# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/f_1(xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$f_1(\xi )$">|; 

$key = q/g;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$g$">|; 

$key = q/g_1=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$g_1 = 0$">|; 

$key = q/displaystylep_z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle p_z$">|; 

$key = q/{displaymath}left|array{{cccc}1&1&1&1x&x_1&x_2&x_3x^2&x_1^2&x_2^2&x_3^2y&y_1&y_2&y_3array{right|=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="93" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="\begin{displaymath}\left\vert \begin{array}{cccc}
1 &amp; 1 &amp; 1 &amp; 1 \\\\
x &amp; x_1 ...
...&amp; x_3^2 \\\\
y &amp; y_1 &amp; y_2 &amp; y_3
\end{array} \right\vert = 0 \end{displaymath}">|; 

$key = q/displaystylefrac{1}{2m}left[{{bf{p}-frac{e}{c}{{bf{A}right]^2+V;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle \frac{1}{2m}\left[{\bf p}-\frac{e}{c}{\bf A}\right]^2+V$">|; 

$key = q/s_1=s_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$s_1 = s_2$">|; 

$key = q/Q_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$Q_i$">|; 

$key = q/xi=pm1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\xi=\pm1$">|; 

$key = q/{eqnarraystar}y^{primeprimeprime}&=&frac{partial}{partialy}(F_ycdotF+F_t)cdotF+Ft)+frac{partial}{partialt}(F_ycdotF+F_t){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="499" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="\begin{eqnarray*}
y^{\prime\prime\prime} &amp; = &amp; \frac{\partial}{\partial y}
(...
...\cdot F+F_t) +
\frac{\partial}{\partial t}(F_y\cdot F + F_t)
\end{eqnarray*}">|; 

$key = q/s_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$s_2$">|; 

$key = q/k_{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$k_{2}$">|; 

$key = q/{eqnarraystar}V&=&frac{z_1e}{r_1}+frac{z_2e}{r_2}+frac{g_1^2}{r_1^2}+frac{g_2^2}+frac{(p_phi+g_+eta)^2}{r_1r_2(1-eta^2)}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="\begin{eqnarray*}
V &amp;=&amp; \frac {z_1e}{r_1}+\frac {z_2e}{r_2}+\frac {g_1^2}{r_1^...
..._2(\xi^2-1)}+
\frac {(p_\phi + g_+\eta)^2}{r_1r_2(1-\eta^2)}
\end{eqnarray*}">|; 

$key = q/{figure}{centering{{epsfxsize{=320pt{epsffile{img26_102.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="329" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="\begin{figure}
\centering
\epsfxsize =320pt \epsffile{img26_102.eps}
\end{figure}">|; 

$key = q/displaystylevarepsilon_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle \varepsilon_+$">|; 

$key = q/xi>1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$\xi &gt; 1$">|; 

$key = q/{eqnarraystar}f_1&=&hxi^2-varepsilon_+xi-alphaf_2&=&frac{p_phi^2}{xi^2-1}s_1&=&hn_-eta-alphas_2&=&frac{p_phi^2}{eta^2-1}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="157" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="\begin{eqnarray*}
f_1 &amp;=&amp; h \xi^2-\varepsilon_+ \xi- \alpha\\\\
f_2 &amp;=&amp; \frac...
...arepsilon_- \eta- \alpha\\\\
s_2 &amp;=&amp; \frac{p_\phi^2}{\eta^2-1}
\end{eqnarray*}">|; 

$key = q/{displaymath}p_phi^{2}>frac{g_-^2}{2}eqno{(1)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="\begin{displaymath}p_\phi^{2} &gt; \frac{g_-^2}{2} \eqno{(1)} \end{displaymath}">|; 

$key = q/displaystyleheta^2+(1-eta^2)p_{eta}^2+frac{(p_{phi}+g_+eta)^2}{1-eta^2}+varepsilon_-eta+g_+^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle h\eta^2+(1-\eta^2)p_{\eta}^2+\frac{(p_{\phi}+g_+\eta)^2}{1-\eta^2}
+\varepsilon_-\eta+g_+^2$">|; 

$key = q/{{bf{A}_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="${\bf A}_2$">|; 

$key = q/displaystyleint{{bf{B}cdothat{{bf{r}dOmega;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle \int{\bf B}\cdot\hat{\bf r} d\Omega$">|; 

$key = q/1slashr^2:;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$1/r^2 \:$">|; 

$key = q/frac1{r^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$\frac 1 {r^2}$">|; 

$key = q/{eqnarraystar}p_phi^2&<&g_-^2p_phi^2&<&g_+^2p_phi^2&<&2alpha2alpha&<&p_phi^2{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="119" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="\begin{eqnarray*}
p_\phi^2 &amp;&lt;&amp; g_-^2\\\\
p_\phi^2 &amp;&lt;&amp; g_+^2\\\\
p_\phi^2 &amp;&lt;&amp; 2\alpha\\\\
2\alpha &amp;&lt;&amp; p_\phi^2
\end{eqnarray*}">|; 

$key = q/displaystylex^2+y^2=d^2(xi^2-1)(1-eta^2)quadmbox{(radiocil'{i}ndrico)};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle x^2+y^2 = d^2 (\xi^2-1)(1-\eta^2) \quad \mbox{ (radio cil\'{\i}ndrico)}$">|; 

$key = q/y^{prime}=-y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$y^{\prime}=-y$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140f.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="643" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140f.eps}
\end{figure}">|; 

$key = q/F_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$F_2$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140e.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="718" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140e.eps}
\end{figure}">|; 

$key = q/k_{1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$k_{1}$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img16_49.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="269" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img16_49.eps}
\end{figure}">|; 

$key = q/-g_{+};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$-g_{+}$">|; 

$key = q/(-p_phislashg_-<1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="\(-p_\phi / g_- &lt; 1 \)">|; 

$key = q/p_phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$p_\phi$">|; 

$key = q/{displaymath}left(frac{varepsilon_+}{2h},-frac{varepsilon_+^2}{4h}-alpharight)quilon_-}{2h},frac{varepsilon_-^2}{4h}-alpharight){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="\begin{displaymath}
\left( \frac{\varepsilon_+}{2h},-\frac{\varepsilon_+^2}{4h...
...c{\varepsilon_-}{2h},\frac{\varepsilon_-^2}{4h}-\alpha\right)
\end{displaymath}">|; 

$key = q/(-3,3);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$(-3,3)$">|; 

$key = q/k_{0}slash6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$k_{0}/6$">|; 

$key = q/{eqnarraystar}r^2&=&x^2+y^2+z^2costheta&=&frac{z}{r}tantheta&=&frac{y}{x}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="105" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="\begin{eqnarray*}
r^2 &amp; = &amp; x^2 + y^2 + z^2 \\\\
\cos\theta &amp; = &amp; \frac{z}{r} \\\\
\tan\theta &amp; = &amp; \frac{y}{x}
\end{eqnarray*}">|; 

$key = q/y_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="$y_i$">|; 

$key = q/s_1<s_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$s_1 &lt; s_2$">|; 

$key = q/{displaymath}2alpha<p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="\begin{displaymath}
2\alpha &lt; p_\phi^2
\end{displaymath}">|; 

$key = q/alpha_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$\alpha_0$">|; 

$key = q/displaystylefrac{zxi-deta}{d^2(xi^2-eta^2)}p_xi-frac{zeta-dxi}{d^2(xi^2-eta^2)}p_eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle \frac{z\xi -d\eta}{d^2(\xi^2-\eta^2)}p_\xi -
\frac{z\eta -d\xi}{d^2(\xi^2-\eta^2)}p_\eta$">|; 

$key = q/displaystyley_0+hy'_0frac{h^2}{2!}y^{primeprime}_0+frac{h^3}{3!}y^{primeprimeprime}_0+cdots;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$\displaystyle y_0+hy'_0\frac{h^2}{2!}y^{\prime\prime}_0+
\frac{h^3}{3!}y^{\prime\prime\prime}_0+\cdots$">|; 

$key = q/p_{phi}=pmg_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$p_{\phi}=\pm g_-$">|; 

$key = q/displaystyledotxi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \dot\xi$">|; 

$key = q/{displaymath}frac{g_-^2}{2}-p_phi^2leq-alphaleqfrac{g_-^2}{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="\begin{displaymath}\frac{g_-^2}{2} - p_\phi^2 \leq -\alpha \leq \frac{g_-^2}{2}\end{displaymath}">|; 

$key = q/{eqnarraystar}Q_i&=&-frac{partialF}{partialp_i}P_i&=&frac{partialF}{partialq_i}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="91" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="\begin{eqnarray*}
Q_i &amp; = &amp; -\frac{\partial F}{\partial p_i} \\\\
P_i &amp; = &amp; \frac{\partial F}{\partial q_i}
\end{eqnarray*}">|; 

$key = q/{eqnarraystar}{{em{B}_x&=&(nablatimes{{bf{A})_x=frac{partial{{bf{A}_y}{partialz}-frac{partial{{bf{A}_z}{partialy}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="\begin{eqnarray*}
{\em B}_x &amp; = &amp; (\nabla \times {\bf A})_x
= \frac{\partial {\bf A}_y}{\partial z} -
\frac{\partial {\bf A}_z}{\partial y}
\end{eqnarray*}">|; 

$key = q/rho-z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$\rho-z$">|; 

$key = q/{eqnarraystar}-frac{(g_1^2+g_2^2)(xi^2+eta^2)-2(g_1^2-g_2^2)xieta}{d^2(xi^2-eta^c{g_1^2}{r_1^2}+frac{g_2^2}{r_2^2}right){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="\begin{eqnarray*}
-\frac{(g_1^2 + g_2^2)(\xi^2 + \eta^2) - 2(g_1^2 -
g_2^2)\x...
...)} &amp;=&amp;
-\left(\frac{g_1^2}{r_1^2} + \frac{g_2^2}{r_2^2}\right)
\end{eqnarray*}">|; 

$key = q/g_+^2-p_phi^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$g_+^2 - p_\phi^2$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img31_137d.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="690" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img31_137d.eps}
\end{figure}">|; 

$key = q/{displaymath}array{{ccl}F(y_0+lambdahF_0,t_0+muh)&=&F(y_0,t_0)+lambdahFfrac{part^2frac{partial^2F}{partialt^2}+cdotsright)array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="568" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="\begin{displaymath}
\begin{array}{ccl}
F(y_0+\lambda hF_0,t_0+\mu h) &amp; = &amp; F(...
...{\partial^2 F}{\partial t^2} + \cdots
\right)
\end{array}
\end{displaymath}">|; 

