rm i}{k} \nabla\times c {\bf B}_{lm}^{(E)}.$">|; 

$key = q/';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2430.png"
 ALT="$ '$">|; 

$key = q/displaystyleR=-{rmi},expleft(2,{rmi},kint_0^{z_0}!q(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2315.png"
 ALT="$\displaystyle R = -{\rm i} \exp\left(2 {\rm i} k\int_0^{z_0} \!q(z')  dz'\right),$">|; 

$key = q/u(z_0)=v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2363.png"
 ALT="$ u(z_0) = v$">|; 

$key = q/{bfX}_{lm}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3313.png"
 ALT="$ {\bf X}_{lm}^{ \ast}$">|; 

$key = q/|z|rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1140.png"
 ALT="$ \vert z\vert\rightarrow \infty$">|; 

$key = q/f_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1912.png"
 ALT="$ f_s$">|; 

$key = q/displaystyle=-v^{,2},frac{partialD_y}{partialx},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2094.png"
 ALT="$\displaystyle =-v^{ 2} \frac{\partial D_y}{\partial x},$">|; 

$key = q/x'=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3460.png"
 ALT="$ x'=0$">|; 

$key = q/displaystylepsi(r)=A,K_0(k_t,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2926.png"
 ALT="$\displaystyle \psi (r)= A K_0(k_t  r)$">|; 

$key = q/displaystyleQ=2pi,frac{mbox{energystoredincavity}}{mbox{energylostpercycletowalls}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2800.png"
 ALT="$\displaystyle Q = 2\pi \frac{\mbox{energy stored in cavity}}{\mbox{ energy lost per cycle to walls}}.$">|; 

$key = q/Nsim3times10^{11},{rmm}^{-3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2222.png"
 ALT="$ N\sim 3\times 10^{11} {\rm m}^{-3}$">|; 

$key = q/displaystylefrac{partialU}{partialt}+nablacdot{bfu}=-{bfE}cdot{bfj},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$\displaystyle \frac{\partial U}{\partial t} + \nabla\cdot{\bf u} = -{\bf E}\cdot {\bf j},$">|; 

$key = q/N_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1063.png"
 ALT="$ N_i$">|; 

$key = q/displaystyleH_theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2933.png"
 ALT="$\displaystyle H_\theta$">|; 

$key = q/{bfR}={bfr-r}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$ {\bf R} = {\bf r - r}'$">|; 

$key = q/displaystyle=cosphi_t,psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2146.png"
 ALT="$\displaystyle = \cos\phi_t \psi_t,$">|; 

$key = q/{bfF}({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="$ {\bf F}({\bf r},{\bf r}')$">|; 

$key = q/A^mu=(dot{bfu},,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4072.png"
 ALT="$ A^\mu =
(\dot{\bf u},  0)$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0,I}{4pi}frac{2}{k,r}frac{cos(picosthetaslash2)}{sin^2theta},{rme}^{,{rmi},(k,r-omega,t)},{bfe}_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2691.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = \frac{\mu_0 I}{4\pi} \frac{2 }{k r} \frac{\c...
...s\theta/2)}{\sin^2 \theta} {\rm e}^{ {\rm i} ( k r-\omega  t)} {\bf e}_z,$">|; 

$key = q/displaystyleint_Vleft[G_D({bfr},{bfr}'),delta({bfr}''-{bfr}')-G_D({bfr}'',{bfr}'),delta({bfr}-{bfr}')right]dV'=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="$\displaystyle \int_V\left[G_D({\bf r},{\bf r}') \delta({\bf r}''-{\bf r}')-G_D({\bf r}'',{\bf r}') \delta({\bf r}-{\bf r}')\right]dV'=0,$">|; 

$key = q/omega=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1945.png"
 ALT="$ \omega=0$">|; 

$key = q/r=a+dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="$ r=a+d/2$">|; 

$key = q/{mitDelta}varphisimeqlambdaslashN,{mitDelta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2711.png"
 ALT="$ {\mit \Delta}\varphi\simeq \lambda/N 
{\mit\Delta}$">|; 

$key = q/rho=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="$ \rho=0$">|; 

$key = q/displaystylefrac{4pi}{mu_0,e},{bfB}=frac{{bfu}times{bfr}}{s^{,3}}left(1-frac{u^{imesleft[left({bfr}-frac{r,{bfu}}{c}right)timesdot{bfu}right]right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4014.png"
 ALT="$\displaystyle \frac{4\pi}{\mu_0 e}  {\bf B} = \frac{{\bf u}\times{\bf r}}{s^{...
...t[ \left({\bf r} - \frac{r {\bf u}}{c}\right)\times\dot{\bf u}\right] \right).$">|; 

$key = q/displaystylenabla^{,2}{bfA}=-mu_0,{bfj}_m,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1493.png"
 ALT="$\displaystyle \nabla^{ 2}{\bf A} =- \mu_0  {\bf j}_m,$">|; 

$key = q/displaystyleI_m(p)=frac{1}{pi}int_0^pi{rme}^{,p,costheta},cos(m,theta),dtheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img937.png"
 ALT="$\displaystyle I_m(p) = \frac{1}{\pi}\int_0^\pi {\rm e}^{ p \cos\theta} \cos(m \theta) d\theta.$">|; 

$key = q/displaystylefrac{epsilon_1,J_1(k_s,a)}{k_s,J_0(k_s,a)}+frac{K_1(k_t,a)}{k_t,K_0(k_t,a)}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2991.png"
 ALT="$\displaystyle \frac{\epsilon_1 J_1(k_s  a)}{k_s J_0(k_s  a)} + \frac{K_1(k_t  a)}{k_t K_0(k_t  a)}= 0.$">|; 

$key = q/displaystylefrac{{mitDelta}E}{m_0,c^{,2}}=frac{4pi}{3}frac{r_0}{a},beta^{,3},gamma^{,4}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4148.png"
 ALT="$\displaystyle \frac{{\mit\Delta} E}{m_0  c^{ 2}} = \frac{4\pi}{3} \frac{r_0}{a}  \beta^{ 3}  \gamma^{ 4}.$">|; 

$key = q/displaystylemu_0,beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1567.png"
 ALT="$\displaystyle \mu_0 \beta$">|; 

$key = q/displaystylesigma_b(theta)=-P,costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1237.png"
 ALT="$\displaystyle \sigma_b(\theta) = -P  \cos\theta$">|; 

$key = q/displaystyle=intr^{,l},Y_{lm}^{,ast},c,rho,dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3234.png"
 ALT="$\displaystyle = \int r^{ l}  Y_{lm}^{ \ast} c \rho dV,$">|; 

$key = q/E_1<E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1182.png"
 ALT="$ E_1&lt;E_0$">|; 

$key = q/displaystylenablatimes{bfH}={bfj}_t+frac{partial{bfD}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1441.png"
 ALT="$\displaystyle \nabla\times{\bf H} = {\bf j}_t + \frac{\partial{\bf D}}{\partial t},$">|; 

$key = q/mu=mu(B);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1539.png"
 ALT="$ \mu=\mu(B)$">|; 

$key = q/displaystyle=E_parallel,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3852.png"
 ALT="$\displaystyle = E_\parallel,$">|; 

$key = q/y=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3453.png"
 ALT="$ y=0$">|; 

$key = q/psi(x,y),{rme}^{,{rmi},k_g,z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2908.png"
 ALT="$ \psi(x,y)  {\rm e}^{ {\rm i}  k_g  z}$">|; 

$key = q/displaystylelanglePrangle=int_{-infty}^{infty}P(x),dx.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1980.png"
 ALT="$\displaystyle \langle P\rangle = \int_{-\infty}^{\infty}P(x) dx.
$">|; 

$key = q/(-q);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="$ (-q)$">|; 

$key = q/displaystyledelta({bfr}-{bfr}')=frac{delta(r-r')}{r^{,2}},delta(varphi-varphi'),delta(costheta-costheta').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3177.png"
 ALT="$\displaystyle \delta({\bf r}-{\bf r}') = \frac{\delta(r-r')}{r^{ 2}}  \delta(\varphi-\varphi')  \delta(\cos\theta-\cos\theta').$">|; 

$key = q/beta_{l,m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="$ \beta_{l,m}$">|; 

$key = q/displaystylefrac{1}{pi}int_0^wv^{-1slash2},(w-v)^{-1slash2},h(v^{,1slash2}),dv=f_0(v^{,1slash2})}!frac{dz}{(w-v)^{1slash2},(v-u)^{1slash2}}right]dv.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2367.png"
 ALT="$\displaystyle \frac{1}{\pi}\int_0^w v^{-1/2}  (w-v)^{-1/2}  h(v^{ 1/2}) dv ...
...left[\int_0^{z_0(v^{ 1/2})} \! \frac{dz}{(w-v)^{1/2}  (v-u)^{1/2}}\right] dv.$">|; 

$key = q/displaystyleG({bfr},{bfr}')=G(|{bfr}-{bfr}'|)=frac{1}{4pi,|{bfr}-{bfr'}|}=frac{1}{4pi,R}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle G({\bf r}, {\bf r}')=G(\vert{\bf r}-{\bf r}'\vert) = \frac{1}{4\pi \vert{\bf r}-{\bf r'}\vert}= \frac{1}{4\pi  R}.$">|; 

$key = q/displaystylef(z)simeqphi(z)sum_{p=0,infty}frac{A_p}{z^{,p}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2407.png"
 ALT="$\displaystyle f(z) \simeq \phi(z) \sum_{p=0,\infty} \frac{A_p}{z^{ p}},$">|; 

$key = q/displaystyle=intrho({bfr}),y,dV=intrho({bfr}),r,sintheta,sinvarphi,dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="$\displaystyle = \int \rho({\bf r}) y dV = \int\rho({\bf r}) r \sin\theta \sin\varphi dV,$">|; 

$key = q/displaystyleQ_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3233.png"
 ALT="$\displaystyle Q_{lm}$">|; 

$key = q/G_3({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="$ G_3({\bf r},{\bf r}')$">|; 

$key = q/g_ill1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1657.png"
 ALT="$ g_i\ll 1$">|; 

$key = q/displaystyle=-frac{mu_0}{4pi}intleft(frac{{bfR}times[{bfj}]}{R^{,3}}+frac{{bfR}times[partial{bfj}slashpartialt]}{c,R^{,2}}right)dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle = -\frac{\mu_0}{4\pi} \int \left( \frac{{\bf R} \times [{\bf j}]}...
...} + \frac{{\bf R} \times [\partial {\bf j}/\partial t]}{c R^{ 2}} \right)dV'.$">|; 

$key = q/displaystyle=left(frac{[x,j_l(x)]'}{[x,y_l(x)]'}right)_{x=k,a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3378.png"
 ALT="$\displaystyle = \left(\frac{[x  j_l(x)]'} {[x  y_l(x)]'}\right)_{x=k a}.$">|; 

$key = q/T^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3636.png"
 ALT="$ T^{ \mu}$">|; 

$key = q/omega^{,2}=v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2360.png"
 ALT="$ \omega^{ 2} =v$">|; 

$key = q/{bfr}cdot{bfE}_{lm}^{(M)}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3092.png"
 ALT="$ {\bf r}\cdot{\bf E}_{lm}^{(M)}=0$">|; 

$key = q/displaystyleP_l^{,m}(x)=frac{(-1)^{,l+m}}{2^{,l},l!},(1-x^{,2})^{,mslash2},frac{d^{,l+m}}{dx^{,l+m}},(1-x^{,2})^{,l},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$\displaystyle P_l^{ m}(x)= \frac{(-1)^{ l+m}}{2^{ l} l!} (1-x^{ 2})^{ m/2} \frac{d^{ l+m}}{dx^{ l+m}} (1-x^{ 2})^{ l},$">|; 

$key = q/displaystylenablacdot(phi,nablapsi)equivphi,nabla^{,2}psi+nablaphicdotnablapsi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="$\displaystyle \nabla\cdot(\phi \nabla\psi) \equiv \phi \nabla^{ 2}\psi + \nabla\phi\cdot\nabla\psi.$">|; 

$key = q/r_>=r';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3293.png"
 ALT="$ r_&gt;=r'$">|; 

$key = q/displaystyle{bfE}'cdot{bfj}_t=frac{j_t^{,2}}{sigma}-{bfE}cdot{bfj}_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1582.png"
 ALT="$\displaystyle {\bf E}'\cdot{\bf j}_t = \frac{j_t^{ 2}}{\sigma} -{\bf E}\cdot{\bf j}_t.$">|; 

$key = q/displaystyle{bfE}={bfE}_0,exp(,{rmi},[{rmRe}(k),x-omega,t])exp[-{rmIm}(k),x].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1613.png"
 ALT="$\displaystyle {\bf E} = {\bf E}_0 \exp( {\rm i} [{\rm Re}(k)  x -\omega  t]) \exp[-{\rm Im}(k)  x].$">|; 

$key = q/displaystyle{mitPhi}^{,mu}rightarrow{mitPhi}^{,mu}+c,partial^{,mu}psi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3737.png"
 ALT="$\displaystyle {\mit \Phi}^{ \mu} \rightarrow {\mit \Phi}^{ \mu} + c \partial^{ \mu} \psi.$">|; 

$key = q/displaystyle{bfH}=frac{bfB}{mu_0}-{bfM};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1442.png"
 ALT="$\displaystyle {\bf H} = \frac{\bf B}{\mu_0} - {\bf M}$">|; 

$key = q/1slashgamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4137.png"
 ALT="$ 1/\gamma$">|; 

$key = q/partialslashpartialzequiv0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="$ \partial/\partial z\equiv 0$">|; 

$key = q/Y_m(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2863.png"
 ALT="$ Y_m(k_s  r)$">|; 

$key = q/displaystyle{bfr}cdotintj_i({bfr}'),{bfr}',dV'=x_jintx'_j,j_i,dV'=-frac{1}{2}x_jint(x_i',j_j-x_j',j_i),dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1400.png"
 ALT="$\displaystyle {\bf r}\cdot\int j_i({\bf r}') {\bf r}' dV' = x_j\int x'_j j_i dV'= -\frac{1}{2}x_j\int(x_i' j_j-x_j' j_i) dV',$">|; 

$key = q/E^{,i}rightarrow-c,B^{,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3832.png"
 ALT="$ E^{ i}\rightarrow -c B^{ i}$">|; 

$key = q/displaystyle{bfj}_perp={bfj}-frac{({bfj}cdot{bfR})}{R^{,2}},{bfR}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$\displaystyle {\bf j}_\perp = {\bf j} - \frac{({\bf j} \cdot {\bf R})}{R^{ 2}}  {\bf R}.$">|; 

$key = q/{bfe}timeshat{bfk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2729.png"
 ALT="$ {\bf e}\times\hat{\bf k}$">|; 

$key = q/q^{1slash2}(hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2492.png"
 ALT="$ q^{1/2}(\hat{z})$">|; 

$key = q/x^{,4'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4043.png"
 ALT="$ x^{ 4'}$">|; 

$key = q/displaystyle{rme}^{+{rmi},k,R}sum_{n=0,infty}left[-frac{2,{rmi},k,n}{R^{,n+1}}+frac{n,(n+1)}{R^{,n+2}}+frac{D}{R^{,n+2}}right]f_n=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$\displaystyle {\rm e}^{+{\rm i} k R} \sum_{n=0,\infty} \left[-\frac{2 {\rm i...
...n}{R^{ n+1}} +\frac{n (n+1)}{R^{ n+2}} + \frac{D}{R^{ n+2}}\right] f_n = 0.$">|; 

$key = q/{bfm}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1422.png"
 ALT="$ {\bf m}_1$">|; 

$key = q/displaystylemu_0left(-frac{B_0}{mu_0}-frac{2,alpha}{b^{,3}}right)=muleft(beta-frac{2,gamma}{b^{,3}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1564.png"
 ALT="$\displaystyle \mu_0\left(-\frac{B_0}{\mu_0} -\frac{2 \alpha}{b^{ 3}}\right) = \mu \left(\beta - \frac{2 \gamma} {b^{ 3}}\right).$">|; 

$key = q/displaystylealpha_pm(l);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3369.png"
 ALT="$\displaystyle \alpha_\pm (l)$">|; 

$key = q/rho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$ \rho$">|; 

$key = q/epsilonrightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1263.png"
 ALT="$ \epsilon\rightarrow 0$">|; 

$key = q/displaystyleq_{2,-2}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="$\displaystyle q_{2,-2}^{ \ast}$">|; 

$key = q/displaystyleM=frac{mu_0}{4pi}oint_1oint_2frac{d{bfr}_1cdotd{bfr}_2}{|{bfr}_2-{bfr}_1|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1417.png"
 ALT="$\displaystyle M = \frac{\mu_0}{4\pi}\oint_1\oint_2 \frac{d{\bf r}_1\cdot d{\bf r}_2}{\vert{\bf r}_2-{\bf r}_1\vert}.
$">|; 

$key = q/displaystyleB_phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4035.png"
 ALT="$\displaystyle B_\phi$">|; 

$key = q/displaystyleW=frac{epsilon_0}{2}intphi,nablacdot{bfE},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$\displaystyle W =\frac{\epsilon_0}{2}\int\phi  \nabla \cdot {\bf E}  dV.$">|; 

$key = q/{bfj}_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1434.png"
 ALT="$ {\bf j}_t$">|; 

$key = q/y(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1658.png"
 ALT="$ y(x)$">|; 

$key = q/displaystylefrac{partialE_x}{partialz}={rmi},k,frac{q^{,2}}{n^{,2}},c,B_y.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2317.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial z} = {\rm i} k \frac{q^{ 2}}{n^{ 2}}  c B_y.$">|; 

$key = q/displaystyleE_x(z,t)=E_0,{rme}^{-zslashd},cos(omega,t-zslashd),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1987.png"
 ALT="$\displaystyle E_x(z,t) = E_0 {\rm e}^{-z/d} \cos(\omega t-z/d),
$">|; 

$key = q/{bfr}times{bfj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3246.png"
 ALT="$ {\bf r}\times{\bf j}$">|; 

$key = q/+sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$ +\sigma$">|; 

$key = q/displaystyle{bfB}(r>a)=frac{mu_0}{4pi}left[-frac{{bfm}}{r^{,3}}+frac{3,({bfm}cdot{bfr}),{bfr}}{r^{,5}}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1516.png"
 ALT="$\displaystyle {\bf B}(r&gt;a) = \frac{\mu_0}{4\pi}\left[ -\frac{{\bf m}}{r^{ 3}} + \frac{3 ({\bf m}\cdot{\bf r}) {\bf r}}{r^{ 5}} \right],$">|; 

$key = q/displaystylerho,{bfE}+{bfj}times{bfB}=nablacdot{bfT}-frac{partial}{partialt}left(epsilon_0,{bfE}times{bfB}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$\displaystyle \rho {\bf E} + {\bf j}\times{\bf B} = \nabla\cdot {\bf T} -\frac{\partial}{\partial t}\left(\epsilon_0 {\bf E}\times{\bf B}\right),$">|; 

$key = q/displaystylez(omega_p)=frac{2}{pi}int_0^{pislash2}h(omega_p,sinalpha),dalpha.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2379.png"
 ALT="$\displaystyle z(\omega_p) = \frac{2}{\pi}\int_0^{\pi/2} h(\omega_p \sin\alpha) d\alpha.$">|; 

$key = q/displaystyle{bff}=rho,{bfE}+{bfj}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle {\bf f} = \rho {\bf E} + {\bf j}\times {\bf B}.$">|; 

$key = q/displaystylecoshtheta_t=sintheta_t=frac{n_1}{n_2},sintheta_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2144.png"
 ALT="$\displaystyle \cosh\theta_t = \sin\theta_t=\frac{n_1}{n_2} \sin\theta_i.$">|; 

$key = q/j_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3304.png"
 ALT="$ j_l(k r)$">|; 

$key = q/displaystyle=tau,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2755.png"
 ALT="$\displaystyle = \tau,$">|; 

$key = q/displaystylenablatimes{bfB}=nablatimes(nablatimes{bfA})equivnabla(nablacdot{bfA})-nabla^{,2}{bfA}=-nabla^{,2}{bfA},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1317.png"
 ALT="$\displaystyle \nabla\times {\bf B} = \nabla\times (\nabla\times {\bf A}) \equiv \nabla(\nabla\cdot{\bf A})-\nabla^{ 2}{\bf A} = -\nabla^{ 2}{\bf A},$">|; 

$key = q/m=-l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="$ m=-l$">|; 

$key = q/displaystylefrac{omega^{,2}}{c^{,2}}=k_1^{,2}+k_2^{,2}+k_3^{,2}=pi^2left(frac{l^{,2}}{a^{,2}}+frac{m^{,2}}{b^{,2}}+frac{n^{,2}}{c^{,2}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2790.png"
 ALT="$\displaystyle \frac{\omega^{ 2}}{c^{ 2}} = k_1^{ 2}+k_2^{ 2}+k_3^{ 2}=\pi^...
...c{l^{ 2}}{a^{ 2}} + \frac{m^{ 2}}{b^{ 2}} + \frac{n^{ 2}}{c^{ 2}}\right).$">|; 

$key = q/displaystyle{bfR}={bfr}-{bfr}',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\displaystyle {\bf R} = {\bf r} - {\bf r}',$">|; 

$key = q/displaystyle=E_0sin[(omegaslashc),(n_+z-c,t)].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1738.png"
 ALT="$\displaystyle = E_0 \sin[(\omega/c) (n_+ z-c t)].$">|; 

$key = q/displaystylec,{bfB}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3142.png"
 ALT="$\displaystyle c {\bf B}^{(E)}$">|; 

$key = q/0<{rmarg}(z)<pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2434.png"
 ALT="$ 0 &lt; {\rm arg}(z) &lt; \pi$">|; 

$key = q/beta=exp(,{rmi},alpha);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2694.png"
 ALT="$ \beta = \exp( {\rm i} \alpha)$">|; 

$key = q/x_0=6sqrt{3},h_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2594.png"
 ALT="$ x_0=6\sqrt{3} h_0$">|; 

$key = q/displaystylebeta_pm(l)+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3364.png"
 ALT="$\displaystyle \beta_\pm (l) + 1$">|; 

$key = q/xslashv_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1883.png"
 ALT="$ x/v_g$">|; 

$key = q/displaystylebeta,a+frac{gamma}{a^{,2}}=delta,a,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1561.png"
 ALT="$\displaystyle \beta  a + \frac{\gamma}{a^{ 2}} = \delta  a,$">|; 

$key = q/displaystylesigma=frac{f_0,N,e^{,2}}{m,(gamma_0-{rmi},omega)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1684.png"
 ALT="$\displaystyle \sigma = \frac{f_0  N  e^{ 2}}{m (\gamma_0 - {\rm i} \omega)}.$">|; 

$key = q/phistackrel{_{normalsize<}}{_{normalsizesim}}{mitDelta}theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4152.png"
 ALT="$ \phi \stackrel {_{\normalsize &lt;}}{_{\normalsize\sim}}{\mit\Delta}\theta$">|; 

$key = q/k_s^{,2},a^{,2}=(epsilon_1-1),omega^{,2},a^{,2}slashc^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2967.png"
 ALT="$ k_s^{ 2}  a^{ 2} = (\epsilon_1-1) \omega^{ 2} a^{ 2}/c^{ 2}$">|; 

$key = q/displaystyleF_{munu}=leftlgroup{array}{cccc}0&-c,B_z&+c,B_y&-E_x[0.5ex]+c,B_z&0&0.5ex]-c,B_y&+c,B_x&0&-E_z[0.5ex]+E_x&+E_y&+E_z&0{array}rightrgroup.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="105" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3797.png"
 ALT="$\displaystyle F_{\mu\nu} = \left\lgroup \begin{array}{cccc} 0 &amp; -c B_z &amp; +c B...
...B_y&amp; +c B_x&amp; 0&amp; -E_z\ [0.5ex] +E_x &amp; +E_y &amp;+E_z &amp; 0\end{array}\right \rgroup.$">|; 

$key = q/displaystyleQ=frac{1}{c}intJ^{,4},d^{,3}x=intrho,d^{,3}x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4060.png"
 ALT="$\displaystyle Q = \frac{1}{c} \int J^{ 4} d^{ 3} x= \int \rho d^{ 3} x$">|; 

$key = q/displaystylexi=frac{omega_p^{,2}}{2,c},x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1858.png"
 ALT="$\displaystyle \xi = \frac{\omega_p^{ 2}}{2 c}  x,$">|; 

$key = q/displaystyleG_{ij}=epsilon_0,(E^{,2},delta_{ij}slash2-E_i,E_j)+(B^{,2},delta_{ij}slash2-B_i,B_j)slashmu_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$\displaystyle G_{ij} = \epsilon_0 (E^{ 2} \delta_{ij}/2-E_i E_j) + (B^{ 2} \delta_{ij}/2-B_i B_j)/ \mu_0.$">|; 

$key = q/displaystylep_{mu}^{,mu'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3647.png"
 ALT="$\displaystyle p_{\mu}^{ \mu'}$">|; 

$key = q/{mitPhi}_mu=(-c,{bfA},,phi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3780.png"
 ALT="$ {\mit\Phi}_\mu = (-c {\bf A},  \phi)$">|; 

$key = q/partialslashpartialx^{,i}|_{t'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3997.png"
 ALT="$ \partial/
\partial x^{ i}\vert _{t'}$">|; 

$key = q/k_{i,y}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2027.png"
 ALT="$ k_{i y}=0$">|; 

$key = q/displaystylephi(omega)=phi_s+frac{1}{2},phi''_s,(omega-omega_s)^{,2}+cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1905.png"
 ALT="$\displaystyle \phi(\omega) = \phi_s + \frac{1}{2}  \phi''_s (\omega-\omega_s)^{ 2}+\cdots.$">|; 

$key = q/56.3^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$ 56.3^\circ $">|; 

$key = q/displaystyleR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2085.png"
 ALT="$\displaystyle R$">|; 

$key = q/P_l(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1171.png"
 ALT="$ P_l(\cos\theta)$">|; 

$key = q/displaystyle{mitPhi}(theta,z)=sum_{m=0,infty}sum_{n=1,infty}sin(k_n,z)left[C_{mn},cos(m,theta)+S_{mn},sin(m,theta)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img944.png"
 ALT="$\displaystyle {\mit\Phi}(\theta,z) = \sum_{m=0,\infty}\sum_{n=1,\infty}\sin(k_n z)\left[C_{mn} \cos(m \theta)+S_{mn} \sin(m \theta)\right],$">|; 

$key = q/displaystyleT^{,2'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3640.png"
 ALT="$\displaystyle T^{ 2'}$">|; 

$key = q/displaystyle=q^{-1slash4}(x),expleft(,{rmi},hint_0^{x}q^{,1slash2}(x'),dx'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2536.png"
 ALT="$\displaystyle = q^{-1/4}(x)  \exp\left( {\rm i} h\int_0^{x} q^{ 1/2}(x')  dx'\right),$">|; 

$key = q/n^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3526.png"
 ALT="$ n^2$">|; 

$key = q/displaystyle{bfF}'=-left.q,nablaphi'right|_{r=b,theta=0}=-frac{q^2}{4pi,epsilon_0},frac{b,a}{(b^{,2}-a^{,2})^2},{bfe}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="$\displaystyle {\bf F}' = -\left.q \nabla\phi'\right\vert _{r=b,\theta=0} =- \frac{q^2}{4\pi \epsilon_0} \frac{b a}{(b^{ 2}-a^{ 2})^2} {\bf e}_z.$">|; 

$key = q/displaystyle=-G^{4i}=-c,B^i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3824.png"
 ALT="$\displaystyle = - G^{4i} = - c B^i,$">|; 

$key = q/displaystyleE_1=frac{3}{2+epsilon},E_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1181.png"
 ALT="$\displaystyle E_1 = \frac{3}{2+\epsilon} E_0.$">|; 

$key = q/displaystyleG_omega({bfr},{bfr}')=sum_{l,m}g_l(r,r'),Y_{lm}^{,ast}(theta',varphi'),Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3179.png"
 ALT="$\displaystyle G_\omega({\bf r}, {\bf r}') =\sum_{l,m} g_l(r, r')  Y_{lm}^{ \ast}(\theta',\varphi')  Y_{lm}(\theta,\varphi).$">|; 

$key = q/displaystyle=frac{langle{calI}_zrangle_t}{langle{calI}_zrangle_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2088.png"
 ALT="$\displaystyle = \frac{\langle {\cal I}_z\rangle_t}{\langle {\cal I}_z\rangle_i},$">|; 

$key = q/displaystyleY_{l,1}(theta,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1339.png"
 ALT="$\displaystyle Y_{l,1}(\theta,0)$">|; 

$key = q/displaystyleleft[z^{,2},frac{d^2}{dz^2}+z,frac{d}{dz}-(z^{,2}+m^{,2})right]psi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2918.png"
 ALT="$\displaystyle \left[z^{ 2} \frac{d^2}{d z^2} + z \frac{d}{dz} - (z^{ 2}+m^{ 2})\right] \psi = 0.$">|; 

$key = q/displaystyledx'^{,2}+dy'^{,2}+dz'^{,2}-c^{,2},dt'^{,2}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3416.png"
 ALT="$\displaystyle dx'^{ 2} + dy'^{ 2} + dz'^{ 2} -c^{ 2}  dt'^{ 2} = 0$">|; 

$key = q/vllc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3475.png"
 ALT="$ v \ll c$">|; 

$key = q/{bfj}({bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1383.png"
 ALT="$ {\bf j}({\bf r}')$">|; 

$key = q/f(t)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1774.png"
 ALT="$ f(t) =0$">|; 

$key = q/displaystylephi_m(r,theta)=frac{M_0,a^{,2}}{3}frac{a}{r^{,2}}costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1514.png"
 ALT="$\displaystyle \phi_m(r, \theta) = \frac{M_0  a^{ 2}}{3} \frac{a}{r^{ 2}} \cos\theta$">|; 

$key = q/displaystylembox{hspace{0.5cm}forhspace{0.5cm}{tneqt'{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle \mbox{\hspace{0.5cm}for\hspace{0.5cm}$t\neq t'$}$">|; 

$key = q/displaystylen^{,2}=1-frac{omega_p^{,2}}{omega,(omega+{rmi},nu)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2218.png"
 ALT="$\displaystyle n^{ 2} = 1 - \frac{\omega_p^{ 2}}{\omega (\omega+ {\rm i} \nu)},$">|; 

$key = q/displaystyleI(z)=I_0,(1-2,|z|slashd);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2634.png"
 ALT="$\displaystyle I(z) = I_0  (1- 2 \vert z\vert/d)$">|; 

$key = q/displaystyleA_{rmeff}=1.64,A_0=frac{lambda}{2},(0.26,lambda).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2689.png"
 ALT="$\displaystyle A_{\rm eff} = 1.64  A_0 = \frac{\lambda}{2}  (0.26 \lambda).$">|; 

$key = q/displaystylepsi_i+cosphi_r,psi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2145.png"
 ALT="$\displaystyle \psi_i + \cos\phi_r \psi_r$">|; 

$key = q/B^i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3604.png"
 ALT="$ B^i$">|; 

$key = q/displaystylez_0(w^{,1slash2})=frac{1}{pi}int_0^wv^{-1slash2},(w-v)^{-1slash2},h(v^{,1slash2}),dv.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2374.png"
 ALT="$\displaystyle z_0(w^{ 1/2}) = \frac{1}{\pi}\int_0^w v^{-1/2}  (w-v)^{-1/2}  h(v^{ 1/2}) dv.$">|; 

$key = q/E>c,B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4182.png"
 ALT="$ E&gt;c B$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}intleft(nablaleft(R^{,-1}right)times[{bfj}]+frac{nablat_rtimes[partial{bfj}slashpartialt]}{R}right)dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} \int \left( \nabla\left(R^{ -1}\right) \times [{\bf j}] + \frac{\nabla t_r\times [\partial {\bf j}/\partial t]}{R} \right)dV'$">|; 

$key = q/nrightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2412.png"
 ALT="$ n\rightarrow \infty$">|; 

$key = q/psi({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="$ \psi({\bf r})$">|; 

$key = q/displaystyle=-epsilon_0,phi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="$\displaystyle = -\epsilon_0 \phi.$">|; 

$key = q/displaystyleB_r(r,theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1354.png"
 ALT="$\displaystyle B_r(r,\theta)$">|; 

$key = q/{bfr}cdot{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3080.png"
 ALT="$ {\bf r}\cdot
{\bf B}$">|; 

$key = q/displaystyleq_{1,+1}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="$\displaystyle q_{1,+1}^{ \ast}$">|; 

$key = q/partialslashpartialt|_{x^{,i}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3994.png"
 ALT="$ \partial/\partial t\vert _{x^{ i}}$">|; 

$key = q/displaystylefrac{partialwidetilde{G}_N({bfr},{bfr}')}{partialn'}=1leftslashint_SdS'right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="$\displaystyle \frac{\partial \widetilde{G}_N({\bf r},{\bf r}')}{\partial n'} = 1\left/\int_S dS'\right.$">|; 

$key = q/R^{,mu}=({bfr},,c,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3771.png"
 ALT="$ R^{ \mu} = ({\bf r},  c t)$">|; 

$key = q/displaystyle~~~~+psi_r,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z+phi_r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2138.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\psi_r \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z+\phi_r),$">|; 

$key = q/displaystyleE_y(z)=n^{-1slash2}(z),expleft(pm{rmi},kint^zn(z'),dz'right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2450.png"
 ALT="$\displaystyle E_y(z) = n^{-1/2}(z)  \exp\left(\pm {\rm i}  k \int^z n(z') dz'\right)$">|; 

$key = q/(r'slashr)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2605.png"
 ALT="$ (r'/r)^2$">|; 

$key = q/displaystylefrac{omega^{,2}}{c^{,2}}=k^{,2}=k_l^{,2}+frac{n^{,2},pi^2}{L^2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2869.png"
 ALT="$\displaystyle \frac{\omega^{ 2}}{c^{ 2}} = k^{ 2} = k_l^{ 2} + \frac{n^{ 2} \pi^2}{L^2}.$">|; 

$key = q/displaystylesimeqfrac{1}{4pi,epsilon_0}intleft(frac{rho,{bfR}}{R^{,3}}-frac{1}{2{c^{,2},R}-frac{partial{bfj}slashpartialt}{c^{,2},R}+cdotsright)dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$\displaystyle \simeq \frac{1}{4\pi  \epsilon_0} \int \left( \frac{\rho {\bf R...
...^{ 2}  R} - \frac{\partial {\bf j}/\partial t}{c^{ 2}  R}+\cdots\right)dV',$">|; 

$key = q/epsilon=n_0^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1686.png"
 ALT="$ \epsilon=n_0^{ 2}$">|; 

$key = q/displaystyle=left(frac{3}{4pi}right)^{1slash2}intrho({bfr}),r,costheta,dV=left(frac{3}{4pi}right)^{1slash2}p_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="$\displaystyle = \left(\frac{3}{4\pi}\right)^{1/2}\int\rho({\bf r}) r \cos\theta dV = \left(\frac{3}{4\pi}\right)^{1/2}p_z,$">|; 

$key = q/displaystyle1slashtausimomega_0simomega_pllxi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1964.png"
 ALT="$\displaystyle 1/\tau \sim \omega_0 \sim \omega_p \ll \xi,$">|; 

$key = q/displaystyleA^{,mu}=frac{d^{,2}x^{,mu}}{dtau^{,2}}=frac{dU^{,mu}}{dtau};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3702.png"
 ALT="$\displaystyle A^{ \mu} = \frac{d^{ 2}x^{ \mu}}{d\tau^{ 2}} = \frac{dU^{ \mu}}{d\tau}$">|; 

$key = q/displaystylenabla^{,2}G({bfr},{bfr}')=delta({bfr}-{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$\displaystyle \nabla^{ 2}G({\bf r},{\bf r}') = \delta({\bf r}-{\bf r}'),$">|; 

$key = q/displaystyleB_3=frac{1}{2pi},{rmRe},(2pi,{rmi},,{rme}^{-2pi,{rmi},tslashtau})=sinleft(frac{2pi,t}{tau}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1803.png"
 ALT="$\displaystyle B_3 = \frac{1}{2\pi}  {\rm Re}  (2\pi  {\rm i}  {\rm e}^{-2\pi  {\rm i} t/\tau}) = \sin\left(\frac{2\pi  t}{\tau}\right).$">|; 

$key = q/displaystyle=frac{rho}{epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle =\frac{\rho}{\epsilon_0},$">|; 

$key = q/displaystylek=frac{omega}{c}sqrt{frac{omega_{1+}-omega}{omega_{0+}-omega}}sqrt{frac{omega_{1-}-omega}{omega_{0-}-omega}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1816.png"
 ALT="$\displaystyle k = \frac{\omega}{c}\sqrt{ \frac{\omega_{1+}-\omega} {\omega_{0+} -\omega}} \sqrt{ \frac{\omega_{1-}-\omega} {\omega_{0-} -\omega}},$">|; 

$key = q/rhorightarrowalpha,rho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$ \rho\rightarrow \alpha \rho$">|; 

$key = q/displaystyle=frac{1}{2pi}sum_{m=-infty,infty}{rme}^{,{rmi},m,(theta-theta')},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img955.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\sum_{m=-\infty,\infty} {\rm e}^{ {\rm i} m (\theta-\theta')},$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{{rme}^{,{rmi},k,|{bfr}-{bfr}'|}}{4pi,|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2598.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\frac{{\rm e}^{ {\rm i} k \vert{\bf r}-{\bf r}'\vert}}{4\pi \vert{\bf r}-{\bf r}'\vert}.$">|; 

$key = q/displaystylephi(r,theta)=sum_{l=0,infty}left[A_l,r^{,l}+B_l,r^{,-(l+1)}right]P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1157.png"
 ALT="$\displaystyle \phi(r,\theta) = \sum_{l=0,\infty}\left[A_l  r^{ l} + B_l  r^{ -(l+1)}\right] P_l(\cos\theta),$">|; 

$key = q/displaystyle{bfm}=I,A,{bfn},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1411.png"
 ALT="$\displaystyle {\bf m} = I A {\bf n},$">|; 

$key = q/displaystyleF^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3803.png"
 ALT="$\displaystyle F^{ ij}$">|; 

$key = q/displaystyledelta(z-z');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img956.png"
 ALT="$\displaystyle \delta(z-z')$">|; 

$key = q/displaystyle{bfL}=-{rmi},{bfr}timesnabla;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3048.png"
 ALT="$\displaystyle {\bf L} = -{\rm i} {\bf r}\times \nabla$">|; 

$key = q/displaystyleP_2^{,+2}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$\displaystyle P_2^{ +2}(x)$">|; 

$key = q/theta>pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4100.png"
 ALT="$ \theta&gt;\pi/2$">|; 

$key = q/displaystyleE_y(t)=int_{-infty}^{infty}F(omega),{rme}^{-{rmi},omega,t},domega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2330.png"
 ALT="$\displaystyle E_y(t) = \int_{-\infty}^{\infty} F(\omega) {\rm e}^{-{\rm i}   \omega  t} d\omega,$">|; 

$key = q/displaystylenabla^{,2}phi=-frac{rho}{epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="$\displaystyle \nabla^{ 2}\phi = -\frac{\rho}{\epsilon_0},$">|; 

$key = q/displaystylephi(r,z)=frac{q}{4pi,epsilon_0,a}int_0^inftye^{-k,|z|},J_0(k,r),frac{sin(k,a)}{k},dk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1054.png"
 ALT="$\displaystyle \phi(r,z) =\frac{q}{4\pi \epsilon_0 a}\int_0^\infty e^{-k \vert z\vert} J_0(k r) \frac{\sin(k a)}{k} dk
$">|; 

$key = q/displaystyle{bfP}=-N,e,{bfs},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1616.png"
 ALT="$\displaystyle {\bf P} = - N e {\bf s},$">|; 

$key = q/displaystyle=z',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3479.png"
 ALT="$\displaystyle = z',$">|; 

$key = q/displaystylew''+h^{,2},q(x),w=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2527.png"
 ALT="$\displaystyle w'' + h^{ 2}  q(x)  w = 0,$">|; 

$key = q/displaystyleE_1=frac{3,epsilon}{2,epsilon+1},E_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1189.png"
 ALT="$\displaystyle E_1 = \frac{3 \epsilon}{2 \epsilon + 1}  E_0.$">|; 

$key = q/{bfn}={bfr}slashr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2602.png"
 ALT="$ {\bf n} = {\bf r}/r$">|; 

$key = q/displaystyle{bfB}=mu_0,{bfH}=-mu_0,nablaphi_m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1515.png"
 ALT="$\displaystyle {\bf B} = \mu_0  {\bf H} = -\mu_0  \nabla\phi_m.$">|; 

$key = q/displaystylefrac{Depsilon}{Dt}=frac{depsilon}{drho_m}frac{Drho_m}{Dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1219.png"
 ALT="$\displaystyle \frac{D\epsilon}{Dt} = \frac{d\epsilon}{d\rho_m} \frac{D\rho_m}{Dt},$">|; 

$key = q/2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1859.png"
 ALT="$ 2\pi/\tau$">|; 

$key = q/displaystylephi_{l,m}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="$\displaystyle \phi_{l,m}(r)$">|; 

$key = q/alpha=k,{mitDelta},sintheta,cosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2692.png"
 ALT="$ \alpha = k {\mit\Delta} 
\sin\theta \cos\varphi$">|; 

$key = q/E^{,4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4092.png"
 ALT="$ E^{ 4}$">|; 

$key = q/|{bfr}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$ \vert{\bf r}\vert$">|; 

$key = q/displaystyle=sum_la_E(l,m),h_l^{(1)}(k,r),{rme}^{-{rmi}{,omega,t}},{bfX}_{lm},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3153.png"
 ALT="$\displaystyle = \sum_l a_E(l,m)   h_l^{(1)}(k r) {\rm e}^{-{\rm i}{  \omega  t}} {\bf X}_{lm},$">|; 

$key = q/displaystyleH_y(x,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2136.png"
 ALT="$\displaystyle H_y(x,z,t)$">|; 

$key = q/displaystyle{bfH}={rme}^{,{rmi},pislash4},sqrt{frac{sigma}{mu_0,omega}},{bfn}times{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2773.png"
 ALT="$\displaystyle {\bf H} = {\rm e}^{ {\rm i} \pi/4}  \sqrt{\frac{\sigma}{\mu_0 \omega}}  {\bf n}\times{\bf E}$">|; 

$key = q/displaystyle=nabla^{,2}L_j,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3069.png"
 ALT="$\displaystyle = \nabla^{ 2} L_j,$">|; 

$key = q/gamma(u);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3694.png"
 ALT="$ \gamma(u)$">|; 

$key = q/M_0=B-mu_0,H;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1529.png"
 ALT="$ M_0 = B - \mu_0  H$">|; 

$key = q/displaystylez_0(omega)=frac{2}{pi}int_0^{pislash2}h(omega,sinalpha),dalpha.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2377.png"
 ALT="$\displaystyle z_0(\omega) = \frac{2}{\pi}\int_0^{\pi/2} h(\omega \sin\alpha) d\alpha.$">|; 

$key = q/u=a,omega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4118.png"
 ALT="$ u=a \omega_0$">|; 

$key = q/partialslashpartialt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2718.png"
 ALT="$ \partial/\partial t$">|; 

$key = q/displaystyle{bfD}=epsilon_0,epsilon,{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1074.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0 \epsilon {\bf E},$">|; 

$key = q/r'=a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="$ r'=a$">|; 

$key = q/displaystyle{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2847.png"
 ALT="$\displaystyle {\bf H}$">|; 

$key = q/displaystyleF^{,munu}=frac{e}{4pi,epsilon_0,c,{r'}^{,3}},(U^{,mu},R^{,nu}-U^{,nu},R^{,mu}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3892.png"
 ALT="$\displaystyle F^{ \mu\nu} = \frac{e}{4\pi \epsilon_0 c {r'}^{ 3}} (U^{ \mu}  R^{ \nu} -U^{ \nu}  R^{ \mu}).$">|; 

$key = q/k_{i,x}=k_{r,x};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2041.png"
 ALT="$ k_{i x}= k_{r x}$">|; 

$key = q/displaystylev({bfr},t)=int_{-infty}^{infty}v_omega({bfr}),{rme}^{-{rmi},omega,t},domega.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle v({\bf r}, t) = \int_{-\infty}^{\infty} v_\omega({\bf r}) {\rm e}^{-{\rm i}  \omega  t} d\omega.$">|; 

$key = q/displaystyleomega_p=sqrt{frac{N,e^2}{epsilon_0,m}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2220.png"
 ALT="$\displaystyle \omega_p = \sqrt{\frac{N  e^2}{\epsilon_0  m}}$">|; 

$key = q/theta=pmpislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2645.png"
 ALT="$ \theta=\pm \pi/2$">|; 

$key = q/m';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3114.png"
 ALT="$ m'$">|; 

$key = q/displaystyle=-left(frac{5}{24pi}right)^{1slash2},(Q_{13}-{rmi},Q_{23}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="$\displaystyle =-\left(\frac{5}{24\pi}\right)^{1/2} (Q_{13}-{\rm i} Q_{23}),$">|; 

$key = q/displaystylelim_{|z|rightarrowinfty}left(z^{,n}left[frac{f(z)}{phi(z)}-sum_{p=0,n}frac{A_p}{z^{,p}}right]right)rightarrow0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2408.png"
 ALT="$\displaystyle \lim_{\vert z\vert\rightarrow\infty} \left( z^{ n} \left[ \frac{f(z)}{\phi(z)} - \sum_{p=0,n}\frac{A_p}{z^{ p}}\right]\right) \rightarrow 0.$">|; 

$key = q/displaystyleP=frac{mu_0,c,I^{,2}}{4pi}int_0^pifrac{cos^2(pi,costhetaslash2)}{sintheta},dtheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2646.png"
 ALT="$\displaystyle P = \frac{\mu_0  c I^{ 2}}{4\pi} \int_0^\pi \frac{\cos^2(\pi  \cos\theta/2)} {\sin\theta} d\theta.$">|; 

$key = q/S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$ S$">|; 

$key = q/(mu_0slash4pi),(gslashr^{,2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$ (\mu_0/4\pi) (g/r^{ 2})$">|; 

$key = q/displaystyle{bfM}={bfr}times{bfG},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$\displaystyle {\bf M} = {\bf r}\times {\bf G},
$">|; 

$key = q/displaystylew(4)=A,(hat{z},0)_d+{rmi},A,(0,hat{z})_s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2557.png"
 ALT="$\displaystyle w(4) = A  (\hat{z},0)_d + {\rm i} A (0,\hat{z})_s.$">|; 

$key = q/displaystyleA_varphi(r,theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1368.png"
 ALT="$\displaystyle A_\varphi(r,\theta)$">|; 

$key = q/displaystyleint{bfE}cdot(nablatimes{bfH}),dV=-int{bfH}cdotfrac{partial{bfB}}{partialt},dV-int({bfE}times{bfH})cdotd{bfS}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1586.png"
 ALT="$\displaystyle \int{\bf E}\cdot(\nabla\times{\bf H}) d V = -\int {\bf H}\cdot\frac{\partial{\bf B}}{\partial t} dV - \int({\bf E}\times{\bf H})\cdot d{\bf S}.$">|; 

$key = q/D_{l,m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$ D_{l,m}$">|; 

$key = q/omega>-{mitOmega}slash2+sqrt{{mitOmega}^{,2}slash4+omega_p^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2009.png"
 ALT="$ \omega &gt; -{\mit\Omega}/2 + \sqrt{{\mit\Omega}^{ 2}/4+\omega_p^{ 2}}$">|; 

$key = q/x=v,t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3461.png"
 ALT="$ x=v t$">|; 

$key = q/displaystyle=-frac{psi_t,sintheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x-n_2,k_0,costheta_t,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2064.png"
 ALT="$\displaystyle =-\frac{\psi_t \sin\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x-n_2 k_0 \cos\theta_t z)$">|; 

$key = q/z<dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3260.png"
 ALT="$ z&lt;d/2$">|; 

$key = q/A_l=C_l=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1174.png"
 ALT="$ A_l = C_l = 0$">|; 

$key = q/displaystyle[rho]simeqrho-frac{partialrho}{partialt}frac{R}{c}+frac{1}{2}frac{partial^{,2}rho}{partialt^{,2}}frac{R^{,2}}{c^{,2}}+cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$\displaystyle [\rho] \simeq \rho - \frac{\partial \rho}{\partial t} \frac{R}{c}...
... \frac{\partial^{ 2} \rho}{\partial t^{ 2}} \frac{R^{ 2}}{c^{ 2}} + \cdots.$">|; 

$key = q/J^{,mu}=e,n_0,U^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3944.png"
 ALT="$ J^{ \mu} = e  n_0  U^{ \mu}$">|; 

$key = q/displaystyleleft[nabla_s^{,2}+left(frac{omega^{,2}}{c^{,2}}-k_g^{,2}right)right]psi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2907.png"
 ALT="$\displaystyle \left[ \nabla_s^{ 2} +\left( \frac{\omega^{ 2}}{c^{ 2}} - k_g^{ 2}\right) \right]\psi = 0.$">|; 

$key = q/displaystyle=frac{dy}{dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3487.png"
 ALT="$\displaystyle = \frac{dy}{dt},$">|; 

$key = q/displaystyle=frac{q}{pi,L}sum_{n=1,infty}cos(n,pi)left(frac{n,pi}{L}right)sinleft(frac{n,pi}{L},z_0right),K_0left(frac{n,pi}{L},rright),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1053.png"
 ALT="$\displaystyle = \frac{q}{\pi L}\sum_{n=1,\infty}\cos(n \pi)\left(\frac{n \pi...
...t) \sin\left(\frac{n \pi}{L} z_0\right) K_0\left(\frac{n \pi}{L} r\right),$">|; 

$key = q/Y_m(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2861.png"
 ALT="$ Y_m(z)$">|; 

$key = q/displaystylew(hat{z},h)=q^{-1slash4}(hat{z}),expleft(pm{rmi},hint^{hat{z}}q(hat{dhat{z}'right)left[1+sum_{p=1,infty}frac{A_p(hat{z})}{h^{,p}}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2469.png"
 ALT="$\displaystyle w(\hat{z}, h) = q^{-1/4}(\hat{z})  \exp\left( \pm {\rm i}  h\in...
...,d\hat{z}'\right)\left[1+\sum_{p=1,\infty} \frac{A_p(\hat{z})}{h^{ p}}\right].$">|; 

$key = q/A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$ A$">|; 

$key = q/displaystyleL^2=-frac{1}{sintheta}frac{partial}{partialtheta},sintheta,frac{partialtheta}-frac{1}{sin^2theta}frac{partial^{,2}}{partialvarphi^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3057.png"
 ALT="$\displaystyle L^2 = - \frac{1}{\sin\theta}\frac{\partial}{\partial\theta}  \si...
...ial\theta}-\frac{1}{\sin^2\theta} \frac{\partial^{ 2}}{\partial\varphi^{ 2}}.$">|; 

$key = q/nablaphi=-{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$ \nabla\phi = - {\bf E}$">|; 

$key = q/displaystylefrac{partialx^{,i'}}{partialx^{,i}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3537.png"
 ALT="$\displaystyle \frac{\partial x^{ i'}}{\partial x^{ i}}$">|; 

$key = q/n_+=n_-=n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1745.png"
 ALT="$ n_+=n_-=n$">|; 

$key = q/displaystylew(3)=A,(hat{z},0)_d.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2556.png"
 ALT="$\displaystyle w(3) = A (\hat{z},0)_d.$">|; 

$key = q/dt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3409.png"
 ALT="$ dt$">|; 

$key = q/n_0^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1680.png"
 ALT="$ n_0^{ 2}$">|; 

$key = q/k_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2865.png"
 ALT="$ k_l$">|; 

$key = q/{rmarg}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2446.png"
 ALT="$ {\rm arg}(z)$">|; 

$key = q/displaystylefrac{partial^{,2}E_x}{partialt^{,2}}+frac{sigma}{epsilon_0},frac{partialE_x}{partialt}=c^{,2},frac{partial^{,2}E_x}{partialz^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1998.png"
 ALT="$\displaystyle \frac{\partial^{ 2} E_x}{\partial t^{ 2}} + \frac{\sigma}{\epsi...
...artial E_x}{\partial t}= c^{ 2} \frac{\partial^{ 2} E_x}{\partial z^{ 2}},
$">|; 

$key = q/displaystyleepsilon_pmequivn^{,2}_pm=1+frac{P_pm}{epsilon_0,E_pm},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1734.png"
 ALT="$\displaystyle \epsilon_\pm\equiv n^{ 2}_\pm= 1 + \frac{P_\pm}{\epsilon_0 E_\pm},$">|; 

$key = q/displaystylealpha_pm(1)=-frac{beta_pm(1)}{2}simeq-frac{2,{rmi}}{3},(k,a)^3.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3383.png"
 ALT="$\displaystyle \alpha_\pm(1) = -\frac{\beta_\pm(1)}{2} \simeq -\frac{2 {\rm i}}{3} (k a)^3.$">|; 

$key = q/displaystyle=frac{1}{2pi}ointfrac{rho(r',theta',z')}{epsilon_0},{rme}^{-{rmi},m,theta'}dtheta'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img992.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\oint \frac{\rho(r',\theta',z')}{\epsilon_0} {\rm e}^{-{\rm i} m \theta'}d\theta'.$">|; 

$key = q/displaystylerggfrac{k,d^{,2}}{16pi}=frac{d^{,2}}{8,lambda},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2608.png"
 ALT="$\displaystyle r \gg \frac{k  d^{ 2}}{16\pi} = \frac{d^{ 2}}{8 \lambda},$">|; 

$key = q/displaystyleointY_{lm}^{,ast}left[delta(costheta-1)-delta(costheta+1)right]dOmega=sqrt{4pi,(2,l+1)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3256.png"
 ALT="$\displaystyle \oint Y_{lm}^{ \ast}\left[\delta(\cos\theta-1) -\delta(\cos\theta+1)\right] d\Omega = \sqrt{4\pi (2 l+1)}.$">|; 

$key = q/displaystyleleft[frac{partialphi_m}{partialr}right]_{r=a-}^{r=a+}=-sigma_m=-M_0costheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1503.png"
 ALT="$\displaystyle \left[\frac{\partial\phi_m}{\partial r}\right]_{r=a-}^{r=a+} = -\sigma_m = -M_0 \cos\theta.$">|; 

$key = q/t^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3466.png"
 ALT="$ t^{ 2}$">|; 

$key = q/displaystyle-int_Vphi,nablacdot(rho_f,{bfu}),dV=int_Vrho_f,nablaphicdot{bfu},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1226.png"
 ALT="$\displaystyle -\int_V\phi \nabla \cdot (\rho_f {\bf u})  dV = \int_V \rho_f  \nabla\phi \cdot {\bf u} dV.$">|; 

$key = q/displaystyle=(1slash2),(1-x^{,2})^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="$\displaystyle = (1/2) (1-x^{ 2})^{1/2},$">|; 

$key = q/displaystylet_0<t_1<t_2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1975.png"
 ALT="$\displaystyle t_0 &lt; t_1 &lt; t_2.$">|; 

$key = q/D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$ D$">|; 

$key = q/displaystylek^{,2}=frac{omega^{,2}}{c^{,2}}left(1+frac{N,e^{,2}slashepsilon_0,m}{omega_0^{,2}-omega^{,2}-{rmi},g,omega,omega_0}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1807.png"
 ALT="$\displaystyle k^{ 2} = \frac{\omega^{ 2}}{c^{ 2}}\left( 1 + \frac{N e^{ 2}...
...lon_0  m} {\omega_0^{ 2} -\omega^{ 2} -{\rm i} g \omega \omega_0}\right).$">|; 

$key = q/{mitDelta}thetasim1slashgamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4151.png"
 ALT="$ {\mit\Delta}\theta \sim 1/\gamma$">|; 

$key = q/displaystyleleft(frac{1}{c^{,2}}frac{partial^{,2}}{partialt^{,2}}-nabla^{,2}right)G({bfr},{bfr'};t,t')=delta({bfr}-{bfr}'),delta(t-t').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \left(\frac{1}{c^{ 2}}\frac{\partial^{ 2}}{\partial t^{ 2}}-\n...
...right) G({\bf r}, {\bf r'}; t, t') = \delta({\bf r} - {\bf r}')  \delta(t-t').$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=-frac{1}{4pi,|{bfr}'-{bfr}|}+frac{a}{4pi,r',|a^{,2},{bfr}'slashr'^{,2}-{bfr}|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}') = -\frac{1}{4\pi \vert{\bf r}'-{\bf r}\vert}+ \frac{a}{4\pi r' \vert a^{ 2} {\bf r}'/r'^{ 2}-{\bf r}\vert}.$">|; 

$key = q/Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$ Q$">|; 

$key = q/displaystyle=-frac{q}{pi,L}sum_{n=1,infty}left(frac{n,pi}{L}right)sinleft(frac{n,pi}{L},z_0right),K_0left(frac{n,pi}{L},rright),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1051.png"
 ALT="$\displaystyle = - \frac{q}{\pi L}\sum_{n=1,\infty}\left(\frac{n \pi}{L}\right)\sin\left(\frac{n \pi}{L} z_0\right) K_0\left(\frac{n \pi}{L} r\right),$">|; 

$key = q/{mitDelta}phi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2183.png"
 ALT="$ {\mit\Delta}\phi_r$">|; 

$key = q/omega_0=e,Bslash(m_0,gamma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4145.png"
 ALT="$ \omega_0 = e  B/(m_0 \gamma)$">|; 

$key = q/displaystyledllsqrt{lambda,r}llr.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2620.png"
 ALT="$\displaystyle d \ll \sqrt{\lambda  r} \ll r.$">|; 

$key = q/displaystyleK_0'(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2950.png"
 ALT="$\displaystyle K_0'(z)$">|; 

$key = q/displaystyledelta({bfr}-{bfr}')=frac{1}{r},delta(r-r'),delta(theta-theta'),delta(z-z').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img951.png"
 ALT="$\displaystyle \delta({\bf r}-{\bf r}') = \frac{1}{r} \delta(r-r') \delta(\theta-\theta') \delta(z-z').$">|; 

$key = q/displaystylefrac{2pi,N,{mitDelta}}{lambda}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2712.png"
 ALT="$\displaystyle \frac{2\pi N {\mit \Delta}}{\lambda}.$">|; 

$key = q/gamma=(1-v^{,2}slashc^{,2})^{-1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4171.png"
 ALT="$ \gamma = (1-v^{ 2}/c^{ 2})^{-1/2}$">|; 

$key = q/displaystyle-epsilon_0,frac{partial{bfE}}{partialt}times{bfB}=frac{{bfB}times(nablatimes{bfB})}{mu_0}+{bfj}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="$\displaystyle -\epsilon_0 \frac{\partial {\bf E}}{\partial t}\times {\bf B} = \frac{{\bf B}\times(\nabla\times {\bf B})}{\mu_0} + {\bf j}\times {\bf B}.$">|; 

$key = q/displaystylenabla^{,2}{bfE}-frac{epsilon}{c^{,2}},frac{partial^{,2}{bfE}}{partialt^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2572.png"
 ALT="$\displaystyle \nabla^{ 2}{\bf E} - \frac{\epsilon}{c^{ 2}} \frac{\partial^{ 2}{\bf E}}{\partial t^{ 2}}$">|; 

$key = q/P_l(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$ P_l(x)$">|; 

$key = q/n^2=1-alpha,(z-h_0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2588.png"
 ALT="$ n^2=1-\alpha (z-h_0)$">|; 

$key = q/displaystyle=frac{nabla_s(partialE_zslashpartialz)}{k^{,2}-k_3^{,2}}+frac{{rmi},omega,mu_0}{k^{,2}-k_3^{,2}},nabla_stimes{bfH}_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2826.png"
 ALT="$\displaystyle =\frac{\nabla_s(\partial E_z/\partial z)}{k^{ 2} - k_3^{ 2}} + \frac{{\rm i} \omega \mu_0}{k^{ 2}-k_3^{ 2}}  \nabla_s\times{\bf H}_z,$">|; 

$key = q/displaystylealpha(r'),I_m(k_n,r')=beta(r')left[I_m(k_n,r'),K_m(k_n,a)-I_m(k_n,a),K_m(k_n,r')right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1010.png"
 ALT="$\displaystyle \alpha(r') I_m(k_n r') = \beta(r')\left[I_m(k_n r') K_m(k_n a)-I_m(k_n a) K_m(k_n r')\right].$">|; 

