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


$key = q/(2N_{tr}+1)(N_{tr}+1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$ (2N_{tr}+1) (N_{tr}+1) $">|; 

$key = q/displaystyleDD{S}{z}<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$\displaystyle \DD{S}{z} &lt; 0$">|; 

$key = q/p_s=hat{p_s}+Deltap_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$ p_s = \hat{p_s} + \Delta p_s$">|; 

$key = q/displaystyle{calF}_varphi(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\displaystyle {\cal F}_\varphi  (\varphi, \lambda, \sigma)$">|; 

$key = q/f^{(n)}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="$ f^{(n)}=0$">|; 

$key = q/displaystyle=T_k-overline{T}_k,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\displaystyle = T_k - \overline{T}_k,$">|; 

$key = q/displaystyletilde{P}_n^mequivfrac{(1-mu^2)^{frac{|m|}{2}}}{2^nn!}DD[n+|m|]{}{mu}(mu^2-1)^n.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="$\displaystyle \tilde{P}_n^m \equiv \frac{ (1-\mu^2)^{\frac{\vert m\vert}{2}} }{2^n n!} \DD[n+\vert m\vert]{}{\mu} (\mu^2-1)^n .$">|; 

$key = q/tau_{S,i}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="$ \tau_{S,i}(z)$">|; 

$key = q/JleKle2J-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="$ J \le K \le 2J-1$">|; 

$key = q/dot{calA}_{dif};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$ \dot{\cal A}_{dif} $">|; 

$key = q/I=128;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="$ I=128$">|; 

$key = q/i=1,2,cdots,I.quadj=1,2,cdots,J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$ i=1,2,\cdots,I. \quad j=1,2,\cdots,J$">|; 

$key = q/displaystyle=Dinv{acosvarphi}left{DP{{u_A}_{,k}}{lambda}+DP{({v_A}_{,k}cosvarphihi}right}-nabla^{2}_{sigma}(Phi_k+C_{p}hat{kappa}_koverline{T}_kpi+(;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle = \Dinv{a \cos \varphi} \left\{ \DP{{u_A}_{,k}}{\lambda} + \DP{({...
...\} - \nabla^{2}_{\sigma} ( \Phi_k + C_{p} \hat{\kappa}_k \overline{T}_k \pi + ($">|; 

$key = q/Dvect{D}={D_{k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$ \Dvect{D}=\{ D_{k} \}$">|; 

$key = q/tilde{A}_n^m;(m=-M,-M+1,cdots,M,;n=|m|,|m|+1,cdots,N(m));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="$ \tilde{A}_n^m \;
(m=-M,-M+1, \cdots,M, \; n=\vert m\vert,\vert m\vert+1,\cdots,N(m))$">|; 

$key = q/displaystyle=sum_{k=0}^{J-1}(2k+1)(mu-mu_j)tilde{P}_k(mu)tilde{P}_k(mu_j).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="$\displaystyle = \sum_{k=0}^{J-1} (2k+1) (\mu-\mu_j) \tilde{P}_k(\mu) \tilde{P}_k(\mu_j).$">|; 

$key = q/displaystylenabla^{2}_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle \nabla^{2}_{\sigma}$">|; 

$key = q/displaystyleDP{zeta}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle \DP{\zeta}{t}  $">|; 

$key = q/A_{zeta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ A_{\zeta }$">|; 

$key = q/-1leqmuleq1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="$ -1 \leq \mu \leq 1$">|; 

$key = q/displaystylesum_{i=1}^Iexp(i(m'-m)lambda)=Idelta_{mm'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="$\displaystyle \sum_{i=1}^I \exp(i(m'-m) \lambda) = I \delta_{mm'} ,$">|; 

$key = q/mu=mu_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$ \mu=\mu_j$">|; 

$key = q/r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="$ r$">|; 

$key = q/displaystyleequivT-overline{T},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle \equiv T - \overline{T},$">|; 

$key = q/tau_i(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="$ \tau_i(z)$">|; 

$key = q/displaystyleequivleft[DP{}{lambda}left(sum_{m,n}tilde{f}_n^mY_n^m(lambda,varphi)right)right]_{ij}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="$\displaystyle \equiv \left[ \DP{}{\lambda} \left( \sum_{m,n} \tilde{f}_n^m Y_n^m (\lambda, \varphi) \right) \right]_{ij} .$">|; 

$key = q/{displaystylew_jequivfrac{(2J-1)(1-sin^2varphi_j)}{left{JP_{J-1}(sinvarphi_j)right}^2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$ {\displaystyle w_j \equiv
\frac{(2J-1)(1-\sin^2 \varphi_j)}
{\left\{J P_{J-1}(\sin \varphi_j)\right\}^2 } }$">|; 

$key = q/displaystyle=frac{I}{2}int_{-1}^{1}f_{n'}^{m}P_{n}^{m}(varphi)DD{P_{n'}^m}{varphi}dvarphidelta_{mm'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="$\displaystyle = \frac{I}{2} \int_{-1}^{1} f_{n'}^{m} P_{n}^{m}(\varphi) \DD{P_{n'}^m}{\varphi} d \varphi \delta_{m m'} .$">|; 

$key = q/p^{*}_{0}=1.4times10^{11};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="$ p^{*}_{0} = 1.4 \times 10^{11}$">|; 

$key = q/displaystyleequivfrac{1}{2Deltat}left({calA}^{t+Deltat}-{calA}^{t-Deltat}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$\displaystyle \equiv \frac{1}{2 \Delta t} \left( {\cal A}^{t+\Delta t} - {\cal A}^{t-\Delta t} \right) ,$">|; 

$key = q/displaystyleDP{D}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \DP{D}{t}  $">|; 

$key = q/displaystylew_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="$\displaystyle w_j$">|; 

$key = q/{displaystyleleft(int_a^bf_k(mu)f_{k'}(mu)w(mu)dmu=lambda_kdelta_{kk'}right)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="$ {\displaystyle
\left( \int_a^b f_k (\mu) f_{k'} (\mu) w(\mu) d \mu
= \lambda_k \delta_{kk'} \right) }$">|; 

$key = q/displaystyle=frac{1}{2Jtilde{P}_{J-1}(mu_j)tilde{P}^{'}_{J}(mu_j)}sum_{k=0}^{J-1}(2k+1)tilde{P}_k(mu_j)int_{-1}^1tilde{P}_k(mu)dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="$\displaystyle = \frac{1}{2 J \tilde{P}_{J-1}(\mu_j) \tilde{P}^{'}_{J} (\mu_j)} \sum_{k=0}^{J-1} (2k+1) \tilde{P}_k(\mu_j) \int_{-1}^1 \tilde{P}_k(\mu) d \mu$">|; 

$key = q/T^c_k=T^a_k,q^c_k=q^a_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$ T^c_k = T^a_k, q^c_k = q^a_k$">|; 

$key = q/{align*}{split}nabla_H^2Y_n^m&equivfrac{1}{r^2}left[DP{}{mu}left((1-mu^2)DP{}{mus^2varphi}DP[2]{}{lambda}right]Y_n^m&=-frac{n(n+1)}{r^2}Y_n^m{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="130" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="\begin{align*}\begin{split}\nabla_H^2 Y_n^m &amp;\equiv \frac{1}{r^2} \left[ \DP{}{\...
...{\lambda} \right] Y_n^m \ &amp;= - \frac{n(n+1)}{r^2} Y_n^m \end{split}\end{align*}">|; 

$key = q/displaystyle=-frac{1}{I}sum_{i,j}f_{ij}left.DD{}{varphi}left(cos^2varphiP_n^mright)right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="$\displaystyle = - \frac{1}{I} \sum_{i,j} f_{ij} \left. \DD{}{\varphi} \left( \cos^2\varphi P_n^m \right) \right\vert _j \exp(-im \lambda_i) w_j$">|; 

$key = q/Jgefrac{2N_{{rmmax}}+1}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="$ J \ge \frac{2N_{{\rm max}}+1}{2}$">|; 

$key = q/displaystyle(hat{p_s}+Deltap_s)q,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="$\displaystyle (\hat{p_s} + \Delta p_s) q,$">|; 

$key = q/{displaystyle(g_{ij}=)sum_{m,n}imtilde{f}_n^mY_n^m=sum_{m,n}tilde{g}_n^mY_n^m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="$ {\displaystyle (g_{ij}=)
\sum_{m,n} im \tilde{f}_n^m Y_n^m
= \sum_{m,n} \tilde{g}_n^m Y_n^m }$">|; 

$key = q/displaystyle{calD}(q)=-(-1)^{N_Dslash2}K_{HD}nabla^{N_D}q.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$\displaystyle {\cal D}(q) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} q .$">|; 

$key = q/{align*}{split}DP{q}{t}&=-Dinv{acosvarphi}left{DP{(uq)}{lambda}+DP{(vqcosvarphi)varphi}right}+qD&quad-dot{sigma}DP{q}{sigma}+S_{q}+{calD}(q).{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="84" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="\begin{align*}\begin{split}\DP{q}{t}  &amp;=  - \Dinv{a \cos \varphi} \left\{ \DP{...
...uad - \dot{\sigma} \DP{q}{\sigma} + S_{q} + {\cal D}(q). \end{split}\end{align*}">|; 

$key = q/[a,b];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="$  [ a ,b ]  $">|; 

$key = q/displaystyleDeltap_s=ginthat{rho}Deltaqdhat{z}=-ginthat{rho}Deltaqfrac{dhat{p}}{-hat{rho}g}=intDeltaqdhat{p}=hat{p_s}intDeltaqdsigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="$\displaystyle \Delta p_s = g \int \hat{\rho} \Delta q d \hat{z}
= -g \int \hat{...
...}}{- \hat{\rho} g}
= \int \Delta q d \hat{p}
= \hat{p_s} \int \Delta q d \sigma$">|; 

$key = q/displaystyle(n-|m|+1)tilde{P}_{n+1}^m-(2n+1)mutilde{P}_n^m+(n+|m|)tilde{P}_{n-1}^m=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="394" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="$\displaystyle (n-\vert m\vert+1) \tilde{P}_{n+1}^m - (2n+1) \mu \tilde{P}_n^m +(n+\vert m\vert) \tilde{P}_{n-1}^m = 0 .$">|; 

$key = q/Jslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$ J/2$">|; 

$key = q/displaystyleH=lambda-lambda_{subsolar}*frac{180}{pi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="$\displaystyle H = \lambda - \lambda_{subsolar} * \frac{180}{\pi}$">|; 

$key = q/displaystyleF_S(0)=sum_i^{N_S}a_i(1-alpha_g)(1-alpha_A)F_S^Iexp(-tau_{S,i}(0)seczeta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="$\displaystyle F_S(0) = \sum_i^{N_S} a_i (1-\alpha_g) (1-\alpha_A) F_S^I \exp ( - \tau_{S,i}(0)\sec \zeta ) ,$">|; 

$key = q/displaystyleDP{Dvect{T}}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle \DP{\Dvect{T}}{t}$">|; 

$key = q/displaystyleq^a_{k+1}leftarrowq^a_{k+1}-frac{L}{C_p}DP{q^*}{T}frac{q^a_{k+1}-q^*(T^a_{k+1},p_{k+1})}{displaystyle1+frac{L}{C_p}DP{q^*}{T}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="79" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="$\displaystyle q^a_{k+1} \leftarrow q^a_{k+1} - \frac{L}{C_p} \DP{q^*}{T} \frac{...
...1} - q^*( T^a_{k+1},p_{k+1}) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} } ,$">|; 

$key = q/displaystylehat{T}_{k-1}+DeltaT_{k-1}-left(hat{T}_{k}+DeltaT_{k}right)+frac{L}{C_{k-1}-q^{*}(hat{T}_{k})-left.DP{q^{*}}{T}right|_{k}DeltaT_{k}right};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="627" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="$\displaystyle \hat{T}_{k-1} + \Delta T_{k-1} - \left( \hat{T}_{k} + \Delta T_{k...
...{*} (\hat{T}_{k}) - \left. \DP{q^{*}}{T} \right\vert _{k} \Delta T_{k} \right\}$">|; 

$key = q/|m'-m|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="$ \vert m'-m\vert$">|; 

$key = q/0lelambda<2pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="$ 0 \le \lambda &lt; 2 \pi$">|; 

$key = q/displaystyle=Isum_{j=1}^{J}P_n^m(mu_j)P_{n'}^{m}(mu_j)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="$\displaystyle = I \sum_{j=1}^{J} P_n^m (\mu_j) P_{n'}^{m} (\mu_j) w_j$">|; 

$key = q/displaystyleT_{k-1}-T_{k}+frac{L}{C_p}left{q^{*}(T_{k-1},p_{k-1})-q^{*}(T_{k},p_C_p}frac{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{T_{k-1}+T_{k}}{2}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="533" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$\displaystyle T_{k-1} - T_{k} + \frac{L}{C_p} \left\{ q^{*} (T_{k-1}, p_{k-1}) ...
...\frac{R}{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{T_{k-1} + T_{k}}{2} = 0,$">|; 

$key = q/displaystylep_{ij}equivleft[DP{}{varphi}left(sum_{m,n}tilde{f}_n^mY_n^mright)right]_{ij}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="$\displaystyle p_{ij} \equiv \left[ \DP{}{\varphi} \left( \sum_{m,n} \tilde{f}_n^m Y_n^m \right) \right]_{ij} .$">|; 

$key = q/I=2M+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="$ I=2M+1$">|; 

$key = q/displaystyle{calD}(D);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle {\cal D}(D)$">|; 

$key = q/tilde{B}_n^m,tilde{C}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="$ \tilde{B}_n^m,\tilde{C}_n^m$">|; 

$key = q/displaystyle:qquad小規模運動過程(緯度方向),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$\displaystyle : \qquad 小規模運動過程 (緯度方向),$">|; 

$key = q/displaystyle=left|{array}{ll}(2n+1)xtilde{P}_n(x)-ntilde{P}_{n-1}(x)&tilde{P}_n(x)(2n+1)ytilde{P}_n(y)-ntilde{P}_{n-1}(y)&tilde{P}_n(y){array}right|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="$\displaystyle = \left\vert \begin{array}{ll} (2n+1)x \tilde{P}_n(x)-n\tilde{P}_...
...1)y \tilde{P}_n(y)-n\tilde{P}_{n-1}(y) &amp; \tilde{P}_n(y) \end{array} \right\vert$">|; 

$key = q/m,m',n,n';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="$ m,m',n,n'$">|; 

$key = q/p_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ p_s$">|; 

$key = q/I=2M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="$ I=2M$">|; 

$key = q/k_B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$ k_B$">|; 

$key = q/displaystylesum_{n=0}^{J-1}P_n(mu_j)P_n(mu_{j'})=frac{1}{w_j}delta_{jj'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="$\displaystyle \sum_{n=0}^{J-1} P_n (\mu_j) P_n (\mu_{j'}) = \frac{1}{w_j} \delta_{jj'}$">|; 

$key = q/displaystylehspace{4em}=-S_{k-1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$\displaystyle \hspace{4em} = - S_{k-1/2}$">|; 

$key = q/displaystyle=frac{1}{I}sum_{m'=-M}^{M}sum_{n'=|m'|}^Nsum_{m''=-M}^{M}sum_{n''=|m''|}^Ntilde{B}_{n'}^{m'}tilde{C}_{n''}^{m''};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{m'=-M}^{M} \sum_{n'=\vert m'\vert}^N \sum_{m''=-M}^{M} \sum_{n''=\vert m''\vert}^N \tilde{B}_{n'}^{m'} \tilde{C}_{n''}^{m''}$">|; 

$key = q/{align*}{split}DP{tilde{q}_n^m}{t}&=-frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}imu_{ij}(lambda_i,varphi_j)w_j&quad+tilde{calD}_{H,n}^mtilde{q}_n^m.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="204" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="\begin{align*}\begin{split}\DP{\tilde{q}_n^m}{t} &amp; = - \frac{1}{I} \sum_{i=1}^{I...
... w_j \ &amp; \quad + \tilde{\cal D}_{H,n}^m \tilde{q}_n^m . \end{split}\end{align*}">|; 

$key = q/displaystyleq_{ij}=cos^2varphi_jsum_{m,n}tilde{f}_n^mleft.DD{P_n^m}{varphi}right|_jexp(imlambda_i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="$\displaystyle q_{ij} = \cos^2\varphi_j \sum_{m,n} \tilde{f}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _j \exp(im \lambda_i)$">|; 

