# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/displaystylefrac{2u_{0}}{a}sintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$\displaystyle \frac{2u_{0}}{a}\sin \theta,$">|; 

$key = q/2.94times10^{4}slashg;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$2.94\times 10^{4}/g$">|; 

$key = q/displaystyle-u_{0}sinlambdasinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle - u_{0}\sin \lambda \sin \alpha$">|; 

$key = q/displaystyleDP{zeta}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\displaystyle \DP{\zeta }{t}$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$T$">|; 

$key = q/displaystyle6.37122times10^{6}mbox{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle 6.37122 \times 10^{6} \mbox{ m}$">|; 

$key = q/nabla^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\nabla ^{2}$">|; 

$key = q/displaystylel_{infty}(Dvect{v});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle l_{\infty}(\Dvect{v})$">|; 

$key = q/displaystylenabla^{2}A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle \nabla^{2} A$">|; 

$key = q/h_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$h_{s}$">|; 

$key = q/displaystyle-K_{m}left[(-1)^{N_{d}slash2}nabla^{N_{d}}-left(frac{2}{a^{2}}right)^{N_{d}slash2}right]D+F_{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}}
- \left(\frac{2}{a^{2}}\right)^{N_{d}/2}\right]D + F_{D}$">|; 

$key = q/Deltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\Delta t$">|; 

$key = q/displaystylel_{1}(Dvect{v});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle l_{1}(\Dvect{v})$">|; 

$key = q/displaystyleA(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\displaystyle A(\phi)$">|; 

$key = q/chi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\chi$">|; 

$key = q/displaystylezeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle \zeta$">|; 

$key = q/{displaymath}r=aarccos(sinphi_{c}sinphi+cosphi_{c}cosphicos(lambda-lambda_{c})){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="\begin{displaymath}
r = a \arccos (\sin \phi _{c}\sin \phi +
\cos \phi _{c}\cos \phi \cos (\lambda -\lambda _{c}))
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}DP{(F_{v}cosphi)}{lambda}-frac{1}{a}DP{(F_{u}cosphi)}{mu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle \frac{1}{a(1-\mu ^{2})}\DP{(F_{v}\cos \phi)}{\lambda} - \frac{1}{a}\DP{(F_{u}\cos \phi)}{\mu},$">|; 

$key = q/displaystyle2omegasinphi-Ksinphicos^{R}phi(R^{2}+3R+2)cosRlambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle 2\omega\sin \phi - K\sin \phi \cos ^{R}\phi (R^{2}+3R+2)\cos R\lambda,$">|; 

$key = q/sim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\sim$">|; 

$key = q/displaystyle7.292times10^{-5}mbox{sec}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle 7.292 \times 10^{-5} \mbox{ sec}^{-1}$">|; 

$key = q/displaystylepsi_{0}expleft(-sigmafrac{1-C}{1+C}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle \psi _{0}\exp \left(-\sigma \frac{1-C}{1+C}\right),$">|; 

$key = q/displaystylesinphi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle \sin \phi '$">|; 

$key = q/(lambda,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$(\lambda, \phi)$">|; 

$key = q/displaystyle-au_{0}(sinphicosalpha-coslambdacosphisinalpha),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle - a u_{0}
(\sin \phi \cos \alpha - \cos \lambda \cos \phi \sin \alpha),$">|; 

$key = q/displaystyle0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle 0,$">|; 

$key = q/h(lambda,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$h(\lambda, \phi)$">|; 

$key = q/{displaymath}f=2Omega(-coslambdacosphisinalpha+sinphicosalpha).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="\begin{displaymath}
f = 2\Omega(-\cos \lambda \cos \phi \sin \alpha + \sin \phi \cos \alpha).
\end{displaymath}">|; 

$key = q/displaystyleDP{D}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\displaystyle \DP{D}{t}$">|; 

$key = q/displaystyle+frac{1}{4}K^{2}cos^{2R}[(R+1)cos^{2}phi+(2R^{2}-R-2)-2R^{2}cos^{-2}phi],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="479" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle + \frac{1}{4}K^{2}\cos ^{2R}[(R+1)\cos^{2}\phi
+ (2R^{2} - R - 2) - 2R^{2}cos^{-2}\phi],$">|; 