$key = q/k_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$k_0$">|; 

$key = q/{displaymath}array{{rcl}y_{n+1}&=&y_n+frac{1}{2}kappa_0+frac{1}{2}kappa_1kappa_0hF(y_n,t_n)kappa_1&=&hF(y_n+kappa_0,t_n+h)array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="72" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
y_{n+1} &amp; = &amp; y_n + \frac{1}{2}\kappa_...
..._n) \\\\
\kappa_1 &amp; = &amp; h F(y_n+\kappa_0,t_n+h)
\end{array}
\end{displaymath}">|; 

$key = q/-g_-slashp_phi;;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$-g_-/ p_\phi \;$">|; 

$key = q/{displaymath}array{{rcl}y_{n+1}&=&y_n+frac{1}{6}(kappa_0+4kappa_1+kappa_2)&&kapp&hF(y_n+frac{3}{2}kappa_0,t_n+frac{3}{2}h)array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="158" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
y_{n+1} &amp;=&amp; y_n + \frac{1}{6}(\kappa_0...
...=&amp; h F(y_n+\frac{3}{2}\kappa_0,t_n+\frac{3}{2}h)
\end{array}
\end{displaymath}">|; 

$key = q/{eqnarraystar}(xi^2-eta^2)h&=&left{(xi^2-1)p_{xi}^2+(1-eta^2)p_{eta}^2+frac{(p_{repsilon_-eta+frac{g_+^2-g_-^2}{2}right}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="549" HEIGHT="109" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="\begin{eqnarray*}
(\xi^2-\eta^2)h &amp;=&amp; \left\{(\xi^2-1)p_{\xi}^2+(1-\eta^2)p_{\...
...repsilon_+\xi + \varepsilon_-\eta+\frac{g_+^2-g_-^2}{2}\right\}
\end{eqnarray*}">|; 

$key = q/{eqnarraystar}p_phi^2&>&g_-^2g_-^2&geq&2alphap_phi^2&>&g_+^2p_phi^2&<&2alpha{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="117" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="\begin{eqnarray*}
p_\phi^2 &amp; &gt; &amp; g_-^2 \\\\
g_-^2 &amp; \geq &amp; 2\alpha \\\\
p_\phi^2 &amp; &gt; &amp; g_+^2 \\\\
p_\phi^2 &amp; &lt; &amp; 2\alpha
\end{eqnarray*}">|; 

$key = q/x_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$x_i$">|; 

$key = q/H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="$H$">|; 

$key = q/-p_phislashg_+>1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$-p_\phi / g_+ &gt; 1$">|; 

$key = q/{displaymath}midalphamidleqfrac{g_-^2}{2}eqno{(2)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="\begin{displaymath}\mid \alpha \mid \leq \frac{g_-^2}{2} \eqno{(2)} \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140m.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="653" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140m.eps}
\end{figure}">|; 

$key = q/(-alphaleq-p_phi^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="\(-\alpha \leq -p_\phi^2\)">|; 

$key = q/2cdotG1cdotG2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$2\cdot G1\cdot G2$">|; 

$key = q/{eqnarraystar}frac{dy_1}{dt}&=&F_1(y_1,y_2,y_3,ldots,y_6,t)frac{dy_2}{dt}&=&F_2(dy_6}{dt}&=&F_6(y_1,y_2,y_3,ldots,y_6,t){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="157" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="\begin{eqnarray*}
\frac{dy_1}{dt} &amp; = &amp; F_1(y_1,y_2,y_3,\ldots,y_6,t) \\\\
\f...
...vdots \\\\
\frac{dy_6}{dt} &amp; = &amp; F_6(y_1,y_2,y_3,\ldots,y_6,t)
\end{eqnarray*}">|; 

$key = q/{displaymath}left.array{{lcr}g_-^2geq2alphag_+^2leq2alphaarray{right}quadg_-^2geq2alphageqg_+^2quadrightarrowquadg_-^2>g_+^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="\begin{displaymath}\left. \begin{array}{lcr}
g_-^2 \geq 2\alpha \\\\
g_+^2 \l...
... \geq 2\alpha \geq g_+^2 \quad \rightarrow
\quad g_-^2 &gt; g_+^2\end{displaymath}">|; 

$key = q/1slashr;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$1/r$">|; 

$key = q/{displaymath}hxi+left(frac{g_-^2}{2}-alpharight)=frac{(p_phi+g_-xi)^2}{{xi}^2-1}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="\begin{displaymath}h\xi + \left(\frac{g_-^2}{2} - \alpha \right) =
\frac{(p_\phi + g_- \xi )^2}{{\xi}^2 - 1} \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140l.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="672" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140l.eps}
\end{figure}">|; 

$key = q/{eqnarraystar}p_x&=&frac{partialF_2}{partialx}=frac{partialxi}{partialx}p_{xi}+f_{eta}+frac{partialphi}{partialx}p_{phi}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="\begin{eqnarray*}
p_x &amp; = &amp; \frac{\partial F_2}{\partial x}
= \frac{\partial...
...partial x}p_{\eta} +
\frac{\partial \phi}{\partial x}p_{\phi}
\end{eqnarray*}">|; 

$key = q/(alphageqp_phi^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="\(\alpha \geq p_\phi^2\)">|; 

$key = q/{figure}{centering{{epsfxsize{=260pt{epsffile{img4_23.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="270" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="\begin{figure}
\centering
\epsfxsize =260pt \epsffile{img4_23.eps}
\end{figure}">|; 

$key = q/{displaymath}p_{eta}^2=frac{1}{(1-eta^2)^2}left{heta^4+varepsilon_-eta^3-(alpha+_-+2p_{phi}g_+)eta+(alpha-kappa-p_{phi}^2)right}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="632" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="\begin{displaymath}
p_{\eta}^2 = \frac{1}{(1-\eta^2)^2}\left\{h\eta^4+\varepsi...
...ilon_-+2p_{\phi}g_+)\eta + (\alpha-\kappa-p_{\phi}^2)\right\}
\end{displaymath}">|; 

$key = q/g_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$g_-$">|; 

$key = q/{figure}{centering{{epsfxsize{=420pt{epsffile{porunam.eps}{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="534" HEIGHT="670" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{figure}
\centering
\epsfxsize =420pt \epsffile{porunam.eps}
\end{figure}">|; 

$key = q/{eqnarraystar}y^{prime}_0&=&-1y^{primeprime}_0&=&(y^{prime}_0)^{prime}=-(y_0)^{pprimeprime})^{prime}=-1cdots&cdots&cdots{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="106" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{eqnarray*}
y^{\prime}_0 &amp; = &amp; -1 \\\\
y^{\prime\prime}_0 &amp; = &amp; (y^{\pr...
..._0^{\prime\prime})^{\prime} = -1\\\\
\cdots &amp; \cdots &amp; \cdots
\end{eqnarray*}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140n.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="633" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140n.eps}
\end{figure}">|; 

$key = q/displaystylefrac{z}{d}quadLongrightarrowquadz=xi;eta;d;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \frac{z}{d} \quad \Longrightarrow \quad z = \xi \; \eta \; d$">|; 

$key = q/X;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$X$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img33_137f.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="670" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img33_137f.eps}
\end{figure}">|; 

$key = q/displaystylefrac{4}{3}piq;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle \frac{4}{3}\pi q$">|; 

$key = q/alpha_1=c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$\alpha_1=c$">|; 

$key = q/{eqnarraystar}{{bf{A}^2&=&left[frac{(g_1+g_2)(xi^2-1)eta+(g_1-g_2)(1-eta^2)xi}{(xi^2-1)(1-eta^2)(xi^2-eta^2)}right]^2{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="389" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="\begin{eqnarray*}
{\bf A}^2 &amp; = &amp; \left[\frac{(g_1+g_2)(\xi^2-1)\eta+
(g_1-g_2)(1-\eta^2)\xi}{(\xi^2-1)(1-\eta^2)(\xi^2-\eta^2)}\right]^2
\end{eqnarray*}">|; 

$key = q/displaystylefrac{2p_{xi}(xi^2-1)}{xi^2-eta^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle \frac{2p_{\xi}(\xi^2-1)}{\xi^2-\eta^2}$">|; 

$key = q/Z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$Z$">|; 

$key = q/xi+eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$\xi + \eta$">|; 

$key = q/{displaymath}s_2left(-frac{varepsilon_-}{2h}right)=frac{p_phi^2}{varepsilon_-^2s-^2-4h^2}=frac{(2p_phih)^2}{varepsilon_-^2-4h^2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="\begin{displaymath}
s_2\left(-\frac{\varepsilon_-}{2h}\right) =
\frac{p_\phi^...
...silon_-^2-4h^2} = \frac{(2p_\phi
h)^2}{\varepsilon_-^2-4h^2}
\end{displaymath}">|; 

$key = q/-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$-1$">|; 

$key = q/1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$1$">|; 

$key = q/varepsilon_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\varepsilon_-$">|; 

$key = q/calZ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$\cal Z$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img19_55.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="239" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img19_55.eps}
\end{figure}">|; 

$key = q/xileq10;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="$\xi\leq10$">|; 

$key = q/{displaymath}-(z_1+z_2)>0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="\begin{displaymath}-(z_1 +z_2) &gt; 0 \end{displaymath}">|; 

$key = q/q_j;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$q_j$">|; 

$key = q/frac{partialH}{partialx_i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\frac{\partial H}{\partial x_i}$">|; 

$key = q/hF(y_n+k_0slash2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$hF(y_n+k_0/2)$">|; 

$key = q/{{bf{B}_y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="${\bf B}_y$">|; 

$key = q/eta=-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\eta = -1$">|; 

$key = q/displaystylefrac{r_1r_2}{d^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \frac{r_1r_2}{d^2}$">|; 

$key = q/{figure}{centering{{epsfxsize{=220pt{epsffile{img9_31.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="268" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="\begin{figure}
\centering
\epsfxsize =220pt \epsffile{img9_31.eps}
\end{figure}">|; 

$key = q/V_r;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$V_r$">|; 

$key = q/displaystyledoteta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle \dot\eta$">|; 

$key = q/{displaymath}s_1left(-frac{varepsilon_-}{2h}right)=-frac{varepsilon_-^2}{4h}-alpha{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="\begin{displaymath}
s_1\left(-\frac{\varepsilon_-}{2h}\right) =
-\frac{\varepsilon_-^2}{4h}-\alpha
\end{displaymath}">|; 

