File: /home/harmonyg/public_html/test/PresentationInTex/images.pl
# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.
$key = q/{displaymath}Deltay'=frac{{Nr_e}}{gamma}ky{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="104" HEIGHT="46" BORDER="0"
SRC="|."$dir".q|img3.gif"
ALT="\begin{displaymath}
\Delta y' = \frac{{Nr_e }}{\gamma }ky
\end{displaymath}">|;
$key = q/K;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img37.gif"
ALT="$K$">|;
$key = q/{displaymath}w_t(s,m)=2left({frac{1}{{b^{2m}}}}right)e^{-nsslashb}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="201" HEIGHT="45" BORDER="0"
SRC="|."$dir".q|img30.gif"
ALT="\begin{displaymath}
w_t (s,m) = 2\left( {\frac{1}{{b^{2m} }}} \right)e^{ - ns/b}
\end{displaymath}">|;
$key = q/overline{r^m};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img23.gif"
ALT="$\overline{r^m}$">|;
$key = q/{displaymath}w_{l,t}(omega)=frac{{1,i}}{{2pi}}intlimits_{-infty}^infty{domega}e^{-iomegasslashc}Z_{l,t}(omega){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="252" HEIGHT="65" BORDER="0"
SRC="|."$dir".q|img32.gif"
ALT="\begin{displaymath}
w_{l,t} (\omega ) = \frac{{1,i}}{{2\pi }}\int\limits_{ - \infty
}^\infty {d\omega } e^{ - i\omega s/c} Z_{l,t} (\omega )
\end{displaymath}">|;
$key = q/rho(r,theta,z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="67" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img19.gif"
ALT="$\rho(r,\theta,z)$">|;
$key = q/Q(z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img24.gif"
ALT="$Q(z)$">|;
$key = q/{displaymath}w_t(s,1)=left({frac{1}{{b^2}}}right){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="118" HEIGHT="45" BORDER="0"
SRC="|."$dir".q|img31.gif"
ALT="\begin{displaymath}
w_t (s,1) = \left( {\frac{1}{{b^2 }}} \right)
\end{displaymath}">|;
$key = q/r,theta,z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img13.gif"
ALT="$r,\theta,z$">|;
$key = q/frac{1}{L};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="17" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img10.gif"
ALT="$\frac{1}{L}$">|;
$key = q/{displaymath}w_t(s,m)=2left({frac{1}{{b^{2m}}}}right){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="148" HEIGHT="45" BORDER="0"
SRC="|."$dir".q|img29.gif"
ALT="\begin{displaymath}
w_t (s,m) = 2\left( {\frac{1}{{b^{2m} }}} \right)
\end{displaymath}">|;
$key = q/z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img15.gif"
ALT="$z$">|;
$key = q/{displaymath}W_m(z)=2left({1overa^{2m}}-{1overb^{2m}}right)e^{-mzslasha}Theta(z){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="283" HEIGHT="45" BORDER="0"
SRC="|."$dir".q|img27.gif"
ALT="\begin{displaymath}W_m(z)=2 \left( {1 \over a^{2m}} - {1 \over b^{2m}} \right) e^{-mz/a} \Theta(z)\end{displaymath}">|;
$key = q/{displaymath}Deltay'={Nr_eovergamma}Ky{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="110" HEIGHT="46" BORDER="0"
SRC="|."$dir".q|img38.gif"
ALT="\begin{displaymath}\Delta y' = {N r_e \over \gamma} K y\end{displaymath}">|;
$key = q/{displaymath}w_t(s,m)=frac{2}{{pib^{2m+1}}}sqrt{frac{c}{sigma}}frac{L}{{sqrts}}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="200" HEIGHT="48" BORDER="0"
SRC="|."$dir".q|img35.gif"
ALT="\begin{displaymath}
w_t (s,m) = \frac{2}{{\pi b^{2m + 1} }}\sqrt {\frac{c}{\sigma }}
\frac{L}{{\sqrt s }}
\end{displaymath}">|;
$key = q/{displaymath}e^{i(k(z-vt))}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="68" HEIGHT="27" BORDER="0"
SRC="|."$dir".q|img6.gif"
ALT="\begin{displaymath}
e^{i(k(z - vt))}
\end{displaymath}">|;
$key = q/{displaymath}array{{l}w_l(rho,s)=-frac{1}{q}left.{E_z}right|_{z=ct-s}w_t(rho,s)=-frac{1}{q}[E_t+ztimesB]_{z=ct-s}array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="242" HEIGHT="54" BORDER="0"
SRC="|."$dir".q|img9.gif"
ALT="\begin{displaymath}
\begin{array}{l}
w_l (\rho ,s) = - \frac{1}{q}\left. {E_z }...