$key = q/displaystylenabla^{2}psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \nabla ^{2} \psi,$">|; 

$key = q/v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$v$">|; 

$key = q/times10^{15};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\times 10^{15}$">|; 

$key = q/times10^{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\times 10^{12}$">|; 

$key = q/displaystyle-u_{0}asintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$\displaystyle -u_{0}a\sin \theta,$">|; 

$key = q/K_{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$K_{h}$">|; 

$key = q/0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$0$">|; 

$key = q/displaystyleu_{0}cosphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$\displaystyle u_{0}\cos \phi,$">|; 

$key = q/displaystylefrac{2(Omega+omega)K}{(R+1)(R+2)}cos^{R}phi[(R^{2}+2R+2)-(R+1)^{2}cos^{2}phi],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle \frac{2(\Omega + \omega)K}{(R+1)(R+2)}\cos ^{R}\phi
[(R^{2} + 2R +2) - (R + 1)^{2}\cos ^{2}\phi],$">|; 

$key = q/displaystyle9.80616mbox{msec}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle 9.80616 \mbox{ msec}^{-2}$">|; 

$key = q/mathop{mathgroupsymoperatorscos}nolimits;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\mathop {\mathgroup \symoperators cos}\nolimits $">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$M$">|; 

$key = q/displaystylev;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle v$">|; 

$key = q/h_{s}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$h_{s}=0$">|; 

$key = q/displaystyle-0.03frac{gh_{0}}{2Omegasin(pislash4)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle -0.03\frac{gh_{0}}{2\Omega \sin (\pi/4)},$">|; 

$key = q/u,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$u, v$">|; 

$key = q/displaystyle0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle 0$">|; 

$key = q/displaystylefrac{sqrt{I[(u(lambda,phi)-u_{T}(lambda,Phi))^{2}+(v(lambda,phi)-v_{{2}]}}{sqrt{I[u_{T}(lambda,Phi)^{2}+v_{T}(lambda,Phi)^{2}]}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="81" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle \frac{\sqrt{I[
(u(\lambda, \phi) - u_{T}(\lambda, \Phi))^{2}+
(v(...
... \Phi))^{2}]}}
{\sqrt{I[u_{T}(\lambda, \Phi)^{2} + v_{T}(\lambda, \Phi)^{2}]}},$">|; 

$key = q/psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\psi $">|; 

$key = q/{displaymath}x=x_{e}frac{phi'-phi_{b}}{phi_{e}-phi_{b}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="\begin{displaymath}
x = x_{e}\frac{\phi ' - \phi _{b}}{\phi _{e}-\phi_{b}}
\end{displaymath}">|; 

$key = q/displaystylev';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle v'$">|; 

$key = q/I>3M+1,J>3Mslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$I&gt;3M+1,
J&gt;3M/2$">|; 

$key = q/displaystyle-frac{1-mu^{2}}{a}DP{psi}{mu}+frac{1}{asqrt{1-mu^{2}}}DP{chi}{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle -\frac{1-\mu^ {2}}{a}\DP{\psi}{\mu}
+\frac{1}{a\sqrt{1-\mu ^{2}}}\DP{\chi}{\lambda},$">|; 

$key = q/displaystyleF_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle F_{v}$">|; 

$key = q/displaystylel_{2}(h);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle l_{2}(h)$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$A$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\lambda$">|; 

$key = q/pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$pi/2$">|; 

$key = q/displaystyleC(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle C(\phi)$">|; 

$key = q/h';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$h'$">|; 

$key = q/displaystyletilde{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle \tilde{h}$">|; 

$key = q/displaystyleh_{0}-frac{a}{g}int_{-pislash2}^{phi'}left(2Omegasintau+frac{u'(tau)tantau}{a}right)u'(tau)Ddtau.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle h_{0} - \frac{a}{g}\int _{-\pi/2}^{\phi '}
\left(2\Omega \sin \tau + \frac{u'(\tau)\tan \tau}{a}\right)
u'(\tau)\Dd \tau.$">|; 

$key = q/1000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$1000$">|; 