$key = q/displaystyle(n-|m|+1)sqrt{frac{1}{2n+3}frac{(n+1+|m|)!}{(n+1-|m|)!}}P_{n+1}^m-(2n+1)sqrt{frac{1}{2n+1}frac{(n+|m|)!}{(n-|m|)!}}muP_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="$\displaystyle (n-\vert m\vert+1) \sqrt{ \frac{1}{2n+3} \frac{(n+1+\vert m\vert)...
...) \sqrt{ \frac{1}{2n+1} \frac{(n+\vert m\vert)!}{(n-\vert m\vert)!} } \mu P_n^m$">|; 

$key = q/displaystyle=hat{kappa}_{k}C_{p}overline{T}_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$\displaystyle = \hat{\kappa}_{k} C_{p} \overline{T}_{k} ,$">|; 

$key = q/displaystyleT_v(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$\displaystyle T_v (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystyle=frac{1}{Deltasigma_{k}}(hat{overline{T}}_{k-1slash2}-overline{T}_{kgma_{k}}(overline{T}_{k}-hat{overline{T}}_{k+1slash2})delta_{k+1=l},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle = \frac{1}{\Delta \sigma_{k}} ( \hat{\overline{T}}_{k-1/2} - \ove...
... \sigma_{k}} ( \overline{T}_{k} - \hat{\overline{T}}_{k+1/2} ) \delta_{k+1=l} ,$">|; 

$key = q/displaystylequad+n(-tilde{P}_{n-1}(x)tilde{P}_n(y)+tilde{P}_{n-1}(y)tilde{P}_n(x));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="$\displaystyle \quad +n (- \tilde{P}_{n-1}(x) \tilde{P}_n(y) + \tilde{P}_{n-1}(y) \tilde{P}_n(x) )$">|; 

$key = q/0lemleM,|m|lenleN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="$ 0 \le m \le M, \vert m\vert \le n \le N$">|; 

$key = q/{align*}{split}DP{T}{t}&=-Dinv{acosvarphi}left{DP{(uT^{prime})}{lambda}+DP{(vT^{sigma}right)+frac{Q}{C_p}+{calD}(T)+{calD}^{prime}(Dvect{v}).{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="541" HEIGHT="90" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="\begin{align*}\begin{split}\DP{T}{t}  &amp;=  - \Dinv{a \cos \varphi} \left\{ \DP{...
...ac{Q}{C_p} + {\cal D}(T) + {\cal D}^{\prime}(\Dvect{v}). \end{split}\end{align*}">|; 

$key = q/Y_n^m(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$ Y_n^m(\lambda,\varphi)$">|; 

$key = q/k=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="$ k=0$">|; 

$key = q/displaystyle=q^{*}(hat{T}_{k},p_{k})+left.DP{q^{*}}{T}right|_{hat{T}_{k}}DeltaT_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$\displaystyle = q^{*} (\hat{T}_{k},p_{k}) + \left. \DP{q^{*}}{T} \right\vert _{\hat{T}_{k}} \Delta T_{k},$">|; 

$key = q/displaystylefrac{1}{2pi}int_0^{2pi}g(lambda)dlambda=frac{1}{I}sum_{n=1}^{I}g(lambda_n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="$\displaystyle \frac{1}{2\pi} \int_0^{2\pi} g(\lambda) d \lambda = \frac{1}{I} \sum_{n=1}^{I} g(\lambda_n)$">|; 

$key = q/displaystyledot{sigma}=0atsigma=0,1.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle \dot{\sigma} = 0    at   \sigma = 0 ,  1 .$">|; 

$key = q/displaystyle=Dinv{acosvarphi}left{DP{{v_A}_{,k}}{lambda}-DP{({u_A}_{,k}cosvarphi)}{varphi}right}+{calD}(zeta_k),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle = \Dinv{a \cos \varphi} \left\{ \DP{{v_A}_{,k}}{\lambda} - \DP{({u_A}_{,k} \cos \varphi)}{\varphi} \right\} + {\cal D}(\zeta_k),$">|; 

$key = q/displaystylehspace{2em}=-S_{k-1slash2}-left(1+gamma_{k-1}-kappafrac{Deltap_{k-1st)frac{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$\displaystyle \hspace{2em} = - S_{k-1/2} - \left( 1 + \gamma_{k-1} - \kappa \fr...
...rac{1}{ 1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$">|; 

$key = q/tilde{P}_J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$ \tilde{P}_J$">|; 

$key = q/I,J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="$ I,J$">|; 

$key = q/n=0,1,cdots,n-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="$ n=0,1,\cdots,n-1$">|; 

$key = q/displaystyle=-sum_{k=1}^{K}(D_k+Dvect{v}_kcdotnablapi)Deltasigma_k,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$\displaystyle = - \sum_{k=1}^{K} ( D_k + \Dvect{v}_k \cdot \nabla \pi ) \Delta \sigma_k,$">|; 

$key = q/displaystyletilde{calD}_{M,n}^m=-K_{HD}left[left(frac{-n(n+1)}{a^{2}}right)^{N_Dslash2}-left(frac{2}{a}right)^{N_D}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\displaystyle \tilde{\cal D}_{M,n}^m = - K_{HD} \left[ \left( \frac{-n(n+1)}{a^{2}} \right)^{N_D/2} - \left( \frac{2}{a} \right)^{N_D} \right] .$">|; 

$key = q/displaystylehat{T}_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="$\displaystyle \hat{T}_{k-1}$">|; 

$key = q/{displaystylefrac{1}{r}DP{f}{varphi}left(=frac{cosvarphi}{r}DP{f}{mu}right)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="$ {\displaystyle \frac{1}{r} \DP{f}{\varphi}
\left( = \frac{\cos \varphi}{r} \DP{f}{\mu} \right) }$">|; 

$key = q/{align*}{split}hat{T}_{k-1slash2}&=frac{left[left(displaystylefrac{sigma_{k-1sla{sigma_{k-1}^{kappa}-sigma_k^{kappa}}&=a_kT_k+b_{k-1}T_{k-1},{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="448" HEIGHT="99" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="\begin{align*}\begin{split}\hat{T}_{k-1/2} &amp; = \frac{ \left[ \left( \displaystyl...
... - \sigma_k^{\kappa} } \ &amp; = a_k T_k + b_{k-1} T_{k-1}, \end{split}\end{align*}">|; 

$key = q/J=63,N=21;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="$ J=63, N=21$">|; 

$key = q/displaystyleu_A(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$\displaystyle u_A (\varphi, \lambda, \sigma)$">|; 

$key = q/M,N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="$ M,N$">|; 

$key = q/{align*}{split}zeta&=frac{1}{rcosvarphi}DP{v}{lambda}-frac{1}{rcosvarphi}DP{}{varphi}(ucosvarphi).{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="43" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="\begin{align*}\begin{split}\zeta &amp;= \frac{1}{r \cos \varphi} \DP{v}{\lambda} - \frac{1}{r \cos \varphi} \DP{}{\varphi}(u \cos \varphi) . \end{split}\end{align*}">|; 

$key = q/displaystylew_j=frac{(2J-1)(1-mu_j^2)}{(JP_{J-1}(mu_j))^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="$\displaystyle w_j = \frac{(2J-1)(1-\mu_j^2)}{(J P_{J-1}(\mu_j))^2 }$">|; 

$key = q/zeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$ \zeta$">|; 

$key = q/0le|m'|len';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="$ 0 \le \vert m'\vert \le n'$">|; 

$key = q/{displaystylesin^{-1}left(cosfrac{j-1slash2}{J}piright)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$ {\displaystyle
\sin^{-1} \left( \cos \frac{j-1/2}{J}\pi \right)
}$">|; 

$key = q/tilde{P}_n^m(mu)(n=|m|,|m+1,cdots);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="$ \tilde{P}_n^m(\mu)  (n=\vert m\vert,\vert m+1, \cdots)$">|; 

$key = q/hat{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="$ \hat{q}$">|; 

$key = q/Leftrightarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="$ \Leftrightarrow$">|; 

$key = q/displaystyle=frac{1}{2}int_{-1}^1frac{tilde{P}_J(mu)}{(mu-mu_j)tilde{P}^{'}_J(mu_j)}dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="$\displaystyle = \frac{1}{2} \int_{-1}^1 \frac{\tilde{P}_J(\mu)} {(\mu-\mu_j) \tilde{P}^{'}_J(\mu_j)} d \mu$">|; 

$key = q/zeta_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$ \zeta_0$">|; 

$key = q/frac{I}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="$ \frac{I}{2}$">|; 

$key = q/P_n^m(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="$ P_n^m(\mu)$">|; 

$key = q/displaystyle(n+1)tilde{P}_{n+1}(mu)=(2n+1)mutilde{P}_n(mu)-ntilde{P}_{n-1}(mu)(n=0,1,2,cdots);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="$\displaystyle (n+1) \tilde{P}_{n+1}(\mu) = (2n+1) \mu \tilde{P}_n(\mu) - n \tilde{P}_{n-1}(\mu)     (n=0,1,2,\cdots)$">|; 

$key = q/T^c_k,q^c_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="$ T^c_k, q^c_k$">|; 

$key = q/displaystyleZequiv-sum_{k=1}^{K}Dvect{v}_kcdotnablapi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle Z \equiv - \sum_{k=1}^{K} \Dvect{v}_k \cdot \nabla \pi.$">|; 

$key = q/displaystyleDeltaq_{cond}=S^{cond}_{q}Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="$\displaystyle \Delta q_{cond}
= S^{cond}_{q} \Delta t$">|; 

$key = q/displaystylehspace{2em}+left(1+gamma_{k-1}-kappafrac{Deltap_{k-1slash2}}{2p_{k-1{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="582" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="$\displaystyle \hspace{2em} + \left( 1 + \gamma_{k-1} - \kappa \frac{\Delta p_{k...
...1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}} \right)$">|; 

$key = q/displaystyleint_{-1}^{1}f(mu)dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="$\displaystyle \int_{-1}^{1} f(\mu) d \mu$">|; 

$key = q/displaystyleS_q(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$\displaystyle S_q  (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="$\displaystyle =$">|; 

$key = q/tilde{P}_0=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="$ \tilde{P}_0 = 1$">|; 

$key = q/displaystylesum_{i=0}^{I-1}exp(imlambda_i)exp(-im'lambda_i)=Idelta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="$\displaystyle \sum_{i=0}^{I-1} \exp(i m \lambda_i) \exp(-i m' \lambda_i) = I \delta_{mm'}$">|; 

$key = q/displaystyle:qquad放射,凝結,小規模運動過程等による加熱・温度変化,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle : \qquad 放射, 凝結, 小規模運動過程等による加熱・温度変化,$">|; 

$key = q/displaystyle:qquad温度水平拡散,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle : \qquad 温度水平拡散,$">|; 

$key = q/displaystylequadsum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}cos^2varphi_jP_{n}^{m}(varphi_j(imlambda_i)left.DD{P_{n'}^{m'}}{varphi}right|_jexp(-im'lambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="$\displaystyle \quad \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} \cos^2\varphi_j P_{n}...
...mbda_i) \left. \DD{P_{n'}^{m'}}{\varphi}\right\vert _j \exp(-im' \lambda_i) w_j$">|; 

$key = q/S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$ S$">|; 

$key = q/nabla^{N_D};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$ \nabla^{N_D}$">|; 

$key = q/displaystyleequivfrac{1}{2}left({calA}^{t+Deltat}+{calA}^{t-Deltat}right)={calA}^{t-Deltat}+delta_{t}{calA}Deltat.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$\displaystyle \equiv \frac{1}{2} \left( {\cal A}^{t+\Delta t} + {\cal A}^{t-\Delta t} \right) = {\cal A}^{t-\Delta t} + \delta_{t} {\cal A} \Delta t .$">|; 

$key = q/displaystyleequivgz:quadジオポテンシャル高度[mathrm{m}^{2}mathrm{s}^{-2}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle \equiv gz : \quad ジオポテンシャル高度 [\mathrm{m}^{2} \mathrm{s}^{-2}],$">|; 

$key = q/displaystyleDeltahat{Q}equivleft{hat{q}_{k-1}-q^{*}(hat{T}_{k-1})right}Deltap_{k-1}+left{hat{q}_{k}-q^{*}(hat{T}_{k})right}Deltap_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$\displaystyle \Delta \hat{Q} \equiv \left\{ \hat{q}_{k-1} - q^{*} (\hat{T}_{k-1...
...Delta p_{k-1} + \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\} \Delta p_{k}$">|; 

$key = q/hat{calA}^{t+Deltat};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$ \hat{\cal A}^{t+\Delta t} $">|; 

$key = q/{align*}{split}{u_A}_{,k}&=(zeta_k+f)v_k-frac{1}{2Deltasigma_k}[dot{sigma}_{k-1sT_{v,k}^{prime}}{acosvarphi}DP{pi}{lambda}+{calF}_{lambda,k},{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="86" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="\begin{align*}\begin{split}{u_A}_{,k} &amp; = ( \zeta_k + f ) v_k - \frac{1}{2 \Delt...
...\cos \varphi} \DP{\pi}{\lambda} + {\cal F}_{\lambda, k}, \end{split}\end{align*}">|; 

$key = q/displaystyleR_k=q_kD_k-frac{1}{2Deltasigma_k}left[dot{sigma}_{k-1slash2}(q_{k-1}-q_k)+dot{sigma}_{k+1slash2}(q_k-q_{k+1})right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle R_k = q_k D_k - \frac{1}{2 \Delta \sigma_k} \left[ \dot{\sigma}_{k-1/2} ( q_{k-1} - q_k ) + \dot{\sigma}_{k+1/2} ( q_k - q_{k+1} ) \right].$">|; 

$key = q/Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$ \Delta t$">|; 

$key = q/r_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$ r_S$">|; 

$key = q/displaystyleA(lambda,varphi)=sum_{m=0}^{infty}sum_{n=|m|}^{infty}tilde{A}_n^mY_n^m(lambda,varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="$\displaystyle A(\lambda, \varphi) = \sum_{m=0}^{\infty} \sum_{n=\vert m\vert}^{\infty} \tilde{A}_n^m Y_n^m(\lambda,\varphi) ,$">|; 

$key = q/{align*}{split}H_k&=T_{k}^{prime}D_{k}&quad-frac{1}{Deltasigma_{k}}[dot{sigma}_{{k}}{Deltasigma_{k}}T'_{v,k}sum_{l=k+1}^{K}D_lDeltasigma_{l}.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="257" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="\begin{align*}\begin{split}H_k &amp; = T_{k}^{\prime} D_{k} \ &amp; \quad - \frac{1}{\D...
..._{k} } T'_{v,k} \sum_{l=k+1}^{K} D_l \Delta \sigma_{l} . \end{split}\end{align*}">|; 

$key = q/displaystyletilde{h}_n^m=-frac{n(n+1)}{r^2}tilde{f}_n^m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="$\displaystyle \tilde{h}_n^m = -\frac{n(n+1)}{r^2} \tilde{f}_n^m .$">|; 

$key = q/B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="$ B$">|; 

$key = q/P_J(sinvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$ P_J(\sin \varphi)$">|; 

$key = q/displaystyle=1-left(frac{sigma_{k+1slash2}}{sigma_k}right)^{kappa}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle = 1- \left( \frac{ \sigma_{k+1/2} } { \sigma_k } \right)^{\kappa} .$">|; 

$key = q/hat{T};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="$ \hat{T}$">|; 

$key = q/displaystyleD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystyleint^{1}_{-1}f(mu)dmu=2sum_{j=1}^{J}f(mu_j)w_j,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="$\displaystyle \int^{1}_{-1} f(\mu) d \mu = 2 \sum_{j=1}^{J} f(\mu_j) w_j ,$">|; 

$key = q/displaystyleint_{-1}^1tilde{P}_n(mu)tilde{P}_{n'}(mu)dmu=frac{2}{2n+1}delta_{nn'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="$\displaystyle \int_{-1}^1 \tilde{P}_n(\mu) \tilde{P}_{n'}(\mu) d \mu = \frac{2}{2n+1} \delta_{nn'} .$">|; 

$key = q/dot{calA}_{phy};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$ \dot{\cal A}_{phy} $">|; 

$key = q/tilde{P}_J(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$ \tilde{P}_J(\mu)$">|; 

$key = q/n+n'+n'';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$ n+n'+n''$">|; 

$key = q/*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$ *$">|; 

$key = q/A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$ A$">|; 

$key = q/chi_n^m,psi_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="$ \chi_n^m,\psi_n^m$">|; 