$key = q/{displaymath}array{{ccl}y^{prime}&=&F(y,t)y^{primeprime}&=&F_ycdotF+F_ty^{primep&F_{yy}F^2+2F_y^2F+2F_{yt}F+2F_yF_t+F_{tt}array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="94" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="\begin{displaymath}
\begin{array}{ccl}
y^{\prime} &amp; = &amp; F(y,t) \\\\
y^{\prim...
...&amp; = &amp; F_{yy}F^2+2F_y^2F+2F_{yt}F+2F_yF_t+F_{tt}
\end{array}
\end{displaymath}">|; 

$key = q/z_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$z_1$">|; 

$key = q/{eqnarraystar}y&=&y_0+alphaF(y_1,t_1)+betaF(y_2,t_2)+gammaF(y_3,t_3)+cdots{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="\begin{eqnarray*}
y &amp;=&amp; y_0+\alpha F(y_1,t_1)+\beta F(y_2,t_2)+\gamma F(y_3,t_3)+\cdots
\end{eqnarray*}">|; 

$key = q/B_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$B_4$">|; 

$key = q/(0,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$( 0, 1 )$">|; 

$key = q/{displaymath}frac{eta}{0.02}+50=etatimes50+50.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="\begin{displaymath}\frac{\eta}{0.02}+50 = \eta \times 50 + 50.\end{displaymath}">|; 

$key = q/=k_{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$ = k_{2}$">|; 

$key = q/{displaymath}V=frac{z_1e}{r_1}+frac{z_2e}{r_2}-frac{{g_1}^2}{{r_1}^2}-frac{{g_2}i)}^2}{xi^2-1}+frac{{(p_phi+g_+eta)}^2}{1-eta^2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="\begin{displaymath}V = \frac{z_1e}{r_1} +\frac{z_2e}{r_2} -
\frac{{g_1}^2}{{r_...
...i)}^2}{\xi^2 - 1} +
\frac{{(p_\phi + g_+\eta)}^2}{1 -\eta^2} \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140k.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="707" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140k.eps}
\end{figure}">|; 

$key = q/c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$c$">|; 

$key = q/{displaymath}array{{rcl}y_{n+1}&=&y_n+frac{1}{4}(kappa_0+3kappa_2)&&kappa_0&=&hF&hF(y_n+frac{3}{2}kappa_1,t_n+frac{3}{2}h)array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="158" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
y_{n+1} &amp;=&amp; y_n + \frac{1}{4}(\kappa_0...
...=&amp; h F(y_n+\frac{3}{2}\kappa_1,t_n+\frac{3}{2}h)
\end{array}
\end{displaymath}">|; 

$key = q/(frac{g_-^2}2-alpha);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$(\frac{g_-^2} 2-\alpha)$">|; 

$key = q/{displaymath}-frac{g_-}{p_phi}>1qquadlongrightarrowqquadg_-^2>p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="\begin{displaymath}-\frac{g_-}{p_\phi} &gt; 1 \qquad \longrightarrow \qquad g_-^2 &gt; p_\phi^2\end{displaymath}">|; 

$key = q/{displaymath}0leqfrac{g_{-}^{2}}{2}-alphaleqg_{-}^{2}qquadrightarrowqquad-frac{g_{-}^{2}}{2}leq-alphaleqfrac{g_{-}^{2}}{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="\begin{displaymath}
0 \leq \frac{g_{-}^{2}}{2} - \alpha
\leq g_{-}^{2} \qqua...
...- \frac{g_{-}^{2}}{2} \leq -\alpha
\leq \frac{g_{-}^{2}}{2}
\end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=360pt{epsffile{img14_43.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="259" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="\begin{figure}
\centering
\epsfxsize =360pt \epsffile{img14_43.eps}
\end{figure}">|; 

$key = q/displaystyledot{p_eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle \dot{p_\eta}$">|; 

$key = q/0.02;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$0.02$">|; 

$key = q/{displaymath}p_phi^2<g_+^2leq2alphaquadrightarrowquadp_phi^2<2alpha{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="\begin{displaymath}
p_\phi^2 &lt; g_+^2
\leq 2\alpha \quad \rightarrow \quad
p_\phi^2 &lt; 2\alpha
\end{displaymath}">|; 

$key = q/displaystyley_0+alpha_0kappa_0+alpha_1kappa_1+cdots;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle y_0+\alpha_0\kappa_0+\alpha_1\kappa_1 + \cdots$">|; 

$key = q/p_phi^2<g_+^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$p_\phi^2 &lt; g_+^2$">|; 

$key = q/{eqnarraystar}y^{primeprimeprime}&=&frac{d}{dt}F_ycdotF+F_ycdotfrac{dF}{dt}+frac{prime}+frac{partial}{partialt}F^{prime}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="\begin{eqnarray*}
y^{\prime\prime\prime} &amp; = &amp; \frac{d}{dt}F_y\cdot F +
F_y\...
...
F_y\cdot F^{\prime} + \frac{\partial}{\partial t}F^{\prime}
\end{eqnarray*}">|; 

$key = q/g_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$g_+$">|; 

$key = q/xi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\xi $">|; 

$key = q/varepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\varepsilon$">|; 

$key = q/F^{prime};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$F^{\prime}$">|; 

$key = q/-p_{phi}slashg_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$-p_{\phi}/g_-$">|; 

$key = q/20032;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$20032$">|; 

$key = q/{displaymath}frac{g_+^2}{2}-alphaleqg_+^2-p^2quadrightarrowquadp_phi^2leqalpha+f2p_phi^2-g_+^2;=;p_phi^2+p_phi^2-g_+^2;>;p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="599" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="\begin{displaymath}
\frac{g_+^2}{2}-\alpha \leq g_+^2-p^2 \quad \rightarrow\qu...
...2-g_+^2
\; = \; p_\phi^2+ p_\phi^2-g_+^2
\; &gt; \; p_\phi^2
\end{displaymath}">|; 

$key = q/displaystylexi^2+eta^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \xi^2+\eta^2$">|; 

$key = q/{{bf{A}_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="${\bf A}_0$">|; 

$key = q/p_eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$p_\eta$">|; 

$key = q/(y_n+kappa,t_n+h);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$(y_n+\kappa,t_n+h)$">|; 

$key = q/displaystyledot{p_xi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle \dot{p_\xi}$">|; 

$key = q/{figure}{centering{{epsfxsize{=220pt{epsffile{img6_26.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="213" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="\begin{figure}
\centering
\epsfxsize =220pt \epsffile{img6_26.eps}
\end{figure}">|; 

$key = q/(-2pi,2pi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$(-2\pi,
2\pi)$">|; 

$key = q/{figure}{centering{{epsfxsize{=320pt{epsffile{img23_90.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="234" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="\begin{figure}
\centering
\epsfxsize =320pt \epsffile{img23_90.eps}
\end{figure}">|; 

$key = q/{displaymath}V=frac{z_1e}{r_1}+frac{z_2e}{r_2}=frac{1}{2md^2(xi^2-eta^2)}left{:2mdexi(z_1+z_2)+2mdeeta(z_1-z_2):right}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="529" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="\begin{displaymath}
V = \frac{z_1e}{r_1}+\frac{z_2e}{r_2}
= \frac{1}{2md^2(\...
...}
\left\{ \: 2mde\xi(z_1+z_2)+2mde\eta(z_1-z_2) \: \right\}
\end{displaymath}">|; 

$key = q/displaystyley_0+y^{prime}cdoth;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle y_0 + y^{\prime}\cdot h$">|; 

$key = q/displaystyley_0+hy^{prime}+frac{h^2}{2}y^{primeprime}+cdots;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle y_0+hy^{\prime}+\frac{h^2}{2}y^{\prime\prime} + \cdots$">|; 

$key = q/p_xi;;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$p_\xi \;$">|; 

$key = q/{eqnarraystar}y_{n+1}&=&y_n+alpha_0kappa_0+alpha_1kappa_1{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="\begin{eqnarray*}
y_{n+1} &amp; = &amp; y_n+\alpha_0\kappa_0+\alpha_1\kappa_1
\end{eqnarray*}">|; 

$key = q/{displaymath}frac{-varepsilon_-pmsqrt{varepsilon_-^2+4halpha}}{2h}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="\begin{displaymath}
\frac{-\varepsilon_- \pm \sqrt{\varepsilon_-^2+4h\alpha}}{2h}
\end{displaymath}">|; 

$key = q/(y_{n}+k_{2})=k_{3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$( y_{n} + k_{2}) = k_{3}$">|; 

$key = q/{figure}{centering{{epsfxsize{=320pt{epsffile{img24_94.eps}{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="507" HEIGHT="873" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="\begin{figure}
\centering
\epsfxsize =320pt \epsffile{img24_94.eps}
\end{figure}">|; 

$key = q/mv;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$mv$">|; 

$key = q/displaystyle2e^2frac{g_1g_2}{c^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle 2e^2\frac{g_1g_2}{c^2}$">|; 

$key = q/{displaymath}f_1(xi)=f_2(xi){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="\begin{displaymath}f_1(\xi) = f_2(\xi) \end{displaymath}">|; 

$key = q/p;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$p$">|; 

$key = q/{displaymath}y=y_1frac{(x-x_2)(x-x_3)}{(x_1-x_2)(x_1-x_3)}+y_2frac{(x-x_1)(x-x_3_3)}+y_3frac{(x-x_1)(x-x_2)}{(x_3-x_1)(x_3-x_2)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="\begin{displaymath}
y = y_1\frac{(x-x_2)(x-x_3)}{(x_1-x_2)(x_1-x_3)} +
y_2\f...
...1)(x_2-x_3)}
+ y_3\frac{(x-x_1)(x-x_2)}{(x_3-x_1)(x_3-x_2)}
\end{displaymath}">|; 

$key = q/xi>100;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$\xi&gt;100$">|; 

$key = q/-p_phislashg_+<1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="$-p_\phi / g_+ &lt; 1 $">|; 

$key = q/displaystyle2mde(z_1+z_2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle 2mde(z_1+z_2)$">|; 

$key = q/{displaymath}left.array{{ccc}hxi^2-varepsilon_+xi+left(frac{g_-^2}{2}-alpharight{(p_phi+g_+eta)^2}{eta^2-1}array{right}eqno{(2)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="105" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="\begin{displaymath}
\left.
\begin{array}{ccc}
h \xi^2-\varepsilon_+\xi+\left...
...phi + g_+\eta)^2}{\eta^2-1}
\end{array}
\right\} \eqno{(2)}
\end{displaymath}">|; 