$key = q/displaystyleOmega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle \Omega$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{(f+zeta)U}{lambda}-frac{1}{a}DP{(f+zeta)V}{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle -\frac{1}{a(1-\mu ^{2})}
\DP{(f+\zeta)U}{\lambda}
- \frac{1}{a}\DP{(f+\zeta)V}{\mu}$">|; 

$key = q/displaystylefrac{I[sqrt{(u(lambda,phi)-u_{T}(lambda,Phi))^{2}+(v(lambda,phi)-v_{{2}}]}{I[sqrt{u_{T}(lambda,Phi)^{2}+v_{T}(lambda,Phi)^{2}}]},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="81" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle \frac{I[
\sqrt{(u(\lambda, \phi) - u_{T}(\lambda, \Phi))^{2}+
(v(...
... \Phi))^{2}}]}
{I[\sqrt{u_{T}(\lambda, \Phi)^{2} + v_{T}(\lambda, \Phi)^{2}}]},$">|; 

$key = q/displaystylel_{2}(Dvect{v});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle l_{2}(\Dvect{v})$">|; 

$key = q/lambda'_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\lambda '_{p}$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{(hU)}{lambda}-frac{1}{a}DP{(hV)}{mu}-(-1)^{N_{d}slash2}K_{h}nabla^{N_{d}}h+F_{h}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu ^{2})}\DP{(hU)}{\lambda}
- \frac{1}{a}\DP{(hV)}{\mu}
- (-1)^{N_{d}/2}K_{h}\nabla ^{N_{d}}h+F_{h}.$">|; 

$key = q/displaystyleoverline{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle \overline{h}$">|; 

$key = q/displaystyleh_{0}-frac{a}{g}int_{-pislash2}^{phi}left(2Omegasintau+frac{overline{u}(tau)tantau}{a}right)overline{u}(tau)Ddtau,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle h_{0} - \frac{a}{g}\int _{-\pi/2}^{\phi}
\left(2\Omega \sin \tau + \frac{\overline{u}(\tau)\tan \tau}{a}\right)
\overline{u}(\tau)\Dd \tau,$">|; 

$key = q/lambda';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\lambda '$">|; 

$key = q/displaystyleucoslambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle u\cos \lambda$">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\sigma $">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$u$">|; 

$key = q/displaystylefrac{U^{2}+V^{2}}{2(1-mu^{2})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle \frac{U^{2}+V^{2}}{2(1-\mu ^{2})},$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$R$">|; 

$key = q/7.848times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$7.848\times 10^{-6}$">|; 

$key = q/{}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="${}^{-1}$">|; 

$key = q/displaystylepsi_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle \psi _{0}$">|; 

$key = q/displaystylefrac{1}{acosphi}DP{overline{psi}}{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle \frac{1}{a\cos \phi}\DP{\overline{\psi}}{\lambda},$">|; 

$key = q/K_{m},K_{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$K_{m}, K_{h}$">|; 

$key = q/displaystyleu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle u$">|; 

$key = q/equivsinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\equiv \sin \phi$">|; 

$key = q/{displaymath}f=2Omega(-coslambdacosphisinalpha+sinphicosalpha){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="\begin{displaymath}
f = 2\Omega(-\cos \lambda \cos \phi \sin \alpha + \sin \phi \cos \alpha)
\end{displaymath}">|; 

$key = q/{}^{4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="${}^{4}$">|; 

$key = q/displaystyle-K_{m}left[(-1)^{N_{d}slash2}nabla^{N_{d}}-left(frac{2}{a^{2}}right)^{N_{d}}right]zeta+F_{zeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="317" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}}
- \left(\frac{2}{a^{2}}\right)^{N_{d}}\right]\zeta + F_{\zeta}$">|; 

$key = q/2piaslash(12;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$2\pi a/(12$">|; 

$key = q/displaystylefrac{I[|h(lambda,phi)-h_{T}(lambda,Phi)|]}{I[|h_{T}(lambda,Phi)|]},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle \frac{I[\vert h(\lambda, \phi) - h_{T}(\lambda, \Phi)\vert]}
{I[\vert h_{T}(\lambda, \Phi)\vert]},$">|; 

$key = q/2Omegasinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$2\Omega \sin \phi$">|; 