$key = q/c,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3139.png"
 ALT="$ c {\bf B}$">|; 

$key = q/displaystylesigma(theta)=-epsilon_0left.frac{partialphi}{partialr}right|_{r=a}=-,a},frac{(b^{,2}-a^{,2})}{(a^{,2}-2,a,b,costheta+b^{,2})^{3slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$\displaystyle \sigma(\theta)= -\epsilon_0\left.\frac{\partial\phi}{\partial r}\...
...\pi a} \frac{(b^{ 2}-a^{ 2})}{(a^{ 2}-2 a b \cos\theta+b^{ 2})^{3/2}}.$">|; 

$key = q/displaystyleR=-{rmi},expleft(2,{rmi},kint_0^{z_0}!n(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2281.png"
 ALT="$\displaystyle R = -{\rm i}  \exp\left(2 {\rm i}  k\int_0^{z_0} \!n(z') dz'\right).$">|; 

$key = q/displaystyled^{,4}x'={calJ},d^{,4}x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3695.png"
 ALT="$\displaystyle d^{ 4} x' = {\cal J}  d^{ 4} x,$">|; 

$key = q/displaystyleF(omega)=frac{1}{tau}frac{1}{omega^{,2}-(2pislashtau)^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1898.png"
 ALT="$\displaystyle F(\omega) = \frac{1}{\tau}\frac{1}{\omega^{ 2}-(2\pi/\tau)^{ 2}},$">|; 

$key = q/displaystyleE=m,c^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3919.png"
 ALT="$\displaystyle E = m  c^{ 2}.$">|; 

$key = q/n=n(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2229.png"
 ALT="$ n=n(z)$">|; 

$key = q/displaystyle=-frac{{rmi},omega,mu_0}{k_s^{,2}},{bfe}_ztimesnabla_sH_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2852.png"
 ALT="$\displaystyle = - \frac{{\rm i}  \omega \mu_0}{k_s^{ 2}} {\bf e}_z\times \nabla_s H_z,$">|; 

$key = q/displaystylefrac{d^{,2}phi}{dz^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2323.png"
 ALT="$\displaystyle \frac{d^{ 2}\phi}{dz^{ 2}}$">|; 

$key = q/displaystylerightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img966.png"
 ALT="$\displaystyle \rightarrow \infty$">|; 

$key = q/displaystylenablacdot{bfE}=frac{rho}{epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="$\displaystyle \nabla\cdot{\bf E} = \frac{\rho}{\epsilon_0},$">|; 

$key = q/z=z_0(v^{,1slash2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2370.png"
 ALT="$ z=z_0(v^{ 1/2})$">|; 

$key = q/displaystylefrac{|E_parallel|}{|E_perp|}simeqksqrt{frac{2}{mu_0,omega,sigma}}=frac{d}{lambdabar},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2775.png"
 ALT="$\displaystyle \frac{\vert E_\parallel\vert}{\vert E_\perp\vert}\simeq k \sqrt{\frac{2}{\mu_0  \omega \sigma}} = \frac{d}{\lambdabar},$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),({bfr}cdot{bfB});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3082.png"
 ALT="$\displaystyle (\nabla^{ 2}+k^{ 2}) ({\bf r}\cdot{\bf B})$">|; 

$key = q/displaystyleq_{0,0}^{,ast}=intrho({bfr}'),Y_{0,0}^{,ast}(theta,varphi),dV=frac{1}{sqrt{4pi}}intrho({bfr}),dV=frac{Q}{sqrt{4pi}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="$\displaystyle q_{0,0}^{ \ast}=\int \rho({\bf r}') Y_{0,0}^{ \ast}(\theta,\varphi) dV = \frac{1}{\sqrt{4\pi}}\int\rho({\bf r}) dV = \frac{Q}{\sqrt{4\pi}},$">|; 

$key = q/delta_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$ \delta_{ij}$">|; 

$key = q/lambdaggd;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2639.png"
 ALT="$ \lambda\gg d$">|; 

$key = q/displaystyleintT^{,4},dS_4+intT^{,4'},dS_{4'}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4045.png"
 ALT="$\displaystyle \int T^{ 4} dS_4 + \int T^{ 4'} dS_{4'} = 0.$">|; 

$key = q/v_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1882.png"
 ALT="$ v_g$">|; 

$key = q/F(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1900.png"
 ALT="$ F(\omega)$">|; 

$key = q/H;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1523.png"
 ALT="$ H$">|; 

$key = q/displaystylefrac{dp}{dt}=m_0,gamma^{,3},dot{u},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4076.png"
 ALT="$\displaystyle \frac{d p}{dt} = m_0  \gamma^{ 3} \dot{u},$">|; 

$key = q/n_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1676.png"
 ALT="$ n_0$">|; 

$key = q/t>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1798.png"
 ALT="$ t&gt;0$">|; 

$key = q/f_1=f_2=cdots=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$ f_1=f_2=\cdots = 0$">|; 

$key = q/cslashv_g(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$ c/v_g(\omega )$">|; 

$key = q/displaystylenabla^{,2}psi-frac{1}{c^{,2}}frac{partial^{,2}psi}{partialt^{,2}}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2777.png"
 ALT="$\displaystyle \nabla^{ 2}\psi - \frac{1}{c^{ 2}}\frac{\partial^{ 2}\psi}{\partial t^{ 2}}=0,$">|; 

$key = q/g_{44}=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3628.png"
 ALT="$ g_{44}=1$">|; 

$key = q/displaystyle=-frac{k,mu_0,c}{4pi}intfrac{{rme}^{,{rmi},k,|{bfr}-{bfr}'|}}{|{bfr}cdotleft[{bfM}({bfr}')+frac{nabla'times{bfj}({bfr}')}{k^2}right]dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3213.png"
 ALT="$\displaystyle = -\frac{k \mu_0   c}{4\pi}\int \frac{{\rm e}^{ {\rm i} k \v...
...t\left[{\bf M}({\bf r}')+\frac{\nabla'\times {\bf j}({\bf r}')}{k^2}\right]dV'.$">|; 

$key = q/displaystyle=mu_0,{bfj}+mu_0,epsilon_0,frac{partial{bfE}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle =\mu_0 {\bf j} + \mu_0 \epsilon_0 \frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/displaystylesimeqfrac{e}{4pi,epsilon_0,c^{,2}}frac{sintheta}{r},dot{u},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4034.png"
 ALT="$\displaystyle \simeq \frac{e}{4\pi \epsilon_0  c^{ 2}} \frac{\sin\theta}{r}  \dot{u},$">|; 

$key = q/Q^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3661.png"
 ALT="$ Q^{ \mu}$">|; 

$key = q/displaystylefrac{partialA_{kcdotsl}^{icdotsj}}{partialx^{,m}}=A^{icdotsj}_{kcdotsl,m}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3580.png"
 ALT="$\displaystyle \frac{\partial A_{k\cdots l}^{i\cdots j} }{\partial x^{ m}} = A^{i \cdots j}_{k\cdots l,m}.$">|; 

$key = q/displaystylenablacdot{bfB}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1312.png"
 ALT="$\displaystyle \nabla\cdot{\bf B} =0,$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),G_omega({bfr},{bfr}')=-delta({bfr}-{bfr}').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2}) G_\omega ({\bf r}, {\bf r}')= -\delta({\bf r} - {\bf r}').$">|; 

$key = q/phi=phi(r,theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1155.png"
 ALT="$ \phi
=\phi(r,\theta)$">|; 

$key = q/displaystyleds^{,2}={dx'}^{,2}+{dy'}^{,2}+{dz'}^{,2}-c^{,2},{dt'}^{,2}={dx}^{,2}+{dy}^{,2}+{dz}^{,2}-c^{,2},{dt}^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3672.png"
 ALT="$\displaystyle ds^{ 2} = {dx'}^{ 2} + {dy'}^{ 2} + {dz'}^{ 2} - c^{ 2}  {dt'}^{ 2} = {dx}^{ 2} + {dy}^{ 2} + {dz}^{ 2} - c^{ 2}  {dt}^{ 2},$">|; 

$key = q/{bfa}=d{bfu}slash{dt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3705.png"
 ALT="$ {\bf a} = d{\bf u}/{dt}$">|; 

$key = q/omega_0^{,2}-omega^{,2}-{rmi},g,omega,omega_0simeqomega_0^{,2}-omega^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1629.png"
 ALT="$ \omega_0^{ 2}
-\omega^{ 2} - {\rm i} g \omega \omega_0\simeq\omega_0^{ 2}
-\omega^{ 2}$">|; 

$key = q/x<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="$ x&lt;0$">|; 

$key = q/displaystyleU=int_Vint_0^Efrac{epsilon_0,epsilon,delta(E^{,2})}{2},dV=frac{1}{2}int_Vepsilon_0,epsilon,E^{,2},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1202.png"
 ALT="$\displaystyle U = \int_V \int_0^E \frac{\epsilon_0 \epsilon  \delta (E^{ 2})}{2} dV = \frac{1}{2} \int_V \epsilon_0 \epsilon  E^{ 2} dV,$">|; 

$key = q/omegaggomega_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1704.png"
 ALT="$ \omega\gg \omega_p$">|; 

$key = q/hat{z}=hat{z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2480.png"
 ALT="$ \hat{z}=\hat{z}$">|; 

$key = q/displaystyle=E_t,{rme}^{-zslashd},cos(omega,t-zslashd+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2194.png"
 ALT="$\displaystyle = E_t {\rm e}^{-z/d} \cos(\omega t-z/d+\phi_t),$">|; 

$key = q/displaystyle=frac{psi_i^{,2},costheta_i}{2,epsilon_0,c,n_1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2080.png"
 ALT="$\displaystyle = \frac{\psi_i^{ 2} \cos\theta_i}{2 \epsilon_0 c n_1},$">|; 

$key = q/displaystyle{rme}^{,{rmi},{bfk}cdot{bfr}}=sum_{l=0,infty}{rmi}^l,(2,l+1),j_l(k,r),P_l(cosgamma),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3298.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} {\bf k}\cdot{\bf r}}= \sum_{l=0,\infty} {\rm i}^l (2 l+1) j_l(k r)  P_l(\cos\gamma),$">|; 

$key = q/displaystylephi(x^{,i},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3991.png"
 ALT="$\displaystyle \phi(x^{ i}, t)$">|; 

$key = q/displaystyle{rmRe}left({rmi}!int_0^{hat{z}}q^{1slash2}(hat{z}'),dhat{z}'right)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2489.png"
 ALT="$\displaystyle {\rm Re} \left( {\rm i}\! \int_0^{\hat{z}} q^{1/2}(\hat{z}')  d\hat{z}' \right) = 0.$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),{bfr}cdotc,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3206.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2}) {\bf r}\cdot c {\bf B}$">|; 

$key = q/psi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2021.png"
 ALT="$ \psi_r$">|; 

$key = q/phi_s''=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1947.png"
 ALT="$ \phi_s''=0$">|; 

$key = q/partialslashpartialx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2292.png"
 ALT="$ \partial/\partial x$">|; 

$key = q/displaystylek-frac{omega}{c}simeqfrac{omega}{c}left(sqrt{1-frac{omega_p^{,2}}{omega^{,2}}}-1right)simeq-frac{omega_p^{,2}}{2,c,omega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="77" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1857.png"
 ALT="$\displaystyle k -\frac{\omega}{c} \simeq \frac{\omega}{c} \left(\sqrt{1-\frac{\...
...p^{ 2}}{\omega^{ 2}}} - 1\right) \simeq - \frac{\omega_p^{ 2}}{2 c \omega}$">|; 

$key = q/|{bfr}|rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3136.png"
 ALT="$ \vert{\bf r}\vert\rightarrow\infty$">|; 

$key = q/displaystyleF_{ij}=partial_i{mitPhi}_j-partial_j{mitPhi}_i=-c,B_{ij}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3792.png"
 ALT="$\displaystyle F_{ij} = \partial_i{\mit\Phi}_j -\partial_j{\mit\Phi}_i= - c  B_{ij}.$">|; 

$key = q/displaystyleH_r(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2941.png"
 ALT="$\displaystyle H_r (r)$">|; 

$key = q/(0,0,pm1,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3429.png"
 ALT="$ (0, 0, \pm 1, 1)$">|; 

$key = q/costheta={bfn}cdot{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2626.png"
 ALT="$ \cos\theta = {\bf n}\cdot{\bf e}_z$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}=frac{e^{,2},r}{16pi^2,epsilon_0,c^{,3}}frac{[{bfr}times({bfr}_utimesdot{bfu})]^2}{s^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4097.png"
 ALT="$\displaystyle \frac{dP(t')}{d{\mit\Omega}} = \frac{e^{ 2}  r}{16\pi^2  \epsilon_0  c^{ 3}} \frac{[{\bf r}\times({\bf r}_u\times\dot{\bf u})]^2}{s^{ 5}}.$">|; 

$key = q/displaystyleP=frac{mu_0,c,I_0^{,2},(k,d)^2}{48pi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2635.png"
 ALT="$\displaystyle P = \frac{\mu_0  c I_0^{ 2}  (k d)^2}{48\pi}.$">|; 

$key = q/A_{klm}^{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3569.png"
 ALT="$ A_{klm}^{ij}$">|; 

$key = q/displaystyle=-frac{partial{bfB}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3841.png"
 ALT="$\displaystyle = -\frac{\partial{\bf B}}{\partial t}.$">|; 

$key = q/N^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2709.png"
 ALT="$ N^{ 2}$">|; 

$key = q/displaystyle={rmi},nabla!cdot!({bfr}times{bfA}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3224.png"
 ALT="$\displaystyle = {\rm i} \nabla\!\cdot\!({\bf r}\times {\bf A}),$">|; 

$key = q/displaystyleB_m(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img926.png"
 ALT="$\displaystyle B_m(k)$">|; 

$key = q/displaystyle=frac{hat{alpha}}{beta},cosphi_t,psi_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2151.png"
 ALT="$\displaystyle =\frac{\hat{\alpha}}{\beta} \cos\phi_t \psi_t.$">|; 

$key = q/Q<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4189.png"
 ALT="$ Q&lt;0$">|; 

$key = q/displaystyle=sum_{l,m}left[a_E(l,m),f_l(k,r),{bfX}_{lm}-frac{rmi}{k},a_M(l,m),nablatimesg_l(k,r),{bfX}_{lm}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3116.png"
 ALT="$\displaystyle = \sum_{l,m}\left[a_E(l,m) f_l(k r) {\bf X}_{lm} -\frac{\rm i}{k}  a_M(l,m)  \nabla\times g_l(k r)  {\bf X}_{lm}\right],$">|; 

$key = q/displaystylealpha_{l,m}(r',theta',varphi')=-left(frac{l+1}{2,l+1}right)frac{r'^{,l}}{a^{,l+2}},Y_{l,m}^ast(theta',varphi');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="$\displaystyle \alpha_{l,m}(r',\theta',\varphi') = - \left(\frac{l+1}{2 l+1}\right)\frac{r'^{ l}}{a^{ l+2}} Y_{l,m}^\ast(\theta',\varphi')$">|; 

$key = q/E_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1997.png"
 ALT="$ E_x$">|; 

$key = q/displaystyleE_y(x,z)=int_{0}^1frac{F(S)}{q^{,1slash2}(z,S)},{rme}^{,{rmi},phi(x,z,S)},dS,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2388.png"
 ALT="$\displaystyle E_y(x,z) =\int_{0}^1 \frac{F(S)}{q^{ 1/2}(z,S)}  {\rm e}^{ {\rm i} \phi (x,z,S)} dS,$">|; 

$key = q/s=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1835.png"
 ALT="$ s=0$">|; 

$key = q/displaystyleepsilon=1+chi_e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1075.png"
 ALT="$\displaystyle \epsilon= 1 + \chi_e$">|; 

$key = q/displaystyle{bfB}simeqfrac{3}{2},frac{mu_0}{mu},frac{a}{d},{bfB}_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1575.png"
 ALT="$\displaystyle {\bf B} \simeq \frac{3}{2}  \frac{\mu_0}{\mu}  \frac{a}{d}  {\bf B}_0.$">|; 

$key = q/{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$ {\bf r}$">|; 

$key = q/k,d=2pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2641.png"
 ALT="$ k d=2\pi$">|; 

$key = q/B=mu,H;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1527.png"
 ALT="$ B = \mu  H$">|; 

$key = q/{rmRe}(z)<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2443.png"
 ALT="$ {\rm Re}(z) &lt; 0$">|; 

$key = q/l+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="$ l+1$">|; 

$key = q/displaystylepsi_i-psi_r=frac{alpha}{beta},psi_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2069.png"
 ALT="$\displaystyle \psi_i-\psi_r= \frac{\alpha}{\beta} \psi_t.$">|; 

$key = q/(RslashR_0)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$ (R/R_0)^2$">|; 

$key = q/v_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4166.png"
 ALT="$ v_2$">|; 

$key = q/displaystyledx'^{,2}+dy'^{,2}+dz'^{,2}-c^{,2},dt'^{,2}=dx^{,2}+dy^{,2}+dz^{,2}-c^{,2},dt^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3443.png"
 ALT="$\displaystyle dx'^{ 2} + dy'^{ 2} + dz'^{ 2} -c^{ 2}  dt'^{ 2} =dx^{ 2} + dy^{ 2} + dz^{ 2} -c^{ 2}  dt^{ 2}.$">|; 

$key = q/displaystyle=-G_{4i}=+cB_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3834.png"
 ALT="$\displaystyle = - G_{4i} = + cB_i,$">|; 

$key = q/displaystyleint_V|nablaphi|^{,2},dV=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$\displaystyle \int_V \vert\nabla \phi\vert^{ 2}  dV = 0,$">|; 

$key = q/displaystyleE_y(z)=A,{rme}^{,{rmi},phi(z)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2244.png"
 ALT="$\displaystyle E_y(z) = A {\rm e}^{ {\rm i} \phi(z)},$">|; 

$key = q/displaystyle|E(omega)|^{,2}proptofrac{1}{(omega-omega_0-{mitDelta}omega)^{,2}+(omega_0slash2,Q)^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2808.png"
 ALT="$\displaystyle \vert E(\omega)\vert^{ 2} \propto \frac{1}{(\omega-\omega_0-{\mit\Delta}\omega)^{ 2} +(\omega_0/2 Q)^{ 2}}.$">|; 

$key = q/displaystyleP=frac{e^{,2}}{6pi,epsilon_0,m_0^{,2},c^{,3}}left(frac{dp}{dt}right)^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4078.png"
 ALT="$\displaystyle P= \frac{e^{ 2}}{6\pi \epsilon_0  m_0^{ 2}  c^{ 3}}\left(\frac{dp}{dt}\right)^2.$">|; 

$key = q/q^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2309.png"
 ALT="$ q^{ 2}$">|; 

$key = q/displaystylec,B_{ij}=-partial_i{mitPhi}_j+partial_j{mitPhi}_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3787.png"
 ALT="$\displaystyle c B_{ij} = -\partial_i {\mit \Phi}_j + \partial_j {\mit \Phi}_i,$">|; 

$key = q/displaystylephi(x,z,S)=kint_0^zq(z,S),dz+k,S,x.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2389.png"
 ALT="$\displaystyle \phi(x,z,S) = k\int_0^z q(z,S) dz + k S x.$">|; 

$key = q/n=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2268.png"
 ALT="$ n=0$">|; 

$key = q/displaystylefrac{partial,c,B_x}{partialz}-{rmi},k,S,c,B_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2301.png"
 ALT="$\displaystyle \frac{\partial c  B_x}{\partial z} - {\rm i} k  S  c B_z$">|; 

$key = q/displaystyleM=frac{mu,N_1,N_2,A}{2pi,a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1601.png"
 ALT="$\displaystyle M = \frac{\mu N_1 N_2 A}{2\pi a}.
$">|; 

$key = q/displaystylepartial^{,mu}equivfrac{partial}{partialx_mu}=left(-nabla,frac{1}{c}frac{partial}{partialt}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3667.png"
 ALT="$\displaystyle \partial^{ \mu} \equiv \frac{\partial}{\partial x_\mu} = \left(-\nabla, \frac{1}{c}\frac{\partial}{\partial t}\right),$">|; 

$key = q/displaystyle=P(z-u,t),{bfe}_x+Q(z-u,t),{bfe}_y+R(z-u,t),{bfe}_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1976.png"
 ALT="$\displaystyle = P(z-u t) {\bf e}_x + Q(z-u t) {\bf e}_y+ R(z-u t) {\bf e}_z,$">|; 

$key = q/displaystyleW=frac{3}{5}frac{Q^{,2}}{4pi,epsilon_0,a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$\displaystyle W = \frac{3}{5} \frac{Q^{ 2}}{4\pi \epsilon_0  a}.$">|; 

$key = q/0<z<z_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2271.png"
 ALT="$ 0&lt;z&lt;z_0$">|; 

$key = q/displaystyle=1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="$\displaystyle = 1,$">|; 

$key = q/t=t_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1944.png"
 ALT="$ t=t_1$">|; 

$key = q/displaystyletheta_B=tan^{-1}left(frac{n_2}{n_1}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2129.png"
 ALT="$\displaystyle \theta_B = \tan^{-1}\left(\frac{n_2}{n_1}\right).$">|; 

$key = q/4sqrt{6pi},(mu_0,c,Islash4pi,d);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3267.png"
 ALT="$ 4\sqrt{6\pi} (\mu_0  c I/4\pi  d)$">|; 

$key = q/displaystyleint_Sfrac{partialG({bfr},{bfr}')}{partialn'},dS'=1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="$\displaystyle \int_S \frac{\partial G({\bf r},{\bf r}')}{\partial n'} dS'=1.$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}intfrac{rho({bfr}')}{|{bfr}-{bfr}'|},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dV',$">|; 

$key = q/displaystylesimeqA,n^{-1slash2}(z),expleft(pm{rmi},kint^z!n(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2261.png"
 ALT="$\displaystyle \simeq A n^{-1/2}(z) \exp\left(\pm {\rm i}  k \int^z \!n(z') dz'\right),$">|; 

$key = q/displaystylerightarrow-{rmi},(hat{z},0),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2508.png"
 ALT="$\displaystyle \rightarrow -{\rm i} (\hat{z}, 0),$">|; 

$key = q/{mitPhi}(r,theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$ {\mit\Phi}(r,\theta)$">|; 

$key = q/p=p(rho_m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1256.png"
 ALT="$ p=p(\rho_m)$">|; 

$key = q/x=infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1769.png"
 ALT="$ x=\infty$">|; 

$key = q/R^{,mu}=(x^{,1},,x^{,2},,x^{,3},,x^{,4});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3653.png"
 ALT="$ R^{ \mu}= (x^{ 1},  x^{ 2},  x^{ 3},  x^{ 4})$">|; 

$key = q/displaystyleL_j,nabla^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3068.png"
 ALT="$\displaystyle L_j  \nabla^{ 2}$">|; 

$key = q/nablacdot{bfE}'=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3203.png"
 ALT="$ \nabla\cdot{\bf E}' = 0$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0}{4pi},frac{{bfm}times{bfr}}{r^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1405.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = \frac{\mu_0}{4\pi} \frac{{\bf m}\times {\bf r}}{r^{ 3}}.$">|; 

$key = q/d,sigmarightarrowD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="$ d \sigma\rightarrow D$">|; 

$key = q/displaystyleoint{bfX}_{l'm'}^{,ast}cdot({bfr}times{bfX}_{lm}),d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3112.png"
 ALT="$\displaystyle \oint {\bf X}_{l'm'}^{ \ast} \cdot({\bf r}\times {\bf X}_{lm}) d {\mit\Omega}$">|; 

$key = q/dslashdz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2242.png"
 ALT="$ d/dz$">|; 

$key = q/displaystyle{bfA}=A_varphi(r,theta),{bfe}_varphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1332.png"
 ALT="$\displaystyle {\bf A}= A_\varphi(r,\theta) {\bf e}_\varphi,$">|; 

$key = q/displaystylephi_m=delta,rcostheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1559.png"
 ALT="$\displaystyle \phi_m = \delta r\cos\theta$">|; 

$key = q/displaystyle={rmi},A,frac{k_g}{k_t},K_1(k_t,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2946.png"
 ALT="$\displaystyle = {\rm i} A \frac{ k_g }{k_t}  K_1(k_t  r),$">|; 

$key = q/{mitOmega}leqomegaleq{mitOmega}slash2+sqrt{{mitOmega}^{,2}slash4+omega_p^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2011.png"
 ALT="$ {\mit\Omega}\leq \omega\leq{\mit \Omega}/2 + \sqrt{{\mit\Omega}^{ 2}/4+\omega_p^{ 2}}$">|; 

$key = q/displaystylenabla's=frac{{bfr}}{r}-frac{{bfu}}{c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4008.png"
 ALT="$\displaystyle \nabla' s = \frac{{\bf r}}{r} - \frac{{\bf u}}{c},$">|; 

$key = q/B_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3799.png"
 ALT="$ B_x$">|; 

$key = q/displaystylenablatimes{bfH}=nablatimes({bfB}slashmu_0-{bfM})={bf0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1492.png"
 ALT="$\displaystyle \nabla\times{\bf H} = \nabla\times({\bf B}/\mu_0 - {\bf M}) = {\bf0},$">|; 

$key = q/B_{ijk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3565.png"
 ALT="$ B_{ijk}$">|; 

$key = q/G_omega(R)rightarrowG(R);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$ G_\omega(R)\rightarrow G(R)$">|; 

$key = q/{bfE}=E_r(r),{bfe}_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$ {\bf E} = E_r(r) 
{\bf e}_r$">|; 

$key = q/x_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$ x_1$">|; 

$key = q/{bfp}=q,{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1058.png"
 ALT="$ {\bf p} = q  {\bf r}$">|; 

$key = q/dt'=gamma,(dt-v,dxslashc^{,2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3500.png"
 ALT="$ dt'=
\gamma (dt-v dx/c^{ 2})$">|; 

$key = q/e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$ e$">|; 

$key = q/displaystylea_pm(l,m)={rmi}^{,l},sqrt{4pi,(2,l+1)},delta_{m,pm1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3322.png"
 ALT="$\displaystyle a_\pm(l,m) = {\rm i}^{ l}  \sqrt{4\pi (2 l+1)} \delta_{m,\pm 1}.$">|; 

$key = q/{figure}{epsfysize{=2.75in{centerline{epsffile{Chapter06slashcont1.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="623" HEIGHT="310" BORDER="0"
 SRC="|."$dir".q|img1794.png"
 ALT="\begin{figure}
\epsfysize =2.75in
\centerline{\epsffile{Chapter06/cont1.eps}}
\end{figure}">|; 

$key = q/theta_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2031.png"
 ALT="$ \theta_r$">|; 

$key = q/displaystyleleft[frac{d^{,2}}{dr^{,2}}+frac{2}{r}frac{d}{dr}+k^{,2}-frac{l,(l+1)}{r^{,2}}right]g_l=-frac{delta(r-r')}{r^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3180.png"
 ALT="$\displaystyle \left[\frac{d^{ 2}}{dr^{ 2}} +\frac{2}{r}\frac{d}{dr}+k^{ 2} -\frac{l (l+1)}{r^{ 2}}\right] g_l = - \frac{\delta(r-r')}{r^{ 2}}.$">|; 

$key = q/zsim1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1961.png"
 ALT="$ z\sim 1$">|; 

$key = q/displaystyle=frac{1}{2,{rmi}},(E_+-E_-).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1727.png"
 ALT="$\displaystyle = \frac{1}{2 {\rm i}}  (E_+-E_-).$">|; 

$key = q/displaystylesigma_+(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1052.png"
 ALT="$\displaystyle \sigma_+(r)$">|; 

$key = q/displaystyleB_theta({bf0});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1362.png"
 ALT="$\displaystyle B_\theta({\bf0})$">|; 

$key = q/|{bfr}'|rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1387.png"
 ALT="$ \vert{\bf r}'\vert\rightarrow\infty$">|; 

$key = q/displaystyle=-frac{e}{m},E_-.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1731.png"
 ALT="$\displaystyle = -\frac{e}{m} E_-.$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),psi({bfr},omega)=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2998.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2}) \psi({\bf r}, \omega) = 0,$">|; 

$key = q/displaystyleointY_{lm}^{,ast}left[delta(costheta-1)-delta(costheta+1)right]d{mitOmega}=2pi,delta_{m0},left[Y_{l0}(0)-Y_{l0}(pi)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3255.png"
 ALT="$\displaystyle \oint Y_{lm}^{ \ast}\left[\delta(\cos\theta-1) -\delta(\cos\thet...
...right]d{\mit\Omega} = 2\pi \delta_{m0}  \left[Y_{l0}(0) - Y_{l0}(\pi)\right],$">|; 

$key = q/displaystyle{bfu}=frac{{bfE}times{bfB}}{mu_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle {\bf u} = \frac{{\bf E}\times{\bf B}}{\mu_0}$">|; 

$key = q/u;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1865.png"
 ALT="$ u$">|; 

$key = q/2pislashn,k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2452.png"
 ALT="$ 2\pi/n  k$">|; 

$key = q/1.64;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2653.png"
 ALT="$ 1.64$">|; 

$key = q/displaystylec,B_x(z)simeqmpA,n^{,1slash2}(z),expleft(pm{rmi},kint^z!n(z'),dz'rign^{,3slash2}(z)}frac{dn}{dz},expleft(pm{rmi},kint^z!n(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="532" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2257.png"
 ALT="$\displaystyle c B_x(z)\simeq \mp A  n^{ 1/2}(z) \exp\left(\pm {\rm i} k \i...
... 3/2}(z)} \frac{dn} {dz} \exp\left(\pm {\rm i} k \int^z \!n(z') dz'\right).$">|; 

$key = q/N_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1599.png"
 ALT="$ N_1$">|; 

$key = q/displaystylesum_{rmmols}x,y=sum_{rmmols}y,z=sum_{rmmols}z,x=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1248.png"
 ALT="$\displaystyle \sum_{\rm mols} x y = \sum_{\rm mols} y z = \sum_{\rm mols} z x = 0.$">|; 

$key = q/displaystyle=frac{J_1(k_s,a)}{k_s}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2958.png"
 ALT="$\displaystyle = \frac{J_1(k_s  a)}{k_s}.$">|; 

$key = q/-q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="$ -q$">|; 

$key = q/{rmIm}(z)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2447.png"
 ALT="$ {\rm Im }(z)=0$">|; 

$key = q/displaystylefrac{dE}{dt}=f,u=m_0,gamma^{,3},u,frac{du}{dt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3917.png"
 ALT="$\displaystyle \frac{dE}{dt} = f u = m_0  \gamma^{ 3}  u  \frac{du}{dt}.$">|; 

$key = q/4pisqrt{6pi},(mu_0,c,Islash4pi,d);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3270.png"
 ALT="$ 4\pi\sqrt{6\pi} (\mu_0  c I/4\pi  d)$">|; 

$key = q/displaystyleJ_0'(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2948.png"
 ALT="$\displaystyle J_0'(z)$">|; 

$key = q/sigma';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="$ \sigma'$">|; 

$key = q/B=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$ B=0$">|; 

$key = q/displaystyledW=frac{1}{4pi,epsilon_0}frac{q(r),dq}{r}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$\displaystyle dW = \frac{1}{4\pi \epsilon_0} \frac{ q(r) dq}{r}.$">|; 

$key = q/displaystylehat{alpha}=frac{sinhtheta_t}{costheta_i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2152.png"
 ALT="$\displaystyle \hat{\alpha} = \frac{\sinh\theta_t}{\cos\theta_i}.$">|; 

$key = q/displaystyle{bfr}cdot{bfE}'({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3212.png"
 ALT="$\displaystyle {\bf r}\cdot {\bf E}'({\bf r})$">|; 

$key = q/J_m(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2860.png"
 ALT="$ J_m(z)$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}intfrac{{bfj}({bfr'},t-|{bfr}-{bfr'}|slashc)}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi } \int \frac{{\bf j}({\bf r'},t- \vert{\bf r} -{\bf r '}\vert/c )}{\vert{\bf r} - {\bf r}'\vert}  dV'.$">|; 

$key = q/partialslashpartialt'|_{x^{,i}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3996.png"
 ALT="$ \partial/\partial t'\vert _{x^{ i}}$">|; 

$key = q/displaystylefrac{dsigma_{rmsc}}{d{mitOmega}}simeqa^{,2}(k,a)^4left[frac{5}{8},(1+cos^2theta)-costhetaright].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3387.png"
 ALT="$\displaystyle \frac{d\sigma_{\rm sc}}{d{\mit \Omega}} \simeq a^{ 2} (k a)^4\left[ \frac{5}{8}  (1+\cos^2\theta) -\cos\theta\right].$">|; 

$key = q/displaystyleu_g=frac{domega}{dk_g}=c,sqrt{1-omega_c^{,2}slashomega^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2886.png"
 ALT="$\displaystyle u_g = \frac{d\omega}{dk_g} = c  \sqrt{1-\omega_c^{ 2}/\omega^{ 2}}.$">|; 

$key = q/{bfP}=epsilon_0,(epsilon-1),{bfE}_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1250.png"
 ALT="$ {\bf P} =\epsilon_0 
(\epsilon-1)  {\bf E}_0$">|; 

$key = q/+V;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="$ +V$">|; 

$key = q/displaystylec,{bfB}_{rmsc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3332.png"
 ALT="$\displaystyle c {\bf B}_{\rm sc}$">|; 

$key = q/P_l(x)=-x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1358.png"
 ALT="$ P_l(x)=-x$">|; 

$key = q/c,B_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1696.png"
 ALT="$ c  B_0$">|; 

$key = q/k_s^{,2}>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2838.png"
 ALT="$ k_s^{ 2}&gt;0$">|; 

$key = q/n_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2013.png"
 ALT="$ n_2$">|; 

$key = q/displaystyleE_pm=E_xpm{rmi},E_y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1722.png"
 ALT="$\displaystyle E_\pm = E_x \pm {\rm i} E_y,$">|; 

$key = q/displaystylerightarrow-frac{cos(z-l,pislash2)}{z},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3038.png"
 ALT="$\displaystyle \rightarrow -\frac{\cos(z-l \pi/2)}{z},$">|; 

$key = q/c-v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3405.png"
 ALT="$ c-v$">|; 

$key = q/displaystyle=mu_0,c,({bfj}+nablatimes{bfM}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3193.png"
 ALT="$\displaystyle = \mu_0  c  ({\bf j} + \nabla\times {\bf M}),$">|; 

$key = q/j_{01}=2.405;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="$ j_{01}=2.405$">|; 

$key = q/displaystyleU^{,mu}=frac{dx^{,mu}}{dtau}=frac{dx^{,mu}}{dt}frac{dt}{dtau}=gamma(u),({bfu},,c),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3703.png"
 ALT="$\displaystyle U^{ \mu} = \frac{dx^{ \mu}}{d\tau} = \frac{dx^{ \mu}}{dt}\frac{dt}{d\tau} = \gamma(u)  ({\bf u},  c),$">|; 

$key = q/t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$ t$">|; 

$key = q/displaystylef_nu=epsilon_0,F_{nusigma},partial_muF^{,musigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3948.png"
 ALT="$\displaystyle f_\nu = \epsilon_0  F_{\nu\sigma} \partial_\mu F^{ \mu\sigma}.$">|; 

$key = q/G({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$ G({\bf r},{\bf r}')$">|; 

$key = q/[cdots];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$ [\cdots]$">|; 

$key = q/displaystyle{bfE}_{lm}^{(E)}=frac{(-{rmi})^{,l}}{k^{,2}}left[nablaleft(frac{{rmefL},Y_{lm}+frac{{rme}^{,{rmi},k,r}}{r},nablatimes{bfL},Y_{lm}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3146.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(E)} = \frac{(-{\rm i})^{ l}}{k^{ 2}}\left[\nabla...
...} +\frac{{\rm e}^{ {\rm i} k r}}{r}  \nabla\times {\bf L}  Y_{lm} \right].$">|; 

$key = q/v=u(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2371.png"
 ALT="$ v=u(z)$">|; 

$key = q/displaystyle=frac{hat{alpha}}{beta},sinphi_t,psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2150.png"
 ALT="$\displaystyle = \frac{\hat{\alpha}}{\beta} \sin\phi_t \psi_t,$">|; 

$key = q/displaystyle{bfr}cdot{bfL}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3056.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf L} = 0.$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3072.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2})  {\bf B}$">|; 

$key = q/displaystyle2,{rmi},k,(n+1)f_{n+1}=[n,(n+1)+D],f_n.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle 2 {\rm i}  k (n+1) f_{n+1} = [n (n+1)+D] f_n.$">|; 

$key = q/r'llr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2603.png"
 ALT="$ r'\ll r$">|; 

$key = q/|z|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2862.png"
 ALT="$ \vert z\vert$">|; 

$key = q/mu_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2577.png"
 ALT="$ \mu_2$">|; 

$key = q/displaystyledeltaE({rmMeV})=8.85times10^{-2},frac{[E({rmGeV})]^4}{rho({rmmeters})}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4088.png"
 ALT="$\displaystyle \delta E ({\rm MeV}) = 8.85\times 10^{-2}  \frac{[E({\rm GeV})]^4}{\rho ({\rm meters})}.$">|; 

$key = q/x,,y,,z,rightarrow-x,,-y,,-z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3768.png"
 ALT="$ x, y, z,\rightarrow -x, -y, -z$">|; 

$key = q/displaystylerightarrowsqrt{frac{pi}{2,p}},{rme}^{-p};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img968.png"
 ALT="$\displaystyle \rightarrow \sqrt{\frac{\pi}{2 p}} {\rm e}^{-p}$">|; 

$key = q/s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1836.png"
 ALT="$ s$">|; 

$key = q/displaystyle=nablatimes{bfA}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle = \nabla\times{\bf A}.$">|; 

$key = q/nablacdot{bfE}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1110.png"
 ALT="$ \nabla \cdot {\bf E} = 0$">|; 

$key = q/displaystyleE_z(x,y,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2782.png"
 ALT="$\displaystyle E_z(x,y,z,t)$">|; 

$key = q/displaystylef^{,nu}=-partial_muT^{,munu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3962.png"
 ALT="$\displaystyle f^{ \nu} =-\partial_\mu T^{ \mu\nu},$">|; 

$key = q/zgeqh_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2586.png"
 ALT="$ z\geq h_0$">|; 

$key = q/displaystyle{bfD}=epsilon_0,{bfE}+{bfP},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1614.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0  {\bf E} + {\bf P},$">|; 

$key = q/R_0=c,t_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$ R_0 = c  t_0$">|; 

$key = q/x>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="$ x&gt;0$">|; 

$key = q/I_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1298.png"
 ALT="$ I_1$">|; 

$key = q/mu=mu({bfH});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1459.png"
 ALT="$ \mu = \mu({\bf H})$">|; 

$key = q/omega_{0+};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1821.png"
 ALT="$ \omega_{0+}$">|; 

$key = q/displaystyle|{bfr}|rightarrowinfty,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$\displaystyle \vert{\bf r}\vert\rightarrow \infty,$">|; 

$key = q/displaystyler,Y_{1,0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="$\displaystyle r Y_{1,0}$">|; 

$key = q/langle{bfp}_irangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1062.png"
 ALT="$ \langle {\bf p}_i\rangle$">|; 

$key = q/omega>omega_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1928.png"
 ALT="$ \omega&gt;\omega_1$">|; 

$key = q/displaystylef(z)=phi(z)left(A_0+frac{A_1}{z}+frac{A_2}{z^{,2}}+cdotsright),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2404.png"
 ALT="$\displaystyle f(z) = \phi(z) \left( A_0 + \frac{A_1}{z} + \frac{A_2}{z^{ 2}}+\cdots\right),$">|; 

$key = q/chi_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1446.png"
 ALT="$ \chi_m$">|; 

$key = q/Q_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="$ Q_i$">|; 

$key = q/{bfE}_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1236.png"
 ALT="$ {\bf E}_0$">|; 

$key = q/{figure}{epsfysize{=3.75in{centerline{epsffile{Chapter06slashj1.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="422" BORDER="0"
 SRC="|."$dir".q|img1874.png"
 ALT="\begin{figure}
\epsfysize =3.75in
\centerline{\epsffile{Chapter06/j1.eps}}
\end{figure}">|; 

$key = q/(2l+1)!!=(2l+1),(2l-1),(2l-3)cdots5cdot3cdot1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3036.png"
 ALT="$ (2l+1)!! = (2l+1) (2l-1)  (2l-3)\cdots 5\cdot 3\cdot 1$">|; 

$key = q/displaystylepartial_muT^{,munu}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4062.png"
 ALT="$\displaystyle \partial_\mu T^{ \mu\nu} = 0,$">|; 

$key = q/omega>omega_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1638.png"
 ALT="$ \omega &gt;\omega_i$">|; 

$key = q/w(hat{z},h)equivE_y(L,hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2455.png"
 ALT="$ w(\hat{z},h)\equiv E_y(L  \hat{z})$">|; 

$key = q/displaystylef_1(xi,t)=frac{{rmi}}{tau}sqrt{frac{s}{xi}}int_0^{2pi}expleft(-2,{rmi},sqrt{xis},cosuright),cosu,du.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1869.png"
 ALT="$\displaystyle f_1(\xi, t) = \frac{{\rm i}}{\tau} \sqrt{\frac{s}{\xi}}\int_0^{2\pi} \exp\left(-2 {\rm i}  \sqrt{\xi s}  \cos u\right) \cos u  du.$">|; 

$key = q/displaystyle0=1+v,u.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2520.png"
 ALT="$\displaystyle 0 = 1 + v u.$">|; 

$key = q/displaystyledeltaU=int_Vphi,nablacdotdelta{bfD},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1194.png"
 ALT="$\displaystyle \delta U = \int_V \phi \nabla \cdot\delta {\bf D} dV,$">|; 

$key = q/displaystylet=int_0^zfrac{dz'}{u_z}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2341.png"
 ALT="$\displaystyle t =\int_0^z \frac{dz'}{u_z}.$">|; 

$key = q/g_m(r',r)=g_m(r,r');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img972.png"
 ALT="$ g_m(r',r)=g_m(r,r')$">|; 

$key = q/omegarightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1934.png"
 ALT="$ \omega\rightarrow\infty$">|; 

$key = q/cosgamma={bfr}cdot{bfr}'slash(r,r');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="$ \cos\gamma={\bf r}\cdot{\bf r}'/(r r')$">|; 

$key = q/displaystyleint_{-1}^1P_l(x),P_k(x),dx=frac{2}{(2,l+1)},delta_{lk}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="$\displaystyle \int_{-1}^1P_l(x) P_k(x) dx = \frac{2}{(2 l+1)} \delta_{lk}.$">|; 

$key = q/h=k,L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2458.png"
 ALT="$ h= k L$">|; 

$key = q/rho_msimeq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1257.png"
 ALT="$ \rho_m\simeq$">|; 

$key = q/V;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ V$">|; 

$key = q/n(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ n(\omega )$">|; 

$key = q/(hat{z},0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2488.png"
 ALT="$ (\hat{z},0 )$">|; 

$key = q/displaystyledeltaU=int{bfH}cdotdelta{bfB},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1591.png"
 ALT="$\displaystyle \delta U = \int {\bf H}\cdot\delta {\bf B} dV.$">|; 

$key = q/displaystyle-frac{partial}{partialt}left(epsilon_0,{bfE}times{bfB}right)_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="$\displaystyle -\frac{\partial}{\partial t} \left(\epsilon_0 {\bf E}\times{\bf B}\right)_i$">|; 

$key = q/displaystylef_n(x)=sum_{p=0,n}frac{(-1)^pp!}{x^{,p}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2419.png"
 ALT="$\displaystyle f_n(x) = \sum_{p=0,n}\frac{(-1)^p p!}{x^{ p}}$">|; 

$key = q/{bfm}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1423.png"
 ALT="$ {\bf m}_2$">|; 

$key = q/sigmaslashepsilon_1,epsilon_0,omegagg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2763.png"
 ALT="$ \sigma /\epsilon_1 \epsilon_0 \omega
\gg 1$">|; 

$key = q/displaystyleg_{mu'nu'},p_{sigma}^{,mu'},p_{numu}^{,nu'}+g_{mu'nu'},p_{mu}^{,mu'},p_{nusigma}^{,nu'}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3680.png"
 ALT="$\displaystyle g_{\mu'\nu'} p_{\sigma}^{ \mu'}  p_{\nu\mu}^{ \nu'} + g_{\mu'\nu'}  p_{\mu}^{ \mu'} p_{\nu\sigma}^{ \nu'} = 0,$">|; 

$key = q/displaystylephantom{==}left[I_m(k_n,a),K_m(k_n,r_>)-I_m(k_n,r_>),K_m(k_n,a)right],frac{I_m(k_n,r_<)}{I_m(k_n,a)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1015.png"
 ALT="$\displaystyle \phantom{==}\left[I_m(k_n a) K_m(k_n r_&gt;)- I_m(k_n r_&gt;) K_m(k_n a)\right] \frac{I_m(k_n r_&lt;)}{I_m(k_n a)}.$">|; 

$key = q/{calM}_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3244.png"
 ALT="$ {\cal M}_{lm}$">|; 

$key = q/beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1560.png"
 ALT="$ \beta$">|; 

$key = q/displaystylev_g(omega)=frac{domega}{dk_-}simeq2,c,frac{sqrt{omega,{mitOmega}}}{omega_p}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1768.png"
 ALT="$\displaystyle v_g(\omega) = \frac{d\omega}{dk_-} \simeq 2 c  \frac{\sqrt{\omega {\mit\Omega}}}{\omega_p}.$">|; 

$key = q/psi({bfr}')=G_D({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="$ \psi({\bf r}')=G_D({\bf r},{\bf r}')$">|; 

$key = q/{bfr}cdot{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3204.png"
 ALT="$ {\bf r}\cdot{\bf E}'$">|; 

$key = q/displaystyle{bfr}cdot(nablatimes{bfA})=({bfr}timesnabla)cdot{bfA}={rmi},{bfL}cdot{bfA},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3205.png"
 ALT="$\displaystyle {\bf r}\cdot(\nabla\times{\bf A}) = ({\bf r}\times\nabla)\cdot {\bf A} = {\rm i} {\bf L}\cdot{\bf A},$">|; 

$key = q/arightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1374.png"
 ALT="$ a\rightarrow 0$">|; 

$key = q/|r|rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2923.png"
 ALT="$ \vert r\vert\rightarrow \infty$">|; 

$key = q/phisimeq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4149.png"
 ALT="$ \phi \simeq 0$">|; 

$key = q/displaystyleL^2,{bfL};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3064.png"
 ALT="$\displaystyle L^2 {\bf L}$">|; 

$key = q/dx^{,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3556.png"
 ALT="$ dx^{ i}$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0,I_1}{4pi}oint_1frac{d{bfr}_1}{|{bfr}-{bfr}_1|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1415.png"
 ALT="$\displaystyle {\bf A}({\bf r})= \frac{\mu_0 I_1}{4\pi}\oint_1\frac{d{\bf r}_1}{\vert{\bf r}-{\bf r}_1\vert}.
$">|; 

$key = q/displaystylef_i=e,(E_i+B_{ij},u^{,j}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3930.png"
 ALT="$\displaystyle f_i = e (E_i + B_{ij}  u^{ j}),$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{epsilon_0}intG({bfr},{bfr}'),rho({bfr}'),dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="$\displaystyle \phi({\bf r})=-\frac{1}{\epsilon_0}\int G({\bf r},{\bf r}') \rho({\bf r}') dV'.$">|; 

$key = q/48.8^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$ 48.8^\circ $">|; 

$key = q/displaystyle{bfB}=mu,{bfH},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1454.png"
 ALT="$\displaystyle {\bf B} = \mu  {\bf H},$">|; 

$key = q/displaystylen_n,sintheta_n=sintheta_I.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2289.png"
 ALT="$\displaystyle n_n \sin\theta_n =\sin\theta_I.$">|; 

$key = q/J^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3720.png"
 ALT="$ J^{ \mu}$">|; 

$key = q/displaystyle=n_1,k_0,(sintheta_r,,0,-costheta_r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2036.png"
 ALT="$\displaystyle =n_1  k_0 (\sin\theta_r, 0,-\cos\theta_r),$">|; 

$key = q/1slashh^{,n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2470.png"
 ALT="$ 1/h^{ n}$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06slashhyperg.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="443" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img2448.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06/hyperg.eps}}
\end{figure}">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),{bfr}cdot{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3208.png"
 ALT="$\displaystyle (\nabla^{ 2}+k^{ 2}) {\bf r}\cdot{\bf E}'$">|; 

$key = q/displaystylephantom{=}+frac{1}{4pi}int_0^piint_0^{2pi}frac{phi_S(theta',varphi')ntheta',dtheta',dvarphi'}{(r^{,2}-2,r,a,cosgamma+a^{,2})^{3slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="$\displaystyle \phantom{=}+\frac{1}{4\pi}\int_0^\pi\int_0^{2\pi}\frac{\phi_S(\th...
...\sin\theta' d\theta' d\varphi'}{(r^{ 2}-2 r a \cos\gamma+a^{ 2})^{3/2}},$">|; 

$key = q/G^{,munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3817.png"
 ALT="$ G^{ \mu\nu}$">|; 

$key = q/displaystylea^{,2}=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1645.png"
 ALT="$\displaystyle a^{ 2} =$">|; 

$key = q/displaystyleE_z(r,varphi,z,t)=A,f(r,varphi),cos(k_3,z),{rme}^{-{rmi},omega,t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2853.png"
 ALT="$\displaystyle E_z(r,\varphi,z,t) = A  f(r,\varphi)  \cos(k_3  z)  {\rm e}^{-{\rm i} \omega  t},$">|; 

$key = q/{bfm}=int{bfM},dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1485.png"
 ALT="$ {\bf m} = \int{\bf M} dV$">|; 

$key = q/P_{-1}(cosalpha)=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1039.png"
 ALT="$ P_{-1}(\cos\alpha)=-1$">|; 

$key = q/displaystyle{bfE}=left{{array}{lll}[qslash(4pi,epsilon_0,r^{,2})],{bfe}_r&mbox{hspace{0.5cm}}&r<a[0.5ex]{bf0}&&r>a{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="$\displaystyle {\bf E} = \left\{ \begin{array}{lll} [q/(4\pi \epsilon_0 r^{ 2...
...,{\bf e}_r&amp;\mbox{\hspace{0.5cm}}&amp; r&lt;a\ [0.5ex] {\bf0}&amp;&amp;r&gt;a \end{array}\right.,$">|; 

$key = q/displaystyleu_p=frac{omega}{k_g}=frac{c}{sqrt{1-omega_c^{,2}slashomega^{,2}}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2885.png"
 ALT="$\displaystyle u_p = \frac{\omega}{k_g} = \frac{c}{\sqrt{1-\omega_c^{ 2}/\omega^{ 2}}}.$">|; 

$key = q/displaystyle=left(frac{5}{16pi}right)^{1slash2}(3,cos^2theta-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="$\displaystyle =\left(\frac{5}{16\pi}\right)^{1/2}(3 \cos^2\theta-1)$">|; 

$key = q/displaystyle=mu,frac{partialphi_m(r=b-,theta)}{partialr}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1554.png"
 ALT="$\displaystyle = \mu  \frac{\partial\phi_m(r=b-,\theta)}{\partial r}.$">|; 

$key = q/L_pm;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3319.png"
 ALT="$ L_\pm$">|; 

$key = q/omega<omega_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1637.png"
 ALT="$ \omega &lt;\omega_i$">|; 

$key = q/x^{,mu'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4044.png"
 ALT="$ x^{ \mu'}$">|; 

$key = q/B_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1799.png"
 ALT="$ B_1$">|; 

$key = q/{bfE}cdot{bfj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$ {\bf E}\cdot{\bf j}$">|; 

$key = q/(x,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2540.png"
 ALT="$ (x,0)$">|; 

$key = q/dot{u}=a,omega_0^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4119.png"
 ALT="$ \dot{u}=a \omega_0^{ 2}$">|; 

$key = q/(x,0)_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2546.png"
 ALT="$ (x,0)_s$">|; 

$key = q/displaystyleU=frac{1}{2}int{bfH}cdot{bfB},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1592.png"
 ALT="$\displaystyle U = \frac{1}{2} \int {\bf H}\cdot{\bf B}  dV.$">|; 

$key = q/beta=uslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4144.png"
 ALT="$ \beta=u/c$">|; 

$key = q/EslashB;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4191.png"
 ALT="$ E/B$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}int_Vfrac{rho({bfr}')}{|{bfr}-{bfr}'|},dV'+frac{1}{4pi,epsilon_0}int_Sfrac{sigma({bfr}')}{|{bfr}-{bfr}'|},dS';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="$\displaystyle = \frac{1}{4\pi \epsilon_0}\int_V \frac{\rho({\bf r}')}{\vert{\b...
...\pi \epsilon_0}\int_S \frac{\sigma({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dS'$">|; 

$key = q/displaystylefrac{c,B_0}{E_0}=frac{k,c}{omega}={rme}^{,{rmi},pislash4}sqrt{frac{sigma}{epsilon_0,omega}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1694.png"
 ALT="$\displaystyle \frac{c  B_0}{E_0} = \frac{k c}{\omega} = {\rm e}^{ {\rm i} \pi/4} \sqrt{\frac{\sigma} {\epsilon_0 \omega}}.$">|; 

$key = q/displaystyleR_s=frac{1}{sigma,d}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2799.png"
 ALT="$\displaystyle R_s = \frac{1}{\sigma  d}.$">|; 

$key = q/l,x+m,y+n,z+p=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3444.png"
 ALT="$ l x + m  y + n  z + p=0$">|; 

$key = q/U^{,mu}=({bf0},,c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3706.png"
 ALT="$ U^{ \mu}=({\bf0},  c)$">|; 

$key = q/z=+dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$ z=+d/2$">|; 

$key = q/displaystylem,ddot{bfs}+f,{bfs}=-e,({bfE}+dot{bfs}times{bfB}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1715.png"
 ALT="$\displaystyle m \ddot{\bf s} +f {\bf s} = - e ({\bf E} + \dot{\bf s}\times{\bf B}),$">|; 

$key = q/displaystylephi(r,theta)=frac{Q}{8pi,epsilon_0}sum_{l=0,infty}frac{1}{2,l+1}left(alpha)-P_{l-1}(cosalpha)right]frac{r^{,l}}{R^{,l+1}},P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="444" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1038.png"
 ALT="$\displaystyle \phi(r,\theta) = \frac{Q}{8\pi \epsilon_0}\sum_{l=0,\infty}\frac...
...\alpha)-P_{l-1}(\cos\alpha)\right]\frac{r^{ l}}{R^{ l+1}} 
P_l(\cos\theta),
$">|; 

$key = q/displaystyle=frac{u'_1+v}{1+u'_1,vslashc^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3505.png"
 ALT="$\displaystyle = \frac{u'_1+v}{1+u'_1  v/c^{ 2}},$">|; 

$key = q/dq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="$ dq$">|; 

$key = q/displaystyle=-{rmi},frac{k_g}{k_s},J_1(k_s,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2942.png"
 ALT="$\displaystyle =-{\rm i} \frac{k_g}{k_s}  J_1(k_s  r),$">|; 

$key = q/F_{munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3798.png"
 ALT="$ F_{\mu\nu}$">|; 

$key = q/displaystyleP(t')=frac{e^{,2},dot{u}^{,2}}{8pi,epsilon_0,c^{,3}}int_0^pifrac{sin_0,c^{,3}}int_{-1}^{+1}frac{(1-mu^{,2}),dmu}{[1-(uslashc),mu]^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4107.png"
 ALT="$\displaystyle P(t')= \frac{e^{ 2} \dot{u}^{ 2}}{8\pi  \epsilon_0  c^{ 3}}...
...n_0  c^{ 3}} \int_{-1}^{+1} \frac{(1-\mu^{ 2}) d\mu}{[1-(u/c) \mu]^{ 5}}.$">|; 

$key = q/displaystyle=psi_t,sintheta_t,cos(omega,t-n_1,k_0,sintheta_i,x-n_2,k_0,costheta_t,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2112.png"
 ALT="$\displaystyle =\psi_t \sin\theta_t \cos(\omega t-n_1 k_0 \sin\theta_i x-n_2 k_0 \cos\theta_t z)$">|; 

$key = q/displaystyle=-frac{psi_r^{,2},costheta_i}{2,epsilon_0,c,n_1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2082.png"
 ALT="$\displaystyle = -\frac{\psi_r^{ 2} \cos\theta_i}{2 \epsilon_0 c n_1},$">|; 

$key = q/epsilon_1=epsilon_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1289.png"
 ALT="$ \epsilon_1=\epsilon_2$">|; 

$key = q/A_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2688.png"
 ALT="$ A_r$">|; 

$key = q/displaystylec,{bfB}_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3152.png"
 ALT="$\displaystyle c {\bf B}_l$">|; 

$key = q/displaystylerightarrowfrac{1}{m!}left(frac{p}{2}right)^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="$\displaystyle \rightarrow \frac{1}{m!}\left(\frac{p}{2}\right)^m$">|; 

$key = q/omega=-omega_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1936.png"
 ALT="$ \omega=-\omega_s$">|; 

$key = q/-pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2282.png"
 ALT="$ -\pi/2$">|; 

$key = q/displaystyle=frac{u_1-v}{1-u_1,vslashc^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3502.png"
 ALT="$\displaystyle = \frac{u_1-v}{1-u_1  v/c^{ 2}},$">|; 

$key = q/displaystyleG^{i4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3823.png"
 ALT="$\displaystyle G^{i4}$">|; 

$key = q/displaystylefrac{1}{c^{,2}}frac{partialphi}{partialt}+nablacdot{bfA}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3735.png"
 ALT="$\displaystyle \frac{1}{c^{ 2}} \frac{\partial\phi}{\partial t} + \nabla\cdot {\bf A} =0.$">|; 

$key = q/displaystylek_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2784.png"
 ALT="$\displaystyle k_1$">|; 

$key = q/displaystyleE_y(x,y,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2780.png"
 ALT="$\displaystyle E_y(x,y,z,t)$">|; 

$key = q/displaystyle{bfg}=epsilon_0,({bfE}times{bfB}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$\displaystyle {\bf g} = \epsilon_0 ({\bf E}\times {\bf B}),$">|; 

$key = q/hat{z}=hat{z}_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2483.png"
 ALT="$ \hat{z}=\hat{z}_0$">|; 

$key = q/displaystylefrac{d^{,2}R}{dr^{,2}}+frac{1}{r},frac{dR}{dr}-left(k^{,2}+frac{m^{,2}}{r^{,2}}right)R=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img931.png"
 ALT="$\displaystyle \frac{d^{ 2} R}{dr^{ 2}} + \frac{1}{r} \frac{dR}{dr}-\left(k^{ 2}+\frac{m^{ 2}}{r^{ 2}}\right) R = 0.$">|; 

$key = q/displaystyleD=frac{1}{sintheta}frac{partial}{partialtheta}left(sintheta,frac{paright)+frac{1}{sin^{,2}theta},frac{partial^{,2}}{partialvarphi^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle D= \frac{1}{\sin\theta} \frac{\partial}{\partial\theta}\left( \si...
...ght) +\frac{1}{\sin^{ 2}\theta} \frac{\partial^{ 2}}{\partial\varphi^{ 2}}.$">|; 

$key = q/R(r)=J_m(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img918.png"
 ALT="$ R(r)=J_m(k r)$">|; 

$key = q/7;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2217.png"
 ALT="$ 7$">|; 

$key = q/displaystyleleft[frac{,{rmi},alpha_pm(l)}{k},frac{1}{r}frac{d[r,h_l^{(1)}(k,r)]}pm1}mp{rmi},beta_pm(l),h_l^{(1)}(k,r),{bfn}times{bfX}_{l,pm1}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3347.png"
 ALT="$\displaystyle \left[ \frac{ {\rm i}  \alpha_\pm(l)}{k} \frac{1}{r}\frac{d[r ...
...\rm i}  \beta_\pm(l) h_l^{(1)}(k r) {\bf n}\times {\bf X}_{l,\pm 1}\right].$">|; 

$key = q/H_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2831.png"
 ALT="$ H_z$">|; 

$key = q/1slash(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3148.png"
 ALT="$ 1/(k r)$">|; 

$key = q/alpha=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2707.png"
 ALT="$ \alpha=0$">|; 