$key = q/{displaymath}2alphaleq2p_phi^2-g_+^2=p_phi^2+p_phi^2-g_+^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="\begin{displaymath}
2\alpha \leq 2 p_\phi^2-g_+^2= p_\phi^2+p_\phi^2-g_+^2
\end{displaymath}">|; 

$key = q/displaystyleH;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle H$">|; 

$key = q/eta=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$\eta = 1$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140h.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="622" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140h.eps}
\end{figure}">|; 

$key = q/-p_{phi}^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$-p_{\phi}^2$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img20_55.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img20_55.eps}
\end{figure}">|; 

$key = q/displaystylefrac{g_+^2-g_-^2}{2}=kappa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle \frac{g_+^2-g_-^2}{2} = \kappa$">|; 

$key = q/{displaymath}-frac{p_phi}{g_{-}}>1qquadrightarrowqquadp_phi^{2}>g_{-}^{2}qquadrightarrowqquadp_phi^{2}>frac{g_{-}^{2}}{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="\begin{displaymath}
-\frac{p_\phi}{g_{-}} &gt; 1 \qquad \rightarrow \qquad
p_\p...
... \qquad \rightarrow \qquad
p_\phi^{2} &gt; \frac{g_{-}^{2}}{2}
\end{displaymath}">|; 

$key = q/X-Y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$X-Y$">|; 

$key = q/displaystylefrac{z(g_1r_2+g_2r_1)+d(g_1r_2-g_2r_1)}{r^2r_1r_2}left(y,-x,0right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \frac{z(g_1r_2+g_2r_1)+d(g_1r_2-g_2r_1)}{r^2r_1r_2}
\left(y,-x,0\right)$">|; 

$key = q/(varepsilon_+slash2h,alpha-g_-^2slash2+varepsilon_+^2slash4h);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$(\varepsilon_+/2h,
\alpha-g_-^2/2+\varepsilon_+^2/4h)$">|; 

$key = q/{displaymath}hleft(-frac{varepsilon_-}{2h}right)^2+varepsilon_-left(-frac{varepsn_-^2}{2h}-alpha=-frac{varepsilon_-^2}{4h}-alpha{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="433" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="\begin{displaymath}
h\left(-\frac{\varepsilon_-}{2h}\right)^2 + \varepsilon_-
...
...psilon_-^2}{2h}-\alpha =
-\frac{\varepsilon_-^2}{4h}-\alpha
\end{displaymath}">|; 

$key = q/f_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$f_1$">|; 

$key = q/(-1,+1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$(-1,+1)$">|; 

$key = q/p_phi^2>g_-^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$p_\phi^2 &gt; g_-^2$">|; 

$key = q/displaystylefrac{2}{xi^2-eta^2}left{frac{p_{phi}+g_-xi}{xi^2-1}+frac{p_{phi}+g_+eta}{1-eta^2}right};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \frac{2}{\xi^2-\eta^2}\left\{
\frac{p_{\phi}+g_-\xi}{\xi^2-1}+
\frac{p_{\phi}+g_+\eta}{1-\eta^2}\right\}$">|; 

$key = q/displaystyle2md^2H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle 2md^2H$">|; 

$key = q/{displaymath}heta^2+left(frac{g_+^2}{2}-alpharight)=frac{(p_phi+g_+eta)^2}{eta^2-1}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="\begin{displaymath}h\eta^2 + \left(\frac{g_+^2}{2} - \alpha \right) =
\frac{(p_\phi + g_+\eta)^2 }{\eta^2 - 1}
\end{displaymath}">|; 

$key = q/displaystyley;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle y$">|; 

$key = q/kappa_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\kappa_1$">|; 

$key = q/{figure}{centering{{epsfxsize{=220pt{epsffile{img7_27.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="259" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="\begin{figure}
\centering
\epsfxsize =220pt \epsffile{img7_27.eps}
\end{figure}">|; 

$key = q/-pslashg_-<1rightarrowp_phi^2<g_-^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$-p/g_- &lt; 1 \rightarrow p_\phi^2 &lt; g_-^2 $">|; 

$key = q/{displaymath}g_-^2>p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="\begin{displaymath}g_-^2 &gt; p_\phi^2 \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img32_137e.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="711" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img32_137e.eps}
\end{figure}">|; 

$key = q/xirightarrow1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\xi \rightarrow 1$">|; 

$key = q/p_{xi}^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$p_{\xi}^2$">|; 

$key = q/{displaymath}left.array{{ccl}f_1(xi)&=&hxi^2-varepsilon_+xi+left(frac{g_-^2}{2}-{(p_phi+g_+eta)^2}{eta^2-1}array{right}eqno{(3)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="207" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="\begin{displaymath}
\left.
\begin{array}{ccl}
f_1(\xi) &amp;=&amp; h\xi^2-\varepsilo...
...hi +g_+\eta)^2}{\eta^2-1}
\end{array}
\right\} \eqno{(3)}
\end{displaymath}">|; 

$key = q/{displaymath}xi=frac{varepsilon_+pmsqrt{varepsilon_+^2+4hleft(frac{g_-^2}{2}-alpharight)}}{2h}eqno{(4)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="74" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{displaymath}
\xi = \frac {\varepsilon_+ \pm \sqrt{\varepsilon_+^2+
4h\left(\frac{g_-^2}{2}-\alpha\right)}}{2h}
\eqno{(4)}
\end{displaymath}">|; 

$key = q/displaystyleh;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle h$">|; 

$key = q/H=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$H=0$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140r.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="641" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140r.eps}
\end{figure}">|; 

$key = q/dyslashdt;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$dy/dt$">|; 

$key = q/displaystyleg_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle g_+$">|; 

$key = q/-1leqetaleq1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$-1 \leq \eta \leq
1$">|; 

$key = q/z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$z$">|; 

$key = q/{displaymath}g_-^2-P_phi^2leqfrac{g_-^2}{2}-alphaleqg_-^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="\begin{displaymath}g_-^2 - P_\phi^2 \leq \frac{g_-^2}{2} - \alpha \leq g_-^2\end{displaymath}">|; 

$key = q/4pi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$4\pi$">|; 

$key = q/;p_{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="$\; p_{\eta}$">|; 

$key = q/{eqnarraystar}{{bf{A}_1&=&g_1left(frac{y(z+d)}{r^2r_1},frac{-x(z+d)}{r^2r_1},0ri)}{r^2r_2},frac{-x(z-d)}{r^2r_2},0right){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="116" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="\begin{eqnarray*}
{\bf A}_1 &amp; = &amp; g_1\left(\frac{y(z+d)}{r^2r_1},
\frac{-x(z...
...ft(\frac{y(z-d)}{r^2r_2},
\frac{-x(z-d)}{r^2r_2},0\right) \\\\
\end{eqnarray*}">|; 

$key = q/frac{alpha^2}{gamma^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\frac{\alpha^2}{\gamma^2}$">|; 

$key = q/phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\phi$">|; 

$key = q/displaystylealpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/displaystylefrac{1}{2m}({{bf{p}-frac{e}{c}{{bf{A})^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \frac{1}{2m}({\bf p}-\frac{e}{c}{\bf A})^2$">|; 

$key = q/{displaymath}frac{1}{xi+eta}+frac{1}{xi-eta}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="\begin{displaymath}\frac{1}{\xi+\eta}+\frac{1}{\xi-\eta}\end{displaymath}">|; 

$key = q/{eqnarraystar}p^2+frac{alpha^2}{r^2}&=&p_r^2+frac{p_theta^2+alpha^2}{r^2}+frac{p_phi^2}{r^2{mbox{sen}^2theta}}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="\begin{eqnarray*}
p^2 +\frac{\alpha^2}{r^2} &amp; = &amp;
p_r^2 + \frac{p_\theta^2 + \alpha^2}{r^2} +
\frac{p_\phi^2}{r^2{\mbox{sen}^2\theta}}
\end{eqnarray*}">|; 

$key = q/10leqxileq100;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$10\leq\xi\leq100$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140j.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="684" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140j.eps}
\end{figure}">|; 

$key = q/{displaymath}{{bf{A}_r=0,qquad{{bf{A}_{theta}=0,qquad{{bf{A}_{phi}=frac{g}{r}tanfrac{theta}{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="\begin{displaymath}
{\bf A}_r = 0, \qquad
{\bf A}_{\theta} = 0, \qquad
{\bf A}_{\phi} = \frac{g}{r}\tan\frac{\theta}{2}
\end{displaymath}">|; 

$key = q/Y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$Y$">|; 

$key = q/{eqnarraystar}-frac{varepsilon_-^2}{4h}-alpha&<&frac{(2p_phih)^2}{varepsilon_-^2>&frac{(2p_phih)^2}{varepsilon_-^2-4h^2}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="153" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="\begin{eqnarray*}
-\frac{\varepsilon_-^2}{4h}-\alpha &amp;&lt;&amp;
\frac{(2p_\phi h)^2...
...^2}{4h}-\alpha &amp;&gt;&amp;
\frac{(2p_\phi h)^2}{\varepsilon_-^2-4h^2}
\end{eqnarray*}">|; 

$key = q/displaystyle-frac{1}{xi^2-eta^2}left{2etaleft[h+p_{eta}^2-frac{(p_{phi}+g_+eta)^}right]-frac{2g_+(p_{phi}+g_+eta)}{xi^2-1}-varepsilon_-right};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="482" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle -\frac{1}{\xi^2-\eta^2}\left\{2\eta\left[
h+p_{\eta}^2-\frac{(p_{...
...eta^2)^2}\right]
-\frac{2g_+(p_{\phi}+g_+\eta)}{\xi^2-1}
-\varepsilon_-\right\}$">|; 

$key = q/displaystyler_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle r_2$">|; 

$key = q/{displaymath}B_4eta^4+B_3eta^3+B_2eta^2+B_1eta+B_0=P(eta){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="\begin{displaymath}B_4\eta^4 + B_3\eta^3 +B_2\eta^2 + B_1\eta + B_0 = P(\eta)\end{displaymath}">|; 

$key = q/{displaymath}array{{rcl}kappa_0&=&hF(y_n,t_n)&&kappa_1&=&hF(y_n+frac{1}{2}kappa_c{1}{2}h)&&kappa_2&=&hF(y_n+kappa_2,t_n+h)array{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="158" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
\kappa_0 &amp; = &amp; h F(y_n,t_n) \\\\
&amp; &amp; ...
...&amp; &amp; \\\\
\kappa_2 &amp; = &amp; h F(y_n+\kappa_2,t_n+h)
\end{array}
\end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=240pt{epsffile{img2_10.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="237" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\begin{figure}
\centering
\epsfxsize =240pt \epsffile{img2_10.eps}
\end{figure}">|; 