$key = q/displaystylel_{infty}(h);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle l_{\infty}(h)$">|; 

$key = q/aslash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$a/3$">|; 

$key = q/displaystylefrac{1}{asqrt{1-mu^{2}}}DP{psi}{lambda}+frac{1-mu^{2}}{a}DP{chi}{mu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \frac{1}{a\sqrt{1-\mu ^{2}}}\DP{\psi}{\lambda}
+ \frac{1-\mu^{2}}{a}\DP{\chi}{\mu},$">|; 

$key = q/displaystylesinlambda'costheta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle \sin \lambda '\cos \theta '$">|; 

$key = q/displaystylevcosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle v\cos \phi$">|; 

$key = q/displaystyleoverline{h}+frac{f}{g}overline{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$\displaystyle \overline{h} + \frac{f}{g}\overline{\psi}$">|; 

$key = q/tilde{u},tilde{v},tilde{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\tilde{u}, \tilde{v}, \tilde{h}$">|; 

$key = q/I,J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$I,J$">|; 

$key = q/displaystylesinphicosalpha-cosalphacoslambdasinalpha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \sin \phi \cos \alpha - \cos \alpha \cos \lambda \sin \alpha,$">|; 

$key = q/times10^{16};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\times 10^{16}$">|; 

$key = q/displaystylefrac{omega}{2}(2Omega+omega)cos^{2}phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$\displaystyle \frac{\omega}{2}(2\Omega + \omega)\cos^{2} \phi$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$t$">|; 

$key = q/displaystylefrac{sqrt{I[(h(lambda,phi)-h_{T}(lambda,Phi))^{2}]}}{sqrt{I[h_{T}(lambda,Phi)^{2}]}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="81" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\displaystyle \frac{\sqrt{I[(h(\lambda, \phi) - h_{T}(\lambda, \Phi))^{2}]}}
{\sqrt{I[h_{T}(\lambda, \Phi)^{2}]}},$">|; 

$key = q/u_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$u_{0}$">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}DP{(f+zeta)V}{lambda}-frac{1}{a}DP{(f+zeta)U}{mu}-Dlaplaleft[g(h+h_{s})+Eright];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\displaystyle \frac{1}{a(1-\mu ^{2})}
\DP{(f+\zeta)V}{\lambda}
- \frac{1}{a}\DP{(f+\zeta)U}{\mu}
- \Dlapla \left[g (h+h_{s}) + E\right]$">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}DP{V}{lambda}-frac{1}{a}DP{U}{mu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle \frac{1}{a(1-\mu ^{2})}\DP{V}{\lambda} - \frac{1}{a}\DP{U}{\mu},$">|; 

$key = q/u,v,h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$u, v, h$">|; 

$key = q/displaystyleDP{h}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle \DP{h}{t}$">|; 

$key = q/{displaymath}I(h)=frac{1}{4pi}int_{0}^{2pi}int_{-pislash2}^{pislash2}h(lambda,phi)sinphiDdphiDdlambda{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="\begin{displaymath}
I(h) = \frac{1}{4\pi}\int _{0}^{2\pi}\int _{-\pi/2}^{\pi/2}
h(\lambda, \phi)\sin \phi \Dd \phi \Dd \lambda
\end{displaymath}">|; 

$key = q/displaystyle-u'sinalphasinlambda',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle - u'\sin \alpha \sin \lambda ',$">|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\mu $">|; 

$key = q/displaystyleDD{tilde{v}}{t}+frac{tilde{u}tilde{v}tanphi}{a}+ftilde{v}+frac{g}{a}DP{tilde{h}}{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle \DD{\tilde{v}}{t} + \frac{\tilde{u}\tilde{v}\tan \phi}{a}
+ f \tilde{v} + \frac{g}{a}\DP{\tilde{h}}{\lambda},$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$K$">|; 

$key = q/displaystylechi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \chi$">|; 

$key = q/{displaymath}mbox{spmodel@gfd-dennou.org}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="\begin{displaymath}
\mbox{spmodel@gfd-dennou.org}
\end{displaymath}">|; 