$key = q/displaystyle=left(frac{1-alpha,beta}{1+alpha,beta}right)^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2121.png"
 ALT="$\displaystyle =\left(\frac{1-\alpha \beta}{1+\alpha \beta}\right)^2,$">|; 

$key = q/displaystyle{bfj}({bfr})=Isin(k,dslash2-k,|z|),delta(x),delta(y),{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2621.png"
 ALT="$\displaystyle {\bf j}({\bf r}) = I \sin (k d/2-k \vert z\vert) \delta(x) \delta(y) {\bf e}_z$">|; 

$key = q/displaystylefrac{dsigma_{rmsc}}{d{mitOmega}}=-frac{a^{,2}}{2},{rmRe},[{bfE}_{rmsc}cdot({bfn}timesc,{bfB}_{rmsc}^{,ast})]_{r=a}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3342.png"
 ALT="$\displaystyle \frac{d\sigma_{\rm sc}}{d{\mit \Omega}} = - \frac{a^{ 2}}{2}   ...
...e} [{\bf E}_{\rm sc}\cdot ({\bf n}\times c {\bf B}_{\rm sc}^{ \ast})]_{r=a}.$">|; 

$key = q/S=-Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1983.png"
 ALT="$ S=-Q$">|; 

$key = q/A^{icdotsj}_{kcdotsl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3551.png"
 ALT="$ A^{i\cdots j}_{k\cdots l}$">|; 

$key = q/displaystylefrac{d}{dt}int_Vrho,dV+int_S{bfj}cdotd{bfS}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \frac{d}{dt}\int_V \rho dV +\int_S {\bf j}\cdot d{\bf S} = 0,$">|; 

$key = q/mu=costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="$ \mu=\cos\theta$">|; 

$key = q/displaystyle{mitPhi}^{,mu}=frac{1}{4pi,epsilon_0,c}intfrac{[J^{,mu}]}{r},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3883.png"
 ALT="$\displaystyle {\mit\Phi}^{ \mu} = \frac{1}{4\pi \epsilon_0 c}\int \frac{[J^{ \mu}]}{r} dV,$">|; 

$key = q/displaystylerho_{l,m}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="$\displaystyle \rho_{l,m}(r)$">|; 

$key = q/displaystylen(omega,z)=left(1-frac{omega_p^{,2}(z)}{omega^{,2}}right)^{1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2344.png"
 ALT="$\displaystyle n(\omega,z) = \left(1-\frac{\omega_p^{ 2}(z)}{\omega^{ 2}}\right)^{1/2},$">|; 

$key = q/displaystyle=-frac{mu_0,I}{4pi,a}intfrac{sinvarphi',delta(costheta'),delta(r'-a)}{|{bfr}-{bfr}'|_{varphi=0}},r'^{,2},dr',d{mitOmega}',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1324.png"
 ALT="$\displaystyle = - \frac{\mu_0 I}{4\pi a}\int \frac{\sin\varphi' \delta(\cos\...
...r'-a)}{\vert{\bf r}-{\bf r}'\vert _{\varphi=0}} r'^{ 2} dr' d{\mit\Omega}',$">|; 

$key = q/displaystyleg_m(r,r')=A,I_m(k,r_<),K_m(k,r_>),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img973.png"
 ALT="$\displaystyle g_m(r,r') = A I_m(k r_&lt;) K_m(k r_&gt;),$">|; 

$key = q/displaystyleA_m(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img924.png"
 ALT="$\displaystyle A_m(k)$">|; 

$key = q/displaystyleR_m(r',k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img989.png"
 ALT="$\displaystyle R_m(r',k)$">|; 

$key = q/g_{m,n}(r,r');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1005.png"
 ALT="$ g_{m,n}(r,r')$">|; 

$key = q/z<h_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2584.png"
 ALT="$ z&lt;h_0$">|; 

$key = q/depsilonslashdrho_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1230.png"
 ALT="$ d\epsilon/d\rho_m$">|; 

$key = q/x^{,3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3652.png"
 ALT="$ x^{ 3}$">|; 

$key = q/vslashcrightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3472.png"
 ALT="$ v/c\rightarrow 0$">|; 

$key = q/q''(hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2461.png"
 ALT="$ q''(\hat{z})$">|; 

$key = q/z=k_s,r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2859.png"
 ALT="$ z=k_s  r$">|; 

$key = q/G_N({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="$ G_N({\bf r},{\bf r}')$">|; 

$key = q/displaystyleE_i,cos(omega,t)+E_r,cos(omega,t+phi_r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2199.png"
 ALT="$\displaystyle E_i \cos(\omega t) + E_r \cos(\omega t+\phi_r)$">|; 

$key = q/displaystyle=mu_0left({bfj}+epsilon_0,frac{partial{bfE}}{partialt}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3806.png"
 ALT="$\displaystyle = \mu_0 \left({\bf j} + \epsilon_0  \frac{\partial {\bf E}} {\partial t}\right).$">|; 

$key = q/[,];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$ [ ]$">|; 

$key = q/+k^{,2},Z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="$ +k^{ 2} Z$">|; 

$key = q/chi_e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1073.png"
 ALT="$ \chi_e$">|; 

$key = q/musimeq10^5mu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1576.png"
 ALT="$ \mu\simeq 10^5 \mu_0$">|; 

$key = q/displaystylesigma_b(r)=-frac{q}{2pi,epsilon_1}left(frac{epsilon_2-epsilon_1}{epsilon_2+epsilon_1}right)frac{d}{(r^{,2}+d^{,2})^{3slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1127.png"
 ALT="$\displaystyle \sigma_b(r) = -\frac{q}{2\pi \epsilon_1} \left(\frac{\epsilon_2-\epsilon_1} {\epsilon_2+\epsilon_1}\right) \frac{d}{(r^{ 2}+d^{ 2})^{3/2}}.$">|; 

$key = q/displaystyler'=-c,t'=-c,gamma,left(t-frac{v,x}{c^{,2}}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3747.png"
 ALT="$\displaystyle r' = -c t' =- c \gamma \left(t - \frac{v x}{c^{ 2}}\right),$">|; 

$key = q/E^{,23};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3828.png"
 ALT="$ E^{ 23}$">|; 

$key = q/displaystyle=left(frac{1-alpha,beta}{1+alpha,beta}right)psi_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2118.png"
 ALT="$\displaystyle =\left(\frac{1-\alpha \beta}{1+\alpha \beta}\right)\psi_i,$">|; 

$key = q/displaystylen^{,2}=n_i^{,2}+frac{N,e^{,2},f_islashepsilon_0,m}{omega_i^{,2}-omega^{,2}-{rmi},g_i,omega,omega_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1640.png"
 ALT="$\displaystyle n^{ 2} = n_i^{ 2} + \frac{N e^{ 2}  f_i/\epsilon_0  m}{\omega_i^{ 2}-\omega^{ 2} -{\rm i} g_i \omega \omega_i},$">|; 

$key = q/displaystyle=int_0^inftyJ_m(k,r),B_m(k),dk.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img922.png"
 ALT="$\displaystyle = \int_0^\infty J_m(k r) B_m(k) dk.$">|; 

$key = q/displaystyleint_Sphi,nablaphicdotd{bfS}=int_Vleft(phi,nabla^{,2}phi+nablaphicdotnablaphiright)dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$\displaystyle \int_S \phi \nabla\phi\cdot d{\bf S} = \int_V\left( \phi \nabla^{ 2} \phi + \nabla \phi\cdot \nabla \phi\right) dV.$">|; 

$key = q/g=x_j';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1397.png"
 ALT="$ g=x_j'$">|; 

$key = q/displaystylefrac{partialD_z}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2047.png"
 ALT="$\displaystyle \frac{\partial D_z}{\partial t}$">|; 

$key = q/mu';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1603.png"
 ALT="$ \mu'$">|; 

$key = q/displaystyleY_{2,-2}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="$\displaystyle Y_{2,-2}(\theta,\varphi)$">|; 

$key = q/displaystylefrac{partialH_z}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2093.png"
 ALT="$\displaystyle \frac{\partial H_z}{\partial t}$">|; 

$key = q/S'(x',y',z',t');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3392.png"
 ALT="$ S'(x',y',z',t')$">|; 

$key = q/displaystyleP_{rmload}=frac{E_0^{,2},d^{,2}}{32,R_{rmrad}}=frac{epsilon_0,c,E_0^{,2}}{2},A_{rmeff},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2672.png"
 ALT="$\displaystyle P_{\rm load} =\frac{ E_0^{ 2}  d^{ 2}}{32  R_{\rm rad} } = \frac{\epsilon_0  c  E_0^{ 2}}{2}  A_{\rm eff},$">|; 

$key = q/displaystylep_{musigma}^{,mu'}=frac{partialp_mu^{,mu'}}{partialx^{,sigma}}=frac{l^{,2}x^{,mu'}}{partialx^{,mu}partialx^{,sigma}}=p_{sigmamu}^{,mu'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3678.png"
 ALT="$\displaystyle p_{\mu\sigma}^{ \mu'} = \frac{\partial p_\mu^{ \mu'} }{\partial...
...2} x^{ \mu'}}{\partial x^{ \mu}\partial x^{ \sigma}}=p_{\sigma\mu}^{ \mu'},$">|; 

$key = q/displaystyle(hat{z},a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2474.png"
 ALT="$\displaystyle (\hat{z}, a)$">|; 

$key = q/displaystyle{bfE}'={bfE}+frac{rmi}{epsilon_0,omega},{bfj}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3195.png"
 ALT="$\displaystyle {\bf E}' = {\bf E} + \frac{\rm i}{\epsilon_0  \omega}  {\bf j}.$">|; 

$key = q/{bff}=-nablaW;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="$ {\bf f} = - \nabla W$">|; 

$key = q/displaystyle=-intr^{,l},Y_{lm}^{,ast},nablacdot{bfM},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3243.png"
 ALT="$\displaystyle = -\int r^{ l} Y_{lm}^{ \ast}  \nabla\cdot{\bf M}  dV.$">|; 

$key = q/displaystyleW=frac{epsilon_0}{2}intE^{,2},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$\displaystyle W = \frac{\epsilon_0}{2} \int E^{ 2} dV,$">|; 

$key = q/S';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="$ S'$">|; 

$key = q/displaystyleW=frac{1}{2},{bfE}cdot{bfD}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1204.png"
 ALT="$\displaystyle W = \frac{1}{2} {\bf E}\cdot{\bf D}.$">|; 

$key = q/pislash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1695.png"
 ALT="$ \pi/4$">|; 

$key = q/displaystylefrac{1}{|{bfr}-{bfr}'+{bfd}|}simeqfrac{1}{|{bfr}-{bfr}'|}-frac{{bfd}cdot({bfr}-{bfr}')}{|{bfr}-{bfr}'|^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="$\displaystyle \frac{1}{\vert{\bf r}-{\bf r}'+{\bf d}\vert} \simeq \frac{1}{\ver...
...vert}-\frac{{\bf d}\cdot ({\bf r}-{\bf r}')}{\vert{\bf r}-{\bf r}'\vert^{ 3}}.$">|; 

$key = q/displaystylesimeqfrac{mu_0}{4pi}intfrac{[partial{bfj}_perpslashpartialt]times{bfR}}{c,R^{,2}},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$\displaystyle \simeq \frac{\mu_0}{4\pi} \int \frac{ [\partial {\bf j}_\perp/\partial t]\times {\bf R} } {c R^{ 2}} dV',$">|; 

$key = q/dS_{4'}=d^{,3}x';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4048.png"
 ALT="$ dS_{4'} = d^{ 3}x'$">|; 

$key = q/x=-dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="$ x=-d/2$">|; 

$key = q/displaystyle=-frac{q}{4pi,a^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="$\displaystyle = - \frac{q}{4\pi a^{ 2}},$">|; 

$key = q/displaystyle{bfF}=frac{q,q'}{4pi,epsilon_0},frac{{bfr}-{bfr}'}{|{bfr}-{bfr}'|^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="$\displaystyle {\bf F} = \frac{q q'}{4\pi \epsilon_0}  \frac{{\bf r}-{\bf r}'}{\vert{\bf r}-{\bf r}'\vert^{ 3}}.$">|; 

$key = q/displaystyle({bfa}times{bfb})^i=epsilon^{,ijk},a_j,b_k,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3762.png"
 ALT="$\displaystyle ({\bf a}\times{\bf b})^i = \epsilon^{ ijk} a_j  b_k,$">|; 

$key = q/displaystyle=-frac{k}{sqrt{l,(l+1)}}ointY_{lm}^{,ast},{bfr}cdot{bfE},d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3125.png"
 ALT="$\displaystyle = - \frac{k}{\sqrt{l (l+1)}} \oint Y_{lm}^{ \ast}  {\bf r} \cdot{\bf E} d{\mit\Omega}.$">|; 

$key = q/displaystylemu_0=4pitimes10^{-7},{rmN,A^{,-2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle \mu_0 = 4\pi\times 10^{-7} {\rm N A^{ -2}}$">|; 

$key = q/{bfm}=m,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1376.png"
 ALT="$ {\bf m} = m {\bf e}_z$">|; 

$key = q/displaystylefrac{dU}{dt}=int_Vleft[-phi,nablacdot(rho_f,{bfu})+frac{epsilon_0}{2cdot{bfu}+frac{epsilon_0}{2},E^{,2},nablaepsilon,cdot{bfu}right],dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1225.png"
 ALT="$\displaystyle \frac{dU}{dt} = \int_V\left[-\phi \nabla \cdot(\rho_f {\bf u}) ...
...u} + \frac{\epsilon_0}{2}  E^{ 2} \nabla\epsilon  \cdot {\bf u}\right] dV.$">|; 

$key = q/displaystyle=int_{-infty}^infty{mitPhi}_m(r,k),{rme}^{,{rmi},k,z},dk,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img986.png"
 ALT="$\displaystyle = \int_{-\infty}^\infty {\mit\Phi}_m(r,k) {\rm e}^{ {\rm i} k z} dk,$">|; 

$key = q/displaystylefrac{c}{v_g}=frac{c,t}{x},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1915.png"
 ALT="$\displaystyle \frac{c}{v_g} = \frac{c t}{x},$">|; 

$key = q/'equivdslashdhat{z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2457.png"
 ALT="$ '\equiv d/d\hat{z}$">|; 

$key = q/delta{bfD};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1195.png"
 ALT="$ \delta{\bf D}$">|; 

$key = q/v=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2366.png"
 ALT="$ v=0$">|; 

$key = q/K_m(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2920.png"
 ALT="$ K_m(z)$">|; 

$key = q/displaystylenabla'^{,2}G_3({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="$\displaystyle \nabla'^{ 2} G_3({\bf r},{\bf r}')=0$">|; 

$key = q/phi({bfr}')=G_D({bfr}'',{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="$ \phi({\bf r}')=G_D({\bf r}'',{\bf r}')$">|; 

$key = q/displaystyleg_{m,n}(r,r')=-left[I_m(k_n,a),K_m(k_n,r_>)-I_m(k_n,r_>),K_m(k_n,a)right],frac{I_m(k_n,r_<)}{I_m(k_n,a)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1012.png"
 ALT="$\displaystyle g_{m,n}(r,r') = -\left[I_m(k_n a) K_m(k_n r_&gt;)- I_m(k_n r_&gt;) K_m(k_n a)\right] \frac{I_m(k_n r_&lt;)}{I_m(k_n a)}.$">|; 

$key = q/v({bfr})=-rho({bfr})slashepsilon_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="$ v({\bf r})=-\rho({\bf r})/\epsilon_0$">|; 

$key = q/displaystyle=T^{,3},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3643.png"
 ALT="$\displaystyle = T^{ 3},$">|; 

$key = q/displaystyleomega^{,2}=k^{,2},c^{,2}+omega_0^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2579.png"
 ALT="$\displaystyle \omega^{ 2} = k^{ 2} c^{ 2}+\omega_0^{ 2},
$">|; 

$key = q/D=epsilon_0,E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1133.png"
 ALT="$ D= \epsilon_0  E_0$">|; 

$key = q/n^2=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2589.png"
 ALT="$ n^2=1$">|; 

$key = q/phi_2({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$ \phi_2({\bf r})$">|; 

$key = q/epsilon_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1082.png"
 ALT="$ \epsilon_2$">|; 

$key = q/displaystyle=z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3402.png"
 ALT="$\displaystyle = z,$">|; 

$key = q/nu';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3681.png"
 ALT="$ \nu'$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}frac{q}{|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$\displaystyle \phi({\bf r})= \frac{1}{4\pi \epsilon_0} \frac{q}{\vert{\bf r} - {\bf r}'\vert}.$">|; 

$key = q/displaystylenablap={bff}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1253.png"
 ALT="$\displaystyle \nabla p = {\bf f}.$">|; 

$key = q/G({bfr},{bfr}')rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$ G({\bf r}, {\bf r}')\rightarrow 0$">|; 

$key = q/G_omega({bfr}-{bfr}')=G_omega(|{bfr}-{bfr}'|);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$ G_\omega({\bf r}-{\bf r}')=G_\omega(\vert{\bf r}-{\bf r}'\vert)$">|; 

$key = q/g({bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1385.png"
 ALT="$ g({\bf r}')$">|; 

$key = q/displaystylesimeqfrac{pi}{4}-frac{alpha}{sqrt{2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2211.png"
 ALT="$\displaystyle \simeq \frac{\pi}{4}-\frac{\alpha}{\sqrt{2}}.$">|; 

$key = q/displaystyleoint[f_l(r),{bfX}_{l'm'}]^{,ast}cdot[nablatimesg_l(r),{bfX}_{lm}],d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3311.png"
 ALT="$\displaystyle \oint [f_l(r)  {\bf X}_{l'm'}]^{ \ast} \cdot [\nabla\times g_l(r)  {\bf X}_{lm}] d{\mit\Omega}$">|; 

$key = q/displaystyle[E_y]_{z=0_-}^{z=0_+}=[D_yslash(epsilon,epsilon_0)]_{z=0_-}^{z=0_+}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2117.png"
 ALT="$\displaystyle [E_y]_{z=0_-}^{z=0_+} = [D_y/(\epsilon \epsilon_0)]_{z=0_-}^{z=0_+}=0,$">|; 

$key = q/displaystyleK=intleft[-g,nabla'cdot(f,{bfj})+g,{bfj}cdotnabla'fright]dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1388.png"
 ALT="$\displaystyle K=\int\left[-g \nabla'\cdot(f {\bf j})+g {\bf j}\cdot\nabla' f\right]dV'$">|; 

$key = q/l';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3113.png"
 ALT="$ l'$">|; 

$key = q/alpha_{0,0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="$ \alpha_{0,0}$">|; 

$key = q/displaystyle{bfE}=-nablaphi-frac{partial{bfA}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle {\bf E} = -\nabla\phi- \frac{\partial {\bf A}}{\partial t},$">|; 

$key = q/displaystyle=-frac{omega,mu_0}{k_g},H_r,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2932.png"
 ALT="$\displaystyle =- \frac{\omega \mu_0}{k_g}  H_r,$">|; 

$key = q/displaystylex_0=2,h_0,tantheta+frac{2}{alpha},sin2theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2590.png"
 ALT="$\displaystyle x_0 = 2 h_0 \tan\theta + \frac{2}{\alpha} \sin2\theta
$">|; 

$key = q/1slash(mu_0,c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3341.png"
 ALT="$ 1/(\mu_0  c)$">|; 

$key = q/x^irightarrowx^{i'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3546.png"
 ALT="$ x^i\rightarrow x^{i'}$">|; 

$key = q/displaystyle=frac{k}{sqrt{l,(l+1)}}ointY_{lm}^{,ast},{bfr}cdotc,{bfB},d{mitOmega},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3123.png"
 ALT="$\displaystyle = \frac{k}{\sqrt{l (l+1)}}\oint Y_{lm}^{ \ast}  {\bf r} \cdot c {\bf B} d{\mit\Omega},$">|; 

$key = q/theta=alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1037.png"
 ALT="$ \theta=\alpha$">|; 

$key = q/displaystyleboxempty{mitPhi}^{,mu}=frac{J^{,mu}}{c,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3730.png"
 ALT="$\displaystyle \boxempty {\mit \Phi}^{ \mu} = \frac{J^{ \mu}}{c \epsilon_0}.$">|; 

$key = q/U_mu,A^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3709.png"
 ALT="$ U_\mu  A^{ \mu}$">|; 

$key = q/displaystyle{mitDelta}tsimfrac{b}{gamma,c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3904.png"
 ALT="$\displaystyle {\mit\Delta} t \sim \frac{b}{\gamma  c},$">|; 

$key = q/displaystylep_{l,m}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="$\displaystyle p_{l,m}(r)$">|; 

$key = q/E_1rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1138.png"
 ALT="$ E_1\rightarrow 0$">|; 

$key = q/displaystylesum_{l=0,infty}sum_{m=-l,+l}Y^{,ast}_{lm}(theta',varphi'),Y_{lm}(theta,varphi)=delta(varphi-varphi'),delta(costheta-costheta').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3176.png"
 ALT="$\displaystyle \sum_{l=0,\infty} \sum_{m=-l,+l}Y^{ \ast}_{lm}(\theta',\varphi')...
...m}(\theta,\varphi) = \delta(\varphi-\varphi') \delta(\cos\theta -\cos\theta').$">|; 

$key = q/displaystyle=-(dx^1)^2-(dx^2)^2-(dx^3)^2+(dx^4)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3623.png"
 ALT="$\displaystyle = -(dx^1)^2 -(dx^2)^2 -(dx^3)^2 + (dx^4)^2$">|; 

$key = q/displaystyle(0,x)_d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2542.png"
 ALT="$\displaystyle (0,x)_d$">|; 

$key = q/J_1(2,sqrt{xi,s});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1885.png"
 ALT="$ J_1(2 \sqrt{\xi s})$">|; 

$key = q/displaystyle=frac{1}{2,l+1}int_0^rfrac{rho_{l,m}(r')}{epsilon_0}left(frac{r'^{,ll+1}}+frac{l+1}{l},frac{r'^{,l},r^{,l}}{a^{,2,l+1}}right)r'^{,2},dr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="317" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="$\displaystyle = \frac{1}{2 l+1}\int_0^r \frac{\rho_{l,m}(r')}{\epsilon_0}\left...
...l+1}}+\frac{l+1}{l} \frac{r'^{ l} r^{ l}}{a^{ 2 l+1}}\right)r'^{ 2} dr'$">|; 

$key = q/displaystyle=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1352.png"
 ALT="$\displaystyle =0.$">|; 

$key = q/displaystylefrac{partialt'}{partialt}=frac{1}{1-{bfr}cdot{bfu}slashr,c}=frac{r}{s},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4001.png"
 ALT="$\displaystyle \frac{\partial t'}{\partial t} = \frac{1}{1- {\bf r}\cdot {\bf u}/r c} = \frac{r}{s},$">|; 

$key = q/displaystylenablap=-frac{epsilon_0}{2},E^{,2},nablaepsilon+frac{epsilon_0}{2},nac{epsilon_0,rho_m}{2},nabla!left(E^{,2}frac{depsilon}{drho_m}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1254.png"
 ALT="$\displaystyle \nabla p = - \frac{\epsilon_0}{2}  E^{ 2} \nabla\epsilon + \fr...
...psilon_0 \rho_m}{2}  \nabla\!\left(E^{ 2} \frac{d\epsilon}{d\rho_m} \right).$">|; 

$key = q/displaystylephi_m(r=a_+,theta)=phi_m(r=a_-,theta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1502.png"
 ALT="$\displaystyle \phi_m(r=a_+,\theta) = \phi_m(r=a_-,\theta).$">|; 

$key = q/displaystyleR=-{rmi},expleft(2,{rmi},hint_a^0q^{,1slash2}(x'),dx'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2565.png"
 ALT="$\displaystyle R = -{\rm i}  \exp\left(2 {\rm i} h\int_a^0 q^{ 1/2}(x') dx'\right).$">|; 

$key = q/displaystyle{bfM}({bfr})=frac{1}{2},{bfr}times{bfj}({bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1403.png"
 ALT="$\displaystyle {\bf M}({\bf r}) = \frac{1}{2} {\bf r}\times {\bf j}({\bf r}).$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{epsilon_0}int_VG_N({bfr},{bfr}'),rho({bfr}'),dV'-int_SG_N({bfr},{bfr}'),frac{partialphi({bfr}')}{dn'},dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="$\displaystyle \phi({\bf r}) = -\frac{1}{\epsilon_0}\int_V G_N({\bf r},{\bf r}')...
...,dV' - \int_S G_N({\bf r}, {\bf r}') \frac{\partial \phi({\bf r}')}{dn'} dS',$">|; 

$key = q/displaystyleleft(-nabla^{,2}+frac{1}{c^{,2}}frac{partial^{,2}}{partialt^{,2}}right)phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3723.png"
 ALT="$\displaystyle \left(-\nabla^{ 2}+\frac{1}{c^{ 2}} \frac{\partial^{ 2}}{\partial t^{ 2}}\right)\phi$">|; 

$key = q/displaystylephi(r,theta)=frac{q}{4pi,epsilon_0}left[frac{1}{(r^{,2}-2,r,b,costhe1}{(r^{,2},b^{,2}slasha^{,2}-2,r,b,costheta+a^{,2})^{1slash2}}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="493" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="$\displaystyle \phi(r,\theta) = \frac{q}{4\pi \epsilon_0}\left[\frac{1}{(r^{ 2...
...- \frac{1}{(r^{ 2} b^{ 2}/a^{ 2}-2 r b \cos\theta+a^{ 2})^{1/2}}\right]$">|; 

$key = q/E_theta=E_varphi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1243.png"
 ALT="$ E_\theta =E_\varphi=0$">|; 

$key = q/D_zrightarrowH_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2099.png"
 ALT="$ D_z\rightarrow H_z$">|; 

$key = q/displaystyleB_r({bf0});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1360.png"
 ALT="$\displaystyle B_r({\bf0})$">|; 

$key = q/displaystyle=frac{rmi}{epsilon_0,omega},nablatimes{bfj},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3198.png"
 ALT="$\displaystyle = \frac{\rm i}{\epsilon_0  \omega}  \nabla\times{\bf j},$">|; 

$key = q/displaystyleint_{-1}^{+1}frac{(1-mu^{,2}),dmu}{[1-(uslashc),mu]^{,5}}=frac{4}{3},gamma^{,6}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4108.png"
 ALT="$\displaystyle \int_{-1}^{+1}\frac{(1-\mu^{ 2}) d\mu}{[1-(u/c) \mu]^{ 5}} = \frac{4}{3} \gamma^{ 6}.$">|; 

$key = q/displaystyledeltaU=-int_Vnablaphicdotdelta{bfD},dV=int_V{bfE}cdotdelta{bfD},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1198.png"
 ALT="$\displaystyle \delta U = -\int_V\nabla\phi \cdot \delta{\bf D} dV = \int_V {\bf E}\cdot \delta {\bf D} dV.$">|; 

$key = q/displaystyle{bfB}({bfr})=frac{mu_0}{4pi}left[frac{3,({bfr}cdot{bfm}),{bfr}-r^2,{bfm}}{r^{,5}}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1419.png"
 ALT="$\displaystyle {\bf B}({\bf r}) = \frac{\mu_0}{4\pi}\left[\frac{3 ({\bf r}\cdot{\bf m}) {\bf r}- r^2 {\bf m}}{r^{ 5}}\right].
$">|; 

$key = q/displaystyle=g_{munu},dx^{,mu},dx^{,nu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3624.png"
 ALT="$\displaystyle = g_{\mu \nu}  dx^{ \mu}  dx^{ \nu},$">|; 

$key = q/displaystyle=E_i,cos[k_0,(c,t-z)]+E_r,cos[k_0,(c,t+z)+phi_r],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2190.png"
 ALT="$\displaystyle = E_i \cos[k_0 (c t-z)] + E_r \cos[k_0 (c t+z)+\phi_r],$">|; 

$key = q/displaystylefrac{P}{m_0,c^{,2}}=frac{2}{3}frac{omega_0^{,2},r_0}{c},beta^{,2},gamma^{,4},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4142.png"
 ALT="$\displaystyle \frac{P}{m_0 c^{ 2}} = \frac{2}{3} \frac{\omega_0^{ 2}  r_0}{c}  \beta^{ 2} \gamma^{ 4},$">|; 

$key = q/displaystyle{bfE}_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3154.png"
 ALT="$\displaystyle {\bf E}_l$">|; 

$key = q/{bfD}=D,{bfe}_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="$ {\bf D} = D {\bf e}_r$">|; 

$key = q/{bfv};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$ {\bf v}$">|; 

$key = q/displaystyleE_y(z,t)=int_{-infty}^{infty}frac{F(omega)}{n^{,1slash2}(omega,z)},,{rme}^{,{rmi},phi(omega,z,t)},domega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2334.png"
 ALT="$\displaystyle E_y(z,t) = \int_{-\infty}^{\infty} \frac{F(\omega)}{n^{ 1/2}(\omega, z)}   {\rm e}^{ {\rm i}  \phi(\omega, z,t)} d\omega,$">|; 

$key = q/displaystyleA_{rmeff}=G,pi,lambdabar^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2679.png"
 ALT="$\displaystyle A_{\rm eff} = G \pi  \lambdabar^{ 2}.$">|; 

$key = q/Y_{l,m}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="$ Y_{l,m}(\theta,\varphi)$">|; 

$key = q/displaystyle{bfB}({bfr})=frac{mu_0,I_1}{4pi}oint_1frac{d{bfr}_1times({bfr}-{bfr}_1)}{|{bfr}-{bfr}_1|^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1299.png"
 ALT="$\displaystyle {\bf B}({\bf r}) = \frac{\mu_0 I_1}{4\pi}\oint_1 \frac{d{\bf r}_1\times ({\bf r}-{\bf r}_1)}{\vert{\bf r}-{\bf r}_1\vert^{ 3}}.$">|; 

$key = q/displaystylelangle{calI}_zrangle_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2081.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle_r$">|; 

$key = q/dx'^{,2}+dy'^{,2}+dz'^{,2}-c^{,2},dt'^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3442.png"
 ALT="$ dx'^{ 2} + dy'^{ 2} + dz'^{ 2} -c^{ 2}  dt'^{ 2}$">|; 

$key = q/displaystyle=E_0,R,n^{-1slash2}(z)expleft(-{rmi},kint_0^z!n(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2277.png"
 ALT="$\displaystyle = E_0 R n^{-1/2}(z) \exp\left(-{\rm i} k \int_0^z\! n(z') dz'\right),$">|; 

$key = q/displaystylerightarrow(-{rmi})^{,l+1},frac{{rme}^{+{rmi},z}}{z},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3039.png"
 ALT="$\displaystyle \rightarrow (-{\rm i})^{ l+1}  \frac{ {\rm e}^{+{\rm i} z} }{z},$">|; 

$key = q/{bfv}=c,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4199.png"
 ALT="$ {\bf v}=c $">|; 

$key = q/displaystylemu=-2,mu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1528.png"
 ALT="$\displaystyle \mu = -2  \mu_0$">|; 

$key = q/{bfG}^{(i)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$ {\bf G}^{(i)}$">|; 

$key = q/displaystyledeltaU=int_Sphi,delta{bfD}cdotd{bfS}-int_Vnablaphicdotdelta{bfD},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1197.png"
 ALT="$\displaystyle \delta U = \int_S \phi  \delta{\bf D}\cdot d{\bf S} - \int_V \nabla\phi\cdot\delta{\bf D} dV,$">|; 

$key = q/t<t_0equivxslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1932.png"
 ALT="$ t&lt;t_0 \equiv x/c$">|; 

$key = q/{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1580.png"
 ALT="$ {\bf E}'$">|; 

$key = q/displaystyle=frac{g_isqrt{1+x}}{x^{,2}+g_i^{,2},(1+x)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1656.png"
 ALT="$\displaystyle = \frac{g_i \sqrt{1+x}}{x^{ 2} + g_i^{ 2} (1+x) }.$">|; 

$key = q/psi(r)proptoJ_0(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2914.png"
 ALT="$ \psi(r)\propto J_0(k_s  r)$">|; 

$key = q/g_{munu},dx^{,mu},dx^{,nu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3673.png"
 ALT="$ g_{\mu\nu}  dx^{ \mu}  dx^{ \nu}$">|; 

$key = q/displaystyleint{bfE}'cdot(nablatimes{bfH}),dV=intfrac{(nablatimes{bfH})^2}{sigma},dV+int{bfH}cdotfrac{partial{bfB}}{partialt},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1590.png"
 ALT="$\displaystyle \int {\bf E}'\cdot(\nabla\times{\bf H}) dV = \int\frac{(\nabla\t...
...H})^2}{\sigma}  dV + \int {\bf H}\cdot\frac{\partial{\bf B}}{\partial t}  dV.$">|; 

$key = q/displaystylef(t)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1797.png"
 ALT="$\displaystyle f(t) =0$">|; 

$key = q/F(a,c,0)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2429.png"
 ALT="$ F(a,c,0)=1$">|; 

$key = q/G({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1006.png"
 ALT="$ G({\bf r}, {\bf r}')=0$">|; 

$key = q/-1leqxleq+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="$ -1\leq x\leq +1$">|; 

$key = q/displaystylefrac{|t-t_r|}{t_0}=frac{R}{R_0}ll1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$\displaystyle \frac{\vert t -t_r\vert}{t_0} = \frac{R}{R_0} \ll 1,$">|; 

$key = q/epsilon_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$ \epsilon_0$">|; 

$key = q/rho_m,g,h;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1274.png"
 ALT="$ \rho_m  g  h$">|; 

$key = q/omega_p(z)propto[N(z)]^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2380.png"
 ALT="$ \omega_p(z)
\propto [N(z)]^{1/2}$">|; 

$key = q/displaystylenabla^{,2}{bfE}-frac{1}{c^{,2}},frac{partial^{,2}{bfE}}{partialt^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2750.png"
 ALT="$\displaystyle \nabla^{ 2}{\bf E} - \frac{1}{c^{ 2}} \frac{\partial^{ 2} {\bf E}}{\partial t^{ 2}}$">|; 

$key = q/k,all1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3379.png"
 ALT="$ k a\ll 1$">|; 

$key = q/B_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="$ B_{mn}$">|; 

$key = q/displaystyle(hat{z},0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2509.png"
 ALT="$\displaystyle (\hat{z}, 0)$">|; 

$key = q/{bfG}({bfr}',{bfr})=G({bfr},{bfr'});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img950.png"
 ALT="$ {\bf G}({\bf r}',{\bf r})=G({\bf r},{\bf r'})$">|; 

$key = q/displaystylephantom{=}+left(rho,{bfE}+{bfj}times{bfB}right)_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$\displaystyle \phantom{=}+ \left(\rho {\bf E}+{\bf j}\times {\bf B}\right)_i,$">|; 

$key = q/displaystyleE_theta(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2943.png"
 ALT="$\displaystyle E_\theta(r)$">|; 

$key = q/displaystylek_0'''equivleft(frac{d^{,3}k}{domega^{,3}}right)_{omega=0}=frac{3,omega_p^{,2}}{c,n(0),omega_0^{,4}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1950.png"
 ALT="$\displaystyle k_0'''\equiv\left(\frac{d^{ 3} k}{d\omega^{ 3}}\right)_{\omega=0} = \frac{3 \omega_p^{ 2}} {c  n(0)  \omega_0^{ 4}}$">|; 

$key = q/displaystyle=frac{t'+v,x'slashc^{,2}}{(1-v^{,2}slashc^{,2})^{1slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3481.png"
 ALT="$\displaystyle = \frac{t'+v x'/c^{ 2}}{(1-v^{ 2}/c^{ 2})^{1/2}}.$">|; 

$key = q/displaystyleint_x^{infty}frac{{rme}^{-t}}{t^{,n+2}},dt<frac{1}{x^{,n+2}}int_x^infty{rme}^{-t},dt=frac{{rme}^{-x}}{x^{,n+2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2416.png"
 ALT="$\displaystyle \int_x^{\infty} \frac{{\rm e}^{-t}}{t^{ n+2}}  dt &lt; \frac{1}{x^{ n+2}}\int_x^\infty {\rm e}^{-t}  dt = \frac{{\rm e}^{-x}} {x^{ n+2}}.$">|; 

$key = q/Z(0)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="$ Z(0) = 0$">|; 

$key = q/displaystyledeltaU=-frac{epsilon_0}{2}int_VE^{,2},deltaepsilon,dV+int_V{bfE}cdotdelta{bfD},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1212.png"
 ALT="$\displaystyle \delta U = -\frac{\epsilon_0}{2}\int_V E^{ 2} \delta\epsilon   dV + \int_V {\bf E} \cdot \delta{\bf D} dV.$">|; 

$key = q/displaystyle~~~~+psi_r,costheta_i,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2106.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\psi_r \cos\theta_i \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z),$">|; 

$key = q/theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="$ \theta$">|; 

$key = q/U=T^{,44};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3971.png"
 ALT="$ U=T^{ 44}$">|; 

$key = q/displaystylea_M(l,m)=frac{mu_0,c,k^{,2}}{{rmi},sqrt{l,(l+1)}}intY_{lm}^{,ast}lefbfM},frac{d[r,j_l(k,r)]}{dr}-k^2,({bfr}cdot{bfM}),j_l(k,r)right],dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="575" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3231.png"
 ALT="$\displaystyle a_M(l,m) = \frac{\mu_0  c k^{ 2}}{{\rm i} \sqrt{l (l+1)}} \i...
...\frac{d [r j_l(k r)]}{d r}-k^2 ({\bf r}\cdot{\bf M}) j_l(k r) \right] dV.$">|; 

$key = q/displaystyle{bfn}times{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2769.png"
 ALT="$\displaystyle {\bf n}\times {\bf E}$">|; 

$key = q/hat{z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2478.png"
 ALT="$ \hat{z}$">|; 

$key = q/alphall1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2203.png"
 ALT="$ \alpha\ll 1$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{epsilon_0}int_VG({bfr},{bfr}'),rho({bfr}'),dV'-iialn'}-phi({bfr}'),frac{partialG({bfr},{bfr}')}{partialn'}right]dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="$\displaystyle \phi({\bf r})=-\frac{1}{\epsilon_0} \int_V G({\bf r},{\bf r}') \...
...'}-\phi({\bf r}') \frac{\partial G({\bf r},{\bf r}')}{\partial n'}\right]d S'.$">|; 

$key = q/displaystylenablacdot{bfE}=frac{rho_f}{epsilon_0,epsilon}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1076.png"
 ALT="$\displaystyle \nabla\cdot{\bf E} = \frac{\rho_f}{\epsilon_0 \epsilon}.$">|; 

$key = q/displaystyle{bfp}=alpha,epsilon_0,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1231.png"
 ALT="$\displaystyle {\bf p} = \alpha  \epsilon_0  {\bf E}$">|; 

$key = q/B_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1801.png"
 ALT="$ B_2$">|; 

$key = q/displaystylefrac{{bfr}-{bfr}'}{|{bfr}-{bfr}'|^{,3}}=-nablaleft(frac{1}{|{bfr}-{bfr}'|}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$\displaystyle \frac{{\bf r}-{\bf r}'}{\vert{\bf r}-{\bf r}'\vert^{ 3}} = -\nabla\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right).$">|; 

$key = q/h_l^{(1)}(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3043.png"
 ALT="$ h_l^{(1)}(k r)$">|; 

$key = q/U^{,mu}=gamma,({bfu},,c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3932.png"
 ALT="$ U^{ \mu} = \gamma ({\bf u},  c)$">|; 

$key = q/displaystylembox{hspace{1cm}as{|{{bf{r}|rightarrowinfty{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img947.png"
 ALT="$\displaystyle \mbox{\hspace{1cm}as $\vert{\bf r}\vert\rightarrow\infty$}$">|; 

$key = q/displaystyled^{,4}x'=d^{,4}x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3698.png"
 ALT="$\displaystyle d^{ 4} x' = d^{ 4} x$">|; 

$key = q/{bfr}_u={bfr}-r,{bfu}slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4016.png"
 ALT="$ {\bf r}_u =
{\bf r} - r  {\bf u}/c$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06slashcont2.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="486" HEIGHT="339" BORDER="0"
 SRC="|."$dir".q|img1804.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06/cont2.eps}}
\end{figure}">|; 

$key = q/displaystylev=sqrt{frac{x,k_0'''}{2,|t-t_1|}},,omega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1953.png"
 ALT="$\displaystyle v = \sqrt{\frac{x k_0'''}{2 \vert t-t_1\vert}}  \omega,$">|; 

$key = q/displaystylefrac{4pi,epsilon_0}{e},{bfE}=frac{1}{s^{,3}}left({bfr}-frac{r,{bfu}}imesleft[left({bfr}-frac{r,{bfu}}{c}right)timesdot{bfu}right]right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4011.png"
 ALT="$\displaystyle \frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{1}{s^{ 3}} \left({...
...t[ \left({\bf r} - \frac{r {\bf u}}{c}\right)\times\dot{\bf u}\right] \right).$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0}{4pi}intfrac{{bfj}({bfr}'),{rme}^{,{rmi},k,|{bfr}-{bfr}'|}}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2599.png"
 ALT="$\displaystyle {\bf A}({\bf r}) =\frac{\mu_0}{4\pi} \int \frac{{\bf j}({\bf r}')...
...^{ {\rm i} k \vert{\bf r}-{\bf r}'\vert}}{\vert{\bf r}-{\bf r}'\vert}  dV'.$">|; 

$key = q/{mitDelta}t'<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3523.png"
 ALT="$ {\mit\Delta} t'&lt;0$">|; 

$key = q/H_r(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2953.png"
 ALT="$ H_r(r)$">|; 

$key = q/displaystylefrac{{rme}^{,{rmi},k,r'}}{4pi,r'},{rme}^{-{rmi},k,{bfn}cdot{bfr}}={r})^{l+1}j_l(k,r),Y_{lm}^{,ast}(theta',varphi'),Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3294.png"
 ALT="$\displaystyle \frac{{\rm e}^{ {\rm i} k r'}}{4\pi r'}  {\rm e}^{-{\rm i} ...
...^{l+1} j_l(k r)  Y_{lm}^{ \ast}(\theta', \varphi')  Y_{lm}(\theta,\varphi).$">|; 

$key = q/omega_srightarrow2pislashtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1971.png"
 ALT="$ \omega_s\rightarrow
2\pi/\tau$">|; 

$key = q/epsilon>1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1183.png"
 ALT="$ \epsilon &gt;1$">|; 

$key = q/displaystylefrac{1}{|{bfr}-{bfr}'|}=frac{1}{|{bfr}|}+frac{{bfr}cdot{bfr}'}{|{bfr}|^{,3}}+cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1380.png"
 ALT="$\displaystyle \frac{1}{\vert{\bf r}-{\bf r}'\vert}= \frac{1}{\vert{\bf r}\vert}+\frac{{\bf r}\cdot{\bf r}'}{\vert{\bf r}\vert^{ 3}}+\cdots.$">|; 

$key = q/displaystyle=pmk,frac{dq}{dz}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2324.png"
 ALT="$\displaystyle = \pm k  \frac{dq}{d z}.$">|; 

$key = q/displaystyleF({bfr})=-left.int_SG_N({bfr},{bfr}'),dS'rightslashint_SdS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="$\displaystyle F({\bf r}) = -\left.\int_S G_N({\bf r},{\bf r}') dS'\right/\int_S dS'.$">|; 

$key = q/displaystylephi(r,theta,z)=R(r),Q(theta),Z(z).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="$\displaystyle \phi(r,\theta,z) = R(r) Q(\theta) Z(z).$">|; 

$key = q/displaystyle=left(frac{2,beta}{beta+alpha}right)psi_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2077.png"
 ALT="$\displaystyle =\left(\frac{2 \beta}{\beta+\alpha}\right)\psi_i.$">|; 

$key = q/E_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3814.png"
 ALT="$ E_{ij}$">|; 

$key = q/displaystyle=-{rmi},A,frac{omega,mu_0}{k_t},K_1(k_t,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2947.png"
 ALT="$\displaystyle = -{\rm i} A  \frac{\omega \mu_0}{k_t}  K_1(k_t  r)$">|; 

$key = q/displaystylefrac{P_{rmout}}{P_{rmin}}=G_t,G_rleft(frac{lambda}{4pi,r}right)^2=frac{A_t,A_r}{lambda^{,2},r^2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2686.png"
 ALT="$\displaystyle \frac{P_{\rm out}}{P_{\rm in}} = G_t  G_r \left(\frac{\lambda}{4\pi  r}\right)^2 = \frac{A_t  A_r}{\lambda^{ 2}  r^2},$">|; 

$key = q/displaystyle=epsilon_1,frac{J_1(k_s,a)}{k_s}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2990.png"
 ALT="$\displaystyle = \epsilon_1  \frac{J_1(k_s  a)}{k_s}.$">|; 

$key = q/displaystyle={rme}^{,{rmi},pislash4},{|q(x)|^{-1slash4}},expleft(-hint_0^x|q(x')|^{,1slash2},dx'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2545.png"
 ALT="$\displaystyle ={\rm e}^{ {\rm i} \pi/4} {\vert q(x)\vert^{-1/4}}  \exp\left( -h \int_0^x \vert q(x')\vert^{ 1/2} dx'\right).$">|; 

$key = q/displaystyle=frac{-{rmi},k}{l+1}intr^{,l},Y_{lm}^ast,nablacdot({bfr}times{bfM}),dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3236.png"
 ALT="$\displaystyle = \frac{-{\rm i} k}{l+1} \int r^{ l}  Y_{lm}^\ast  \nabla\cdot({\bf r}\times{\bf M}) dV.$">|; 

$key = q/displaystylew(1)=A,(hat{z},0)_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2554.png"
 ALT="$\displaystyle w(1) = A  (\hat{z},0)_s,$">|; 

$key = q/displaystyleP_l(cosgamma)=frac{4pi}{2,l+1}sum_{m=-l,+l}Y_{lm}^{,ast}(theta,varphi),Y_{lm}(theta',varphi'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3297.png"
 ALT="$\displaystyle P_l(\cos\gamma) = \frac{4\pi}{2 l+1} \sum_{m=-l,+l}Y_{lm}^{ \ast} (\theta,\varphi)  Y_{lm}(\theta',\varphi'),$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}intfrac{nabla'cdot{bfj}({bfr}')}{|{bfr}-{bfr}'|},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1315.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi}\int \frac{\nabla'\cdot{\bf j}({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dV',$">|; 

$key = q/sinz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2426.png"
 ALT="$ \sin z$">|; 

$key = q/displaystylelim_{nrightarrowinfty}left|frac{u_{n+1}}{u_n}right|=lim_{nrightarrowinfty}left(frac{n}{x}right)rightarrowinfty.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2413.png"
 ALT="$\displaystyle \lim_{n\rightarrow\infty} \left\vert\frac{u_{n+1}}{u_n}\right\vert =\lim_{n\rightarrow\infty} \left(\frac{n}{x}\right)\rightarrow\infty.$">|; 

$key = q/displaystylefrac{df_l(z)}{dz},f_{l'}^{,ast}(z)-frac{df_{l'}^{,ast}(z)}{dz},f_{l}(z)=frac{2,{rmi}}{z^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3349.png"
 ALT="$\displaystyle \frac{d f_l(z)}{dz}  f_{l'}^{ \ast}(z)- \frac{d f_{l'}^{ \ast}(z)}{dz}  f_{l}(z) = \frac{2 {\rm i}}{z^{ 2}},$">|; 

$key = q/displaystyle=E_0,R,n^{,1slash2}(z)expleft(-{rmi},kint_0^z!n(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2278.png"
 ALT="$\displaystyle = E_0 R n^{ 1/2}(z) \exp\left(-{\rm i} k \int_0^z\! n(z') dz'\right),$">|; 

$key = q/displaystyle=c,t,coshvarphi-x,sinhvarphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4161.png"
 ALT="$\displaystyle = c t \cosh\varphi - x \sinh\varphi,$">|; 

$key = q/q'(hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2460.png"
 ALT="$ q'(\hat{z})$">|; 

$key = q/displaystyleD_y(x,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2101.png"
 ALT="$\displaystyle D_y(x,z,t)$">|; 

$key = q/displaystyleint_Vleft[psi({bfr}'),nabla'^{,2}phi({bfr}')-phi({bfr}'),nabla'^{,2}partialn'}-phi({bfr}'),frac{partialpsi({bfr}')}{partialn'}right]dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="$\displaystyle \int_V \left[\psi({\bf r}') \nabla'^{ 2}\phi({\bf r}')-\phi({\b...
...tial n'}-\phi({\bf r}') \frac{\partial\psi({\bf r}')}{\partial n'}\right] dS',$">|; 

$key = q/displaystyleequiv0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2298.png"
 ALT="$\displaystyle \equiv 0.$">|; 

$key = q/displaystyle=frac{{rmi},omega,epsilon_0}{k_s^{,2}},{bfe}_ztimesnabla_sE_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2848.png"
 ALT="$\displaystyle =\frac{{\rm i} \omega \epsilon_0}{k_s^{ 2}}  {\bf e}_z\times \nabla_s E_z.$">|; 

$key = q/displaystylef(t)=frac{2}{tau}int_0^inftyfrac{domega}{omega^{,2}-(2pislashtau)^{,2}}left(cos[omega,(t-T)]-cos[omega,t]right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1784.png"
 ALT="$\displaystyle f(t) = \frac{2}{\tau} \int_0^\infty \frac{d\omega}{\omega^{ 2} -(2\pi/\tau)^{ 2}} \left(\cos[\omega (t-T)] -\cos[\omega  t]\right).$">|; 

$key = q/displaystyle=left(frac{5}{16pi}right)^{1slash2},Q_{33},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="$\displaystyle =\left(\frac{5}{16\pi}\right)^{1/2} Q_{33},$">|; 

$key = q/U;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="$ U$">|; 

$key = q/partialslashpartialn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$ \partial/\partial n$">|; 

$key = q/displaystyle=2,E_0cos[(omegaslashc),(n,z-c,t)]cos[(omegaslash2,c),(n_+-n_-),z],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1748.png"
 ALT="$\displaystyle =2 E_0 \cos[(\omega/c) (n z -c t)]\cos[(\omega/2 c) (n_+-n_-) z],$">|; 

$key = q/displaystyleint_Vphi({bfr}'),delta({bfr}-{bfr}'),dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="$\displaystyle \int_V \phi({\bf r}') \delta({\bf r}-{\bf r}') dV'$">|; 

$key = q/displaystylev^{-1slash2},h(v^{,1slash2})=int_0^{z_0(v^{,1slash2})}frac{dz}{[v-u(z)]^{1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2362.png"
 ALT="$\displaystyle v^{-1/2} h(v^{ 1/2}) = \int_0^{z_0(v^{ 1/2})} \frac{dz}{[v-u(z)]^{1/2}},$">|; 

$key = q/b_pm(l,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3308.png"
 ALT="$ b_\pm(l,m)$">|; 

$key = q/-omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1788.png"
 ALT="$ -\omega$">|; 

$key = q/dtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3689.png"
 ALT="$ d\tau$">|; 

$key = q/-e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1283.png"
 ALT="$ -e$">|; 

$key = q/langle{bfm}_irangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1430.png"
 ALT="$ \langle {\bf m}_i\rangle$">|; 

$key = q/dx'^{,2}+dy'^{,2}+dz'^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3434.png"
 ALT="$ dx'^{ 2}+dy'^{ 2} + dz'^{ 2}$">|; 

$key = q/n^{,2}=S^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2314.png"
 ALT="$ n^{ 2}=S^{ 2}$">|; 

$key = q/displaystyleP_{rmload}=frac{E_0^{,2}d^{,2}}{32,R_{rmrad}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2669.png"
 ALT="$\displaystyle P_{\rm load} = \frac{E_0^{ 2} d^{ 2}}{32  R_{\rm rad}}.$">|; 

$key = q/displaystylepartial_muJ_m^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4207.png"
 ALT="$\displaystyle \partial_\mu J_m^{ \mu}$">|; 

$key = q/B_{23};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3800.png"
 ALT="$ B_{23}$">|; 

$key = q/displaystylefrac{d^{,2}R}{dr^{,2}}+frac{1}{r},frac{dR}{dr}+left(k^{,2}-frac{m^{,2}}{r^{,2}}right)R=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="$\displaystyle \frac{d^{ 2} R}{dr^{ 2}} + \frac{1}{r} \frac{dR}{dr}+\left(k^{ 2}-\frac{m^{ 2}}{r^{ 2}}\right) R = 0.$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06slashfig19.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img2533.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06/fig19.eps}}
\end{figure}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter05slashbh1.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="335" BORDER="0"
 SRC="|."$dir".q|img1460.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter05/bh1.eps}}
\end{figure}">|; 

$key = q/displaystyle=-left(frac{3}{2+epsilon}right),E_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1176.png"
 ALT="$\displaystyle = -\left(\frac{3}{2+\epsilon}\right)  E_0,$">|; 

$key = q/displaystyley=A,y'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3456.png"
 ALT="$\displaystyle y = A y'.$">|; 

$key = q/u_z(omega_0,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2339.png"
 ALT="$ u_z(\omega_0,z)$">|; 

$key = q/f_0=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$ f_0=0$">|; 

$key = q/displaystyle=epsilon_0,{bfE}times(nablatimes{bfE})+frac{{bfB}times(nablatimes{bfB})}{mu_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$\displaystyle = \epsilon_0 {\bf E}\times (\nabla\times{\bf E})+\frac{{\bf B}\times(\nabla\times {\bf B})}{\mu_0}$">|; 

$key = q/{bfM}({bfr}),{rme}^{-{rmi},omega,t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3190.png"
 ALT="$ {\bf M}({\bf r})  {\rm e}^{-{\rm i} \omega  t}$">|; 

$key = q/displaystyleg_{mu'nu'},p_{musigma}^{,mu'},p_{nu}^{,nu'},p_{sigma'}^{,nu}=g_{mu'sigma'},p_{musigma}^{,mu'}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3684.png"
 ALT="$\displaystyle g_{\mu'\nu'}  p_{\mu\sigma}^{ \mu'}  p_{\nu}^{ \nu'} p_{\sigma'}^{ \nu} = g_{\mu'\sigma'} p_{\mu\sigma}^{ \mu'} =0.$">|; 

$key = q/displaystylephi_{0,0}(r)=int_0^rfrac{rho_{0,0}(r')}{epsilon_0}left(frac{1}{r}-fro_{0,0}(r')}{epsilon_0}left(frac{1}{r'}-frac{1}{a}right)r'^{,2},dr',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="435" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="$\displaystyle \phi_{0,0}(r) = \int_0^r\frac{\rho_{0,0}(r')}{\epsilon_0}\left(\f...
...{\rho_{0,0}(r')}{\epsilon_0}\left(\frac{1}{r'}-\frac{1}{a}\right)r'^{ 2} dr',$">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ x$">|; 

$key = q/I_0^{,2}slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2637.png"
 ALT="$ I_0^{ 2}/2$">|; 

$key = q/displaystyleP_{rmin}=langleV,Irangle=frac{V_0^{,2}}{2,(R_{rmrad}+R_{rmload})}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2659.png"
 ALT="$\displaystyle P_{\rm in} = \langle V I\rangle = \frac{V_0^{ 2}}{2 (R_{\rm rad} + R_{\rm load})}.$">|; 

$key = q/displaystyle=left(frac{pi}{2,z}right)^{1slash2}J_{l+1slash2}(z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3021.png"
 ALT="$\displaystyle = \left(\frac{\pi}{2  z}\right)^{1/2} J_{l+1/2}(z),$">|; 

$key = q/displaystylefrac{{bfE}_{rmrad},times{bfB}_{rmrad}}{mu_0}=epsilon_0,c,E_{rmrad}^{,2},frac{{bfr}}{r},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4094.png"
 ALT="$\displaystyle \frac{{\bf E}_{\rm rad} \times{\bf B}_{\rm rad}}{\mu_0} = \epsilon_0  c E_{\rm rad}^{ 2}  \frac{{\bf r}}{r},$">|; 

$key = q/rrightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$ r\rightarrow \infty$">|; 

$key = q/displaystyle=frac{t-v,xslashc^{,2}}{(1-v^{,2}slashc^{,2})^{1slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3474.png"
 ALT="$\displaystyle = \frac{t-v x/c^{ 2}}{(1-v^{ 2}/c^{ 2})^{1/2}}.$">|; 

$key = q/displaystyle=nabla_stimes{bfE}_z+nabla_ztimes{bfE}_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2822.png"
 ALT="$\displaystyle = \nabla_s\times{\bf E}_z +\nabla_z\times{\bf E}_s,$">|; 

$key = q/K_1(k_t,a)slashk_t,K_0(k_t,a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2962.png"
 ALT="$ K_1(k_t  a) / k_t  K_0(k_t  a)$">|; 

$key = q/displaystyleH_n^{,2}(rho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle H_n^{ 2}(\rho)$">|; 

$key = q/z<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1095.png"
 ALT="$ z&lt;0$">|; 

$key = q/displaystyle=p_i^{,i'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3538.png"
 ALT="$\displaystyle = p_i^{ i'},$">|; 

$key = q/displaystylenabla'^{,2}G_D({bfr},{bfr}')=nabla^{,2}G_D({bfr},{bfr}')=delta({bfr}-{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$\displaystyle \nabla'^{ 2}G_D({\bf r},{\bf r}')=\nabla^{ 2}G_D({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}'),$">|; 

$key = q/l,(l+1)slashk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3088.png"
 ALT="$ l (l+1)/k$">|; 

$key = q/H_y(z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1993.png"
 ALT="$ H_y(z,t)$">|; 

$key = q/displaystylefrac{pi}{2},t^{,2}=frac{1}{2},phi_s'',(omega-omega_s)^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1909.png"
 ALT="$\displaystyle \frac{\pi}{2}  t^{ 2} = \frac{1}{2}  \phi_s''  (\omega-\omega_s)^{ 2}.$">|; 

$key = q/displaystylec,{bfB}=-frac{rmi}{k},nablatimes{bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3075.png"
 ALT="$\displaystyle c {\bf B} =- \frac{\rm i}{k} \nabla\times{\bf E}.$">|; 

$key = q/I_m(p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img978.png"
 ALT="$ I_m(p)$">|; 

$key = q/phi(r,theta,0)={mitPhi}(r,theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img916.png"
 ALT="$ \phi(r,\theta,0)={\mit\Phi}(r,\theta)$">|; 

$key = q/{bfj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$ {\bf j}$">|; 

$key = q/gammarightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3906.png"
 ALT="$ \gamma\rightarrow \infty$">|; 

$key = q/displaystyleB_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1511.png"
 ALT="$\displaystyle B_1$">|; 

$key = q/displaystyle{bfP}_i=epsilon_0,(epsilon_i-1),{bfE}=-epsilon_0,({epsilon}_i-1),nablaphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1126.png"
 ALT="$\displaystyle {\bf P}_i = \epsilon_0  (\epsilon_i -1) {\bf E} = - \epsilon_0  ({\epsilon}_i - 1) \nabla\phi$">|; 

$key = q/displaystyleB_3={rme}^{-{rmIm}(k_tau),x}sinleft[2pi,frac{t}{tau}-{rmRe}(k_tau),xright].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1830.png"
 ALT="$\displaystyle B_3 = {\rm e}^{-{\rm Im}(k_\tau)  x} \sin\left[2\pi \frac{t}{\tau} -{\rm Re}(k_\tau) x\right].$">|; 

$key = q/{A^i}_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3598.png"
 ALT="$ {A^i}_j$">|; 

$key = q/displaystyle=frac{mu_0}{4pi}intfrac{left[{bfj}({bfr}')right]}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} \int \frac{\left[{\bf j}({\bf r}')\right]}{\vert{\bf r} - {\bf r}'\vert} dV'.$">|; 

$key = q/displaystyleL_-;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3052.png"
 ALT="$\displaystyle L_-$">|; 

$key = q/z_0(w^{1slash2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2373.png"
 ALT="$ z_0(w^{1/2})$">|; 

$key = q/displaystyle-{bfE}cdot{bfj}=-frac{{bfE}cdotnablatimes{bfB}}{mu_0}+epsilon_0,{bfE}cdotfrac{partial{bfE}}{partialt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle - {\bf E} \cdot {\bf j} = - \frac{ {\bf E}\cdot \nabla\times{\bf B}}{\mu_0} +\epsilon_0  {\bf E}\cdot \frac{\partial {\bf E}}{\partial t},$">|; 