$key = q/-V_r;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$-V_r$">|; 

$key = q/{eqnarraystar}{r_1}^2=r^2+{(d+z)}^2{r_2}^2=r^2+{(d-z)}^2{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="\begin{eqnarray*}
{r_1}^2 = r^2 + {(d +z)}^2\\\\
{r_2}^2 = r^2 + {(d-z)}^2
\end{eqnarray*}">|; 

$key = q/displaystylefrac{e}{c}(g_1-g_2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\displaystyle \frac{e}{c}(g_1-g_2)$">|; 

$key = q/displaystylexi^2-eta^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle \xi^2-\eta^2$">|; 

$key = q/z_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$z_2$">|; 

$key = q/xi=-g_-slashp_{phi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\xi=-g_-/p_{\phi}$">|; 

$key = q/h^3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$h^3$">|; 

$key = q/{displaymath}frac{(p_{phi}+g_-xi_{ext})^2}{xi_{ext}^2-1}=frac{(p_phi+g_-[-frac{g_phi}])^2}{frac{g_-^2}{p_phi^2}-1}=g_-^2-p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="71" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="\begin{displaymath}
\frac{(p_{\phi} + g_-\xi_{ext})^2}{\xi_{ext}^2 - 1} =
\fra...
...}{p_\phi}])^2}{\frac{g_-^2}{p_\phi^2}
-1} = g_-^2 - p_\phi^2
\end{displaymath}">|; 

$key = q/s_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$s_1$">|; 

$key = q/p_phi^2>g_+^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$p_\phi^2 &gt; g_+^2$">|; 

$key = q/displaystylercosphi=dsqrt{(xi^2-1)(1-eta^2)}cosphi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle r \cos \phi = d\sqrt{(\xi^2-1)(1-\eta^2)}\cos \phi$">|; 

$key = q/;g_-^2-p_phi^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$ \; g_-^2 - p_\phi^2$">|; 

$key = q/displaystylefrac{1}{2m}left({{bf{p}-frac{e}{c}{{bf{A}right)^2=frac{{{bf{p}^2}{2m}-frac{e}{mc}{{bf{p}cdot{{bf{A}+frac{e^2}{2mc^2}{{{bf{A}^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \frac{1}{2m}\left({\bf p}-\frac{e}{c}{\bf A}\right)^2
= \frac{{\bf p}^2}{2m}-\frac{e}{mc}{\bf p}\cdot{\bf A} +
\frac{e^2}{2mc^2}{{\bf A}^2}$">|; 

$key = q/{eqnarraystar}kappa_0&=&hF(y_0,t_0)=hFkappa_1&=&hF(y_0+lambdakappa_0,t_0+muh){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="\begin{eqnarray*}
\kappa_0 &amp; = &amp; h F(y_0,t_0) = h F \\\\
\kappa_1 &amp; = &amp; h F(y_0+\lambda\kappa_0,t_0+\mu h)
\end{eqnarray*}">|; 

$key = q/{eqnarraystar}F_2&=&xip_{xi}+etap_{eta}+phip_{phi}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="\begin{eqnarray*}
F_2 &amp; = &amp; \xi p_{\xi}+\eta p_{\eta}+\phi p_{\phi}
\end{eqnarray*}">|; 

$key = q/(x,y,z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$(x,y,z)$">|; 

$key = q/2pi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$2\pi$">|; 

$key = q/displaystylenablatimes{{bf{A};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle \nabla \times {\bf A}$">|; 

$key = q/kappa_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$\kappa_0$">|; 

$key = q/displaystylexi;eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \xi \; \eta$">|; 

$key = q/y=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$y=1$">|; 

$key = q/{displaymath}frac{g_-^2}{2}-alphageq0quadlongrightarrowquadg_-^2geq2alpha{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="\begin{displaymath}\frac{g_-^2}{2} - \alpha \geq 0 \quad \longrightarrow \quad g_-^2 \geq 2\alpha \end{displaymath}">|; 

$key = q/xi-eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$\xi - \eta$">|; 

$key = q/displaystylexi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle \xi$">|; 

$key = q/(-p_phislashg_+>1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="\(-p_\phi / g_+ &gt; 1\)">|; 

$key = q/k_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$k_1$">|; 

$key = q/rho;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\rho $">|; 

$key = q/{displaymath}-varepsilon_-xi+left(frac{g_-^2}{2}-alpharight){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="\begin{displaymath}-\varepsilon_-\xi+\left(\frac{g_-^2}{2}-\alpha\right) \end{displaymath}">|; 

$key = q/s_2(eta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$s_2(\eta )$">|; 

$key = q/displaystylex;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle x$">|; 

$key = q/displaystyleheta^4+varepsilon_-eta^3-(g_+^2+h+alpha-kappa)eta^2-(varepsilon_-+2p_{phi}g_+)eta+(alpha-p_{phi}^2-kappa);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="503" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\displaystyle h\eta^4+\varepsilon_-\eta^3-(g_+^2+h+\alpha-\kappa)\eta^2-
(\varepsilon_-+2p_{\phi}g_+)\eta+
(\alpha-p_{\phi}^2-\kappa)$">|; 

$key = q/f_{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$f_{2}$">|; 

$key = q/displaystyledot{p_phi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \dot{p_\phi}$">|; 

$key = q/r_1r_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$r_1r_2$">|; 

$key = q/displaystylehxi^2-(xi^2-1)p_{xi}^2-frac{(p_{phi}+g_-xi)^2}{xi^2-1}-varepsilon_+xi+g_-^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle h\xi^2-(\xi^2-1)p_{\xi}^2-\frac{(p_{\phi}+g_-\xi)^2}{\xi^2-1}
-\varepsilon_+\xi+g_-^2$">|; 

$key = q/{displaymath}V_r=-2mdefrac{(g_1^2+g_2^2)(xi^2+eta^2)-2(g_1-g_2)xieta}{d^2(xi^2-eleft(frac{g_1^2}{r_1^2}+frac{g_2^2}{r_2^2}right){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="\begin{displaymath}
V_r = -2mde\frac{(g_1^2+g_2^2)(\xi^2+\eta^2)-2(g_1-g_2)\xi...
...
= -2mde\left(\frac{g_1^2}{r_1^2}+\frac{g_2^2}{r_2^2}\right)
\end{displaymath}">|; 

$key = q/f_2(xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$f_2(\xi )$">|; 

$key = q/{figure}{centering{{epsfxsize{=220pt{epsffile{img5_24.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="261" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="\begin{figure}
\centering
\epsfxsize =220pt \epsffile{img5_24.eps}
\end{figure}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img18_54.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="455" HEIGHT="324" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img18_54.eps}
\end{figure}">|; 

$key = q/s_{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="$s_{2}$">|; 

$key = q/p_z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$p_z$">|; 

$key = q/y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$y$">|; 

$key = q/2md^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$2md^2$">|; 

$key = q/-varepsilon_-slash2h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$-\varepsilon_- / 2h$">|; 

$key = q/quadp_phi^2-g_+^2<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$\quad p_\phi^2 -g_+^2 &lt; 0$">|; 

$key = q/{displaymath}2alpha>p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="\begin{displaymath}2\alpha &gt; p_\phi^2\end{displaymath}">|; 

$key = q/{displaymath}-varepsilon_+>0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="\begin{displaymath}-\varepsilon_+ &gt; 0 \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140q.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="678" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140q.eps}
\end{figure}">|; 

$key = q/+1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$+1$">|; 

$key = q/{eqnarraystar}{{bf{A}&=&frac{(g_1+g_2)(xi^2-1)eta+(g_1-g_2)(1-eta^2)xi}{d^2(xi^2)(1-eta^2)(xi^2-eta^2)}left(y,-x,0right){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="\begin{eqnarray*}
{\bf A} &amp; = &amp; \frac{(g_1+g_2)(\xi^2-1)\eta+(g_1-g_2)(1-\eta^2)\xi}{
d^2(\xi^2-1)(1-\eta^2)(\xi^2-\eta^2)}\left(y,-x,0\right)
\end{eqnarray*}">|; 

$key = q/{displaymath}2alphaleqp_phi^2+{p_phi}^2-g_+^2<p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="\begin{displaymath}
2\alpha \leq p_\phi^2+{p_\phi}^2-g_+^2 &lt; p_\phi^2
\end{displaymath}">|; 

$key = q/Fe_3O_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$Fe_3O_4$">|; 

$key = q/s_1>s_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$s_1 &gt; s_2$">|; 

$key = q/y';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$y'$">|; 

$key = q/displaystylevarepsilon_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\displaystyle \varepsilon_-$">|; 

$key = q/displaystylefrac{e}{c}(g_1+g_2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \frac{e}{c}(g_1+g_2)$">|; 

$key = q/(xi^2-eta^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$(\xi^2-\eta^2)$">|; 

$key = q/displaystyler;mbox{sen}phi=dsqrt{(xi^2-1)(1-eta^2)};mbox{sen}phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle r \; \mbox{sen}\phi = d\sqrt{(\xi^2-1)(1-\eta^2)}\;\mbox{sen}\phi$">|; 

$key = q/displaystylegleft(frac{yz}{r^3rho},-frac{xz}{r^3rho},0right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle g\left(\frac{yz}{r^3\rho},
-\frac{xz}{r^3\rho},0\right)$">|; 

$key = q/displaystylesum_iQ_i(q_j)P_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle \sum_iQ_i(q_j)P_i$">|; 

$key = q/{displaymath}T=frac{p^2}{2m}=frac{p_x^2+p_y^2+p_z^2}{2m}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="\begin{displaymath}
T = \frac{p^2}{2m} = \frac{p_x^2+p_y^2+p_z^2}{2m}
\end{displaymath}">|; 

$key = q/displaystyley_0+alpha_0Fh+alpha_1h(F+lambdahFF_y+muhF_t)+oh^3+cdots;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle y_0+\alpha_0Fh+\alpha_1 h(F+\lambda h F F_y +\mu hF_t)+oh^3+\cdots$">|; 

$key = q/displaystylehxi^4-varepsilon_+xi^3+(g_-^2-h+alpha)xi^2-(varepsilon_++2p_{phi}g_-)xi-(alpha-p_{phi}^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle h\xi^4-\varepsilon_+\xi^3+(g_-^2-h+\alpha)\xi^2
-(\varepsilon_++2p_{\phi}g_-)\xi-(\alpha-p_{\phi}^2)$">|; 

$key = q/{{rm{arctan}(yslashx);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="${\rm arctan}(y/x)$">|; 

$key = q/t=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$t=0$">|; 

