# LaTeX2HTML 2021 (Released January 1, 2021)
# Associate images original text with physical files.


$key = q//;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img131.png"
 ALT="$\qopname \relax o{log}_{10}(\tau _{{\rm th}}) = -28.9 - 1.60\tmspace +\thinmusk...
...e +\thinmuskip {.1667em}2/3} + 1.61\tmspace +\thinmuskip {.1667em}Z_1/\sqrt {E}$">|; 

$key = q/';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.67ex; vertical-align: 0.76ex; " SRC="|."$dir".q|img3755.png"
 ALT="$'$">|; 

$key = q/(0,,0,,hat{E}_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2846.png"
 ALT="$(0, 0, \hat{E}_z)$">|; 

$key = q/(1+2,alpha)^{1slash2},omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img762.png"
 ALT="$(1+2 \alpha)^{1/2} \omega_0$">|; 

$key = q/(1slash2),k,d,sintheta-(1slash2),(phi_1-phi_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3322.png"
 ALT="$(1/2) k d \sin\theta-(1/2) (\phi_1-\phi_2)$">|; 

$key = q/(1slash2),rho,g,a^{,2},w,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3076.png"
 ALT="$(1/2) \rho g a^{ 2} w V$">|; 

$key = q/(1slash2),rho,g,a^{,2},w,v_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3078.png"
 ALT="$(1/2) \rho g a^{ 2} w v_g$">|; 

$key = q/(1slash2),skew{3}hat{V}^{,2}slashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img587.png"
 ALT="$(1/2) \skew{3}\hat{V}^{ 2}/R$">|; 

$key = q/(1slash6),m,v^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img371.png"
 ALT="$(1/6) m v^{ 2}$">|; 

$key = q/(2,KslashM)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1303.png"
 ALT="$(2 K/M)^{1/2}$">|; 

$key = q/(2,Kslashm)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1304.png"
 ALT="$(2 K/m)^{1/2}$">|; 

$key = q/(2pi+phi)slashomega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img483.png"
 ALT="$(2\pi+\phi)/\omega_1$">|; 

$key = q/(2pi,sigma_k)^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2377.png"
 ALT="$(2\pi \sigma_k)^{-1/2}$">|; 

$key = q/(2slash3),l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img385.png"
 ALT="$(2/3) l$">|; 

$key = q/(2slashl),cos[(n-1slash2),pi,xslashl];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1196.png"
 ALT="$(2/l) \cos[(n-1/2) \pi x/l]$">|; 

$key = q/(2slashl),sin(n,pi,xslashl);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1037.png"
 ALT="$(2/l) \sin (n \pi x/l)$">|; 

$key = q/(2slashtau),cos(n,omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1264.png"
 ALT="$(2/\tau) \cos(n \omega t)$">|; 

$key = q/(2slashtau),sin(n,omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1266.png"
 ALT="$(2/\tau) \sin(n \omega t)$">|; 

$key = q/(3slash2),k_B,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4179.png"
 ALT="$(3/2) k_B T$">|; 

$key = q/(Omega,{rmm})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2927.png"
 ALT="$(\Omega {\rm m})^{-1}$">|; 

$key = q/(X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3251.png"
 ALT="$(X$">|; 

$key = q/(g,d)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3084.png"
 ALT="$(g d)^{1/2}$">|; 

$key = q/(hat{E}_x,,-hat{E}_x,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2852.png"
 ALT="$(\hat{E}_x,  -\hat{E}_x,  0)$">|; 

$key = q/(hat{E}_x,,hat{E}_x,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2850.png"
 ALT="$(\hat{E}_x,  \hat{E}_x, 0)$">|; 

$key = q/(l>0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1331.png"
 ALT="$(l&gt;0)$">|; 

$key = q/(lambda-y^{,2})^{1slash2}=y,tany;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4239.png"
 ALT="$(\lambda-y^{ 2})^{1/2} = y \tan y$">|; 

$key = q/(lambda-y^{,2})^{1slash2}slashy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3980.png"
 ALT="$(\lambda - y^{ 2})^{1/2}/y$">|; 

$key = q/(lambda-y^{tmspace+thinmuskip{.1667em}2})^{1slash2}slashy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img118.png"
 ALT="$(\lambda - y^{\tmspace +\thinmuskip {.1667em}2})^{1/2}/y$">|; 

$key = q/(omega_0+omega)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img621.png"
 ALT="$(\omega_0+\omega)/2$">|; 

$key = q/(omega_0-omega)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img623.png"
 ALT="$(\omega_0-\omega)/2$">|; 

$key = q/(omegaslashv),a=z_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1917.png"
 ALT="$(\omega/v) a=z_j$">|; 

$key = q/(partial^{,2}zetaslashpartialx^{,2})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3161.png"
 ALT="$(\partial^{ 2}\zeta/\partial x^{ 2})^{-1}$">|; 

$key = q/(psi^ast)^ast=psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3850.png"
 ALT="$(\psi^\ast)^\ast=\psi$">|; 

$key = q/(x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3489.png"
 ALT="$(x'$">|; 

$key = q/(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4477.png"
 ALT="$(x, y, z)$">|; 

$key = q/(x-x')^{,4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3563.png"
 ALT="$(x-x')^{ 4}$">|; 

$key = q/(x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3488.png"
 ALT="$(x$">|; 

$key = q/(x^{,2}+y^{,2})^{1slash2}<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3521.png"
 ALT="$(x^{ 2}+y^{ 2})^{1/2}&lt; a$">|; 

$key = q/(y-y')^{,4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3564.png"
 ALT="$(y-y')^{ 4}$">|; 

$key = q/({mitDelta}x)_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3900.png"
 ALT="$({\mit\Delta} x)_0$">|; 

$key = q/({mitDelta}x)_0simsigma_x=sigma_k^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2576.png"
 ALT="$({\mit\Delta} x)_0\sim \sigma_x=\sigma_k^{ -1}$">|; 

$key = q/+A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1273.png"
 ALT="$+A$">|; 

$key = q/+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img179.png"
 ALT="$+a$">|; 

$key = q/+e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2590.png"
 ALT="$+e$">|; 

$key = q/+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3801.png"
 ALT="$+\infty$">|; 

$key = q/+k,x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img662.png"
 ALT="$+k x$">|; 

$key = q/+omega,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img183.png"
 ALT="$+\omega a$">|; 

$key = q/+omega^{,2},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img186.png"
 ALT="$+\omega^{ 2} a$">|; 

$key = q/+pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3143.png"
 ALT="$+\pi/2$">|; 

$key = q/+pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4.png"
 ALT="$+\pi /4$">|; 

$key = q/+q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1639.png"
 ALT="$+q$">|; 

$key = q/+x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1694.png"
 ALT="$+x$">|; 

$key = q/,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img192.png"
 ALT="$, \omega$">|; 

$key = q/-(phislash2pi),lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1844.png"
 ALT="$-(\phi/2\pi) \lambda$">|; 

$key = q/-1leqcosthetaleq+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img162.png"
 ALT="$-1\leq \cos\theta\leq +1$">|; 

$key = q/-A,[p+deltap(x+deltaxslash2,t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1231.png"
 ALT="$-A [p+\delta p(x+\delta x/2,t)]$">|; 

$key = q/-A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1272.png"
 ALT="$-A$">|; 

$key = q/-K,(psi_i-psi_{i-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1124.png"
 ALT="$-K (\psi_i-\psi_{i-1})$">|; 

$key = q/-Q(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1476.png"
 ALT="$-Q(t)$">|; 

$key = q/-T,sintheta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img891.png"
 ALT="$-T \sin\theta_i$">|; 

$key = q/-V<E<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3977.png"
 ALT="$-V&lt;E&lt;0$">|; 

$key = q/-V_0<E<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4257.png"
 ALT="$-V_0&lt;E&lt;0$">|; 

$key = q/-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img180.png"
 ALT="$-a$">|; 

$key = q/-aslash2<x<aslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3512.png"
 ALT="$-a/2&lt; x&lt;a/2$">|; 

$key = q/-bslash2<y<bslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3513.png"
 ALT="$-b/2&lt;y&lt;b/2$">|; 

$key = q/-c^{,2},n^{,2}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2987.png"
 ALT="$-c^{ 2} n^{ 2}/2$">|; 

$key = q/-e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2588.png"
 ALT="$-e$">|; 

$key = q/-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.89ex; vertical-align: 0.04ex; " SRC="|."$dir".q|img3800.png"
 ALT="$-\infty$">|; 

$key = q/-inftyleqxleqinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img1744.png"
 ALT="$-\infty\leq x\leq \infty$">|; 

$key = q/-k,x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img663.png"
 ALT="$-k x$">|; 

$key = q/-m,nu,dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img646.png"
 ALT="$-m \nu \dot{x}$">|; 

$key = q/-m,nu,omega^{,2},hat{x}^{,2}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img648.png"
 ALT="$-m \nu \omega^{ 2} \hat{x}^{ 2}/2$">|; 

$key = q/-omega,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img182.png"
 ALT="$-\omega a$">|; 

$key = q/-omega^{,2},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img185.png"
 ALT="$-\omega^{ 2} a$">|; 

$key = q/-pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3142.png"
 ALT="$-\pi/2$">|; 

$key = q/-pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img5.png"
 ALT="$-\pi /4$">|; 

$key = q/-q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1641.png"
 ALT="$-q$">|; 

$key = q/-theta_0slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3328.png"
 ALT="$-\theta_0/2$">|; 

$key = q/-x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img656.png"
 ALT="$-x_2$">|; 

$key = q/-yslash(lambda-y^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3987.png"
 ALT="$-y/(\lambda - y^{ 2})^{1/2}$">|; 

$key = q/-yslash(lambda-y^{tmspace+thinmuskip{.1667em}2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img121.png"
 ALT="$-y/(\lambda - y^{\tmspace +\thinmuskip {.1667em}2})^{1/2}$">|; 

$key = q/0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3252.png"
 ALT="$0)$">|; 

$key = q/0.02;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img68.png"
 ALT="$0.02$">|; 

$key = q/0.04;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img69.png"
 ALT="$0.04$">|; 

$key = q/0.08;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img70.png"
 ALT="$0.08$">|; 

$key = q/0.1,{rmmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3732.png"
 ALT="$0.1 {\rm mm}$">|; 

$key = q/0.16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img71.png"
 ALT="$0.16$">|; 

$key = q/0.25,{rmmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3727.png"
 ALT="$0.25 {\rm mm}$">|; 

$key = q/0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2909.png"
 ALT="$0.2$">|; 

$key = q/0.32;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img72.png"
 ALT="$0.32$">|; 

$key = q/0.5,{rmmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3729.png"
 ALT="$0.5 {\rm mm}$">|; 

$key = q/0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img109.png"
 ALT="$0.5$">|; 

$key = q/0.64;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img73.png"
 ALT="$0.64$">|; 

$key = q/0.90,{rmeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img4229.png"
 ALT="$0.90 {\rm eV}$">|; 

$key = q/0<theta<theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3750.png"
 ALT="$0&lt;\theta&lt;\theta_0$">|; 

$key = q/0<x_1<x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4071.png"
 ALT="$0&lt;x_1&lt;x_2$">|; 

$key = q/0<y<lambda^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3976.png"
 ALT="$0&lt;y&lt;\lambda^{1/2}$">|; 

$key = q/0<{rmFr}<{rmFr}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3099.png"
 ALT="$0&lt;{\rm Fr}&lt;{\rm Fr}_c$">|; 

$key = q/0leqthetaleqpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3546.png"
 ALT="$0\leq\theta\leq \pi/2$">|; 

$key = q/0leqxleqa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img1203.png"
 ALT="$0\leq x\leq a$">|; 

$key = q/0leqxleql;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img966.png"
 ALT="$0\leq x\leq l$">|; 

$key = q/1,{rmmW};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4225.png"
 ALT="$1 {\rm mW}$">|; 

$key = q/1,{rmmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3737.png"
 ALT="$1 {\rm mm}$">|; 

$key = q/1-costhetaequiv2,sin^2(thetaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img921.png"
 ALT="$1-\cos\theta \equiv 2 \sin^2(\theta/2)$">|; 

$key = q/1.055times10^{-34};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4262.png"
 ALT="$1.055\times 10^{-34}$">|; 

$key = q/1.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img103.png"
 ALT="$1.0$">|; 

$key = q/1.1times10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1372.png"
 ALT="$1.1\times 10^4$">|; 

$key = q/1.1times10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1365.png"
 ALT="$1.1\times 10^{11}$">|; 

$key = q/1.257times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4266.png"
 ALT="$1.257\times 10^{-6}$">|; 

$key = q/1.28;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img74.png"
 ALT="$1.28$">|; 

$key = q/1.2times10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1368.png"
 ALT="$1.2\times 10^{11}$">|; 

$key = q/1.35;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1796.png"
 ALT="$1.35$">|; 

$key = q/1.36;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3740.png"
 ALT="$1.36$">|; 

$key = q/1.40;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1219.png"
 ALT="$1.40$">|; 

$key = q/1.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4215.png"
 ALT="$1.4$">|; 

$key = q/1.52;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2094.png"
 ALT="$1.52$">|; 

$key = q/1.602times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4268.png"
 ALT="$1.602\times 10^{-19}$">|; 

$key = q/1.673times10^{-27};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4270.png"
 ALT="$1.673\times 10^{-27}$">|; 

$key = q/1.6times10^{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1378.png"
 ALT="$1.6\times 10^{10}$">|; 

$key = q/10,mu{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img359.png"
 ALT="$10 \mu{\rm m}$">|; 

$key = q/10.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img107.png"
 ALT="$10.0$">|; 

$key = q/100%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2039.png"
 ALT="$100\%$">|; 

$key = q/1000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3795.png"
 ALT="$1000$">|; 

$key = q/100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3797.png"
 ALT="$100$">|; 

$key = q/1010,{rmV},{rmm}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1797.png"
 ALT="$1010 {\rm V} {\rm m}^{-1}$">|; 

$key = q/10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3796.png"
 ALT="$10$">|; 

$key = q/10^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4247.png"
 ALT="$10^{ -1}$">|; 

$key = q/10^{,-38};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4248.png"
 ALT="$10^{ -38}$">|; 

$key = q/10^{,-8},{rms};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3314.png"
 ALT="$10^{ -8} {\rm s}$">|; 

$key = q/10^{,-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3319.png"
 ALT="$10^{ -8}$">|; 

$key = q/10^{,7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2504.png"
 ALT="$10^{ 7}$">|; 

$key = q/10^{-10},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3784.png"
 ALT="$10^{-10} {\rm m}$">|; 

$key = q/10^{-14};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4113.png"
 ALT="$10^{-14}$">|; 

$key = q/10^{-15},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3783.png"
 ALT="$10^{-15} {\rm m}$">|; 

$key = q/10^{-16},{rms};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3904.png"
 ALT="$10^{-16} {\rm s}$">|; 

$key = q/10^{-2},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img358.png"
 ALT="$10^{-2} {\rm m}$">|; 

$key = q/10^{18},{rmHz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2903.png"
 ALT="$10^{18} {\rm Hz}$">|; 

$key = q/1100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1379.png"
 ALT="$1100$">|; 

$key = q/12.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img476.png"
 ALT="$12.6$">|; 

$key = q/1481,{rmm,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2246.png"
 ALT="$1481 {\rm m s}^{-1}$">|; 

$key = q/1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img945.png"
 ALT="$1$">|; 

$key = q/1slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img26.png"
 ALT="$1/16$">|; 

$key = q/1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img23.png"
 ALT="$1/2$">|; 

$key = q/1slash30;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2501.png"
 ALT="$1/30$">|; 

$key = q/1slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img24.png"
 ALT="$1/4$">|; 

$key = q/1slash50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2498.png"
 ALT="$1/50$">|; 

$key = q/1slash6+1slash6=1slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3845.png"
 ALT="$1/6+1/6=1/3$">|; 

$key = q/1slash6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3843.png"
 ALT="$1/6$">|; 

$key = q/1slash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img25.png"
 ALT="$1/8$">|; 

$key = q/1slashA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3500.png"
 ALT="$1/A$">|; 

$key = q/1slashT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1327.png"
 ALT="$1/T$">|; 

$key = q/1slashf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1465.png"
 ALT="$1/f$">|; 

$key = q/1slashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1280.png"
 ALT="$1/n$">|; 

$key = q/1slashsqrt{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img555.png"
 ALT="$1/\sqrt{2}$">|; 

$key = q/1slashtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1328.png"
 ALT="$1/\tau$">|; 

$key = q/1slash{mitDelta}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2497.png"
 ALT="$1/{\mit\Delta} t$">|; 

$key = q/1slash{rme};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img630.png"
 ALT="$1/{\rm e}$">|; 

$key = q/2,J_1(z)slashz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3520.png"
 ALT="$2 J_1(z)/z$">|; 

$key = q/2,l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img360.png"
 ALT="$2 l$">|; 

$key = q/2,omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1150.png"
 ALT="$2 \omega_0$">|; 

$key = q/2,sina,sinbequivcos(a-b)-cos(a+b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1030.png"
 ALT="$2 \sin a \sin b \equiv \cos(a-b)-\cos(a+b)$">|; 

$key = q/2,tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1281.png"
 ALT="$2 \tau$">|; 

$key = q/2,{rmkV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4233.png"
 ALT="$2 {\rm kV}$">|; 

$key = q/2.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img104.png"
 ALT="$2.0$">|; 

$key = q/2.0times10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1361.png"
 ALT="$2.0\times 10^{11}$">|; 

$key = q/2.3,{rmeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4227.png"
 ALT="$2.3 {\rm eV}$">|; 

$key = q/2.5,{rmmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3734.png"
 ALT="$2.5 {\rm mm}$">|; 

$key = q/2.5times10^{,5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2500.png"
 ALT="$2.5\times 10^{ 5}$">|; 

$key = q/2.7,{rmA},{rmm}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1798.png"
 ALT="$2.7 {\rm A} {\rm m}^{-1}$">|; 

$key = q/2.7times10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1358.png"
 ALT="$2.7\times 10^3$">|; 

$key = q/2.7times10^{,3},{rmkg,m}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1299.png"
 ALT="$2.7\times 10^{ 3} {\rm kg m}^{-3}$">|; 

$key = q/2.998times10^{+8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img4260.png"
 ALT="$2.998\times 10^{+8}$">|; 

$key = q/200,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4228.png"
 ALT="$200 {\rm nm}$">|; 

$key = q/20^circ,{rmC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2233.png"
 ALT="$20^\circ {\rm C}$">|; 

$key = q/210,{rmMHz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2509.png"
 ALT="$210 {\rm MHz}$">|; 

$key = q/256;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img634.png"
 ALT="$256$">|; 

$key = q/258,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4230.png"
 ALT="$258 {\rm nm}$">|; 

$key = q/2600;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1377.png"
 ALT="$2600$">|; 

$key = q/261.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1064.png"
 ALT="$261.6$">|; 

$key = q/2700;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1374.png"
 ALT="$2700$">|; 

$key = q/27;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1301.png"
 ALT="$27$">|; 

$key = q/2800;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1373.png"
 ALT="$2800$">|; 

$key = q/2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3844.png"
 ALT="$2$">|; 

$key = q/2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img166.png"
 ALT="$2\pi$">|; 

$key = q/2pislashomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img169.png"
 ALT="$2\pi/\omega$">|; 

$key = q/2pislash{mitDelta}omega=tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3318.png"
 ALT="$2\pi/{\mit\Delta}\omega = \tau$">|; 

$key = q/2slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1243.png"
 ALT="$2/3$">|; 

$key = q/2slashpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img389.png"
 ALT="$2/\pi$">|; 

$key = q/2sqrt{Lslashg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img3177.png"
 ALT="$2\sqrt{L/g}$">|; 

$key = q/2times2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img686.png"
 ALT="$2\times 2$">|; 

$key = q/2tmspace+thinmuskip{.1667em}J_1(z)slashz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img98.png"
 ALT="$2\tmspace +\thinmuskip {.1667em}J_1(z)/z$">|; 

$key = q/3,E_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4168.png"
 ALT="$3 E_1$">|; 

$key = q/3,f_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1809.png"
 ALT="$3 f_0$">|; 

$key = q/3,{mitDelta}k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3894.png"
 ALT="$3 {\mit\Delta}k$">|; 

$key = q/3,{mitDelta}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3875.png"
 ALT="$3 {\mit\Delta} x$">|; 

$key = q/3.76times10^{,5},{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3741.png"
 ALT="$3.76\times 10^{ 5} {\rm km}$">|; 

$key = q/30times2.5times10^{,5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2502.png"
 ALT="$30\times 2.5\times 10^{ 5}$">|; 

$key = q/3600;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1369.png"
 ALT="$3600$">|; 

$key = q/3800;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1370.png"
 ALT="$3800$">|; 

$key = q/3900;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1367.png"
 ALT="$3900$">|; 

$key = q/3^{1slash2},k_c^{-1}simeq4.8,{rmmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3250.png"
 ALT="$3^{1/2} k_c^{-1}\simeq 4.8 {\rm mm}$">|; 

$key = q/3pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img55.png"
 ALT="$3\pi /2$">|; 

$key = q/3pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img557.png"
 ALT="$3\pi/4$">|; 

$key = q/3pislash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img52.png"
 ALT="$3\pi /8$">|; 

$key = q/3slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img61.png"
 ALT="$3/16$">|; 

$key = q/3slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3174.png"
 ALT="$3/2$">|; 

$key = q/3slash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img63.png"
 ALT="$3/8$">|; 

$key = q/3times10^{-10},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4232.png"
 ALT="$3\times 10^{-10} {\rm m}$">|; 

$key = q/3times3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img794.png"
 ALT="$3\times 3$">|; 

$key = q/4%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img475.png"
 ALT="$4\%$">|; 

$key = q/4.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img105.png"
 ALT="$4.0$">|; 

$key = q/45^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2095.png"
 ALT="$45^\circ$">|; 

$key = q/47.6^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2091.png"
 ALT="$47.6^\circ$">|; 

$key = q/4700;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1363.png"
 ALT="$4700$">|; 

$key = q/48.8^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img88.png"
 ALT="$48.8^\circ $">|; 

$key = q/4900;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1364.png"
 ALT="$4900$">|; 

$key = q/4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3938.png"
 ALT="$4$">|; 

$key = q/4slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1241.png"
 ALT="$4/3$">|; 

$key = q/4slash5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1242.png"
 ALT="$4/5$">|; 

$key = q/5,f_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1810.png"
 ALT="$5 f_0$">|; 

$key = q/5,{rmHz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img357.png"
 ALT="$5 {\rm Hz}$">|; 

$key = q/5,{rmMHz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2507.png"
 ALT="$5 {\rm MHz}$">|; 

$key = q/5,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3731.png"
 ALT="$5 {\rm m}$">|; 

$key = q/5.0times10^{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1375.png"
 ALT="$5.0\times 10^{10}$">|; 

$key = q/50,{rmOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1508.png"
 ALT="$50 {\rm\Omega}$">|; 

$key = q/50,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3733.png"
 ALT="$50 {\rm cm}$">|; 

$key = q/50,{rmcm}times50,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2499.png"
 ALT="$50 {\rm cm}\times 50 {\rm cm}$">|; 

$key = q/5000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1360.png"
 ALT="$5000$">|; 

$key = q/5100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1359.png"
 ALT="$5100$">|; 

$key = q/55.5^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2092.png"
 ALT="$55.5^\circ$">|; 

$key = q/55;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2508.png"
 ALT="$55$">|; 

$key = q/56.3^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img85.png"
 ALT="$56.3^\circ $">|; 

$key = q/589.0,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3738.png"
 ALT="$589.0 {\rm nm}$">|; 

$key = q/589.6,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3739.png"
 ALT="$589.6 {\rm nm}$">|; 

$key = q/5pislash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img54.png"
 ALT="$5\pi /8$">|; 

$key = q/5slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img62.png"
 ALT="$5/16$">|; 

$key = q/5slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1386.png"
 ALT="$5/3$">|; 

$key = q/5slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3224.png"
 ALT="$5/4$">|; 

$key = q/5times10,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3223.png"
 ALT="$5\times 10 {\rm cm}$">|; 

$key = q/6,E_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4169.png"
 ALT="$6 E_1$">|; 

$key = q/6,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2905.png"
 ALT="$6 {\rm cm}$">|; 

$key = q/6.022times10^{+23};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4276.png"
 ALT="$6.022\times 10^{+23}$">|; 

$key = q/6.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img106.png"
 ALT="$6.0$">|; 

$key = q/6.3times10^{,7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2926.png"
 ALT="$6.3\times 10^{ 7}$">|; 

$key = q/6.674times10^{-11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4271.png"
 ALT="$6.674\times 10^{-11}$">|; 

$key = q/632.8,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3730.png"
 ALT="$632.8 {\rm nm}$">|; 

$key = q/650,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1807.png"
 ALT="$650 {\rm nm}$">|; 

$key = q/6^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img345.png"
 ALT="$6^\circ$">|; 

$key = q/6times10^{7},(Omega,{rmm})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2902.png"
 ALT="$6\times
10^{7} (\Omega {\rm m})^{-1}$">|; 

$key = q/7%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2930.png"
 ALT="$7\%$">|; 

$key = q/7.0times10^{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1357.png"
 ALT="$7.0\times 10^{10}$">|; 

$key = q/7.1times10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1366.png"
 ALT="$7.1\times 10^3$">|; 

$key = q/7.4times10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1376.png"
 ALT="$7.4\times 10^3$">|; 

$key = q/73,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1606.png"
 ALT="$73 \Omega$">|; 

$key = q/7pislash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img56.png"
 ALT="$7\pi /8$">|; 

$key = q/7slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img64.png"
 ALT="$7/16$">|; 

$key = q/7times10^{10},{rmN,m}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1300.png"
 ALT="$7\times 10^{10} {\rm N m}^{-2}$">|; 

$key = q/8.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img110.png"
 ALT="$8.0$">|; 

$key = q/8.3145;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4273.png"
 ALT="$8.3145$">|; 

$key = q/8.3times10^{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1371.png"
 ALT="$8.3\times 10^{10}$">|; 

$key = q/8.5times10^{28},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4259.png"
 ALT="$8.5\times 10^{28} {\rm m}^{-3}$">|; 

$key = q/8.854times10^{-12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4264.png"
 ALT="$8.854\times 10^{-12}$">|; 

$key = q/8.9times10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1362.png"
 ALT="$8.9\times 10^3$">|; 

$key = q/84%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3756.png"
 ALT="$84\%$">|; 

$key = q/8times10^{,6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2503.png"
 ALT="$8\times 10^{ 6}$">|; 

$key = q/9.109times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img4269.png"
 ALT="$9.109\times 10^{-31}$">|; 

$key = q/A'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3117.png"
 ALT="$A''$">|; 

$key = q/A';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3101.png"
 ALT="$A'$">|; 

$key = q/A'E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3106.png"
 ALT="$A'E$">|; 

$key = q/A'P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3128.png"
 ALT="$A'P$">|; 

$key = q/A(t)-A_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2460.png"
 ALT="$A(t)-A_0$">|; 

$key = q/A(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1730.png"
 ALT="$A(x)$">|; 

$key = q/A(x)propto[Z(x)]^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1732.png"
 ALT="$A(x)\propto [Z(x)]^{-1/2}$">|; 

$key = q/A(x,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2944.png"
 ALT="$A(x,z)$">|; 

$key = q/A,Y,epsilon(x+deltaxslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1170.png"
 ALT="$A Y \epsilon(x+\delta x/2)$">|; 

$key = q/A,Y,epsilon(x-deltaxslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1169.png"
 ALT="$A Y \epsilon(x-\delta x/2)$">|; 

$key = q/A,[p+deltap(x-deltaxslash2,t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1230.png"
 ALT="$A [p+\delta p(x-\delta x/2,t)]$">|; 

$key = q/A,cosh[k,(d-h)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3243.png"
 ALT="$A \cosh[k (d-h)]$">|; 

$key = q/A,sin(k,x_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img911.png"
 ALT="$A \sin(k x_i)$">|; 

$key = q/A,sinh[k,(d-h)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3244.png"
 ALT="$A \sinh[k (d-h)]$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img245.png"
 ALT="$A$">|; 

$key = q/A=(8slasha,b,c)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4237.png"
 ALT="$A=(8/a b c)^{1/2}$">|; 

$key = q/A=a,cosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img237.png"
 ALT="$A= a \cos\phi$">|; 

$key = q/A>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img910.png"
 ALT="$A&gt;0$">|; 

$key = q/AA';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3105.png"
 ALT="$AA'$">|; 

$key = q/AA'E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3104.png"
 ALT="$AA'E$">|; 

$key = q/AB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3145.png"
 ALT="$AB$">|; 

$key = q/AD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3146.png"
 ALT="$AD$">|; 

$key = q/APD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3126.png"
 ALT="$APD$">|; 

$key = q/A_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1450.png"
 ALT="$A_+$">|; 

$key = q/A_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.07ex; " SRC="|."$dir".q|img1451.png"
 ALT="$A_-$">|; 

$key = q/A_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1734.png"
 ALT="$A_0$">|; 

$key = q/A_1+A_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1408.png"
 ALT="$A_1+A_2$">|; 

$key = q/A_1,A_2>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1399.png"
 ALT="$A_1, A_2&gt;0$">|; 

$key = q/A_1=A-4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4091.png"
 ALT="$A_1=A-4$">|; 

$key = q/A_1=A_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1409.png"
 ALT="$A_1=A_2$">|; 

$key = q/A_1>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1410.png"
 ALT="$A_1&gt;0$">|; 

$key = q/A_2=4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4093.png"
 ALT="$A_2=4$">|; 

$key = q/A_2>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1411.png"
 ALT="$A_2&gt;0$">|; 

$key = q/A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1519.png"
 ALT="$A_i$">|; 

$key = q/A_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1920.png"
 ALT="$A_j$">|; 

$key = q/A_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img928.png"
 ALT="$A_n$">|; 

$key = q/A_n=(C_n^{,2}+S_n^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1199.png"
 ALT="$A_n = (C_n^{ 2}+S_n^{ 2})^{1/2}$">|; 

$key = q/A_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1063.png"
 ALT="$A_n=0$">|; 

$key = q/A_n=C_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1056.png"
 ALT="$A_n = C_n$">|; 

$key = q/A_nslashA_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1066.png"
 ALT="$A_n/A_1$">|; 

$key = q/A_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1522.png"
 ALT="$A_r$">|; 

$key = q/A_r=-A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1549.png"
 ALT="$A_r=-A_i$">|; 

$key = q/A_r=A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1558.png"
 ALT="$A_r=A_i$">|; 

$key = q/A_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1526.png"
 ALT="$A_t$">|; 

$key = q/A_t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1550.png"
 ALT="$A_t=0$">|; 

$key = q/A_t=2,A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1559.png"
 ALT="$A_t=2 A_i$">|; 

$key = q/A_{-n}=-A_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img937.png"
 ALT="$A_{-n}=-A_n$">|; 

$key = q/A_{N+1+n}=-A_{N+1-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img943.png"
 ALT="$A_{N+1+n}=-A_{N+1-n}$">|; 

$key = q/A_{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img1902.png"
 ALT="$A_{m,n}$">|; 

$key = q/Aproptor^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1868.png"
 ALT="$A\propto r^{ 2}$">|; 

$key = q/Aproptorho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1856.png"
 ALT="$A\propto \rho$">|; 

$key = q/AslashB=exp(q,aslash2),cos(k,aslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3995.png"
 ALT="$A/B= \exp(q a/2) \cos(k a/2)$">|; 

$key = q/B'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3118.png"
 ALT="$B''$">|; 

$key = q/B';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3115.png"
 ALT="$B'$">|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img246.png"
 ALT="$B$">|; 

$key = q/B=4.5times10^{10},{rmN},{rmm}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4194.png"
 ALT="$B= 4.5\times 10^{10} {\rm N} {\rm m}^{-2}$">|; 

$key = q/B=A,exp(-2,k,d);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3043.png"
 ALT="$B = A \exp(-2 k d)$">|; 

$key = q/B=a,sinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img238.png"
 ALT="$B=a \sin\phi$">|; 

$key = q/BC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3127.png"
 ALT="$BC$">|; 

$key = q/BCD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3144.png"
 ALT="$BCD$">|; 

$key = q/B_0(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2693.png"
 ALT="$B_0(z)$">|; 

$key = q/B_0,vslashE_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2580.png"
 ALT="$B_0 v/E_0$">|; 

$key = q/B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2697.png"
 ALT="$B_0$">|; 

$key = q/B_0=E_0slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2582.png"
 ALT="$B_0=E_0/c$">|; 

$key = q/B_0^{,2}slashmu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2842.png"
 ALT="$B_0^{ 2}/\mu_0$">|; 

$key = q/Bsim6.4times10^{10},{rmN},{rmm}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4193.png"
 ALT="$B\sim 6.4\times 10^{10} {\rm N} {\rm m}^{-2}$">|; 

$key = q/C'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3119.png"
 ALT="$C''$">|; 

$key = q/C';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3116.png"
 ALT="$C'$">|; 

$key = q/C'D';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3102.png"
 ALT="$C'D'$">|; 

$key = q/C(-k)=C(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2345.png"
 ALT="$C(-k)=C(k)$">|; 

$key = q/C(-omega)=C(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2455.png"
 ALT="$C(-\omega)=C(\omega)$">|; 

$key = q/C(-z)=-C(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3624.png"
 ALT="$C(-z)=-C(z)$">|; 

$key = q/C(infty)=S(infty)=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3626.png"
 ALT="$C(\infty)=S(\infty) = 1/2$">|; 

$key = q/C(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2347.png"
 ALT="$C(k)$">|; 

$key = q/C(k)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2356.png"
 ALT="$C(k)=0$">|; 

$key = q/C(k)=C(-k)=C_nslash(2,deltak);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2339.png"
 ALT="$C(k)=C(-k)= C_n/(2 \delta k)$">|; 

$key = q/C(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2449.png"
 ALT="$C(\omega)$">|; 

$key = q/C(omega)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2458.png"
 ALT="$C(\omega)=0$">|; 

$key = q/C(v',-infty,infty)=S(v',-infty,infty)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3632.png"
 ALT="$C(v',-\infty,\infty)=S(v',-\infty,\infty)=1$">|; 

$key = q/C(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img99.png"
 ALT="$C(z)$">|; 

$key = q/C,L^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img291.png"
 ALT="$C L^2$">|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img270.png"
 ALT="$C$">|; 

$key = q/C={calC},deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img1097.png"
 ALT="$C={\cal C} \delta x$">|; 

$key = q/CD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3103.png"
 ALT="$CD$">|; 

$key = q/C^{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4200.png"
 ALT="$C^{12}$">|; 

$key = q/C_+(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2407.png"
 ALT="$C_+(k)$">|; 

$key = q/C_+=A,cosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2401.png"
 ALT="$C_+=A \cos\phi$">|; 

$key = q/C_-(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2409.png"
 ALT="$C_-(k)$">|; 

$key = q/C_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img75.png"
 ALT="$C_0$">|; 

$key = q/C_n'=C_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1313.png"
 ALT="$C_n'=C_n$">|; 

$key = q/C_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1255.png"
 ALT="$C_n$">|; 

$key = q/C_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1205.png"
 ALT="$C_n=0$">|; 

$key = q/C_n=A_n,cosphi_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1246.png"
 ALT="$C_n=A_n \cos\phi_n$">|; 

$key = q/D,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3079.png"
 ALT="$D V$">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3073.png"
 ALT="$D$">|; 

$key = q/D=2,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3537.png"
 ALT="$D=2 a$">|; 

$key = q/DAE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3114.png"
 ALT="$DAE$">|; 

$key = q/D_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2071.png"
 ALT="$D_x$">|; 

$key = q/D_xrightarrowH_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2007.png"
 ALT="$D_x\rightarrow H_x$">|; 

$key = q/D_zrightarrowH_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2008.png"
 ALT="$D_z\rightarrow H_z$">|; 

$key = q/Drightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3087.png"
 ALT="$D\rightarrow 0$">|; 

$key = q/E(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1436.png"
 ALT="$E(t)$">|; 

$key = q/E+V>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3951.png"
 ALT="$E+V&gt;0$">|; 

$key = q/E,v_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3077.png"
 ALT="$E v_g$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img125.png"
 ALT="$E$">|; 

$key = q/E<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3950.png"
 ALT="$E&lt;0$">|; 

$key = q/E<U(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4070.png"
 ALT="$E&lt;U(x)$">|; 

$key = q/E<V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4035.png"
 ALT="$E&lt; V$">|; 

$key = q/E=E_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3931.png"
 ALT="$E=E_n$">|; 

$key = q/E=hbar,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3917.png"
 ALT="$E=\hbar \omega$">|; 

$key = q/E=m,c^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1799.png"
 ALT="$E=m c^{ 2}$">|; 

$key = q/E=p^{,2}slash2,m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3944.png"
 ALT="$E=p^{ 2}/2 m$">|; 

$key = q/E>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4001.png"
 ALT="$E&gt;0$">|; 

$key = q/E>U(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3996.png"
 ALT="$E&gt;U(x)$">|; 

$key = q/E>V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4010.png"
 ALT="$E&gt;V$">|; 

$key = q/E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2581.png"
 ALT="$E_0$">|; 

$key = q/E_1=hbar^{,2},pi^{,2}slash(2,m,a^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3940.png"
 ALT="$E_1= \hbar^{ 2} \pi^{ 2}/(2 m a^{ 2})$">|; 

$key = q/E_Fproptoa^{,-2}=V^{,-2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4185.png"
 ALT="$E_F\propto a^{ -2}=V^{ -2/3}$">|; 

$key = q/E_Fpropton^{,2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4188.png"
 ALT="$E_F\propto n^{ 2/3}$">|; 

$key = q/E_L=(hat{E}_x-hat{E}_y)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2815.png"
 ALT="$E_L=(\hat{E}_x-\hat{E}_y)/2$">|; 

$key = q/E_P=hat{E}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2816.png"
 ALT="$E_P=\hat{E}_z$">|; 

$key = q/E_R=(hat{E}_x+hat{E}_y)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2814.png"
 ALT="$E_R=(\hat{E}_x+\hat{E}_y)/2$">|; 

$key = q/E_R=E_L=E_0slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2676.png"
 ALT="$E_R=E_L=E_0/2$">|; 

$key = q/E_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1670.png"
 ALT="$E_i$">|; 

$key = q/E_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1671.png"
 ALT="$E_r$">|; 

$key = q/E_r=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1689.png"
 ALT="$E_r=0$">|; 

$key = q/E_rsimeq-E_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2925.png"
 ALT="$E_r\simeq -E_i$">|; 

$key = q/E_rslashE_i<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1692.png"
 ALT="$E_r/E_i&lt;0$">|; 

$key = q/E_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1676.png"
 ALT="$E_t$">|; 

$key = q/E_t=E_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1690.png"
 ALT="$E_t=E_i$">|; 

$key = q/E_x(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1612.png"
 ALT="$E_x(z,t)$">|; 

$key = q/E_x,(1,,-SslashD,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2877.png"
 ALT="$E_x (1, -S/D,  0)$">|; 

$key = q/E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1615.png"
 ALT="$E_x$">|; 

$key = q/E_x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3209.png"
 ALT="$E_x=0$">|; 

$key = q/E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2127.png"
 ALT="$E_y$">|; 

$key = q/E_y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3208.png"
 ALT="$E_y=0$">|; 

$key = q/E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2128.png"
 ALT="$E_z$">|; 

$key = q/E_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3204.png"
 ALT="$E_z=0$">|; 

$key = q/E_{rmion}=13.6,{rmeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4226.png"
 ALT="$E_{\rm ion}= 13.6 {\rm eV}$">|; 

$key = q/EllE_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4106.png"
 ALT="$E\ll E_c$">|; 

$key = q/Eproptol^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4178.png"
 ALT="$E\propto l^{ 2}$">|; 

$key = q/F(-x)=-F(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2355.png"
 ALT="$F(-x)=-F(x)$">|; 

$key = q/F(-x)=F(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2353.png"
 ALT="$F(-x)=F(x)$">|; 

$key = q/F(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2386.png"
 ALT="$F(k)$">|; 

$key = q/F(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2447.png"
 ALT="$F(t)$">|; 

$key = q/F(t)=cos(omega_0,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2537.png"
 ALT="$F(t)=\cos(\omega_0 t)$">|; 

$key = q/F(v,t-x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2436.png"
 ALT="$F(v t-x)$">|; 

$key = q/F(v,t-x)=c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2437.png"
 ALT="$F(v t-x)=c$">|; 

$key = q/F(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2321.png"
 ALT="$F(x)$">|; 

$key = q/F(x)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2378.png"
 ALT="$F(x)=1$">|; 

$key = q/F(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3499.png"
 ALT="$F(x,y)$">|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2540.png"
 ALT="$F$">|; 

$key = q/F_0,cos(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img850.png"
 ALT="$F_0 \cos(\omega t)$">|; 

$key = q/F_0slash(m_1,omega^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img851.png"
 ALT="$F_0/(m_1 \omega^{ 2})$">|; 

$key = q/F_2(x');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3465.png"
 ALT="$F_2(x')$">|; 

$key = q/F_2(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3455.png"
 ALT="$F_2(x)$">|; 

$key = q/G(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2526.png"
 ALT="$G(t)$">|; 

$key = q/G(v,t+x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2439.png"
 ALT="$G(v t+x)$">|; 

$key = q/G(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2518.png"
 ALT="$G(x)$">|; 

$key = q/G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4198.png"
 ALT="$G$">|; 

$key = q/H(t)=F(t),G(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2533.png"
 ALT="$H(t)=F(t) G(t)$">|; 

$key = q/H_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2129.png"
 ALT="$H_x$">|; 

$key = q/H_y(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1613.png"
 ALT="$H_y(z,t)$">|; 

$key = q/H_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1616.png"
 ALT="$H_y$">|; 

$key = q/H_yrightarrow-v^{,2},D_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2006.png"
 ALT="$H_y\rightarrow -v^{ 2} D_y$">|; 

$key = q/H_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2130.png"
 ALT="$H_z$">|; 

$key = q/H_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3216.png"
 ALT="$H_z=0$">|; 

$key = q/I(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img295.png"
 ALT="$I(0) = 0$">|; 

$key = q/I(0)=I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img299.png"
 ALT="$I(0)=I_0$">|; 

$key = q/I(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img271.png"
 ALT="$I(t)$">|; 

$key = q/I(t)slashhat{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img310.png"
 ALT="$I(t)/\hat{I}$">|; 

$key = q/I(t)slashmathaccentV{hat}05E{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img15.png"
 ALT="$I(t)/\mathaccentV {hat}05E{I}$">|; 

$key = q/I(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1473.png"
 ALT="$I(x,t)$">|; 

$key = q/I(x_i,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1095.png"
 ALT="$I(x_i,t)$">|; 

$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img318.png"
 ALT="$I$">|; 

$key = q/I=I(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1102.png"
 ALT="$I=I(x,t)$">|; 

$key = q/I=dot{Q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img275.png"
 ALT="$I = \dot{Q}$">|; 

$key = q/I=hat{I},cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img307.png"
 ALT="$I=\hat{I} \cos(\omega t-\phi)$">|; 

$key = q/I=m,l^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img325.png"
 ALT="$I=m l^{ 2}$">|; 

$key = q/I=mathaccentV{hat}05E{I}tmspace+thinmuskip{.1667em}qopnamerelaxo{cos}(omegatmspace+thinmuskip{.1667em}t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img12.png"
 ALT="$I=\mathaccentV {hat}05E{I}\tmspace +\thinmuskip {.1667em}\qopname \relax o{cos}(\omega \tmspace +\thinmuskip {.1667em}t-\phi )$">|; 

$key = q/I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img297.png"
 ALT="$I_0$">|; 

$key = q/I_0=I_{N+1}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1078.png"
 ALT="$I_0=I_{N+1}=0$">|; 

$key = q/I_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img736.png"
 ALT="$I_1(t)$">|; 

$key = q/I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img43.png"
 ALT="$I_1$">|; 

$key = q/I_1=0.9,I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img769.png"
 ALT="$I_1=0.9 I_0$">|; 

$key = q/I_1=0.9tmspace+thinmuskip{.1667em}I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img40.png"
 ALT="$I_1=0.9\tmspace +\thinmuskip {.1667em}I_0$">|; 

$key = q/I_1=eta_1+eta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img781.png"
 ALT="$I_1=\eta_1+\eta_2$">|; 

$key = q/I_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img737.png"
 ALT="$I_2(t)$">|; 

$key = q/I_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img44.png"
 ALT="$I_2$">|; 

$key = q/I_2=0.1,I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img770.png"
 ALT="$I_2=0.1 I_0$">|; 

$key = q/I_2=0.1tmspace+thinmuskip{.1667em}I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img41.png"
 ALT="$I_2=0.1\tmspace +\thinmuskip {.1667em}I_0$">|; 

$key = q/I_2=eta_1-eta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img782.png"
 ALT="$I_2=\eta_1-\eta_2$">|; 

$key = q/I_3(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img738.png"
 ALT="$I_3(t)$">|; 

$key = q/I_3=-(I_1+I_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img739.png"
 ALT="$I_3=-(I_1+I_2)$">|; 

$key = q/I_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1076.png"
 ALT="$I_i(t)$">|; 

$key = q/I_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1598.png"
 ALT="$I_i$">|; 

$key = q/I_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1599.png"
 ALT="$I_r$">|; 

$key = q/J_0'(z)=-J_1(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img3754.png"
 ALT="$J_0'(z)=-J_1(z)$">|; 

$key = q/J_0(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img80.png"
 ALT="$J_0(z)$">|; 

$key = q/J_0(z)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1915.png"
 ALT="$J_0(z)=0$">|; 

$key = q/J_1'(z)=J_0(z)-J_1(z)slashz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3753.png"
 ALT="$J_1'(z)=J_0(z)-J_1(z)/z$">|; 

$key = q/J_1[2pi,a,r'slash(lambda,R)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3717.png"
 ALT="$J_1[2\pi a r'/(\lambda R)]$">|; 

$key = q/J_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3762.png"
 ALT="$J_n$">|; 

$key = q/K(0)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3570.png"
 ALT="$K(0)=1$">|; 

$key = q/K(t)slashE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img9.png"
 ALT="$K(t)/E$">|; 

$key = q/K(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3544.png"
 ALT="$K(\theta)$">|; 

$key = q/K(theta)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3547.png"
 ALT="$K(\theta)=0$">|; 

$key = q/K(theta)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3545.png"
 ALT="$K(\theta)=1$">|; 

$key = q/K,(psi_{i+1}-psi_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1125.png"
 ALT="$K (\psi_{i+1}-\psi_i)$">|; 

$key = q/K,e^{,2},a^{,2}slashc^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img635.png"
 ALT="$K e^{ 2} a^{ 2}/c^{ 3}$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img114.png"
 ALT="$K$">|; 

$key = q/K=2.2times10^9,{rmN,m}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2234.png"
 ALT="$K=2.2\times 10^9 {\rm N m}^{-2}$">|; 

$key = q/K=6times10^{,9},{rmN,m^{,2}}slash{rmC^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img636.png"
 ALT="$K=6\times 10^{ 9} {\rm N m^{ 2}}/{\rm C^{ 2}}$">|; 

$key = q/K=A,Yslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1185.png"
 ALT="$K=A Y/a$">|; 

$key = q/K=gamma,p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2243.png"
 ALT="$K=\gamma p$">|; 

$key = q/K=rho,partialpslashpartialrho=-V,partialpslashpartialV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3007.png"
 ALT="$K=\rho \partial p/\partial\rho=-V \partial p/\partial V$">|; 

$key = q/K^{,-1},tilde{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2249.png"
 ALT="$K^{ -1} \tilde{p}$">|; 

$key = q/Krightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3005.png"
 ALT="$K\rightarrow \infty$">|; 

$key = q/L,dot{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img272.png"
 ALT="$L \dot{I}$">|; 

$key = q/L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img269.png"
 ALT="$L$">|; 

$key = q/L=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2878.png"
 ALT="$L=0$">|; 

$key = q/L={calL},deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.28ex; " SRC="|."$dir".q|img1098.png"
 ALT="$L={\cal L} \delta x$">|; 

$key = q/L_c=cslashf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1466.png"
 ALT="$L_c=c/f$">|; 

$key = q/L_csim3,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1471.png"
 ALT="$L_c\sim 3 {\rm cm}$">|; 

$key = q/L_csim30,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1469.png"
 ALT="$L_c\sim 30 {\rm km}$">|; 

$key = q/L_csim30,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1470.png"
 ALT="$L_c\sim 30 {\rm m}$">|; 

$key = q/L_csim5000,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1468.png"
 ALT="$L_c\sim 5000 {\rm km}$">|; 

$key = q/LggD,,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3326.png"
 ALT="$L\gg D, d$">|; 

$key = q/Lrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2333.png"
 ALT="$L\rightarrow\infty$">|; 

$key = q/Lslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1464.png"
 ALT="$L/c$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img346.png"
 ALT="$M$">|; 

$key = q/M_odot=2times10^{30},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4211.png"
 ALT="$M_\odot = 2\times 10^{30} {\rm kg}$">|; 

$key = q/N(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4121.png"
 ALT="$N(0)$">|; 

$key = q/N(t)gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4115.png"
 ALT="$N(t)\gg 1$">|; 

$key = q/N+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1075.png"
 ALT="$N+1$">|; 

$key = q/N+dN;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4116.png"
 ALT="$N+dN$">|; 

$key = q/N-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3384.png"
 ALT="$N-1$">|; 

$key = q/N-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3385.png"
 ALT="$N-2$">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img695.png"
 ALT="$N$">|; 

$key = q/N=10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img93.png"
 ALT="$N=10$">|; 

$key = q/N=8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img948.png"
 ALT="$N=8$">|; 

$key = q/N>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1780.png"
 ALT="$N&gt;1$">|; 

$key = q/N^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3381.png"
 ALT="$N^{ 2}$">|; 

$key = q/N_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4275.png"
 ALT="$N_A$">|; 

$key = q/Nrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img964.png"
 ALT="$N\rightarrow\infty$">|; 

$key = q/O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2874.png"
 ALT="$O$">|; 

$key = q/O^{16};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4201.png"
 ALT="$O^{16}$">|; 

$key = q/P(t)slash(hat{I},hat{V});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img312.png"
 ALT="$P(t)/(\hat{I} \hat{V})$">|; 

$key = q/P(t)slash(mathaccentV{hat}05E{I}tmspace+thinmuskip{.1667em}mathaccentV{hat}05E{V});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img17.png"
 ALT="$P(t)/(\mathaccentV {hat}05E{I}\tmspace +\thinmuskip {.1667em}\mathaccentV {hat}05E{V})$">|; 

$key = q/P-n^{,2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2872.png"
 ALT="$P-n^{ 2} =0$">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img319.png"
 ALT="$P$">|; 

$key = q/P=I,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img309.png"
 ALT="$P=I V$">|; 

$key = q/P=Itmspace+thinmuskip{.1667em}V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img14.png"
 ALT="$P=I\tmspace +\thinmuskip {.1667em}V$">|; 

$key = q/P=n,k_B,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4186.png"
 ALT="$P= n k_B T$">|; 

$key = q/PC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img349.png"
 ALT="$PC$">|; 

$key = q/P_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2599.png"
 ALT="$P_x$">|; 

$key = q/P_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2664.png"
 ALT="$P_y$">|; 

$key = q/P_{rmout}simeq(pi^{,2}slash4)slashlambda^{,3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4242.png"
 ALT="$P_{\rm out}\simeq (\pi^{ 2}/4) / \lambda^{ 3/2}$">|; 

$key = q/P_{rmout}simeq1-2,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4241.png"
 ALT="$P_{\rm out}\simeq 1 - 2 \lambda$">|; 

$key = q/PproptoV^{,-5slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4190.png"
 ALT="$P\propto V^{ -5/3}$">|; 

$key = q/Q(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1475.png"
 ALT="$Q(t)$">|; 

$key = q/Q(t)={calC},deltax,V(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1478.png"
 ALT="$Q(t) = {\cal C} \delta x V(x,t)$">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img274.png"
 ALT="$Q$">|; 

$key = q/Q_1slashC+L,dot{I}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img740.png"
 ALT="$Q_1/C+L \dot{I}_1$">|; 

$key = q/Q_2slashC+L,dot{I}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img742.png"
 ALT="$Q_2/C+L \dot{I}_2$">|; 

$key = q/Q_3=-(Q_1+Q_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img745.png"
 ALT="$Q_3=-(Q_1+Q_2)$">|; 

$key = q/Q_3slashC';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img741.png"
 ALT="$Q_3/C'$">|; 

$key = q/Q_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img474.png"
 ALT="$Q_f$">|; 

$key = q/Q_f=omega_0slashnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img613.png"
 ALT="$Q_f=\omega_0/\nu$">|; 

$key = q/Q_f^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -1.09ex; " SRC="|."$dir".q|img560.png"
 ALT="$Q_f^{ -1}$">|; 

$key = q/Q_fgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img559.png"
 ALT="$Q_f\gg 1$">|; 

$key = q/QslashC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img492.png"
 ALT="$Q/C$">|; 

$key = q/R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3491.png"
 ALT="$R)$">|; 

$key = q/R,I^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img507.png"
 ALT="$R I^{ 2}$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img351.png"
 ALT="$R$">|; 

$key = q/R<2sqrt{LslashC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img500.png"
 ALT="$R&lt;2\sqrt{L/C}$">|; 

$key = q/R=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1589.png"
 ALT="$R=0$">|; 

$key = q/R=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1551.png"
 ALT="$R=1$">|; 

$key = q/R=1slash9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1769.png"
 ALT="$R=1/9$">|; 

$key = q/R=8.3145,{rmJ,mol}^{-1},{rmK}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1381.png"
 ALT="$R=8.3145 {\rm J mol}^{-1} {\rm K}^{-1}$">|; 

$key = q/R^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4213.png"
 ALT="$R^{ -1}$">|; 

$key = q/R^{,-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4214.png"
 ALT="$R^{ -2}$">|; 

$key = q/R_L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1595.png"
 ALT="$R_L$">|; 

$key = q/R_L=Z_1-Z_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1759.png"
 ALT="$R_L=Z_1-Z_2$">|; 

$key = q/R_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img4206.png"
 ALT="$R_\ast$">|; 

$key = q/R_odot=7times10^5,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4210.png"
 ALT="$R_\odot= 7\times 10^5 {\rm km}$">|; 

$key = q/Rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2856.png"
 ALT="$R\rightarrow\infty$">|; 

$key = q/Rsimeq93.3%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2929.png"
 ALT="$R\simeq 93.3\%$">|; 

$key = q/S(-k)=-S(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2346.png"
 ALT="$S(-k)=-S(k)$">|; 

$key = q/S(-omega)=-S(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2456.png"
 ALT="$S(-\omega)=-S(\omega)$">|; 

$key = q/S(-z)=-S(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3625.png"
 ALT="$S(-z)=-S(z)$">|; 

$key = q/S(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2348.png"
 ALT="$S(k)$">|; 

$key = q/S(k)=-S(-k)=S_nslash(2,deltak);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2340.png"
 ALT="$S(k)=-S(-k)=S_n/(2 \delta k)$">|; 

$key = q/S(k)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2354.png"
 ALT="$S(k)=0$">|; 

$key = q/S(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2450.png"
 ALT="$S(\omega)$">|; 

$key = q/S(omega)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2457.png"
 ALT="$S(\omega)=0$">|; 

$key = q/S(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img100.png"
 ALT="$S(z)$">|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2977.png"
 ALT="$S$">|; 

$key = q/S^{,2}-D^{,2}=R,L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2875.png"
 ALT="$S^{ 2}-D^{ 2}=R L$">|; 

$key = q/S_+(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2408.png"
 ALT="$S_+(k)$">|; 

$key = q/S_+=A,sinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2402.png"
 ALT="$S_+=A \sin\phi$">|; 

$key = q/S_-(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2410.png"
 ALT="$S_-(k)$">|; 

$key = q/S_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1283.png"
 ALT="$S_0$">|; 

$key = q/S_n'=-S_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1314.png"
 ALT="$S_n'=-S_n$">|; 

$key = q/S_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1055.png"
 ALT="$S_n$">|; 

$key = q/S_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1295.png"
 ALT="$S_n=0$">|; 

$key = q/S_n=A_n,sinphi_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1247.png"
 ALT="$S_n=A_n \sin\phi_n$">|; 

$key = q/T,sintheta_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img892.png"
 ALT="$T \sin\theta_{i+1}$">|; 

$key = q/T,{mitDelta}s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1416.png"
 ALT="$T {\mit\Delta} s$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img328.png"
 ALT="$T$">|; 

$key = q/T=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1552.png"
 ALT="$T=0$">|; 

$key = q/T=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1590.png"
 ALT="$T=1$">|; 

$key = q/T=1slashf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1339.png"
 ALT="$T=1/f$">|; 

$key = q/T=2pislashomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img216.png"
 ALT="$T=2\pi/\omega$">|; 

$key = q/T=4,m,a^{,2}slashpi,hbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4235.png"
 ALT="$T=4 m a^{ 2}/\pi \hbar$">|; 

$key = q/T_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img407.png"
 ALT="$T_0$">|; 

$key = q/T_0=2pislashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img18.png"
 ALT="$T_0=2\pi /\omega _0$">|; 

$key = q/T_2=T_3=4slash9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1770.png"
 ALT="$T_2=T_3=4/9$">|; 

$key = q/T_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img904.png"
 ALT="$T_i$">|; 

$key = q/T_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img905.png"
 ALT="$T_{i+1}$">|; 

$key = q/Tsimeq7times10^{-2},{rmN,m}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3159.png"
 ALT="$T\simeq 7\times 10^{-2} {\rm N m}^{-1}$">|; 

$key = q/Tslash[rho,(deltax)^{,2}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img976.png"
 ALT="$T/[\rho (\delta x)^{ 2}]$">|; 

$key = q/U(-x)=U(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3953.png"
 ALT="$U(-x)=U(x)$">|; 

$key = q/U(t)slashE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img10.png"
 ALT="$U(t)/E$">|; 

$key = q/U(x)-E=W-e,{calE},x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4083.png"
 ALT="$U(x)-E=W-e {\cal E} x$">|; 

$key = q/U(x)-E=W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4082.png"
 ALT="$U(x)-E=W$">|; 

$key = q/U(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3827.png"
 ALT="$U(x)$">|; 

$key = q/U(x)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4250.png"
 ALT="$U(x)=0$">|; 

$key = q/U(x)=W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4251.png"
 ALT="$U(x)=W$">|; 

$key = q/U(x)>E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3994.png"
 ALT="$U(x)&gt;E$">|; 

$key = q/U(x)rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3948.png"
 ALT="$U(x)\rightarrow 0$">|; 

$key = q/U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4196.png"
 ALT="$U$">|; 

$key = q/U=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3836.png"
 ALT="$U=0$">|; 

$key = q/U=T,{mitDelta}s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1423.png"
 ALT="$U=T {\mit\Delta} s$">|; 

$key = q/U_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3703.png"
 ALT="$U_n$">|; 

$key = q/V(0)=-L,dot{I}(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img298.png"
 ALT="$V(0)=-L \dot{I}(0)=0$">|; 

$key = q/V(0)=-L,dot{I}(0)=V_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img294.png"
 ALT="$V(0)=-L \dot{I}(0)=V_0$">|; 

$key = q/V(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img572.png"
 ALT="$V(t)$">|; 

$key = q/V(t)slashhat{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img311.png"
 ALT="$V(t)/\hat{V}$">|; 

$key = q/V(t)slashmathaccentV{hat}05E{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img16.png"
 ALT="$V(t)/\mathaccentV {hat}05E{V}$">|; 

$key = q/V(x+deltax,t)-V(x,t)=-{calL},deltax,partialI(x,t)slashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1479.png"
 ALT="$V(x+\delta x,t)-V(x,t) = -{\cal L} \delta x \partial I(x,t)/\partial t$">|; 

$key = q/V(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1105.png"
 ALT="$V(x,t)$">|; 

$key = q/V,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3107.png"
 ALT="$V t$">|; 

$key = q/V-E=1,{rmeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4246.png"
 ALT="$V-E = 1 {\rm eV}$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img124.png"
 ALT="$V$">|; 

$key = q/V<E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4032.png"
 ALT="$V &lt; E$">|; 

$key = q/V=(4slash3),E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4047.png"
 ALT="$V = (4/3) E$">|; 

$key = q/V=(4slash3)tmspace+thinmuskip{.1667em}E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img128.png"
 ALT="$V = (4/3)\tmspace +\thinmuskip {.1667em}E$">|; 

$key = q/V=-L,dot{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img282.png"
 ALT="$V= -L \dot{I}$">|; 

$key = q/V=0.75,E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4028.png"
 ALT="$V= 0.75 E$">|; 

$key = q/V=0.75tmspace+thinmuskip{.1667em}E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img126.png"
 ALT="$V= 0.75\tmspace +\thinmuskip {.1667em}E$">|; 

$key = q/V=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3356.png"
 ALT="$V=0$">|; 

$key = q/V=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3355.png"
 ALT="$V=1$">|; 

$key = q/V=I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img493.png"
 ALT="$V=I R$">|; 

$key = q/V=QslashC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img273.png"
 ALT="$V=Q/C$">|; 

$key = q/V=hat{V},sin(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img308.png"
 ALT="$V=\hat{V} \sin(\omega t-\phi)$">|; 

$key = q/V=mathaccentV{hat}05E{V}tmspace+thinmuskip{.1667em}qopnamerelaxo{sin}(omegatmspace+thinmuskip{.1667em}t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img13.png"
 ALT="$V=\mathaccentV {hat}05E{V}\tmspace +\thinmuskip {.1667em}\qopname \relax o{sin}(\omega \tmspace +\thinmuskip {.1667em}t-\phi )$">|; 

$key = q/V=v_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3081.png"
 ALT="$V=v_p$">|; 

$key = q/V>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3946.png"
 ALT="$V&gt;0$">|; 

$key = q/V>E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4052.png"
 ALT="$V &gt; E$">|; 

$key = q/V_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img293.png"
 ALT="$V_0$">|; 

$key = q/V_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4256.png"
 ALT="$V_0&gt; 0$">|; 

$key = q/V_Allc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2840.png"
 ALT="$V_A\ll c$">|; 

$key = q/V_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1104.png"
 ALT="$V_i(t)$">|; 

$key = q/V_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3699.png"
 ALT="$V_n$">|; 

$key = q/VggE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4051.png"
 ALT="$V\gg E$">|; 

$key = q/VllE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4031.png"
 ALT="$V\ll E$">|; 

$key = q/Vrightarrow(g,d)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3085.png"
 ALT="$V\rightarrow (g d)^{1/2}$">|; 

$key = q/Vsim0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3359.png"
 ALT="$V\sim 0$">|; 

$key = q/Vsim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3358.png"
 ALT="$V\sim 1$">|; 

$key = q/W(<E);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4249.png"
 ALT="$W (&lt;E)$">|; 

$key = q/W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3789.png"
 ALT="$W$">|; 

$key = q/Wslashhbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3792.png"
 ALT="$W/\hbar$">|; 

$key = q/X(0)=X(a)=Y(0)=Y(b)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1879.png"
 ALT="$X(0)=X(a)=Y(0)=Y(b)=0$">|; 

$key = q/X(0)=Y(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1894.png"
 ALT="$X(0)=Y(0)=0$">|; 

$key = q/X(a)=Y(b)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1895.png"
 ALT="$X(a)=Y(b)=0$">|; 

$key = q/X(beta)=V,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3136.png"
 ALT="$X(\beta)=V t$">|; 

$key = q/X(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img509.png"
 ALT="$X(t)$">|; 

$key = q/X,sin^3beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3253.png"
 ALT="$X \sin^3\beta$">|; 

$key = q/X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2890.png"
 ALT="$X$">|; 

$key = q/X_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1893.png"
 ALT="$X_0$">|; 

$key = q/X_0=2,j,lambda_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3154.png"
 ALT="$X_0=2 j \lambda_0$">|; 

$key = q/Y,({rmN,m}^{-2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1353.png"
 ALT="$Y  ({\rm N m}^{-2})$">|; 

$key = q/Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1166.png"
 ALT="$Y$">|; 

$key = q/Y_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1084.png"
 ALT="$Y_0$">|; 

$key = q/Z(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1720.png"
 ALT="$Z(x)$">|; 

$key = q/Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img133.png"
 ALT="$Z$">|; 

$key = q/Z=R_L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1605.png"
 ALT="$Z=R_L$">|; 

$key = q/Z=Z_0slashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2314.png"
 ALT="$Z=Z_0/n$">|; 

$key = q/Z=sqrt{{calL}slash{calC}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.48ex; " SRC="|."$dir".q|img1793.png"
 ALT="$Z=\sqrt{{\cal L}/{\cal C}}$">|; 

$key = q/Z^{,-1}propton;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1681.png"
 ALT="$Z^{ -1}\propto n$">|; 

$key = q/Z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1627.png"
 ALT="$Z_0$">|; 

$key = q/Z_0=sqrt{mu_0slashepsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1822.png"
 ALT="$Z_0=\sqrt{\mu_0/\epsilon_0}$">|; 

$key = q/Z_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1591.png"
 ALT="$Z_1$">|; 

$key = q/Z_1=Z-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img132.png"
 ALT="$Z_1=Z-2$">|; 

$key = q/Z_1=Z_0slashn_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1673.png"
 ALT="$Z_1=Z_0/n_1$">|; 

$key = q/Z_1=rho_1,v_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2318.png"
 ALT="$Z_1=\rho_1 v_1$">|; 

$key = q/Z_1=sqrt{rho_1,T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img1537.png"
 ALT="$Z_1=\sqrt{\rho_1 T}$">|; 

$key = q/Z_1>Z_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1752.png"
 ALT="$Z_1&gt;Z_2$">|; 

$key = q/Z_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1592.png"
 ALT="$Z_2$">|; 

$key = q/Z_2=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4092.png"
 ALT="$Z_2=2$">|; 

$key = q/Z_2=Z_0slashn_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1678.png"
 ALT="$Z_2=Z_0/n_2$">|; 

$key = q/Z_2=rho_2,v_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2319.png"
 ALT="$Z_2=\rho_2 v_2$">|; 

$key = q/Z_2=sqrt{rho_2,T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img1538.png"
 ALT="$Z_2=\sqrt{\rho_2 T}$">|; 

$key = q/Z_2=sqrt{rho_2,T}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img1557.png"
 ALT="$Z_2=\sqrt{\rho_2 T}\rightarrow 0$">|; 

$key = q/Z_2=sqrt{rho_2,T}rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img1548.png"
 ALT="$Z_2=\sqrt{\rho_2 T}\rightarrow\infty$">|; 

$key = q/Z_2neqZ_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1593.png"
 ALT="$Z_2\neq Z_1$">|; 

$key = q/Z_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1763.png"
 ALT="$Z_3$">|; 

$key = q/Z_3=sqrt{Z_1,Z_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.50ex; " SRC="|."$dir".q|img1588.png"
 ALT="$Z_3=\sqrt{Z_1 Z_2}$">|; 

$key = q/Zgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4095.png"
 ALT="$Z\gg 1$">|; 

$key = q/ZllZ_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1507.png"
 ALT="$Z\ll Z_0$">|; 

$key = q/[(k_1+k_2)slashm]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img365.png"
 ALT="$[(k_1+k_2)/m]^{1/2}$">|; 

$key = q/[2,K,(1slashM+1slashm)]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1305.png"
 ALT="$[2 K (1/M+1/m)]^{1/2}$">|; 

$key = q/[K(t)+U(t)]slashE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img11.png"
 ALT="$[K(t)+U(t)]/E$">|; 

$key = q/[bar{F}_1(theta)]^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3476.png"
 ALT="$[\bar{F}_1(\theta)]^{ 2}$">|; 

$key = q/[bar{F}_2(theta)]^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3482.png"
 ALT="$[\bar{F}_2(\theta)]^{ 2}$">|; 

$key = q/[bar{F}_2(theta-theta_0)]^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3478.png"
 ALT="$[\bar{F}_2(\theta-\theta_0)]^{ 2}$">|; 

$key = q/[k_1,k_2slash(k_1+k_2),m]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img366.png"
 ALT="$[k_1 k_2/(k_1+k_2) m]^{1/2}$">|; 

$key = q/a(t)=(hat{X}slash2),omega_0,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img628.png"
 ALT="$a(t) = (\hat{X}/2) \omega_0 t$">|; 

$key = q/a(t)=a,exp(-gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img427.png"
 ALT="$a(t)=a \exp(-\gamma t)$">|; 

$key = q/a(t)=hat{X},Q_fleft(1-{rme}^{-nu,tslash2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img614.png"
 ALT="$a(t) = \hat{X} Q_f\left(1-{\rm e}^{-\nu t/2}\right)$">|; 

$key = q/a(t)=hat{X},[omega_0slash(omega_0-omega)],sin[(omega_0-omega)slasht];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img622.png"
 ALT="$a(t) = \hat{X} [\omega_0/(\omega_0-\omega)] \sin[(\omega_0-\omega)/t]$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img82.png"
 ALT="$a$">|; 

$key = q/a<l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1080.png"
 ALT="$a&lt;l$">|; 

$key = q/a=0.5,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4045.png"
 ALT="$a=0.5 \lambda$">|; 

$key = q/a=0.5tmspace+thinmuskip{.1667em}lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img127.png"
 ALT="$a=0.5\tmspace +\thinmuskip {.1667em}\lambda $">|; 

$key = q/a=1.25,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4026.png"
 ALT="$a=1.25 \lambda$">|; 

$key = q/a=1.25tmspace+thinmuskip{.1667em}lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img122.png"
 ALT="$a=1.25\tmspace +\thinmuskip {.1667em}\lambda $">|; 

$key = q/a=2,b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1872.png"
 ALT="$a=2 b$">|; 

$key = q/a=2tmspace+thinmuskip{.1667em}b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img79.png"
 ALT="$a=2\tmspace +\thinmuskip {.1667em}b$">|; 

$key = q/a=deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img972.png"
 ALT="$a=\delta x$">|; 

$key = q/a=lslash10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1081.png"
 ALT="$a=l/10$">|; 

$key = q/a>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img148.png"
 ALT="$a&gt;0$">|; 

$key = q/agglambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4056.png"
 ALT="$a\gg\lambda$">|; 

$key = q/alpha,s_1+beta,s_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img258.png"
 ALT="$\alpha s_1+\beta s_2$">|; 

$key = q/alpha,x_1(t)+beta,x_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img468.png"
 ALT="$\alpha x_1(t)+\beta x_2(t)$">|; 

$key = q/alpha,x_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img707.png"
 ALT="$\alpha x_1(t)$">|; 

$key = q/alpha,x_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img708.png"
 ALT="$\alpha x_2(t)$">|; 

$key = q/alpha,y(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1012.png"
 ALT="$\alpha y(x,t)$">|; 

$key = q/alpha,{bfx}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img808.png"
 ALT="$\alpha {\bf x}(t)$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img130.png"
 ALT="$\alpha $">|; 

$key = q/alpha=0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img45.png"
 ALT="$\alpha = 0.5$">|; 

$key = q/alpha=2,d^{,2}f(0)slashdx^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img420.png"
 ALT="$\alpha=2 d^{ 2}f(0)/dx^{ 2}$">|; 

$key = q/alpha=CslashC';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img752.png"
 ALT="$\alpha=C/C'$">|; 

$key = q/alpha=L'slashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img837.png"
 ALT="$\alpha=L'/L$">|; 

$key = q/alpha=beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2218.png"
 ALT="$\alpha=\beta$">|; 

$key = q/alpha=k'slashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img833.png"
 ALT="$\alpha=k'/k$">|; 

$key = q/alpha=m'slashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img835.png"
 ALT="$\alpha=m'/m$">|; 

$key = q/alpha^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1887.png"
 ALT="$\alpha^{ 2}$">|; 

$key = q/alphall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2919.png"
 ALT="$\alpha\ll 1$">|; 

$key = q/aproptod^{,-1slash4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3242.png"
 ALT="$a\propto d^{ -1/4}$">|; 

$key = q/aslashl=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1212.png"
 ALT="$a/l=0.1$">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img381.png"
 ALT="$b$">|; 

$key = q/b=2,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3511.png"
 ALT="$b=2 a$">|; 

$key = q/b=2tmspace+thinmuskip{.1667em}a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img97.png"
 ALT="$b=2\tmspace +\thinmuskip {.1667em}a$">|; 

$key = q/bar{F}(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2527.png"
 ALT="$\bar{F}(\omega)$">|; 

$key = q/bar{F}(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3427.png"
 ALT="$\bar{F}(\theta)$">|; 

$key = q/bar{F}_1(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3474.png"
 ALT="$\bar{F}_1(\theta)$">|; 

$key = q/bar{F}_2(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3475.png"
 ALT="$\bar{F}_2(\theta)$">|; 

$key = q/bar{G}(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2528.png"
 ALT="$\bar{G}(\omega)$">|; 

$key = q/bar{H}(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2534.png"
 ALT="$\bar{H}(\omega)$">|; 

$key = q/bar{f}(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3871.png"
 ALT="$\bar{f}(k)$">|; 

$key = q/bar{f}(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3600.png"
 ALT="$\bar{f}(u,v)$">|; 

$key = q/bar{psi}(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3868.png"
 ALT="$\bar{\psi}(k)$">|; 

$key = q/bar{psi}(u',v',t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3609.png"
 ALT="$\bar{\psi}(u',v',t)$">|; 

$key = q/bar{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3865.png"
 ALT="$\bar{\psi}$">|; 

$key = q/beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img219.png"
 ALT="$\beta$">|; 

$key = q/beta=2,(k-k_0),{mitDelta}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3884.png"
 ALT="$\beta = 2 (k-k_0) {\mit\Delta}x$">|; 

$key = q/beta=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3147.png"
 ALT="$\beta=\pi/2$">|; 

$key = q/beta=pmtan^{-1}left(sqrt{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3149.png"
 ALT="$\beta=\pm \tan^{-1}\left(\sqrt{2}\right)$">|; 

$key = q/beta^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1888.png"
 ALT="$\beta^{ 2}$">|; 

$key = q/bm{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2100.png"
 ALT="$\bm{\epsilon}$">|; 

$key = q/bm{mathcal{I}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2143.png"
 ALT="$\bm{\mathcal{I}}$">|; 

$key = q/c,d^{,2}sslashdt^{,2}=d^{,2}(c,s)slashdt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img249.png"
 ALT="$c d^{ 2}s/dt^{ 2}=d^{ 2}(c s)/dt^{ 2}$">|; 

$key = q/c,s(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img248.png"
 ALT="$c s(t)$">|; 

$key = q/c,x(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img465.png"
 ALT="$c x(t)$">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img244.png"
 ALT="$c$">|; 

$key = q/c=1slash(epsilon_0,mu_0)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1654.png"
 ALT="$c=1/(\epsilon_0 \mu_0)^{1/2}$">|; 

$key = q/c=1slashsqrt{epsilon_0,mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img1816.png"
 ALT="$c=1/\sqrt{\epsilon_0 \mu_0}$">|; 

$key = q/c=sqrt{Kslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img3028.png"
 ALT="$c=\sqrt{K/\rho}$">|; 

$key = q/c^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3178.png"
 ALT="$c^{ 2}$">|; 

$key = q/cos(-k,x)=cos(k,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2351.png"
 ALT="$\cos(-k x)=\cos(k x)$">|; 

$key = q/cos(-theta)equivcostheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img200.png"
 ALT="$\cos(-\theta) \equiv\cos\theta$">|; 

$key = q/cos(2,theta)equivcos^2theta-sin^2theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img314.png"
 ALT="$\cos(2 \theta)\equiv \cos^2\theta-\sin^2\theta$">|; 

$key = q/cos(a+b)equivcosa,cosb-sina,sinb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1401.png"
 ALT="$\cos(a+b)\equiv \cos a \cos b-\sin a \sin b$">|; 

$key = q/cos(a-b)equivcosa,cosb+sina,sinb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1400.png"
 ALT="$\cos(a-b)\equiv \cos a \cos b+\sin a \sin b$">|; 

$key = q/cos(k,x)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1403.png"
 ALT="$\cos(k x)=0$">|; 

$key = q/cos(k,x)=pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1190.png"
 ALT="$\cos(k x)=\pm 1$">|; 

$key = q/cos(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img528.png"
 ALT="$\cos(\omega t)$">|; 

$key = q/cos(omega,t+k_3,a)=-sin(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1577.png"
 ALT="$\cos(\omega t+k_3 a)=-\sin(\omega t)$">|; 

$key = q/cos(omega,t-k,x-phi)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1342.png"
 ALT="$\cos(\omega t-k x-\phi)=1$">|; 

$key = q/cos(omega,t-k_2,a-phi_t)=sin(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1578.png"
 ALT="$\cos(\omega t-k_2 a-\phi_t)=\sin(\omega t)$">|; 

$key = q/cos(omega,t-k_3,a)=sin(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1576.png"
 ALT="$\cos(\omega t-k_3 a)= \sin(\omega t)$">|; 

$key = q/cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img679.png"
 ALT="$\cos(\omega t-\phi)$">|; 

$key = q/cos(omega,t-phi)equivcos(-omega,t+phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img693.png"
 ALT="$\cos(\omega t-\phi)\equiv \cos(-\omega t+\phi)$">|; 

$key = q/cos(omega,t-phi_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1534.png"
 ALT="$\cos(\omega t-\phi_i)$">|; 

$key = q/cos(omega,t-varphi)equivcos(omega,t),cosvarphi+sin(omega,t),sinvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img524.png"
 ALT="$\cos(\omega t-\varphi)\equiv \cos(\omega t) \cos\varphi + \sin(\omega t) \sin\varphi$">|; 

$key = q/cos(omega_n,t-phi_n)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1129.png"
 ALT="$\cos(\omega_n t-\phi_n)=1$">|; 

$key = q/cos(theta+2pi)equivcostheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img167.png"
 ALT="$\cos(\theta+2\pi) \equiv \cos\theta$">|; 

$key = q/cos(theta+n,2pi)=costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2325.png"
 ALT="$\cos(\theta+n 2\pi)=\cos\theta$">|; 

$key = q/cos(theta+n,2pi)equivcostheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1251.png"
 ALT="$\cos(\theta+n 2\pi)\equiv \cos\theta$">|; 

$key = q/cos(theta-pislash2)equivsintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img305.png"
 ALT="$\cos(\theta-\pi/2)\equiv \sin\theta$">|; 

$key = q/cos(x+pislash2)=-sin(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3562.png"
 ALT="$\cos(x+\pi/2)=-\sin(x)$">|; 

$key = q/cos(x-y)equivcosx,cosy+sinx,siny;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img239.png"
 ALT="$\cos(x-y) \equiv \cos x \cos y+\sin x \sin y$">|; 

$key = q/cos(x-y)equivcosx,cosy-sinx,siny;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3468.png"
 ALT="$\cos(x-y)\equiv \cos x \cos y-\sin x \sin y$">|; 

$key = q/cos[k,(x_0-aslash2)]=cos(-k,aslash2)=cos(k,aslash2)=cos[k,(x_1-aslash2)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1139.png"
 ALT="$\cos[k (x_0-a/2)]=\cos(-k a/2)=\cos(k a/2)=\cos[k (x_1-a/2)]$">|; 

$key = q/cos[pi,(dslashlambda),theta_0]=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3347.png"
 ALT="$\cos[\pi (d/\lambda) \theta_0]=0$">|; 

$key = q/cos[pi,(dslashlambda),theta_0]simeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3350.png"
 ALT="$\cos[\pi (d/\lambda) \theta_0]\simeq 1$">|; 

$key = q/cos^2thetaequiv(1+cos2theta)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3344.png"
 ALT="$\cos^2\theta\equiv (1+\cos 2\theta)/2$">|; 

$key = q/cosa+cosbequiv2,cos[(a+b)slash2],cos[(a-b)slash2];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img723.png"
 ALT="$\cos a + \cos b\equiv 2 \cos[(a+b)/2] \cos[(a-b)/2]$">|; 

$key = q/cosa-cosbequiv-2,sin[(a+b)slash2],sin[(a-b)slash2];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img620.png"
 ALT="$\cos a - \cos b \equiv -2 \sin[(a+b)/2] \sin[(a-b)/2]$">|; 

$key = q/cosa-cosbequiv2,sin[(a+b)slash2],sin[(b-a)slash2];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1556.png"
 ALT="$\cos a-\cos b \equiv 2 \sin[(a+b)/2] \sin[(b-a)/2]$">|; 

$key = q/costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img164.png"
 ALT="$\cos\theta$">|; 

$key = q/costheta_isimeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img907.png"
 ALT="$\cos\theta_i\simeq 1$">|; 

$key = q/costhetaequivsin(theta+pislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img242.png"
 ALT="$\cos\theta \equiv \sin(\theta+\pi/2)$">|; 

$key = q/cosx+cosyequiv2,cos[(x+y)slash2],cos((x-y)slash2];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3345.png"
 ALT="$\cos x + \cos y \equiv 2 \cos[(x+y)/2] \cos((x-y)/2]$">|; 

$key = q/cosx+cosyequiv2,cos[(x+y)slash2],cos[(x-y)slash2];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3273.png"
 ALT="$\cos x + \cos y\equiv 2 \cos[(x+y)/2] \cos[(x-y)/2]$">|; 

$key = q/cslashf=lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1467.png"
 ALT="$c/f=\lambda$">|; 

$key = q/d(costheta)slashdtheta=-sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img151.png"
 ALT="$d(\cos\theta)/d\theta = -\sin\theta$">|; 

$key = q/d(sintheta)slashdtheta=costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img152.png"
 ALT="$d (\sin\theta)/d\theta = \cos\theta$">|; 

$key = q/d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img348.png"
 ALT="$d$">|; 

$key = q/d=v,t-j,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1830.png"
 ALT="$d=v t-j \lambda$">|; 

$key = q/d>2,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1509.png"
 ALT="$d&gt;2 a$">|; 

$key = q/d>delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3261.png"
 ALT="$d&gt;\delta$">|; 

$key = q/dEslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1438.png"
 ALT="$dE/dt$">|; 

$key = q/dQslashdt=I(x,t)-I(x+deltax,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1477.png"
 ALT="$dQ/dt = I(x,t)-I(x+\delta x,t)$">|; 

$key = q/dS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3543.png"
 ALT="$dS$">|; 

$key = q/d^{,2}omegaslashdk^{,2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2578.png"
 ALT="$d^{ 2}\omega/dk^{ 2}=0$">|; 

$key = q/d^{,2}psislashdx^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3924.png"
 ALT="$d^{ 2}\psi/dx^{ 2}$">|; 

$key = q/d^{,2}s_1slashdt^{,2}+d^{,2}s_2slashdt^{,2}=d^{,2}(s_1+s_2)slashdt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img255.png"
 ALT="$d^{ 2}s_1/dt^{ 2}+d^{ 2} s_2/dt^{ 2}=d^{ 2}(s_1+s_2)/dt^{ 2}$">|; 

$key = q/d_1=v,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1706.png"
 ALT="$d_1=v t$">|; 

$key = q/d_2=v,(t-T)+u_s,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1707.png"
 ALT="$d_2 =v (t-T) + u_s T$">|; 

$key = q/ddot{phantom{x}}equivd^{,2}slashdt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img146.png"
 ALT="$\ddot{\phantom{x}} \equiv d^{ 2}/dt^{ 2}$">|; 

$key = q/ddot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img184.png"
 ALT="$\ddot{x}$">|; 

$key = q/ddot{x}=-omega^{,2},a,cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img154.png"
 ALT="$\ddot{x} = -\omega^{ 2} a \cos(\omega t-\phi)$">|; 

$key = q/ddot{y}_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img973.png"
 ALT="$\ddot{y}_i(t)$">|; 

$key = q/delta(0)=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2383.png"
 ALT="$\delta(0)=\infty$">|; 

$key = q/delta(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2379.png"
 ALT="$\delta (k)$">|; 

$key = q/delta(k)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2381.png"
 ALT="$\delta(k)=0$">|; 

$key = q/delta(k-k');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2388.png"
 ALT="$\delta(k-k')$">|; 

$key = q/delta(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3422.png"
 ALT="$\delta(x)$">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3258.png"
 ALT="$\delta$">|; 

$key = q/delta<d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3451.png"
 ALT="$\delta &lt; d$">|; 

$key = q/delta=2,Zslash{calR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1792.png"
 ALT="$\delta = 2 Z/{\cal R}$">|; 

$key = q/delta=2,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3410.png"
 ALT="$\delta=2 t$">|; 

$key = q/delta=2slash(Z_0,sigma);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1821.png"
 ALT="$\delta = 2/(Z_0 \sigma)$">|; 

$key = q/delta=2times10^{,-4},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3201.png"
 ALT="$\delta=2\times 10^{ -4} {\rm m}$">|; 

$key = q/deltaV(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1224.png"
 ALT="$\delta V(x,t)$">|; 

$key = q/deltaV=A,[psi(x+deltaxslash2,t)-psi(x-deltaxslash2,t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1220.png"
 ALT="$\delta V = A [\psi(x+\delta x/2,t)-\psi(x-\delta x/2,t)]$">|; 

$key = q/deltaVslashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1228.png"
 ALT="$\delta V/V$">|; 

$key = q/delta_{n,n'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img2330.png"
 ALT="$\delta_{n,n'}$">|; 

$key = q/deltagglambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3434.png"
 ALT="$\delta\gg \lambda$">|; 

$key = q/deltagtrsimlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3419.png"
 ALT="$\delta\gtrsim \lambda$">|; 

$key = q/deltakrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2334.png"
 ALT="$\delta k\rightarrow 0$">|; 

$key = q/deltalllambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3264.png"
 ALT="$\delta\ll \lambda$">|; 

$key = q/deltap(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1248.png"
 ALT="$\delta p(t)$">|; 

$key = q/deltap(t+tau')=deltap(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1254.png"
 ALT="$\delta p(t+\tau')=\delta p(t)$">|; 

$key = q/deltap(t+tau)=deltap(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1250.png"
 ALT="$\delta p(t+\tau)=\delta p(t)$">|; 

$key = q/deltap(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1223.png"
 ALT="$\delta p(x,t)$">|; 

$key = q/deltapslashp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1229.png"
 ALT="$\delta p/p$">|; 

$key = q/deltaslashlambda=20;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img94.png"
 ALT="$\delta /\lambda = 20$">|; 

$key = q/deltaslashlambda=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img96.png"
 ALT="$\delta /\lambda =2$">|; 

$key = q/deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3450.png"
 ALT="$\delta\theta$">|; 

$key = q/deltatheta=lambdaslashD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3446.png"
 ALT="$\delta\theta=\lambda/D$">|; 

$key = q/deltatheta=z_1slash(k,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3534.png"
 ALT="$\delta\theta=z_1/(k a)$">|; 

$key = q/deltatheta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3397.png"
 ALT="$\delta\theta_j$">|; 

$key = q/deltathetasimeq(1slashN),(lambdaslashd);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3386.png"
 ALT="$\delta\theta \simeq (1/N) (\lambda/d)$">|; 

$key = q/deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1155.png"
 ALT="$\delta x$">|; 

$key = q/deltaxrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img982.png"
 ALT="$\delta x\rightarrow 0$">|; 

$key = q/df(0)slashdx<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img417.png"
 ALT="$df(0)/dx&lt;0$">|; 

$key = q/dgglambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3306.png"
 ALT="$d\gg \lambda$">|; 

$key = q/displaystyle%label{e7.57}frac{R_ast}{R_odot}=0.010left(frac{M_odot}{M}right)^{1slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.02ex; " SRC="|."$dir".q|img4209.png"
 ALT="$\displaystyle %\label{e7.57}
\frac{R_\ast}{R_\odot}= 0.010\left(\frac{M_\odot}{M}\right)^{1/3},$">|; 

$key = q/displaystyle(1+deltapslashp),(1+deltaVslashV)^gammasimeq1+deltapslashp+gamma,deltaVslashV=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1226.png"
 ALT="$\displaystyle (1+\delta p/p) (1+\delta V/V)^\gamma \simeq 1+ \delta p/p + \gamma \delta V/V=1,$">|; 

$key = q/displaystyle(1+x)^alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4312.png"
 ALT="$\displaystyle (1+x)^\alpha$">|; 

$key = q/displaystyle(hat{omega}^{,2}-2),(hat{omega}^{,2}-2)-1=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img685.png"
 ALT="$\displaystyle (\hat{\omega}^{ 2}-2) (\hat{\omega}^{ 2}-2)-1 = 0.$">|; 

$key = q/displaystyle(hat{omega}^{,2}-2),hat{x}_1+hat{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img680.png"
 ALT="$\displaystyle (\hat{\omega}^{ 2}-2) \hat{x}_1 +\hat{x}_2$">|; 

$key = q/displaystyle(hat{omega}^{,2}-2),left[hat{omega}^{,2}-2-sqrt{2}right],left[hat{omega}^{,2}-2+sqrt{2}right]=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img797.png"
 ALT="$\displaystyle (\hat{\omega}^{ 2}-2) \left[\hat{\omega}^{ 2}-2-\sqrt{2}\right] \left[
\hat{\omega}^{ 2}-2+\sqrt{2}\right]=0.$">|; 

$key = q/displaystyle(hat{omega}^{,2}-2)left[(hat{omega}^{,2}-2)^2-1right]-(hat{omega}^{,2}-2)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img796.png"
 ALT="$\displaystyle (\hat{\omega}^{ 2}-2)\left[(\hat{\omega}^{ 2}-2)^2-1\right]-(\hat{\omega}^{ 2}-2)=0,$">|; 

$key = q/displaystyle(p+deltap),(V+deltaV)^gamma=p,V^{,gamma},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1225.png"
 ALT="$\displaystyle (p+\delta p) (V+\delta V)^\gamma = p V^{ \gamma},$">|; 

$key = q/displaystyle+hat{x}left[left(omega_0^{,2}-omega^{,2}right)sinvarphi-nu,omega,cosvarphiright]sin(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img527.png"
 ALT="$\displaystyle +\hat{x}\left[\left(\omega_0^{ 2}-\omega^{ 2}\right)\sin\varphi-\nu \omega \cos\varphi\right]\sin(\omega t)$">|; 

$key = q/displaystyle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.56ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1271.png"
 ALT="$\displaystyle ,$">|; 

$key = q/displaystyle,frac{hbar}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4143.png"
 ALT="$\displaystyle  \frac{\hbar}{2},$">|; 

$key = q/displaystyle,frac{hbar}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4146.png"
 ALT="$\displaystyle  \frac{\hbar}{2}.$">|; 

$key = q/displaystyle-S_+(k)+S_-(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2416.png"
 ALT="$\displaystyle -S_+(k) + S_-(k)$">|; 

$key = q/displaystyle-frac{1}{epsilon_0},frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1609.png"
 ALT="$\displaystyle - \frac{1}{\epsilon_0} \frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyle-frac{1}{mu_0},frac{partialE_x}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1611.png"
 ALT="$\displaystyle -\frac{1}{\mu_0} \frac{\partial E_x}{\partial z},$">|; 

$key = q/displaystyle-frac{1}{pi}int_0^picosleft[(n+n'),thetaright]dtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1025.png"
 ALT="$\displaystyle -\frac{1}{\pi}\int_0^\pi\cos\left[(n+n') \theta\right] d\theta$">|; 

$key = q/displaystyle-frac{hbar^{,2}}{2,m},frac{d^{,2}psi}{dx^{,2}}+U(x),psi=E,psi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3920.png"
 ALT="$\displaystyle -\frac{\hbar^{ 2}}{2 m} \frac{d^{ 2}\psi}{d x^{ 2}} + U(x) \psi = E \psi.$">|; 

$key = q/displaystyle-frac{hbar^{,2}}{2,m},frac{d^{,2}psi}{dx^{,2}}=E,psi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3922.png"
 ALT="$\displaystyle -\frac{\hbar^{ 2}}{2 m} \frac{d^{ 2}\psi}{d x^{ 2}} = E \psi.$">|; 

$key = q/displaystyle-frac{hbar^{,2}}{2,m},nabla^{,2}psi+U({bfr}),psi=E,psi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4149.png"
 ALT="$\displaystyle - \frac{\hbar^{ 2}}{2 m} \nabla^{ 2}\psi + U({\bf r}) \psi = E \psi.$">|; 

$key = q/displaystyle-frac{hbar^{,2}}{2,m},nabla^{,2}psi=E,psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4151.png"
 ALT="$\displaystyle - \frac{\hbar^{ 2}}{2 m} \nabla^{ 2}\psi = E \psi,$">|; 

$key = q/displaystyle-frac{y}{sqrt{lambda-y^{,2}}}=tany.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img3988.png"
 ALT="$\displaystyle -\frac{y}{\sqrt{\lambda-y^{ 2}}} = \tan y.$">|; 

$key = q/displaystyle-m,omega^{,2},a,cos(omega,t-phi)=-k,a,cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle -m \omega^{ 2} a \cos(\omega t-\phi) =- k a \cos(\omega t-\phi).$">|; 

$key = q/displaystyle-omega^{,2},A,sin(k,x_i),cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img914.png"
 ALT="$\displaystyle -\omega^{ 2} A \sin(k x_i) \cos(\omega t-\phi)$">|; 

$key = q/displaystyle-omega^{,2},hat{x}_1,cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img675.png"
 ALT="$\displaystyle -\omega^{ 2} \hat{x}_1 \cos(\omega t-\phi)$">|; 