$key = q/displaystylef_s=frac{sigma^{,2}}{2,epsilon_0,epsilon};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1282.png"
 ALT="$\displaystyle f_s = \frac{\sigma^{ 2}}{2 \epsilon_0 \epsilon}$">|; 

$key = q/z(t')=a,cos(omega_0,t');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4213.png"
 ALT="$ z(t')=a  \cos(\omega_0  t')$">|; 

$key = q/displaystylerightarrowleft(frac{2}{pi,p}right)^{1slash2},cosleft(p-m,frac{pi}{2}-frac{pi}{4}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="$\displaystyle \rightarrow \left(\frac{2}{\pi p}\right)^{1/2} \cos\left(p - m \frac{\pi}{2}-\frac{\pi}{4}\right)$">|; 

$key = q/(1slashsqrt{2},1slashsqrt{2},0,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3432.png"
 ALT="$ (1/\sqrt{2}, 1/\sqrt{2}, 0, 1)$">|; 

$key = q/displaystyle{bfE}=left{{array}{rll}{bf0}&mbox{hspace{0.5cm}}&r<a[0.5ex]{bf0}&&r>a{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="$\displaystyle {\bf E} = \left\{ \begin{array}{rll} {\bf0}&amp;\mbox{\hspace{0.5cm}}&amp; r&lt;a\ [0.5ex] {\bf0}&amp;&amp;r&gt;a \end{array}\right.,$">|; 

$key = q/displaystyle{bfA}({bfr})simeqfrac{mu_0}{4pi}frac{{rme}^{,{rmi},k,r}}{r}int{bfj}({bfr}'),{rme}^{-{rmi},k,{bfn}cdot{bfr}'},dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2613.png"
 ALT="$\displaystyle {\bf A}({\bf r}) \simeq \frac{\mu_0}{4\pi}\frac{{\rm e}^{ {\rm i...
...}}{r} \int {\bf j}({\bf r}') {\rm e}^{-{\rm i} k {\bf n}\cdot {\bf r}'} dV'$">|; 

$key = q/displaystyle{mitPhi}_{m,n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1025.png"
 ALT="$\displaystyle {\mit\Phi}_{m,n}$">|; 

$key = q/a_pm(l,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3307.png"
 ALT="$ a_\pm(l,m)$">|; 

$key = q/dE;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4066.png"
 ALT="$ dE$">|; 

$key = q/{bfM}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1471.png"
 ALT="$ {\bf M}_1$">|; 

$key = q/t';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$ t'$">|; 

$key = q/displaystylephi(z<0)=frac{1}{4pi,epsilon_0,epsilon_2}frac{q''}{R_1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1112.png"
 ALT="$\displaystyle \phi(z&lt;0) = \frac{1}{4\pi \epsilon_0 \epsilon_2} \frac{q''}{R_1}.$">|; 

$key = q/g_{11}=g_{22}=g_{33}=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3627.png"
 ALT="$ g_{11}=g_{22}=g_{33}=-1$">|; 

$key = q/h_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2581.png"
 ALT="$ h_0$">|; 

$key = q/i=3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$ i=3$">|; 

$key = q/0leqmleql;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="$ 0\leq m\leq l$">|; 

$key = q/exp(,{rmi},phi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1903.png"
 ALT="$ \exp( {\rm i} \phi)$">|; 

$key = q/displaystyle=intrho({bfr}),z,dV=intrho({bfr}),r,costheta,dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="$\displaystyle = \int \rho({\bf r}) z dV = \int\rho({\bf r}) r \cos\theta dV.$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),c,{bfB}=-mu_0,c,nablatimes({bfj}+nablatimes{bfM}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3201.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2}) c {\bf B} = -\mu_0  c  \nabla\times({\bf j}+\nabla\times{\bf M}),$">|; 

$key = q/displaystyleY_{l,0}(theta,varphi)=left(frac{2,l+1}{4pi}right)^{1slash2}P_l(costheta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="$\displaystyle Y_{l,0}(\theta,\varphi) = \left(\frac{2 l+1}{4\pi}\right)^{1/2} P_l(\cos\theta).$">|; 

$key = q/G_omega({bfr},{bfr}')rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$ G_\omega({\bf r}, {\bf r}')\rightarrow 0$">|; 

$key = q/displaystylet=frac{1}{c}int_0^zleft[frac{partial(omega,n)}{partialomega}right]_{omega=omega_0},dz'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2338.png"
 ALT="$\displaystyle t = \frac{1}{c} \int_0^z \left[\frac{\partial(\omega  n)}{\partial\omega} \right]_{\omega=\omega_0}  dz'.$">|; 

$key = q/pm;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2291.png"
 ALT="$ \pm$">|; 

$key = q/displaystyle{rmi},k,S,E_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2299.png"
 ALT="$\displaystyle {\rm i}   k S E_y$">|; 

$key = q/displaystylephi=left{{array}{rll}Dslash(2,epsilon_0)&mbox{hspace{0.5cm}}&x>0[0.5ex]-Dslash(2,epsilon_0)&&x<0{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="$\displaystyle \phi = \left\{ \begin{array}{rll} D/(2 \epsilon_0)&amp;\mbox{\hspace{0.5cm}}&amp; x&gt;0\ [0.5ex] -D/(2 \epsilon_0)&amp;&amp;x&lt;0 \end{array}\right.,$">|; 

$key = q/G;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2678.png"
 ALT="$ G$">|; 

$key = q/displaystyle,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="8" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle ,$">|; 

$key = q/displaystyle~~~~+psi_r,sintheta_i,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2109.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\psi_r \sin\theta_i \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z)$">|; 

$key = q/displaystyleZ_g=sqrt{frac{mu_0}{epsilon_0}}sqrt{1-omega_c^{,2}slashomega^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2904.png"
 ALT="$\displaystyle Z_g = \sqrt{\frac{\mu_0}{\epsilon_0}} \sqrt{1-\omega_c^{ 2}/\omega^{ 2}}$">|; 

$key = q/displaystylek_s^{,2}=epsilon_1,frac{omega^{,2}}{c^{,2}}-k_g^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2909.png"
 ALT="$\displaystyle k_s^{ 2} = \epsilon_1  \frac{\omega^{ 2}}{c^{ 2}} -k_g^{ 2}$">|; 

$key = q/displaystyleY_{1,0}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="$\displaystyle  Y_{1,0}(\theta,\varphi)$">|; 

$key = q/displaystyle-{bfE}cdot{bfj}=nablacdotleft(frac{{bfE}times{bfB}}{mu_0}right)+mu_0tialt}+frac{partial}{partialt}!left(frac{epsilon_0,E^{,2}}{2}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle - {\bf E} \cdot {\bf j} = \nabla \cdot \left(\frac{{\bf E}\times{...
...l t} + \frac{\partial}{\partial t}\!\left(\frac{\epsilon_0 E^{ 2}}{2}\right),$">|; 

$key = q/displaystyleB^{ij}=B_{ij}=left({array}{ccc}0&B_z&-B_y[0.5ex]-B_z&0&B_x[0.5ex]B_y&-B_x&0{array}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="81" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3778.png"
 ALT="$\displaystyle B^{ij}=B_{ij} = \left(\begin{array}{ccc} 0&amp; B_z &amp; -B_y\ [0.5ex] -B_z &amp; 0 &amp; B_x \ [0.5ex] B_y &amp; -B_x &amp; 0 \end{array} \right),$">|; 

$key = q/displaystylef(x,t)=frac{tau}{sqrt{2},pi^{,2}}sqrt{frac{|t-t_1|}{x,k_0'''}}int_0^inftycos!left[frac{3}{2},zleft(frac{v^{,3}}{3}pmvright)right],dv,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1952.png"
 ALT="$\displaystyle f(x,t) = \frac{\tau}{\sqrt{2} \pi^{ 2}}\sqrt{\frac{\vert t-t_1\...
...y \cos\!\left[ \frac{3}{2}  z\left(\frac{v^{ 3}}{3} \pm v\right) \right] dv,$">|; 

$key = q/displaystylefrac{partial}{partialy};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2297.png"
 ALT="$\displaystyle \frac{\partial}{\partial y}$">|; 

$key = q/{bfP}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="$ {\bf P}({\bf r})$">|; 

$key = q/displaystyle=E_2,sin(k_1,x)cos(k_2,y)sin(k_3,z),{rme}^{-{rmi},omega,t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2781.png"
 ALT="$\displaystyle = E_2  \sin(k_1  x)\cos(k_2  y) \sin(k_3  z)  {\rm e}^{-{\rm i} \omega  t},$">|; 

$key = q/s=r-{bfr}cdot{bfu}slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3993.png"
 ALT="$ s = r - {\bf r}\cdot{\bf u}/c$">|; 

$key = q/2,l+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="$ 2 l+1$">|; 

$key = q/displaystylerightarrow-frac{(2,l-1)!!}{z^{,l+1}}left[1+{calO}(z^2)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3035.png"
 ALT="$\displaystyle \rightarrow -\frac{(2 l-1)!!}{z^{ l+1}}\left[1+ {\cal O}(z^2)\right],$">|; 

$key = q/displaystyleE_y(z=0_+);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1101.png"
 ALT="$\displaystyle E_y (z=0_+)$">|; 

$key = q/displaystylec,A_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3869.png"
 ALT="$\displaystyle c A_1$">|; 

$key = q/B_5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1826.png"
 ALT="$ B_5$">|; 

$key = q/I=I_0,cos(omega,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2658.png"
 ALT="$ I= I_0 \cos(\omega  t)$">|; 

$key = q/l,(a_1,x'+b_1,y'+c_1,z'+d_1,t'+e_1)+m,(a_2,x'+cdots)+n,(a_3,x'+cdots)+p=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3445.png"
 ALT="$ l (a_1  x' + b_1  y'
+c_1  z' +d_1  t' + e_1) + m (a_2  x' +\cdots) +n (a_3  x'+\cdots) + p =0$">|; 

$key = q/e^{,2}slash(4pi,epsilon_0,m_e,c^{,2})=2.8times10^{-15};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2741.png"
 ALT="$ e^{ 2}/(4\pi \epsilon_0  m_e  c^{ 2})=2.8 \times 10^{-15}$">|; 

$key = q/displaystylephi_2-phi_1=frac{D}{epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="$\displaystyle \phi_2-\phi_1 = \frac{D}{\epsilon_0},$">|; 

$key = q/displaystyle{bfE}({bfr})=-nablaphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = -\nabla\phi,$">|; 

$key = q/displaystyle{mitDelta}chisimeqfrac{e^{,3}}{2,epsilon_0,m^{,2},c,omega^{,2}}intN(l),B_parallel(l),dl,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1761.png"
 ALT="$\displaystyle {\mit\Delta}\chi \simeq \frac{e^{ 3}}{2 \epsilon_0  m^{ 2}  c \omega^{ 2}} \int N(l)  B_\parallel(l)  dl,$">|; 

$key = q/{bfu}=u^{,i}=dx^{,i}slashdt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3634.png"
 ALT="$ {\bf u} = u^{ i} = dx^{ i}/dt$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),w=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2})  w =0,$">|; 

$key = q/displaystyle{bfn}cdot({bfB}_1-{bfB}_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2758.png"
 ALT="$\displaystyle {\bf n}\cdot({\bf B}_1 - {\bf B}_2)$">|; 

$key = q/displaystyle=sum_{n=1,infty}A_{mn},sinh(j_{mn},Lslasha),J_m(j_{mn},rslasha),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="$\displaystyle = \sum_{n=1,\infty}A_{mn} \sinh(j_{mn} L/a) J_m(j_{mn} r/a),$">|; 

$key = q/displaystyle=frac{2,beta}{(beta^{,2}+hat{alpha}^{,2})^{1slash2}},psi_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2159.png"
 ALT="$\displaystyle =\frac{2 \beta}{(\beta^{ 2}+\hat{\alpha}^{ 2})^{1/2}} \psi_i.$">|; 

$key = q/n_2=1.0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$ n_2=1.0$">|; 

$key = q/epsilon_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1081.png"
 ALT="$ \epsilon_1$">|; 

$key = q/displaystyle=sqrt{(l-m),(l+m+1)},Y_{l,m+1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3059.png"
 ALT="$\displaystyle = \sqrt{(l-m) (l+m+1)} Y_{l,m+1},$">|; 

$key = q/theta_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2179.png"
 ALT="$ \theta_c$">|; 

$key = q/gamma_0=lim_{omega_0rightarrow0}g_0,omega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1677.png"
 ALT="$ \gamma_0=\lim_{\omega_0\rightarrow 0} g_0 \omega_0$">|; 

$key = q/displaystyle=psi_t,coshtheta_t,{rme}^{-n_2,k_0,sinhtheta_t,z},cos(omega,t-n_1,k_0,sintheta_i,x+phi_t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2170.png"
 ALT="$\displaystyle =\psi_t \cosh\theta_t {\rm e}^{-n_2 k_0 \sinh\theta_t z} \cos(\omega t-n_1 k_0 \sin\theta_i x+\phi_t)$">|; 

$key = q/{bfe}_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$ {\bf e}_j$">|; 

$key = q/displaystyle{mitDelta}t_0simfrac{pi^2}{2,xi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1895.png"
 ALT="$\displaystyle {\mit\Delta} t_0 \sim \frac{ \pi^2}{2 \xi},$">|; 

$key = q/displaystyle=-frac{partialH_z}{partialx}+frac{partialH_x}{partialz}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2096.png"
 ALT="$\displaystyle =-\frac{\partial H_z}{\partial x}+ \frac{\partial H_x}{\partial z}.$">|; 

$key = q/displaystylepsi({bfr})=sum_{l,m}left[A_{lm}^{(1)},h_l^{(1)}(k,r)+A_{lm}^{(2)},h_l^{(2)}(k,r)right]Y_{lm}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3076.png"
 ALT="$\displaystyle \psi({\bf r}) = \sum_{l,m}\left[A_{lm}^{(1)}  h_l^{(1)}(k r) +A_{lm}^{(2)}  h_l^{(2)}(k r)\right] Y_{lm}(\theta,\varphi),$">|; 

$key = q/int{bfE}cdot{bfD},dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1296.png"
 ALT="$ \int {\bf E}\cdot{\bf D} dV$">|; 

$key = q/muneqnu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3630.png"
 ALT="$ \mu\neq \nu$">|; 

$key = q/{bfp}=p,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1291.png"
 ALT="$ {\bf p} = p {\bf e}_z$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}intfrac{left[rho({bfr}')right]}{|{bfr}-{bfr}'|},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle = \frac{1}{4\pi  \epsilon_0} \int \frac{\left[\rho({\bf r}')\right]}{\vert{\bf r} - {\bf r}'\vert} dV',$">|; 

$key = q/A^mu=({bfA},,A^0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3669.png"
 ALT="$ A^\mu= ({\bf A},  A^0)$">|; 

$key = q/sigmaslashepsilon,epsilon_0,omegagg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1692.png"
 ALT="$ \sigma/\epsilon \epsilon_0 \omega\gg 1$">|; 

$key = q/displaystyle{mitDelta}t_0sim(x,k_0''')^{1slash3}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1962.png"
 ALT="$\displaystyle {\mit\Delta} t_0 \sim (x  k_0''')^{1/3}.$">|; 

$key = q/displaystyle=frac{S_{mn}}{I_m(k_n,a)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img946.png"
 ALT="$\displaystyle = \frac{S_{mn}}{I_m(k_n a)}.$">|; 

$key = q/displaystyle~~~+frac{1}{2,l+1}int_r^inftyfrac{rho_{l,m}(r')}{epsilon_0}left(frac,r^{,l+1}}right)r'^{,2},dr'+phi_{l,m}(a)left(frac{a}{r}right)^{l+1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;+\frac{1}{2 l+1}\int_r^\infty \frac{\rho_{l,m}(r')}{\epsilon_...
...} r^{ l+1}}\right)r'^{ 2} dr' +\phi_{l,m}(a)\left(\frac{a}{r}\right)^{l+1}.$">|; 

$key = q/displaystylec,A_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3871.png"
 ALT="$\displaystyle c A_2$">|; 

$key = q/r^{,i}=x^{,i}-x^{,i'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3986.png"
 ALT="$ r^{ i} = x^{ i} - x^{ i'}$">|; 

$key = q/displaystyle(0,hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2507.png"
 ALT="$\displaystyle (0,\hat{z})$">|; 

$key = q/displaystylephantom{=}+I_m(k_n,r)int_r^inftyR_{m,n}(r'),left[K_m(k_n,r')-frac{I_m(k_n,r'),K_m(k_n,a)}{I_m(k_n,a)}right]r',dr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1020.png"
 ALT="$\displaystyle \phantom{=}+I_m(k_n r)\int_r^\infty R_{m,n}(r') \left[K_m(k_n r')-\frac{I_m(k_n r') K_m(k_n a)}{I_m(k_n a)}\right]r' dr'$">|; 

$key = q/displaystylephi(z>0)=frac{1}{4pi,epsilon_0,epsilon_1}left(frac{q}{R_1}+frac{q'}{R_2}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1107.png"
 ALT="$\displaystyle \phi(z&gt;0) = \frac{1}{4\pi \epsilon_0  \epsilon_1}\left(\frac{q}{R_1} + \frac{q'}{R_2}\right),$">|; 

$key = q/displaystyle={bfB}_0-frac{1}{3},mu_0,{bfM},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1535.png"
 ALT="$\displaystyle = {\bf B}_0 - \frac{1}{3} \mu_0  {\bf M},$">|; 

$key = q/A^{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3530.png"
 ALT="$ A^{ij}$">|; 

$key = q/g_{munu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3626.png"
 ALT="$ g_{\mu \nu}$">|; 

$key = q/displaystyle=-left(frac{3}{8pi}right)^{1slash2}sintheta,,{rme}^{+{rmi},varphi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="$\displaystyle =- \left(\frac{3}{8\pi}\right)^{1/2}\sin\theta  {\rm e}^{+{\rm i} \varphi},$">|; 

$key = q/displaystyleC_m(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="$\displaystyle C_m(r)$">|; 

$key = q/u({bfr},t)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$ u({\bf r}, t)=0$">|; 

$key = q/k,rgg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3144.png"
 ALT="$ k r\gg 1$">|; 

$key = q/displaystyleA,K_0(k_t,a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2955.png"
 ALT="$\displaystyle A K_0(k_t  a)$">|; 

$key = q/displaystylepartial_muF^{,munu}=frac{J^{,nu}}{c,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3812.png"
 ALT="$\displaystyle \partial_\mu F^{ \mu\nu} = \frac{J^{ \nu}}{c \epsilon_0}.$">|; 

$key = q/displaystyle{r'}^{,2}=r^{,2}+c^{,2},{t'}^{,2}=r^{,2}+frac{gamma^{,2},u^{,2},x^{,2}}{c^{,2}}=r^{,2}left(1+frac{gamma^{,2},u_r^{,2}}{c^{,2}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3899.png"
 ALT="$\displaystyle {r'}^{ 2} = r^{ 2} + c^{ 2}  {t'}^{ 2} = r^{ 2} +\frac{ \ga...
...}}{c^{ 2}} = r^{ 2}\left(1 + \frac{\gamma^{ 2}  u_r^{ 2}}{c^{ 2}}\right).$">|; 

$key = q/displaystyle=frac{mu_0}{4pi},m,frac{sintheta}{r^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1369.png"
 ALT="$\displaystyle = \frac{\mu_0}{4\pi} m \frac{\sin\theta}{r^{ 2}},$">|; 

$key = q/displaystylec^{,2}-u^{,2}=frac{c^{,2},(c^{,2}-u'^{,2}),(c^{,2}-v^{,2})}{(c^{,2}+u'_1,v)^2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3513.png"
 ALT="$\displaystyle c^{ 2} - u^{ 2} = \frac{c^{ 2}  (c^{ 2}-u'^{ 2})  (c^{ 2}-v^{ 2})}{(c^{ 2} + u'_1  v)^2}.$">|; 

$key = q/displaystylefrac{1}{2},F_{munu},F^{,munu}=c^{,2},B^{,2}-E^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3859.png"
 ALT="$\displaystyle \frac{1}{2}  F_{\mu\nu}  F^{ \mu\nu} = c^{ 2}  B^{ 2} - E^{ 2},$">|; 

$key = q/displaystyle-sum_{l=0,infty}sum_{m=-l,+l}frac{1}{2,l+1},frac{r_<^{,l}}{r_>^{,l+1}},Y_{l,m}^ast(theta',varphi'),Y_{l,m}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="$\displaystyle -\sum_{l=0,\infty}\sum_{m=-l,+l}\frac{1}{2 l+1} \frac{r_&lt;^{ l}}{r_&gt;^{ l+1}} Y_{l,m}^\ast(\theta',\varphi') Y_{l,m}(\theta,\varphi)$">|; 

$key = q/f_mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3943.png"
 ALT="$ f_\mu$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$ \alpha$">|; 

$key = q/displaystyle-frac{partial,c,B_y}{partialz};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2238.png"
 ALT="$\displaystyle -\frac{\partial  c  B_y}{\partial z}$">|; 

$key = q/displaystylenablacdot{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle \nabla\cdot{\bf B}$">|; 

$key = q/displaystylefrac{dphi}{dz}=pmk,q+frac{rmi}{2,q}frac{dq}{dz}-frac{{rmi}}{n}frac{dn}{dz}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2326.png"
 ALT="$\displaystyle \frac{d\phi}{dz} = \pm k  q +\frac{\rm i}{2 q} \frac{dq}{dz} -\frac{{\rm i}}{n} \frac{dn}{dz}.$">|; 

$key = q/u_z(omega,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2351.png"
 ALT="$ u_z(\omega, z)$">|; 

$key = q/varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="$ \varphi$">|; 

$key = q/displaystylen_1,sintheta_i=n_2,sintheta_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2044.png"
 ALT="$\displaystyle n_1 \sin\theta_i = n_2 \sin\theta_t.$">|; 

$key = q/displaystyleint_{-infty}^inftyf(t),delta(t-t'),dt'=f(t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle \int_{-\infty}^\infty f(t) \delta(t-t') dt' = f(t),$">|; 

$key = q/displaystyleG^{munu}=leftlgroup{array}{cccc}0&-E_z&+E_y&-c,B_x[0.5ex]+E_z&0&-E_xx]-E_y&+E_x&0&-c,B_z[0.5ex]+c,B_x&+c,B_y&+c,B_z&0{array}rightrgroup.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="105" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3827.png"
 ALT="$\displaystyle G^{\mu\nu} = \left\lgroup \begin{array}{cccc} 0 &amp; -E_z &amp; +E_y &amp; -...
...&amp; 0&amp; -c B_z\ [0.5ex] +c B_x &amp;+ c B_y &amp;+c B_z &amp; 0\end{array}\right \rgroup.$">|; 

$key = q/displaystyle-frac{partial}{partialt}left(epsilon_0,{bfE}times{bfB}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$\displaystyle -\frac{\partial}{\partial t} \left(\epsilon_0 {\bf E}\times{\bf B}\right)$">|; 

$key = q/displaystyle=frac{mu_0,e}{4pi}frac{[{bfu}]}{[r+{bfr}cdot{bfu}slashc]},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3881.png"
 ALT="$\displaystyle = \frac{\mu_0 e}{4\pi} \frac{[{\bf u}]}{[r+ {\bf r}\cdot{\bf u}/c]},$">|; 

$key = q/displaystylenablacdot{bfE}=frac{rho}{epsilon_0}=frac{rho_f+rho_b}{epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1068.png"
 ALT="$\displaystyle \nabla \cdot{\bf E} = \frac{\rho}{\epsilon_0} = \frac{\rho_f + \rho_b}{\epsilon_0}.$">|; 

$key = q/displaystyle{rmi},frac{d^{,2}phi}{dz^{,2}}-left(frac{dphi}{dz}right)^2-frac{{rmi}}{n^{,2}}frac{dn^{,2}}{dz}frac{dphi}{dz}+k^{,2}q^{,2},phi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2320.png"
 ALT="$\displaystyle {\rm i} \frac{d^{ 2}\phi}{dz^{ 2}} -\left(\frac{d\phi}{dz}\rig...
...m i}}{n^{ 2}}\frac{dn^{ 2}}{dz} \frac{d\phi}{dz} + k^{ 2} q^{ 2} \phi = 0.$">|; 

$key = q/displaystyle=frac{u_3}{gamma,(1-u_1,vslashc^{,2})}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3504.png"
 ALT="$\displaystyle = \frac{u_3}{\gamma (1-u_1  v/c^{ 2})}.$">|; 

$key = q/displaystylefrac{d({A^{icdotsj}}_{kcdotsl})}{ds}={A^{icdotsj}}_{kcdotsl,m}frac{dx^{,m}}{ds},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3609.png"
 ALT="$\displaystyle \frac{d({A^{i\cdots j}}_{k\cdots l})}{ds} = {A^{i\cdots j}}_{k\cdots l,m} \frac{d x^{ m}}{ds},$">|; 

$key = q/displaystyle=sum_{l=1,infty}{rmi}^{,l}sqrt{4pi,(2,l+1)}left[j_l(k,r),{bfX}_{l,pm1}pmfrac{1}{k},nablatimesj_l(k,r),{bfX}_{l,pm1}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="367" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3324.png"
 ALT="$\displaystyle = \sum_{l=1,\infty} {\rm i}^{ l}\sqrt{4\pi (2 l+1)}\left[j_l(k...
... X}_{l,\pm 1}\pm\frac{1}{k} \nabla\times j_l(k r) {\bf X}_{l,\pm 1} \right],$">|; 

$key = q/A_mu,B^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4058.png"
 ALT="$ A_\mu  B^{ \mu}$">|; 

$key = q/displaystyle{bfE}({bfr})=frac{q'}{4pi,epsilon_0},frac{{bfr}-{bfr}'}{|{bfr}-{bfr}'|^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = \frac{q'}{4\pi \epsilon_0} \frac{{\bf r}-{\bf r}'}{\vert{\bf r}-{\bf r}'\vert^{ 3}}.$">|; 

$key = q/{bfn}timesc,{bfB}_{sc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3344.png"
 ALT="$ {\bf n}\times c {\bf B}_{sc}$">|; 

$key = q/t-|{bfr}-{bfr}'|slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$ t-\vert{\bf r} -{\bf r}'\vert/c$">|; 

$key = q/displaystyle{bfD}=epsilon_0,epsilon,{bfE}=epsilon_0,{bfE}+{bfP},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1625.png"
 ALT="$\displaystyle {\bf D} =\epsilon_0 \epsilon  {\bf E} = \epsilon_0  {\bf E} + {\bf P},$">|; 

$key = q/n_1=1.52;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$ n_1=1.52$">|; 

$key = q/displaystyle=f_l(k,r),{bfL},Y_{lm}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3104.png"
 ALT="$\displaystyle = f_l(k r) {\bf L}  Y_{lm}(\theta,\varphi),$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{2pi,epsilon_0}intrho({bfr}'),ln|{bfr}-{bfr'}|,dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="$\displaystyle \phi({\bf r}) = - \frac{1}{2\pi \epsilon_0}\int\rho({\bf r}') \ln\vert{\bf r}-{\bf r'}\vert dV'.
$">|; 

$key = q/displaystyleP_0^{,0}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="$\displaystyle P_0^{ 0}(x)$">|; 

$key = q/q<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2530.png"
 ALT="$ q&lt;0$">|; 

$key = q/sigma_{rmsc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3357.png"
 ALT="$ \sigma_{\rm sc}$">|; 

$key = q/displaystyleint_V{bfE}cdotdelta{bfD},dV=-int_Vnablaphicdotdelta{bfD},dV=int_Vphi,nablacdotdelta{bfD},dV=int_Vphi,deltarho_f,dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1213.png"
 ALT="$\displaystyle \int_V{\bf E}\cdot \delta{\bf D} dV = - \int_V\nabla\phi \cdot \...
...=\int_V \phi  \nabla \cdot \delta {\bf D} dV = \int_V \phi \delta\rho_f dV,$">|; 

$key = q/displaystylek_s^{,2}=frac{int_V(nabla_sf)^{,2},dV}{int_Vf^{,2},dV}>0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2843.png"
 ALT="$\displaystyle k_s^{ 2} = \frac{\int_V (\nabla_s f)^{ 2} dV} {\int_V f^{ 2} dV} &gt; 0.$">|; 

$key = q/phi=omega_0,t';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4113.png"
 ALT="$ \phi = \omega_0  t'$">|; 

$key = q/displaystyleG^{(pm)}({bfr},{bfr}';t,t')=frac{delta(t'-[tmp|{bfr}-{bfr'}|slashc])}{4pi,|{bfr}-{bfr}'|},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle G^{(\pm)} ({\bf r}, {\bf r}'; t, t') = \frac{\delta(t'-[t\mp \vert{\bf r}- {\bf r'}\vert/c])}{4\pi  \vert{\bf r}-{\bf r}'\vert},$">|; 

$key = q/{calM}_{lm}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3245.png"
 ALT="$ {\cal M}_{lm}'$">|; 

$key = q/displaystylefrac{partial}{partialz}!left(frac{1}{R_1}right)_{z=0}=-frac{partial}z}!left(frac{1}{R_2}right)_{z=0}=frac{d}{(r^{,2}+d^{,2})^{3slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1117.png"
 ALT="$\displaystyle \frac{\partial}{\partial z}\!\left(\frac{1}{R_1}\right)_{z=0} =- ...
...rtial z}\!\left(\frac{1}{R_2}\right)_{z=0} = \frac{d}{(r^{ 2}+d^{ 2})^{3/2}}.$">|; 

$key = q/{bfr}cdot{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3077.png"
 ALT="$ {\bf r}\cdot{\bf A}$">|; 

$key = q/{bfj}_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1435.png"
 ALT="$ {\bf j}_p$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0}{4pi}intfrac{nabla'times{bfM}({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1496.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = \frac{\mu_0}{4\pi}\int \frac{\nabla'\times {\bf M}({\bf r}')} {\vert{\bf r}- {\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle=frac{rmi}{k},nablatimesc,{bfB}_{l}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3155.png"
 ALT="$\displaystyle = \frac{\rm i}{k} \nabla\times c  {\bf B}_{l}.$">|; 

$key = q/1slashr^{,3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1589.png"
 ALT="$ 1/r^{ 3}$">|; 

$key = q/A_l^{(2)}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3214.png"
 ALT="$ A_l^{(2)} = 0$">|; 

$key = q/{bfs};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1615.png"
 ALT="$ {\bf s}$">|; 

$key = q/{bfp}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="$ {\bf p}_1$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}}{partialz}=-sigma,E_x^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1994.png"
 ALT="$\displaystyle \frac{\partial{\cal E}}{\partial t} + \frac{\partial {\cal I}}{\partial z} =- \sigma E_x^{ 2},
$">|; 

$key = q/displaystyle=frac{m,pi}{b},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2787.png"
 ALT="$\displaystyle = \frac{m \pi}{b},$">|; 

$key = q/-J_1(k_s,a)slashk_s,J_0(k_s,a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2964.png"
 ALT="$ -J_1(k_s  a)/k_s  J_0(k_s  a)$">|; 

$key = q/F^{,ij}=-c,B^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3891.png"
 ALT="$ F^{ ij} = - c B^{ ij}$">|; 

$key = q/B_j^i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3531.png"
 ALT="$ B_j^i$">|; 

$key = q/displaystylek=n,frac{omega}{c}simeqsqrt{epsilon},frac{omega}{c}+{rmi},frac{sigma}{2sqrt{epsilon},epsilon_0,c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1689.png"
 ALT="$\displaystyle k = n  \frac{\omega}{c} \simeq \sqrt{\epsilon} \frac{\omega}{c} + {\rm i}  \frac{\sigma}{2\sqrt{\epsilon}  \epsilon_0  c}.$">|; 

$key = q/displaystyle{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$\displaystyle {\bf B}$">|; 

$key = q/D(z)=epsilon_0,epsilon(z),E(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1142.png"
 ALT="$ D(z) = \epsilon_0  \epsilon(z) E(z)$">|; 

$key = q/displaystylesimeq-left(1-sqrt{2},alpharight),E_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2205.png"
 ALT="$\displaystyle \simeq-\left(1-\sqrt{2} \alpha\right) E_i,$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=lambda,frac{3,mu_0,c,I^{,2}}{pi^3}frac{3,sin^2sqrt{frac{7}{8}}frac{a_E(3,0)}{a_E(1,0)},(5cos^2theta-1)right|^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3284.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} = \lambda \frac{3 \mu_0  c  I^{ 2}...
...qrt{\frac{7}{8}}\frac{a_E(3,0)}{a_E(1,0)}  (5\cos^2\theta-1)\right\vert^{ 2},$">|; 

$key = q/phi_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="$ \phi_i$">|; 

$key = q/displaystyleU=int_{bf0}^{bfD}int_V{bfE}cdotdelta{bfD},dV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1294.png"
 ALT="$\displaystyle U = \int_{\bf0}^{\bf D }\int_V {\bf E} \cdot
\delta{\bf D} dV
$">|; 

$key = q/displaystyle{bfB}=frac{mu_0}{4pi}left[frac{3,({bfm}cdot{bfr}),{bfr}-r^{,2},{bfm}}{r^{,5}}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1378.png"
 ALT="$\displaystyle {\bf B} =\frac{\mu_0}{4\pi}\left[\frac{3 ({\bf m}\cdot{\bf r}) {\bf r} -r^{ 2} {\bf m}}{r^{ 5}}\right],$">|; 

$key = q/{rme}^{-{rmi},omega,t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1800.png"
 ALT="$ {\rm e}^{-{\rm i} \omega  t}$">|; 

$key = q/displaystylefrac{P}{m_0,c^{,2}}=frac{2}{3}left(frac{e,B}{m_0}right)^{2}frac{r_0}{c},(beta,gamma)^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4146.png"
 ALT="$\displaystyle \frac{P}{m_0  c^{ 2}} =\frac{2}{3} \left(\frac{e B}{m_0}\right)^{2} \frac{r_0}{c}  (\beta \gamma)^{ 2},$">|; 

$key = q/K=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3440.png"
 ALT="$ K=-1$">|; 

$key = q/displaystyle{bfE}_{rmradiation}=frac{e}{4pi,epsilon_0,c^{,2}}frac{{bfr}times({bfr}_utimesdot{bfu})}{s^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4026.png"
 ALT="$\displaystyle {\bf E}_{\rm radiation} = \frac{e}{4\pi \epsilon_0  c^{ 2}} \frac{{\bf r}\times ({\bf r}_u\times\dot{\bf u})}{s^{ 3}},$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{Chapter06slashfig18.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img2496.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{Chapter06/fig18.eps}}
\end{figure}">|; 

$key = q/q>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2529.png"
 ALT="$ q&gt;0$">|; 

$key = q/(d_1,d_2,d_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3448.png"
 ALT="$ (d_1, d_2, d_3)$">|; 

$key = q/displaystylefrac{partials}{partialt'}=frac{partialr}{partialt'}-frac{{bfr}cdotdo-frac{{bfr}cdot{bfu}}{r}-frac{{bfr}cdotdot{bfu}}{c}+frac{u^{,2}}{c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4009.png"
 ALT="$\displaystyle \frac{\partial s}{\partial t'} = \frac{\partial r}{\partial t'} -...
...f r} \cdot{\bf u}}{r} - \frac{ {\bf r}\cdot\dot{\bf u}}{c} + \frac{u^{ 2}}{c}.$">|; 

$key = q/displaystyle=-frac{e}{4pi,epsilon_0}frac{gamma}{r^{,3},(1+u_r^{,2},gamma^{,2}slashc^{,2})^{3slash2}},{bfr},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3900.png"
 ALT="$\displaystyle = - \frac{e}{4\pi \epsilon_0} \frac{\gamma}{r^{ 3}  (1+ u_r^{ 2}  \gamma^{ 2}/c^{ 2})^{3/2}} {\bf r},$">|; 

$key = q/displaystyle=-frac{psi_i,sintheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2061.png"
 ALT="$\displaystyle = -\frac{\psi_i \sin\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x-n_1 k_0 \cos\theta_i z)$">|; 

$key = q/displaystyleJ^{,mu}=rho_0,frac{dx^{,mu}}{dtau}=rho_0,U^{,mu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3717.png"
 ALT="$\displaystyle J^{ \mu} = \rho_0  \frac{dx^{ \mu}}{d\tau} = \rho_0  U^{ \mu}.$">|; 

$key = q/displaystylep=4pi,epsilon_0left(frac{epsilon-1}{epsilon+2}right),a^{,3},E_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1184.png"
 ALT="$\displaystyle p = 4\pi \epsilon_0 \left(\frac{\epsilon-1}{\epsilon +2} \right)  a^{ 3}  E_0.$">|; 

$key = q/A_{i'j'k'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3536.png"
 ALT="$ A_{i'j'k'}$">|; 

$key = q/nabla^{,2}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2832.png"
 ALT="$ \nabla^{ 2}_s$">|; 

$key = q/Q_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3237.png"
 ALT="$ Q_{lm}$">|; 

$key = q/displaystylephi(r,theta)=sum_{l=0,infty}left(alpha_l,r^{,l}+beta_l,r^{-l-1}right)P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1030.png"
 ALT="$\displaystyle \phi(r,\theta) = \sum_{l=0,\infty} \left(\alpha_l r^{ l} +\beta_l r^{-l-1}\right)P_l(\cos\theta),
$">|; 

$key = q/v=w,cos^{,2}theta+u,sin^{,2}theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2372.png"
 ALT="$ v=w \cos^{ 2}\theta+u \sin^{ 2}\theta$">|; 

$key = q/displaystylea_pm(l,m),j_l(k,r)=frac{sqrt{(lpmm),(lmpm+1)}}{sqrt{l,(l+1)}}ointY_{l,mmp1}^{,ast},{rme}^{,{rmi},k,z},d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3320.png"
 ALT="$\displaystyle a_\pm(l,m) j_l(k r) = \frac{\sqrt{(l\pm m) (l\mp m+1)}}{\sqrt{l (l+1)}} \oint Y_{l,m\mp 1}^{ \ast} {\rm e}^{ {\rm i} k z} d{\mit \Omega}.$">|; 

$key = q/hbar,omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2738.png"
 ALT="$ \hbar \omega$">|; 

$key = q/displaystylebeta^{,2}=frac{cos^2theta_t}{cos^2theta_i}=frac{1-sin^2theta_t}{1-sin^2theta_i}=frac{1-sin^2theta_islashbeta^{,2}}{1-sin^2theta_i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2125.png"
 ALT="$\displaystyle \beta^{ 2} = \frac{\cos^2\theta_t}{\cos^2\theta_i} = \frac{1-\si...
...eta_t}{1-\sin^2\theta_i}=\frac{1-\sin^2\theta_i/\beta^{ 2}}{1-\sin^2\theta_i},$">|; 

$key = q/{bfH}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2833.png"
 ALT="$ {\bf H}_s$">|; 

$key = q/displaystyle{bfE}({bfr})=-nablaleft(frac{1}{4pi,epsilon_0},frac{{bfp}cdot({bfr}-{bfr}')}{|{bfr}-{bfr}'|^{,3}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="$\displaystyle {\bf E}({\bf r}) =-\nabla\left(\frac{1}{4\pi \epsilon_0} \frac{{\bf p}\cdot({\bf r}-{\bf r}')}{\vert{\bf r}-{\bf r}'\vert^{ 3}}\right).$">|; 

$key = q/displaystylef(x,t)=f_1(xi,t)simeqfrac{1}{tau}oint_Sexpleft[,{rmi}left(-frac{xi}{omega}-omega,sright)right]frac{domega}{omega^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1860.png"
 ALT="$\displaystyle f(x,t) = f_1(\xi,t) \simeq\frac{1}{\tau} \oint_S \exp\left[ {\rm...
...eft( -\frac{\xi}{\omega} -\omega  s\right)\right]\frac{d\omega} {\omega^{ 2}}$">|; 

$key = q/displaystyle{bfX}_{lm}(theta,varphi)=frac{1}{sqrt{l,(l+1)}},{bfL},Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3109.png"
 ALT="$\displaystyle {\bf X}_{lm}(\theta,\varphi) = \frac{1}{\sqrt{l (l+1)}} {\bf L}   Y_{lm}(\theta,\varphi).$">|; 

$key = q/{bfj}'=sigma,{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4197.png"
 ALT="$ {\bf j}' = \sigma  {\bf E}'$">|; 

$key = q/B_0ggB_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1546.png"
 ALT="$ B_0\gg B_s$">|; 

$key = q/f(alpha);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2700.png"
 ALT="$ f(\alpha)$">|; 

$key = q/displaystyle({mitDelta}t_0,omega_p)_{rmbrillouin}simleft(frac{xi}{omega_p}right)^{1slash3}gg1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1965.png"
 ALT="$\displaystyle ({\mit\Delta} t_0  \omega_p)_{\rm brillouin} \sim \left(\frac{\xi} {\omega_p}\right)^{1/3} \gg 1,$">|; 

$key = q/displaystyleepsilon(omega)equivn^{,2}(omega)=n_0^{,2}+{rmi},frac{sigma}{epsilon_0,omega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1683.png"
 ALT="$\displaystyle \epsilon(\omega) \equiv n^{ 2}(\omega) = n_0^{ 2} + {\rm i}  \frac{\sigma}{\epsilon_0  \omega}.$">|; 

$key = q/nabla;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$ \nabla$">|; 

$key = q/g_{ij},dx^{,i},dx^{,j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3601.png"
 ALT="$ g_{ij} dx^{ i}  dx^{ j}$">|; 

$key = q/displaystylephi_i=frac{1}{4pi,epsilon_0}sum_{j=1,N}^{jneqi}frac{q_j}{|{bfr}_i-{bfr}_j|};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="$\displaystyle \phi_i = \frac{1}{4\pi \epsilon_0}\sum_{j=1,N}^{j\neq i} \frac{q_j}{\vert{\bf r}_i - {\bf r}_j\vert}$">|; 

$key = q/J_m(j_{ml})=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2871.png"
 ALT="$ J_m(j_{ml})=0$">|; 

$key = q/displaystyleH_z(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2939.png"
 ALT="$\displaystyle H_z(r)$">|; 

$key = q/displaystyle{calJ}=frac{partial(x^{,1'},x^{,2'},x^{,3'},x^{,4'})}{partial(x^{,1},x^{,2},x^{,3},x^{,4})};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3696.png"
 ALT="$\displaystyle {\cal J} = \frac{\partial(x^{ 1'}, x^{ 2'}, x^{ 3'}, x^{ 4'})} {\partial (x^{ 1}, x^{ 2}, x^{ 3}, x^{ 4})}$">|; 

$key = q/displaystyle=-{T^{,4}}_i=frac{epsilon^{,ijk},E_j,B_k}{mu_0,c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3959.png"
 ALT="$\displaystyle = - {T^{ 4}}_i = \frac{\epsilon^{ ijk}  E_j  B_k}{\mu_0  c},$">|; 

$key = q/displaystyleh_l^{(1)}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3026.png"
 ALT="$\displaystyle h_l^{(1)} (z)$">|; 

$key = q/displaystyledeltaU=int_Vnablacdot(phi,delta{bfD}),dV-int_Vnablaphicdotdelta{bfD},dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1196.png"
 ALT="$\displaystyle \delta U = \int_V \nabla \cdot (\phi \delta{\bf D}) dV - \int_V \nabla\phi \cdot\delta{\bf D} dV,$">|; 

$key = q/nabla'cdot{bfj}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1390.png"
 ALT="$ \nabla'\cdot{\bf j}= 0$">|; 

$key = q/displaystylenabla'^{,2}G_N({bfr},{bfr}')=delta({bfr}-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="$\displaystyle \nabla'^{ 2}G_N({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}')$">|; 

$key = q/displaystyle{bfr}cdotc,{bfB}=frac{1}{k}sum_{l,m}a_M(l,m),g_l(k,r),{bfL},{bfX}_{lm}=frac{1}{k}sum_{l,m}a_M(l,m),g_l(k,r)sqrt{l,(l+1)},Y_{lm},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3120.png"
 ALT="$\displaystyle {\bf r}\cdot c {\bf B} = \frac{1}{k}\sum_{l,m} a_M(l,m)  g_l(k\...
... X}_{lm}=\frac{1}{k} \sum_{l,m} a_M(l,m)  g_l(k r) \sqrt{l (l+1)}   Y_{lm},$">|; 

$key = q/displaystyleL_-,Y_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3060.png"
 ALT="$\displaystyle L_- Y_{lm}$">|; 

$key = q/displaystyle{bfF}=q,({bfE}+{bfv}times{bfB}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle {\bf F} = q ({\bf E} + {\bf v}\times {\bf B}).$">|; 

$key = q/A=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img981.png"
 ALT="$ A=-1$">|; 

$key = q/E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1131.png"
 ALT="$ E_0$">|; 

$key = q/displaystyle=frac{psi_t^{,2},costheta_t}{2,epsilon_0,c,n_2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2084.png"
 ALT="$\displaystyle = \frac{\psi_t^{ 2} \cos\theta_t}{2 \epsilon_0 c n_2},$">|; 

$key = q/displaystyle|{bfL}Y_{3,0}|^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3280.png"
 ALT="$\displaystyle \vert{\bf L} Y_{3,0}\vert^{ 2}$">|; 

$key = q/displaystyleB_{ij}=-B_{ji}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3776.png"
 ALT="$\displaystyle B_{ij} = -B_{ji}.$">|; 

$key = q/displaystylew(7)=A,(0,hat{z})_d+B,(hat{z},0)_s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2498.png"
 ALT="$\displaystyle w(7) = A (0,\hat{z})_d + B (\hat{z},0)_s.$">|; 

$key = q/omega_0>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4150.png"
 ALT="$ \omega_0&gt;0$">|; 

$key = q/delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2582.png"
 ALT="$ \delta$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),G_omega(R,theta,varphi)=-delta({bfR})?;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle (\nabla^{ 2} + k^{ 2})  G_\omega(R, \theta, \varphi) = - \delta({\bf R}) ?$">|; 

$key = q/k_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2811.png"
 ALT="$ k_2$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi,r'}sum_{l=0,infty}left(frac{r}{r'}right)^{l}P_l(cosgamma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\frac{1}{4\pi r'}\sum_{l=0,\infty}\left(\frac{r}{r'}\right)^{l}P_l(\cos\gamma)$">|; 

$key = q/displaystyle=A,{rme}^{,{rmi},pislash4},|n(z)|^{-1slash2}expleft(pmkint^z!|n(z')|,dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2275.png"
 ALT="$\displaystyle = A {\rm e}^{ {\rm i} \pi/4}  \vert n(z)\vert^{-1/2} \exp\left(\pm k\int^z \!\vert n(z')\vert dz'\right),$">|; 

$key = q/G({bfr},{bfr'});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img970.png"
 ALT="$ G({\bf r},{\bf r'})$">|; 

$key = q/displaystyleZ(z)=sum_{n=1,infty}Z_n,sin(k_n,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img997.png"
 ALT="$\displaystyle Z(z) = \sum_{n=1,\infty} Z_n \sin(k_n z),$">|; 

$key = q/displaystylealpha_pm(l)+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3362.png"
 ALT="$\displaystyle \alpha_\pm (l) + 1$">|; 

$key = q/displaystylefrac{partial{bfg}}{partialt}+nablacdot{bfG}=-(rho,{bfE}+{bfj}times{bfB}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="$\displaystyle \frac{\partial {\bf g}}{\partial t} + \nabla\cdot{\bf G} = - (\rho {\bf E} + {\bf j}\times {\bf B}),$">|; 

$key = q/+e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1285.png"
 ALT="$ +e$">|; 

$key = q/bgeqrgeqa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1558.png"
 ALT="$ b\geq r\geq a$">|; 

$key = q/theta=pislash3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2593.png"
 ALT="$ \theta=\pi/3$">|; 

$key = q/displaystyleR_{rmrad}=frac{0.6094}{pi}sqrt{frac{mu_0}{epsilon_0}}=73,,{rmohms}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2650.png"
 ALT="$\displaystyle R_{\rm rad} = \frac{0.6094}{\pi} \sqrt{\frac{\mu_0}{\epsilon_0}} = 73   {\rm ohms}.$">|; 

$key = q/displaystyleintoverline{N_z},dS=frac{Z_g}{2}intH_{s,0}^{,2},dS.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2902.png"
 ALT="$\displaystyle \int \overline{N_z}  dS = \frac{Z_g}{2} \int H_{s 0}^{ 2}  dS.$">|; 

$key = q/displaystyle=delta_{ll'},delta_{mm'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3111.png"
 ALT="$\displaystyle =\delta_{ll'}  \delta_{m m'},$">|; 

$key = q/g(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1891.png"
 ALT="$ g(z)$">|; 

$key = q/R_mu,Q^{,mu}=-{bfr}cdot{bfq}+c,t,k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3660.png"
 ALT="$ R_\mu  Q^{ \mu} = - {\bf r}\cdot{\bf q} + c t k$">|; 

$key = q/displaystylephi(z=0_+)=phi(z=0_-).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1113.png"
 ALT="$\displaystyle \phi(z=0_+) = \phi(z=0_-).$">|; 

$key = q/displaystyle{bfE}({bfr})=sum_{i=1,N}frac{q_i}{4pi,epsilon_0},frac{{bfr}-{bfr}_i}{|{bfr}-{bfr}_i|^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = \sum_{i=1,N}\frac{q_i}{4\pi \epsilon_0} \frac{{\bf r}-{\bf r}_i}{\vert{\bf r}-{\bf r}_i\vert^{ 3}}.$">|; 

$key = q/displaystyle{bfu}'=frac{{bfu}+left[(gamma-1),{bfu}cdot{bfv}slashc^{,2}-gammaright]{bfv}}{gamma,(1-{bfu}cdot{bfv}slashc^{,2})}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4174.png"
 ALT="$\displaystyle {\bf u}' = \frac{{\bf u}+ \left[(\gamma-1) {\bf u}\cdot{\bf v}/c^{ 2} - \gamma\right]{\bf v}}{\gamma (1-{\bf u}\cdot{\bf v}/c^{ 2})}.
$">|; 

$key = q/u_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$ u_2$">|; 

$key = q/{bfB}=nablatimes{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1490.png"
 ALT="$ {\bf B} = \nabla\times{\bf A}$">|; 

$key = q/g^{,i}=T^{,4i}slashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3977.png"
 ALT="$ g^{ i} = T^{ 4i}/c$">|; 

$key = q/phi({bfr}')=widetilde{G}_N({bfr}'',{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="$ \phi({\bf r}')=\widetilde{G}_N({\bf r}'',{\bf r}')$">|; 

$key = q/displaystyle=-left(frac{15}{8pi}right)^{1slash2}sintheta,costheta,{rme}^{+{rmi},varphi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="$\displaystyle =-\left(\frac{15}{8\pi}\right)^{1/2}\sin\theta \cos\theta {\rm e}^{+{\rm i} \varphi},$">|; 

$key = q/displaystyle={rmi},frac{k_g}{k_s^{,2}}frac{partialH_z}{partialr},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2930.png"
 ALT="$\displaystyle = {\rm i} \frac{k_g}{k_s^{ 2}} \frac{\partial H_z}{\partial r},$">|; 

$key = q/displaystyleint_{-1}^1P_l^{,m}(x),P_k^{,m}(x),dx=frac{2,(l+m)!}{(2,l+1),(l-m)!},delta_{lk},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img680.png"
 ALT="$\displaystyle \int_{-1}^1P_l^{ m}(x) P_k^{ m}(x) dx = \frac{2 (l+m)!}{(2 l+1) (l-m)!} \delta_{lk},$">|; 

$key = q/theta_c=48.8^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2180.png"
 ALT="$ \theta_c= 48.8^\circ$">|; 

$key = q/P_l(costheta)=costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1508.png"
 ALT="$ P_l(\cos\theta)=\cos\theta$">|; 

$key = q/M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1235.png"
 ALT="$ M$">|; 

$key = q/displaystyle=frac{mu_0,c,k^{,2}}{2pisqrt{l,(l+1)}}int_0^{dslash2}left{kr,j_l(k,r),I(r)-frac{1}{k}frac{dI(r)}{dr}frac{d[r,j_l(k,r)]}{dr}right}dr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3253.png"
 ALT="$\displaystyle =\frac{\mu_0  c k^{ 2}}{2\pi\sqrt{l (l+1)}} \int_0^{d/2}\left...
...(k r) I(r) -\frac{1}{k} \frac{dI(r)}{dr} \frac{d[r j_l(k r)]}{dr}\right\}dr$">|; 

$key = q/displaystylephi_m(r,theta)=sum_{l=0,infty}A_l,r^{,l}P_l(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1504.png"
 ALT="$\displaystyle \phi_m(r,\theta) =\sum_{l=0,\infty}A_l  r^{ l} P_l(\cos\theta)$">|; 

$key = q/dx^{,2}+dy^{,2}+dz^{,2}-c^{,2},dt^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3441.png"
 ALT="$ dx^{ 2} + dy^{ 2} + dz^{ 2} -c^{ 2}  dt^{ 2}$">|; 

$key = q/displaystyle=-frac{nablaepsilontimes(nablatimes{bfB})}{epsilon}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2575.png"
 ALT="$\displaystyle = - \frac{\nabla\epsilon\times (\nabla\times {\bf B})}{\epsilon}.$">|; 

$key = q/displaystylebeta_pm(l);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3371.png"
 ALT="$\displaystyle \beta_\pm (l)$">|; 

$key = q/displaystyle=E_0cos[(omegaslashc),(n_+z-c,t)],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1737.png"
 ALT="$\displaystyle = E_0 \cos[(\omega/c) (n_+ z -c  t)],$">|; 

$key = q/{mitDelta}t_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1896.png"
 ALT="$ {\mit\Delta} t_0$">|; 

$key = q/phi=phi(x^{,1},cdots,x^{,n});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3558.png"
 ALT="$ \phi=\phi(x^{ 1}, \cdots, x^{ n})$">|; 

$key = q/displaystyleepsilon_1nablacdot{bfE}=frac{rho}{epsilon_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1092.png"
 ALT="$\displaystyle \epsilon_1 \nabla \cdot {\bf E} = \frac{\rho}{\epsilon_0}$">|; 

$key = q/displaystyle{bfA}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3864.png"
 ALT="$\displaystyle {\bf A}'$">|; 

$key = q/b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="$ b$">|; 

$key = q/displaystylembox{hspace{1.7cm}as{prightarrow0{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img939.png"
 ALT="$\displaystyle \mbox{\hspace{1.7cm}as $p\rightarrow 0$}$">|; 

$key = q/k(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1946.png"
 ALT="$ k(\omega)$">|; 

$key = q/displaystyle-left(frac{1}{r_>}-frac{1}{a}right)Y_{0,0}^ast(theta',varphi'),Y_{0,0}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="$\displaystyle -\left(\frac{1}{r_&gt;}-\frac{1}{a}\right)Y_{0,0}^\ast(\theta',\varphi') Y_{0,0}(\theta,\varphi)$">|; 

$key = q/displaystyleleft(frac{partialr}{partialt'}right)_{x^{,i}}=-frac{{bfr}cdot{bfu}}{r}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3999.png"
 ALT="$\displaystyle \left(\frac{\partial r}{\partial t'}\right)_{x^{ i}} = - \frac{{\bf r} \cdot {\bf u}}{r}.$">|; 

$key = q/displaystyle{rmi},k,S,c,B_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2304.png"
 ALT="$\displaystyle {\rm i} k  S c B_y$">|; 

$key = q/J_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1880.png"
 ALT="$ J_1$">|; 

$key = q/G_D({bfr},{bfr}')rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="$ G_D({\bf r},{\bf r}')\rightarrow 0$">|; 

$key = q/displaystylew''+h^2,q(hat{z}),w=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2471.png"
 ALT="$\displaystyle w'' + h^2 q(\hat{z}) w = 0,$">|; 

$key = q/sigmaslashepsilon,epsilon_0,omegall1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1688.png"
 ALT="$ \sigma/\epsilon \epsilon_0 \omega\ll 1$">|; 

$key = q/tau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="$ \tau$">|; 

$key = q/k,d=pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2640.png"
 ALT="$ k  d=\pi$">|; 

$key = q/k_3=n,pislashL;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2815.png"
 ALT="$ k_3 = n \pi/L$">|; 

$key = q/displaystylephi({bfr})=frac{1}{epsilon_0}sum_{l=0,infty}sum_{m=-l,+l}frac{q_{l,m}^{,ast}}{2,l+1},frac{Y_{l,m}(theta,varphi)}{r^{,l+1}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{\epsilon_0}\sum_{l=0,\infty}\sum_{m=-l,+l} \frac{q_{l,m}^{ \ast}}{2 l+1} \frac{Y_{l,m}(\theta,\varphi)}{r^{ l+1}},$">|; 

$key = q/displaystylephi_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2210.png"
 ALT="$\displaystyle \phi_t$">|; 

$key = q/l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$ l$">|; 

$key = q/displaystyle=sinphi_t,psi_t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2148.png"
 ALT="$\displaystyle =\sin\phi_t \psi_t,$">|; 

$key = q/displaystyle|{bfB}|=frac{n}{c},|{bfE}|,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1713.png"
 ALT="$\displaystyle \vert{\bf B}\vert = \frac{n}{c}  \vert{\bf E}\vert,$">|; 

$key = q/displaystylesin^2theta=1-cos^2psi,sin^2varphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2734.png"
 ALT="$\displaystyle \sin^2\theta = 1-\cos^2\psi  \sin^2\varphi.$">|; 

$key = q/displaystylex^{,2}+y^{,2}+z^{,2}-c^{,2},t^{,2}=x'^{,2}+y'^{,2}+z'^{,2}-c^{,2},t'^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3452.png"
 ALT="$\displaystyle x^{ 2} + y^{ 2} + z^{ 2} -c^{ 2}  t^{ 2} = x'^{ 2} + y'^{ 2} + z'^{ 2} - c^{ 2}  t'^{ 2}.$">|; 

$key = q/displaystylesigmasimeqsigma_{rmThomson}left(frac{omega}{omega_0}right)^{,4},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2749.png"
 ALT="$\displaystyle \sigma \simeq \sigma_{\rm Thomson} \left(\frac{\omega}{\omega_0}\right)^{ 4},$">|; 

$key = q/displaystyle=frac{{rmi},k_g}{k_s^{,2}},nabla_sH_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2892.png"
 ALT="$\displaystyle = \frac{{\rm i} k_g}{k_s^{ 2}} \nabla_s H_z,$">|; 

$key = q/partialepsilonslashpartialt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1216.png"
 ALT="$ \partial\epsilon/\partial t$">|; 

$key = q/displaystylephi(z)=frac{V}{2},(z^{,2}-a^{,2}),aleft[int_0^1frac{dmu}{(z^{,2}-2,zsh2}}-int_{-1}^0frac{dmu}{(z^{,2}-2,z,a,mu+a^{,2})^{3slash2}}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="$\displaystyle \phi(z) = \frac{V}{2} (z^{ 2}-a^{ 2}) a\left[\int_0^1 \frac{d...
...2})^{3/2}}-\int_{-1}^0\frac{d\mu}{(z^{ 2}-2 z a \mu+a^{ 2})^{3/2}}\right],$">|; 

$key = q/displaystyleJ_1(z)=frac{z}{2}+{calO}(z^{,3}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1876.png"
 ALT="$\displaystyle J_1(z) = \frac{z}{2} + {\cal O}(z^{ 3}).$">|; 

$key = q/displaystyle=frac{2}{a^2,J_{m+1}^{,2}(j_{mn}),sinh(j_{mn},Lslasha)},int_0^ar,S_m(r),J_m(j_{mn},rslasha),dr,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="$\displaystyle = \frac{2}{a^2 J_{m+1}^{ 2}(j_{mn}) \sinh(j_{mn} L/a)} \int_0^a r S_m(r) J_m(j_{mn} r/a) dr,$">|; 

$key = q/(0,1slashsqrt{2},1slashsqrt{2},1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3430.png"
 ALT="$ (0, 1/\sqrt{2}, 1/\sqrt{2},
1)$">|; 

$key = q/displaystyle=K_m(k,r)int_0^rR_m(r',k),I_m(k,r'),r',dr'+I_m(k,r)int_r^inftyR_m(r',k),K_m(k,r'),r',dr',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img988.png"
 ALT="$\displaystyle = K_m(k r)\int_0^r R_m(r',k) I_m(k r') r' dr'+I_m(k r)\int_r^\infty R_m(r',k) K_m(k r') r' dr',$">|; 

$key = q/displaystylecdot{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1293.png"
 ALT="$\displaystyle \cdot{\bf E},
$">|; 