$key = q/{eqnarraystar}alpha_1=frac{1}{2}&qquad&lambda=1alpha_0=frac{1}{2}&qquad&mu=1{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="97" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="\begin{eqnarray*}
\alpha_1 = \frac{1}{2} &amp; \qquad &amp; \lambda = 1 \\\\
\alpha_0 = \frac{1}{2} &amp; \qquad &amp; \mu = 1 \\\\
\end{eqnarray*}">|; 

$key = q/displaystylefrac{yxip_{xi}}{d^2(xi^2-eta^2)}-frac{yetap_{eta}}{d^2(xi^2-eta^2)}+frac{xp_{phi}}{(x^2+y^2)};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \frac{y\xi p_{\xi}}{d^2(\xi^2-\eta^2)} -
\frac{y\eta p_{\eta}}{d^2(\xi^2-\eta^2)} +
\frac{x p_{\phi}}{(x^2+y^2)}$">|; 

$key = q/r;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$r$">|; 

$key = q/y_{n+1}-y_{n};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$y_{n+1} - y_{n}$">|; 

$key = q/{displaymath}varepsilon_-^2<4h^2quadrightarrowquadleft(frac{varepsilon_-}{2h}right)^2<1{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="\begin{displaymath}\varepsilon_-^2 &lt; 4h^2 \quad \rightarrow \quad
\left(\frac{\varepsilon_-}{2h}\right)^2 &lt; 1\end{displaymath}">|; 

$key = q/{{bf{F};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="${\bf F}$">|; 

$key = q/r_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$r_2$">|; 

$key = q/-g_{-};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$-g_{-}$">|; 

$key = q/kappa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\kappa$">|; 

$key = q/{displaymath}frac{g_-^2}{2}-alphageqg_-^2-p_phi^2quadrightarrowquadp_phi^2geqalpha+frac{g_+^2}{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="\begin{displaymath}
\frac{g_-^2}{2}-\alpha \geq g_-^2-p_\phi^2 \quad
\rightarrow\quad p_\phi^2 \geq \alpha+\frac{g_+^2}{2}
\end{displaymath}">|; 

$key = q/Y=(50-I)(0.082);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$Y=(50-I)(0.082)$">|; 

$key = q/{figure}{centering{{epsfxsize{=360pt{epsffile{img27_111.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="547" HEIGHT="459" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="\begin{figure}
\centering
\epsfxsize =360pt \epsffile{img27_111.eps}
\end{figure}">|; 

$key = q/displaystyle0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle 0$">|; 

$key = q/frac12;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$\frac 1 2$">|; 

$key = q/displaystylep_y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle p_y$">|; 

$key = q/eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\eta$">|; 

$key = q/10<xileq100;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$10&lt;\xi\leq100$">|; 

$key = q/{P}(xi)slashH;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="${P}(\xi)/H$">|; 

$key = q/x-y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$x-y$">|; 

$key = q/{displaymath}p_{xi}^2=frac{1}{(xi^2-1)^2}left{hxi^4-varepsilon_+xi^3+(g_-^2-h+alp_{phi}g_-)xiright.left.-(alpha-p_{phi}^2)right}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="565" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="\begin{displaymath}
p_{\xi}^2 = \frac{1}{(\xi^2-1)^2}\left\{h\xi^4-\varepsilon...
...p_{\phi}g_-)\xi \right.
\left. -(\alpha-p_{\phi}^2)\right\}
\end{displaymath}">|; 

$key = q/displaystylesqrt{x^2+y^2+(z-d)^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle \sqrt{x^2+y^2+(z-d)^2}$">|; 

$key = q/{displaymath}-1<frac{varepsilon_-}{2h}<1{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="\begin{displaymath}-1 &lt; \frac{\varepsilon_-}{2h} &lt; 1\end{displaymath}">|; 

$key = q/displaystyleF(y,t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\displaystyle F(y,t)$">|; 

$key = q/{displaymath}h=frac{1}{xi^2-eta^2}left{(xi^2-1)p_{xi}^2+(1-eta^2)p_{eta}^2+frac{}+varepsilon_+xi+varepsilon_-eta+kapparight}+V_r{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="681" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="\begin{displaymath}
h = \frac{1}{\xi^2-\eta^2}\left\{(\xi^2-1)p_{\xi}^2+
(1-...
...a^2}+\varepsilon_+\xi+
\varepsilon_-\eta+\kappa\right\}+V_r
\end{displaymath}">|; 

$key = q/P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$P$">|; 

$key = q/1slash{r^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="$1/{r^2}$">|; 

$key = q/1slashh;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$1/h$">|; 

$key = q/{displaymath}A_4xi^4+A_3xi^3+A_2xi^2+A_1xi+A_0=P(xi){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="\begin{displaymath}A_4\xi^4 + A_3\xi^3 + A_2\xi^2 + A_1\xi + A_0 =P(\xi)\end{displaymath}">|; 

$key = q/2d;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$2d$">|; 

$key = q/p_xi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="$p_\xi$">|; 

$key = q/{displaymath}frac{(D+Ex)^2}{x^2-1}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="\begin{displaymath}\frac{(D + Ex)^2}{x^2-1} \end{displaymath}">|; 

$key = q/{displaymath}alpha_0+alpha_1=1quad,quadlambdaalpha_1=frac{1}{2}quad,quadmualpha_1=frac{1}{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="\begin{displaymath}
\alpha_0 + \alpha_1 = 1 \quad , \quad
\lambda \alpha_1 = \frac{1}{2} \quad , \quad
\mu \alpha_1 = \frac{1}{2}
\end{displaymath}">|; 

$key = q/f_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$f_2$">|; 

$key = q/frac{1}{2}(g_+^2-g_-^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\frac{1}{2}
(g_+^2-g_-^2)$">|; 

$key = q/{displaymath}frac{g_1^2}{r_1^2}+frac{g_2^2}{r_2^2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="\begin{displaymath}\frac{g_1^2}{r_1^2}+\frac{g_2^2}{r_2^2}\end{displaymath}">|; 

$key = q/displaystyle{{bf{A};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle {\bf A}$">|; 

$key = q/varepsilon_+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\varepsilon_+$">|; 

$key = q/{{bf{A}_z=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="${\bf A}_z=0$">|; 

$key = q/h;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$h$">|; 

$key = q/-frac{g_-}{-p_phi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$ -\frac{g_-}{-p_\phi }$">|; 

$key = q/displaystyledot{p}_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle \dot{p}_i$">|; 

$key = q/{{bf{A};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="${\bf A}$">|; 

$key = q/{displaymath}alphageqp_phi^2eqno{(3)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="\begin{displaymath}\alpha \geq  p_\phi^2 \eqno{(3)} \end{displaymath}">|; 

$key = q/{{bf{B}_z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="${\bf B}_z$">|; 

$key = q/kappa=frac{1}{2}(g_+^2-g_-^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$\kappa=\frac{1}{2}(g_+^2-g_-^2)$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img8_31.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="280" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img8_31.eps}
\end{figure}">|; 

$key = q/F(y,t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$F(y,t)$">|; 

$key = q/2pislash100=0.0628314;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$2\pi/100 = 0.0628314$">|; 

$key = q/{displaymath}Ax^2+Bx+C{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="\begin{displaymath}Ax^2 + Bx + C \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140d.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="673" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140d.eps}
\end{figure}">|; 

$key = q/:1slashr;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\:1/r$">|; 

$key = q/displaystylefrac{q}{r^3}{{bf{r}=frac{q}{r^2}{hat{{bf{r}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle \frac{q}{r^3} {\bf r}
= \frac{q}{r^2}{\hat{\bf r}}$">|; 

$key = q/X=Jcdot0.5-3.0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$X=J\cdot 0.5-3.0$">|; 

$key = q/{eqnarraystar}{{bf{B}_x&=&-frac{gx}{rho^2}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="\begin{eqnarray*}
{\bf B}_x &amp; = &amp; -\frac{gx}{\rho^2}
\end{eqnarray*}">|; 

$key = q/{{bf{kappa};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="${\bf\kappa}$">|; 

$key = q/{eqnarraystar}p_phi^2&<&g_-^2p_phi^2&<&g_+^2p_phi^2&>&2alphag_+^2&leq&2alpha{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="118" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="\begin{eqnarray*}
p_\phi^2 &amp;&lt;&amp; g_-^2\\\\
p_\phi^2 &amp;&lt;&amp; g_+^2\\\\
p_\phi^2 &amp;&gt;&amp; 2\alpha\\\\
g_+^2 &amp;\leq&amp; 2\alpha
\end{eqnarray*}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img29_137b.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="654" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img29_137b.eps}
\end{figure}">|; 

$key = q/(-1,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$(-1,1)$">|; 

$key = q/k_{3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$k_{3}$">|; 

$key = q/{displaymath}xi^2h-(xi^2-1)p_{xi}^2-frac{(p_{phi}+g_-xi)^2}{xi^2-1}-varepsilon_+_{phi}+g_+eta)^2}{1-eta^2}-varepsilon_-eta+g_+^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="601" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="\begin{displaymath}\xi^2h-(\xi^2-1)p_{\xi}^2-\frac{(p_{\phi}+g_-\xi)^2}{\xi^2-1}...
...frac{(p_{\phi}+g_+\eta)^2}{1-\eta^2}
-\varepsilon_-\eta+g_+^2\end{displaymath}">|; 

$key = q/{eqnarraystar}V&=&frac{Z_1^2}{r_1}+frac{Z_2^2}{r_2}-left(frac{g_1^2}{r_1^2}+frac(p_phi+g_+eta)^2}{(xi^2-eta^2)(1-eta^2)}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="541" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="\begin{eqnarray*}
V &amp; = &amp; \frac{Z_1^2}{r_1} + \frac{Z_2^2}{r_2} -
\left(\fra...
...} +
\frac{(p_\phi + g_+\eta)^2}{(\xi^2 - \eta^2)(1 - \eta^2)}
\end{eqnarray*}">|; 

$key = q/-varepsilon_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$-\varepsilon_-$">|; 

$key = q/displaystyle{{bf{A}_0+nablaPhi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle {\bf A}_0 + \nabla\Phi$">|; 

$key = q/{figure}{centering{{epsfxsize{=320pt{epsffile{img17_50.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="498" HEIGHT="215" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="\begin{figure}
\centering
\epsfxsize =320pt \epsffile{img17_50.eps}
\end{figure}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img25_100.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="307" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img25_100.eps}
\end{figure}">|; 