$key = q/displaystyleg(lambda)=sum_{m=-M}^{m=M}g_mexp(imlambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="$\displaystyle g(\lambda) = \sum_{m=-M}^{m=M} g_m \exp( i m \lambda )$">|; 

$key = q/displaystyle:quad乾燥大気の気体定数[mathrm{Jkg}^{-1}mathrm{K}^{-1}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle : \quad 乾燥大気の気体定数 [\mathrm{J kg}^{-1} \mathrm{K}^{-1}],$">|; 

$key = q/displaystyle=frac{1}{I}sum_{n=1}^{I}sum_{m=-M}^{M}g_mexp(imlambda_n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{n=1}^{I} \sum_{m=-M}^{M} g_m \exp(i m \lambda_n)$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}left(cos^2varphi_jsum_{m',n'}tilde{f}_{n'}^{m'}lphi}right|_jexp(im'lambda_i)right)P_n^m(varphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} \left( \cos^2\varphi_j \sum_{m',n'} \til...
...t\vert _j \exp(i m' \lambda_i) \right) P_n^m(\varphi_j) \exp(-im \lambda_i) w_j$">|; 

$key = q/{calA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$ {\cal A}$">|; 

$key = q/displaystyleleft(-1-gamma_{k}-frac{R}{C_p}frac{Deltap_{k-1slash2}}{2p_{k-1slash2}}right)DeltaT_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$\displaystyle \left( - 1 - \gamma_{k} - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) \Delta T_{k}$">|; 

$key = q/displaystyle=frac{1}{Jtilde{P}_{J-1}(mu_j)tilde{P}^{'}_{J}(mu_j)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="$\displaystyle = \frac{1}{J \tilde{P}_{J-1}(\mu_j) \tilde{P}^{'}_{J} (\mu_j)}$">|; 

$key = q/displaystyle=sigma_{k-1slash2}Deltasigma_{l}-Deltasigma_{l}delta_{kleql},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle = \sigma_{k-1/2} \Delta \sigma_{l} - \Delta \sigma_{l} \delta_{k \leq l } ,$">|; 

$key = q/displaystyleleft[frac{1}{cosvarphi}DP{}{varphi}left(cosvarphiDP{}{varphi}right)+frac{1}{cos^2varphi}DP[2]{}{lambda}+n(n+1)right]Y_n^m=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="$\displaystyle \left[ \frac{1}{\cos \varphi} \DP{}{\varphi} \left( \cos \varphi ...
...right) + \frac{1}{\cos^2 \varphi} \DP[2]{}{\lambda} + n(n+1) \right] Y_n^m =0 .$">|; 

$key = q/displaystyle=g_0+sum_{m=-M,mneq0}^{M}frac{g_m}{I}sum_{n=1}^{I}left(exp(frac{2piim}{I})right)^{n-1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="$\displaystyle = g_0 + \sum_{m=-M, m\neq0}^{M} \frac{g_m}{I} \sum_{n=1}^{I} \left( \exp(\frac{2 \pi i m}{I}) \right)^{n-1} .$">|; 

$key = q/f_J(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="$ f_J(\mu)$">|; 

$key = q/displaystyletilde{A}_n^m=frac{1}{2}int_{-1}^1A(mu)P_n^m(mu)dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="$\displaystyle \tilde{A}_n^m = \frac{1}{2} \int_{-1}^1 A(\mu) P_n^m(\mu) d \mu$">|; 

$key = q/x=-1,alpha,1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="$ x=-1,\alpha,1$">|; 

$key = q/displaystyleS_{k-1slash2}equivhat{T}_{k-1}-hat{T}_{k}+frac{L}{C_p}left{q^{*}(hatc{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_{k-1}+hat{T}_{k}}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="$\displaystyle S_{k-1/2} \equiv \hat{T}_{k-1} - \hat{T}_{k} + \frac{L}{C_p} \lef...
...{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$">|; 

$key = q/displaystyleequivsum_{m=-M}^{M}sum_{n=|m|}^{N}tilde{A}_n^mY_n^m(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle \equiv \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \tilde{A}_n^m Y_n^m (\lambda, \varphi)$">|; 

$key = q/{align*}{split}DP{tilde{D}_n^m}{t}&=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}im(u_A)_}hat{kappa}_kbar{T}_kpi_n^m)+tilde{calD}_{M,n}^mtilde{D}_n^m.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="214" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="\begin{align*}\begin{split}\DP{\tilde{D}_n^m}{t} &amp; = \frac{1}{I} \sum_{i=1}^{I} ...
...{T}_k \pi_n^m ) + \tilde{\cal D}_{M,n}^m \tilde{D}_n^m . \end{split}\end{align*}">|; 

$key = q/displaystyle(C_pT_{k}+Lq_{k})Deltap_{k}+(C_pT_{k-1}+Lq_{k-1})Deltap_{k-1}=(C_pha+Lhat{q}_{k})Deltap_{k}+(C_phat{T}_{k-1}+Lhat{q}_{k-1})Deltap_{k-1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="654" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$\displaystyle (C_p T_{k} + L q_{k}) \Delta p_{k} + (C_p T_{k-1} + L q_{k-1}) \D...
...at{q}_{k}) \Delta p_{k} + (C_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}.$">|; 

$key = q/displaystylep_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="$\displaystyle p_n^m$">|; 

$key = q/displaystyleDeltaq_{evap}=F_{evap}frac{g}{LDeltap}Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="$\displaystyle \Delta q_{evap}
= F_{evap} \frac{g}{L \Delta p} \Delta t$">|; 

$key = q/{figure}center{picture{(300,100)(10,-10)put(20,10){vector(1,0){85}}put(30,0){vec0,-20){shortstack{三角形切断}}{par{picture{center{{{{figure};MSF=1.6;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="139" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="\begin{figure}\begin{center}
\begin{picture}(300,100)(10,-10)
\put(20 , 10){\v...
...00,-20) \{ shortstack\{三角形切断\}\}
\par
\end{picture}\end{center}\end{figure}">|; 

$key = q/(u,v);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ (u,v)$">|; 

$key = q/P_n^mP_{n'}^{m'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$ P_n^m P_{n'}^{m'} $">|; 

$key = q/{picture}(300,150)(50,10)put(50,20){line(1,0){220}}put(50,40){line(1,0){220}}put){shortstack{{sigma=1{}}put(280,136){shortstack{{sigma=0{}}{picture};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="465" HEIGHT="208" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="\begin{picture}(300,150)(50,10)
\put(50,20){\line(1,0){220}}
\put(50,40){\line...
...){\shortstack{$\sigma=1$}}
\put(280,136){\shortstack{$\sigma=0$}}
\end{picture}">|; 

$key = q/Y_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ Y_n^m$">|; 

$key = q/{align*}{split}DP{T_k}{t}&=-Dinv{acosvarphi}left{DP{(u_kT^{prime}_k)}{lambda}+DPhat{H}_k&quad+frac{Q_k}{C_{p}}+{calD}(T_k)+{calD}'(Dvect{v}).{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="88" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="\begin{align*}\begin{split}\DP{T_k}{t} &amp; = - \Dinv{a \cos \varphi} \left\{ \DP{(...
...frac{Q_k}{C_{p}} + {\cal D}(T_k) + {\cal D}'(\Dvect{v}). \end{split}\end{align*}">|; 

$key = q/displaystyleQ_{kl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle Q_{kl}$">|; 

$key = q/displaystylefrac{hat{p_{s}}sigma}{RT}hat{q}=frac{p_{s}sigma}{RT}q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="$\displaystyle \frac{\hat{p_{s}} \sigma}{RT} \hat{q} = \frac{p_{s} \sigma}{RT} q$">|; 

$key = q/mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="$ \mu$">|; 

$key = q/displaystyleleft[left(-1-gamma_{k}right)-kappafrac{Deltap_{k-1slash2}}{2p_{k-1sl}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}right)right]DeltaT_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="$\displaystyle \left[ \left( - 1 - \gamma_{k} \right) - \kappa \frac{\Delta p_{k...
... \gamma_{k-1}} \frac{\Delta p_{k}}{\Delta p_{k-1}} \right) \right] \Delta T_{k}$">|; 

$key = q/displaystyleDD{}{mu}left{(1-mu^2)DD{}{mu}P_n^mright}+left{n(n+1)-frac{m^2}{1-mu^2}right}P_n^m=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="$\displaystyle \DD{}{\mu} \left\{ (1-\mu^2) \DD{}{\mu} P_n^m \right\} + \left\{ n(n+1) - \frac{m^2}{1-\mu^2} \right\} P_n^m = 0 .$">|; 

$key = q/displaystyleint_{-1}^1P_n^m(mu)P_{n'}^m(mu)dmu=2delta_{nn'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \int_{-1}^1 P_n^m(\mu) P_{n'}^m(\mu) d \mu = 2 \delta_{nn'}$">|; 

$key = q/displaystyle=-sum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}left.DD{}{varphi}left(cos^2varphight)right|_jexp(-imlambda_i)P_{n'}^{m'}(varphi_j)exp(im'lambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="$\displaystyle = - \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} \left. \DD{}{\varphi} \...
...ight\vert _j \exp(-im \lambda_i) P_{n'}^{m'}(\varphi_j) \exp(im' \lambda_i) w_j$">|; 

$key = q/displaystylesigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\displaystyle \sigma$">|; 

$key = q/displaystyleequivDD{sigma}{t}equivDP{sigma}{t}+frac{u}{acosvarphi}DP{sigma}{lambda}+frac{v}{a}DP{sigma}{varphi}+DP{sigma}{sigma},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \equiv \DD{\sigma}{t}  \equiv  \DP{\sigma}{t} + \frac{u}{a \cos...
... \DP{\sigma}{\lambda} + \frac{v}{a} \DP{\sigma}{\varphi} + \DP{\sigma}{\sigma},$">|; 

$key = q/displaystylehspace{-7em}=-left[DeltaT_{k}+frac{L}{C_p}left{q^{*}(T_{k})+left.DP{q^{*}}{T}right|_{k}DeltaT_{k}-hat{q}_{k}right}right]Deltap_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$\displaystyle \hspace{-7em} = - \left[ \Delta T_{k} + \frac{L}{C_p} \left\{ q^{...
...}{T} \right\vert _{k} \Delta T_{k} - \hat{q}_{k} \right\} \right] \Delta p_{k},$">|; 

$key = q/displaystyleq^a_{k+1}>q^*(T^a_{k+1},p_{k+1});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$\displaystyle q^a_{k+1} &gt; q^*( T^a_{k+1}, p_{k+1} )$">|; 

$key = q/2Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$ 2 \Delta t$">|; 

$key = q/displaystyleu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="$\displaystyle u$">|; 

$key = q/{displaystyleint_{-1}^1fdmu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="$ {\displaystyle \int_{-1}^1 f d \mu }$">|; 

$key = q/P_{J};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="$ P_{J}$">|; 

$key = q/L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$ L$">|; 

$key = q/K=2N_{tr},J=M=N_{tr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="$ K=2N_{tr}, J=M=N_{tr} $">|; 

$key = q/2J-1ge{rmmax}[n+n']=2{rmmax}[N];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="$ 2J-1 \ge {\rm max}[n+n'] = 2 {\rm max}[N]$">|; 

$key = q/alpha_A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$ \alpha_A$">|; 

$key = q/N=64;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="$ N=64$">|; 

$key = q/Jge65;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="$ J \ge 65$">|; 

$key = q/sigma=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$ \sigma=0$">|; 

$key = q/displaystylehequivfrac{g}{rcos^2varphi}=frac{1}{rcos^2varphi}DP{f}{lambda}left[=DP{}{x}left(frac{f}{cosvarphi}right)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="$\displaystyle h \equiv \frac{g}{r \cos^2 \varphi} = \frac{1}{r \cos^2 \varphi} ...
...f}{\lambda}   \left[ = \DP{}{x} \left( \frac{f}{\cos \varphi} \right) \right]$">|; 

$key = q/displaystyleoverline{coszeta}simeqA_{zeta}+B_{zeta}cos^2varphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="$\displaystyle \overline{\cos \zeta} \simeq A_{\zeta} + B_{\zeta} \cos^2 \varphi .$">|; 

$key = q/f''=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="$ f''=0$">|; 

$key = q/displaystyleDP{tilde{pi}_n^m}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$\displaystyle \DP{\tilde{\pi}_n^m}{t}$">|; 

$key = q/F_{evap}simLC(q^{*}-q_s)rho_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="$ F_{evap} \sim L C (q^{*} - q_s) \rho_s$">|; 

$key = q/{P_n^m|n=|m|,|m+1|,cdots};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="$ \{ P_n^m \vert n=\vert m\vert,\vert m+1\vert,\cdots \}$">|; 

$key = q/u,v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="$ u, v$">|; 

$key = q/displaystyle:quad水平平均気温[mathrm{K}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle : \quad 水平平均気温 [\mathrm{K}],$">|; 

$key = q/displaystylehspace*{2.5cm}-sqrt{frac{(2n+1)(2n+3)}{(n-|m|+1)(n+|m|+1)}}sqrt{frac{(n-|m|)(n+|m|)}{(2n+1)(2n-1)}}P_{n-1}^m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="$\displaystyle \hspace*{2.5cm} - \sqrt{ \frac{(2n+1)(2n+3)}{(n-\vert m\vert+1)(n...
...)} } \sqrt{ \frac{(n-\vert m\vert)(n+\vert m\vert)}{(2n+1)(2n-1)} } P_{n-1}^m .$">|; 

$key = q/D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="$ D$">|; 

$key = q/displaystyleqquad-frac{R}{C_p}frac{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_{k-1}+DeltaT_{k-1}+hat{T}_{k}+DeltaT_{k}}{2}=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$\displaystyle \qquad - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k}}{2} = 0,$">|; 

$key = q/displaystyle(n+1)left|{array}{ll}tilde{P}_{n+1}(x)&tilde{P}_n(x)tilde{P}_{n+1}(y)&tilde{P}_n(y){array}right|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="$\displaystyle (n+1) \left\vert \begin{array}{ll} \tilde{P}_{n+1}(x) &amp; \tilde{P}_n(x) \ \tilde{P}_{n+1}(y) &amp; \tilde{P}_n(y) \end{array} \right\vert$">|; 

$key = q/M=N_{tr},N(m)=N_{tr}+|m|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$ M= N_{tr},  N(m) =N_{tr}+\vert m\vert$">|; 

$key = q/{calT}^f(z_1,z_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$ {\cal T}^f(z_1,z_2)$">|; 

$key = q/A(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="$ A(\mu)$">|; 

$key = q/displaystylew_j=frac{1}{2}int_{-1}^{1}frac{P_J(mu)}{(mu-mu_j)P^{'}_J(mu_i)}dmu=frac{(2J-1)(1-mu_j^2)}{(JP_{J-1}(mu_j))^2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="$\displaystyle w_j = \frac{1}{2} \int_{-1}^{1} \frac{P_J(\mu)}{(\mu-\mu_j) P^{'}_J (\mu_i)}d \mu = \frac{(2J-1)(1-\mu_j^2)}{(J P_{J-1}(\mu_j))^2 } .$">|; 

$key = q/displaystylehat{hat{T}}_{k+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="$\displaystyle \hat{\hat{T}}_{k+1}$">|; 

$key = q/R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$ R$">|; 

$key = q/displaystyleI=sum_{k=k_B}^{k_T}(hat{q}_k-bar{q}_k^{t-Deltat})frac{Deltap_k}{g}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$\displaystyle I = \sum_{k=k_B}^{k_T} ( \hat{q}_k - \bar{q}_k^{t-\Delta t} ) \frac{\Delta p_k}{g} .$">|; 

$key = q/displaystylesum_{n=1}^{I}left(exp(frac{2piim}{I})right)^{n-1}=0(mneq0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="$\displaystyle \sum_{n=1}^{I} \left( \exp(\frac{2 \pi i m}{I}) \right)^{n-1} =0     (m \neq 0)$">|; 

$key = q/{align*}{split}Deltasigma_k&equivsigma_{k-1slash2}-sigma_{k+1slash2},qquad(1<k<Ksigma_{K+1slash2}&equivsigma_{K}-sigma_{K+1slash2}=sigma_{K}.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="88" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="\begin{align*}\begin{split}\Delta \sigma_k &amp;\equiv \sigma_{k-1/2} - \sigma_{k+1/...
...K+1/2} &amp;\equiv \sigma_{K} - \sigma_{K+1/2} = \sigma_{K}. \end{split}\end{align*}">|; 

$key = q/N_D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$ N_D$">|; 