$key = q/displaystylefrac{[{rmRe}(n)]^{,2}-[{rmIm}(n)]^{,2}}{a^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1650.png"
 ALT="$\displaystyle \frac{[{\rm Re}(n)]^{ 2} - [{\rm Im}(n)]^{ 2}}{a^{ 2}},$">|; 

$key = q/nabla^{,2}(|{bfr}-{bfr}'|^{-1})=nabla'^{,2}(|{bfr}-{bfr}'|^{-1});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="$ \nabla^{ 2}(\vert{\bf r}-{\bf r}'\vert^{-1})=\nabla'^{ 2}(\vert{\bf r}-{\bf r}'\vert^{-1})$">|; 

$key = q/displaystyleq(r)=frac{4pi}{3},r^{,3},rho,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="$\displaystyle q(r) = \frac{4\pi}{3}  r^{ 3} \rho,$">|; 

$key = q/displaystylenabla^{,2}left(frac{1}{|{bfr}-{bfr}'|}right)=-4pi,delta({bfr}-{bfr}').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \nabla^{ 2}\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)=-4\pi \delta({\bf r}-{\bf r}').$">|; 

$key = q/displaystyle{bfE}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2825.png"
 ALT="$\displaystyle {\bf E}_s$">|; 

$key = q/displaystylet;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3480.png"
 ALT="$\displaystyle t$">|; 

$key = q/A_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="$ A_{mn}$">|; 

$key = q/displaystyles=t-frac{x}{c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1808.png"
 ALT="$\displaystyle s = t - \frac{x}{c}.$">|; 

$key = q/displaystyleequiv-J_1(z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2949.png"
 ALT="$\displaystyle \equiv -J_1(z),$">|; 

$key = q/displaystyle=int_0^rointr'^{,l},rho(r',theta,varphi),Y_{l,m}(theta,varphi),r'^{,2},d{mitOmega},dr'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="$\displaystyle = \int_0^r \oint r'^{ l} \rho(r',\theta,\varphi) Y_{l,m}(\theta,\varphi) r'^{ 2} d{\mit\Omega} dr'.$">|; 

$key = q/displaystyle{bfD}=epsilon_0,{bfE}+{bfP};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1070.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0  {\bf E} + {\bf P}$">|; 

$key = q/displaystylenablatimes{bfB}=-{rmi},epsilon_0,mu_0,omegaleft(n_0^{,2}+{rmi},frac{sigma}{epsilon_0,omega}right){bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1682.png"
 ALT="$\displaystyle \nabla\times{\bf B} = -{\rm i} \epsilon_0 \mu_0 \omega\left( n_0^{ 2} + {\rm i}  \frac{\sigma}{\epsilon_0  \omega}\right) {\bf E}.$">|; 

$key = q/hgg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2463.png"
 ALT="$ h\gg 1$">|; 

$key = q/f(x)=x,exp(x),{rmE}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2418.png"
 ALT="$ f(x) = x  \exp(x) {\rm E}(x)$">|; 

$key = q/x^{,i'}(t');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3983.png"
 ALT="$ x^{ i'}(t')$">|; 

$key = q/+infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1792.png"
 ALT="$ +\infty$">|; 

$key = q/displaystyle{mitDelta}tsimeqfrac{{mitDelta}theta}{2,omega_0,gamma^{,2}}simfrac{1}{omega_0,gamma^{,3}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4155.png"
 ALT="$\displaystyle {\mit\Delta} t \simeq \frac{{\mit\Delta}\theta}{2 \omega_0  \gamma^{ 2}} \sim \frac{1}{\omega_0 \gamma^{ 3}},$">|; 

$key = q/displaystyle{bfE}_{lm}^{(M)}=g_l(k,r),{bfL},Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3096.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(M)} = g_l(k r) {\bf L}  Y_{lm}(\theta,\varphi).$">|; 

$key = q/displaystyle{bfF}_{12}=-{bfF}_{21},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1414.png"
 ALT="$\displaystyle {\bf F}_{12} = -{\bf F}_{21},
$">|; 

$key = q/displaystylef(t)=frac{1}{tau}int_C{rme}^{-{rmi},omega,t},frac{domega}{omega^{,2}-(2pislashtau)^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1839.png"
 ALT="$\displaystyle f(t) = \frac{1}{\tau} \int _C{\rm e}^{-{\rm i} \omega  t}  \frac{d\omega}{\omega^{ 2} - (2\pi/\tau)^{ 2}}.$">|; 

$key = q/x,t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3465.png"
 ALT="$ x t$">|; 

$key = q/f(t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$ f(t)$">|; 

$key = q/-lleqmleql;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="$ -l\leq m\leq l$">|; 

$key = q/omega_0=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1674.png"
 ALT="$ \omega_0=0$">|; 

$key = q/displaystyleoverline{N_z}=sqrt{frac{mu_0}{epsilon_0}}frac{1}{sqrt{1-omega_c^{,2}slashomega^{,2}}}frac{H_{s,0}^{,2}}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2896.png"
 ALT="$\displaystyle \overline{N_z} = \sqrt{\frac{\mu_0}{\epsilon_0}} \frac{1}{\sqrt{1-\omega_c^{ 2}/\omega^{ 2}}}\frac{H_{s 0}^{ 2}}{2}$">|; 

$key = q/displaystylefrac{partialG_N({bfr},{bfr}')}{partialn}=1leftslashint_SdSright..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="$\displaystyle \frac{\partial G_N({\bf r},{\bf r}')}{\partial n} = 1\left/\int_S dS\right..$">|; 

$key = q/displaystyle[E_x]_{z=0_-}^{z=0_+}=[D_xslash(epsilon,epsilon_0)]_{z=0_-}^{z=0_+}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2068.png"
 ALT="$\displaystyle [E_x]_{z=0_-}^{z=0_+}=[D_x/(\epsilon \epsilon_0)]_{z=0_-}^{z=0_+} = 0.$">|; 

$key = q/displaystyle=-frac{e}{m},E_+,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1729.png"
 ALT="$\displaystyle = -\frac{e}{m} E_+,$">|; 

$key = q/w(hat{z},h);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2550.png"
 ALT="$ w(\hat{z},h)$">|; 

$key = q/-(E_y,B_x^{,ast}+E_y^{,ast},B_x)slash(4,mu_0)=(epsilon_0slashmu_0)^{1slash2},|E_0|^{,2}slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2274.png"
 ALT="$ -(E_y  B_x^{ \ast} + E_y^{ \ast}  B_x)/(4 \mu_0)
= (\epsilon_0/\mu_0)^{1/2}  \vert E_0\vert^{ 2}/2$">|; 

$key = q/displaystyleP_{rmrad}=langleI^{,2},R_{rmrad}rangle=frac{R_{rmrad},V_0^{,2}}{2,(R_{rmrad}+R_{rmload})^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2661.png"
 ALT="$\displaystyle P_{\rm rad} = \langle I^{ 2}  R_{\rm rad}\rangle = \frac{R_{\rm rad}  V_0^{ 2}} {2 (R_{\rm rad} + R_{\rm load})^{ 2}}.$">|; 

$key = q/displaystyle{bfE}=E_0,cos(omega,t-k,z),{bfe}_x+E_0,sin(omega,t-k,z),{bfe}_y.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1710.png"
 ALT="$\displaystyle {\bf E} = E_0 \cos(\omega t-k z) {\bf e}_x+E_0 \sin(\omega t-k z) {\bf e}_y.$">|; 

$key = q/displaystyle=frac{1}{2}sum_{l=1,infty}{rmi}^{,l}sqrt{4pi,(2,l+1)}left[frac{-{rmi,{bfX}_{l,pm1}mp{rmi},beta_pm(l),h_l^{(1)}(k,r),{bfX}_{l,pm1}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="486" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3333.png"
 ALT="$\displaystyle =\frac{1}{2}\sum_{l=1,\infty} {\rm i}^{ l}\sqrt{4\pi (2 l+1)} ...
...l,\pm 1} \mp {\rm i}  \beta_\pm(l) h_l^{(1)}(k r) {\bf X}_{l,\pm 1}\right].$">|; 

$key = q/{bfB}_{rmrad}=({bfr}times{bfE}_{rmrad})slashr,c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4095.png"
 ALT="$ {\bf B}_{\rm rad} = ({\bf r}\times
{\bf E}_{\rm rad})/r c$">|; 

$key = q/omega<omega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1926.png"
 ALT="$ \omega&lt;\omega_0$">|; 

$key = q/displaystylev_z,u_z=c^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2347.png"
 ALT="$\displaystyle v_z u_z = c^{ 2}.$">|; 

$key = q/displaystyledelta(theta-theta');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img954.png"
 ALT="$\displaystyle \delta(\theta-\theta')$">|; 

$key = q/displaystylenabla^{,2}G({bfr},{bfr}')=delta({bfr}-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img994.png"
 ALT="$\displaystyle \nabla^{ 2} G({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}')$">|; 

$key = q/displaystyle=mu_0,{bfj},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle = \mu_0 {\bf j},$">|; 

$key = q/U>c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3519.png"
 ALT="$ U&gt;c$">|; 

$key = q/displaystylephi(r,theta)=-left(frac{3}{2+epsilon}right),E_0,r,costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1179.png"
 ALT="$\displaystyle \phi(r,\theta) = - \left(\frac{3}{2+\epsilon}\right) E_0 r \cos\theta$">|; 

$key = q/displaystyle=epsilon_2,E_z(z=0_-),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1098.png"
 ALT="$\displaystyle = \epsilon_2  E_z (z=0_-),$">|; 

$key = q/displaystyleF^{,mu'nu'}=F^{,munu},p_mu^{,mu'},p_{nu}^{,nu'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3850.png"
 ALT="$\displaystyle F^{ \mu'\nu'} = F^{ \mu\nu}  p_\mu^{ \mu'}  p_{\nu}^{ \nu'}.$">|; 

$key = q/1slashr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$ 1/r$">|; 

$key = q/{bfB}=mu,{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1548.png"
 ALT="$ {\bf B} = \mu  {\bf H}$">|; 

$key = q/displaystyle-A,frac{K_1(k_t,r)}{k_t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2957.png"
 ALT="$\displaystyle -A  \frac{K_1(k_t  r) }{k_t}$">|; 

$key = q/displaystylenabla'^{,2}G({bfr},{bfr}')=delta({bfr}-{bfr}').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="$\displaystyle \nabla'^{ 2}G({\bf r},{\bf r}') = \delta({\bf r}-{\bf r}').$">|; 

$key = q/displaystylenablacdot{bfB}=mu_0,nablacdot({bfH}+{bfM})=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1476.png"
 ALT="$\displaystyle \nabla\cdot{\bf B} = \mu_0  \nabla\cdot({\bf H} + {\bf M}) = 0.$">|; 

$key = q/displaystylef(x,t)simeqF(0)int_{infty}^{-infty}expleft[{rmi},omega,(t_1-t)+{rmi},frac{x}{6},k_0''',omega^{,3}right]domega.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1951.png"
 ALT="$\displaystyle f(x,t) \simeq F(0) \int_{\infty}^{-\infty} \exp\left[{\rm i} \omega (t_1-t) + {\rm i} \frac{x}{6}  k_0'''  \omega^{ 3}\right]d\omega.$">|; 

$key = q/(pm1,0,0,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3427.png"
 ALT="$ (\pm 1, 0, 0, 1)$">|; 

$key = q/n^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2224.png"
 ALT="$ n^{ 2}$">|; 

$key = q/displaystyleu({bfr},t)=int_{-infty}^{infty}u_omega({bfr}),{rme}^{-{rmi},omega,t},domega,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\displaystyle u({\bf r}, t) = \int_{-\infty}^{\infty} u_\omega({\bf r}) {\rm e}^{-{\rm i}  \omega  t} d\omega,$">|; 

$key = q/cslashn_+;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1739.png"
 ALT="$ c/n_+$">|; 

$key = q/displaystyleF_{i4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3793.png"
 ALT="$\displaystyle F_{i4}$">|; 

$key = q/nablatimes{bfE}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1104.png"
 ALT="$ \nabla\times{\bf E} = 0$">|; 

$key = q/r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$ r$">|; 

$key = q/A'=A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3555.png"
 ALT="$ A'= A$">|; 

$key = q/displaystyleI^{,2}=left(frac{B^{,2}}{mu_0}-epsilon_0,E^{,2}right)^2+frac{4,epsilon_0}{mu_0},({bfE}cdot{bfB})^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4212.png"
 ALT="$\displaystyle I^{ 2} = \left(\frac{B^{ 2}}{\mu_0}- \epsilon_0  E^{ 2}\right)^2
+ \frac{4 \epsilon_0}{\mu_0}  ({\bf E}\cdot{\bf B})^2.
$">|; 

$key = q/displaystyleB^{,mu}=intQ^{,4mu},d^{,3}x.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4057.png"
 ALT="$\displaystyle B^{ \mu} = \int Q^{ 4\mu} d^{ 3} x.$">|; 

$key = q/displaystylenabla^{,2}phi_m=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1500.png"
 ALT="$\displaystyle \nabla^{ 2}\phi_m = 0,$">|; 

$key = q/omega_0=sqrt{fslashm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1720.png"
 ALT="$ \omega_0=\sqrt{f/m}$">|; 

$key = q/displaystyleR_{rmrad}=sqrt{frac{mu_0}{epsilon_0}},frac{(k,d)^{,2}}{24pi}=197left(frac{d}{lambda}right)^{,2},,{rmohms}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2638.png"
 ALT="$\displaystyle R_{\rm rad} = \sqrt{\frac{\mu_0}{\epsilon_0}} \frac{(k d)^{ 2}}{24\pi} = 197\left(\frac{d}{\lambda}\right)^{ 2}  {\rm ohms}.$">|; 

$key = q/displaystyleE_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2204.png"
 ALT="$\displaystyle E_r$">|; 

$key = q/nu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2219.png"
 ALT="$ \nu$">|; 

$key = q/-k^{,2},Z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="$ -k^{ 2} Z$">|; 

$key = q/displaystyleq_{l,m}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="$\displaystyle q_{l,m}(r)$">|; 

$key = q/displaystyle|{bfr}-{bfr}'|=rleft[1-frac{{bfn}cdot{bfr}'}{r}+frac{{r'}^{,2}}{2,r^{,2}}-frac{1}{8}left(frac{2,{bfn}cdot{bfr}'}{r}right)^2+cdotsright],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2604.png"
 ALT="$\displaystyle \vert{\bf r} -{\bf r}'\vert = r\left[ 1-\frac{{\bf n}\cdot{\bf r}...
...}} -\frac{1}{8}\left(\frac{2 {\bf n}\cdot{\bf r}'}{r}\right)^2 +\cdots\right],$">|; 

$key = q/A_{i'j'cdotsk'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3545.png"
 ALT="$ A_{i'j'\cdots k'}$">|; 

$key = q/displaystyleF^{munu}=leftlgroup{array}{cccc}0&-c,B_z&+c,B_y&+E_x[0.5ex]+c,B_z&0&0.5ex]-c,B_y&+c,B_x&0&+E_z[0.5ex]-E_x&-E_y&-E_z&0{array}rightrgroup.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="105" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3805.png"
 ALT="$\displaystyle F^{\mu\nu} = \left\lgroup \begin{array}{cccc} 0 &amp; -c B_z &amp; +c B...
...B_y&amp; +c B_x&amp; 0&amp; +E_z\ [0.5ex] -E_x &amp; -E_y &amp;-E_z &amp; 0\end{array}\right \rgroup.$">|; 

$key = q/K_m(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img963.png"
 ALT="$ K_m(k r)$">|; 

$key = q/{bfp}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="$ {\bf p}_2$">|; 

$key = q/{mitDelta}omegaslashomega_ssim1slash!sqrt{k(omega_s),x};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1913.png"
 ALT="$ {\mit\Delta} \omega/\omega_s \sim 1/\!\sqrt{k(\omega_s)  x}$">|; 

$key = q/A_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2830.png"
 ALT="$ A_z$">|; 

$key = q/displaystyle=frac{{rmi},mu_0,c}{4pi}intfrac{{rme}^{,{rmi},k,|{bfr}-{bfr}'|}}{|{b}'|},{bfL}'cdotleft[{bfj}({bfr}')+nabla'times{bfM}({bfr}')right]dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3211.png"
 ALT="$\displaystyle =\frac{{\rm i} \mu_0  c}{4\pi} \int\frac{{\rm e}^{ {\rm i} k\...
...\bf L}'\cdot\left[{\bf j}({\bf r}') +\nabla'\times {\bf M}({\bf r}')\right]dV',$">|; 

$key = q/k_g=omegaslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2978.png"
 ALT="$ k_g = \omega/c$">|; 

$key = q/displaystyleleft(frac{epsilon}{c^{,2}}frac{partial^{,2}}{partialt^{,2}}-nabla^{,2}right){bfE}={bf0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1604.png"
 ALT="$\displaystyle \left(\frac{\epsilon}{c^{ 2}}\frac{\partial^{ 2}}{\partial t^{ 2}}-\nabla^{ 2}\right) {\bf E} = {\bf0},$">|; 

$key = q/rslasharightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1367.png"
 ALT="$ r/a\rightarrow\infty$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0},frac{{bfp}cdot({bfr}-{bfr}')}{|{bf1}{4pi,epsilon_0},{bfp}cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0} \frac{{\bf p}\cdot({\...
...silon_0} {\bf p}\cdot\nabla'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right).$">|; 

$key = q/displaystylewidetilde{G}_N({bfr},{bfr}')=G_N({bfr},{bfr}')+F({bfr}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="$\displaystyle \widetilde{G}_N({\bf r},{\bf r}')= G_N({\bf r},{\bf r}')+F({\bf r}),$">|; 

$key = q/displaystyleP=frac{1}{2,mu_0,c,k^{,2}}sum_{l,{rmodd}}|a_E(l,0)|^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3290.png"
 ALT="$\displaystyle P = \frac{1}{2 \mu_0  c k^{ 2}} \sum_{l {\rm odd}} \vert a_E(l,0)\vert^{ 2},$">|; 

$key = q/displaystyle=E_t,cos(omega,t+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2200.png"
 ALT="$\displaystyle = E_t \cos(\omega t+\phi_t),$">|; 

$key = q/t=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1770.png"
 ALT="$ t=0$">|; 

$key = q/B_4+B_5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1847.png"
 ALT="$ B_4+B_5$">|; 

$key = q/displaystyleA_varphi(r,theta)=mu_0,I,a,,{rmRe}!sum_{l=0,infty}sum_{m=-l,+l}frac{right)ointY_{l,m}(pislash2,varphi'),{rme}^{,{rmi},varphi'},dvarphi',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1336.png"
 ALT="$\displaystyle A_\varphi(r,\theta)= \mu_0 I a  {\rm Re}\!\sum_{l=0,\infty}\s...
...\right)\oint Y_{l,m}(\pi/2,\varphi') {\rm e}^{ {\rm i} \varphi'} d\varphi',$">|; 

$key = q/mslashM;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1671.png"
 ALT="$ m/M$">|; 

$key = q/(0,0,0,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3449.png"
 ALT="$ (0,0,0,0)$">|; 

$key = q/displaystylenabla'^{,2}G_N({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="$\displaystyle \nabla'^{ 2}G_N({\bf r},{\bf r}')$">|; 

$key = q/ullc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4027.png"
 ALT="$ u\ll c$">|; 

$key = q/displaystyle=-psi_i,costheta_i,cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2105.png"
 ALT="$\displaystyle =-\psi_i \cos\theta_i \cos(\omega t-n_1 k_0 \sin\theta_i x-n_1 k_0 \cos\theta_i z)$">|; 

$key = q/k,dll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2631.png"
 ALT="$ k d\ll 1$">|; 

$key = q/displaystylef(t)=left{{array}{ccl}0&mbox{hspace{2cm}}&mbox{fort<0},[0.5ex]sin!left(2pi,tslashtauright)&&mbox{fortgeq0}.{array}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1771.png"
 ALT="$\displaystyle f(t) =\left\{\begin{array}{ccl} 0 &amp;\mbox{\hspace{2cm}}&amp; \mbox{for...
...5ex] \sin\!\left(2\pi  t/\tau\right)&amp;&amp;\mbox{for $t\geq 0$}. \end{array}\right.$">|; 

$key = q/nablacdot{bfB}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1491.png"
 ALT="$ \nabla\cdot{\bf B} = 0$">|; 

$key = q/r=r';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img974.png"
 ALT="$ r=r'$">|; 

$key = q/{bfp}={bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="$ {\bf p}={\bf0}$">|; 

$key = q/displaystyle=q^{-1slash4}(hat{z}),expleft(,{rmi},hint_a^{hat{z}}q^{,1slash2}(hat{z}),dhat{z}'right)left[1+{calO}left(frac{1}{h}right)right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2473.png"
 ALT="$\displaystyle = q^{-1/4}(\hat{z})  \exp\left( {\rm i} h\int_a^{\hat{z}} q^{ 1/2}(\hat{z}) d\hat{z}'\right) \left[1+{\cal O}\left(\frac{1}{h}\right)\right],$">|; 

$key = q/displaystylephi(z)=pmk,n,z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2245.png"
 ALT="$\displaystyle \phi(z) = \pm k n z.$">|; 

$key = q/hat{bfk}={bfk}slashk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2731.png"
 ALT="$ \hat{\bf k}={\bf k}/k$">|; 

$key = q/displaystyle=frac{d{bfu}}{dt'}=-dot{u},(cosphi,,sinphi,,0),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4117.png"
 ALT="$\displaystyle = \frac{d{\bf u}}{dt'} = -\dot{u} (\cos\phi,  \sin\phi,  0),$">|; 

$key = q/k=k_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2879.png"
 ALT="$ k=k_s$">|; 

$key = q/omega_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1970.png"
 ALT="$ \omega_s$">|; 

$key = q/displaystylefrac{1}{r}frac{partial}{partialr}!left(r,frac{partialf}{partialr}rig+frac{1}{r^{,2}}frac{partial^{,2}f}{partialvarphi^{,2}}+k_s^{,2}f=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2855.png"
 ALT="$\displaystyle \frac{1}{r} \frac{\partial}{\partial r}\!\left(r \frac{\partial ...
...{1}{r^{ 2}} \frac{\partial^{ 2} f}{\partial \varphi^{ 2}} + k_s^{ 2} f = 0,$">|; 

$key = q/1slashomega^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1837.png"
 ALT="$ 1/\omega^{ 2}$">|; 

$key = q/displaystyle-partial_i,(c,B^{,i})=partial_iG^{,i4}+partial_4G^{,44}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3842.png"
 ALT="$\displaystyle -\partial_i (c B^{ i}) = \partial_i G^{ i4} +\partial_4 G^{ 44} = 0,$">|; 

$key = q/n_-;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1740.png"
 ALT="$ n_-$">|; 

$key = q/displaystyleomega_{0pm}=-{rmi},rhopmsqrt{omega_0^{~2}-rho^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1817.png"
 ALT="$\displaystyle \omega_{0\pm} = -{\rm i} \rho \pm\sqrt{\omega_0^{&nbsp;2}-\rho^{ 2}},$">|; 

$key = q/displaystylefrac{1}{c^{,2}},frac{partial^{,2}{bfA}}{partialt^{,2}}-nabla^{,2}{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle \frac{1}{c^{ 2}} \frac{\partial^{ 2}{\bf A}}{\partial t^{ 2}} - \nabla^{ 2}{\bf A}$">|; 

$key = q/displaystyle~~~~-frac{psi_r,sintheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2062.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;-\frac{\psi_r \sin\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z)$">|; 

$key = q/displaystyle=frac{J_m^{,nu}}{epsilon_0,c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4209.png"
 ALT="$\displaystyle = \frac{J_m^{ \nu}}{\epsilon_0 c}.$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{Chapter06bslashfig11.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="399" BORDER="0"
 SRC="|."$dir".q|img2186.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{Chapter06b/fig11.eps}}
\end{figure}">|; 

$key = q/displaystylerho=frac{g,omega_0}{2}llomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1820.png"
 ALT="$\displaystyle \rho = \frac{g \omega_0}{2}\ll \omega_0$">|; 

$key = q/displaystyleA^{,mu}=frac{dU^{,mu}}{dtau}=gamma,frac{dU^{,mu}}{dt}=gammafrac{d}{dmaleft(frac{dgamma}{dt},{bfu}+gamma,{bfa},,c,frac{dgamma}{dt}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3704.png"
 ALT="$\displaystyle A^{ \mu} = \frac{dU^{ \mu}}{d\tau} = \gamma \frac{dU^{ \mu}}{...
...\frac{d\gamma}{dt}  {\bf u} + \gamma {\bf a},  c \frac{d\gamma}{dt}\right),$">|; 

$key = q/E_1>E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1190.png"
 ALT="$ E_1 &gt; E_0$">|; 

$key = q/displaystyleV_0=E_0,dslash2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2667.png"
 ALT="$\displaystyle V_0 = E_0  d/2.$">|; 

$key = q/displaystylephi(r,theta,varphi)=sum_{l=0,infty}sum_{m=-l,+l}left[alpha_{l,m},r^{,l}+beta_{l,m},r^{-(l+1)}right]Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="$\displaystyle \phi(r,\theta,\varphi)= \sum_{l=0,\infty}\sum_{m=-l,+l}\left[\alpha_{l,m} r^{ l}+\beta_{l,m} r^{-(l+1)}\right]Y_{l,m}(\theta,\varphi).$">|; 

$key = q/k_{i,x}=k_{t,x};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2043.png"
 ALT="$ k_{i x}=k_{t x}$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0}{4pi}intfrac{{bfj}_m({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1495.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = \frac{\mu_0}{4\pi}\int \frac{{\bf j}_m({\bf r}')} {\vert{\bf r}- {\bf r}'\vert} dV'.$">|; 

$key = q/dt=dzslashu_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2340.png"
 ALT="$ dt = dz/u_z$">|; 

$key = q/displaystyle{bfL}cdot{bfE}_{lm}^{(M)}(r,theta,varphi)=l,(l+1),g_l(k,r),Y_{lm}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3091.png"
 ALT="$\displaystyle {\bf L}\cdot{\bf E}_{lm}^{(M)} (r,\theta,\varphi) =l (l+1)  g_l(k r)  Y_{lm}(\theta,\varphi),$">|; 

$key = q/n_-^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1764.png"
 ALT="$ n_-^{ 2}$">|; 

$key = q/displaystyle{bfk}_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2033.png"
 ALT="$\displaystyle {\bf k}_i$">|; 

$key = q/r<dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3251.png"
 ALT="$ r&lt;d/2$">|; 

$key = q/displaystyle{bfB}_0=frac{{bfk}times{bfE}_0}{omega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1609.png"
 ALT="$\displaystyle {\bf B}_0 = \frac{{\bf k}\times{\bf E}_0}{\omega}.$">|; 

$key = q/displaystylenablatimes{bfH}={bfj}_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1467.png"
 ALT="$\displaystyle \nabla\times{\bf H} = {\bf j}_t.$">|; 

$key = q/A_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1330.png"
 ALT="$ A_y$">|; 

$key = q/q(hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2459.png"
 ALT="$ q(\hat{z})$">|; 

$key = q/displaystyle{bfm}=frac{4}{3},pi,a^{,3},{bfM}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1517.png"
 ALT="$\displaystyle {\bf m} = \frac{4}{3} \pi  a^{ 3}  {\bf M}.$">|; 

$key = q/displaystyle{bfE}=left{{array}{lll}{bf0}&mbox{hspace{0.5cm}}&r<a[0.5ex](sigmaslashepsilon_0),(aslashr)^2,{bfe}_r&&r>a{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="$\displaystyle {\bf E} = \left\{ \begin{array}{lll} {\bf0}&amp;\mbox{\hspace{0.5cm}}&amp; r&lt;a\ [0.5ex] (\sigma/\epsilon_0) (a/r)^2 {\bf e}_r &amp;&amp;r&gt;a \end{array}\right.,$">|; 

$key = q/displaystylefrac{dsigma_{rmsc}}{d{mitOmega}}simeqfrac{2pi}{3},a^{,2}(k,a)^4left|{bfX}_{1,pm1}mp2,{rmi},{bfn}times{bfX}_{1,pm1}right|^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3384.png"
 ALT="$\displaystyle \frac{d\sigma_{\rm sc}}{d{\mit \Omega}} \simeq \frac{2\pi}{3}  a...
...f X}_{1,\pm 1} \mp 2 {\rm i} {\bf n}\times{\bf X}_{1,\pm 1}\right\vert^{ 2}.$">|; 

$key = q/F({bfr})=G_3({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="$ F({\bf r})=G_3({\bf r},{\bf r}')=0$">|; 

$key = q/E_z(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2987.png"
 ALT="$ E_z(r)$">|; 

$key = q/displaystyleepsilon^{,alphabetagammadelta},p_{alpha}^{,alpha'},p_{beta}^{,beta'}beta'gamma'delta'},|p_mu^{,mu'}|=epsilon^{,alpha'beta'gamma'delta'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3758.png"
 ALT="$\displaystyle \epsilon^{ \alpha\beta\gamma\delta}  p_{\alpha}^{ \alpha'} p_...
...elta'}  \vert p_\mu^{ \mu'}\vert = \epsilon^{ \alpha' \beta'\gamma'\delta'},$">|; 

$key = q/displaystyle=frac{dx}{dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3485.png"
 ALT="$\displaystyle = \frac{dx}{dt},$">|; 

$key = q/displaystyleD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystylep_A-p_B=frac{epsilon_0,(epsilon-1)}{2}left[E_parallel^{,2}+frac{E_perp^{,2}}{epsilon}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1273.png"
 ALT="$\displaystyle p_A - p_B = \frac{\epsilon_0 (\epsilon-1)}{2} \left[E_\parallel^{ 2} +\frac{E_\perp^{ 2}}{\epsilon}\right].$">|; 

$key = q/Fslashn^{,1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2336.png"
 ALT="$ F/n^{ 1/2}$">|; 

$key = q/displaystylephi(r,theta,L);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="$\displaystyle \phi(r,\theta,L)$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{|a_E(l,0)|^{,2}}{4,mu_0,c,k^{,2}},left|{bfL}Y_{1,0}-frac{a_E(3,0)}{sqrt{6},a_E(1,0)},{bfL}Y_{3,0}right|^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3277.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} = \frac{\vert a_E(l,0)\vert^{ 2}}{4 \...
..._{1,0} - \frac{a_E(3,0)}{\sqrt{6} a_E(1,0)} {\bf L} Y_{3,0}\right\vert^{ 2},$">|; 

$key = q/displaystyle=delta({bfr}-{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="$\displaystyle =\delta({\bf r}-{\bf r}'),$">|; 

$key = q/d{bfS};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$ d{\bf S}$">|; 

$key = q/displaystyleleft[nabla_s^{,2}+left(epsilon_1,frac{omega^{,2}}{c^{,2}}-k_g^{,2}right)right]psi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2906.png"
 ALT="$\displaystyle \left[ \nabla_s^{ 2} +\left(\epsilon_1  \frac{\omega^{ 2}}{c^{ 2}} - k_g^{ 2}\right) \right]\psi = 0.$">|; 

$key = q/muggmu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1542.png"
 ALT="$ \mu\gg \mu_0$">|; 

$key = q/omegarightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1672.png"
 ALT="$ \omega\rightarrow 0$">|; 

$key = q/displaystylephi_{l,m}(r)=alpha_{l,m},r^{,l}+beta_{l,m},r^{-(l+1)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="$\displaystyle \phi_{l,m}(r)=\alpha_{l,m} r^{ l} + \beta_{l,m} r^{-(l+1)},$">|; 

$key = q/displaystyle=-frac{mu_0,I}{2,a}sum_{l=1,3,5,cdots}P_l^1(0)left(frac{a}{r}right)^{l+2}P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1365.png"
 ALT="$\displaystyle = -\frac{\mu_0 I}{2 a}\sum_{l=1,3,5,\cdots}P_l^1(0)\left(\frac{a}{r}\right)^{l+2}P_l(\cos\theta),$">|; 

$key = q/displaystylesigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="$\displaystyle \sigma$">|; 

$key = q/|z|geqa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img636.png"
 ALT="$ \vert z\vert\geq a$">|; 

$key = q/displaystyleG({bfr},{bfr}')rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$\displaystyle G({\bf r}, {\bf r}') \rightarrow 0$">|; 

$key = q/displaystyleleft(z^{,2},frac{d^{,2}}{dz^{,2}}+z,frac{d}{dz}-z^{,2}right)psi=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2916.png"
 ALT="$\displaystyle \left(z^{ 2} \frac{d^{ 2}}{d z^{ 2}} + z \frac{d}{dz} - z^{ 2}\right) \psi = 0,$">|; 

$key = q/displaystyle{bfA}({bfr})=-frac{mu_0}{8pi},frac{{bfr}}{|{bfr}|^{,3}}timesint({bfr}'times{bfj}),dV'+cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1402.png"
 ALT="$\displaystyle {\bf A}({\bf r})=-\frac{\mu_0}{8\pi} \frac{{\bf r}}{\vert{\bf r}\vert^{ 3}}\times \int ({\bf r}'\times {\bf j}) dV'+\cdots.$">|; 

$key = q/displaystyle=int_0^inftyk,r,J_m(k,r),S_m(r),dr,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img927.png"
 ALT="$\displaystyle = \int_0^\infty k r J_m(k r) S_m(r) dr,$">|; 

$key = q/displaystyleU=frac{1}{2}int_V{bfE}cdot{bfD},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1203.png"
 ALT="$\displaystyle U = \frac{1}{2} \int_V {\bf E}\cdot{\bf D} dV.$">|; 

$key = q/displaystyleL_+;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3050.png"
 ALT="$\displaystyle L_+$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{e^{,2},c,beta^{,4}}{128pi^2,epsilon_0,a^{2},cos^2theta}{(1-beta^{,2},cos^2theta)^{,7slash2}}right]sin^2theta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4216.png"
 ALT="$\displaystyle \frac{dP}{d{\mit\Omega}} = \frac{e^{ 2}  c  \beta^{ 4}}{128\p...
...,2} \cos^2\theta}{(1-\beta^{ 2} \cos^2\theta)^{ 7/2}}\right] \sin^2\theta.
$">|; 

$key = q/displaystylesimeq-sqrt{2},alpha,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2207.png"
 ALT="$\displaystyle \simeq - \sqrt{2} \alpha,$">|; 

$key = q/displaystylef_{lm}(r)=frac{A_{lm}}{r^{,1slash2}},J_{l+1slash2}(k,r)+frac{B_{lm}}{r^{,1slash2}},Y_{l+1slash2}(k,r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3012.png"
 ALT="$\displaystyle f_{lm}(r) = \frac{A_{lm}}{r^{ 1/2}} J_{l+1/2}(k r) + \frac{B_{lm}}{r^{ 1/2}}  Y_{l+1/2}(k r),$">|; 

$key = q/displaystyle{bfJ}_m={bfn}_{21}times({bfM}_2-{bfM}_1),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1470.png"
 ALT="$\displaystyle {\bf J}_m = {\bf n}_{21}\times({\bf M}_2 - {\bf M}_1),$">|; 

$key = q/displaystyleA_varphi(r,theta)=frac{mu_0,I,a}{4pi}ointfrac{cosvarphi',dvarphi'}{|phi',dvarphi'}{(r^{,2}+a^{,2}-2,a,r,sintheta,cosvarphi')^{1slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1334.png"
 ALT="$\displaystyle A_\varphi(r,\theta) =\frac{\mu_0 I a}{4\pi}\oint \frac{\cos\var...
...arphi' d\varphi'}{(r^{ 2}+a^{ 2} -2 a r \sin\theta \cos\varphi')^{1/2}}.$">|; 

$key = q/displaystylefrac{d}{dr}!left(r^{,2},frac{dphi_{l,m}}{dr}right)-l,(l+1),phi_{l,m}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="$\displaystyle \frac{d}{dr}\!\left(r^{ 2} \frac{d\phi_{l,m}}{dr}\right)-l (l+1) \phi_{l,m}=0,$">|; 

$key = q/displaystyleddot{bfs}=frac{omega^{,2}}{omega_0^{,2}-omega^{,2}-{rmi},gamma_0,omega},frac{e}{m_e},{bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2744.png"
 ALT="$\displaystyle \ddot{\bf s} = \frac{ \omega^{ 2}}{\omega_0^{ 2} -\omega^{ 2} -{\rm i}  \gamma_0 \omega} \frac{e}{m_e}  {\bf E}.$">|; 

$key = q/t<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1775.png"
 ALT="$ t&lt;0$">|; 

$key = q/xi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1884.png"
 ALT="$ \xi$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=sum_{m=0,infty}left[C_m(r),cos(m,theta)+S_m(r),sin(m,theta)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img920.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = \sum_{m=0,\infty}\left[C_m(r) \cos(m \theta)+ S_m(r) \sin(m \theta)\right]$">|; 

$key = q/displaystylephi(r,theta)=frac{q}{4pi,epsilon_0}sum_{l=0,infty}frac{r_<^{,l}}{r_>^{,l+1}},P_l(0),P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="$\displaystyle \phi(r,\theta) = \frac{q}{4\pi \epsilon_0}\sum_{l=0,\infty} \frac{r_&lt;^{ l}}{r_&gt;^{ l+1}} P_l(0) P_l(\cos\theta),$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0}{4pi}intfrac{{bfj}({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1310.png"
 ALT="$\displaystyle {\bf A}({\bf r}) = \frac{\mu_0}{4\pi}\int\frac{{\bf j}({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle{bfn}times({bfH}_1-{bfH}_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2759.png"
 ALT="$\displaystyle {\bf n}\times ({\bf H}_1-{\bf H}_2)$">|; 

$key = q/displaystyle=-left[frac{3,(mu-mu_0),mu_0}{(2,mu+mu_0),(mu+2,mu_0)-2,(a^{,3}slashb^{,3}),(mu-mu_0)^{,2}}right]a^{,3}B_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1570.png"
 ALT="$\displaystyle = - \left[ \frac{3 (\mu-\mu_0) \mu_0} {(2 \mu+\mu_0) (\mu+2 \mu_0) - 2 (a^{ 3}/b^{ 3}) (\mu-\mu_0)^{ 2}}\right] a^{ 3} B_0,$">|; 

$key = q/displaystyle{bfj}_p=frac{partial{bfP}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1436.png"
 ALT="$\displaystyle {\bf j}_p = \frac{\partial{\bf P}}{\partial t}.$">|; 

$key = q/displaystylenablacdot{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3196.png"
 ALT="$\displaystyle \nabla\cdot{\bf E}'$">|; 

$key = q/displaystylea_M(l,m)simeqfrac{mu_0,c,,{rmi},k^{,l+2}}{(2,l+1)!!},left(frac{l+1}{l}right)^{1slash2}({calM}_{lm}+{calM}_{lm}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3239.png"
 ALT="$\displaystyle a_M(l,m) \simeq \frac{\mu_0  c   {\rm i}  k^{ l+2}}{ (2 l+1)!!} \left(\frac{l+1}{l}\right)^{1/2} ({\cal M}_{lm}+{\cal M}_{lm}'),$">|; 

$key = q/displaystyle=B_parallel,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3854.png"
 ALT="$\displaystyle = B_\parallel,$">|; 

$key = q/t>t_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1956.png"
 ALT="$ t&gt;t_1$">|; 

$key = q/z>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1093.png"
 ALT="$ z&gt;0$">|; 

$key = q/{bfj}({bfr})=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2623.png"
 ALT="$ {\bf j}({\bf r}) =0$">|; 

$key = q/a=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2486.png"
 ALT="$ a=0$">|; 

$key = q/displaystyle=-frac{1}{4pi,epsilon_0}intleft(frac{[rho]}{R^{,3}},{bfR}+frac{[partialrhoslashpartialt]}{c,R^{,2}},{bfR}right),dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\displaystyle = - \frac{1}{4\pi \epsilon_0} \int \left( \frac{[\rho]}{R^{ 3}} {\bf R} + \frac{[\partial\rho/\partial t]}{c R^{ 2}} {\bf R} \right)  dV',$">|; 

$key = q/displaystylephi_m(r,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img985.png"
 ALT="$\displaystyle \phi_m(r,z)$">|; 

$key = q/displaystyleR(theta)=R_0left[1+beta,P_2(costheta)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3389.png"
 ALT="$\displaystyle R(\theta)=R_0\left[1+\beta P_2(\cos\theta)\right]
$">|; 

$key = q/[J^{,mu}],dVslashr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3756.png"
 ALT="$ [J^{ \mu}] dV/r$">|; 

$key = q/dz'=dz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3499.png"
 ALT="$ dz'=dz$">|; 

$key = q/sigma_{rmabs};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3358.png"
 ALT="$ \sigma_{\rm abs}$">|; 

$key = q/displaystyleW=frac{Q^{,2}}{8pi,epsilon_0}left(frac{1}{a^{,6}}int_0^ar^{,4},dr+int_a^inftyfrac{dr}{r^{,2}}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="$\displaystyle W = \frac{Q^{ 2}}{8\pi \epsilon_0} \left( \frac{1}{a^{ 6}} \int_0^a r^{ 4} dr + \int_a^\infty \frac{dr}{r^{ 2}} \right),$">|; 

$key = q/displaystyleh(omega)=int_0^{z_0(omega)}!left(1-frac{omega_p^{,2}(z)}{omega^2}right)^{-1slash2}dz.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2355.png"
 ALT="$\displaystyle h(\omega) = \int_0^{z_0(\omega)} \!\left(1-\frac{\omega_p^{ 2}(z)} {\omega^2}\right)^{-1/2} dz.$">|; 

$key = q/displaystylephi(r,theta,z)=sum_{m=0,infty}sum_{n=1,infty}sin(k_n,z),I_m(k_n,z)left[A_{mn},cos(m,theta)+B_{mn},sin(m,theta)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img943.png"
 ALT="$\displaystyle \phi(r,\theta,z) =\sum_{m=0,\infty} \sum_{n=1,\infty}\sin(k_n z) I_m(k_n z)\left[A_{mn} \cos(m \theta)+B_{mn} \sin(m \theta)\right].$">|; 

$key = q/|f_n(x)-f(x)|slashf(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2420.png"
 ALT="$ \vert f_n(x) - f(x)\vert/f(x)$">|; 

$key = q/displaystyleC;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3469.png"
 ALT="$\displaystyle C$">|; 

$key = q/displaystyle=left[K_m(k_n,r)-frac{I_m(k_n,r),K_m(k_n,a)}{I_m(k_n,a)}right]int_0^rR_{m,n}(r'),I_m(k_n,r'),r',dr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1019.png"
 ALT="$\displaystyle = \left[K_m(k_n r)-\frac{I_m(k_n r) K_m(k_n a)}{I_m(k_n a)}\right]\int_0^r R_{m,n}(r') I_m(k_n r') r' dr'$">|; 

$key = q/displaystyledtau^{,2}=-frac{dx^{,2}+dy^{,2}+dz^{,2}}{c^{,2}}+dt^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3690.png"
 ALT="$\displaystyle d\tau^{ 2} = - \frac{dx^{ 2}+dy^{ 2}+dz^{ 2}}{c^{ 2}} + dt^{ 2}.$">|; 

$key = q/displaystylephi({bfr})=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="$\displaystyle \phi({\bf r}) = 0$">|; 

$key = q/d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="$ d$">|; 

$key = q/displaystyle=frac{2,beta}{(1+hat{alpha}^{,2},beta^{,2})^{1slash2}},psi_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2177.png"
 ALT="$\displaystyle =\frac{2 \beta}{(1+\hat{\alpha}^{ 2} \beta^{ 2})^{1/2}} \psi_i.$">|; 

$key = q/displaystyleE_y(z)simeqA,n^{-1slash2}(z),expleft(pm{rmi},kint^z!n(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2256.png"
 ALT="$\displaystyle E_y(z) \simeq A n^{-1/2}(z) \exp\left(\pm {\rm i}  k \int^z \!n(z') dz'\right).$">|; 

$key = q/displaystyleJ_m(p)=frac{1}{pi}int_0^picos(p,sintheta-m,theta),dtheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="$\displaystyle J_m(p) = \frac{1}{\pi}\int_0^\pi \cos(p \sin\theta-m \theta) d\theta.$">|; 

$key = q/displaystyledelta(t'-t)=delta(t-t').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle \delta(t'-t) = \delta(t-t').$">|; 

$key = q/{bfJ}_m={bfM}times{bfn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1498.png"
 ALT="$ {\bf J}_m = {\bf M} \times {\bf n}$">|; 

$key = q/{bfr}={bfr}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$ {\bf r}={\bf r}'$">|; 

$key = q/displaystyle=-{rmi},mu_0,c,{bfL}cdot({bfj}+nablatimes{bfM}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3207.png"
 ALT="$\displaystyle = -{\rm i} \mu_0  c {\bf L}\cdot({\bf j} + \nabla\times{\bf M}),$">|; 

$key = q/theta_i=theta_B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2128.png"
 ALT="$ \theta_i=\theta_B$">|; 

$key = q/displaystylefrac{partial{bfg}}{partialt}+nablacdot{bfG}=-rho,{bfE}-{bfj}times{bfB},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3975.png"
 ALT="$\displaystyle \frac{\partial{\bf g}}{\partial t}+\nabla\cdot {\bf G}= -\rho  {\bf E} - {\bf j}\times{\bf B},$">|; 

$key = q/R=U=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1982.png"
 ALT="$ R=U=0$">|; 

$key = q/displaystylef_{lm}(r)=A_{lm},h_l^{(1)}(k,r)+B_{lm},h_l^{(2)}(k,r).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3041.png"
 ALT="$\displaystyle f_{lm}(r) = A_{lm} h_l^{(1)}(k r) + B_{lm} h_l^{(2)}(k r).$">|; 

$key = q/y=y';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3458.png"
 ALT="$ y=y'$">|; 

$key = q/(0,x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2539.png"
 ALT="$ (0,x)$">|; 

$key = q/epsilon=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1267.png"
 ALT="$ \epsilon=1$">|; 

$key = q/displaystylephi({bfr})simeqphi_0({bfr})+phi_1({bfr})+phi_2({bfr})=frac{Q}{4pi,epn_0,r^{,3}}+sum_{i,j=1,3}frac{Q_{ij},x_i,x_j}{8pi,epsilon_0,r^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="$\displaystyle \phi({\bf r})\simeq \phi_0({\bf r})+\phi_1({\bf r})+\phi_2({\bf r...
..._0 r^{ 3}}+ \sum_{i,j=1,3}\frac{Q_{ij} x_i x_j}{8\pi \epsilon_0 r^{ 5}}.$">|; 

$key = q/displaystyle(omega_0^{,2}-omega^{,2}),s_y+{rmi},omega,{mitOmega},s_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1718.png"
 ALT="$\displaystyle (\omega_0^{ 2} -\omega^{ 2}) s_y +{\rm i}  \omega {\mit\Omega}  s_x$">|; 

$key = q/P_{rmin};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2680.png"
 ALT="$ P_{\rm in}$">|; 

$key = q/displaystyle=frac{1}{2}sum_{l=1,infty}{rmi}^{,l}sqrt{4pi,(2,l+1)}left[alpha_pm(l}pmfrac{beta_pm(l)}{k},nablatimesh_l^{(1)}(k,r),{bfX}_{l,pm1}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="461" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3331.png"
 ALT="$\displaystyle = \frac{1}{2}\sum_{l=1,\infty} {\rm i}^{ l}\sqrt{4\pi (2 l+1)}...
...rac{\beta_\pm(l)}{k} \nabla\times h_l^{(1)}(k r)  {\bf X}_{l,\pm 1} \right],$">|; 

$key = q/displaystyle=frac{{rmi},k_g}{k_s^{,2}},nabla_sE_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2889.png"
 ALT="$\displaystyle = \frac{{\rm i}  k_g}{k_s^{ 2}} \nabla_s E_z,$">|; 

$key = q/omega_p^{,2}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2358.png"
 ALT="$ \omega_p^{ 2}(z)$">|; 

$key = q/displaystylev_g=frac{domega}{dk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1916.png"
 ALT="$\displaystyle v_g = \frac{d \omega}{d k}$">|; 

$key = q/displaystylea_pm(l,m),j_l(k,r)=ointfrac{(L_mp,Y_{lm})^{,ast}}{sqrt{l,(l+1)}},{rme}^{,{rmi},k,z},d{mitOmega},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3318.png"
 ALT="$\displaystyle a_\pm(l,m) j_l(k r) = \oint \frac{(L_\mp Y_{lm})^{ \ast}}{\sqrt{l (l+1)}}  {\rm e}^{ {\rm i} k z} d{\mit \Omega},$">|; 

$key = q/displaystylef=frac{d(m,u)}{dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3915.png"
 ALT="$\displaystyle f = \frac{d(m u)}{dt},$">|; 

$key = q/aleqrleqb;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1029.png"
 ALT="$ a\leq r\leq b$">|; 

$key = q/displaystylepartial_muJ^{,mu}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3722.png"
 ALT="$\displaystyle \partial_\mu J^{ \mu} =0.$">|; 

$key = q/exp(-{rmi},omega,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1681.png"
 ALT="$ \exp(-{\rm i} \omega  t)$">|; 

$key = q/displaystylem,ddot{bfs}+f,{bfs}=-e,{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1617.png"
 ALT="$\displaystyle m \ddot{\bf s} + f {\bf s} = - e  {\bf E},$">|; 

$key = q/p=k,r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="$ p=k r$">|; 

$key = q/-{bfE}cdot{bfj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$ -{\bf E}\cdot{\bf j}$">|; 

$key = q/displaystylealpha_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1031.png"
 ALT="$\displaystyle \alpha_l$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$ i$">|; 

$key = q/c,tslashx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1931.png"
 ALT="$ c t/x$">|; 

$key = q/nullomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2223.png"
 ALT="$ \nu\ll \omega$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0,I}{4pi}frac{{rme}^{,{rmi},k,r}}{r}int_{-dslasdslash2}sin(k,dslash2-k,|z|),{rme}^{-{rmi},k,z,costheta},dz,{bfe}_z,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2625.png"
 ALT="$\displaystyle {\bf A}({\bf r}) =\frac{\mu_0  I}{4\pi} \frac{{\rm e}^{ {\rm i}...
...k d/2-k \vert z\vert) {\rm e}^{-{\rm i} k  z  \cos\theta} dz {\bf e}_z,$">|; 

$key = q/displaystyleboxemptypsi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3738.png"
 ALT="$\displaystyle \boxempty \psi = 0.$">|; 

$key = q/displaystylenablatimes{bfB}=mu_0,{bfj},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1319.png"
 ALT="$\displaystyle \nabla\times {\bf B} = \mu_0 {\bf j},$">|; 

$key = q/Pslash(I^{,2}slash2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2649.png"
 ALT="$ P/(I^{ 2}/2)$">|; 

$key = q/displaystyleint_0^inftycos!left[frac{3}{2},zleft(frac{v^{,3}}{3}-vright)right],dv=frac{pi}{3}left[J_{1slash3}(z)+J_{-1slash3}(z)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1959.png"
 ALT="$\displaystyle \int_0^\infty \cos\!\left[ \frac{3}{2}  z\left(\frac{v^{ 3}}{3} - v\right) \right] dv= \frac{\pi}{3} \left[ J_{1/3}(z) + J_{-1/3}(z)\right].$">|; 

$key = q/displaystyleG_omega(R)=frac{A,{rme}^{+{rmi},k,R}+B,{rme}^{-{rmi},k,R}}{4pi,R}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle G_\omega (R) = \frac{A  {\rm e}^{+{\rm i}  k R} + B  {\rm e}^{-{\rm i}  k R}}{4\pi  R}.$">|; 

$key = q/displaystyleZ_g=sqrt{frac{mu_0}{epsilon_0}}frac{1}{sqrt{1-omega_c^{,2}slashomega^{,2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2903.png"
 ALT="$\displaystyle Z_g = \sqrt{\frac{\mu_0}{\epsilon_0}} \frac{1}{\sqrt{1-\omega_c^{ 2}/\omega^{ 2}}}$">|; 

$key = q/(0,hat{z})_dleftrightarrow(0,hat{z})_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2490.png"
 ALT="$ (0,\hat{z})_d \leftrightarrow (0,\hat{z})_s$">|; 

$key = q/dt>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3415.png"
 ALT="$ dt&gt;0$">|; 

$key = q/displaystyle=(1slash8),(1-x^{,2}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="$\displaystyle =(1/8) (1-x^{ 2}),$">|; 

$key = q/displaystylef(p)=sum_{n=1,infty}a_{mn},J_m(j_{mn},p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="$\displaystyle f(p) = \sum_{n=1,\infty} a_{mn} J_m(j_{mn} p)$">|; 

$key = q/displaystyleW=frac{1}{4pi,epsilon_0}sum_{i=1,N}sum_{j=1,i-1}frac{q_i,q_j}{|{bfr}_i-{bfr}_j|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="$\displaystyle W = \frac{1}{4\pi \epsilon_0} \sum_{i=1,N} \sum_{j=1,i-1}\frac{q_i  q_j}{\vert{\bf r}_i -{\bf r}_j\vert}.$">|; 

$key = q/displaystyle{bfL}cdot{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3223.png"
 ALT="$\displaystyle {\bf L}\cdot{\bf A}$">|; 

$key = q/(x^{,i},,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3981.png"
 ALT="$ (x^{ i},  t)$">|; 

$key = q/displaystyleint_0^{hat{z}}q^{,1slash2}(hat{z}),dhat{z}'simeqfrac{2sqrt{a_1}}{3},hat{z}^{,3slash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2494.png"
 ALT="$\displaystyle \int_0^{\hat{z}} q^{ 1/2}(\hat{z})  d\hat{z}' \simeq \frac{2\sqrt{a_1}}{3}  \hat{z}^{ 3/2}.$">|; 

$key = q/z';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3396.png"
 ALT="$ z'$">|; 

$key = q/displaystylen_+-n_-simeqfrac{N,e^{,2}}{epsilon_0,m,n}frac{omega,{mitOmega}}{(omega_0^{,2}-omega^{,2})^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1755.png"
 ALT="$\displaystyle n_+-n_- \simeq \frac{N e^{ 2}}{\epsilon_0  m  n} \frac{\omega  {\mit \Omega}}{(\omega_0^{ 2} -\omega^{ 2})^{ 2}}.$">|; 

$key = q/f_n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$ f_n$">|; 

$key = q/displaystylephi({bfr})=frac{1}{epsilon_0}sum_{l=0,infty}sum_{m=-l,+l}frac{1}{2,lst}(r)+frac{q_{l,m}^{,ast}(r)}{r^{,l+1}}right]Y_{l,m}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{\epsilon_0}\sum_{l=0,\infty}\sum_{m=-l,+...
...,\ast}(r)+ \frac{q_{l,m}^{ \ast}(r)}{r^{ l+1}}\right]Y_{l,m}(\theta,\varphi),$">|; 

$key = q/phi';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="$ \phi'$">|; 

$key = q/displaystyle=left(frac{3}{4pi}right)^{1slash2}costheta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="$\displaystyle = \left(\frac{3}{4\pi}\right)^{1/2}\cos\theta,$">|; 

$key = q/displaystylea_E(l,m)=-frac{mu_0,c,,k^{,3}}{sqrt{l,(l+1)}}intj_l(k,r),Y_{lm}^{,as^{,2}}-{rmi},frac{c}{k,r}frac{partial(r^{,2}rho)}{partialr}right]dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="505" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3227.png"
 ALT="$\displaystyle a_E(l,m) = - \frac{\mu_0  c  k^{ 3}}{\sqrt{l (l+1)}} \int j_...
...}} -{\rm i} \frac{c}{k r} \frac{\partial(r^{ 2} \rho)}{\partial r}\right]dV,$">|; 

$key = q/displaystylesigma_b(theta)=3,epsilon_0left(frac{epsilon-1}{epsilon+2}right),E_0,costheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1187.png"
 ALT="$\displaystyle \sigma_b(\theta) = 3 \epsilon_0 \left(\frac{\epsilon-1}{\epsilon+2}\right) E_0 \cos\theta.$">|; 

$key = q/displaystyleP_l(cosgamma)=frac{4pi}{2,l+1}sum_{m=-l,+l}Y^{,ast}_{l,m}(theta',varphi'),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="$\displaystyle P_l(\cos\gamma) =\frac{4\pi}{2 l+1}\sum_{m=-l,+l}Y^{ \ast}_{l,m}(\theta',\varphi') Y_{l,m}(\theta,\varphi).$">|; 

$key = q/displaystylefrac{d^{,2}Q}{dtheta^{,2}}+m^{,2},Q=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="$\displaystyle \frac{d^{ 2} Q}{d\theta^{ 2}}+m^{ 2} Q=0,$">|; 

$key = q/displaystylenablacdot{bfA}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1316.png"
 ALT="$\displaystyle \nabla\cdot{\bf A} = 0.$">|; 

$key = q/displaystylew(x,h);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2560.png"
 ALT="$\displaystyle w(x,h)$">|; 

$key = q/{bfu}^i=c,T^{,i4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3972.png"
 ALT="$ {\bf u}^i = c  T^{ i4}$">|; 

$key = q/theta_{rmmax}rightarrowpislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4104.png"
 ALT="$ \theta_{\rm max} \rightarrow \pi/2$">|; 

$key = q/displaystylep_A-p_B=frac{epsilon_0}{2}left[E_parallel^{,2},(epsilon-1)+epsilon^{_perp^{,2}(epsilon),int_1^epsilonfrac{depsilon}{epsilon^{,2}}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1272.png"
 ALT="$\displaystyle p_A - p_B = \frac{\epsilon_0}{2}\left[ E_\parallel^{ 2}  (\epsi...
...perp^{ 2}(\epsilon)  \int_1^\epsilon \frac{d\epsilon}{\epsilon^{ 2}}\right],$">|; 

$key = q/displaystyleE(t)=E_0,{rme}^{-omega_0,tslash2,Q},{rme}^{-{rmi},(omega_0+{mitDelta}omega),t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2803.png"
 ALT="$\displaystyle E(t) = E_0  {\rm e}^{-\omega_0  t/2 Q}  {\rm e}^{-{\rm i} (\omega_0+{\mit\Delta}\omega) t},$">|; 

$key = q/displaystyle=-left(frac{[x,h_l^{(2)}(x)]'}{[x,h_l^{(1)}(x)]'}right)_{x=k,a},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3365.png"
 ALT="$\displaystyle = -\left(\frac{[x  h_l^{(2)}(x)]'} {[x  h_l^{(1)}(x)]'}\right)_{x=k a},$">|; 

$key = q/displaystylemu_0,gamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1569.png"
 ALT="$\displaystyle \mu_0 \gamma$">|; 

$key = q/B_{ij}=-B_{ji};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3788.png"
 ALT="$ B_{ij} = -B_{ji}$">|; 

$key = q/displaystyle={rme}^{,2,{rmi},delta_l'}-1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3372.png"
 ALT="$\displaystyle ={\rm e}^{ 2 {\rm i} \delta_l'} -1,$">|; 

$key = q/A,(0,hat{z})_d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2515.png"
 ALT="$ A (0,\hat{z})_d$">|; 

$key = q/displaystyleointY^{,ast}_{lm}(theta,varphi),frac{{rme}^{,{rmi},k,|{bfr}-{bfr}'|}ega}={rmi},k,h_l^{(1)}(k,r),j_l(k,r'),Y_{lm}^{,ast}(theta',varphi').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3218.png"
 ALT="$\displaystyle \oint Y^{ \ast}_{lm}(\theta,\varphi) \frac{{\rm e}^{ {\rm i} ...
...={\rm i} k  h_l^{(1)}(k r)  j_l(k r')  Y_{lm}^{ \ast}(\theta',\varphi').$">|; 

$key = q/A_i^j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3573.png"
 ALT="$ A_i^j$">|; 

$key = q/displaystyle=frac{2}{a^2,J_{m+1}^{,2}(j_{mn}),sinh(j_{mn},Lslasha)},int_0^ar,C_m(r),J_m(j_{mn},rslasha),dr,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="$\displaystyle = \frac{2}{a^2 J_{m+1}^{ 2}(j_{mn}) \sinh(j_{mn} L/a)} \int_0^a r C_m(r) J_m(j_{mn} r/a) dr,$">|; 

$key = q/x^{,1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3651.png"
 ALT="$ x^{ 1}$">|; 

$key = q/q_l=q,a^{,l},P_l(0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="$ q_l=q a^{ l} P_l(0)$">|; 