$key = q/{displaymath}h_{s}=h_{s0}left(1-frac{1}{R}sqrt{mbox{min}[R^{2},(lambda-lambda_{c})^{2}+(phi-phi_{c})^{2}]}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{displaymath}
h_{s} = h_{s0} \left(1 - \frac{1}{R}\sqrt{\mbox{min}[R^{2}, (\lambda -\lambda _{c})^{2}+(\phi - \phi _{c})^{2}]}\right)
\end{displaymath}">|; 

$key = q/phi_{e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\phi _{e}$">|; 

$key = q/phi_{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\phi _{b}$">|; 

$key = q/{displaymath}b(x)=left{array{{lc}0&xle0e^{-x^{-1}}&0<xarray{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="\begin{displaymath}
b(x) = \left\{
\begin{array}{lc}
0 &amp; x\le 0 \\\\
e^{-x^{-1}} &amp; 0 &lt; x
\end{array}\right.
\end{displaymath}">|; 

$key = q/displaystyleDD{tilde{u}}{t}-frac{tilde{u}tilde{v}tanphi}{a}-ftilde{v}+frac{g}{acosphi}DP{tilde{h}}{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \DD{\tilde{u}}{t} - \frac{\tilde{u}\tilde{v}\tan \phi}{a}
- f \tilde{v} + \frac{g}{a\cos \phi}\DP{\tilde{h}}{\lambda},$">|; 

$key = q/{displaymath}h=left{array{{ll}(h_{0}slash2)(1+cos(pirslashR))&(r<R)0&(rgeR)array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="\begin{displaymath}
h = \left\{
\begin{array}{ll}
(h_{0}/2)( 1 + \cos (\pi r/R) ) &amp; (r &lt; R) \\\\
0 &amp; (r \ge R)
\end{array}\right.
\end{displaymath}">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$h$">|; 

$key = q/I(h);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$I(h)$">|; 

$key = q/lambda_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\lambda _{c}$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$E$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\phi$">|; 

$key = q/{displaymath}h=h_{0}+[a^{2}A(phi)+a^{2}B(phi)cosRlambda+a^{2}C(phi)cos2Rlambda]slashg{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="\begin{displaymath}
h = h_{0} + [a^{2}A(\phi) + a^{2}B(\phi)\cos R\lambda +a^{2}C(\phi)\cos 2R\lambda]/g
\end{displaymath}">|; 

$key = q/pislash6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\pi/6$">|; 

$key = q/alpha=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$\alpha =0$">|; 

$key = q/displaystyleh';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle h'$">|; 

$key = q/zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\zeta $">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$\pi$">|; 

$key = q/displaystylenabla^{2}chi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle \nabla ^{2} \chi$">|; 

$key = q/displaystyletilde{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle \tilde{u}$">|; 

$key = q/3pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$3\pi/2$">|; 

$key = q/displaystyleh;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle h$">|; 

$key = q/displaystyle-u_{0}sinlambdasinalpha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle - u_{0}\sin \lambda \sin \alpha,$">|; 

$key = q/displaystyleF_{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle F_{h}$">|; 

$key = q/displaystyleE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle E$">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}DP{U}{lambda}+frac{1}{a}DP{V}{mu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \frac{1}{a(1-\mu ^{2})}\DP{U}{\lambda} + \frac{1}{a}\DP{V}{\mu},$">|; 

$key = q/N_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$N_{d}$">|; 

$key = q/displaystyleoverline{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle \overline{u}$">|; 

$key = q/lambda_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\lambda _{0}$">|; 

$key = q/vcosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$v\cos \phi $">|; 

$key = q/displaystyleF_{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle F_{D}$">|; 

$key = q/displaystylesinlambdacosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle \sin \lambda \cos \phi$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$V$">|; 

$key = q/(lambda',phi');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$(\lambda ', \phi')$">|; 

$key = q/displaystylel_{1}(h);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle l_{1}(h)$">|; 

$key = q/(12.74244)^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$(12.74244)^{2}$">|; 

$key = q/displaystyleB(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle B(\phi)$">|; 

$key = q/F_{zeta},F_{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$F_{\zeta}, F_{D}$">|; 

$key = q/cos;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\cos$">|; 

$key = q/displaystyleoverline{u}-frac{1}{a}DP{overline{psi}}{phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\displaystyle \overline{u} - \frac{1}{a}\DP{\overline{\psi}}{\phi},$">|; 