$key = q/{displaymath}y_{n+1}=y_n+frac{1}{6}(kappa_0+2kappa_1+2kappa_2+kappa_3)+o(h^4){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="\begin{displaymath}
y_{n+1} = y_n + \frac{1}{6}(\kappa_0+2\kappa_1+2\kappa_2+\kappa_3)
+ o(h^4)
\end{displaymath}">|; 

$key = q/k_{0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$k_{0}$">|; 

$key = q/frac{partialh}{partialx_i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\frac{\partial h}
{\partial x_i}$">|; 

$key = q/displaystyleleft(frac{gx}{rho^2},frac{-gy}{rho^2},frac{-gz}{rho^2}right)=-frac{g}{rho^2}{{bf{r};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \left(\frac{gx}{\rho^2},\frac{-gy}{\rho^2},
\frac{-gz}{\rho^2}\right)
= -\frac{g}{\rho^2} {\bf r}$">|; 

$key = q/{displaymath}(((a_4xi+a_3)xi+a_2)xi+a_1)xi+a_0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="\begin{displaymath}(((a_4\xi + a_3)\xi + a_2)\xi + a_1)\xi + a_0\end{displaymath}">|; 

$key = q/(g_-^2>p_phi^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="\(g_-^2 &gt; p_\phi^2\)">|; 

$key = q/{eqnarraystar}Fhalpha_0+Fhalpha_1&approx&hFh^2(lambdaalpha_1FF_y+alpha_1muF_t)&approx&(FF_y+F_t)h^2{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="\begin{eqnarray*}
Fh\alpha_0+Fh\alpha_1 &amp; \approx &amp; hF \\\\
h^2(\lambda \alpha_1FF_y+\alpha_1\mu F_t) &amp; \approx &amp; (FF_y+F_t)h^2
\end{eqnarray*}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140p.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="688" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140p.eps}
\end{figure}">|; 

$key = q/displaystyleheta^2+(1-eta^2)p_{eta}^2+frac{(p_{phi}+g_+eta)^2}{1-eta^2}+varepsilon_-eta+kappa;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle h\eta^2+(1-\eta^2)p_{\eta}^2+\frac{(p_{\phi}+g_+\eta)^2}{1-\eta^2}
+\varepsilon_-\eta +\kappa$">|; 

$key = q/2varepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$2\varepsilon$">|; 

$key = q/alpha_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$\alpha_1$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img3_21.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="311" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img3_21.eps}
\end{figure}">|; 

$key = q/displaystylesqrt{x^2+y^2+(z+d)^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle \sqrt{x^2+y^2+(z+d)^2}$">|; 

$key = q/X_{0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$X_{0}$">|; 

$key = q/textstyle=;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\textstyle =$">|; 

$key = q/{figure}{centering{{epsfxsize{=400pt{epsffile{img12_36.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="618" HEIGHT="460" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="\begin{figure}
\centering
\epsfxsize =400pt \epsffile{img12_36.eps}
\end{figure}">|; 

$key = q/displaystylefrac{r_1-r_2}{2d};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle \frac{r_1-r_2}{2d}$">|; 

$key = q/{figure}{centering{{epsfxsize{=310pt{epsffile{img21_61.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="486" HEIGHT="270" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="\begin{figure}
\centering
\epsfxsize =310pt \epsffile{img21_61.eps}
\end{figure}">|; 

$key = q/alpha;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\alpha$">|; 

$key = q/displaystylefrac{xxip_{xi}}{d^2(xi^2-eta^2)}-frac{xetap_{eta}}{d^2(xi^2-eta^2)}-frac{yp_{phi}}{(x^2+y^2)};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \frac{x\xi p_{\xi}}{d^2(\xi^2-\eta^2)} -
\frac{x\eta p_{\eta}}{d^2(\xi^2-\eta^2)} -
\frac{y p_{\phi}}{(x^2+y^2)}$">|; 

$key = q/theta=pi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\theta=\pi$">|; 

$key = q/r_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$r_1$">|; 

$key = q/p_y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$p_y$">|; 

$key = q/displaystylefrac{partialH}{partialp_i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \frac{\partial H}{\partial p_i}$">|; 

$key = q/F;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$F$">|; 

$key = q/displaystyleR(xi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle R(\xi)$">|; 

$key = q/DZslashh;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$DZ/h$">|; 

$key = q/k;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$k$">|; 

$key = q/displaystyledotphi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle \dot\phi$">|; 

$key = q/displaystyle-frac{partialH}{partialq_i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle -\frac{\partial H}{\partial q_i}$">|; 

$key = q/t_0=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$t_0=0$">|; 

$key = q/varepsilon^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$\varepsilon^2$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140a.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="653" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140a.eps}
\end{figure}">|; 

$key = q/{displaymath}frac{g_-^2}{2}-p_phi^2leq-alphaleq-p_phi^2quadlongrightarrowquadfralphaleq0quadlongrightarrowquadfrac{g_-^2}{2}leq0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="\begin{displaymath}\frac{g_-^2}{2} - p_\phi^2 \leq -\alpha \leq
- p_\phi^2 \qu...
...ha \leq 0
\quad \longrightarrow \quad \frac{g_-^2}{2} \leq 0 \end{displaymath}">|; 

$key = q/displaystylep_x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle p_x$">|; 

$key = q/{eqnarraystar}p^2&=&p_r^2+frac{p_theta^2}{r^2}+frac{p_phi^2}{r^2{mbox{sen}^2theta}}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="\begin{eqnarray*}
p^2 &amp; = &amp;
p_r^2 + \frac{p_\theta^2}{r^2} + \frac{p_\phi^2}{r^2{\mbox{sen}^2\theta}}
\end{eqnarray*}">|; 

$key = q/2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$2$">|; 

$key = q/(y_0+lambday^{prime},t_0+muh);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$(y_0+\lambda y^{\prime}, t_0+\mu h)$">|; 

$key = q/{displaymath}-alphaleq-p_phi^{2}qquadrightarrowqquadalphageqp_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="\begin{displaymath}
-\alpha \leq -p_\phi^{2} \qquad \rightarrow \qquad
\alpha \geq p_\phi^2
\end{displaymath}">|; 

$key = q/{displaymath}left.array{{lcr}p_phi^2>g_-^2p_phi^2<g_+^2array{right}quadg_-^2<p_phi^2<g_+^2quadrightarrowquadg_-^2<g_+^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="\begin{displaymath}\left. \begin{array}{lcr}
p_\phi^2 &gt; g_-^2 \\\\
p_\phi^2 &lt;...
...-^2 &lt; p_\phi^2 &lt; g_+^2 \quad \rightarrow \quad
g_-^2 &lt; g_+^2
\end{displaymath}">|; 

$key = q/(y_0,t_0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="$(y_0,t_0)$">|; 

$key = q/1slash(xi^2-eta^2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$1/(\xi^2-\eta^2)$">|; 

$key = q/{eqnarraystar}V_r&=&frac{g_1^2}{r_1^2}+frac{g_2^2}{r_2^2}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="\begin{eqnarray*}
V_r &amp;=&amp; \frac{g_1^2}{r_1^2} + \frac{g_2^2}{r_2^2}
\end{eqnarray*}">|; 

$key = q/-1slashr;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$-1/r$">|; 

$key = q/displaystyledot{q}_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \dot{q}_i$">|; 

$key = q/{figure}{centering{{epsfxsize{=360pt{epsffile{img13_40.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="549" HEIGHT="260" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="\begin{figure}
\centering
\epsfxsize =360pt \epsffile{img13_40.eps}
\end{figure}">|; 

$key = q/V;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$V$">|; 

$key = q/{{bf{A}_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="${\bf A}_1$">|; 

$key = q/{figure}{centering{{epsfxsize{=400pt{epsffile{img11_35.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="636" HEIGHT="655" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="\begin{figure}\centering
\epsfxsize =400pt \epsffile{img11_35.eps}
\end{figure}">|; 

$key = q/frac{a}{r_1}+frac{b}{r_2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\frac{a}{r_1}+\frac{b}{r_2}$">|; 

$key = q/Phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\Phi$">|; 

$key = q/20:12.13;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$20:12.13$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140i.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="615" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140i.eps}
\end{figure}">|; 

$key = q/{eqnarraystar}y&=&y_0+hy^{prime}_0+frac{h^2}{2!}y^{primeprime}_0+frac{h^3}{3!}y^frac{h^2}{2!}-frac{h^3}{3!}+cdots=e^{-h}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="524" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="\begin{eqnarray*}
y &amp; = &amp; y_0+hy^{\prime}_0 +
\frac{h^2}{2!}y^{\prime\prime}...
...
= 1 - h + \frac{h^2}{2!} - \frac{h^3}{3!} + \cdots
= e^{-h}
\end{eqnarray*}">|; 

$key = q/displaystyley(t_0+h);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle y(t_0+h)$">|; 

$key = q/{displaymath}left(xi+frac{varepsilon_+}{2h}right)^2=frac{1}{h}left[f_1+left(alph^2+frac{varepsilon_+^2}{4h}right)right]eqno{(5)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="\begin{displaymath}
\left(\xi+\frac{\varepsilon_+}{2h}\right)^2 = \frac{1}{h}
...
...a-g_-^2+\frac{\varepsilon_+^2}{4h}\right)\right]
\eqno{(5)}
\end{displaymath}">|; 

$key = q/displaystyle2mde(z_1-z_2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle 2mde(z_1-z_2)$">|; 

$key = q/q_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$q_i$">|; 

$key = q/cdotk_{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$\cdot k_{2}$">|; 

$key = q/{eqnarraystar}F(y,t)&=&m(t)cdoty+g(t){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="\begin{eqnarray*}
F(y,t) &amp; = &amp; m(t)\cdot y +g(t)
\end{eqnarray*}">|; 

$key = q/displaystyler_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle r_1$">|; 

$key = q/r=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$r = 0$">|; 

$key = q/{displaymath}g_-^2geq2alpha>p_phi^2{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="\begin{displaymath}g_-^2 \geq 2\alpha &gt; p_\phi^2 \end{displaymath}">|; 

$key = q/displaystyle-frac{1}{xi^2-eta^2}left{2xileft[p_{xi}^2-h-frac{(p_{phi}+g_-xi)^2}{2}right]+frac{2g_-(p_{phi}+g_-xi)}{xi^2-1}+varepsilon_+right};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="479" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle -\frac{1}{\xi^2-\eta^2}\left\{2\xi\left[
p_{\xi}^2-h-\frac{(p_{\p...
...xi^2-1)^2}\right]
+\frac{2g_-(p_{\phi}+g_-\xi)}{\xi^2-1}
+\varepsilon_+\right\}$">|; 