$key = q/displaystyle-omega^{,2},hat{x}_2,cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img677.png"
 ALT="$\displaystyle -\omega^{ 2} \hat{x}_2 \cos(\omega t-\phi)$">|; 

$key = q/displaystyle-omega^{,2},sin(k,x_i)=omega_0^{,2}left(sin[k,(x_i-a)]-2,sin(k,x_i)+sin[k,(x_i+a)]right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img917.png"
 ALT="$\displaystyle -\omega^{ 2} \sin(k x_i)=\omega_0^{ 2}\left(\sin[k (x_i-a)] -2 \sin(k x_i)
+\sin[k (x_i+a)]\right).$">|; 

$key = q/displaystyle-omega^{,2},sin(k,x_i)=omega_0^{,2}left[cos(k,a)-2+cos(k,a)right]sin(k,x_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img919.png"
 ALT="$\displaystyle -\omega^{ 2} \sin(k x_i)=\omega_0^{ 2}\left[\cos(k a)-2+\cos(k a)\right]\sin(k x_i),$">|; 

$key = q/displaystyle0=frac{1}{2pi}int_{-infty}^{infty}sin(k,x),dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2392.png"
 ALT="$\displaystyle 0 = \frac{1}{2\pi}\int_{-\infty}^{\infty} \sin(k x) dx.$">|; 

$key = q/displaystyle1+R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4015.png"
 ALT="$\displaystyle 1 + R$">|; 

$key = q/displaystyle1+frac{1}{8pi^{,2},n^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img632.png"
 ALT="$\displaystyle 1 + \frac{1}{8\pi^{ 2} n^{ 2}}.
$">|; 

$key = q/displaystyle1lesssimfrac{d^{,2}}{lambda,R}llleft(frac{R}{d}right)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3567.png"
 ALT="$\displaystyle 1\lesssim\frac{d^{ 2}}{\lambda R} \ll \left(\frac{R}{d}\right)^2.$">|; 

$key = q/displaystyle2,gamma,omega_1-nu,omega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img438.png"
 ALT="$\displaystyle 2 \gamma \omega_1-\nu \omega_1$">|; 

$key = q/displaystyle2,n,t=(m+1slash2),lambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3417.png"
 ALT="$\displaystyle 2 n t=(m+1/2) \lambda,$">|; 

$key = q/displaystyle2,n,t=m,lambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3418.png"
 ALT="$\displaystyle 2 n t = m \lambda,$">|; 

$key = q/displaystyle2,omega,frac{domega}{dk}=2,k,c^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2610.png"
 ALT="$\displaystyle 2 \omega \frac{d\omega}{dk} = 2 k c^{ 2},$">|; 

$key = q/displaystyle2,t=(m+1slash2),lambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3414.png"
 ALT="$\displaystyle 2 t=(m+1/2) \lambda,$">|; 

$key = q/displaystyle2,t=m,lambda.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3415.png"
 ALT="$\displaystyle 2 t = m \lambda.$">|; 

$key = q/displaystyle=(-8,sin^3alpha+4,sinalpha),cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4374.png"
 ALT="$\displaystyle = (-8 \sin^3\alpha+4 \sin\alpha) \cos\alpha$">|; 

$key = q/displaystyle=(C_n^{,2}+S_n^{,2})^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1050.png"
 ALT="$\displaystyle = (C_n^{ 2} + S_n^{ 2})^{1/2},$">|; 

$key = q/displaystyle=(E_R+E_L),cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2777.png"
 ALT="$\displaystyle = (E_R+E_L) \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=(E_R-E_L),sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2778.png"
 ALT="$\displaystyle = (E_R-E_L) \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=(I_1+I_2)slash2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img773.png"
 ALT="$\displaystyle =(I_1+I_2)/2,$">|; 

$key = q/displaystyle=(I_1-I_2)slash2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img775.png"
 ALT="$\displaystyle =(I_1-I_2)/2.$">|; 

$key = q/displaystyle=(alpha^{,2}+beta^{,2}),v^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1886.png"
 ALT="$\displaystyle = (\alpha^{ 2}+\beta^{ 2}) v^{ 2},$">|; 

$key = q/displaystyle=+cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4330.png"
 ALT="$\displaystyle =+ \cos\alpha$">|; 

$key = q/displaystyle=+coshalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4392.png"
 ALT="$\displaystyle =+ \cosh\alpha$">|; 

$key = q/displaystyle=-2,omega_0^{,2},x_1+omega_0^{,2},x_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img666.png"
 ALT="$\displaystyle = -2 \omega_0^{ 2} x_1+ \omega_0^{ 2} x_2,$">|; 

$key = q/displaystyle=-2,sinleft(frac{alpha+beta}{2}right),sinleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4352.png"
 ALT="$\displaystyle =-2 \sin\left(\frac{\alpha+\beta}{2}\right) \sin\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=-4,sin^3alpha+3,sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4370.png"
 ALT="$\displaystyle =-4 \sin^3\alpha+3 \sin\alpha$">|; 

$key = q/displaystyle=-E_L,sin(omega,t-k_L,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2669.png"
 ALT="$\displaystyle =-E_L \sin(\omega t-k_L z).$">|; 

$key = q/displaystyle=-E_L,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2769.png"
 ALT="$\displaystyle = -E_L \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=-V_0,cos(omega,t+k,x-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1495.png"
 ALT="$\displaystyle =-V_0 \cos(\omega t+k x-\phi),$">|; 

$key = q/displaystyle=-Z^{,-1},E_0,cos(omega,t+k,z-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1637.png"
 ALT="$\displaystyle =-Z^{ -1} E_0 \cos(\omega t+k z-\phi),$">|; 

$key = q/displaystyle=-Z_R^{,-1},E_R,sin(omega,t-k_R,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img2662.png"
 ALT="$\displaystyle = -Z_R^{ -1} E_R \sin(\omega t-k_R z),$">|; 

$key = q/displaystyle=-alpha^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1882.png"
 ALT="$\displaystyle = -\alpha^{ 2},$">|; 

$key = q/displaystyle=-beta^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1884.png"
 ALT="$\displaystyle = -\beta^{ 2},$">|; 

$key = q/displaystyle=-e,E_x-e,B_0,frac{dy_e}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2712.png"
 ALT="$\displaystyle = -e E_x-e B_0 \frac{dy_e}{dt},$">|; 

$key = q/displaystyle=-e,E_x-e,B_0,frac{dy}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2641.png"
 ALT="$\displaystyle = -e E_x-e B_0 \frac{dy}{dt},$">|; 

$key = q/displaystyle=-e,E_y+e,B_0,frac{dx_e}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2714.png"
 ALT="$\displaystyle =-e E_y+e B_0 \frac{dx_e}{dt},$">|; 

$key = q/displaystyle=-e,E_y+e,B_0,frac{dx}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2643.png"
 ALT="$\displaystyle = -e E_y+e B_0 \frac{dx}{dt},$">|; 

$key = q/displaystyle=-e,E_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2716.png"
 ALT="$\displaystyle =-e E_z.$">|; 

$key = q/displaystyle=-e,n_e,x=-frac{n_e,e^{,2},E_R}{m_e,omega,(omega-{mitOmega}_e)},cos(omega,t-k_R,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2655.png"
 ALT="$\displaystyle =-e n_e x= -\frac{n_e e^{ 2} E_R}{m_e \omega (\omega-{\mit\Omega}_e)} \cos(\omega t-k_R z),$">|; 

$key = q/displaystyle=-e,n_e,y=-frac{n_e,e^{,2},E_R}{m_e,omega,(omega-{mitOmega}_e)},sin(omega,t-k_R,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2657.png"
 ALT="$\displaystyle =-e n_e y= -\frac{n_e e^{ 2} E_R}{m_e \omega (\omega-{\mit\Omega}_e)} \sin(\omega t-k_R z),$">|; 

$key = q/displaystyle=-epsilon_0,L,D_L,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2771.png"
 ALT="$\displaystyle = -\epsilon_0 L D_L \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=-epsilon_0left[frac{omega_{p,i}^{,2}}{omega,(omega+{mitOmega}_i)}+frac{omega_{p,e}^{,2}}{omega,(omega-{mitOmega}_e)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.19ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img2748.png"
 ALT="$\displaystyle =-\epsilon_0\left[ \frac{\omega_{p i}^{ 2}}{\omega (\omega+{\mit\Omega}_i)}+\frac{\omega_{p e}^{ 2}}{\omega (\omega-{\mit\Omega}_e)}\right],$">|; 

$key = q/displaystyle=-frac{1}{epsilon,epsilon_0},frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1651.png"
 ALT="$\displaystyle =- \frac{1}{\epsilon \epsilon_0} \frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0},frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2894.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}  \frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialH_x}{partialy}-frac{partialH_y}{partialx}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3221.png"
 ALT="$\displaystyle = -\frac{1}{\epsilon_0}\left(\frac{\partial H_x}{\partial y}-\frac{\partial H_y}{\partial x}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialH_y}{partialz}-frac{partialH_z}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3205.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\frac{\partial H_y}{\partial z}-\frac{\partial H_z}{\partial y}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialH_z}{partialx}-frac{partialH_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3206.png"
 ALT="$\displaystyle = -\frac{1}{\epsilon_0}\left(\frac{\partial H_z}{\partial x}-\frac{\partial H_x}{\partial z}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialP_x}{partialt}+frac{partialH_y}{partialz}-frac{partialH_z}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4449.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\frac{\partial P_x}{\partial t} + \frac{\partial H_y}{\partial z}-\frac{\partial H_z}{\partial y}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialP_x}{partialt}+frac{partialH_y}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1648.png"
 ALT="$\displaystyle = - \frac{1}{\epsilon_0}\left(\frac{\partial P_x}{\partial t}+\frac{\partial H_y}{\partial z}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialP_y}{partialt}+frac{partialH_z}{partialx}-frac{partialH_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4450.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\frac{\partial P_y}{\partial t} + \frac{\partial H_z}{\partial x}-\frac{\partial H_x}{\partial z}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialP_y}{partialt}-frac{partialH_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2659.png"
 ALT="$\displaystyle = -\frac{1}{\epsilon_0}\left(\frac{\partial P_y}{\partial t} - \frac{\partial H_x}{\partial z}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(frac{partialP_z}{partialt}+frac{partialH_x}{partialy}-frac{partialH_y}{partialx}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4451.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\frac{\partial P_z}{\partial t} + \frac{\partial H_x}{\partial y}-\frac{\partial H_y}{\partial x}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(j_x+frac{partialH_y}{partialz}-frac{partialH_z}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4442.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(j_x + \frac{\partial H_y}{\partial z}-\frac{\partial H_z}{\partial y}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(j_y+frac{partialH_z}{partialx}-frac{partialH_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4443.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(j_y + \frac{\partial H_z}{\partial x}-\frac{\partial H_x}{\partial z}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(j_z+frac{partialH_x}{partialy}-frac{partialH_y}{partialx}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4444.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(j_z + \frac{\partial H_x}{\partial y}-\frac{\partial H_y}{\partial x}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(sigma,E_x+frac{partialH_y}{partialz}-frac{partialH_z}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4457.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\sigma E_x+ \frac{\partial H_y}{\partial z}-\frac{\partial H_z}{\partial y}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(sigma,E_y+frac{partialH_z}{partialx}-frac{partialH_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4458.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\sigma E_y + \frac{\partial H_z}{\partial x}-\frac{\partial H_x}{\partial z}\right),$">|; 

$key = q/displaystyle=-frac{1}{epsilon_0}left(sigma,E_z+frac{partialH_x}{partialy}-frac{partialH_y}{partialx}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4459.png"
 ALT="$\displaystyle =-\frac{1}{\epsilon_0}\left(\sigma E_z+ \frac{\partial H_x}{\partial y}-\frac{\partial H_y}{\partial x}\right),$">|; 

$key = q/displaystyle=-frac{1}{mu_0},frac{partialE_x}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1812.png"
 ALT="$\displaystyle = - \frac{1}{\mu_0} \frac{\partial E_x}{\partial z},$">|; 

$key = q/displaystyle=-frac{1}{mu_0},frac{partialE_x}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1650.png"
 ALT="$\displaystyle = -\frac{1}{\mu_0} \frac{\partial E_x}{\partial z}.$">|; 

$key = q/displaystyle=-frac{1}{sqrt{1-x^{,2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4293.png"
 ALT="$\displaystyle = -\frac{1}{\sqrt{1-x^{ 2}}}$">|; 

$key = q/displaystyle=-frac{1}{{calC}},frac{partialI}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.72ex; " SRC="|."$dir".q|img1107.png"
 ALT="$\displaystyle =-\frac{1}{{\cal C}} \frac{\partial I}{\partial x},$">|; 

$key = q/displaystyle=-frac{1}{{calC}},frac{partialI}{partialx},nonumber;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.72ex; " SRC="|."$dir".q|img1784.png"
 ALT="$\displaystyle =-\frac{1}{{\cal C}} \frac{\partial I}{\partial x},\nonumber$">|; 

$key = q/displaystyle=-frac{1}{{calL}},frac{partialV}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img1109.png"
 ALT="$\displaystyle = - \frac{1}{{\cal L}} \frac{\partial V}{\partial x},$">|; 

$key = q/displaystyle=-frac{1}{{calL}},frac{partialV}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img1480.png"
 ALT="$\displaystyle = -\frac{1}{{\cal L}} \frac{\partial V}{\partial x}.$">|; 

$key = q/displaystyle=-frac{2,A}{n,pi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1278.png"
 ALT="$\displaystyle = - \frac{2 A}{n \pi}.$">|; 

$key = q/displaystyle=-frac{e,E_R}{m_i,omega,(omega+{mitOmega}_i)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2745.png"
 ALT="$\displaystyle = -\frac{e E_R}{m_i \omega (\omega+{\mit\Omega}_i)},$">|; 

$key = q/displaystyle=-frac{nu}{2},a,cosphi+omega_1,a,sinphi=-frac{nu,x_0}{2}+omega_1,a,sinphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img456.png"
 ALT="$\displaystyle = - \frac{\nu}{2} a \cos\phi + \omega_1 a \sin\phi = -\frac{\nu x_0}{2}+ \omega_1 a \sin\phi,$">|; 

$key = q/displaystyle=-frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1960.png"
 ALT="$\displaystyle =-\frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyle=-frac{partialH_z}{partialx}+frac{partialH_x}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2005.png"
 ALT="$\displaystyle =-\frac{\partial H_z}{\partial x}+ \frac{\partial H_x}{\partial z}.$">|; 

$key = q/displaystyle=-frac{partial^{,2}phi}{partialx,partialt}=-frac{partialomega}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2953.png"
 ALT="$\displaystyle = -\frac{\partial^{ 2}\phi}{\partial x \partial t} = - \frac{\partial\omega}{\partial x},$">|; 

$key = q/displaystyle=-frac{partial^{,2}phi}{partialz,partialt}=-frac{partialomega}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2955.png"
 ALT="$\displaystyle = -\frac{\partial^{ 2}\phi}{\partial z \partial t} = - \frac{\partial\omega}{\partial z}.$">|; 

$key = q/displaystyle=-frac{partialomega}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2964.png"
 ALT="$\displaystyle =-\frac{\partial\omega}{\partial x},$">|; 

$key = q/displaystyle=-frac{partialomega}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2966.png"
 ALT="$\displaystyle =-\frac{\partial\omega}{\partial z}.$">|; 

$key = q/displaystyle=-frac{partialp_1}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3021.png"
 ALT="$\displaystyle = - \frac{\partial p_1}{\partial x},$">|; 

$key = q/displaystyle=-frac{partialp_1}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3022.png"
 ALT="$\displaystyle = - \frac{\partial p_1}{\partial z}.$">|; 

$key = q/displaystyle=-frac{partialphi}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1727.png"
 ALT="$\displaystyle = -\frac{\partial\phi}{\partial x},$">|; 

$key = q/displaystyle=-frac{partialphi}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2949.png"
 ALT="$\displaystyle = -\frac{\partial\phi}{\partial z},$">|; 

$key = q/displaystyle=-frac{partialtilde{p}}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2225.png"
 ALT="$\displaystyle = -\frac{\partial\tilde{p}}{\partial x},$">|; 

$key = q/displaystyle=-frac{partialtilde{p}}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2227.png"
 ALT="$\displaystyle = -\frac{\partial\tilde{p}}{\partial z},$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1975.png"
 ALT="$\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/displaystyle=-frac{psi_r^{,2},costheta_i}{2,epsilon_0,c,n_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1993.png"
 ALT="$\displaystyle = -\frac{\psi_r^{ 2} \cos\theta_i}{2 \epsilon_0 c n_1},$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1978.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2052.png"
 ALT="$\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/displaystyle=-frac{rho_1,omega,costheta_i}{2,v_1},phi_r^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2281.png"
 ALT="$\displaystyle = -\frac{\rho_1 \omega \cos\theta_i}{2 v_1} \phi_r^{ 2},$">|; 

$key = q/displaystyle=-frac{sigma}{epsilon_0},E_x-frac{1}{epsilon_0},frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1813.png"
 ALT="$\displaystyle =-\frac{\sigma}{\epsilon_0} E_x -\frac{1}{\epsilon_0} \frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyle=-frac{v_1}{v_0},frac{dz}{ds},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3232.png"
 ALT="$\displaystyle =- \frac{v_1}{v_0} \frac{dz}{ds},$">|; 

$key = q/displaystyle=-frac{{calR}}{{calL}},I-frac{1}{calL},frac{partialV}{partialx}nonumber,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img1785.png"
 ALT="$\displaystyle =-\frac{{\cal R}}{{\cal L}} I - \frac{1}{\cal L} \frac{\partial V}{\partial x}\nonumber,$">|; 

$key = q/displaystyle=-gamma,a,{rme}^{-gamma,t},cos(omega_1,t-phi)-omega_1,a,{rme}^{-gamma,t},sin(omega_1,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img429.png"
 ALT="$\displaystyle = - \gamma a {\rm e}^{-\gamma t} \cos(\omega_1 t-\phi) -\omega_1  a {\rm e}^{-\gamma t} \sin(\omega_1 t-\phi),$">|; 

$key = q/displaystyle=-hat{eta}_2,cosleft(sqrt{3},omega_0,t-phi_2right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img704.png"
 ALT="$\displaystyle =-\hat{\eta}_2 \cos\left(\sqrt{3} \omega_0 t-\phi_2\right),$">|; 

$key = q/displaystyle=-hat{x},cosvarphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img603.png"
 ALT="$\displaystyle = -\hat{x} \cos\varphi,$">|; 

$key = q/displaystyle=-hat{x}left[frac{omega,sinvarphi+(nuslash2),cosvarphi}{omega_1}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img605.png"
 ALT="$\displaystyle = -\hat{x}\left[\frac{\omega \sin\varphi + (\nu/2) \cos\varphi}{\omega_1}\right].$">|; 

$key = q/displaystyle=-int_{phislashomega_1}^{(2pi+phi)slashomega_1}frac{dE}{dt},dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.35ex; " SRC="|."$dir".q|img480.png"
 ALT="$\displaystyle = -\int_{\phi/\omega_1}^{(2\pi+\phi)/\omega_1} \frac{dE}{dt} dt$">|; 

$key = q/displaystyle=-k,(x_2-x_1)+k,(-x_2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img661.png"
 ALT="$\displaystyle = -k (x_2-x_1) +k (-x_2).$">|; 

$key = q/displaystyle=-k,(x_2-x_1)+k,(x_3-x_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img786.png"
 ALT="$\displaystyle =-k (x_2-x_1)+k (x_3-x_2),$">|; 

$key = q/displaystyle=-k,(x_3-x_2)+k,(-x_3).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img788.png"
 ALT="$\displaystyle =-k (x_3-x_2)+k (-x_3).$">|; 

$key = q/displaystyle=-k,costheta,(E_R-E_L),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2802.png"
 ALT="$\displaystyle = -k \cos\theta (E_R-E_L),$">|; 

$key = q/displaystyle=-k,costheta,hat{H}_x+k,sintheta,hat{H}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2798.png"
 ALT="$\displaystyle =-k \cos\theta \hat{H}_x+k \sin\theta \hat{H}_z,$">|; 

$key = q/displaystyle=-k,hat{X},hat{x},omega,cos(omega,t),sin(omega,t-varphi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img564.png"
 ALT="$\displaystyle =- k \hat{X} \hat{x} \omega \cos(\omega t) \sin(\omega t-\varphi)$">|; 

$key = q/displaystyle=-k,hat{X},hat{x},omegaleft[cos(omega,t),sin(omega,t),cosvarphi-cos^2(omega,t),sinvarphiright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img565.png"
 ALT="$\displaystyle = -k \hat{X} \hat{x} \omega\left[\cos(\omega t) \sin(\omega t) \cos\varphi - \cos^2(\omega t) \sin\varphi\right].$">|; 

$key = q/displaystyle=-k,sintheta,E_P+k,costheta,(E_R+E_L),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2804.png"
 ALT="$\displaystyle = -k \sin\theta E_P + k \cos\theta (E_R+E_L),$">|; 

$key = q/displaystyle=-k,sintheta,hat{H}_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2800.png"
 ALT="$\displaystyle = - k \sin\theta \hat{H}_y,$">|; 

$key = q/displaystyle=-k,x_1+k,(x_2-x_1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img659.png"
 ALT="$\displaystyle = -k x_1 +k (x_2-x_1),$">|; 

$key = q/displaystyle=-m_1,frac{g}{l},theta_1+k,(theta_2-theta_1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img841.png"
 ALT="$\displaystyle =-m_1 \frac{g}{l} \theta_1+ k (\theta_2-\theta_1),$">|; 

$key = q/displaystyle=-m_2,frac{g}{l},theta_2+k,(theta_1-theta_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img843.png"
 ALT="$\displaystyle =-m_2 \frac{g}{l} \theta_2+ k (\theta_1-\theta_2),$">|; 

$key = q/displaystyle=-omega,hat{x},sin(omega,t-varphi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img521.png"
 ALT="$\displaystyle = -\omega \hat{x} \sin(\omega t-\varphi),$">|; 

$key = q/displaystyle=-omega^{,2},hat{x},cos(omega,t-varphi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img522.png"
 ALT="$\displaystyle =-\omega^{ 2} \hat{x} \cos(\omega t-\varphi),$">|; 

$key = q/displaystyle=-omega_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img934.png"
 ALT="$\displaystyle =-\omega_n,$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2014.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2020.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2077.png"
 ALT="$\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/displaystyle=-sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4328.png"
 ALT="$\displaystyle = -\sin\alpha$">|; 

$key = q/displaystyle=-sinhalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4390.png"
 ALT="$\displaystyle = -\sinh\alpha$">|; 

$key = q/displaystyle=-sinx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4287.png"
 ALT="$\displaystyle = -\sin x$">|; 

$key = q/displaystyle=-tanalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4332.png"
 ALT="$\displaystyle = -\tan\alpha$">|; 

$key = q/displaystyle=-tanhalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4394.png"
 ALT="$\displaystyle = -\tanh\alpha$">|; 

$key = q/displaystyle=-v^{,2},frac{partialD_y}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2003.png"
 ALT="$\displaystyle =-v^{ 2} \frac{\partial D_y}{\partial x},$">|; 

$key = q/displaystyle=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img437.png"
 ALT="$\displaystyle =0,$">|; 

$key = q/displaystyle=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img439.png"
 ALT="$\displaystyle =0.$">|; 

$key = q/displaystyle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4470.png"
 ALT="$\displaystyle = 0$">|; 

$key = q/displaystyle=1+alpha,x+frac{alpha,(alpha-1)}{2!},x^{,2}+frac{alpha,(alpha-1),(alpha-2)}{3!},x^{,3}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4313.png"
 ALT="$\displaystyle = 1 + \alpha x + \frac{\alpha (\alpha-1)}{2!} x^{ 2} + \frac{\alpha (\alpha-1) (\alpha-2)}{3!}  x^{ 3}+\cdots$">|; 

$key = q/displaystyle=1+cosleft(2pi,frac{d}{lambda},thetaright),cosleft(pi,frac{d}{lambda},theta_0right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3343.png"
 ALT="$\displaystyle = 1 + \cos\left(2\pi \frac{d}{\lambda} \theta\right) \cos\left(\pi \frac{d}{\lambda} \theta_0\right),$">|; 

$key = q/displaystyle=1+frac{x^{,2}}{2!}+frac{x^{,4}}{4!}+frac{x^{,6}}{6!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4324.png"
 ALT="$\displaystyle = 1+\frac{x^{ 2}}{2!} + \frac{x^{ 4}}{4!}+\frac{x^{ 6}}{6!} + \cdots$">|; 

$key = q/displaystyle=1+x+frac{x^{,2}}{2!}+frac{x^{,3}}{3!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4314.png"
 ALT="$\displaystyle = 1 + x + \frac{x^{ 2}}{2!}+ \frac{x^{ 3}}{3!} + \cdots$">|; 

$key = q/displaystyle=1+x+frac{x^{,2}}{2!}+frac{x^{,3}}{3!}+frac{x^{,4}}{4!}+frac{x^{,5}}{5!}+frac{x^{,6}}{6!}+frac{x^{,7}}{7!}+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4217.png"
 ALT="$\displaystyle = 1 + x + \frac{x^{ 2}}{2!} + \frac{x^{ 3}}{3!}+\frac{x^{ 4}}{4!}+\frac{x^{ 5}}{5!}+\frac{x^{ 6}}{6!}+\frac{x^{ 7}}{7!}+\cdots,$">|; 

$key = q/displaystyle=1-cosleft(frac{u^{,2}+v^{,2}}{2,u}right)V_0(u,v)-sinleft(frac{u^{,2}+v^{,2}}{2,u}right)V_1(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3707.png"
 ALT="$\displaystyle =1- \cos\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)V_0(u,v)- \sin\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)V_1(u,v)$">|; 

$key = q/displaystyle=1-frac{x^{,2}}{2!}+frac{x^{,4}}{4!}-frac{x^{,6}}{6!}+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4221.png"
 ALT="$\displaystyle =1-\frac{x^{ 2}}{2!} + \frac{x^{ 4}}{4!}-\frac{x^{ 6}}{6!}+\cdots,$">|; 

$key = q/displaystyle=1-frac{x^{,2}}{2!}+frac{x^{,4}}{4!}-frac{x^{,6}}{6!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4318.png"
 ALT="$\displaystyle = 1-\frac{x^{ 2}}{2!} + \frac{x^{ 4}}{4!}-\frac{x^{ 6}}{6!} + \cdots$">|; 

$key = q/displaystyle=1.60,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4132.png"
 ALT="$\displaystyle = 1.60,$">|; 

$key = q/displaystyle=1.61.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4133.png"
 ALT="$\displaystyle = 1.61.$">|; 

$key = q/displaystyle=1.73.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4128.png"
 ALT="$\displaystyle = 1.73.$">|; 

$key = q/displaystyle=1.83,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4126.png"
 ALT="$\displaystyle = 1.83,$">|; 

$key = q/displaystyle=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3608.png"
 ALT="$\displaystyle = 1.$">|; 

$key = q/displaystyle=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4338.png"
 ALT="$\displaystyle =1$">|; 

$key = q/displaystyle=2,A_i,cos(k_1,x),cos(omega,t-phi_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1561.png"
 ALT="$\displaystyle =2 A_i \cos(k_1 x) \cos(\omega t-\phi_i),$">|; 

$key = q/displaystyle=2,A_i,sin(k_1,x),sin(omega,t-phi_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1555.png"
 ALT="$\displaystyle =2 A_i \sin(k_1 x) \sin(\omega t-\phi_i),$">|; 

$key = q/displaystyle=2,coshleft(frac{alpha+beta}{2}right),coshleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4407.png"
 ALT="$\displaystyle =2 \cosh\left(\frac{\alpha+\beta}{2}\right) \cosh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,coshleft(frac{alpha+beta}{2}right),sinhleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4405.png"
 ALT="$\displaystyle =2 \cosh\left(\frac{\alpha+\beta}{2}\right) \sinh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,cosleft(frac{alpha+beta}{2}right),cosleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4350.png"
 ALT="$\displaystyle =2 \cos\left(\frac{\alpha+\beta}{2}\right) \cos\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,cosleft(frac{alpha+beta}{2}right),sinleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4348.png"
 ALT="$\displaystyle =2 \cos\left(\frac{\alpha+\beta}{2}\right) \sin\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,sinalpha,cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4366.png"
 ALT="$\displaystyle = 2 \sin\alpha \cos\alpha$">|; 

$key = q/displaystyle=2,sinhalpha,coshalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4423.png"
 ALT="$\displaystyle = 2 \sinh\alpha \cosh\alpha$">|; 

$key = q/displaystyle=2,sinhleft(frac{alpha+beta}{2}right),coshleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4403.png"
 ALT="$\displaystyle =2 \sinh\left(\frac{\alpha+\beta}{2}\right) \cosh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,sinhleft(frac{alpha+beta}{2}right),sinhleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4409.png"
 ALT="$\displaystyle =2 \sinh\left(\frac{\alpha+\beta}{2}\right) \sinh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,sinleft(frac{alpha+beta}{2}right),cosleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4346.png"
 ALT="$\displaystyle =2 \sin\left(\frac{\alpha+\beta}{2}\right) \cos\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=28.5,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4124.png"
 ALT="$\displaystyle = 28.5,$">|; 

$key = q/displaystyle=28.9,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4131.png"
 ALT="$\displaystyle = 28.9,$">|; 

$key = q/displaystyle=4,cos^3alpha-3,cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4372.png"
 ALT="$\displaystyle =4 \cos^3\alpha-3 \cos\alpha$">|; 

$key = q/displaystyle=8,cos^4alpha-8,cos^2alpha+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4376.png"
 ALT="$\displaystyle =8 \cos^4\alpha-8 \cos^2\alpha+1$">|; 

$key = q/displaystyle=A(t),cos(omega_0,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2463.png"
 ALT="$\displaystyle = A(t) \cos(\omega_0 t)$">|; 

$key = q/displaystyle=A+B,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4016.png"
 ALT="$\displaystyle = A+B,$">|; 

$key = q/displaystyle=A_0,cos(omega_0,t)+frac{1}{2}sum_{n>0}A_n,cos[(omega_0+omega_n),t-phi_n)]+frac{1}{2}sum_{n>0}A_n,cos[(omega_0-omega_n),t+phi_n)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2465.png"
 ALT="$\displaystyle =A_0 \cos(\omega_0 t)+\frac{1}{2}\sum_{n&gt;0}A_n \cos[(\omega_0+...
..._n) t-\phi_n)]+ \frac{1}{2}\sum_{n&gt;0}A_n \cos[(\omega_0-\omega_n) t+\phi_n)]$">|; 

$key = q/displaystyle=A_0,cos(omega_0,t)+frac{1}{2}sum_{n>0}A_n,cosphi_n,cos[(omega_0+omega_n),t];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2466.png"
 ALT="$\displaystyle =A_0 \cos(\omega_0 t)+\frac{1}{2}\sum_{n&gt;0}A_n \cos\phi_n \cos[(\omega_0+\omega_n) t]$">|; 

$key = q/displaystyle=A_0,cos(omega_0,t)+sum_{n>0}A_n,cos(omega_n,t-phi_n),cos(omega_0,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2464.png"
 ALT="$\displaystyle =A_0 \cos(\omega_0 t)+\sum_{n&gt;0} A_n \cos(\omega_n t-\phi_n) \cos(\omega_0 t),$">|; 

$key = q/displaystyle=A_i,cos(omega,t-k_1,x-phi_i)+A_i,cos(omega,t+k_1,x+phi_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1560.png"
 ALT="$\displaystyle = A_i \cos(\omega t-k_1 x-\phi_i) +A_i \cos(\omega t+k_1 x+\phi_i)$">|; 

$key = q/displaystyle=A_i,cos(omega,t-k_1,x-phi_i)-A_i,cos(omega,t+k_1,x+phi_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1554.png"
 ALT="$\displaystyle = A_i \cos(\omega t-k_1 x-\phi_i) -A_i \cos(\omega t+k_1 x+\phi_i)$">|; 

$key = q/displaystyle=A_n,cosphi_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1047.png"
 ALT="$\displaystyle = A_n \cos\phi_n,$">|; 

$key = q/displaystyle=A_n,sinphi_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1048.png"
 ALT="$\displaystyle = A_n \sin\phi_n,$">|; 

$key = q/displaystyle=C(z_2-z')+C(z'-z_1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3617.png"
 ALT="$\displaystyle = C(z_2-z')+C(z'-z_1),$">|; 

$key = q/displaystyle=C_n,cos(n,omega,T)+S_n,sin(n,omega,T),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1317.png"
 ALT="$\displaystyle = C_n \cos(n \omega T) + S_n \sin(n \omega T),$">|; 

$key = q/displaystyle=D_{a,x},D_{b,x}+D_{a,y},D_{b,y}+D_{a,z},D_{b,z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2182.png"
 ALT="$\displaystyle = D_{a x} D_{b x}+D_{a y} D_{b y}+D_{a z} D_{b z}$">|; 

$key = q/displaystyle=E_0,Z^{,-1},{rme}^{-zslashd},cos(omega,t-zslashd-pislash4),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2899.png"
 ALT="$\displaystyle = E_0 Z^{ -1} {\rm e}^{-z/d} \cos(\omega t-z/d-\pi/4),$">|; 

$key = q/displaystyle=E_0,cos(omega,t+k,z-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1635.png"
 ALT="$\displaystyle =E_0 \cos(\omega t+k z-\phi),$">|; 

$key = q/displaystyle=E_0,cos(omega,t-k_0,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2673.png"
 ALT="$\displaystyle = E_0 \cos(\omega t-k_0 z),$">|; 

$key = q/displaystyle=E_0,cos(omega,t-k_0,z),cos({mitDelta}k,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2686.png"
 ALT="$\displaystyle = E_0 \cos(\omega t-k_0 z) \cos({\mit\Delta} k z),$">|; 

$key = q/displaystyle=E_0,cos(omega,t-k_0,z),sin({mitDelta}k,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2688.png"
 ALT="$\displaystyle = E_0 \cos(\omega t-k_0 z) \sin({\mit\Delta} k z).$">|; 

$key = q/displaystyle=E_0,{rme}^{-k,z},cos(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2616.png"
 ALT="$\displaystyle = E_0 {\rm e}^{-k z} \cos(\omega t),$">|; 

$key = q/displaystyle=E_0,{rme}^{-zslashd},cos(omega,t-zslashd),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2898.png"
 ALT="$\displaystyle = E_0 {\rm e}^{-z/d} \cos(\omega t-z/d),$">|; 

$key = q/displaystyle=E_L,cos(omega,t-k_L,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2668.png"
 ALT="$\displaystyle = E_L \cos(\omega t-k_L z),$">|; 

$key = q/displaystyle=E_L,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2768.png"
 ALT="$\displaystyle = E_L \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=E_P,cos(omega,t-{bfk}cdot{bfr}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2773.png"
 ALT="$\displaystyle =E_P \cos(\omega t-{\bf k}\cdot{\bf r}).$">|; 

$key = q/displaystyle=E_R,cos(omega,t-k_R,z)+E_L,cos(omega,t-k_L,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2674.png"
 ALT="$\displaystyle = E_R \cos(\omega t-k_R z) + E_L \cos(\omega t-k_L z),$">|; 

$key = q/displaystyle=E_R,cos(omega,t-k_R,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2644.png"
 ALT="$\displaystyle = E_R \cos(\omega t-k_R z),$">|; 

$key = q/displaystyle=E_R,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2725.png"
 ALT="$\displaystyle = E_R \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=E_R,sin(omega,t-k_R,z)-E_L,sin(omega,t-k_L,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2675.png"
 ALT="$\displaystyle = E_R \sin(\omega t-k_R z) - E_L \sin(\omega t-k_L z),$">|; 

$key = q/displaystyle=E_R,sin(omega,t-k_R,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2646.png"
 ALT="$\displaystyle =E_R \sin(\omega t-k_R z).$">|; 

$key = q/displaystyle=E_R,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2727.png"
 ALT="$\displaystyle = E_R \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2631.png"
 ALT="$\displaystyle =E_i,$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img2623.png"
 ALT="$\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/displaystyle=E_i,cos(omega,t-k_1,z)+E_r,cos(omega,t+k_1,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1668.png"
 ALT="$\displaystyle = E_i \cos(\omega t-k_1 z) + E_r \cos(\omega t+k_1 z),$">|; 

$key = q/displaystyle=E_i,cos[k_0,(c,t-z)]+E_r,cos[k_0,(c,t+z)+phi_r],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2622.png"
 ALT="$\displaystyle = E_i \cos[k_0 (c t-z)] + E_r \cos[k_0 (c t+z)+\phi_r],$">|; 

$key = q/displaystyle=E_t,Z_0^{,-1},alpha,{rme}^{-k_0,alpha,z},sin(omega,t+phi_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img2625.png"
 ALT="$\displaystyle = E_t Z_0^{ -1} \alpha {\rm e}^{-k_0 \alpha z} \sin(\omega t+\phi_t),$">|; 

$key = q/displaystyle=E_t,Z_0^{,-1},alpha^{-1},{rme}^{-zslashd},cos(omega,t-zslashd-pislash4+phi_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img2915.png"
 ALT="$\displaystyle = E_t Z_0^{ -1} \alpha^{-1} {\rm e}^{-z/d} \cos(\omega t-z/d-\pi/4+\phi_t),$">|; 

$key = q/displaystyle=E_t,alpha,sin(omega,t+phi_t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2630.png"
 ALT="$\displaystyle = E_t \alpha \sin(\omega t+\phi_t).$">|; 

$key = q/displaystyle=E_t,cos(omega,t+phi_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2628.png"
 ALT="$\displaystyle = E_t \cos(\omega t+\phi_t),$">|; 

$key = q/displaystyle=E_t,cos(omega,t-k_2,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1674.png"
 ALT="$\displaystyle = E_t \cos(\omega t-k_2 z),$">|; 

$key = q/displaystyle=E_t,cos(omega,t-pislash4+phi_t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2918.png"
 ALT="$\displaystyle =E_t \cos(\omega t-\pi/4+\phi_t).$">|; 

$key = q/displaystyle=E_t,{rme}^{-k_0,alpha,z},cos(omega,t+phi_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2624.png"
 ALT="$\displaystyle =E_t {\rm e}^{-k_0 \alpha z} \cos(\omega t+\phi_t),$">|; 

$key = q/displaystyle=E_t,{rme}^{-zslashd},cos(omega,t-zslashd+phi_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2914.png"
 ALT="$\displaystyle = E_t {\rm e}^{-z/d} \cos(\omega t-z/d+\phi_t),$">|; 

$key = q/displaystyle=E_x,H_y-E_y,H_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4463.png"
 ALT="$\displaystyle = E_x H_y-E_y H_x,$">|; 

$key = q/displaystyle=E_y,H_z-E_z,H_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4460.png"
 ALT="$\displaystyle = E_y H_z-E_z H_y,$">|; 

$key = q/displaystyle=E_z,H_x-E_x,H_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4462.png"
 ALT="$\displaystyle = E_z H_x-E_x H_z,$">|; 

$key = q/displaystyle=F(t),dot{x}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img563.png"
 ALT="$\displaystyle = F(t) \dot{x}(t)$">|; 

$key = q/displaystyle=F(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1741.png"
 ALT="$\displaystyle = F(x),$">|; 

$key = q/displaystyle=F(x,y),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2296.png"
 ALT="$\displaystyle = F(x,y),$">|; 

$key = q/displaystyle=G(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1743.png"
 ALT="$\displaystyle =G(x),$">|; 

$key = q/displaystyle=G(x,y).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2298.png"
 ALT="$\displaystyle = G(x,y).$">|; 

$key = q/displaystyle=I_0,cos(omega,t+k,x-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1493.png"
 ALT="$\displaystyle = I_0 \cos(\omega t+k x-\phi),$">|; 

$key = q/displaystyle=I_i,Z,cos(omega,t-k,x)-I_r,Z,cos(omega,t+k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1597.png"
 ALT="$\displaystyle = I_i Z \cos(\omega t-k x) - I_r Z \cos(\omega t+k x),$">|; 

$key = q/displaystyle=I_i,cos(omega,t-k,x)+I_r,cos(omega,t+k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1596.png"
 ALT="$\displaystyle = I_i \cos(\omega t-k x) + I_r \cos(\omega t+k x),$">|; 

$key = q/displaystyle=J_0(v,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3684.png"
 ALT="$\displaystyle = J_0(v z),$">|; 

$key = q/displaystyle=P,R,L.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3190.png"
 ALT="$\displaystyle = P R L.$">|; 

$key = q/displaystyle=Q_3slashC'=-(Q_1+Q_2)slashC',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img747.png"
 ALT="$\displaystyle = Q_3/C' = -(Q_1+Q_2)/C',$">|; 

$key = q/displaystyle=Q_3slashC'=-(Q_1+Q_2)slashC'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img749.png"
 ALT="$\displaystyle = Q_3/C' = -(Q_1+Q_2)/C'.$">|; 

$key = q/displaystyle=R,L,sin^2theta+P,S,(1+cos^2theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3188.png"
 ALT="$\displaystyle = R L \sin^2\theta + P S (1+\cos^2\theta),$">|; 

$key = q/displaystyle=S(z_2-z')+S(z'-z_1).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3619.png"
 ALT="$\displaystyle = S(z_2-z')+S(z'-z_1).$">|; 

$key = q/displaystyle=S,sin^2theta+P,cos^2theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3187.png"
 ALT="$\displaystyle = S \sin^2\theta + P \cos^2\theta,$">|; 

$key = q/displaystyle=S_n,cos(n,omega,T)-C_n,sin(n,omega,T).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1319.png"
 ALT="$\displaystyle = S_n \cos(n \omega T) - C_n \sin(n \omega T).$">|; 

$key = q/displaystyle=T,{rme}^{,{rmi},k,a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4020.png"
 ALT="$\displaystyle = T {\rm e}^{ {\rm i} k a},$">|; 

$key = q/displaystyle=V,t-v_g,t,sinbeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3130.png"
 ALT="$\displaystyle = V t-v_g t \sin\beta,$">|; 

$key = q/displaystyle=X_0,sin(alpha,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1890.png"
 ALT="$\displaystyle = X_0 \sin(\alpha x),$">|; 

$key = q/displaystyle=X_0,sinbetaleft(1-frac{1}{2},sin^2betaright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3140.png"
 ALT="$\displaystyle = X_0 \sin\beta\left(1-\frac{1}{2} \sin^2\beta\right),$">|; 

$key = q/displaystyle=Xleft(1-frac{1}{2},sin^2betaright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3134.png"
 ALT="$\displaystyle = X\left(1-\frac{1}{2} \sin^2\beta\right),$">|; 

$key = q/displaystyle=Y_0,sin(beta,y),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1892.png"
 ALT="$\displaystyle = Y_0 \sin(\beta y),$">|; 

$key = q/displaystyle=Z^{,-1},E_0,{rme}^{-k,z},sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2617.png"
 ALT="$\displaystyle =Z^{ -1} E_0 {\rm e}^{-k z} \sin(\omega t).$">|; 

$key = q/displaystyle=Z_1^{,-1},E_i,cos(omega,t-k_1,z)-Z_1^{,-1},E_r,cos(omega,t+k_1,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img1669.png"
 ALT="$\displaystyle =Z_1^{ -1} E_i \cos(\omega t-k_1 z)- Z_1^{ -1} E_r \cos(\omega t+k_1 z),$">|; 

$key = q/displaystyle=Z_2^{,-1},E_t,cos(omega,t-k_2,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img1675.png"
 ALT="$\displaystyle =Z_2^{ -1} E_t \cos(\omega t-k_2 z),$">|; 

$key = q/displaystyle=Z_R^{,-1},E_R,cos(omega,t-k_R,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img2663.png"
 ALT="$\displaystyle = Z_R^{ -1} E_R \cos(\omega t-k_R z),$">|; 

$key = q/displaystyle=[x_1(t)+x_2(t)]slash2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img727.png"
 ALT="$\displaystyle = [x_1(t) + x_2(t)]/2,$">|; 

$key = q/displaystyle=[x_1(t)-x_2(t)]slash2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img729.png"
 ALT="$\displaystyle = [x_1(t)-x_2(t)]/2.$">|; 

$key = q/displaystyle=a,cos(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img394.png"
 ALT="$\displaystyle =a \cos(\omega t),$">|; 

$key = q/displaystyle=a,cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img396.png"
 ALT="$\displaystyle =a \cos(\omega t-\phi).$">|; 

$key = q/displaystyle=a,cosphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img454.png"
 ALT="$\displaystyle =a \cos\phi,$">|; 

$key = q/displaystyle=a,omega,frac{cosh[k,(z+d)]}{sinh(k,d)},sin(omega,t-k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3050.png"
 ALT="$\displaystyle =a \omega \frac{\cosh[k (z+d)]}{\sinh(k d)} \sin(\omega t-k x),$">|; 

$key = q/displaystyle=a,omega,frac{sinh[k,(z+d)]}{sinh(k,d)},cos(omega,t-k,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3052.png"
 ALT="$\displaystyle =a \omega \frac{\sinh[k (z+d)]}{\sinh(k d)} \cos(\omega t-k x).$">|; 

$key = q/displaystyle=alpha.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2634.png"
 ALT="$\displaystyle = \alpha.$">|; 

$key = q/displaystyle=beta^{,-1},cosphi_t,psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2079.png"
 ALT="$\displaystyle = \beta^{ -1} \cos\phi_t \psi_t $">|; 

$key = q/displaystyle=beta^{,-1},sinphi_t,psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2080.png"
 ALT="$\displaystyle =\beta^{ -1} \sin\phi_t \psi_t,$">|; 

$key = q/displaystyle=c,S,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2979.png"
 ALT="$\displaystyle = c S,$">|; 

$key = q/displaystyle=cos^2alpha-sin^2alpha=2,cos^2alpha-1=1-2,sin^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4368.png"
 ALT="$\displaystyle =\cos^2\alpha-\sin^2\alpha = 2 \cos^2\alpha-1=1-2 \sin^2\alpha$">|; 

$key = q/displaystyle=cosalpha,cosbetampsinalpha,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4342.png"
 ALT="$\displaystyle =\cos\alpha \cos\beta\mp \sin\alpha \sin\beta$">|; 

$key = q/displaystyle=cosh^2alpha+sinh^2alpha=2,cosh^2alpha-1=2,sinh^2alpha+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4425.png"
 ALT="$\displaystyle =\cosh^2\alpha+\sinh^2\alpha = 2 \cosh^2\alpha-1=2 \sinh^2\alpha+1$">|; 

$key = q/displaystyle=coshalpha,coshbetapmsinhalpha,sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4399.png"
 ALT="$\displaystyle =\cosh\alpha \cosh\beta\pm \sinh\alpha \sinh\beta$">|; 

$key = q/displaystyle=coshtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4435.png"
 ALT="$\displaystyle = \cosh\theta$">|; 

$key = q/displaystyle=coshx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4297.png"
 ALT="$\displaystyle =\cosh x$">|; 

$key = q/displaystyle=cosleft(frac{u^{,2}+v^{,2}}{2,u}right)U_1(u,v)+sinleft(frac{u^{,2}+v^{,2}}{2,u}right)U_2(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3708.png"
 ALT="$\displaystyle = \cos\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)U_1(u,v)+ \sin\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)U_2(u,v),$">|; 

$key = q/displaystyle=cosleft(frac{u}{2}right)U_1(u,v)+sinleft(frac{u}{2}right)U_2(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3704.png"
 ALT="$\displaystyle =\cos\left(\frac{u}{2}\right)U_1(u,v)+\sin\left(\frac{u}{2}\right)U_2(u,v),$">|; 

$key = q/displaystyle=cosleft(frac{v^{,2}}{2,u}right),{calC}(u,v)-sinleft(frac{v^{,2}}{2,v}right){calS}(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3687.png"
 ALT="$\displaystyle = \cos\left(\frac{v^{ 2}}{2 u}\right) {\cal C}(u,v) -\sin\left(\frac{v^{ 2}}{2 v}\right){\cal S}(u,v),$">|; 

$key = q/displaystyle=cosleft(frac{v^{,2}}{2,u}right)-cosleft(frac{u}{2}right)V_0(u,v)-sinleft(frac{u}{2}right)V_1(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3771.png"
 ALT="$\displaystyle =\cos\left(\frac{v^{ 2}}{2 u}\right)-\cos\left(\frac{u}{2}\right)V_0(u,v)-\sin\left(\frac{u}{2}\right)V_1(u,v),$">|; 

$key = q/displaystyle=cosleft(frac{v^{,2}}{2,u}right)-cosleft(frac{u}{2}right)V_0(u,v)-sinleft(frac{u}{2}right)V_1(u,v).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3701.png"
 ALT="$\displaystyle =\cos\left(\frac{v^{ 2}}{2 u}\right)-\cos\left(\frac{u}{2}\right)V_0(u,v)-\sin\left(\frac{u}{2}\right)V_1(u,v).$">|; 

$key = q/displaystyle=cosphi_t,psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2055.png"
 ALT="$\displaystyle = \cos\phi_t \psi_t,$">|; 

$key = q/displaystyle=costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4439.png"
 ALT="$\displaystyle = \cos\theta$">|; 

$key = q/displaystyle=cosx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4285.png"
 ALT="$\displaystyle = \cos x$">|; 

$key = q/displaystyle=delta_{n,n'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img1261.png"
 ALT="$\displaystyle = \delta_{n,n'},$">|; 

$key = q/displaystyle=dot{eta}_1^{,2}+omega_0^{,2},eta_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img857.png"
 ALT="$\displaystyle = \dot{\eta}_1^{ 2}+ \omega_0^{ 2} \eta_1^{ 2},$">|; 

$key = q/displaystyle=dot{eta}_2^{,2}+3,omega_0^{,2},eta_2^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img859.png"
 ALT="$\displaystyle =\dot{\eta}_2^{ 2} + 3 \omega_0^{ 2} \eta_2^{ 2},$">|; 

$key = q/displaystyle=e,E_x+e,B_0,frac{dy_i}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2705.png"
 ALT="$\displaystyle = e E_x+e B_0 \frac{dy_i}{dt},$">|; 

$key = q/displaystyle=e,E_y-e,B_0,frac{dx_i}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2707.png"
 ALT="$\displaystyle =e E_y-e B_0 \frac{dx_i}{dt},$">|; 

$key = q/displaystyle=e,E_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2709.png"
 ALT="$\displaystyle =e E_z,$">|; 

$key = q/displaystyle=e,n_e,(x_i-x_e),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2718.png"
 ALT="$\displaystyle =e n_e (x_i-x_e),$">|; 

$key = q/displaystyle=e,n_e,(y_i-y_e),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2720.png"
 ALT="$\displaystyle =e n_e (y_i-y_e),$">|; 

$key = q/displaystyle=e,n_e,(z_i-z_e).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2722.png"
 ALT="$\displaystyle =e n_e (z_i-z_e).$">|; 

$key = q/displaystyle=epsilon_0,(R,E_R+L,E_L),cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2779.png"
 ALT="$\displaystyle =\epsilon_0  (R E_R+L E_L) \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=epsilon_0,(R,E_R-L,E_L),sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2780.png"
 ALT="$\displaystyle = \epsilon_0 (R E_R-L E_L) \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=epsilon_0,L,D_L,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2770.png"
 ALT="$\displaystyle = \epsilon_0 L D_L \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=epsilon_0,P,E_P,cos(omega,t-{bfk}cdot{bfr}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2781.png"
 ALT="$\displaystyle =\epsilon_0 P E_P \cos(\omega t-{\bf k}\cdot{\bf r}).$">|; 

$key = q/displaystyle=epsilon_0,P,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2774.png"
 ALT="$\displaystyle =\epsilon_0 P \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=epsilon_0,R,E_R,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2763.png"
 ALT="$\displaystyle = \epsilon_0 R E_R \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=epsilon_0,R,E_R,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2765.png"
 ALT="$\displaystyle = \epsilon_0 R E_R \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=epsilon_0left(epsilon_{xx},E_x+epsilon_{xy},E_y+epsilon_{xz},E_zright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2102.png"
 ALT="$\displaystyle = \epsilon_0\left(\epsilon_{xx} E_x+\epsilon_{xy} E_y+\epsilon_{xz} E_z\right),$">|; 

$key = q/displaystyle=epsilon_0left(epsilon_{yx},E_x+epsilon_{yy},E_y+epsilon_{yz},E_zright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2104.png"
 ALT="$\displaystyle = \epsilon_0\left(\epsilon_{yx} E_x+\epsilon_{yy} E_y+\epsilon_{yz} E_z\right),$">|; 

$key = q/displaystyle=epsilon_0left(epsilon_{zx},E_x+epsilon_{zy},E_y+epsilon_{zz},E_zright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2106.png"
 ALT="$\displaystyle = \epsilon_0\left(\epsilon_{zx} E_x+\epsilon_{zy} E_y+\epsilon_{zz} E_z\right).$">|; 

$key = q/displaystyle=f(a)+frac{(x-a)}{1!},f^{,(1)}(a)+frac{(x-a)^2}{2!},f^{,(2)}(a)+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4311.png"
 ALT="$\displaystyle = f(a) + \frac{(x-a)}{1!} f^{ (1)}(a) + \frac{(x-a)^2}{2!} f^{ (2)}(a)+\cdots$">|; 

$key = q/displaystyle=frac{-langle{calI}_zrangle_r}{langle{calI}_zrangle_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1996.png"
 ALT="$\displaystyle = \frac{-\langle {\cal I}_z\rangle_r}{\langle {\cal I}_z\rangle_i},$">|; 

$key = q/displaystyle=frac{1}{1+x^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4295.png"
 ALT="$\displaystyle = \frac{1}{1+x^{ 2}}$">|; 

$key = q/displaystyle=frac{1}{1-x^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4307.png"
 ALT="$\displaystyle = \frac{1}{1-x^{ 2}}$">|; 

$key = q/displaystyle=frac{1}{2,{rmi}}left({rme}^{,{rmi},theta}-{rme}^{-{rmi},theta}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4429.png"
 ALT="$\displaystyle = \frac{1}{2 {\rm i}}\left({\rm e}^{ {\rm i} \theta}-{\rm e}^{-{\rm i} \theta}\right)$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftyF(t),cos(omega,t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2452.png"
 ALT="$\displaystyle =\frac{1}{2\pi}\int_{-\infty}^\infty F(t) \cos(\omega t) dt,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftyF(t),sin(omega,t),dt.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2454.png"
 ALT="$\displaystyle =\frac{1}{2\pi}\int_{-\infty}^\infty F(t) \sin(\omega t) dt.$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftyF(x),cos(k,x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2342.png"
 ALT="$\displaystyle =\frac{1}{2\pi}\int_{-\infty}^\infty F(x) \cos(k x) dx,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftyF(x),sin(k,x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2344.png"
 ALT="$\displaystyle =\frac{1}{2\pi}\int_{-\infty}^\infty F(x) \sin(k x) dx,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftypsi(t),cos(omega,t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2469.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^\infty \psi(t) \cos(\omega t) dt,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^inftypsi(t),sin(omega,t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2470.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^\infty \psi(t) \sin(\omega t) dt,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}F(x),cos(k,x),dx=frac{1}{sqrt{2pi,sigma_k^{,2}}},expleft(-frac{k^{,2}}{2,sigma_k^{,2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.31ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img2515.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(x) \cos(k x) dx
= \f...
...t{2\pi \sigma_k^{ 2}}} \exp \left(-\frac{k^{ 2}}{2 \sigma_k^{ 2}}\right),$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}F(x),sin(k,x),dx=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2516.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(x) \sin(k x) dx=0.$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}dot{psi}(x,0),cos(k,x),dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2422.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^{\infty} \dot{\psi}(x,0) \cos(k x) dx.$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}dot{psi}(x,0),sin(k,x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2420.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^{\infty} \dot{\psi}(x,0) \sin(k x) dx,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}expleft(-frac{t^{,2}}{2,sigma_t^{,2}}right)cos(omega_0,t),cos(omega,t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img2486.png"
 ALT="$\displaystyle =\frac{1}{2\pi}\int_{-\infty}^{\infty} \exp\left(-\frac{t^{ 2}}{2 \sigma_t^{ 2}}\right)\cos(\omega_0 t) \cos(\omega t) dt,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}psi(x,0),cos(k,x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2415.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^{\infty} \psi(x,0) \cos(k x) dx,$">|; 

$key = q/displaystyle=frac{1}{2pi}int_{-infty}^{infty}psi(x,0),sin(k,x),dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2417.png"
 ALT="$\displaystyle = \frac{1}{2\pi}\int_{-\infty}^{\infty} \psi(x,0) \sin(k x) dx.$">|; 

$key = q/displaystyle=frac{1}{2}+C(u'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3642.png"
 ALT="$\displaystyle = \frac{1}{2}+C(u'),$">|; 

$key = q/displaystyle=frac{1}{2}+S(u').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3644.png"
 ALT="$\displaystyle = \frac{1}{2}+S(u').$">|; 

$key = q/displaystyle=frac{1}{2},(1+cos2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4380.png"
 ALT="$\displaystyle =\frac{1}{2} (1+\cos 2\alpha)$">|; 

$key = q/displaystyle=frac{1}{2},(1-cos2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4378.png"
 ALT="$\displaystyle =\frac{1}{2} (1-\cos 2\alpha)$">|; 

$key = q/displaystyle=frac{1}{2},C(u',u_1,u_2),C(v',v_1,v_2)-frac{1}{2},S(u',u_1,u_2),S(v',v_1,v_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3614.png"
 ALT="$\displaystyle = \frac{1}{2} C(u',u_1,u_2) C(v',v_1,v_2) -\frac{1}{2} S(u',u_1,u_2) S(v',v_1,v_2),$">|; 

$key = q/displaystyle=frac{1}{2},C(u',u_1,u_2)-frac{1}{2},S(u',u_1,u_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3634.png"
 ALT="$\displaystyle = \frac{1}{2} C(u',u_1,u_2)-\frac{1}{2} S(u',u_1,u_2)$">|; 

$key = q/displaystyle=frac{1}{2},S(u',u_1,u_2)+frac{1}{2},C(u',u_1,u_2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3636.png"
 ALT="$\displaystyle = \frac{1}{2} S(u',u_1,u_2) + \frac{1}{2} C(u',u_1,u_2).$">|; 

$key = q/displaystyle=frac{1}{2},S(u',u_1,u_2),C(v',v_1,v_2)+frac{1}{2},C(u',u_1,u_2),S(v',v_1,v_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3615.png"
 ALT="$\displaystyle = \frac{1}{2} S(u',u_1,u_2) C(v',v_1,v_2) + \frac{1}{2} C(u',u_1,u_2) S(v',v_1,v_2),$">|; 

$key = q/displaystyle=frac{1}{2},X,sinbeta,cosbeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3135.png"
 ALT="$\displaystyle =\frac{1}{2} X \sin\beta \cos\beta,$">|; 

$key = q/displaystyle=frac{1}{2},X_0,sin^2beta,cosbeta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3141.png"
 ALT="$\displaystyle =\frac{1}{2} X_0 \sin^2\beta \cos\beta.$">|; 

$key = q/displaystyle=frac{1}{2},epsilon_0,frac{partial}{partialt}left(epsilon_{xx},E_x^{,2}+epsilon_{yy},E_y^{,2}+epsilon_{zz},E_z^{,2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2135.png"
 ALT="$\displaystyle =\frac{1}{2} \epsilon_0 \frac{\partial}{\partial t}\left(\epsilon_{xx} E_x^{ 2}
+\epsilon_{yy} E_y^{ 2}+\epsilon_{zz} E_z^{ 2}\right)$">|; 

$key = q/displaystyle=frac{1}{2},frac{partial}{partialt}left(E_x,D_x+E_y,D_y+E_z,D_zright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2136.png"
 ALT="$\displaystyle =\frac{1}{2} \frac{\partial}{\partial t}\left(E_x D_x+E_y D_y+E_z D_z\right).$">|; 

$key = q/displaystyle=frac{1}{2},rho,v_x^{,2}+frac{1}{2},rho,v_z^{,2}+frac{1}{2},frac{tilde{p}^{,2}}{K},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2251.png"
 ALT="$\displaystyle = \frac{1}{2} \rho v_x^{ 2} + \frac{1}{2} \rho v_z^{ 2}+ \frac{1}{2} \frac{\tilde{p}^{ 2}}{K},$">|; 

$key = q/displaystyle=frac{1}{2},{bfE}cdot{bfD}+frac{1}{2},{bfB}cdot{bfH},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2140.png"
 ALT="$\displaystyle = \frac{1}{2} {\bf E}\cdot{\bf D} + \frac{1}{2} {\bf B}\cdot{\bf H},$">|; 

$key = q/displaystyle=frac{1}{2}int_{-infty}^inftybar{f}(u,v),cosleft[frac{pi}{2},(u-u')^{,2}+frac{pi}{2},(v-v')^{,2}right]du,dv,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3603.png"
 ALT="$\displaystyle =\frac{1}{2}\int_{-\infty}^\infty \bar{f}(u,v) \cos\left[\frac{\pi}{2} (u-u')^{ 2} +\frac{\pi}{2} (v-v')^{ 2}\right]
du dv,$">|; 

$key = q/displaystyle=frac{1}{2}int_{-infty}^inftybar{f}(u,v),sinleft[frac{pi}{2},(u-u')^{,2}+frac{pi}{2},(v-v')^{,2}right]du,dv.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3605.png"
 ALT="$\displaystyle =\frac{1}{2}\int_{-\infty}^\infty \bar{f}(u,v) \sin\left[\frac{\pi}{2} (u-u')^{ 2} +\frac{\pi}{2} (v-v')^{ 2}\right]
du dv.$">|; 

$key = q/displaystyle=frac{1}{2}int_{-infty}^inftyint_{-infty}^inftyf(u,v),cosleft[frac{pi}{2},(u-u')^{,2}+frac{pi}{2},(v-v')^{,2}right]du,dv,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3583.png"
 ALT="$\displaystyle =\frac{1}{2}\int_{-\infty}^\infty \int_{-\infty}^\infty f(u,v) \cos\left[\frac{\pi}{2} (u-u')^{ 2} +\frac{\pi}{2} (v-v')^{ 2}\right]
du dv,$">|; 

$key = q/displaystyle=frac{1}{2}int_{-infty}^inftyint_{-infty}^inftyf(u,v),cosleft[pi,(u,u'+v,v')right],du,dv,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3746.png"
 ALT="$\displaystyle =\frac{1}{2}\int_{-\infty}^\infty\int_{-\infty}^\infty f(u,v) \cos\left[\pi (u u'+v v')\right] du dv,$">|; 

$key = q/displaystyle=frac{1}{2}int_{-infty}^inftyint_{-infty}^inftyf(u,v),sinleft[frac{pi}{2},(u-u')^{,2}+frac{pi}{2},(v-v')^{,2}right]du,dv.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3585.png"
 ALT="$\displaystyle =\frac{1}{2}\int_{-\infty}^\infty \int_{-\infty}^\infty f(u,v) \sin\left[\frac{\pi}{2} (u-u')^{ 2} +\frac{\pi}{2} (v-v')^{ 2}\right]
du dv.$">|; 

$key = q/displaystyle=frac{1}{2}int_{-infty}^inftyint_{-infty}^inftyf(u,v),sinleft[pi,(u,u'+v,v')right],du,dv.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3748.png"
 ALT="$\displaystyle =\frac{1}{2}\int_{-\infty}^\infty\int_{-\infty}^\infty f(u,v) \sin\left[\pi (u u'+v v')\right] du dv.$">|; 

$key = q/displaystyle=frac{1}{2}left({rme}^{,theta}+{rme}^{-theta}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4431.png"
 ALT="$\displaystyle = \frac{1}{2}\left({\rm e}^{ \theta}+{\rm e}^{-\theta}\right)$">|; 

$key = q/displaystyle=frac{1}{2}left({rme}^{,theta}-{rme}^{-theta}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4433.png"
 ALT="$\displaystyle = \frac{1}{2}\left({\rm e}^{ \theta}-{\rm e}^{-\theta}\right)$">|; 

$key = q/displaystyle=frac{1}{2}left({rme}^{,{rmi},theta}+{rme}^{-{rmi},theta}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4427.png"
 ALT="$\displaystyle = \frac{1}{2}\left({\rm e}^{ {\rm i} \theta}+{\rm e}^{-{\rm i} \theta}\right)$">|; 

$key = q/displaystyle=frac{1}{2}left[1+C(u')+S(u')right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3646.png"
 ALT="$\displaystyle =\frac{1}{2}\left[ 1+ C(u')+S(u')\right],$">|; 

$key = q/displaystyle=frac{1}{2}left[C(u')-S(u')right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3645.png"
 ALT="$\displaystyle = \frac{1}{2}\left[ C(u')-S(u')\right],$">|; 

$key = q/displaystyle=frac{1}{2}left[cos(alpha-beta)+cos(alpha+beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4356.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cos(\alpha-\beta)+\cos(\alpha+\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[cos(alpha-beta)-cos(alpha+beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4354.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cos(\alpha-\beta)-\cos(\alpha+\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[cosh(alpha+beta)+cosh(alpha-beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4413.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cosh(\alpha+\beta)+\cosh(\alpha-\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[cosh(alpha+beta)-cosh(alpha-beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4411.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cosh(\alpha+\beta)-\cosh(\alpha-\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[delta(k-k')-delta(k+k')right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2396.png"
 ALT="$\displaystyle = \frac{1}{2}\left[\delta(k-k') - \delta(k+k')\right],$">|; 

$key = q/displaystyle=frac{1}{2}left[sin(alpha-beta)+sin(alpha+beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4358.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\sin(\alpha-\beta)+\sin(\alpha+\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[sinh(alpha+beta)+sinh(alpha-beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4415.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\sinh(\alpha+\beta)+\sinh(\alpha-\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{4pi}left[-int_{-infty}^{infty}psi(x,0),sin(k,x),dx+int_{-infty}^inftyfrac{dot{psi}(x,0)}{k,v},cos(k,x),dxright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2428.png"
 ALT="$\displaystyle =\frac{1}{4\pi}\left[-\int_{-\infty}^{\infty}\psi(x,0) \sin(k x) dx
+ \int_{-\infty}^\infty \frac{\dot{\psi}(x,0)}{k v} \cos(k x) dx\right],$">|; 

$key = q/displaystyle=frac{1}{4pi}left[int_{-infty}^{infty}psi(x,0),cos(k,x),dx+int_{-infty}^inftyfrac{dot{psi}(x,0)}{k,v},sin(k,x),dxright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2424.png"
 ALT="$\displaystyle =\frac{1}{4\pi}\left[\int_{-\infty}^{\infty}\psi(x,0) \cos(k x) dx
+ \int_{-\infty}^\infty \frac{\dot{\psi}(x,0)}{k v} \sin(k x) dx\right],$">|; 

$key = q/displaystyle=frac{1}{4pi}left[int_{-infty}^{infty}psi(x,0),cos(k,x),dx-int_{-infty}^inftyfrac{dot{psi}(x,0)}{k,v},sin(k,x),dxright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2426.png"
 ALT="$\displaystyle =\frac{1}{4\pi}\left[\int_{-\infty}^{\infty}\psi(x,0) \cos(k x) dx
- \int_{-\infty}^\infty \frac{\dot{\psi}(x,0)}{k v} \sin(k x) dx\right],$">|; 

$key = q/displaystyle=frac{1}{4pi}left[int_{-infty}^{infty}psi(x,0),sin(k,x),dx+int_{-infty}^inftyfrac{dot{psi}(x,0)}{k,v},cos(k,x),dxright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2430.png"
 ALT="$\displaystyle =\frac{1}{4\pi}\left[\int_{-\infty}^{\infty}\psi(x,0) \sin(k x) dx
+\int_{-\infty}^\infty \frac{\dot{\psi}(x,0)}{k v} \cos(k x) dx\right].$">|; 

$key = q/displaystyle=frac{1}{4},(3,cosalpha+cos3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4384.png"
 ALT="$\displaystyle =\frac{1}{4} (3 \cos\alpha+\cos 3\alpha)$">|; 

$key = q/displaystyle=frac{1}{4},(3,sinalpha-sin3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4382.png"
 ALT="$\displaystyle = \frac{1}{4} (3 \sin\alpha-\sin 3\alpha)$">|; 

$key = q/displaystyle=frac{1}{4}sum_{n>0}A_n,sinphi_nleft[delta(omega-omega_0-omega_n)-delta(omega-omega_0+omega_n)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2474.png"
 ALT="$\displaystyle = \frac{1}{4}\sum_{n&gt;0} A_n \sin\phi_n\left[\delta(\omega-\omega_0-\omega_n) - \delta(\omega-\omega_0+\omega_n)\right].$">|; 

$key = q/displaystyle=frac{1}{8},(3+4,cos2alpha+cos4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4388.png"
 ALT="$\displaystyle = \frac{1}{8} (3+4 \cos 2\alpha+\cos 4\alpha)$">|; 

$key = q/displaystyle=frac{1}{8},(3-4,cos2alpha+cos4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4386.png"
 ALT="$\displaystyle = \frac{1}{8} (3-4 \cos 2\alpha+\cos 4\alpha)$">|; 

$key = q/displaystyle=frac{1}{N}sum_{n=1,N}int_{-infty}^inftyF_2(x-x_n),cos(k,sintheta,x),dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3459.png"
 ALT="$\displaystyle = \frac{1}{N}\sum_{n=1,N}\int_{-\infty}^\infty F_2(x-x_n) \cos(k \sin\theta x) dx$">|; 

$key = q/displaystyle=frac{1}{N}sum_{n=1,N}left[cos(k,sintheta,x_n),int_{-infty}^inftyF_2(x'),cos(k,sintheta,x'),dx'right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3460.png"
 ALT="$\displaystyle =\frac{1}{N}\sum_{n=1,N} \left[\cos(k \sin\theta x_n) \int_{-\infty}^\infty F_2(x') \cos(k \sin\theta x') dx'\right.$">|; 

$key = q/displaystyle=frac{1}{cos^2x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4289.png"
 ALT="$\displaystyle = \frac{1}{\cos^2 x}$">|; 

$key = q/displaystyle=frac{1}{cosh^2x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.92ex; " SRC="|."$dir".q|img4301.png"
 ALT="$\displaystyle = \frac{1}{\cosh^2 x}$">|; 

$key = q/displaystyle=frac{1}{epsilon_0,mu_0},frac{partial^{,2}E_x}{partialz^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1619.png"
 ALT="$\displaystyle =\frac{1}{\epsilon_0 \mu_0} \frac{\partial^{ 2} E_x}{\partial z^{ 2}},$">|; 

$key = q/displaystyle=frac{1}{epsilon_0,mu_0},frac{partial^{,2}H_y}{partialz^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1621.png"
 ALT="$\displaystyle =\frac{1}{\epsilon_0 \mu_0} \frac{\partial^{ 2} H_y}{\partial z^{ 2}}.$">|; 

$key = q/displaystyle=frac{1}{epsilon_0},frac{partialH_x}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3219.png"
 ALT="$\displaystyle =\frac{1}{\epsilon_0} \frac{\partial H_x}{\partial z},$">|; 

$key = q/displaystyle=frac{1}{l}int_0^lv_0(x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1089.png"
 ALT="$\displaystyle =\frac{1}{l}\int_0^l v_0(x) dx,$">|; 

$key = q/displaystyle=frac{1}{l}int_0^ly_0(x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1087.png"
 ALT="$\displaystyle =\frac{1}{l}\int_0^l y_0(x) dx,$">|; 

$key = q/displaystyle=frac{1}{mu_0},frac{partialE_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2660.png"
 ALT="$\displaystyle =\frac{1}{\mu_0} \frac{\partial E_y}{\partial z},$">|; 

$key = q/displaystyle=frac{1}{mu_0}left(frac{partialE_x}{partialy}-frac{partialE_y}{partialx}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3207.png"
 ALT="$\displaystyle = \frac{1}{\mu_0}\left(\frac{\partial E_x}{\partial y}-\frac{\partial E_y}{\partial x}\right),$">|; 

$key = q/displaystyle=frac{1}{mu_0}left(frac{partialE_x}{partialy}-frac{partialE_y}{partialx}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4447.png"
 ALT="$\displaystyle =\frac{1}{\mu_0}\left(\frac{\partial E_x}{\partial y}-\frac{\partial E_y}{\partial x}\right).$">|; 

$key = q/displaystyle=frac{1}{mu_0}left(frac{partialE_x}{partialy}-frac{partialE_y}{partialx}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4445.png"
 ALT="$\displaystyle =\frac{1}{\mu_0}\left(\frac{\partial E_x}{\partial y}-\frac{\partial E_y}{\partial x}\right)$">|; 

$key = q/displaystyle=frac{1}{mu_0}left(frac{partialE_y}{partialz}-frac{partialE_z}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3217.png"
 ALT="$\displaystyle =\frac{1}{\mu_0}\left(\frac{\partial E_y}{\partial z}-\frac{\partial E_z}{\partial y}\right),$">|; 

$key = q/displaystyle=frac{1}{mu_0}left(frac{partialE_z}{partialx}-frac{partialE_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3218.png"
 ALT="$\displaystyle = \frac{1}{\mu_0}\left(\frac{\partial E_z}{\partial x}-\frac{\partial E_x}{\partial z}\right),$">|; 

$key = q/displaystyle=frac{1}{sqrt{1-x^{,2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4291.png"
 ALT="$\displaystyle = \frac{1}{\sqrt{1-x^{ 2}}}$">|; 

$key = q/displaystyle=frac{1}{sqrt{L,C}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img497.png"
 ALT="$\displaystyle = \frac{1}{\sqrt{L C}},$">|; 

$key = q/displaystyle=frac{1}{sqrt{x^{,2}+1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4303.png"
 ALT="$\displaystyle = \frac{1}{\sqrt{x^{ 2}+1}}$">|; 

$key = q/displaystyle=frac{1}{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4283.png"
 ALT="$\displaystyle = \frac{1}{x}$">|; 

$key = q/displaystyle=frac{2,E_i}{(1+alpha^{,2})^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2633.png"
 ALT="$\displaystyle = \frac{2 E_i}{(1+\alpha^{ 2})^{1/2}},$">|; 

$key = q/displaystyle=frac{2,alpha}{1-alpha^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2632.png"
 ALT="$\displaystyle = \frac{2 \alpha}{1-\alpha^{ 2}},$">|; 

$key = q/displaystyle=frac{2,beta}{(1+hat{alpha}^{,2},beta^{,2})^{1slash2}},psi_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2085.png"
 ALT="$\displaystyle =\frac{2 \beta}{(1+\hat{\alpha}^{ 2} \beta^{ 2})^{1/2}} \psi_i.$">|; 

$key = q/displaystyle=frac{2,beta}{(beta^{,2}+hat{alpha}^{,2})^{1slash2}},psi_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2068.png"
 ALT="$\displaystyle =\frac{2 \beta}{(\beta^{ 2}+\hat{\alpha}^{ 2})^{1/2}} \psi_i.$">|; 

$key = q/displaystyle=frac{2,hat{alpha},beta}{1-hat{alpha}^{,2},beta^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2083.png"
 ALT="$\displaystyle =\frac{2 \hat{\alpha} \beta}{1-\hat{\alpha}^{ 2} \beta^{ 2}},$">|; 

$key = q/displaystyle=frac{2,hat{alpha},beta}{beta^{,2}-hat{alpha}^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2063.png"
 ALT="$\displaystyle =\frac{2 \hat{\alpha} \beta}{\beta^{ 2}-\hat{\alpha}^{ 2}},$">|; 

$key = q/displaystyle=frac{2pi}{lambda},frac{a}{R},a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3672.png"
 ALT="$\displaystyle = \frac{2\pi}{\lambda} \frac{a}{R} a,$">|; 

$key = q/displaystyle=frac{2pi}{lambda},frac{a}{R},r'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3673.png"
 ALT="$\displaystyle = \frac{2\pi}{\lambda} \frac{a}{R} r'.$">|; 

$key = q/displaystyle=frac{2}{L}int_{-Lslash2}^{Lslash2}F(x),cos(n,deltak,x),dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2331.png"
 ALT="$\displaystyle =\frac{2}{L}\int_{-L/2}^{L/2} F(x) \cos(n \delta k x) dx,$">|; 

$key = q/displaystyle=frac{2}{L}int_{-Lslash2}^{Lslash2}F(x),sin(n,deltak,x),dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2332.png"
 ALT="$\displaystyle =\frac{2}{L}\int_{-L/2}^{L/2} F(x) \sin(n \delta k x) dx.$">|; 

$key = q/displaystyle=frac{2}{l}int_0^lv_0(x),cosleft(n,pi,frac{x}{l}right)dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1094.png"
 ALT="$\displaystyle = \frac{2}{l}\int_0^l v_0(x) \cos\left(n \pi \frac{x}{l}\right) dx.$">|; 

$key = q/displaystyle=frac{2}{l}int_0^ly_0(x),cosleft(n,pi,frac{x}{l}right)dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1093.png"
 ALT="$\displaystyle = \frac{2}{l}\int_0^l y_0(x) \cos\left(n \pi \frac{x}{l}\right) dx,$">|; 

$key = q/displaystyle=frac{2}{l}int_0^ly_0(x),sinleft(n,pi,frac{x}{l}right)dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1043.png"
 ALT="$\displaystyle = \frac{2}{l}\int_0^l y_0(x) \sin\left(n \pi \frac{x}{l}\right)dx,$">|; 

$key = q/displaystyle=frac{2}{n,pi,v}int_0^lv_0(x),sinleft(n,pi,frac{x}{l}right)dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1045.png"
 ALT="$\displaystyle = \frac{2}{n \pi v}\int_0^l v_0(x) \sin\left(n \pi \frac{x}{l}\right)dx,$">|; 

$key = q/displaystyle=frac{2}{tau}int_0^tauA,(2,tslashtau-1),cos(n,omega,t),dt=frac{A}{pi^{,2}}int_0^{2pi}(theta-pi),cos(n,theta),dtheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1275.png"
 ALT="$\displaystyle = \frac{2}{\tau}\int_0^\tau A (2 t/\tau-1) \cos(n \omega t) dt = \frac{A}{\pi^{ 2}}\int_0^{2\pi} (\theta-\pi) \cos(n \theta) d\theta,$">|; 

$key = q/displaystyle=frac{2}{tau}int_0^tauA,(2,tslashtau-1),sin(n,omega,t),dt=frac{A}{pi^{,2}}int_0^{2pi}(theta-pi),sin(n,theta),dtheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1276.png"
 ALT="$\displaystyle = \frac{2}{\tau}\int_0^\tau A (2 t/\tau-1) \sin(n \omega t) dt = \frac{A}{\pi^{ 2}}\int_0^{2\pi} (\theta-\pi) \sin(n \theta) d\theta,$">|; 

$key = q/displaystyle=frac{3}{20}left(frac{9pi}{8}right)^{2slash3}frac{hbar^{,2}}{m_e}left(frac{M}{m_p}right)^{5slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4204.png"
 ALT="$\displaystyle = \frac{3}{20}\left(\frac{9\pi}{8}\right)^{2/3}\frac{\hbar^{ 2}}{m_e}
\left(\frac{M}{m_p}\right)^{5/3},$">|; 

$key = q/displaystyle=frac{3}{2},X_0,frac{cosbeta}{sin^2beta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.35ex; " SRC="|."$dir".q|img3255.png"
 ALT="$\displaystyle = \frac{3}{2} X_0 \frac{\cos\beta}{\sin^2\beta}.$">|; 

$key = q/displaystyle=frac{3}{5},G,M^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4205.png"
 ALT="$\displaystyle = \frac{3}{5} G M^{ 2}.$">|; 

$key = q/displaystyle=frac{4,Z_1,Z_1}{(R_L+Z_1+Z_2)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1756.png"
 ALT="$\displaystyle = \frac{4 Z_1 Z_1}{(R_L+Z_1+Z_2)^2},$">|; 

$key = q/displaystyle=frac{4,Z_1,Z_2,Z_3^{,2}}{[Z_2,Z_3+Z_1,(Z_2+Z_3)]^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1766.png"
 ALT="$\displaystyle = \frac{4 Z_1 Z_2 Z_3^{ 2}}{[Z_2 Z_3+Z_1 (Z_2+Z_3)]^{ 2}},$">|; 

$key = q/displaystyle=frac{4,Z_1,Z_2,costheta_i,costheta_t}{(Z_1,costheta_i+Z_2,costheta_t)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2313.png"
 ALT="$\displaystyle = \frac{4 Z_1 Z_2 \cos\theta_i \cos\theta_t}{(Z_1 \cos\theta_i+Z_2 \cos\theta_t)^2},$">|; 

$key = q/displaystyle=frac{4,Z_1,Z_2^{,2},Z_3}{[Z_2,Z_3+Z_1,(Z_2+Z_3)]^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1768.png"
 ALT="$\displaystyle = \frac{4 Z_1 Z_2^{ 2} Z_3}{[Z_2 Z_3+Z_1 (Z_2+Z_3)]^{ 2}},$">|; 

$key = q/displaystyle=frac{4,Z_2,Z_1,costheta_i,costheta_t}{(Z_2,costheta_i+Z_1,costheta_t)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2317.png"
 ALT="$\displaystyle = \frac{4 Z_2 Z_1 \cos\theta_i \cos\theta_t}{(Z_2 \cos\theta_i+Z_1 \cos\theta_t)^2},$">|; 

$key = q/displaystyle=frac{4,Z_2,Z_1,costheta_i,costheta_t}{(Z_2,costheta_i+Z_1,costheta_t)^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2316.png"
 ALT="$\displaystyle = \frac{4 Z_2 Z_1 \cos\theta_i \cos\theta_t}{(Z_2 \cos\theta_i+Z_1 \cos\theta_t)^2}.$">|; 

$key = q/displaystyle=frac{4,alpha,beta}{(1+alpha,beta)^2}=1-R,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2031.png"
 ALT="$\displaystyle =\frac{4 \alpha \beta}{(1+\alpha \beta)^2} = 1-R,$">|; 

$key = q/displaystyle=frac{4,alpha,beta}{(beta+alpha)^2}=1-R.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1999.png"
 ALT="$\displaystyle =\frac{4 \alpha \beta}{(\beta+\alpha)^2} = 1-R.$">|; 

$key = q/displaystyle=frac{4}{a,b,omega_{m,n}}int_0^aint_0^bG(x,y),sinleft(m,pi,frac{x}{a}right)sinleft(n,pi,frac{y}{b}right),dx,dy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.16ex; " SRC="|."$dir".q|img2306.png"
 ALT="$\displaystyle = \frac{4}{a b \omega_{m,n}}\int_0^a\int_0^b G(x,y) \sin\left(m \pi \frac{x}{a}\right)\sin\left(n \pi \frac{y}{b}\right)  dx dy.$">|; 

$key = q/displaystyle=frac{4}{a,b}int_0^aint_0^bF(x,y),sinleft(m,pi,frac{x}{a}right)sinleft(n,pi,frac{y}{b}right),dx,dy,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2304.png"
 ALT="$\displaystyle = \frac{4}{a b}\int_0^a\int_0^b F(x,y) \sin\left(m \pi \frac{x}{a}\right)\sin\left(n \pi \frac{y}{b}\right)  dx dy,$">|; 

$key = q/displaystyle=frac{K}{rho},frac{partialtilde{rho}}{partialt}=-Kleft(frac{partialv_x}{partialx}+frac{partialv_z}{partialz}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2229.png"
 ALT="$\displaystyle =\frac{K}{\rho} \frac{\partial\tilde{\rho}}{\partial t} = -K\left(\frac{\partial v_x}{\partial x}+
\frac{\partial v_z}{\partial z}\right).$">|; 

$key = q/displaystyle=frac{R+L}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2820.png"
 ALT="$\displaystyle = \frac{R+L}{2},$">|; 

$key = q/displaystyle=frac{R-L}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2822.png"
 ALT="$\displaystyle =\frac{R-L}{2}.$">|; 

$key = q/displaystyle=frac{R}{L}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img499.png"
 ALT="$\displaystyle = \frac{R}{L}.$">|; 

$key = q/displaystyle=frac{X_0}{sin^3beta}left(1-frac{3}{2},sin^2betaright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.35ex; " SRC="|."$dir".q|img3254.png"
 ALT="$\displaystyle = \frac{X_0}{\sin^3\beta}\left(1-\frac{3}{2} \sin^2\beta\right),$">|; 

$key = q/displaystyle=frac{a}{2},cos(omega_0,t)+frac{a}{2},cos(sqrt{3},omega_0,t)=a,cos(omega_-,t),cos(omega_+,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img720.png"
 ALT="$\displaystyle =\frac{a}{2} \cos(\omega_0 t)+\frac{a}{2} \cos(\sqrt{3} \omega_0 t)= a \cos(\omega_- t) \cos(\omega_+ t),$">|; 

$key = q/displaystyle=frac{a}{2},cos(omega_0,t)-frac{a}{2},cos(sqrt{3},omega_0,t)=a,sin(omega_-,t),sin(omega_+,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img721.png"
 ALT="$\displaystyle =\frac{a}{2} \cos(\omega_0 t)-\frac{a}{2} \cos(\sqrt{3} \omega_0 t)=a \sin(\omega_- t) \sin(\omega_+ t),$">|; 

$key = q/displaystyle=frac{costheta_t}{costheta_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1984.png"
 ALT="$\displaystyle =\frac{\cos\theta_t}{\cos\theta_i},$">|; 

$key = q/displaystyle=frac{dot{x}(t=0)}{omega}=a,sinphi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle = \frac{\dot{x}(t=0)}{\omega}=a \sin\phi.$">|; 

$key = q/displaystyle=frac{e,B_0}{m_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2752.png"
 ALT="$\displaystyle = \frac{e B_0}{m_e},$">|; 

$key = q/displaystyle=frac{e,B_0}{m_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2750.png"
 ALT="$\displaystyle = \frac{e B_0}{m_i},$">|; 

$key = q/displaystyle=frac{e,E_R}{m_e,omega,(omega-{mitOmega}_e)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2651.png"
 ALT="$\displaystyle = \frac{e E_R}{m_e \omega (\omega-{\mit\Omega}_e)},$">|; 

$key = q/displaystyle=frac{hat{D}}{epsilon_0,epsilon_perp}(sinphi,,-cosphi,,0)=frac{hat{bfD}}{epsilon_0,epsilon_perp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2199.png"
 ALT="$\displaystyle = \frac{\hat{D}}{\epsilon_0 \epsilon_\perp}(\sin\phi, -\cos\phi, 0)=\frac{\hat{\bf D}}{\epsilon_0  \epsilon_\perp},$">|; 

$key = q/displaystyle=frac{hat{alpha}}{beta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2065.png"
 ALT="$\displaystyle = \frac{\hat{\alpha}}{\beta},$">|; 

$key = q/displaystyle=frac{hat{alpha}}{beta},cosphi_t,psi_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2060.png"
 ALT="$\displaystyle =\frac{\hat{\alpha}}{\beta} \cos\phi_t \psi_t.$">|; 

$key = q/displaystyle=frac{hat{alpha}}{beta},sinphi_t,psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2059.png"
 ALT="$\displaystyle = \frac{\hat{\alpha}}{\beta} \sin\phi_t \psi_t,$">|; 

$key = q/displaystyle=frac{k_x,c^{,2}}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2972.png"
 ALT="$\displaystyle = \frac{k_x c^{ 2}}{\omega},$">|; 

$key = q/displaystyle=frac{k_z,c^{,2}}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2973.png"
 ALT="$\displaystyle = \frac{k_z c^{ 2}}{\omega},$">|; 

$key = q/displaystyle=frac{langle{calI}_zrangle_t}{langle{calI}_zrangle_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1997.png"
 ALT="$\displaystyle = \frac{\langle {\cal I}_z\rangle_t}{\langle {\cal I}_z\rangle_i},$">|; 

$key = q/displaystyle=frac{m,pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1897.png"
 ALT="$\displaystyle = \frac{m \pi}{a},$">|; 

$key = q/displaystyle=frac{n,pi}{b},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1899.png"
 ALT="$\displaystyle = \frac{n \pi}{b},$">|; 

$key = q/displaystyle=frac{omega,skew{3}hat{V}slashL}{left[(omega_0^{,2}-omega^{,2})^{,2}+nu^{,2},omega^{,2}right]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.03ex; vertical-align: -3.62ex; " SRC="|."$dir".q|img582.png"
 ALT="$\displaystyle =\frac{\omega \skew{3}\hat{V}/L}{\left[(\omega_0^{ 2}-\omega^{ 2})^{ 2}+\nu^{ 2} \omega^{ 2}\right]^{1/2}},$">|; 

$key = q/displaystyle=frac{omega_0^{,2},hat{X}}{left[(omega_0^{,2}-omega^{,2})^{,2}+nu^{,2},omega^{,2}right]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.25ex; vertical-align: -3.62ex; " SRC="|."$dir".q|img590.png"
 ALT="$\displaystyle = \frac{\omega_0^{ 2} \hat{X}}{\left[(\omega_0^{ 2}-\omega^{ 2})^{ 2}+\nu^{ 2} \omega^{ 2}\right]^{1/2}},$">|; 

$key = q/displaystyle=frac{omega_0^{,2},hat{X}}{left[left(omega_0^{,2}-omega^{,2}right)^{,2}+nu^{,2},omega^{,2}right]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.25ex; vertical-align: -4.69ex; " SRC="|."$dir".q|img533.png"
 ALT="$\displaystyle = \frac{\omega_0^{ 2} \hat{X}}{\left[\left(\omega_0^{ 2}-\omega^{ 2}\right)^{ 2}+\nu^{ 2} \omega^{ 2}\right]^{1/2}},$">|; 

$key = q/displaystyle=frac{omega}{v_1},(sintheta_i,,0,,costheta_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2260.png"
 ALT="$\displaystyle = \frac{\omega}{v_1} (\sin\theta_i, 0, \cos\theta_i),$">|; 

$key = q/displaystyle=frac{omega}{v_1},(sintheta_r,,0,,-costheta_r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2261.png"
 ALT="$\displaystyle = \frac{\omega}{v_1} (\sin\theta_r, 0, -\cos\theta_r),$">|; 

$key = q/displaystyle=frac{omega}{v_2},(sintheta_t,,0,,costheta_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2262.png"
 ALT="$\displaystyle =\frac{\omega}{v_2} (\sin\theta_t, 0, \cos\theta_t),$">|; 

$key = q/displaystyle=frac{partialE_x}{partialy}-frac{partialE_y}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2123.png"
 ALT="$\displaystyle = \frac{\partial E_x}{\partial y}-\frac{\partial E_y}{\partial x},$">|; 

$key = q/displaystyle=frac{partialE_x}{partialy}-frac{partialE_y}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2776.png"
 ALT="$\displaystyle =\frac{\partial E_x}{\partial y}-\frac{\partial E_y}{\partial x}.$">|; 

$key = q/displaystyle=frac{partialE_y}{partialz}-frac{partialE_z}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2119.png"
 ALT="$\displaystyle = \frac{\partial E_y}{\partial z}-\frac{\partial E_z}{\partial y},$">|; 

$key = q/displaystyle=frac{partialE_z}{partialx}-frac{partialE_x}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2121.png"
 ALT="$\displaystyle = \frac{\partial E_z}{\partial x}-\frac{\partial E_x}{\partial z},$">|; 

$key = q/displaystyle=frac{partialH_x}{partialz}-frac{partialH_z}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2116.png"
 ALT="$\displaystyle = \frac{\partial H_x}{\partial z}-\frac{\partial H_z}{\partial x},$">|; 

$key = q/displaystyle=frac{partialH_y}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1962.png"
 ALT="$\displaystyle =\frac{\partial H_y}{\partial x},$">|; 

$key = q/displaystyle=frac{partialH_y}{partialx}-frac{partialH_x}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2117.png"
 ALT="$\displaystyle = \frac{\partial H_y}{\partial x}-\frac{\partial H_x}{\partial y},$">|; 

$key = q/displaystyle=frac{partialH_z}{partialy}-frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2115.png"
 ALT="$\displaystyle = \frac{\partial H_z}{\partial y}-\frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystyle=frac{partialomega}{partialk_x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2960.png"
 ALT="$\displaystyle = \frac{\partial\omega}{\partial k_x},$">|; 

$key = q/displaystyle=frac{partialomega}{partialk_z},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2965.png"
 ALT="$\displaystyle =\frac{\partial\omega}{\partial k_z},$">|; 

$key = q/displaystyle=frac{partialomega}{partialk_z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2962.png"
 ALT="$\displaystyle =\frac{\partial\omega}{\partial k_z}.$">|; 

$key = q/displaystyle=frac{partialphi}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1725.png"
 ALT="$\displaystyle = \frac{\partial\phi}{\partial t},$">|; 

$key = q/displaystyle=frac{partialphi}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2236.png"
 ALT="$\displaystyle = \frac{\partial\phi}{\partial x},$">|; 

$key = q/displaystyle=frac{partialphi}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2238.png"
 ALT="$\displaystyle =\frac{\partial\phi}{\partial z},$">|; 

$key = q/displaystyle=frac{partialphi}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3026.png"
 ALT="$\displaystyle =\frac{\partial \phi}{\partial z}.$">|; 