$key = q/k_{S,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$ k_{S,i}$">|; 

$key = q/displaystyle=Idelta_{nn'}delta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="$\displaystyle = I \delta_{nn'} \delta_{mm'}$">|; 

$key = q/S_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$ S_0$">|; 

$key = q/displaystyletilde{g}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="$\displaystyle \tilde{g}_n^m$">|; 

$key = q/displaystyle=frac{displaystyle-S_{k-1slash2}-left(1+gamma_{k-1}-kappafrac{Deltaprac{1+gamma_{k}}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}right)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="100" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$\displaystyle = \frac{ \displaystyle - S_{k-1/2} - \left( 1 + \gamma_{k-1} - \k...
...+ \gamma_{k} }{ 1 + \gamma_{k-1}} \frac{\Delta p_{k}}{\Delta p_{k-1}} \right) }$">|; 

$key = q/^{-2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="$ ^{-2}$">|; 

$key = q/displaystyleDD{}{mu}left{(1-mu^2)DD{}{mu}tilde{P}_n^mright}+left{n(n+1)-frac{m^2}{1-mu^2}right}tilde{P}_n^m=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="$\displaystyle \DD{}{\mu} \left\{ (1-\mu^2) \DD{}{\mu} \tilde{P}_n^m \right\} + \left\{ n(n+1) - \frac{m^2}{1-\mu^2} \right\} \tilde{P}_n^m = 0 .$">|; 

$key = q/displaystyleleft.-alpha_g(1-alpha_A)F_S^Iexpleft(-tau_{S,i}(0)seczetaright)expleft(-(tau_{S,i}(0)-tau_i(z))seczeta_0right)right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$\displaystyle \left. - \alpha_g (1-\alpha_A) F_S^I
\exp \left( - \tau_{S,i}(0) ...
... \right)
\exp \left( - ( \tau_{S,i}(0)-\tau_i(z) ) \sec \zeta_0 \right)
\right]$">|; 

$key = q/{align*}{split}(mbox{rot}Dvect{v})_r&equivfrac{1}{rcosvarphi}DP{v_2}{lambda}-frat{1-mu^2}}DP{v_2}{lambda}-frac{1}{r}DP{}{mu}(sqrt{1-mu^2}v_1){split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="88" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="\begin{align*}\begin{split}(\mbox{rot} \Dvect{v})_r &amp;\equiv \frac{1}{r \cos \var...
..._2}{\lambda} - \frac{1}{r} \DP{}{\mu}(\sqrt{1-\mu^2}v_1) \end{split}\end{align*}">|; 

$key = q/(T^a_k,q^a_k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$ (T^a_k, q^a_k)$">|; 

$key = q/displaystyleY_n^m(lambda,varphi)equivP_n^m(sinvarphi)exp(imlambda).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="$\displaystyle Y_n^m(\lambda, \varphi) \equiv P_n^m(\sin \varphi) \exp(i m \lambda) .$">|; 

$key = q/B_{ins};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ B_{ins}$">|; 

$key = q/{displaystylew_j=frac{1}{2}int_{-1}^1frac{tilde{P}_J(mu)}{(mu-mu_j)tilde{P}^{'}_J(mu_j)}dmu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="$ {\displaystyle w_j
= \frac{1}{2} \int_{-1}^1
\frac{\tilde{P}_J(\mu)}
{(\mu-\mu_j)\tilde{P}^{'}_J(\mu_j)} d \mu
}$">|; 

$key = q/displaystyledot{sigma}_{k-1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\displaystyle \dot{\sigma}_{k-1/2}$">|; 

$key = q/displaystyle=-sum_{k=1}^{K}(tilde{D}_n^m)_kDeltasigma_k+frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}Z_{ij}Y_n^{m*}(lambda_i,mu_j)w_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$\displaystyle = - \sum_{k=1}^{K} (\tilde{D}_n^m)_k \Delta \sigma_k + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J} Z_{ij} Y_n^{m *} ( \lambda_i, \mu_j ) w_j.$">|; 

$key = q/displaystyle{calD}(q);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle {\cal D}(q)$">|; 

$key = q/displaystyle=widetilde{left[DP{}{lambda}left(frac{f}{rcos^2varphi}right)right]_n^m}=imwidetilde{left(frac{f}{rcos^2varphi}right)_n^m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="$\displaystyle = \widetilde{ \left[ \DP{}{\lambda} \left( \frac{f}{r \cos^2 \var...
... \right]_n^m } = im \widetilde{ \left( \frac{f}{r \cos^2 \varphi} \right)_n^m }$">|; 

$key = q/displaystyleT^{prime}(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle T^{\prime} (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystyleequivsum_{m=-M}^Msum_{n=|m|}^Ntilde{A}_n^mP_n^{m}(sinvarphi_j)exp(imlambda_i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="$\displaystyle \equiv \sum_{m=-M}^M \sum_{n=\vert m\vert}^N \tilde{A}_n^m P_n^{m}(\sin \varphi_j) \exp(im \lambda_i)$">|; 

$key = q/z=z_1,z_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$ z=z_1,z_2$">|; 

$key = q/displaystyleT=hat{T}+frac{L}{C_p}frac{hat{q}-q^*(hat{T},p)}{displaystyle1+frac{L}{C_p}DP{q^*}{T}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="79" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="$\displaystyle T = \hat{T} + \frac{L}{C_p} \frac{ \hat{q} - q^*(\hat{T},p) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} }$">|; 

$key = q/-1<beta_1<beta_2<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="$ -1 &lt; \beta_1 &lt; \beta_2 &lt; 1$">|; 

$key = q/displaystyle=left(DP{Dvect{T}}{t}right)_{rmNG}-underline{h}Dvect{D}+{calD}_HDvect{T}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$\displaystyle = \left( \DP{\Dvect{T}}{t} \right)_{\rm NG} - \underline{h} \Dvect{D} + {\cal D}_H \Dvect{T} .$">|; 

$key = q/DeltaT_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$ \Delta T_{k-1}$">|; 

$key = q/displaystylequadsum_{j=1}^{J}sum_{i=1}^{I}P_n^m(mu_j)P_{n'}^{m'}(mu_j)exp(imlambda_i)exp(-im'lambda_{i})w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="363" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="$\displaystyle \quad \sum_{j=1}^{J} \sum_{i=1}^{I} P_n^m (\mu_j) P_{n'}^{m'} (\mu_j) \exp(i m \lambda_i) \exp(-i m' \lambda_{i}) w_j$">|; 

$key = q/P_n^m(sinvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$ P_n^m(\sin \varphi)$">|; 

$key = q/displaystyleP=frac{Deltap}{g}(hat{q}-q).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="$\displaystyle P = \frac{\Delta p}{g} ( \hat{q} - q ) .$">|; 

$key = q/displaystyleP_n^mequivsqrt{frac{(2n+1)(n-|m|)!}{(n+|m|)!}}tilde{P}_n^m=sqrt{fracm|)!}}frac{(1-mu^2)^{frac{|m|}{2}}}{2^nn!}DD[n+|m|]{}{mu}(mu^2-1)^n.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="595" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="$\displaystyle P_n^m \equiv \sqrt{ \frac{(2n+1)(n-\vert m\vert)!}{(n+\vert m\ver...
...^2)^{\frac{\vert m\vert}{2}} }{2^n n!} \DD[n+\vert m\vert]{}{\mu} (\mu^2-1)^n .$">|; 

$key = q/nabla_H^2Y^m_n(lambda,varphi)=-frac{n(n+1)}{r^2}Y^m_n(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="$ \nabla_H^2 Y^m_n(\lambda, \varphi)
=- \frac{n(n+1)}{r^2} Y^m_n(\lambda,\varphi)$">|; 

$key = q/displaystylehat{rho}hat{q}=rhoq,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="$\displaystyle \hat{\rho} \hat{q} = \rho q,$">|; 

$key = q/displaystyleequivDP{f}{lambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="$\displaystyle \equiv \DP{f}{\lambda}$">|; 

$key = q/displaystyleJtilde{P}_J(mu)tilde{P}_{J-1}(mu_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="$\displaystyle J \tilde{P}_J (\mu) \tilde{P}_{J-1} (\mu_j)$">|; 

$key = q/displaystyleDeltaT_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$\displaystyle \Delta T_{k}$">|; 

$key = q/x=-1,1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="$ x=-1,1$">|; 

$key = q/{P_n^m}(n=|m|,|m|+1,|m|+2,cdots,N);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="$ \{ P_n^m \} (n=\vert m\vert,\vert m\vert+1,\vert m\vert+2,\cdots,N)$">|; 

$key = q/Y_n^m(lambda',varphi');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="$ Y_n^m(\lambda',\varphi')$">|; 

$key = q/A_{i,j}-A_{i,J-j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$ A_{i,j}-A_{i,J-j}$">|; 

$key = q/displaystyle{calD}'(Dvect{v});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\displaystyle {\cal D}'  (\Dvect{v})$">|; 

$key = q/{align*}{split}Phi_k-Phi_{k-1}&=C_{p}left[left(frac{sigma_{k-1slash2}}{sigma_k}right]T_{v,k-1}&=C_{p}alpha_kT_{v,k}+C_{p}beta_{k-1}T_{v,k-1}.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="76" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="\begin{align*}\begin{split}\Phi_k - \Phi_{k-1} &amp; = C_{p} \left[ \left( \frac{ \s...
... = C_{p} \alpha_k T_{v,k} + C_{p} \beta_{k-1} T_{v,k-1}. \end{split}\end{align*}">|; 

$key = q/displaystylefrac{1}{rcosvarphi}DP{Y_n^m}{lambda}=frac{1}{rcosvarphi}DP{}{lambda}p(imlambda)right)=frac{im}{rcosvarphi}P_n^m(sinvarphi)exp(imlambda).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="548" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="$\displaystyle \frac{1}{r \cos \varphi} \DP{Y_n^m}{\lambda} = \frac{1}{r \cos \v...
...da) \right) = \frac{im}{r \cos \varphi} P_n^m (\sin \varphi) \exp(im \lambda) .$">|; 

$key = q/F_S^I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="$ F_S^I$">|; 

$key = q/P_n^mP_{n'}^{m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="$ P_n^m P_{n'}^{m} $">|; 

$key = q/displaystyle{calD}(T);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle {\cal D}(T)$">|; 

$key = q/bar{calA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$ \bar{\cal A}$">|; 

$key = q/chi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="$ \chi$">|; 

$key = q/displaystyledelta_{t}{calA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle \delta_{t} {\cal A}$">|; 

$key = q/displaystyleh_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="$\displaystyle h_{ij}$">|; 

$key = q/displaystyleequivpslashp_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle \equiv p/p_s,$">|; 

$key = q/displaystylesum^{KMAX}_{k=1}c_vDeltaT_{k}Deltap_{k}=sum^{KMAX}_{k=1}c_vS_{grst}(T_{Bk}-T_{k})(p_sDeltasigma_{k});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="$\displaystyle \sum^{KMAX}_{k=1} c_v \Delta T_{k} \Delta p_{k}
= \sum^{KMAX}_{k=1} c_v S_{grst} (T_{Bk} - T_{k}) (p_s \Delta \sigma_{k})$">|; 

$key = q/{displaystylesum_{i=1}^{I}sum_{j=1}^{J}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="$ {\displaystyle \sum_{i=1}^{I} \sum_{j=1}^{J} }$">|; 

$key = q/displaystylehat{T}_{k}=T_{k}+S_{grst}(T_{Bk}-T_{k})-frac{sum^{KMAX}_{k=1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{KMAX}_{k=1}Deltap_{k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="418" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="$\displaystyle \hat{T}_{k}
= T_{k} + S_{grst} (T_{Bk} - T_{k})
- \frac{
\sum^{KM...
...k=1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{KMAX}_{k=1} \Delta p_{k}
}$">|; 

$key = q/displaystyleequiv(zeta+f)v-dot{sigma}DP{u}{sigma}-frac{RT_v^{prime}}{acosvarphi}DP{pi}{lambda}+{calF}_{lambda},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\displaystyle \equiv ( \zeta + f ) v - \dot{\sigma} \DP{u}{\sigma} - \frac{R T_v^{\prime}}{a \cos \varphi} \DP{\pi}{\lambda} + {\cal F}_{\lambda},$">|; 

$key = q/Deltap_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="$ \Delta p_s$">|; 

$key = q/P_n^0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$ P_n^0$">|; 

$key = q/1leileI,1lejleJ;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="$ 1 \le i \le I,1 \le j \le J$">|; 

$key = q/displaystyledot{sigma}=-sigmaDP{pi}{t}-int_{0}^{sigma}Ddsigma-int_{0}^{sigma}Dvect{v}_{H}cdotnabla_{sigma}pidsigma,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$\displaystyle \dot{\sigma} = - \sigma \DP{\pi}{t} - \int_{0}^{\sigma} D d \sigma - \int_{0}^{\sigma} \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma ,$">|; 

$key = q/displaystylehat{T}_{k+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="$\displaystyle \hat{T}_{k+1}$">|; 

$key = q/I=64,J=65;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="$ I=64, J=65$">|; 

$key = q/displaystyleleft(DP{f}{varphi}right)_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle \left(\DP{f}{\varphi}\right)_{ij}$">|; 

$key = q/H;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$ H$">|; 

$key = q/displaystyleL(mu)equivsum_{j=1}^{J}f(mu_j)prod_{k=1,kneqj}^{J}frac{mu-mu_k}{mu_j-mu_k}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="$\displaystyle L(\mu) \equiv \sum_{j=1}^{J} f(\mu_j) \prod_{k=1,k \neq j}^{J} \frac{ \mu-\mu_k}{\mu_j-\mu_k} .$">|; 

$key = q/tilde{P}_J(mu)S(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="$ \tilde{P}_J(\mu) S(\mu)$">|; 

$key = q/C_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="$ C_v$">|; 

$key = q/displaystyleleft(DP{pi}{t}right)^{rmNG}=-sum_{k=1}^{K}Dvect{v}_{k}cdotnablapiDeltasigma_{k}=Z_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$\displaystyle \left( \DP{\pi}{t} \right)^{\rm NG} = - \sum_{k=1}^{K} \Dvect{v}_{k} \cdot \nabla \pi \Delta \sigma_{k} = Z_{k} ,$">|; 

$key = q/overline{P_n^1}=P_n^1slashsqrt{2},overline{P_n^2}=P_n^2slashsqrt{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="$ \overline{P_n^1} = P_n^1/\sqrt{2},
\overline{P_n^2} = P_n^2/\sqrt{2}$">|; 

$key = q/displaystyleg;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$\displaystyle g$">|; 

$key = q/displaystyleleft(DP{D}{t}right)^{rmNG}=Dinv{acosvarphi}left{DP{{u_A}_{,k}}{lambda}+DP{({v_A}_{,k}cosvarphi)}{varphi}right}-nabla^{2}_{sigma}(;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle \left( \DP{D}{t} \right)^{\rm NG} = \Dinv{a \cos \varphi} \left\{...
...bda} + \DP{({v_A}_{,k} \cos \varphi)}{\varphi} \right\} - \nabla^{2}_{\sigma} ($">|; 

$key = q/displaystyletilde{h}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="$\displaystyle \tilde{h}_n^m$">|; 

$key = q/k+2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="$ k+2$">|; 

$key = q/M=21,N=42;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="$ M=21, N=42$">|; 

$key = q/displaystyle:qquad小規模運動過程(経度方向),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle : \qquad 小規模運動過程 (経度方向),$">|; 

$key = q/|m|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="$ \vert m\vert$">|; 

$key = q/{displaystylesum_{i,j}Y_n^{m*}(lambda_i,varphi_j)w_j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="$ {\displaystyle \sum_{i,j} Y_n^{m*}(\lambda_i,\varphi_j)w_j}$">|; 

$key = q/f=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="$ f=0$">|; 

$key = q/displaystyle:qquad発散水平拡散,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle : \qquad 発散水平拡散,$">|; 

$key = q/displaystyletilde{g}_n^m=imtilde{f}_n^m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="$\displaystyle \tilde{g}_n^m = im \tilde{f}_n^m .$">|; 

$key = q/displaystyle)_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle )_k$">|; 

$key = q/displaystylequadtimesleft(sum_{m''=-M}^{M}sum_{n''=|m''|}^Ntilde{C}_{n''}^{m''}en''}^{m''}(sinvarphi_j)right)P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="$\displaystyle \quad \times \left( \sum_{m''=-M}^{M} \sum_{n''=\vert m''\vert}^N...
...}^{m''}(\sin \varphi_j) \right) P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$">|; 