$key = q/displaystyled=sqrt{frac{2}{mu_0,sigma,omega}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1699.png"
 ALT="$\displaystyle d = \sqrt{\frac{2}{\mu_0 \sigma \omega}}$">|; 

$key = q/displaystylefrac{dU}{dt}=int_Vleft(phi,frac{partialrho_f}{partialt}-frac{epsilon_0}{2},E^{,2},frac{partialepsilon}{partialt}right),dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1214.png"
 ALT="$\displaystyle \frac{dU}{dt} = \int_V\left(\phi \frac{\partial\rho_f}{\partial ...
...frac{\epsilon_0}{2}  E^{ 2}  \frac{\partial\epsilon}{\partial t}\right) dV.$">|; 

$key = q/t=dt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4061.png"
 ALT="$ t=dt$">|; 

$key = q/a_E(l,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3118.png"
 ALT="$ a_E(l,m)$">|; 

$key = q/displaystyle{bfm}=frac{1}{2}int{bfr}'times{bfj}'({bfr}'),dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1404.png"
 ALT="$\displaystyle {\bf m} = \frac{1}{2}\int{\bf r}'\times {\bf j}'({\bf r}') dV'.$">|; 

$key = q/mu(B);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1531.png"
 ALT="$ \mu(B)$">|; 

$key = q/1slashh;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2466.png"
 ALT="$ 1/h$">|; 

$key = q/q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$ q$">|; 

$key = q/{mitPhi}(theta,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img929.png"
 ALT="$ {\mit\Phi}(\theta,z)$">|; 

$key = q/displaystyle(omega_0^{,2}-omega^{,2}),s_x-{rmi},omega,{mitOmega},s_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1716.png"
 ALT="$\displaystyle (\omega_0^{ 2} -\omega^{ 2}) s_x -{\rm i}  \omega {\mit\Omega}  s_y$">|; 

$key = q/displaystyleW=frac{epsilon_0}{2}left(int_Sphi,{bfE}cdotd{bfS}+int_VE^{,2},dVright),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$\displaystyle W = \frac{\epsilon_0}{2} \left(\int_S \phi {\bf E} \cdot d{\bf S}+ \int_V E^{ 2} dV\right),$">|; 

$key = q/i=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$ i=2$">|; 

$key = q/displaystyleq(hat{z})=a_1,hat{z}+a_2,hat{z}^{,2}+cdots,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2484.png"
 ALT="$\displaystyle q(\hat{z})= a_1 \hat{z} + a_2 \hat{z}^{ 2} + \cdots,$">|; 

$key = q/displaystylev_p=frac{2pi}{tau,{rmRe}(k_tau)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1849.png"
 ALT="$\displaystyle v_p = \frac{2\pi}{\tau {\rm Re}(k_\tau)}$">|; 

$key = q/displaystylef(x,t)={rme}^{-{rmIm}(k_tau),x}sin!left[2pi,frac{t}{tau}-{rmRe}(k_tau),xright]+B_4+B_5=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1844.png"
 ALT="$\displaystyle f(x,t) = {\rm e}^{-{\rm Im}(k_\tau)  x} \sin\!\left[2\pi \frac{t}{\tau} -{\rm Re}(k_\tau) x\right]+ B_4 + B_5 = 0$">|; 

$key = q/H_z(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2952.png"
 ALT="$ H_z(r)$">|; 

$key = q/n(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2247.png"
 ALT="$ n(z)$">|; 

$key = q/displaystyle={mitPhi}(r,theta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="$\displaystyle = {\mit\Phi}(r,\theta),$">|; 

$key = q/|z|rightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3017.png"
 ALT="$ \vert z\vert\rightarrow 0$">|; 

$key = q/E(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1141.png"
 ALT="$ E(z)$">|; 

$key = q/zslashg_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ z/g_i$">|; 

$key = q/{bfP}=epsilon_0,chi_e,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1122.png"
 ALT="$ {\bf P}=\epsilon_0 \chi_e  {\bf E}$">|; 

$key = q/displaystyle=y',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3478.png"
 ALT="$\displaystyle = y',$">|; 

$key = q/displaystyle({bfD}_2-{bfD}_1)cdot{bfn}_{21}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1088.png"
 ALT="$\displaystyle ({\bf D}_2 - {\bf D}_1) \cdot {\bf n}_{21} = 0,$">|; 

$key = q/displaystylefrac{E_theta,B_phi}{mu_0}=frac{e^{,2}}{16pi^2,epsilon_0,c^{,3}}frac{sin^2theta}{r^{,2}},dot{u}^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4037.png"
 ALT="$\displaystyle \frac{E_\theta  B_\phi}{\mu_0} = \frac{e^{ 2}} {16\pi^2  \epsilon_0  c^{ 3}}\frac{\sin^2\theta}{r^{ 2}}  \dot{u}^{ 2}.$">|; 

$key = q/displaystylepsi_i-cosphi_r,psi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2149.png"
 ALT="$\displaystyle \psi_i -\cos\phi_r \psi_r$">|; 

$key = q/{bfr}times{bfj}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3249.png"
 ALT="$ {\bf r}\times{\bf j} = 0$">|; 

$key = q/displaystyledtau^{,2}=dt^{,2}left(-frac{dx^{,2}+dy^{,2}+dz^{,2}}{c^{,2},dt^{,2}}+1right)=dt^{,2}left(1-frac{u^{,2}}{c^{,2}}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3691.png"
 ALT="$\displaystyle d\tau^{ 2} = dt^{ 2}\left( -\frac{dx^{ 2}+dy^{ 2}+dz^{ 2}}{c^{ 2}  dt^{ 2}} + 1\right) =dt^{ 2}\left(1-\frac{u^{ 2}}{c^{ 2}}\right),$">|; 

$key = q/displaystyle=frac{psi_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2102.png"
 ALT="$\displaystyle = \frac{\psi_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x-n_1 k_0 \cos\theta_i z)$">|; 

$key = q/displaystylenabla'^{,2}G_D({bfr},{bfr}')=delta({bfr}-{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="$\displaystyle \nabla'^{ 2} G_D({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}'),$">|; 

$key = q/{mitGamma}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2587.png"
 ALT="$ {\mit\Gamma}(z)$">|; 

$key = q/l+1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3011.png"
 ALT="$ l+1/2$">|; 

$key = q/displaystyleY_{2,-1}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="$\displaystyle Y_{2,-1}(\theta,\varphi)$">|; 

$key = q/B^{,1}=B_1equivB_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3779.png"
 ALT="$ B^{ 1}=B_1 \equiv B_x$">|; 

$key = q/w(hat{z},h)=w(x,h);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2552.png"
 ALT="$ w(\hat{z}, h) = w(x,h)$">|; 

$key = q/P_{rmout};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2681.png"
 ALT="$ P_{\rm out}$">|; 

$key = q/displaystyle{mitDelta}t_msimfrac{m,pi^2}{2,xi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1894.png"
 ALT="$\displaystyle {\mit\Delta} t_m \sim \frac{m  \pi^2}{2 \xi}.$">|; 

$key = q/displaystyle=-frac{psi_t,sintheta_i}{v_1},{rme}^{-n_2,k_0,sinhtheta_t,z},cos(omega,t-n_1,k_0,sintheta_i,x+phi_t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2143.png"
 ALT="$\displaystyle =-\frac{\psi_t \sin\theta_i}{v_1} {\rm e}^{-n_2 k_0 \sinh\theta_t z} \cos(\omega t-n_1 k_0 \sin\theta_i x+\phi_t)$">|; 

$key = q/beta=-uslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3876.png"
 ALT="$ \beta=-u/c$">|; 

$key = q/F;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3419.png"
 ALT="$ F$">|; 

$key = q/displaystylefrac{1}{k^{,2}}left|frac{3}{4}left(frac{1}{n^{,2}}frac{dn}{dz}right)^2-frac{1}{2,n^{,3}}frac{d^{,2}n}{dz^{,2}}right|ll1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2259.png"
 ALT="$\displaystyle \frac{1}{k^{ 2}}\left\vert \frac{3}{4}\left(\frac{1}{n^{ 2}} \f...
...{dz}\right)^2 -\frac{1}{2 n^{ 3}}\frac{d^{ 2} n}{dz^{ 2}}\right\vert \ll 1.$">|; 

$key = q/displaystylerho_b=epsilon_0,frac{dE(z)}{dz}=epsilon_0,E_0frac{d}{dz}!left[frac{1}{epsilon(z)}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1146.png"
 ALT="$\displaystyle \rho_b = \epsilon_0  \frac{d E(z)}{d z} = \epsilon_0  E_0\frac{d}{dz} \!\left[\frac{1}{\epsilon(z)}\right].$">|; 

$key = q/displaystyle=left(frac{15}{8pi}right)^{1slash2}sintheta,costheta,{rme}^{-{rmi},varphi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="$\displaystyle =\left(\frac{15}{8\pi}\right)^{1/2}\sin\theta \cos\theta {\rm e}^{-{\rm i} \varphi},$">|; 

$key = q/displaystylefrac{1}{r},frac{d}{dr}!left(r,frac{dg_{m,n}}{dr}right)-left(k_n^{,2}+frac{m^{,2}}{r^{,2}}right)g_{m,n}=frac{1}{r},delta(r-r').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1004.png"
 ALT="$\displaystyle \frac{1}{r} \frac{d}{dr}\!\left(r \frac{d g_{m,n}}{dr}\right) -...
...t(k_n^{ 2}+\frac{m^{ 2}}{r^{ 2}}\right) g_{m,n} = \frac{1}{r} \delta(r-r').$">|; 

$key = q/displaystyle=left(frac{3}{8pi}right)^{1slash2}sintheta,,{rme}^{-{rmi},varphi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="$\displaystyle = \left(\frac{3}{8\pi}\right)^{1/2}\sin\theta  {\rm e}^{-{\rm i} \varphi},$">|; 

$key = q/displaystyleF_{munu}=-F_{numu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3790.png"
 ALT="$\displaystyle F_{\mu\nu} = -F_{\nu\mu}.$">|; 

$key = q/displaystyleE_y(x)=int_{0}^{1}F(S),{rme}^{,{rmi},k,S,x},dS,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2384.png"
 ALT="$\displaystyle E_y(x) = \int_{0}^{1} F(S)  {\rm e}^{ {\rm i} k  S x} dS,$">|; 

$key = q/+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3770.png"
 ALT="$ +1$">|; 

$key = q/displaystylefrac{B}{B_0}=1+2,frac{B_s}{B_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1545.png"
 ALT="$\displaystyle \frac{B}{B_0} = 1 + 2 \frac{B_s}{B_0}.$">|; 

$key = q/{bfM};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$ {\bf M}$">|; 

$key = q/x=10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2421.png"
 ALT="$ x=10$">|; 

$key = q/displaystyleg_{ij},A^i,B^{,j}=A_i,B^{,i}=A^i,B_i=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3605.png"
 ALT="$\displaystyle g_{ij}  A^i  B^{ j} = A_i  B^{ i} = A^i  B_i = 0.$">|; 

$key = q/pmalpha=0,2pi,cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2702.png"
 ALT="$ \pm\alpha= 0, 2\pi, \cdots $">|; 

$key = q/displaystylemu_0,frac{partialphi_m(r=b+,theta)}{partialr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1553.png"
 ALT="$\displaystyle \mu_0 \frac{\partial\phi_m(r=b+,\theta)}{\partial r}$">|; 

$key = q/displaystylephi(z)simeqpmkint^z!n(z'),dz'+{rmi},log(n^{,1slash2}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2255.png"
 ALT="$\displaystyle \phi(z) \simeq \pm k \int^z \!n(z') dz' +{\rm i} \log(n^{ 1/2}).$">|; 

$key = q/omega=k,c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1707.png"
 ALT="$ \omega=k c$">|; 

$key = q/phi(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2246.png"
 ALT="$ \phi(z)$">|; 

$key = q/x=dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="$ x=d/2$">|; 

$key = q/displaystyleA_varphi(r,theta)=frac{mu_0,I}{4pi,a}intfrac{cosvarphi',delta(costheta'),delta(r'-a)}{|{bfr}-{bfr}'|},r'^{,2},dr',d{mitOmega}',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1333.png"
 ALT="$\displaystyle A_\varphi(r,\theta) = \frac{\mu_0 I}{4\pi a}\int \frac{\cos\var...
...ta') \delta(r'-a)}{\vert{\bf r}-{\bf r}'\vert} r'^{ 2} dr' d{\mit\Omega}',$">|; 

$key = q/r_>;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="$ r_&gt;$">|; 

$key = q/P=(0,0,0,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3437.png"
 ALT="$ P=(0,0,0,0)$">|; 

$key = q/displaystylep_{i'}^{,i},p_{j}^{,i'}=delta_j^{,i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3541.png"
 ALT="$\displaystyle p_{i'}^{ i}  p_{j}^{ i'} = \delta_j^{ i},$">|; 

$key = q/displaystyle=sum_{l=0,infty}sum_{m=-l,+l}phi_{l,m}(r),Y_{l,m}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="$\displaystyle =\sum_{l=0,\infty}\sum_{m=-l,+l}\phi_{l,m}(r) Y_{l,m}(\theta,\varphi),$">|; 

$key = q/displaystyle{bfn}times{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2771.png"
 ALT="$\displaystyle {\bf n}\times {\bf H}$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}intfrac{[rho]}{R},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle = \frac{1}{4\pi  \epsilon_0} \int \frac{[\rho]}{R}  dV',$">|; 

$key = q/z=dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2607.png"
 ALT="$ z=d/2$">|; 

$key = q/displaystyledU=frac{epsilon_0,dr}{2,k^{,2}}sum_{m,m'}a_E^ast(l,m'),a_E(l,m)oint{bfX}_{lm'}^ast!cdot{bfX}_{lm},d{mitOmega},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3157.png"
 ALT="$\displaystyle dU = \frac{\epsilon_0 dr}{2 k^{ 2}}\sum_{m,m'} a_E^\ast(l,m')  a_E(l,m) \oint {\bf X}_{lm'}^\ast\!\cdot{\bf X}_{lm}  d{\mit\Omega},$">|; 

$key = q/displaystyle{bfL}cdot(nablatimes{bfA});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3225.png"
 ALT="$\displaystyle {\bf L}\cdot(\nabla\times{\bf A})$">|; 

$key = q/displaystylef(x,t)=frac{1}{tau}oint_S{rme}^{,{rmi},([k-omegaslashc],x-omega,s)}frac{domega}{omega^{,2}-(2pislashtau)^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1855.png"
 ALT="$\displaystyle f(x,t) = \frac{1}{\tau}\oint_S{\rm e}^{ {\rm i} ([k-\omega/c] x-\omega  s)} \frac{d\omega}{\omega^{ 2} -(2\pi/\tau)^{ 2}}$">|; 

$key = q/displaystyle{bfE}_{lm}^{(E)}rightarrowfrac{-{rmi}}{l},nablatimes{bfL}left(frac{Y_{lm}}{r^{,l+1}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3131.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(E)} \rightarrow \frac{-{\rm i}}{l} \nabla\times {\bf L} \left(\frac{Y_{lm}}{r^{ l+1}}\right).$">|; 

$key = q/r'=sqrt{x^{',2}+y^{',2}+z^{',2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3867.png"
 ALT="$ r'=\sqrt{x^{' 2}+y^{' 2}+z^{' 2}}$">|; 

$key = q/displaystylelangleu_{rmin}rangle=frac{epsilon_0,c,E_0^{,2}}{2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2668.png"
 ALT="$\displaystyle \langle u_{\rm in}\rangle = \frac{\epsilon_0  c  E_0^{ 2}}{2},$">|; 

$key = q/displaystyleointY_{lm}^{,ast}left[delta(costheta-1)-delta(costheta+1)right]d{mitOmega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3254.png"
 ALT="$\displaystyle \oint Y_{lm}^{ \ast}\left[\delta(\cos\theta-1) -\delta(\cos\theta+1)\right]d{\mit\Omega}.$">|; 

$key = q/displaystyleB_l=A_l,a^{,2,l+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1506.png"
 ALT="$\displaystyle B_l = A_l  a^{ 2 l+1}$">|; 

$key = q/displaystyle=left(frac{beta-alpha}{beta+alpha}right)^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2089.png"
 ALT="$\displaystyle =\left(\frac{\beta-\alpha}{\beta+\alpha}\right)^2,$">|; 

$key = q/epsilon^{,alphabetagammadelta}rightarrow-epsilon^{,alphabetagammadelta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3772.png"
 ALT="$ \epsilon^{ \alpha\beta\gamma\delta}
\rightarrow -\epsilon^{ \alpha\beta\gamma\delta}$">|; 

$key = q/displaystyleoint_S{bfD}cdotd{bfS}=int_Vrho_f,dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1071.png"
 ALT="$\displaystyle \oint_S {\bf D}\cdot d{\bf S} = \int_V \rho_f dV.$">|; 

$key = q/dS_4=-d^{,3}x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4047.png"
 ALT="$ dS_4=-d^{ 3} x$">|; 

$key = q/displaystyleL_+,Y_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3058.png"
 ALT="$\displaystyle L_+  Y_{lm}$">|; 

$key = q/displaystyleepsilon(omega)equivn^{,2}(omega)=n_0^{,2}+{rmi},frac{N,e^{,2}}{epsilon_0,m}frac{f_0}{omega,(gamma_0-{rmi},omega)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1675.png"
 ALT="$\displaystyle \epsilon(\omega) \equiv n^{ 2}(\omega) =n_0^{ 2} + {\rm i} \frac{N e^{ 2}}{\epsilon_0  m} \frac{f_0}{\omega (\gamma_0-{\rm i} \omega)},$">|; 

$key = q/displaystyleg_{m,n}(r,r')=left{{array}{ccc}alpha(r'),I_m(k_n,r)&mbox{hspace{1cm}_m(k_n,r),K_m(k_n,a)-I_m(k_n,a),K_m(k_n,r)right]&&r>r'{array}right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="503" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1008.png"
 ALT="$\displaystyle g_{m,n}(r,r')=\left\{\begin{array}{ccc}\alpha(r') I_m(k_n r)&amp;\m...
...m(k_n r) K_m(k_n a)-I_m(k_n a) K_m(k_n r)\right]&amp;&amp;r&gt;r'\end{array}\right..$">|; 

$key = q/displaystylenablatimes{bfB}=mu_0,{bfj}+epsilon_0,mu_0frac{partial{bfE}}{partialt}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle \nabla\times{\bf B} = \mu_0  {\bf j} +\epsilon_0 \mu_0 \frac{\partial {\bf E}} {\partial t}.$">|; 

$key = q/displaystylenablatimesc,{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2227.png"
 ALT="$\displaystyle \nabla\times c {\bf B}$">|; 

$key = q/displaystyleY_{2,0}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$\displaystyle Y_{2,0}(\theta,\varphi)$">|; 

$key = q/displaystyle{mitDelta}omega=gamma^{,3},omega_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4157.png"
 ALT="$\displaystyle {\mit\Delta}\omega = \gamma^{ 3} \omega_0.$">|; 

$key = q/displaystyle(omega_0^{,2}-omega^{,2}-omega,{mitOmega}),s_+;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1728.png"
 ALT="$\displaystyle (\omega_0^{ 2} -\omega^{ 2} -\omega {\mit \Omega}) s_+$">|; 

$key = q/displaystylew(hat{z},h)=A,(0,hat{z})+B,(hat{z},0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2497.png"
 ALT="$\displaystyle w(\hat{z}, h) = A (0,\hat{z}) + B (\hat{z},0)$">|; 

$key = q/displaystylefrac{dgamma}{dt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3911.png"
 ALT="$\displaystyle \frac{d\gamma}{dt}$">|; 

$key = q/partialphi({bfr}')slashpartialn';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="$ \partial\phi({\bf r}')/\partial n'$">|; 

$key = q/displaystyle=T^{,4i}=frac{({bfE}times{bfB})^{,i}}{mu_0,c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3967.png"
 ALT="$\displaystyle = T^{ 4i} = \frac{({\bf E}\times{\bf B})^{ i}}{\mu_0  c},$">|; 

$key = q/displaystyleA_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1175.png"
 ALT="$\displaystyle A_1$">|; 

$key = q/{bfk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1612.png"
 ALT="$ {\bf k}$">|; 

$key = q/phi_3({bfr})=phi_1({bfr})-phi_2({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$ \phi_3({\bf r})=\phi_1({\bf r})-\phi_2({\bf r})$">|; 

$key = q/phi_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1475.png"
 ALT="$ \phi_m$">|; 

$key = q/displaystylenabla'left(frac{1}{|{bfr}-{bfr}'|}right)=-nablaleft(frac{1}{|{bfr}-{bfr}'|}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1482.png"
 ALT="$\displaystyle \nabla'\left(\frac{1}{\vert{\bf r} - {\bf r}'\vert}\right)= - \nabla\left(\frac{1}{\vert{\bf r} - {\bf r}'\vert}\right),$">|; 

$key = q/{bfD}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1087.png"
 ALT="$ {\bf D}_1$">|; 

$key = q/omega=omega_p(z_0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2348.png"
 ALT="$ \omega
=\omega_p(z_0)$">|; 

$key = q/displaystyle{bfD}_1cdotd{bfS}_1+{bfD}_2cdotd{bfS}_2=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1086.png"
 ALT="$\displaystyle {\bf D}_1 \cdot d{\bf S}_1 + {\bf D}_2 \cdot d{\bf S}_2 = 0,$">|; 

$key = q/displaystylev_omega({bfr})=frac{1}{2pi}int_{-infty}^{infty}v({bfr},t),{rme}^{+{rmi},omega,t},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle v_\omega({\bf r}) = \frac{1}{2\pi} \int_{-\infty}^{\infty} v({\bf r}, t)  {\rm e}^{+{\rm i}  \omega  t} d t.$">|; 

$key = q/partial_muJ^{,mu}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3813.png"
 ALT="$ \partial_\mu J^{ \mu} =0$">|; 

$key = q/displaystylepsi_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2076.png"
 ALT="$\displaystyle \psi_t$">|; 

$key = q/displaystyle=frac{mu_0,I}{2,a}sum_{l=1,3,5,cdots}frac{P_l^1(0)}{l+1}left(frac{a}{r}right)^{l+2}P_l^1(costheta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1366.png"
 ALT="$\displaystyle = \frac{\mu_0 I}{2 a}\sum_{l=1,3,5,\cdots}\frac{P_l^1(0)}{l+1}\left(\frac{a}{r}\right)^{l+2}P_l^1(\cos\theta)$">|; 

$key = q/epsilon_{,iab};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3784.png"
 ALT="$ \epsilon_{ iab}$">|; 

$key = q/delta_j^{,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3542.png"
 ALT="$ \delta_j^{ i}$">|; 

$key = q/displaystylephi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2206.png"
 ALT="$\displaystyle \phi_r$">|; 

$key = q/displaystyleu_omega({bfr})=frac{1}{2pi}int_{-infty}^{infty}u({bfr},t),{rme}^{+{rmi},omega,t},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle u_\omega({\bf r}) = \frac{1}{2\pi} \int_{-\infty}^{\infty} u({\bf r}, t)  {\rm e}^{+{\rm i}  \omega  t} d t.$">|; 

$key = q/displaystyleP^{,mu}=frac{1}{c}intT^{,4mu},d^{,3}x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4063.png"
 ALT="$\displaystyle P^{ \mu} = \frac{1}{c}\int T^{ 4\mu} d^{ 3} x$">|; 

$key = q/displaystyleP=frac{e^{,2}}{6pi,epsilon_0,m_0^{,2},c^{,3}}left(frac{dE}{dx}right)^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4079.png"
 ALT="$\displaystyle P= \frac{e^{ 2}}{6\pi \epsilon_0  m_0^{ 2}  c^{ 3}}\left(\frac{dE}{dx}\right)^2.$">|; 

$key = q/displaystyleJ_m'(k_l,a)=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2868.png"
 ALT="$\displaystyle J_m'(k_l  a) = 0,$">|; 

$key = q/displaystylefrac{dt}{dtau}=gamma(u).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3692.png"
 ALT="$\displaystyle \frac{dt}{d\tau} = \gamma(u).$">|; 

$key = q/displaystyle=-epsilon_0,E^{,i},E^{,j}-frac{B^{,i},B^{,j}}{mu_0}+delta^{,ij},frac{1}{2}left(epsilon_0,E^{,2}+frac{B^{,2}}{mu_0}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3965.png"
 ALT="$\displaystyle = -\epsilon_0  E^{ i}  E^{ j} - \frac{B^{ i}  B^{ j}}{\mu_...
...a^{ ij} \frac{1}{2} \left(\epsilon_0  E^{ 2} +\frac{B^{ 2}}{\mu_0}\right),$">|; 

$key = q/displaystylefrac{1}{R}frac{d^{,2}(R,G_omega)}{dR^{,2}}+k^{,2},G_omega=-delta({bfR}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \frac{1}{R}\frac{d^{ 2}(R  G_\omega)}{dR^{ 2}} + k^{ 2}  G_\omega = -\delta({\bf R}),$">|; 

$key = q/displaystyleq'=intsigma,dS=2pi,a^{,2}int_0^pisigma(theta),dtheta=-q,frac{a}{b}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="$\displaystyle q' = \int\sigma dS= 2\pi a^{ 2}\int_0^\pi\sigma(\theta) d\theta = - q \frac{a}{b}.$">|; 

$key = q/d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$ d{\mit\Omega}$">|; 

$key = q/6.3times10^7,(Omega,{rmm})^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2214.png"
 ALT="$ 6.3\times 10^7 (\Omega {\rm m})^{-1}$">|; 

$key = q/displaystyledt=-frac{dr}{c}=-frac{dx}{c},costheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3752.png"
 ALT="$\displaystyle dt = -\frac{dr}{c} = -\frac{dx}{c} \cos\theta.$">|; 

$key = q/displaystyle{calF}^{,mu}=gammaleft({bff},,c,frac{dm}{dt}right)=gammaleft({bff},,frac{{bff}cdot{bfu}}{c}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3926.png"
 ALT="$\displaystyle {\cal F}^{ \mu} = \gamma\left({\bf f},  c  \frac{dm}{dt}\right) = \gamma \left( {\bf f},  \frac{{\bf f}\cdot{\bf u}}{c}\right),$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^infty{rme}^{,{rmi},k,(z-z')},dk,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img957.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^\infty {\rm e}^{ {\rm i} k (z-z')} dk,$">|; 

$key = q/displaystylesum_if_i=Z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1635.png"
 ALT="$\displaystyle \sum_i f_i = Z.$">|; 

$key = q/{bfK};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2761.png"
 ALT="$ {\bf K}$">|; 

$key = q/theta';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="$ \theta'$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=left(frac{q^{,2}}{4pi,epsilon_0,m,c^{,2}}right)^2frac{epsilon_0,c,E_0^{,2}}{2}sin^2theta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2722.png"
 ALT="$\displaystyle \frac{d P}{d {\mit \Omega}}=\left( \frac{q^{ 2}}{4\pi \epsilon_0  m  c^{ 2}}\right)^2 \frac{\epsilon_0  c E_0^{ 2}}{2} \sin^2\theta.$">|; 

$key = q/displaystylenabla'^{,2}F({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="$\displaystyle \nabla'^{ 2} F({\bf r}, {\bf r}')=0$">|; 

$key = q/d{mitOmega}=sinalpha,dalpha,dphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4139.png"
 ALT="$ d{\mit\Omega} = \sin\alpha d\alpha d\phi$">|; 

$key = q/displaystyleE_r(r)=frac{Q}{4pi,epsilon_0}frac{r}{a^{,3}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$\displaystyle E_r(r) = \frac{Q}{4\pi \epsilon_0} \frac{r}{a^{ 3}}$">|; 

$key = q/l=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="$ l=1$">|; 

$key = q/A_{k'cdotsl',m'}^{i'cdotsj'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3584.png"
 ALT="$ A_{k'\cdots l', m'}^{i'\cdots j'}$">|; 

$key = q/displaystyle=frac{psi_t}{v_2},cos(omega,t-n_1,k_0,sintheta_i,x-n_2,k_0,costheta_t,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2110.png"
 ALT="$\displaystyle = \frac{\psi_t}{v_2} \cos(\omega t-n_1 k_0 \sin\theta_i x-n_2 k_0 \cos\theta_t z),$">|; 

$key = q/R_{rmload};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2656.png"
 ALT="$ R_{\rm load}$">|; 

$key = q/(x,y,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3450.png"
 ALT="$ (x, y, z, t)$">|; 

$key = q/displaystylef(t)=frac{1}{2pi}int_0^inftydomegaleft(frac{cos[2pi,t'slashtau+omegapi,t'slashtau-omega,(t-t')]}{omega+2pislashtau}right)_{t'=0}^{t'=T}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1782.png"
 ALT="$\displaystyle f(t) =\frac{1}{2\pi}\int_0^\infty d\omega\left( \frac{\cos[2\pi \...
...c{\cos[2\pi  t'/\tau -\omega (t-t')]}{\omega+2\pi/\tau}\right)_{t'=0}^{t'=T}.$">|; 

$key = q/displaystylefrac{dchi}{dl}simeqfrac{e^{,3}}{2,epsilon_0,m^{,2},c}frac{N,B_parallel}{omega^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1760.png"
 ALT="$\displaystyle \frac{d\chi}{dl} \simeq \frac{e^{ 3}}{2 \epsilon_0  m^{ 2}  c} \frac{N  B_\parallel} {\omega^{ 2}}.$">|; 

$key = q/d{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1407.png"
 ALT="$ d{\bf r}$">|; 

$key = q/displaystyle=E_t,cos(omega,t-pislash4+phi_t).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2202.png"
 ALT="$\displaystyle =E_t \cos(\omega t-\pi/4+\phi_t).$">|; 

$key = q/displaystyle{rmi},nablatimes{bfL}equiv{bfr},nabla^{,2}-nabla!left(1+r,frac{partial}{partialr}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3130.png"
 ALT="$\displaystyle {\rm i} \nabla\times{\bf L} \equiv {\bf r} \nabla^{ 2} -\nabla\!\left( 1+ r \frac{\partial}{\partial r}\right).$">|; 

$key = q/displaystylesimeq-frac{(l+1)}{l},alpha_pm(l),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3381.png"
 ALT="$\displaystyle \simeq -\frac{(l+1)}{l} \alpha_\pm(l),$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}intfrac{rho({bfr'})}{|{bfr}-{bfr}'|},dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho({\bf r'})}{\vert{\bf r}-{\bf r}'\vert} dV'$">|; 

$key = q/displaystyle{mitDelta}t=frac{{mitDelta}theta}{omega_0}left(1-frac{u}{c}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4154.png"
 ALT="$\displaystyle {\mit\Delta} t = \frac{{\mit\Delta} \theta}{\omega_0} \left(1-\frac{u}{c}\right),$">|; 

$key = q/displaystyle=-F_{4i}=-E_i,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3794.png"
 ALT="$\displaystyle =-F_{4i} = -E_i,$">|; 

$key = q/displaystyle=frac{J^{,nu}}{c,epsilon_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3848.png"
 ALT="$\displaystyle = \frac{J^{ \nu}}{c \epsilon_0},$">|; 

$key = q/pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1893.png"
 ALT="$ \pi$">|; 

$key = q/displaystyledx'=frac{partialF}{partialx},dx+frac{partialF}{partialy},dy+frac{partialF}{partialz},dz+frac{partialF}{partialt},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3420.png"
 ALT="$\displaystyle dx' = \frac{\partial F}{\partial x} dx + \frac{\partial F}{\part...
...y} dy + \frac{\partial F}{\partial z} dz + \frac{\partial F}{\partial t} dt.$">|; 

$key = q/displaystylefrac{dphi}{dz}simeqpmleft(k^{,2}n^{,2}pm{rmi},k,frac{dn}{dz}right)^{1slash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2253.png"
 ALT="$\displaystyle \frac{d\phi}{dz} \simeq \pm \left(k^{ 2} n^{ 2} \pm {\rm i}  k  \frac{dn}{dz}\right)^{1/2}.$">|; 

$key = q/displaystylenablacdot(psi,nablaphi)equivpsi,nabla^{,2}phi+nablapsicdotnablaphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="$\displaystyle \nabla\cdot(\psi \nabla\phi) \equiv \psi \nabla^{ 2}\phi + \nabla\psi\cdot\nabla\phi,$">|; 

$key = q/displaystyle=frac{-vslashc^2}{pm(1-v^{,2}slashc^{,2})^{1slash2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3470.png"
 ALT="$\displaystyle = \frac{- v/c^2}{\pm(1-v^{ 2}/c^{ 2})^{1/2}}.$">|; 

$key = q/displaystyleT^{,3'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3642.png"
 ALT="$\displaystyle T^{ 3'}$">|; 

$key = q/-{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3773.png"
 ALT="$ -{\bf B}$">|; 

$key = q/displaystyle{mitPhi}^{,mu}=(c,{bfA},,phi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3729.png"
 ALT="$\displaystyle {\mit \Phi}^{ \mu} = (c {\bf A},  \phi)$">|; 

$key = q/displaystyleoint[f_l(r),{bfX}_{l'm'}]^{,ast}cdot[g_l(r),{bfX}_{lm}],d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3309.png"
 ALT="$\displaystyle \oint [f_l(r) {\bf X}_{l'm'}]^{ \ast} \cdot [g_l(r)  {\bf X}_{lm}] d{\mit\Omega}$">|; 

$key = q/omega_0leqomegaleqomega_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1927.png"
 ALT="$ \omega_0
\leq \omega\leq \omega_1$">|; 

$key = q/displaystylefrac{dM_y}{dr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3170.png"
 ALT="$\displaystyle \frac{d M_y}{dr}$">|; 

$key = q/6.8times10^{-5};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1450.png"
 ALT="$ 6.8\times 10^{-5}$">|; 

$key = q/deltaU;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1206.png"
 ALT="$ \delta U$">|; 

$key = q/g,omega_0,dot{bfs};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1622.png"
 ALT="$ g \omega_0 \dot{\bf s}$">|; 

$key = q/displaystylepartial_mu{mitPhi}^{,mu}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3736.png"
 ALT="$\displaystyle \partial_\mu {\mit \Phi}^{ \mu} =0.$">|; 

$key = q/{bfL};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$ {\bf L}$">|; 

$key = q/(hat{z},0)_dleftrightarrow(hat{z},0)_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2491.png"
 ALT="$ (\hat{z},0)_d \leftrightarrow (\hat{z},0)_s$">|; 

$key = q/mu_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2576.png"
 ALT="$ \mu_1$">|; 

$key = q/B_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3563.png"
 ALT="$ B_{ij}$">|; 

$key = q/displaystylefrac{{rme}^{,{rmi},N,alpha}-1}{{rme}^{,{rmi},alpha}-1}={rme}^{,{rmi},(N-1),alphaslash2},frac{sin(N,alphaslash2)}{sin(alphaslash2)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2696.png"
 ALT="$\displaystyle \frac{{\rm e}^{ {\rm i} N \alpha}-1}{{\rm e}^{ {\rm i} \alph...
...rm e}^{ {\rm i} (N-1) \alpha/2}  \frac{\sin(N \alpha/2)}{\sin(\alpha /2)}.$">|; 

$key = q/gpropto{rme}^{,{rmi},k,r};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3182.png"
 ALT="$ g\propto {\rm e}^{ {\rm i} k r}$">|; 

$key = q/displaystylef(t)=frac{1}{4pi}int_{-infty}^{infty}frac{domega}{omega-2pislashtau}ashtau}left[{rme}^{+{rmi},omega,(t-T)}-{rme}^{+{rmi},omega,t}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="540" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1787.png"
 ALT="$\displaystyle f(t) = \frac{1}{4\pi} \int_{-\infty}^{\infty} \frac{d\omega}{\ome...
...\left[{\rm e}^{+{\rm i} \omega (t-T)} -{\rm e}^{+{\rm i} \omega  t}\right].$">|; 

$key = q/H_{parallel,0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2796.png"
 ALT="$ H_{\parallel  0}$">|; 

$key = q/displaystylefrac{{bff}cdot{bfu}}{c}=frac{e}{c},{bfE}cdot{bfu}=frac{e}{c},E_i,u^{,i}=frac{e}{gamma,c}(F_{4i},U^{,i}+F_{44},U^{,4}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3933.png"
 ALT="$\displaystyle \frac{{\bf f}\cdot{\bf u}}{c} = \frac{e}{c}  {\bf E}\cdot{\bf u}...
...c}  E_i  u^{ i} = \frac{e}{\gamma c} (F_{4i}  U^{ i} + F_{44}  U^{ 4}).$">|; 

$key = q/displaystylefrac{partialD_y}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2095.png"
 ALT="$\displaystyle \frac{\partial D_y}{\partial t}$">|; 

$key = q/{bfr}cdot{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3079.png"
 ALT="$ {\bf r}\cdot
{\bf E}$">|; 

$key = q/displaystylerho_m(r',z');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img991.png"
 ALT="$\displaystyle \rho_m(r',z')$">|; 

$key = q/displaystylenablatimes{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2819.png"
 ALT="$\displaystyle \nabla\times{\bf H}$">|; 

$key = q/S=sintheta_I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2294.png"
 ALT="$ S=\sin\theta_I$">|; 

$key = q/displaystylephi(r,theta)=sum_{l=0,infty}left[B_l,r^{,l}+C_l,r^{,-(l+1)}right]P_l(costheta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1164.png"
 ALT="$\displaystyle \phi(r,\theta) = \sum_{l=0,\infty}\left[B_l r^{ l} + C_l  r^{ -(l+1)}\right]P_l(\cos \theta).$">|; 

$key = q/displaystyleL^2=L_x^{,2}+L_y^{,2}+L_z^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3047.png"
 ALT="$\displaystyle L^2 = L_x^{ 2} + L_y^{ 2} + L_z^{ 2},$">|; 

$key = q/G_3({bfr},{bfr}')=G_1({bfr},{bfr}')-G_2({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$ G_3({\bf r},{\bf r}')
=G_1({\bf r},{\bf r}')-G_2({\bf r},{\bf r}')$">|; 

$key = q/r=z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="$ r=z$">|; 

$key = q/displaystylenablaequivfrac{bfr}{r},frac{partial}{partialr}-frac{rmi}{r^{,2}},{bfr}times{bfL}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3312.png"
 ALT="$\displaystyle \nabla \equiv \frac{\bf r}{r}  \frac{\partial}{\partial r} - \frac{\rm i}{r^{ 2}}  {\bf r}\times{\bf L}.$">|; 

$key = q/j_{ml}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2873.png"
 ALT="$ j_{m l}'$">|; 

$key = q/{rme}^{,{rmi},k,z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3321.png"
 ALT="$ {\rm e}^{ {\rm i} 
k z}$">|; 

$key = q/displaystyle{bfE}=frac{e}{4pi,epsilon_0}frac{1-u^{,2}slashc^{,2}}{r_0^{,3},(1-u^{,2}slashc^{,2}+u_r^{,2}slashc^{,2})^{3slash2}},{bfr}_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4019.png"
 ALT="$\displaystyle {\bf E} = \frac{e}{4\pi \epsilon_0} \frac{1-u^{ 2}/c^{ 2}}{r_0^{ 3} (1-u^{ 2}/c^{ 2} + u_r^{ 2}/c^{ 2})^{3/2}} {\bf r}_0,$">|; 

$key = q/{T^{,mu}}_nu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3955.png"
 ALT="$ {T^{ \mu}}_\nu$">|; 

$key = q/displaystyle{bfB}({bfr})=nablatimes{bfA}=frac{mu_0}{4pi}left[frac{3,({bfm}cdot{bfr}),{bfr}-r^{,2},{bfm}}{r^{,5}}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1406.png"
 ALT="$\displaystyle {\bf B}({\bf r}) = \nabla\times {\bf A} = \frac{\mu_0}{4\pi}\left[\frac{3 ({\bf m}\cdot{\bf r}) {\bf r} -r^{ 2} {\bf m}}{r^{ 5}}\right].$">|; 

$key = q/displaystyle=frac{1}{2}sum_{l=1,infty}{rmi}^{,l}sqrt{4pi,(2,l+1)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3346.png"
 ALT="$\displaystyle = \frac{1}{2}\sum_{l=1,\infty} {\rm i}^{ l}\sqrt{4\pi (2 l+1)}$">|; 

$key = q/displaystyle0=frac{1}{4pi,epsilon_0}int_Vfrac{rho({bfr}')}{|{bfr}-{bfr}'|},dV'+fr}'),frac{partial}{partialn'}!left(frac{1}{|{bfr}-{bfr}'|}right)dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="538" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="$\displaystyle 0= \frac{1}{4\pi \epsilon_0}\int_V \frac{\rho({\bf r}')}{\vert{\...
...c{\partial}{\partial n'}\!\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dS'.$">|; 

$key = q/(1slashsqrt{2},0,1slashsqrt{2},1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3431.png"
 ALT="$ (1/\sqrt{2}, 0, 1/\sqrt{2}, 1)$">|; 

$key = q/omega=omega_0+{mitDelta}omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2805.png"
 ALT="$ \omega=\omega_0+{\mit\Delta}\omega$">|; 

$key = q/displaystyleI_m(p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img938.png"
 ALT="$\displaystyle I_m(p)$">|; 

$key = q/displaystylembox{hspace{2.4cm}as{prightarrow0{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img967.png"
 ALT="$\displaystyle \mbox{\hspace{2.4cm}as $p\rightarrow 0$}$">|; 

$key = q/displaystylefrac{dE}{dt}={bff}cdot{bfu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3927.png"
 ALT="$\displaystyle \frac{d E}{dt} = {\bf f}\cdot{\bf u}.$">|; 

$key = q/p_{ij}=p_{ji};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="$ p_{ij} = p_{ji}$">|; 

$key = q/r'=infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="$ r'=\infty$">|; 

$key = q/{bfB}rightarrow-{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3774.png"
 ALT="$ {\bf B}\rightarrow -{\bf B}$">|; 

$key = q/E_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2192.png"
 ALT="$ E_i$">|; 

$key = q/displaystylep_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="$\displaystyle p_z$">|; 

$key = q/P_1^1(x)=-(1-x^2)^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1359.png"
 ALT="$ P_1^1(x)=-(1-x^2)^{1/2}$">|; 

$key = q/displaystyle=-frac{e}{m},E_y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1719.png"
 ALT="$\displaystyle = -\frac{e}{m}  E_y,$">|; 

$key = q/m,c^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2739.png"
 ALT="$ m  c^{ 2}$">|; 

$key = q/q_l=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="$ q_l=0$">|; 

$key = q/displaystyleG_3({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$\displaystyle G_3({\bf r},{\bf r}')= 0$">|; 

$key = q/displaystyleF^{,4i}=-E^{,i}=frac{e,gamma}{4pi,epsilon_0,{r'}^{,3}},r^{,i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3896.png"
 ALT="$\displaystyle F^{ 4i} = -E^{ i} = \frac{e \gamma}{4\pi \epsilon_0 {r'}^{ 3}} r^{ i},$">|; 

$key = q/R=|{bfR}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$ R=\vert{\bf R}\vert$">|; 

$key = q/displaystylefrac{dM_z}{dr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3173.png"
 ALT="$\displaystyle \frac{d M_z}{dr}$">|; 

$key = q/Q_{ji}=Q_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="$ Q_{ji}=Q_{ij}$">|; 

$key = q/displaystylex=-int_0^zleft(frac{partialq}{partialS}right)_{S=S_0},dz.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2393.png"
 ALT="$\displaystyle x = - \int_0^z \left(\frac{\partial q}{\partial S}\right)_{S=S_0} dz.$">|; 

$key = q/theta_I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2284.png"
 ALT="$ \theta_I$">|; 

$key = q/displaystylephi_1({bfr})=frac{1}{3,epsilon_0}left(frac{q_{1,-1}^{,ast},r,Y_{1,-1+q_{1,0}^{,ast},r,Y_{1,0}+q_{1,+1}^{,ast},r,Y_{1,+1}}{r^{,3}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="$\displaystyle \phi_1({\bf r}) = \frac{1}{3 \epsilon_0}\left(\frac{q_{1,-1}^{ ...
...}+q_{1,0}^{ \ast} r Y_{1,0}+q_{1,+1}^{ \ast} r Y_{1,+1}}{r^{ 3}}\right).$">|; 

$key = q/displaystyleepsilon^{,ijk},partial_j(c,B_k)-partial_4E^{,i}=epsilon^{,ijk},partiepsilon_{kab},c,B^{,ab})+partial_4F^{,4i}=frac{J^{,i}}{c,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3810.png"
 ALT="$\displaystyle \epsilon^{ ijk}  \partial_j( c B_k) - \partial_4 E^{ i} = \ep...
...n_{kab}  c  B^{ ab} ) + \partial_4 F^{ 4i} = \frac{J^{ i}}{c \epsilon_0}.$">|; 

$key = q/l>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="$ l&gt;0$">|; 

$key = q/k_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2812.png"
 ALT="$ k_3$">|; 

$key = q/1slashomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2332.png"
 ALT="$ 1/\omega_0$">|; 

$key = q/displaystyle=gamma,{bfB}+frac{1-gamma}{v^{,2}},({bfv}cdot{bfB}),{bfv}-frac{gamma}{c^{,2}},({bfv}times{bfE}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4178.png"
 ALT="$\displaystyle =\gamma {\bf B} + \frac{1-\gamma}{v^{ 2}} ({\bf v}\cdot{\bf B}) {\bf v} - \frac{\gamma}{c^{ 2}} ({\bf v}\times {\bf E}),$">|; 

$key = q/displaystyleleft[frac{dg_m}{dr}right]_{r=r'_-}^{r=r'_+}=frac{1}{r'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img975.png"
 ALT="$\displaystyle \left[\frac{d g_m}{dr}\right]_{r=r'_-}^{r=r'_+} = \frac{1}{r'},$">|; 

$key = q/{rme}^{,{rmi},(k,S,x-omega,t)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2312.png"
 ALT="$ {\rm e}^{ {\rm i}  (k S x -\omega  t)}$">|; 

$key = q/displaystylefrac{dgamma}{dt}=gamma^{,3},frac{{bfu}cdotdot{bfu}}{c^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4074.png"
 ALT="$\displaystyle \frac{d\gamma}{dt} = \gamma^{ 3} \frac{{\bf u} \cdot\dot{\bf u}}{c^{ 2}}.$">|; 

$key = q/N_A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1234.png"
 ALT="$ N_A$">|; 

$key = q/{bfG}({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img949.png"
 ALT="$ {\bf G}({\bf r},{\bf r}')$">|; 

$key = q/rho({bfr}'),dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="$ \rho({\bf r}') dV'$">|; 

$key = q/displaystylerightarrow-c,{bfB}^{(M)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3141.png"
 ALT="$\displaystyle \rightarrow -c {\bf B}^{(M)},$">|; 

$key = q/displaystyleL_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3054.png"
 ALT="$\displaystyle L_z$">|; 

$key = q/k,r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3138.png"
 ALT="$ k r$">|; 

$key = q/dy;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3407.png"
 ALT="$ dy$">|; 

$key = q/5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3263.png"
 ALT="$ 5$">|; 

$key = q/displaystyleds^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3621.png"
 ALT="$\displaystyle ds^{ 2}$">|; 

$key = q/omega_0<omega<omega_1equiv(omega_0^{,2}+omega_p^{,2})^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1924.png"
 ALT="$ \omega_0&lt;\omega&lt;
\omega_1\equiv(\omega_0^{ 2} +\omega_p^{ 2})^{1/2}$">|; 

$key = q/displaystylefrac{1}{pi}int_0^{z_0(w^{,1slash2})}left[int_{u(z)}^wfrac{dv}{(w-v)^{1slash2},(v-u)^{1slash2}}right],dz.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2369.png"
 ALT="$\displaystyle \frac{1}{\pi} \int_0^{z_0(w^{ 1/2})} \left[ \int_{u(z)}^w \frac{dv} {(w-v)^{1/2} (v-u)^{1/2}}\right] dz.$">|; 

$key = q/displaystyle-{rmi},omega,epsilon_0,{bfE}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2823.png"
 ALT="$\displaystyle -{\rm i} \omega  \epsilon_0  {\bf E}_s$">|; 

$key = q/psi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2023.png"
 ALT="$ \psi$">|; 

$key = q/displaystyle=epsilon_0left[nabla(E^{,2}slash2)-(nablacdot{bfE}),{bfE}-({bfE}cdotnabla),{bfE}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$\displaystyle = \epsilon_0\left[\nabla(E^{ 2}/2) - (\nabla\cdot {\bf E}) {\bf E} - ({\bf E}\cdot\nabla) {\bf E}\right]$">|; 

$key = q/S_0=sintheta_I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2387.png"
 ALT="$ S_0= \sin\theta_I$">|; 

$key = q/f=x_i';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1396.png"
 ALT="$ f=x_i'$">|; 

$key = q/widetilde{G}({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="$ \widetilde{G}({\bf r},{\bf r}')$">|; 

$key = q/displaystyle=frac{psi_t,costheta_t}{v_2},cos(omega,t-n_1,k_0,sintheta_i,x-n_2,k_0,costheta_t,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2063.png"
 ALT="$\displaystyle =\frac{\psi_t \cos\theta_t}{v_2} \cos(\omega t-n_1 k_0 \sin\theta_i x-n_2 k_0 \cos\theta_t z),$">|; 

$key = q/w(x,h);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2553.png"
 ALT="$ w(x,h)$">|; 

$key = q/displaystyle=l,(l+1),Y_{lm},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3006.png"
 ALT="$\displaystyle = l (l+1) Y_{lm},$">|; 

$key = q/displaystylesigma_{rmThomson}=frac{8pi}{3}left(frac{e^{,2}}{4pi,epsilon_0,m_e,c^{,2}}right)^2=6.65times10^{-29},{rmm}^2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2740.png"
 ALT="$\displaystyle \sigma_{\rm Thomson} = \frac{8\pi}{3}\left( \frac{e^{ 2}}{4\pi \epsilon_0  m_e  c^{ 2}}\right)^2 = 6.65\times 10^{-29} {\rm m}^2.$">|; 

$key = q/displaystylefrac{partialE_x}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1990.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial t}$">|; 

$key = q/displaystyle=frac{4,alpha,beta}{(1+alpha,beta)^2}=1-R,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2122.png"
 ALT="$\displaystyle =\frac{4 \alpha \beta}{(1+\alpha \beta)^2} = 1-R,$">|; 

$key = q/v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$ v$">|; 

$key = q/t>xslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1846.png"
 ALT="$ t&gt; x/c$">|; 

$key = q/displaystylefrac{partialE_x}{partialz}-{rmi},k,S,E_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2302.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial z} -{\rm i}  k S  E_z$">|; 

$key = q/(hat{z},0)_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2513.png"
 ALT="$ (\hat{z},0)_s$">|; 

$key = q/Z=(epsilon_0,omegaslashsigma)^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1986.png"
 ALT="$ Z=(\epsilon_0 \omega/\sigma)^{1/2}$">|; 

$key = q/3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="$ 3$">|; 

$key = q/displaystylec,{bfB}_{lm}^{(E)}rightarrow-frac{k}{l},{bfL},frac{Y_{lm}}{r^{,l+1}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3129.png"
 ALT="$\displaystyle c {\bf B}_{lm}^{(E)} \rightarrow -\frac{k}{l}  {\bf L}  \frac{Y_{lm}}{r^{ l+1}},$">|; 

$key = q/displaystyleW=frac{epsilon_0}{2}intE^{,2},dV=frac{1}{2}sum_{i=1,N}q_i,phi_i+sum_{i=1,N}W_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$\displaystyle W = \frac{\epsilon_0}{2} \int E^{ 2}  dV = \frac{1}{2} \sum_{i=1,N} q_i  \phi_i + \sum_{i=1,N} W_i$">|; 

$key = q/{mitDelta}omega,{mitDelta}tsim1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4156.png"
 ALT="$ {\mit\Delta}\omega {\mit\Delta} t\sim 1$">|; 

$key = q/displaystyleE(z)=frac{E_0}{epsilon(z)}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1145.png"
 ALT="$\displaystyle E(z) = \frac{E_0}{\epsilon(z)}.$">|; 

$key = q/displaystylef(r,varphi)=g(r),{rme}^{,{rmi},m,varphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2856.png"
 ALT="$\displaystyle f(r,\varphi) = g(r)  {\rm e}^{ {\rm i} m \varphi}.$">|; 

$key = q/j_l(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3018.png"
 ALT="$ j_l(r)$">|; 

$key = q/displaystyleP=frac{e^{,2}}{6pi,epsilon_0,c^{,3}},gamma^{,6}left[dot{bfu}^{,2}-frac{({bfu}timesdot{bfu})^{,2}}{c^{,2}}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4075.png"
 ALT="$\displaystyle P= \frac{e^{ 2}}{6\pi \epsilon_0  c^{ 3}}  \gamma^{ 6} \left[ \dot{\bf u}^{ 2} - \frac{({\bf u}\times\dot{\bf u})^{ 2}}{c^{ 2}}\right].$">|; 

$key = q/displaystyledelta(z-z')=frac{2}{L}sum_{n=1,infty}sin(k_n,z),sin(k_n,z').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1002.png"
 ALT="$\displaystyle \delta(z-z') = \frac{2}{L}\sum_{n=1,\infty} \sin(k_n z) \sin(k_n z').$">|; 

$key = q/lambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3285.png"
 ALT="$ \lambda$">|; 

$key = q/displaystylephi({bfr})simeqphi_0({bfr})=frac{q_{0,0}^{,ast}}{epsilon_0},frac{Y_{0,0}(theta,varphi)}{r}=frac{Q}{4pi,epsilon_0,r}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="$\displaystyle \phi({\bf r})\simeq \phi_0({\bf r})=\frac{q_{0,0}^{ \ast}}{\epsilon_0} \frac{Y_{0,0}(\theta,\varphi)}{r} = \frac{Q}{4\pi \epsilon_0 r}.$">|; 

$key = q/-pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2283.png"
 ALT="$ -\pi$">|; 

$key = q/J^{,mu}=({bfj},,rho,c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3807.png"
 ALT="$ J^{ \mu} = ({\bf j},  \rho  c)$">|; 

$key = q/displaystylesigma_{rmabs}=frac{pi}{2,k^{,2}}sum_l(2,l+1)left[2-|alpha_pm(l)+1|^{,2}-|beta_pm(l)+1|^{,2}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3356.png"
 ALT="$\displaystyle \sigma_{\rm abs} = \frac{\pi}{2 k^{ 2}} \sum_l (2 l+1)\left[ 2 -\vert\alpha_\pm(l)+1\vert^{ 2} -\vert\beta_\pm(l)+1\vert^{ 2}\right].$">|; 

$key = q/{figure}{epsfysize{=4in{centerline{epsffile{Chapter06slashdisp.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="451" BORDER="0"
 SRC="|."$dir".q|img1930.png"
 ALT="\begin{figure}
\epsfysize =4in
\centerline{\epsffile{Chapter06/disp.eps}}
\end{figure}">|; 

$key = q/1.52;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2187.png"
 ALT="$ 1.52$">|; 

$key = q/displaystylefrac{dphi}{dz}simeqpmk,n,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2250.png"
 ALT="$\displaystyle \frac{d\phi}{dz} \simeq \pm k n,$">|; 

$key = q/displaystyle{bfr}cdotc,{bfB}_{lm}^{(M)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3084.png"
 ALT="$\displaystyle {\bf r}\cdot c {\bf B}_{lm}^{(M)}$">|; 

$key = q/A=pm1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3457.png"
 ALT="$ A=\pm 1$">|; 

$key = q/displaystylepartial_iE^{,i}=partial_iF^{,i4}+partial_4F^{,44}=frac{J^{,4}}{c,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3808.png"
 ALT="$\displaystyle \partial_i E^{ i} = \partial_i F^{ i4} +\partial_4 F^{ 44} = \frac{J^{ 4}}{c \epsilon_0}.$">|; 

$key = q/displaystyleg(z)=sqrt{z},J_1(sqrt{z}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1890.png"
 ALT="$\displaystyle g(z) = \sqrt{z}  J_1(\sqrt{z}).$">|; 

$key = q/F(S);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2385.png"
 ALT="$ F(S)$">|; 

$key = q/displaystyle=left[frac{(2,mu+mu_0),(mu-mu_0)}{(2,mu+mu_0),(mu+2,mu_0)-2,(a^{,3}slashb^{,3}),(mu-mu_0)^{,2}}right](b^{,3}-a^{,3}),B_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1566.png"
 ALT="$\displaystyle = \left[ \frac{(2 \mu+\mu_0) (\mu-\mu_0) } {(2 \mu+\mu_0) (\m...
...mu_0) - 2 (a^{ 3}/b^{ 3}) (\mu-\mu_0)^{ 2}}\right](b^{ 3}-a^{ 3})  B_0,$">|; 

$key = q/displaystyleu({bfr},t)=int!intv({bfr'},t'),G({bfr},{bfr'};t,t'),dV'dt'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle u({\bf r}, t) =\int\!\int v({\bf r'}, t')  G({\bf r}, {\bf r'}; t, t')  dV' dt'.$">|; 

$key = q/displaystyleint_S{bfE}cdotd{bfS}=frac{1}{epsilon_0}int_Vrho,dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$\displaystyle \int_S {\bf E} \cdot d{\bf S} = \frac{1}{\epsilon_0} \int_V \rho  dV,$">|; 

$key = q/displaystyle{bfE}_{rminduction}=frac{e}{4pi,epsilon_0}frac{1-u^{,2}slashc^{,2}}{s^{,3}},{bfr}_u.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4018.png"
 ALT="$\displaystyle {\bf E}_{\rm induction} = \frac{e}{4\pi \epsilon_0} \frac{1-u^{ 2}/c^{ 2}}{s^{ 3}} {\bf r}_u.$">|; 

$key = q/displaystyle=q^{-1slash4}(hat{z}),expleft(-{rmi},hint_a^{hat{z}}q^{,1slash2}(hat{z}),dhat{z}'right)left[1+{calO}left(frac{1}{h}right)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2475.png"
 ALT="$\displaystyle = q^{-1/4}(\hat{z})  \exp\left(-{\rm i} h\int_a^{\hat{z}} q^{ 1/2}(\hat{z}) d\hat{z}'\right)\left[1+{\cal O}\left(\frac{1}{h}\right)\right].$">|; 

$key = q/displaystyleleft(r^{,2},frac{d^2}{dr^{2}}+r,frac{d}{dr}+r^{,2},k_s^{,2}right)psi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2911.png"
 ALT="$\displaystyle \left(r^{ 2} \frac{d^2}{d r^{2}} + r \frac{d}{dr} + r^{ 2}  k_s^{ 2}\right) \psi = 0$">|; 

$key = q/{figure}{epsfysize{=2.75in{centerline{epsffile{Chapter06bslashfig08.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="703" HEIGHT="304" BORDER="0"
 SRC="|."$dir".q|img2123.png"
 ALT="\begin{figure}
\epsfysize =2.75in
\centerline{\epsffile{Chapter06b/fig08.eps}}
\end{figure}">|; 

$key = q/displaystylephi({bfr})=phi_S({bfr}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="$\displaystyle \phi({\bf r})= \phi_S({\bf r}),$">|; 

$key = q/displaystyleomega_{1pm}=-{rmi},rhopmsqrt{omega_0^{,2}+omega_p^{,2}-rho^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1818.png"
 ALT="$\displaystyle \omega_{1\pm} = -{\rm i} \rho \pm \sqrt{\omega_0^{ 2} +\omega_p^{ 2} -\rho^{ 2}}.$">|; 

$key = q/displaystyle{bfP}=N,{bfp}=N,alpha,epsilon_0,{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1232.png"
 ALT="$\displaystyle {\bf P} = N  {\bf p} = N \alpha  \epsilon_0  {\bf E},$">|; 

$key = q/displaystylephi_m=-frac{B_0}{mu_0},rcostheta+frac{alpha}{r^{,2}}costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1555.png"
 ALT="$\displaystyle \phi_m = - \frac{B_0}{\mu_0} r\cos\theta + \frac{\alpha}{r^{ 2}} \cos\theta$">|; 

$key = q/pmsigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1276.png"
 ALT="$ \pm\sigma$">|; 

$key = q/displaystyleleft(r^{,2},frac{d^{,2}}{dr^{,2}}+r,frac{d}{dr}-r^{,2},k_t^{,2}right)psi=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2915.png"
 ALT="$\displaystyle \left(r^{ 2} \frac{d^{ 2}}{d r^{ 2}} + r \frac{d}{dr} - r^{ 2}  k_t^{ 2}\right) \psi = 0.$">|; 