$key = q/displaystyle=frac{partial}{partialz}left(frac{c^{,2},n^{,2}}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2986.png"
 ALT="$\displaystyle = \frac{\partial}{\partial z}\left(\frac{c^{ 2} n^{ 2}}{2}\right).$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1972.png"
 ALT="$\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/displaystyle=frac{psi_i^{,2},costheta_i}{2,epsilon_0,c,n_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1991.png"
 ALT="$\displaystyle = \frac{\psi_i^{ 2} \cos\theta_i}{2 \epsilon_0 c n_1},$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2011.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1977.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2051.png"
 ALT="$\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{psi_t^{,2},costheta_t}{2,epsilon_0,c,n_2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1995.png"
 ALT="$\displaystyle = \frac{\psi_t^{ 2} \cos\theta_t}{2 \epsilon_0 c n_2},$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2019.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2076.png"
 ALT="$\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/displaystyle=frac{rho_1,omega,costheta_i}{2,v_1},phi_i^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2280.png"
 ALT="$\displaystyle = \frac{\rho_1 \omega \cos\theta_i}{2 v_1} \phi_i^{ 2},$">|; 

$key = q/displaystyle=frac{rho_2,omega,costheta_t}{2,v_2},phi_t^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2282.png"
 ALT="$\displaystyle = \frac{\rho_2 \omega \cos\theta_t}{2 v_2} \phi_t^{ 2},$">|; 

$key = q/displaystyle=frac{sintheta_t}{v_2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2272.png"
 ALT="$\displaystyle =\frac{\sin\theta_t}{v_2}.$">|; 

$key = q/displaystyle=frac{tanalphapmtanbeta}{1mptanalpha,tanbeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4344.png"
 ALT="$\displaystyle = \frac{\tan\alpha\pm \tan\beta}{1\mp \tan\alpha \tan\beta}$">|; 

$key = q/displaystyle=frac{tanhalphapmtanhbeta}{1pmtanhalpha,tanhbeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4401.png"
 ALT="$\displaystyle = \frac{\tanh\alpha\pm\tanh\beta}{1\pm\tanh\alpha \tanh\beta}$">|; 

$key = q/displaystyle=frac{v_0+nu,x_0slash2}{omega_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img460.png"
 ALT="$\displaystyle = \frac{v_0 + \nu x_0/2}{\omega_1},$">|; 

$key = q/displaystyle=frac{v_1}{v_0},frac{dx}{ds},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3234.png"
 ALT="$\displaystyle =\frac{v_1}{v_0} \frac{dx}{ds},$">|; 

$key = q/displaystyle=frac{v_1}{v_2}=frac{n_2}{n_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1985.png"
 ALT="$\displaystyle =\frac{v_1}{v_2}=\frac{n_2}{n_1}.$">|; 

$key = q/displaystyle=frac{v}{l}sum_{n'=1,infty}n',pi,A_{n'},sinphi_{n'},sinleft(n',pi,frac{x}{l}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1020.png"
 ALT="$\displaystyle = \frac{v}{l}\sum_{n'=1,\infty} n' \pi A_{n'} \sin\phi_{n'} \sin\left(n' \pi \frac{x}{l}\right).$">|; 

$key = q/displaystyle=frac{v}{v_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3228.png"
 ALT="$\displaystyle = \frac{v}{v_0},$">|; 

$key = q/displaystyle=hat{D},(costheta,cosphi,,costheta,sinphi,,-sintheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2209.png"
 ALT="$\displaystyle = \hat{D} (\cos\theta \cos\phi, \cos\theta \sin\phi, -\sin\theta),$">|; 

$key = q/displaystyle=hat{D},(sinphi,,-cosphi,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2197.png"
 ALT="$\displaystyle = \hat{D} (\sin\phi, -\cos\phi, 0),$">|; 

$key = q/displaystyle=hat{E}_x,cos(omega,t-k,sintheta,x-k,costheta,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2809.png"
 ALT="$\displaystyle = \hat{E}_x \cos(\omega t-k \sin\theta x-k \cos\theta z),$">|; 

$key = q/displaystyle=hat{E}_y,sin(omega,t-k,sintheta,x-k,costheta,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2811.png"
 ALT="$\displaystyle = \hat{E}_y \sin(\omega t-k \sin\theta x-k \cos\theta z),$">|; 

$key = q/displaystyle=hat{E}_z,cos(omega,t-k,sintheta,x-k,costheta,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2813.png"
 ALT="$\displaystyle = \hat{E}_z \cos(\omega t-k \sin\theta x-k \cos\theta z).$">|; 

$key = q/displaystyle=hat{H}_x,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2783.png"
 ALT="$\displaystyle = \hat{H}_x \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=hat{H}_y,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2785.png"
 ALT="$\displaystyle = \hat{H}_y \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=hat{H}_z,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2787.png"
 ALT="$\displaystyle =\hat{H}_z \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=hat{I}_1,cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img755.png"
 ALT="$\displaystyle =\hat{I}_1 \cos(\omega t-\phi),$">|; 

$key = q/displaystyle=hat{I}_2,cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img757.png"
 ALT="$\displaystyle =\hat{I}_2 \cos(\omega t-\phi).$">|; 

$key = q/displaystyle=hat{P}_x,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2740.png"
 ALT="$\displaystyle =\hat{P}_x \cos(\omega t-{\bf k}\cdot {\bf r}),$">|; 

$key = q/displaystyle=hat{P}_y,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2742.png"
 ALT="$\displaystyle = \hat{P}_y \sin(\omega t-{\bf k}\cdot {\bf r}),$">|; 

$key = q/displaystyle=hat{alpha},beta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2084.png"
 ALT="$\displaystyle = \hat{\alpha} \beta,$">|; 

$key = q/displaystyle=hat{alpha},cosphi_t,psi_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2082.png"
 ALT="$\displaystyle =\hat{\alpha} \cos\phi_t \psi_t.$">|; 

$key = q/displaystyle=hat{alpha},sinphi_t,psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2081.png"
 ALT="$\displaystyle = \hat{\alpha} \sin\phi_t \psi_t,$">|; 

$key = q/displaystyle=hat{bfD},cosleft[k,(v,t-{bfn}cdot{bfr})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2148.png"
 ALT="$\displaystyle = \hat{\bf D} \cos\left[k (v t-{\bf n}\cdot{\bf r})\right],$">|; 

$key = q/displaystyle=hat{bfE},cosleft[k,(v,t-{bfn}cdot{bfr})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2146.png"
 ALT="$\displaystyle = \hat{\bf E} \cos\left[k (v t-{\bf n}\cdot{\bf r})\right],$">|; 

$key = q/displaystyle=hat{bfH},cosleft[k,(v,t-{bfn}cdot{bfr})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2150.png"
 ALT="$\displaystyle = \hat{\bf H} \cos\left[k (v t-{\bf n}\cdot{\bf r})\right],$">|; 

$key = q/displaystyle=hat{eta}_1,cos(omega_0,t-phi_1)+hat{eta}_2,cosleft(sqrt{3},omega_0,t-phi_2right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img709.png"
 ALT="$\displaystyle = \hat{\eta}_1 \cos(\omega_0 t-\phi_1)+ \hat{\eta}_2 \cos\left(\sqrt{3} \omega_0 t-\phi_2\right),$">|; 

$key = q/displaystyle=hat{eta}_1,cos(omega_0,t-phi_1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img698.png"
 ALT="$\displaystyle = \hat{\eta}_1 \cos(\omega_0 t-\phi_1),$">|; 

$key = q/displaystyle=hat{eta}_1,cos(omega_0,t-phi_1)-hat{eta}_2,cosleft(sqrt{3},omega_0,t-phi_2right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img710.png"
 ALT="$\displaystyle = \hat{\eta}_1 \cos(\omega_0 t-\phi_1)-\hat{ \eta}_2 \cos\left(\sqrt{3} \omega_0 t-\phi_2\right).$">|; 

$key = q/displaystyle=hat{eta}_1,cos(omega_1,t-phi_1)+hat{eta}_2,cos(omega_0,t-phi_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img766.png"
 ALT="$\displaystyle = \hat{\eta}_1 \cos(\omega_1 t-\phi_1)+\hat{\eta}_2 \cos(\omega_0 t-\phi_2),$">|; 

$key = q/displaystyle=hat{eta}_1,cos(omega_1,t-phi_1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img778.png"
 ALT="$\displaystyle =\hat{\eta}_1 \cos(\omega_1 t-\phi_1),$">|; 

$key = q/displaystyle=hat{eta}_1,cos(omega_1,t-phi_1)-hat{eta}_2,cos(omega_0,t-phi_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img767.png"
 ALT="$\displaystyle = \hat{\eta}_1 \cos(\omega_1 t-\phi_1)-\hat{\eta}_2 \cos(\omega_0 t-\phi_2),$">|; 

$key = q/displaystyle=hat{eta}_1,cosleft(omega_0,t-phi_1right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img730.png"
 ALT="$\displaystyle =\hat{\eta}_1 \cos\left(\omega_0 t-\phi_1\right),$">|; 

$key = q/displaystyle=hat{eta}_1,cosphi_1+hat{eta}_2,cosphi_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img714.png"
 ALT="$\displaystyle =\hat{\eta}_1 \cos\phi_1 + \hat{\eta}_2 \cos\phi_2,$">|; 

$key = q/displaystyle=hat{eta}_1,cosphi_1-hat{eta}_2,cosphi_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img716.png"
 ALT="$\displaystyle =\hat{\eta}_1 \cos\phi_1 -\hat{\eta}_2 \cos\phi_2,$">|; 

$key = q/displaystyle=hat{eta}_1,sinphi_1+sqrt{3},hat{eta}_2,sinphi_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img715.png"
 ALT="$\displaystyle =\hat{\eta}_1 \sin\phi_1+\sqrt{3} \hat{\eta}_2 \sin\phi_2,$">|; 

$key = q/displaystyle=hat{eta}_1,sinphi_1-sqrt{3},hat{eta}_2,sinphi_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img717.png"
 ALT="$\displaystyle =\hat{\eta}_1 \sin\phi_1-\sqrt{3} \hat{\eta}_2 \sin\phi_2,$">|; 

$key = q/displaystyle=hat{eta}_2,cos(omega_0,t-phi_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img779.png"
 ALT="$\displaystyle =\hat{\eta}_2 \cos(\omega_0 t-\phi_2),$">|; 

$key = q/displaystyle=hat{eta}_2,cos(omega_2,t-phi_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img821.png"
 ALT="$\displaystyle =\hat{\eta}_2 \cos(\omega_2 t-\phi_2),$">|; 

$key = q/displaystyle=hat{eta}_2,cosleft(sqrt{3},omega_0,t-phi_2right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img703.png"
 ALT="$\displaystyle = \hat{\eta}_2 \cos\left(\sqrt{3} \omega_0 t-\phi_2\right),$">|; 

$key = q/displaystyle=hat{eta}_2,cosleft(sqrt{3},omega_0,t-phi_2right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img731.png"
 ALT="$\displaystyle =\hat{\eta}_2 \cos\left(\sqrt{3} \omega_0 t-\phi_2\right).$">|; 

$key = q/displaystyle=hat{eta}_3,cos(omega_3,t-phi_3).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img823.png"
 ALT="$\displaystyle =\hat{\eta}_3 \cos(\omega_3 t-\phi_3).$">|; 

$key = q/displaystyle=hat{x},cos(omega,t-varphi)+A,{rme}^{-nu,tslash2},cos(omega_1,t)+B,{rme}^{-nu,tslash2},sin(omega_1,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img593.png"
 ALT="$\displaystyle = \hat{x} \cos(\omega t-\varphi) + A {\rm e}^{-\nu t/2} \cos(\omega_1 t) + B {\rm e}^{-\nu t/2} \sin(\omega_1 t).$">|; 

$key = q/displaystyle=hat{x},cosvarphi+A=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img599.png"
 ALT="$\displaystyle =\hat{x} \cos\varphi +A=0,$">|; 

$key = q/displaystyle=hat{x},omega,sinvarphi-frac{nu}{2},A+omega_1,B=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img601.png"
 ALT="$\displaystyle = \hat{x} \omega \sin\varphi - \frac{\nu}{2} A+\omega_1 B=0.$">|; 

$key = q/displaystyle=hat{x}_1,cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img670.png"
 ALT="$\displaystyle = \hat{x}_1 \cos(\omega t-\phi),$">|; 

$key = q/displaystyle=hat{x}_2,cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img672.png"
 ALT="$\displaystyle =\hat{x}_2 \cos(\omega t-\phi),$">|; 

$key = q/displaystyle=hat{x}_3,cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img793.png"
 ALT="$\displaystyle =\hat{x}_3 \cos(\omega t-\phi).$">|; 

$key = q/displaystyle=hat{x}_e,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2735.png"
 ALT="$\displaystyle = \hat{x}_e \cos(\omega t-{\bf k}\cdot {\bf r}),$">|; 

$key = q/displaystyle=hat{x}_i,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2730.png"
 ALT="$\displaystyle = \hat{x}_i \cos(\omega t-{\bf k}\cdot {\bf r}),$">|; 

$key = q/displaystyle=hat{y}_e,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2737.png"
 ALT="$\displaystyle = \hat{y}_e \sin(\omega t-{\bf k}\cdot {\bf r}),$">|; 

$key = q/displaystyle=hat{y}_i,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2732.png"
 ALT="$\displaystyle = \hat{y}_i \sin(\omega t-{\bf k}\cdot {\bf r}),$">|; 

$key = q/displaystyle=int_0^zcosleft(frac{pi}{2},t^{,2}right)dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3621.png"
 ALT="$\displaystyle =\int_0^z \cos\left(\frac{\pi}{2} t^{ 2}\right)dt,$">|; 

$key = q/displaystyle=int_0^zsinleft(frac{pi}{2},t^{,2}right)dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3623.png"
 ALT="$\displaystyle = \int_0^z \sin\left(\frac{\pi}{2} t^{ 2}\right)dt$">|; 

$key = q/displaystyle=int_{-infty}^inftybar{F}(omega),cos(omega,t),domega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2530.png"
 ALT="$\displaystyle =\int_{-\infty}^\infty \bar{F}(\omega) \cos(\omega t) d\omega,$">|; 

$key = q/displaystyle=int_{-infty}^inftybar{G}(omega),cos(omega,t),domega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2532.png"
 ALT="$\displaystyle =\int_{-\infty}^\infty \bar{G}(\omega) \cos(\omega t) d\omega.$">|; 

$key = q/displaystyle=int_{-infty}^inftyleft[C_+(k),cos(k,x)+S_+(k),sin(k,x)right]dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2433.png"
 ALT="$\displaystyle = \int_{-\infty}^\infty\left[C_+(k) \cos(k x)+ S_+(k) \sin(k x)\right] dk,$">|; 

$key = q/displaystyle=int_{-infty}^inftyleft[C_-(k),cos(k,x)+S_-(k),sin(k,x)right]dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2435.png"
 ALT="$\displaystyle = \int_{-\infty}^\infty\left[C_-(k) \cos(k x)+ S_-(k) \sin(k x)\right] dk.$">|; 

$key = q/displaystyle=int_{-infty}^{infty}C_+(k),cos[k,(v,t-x)],dk+int_{-infty}^{infty}S_+(k),sin[k,(v,t-x)],dk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2405.png"
 ALT="$\displaystyle = \int_{-\infty}^{\infty} C_+(k) \cos[k (v t-x)] dk+ \int_{-\infty}^{\infty} S_+(k) \sin[k (v t-x)] dk$">|; 

$key = q/displaystyle=int_{x_1}^{x_2}left{left[1+left(frac{partialy}{partialx}right)^2right]^{1slash2}-1right}dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.86ex; vertical-align: -2.76ex; " SRC="|."$dir".q|img1420.png"
 ALT="$\displaystyle = \int_{x_1}^{x_2} \left\{\left[1+ \left(\frac{\partial y}{\partial x}\right)^2\right]^{1/2}-1\right\} dx$">|; 

$key = q/displaystyle=k,T,{rme}^{,{rmi},k,a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4022.png"
 ALT="$\displaystyle =k T {\rm e}^{ {\rm i} k a}.$">|; 

$key = q/displaystyle=k,costheta,hat{H}_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2796.png"
 ALT="$\displaystyle = k \cos\theta \hat{H}_y,$">|; 

$key = q/displaystyle=k,sintheta,(E_R-E_L),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2806.png"
 ALT="$\displaystyle = k \sin\theta (E_R-E_L),$">|; 

$key = q/displaystyle=l_x,frac{pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4155.png"
 ALT="$\displaystyle = l_x \frac{\pi}{a},$">|; 

$key = q/displaystyle=l_y,frac{pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4157.png"
 ALT="$\displaystyle =l_y \frac{\pi}{a},$">|; 

$key = q/displaystyle=l_z,frac{pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4158.png"
 ALT="$\displaystyle = l_z \frac{\pi}{a},$">|; 

$key = q/displaystyle=left(-2,omega_0^{,2},hat{x}_1+omega_0^{,2},hat{x}_2right),cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img676.png"
 ALT="$\displaystyle =\left( -2 \omega_0^{ 2} \hat{x}_1+ \omega_0^{ 2} \hat{x}_2\right) \cos(\omega t-\phi),$">|; 

$key = q/displaystyle=left(1-frac{v^{,2}}{v_0^{,2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img3230.png"
 ALT="$\displaystyle =\left(1-\frac{v^{ 2}}{v_0^{ 2}}\right),$">|; 

$key = q/displaystyle=left(I_{m,n}^{,2}+J_{m,n}^{,2}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2300.png"
 ALT="$\displaystyle = \left(I_{m,n}^{ 2}+J_{m,n}^{ 2}\right)^{1/2},$">|; 

$key = q/displaystyle=left(frac{1-alpha,beta}{1+alpha,beta}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2030.png"
 ALT="$\displaystyle =\left(\frac{1-\alpha \beta}{1+\alpha \beta}\right)^2,$">|; 

$key = q/displaystyle=left(frac{1-alpha,beta}{1+alpha,beta}right)psi_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2027.png"
 ALT="$\displaystyle =\left(\frac{1-\alpha \beta}{1+\alpha \beta}\right)\psi_i,$">|; 

$key = q/displaystyle=left(frac{2,Z_1,Z_3}{Z_1,Z_2+Z_3^{,2}}right)A_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img1585.png"
 ALT="$\displaystyle =\left(\frac{2 Z_1 Z_3}{Z_1 Z_2+Z_3^{ 2}}\right) A_i.$">|; 

$key = q/displaystyle=left(frac{2,Z_1}{Z_1+Z_2}right)A_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1544.png"
 ALT="$\displaystyle = \left(\frac{2 Z_1}{Z_1+Z_2}\right) A_i.$">|; 

$key = q/displaystyle=left(frac{2,beta}{1+alpha,beta}right)psi_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2028.png"
 ALT="$\displaystyle =\left(\frac{2 \beta}{1+\alpha \beta}\right)\psi_i.$">|; 

$key = q/displaystyle=left(frac{2,beta}{beta+alpha}right)psi_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1989.png"
 ALT="$\displaystyle =\left(\frac{2 \beta}{\beta+\alpha}\right)\psi_i.$">|; 

$key = q/displaystyle=left(frac{2,n_1}{n_1+n_2}right)E_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1685.png"
 ALT="$\displaystyle =\left(\frac{2 n_1}{n_1+n_2}\right)E_i.$">|; 

$key = q/displaystyle=left(frac{2,rho_1,tantheta_t}{rho_2,tantheta_t+rho_1,tantheta_i}right)phi_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2279.png"
 ALT="$\displaystyle = \left(\frac{2 \rho_1 \tan\theta_t}{\rho_2 \tan\theta_t+\rho_1 \tan\theta_i}\right)\phi_i.$">|; 

$key = q/displaystyle=left(frac{2}{lambda,R}right)^{1slash2}x',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3574.png"
 ALT="$\displaystyle = \left(\frac{2}{\lambda R}\right)^{1/2}x',$">|; 

$key = q/displaystyle=left(frac{2}{lambda,R}right)^{1slash2}x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3572.png"
 ALT="$\displaystyle = \left(\frac{2}{\lambda R}\right)^{1/2}x,$">|; 

$key = q/displaystyle=left(frac{2}{lambda,R}right)^{1slash2}y'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3578.png"
 ALT="$\displaystyle = \left(\frac{2}{\lambda R}\right)^{1/2}y'.$">|; 

$key = q/displaystyle=left(frac{2}{lambda,R}right)^{1slash2}y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3576.png"
 ALT="$\displaystyle = \left(\frac{2}{\lambda R}\right)^{1/2}y,$">|; 

$key = q/displaystyle=left(frac{R_L-Z_1+Z_2}{R_L+Z_1+Z_2}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1754.png"
 ALT="$\displaystyle =\left(\frac{R_L-Z_1+Z_2}{R_L+Z_1+Z_2}\right)^2,$">|; 

$key = q/displaystyle=left(frac{Z_1,Z_2-Z_3^{,2}}{Z_1,Z_2+Z_3^{,2}}right)A_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img1584.png"
 ALT="$\displaystyle = \left(\frac{Z_1 Z_2-Z_3^{ 2}}{Z_1 Z_2+Z_3^{ 2}}\right)A_i,$">|; 

$key = q/displaystyle=left(frac{Z_1,costheta_i-Z_2,costheta_t}{Z_1,costheta_i+Z_2,costheta_t}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2312.png"
 ALT="$\displaystyle = \left(\frac{Z_1 \cos\theta_i-Z_2 \cos\theta_t}{Z_1 \cos\theta_i+Z_2 \cos\theta_t}\right)^2,$">|; 

$key = q/displaystyle=left(frac{Z_1-Z_2}{Z_1+Z_2}right)A_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1542.png"
 ALT="$\displaystyle =\left(\frac{Z_1-Z_2}{Z_1+Z_2}\right) A_i,$">|; 

$key = q/displaystyle=left(frac{Z_2,costheta_i-Z_1,costheta_t}{Z_2,costheta_i+Z_1,costheta_t}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2315.png"
 ALT="$\displaystyle = \left(\frac{Z_2 \cos\theta_i-Z_1 \cos\theta_t}{Z_2 \cos\theta_i+Z_1 \cos\theta_t}\right)^2,$">|; 

$key = q/displaystyle=left(frac{beta-alpha}{beta+alpha}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1998.png"
 ALT="$\displaystyle =\left(\frac{\beta-\alpha}{\beta+\alpha}\right)^2,$">|; 

$key = q/displaystyle=left(frac{beta-alpha}{beta+alpha}right)psi_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1987.png"
 ALT="$\displaystyle =\left(\frac{\beta-\alpha}{\beta+\alpha}\right)\psi_i,$">|; 

$key = q/displaystyle=left(frac{coshalpha+1}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4419.png"
 ALT="$\displaystyle =\left(\frac{\cosh\alpha+1}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=left(frac{n_1-n_2}{n_1+n_2}right)E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1683.png"
 ALT="$\displaystyle =\left(\frac{n_1-n_2}{n_1+n_2}\right)E_i,$">|; 

$key = q/displaystyle=left(frac{n_e,e^{,2}}{epsilon_0,m_e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2754.png"
 ALT="$\displaystyle = \left(\frac{n_e e^{ 2}}{\epsilon_0 m_e}\right)^{1/2},$">|; 

$key = q/displaystyle=left(frac{n_e,e^{,2}}{epsilon_0,m_i}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2756.png"
 ALT="$\displaystyle = \left(\frac{n_e e^{ 2}}{\epsilon_0 m_i}\right)^{1/2}.$">|; 

$key = q/displaystyle=left(frac{rho_2,tantheta_t-rho_1,tantheta_i}{rho_2,tantheta_t+rho_1,tantheta_i}right)phi_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2277.png"
 ALT="$\displaystyle = \left(\frac{\rho_2 \tan\theta_t-\rho_1 \tan\theta_i}{\rho_2 \tan\theta_t+\rho_1 \tan\theta_i}\right)\phi_i,$">|; 

$key = q/displaystyle=left(gamma^{,2}-omega_1^{,2}right)a,{rme}^{-gamma,t},cos(omega_1,t-phi)+2,gamma,omega_1,a,{rme}^{-gamma,t},sin(omega_1,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img431.png"
 ALT="$\displaystyle = \left(\gamma^{ 2}-\omega_1^{ 2}\right)a {\rm e}^{-\gamma t}...
...t-\phi) +2 \gamma \omega_1  a {\rm e}^{-\gamma t} \sin(\omega_1 t-\phi).$">|; 

$key = q/displaystyle=left(omega_0^{,2},hat{x}_1-2,omega_0^{,2},hat{x}_2right),cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img678.png"
 ALT="$\displaystyle =\left( \omega_0^{ 2} \hat{x}_1-2 \omega_0^{ 2} \hat{x}_2\right) \cos(\omega t-\phi),$">|; 

$key = q/displaystyle=left[(x-x')^{,2}+(y-y')^{,2}+R^{,2}right]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3555.png"
 ALT="$\displaystyle =\left[(x-x')^{ 2}+(y-y')^{ 2}+R^{ 2}\right]^{1/2}$">|; 

$key = q/displaystyle=left[frac{1}{N}sum_{n=1,N}cos(k,sintheta,x_n)right]int_{-infty}^inftyF_2(x'),cos(k,sintheta,x'),dx',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3462.png"
 ALT="$\displaystyle =\left[\frac{1}{N}\sum_{n=1,N} \cos(k \sin\theta x_n)\right] \int_{-\infty}^\infty F_2(x') \cos(k \sin\theta x') dx',$">|; 

$key = q/displaystyle=left[int_{-infty}^inftycosleft(frac{pi}{2},t^{,2}right)dtright]left[int_{-infty}^inftysinleft(frac{pi}{2},t^{,2}right)dtright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3588.png"
 ALT="$\displaystyle =\left[\int_{-\infty}^\infty \cos\left(\frac{\pi}{2} t^{ 2}\rig...
...t]\left[\int_{-\infty}^\infty \sin\left(\frac{\pi}{2} t^{ 2}\right)dt\right].$">|; 

$key = q/displaystyle=left[left(gamma^{,2}-omega_1^{,2}right)-nu,gamma+omega_0^{,2}right]a,{rme}^{-gamma,t},cos(omega_1,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img432.png"
 ALT="$\displaystyle =\left[ \left(\gamma^{ 2}-\omega_1^{ 2}\right) -\nu \gamma + \omega_0^{ 2}\right]a {\rm e}^{-\gamma t} \cos(\omega_1 t-\phi)$">|; 

$key = q/displaystyle=left[x_0^{,2}+left(frac{v_0+nu,x_0slash2}{omega_1}right)^2right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.30ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img462.png"
 ALT="$\displaystyle =\left[x_0^{ 2} + \left(\frac{v_0+\nu x_0/2}{\omega_1}\right)^2\right]^{1/2},$">|; 

$key = q/displaystyle=mleft({calE}_1+{calE}_2right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img855.png"
 ALT="$\displaystyle = m\left({\cal E}_1+{\cal E}_2\right),$">|; 

$key = q/displaystyle=mpsinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4336.png"
 ALT="$\displaystyle =\mp \sin\alpha$">|; 

$key = q/displaystyle=mu_0,hat{H}_x,sin(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2789.png"
 ALT="$\displaystyle = \mu_0 \hat{H}_x \sin(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=mu_0,hat{H}_y,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2791.png"
 ALT="$\displaystyle = \mu_0 \hat{H}_y \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystyle=mu_0,hat{H}_z,sin(omega,t-{bfk}cdot{bfr}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2793.png"
 ALT="$\displaystyle =\mu_0 \hat{H}_z \sin(\omega t-{\bf k}\cdot{\bf r}).$">|; 

$key = q/displaystyle=n,x^{,n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4279.png"
 ALT="$\displaystyle = n x^{ n-1}$">|; 

$key = q/displaystyle=n_1,k_0,(sintheta_i,,0,,costheta_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1948.png"
 ALT="$\displaystyle = n_1 k_0 (\sin\theta_i, 0, \cos\theta_i),$">|; 

$key = q/displaystyle=n_1,k_0,(sintheta_r,,0,-costheta_r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1950.png"
 ALT="$\displaystyle =n_1  k_0 (\sin\theta_r, 0,-\cos\theta_r),$">|; 

$key = q/displaystyle=n_2,k_0,(sintheta_t,,0,,costheta_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1952.png"
 ALT="$\displaystyle =n_2 k_0 (\sin\theta_t, 0, \cos\theta_t),$">|; 

$key = q/displaystyle=omega_0^{,2},Aleft[sin(k,x_{i-1})-2,sin(k,x_i)right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img915.png"
 ALT="$\displaystyle =\omega_0^{ 2} A\left[\sin(k x_{i-1})-2 \sin(k x_i)\right.$">|; 

$key = q/displaystyle=omega_0^{,2},x_1-2,omega_0^{,2},x_2+omega_0^{,2},x_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img789.png"
 ALT="$\displaystyle =\omega_0^{ 2} x_1-2 \omega_0^{ 2} x_2+\omega_0^{ 2} x_3,$">|; 

$key = q/displaystyle=omega_0^{,2},x_1-2,omega_0^{,2},x_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img668.png"
 ALT="$\displaystyle = \omega_0^{ 2} x_1 - 2 \omega_0^{ 2} x_2,$">|; 

$key = q/displaystyle=omega_0^{,2},x_2-2,omega_0^{,2},x_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img791.png"
 ALT="$\displaystyle =\omega_0^{ 2} x_2-2 \omega_0^{ 2} x_3,$">|; 

$key = q/displaystyle=omega_{N+1-n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img940.png"
 ALT="$\displaystyle =\omega_{N+1-n},$">|; 

$key = q/displaystyle=phi_i,cos[omega,(t-sintheta_i,xslashv_1-costheta_i,zslashv_1)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2264.png"
 ALT="$\displaystyle = \phi_i \cos[\omega (t-\sin\theta_i x/v_1-\cos\theta_i z/v_1)]$">|; 

$key = q/displaystyle=pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img488.png"
 ALT="$\displaystyle =\pi,$">|; 

$key = q/displaystyle=pmcosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4334.png"
 ALT="$\displaystyle =\pm\cos\alpha$">|; 

$key = q/displaystyle=pmcsqrt{n^{,2}-S^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.16ex; " SRC="|."$dir".q|img2980.png"
 ALT="$\displaystyle =\pm c\sqrt{n^{ 2}-S^{2}}.$">|; 

$key = q/displaystyle=pmfrac{1}{sqrt{x^{,2}-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4305.png"
 ALT="$\displaystyle =\pm \frac{1}{\sqrt{x^{ 2}-1}}$">|; 

$key = q/displaystyle=pmleft(frac{1+cosalpha}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4362.png"
 ALT="$\displaystyle = \pm \left(\frac{1+\cos\alpha}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=pmleft(frac{1-cosalpha}{1+cosalpha}right)^{1slash2}=frac{1-cosalpha}{sinalpha}=frac{sinalpha}{1+cosalpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4364.png"
 ALT="$\displaystyle = \pm\left(\frac{1-\cos\alpha}{1+\cos\alpha}\right)^{1/2} = \frac{1-\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1+\cos\alpha}$">|; 

$key = q/displaystyle=pmleft(frac{1-cosalpha}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4360.png"
 ALT="$\displaystyle = \pm\left(\frac{1-\cos\alpha}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=pmleft(frac{coshalpha-1}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4417.png"
 ALT="$\displaystyle =\pm \left(\frac{\cosh\alpha-1}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=pmleft(frac{coshalpha-1}{coshalpha+1}right)^{1slash2}=frac{coshalpha-1}{sinhalpha}=frac{sinhalpha}{coshalpha+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4421.png"
 ALT="$\displaystyle =\pm \left(\frac{\cosh\alpha-1}{\cosh\alpha+1}\right)^{1/2}=\frac{\cosh\alpha-1}{\sinh\alpha}=
\frac{\sinh\alpha}{\cosh\alpha+1}$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2046.png"
 ALT="$\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=psi_i,sintheta_i,cos(omega,t-n_1,k_0,sintheta_i,x-n_1,k_0,costheta_i,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2017.png"
 ALT="$\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/displaystyle=psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2067.png"
 ALT="$\displaystyle = \psi_t,$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2078.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2021.png"
 ALT="$\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=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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2050.png"
 ALT="$\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/displaystyle=q,(A-B).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4018.png"
 ALT="$\displaystyle = q (A-B).$">|; 

$key = q/displaystyle=qleft(E_x+B_z,frac{dy}{dt}-B_y,frac{dz}{dt}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4472.png"
 ALT="$\displaystyle = q\left(E_x + B_z \frac{d y}{d t}-B_y \frac{d z}{d t}\right),$">|; 

$key = q/displaystyle=qleft(E_y+B_x,frac{dz}{dt}-B_z,frac{dx}{dt}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4474.png"
 ALT="$\displaystyle = q\left(E_y + B_x \frac{dz}{d t}-B_z \frac{d x}{d t}\right),$">|; 

$key = q/displaystyle=qleft(E_z+B_y,frac{dx}{dt}-B_x,frac{dy}{dt}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4476.png"
 ALT="$\displaystyle = q\left(E_z + B_y \frac{d x}{d t}-B_x \frac{d y}{d t}\right),$">|; 

$key = q/displaystyle=sinalpha,cosbetapmcosalpha,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4340.png"
 ALT="$\displaystyle =\sin\alpha \cos\beta\pm \cos\alpha \sin\beta$">|; 

$key = q/displaystyle=sinhalpha,coshbetapmcoshalpha,sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4397.png"
 ALT="$\displaystyle =\sinh\alpha \cosh\beta\pm \cosh\alpha \sinh\beta$">|; 

$key = q/displaystyle=sinhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4299.png"
 ALT="$\displaystyle = \sinh x$">|; 

$key = q/displaystyle=sinleft(frac{u^{,2}+v^{,2}}{2,u}right)U_1(u,v)-cosleft(frac{u^{,2}+v^{,2}}{2,u}right)U_2(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3709.png"
 ALT="$\displaystyle =\sin\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)U_1(u,v)- \cos\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)U_2(u,v)$">|; 

$key = q/displaystyle=sinleft(frac{u^{,2}+v^{,2}}{2,u}right)V_0(u,v)-cosleft(frac{u^{,2}+v^{,2}}{2,u}right)V_1(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3706.png"
 ALT="$\displaystyle = \sin\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)V_0(u,v)- \cos\left(\frac{u^{ 2}+v^{ 2}}{2 u}\right)V_1(u,v),$">|; 

$key = q/displaystyle=sinleft(frac{u}{2}right)U_1(u,v)-cosleft(frac{u}{2}right)U_2(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3768.png"
 ALT="$\displaystyle =\sin\left(\frac{u}{2}\right)U_1(u,v)-\cos\left(\frac{u}{2}\right)U_2(u,v),$">|; 

$key = q/displaystyle=sinleft(frac{u}{2}right)U_1(u,v)-cosleft(frac{u}{2}right)U_2(u,v).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3705.png"
 ALT="$\displaystyle =\sin\left(\frac{u}{2}\right)U_1(u,v)-\cos\left(\frac{u}{2}\right)U_2(u,v).$">|; 

$key = q/displaystyle=sinleft(frac{v^{,2}}{2,u}right)+sinleft(frac{u}{2}right)V_0(u,v)-cosleft(frac{u}{2}right)V_1(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3700.png"
 ALT="$\displaystyle =\sin\left(\frac{v^{ 2}}{2 u}\right)+\sin\left(\frac{u}{2}\right)V_0(u,v)-\cos\left(\frac{u}{2}\right)V_1(u,v),$">|; 

$key = q/displaystyle=sinleft(frac{v^{,2}}{2,u}right),{calC}(u,v)+cosleft(frac{v^{,2}}{2,v}right){calS}(u,v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3688.png"
 ALT="$\displaystyle = \sin\left(\frac{v^{ 2}}{2 u}\right) {\cal C}(u,v) + \cos\left(\frac{v^{ 2}}{2 v}\right){\cal S}(u,v),$">|; 

$key = q/displaystyle=sinphi_t,psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2057.png"
 ALT="$\displaystyle =\sin\phi_t \psi_t,$">|; 

$key = q/displaystyle=sintheta_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2270.png"
 ALT="$\displaystyle = \sin\theta_r$">|; 

$key = q/displaystyle=sum_{n'=1,infty}!!!A_{n'},cosphi_{n'},frac{2}{l}int_0^pisinleft(n',pi,frac{x}{l}right),sinleft(n,pi,frac{x}{l}right)dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1039.png"
 ALT="$\displaystyle =\sum_{n'=1,\infty} \!\!\!A_{n'} \cos\phi_{n'} \frac{2}{l}\int_0^\pi\sin\left(n' \pi \frac{x}{l}\right) \sin\left(n \pi \frac{x}{l}\right)dx$">|; 

$key = q/displaystyle=sum_{n'=1,infty}A_{n'},cosphi_{n'},delta_{n,n'}=A_ncosphi_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1040.png"
 ALT="$\displaystyle =\sum_{n'=1,\infty} A_{n'} \cos\phi_{n'} \delta_{n,n'}
= A_n\cos\phi_n,$">|; 

$key = q/displaystyle=sum_{n'=1,infty}A_{n'},cosphi_{n'},sinleft(n',pi,frac{x}{l}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1018.png"
 ALT="$\displaystyle =\sum_{n'=1,\infty} A_{n'} \cos\phi_{n'} \sin\left(n' \pi \frac{x}{l}\right),$">|; 

$key = q/displaystyle=sum_{s=0,infty}(-1)^sleft(frac{u}{v}right)^{n+2s}J_{n+2s}(v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3694.png"
 ALT="$\displaystyle =\sum_{s=0,\infty} (-1)^s\left(\frac{u}{v}\right)^{n+2s}J_{n+2s}(v),$">|; 

$key = q/displaystyle=sum_{s=0,infty}(-1)^sleft(frac{v}{u}right)^{n+2s}J_{n+2s}(v).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3696.png"
 ALT="$\displaystyle =\sum_{s=0,\infty} (-1)^s\left(\frac{v}{u}\right)^{n+2s}J_{n+2s}(v).$">|; 

$key = q/displaystyle=tan^{-1}(S_nslashC_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1090.png"
 ALT="$\displaystyle =\tan^{-1}(S_n/C_n),$">|; 

$key = q/displaystyle=tan^{-1}(S_nslashC_n).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1052.png"
 ALT="$\displaystyle = \tan^{-1}(S_n/C_n).$">|; 

$key = q/displaystyle=tan^{-1}left(frac{J_{m,n}}{I_{m,n}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2302.png"
 ALT="$\displaystyle =\tan^{-1}\left(\frac{J_{m,n}}{I_{m,n}}\right),$">|; 

$key = q/displaystyle=tan^{-1}left(frac{nu,omega}{omega_0^{,2}-omega^{,2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img535.png"
 ALT="$\displaystyle =\tan^{-1}\left(\frac{\nu \omega}{\omega_0^{ 2}-\omega^{ 2}}\right).$">|; 

$key = q/displaystyle=tan^{-1}left(frac{v_0+nu,x_0slash2}{omega_1,x_0}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img464.png"
 ALT="$\displaystyle = \tan^{-1}\left(\frac{v_0+\nu x_0/2}{\omega_1 x_0}\right).$">|; 

$key = q/displaystyle=tilde{p},v_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2253.png"
 ALT="$\displaystyle = \tilde{p} v_x,$">|; 

$key = q/displaystyle=tilde{p},v_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2255.png"
 ALT="$\displaystyle = \tilde{p} v_z.$">|; 

$key = q/displaystyle=uint_0^1cosleft(frac{u,z^{,2}}{2}right)J_0(v,z),z,dz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3690.png"
 ALT="$\displaystyle = u\int_0^1 \cos\left(\frac{u z^{ 2}}{2}\right)J_0(v z) z dz,$">|; 

$key = q/displaystyle=uint_0^1ointcosleft(frac{v^{,2}}{2,u}+frac{u,z^{,2}}{2}-v,z,costhetaright)z,dz,frac{dtheta}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3679.png"
 ALT="$\displaystyle = u\int_0^1\oint \cos\left(\frac{v^{ 2}}{2 u} + \frac{u z^{ 2}}{2}-v z \cos\theta\right)z dz \frac{d\theta}{2\pi},$">|; 

$key = q/displaystyle=uint_0^1ointsinleft(frac{v^{,2}}{2,u}+frac{u,z^{,2}}{2}-v,z,costhetaright)z,dz,frac{dtheta}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3681.png"
 ALT="$\displaystyle = u\int_0^1\oint \sin\left(\frac{v^{ 2}}{2 u} + \frac{u z^{ 2}}{2}-v z \cos\theta\right)z dz \frac{d\theta}{2\pi},$">|; 

$key = q/displaystyle=uint_0^1sinleft(frac{u,z^{,2}}{2}right)J_0(v,z),z,dz.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3692.png"
 ALT="$\displaystyle = u\int_0^1 \sin\left(\frac{u z^{ 2}}{2}\right)J_0(v z) z dz.$">|; 

$key = q/displaystyle=v,hat{D},(-sinphi,,cosphi,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2211.png"
 ALT="$\displaystyle = v \hat{D} (-\sin\phi, \cos\phi, 0),$">|; 

$key = q/displaystyle=v^{,2},frac{partialD_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2001.png"
 ALT="$\displaystyle =v^{ 2} \frac{\partial D_y}{\partial z},$">|; 

$key = q/displaystyle=v^{,2}left(frac{partialD_x}{partialy}-frac{partialD_y}{partialx}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4455.png"
 ALT="$\displaystyle = v^{ 2}\left(\frac{\partial D_x}{\partial y}-\frac{\partial D_y}{\partial x}\right),$">|; 

$key = q/displaystyle=v^{,2}left(frac{partialD_y}{partialz}-frac{partialD_z}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4454.png"
 ALT="$\displaystyle = v^{ 2}\left(\frac{\partial D_y}{\partial z}-\frac{\partial D_z}{\partial y}\right),$">|; 

$key = q/displaystyle=v^{,2}left(frac{partialD_z}{partialx}-frac{partialD_x}{partialz}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1963.png"
 ALT="$\displaystyle =v^{ 2}\left(\frac{\partial D_z}{\partial x}- \frac{\partial D_x}{\partial z}\right),$">|; 

$key = q/displaystyle=v_g,t,cosbeta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3131.png"
 ALT="$\displaystyle =v_g t \cos\beta.$">|; 

$key = q/displaystyle=v_perp,hat{D},(costheta,cosphi,,costheta,sinphi,,-sintheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2201.png"
 ALT="$\displaystyle = v_\perp \hat{D} (\cos\theta \cos\phi, \cos\theta \sin\phi, -\sin\theta),$">|; 

$key = q/displaystyle=x(t=0)=a,cosphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img197.png"
 ALT="$\displaystyle = x(t=0) = a \cos\phi,$">|; 

$key = q/displaystyle=x+frac{x^{,3}}{3!}+frac{x^{,5}}{5!}+frac{x^{,7}}{7!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4322.png"
 ALT="$\displaystyle = x + \frac{x^{ 3}}{3!} +\frac{x^{ 5}}{5!} + \frac{x^{ 7}}{7!} + \cdots$">|; 

$key = q/displaystyle=x+frac{x^{,3}}{3}+frac{2,x^{,5}}{15}+frac{17,x^{,7}}{315}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4320.png"
 ALT="$\displaystyle = x + \frac{x^{ 3}}{3} + \frac{2 x^{ 5}}{15} + \frac{17 x^{ 7}}{315}+\cdots$">|; 

$key = q/displaystyle=x-frac{x^{,2}}{2}+frac{x^{,3}}{3}-frac{x^{,4}}{4}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4316.png"
 ALT="$\displaystyle = x - \frac{x^{ 2}}{2}+\frac{x^{ 3}}{3}-\frac{x^{ 4}}{4}+\cdots$">|; 

$key = q/displaystyle=x-frac{x^{,3}}{3!}+frac{x^{,5}}{5!}-frac{x^{,7}}{7!}+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4219.png"
 ALT="$\displaystyle = x - \frac{x^{ 3}}{3!} + \frac{x^{ 5}}{5!}-\frac{x^{ 7}}{7!}+\cdots,$">|; 

$key = q/displaystyle=x-frac{x^{,3}}{3!}+frac{x^{,5}}{5!}-frac{x^{,7}}{7!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4317.png"
 ALT="$\displaystyle =x - \frac{x^{ 3}}{3!} +\frac{x^{ 5}}{5!} - \frac{x^{ 7}}{7!} + \cdots$">|; 

$key = q/displaystyle=x-frac{x^{,3}}{3}+frac{2,x^{,5}}{15}-frac{17,x^{,7}}{315}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4326.png"
 ALT="$\displaystyle = x - \frac{x^{ 3}}{3} + \frac{2 x^{ 5}}{15} - \frac{17 x^{ 7}}{315}+\cdots$">|; 

$key = q/displaystyle=x_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img458.png"
 ALT="$\displaystyle = x_0,$">|; 

$key = q/displaystyle=x_0,cos(omega,t-k_R,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2648.png"
 ALT="$\displaystyle = x_0 \cos(\omega t-k_R z),$">|; 

$key = q/displaystyle=x_{ta}(t)+x_{tr}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img592.png"
 ALT="$\displaystyle = x_{ta}(t) + x_{tr}(t)$">|; 

$key = q/displaystyle=y_0,sin(omega,t-k_R,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2650.png"
 ALT="$\displaystyle = y_0 \sin(\omega t-k_R z).$">|; 

$key = q/displaystyle=y_n(x,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img996.png"
 ALT="$\displaystyle = y_n(x,t),$">|; 

$key = q/displaystyle=y_{N+1-n,i}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img942.png"
 ALT="$\displaystyle =y_{N+1-n,i}(t),$">|; 

$key = q/displaystyle=y_{n,i}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img936.png"
 ALT="$\displaystyle = y_{n,i}(t),$">|; 

$key = q/displaystyle={bfE}times{bfH}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2142.png"
 ALT="$\displaystyle = {\bf E}\times {\bf H}.$">|; 

$key = q/displaystyle={rme}^x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4281.png"
 ALT="$\displaystyle = {\rm e}^x$">|; 

$key = q/displaystyle={rmi},k,T,{rme}^{,{rmi},k,a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4042.png"
 ALT="$\displaystyle = {\rm i} k T {\rm e}^{ {\rm i} k a}.$">|; 

$key = q/displaystyle={rmi},sinhtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4437.png"
 ALT="$\displaystyle = {\rm i} \sinh\theta$">|; 

$key = q/displaystyle={rmi},sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4441.png"
 ALT="$\displaystyle = {\rm i} \sin\theta$">|; 

$key = q/displaystyle={};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.61ex; vertical-align: 0.21ex; " SRC="|."$dir".q|img1023.png"
 ALT="$\displaystyle ={}$">|; 

$key = q/displaystyleA(t)=A_0+sum_{n>0}A_n,cos(omega_n,t-phi_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2459.png"
 ALT="$\displaystyle A(t) = A_0 + \sum_{n&gt;0} A_n \cos(\omega_n t-\phi_n),$">|; 

$key = q/displaystyleA,cos(k,x)+B,sin(k,x)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1333.png"
 ALT="$\displaystyle A \cos(k x)+ B \sin(k x) = 0,$">|; 

$key = q/displaystyleA,kleft(1-{rme}^{-2,k,d}right)cos(omega,t-k,x)=A,frac{omega^{,2}}{g}left(1+{rme}^{-2,k,d}right)cos(omega,t-k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3045.png"
 ALT="$\displaystyle A k\left(1-{\rm e}^{-2 k d}\right)\cos(\omega t-k x) = A \frac{\omega^{ 2}}{g}\left(1+{\rm e}^{-2 k d}\right)\cos(\omega t-k x),$">|; 

$key = q/displaystyleA,n^{,4}-B,n^{,2}+C=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3186.png"
 ALT="$\displaystyle A n^{ 4}-B n^{ 2}+C =0,
$">|; 

$key = q/displaystyleA,{rme}^{,q,a}+B,{rme}^{-q,a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4040.png"
 ALT="$\displaystyle A  {\rm e}^{ q a}+ B  {\rm e}^{-q a}$">|; 

$key = q/displaystyleA,{rme}^{,{rmi},q,a}+B,{rme}^{-{rmi},q,a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4019.png"
 ALT="$\displaystyle A  {\rm e}^{ {\rm i} q a}+ B  {\rm e}^{-{\rm i} q a}$">|; 

$key = q/displaystyleA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img602.png"
 ALT="$\displaystyle A$">|; 

$key = q/displaystyleA=1-frac{Z_2}{Z_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1758.png"
 ALT="$\displaystyle A=1-\frac{Z_2}{Z_1}.
$">|; 

$key = q/displaystyleA=frac{N-2}{N-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1782.png"
 ALT="$\displaystyle A = \frac{N-2}{N-1}
$">|; 

$key = q/displaystyleA=left(1-frac{Z_2}{Z_1}right)frac{Z_2}{Z_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1761.png"
 ALT="$\displaystyle A = \left(1-\frac{Z_2}{Z_1}\right)\frac{Z_2}{Z_1}.
$">|; 

$key = q/displaystyleA=left(frac{u^{,2},b^{,2}-v^{,2},a^{,2}}{u^{,2}-v^{,2}}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img383.png"
 ALT="$\displaystyle A= \left(\frac{u^{ 2} b^{ 2}-v^{ 2} a^{ 2}}{u^{ 2}-v^{ 2}}\right)^{1/2}.
$">|; 

$key = q/displaystyleA_+,cos(omega,t-k_3,a)+A_-,cos(omega,t+k_3,a)=A_t,cos(omega,t-k_2,a-phi_t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1573.png"
 ALT="$\displaystyle A_+ \cos(\omega t-k_3 a)+ A_- \cos(\omega t+k_3 a)=
A_t \cos(\omega t-k_2 a-\phi_t).$">|; 

$key = q/displaystyleA_+-A_-=A_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1579.png"
 ALT="$\displaystyle A_+-A_- = A_t.$">|; 

$key = q/displaystyleA_i+A_r=A_++A_-,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1570.png"
 ALT="$\displaystyle A_i + A_r=A_+ + A_-,$">|; 

$key = q/displaystyleA_i+A_r=A_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1535.png"
 ALT="$\displaystyle A_i + A_r = A_t.$">|; 

$key = q/displaystyleA_i+A_r=frac{Z_2}{Z_3},A_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1582.png"
 ALT="$\displaystyle A_i + A_r = \frac{Z_2}{Z_3} A_t,$">|; 

$key = q/displaystyleA_i,cos(omega,t-phi_i)+A_r,cos(omega,t-phi_r)=A_t,cos(omega,t-phi_t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1532.png"
 ALT="$\displaystyle A_i \cos(\omega t-\phi_i) +A_r \cos(\omega t-\phi_r)=A_t \cos(\omega t-\phi_t).$">|; 

$key = q/displaystyleA_i-A_r=frac{Z_3}{Z_1},A_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1583.png"
 ALT="$\displaystyle A_i-A_r=\frac{Z_3}{Z_1} A_t.$">|; 

$key = q/displaystyleA_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1049.png"
 ALT="$\displaystyle A_n$">|; 

$key = q/displaystyleA_n=2,A,frac{sin(n,pislash2)}{(n,pislash2)^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1062.png"
 ALT="$\displaystyle A_n = 2 A \frac{\sin(n \pi/2)}{(n \pi/2)^{ 2}}.$">|; 

$key = q/displaystyleA_n=S_n=frac{V_0,a}{v},frac{2}{pi},frac{sin[(n-1slash2),pi,aslashl]}{(n-1slash2)^{,2},pi,aslashl},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1207.png"
 ALT="$\displaystyle A_n =S_n= \frac{V_0 a}{v} \frac{2}{\pi} \frac{\sin[(n-1/2) \pi a/l]}{(n-1/2)^{ 2} \pi a/l},$">|; 

$key = q/displaystyleA_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1541.png"
 ALT="$\displaystyle A_r$">|; 

$key = q/displaystyleA_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1543.png"
 ALT="$\displaystyle A_t$">|; 

$key = q/displaystyleA_{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img2299.png"
 ALT="$\displaystyle A_{m,n}$">|; 

$key = q/displaystyleB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img604.png"
 ALT="$\displaystyle B$">|; 

$key = q/displaystyleB=-V,frac{partialP}{partialV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4189.png"
 ALT="$\displaystyle B = - V \frac{\partial P}{\partial V}$">|; 

$key = q/displaystyleB=frac{5}{3},P=frac{pi^{,3},hbar^{,2}}{9,m_e}left(frac{3,n}{pi}right)^{5slash3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4191.png"
 ALT="$\displaystyle B = \frac{5}{3} P = \frac{\pi^{ 3} \hbar^{ 2}}{9 m_e}\left(\frac{3 n}{\pi}\right)^{5/3}.$">|; 

$key = q/displaystyleB_x({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2788.png"
 ALT="$\displaystyle B_x({\bf r},t)$">|; 

$key = q/displaystyleB_y({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2790.png"
 ALT="$\displaystyle B_y({\bf r},t)$">|; 

$key = q/displaystyleB_z({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2792.png"
 ALT="$\displaystyle B_z({\bf r},t)$">|; 

$key = q/displaystyleC(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2341.png"
 ALT="$\displaystyle C(k)$">|; 

$key = q/displaystyleC(k)=frac{1}{(2pi,sigma_k^{,2})^{1slash2}},expleft(-frac{k^{,2}}{2,sigma_k^{,2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2362.png"
 ALT="$\displaystyle C(k) = \frac{1}{(2\pi \sigma_k^{ 2})^{1/2}} \exp\left(-\frac{k^{ 2}}{2 \sigma_k^{ 2}}\right),$">|; 

$key = q/displaystyleC(k)=frac{1}{2pi}int_{-infty}^inftyF(x),cos(k,x),dx=frac{l}{4pi},frac{sin^2(k,lslash4)}{(k,lslash4)^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2442.png"
 ALT="$\displaystyle C(k)=\frac{1}{2\pi}\int_{-\infty}^\infty F(x) \cos(k x) dx = \frac{l}{4\pi} \frac{\sin^2(k l/4)}{(k l/4)^{ 2}}.$">|; 

$key = q/displaystyleC(k)=frac{1}{2pi}int_{-lslash2}^{lslash2},cos(k,x),dx=frac{l}{2pi},frac{sin(k,lslash2)}{k,lslash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2357.png"
 ALT="$\displaystyle C(k) = \frac{1}{2\pi}\int_{-l/2}^{l/2} \cos(k  x) dx = \frac{l}{2\pi} \frac{\sin(k l/2)}{k l/2}.$">|; 

$key = q/displaystyleC(k)=frac{1}{sqrt{2pi,sigma_k^{,2}}},expleft[-frac{(k-k_0)^{,2}}{2,sigma_k^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.31ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img2550.png"
 ALT="$\displaystyle C(k) = \frac{1}{\sqrt{2\pi \sigma_k^{ 2}}} \exp\left[-\frac{(k-k_0)^{ 2}}{2 \sigma_k^{ 2}}\right].$">|; 

$key = q/displaystyleC(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2451.png"
 ALT="$\displaystyle C(\omega)$">|; 

$key = q/displaystyleC(omega>0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2471.png"
 ALT="$\displaystyle C(\omega&gt;0)$">|; 

$key = q/displaystyleC(omega>0)=frac{1}{2,(2pi,sigma_omega^{,2})^{1slash2}},expleft[-frac{(omega-omega_0)^{,2}}{2,sigma_omega^{,2}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2488.png"
 ALT="$\displaystyle C(\omega&gt;0) = \frac{1}{2 (2\pi \sigma_\omega^{ 2})^{1/2}} \exp\left[-\frac{(\omega-\omega_0)^{ 2}}{2 \sigma_\omega^{ 2}}\right],$">|; 

$key = q/displaystyleC(u',0,infty);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3641.png"
 ALT="$\displaystyle C(u',0,\infty)$">|; 

$key = q/displaystyleC(z',z_1,z_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3616.png"
 ALT="$\displaystyle C(z',z_1,z_2)$">|; 

$key = q/displaystyleC(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3620.png"
 ALT="$\displaystyle C(z)$">|; 

$key = q/displaystyleC(z)simeqfrac{1}{2}+frac{1}{pi,z},sinleft(frac{pi,z^{,2}}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3757.png"
 ALT="$\displaystyle C(z) \simeq \frac{1}{2}+\frac{1}{\pi z} \sin\left(\frac{\pi z^{ 2}}{2}\right),$">|; 

$key = q/displaystyleC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3189.png"
 ALT="$\displaystyle C$">|; 

$key = q/displaystyleC=frac{sin(N,alpha,dslash2)}{sin(alpha,dslash2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3726.png"
 ALT="$\displaystyle C = \frac{\sin(N \alpha d/2)}{\sin(\alpha d/2)}.
$">|; 

$key = q/displaystyleC=sum_{n=1,N}cos(alpha,x_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3725.png"
 ALT="$\displaystyle C=\sum_{n=1,N} \cos(\alpha x_n),
$">|; 

$key = q/displaystyleC_+(k)+C_-(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2414.png"
 ALT="$\displaystyle C_+(k) + C_-(k)$">|; 

$key = q/displaystyleC_+(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2423.png"
 ALT="$\displaystyle C_+(k)$">|; 

$key = q/displaystyleC_-(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2425.png"
 ALT="$\displaystyle C_-(k)$">|; 

$key = q/displaystyleC_0=frac{1}{tau}int_0^tauy(t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1288.png"
 ALT="$\displaystyle C_0 = \frac{1}{\tau}\int_0^\tau y(t) dt,$">|; 

$key = q/displaystyleC_0=frac{A}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1293.png"
 ALT="$\displaystyle C_0 = \frac{A}{2},$">|; 

$key = q/displaystyleC_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4123.png"
 ALT="$\displaystyle C_1$">|; 

$key = q/displaystyleC_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4125.png"
 ALT="$\displaystyle C_2$">|; 

$key = q/displaystyleC_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4127.png"
 ALT="$\displaystyle C_3$">|; 

$key = q/displaystyleC_n'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1316.png"
 ALT="$\displaystyle C_n''$">|; 

$key = q/displaystyleC_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1042.png"
 ALT="$\displaystyle C_n$">|; 

$key = q/displaystyleC_n=-A,frac{sin^2(n,pislash2)}{(n,pislash2)^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1294.png"
 ALT="$\displaystyle C_n = - A \frac{\sin^2(n \pi/2)}{(n \pi/2)^{ 2}}$">|; 

$key = q/displaystyleC_n=frac{2}{l}int_0^lpsi(x,0),cosleft[(n-1slash2),pi,frac{x}{l}right]dx=A_n,cosphi_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1197.png"
 ALT="$\displaystyle C_n = \frac{2}{l} \int_0^l\psi(x,0) \cos\left[(n-1/2) \pi \frac{x}{l}\right]dx = A_n \cos\phi_n,$">|; 

$key = q/displaystyleC_n=frac{2}{tau}int_0^tauy(t),cos(n,omega,t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1265.png"
 ALT="$\displaystyle C_n = \frac{2}{\tau}\int_0^\tau y(t) \cos(n \omega t) dt,$">|; 

$key = q/displaystyleD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2821.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystyleD=frac{1}{2},,rho,g,a^{,2},wleft(1-frac{v_g}{v_p}right)=frac{1}{4},rho,g,a^{,2},wleft[1-frac{2,k,d}{sinh(2,k,d)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3082.png"
 ALT="$\displaystyle D = \frac{1}{2}  \rho g a^{ 2} w\left(1-\frac{v_g}{v_p}\right)=\frac{1}{4} \rho g a^{ 2} w\left[1-\frac{2 k d}{\sinh(2 k d)}\right],$">|; 

$key = q/displaystyleD=frac{1}{4},rho,g,a^{,2},w.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3088.png"
 ALT="$\displaystyle D = \frac{1}{4} \rho g a^{ 2} w.$">|; 

$key = q/displaystyleD_x(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1971.png"
 ALT="$\displaystyle D_x(x,z,t)$">|; 

$key = q/displaystyleD_x({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2762.png"
 ALT="$\displaystyle D_x({\bf r},t)$">|; 

$key = q/displaystyleD_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2101.png"
 ALT="$\displaystyle D_x$">|; 

$key = q/displaystyleD_y(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2010.png"
 ALT="$\displaystyle D_y(x,z,t)$">|; 

$key = q/displaystyleD_y({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2764.png"
 ALT="$\displaystyle D_y({\bf r},t)$">|; 

$key = q/displaystyleD_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2103.png"
 ALT="$\displaystyle D_y$">|; 

$key = q/displaystyleD_z(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1974.png"
 ALT="$\displaystyle D_z(x,z,t)$">|; 

$key = q/displaystyleD_z({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2766.png"
 ALT="$\displaystyle D_z({\bf r},t)$">|; 

$key = q/displaystyleD_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2105.png"
 ALT="$\displaystyle D_z$">|; 

$key = q/displaystyleDproptoa^{,2}proptoleft[{rmsinc}left(pi-F^{,-2}right)+{rmsinc}left(pi+F^{,-2}right)right]^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3094.png"
 ALT="$\displaystyle D\propto a^{ 2}\propto \left[{\rm sinc}\left(\pi-F^{ -2}\right)+{\rm sinc}\left(\pi+F^{ -2}\right)\right]^{ 2},$">|; 

$key = q/displaystyleE,psi=(K+U),psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3830.png"
 ALT="$\displaystyle E \psi = (K+U) \psi$">|; 

$key = q/displaystyleE,psi={rmi},hbar,frac{partialpsi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3832.png"
 ALT="$\displaystyle E \psi= {\rm i} \hbar \frac{\partial\psi}{\partial t}.$">|; 

$key = q/displaystyleE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img854.png"
 ALT="$\displaystyle E$">|; 

$key = q/displaystyleE=E_0,y^{,2}-V,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3972.png"
 ALT="$\displaystyle E = E_0 y^{ 2} - V,$">|; 

$key = q/displaystyleE=K+U,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3828.png"
 ALT="$\displaystyle E = K+ U,$">|; 

$key = q/displaystyleE=K+U=frac{1}{2},k,a^{,2}=frac{1}{2},m,omega^{,2},a^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle E = K + U =\frac{1}{2}  k a^{ 2}= \frac{1}{2} m \omega^{ 2} a^{ 2},$">|; 

$key = q/displaystyleE=K+U=frac{1}{2},rho,g,a^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3072.png"
 ALT="$\displaystyle E = K+ U = \frac{1}{2} \rho g a^{ 2}.$">|; 

$key = q/displaystyleE=frac{1}{2},C,V^{,2}+frac{1}{2},L,I^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img292.png"
 ALT="$\displaystyle E = \frac{1}{2} C V^{ 2} + \frac{1}{2} L I^{ 2}.$">|; 

$key = q/displaystyleE=frac{1}{2},L,I^{,2}+frac{1}{2},frac{Q^{,2}}{C}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img506.png"
 ALT="$\displaystyle E = \frac{1}{2} L I^{ 2} + \frac{1}{2} \frac{Q^{ 2}}{C}.$">|; 

$key = q/displaystyleE=frac{1}{2},m,dot{x}^{,2}+frac{1}{2},k,x^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img471.png"
 ALT="$\displaystyle E = \frac{1}{2} m \dot{x}^{ 2}+\frac{1}{2} k x^{ 2}$">|; 

$key = q/displaystyleE=frac{1}{2},m,l^{,2},skew{3}dot{theta}^{,2}+m,g,l,(1-costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img404.png"
 ALT="$\displaystyle E = \frac{1}{2} m l^{ 2} \skew{3}\dot{\theta}^{ 2} + m g l (1-\cos\theta)
$">|; 

$key = q/displaystyleE=frac{1}{2},m,omega_0^{,2},a^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img490.png"
 ALT="$\displaystyle E = \frac{1}{2} m \omega_0^{ 2} a^{ 2}.$">|; 

$key = q/displaystyleE=frac{1}{2}int_0^lleft[rholeft(frac{partialy}{partialt}right)^2+Tleft(frac{partialy}{partialx}right)^2right]dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1111.png"
 ALT="$\displaystyle E = \frac{1}{2}\int_0^l\left[\rho\left(\frac{\partial y}{\partial t}\right)^2
+ T\left(\frac{\partial y}{\partial x}\right)^2\right] dx,
$">|; 

$key = q/displaystyleE=frac{hbar^{,2}}{2,m},(k_x^{,2}+k_y^{,2}+k_z^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4162.png"
 ALT="$\displaystyle E = \frac{\hbar^{ 2}}{2 m} (k_x^{ 2} + k_y^{ 2}+k_z^{ 2}).$">|; 

$key = q/displaystyleE=hbar,omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4137.png"
 ALT="$\displaystyle E = \hbar \omega,$">|; 

$key = q/displaystyleE=hbar,omega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3785.png"
 ALT="$\displaystyle E = \hbar \omega.$">|; 

$key = q/displaystyleE=int_{x_1}^{x_2}frac{1}{2}left[rholeft(frac{partialy}{partialt}right)^2+Tleft(frac{partialy}{partialx}right)^2right]dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1425.png"
 ALT="$\displaystyle E = \int_{x_1}^{x_2}\frac{1}{2}\left[\rho\left(\frac{\partial y}{\partial t}\right)^2
+ T\left(\frac{\partial y}{\partial x}\right)^2\right] dx.$">|; 

$key = q/displaystyleE=mleft[frac{1}{2}left(dot{x}_1^{,2}+dot{x}_2^{,2}right)+omega_0^{,2}left(x_1^{,2}-x_1,x_2+x_2^{,2}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img852.png"
 ALT="$\displaystyle E = m\left[\frac{1}{2}\left(\dot{x}_1^{ 2}+\dot{x}_2^{ 2}\right) + \omega_0^{ 2}\left(x_1^{ 2}-x_1 x_2+x_2^{ 2}\right)\right].
$">|; 

$key = q/displaystyleE=mleft[left(dot{eta}_1^{,2}+dot{eta}_2^{,2}right)+omega_0^{,2}left(eta_1^{,2}+3,eta_2^{,2}right)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img853.png"
 ALT="$\displaystyle E= m\left[\left(\dot{\eta}_1^{ 2}+\dot{\eta}_2^{ 2}\right) + \omega_0^{ 2}\left(\eta_1^{ 2}+3 \eta_2^{ 2}\right)\right]
$">|; 

$key = q/displaystyleE=sum_{n=1,infty}E_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1113.png"
 ALT="$\displaystyle E = \sum_{n=1,\infty} E_n,
$">|; 

$key = q/displaystyleE_0=frac{2,hbar^{,2}}{m,a^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3973.png"
 ALT="$\displaystyle E_0 = \frac{2 \hbar^{ 2}}{m a^{ 2}}.$">|; 

$key = q/displaystyleE_1=frac{hbar^{,2}}{2,m,a^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4166.png"
 ALT="$\displaystyle E_1 = \frac{\hbar^{ 2}}{2 m a^{ 2}}.$">|; 

$key = q/displaystyleE_F=frac{l_F^{,2},pi^{,2},hbar^{,2}}{2,m_e,a^{,2}}=frac{pi^{,2},hbar^{,2}}{2,m_e,a^{,2}}left(frac{3,N}{pi}right)^{2slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4174.png"
 ALT="$\displaystyle E_F = \frac{l_F^{ 2} \pi^{ 2} \hbar^{ 2}}{2 m_e a^{ 2}}=\frac{\pi^{ 2} \hbar^{ 2}}{2 m_e a^{ 2}}\left(\frac{3 N}{\pi}\right)^{2/3},$">|; 

$key = q/displaystyleE_F=frac{pi^{,2},hbar^{,2}}{2,m_e}left(frac{3,n}{pi}right)^{2slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4175.png"
 ALT="$\displaystyle E_F = \frac{\pi^{ 2} \hbar^{ 2}}{2 m_e}\left(\frac{3 n}{\pi}\right)^{2/3},$">|; 

$key = q/displaystyleE_c=frac{Z_1,Z_2,e^{,2}}{4pi,epsilon_0,R}=1.44,Z_1^{,2slash3},,{rmMeV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4105.png"
 ALT="$\displaystyle E_c = \frac{Z_1 Z_2 e^{ 2}}{4\pi \epsilon_0 R} = 1.44 Z_1^{ 2/3}  {\rm MeV}$">|; 

$key = q/displaystyleE_i+E_r=E_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1679.png"
 ALT="$\displaystyle E_i + E_r = E_t,$">|; 

$key = q/displaystyleE_i,cos(omega,t)+E_r,cos(omega,t+phi_r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2627.png"
 ALT="$\displaystyle E_i \cos(\omega t) + E_r \cos(\omega t+\phi_r)$">|; 

$key = q/displaystyleE_i,cos(omega,t)-E_r,cos(omega,t+phi_r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2629.png"
 ALT="$\displaystyle E_i \cos(\omega t) - E_r \cos(\omega t+\phi_r)$">|; 

$key = q/displaystyleE_n=frac{1}{4},m,omega_n^{,2},A_n^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1114.png"
 ALT="$\displaystyle E_n = \frac{1}{4} m \omega_n^{ 2} A_n^{ 2}
$">|; 

$key = q/displaystyleE_n=n^{,2},frac{hbar^{,2},pi^{,2}}{2,m,a^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3932.png"
 ALT="$\displaystyle E_n = n^{ 2} \frac{\hbar^{ 2} \pi^{ 2}}{2 m a^{ 2}}.$">|; 

$key = q/displaystyleE_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1682.png"
 ALT="$\displaystyle E_r$">|; 

$key = q/displaystyleE_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1684.png"
 ALT="$\displaystyle E_t$">|; 

$key = q/displaystyleE_x(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2808.png"
 ALT="$\displaystyle E_x(x,z,t)$">|; 

$key = q/displaystyleE_x(z,r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2685.png"
 ALT="$\displaystyle E_x(z,r)$">|; 

$key = q/displaystyleE_x(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1634.png"
 ALT="$\displaystyle E_x(z,t)$">|; 

$key = q/displaystyleE_x(z,t)=E_0,cos(omega,t-k,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2584.png"
 ALT="$\displaystyle E_x(z,t) = E_0 \cos(\omega t-k z),$">|; 

$key = q/displaystyleE_x(z,t)=E_0,cos(omega,t-k,z-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1623.png"
 ALT="$\displaystyle E_x(z,t)=E_0 \cos(\omega t-k z-\phi).$">|; 

$key = q/displaystyleE_x(z,t)=E_0,{rme}^{-zslashd},cos(omega,t-zslashd),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3198.png"
 ALT="$\displaystyle E_x(z,t) = E_0 {\rm e}^{-z/d} \cos(\omega t-z/d),
$">|; 

$key = q/displaystyleE_x({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2724.png"
 ALT="$\displaystyle E_x({\bf r},t)$">|; 

$key = q/displaystyleE_x,frac{partialD_x}{partialt}+E_y,frac{partialD_y}{partialt}+E_z,frac{partialD_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2133.png"
 ALT="$\displaystyle E_x \frac{\partial D_x}{\partial t} + E_y \frac{\partial D_y}{\partial t}+E_z \frac{\partial D_z}{\partial t}$">|; 

$key = q/displaystyleE_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2896.png"
 ALT="$\displaystyle E_x$">|; 

$key = q/displaystyleE_y(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2810.png"
 ALT="$\displaystyle E_y(x,z,t)$">|; 

$key = q/displaystyleE_y(z,r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2687.png"
 ALT="$\displaystyle E_y(z,r)$">|; 

$key = q/displaystyleE_y(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2645.png"
 ALT="$\displaystyle E_y(z,t)$">|; 

$key = q/displaystyleE_y({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2726.png"
 ALT="$\displaystyle E_y({\bf r},t)$">|; 

$key = q/displaystyleE_z(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2812.png"
 ALT="$\displaystyle E_z(x,z,t)$">|; 

$key = q/displaystyleE_z({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2728.png"
 ALT="$\displaystyle E_z({\bf r},t)$">|; 

$key = q/displaystyleE_{1,1,1}=3,E_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img4165.png"
 ALT="$\displaystyle E_{1,1,1} = 3 E_1.$">|; 

$key = q/displaystyleE_{l_x,l_y,l_z}=frac{hbar^{,2}}{2,m,a^{,2}},(l_x^{,2}+l_y^{,2}+l_z^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4163.png"
 ALT="$\displaystyle E_{l_x,l_y,l_z} = \frac{\hbar^{ 2}}{2 m a^{ 2}} (l_x^{ 2}+l_y^{ 2}+l_z^{ 2}).$">|; 

$key = q/displaystyleE_{rmtotal}=N,overline{E}=frac{3}{5},N,E_F.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4183.png"
 ALT="$\displaystyle E_{\rm total} = N \overline{E} = \frac{3}{5} N E_F.$">|; 

$key = q/displaystyleEsimfrac{p^{,2}}{m}simfrac{hbar^{,2}}{m,a^{,2}}simE_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3945.png"
 ALT="$\displaystyle E \sim \frac{p^{ 2}}{m}\sim \frac{\hbar^{ 2}}{m a^{ 2}}\sim E_1.$">|; 

$key = q/displaystyleF(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2529.png"
 ALT="$\displaystyle F(t)$">|; 

$key = q/displaystyleF(t)=int_{-infty}^inftyC(omega),cos(omega,t),domega+int_{-infty}^inftyS(omega),sin(omega,t),domega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2521.png"
 ALT="$\displaystyle F(t) = \int_{-\infty}^\infty C(\omega) \cos(\omega t) d\omega + \int_{-\infty}^\infty S(\omega) \sin(\omega t) d\omega.
$">|; 

$key = q/displaystyleF(t)=int_{-infty}^inftyC(omega),cos(omega,t),domega+int_{-infty}^{infty}S(omega),sin(omega,t),domega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2448.png"
 ALT="$\displaystyle F(t) = \int_{-\infty}^\infty C(\omega) \cos(\omega t) d\omega + \int_{-\infty}^{\infty}
S(\omega) \sin(\omega t) d\omega,$">|; 

$key = q/displaystyleF(t)=k,hat{X},cos(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img561.png"
 ALT="$\displaystyle F(t) = k \hat{X} \cos(\omega t).$">|; 

$key = q/displaystyleF(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2432.png"
 ALT="$\displaystyle F(x)$">|; 

$key = q/displaystyleF(x)=expleft(-frac{x^{,2}}{2,sigma_x^{,2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2359.png"
 ALT="$\displaystyle F(x) =\exp\left(-\frac{x^{ 2}}{2 \sigma_x^{ 2}}\right).$">|; 

$key = q/displaystyleF(x)=frac{1}{N}sum_{n=1,N}F_2(x-x_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3452.png"
 ALT="$\displaystyle F(x) = \frac{1}{N}\sum_{n=1,N} F_2(x-x_n),$">|; 

$key = q/displaystyleF(x)=frac{1}{N}sum_{n=1,N}delta(x-x_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3421.png"
 ALT="$\displaystyle F(x)=\frac{1}{N}\sum_{n=1,N} \delta(x-x_n),$">|; 

$key = q/displaystyleF(x)=int_{-infty}^inftyC(k),cos(k,x),dk+int_{-infty}^inftyS(k),sin(k,x),dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2337.png"
 ALT="$\displaystyle F(x)=\int_{-\infty}^\infty C(k) \cos(k x) dk + \int_{-\infty}^\infty S(k) \sin(k x) dk,$">|; 

$key = q/displaystyleF(x)=int_{-infty}^inftyC(k),cos(k,x),dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2365.png"
 ALT="$\displaystyle F(x)=\int_{-\infty}^\infty C(k) \cos(k x) dk.$">|; 

$key = q/displaystyleF(x)=sum_{n=1,infty}frac{C_n}{deltak},cos(n,deltak,x),deltak+sum_{n=1,infty}frac{S_n}{deltak},sin(n,deltak,x),deltak.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2336.png"
 ALT="$\displaystyle F(x) = \sum_{n=1,\infty} \frac{C_n}{\delta k} \cos(n \delta k ...
...lta k+ \sum_{n=1,\infty} \frac{S_n}{\delta k}  \sin(n \delta k x) \delta k.$">|; 

$key = q/displaystyleF(x)=sum_{n=1,infty}left[C_n,cos(n,deltak,x)+S_n,sin(n,deltak,x)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2323.png"
 ALT="$\displaystyle F(x)= \sum_{n=1,\infty} \left[C_n \cos(n \delta k x) + S_n \sin(n \delta k x)\right],$">|; 

$key = q/displaystyleF(x)rightarrow1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2375.png"
 ALT="$\displaystyle F(x)\rightarrow 1.$">|; 

$key = q/displaystyleF(x+L)=F(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2322.png"
 ALT="$\displaystyle F(x+L) = F(x)$">|; 

$key = q/displaystyleF=(R,L-P,S)^2,sin^4theta+4,P^{,2},D^{,2},cos^2theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3192.png"
 ALT="$\displaystyle F= (R L-P S)^2 \sin^4\theta + 4 P^{ 2} D^{ 2} \cos^2\theta.
$">|; 

$key = q/displaystyleF=frac{V}{(g,l)^{1slash2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3095.png"
 ALT="$\displaystyle F = \frac{V}{(g l)^{1/2}}$">|; 

$key = q/displaystyleF_1(x)=frac{1}{N}sum_{n=1,N}delta(x-x_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3471.png"
 ALT="$\displaystyle F_1(x) = \frac{1}{N} \sum_{n=1,N} \delta(x-x_n),$">|; 

$key = q/displaystyleF_c(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3745.png"
 ALT="$\displaystyle F_c(u',v')$">|; 

$key = q/displaystyleF_s(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3747.png"
 ALT="$\displaystyle F_s(u',v')$">|; 

$key = q/displaystyleG(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2531.png"
 ALT="$\displaystyle G(t)$">|; 

$key = q/displaystyleG(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2434.png"
 ALT="$\displaystyle G(x)$">|; 

$key = q/displaystyleH(t)=int_{-infty}^inftybar{H}(omega),cos(omega,t),domega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2535.png"
 ALT="$\displaystyle H(t)= \int_{-\infty}^\infty \bar{H}(\omega) \cos(\omega t) d\omega.
$">|; 

$key = q/displaystyleH_x(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2013.png"
 ALT="$\displaystyle H_x(x,z,t)$">|; 

$key = q/displaystyleH_x(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2661.png"
 ALT="$\displaystyle H_x(z,t)$">|; 

$key = q/displaystyleH_x({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2782.png"
 ALT="$\displaystyle H_x({\bf r},t)$">|; 

$key = q/displaystyleH_y(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2045.png"
 ALT="$\displaystyle H_y(x,z,t)$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1968.png"
 ALT="$\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/displaystyleH_y(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1636.png"
 ALT="$\displaystyle H_y(z,t)$">|; 

$key = q/displaystyleH_y(z,t)=Z^{,-1},E_0,cos(omega,t-k,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2598.png"
 ALT="$\displaystyle H_y(z,t) = Z^{ -1} E_0 \cos(\omega t-k z),$">|; 

$key = q/displaystyleH_y(z,t)=Z^{,-1},E_0,cos(omega,t-k,z-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1625.png"
 ALT="$\displaystyle H_y(z,t)=Z^{ -1} E_0 \cos(\omega t-k z-\phi),$">|; 

$key = q/displaystyleH_y({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2784.png"
 ALT="$\displaystyle H_y({\bf r},t)$">|; 

$key = q/displaystyleH_z(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2016.png"
 ALT="$\displaystyle H_z(x,z,t)$">|; 

$key = q/displaystyleH_z({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2786.png"
 ALT="$\displaystyle H_z({\bf r},t)$">|; 

$key = q/displaystyleI(t)=-frac{V_0}{sqrt{LslashC}},sin(omega,t)+I_0,cos(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img301.png"
 ALT="$\displaystyle I(t) = -\frac{V_0}{\sqrt{L/C}} \sin(\omega t) + I_0 \cos(\omega t).$">|; 

$key = q/displaystyleI(t)=-frac{V_0}{sqrt{LslashC}},sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img296.png"
 ALT="$\displaystyle I(t) = -\frac{V_0}{\sqrt{L/C}} \sin(\omega t).$">|; 

$key = q/displaystyleI(t)=I_0,cos(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img300.png"
 ALT="$\displaystyle I(t) = I_0 \cos(\omega t).$">|; 

$key = q/displaystyleI(t)=hat{I},cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle I(t) = \hat{I} \cos(\omega t-\phi),$">|; 

$key = q/displaystyleI(t)=hat{I},cos(omega,t-varphi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img580.png"
 ALT="$\displaystyle I(t) = \hat{I} \cos(\omega t-\varphi),$">|; 

$key = q/displaystyleI(t)=hat{I},{rme}^{-nu,tslash2},cos(omega_1,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img501.png"
 ALT="$\displaystyle I(t) = \hat{I} {\rm e}^{-\nu t/2} \cos(\omega_1 t-\phi),$">|; 

$key = q/displaystyleI(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1492.png"
 ALT="$\displaystyle I(x,t)$">|; 

$key = q/displaystyleI(x,t)=I_0,cos(omega,t-k,x-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1487.png"
 ALT="$\displaystyle I(x,t) = I_0 \cos(\omega t-k x-\phi),$">|; 

$key = q/displaystyleI(x,t)=I_i,cos(omega,t-k,x)+I_r,cos(omega,t+k,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1749.png"
 ALT="$\displaystyle I(x,t) = I_i \cos(\omega t-k x)+ I_r \cos(\omega t+k x)
$">|; 

$key = q/displaystyleI,skew{3}ddot{theta}=-M,g,d,sintheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img352.png"
 ALT="$\displaystyle I \skew{3}\ddot{\theta} = - M g d \sin\theta.$">|; 

$key = q/displaystyleI,skew{3}ddot{theta}=tau,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img323.png"
 ALT="$\displaystyle I \skew{3}\ddot{\theta} = \tau,$">|; 

$key = q/displaystyleI,skew{3}ddot{theta}simeq-M,g,d,theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img353.png"
 ALT="$\displaystyle I \skew{3}\ddot{\theta} \simeq - M g d \theta.$">|; 

$key = q/displaystyleI_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img754.png"
 ALT="$\displaystyle I_1(t)$">|; 

$key = q/displaystyleI_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img756.png"
 ALT="$\displaystyle I_2(t)$">|; 

$key = q/displaystyleI_r=left(frac{Z-R_L}{Z+R_L}right)I_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1602.png"
 ALT="$\displaystyle I_r = \left(\frac{Z-R_L}{Z+R_L}\right) I_i.$">|; 

$key = q/displaystyleI_{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img2303.png"
 ALT="$\displaystyle I_{m,n}$">|; 

$key = q/displaystyleJ_0(z)=frac{1}{pi}int_0^picos(z,sinnu),dnu.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1914.png"
 ALT="$\displaystyle J_0(z)= \frac{1}{\pi}\int_0^\pi\cos(z \sin\nu) d\nu.$">|; 

$key = q/displaystyleJ_1(z)=frac{1}{pi}int_0^picos(z,sinnu-nu),dnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3532.png"
 ALT="$\displaystyle J_1(z) = \frac{1}{\pi}\int_0^\pi \cos(z \sin\nu -\nu) d\nu$">|; 

$key = q/displaystyleJ_n(z)=frac{1}{pi}int_0^picos(z,sintheta-n,theta),dtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3686.png"
 ALT="$\displaystyle J_n(z)=\frac{1}{\pi}\int_0^\pi \cos(z \sin\theta-n \theta) d\theta$">|; 

$key = q/displaystyleJ_{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img2305.png"
 ALT="$\displaystyle J_{m,n}$">|; 

$key = q/displaystyleK(theta)=frac{1}{2}left(1+costhetaright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3549.png"
 ALT="$\displaystyle K(\theta) = \frac{1}{2}\left(1+\cos\theta\right),$">|; 

$key = q/displaystyleK,psi=frac{p^{,2}}{2,m},psi=-frac{hbar^{,2}}{2,m},frac{partial^{,2}psi}{partialx^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3834.png"
 ALT="$\displaystyle K \psi=\frac{p^{ 2}}{2 m} \psi = -\frac{\hbar^{ 2}}{2 m} \frac{\partial^{ 2}\psi}{\partial x^{ 2}}.$">|; 

$key = q/displaystyleK=N,overline{E}=frac{3}{5},N,E_F=frac{3}{5},N,frac{pi^{,2},hbar^{,2}}{2,m_e}left(frac{3,N}{pi,V}right)^{2slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4199.png"
 ALT="$\displaystyle K = N \overline{E} = \frac{3}{5} N E_F = \frac{3}{5} N \frac{\pi^{ 2} \hbar^{ 2}}{2 m_e}\left(\frac{3 N}{\pi V}\right)^{2/3},$">|; 

$key = q/displaystyleK=frac{1}{2},m,dot{x}^{,2}=frac{1}{2},m,a^{,2},omega^{,2},sin^2(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img206.png"
 ALT="$\displaystyle K = \frac{1}{2} m \dot{x}^{ 2} = \frac{1}{2} m a^{ 2} \omega^{ 2} \sin^2(\omega t-\phi).$">|; 

$key = q/displaystyleK=frac{1}{4},rho,g,a^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3068.png"
 ALT="$\displaystyle K = \frac{1}{4} \rho g a^{ 2}.$">|; 

$key = q/displaystyleK=frac{p^{,2}}{2,m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3829.png"
 ALT="$\displaystyle K = \frac{p^{ 2}}{2 m}$">|; 

$key = q/displaystyleK=hbar,omega-W.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3791.png"
 ALT="$\displaystyle K = \hbar \omega - W.$">|; 

$key = q/displaystyleK=int_{x_1}^{x_2}frac{1}{2},rholeft(frac{partialy}{partialt}right)^2dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img1414.png"
 ALT="$\displaystyle K = \int_{x_1}^{x_2}\frac{1}{2} \rho\left(\frac{\partial y}{\partial t}\right)^2 dx,$">|; 

$key = q/displaystyleK=leftlangleint_{-d}^zetafrac{1}{2},rho,v^{,2},dzrightrangle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3063.png"
 ALT="$\displaystyle K = \left\langle\int_{-d}^\zeta \frac{1}{2} \rho v^{ 2} dz\right\rangle,$">|; 

$key = q/displaystyleK=rho,frac{dp}{drho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2231.png"
 ALT="$\displaystyle K = \rho \frac{dp}{d\rho}$">|; 

$key = q/displaystyleL,dot{I}+QslashC=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle L \dot{I}+Q/C = 0.$">|; 

$key = q/displaystyleL,dot{I}+R,I+QslashC=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img494.png"
 ALT="$\displaystyle L \dot{I} + R I + Q/C=0.$">|; 

$key = q/displaystyleL,dot{I}+R,I+QslashC=V,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img573.png"
 ALT="$\displaystyle L \dot{I} + R I+ Q/C = V,$">|; 

$key = q/displaystyleL,dot{I},I+R,I^{,2}+dot{Q},QslashC=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img504.png"
 ALT="$\displaystyle L \dot{I} I + R I^{ 2}+\dot{Q} Q/C = 0,$">|; 

$key = q/displaystyleL=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3196.png"
 ALT="$\displaystyle L=0.
$">|; 

$key = q/displaystyleL=frac{I}{M,d}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img355.png"
 ALT="$\displaystyle L = \frac{I}{M d}.$">|; 

$key = q/displaystyleLggfrac{d,D}{lambda}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3363.png"
 ALT="$\displaystyle L\gg \frac{d D}{\lambda}.$">|; 

$key = q/displaystyleM=2,N,m_p,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4202.png"
 ALT="$\displaystyle M = 2 N m_p,$">|; 

$key = q/displaystyleN(t)=N(0),expleft(-nu,|T|^{,2},tright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4119.png"
 ALT="$\displaystyle N(t) = N(0) \exp\left(-\nu \vert T\vert^{ 2} t\right).$">|; 

$key = q/displaystyleN=2timesfrac{1}{8}timesfrac{4pi}{3},l_F^{,3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4172.png"
 ALT="$\displaystyle N = 2\times\frac{1}{8}\times \frac{4\pi}{3} l_F^{ 3}.$">|; 

$key = q/displaystyleN=frac{a^{,2}}{lambda,R},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3775.png"
 ALT="$\displaystyle N = \frac{a^{ 2}}{\lambda R},
$">|; 

$key = q/displaystyleP(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img562.png"
 ALT="$\displaystyle P(t)$">|; 

$key = q/displaystyleP(t)=I(t),V(t)=I_0,V_0,cos(2,omega,t)+frac{1}{2}left(I_0^{,2},sqrt{frac{L}{C}}-frac{V_0^{,2}}{sqrt{LslashC}}right)sin(2,omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img313.png"
 ALT="$\displaystyle P(t)=I(t) V(t) = I_0 V_0 \cos(2 \omega t) + \frac{1}{2}\left...
...,2} \sqrt{\frac{L}{C}}- \frac{V_0^{ 2}}{\sqrt{L/C}}\right)\sin(2 \omega t),$">|; 

$key = q/displaystyleP(t)=int_{-infty}^infty|psi(x,t)|^{,2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3841.png"
 ALT="$\displaystyle P(t) = \int_{-\infty}^\infty \vert\psi(x,t)\vert^{ 2} dx$">|; 

$key = q/displaystyleP(x,t)=|psi(x,t)|^{,2},dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3840.png"
 ALT="$\displaystyle P(x,t) = \vert\psi(x,t)\vert^{ 2} dx.$">|; 

$key = q/displaystyleP(x,t)=|psi(x,t)|^{,2},dx=|psi(x)|^{,2},dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3919.png"
 ALT="$\displaystyle P(x,t) = \vert\psi(x,t)\vert^{ 2} dx = \vert\psi(x)\vert^{ 2} dx.$">|; 

$key = q/displaystyleP(x,t)propto|psi(x,t)|^{,2},dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3861.png"
 ALT="$\displaystyle P(x,t)\propto \vert\psi(x,t)\vert^{ 2} dx.$">|; 

$key = q/displaystyleP(x,y,z,t)=|psi(x,y,z,t)|^{,2},dx,dy,dz.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4140.png"
 ALT="$\displaystyle P(x,y,z,t) = \vert\psi(x,y,z,t)\vert^{ 2} dx dy dz.$">|; 

$key = q/displaystyleP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2826.png"
 ALT="$\displaystyle P$">|; 

$key = q/displaystyleP=-frac{partialE_{rmtotal}}{partialV}=frac{2}{5},n,E_F,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4184.png"
 ALT="$\displaystyle P = -\frac{\partial E_{\rm total}}{\partial V} = \frac{2}{5} n E_F,$">|; 

$key = q/displaystyleP=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3194.png"
 ALT="$\displaystyle P=0,
$">|; 

$key = q/displaystyleP=1-frac{omega_{p,i}^{,2}}{omega^{,2}}-frac{omega_{p,e}^{,2}}{omega^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2775.png"
 ALT="$\displaystyle P= 1-\frac{\omega_{p i}^{ 2}}{\omega^{ 2}}-\frac{\omega_{p e}^{ 2}}{\omega^{ 2}}.$">|; 

$key = q/displaystyleP=f,dot{x}=-k,dot{x},x-m,nu,dot{x}^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img472.png"
 ALT="$\displaystyle P = f \dot{x} = -k \dot{x} x-m \nu \dot{x}^{ 2}.$">|; 

$key = q/displaystyleP_x(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2654.png"
 ALT="$\displaystyle P_x(z,t)$">|; 

$key = q/displaystyleP_x(z,t)=-frac{n_e,e^{,2},E_0}{m_e,omega^{,2}},cos(omega,t-k,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2597.png"
 ALT="$\displaystyle P_x(z,t)= - \frac{n_e e^{ 2} E_0}{m_e \omega^{ 2}} \cos(\omega t-k z).$">|; 

$key = q/displaystyleP_x(z,t)=-frac{n_e,e^{,2},E_0}{m_e,omega^{,2}},{rme}^{-k,z},cos(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2618.png"
 ALT="$\displaystyle P_x(z,t) = - \frac{n_e e^{ 2} E_0}{m_e \omega^{ 2}} {\rm e}^{-k z} \cos(\omega t).$">|; 

$key = q/displaystyleP_x({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2739.png"
 ALT="$\displaystyle P_x({\bf r},t)$">|; 

$key = q/displaystyleP_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2717.png"
 ALT="$\displaystyle P_x$">|; 

$key = q/displaystyleP_x=n_e,p_x=-n_e,e,x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2594.png"
 ALT="$\displaystyle P_x = n_e p_x = -n_e e x.$">|; 

$key = q/displaystyleP_y(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2656.png"
 ALT="$\displaystyle P_y(z,t)$">|; 

$key = q/displaystyleP_y({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2741.png"
 ALT="$\displaystyle P_y({\bf r},t)$">|; 

$key = q/displaystyleP_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2719.png"
 ALT="$\displaystyle P_y$">|; 

$key = q/displaystyleP_z({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2743.png"
 ALT="$\displaystyle P_z({\bf r},t)$">|; 

$key = q/displaystyleP_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2721.png"
 ALT="$\displaystyle P_z$">|; 

$key = q/displaystyleP_{rmout}simeq1-2,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3997.png"
 ALT="$\displaystyle P_{\rm out}\simeq 1-2 \lambda$">|; 

$key = q/displaystyleP_{rmout}simeqfrac{pi^{,2}}{4},frac{1}{lambda^{,3slash2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3999.png"
 ALT="$\displaystyle P_{\rm out}\simeq \frac{\pi^{ 2}}{4} \frac{1}{\lambda^{ 3/2}}$">|; 

$key = q/displaystylePsimeq1-frac{omega_{p,e}^{,2}}{omega^{,2}}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2845.png"
 ALT="$\displaystyle P \simeq 1 - \frac{\omega_{p e}^{ 2}}{\omega^{ 2}} = 0,$">|; 

$key = q/displaystyleQ_1slashC+L,dot{I}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img746.png"
 ALT="$\displaystyle Q_1/C + L \dot{I}_1$">|; 