$key = q/displaystyleequivRslashC_p,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle \equiv R/C_p,$">|; 

$key = q/displaystyleP=(1-b)I.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$\displaystyle P = (1-b) I .$">|; 

$key = q/displaystylelangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="$\displaystyle \langle$">|; 

$key = q/k_{R,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="$ k_{R,i}$">|; 

$key = q/displaystyleDeltap_s=F_{evap}frac{g}{L}Deltat+hat{p_s}intS^{cond}_{q}Deltatdsigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="$\displaystyle \Delta p_s = F_{evap} \frac{g}{L} \Delta t + \hat{p_s} \int S^{cond}_{q} \Delta t d \sigma$">|; 

$key = q/{rmmax}[N];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="$ {\rm max}[N]$">|; 

$key = q/I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$ I$">|; 

$key = q/displaystylesum_{j=1}^{J}P_n^m(mu_j)P_{n'}^m(mu_j)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle \sum_{j=1}^{J} P_n^m (\mu_j) P_{n'}^m (\mu_j) w_j$">|; 

$key = q/q^c_k=q^*(T^c_k,p_k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$ q^c_k = q^*( T^c_k, p_k ) $">|; 

$key = q/{figure}center{picture{(300,170)(10,-20)put(20,10){vector(1,0){95}}put(30,0){vec0,-20){shortstack{五角形切断}}{par{picture{center{{{{figure};MSF=1.6;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="200" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="\begin{figure}\begin{center}
\begin{picture}(300,170)(10,-20)
\put(20 , 10){\v...
...00,-20) \{ shortstack\{五角形切断\}\}
\par
\end{picture}\end{center}\end{figure}">|; 

$key = q/displaystyle=sum_{k=0}^{n-1}(2k+1)(x-y)tilde{P}_k(x)tilde{P}_k(y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="$\displaystyle = \sum_{k=0}^{n-1} (2k+1)(x-y)\tilde{P}_k(x)\tilde{P}_k(y)$">|; 

$key = q/displaystyleoverline{F_S^I}(varphi)simeq-S_0(1-mathcal{A})(A_{ins}+B_{ins}cos^2varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="$\displaystyle \overline{F_S^I} (\varphi) \simeq - S_0 (1 - \mathcal{A})( A_{ins} + B_{ins} \cos^2 \varphi )$">|; 

$key = q/displaystyle=(2n+1)(x-y)tilde{P}_n(x)tilde{P}_n(y)+nleft|{array}{ll}tilde{P}_{n}(x)&tilde{P}_{n-1}(x)tilde{P}_{n}(y)&tilde{P}_{n-1}(y){array}right|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="$\displaystyle = (2n+1)(x-y)\tilde{P}_n(x)\tilde{P}_n(y) + n \left\vert \begin{a...
...de{P}_{n-1}(x) \ \tilde{P}_{n}(y) &amp; \tilde{P}_{n-1}(y) \end{array} \right\vert$">|; 

$key = q/displaystyleint_{-1}^1f(mu)P_n(mu)dmu=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="$\displaystyle \int_{-1}^1 f(\mu) P_n(\mu) d \mu = 0$">|; 

$key = q/displaystylea;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle a$">|; 

$key = q/K;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="$ K$">|; 

$key = q/I=128,J=65;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="$ I=128, J=65$">|; 

$key = q/M,N(m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="$ M,N(m)$">|; 

$key = q/displaystylepi(varphi,lambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \pi (\varphi, \lambda)$">|; 

$key = q/displaystyle=Idelta_{mm'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle = I \delta_{mm'}.$">|; 

$key = q/displaystyleA(mu)=sum_{n=|m|}^{infty}tilde{A}_n^mtilde{P}_n^m(mu),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="$\displaystyle A(\mu) = \sum_{n=\vert m\vert}^{\infty} \tilde{A}_n^m \tilde{P}_n^m(\mu),$">|; 

$key = q/displaystyle(1-mu^2)DD{}{mu}tilde{P}_{n}^{m}=(n+|m|)tilde{P}_{n-1}^m-nmutilde{P}_n^m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="$\displaystyle (1-\mu^2) \DD{}{\mu}\tilde{P}_{n}^{m} = (n+\vert m\vert) \tilde{P}_{n-1}^m - n \mu \tilde{P}_n^m .$">|; 

$key = q/{f_k(mu)}(k=0,1,2,cdots);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="$ \{ f_k(\mu) \}(k=0,1,2,\cdots) $">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^Jleft(sum_{m'=-M}^{M}sum_{n'=|m'|}^Ntilde{B}_{n'}^{m'}exp(im'lambda_i)P_{n'}^{m'}(sinvarphi_j)right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="401" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J \left( \sum_{m'=-M}^{M} \...
...}^N \tilde{B}_{n'}^{m'} \exp(im' \lambda_i) P_{n'}^{m'}(\sin \varphi_j) \right)$">|; 

$key = q/displaystyle=Dinv{acosvarphi}left{DP{u_A}{lambda}+DP{(v_Acosvarphi)}{varphi}right}-nabla^{2}_{sigma}(Phi+Roverline{T}pi+;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle =  \Dinv{a \cos \varphi} \left\{ \DP{u_A}{\lambda} + \DP{(v_A \cos \varphi)}{\varphi} \right\} - \nabla^{2}_{\sigma} ( \Phi + R \overline{T} \pi +$">|; 

$key = q/P_J(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$ P_J (\mu)$">|; 

$key = q/displaystylesum_{j=0}^{J-1}f_k(mu_j)f_{k'}(mu_{j})w_j=lambda_kdelta_{kk'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="$\displaystyle \sum_{j=0}^{J-1} f_k (\mu_j) f_{k'} (\mu_{j}) w_j = \lambda_k \delta_{kk'}$">|; 

$key = q/Jgefrac{3N_{{rmmax}}+1}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="$ J \ge \frac{3N_{{\rm max}}+1}{2}$">|; 

$key = q/Idelta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$ I \delta_{mm'}$">|; 

$key = q/displaystyleequivsum_{m=-M}^{M}sum_{n=|m|}^{N}tilde{A}_n^mY_n^m(lambda_i,varphi_j),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle \equiv \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \tilde{A}_n^m Y_n^m (\lambda_i,\varphi_j),$">|; 

$key = q/F_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="$ F_S$">|; 

$key = q/displaystyletau_{R,i}(z)=int_z^inftyk_{R,i}rhoqdz+int_z^inftybar{k}_{R,i}rhodz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="$\displaystyle \tau_{R,i}(z) = \int_z^\infty k_{R,i} \rho q dz + \int_z^\infty \bar{k}_{R,i} \rho dz$">|; 

$key = q/displaystyledelta_{t}Dvect{D}=left(DP{Dvect{D}}{t}right)_{rmNG}-nabla^{2}_{sigmaine{pi}^{t})+{calD}_M(Dvect{D}^{t-Deltat}+2Deltatdelta_{t}Dvect{D}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="489" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$\displaystyle \delta_{t} \Dvect{D} = \left( \DP{\Dvect{D}}{t} \right)_{\rm NG} ...
...} ) + {\cal D}_M ( \Dvect{D}^{t-\Delta t} + 2 \Delta t \delta_{t} \Dvect{D} ) ,$">|; 

$key = q/displaystylenabla^{2}_{sigma}=-frac{n(n+1)}{a^{2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$\displaystyle \nabla^{2}_{\sigma} = - \frac{n(n+1)}{a^{2}}$">|; 

$key = q/displaystyleDeltaT_{k-1}-DeltaT_{k}+gamma_{k-1}DeltaT_{k-1}-gamma_{k}DeltaT_{k}-p}frac{Deltap_{k-1slash2}}{2p_{k-1slash2}}DeltaT_{k}=-S_{k-1slash2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="633" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$\displaystyle \Delta T_{k-1} - \Delta T_{k} + \gamma_{k-1} \Delta T_{k-1} - \ga...
... \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \Delta T_{k} = - S_{k-1/2},$">|; 

$key = q/displaystyleq_k=bar{q}_k^{t-Deltat}+bIfrac{(q^c_k-q_k)}{displaystylesum_{k=k_B}^{k_T}(q^c_k-q_k)frac{Deltap_k}{g}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="108" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$\displaystyle q_k = \bar{q}_k^{t-\Delta t} + b I \frac{( q^c_k - q_k )} {\displaystyle \sum_{k=k_B}^{k_T} ( q^c_k - q_k ) \frac{\Delta p_k}{g} }$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$ i$">|; 

$key = q/n=0,1,2,cdots,N<J-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="$ n=0,1,2,\cdots,N &lt; J-1$">|; 

$key = q/^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="$ ^{-1}$">|; 

$key = q/times10^{-8};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="$ \times 10^{-8}$">|; 

$key = q/S(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="$ S(\mu)$">|; 

$key = q/displaystyle=sum_{j=1}^{J}f(mu_j)int^1_{-1}frac{{displaystyleprod_{k=1}^{J}(mu-mu_k)}}{(mu-mu_j){displaystyleprod_{k=1,kneqj}^{J}(mu_j-mu_k)}}dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="120" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="$\displaystyle = \sum_{j=1}^{J} f(\mu_j) \int^1_{-1} \frac{ {\displaystyle \prod...
... } { (\mu-\mu_j) {\displaystyle \prod_{k=1,k \neq j}^{J}(\mu_j-\mu_k) } } d \mu$">|; 

$key = q/-1<mu<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$ -1 &lt; \mu &lt; 1$">|; 

$key = q/128times64=8192;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="$ 128 \times 64 = 8192 $">|; 

$key = q/A_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$ A_{ij}$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}p_{ij}Y_n^{m*}w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} p_{ij} Y_n^{m*} w_j$">|; 

$key = q/displaystyleleft{1+frac{L}{C_p}left.DP{q^{*}}{T}right|_{k-1}right}DeltaT_{k-1}De}left{q^{*}(hat{T}_{k-1})-hat{q}_{k-1}right}Deltap_{k-1}hspace{-7em};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$\displaystyle \left\{ 1+ \frac{L}{C_p} \left. \DP{q^{*}}{T} \right\vert _{k-1} ...
...\{ q^{*} (\hat{T}_{k-1} ) - \hat{q}_{k-1} \right\} \Delta p_{k-1} \hspace{-7em}$">|; 

$key = q/{rmmax}[n+n'+n''];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="$ {\rm max}[n+n'+n'']$">|; 

$key = q/a_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="$ a_i$">|; 

$key = q/displaystylesum_{j=1}^JP_n^{m}(sinvarphi_j)P_{n'}^{m}(sinvarphi_j)w_j=delta_{nn'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="$\displaystyle \sum_{j=1}^J P_n^{m}(\sin \varphi_j) P_{n'}^{m}(\sin \varphi_j) w_j = \delta_{nn'}$">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ x$">|; 

$key = q/f-L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="$ f-L$">|; 

$key = q/-1lemule1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="$ -1 \le \mu \le 1$">|; 

$key = q/tilde{P}_J(mu_j)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$ \tilde{P}_J(\mu_j)=0$">|; 

$key = q/h=nabla_H^2f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="$ h = \nabla_H^2 f$">|; 

$key = q/B,C;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="$ B,C$">|; 

$key = q/displaystyleC_pT+Lq=C_phat{T}+Lhat{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="$\displaystyle C_p T + L q = C_p \hat{T} + L \hat{q}$">|; 

$key = q/displaystyleDP{Phi}{sigma}=-frac{RT_v}{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle \DP{\Phi}{\sigma} = - \frac{RT_v}{\sigma}.$">|; 

$key = q/displaystyleoverline{calA}^{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$\displaystyle \overline{\cal A}^{t}$">|; 

$key = q/hat{T},hat{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$ \hat{T}, \hat{q}$">|; 

$key = q/Deltaq_{evap};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$ \Delta q_{evap}$">|; 

$key = q/B_{zeta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ B_{\zeta }$">|; 

$key = q/j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$ j$">|; 

$key = q/J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$ J$">|; 

$key = q/displaystyle=-frac{1}{r}DP{psi}{varphi}+frac{1}{rcosvarphi}DP{chi}{lambda},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="$\displaystyle = - \frac{1}{r} \DP{\psi}{\varphi} + \frac{1}{r\cos\varphi} \DP{\chi}{\lambda} ,$">|; 

$key = q/displaystyle=-Dinv{acosvarphi}left{DP{(u_kq_k)}{lambda}+DP{(v_kq_kcosvarphi)}{varphi}right}+R_k+S_{q,k}+{calD}(q_k).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle = - \Dinv{a \cos \varphi} \left\{ \DP{(u_k q_k)}{\lambda} + \DP{(v_k q_k \cos \varphi)}{\varphi} \right\} + R_k + S_{q,k} + {\cal D}(q_k).$">|; 

$key = q/displaystyle%T_{v,k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle %
T_{v,k}$">|; 

$key = q/displaystyle=frac{{displaystylesum_{k=0}^{J-1}(2k+1)tilde{P}_k(mu)tilde{P}_k(mu_j)}}{Jtilde{P}_{J-1}(mu_j)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="120" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="$\displaystyle = \frac{ {\displaystyle \sum_{k=0}^{J-1} (2k+1) \tilde{P}_k(\mu) \tilde{P}_k(\mu_j) } } {J \tilde{P}_{J-1}(\mu_j)}$">|; 

$key = q/qll1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$ q \ll 1$">|; 

$key = q/displaystylepequivDP{f}{varphi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="$\displaystyle p \equiv \DP{f}{\varphi}$">|; 

$key = q/m=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="$ m=0$">|; 

$key = q/displaystylekappa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\displaystyle \kappa$">|; 

$key = q/displaystyle=Dinv{acosvarphi}left{DP{v_A}{lambda}-DP{(u_Acosvarphi)}{varphi}right}+{calD}(zeta),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle =  \Dinv{a \cos \varphi} \left\{ \DP{v_A}{\lambda} - \DP{(u_A \cos \varphi)}{\varphi} \right\} + {\cal D}(\zeta),$">|; 

$key = q/k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$ k$">|; 

$key = q/displaystyle:qquad比湿水平拡散,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle : \qquad 比湿水平拡散,$">|; 

$key = q/displaystyle=left{{array}{ll}{displaystylefrac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}}Aij}Y_n^{m*}(lambda_i,varphi_j)w_j,&1lemleM,quadmlenleN.{array}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="464" HEIGHT="119" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle = \left\{ \begin{array}{ll} {\displaystyle \frac{1}{I} \sum_{i=1}...
...varphi_j) w_j , &amp;    1 \le m \le M, \quad m \le n \le N. \end{array} \right.$">|; 

$key = q/N_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="$ N_R$">|; 

$key = q/displaystylef;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\displaystyle f$">|; 

$key = q/[];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$ [  ]$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}q_{ij}Y_n^{m*}w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} q_{ij} Y_n^{m*} w_j$">|; 

$key = q/P_n^m(sinvarphi)exp(imlambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="$ P_n^m(\sin \varphi) \exp(im \lambda)$">|; 

$key = q/k+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$ k+1$">|; 

$key = q/displaystyleY^m_n(lambda,varphi)=sum_{m'=-n}^{n}A_n^{m'}Y^{m'*}_n(lambda',varphi').;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="$\displaystyle Y^m_n(\lambda, \varphi) = \sum_{m'=-n}^{n} A_n^{m'} Y^{m'*}_n(\lambda',\varphi') .$">|; 

$key = q/displaystylefrac{1}{I}sum_{n=1}^{I}g(lambda_n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="$\displaystyle \frac{1}{I} \sum_{n=1}^{I} g(\lambda_n)$">|; 

$key = q/F_R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="$ F_R$">|; 

$key = q/A(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$ A(\lambda,\varphi)$">|; 

$key = q/T^a_1=hat{T}_1,q^a_1=hat{q}_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$ T^a_1=\hat{T}_1, q^a_1=\hat{q}_1 $">|; 

$key = q/nabla^{'2}_HY_n^m=-frac{n(n+1)}{r^2}Y_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="$ \nabla^{'2}_H Y_n^m = -\frac{n(n+1)}{r^2} Y_n^m $">|; 

$key = q/displaystyleequivDinv{acosvarphi}left{DP{v}{lambda}-DP{(ucosvarphi)}{varphi}right}:quad渦度[mathrm{s}^{-1}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle \equiv \Dinv{a \cos \varphi} \left\{ \DP{v}{\lambda} - \DP{(u \cos \varphi)}{\varphi} \right\} : \quad 渦度 [\mathrm{s}^{-1}],$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}imleft(frac{f}{rcos^2varphi}right)_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} im \left( \frac{f}{r \cos^2 \varphi} \right)_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j$">|; 