$key = q/displaystylepsi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle \psi$">|; 

$key = q/displaystyleV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle V$">|; 

$key = q/h_{T}(lambda,Phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$h_{T}(\lambda, \Phi)$">|; 

$key = q/J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$J$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$g$">|; 

$key = q/{displaymath}lambda'=left{array{{lc}lambda'_{p}&cosalphacoslambdacosphi+sinalphalphacoslambdacosphi+sinalphasinphi<0array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="\begin{displaymath}
\lambda ' = \left\{
\begin{array}{lc}
\lambda '_{p} &amp; \cos ...
...ambda \cos \phi + \sin \alpha \sin \phi &lt; 0
\end{array}\right.
\end{displaymath}">|; 

$key = q/displaystyle-a^{2}omegasinphi+a^{2}Kcos^{R}phicosRlambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle -a^{2}\omega \sin \phi + a^{2}K\cos ^{R}\phi \cos R\lambda,$">|; 

$key = q/{displaymath}DD{}{t}=DP{}{t}+frac{u}{acosphi}DP{}{lambda}+frac{v}{a}DP{}{phi}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="\begin{displaymath}
\DD{}{t} = \DP{}{t} + \frac{u}{a\cos \phi}\DP{}{\lambda} +
\frac{v}{a}\DP{}{\phi}
\end{displaymath}">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$D$">|; 

$key = q/-pislash6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$-pi/6$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$a$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\alpha $">|; 

$key = q/displaystyleg;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle g$">|; 

$key = q/displaystylevsinphisinlambda+u'coslambda'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle v\sin \phi \sin \lambda + u'\cos \lambda '.$">|; 

$key = q/a,Omega,g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$a, \Omega, g$">|; 

$key = q/displaystyleD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystyleoverline{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle \overline{\psi}$">|; 

$key = q/displaystyle0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$\displaystyle 0.$">|; 

$key = q/h_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$h_{0}$">|; 

$key = q/displaystylefrac{1}{a^{2}(1-mu^{2})}DP[2]{A}{lambda}+frac{1}{a^{2}}DP{}{mu}left[(1-mu^{2})DP{A}{mu}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle \frac{1}{a^{2}(1-\mu ^{2})}\DP[2]{A}{\lambda}
+ \frac{1}{a^{2}}\DP{}{\mu}\left[(1-\mu^{2})\DP{A}{\mu}\right].$">|; 

$key = q/displaystyleaomegacosphi+aKcos^{R-1}phi(Rsin^{2}phi-cos^{2}phi)cosRlambda,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\displaystyle a\omega \cos \phi + aK\cos ^{R-1}\phi (R\sin ^{2}\phi - \cos ^{2}\phi)\cos R\lambda,$">|; 

$key = q/displaystylea;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle a$">|; 

$key = q/displaystyleu_{0}b(x)b(x_{e}-x)e^{4slashx_{e}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle u_{0}b(x)b(x_{e}-x)e^{4/x_{e}},$">|; 

$key = q/U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$U$">|; 

$key = q/times10^{14};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\times 10^{14}$">|; 

$key = q/K_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$K_{m}$">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}DP{(F_{u}cosphi)}{lambda}+frac{1}{a}DP{(F_{v}cosphi)}{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle \frac{1}{a(1-\mu ^{2})}\DP{(F_{u}\cos \phi)}{\lambda} + \frac{1}{a}\DP{(F_{v}\cos \phi)}{\mu}$">|; 

$key = q/0,quad0.05,quadpislash2-0.05,quadpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$0, \quad 0.05, \quad \pi/2 - 0.05,\quad \pi/2$">|; 

$key = q/displaystylesinphi_{0}sinphi+cosphi_{0}cosphileft(lambda-frac{u_{0}}{a}t-lambda_{0}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\displaystyle \sin \phi _{0}\sin \phi
+ \cos \phi_{0}\cos \phi
\left(\lambda - \frac{u_{0}}{a}t - \lambda _{0}\right)$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\textstyle =$">|; 

$key = q/displaystyleU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle U$">|; 