$key = q/displaystyleQ_2slashC+L,dot{I}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img748.png"
 ALT="$\displaystyle Q_2/C+L \dot{I}_2$">|; 

$key = q/displaystyleQ_f=2pi,frac{E}{{mitDelta}E}=frac{omega_1}{nu}simeqfrac{omega_0}{nu}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img491.png"
 ALT="$\displaystyle Q_f = 2\pi \frac{E}{{\mit\Delta} E} = \frac{\omega_1}{\nu}\simeq \frac{\omega_0}{\nu}.$">|; 

$key = q/displaystyleQ_f=frac{sqrt{LslashC}}{R}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img508.png"
 ALT="$\displaystyle Q_f = \frac{\sqrt{L/C}}{R}.$">|; 

$key = q/displaystyleR+T=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1547.png"
 ALT="$\displaystyle R+T=1.$">|; 

$key = q/displaystyleR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1753.png"
 ALT="$\displaystyle R$">|; 

$key = q/displaystyleR=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3195.png"
 ALT="$\displaystyle R=0,
$">|; 

$key = q/displaystyleR=1.5times10^{-15},A^{1slash3},{rmm}=2.0times10^{-15},Z_1^{,1slash3},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img4094.png"
 ALT="$\displaystyle R = 1.5\times 10^{-15} A^{1/3} {\rm m}=2.0\times 10^{-15} Z_1^{ 1/3} {\rm m}$">|; 

$key = q/displaystyleR=frac{(n-1)^{,2},cos^2[(pislash2),(lambda_0slashlambda)]}{4,n+(n-1)^{,2},cos^2[(pislash2),(lambda_0slashlambda)]},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1803.png"
 ALT="$\displaystyle R = \frac{(n-1)^{ 2} \cos^2[(\pi/2) (\lambda_0/\lambda)]}{4 n+(n-1)^{ 2}  \cos^2[(\pi/2) (\lambda_0/\lambda)]},
$">|; 

$key = q/displaystyleR=frac{v_0}{v_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img3236.png"
 ALT="$\displaystyle R = \frac{v_0}{v_1},
$">|; 

$key = q/displaystyleR=left(1-frac{Z_2}{Z_1}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1760.png"
 ALT="$\displaystyle R=\left(1-\frac{Z_2}{Z_1}\right)^2,
$">|; 

$key = q/displaystyleR=left(frac{A_r}{A_i}right)^2=left(frac{Z_1,Z_2-Z_3^{,2}}{Z_1,Z_2+Z_3^{,2}}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.36ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img1586.png"
 ALT="$\displaystyle R = \left(\frac{A_r}{A_i}\right)^2 = \left(\frac{Z_1 Z_2-Z_3^{ 2}}{Z_1 Z_2+Z_3^{ 2}}\right)^2,$">|; 

$key = q/displaystyleR=left(frac{A_r}{A_i}right)^2=left(frac{Z_1-Z_2}{Z_1+Z_2}right)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1545.png"
 ALT="$\displaystyle R = \left(\frac{A_r}{A_i}\right)^2 = \left(\frac{Z_1-Z_2}{Z_1+Z_2}\right)^2.$">|; 

$key = q/displaystyleR=left(frac{E_r}{E_i}right)^2=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2635.png"
 ALT="$\displaystyle R = \left(\frac{E_r}{E_i}\right)^2 =1,$">|; 

$key = q/displaystyleR=left(frac{E_r}{E_i}right)^2=left(frac{n_1-n_2}{n_1+n_2}right)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1686.png"
 ALT="$\displaystyle R = \left(\frac{E_r}{E_i}\right)^2 = \left(\frac{n_1-n_2}{n_1+n_2}\right)^2.$">|; 

$key = q/displaystyleR=left(frac{I_r}{I_i}right)^2=left(frac{Z-R_L}{Z+R_L}right)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1603.png"
 ALT="$\displaystyle R = \left(\frac{I_r}{I_i}\right)^2=\left(\frac{Z-R_L}{Z+R_L}\right)^2.$">|; 

$key = q/displaystyleR=left(frac{R_L-Zslash3}{R_L+Z}right)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1777.png"
 ALT="$\displaystyle R =\left(\frac{R_L-Z/3}{R_L+Z}\right)^2
$">|; 

$key = q/displaystyleR=left(frac{Z_2}{Z_2+Z_3}right)^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1774.png"
 ALT="$\displaystyle R=\left(\frac{Z_2}{Z_2+Z_3}\right)^{ 2}.
$">|; 

$key = q/displaystyleR=left(frac{Z_3}{Z_2+Z_3}right)^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1775.png"
 ALT="$\displaystyle R=\left(\frac{Z_3}{Z_2+Z_3}\right)^{ 2}
$">|; 

$key = q/displaystyleR=left(frac{k-q}{k+q}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4252.png"
 ALT="$\displaystyle R = \left(\frac{k-q}{k+q}\right)^2,
$">|; 

$key = q/displaystyleR=left[frac{Z_2,Z_3-Z_1,(Z_2+Z_3)}{Z_2,Z_3+Z_1,(Z_2+Z_3)}right]^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1764.png"
 ALT="$\displaystyle R = \left[\frac{Z_2 Z_3-Z_1 (Z_2+Z_3)}{Z_2 Z_3+Z_1 (Z_2+Z_3)}\right]^{ 2},
$">|; 

$key = q/displaystyleR_L=Z_1-Z_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1757.png"
 ALT="$\displaystyle R_L= Z_1-Z_2
$">|; 

$key = q/displaystyleR_L=frac{Z}{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1779.png"
 ALT="$\displaystyle R_L = \frac{Z}{3}
$">|; 

$key = q/displaystyleR_L=left(1-frac{2}{N}right)Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1781.png"
 ALT="$\displaystyle R_L = \left(1-\frac{2}{N}\right)Z
$">|; 

$key = q/displaystyleR_ast=frac{(9pi)^{2slash3}}{8},frac{hbar^{,2}}{G,m_e,m_p^{,5slash3},M^{,1slash3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.66ex; " SRC="|."$dir".q|img4208.png"
 ALT="$\displaystyle R_\ast = \frac{(9\pi)^{2/3}}{8} \frac{\hbar^{ 2}}{G m_e m_p^{ 5/3} 
M^{ 1/3}}.$">|; 

$key = q/displaystyleR_ast=frac{2,A}{B},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4207.png"
 ALT="$\displaystyle R_\ast = \frac{2 A}{B},$">|; 

$key = q/displaystyleRggd,,frac{d^{,2}}{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3487.png"
 ALT="$\displaystyle R\gg d, \frac{d^{ 2}}{\lambda},$">|; 

$key = q/displaystyleRggd,,lambda,,frac{d^{,2}}{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3279.png"
 ALT="$\displaystyle R\gg d, \lambda, \frac{d^{ 2}}{\lambda},$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2924.png"
 ALT="$\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/displaystyleS(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2343.png"
 ALT="$\displaystyle S(k)$">|; 

$key = q/displaystyleS(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2453.png"
 ALT="$\displaystyle S(\omega)$">|; 

$key = q/displaystyleS(omega>0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2473.png"
 ALT="$\displaystyle S(\omega&gt;0)$">|; 

$key = q/displaystyleS(u',0,infty);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3643.png"
 ALT="$\displaystyle S(u',0,\infty)$">|; 

$key = q/displaystyleS(z',z_1,z_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3618.png"
 ALT="$\displaystyle S(z',z_1,z_2)$">|; 

$key = q/displaystyleS(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3622.png"
 ALT="$\displaystyle S(z)$">|; 

$key = q/displaystyleS(z)simeqfrac{1}{2}-frac{1}{pi,z},cosleft(frac{pi,z^{,2}}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3758.png"
 ALT="$\displaystyle S(z)\simeq \frac{1}{2}-\frac{1}{\pi z} \cos\left(\frac{\pi z^{ 2}}{2}\right)$">|; 

$key = q/displaystyleS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2819.png"
 ALT="$\displaystyle S$">|; 

$key = q/displaystyleS=1-frac{omega_{p,e}^{,2}}{omega^{,2}-{mitOmega}_e^{,2}}-frac{omega_{p,i}^{,2}}{omega^{,2}-{mitOmega}_i^{,2}}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2880.png"
 ALT="$\displaystyle S = 1- \frac{\omega_{p e}^{ 2}}{\omega^{ 2}-{\mit\Omega}_e^{ 2}}
- \frac{\omega_{p i}^{ 2}}{\omega^{ 2}-{\mit\Omega}_i^{ 2}}=0.$">|; 

$key = q/displaystyleS=frac{1-z^{,N}}{1-z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3720.png"
 ALT="$\displaystyle S = \frac{1-z^{ N}}{1-z}.
$">|; 

$key = q/displaystyleS=sum_{n=0,N-1}z^{,n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3719.png"
 ALT="$\displaystyle S= \sum_{n=0,N-1} z^{ n},
$">|; 

$key = q/displaystyleS={rme}^{,{rmi},(N-1),thetaslash2},frac{sin(N,thetaslash2)}{sin(thetaslash2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3723.png"
 ALT="$\displaystyle S = {\rm e}^{ {\rm i} (N-1) \theta/2} \frac{\sin(N \theta/2)}{\sin(\theta/2)}.
$">|; 

$key = q/displaystyleS_+(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2427.png"
 ALT="$\displaystyle S_+(k)$">|; 

$key = q/displaystyleS_-(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2429.png"
 ALT="$\displaystyle S_-(k)$">|; 

$key = q/displaystyleS_n'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1318.png"
 ALT="$\displaystyle S_n''$">|; 

$key = q/displaystyleS_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1044.png"
 ALT="$\displaystyle S_n$">|; 

$key = q/displaystyleS_n=frac{2}{tau}int_0^tauy(t),sin(n,omega,t),dt.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1267.png"
 ALT="$\displaystyle S_n = \frac{2}{\tau}\int_0^\tau y(t) \sin(n \omega t) dt.$">|; 

$key = q/displaystyleS_n=frac{2}{v,(n-1slash2),pi}int_0^ldot{psi}(x,0),cosleft[(n-1slash2),pi,frac{x}{l}right]dx=A_n,sinphi_n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1198.png"
 ALT="$\displaystyle S_n =\frac{2}{v (n-1/2) \pi} \int_0^l\dot{\psi}(x,0) \cos\left[(n-1/2) \pi \frac{x}{l}\right]dx = A_n \sin\phi_n.$">|; 

$key = q/displaystyleT,frac{partial^{,2}zeta}{partialx^{,2}}=rho,g,zeta-left.p_1right|_{z=0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3162.png"
 ALT="$\displaystyle T \frac{\partial^{ 2}\zeta}{\partial x^{ 2}} = \rho g \zeta- \left. p_1\right\vert _{z=0},$">|; 

$key = q/displaystyleT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1755.png"
 ALT="$\displaystyle T$">|; 

$key = q/displaystyleT=1-R=frac{4,Z,R_L}{(Z+R_L)^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1604.png"
 ALT="$\displaystyle T = 1-R = \frac{4 Z R_L}{(Z+R_L)^2}.$">|; 

$key = q/displaystyleT=2pi,sqrt{frac{V}{g,A}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img376.png"
 ALT="$\displaystyle T = 2\pi \sqrt{\frac{V}{g A}}.
$">|; 

$key = q/displaystyleT=2pileft(frac{b^{,2}-a^{,2}}{u^{,2}-v^{,2}}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img382.png"
 ALT="$\displaystyle T = 2\pi\left(\frac{b^{ 2}-a^{ 2}}{u^{ 2}-v^{ 2}}\right)^{1/2}.
$">|; 

$key = q/displaystyleT=4left(frac{Zslash3}{R_L+Z}right)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1778.png"
 ALT="$\displaystyle T = 4\left(\frac{Z/3}{R_L+Z}\right)^2
$">|; 

$key = q/displaystyleT=frac{2pi}{omega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle T = \frac{2\pi}{\omega}.$">|; 

$key = q/displaystyleT=frac{Z_2}{Z_1}left(frac{A_t}{A_i}right)^2=frac{4,Z_1,Z_2,Z_3^{,2}}{(Z_1,Z_2+Z_3^{,2})^2}=1-R.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img1587.png"
 ALT="$\displaystyle T = \frac{Z_2}{Z_1}\left(\frac{A_t}{A_i}\right)^2= \frac{4 Z_1 Z_2 Z_3^{ 2}}{(Z_1 Z_2+Z_3^{ 2})^2}=1-R.$">|; 

$key = q/displaystyleT=frac{Z_2}{Z_1}left(frac{A_t}{A_i}right)^2=frac{4,Z_1,Z_2}{(Z_1+Z_2)^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1546.png"
 ALT="$\displaystyle T = \frac{Z_2}{Z_1}\left(\frac{A_t}{A_i}\right)^2= \frac{4 Z_1 Z_2}{(Z_1+Z_2)^2}.$">|; 

$key = q/displaystyleT_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1765.png"
 ALT="$\displaystyle T_2$">|; 

$key = q/displaystyleT_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1767.png"
 ALT="$\displaystyle T_3$">|; 

$key = q/displaystyleT_i,costheta_i=T_{i+1},costheta_{i+1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img906.png"
 ALT="$\displaystyle T_i \cos\theta_i = T_{i+1} \cos\theta_{i+1}.$">|; 

$key = q/displaystyleT_isimeqT_{i+1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img908.png"
 ALT="$\displaystyle T_i\simeq T_{i+1}.$">|; 

$key = q/displaystyleU(r)=frac{Z_1,Z_2,e^{,2}}{4pi,epsilon_0,r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4096.png"
 ALT="$\displaystyle U(r) = \frac{Z_1 Z_2 e^{ 2}}{4\pi \epsilon_0 r}$">|; 

$key = q/displaystyleU(x)=left{{array}{lll}infty&mbox{hspace{1cm}}&xleq0-V_0&&0<x<L0&&xgeqL{array}right.,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.64ex; vertical-align: -3.36ex; " SRC="|."$dir".q|img4255.png"
 ALT="$\displaystyle U(x) = \left\{\begin{array}{lll}
\infty&amp;\mbox{\hspace{1cm}}&amp;x\leq 0\\\\
-V_0&amp;&amp;0&lt;x&lt;L\\\\
0 &amp;&amp;x\geq L
\end{array}\right.,
$">|; 

$key = q/displaystyleU(x)=left{{array}{rcl}V&mbox{hspace{1cm}}&mbox{for0leqxleqa}[0.5ex]0&&mbox{otherwise}{array}right.,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img4002.png"
 ALT="$\displaystyle U(x) = \left\{\begin{array}{rcl}
V&amp;\mbox{\hspace{1cm}}&amp;\mbox{for $0\leq x\leq a$}\ [0.5ex]
0&amp;&amp;\mbox{otherwise}
\end{array}\right.,$">|; 

$key = q/displaystyleU=-frac{3}{5}frac{G,M^{,2}}{R},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4197.png"
 ALT="$\displaystyle U = -\frac{3}{5}\frac{G M^{ 2}}{R},$">|; 

$key = q/displaystyleU=frac{1}{2},k,x^{,2}=frac{1}{2},k,a^{,2},cos^2(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle U = \frac{1}{2} k x^{ 2}= \frac{1}{2} k a^{ 2} \cos^2(\omega t-\phi).$">|; 

$key = q/displaystyleU=frac{1}{4},rho,g,a^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3071.png"
 ALT="$\displaystyle U = \frac{1}{4} \rho g a^{ 2}.$">|; 

$key = q/displaystyleU=int_{x_1}^{x_2}frac{1}{2},Tleft(frac{partialy}{partialx}right)^2dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img1424.png"
 ALT="$\displaystyle U = \int_{x_1}^{x_2}\frac{1}{2} T\left(\frac{\partial y}{\partial x}\right)^2 dx.$">|; 

$key = q/displaystyleU=leftlanglefrac{1}{2},rho,g,(zeta^{,2}-d^{,2})rightrangle+frac{1}{2},rho,g,d^{,2}=frac{1}{2},rho,g,langlezeta^{,2}rangle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3070.png"
 ALT="$\displaystyle U = \left\langle \frac{1}{2} \rho g (\zeta^{ 2}-d^{ 2})\righ...
...frac{1}{2} \rho g d^{ 2} = \frac{1}{2} \rho g \langle\zeta^{ 2}\rangle,$">|; 

$key = q/displaystyleU=leftlangleint_{-d}^zetarho,g,z,dzrightrangle+frac{1}{2},rho,g,d^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3069.png"
 ALT="$\displaystyle U = \left\langle\int_{-d}^\zeta \rho g z dz\right\rangle + \frac{1}{2} \rho g d^{ 2},$">|; 

$key = q/displaystyleU_n(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3693.png"
 ALT="$\displaystyle U_n(u,v)$">|; 

$key = q/displaystyleU_n(u,v)=sum_{s=0,infty}(-1)^sleft(frac{u}{v}right)^{n+2s}J_{n+2s}(v).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3769.png"
 ALT="$\displaystyle U_n(u,v)=\sum_{s=0,\infty} (-1)^s\left(\frac{u}{v}\right)^{n+2s}J_{n+2s}(v).
$">|; 

$key = q/displaystyleV(0,t)=I(0,t),R_L.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1601.png"
 ALT="$\displaystyle V(0,t) = I(0,t) R_L.$">|; 

$key = q/displaystyleV(t)=-V_0,sin(omega,t-pislash2)+sqrt{frac{L}{C}},I_0,cos(omega,t-pislash2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img302.png"
 ALT="$\displaystyle V(t)= - V_0 \sin(\omega t-\pi/2) + \sqrt{\frac{L}{C}} I_0 \cos(\omega t-\pi/2),$">|; 

$key = q/displaystyleV(t)=V_0,cos(omega,t)+sqrt{frac{L}{C}},I_0,sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img303.png"
 ALT="$\displaystyle V(t) = V_0 \cos(\omega t) + \sqrt{\frac{L}{C}} I_0 \sin(\omega t).$">|; 

$key = q/displaystyleV(t)=skew{3}hat{V},sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img576.png"
 ALT="$\displaystyle V(t) = \skew{3}\hat{V} \sin(\omega t).$">|; 

$key = q/displaystyleV(t)=sqrt{frac{L}{C}},Ileft(t-frac{T}{4}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img286.png"
 ALT="$\displaystyle V(t) = \sqrt{\frac{L}{C}} I\left(t-\frac{T}{4}\right),$">|; 

$key = q/displaystyleV(t)=sqrt{frac{L}{C}},hat{I},sin(omega,t-phi)=sqrt{frac{L}{C}},hat{I},cos(omega,t-phi-pislash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle V(t) = \sqrt{\frac{L}{C}} \hat{I} \sin (\omega t-\phi) = \sqrt{\frac{L}{C}} \hat{I} \cos(\omega t-\phi-\pi/2).$">|; 

$key = q/displaystyleV(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1494.png"
 ALT="$\displaystyle V(x,t)$">|; 

$key = q/displaystyleV(x,t)=V_0,cos(omega,t-k,x-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1488.png"
 ALT="$\displaystyle V(x,t) = V_0 \cos(\omega t-k x-\phi),$">|; 

$key = q/displaystyleV=frac{{calI}_{rmmax}-{calI}_{rmmin}}{{calI}_{rmmax}+{calI}_{rmmin}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3354.png"
 ALT="$\displaystyle V = \frac{{\cal I}_{\rm max} - {\cal I}_{\rm min}}{{\cal I}_{\rm max} + {\cal I}_{\rm min}},$">|; 

$key = q/displaystyleV=left|{rmsinc}left(pi,frac{d}{lambda},theta_0right)right|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.31ex; " SRC="|."$dir".q|img3357.png"
 ALT="$\displaystyle V = \left\vert{\rm sinc}\left(\pi \frac{d}{\lambda} \theta_0\right)\right\vert.$">|; 

$key = q/displaystyleV>(g,d)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3113.png"
 ALT="$\displaystyle V &gt;(g d)^{1/2}.$">|; 

$key = q/displaystyleV_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1088.png"
 ALT="$\displaystyle V_0$">|; 

$key = q/displaystyleV_0=I_0,Z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1489.png"
 ALT="$\displaystyle V_0 = I_0 Z.$">|; 

$key = q/displaystyleV_A=sqrt{frac{B_0^{,2}}{mu_0,rho}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2837.png"
 ALT="$\displaystyle V_A = \sqrt{\frac{B_0^{ 2}}{\mu_0 \rho}}$">|; 

$key = q/displaystyleV_c=0.56,(g,l)^{1slash2}=1.75,[l({rmm})]^{1slash2},{rmmslashs}=3.4,[l({rmm})]^{1slash2},{rmkts}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3100.png"
 ALT="$\displaystyle V_c = 0.56 (g l)^{1/2} = 1.75 [l({\rm m})]^{1/2} {\rm m/s} = 3.4 [l({\rm m})]^{1/2} {\rm kts}.$">|; 

$key = q/displaystyleV_n(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3695.png"
 ALT="$\displaystyle V_n(u,v)$">|; 

$key = q/displaystyleV_n(u,v)=sum_{s=0,infty}(-1)^sleft(frac{v}{u}right)^{n+2s}J_{n+2s}(v).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3772.png"
 ALT="$\displaystyle V_n(u,v)=\sum_{s=0,\infty} (-1)^s\left(\frac{v}{u}\right)^{n+2s}J_{n+2s}(v).
$">|; 

$key = q/displaystyleVll(g,d)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3157.png"
 ALT="$\displaystyle V \ll (g d)^{1/2}.$">|; 

$key = q/displaystyleX(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1889.png"
 ALT="$\displaystyle X(x)$">|; 

$key = q/displaystyleX=X_0,sinbeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3139.png"
 ALT="$\displaystyle X = X_0 \sin\beta,$">|; 

$key = q/displaystyleY(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1891.png"
 ALT="$\displaystyle Y(y)$">|; 

$key = q/displaystyleY_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1086.png"
 ALT="$\displaystyle Y_0$">|; 

$key = q/displaystyleZ=(2pi)^{-1}lnleft(frac{b}{a}right),Z_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1513.png"
 ALT="$\displaystyle Z = (2\pi)^{-1}\ln\left(\frac{b}{a}\right) Z_0.$">|; 

$key = q/displaystyleZ=Z_0,frac{omega}{k,c}=Z_0left(frac{omega_{p,e}^{,2}}{omega^{,2}}-1right)^{-1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2620.png"
 ALT="$\displaystyle Z = Z_0 \frac{\omega}{k c}= Z_0\left(\frac{\omega_{p e}^{ 2}}{\omega^{ 2}}-1\right)^{-1/2}.$">|; 

$key = q/displaystyleZ=Z_0equivsqrt{frac{mu_0}{epsilon_0}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img1626.png"
 ALT="$\displaystyle Z= Z_0 \equiv \sqrt{\frac{\mu_0}{\epsilon_0}},$">|; 

$key = q/displaystyleZ=frac{1}{2pisqrt{epsilon}},lnleft(frac{b}{a}right),Z_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1661.png"
 ALT="$\displaystyle Z = \frac{1}{2\pi\sqrt{\epsilon}} \ln\left(\frac{b}{a}\right) Z_0.$">|; 

$key = q/displaystyleZ=frac{Z_0}{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2602.png"
 ALT="$\displaystyle Z = \frac{Z_0}{n},$">|; 

$key = q/displaystyleZ=frac{Z_0}{{calC}slashepsilon_0}=pi^{-1}cosh^{-1}left(frac{d}{2,a}right),Z_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1511.png"
 ALT="$\displaystyle Z = \frac{Z_0}{{\cal C}/\epsilon_0}= \pi^{-1}\cosh^{-1}\left(\frac{d}{2 a}\right) Z_0.$">|; 

$key = q/displaystyleZ=left(frac{mu_0,omega}{sigma}right)^{1slash2}=left(frac{epsilon_0,omega}{sigma}right)^{1slash2},Z_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2901.png"
 ALT="$\displaystyle Z = \left(\frac{\mu_0 \omega}{\sigma}\right)^{1/2} = \left(\frac{\epsilon_0 \omega}{\sigma}\right)^{1/2} Z_0.$">|; 

$key = q/displaystyleZ=sqrt{frac{mu_0}{epsilon,epsilon_0}}=frac{Z_0}{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img1657.png"
 ALT="$\displaystyle Z = \sqrt{\frac{\mu_0}{\epsilon \epsilon_0}} = \frac{Z_0}{n},$">|; 

$key = q/displaystyleZ=sqrt{frac{{calL}}{{calC}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img1490.png"
 ALT="$\displaystyle Z = \sqrt{\frac{{\cal L}}{{\cal C}}}$">|; 

$key = q/displaystyleZ=sqrt{frac{{calL}}{{calC}}}=frac{Z_0}{{calC}slashepsilon_0}=frac{d}{w},Z_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1505.png"
 ALT="$\displaystyle Z = \sqrt{\frac{{\cal L}}{{\cal C}}} = \frac{Z_0}{{\cal C}/\epsilon_0}=\frac{d}{w} Z_0,$">|; 

$key = q/displaystyleZ=sqrt{rho,T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img1447.png"
 ALT="$\displaystyle Z = \sqrt{\rho T}$">|; 

$key = q/displaystyleZ=sqrt{rho,Y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img1462.png"
 ALT="$\displaystyle Z = \sqrt{\rho Y}$">|; 

$key = q/displaystyleZ=sqrt{rho,gamma,p}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img1463.png"
 ALT="$\displaystyle Z = \sqrt{\rho \gamma p}.$">|; 

$key = q/displaystyleZ_0=sqrt{frac{mu_0}{epsilon_0}}=376.73,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img1506.png"
 ALT="$\displaystyle Z_0 = \sqrt{\frac{\mu_0}{\epsilon_0}} = 376.73 \Omega$">|; 

$key = q/displaystyleZ_1,(A_i+A_r),(A_i-A_r)=Z_2,A_t^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1539.png"
 ALT="$\displaystyle Z_1 (A_i+A_r) (A_i-A_r) = Z_2 A_t^{ 2},$">|; 

$key = q/displaystyleZ_1,(A_i-A_r)=Z_2,A_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1540.png"
 ALT="$\displaystyle Z_1 (A_i-A_r) = Z_2 A_t.$">|; 

$key = q/displaystyleZ_1,(A_i-A_r)=Z_3,(A_+-A_-).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1572.png"
 ALT="$\displaystyle Z_1 (A_i-A_r)= Z_3 (A_+-A_-).$">|; 

$key = q/displaystyleZ_1,(A_i^{,2}-A_r^{,2})=Z_3,(A_+^{,2}-A_-^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1571.png"
 ALT="$\displaystyle Z_1 (A_i^{ 2}-A_r^{ 2}) = Z_3 (A_+^{ 2}-A_-^{ 2}),$">|; 

$key = q/displaystyleZ_3,(A_++A_-)=Z_2,A_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1581.png"
 ALT="$\displaystyle Z_3 (A_+ + A_-)= Z_2 A_t.$">|; 

$key = q/displaystyleZ_3,(A_+^{,2}-A_-^{,2})=Z_2,A_t^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img1580.png"
 ALT="$\displaystyle Z_3 (A_+^{ 2}-A_-^{ 2}) = Z_2 A_t^{ 2}.$">|; 

$key = q/displaystyleZ_L=frac{Z_0}{n_L}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2672.png"
 ALT="$\displaystyle Z_L = \frac{Z_0}{n_L}.$">|; 

$key = q/displaystyleZ_R=frac{Z_0}{n_R}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2667.png"
 ALT="$\displaystyle Z_R = \frac{Z_0}{n_R}.$">|; 

$key = q/displaystyle[D_z]_{z=0_-}^{z=0^+}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.90ex; vertical-align: -0.93ex; " SRC="|."$dir".q|img1981.png"
 ALT="$\displaystyle [D_z]_{z=0_-}^{z=0^+} = 0,$">|; 

$key = q/displaystyle[D_z]_{z=0_-}^{z=0_+};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4466.png"
 ALT="$\displaystyle [D_z]_{z=0_-}^{z=0_+}$">|; 

$key = q/displaystyle[E_x]_{z=0_-}^{z=0_+};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4464.png"
 ALT="$\displaystyle [E_x]_{z=0_-}^{z=0_+}$">|; 

$key = q/displaystyle[E_x]_{z=0_-}^{z=0_+}=left[frac{D_x}{epsilon,epsilon_0}right]_{z=0_-}^{z=0_+}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img1982.png"
 ALT="$\displaystyle [E_x]_{z=0_-}^{z=0_+}=\left[\frac{D_x}{\epsilon \epsilon_0}\right]_{z=0_-}^{z=0_+} = 0.$">|; 

$key = q/displaystyle[E_y]_{z=0_-}^{z=0_+};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4465.png"
 ALT="$\displaystyle [E_y]_{z=0_-}^{z=0_+}$">|; 

$key = q/displaystyle[E_y]_{z=0_-}^{z=0_+}=left[frac{D_y}{epsilon,epsilon_0}right]_{z=0_-}^{z=0_+}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2026.png"
 ALT="$\displaystyle [E_y]_{z=0_-}^{z=0_+} = \left[\frac{D_y}{\epsilon \epsilon_0}\right]_{z=0_-}^{z=0_+}=0,$">|; 

$key = q/displaystyle[H_x]_{z=0_+}^{z=0_-};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.90ex; vertical-align: -1.02ex; " SRC="|."$dir".q|img2023.png"
 ALT="$\displaystyle [H_x]_{z=0_+}^{z=0_-}$">|; 

$key = q/displaystyle[H_x]_{z=0_-}^{z=0_+};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4467.png"
 ALT="$\displaystyle [H_x]_{z=0_-}^{z=0_+}$">|; 

$key = q/displaystyle[H_y]_{z=0_-}^{z=0_+};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4468.png"
 ALT="$\displaystyle [H_y]_{z=0_-}^{z=0_+}$">|; 

$key = q/displaystyle[H_y]_{z=0_-}^{z=0_+}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img1979.png"
 ALT="$\displaystyle [H_y]_{z=0_-}^{z=0_+}=0,$">|; 

$key = q/displaystyle[H_z]_{z=0_+}^{z=0_-};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.90ex; vertical-align: -1.02ex; " SRC="|."$dir".q|img2022.png"
 ALT="$\displaystyle [H_z]_{z=0_+}^{z=0_-}$">|; 

$key = q/displaystyle[H_z]_{z=0_-}^{z=0_+};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4469.png"
 ALT="$\displaystyle [H_z]_{z=0_-}^{z=0_+}$">|; 

$key = q/displaystyle[p]_{z=0_-}^{z=0_+}=T,frac{partial^{,2}zeta}{partialx^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3160.png"
 ALT="$\displaystyle [p]_{z=0_-}^{z=0_+} = T \frac{\partial^{ 2} \zeta}{\partial x^{ 2}}$">|; 

$key = q/displaystyle[tilde{p}]_{z=0_-}^{z=0_+}=-left[rho,frac{partialphi}{partialt}right]_{z=0_-}^{z=0_+}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2267.png"
 ALT="$\displaystyle [\tilde{p}]_{z=0_-}^{z=0_+}=-\left[\rho \frac{\partial\phi}{\partial t}\right]_{z=0_-}^{z=0_+}=0.$">|; 

$key = q/displaystyle[v_z]_{z=0_-}^{z=0_+}=left[frac{partialphi}{partialz}right]_{z=0_-}^{z=0_+}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2274.png"
 ALT="$\displaystyle [v_z]_{z=0_-}^{z=0_+} = \left[\frac{\partial\phi}{\partial z}\right]_{z=0_-}^{z=0_+} = 0.$">|; 

$key = q/displaystylea,cosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img457.png"
 ALT="$\displaystyle a \cos\phi$">|; 

$key = q/displaystylea,sinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img459.png"
 ALT="$\displaystyle a \sin\phi$">|; 

$key = q/displaystylea;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img461.png"
 ALT="$\displaystyle a$">|; 

$key = q/displaystylea=sqrt{x_0^{,2}+left(frac{v_0}{omega}right)^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.75ex; " SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle a = \sqrt{x_0^{ 2} + \left(\frac{v_0}{\omega}\right)^{ 2}},$">|; 

$key = q/displaystylealpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1896.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/displaystylealpha=beta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2033.png"
 ALT="$\displaystyle \alpha=\beta,$">|; 

$key = q/displaystylealpha=frac{Z}{Z_0}=left(frac{epsilon_0,omega}{sigma}right)^{1slash2}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2916.png"
 ALT="$\displaystyle \alpha = \frac{Z}{Z_0}=\left(\frac{\epsilon_0 \omega}{\sigma}\right)^{1/2}\ll 1.$">|; 

$key = q/displaystylealpha=frac{k,c}{omega}=left(frac{omega_{p,e}^{,2}}{omega^{,2}}-1right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2626.png"
 ALT="$\displaystyle \alpha =\frac{k c}{\omega}= \left(\frac{\omega_{p e}^{ 2}}{\omega^{ 2}}-1\right)^{1/2}.$">|; 

$key = q/displaystylealpha^{,2}=2,m,(V-E)slashhbar^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4244.png"
 ALT="$\displaystyle \alpha^{ 2} = 2 m (V-E)/\hbar^{ 2}.
$">|; 

$key = q/displaystylealphaleft[E_i,cos(omega,t)-E_r,cos(omega,t+phi_r)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img2917.png"
 ALT="$\displaystyle \alpha\left[E_i \cos(\omega t) - E_r \cos(\omega t+\phi_r)\right]$">|; 

$key = q/displaystyleaproptofrac{1}{l}int_0^lcosleft(pi,frac{x}{l}right)cos(k,x),dx=frac{1}{2}left[{rmsinc}(pi-k,l)+{rmsinc}(pi+k,l)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3093.png"
 ALT="$\displaystyle a\propto \frac{1}{l}\int_0^l\cos\left(\pi \frac{x}{l}\right)\cos(k x) dx = \frac{1}{2}\left[{\rm sinc}(\pi-k l)+{\rm sinc}(\pi+k l)\right],$">|; 

$key = q/displaystylebar{F}(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3458.png"
 ALT="$\displaystyle \bar{F}(\theta)$">|; 

$key = q/displaystylebar{F}(theta)=bar{F}_1(theta),bar{F}_2(theta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3469.png"
 ALT="$\displaystyle \bar{F}(\theta) = \bar{F}_1(\theta) \bar{F}_2(\theta).$">|; 

$key = q/displaystylebar{F}(theta)=int_{-infty}^inftyF(x),cos[k,(sintheta-sintheta_0),x],dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3426.png"
 ALT="$\displaystyle \bar{F}(\theta) = \int_{-\infty}^\infty F(x) \cos[k (\sin\theta-\sin\theta_0) x] dx.$">|; 

$key = q/displaystylebar{F}(theta)=int_{-infty}^{infty}F(x),cos(k,sintheta,x),dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3457.png"
 ALT="$\displaystyle \bar{F}(\theta) = \int_{-\infty}^{\infty} F(x) \cos(k \sin\theta x) dx.$">|; 

$key = q/displaystylebar{F}_2(theta)=int_{-infty}^inftyF_2(x),cos(k,sintheta,x),dx={rmsinc}left[pi,frac{delta}{lambda},sinthetaright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3472.png"
 ALT="$\displaystyle \bar{F}_2(\theta) = \int_{-\infty}^\infty F_2(x) \cos(k \sin\theta x) dx = {\rm sinc}\left[\pi \frac{\delta}{\lambda} \sin\theta\right],$">|; 

$key = q/displaystylebar{H}(omega)=frac{1}{2}int_{-infty}^inftybar{F}(omega')left[bar{G}(omega'+omega)+bar{G}(omega'-omega)right]domega'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2536.png"
 ALT="$\displaystyle \bar{H}(\omega) = \frac{1}{2}\int_{-\infty}^\infty \bar{F}(\omega')\left[\bar{G}(\omega'+\omega) + \bar{G}(\omega'-\omega)\right] d\omega'.
$">|; 

$key = q/displaystylebar{H}(omega)=frac{1}{2}left[bar{G}(omega-omega_0)+bar{G}(omega+omega_0)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2538.png"
 ALT="$\displaystyle \bar{H}(\omega) = \frac{1}{2}\left[\bar{G}(\omega-\omega_0) + \bar{G}(\omega+\omega_0)\right].
$">|; 

$key = q/displaystylebar{f}(k)=frac{1}{2pi}int_{-infty}^inftyf(x),{rme}^{-{rmi},k,x},dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3870.png"
 ALT="$\displaystyle \bar{f}(k) = \frac{1}{2\pi}\int_{-\infty}^\infty f(x) {\rm e}^{-{\rm i} k x} dx.$">|; 

$key = q/displaystylebar{f}_c(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3602.png"
 ALT="$\displaystyle \bar{f}_c(u',v')$">|; 

$key = q/displaystylebar{f}_s(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3604.png"
 ALT="$\displaystyle \bar{f}_s(u',v')$">|; 

$key = q/displaystylebar{psi}(k)proptoexpleft[-{rmi},k,x_0-frac{(k-k_0)^{,2}}{4,({mitDelta}k)^{,2}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3887.png"
 ALT="$\displaystyle \bar{\psi}(k) \propto \exp\left[-{\rm i} k x_0 - \frac{(k-k_0)^{ 2}}{4 ({\mit\Delta}k)^{ 2}}\right],$">|; 

$key = q/displaystylebar{psi}(k)proptoint_{-infty}^{infty}psi(x,0),{rme}^{-{rmi},k,x},dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3880.png"
 ALT="$\displaystyle \bar{\psi}(k)\propto \int_{-\infty}^{\infty} \psi(x,0) {\rm e}^{-{\rm i} k x} dx.$">|; 

$key = q/displaystylebar{psi}(k)propto{rme}^{-{rmi},k,x_0-beta^{,2}slash4}int_{-infty}^{infty}{rme}^{-(y-y_0)^{,2}},dy,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3883.png"
 ALT="$\displaystyle \bar{\psi}(k) \propto {\rm e}^{-{\rm i} k x_0 - \beta^{ 2}/4}\int_{-\infty}^{\infty} {\rm e}^{-(y-y_0)^{ 2}} dy,$">|; 

$key = q/displaystylebar{psi}(u',v',t)simeq-psi_0,sin(omega,t-k,R-phi),bar{f}_c(u',v')+psi_0,cos(omega,t-k,R-phi),bar{f}_s(u',v').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3610.png"
 ALT="$\displaystyle \bar{\psi}(u',v',t)\simeq -\psi_0 \sin(\omega t-k R-\phi) \bar{f}_c(u',v') + \psi_0 \cos(\omega t-k R-\phi) \bar{f}_s(u',v').$">|; 

$key = q/displaystylebeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1898.png"
 ALT="$\displaystyle \beta$">|; 

$key = q/displaystylebeta=left(frac{Z_1,Z_2,e^{,2},m,R}{4pi,epsilon_0,hbar^{,2}}right)^{1slash2}=0.74,Z_1^{,2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4104.png"
 ALT="$\displaystyle \beta = \left(\frac{Z_1 Z_2 e^{ 2} m R}{4\pi \epsilon_0 \hbar^{ 2}}\right)^{1/2} = 0.74 Z_1^{ 2/3}$">|; 

$key = q/displaystylebeta=sin^{-1}left[frac{(g,d)^{1slash2}}{V}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3112.png"
 ALT="$\displaystyle \beta = \sin^{-1}\left[\frac{(g d)^{1/2}}{V}\right].$">|; 

$key = q/displaystylebm{mathcal{I}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2141.png"
 ALT="$\displaystyle \bm{\mathcal{I} }$">|; 

$key = q/displaystylec=frac{1}{sqrt{epsilon_0,mu_0}}=2.998times10^8,{rmm,s}^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.33ex; " SRC="|."$dir".q|img1622.png"
 ALT="$\displaystyle c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}=2.998\times 10^8 {\rm m s}^{-1}.$">|; 

$key = q/displaystylecos(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4329.png"
 ALT="$\displaystyle \cos(-\alpha)$">|; 

$key = q/displaystylecos(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4367.png"
 ALT="$\displaystyle \cos(2\alpha)$">|; 

$key = q/displaystylecos(3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4371.png"
 ALT="$\displaystyle \cos(3\alpha)$">|; 

$key = q/displaystylecos(4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4375.png"
 ALT="$\displaystyle \cos(4\alpha)$">|; 

$key = q/displaystylecos(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4341.png"
 ALT="$\displaystyle \cos(\alpha\pm \beta)$">|; 

$key = q/displaystylecos(alphapmpislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4335.png"
 ALT="$\displaystyle \cos(\alpha\pm\pi/2)$">|; 

$key = q/displaystylecos(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4361.png"
 ALT="$\displaystyle \cos(\alpha/2)$">|; 

$key = q/displaystylecos(k,l)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1182.png"
 ALT="$\displaystyle \cos(k l) = 0,$">|; 

$key = q/displaystylecos(omega,t-k,R-phi)int_{-infty}^inftyint_{-infty}^inftyF(x,y),cos(k,theta_x,x+k,theta_y,y),dx,dy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3506.png"
 ALT="$\displaystyle \cos(\omega t-k R-\phi)\int_{-\infty}^\infty\int_{-\infty}^\infty F(x,y) \cos(k \theta_x x+k \theta_y y) dx dy.$">|; 

$key = q/displaystylecos(omega,t-k,R-phi)int_{-infty}^inftyint_{-infty}^inftyF(x,y),cos(k,theta_x,x+k,theta_y,y),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3504.png"
 ALT="$\displaystyle \cos(\omega t-k R-\phi)\int_{-\infty}^\infty\int_{-\infty}^\infty F(x,y) \cos(k \theta_x x+k \theta_y y) dx dy$">|; 

$key = q/displaystylecos({rmi},theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4434.png"
 ALT="$\displaystyle \cos({\rm i} \theta)$">|; 

$key = q/displaystylecos[k,(x_{N+1}-aslash2)]=cos[(N+1slash2),k,a]=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1140.png"
 ALT="$\displaystyle \cos[k (x_{N+1}-a/2)] = \cos[(N+1/2) k a] = 0,$">|; 

$key = q/displaystylecos^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4379.png"
 ALT="$\displaystyle \cos^2\alpha$">|; 

$key = q/displaystylecos^3alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4383.png"
 ALT="$\displaystyle \cos^3\alpha$">|; 

$key = q/displaystylecos^4alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4387.png"
 ALT="$\displaystyle \cos^4\alpha$">|; 

$key = q/displaystylecosalpha+cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4349.png"
 ALT="$\displaystyle \cos\alpha+\cos\beta$">|; 

$key = q/displaystylecosalpha,cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4355.png"
 ALT="$\displaystyle \cos\alpha \cos\beta$">|; 

$key = q/displaystylecosalpha-cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4351.png"
 ALT="$\displaystyle \cos\alpha-\cos\beta$">|; 

$key = q/displaystylecosh(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4391.png"
 ALT="$\displaystyle \cosh(-\alpha)$">|; 

$key = q/displaystylecosh(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4424.png"
 ALT="$\displaystyle \cosh(2\alpha)$">|; 

$key = q/displaystylecosh(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4398.png"
 ALT="$\displaystyle \cosh(\alpha\pm \beta)$">|; 

$key = q/displaystylecosh(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4418.png"
 ALT="$\displaystyle \cosh(\alpha/2)$">|; 

$key = q/displaystylecosh({rmi},theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4438.png"
 ALT="$\displaystyle \cosh({\rm i} \theta)$">|; 

$key = q/displaystylecosh^2alpha-sinh^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4395.png"
 ALT="$\displaystyle \cosh^2\alpha-\sinh^2\alpha$">|; 

$key = q/displaystylecoshalpha+coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4406.png"
 ALT="$\displaystyle \cosh\alpha+\cosh\beta$">|; 

$key = q/displaystylecoshalpha,coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4412.png"
 ALT="$\displaystyle \cosh\alpha \cosh\beta$">|; 

$key = q/displaystylecoshalpha-coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4408.png"
 ALT="$\displaystyle \cosh\alpha-\cosh\beta$">|; 

$key = q/displaystylecoshtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4430.png"
 ALT="$\displaystyle \cosh\theta$">|; 

$key = q/displaystylecoshtheta_t=sintheta_t=frac{n_1}{n_2},sintheta_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2053.png"
 ALT="$\displaystyle \cosh\theta_t = \sin\theta_t=\frac{n_1}{n_2} \sin\theta_i.$">|; 

$key = q/displaystylecoshx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4323.png"
 ALT="$\displaystyle \cosh x$">|; 

$key = q/displaystylecostheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4426.png"
 ALT="$\displaystyle \cos\theta$">|; 

$key = q/displaystylecosvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img537.png"
 ALT="$\displaystyle \cos\varphi$">|; 

$key = q/displaystylecosx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4220.png"
 ALT="$\displaystyle \cos x$">|; 

$key = q/displaystyled=left(frac{2}{mu_0,sigma,omega}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2900.png"
 ALT="$\displaystyle d = \left(\frac{2}{\mu_0 \sigma \omega}\right)^{1/2},$">|; 

$key = q/displaystyled=sqrt{frac{2}{mu_0,sigma,omega}}simeqfrac{6}{sqrt{f({rmHz})}},{rmcm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.86ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img2904.png"
 ALT="$\displaystyle d = \sqrt{\frac{2}{\mu_0 \sigma \omega}} \simeq \frac{6}{\sqrt{f({\rm Hz})}} {\rm cm}.$">|; 

$key = q/displaystyledN=-N,nu,|T|^{,2},dt.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4118.png"
 ALT="$\displaystyle dN = - N \nu \vert T\vert^{ 2} dt.$">|; 

$key = q/displaystyleddot{I}+nu,dot{I}+omega_0^{,2},I=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img495.png"
 ALT="$\displaystyle \ddot{I} + \nu \dot{I} + \omega_0^{ 2} I=0,$">|; 

$key = q/displaystyleddot{I}+nu,dot{I}+omega_0^{,2},I=frac{omega,skew{3}hat{V}}{L},cos(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img577.png"
 ALT="$\displaystyle \ddot{I} + \nu \dot{I} + \omega_0^{ 2} I = \frac{\omega \skew{3}\hat{V}}{L} \cos(\omega t),$">|; 

$key = q/displaystyleddot{I}+omega^{,2},I=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img277.png"
 ALT="$\displaystyle \ddot{I} + \omega^{ 2} I = 0,$">|; 

$key = q/displaystyleddot{I}_1+omega_0^{,2},(1+alpha),I_1+omega_0^{,2},alpha,I_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img750.png"
 ALT="$\displaystyle \ddot{I}_1 + \omega_0^{ 2} (1+\alpha) I_1+\omega_0^{ 2}  \alpha I_2$">|; 

$key = q/displaystyleddot{I}_2+omega_0^{,2},(1+alpha),I_2+omega_0^{,2},alpha,I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img751.png"
 ALT="$\displaystyle \ddot{I}_2 + \omega_0^{ 2} (1+\alpha) I_2+ \omega_0^{ 2} \alpha I_1$">|; 

$key = q/displaystyleddot{I}_i=omega_0^{,2},(I_{i-1}-2,I_i+I_{i+1}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1077.png"
 ALT="$\displaystyle \ddot{I}_i = \omega_0^{ 2} (I_{i-1}-2 I_i+I_{i+1}),
$">|; 

$key = q/displaystyleddot{eta}_1+(1+2,alpha),omega_0^{,2},eta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img776.png"
 ALT="$\displaystyle \ddot{\eta}_1+(1+2 \alpha) \omega_0^{ 2} \eta_1$">|; 

$key = q/displaystyleddot{eta}_1=-omega_0^{,2},eta_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img732.png"
 ALT="$\displaystyle \ddot{\eta}_1 = -\omega_0^{ 2} \eta_1,$">|; 

$key = q/displaystyleddot{eta}_2+omega_0^{,2},eta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img777.png"
 ALT="$\displaystyle \ddot{\eta}_2+\omega_0^{ 2} \eta_2$">|; 

$key = q/displaystyleddot{eta}_2=-3,omega_0^{,2},eta_2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img733.png"
 ALT="$\displaystyle \ddot{\eta}_2 = -3 \omega_0^{ 2} \eta_2.$">|; 

$key = q/displaystyleddot{psi}_i=-frac{g}{l},psi_i+frac{K}{m},(psi_{i-1}-2,psi_i+psi_{i+1}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1307.png"
 ALT="$\displaystyle \ddot{\psi}_i = - \frac{g}{l} \psi_i + \frac{K}{m} (\psi_{i-1}-2 \psi_i+\psi_{i+1}).
$">|; 

$key = q/displaystyleddot{psi}_i=omega_0^{,2},(psi_{i-1}-2,psi_i+psi_{i+1}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1126.png"
 ALT="$\displaystyle \ddot{\psi}_i = \omega_0^{ 2} (\psi_{i-1} -2 \psi_i+ \psi_{i+1}),$">|; 

$key = q/displaystyleddot{s}+omega^{,2},s=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle \ddot{s}+ \omega^{ 2} s=0,$">|; 

$key = q/displaystyleddot{s}_1=-omega^{,2},s_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle \ddot{s}_1=-\omega^{ 2} s_1,$">|; 

$key = q/displaystyleddot{s}_2=-omega^{,2},s_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img253.png"
 ALT="$\displaystyle \ddot{s}_2=-\omega^{ 2} s_2,$">|; 

$key = q/displaystyleddot{x}+nu,dot{x}+omega_0^{,2},x=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img414.png"
 ALT="$\displaystyle \ddot{x} + \nu \dot{x} + \omega_0^{ 2} x = 0,$">|; 

$key = q/displaystyleddot{x}+nu,dot{x}+omega_0^{,2},x=omega_0^{,2},X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img513.png"
 ALT="$\displaystyle \ddot{x} + \nu \dot{x} + \omega_0^{ 2} x = \omega_0^{ 2} X,$">|; 

$key = q/displaystyleddot{x}+nu,dot{x}+omega_0^{,2},x=omega_0^{,2},hat{X},cos(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img516.png"
 ALT="$\displaystyle \ddot{x} + \nu \dot{x} + \omega_0^{ 2} x = \omega_0^{ 2} \hat{X} \cos(\omega t).$">|; 

$key = q/displaystyleddot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img430.png"
 ALT="$\displaystyle \ddot{x}$">|; 

$key = q/displaystyleddot{x}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img665.png"
 ALT="$\displaystyle \ddot{x}_1$">|; 

$key = q/displaystyleddot{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img667.png"
 ALT="$\displaystyle \ddot{x}_2$">|; 

$key = q/displaystyleddot{x}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img790.png"
 ALT="$\displaystyle \ddot{x}_3$">|; 

$key = q/displaystyleddot{y}_i=omega_0^{,2}left(y_{i-1}-2,y_i+y_{i+1}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img895.png"
 ALT="$\displaystyle \ddot{y}_i = \omega_0^{ 2}\left(y_{i-1}-2 y_i+y_{i+1}\right),$">|; 

$key = q/displaystyleddot{y}_isimeqfrac{T}{m}left(theta_{i+1}-theta_iright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img894.png"
 ALT="$\displaystyle \ddot{y}_i\simeq \frac{T}{m}\left(\theta_{i+1}-\theta_i\right).$">|; 

$key = q/displaystyledelta(k)=frac{1}{2pi}int_{-infty}^infty{rme}^{,{rmi},k,x},dx,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4223.png"
 ALT="$\displaystyle \delta(k) = \frac{1}{2\pi}\int_{-\infty}^\infty {\rm e}^{ {\rm i} k x} dx,
$">|; 

$key = q/displaystyledelta(k)=frac{1}{2pi}int_{-infty}^{infty}cos(k,x),dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2391.png"
 ALT="$\displaystyle \delta (k) = \frac{1}{2\pi}\int_{-\infty}^{\infty} \cos(k x) dx.$">|; 

$key = q/displaystyledelta(k)=lim_{sigma_krightarrow0}frac{1}{(2pi,sigma_k^{,2})^{1slash2}},expleft(-frac{k^{,2}}{2,sigma_k^{,2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2380.png"
 ALT="$\displaystyle \delta (k)= \lim_{\sigma_k\rightarrow 0}\frac{1}{(2\pi \sigma_k^{ 2})^{1/2}} \exp\left(-\frac{k^{ 2}}{2 \sigma_k^{ 2}}\right).$">|; 

$key = q/displaystyledeltak=frac{2pi}{L}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2324.png"
 ALT="$\displaystyle \delta k = \frac{2\pi}{L}.$">|; 

$key = q/displaystyledeltap(t)=sum_{n=1,infty}A_{n},cos(n,omega,t-phi_{n}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1244.png"
 ALT="$\displaystyle \delta p(t) = \sum_{n=1,\infty} A_{n} \cos(n \omega t-\phi_{n}),$">|; 

$key = q/displaystyledeltap(t)=sum_{n=1,infty}left[C_{n},cos(n,omega,t)+S_{n},sin(n,omega,t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1245.png"
 ALT="$\displaystyle \delta p(t) = \sum_{n=1,\infty} \left[C_{n} \cos(n \omega t)+ S_{n} \sin(n \omega t)\right],$">|; 

$key = q/displaystyledeltap=-gamma,p,frac{deltaV}{V}=-gamma,p,frac{partialpsi}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1227.png"
 ALT="$\displaystyle \delta p = - \gamma p \frac{\delta V}{V}= -\gamma p \frac{\partial\psi}{\partial x},$">|; 

$key = q/displaystyledeltatheta=1.22,frac{lambda}{D},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3540.png"
 ALT="$\displaystyle \delta\theta = 1.22 \frac{\lambda}{D},$">|; 

$key = q/displaystyledeltatheta=frac{3.83171}{pi},frac{lambda}{D}=1.22,frac{lambda}{D},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3536.png"
 ALT="$\displaystyle \delta\theta= \frac{3.83171}{\pi} \frac{\lambda}{D} = 1.22 \frac{\lambda}{D},$">|; 

$key = q/displaystyledeltatheta=frac{lambda}{delta};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3440.png"
 ALT="$\displaystyle \delta\theta = \frac{\lambda}{\delta};$">|; 

$key = q/displaystyledeltatheta_j=frac{tantheta_j}{N,j}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3398.png"
 ALT="$\displaystyle \delta\theta_j = \frac{\tan\theta_j}{N j}.$">|; 

$key = q/displaystyledeltathetasimeqfrac{lambda}{D}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3449.png"
 ALT="$\displaystyle \delta\theta \simeq \frac{\lambda}{D}.$">|; 

$key = q/displaystyledeltau=frac{2}{{mitDelta}u}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3668.png"
 ALT="$\displaystyle \delta u = \frac{2}{{\mit\Delta} u}.$">|; 

$key = q/displaystyledot{psi}(x,0)=frac{pi,v}{l}sum_{n'=1,infty}(n'-1slash2),A_{n'},sinphi_{n'},cosleft[(n'-1slash2),pi,frac{x}{l}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1194.png"
 ALT="$\displaystyle \dot{\psi}(x,0) = \frac{\pi v}{l}\sum_{n'=1,\infty} (n'-1/2) A_{n'} \sin \phi_{n'} \cos\left[(n'-1/2) \pi \frac{x}{l}\right].$">|; 

$key = q/displaystyledot{psi}(x,y,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2297.png"
 ALT="$\displaystyle \dot{\psi}(x,y,0)$">|; 

$key = q/displaystyledot{s},ddot{s}+omega^{,2},dot{s},s=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle \dot{s} \ddot{s} + \omega^{ 2} \dot{s} s=0.$">|; 

$key = q/displaystyledot{s}_{rmmax}=sqrt{2,{calE}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img235.png"
 ALT="$\displaystyle \dot{s}_{\rm max} = \sqrt{2 {\cal E}},$">|; 

$key = q/displaystyledot{x}(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img600.png"
 ALT="$\displaystyle \dot{x}(0)$">|; 

$key = q/displaystyledot{x},ddot{x}+nu,dot{x}^{,2}+omega_0^{,2},dot{x},x=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img469.png"
 ALT="$\displaystyle \dot{x} \ddot{x} + \nu \dot{x}^{ 2}+ \omega_0^{ 2} \dot{x} x=0,$">|; 

$key = q/displaystyledot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img428.png"
 ALT="$\displaystyle \dot{x}$">|; 

$key = q/displaystyledot{x}=-frac{a,nu}{2},{rme}^{-nu,tslash2},cos(omega_1,t-phi)-a,omega_1,{rme}^{-nu,tslash2},sin(omega_1,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img478.png"
 ALT="$\displaystyle \dot{x} =- \frac{a \nu}{2} {\rm e}^{-\nu t/2} \cos(\omega_1 t-\phi)-
a \omega_1 {\rm e}^{-\nu t/2} \sin(\omega_1 t-\phi).$">|; 

$key = q/displaystyledot{y}(x,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1742.png"
 ALT="$\displaystyle \dot{y}(x,0)$">|; 

$key = q/displaystyleds=(dx^{,2}+dy^{,2})^{1slash2}=left[1+left(frac{partialy}{partialx}right)^2right]^{1slash2}dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.30ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1418.png"
 ALT="$\displaystyle ds = (dx^{ 2}+dy^{ 2})^{1/2} = \left[1+ \left(\frac{\partial y}{\partial x}\right)^2\right]^{1/2} dx.$">|; 

$key = q/displaystyledsimn^{-1slash3}simfrac{h}{sqrt{m_e,E}}simfrac{h}{p}simlambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4187.png"
 ALT="$\displaystyle d\sim n^{-1/3}\sim \frac{h}{\sqrt{m_e E}}\sim \frac{h}{p}\sim \lambda,$">|; 

$key = q/displaystyleepsilon(x,t)=frac{partialpsi(x,t)}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1162.png"
 ALT="$\displaystyle \epsilon(x,t) = \frac{\partial \psi(x,t)}{\partial x}.$">|; 

$key = q/displaystyleepsilon(x,t)=frac{psi(x+deltaxslash2,t)-psi(x-deltaxslash2,t)}{deltax}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1161.png"
 ALT="$\displaystyle \epsilon(x,t) = \frac{ \psi(x+\delta x/2,t)-\psi(x-\delta x/2,t)}{\delta x}.$">|; 

$key = q/displaystyleepsilon_0,omega,(R,E_R+L,E_L);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2795.png"
 ALT="$\displaystyle \epsilon_0 \omega (R E_R+L E_L)$">|; 

$key = q/displaystyleepsilon_0,omega,(R,E_R-L,E_L);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2797.png"
 ALT="$\displaystyle \epsilon_0 \omega (R E_R-L E_L)$">|; 

$key = q/displaystyleepsilon_0,omega,P,E_P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2799.png"
 ALT="$\displaystyle \epsilon_0 \omega P E_P$">|; 

$key = q/displaystyleeta_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img726.png"
 ALT="$\displaystyle \eta_1(t)$">|; 

$key = q/displaystyleeta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img772.png"
 ALT="$\displaystyle \eta_1$">|; 

$key = q/displaystyleeta_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img728.png"
 ALT="$\displaystyle \eta_2(t)$">|; 

$key = q/displaystyleeta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img774.png"
 ALT="$\displaystyle \eta_2$">|; 

$key = q/displaystyleeta_3(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img822.png"
 ALT="$\displaystyle \eta_3(t)$">|; 

$key = q/displaystylef'=frac{f}{1-u_sslashv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1713.png"
 ALT="$\displaystyle f' = \frac{f}{1-u_s/v},$">|; 

$key = q/displaystylef'=left(1-frac{u_o}{v}right),f,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1701.png"
 ALT="$\displaystyle f' = \left(1 - \frac{u_o}{v}\right) f,$">|; 

$key = q/displaystylef'=left(1mpfrac{u_o}{v}right),f,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1703.png"
 ALT="$\displaystyle f' = \left(1 \mp \frac{u_o}{v}\right) f,$">|; 

$key = q/displaystylef'=left(frac{1mpu_oslashv}{1pmu_sslashv}right)f,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1714.png"
 ALT="$\displaystyle f' = \left(\frac{1\mp u_o/v}{1\pm u_s/v}\right) f,$">|; 

$key = q/displaystylef'=left[1-frac{u}{c}+{calO}left(frac{u^{,2}}{c^{,2}}right)right]f,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1718.png"
 ALT="$\displaystyle f'=\left[1-\frac{u}{c}+{\cal O}\left(\frac{u^{ 2}}{c^{ 2}}\right)\right]f,$">|; 

$key = q/displaystylef(u,v)+bar{f}(u,v)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3601.png"
 ALT="$\displaystyle f(u,v)+\bar{f}(u,v) = 1$">|; 

$key = q/displaystylef(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4310.png"
 ALT="$\displaystyle f(x)$">|; 

$key = q/displaystylef(x)=-k,x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle f (x)= -k x.$">|; 

$key = q/displaystylef(x)=int_{-infty}^{infty}bar{f}(k),{rme}^{,{rmi},k,x},dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3869.png"
 ALT="$\displaystyle f(x) = \int_{-\infty}^{\infty} \bar{f}(k) {\rm e}^{ {\rm i} k x} dk,$">|; 

$key = q/displaystylef(x)simeq-k,x+alpha,x^{,2}+{calO}left(x^{,3}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img418.png"
 ALT="$\displaystyle f(x) \simeq -k x+\alpha x^{ 2} + {\cal O}\left(x^{ 3}\right),$">|; 

$key = q/displaystylef(x,dot{x})=-k,x-m,nu,dot{x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img411.png"
 ALT="$\displaystyle f (x,\dot{x})= - k x -m \nu \dot{x},$">|; 

$key = q/displaystylef=-k,(x-X)-m,nu,dot{x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img512.png"
 ALT="$\displaystyle f = - k (x-X)-m \nu \dot{x}.$">|; 

$key = q/displaystylef=frac{1}{T}=frac{omega}{2pi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle f = \frac{1}{T} = \frac{\omega}{2\pi}.$">|; 

$key = q/displaystylef=left(frac{V-v+w}{V-u+w}right)f_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1824.png"
 ALT="$\displaystyle f =\left(\frac{V-v+w}{V-u+w}\right)f_0,
$">|; 

$key = q/displaystylef_c(u');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3633.png"
 ALT="$\displaystyle f_c(u')$">|; 

$key = q/displaystylef_c(u',v')+bar{f}_c(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3606.png"
 ALT="$\displaystyle f_c(u',v')+\bar{f}_c(u',v')$">|; 

$key = q/displaystylef_c(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3582.png"
 ALT="$\displaystyle f_c(u',v')$">|; 

$key = q/displaystylef_c(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3678.png"
 ALT="$\displaystyle f_c(u,v)$">|; 

$key = q/displaystylef_n=(2,n-1),f_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1238.png"
 ALT="$\displaystyle f_n = (2 n-1) f_1,$">|; 

$key = q/displaystylef_s(u');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3635.png"
 ALT="$\displaystyle f_s(u')$">|; 

$key = q/displaystylef_s(u',v')+bar{f}_s(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3607.png"
 ALT="$\displaystyle f_s(u',v')+\bar{f}_s(u',v')$">|; 

$key = q/displaystylef_s(u',v');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3584.png"
 ALT="$\displaystyle f_s(u',v')$">|; 

$key = q/displaystylef_s(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3680.png"
 ALT="$\displaystyle f_s(u,v)$">|; 

$key = q/displaystylefrac{1}{2pi}int_0^{2pi}cos(z,cosnu),dnu=frac{1}{pi}int_0^picos(z,sinnu),dnu=J_0(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3529.png"
 ALT="$\displaystyle \frac{1}{2\pi}\int_0^{2\pi}\cos(z \cos\nu) d\nu=\frac{1}{\pi}\int_0^\pi\cos(z \sin\nu) d\nu=J_0(z),$">|; 

$key = q/displaystylefrac{1}{2pi}int_{-infty}^inftycos(k,x),cos(k',x),dx=frac{1}{2}left[delta(k-k')+delta(k+k')right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2394.png"
 ALT="$\displaystyle \frac{1}{2\pi}\int_{-\infty}^\infty \cos(k x) \cos(k' x) dx= \frac{1}{2}\left[\delta(k-k') + \delta(k+k')\right],$">|; 

$key = q/displaystylefrac{1}{2pi}int_{-infty}^inftycos(k,x),sin(k',x),dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2397.png"
 ALT="$\displaystyle \frac{1}{2\pi}\int_{-\infty}^\infty \cos(k x) \sin(k' x) dx$">|; 

$key = q/displaystylefrac{1}{2pi}int_{-infty}^inftysin(k,x),sin(k',x),dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2395.png"
 ALT="$\displaystyle \frac{1}{2\pi}\int_{-\infty}^\infty \sin(k x) \sin(k' x) dx$">|; 

$key = q/displaystylefrac{1}{2},omega^{,2},Z_1,(A_i^{,2}-A_r^{,2})=frac{1}{2},omega^{,2},Z_2,A_t^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1536.png"
 ALT="$\displaystyle \frac{1}{2} \omega^{ 2} Z_1 (A_i^{ 2}-A_r^{ 2}) = \frac{1}{2} \omega^{ 2} Z_2 A_t^{ 2},$">|; 

$key = q/displaystylefrac{1}{2},rho,g,a^{,2},w,V=frac{1}{2},rho,g,a^{,2},w,v_g+D,V.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3080.png"
 ALT="$\displaystyle \frac{1}{2} \rho g a^{ 2} w V= \frac{1}{2} \rho g a^{ 2} w v_g + D V.$">|; 

$key = q/displaystylefrac{1}{2}left(frac{m}{l},dyright)left(frac{y}{l},vright)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle \frac{1}{2}\left(\frac{m}{l} dy\right)\left(\frac{y}{l} v\right)^2,
$">|; 

$key = q/displaystylefrac{1}{X},frac{d^{,2}X}{dx^{,2}}+frac{1}{Y},frac{d^{,2}Y}{dy^{,2}}+frac{omega^{,2}}{v^{,2}}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1880.png"
 ALT="$\displaystyle \frac{1}{X} \frac{d^{ 2}X}{dx^{ 2}} + \frac{1}{Y} \frac{d^{ 2}Y}{dy^{ 2}}+\frac{\omega^{ 2}}{v^{ 2}} = 0.$">|; 

$key = q/displaystylefrac{1}{X},frac{d^{,2}X}{dx^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1881.png"
 ALT="$\displaystyle \frac{1}{X} \frac{d^{ 2}X}{dx^{ 2}}$">|; 

$key = q/displaystylefrac{1}{Y},frac{d^{,2}Y}{dy^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1883.png"
 ALT="$\displaystyle \frac{1}{Y} \frac{d^{ 2}Y}{dy^{ 2}}$">|; 

$key = q/displaystylefrac{1}{Z_1}=frac{1}{Z_2}+frac{1}{Z_3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1773.png"
 ALT="$\displaystyle \frac{1}{Z_1}=\frac{1}{Z_2}+\frac{1}{Z_3},
$">|; 

$key = q/displaystylefrac{1}{Z_1}=frac{1}{Z_2}+frac{1}{Z_3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1771.png"
 ALT="$\displaystyle \frac{1}{Z_1}=\frac{1}{Z_2}+\frac{1}{Z_3}
$">|; 

$key = q/displaystylefrac{1}{epsilon^{,2}}=frac{cos^2theta}{epsilon_perp^{,2}}+frac{sin^2theta}{epsilon_parallel^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img2213.png"
 ALT="$\displaystyle \frac{1}{\epsilon^{ 2}} = \frac{\cos^2\theta}{\epsilon_\perp^{ 2}}+ \frac{\sin^2\theta}{\epsilon_\parallel^{ 2}}.$">|; 

$key = q/displaystylefrac{1}{pi}int_0^picosleft[(n-n'),thetaright]dtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1024.png"
 ALT="$\displaystyle \frac{1}{\pi}\int_0^\pi \cos\left[(n-n') \theta\right]d\theta$">|; 

$key = q/displaystylefrac{1}{pi}left[frac{sinleft[(n-n'),thetaright]}{n-n'}-frac{sinleft[(n+n'),thetaright]}{n+n'}right]_0^{pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1026.png"
 ALT="$\displaystyle \frac{1}{\pi}\left[\frac{\sin\left[(n-n') \theta\right]}{n-n'}-
\frac{\sin\left[(n+n') \theta\right]}{n+n'}\right]_0^{\pi}$">|; 

$key = q/displaystylefrac{2}{L}int_{-Lslash2}^{Lslash2}cos(n,deltak,x),cos(n',deltak,x),dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2327.png"
 ALT="$\displaystyle \frac{2}{L}\int_{-L/2}^{L/2}\cos(n \delta k x) \cos(n' \delta k  x) dx$">|; 

$key = q/displaystylefrac{2}{L}int_{-Lslash2}^{Lslash2}cos(n,deltak,x),sin(n',deltak,x),dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2329.png"
 ALT="$\displaystyle \frac{2}{L}\int_{-L/2}^{L/2}\cos(n \delta k x) \sin(n' \delta k  x) dx$">|; 

$key = q/displaystylefrac{2}{L}int_{-Lslash2}^{Lslash2}sin(n,deltak,x),sin(n',deltak,x),dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2328.png"
 ALT="$\displaystyle \frac{2}{L}\int_{-L/2}^{L/2}\sin(n \delta k x) \sin(n' \delta k  x) dx$">|; 

$key = q/displaystylefrac{2}{l}int_0^lcosleft(n,pi,frac{x}{l}right)cosleft(n',pifrac{x}{l}right)dx=delta_{n,n'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1085.png"
 ALT="$\displaystyle \frac{2}{l}\int_0^l\cos\left(n \pi \frac{x}{l}\right)\cos\left(n' \pi\frac{x}{l}\right)dx=\delta_{n,n'},
$">|; 

$key = q/displaystylefrac{2}{l}int_0^lcosleft[(n-1slash2),pi,frac{x}{l}right],cosleft[(n'-1slash2),pi,frac{x}{l}right]dx=delta_{n,n'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1195.png"
 ALT="$\displaystyle \frac{2}{l}\int_0^l \cos\left[(n-1/2) \pi \frac{x}{l}\right] \cos\left[(n'-1/2) \pi \frac{x}{l}\right]dx = \delta_{n,n'}.$">|; 

$key = q/displaystylefrac{2}{l}int_0^lsinleft(n,pi,frac{x}{l}right),sinleft(n',pi,frac{x}{l}right)dx=delta_{n,n'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1035.png"
 ALT="$\displaystyle \frac{2}{l}\int_0^l\sin\left(n \pi \frac{x}{l}\right) \sin\left(n' \pi \frac{x}{l}\right)dx
= \delta_{n,n'}.$">|; 

$key = q/displaystylefrac{2}{l}int_0^lsinleft(n,pi,frac{x}{l}right),sinleft(n',pi,frac{x}{l}right)dx={};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1021.png"
 ALT="$\displaystyle \frac{2}{l}\int_0^l\sin\left(n \pi \frac{x}{l}\right) \sin\left(n' \pi \frac{x}{l}\right)dx={}$">|; 

$key = q/displaystylefrac{2}{l}int_0^ly_0(x),sinleft(n,pi,frac{x}{l}right)dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1038.png"
 ALT="$\displaystyle \frac{2}{l}\int_0^l y_0(x) \sin\left(n \pi \frac{x}{l}\right)dx$">|; 

$key = q/displaystylefrac{2}{pi}int_0^pisinleft(n,thetaright),sinleft(n',thetaright)dtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1022.png"
 ALT="$\displaystyle \frac{2}{\pi}\int_0^\pi \sin\left(n \theta\right) \sin\left(n' \theta\right)d\theta$">|; 

$key = q/displaystylefrac{2}{tau}int_0^taucos(n,omega,t),cos(n',omega,t),dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1260.png"
 ALT="$\displaystyle \frac{2}{\tau} \int_0^\tau \cos(n \omega t) \cos(n' \omega t) dt$">|; 

$key = q/displaystylefrac{2}{tau}int_0^taucos(n,omega,t),dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1285.png"
 ALT="$\displaystyle \frac{2}{\tau} \int_0^\tau \cos(n \omega t) dt$">|; 

$key = q/displaystylefrac{2}{tau}int_0^taucos(n,omega,t),sin(n',omega,t),dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1263.png"
 ALT="$\displaystyle \frac{2}{\tau} \int_0^\tau \cos(n \omega t) \sin(n' \omega t) dt$">|; 

$key = q/displaystylefrac{2}{tau}int_0^tausin(n,omega,t),,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1286.png"
 ALT="$\displaystyle \frac{2}{\tau} \int_0^\tau \sin(n \omega t)  dt$">|; 

$key = q/displaystylefrac{2}{tau}int_0^tausin(n,omega,t),sin(n',omega,t),dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1262.png"
 ALT="$\displaystyle \frac{2}{\tau} \int_0^\tau \sin(n \omega t) \sin(n' \omega t) dt$">|; 

$key = q/displaystylefrac{2}{v}int_0^lv_0(x),sinleft(n,pi,frac{x}{l}right)dx=n,pi,A_n,sinphi_n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1041.png"
 ALT="$\displaystyle \frac{2}{v}\int_0^l v_0(x) \sin\left(n \pi \frac{x}{l}\right)dx = n \pi  A_n \sin\phi_n.$">|; 

$key = q/displaystylefrac{P_{rmout}}{P_{rmin}}=frac{cos^3y}{siny,(y+siny,cosy)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4238.png"
 ALT="$\displaystyle \frac{P_{\rm out}}{P_{\rm in}}= \frac{\cos^3 y}{\sin y (y + \sin y \cos y)},
$">|; 

$key = q/displaystylefrac{T_2}{T_3}=frac{Z_3}{Z_2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1772.png"
 ALT="$\displaystyle \frac{T_2}{T_3} = \frac{Z_3}{Z_2}.
$">|; 

$key = q/displaystylefrac{T}{T_0}=1+frac{skew{3}hat{theta}^{,2}}{16}+{calO}left(skew{3}hat{theta}^{,4}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img410.png"
 ALT="$\displaystyle \frac{T}{T_0} = 1+ \frac{\skew{3}\hat{\theta}^{ 2}}{16}+{\cal O}\left(\skew{3}\hat{\theta}^{ 4}\right).
$">|; 

$key = q/displaystylefrac{T}{T_0}=frac{1}{pi}int_0^{skew{3}hat{theta}}frac{dtheta}{sqrt{sin^2(skew{3}hat{theta}slash2)-sin^2(thetaslash2)}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.47ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img406.png"
 ALT="$\displaystyle \frac{T}{T_0} = \frac{1}{\pi}\int_0^{\skew{3}\hat{\theta}}\frac{d\theta}{\sqrt{\sin^2(\skew{3}\hat{\theta}/2)-\sin^2(\theta/2)}},
$">|; 

$key = q/displaystylefrac{T}{T_0}=frac{2}{pi}int_0^{pislash2}frac{du}{sqrt{1-sin^2(skew{3}hat{theta}slash2),sin^2u}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img409.png"
 ALT="$\displaystyle \frac{T}{T_0} = \frac{2}{\pi}\int_0^{\pi/2}\frac{du}{\sqrt{1-\sin^2(\skew{3}\hat{\theta}/2) \sin^2 u}}.
$">|; 

$key = q/displaystylefrac{calL}{mu_0}=frac{epsilon_0}{calC}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1504.png"
 ALT="$\displaystyle \frac{\cal L}{\mu_0} = \frac{\epsilon_0}{\cal C}.$">|; 

$key = q/displaystylefrac{dE}{dt}=-R,I^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img505.png"
 ALT="$\displaystyle \frac{dE}{dt} = - R I^{ 2},$">|; 

$key = q/displaystylefrac{dE}{dt}=-m,nu,dot{x}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img470.png"
 ALT="$\displaystyle \frac{dE}{dt} = - m \nu \dot{x}^{ 2},$">|; 

$key = q/displaystylefrac{dE}{dt}={calI}(x_1,t)-{calI}(x_2,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1435.png"
 ALT="$\displaystyle \frac{d E}{dt} = {\cal I}(x_1,t)-{\cal I}(x_2,t).$">|; 

$key = q/displaystylefrac{dX}{dbeta}=frac{X}{tanbeta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3138.png"
 ALT="$\displaystyle \frac{dX}{d\beta} = \frac{X}{\tan\beta}.$">|; 

$key = q/displaystylefrac{d^{,2}F}{dz^{,2}}-k^{,2},F=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3039.png"
 ALT="$\displaystyle \frac{d^{ 2} F}{dz^{ 2}} - k^{ 2} F= 0,$">|; 

$key = q/displaystylefrac{d^{,2}hat{psi}}{drho^{,2}}+frac{1}{rho},frac{dhat{psi}}{drho}+frac{omega^{,2}}{v^{,2}},hat{psi}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1910.png"
 ALT="$\displaystyle \frac{d^{ 2}\hat{\psi}}{d\rho^{ 2}} + \frac{1}{\rho} \frac{d\hat{\psi}}{d\rho}+ \frac{\omega^{ 2}}{v^{ 2}} \hat{\psi} = 0,$">|; 

$key = q/displaystylefrac{d^{,2}hat{psi}}{dz^{,2}}+frac{1}{z},frac{dhat{psi}}{dz}+hat{psi}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1913.png"
 ALT="$\displaystyle \frac{d^{ 2}\hat{\psi}}{dz^{ 2}} + \frac{1}{z} \frac{d\hat{\psi}}{dz}+\hat{\psi}=0.$">|; 

$key = q/displaystylefrac{d^{,2}psi(x)}{dx^{,2}}=-k^{,2}(x),psi(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4057.png"
 ALT="$\displaystyle \frac{d^{ 2}\psi(x)}{dx^{ 2}} = - k^{ 2}(x) \psi(x),$">|; 

$key = q/displaystylefrac{d^{,2}psi(x)}{dx^{,2}}={rmi},k'(x),psi(x)-k^{,2}(x),psi(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4064.png"
 ALT="$\displaystyle \frac{d^{ 2}\psi(x)}{dx^{ 2}} = {\rm i} k'(x) \psi(x) - k^{ 2}(x) \psi(x),$">|; 

$key = q/displaystylefrac{d^{,2}psi}{dx^{,2}}=-k^{,2},psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4003.png"
 ALT="$\displaystyle \frac{d^{ 2} \psi}{d x^{ 2}} = - k^{ 2} \psi,$">|; 

$key = q/displaystylefrac{d^{,2}psi}{dx^{,2}}=-q^{,2},psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4011.png"
 ALT="$\displaystyle \frac{d^{ 2}\psi}{dx^{ 2}} =-q^{ 2} \psi,$">|; 

$key = q/displaystylefrac{d^{,2}psi}{dx^{,2}}=q^{,2},psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4036.png"
 ALT="$\displaystyle \frac{d^{ 2} \psi}{d x^{ 2}} = q^{ 2} \psi,$">|; 

$key = q/displaystylefrac{d^{,2}x}{ds^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3231.png"
 ALT="$\displaystyle \frac{d^{ 2} x}{ds^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}z}{ds^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3233.png"
 ALT="$\displaystyle \frac{d^{ 2} z}{ds^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}}{lambda,R}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3566.png"
 ALT="$\displaystyle \frac{d^{ 2}}{\lambda R} \ll 1.$">|; 

$key = q/displaystylefrac{d^{,4}}{lambda,R^{,3}}ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3565.png"
 ALT="$\displaystyle \frac{d^{ 4}}{\lambda R^{ 3}} \ll 1.$">|; 

$key = q/displaystylefrac{deltaV(x,t)}{V}=frac{partialpsi(x,t)}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1222.png"
 ALT="$\displaystyle \frac{\delta V(x,t)}{V} = \frac{\partial\psi(x,t)}{\partial x}.$">|; 

$key = q/displaystylefrac{deltaV}{V}=frac{A,[psi(x+deltaxslash2,t)-psi(x-deltaxslash2,t)]}{A,deltax}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1221.png"
 ALT="$\displaystyle \frac{\delta V}{V} = \frac{A [\psi(x+\delta x/2,t)-\psi(x-\delta x/2,t)]}{A \delta x}.$">|; 

$key = q/displaystylefrac{deltatheta}{{mitDelta}theta}simeqfrac{1}{N}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3387.png"
 ALT="$\displaystyle \frac{\delta\theta}{{\mit\Delta}\theta}\simeq \frac{1}{N}.$">|; 

$key = q/displaystylefrac{dpsi(x)}{dx}={rmi},k(x),psi(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4063.png"
 ALT="$\displaystyle \frac{d\psi(x)}{dx} = {\rm i} k(x) \psi(x),$">|; 

$key = q/displaystylefrac{dx}{ds};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3227.png"
 ALT="$\displaystyle \frac{dx}{ds}$">|; 

$key = q/displaystylefrac{dx}{dt}=-frac{omega}{k}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1390.png"
 ALT="$\displaystyle \frac{dx}{dt} =-\frac{ \omega}{k}.$">|; 

$key = q/displaystylefrac{dx}{dt}=frac{domega}{dk}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2956.png"
 ALT="$\displaystyle \frac{dx}{dt} = \frac{d\omega}{dk}.$">|; 

$key = q/displaystylefrac{dx}{dt}=frac{omega}{k}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1344.png"
 ALT="$\displaystyle \frac{dx}{dt}=\frac{\omega}{k}.$">|; 

$key = q/displaystylefrac{dy}{dx}=tanbeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3132.png"
 ALT="$\displaystyle \frac{dy}{dx} = \tan\beta,$">|; 

$key = q/displaystylefrac{dz}{ds};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3229.png"
 ALT="$\displaystyle \frac{dz}{ds}$">|; 

$key = q/displaystylefrac{d{calE}_1}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img860.png"
 ALT="$\displaystyle \frac{d{\cal E}_1}{dt}$">|; 

$key = q/displaystylefrac{d{calE}_2}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img861.png"
 ALT="$\displaystyle \frac{d{\cal E}_2}{dt}$">|; 

$key = q/displaystylefrac{d{calE}}{dt}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle \frac{d{\cal E}}{dt} = 0,$">|; 

$key = q/displaystylefrac{d}{R}ll1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3558.png"
 ALT="$\displaystyle \frac{d}{R}\ll 1,$">|; 

$key = q/displaystylefrac{d}{R}ll|theta_x|,,|theta_y|ll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3495.png"
 ALT="$\displaystyle \frac{d}{R}\ll \vert\theta_x\vert, \vert\theta_y\vert\ll 1.$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{1}{2},dot{s}^{,2}right)+frac{d}{dt}!left(frac{1}{2},omega^{,2},s^{,2}right)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{1}{2} \dot{s}^{ 2}\right) +\frac{d}{dt}\!\left(
\frac{1}{2} \omega^{ 2} s^{ 2}\right)=0,$">|; 

$key = q/displaystylefrac{d}{dt}int_{-infty}^infty|psi|^{,2},dx=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3857.png"
 ALT="$\displaystyle \frac{d}{dt}\int_{-\infty}^\infty \vert\psi\vert^{ 2} dx=0.$">|; 

$key = q/displaystylefrac{d}{dt}int_{x_1}^{x_2}{calE},dx+{calI}(x_2,t)-{calI}(x_1,t)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img1434.png"
 ALT="$\displaystyle \frac{d}{dt} \int_{x_1}^{x_2} {\cal E} dx + {\cal I}(x_2,t)-{\cal I}(x_1,t) = 0,$">|; 

$key = q/displaystylefrac{d}{dx},cos^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4292.png"
 ALT="$\displaystyle \frac{d}{dx} \cos^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},cosh^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4304.png"
 ALT="$\displaystyle \frac{d}{dx} \cosh^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},coshx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4298.png"
 ALT="$\displaystyle \frac{d}{dx} \cosh x$">|; 

$key = q/displaystylefrac{d}{dx},cosx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4286.png"
 ALT="$\displaystyle \frac{d}{dx} \cos x$">|; 

$key = q/displaystylefrac{d}{dx},lnx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4282.png"
 ALT="$\displaystyle \frac{d}{dx} \ln x$">|; 

$key = q/displaystylefrac{d}{dx},sin^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4290.png"
 ALT="$\displaystyle \frac{d}{dx} \sin^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},sinh^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4302.png"
 ALT="$\displaystyle \frac{d}{dx} \sinh^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},sinhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4296.png"
 ALT="$\displaystyle \frac{d}{dx} \sinh x$">|; 

$key = q/displaystylefrac{d}{dx},sinx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4284.png"
 ALT="$\displaystyle \frac{d}{dx} \sin x$">|; 

$key = q/displaystylefrac{d}{dx},tan^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4294.png"
 ALT="$\displaystyle \frac{d}{dx} \tan^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},tanh^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4306.png"
 ALT="$\displaystyle \frac{d}{dx} \tanh^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},tanhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4300.png"
 ALT="$\displaystyle \frac{d}{dx} \tanh x$">|; 

$key = q/displaystylefrac{d}{dx},tanx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4288.png"
 ALT="$\displaystyle \frac{d}{dx} \tan x$">|; 

$key = q/displaystylefrac{d}{dx},x^{,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4278.png"
 ALT="$\displaystyle \frac{d}{dx} x^{ n}$">|; 

$key = q/displaystylefrac{d}{dx},{rme}^x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4280.png"
 ALT="$\displaystyle \frac{d}{dx} {\rm e}^x$">|; 

$key = q/displaystylefrac{d}{dx}left(fleft[g(x)right]right)equivfrac{df}{dg},frac{dg}{dx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \frac{d}{dx}\left(f\left[g(x)\right]\right)\equiv \frac{df}{dg} \frac{dg}{dx},$">|; 

$key = q/displaystylefrac{d}{dz}left[z^{,n+1},J_{n+1}(z)right]=z^{,n+1},J_n(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3763.png"
 ALT="$\displaystyle \frac{d}{dz}\left[z^{ n+1} J_{n+1}(z)\right]=z^{ n+1} J_n(z),
$">|; 

$key = q/displaystylefrac{d}{dz}left[z^{-n},J_{n}(z)right]=-z^{-n},J_{n+1}(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3770.png"
 ALT="$\displaystyle \frac{d}{dz}\left[z^{-n} J_{n}(z)\right]=-z^{-n} J_{n+1}(z),
$">|; 

$key = q/displaystylefrac{hat{I}_1}{hat{I}_2}=frac{alpha}{hat{omega}^{,2}-(1+alpha)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.23ex; " SRC="|."$dir".q|img763.png"
 ALT="$\displaystyle \frac{\hat{I}_1}{\hat{I}_2}= \frac{\alpha}{\hat{\omega}^{ 2}-(1+\alpha)}.$">|; 

$key = q/displaystylefrac{hat{x}(omega)}{hat{x}(omega=omega_0)}simeqsinvarphisimeqfrac{nu}{[4,(omega_0-omega)^{,2}+nu^{,2}]^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img552.png"
 ALT="$\displaystyle \frac{\hat{x}(\omega)}{\hat{x}(\omega=\omega_0)}\simeq \sin\varphi\simeq \frac{\nu}{[4 (\omega_0-\omega)^{ 2} + \nu^{ 2}]^{1/2}}.$">|; 

$key = q/displaystylefrac{hat{x}(omega=omega_0)}{hat{X}}=frac{omega_0}{nu}=Q_f.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.90ex; " SRC="|."$dir".q|img550.png"
 ALT="$\displaystyle \frac{\hat{x}(\omega=\omega_0)}{\hat{X}} = \frac{\omega_0}{\nu}
=Q_f.$">|; 

$key = q/displaystylefrac{hat{x}_1}{hat{x}_2}=-frac{1}{(hat{omega}^{,2}-2)}=-(hat{omega}^{,2}-2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img684.png"
 ALT="$\displaystyle \frac{\hat{x}_1}{\hat{x}_2}=-\frac{1}{(\hat{\omega}^{ 2}-2)} =-( \hat{\omega}^{ 2}-2).$">|; 

$key = q/displaystylefrac{hbar^{,2},k^{,2}}{2,m}=E.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3926.png"
 ALT="$\displaystyle \frac{\hbar^{ 2} k^{ 2}}{2 m} = E.$">|; 

$key = q/displaystylefrac{k,d^{,2}}{R},,frac{1}{k,R},,frac{d}{R}ll1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3276.png"
 ALT="$\displaystyle \frac{k d^{ 2}}{R}, \frac{1}{k R},  \frac{d}{R}\ll 1,$">|; 

$key = q/displaystylefrac{k}{|k'|}ggk^{,-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img4067.png"
 ALT="$\displaystyle \frac{k}{\vert k'\vert}\gg k^{ -1}.$">|; 

$key = q/displaystylefrac{n_x^{,2}}{v^{,2}-v_x^{,2}}+frac{n_y^{,2}}{v^{,2}-v_y^{,2}}+frac{n_z^{,2}}{v^{,2}-v_z^{,2}}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img2168.png"
 ALT="$\displaystyle \frac{n_x^{ 2}}{v^{ 2}-v_x^{ 2}}+ \frac{n_y^{ 2}}{v^{ 2}-v_y^{ 2}}+\frac{n_z^{ 2}}{v^{ 2}-v_z^{ 2}}=0,$">|; 

$key = q/displaystylefrac{omega_{p,i}^{,2}}{{mitOmega}_i^{,2}}=frac{c^{,2}}{B_0^{,2}slash(mu_0,rho)}=frac{c^{,2}}{V_A^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.19ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2835.png"
 ALT="$\displaystyle \frac{\omega_{p i}^{ 2}}{{\mit\Omega}_i^{ 2}} = \frac{c^{ 2}}{B_0^{ 2}/(\mu_0 \rho)}
= \frac{c^{ 2}}{V_A^{ 2}}.$">|; 

$key = q/displaystylefrac{omega}{k},frac{domega}{dk}=v_p,v_g=c^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2611.png"
 ALT="$\displaystyle \frac{\omega}{k} \frac{d\omega}{dk }= v_p v_g = c^{ 2}.$">|; 

$key = q/displaystylefrac{partialB_x}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2118.png"
 ALT="$\displaystyle \frac{\partial B_x}{\partial t}$">|; 

$key = q/displaystylefrac{partialB_y}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2120.png"
 ALT="$\displaystyle \frac{\partial B_y}{\partial t}$">|; 

$key = q/displaystylefrac{partialB_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2122.png"
 ALT="$\displaystyle \frac{\partial B_z}{\partial t}$">|; 

$key = q/displaystylefrac{partialD_x}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1959.png"
 ALT="$\displaystyle \frac{\partial D_x}{\partial t}$">|; 

$key = q/displaystylefrac{partialD_y}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2004.png"
 ALT="$\displaystyle \frac{\partial D_y}{\partial t}$">|; 

$key = q/displaystylefrac{partialD_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1961.png"
 ALT="$\displaystyle \frac{\partial D_z}{\partial t}$">|; 

$key = q/displaystylefrac{partialE_x}{partialt}+frac{sigma}{epsilon_0},E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2893.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial t} +\frac{\sigma}{\epsilon_0} E_x$">|; 

$key = q/displaystylefrac{partialE_x}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1647.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial t}$">|; 

$key = q/displaystylefrac{partialE_x}{partialt}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1608.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial t} =$">|; 

$key = q/displaystylefrac{partialE_y}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2658.png"
 ALT="$\displaystyle \frac{\partial E_y}{\partial t}$">|; 

$key = q/displaystylefrac{partialE_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3220.png"
 ALT="$\displaystyle \frac{\partial E_z}{\partial t}$">|; 

$key = q/displaystylefrac{partialH_x}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2000.png"
 ALT="$\displaystyle \frac{\partial H_x}{\partial t}$">|; 

$key = q/displaystylefrac{partialH_y}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1649.png"
 ALT="$\displaystyle \frac{\partial H_y}{\partial t}$">|; 

$key = q/displaystylefrac{partialH_y}{partialt}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1610.png"
 ALT="$\displaystyle \frac{\partial H_y}{\partial t} =$">|; 

$key = q/displaystylefrac{partialH_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2002.png"
 ALT="$\displaystyle \frac{\partial H_z}{\partial t}$">|; 

$key = q/displaystylefrac{partialI}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1108.png"
 ALT="$\displaystyle \frac{\partial I}{\partial t}$">|; 

$key = q/displaystylefrac{partialV}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1106.png"
 ALT="$\displaystyle \frac{\partial V}{\partial t}$">|; 

$key = q/displaystylefrac{partial^{,2}E_x}{partialt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1618.png"
 ALT="$\displaystyle \frac{\partial^{ 2} E_x}{\partial t^{ 2}}$">|; 

$key = q/displaystylefrac{partial^{,2}H_y}{partialt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1620.png"
 ALT="$\displaystyle \frac{\partial^{ 2} H_y}{\partial t^{ 2}}$">|; 

$key = q/displaystylefrac{partial^{,2}I}{partialt^{,2}}=v^{,2},frac{partial^{,2}I}{partialx^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1101.png"
 ALT="$\displaystyle \frac{\partial^{ 2} I}{\partial t^{ 2}} = v^{ 2} \frac{\partial^{ 2} I}{\partial x^{ 2}},
$">|; 

$key = q/displaystylefrac{partial^{,2}V}{partialt^{,2}}=frac{1}{{calL},{calC}},frac{partial^{,2}V}{partialx^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img1481.png"
 ALT="$\displaystyle \frac{\partial^{ 2} V}{\partial t^{ 2}} = \frac{1}{{\cal L} {\cal C}} \frac{\partial^{ 2} V}{\partial x^{ 2}},$">|; 

$key = q/displaystylefrac{partial^{,2}V}{partialt^{,2}}=v^{,2},frac{partial^{,2}V}{partialx^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1110.png"
 ALT="$\displaystyle \frac{\partial^{ 2} V}{\partial t^{ 2}} = v^{ 2} \frac{\partial^{ 2} V}{\partial x^{ 2}}.
$">|; 

$key = q/displaystylefrac{partial^{,2}hat{psi}}{partialx^{,2}}+frac{partial^{,2}hat{psi}}{partialy^{,2}}+frac{omega^{,2}}{v^{,2}},hat{psi}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1876.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\hat{\psi}}{\partial x^{ 2}} + \frac{\partia...
...2}\hat{\psi}}{\partial y^{ 2}} + \frac{\omega^{ 2}}{v^{ 2}} \hat{\psi} = 0,$">|; 