$key = q/displaystylesum^{KMAX}_{k=1}DeltaT_{k}Deltap_{k}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="$\displaystyle \sum^{KMAX}_{k=1} \Delta T_{k} \Delta p_{k} = 0$">|; 

$key = q/R_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="$ R_v$">|; 

$key = q/Ige2M+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="$ I \ge 2M+1$">|; 

$key = q/sinvarphi=mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$ \sin \varphi = \mu$">|; 

$key = q/displaystyleqequivcos^2varphiDP{f}{varphi}=cos^2varphip;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="$\displaystyle q \equiv \cos^2\varphi \DP{f}{\varphi} = \cos^2\varphi p$">|; 

$key = q/displaystyle{calT}^f(z_1,z_2)=sum_{i=1}^{N_R}b_iexpleft(-delta_R|tau_{R,i}(z_1)-tau_{R,i}(z_2)|right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="$\displaystyle {\cal T}^f(z_1,z_2) = \sum_{i=1}^{N_R} b_i \exp \left( - \delta_R \vert \tau_{R,i}(z_1) - \tau_{R,i}(z_2) \vert \right)$">|; 

$key = q/displaystylehat{q}>q^*(hat{T},p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$\displaystyle \hat{q} &gt; q^*(\hat{T},p)$">|; 

$key = q/displaystylehspace*{2cm}+(n+|m|)sqrt{frac{1}{2n-1}frac{(n-1+|m|)!}{(n-1-|m|)!}}P_{n-1}^m=0,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="$\displaystyle \hspace*{2cm} +(n+\vert m\vert) \sqrt{ \frac{1}{2n-1} \frac{(n-1+\vert m\vert)!}{(n-1-\vert m\vert)!} } P_{n-1}^m = 0 ,$">|; 

$key = q/displaystylePhi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle \Phi$">|; 

$key = q/-frac{n(n+1)}{r^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="$ - \frac{n(n+1)}{r^2}$">|; 

$key = q/displaystyleint_{-1}^1P_n(mu)P_n'(mu)dmu=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="$\displaystyle \int_{-1}^1 P_n(\mu) P_n'(\mu) d \mu = 2$">|; 

$key = q/displaystylev=frac{1}{rcosvarphi}DP{psi}{lambda}+frac{1}{r}DP{chi}{varphi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="$\displaystyle v = \frac{1}{r\cos\varphi} \DP{\psi}{\lambda} + \frac{1}{r} \DP{\chi}{\varphi}$">|; 

$key = q/M=21;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="$ M=21$">|; 

$key = q/displaystyleb_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle b_k$">|; 

$key = q/displaystyledelta_{t}Dvect{T}=left(DP{Dvect{T}}{t}right)_{rmNG}-underline{h}overvect{D}}^{t}+{calD}_H(Dvect{T}^{t-Deltat}+2Deltatdelta_{t}Dvect{T}).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle \delta_{t} \Dvect{T} = \left( \DP{\Dvect{T}}{t} \right)_{\rm NG} ...
...{t} + {\cal D}_H ( \Dvect{T}^{t-\Delta t} + 2 \Delta t \delta_{t} \Dvect{T} ) .$">|; 

$key = q/displaystyleDP{zeta_k}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\displaystyle \DP{\zeta_k}{t}$">|; 

$key = q/displaystyleW_{kl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$\displaystyle W_{kl}$">|; 

$key = q/n-m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$ n-m$">|; 

$key = q/displaystyledot{sigma}^{rmNG}_{k-1slash2}=-sigma_{k-1slash2}left(DP{pi}{t}right)^{rmNG}-sum_{l=k}^{K}Dvect{v}_{l}cdotnablapiDeltasigma_{l},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle \dot{\sigma}^{\rm NG}_{k-1/2} = - \sigma_{k-1/2} \left( \DP{\pi}{...
...t)^{\rm NG} - \sum_{l=k}^{K} \Dvect{v}_{l} \cdot \nabla \pi \Delta \sigma_{l} ,$">|; 

$key = q/displaystyle=left(frac{sigma_{k-1slash2}}{sigma_k}right)^{kappa}-1,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle = \left( \frac{ \sigma_{k-1/2} } { \sigma_k } \right)^{\kappa} -1 ,$">|; 

$key = q/displaystylev_A(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle v_A (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystyleoverline{T}(sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \overline{T} (\sigma)$">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$ N$">|; 

$key = q/displaystylehat{T}_{k+1}+S_{grst}(T_{Bk+1}-hat{T}_{k+1})-frac{sum^{k+2}_{k=k}S_{grst}(T_{Bk}-hat{T}_{k})Deltap_{k}}{sum^{k+2}_{k=k}Deltap_{k}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="$\displaystyle \hat{T}_{k+1} + S_{grst} (T_{Bk+1} - \hat{T}_{k+1})
- \frac{
\sum...
..._{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k}
}{
\sum^{k+2}_{k=k} \Delta p_{k}
},$">|; 

$key = q/{Y_n^m|m=0,1,2,cdots,n=|m|,|m+1|,cdots};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="$ \{ Y_n^m \vert m=0,1,2,\cdots,  n=\vert m\vert,\vert m+1\vert,\cdots \}$">|; 

$key = q/displaystylefrac{(hat{p_s}+Deltap_s)sigma}{RT}q,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img468.png"
 ALT="$\displaystyle \frac{(\hat{p_s} + \Delta p_s) \sigma}{RT} q,$">|; 

$key = q/displaystyle=sum_{m,n}imtilde{f}_n^mY_n^m(lambda_i,varphi_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="$\displaystyle = \sum_{m,n} im \tilde{f}_n^m Y_n^m (\lambda_i,\varphi_j)$">|; 

$key = q/displaystyleC=sum_{m=-M}^{M}sum_{n=|m|}^{N}left(tilde{C}_n^mexp(imlambda)right)P_n^m(sinvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="$\displaystyle C= \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \left( \tilde{C}_n^m \exp(im \lambda) \right) P_n^m(\sin \varphi)$">|; 

$key = q/2J-1ge{rmmax}[n+n'+n'']=3{rmmax}[N];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="$ 2J-1 \ge {\rm max}[n+n'+n''] = 3 {\rm max}[N]$">|; 

$key = q/q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$ q$">|; 

$key = q/N_{{rmmax}}=M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="$ N_{{\rm max}}=M$">|; 

$key = q/-1<alpha<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="$ -1&lt;\alpha&lt;1$">|; 

$key = q/displaystyle:quad気温[mathrm{K}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle : \quad 気温 [\mathrm{K}],$">|; 

$key = q/Dvect{T}={T_{k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$ \Dvect{T}=\{ T_{k} \}$">|; 

$key = q/bar{k}_{S,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="$ \bar{k}_{S,i}$">|; 

$key = q/mu_j,mu_{j'}(1lej,j'leJ);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="$ \mu_j, \mu_{j'}(1 \le j,j' \le J)$">|; 

$key = q/A_{ij}^{odd};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$ A_{ij}^{odd}$">|; 

$key = q/displaystylesum_{j=1}^{J}sum_{i=1}^{I}P_n^m(mu_j)P_{n'}^{m'}(mu_j)exp(imlambda_i)exp(-im'lambda_i)w_j=Idelta_{nn'}delta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="$\displaystyle \sum_{j=1}^{J} \sum_{i=1}^{I} P_n^m (\mu_j) P_{n'}^{m'} (\mu_j) \exp(i m \lambda_i) \exp(-i m' \lambda_i) w_j = I \delta_{nn'} \delta_{mm'}$">|; 

$key = q/sigma=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$ \sigma=1$">|; 

$key = q/displaystyleT(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle T (\varphi, \lambda, \sigma)$">|; 

$key = q/J=K=M=N_{tr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="$ J=K=M =N_{tr} $">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}imf_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} im f_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j$">|; 

$key = q/displaystyleequiv-(zeta+f)u-dot{sigma}DP{v}{sigma}-frac{RT_v^{prime}}{a}DP{pi}{varphi}+{calF}_{varphi},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle \equiv - ( \zeta + f ) u - \dot{\sigma} \DP{v}{\sigma} - \frac{R T_v^{\prime}}{a} \DP{\pi}{\varphi} + {\cal F}_{\varphi},$">|; 

$key = q/m,n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$ m,n$">|; 

$key = q/displaystylehat{p_{s}}hat{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="$\displaystyle \hat{p_{s}} \hat{q}$">|; 

$key = q/{P_n}(n=0,1,2,cdots,J-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="$ \{ P_n \}(n=0,1,2,\cdots,J-1) $">|; 

$key = q/tilde{B}_n^m=tilde{B}_n^{m*},{itetc.};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="$ \tilde{B}_n^m = \tilde{B}_n^{m*}, {\it etc.}$">|; 

$key = q/displaystyleR_{kl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="$\displaystyle R_{kl}$">|; 

$key = q/displaystyle:quad水蒸気分子量比.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle : \quad 水蒸気分子量比.$">|; 

$key = q/(2times21+1)times(21+1)=946;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="$ (2 \times 21 +1) \times (21+1)= 946$">|; 

$key = q/P_J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="$ P_J$">|; 

$key = q/{align*}{split}D&=frac{1}{rcosvarphi}DP{u}{lambda}+frac{1}{rcosvarphi}DP{}{varphi}(vcosvarphi).{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="43" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="\begin{align*}\begin{split}D &amp;= \frac{1}{r \cos \varphi} \DP{u}{\lambda} + \frac{1}{r \cos \varphi} \DP{}{\varphi} (v \cos \varphi) . \end{split}\end{align*}">|; 

$key = q/f(mu)-L(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img680.png"
 ALT="$ f(\mu)-L(\mu)$">|; 

$key = q/displaystyle%(;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle %
($">|; 

$key = q/displaystyledot{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle \dot{\sigma}$">|; 

$key = q/S^{cond}_{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="$ S^{cond}_{q}$">|; 

$key = q/displaystyleF_S(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$\displaystyle F_S(z)$">|; 

$key = q/mathcal{A};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="$ \mathcal{A}$">|; 

$key = q/times10^6;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="$ \times 10^6$">|; 

$key = q/{displaystylex_j=cosfrac{j-1slash2}{n}pi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="$ {\displaystyle x_j=\cos \frac{j-1/2}{n}\pi }$">|; 

$key = q/displaystylehspace{3em}=-left(1+gamma_{k}right)DeltaT_{k}Deltap_{k}+frac{L}{C_p}Deltap_{k-1}+left{hat{q}_{k}-q^{*}(hat{T}_{k})right}Deltap_{k}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="588" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$\displaystyle \hspace{3em} = - \left( 1 + \gamma_{k} \right) \Delta T_{k} \Delt...
...{k-1} + \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\} \Delta p_{k} \right]$">|; 

$key = q/f'(alpha)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="$ f'(\alpha)=0$">|; 

$key = q/C;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="$ C$">|; 

$key = q/Deltasigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$ \Delta \sigma$">|; 

$key = q/{align*}{split}&left{(1-2Deltat{calD}_H)(1-2Deltat{calD}_M)underline{I}-(Deltat)[pi^{t-Deltat}+Deltatleft(DP{pi}{t}right)_{rmNG}right]right}.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="546" HEIGHT="167" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="\begin{align*}\begin{split}&amp; \left\{ ( 1-2\Delta t {\cal D}_H )( 1-2\Delta t {\c...
...t \left( \DP{\pi}{t} \right)_{\rm NG} \right] \right\} . \end{split}\end{align*}">|; 

$key = q/displaystyle=q^{*}(T_{k},p_{k}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$\displaystyle = q^{*} (T_{k}, p_{k}),$">|; 

$key = q/{displaystylesigmaequivfrac{p}{p_s}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$ {\displaystyle \sigma \equiv \frac{p}{p_s} }$">|; 

$key = q/displaystyle(1-mu^2)DD{}{mu}P_n^m=(n+|m|)sqrt{frac{(n-|m|)(2n+1)}{(n+|m|)(2n-1)}}P_{n-1}^m-nmuP_n^m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$\displaystyle (1-\mu^2) \DD{}{\mu} P_n^m = (n+\vert m\vert) \sqrt{ \frac{(n-\vert m\vert)(2n+1)}{(n+\vert m\vert)(2n-1)} } P_{n-1}^m - n \mu P_n^m .$">|; 

$key = q/displaystyle{calD}(zeta)=-K_{HD}left[(-1)^{N_Dslash2}nabla^{N_D}-left(frac{2}{a^2}right)^{N_Dslash2}right]zeta,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$\displaystyle {\cal D}(\zeta) = - K_{HD} \left[ (-1)^{N_D/2} \nabla^{N_D} - \left( \frac{2}{a^2} \right)^{N_D/2} \right] \zeta ,$">|; 

$key = q/displaystylecoszeta=cosvarphicosdelta_ScosH+sinvarphisindelta_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="$\displaystyle \cos \zeta = \cos \varphi \cos \delta_S \cos H + \sin \varphi \sin \delta_S$">|; 

$key = q/P_n(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="$ P_n(\mu)$">|; 

$key = q/(n,m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="$ (n,m)$">|; 

$key = q/displaystyleS_{kl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$\displaystyle S_{kl}$">|; 

$key = q/displaystyle=-left{DeltaT_{k}+frac{L}{C_p}(q_{k}-hat{q}_{k})right}Deltap_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$\displaystyle = - \left\{ \Delta T_{k} + \frac{L}{C_p} (q_{k} - \hat{q}_{k}) \right\} \Delta p_{k},$">|; 

$key = q/displaystylesigma_k=left{frac{1}{1+kappa}left(frac{sigma^{kappa+1}_{k-1slash2}-sh2}}{sigma_{k-1slash2}-sigma_{k+1slash2}}right)right}^{1slashkappa}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \sigma_k = \left\{ \frac{1}{1+\kappa} \left( \frac{ \sigma^{\kapp...
... +1}_{k+1/2} } { \sigma_{k-1/2} - \sigma_{k+1/2} } \right) \right\}^{1/\kappa}.$">|; 

$key = q/n=|m|,|m|+1,cdots,|m|+J-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="$ n=\vert m\vert, \vert m\vert+1, \cdots, \vert m\vert+J-1$">|; 

$key = q/displaystyle=frac{1}{rcos^2varphi_i}g_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="$\displaystyle = \frac{1}{r \cos^2 \varphi_i} g_{ij}$">|; 

$key = q/displaystyleB=sum_{m=-M}^{M}sum_{n=|m|}^{N}left(tilde{B}_n^mexp(imlambda)right)P_n^m(sinvarphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="$\displaystyle B= \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \left( \tilde{B}_n^m \exp(im \lambda) \right) P_n^m(\sin \varphi) ,$">|; 

$key = q/T^a_{k_B}=hat{T}_{k_B},q^a_{k_B}=q^*(hat{T}_{k_B},p_{k_B});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$ T^a_{k_B} = \hat{T}_{k_B},
q^a_{k_B} = q^*( \hat{T}_{k_B}, p_{k_B} ) $">|; 

$key = q/q^{*};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$ q^{*}$">|; 

$key = q/displaystyle=sum_{j=1}^{J}f(mu_j)int_{-1}^1frac{tilde{P}_J(mu)}{(mu-mu_j)tilde{P}^{'}_J(mu_j)}dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="$\displaystyle = \sum_{j=1}^{J} f(\mu_j) \int_{-1}^1 \frac{\tilde{P}_J(\mu)} {(\mu-\mu_j)\tilde{P}^{'}_J(\mu_j)} d \mu$">|; 

$key = q/{align*}{split}mbox{div}_HDvect{v}&equivfrac{1}{rcosvarphi}DP{v_1}{lambda}+frac{t{1-mu^2}}DP{v_1}{lambda}+frac{1}{r}DP{}{mu}(sqrt{1-mu^2}v_2){split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="88" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="\begin{align*}\begin{split}\mbox{div}_H \Dvect{v} &amp;\equiv \frac{1}{r \cos \varph...
...{\lambda} + \frac{1}{r} \DP{}{\mu}( \sqrt{1-\mu^2} v_2 ) \end{split}\end{align*}">|; 

$key = q/displaystyleequivnabla_H^2psi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="$\displaystyle \equiv \nabla_H^2 \psi$">|; 

$key = q/f'=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$ f'=0$">|; 