$key = q/n_n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2285.png"
 ALT="$ n_n$">|; 

$key = q/a<d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1287.png"
 ALT="$ a&lt;d$">|; 

$key = q/|a_E|^{,2}+|a_M|^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3161.png"
 ALT="$ \vert a_E\vert^{ 2}+\vert a_M\vert^{ 2}$">|; 

$key = q/{bfE}rightarrow{bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1129.png"
 ALT="$ {\bf E}\rightarrow
{\bf0}$">|; 

$key = q/w;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$ w$">|; 

$key = q/displaystyle{bfk}_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2035.png"
 ALT="$\displaystyle {\bf k}_r$">|; 

$key = q/displaystyle=frac{1}{4pi,epsilon_0}intleft([rho],nablaleft(R^{,-1}right)+frac{[partialrhoslashpartialt]}{R},nablat_rright)dV';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\displaystyle = \frac{1}{4\pi \epsilon_0}\int \left( [\rho]  \nabla\left(R^{ -1}\right) + \frac{[\partial\rho/\partial t]}{R}  \nabla t_r\right)dV'$">|; 

$key = q/1slashz^{,n+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2406.png"
 ALT="$ 1/z^{ n+1}$">|; 

$key = q/z>z_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2270.png"
 ALT="$ z&gt;z_0$">|; 

$key = q/displaystyle=frac{l,pi}{a},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2785.png"
 ALT="$\displaystyle = \frac{l \pi}{a},$">|; 

$key = q/displaystyleG({bfr},{bfr}';t,t')=G^{(+)}({bfr},{bfr}';t,t')=frac{delta(t'-[t-|{bfr}-{bfr'}|slashc])}{4pi,|{bfr}-{bfr}'|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle G ({\bf r}, {\bf r}'; t, t')= G^{(+)} ({\bf r}, {\bf r}'; t, t') ...
...ta(t'-[t - \vert{\bf r}- {\bf r'}\vert/c])}{4\pi  \vert{\bf r}-{\bf r}'\vert}.$">|; 

$key = q/omegaggsigmaslashepsilon_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2000.png"
 ALT="$ \omega\gg \sigma/\epsilon_0$">|; 

$key = q/4.95times10^{-2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3268.png"
 ALT="$ 4.95\times 10^{-2}$">|; 

$key = q/dx^{,2}+dy^{,2}+dz^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3433.png"
 ALT="$ dx^{ 2} + dy^{ 2} +dz^{ 2}$">|; 

$key = q/|q|,|{bfd}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="$ \vert q\vert \vert{\bf d}\vert$">|; 

$key = q/b>a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="$ b&gt;a$">|; 

$key = q/gamma^{,3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4158.png"
 ALT="$ \gamma^{ 3}$">|; 

$key = q/displaystylep_A-p_B=frac{epsilon_0}{2}left(1-frac{1}{epsilon}right)E^{,2}=frac{sigma^{,2}}{2,epsilon_0}left(1-frac{1}{epsilon}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1280.png"
 ALT="$\displaystyle p_A - p_B = \frac{\epsilon_0}{2}\left(1-\frac{1}{\epsilon}\right) E^{ 2} = \frac{\sigma^{ 2}}{2 \epsilon_0}\left(1-\frac{1}{\epsilon}\right),$">|; 

$key = q/rleqa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1162.png"
 ALT="$ r\leq a$">|; 

$key = q/psi({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$ \psi({\bf r},t)$">|; 

$key = q/r';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$ r'$">|; 

$key = q/displaystylepsi_i-psi_r=alpha,psi_t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2116.png"
 ALT="$\displaystyle \psi_i-\psi_r = \alpha \psi_t.$">|; 

$key = q/displaystyle{bfE}_parallel={rme}^{-{rmi},pislash4},sqrt{frac{mu_0,omega}{sigma}},{bfH}_paralleltimes{bfn}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2793.png"
 ALT="$\displaystyle {\bf E}_\parallel = {\rm e}^{-{\rm i} \pi/4}  \sqrt{\frac{\mu_0 \omega}{\sigma}}  {\bf H}_\parallel \times{\bf n}.$">|; 

$key = q/partialslashpartialt=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1307.png"
 ALT="$ \partial/\partial t =0 $">|; 

$key = q/displaystyle=y,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3400.png"
 ALT="$\displaystyle = y,$">|; 

$key = q/epsilon^{,ijk};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3760.png"
 ALT="$ \epsilon^{ ijk}$">|; 

$key = q/displaystylepartial_mu,A^{nusigma}equiv{A^{nusigma}}_{,mu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3666.png"
 ALT="$\displaystyle \partial_\mu  A^{\nu\sigma} \equiv {A^{\nu\sigma}}_{,\mu}.$">|; 

$key = q/n^{,2}_-(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1765.png"
 ALT="$ n^{ 2}_-(\omega)$">|; 

$key = q/{bfj}_t=sigma,{bfE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1679.png"
 ALT="$ {\bf j}_t
= \sigma  {\bf E}$">|; 

$key = q/sigma,[aslash(a+dslash2)]^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="$ \sigma [a/(a+d/2)]^{ 2}$">|; 

$key = q/displaystylep=frac{3}{2},epsilon_0,E_0^{,2},frac{epsilon-1}{epsilon+2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1260.png"
 ALT="$\displaystyle p = \frac{3}{2}  \epsilon_0  E_0^{ 2}  \frac{\epsilon-1}{\epsilon + 2}.$">|; 

$key = q/displaystylephantom{=}-frac{1}{4pi,epsilon_0}int_a^inftyint_0^piint_0^{2pi}frac{rphi'}{(r^{,2},r'^{,2}slasha^{,2}-2,r,r',cosgamma+a^{,2})^{1slash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="$\displaystyle \phantom{=}-\frac{1}{4\pi \epsilon_0}\int_a^\infty\int_0^\pi\int...
...ta' d\varphi'}{(r^{ 2} r'^{ 2}/a^{ 2}-2 r r' \cos\gamma+a^{ 2})^{1/2}}$">|; 

$key = q/xrightarrow+infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2548.png"
 ALT="$ x\rightarrow +\infty$">|; 

$key = q/displaystyleT^{,1'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3638.png"
 ALT="$\displaystyle T^{ 1'}$">|; 

$key = q/{bfB}_{rminc};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3329.png"
 ALT="$ {\bf B}_{\rm inc}$">|; 

$key = q/Q^{,mu}=({bfq},k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3659.png"
 ALT="$ Q^{ \mu} = ({\bf q}, k)$">|; 

$key = q/d{bfS}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1084.png"
 ALT="$ d{\bf S}_2$">|; 

$key = q/displaystyleG^{,ij}=frac{1}{2},(epsilon^{,ijk4},F_{k4}+epsilon^{,ij4k},F_{4k})=epsilon^{,ijk},F_{k4},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3820.png"
 ALT="$\displaystyle G^{ ij} = \frac{1}{2} (\epsilon^{ ijk4}  F_{k4} + \epsilon^{ ij4k}  F_{4k}) = \epsilon^{ ijk}  F_{k4},$">|; 

$key = q/C_{ij}=A_{ij}pmB_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3564.png"
 ALT="$ C_{ij} = A_{ij} \pm B_{ij}$">|; 

$key = q/displaystyleomegasqrt{frac{s}{xi}}={rme}^{,{rmi},u}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1862.png"
 ALT="$\displaystyle \omega \sqrt{\frac{s}{\xi}} = {\rm e}^{ {\rm i} u}.$">|; 

$key = q/displaystyle=mu_0,c,nablatimes{bfM}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3200.png"
 ALT="$\displaystyle = \mu_0  c  \nabla\times {\bf M}.$">|; 

$key = q/displaystylebeta_{l,m}=frac{1}{2,l+1},frac{a^{,2,l+1}}{r'^{,l+1}},Y_{l,m}^ast(theta',varphi').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="$\displaystyle \beta_{l,m}=\frac{1}{2 l+1} \frac{a^{ 2 l+1}}{r'^{ l+1}} Y_{l,m}^\ast(\theta',\varphi').$">|; 

$key = q/displaystyle=A,q^{-1slash2}(z)expleft(pm{rmi},kint^z!q(z'),dz'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2310.png"
 ALT="$\displaystyle = A  q^{-1/2}(z) \exp\left(\pm {\rm i} k\int^z\!q(z') dz'\right),$">|; 

$key = q/phi_S({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="$ \phi_S({\bf r})$">|; 

$key = q/displaystyleh(omega)=int_0^{z_0(omega)}frac{c}{u_z(omega,z)},dz.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2354.png"
 ALT="$\displaystyle h(\omega) = \int_0^{z_0(\omega)}\frac{c}{u_z(\omega,z)}  dz.$">|; 

$key = q/displaystyle{T^{,mu}}_nu=epsilon_0left[F^{,musigma},F_{sigmanu}+frac{1}{4},delta_nu^{,mu},(F^{,rhosigma},F_{rhosigma})right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3954.png"
 ALT="$\displaystyle {T^{ \mu}}_\nu = \epsilon_0\left[ F^{ \mu\sigma} F_{\sigma\nu} + \frac{1}{4}  \delta_\nu^{ \mu}  (F^{ \rho\sigma} F_{\rho\sigma})\right]$">|; 

$key = q/100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2130.png"
 ALT="$ 100$">|; 

$key = q/displaystyle{bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3733.png"
 ALT="$\displaystyle {\bf A}$">|; 

$key = q/R_mu=(-{bfr},c,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3655.png"
 ALT="$ R_\mu = (-{\bf r}, c t)$">|; 

$key = q/v<c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3515.png"
 ALT="$ v&lt;c$">|; 

$key = q/C^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3574.png"
 ALT="$ C^{ ij}$">|; 

$key = q/delta=2slash(Z_0,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2005.png"
 ALT="$ \delta = 2/(Z_0 \sigma)$">|; 

$key = q/delta_{ij}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$ \delta_{ij}=0$">|; 

$key = q/displaystylepmalpha=frac{3pi}{N},frac{5pi}{N},cdotsfrac{(2,N-3),2pi}{N},frac{(2,N+3),2pi}{N}cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2704.png"
 ALT="$\displaystyle \pm\alpha = \frac{3\pi}{N}, \frac{5\pi}{N}, \cdots \frac{(2 N-3) 2\pi}{N}, \frac{(2 N+3) 2\pi}{N}\cdots.$">|; 

$key = q/J_m'(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2872.png"
 ALT="$ J_m'(z)$">|; 

$key = q/displaystylec,B_x(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2262.png"
 ALT="$\displaystyle c B_x(z)$">|; 

$key = q/displaystyleR=-{rmi},expleft(2,{rmi},hint_a^{hat{z}_0}q^{,1slash2}(hat{z}'),dhat{z}'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2569.png"
 ALT="$\displaystyle R = -{\rm i}  \exp\left(2 {\rm i}  h\int_a^{\hat{z}_0} q^{ 1/2}(\hat{z}')  d\hat{z}'\right).$">|; 

$key = q/G_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2684.png"
 ALT="$ G_t$">|; 

$key = q/displaystyle=t.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3404.png"
 ALT="$\displaystyle = t.$">|; 

$key = q/displaystyle=psi_i,cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2137.png"
 ALT="$\displaystyle = \psi_i \cos(\omega t-n_1 k_0 \sin\theta_i x-n_1 k_0 \cos\theta_i z)$">|; 

$key = q/displaystyle=-{rmi},k,n^{,2},E_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2305.png"
 ALT="$\displaystyle = -{\rm i} k n^{ 2} E_z.$">|; 

$key = q/displaystyle{bfE}=E_0,cos(omega,t-k,z),{bfe}_x-E_0,sin(omega,t-k,z),{bfe}_y.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1711.png"
 ALT="$\displaystyle {\bf E} = E_0 \cos(\omega t-k z) {\bf e}_x-E_0 \sin(\omega t-k z) {\bf e}_y.$">|; 

$key = q/t=xslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1845.png"
 ALT="$ t=x/c$">|; 

$key = q/displaystylenabla^{,2}phi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1147.png"
 ALT="$\displaystyle \nabla^{ 2}\phi = 0$">|; 

$key = q/displaystyle1=-{rmi},(t+v+v,u,t).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2522.png"
 ALT="$\displaystyle 1 = -{\rm i} (t + v + v u t).$">|; 

$key = q/u=c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3518.png"
 ALT="$ u=c$">|; 

$key = q/displaystyle=-frac{1}{l+1}intr^{,l},Y_{lm}^{,ast},nablacdot({bfr}times{bfj}),dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3241.png"
 ALT="$\displaystyle = -\frac{1}{l+1} \int r^{ l} Y_{lm}^{ \ast}  \nabla\cdot({\bf r}\times{\bf j}) dV,$">|; 

$key = q/displaystylenabla=nabla'-frac{{bfr}}{s,c},frac{partial}{partialt'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4005.png"
 ALT="$\displaystyle \nabla = \nabla' - \frac{{\bf r}}{s c}  \frac{\partial}{\partial t'}.$">|; 

$key = q/mu,nu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3625.png"
 ALT="$ \mu, \nu$">|; 

$key = q/displaystylerho({bfr})=frac{1}{{rmi},omega}frac{dI(r)}{dr}left[frac{delta(costheta-1)-delta(costheta+1)}{2pi,r^{,2}}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3252.png"
 ALT="$\displaystyle \rho({\bf r}) = \frac{1}{{\rm i} \omega} \frac{d I(r)}{dr} \left[\frac{\delta(\cos\theta-1) -\delta(\cos\theta+1)}{2\pi  r^{ 2}}\right],$">|; 

$key = q/displaystyleV_0,cos(omega,t)=I_0,cos(omega,t),(R_{rmrad}+R_{rmload}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2657.png"
 ALT="$\displaystyle V_0  \cos(\omega  t) = I_0  \cos(\omega  t)  (R_{\rm rad} + R_{\rm load}),$">|; 

$key = q/displaystyle~~~~-frac{psi_r,costheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z+phi_r),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2139.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;-\frac{\psi_r \cos\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z+\phi_r),$">|; 

$key = q/displaystylesintheta_t=frac{n_1}{n_2},sintheta_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2131.png"
 ALT="$\displaystyle \sin\theta_t = \frac{n_1}{n_2} \sin\theta_i.$">|; 

$key = q/displaystylesigma_b=-({bfP}_2-{bfP}_1)cdot{bfn}_{21},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1125.png"
 ALT="$\displaystyle \sigma_b = - ({\bf P}_2-{\bf P}_1) \cdot {\bf n}_{21},$">|; 

$key = q/displaystyleq_{1,0}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$\displaystyle q_{1,0}^{ \ast}$">|; 

$key = q/displaystyle=left(frac{15}{32pi}right)^{1slash2}sin^2theta,{rme}^{+2,{rmi},varphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$\displaystyle =\left(\frac{15}{32\pi}\right)^{1/2}\sin^2\theta {\rm e}^{+2 {\rm i} \varphi}.$">|; 

$key = q/displaystyle{bfE}_{lm}^{(E)}rightarrow-nablaleft(frac{Y_{lm}}{r^{,l+1}}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3133.png"
 ALT="$\displaystyle {\bf E}_{lm}^{(E)} \rightarrow -\nabla\left(\frac{Y_{lm}}{r^{ l+1}}\right).$">|; 

$key = q/(a,hat{z});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2477.png"
 ALT="$ (a, \hat{z})$">|; 

$key = q/uslashcrightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3902.png"
 ALT="$ u/c\rightarrow 0$">|; 

$key = q/displaystyle=-{rmi},frac{partial}{partialvarphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3055.png"
 ALT="$\displaystyle = -{\rm i}  \frac{\partial}{\partial\varphi}.$">|; 

$key = q/displaystyle=E_y(z=0_-).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1102.png"
 ALT="$\displaystyle = E_y(z=0_-).$">|; 

$key = q/displaystyleint_Vnabla^{,2}left(frac{1}{|{bfr}-{bfr}'|}right)dV=-4pi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle \int_V \nabla^{ 2}\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right)dV =- 4\pi,$">|; 

$key = q/displaystyle{bfE}=E_0,cos(omega,t-k,z),{bfe}_x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1706.png"
 ALT="$\displaystyle {\bf E} = E_0 \cos(\omega t-k z) {\bf e}_x,$">|; 

$key = q/displaystylez,F''+(c-z),F'-a,F=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2428.png"
 ALT="$\displaystyle z  F'' +(c-z) F' - a  F = 0$">|; 

$key = q/displaystyle=L_x-{rmi},L_y={rme}^{-{rmi},varphi}left(-frac{partial}{partialtheta}+{rmi},cottheta,frac{partial}{partialvarphi}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3053.png"
 ALT="$\displaystyle = L_x - {\rm i} L_y={\rm e}^{-{\rm i} \varphi} \left(-\frac{\pa...
...\partial\theta} +{\rm i} \cot\theta  \frac{\partial}{\partial\varphi}\right),$">|; 

$key = q/displaystylefrac{D}{Dt}equivfrac{partial}{partialt}+{bfu}cdotnabla;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1220.png"
 ALT="$\displaystyle \frac{D}{Dt} \equiv \frac{\partial}{\partial t} + {\bf u}\cdot\nabla$">|; 

$key = q/1slashr^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="$ 1/r^{ 2}$">|; 

$key = q/displaystyle=frac{psi_t}{v_2},{rme}^{-n_2,k_0,sinhtheta_t,z},cos(omega,t-n_1,k_0,sintheta_i,x+phi_t),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2168.png"
 ALT="$\displaystyle = \frac{\psi_t}{v_2} {\rm e}^{-n_2 k_0 \sinh\theta_t z} \cos(\omega t-n_1 k_0 \sin\theta_i x+\phi_t),$">|; 

$key = q/displaystyleg_{mu'nu'},p_{musigma}^{,mu'},p_{nu}^{,nu'}+g_{mu'nu'},p_{sigma}^{,mu'},p_{numu}^{,nu'}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3679.png"
 ALT="$\displaystyle g_{\mu'\nu'} p_{\mu\sigma}^{ \mu'}   p_{\nu}^{ \nu'} + g_{\mu'\nu'} p_{\sigma}^{ \mu'}  p_{\nu\mu}^{ \nu'} = 0.$">|; 

$key = q/displaystylef_i=-frac{e}{gamma,c},(F_{i4},U^{,4}+F_{ij},U^{,j}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3931.png"
 ALT="$\displaystyle f_i = -\frac{e}{\gamma c}  (F_{i4}  U^{ 4} + F_{ij}  U^{ j}),$">|; 

$key = q/displaystyle[pm{rmi},({bfn}times{bfX}_{1,pm1}^{,ast})cdot{bfX}_{1,pm1}]=-frac{3pi}{8},costheta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3386.png"
 ALT="$\displaystyle [\pm{\rm i} ({\bf n}\times{\bf X}_{1,\pm 1}^{ \ast})\cdot {\bf X}_{1,\pm 1}] = -\frac{3\pi}{8} \cos\theta.$">|; 

$key = q/displaystylerightarrow(+{rmi})^{,l+1},frac{{rme}^{-{rmi},z}}{z}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3040.png"
 ALT="$\displaystyle \rightarrow (+{\rm i})^{ l+1}  \frac{ {\rm e}^{-{\rm i} z} }{z}.$">|; 

$key = q/partialrhoslashpartialt;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1215.png"
 ALT="$ \partial\rho/\partial t$">|; 

$key = q/r=b>a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="$ r=b&gt;a$">|; 

$key = q/epsilongg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1137.png"
 ALT="$ \epsilon\gg 1$">|; 

$key = q/displaystyleG_N({bfr},{bfr}')=G_N({bfr}',{bfr}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="$\displaystyle G_N({\bf r},{\bf r}')= G_N({\bf r}',{\bf r}).$">|; 

$key = q/displaystyleT^{,i4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3966.png"
 ALT="$\displaystyle T^{ i4}$">|; 

$key = q/{bfD}=D,{bfe}_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="$ {\bf D} = D {\bf e}_x$">|; 

$key = q/displaystyle=left(frac{5}{96pi}right)^{1slash2},(Q_{11}-2,{rmi},Q_{12}-Q_{22}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="$\displaystyle =\left(\frac{5}{96\pi}\right)^{1/2} (Q_{11}-2 {\rm i} Q_{12}-Q_{22}).$">|; 

$key = q/theta=pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1035.png"
 ALT="$ \theta=\pi/2$">|; 

$key = q/displaystylemu_0,{bfM}=3left(frac{mu-mu_0}{mu+2,mu_0}right){bfB}_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1537.png"
 ALT="$\displaystyle \mu_0 {\bf M} = 3\left(\frac{\mu-\mu_0}{\mu+2 \mu_0}\right) {\bf B}_0,$">|; 

$key = q/r>a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="$ r&gt;a$">|; 

$key = q/displaystyleint_SG_N({bfr},{bfr}'),dS'leftslashint_SdS'right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="$\displaystyle \int_S G_N({\bf r},{\bf r}') dS'\left/\int_S dS'\right.$">|; 

$key = q/displaystyle{bfE}({bf0})=frac{Q}{16,pi,epsilon_0,R^{,2}},sin^2alpha,{bfe}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1040.png"
 ALT="$\displaystyle {\bf E}({\bf0}) = \frac{Q}{16 \pi \epsilon_0 R^{ 2}} \sin^2\alpha {\bf e}_z.
$">|; 

$key = q/displaystyle=gammaleft(phi'+frac{u}{c},c,A_1'right)=frac{gamma,e}{4pi,epsilon_0,r'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3875.png"
 ALT="$\displaystyle = \gamma\left(\phi' + \frac{u }{c}  c A_1'\right)= \frac{\gamma  e} {4\pi \epsilon_0 r'},$">|; 

$key = q/{multline}int_Vleft[G_D({{bf{r},{{bf{r}'),nabla'^{,2}G_D({{bf{r}'',{{bf{r}')-G_D,{{bf{r}'),frac{partialG_D({{bf{r},{{bf{r}')}{partialn'}right]dS'.{multline};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="536" HEIGHT="96" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="\begin{multline}
\int_V\left[G_D({\bf r},{\bf r}') \nabla'^{ 2}G_D({\bf r}'',{...
...') \frac{\partial G_D({\bf r},{\bf r}')}{\partial n'}\right]dS'.
\end{multline}">|; 

$key = q/displaystyle{rme}^{,{rmi},{bfk}cdot{bfr}}=4pisum_{l=0,infty}{rmi}^l,j_l(k,r)sum_{m=-l,+l}Y_{lm}^{,ast}(theta,varphi),Y_{lm}(theta',varphi'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3296.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} {\bf k}\cdot{\bf r}}=4\pi \sum_{l=0,\infty} {...
...k r) \sum_{m=-l,+l}Y_{lm}^{ \ast}(\theta,\varphi)  Y_{lm}(\theta',\varphi'),$">|; 

$key = q/displaystylef(t)=frac{1}{pi}int_0^{infty}domegaint_0^Tf(t'),cos[omega,(t-t')],dt'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1780.png"
 ALT="$\displaystyle f(t) = \frac{1}{\pi}\int_0^{\infty} d\omega \int_0^Tf(t') \cos[\omega (t-t')] dt'.$">|; 

$key = q/displaystylesimeq-frac{1}{4pi,epsilon_0}intfrac{[partial{bfj}_perpslashpartialt]}{c^{,2},R},dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$\displaystyle \simeq -\frac{1}{4\pi \epsilon_0}\int\frac{[\partial {\bf j}_\perp /\partial t]}{c^{ 2}  R}  dV',$">|; 

$key = q/displaystyle{bfH}=-frac{{bfM}}{3},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1521.png"
 ALT="$\displaystyle {\bf H} = -\frac{{\bf M}}{3},$">|; 

$key = q/(n+1)!,{rme}^{-x}slashx^{,n+2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2417.png"
 ALT="$ (n+1)!  {\rm e}^{-x}/x^{ n+2}$">|; 

$key = q/displaystyley';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3399.png"
 ALT="$\displaystyle y'$">|; 

$key = q/(x_1,,y_1,,z_1,,t_1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3614.png"
 ALT="$ (x_1,  y_1,  z_1,  t_1)$">|; 

$key = q/B^{,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3596.png"
 ALT="$ B^{ i}$">|; 

$key = q/P_pm=P_xpm{rmi},P_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1732.png"
 ALT="$ P_\pm = P_x\pm{\rm i} P_y$">|; 

$key = q/{bfn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="$ {\bf n}$">|; 

$key = q/zll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1875.png"
 ALT="$ z\ll 1$">|; 

$key = q/displaystylemu_0,{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1534.png"
 ALT="$\displaystyle \mu_0 {\bf H}$">|; 

$key = q/displaystyle=-frac{l,(l+1)}{k},f_l(k,r),Y_{lm}(theta,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3101.png"
 ALT="$\displaystyle = -\frac{l (l+1)}{k} f_l(k r)  Y_{lm}(\theta,\varphi),$">|; 

$key = q/T^{,mu},dS_mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4046.png"
 ALT="$ T^{ \mu} dS_\mu$">|; 

$key = q/displaystylehat{z}=frac{z}{L},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2453.png"
 ALT="$\displaystyle \hat{z} = \frac{z}{L},$">|; 

$key = q/displaystylej_l(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3020.png"
 ALT="$\displaystyle j_l(z)$">|; 

$key = q/g^{,nu'sigma'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3685.png"
 ALT="$ g^{ \nu'\sigma'}$">|; 

$key = q/x^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3464.png"
 ALT="$ x^{ 2}$">|; 

$key = q/displaystyle{bff}=-e,({bfE}+{bfv}times{bfB}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1712.png"
 ALT="$\displaystyle {\bf f} = -e ({\bf E} + {\bf v}\times{\bf B}).$">|; 

$key = q/T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1978.png"
 ALT="$ T$">|; 

$key = q/displaystyledot{bfu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4116.png"
 ALT="$\displaystyle \dot{\bf u}$">|; 

$key = q/displaystyleepsilon_{iab},epsilon^{,ijk}=delta_a^{,j},delta_b^{,k}-delta_b^{,j},delta_a^{,k}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3785.png"
 ALT="$\displaystyle \epsilon_{iab}  \epsilon^{ ijk} = \delta_a^{ j}  \delta_b^{ k} - \delta_b^{ j} \delta_a^{ k}.$">|; 

$key = q/b=a+d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1573.png"
 ALT="$ b=a+d$">|; 

$key = q/displaystyle=oint{bfX}_{lm}^{,ast}cdot{bfE},d{mitOmega},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3315.png"
 ALT="$\displaystyle = \oint {\bf X}_{lm}^{ \ast}\cdot{\bf E} d {\mit \Omega},$">|; 

$key = q/nabla^{,2}phiequivnablacdotnablaphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$ \nabla^{ 2}\phi \equiv \nabla\cdot\nabla\phi$">|; 

$key = q/-{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1056.png"
 ALT="$ -{\bf r}$">|; 

$key = q/displaystylesigma=frac{mbox{totalre-radiatedpower}}{langleurangle}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2724.png"
 ALT="$\displaystyle \sigma = \frac{\mbox{total re-radiated power}}{\langle u \rangle}.$">|; 

$key = q/displaystyle={rme}^{,{rmi},pislash4},|q(x)|^{-1slash4},expleft(+hint_0^x|q(x')|^{,1slash2},dx'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2543.png"
 ALT="$\displaystyle = {\rm e}^{ {\rm i} \pi/4}  \vert q(x)\vert^{-1/4}  \exp\left( +h\int_0^x \vert q(x')\vert^{ 1/2} dx'\right),$">|; 

$key = q/+v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3483.png"
 ALT="$ +v$">|; 

$key = q/{bfD};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ {\bf D}$">|; 

$key = q/displaystyle=frac{psi_i,costheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2058.png"
 ALT="$\displaystyle = \frac{\psi_i \cos\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x-n_1 k_0 \cos\theta_i z)$">|; 

$key = q/displaystylephi'(hat{z},h)=pmq^{1slash2}(hat{z})+frac{rmi}{4,h}frac{q'(hat{z})}{q(hat{z})}+{calO}left(frac{1}{h^{,2}}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2467.png"
 ALT="$\displaystyle \phi'(\hat{z},h) = \pm q^{1/2}(\hat{z}) + \frac{\rm i}{4  h} \frac{q'(\hat{z})}{q(\hat{z})} + {\cal O}\left(\frac{1}{h^{ 2}}\right),$">|; 

$key = q/displaystylefrac{dP}{d{mitOmega}}=frac{{rmRe},({bfn}cdot{bfE}times{bfB}^{,ast}),r^{,2}}{2,mu_0}=frac{c,k^{,2},sin^2theta,|A|^{,2},r^{,2}}{2,mu_0},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2628.png"
 ALT="$\displaystyle \frac{dP}{d{\mit \Omega}} =\frac{{\rm Re} ({\bf n}\cdot {\bf E}\...
...mu_0} = \frac{c k^{ 2} \sin^2\theta \vert A\vert^{ 2} r^{ 2}}{2 \mu_0},$">|; 

$key = q/displaystyleP_2^{,+1}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="$\displaystyle P_2^{ +1}(x)$">|; 

$key = q/psi({bfr}')=widetilde{G}_N({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="$ \psi({\bf r}')=\widetilde{G}_N({\bf r},{\bf r}')$">|; 

$key = q/displaystyle=frac{1}{2},(E_++E_-),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1725.png"
 ALT="$\displaystyle = \frac{1}{2}  (E_+ + E_-),$">|; 

$key = q/D=epsilon_0,epsilon,E_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1134.png"
 ALT="$ D= \epsilon_0 \epsilon  E_1$">|; 

$key = q/displaystylex^{,1}=x,~~x^{,2}=y,~~x^{,3}=z,~~x^{,4}=c,t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3619.png"
 ALT="$\displaystyle x^{ 1}=x,&nbsp;&nbsp;x^{ 2}=y,&nbsp;&nbsp;x^{ 3}= z,&nbsp;&nbsp;x^{ 4}=c t,$">|; 

$key = q/cslashn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1747.png"
 ALT="$ c/n$">|; 

$key = q/xsimeqpmg_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1659.png"
 ALT="$ x\simeq \pm g_i$">|; 

$key = q/{bfg};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$ {\bf g}$">|; 

$key = q/r=a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="$ r=a$">|; 

$key = q/G_D({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="$ G_D({\bf r},{\bf r}')$">|; 

$key = q/displaystylesimeqE_0,cos[k,(c,t-z)],{rme}^{-zslashdelta},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2002.png"
 ALT="$\displaystyle \simeq E_0 \cos[k (c t-z)] {\rm e}^{-z/\delta},$">|; 

$key = q/displaystyleint_SG_N({bfr},{bfr}'),dS=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="$\displaystyle \int_S G_N({\bf r},{\bf r}') dS = 0,$">|; 

$key = q/displaystylelangle{calI}_zrangle_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2079.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle_i$">|; 

$key = q/h_l^{(2)}(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3044.png"
 ALT="$ h_l^{(2)}(k r)$">|; 

$key = q/displaystyleJ^{,mu}=rho_0,gamma(u),({bfu},,c)=({bfj},,rho,c),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3718.png"
 ALT="$\displaystyle J^{ \mu} = \rho_0 \gamma(u)  ({\bf u},  c) = ({\bf j},  \rho  c),$">|; 

$key = q/epsilon_1gg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2993.png"
 ALT="$ \epsilon_1\gg 1$">|; 

$key = q/displaystyle=3,(1-x^{,2}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$\displaystyle =3 (1-x^{ 2}).$">|; 

$key = q/displaystyle({bfL}Y_{1,0})^{,ast}cdot({bfL}Y_{3,0});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3282.png"
 ALT="$\displaystyle ({\bf L} Y_{1,0})^{ \ast}\cdot ({\bf L} Y_{3,0})$">|; 

$key = q/J_0'(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2875.png"
 ALT="$ J_0'(z)$">|; 

$key = q/beta^{,2}-R,beta+1=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4194.png"
 ALT="$ \beta^{ 2}-R \beta+1=0$">|; 

$key = q/displaystylef_1(xi,t)=frac{2pi}{tau}sqrt{frac{s}{xi}},J_1(2sqrt{xis}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1872.png"
 ALT="$\displaystyle f_1(\xi, t) = \frac{2\pi}{\tau} \sqrt{\frac{s}{\xi}}  J_1(2\sqrt{\xi s}).$">|; 

$key = q/displaystyleH_n^1(rho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle H_n^1(\rho)$">|; 

$key = q/L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="$ L$">|; 

$key = q/displaystyle{bfA}({bfr})=frac{mu_0,I}{4pi}frac{2}{k,r}frac{cos(picosthetaslash2)me}^{,(N-1),{rmi},alpha}right],{rme}^{,{rmi},(k,r-omega,t)},{bfe}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="478" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2693.png"
 ALT="$\displaystyle {\bf A}({\bf r}) =\frac{\mu_0 I}{4\pi} \frac{2 }{k r} \frac{\co...
... {\rm i} \alpha}\right]  {\rm e}^{ {\rm i} (k r-\omega  t)}  {\bf e}_z.$">|; 

$key = q/pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1709.png"
 ALT="$ \pi/2$">|; 

$key = q/displaystylenablatimes{bfH}={bf0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1473.png"
 ALT="$\displaystyle \nabla\times{\bf H} = {\bf0}.$">|; 

$key = q/E_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2241.png"
 ALT="$ E_y$">|; 

$key = q/{bfr}_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$ {\bf r}_3$">|; 

$key = q/Y_0(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2913.png"
 ALT="$ Y_0(k_s  r)$">|; 

$key = q/displaystyleomega_ssimeqomega_psqrt{frac{t_0}{2,(t-t_0)}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1935.png"
 ALT="$\displaystyle \omega_s \simeq \omega_p \sqrt{\frac{t_0}{2 (t-t_0)}}.$">|; 

$key = q/displaystyleA_varphi(r,theta)=frac{1}{2},mu_0,I,asum_{l=1,3,5,cdots}frac{P_l^1(0)}{l,(l+1)}left(frac{r_<^{,l}}{r_>^{,l+1}}right)P_l^1(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1343.png"
 ALT="$\displaystyle A_\varphi(r,\theta) =\frac{1}{2} \mu_0 I a \sum_{l=1,3,5,\cdot...
...P_l^1(0)}{l (l+1)}\left(\frac{r_&lt;^{ l}}{r_&gt;^{ l+1}}\right)P_l^1(\cos\theta),$">|; 

$key = q/displaystyleP_pm=frac{(N,e^{,2}slashm),E_pm}{omega_0^{,2}-omega^{,2}mpomega,{mitOmega}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1733.png"
 ALT="$\displaystyle P_\pm = \frac{(N  e^{ 2}/m) E_\pm}{\omega_0^{ 2} -\omega^{ 2} \mp \omega  {\mit\Omega}}.$">|; 

$key = q/a_E(5,0)slasha_E(1,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3266.png"
 ALT="$ a_E(5,0)/a_E(1,0)$">|; 

$key = q/displaystyleksimeq{rme}^{,{rmi},pislash4}sqrt{mu_0,sigma,omega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1693.png"
 ALT="$\displaystyle k \simeq {\rm e}^{ {\rm i} \pi/4} \sqrt{\mu_0  \sigma  \omega}.$">|; 

$key = q/displaystylek=n,frac{omega}{c}=frac{(omega^{,2}-omega_p^{,2})^{1slash2}}{c}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1703.png"
 ALT="$\displaystyle k = n \frac{\omega}{c} = \frac{(\omega^{ 2} - \omega_p^{ 2})^{1/2}}{c}.$">|; 

$key = q/displaystylefrac{1}{R^{,2}},frac{d}{dR}!left[R^{,2},frac{d}{dR}!left(frac{1}{R}right)right]=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle \frac{1}{R^{ 2}} \frac{d}{dR}\!\left[R^{ 2} \frac{d}{dR}\!\left(\frac{1}{R}\right)\right]=0$">|; 

$key = q/displaystyle{bfB}=nablatimes{bfA},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle {\bf B} = \nabla\times {\bf A},$">|; 

$key = q/k_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2880.png"
 ALT="$ k_c$">|; 

$key = q/displaystyleA_0=pilambdabar^{,2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2675.png"
 ALT="$\displaystyle A_0 = \pi \lambdabar^{ 2},$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{Chapter06slashcont4.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="398" BORDER="0"
 SRC="|."$dir".q|img1856.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{Chapter06/cont4.eps}}
\end{figure}">|; 

$key = q/S_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3710.png"
 ALT="$ S_0$">|; 

$key = q/displaystylelangleurangle=G_t,frac{P_{rmin}}{4pi,r^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2682.png"
 ALT="$\displaystyle \langle u\rangle = G_t \frac{P_{\rm in}}{4\pi  r^2}$">|; 

$key = q/displaystyleint_SG_3({bfr},{bfr}'),dS'leftslashint_SdS'right.=F({bfr})=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="$\displaystyle \int_S G_3({\bf r},{\bf r}') dS'\left/\int_S dS' \right.= F({\bf r}) = 0.$">|; 

$key = q/r',|a^{,2},{bfr}'slashr'^{,2}-{bfr}|=r,|a^{,2},{bfr}slashr^{,2}-{bfr}'|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="$ r' \vert a^{ 2} {\bf r}'/r'^{ 2}-{\bf r}\vert=
r \vert a^{ 2} {\bf r}/r^{ 2}-{\bf r}'\vert$">|; 

$key = q/phi_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="$ \phi_1$">|; 

$key = q/displaystylec,{bfB}({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3302.png"
 ALT="$\displaystyle c {\bf B}({\bf r})$">|; 

$key = q/displaystyle={rmi},omega,mu_0,{bfH},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2818.png"
 ALT="$\displaystyle = {\rm i} \omega  \mu_0 {\bf H},$">|; 

$key = q/displaystyle=-E_0,n^{,1slash2}(z)expleft(,{rmi},kint_0^z!n(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2273.png"
 ALT="$\displaystyle = -E_0 n^{ 1/2}(z) \exp\left( {\rm i} k \int_0^z\! n(z') dz'\right).$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{epsilon_0}int_VG_D({bfr},{bfr}'),rho({bfr}'),dV'-int_Sphi_S({bfr}'),frac{partialG_D({bfr},{bfr}')}{partialr'},dS'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="$\displaystyle \phi({\bf r})=-\frac{1}{\epsilon_0} \int_V G_D({\bf r},{\bf r}')\...
..._S \phi_S({\bf r}') \frac{\partial G_D({\bf r},{\bf r}')}{\partial r'}  d S'.$">|; 

$key = q/l=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="$ l=0$">|; 

$key = q/omegallomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2748.png"
 ALT="$ \omega\ll \omega_0$">|; 

$key = q/displaystyleoint({bfn}times{bfX}_{l'm'}^{,ast})cdot({bfn}times{bfX}_{lm}),d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3352.png"
 ALT="$\displaystyle \oint ({\bf n}\times{\bf X}_{l'm'}^{ \ast}) \cdot({\bf n}\times{\bf X}_{lm}) d{\mit \Omega}$">|; 

$key = q/dt';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3413.png"
 ALT="$ dt'$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}sum_{l=0,infty}left[r^{,l},p_{l}(r)+frac{q_{l}(r)}{r^{,l+1}}right]P_l(costheta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\sum_{l=0,\infty}\left[r^{ l} p_{l}(r)+ \frac{q_{l}(r)}{r^{ l+1}}\right]P_l(\cos\theta),$">|; 

$key = q/H_n^{1,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$ H_n^{1,2}$">|; 

$key = q/{bfk}_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2014.png"
 ALT="$ {\bf k}_i$">|; 

$key = q/theta_r=theta_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2055.png"
 ALT="$ \theta_r=\theta_i$">|; 

$key = q/sigma_m={bfn}cdot{bfM};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1489.png"
 ALT="$ \sigma_m = {\bf n}\cdot{\bf M}$">|; 

$key = q/nabla^{,2}F=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="$ \nabla^{ 2} F=0$">|; 

$key = q/displaystyle[rho({bfr}',t)]simeqrho({bfr}',t-rslashc),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\displaystyle [ \rho({\bf r}', t)] \simeq \rho({\bf r}', t - r/c),$">|; 

$key = q/mu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$ \mu_0$">|; 

$key = q/displaystyle=sum_{n=1,infty}B_{mn},sinh(j_{mn},Lslasha),J_m(j_{mn},rslasha).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="$\displaystyle = \sum_{n=1,\infty}B_{mn} \sinh(j_{mn} L/a) J_m(j_{mn} r/a).$">|; 

$key = q/displaystylea_pm(l,m),j_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3314.png"
 ALT="$\displaystyle a_\pm(l,m) j_l(k r)$">|; 

$key = q/displaystylenablacdot({bfE}times{bfH})equiv{bfH}cdot(nablatimes{bfE})-{bfE}cdot(nablatimes{bfH}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1585.png"
 ALT="$\displaystyle \nabla\cdot({\bf E}\times{\bf H}) \equiv {\bf H}\cdot(\nabla\times {\bf E}) - {\bf E}\cdot(\nabla\times{\bf H}).$">|; 

$key = q/displaystyleg_{mu'sigma'},g^{,nu'sigma'},p_{musigma}^{,mu'}=p_{musigma}^{,nu'}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3686.png"
 ALT="$\displaystyle g_{\mu'\sigma'} g^{ \nu'\sigma'} p_{\mu\sigma}^{ \mu'} = p_{\mu\sigma}^{ \nu'} =0.$">|; 

$key = q/B_{ik};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3775.png"
 ALT="$ B_{ik}$">|; 

$key = q/displaystylenabla^{,2}phi=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="$\displaystyle \nabla^{ 2}\phi = 0,$">|; 

$key = q/displaystyle{bfH}=-nablaphi_m,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1474.png"
 ALT="$\displaystyle {\bf H} = - \nabla\phi_m,$">|; 

$key = q/q(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2528.png"
 ALT="$ q(x)$">|; 

$key = q/J_0(z)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2970.png"
 ALT="$ J_0(z)=0$">|; 

$key = q/dz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3408.png"
 ALT="$ dz$">|; 

$key = q/displaystylesigma=sigma_{rmThomson},frac{omega^{,4}}{(omega_0^{,2}-omega^{,2})^{,2}+(gamma_0,omega)^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2745.png"
 ALT="$\displaystyle \sigma = \sigma_{\rm Thomson}  \frac{\omega^{ 4}}{(\omega_0^{ 2}-\omega^{ 2})^{ 2} + (\gamma_0 \omega)^{ 2}}.$">|; 

$key = q/dP_{rmsc}slashd{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3340.png"
 ALT="$ d P_{\rm sc}/d{\mit \Omega}$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}int_Vfrac{rho({bfr}')}{|{bfr}-{bfr},epsilon_0}int_{skew{3}bar{V}}frac{rho({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int_V \frac{\rho({\bf ...
...}\int_{\skew{3}\bar{V}} \frac{\rho({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dV'.$">|; 

$key = q/displaystyle{bfB}=frac{mu_0}{4pi}intleft(frac{[{bfj}]times{bfR}}{R^{,3}}+frac{[partial{bfj}slashpartialt]times{bfR}}{c,R^{,2}}right)dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle {\bf B} = \frac{\mu_0}{4\pi} \int \left( \frac{ [{\bf j}]\times {...
...+ \frac{ [\partial {\bf j}/\partial t]\times {\bf R} } {c R^{ 2}} \right)dV'.$">|; 

$key = q/displaystyle~~~~-frac{psi_r,costheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2059.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;-\frac{\psi_r \cos\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z),$">|; 

$key = q/55.5^circ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2185.png"
 ALT="$ 55.5^\circ$">|; 

$key = q/displaystylefrac{dphi}{dz};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2321.png"
 ALT="$\displaystyle \frac{d\phi}{dz}$">|; 

$key = q/displaystyle|{bfr}-{bfr}'|simeqr-{bfn}cdot{bfr}'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2610.png"
 ALT="$\displaystyle \vert{\bf r} - {\bf r}'\vert \simeq r - {\bf n}\cdot{\bf r}'.$">|; 

$key = q/displaystyle=frac{x-v,t}{(1-v^{,2}slashc^{,2})^{1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3473.png"
 ALT="$\displaystyle = \frac{x-v t}{(1-v^{ 2}/c^{ 2})^{1/2}},$">|; 

$key = q/alpharightarrowpi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1043.png"
 ALT="$ \alpha\rightarrow\pi$">|; 

$key = q/langlephirangle_S=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="$ \langle\phi\rangle_S = 0$">|; 

$key = q/displaystyle(nabla^{,2}+k^{,2}),{bfA}=-mu_0,{bfj},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2597.png"
 ALT="$\displaystyle (\nabla^{ 2}+k^{ 2}) {\bf A} = - \mu_0  {\bf j},$">|; 

$key = q/A_mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4053.png"
 ALT="$ A_\mu$">|; 

$key = q/displaystylephi(r,theta,z)=sum_{m=0,infty}int_0^infty{rme}^{-k,z},J_m(k,r),left[A_m(k),cos(m,theta)+B_m(k),sin(m,theta)right],dk.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img919.png"
 ALT="$\displaystyle \phi(r,\theta,z) = \sum_{m=0,\infty} \int_0^\infty {\rm e}^{-k z} J_m(k r) \left[A_m(k) \cos (m \theta)+B_m(k) \sin(m \theta)\right] dk.$">|; 

$key = q/R_1=sqrt{r^{,2}+(d-z)^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1108.png"
 ALT="$ R_1= \sqrt{r^{ 2}+(d-z)^{ 2}}$">|; 

$key = q/displaystyle={rmi},A,frac{k_g}{k_t},K_1(k_t,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2986.png"
 ALT="$\displaystyle = {\rm i} A  \frac{k_g}{k_t}  K_1(k_t  r)$">|; 

$key = q/displaystyleG_3({bfr},{bfr}')=F({bfr}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="$\displaystyle G_3({\bf r},{\bf r}')=F({\bf r}),$">|; 

$key = q/I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$ I$">|; 

$key = q/alpha(l);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3337.png"
 ALT="$ \alpha(l)$">|; 

$key = q/displaystylenabla^{,2}phi({bfr})=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="$\displaystyle \nabla^{ 2} \phi({\bf r}) = 0,$">|; 

$key = q/displaystyle=leftlgroup{array}{cccc}+gamma&0&0&+gamma,beta0&1&0&00&0&1&0+gamma,beta&0&0&+gamma{array}rightrgroup.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="94" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3650.png"
 ALT="$\displaystyle = \left\lgroup \begin{array}{cccc} +\gamma &amp; 0 &amp; 0 &amp; +\gamma \be...
... \ 0 &amp; 0 &amp; 1 &amp; 0 \ +\gamma \beta &amp; 0 &amp; 0 &amp; +\gamma \end{array}\right\rgroup.$">|; 

$key = q/omegasimeqomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2746.png"
 ALT="$ \omega\simeq \omega_0$">|; 

$key = q/n_1=1.33;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ n_1=1.33$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}=frac{e^{,2},dot{u}^{,2}}{16pi^2,epsilon_0,c^{,3}}frac{sin^2theta}{[1-(uslashc),costheta]^5}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4098.png"
 ALT="$\displaystyle \frac{d P(t')}{d{\mit\Omega}} = \frac{e^{ 2} \dot{u}^{ 2}}{16\pi^2  \epsilon_0  c^{ 3}} \frac{\sin^2\theta}{[1-(u/c) \cos\theta]^5}.$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}simeqfrac{e^{,2},dot{u}^{,2}}{2pi^2epsilon_{,6},frac{[1-(gamma,theta)^{,2}]^{,2}}{[1+(gamma,theta)^{,2}]^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4136.png"
 ALT="$\displaystyle \frac{dP(t')}{d{\mit\Omega}} \simeq \frac{e^{ 2}  \dot{u}^{ 2}...
...,6} \frac{[1-(\gamma \theta)^{ 2}]^{ 2}}{[1+(\gamma \theta)^{ 2}]^{ 5}}.$">|; 

$key = q/displaystyle{bfP}=epsilon_0,(epsilon-1),E_1,{bfe}_z=3,epsilon_0left(frac{epsilon-1}{epsilon+2}right),E_0,{bfe}_z.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1185.png"
 ALT="$\displaystyle {\bf P} = \epsilon_0  (\epsilon -1) E_1 {\bf e}_z = 3 \epsilon_0 \left(\frac{\epsilon-1}{\epsilon+2}\right) E_0 {\bf e}_z.$">|; 

$key = q/(N-2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2705.png"
 ALT="$ (N-2)$">|; 

$key = q/p=k_n,r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img935.png"
 ALT="$ p=k_n r$">|; 

$key = q/displaystylebeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2072.png"
 ALT="$\displaystyle \beta$">|; 

$key = q/omega_p(z)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2583.png"
 ALT="$ \omega_p(z)=0$">|; 

$key = q/displaystyle=frac{dz'}{dt'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3496.png"
 ALT="$\displaystyle = \frac{dz'}{dt'}.$">|; 

$key = q/displaystyleD_x(x,z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2057.png"
 ALT="$\displaystyle D_x(x,z,t)$">|; 

$key = q/displaystyle=y(x=-g_i)=frac{n_i^{,2}}{a^{,2}}+frac{1}{2,g_i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1663.png"
 ALT="$\displaystyle = y(x=-g_i) = \frac{n_i^{ 2}}{a^{ 2}} + \frac{1}{2 g_i}.$">|; 

$key = q/G^{(+)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$ G^{(+)}$">|; 

$key = q/{rmTE}_{mn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2996.png"
 ALT="$ {\rm TE}_{mn}$">|; 

$key = q/displaystyle1=-{rmi},u.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2516.png"
 ALT="$\displaystyle 1 = -{\rm i}  u.$">|; 

$key = q/dt'^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3436.png"
 ALT="$ dt'^{ 2}$">|; 

$key = q/displaystyle=-frac{q}{4pi,a},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="$\displaystyle = -\frac{q}{4\pi a},$">|; 

$key = q/displaystyleleft(frac{1}{c^{,2}},frac{partial^{,2}}{partialt^{,2}}-nabla^{,2}right){bfA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle \left(\frac{1}{c^{ 2}} \frac{\partial^{ 2}}{\partial t^{ 2}}-\nabla^{ 2} \right) {\bf A}$">|; 

$key = q/B_0stackrel{_{normalsize>}}{_{normalsizesim}}1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1579.png"
 ALT="$ B_0\stackrel {_{\normalsize &gt;}}{_{\normalsize\sim}}1$">|; 

$key = q/alpharightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1041.png"
 ALT="$ \alpha\rightarrow 0$">|; 

$key = q/displaystyle=frac{V}{2}left[frac{a^{-l}-(-1)^l,b^{-l}}{a^{-2,l-1}-b^{-2,l-1}}right]left[P_{l-1}(0)-P_{l+1}(0)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1034.png"
 ALT="$\displaystyle = \frac{V}{2}\left[\frac{a^{-l}-(-1)^l b^{-l}}{a^{-2 l-1}-b^{-2 l-1}}\right]\left[P_{l-1}(0)-P_{l+1}(0)\right].$">|; 

$key = q/displaystyleA_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1323.png"
 ALT="$\displaystyle A_x$">|; 

$key = q/displaystyle={rmi},frac{omega,epsilon_0,epsilon_1}{k_s^{,2}}frac{partialE_z}{partialr},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2934.png"
 ALT="$\displaystyle = {\rm i}  \frac{\omega \epsilon_0 \epsilon_1}{k_s^{ 2}} \frac{\partial E_z}{\partial r},$">|; 

$key = q/displaystyle=frac{J^{,nu}}{epsilon_0,c},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4208.png"
 ALT="$\displaystyle = \frac{J^{ \nu}}{\epsilon_0 c},$">|; 

$key = q/displaystyle{bfE}=-frac{e,gamma}{4pi,epsilon_0,{r'}^{,3}}{bfr}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3897.png"
 ALT="$\displaystyle {\bf E} = -\frac{e \gamma}{4\pi \epsilon_0 {r'}^{ 3}} {\bf r}.$">|; 

$key = q/psi_{i,r,t}rightarrow-v,psi_{i,r,t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2100.png"
 ALT="$ \psi_{i,r,t}\rightarrow -v \psi_{i,r,t}$">|; 

$key = q/j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$ j$">|; 

$key = q/displaystylebeta,b+frac{gamma}{b^{,2}}=-frac{B_0}{mu_0},b+frac{alpha}{b^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1562.png"
 ALT="$\displaystyle \beta  b + \frac{\gamma}{b^{ 2}} = - \frac{B_0}{\mu_0}  b + \frac{\alpha}{b^{ 2}}.$">|; 

$key = q/displaystyle{bfB}_{rmradiation};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4032.png"
 ALT="$\displaystyle {\bf B}_{\rm radiation}$">|; 

$key = q/displaystylex_0=2,Sint_0^{z_0(S)}frac{dz}{sqrt{n^{,2}(z)-S^{,2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2398.png"
 ALT="$\displaystyle x_0 = 2  S\int_0^{z_0(S)} \frac{dz}{\sqrt{n^{ 2}(z)-S^{ 2}} }$">|; 

$key = q/u^{,i}=u_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3635.png"
 ALT="$ u^{ i}=u_i$">|; 

$key = q/Q=(4pislash3),a^{,3},rho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="$ Q = (4\pi/3) a^{ 3}  \rho$">|; 

$key = q/displaystyleleft.frac{partialG_D}{partialr'}right|_{r'=a}=-sum_{l=0,infty}sum_{-{,l-1}}{r^{,l+1}},Y_{l,m}^ast(theta',varphi'),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="$\displaystyle \left.\frac{\partial G_D}{\partial r'}\right\vert _{r'=a} = -\sum...
...a^{ l-1}}{r^{ l+1}} Y_{l,m}^\ast(\theta',\varphi') Y_{l,m}(\theta,\varphi).$">|; 

$key = q/displaystylef_1(xi,t)=frac{1}{tau}oint_Sexpleft[,-{rmi},sqrt{xi,s}left(frac{1}{o{xi}{s}}+omegasqrt{frac{s}{xi}}right)right]frac{domega}{omega^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1861.png"
 ALT="$\displaystyle f_1(\xi,t) = \frac{1}{\tau} \oint_S \exp\left[ -{\rm i}  \sqrt{...
...xi}{s}}+\omega \sqrt{\frac{s}{\xi}}\right)\right] \frac{d\omega}{\omega^{ 2}}.$">|; 

$key = q/displaystyle-epsilon_0,frac{partial{bfE}}{partialt}times{bfB}-epsilon_0,{bfE}timtimes{bfE})+frac{{bfB}times(nablatimes{bfB})}{mu_0}+{bfj}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle -\epsilon_0 \frac{\partial {\bf E}}{\partial t}\times {\bf B}-\e...
... E})+\frac{{\bf B}\times(\nabla\times {\bf B})}{\mu_0} + {\bf j}\times {\bf B}.$">|; 

$key = q/(5,cos^2theta-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3287.png"
 ALT="$ (5 \cos^2\theta -1)$">|; 

$key = q/{bfm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1418.png"
 ALT="$ {\bf m}$">|; 

$key = q/displaystyleepsilon_0=8.8542times10^{-12},{rmC^{,2},N^{,-1},m^{-2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \epsilon_0 = 8.8542\times 10^{-12} {\rm C^{ 2} N^{ -1} m^{-2}}$">|; 

$key = q/displaystyle{bfr}cdot{bfE}_{lm}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3100.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf E}_{lm}^{(E)}$">|; 

$key = q/displaystyle{bfE}({bfr})=-nablaleft(frac{q}{4pi,epsilon_0},frac{1}{|{bfr}-{bfr}'|}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$\displaystyle {\bf E}({\bf r}) = -\nabla\left(\frac{q}{4\pi \epsilon_0} \frac{1}{\vert{\bf r}-{\bf r}'\vert}\right).$">|; 

$key = q/|z|gg1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2441.png"
 ALT="$ \vert z\vert\gg 1$">|; 

$key = q/c,tauslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2349.png"
 ALT="$ c \tau/2$">|; 

$key = q/{figure}{epsfysize{=4in{centerline{epsffile{Chapter08slashcross.eps}}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="485" HEIGHT="456" BORDER="0"
 SRC="|."$dir".q|img2963.png"
 ALT="\begin{figure}
\epsfysize =4in
\centerline{\epsffile{Chapter08/cross.eps}}\end{figure}">|; 

$key = q/|{bfr}-{bfr}'|simeqr'-{bfn}cdot{bfr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3291.png"
 ALT="$ \vert{\bf r} - {\bf r}'\vert\simeq
r'-{\bf n}\cdot{\bf r}$">|; 

$key = q/t=t';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$ t=t'$">|; 

$key = q/costheta={bfe}cdot{bfn};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2728.png"
 ALT="$ \cos\theta ={\bf e}\cdot{\bf n}$">|; 

$key = q/u'=c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3517.png"
 ALT="$ u'=c$">|; 

$key = q/displaystylenabla'^{,2}widetilde{G}_N({bfr},{bfr}')=delta({bfr}-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="$\displaystyle \nabla'^{ 2}\widetilde{G}_N({\bf r},{\bf r}')=\delta({\bf r}-{\bf r}')$">|; 

$key = q/displaystylephi=left{{array}{lll}sigma,aslashepsilon_0&mbox{hspace{0.5cm}}&r<a[0.5ex](sigma,aslashepsilon_0),(aslashr)&&r>a{array}right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="$\displaystyle \phi = \left\{ \begin{array}{lll} \sigma a/\epsilon_0&amp;\mbox{\hspace{0.5cm}}&amp; r&lt;a\ [0.5ex] (\sigma a/\epsilon_0) (a/r)&amp;&amp;r&gt;a \end{array}\right..$">|; 

$key = q/displaystylephi(r,theta,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="$\displaystyle \phi(r,\theta,0)$">|; 

$key = q/displaystylefrac{partial^{,2}B_y}{partialz^{,2}}-frac{1}{n^{,2}}frac{dn^{,2}}{dz}frac{partialB_y}{partialz}+k^{,2},q^{,2},B_y=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2318.png"
 ALT="$\displaystyle \frac{\partial^{ 2} B_y}{\partial z^{ 2}} - \frac{1}{n^{ 2}} \frac{d n^{ 2}}{dz} \frac{\partial B_y}{\partial z} + k^{ 2}  q^{ 2}  B_y = 0.$">|; 

$key = q/displaystylenablacdot({bfE},phi)equivphi,nablacdot{bfE}+{bfE}cdotnablaphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="$\displaystyle \nabla \cdot({\bf E}  \phi) \equiv \phi \nabla\cdot{\bf E} +{\bf E} \cdot \nabla\phi,$">|; 

$key = q/displaystyleE^{,ij}=E_{ij}=left({array}{ccc}0&E_z&-E_y[0.5ex]-E_z&0&E_x[0.5ex]E_y&-E_x&0{array}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="81" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3816.png"
 ALT="$\displaystyle E^{ ij}=E_{ij} = \left(\begin{array}{ccc} 0&amp; E_z &amp; -E_y\ [0.5ex] -E_z &amp; 0 &amp; E_x \ [0.5ex] E_y &amp; -E_x &amp; 0 \end{array} \right),$">|; 

$key = q/{bfB}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$ {\bf B}({\bf r},t)$">|; 

$key = q/displaystyle=epsilon_0,{bfn}cdotnablaphi=-epsilon_0,{bfn}cdot{bfE},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="$\displaystyle = \epsilon_0 {\bf n}\cdot\nabla\phi =-\epsilon_0 {\bf n}\cdot{\bf E},$">|; 

$key = q/g^{,ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3591.png"
 ALT="$ g^{ ij}$">|; 

$key = q/J_1(z)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1892.png"
 ALT="$ J_1(z)=0$">|; 

$key = q/tanhvarphi=vslashc;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4162.png"
 ALT="$ \tanh\varphi = v/c$">|; 

$key = q/D({bfr});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="$ D({\bf r})$">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$ N$">|; 

$key = q/displaystylefrac{d^{,2}E_y}{dz^{,2}}+k^{,2},n^{,2},E_y=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2240.png"
 ALT="$\displaystyle \frac{d^{ 2} E_y}{d z^{ 2}} + k^{ 2}  n^{ 2} E_y = 0.$">|; 

$key = q/displaystyle=frac{d{mbox{boldmathrho}}}{dt'}=u,(-sinphi,,cosphi,,0),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4115.png"
 ALT="$\displaystyle =\frac{d{\mbox{\boldmath$\rho$}}}{dt'}= u (-\sin\phi,  \cos\phi,  0),$">|; 

$key = q/q'';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1111.png"
 ALT="$ q''$">|; 

$key = q/{bfE}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="$ {\bf E}_2$">|; 