$key = q/displaystylefrac{partial^{,2}phi}{partialt^{,2}}=v^{,2}left(frac{partial^{,2}phi}{partialx^{,2}}+frac{partial^{,2}phi}{partialz^{,2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2241.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\phi}{\partial t^{ 2}} = v^{ 2}\left(\frac{...
... 2}\phi}{\partial x^{ 2}}+\frac{\partial^{ 2}\phi}{\partial z^{ 2}}\right),$">|; 

$key = q/displaystylefrac{partial^{,2}phi}{partialx^{,2}}+frac{partial^{,2}phi}{partialz^{,2}}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3029.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\phi}{\partial x^{ 2}} + \frac{\partial^{ 2}\phi}{\partial z^{ 2}} = 0.$">|; 

$key = q/displaystylefrac{partial^{,2}psi}{partialt^{,2}}=c^{,2}left(frac{partial^{,2}}{partialx^{,2}}+frac{partial^{,2}}{partialz^{,2}}right)psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2932.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\psi}{\partial t^{ 2}} = c^{ 2}\left(\frac{...
...l^{ 2}}{\partial x^{ 2}}+ \frac{\partial^{ 2}}{\partial z^{ 2}}\right)\psi,$">|; 

$key = q/displaystylefrac{partial^{,2}psi}{partialt^{,2}}=v^{,2},frac{partial^{,2}psi}{partialx^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1174.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\psi}{\partial t^{ 2}} = v^{ 2} \frac{\partial^{ 2}\psi}{\partial x^{ 2}},$">|; 

$key = q/displaystylefrac{partial^{,2}psi}{partialt^{,2}}=v^{,2}left(frac{partial^{,2}psi}{partialr^{,2}}+frac{2}{r},frac{partialpsi}{partialr}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1862.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\psi}{\partial t^{ 2}} = v^{ 2}\left(\frac{...
...}\psi}{\partial r^{ 2}} + \frac{2}{r} \frac{\partial\psi}{\partial r}\right),$">|; 

$key = q/displaystylefrac{partial^{,2}psi}{partialt^{,2}}=v^{,2}left(frac{partial^{,2}psi}{partialr^{,2}}+frac{2}{r},frac{partialpsi}{partialr}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2293.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\psi}{\partial t^{ 2}} = v^{ 2}\left(\frac{...
...\psi}{\partial r^{ 2}} + \frac{2}{r} \frac{\partial\psi}{\partial r}\right).
$">|; 

$key = q/displaystylefrac{partial^{,2}psi}{partialt^{,2}}=v^{,2}left(frac{partial^{,2}psi}{partialx^{,2}}+frac{partial^{,2}psi}{partialy^{,2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1869.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\psi}{\partial t^{ 2}} = v^{ 2}\left(\frac{...
... 2}\psi}{\partial x^{ 2}}+\frac{\partial^{ 2}\psi}{\partial y^{ 2}}\right).$">|; 

$key = q/displaystylefrac{partial^{,2}psi}{partialx^{,2}}=-k^{,2},psi_0,{rme}^{-{rmi},(k,x-omega,t)}=-frac{p^{,2}}{hbar^{,2}},psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3833.png"
 ALT="$\displaystyle \frac{\partial^{ 2}\psi}{\partial x^{ 2}} = - k^{ 2} \psi_0  {\rm e}^{-{\rm i} (k x-\omega t)} = - \frac{p^{ 2}}{\hbar^{ 2}} \psi,$">|; 

$key = q/displaystylefrac{partial^{,2}x}{partialt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2984.png"
 ALT="$\displaystyle \frac{\partial^{ 2} x}{\partial t^{ 2}}$">|; 

$key = q/displaystylefrac{partial^{,2}y(x,t)}{partialt^{,2}}=frac{T}{rho}left[frac{y(x-deltax,t)-2,y(x,t)+y(x+deltax,t)}{(deltax)^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img978.png"
 ALT="$\displaystyle \frac{\partial^{ 2} y(x,t)}{\partial t^{ 2}} = \frac{T}{\rho}\left[\frac{y(x-\delta x,t)-2 y(x,t)+y(x+\delta x,t)}{(\delta x)^{ 2}}\right].$">|; 

$key = q/displaystylefrac{partial^{,2}y}{partialt^{,2}}=v^{,2},frac{partial^{,2}y}{partialx^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img983.png"
 ALT="$\displaystyle \frac{\partial^{ 2} y}{\partial t^{ 2}} = v^{ 2} \frac{\partial^{ 2} y}{\partial x^{ 2}},$">|; 

$key = q/displaystylefrac{partial^{,2}y}{partialt^{,2}}=v^{,2}frac{partial^{,2}y}{partialx^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1739.png"
 ALT="$\displaystyle \frac{\partial^{ 2} y}{\partial t^{ 2}} = v^{ 2}\frac{\partial^{ 2} y}{\partial x^{ 2}},
$">|; 

$key = q/displaystylefrac{partial^{,2}z}{partialt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2985.png"
 ALT="$\displaystyle \frac{\partial^{ 2} z}{\partial t^{ 2}}$">|; 

$key = q/displaystylefrac{partialk_x}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2952.png"
 ALT="$\displaystyle \frac{\partial k_x}{\partial t}$">|; 

$key = q/displaystylefrac{partialk_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2954.png"
 ALT="$\displaystyle \frac{\partial k_z}{\partial t}$">|; 

$key = q/displaystylefrac{partialpsi}{partialt}=-{rmi},omega,psi_0,{rme}^{-{rmi},(omega,t-k,x)}=-{rmi},frac{E}{hbar},psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3831.png"
 ALT="$\displaystyle \frac{\partial \psi}{\partial t} = -{\rm i} \omega \psi_0 {\rm e}^{-{\rm i} (\omega t-k x)} = -{\rm i} \frac{E}{\hbar} \psi,$">|; 

$key = q/displaystylefrac{partialtilde{p}}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2228.png"
 ALT="$\displaystyle \frac{\partial\tilde{p}}{\partial t}$">|; 

$key = q/displaystylefrac{partialv_x}{partialx}+frac{partialv_z}{partialz}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3004.png"
 ALT="$\displaystyle \frac{\partial v_x}{\partial x} + \frac{\partial v_z}{\partial z} = 0,$">|; 

$key = q/displaystylefrac{partialv_x}{partialz}-frac{partialv_z}{partialx}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3025.png"
 ALT="$\displaystyle \frac{\partial v_x}{\partial z} -\frac{\partial v_z}{\partial x} = 0.$">|; 

$key = q/displaystylefrac{partialx}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2959.png"
 ALT="$\displaystyle \frac{\partial x}{\partial t}$">|; 

$key = q/displaystylefrac{partialzeta}{partialt}=left.v_zright|_{z=0}=left.frac{partialphi}{partialz}right|_{z=0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.04ex; " SRC="|."$dir".q|img3035.png"
 ALT="$\displaystyle \frac{\partial \zeta}{\partial t} = \left.v_z\right\vert _{z=0}=\left.\frac{\partial \phi}{\partial z}\right\vert _{z=0}.$">|; 

$key = q/displaystylefrac{partialz}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2961.png"
 ALT="$\displaystyle \frac{\partial z}{\partial t}$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}_x}{partialx}+frac{partial{calI}_y}{partialy}+frac{partial{calI}_z}{partialz}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2138.png"
 ALT="$\displaystyle \frac{\partial{\cal E}}{\partial t}+\frac{\partial{\cal I}_x}{\pa...
...frac{\partial {\cal I}_y}{\partial y}+\frac{\partial {\cal I}_z}{\partial z}=0,$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}_x}{partialx}+frac{partial{calI}_z}{partialz}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2250.png"
 ALT="$\displaystyle \frac{\partial {\cal E}}{\partial t} + \frac{\partial{\cal I}_x}{\partial x}+ \frac{\partial {\cal I}_z}{\partial z} = 0,$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}_z}{partialz}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1630.png"
 ALT="$\displaystyle \frac{\partial{\cal E}}{\partial t} + \frac{\partial{\cal I}_z}{\partial z} =0,$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}}{partialx}=-{calR},I^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1786.png"
 ALT="$\displaystyle \frac{\partial{\cal E}}{\partial t} + \frac{\partial {\cal I}}{\partial x} =- {\cal R} I^{ 2},
$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}}{partialx}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1431.png"
 ALT="$\displaystyle \frac{\partial {\cal E}}{\partial t} + \frac{\partial {\cal I}}{\partial x} = 0,$">|; 

$key = q/displaystylefrac{partial{calE}}{partialt}+frac{partial{calI}}{partialz}=-sigma,E_x^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1814.png"
 ALT="$\displaystyle \frac{\partial{\cal E}}{\partial t} + \frac{\partial {\cal I}}{\partial z} =- \sigma E_x^{ 2},
$">|; 

$key = q/displaystylefrac{sin(k,pi)}{k,pi}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1031.png"
 ALT="$\displaystyle \frac{\sin(k \pi)}{k \pi} =0.$">|; 

$key = q/displaystylefrac{sinleft[(n-n'),piright]}{(n-n'),pi}-frac{sinleft[(n+n'),piright]}{(n+n'),pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1027.png"
 ALT="$\displaystyle \frac{\sin\left[(n-n') \pi\right]}{(n-n') \pi}-
\frac{\sin\left[(n+n') \pi\right]}{(n+n') \pi},$">|; 

$key = q/displaystylefrac{sintheta_i}{v_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2271.png"
 ALT="$\displaystyle \frac{\sin\theta_i}{v_1}$">|; 

$key = q/displaystylefrac{sqrt{lambda-y^{,2}}}{y}=tany,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3974.png"
 ALT="$\displaystyle \frac{\sqrt{\lambda-y^{ 2}}}{y} = \tan y,$">|; 

$key = q/displaystylefrac{tanh(k,d)}{k,d}=frac{V^{,2}}{g,d}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3075.png"
 ALT="$\displaystyle \frac{\tanh(k d)}{k d} = \frac{V^{ 2}}{g d}.$">|; 

$key = q/displaystylefrac{v_0}{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img198.png"
 ALT="$\displaystyle \frac{v_0}{\omega}$">|; 

$key = q/displaystylefrac{v_g}{v_p}=frac{k}{omega},frac{domega}{dk}=frac{1}{2}left[1+frac{2,k,d}{sinh(2,k,d)}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3048.png"
 ALT="$\displaystyle \frac{v_g}{v_p} =\frac{k}{\omega} \frac{d\omega}{dk}=\frac{1}{2}\left[1+\frac{2 k d}{\sinh(2 k d)}\right].$">|; 

$key = q/displaystylefrac{v_g}{v_p}=frac{k}{omega},frac{domega}{dk}=frac{1}{2}left[frac{1+3,T,k^{,2}slash(rho,g)}{1+T,k^{,2}slash(rho,g)}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img3166.png"
 ALT="$\displaystyle \frac{v_g}{v_p} = \frac{k}{\omega} \frac{d\omega}{dk}=\frac{1}{2}\left[\frac{1+3 T k^{ 2}/(\rho g)}{1+T k^{ 2}/(\rho g)}\right].$">|; 

$key = q/displaystylefrac{{calI}(0,0)}{{calI}_0}=left(frac{A}{lambda,R}right)^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3749.png"
 ALT="$\displaystyle \frac{{\cal I}(0,0)}{{\cal I}_0} = \left(\frac{A}{\lambda R}\right)^{ 2},
$">|; 

$key = q/displaystylefrac{{calI}(u')}{{calI}_0}=f_c^{,2}(u')+f_s^{,2}(u').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3637.png"
 ALT="$\displaystyle \frac{{\cal I}(u')}{{\cal I}_0} = f_c^{ 2}(u')+f_s^{ 2}(u').$">|; 

$key = q/displaystylefrac{{calI}(u')}{{calI}_0}=frac{1}{2}left[C(u')+frac{1}{2}right]^{,2}+frac{1}{2}left[S(u')+frac{1}{2}right]^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3647.png"
 ALT="$\displaystyle \frac{{\cal I}(u')}{{\cal I}_0} = \frac{1}{2}\left[C(u')+\frac{1}{2}\right]^{ 2} + \frac{1}{2}\left[S(u')+\frac{1}{2}\right]^{ 2}.$">|; 

$key = q/displaystylefrac{{calI}(u')}{{calI}_0}simeqfrac{1}{2,pi^{,2},|u'|^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img3760.png"
 ALT="$\displaystyle \frac{{\cal I}(u') }{{\cal I}_0}\simeq \frac{1}{2 \pi^{ 2} \vert u'\vert^{ 2}}
$">|; 

$key = q/displaystylefrac{{calI}(u',v')}{{calI}_0}=F_c^{,2}(u',v')+F_s^{,2}(u',v'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3744.png"
 ALT="$\displaystyle \frac{{\cal I}(u',v')}{{\cal I}_0} = F_c^{ 2}(u',v')+F_s^{ 2}(u',v'),
$">|; 

$key = q/displaystylefrac{{calI}(u',v')}{{calI}_0}=f_c^{,2}(u',v')+f_s^{,2}(u',v'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3595.png"
 ALT="$\displaystyle \frac{{\cal I}(u',v')}{{\cal I}_0}=f_c^{ 2}(u',v') + f_s^{ 2}(u',v'),$">|; 

$key = q/displaystylefrac{{calI}(v)}{{calI}_0}=V_0^{,2}(u,v)+V_1^{,2}(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3714.png"
 ALT="$\displaystyle \frac{{\cal I}(v)}{{\cal I}_0}= V_0^{ 2}(u,v)+V_1^{ 2}(u,v)$">|; 

$key = q/displaystylefrac{{calI}(v)}{{calI}_0}=left[U_1^{,2}(u,v)+U_2^{,2}(u,v)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3712.png"
 ALT="$\displaystyle \frac{{\cal I}(v)}{{\cal I}_0}= \left[U_1^{ 2}(u,v)+U_2^{ 2}(u,v)\right]$">|; 

$key = q/displaystylefrac{{mitDelta}lambda}{lambda}>frac{1}{N,j}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3406.png"
 ALT="$\displaystyle \frac{{\mit\Delta}\lambda}{\lambda} &gt; \frac{1}{N j}.$">|; 

$key = q/displaystylefrac{{mitDelta}omega}{omega_0}=frac{nu}{omega_0}=frac{1}{Q_f}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img558.png"
 ALT="$\displaystyle \frac{{\mit\Delta} \omega}{\omega_0} = \frac{\nu}{\omega_0} = \frac{1}{Q_f}.$">|; 

$key = q/displaystylegamma=nuslash2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img440.png"
 ALT="$\displaystyle \gamma= \nu/2,$">|; 

$key = q/displaystyleh(omega)=int_0^{z_0}frac{dz}{[1-omega_{p,e}^{,2}(z)slashomega^{,2}]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img3181.png"
 ALT="$\displaystyle h(\omega) = \int_0^{z_0}\frac{dz}{[1-\omega_{p e}^{ 2}(z)/\omega^{ 2}]^{1/2}},
$">|; 

$key = q/displaystylehat{D}_{a,x}=-frac{epsilon_0,c^{,2},({bfn}cdothat{bfE}_a),n_x}{v_a^{,2}-v_x^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img2175.png"
 ALT="$\displaystyle \hat{D}_{a x} = -\frac{\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}_a) n_x}{v_a^{ 2}-v_x^{ 2}},$">|; 

$key = q/displaystylehat{D}_{a,y}=-frac{epsilon_0,c^{,2},({bfn}cdothat{bfE}_a),n_y}{v_a^{,2}-v_y^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img2176.png"
 ALT="$\displaystyle \hat{D}_{a y} = -\frac{\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}_a) n_y}{v_a^{ 2}-v_y^{ 2}},$">|; 

$key = q/displaystylehat{D}_{a,z}=-frac{epsilon_0,c^{,2},({bfn}cdothat{bfE}_a),n_z}{v_a^{,2}-v_z^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img2177.png"
 ALT="$\displaystyle \hat{D}_{a z} = -\frac{\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}_a) n_z}{v_a^{ 2}-v_z^{ 2}},$">|; 

$key = q/displaystylehat{D}_{b,x}=-frac{epsilon_0,c^{,2},({bfn}cdothat{bfE}_b),n_x}{v_b^{,2}-v_x^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2178.png"
 ALT="$\displaystyle \hat{D}_{b x} = -\frac{\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}_b) n_x}{v_b^{ 2}-v_x^{ 2}},$">|; 

$key = q/displaystylehat{D}_{b,y}=-frac{epsilon_0,c^{,2},({bfn}cdothat{bfE}_b),n_y}{v_b^{,2}-v_y^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.19ex; vertical-align: -2.59ex; " SRC="|."$dir".q|img2179.png"
 ALT="$\displaystyle \hat{D}_{b y} = -\frac{\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}_b) n_y}{v_b^{ 2}-v_y^{ 2}},$">|; 

$key = q/displaystylehat{D}_{b,z}=-frac{epsilon_0,c^{,2},({bfn}cdothat{bfE}_b),n_z}{v_b^{,2}-v_z^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2180.png"
 ALT="$\displaystyle \hat{D}_{b z} = -\frac{\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}_b) n_z}{v_b^{ 2}-v_z^{ 2}}.$">|; 

$key = q/displaystylehat{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img581.png"
 ALT="$\displaystyle \hat{I}$">|; 

$key = q/displaystylehat{P}_x=hat{P}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2747.png"
 ALT="$\displaystyle \hat{P}_x=\hat{P}_y$">|; 

$key = q/displaystylehat{alpha}=frac{sinhtheta_t}{costheta_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2061.png"
 ALT="$\displaystyle \hat{\alpha} = \frac{\sinh\theta_t}{\cos\theta_i}.$">|; 

$key = q/displaystylehat{bfD};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2196.png"
 ALT="$\displaystyle \hat{\bf D}$">|; 

$key = q/displaystylehat{bfD}_acdothat{bfD}_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2181.png"
 ALT="$\displaystyle \hat{\bf D}_a\cdot\hat{\bf D}_b$">|; 

$key = q/displaystylehat{bfD}_acdothat{bfD}_b=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2186.png"
 ALT="$\displaystyle \hat{\bf D}_a\cdot\hat{\bf D}_b=0.$">|; 

$key = q/displaystylehat{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2198.png"
 ALT="$\displaystyle \hat{\bf E}$">|; 

$key = q/displaystylehat{bfH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2200.png"
 ALT="$\displaystyle \hat{\bf H}$">|; 

$key = q/displaystylehat{bfH}cdothat{bfD}=hat{bfH}cdothat{bfE}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2156.png"
 ALT="$\displaystyle \hat{\bf H}\cdot\hat{\bf D}=\hat{\bf H}\cdot\hat{\bf E} = 0.$">|; 

$key = q/displaystylehat{bfx}_1=left(frac{1}{2},,frac{1}{sqrt{2}},,frac{1}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img811.png"
 ALT="$\displaystyle \hat{\bf x}_1 = \left(\frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{2}\right).$">|; 

$key = q/displaystylehat{bfx}_2=left(-frac{1}{sqrt{2}},,0,,frac{1}{sqrt{2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img813.png"
 ALT="$\displaystyle \hat{\bf x}_2 = \left(-\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}\right).$">|; 

$key = q/displaystylehat{bfx}_3=left(frac{1}{2},-frac{1}{sqrt{2}},,frac{1}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img815.png"
 ALT="$\displaystyle \hat{\bf x}_3 =\left(\frac{1}{2},-\frac{1}{\sqrt{2}}, \frac{1}{2}\right).$">|; 

$key = q/displaystylehat{omega}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img689.png"
 ALT="$\displaystyle \hat{\omega} = 1$">|; 

$key = q/displaystylehat{omega}^{,4}-2,(1+alpha),hat{omega}^{,2}+1+2,alpha=left(hat{omega}^{,2}-1right)left(hat{omega}^{,2}-[1+2,alpha]right)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img760.png"
 ALT="$\displaystyle \hat{\omega}^{ 4} - 2 (1+\alpha) \hat{\omega}^{ 2}+1+2 \alph...
...eft(\hat{\omega}^{ 2}-1\right)\left(\hat{\omega}^{ 2}-[1+2 \alpha]\right)=0.$">|; 

$key = q/displaystylehat{omega}^{,4}-4,hat{omega}^2+3=(hat{omega}^{,2}-1),(hat{omega}^{,2}-3)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img688.png"
 ALT="$\displaystyle \hat{\omega}^{ 4} - 4 \hat{\omega}^2+3 = (\hat{\omega}^{ 2}-1) (\hat{\omega}^{ 2}-3)=0.$">|; 

$key = q/displaystylehat{psi}(x,y)=X(x),Y(y).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1878.png"
 ALT="$\displaystyle \hat{\psi}(x,y)= X(x) Y(y).$">|; 

$key = q/displaystylehat{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img532.png"
 ALT="$\displaystyle \hat{x}$">|; 

$key = q/displaystylehat{x}_1+(hat{omega}^{,2}-2),hat{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img681.png"
 ALT="$\displaystyle \hat{x}_1 + (\hat{\omega}^{ 2}-2) \hat{x}_2$">|; 

$key = q/displaystylehat{x}_1:hat{x}_2:hat{x}_3::-1:0:1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img803.png"
 ALT="$\displaystyle \hat{x}_1:\hat{x}_2:\hat{x}_3 :: -1:0:1$">|; 

$key = q/displaystylehat{x}_1:hat{x}_2:hat{x}_3::1:2-hat{omega}^{,2}:1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img801.png"
 ALT="$\displaystyle \hat{x}_1:\hat{x}_2:\hat{x}_3 :: 1:2- \hat{\omega}^{ 2}:1,$">|; 

$key = q/displaystylehat{x}_e=hat{y_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2746.png"
 ALT="$\displaystyle \hat{x}_e=\hat{y_e}$">|; 

$key = q/displaystylehat{x}_i=hat{y_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2744.png"
 ALT="$\displaystyle \hat{x}_i=\hat{y_i}$">|; 

$key = q/displaystylehat{x}left(omega_0^{,2}-omega^{,2}right)cosvarphi+hat{x},nu,omega,sinvarphi-omega_0^{,2},hat{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img530.png"
 ALT="$\displaystyle \hat{x}\left(\omega_0^{ 2}-\omega^{ 2}\right)\cos\varphi + \hat{x} \nu \omega \sin\varphi -\omega_0^{ 2} \hat{X}$">|; 

$key = q/displaystyleindex{dispersionrelation!ofelectromagneticwaveindielectricmedium}omega=k,v=frac{k,c}{n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1656.png"
 ALT="$\displaystyle \index{dispersion relation!of electromagnetic wave in dielectric medium}
\omega = k v = \frac{k c}{n}.$">|; 

$key = q/displaystyleint_0^a,|psi(x)|^{,2},dx=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3934.png"
 ALT="$\displaystyle \int_0^a \vert\psi(x)\vert^{ 2} dx = 1.$">|; 

$key = q/displaystyleint_0^z,J_0(z'),z',dz'=z,J_1(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3531.png"
 ALT="$\displaystyle \int_0^z J_0(z') z' dz' = z J_1(z),$">|; 

$key = q/displaystyleint_0^{2pi}cos^2theta,dtheta=int_0^{2pi}sin^2theta,dtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img487.png"
 ALT="$\displaystyle \int_0^{2\pi}\cos^2\theta d\theta = \int_0^{2\pi}\sin^2\theta d\theta$">|; 

$key = q/displaystyleint_0^{2pi}costheta,sintheta,dtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img489.png"
 ALT="$\displaystyle \int_0^{2\pi}\cos\theta \sin\theta d\theta$">|; 

$key = q/displaystyleint_1^{1slashepsilon}left(frac{1}{y}-epsilonright)^{1slash2}dysimeqfrac{pi}{2sqrt{epsilon}}-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4107.png"
 ALT="$\displaystyle \int_1^{1/\epsilon}\left(\frac{1}{y} - \epsilon\right)^{1/2} dy \simeq
\frac{\pi}{2\sqrt{\epsilon}}-2$">|; 

$key = q/displaystyleint_{-infty}^inftyF(k),delta(k),dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2385.png"
 ALT="$\displaystyle \int_{-\infty}^\infty F(k) \delta(k) dk,$">|; 

$key = q/displaystyleint_{-infty}^inftyF^{,2}(t),dt=2piint_{-infty}^inftyleft[C^{,2}(omega)+S^{,2}(omega)right]domega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2525.png"
 ALT="$\displaystyle \int_{-\infty}^\infty F^{ 2}(t) dt= 2\pi\int_{-\infty}^\infty\left[C^{ 2}(\omega)+S^{ 2}(\omega)\right]d\omega,
$">|; 

$key = q/displaystyleint_{-infty}^inftycosleft(frac{pi}{2},t^{,2}right)dt=int_{-infty}^inftysinleft(frac{pi}{2},t^{,2}right)dt=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3589.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \cos\left(\frac{\pi}{2} t^{ 2}\right)dt= \int_{-\infty}^\infty \sin\left(\frac{\pi}{2} t^{ 2}\right)dt=1.$">|; 

$key = q/displaystyleint_{-infty}^inftydelta(k),dk=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2384.png"
 ALT="$\displaystyle \int_{-\infty}^\infty\delta (k) dk = 1.$">|; 

$key = q/displaystyleint_{-infty}^inftyfrac{1}{(2pi,sigma_k^{,2})^{1slash2}},expleft(-frac{k^{,2}}{2,sigma_k^{,2}}right)dk=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2372.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \frac{1}{(2\pi \sigma_k^{ 2})^{1/2}} \exp\left(-\frac{k^{ 2}}{2 \sigma_k^{ 2}}\right) dk = 1.$">|; 

$key = q/displaystyleint_{-infty}^inftyint_{-infty}^inftyint_{-infty}^infty|psi(x,y,z,t)|^{,2},dx,dy,dz=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4141.png"
 ALT="$\displaystyle \int_{-\infty}^\infty\int_{-\infty}^\infty\int_{-\infty}^\infty\vert\psi(x,y,z,t)\vert^{ 2} dx dy dz =1.$">|; 

$key = q/displaystyleint_{-infty}^infty|psi(x,t)|^{,2},dx=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3846.png"
 ALT="$\displaystyle \int_{-\infty}^\infty \vert\psi(x,t)\vert^{ 2} dx=1$">|; 

$key = q/displaystyleint_{-infty}^{infty}F(k),delta(k),dk=int_{-infty}^inftyF(0),delta(k),dk=F(0),int_{-infty}^{infty}delta(k),dk=F(0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2387.png"
 ALT="$\displaystyle \int_{-\infty}^{\infty} F(k) \delta(k) dk = \int_{-\infty}^\infty F(0) \delta (k) dk=F(0) \int_{-\infty}^{\infty} \delta(k) dk = F(0),$">|; 

$key = q/displaystyleint_{-infty}^{infty}F(k),delta(k-k'),dk=F(k'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2390.png"
 ALT="$\displaystyle \int_{-\infty}^{\infty} F(k) \delta(k-k') dk = F(k'),$">|; 

$key = q/displaystyleint_{-infty}^{infty}frac{1}{(2pi,sigma_k^{,2})^{1slash2}},expleft(-frac{k^{,2}}{2,sigma_k^{,2}}right)dk=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2517.png"
 ALT="$\displaystyle \int_{-\infty}^{\infty} \frac{1}{(2\pi \sigma_k^{ 2})^{1/2}} \exp \left(-\frac{k^{ 2}}{2 \sigma_k^{ 2}}\right)dk = 1.
$">|; 

$key = q/displaystylek(x)=frac{omega}{v(x)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1722.png"
 ALT="$\displaystyle k(x) = \frac{\omega}{v(x)}.$">|; 

$key = q/displaystylek,(1-R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4017.png"
 ALT="$\displaystyle k (1-R)$">|; 

$key = q/displaystylek,a=frac{(n-1slash2),pi}{N+1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1141.png"
 ALT="$\displaystyle k a = \frac{(n-1/2) \pi}{N+1/2},$">|; 

$key = q/displaystylek,c=sqrt{omega_{p,e}^{,2}-omega^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.47ex; " SRC="|."$dir".q|img2619.png"
 ALT="$\displaystyle k c=\sqrt{\omega_{p e}^{ 2}-\omega^{ 2}},$">|; 

$key = q/displaystylek,l=(n-1slash2),pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1183.png"
 ALT="$\displaystyle k l = (n-1/2) \pi,$">|; 

$key = q/displaystylek,l=(n-1slash2),pi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1337.png"
 ALT="$\displaystyle k l = (n-1/2) \pi.$">|; 

$key = q/displaystylek,l=n,pi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1336.png"
 ALT="$\displaystyle k l = n \pi.$">|; 

$key = q/displaystylek,v,[C_+(k)-C_-(k)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2419.png"
 ALT="$\displaystyle k v [C_+(k) - C_-(k)]$">|; 

$key = q/displaystylek,v,[S_+(k)+S_-(k)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2421.png"
 ALT="$\displaystyle k v [S_+(k) + S_-(k)]$">|; 

$key = q/displaystylek;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1726.png"
 ALT="$\displaystyle k$">|; 

$key = q/displaystylek=(2,n-1),frac{pi}{a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3985.png"
 ALT="$\displaystyle k = (2 n-1) \frac{\pi}{a}.$">|; 

$key = q/displaystylek=2,n,frac{pi}{a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3992.png"
 ALT="$\displaystyle k= 2 n \frac{\pi}{a}.$">|; 

$key = q/displaystylek=frac{n}{N+1},frac{pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img924.png"
 ALT="$\displaystyle k = \frac{n}{N+1} \frac{\pi}{a},$">|; 

$key = q/displaystylek=left[frac{sinh(2,k,d)-2,k,d}{sinh(2,k,d)+2,k,d}right]^{1slash2}k_c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3248.png"
 ALT="$\displaystyle k = \left[\frac{\sinh(2 k d)-2 k d}{\sinh(2 k d)+2 k d}\right]^{1/2} k_c,
$">|; 

$key = q/displaystylek=n,frac{pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3929.png"
 ALT="$\displaystyle k= n \frac{\pi}{a},$">|; 

$key = q/displaystylek=n,frac{pi}{l},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img990.png"
 ALT="$\displaystyle k = n \frac{\pi}{l},$">|; 

$key = q/displaystylek=sqrt{frac{2,m,(V+E)}{hbar^{,2}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img3967.png"
 ALT="$\displaystyle k= \sqrt{\frac{2 m (V+E)}{\hbar^{ 2}}},$">|; 

$key = q/displaystylek=sqrt{frac{2,m,E}{hbar^{,2}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img4004.png"
 ALT="$\displaystyle k = \sqrt{\frac{2 m E}{\hbar^{ 2}}}.$">|; 

$key = q/displaystylek^{,2}(x)=frac{2,m,[E-U(x)]}{hbar^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4058.png"
 ALT="$\displaystyle k^{ 2}(x) = \frac{2 m [E-U(x)]}{\hbar^2}.$">|; 

$key = q/displaystylek_0=frac{g}{V^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3123.png"
 ALT="$\displaystyle k_0 = \frac{g}{V^{ 2}}$">|; 

$key = q/displaystylek_L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2681.png"
 ALT="$\displaystyle k_L$">|; 

$key = q/displaystylek_R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2679.png"
 ALT="$\displaystyle k_R$">|; 

$key = q/displaystylek_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2947.png"
 ALT="$\displaystyle k_x$">|; 

$key = q/displaystylek_x=j,frac{pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2937.png"
 ALT="$\displaystyle k_x = j \frac{\pi}{a},$">|; 

$key = q/displaystylek_x=k_x(z=0)=frac{omega}{c},S,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2976.png"
 ALT="$\displaystyle k_x = k_x(z=0)= \frac{\omega}{c} S,$">|; 

$key = q/displaystylek_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4156.png"
 ALT="$\displaystyle k_y$">|; 

$key = q/displaystylek_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2948.png"
 ALT="$\displaystyle k_z$">|; 

$key = q/displaystylek_z=pmfrac{omega}{c}sqrt{n^{,2}-S^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2978.png"
 ALT="$\displaystyle k_z = \pm\frac{\omega}{c}\sqrt{n^{ 2}-S^{2}}.$">|; 

$key = q/displaystylek_{i,x}=k_{r,x}=k_{t,x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1940.png"
 ALT="$\displaystyle k_{i x} = k_{r x} = k_{t x},$">|; 

$key = q/displaystylek_{i,y}=k_{r,y}=k_{t,y}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1941.png"
 ALT="$\displaystyle k_{i y} = k_{r y} = k_{t y}.$">|; 

$key = q/displaystylek_{m,n}=pileft(frac{m^{,2}}{l^{,2}}+frac{n^{,2}}{b^{,2}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3246.png"
 ALT="$\displaystyle k_{m,n} = \pi\left(\frac{m^{ 2}}{l^{ 2}}+\frac{n^{ 2}}{b^{ 2}}\right)^{1/2},
$">|; 

$key = q/displaystylel,skew{3}ddot{theta}+g,sintheta=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img333.png"
 ALT="$\displaystyle l \skew{3}\ddot{\theta} + g \sin\theta=0.$">|; 

$key = q/displaystylel_F=left(frac{3,N}{pi}right)^{1slash3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4173.png"
 ALT="$\displaystyle l_F = \left(\frac{3 N}{\pi}\right)^{1/3}.$">|; 

$key = q/displaystylelambda'=d_1-d_2=(v-u_s),T.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1710.png"
 ALT="$\displaystyle \lambda' = d_1-d_2 = (v - u_s) T.$">|; 

$key = q/displaystylelambda=1.23times10^{-9},V^{,-1slash2},{rmm},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4231.png"
 ALT="$\displaystyle \lambda = 1.23\times 10^{-9} V^{ -1/2} {\rm m},
$">|; 

$key = q/displaystylelambda=frac{V}{E_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3975.png"
 ALT="$\displaystyle \lambda = \frac{V}{E_0}.$">|; 

$key = q/displaystylelambda_e=1.2times10^{-9},[E({rmeV})]^{-1slash2},{rmm},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3794.png"
 ALT="$\displaystyle \lambda_e = 1.2\times 10^{-9} [E({\rm eV})]^{-1/2} {\rm m},$">|; 

$key = q/displaystylelambda_n=frac{4,l}{2,n-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1237.png"
 ALT="$\displaystyle \lambda_n =\frac{4 l}{2 n-1},$">|; 

$key = q/displaystylelambda_p=2.9times10^{-11},[E({rmeV})]^{-1slash2},{rmm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3798.png"
 ALT="$\displaystyle \lambda_p = 2.9\times 10^{-11} [E({\rm eV})]^{-1/2} {\rm m}.$">|; 

$key = q/displaystylelanglePrangle=frac{1}{2},k,hat{X},,hat{x},omega,sinvarphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img566.png"
 ALT="$\displaystyle \langle P\rangle = \frac{1}{2} k \hat{X}  \hat{x} \omega \sin\varphi,$">|; 

$key = q/displaystylelanglePrangleequivfrac{1}{T}int_0^TP(t),dt,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img316.png"
 ALT="$\displaystyle \langle P\rangle \equiv \frac{1}{T}\int_0^T P(t) dt,$">|; 

$key = q/displaystylelanglePranglesimeqfrac{1}{2},frac{skew{3}hat{V}^{,2}}{R}left[frac{nu^{,2}}{4,(omega_0-omega)^{,2}+nu^{,2}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img586.png"
 ALT="$\displaystyle \langle P\rangle \simeq \frac{1}{2} \frac{\skew{3}\hat{V}^{ 2}}{R}\left[\frac{\nu^{ 2}}{4 (\omega_0-\omega)^{ 2}+\nu^{ 2}}\right]$">|; 

$key = q/displaystylelanglePranglesimeqfrac{1}{2},omega_0,k,hat{X}^{,2},Q_fleft[frac{nu^{,2}}{4,(omega_0-omega)^{,2}+nu^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img569.png"
 ALT="$\displaystyle \langle P\rangle \simeq \frac{1}{2} \omega_0 k \hat{X}^{ 2} Q_f\left[\frac{\nu^{ 2}}{4 (\omega_0-\omega)^{ 2}+\nu^{ 2}}\right].$">|; 

$key = q/displaystylelanglebm{mathcal{I}}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2202.png"
 ALT="$\displaystyle \langle\bm{\mathcal{I}}\rangle$">|; 

$key = q/displaystylelanglecdotsrangle=int_0^{2pi}(cdots),frac{d(k,x)}{2pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3065.png"
 ALT="$\displaystyle \langle \cdots\rangle = \int_0^{2\pi} (\cdots) \frac{d(k x)}{2\pi}$">|; 

$key = q/displaystylelangle{calI}_zrangle=-frac{1}{2},frac{E_0^{,2}}{Z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1638.png"
 ALT="$\displaystyle \langle {\cal I}_z \rangle =- \frac{1}{2} \frac{E_0^{ 2}}{Z}.$">|; 

$key = q/displaystylelangle{calI}_zrangle=frac{1}{2},epsilon_0,E_0^{,2},n,c=frac{1}{2},epsilon_0,E_0^{,2},v_g,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2614.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle = \frac{1}{2} \epsilon_0 E_0^{ 2} n c = \frac{1}{2} \epsilon_0 E_0^{ 2} v_g,$">|; 

$key = q/displaystylelangle{calI}_zrangle=frac{1}{2},frac{E_0^{,2}}{Z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1633.png"
 ALT="$\displaystyle \langle {\cal I}_z \rangle = \frac{1}{2} \frac{E_0^{ 2}}{Z}.$">|; 

$key = q/displaystylelangle{calI}_zrangle=langleE_x,H_yrangle=E_0^{,2},Z^{,-1},{rme}^{-2,k,z},langlecos(omega,t),sin(omega,t)rangle=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2621.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle =\langle E_x H_y\rangle = E_0^{ 2} Z^{ -1} {\rm e}^{-2 k z} \langle\cos(\omega t) \sin(\omega t)\rangle=0.$">|; 

$key = q/displaystylelangle{calI}_zrangle_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1990.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle_i$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2069.png"
 ALT="$\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/displaystylelangle{calI}_zrangle_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1992.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle_r$">|; 

$key = q/displaystylelangle{calI}_zrangle_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1994.png"
 ALT="$\displaystyle \langle {\cal I}_z\rangle_t$">|; 

$key = q/displaystylelangle{calI}_zrangle_t=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2070.png"
 ALT="$\displaystyle \langle{\cal I}_z\rangle_t= 0.$">|; 

$key = q/displaystylelangle{calI}rangle=-frac{1}{2},I_0,V_0=-frac{1}{2},Z,I_0^{,2}=-frac{1}{2},frac{V_0^{,2}}{Z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1496.png"
 ALT="$\displaystyle \langle {\cal I}\rangle =-\frac{1}{2} I_0 V_0= -\frac{1}{2} Z I_0^{ 2} =- \frac{1}{2} \frac{V_0^{ 2}}{Z}.$">|; 

$key = q/displaystylelangle{calI}rangle=-frac{1}{2},omega^{,2},Z,A^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1449.png"
 ALT="$\displaystyle \langle {\cal I}\rangle =- \frac{1}{2} \omega^{ 2} Z A^2.$">|; 

$key = q/displaystylelangle{calI}rangle=frac{1}{2},omega^{,2},Z(x)left[A(x)right]^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1731.png"
 ALT="$\displaystyle \langle {\cal I}\rangle = \frac{1}{2} \omega^{ 2} Z(x)\left[A(x)\right]^{ 2}.$">|; 

$key = q/displaystylelangle{calI}rangle=frac{1}{2},omega^{,2},Z,A^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1443.png"
 ALT="$\displaystyle \langle {\cal I}\rangle = \frac{1}{2} \omega^{ 2} Z A^2,$">|; 

$key = q/displaystylelangle{calI}rangle=frac{1}{2},omega^{,2},Z,A_+^{,2}-frac{1}{2},omega^{,2},Z,A_-^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1457.png"
 ALT="$\displaystyle \langle {\cal I}\rangle = \frac{1}{2} \omega^{ 2} Z A_+^{ 2} - \frac{1}{2} \omega^{ 2} Z A_-^{ 2},$">|; 

$key = q/displaystylelangle{calI}rangle=langleI,Vrangle=frac{1}{2},I_0,V_0=frac{1}{2},Z,I_0^{,2}=frac{1}{2},frac{V_0^{,2}}{Z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1491.png"
 ALT="$\displaystyle \langle {\cal I}\rangle =\langle I V\rangle= \frac{1}{2} I_0 V_0= \frac{1}{2} Z I_0^{ 2} = \frac{1}{2} \frac{V_0^{ 2}}{Z}.$">|; 

$key = q/displaystylelangle{calI}rangle=v,langle{calE}rangle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1746.png"
 ALT="$\displaystyle \langle {\cal I}\rangle = v \langle {\cal E}\rangle,
$">|; 

$key = q/displaystyleleft(gamma^{,2}-omega_1^{,2}right)-nu,gamma+omega_0^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img436.png"
 ALT="$\displaystyle \left(\gamma^{ 2}-\omega_1^{ 2}\right) -\nu \gamma+\omega_0^{ 2}$">|; 

$key = q/displaystyleleft(omega_0^{,2}-omega^{,2}right)sinvarphi-nu,omega,cosvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img531.png"
 ALT="$\displaystyle \left(\omega_0^{ 2}-\omega^{ 2}\right)\sin\varphi-\nu \omega \cos\varphi$">|; 

$key = q/displaystyleleft(v^{,2}-v_x^{,2}right)hat{D}_x=-epsilon_0,c^{,2},({bfn}cdothat{bfE}),n_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2162.png"
 ALT="$\displaystyle \left(v^{ 2}-v_x^{ 2}\right)\hat{D}_x = -\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}) n_x,$">|; 

$key = q/displaystyleleft(v^{,2}-v_y^{,2}right)hat{D}_x=-epsilon_0,c^{,2},({bfn}cdothat{bfE}),n_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2163.png"
 ALT="$\displaystyle \left(v^{ 2}-v_y^{ 2}\right)\hat{D}_x = -\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}) n_y,$">|; 

$key = q/displaystyleleft(v^{,2}-v_z^{,2}right)hat{D}_x=-epsilon_0,c^{,2},({bfn}cdothat{bfE}),n_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2164.png"
 ALT="$\displaystyle \left(v^{ 2}-v_z^{ 2}\right)\hat{D}_x = -\epsilon_0 c^{ 2} ({\bf n}\cdot\hat{\bf E}) n_z.$">|; 

$key = q/displaystyleleft.frac{partialphi}{partialz}right|_{z=-d}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.04ex; " SRC="|."$dir".q|img3033.png"
 ALT="$\displaystyle \left.\frac{\partial \phi}{\partial z}\right\vert _{z=-d} = 0.$">|; 

$key = q/displaystyleleft.frac{partialphi}{partialz}right|_{z=0}=-g^{-1}left.frac{partial^{,2}phi}{partialt^{,2}}right|_{z=0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.50ex; " SRC="|."$dir".q|img3037.png"
 ALT="$\displaystyle \left.\frac{\partial \phi}{\partial z}\right\vert _{z=0} = -g^{-1}\left.\frac{\partial^{ 2}\phi}{\partial t^{ 2}}\right\vert _{z=0}.$">|; 

$key = q/displaystyleleft[A_+,sin(omega,t-k,x-phi_+)-A_-,sin(omega,t+k,x-phi_-)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img1455.png"
 ALT="$\displaystyle \left[A_+ \sin(\omega t-k x-\phi_+)-A_- \sin(\omega t+k x-\phi_-)\right]$">|; 

$key = q/displaystyleleft[frac{v_x(x+dx,z,t)-v_x(x,z,t)}{dx}+frac{v_z(x,z+dz,t)-v_z(x,z,t)}{dz}right]dx,dy,dz=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3003.png"
 ALT="$\displaystyle \left[\frac{v_x(x+dx,z,t)-v_x(x,z,t)}{dx} + \frac{v_z(x,z+dz,t)-v_z(x,z,t)}{dz} \right]dx dy dz=0.$">|; 

$key = q/displaystyleleft[frac{y(x-deltax,t)-2,y(x,t)+y(x+deltax,t)}{(deltax)^{,2}}right]=frac{partial^{,2}y(x,t)}{partialx^{,2}}+{calO}(deltax).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img981.png"
 ALT="$\displaystyle \left[\frac{y(x-\delta x,t)-2 y(x,t)+y(x+\delta x,t)}{(\delta x)...
...}}\right]
=\frac{\partial^{ 2} y(x,t)}{\partial x^{ 2}} + {\cal O}(\delta x).$">|; 

$key = q/displaystyleleft[hat{omega}^{,2}-(1+alpha)right]^{,2}-alpha^{,2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img759.png"
 ALT="$\displaystyle \left[\hat{\omega}^{ 2}-(1+\alpha)\right]^{ 2}-\alpha^{ 2} = 0,$">|; 

$key = q/displaystyleleft[hat{x}left(omega_0^{,2}-omega^{,2}right)cosvarphi+hat{x},nu,omega,sinvarphi-omega_0^{,2},hat{X}right]cos(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img526.png"
 ALT="$\displaystyle \left[\hat{x}\left(\omega_0^{ 2}-\omega^{ 2}\right)\cos\varphi + \hat{x} \nu \omega \sin\varphi -\omega_0^{ 2} \hat{X}\right]\cos(\omega t)$">|; 

$key = q/displaystylelim_{xrightarrow0}frac{sinx}{x}=lim_{xrightarrow0}frac{d(sinx)slashdx}{dxslashdx}=lim_{xrightarrow0}frac{cosx}{1}=1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1033.png"
 ALT="$\displaystyle \lim_{x\rightarrow 0} \frac{\sin x}{x} = \lim_{x\rightarrow 0} \frac{d(\sin x)/dx}{dx/dx}
= \lim_{x\rightarrow 0} \frac{\cos x}{1} = 1.$">|; 

$key = q/displaystyleln(1+x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4315.png"
 ALT="$\displaystyle \ln(1+x)$">|; 

$key = q/displaystylelog_{10}[tau({rmyr})]=-C_1-C_2,Z_1^{,2slash3}+C_3,frac{Z_1}{sqrt{E({rmMeV})}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4122.png"
 ALT="$\displaystyle \log_{10}[\tau ({\rm yr})] = -C_1 - C_2 Z_1^{ 2/3} + C_3 \frac{Z_1}{\sqrt{E({\rm MeV})}},$">|; 

$key = q/displaystylem,ddot{x}=-k,x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle m \ddot{x} = - k x,$">|; 

$key = q/displaystylem,ddot{x}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img658.png"
 ALT="$\displaystyle m \ddot{x}_1$">|; 

$key = q/displaystylem,ddot{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img660.png"
 ALT="$\displaystyle m \ddot{x}_2$">|; 

$key = q/displaystylem,ddot{x}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img787.png"
 ALT="$\displaystyle m \ddot{x}_3$">|; 

$key = q/displaystylem,ddot{x}_i=-T_i,costheta_i+T_{i+1},costheta_{i+1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img903.png"
 ALT="$\displaystyle m \ddot{x}_i=-T_i \cos\theta_i +T_{i+1} \cos\theta_{i+1},$">|; 

$key = q/displaystylem,ddot{y}_i=-T,sintheta_i+T,sintheta_{i+1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img893.png"
 ALT="$\displaystyle m \ddot{y}_i = -T \sin\theta_i + T \sin\theta_{i+1}.$">|; 

$key = q/displaystylem,frac{d^{,2}x}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4471.png"
 ALT="$\displaystyle m \frac{d^{ 2}x}{dt^{ 2}}$">|; 

$key = q/displaystylem,frac{d^{,2}x}{dt^{,2}}=q,E_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2585.png"
 ALT="$\displaystyle m \frac{d^{ 2} x}{dt^{ 2}} = q E_x,$">|; 

$key = q/displaystylem,frac{d^{,2}y}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4473.png"
 ALT="$\displaystyle m \frac{d^{ 2}y}{dt^{ 2}}$">|; 

$key = q/displaystylem,frac{d^{,2}z}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4475.png"
 ALT="$\displaystyle m \frac{d^{ 2}z}{dt^{ 2}}$">|; 

$key = q/displaystylem_1,skew{3}ddot{theta}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img840.png"
 ALT="$\displaystyle m_1 \skew{3}\ddot{\theta}_1$">|; 

$key = q/displaystylem_2,skew{3}ddot{theta}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img842.png"
 ALT="$\displaystyle m_2 \skew{3}\ddot{\theta}_2$">|; 

$key = q/displaystylem_e,frac{d^{,2}x_e}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2711.png"
 ALT="$\displaystyle m_e \frac{d^{ 2}x_e}{dt^{ 2}}$">|; 

$key = q/displaystylem_e,frac{d^{,2}x}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2640.png"
 ALT="$\displaystyle m_e \frac{d^{ 2}x}{dt^{ 2}}$">|; 

$key = q/displaystylem_e,frac{d^{,2}y_e}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2713.png"
 ALT="$\displaystyle m_e \frac{d^{ 2} y_e}{dt^{ 2}}$">|; 

$key = q/displaystylem_e,frac{d^{,2}y}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2642.png"
 ALT="$\displaystyle m_e \frac{d^{ 2} y}{dt^{ 2}}$">|; 

$key = q/displaystylem_e,frac{d^{,2}z_e}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2715.png"
 ALT="$\displaystyle m_e \frac{d^{ 2} z_e}{dt^{ 2}}$">|; 

$key = q/displaystylem_i,frac{d^{,2}x_i}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2704.png"
 ALT="$\displaystyle m_i \frac{d^{ 2}x_i}{dt^{ 2}}$">|; 

$key = q/displaystylem_i,frac{d^{,2}y_i}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2706.png"
 ALT="$\displaystyle m_i \frac{d^{ 2} y_i}{dt^{ 2}}$">|; 

$key = q/displaystylem_i,frac{d^{,2}z_i}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2708.png"
 ALT="$\displaystyle m_i \frac{d^{ 2} z_i}{dt^{ 2}}$">|; 

$key = q/displaystylembox{hspace{0.5cm}ashspace{0.5cm}{|x|rightarrowinfty{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3957.png"
 ALT="$\displaystyle \mbox{\hspace{0.5cm}as\hspace{0.5cm}$\vert x\vert\rightarrow\infty$}$">|; 

$key = q/displaystylembox{hspace{0.5cm}{0leqtslashtauleq1{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1270.png"
 ALT="$\displaystyle \mbox{\hspace{0.5cm}$0\leq t/\tau \leq 1$}$">|; 

$key = q/displaystylemu_0,omega,hat{H}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2801.png"
 ALT="$\displaystyle \mu_0 \omega \hat{H}_x$">|; 

$key = q/displaystylemu_0,omega,hat{H}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2803.png"
 ALT="$\displaystyle \mu_0 \omega \hat{H}_y$">|; 

$key = q/displaystylemu_0,omega,hat{H}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2805.png"
 ALT="$\displaystyle \mu_0 \omega \hat{H}_z$">|; 

$key = q/displaystylen(z)=frac{(k_x^{,2}+k_z^{,2})^{1slash2},c}{omega}=left(1-frac{omega_{p,e}^{,2}}{omega^{,2}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2974.png"
 ALT="$\displaystyle n(z) = \frac{(k_x^{ 2}+k_z^{ 2})^{1/2} c}{\omega} = \left(1-\frac{\omega_{p e}^{ 2}}{\omega^{ 2}}\right)^{1/2},$">|; 

$key = q/displaystylen=frac{c,k}{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2818.png"
 ALT="$\displaystyle n = \frac{c k}{\omega}$">|; 

$key = q/displaystylen=frac{k,c}{omega}=left(1-frac{omega_{p,e}^{,2}}{omega^{,2}}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2603.png"
 ALT="$\displaystyle n = \frac{k c}{\omega} = \left(1-\frac{\omega_{p e}^{ 2}}{\omega^{ 2}}\right)^{1/2}$">|; 

$key = q/displaystylen=sqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.48ex; " SRC="|."$dir".q|img1655.png"
 ALT="$\displaystyle n = \sqrt{\epsilon}$">|; 

$key = q/displaystylen^{,2},cos^2theta=1+frac{omega_{p,i}^{,2}}{{mitOmega}_i^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2833.png"
 ALT="$\displaystyle n^{ 2} \cos^2\theta = 1 + \frac{\omega_{p i}^{ 2}}{{\mit\Omega}_i^{ 2}},$">|; 

$key = q/displaystylen^{,2}=1+frac{omega_{p,i}^{,2}}{{mitOmega}_i^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2834.png"
 ALT="$\displaystyle n^{ 2} = 1 + \frac{\omega_{p i}^{ 2}}{{\mit\Omega}_i^{ 2}}.$">|; 

$key = q/displaystylen^{,2}=Lsimeq1-frac{omega_{p,e}^{,2}}{(omega+{mitOmega}_e),(omega-{mitOmega}_i)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2851.png"
 ALT="$\displaystyle n^{ 2} = L\simeq 1 - \frac{\omega_{p e}^{ 2}}{(\omega+{\mit\Omega}_e) 
(\omega-{\mit\Omega}_i)},$">|; 

$key = q/displaystylen^{,2}=Rsimeq1-frac{omega_{p,e}^{,2}}{(omega-{mitOmega}_e),(omega+{mitOmega}_i)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2849.png"
 ALT="$\displaystyle n^{ 2} = R \simeq 1 - \frac{\omega_{p e}^{ 2}}{(\omega-{\mit\Omega}_e)
 (\omega+{\mit\Omega}_i)},$">|; 

$key = q/displaystylen^{,2}=frac{BpmF}{2,A},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3191.png"
 ALT="$\displaystyle n^{ 2} = \frac{B\pm F}{2 A},
$">|; 

$key = q/displaystylen^{,2}=frac{R,L}{S},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2876.png"
 ALT="$\displaystyle n^{ 2} = \frac{R L}{S},$">|; 

$key = q/displaystylen^{,2}=frac{k^{,2},c^{,2}}{omega^{,2}}simeqfrac{omega_{p,e}^{,2}}{omega,{mitOmega}_e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2866.png"
 ALT="$\displaystyle n^{ 2} = \frac{k^{ 2} c^{ 2}}{\omega^{ 2}}\simeq \frac{\omega_{p e}^{ 2}}
{\omega {\mit\Omega}_e}.$">|; 

$key = q/displaystylen_1,(E_i-E_r)=n_2,E_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1680.png"
 ALT="$\displaystyle n_1 (E_i-E_r) = n_2 E_t,$">|; 

$key = q/displaystylen_1,sintheta_i=n_2,sintheta_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1958.png"
 ALT="$\displaystyle n_1 \sin\theta_i = n_2 \sin\theta_t.$">|; 

$key = q/displaystylen_L=frac{k_L,c}{omega}=left[1-frac{omega_{p,e}^{,2}}{omega,(omega+{mitOmega}_e)}right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2671.png"
 ALT="$\displaystyle n_L = \frac{k_L c}{\omega} = \left[1-\frac{\omega_{p e}^{ 2}}{\omega (\omega+{\mit\Omega}_e)}\right]^{1/2},$">|; 

$key = q/displaystylen_R=frac{k_R,c}{omega}=left[1-frac{omega_{p,e}^{,2}}{omega,(omega-{mitOmega}_e)}right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2666.png"
 ALT="$\displaystyle n_R = \frac{k_R c}{\omega} = \left[1-\frac{\omega_{p e}^{ 2}}{\omega (\omega-{\mit\Omega}_e)}\right]^{1/2},$">|; 

$key = q/displaystylenabla^{,2}equivfrac{partial^{,2}}{partialx^{,2}}+frac{partial^{,2}}{partialy^{,2}}+frac{partial^{,2}}{partialz^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4139.png"
 ALT="$\displaystyle \nabla^{ 2} \equiv \frac{\partial^{ 2}}{\partial x^{ 2}} + \frac{\partial^{ 2} }{\partial y^{ 2}} + \frac{\partial^{ 2}}{\partial z^{ 2}}$">|; 

$key = q/displaystylenu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img498.png"
 ALT="$\displaystyle \nu$">|; 

$key = q/displaystylenusimeq2times10^{28},,{rmyr}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4112.png"
 ALT="$\displaystyle \nu\simeq 2\times 10^{28}  {\rm yr}^{-1}$">|; 

$key = q/displaystyleointcos(v,z,costheta),frac{dtheta}{2pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3683.png"
 ALT="$\displaystyle \oint \cos(v z \cos\theta) \frac{d\theta}{2\pi}$">|; 

$key = q/displaystyleointsin(v,z,costheta),frac{dtheta}{2pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3685.png"
 ALT="$\displaystyle \oint \sin(v z \cos\theta) \frac{d\theta}{2\pi}$">|; 

$key = q/displaystyleomega'=omega-k,u_o.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1699.png"
 ALT="$\displaystyle \omega' = \omega - k  u_o.$">|; 

$key = q/displaystyleomega,t+k,x-phi=n,2pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1389.png"
 ALT="$\displaystyle \omega t+k x-\phi = n 2\pi,$">|; 

$key = q/displaystyleomega,t-k,x-phi=n,2pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1343.png"
 ALT="$\displaystyle \omega t-k x-\phi = n 2\pi,$">|; 

$key = q/displaystyleomega,t-k,x=j,2pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1827.png"
 ALT="$\displaystyle \omega t -k x = j 2\pi,$">|; 

$key = q/displaystyleomega,t-k,xsimeqomega_0,t-k_0,x+(k-k_0),(v_g,t-x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2557.png"
 ALT="$\displaystyle \omega t-k x\simeq \omega_0 t-k_0 x+ (k-k_0) (v_g t-x),$">|; 

$key = q/displaystyleomega,t-{bfk}cdot{bfr}=j,2pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1839.png"
 ALT="$\displaystyle \omega t-{\bf k}\cdot{\bf r} = j 2\pi,$">|; 

$key = q/displaystyleomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1724.png"
 ALT="$\displaystyle \omega$">|; 

$key = q/displaystyleomega=2,omega_0,sin(k,aslash2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img920.png"
 ALT="$\displaystyle \omega = 2 \omega_0 \sin(k a/2),$">|; 

$key = q/displaystyleomega=2,omega_0,sin(k,aslash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1142.png"
 ALT="$\displaystyle \omega = 2 \omega_0 \sin(k a/2).$">|; 

$key = q/displaystyleomega=frac{1}{sqrt{L,C}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle \omega = \frac{1}{\sqrt{L C}}.$">|; 

$key = q/displaystyleomega=frac{2pi}{tau}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1259.png"
 ALT="$\displaystyle \omega=\frac{2\pi}{\tau}.$">|; 

$key = q/displaystyleomega=frac{hbar}{2,m},k^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3837.png"
 ALT="$\displaystyle \omega = \frac{\hbar}{2 m} k^{ 2}.$">|; 

$key = q/displaystyleomega=frac{k,V_A,costheta}{sqrt{1+V_A^{,2}slashc^{,2}}}simeqk,V_A,costheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.08ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img2838.png"
 ALT="$\displaystyle \omega = \frac{k V_A \cos\theta}{\sqrt{1+V_A^{ 2}/c^{ 2}}}\simeq k V_A \cos\theta,$">|; 

$key = q/displaystyleomega=frac{k,V_A}{sqrt{1+V_A^{,2}slashc^{,2}}}simeqk,V_A,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.08ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img2839.png"
 ALT="$\displaystyle \omega = \frac{k V_A}{\sqrt{1+V_A^{ 2}/c^{ 2}}}\simeq k V_A,$">|; 

$key = q/displaystyleomega=k(x),v(x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1721.png"
 ALT="$\displaystyle \omega= k(x) v(x).$">|; 

$key = q/displaystyleomega=k,c.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1624.png"
 ALT="$\displaystyle \omega=k c.$">|; 

$key = q/displaystyleomega=k,sqrt{g,d}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img3054.png"
 ALT="$\displaystyle \omega = k \sqrt{g d}.$">|; 

$key = q/displaystyleomega=k,v,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2544.png"
 ALT="$\displaystyle \omega = k v,$">|; 

$key = q/displaystyleomega=k,v.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img986.png"
 ALT="$\displaystyle \omega = k v.$">|; 

$key = q/displaystyleomega=k,v;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2399.png"
 ALT="$\displaystyle \omega = k v;$">|; 

$key = q/displaystyleomega=left(k_x^{,2},c^{,2}+k_z^{,2},c^{,2}+omega_{p,e}^{,2}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2970.png"
 ALT="$\displaystyle \omega = \left(k_x^{ 2} c^{ 2}+k_z^{ 2} c^{ 2}+\omega_{p e}^{ 2}\right)^{1/2},$">|; 

$key = q/displaystyleomega=omega(k).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2543.png"
 ALT="$\displaystyle \omega = \omega(k).$">|; 

$key = q/displaystyleomega=sqrt{frac{2}{3},frac{m}{M},frac{g}{a}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img388.png"
 ALT="$\displaystyle \omega =\sqrt{\frac{2}{3} \frac{m}{M} \frac{g}{a}}.
$">|; 

$key = q/displaystyleomega=sqrt{frac{M,g,d}{I}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.79ex; " SRC="|."$dir".q|img354.png"
 ALT="$\displaystyle \omega = \sqrt{\frac{M g d}{I}}.$">|; 

$key = q/displaystyleomega=sqrt{frac{g}{L}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle \omega = \sqrt{\frac{g}{L}},$">|; 

$key = q/displaystyleomega=sqrt{frac{g}{l}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.06ex; " SRC="|."$dir".q|img340.png"
 ALT="$\displaystyle \omega = \sqrt{\frac{g}{l}}.$">|; 

$key = q/displaystyleomega=sqrt{frac{k}{M+mslash3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img372.png"
 ALT="$\displaystyle \omega=\sqrt{\frac{k}{M+m/3}}.
$">|; 

$key = q/displaystyleomega=sqrt{frac{k}{m}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle \omega = \sqrt{\frac{k}{m}}.$">|; 

$key = q/displaystyleomega=sqrt{g,k+frac{T}{rho},k^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img2549.png"
 ALT="$\displaystyle \omega = \sqrt{g k+ \frac{T}{\rho} k^{ 3}},$">|; 

$key = q/displaystyleomega=sqrt{g,k+frac{T}{rho},k^{,3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img3164.png"
 ALT="$\displaystyle \omega = \sqrt{g k + \frac{T}{\rho} k^{ 3}}.$">|; 

$key = q/displaystyleomega=sqrt{k,g}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img3058.png"
 ALT="$\displaystyle \omega = \sqrt{k g}.$">|; 

$key = q/displaystyleomega=sqrt{k^{,2},c^{,2}+omega_{p,e}^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.47ex; " SRC="|."$dir".q|img2547.png"
 ALT="$\displaystyle \omega = \sqrt{k^{ 2} c^{ 2} + \omega_{p e}^{ 2}},$">|; 

$key = q/displaystyleomega=|{bfk}|,v.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2291.png"
 ALT="$\displaystyle \omega = \vert{\bf k}\vert v.
$">|; 

$key = q/displaystyleomega^{,2},Zleft[A_+,sin(omega,t-k,x-phi_+)+A_-,sin(omega,t+k,x-phi_-)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img1454.png"
 ALT="$\displaystyle \omega^{ 2} Z\left[A_+ \sin(\omega t-k x-\phi_+)+A_- \sin(\omega t+k x-\phi_-)\right]$">|; 

$key = q/displaystyleomega^{,2},Zleft[A_+^{,2},sin^2(omega,t-k,x-phi_+)-A_-^{,2},sin^2(omega,t+k,x-phi_-)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1456.png"
 ALT="$\displaystyle \omega^{ 2} Z\left[A_+^{ 2} \sin^2(\omega t-k x-\phi_+) - A_-^{ 2} \sin^2(\omega t+k x-\phi_-)\right].$">|; 

$key = q/displaystyleomega^{,2}-{mitOmega}_e,omega-omega_{p,e}^{,2}simeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2861.png"
 ALT="$\displaystyle \omega^{ 2}-{\mit\Omega}_e \omega- \omega_{p e}^{ 2}\simeq 0,$">|; 

$key = q/displaystyleomega^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1885.png"
 ALT="$\displaystyle \omega^{ 2}$">|; 

$key = q/displaystyleomega^{,2}=frac{g}{l}+frac{4,K}{m},sin^2(k,aslash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1309.png"
 ALT="$\displaystyle \omega^{ 2}= \frac{g}{l} + \frac{4 K}{m} \sin^2(k a/2).
$">|; 

$key = q/displaystyleomega^{,2}=g,k,tanh(k,d).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3046.png"
 ALT="$\displaystyle \omega^{ 2} = g k \tanh(k d).$">|; 

$key = q/displaystyleomega^{,2}=k^{,2},c^{,2}+omega_0^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img2938.png"
 ALT="$\displaystyle \omega^{ 2} = k^{ 2} c^{ 2}+\omega_0^{ 2},$">|; 

$key = q/displaystyleomega^{,2}=k^{,2},c^{,2}+omega_{m,n}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.85ex; " SRC="|."$dir".q|img3213.png"
 ALT="$\displaystyle \omega^{ 2} = k^{ 2} c^{ 2} + \omega_{m,n}^{ 2},
$">|; 

$key = q/displaystyleomega^{,2}=k^{,2},c^{,2}+omega_{p,e}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2600.png"
 ALT="$\displaystyle \omega^{ 2} = k^{ 2} c^{ 2}+\omega_{p e}^{ 2},$">|; 

$key = q/displaystyleomega^{,2}=k^{,2},c^{,2}pmomega_0^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img3179.png"
 ALT="$\displaystyle \omega^{ 2} = k^{ 2} c^{ 2}\pm\omega_0^{ 2},
$">|; 

$key = q/displaystyleomega^{,2}=k_L^{,2},c^{,2}+frac{omega,omega_{p,e}^{,2}}{omega+{mitOmega}_e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2670.png"
 ALT="$\displaystyle \omega^{ 2} = k_L^{ 2} c^{ 2} + \frac{\omega \omega_{p e}^{ 2}}{\omega+{\mit\Omega}_e}.$">|; 

$key = q/displaystyleomega^{,2}=k_R^{,2},c^{,2}+frac{omega,omega_{p,e}^{,2}}{omega-{mitOmega}_e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2665.png"
 ALT="$\displaystyle \omega^{ 2} = k_R^{ 2} c^{ 2} + \frac{\omega \omega_{p e}^{ 2}}{\omega-{\mit\Omega}_e},$">|; 

$key = q/displaystyleomega^{,2}=left(g,k+frac{T}{rho},k^{,3}right)tanh(k,d);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3247.png"
 ALT="$\displaystyle \omega^{ 2} = \left(g k + \frac{T}{\rho} k^{ 3}\right)\tanh(k d)
$">|; 

$key = q/displaystyleomega^{,2}=omega_{p,e}^{,2}+k^{,2},c^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2873.png"
 ALT="$\displaystyle \omega^{ 2} =\omega_{p e}^{ 2} +k^{ 2} c^{ 2},$">|; 

$key = q/displaystyleomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img496.png"
 ALT="$\displaystyle \omega_0$">|; 

$key = q/displaystyleomega_0=frac{pi,c}{a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2939.png"
 ALT="$\displaystyle \omega_0 = \frac{\pi c}{a}.$">|; 

$key = q/displaystyleomega_1=left(omega_0^{,2}-nu^{,2}slash4right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img441.png"
 ALT="$\displaystyle \omega_1 =\left(\omega_0^{ 2}-\nu^{ 2}/4\right)^{1/2}.$">|; 

$key = q/displaystyleomega_1simeq{mitOmega}_eslash2+sqrt{{mitOmega}_e^{,2}slash4+omega_{p,e}^{,2}}>{mitOmega}_e.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.47ex; " SRC="|."$dir".q|img2863.png"
 ALT="$\displaystyle \omega_1 \simeq {\mit\Omega}_e/2 + \sqrt{{\mit\Omega}_e^{ 2}/4
+\omega_{p e}^{ 2}}&gt;{\mit\Omega}_e.$">|; 

$key = q/displaystyleomega_2simeq-{mitOmega}_eslash2+sqrt{{mitOmega}_e^{,2}slash4+omega_{p,e}^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.47ex; " SRC="|."$dir".q|img2869.png"
 ALT="$\displaystyle \omega_2 \simeq -{\mit\Omega}_e/2 +
\sqrt{{\mit\Omega}_e^{ 2}/4 + \omega_{p e}^{ 2}}.$">|; 

$key = q/displaystyleomega_j=j,pi,frac{v}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2310.png"
 ALT="$\displaystyle \omega_j = j \pi \frac{v}{a},
$">|; 

$key = q/displaystyleomega_j=z_j,frac{v}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1919.png"
 ALT="$\displaystyle \omega_j = z_j \frac{v}{a},$">|; 

$key = q/displaystyleomega_n=(n-1slash2),frac{pi,v}{l}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1187.png"
 ALT="$\displaystyle \omega_n = (n-1/2) \frac{\pi v}{l}.$">|; 

$key = q/displaystyleomega_n=2,omega_0,sinleft(frac{n-1slash2}{N+1slash2},frac{pi}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1144.png"
 ALT="$\displaystyle \omega_n = 2 \omega_0 \sin\left(\frac{n-1/2}{N+1/2} \frac{\pi}{2}\right),$">|; 

$key = q/displaystyleomega_n=2,omega_0,sinleft(frac{n}{N+1},frac{pi}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img927.png"
 ALT="$\displaystyle \omega_n = 2 \omega_0 \sin\left(\frac{n}{N+1} \frac{\pi}{2}\right).$">|; 

$key = q/displaystyleomega_n=2,omega_0,sinleft(frac{n}{N},frac{pi}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1073.png"
 ALT="$\displaystyle \omega_n = 2 \omega_0 \sin\left(\frac{n}{N} \frac{\pi}{2}\right),
$">|; 

$key = q/displaystyleomega_n=frac{n,pi}{N+1},omega_0=frac{n,pi}{N+1}left(frac{T}{m,a}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1009.png"
 ALT="$\displaystyle \omega_n = \frac{n \pi}{N+1} \omega_0= \frac{n \pi}{N+1}\left(\frac{T}{m a}\right)^{1/2}.$">|; 

$key = q/displaystyleomega_n=frac{n,pi}{l}left(frac{T}{rho}right)^{1slash2}=n,frac{pi,v}{l},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1011.png"
 ALT="$\displaystyle \omega_n = \frac{n \pi}{l}\left(\frac{T}{\rho}\right)^{1/2} =n  \frac{\pi v}{l},$">|; 

$key = q/displaystyleomega_n=n,frac{pi,v}{l}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img993.png"
 ALT="$\displaystyle \omega_n = n \frac{\pi v}{l}.$">|; 

$key = q/displaystyleomega_nsimeq(k,a),omega_0=left(frac{n}{N+1}right)pi,omega_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img960.png"
 ALT="$\displaystyle \omega_n \simeq (k a) \omega_0 = \left(\frac{n}{N+1}\right)\pi \omega_0.$">|; 

$key = q/displaystyleomega_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img933.png"
 ALT="$\displaystyle \omega_{-n}$">|; 

$key = q/displaystyleomega_{N+1+n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img939.png"
 ALT="$\displaystyle \omega_{N+1+n}$">|; 

$key = q/displaystyleomega_{m,n}=left[g,k_{m,n},tanh(k_{m,n},d)right]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img3245.png"
 ALT="$\displaystyle \omega_{m,n}=\left[g k_{m,n} \tanh(k_{m,n} d)\right]^{1/2}
$">|; 

$key = q/displaystyleomega_{m,n}=pi,cleft(frac{m^{,2}}{a^{,2}}+frac{n^{,2}}{b^{,2}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3214.png"
 ALT="$\displaystyle \omega_{m,n} = \pi c\left(\frac{m^{ 2}}{a^{ 2}}+\frac{n^{ 2}}{b^{ 2}}\right)^{1/2},
$">|; 

$key = q/displaystyleomega_{m,n}=pileft(frac{m^{,2}}{a^{,2}}+frac{n^{,2}}{b^{,2}}right)^{1slash2}v.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1901.png"
 ALT="$\displaystyle \omega_{m,n} = \pi\left(\frac{m^{ 2}}{a^{ 2}}+ \frac{n^{ 2}}{b^{ 2}}\right)^{1/2}v.$">|; 

$key = q/displaystyleomega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2753.png"
 ALT="$\displaystyle \omega_{p e}$">|; 

$key = q/displaystyleomega_{p,e}=left(frac{n_e,e^{,2}}{epsilon_0,m_e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2601.png"
 ALT="$\displaystyle \omega_{p e} = \left(\frac{n_e e^{ 2}}{\epsilon_0 m_e}\right)^{1/2},$">|; 

$key = q/displaystyleomega_{p,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2755.png"
 ALT="$\displaystyle \omega_{p i}$">|; 

$key = q/displaystyleomega_{rmLH}<omega_2<omega_{rmUH}<omega_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2889.png"
 ALT="$\displaystyle \omega_{\rm LH} &lt; \omega_2 &lt; \omega_{\rm UH} &lt; \omega_1,$">|; 

$key = q/displaystyleomega_{rmUH}=sqrt{omega_{p,e}^{,2}+{mitOmega}_e^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.47ex; " SRC="|."$dir".q|img2882.png"
 ALT="$\displaystyle \omega_{\rm UH} = \sqrt{\omega_{p e}^{ 2} + {\mit\Omega}_e^{ 2}}.$">|; 

$key = q/displaystyleomegasimeqk,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1151.png"
 ALT="$\displaystyle \omega\simeq k v$">|; 

$key = q/displaystyleomegasimeqomega(k_0)+(k-k_0),frac{domega(k_0)}{dk}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2556.png"
 ALT="$\displaystyle \omega \simeq \omega(k_0) + (k-k_0) \frac{d\omega(k_0)}{dk}.$">|; 

$key = q/displaystyleoverline{E}=E_Fleft.int_0^{l_F}l^{,2},4pi,l^{,2},dlrightslashfrac{4}{3},pi,l_F^{,5}=frac{3}{5},E_F,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4177.png"
 ALT="$\displaystyle \overline{E} = E_F\left.\int_0^{l_F}l^{ 2} 4\pi l^{ 2} dl\right/\frac{4}{3} \pi l_F^{ 5}=
\frac{3}{5} E_F,$">|; 

$key = q/displaystylep,V=frac{m}{M},R,T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1380.png"
 ALT="$\displaystyle p V = \frac{m}{M} R T,$">|; 

$key = q/displaystylep,V^{,gamma}={rmconstant},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1217.png"
 ALT="$\displaystyle p V^{ \gamma} = {\rm constant},$">|; 

$key = q/displaystylep=hbar,k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3793.png"
 ALT="$\displaystyle p = \hbar k$">|; 

$key = q/displaystylep=p_0-rho,g,z+p_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3017.png"
 ALT="$\displaystyle p = p_0-\rho g z+p_1,$">|; 

$key = q/displaystylep_0=p_0-rho,g,zeta(x,t)+p_1(x,0,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3036.png"
 ALT="$\displaystyle p_0 = p_0 -\rho g \zeta(x,t) + p_1(x,0,t).$">|; 

$key = q/displaystylep_1=-rho,frac{partialphi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3030.png"
 ALT="$\displaystyle p_1 = -\rho \frac{\partial \phi}{\partial t}.$">|; 

$key = q/displaystylephi(x,t)=omegaleft(t-int^xleft[v(x')right]^{-1},dx'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1728.png"
 ALT="$\displaystyle \phi(x,t) = \omega\left(t-\int^x\left[v(x')\right]^{-1} dx'\right).$">|; 

$key = q/displaystylephi(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2263.png"
 ALT="$\displaystyle \phi(x,z,t)$">|; 

$key = q/displaystylephi(x,z,t)=A,{rme}^{,k,z},cos(omega,t-k,x)+B,{rme}^{-k,z},cos(omega,t-k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3042.png"
 ALT="$\displaystyle \phi(x,z,t) = A {\rm e}^{ k z} \cos(\omega t-k x) + B {\rm e}^{-k z} \cos(\omega t-k x),$">|; 

$key = q/displaystylephi(x,z,t)=Aleft[{rme}^{,k,z}+{rme}^{-k,(z+2,d)}right]cos(omega,t-k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3044.png"
 ALT="$\displaystyle \phi(x,z,t) = A\left[{\rm e}^{ k z} + {\rm e}^{-k (z+2 d)}\right]\cos(\omega t-k x),$">|; 

$key = q/displaystylephi(x,z,t)=F(z),cos(omega,t-k,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3038.png"
 ALT="$\displaystyle \phi(x,z,t) = F(z) \cos(\omega t-k x).$">|; 

$key = q/displaystylephi(x,z,t)=phi_t,cos[omega,(t-sintheta_t,xslashv_2-costheta_t,zslashv_2)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2266.png"
 ALT="$\displaystyle \phi(x,z,t) = \phi_t \cos[\omega (t-\sin\theta_t x/v_2-\cos\theta_t z/v_2)],$">|; 

$key = q/displaystylephi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img463.png"
 ALT="$\displaystyle \phi$">|; 

$key = q/displaystylephi=tan^{-1}!left(frac{v_0}{omega,x_0}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle \phi =\tan^{-1}\!\left(\frac{v_0}{\omega x_0}\right),$">|; 

$key = q/displaystylephi_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1051.png"
 ALT="$\displaystyle \phi_n$">|; 

$key = q/displaystylephi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2276.png"
 ALT="$\displaystyle \phi_r$">|; 

$key = q/displaystylephi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2278.png"
 ALT="$\displaystyle \phi_t$">|; 

$key = q/displaystylephi_{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img2301.png"
 ALT="$\displaystyle \phi_{m,n}$">|; 

$key = q/displaystylephisimeqphi_0+x,frac{partialphi}{partialx}+z,frac{partialphi}{partialz}+t,frac{partialphi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2945.png"
 ALT="$\displaystyle \phi\simeq \phi_0 + x \frac{\partial \phi}{\partial x} + z \frac{\partial\phi}{\partial z} + t \frac{\partial\phi}{\partial t}.$">|; 

$key = q/displaystylepropto;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.89ex; vertical-align: 0.04ex; " SRC="|."$dir".q|img3503.png"
 ALT="$\displaystyle \propto$">|; 

$key = q/displaystyleproptocos(omega,t-k,R-phi),cosleft[frac{1}{2},k,d,(sintheta-sintheta_0)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3305.png"
 ALT="$\displaystyle \propto \cos(\omega t-k R-\phi) \cos
\left[\frac{1}{2} k d (\sin\theta-\sin\theta_0)\right].$">|; 

$key = q/displaystyleproptocos(omega,t-k,R-phi_A),cosleft[frac{1}{2},k,d,(theta-theta_0slash2)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3332.png"
 ALT="$\displaystyle \propto \cos(\omega t-k R-\phi_A) \cos\left[\frac{1}{2} k d (\theta-\theta_0/2)\right]$">|; 

$key = q/displaystyleproptocos^2left[frac{1}{2},k,d,(theta-theta_0slash2)right]+cos^2left[frac{1}{2},k,d,(theta+theta_0slash2)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3342.png"
 ALT="$\displaystyle \propto\cos^2\left[\frac{1}{2} k d (\theta-\theta_0/2)\right]+ \cos^2\left[\frac{1}{2} k d (\theta+\theta_0/2)\right]$">|; 

$key = q/displaystyleproptocosleft[omega,t-k,R-frac{1}{2},(phi_1+phi_2)right]cosleft[frac{1}{2},k,d,sintheta-frac{1}{2},(phi_1-phi_2)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3304.png"
 ALT="$\displaystyle \propto \cos\left[\omega t-k R-\frac{1}{2} (\phi_1+\phi_2)\right]\cos
\left[\frac{1}{2} k d \sin\theta-\frac{1}{2} (\phi_1-\phi_2)\right]$">|; 

$key = q/displaystyleproptolangle,cos^2(omega,t-k,R-phi_A)ranglecos^2left[frac{1}{2},k,d,(theta-theta_0slash2)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3335.png"
 ALT="$\displaystyle \propto \langle \cos^2 (\omega t-k R-\phi_A)\rangle\cos^2\left[\frac{1}{2} k d (\theta-\theta_0/2)\right]$">|; 

$key = q/displaystylepsi(0)=psi(a)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3923.png"
 ALT="$\displaystyle \psi(0) = \psi(a) = 0.$">|; 

$key = q/displaystylepsi(0,y,z)=psi(x,0,z)=psi(x,y,0)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4152.png"
 ALT="$\displaystyle \psi(0,y,z) = \psi(x,0,z)=\psi(x,y,0) =0,$">|; 

$key = q/displaystylepsi(0,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2934.png"
 ALT="$\displaystyle \psi(0,z,t)$">|; 

$key = q/displaystylepsi(a,y,z)=psi(x,a,z)=psi(x,y,a)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4153.png"
 ALT="$\displaystyle \psi(a,y,z) = \psi(x,a,z)=\psi(x,y,a) =0,$">|; 

$key = q/displaystylepsi(a,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2935.png"
 ALT="$\displaystyle \psi(a,z,t)$">|; 

$key = q/displaystylepsi(r,t)=frac{F(v,t-r)}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2541.png"
 ALT="$\displaystyle \psi(r,t)= \frac{F(v t-r)}{r},
$">|; 

$key = q/displaystylepsi(r,t)=frac{psi_0}{r},cos(omega,t-k,r-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1863.png"
 ALT="$\displaystyle \psi(r,t) =\frac{ \psi_0}{r} \cos(\omega t-k r-\phi).$">|; 

$key = q/displaystylepsi(r,t)=frac{psi_0}{r},cos(omega,t-k,r-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2294.png"
 ALT="$\displaystyle \psi(r,t) =\frac{ \psi_0}{r} \cos(\omega t-k r-\phi)
$">|; 

$key = q/displaystylepsi(r,t)=sum_{j=1,infty}A_j,{rmsinc}left(j,pi,frac{r}{a}right),cos(omega_j,t-phi_j),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2308.png"
 ALT="$\displaystyle \psi(r,t)=\sum_{j=1,\infty} A_j {\rm sinc}\left(j \pi \frac{r}{a}\right) \cos(\omega_j t-\phi_j),
$">|; 

$key = q/displaystylepsi(r,theta,t)=frac{psi_0,K(theta),cos(omega,t-k,r-phi+pislash2)}{lambda,r},dS,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3542.png"
 ALT="$\displaystyle \psi(r,\theta,t) = \frac{\psi_0 K(\theta) \cos(\omega t-k r-\phi+\pi/2)}{\lambda r} dS,$">|; 

$key = q/displaystylepsi(rho,t)=hat{psi}(rho),cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1909.png"
 ALT="$\displaystyle \psi(\rho,t) = \hat{\psi}(\rho) \cos(\omega t-\phi).$">|; 

$key = q/displaystylepsi(rho,t)simeqfrac{psi_0}{rho^{1slash2}},cos(omega,t-k,rho-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1850.png"
 ALT="$\displaystyle \psi(\rho,t) \simeq \frac{\psi_0}{\rho^{1/2}} \cos(\omega t-k \rho-\phi)$">|; 

$key = q/displaystylepsi(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2462.png"
 ALT="$\displaystyle \psi(t)$">|; 

$key = q/displaystylepsi(t)=expleft(-frac{t^{,2}}{2,sigma_t^{,2}}right),cos(omega_0,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img2483.png"
 ALT="$\displaystyle \psi(t) = \exp\left(-\frac{t^{ 2}}{2 \sigma_t^{ 2}}\right) \cos(\omega_0 t).$">|; 

$key = q/displaystylepsi(theta,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3303.png"
 ALT="$\displaystyle \psi(\theta,t)$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega,t-k,R-phi),bar{F}(theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3425.png"
 ALT="$\displaystyle \psi(\theta,t) \propto \cos(\omega t-k R-\phi) \bar{F}(\theta),$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega,t-k,R-phi),cosleft(frac{1}{2},k,d,sinthetaright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3277.png"
 ALT="$\displaystyle \psi(\theta,t)\propto \cos(\omega t-k R-\phi) \cos\left(\frac{1}{2} k d \sin\theta\right).$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega,t-k,R-phi)sum_{n=1,N}cos(k,x_n,sintheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3372.png"
 ALT="$\displaystyle \psi(\theta,t)\propto \cos(\omega t-k R-\phi)\sum_{n=1,N} \cos(k x_n \sin\theta).$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega,t-k,R-phi)sum_{n=1,N}cos(k,x_n,sintheta)sin(omega,t-k,R-phi)sum_{n=1,N}sin(k,x_n,sintheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3371.png"
 ALT="$\displaystyle \psi(\theta,t)\propto \cos(\omega t-k R-\phi)\sum_{n=1,N} \cos(k x_n \sin\theta) \sin(\omega t-k R-\phi)\sum_{n=1,N}\sin(k x_n \sin\theta),$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega,t-k,R-phi)sum_{n=1,N}cos[k,x_n,(sintheta-sintheta_0)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3423.png"
 ALT="$\displaystyle \psi(\theta,t)\propto \cos(\omega t-k R-\phi)\sum_{n=1,N} \cos[k x_n (\sin\theta-\sin\theta_0)].$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega,t-k,rho_1-phi)+cos(omega,t-k,rho_2-phi)+{calO}left(frac{1}{k,R}right)+{calO}left(frac{d}{R}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3272.png"
 ALT="$\displaystyle \psi(\theta,t)\propto\cos(\omega t-k \rho_1-\phi)+ \cos(\omega\...
...2-\phi)+ {\cal O}\left(\frac{1}{k R}\right)+ {\cal O}\left(\frac{d}{R}\right),$">|; 

$key = q/displaystylepsi(theta,t)proptocos(omega-k,R-phi),cosleft[frac{1}{2},k,d,(theta-theta_0)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3307.png"
 ALT="$\displaystyle \psi(\theta,t)\propto \cos(\omega-k R-\phi) \cos
\left[\frac{1}{2} k d (\theta-\theta_0)\right],$">|; 

$key = q/displaystylepsi(theta,t)proptofrac{cos(omega,t-k,rho_1-phi_1)}{rho_1^{,1slash2}}+frac{cos(omega,t-k,rho_2-phi_2)}{rho_2^{,1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.68ex; " SRC="|."$dir".q|img3300.png"
 ALT="$\displaystyle \psi(\theta,t)\propto\frac{\cos(\omega t-k \rho_1-\phi_1)}{\rho_1^{ 1/2}}
+\frac{\cos(\omega t-k \rho_2-\phi_2)}{\rho_2^{ 1/2}},$">|; 

$key = q/displaystylepsi(theta,t)proptosum_{n=1,N}cos(omega,t-k,R-phi+k,x_n,sintheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3370.png"
 ALT="$\displaystyle \psi(\theta,t)\propto \sum_{n=1,N}\cos(\omega t - k R -\phi+k x_n \sin\theta),$">|; 

$key = q/displaystylepsi(theta_x,theta_y,t)propto;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3501.png"
 ALT="$\displaystyle \psi(\theta_x,\theta_y,t)\propto$">|; 

$key = q/displaystylepsi(theta_x,theta_y,t)proptoint_{-infty}^inftyint_{-infty}^inftyF(x,y),cos(omega,t-k,r-phi),dx,dy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3498.png"
 ALT="$\displaystyle \psi(\theta_x,\theta_y,t)\propto \int_{-\infty}^\infty\int_{-\infty}^\infty F(x,y)  \cos(\omega t-k r-\phi) dx dy.$">|; 

$key = q/displaystylepsi(u',v',t)+bar{psi}(u',v',t)=psi_0,cos(omega,t-k,R-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3611.png"
 ALT="$\displaystyle \psi(u',v',t)+\bar{\psi}(u',v',t) = \psi_0 \cos(\omega t-k R-\phi).$">|; 

$key = q/displaystylepsi(u',v',t)=psi_0,cos(omega,t-k,R-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3592.png"
 ALT="$\displaystyle \psi(u',v',t)= \psi_0 \cos(\omega t-k R-\phi).$">|; 

$key = q/displaystylepsi(u',v',t)simeq-psi_0,sin(omega,t-k,R-phi),f_c(u',v')+psi_0,cos(omega,t-k,R-phi),f_s(u',v'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3581.png"
 ALT="$\displaystyle \psi(u',v',t)\simeq -\psi_0 \sin(\omega t-k R-\phi) f_c(u',v') + \psi_0 \cos(\omega t-k R-\phi) f_s(u',v'),$">|; 

$key = q/displaystylepsi(x',t)=psi_0,cos,(omega',t-k,x'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1698.png"
 ALT="$\displaystyle \psi(x',t) = \psi_0 \cos (\omega' t-k x'),$">|; 

$key = q/displaystylepsi(x',y',t)=frac{psi_0}{lambda}int_{-infty}^inftyint_{-infty}^inftyf(x,y),K(theta),frac{cos(omega,t-k,r-phi+pislash2)}{r},dx,dy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3553.png"
 ALT="$\displaystyle \psi(x',y',t) = \frac{\psi_0}{\lambda} \int_{-\infty}^\infty\int_...
...}^\infty f(x,y) K(\theta) 
\frac{\cos(\omega t-k r-\phi+\pi/2)}{r} dx dy.$">|; 

$key = q/displaystylepsi(x)=A,{rme}^{,q,x}+B,{rme}^{-q,x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4038.png"
 ALT="$\displaystyle \psi(x) = A {\rm e}^{ q x} + B {\rm e}^{-q x}.$">|; 

$key = q/displaystylepsi(x)=A,{rme}^{,q,x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3961.png"
 ALT="$\displaystyle \psi(x) = A {\rm e}^{ q x},$">|; 

$key = q/displaystylepsi(x)=A,{rme}^{,{rmi},q,x}+B,{rme}^{-{rmi},q,x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4013.png"
 ALT="$\displaystyle \psi(x) = A {\rm e}^{ {\rm i} q x}+B {\rm e}^{-{\rm i} q x}.$">|; 

$key = q/displaystylepsi(x)=A,{rme}^{-q,x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3964.png"
 ALT="$\displaystyle \psi(x) = A {\rm e}^{- q x}.$">|; 

$key = q/displaystylepsi(x)=B,cos(k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3966.png"
 ALT="$\displaystyle \psi(x) = B \cos(k x),$">|; 

$key = q/displaystylepsi(x)=T,{rme}^{,{rmi},k,x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4008.png"
 ALT="$\displaystyle \psi(x) = T {\rm e}^{ {\rm i} k x}.$">|; 

$key = q/displaystylepsi(x)=psi_0,expleft(int_0^x{rmi},k(x'),dx'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4059.png"
 ALT="$\displaystyle \psi(x) = \psi_0 \exp\left(\int_0^x{\rm i} k(x') dx'\right),$">|; 

$key = q/displaystylepsi(x)=psi_0,sin(k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3925.png"
 ALT="$\displaystyle \psi(x) = \psi_0 \sin(k x),$">|; 

$key = q/displaystylepsi(x)=psi_1,expleft(-int_{x_1}^x|k(x')|,dx'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img4072.png"
 ALT="$\displaystyle \psi(x) = \psi_1 \exp\left(-\int_{x_1}^x \vert k(x')\vert dx'\right),$">|; 

$key = q/displaystylepsi(x)={rme}^{,{rmi},k,x}+R,{rme}^{-{rmi},k,x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4005.png"
 ALT="$\displaystyle \psi(x) = {\rm e}^{ {\rm i} k x} + R {\rm e}^{-{\rm i} k x}.$">|; 

$key = q/displaystylepsi(x,0)=int_{-infty}^{infty}bar{psi}(k),{rme}^{,{rmi},k,x},dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3879.png"
 ALT="$\displaystyle \psi(x,0) = \int_{-\infty}^{\infty} \bar{\psi}(k) {\rm e}^{ {\rm i} k x} dk.$">|; 

$key = q/displaystylepsi(x,0)=int_{-infty}^{infty}left[C_+(k)+C_-(k)right],cos(k,x),dk+int_{-infty}^{infty}left[-S_+(k)+S_-(k)right],sin(k,x),dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2413.png"
 ALT="$\displaystyle \psi(x,0) = \int_{-\infty}^{\infty}\left[C_+(k)+C_-(k)\right] \cos(k x) dk+ \int_{-\infty}^{\infty}\left[-S_+(k)+S_-(k)\right] \sin(k x) dk.$">|; 

$key = q/displaystylepsi(x,0)=sum_{n'=1,infty}A_{n'},cosphi_{n'},cosleft[(n'-1slash2),pi,frac{x}{l}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1193.png"
 ALT="$\displaystyle \psi(x,0) = \sum_{n'=1,\infty} A_{n'} \cos \phi_{n'} \cos\left[(n'-1/2) \pi \frac{x}{l}\right],$">|; 

$key = q/displaystylepsi(x,0)proptoexpleft[{rmi},k_0,x-frac{(x-x_0)^{,2}}{4,({mitDelta}x)^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3873.png"
 ALT="$\displaystyle \psi(x,0) \propto \exp\left[{\rm i} k_0 x - \frac{(x-x_0)^{ 2}}{4 ({\mit\Delta}x)^{ 2}}\right].$">|; 

$key = q/displaystylepsi(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2404.png"
 ALT="$\displaystyle \psi(x,t)$">|; 

$key = q/displaystylepsi(x,t)=(A_1+A_2),cos(k,x),cos(omega,t)+(A_1-A_2),sin(k,x),sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1402.png"
 ALT="$\displaystyle \psi(x,t)= (A_1+A_2) \cos(k x) \cos(\omega t) + (A_1-A_2) \sin(k x) \sin(\omega t).$">|; 

$key = q/displaystylepsi(x,t)=2,A,cos(k,x),cos(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1395.png"
 ALT="$\displaystyle \psi(x,t) = 2 A \cos(k x) \cos(\omega t),$">|; 