$key = q/displaystyle=frac{displaystyle(1+gamma_{k-1})Deltap_{k-1}S_{k-1slash2}+left(1+gaac{Deltap_{k-1slash2}}{2p_{k-1slash2}}right)(1+gamma_{k})Deltap_{k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="687" HEIGHT="100" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="$\displaystyle = \frac{ \displaystyle (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2...
...pa \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) (1 + \gamma_{k}) \Delta p_{k} }$">|; 

$key = q/(k-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="$ (k-1)$">|; 

$key = q/displaystyledot{sigma}_{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle \dot{\sigma}_{1/2}$">|; 

$key = q/displaystyle=-left(frac{alpha_{k}}{Deltasigma_{k}}Deltasigma_{l}delta_{kleql}+fr}{Deltasigma_{k}}Deltasigma_{l}delta_{k+1leql}right)overline{T}_{k}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$\displaystyle = - \left( \frac{ \alpha_{k} }{ \Delta \sigma_{k} } \Delta \sigma...
...a \sigma_{k} } \Delta \sigma_{l} \delta_{k+1 \leq l} \right) \overline{T}_{k} .$">|; 

$key = q/displaystylewidetilde{left(DP{f}{varphi}right)}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle \widetilde{\left(\DP{f}{\varphi}\right)}_n^m$">|; 

$key = q/m=n=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="$ m=n=0$">|; 

$key = q/displaystyleleft{1+gamma_{k-1}right}DeltaT_{k-1}Deltap_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$\displaystyle \left\{ 1 + \gamma_{k-1} \right\} \Delta T_{k-1} \Delta p_{k-1}$">|; 

$key = q/displaystyle=-sum_{i}sum_{j}f_{n'}^{m'}P_{n'}^{m'}(varphi_j)exp(im'lambda_i)left.DD{P_{n}^{m}}{varphi}right|_jexp(-imlambda_i)w_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="$\displaystyle = - \sum_{i} \sum_{j} f_{n'}^{m'} P_{n'}^{m'}(\varphi_j) \exp(im' \lambda_i) \left. \DD{P_{n}^{m}}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j .$">|; 

$key = q/displaystyle:qquad凝結,小規模運動過程等による水蒸気ソース,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle : \qquad 凝結, 小規模運動過程等による水蒸気ソース,$">|; 

$key = q/displaystylesum_{k=0}^{J-1}frac{f_k(mu_j)f_k(mu_{j'})}{lambda_k}=frac{1}{w_j}delta_{jj'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="$\displaystyle \sum_{k=0}^{J-1} \frac{f_k (\mu_j) f_k (\mu_{j'}) }{\lambda_k} = \frac{1}{w_j} \delta_{jj'}$">|; 

$key = q/displaystyle=frac{I}{2}int_{-1}^1P_n^m(mu)P_{n'}^{m}(mu)dmu.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="$\displaystyle = \frac{I}{2} \int_{-1}^1 P_n^m (\mu) P_{n'}^{m} (\mu) d\mu .$">|; 

$key = q/displaystyle=frac{1}{I}sum_{m'=-M}^{M}sum_{n'=|m'|}^Ntilde{A}_{n'}^{m'}sum_{i=1}-m)lambda)sum_{j=1}^JP_n^{m}(sinvarphi_j)P_{n'}^{m'}(sinvarphi_j)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="510" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{m'=-M}^{M} \sum_{n'=\vert m'\vert}^N \tilde{A...
...) \lambda) \sum_{j=1}^J P_n^{m}(\sin \varphi_j) P_{n'}^{m'}(\sin \varphi_j) w_j$">|; 

$key = q/displaystyle=-frac{1}{I}sum_{i,j}left(sum_{m',n'}tilde{f}_{n'}^{m'}P_{n'}^{m'}(varphi_j)exp(im'lambda_i)right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="$\displaystyle = - \frac{1}{I} \sum_{i,j} \left( \sum_{m',n'} \tilde{f}_{n'}^{m'} P_{n'}^{m'}(\varphi_j) \exp(i m' \lambda_i) \right)$">|; 

$key = q/displaystyle:quad経度[mathrm{deg.}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle : \quad 経度 [\mathrm{deg.}],$">|; 

$key = q/displaystyleT^a_{k+1}>hat{T}_{k+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="$\displaystyle T^a_{k+1} &gt; \hat{T}_{k+1}$">|; 

$key = q/1leileI,1lejleJ,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="$ 1 \le i \le I , 1 \le j \le J, $">|; 

$key = q/L-f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="$ L-f$">|; 

$key = q/displaystylevarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle \varphi$">|; 

$key = q/hat{rho};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="$ \hat{\rho}$">|; 

$key = q/displaystyle(1-mu^2)DP{tilde{P}_n}{mu}=ntilde{P}_{n-1}(mu)-nmutilde{P}_n(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="$\displaystyle (1-\mu^2) \DP{\tilde{P}_n}{\mu} = n \tilde{P}_{n-1}(\mu) - n \mu \tilde{P}_n(\mu)$">|; 

$key = q/displaystyle=alpha_kleft[1-left(frac{sigma_k}{sigma_{k-1}}right)^{kappa}right]^{-1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle = \alpha_k \left[ 1- \left( \frac{ \sigma_k }{ \sigma_{k-1} } \right)^{\kappa} \right]^{-1},$">|; 

$key = q/g(lambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="$ g(\lambda)$">|; 

$key = q/Dvect{v};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="$ \Dvect{v}$">|; 

$key = q/displaystyleT_{k+1}+S_{grst}(T_{Bk+1}-T_{k+1})-frac{sum^{k+1}_{k=k-1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{k+1}_{k=k-1}Deltap_{k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="$\displaystyle T_{k+1} + S_{grst} (T_{Bk+1} - T_{k+1})
- \frac{
\sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{k+1}_{k=k-1} \Delta p_{k}
}$">|; 

$key = q/tilde{P}_n^0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="$ \tilde{P}_n^0$">|; 

$key = q/P_n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$ P_n$">|; 

$key = q/times10^{10};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="$ \times 10^{10}$">|; 

$key = q/M=42,N=42;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="$ M=42, N=42$">|; 

$key = q/{tilde{P}_n^m|n=|m|,|m+1|,cdots};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="$ \{ \tilde{P}_n^m \vert n=\vert m\vert,\vert m+1\vert,\cdots \}$">|; 

$key = q/n=J,mu=mu_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="$ n=J, \mu=\mu_j$">|; 

$key = q/sigma_{k-1slash2}(k=1,2,cdots,K);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$ \sigma_{k-1/2}  (k=1,2,\cdots,K)$">|; 

$key = q/displaystyleA_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle A_{ij}$">|; 

$key = q/u;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$ u$">|; 

$key = q/displaystyle)_{k}-nabla^{2}_{sigma}sum_{k=1}^{K}W_{kl}(T_{v,l}-T_{l})+{calD}(D_{k}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$\displaystyle )_{k} - \nabla^{2}_{\sigma} \sum_{k=1}^{K} W_{kl} ( T_{v,l}-T_{l} ) + {\cal D}(D_{k}) ,$">|; 

$key = q/displaystyleequivsum_{m=-M}^Msum_{n=|m|}^Ntilde{f}_n^mleft.DD{P_n^m}{varphi}right|_jexp(imlambda_i),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \equiv \sum_{m=-M}^M \sum_{n=\vert m\vert}^N \tilde{f}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _j \exp(im \lambda_i) ,$">|; 

$key = q/exp(imlambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="$ \exp(im\lambda)$">|; 

$key = q/displaystylequadtimessum_{i=1}^Iexp(i(m'+m''-m)lambda_i)sum_{j=1}^JP_{n'}^{m'}(sinvarphi_j)P_{n''}^{m''}(sinvarphi_j)P_n^{m}(sinvarphi_j)w_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="515" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="$\displaystyle \quad \times \sum_{i=1}^I \exp(i(m'+m''-m) \lambda_i) \sum_{j=1}^...
...m'}(\sin \varphi_j) P_{n''}^{m''}(\sin \varphi_j) P_n^{m}(\sin \varphi_j) w_j .$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^JB_{ij}C_{ij}P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J B_{ij} C_{ij} P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$">|; 

$key = q/displaystyle:quad緯度[mathrm{deg.}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle : \quad 緯度 [\mathrm{deg.}],$">|; 

$key = q/displaystylebeta_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle \beta_k$">|; 

$key = q/f'=2nx(x^2-1)^{n-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="$ f'=2nx(x^2-1)^{n-1}$">|; 

$key = q/displaystyle∴P_{n+1}^m=sqrt{frac{(2n+1)(2n+3)}{(n-|m|+1)(n+|m|+1)}}muP_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="$\displaystyle ∴ P_{n+1}^m = \sqrt{ \frac{(2n+1)(2n+3)}{(n-\vert m\vert+1)(n+\vert m\vert+1)} } \mu P_n^m$">|; 

$key = q/displaystyleleft(DP{f}{lambda}right)_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle \left( \DP{f}{\lambda} \right)_{ij}$">|; 

$key = q/{Y_n^m|m=-n,-n+1,cdots,n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="$ \{Y_n^m \vert m= -n, -n+1,\cdots,n \}$">|; 

$key = q/T,q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="$ T,q$">|; 

$key = q/tilde{P}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="$ \tilde{P}_n^m$">|; 

$key = q/frac{I-1}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="$ \frac{I-1}{2}$">|; 

$key = q/J-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="$ J-1$">|; 

$key = q/tilde{A}_n^m(-MlemleM,|m|lenleN);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="$ \tilde{A}_n^m ( -M \le m \le M,  \vert m\vert \le n \le N) $">|; 

$key = q/displaystyle=-Isum_{j}f_{n'}^{m}P_{n'}^{m}(varphi_j)left.DD{P_{n}^{m}}{varphi}right|_jw_jdelta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="$\displaystyle = - I \sum_{j} f_{n'}^{m} P_{n'}^{m}(\varphi_j) \left.\DD{P_{n}^{m}}{\varphi}\right\vert _j w_j \delta_{mm'}$">|; 

$key = q/M<I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="$ M &lt; I$">|; 

$key = q/sim;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$ \sim$">|; 

$key = q/mu_j（j=1,2,cdots,J）;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$ \mu_j（j=1,2,\cdots,J）$">|; 

$key = q/displaystylezeta(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \zeta (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystyleF_S^I(lambda,varphi)=-S_0r_S^{-2}coszeta.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$\displaystyle F_S^I (\lambda, \varphi)= - S_0 r_S^{-2} \cos \zeta .$">|; 

$key = q/{displaystyleleft{tilde{A}^m_nexp(imlambda)right}^*=tilde{A}^{-m}_nexp(-imlambda)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$ {\displaystyle
\left\{\tilde{A}^m_n \exp(im\lambda) \right\}^*
= \tilde{A}^{-m}_n \exp(-im\lambda) }$">|; 

$key = q/displaystyle=Deltasigma_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$\displaystyle = \Delta \sigma_{k} ,$">|; 

$key = q/displaystylesum_{i=1}^{I}exp(imlambda_i)exp(-im'lambda_i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \sum_{i=1}^{I} \exp(im \lambda_i) \exp(-im' \lambda_i)$">|; 

$key = q/P_n,P_n^1,P_n^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="$ P_n,P_n^1,P_n^2$">|; 

$key = q/tilde{A}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$ \tilde{A}_n^m$">|; 

$key = q/hat{T}_{k+2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="$ \hat{T}_{k+2}$">|; 

$key = q/displaystyleDeltaT_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$\displaystyle \Delta T_{k-1}$">|; 

$key = q/displaystylefrac{Deltaq_{evap}}{Deltat}=frac{F_{evap}L^{-1}rho_s^{-1}}{Deltaz}=fevap}L^{-1}rho_s^{-1}}{Deltapslash(rho_sg)}=F_{evap}frac{g}{LDeltap};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="381" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$\displaystyle \frac{\Delta q_{evap}}{\Delta t}
= \frac{ F_{evap} L^{-1} \rho_s^...
...vap} L^{-1} \rho_s^{-1}}{\Delta p / (\rho_s g)}
= F_{evap} \frac{g}{L \Delta p}$">|; 

$key = q/displaystyleDP{T}{z}-frac{RT}{C_pp}DP{p}{z}+frac{L}{C_p}DP{q^*}{z}<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="$\displaystyle \DP{T}{z} - \frac{RT}{C_p p} \DP{p}{z} + \frac{L}{C_p} \DP{q^*}{z} &lt; 0$">|; 

$key = q/sigma_k(k=1,2,ldotsK);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$ \sigma_k  (k=1,2,\ldots K)$">|; 

$key = q/im'tilde{f}_{n'}^{m'}=tilde{g}_{n'}^{m'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="$ im' \tilde{f}_{n'}^{m'}
= \tilde{g}_{n'}^{m'} $">|; 

$key = q/displaystylew_j=frac{1-mu_j^2}{(Jsqrt{frac{1}{2J-1}}P_{J-1}(mu_j))^2}=frac{(2J-1)(1-mu_j^2)}{(JP_{J-1}(mu_j))^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="$\displaystyle w_j = \frac{1-\mu_j^2} {(J \sqrt{ \frac{1}{2J-1} } P_{J-1}(\mu_j))^2 } = \frac{(2J-1)(1-\mu_j^2)} {(J P_{J-1}(\mu_j))^2 }$">|; 

$key = q/displaystyleA(mu)=sum_{n=|m|}^{infty}tilde{A}_n^mP_n^m(mu),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="$\displaystyle A(\mu) = \sum_{n=\vert m\vert}^{\infty} \tilde{A}_n^m P_n^m(\mu),$">|; 

$key = q/{displaystylefrac{I}{3}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="$ {\displaystyle \frac{I}{3} }$">|; 

$key = q/displaystyleq^{*}(T,p)=p^{*}_{0}expleft(-frac{L}{RT}right)frac{1}{p};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="$\displaystyle q^{*}(T, p) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right) \frac{1}{p}$">|; 

$key = q/{displaystyleJgefrac{3N_{tr}+1}{2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$ {\displaystyle J \ge \frac{3N_{tr}+1}{2} }$">|; 

$key = q/displaystyleY_n^m(lambda,varphi)equivP_n^m(sinvarphi)exp(imlambda),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle Y_n^m(\lambda,\varphi) \equiv P_n^m(\sin \varphi) \exp(im \lambda),$">|; 

$key = q/f';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="$ f'$">|; 

$key = q/equivhat{q}slashq^*(hat{T},p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$ \equiv \hat{q}/q^*(\hat{T},p)$">|; 

$key = q/displaystylea_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\displaystyle a_k$">|; 

$key = q/epsilon_f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$ \epsilon_f$">|; 

$key = q/displaystyle{calD}(zeta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle {\cal D}(\zeta)$">|; 

$key = q/K=42,J=M=21;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="$ K=42, J=M=21$">|; 

$key = q/displaystyledelta_{t}pi=left(DP{pi}{t}right)_{rmNG}-Dvect{C}cdotoverline{Dvect{D}}^{t},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="$\displaystyle \delta_{t} \pi = \left( \DP{\pi}{t} \right)_{\rm NG} - \Dvect{C} \cdot \overline{ \Dvect{D} }^{t} ,$">|; 

$key = q/y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ y$">|; 

$key = q/displaystyleT_v^{prime}(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$\displaystyle T_v^{\prime} (\varphi, \lambda, \sigma)$">|; 

$key = q/I=64,J=64;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$ I=64, J=64$">|; 

$key = q/displaystyleoverline{F_S^I}(varphi)simeq-S_0(A_{ins}+B_{ins}cos^2varphi),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$\displaystyle \overline{F_S^I} (\varphi) \simeq - S_0 ( A_{ins} + B_{ins} \cos^2 \varphi ) ,$">|; 

$key = q/displaystyleequivlnp_s,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \equiv \ln p_s,$">|; 

$key = q/A{i,J-j}=A_{ij}^{even}-A_{ij}^{odd};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$ A{i,J-j}=A_{ij}^{even}-A_{ij}^{odd}$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="$ \alpha$">|; 

$key = q/displaystylefrac{1}{2pi}int_0^{2pi}g(lambda)dlambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="$\displaystyle \frac{1}{2\pi} \int_0^{2\pi} g(\lambda) d \lambda$">|; 

$key = q/displaystyle=-sum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}left.DD{P_{n}^{m}}{varphi}right|_jexp(-imlambda_i)P_{n'}^{m'}(varphi_j)exp(im'lambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="$\displaystyle = - \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} \left. \DD{P_{n}^{m}}{\...
...ight\vert _j \exp(-im \lambda_i) P_{n'}^{m'}(\varphi_j) \exp(im' \lambda_i) w_j$">|; 