$key = q/theta,varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3093.png"
 ALT="$ \theta, \varphi$">|; 

$key = q/displaystyleG_D({bfr}',{bfr})=G_D({bfr},{bfr}').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="$\displaystyle G_D({\bf r}',{\bf r})=G_D({\bf r},{\bf r}').$">|; 

$key = q/{bfM}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1540.png"
 ALT="$ {\bf M}_s$">|; 

$key = q/displaystylerightarrow{bfA}-nablapsi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3734.png"
 ALT="$\displaystyle \rightarrow {\bf A} - \nabla\psi,$">|; 

$key = q/B_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1802.png"
 ALT="$ B_3$">|; 

$key = q/displaystylefrac{dD(z)}{dz}=epsilon_0,frac{d[epsilon(z),E(z)]}{dz}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1143.png"
 ALT="$\displaystyle \frac{d D(z)}{dz} = \epsilon_0  \frac{d [\epsilon(z)  E(z)]}{d z} = 0.$">|; 

$key = q/displaystyle=-{rmi},frac{k_g}{k_s},J_1(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2984.png"
 ALT="$\displaystyle = -{\rm i}  \frac{k_g}{k_s}  J_1(k_s  r)$">|; 

$key = q/displaystylen(omega)=frac{c,k}{omega}=sqrt{frac{omega_0^{~2}+omega_p^{,2}-omega^{,2}}{omega_0^{,2}-omega^{,2}}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1921.png"
 ALT="$\displaystyle n(\omega) =\frac{c  k}{\omega} = \sqrt{\frac{\omega_0^{&nbsp;2} + \omega_p^{ 2}-\omega^{ 2}}{\omega_0^{ 2}-\omega^{ 2}}}.$">|; 

$key = q/h^{(1)}_l(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3031.png"
 ALT="$ h^{(1)}_l(z)$">|; 

$key = q/displaystyleY_{2,+2}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="$\displaystyle Y_{2,+2}(\theta,\varphi)$">|; 

$key = q/displaystyle=-{rmi},k,n^{,2},E_x,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2303.png"
 ALT="$\displaystyle =-{\rm i} k n^{ 2} E_x,$">|; 

$key = q/displaystyle{mitDelta}t'=gamma,({mitDelta}t-v,{mitDelta}xslashc^{,2})=gamma,{mitDelta}t,(1-v,Uslashc^2).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3522.png"
 ALT="$\displaystyle {\mit\Delta} t' = \gamma ({\mit\Delta} t - v {\mit\Delta} x/c^{ 2}) = \gamma {\mit\Delta} t  (1-v  U/c^2).$">|; 

$key = q/displaystylet'=C,x+D,t,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3463.png"
 ALT="$\displaystyle t' = C  x + D  t,$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi}sum_{l=0,infty}frac{r_<^{,l}}{r_>^{,l+1}},P_l(costheta'),P_l(costheta).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\frac{1}{4\pi} \sum_{l=0,\infty}\frac{r_&lt;^{ l}}{r_&gt;^{ l+1}} P_l(\cos\theta') P_l(\cos\theta).$">|; 

$key = q/(x,,y,,z,,c,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3746.png"
 ALT="$ (x, y, z, c t)$">|; 

$key = q/(0,,0,,0,,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3745.png"
 ALT="$ (0, 0, 0, 0)$">|; 

$key = q/cos^2theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4130.png"
 ALT="$ \cos^2\theta$">|; 

$key = q/displaystyleH_theta(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2981.png"
 ALT="$\displaystyle H_\theta(r)$">|; 

$key = q/displaystyleE_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1724.png"
 ALT="$\displaystyle E_x$">|; 

$key = q/displaystyleint_{p_1}^{p_2}frac{dp}{rho_m}=frac{epsilon_0}{2}left(left[E^{,2}fraon}{drho_m}right]_2-left[E^{,2}frac{depsilon}{drho_m}right]_1right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1255.png"
 ALT="$\displaystyle \int_{p_1}^{p_2} \frac{dp}{\rho_m} =\frac{\epsilon_0}{2} \left(\l...
...on}{d\rho_m}\right]_2 - \left[E^{ 2}\frac{d\epsilon}{d\rho_m}\right]_1\right),$">|; 

$key = q/displaystylef(x,t)=frac{1}{tau}int_C{rme}^{,{rmi},([k-omegaslashc],x-omega,s)}frac{domega}{omega^{,2}-(2pislashtau)^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1853.png"
 ALT="$\displaystyle f(x,t) = \frac{1}{\tau}\int_C {\rm e}^{ {\rm i} ([k-\omega/c] x-\omega  s)} \frac{d\omega}{\omega^{ 2} -(2\pi/\tau)^{ 2}}.$">|; 

$key = q/displaystylef_mu=c^{,-1},F_{munu},J^{,nu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3942.png"
 ALT="$\displaystyle f_\mu = c^{ -1}  F_{\mu\nu}  J^{ \nu}$">|; 

$key = q/displaystylenabla^{,2}G_3({bfr},{bfr}')=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$\displaystyle \nabla^{ 2}G_3({\bf r},{\bf r}') = 0,$">|; 

$key = q/displaystyle=j_l(z)-{rmi},y_l(z).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3029.png"
 ALT="$\displaystyle = j_l(z)- {\rm i} y_l(z).$">|; 

$key = q/j_{0l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$ j_{0l}$">|; 

$key = q/displaystyle=-F^{,ji}=-c,B^{,ij},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3804.png"
 ALT="$\displaystyle = -F^{ ji} = -c B^{ ij},$">|; 

$key = q/displaystyleW=frac{1}{2},{bfH}cdot{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1593.png"
 ALT="$\displaystyle W= \frac{1}{2} {\bf H}\cdot{\bf B}.$">|; 

$key = q/dz';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3412.png"
 ALT="$ dz'$">|; 

$key = q/j=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="$ j=1$">|; 

$key = q/R_2=sqrt{r^{,2}+(d+z)^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1109.png"
 ALT="$ R_2= \sqrt{r^{ 2}+(d+z)^{ 2}}$">|; 

$key = q/displaystyleJ_m=({bfj}_m,,rho_m,c),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4205.png"
 ALT="$\displaystyle J_m = ({\bf j}_m, \rho_m c),
$">|; 

$key = q/phi_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="$ \phi_2$">|; 

$key = q/displaystylephi_m=left(beta,r+frac{gamma}{r^{,2}}right)costheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1557.png"
 ALT="$\displaystyle \phi_m = \left(\beta  r + \frac{\gamma}{r^{ 2}}\right) \cos\theta$">|; 

$key = q/-0.98times10^{-5};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1448.png"
 ALT="$ -0.98\times 10^{-5}$">|; 

$key = q/displaystyleepsilon_2nablacdot{bfE}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1094.png"
 ALT="$\displaystyle \epsilon_2\nabla \cdot {\bf E} = 0$">|; 

$key = q/displaystylefrac{partialx^{,i}}{partialx^{,i'}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3539.png"
 ALT="$\displaystyle \frac{\partial x^{ i}}{\partial x^{ i'}}$">|; 

$key = q/phi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="$ \phi=0$">|; 

$key = q/omega_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1632.png"
 ALT="$ \omega_i$">|; 

$key = q/displaystylesigma_b(z=b)=-sigma_b(z=0)=epsilon_0left(frac{epsilon-1}{epsilon}right)E_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1136.png"
 ALT="$\displaystyle \sigma_b(z=b)=-\sigma_b (z=0) = \epsilon_0 \left(\frac{\epsilon-1}{\epsilon}\right)E_0.$">|; 

$key = q/t=infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1773.png"
 ALT="$ t=\infty$">|; 

$key = q/q';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$ q'$">|; 

$key = q/displaystyle{bfE}=frac{e}{4pi,epsilon_0}frac{1-u^{,2}slashc^{,2}}{s^{,3}},{bfr}_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4024.png"
 ALT="$\displaystyle {\bf E} = \frac{e}{4\pi \epsilon_0} \frac{1-u^{ 2}/c^{ 2}}{s^{ 3}} {\bf r}_0.$">|; 

$key = q/{bfB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ {\bf B}$">|; 

$key = q/displaystyleepsilon,l,A_l=-(l+1),frac{C_l}{a^{,2,l+1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1173.png"
 ALT="$\displaystyle \epsilon  l  A_l = - (l+1) \frac{C_l}{a^{ 2 l+1}}$">|; 

$key = q/displaystyle=4pi,R^{,2},frac{d}{dR}!left(frac{1}{R}right)=-4pi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\displaystyle = 4\pi R^{ 2} \frac{d}{dR}\!\left(\frac{1}{R}\right) = -4\pi.$">|; 

$key = q/x_1=x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="$ x_1=x$">|; 

$key = q/displaystylepartial_muG^{,munu}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3846.png"
 ALT="$\displaystyle \partial_\mu G^{ \mu\nu} = 0.$">|; 

$key = q/displaystyle=ointphi(r,theta,varphi),Y_{l,m}^ast(theta,varphi),d{mitOmega},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="$\displaystyle =\oint \phi(r,\theta,\varphi) Y_{l,m}^\ast(\theta,\varphi) d{\mit\Omega},$">|; 

$key = q/displaystyleoint{bfX}_{l'm'}^{,ast}cdot({bfn}times{bfX}_{lm}),d{mitOmega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3351.png"
 ALT="$\displaystyle \oint{ \bf X}_{l'm'}^{ \ast} \cdot ({\bf n}\times{\bf X}_{lm}) d{\mit \Omega}$">|; 

$key = q/displaystylef(t)=frac{1}{2pi},{rmRe}int_C{rme}^{-{rmi},omega,t}frac{domega}{omeg{rmRe}int_C{rme}^{-{rmi},omega,(t-T)}frac{domega}{omega-2pislashtau};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1791.png"
 ALT="$\displaystyle f(t) = \frac{1}{2\pi} {\rm Re}\int_C {\rm e}^{-{\rm i} \omega ...
...m Re}\int_C{\rm e}^{-{\rm i} \omega  (t-T)} \frac{d\omega}{\omega -2\pi/\tau}$">|; 

$key = q/displaystylesinz=z-frac{z^{,3}}{3!}+frac{z^{,5}}{5!}-frac{z^{,7}}{7!}+cdots.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2425.png"
 ALT="$\displaystyle \sin z = z - \frac{z^{ 3}}{3!} + \frac{z^{ 5}}{5!} -\frac{z^{ 7}}{7!} + \cdots .$">|; 

$key = q/displaystyleP_1^{,0}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$\displaystyle  P_1^{ 0}(x)$">|; 

$key = q/displaystylew(hat{z},h)=q^{-1slash4}(hat{z}),expleft(pm{rmi},hint^{hat{z}}q(hat{z}'),dhat{z}'right)left[1+Oleft(frac{1}{h}right)right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2468.png"
 ALT="$\displaystyle w(\hat{z}, h) = q^{-1/4}(\hat{z})  \exp\left( \pm {\rm i}  h\int^{\hat{z}} q(\hat{z}') d\hat{z}'\right)\left[1+O\left(\frac{1}{h}\right)\right].$">|; 

$key = q/displaystylewidetilde{G}_N({bfr},{bfr}'')-widetilde{G}_N({bfr}'',{bfr})=int_Slefr}')-widetilde{G}_N({bfr}'',{bfr}')right]dS'leftslashint_SdS'right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="$\displaystyle \widetilde{G}_N({\bf r},{\bf r}'')-\widetilde{G}_N({\bf r}'',{\bf...
...{\bf r}')-\widetilde{G}_N({\bf r}'',{\bf r}')\right]dS'\left/\int_S dS'\right..$">|; 

$key = q/displaystyle{rmi},omega,rho=nablacdot{bfj}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3194.png"
 ALT="$\displaystyle {\rm i} \omega  \rho = \nabla\cdot{\bf j}.$">|; 

$key = q/i,j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="$ i,j$">|; 

$key = q/displaystylef(alpha)=frac{sin^2(N,alphaslash2)}{sin^2(alphaslash2)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2698.png"
 ALT="$\displaystyle f(\alpha) = \frac{\sin^2(N \alpha/2)}{\sin^2(\alpha /2)},$">|; 

$key = q/displaystyle=intrho({bfr}),x,dV=intrho({bfr}),r,sintheta,cosvarphi,dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="$\displaystyle = \int \rho({\bf r}) x dV= \int\rho({\bf r}) r \sin\theta \cos\varphi dV,$">|; 

$key = q/displaystyleT=N,tau,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1783.png"
 ALT="$\displaystyle T= N \tau,$">|; 

$key = q/displaystyle={bfm}times{bfB}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1420.png"
 ALT="$\displaystyle = {\bf m}\times {\bf B}.
$">|; 

$key = q/rho=e,n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3713.png"
 ALT="$ \rho = e n$">|; 

$key = q/3times10^{14};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4084.png"
 ALT="$ 3\times 10^{14}$">|; 

$key = q/displaystylephi_{i'}=frac{partialphi}{partialx^{,i'}}=frac{partialphi}{partialx^{,i}}frac{partialx^{,i}}{partialx^{,i'}}=phi_i,p_{i'}^{,i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3560.png"
 ALT="$\displaystyle \phi_{i'} = \frac{\partial\phi}{\partial x^{ i'}} = \frac{\parti...
...ial x^{ i}} \frac{\partial x^{ i}}{\partial x^{ i'}} =\phi_i  p_{i'}^{ i}.$">|; 

$key = q/displaystyle{bfB}({bfr})=frac{mu_0}{4pi}intfrac{{bfj}({bfr}')times({bfr}-{bfr'})}{|{bfr}-{bfr}'|^{,3}},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1306.png"
 ALT="$\displaystyle {\bf B}({\bf r}) = \frac{\mu_0}{4\pi}\int \frac{{\bf j}({\bf r}')\times ({\bf r}-{\bf r'})}{\vert{\bf r}-{\bf r}'\vert^{ 3}} dV'.$">|; 

$key = q/displaystyleq_{2,0}^{,ast};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="$\displaystyle q_{2,0}^{ \ast}$">|; 

$key = q/displaystylec,B_y(z)=A,n(z),q^{-1slash2}(z),expleft(pm{rmi},kint^z!q(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2327.png"
 ALT="$\displaystyle c  B_y(z) = A n(z) q^{-1/2}(z)  \exp\left(\pm {\rm i}  k \int^z\!q(z') dz'\right).$">|; 

$key = q/R_{rmrad};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2655.png"
 ALT="$ R_{\rm rad}$">|; 

$key = q/displaystylef_ssimeq-sqrt{frac{2pi,{rmi}}{phi_s''}},F(omega_s),{rme}^{,{rmi},phi_s}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1911.png"
 ALT="$\displaystyle f_s \simeq - \sqrt{\frac{2\pi {\rm i}}{\phi_s''}}   F(\omega_s)  {\rm e}^{ {\rm i} \phi_s}.$">|; 

$key = q/209.0times10^{-8};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1452.png"
 ALT="$ 209.0\times 10^{-8}$">|; 

$key = q/Y_{lm}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3002.png"
 ALT="$ Y_{lm}(\theta,\varphi)$">|; 

$key = q/displaystylet';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3403.png"
 ALT="$\displaystyle t'$">|; 

$key = q/|{bfr}-{bfr}'|rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$ \vert{\bf r} -{\bf r}'\vert\rightarrow
\infty$">|; 

$key = q/(w-v)^{-1slash2}slashpi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2365.png"
 ALT="$ (w-v)^{-1/2}/\pi$">|; 

$key = q/displaystyleT^{,44};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3968.png"
 ALT="$\displaystyle T^{ 44}$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}int{bfP}({bfr'})cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right)dV',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int {\bf P}({\bf r'})\cdot\nabla'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right) dV',$">|; 

$key = q/j_{0l}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$ j_{0l}'$">|; 

$key = q/displaystylephi({bfr})=frac{1}{4pi,epsilon_0}int_SD({bfr'}),{bfn}'cdotnabla'left(frac{1}{|{bfr}-{bfr}'|}right)dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="$\displaystyle \phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int_S D({\bf r'}) {\bf n}'\cdot\nabla'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert}\right) dS',$">|; 

$key = q/{bfM}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3187.png"
 ALT="$ {\bf M}({\bf r}, t)$">|; 

$key = q/G^{,44}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3843.png"
 ALT="$ G^{ 44}=0$">|; 

$key = q/displaystyle{rmi},omega,mu_0,{bfH}_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2821.png"
 ALT="$\displaystyle {\rm i} \omega  \mu_0 {\bf H}_s$">|; 

$key = q/displaystyle=frac{mu_0,I}{4pi,a}intfrac{cosvarphi',delta(costheta'),delta(r'-a)}{|{bfr}-{bfr}'|_{varphi=0}},r'^{,2},dr',d{mitOmega}',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1326.png"
 ALT="$\displaystyle = \frac{\mu_0 I}{4\pi a}\int \frac{\cos\varphi' \delta(\cos\th...
...r'-a)}{\vert{\bf r}-{\bf r}'\vert _{\varphi=0}} r'^{ 2} dr' d{\mit\Omega}',$">|; 

$key = q/displaystylenabla^{,2}=frac{1}{r^{,2}}frac{partial}{partialr},r^{,2}frac{partial}{partialr}-frac{L^2}{r^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3070.png"
 ALT="$\displaystyle \nabla^{ 2} = \frac{1}{r^{ 2}}\frac{\partial}{\partial r}  r^{ 2}\frac{\partial}{\partial r} - \frac{L^2}{r^{ 2}}.$">|; 

$key = q/f^{,mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3946.png"
 ALT="$ f^{ \mu}$">|; 

$key = q/displaystyle-{rmi},expleft(2,{rmi},hint_a^0q^{1slash2}(x'),dx'right),,q^{-1slash4}(x),expleft(-{rmi},hint_a^xq^{,1slash2}(x'),dx'right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2562.png"
 ALT="$\displaystyle - {\rm i}  \exp\left(2 {\rm i} h\int_a^0 q^{1/2}(x') dx'\right)   q^{-1/4}(x)  \exp\left(-{\rm i} h\int_a^x q^{ 1/2}(x') dx'\right),$">|; 

$key = q/displaystyle=frac{1}{k_s^{,2}},nabla_sfrac{partialH_z}{partialz},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2851.png"
 ALT="$\displaystyle = \frac{1}{k_s^{ 2}}  \nabla_s \frac{\partial H_z}{\partial z} ,$">|; 

$key = q/displaystyle-left(frac{1}{sintheta}frac{partial}{partialtheta},sintheta,frac{parrac{1}{sin^2theta}frac{partial^{,2}}{partialvarphi^{,2}}right)Y_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3005.png"
 ALT="$\displaystyle -\left(\frac{1}{\sin\theta}\frac{\partial}{\partial\theta}  \sin...
...rac{1}{\sin^2\theta}\frac{\partial^{ 2} }{\partial \varphi^{ 2}}\right)Y_{lm}$">|; 

$key = q/q^{,1slash4}rightarrow-{rmi},q^{,1slash4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2506.png"
 ALT="$ q^{ 1/4}\rightarrow
-{\rm i} q^{ 1/4}$">|; 

$key = q/displaystyle=left[frac{(2,l+1)}{4pi,l,(l+1)}right]^{1slash2},P_l^{,1}(0).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1342.png"
 ALT="$\displaystyle = \left[\frac{(2 l+1)}{4\pi l (l+1)}\right]^{1/2} P_l^{ 1}(0).$">|; 

$key = q/displaystylefrac{1}{r},frac{partial}{partialr}left(r,frac{partialphi}{partialr}r^{,2}phi}{partialtheta^{,2}}+frac{partial^{,2}phi}{partialz^{,2}}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$\displaystyle \frac{1}{r} \frac{\partial}{\partial r}\left(r \frac{\partial\p...
...{ 2}\phi}{\partial\theta^{ 2}}+\frac{\partial^{ 2}\phi}{\partial z^{ 2}}=0.$">|; 

$key = q/displaystyle=2,delta_b^{,k}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3767.png"
 ALT="$\displaystyle = 2 \delta_b^{ k}.$">|; 

$key = q/displaystyle=-frac{e}{4pi,epsilon_0}frac{{bfr}'}{{r'}^{,3}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3886.png"
 ALT="$\displaystyle = -\frac{e}{4\pi \epsilon_0} \frac{{\bf r}'}{{r'}^{ 3}}.$">|; 

$key = q/displaystyleR=-expleft(2,{rmi},kint_0^{z_0}!n(z'),dz'right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2280.png"
 ALT="$\displaystyle R = -\exp\left(2 {\rm i}  k\int_0^{z_0}\! n(z') dz'\right).$">|; 

$key = q/displaystyle=left.frac{partialphi}{partialtheta}right|_{r=a_{+}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1151.png"
 ALT="$\displaystyle = \left. \frac{\partial\phi}{\partial \theta}\right\vert _{r=a_{+}}.$">|; 

$key = q/displaystyleE_z=-frac{1}{4pi,epsilon_0}sum_{rmmols}left[frac{p_z}{r^{,3}}-frac{3,(p_x,x,z+p_y,y,z+p_z,z^{,2})}{r^{,5}}right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1246.png"
 ALT="$\displaystyle E_z = -\frac{1}{4\pi \epsilon_0}\sum_{\rm mols}\left[\frac{ p_z}{r^{ 3}} - \frac{3 (p_x  x z + p_y  y z + p_z  z^{ 2})}{r^{ 5}}\right],$">|; 

$key = q/Rsimeq93.3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2216.png"
 ALT="$ R\simeq 93.3$">|; 

$key = q/(hat{z},a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2479.png"
 ALT="$ (\hat{z},a)$">|; 

$key = q/z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ z$">|; 

$key = q/gll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1628.png"
 ALT="$ g\ll 1$">|; 

$key = q/displaystylefrac{omega^{,2}-omega_i^{,2}}{omega_i^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1648.png"
 ALT="$\displaystyle \frac{\omega^{ 2}-\omega_i^{ 2}}{\omega_i^{ 2}},$">|; 

$key = q/displaystyle=frac{2,hat{alpha},beta}{1-hat{alpha}^{,2},beta^{,2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2175.png"
 ALT="$\displaystyle =\frac{2 \hat{\alpha} \beta}{1-\hat{\alpha}^{ 2} \beta^{ 2}},$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi^2}sum_{m=-infty,infty}int_{-infty}^inft,k,(z-z')},{rme}^{,{rmi},m,(theta-theta')},I_m(k,r_<),K_m(k,r_>),dk.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="422" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img982.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') =-\frac{1}{4\pi^2}\sum_{m=-\infty,\infty}\int...
...-z')} {\rm e}^{ {\rm i} m (\theta-\theta')}  I_m(k r_&lt;) K_m(k r_&gt;) dk.$">|; 

$key = q/displaystylesigma_{rmsc}=frac{pi}{2,k^{,2}}sum_l(2,l+1)left[|alpha_pm(l)|^{,2}+|beta_pm(l)|^{,2}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3354.png"
 ALT="$\displaystyle \sigma_{\rm sc} = \frac{\pi}{2 k^{ 2}} \sum_l (2 l+1)\left[\vert\alpha_\pm(l)\vert^{ 2} +\vert\beta_\pm(l)\vert^{ 2}\right].$">|; 

$key = q/displaystylefrac{1}{c^{,2}},frac{partial^{,2}phi}{partialt^{,2}}-nabla^{,2}phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle \frac{1}{c^{ 2}} \frac{\partial^{ 2}\phi}{\partial t^{ 2}} - \nabla^{ 2}\phi$">|; 

$key = q/G_3({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="$ G_3({\bf r},{\bf r}')=0$">|; 

$key = q/displaystyleE_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2208.png"
 ALT="$\displaystyle E_t$">|; 

$key = q/displaystyle{mitPhi}_{21}=frac{mu_0,I_1}{4pi}oint_1oint_2frac{d{bfr}_2cdotd{bfr}_1}{|{bfr}_1-{bfr}_2|}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1416.png"
 ALT="$\displaystyle {\mit\Phi}_{21} = \frac{\mu_0 I_1}{4\pi}\oint_1\oint_2 \frac{d{\bf r}_2\cdot d{\bf r}_1}{\vert{\bf r}_1-{\bf r}_2\vert}.
$">|; 

$key = q/z=L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="$ z=L$">|; 

$key = q/nabla'^{,2}G_D({bfr}'',{bfr}')=delta({bfr}''-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="$ \nabla'^{ 2}G_D({\bf r}'',{\bf r}')=\delta({\bf r}''-{\bf r}')$">|; 

$key = q/displaystyle=(-z)^{,l}left(frac{1}{z}frac{d}{dz}right)^lleft(frac{sinz}{z}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3032.png"
 ALT="$\displaystyle = (-z)^{ l} \left(\frac{1}{z}\frac{d}{dz}\right)^l \left(\frac{\sin z}{z}\right),$">|; 

$key = q/displaystyleq_{l}(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="$\displaystyle q_{l}(r)$">|; 

$key = q/displaystyle{bfr}cdot{bfB}_{lm}^{(E)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3102.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf B}_{lm}^{(E)}$">|; 

$key = q/displaystyleq^{,2}=n^{,2}-S^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2307.png"
 ALT="$\displaystyle q^{ 2} = n^{ 2} - S^{ 2}.$">|; 

$key = q/H_yrightarrow-v^{,2},D_y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2097.png"
 ALT="$ H_y\rightarrow -v^{ 2} D_y$">|; 

$key = q/pislash2<theta<pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4132.png"
 ALT="$ \pi/2&lt;\theta&lt;\pi$">|; 

$key = q/A';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1106.png"
 ALT="$ A'$">|; 

$key = q/omega_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1851.png"
 ALT="$ \omega_p$">|; 

$key = q/H_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2936.png"
 ALT="$ H_r$">|; 

$key = q/lgeq1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3382.png"
 ALT="$ l\geq 1$">|; 

$key = q/displaystylefrac{{mitGamma}(a),{mitGamma}(c-a)}{{mitGamma}(c)},F(a,c,z)simeq{mit),z^{-a},{rme}^{-{rmi},pi,a}left[1+{calO}left(frac{1}{z}right)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2431.png"
 ALT="$\displaystyle \frac{{\mit\Gamma}(a) {\mit\Gamma}(c-a)}{{\mit\Gamma}(c)}  F(a,...
...a}  {\rm e}^{-{\rm i} \pi  a}\left[1+{\cal O}\left(\frac{1}{z}\right)\right]$">|; 

$key = q/displaystylesimeq{mitGamma}(c-a),z^{,a-c},{rme}^{-{rmi},2pi,(a-c)},{rme}^{,z}left[1+{calO}left(frac{1}{z}right)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2436.png"
 ALT="$\displaystyle \simeq {\mit\Gamma}(c-a) z^{ a-c}  {\rm e}^{-{\rm i}  2\pi (a-c)}  {\rm e}^{ z}\left[1+{\cal O}\left(\frac{1}{z}\right)\right]$">|; 

$key = q/displaystyle=frac{j_l(k,a)}{y_l(k,a)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3376.png"
 ALT="$\displaystyle = \frac{j_l(k a)}{y_l(k a)},$">|; 

$key = q/displaystyleL^2,Y_{lm}=l,(l+1),Y_{lm}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3045.png"
 ALT="$\displaystyle L^2  Y_{lm} = l (l+1) Y_{lm}.$">|; 

$key = q/{bfj}'({bfr}')rightarrow{bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1386.png"
 ALT="$ {\bf j}'({\bf r}')\rightarrow {\bf0}$">|; 

$key = q/displaystyle{bfD}=epsilon_0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1078.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0  $">|; 

$key = q/displaystyleG({bfr},{bfr}';t,t')=A,G^{(+)}({bfr},{bfr}';t,t')+B,G^{(-)}({bfr},{bfr}';t,t'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle G({\bf r}, {\bf r}'; t, t') = A G^{(+)} ({\bf r}, {\bf r}'; t, t') + B  G^{(-)} ({\bf r}, {\bf r}'; t, t'),$">|; 

$key = q/u({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$ u({\bf r}, t)$">|; 

$key = q/m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="$ m$">|; 

$key = q/displaystyleW=frac{epsilon_0}{2}left[intnablacdot({bfE},phi),dV+intE^{,2},dVright].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="$\displaystyle W = \frac{\epsilon_0}{2} \left[\int \nabla \cdot ({\bf E} \phi) dV + \int E^{ 2} dV\right].$">|; 

$key = q/displaystylenablacdot(phi,nablaphi)equivphi,nabla^{,2}phi+nablaphicdotnablaphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$\displaystyle \nabla\cdot (\phi \nabla \phi) \equiv \phi \nabla^{ 2} \phi + \nabla \phi\cdot \nabla \phi.$">|; 

$key = q/delta({bfr}-{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$ \delta({\bf r}-{\bf r}')$">|; 

$key = q/Z_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2901.png"
 ALT="$ Z_g$">|; 

$key = q/v_p=cslashn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1925.png"
 ALT="$ v_p=c/n$">|; 

$key = q/displaystyleE_1=frac{E_0}{epsilon}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1135.png"
 ALT="$\displaystyle E_1=\frac{E_0}{\epsilon}.$">|; 

$key = q/displaystylew(7)=-{rmi},(A+t,B+v,{B+u,[A+t,B]}),(hat{z},0)_s-{rmi},(B+u,[A+t,B]),(0,hat{z})_d.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2512.png"
 ALT="$\displaystyle w(7) =-{\rm i} ( A+t B +v \{B+ u [A+t B]\})  (\hat{z},0)_s -{\rm i} (B+ u [A+t B]) (0,\hat{z})_d.$">|; 

$key = q/displaystyleG^{,ij}=-epsilon^{,ijk},E_k=-frac{1}{2},epsilon^{,ijk}epsilon_{kab},E^{,ab}=-E^{,ij}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3822.png"
 ALT="$\displaystyle G^{ ij} = -\epsilon^{ ijk}  E_k =-\frac{1}{2} \epsilon^{ ijk} \epsilon_{kab}  E^{ ab} = - E^{ ij}.$">|; 

$key = q/displaystylen^{,2}(omega)=epsilon+{rmi},frac{sigma}{epsilon_0,omega}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1687.png"
 ALT="$\displaystyle n^{ 2}(\omega) = \epsilon + {\rm i} \frac{\sigma}{\epsilon_0  \omega}.$">|; 

$key = q/n_1>n_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2133.png"
 ALT="$ n_1&gt; n_2$">|; 

$key = q/P;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$ P$">|; 

$key = q/displaystyle{T^{,mu}}_mu=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4210.png"
 ALT="$\displaystyle {T^{ \mu}}_\mu = 0,
$">|; 

$key = q/omegaggomega_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1700.png"
 ALT="$ \omega\gg \omega_i$">|; 

$key = q/sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="$ \sigma$">|; 

$key = q/displaystylek_t^{,2}=k_g^{,2}-frac{omega^{,2}}{c^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2910.png"
 ALT="$\displaystyle k_t^{ 2} = k_g^{ 2} - \frac{\omega^{ 2}}{c^{ 2}}$">|; 

$key = q/displaystylepsi({bfr},omega)=sum_{l=0,infty}sum_{m=-l,+l}f_{lm}(r),Y_{lm}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3001.png"
 ALT="$\displaystyle \psi({\bf r}, \omega) = \sum_{l=0,\infty}\sum_{m=-l,+l} f_{lm}(r)  Y_{lm}(\theta,\varphi).$">|; 

$key = q/B_0,{bfe}_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2008.png"
 ALT="$ B_0 {\bf e}_z$">|; 

$key = q/displaystyleG({bfr},{bfr}')=-frac{1}{4pi,|{bfr}-{bfr}'|}+F({bfr},{bfr}'),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="$\displaystyle G({\bf r},{\bf r}') = -\frac{1}{4\pi \vert{\bf r}-{\bf r}'\vert} + F({\bf r},{\bf r}'),$">|; 

$key = q/displaystyle=p_{i'}^{,i}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3540.png"
 ALT="$\displaystyle = p_{i'}^{ i}.$">|; 

$key = q/n=sqrt{epsilon};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2052.png"
 ALT="$ n=\sqrt{\epsilon}$">|; 

$key = q/rrightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1153.png"
 ALT="$ r\rightarrow 0$">|; 

$key = q/displaystyleA_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1327.png"
 ALT="$\displaystyle A_z$">|; 

$key = q/rgeqa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="$ r\geq a$">|; 

$key = q/displaystyleleft(frac{partial^{,2}}{partialz^{,2}}+k_3^{,2}right)psi=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2816.png"
 ALT="$\displaystyle \left(\frac{\partial^{ 2}}{\partial z^{ 2}} + k_3^{ 2}\right)\psi =0,$">|; 

$key = q/R^{,mu}=({bfr},c,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3654.png"
 ALT="$ R^{ \mu} = ({\bf r}, c t)$">|; 

$key = q/g_{mu'nu'},dx^{,mu'},dx^{,nu'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3674.png"
 ALT="$ g_{\mu'\nu'}  dx^{ \mu'}  dx^{ \nu'}$">|; 

$key = q/ds;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3618.png"
 ALT="$ ds$">|; 

$key = q/icdotsj;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3552.png"
 ALT="$ i\cdots j$">|; 

$key = q/{bfr}_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$ {\bf r}_2$">|; 

$key = q/displaystyleepsilon^{,alphabetagammadelta}=left{{array}{rcl}+1&mbox{hspace{1cm}}onof1,2,3,4}[0.5ex]0&mbox{hspace{1cm}}&mbox{otherwise}{array}right..;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="81" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3757.png"
 ALT="$\displaystyle \epsilon^{ \alpha\beta\gamma\delta} =\left\{ \begin{array}{rcl} ...
...1,2,3,4$}\ [0.5ex] 0&amp;\mbox{\hspace{1cm}}&amp;\mbox{otherwise} \end{array}\right. .$">|; 

$key = q/displaystylefrac{dU}{dt}=-int_V{bff}cdot{bfu},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1209.png"
 ALT="$\displaystyle \frac{dU}{dt} = - \int_V {\bf f}\cdot {\bf u} dV.$">|; 

$key = q/|omega|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1842.png"
 ALT="$ \vert\omega\vert$">|; 

$key = q/displaystyle{bff}=frac{d{bfp}}{dt},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3921.png"
 ALT="$\displaystyle {\bf f} = \frac{d{\bf p}}{dt},$">|; 

$key = q/displaystyleP_2^{,-2}(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="$\displaystyle P_2^{ -2}(x)$">|; 

$key = q/displaystylephi(r,theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="$\displaystyle \phi(r,\theta,\varphi)$">|; 

$key = q/displaystyle{rmE}_1(x)=frac{{rme}^{-x}}{x}-int_x^inftyfrac{{rme}^{-t}}{t^{,2}},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2410.png"
 ALT="$\displaystyle {\rm E}_1(x) = \frac{{\rm e}^{-x}}{x} -\int_x^\infty \frac{{\rm e}^{-t}}{t^{ 2}} dt.$">|; 

$key = q/-{rmi},omega,t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1796.png"
 ALT="$ -{\rm i} \omega  t$">|; 

$key = q/displaystyleg_{munu}=g_{mu'nu'},p_{mu}^{,mu'},p_{nu}^{,nu'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3675.png"
 ALT="$\displaystyle g_{\mu\nu} = g_{\mu'\nu'} p_{\mu}^{ \mu'}  p_{\nu}^{ \nu'}.$">|; 

$key = q/displaystyleG_D({bfr},{bfr}')=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="$\displaystyle G_D({\bf r},{\bf r}')=0$">|; 

$key = q/displaystyle|H_{parallel}|simeqfrac{k}{mu_0,omega},|E_perp|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2774.png"
 ALT="$\displaystyle \vert H_{\parallel}\vert \simeq \frac{k}{\mu_0 \omega}  \vert E_\perp\vert$">|; 

$key = q/Sigma_infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$ \Sigma_\infty$">|; 

$key = q/displaystyleW=frac{1}{2}intrho({bfr}),phi({bfr}),dV,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$\displaystyle W = \frac{1}{2} \int \rho({\bf r}) \phi({\bf r}) dV,$">|; 

$key = q/{bfP};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1059.png"
 ALT="$ {\bf P}$">|; 

$key = q/displaystyle={bfK},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2760.png"
 ALT="$\displaystyle = {\bf K},$">|; 

$key = q/omega_1=(omega_0^{nobreakspace{}2}+omega_p^{nobreakspace{}2})^{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ \omega _1=(\omega _0^{\nobreakspace {}2} + \omega _p^{\nobreakspace {}2})^{1/2}$">|; 

$key = q/k_tau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1828.png"
 ALT="$ k_\tau$">|; 

$key = q/displaystylefrac{dP(t')}{d{mitOmega}}simeqfrac{2,e^{,2},dot{u}^{,2}}{pi^2,epsilo3}},gamma^{,8}frac{(gamma,theta)^{,2}}{[1+(gamma,theta)^{,2}]^{,5}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4106.png"
 ALT="$\displaystyle \frac{dP(t')}{d{\mit\Omega}} \simeq \frac{2  e^{ 2} \dot{u}^{\...
...,\gamma^{ 8} \frac{(\gamma \theta)^{ 2}}{[1+ (\gamma \theta)^{ 2}]^{ 5}}.$">|; 

$key = q/Fslashq^{,1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2390.png"
 ALT="$ F/q^{ 1/2}$">|; 

$key = q/displaystyleA_i({bfr})=frac{mu_0}{4pi},frac{1}{|{bfr}|}intj_i({bfr}'),dV'+frac{m0}{4pi},frac{{bfr}}{|{bfr}|^{,3}}cdotintj_i({bfr}'),{bfr}',dV'+cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1381.png"
 ALT="$\displaystyle A_i({\bf r})= \frac{\mu_0}{4\pi} \frac{1}{\vert{\bf r}\vert}\int...
...{{\bf r}}{\vert{\bf r}\vert^{ 3}}\cdot\int j_i({\bf r}') {\bf r}' dV'+\cdots$">|; 

$key = q/mu_0,{bfH};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1464.png"
 ALT="$ \mu_0 {\bf H}$">|; 

$key = q/displaystyle=left(frac{5}{96pi}right)^{1slash2},(Q_{11}+2,{rmi},Q_{12}-Q_{22}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="$\displaystyle =\left(\frac{5}{96\pi}\right)^{1/2} (Q_{11}+2 {\rm i} Q_{12}-Q_{22}),$">|; 

$key = q/displaystyleE_z(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2979.png"
 ALT="$\displaystyle E_z(r)$">|; 

$key = q/E_theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2937.png"
 ALT="$ E_\theta$">|; 

$key = q/(n,0)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$ (n,0) =1$">|; 

$key = q/displaystyleint_0^inftycos!left[frac{3}{2},zleft(frac{v^{,3}}{3}+vright)right],dv=frac{1}{sqrt{3}},K_{1slash3}(z),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1958.png"
 ALT="$\displaystyle \int_0^\infty \cos\!\left[ \frac{3}{2}  z\left(\frac{v^{ 3}}{3} + v\right) \right] dv= \frac{1}{\sqrt{3}}  K_{1/3}(z),$">|; 

$key = q/displaystyleH_y(z,t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2003.png"
 ALT="$\displaystyle H_y(z,t)$">|; 

$key = q/|z|geqdslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2624.png"
 ALT="$ \vert z\vert\geq d/2$">|; 

$key = q/displaystylex^{,2}-c^{,2},t^{,2}=x'^{,2}-c^{,2},t'^{,2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3459.png"
 ALT="$\displaystyle x^{ 2} - c^{ 2}  t^{ 2} = x'^{ 2} - c^{ 2}  t'^{ 2}.$">|; 

$key = q/displaystyleK_m(p)=int_0^infty{rme}^{-,p,cosht},cosh(m,t),dt,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img964.png"
 ALT="$\displaystyle K_m(p) = \int_0^\infty {\rm e}^{- p \cosh t} \cosh(m t) dt,$">|; 

$key = q/displaystylephi({bfr})=-int_VG({bfr},{bfr}'),frac{rho({bfr}')}{epsilon_0},dV'+int_Sphi({bfr}'),frac{partialG({bfr},{bfr}')}{partialn'},dS',;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img993.png"
 ALT="$\displaystyle \phi({\bf r}) = - \int_VG({\bf r},{\bf r}') \frac{\rho({\bf r}')...
... + \int_S\phi({\bf r}') \frac{\partial G({\bf r},{\bf r}')}{\partial n'} dS',$">|; 

$key = q/u<c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3516.png"
 ALT="$ u&lt;c$">|; 

$key = q/displaystylemu_0,alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1565.png"
 ALT="$\displaystyle \mu_0 \alpha$">|; 

$key = q/displaystyle{bfE}=frac{bfP}{3,epsilon_0}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1244.png"
 ALT="$\displaystyle {\bf E} = \frac{\bf P}{3 \epsilon_0}.$">|; 

$key = q/k_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2968.png"
 ALT="$ k_t$">|; 

$key = q/q(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$ q(r)$">|; 

$key = q/displaystylefrac{d^{,2}R}{dp^{,2}}+frac{1}{p},frac{dR}{dp}+left(1-frac{m^{,2}}{p^{,2}}right)R=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="$\displaystyle \frac{d^{ 2} R}{dp^{ 2}} + \frac{1}{p} \frac{dR}{dp}+\left(1-\frac{m^{ 2}}{p^{ 2}}\right) R = 0.$">|; 

$key = q/phi_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="$ \phi_S$">|; 

$key = q/{bfu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$ {\bf u}$">|; 

$key = q/n_1=1.0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ n_1=1.0$">|; 

$key = q/displaystylenabla^{,2}{bfB}-frac{epsilon}{c^{,2}},frac{partial^{,2}{bfB}}{partialt^{,2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2574.png"
 ALT="$\displaystyle \nabla^{ 2}{\bf B} - \frac{\epsilon}{c^{ 2}} \frac{\partial^{ 2}{\bf B}}{\partial t^{ 2}}$">|; 

$key = q/displaystylekappa(omega)=frac{e^{,3}}{2,epsilon_0,m^{,2},c}frac{omega^{,2}}{(omega_0^{,2}-omega^{,2})^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1758.png"
 ALT="$\displaystyle \kappa(\omega) = \frac{e^{ 3}}{2 \epsilon_0  m^{ 2}  c} \frac{\omega^{ 2}} {(\omega_0^{ 2} -\omega^{ 2})^{ 2}}.$">|; 

$key = q/displaystyle{bfE}({bfr},t)simeq-frac{1}{4pi,epsilon_0}frac{left[intpartial{bfj}_perpslashpartialt,,dV'right]}{c^{,2},r},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle {\bf E}({\bf r},t) \simeq -\frac{1}{4\pi \epsilon_0} \frac{\left[ \int \partial {\bf j}_\perp/\partial t  dV'\right]}{c^{ 2}  r},$">|; 

$key = q/displaystyle=frac{x'+v,t'}{(1-v^{,2}slashc^{,2})^{1slash2}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3477.png"
 ALT="$\displaystyle = \frac{x'+v t'}{(1-v^{ 2}/c^{ 2})^{1/2}},$">|; 

$key = q/displaystyle{mitPhi}^{,mu}=frac{1}{4pi,epsilon_0,c}intfrac{[J^{,mu}]}{r},dV.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3742.png"
 ALT="$\displaystyle {\mit \Phi}^{ \mu} = \frac{1}{4\pi \epsilon_0 c}\int \frac{[J^{ \mu}]} { r} dV.$">|; 

$key = q/displaystyle{bfE}({bfr},t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\displaystyle {\bf E}({\bf r},t)$">|; 

$key = q/displaystyle=left(frac{epsilon-1}{epsilon+2}right),a^{,3},E_0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1178.png"
 ALT="$\displaystyle = \left(\frac{\epsilon-1}{\epsilon+2}\right) a^{ 3}  E_0.$">|; 

$key = q/displaystylef_ssimeqfrac{2sqrt{pi}}{tau},frac{(t-t_0)^{1slash4}}{xi^{,3slash4}}cos!left[2sqrt{xi,(t-t_0)}-3pislash4right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1941.png"
 ALT="$\displaystyle f_s \simeq \frac{ 2\sqrt{\pi}}{\tau}  \frac{(t-t_0)^{1/4}}{\xi^{ 3/4}} \cos\!\left[2\sqrt{\xi (t-t_0)} - 3\pi/4\right].$">|; 

$key = q/displaystylew(3)=(A+t,B),(0,hat{z})_d+B,(hat{z},0)_s.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2501.png"
 ALT="$\displaystyle w(3) =( A+t B) (0,\hat{z})_d + B (\hat{z},0)_s.$">|; 

$key = q/displaystylez';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3401.png"
 ALT="$\displaystyle z'$">|; 

$key = q/displaystyleW=-{bfp}cdot{bfE}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$\displaystyle W =- {\bf p}\cdot{\bf E}.
$">|; 

$key = q/displaystylef_s=frac{sigma^{,2}}{2,epsilon_0,epsilon}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1279.png"
 ALT="$\displaystyle f_s = \frac{\sigma^{ 2}}{2 \epsilon_0 \epsilon}.$">|; 

$key = q/z_0(v^{,1slash2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2368.png"
 ALT="$ z_0(v^{ 1/2})$">|; 

$key = q/partialslashpartialz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2243.png"
 ALT="$ \partial/\partial z$">|; 

$key = q/displaystyle{rmE}_1(x)=frac{{rme}^{-x}}{x}left[1-frac{1}{x}+frac{2!}{x^{,2}}-fra,n}}right]+(-1)^{n+1}(n+1)!int_x^inftyfrac{{rme}^{-t}}{t^{,n+2}},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="510" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2411.png"
 ALT="$\displaystyle {\rm E}_1(x) = \frac{{\rm e}^{-x}}{x}\left[ 1-\frac{1}{x} + \frac...
... n}}\right] +(-1)^{n+1}(n+1)!\int_x^\infty \frac{{\rm e}^{-t}}{t^{ n+2}} dt.$">|; 

$key = q/displaystyleP_l^{,-m}(x)=(-1)^{,m},frac{(l-m)!}{(l+m)!},P_l^{,m}(x).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="$\displaystyle P_l^{ -m}(x)= (-1)^{ m} \frac{(l-m)!}{(l+m)!} P_l^{ m}(x).$">|; 

$key = q/G_{ij}={bfG}^{(i)}cdot{bfe}_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$ G_{ij}= {\bf G}^{(i)}\cdot{\bf e}_j$">|; 

$key = q/q(hat{z})=q(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2532.png"
 ALT="$ q(\hat{z})=q(x)$">|; 

$key = q/partialphislashpartialS=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2391.png"
 ALT="$ \partial\phi/\partial S = 0$">|; 

$key = q/displaystyle{bfE}';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3885.png"
 ALT="$\displaystyle {\bf E}'$">|; 

$key = q/{rme}^{,{rmi},k,r'}slashr';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3295.png"
 ALT="$ {\rm e}^{ {\rm i}  k r'}/r'$">|; 

$key = q/{rmRe}(n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1668.png"
 ALT="$ {\rm Re}(n)$">|; 

$key = q/g_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3095.png"
 ALT="$ g_l(k r)$">|; 

$key = q/|omega-omega_i|slashomega_i<{calO}(g_i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1670.png"
 ALT="$ \vert\omega-\omega_i\vert/\omega_i&lt;{\cal O}(g_i)$">|; 

$key = q/displaystyleu_z(omega,z)=c,left(1-frac{omega_p^{,2}(z)}{omega^{,2}}right)^{1slash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2346.png"
 ALT="$\displaystyle u_z(\omega,z) = c  \left(1-\frac{\omega_p^{ 2}(z)}{\omega^{ 2}}\right)^{1/2}.$">|; 

$key = q/r'>r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="$ r'&gt;r$">|; 

$key = q/displaystyleointY_{l,m}(theta,varphi),Y^{,ast}_{l',m'}(theta,varphi),d{mitOmega}=delta_{ll'},delta_{mm'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="$\displaystyle \oint Y_{l,m}(\theta,\varphi) Y^{ \ast}_{l',m'}(\theta,\varphi) d{\mit\Omega}= \delta_{ll'} \delta_{mm'},$">|; 

$key = q/displaystyleF^{,munu}=frac{e}{4pi,epsilon_0,c,{r'}^{,3}},U^{,mu},R^{,nu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3889.png"
 ALT="$\displaystyle F^{ \mu\nu} = \frac{e}{4\pi \epsilon_0 c {r'}^{ 3}} U^{ \mu}  R^{ \nu}.$">|; 

$key = q/displaystyle|{bfr}|rightarrowinfty.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="$\displaystyle \vert{\bf r}\vert\rightarrow \infty.$">|; 

$key = q/displaystyleE_theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2931.png"
 ALT="$\displaystyle E_\theta$">|; 

$key = q/displaystyleF_{4i}=partial_4{mitPhi}_i-partial_i{mitPhi}_4=E_i.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3791.png"
 ALT="$\displaystyle F_{4i} = \partial_4{\mit\Phi}_i -\partial_i{\mit\Phi}_4 = E_i.$">|; 

$key = q/displaystyleL_z,Y_{lm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3062.png"
 ALT="$\displaystyle L_z Y_{lm}$">|; 

$key = q/{mitOmega}=e,Bslash(gamma,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4218.png"
 ALT="$ {\mit\Omega} = e B/(\gamma  m)$">|; 

$key = q/displaystylea_E(l,m),f_l(k,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3124.png"
 ALT="$\displaystyle a_E(l,m) f_l(k r)$">|; 

$key = q/Qslash4pi,R^{,2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1036.png"
 ALT="$ Q/4\pi R^{ 2}$">|; 

$key = q/displaystylen_{n-1},sintheta_{n-1}=n_n,sintheta_n.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2287.png"
 ALT="$\displaystyle n_{n-1} \sin\theta_{n-1} = n_n \sin\theta_n.$">|; 

$key = q/epsilon(rho_m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1218.png"
 ALT="$ \epsilon(\rho_m)$">|; 

$key = q/displaystylesigma_-(r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1050.png"
 ALT="$\displaystyle \sigma_-(r)$">|; 

$key = q/dx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3406.png"
 ALT="$ dx$">|; 

$key = q/n=x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2414.png"
 ALT="$ n=x$">|; 

$key = q/displaystyle{bfE}_{rmradiation};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4030.png"
 ALT="$\displaystyle {\bf E}_{\rm radiation}$">|; 

$key = q/displaystyle~~~~-frac{psi_r,sintheta_i}{v_1},cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z+phi_r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2140.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;-\frac{\psi_r \sin\theta_i}{v_1} \cos(\omega t-n_1 k_0 \sin\theta_i x+n_1 k_0 \cos\theta_i z+\phi_r)$">|; 

$key = q/OB;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2534.png"
 ALT="$ OB$">|; 

$key = q/I_m(z)rightarrowinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2921.png"
 ALT="$ I_m(z)\rightarrow\infty$">|; 

$key = q/dot{u}=u^{,2}slashrho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4086.png"
 ALT="$ \dot{u} = u^{ 2}/\rho$">|; 

$key = q/displaystyleC_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1177.png"
 ALT="$\displaystyle C_1$">|; 

$key = q/{mitDelta}t'={mitDelta}thetaslashomega_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4153.png"
 ALT="$ {\mit\Delta} t' ={\mit\Delta}\theta/\omega_0$">|; 

$key = q/displaystyle={rmi},frac{omega,mu_0}{k_s},J_1(k_s,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2944.png"
 ALT="$\displaystyle = {\rm i}  \frac{\omega \mu_0}{k_s}  J_1(k_s  r)$">|; 

$key = q/displaystylephi({bfr})=-frac{1}{4pi}intfrac{v({bfr}')}{|{bfr}-{bfr}'|},dV'.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="$\displaystyle \phi({\bf r})= - \frac{1}{4\pi}\int \frac{v({\bf r}')}{\vert{\bf r}-{\bf r}'\vert} dV'.$">|; 

$key = q/displaystylev=frac{v_1+v_2}{1+v_1,v_2slashc^{,2}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4167.png"
 ALT="$\displaystyle v = \frac{v_1+v_2}{1+v_1 v_2/c^{ 2}}.
$">|; 

$key = q/I(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3258.png"
 ALT="$ I(z)$">|; 

$key = q/Y_{l,m-1}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3097.png"
 ALT="$ Y_{l,m-1}(\theta,\varphi)$">|; 

$key = q/k_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2878.png"
 ALT="$ k_g$">|; 

$key = q/displaystyleepsilon_0,mu_0,frac{partialphi}{partialt}+nablacdot{bfA}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle \epsilon_0 \mu_0 \frac{\partial\phi}{\partial t} +\nabla\cdot{\bf A} = 0.$">|; 

$key = q/displaystylec,B_y=A,{rme}^{,{rmi},phi(z)},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2319.png"
 ALT="$\displaystyle c  B_y = A  {\rm e}^{ {\rm i} \phi(z)},$">|; 

$key = q/E_parallel;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1270.png"
 ALT="$ E_\parallel$">|; 

$key = q/displaystyleleft[frac{d^{,2}}{dr^{,2}}+frac{2}{r}frac{d}{dr}+k^{,2}-frac{l,(l+1)}{r^{,2}}right]f_{lm}(r)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3008.png"
 ALT="$\displaystyle \left[\frac{d^{ 2}}{dr^{ 2}} + \frac{2}{r}\frac{d}{dr} + k^{ 2} - \frac{l (l+1)}{r^{ 2}} \right]f_{lm}(r) =0.$">|; 

$key = q/Qneq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4187.png"
 ALT="$ Q\neq 0$">|; 

$key = q/dS';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="$ dS'$">|; 

$key = q/displaystyleJ_m(k_l,a)=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2866.png"
 ALT="$\displaystyle J_m(k_l  a) = 0.$">|; 

$key = q/displaystylembox{hspace{2cm}as{prightarrowinfty{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img941.png"
 ALT="$\displaystyle \mbox{\hspace{2cm}as $p\rightarrow \infty$}$">|; 

$key = q/displaystylerho_m=-nablacdot{bfM}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1478.png"
 ALT="$\displaystyle \rho_m = -\nabla\cdot{\bf M}.$">|; 

$key = q/displaystyleB=D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3467.png"
 ALT="$\displaystyle B=D$">|; 

$key = q/G_omega({bfr},{bfr}');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$ G_\omega({\bf r}, {\bf r}')$">|; 

$key = q/R>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$ R&gt;0$">|; 

$key = q/displaystyleI=intA_nu,Q^{,4nu},d^{,3}x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4055.png"
 ALT="$\displaystyle I = \int A_\nu  Q^{ 4\nu}  d^{ 3} x$">|; 

$key = q/(dnslashdz)slash(k,n^{,2})ll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2252.png"
 ALT="$ (dn/dz)/(k n^{ 2})\ll 1$">|; 

$key = q/x_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$ x_2$">|; 

$key = q/h(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2350.png"
 ALT="$ h(\omega)$">|; 

$key = q/displaystylebeta_l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1033.png"
 ALT="$\displaystyle \beta_l$">|; 

$key = q/displaystyler'=-c,t'=-c,gamma,(t-u,xslashc^{,2})=r,gamma,(1+u_rslashc),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3879.png"
 ALT="$\displaystyle r'=-c t' =-c \gamma (t-u x/c^{ 2}) = r \gamma (1+u_r/c),$">|; 

$key = q/displaystyleb_pm(l,m)=mp,{rmi},a_pm(l,m).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3323.png"
 ALT="$\displaystyle b_\pm(l,m) = \mp  {\rm i} a_\pm(l,m).$">|; 

$key = q/displaystyledx^{,i'}=frac{partialx^{,i'}}{partialx^{,i}},dx^{,i}=dx^{,i},p_i^{,i'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3557.png"
 ALT="$\displaystyle dx^{ i'} = \frac{\partial x^{ i'}}{\partial x^{ i}}  dx^{ i} = dx^{ i}  p_i^{ i'}.$">|; 

$key = q/displaystylepsi_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2074.png"
 ALT="$\displaystyle \psi_r$">|; 

$key = q/A_i^i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3572.png"
 ALT="$ A_i^i$">|; 

$key = q/displaystyleointY_{l,m}^{,ast}(theta',varphi'),{rme}^{,{rmi},varphi'},dvarphi'=2pi,Y_{l,m}^{,ast}(theta',varphi'),{rme}^{,{rmi},varphi'},delta_{m1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1337.png"
 ALT="$\displaystyle \oint Y_{l,m}^{ \ast}(\theta',\varphi') {\rm e}^{ {\rm i} \va...
...Y_{l,m}^{ \ast}(\theta',\varphi') {\rm e}^{ {\rm i} \varphi'} \delta_{m1}.$">|; 

$key = q/dlla;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1602.png"
 ALT="$ d\ll a$">|; 

$key = q/displaystyle=-F^{,4i}=+E^{,i},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3802.png"
 ALT="$\displaystyle =-F^{ 4i} = +E^{ i},$">|; 

$key = q/displaystyle=frac{omega,epsilon_0}{k_g},{bfe}_ztimes{bfE}_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2890.png"
 ALT="$\displaystyle = \frac{\omega \epsilon_0}{k_g}  {\bf e}_z\times{\bf E}_s,$">|; 

$key = q/i,j,k,cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3529.png"
 ALT="$ i,j,k,\cdots$">|; 

$key = q/displaystyleY_{2,+1}(theta,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="$\displaystyle Y_{2,+1}(\theta,\varphi)$">|; 

$key = q/{bfA}rightarrow{bfA}-nablapsi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$ {\bf A}\rightarrow {\bf A}-\nabla\psi$">|; 

$key = q/displaystyle{rmE}_1(x)=int_x^inftyfrac{{rme}^{-t}}{t},dt.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2409.png"
 ALT="$\displaystyle {\rm E}_1(x) = \int_x^\infty \frac{{\rm e}^{-t}}{t} dt.$">|; 

$key = q/displaystyle=sum_{m=-infty,infty}phi_m(r,z),{rme}^{,{rmi},m,theta},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img984.png"
 ALT="$\displaystyle =\sum_{m=-\infty,\infty}\phi_m(r,z) {\rm e}^{ {\rm i} m \theta},$">|; 

$key = q/displaystylephi(r,theta,varphi)=sum_{l=0,infty}sum_{m=-l,+l}phi_{l,m}(r),Y_{l,m}(theta,varphi).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="$\displaystyle \phi(r,\theta,\varphi) = \sum_{l=0,\infty}\sum_{m=-l,+l}\phi_{l,m}(r) Y_{l,m}(\theta,\varphi).$">|; 

$key = q/K_1(k_ttmspace+thinmuskip{.1667em}a)slashk_ttmspace+thinmuskip{.1667em}K_0(k_ttmspace+thinmuskip{.1667em}a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$ K_1(k_t \tmspace +\thinmuskip {.1667em}a) / k_t\tmspace +\thinmuskip {.1667em} K_0(k_t\tmspace +\thinmuskip {.1667em} a)$">|; 

$key = q/displaystylew''+h^{,2},q,w=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2454.png"
 ALT="$\displaystyle w'' + h^{ 2}  q  w = 0,$">|; 

$key = q/displaystyleh_l^{(1,2)}(rho)=sqrt{frac{pi}{2,rho}},H_{l+1slash2}^{1,2}(rho),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle h_l^{(1,2)}(\rho) = \sqrt{\frac{\pi}{2 \rho}} H_{l+1/2}^{1,2} (\rho),$">|; 

$key = q/grightarrow0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1920.png"
 ALT="$ g\rightarrow 0$">|; 

$key = q/{bfk}_r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2015.png"
 ALT="$ {\bf k}_r$">|; 

$key = q/nablaphi={bf0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$ \nabla\phi={\bf0}$">|; 

$key = q/displaystyleP_{rmload}=langleu_{rmin}rangle,A_{rmeff}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2671.png"
 ALT="$\displaystyle P_{\rm load} = \langle u_{\rm in}\rangle  A_{\rm eff}.$">|; 

$key = q/displaystyle{bfL}={bfr}times{bfg},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$\displaystyle {\bf L} = {\bf r}\times {\bf g},
$">|; 

$key = q/displaystylephantom{=}+{mitGamma}(a),z^{-a},{rme}^{,{rmi},pi,a}left[1+{calO}left(frac{1}{z}right)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2437.png"
 ALT="$\displaystyle \phantom{=} +{\mit\Gamma}(a) z^{-a}  {\rm e}^{ {\rm i} \pi  a}\left[1+{\cal O}\left(\frac{1}{z}\right)\right]$">|; 

$key = q/displaystyle=-{rmi},k,n^{,2},E_x.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2239.png"
 ALT="$\displaystyle = -{\rm i} k n^{ 2}  E_x.$">|; 

$key = q/z=k_t,r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2917.png"
 ALT="$ z=k_t  r$">|; 

1;