$key = q/displaystylepsi(x,t)=A(x),cos[phi(x,t)]=A(x),cosleft[omegaleft(t-int^xleft[v(x')right]^{-1},dx'right)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1729.png"
 ALT="$\displaystyle \psi(x,t) = A(x) \cos[\phi(x,t)]= A(x) \cos\left[ \omega\left(t-\int^x\left[v(x')\right]^{-1} dx'\right)\right],$">|; 

$key = q/displaystylepsi(x,t)=A,(1+R),cos(k,x),cos(omega,t)+A,(1-R),sin(k,x),sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1738.png"
 ALT="$\displaystyle \psi(x,t) = A (1+R) \cos(k x) \cos(\omega t) + A (1-R) \sin(k x) \sin(\omega t).
$">|; 

$key = q/displaystylepsi(x,t)=A,cos(k,x),cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1181.png"
 ALT="$\displaystyle \psi(x,t) = A \cos(k x) \cos(\omega t-\phi),$">|; 

$key = q/displaystylepsi(x,t)=A,cos(omega,t+k,x-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1388.png"
 ALT="$\displaystyle \psi(x,t) = A \cos(\omega t+k x-\phi),$">|; 

$key = q/displaystylepsi(x,t)=A,cos(omega,t-k,x)+A,R,cos(omega,t+k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1737.png"
 ALT="$\displaystyle \psi(x,t)= A \cos(\omega t-k x)+ A R \cos(\omega t+k x),
$">|; 

$key = q/displaystylepsi(x,t)=A,cos(omega,t-k,x)+A,cos(omega,t+k,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1393.png"
 ALT="$\displaystyle \psi(x,t) = A \cos(\omega t-k x) + A \cos(\omega t+k x).$">|; 

$key = q/displaystylepsi(x,t)=A,cos(omega,t-k,x-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1338.png"
 ALT="$\displaystyle \psi(x,t) = A \cos(\omega t-k x-\phi),$">|; 

$key = q/displaystylepsi(x,t)=A,cos(omega,t-k,x-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2398.png"
 ALT="$\displaystyle \psi(x,t) = A \cos(\omega t-k x-\phi)$">|; 

$key = q/displaystylepsi(x,t)=A,expleft[-a,(m,x^{,2}slashhbar+{rmi},t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4234.png"
 ALT="$\displaystyle \psi(x,t)= A \exp\left[-a (m x^{ 2}/\hbar+ {\rm i} t)\right],
$">|; 

$key = q/displaystylepsi(x,t)=A,sin(k,x),cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1236.png"
 ALT="$\displaystyle \psi(x,t) = A \sin(k x) \cos(\omega t-\phi),$">|; 

$key = q/displaystylepsi(x,t)=A_1,cos(omega,t-k,x)+A_2,cos(omega,t+k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1398.png"
 ALT="$\displaystyle \psi(x,t) = A_1 \cos(\omega t-k x) + A_2 \cos(\omega t+k x),$">|; 

$key = q/displaystylepsi(x,t)=C_+,cos[k,(v,t-x)]+S_+,sin[k,(v,t-x)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2400.png"
 ALT="$\displaystyle \psi(x,t) = C_+ \cos[k (v t-x)] + S_+ \sin[k (v t-x)],$">|; 

$key = q/displaystylepsi(x,t)=C_-,cos[k,(v,t+x)]+S_-,sin[k,(v,t+x)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2403.png"
 ALT="$\displaystyle \psi(x,t) = C_- \cos[k (v t+x)] + S_- \sin[k (v t+x)].$">|; 

$key = q/displaystylepsi(x,t)=F(v,t-x)+G(v,t+x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2431.png"
 ALT="$\displaystyle \psi(x,t) = F(v t-x)+ G(v t+x),$">|; 

$key = q/displaystylepsi(x,t)=[A,cos(k,x)+B,sin(k,x)],cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1332.png"
 ALT="$\displaystyle \psi(x,t) =[A \cos(k x)+B \sin(k x)] \cos(\omega t-\phi).$">|; 

$key = q/displaystylepsi(x,t)=bar{psi},{rme}^{-{rmi},(omega,t-k,x)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3862.png"
 ALT="$\displaystyle \psi(x,t) = \bar{\psi} {\rm e}^{-{\rm i} (\omega t-k x)},$">|; 

$key = q/displaystylepsi(x,t)=frac{1}{4pi}int_{-infty}^inftyfrac{sin^2(k,lslash4)}{(k,lslash4)^{,2}},cos[k,(v,t+x)],l,dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2446.png"
 ALT="$\displaystyle \psi(x,t) =\frac{1}{4\pi} \int_{-\infty}^\infty \frac{\sin^2(k l/4)}{(k l/4)^{ 2}} \cos[k (v t+x)] l dk.$">|; 

$key = q/displaystylepsi(x,t)=frac{1}{4pi}int_{-infty}^inftyfrac{sin^2(k,lslash4)}{(k,lslash4)^{,2}},cos[k,(v,t-x)],l,dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img2444.png"
 ALT="$\displaystyle \psi(x,t) =\frac{1}{4\pi} \int_{-\infty}^\infty \frac{\sin^2(k l/4)}{(k l/4)^{ 2}} \cos[k (v t-x)] l dk.$">|; 

$key = q/displaystylepsi(x,t)=frac{A_0}{[Z(x)]^{1slash2}},cosleft[omegaleft(t-int^xleft[v(x')right]^{-1},dx'right)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1733.png"
 ALT="$\displaystyle \psi(x,t) = \frac{A_0}{[Z(x)]^{1/2}} \cos\left[ \omega\left(t-\int^x\left[v(x')\right]^{-1} dx'\right)\right],$">|; 

$key = q/displaystylepsi(x,t)=int_{-infty}^inftyC(k),cos(omega,t-k,x),dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2542.png"
 ALT="$\displaystyle \psi(x,t) = \int_{-\infty}^\infty C(k) \cos(\omega t-k x) dk,$">|; 

$key = q/displaystylepsi(x,t)=int_{-infty}^inftyC(k),cos[k,(v,t-x)],dk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2546.png"
 ALT="$\displaystyle \psi(x,t)=\int_{-\infty}^\infty C(k) \cos[k (v t-x)] dk,$">|; 

$key = q/displaystylepsi(x,t)=int_{-infty}^inftyfrac{1}{sqrt{2pi,sigma_k^{,2}}},expleft[-frac{(k-k_0)^{,2}}{2,sigma_k^{,2}}right]cos(omega,t-k,x),dk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.31ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img2554.png"
 ALT="$\displaystyle \psi(x,t) = \int_{-\infty}^\infty\frac{1}{\sqrt{2\pi \sigma_k^{\...
...xp\left[-\frac{(k-k_0)^{ 2}}{2 \sigma_k^{ 2}}\right]\cos(\omega t-k x) dk$">|; 

$key = q/displaystylepsi(x,t)=int_{-infty}^{infty}bar{psi}(k),{rme}^{-{rmi},(omega,t-k,x)},dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3867.png"
 ALT="$\displaystyle \psi(x,t) = \int_{-\infty}^{\infty} \bar{\psi}(k) {\rm e}^{-{\rm i} (\omega t-k x)} dk.$">|; 

$key = q/displaystylepsi(x,t)=psi(x),{rme}^{-{rmi},(Eslashhbar),t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3952.png"
 ALT="$\displaystyle \psi(x,t) = \psi(x) {\rm e}^{-{\rm i} (E/\hbar) t},$">|; 

$key = q/displaystylepsi(x,t)=psi(x),{rme}^{-{rmi},(Eslashhbar),t}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3918.png"
 ALT="$\displaystyle \psi(x,t) = \psi(x) {\rm e}^{-{\rm i} (E/\hbar) t}.$">|; 

$key = q/displaystylepsi(x,t)=psi(x),{rme}^{-{rmi},omega,t}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3916.png"
 ALT="$\displaystyle \psi(x,t) = \psi(x) {\rm e}^{-{\rm i} \omega t}.$">|; 

$key = q/displaystylepsi(x,t)=psi_0,cos(omega,t-k,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1826.png"
 ALT="$\displaystyle \psi(x,t)=\psi_0 \cos(\omega t-k x).$">|; 

$key = q/displaystylepsi(x,t)=psi_0,cos,(omega,t-k,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1695.png"
 ALT="$\displaystyle \psi(x,t) = \psi_0 \cos (\omega t-k x).$">|; 

$key = q/displaystylepsi(x,t)=psi_0,{rme}^{-{rmi},(omega,t-k,x)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3822.png"
 ALT="$\displaystyle \psi(x,t) = \psi_0 {\rm e}^{-{\rm i} (\omega t-k x)},$">|; 

$key = q/displaystylepsi(x,t)=psi_0,{rme}^{-{rmi},(omega,t-k,x)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3826.png"
 ALT="$\displaystyle \psi(x,t) = \psi_0 {\rm e}^{-{\rm i} (\omega t-k x)}.$">|; 

$key = q/displaystylepsi(x,t)=sum_{n'=1,infty}A_{n'},cosleft[(n'-1slash2),pi,frac{x}{l}right],cosleft[(n'-1slash2),pi,frac{v,t}{l}-phi_{n'}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1192.png"
 ALT="$\displaystyle \psi(x,t) = \sum_{n'=1,\infty} A_{n'} \cos\left[(n'-1/2) \pi \frac{x}{l}\right] \cos\left[(n'-1/2) \pi \frac{v t}{l}-\phi_{n'}\right].$">|; 

$key = q/displaystylepsi(x,t)=sum_{n=1,infty}A_n,cosleft[(n-1slash2),pi,frac{x}{l}right]sinleft[(n-1slash2),pi,frac{t}{tau}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1208.png"
 ALT="$\displaystyle \psi(x,t) = \sum_{n=1,\infty} A_n \cos\left[(n-1/2) \pi \frac{x}{l}\right]\sin\left[(n-1/2) \pi \frac{t}{\tau}\right],$">|; 

$key = q/displaystylepsi(x,t)simeqexpleft[-frac{(v_g,t-x)^{,2}}{2,sigma_x^{,2}}right],cos(omega_0,t-k_0,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2565.png"
 ALT="$\displaystyle \psi(x,t)\simeq \exp\left[-\frac{(v_g t-x)^{ 2}}{2 \sigma_x^{ 2}}\right] \cos(\omega_0 t-k_0 x).$">|; 

$key = q/displaystylepsi(x,y,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2295.png"
 ALT="$\displaystyle \psi(x,y,0)$">|; 

$key = q/displaystylepsi(x,y,t)=hat{psi}(x,y),cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1875.png"
 ALT="$\displaystyle \psi(x,y,t)=\hat{\psi}(x,y) \cos(\omega t-\phi).$">|; 

$key = q/displaystylepsi(x,y,z)=A,sinleft(l_x,pi,frac{x}{a}right)sinleft(l_y,pi,frac{y}{b}right)sinleft(l_z,pi,frac{z}{c}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4236.png"
 ALT="$\displaystyle \psi(x,y,z) = A \sin\left(l_x \pi \frac{x}{a}\right)\sin\left(l_y \pi \frac{y}{b}\right)\sin\left(l_z \pi \frac{z}{c}\right)
$">|; 

$key = q/displaystylepsi(x,y,z)=psi_0,sin(k_x,x),sin(k_y,y),sin(k_z,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4154.png"
 ALT="$\displaystyle \psi(x,y,z) =\psi_0 \sin(k_x x) \sin(k_y y) \sin(k_z z).$">|; 

$key = q/displaystylepsi(x,y,z,t)=psi(x,y,z),{rme}^{-{rmi},(Eslashhbar),t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4147.png"
 ALT="$\displaystyle \psi(x,y,z,t) = \psi(x,y,z) {\rm e}^{-{\rm i} (E/\hbar) t},$">|; 

$key = q/displaystylepsi(x,y,z,t)=psi_0,cos(omega,t-{bfk}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1836.png"
 ALT="$\displaystyle \psi(x,y,z,t)=\psi_0 \cos(\omega t-{\bf k}\cdot{\bf r}),$">|; 

$key = q/displaystylepsi(x,y,z,t)=psi_0,{rme}^{-{rmi},(omega,t-{bfk}cdot{bfr})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4134.png"
 ALT="$\displaystyle \psi(x,y,z,t) = \psi_0 {\rm e}^{-{\rm i} (\omega t-{\bf k}\cdot{\bf r})},$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1932.png"
 ALT="$\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/displaystylepsi(x,y,z,t)=psi_t,cos(omega,t-{bfk}_tcdot{bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1933.png"
 ALT="$\displaystyle \psi(x,y,z,t)= \psi_t \cos(\omega t-{\bf k}_t\cdot{\bf r})$">|; 

$key = q/displaystylepsi(x,z,t)=A(x,z),cosleft[phi(x,z,t)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img2943.png"
 ALT="$\displaystyle \psi(x,z,t) = A(x,z) \cos\left[\phi(x,z,t)\right].$">|; 

$key = q/displaystylepsi(x,z,t)=A,cos(omega,t-k_x,x-k_z,z+phi_0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2946.png"
 ALT="$\displaystyle \psi(x,z,t) = A \cos(\omega t-k_x x-k_z z+\phi_0),$">|; 

$key = q/displaystylepsi(x,z,t)=psi_0,cos(omega,t-k,x,sintheta_0-k,z,costheta_0-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3297.png"
 ALT="$\displaystyle \psi(x,z,t) = \psi_0 \cos(\omega t-k x \sin\theta_0- k z \cos\theta_0-\phi).$">|; 

$key = q/displaystylepsi(x,z,t)=psi_0,sin(k_x,x),cos(omega,t-k,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2936.png"
 ALT="$\displaystyle \psi(x,z,t)= \psi_0 \sin(k_x x) \cos(\omega t-k z),$">|; 

$key = q/displaystylepsi(z,t)=psi_0,cos(omega,t-k,z-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3256.png"
 ALT="$\displaystyle \psi(z,t) = \psi_0 \cos(\omega t-k z-\phi).$">|; 

$key = q/displaystylepsi({bfr},t)=F(v,t-{bfn}cdot{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2539.png"
 ALT="$\displaystyle \psi({\bf r}, t)= F(v t-{\bf n}\cdot{\bf r}),
$">|; 

$key = q/displaystylepsi_0=A,{rme}^{,{rmi},phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3823.png"
 ALT="$\displaystyle \psi_0 = A {\rm e}^{ {\rm i} \phi},$">|; 

$key = q/displaystylepsi_1=psi_0,expleft(int_0^{x_1}{rmi},k(x'),dx'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4073.png"
 ALT="$\displaystyle \psi_1=\psi_0 \exp\left(\int_0^{x_1}{\rm i} k(x') dx'\right).$">|; 

$key = q/displaystylepsi_i(t)=A,cos[k,(x_i-aslash2)],cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1138.png"
 ALT="$\displaystyle \psi_i(t) = A \cos[k (x_i-a/2)] \cos(\omega t-\phi),$">|; 

$key = q/displaystylepsi_i(t)=[A,sin(k,x_i)+B,cos(k,x_i)],cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1308.png"
 ALT="$\displaystyle \psi_i(t) = [A \sin (k x_i)+ B \cos(k x_i)] \cos(\omega t-\phi).
$">|; 

$key = q/displaystylepsi_i+cosphi_r,psi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2054.png"
 ALT="$\displaystyle \psi_i + \cos\phi_r \psi_r$">|; 

$key = q/displaystylepsi_i+psi_r=beta^{,-1},psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2024.png"
 ALT="$\displaystyle \psi_i+\psi_r = \beta^{ -1} \psi_t,$">|; 

$key = q/displaystylepsi_i+psi_r=psi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1980.png"
 ALT="$\displaystyle \psi_i+\psi_r=\psi_t$">|; 

$key = q/displaystylepsi_i,cos(omega,t-k_{i,x},x-k_{i,y},y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1938.png"
 ALT="$\displaystyle \psi_i \cos(\omega t-k_{i x} x-k_{i y} y)$">|; 

$key = q/displaystylepsi_i-cosphi_r,psi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2058.png"
 ALT="$\displaystyle \psi_i -\cos\phi_r \psi_r$">|; 

$key = q/displaystylepsi_i-psi_r=alpha,psi_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2025.png"
 ALT="$\displaystyle \psi_i-\psi_r = \alpha \psi_t.$">|; 

$key = q/displaystylepsi_i-psi_r=frac{alpha}{beta},psi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1983.png"
 ALT="$\displaystyle \psi_i-\psi_r= \frac{\alpha}{\beta} \psi_t,$">|; 

$key = q/displaystylepsi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2066.png"
 ALT="$\displaystyle \psi_i$">|; 

$key = q/displaystylepsi_j(rho,t)=A_j,J_0left(frac{z_j,rho}{a}right)cos(omega_j,t-phi_j),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1918.png"
 ALT="$\displaystyle \psi_j(\rho,t) = A_j  J_0\left(\frac{z_j \rho}{a}\right)\cos(\omega_j t-\phi_j),$">|; 

$key = q/displaystylepsi_n(x,t)=A_n,cosleft[(n-1slash2),pi,frac{x}{l}right]cos(omega_n,t-phi_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1186.png"
 ALT="$\displaystyle \psi_n(x,t) = A_n \cos\left[(n-1/2) \pi \frac{x}{l}\right]\cos(\omega_n t-\phi_n),$">|; 

$key = q/displaystylepsi_n(x,t)=A_n,sinleft(n,pi,frac{x}{a}right),expleft(-{rmi},n^{,2},frac{E_1}{hbar},tright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3933.png"
 ALT="$\displaystyle \psi_n(x,t) = A_n \sin\left(n \pi \frac{x}{a}\right) \exp\left(-{\rm i} n^{ 2} \frac{E_1}{\hbar} t\right),$">|; 

$key = q/displaystylepsi_n(x,t)=left(frac{2}{a}right)^{1slash2},sinleft(n,pi,frac{x}{a}right),expleft(-{rmi},n^{,2},frac{E_1}{hbar},tright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3936.png"
 ALT="$\displaystyle \psi_n(x,t) = \left(\frac{2}{a}\right)^{1/2} \sin\left(n \pi \frac{x}{a}\right) \exp\left(-{\rm i} n^{ 2} \frac{E_1}{\hbar} t\right).$">|; 

$key = q/displaystylepsi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1986.png"
 ALT="$\displaystyle \psi_r$">|; 

$key = q/displaystylepsi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1988.png"
 ALT="$\displaystyle \psi_t$">|; 

$key = q/displaystylepsi_{m,n}(x,y,t)=A_{m,n},sinleft(m,pi,frac{x}{a}right),sinleft(n,pi,frac{y}{b}right),cos(omega_{m,n},t-phi_{m,n}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1900.png"
 ALT="$\displaystyle \psi_{m,n}(x,y,t) = A_{m,n} \sin\left(m \pi \frac{x}{a}\right) \sin\left(n \pi \frac{y}{b}\right) \cos(\omega_{m,n} t-\phi_{m,n}),$">|; 

$key = q/displaystylepsi_{n,i}(t)=A_n,cosleft[frac{(n-1slash2),(i-1slash2)}{N+1slash2},piright]cos(omega_n-phi_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1143.png"
 ALT="$\displaystyle \psi_{n,i} (t) = A_n \cos\left[\frac{(n-1/2) (i-1/2)}{N+1/2} \pi\right]\cos(\omega_n-\phi_n),$">|; 

$key = q/displaystylepsirightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3956.png"
 ALT="$\displaystyle \psi\rightarrow 0$">|; 

$key = q/displaystyleq,a=n,pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4033.png"
 ALT="$\displaystyle q a = n \pi,$">|; 

$key = q/displaystyleq=k,tan(k,aslash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img3970.png"
 ALT="$\displaystyle q = k \tan(k a/2).$">|; 

$key = q/displaystyleq=sqrt{frac{2,m,(-E)}{hbar^{,2}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img3962.png"
 ALT="$\displaystyle q = \sqrt{\frac{2 m (-E)}{\hbar^{ 2}}},$">|; 

$key = q/displaystyleq=sqrt{frac{2,m,(E-V)}{hbar^{,2}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img4012.png"
 ALT="$\displaystyle q = \sqrt{\frac{2 m (E-V)}{\hbar^{ 2}}}.$">|; 

$key = q/displaystyleq=sqrt{frac{2,m,(V-E)}{hbar^{,2}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img4037.png"
 ALT="$\displaystyle q = \sqrt{\frac{2 m (V-E)}{\hbar^{ 2}}}.$">|; 

$key = q/displaystyleqleft(A,{rme}^{,q,a}-B,{rme}^{-q,a}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img4041.png"
 ALT="$\displaystyle q\left(A  {\rm e}^{ q a}-B  {\rm e}^{-q a}\right)$">|; 

$key = q/displaystyleqleft(A,{rme}^{,{rmi},q,a}-B,{rme}^{-{rmi},q,a}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4021.png"
 ALT="$\displaystyle q\left(A {\rm e}^{ {\rm i} q a} -B  {\rm e}^{-{\rm i} q a}\right)$">|; 

$key = q/displaystyler;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3554.png"
 ALT="$\displaystyle r$">|; 

$key = q/displaystyler=left(frac{2,v_0,h}{v_1}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3240.png"
 ALT="$\displaystyle r = \left(\frac{2 v_0 h}{v_1}\right)^{1/2}.
$">|; 

$key = q/displaystylerho,A,deltax,frac{partial^{,2}psi(x,t)}{partialt^{,2}}=-Aleft[deltap(x+deltaxslash2,t)-deltap(x-deltaxslash2,t)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1232.png"
 ALT="$\displaystyle \rho A \delta x \frac{\partial^{ 2}\psi(x,t)}{\partial t^{ 2}} = -A\left[\delta p(x+\delta x/2,t)-\delta p(x-\delta x/2,t)\right].$">|; 

$key = q/displaystylerho,A,deltax,frac{partial^{,2}psi(x,t)}{partialt^{,2}}=A,Yleft[epsilon(x+deltaxslash2,t)-epsilon(x-deltaxslash2,t)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1172.png"
 ALT="$\displaystyle \rho A \delta x \frac{\partial^{ 2}\psi(x,t)}{\partial t^{ 2}} = A Y\left[\epsilon(x+\delta x/2,t)-\epsilon(x-\delta x/2,t)\right].$">|; 

$key = q/displaystylerho,dx,dy,dz,frac{partialv_x(x,z,t)}{partialt}=-left[frac{p(x+dx,z,t)-p(x,z,t)}{dx}right]dx,dy,dz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3013.png"
 ALT="$\displaystyle \rho dx dy dz \frac{\partial v_x(x,z,t)}{\partial t} = -\left[\frac{p(x+dx,z,t)-p(x,z,t)}{dx}\right]dx dy dz,$">|; 

$key = q/displaystylerho,frac{partial^{,2}psi(x,t)}{partialt^{,2}}=-frac{partial,deltap(x,t)}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1233.png"
 ALT="$\displaystyle \rho \frac{\partial^{ 2}\psi(x,t)}{\partial t^{ 2}} = - \frac{\partial \delta p(x,t)}{\partial x}.$">|; 

$key = q/displaystylerho,frac{partial^{,2}psi(x,t)}{partialt^{,2}}=Y,frac{partialepsilon(x,t)}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1173.png"
 ALT="$\displaystyle \rho \frac{\partial^{ 2}\psi(x,t)}{\partial t^{ 2}} = Y \frac{\partial\epsilon(x,t)}{\partial x},$">|; 

$key = q/displaystylerho,frac{partialv_x}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2224.png"
 ALT="$\displaystyle \rho \frac{\partial v_x}{\partial t}$">|; 

$key = q/displaystylerho,frac{partialv_x}{partialt}=-frac{partialp}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3014.png"
 ALT="$\displaystyle \rho \frac{\partial v_x}{\partial t} = - \frac{\partial p}{\partial x}.$">|; 

$key = q/displaystylerho,frac{partialv_z}{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2226.png"
 ALT="$\displaystyle \rho \frac{\partial v_z}{\partial t}$">|; 

$key = q/displaystylerho,frac{partialv_z}{partialt}=-frac{partialp}{partialz}-rho,g.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3016.png"
 ALT="$\displaystyle \rho \frac{\partial v_z}{\partial t} = -\frac{\partial p}{\partial z} - \rho g.$">|; 

$key = q/displaystylerho,frac{partialy}{partialt},frac{partial^{,2}y}{partialt^{,2}}=T,frac{partialy}{partialt},frac{partial^{,2}y}{partialx^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1427.png"
 ALT="$\displaystyle \rho \frac{\partial y}{\partial t}  \frac{\partial^{ 2} y}{\pa...
...= T  \frac{\partial y}{\partial t} \frac{\partial^{ 2} y}{\partial x^{ 2}},$">|; 

$key = q/displaystylerho,frac{partial}{partialt}!left(frac{partialv_x}{partialz}-frac{partialv_z}{partialx}right)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3024.png"
 ALT="$\displaystyle \rho \frac{\partial}{\partial t}\!\left(\frac{\partial v_x}{\partial z} -\frac{\partial v_z}{\partial x}\right) = 0,$">|; 

$key = q/displaystylerho_1,(phi_i+phi_r)=rho_2,phi_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2273.png"
 ALT="$\displaystyle \rho_1 (\phi_i+\phi_r) = \rho_2 \phi_t.$">|; 

$key = q/displaystylerho_2-rho_1=d,sintheta=(j+1slash2),lambda.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3291.png"
 ALT="$\displaystyle \rho_2-\rho_1=d \sin\theta= (j+1/2) \lambda.$">|; 

$key = q/displaystylerho_2-rho_1=d,sintheta=j,lambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3290.png"
 ALT="$\displaystyle \rho_2-\rho_1 = d \sin\theta = j \lambda,$">|; 

$key = q/displaystylerho_2=Rleft[1+frac{1}{2},frac{d}{R},sintheta+{calO}!left(frac{d^{,2}}{R^{,2}}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3271.png"
 ALT="$\displaystyle \rho_2 = R\left[1+\frac{1}{2} \frac{d}{R} \sin\theta + {\cal O}\!\left(\frac{d^{ 2}}{R^{ 2}}\right)\right].$">|; 

$key = q/displaystylerho_n=Rleft[1-frac{x_n}{R},sintheta+{calO}left(frac{x_n^{,2}}{R^{,2}}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3369.png"
 ALT="$\displaystyle \rho_n = R\left[1-\frac{x_n}{R} \sin\theta + {\cal O}\left(\frac{x_n^{ 2}}{R^{ 2}}\right)\right].$">|; 

$key = q/displaystyles(t)=A,cos(omega,t)+B,sin(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle s(t) = A \cos(\omega t) + B \sin(\omega t),$">|; 

$key = q/displaystyles(t)=a,cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle s(t) = a \cos(\omega t-\phi),$">|; 

$key = q/displaystyles(t)=a,sin(omega,t-phi'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img240.png"
 ALT="$\displaystyle s(t) = a \sin(\omega t-\phi'),$">|; 

$key = q/displaystyles(t)=s_0,cos(omega,t)+frac{dot{s}_0}{omega},sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle s(t) = s_0 \cos(\omega t)+ \frac{\dot{s}_0}{\omega} \sin(\omega t).$">|; 

$key = q/displaystyles(t)=s_0,s_1(t)+dot{s}_0,s_2(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle s(t)=s_0 s_1(t) + \dot{s}_0 s_2(t),$">|; 

$key = q/displaystyles=frac{d,sin(theta_1-theta_2)}{costheta_2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2311.png"
 ALT="$\displaystyle s = \frac{d \sin(\theta_1-\theta_2)}{\cos\theta_2},
$">|; 

$key = q/displaystyles_1(t)=cos(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle s_1(t) = \cos(\omega t).$">|; 

$key = q/displaystyles_2(t)=omega^{-1},sin(omega,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle s_2(t) = \omega^{-1} \sin(\omega t).$">|; 

$key = q/displaystyles_{rmmax}=frac{sqrt{2,{calE}}}{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle s_{\rm max} = \frac{\sqrt{2 {\cal E}}}{\omega},$">|; 

$key = q/displaystylesigma=Y,epsilon.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1165.png"
 ALT="$\displaystyle \sigma = Y \epsilon.$">|; 

$key = q/displaystylesigma_k=frac{1}{sigma_x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2363.png"
 ALT="$\displaystyle \sigma_k=\frac{1}{\sigma_x}.$">|; 

$key = q/displaystylesigma_omega=frac{1}{sigma_t}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2489.png"
 ALT="$\displaystyle \sigma_\omega = \frac{1}{\sigma_t}.$">|; 

$key = q/displaystylesimeq-frac{1}{sigma},frac{partialH_y}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2897.png"
 ALT="$\displaystyle \simeq- \frac{1}{\sigma} \frac{\partial H_y}{\partial z},$">|; 

$key = q/displaystylesimeq-frac{omega_{p,e}^{,2}}{omega^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2827.png"
 ALT="$\displaystyle \simeq -\frac{\omega_{p e}^{ 2}}{\omega^{ 2}}.$">|; 

$key = q/displaystylesimeq-left(1-sqrt{2},alpharight),E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2920.png"
 ALT="$\displaystyle \simeq-\left(1-\sqrt{2} \alpha\right) E_i,$">|; 

$key = q/displaystylesimeq-sqrt{2},alpha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2921.png"
 ALT="$\displaystyle \simeq - \sqrt{2} \alpha,$">|; 

$key = q/displaystylesimeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2825.png"
 ALT="$\displaystyle \simeq 0,$">|; 

$key = q/displaystylesimeq1+frac{omega_{p,i}^{,2}}{{{mitOmega}}_i^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.43ex; " SRC="|."$dir".q|img2824.png"
 ALT="$\displaystyle \simeq 1 +\frac{\omega_{p i}^{ 2}}{{{\mit\Omega}}_i^{ 2}},$">|; 

$key = q/displaystylesimeq2,alpha,E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2922.png"
 ALT="$\displaystyle \simeq 2 \alpha E_i,$">|; 

$key = q/displaystylesimeqE_0,cos[k,(v,t-z)],{rme}^{-zslashdelta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1818.png"
 ALT="$\displaystyle \simeq E_0 \cos[k (v t-z)] {\rm e}^{-z/\delta},$">|; 

$key = q/displaystylesimeqI_0,cos[k,(v,t-x)],{rme}^{-xslashdelta},nonumber;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1790.png"
 ALT="$\displaystyle \simeq I_0 \cos[k (v t-x)] {\rm e}^{-x/\delta},\nonumber$">|; 

$key = q/displaystylesimeqZ,I_0,cos[k,(v,t-x)-1slash(k,delta)],{rme}^{-xslashdelta},nonumber;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1791.png"
 ALT="$\displaystyle \simeq Z I_0 \cos[k (v t-x)-1/(k \delta)] {\rm e}^{-x/\delta},\nonumber$">|; 

$key = q/displaystylesimeqZ_0^{,-1},E_0,cos[k,(v,t-z)-1slash(k,delta)],{rme}^{-zslashdelta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1819.png"
 ALT="$\displaystyle \simeq Z_0^{ -1} E_0 \cos[k (v t-z)-1/(k \delta)] {\rm e}^{-z/\delta},$">|; 

$key = q/displaystylesimeqfrac{2,(omega_0-omega)}{[4,(omega_0-omega)^{,2}+nu^{,2}]^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img609.png"
 ALT="$\displaystyle \simeq \frac{2 (\omega_0-\omega)}{[4 (\omega_0-\omega)^{ 2}+\nu^{ 2}]^{1/2}}.$">|; 

$key = q/displaystylesimeqfrac{nu}{[4,(omega_0-omega)^{,2}+nu^{,2}]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img608.png"
 ALT="$\displaystyle \simeq \frac{\nu}{[4 (\omega_0-\omega)^{ 2}+\nu^{ 2}]^{1/2}},$">|; 

$key = q/displaystylesimeqfrac{nu}{left[4,(omega-omega_0)^{,2}+nu^{,2}right]^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.54ex; " SRC="|."$dir".q|img584.png"
 ALT="$\displaystyle \simeq \frac{\nu}{\left[4 (\omega-\omega_0)^{ 2}+\nu^{ 2}\right]^{1/2}}.$">|; 

$key = q/displaystylesimeqfrac{omega_0,hat{X}}{[4,(omega_0-omega)^{,2}+nu^{,2}]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img607.png"
 ALT="$\displaystyle \simeq \frac{\omega_0 \hat{X}}{[4 (\omega_0-\omega)^{ 2}+\nu^{ 2}]^{1/2}},$">|; 

$key = q/displaystylesimeqfrac{pi}{4}-frac{alpha}{sqrt{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img2923.png"
 ALT="$\displaystyle \simeq \frac{\pi}{4}-\frac{\alpha}{\sqrt{2}}.$">|; 

$key = q/displaystylesimeqfrac{skew{3}hat{V}}{R},frac{nu}{left[4,(omega_0-omega)^{,2}+nu^{,2}right]^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.97ex; vertical-align: -2.54ex; " SRC="|."$dir".q|img583.png"
 ALT="$\displaystyle \simeq \frac{\skew{3}\hat{V}}{R} \frac{\nu}{\left[4 (\omega_0-\omega)^{ 2}+\nu^{ 2}\right]^{1/2}},$">|; 

$key = q/displaystylesimeqfrac{y_i-y_{i-1}}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img887.png"
 ALT="$\displaystyle \simeq \frac{y_i-y_{i-1}}{a},$">|; 

$key = q/displaystylesimeqfrac{y_{i+1}-y_{i}}{a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img889.png"
 ALT="$\displaystyle \simeq \frac{y_{i+1}-y_{i}}{a}.$">|; 

$key = q/displaystylesimeqk_0+{mitDelta}k,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2682.png"
 ALT="$\displaystyle \simeq k_0+{\mit\Delta} k,$">|; 

$key = q/displaystylesimeqk_0-{mitDelta}k,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2680.png"
 ALT="$\displaystyle \simeq k_0-{\mit\Delta} k,$">|; 

$key = q/displaystylesin(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4327.png"
 ALT="$\displaystyle \sin(-\alpha)$">|; 

$key = q/displaystylesin(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4365.png"
 ALT="$\displaystyle \sin(2\alpha)$">|; 

$key = q/displaystylesin(3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4369.png"
 ALT="$\displaystyle \sin(3\alpha)$">|; 

$key = q/displaystylesin(4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4373.png"
 ALT="$\displaystyle \sin(4\alpha)$">|; 

$key = q/displaystylesin(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4339.png"
 ALT="$\displaystyle \sin(\alpha\pm\beta)$">|; 

$key = q/displaystylesin(alphapmpislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4333.png"
 ALT="$\displaystyle \sin(\alpha\pm\pi/2)$">|; 

$key = q/displaystylesin(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4359.png"
 ALT="$\displaystyle \sin(\alpha/2)$">|; 

$key = q/displaystylesin(k,x_{N+1})=sin[(N+1),k,a]=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img923.png"
 ALT="$\displaystyle \sin(k x_{N+1}) = \sin[(N+1) k a] = 0.$">|; 

$key = q/displaystylesin({rmi},theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4436.png"
 ALT="$\displaystyle \sin({\rm i} \theta)$">|; 

$key = q/displaystylesin^2alpha+cos^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4337.png"
 ALT="$\displaystyle \sin^2\alpha+\cos^2\alpha$">|; 

$key = q/displaystylesin^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4377.png"
 ALT="$\displaystyle \sin^2\alpha$">|; 

$key = q/displaystylesin^3alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4381.png"
 ALT="$\displaystyle \sin^3\alpha$">|; 

$key = q/displaystylesin^4alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4385.png"
 ALT="$\displaystyle \sin^4\alpha$">|; 

$key = q/displaystylesinalpha+sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4345.png"
 ALT="$\displaystyle \sin\alpha+\sin\beta$">|; 

$key = q/displaystylesinalpha,cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4357.png"
 ALT="$\displaystyle \sin\alpha \cos\beta$">|; 

$key = q/displaystylesinalpha,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4353.png"
 ALT="$\displaystyle \sin\alpha \sin\beta$">|; 

$key = q/displaystylesinalpha-sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4347.png"
 ALT="$\displaystyle \sin\alpha-\sin\beta$">|; 

$key = q/displaystylesinbeta=frac{v_p}{V}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.24ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3109.png"
 ALT="$\displaystyle \sin\beta =\frac{v_p}{V}.$">|; 

$key = q/displaystylesinbeta=frac{v_p}{V}=left(frac{g}{k,V^{,2}}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3122.png"
 ALT="$\displaystyle \sin\beta =\frac{v_p}{V}=\left( \frac{g}{k V^{ 2}}\right)^{1/2}.$">|; 

$key = q/displaystylesinh(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4389.png"
 ALT="$\displaystyle \sinh(-\alpha)$">|; 

$key = q/displaystylesinh(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4422.png"
 ALT="$\displaystyle \sinh(2\alpha)$">|; 

$key = q/displaystylesinh(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4396.png"
 ALT="$\displaystyle \sinh(\alpha\pm\beta)$">|; 

$key = q/displaystylesinh(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4416.png"
 ALT="$\displaystyle \sinh(\alpha/2)$">|; 

$key = q/displaystylesinh({rmi},theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4440.png"
 ALT="$\displaystyle \sinh({\rm i} \theta)$">|; 

$key = q/displaystylesinhalpha+sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4402.png"
 ALT="$\displaystyle \sinh\alpha+\sinh\beta$">|; 

$key = q/displaystylesinhalpha,coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4414.png"
 ALT="$\displaystyle \sinh\alpha \cosh\beta$">|; 

$key = q/displaystylesinhalpha,sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4410.png"
 ALT="$\displaystyle \sinh\alpha \sinh\beta$">|; 

$key = q/displaystylesinhalpha-sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4404.png"
 ALT="$\displaystyle \sinh\alpha-\sinh\beta$">|; 

$key = q/displaystylesinhtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4432.png"
 ALT="$\displaystyle \sinh\theta$">|; 

$key = q/displaystylesinhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4321.png"
 ALT="$\displaystyle \sinh x$">|; 

$key = q/displaystylesinphi_r,psi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2056.png"
 ALT="$\displaystyle \sin\phi_r \psi_r$">|; 

$key = q/displaystylesintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4428.png"
 ALT="$\displaystyle \sin\theta$">|; 

$key = q/displaystylesintheta=frac{l}{N},frac{lambda}{d},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3383.png"
 ALT="$\displaystyle \sin\theta=\frac{l}{N} \frac{\lambda}{d},$">|; 

$key = q/displaystylesintheta=j,frac{lambda}{d},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3379.png"
 ALT="$\displaystyle \sin\theta=j \frac{\lambda}{d},$">|; 

$key = q/displaystylesintheta=theta-frac{theta^{,3}}{6}+frac{theta^{,5}}{120}+{calO}(theta^{,7}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img336.png"
 ALT="$\displaystyle \sin\theta = \theta - \frac{\theta^{ 3}}{6} + \frac{\theta^{ 5}}{120} + {\cal O}(\theta^{ 7}).$">|; 

$key = q/displaystylesintheta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2269.png"
 ALT="$\displaystyle \sin\theta_i$">|; 

$key = q/displaystylesintheta_i=frac{beta}{sqrt{1+beta^{,2}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img2035.png"
 ALT="$\displaystyle \sin\theta_i = \frac{\beta}{\sqrt{1+\beta^{ 2}}},$">|; 

$key = q/displaystylesintheta_i=sintheta_r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1956.png"
 ALT="$\displaystyle \sin\theta_i=\sin\theta_r,$">|; 

$key = q/displaystylesintheta_t=frac{n_1}{n_2},sintheta_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2040.png"
 ALT="$\displaystyle \sin\theta_t = \frac{n_1}{n_2} \sin\theta_i.$">|; 

$key = q/displaystylesinthetaequivfrac{1}{2,{rmi}}left({rme}^{,{rmi},theta}-{rme}^{-{rmi},theta}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3722.png"
 ALT="$\displaystyle \sin\theta \equiv \frac{1}{2 {\rm i}}\left({\rm e}^{ {\rm i} \theta} - {\rm e}^{-{\rm i} \theta}\right),
$">|; 

$key = q/displaystylesinvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img539.png"
 ALT="$\displaystyle \sin\varphi$">|; 

$key = q/displaystylesinx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4218.png"
 ALT="$\displaystyle \sin x$">|; 

$key = q/displaystyleskew{3}ddot{theta}+omega^{,2},thetasimeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img339.png"
 ALT="$\displaystyle \skew{3}\ddot{\theta} +\omega^{ 2} \theta\simeq 0,$">|; 

$key = q/displaystyleskew{3}hat{theta}=2,sin^{-1}left(frac{E}{2,m,g,l}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img405.png"
 ALT="$\displaystyle \skew{3}\hat{\theta} = 2 \sin^{-1}\left(\frac{E}{2 m g l}\right)^{1/2}.
$">|; 

$key = q/displaystylesqrt{3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.23ex; " SRC="|."$dir".q|img690.png"
 ALT="$\displaystyle \sqrt{3}.$">|; 

$key = q/displaystylet_{rmmax}=left(n+frac{phi}{2pi}right)T.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle t_{\rm max} = \left(n + \frac{\phi}{2\pi}\right)T.$">|; 

$key = q/displaystyletan(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4331.png"
 ALT="$\displaystyle \tan(-\alpha)$">|; 

$key = q/displaystyletan(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4343.png"
 ALT="$\displaystyle \tan(\alpha\pm \beta)$">|; 

$key = q/displaystyletan(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4363.png"
 ALT="$\displaystyle \tan(\alpha/2)$">|; 

$key = q/displaystyletan^2theta=-frac{P,(n^{,2}-R),(n^{,2}-L)}{(S,n^{,2}-R,L),(n^{,2}-P)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3193.png"
 ALT="$\displaystyle \tan^2\theta = - \frac{P (n^{ 2}-R) (n^{ 2}-L)}{(S n^{ 2}-R L) (n^{ 2}-P)}.
$">|; 

$key = q/displaystyletan^2theta=-frac{P}{S}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3197.png"
 ALT="$\displaystyle \tan^2\theta = -\frac{P}{S}.
$">|; 

$key = q/displaystyletan^2theta_i=frac{(Z_2slashZ_1)^2-1}{1-(v_2slashv_1)^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2320.png"
 ALT="$\displaystyle \tan^2\theta_i = \frac{(Z_2/Z_1)^2-1}{1-(v_2/v_1)^2}.
$">|; 

$key = q/displaystyletan^2theta_i=frac{rho_2^{,2},v_2^{,2}-rho_1^{,2},v_1^{,2}}{rho_1^{,2},(v_1^{,2}-v_2^{,2})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img2286.png"
 ALT="$\displaystyle \tan^2\theta_i = \frac{\rho_2^{ 2} v_2^{ 2}-\rho_1^{ 2} v_1^{ 2}}{\rho_1^{ 2} (v_1^{ 2}-v_2^{ 2})},$">|; 

$key = q/displaystyletanh(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4393.png"
 ALT="$\displaystyle \tanh(-\alpha)$">|; 

$key = q/displaystyletanh(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4400.png"
 ALT="$\displaystyle \tanh(\alpha\pm \beta)$">|; 

$key = q/displaystyletanh(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4420.png"
 ALT="$\displaystyle \tanh(\alpha/2)$">|; 

$key = q/displaystyletanhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4325.png"
 ALT="$\displaystyle \tanh x$">|; 

$key = q/displaystyletanleft(sqrt{2,m,(V_0+E)},,Lslashhbarright)=-sqrt{(V_0+E)slash(-E)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4258.png"
 ALT="$\displaystyle \tan\left(\sqrt{2 m (V_0+E)}  L/\hbar\right) = - \sqrt{(V_0+E)/(-E)}.
$">|; 

$key = q/displaystyletanphi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2062.png"
 ALT="$\displaystyle \tan\phi_r$">|; 

$key = q/displaystyletanphi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2064.png"
 ALT="$\displaystyle \tan\phi_t$">|; 

$key = q/displaystyletantheta_i=frac{y_i-y_{i-1}}{x_i-x_{i-1}}=frac{y_i-y_{i-1}}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img882.png"
 ALT="$\displaystyle \tan\theta_i = \frac{y_i-y_{i-1}}{x_i-x_{i-1}} = \frac{y_i-y_{i-1}}{a},$">|; 

$key = q/displaystyletantheta_t,(phi_i-phi_r)=tantheta_i,phi_t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2275.png"
 ALT="$\displaystyle \tan\theta_t (\phi_i-\phi_r) = \tan\theta_i \phi_t,$">|; 

$key = q/displaystyletantheta_{i+1}=frac{y_{i+1}-y_{i}}{a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img883.png"
 ALT="$\displaystyle \tan\theta_{i+1} = \frac{y_{i+1}-y_{i}}{a}.$">|; 

$key = q/displaystyletanvarphi=frac{nu,omega}{omega_0^{,2}-omega^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img536.png"
 ALT="$\displaystyle \tan\varphi = \frac{\nu \omega}{\omega_0^{ 2}-\omega^{ 2}},$">|; 

$key = q/displaystyletanx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4319.png"
 ALT="$\displaystyle \tan x$">|; 

$key = q/displaystyletau=-M,g,d,sintheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img350.png"
 ALT="$\displaystyle \tau = - M g d \sin\theta.$">|; 

$key = q/displaystyletau=-m,g,l,sintheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img332.png"
 ALT="$\displaystyle \tau = - m g l \sin\theta.$">|; 

$key = q/displaystyletau=frac{ln2}{nu,|T|^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img4120.png"
 ALT="$\displaystyle \tau = \frac{\ln 2}{\nu \vert T\vert^{ 2}}.$">|; 

$key = q/displaystyletheta(t)=skew{3}hat{theta},cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img341.png"
 ALT="$\displaystyle \theta(t) = \skew{3}\hat{\theta} \cos(\omega t-\phi),$">|; 

$key = q/displaystyletheta=theta_0+j,frac{lambda}{d},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3309.png"
 ALT="$\displaystyle \theta = \theta_0 + j \frac{\lambda}{d},$">|; 

$key = q/displaystyletheta_0llfrac{lambda}{d}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3362.png"
 ALT="$\displaystyle \theta_0\ll \frac{\lambda}{d}.$">|; 

$key = q/displaystyletheta_B=tan^{-1}left(frac{n_2}{n_1}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2038.png"
 ALT="$\displaystyle \theta_B = \tan^{-1}\left(\frac{n_2}{n_1}\right).$">|; 

$key = q/displaystyletheta_c=sin^{-1}left(frac{n_2}{n_1}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2044.png"
 ALT="$\displaystyle \theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right).$">|; 

$key = q/displaystyletheta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img886.png"
 ALT="$\displaystyle \theta_i$">|; 

$key = q/displaystyletheta_j=sin^{-1}left(j,frac{lambda}{d}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3477.png"
 ALT="$\displaystyle \theta_j = \sin^{-1}\left(j \frac{\lambda}{d}\right),$">|; 

$key = q/displaystyletheta_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img888.png"
 ALT="$\displaystyle \theta_{i+1}$">|; 

$key = q/displaystyletilde{p}=-rho,frac{partialphi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2240.png"
 ALT="$\displaystyle \tilde{p} = -\rho \frac{\partial \phi}{\partial t}.$">|; 

$key = q/displaystyletimescosleft[frac{1}{2},k,d,(theta-theta_0slash2)right],cosleft[frac{1}{2},k,d,(theta+theta_0slash2)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3337.png"
 ALT="$\displaystyle \times \cos\left[\frac{1}{2} k d (\theta-\theta_0/2)\right] \cos\left[\frac{1}{2} k d (\theta+\theta_0/2)\right]$">|; 

$key = q/displaystyletsimeqt_0+frac{e^{,2}}{2,epsilon_0,m_e,c,omega^{,2}},int_0^zn_e(z'),dz'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2701.png"
 ALT="$\displaystyle t \simeq t_0+ \frac{e^{ 2}}{2 \epsilon_0 m_e c \omega^{ 2}} \int_0^z n_e(z') dz'.$">|; 

$key = q/displaystyleu';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3573.png"
 ALT="$\displaystyle u'$">|; 

$key = q/displaystyleu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3571.png"
 ALT="$\displaystyle u$">|; 

$key = q/displaystyleuint_0^1cosleft(frac{u,z^{,2}}{2}right)J_0(v,z),z,dz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3765.png"
 ALT="$\displaystyle u\int_0^1\cos\left(\frac{u z^{ 2}}{2}\right) J_0(v z) z dz,$">|; 

$key = q/displaystyleuint_0^1sinleft(frac{u,z^{,2}}{2}right)J_0(v,z),z,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3767.png"
 ALT="$\displaystyle u\int_0^1\sin\left(\frac{u z^{ 2}}{2}\right) J_0(v z) z dz$">|; 

$key = q/displaystylev';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3577.png"
 ALT="$\displaystyle v'$">|; 

$key = q/displaystylev(z)=v_0-v_1,z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3238.png"
 ALT="$\displaystyle v(z)=v_0-v_1 z,
$">|; 

$key = q/displaystylev(z)=v_0-v_1,z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3225.png"
 ALT="$\displaystyle v(z) = v_0-v_1 z.
$">|; 

$key = q/displaystylev,hat{bfD}=hat{{bfH}}times{bfn},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2153.png"
 ALT="$\displaystyle v \hat{\bf D} = \hat{{\bf H}}\times {\bf n},$">|; 

$key = q/displaystylev,hat{bfH}=epsilon_0,c^{,2},{bfn}timeshat{bfE}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2154.png"
 ALT="$\displaystyle v \hat{\bf H}=\epsilon_0 c^{ 2} {\bf n}\times \hat{\bf E}.$">|; 

$key = q/displaystylev;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3575.png"
 ALT="$\displaystyle v$">|; 

$key = q/displaystylev=f,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1387.png"
 ALT="$\displaystyle v = f \lambda$">|; 

$key = q/displaystylev=frac{1}{sqrt{epsilon,epsilon_0,mu_0}}=frac{c}{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.33ex; " SRC="|."$dir".q|img1653.png"
 ALT="$\displaystyle v = \frac{1}{\sqrt{\epsilon \epsilon_0 \mu_0}} = \frac{c}{n},$">|; 

$key = q/displaystylev=frac{1}{sqrt{{calL},{calC}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1482.png"
 ALT="$\displaystyle v=\frac{1}{\sqrt{{\cal L} {\cal C}}}.$">|; 

$key = q/displaystylev=frac{1}{sqrt{{calL},{calC}}}=frac{1}{sqrt{epsilon_0,mu_0}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.33ex; " SRC="|."$dir".q|img1503.png"
 ALT="$\displaystyle v = \frac{1}{\sqrt{{\cal L} {\cal C}}} = \frac{1}{\sqrt{\epsilon_0 \mu_0}},$">|; 

$key = q/displaystylev=frac{c}{sqrt{epsilon}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1659.png"
 ALT="$\displaystyle v = \frac{c}{\sqrt{\epsilon}}.$">|; 

$key = q/displaystylev=left(frac{gamma,R,T}{M}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1384.png"
 ALT="$\displaystyle v= \left(\frac{\gamma R T}{M}\right)^{1/2}.$">|; 

$key = q/displaystylev=sqrt{frac{K}{rho}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img2242.png"
 ALT="$\displaystyle v = \sqrt{\frac{K}{\rho}}.$">|; 

$key = q/displaystylev=sqrt{frac{T}{rho}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img984.png"
 ALT="$\displaystyle v = \sqrt{\frac{T}{\rho}}$">|; 

$key = q/displaystylev=sqrt{frac{Y}{rho}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img1175.png"
 ALT="$\displaystyle v=\sqrt{\frac{Y}{\rho}}$">|; 

$key = q/displaystylev=sqrt{frac{gamma,p}{rho}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img1234.png"
 ALT="$\displaystyle v=\sqrt{\frac{\gamma p}{\rho}}$">|; 

$key = q/displaystylev=v_perp.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2205.png"
 ALT="$\displaystyle v=v_\perp.$">|; 

$key = q/displaystylev^{,2},hat{bfD}=epsilon_0,c^{,2}left[hat{bfE}-({bfn}cdothat{bfE}),{bfn}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2157.png"
 ALT="$\displaystyle v^{ 2} \hat{\bf D} = \epsilon_0 c^{ 2}\left[\hat{\bf E} - ({\bf n}\cdot\hat{\bf E}) {\bf n}\right],$">|; 

$key = q/displaystylev^{,2}=cos^2theta,,v_perp^{,2}+sin^2theta,,v_parallel^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.93ex; " SRC="|."$dir".q|img2208.png"
 ALT="$\displaystyle v^{ 2} = \cos^2\theta  v_\perp^{ 2} + \sin^2\theta  v_\parallel^{ 2}.$">|; 

$key = q/displaystylev_0(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1019.png"
 ALT="$\displaystyle v_0(x)$">|; 

$key = q/displaystylev_0(x)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1053.png"
 ALT="$\displaystyle v_0(x) = 0,$">|; 

$key = q/displaystylev_0(x)equivfrac{partialy(x,0)}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1015.png"
 ALT="$\displaystyle v_0(x) \equiv \frac{\partial y(x,0)}{\partial t}.$">|; 

$key = q/displaystylev_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img455.png"
 ALT="$\displaystyle v_0$">|; 

$key = q/displaystylev_g=frac{domega(k_0)}{dk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3896.png"
 ALT="$\displaystyle v_g = \frac{d\omega(k_0)}{dk},$">|; 

$key = q/displaystylev_g=frac{domega(k_0)}{dk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2559.png"
 ALT="$\displaystyle v_g = \frac{d\omega(k_0)}{dk}$">|; 

$key = q/displaystylev_g=frac{domega}{dk}=2,c,frac{sqrt{omega,{mitOmega}_e}}{omega_{p,e}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2867.png"
 ALT="$\displaystyle v_g = \frac{d\omega}{dk} = 2 c \frac{\sqrt{\omega {\mit\Omega}_e}}{\omega_{p e}}.$">|; 

$key = q/displaystylev_g=frac{domega}{dk}=csqrt{1-omega_0^{,2}slashomega^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2942.png"
 ALT="$\displaystyle v_g= \frac{d\omega}{dk} = c\sqrt{1-\omega_0^{ 2}/\omega^{ 2}},$">|; 

$key = q/displaystylev_g=frac{hbar,k_0}{m}=frac{p}{m},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3898.png"
 ALT="$\displaystyle v_g = \frac{\hbar k_0}{m} = \frac{p}{m},$">|; 

$key = q/displaystylev_g=n,c=(1-omega_{p,e}^{,2}slashomega^{,2})^{1slash2},c.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2612.png"
 ALT="$\displaystyle v_g = n c=(1-\omega_{p e}^{ 2}/\omega^{ 2})^{1/2} c.$">|; 

$key = q/displaystylev_p=(g,d)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3111.png"
 ALT="$\displaystyle v_p = (g d)^{1/2},$">|; 

$key = q/displaystylev_p=frac{omega}{k}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1345.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k}.$">|; 

$key = q/displaystylev_p=frac{omega}{k}=(g,d)^{1slash2}left[frac{tanh(k,d)}{k,d}right]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3047.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k}=(g d)^{1/2}\left[\frac{\tanh(k d)}{k d}\right]^{1/2}.$">|; 

$key = q/displaystylev_p=frac{omega}{k}=frac{c}{n}=frac{c}{(1-omega_{p,e}^{,2}slashomega^{,2})^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img2608.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k} = \frac{c}{n}=\frac{c}{(1-\omega_{p e}^{ 2}/\omega^{ 2})^{1/2}}.$">|; 

$key = q/displaystylev_p=frac{omega}{k}=frac{c}{sqrt{1-omega_0^{,2}slashomega^{,2}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.52ex; vertical-align: -4.12ex; " SRC="|."$dir".q|img2941.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k} = \frac{c}{\sqrt{1-\omega_0^{ 2}/\omega^{ 2}}},$">|; 

$key = q/displaystylev_p=frac{omega}{k}=frac{hbar,k}{2,m}=frac{p}{2,m},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3838.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k} = \frac{\hbar k}{2 m} = \frac{p}{2 m},$">|; 

$key = q/displaystylev_p=frac{omega}{k}=sqrt{frac{g}{k}+frac{T}{rho},k},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img3165.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k} = \sqrt{\frac{g}{k} + \frac{T}{\rho} k},$">|; 

$key = q/displaystylev_p=frac{omega}{k}=v,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2545.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k} = v,$">|; 

$key = q/displaystylev_p=frac{omega}{k}=v;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1348.png"
 ALT="$\displaystyle v_p = \frac{\omega}{k} = v;$">|; 

$key = q/displaystylev_p=v_0,frac{sin(k,aslash2)}{(k,aslash2)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3175.png"
 ALT="$\displaystyle v_p = v_0 \frac{\sin(k a/2)}{(k a/2)},
$">|; 

$key = q/displaystylev_x(x,z,t),dy,dz+v_z(x,z,t),dx,dy=v_x(x+dx,z,t),dy,dz+v_z(x,z+dz,t),dx,dy,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3002.png"
 ALT="$\displaystyle v_x(x,z,t) dy dz + v_z(x,z,t) dx dy = v_x(x+dx,z,t) dy dz + v_z(x,z+dz,t) dx dy,$">|; 

$key = q/displaystylev_x(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3049.png"
 ALT="$\displaystyle v_x(x,z,t)$">|; 

$key = q/displaystylev_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2235.png"
 ALT="$\displaystyle v_x$">|; 

$key = q/displaystylev_z(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3051.png"
 ALT="$\displaystyle v_z(x,z,t)$">|; 

$key = q/displaystylev_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2237.png"
 ALT="$\displaystyle v_z$">|; 

$key = q/displaystylevarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img534.png"
 ALT="$\displaystyle \varphi$">|; 

$key = q/displaystylevarphi=tan^{-1}left(frac{E_y}{E_x}right)={mitDelta}k,,z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2690.png"
 ALT="$\displaystyle \varphi = \tan^{-1}\left(\frac{E_y}{E_x}\right) = {\mit\Delta} k  z,$">|; 

$key = q/displaystylex(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img598.png"
 ALT="$\displaystyle x(0)$">|; 

$key = q/displaystylex(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img393.png"
 ALT="$\displaystyle x(t)$">|; 

$key = q/displaystylex(t)=a,cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle x(t) = a \cos(\omega t-\phi),$">|; 

$key = q/displaystylex(t)=a,cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img390.png"
 ALT="$\displaystyle x(t) = a \cos(\omega t-\phi).
$">|; 

$key = q/displaystylex(t)=a,{rme}^{-gamma,t},cos(omega_1,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img423.png"
 ALT="$\displaystyle x(t) = a {\rm e}^{-\gamma t} \cos(\omega_1 t-\phi),$">|; 

$key = q/displaystylex(t)=a,{rme}^{-nu,tslash2},cosleft(omega_1,t-phiright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img442.png"
 ALT="$\displaystyle x(t) = a {\rm e}^{-\nu t/2} \cos\left(\omega_1  t-\phi\right),$">|; 

$key = q/displaystylex(t)=frac{hat{X}}{2},omega_0,tsin(omega_0,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img625.png"
 ALT="$\displaystyle x(t) = \frac{\hat{X}}{2} \omega_0 t\sin(\omega_0 t),$">|; 

$key = q/displaystylex(t)=hat{X},Q_fleft(1-{rme}^{-nu,tslash2}right)sin(omega_0,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img612.png"
 ALT="$\displaystyle x(t)= \hat{X} Q_f\left(1-{\rm e}^{-\nu t/2}\right)\sin(\omega_0 t),$">|; 

$key = q/displaystylex(t)=hat{x},cos(omega,t-varphi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img518.png"
 ALT="$\displaystyle x(t)=\hat{x} \cos(\omega t-\varphi).$">|; 

$key = q/displaystylex(t)=left(x_0+left[v_0+omega_0,x_0right]tright){rme}^{-omega_0,t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img641.png"
 ALT="$\displaystyle x(t) = \left(x_0 + \left[v_0+ \omega_0 x_0\right]t\right){\rm e}^{-\omega_0 t},
$">|; 

$key = q/displaystylex;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2647.png"
 ALT="$\displaystyle x$">|; 

$key = q/displaystylex=-frac{q,E_0}{m,omega^{,2}},cos(omega,t-k,z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2586.png"
 ALT="$\displaystyle x = -\frac{q E_0}{m \omega^{ 2}} \cos(\omega t-k z).$">|; 

$key = q/displaystylex=a,{rme}^{-nu,tslash2},cos(omega_1,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img477.png"
 ALT="$\displaystyle x = a {\rm e}^{-\nu t/2} \cos(\omega_1 t-\phi).$">|; 

$key = q/displaystylex=d,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1829.png"
 ALT="$\displaystyle x= d,$">|; 

$key = q/displaystylex=frac{F_0,sin(omega,t)}{m,(omega_0^{,2}-omega^{,2})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img650.png"
 ALT="$\displaystyle x = \frac{F_0 \sin(\omega t)}{m (\omega_0^{ 2}-\omega^{ 2})},
$">|; 

$key = q/displaystylex=frac{F_0}{m,(omega_0^{,2}-omega^{,2})}left[sin(omega,t)-frac{omega}{omega_0},sin(omega_0,t)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img653.png"
 ALT="$\displaystyle x =\frac{ F_0}{m (\omega_0^{ 2}-\omega^{ 2})}\left[\sin(\omega t)-\frac{\omega}{\omega_0} \sin(\omega_0 t)\right].
$">|; 

$key = q/displaystylex=v_g,t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2567.png"
 ALT="$\displaystyle x = v_g t.$">|; 

$key = q/displaystylex_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img196.png"
 ALT="$\displaystyle x_0$">|; 

$key = q/displaystylex_0=2,Sint_0^{z_0(S)}frac{dz}{sqrt{n^{,2}(z)-S^{2}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.70ex; " SRC="|."$dir".q|img2983.png"
 ALT="$\displaystyle x_0 = 2 S\int_0^{z_0(S)} \frac{dz}{\sqrt{n^{ 2}(z)-S^{2}}}.$">|; 

$key = q/displaystylex_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img669.png"
 ALT="$\displaystyle x_1(t)$">|; 

$key = q/displaystylex_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img671.png"
 ALT="$\displaystyle x_2(t)$">|; 

$key = q/displaystylex_3(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img792.png"
 ALT="$\displaystyle x_3(t)$">|; 

$key = q/displaystylex_e({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2734.png"
 ALT="$\displaystyle x_e({\bf r},t)$">|; 

$key = q/displaystylex_i({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2729.png"
 ALT="$\displaystyle x_i({\bf r},t)$">|; 

$key = q/displaystylex_i=i,a+psi_i(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1118.png"
 ALT="$\displaystyle x_i = i a + \psi_i(t),$">|; 

$key = q/displaystylex_i=i,a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img865.png"
 ALT="$\displaystyle x_i = i a,$">|; 

$key = q/displaystylex_n=[n-(N+1)slash2],d,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3453.png"
 ALT="$\displaystyle x_n = [n-(N+1)/2] d,$">|; 

$key = q/displaystylex_n=[n-(N+1)slash2],d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3376.png"
 ALT="$\displaystyle x_n = [n-(N+1)/2] d$">|; 

$key = q/displaystylex_{n,j}=left(frac{j}{n}right)l,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1002.png"
 ALT="$\displaystyle x_{n,j} = \left(\frac{j}{n}\right)l,$">|; 

$key = q/displaystylex_{ta}(t)=hat{x},cos(omega,t-varphi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img589.png"
 ALT="$\displaystyle x_{ta}(t)=\hat{x} \cos(\omega t-\varphi),$">|; 

$key = q/displaystylex_{tr}(t)=A,{rme}^{-nu,tslash2},cos(omega_1,t)+B,{rme}^{-nu,tslash2},sin(omega_1,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img591.png"
 ALT="$\displaystyle x_{tr}(t) = A {\rm e}^{-\nu t/2} \cos(\omega_1 t) + B {\rm e}^{-\nu t/2} \sin(\omega_1 t),$">|; 

$key = q/displaystylexsimeqfrac{F_0}{2,m,omega_0^{,2}}left[sin(omega_0,t)-omega_0,t,cos(omega_0,t)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img654.png"
 ALT="$\displaystyle x\simeq \frac{F_0}{2 m \omega_0^{ 2}}\left[\sin(\omega_0 t)-\omega_0 t \cos(\omega_0 t)\right].
$">|; 

$key = q/displaystyley(-t)=C_0+sum_{n>0}left[C_n',cos(n,omega,t)+S_n',sin(n,omega,t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img1312.png"
 ALT="$\displaystyle y(-t) = C_0 + \sum_{n&gt;0}\left[C_n' \cos(n \omega t) + S_n' \sin(n \omega t)\right],
$">|; 

$key = q/displaystyley(0,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img987.png"
 ALT="$\displaystyle y(0, t)$">|; 

$key = q/displaystyley(0_-,t)=y(0_+,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1531.png"
 ALT="$\displaystyle y(0_-,t) = y(0_+,t),$">|; 

$key = q/displaystyley(l,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img988.png"
 ALT="$\displaystyle y(l,t)$">|; 

$key = q/displaystyley(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img395.png"
 ALT="$\displaystyle y(t)$">|; 

$key = q/displaystyley(t)=-frac{2,A}{pi}sum_{n=1,infty}frac{sin(n,2pi,tslashtau)}{n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1279.png"
 ALT="$\displaystyle y(t) = - \frac{2 A}{\pi}\sum_{n=1,\infty} \frac{\sin(n 2\pi t/\tau)}{n}.$">|; 

$key = q/displaystyley(t)=-frac{4,A}{pi}left[frac{sin(omega,t)}{1}+frac{sin(3,omega,t)}{3}+frac{sin(5,omega,t)}{5}+cdotsright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1321.png"
 ALT="$\displaystyle y(t) = -\frac{4 A}{\pi}\left[\frac{\sin(\omega t)}{1}+ \frac{\sin(3 \omega t)}{3}+ \frac{\sin(5 \omega t)}{5}+\cdots\right].
$">|; 

$key = q/displaystyley(t)=A,(2,tslashtau-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1269.png"
 ALT="$\displaystyle y(t) = A (2 t/\tau-1)$">|; 

$key = q/displaystyley(t)=A,frac{tau}{T}+frac{2,A}{pi}sum_{n=1,infty}(-1)^{,n},frac{sin(n,pi,tauslashT)}{n},cos(n,2pi,tslashT).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1325.png"
 ALT="$\displaystyle y(t) =A \frac{\tau}{T} +\frac{2 A}{\pi}\sum_{n=1,\infty} (-1)^{ n} \frac{\sin (n \pi \tau/T)}{n} \cos(n 2\pi t/T).
$">|; 

$key = q/displaystyley(t)=Aleft{{array}{ccc}-1&mbox{hspace{1cm}}&0leqtslashtauleq1slash2[0.5ex]+1&&1slash2<tslashtauleq1{array}right.,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img1320.png"
 ALT="$\displaystyle y(t)=A\left\{\begin{array}{ccc}
-1&amp;\mbox{\hspace{1cm}}&amp;0\leq t/\tau\leq 1/2\ [0.5ex]
+1 &amp;&amp;1/2&lt;t/\tau \leq 1
\end{array}\right.,
$">|; 

$key = q/displaystyley(t)=Aleft{{array}{ccl}1&mbox{hspace{1cm}}&|t-Tslash2|leqtauslash2[0.5ex]0&&mbox{otherwise}{array}right.,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img1322.png"
 ALT="$\displaystyle y(t)=A\left\{\begin{array}{ccl}
1&amp;\mbox{\hspace{1cm}}&amp;\vert t-T/2\vert\leq \tau/2\ [0.5ex]
0 &amp;&amp;\mbox{otherwise}
\end{array}\right.,
$">|; 

$key = q/displaystyley(t)=C_0+sum_{n'=1,infty}left[C_{n'},cos(n',omega,t)+S_{n'},sin(n',omega,t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1282.png"
 ALT="$\displaystyle y(t) = C_0+ \sum_{n'=1,\infty} \left[C_{n'} \cos(n' \omega t)+ S_{n'} \sin(n' \omega t)\right],$">|; 

$key = q/displaystyley(t)=C_0+sum_{n>0}left[C_n,cos(n,omega,t)+S_n,sin(n,omega,t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img1311.png"
 ALT="$\displaystyle y(t) = C_0 + \sum_{n&gt;0}\left[C_n \cos(n \omega t) + S_n \sin(n \omega t)\right],
$">|; 

$key = q/displaystyley(t)=frac{A}{2}-frac{4,A}{pi^{,2}}sum_{n=1,3,5,cdots}frac{cos(n,2pi,tslashtau)}{n^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img1296.png"
 ALT="$\displaystyle y(t) = \frac{A}{2} - \frac{4 A}{\pi^{ 2}}\sum_{n=1,3,5,\cdots} \frac{\cos(n 2\pi t/\tau)}{n^{ 2}}.$">|; 

$key = q/displaystyley(t)=sum_{n'=1,infty}left[C_{n'},cos(n',omega,t)+S_{n'},sin(n',omega,t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1258.png"
 ALT="$\displaystyle y(t) = \sum_{n'=1,\infty} \left[C_{n'} \cos(n' \omega t)+ S_{n'} \sin(n' \omega t)\right],$">|; 

$key = q/displaystyley(t+T)=C_0+sum_{n>0}left[C_n'',cos(n,omega,t)+S_n'',sin(n,omega,t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img1315.png"
 ALT="$\displaystyle y(t+T) = C_0 + \sum_{n&gt;0}\left[C_n'' \cos(n \omega t) + S_n'' \sin(n \omega t)\right],
$">|; 

$key = q/displaystyley(x,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1740.png"
 ALT="$\displaystyle y(x,0)$">|; 

$key = q/displaystyley(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1553.png"
 ALT="$\displaystyle y(x,t)$">|; 

$key = q/displaystyley(x,t)=A,cos(omega,t+k,x-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1448.png"
 ALT="$\displaystyle y(x,t) = A \cos(\omega t+k x-\phi).$">|; 

$key = q/displaystyley(x,t)=A,cos(omega,t-k,x-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1441.png"
 ALT="$\displaystyle y(x,t) = A \cos(\omega t-k x-\phi).$">|; 

$key = q/displaystyley(x,t)=A,sin(k,x),cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img985.png"
 ALT="$\displaystyle y(x,t) = A \sin(k x) \cos(\omega t-\phi),$">|; 

$key = q/displaystyley(x,t)=A_+,cos(omega,t-k,x-phi_+)+A_-,cos(omega,t+k,x-phi_-).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1452.png"
 ALT="$\displaystyle y(x,t) = A_+ \cos(\omega t-k x-\phi_+) + A_- \cos(\omega t+k x-\phi_-).$">|; 

$key = q/displaystyley(x,t)=A_+,cos(omega,t-k_3,x)+A_-,cos(omega,t+k_3,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1568.png"
 ALT="$\displaystyle y(x,t) = A_+ \cos(\omega t-k_3 x) + A_- \cos(\omega t+k_3 x),$">|; 

$key = q/displaystyley(x,t)=A_i,cos(omega,t-k_1,x)+A_r,cos(omega,t+k_1,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1564.png"
 ALT="$\displaystyle y(x,t) = A_i \cos(\omega t-k_1 x) + A_r \cos(\omega t+k_1 x),$">|; 

$key = q/displaystyley(x,t)=A_i,cos(omega,t-k_1,x-phi_i)+A_r,cos(omega,t+k_1,x-phi_r).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1518.png"
 ALT="$\displaystyle y(x,t)= A_i \cos(\omega t-k_1 x-\phi_i) + A_r \cos(\omega t+k_1 x-\phi_r).$">|; 

$key = q/displaystyley(x,t)=A_t,cos(omega,t-k_2,x-phi_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1566.png"
 ALT="$\displaystyle y(x,t) = A_t \cos(\omega t-k_2 x-\phi_t),$">|; 

$key = q/displaystyley(x,t)=A_t,cos(omega,t-k_2,x-phi_t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1525.png"
 ALT="$\displaystyle y(x,t)= A_t \cos(\omega t-k_2 x-\phi_t).$">|; 

$key = q/displaystyley(x,t)=Y_0+V_0,t+sum_{n>0}A_n,cosleft(n,pi,frac{x}{l}right)cosleft(n,pi,frac{v,t}{l}-phi_nright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img1082.png"
 ALT="$\displaystyle y(x,t) = Y_0 + V_0 t + \sum_{n&gt;0} A_n \cos\left(n \pi \frac{x}{l}\right)\cos\left(n \pi \frac{v t}{l}-\phi_n\right),
$">|; 

$key = q/displaystyley(x,t)=frac{1}{2}left[F(x-v,t)+F(x+v,t)+frac{1}{v}int_{x-v,t}^{x+v,t}G(x'),dx'right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1745.png"
 ALT="$\displaystyle y(x,t)=\frac{1}{2}\left[F(x-v t)+F(x+v t) + \frac{1}{v}\int_{x-v t}^{x+v t}G(x') dx'\right].
$">|; 

$key = q/displaystyley(x,t)=sum_{n=1,infty}A_n,sinleft(n,pi,frac{x}{l}right),cosleft(n,2pi,frac{t}{tau}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1058.png"
 ALT="$\displaystyle y(x,t) = \sum_{n=1,\infty}A_n \sin\left(n \pi \frac{x}{l}\right) \cos\left(n 2\pi \frac{t}{\tau}\right),$">|; 

$key = q/displaystyley(x,t)=sum_{n=1,infty}A_n,sinleft(n,pi,frac{x}{l}right)cosleft(n,pi,frac{v,t}{l}-phi_nright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1112.png"
 ALT="$\displaystyle y(x,t) = \sum_{n=1,\infty}A_n \sin\left(n \pi \frac{x}{l}\right)\cos\left(n \pi \frac{v t}{l}-\phi_n\right),
$">|; 

$key = q/displaystyley;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2649.png"
 ALT="$\displaystyle y$">|; 

$key = q/displaystyley_0(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1017.png"
 ALT="$\displaystyle y_0(x)$">|; 

$key = q/displaystyley_0(x)equivy(x,0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1014.png"
 ALT="$\displaystyle y_0(x) \equiv y(x,0).$">|; 

$key = q/displaystyley_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2652.png"
 ALT="$\displaystyle y_0$">|; 

$key = q/displaystyley_e({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2736.png"
 ALT="$\displaystyle y_e({\bf r},t)$">|; 

$key = q/displaystyley_i(t)=A,sin(k,x_i),cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img909.png"
 ALT="$\displaystyle y_i(t) = A \sin(k x_i) \cos(\omega t-\phi),$">|; 

$key = q/displaystyley_i({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2731.png"
 ALT="$\displaystyle y_i({\bf r},t)$">|; 

$key = q/displaystyley_n(x,t)=A_n,sinleft(n,pi,frac{x}{l}right),cos(omega_n,t-phi_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img992.png"
 ALT="$\displaystyle y_n(x,t) = A_n \sin\left(n \pi \frac{x}{l}\right) \cos(\omega_n t-\phi_n),$">|; 

$key = q/displaystyley_{-n,i}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img935.png"
 ALT="$\displaystyle y_{-n,i}(t)$">|; 

$key = q/displaystyley_{-n}(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img995.png"
 ALT="$\displaystyle y_{-n}(x,t)$">|; 

$key = q/displaystyley_{N+1+n,i}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img941.png"
 ALT="$\displaystyle y_{N+1+n,i}(t)$">|; 

$key = q/displaystyley_{n,i}(t)=A_n,cosleft[frac{n,(i-1slash2)}{N},piright],cos(omega_n,t-phi_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1072.png"
 ALT="$\displaystyle y_{n,i}(t) = A_n \cos\left[\frac{n (i-1/2)}{N} \pi\right] \cos(\omega_n t-\phi_n),
$">|; 

$key = q/displaystyley_{n,i}(t)=A_n,sinleft(frac{n,i}{N+1},piright),cos(omega_n,t-phi_n),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img926.png"
 ALT="$\displaystyle y_{n,i}(t)=A_n \sin\left(\frac{n i}{N+1} \pi\right) \cos(\omega_n t-\phi_n),$">|; 

$key = q/displaystylez=r,{rme}^{,{rmi},theta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3821.png"
 ALT="$\displaystyle z = r {\rm e}^{ {\rm i} \theta},$">|; 

$key = q/displaystylez=x+{rmi},y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3803.png"
 ALT="$\displaystyle z = x + {\rm i} y,$">|; 

$key = q/displaystylez_e({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2738.png"
 ALT="$\displaystyle z_e({\bf r},t)$">|; 

$key = q/displaystylez_i({bfr},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2733.png"
 ALT="$\displaystyle z_i({\bf r},t)$">|; 

$key = q/displaystylezeta(x)proptocosleft(pi,frac{x}{l}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3089.png"
 ALT="$\displaystyle \zeta(x)\propto \cos\left(\pi \frac{x}{l}\right).$">|; 

$key = q/displaystylezeta(x,t)=a,sin(omega,t-k,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3064.png"
 ALT="$\displaystyle \zeta(x,t) = a \sin(\omega t-k x)$">|; 

$key = q/displaystyle{bfD}(x,y,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2147.png"
 ALT="$\displaystyle {\bf D}(x,y,z,t)$">|; 

$key = q/displaystyle{bfD}=epsilon_0,bm{epsilon}cdot{bfE}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2097.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0 \bm{\epsilon}\cdot {\bf E}.$">|; 

$key = q/displaystyle{bfD}=epsilon_0,epsilon,{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4453.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0 \epsilon {\bf E},$">|; 

$key = q/displaystyle{bfD}=epsilon_0,epsilon,{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1964.png"
 ALT="$\displaystyle {\bf D} = \epsilon_0 \epsilon {\bf E}$">|; 

$key = q/displaystyle{bfD}=epsilon_0,{bfE}+{bfP}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2723.png"
 ALT="$\displaystyle {\bf D}= \epsilon_0 {\bf E}+ {\bf P}.$">|; 

$key = q/displaystyle{bfE}(x,y,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2145.png"
 ALT="$\displaystyle {\bf E}(x,y,z,t)$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1927.png"
 ALT="$\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{bfE}=E_0,cos(omega,t-k,z),{bfe}_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1924.png"
 ALT="$\displaystyle {\bf E} = E_0 \cos(\omega t-k z) {\bf e}_x,$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1928.png"
 ALT="$\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{bfE}=E_0,cos(omega,t-k,z),{bfe}_y.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1926.png"
 ALT="$\displaystyle {\bf E} = E_0 \cos(\omega t-k z) {\bf e}_y.$">|; 

$key = q/displaystyle{bfH}(x,y,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2149.png"
 ALT="$\displaystyle {\bf H}(x,y,z,t)$">|; 

$key = q/displaystyle{bfP}=epsilon_0,(epsilon-1),{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1645.png"
 ALT="$\displaystyle {\bf P} = \epsilon_0 (\epsilon-1) {\bf E},$">|; 

$key = q/displaystyle{bfP}=epsilon_0,{bfE}+{bfP}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4452.png"
 ALT="$\displaystyle {\bf P}= \epsilon_0 {\bf E}+{\bf P}.$">|; 

$key = q/displaystyle{bfj}=frac{partial{bfP}}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4448.png"
 ALT="$\displaystyle {\bf j} = \frac{\partial{\bf P}}{\partial t},$">|; 

$key = q/displaystyle{bfj}=sigma,{bfE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img2891.png"
 ALT="$\displaystyle {\bf j} = \sigma {\bf E},$">|; 

$key = q/displaystyle{bfj}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img4446.png"
 ALT="$\displaystyle {\bf j} = {\bf0}.$">|; 

$key = q/displaystyle{bfk}=k,(sintheta,,0,,costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2794.png"
 ALT="$\displaystyle {\bf k} = k (\sin\theta, 0, \cos\theta),$">|; 

$key = q/displaystyle{bfk}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1947.png"
 ALT="$\displaystyle {\bf k}_i$">|; 

$key = q/displaystyle{bfk}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1949.png"
 ALT="$\displaystyle {\bf k}_r$">|; 

$key = q/displaystyle{bfk}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1951.png"
 ALT="$\displaystyle {\bf k}_t$">|; 

$key = q/displaystyle{bfn}=(sintheta,cosphi,,sintheta,sinphi,,costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2194.png"
 ALT="$\displaystyle {\bf n} = (\sin\theta \cos\phi, \sin\theta \sin\phi, \cos\theta).$">|; 

$key = q/displaystyle{bfn}cdothat{bfD}=n_x,hat{D}_x+n_y,hat{D}_y+n_z,hat{D}_z=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2165.png"
 ALT="$\displaystyle {\bf n} \cdot\hat{\bf D}= n_x \hat{D}_x+n_y \hat{D}_y+n_z \hat{D}_z=0,$">|; 

$key = q/displaystyle{bfn}cdothat{bfD}={bfn}cdothat{bfH}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2155.png"
 ALT="$\displaystyle {\bf n}\cdot\hat{\bf D}= {\bf n}\cdot\hat{\bf H} =0,$">|; 

$key = q/displaystyle{bfn}cdot{bfr}=d,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1832.png"
 ALT="$\displaystyle {\bf n}\cdot{\bf r} = d,$">|; 

$key = q/displaystyle{bfn}cdot{bfr}=v,t-j,lambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1840.png"
 ALT="$\displaystyle {\bf n}\cdot{\bf r} = v t-j \lambda,$">|; 

$key = q/displaystyle{bfp}=hbar,{bfk},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4136.png"
 ALT="$\displaystyle {\bf p} = \hbar {\bf k},$">|; 

$key = q/displaystyle{bfv}_g=left(frac{partialomega}{partialk_x},,0,,frac{partialomega}{partialk_z}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2958.png"
 ALT="$\displaystyle {\bf v}_g = \left(\frac{\partial\omega}{\partial k_x}, 0, \frac{\partial\omega}{\partial k_z}\right).$">|; 

$key = q/displaystyle{bfx}(t)=eta_1(t),hat{bfx}_1+eta_2(t),hat{bfx}_2+eta_3(t),hat{bfx}_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img820.png"
 ALT="$\displaystyle {\bf x}(t) = \eta_1(t) \hat{\bf x}_1 + \eta_2(t) \hat{\bf x}_2+\eta_3(t) \hat{\bf x}_3,$">|; 

$key = q/displaystyle{calC}(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3689.png"
 ALT="$\displaystyle {\cal C}(u,v)$">|; 

$key = q/displaystyle{calC}(u,v)=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3764.png"
 ALT="$\displaystyle {\cal C}(u,v) =$">|; 

$key = q/displaystyle{calC}=epsilon_0,frac{w}{d},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1499.png"
 ALT="$\displaystyle {\cal C} = \epsilon_0 \frac{w}{d},$">|; 

$key = q/displaystyle{calC}=frac{2pi,epsilon_0}{ln(bslasha)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1512.png"
 ALT="$\displaystyle {\cal C} = \frac{2\pi \epsilon_0}{\ln(b/a)}.$">|; 

$key = q/displaystyle{calC}=frac{pi,epsilon_0}{cosh^{-1}(dslash2,a)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img1510.png"
 ALT="$\displaystyle {\cal C} = \frac{\pi \epsilon_0}{\cosh^{-1}(d/2 a)}.$">|; 

$key = q/displaystyle{calE}(x,t)=frac{1}{2}left[rholeft(frac{partialy}{partialt}right)^2+Tleft(frac{partialy}{partialx}right)^2right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1432.png"
 ALT="$\displaystyle {\cal E}(x,t) = \frac{1}{2}\left[\rho \left(\frac{\partial y}{\partial t}\right)^2
+ T\left(\frac{\partial y}{\partial x}\right)^2\right]$">|; 

$key = q/displaystyle{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2139.png"
 ALT="$\displaystyle {\cal E}$">|; 

$key = q/displaystyle{calE}=K+U,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4195.png"
 ALT="$\displaystyle {\cal E} = K + U,$">|; 

$key = q/displaystyle{calE}=frac{1}{2},dot{I}^{,2}+frac{1}{2},omega^{,2},I^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle {\cal E} = \frac{1}{2} \dot{I}^{ 2} +\frac{1}{2}  \omega^{ 2} I^{ 2}$">|; 

$key = q/displaystyle{calE}=frac{1}{2},dot{s}^{,2}+frac{1}{2},omega^{,2},s^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img224.png"
 ALT="$\displaystyle {\cal E} = \frac{1}{2} \dot{s}^{ 2} + \frac{1}{2} \omega^{ 2} s^{ 2}.$">|; 

$key = q/displaystyle{calE}=frac{1}{2},{calL},I^{,2}+frac{1}{2},{calC},V^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1485.png"
 ALT="$\displaystyle {\cal E} = \frac{1}{2} {\cal L} I^{ 2} + \frac{1}{2} {\cal C} V^{ 2}$">|; 

$key = q/displaystyle{calE}=frac{1}{2}left(epsilon_0,E_x^{,2}+mu_0,H_y^{,2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1631.png"
 ALT="$\displaystyle {\cal E} = \frac{1}{2}\left(\epsilon_0 E_x^{ 2} + \mu_0 H_y^{ 2}\right)$">|; 

$key = q/displaystyle{calE}=frac{1}{2}left[rholeft(frac{partialpsi}{partialt}right)^2+Yleft(frac{partialpsi}{partialx}right)^2right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1459.png"
 ALT="$\displaystyle {\cal E} = \frac{1}{2}\left[\rho\left(\frac{\partial\psi}{\partial t}\right)^2 + Y\left(\frac{\partial \psi}{\partial x}\right)^2\right]$">|; 

$key = q/displaystyle{calE}=frac{A}{R^{,2}}-frac{B}{R},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4203.png"
 ALT="$\displaystyle {\cal E} = \frac{A}{R^{ 2}} - \frac{B}{R},$">|; 

$key = q/displaystyle{calE}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img856.png"
 ALT="$\displaystyle {\cal E}_1$">|; 

$key = q/displaystyle{calE}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img858.png"
 ALT="$\displaystyle {\cal E}_2$">|; 

$key = q/displaystyle{calI}(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3341.png"
 ALT="$\displaystyle {\cal I}(\theta)$">|; 

$key = q/displaystyle{calI}(theta)propto1+cosleft(2pi,frac{d}{lambda},thetaright),{rmsinc}left(pi,frac{d}{lambda},theta_0right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3353.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto 1 + \cos\left(2\pi \frac{d}{\lambda} \theta\right) {\rm sinc}\left(\pi \frac{d}{\lambda} \theta_0\right),$">|; 

$key = q/displaystyle{calI}(theta)proptocos^2left(pi,frac{d}{lambda},sinthetaright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3288.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto \cos^2\left(\pi \frac{d}{\lambda} \sin\theta\right).$">|; 

$key = q/displaystyle{calI}(theta)proptocos^2left(pi,frac{d}{lambda},sinthetaright){rmsinc}^2left(pi,frac{delta}{lambda},sinthetaright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3742.png"
 ALT="$\displaystyle {\cal I}(\theta)\propto \cos^2\left(\pi \frac{d}{\lambda} \sin\theta\right){\rm sinc}^2\left(\pi \frac{\delta}{\lambda} \sin\theta\right).
$">|; 

$key = q/displaystyle{calI}(theta)proptocos^2left(pi,frac{d}{lambda},thetaright){rmsinc}^2left(frac{pi}{2},frac{d}{lambda},theta_0right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3365.png"
 ALT="$\displaystyle {\cal I}(\theta)\propto \cos^2\left(\pi \frac{d}{\lambda} \theta\right){\rm sinc}^2\left(\frac{\pi}{2} \frac{d}{\lambda} \theta_0\right).$">|; 

$key = q/displaystyle{calI}(theta)proptocos^2left[pi,frac{d}{lambda},(theta-theta_0)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3308.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto\cos^2\left[\pi \frac{d}{\lambda} (\theta-\theta_0)\right].$">|; 

$key = q/displaystyle{calI}(theta)proptofrac{sin^2[pi,N,(dslashlambda),sintheta]}{sin^2[pi,(dslashlambda),sintheta)]}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.29ex; " SRC="|."$dir".q|img3378.png"
 ALT="$\displaystyle {\cal I}(\theta)\propto \frac{\sin^2[\pi N (d/\lambda) \sin\theta]}{\sin^2[\pi (d/\lambda) \sin\theta)]}.$">|; 

$key = q/displaystyle{calI}(theta)proptolanglepsi^{,2}(theta,t)rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3334.png"
 ALT="$\displaystyle {\cal I}(\theta)\propto \langle \psi^{ 2}(\theta,t)\rangle$">|; 

$key = q/displaystyle{calI}(theta)proptolanglepsi^{,2}(theta,t)rangleproptoleft[sum_{n=1,N}cosleft(2pi,frac{x_n}{lambda},sinthetaright)right]^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.08ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3374.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto \langle \psi^{ 2}(\theta,t)\rangle \pro...
...um_{n=1,N} \cos\left(2\pi \frac{x_n}{\lambda} \sin\theta\right)\right]^{ 2},$">|; 

$key = q/displaystyle{calI}(theta)proptoleft(int_0^aint_0^{2pi}cos(k,rho,theta,cosnu),dnu,frac{rho,drho}{pi,a^{,2}}right)^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3527.png"
 ALT="$\displaystyle {\cal I}(\theta)\propto \left(\int_0^a\int_0^{2\pi}\cos(k \rho \theta \cos\nu) d\nu \frac{\rho d\rho}{\pi a^{ 2}}\right)^{ 2},$">|; 

$key = q/displaystyle{calI}(theta)proptoleft[bar{F}(theta)right]^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3428.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto \left[\bar{F}(\theta)\right]^{ 2}.$">|; 

$key = q/displaystyle{calI}(theta)proptoleft[frac{2,J_1(k,a,theta)}{k,a,theta}right]^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3533.png"
 ALT="$\displaystyle {\cal I}(\theta)\propto \left[\frac{2 J_1(k a \theta)}{k a \theta}\right]^{ 2}.$">|; 

$key = q/displaystyle{calI}(theta)proptoleft[sum_{n=1,N}cosleft(2pi,[n-(N+1)slash2],frac{d}{lambda},sinthetaright)right]^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.08ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img3377.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto \left[\sum_{n=1,N} \cos\left(2\pi [n-(N+1)/2] \frac{d}{\lambda} \sin\theta\right)\right]^{ 2},$">|; 

$key = q/displaystyle{calI}(theta)propto{rmsinc}^2left[pi,frac{delta}{lambda},(theta-theta_0)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3435.png"
 ALT="$\displaystyle {\cal I}(\theta) \propto {\rm sinc}^2\left[\pi \frac{\delta}{\lambda} (\theta-\theta_0)\right].$">|; 

$key = q/displaystyle{calI}(theta,phi')proptoleft(int_0^aint_0^{2pi}cos[k,rho,theta,cos(phi-phi')],frac{rho,dphi,drho}{pi,a^{,2}}right)^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3526.png"
 ALT="$\displaystyle {\cal I}(\theta,\phi') \propto\left(\int_0^a\int_0^{2\pi}\cos[k ...
...theta \cos(\phi-\phi')] \frac{\rho d\phi d\rho}{\pi a^{ 2}}\right)^{ 2},$">|; 

$key = q/displaystyle{calI}(theta_x,theta_y)propto{rmsinc}^{2}left(pi,frac{a}{lambda},theta_xright){rmsinc}^{2}left(pi,frac{b}{lambda},theta_yright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3515.png"
 ALT="$\displaystyle {\cal I}(\theta_x,\theta_y)\propto {\rm sinc}^{2}\left(\pi \frac...
...a} \theta_x\right){\rm sinc}^{2}\left(\pi \frac{b}{\lambda} \theta_y\right).$">|; 

$key = q/displaystyle{calI}(u',v')proptolanglepsi^{,2}(u',v',t)rangle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3594.png"
 ALT="$\displaystyle {\cal I}(u',v') \propto
\langle \psi^{ 2}(u',v',t)\rangle,$">|; 

$key = q/displaystyle{calI}(x,t)=-T,frac{partialy}{partialt},frac{partialy}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1433.png"
 ALT="$\displaystyle {\cal I}(x,t) = - T \frac{\partial y}{\partial t} \frac{\partial y}{\partial x}.$">|; 

$key = q/displaystyle{calI}(x,t)=T,k,omega,A^2,sin^2(omega,t-k,x-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1442.png"
 ALT="$\displaystyle {\cal I}(x,t) = T k \omega A^2 \sin^2(\omega t-k x-\phi).$">|; 

$key = q/displaystyle{calI}(x,t)={};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1453.png"
 ALT="$\displaystyle {\cal I}(x,t)={}$">|; 

$key = q/displaystyle{calI}=-Y,frac{partialpsi}{partialt},frac{partialpsi}{partialx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1460.png"
 ALT="$\displaystyle {\cal I} = - Y \frac{\partial\psi}{\partial t} \frac{\partial\psi}{\partial x}$">|; 

$key = q/displaystyle{calI}=4,{calI}_0,sin^{2}left(frac{pi}{2},frac{a^{,2}}{lambda,R}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3774.png"
 ALT="$\displaystyle {\cal I} = 4 {\cal I}_0 \sin^{2}\left(\frac{\pi}{2} \frac{a^{ 2}}{\lambda R}\right),
$">|; 

$key = q/displaystyle{calI}=I,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img1486.png"
 ALT="$\displaystyle {\cal I} = I V$">|; 

$key = q/displaystyle{calI}={calI}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3781.png"
 ALT="$\displaystyle {\cal I} = {\cal I}_0,
$">|; 

$key = q/displaystyle{calI}={calI}_0left[1-frac{2,a}{r'},J_1left(2pi,frac{a,r'}{lambda,R}right)sinleft(pi,frac{r'^{,2}}{lambda,R}right)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3782.png"
 ALT="$\displaystyle {\cal I}= {\cal I}_0\left[1-\frac{2 a}{r'} J_1\left(2\pi \frac...
...r'}{\lambda R}\right)\sin\left(\pi \frac{r'^{ 2}}{\lambda R}\right)\right]
$">|; 