...= - \frac{1}{q}[E_t + z \times B]_{z = ct - s} \\\\
\end{array}\end{displaymath}">|;
$key = q/{eqnarraystar}overlineF_perp=&-e&sum_{m=1}^inftyW_m(z)mr^{m-1}Big[hatrleft(Q_mcoQ_msinmtheta+tildeQ_mcosmthetaright)Big]{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="429" HEIGHT="98" BORDER="0"
SRC="|."$dir".q|img16.gif"
ALT="\begin{eqnarray*}
\overline F_\perp =& \ -e &\sum_{m=1}^\infty W_m(z) m r^{m-1}...
...left( Q_m \sin m \theta + \tilde Q_m \cos m \theta \right)
\Big]
\end{eqnarray*}">|;
$key = q/e^{ltheta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img11.gif"
ALT="$e^{l\theta }$">|;
$key = q/{displaymath}tildeQ_m=int_0^{2pi}dtheta'int_0^inftydr'r'^{m+1}sinmtheta'rho(r',theta',z){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="331" HEIGHT="46" BORDER="0"
SRC="|."$dir".q|img18.gif"
ALT="\begin{displaymath}
\tilde Q_m=\int_0^{2 \pi} d \theta' \int_0^\infty dr' r'^{m+1} sin m
\theta' \rho(r',\theta',z) \end{displaymath}">|;
$key = q/{displaymath}vapproxc;gamma>>1{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="103" HEIGHT="30" BORDER="0"
SRC="|."$dir".q|img7.gif"
ALT="\begin{displaymath}
v \approx c;\gamma > > 1
\end{displaymath}">|;
$key = q/{displaymath}lambda_i(s_i){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="40" HEIGHT="31" BORDER="0"
SRC="|."$dir".q|img5.gif"
ALT="\begin{displaymath}
\lambda _i (s_i )
\end{displaymath}">|;
$key = q/{displaymath}array{{l}left({array{{*{20}c}{E_z(r,s)}{E_r(r,s)}{E_theta(r,s)}arrak_n^{}s}{sink_n^{}s}array{}right)Theta(-s)array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="500" HEIGHT="152" BORDER="0"
SRC="|."$dir".q|img34.gif"
ALT="\begin{displaymath}
\begin{array}{l}
\left( {\begin{array}{*{20}c}
{E_z (r,s)}...
..._n^{} s} \\\\
\end{array}} \right)\Theta ( - s) \\\\
\end{array}\end{displaymath}">|;
$key = q/{displaymath}frac{{Deltap_z}}{p}=frac{{Ne^2}}{{pc}}sumlimits_{i+1}^{nbins}{}ds'l2sumlimits_{i+1}^{nbins}{ds'lambda(s')}w_t(s'-s){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="566" HEIGHT="60" BORDER="0"
SRC="|."$dir".q|img36.gif"
ALT="\begin{displaymath}
\frac{{\Delta p_z }}{p} = \frac{{Ne^2 }}{{pc}}\sum\limits_{i...