$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$x$">|; 

$key = q/P_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$P_i$">|; 

$key = q/{eqnarraystar}hleft(xi-frac{varepsilon_+}{2h}right)^2&=&f_1+(alpha-g_-^2)+frac{varepsilon_+^2}{4h}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="\begin{eqnarray*}
h \left(\xi-\frac{\varepsilon_+}{2h}\right)^2 &amp;=&amp;
f_1+(\alpha-g_-^2)+\frac{\varepsilon_+^2}{4h}
\end{eqnarray*}">|; 

$key = q/{eqnarraystar}alpha_1=cqquad&&qquadlambda=frac{1}{2c}alpha_0=1-c&&qquadmu=frac{1}{2c}{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="97" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="\begin{eqnarray*}
\alpha_1 = c \qquad &amp; &amp; \qquad \lambda = \frac{1}{2c} \\\\
\alpha_0 = 1 - c &amp; &amp; \qquad \mu = \frac{1}{2c}\\\\
\end{eqnarray*}">|; 

$key = q/S_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$S_2$">|; 

$key = q/displaystyleR(eta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle R(\eta)$">|; 

$key = q/-pileqphileqpi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$-\pi \leq \phi \leq
\pi$">|; 

$key = q/{eqnarraystar}y^{prime}&=&F(y,t)y^{primeprime}&=&frac{d}{dt}F(y,t)=frac{partialFeprimeprime}&=&frac{d}{dt}(F_ycdotF+F_t){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="142" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="\begin{eqnarray*}
y^{\prime} &amp; = &amp; F(y,t) \\\\
y^{\prime\prime} &amp; = &amp; \frac{d...
...
y^{\prime\prime\prime} &amp; = &amp; \frac{d}{dt}(F_y\cdot F + F_t)
\end{eqnarray*}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img30_137c.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="638" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img30_137c.eps}
\end{figure}">|; 

$key = q/23616;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$23616$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140g.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="638" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140g.eps}
\end{figure}">|; 

$key = q/A_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$A_4$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img28_137a.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="724" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img28_137a.eps}
\end{figure}">|; 

$key = q/p_{phi};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$p_{\phi}$">|; 

$key = q/varepsilon^3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$\varepsilon^3$">|; 

$key = q/y(t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$y(t)$">|; 

$key = q/(-p_phislashg_+<1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="\(-p_\phi / g_+ &lt; 1\)">|; 

$key = q/{displaymath}frac{varepsilon_+pmsqrt{varepsilon_+^2+4halpha}}{2h}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="\begin{displaymath}
\frac{\varepsilon_+ \pm \sqrt{\varepsilon_+^2+4h\alpha}}{2h}
\end{displaymath}">|; 

$key = q/displaystyleg_-;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle g_-$">|; 

$key = q/{{bf{y};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="${\bf y}$">|; 

$key = q/-p_phislashg_->1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$-p_\phi / g_- &gt; 1$">|; 

$key = q/displaystylefrac{dy}{dt};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\displaystyle \frac{dy}{dt}$">|; 

$key = q/{figure}{centering{{epsfxsize{=400pt{epsffile{img10_33.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="627" HEIGHT="422" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="\begin{figure}
\centering
\epsfxsize =400pt \epsffile{img10_33.eps}
\end{figure}">|; 

$key = q/{eqnarraystar}{{bf{y}^{prime}&=&{{bf{F}({{bf{y},t){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="\begin{eqnarray*}
{\bf y}^{\prime} &amp; = &amp; {\bf F}({\bf y},t)
\end{eqnarray*}">|; 

$key = q/displaystyley(t_0)+hcdotF(y,t);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle y(t_0) + h\cdot F(y,t)$">|; 

$key = q/displaystyle{{bf{B};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle {\bf B}$">|; 

$key = q/s_1(eta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$s_1(\eta )$">|; 

$key = q/-g_+slashp_phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="$-g_+ / p_\phi$">|; 

$key = q/displaystylefrac{r_1^2+r_2^2}{2d^2}=frac{x^2+y^2+z^2+d^2}{d^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle \frac{r_1^2+r_2^2}{2d^2} = \frac{x^2+y^2+z^2+d^2}{d^2}$">|; 

$key = q/B_4longrightarrowB(1),quadB_3longrightarrowB(2),quadB_2longrightarrowB(3),quadB_1longrightarrowB(4),quadB_0longrightarrowB(5);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="576" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$B_4 \longrightarrow B(1) , \quad B_3 \longrightarrow B(2) ,
\quad B_2 \longrightarrow B(3), \quad B_1 \longrightarrow B(4) ,
\quad B_0 \longrightarrow B(5)$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140b.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="635" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140b.eps}
\end{figure}">|; 

$key = q/{eqnarraystar}frac{e}{c}{{bf{p}cdot{{bf{A}&=&-frac{p_{phi}}{d^2}left[frac{(g_1+gxi}{(xi^2-1)(1-eta^2)(xi^2-eta^2)}right]{eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="\begin{eqnarray*}
\frac{e}{c}{\bf p}\cdot{\bf A} &amp; = &amp;
-\frac{p_{\phi}}{d^2}...
..._1-g_2)(1-\eta^2)\xi}{(\xi^2-1)(1-\eta^2)(\xi^2-\eta^2)}\right]
\end{eqnarray*}">|; 

$key = q/F^{primeprime};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$F^{\prime\prime}$">|; 

$key = q/displaystyler^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle r^2$">|; 

$key = q/19624;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$19624$">|; 

$key = q/{displaymath}alpha;geq;p_phi^2;>;frac{g_-^2}{2};geq;alphaeqno{(4)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="\begin{displaymath}\alpha \; \geq \; p_\phi^2 \;
&gt; \; \frac{g_-^2}{2} \; \geq \; \alpha \eqno{(4)} \end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=210pt{epsffile{img15_46.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="393" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="\begin{figure}
\centering
\epsfxsize =210pt \epsffile{img15_46.eps}
\end{figure}">|; 

$key = q/{displaymath}frac{g_+^{2}}{2}-alphaleqp_phi^{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="\begin{displaymath}\frac{g_+^{2}}{2} - \alpha \leq p_\phi^{2}\end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=240pt{epsffile{img1_4.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="193" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="\begin{figure}
\centering
\epsfxsize =240pt \epsffile{img1_4.eps}
\end{figure}">|; 

$key = q/displaystyleeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle \eta$">|; 

$key = q/Ax^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="$Ax^2$">|; 

$key = q/{displaymath}left.array{{ccc}hxi^2-(xi^2-1)p_xi^2-frac{(p_phi+g_-xi)^2}{xi^2-1}-ta+frac{g_+^2}{2}-alpha&=&0array{right}eqno{(1)}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="479" HEIGHT="89" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="\begin{displaymath}
\left.
\begin{array}{ccc}
h\xi^2 -(\xi^2-1)p_\xi^2-\frac...
...{g_+^2}{2}-\alpha &amp; = &amp; 0
\end{array}
\right\} \eqno{(1)}
\end{displaymath}">|; 

$key = q/(frac{g_-^2}{2}-p_phi^2leq-alphaleqfrac{g_-^2}{2});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="\(\frac{g_-^2}{2} - p_\phi^2 \leq -\alpha \leq
\frac{g_-^2}{2}\)">|; 

$key = q/displaystyleF_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle F_2$">|; 

$key = q/p_{eta}^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$p_{\eta}^2$">|; 

$key = q/{displaymath}frac{g_+^2}{2}-alphaleq0quadlongrightarrowquadg_+^2leq2alpha{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="\begin{displaymath}\frac{g_+^2}{2}-\alpha \leq 0 \quad \longrightarrow \quad g_+^2 \leq 2\alpha \end{displaymath}">|; 

$key = q/{displaymath}2mdT=frac{1}{xi^2-eta^2}left{(xi^2-1)p_{xi}^2+(1-eta^2)p_{eta}^2+le1}{xi^2-1}+frac{1}{1-eta^2}right)p_{phi}^2right}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="513" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="\begin{displaymath}
2 m d T = \frac{1}{\xi^2-\eta^2}
\left\{(\xi^2-1) p_{\xi...
...1}{\xi^2-1} +\frac{1}{ 1-\eta^2 } \right) p_{\phi}^2 \right\}
\end{displaymath}">|; 

$key = q/{figure}{centering{{epsfxsize{=240pt{epsffile{img22_75.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="21" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="\begin{figure}
\centering
\epsfxsize =240pt \epsffile{img22_75.eps}
\end{figure}">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140c.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="616" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140c.eps}
\end{figure}">|; 

$key = q/g_-^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$g_-^2$">|; 

$key = q/{figure}{centering{{epsfxsize{=300pt{epsffile{img34_140o.eps}{{{{figure};LFS=11;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="631" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="\begin{figure}
\centering
\epsfxsize =300pt \epsffile{img34_140o.eps}
\end{figure}">|; 

$key = q/displaystylehxi^2-(xi^2-1)p_{xi}^2-frac{(p_{phi}+g_-xi)^2}{xi^2-1}-varepsilon_+xi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle h\xi^2-(\xi^2-1)p_{\xi}^2-\frac{(p_{\phi}+g_-\xi)^2}{\xi^2-1}
-\varepsilon_+\xi$">|; 

$key = q/{displaymath}z_1=aqquadg_1=bqquadz_2=0qquadg_2=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="\begin{displaymath}
z_1 = a \qquad
g_1 = b \qquad
z_2 = 0 \qquad
g_2 = 0
\end{displaymath}">|; 

$key = q/displaystylefrac{2p_{eta}(1-eta^2)}{xi^2-eta^2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \frac{2p_{\eta}(1-\eta^2)}{\xi^2-\eta^2}$">|; 

$key = q/{eqnarraystar}kappa_0&=&hF(y_n,t_n)kappa_1&=&hF(y_n+lambdakappa_0,t_n+muh){eqnarraystar};MSF=1.6;LFS=11;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="\begin{eqnarray*}
\kappa_0 &amp; = &amp; h F(y_n,t_n) \\\\
\kappa_1 &amp; = &amp; h F(y_n+\lambda\kappa_0,t_n+\mu h)
\end{eqnarray*}">|; 

$key = q/displaystylefrac{r_1+r_2}{2d};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle \frac{r_1+r_2}{2d}$">|; 

$key = q/p_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$p_i$">|; 

$key = q/displaystyley_0+hF+frac{h^2}{2}(FF_y+F_t)+oh^3+cdots;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle y_0+hF+\frac{h^2}{2}(FF_y+F_t)+oh^3+\cdots$">|; 

1;