$key = q/displaystyle{calI}={calI}_0left[frac{a}{r'},J_1left(2pi,frac{a,r'}{lambda,R}right)right]^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3779.png"
 ALT="$\displaystyle {\cal I}= {\cal I}_0\left[\frac{a}{r'} J_1\left(2\pi \frac{a r'}{\lambda R}\right)\right]^{ 2}
$">|; 

$key = q/displaystyle{calI}_0,pi,a^{,2}left[1-J_0^{,2}(k,a,theta_0)-J_1^{,2}(k,a,theta_0)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3751.png"
 ALT="$\displaystyle {\cal I}_0 \pi a^{ 2}\left[1-J_0^{ 2}(k a \theta_0)-J_1^{ 2}(k a \theta_0)\right],
$">|; 

$key = q/displaystyle{calI}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2252.png"
 ALT="$\displaystyle {\cal I}_x$">|; 

$key = q/displaystyle{calI}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4461.png"
 ALT="$\displaystyle {\cal I}_y$">|; 

$key = q/displaystyle{calI}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2254.png"
 ALT="$\displaystyle {\cal I}_z$">|; 

$key = q/displaystyle{calI}_z=-E_y,H_x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2029.png"
 ALT="$\displaystyle {\cal I}_z = -E_y H_x.$">|; 

$key = q/displaystyle{calI}_z=E_x,H_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1632.png"
 ALT="$\displaystyle {\cal I}_z = E_x H_y$">|; 

$key = q/displaystyle{calL}=mu_0,frac{d}{w},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1501.png"
 ALT="$\displaystyle {\cal L} = \mu_0 \frac{d}{w},$">|; 

$key = q/displaystyle{calS}(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3691.png"
 ALT="$\displaystyle {\cal S}(u,v)$">|; 

$key = q/displaystyle{calS}(u,v)=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3766.png"
 ALT="$\displaystyle {\cal S}(u,v) =$">|; 

$key = q/displaystyle{mitDelta}E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img479.png"
 ALT="$\displaystyle {\mit\Delta} E$">|; 

$key = q/displaystyle{mitDelta}f,{mitDelta}tsimeq1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2495.png"
 ALT="$\displaystyle {\mit\Delta} f {\mit\Delta} t\simeq 1,$">|; 

$key = q/displaystyle{mitDelta}k=frac{1}{2,{mitDelta}x}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3888.png"
 ALT="$\displaystyle {\mit\Delta} k = \frac{1}{2 {\mit\Delta} x}.$">|; 

$key = q/displaystyle{mitDelta}k=frac{1}{2}left(frac{omega_{p,e}}{omega}right)^2left(frac{{mitOmega}_e}{c}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2684.png"
 ALT="$\displaystyle {\mit\Delta} k = \frac{1}{2}\left(\frac{\omega_{p e}}{\omega}\right)^2\left(\frac{{\mit\Omega}_e}{c}\right).$">|; 

$key = q/displaystyle{mitDelta}omega,{mitDelta}tsimeq2pi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2494.png"
 ALT="$\displaystyle {\mit\Delta}\omega {\mit\Delta} t\simeq 2\pi.$">|; 

$key = q/displaystyle{mitDelta}omegasimfrac{2pi}{tau}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3315.png"
 ALT="$\displaystyle {\mit\Delta}\omega\sim \frac{2\pi}{\tau}.$">|; 

$key = q/displaystyle{mitDelta}pgtrsimfrac{hbar}{2,{mitDelta}x}simfrac{hbar}{a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3942.png"
 ALT="$\displaystyle {\mit\Delta} p \gtrsim \frac{\hbar}{2 {\mit\Delta} x}\sim \frac{\hbar}{a}.$">|; 

$key = q/displaystyle{mitDelta}s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1419.png"
 ALT="$\displaystyle {\mit\Delta} s$">|; 

$key = q/displaystyle{mitDelta}theta>1.22,frac{lambda}{D},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3539.png"
 ALT="$\displaystyle {\mit\Delta}\theta &gt; 1.22 \frac{\lambda}{D},$">|; 

$key = q/displaystyle{mitDelta}theta_j=tantheta_j,frac{{mitDelta}lambda}{lambda}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3404.png"
 ALT="$\displaystyle {\mit\Delta}\theta_j = \tan\theta_j \frac{{\mit\Delta}\lambda}{\lambda}.$">|; 

$key = q/displaystyle{mitDelta}varphi=phi(z)-phi(0)=frac{e^{,3}}{2,epsilon_0,m_e^{,2},c,omega^{,2}}int_0^zn_e(z'),B_0(z'),dz'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img2694.png"
 ALT="$\displaystyle {\mit\Delta}\varphi=\phi(z)-\phi(0)=\frac{e^{ 3}}{2 \epsilon_0 m_e^{ 2} c \omega^{ 2}}\int_0^z n_e(z') B_0(z') dz'.$">|; 

$key = q/displaystyle{mitDelta}x,{mitDelta}k=frac{1}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3895.png"
 ALT="$\displaystyle {\mit\Delta}x {\mit\Delta} k = \frac{1}{2}.$">|; 

$key = q/displaystyle{mitDelta}x,{mitDelta}kgtrsimfrac{1}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3906.png"
 ALT="$\displaystyle {\mit\Delta}x {\mit\Delta} k\gtrsim \frac{1}{2}.$">|; 

$key = q/displaystyle{mitDelta}x,{mitDelta}ksimeq2pi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2370.png"
 ALT="$\displaystyle {\mit\Delta} x {\mit\Delta} k \simeq 2\pi,$">|; 

$key = q/displaystyle{mitDelta}x,{mitDelta}p_xgtrsim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4142.png"
 ALT="$\displaystyle {\mit\Delta} x {\mit\Delta} p_x\gtrsim$">|; 

$key = q/displaystyle{mitDelta}x,{mitDelta}pgtrsimfrac{hbar}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3908.png"
 ALT="$\displaystyle {\mit\Delta}x {\mit\Delta} p \gtrsim \frac{\hbar}{2}.$">|; 

$key = q/displaystyle{mitDelta}xsim({mitDelta}x)_0+frac{d^{,2}omega(k_0)}{dk^{,2}},frac{t}{({mitDelta}x)_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2577.png"
 ALT="$\displaystyle {\mit\Delta} x \sim ({\mit\Delta} x)_0 + \frac{d^{ 2}\omega(k_0)}{dk^{ 2}} \frac{t}{({\mit\Delta} x)_0}.$">|; 

$key = q/displaystyle{mitDelta}xsimeq({mitDelta}x)_0+frac{d^{,2}omega(k_0)}{dk^{,2}},frac{t}{({mitDelta}x)_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3901.png"
 ALT="$\displaystyle {\mit\Delta} x \simeq ({\mit\Delta} x)_0 + \frac{d^{ 2}\omega(k_0)}{dk^{ 2}} \frac{t}{({\mit\Delta} x)_0},$">|; 

$key = q/displaystyle{mitDelta}xsimeq({mitDelta}x)_0+frac{hbar}{m},frac{t}{({mitDelta}x)_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3902.png"
 ALT="$\displaystyle {\mit\Delta} x \simeq ({\mit\Delta} x)_0 + \frac{\hbar}{m} \frac{t}{({\mit\Delta} x)_0}.$">|; 

$key = q/displaystyle{mitDelta}xsimfrac{hbar,t}{m,({mitDelta}x)_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3909.png"
 ALT="$\displaystyle {\mit\Delta} x\sim \frac{\hbar t}{m ({\mit\Delta}x)_0}$">|; 

$key = q/displaystyle{mitDelta}xsim{mitDelta}v,tsimfrac{hbar,t}{m,({mitDelta}x)_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3914.png"
 ALT="$\displaystyle {\mit\Delta} x \sim {\mit\Delta}v t \sim \frac{\hbar t}{m ({\mit\Delta}x)_0},$">|; 

$key = q/displaystyle{mitDelta}y,{mitDelta}p_ygtrsim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4144.png"
 ALT="$\displaystyle {\mit\Delta} y {\mit\Delta} p_y\gtrsim$">|; 

$key = q/displaystyle{mitDelta}z,{mitDelta}p_zgtrsim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4145.png"
 ALT="$\displaystyle {\mit\Delta} z {\mit\Delta} p_z\gtrsim$">|; 

$key = q/displaystyle{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2751.png"
 ALT="$\displaystyle {\mit\Omega}_e$">|; 

$key = q/displaystyle{mitOmega}_e=frac{e,B_0}{m_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2653.png"
 ALT="$\displaystyle {\mit\Omega}_e = \frac{e B_0}{m_e}$">|; 

$key = q/displaystyle{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2749.png"
 ALT="$\displaystyle {\mit\Omega}_i$">|; 

$key = q/displaystyle{rmRe}left[psi_0,{rme}^{-{rmi},(omega,t-k,x)}right]=A,cos(omega,t-k,x-phi)=psi(x,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3825.png"
 ALT="$\displaystyle {\rm Re}\left[\psi_0 {\rm e}^{-{\rm i} (\omega t-k x)}\right] =A \cos(\omega t-k x-\phi)=\psi(x,t).$">|; 

$key = q/displaystyle{rme}^x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4216.png"
 ALT="$\displaystyle {\rm e}^x$">|; 

$key = q/displaystyle{rme}^{,{rmi},n,theta}equivcos(n,theta)+{rmi},sin(n,theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3724.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} n \theta} \equiv \cos(n \theta) + {\rm i} \sin(n \theta),
$">|; 

$key = q/displaystyle{rme}^{,{rmi},phi}equivcosphi+{rmi},sinphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3817.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} \phi} \equiv \cos\phi + {\rm i} \sin\phi,$">|; 

$key = q/displaystyle{rme}^{,{rmi},theta}=costheta+{rmi},sintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4222.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} \theta} = \cos\theta + {\rm i} \sin\theta,
$">|; 

$key = q/displaystyle{rmi},hbar,frac{partialpsi}{partialt},psi^ast=-frac{hbar^{,2}}{2,m},frac{partial^{,2}psi}{partialx^{,2}},psi^ast+U(x),|psi|^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3848.png"
 ALT="$\displaystyle {\rm i} \hbar \frac{\partial\psi}{\partial t} \psi^\ast = -\fr...
...{\partial^{ 2}\psi}{\partial x^{ 2}} \psi^\ast + U(x) \vert\psi\vert^{ 2}.$">|; 

$key = q/displaystyle{rmi},hbar,frac{partialpsi}{partialt}=-frac{hbar^{,2}}{2,m},frac{partial^{,2}psi}{partialx^{,2}}+U(x),psi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3835.png"
 ALT="$\displaystyle {\rm i} \hbar \frac{\partial\psi}{\partial t} = -\frac{\hbar^{ 2}}{2 m} \frac{\partial^{ 2}\psi}{\partial x^{ 2}} + U(x) \psi.$">|; 

$key = q/displaystyle{rmi},hbar,frac{partialpsi}{partialt}=-frac{hbar^{,2}}{2,m},nabla^{,2}psi+U({bfr}),psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4138.png"
 ALT="$\displaystyle {\rm i} \hbar \frac{\partial\psi}{\partial t} = - \frac{\hbar^{ 2}}{2 m} \nabla^{ 2}\psi + U({\bf r}) \psi,$">|; 

$key = q/displaystyle{rmi},k,(1-R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4039.png"
 ALT="$\displaystyle {\rm i} k (1-R)$">|; 

$key = q/displaystyle|T|^{,2}=1-|R|^{,2}=frac{4,k^{,2},q^{,2}}{4,k^{,2},q^{,2}+(k^{,2}+q^{,2})^{,2},sinh^2(q,a)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.36ex; " SRC="|."$dir".q|img4043.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = 1-\vert R\vert^{ 2}= \frac{4 k^{ 2} q^{ 2}}{4 k^{ 2} q^{ 2} + (k^{ 2}+q^{ 2})^{ 2} \sinh^2(q a)}.$">|; 

$key = q/displaystyle|T|^{,2}=1-|R|^{,2}=frac{4,k^{,2},q^{,2}}{4,k^{,2},q^{,2}+(k^{,2}-q^{,2})^{,2},sin^2(q,a)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.36ex; " SRC="|."$dir".q|img4023.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = 1-\vert R\vert^{ 2}= \frac{4 k^{ 2} q^{ 2}}{4 k^{ 2} q^{ 2} + (k^{ 2}-q^{ 2})^{ 2} \sin^2(q a)}.$">|; 

$key = q/displaystyle|T|^{,2}=expleft(-2sqrt{2},frac{m_e^{1slash2},W^{,3slash2}}{hbar,e,{calE}}int_{0}^{1}sqrt{1-y},dyright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4089.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \exp\left(-2\sqrt{2} \frac{m_e^{1/2} W^{ 3/2}}{\hbar e {\cal E}}\int_{0}^{1}
\sqrt{1-y} dy\right),$">|; 

$key = q/displaystyle|T|^{,2}=expleft(-frac{2sqrt{2,m_e}}{hbar}int_{0}^{Wslashe,{calE}}sqrt{W-e,{calE},x},dxright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4088.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \exp\left(-\frac{2\sqrt{2 m_e}}{\hbar}\int_{0}^{W/e {\cal E}}
\sqrt{W-e {\cal E} x } dx\right),$">|; 

$key = q/displaystyle|T|^{,2}=expleft(-frac{2sqrt{2,m_e}}{hbar}int_{x_1}^{x_2}sqrt{U(x)-E},dxright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img4087.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \exp\left(-\frac{2\sqrt{2 m_e}}{\hbar}\int_{x_1}^{x_2}
\sqrt{U(x)- E} dx\right),$">|; 

$key = q/displaystyle|T|^{,2}=expleft(-frac{2sqrt{2,m}}{hbar}int_{r_1}^{r_2}sqrt{U(r)-E},drright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4098.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \exp\left(-\frac{2\sqrt{2 m}}{\hbar}\int_{r_1}^{r_2}
\sqrt{U(r)-E} dr\right),$">|; 

$key = q/displaystyle|T|^{,2}=expleft(-frac{4sqrt{2}}{3},frac{m_e^{1slash2},W^{,3slash2}}{hbar,e,{calE}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4090.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \exp\left(-\frac{4\sqrt{2}}{3} \frac{m_e^{1/2} W^{ 3/2}}{\hbar e {\cal E}}\right).$">|; 

$key = q/displaystyle|T|^{,2}=expleft[-2sqrt{2},betaint_{1}^{E_cslashE}left(frac{1}{y}-frac{E}{E_c}right)^{1slash2}dyright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4103.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \exp\left[-2\sqrt{2} \beta \int_{1}^{E_c/E}\left(\frac{1}{y}-\frac{E}{E_c}\right)^{1/2} dy\right],$">|; 

$key = q/displaystyle|T|^{,2}=frac{|psi_2|^{,2}}{|psi_1|^{,2}}=expleft(-2,int_{x_1}^{x_2}|k(x')|,dx'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img4080.png"
 ALT="$\displaystyle \vert T\vert^{ 2} = \frac{\vert\psi_2\vert^{ 2}}{\vert\psi_1\vert^{ 2}} = \exp\left(-2 \int_{x_1}^{x_2} \vert k(x')\vert dx'\right).$">|; 

$key = q/displaystyle|T|^{,2}simeqexpleft[-2sqrt{2},betaleft(frac{pi}{2}sqrt{frac{E_c}{E}}-2right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img4109.png"
 ALT="$\displaystyle \vert T\vert^{ 2} \simeq \exp\left[-2\sqrt{2} \beta\left(\frac{\pi}{2}\sqrt{\frac{E_c}{E}}-2\right)\right].$">|; 

$key = q/displaystyle|T|^{,2}simeqfrac{4,E}{V},{rme}^{-2,aslashlambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4054.png"
 ALT="$\displaystyle \vert T\vert^{ 2}\simeq \frac{4 E}{V} {\rm e}^{-2 a/\lambda},$">|; 

$key = q/displaystyle|bar{psi}(k)|^{,2}proptoexpleft[-frac{(k-k_0)^{,2}}{2,({mitDelta}k)^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3893.png"
 ALT="$\displaystyle \vert\bar{\psi}(k)\vert^{ 2} \propto \exp\left[- \frac{(k-k_0)^{ 2}}{2 ({\mit\Delta}k)^{ 2}}\right].$">|; 

$key = q/displaystyle|psi(x)|^{,2}=|psi_0|^{,2};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4069.png"
 ALT="$\displaystyle \vert\psi(x)\vert^{ 2} = \vert\psi_0\vert^{ 2};$">|; 

$key = q/displaystyle|psi(x)|^{,2}=|psi_1|^{,2},expleft(-2,int_{x_1}^x|k(x')|,dx'right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img4074.png"
 ALT="$\displaystyle \vert\psi(x)\vert^{ 2} = \vert\psi_1\vert^{ 2} \exp\left(-2 \int_{x_1}^x \vert k(x')\vert dx'\right),$">|; 

$key = q/displaystyle|psi(x,0)|^{,2}proptoexpleft[-frac{(x-x_0)^{,2}}{2,({mitDelta}x)^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3874.png"
 ALT="$\displaystyle \vert\psi(x,0)\vert^{ 2} \propto \exp\left[- \frac{(x-x_0)^{ 2}}{2 ({\mit\Delta}x)^{ 2}}\right].$">|; 

$key = q/displaystyle|psi(x,t)|rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3855.png"
 ALT="$\displaystyle \vert\psi(x,t)\vert\rightarrow 0$">|; 

$key = q/displaystyle|psi_2|^{,2}=|psi_1|^{,2},expleft(-2,int_{x_1}^{x_2}|k(x')|,dx'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img4076.png"
 ALT="$\displaystyle \vert\psi_2\vert^{ 2} = \vert\psi_1\vert^{ 2} \exp\left(-2 \int_{x_1}^{x_2} \vert k(x')\vert dx'\right).$">|; 

$key = q/displaystyle|x|rightarrowinfty,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3856.png"
 ALT="$\displaystyle \vert x\vert\rightarrow\infty,$">|; 

$key = q/displaystyle~~+hat{X}left[frac{omega_0,nu}{4,(omega_0-omega)^{,2}+nu^{,2}}right]left[sin(omega,t)-{rme}^{-nu,tslash2},sin(omega_0,t)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img611.png"
 ALT="$\displaystyle&nbsp;&nbsp;+ \hat{X}\left[\frac{\omega_0 \nu}{4 (\omega_0-\omega)^{ 2}+...
...,2}}\right]\left[\sin(\omega t)-{\rm e}^{-\nu t/2} \sin(\omega_0 t)\right].$">|; 

$key = q/displaystyle~~+left(2,gamma,omega_1-nu,omega_1right)a,{rme}^{-gamma,t},sin(omega_1,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img433.png"
 ALT="$\displaystyle&nbsp;&nbsp;+\left(2 \gamma \omega_1-\nu \omega_1\right) a {\rm e}^{-\gamma t} \sin(\omega_1 t-\phi).$">|; 

$key = q/displaystyle~~left.+sin(k,x_{i+1})right],cos(omega,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img916.png"
 ALT="$\displaystyle&nbsp;&nbsp;\left.+\sin(k x_{i+1})\right] \cos(\omega t-\phi),$">|; 

$key = q/displaystyle~~~+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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1939.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;+ \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).$">|; 

$key = q/displaystyle~~~-frac{1}{2}sum_{n>0}A_n,sinphi_n,sin[(omega_0-omega_n),t].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2468.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;-\frac{1}{2}\sum_{n&gt;0}A_n \sin\phi_n \sin[(\omega_0-\omega_n) t].$">|; 

$key = q/displaystyle~~~~+2,langlecos(omega,t-k,R-phi_A),cos(omega,t-k,R-phi_B)rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3336.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+2 \langle \cos (\omega t-k R-\phi_A) \cos (\omega t-k R-\phi_B)\rangle$">|; 

$key = q/displaystyle~~~~+cos(omega,t-k,R-phi_B),cosleft[frac{1}{2},k,d,(theta+theta_0slash2)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3333.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+ \cos(\omega t-k R-\phi_B) \cos\left[\frac{1}{2} k d (\theta+\theta_0/2)\right].$">|; 

$key = q/displaystyle~~~~+frac{1}{2}sum_{n>0}A_n,sinphi_n,sin[(omega_0+omega_n),t]+frac{1}{2}sum_{n>0}A_n,cosphi_n,cos[(omega_0-omega_n),t];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.64ex; " SRC="|."$dir".q|img2467.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\frac{1}{2}\sum_{n&gt;0}A_n \sin\phi_n \sin[(\omega_0+\omega_n) t]+\frac{1}{2}\sum_{n&gt;0}A_n \cos\phi_n \cos[(\omega_0-\omega_n) t]$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2012.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2073.png"
 ALT="$\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/displaystyle~~~~+int_{-infty}^{infty}C_-(k),cos[k,(v,t+x)],dk+int_{-infty}^{infty}S_-(k),sin[k,(v,t+x)],dk.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2406.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+ \int_{-\infty}^{\infty} C_-(k) \cos[k (v t+x)] dk+ \int_{-\infty}^{\infty} S_-(k) \sin[k (v t+x)] dk.$">|; 

$key = q/displaystyle~~~~+langle,cos^2(omega,t-k,R-phi_B)ranglecos^2left[frac{1}{2},k,d,(theta+theta_0slash2)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3338.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\langle \cos^2 (\omega t-k R-\phi_B)\rangle\cos^2\left[\frac{1}{2} k d (\theta+\theta_0/2)\right].$">|; 

$key = q/displaystyle~~~~+phi_r,cos[omega,(t-sintheta_r,xslashv_1+costheta_r,zslashv_1)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2265.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;+\phi_r \cos[\omega (t-\sin\theta_r x/v_1+\cos\theta_r z/v_1)],$">|; 

$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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2047.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2015.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2074.png"
 ALT="$\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~~~~+psi_r,sintheta_i,cos(omega,t-n_1,k_0,sintheta_i,x+n_1,k_0,costheta_i,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2018.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2075.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1973.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2048.png"
 ALT="$\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/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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img1976.png"
 ALT="$\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{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;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2049.png"
 ALT="$\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/displaystyle~~~~-sin(omega,t-k,R-phi)int_{-infty}^inftyint_{-infty}^inftyF(x,y),sin(k,theta_x,x+k,theta_y,y),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3505.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;-\sin(\omega t-k R-\phi)\int_{-\infty}^\infty\int_{-\infty}^\infty F(x,y) \sin(k \theta_x x+k \theta_y y) dx dy$">|; 

$key = q/displaystyle~~~~left.-sin(k,sintheta,x_n),int_{-infty}^inftyF_2(x'),sin(k,sintheta,x'),dx'right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3461.png"
 ALT="$\displaystyle&nbsp;&nbsp;&nbsp;&nbsp;\left.
- \sin(k \sin\theta x_n) \int_{-\infty}^\infty F_2(x') \sin(k \sin\theta x') dx'\right]$">|; 

$key = q/dllw;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1498.png"
 ALT="$d\ll w$">|; 

$key = q/dot{I}=-VslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img290.png"
 ALT="$\dot{I} = -V/L$">|; 

$key = q/dot{I}_1=dot{I}_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img783.png"
 ALT="$\dot{I}_1=\dot{I}_2=0$">|; 

$key = q/dot{Q}=I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img574.png"
 ALT="$\dot{Q}=I$">|; 

$key = q/dot{Q}_1=I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img743.png"
 ALT="$\dot{Q}_1=I_1$">|; 

$key = q/dot{Q}_2=I_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img744.png"
 ALT="$\dot{Q}_2=I_2$">|; 

$key = q/dot{phantom{x}}equivdslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img139.png"
 ALT="$\dot{\phantom{x}}\equiv d/dt$">|; 

$key = q/dot{psi}(x,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2412.png"
 ALT="$\dot{\psi}(x,0)$">|; 

$key = q/dot{psi}(x,0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1204.png"
 ALT="$\dot{\psi}(x,0)=0$">|; 

$key = q/dot{psi}(x,0)=V_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1202.png"
 ALT="$\dot{\psi}(x,0)=V_0$">|; 

$key = q/dot{s}(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img260.png"
 ALT="$\dot{s}(0) = 0$">|; 

$key = q/dot{s}(0)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img263.png"
 ALT="$\dot{s}(0)=1$">|; 

$key = q/dot{s}(0)=dot{s}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img266.png"
 ALT="$\dot{s}(0)=\dot{s}_0$">|; 

$key = q/dot{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img220.png"
 ALT="$\dot{s}$">|; 

$key = q/dot{s}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img232.png"
 ALT="$\dot{s}=0$">|; 

$key = q/dot{s}=alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img217.png"
 ALT="$\dot{s}=\alpha$">|; 

$key = q/dot{s}=ddot{s}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img227.png"
 ALT="$\dot{s}=\ddot{s}=0$">|; 

$key = q/dot{x}(0)=v_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img453.png"
 ALT="$\dot{x}(0)=v_0$">|; 

$key = q/dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img181.png"
 ALT="$\dot{x}$">|; 

$key = q/dot{x}=-omega,a,sin(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img153.png"
 ALT="$\dot{x} = -\omega a \sin(\omega t-\phi)$">|; 

$key = q/dot{x}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img392.png"
 ALT="$\dot{x}^{ 2}$">|; 

$key = q/dot{x}_1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img711.png"
 ALT="$\dot{x}_1=0$">|; 

$key = q/dot{x}_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img713.png"
 ALT="$\dot{x}_2=0$">|; 

$key = q/dpsi(x)slashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3969.png"
 ALT="$d\psi(x)/dx$">|; 

$key = q/dpsislashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4014.png"
 ALT="$d\psi/d x$">|; 

$key = q/dslashRll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3568.png"
 ALT="$d/R\ll 1$">|; 

$key = q/dslashlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3408.png"
 ALT="$d/\lambda$">|; 

$key = q/dslashlambda=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img92.png"
 ALT="$d/\lambda = 0.1$">|; 

$key = q/dslashlambda=10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img95.png"
 ALT="$d/\lambda = 10$">|; 

$key = q/dslashlambda=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img91.png"
 ALT="$d/\lambda = 1$">|; 

$key = q/dslashlambda=5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img90.png"
 ALT="$d/\lambda = 5$">|; 

$key = q/dslashlambda=8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3743.png"
 ALT="$d/\lambda=8$">|; 

$key = q/dslashlambdall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3294.png"
 ALT="$d/\lambda\ll 1$">|; 

$key = q/dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2997.png"
 ALT="$dx dy$">|; 

$key = q/dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2993.png"
 ALT="$dy dz$">|; 

$key = q/dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img367.png"
 ALT="$dy$">|; 

$key = q/e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img637.png"
 ALT="$e$">|; 

$key = q/epsilon,epsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1652.png"
 ALT="$\epsilon \epsilon_0$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1658.png"
 ALT="$\epsilon$">|; 

$key = q/epsilon>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1646.png"
 ALT="$\epsilon&gt;1$">|; 

$key = q/epsilon_0,E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1628.png"
 ALT="$\epsilon_0 E_x$">|; 

$key = q/epsilon_0,c^{,2},hat{E}_x=c^{,2},hat{D}_xslashepsilon_{xx}=v_x^{,2},hat{D}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img2161.png"
 ALT="$\epsilon_0 c^{ 2} \hat{E}_x = c^{ 2} \hat{D}_x/\epsilon_{xx}= v_x^{ 2} \hat{D}_x$">|; 

$key = q/epsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1617.png"
 ALT="$\epsilon_0$">|; 

$key = q/epsilon_0=8.8542times10^{-12},{rmC}^{,2},{rmN}^{-1},{rmm}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1500.png"
 ALT="$\epsilon_0= 8.8542\times 10^{-12} {\rm C}^{ 2} {\rm N}^{-1} {\rm m}^{-2}$">|; 

$key = q/epsilon_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2112.png"
 ALT="$\epsilon_{xx}$">|; 

$key = q/epsilon_{xx}=epsilon_{yy}=epsilon_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2190.png"
 ALT="$\epsilon_{xx}=\epsilon_{yy}=\epsilon_\perp$">|; 

$key = q/epsilon_{yx}=epsilon_{xy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2107.png"
 ALT="$\epsilon_{yx}=\epsilon_{xy}$">|; 

$key = q/epsilon_{yy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2113.png"
 ALT="$\epsilon_{yy}$">|; 

$key = q/epsilon_{zx}=epsilon_{xz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2108.png"
 ALT="$\epsilon_{zx}=\epsilon_{xz}$">|; 

$key = q/epsilon_{zy}=epsilon_{yz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2109.png"
 ALT="$\epsilon_{zy}=\epsilon_{yz}$">|; 

$key = q/epsilon_{zz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2114.png"
 ALT="$\epsilon_{zz}$">|; 

$key = q/epsilon_{zz}=epsilon_{parallel};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2191.png"
 ALT="$\epsilon_{zz}=\epsilon_{\parallel}$">|; 

$key = q/epsilonll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4108.png"
 ALT="$\epsilon\ll 1$">|; 

$key = q/eta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img38.png"
 ALT="$\eta _1$">|; 

$key = q/eta_1=(m_1,theta_1+m_2,theta_2)slash(m_1+m_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img846.png"
 ALT="$\eta_1=(m_1 \theta_1+m_2 \theta_2)/(m_1+m_2)$">|; 

$key = q/eta_1=hat{bfx}_1cdothat{bfx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img828.png"
 ALT="$\eta_1=\hat{\bf x}_1\cdot \hat{\bf x}$">|; 

$key = q/eta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img39.png"
 ALT="$\eta _2$">|; 

$key = q/eta_2=theta_1-theta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img847.png"
 ALT="$\eta_2=\theta_1-\theta_2$">|; 

$key = q/eta_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img830.png"
 ALT="$\eta_3$">|; 

$key = q/exp(+k,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3040.png"
 ALT="$\exp(+k z)$">|; 

$key = q/exp(,{rmi},theta)equivcostheta+{rmi},sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2514.png"
 ALT="$\exp( {\rm i} \theta)\equiv\cos \theta + {\rm i} \sin \theta$">|; 

$key = q/exp(-gamma,t),cos(omega_1,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img434.png"
 ALT="$\exp(-\gamma t) \cos(\omega_1 t-\phi)$">|; 

$key = q/exp(-gamma,t),sin(omega_1,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img435.png"
 ALT="$\exp(-\gamma t) \sin(\omega_1 t-\phi)$">|; 

$key = q/exp(-k,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3041.png"
 ALT="$\exp(-k z)$">|; 

$key = q/exp(-tslash2,tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2519.png"
 ALT="$\exp(-t/2 \tau)$">|; 

$key = q/exp(-{rmi},E,tslashhbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4006.png"
 ALT="$\exp(-{\rm i} E t/\hbar$">|; 

$key = q/exp(-{rmi},omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4060.png"
 ALT="$\exp(-{\rm i} \omega t)$">|; 

$key = q/f';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1712.png"
 ALT="$f'$">|; 

$key = q/f(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img416.png"
 ALT="$f(0)=0$">|; 

$key = q/f(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3599.png"
 ALT="$f(u,v)$">|; 

$key = q/f(u,v)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3586.png"
 ALT="$f(u,v)=1$">|; 

$key = q/f(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img142.png"
 ALT="$f(x)$">|; 

$key = q/f(x)simeq-k,x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img422.png"
 ALT="$f(x)\simeq -k x$">|; 

$key = q/f(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3550.png"
 ALT="$f(x,y)$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img171.png"
 ALT="$f$">|; 

$key = q/f<100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2910.png"
 ALT="$f&lt; 100$">|; 

$key = q/f=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3552.png"
 ALT="$f=0$">|; 

$key = q/f=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3551.png"
 ALT="$f=1$">|; 

$key = q/f=omegaslash2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img215.png"
 ALT="$f=\omega/2\pi$">|; 

$key = q/f=omegaslash2pi<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2907.png"
 ALT="$f=\omega/2\pi &lt; 1$">|; 

$key = q/f^{,(n)}(x)=d^{,n}f(x)slashdx^{,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4309.png"
 ALT="$f^{ (n)}(x)=d^{ n}f(x)/dx^{ n}$">|; 

$key = q/f_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1808.png"
 ALT="$f_0$">|; 

$key = q/f_1=vslash(4,l);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1239.png"
 ALT="$f_1=v/(4 l)$">|; 

$key = q/f_c(u',v')=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3590.png"
 ALT="$f_c(u',v')=0$">|; 

$key = q/f_s(u',v')=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3591.png"
 ALT="$f_s(u',v')=1$">|; 

$key = q/fsim10^{14},{rmHz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3287.png"
 ALT="$f\sim 10^{14} {\rm Hz}$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img327.png"
 ALT="$g$">|; 

$key = q/gamma,p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2232.png"
 ALT="$\gamma p$">|; 

$key = q/gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1218.png"
 ALT="$\gamma$">|; 

$key = q/gamma>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img424.png"
 ALT="$\gamma&gt;0$">|; 

$key = q/gsimeq9.8,{rmm,s}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3015.png"
 ALT="$g\simeq 9.8 {\rm m s}^{-2}$">|; 

$key = q/h(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3180.png"
 ALT="$h(\omega)$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img377.png"
 ALT="$h$">|; 

$key = q/hat{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img502.png"
 ALT="$\hat{I}$">|; 

$key = q/hat{I}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img281.png"
 ALT="$\hat{I}&gt;0$">|; 

$key = q/hat{I}_1=-hat{I}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img764.png"
 ALT="$\hat{I}_1=-\hat{I}_2$">|; 

$key = q/hat{I}_1=hat{I}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img765.png"
 ALT="$\hat{I}_1=\hat{I}_2$">|; 

$key = q/hat{X},Q_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img616.png"
 ALT="$\hat{X} Q_f$">|; 

$key = q/hat{X}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img515.png"
 ALT="$\hat{X}&gt;0$">|; 

$key = q/hat{bfD};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2214.png"
 ALT="$\hat{\bf D}$">|; 

$key = q/hat{bfD}_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2170.png"
 ALT="$\hat{\bf D}_a$">|; 

$key = q/hat{bfD}_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2173.png"
 ALT="$\hat{\bf D}_b$">|; 

$key = q/hat{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2215.png"
 ALT="$\hat{\bf E}$">|; 

$key = q/hat{bfE}_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2171.png"
 ALT="$\hat{\bf E}_a$">|; 

$key = q/hat{bfE}_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2174.png"
 ALT="$\hat{\bf E}_b$">|; 

$key = q/hat{bfx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img809.png"
 ALT="$\hat{\bf x}$">|; 

$key = q/hat{bfx}=(hat{x}_1,hat{x}_2,hat{x}_3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img806.png"
 ALT="$\hat{\bf x}= (\hat{x}_1,\hat{x}_2,\hat{x}_3)$">|; 

$key = q/hat{bfx}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img816.png"
 ALT="$\hat{\bf x}_1$">|; 

$key = q/hat{bfx}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img817.png"
 ALT="$\hat{\bf x}_2$">|; 

$key = q/hat{bfx}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img818.png"
 ALT="$\hat{\bf x}_3$">|; 

$key = q/hat{bfx}_{1,2,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img826.png"
 ALT="$\hat{\bf x}_{1,2,3}$">|; 

$key = q/hat{eta}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img699.png"
 ALT="$\hat{\eta}_1$">|; 

$key = q/hat{eta}_1=hat{eta}_2=aslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img719.png"
 ALT="$\hat{\eta}_1=\hat{\eta}_2=a/2$">|; 

$key = q/hat{eta}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img705.png"
 ALT="$\hat{\eta}_2$">|; 

$key = q/hat{eta}_{1,2,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img824.png"
 ALT="$\hat{\eta}_{1,2,3}$">|; 

$key = q/hat{omega}=(1+2,alpha)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img761.png"
 ALT="$\hat{\omega}=(1+2 \alpha)^{1/2}$">|; 

$key = q/hat{omega}=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img691.png"
 ALT="$\hat{\omega}=-1$">|; 

$key = q/hat{omega}=-sqrt{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.34ex; " SRC="|."$dir".q|img692.png"
 ALT="$\hat{\omega}=-\sqrt{3}$">|; 

$key = q/hat{omega}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img696.png"
 ALT="$\hat{\omega}=1$">|; 

$key = q/hat{omega}=omegaslashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img682.png"
 ALT="$\hat{\omega}=\omega/\omega_0$">|; 

$key = q/hat{omega}=sqrt{2}left(1-1slashsqrt{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img798.png"
 ALT="$\hat{\omega}= \sqrt{2}\left(1-1/\sqrt{2}\right)^{1/2}$">|; 

$key = q/hat{omega}=sqrt{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.34ex; " SRC="|."$dir".q|img701.png"
 ALT="$\hat{\omega}=\sqrt{3}$">|; 

$key = q/hat{omega}^{,2}=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img804.png"
 ALT="$\hat{\omega}^{ 2} = 2$">|; 

$key = q/hat{omega}^{,2}neq2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img802.png"
 ALT="$\hat{\omega}^{ 2}\neq 2$">|; 

$key = q/hat{omega}_1=sqrt{2},left(1-1slashsqrt{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img810.png"
 ALT="$\hat{\omega}_1=\sqrt{2} \left(1-1/\sqrt{2}\right)^{1/2}$">|; 

$key = q/hat{omega}_2=sqrt{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img812.png"
 ALT="$\hat{\omega}_2=\sqrt{2}$">|; 

$key = q/hat{omega}_3=sqrt{2},left(1+1slashsqrt{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img814.png"
 ALT="$\hat{\omega}_3=\sqrt{2} \left(1+1/\sqrt{2}\right)^{1/2}$">|; 

$key = q/hat{psi}(0,y)=hat{psi}(a,y)=hat{psi}(x,0)=hat{psi}(x,b)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1877.png"
 ALT="$\hat{\psi}(0,y)=\hat{\psi}(a,y)=\hat{\psi}(x,0)=\hat{\psi}(x,b)=0$">|; 

$key = q/hat{psi}(a)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1911.png"
 ALT="$\hat{\psi}(a)=0$">|; 

$key = q/hat{psi}(x,t)=(vslashV_0,a),psi(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1210.png"
 ALT="$\hat{\psi}(x,t)= (v/V_0 a) \psi(x,t)$">|; 

$key = q/hat{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img542.png"
 ALT="$\hat{x}$">|; 

$key = q/hat{x}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img519.png"
 ALT="$\hat{x}&gt;0$">|; 

$key = q/hat{x}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img673.png"
 ALT="$\hat{x}_1$">|; 

$key = q/hat{x}_1=-hat{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img702.png"
 ALT="$\hat{x}_1=-\hat{x}_2$">|; 

$key = q/hat{x}_1=hat{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img697.png"
 ALT="$\hat{x}_1=\hat{x}_2$">|; 

$key = q/hat{x}_1=hat{x}_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img683.png"
 ALT="$\hat{x}_1=\hat{x}_2=0$">|; 

$key = q/hat{x}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img674.png"
 ALT="$\hat{x}_2$">|; 

$key = q/hat{x}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img805.png"
 ALT="$\hat{x}_3$">|; 

$key = q/hat{x}slashhat{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img543.png"
 ALT="$\hat{x}/\hat{X}$">|; 

$key = q/hbar,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3790.png"
 ALT="$\hbar \omega$">|; 

$key = q/hbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3787.png"
 ALT="$\hbar$">|; 

$key = q/hbar=1.055times10^{-34},{rmJ,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3786.png"
 ALT="$\hbar = 1.055\times 10^{-34} {\rm J s}$">|; 

$key = q/hbar=1.055times10^{-34},{rmJ,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3313.png"
 ALT="$\hbar = 1.055\times 10^{-34} {\rm J s}^{-1}$">|; 

$key = q/hbarslash({mitDelta}x)_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3910.png"
 ALT="$\hbar/({\mit\Delta}x)_0$">|; 

$key = q/hllv_0slashv_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3239.png"
 ALT="$h\ll v_0/v_1$">|; 

$key = q/hproptoomega^{,2slashp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3185.png"
 ALT="$h\propto \omega^{ 2/p}$">|; 

$key = q/i+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img873.png"
 ALT="$i+1$">|; 

$key = q/i-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img872.png"
 ALT="$i-1$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img869.png"
 ALT="$i$">|; 

$key = q/i=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img899.png"
 ALT="$i=0$">|; 

$key = q/i=1,2,cdots,N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img866.png"
 ALT="$i=1,2,\cdots, N$">|; 

$key = q/i=1,N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img871.png"
 ALT="$i=1,N$">|; 

$key = q/i=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img897.png"
 ALT="$i=1$">|; 

$key = q/i=N+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img900.png"
 ALT="$i=N+1$">|; 

$key = q/i=N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img898.png"
 ALT="$i=N$">|; 

$key = q/includegraphics[width=0.4textwidth]{Chapter01slashfig1_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="216" STYLE=""
 SRC="|."$dir".q|img287.png"
 ALT="\includegraphics[width=0.4\textwidth]{Chapter01/fig1_06.eps}">;WIDTH="220" HEIGHT="216"|; 

$key = q/includegraphics[width=0.4textwidth]{Chapter07slashfig7_12.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="337" STYLE=""
 SRC="|."$dir".q|img2096.png"
 ALT="\includegraphics[width=0.4\textwidth]{Chapter07/fig7_12.eps}">;WIDTH="222" HEIGHT="337"|; 

$key = q/includegraphics[width=0.5textwidth]{Chapter02slashfig2_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="260" STYLE=""
 SRC="|."$dir".q|img503.png"
 ALT="\includegraphics[width=0.5\textwidth]{Chapter02/fig2_02.eps}">;WIDTH="273" HEIGHT="260"|; 

$key = q/includegraphics[width=0.5textwidth]{Chapter02slashfig2_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="190" STYLE=""
 SRC="|."$dir".q|img644.png"
 ALT="\includegraphics[width=0.5\textwidth]{Chapter02/fig2_10.eps}">;WIDTH="274" HEIGHT="190"|; 

$key = q/includegraphics[width=0.5textwidth]{Chapter07slashfig7_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="291" STYLE=""
 SRC="|."$dir".q|img1845.png"
 ALT="\includegraphics[width=0.5\textwidth]{Chapter07/fig7_02.eps}">;WIDTH="276" HEIGHT="291"|; 

$key = q/includegraphics[width=0.5textwidth]{Chapter11slashfig11_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="248" STYLE=""
 SRC="|."$dir".q|img3788.png"
 ALT="\includegraphics[width=0.5\textwidth]{Chapter11/fig11_01.eps}">;WIDTH="275" HEIGHT="248"|; 

$key = q/includegraphics[width=0.5textwidth]{Chapter11slashfig11_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="275" STYLE=""
 SRC="|."$dir".q|img3816.png"
 ALT="\includegraphics[width=0.5\textwidth]{Chapter11/fig11_02.eps}">;WIDTH="276" HEIGHT="275"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter05slashfig5_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="235" STYLE=""
 SRC="|."$dir".q|img1310.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter05/fig5_08.eps}">;WIDTH="330" HEIGHT="235"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter06slashfig6_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="227" STYLE=""
 SRC="|."$dir".q|img1472.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter06/fig6_01.eps}">;WIDTH="328" HEIGHT="227"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter06slashfig6_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="96" STYLE=""
 SRC="|."$dir".q|img1751.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter06/fig6_02.eps}">;WIDTH="329" HEIGHT="96"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter06slashfig6_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="271" STYLE=""
 SRC="|."$dir".q|img1762.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter06/fig6_03.eps}">;WIDTH="329" HEIGHT="271"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter06slashfig6_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="271" STYLE=""
 SRC="|."$dir".q|img1776.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter06/fig6_04.eps}">;WIDTH="329" HEIGHT="271"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter07slashfig7_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="281" STYLE=""
 SRC="|."$dir".q|img1831.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter07/fig7_01.eps}">;WIDTH="329" HEIGHT="281"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter07slashfig7_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="227" STYLE=""
 SRC="|."$dir".q|img2086.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter07/fig7_10.eps}">;WIDTH="329" HEIGHT="227"|; 

$key = q/includegraphics[width=0.6textwidth]{Chapter11slashfig11_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="439" STYLE=""
 SRC="|."$dir".q|img3915.png"
 ALT="\includegraphics[width=0.6\textwidth]{Chapter11/fig11_04.eps}">;WIDTH="328" HEIGHT="439"|; 

$key = q/includegraphics[width=0.75textwidth]{Chapter01slashfig1_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="276" STYLE=""
 SRC="|."$dir".q|img187.png"
 ALT="\includegraphics[width=0.75\textwidth]{Chapter01/fig1_04.eps}">;WIDTH="413" HEIGHT="276"|; 

$key = q/includegraphics[width=0.75textwidth]{Chapter01slashfig1_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="277" STYLE=""
 SRC="|."$dir".q|img211.png"
 ALT="\includegraphics[width=0.75\textwidth]{Chapter01/fig1_05.eps}">;WIDTH="413" HEIGHT="277"|; 

$key = q/includegraphics[width=0.75textwidth]{Chapter01slashfig1_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="276" STYLE=""
 SRC="|."$dir".q|img306.png"
 ALT="\includegraphics[width=0.75\textwidth]{Chapter01/fig1_07.eps}">;WIDTH="413" HEIGHT="276"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter01slashfig1_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="153" STYLE=""
 SRC="|."$dir".q|img137.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter01/fig1_01.eps}">;WIDTH="379" HEIGHT="153"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter01slashfig1_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="327" STYLE=""
 SRC="|."$dir".q|img320.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter01/fig1_08.eps}">;WIDTH="376" HEIGHT="327"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter02slashfig2_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="192" STYLE=""
 SRC="|."$dir".q|img571.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter02/fig2_06.eps}">;WIDTH="386" HEIGHT="192"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter03slashfig3_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="178" STYLE=""
 SRC="|."$dir".q|img836.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter03/fig3_07.eps}">;WIDTH="383" HEIGHT="178"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter07slashfig7_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="259" STYLE=""
 SRC="|."$dir".q|img1859.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter07/fig7_03.eps}">;WIDTH="388" HEIGHT="259"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter08slashfig8_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="289" STYLE=""
 SRC="|."$dir".q|img2475.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter08/fig8_04.eps}">;WIDTH="385" HEIGHT="289"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter09slashfig9_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="326" STYLE=""
 SRC="|."$dir".q|img2864.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter09/fig9_02.eps}">;WIDTH="384" HEIGHT="326"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter09slashfig9_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="325" STYLE=""
 SRC="|."$dir".q|img2870.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter09/fig9_03.eps}">;WIDTH="384" HEIGHT="325"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter09slashfig9_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="318" STYLE=""
 SRC="|."$dir".q|img2888.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter09/fig9_04.eps}">;WIDTH="385" HEIGHT="318"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter09slashfig9_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="311" STYLE=""
 SRC="|."$dir".q|img3110.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter09/fig9_06.eps}">;WIDTH="384" HEIGHT="311"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter09slashfig9_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="301" STYLE=""
 SRC="|."$dir".q|img3120.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter09/fig9_07.eps}">;WIDTH="384" HEIGHT="301"|; 

$key = q/includegraphics[width=0.7textwidth]{Chapter09slashfig9_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="302" STYLE=""
 SRC="|."$dir".q|img3125.png"
 ALT="\includegraphics[width=0.7\textwidth]{Chapter09/fig9_08.eps}">;WIDTH="385" HEIGHT="302"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter10slashfig10_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="378" STYLE=""
 SRC="|."$dir".q|img3263.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter10/fig10_01.eps}">;WIDTH="437" HEIGHT="378"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="313" STYLE=""
 SRC="|."$dir".q|img3878.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_03.eps}">;WIDTH="469" HEIGHT="313"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="313" STYLE=""
 SRC="|."$dir".q|img3978.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_06.eps}">;WIDTH="468" HEIGHT="313"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="313" STYLE=""
 SRC="|."$dir".q|img3986.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_07.eps}">;WIDTH="468" HEIGHT="313"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="312" STYLE=""
 SRC="|."$dir".q|img4025.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_08.eps}">;WIDTH="467" HEIGHT="312"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="312" STYLE=""
 SRC="|."$dir".q|img4027.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_09.eps}">;WIDTH="467" HEIGHT="312"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="312" STYLE=""
 SRC="|."$dir".q|img4044.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_10.eps}">;WIDTH="467" HEIGHT="312"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="312" STYLE=""
 SRC="|."$dir".q|img4046.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_11.eps}">;WIDTH="467" HEIGHT="312"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_12.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="298" STYLE=""
 SRC="|."$dir".q|img4084.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_12.eps}">;WIDTH="469" HEIGHT="298"|; 

$key = q/includegraphics[width=0.85textwidth]{Chapter11slashfig11_13.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="313" STYLE=""
 SRC="|."$dir".q|img4129.png"
 ALT="\includegraphics[width=0.85\textwidth]{Chapter11/fig11_13.eps}">;WIDTH="470" HEIGHT="313"|; 

$key = q/includegraphics[width=0.8textwidth]{Chapter01slashfig1_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="295" STYLE=""
 SRC="|."$dir".q|img158.png"
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$key = q/includegraphics[width=0.8textwidth]{Chapter01slashfig1_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter01slashfig1_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter02slashfig2_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter02slashfig2_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter02slashfig2_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter02slashfig2_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter02slashfig2_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter02slashfig2_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter03slashfig3_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter03slashfig3_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter03slashfig3_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter03slashfig3_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter03slashfig3_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter04slashfig4_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter04slashfig4_12.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter07slashfig7_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter07slashfig7_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter07slashfig7_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter08slashfig8_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter08slashfig8_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter10slashfig10_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter10slashfig10_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter10slashfig10_13.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter10slashfig10_15.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter10slashfig10_16.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.8textwidth]{Chapter10slashfig10_17.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter02slashfig2_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter04slashfig4_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter05slashfig5_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter07slashfig7_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter07slashfig7_13.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter09slashfig9_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter09slashfig9_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter09slashfig9_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter09slashfig9_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_12.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter10slashfig10_14.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=0.9textwidth]{Chapter11slashfig11_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1.4textwidth]{Chapter05slashfig5_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1.textwidth]{Chapter07slashfig7_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter03slashfig3_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter04slashfig4_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter04slashfig4_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter05slashfig5_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter05slashfig5_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter05slashfig5_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter05slashfig5_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter05slashfig5_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter07slashfig7_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
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$key = q/includegraphics[width=1textwidth]{Chapter07slashfig7_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="276" STYLE=""
 SRC="|."$dir".q|img2032.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter07/fig7_08.eps}">;WIDTH="527" HEIGHT="276"|; 

$key = q/includegraphics[width=1textwidth]{Chapter08slashfig8_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="261" STYLE=""
 SRC="|."$dir".q|img2349.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter08/fig8_01.eps}">;WIDTH="527" HEIGHT="261"|; 

$key = q/includegraphics[width=1textwidth]{Chapter08slashfig8_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="526" HEIGHT="268" STYLE=""
 SRC="|."$dir".q|img2440.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter08/fig8_03.eps}">;WIDTH="526" HEIGHT="268"|; 

$key = q/includegraphics[width=1textwidth]{Chapter10slashfig10_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="328" STYLE=""
 SRC="|."$dir".q|img3325.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter10/fig10_06.eps}">;WIDTH="528" HEIGHT="328"|; 

$key = q/includegraphics[width=1textwidth]{Chapter10slashfig10_18.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="540" STYLE=""
 SRC="|."$dir".q|img3653.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter10/fig10_18.eps}">;WIDTH="527" HEIGHT="540"|; 

$key = q/includegraphics[width=1textwidth]{Chapter10slashfig10_19.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="559" STYLE=""
 SRC="|."$dir".q|img3665.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter10/fig10_19.eps}">;WIDTH="527" HEIGHT="559"|; 

$key = q/includegraphics[width=1textwidth]{Chapter10slashfig10_20.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="227" STYLE=""
 SRC="|."$dir".q|img3710.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter10/fig10_20.eps}">;WIDTH="527" HEIGHT="227"|; 

$key = q/includegraphics[width=1textwidth]{Chapter10slashfig10_21.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="224" STYLE=""
 SRC="|."$dir".q|img3713.png"
 ALT="\includegraphics[width=1\textwidth]{Chapter10/fig10_21.eps}">;WIDTH="527" HEIGHT="224"|; 

$key = q/int_{-infty}^inftyF(x),dx=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.96ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img3420.png"
 ALT="$\int_{-\infty}^\infty F(x) dx = 1$">|; 

$key = q/int_{-infty}^inftyF_2(x'),sin(alpha,x'),dx'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.96ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img3464.png"
 ALT="$\int_{-\infty}^\infty F_2(x') \sin(\alpha x') dx'=0$">|; 

$key = q/int_{-infty}^infty{rme}^{-y^{,2}},dy=sqrt{pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.01ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img2513.png"
 ALT="$\int_{-\infty}^\infty {\rm e}^{-y^{ 2}} dy = \sqrt{\pi}$">|; 

$key = q/int_{-infty}^infty|psi(x,0)|^{,2},dx=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.96ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img3858.png"
 ALT="$\int_{-\infty}^\infty \vert\psi(x,0)\vert^{ 2} dx =1$">|; 

$key = q/int_{-infty}^infty|psi|^{,2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.96ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img3859.png"
 ALT="$\int_{-\infty}^\infty\vert\psi\vert^{ 2} dx$">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1003.png"
 ALT="$j$">|; 

$key = q/j=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1004.png"
 ALT="$j=0$">|; 

$key = q/j=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1005.png"
 ALT="$j=1$">|; 

$key = q/j=5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img81.png"
 ALT="$j=5$">|; 

$key = q/jneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3388.png"
 ALT="$j\neq 0$">|; 

$key = q/k!=k,(k-1),(k-2)..2.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4308.png"
 ALT="$k!= k (k-1) (k-2)..2.1$">|; 

$key = q/k';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img832.png"
 ALT="$k'$">|; 

$key = q/k'equivdkslashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4065.png"
 ALT="$k'\equiv dk/dx$">|; 

$key = q/k(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4062.png"
 ALT="$k(x)$">|; 

$key = q/k(x)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4081.png"
 ALT="$k(x)=0$">|; 

$key = q/k+dk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3891.png"
 ALT="$k+dk$">|; 

$key = q/k,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3593.png"
 ALT="$k R$">|; 

$key = q/k,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img957.png"
 ALT="$k a$">|; 

$key = q/k,a=(nslash9),pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img958.png"
 ALT="$k a = (n/9) \pi$">|; 

$key = q/k,all1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img959.png"
 ALT="$k a\ll 1$">|; 

$key = q/k,arightarrow1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img961.png"
 ALT="$k a\rightarrow 1$">|; 

$key = q/k,asim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1147.png"
 ALT="$k a\sim 1$">|; 

$key = q/k,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3083.png"
 ALT="$k d$">|; 

$key = q/k,deltagg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1794.png"
 ALT="$k \delta \gg 1$">|; 

$key = q/k,deltall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1823.png"
 ALT="$k \delta \ll 1$">|; 

$key = q/k,dgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3057.png"
 ALT="$k d\gg 1$">|; 

$key = q/k,dll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3053.png"
 ALT="$k d\ll 1$">|; 

$key = q/k,drightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3086.png"
 ALT="$k d\rightarrow 0$">|; 

$key = q/k,rho_1,,k,rho_2gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3266.png"
 ALT="$k \rho_1, k \rho_2\gg 1$">|; 

$key = q/k,rhogg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1851.png"
 ALT="$k \rho\gg 1$">|; 

$key = q/k,x=(n-1slash2),pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1396.png"
 ALT="$k x=(n-1/2) \pi$">|; 

$key = q/k,x=n,pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1397.png"
 ALT="$k x=n \pi$">|; 

$key = q/k,|rho_1-rho_2|gtrsimpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3281.png"
 ALT="$k \vert\rho_1-\rho_2\vert\gtrsim \pi$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img193.png"
 ALT="$k$">|; 

$key = q/k=(I_0slashM)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img387.png"
 ALT="$k=(I_0/M)^{1/2}$">|; 

$key = q/k=-df(0)slashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img419.png"
 ALT="$k=-df(0)/dx$">|; 

$key = q/k=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1032.png"
 ALT="$k=0$">|; 

$key = q/k=2pislashlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3752.png"
 ALT="$k=2\pi/\lambda$">|; 

$key = q/k=gslashV^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3092.png"
 ALT="$k=g/V^{ 2}$">|; 

$key = q/k=k';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2389.png"
 ALT="$k=k'$">|; 

$key = q/k=k_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2552.png"
 ALT="$k=k_0$">|; 

$key = q/k=k_0equiv(rho,gslashT)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3168.png"
 ALT="$k=k_0\equiv (\rho g/T)^{1/2}$">|; 

$key = q/k=n,deltak;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2338.png"
 ALT="$k=n \delta k$">|; 

$key = q/k=omegaslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1820.png"
 ALT="$k=\omega/c$">|; 

$key = q/k=omegaslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1600.png"
 ALT="$k=\omega/v$">|; 

$key = q/k=pslashhbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3863.png"
 ALT="$k= p/\hbar$">|; 

$key = q/k=|{bfk}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1842.png"
 ALT="$k= \vert{\bf k}\vert$">|; 

$key = q/k>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img141.png"
 ALT="$k&gt;0$">|; 

$key = q/k^{,-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3171.png"
 ALT="$k^{ -1/2}$">|; 

$key = q/k^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4068.png"
 ALT="$k^{ -1}$">|; 

$key = q/k^{,1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3173.png"
 ALT="$k^{ 1/2}$">|; 

$key = q/k^{,2}<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2940.png"
 ALT="$k^{ 2}&lt;0$">|; 

$key = q/k^{,2}=(2,mslashhbar^{,2}),E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4253.png"
 ALT="$k^{ 2}= (2 m/\hbar^{ 2}) E$">|; 

$key = q/k_0+{mitDelta}kslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2571.png"
 ALT="$k_0+{\mit\Delta} k/2$">|; 

$key = q/k_0,dgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3156.png"
 ALT="$k_0 d\gg 1$">|; 

$key = q/k_0-{mitDelta}kslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2570.png"
 ALT="$k_0-{\mit\Delta} k/2$">|; 

$key = q/k_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2566.png"
 ALT="$k_0$">|; 

$key = q/k_0=(omegaslashc)[1-(1slash2),(omega_{p,e}slashomega)^2];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2683.png"
 ALT="$k_0 = (\omega/c)[1-(1/2) (\omega_{p e}/\omega)^2]$">|; 

$key = q/k_0=omegaslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1953.png"
 ALT="$k_0=\omega/c$">|; 

$key = q/k_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img363.png"
 ALT="$k_1$">|; 

$key = q/k_1=n_1,omegaslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1672.png"
 ALT="$k_1=n_1 \omega/c$">|; 

$key = q/k_1=omegaslash(Tslashrho_1)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1565.png"
 ALT="$k_1=\omega/(T/\rho_1)^{1/2}$">|; 

$key = q/k_1=omegaslashv_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1520.png"
 ALT="$k_1=\omega/v_1$">|; 

$key = q/k_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img364.png"
 ALT="$k_2$">|; 

$key = q/k_2=n_2,omegaslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1677.png"
 ALT="$k_2=n_2 \omega/c$">|; 

$key = q/k_2=omegaslash(Tslashrho_2)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1567.png"
 ALT="$k_2=\omega/(T/\rho_2)^{1/2}$">|; 

$key = q/k_2=omegaslashv_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1527.png"
 ALT="$k_2=\omega/v_2$">|; 

$key = q/k_3,a=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1574.png"
 ALT="$k_3 a=\pi/2$">|; 

$key = q/k_3=omegaslash(Tslashrho_3)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1569.png"
 ALT="$k_3=\omega/(T/\rho_3)^{1/2}$">|; 

$key = q/k_B,TggE_F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4182.png"
 ALT="$k_B T\gg E_F$">|; 

$key = q/k_B,TllE_F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4181.png"
 ALT="$k_B T\ll E_F$">|; 

$key = q/k_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4180.png"
 ALT="$k_B$">|; 

$key = q/k_c=(rho,gslashT)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3249.png"
 ALT="$k_c= (\rho g/T)^{1/2}$">|; 

$key = q/k_n=n,deltak;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2335.png"
 ALT="$k_n=n \delta k$">|; 

$key = q/k_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2967.png"
 ALT="$k_x$">|; 

$key = q/k_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2951.png"
 ALT="$k_z)$">|; 

$key = q/k_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2968.png"
 ALT="$k_z$">|; 

$key = q/k_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3226.png"
 ALT="$k_z=0$">|; 

$key = q/k_{i,x}=k_{r,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1955.png"
 ALT="$k_{i x}= k_{r x}$">|; 

$key = q/k_{i,x}=k_{t,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1957.png"
 ALT="$k_{i x}=k_{t x}$">|; 

$key = q/k_{i,y}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1942.png"
 ALT="$k_{i y}=0$">|; 

$key = q/k_{r,y}=k_{t,y}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1943.png"
 ALT="$k_{r y}=k_{t y}=0$">|; 

$key = q/kggk_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3172.png"
 ALT="$k\gg k_0$">|; 

$key = q/kllk_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3170.png"
 ALT="$k\ll k_0$">|; 

$key = q/kneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img2382.png"
 ALT="$k\neq 0$">|; 

$key = q/l,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img329.png"
 ALT="$l \sin\theta$">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img321.png"
 ALT="$l$">|; 

$key = q/l=(N+1),a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img962.png"
 ALT="$l=(N+1) a$">|; 

$key = q/l=n,lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1335.png"
 ALT="$l = n \lambda/2$">|; 

$key = q/l^{,2}=l_x^{,2}+l_y^{,2}+l_z^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4170.png"
 ALT="$l^{ 2} = l_x^{ 2} + l_y^{ 2}+ l_z^{ 2}$">|; 

$key = q/l_F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4171.png"
 ALT="$l_F$">|; 

$key = q/l_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4159.png"
 ALT="$l_x$">|; 

$key = q/l_x^{,2}+l_y^{,2}+l_z^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4167.png"
 ALT="$l_x^{ 2}+l_y^{ 2}+ l_z^{ 2}$">|; 

$key = q/l_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4160.png"
 ALT="$l_y$">|; 

$key = q/l_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4161.png"
 ALT="$l_z$">|; 

$key = q/lambda';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1709.png"
 ALT="$\lambda'$">|; 

$key = q/lambda+{mitDelta}lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3389.png"
 ALT="$\lambda+{\mit\Delta}\lambda$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img123.png"
 ALT="$\lambda $">|; 

$key = q/lambda<(pislash2)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3989.png"
 ALT="$\lambda &lt; (\pi/2)^2$">|; 

$key = q/lambda=(hbar^{,2}slash2,m,V)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4055.png"
 ALT="$\lambda = (\hbar^{ 2}/2 m V)^{1/2}$">|; 

$key = q/lambda=1.5,pi^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3981.png"
 ALT="$\lambda = 1.5 \pi^{ 2}$">|; 

$key = q/lambda=1.5tmspace+thinmuskip{.1667em}pi^{tmspace+thinmuskip{.1667em}2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img119.png"
 ALT="$\lambda = 1.5\tmspace +\thinmuskip {.1667em}\pi ^{\tmspace +\thinmuskip {.1667em}2}$">|; 

$key = q/lambda=18,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img949.png"
 ALT="$\lambda=18 a$">|; 

$key = q/lambda=2.25,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img952.png"
 ALT="$\lambda = 2.25 a$">|; 

$key = q/lambda=2pislashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img912.png"
 ALT="$\lambda=2\pi/k$">|; 

$key = q/lambda=450,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1806.png"
 ALT="$\lambda=450 {\rm nm}$">|; 

$key = q/lambda=500,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3728.png"
 ALT="$\lambda=500 {\rm nm}$">|; 

$key = q/lambda=633,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4224.png"
 ALT="$\lambda =633 {\rm nm}$">|; 

$key = q/lambda=9,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img951.png"
 ALT="$\lambda = 9 a$">|; 

$key = q/lambda=VslashE_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4240.png"
 ALT="$\lambda = V/E_0$">|; 

$key = q/lambda=cslashf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2931.png"
 ALT="$\lambda = c/f$">|; 

$key = q/lambda>3000,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2911.png"
 ALT="$\lambda &gt; 3000 {\rm km}$">|; 

$key = q/lambda_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1801.png"
 ALT="$\lambda_0$">|; 

$key = q/lambda_0=2pislashk_0=2pi,V^{,2}slashg;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3153.png"
 ALT="$\lambda_0=2\pi/k_0=2\pi V^{ 2}/g$">|; 

$key = q/lambda_0=550,{rmnm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1805.png"
 ALT="$\lambda_0 = 550 {\rm nm}$">|; 

$key = q/lambdagg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3982.png"
 ALT="$\lambda\gg 1$">|; 

$key = q/lambdall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3998.png"
 ALT="$\lambda\ll 1$">|; 

$key = q/lambdalla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3518.png"
 ALT="$\lambda\ll a$">|; 

$key = q/lambdaproptod^{,1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3241.png"
 ALT="$\lambda\propto d^{ 1/2}$">|; 

$key = q/lambdarightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4000.png"
 ALT="$\lambda\rightarrow \infty$">|; 

$key = q/lambdasim2,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3169.png"
 ALT="$\lambda\sim 2 {\rm cm}$">|; 

$key = q/lambdasim300;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2908.png"
 ALT="$\lambda\sim 300$">|; 

$key = q/lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1334.png"
 ALT="$\lambda/2$">|; 

$key = q/lambdaslashD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3444.png"
 ALT="$\lambda/D$">|; 

$key = q/lambdaslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3416.png"
 ALT="$\lambda/n$">|; 

$key = q/langleArangle(x)equiv(omegaslash2pi)int_t^{t+2pislashomega}A(x,t'),dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.35ex; vertical-align: -1.01ex; " SRC="|."$dir".q|img1444.png"
 ALT="$\langle A \rangle(x) \equiv (\omega/2\pi)\int_t^{t+2\pi/\omega}A(x,t')  dt'$">|; 

$key = q/langleErangle=E_0,exp(-nu,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img633.png"
 ALT="$\langle E\rangle = E_0 \exp(-\nu t)$">|; 

$key = q/langlePrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img645.png"
 ALT="$\langle P\rangle$">|; 

$key = q/langlecdotsrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2204.png"
 ALT="$\langle\cdots\rangle$">|; 

$key = q/langlecos(2,omega,t)rangle=langlesin(2,omega,t)rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img317.png"
 ALT="$\langle\cos(2 \omega t)\rangle=\langle \sin(2 \omega t)\rangle=0$">|; 

$key = q/langlecos(omega,t),sin(omega,t)rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img567.png"
 ALT="$\langle \cos(\omega t) \sin(\omega t)\rangle =0$">|; 

$key = q/langlecos(omega,t-k,R-phi),sin(omega,t-k,R-phi)rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3598.png"
 ALT="$\langle \cos(\omega t-k R-\phi) \sin(\omega t-k R-\phi)\rangle=0$">|; 

$key = q/langlecos(omega,t-k,R-phi_A),cos(omega,t-k,R-phi_B)rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3340.png"
 ALT="$\langle \cos (\omega t-k R-\phi_A) \cos (\omega t-k R-\phi_B)\rangle=0$">|; 

$key = q/langlecos^2(omega,t)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img568.png"
 ALT="$\langle \cos^2(\omega t)\rangle =1/2$">|; 

$key = q/langlecos^2(omega,t-k,R-phi)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3286.png"
 ALT="$\langle\cos^2(\omega t-k R-\phi)\rangle=1/2$">|; 

$key = q/langlecos^2(omega,t-k,R-phi)rangle=langlesin^2(omega,t-k,R-phi)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3597.png"
 ALT="$\langle \cos^2(\omega t-k R-\phi)\rangle
=\langle \sin^2(\omega t-k R-\phi)\rangle = 1/2$">|; 

$key = q/langlecos^2(omega,t-k,R-phi_A)rangle=langlecos^2(omega,t-k,R-phi_B)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3339.png"
 ALT="$\langle \cos^2 (\omega t-k R-\phi_A)\rangle= \langle \cos^2 (\omega t-k R-\phi_B)\rangle=1/2$">|; 

$key = q/langlecos^2(omega,t-k,x)rangle=langlesin^2(omega,t-k,x)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3066.png"
 ALT="$\langle \cos^2(\omega t-k x)\rangle =\langle \sin^2(\omega t-k x)\rangle=1/2$">|; 

$key = q/langlesin^2(omega,t+theta)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1446.png"
 ALT="$\langle \sin^2(\omega t+\theta)\rangle=1/2$">|; 

$key = q/langle{calE}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1748.png"
 ALT="$\langle {\cal E}\rangle$">|; 

$key = q/langle{calI}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1747.png"
 ALT="$\langle {\cal I}\rangle$">|; 

$key = q/langle{calP}rangle=langle{calI}rangleslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1800.png"
 ALT="$\langle {\cal P}\rangle = \langle {\cal I}\rangle/c$">|; 

$key = q/lim_{,zrightarrow0}J_n(z)slashz^{,n}=1slash(2^{,n},n!);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3773.png"
 ALT="$\lim_{ z\rightarrow 0} J_n(z)/z^{ n} = 1/(2^{ n} n!)$">|; 

$key = q/log_{10}(tau_{{rmth}})=-28.9-1.60,Z_1^{,2slash3}+1.61,Z_1slashsqrt{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img4130.png"
 ALT="$\log_{10}(\tau_{{\rm th}}) = -28.9 - 1.60 Z_1^{ 2/3} + 1.61 Z_1/\sqrt{E}$">|; 

$key = q/lslash(n-1slash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1189.png"
 ALT="$l/(n-1/2)$">|; 

$key = q/lslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1007.png"
 ALT="$l/n$">|; 

$key = q/m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img834.png"
 ALT="$m'$">|; 

$key = q/m,,n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3215.png"
 ALT="$m, n$">|; 

$key = q/m,ddot{x}+k,x=F_0,sin(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img649.png"
 ALT="$m \ddot{x} + k x = F_0 \sin(\omega t)$">|; 

$key = q/m,g,l,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img330.png"
 ALT="$m g l 
\sin\theta$">|; 

$key = q/m,g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img326.png"
 ALT="$m g$">|; 

$key = q/m,omega^{,2}=k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img209.png"
 ALT="$m \omega^{ 2} = k$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img134.png"
 ALT="$m$">|; 

$key = q/m<M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1302.png"
 ALT="$m&lt;M$">|; 

$key = q/m=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img77.png"
 ALT="$m=2$">|; 

$key = q/m=4,m_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4101.png"
 ALT="$m=4 m_p$">|; 

$key = q/m=m_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2596.png"
 ALT="$m=m_e$">|; 

$key = q/m=rho,A,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1184.png"
 ALT="$m=\rho A a$">|; 

$key = q/m=rho,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1010.png"
 ALT="$m=\rho a$">|; 

$key = q/m=rho,l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1115.png"
 ALT="$m=\rho l$">|; 

$key = q/m>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img412.png"
 ALT="$m&gt;0$">|; 

$key = q/m_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img838.png"
 ALT="$m_1$">|; 

$key = q/m_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img839.png"
 ALT="$m_2$">|; 

$key = q/m_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2587.png"
 ALT="$m_e$">|; 

$key = q/m_ellm_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2592.png"
 ALT="$m_e\ll m_i$">|; 

$key = q/m_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2589.png"
 ALT="$m_i$">|; 

$key = q/m_iggm_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2761.png"
 ALT="$m_i\gg m_e$">|; 

$key = q/m_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4102.png"
 ALT="$m_p$">|; 

$key = q/mslashV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1382.png"
 ALT="$m/V$">|; 

$key = q/mu_0,H_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1629.png"
 ALT="$\mu_0 H_y$">|; 

$key = q/mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1614.png"
 ALT="$\mu_0$">|; 

$key = q/mu_0=4pitimes10^{-7},{rmN},{rmA}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1502.png"
 ALT="$\mu_0 = 4\pi\times 10^{-7} {\rm N} {\rm A}^{-2}$">|; 

$key = q/n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1028.png"
 ALT="$n'$">|; 

$key = q/n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2975.png"
 ALT="$n(z)$">|; 

$key = q/n(z_0)=|S|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2982.png"
 ALT="$n(z_0)=\vert S\vert$">|; 

$key = q/n+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1006.png"
 ALT="$n+1$">|; 

$key = q/n,k_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1954.png"
 ALT="$n k_0$">|; 

$key = q/n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img174.png"
 ALT="$n$">|; 

$key = q/n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img930.png"
 ALT="$n=0$">|; 

$key = q/n=1,,2,,3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3930.png"
 ALT="$n=1, 2, 3,$">|; 

$key = q/n=1,100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1211.png"
 ALT="$n=1,100$">|; 

$key = q/n=1,2,3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img997.png"
 ALT="$n=1,2,3,$">|; 

$key = q/n=1,2,3,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4034.png"
 ALT="$n=1,2,3,\cdots$">|; 

$key = q/n=1,2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1240.png"
 ALT="$n=1, 2$">|; 

$key = q/n=1,N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3367.png"
 ALT="$n=1,N$">|; 

$key = q/n=1,infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1046.png"
 ALT="$n=1,\infty$">|; 

$key = q/n=1.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1804.png"
 ALT="$n=1.5$">|; 

$key = q/n=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img950.png"
 ALT="$n=1$">|; 

$key = q/n=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img48.png"
 ALT="$n=2$">|; 

$key = q/n=3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img78.png"
 ALT="$n=3$">|; 

$key = q/n=4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img58.png"
 ALT="$n=4$">|; 

$key = q/n=8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img953.png"
 ALT="$n=8$">|; 

$key = q/n=N+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img931.png"
 ALT="$n=N+1$">|; 

$key = q/n=Nslasha^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4176.png"
 ALT="$n=N/a^{ 3}$">|; 

$key = q/n=sqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img1966.png"
 ALT="$n=\sqrt{\epsilon}$">|; 

$key = q/n>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1289.png"
 ALT="$n&gt;0$">|; 

$key = q/n>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1067.png"
 ALT="$n&gt;1$">|; 

$key = q/n^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2857.png"
 ALT="$n^{ 2}$">|; 

$key = q/n^{,2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2860.png"
 ALT="$n^{ 2}=0$">|; 

$key = q/n^{,2}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2858.png"
 ALT="$n^{ 2}=1$">|; 

$key = q/n^{,2}rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2854.png"
 ALT="$n^{ 2}\rightarrow\infty$">|; 

$key = q/n_1,sintheta_i=n_2,sintheta_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1970.png"
 ALT="$n_1 \sin\theta_i=n_2 \sin\theta_t$">|; 

$key = q/n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1663.png"
 ALT="$n_1$">|; 

$key = q/n_1<n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2041.png"
 ALT="$n_1&lt; n_2$">|; 

$key = q/n_1=1.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img83.png"
 ALT="$n_1=1.0$">|; 

$key = q/n_1=1.33;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img86.png"
 ALT="$n_1=1.33$">|; 

$key = q/n_1=1.52;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img89.png"
 ALT="$n_1=1.52$">|; 

$key = q/n_1=n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1688.png"
 ALT="$n_1=n_2$">|; 

$key = q/n_1>n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2042.png"
 ALT="$n_1&gt; n_2$">|; 

$key = q/n_1neqn_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1691.png"
 ALT="$n_1\neq n_2$">|; 

$key = q/n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1664.png"
 ALT="$n_2$">|; 

$key = q/n_2=1.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img87.png"
 ALT="$n_2=1.0$">|; 

$key = q/n_2=1.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img84.png"
 ALT="$n_2=1.5$">|; 

$key = q/n_2>n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1693.png"
 ALT="$n_2&gt; n_1$">|; 

$key = q/n_e(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2692.png"
 ALT="$n_e(z)$">|; 

$key = q/n_e,B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2696.png"
 ALT="$n_e B_0$">|; 

$key = q/n_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2591.png"
 ALT="$n_e$">|; 

$key = q/n_eproptoz^{,p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3184.png"
 ALT="$n_e\propto z^{ p}$">|; 

$key = q/ngg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img631.png"
 ALT="$n\gg 1$">|; 

$key = q/nllN;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1146.png"
 ALT="$n\ll N$">|; 

$key = q/nsim8.6times10^{28},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4192.png"
 ALT="$n\sim 8.6\times 10^{28} {\rm m}^{-3}$">|; 

$key = q/nsimN;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1148.png"
 ALT="$n\sim N$">|; 

$key = q/nu,T_0=0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img451.png"
 ALT="$\nu T_0=0.5$">|; 

$key = q/nu,|T|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4114.png"
 ALT="$\nu \vert T\vert^{ 2}$">|; 

$key = q/nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img445.png"
 ALT="$\nu$">|; 

$key = q/nu<2,omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img443.png"
 ALT="$\nu&lt; 2 \omega_0$">|; 

$key = q/nu=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img618.png"
 ALT="$\nu=0$">|; 

$key = q/nu=RslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img579.png"
 ALT="$\nu=R/L$">|; 

$key = q/nu=phi-phi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3528.png"
 ALT="$\nu=\phi-\phi'$">|; 

$key = q/nu>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img413.png"
 ALT="$\nu&gt;0$">|; 

$key = q/nu^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img615.png"
 ALT="$\nu^{ -1}$">|; 

$key = q/nugeq2,omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img449.png"
 ALT="$\nu\geq 2 \omega_0$">|; 

$key = q/null2,omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img473.png"
 ALT="$\nu\ll 2 \omega_0$">|; 

$key = q/nullomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img545.png"
 ALT="$\nu\ll \omega_0$">|; 

$key = q/nurightarrow2,omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img640.png"
 ALT="$\nu\rightarrow2 \omega_0$">|; 

$key = q/nusimeqvslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4111.png"
 ALT="$\nu\simeq v/R$">|; 

$key = q/nuslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img448.png"
 ALT="$\nu/2$">|; 

$key = q/nuslashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img544.png"
 ALT="$\nu/\omega_0$">|; 

$key = q/nuslashomega_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img32.png"
 ALT="$\nu /\omega _0=0$">|; 

$key = q/nuslashomega_0=1slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img28.png"
 ALT="$\nu /\omega _0=1/16$">|; 

$key = q/nuslashomega_0=1slashQ_f=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img22.png"
 ALT="$\nu /\omega _0 = 1/Q_f= 1$">|; 

$key = q/nutmspace+thinmuskip{.1667em}T_0=0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img19.png"
 ALT="$\nu \tmspace +\thinmuskip {.1667em}T_0=0.5$">|; 

$key = q/omega(x,z,k_x,k_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2969.png"
 ALT="$\omega(x,z,k_x,k_z)$">|; 

$key = q/omega+{mitDelta}omegaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3317.png"
 ALT="$\omega+{\mit\Delta}\omega/2$">|; 

$key = q/omega,t+(1slash2),k,d,sintheta_0-phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3299.png"
 ALT="$\omega t+ (1/2) k d \sin\theta_0-\phi$">|; 

$key = q/omega,t+c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img243.png"
 ALT="$\omega t+c$">|; 

$key = q/omega,t-(1slash2),k,d,sintheta_0-phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3298.png"
 ALT="$\omega t- (1/2) k d \sin\theta_0-\phi$">|; 

$key = q/omega,t-k,rho-phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3268.png"
 ALT="$\omega t-k \rho-\phi$">|; 

$key = q/omega,t-k,x-phi={rmconstant};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1347.png"
 ALT="$\omega t-k x-\phi = {\rm constant}$">|; 

$key = q/omega,t-phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img178.png"
 ALT="$\omega t-\phi$">|; 

$key = q/omega,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img168.png"
 ALT="$\omega t$">|; 

$key = q/omega-{mitDelta}omegaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3316.png"
 ALT="$\omega-{\mit\Delta}\omega/2$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img115.png"
 ALT="$\omega $">|; 

$key = q/omega<omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img651.png"
 ALT="$\omega&lt;\omega_0$">|; 

$key = q/omega<omega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2605.png"
 ALT="$\omega&lt;\omega_{p e}$">|; 

$key = q/omega=1slashsqrt{L,C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img279.png"
 ALT="$\omega=1/\sqrt{L C}$">|; 

$key = q/omega=1slashsqrt{L,C}pmRslash(2,L);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img588.png"
 ALT="$\omega=1/\sqrt{L C}\pm R/(2 L)$">|; 

$key = q/omega=2pislashtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1287.png"
 ALT="$\omega=2\pi/\tau$">|; 

$key = q/omega=4times10^{,15},{rmrad.,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2928.png"
 ALT="$\omega = 4\times 10^{ 15} {\rm rad. s}^{-1}$">|; 

$key = q/omega=Eslashhbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3864.png"
 ALT="$\omega = E/\hbar$">|; 

$key = q/omega=Eslashhbar>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4061.png"
 ALT="$\omega=E/\hbar&gt;0$">|; 

$key = q/omega=k,c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1925.png"
 ALT="$\omega=k c$">|; 

$key = q/omega=k,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1394.png"
 ALT="$\omega=k v$">|; 

$key = q/omega=omega(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2555.png"
 ALT="$\omega=\omega(k)$">|; 

$key = q/omega=omega(k_x,k_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2957.png"
 ALT="$\omega=\omega(k_x,k_z)$">|; 

$key = q/omega=omega(x,z,k_x,k_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2963.png"
 ALT="$\omega=\omega(x,z,k_x,k_z)$">|; 

$key = q/omega=omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img570.png"
 ALT="$\omega=\omega_0$">|; 

$key = q/omega=omega_0pmnuslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img556.png"
 ALT="$\omega=\omega_0\pm \nu/2$">|; 

$key = q/omega=omega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2862.png"
 ALT="$\omega=\omega_1$">|; 

$key = q/omega=omega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2615.png"
 ALT="$\omega = \omega_{p e}$">|; 

$key = q/omega=omega_{rmLH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2885.png"
 ALT="$\omega= \omega_{\rm LH}$">|; 

$key = q/omega=omega_{rmUH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2881.png"
 ALT="$\omega=\omega_{\rm UH}$">|; 

$key = q/omega=sqrt{2,Tslashl,m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img362.png"
 ALT="$\omega=\sqrt{2 T/l m}$">|; 

$key = q/omega=sqrt{2,gslashl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img378.png"
 ALT="$\omega=\sqrt{2 g/l}$">|; 

$key = q/omega=sqrt{3},omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img694.png"
 ALT="$\omega=\sqrt{3} \omega_0$">|; 

$key = q/omega=sqrt{gslashR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img379.png"
 ALT="$\omega=\sqrt{g/R}$">|; 

$key = q/omega={mitDelta}{calE}slashhbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3311.png"
 ALT="$\omega={\mit\Delta}{\cal E}/\hbar$">|; 

$key = q/omega>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img149.png"
 ALT="$\omega&gt;0$">|; 

$key = q/omega>omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img652.png"
 ALT="$\omega&gt;\omega_0$">|; 

$key = q/omega>omega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2604.png"
 ALT="$\omega&gt;\omega_{p e}$">|; 

$key = q/omega^{,2}=1slashL,C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img289.png"
 ALT="$\omega^{ 2}=1/L C$">|; 

$key = q/omega^{,2}=k^{,2},c^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2859.png"
 ALT="$\omega^{ 2}=k^{ 2}  c^{ 2}$">|; 

$key = q/omega_0+omega_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2479.png"
 ALT="$\omega_0+\omega_N$">|; 

$key = q/omega_0+omega_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2476.png"
 ALT="$\omega_0+\omega_n$">|; 

$key = q/omega_0,sigma_t=20;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2485.png"
 ALT="$\omega_0 \sigma_t=20$">|; 

$key = q/omega_0,sigma_tgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2484.png"
 ALT="$\omega_0 \sigma_t\gg 1$">|; 

$key = q/omega_0-omega_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2478.png"
 ALT="$\omega_0-\omega_N$">|; 

$key = q/omega_0-omega_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2477.png"
 ALT="$\omega_0-\omega_n$">|; 

$key = q/omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img446.png"
 ALT="$\omega_0$">|; 

$key = q/omega_0=1slashsqrt{L,C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img578.png"
 ALT="$\omega_0=1/\sqrt{L C}$">|; 

$key = q/omega_0=2pislash{mitDelta}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2524.png"
 ALT="$\omega_0 = 2\pi/{\mit\Delta} t$">|; 

$key = q/omega_0=omega(k_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2558.png"
 ALT="$\omega_0=\omega(k_0)$">|; 

$key = q/omega_0=sqrt{Kslashm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1127.png"
 ALT="$\omega_0=\sqrt{K/m}$">|; 

$key = q/omega_0=sqrt{Tslashm,a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img896.png"
 ALT="$\omega_0 = \sqrt{T/ m a}$">|; 

$key = q/omega_0=sqrt{kslashm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img415.png"
 ALT="$\omega_0=\sqrt{k/m}$">|; 

$key = q/omega_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img514.png"
 ALT="$\omega_0&gt;0$">|; 

$key = q/omega_0^{,2}-omega^{,2}=(omega_0+omega),(omega_0-omega)simeq2,omega_0,(omega_0-omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img553.png"
 ALT="$\omega_0^{ 2}-\omega^{ 2}=(\omega_0+\omega) (\omega_0-\omega)\simeq 2 \omega_0 (\omega_0-\omega)$">|; 

$key = q/omega_0^{,2}=Tslash(m,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img975.png"
 ALT="$\omega_0^{ 2}= T/(m a)$">|; 

$key = q/omega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img426.png"
 ALT="$\omega_1$">|; 

$key = q/omega_1=(1+2,alpha)^{1slash2},omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img780.png"
 ALT="$\omega_1=(1+2 \alpha)^{1/2} \omega_0$">|; 

$key = q/omega_1=(omega_0^{,2}-nu^{,2}slash4)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img447.png"
 ALT="$\omega_1=(\omega_0^{ 2}-\nu^{ 2}/4)^{1/2}$">|; 

$key = q/omega_1>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img425.png"
 ALT="$\omega_1&gt;0$">|; 

$key = q/omega_1^{,2}=omega_0^{,2}-nu^{,2}slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img444.png"
 ALT="$\omega_1^{ 2}=\omega_0^{ 2}-\nu^{ 2}/4$">|; 

$key = q/omega_2,t-phi_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img955.png"
 ALT="$\omega_2 t-\phi_2=0$">|; 

$key = q/omega_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2879.png"
 ALT="$\omega_2$">|; 

$key = q/omega_2tmspace+thinmuskip{.1667em}t-phi_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img49.png"
 ALT="$\omega _2\tmspace +\thinmuskip {.1667em}t-\phi _2=0$">|; 

$key = q/omega_4,t-phi_4=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1000.png"
 ALT="$\omega_4 t-\phi_4=0$">|; 

$key = q/omega_4tmspace+thinmuskip{.1667em}t-phi_4=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img59.png"
 ALT="$\omega _4\tmspace +\thinmuskip {.1667em}t-\phi _4=0$">|; 

$key = q/omega_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2480.png"
 ALT="$\omega_N$">|; 

$key = q/omega_n,t-phi_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img947.png"
 ALT="$\omega_n t-\phi_n=0$">|; 

$key = q/omega_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1149.png"
 ALT="$\omega_n$">|; 

$key = q/omega_n=n,pi,vslashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1116.png"
 ALT="$\omega_n = n \pi v/l$">|; 

$key = q/omega_nllomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2461.png"
 ALT="$\omega_n\ll \omega_0$">|; 

$key = q/omega_ntmspace+thinmuskip{.1667em}t-phi_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img47.png"
 ALT="$\omega _n\tmspace +\thinmuskip {.1667em}t-\phi _n=0$">|; 

$key = q/omega_pm=[(sqrt{3}pm1)slash2]],omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img722.png"
 ALT="$\omega_\pm = [(\sqrt{3}\pm 1)/2]] \omega_0$">|; 

$key = q/omega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2548.png"
 ALT="$\omega_{p e}$">|; 

$key = q/omega_{p,e}=omega_{p,e}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2971.png"
 ALT="$\omega_{p e}=\omega_{p e}(z)$">|; 

$key = q/omega_{p,e}^{,2}(z)=n_e(z),e^{,2}slash(epsilon_0,m_e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img3182.png"
 ALT="$\omega_{p e}^{ 2}(z)= n_e(z) e^{ 2}/(\epsilon_0 m_e)$">|; 

$key = q/omega_{p,e}^{,2}(z_0)=omega^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img3183.png"
 ALT="$\omega_{p e}^{ 2}(z_0)=\omega^{ 2}$">|; 

$key = q/omega_{p,e}^{,2}slash({mitOmega}_e,{mitOmega}_i)=omega_{p,i}^{,2}slash{mitOmega}_i^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -1.06ex; " SRC="|."$dir".q|img2828.png"
 ALT="$\omega_{p e}^{ 2}/({\mit\Omega}_e {\mit\Omega}_i)
=\omega_{p i}^{ 2}/ {\mit\Omega}_i^{ 2}$">|; 

$key = q/omega_{p,e}^{,2}slashomega^{,2}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2831.png"
 ALT="$\omega_{p e}^{ 2}/\omega^{ 2}\gg 1$">|; 

$key = q/omega_{p,e}ggomega_{p,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2760.png"
 ALT="$\omega_{p e}\gg \omega_{p i}$">|; 

$key = q/omega_{p,e}proptosqrt{n_e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img2637.png"
 ALT="$\omega_{p e}\propto \sqrt{n_e}$">|; 

$key = q/omega_{p,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2758.png"
 ALT="$\omega_{p i}$">|; 

$key = q/omega_{p,i}^{,2}slash{mitOmega}_i^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -1.06ex; " SRC="|."$dir".q|img2832.png"
 ALT="$\omega_{p i}^{ 2}/{\mit\Omega}_i^{ 2}$">|; 

$key = q/omega_{rmLH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2887.png"
 ALT="$\omega_{\rm LH}$">|; 

$key = q/omega_{rmUH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2883.png"
 ALT="$\omega_{\rm UH}$">|; 

$key = q/omegaggomega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2677.png"
 ALT="$\omega\gg \omega_{p e}$">|; 

$key = q/omegaggsigmaslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1817.png"
 ALT="$\omega\gg \sigma/\epsilon_0$">|; 

$key = q/omegagg{calR}slash{calL};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1789.png"
 ALT="$\omega\gg {\cal R}/{\cal L}$">|; 

$key = q/omegallomega_{p,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2636.png"
 ALT="$\omega\ll \omega_{p e}$">|; 

$key = q/omegall{mitOmega}_i,omega_{p,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2823.png"
 ALT="$\omega\ll {\mit\Omega}_i, \omega_{p i}$">|; 

$key = q/omegall{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2853.png"
 ALT="$\omega\ll {\mit\Omega}_i$">|; 

$key = q/omegarightarrowomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img624.png"
 ALT="$\omega\rightarrow\omega_0$">|; 

$key = q/omegarightarrow{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2855.png"
 ALT="$\omega\rightarrow {\mit\Omega}_e$">|; 

$key = q/omegaslashk=domegaslashdk=v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2569.png"
 ALT="$\omega/k=d\omega/dk = v$">|; 

$key = q/omegaslashk=sqrt{Tslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1445.png"
 ALT="$\omega/k=\sqrt{T/\rho}$">|; 

$key = q/omegaslashk=v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1828.png"
 ALT="$\omega/k=v$">|; 

$key = q/omegaslashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img27.png"
 ALT="$\omega /\omega _0$">|; 

$key = q/omegaslashomega_0=15slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img31.png"
 ALT="$\omega /\omega _0=15/16$">|; 

$key = q/overline{E}proptoM^{,4slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4212.png"
 ALT="$\overline{E}\propto M^{ 4/3}$">|; 

$key = q/p(x,z,t),dy,dz-p(x+dx,z,t),dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3012.png"
 ALT="$p(x,z,t) dy dz -
p(x+dx,z,t) dy dz$">|; 

$key = q/p(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3011.png"
 ALT="$p(x,z,t)$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1216.png"
 ALT="$p$">|; 

$key = q/p=hbar,k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3892.png"
 ALT="$p = \hbar k$">|; 

$key = q/p=hbar,k_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3899.png"
 ALT="$p=\hbar k_0$">|; 

$key = q/p_0+rho,g,h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3020.png"
 ALT="$p_0+\rho g h$">|; 

$key = q/p_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3018.png"
 ALT="$p_0$">|; 

$key = q/p_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3019.png"
 ALT="$p_1$">|; 

$key = q/p_x=-e,x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2593.png"
 ALT="$p_x = -e x$">|; 

$key = q/partialH_zslashpartialx=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3211.png"
 ALT="$\partial H_z/\partial x=0$">|; 

$key = q/partialH_zslashpartialy=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3212.png"
 ALT="$\partial H_z/\partial y=0$">|; 

$key = q/partial^{,2}phislashpartialt^{,2}=c^{,2}(partial^{,2}phislashpartialx^{,2}+partial^{,2}phislashpartialz^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3027.png"
 ALT="$\partial^{ 2}\phi/\partial t^{ 2} = c^{ 2}(\partial^{ 2}\phi/\partial x^{ 2}+\partial^{ 2}\phi/\partial z^{ 2})$">|; 

$key = q/partial^{,2}psi(x,t)slashpartialt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1171.png"
 ALT="$\partial^{ 2}\psi(x,t)/\partial t^{ 2}$">|; 

$key = q/partial^{,2}y(x,t)slashpartialt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img974.png"
 ALT="$\partial^{ 2} y(x,t)/\partial t^{ 2}$">|; 

$key = q/partialpsi(0,t)slashpartialx=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1178.png"
 ALT="$\partial\psi(0,t)/\partial x=0$">|; 

$key = q/partialpsi(l,t)slashpartialx=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1180.png"
 ALT="$\partial\psi(l,t)/\partial x=0$">|; 