...}^2 \sum\limits_{i + 1}^{nbins} {ds'\lambda (s')} w_t (s' - s)
\end{displaymath}">|;
$key = q/{displaymath}array{{l}Z_l(omega)=-frac{{iomegaZ_0}}{{4pic}}intlimits_{-infty}^infty}^infty{dz}left({frac{{b'}}{b}}right)^2array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="193" HEIGHT="89" BORDER="0"
SRC="|."$dir".q|img33.gif"
ALT="\begin{displaymath}
\begin{array}{l}
Z_l (\omega ) = - \frac{{i\omega Z_0 }}{{4...
...^\infty {dz} \left( {\frac{{b'}}{b}} \right)^2 \\\\
\end{array}\end{displaymath}">|;
$key = q/Theta(z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="40" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img28.gif"
ALT="$\Theta(z)$">|;
$key = q/{displaymath}Deltap(rho,rho_1,s)=int{dt[}E(rho,rho_1,z,t)+ztimesB(rho,rho_1,z,t)]_{z=ct-s}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="431" HEIGHT="42" BORDER="0"
SRC="|."$dir".q|img1.gif"
ALT="\begin{displaymath}
\Delta p(\rho ,\rho_1 ,s) = \int {dt[} E(\rho ,\rho_1 ,z,t) + z
\times B(\rho ,\rho_1 ,z,t)]_{z = ct - s}
\end{displaymath}">|;
$key = q/s_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img4.gif"
ALT="$s_i$">|;
$key = q/{displaymath}Q_m=int_0^{2pi}dtheta'int_0^inftydr'{r'}^{m+1}rho(r',theta')=Q(z)overline{r^m}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="344" HEIGHT="46" BORDER="0"
SRC="|."$dir".q|img22.gif"
ALT="\begin{displaymath}Q_m=\int_0^{2\pi} d \theta'
\int_0^\infty dr' {r'}^{m+1} \rho(r',\theta')=Q(z) \overline{r^m}\end{displaymath}">|;
$key = q/{displaymath}F_{perp,m}=-eW_mmr^{m-1}Q_m{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="192" HEIGHT="32" BORDER="0"
SRC="|."$dir".q|img21.gif"
ALT="\begin{displaymath}F_{\perp,m}=-e W_m m r^{m-1} Q_m \end{displaymath}">|;
$key = q/{displaymath}Q_m=int_0^{2pi}dtheta'int_0^inftydr'(r')^{m+1}cosmtheta'rho(r',theta',z){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="344" HEIGHT="46" BORDER="0"
SRC="|."$dir".q|img17.gif"
ALT="\begin{displaymath}Q_m=\int_0^{2 \pi} d \theta' \int_0^\infty dr' (r')^{m+1} cos m
\theta' \rho(r',\theta',z) \end{displaymath}">|;
$key = q/theta'=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="50" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img20.gif"
ALT="$\theta'=0$">|;
$key = q/{displaymath}array{{l}w_l(rho,rho_1,s)=-frac{c}{q}Deltap_z=-frac{c}{q}int{dt}left=-frac{c}{q}int{dt[}E_t+ztimesB]_{z=ct-s}array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="374" HEIGHT="54" BORDER="0"
SRC="|."$dir".q|img2.gif"
ALT="\begin{displaymath}
\begin{array}{l}
w_l (\rho ,\rho_1 ,s) = - \frac{c}{q}\Delt...
...c}{q}\int {dt[} E_t + z \times B]_{z = ct - s} \\\\
\end{array}\end{displaymath}">|;
$key = q/b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img25.gif"
ALT="$b$">|;
$key = q/{displaymath}frac{{partialw_t}}{{partials}}=nabla_rhow_l{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="92" HEIGHT="42" BORDER="0"
SRC="|."$dir".q|img8.gif"
ALT="\begin{displaymath}
\frac{{\partial w_t }}{{\partial s}} = \nabla _\rho w_l
\end{displaymath}">|;
$key = q/dz;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img14.gif"
ALT="$dz$">|;
$key = q/r;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img12.gif"
ALT="$r$">|;
$key = q/a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img26.gif"
ALT="$a$">|;
1;