$key = q/displaystylefrac{mbox{max}_{alllambda,phi}[(u(lambda,phi)-u_{T}(lambda,Phi))^{2}{alllambda,phi}[u_{T}(lambda,Phi)^{2}+v_{T}(lambda,Phi)^{2}]};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle \frac{\mbox{max}_{all \lambda, \phi}
[(u(\lambda, \phi) - u_{T}(\...
...max}_{all \lambda, \phi}
[u_{T}(\lambda, \Phi)^{2} + v_{T}(\lambda, \Phi)^{2}]}$">|; 

$key = q/displaystyleF_{zeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle F_{\zeta}$">|; 

$key = q/phi_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\phi _{c}$">|; 

$key = q/displaystyleu_{0}sin^{14}(2phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\displaystyle u_{0}\sin ^{14}(2\phi),$">|; 

$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$I$">|; 

$key = q/u',v',h';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$u', v', h'$">|; 

$key = q/Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\Omega$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\omega$">|; 

$key = q/x_{e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$x _{e} $">|; 

$key = q/displaystylefrac{mbox{max}_{alllambda,phi}|(h(lambda,phi)-h_{T}(lambda,phi)|}{mbox{max}_{alllambda,phi}|h_{T}(lambda,Phi)|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle \frac{\mbox{max}_{all \lambda, \phi}\vert(h(\lambda, \phi) - h_{T...
...a, \phi)\vert}
{\mbox{max}_{all \lambda, \phi}
\vert h_{T}(\lambda, \Phi)\vert}$">|; 

$key = q/displaystyleu';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle u'$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$f$">|; 

$key = q/ucosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$u\cos \phi $">|; 

$key = q/F_{zeta,D,h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$F_{\zeta, D, h}$">|; 

$key = q/0,quadpislash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$0, \quad \pi/3$">|; 

$key = q/10^{5}slashg;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$10^{5}/g$">|; 

$key = q/displaystyleF_{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle F_{u}$">|; 

$key = q/pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\pi/4$">|; 

$key = q/displaystyletilde{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$\displaystyle \tilde{v}$">|; 

$key = q/sin;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\sin$">|; 

$key = q/displaystyleh_{0}-left(aOmegau_{0}+frac{u_{0}^{2}}{2}right)(sinphi)^{2}slashg.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$\displaystyle h_{0} - \left(a\Omega u_{0} + \frac{u_{0}^{2}}{2}\right)
(\sin \phi)^{2}/g.$">|; 

$key = q/displaystyleu_{0}(cosphicosalpha+sinphicoslambdasinalpha),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle u_{0}(\cos \phi \cos \alpha + \sin \phi \cos \lambda \sin \alpha),$">|; 

$key = q/displaystyleDD{tilde{h}}{t}+frac{tilde{h}}{acosphi}left[DP{tilde{u}}{lambda}+DP{tilde{v}cosphi}{phi}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle \DD{\tilde{h}}{t} + \frac{\tilde{h}}{a\cos \phi}
\left[\DP{\tilde{u}}{\lambda} + \DP{\tilde{v}\cos \phi}{\phi}
\right]$">|; 

$key = q/phi_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\phi _{0}$">|; 

$key = q/h_{s0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$h_{s0}$">|; 

$key = q/displaystyleh_{0}-left(aOmegau_{0}+frac{u_{0}^{2}}{2}right)(-coslambdacosphisinalpha+sinphicosalpha)^{2}slashg.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle h_{0} - \left(a\Omega u_{0} + \frac{u_{0}^{2}}{2}\right)
(-\cos \lambda \cos \phi \sin \alpha + \sin \phi \cos \alpha)^{2}/g.$">|; 

$key = q/displaystyleC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle C$">|; 

$key = q/20,quad40;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$20, \quad 40$">|; 

$key = q/displaystylefrac{1}{4}K^{2}cos^{2R}phi[(R+1)cos^{2}phi-(R+2)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle \frac{1}{4}K^{2}\cos ^{2R}\phi[(R + 1)\cos ^{2}\phi - (R + 2)]$">|; 

$key = q/displaystyle-aKRcos^{R-1}phisinphisinRlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle -aKR\cos ^{R-1}\phi \sin \phi \sin R\lambda$">|; 

1;