$key = q/partialpslashpartialt=-K,(partialv_xslashpartialx+partialv_zslashpartialz);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3008.png"
 ALT="$\partial p/\partial t = -K (\partial v_x/\partial x+\partial v_z/\partial z)$">|; 

$key = q/partialv_xslashpartialx+partialv_zslashpartialz=V^{,-1},partialVslashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3006.png"
 ALT="$\partial v_x/\partial x+ \partial v_z/\partial z = V^{ -1} \partial V/\partial t$">|; 

$key = q/partialyslashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1415.png"
 ALT="$\partial y/\partial t$">|; 

$key = q/phi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img247.png"
 ALT="$\phi'$">|; 

$key = q/phi'=phi-pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img241.png"
 ALT="$\phi'=\phi-\pi/2$">|; 

$key = q/phi(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1723.png"
 ALT="$\phi(x,t)$">|; 

$key = q/phi(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2239.png"
 ALT="$\phi(x,z,t)$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img150.png"
 ALT="$\phi$">|; 

$key = q/phi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3.png"
 ALT="$\phi = 0$">|; 

$key = q/phi=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img398.png"
 ALT="$\phi=\pi/2$">|; 

$key = q/phi=pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img397.png"
 ALT="$\phi=\pi/4$">|; 

$key = q/phi_1-phi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3324.png"
 ALT="$\phi_1-\phi_2$">|; 

$key = q/phi_1-phi_2=k,d,sintheta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3321.png"
 ALT="$\phi_1-\phi_2= k d \sin\theta_0$">|; 

$key = q/phi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img700.png"
 ALT="$\phi_1$">|; 

$key = q/phi_1=(1slash2),k,d,sintheta_0+phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3301.png"
 ALT="$\phi_1= (1/2) k d \sin\theta_0+\phi$">|; 

$key = q/phi_1=phi_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img718.png"
 ALT="$\phi_1=\phi_2=0$">|; 

$key = q/phi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img706.png"
 ALT="$\phi_2$">|; 

$key = q/phi_2=-(1slash2),k,d,sintheta_0+phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3302.png"
 ALT="$\phi_2=-(1/2) k d \sin\theta_0+\phi$">|; 

$key = q/phi_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3329.png"
 ALT="$\phi_A$">|; 

$key = q/phi_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3330.png"
 ALT="$\phi_B$">|; 

$key = q/phi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1521.png"
 ALT="$\phi_i$">|; 

$key = q/phi_i=phi_r=phi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1533.png"
 ALT="$\phi_i=\phi_r=\phi_t$">|; 

$key = q/phi_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1921.png"
 ALT="$\phi_j$">|; 

$key = q/phi_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img929.png"
 ALT="$\phi_n$">|; 

$key = q/phi_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1057.png"
 ALT="$\phi_n=0$">|; 

$key = q/phi_n=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1206.png"
 ALT="$\phi_n=\pi/2$">|; 

$key = q/phi_n=tan^{-1}(S_nslashC_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1200.png"
 ALT="$\phi_n=\tan^{-1}(S_n/C_n)$">|; 

$key = q/phi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1523.png"
 ALT="$\phi_r$">|; 

$key = q/phi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1528.png"
 ALT="$\phi_t$">|; 

$key = q/phi_t=k_3,a-k_2,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1575.png"
 ALT="$\phi_t=k_3 a-k_2 a$">|; 

$key = q/phi_{-n}=-phi_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img938.png"
 ALT="$\phi_{-n}=-\phi_n$">|; 

$key = q/phi_{1,2,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img825.png"
 ALT="$\phi_{1,2,3}$">|; 

$key = q/phi_{N+1+n}=phi_{N+1-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img944.png"
 ALT="$\phi_{N+1+n}=\phi_{N+1-n}$">|; 

$key = q/phi_{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img1903.png"
 ALT="$\phi_{m,n}$">|; 

$key = q/phi_{n,m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img1905.png"
 ALT="$\phi_{n,m}$">|; 

$key = q/pi,N,(dslashlambda),sin(theta_jpmdeltatheta_j)=pi,(N,jpm1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3395.png"
 ALT="$\pi N (d/\lambda) \sin(\theta_j\pm\delta\theta_j)= \pi (N j\pm 1)$">|; 

$key = q/pi,N,(dslashlambda),sintheta_j=pi,N,j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3394.png"
 ALT="$\pi N (d/\lambda) \sin\theta_j = \pi N j$">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img57.png"
 ALT="$\pi $">|; 

$key = q/pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img53.png"
 ALT="$\pi /2$">|; 

$key = q/pislash2<thetaleqpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3548.png"
 ALT="$\pi/2&lt;\theta\leq \pi$">|; 

$key = q/pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img51.png"
 ALT="$\pi /4$">|; 

$key = q/pislash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img50.png"
 ALT="$\pi /8$">|; 

$key = q/pislash[(N+1),a];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img925.png"
 ALT="$\pi/[(N+1) a]$">|; 

$key = q/pislashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img991.png"
 ALT="$\pi/l$">|; 

$key = q/pma(t)slasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img21.png"
 ALT="$\pm a(t)/a$">|; 

$key = q/pma(t)slashhat{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img596.png"
 ALT="$\pm a(t)/\hat{X}$">|; 

$key = q/pma(t)slashmathaccentV{hat}05E{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img30.png"
 ALT="$\pm a(t)/\mathaccentV {hat}05E{X}$">|; 

$key = q/psi(-x)=-psi(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3955.png"
 ALT="$\psi(-x)=-\psi(x)$">|; 

$key = q/psi(-x)=psi(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3954.png"
 ALT="$\psi(-x)=\psi(x)$">|; 

$key = q/psi(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3927.png"
 ALT="$\psi(0)=0$">|; 

$key = q/psi(0,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1176.png"
 ALT="$\psi(0,t)=0$">|; 

$key = q/psi(a)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3928.png"
 ALT="$\psi(a)=0$">|; 

$key = q/psi(a,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2307.png"
 ALT="$\psi(a,t)=0$">|; 

$key = q/psi(l,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1179.png"
 ALT="$\psi(l,t)=0$">|; 

$key = q/psi(r,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1860.png"
 ALT="$\psi(r,t)$">|; 

$key = q/psi(rho,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1847.png"
 ALT="$\psi(\rho,t)$">|; 

$key = q/psi(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3872.png"
 ALT="$\psi(x)$">|; 

$key = q/psi(x+deltaxslash2,t)-psi(x-deltaxslash2,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1160.png"
 ALT="$\psi(x+\delta x/2,t)-\psi(x-\delta x/2,t)$">|; 

$key = q/psi(x+deltaxslash2,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1159.png"
 ALT="$\psi(x+\delta x/2,t)$">|; 

$key = q/psi(x+lambda,t)=psi(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1340.png"
 ALT="$\psi(x+\lambda,t)=\psi(x,t)$">|; 

$key = q/psi(x,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2411.png"
 ALT="$\psi(x,0)$">|; 

$key = q/psi(x,0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1201.png"
 ALT="$\psi(x,0)=0$">|; 

$key = q/psi(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1154.png"
 ALT="$\psi(x,t)$">|; 

$key = q/psi(x,t)=A,cos(k,x),cos(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1736.png"
 ALT="$\psi(x,t)=A \cos(k x) \cos(\omega t)$">|; 

$key = q/psi(x,t)=A,cos(omega,t-k,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1735.png"
 ALT="$\psi(x,t)= A \cos(\omega t-k x)$">|; 

$key = q/psi(x,t)=A,cos(omega,t-k,x-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1461.png"
 ALT="$\psi(x,t)= A \cos(\omega t-k x-\phi)$">|; 

$key = q/psi(x,t+T)=psi(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1341.png"
 ALT="$\psi(x,t+T)=\psi(x,t)$">|; 

$key = q/psi(x,y,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1870.png"
 ALT="$\psi(x,y,t)$">|; 

$key = q/psi(x,y,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4148.png"
 ALT="$\psi(x,y,z)$">|; 

$key = q/psi(x,y,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1838.png"
 ALT="$\psi(x,y,z,t)$">|; 

$key = q/psi(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2933.png"
 ALT="$\psi(x,z,t)$">|; 

$key = q/psi(x-deltaxslash2,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1158.png"
 ALT="$\psi(x-\delta x/2,t)$">|; 

$key = q/psi(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3257.png"
 ALT="$\psi(z,t)$">|; 

$key = q/psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1937.png"
 ALT="$\psi$">|; 

$key = q/psi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1188.png"
 ALT="$\psi=0$">|; 

$key = q/psi=psi_0,cos(omega,t-{bfk}cdot{bfr}-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1843.png"
 ALT="$\psi = \psi_0 \cos(\omega t-{\bf k}\cdot{\bf r}-\phi)$">|; 

$key = q/psi^ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3847.png"
 ALT="$\psi^\ast$">|; 

$key = q/psi^{,2},A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1857.png"
 ALT="$\psi^{ 2} A$">|; 

$key = q/psi^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1858.png"
 ALT="$\psi^{ 2}$">|; 

$key = q/psi_0,cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3541.png"
 ALT="$\psi_0 \cos(\omega t-\phi)$">|; 

$key = q/psi_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1130.png"
 ALT="$\psi_0$">|; 

$key = q/psi_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1134.png"
 ALT="$\psi_0=0$">|; 

$key = q/psi_0=psi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1135.png"
 ALT="$\psi_0=\psi_1$">|; 

$key = q/psi_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1825.png"
 ALT="$\psi_0&gt;0$">|; 

$key = q/psi_0slashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1864.png"
 ALT="$\psi_0/r$">|; 

$key = q/psi_0slashrho^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1852.png"
 ALT="$\psi_0/\rho^{1/2}$">|; 

$key = q/psi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1132.png"
 ALT="$\psi_1$">|; 

$key = q/psi_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1133.png"
 ALT="$\psi_N$">|; 

$key = q/psi_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1119.png"
 ALT="$\psi_i(t)$">|; 

$key = q/psi_i-psi_{i-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1122.png"
 ALT="$\psi_i-\psi_{i-1}$">|; 

$key = q/psi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1934.png"
 ALT="$\psi_i$">|; 

$key = q/psi_n(x)=(2slasha)^{1slash2},sin(n,pi,xslasha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3937.png"
 ALT="$\psi_n(x)= (2/a)^{1/2} \sin(n \pi x/a)$">|; 

$key = q/psi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1935.png"
 ALT="$\psi_r$">|; 

$key = q/psi_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1936.png"
 ALT="$\psi_t$">|; 

$key = q/psi_{N+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1131.png"
 ALT="$\psi_{N+1}$">|; 

$key = q/psi_{N+1}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1136.png"
 ALT="$\psi_{N+1}=0$">|; 

$key = q/psi_{N+1}=psi_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1137.png"
 ALT="$\psi_{N+1}=\psi_N$">|; 

$key = q/psi_{i+1}-psi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1123.png"
 ALT="$\psi_{i+1}-\psi_i$">|; 

$key = q/psi_{i,r,t}rightarrow-v,psi_{i,r,t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img2009.png"
 ALT="$\psi_{i,r,t}\rightarrow -v \psi_{i,r,t}$">|; 

$key = q/psimhbarslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3943.png"
 ALT="$p\sim \hbar/a$">|; 

$key = q/psiproptoE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3285.png"
 ALT="$\psi\propto E$">|; 

$key = q/psirightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3959.png"
 ALT="$\psi\rightarrow 0$">|; 

$key = q/q,agg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4053.png"
 ALT="$q a\gg 1$">|; 

$key = q/q,asim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4050.png"
 ALT="$q a\sim 1$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2579.png"
 ALT="$q$">|; 

$key = q/q=-e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2595.png"
 ALT="$q=-e$">|; 

$key = q/q^{,2}=(2,mslashhbar^{,2}),(E-W);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4254.png"
 ALT="$q^{ 2}= (2 m/\hbar^{ 2}) (E-W)$">|; 

$key = q/qopnamerelaxo{cos}(omega_ntmspace+thinmuskip{.1667em}t-phi_n)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img65.png"
 ALT="$\qopname \relax o{cos}(\omega _n\tmspace +\thinmuskip {.1667em}t-\phi _n)=1$">|; 

$key = q/qopnamerelaxo{tan}y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img117.png"
 ALT="$\qopname \relax o{tan}y$">|; 

$key = q/r';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3778.png"
 ALT="$r'$">|; 

$key = q/r'=(x'^{,2}+y'^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3671.png"
 ALT="$r'=(x'^{ 2}+y'^{ 2})^{1/2}$">|; 

$key = q/r'gga;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3780.png"
 ALT="$r'\gg a$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img386.png"
 ALT="$r$">|; 

$key = q/r=(x^{,2}+y^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3808.png"
 ALT="$r=(x^{ 2}+y^{ 2})^{1/2}$">|; 

$key = q/r=(x^{,2}+y^{,2}+z^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1861.png"
 ALT="$r=(x^{ 2}+y^{ 2}+z^{ 2})^{1/2}$">|; 

$key = q/r=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1865.png"
 ALT="$r=0$">|; 

$key = q/r={rmconst.};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1867.png"
 ALT="$r={\rm const.}$">|; 

$key = q/r=|z|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3819.png"
 ALT="$r=\vert z\vert$">|; 

$key = q/r>R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4097.png"
 ALT="$r&gt;R$">|; 

$key = q/r^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1866.png"
 ALT="$r^{ -1}$">|; 

$key = q/r_1=R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4099.png"
 ALT="$r_1=R$">|; 

$key = q/r_2=Z_1,Z_2,e^{,2}slash(4pi,epsilon_0,E);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4100.png"
 ALT="$r_2 = Z_1 Z_2 e^{ 2}/(4\pi \epsilon_0 E)$">|; 

$key = q/rho,(partialyslashpartialt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1426.png"
 ALT="$\rho (\partial y/\partial t)$">|; 

$key = q/rho,({rmkg,m}^{-3});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1354.png"
 ALT="$\rho  ({\rm kg m}^{-3})$">|; 

$key = q/rho,A,deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1167.png"
 ALT="$\rho A \delta x$">|; 

$key = q/rho,dx,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3009.png"
 ALT="$\rho dx dy dz$">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img373.png"
 ALT="$\rho$">|; 

$key = q/rho<rho_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img375.png"
 ALT="$\rho&lt;\rho_0$">|; 

$key = q/rho=(x^{,2}+y^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1848.png"
 ALT="$\rho= (x^{ 2}+y^{ 2})^{1/2}$">|; 

$key = q/rho=(x^{,2}+z^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3269.png"
 ALT="$\rho=(x^{ 2}+z^{ 2})^{1/2}$">|; 

$key = q/rho=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1853.png"
 ALT="$\rho=0$">|; 

$key = q/rho=1.0times10^3,{rmkg,m}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2244.png"
 ALT="$\rho =1.0\times 10^3 {\rm kg m}^{-3}$">|; 

$key = q/rho=1.0times10^3,{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3010.png"
 ALT="$\rho=1.0\times 10^3 {\rm m}^{-3}$">|; 

$key = q/rho=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1907.png"
 ALT="$\rho=a$">|; 

$key = q/rho=mslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img963.png"
 ALT="$\rho=m/a$">|; 

$key = q/rho=mslashdeltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img977.png"
 ALT="$\rho=m/\delta x$">|; 

$key = q/rho={rmconst.};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1855.png"
 ALT="$\rho={\rm const.}$">|; 

$key = q/rho^{,-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1854.png"
 ALT="$\rho^{ -1/2}$">|; 

$key = q/rho^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3267.png"
 ALT="$\rho^{-1/2}$">|; 

$key = q/rho_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img374.png"
 ALT="$\rho_0$">|; 

$key = q/rho_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1514.png"
 ALT="$\rho_1$">|; 

$key = q/rho_1neqrho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1517.png"
 ALT="$\rho_1\neq \rho_2$">|; 

$key = q/rho_2,tantheta_t=rho_1,tantheta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2285.png"
 ALT="$\rho_2 \tan\theta_t=\rho_1 \tan\theta_i$">|; 

$key = q/rho_2,v_2<rho_1,v_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2289.png"
 ALT="$\rho_2 v_2&lt; \rho_1 v_1$">|; 

$key = q/rho_2,v_2>rho_1,v_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2287.png"
 ALT="$\rho_2 v_2&gt; \rho_1 v_1$">|; 

$key = q/rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1515.png"
 ALT="$\rho_2$">|; 

$key = q/rho_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1562.png"
 ALT="$\rho_3$">|; 

$key = q/rho_n-rho_{n-1}=d,sintheta=j,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3382.png"
 ALT="$\rho_n-\rho_{n-1}=d \sin\theta=j \lambda$">|; 

$key = q/rhosimeqn_e,m_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2836.png"
 ALT="$\rho\simeq n_e m_i$">|; 

$key = q/s(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img262.png"
 ALT="$s(0)=0$">|; 

$key = q/s(0)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img259.png"
 ALT="$s(0) = 1$">|; 

$key = q/s(0)=s_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img265.png"
 ALT="$s(0)=s_0$">|; 

$key = q/s(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img212.png"
 ALT="$s(t)$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img231.png"
 ALT="$s$">|; 

$key = q/s=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img228.png"
 ALT="$s=0$">|; 

$key = q/s=alpha,t+beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img218.png"
 ALT="$s=\alpha t+\beta$">|; 

$key = q/s=v,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3235.png"
 ALT="$s=v t$">|; 

$key = q/s={rmconstant};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img226.png"
 ALT="$s= {\rm constant}$">|; 

$key = q/s_1(t)+s_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img254.png"
 ALT="$s_1(t)+s_2(t)$">|; 

$key = q/s_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img250.png"
 ALT="$s_1(t)$">|; 

$key = q/s_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img256.png"
 ALT="$s_1$">|; 

$key = q/s_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img252.png"
 ALT="$s_2(t)$">|; 

$key = q/s_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img257.png"
 ALT="$s_2$">|; 

$key = q/s_{rmmax}=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img234.png"
 ALT="$s_{\rm max}=a$">|; 

$key = q/sigma(0,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1177.png"
 ALT="$\sigma(0,t)=0$">|; 

$key = q/sigma(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1164.png"
 ALT="$\sigma(x,t)$">|; 

$key = q/sigma(x-deltaxslash2)=Y,epsilon(x-deltaxslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1168.png"
 ALT="$\sigma(x-\delta x/2) = Y \epsilon(x-\delta x/2)$">|; 

$key = q/sigma,E_x^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3199.png"
 ALT="$\sigma E_x^{ 2}$">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1811.png"
 ALT="$\sigma$">|; 

$key = q/sigma=3.5times10^{,7},(Omega,{rmm})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3200.png"
 ALT="$\sigma=3.5\times 10^{ 7} (\Omega {\rm m})^{-1}$">|; 

$key = q/sigma_k,sigma_x=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2371.png"
 ALT="$\sigma_k \sigma_x=1$">|; 

$key = q/sigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2551.png"
 ALT="$\sigma_k$">|; 

$key = q/sigma_k=1slashsigma_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2364.png"
 ALT="$\sigma_k=1/\sigma_x$">|; 

$key = q/sigma_krightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2374.png"
 ALT="$\sigma_k\rightarrow 0$">|; 

$key = q/sigma_omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2491.png"
 ALT="$\sigma_\omega$">|; 

$key = q/sigma_omega=1slashsigma_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2490.png"
 ALT="$\sigma_\omega=1/\sigma_t$">|; 

$key = q/sigma_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2482.png"
 ALT="$\sigma_t$">|; 

$key = q/sigma_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2361.png"
 ALT="$\sigma_x$">|; 

$key = q/sigma_x=1slashsigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2564.png"
 ALT="$\sigma_x=1/\sigma_k$">|; 

$key = q/sigma_xrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2373.png"
 ALT="$\sigma_x\rightarrow \infty$">|; 

$key = q/sigmaggepsilon_0,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2895.png"
 ALT="$\sigma\gg \epsilon_0 \omega$">|; 

$key = q/sigmasimeq5,(Omega,{rmm})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2906.png"
 ALT="$\sigma\simeq 5 (\Omega {\rm m})^{-1}$">|; 

$key = q/sin(-k,x)=-sin(k,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2352.png"
 ALT="$\sin(-k x)=-\sin(k x)$">|; 

$key = q/sin(-theta)equiv-sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img201.png"
 ALT="$\sin(-\theta)
\equiv-\sin\theta$">|; 

$key = q/sin(2,theta)equiv2,sintheta,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img315.png"
 ALT="$\sin(2 \theta)\equiv 2 \sin\theta \cos\theta$">|; 

$key = q/sin(a+b)equivsina,cosb+cosa,sinb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img918.png"
 ALT="$\sin(a+b)\equiv \sin a \cos b + \cos a \sin b$">|; 

$key = q/sin(alpha,x');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3467.png"
 ALT="$\sin(\alpha x')$">|; 

$key = q/sin(c,theta)neqc,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img334.png"
 ALT="$\sin(c \theta)\neq c \sin\theta$">|; 

$key = q/sin(k,l)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img989.png"
 ALT="$\sin(k l)=0$">|; 

$key = q/sin(k,x)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1407.png"
 ALT="$\sin(k x)=0$">|; 

$key = q/sin(n,omega,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1284.png"
 ALT="$\sin (n \omega t)=0$">|; 

$key = q/sin(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img529.png"
 ALT="$\sin(\omega t)$">|; 

$key = q/sin(omega,t-varphi)equivsin(omega,t),cosvarphi-cos(omega,t),sinvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img525.png"
 ALT="$\sin(\omega t-\varphi) \equiv \sin(\omega t) \cos \varphi - \cos(\omega t) \sin\varphi$">|; 

$key = q/sin(theta+2pi)equivsintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img913.png"
 ALT="$\sin(\theta+2\pi)\equiv \sin\theta$">|; 

$key = q/sin(theta+n,2pi)=sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2326.png"
 ALT="$\sin(\theta+n 2\pi)=\sin\theta$">|; 

$key = q/sin(theta+n,2pi)equivsintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1252.png"
 ALT="$\sin(\theta+n 2\pi)\equiv \sin\theta$">|; 

$key = q/sin(theta-pislash2)equiv-costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img304.png"
 ALT="$\sin (\theta-\pi/2)\equiv -\cos\theta$">|; 

$key = q/sin(theta_j+{mitDelta}theta_j)=j,(lambda+{mitDelta}lambda)slashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3402.png"
 ALT="$\sin(\theta_j+{\mit\Delta}\theta_j)= j (\lambda+{\mit\Delta}\lambda)/d$">|; 

$key = q/sin[(k-k_0),(v_g,t-x)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2562.png"
 ALT="$\sin[(k-k_0) (v_g t-x)]$">|; 

$key = q/sin[n,(xslashl),pi]=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1001.png"
 ALT="$\sin [n (x/l) \pi]=0$">|; 

$key = q/sin[pi,N,(dslashlambda),sintheta];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3396.png"
 ALT="$\sin[\pi N (d/\lambda) \sin\theta]$">|; 

$key = q/sin^2theta+cos^2thetaequiv1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img204.png"
 ALT="$\sin^2\theta+\cos^2\theta \equiv 1$">|; 

$key = q/sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img335.png"
 ALT="$\sin\theta$">|; 

$key = q/sintheta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3407.png"
 ALT="$\sin\theta_j$">|; 

$key = q/sintheta_j=j,(lambdaslashd);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3392.png"
 ALT="$\sin\theta_j = j (\lambda/d)$">|; 

$key = q/sintheta_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2043.png"
 ALT="$\sin\theta_t$">|; 

$key = q/sinthetaequivcos(theta-pislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img284.png"
 ALT="$\sin\theta\equiv \cos(\theta-\pi/2)$">|; 

$key = q/sinthetasimeqtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img338.png"
 ALT="$\sin\theta\simeq \theta$">|; 

$key = q/sinu=sin(thetaslash2)slashsin(skew{3}hat{theta}slash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img408.png"
 ALT="$\sin u =\sin(\theta/2)/\sin(\skew{3}\hat{\theta}/2)$">|; 

$key = q/sinxsimeqx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img626.png"
 ALT="$\sin x\simeq x$">|; 

$key = q/skew{3}dot{theta}(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img403.png"
 ALT="$\skew{3}\dot{\theta}(0) = 0$">|; 

$key = q/skew{3}dot{theta}(0)=omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img400.png"
 ALT="$\skew{3}\dot{\theta}(0) = \omega_0$">|; 

$key = q/skew{3}hat{V}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img575.png"
 ALT="$\skew{3}\hat{V}&gt;0$">|; 

$key = q/skew{3}hat{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img343.png"
 ALT="$\skew{3}\hat{\theta}$">|; 

$key = q/skew{3}hat{theta}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img342.png"
 ALT="$\skew{3}\hat{\theta}&gt;0$">|; 

$key = q/sqrt{2},(g,Tslashrho)^{1slash4}sim0.2,{rmm,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3167.png"
 ALT="$\sqrt{2} (g T/\rho)^{1/4}\sim 0.2 {\rm m s}^{-1}$">|; 

$key = q/sqrt{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.32ex; " SRC="|."$dir".q|img799.png"
 ALT="$\sqrt{2}$">|; 

$key = q/sqrt{2}left(1+1slashsqrt{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img800.png"
 ALT="$\sqrt{2}\left(1+1/\sqrt{2}\right)^{1/2}$">|; 

$key = q/sqrt{LslashC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img285.png"
 ALT="$\sqrt{L/C}$">|; 

$key = q/sqrt{Tslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1350.png"
 ALT="$\sqrt{T/\rho}$">|; 

$key = q/sqrt{Yslashrho},({rmm,s}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1355.png"
 ALT="$\sqrt{Y/\rho}  ({\rm m s}^{-1})$">|; 

$key = q/sqrt{Yslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1351.png"
 ALT="$\sqrt{Y/\rho}$">|; 

$key = q/sqrt{Z_1,Z_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.50ex; " SRC="|."$dir".q|img1594.png"
 ALT="$\sqrt{Z_1 Z_2}$">|; 

$key = q/sqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img1660.png"
 ALT="$\sqrt{\epsilon}$">|; 

$key = q/sqrt{g,d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img3056.png"
 ALT="$\sqrt{g d}$">|; 

$key = q/sqrt{gamma,pslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1352.png"
 ALT="$\sqrt{\gamma p/\rho}$">|; 

$key = q/sqrt{mu_0slashepsilon_0},=376.73,Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1795.png"
 ALT="$\sqrt{\mu_0/\epsilon_0} =376.73 \Omega$">|; 

$key = q/sqrt{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1802.png"
 ALT="$\sqrt{n}$">|; 

$key = q/stackrel{,,mbox{large..}}{x}slash(omega^{,2},a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img189.png"
 ALT="$\stackrel{  \mbox{\large ..}}{x}/(\omega^{ 2} a)$">|; 

$key = q/stackrel{,,mbox{large.}}{x}_1=x_2=,stackrel{,,mbox{large.}}{x}_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img725.png"
 ALT="$\stackrel{  \mbox{\large.}}{x}_1 = x_2 =  \stackrel{  \mbox{\large .}}{x}_2=0$">|; 

$key = q/stackrel{,,mbox{large.}}{x}_1=x_2=,stackrel{,mbox{large.}}{x}_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img735.png"
 ALT="$\stackrel{  \mbox{\large .}}{x}_1 = x_2 =  \stackrel{ \mbox{\large .}}{x}_2=0$">|; 

$key = q/stackrel{,,mbox{large.}}{x}slash(omega,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img188.png"
 ALT="$\stackrel{  \mbox{\large .}}{x}/(\omega a)$">|; 

$key = q/stackrel{,mbox{.}}{I}_1=,stackrel{,mbox{.}}{I}_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img771.png"
 ALT="$\stackrel{ \mbox{.}}{I}_1 =
 \stackrel{ \mbox{.}}{I}_2=0$">|; 

$key = q/sum_{n=1,N}sin(alpha,x_n)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img3424.png"
 ALT="$\sum_{n=1,N} \sin(\alpha x_n) =0$">|; 

$key = q/sum_{n=1,N}sin(k,x_n,sintheta)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img3373.png"
 ALT="$\sum_{n=1,N} \sin(k x_n \sin\theta)= 0$">|; 

$key = q/t+dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4117.png"
 ALT="$t+dt$">|; 

$key = q/t-t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2703.png"
 ALT="$t-t_0$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img135.png"
 ALT="$t$">|; 

$key = q/t=-{mitDelta}tslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2522.png"
 ALT="$t=-{\mit\Delta} t/2$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img66.png"
 ALT="$t=0$">|; 

$key = q/t=T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1705.png"
 ALT="$t=T$">|; 

$key = q/t=phislashomega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img482.png"
 ALT="$t=\phi/\omega_1$">|; 

$key = q/t=tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1274.png"
 ALT="$t=\tau$">|; 

$key = q/t=tauslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1292.png"
 ALT="$t=\tau/2$">|; 

$key = q/t={mitDelta}tslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2523.png"
 ALT="$t={\mit\Delta} t/2$">|; 

$key = q/t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2702.png"
 ALT="$t_0$">|; 

$key = q/tan^{-1}left(1slashsqrt{8}right)=19.47^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3155.png"
 ALT="$\tan^{-1}\left(1/\sqrt{8}\right)= 19.47^\circ$">|; 

$key = q/tanhxsimeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3059.png"
 ALT="$\tanh x\simeq 1$">|; 

$key = q/tanhxsimeqx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3055.png"
 ALT="$\tanh x\simeq x$">|; 

$key = q/tantheta_i=beta=n_2slashn_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2036.png"
 ALT="$\tan\theta_i = \beta = n_2/n_1$">|; 

$key = q/tanthetaequivsinthetaslashcostheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img205.png"
 ALT="$\tan\theta \equiv \sin\theta/\cos\theta$">|; 

$key = q/tanthetasimeqtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img885.png"
 ALT="$\tan\theta\simeq \theta$">|; 

$key = q/tany;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3979.png"
 ALT="$\tan y$">|; 

$key = q/tany=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3990.png"
 ALT="$\tan y =0$">|; 

$key = q/tany=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3983.png"
 ALT="$\tan y =\infty$">|; 

$key = q/tau'<tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1253.png"
 ALT="$\tau'&lt;\tau$">|; 

$key = q/tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img324.png"
 ALT="$\tau$">|; 

$key = q/tau<T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1324.png"
 ALT="$\tau &lt; T$">|; 

$key = q/tau=-k,theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img384.png"
 ALT="$\tau = - k \theta$">|; 

$key = q/tau=2,lslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1059.png"
 ALT="$\tau= 2 l/v$">|; 

$key = q/tau=2pislashomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1249.png"
 ALT="$\tau=2\pi/\omega$">|; 

$key = q/tau=lslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1209.png"
 ALT="$\tau=l/v$">|; 

$key = q/tau_{{rmex}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img129.png"
 ALT="$\tau _{{\rm ex}}$">|; 

$key = q/taullT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1326.png"
 ALT="$\tau\ll T$">|; 

$key = q/tausim10^{,-8},{rms};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3735.png"
 ALT="$\tau\sim 10^{ -8} {\rm s}$">|; 

$key = q/tausim10^{,-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3320.png"
 ALT="$\tau\sim 10^{ -8}$">|; 

$key = q/tausim10^{,-9},{rms};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3736.png"
 ALT="$\tau\sim 10^{ -9} {\rm s}$">|; 

$key = q/tgeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img2520.png"
 ALT="$t\geq 0$">|; 

$key = q/theta(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img399.png"
 ALT="$\theta(0)=0$">|; 

$key = q/theta(0)=theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img402.png"
 ALT="$\theta(0)=\theta_0$">|; 

$key = q/theta(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img401.png"
 ALT="$\theta(t)$">|; 

$key = q/theta,,theta_0ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3331.png"
 ALT="$\theta, \theta_0\ll 1$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img165.png"
 ALT="$\theta$">|; 

$key = q/theta=0,pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2219.png"
 ALT="$\theta=0, \pi$">|; 

$key = q/theta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img331.png"
 ALT="$\theta =0$">|; 

$key = q/theta=n,2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img173.png"
 ALT="$\theta=n 2\pi$">|; 

$key = q/theta=omega,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1277.png"
 ALT="$\theta=\omega t$">|; 

$key = q/theta=omega_1,t-phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img485.png"
 ALT="$\theta=\omega_1 t-\phi$">|; 

$key = q/theta=pi,xslashl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1029.png"
 ALT="$\theta=\pi x/l$">|; 

$key = q/theta=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2220.png"
 ALT="$\theta=\pi/2$">|; 

$key = q/theta=skew{3}dot{theta}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img322.png"
 ALT="$\theta=\skew{3}\dot{\theta}=0$">|; 

$key = q/theta=tan^{-1}(yslashx);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3811.png"
 ALT="$\theta=\tan^{-1}(y/x)$">|; 

$key = q/theta=theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3310.png"
 ALT="$\theta=\theta_0$">|; 

$key = q/theta={rmarg}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3820.png"
 ALT="$\theta={\rm arg}(z)$">|; 

$key = q/theta_0+deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3442.png"
 ALT="$\theta_0+\delta\theta$">|; 

$key = q/theta_0-deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3441.png"
 ALT="$\theta_0-\delta\theta$">|; 

$key = q/theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3296.png"
 ALT="$\theta_0$">|; 

$key = q/theta_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3456.png"
 ALT="$\theta_0=0$">|; 

$key = q/theta_0=lambdaslash(2,d);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3346.png"
 ALT="$\theta_0=\lambda/(2 d)$">|; 

$key = q/theta_0^{,-1}int_0^{theta_0}cdots,dtheta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.35ex; vertical-align: -1.02ex; " SRC="|."$dir".q|img3352.png"
 ALT="$\theta_0^{ -1}\int_0^{\theta_0}\cdots d\theta_0$">|; 

$key = q/theta_0gtrsimlambdaslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3360.png"
 ALT="$\theta_0\gtrsim \lambda/d$">|; 

$key = q/theta_0lllambdaslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3349.png"
 ALT="$\theta_0\ll \lambda/d$">|; 

$key = q/theta_0simeqDslashL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3364.png"
 ALT="$\theta_0\simeq D/L$">|; 

$key = q/theta_0slash2simeqDslash(2,L);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3327.png"
 ALT="$\theta_0/2\simeq D/(2 L)$">|; 

$key = q/theta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img844.png"
 ALT="$\theta_1$">|; 

$key = q/theta_1=theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img848.png"
 ALT="$\theta_1=\theta_0$">|; 

$key = q/theta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img845.png"
 ALT="$\theta_2$">|; 

$key = q/theta_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img849.png"
 ALT="$\theta_2=0$">|; 

$key = q/theta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2087.png"
 ALT="$\theta_c$">|; 

$key = q/theta_c<45^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2089.png"
 ALT="$\theta_c&lt;45^\circ$">|; 

$key = q/theta_c=48.8^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2088.png"
 ALT="$\theta_c= 48.8^\circ$">|; 

$key = q/theta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img880.png"
 ALT="$\theta_i$">|; 

$key = q/theta_i=theta_B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2037.png"
 ALT="$\theta_i=\theta_B$">|; 

$key = q/theta_j+deltatheta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3400.png"
 ALT="$\theta_j+\delta\theta_j$">|; 

$key = q/theta_j+{mitDelta}theta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3401.png"
 ALT="$\theta_j+{\mit\Delta}\theta_j$">|; 

$key = q/theta_j-deltatheta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3399.png"
 ALT="$\theta_j-\delta\theta_j$">|; 

$key = q/theta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3391.png"
 ALT="$\theta_j$">|; 

$key = q/theta_jpmdeltatheta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3393.png"
 ALT="$\theta_j\pm \delta\theta_j$">|; 

$key = q/theta_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1945.png"
 ALT="$\theta_r$">|; 

$key = q/theta_r=theta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1969.png"
 ALT="$\theta_r=\theta_i$">|; 

$key = q/theta_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1946.png"
 ALT="$\theta_t$">|; 

$key = q/theta_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3496.png"
 ALT="$\theta_x$">|; 

$key = q/theta_x=theta,cosphi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3524.png"
 ALT="$\theta_x=\theta \cos\phi'$">|; 

$key = q/theta_x=x'slashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3493.png"
 ALT="$\theta_x=x'/R$">|; 

$key = q/theta_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3497.png"
 ALT="$\theta_y$">|; 

$key = q/theta_y=theta,sinphi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3525.png"
 ALT="$\theta_y=\theta \sin\phi'$">|; 

$key = q/theta_y=y'slashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3494.png"
 ALT="$\theta_y=y'/R$">|; 

$key = q/theta_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img881.png"
 ALT="$\theta_{i+1}$">|; 

$key = q/tilde{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2223.png"
 ALT="$\tilde{p}$">|; 

$key = q/tilde{rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2222.png"
 ALT="$\tilde{\rho}$">|; 

$key = q/tslashtau=0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img67.png"
 ALT="$t/\tau =0.01$">|; 

$key = q/tslashtau=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img60.png"
 ALT="$t/\tau = 0$">|; 

$key = q/tslashtau=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1215.png"
 ALT="$t/\tau=1$">|; 

$key = q/u';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3579.png"
 ALT="$u'$">|; 

$key = q/u'<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3650.png"
 ALT="$u'&lt;0$">|; 

$key = q/u'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3651.png"
 ALT="$u'=0$">|; 

$key = q/u'>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3649.png"
 ALT="$u'&gt;0$">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img380.png"
 ALT="$u$">|; 

$key = q/u<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img101.png"
 ALT="$u&lt;0$">|; 

$key = q/u=-{mitDelta}uslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3654.png"
 ALT="$u=-{\mit\Delta }u/2$">|; 

$key = q/u=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img113.png"
 ALT="$u=0.2$">|; 

$key = q/u=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3638.png"
 ALT="$u=0$">|; 

$key = q/u=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img111.png"
 ALT="$u=1$">|; 

$key = q/u=50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img112.png"
 ALT="$u=50$">|; 

$key = q/u=u_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3630.png"
 ALT="$u=u_1$">|; 

$key = q/u=u_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3631.png"
 ALT="$u=u_2$">|; 

$key = q/u={mitDelta}uslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3655.png"
 ALT="$u={\mit\Delta} u/2$">|; 

$key = q/u_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1079.png"
 ALT="$u_0$">|; 

$key = q/u_0slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1716.png"
 ALT="$u_0/c$">|; 

$key = q/u_1<u_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3613.png"
 ALT="$u_1&lt;u_2$">|; 

$key = q/u_1=-{mitDelta}uslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3656.png"
 ALT="$u_1=-{\mit\Delta }u/2$">|; 

$key = q/u_1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3639.png"
 ALT="$u_1=0$">|; 

$key = q/u_2=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3640.png"
 ALT="$u_2=\infty$">|; 

$key = q/u_2={mitDelta}uslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3657.png"
 ALT="$u_2={\mit\Delta}u/2$">|; 

$key = q/u_o;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1696.png"
 ALT="$u_o$">|; 

$key = q/u_s,T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1708.png"
 ALT="$u_s T$">|; 

$key = q/u_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1704.png"
 ALT="$u_s$">|; 

$key = q/u_sllc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1715.png"
 ALT="$u_s\ll c$">|; 

$key = q/u_sslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1717.png"
 ALT="$u_s/c$">|; 

$key = q/ugg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3675.png"
 ALT="$u\gg 1$">|; 

$key = q/ulesssim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3674.png"
 ALT="$u\lesssim 1$">|; 

$key = q/ull1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3716.png"
 ALT="$u\ll1$">|; 

$key = q/v';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3580.png"
 ALT="$v'$">|; 

$key = q/v(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1719.png"
 ALT="$v(x)$">|; 

$key = q/v,({rmm,s}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1356.png"
 ALT="$v ({\rm m s}^{-1})$">|; 

$key = q/v,t-x=F^{,-1}(c)={rmconstant};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2438.png"
 ALT="$v t-x=F^{ -1}(c)={\rm constant}$">|; 

$key = q/v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img370.png"
 ALT="$v$">|; 

$key = q/v<u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3676.png"
 ALT="$v&lt;u$">|; 

$key = q/v=(B_0^{,2}slashmu_0,rho)^{,1slash2}=V_A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2843.png"
 ALT="$v = (B_0^{ 2}/\mu_0 \rho)^{ 1/2} = V_A$">|; 

$key = q/v=(Tslashrho)^{,1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2841.png"
 ALT="$v=(T/\rho)^{ 1/2}$">|; 

$key = q/v=1483,{rmm,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2245.png"
 ALT="$v = 1483 {\rm m s}^{-1}$">|; 

$key = q/v=1slashsqrt{{calL},{calC}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1103.png"
 ALT="$v=1/\sqrt{{\cal L} {\cal C}}$">|; 

$key = q/v=cslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1965.png"
 ALT="$v=c/n$">|; 

$key = q/v=cslashsqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img4456.png"
 ALT="$v=c/\sqrt{\epsilon}$">|; 

$key = q/v=f',lambda';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1711.png"
 ALT="$v=f' \lambda'$">|; 

$key = q/v=omega_0,a=(Kslashm)^{1slash2},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1152.png"
 ALT="$v=\omega_0 a=(K/m)^{1/2} a$">|; 

$key = q/v=omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1702.png"
 ALT="$v=\omega/k$">|; 

$key = q/v=pslashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3839.png"
 ALT="$v=p/m$">|; 

$key = q/v=sqrt{2,Eslashm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4110.png"
 ALT="$v= \sqrt{2 E/m}$">|; 

$key = q/v=sqrt{Tslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1083.png"
 ALT="$v=\sqrt{T/\rho}$">|; 

$key = q/v=sqrt{Yslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1458.png"
 ALT="$v=\sqrt{Y/\rho}$">|; 

$key = q/v=sqrt{gamma,pslashrho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1383.png"
 ALT="$v=\sqrt{\gamma p/\rho}$">|; 

$key = q/v>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1329.png"
 ALT="$v&gt;0$">|; 

$key = q/v>u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3702.png"
 ALT="$v&gt;u$">|; 

$key = q/v^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1349.png"
 ALT="$v^{ 2}$">|; 

$key = q/v^{,2}=Tslashrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1428.png"
 ALT="$v^{ 2}=T/\rho$">|; 

$key = q/v_0(x)equivpartialy(x,0)slashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1092.png"
 ALT="$v_0(x)\equiv \partial y(x,0)/\partial t$">|; 

$key = q/v_0+{mitDelta}vslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3912.png"
 ALT="$v_0+ {\mit\Delta}v/2$">|; 

$key = q/v_0-{mitDelta}vslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3913.png"
 ALT="$v_0-{\mit\Delta}v/2$">|; 

$key = q/v_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img195.png"
 ALT="$v_0$">|; 

$key = q/v_0=dot{x}(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img643.png"
 ALT="$v_0=\dot{x}(0)$">|; 

$key = q/v_0=sqrt{T,aslashm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3176.png"
 ALT="$v_0= \sqrt{T a/m}$">|; 

$key = q/v_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2258.png"
 ALT="$v_1$">|; 

$key = q/v_1<v_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2290.png"
 ALT="$v_1&lt; v_2$">|; 

$key = q/v_1=-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3628.png"
 ALT="$v_1=-\infty$">|; 

$key = q/v_1=sqrt{Tslashrho_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1524.png"
 ALT="$v_1=\sqrt{T/\rho_1}$">|; 

$key = q/v_1>v_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2288.png"
 ALT="$v_1&gt; v_2$">|; 

$key = q/v_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2259.png"
 ALT="$v_2$">|; 

$key = q/v_2=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3629.png"
 ALT="$v_2=\infty$">|; 

$key = q/v_2=sqrt{Tslashrho_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1529.png"
 ALT="$v_2=\sqrt{T/\rho_2}$">|; 

$key = q/v_a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2169.png"
 ALT="$v_a$">|; 

$key = q/v_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2172.png"
 ALT="$v_b$">|; 

$key = q/v_g(k_0+{mitDelta}kslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2574.png"
 ALT="$v_g(k_0+{\mit\Delta} k/2)$">|; 

$key = q/v_g(k_0-{mitDelta}kslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2573.png"
 ALT="$v_g(k_0-{\mit\Delta} k/2)$">|; 

$key = q/v_g,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3129.png"
 ALT="$v_g t$">|; 

$key = q/v_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2568.png"
 ALT="$v_g$">|; 

$key = q/v_g<c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2613.png"
 ALT="$v_g&lt;c$">|; 

$key = q/v_g=(1-omega_{p,e}^{,2}slashomega^{,2})^{1slash2},c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2700.png"
 ALT="$v_g = (1-\omega_{p e}^{ 2}/\omega^{ 2})^{1/2} c$">|; 

$key = q/v_g=domegaslashdk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2609.png"
 ALT="$v_g=d\omega/dk$">|; 

$key = q/v_g=domegaslashdk=(1slash2),sqrt{gslashk}=v_pslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img3062.png"
 ALT="$v_g=d\omega/dk = (1/2) \sqrt{g/k}= v_p/2$">|; 

$key = q/v_g=domegaslashdk=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2847.png"
 ALT="$v_g=d\omega/dk = 0$">|; 

$key = q/v_g=v_pslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3124.png"
 ALT="$v_g=v_p/2$">|; 

$key = q/v_p,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3108.png"
 ALT="$v_p t$">|; 

$key = q/v_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1346.png"
 ALT="$v_p$">|; 

$key = q/v_p=(gslashk)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3121.png"
 ALT="$v_p=(g/k)^{1/2}$">|; 

$key = q/v_p=(omegaslashk)_{k_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3897.png"
 ALT="$v_p = (\omega/k)_{k_0}$">|; 

$key = q/v_p=V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3074.png"
 ALT="$v_p=V$">|; 

$key = q/v_p=omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1391.png"
 ALT="$v_p = \omega/k$">|; 

$key = q/v_p=omegaslashk=cslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2606.png"
 ALT="$v_p=\omega/k = c/n$">|; 

$key = q/v_p=omegaslashk=sqrt{gslashk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img3061.png"
 ALT="$v_p=\omega/k = \sqrt{g/k}$">|; 

$key = q/v_p=v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1392.png"
 ALT="$v_p=v$">|; 

$key = q/v_p>c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2607.png"
 ALT="$v_p&gt;c$">|; 

$key = q/v_parallel=cslashsqrt{epsilon_parallel}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.86ex; " SRC="|."$dir".q|img2193.png"
 ALT="$v_\parallel=c/\sqrt{\epsilon_\parallel}.$">|; 

$key = q/v_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2206.png"
 ALT="$v_\perp$">|; 

$key = q/v_perp=cslashsqrt{epsilon_perp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img2192.png"
 ALT="$v_\perp=c/\sqrt{\epsilon_\perp}$">|; 

$key = q/v_perpneqv_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2189.png"
 ALT="$v_\perp\neq v_\parallel$">|; 

$key = q/v_x(x+dx,z,t),dy,dz+v_z(x,z+dz,t),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3001.png"
 ALT="$v_x(x+dx,z,t) dy dz + v_z(x,z+dz,t) dx dy$">|; 

$key = q/v_x(x+dx,z,t),dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2995.png"
 ALT="$v_x(x+dx,z,t) dy dz$">|; 

$key = q/v_x(x,z,t),dy,dz+v_z(x,z,t),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3000.png"
 ALT="$v_x(x,z,t) dy dz + v_z(x,z,t) dx dy$">|; 

$key = q/v_x(x,z,t),dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2994.png"
 ALT="$v_x(x,z,t) dy dz$">|; 

$key = q/v_x(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2988.png"
 ALT="$v_x(x,z,t)$">|; 

$key = q/v_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2247.png"
 ALT="$v_x$">|; 

$key = q/v_x=cslashsqrt{epsilon_{xx}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img2158.png"
 ALT="$v_x=c/\sqrt{\epsilon_{xx}}$">|; 

$key = q/v_x=v_y=v_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2187.png"
 ALT="$v_x=v_y=v_\perp$">|; 

$key = q/v_y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2996.png"
 ALT="$v_y=0$">|; 

$key = q/v_y=cslashsqrt{epsilon_{yy}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.89ex; " SRC="|."$dir".q|img2159.png"
 ALT="$v_y=c/\sqrt{\epsilon_{yy}}$">|; 

$key = q/v_z(x,-d,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3032.png"
 ALT="$v_z(x,-d,t)=0$">|; 

$key = q/v_z(x,z+dz,t),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2999.png"
 ALT="$v_z(x,z+dz,t) dx dy$">|; 

$key = q/v_z(x,z,t),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2998.png"
 ALT="$v_z(x,z,t) dx dy$">|; 

$key = q/v_z(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2989.png"
 ALT="$v_z(x,z,t)$">|; 

$key = q/v_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2248.png"
 ALT="$v_z$">|; 

$key = q/v_z=cslashsqrt{epsilon_{zz}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img2160.png"
 ALT="$v_z=c/\sqrt{\epsilon_{zz}}$">|; 

$key = q/v_z=v_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2188.png"
 ALT="$v_z=v_\parallel$">|; 

$key = q/v_{rmrms}=sqrt{3,R,TslashM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1385.png"
 ALT="$v_{\rm rms}= \sqrt{3 R T/M}$">|; 

$key = q/varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img520.png"
 ALT="$\varphi$">|; 

$key = q/varphi=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img547.png"
 ALT="$\varphi=\pi/2$">|; 

$key = q/varphi_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2698.png"
 ALT="$\varphi_0$">|; 

$key = q/varphisimeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img546.png"
 ALT="$\varphi\simeq 0$">|; 

$key = q/varphisimeqpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img548.png"
 ALT="$\varphi\simeq \pi$">|; 

$key = q/vslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2583.png"
 ALT="$v/c$">|; 

$key = q/w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1497.png"
 ALT="$w$">|; 

$key = q/x'+u_o,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1700.png"
 ALT="$x'+u_o t$">|; 

$key = q/x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3466.png"
 ALT="$x'$">|; 

$key = q/x'=x-u_0,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1697.png"
 ALT="$x'=x-u_0 t$">|; 

$key = q/x'=x-x_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3463.png"
 ALT="$x'=x-x_n$">|; 

$key = q/x(0)=dot{x}(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img597.png"
 ALT="$x(0)=\dot{x}(0)=0$">|; 

$key = q/x(0)=x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img452.png"
 ALT="$x(0)=x_0$">|; 

$key = q/x(t)-X(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img510.png"
 ALT="$x(t)-X(t)$">|; 

$key = q/x(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img136.png"
 ALT="$x(t)$">|; 

$key = q/x(t)=A,sin(2pi,f,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img638.png"
 ALT="$x(t)= A \sin(2\pi f t)$">|; 

$key = q/x(t)slasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img20.png"
 ALT="$x(t)/a$">|; 

$key = q/x(t)slashhat{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img595.png"
 ALT="$x(t)/\hat{X}$">|; 

$key = q/x(t)slashmathaccentV{hat}05E{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img29.png"
 ALT="$x(t)/\mathaccentV {hat}05E{X}$">|; 

$key = q/x+deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1474.png"
 ALT="$x+\delta x$">|; 

$key = q/x+deltaxslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1157.png"
 ALT="$x+\delta x/2$">|; 

$key = q/x+dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2990.png"
 ALT="$x+dx$">|; 

$key = q/x-deltaxslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1156.png"
 ALT="$x-\delta x/2$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img116.png"
 ALT="$x$">|; 

$key = q/x<-aslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3958.png"
 ALT="$x&lt;-a/2$">|; 

$key = q/x<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img191.png"
 ALT="$x&lt;0$">|; 

$key = q/x=(8slash27)^{1slash2},X_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3150.png"
 ALT="$x=(8/27)^{1/2} X_0$">|; 

$key = q/x=+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img161.png"
 ALT="$x=+a$">|; 

$key = q/x=+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3842.png"
 ALT="$x=+\infty$">|; 

$key = q/x=-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img160.png"
 ALT="$x=-a$">|; 

$key = q/x=-deltaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3429.png"
 ALT="$x=-\delta/2$">|; 

$key = q/x=-dslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3260.png"
 ALT="$x=-d/2$">|; 

$key = q/x=-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1516.png"
 ALT="$x=-\infty$">|; 

$key = q/x=-x_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3368.png"
 ALT="$x=-x_n$">|; 

$key = q/x=0,,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3202.png"
 ALT="$x=0, a$">|; 

$key = q/x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img143.png"
 ALT="$x=0$">|; 

$key = q/x=2times10^{-10},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4245.png"
 ALT="$x=2\times 10^{-10} {\rm m}$">|; 

$key = q/x=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1330.png"
 ALT="$x=$">|; 

$key = q/x=X=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img511.png"
 ALT="$x=X=0$">|; 

$key = q/x=X_0slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3148.png"
 ALT="$x=X_0/2$">|; 

$key = q/x=a,cos(2pi,tslashT-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img177.png"
 ALT="$x=a \cos(2\pi t/T-\phi)$">|; 

$key = q/x=a,cos(omega,t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img159.png"
 ALT="$x=a \cos(\omega t-\phi)$">|; 

$key = q/x=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img172.png"
 ALT="$x=a$">|; 

$key = q/x=atmspace+thinmuskip{.1667em}qopnamerelaxo{cos}(2pitmspace+thinmuskip{.1667em}tslashT-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2.png"
 ALT="$x=a\tmspace +\thinmuskip {.1667em}\qopname \relax o{cos}(2\pi \tmspace +\thinmuskip {.1667em}t/T-\phi )$">|; 

$key = q/x=atmspace+thinmuskip{.1667em}qopnamerelaxo{cos}(omegatmspace+thinmuskip{.1667em}t-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1.png"
 ALT="$x=a\tmspace +\thinmuskip {.1667em}\qopname \relax o{cos}(\omega \tmspace +\thinmuskip {.1667em}t-\phi )$">|; 

$key = q/x=deltaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3430.png"
 ALT="$x=\delta/2$">|; 

$key = q/x=dot{x}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img138.png"
 ALT="$x=\dot{x}=0$">|; 

$key = q/x=dslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3259.png"
 ALT="$x=d/2$">|; 

$key = q/x=hat{x},cos(omega,t-varphi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img647.png"
 ALT="$x = \hat{x} \cos(\omega t - \varphi)$">|; 

$key = q/x=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1530.png"
 ALT="$x=\infty$">|; 

$key = q/x=j,pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3438.png"
 ALT="$x=j \pi$">|; 

$key = q/x=l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1153.png"
 ALT="$x=l$">|; 

$key = q/x=lslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1071.png"
 ALT="$x=l/2$">|; 

$key = q/x=pma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img210.png"
 ALT="$x=\pm a$">|; 

$key = q/x=pmaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3968.png"
 ALT="$x=\pm a/2$">|; 

$key = q/x=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3813.png"
 ALT="$x=r \cos\theta$">|; 

$key = q/x=rho,cosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3522.png"
 ALT="$x=\rho \cos\phi$">|; 

$key = q/x=x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3876.png"
 ALT="$x=x_0$">|; 

$key = q/x=x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1412.png"
 ALT="$x=x_1$">|; 

$key = q/x=x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1413.png"
 ALT="$x=x_2$">|; 

$key = q/x=x_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3366.png"
 ALT="$x=x_n$">|; 

$key = q/x=y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3670.png"
 ALT="$x=y=0$">|; 

$key = q/x=z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3262.png"
 ALT="$x=z=0$">|; 

$key = q/x={rmRe}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3804.png"
 ALT="$x={\rm Re}(z)$">|; 

$key = q/x>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img190.png"
 ALT="$x&gt;0$">|; 

$key = q/x>a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1563.png"
 ALT="$x&gt;a$">|; 

$key = q/x>aslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3963.png"
 ALT="$x&gt;a/2$">|; 

$key = q/x>x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4078.png"
 ALT="$x&gt;x_2$">|; 

$key = q/x^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img391.png"
 ALT="$x^{ 2}$">|; 

$key = q/x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img194.png"
 ALT="$x_0$">|; 

$key = q/x_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img867.png"
 ALT="$x_0=0$">|; 

$key = q/x_0=x(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img642.png"
 ALT="$x_0=x(0)$">|; 

$key = q/x_1(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img466.png"
 ALT="$x_1(t)$">|; 

$key = q/x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img35.png"
 ALT="$x_1$">|; 

$key = q/x_1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4085.png"
 ALT="$x_1=0$">|; 

$key = q/x_1=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img33.png"
 ALT="$x_1=a$">|; 

$key = q/x_1=x_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img657.png"
 ALT="$x_1=x_2=0$">|; 

$key = q/x_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img467.png"
 ALT="$x_2(t)$">|; 

$key = q/x_2-x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img655.png"
 ALT="$x_2-x_1$">|; 

$key = q/x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img36.png"
 ALT="$x_2$">|; 

$key = q/x_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img712.png"
 ALT="$x_2=0$">|; 

$key = q/x_2=Wslash(e,{calE});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4086.png"
 ALT="$x_2 = W / (e {\cal E})$">|; 

$key = q/x_3(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img785.png"
 ALT="$x_3(t)$">|; 

$key = q/x_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img831.png"
 ALT="$x_3$">|; 

$key = q/x_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img875.png"
 ALT="$x_i$">|; 

$key = q/x_i=i,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1117.png"
 ALT="$x_i=i a$">|; 

$key = q/x_i=i,deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1096.png"
 ALT="$x_i=i \delta x$">|; 

$key = q/x_i=x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img971.png"
 ALT="$x_i=x$">|; 

$key = q/x_{N+1}=(N+1),a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img868.png"
 ALT="$x_{N+1}= (N+1) a$">|; 

$key = q/x_{i+1}=x_i+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img876.png"
 ALT="$x_{i+1}=x_i+a$">|; 

$key = q/x_{i-1}=x_i-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img874.png"
 ALT="$x_{i-1}=x_i-a$">|; 

$key = q/xgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3060.png"
 ALT="$x\gg 1$">|; 

$key = q/xleq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img1750.png"
 ALT="$x\leq 0$">|; 

$key = q/xlll;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img361.png"
 ALT="$x\ll l$">|; 

$key = q/xrightarrow-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3960.png"
 ALT="$x\rightarrow -\infty$">|; 

$key = q/xslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img6.png"
 ALT="$x/a$">|; 

$key = q/xslashl=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1213.png"
 ALT="$x/l=0$">|; 

$key = q/xslashl=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1214.png"
 ALT="$x/l=1$">|; 

$key = q/y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3490.png"
 ALT="$y'$">|; 

$key = q/y(-t)=-y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1297.png"
 ALT="$y(-t)=-y(t)$">|; 

$key = q/y(-t)=y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1298.png"
 ALT="$y(-t)=y(t)$">|; 

$key = q/y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1256.png"
 ALT="$y(t)$">|; 

$key = q/y(t+T)=y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1323.png"
 ALT="$y(t+T)=y(t)$">|; 

$key = q/y(t+tau)=y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1257.png"
 ALT="$y(t+\tau)=y(t)$">|; 

$key = q/y(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3133.png"
 ALT="$y(x)$">|; 

$key = q/y(x+deltax,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img970.png"
 ALT="$y(x+\delta x,t)$">|; 

$key = q/y(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img965.png"
 ALT="$y(x,t)$">|; 

$key = q/y(x-deltax,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img968.png"
 ALT="$y(x-\delta x,t)$">|; 

$key = q/y+dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2991.png"
 ALT="$y+dy$">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img368.png"
 ALT="$y$">|; 

$key = q/y=(2,n-1),pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3984.png"
 ALT="$y = (2 n-1) \pi/2$">|; 

$key = q/y=(x-x_0)slash(2,{mitDelta}x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3882.png"
 ALT="$y=(x-x_0)/ (2 {\mit\Delta} x)$">|; 

$key = q/y=0,,b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3203.png"
 ALT="$y=0, b$">|; 

$key = q/y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1873.png"
 ALT="$y=0$">|; 

$key = q/y=b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1874.png"
 ALT="$y=b$">|; 

$key = q/y=k,aslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3971.png"
 ALT="$y=k a/2$">|; 

$key = q/y=n,pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3991.png"
 ALT="$y = n \pi$">|; 

$key = q/y=pm(1slash27)^{1slash2},X_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3151.png"
 ALT="$y=\pm (1/27)^{1/2} X_0$">|; 

$key = q/y=r,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3814.png"
 ALT="$y=r \sin\theta$">|; 

$key = q/y=rho,sinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3523.png"
 ALT="$y=\rho \sin\phi$">|; 

$key = q/y={rmIm}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3805.png"
 ALT="$y={\rm Im}(z)$">|; 

$key = q/y>lambda^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img120.png"
 ALT="$y&gt;\lambda ^{1/2}$">|; 

$key = q/y_0(0)=y_0(l)=v_0(0)=v_0(l)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1016.png"
 ALT="$y_0(0)=y_0(l)=v_0(0)=v_0(l)=0$">|; 

$key = q/y_0(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1069.png"
 ALT="$y_0(x)$">|; 

$key = q/y_0(x)equivy(x,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1091.png"
 ALT="$y_0(x)\equiv y(x,0)$">|; 

$key = q/y_0(x,t)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img994.png"
 ALT="$y_0(x,t)=0$">|; 

$key = q/y_0=-{rmi},betaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3885.png"
 ALT="$y_0 = - {\rm i} \beta/2$">|; 

$key = q/y_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img901.png"
 ALT="$y_0=0$">|; 

$key = q/y_0=y_{N+1}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img922.png"
 ALT="$y_0=y_{N+1}=0$">|; 

$key = q/y_i(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img870.png"
 ALT="$y_i(t)$">|; 

$key = q/y_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img878.png"
 ALT="$y_i$">|; 

$key = q/y_{N+1}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img902.png"
 ALT="$y_{N+1}=0$">|; 

$key = q/y_{i+1}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img969.png"
 ALT="$y_{i+1}(t)$">|; 

$key = q/y_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img879.png"
 ALT="$y_{i+1}$">|; 

$key = q/y_{i-1}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img967.png"
 ALT="$y_{i-1}(t)$">|; 

$key = q/y_{i-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img877.png"
 ALT="$y_{i-1}$">|; 

$key = q/y_{n,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img932.png"
 ALT="$y_{n,i}$">|; 

$key = q/z+dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2992.png"
 ALT="$z+dz$">|; 

$key = q/z,z^ast=x^{,2}+y^{,2}=|z|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3810.png"
 ALT="$z z^\ast = x^{ 2} + y^{ 2}=\vert z\vert^{ 2}$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1607.png"
 ALT="$z$">|; 

$key = q/z<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1665.png"
 ALT="$z&lt;0$">|; 

$key = q/z=(omegaslashv),rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1912.png"
 ALT="$z=(\omega/v) \rho$">|; 

$key = q/z=(x^{,2}+y^{,2})^{1slash2}slasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3682.png"
 ALT="$z=(x^{ 2}+y^{ 2})^{1/2}/a$">|; 

$key = q/z=-d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3031.png"
 ALT="$z=-d$">|; 

$key = q/z=-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1667.png"
 ALT="$z=-\infty$">|; 

$key = q/z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1662.png"
 ALT="$z=0$">|; 

$key = q/z=R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3237.png"
 ALT="$z=R$">|; 

$key = q/z=r,costheta+{rmi},r,sintheta=r,[costheta+{rmi},sintheta];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3818.png"
 ALT="$z=r \cos\theta + {\rm i} r \sin\theta= r [\cos\theta+{\rm i} \sin\theta]$">|; 

$key = q/z=r,costheta+{rmi},rsintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3815.png"
 ALT="$z= r \cos\theta+ {\rm i} r\sin\theta$">|; 

$key = q/z=y-y_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3886.png"
 ALT="$z=y-y_0$">|; 

$key = q/z=z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2981.png"
 ALT="$z=z_0$">|; 

$key = q/z=z_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1916.png"
 ALT="$z=z_j$">|; 

$key = q/z={rme}^{,{rmi},theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3721.png"
 ALT="$z={\rm e}^{ {\rm i} \theta}$">|; 

$key = q/z>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1666.png"
 ALT="$z&gt;0$">|; 

$key = q/z^ast=x-{rmi},y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3806.png"
 ALT="$z^\ast = x-{\rm i} y$">|; 

$key = q/z_1=3.83171;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3535.png"
 ALT="$z_1=3.83171$">|; 

$key = q/z_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2710.png"
 ALT="$z_i$">|; 

$key = q/z_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1922.png"
 ALT="$z_j$">|; 

$key = q/zequiv(x,,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3807.png"
 ALT="$z\equiv (x, y)$">|; 

$key = q/zeta(0)>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3090.png"
 ALT="$\zeta(0)&gt;0$">|; 

$key = q/zeta(l)<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3091.png"
 ALT="$\zeta(l)&lt;0$">|; 

$key = q/zeta(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3034.png"
 ALT="$\zeta(x,t)$">|; 

$key = q/zgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3759.png"
 ALT="$z\gg 1$">|; 

$key = q/{bfB};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2125.png"
 ALT="${\bf B}$">|; 

$key = q/{bfB}=B_0,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2639.png"
 ALT="${\bf B} = B_0 {\bf e}_z$">|; 

$key = q/{bfB}=mu_0,{bfH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2124.png"
 ALT="${\bf B}=\mu_0 {\bf H}$">|; 

$key = q/{bfB}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2848.png"
 ALT="${\bf B}_0$">|; 

$key = q/{bfD};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2110.png"
 ALT="${\bf D}$">|; 

$key = q/{bfD}=epsilon_0,{bfE}+{bfP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2098.png"
 ALT="${\bf D}= \epsilon_0 {\bf E}+{\bf P}$">|; 

$key = q/{bfE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1642.png"
 ALT="${\bf E}$">|; 

$key = q/{bfH};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2126.png"
 ALT="${\bf H}$">|; 

$key = q/{bfP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2099.png"
 ALT="${\bf P}$">|; 

$key = q/{bfP}=N,q,{bfd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1644.png"
 ALT="${\bf P} = N q {\bf d}$">|; 

$key = q/{bfd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1640.png"
 ALT="${\bf d}$">|; 

$key = q/{bfj};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img2892.png"
 ALT="${\bf j}$">|; 

$key = q/{bfk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1841.png"
 ALT="${\bf k}$">|; 

$key = q/{bfk}=(k_x,,k_y,,k_z)=k,{bfn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1837.png"
 ALT="${\bf k} = (k_x, k_y, k_z)=k {\bf n}$">|; 

$key = q/{bfk}=(k_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2950.png"
 ALT="${\bf k}=(k_x$">|; 

$key = q/{bfk}=k,{bfn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2151.png"
 ALT="${\bf k}=k {\bf n}$">|; 

$key = q/{bfk}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1929.png"
 ALT="${\bf k}_i$">|; 

$key = q/{bfk}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1930.png"
 ALT="${\bf k}_r$">|; 

$key = q/{bfk}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1931.png"
 ALT="${\bf k}_t$">|; 

$key = q/{bfn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1835.png"
 ALT="${\bf n}$">|; 

$key = q/{bfn}=(1,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1833.png"
 ALT="${\bf n} = (1, 0, 0)$">|; 

$key = q/{bfn}cdothat{bfE}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2195.png"
 ALT="${\bf n}\cdot\hat{\bf E}=0$">|; 

$key = q/{bfn}cdothat{bfE}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img2167.png"
 ALT="${\bf n}\cdot\hat{\bf E}\neq 0$">|; 

$key = q/{bfn}cdot{bfr}=d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img76.png"
 ALT="${\bf n}\cdot {\bf r} = d$">|; 

$key = q/{bfp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4135.png"
 ALT="${\bf p}$">|; 

$key = q/{bfp}=q,{bfd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1643.png"
 ALT="${\bf p} = q {\bf d}$">|; 

$key = q/{bfr}=(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1834.png"
 ALT="${\bf r}=(x, y, z)$">|; 

$key = q/{bfv}=(v_x,,0,,v_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2230.png"
 ALT="${\bf v} = (v_x, 0, v_z)$">|; 

$key = q/{bfv}_p=v,{bfn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2152.png"
 ALT="${\bf v}_p = v {\bf n}$">|; 

$key = q/{bfx}(t)=(x_1(t),x_2(t),x_3(t));MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img807.png"
 ALT="${\bf x}(t)=(x_1(t),x_2(t),x_3(t))$">|; 

$key = q/{bfx}=(x_1,x_2,x_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img819.png"
 ALT="${\bf x}=(x_1,x_2,x_2)$">|; 

$key = q/{calC}(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3697.png"
 ALT="${\cal C}(u,v)$">|; 

$key = q/{calC},V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img1483.png"
 ALT="${\cal C} V$">|; 

$key = q/{calC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img1099.png"
 ALT="${\cal C}$">|; 

$key = q/{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img225.png"
 ALT="${\cal E}$">|; 

$key = q/{calE}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img229.png"
 ALT="${\cal E}=0$">|; 

$key = q/{calE}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img230.png"
 ALT="${\cal E}&gt;0$">|; 

$key = q/{calE}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img862.png"
 ALT="${\cal E}_1$">|; 

$key = q/{calE}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img863.png"
 ALT="${\cal E}_2$">|; 

$key = q/{calI}(0)={calI}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3718.png"
 ALT="${\cal I}(0)={\cal I}_0$">|; 

$key = q/{calI}(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3293.png"
 ALT="${\cal I}(\theta)$">|; 

$key = q/{calI}(theta)propto1+cos[2pi,(dslashlambda),theta]=2,cos^2[pi,(dslashlambda),theta];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3351.png"
 ALT="${\cal I}(\theta)\propto 1+\cos[2\pi (d/\lambda) \theta]=2  \cos^2[\pi (d/\lambda) \theta]$">|; 

$key = q/{calI}(theta)propto1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3348.png"
 ALT="${\cal I}(\theta)\propto 1$">|; 

$key = q/{calI}(theta)proptocos^2[(1slash2),k,d,sintheta-(1slash2),(phi_1-phi_2)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3323.png"
 ALT="${\cal I}(\theta)\propto \cos^2[(1/2) k d \sin\theta-(1/2) (\phi_1-\phi_2)]$">|; 

$key = q/{calI}(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1437.png"
 ALT="${\cal I}(x,t)$">|; 

$key = q/{calI}(x_1,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1439.png"
 ALT="${\cal I}(x_1,t)$">|; 

$key = q/{calI}(x_2,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1440.png"
 ALT="${\cal I}(x_2,t)$">|; 

$key = q/{calI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img1787.png"
 ALT="${\cal I}$">|; 

$key = q/{calI}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3776.png"
 ALT="${\cal I}=0$">|; 

$key = q/{calI}=4,{calI}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3777.png"
 ALT="${\cal I}=4 {\cal I}_0$">|; 

$key = q/{calI}=N^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img3380.png"
 ALT="${\cal I} = N^{ 2}$">|; 

$key = q/{calI}={calI}_0slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3652.png"
 ALT="${\cal I}= {\cal I}_0/4$">|; 

$key = q/{calI}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3596.png"
 ALT="${\cal I}_0$">|; 

$key = q/{calI}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2256.png"
 ALT="${\cal I}_x$">|; 

$key = q/{calI}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2257.png"
 ALT="${\cal I}_z$">|; 

$key = q/{calI}proptoE^{,2}slashZ_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3284.png"
 ALT="${\cal I} \propto E^{ 2}/Z_0$">|; 

$key = q/{calL},I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.28ex; " SRC="|."$dir".q|img1484.png"
 ALT="${\cal L} I$">|; 

$key = q/{calL};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.28ex; " SRC="|."$dir".q|img1100.png"
 ALT="${\cal L}$">|; 

$key = q/{calR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img1783.png"
 ALT="${\cal R}$">|; 

$key = q/{calS}(u,v);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3698.png"
 ALT="${\cal S}(u,v)$">|; 

$key = q/{displaymath}F(x)=left{{array}{ccc}1&mbox{hspace{1cm}}&|x|leqlslash20&&|x|>lslash2{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img2350.png"
 ALT="\begin{displaymath}F(x)=\left\{
\begin{array}{ccc}
1 &amp;\mbox{\hspace{1cm}}&amp; \vert x\vert\leq l/2\\\\
0 &amp;&amp; \vert x\vert&gt;l/2
\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}F(x)=left{{array}{ccc}1slashdelta&mbox{hspace{0.5cm}}&|x|leqdeltaslash2[0.5ex]0&&|x|>deltaslash2{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img3431.png"
 ALT="\begin{displaymath}F(x)=\left\{
\begin{array}{ccc}
1/\delta&amp;\mbox{\hspace{0.5cm}...
...elta/2\ [0.5ex]
0 &amp;&amp;\vert x\vert&gt; \delta/2
\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}F(x)=left{{array}{lcc}1-2,|x|slashl&mbox{hspace{1cm}}&|x|leqlslash2[0.5ex]0&&|x|>lslash2{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img2441.png"
 ALT="\begin{displaymath}F(x) = \left\{
\begin{array}{lcc}
1 -2 \vert x\vert/l&amp;\mbox{...
...vert\leq l/2\ [0.5ex]
0 &amp;&amp;\vert x\vert&gt;l/2
\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}F_2(x)=left{{array}{ccc}1slashdelta&mbox{hspace{0.5cm}}&|x|leqdeltaslash2[0.5ex]0&&|x|>deltaslash2{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img3454.png"
 ALT="\begin{displaymath}F_2(x)=\left\{
\begin{array}{ccc}
1/\delta&amp;\mbox{\hspace{0.5c...
...elta/2\ [0.5ex]
0 &amp;&amp;\vert x\vert&gt; \delta/2
\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}U(x)=left{{array}{lll}0&mbox{hspace{0.5cm}}&0leqxleqa[0.5ex]infty&&mbox{otherwise}{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img3921.png"
 ALT="\begin{displaymath}U(x) = \left\{
\begin{array}{lll}
0&amp;\mbox{\hspace{0.5cm}}&amp;0\l...
... \leq a\ [0.5ex]
\infty &amp;&amp;\mbox{otherwise}
\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}U(x)=left{{array}{rll}-V&mbox{hspace{0.5cm}}&|x|leqaslash2[0.5ex]0&&mbox{otherwise}{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img3947.png"
 ALT="\begin{displaymath}U(x) = \left\{
\begin{array}{rll}
-V &amp;\mbox{\hspace{0.5cm}}&amp;\...
...\vert\leq a/2\ [0.5ex]
0&amp;&amp;\mbox{otherwise}
\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}bm{epsilon}=left({array}{ccc}epsilon_{xx},&0,&0[0.5ex]0,&epsilon_{yy},&0[0.5ex]0,&0,&epsilon_{zz}{array}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.36ex; " SRC="|."$dir".q|img2111.png"
 ALT="\begin{displaymath}\bm{\epsilon} = \left(
\begin{array}{ccc}
\epsilon_{xx},&amp;0,&amp;0...
...psilon_{yy},&amp;0\ [0.5ex]
0,&amp;0,&amp;\epsilon_{zz}\end{array}\right).\end{displaymath}">|; 

$key = q/{displaymath}delta_{n,n'}=left{{array}{ccc}1&mbox{hspace{0.5cm}}&n=n'[0.5ex]0&&nneqn'{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img1036.png"
 ALT="\begin{displaymath}\delta_{n,n'} = \left\{
\begin{array}{ccc}
1 &amp;\mbox{\hspace{0.5cm}}&amp;n=n'\ [0.5ex]
0&amp;&amp;n\neq n'
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}f(u,v)=left{{array}{lll}1&mbox{hspace{0.5cm}}&mbox{u_1<u<u_2~and~v_1<v<v_2}[0.5ex]0&&mbox{otherwise}{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img3612.png"
 ALT="\begin{displaymath}f(u,v) = \left\{
\begin{array}{lll}
1&amp;\mbox{\hspace{0.5cm}}&amp; ...
...&nbsp;$v_1&lt;v&lt;v_2$}\ [0.5ex]
0&amp;&amp;\mbox{otherwise}\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}f(v)=left{{array}{lll}1&mbox{hspace{0.5cm}}&mbox{v<u}[0.5ex]0&&mbox{otherwise}{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img3677.png"
 ALT="\begin{displaymath}f(v) = \left\{
\begin{array}{lll}
1&amp;\mbox{\hspace{0.5cm}}&amp; \mbox{$v&lt;u$ }\ [0.5ex]
0&amp;&amp;\mbox{otherwise}\end{array}\right..\end{displaymath}">|; 

$key = q/{displaymath}frac{sin(k,pi)}{k,pi}=left{{array}{ccc}1&mbox{hspace{0.5cm}}&k=0[0.5ex]0&&kneq0{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img1034.png"
 ALT="\begin{displaymath}\frac{\sin(k \pi)}{k \pi} = \left\{
\begin{array}{ccc}
1 &amp;\mbox{\hspace{0.5cm}}&amp;k=0\ [0.5ex]
0&amp;&amp;k\neq 0
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}y_0(x)=2,Aleft{{array}{lcc}xslashl&mbox{hspace{0.5cm}}&0leqx<lslash2[0.5ex]1-xslashl&&lslash2leqxleql{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img1054.png"
 ALT="\begin{displaymath}y_0(x) = 2 A\left\{
\begin{array}{lcc}
x/l&amp;\mbox{\hspace{0.5...
... x &lt; l/2\ [0.5ex]
1-x/l &amp;&amp;l/2\leq x\leq l
\end{array}\right. .\end{displaymath}">|; 

$key = q/{mitDeltau}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3669.png"
 ALT="${\mit\Delta u}\gg 1$">|; 

$key = q/{mitDelta}f={mitDelta}omegaslash2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2496.png"
 ALT="${\mit\Delta} f={\mit\Delta}\omega/2\pi$">|; 

$key = q/{mitDelta}fsim1slash{mitDelta}tsim10^{,7},{rmHz}=10,{rmMHz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2506.png"
 ALT="${\mit\Delta} f\sim 1/{\mit\Delta} t\sim 10^{ 7} {\rm Hz}=10 {\rm MHz}$">|; 

$key = q/{mitDelta}k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2689.png"
 ALT="${\mit\Delta} k$">|; 

$key = q/{mitDelta}k=1slash(2,{mitDelta}x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3905.png"
 ALT="${\mit\Delta}k= 1/(2 {\mit\Delta} x)$">|; 

$key = q/{mitDelta}ksimeqsqrt{2pi},sigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2369.png"
 ALT="${\mit\Delta} k \simeq \sqrt{2\pi} \sigma_k$">|; 

$key = q/{mitDelta}ksimsigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2572.png"
 ALT="${\mit\Delta} k \sim \sigma_k$">|; 

$key = q/{mitDelta}lambdalllambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3390.png"
 ALT="${\mit\Delta}\lambda\ll \lambda$">|; 

$key = q/{mitDelta}omega=nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img554.png"
 ALT="${\mit\Delta}\omega = \nu$">|; 

$key = q/{mitDelta}omegasimeqsqrt{2pi},sigma_omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2493.png"
 ALT="${\mit\Delta} \omega\simeq \sqrt{2\pi} \sigma_\omega$">|; 

$key = q/{mitDelta}p=hbar,{mitDelta}k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3907.png"
 ALT="${\mit\Delta}p=\hbar {\mit\Delta}k$">|; 

$key = q/{mitDelta}phi=(m+1slash2),2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3413.png"
 ALT="${\mit\Delta}\phi=(m+1/2) 2\pi$">|; 

$key = q/{mitDelta}phi=k,delta=2pi,deltaslashlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3411.png"
 ALT="${\mit\Delta} \phi = k \delta = 2\pi \delta/\lambda$">|; 

$key = q/{mitDelta}phi=m,2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3412.png"
 ALT="${\mit\Delta}\phi = m 2\pi$">|; 

$key = q/{mitDelta}phi_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2090.png"
 ALT="${\mit\Delta}\phi_r$">|; 

$key = q/{mitDelta}s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1417.png"
 ALT="${\mit\Delta} s$">|; 

$key = q/{mitDelta}theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3445.png"
 ALT="${\mit\Delta}\theta$">|; 

$key = q/{mitDelta}theta<deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3448.png"
 ALT="${\mit\Delta}\theta &lt; \delta\theta$">|; 

$key = q/{mitDelta}theta>deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3447.png"
 ALT="${\mit\Delta}\theta&gt;\delta\theta$">|; 

$key = q/{mitDelta}theta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3403.png"
 ALT="${\mit\Delta}\theta_j$">|; 

$key = q/{mitDelta}theta_j>deltatheta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3405.png"
 ALT="${\mit\Delta}\theta_j&gt;\delta\theta_j$">|; 

$key = q/{mitDelta}thetasimeqlambdaslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3292.png"
 ALT="${\mit\Delta}\theta\simeq \lambda/d$">|; 

$key = q/{mitDelta}tsim10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2505.png"
 ALT="${\mit\Delta} t \sim 10^{-7}$">|; 

$key = q/{mitDelta}tsimeqsqrt{2pi},sigma_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2492.png"
 ALT="${\mit\Delta} t\simeq \sqrt{2\pi} \sigma_t$">|; 

$key = q/{mitDelta}u=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img102.png"
 ALT="${\mit \Delta }u=0.1$">|; 

$key = q/{mitDelta}u=0.25;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img108.png"
 ALT="${\mit \Delta }u=0.25$">|; 

$key = q/{mitDelta}u>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3663.png"
 ALT="${\mit\Delta}u&gt;1$">|; 

$key = q/{mitDelta}ugg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3664.png"
 ALT="${\mit\Delta}u\gg 1$">|; 

$key = q/{mitDelta}ugtrsim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.35ex; " SRC="|."$dir".q|img3662.png"
 ALT="${\mit\Delta}u\gtrsim 1$">|; 

$key = q/{mitDelta}ull1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3661.png"
 ALT="${\mit\Delta}u\ll 1$">|; 

$key = q/{mitDelta}v=hbarslash[m,({mitDelta}x)_0];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3911.png"
 ALT="${\mit\Delta}v = \hbar/[m ({\mit\Delta}x)_0]$">|; 

$key = q/{mitDelta}varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2695.png"
 ALT="${\mit\Delta}\varphi$">|; 

$key = q/{mitDelta}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3877.png"
 ALT="${\mit\Delta} x$">|; 

$key = q/{mitDelta}xsim10^{-10},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3903.png"
 ALT="${\mit\Delta} x\sim 10^{-10} {\rm m}$">|; 

$key = q/{mitDelta}xsima;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3941.png"
 ALT="${\mit\Delta} x\sim a$">|; 

$key = q/{mitDelta}xsimeq2sqrt{pislash2},sigma_x=sqrt{2pi},sigma_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2368.png"
 ALT="${\mit\Delta} x \simeq 2\sqrt{\pi/2} \sigma_x=\sqrt{2\pi} \sigma_x$">|; 

$key = q/{mitDelta}{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3312.png"
 ALT="${\mit\Delta}{\cal E}$">|; 

$key = q/{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2678.png"
 ALT="${\mit\Omega}_e$">|; 

$key = q/{mitOmega}_egg{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2759.png"
 ALT="${\mit\Omega}_e\gg {\mit\Omega}_i$">|; 

$key = q/{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2757.png"
 ALT="${\mit\Omega}_i$">|; 

$key = q/{mitOmega}_illomegall{mitOmega}_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2865.png"
 ALT="${\mit\Omega}_i\ll \omega\ll {\mit\Omega}_e$">|; 

$key = q/{rmF,m}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4265.png"
 ALT="${\rm F m}^{-1}$">|; 

$key = q/{rmFr}={rmFr}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3098.png"
 ALT="${\rm Fr}= {\rm Fr}_c$">|; 

$key = q/{rmFr}={rmFr}_c=1slashsqrt{pi}=0.56;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img3097.png"
 ALT="${\rm Fr}={\rm Fr}_c= 1/\sqrt{\pi}= 0.56$">|; 

$key = q/{rmJ,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4263.png"
 ALT="${\rm J s}$">|; 

$key = q/{rmJ},{rmmol}^{-1},{rmK}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4274.png"
 ALT="${\rm J} {\rm mol}^{-1} {\rm K}^{-1}$">|; 

$key = q/{rmN,A}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4267.png"
 ALT="${\rm N A}^{-2}$">|; 

$key = q/{rmarg}(z)=tan^{-1}(yslashx);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img3812.png"
 ALT="${\rm arg}(z)=\tan^{-1}(y/x)$">|; 

$key = q/{rme};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2512.png"
 ALT="${\rm e}$">|; 

$key = q/{rme}^{-2,alpha,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4243.png"
 ALT="${\rm e}^{-2 \alpha x}$">|; 

$key = q/{rme}^{-2pi}simeq1.9times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img639.png"
 ALT="${\rm e}^{-2\pi}\simeq 1.9\times 10^{-3}$">|; 

$key = q/{rmi},y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3802.png"
 ALT="${\rm i} y$">|; 

$key = q/{rmi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2511.png"
 ALT="${\rm i}$">|; 

$key = q/{rmi}^ast=-{rmi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3851.png"
 ALT="${\rm i}^\ast=-{\rm i}$">|; 

$key = q/{rmi}^{,2}=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3799.png"
 ALT="${\rm i}^{ 2} = -1$">|; 

$key = q/{rmm,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4261.png"
 ALT="${\rm m s}^{-1}$">|; 

$key = q/{rmmol}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4277.png"
 ALT="${\rm mol}^{-1}$">|; 

$key = q/{rmm}^{3},{rmkg}^{-1},{rms}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4272.png"
 ALT="${\rm m}^{3} {\rm kg}^{-1} {\rm s}^{-2}$">|; 

$key = q/{rmsinc}(0)=lim_{xrightarrow0},sinxslashx=lim_{x_rightarrow0},cosxslash1=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img3436.png"
 ALT="${\rm sinc}(0)=\lim_{x\rightarrow 0} \sin x/x = \lim_{x_\rightarrow 0}  \cos x/1=1$">|; 

$key = q/{rmsinc}(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3437.png"
 ALT="${\rm sinc}(x)$">|; 

$key = q/{rmsinc}(x)equivsin(x)slashx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3433.png"
 ALT="${\rm sinc}(x)\equiv \sin(x)/x$">|; 

$key = q/{rmsinc}(x)equivsinxslashx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2309.png"
 ALT="${\rm sinc}(x)\equiv \sin x/x$">|; 

$key = q/{{mitDelta}}varphi(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2699.png"
 ALT="${{\mit\Delta}}\varphi(\omega)$">|; 

$key = q/{{mitOmega}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2868.png"
 ALT="${{\mit\Omega}}_i$">|; 

$key = q/|A_1-A_2|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1405.png"
 ALT="$\vert A_1-A_2\vert$">|; 

$key = q/|A_n|^{,2}=2slasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3935.png"
 ALT="$\vert A_n\vert^{ 2}=2/a$">|; 

$key = q/|E_x|=E_0,{rme}^{-zslashd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2913.png"
 ALT="$\vert E_x\vert = E_0 {\rm e}^{-z/d}$">|; 

$key = q/|R|^{,2}+|T|^{,2}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4024.png"
 ALT="$\vert R\vert^{ 2}+\vert T\vert^{ 2}=1$">|; 

$key = q/|R|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4007.png"
 ALT="$\vert R\vert^{ 2}$">|; 

$key = q/|R|^{,2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4029.png"
 ALT="$\vert R\vert^{ 2}=0$">|; 

$key = q/|R|^{,2}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4048.png"
 ALT="$\vert R\vert^{ 2}=1$">|; 

$key = q/|T|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4009.png"
 ALT="$\vert T\vert^{ 2}$">|; 

$key = q/|T|^{,2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4049.png"
 ALT="$\vert T\vert^{ 2}=0$">|; 

$key = q/|T|^{,2}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4030.png"
 ALT="$\vert T\vert^{ 2}=1$">|; 

$key = q/|bar{psi}(k)|^{,2},dk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3890.png"
 ALT="$\vert\bar{\psi}(k)\vert^{ 2} dk$">|; 

$key = q/|bar{psi}|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3866.png"
 ALT="$\vert\bar{\psi}\vert^{ 2}$">|; 

$key = q/|bm{mathcal{I}}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2144.png"
 ALT="$\vert\bm{\mathcal{I}}\vert$">|; 

$key = q/|cos(k,x)|=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1406.png"
 ALT="$\vert\cos(k x)\vert=1$">|; 

$key = q/|epsilon|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1163.png"
 ALT="$\vert\epsilon\vert\ll 1$">|; 

$key = q/|f|proptox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img144.png"
 ALT="$\vert f\vert\propto x$">|; 

$key = q/|k'|llk^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4066.png"
 ALT="$\vert k'\vert\ll k^{ 2}$">|; 

$key = q/|k-k_0|gtrsim3,sigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2553.png"
 ALT="$\vert k-k_0\vert\gtrsim 3 \sigma_k$">|; 

$key = q/|k|gtrsim3,sigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2366.png"
 ALT="$\vert k\vert\gtrsim 3 \sigma_k$">|; 

$key = q/|k|gtrsimsigma_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2376.png"
 ALT="$\vert k\vert\gtrsim \sigma_k$">|; 

$key = q/|omega-omega_0|simnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img606.png"
 ALT="$\vert\omega-\omega_0\vert\sim \nu$">|; 

$key = q/|omega-omega_0|simnullomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img551.png"
 ALT="$\vert\omega-\omega_0\vert\sim \nu\ll \omega_0$">|; 

$key = q/|partialyslashpartialx|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1422.png"
 ALT="$\vert\partial y/\partial x\vert\ll 1$">|; 

$key = q/|psi(x,0)|^{,2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3889.png"
 ALT="$\vert\psi(x,0)\vert^{ 2} dx$">|; 

$key = q/|psi(x,t)|^{,2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3860.png"
 ALT="$\vert\psi(x,t)\vert^{ 2} dx$">|; 

$key = q/|psi_1|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4075.png"
 ALT="$\vert\psi_1\vert^{ 2}$">|; 

$key = q/|psi_2|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4079.png"
 ALT="$\vert\psi_2\vert^{ 2}$">|; 

$key = q/|psi_2|^{,2}<|psi_1|^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4077.png"
 ALT="$\vert\psi_2\vert^{ 2} &lt; \vert\psi_1\vert^{ 2}$">|; 

$key = q/|psi_i|lla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1120.png"
 ALT="$\vert\psi_i\vert\ll a$">|; 

$key = q/|psi_i|slashall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1306.png"
 ALT="$\vert\psi_i\vert/a\ll 1$">|; 

$key = q/|rho_1-rho_2|slashrho_1ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3280.png"
 ALT="$\vert\rho_1-\rho_2\vert/\rho_1\ll 1$">|; 

$key = q/|sin(k,x)|=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1404.png"
 ALT="$\vert\sin(k x)\vert=1$">|; 

$key = q/|theta_x|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3507.png"
 ALT="$\vert\theta_x\vert$">|; 

$key = q/|theta_x|<lambdaslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3516.png"
 ALT="$\vert\theta_x\vert&lt;\lambda/a$">|; 

$key = q/|theta_y|<lambdaslashb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3517.png"
 ALT="$\vert\theta_y\vert&lt;\lambda/b$">|; 

$key = q/|theta_y|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3508.png"
 ALT="$\vert\theta_y\vert\ll 1$">|; 

$key = q/|theta|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img337.png"
 ALT="$\vert\theta\vert$">|; 

$key = q/|theta|<sin^{-1}(0.5)=pislash6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3485.png"
 ALT="$\vert\theta\vert&lt; \sin^{-1}(0.5) = \pi/6$">|; 

$key = q/|theta|<sin^{-1}(lambdaslashdelta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3483.png"
 ALT="$\vert\theta\vert&lt; \sin^{-1}(\lambda/\delta)$">|; 

$key = q/|theta|>pislash6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3486.png"
 ALT="$\vert\theta\vert&gt; \pi/6$">|; 

$key = q/|theta|>sin^{-1}(lambdaslashdelta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3484.png"
 ALT="$\vert\theta\vert&gt; \sin^{-1}(\lambda/\delta)$">|; 

$key = q/|theta|gtrsimsin^{-1}(lambdaslashdelta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3480.png"
 ALT="$\vert\theta\vert\gtrsim \sin^{-1}(\lambda/\delta)$">|; 

$key = q/|theta|lesssim6^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img344.png"
 ALT="$\vert\theta\vert\lesssim 6^\circ$">|; 

$key = q/|theta|lesssimsin^{-1}(lambdaslashdelta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3479.png"
 ALT="$\vert\theta\vert\lesssim \sin^{-1}(\lambda/\delta)$">|; 

$key = q/|theta|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3569.png"
 ALT="$\vert\theta\vert\ll 1$">|; 

$key = q/|u'|gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3761.png"
 ALT="$\vert u'\vert\gg 1$">|; 

$key = q/|x-x'|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3559.png"
 ALT="$\vert x-x'\vert$">|; 

$key = q/|x|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img421.png"
 ALT="$\vert x\vert$">|; 

$key = q/|x|>aslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3993.png"
 ALT="$\vert x\vert&gt;a/2$">|; 

$key = q/|x|gtrsim3,sigma_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2360.png"
 ALT="$\vert x\vert\gtrsim 3 \sigma_x$">|; 

$key = q/|x|leqaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3965.png"
 ALT="$\vert x\vert\leq a/2$">|; 

$key = q/|x|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img627.png"
 ALT="$\vert x\vert\ll 1$">|; 

$key = q/|x|rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3949.png"
 ALT="$\vert x\vert\rightarrow \infty$">|; 

$key = q/|x|simeqsqrt{pislash2},sigma_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2367.png"
 ALT="$\vert x\vert\simeq \sqrt{\pi/2} \sigma_x$">|; 

$key = q/|y-y'|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3560.png"
 ALT="$\vert y-y'\vert$">|; 

$key = q/|y_i|lla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img884.png"
 ALT="$\vert y_i\vert\ll a$">|; 

$key = q/|z|=(x^{,2}+y^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3809.png"
 ALT="$\vert z\vert=(x^{ 2}+y^{ 2})^{1/2}$">|; 

1;