$key = q/{displaystylesum_{i,j}Y_{n'}^{m'*}|_{ij}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="$ {\displaystyle \sum_{i,j} Y_{n'}^{m'*}\vert _{ij} }$">|; 

$key = q/I=64;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="$ I=64$">|; 

$key = q/frac{1}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$ \frac{1}{2}$">|; 

$key = q/P_0simP_{n-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$ P_0 \sim P_{n-1}$">|; 

$key = q/{displaystyle-frac{I-1}{2}simfrac{I-1}{2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="$ {\displaystyle -\frac{I-1}{2} \sim \frac{I-1}{2} }$">|; 

$key = q/displaystyle=frac{displaystyle(1+gamma_{k-1})Deltap_{k-1}S_{k-1slash2}+left(1+gash2}}left{(1+gamma_{k-1})Deltap_{k-1}-(1+gamma_{k})Deltap_{k}right}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="590" HEIGHT="100" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$\displaystyle = \frac{ \displaystyle (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2...
...\{ (1 + \gamma_{k-1}) \Delta p_{k-1} - (1 + \gamma_{k}) \Delta p_{k} \right\} }$">|; 

$key = q/^{-4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="$ ^{-4}$">|; 

$key = q/alpha_g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$ \alpha_g$">|; 

$key = q/n=J,x=mu,y=mu_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$ n=J,x=\mu,y=\mu_j$">|; 

$key = q/delta_v=epsilon_v^{-1}-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="$ \delta_v = \epsilon_v^{-1} - 1$">|; 

$key = q/varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ \varphi$">|; 

$key = q/displaystyleT_{k-1}+S_{grst}(T_{Bk-1}-T_{k-1})-frac{sum^{k+1}_{k=k-1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{k+1}_{k=k-1}Deltap_{k}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="$\displaystyle T_{k-1} + S_{grst} (T_{Bk-1} - T_{k-1})
- \frac{
\sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{k+1}_{k=k-1} \Delta p_{k}
},$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}imf_{ij}Y_n^{m*}(lambda_ivarphi_j)frac{w_j}{rcos^2varphi_j}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} im f_{ij} Y_n^{m*} (\lambda_i \varphi_j) \frac{w_j}{r \cos^2 \varphi_j} .$">|; 

$key = q/0leKle2J-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$ 0 \le K \le 2J-1$">|; 

$key = q/q_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$ q_{k}$">|; 

$key = q/I=128,J=64;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$ I=128, J=64$">|; 

$key = q/displaystyle:qquad渦度水平拡散,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle : \qquad 渦度水平拡散,$">|; 

$key = q/N_{{rmmax}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="$ N_{{\rm max}}$">|; 

$key = q/displaystyle=T_{k}-hat{T}_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$\displaystyle = T_{k} - \hat{T}_{k} ,$">|; 

$key = q/0le|m|len,n';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="$ 0\le \vert m\vert \le n,n'$">|; 

$key = q/displaystyleh_{ij}=left.left(nabla_H^2sum_{m,n}tilde{f}_n^mY_n^mright)right|_{ij}=-sum_{m,n}frac{n(n+1)}{r^2}left.tilde{f}_n^mY_n^mright|_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="381" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="$\displaystyle h_{ij} = \left. \left(\nabla_H^2 \sum_{m,n} \tilde{f}_n^m Y_n^m \...
... = - \sum_{m,n} \frac{n(n+1)}{r^2} \left. \tilde{f}_n^m Y_n^m \right\vert _{ij}$">|; 

$key = q/displaystyleP_n^m(mu)equivsqrt{frac{(2n+1)(n-|m|)!}{(n+|m|)!}}frac{(1-mu^2)^{frac{|m|}{2}}}{2^nn!}DD[n+|m|]{}{mu}(mu^2-1)^n,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle P_n^m(\mu)\equiv \sqrt{\frac{(2n+1)(n-\vert m\vert)!}{(n+\vert m\...
...u^2)^{\frac{\vert m\vert}{2}} }{2^n n!} \DD[n+\vert m\vert]{}{\mu} (\mu^2-1)^n,$">|; 

$key = q/delta_{kleql};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$ \delta_{k \leq l}$">|; 

$key = q/displaystyleq_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$\displaystyle q_{k}$">|; 

$key = q/Deltaq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="$ \Delta q$">|; 

$key = q/tilde{P}^m_n(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="$ \tilde{P}^m_n(\mu)$">|; 

$key = q/displaystylefrac{tilde{P}_J(mu)}{mu-mu_j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="$\displaystyle \frac{\tilde{P}_J (\mu) }{\mu-\mu_j}$">|; 

$key = q/d_{mathrm{H}_2mathrm{O}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="$ d_{\mathrm{H}_2\mathrm{O}}$">|; 

$key = q/-MlemleM,|m|lenleN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="$ -M \le m \le M, \vert m\vert \le n \le N$">|; 

$key = q/displaystyleT_{Bk}=frac{T_{k+1slash2}+T_{k-1slash2}}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="$\displaystyle T_{Bk} = \frac{T_{k+1/2} + T_{k-1/2}}{2}$">|; 

$key = q/displaystyle=q^{*}(hat{T}_{k-1},p_{k-1})+left.DP{q^{*}}{T}right|_{hat{T}_{k-1}}DeltaT_{k-1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$\displaystyle = q^{*} (\hat{T}_{k-1},p_{k-1}) + \left. \DP{q^{*}}{T} \right\vert _{\hat{T}_{k-1}} \Delta T_{k-1}.$">|; 

$key = q/z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="$ z$">|; 

$key = q/displaystyleequivnabla_H^2chi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="$\displaystyle \equiv \nabla_H^2 \chi ,$">|; 

$key = q/displaystyle{calD}(T)=-(-1)^{N_Dslash2}K_{HD}nabla^{N_D}T,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$\displaystyle {\cal D}(T) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} T ,$">|; 

$key = q/tilde{P}_n^m(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="$ \tilde{P}_n^m(\mu)$">|; 

$key = q/displaystyle=-D-DP{dot{sigma}}{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$\displaystyle = - D - \DP{\dot{\sigma}}{\sigma}.$">|; 

$key = q/dot{calA}_{cnd};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$ \dot{\cal A}_{cnd} $">|; 

$key = q/M=42;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="$ M=42$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="$ a$">|; 

$key = q/displaystylealpha_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle \alpha_k$">|; 

$key = q/{rmmax}[n+n'];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$ {\rm max}[n+n']$">|; 

$key = q/0le|m|len;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$  0 \le \vert m\vert \le n$">|; 

$key = q/displaystylee^{*}(T)=p^{*}_{0}expleft(-frac{L}{RT}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="$\displaystyle e^{*}(T) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right)$">|; 

$key = q/displaystyleA(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle A(\lambda,\varphi)$">|; 

$key = q/displaystyle=Isum_{j}f_{n'}^{m'}P_{n}^{m}(varphi_j)left.DD{P_{n'}^{m'}}{varphi}rP_{n}^{m}(varphi_j)left.DD{P_{n'}^{m}}{varphi}right|_jw_jdelta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="494" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="$\displaystyle = I \sum_{j} f_{n'}^{m'} P_{n}^{m}(\varphi_j) \left.\DD{P_{n'}^{m...
...}^{m}(\varphi_j) \left.\DD{P_{n'}^{m}}{\varphi}\right\vert _j w_j \delta_{m m'}$">|; 

$key = q/displaystylegamma_{k}equivfrac{L}{C_p}left.DP{q^{*}}{T}right|_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$\displaystyle \gamma_{k} \equiv \frac{L}{C_p} \left. \DP{q^{*}}{T} \right\vert _{k}$">|; 

$key = q/displaystyleDP{pi}{t}+frac{u}{acosvarphi}DP{pi}{lambda}+frac{v}{a}DP{pi}{varphi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\displaystyle \DP{\pi}{t} + \frac{u}{a \cos \varphi} \DP{\pi}{\lambda} + \frac{v}{a} \DP{\pi}{\varphi}$">|; 

$key = q/Ige3M+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="$ I \ge 3M+1$">|; 

$key = q/int_0^{2pi}exp(imlambda)dlambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="$ \int_0^{2\pi} \exp(i m \lambda) d \lambda $">|; 

$key = q/T_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="$ T_{k}$">|; 

$key = q/M=64;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img907.png"
 ALT="$ M=64$">|; 

$key = q/displaystylesum_{n=1}^{I}exp(imlambda_n)=left{{array}{ll}I&(m=0),0&(0<|m|<I),{array}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="$\displaystyle \sum_{n=1}^{I} \exp(i m \lambda_n) = \left\{ \begin{array}{ll} I &amp;   (m=0) , \ 0 &amp;   (0 &lt; \vert m\vert &lt; I) , \ \end{array} \right.$">|; 

$key = q/{displaystylefrac{pi}{2}>varphi_1>varphi_2>cdots>varphi_{J}>-frac{pi}{2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$ {\displaystyle \frac{\pi}{2} &gt; \varphi_1 &gt; \varphi_2 &gt;
\cdots &gt; \varphi_{J} &gt; -\frac{\pi}{2} }$">|; 

$key = q/Y_n^mexp(imlambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="$ Y_n^m \exp(im\lambda)$">|; 

$key = q/tilde{P_n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="$ \tilde{P_n}$">|; 

$key = q/T_{k+2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="$ T_{k+2}$">|; 

$key = q/varphi_j(j=1,2,3,cdots,J);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$ \varphi_j (j=1,2,3,\cdots,J) $">|; 

$key = q/displaystyleqquad+DeltaT_{k-1}-DeltaT_{k}+frac{L}{C_p}left.DP{q^{*}}{T}right|_{keltap_{k-1slash2}}{p_{k-1slash2}}frac{DeltaT_{k-1}+DeltaT_{k}}{2}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="655" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$\displaystyle \qquad + \Delta T_{k-1} - \Delta T_{k} + \frac{L}{C_p} \left. \DP...
...\frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\Delta T_{k-1} + \Delta T_{k}}{2} = 0.$">|; 

$key = q/displaystyle(T_{k}-T_{k-1})cdot(T_{k+1}-T_{k})<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="$\displaystyle (T_{k} - T_{k-1}) \cdot (T_{k+1} - T_{k}) &lt; 0$">|; 

$key = q/displaystyleT_k=hat{T}_k+frac{L}{C_p}(1-b)Ifrac{(T^c_k-T_k)}{displaystylesum_{k=k_B}^{k_T}(T^c_k-T_k)frac{Deltap_k}{g}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="108" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="$\displaystyle T_k = \hat{T}_k + \frac{L}{C_p} (1-b) I \frac{( T^c_k - T_k )} {\displaystyle \sum_{k=k_B}^{k_T} ( T^c_k - T_k ) \frac{\Delta p_k}{g} }$">|; 

$key = q/displaystylebar{calA}^{t}=(1-2epsilon_f){calA}^{t}+epsilon_fleft(bar{calA}^{t-Deltat}+{calA}^{t+Deltat}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle \bar{\cal A}^{t} = ( 1-2 \epsilon_f ) {\cal A}^{t} + \epsilon_f \left( \bar{\cal A}^{t-\Delta t} + {\cal A}^{t+\Delta t} \right)$">|; 

$key = q/displaystylehat{T}_{k-1}-hat{T}_{k}+frac{L}{C_p}left{q^{*}(hat{T}_{k-1})-q^{*}(hc{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_{k-1}+hat{T}_{k}}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="443" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$\displaystyle \hat{T}_{k-1} - \hat{T}_{k} + \frac{L}{C_p} \left\{ q^{*} (\hat{T...
...{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$">|; 

$key = q/{Y_n^m(lambda',varphi')|m=-n,-n+1,cdots,n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="$ \{ Y_n^m(\lambda', \varphi') \vert m=-n,-n+1, \cdots, n \} $">|; 

$key = q/{displaystyleM=left[frac{I}{2}right]};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="$ {\displaystyle M= \left[ \frac{I}{2} \right] }$">|; 

$key = q/displaystylev_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="$\displaystyle v_{ij}$">|; 

$key = q/Y_n^m(varphi,lambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="$ Y_n^m(\varphi,\lambda)$">|; 

$key = q/displaystyle=underline{Q}underline{S}-underline{R},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$\displaystyle = \underline{Q}\underline{S} - \underline{R} ,$">|; 

$key = q/Y^m_n(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="$ Y^m_n(\lambda, \varphi)$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^JA_{ij}P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J A_{ij} P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$">|; 

$key = q/displaystyleq=frac{hat{p_s}}{hat{p_s}+Deltap_s}hat{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="$\displaystyle q = \frac{\hat{p_s}}{\hat{p_s} + \Delta p_s} \hat{q}$">|; 

$key = q/piBequivsigma_{SB}T^4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$ \pi B \equiv \sigma_{SB} T^4$">|; 

$key = q/displaystyleF_S^I(lambda,varphi)=-S_0(1-mathcal{A})coszeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="$\displaystyle F_S^I (\lambda, \varphi) = - S_0 (1 - \mathcal{A}) \cos \zeta$">|; 

$key = q/displaystyleD(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle D (\varphi, \lambda, \sigma)$">|; 

$key = q/-MlemleM,|m|lenleN(m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="$ -M \le m \le M, \vert m\vert \le n \le N(m)$">|; 

$key = q/displaystyleleft[DeltaT_{k-1}+frac{L}{C_p}left{q^{*}(hat{T}_{k-1})+left.DP{q^{*}|_{k-1}DeltaT_{k-1}-hat{q}_{k-1}right}right]Deltap_{k-1}hspace{-7em};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="425" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$\displaystyle \left[ \Delta T_{k-1} + \frac{L}{C_p} \left\{ q^{*} (\hat{T}_{k-1...
...1} \Delta T_{k-1} - \hat{q}_{k-1} \right\} \right] \Delta p_{k-1} \hspace{-7em}$">|; 

$key = q/T=overline{T}_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$ T=\overline{T}_k$">|; 

$key = q/displaystyleT_{k+1}+S_{grst}(T_{Bk+2}-T_{k+2})-frac{sum^{k+2}_{k=k}S_{grst}(T_{Bk}-hat{T}_{k})Deltap_{k}}{sum^{k+2}_{k=k}Deltap_{k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="$\displaystyle T_{k+1} + S_{grst} (T_{Bk+2} - T_{k+2})
- \frac{
\sum^{k+2}_{k=k} S_{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k}
}{
\sum^{k+2}_{k=k} \Delta p_{k}
}$">|; 

$key = q/displaystylerangle=frac{displaystylesum_{k=k_B}^{k_T}hat{q}frac{Deltap_k}{g}}{displaystylesum_{k=k_B}^{k_T}q^*(hat{T},p)frac{Deltap_k}{g}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="124" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle \rangle = \frac{\displaystyle \sum_{k=k_B}^{k_T} \hat{q} \frac{\D...
...{g} } {\displaystyle \sum_{k=k_B}^{k_T} q^*(\hat{T},p) \frac{\Delta p_k}{g} } .$">|; 

$key = q/k_T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="$ k_T$">|; 

$key = q/displaystyle=-frac{1+gamma_{k}}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}Delt}+frac{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$\displaystyle = - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}} \frac{\Delta p_{k}...
...rac{1}{ 1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$">|; 

$key = q/T^a_k=hat{T}_k,q^a_k=q^*(hat{T}_k,p_k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="$ T^a_k = \hat{T}_k, q^a_k = q^*( \hat{T}_k, p_k ) $">|; 

$key = q/displaystyleq^a_{k+1}=q^a_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="$\displaystyle q^a_{k+1} = q^a_k$">|; 

$key = q/m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$ m$">|; 

$key = q/displaystyle=sum_{m,n}left(frac{1}{rcosvarphi_j}imtilde{psi}_n^mP_n^m(sinvarphi_tilde{chi}_n^mleft.DD{P_n^m}{varphi}right|_{j}right)exp(imlambda_i).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="$\displaystyle = \sum_{m,n} \left( \frac{1}{r\cos\varphi_j} im \tilde{\psi}_n^m ...
...i}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _{j} \right) \exp(im \lambda_i) .$">|; 

$key = q/pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$ \pi$">|; 

$key = q/displaystyle{calA}^{t+Deltat}=hat{calA}^{t+Deltat}+2Deltatdot{calA}_{dis}left(haDeltat}right)+2Deltatdot{calA}_{cnd}left(hat{calA}^{t+Deltat}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle {\cal A}^{t+\Delta t} = \hat{\cal A}^{t+\Delta t} + 2 \Delta t \d...
...ight) + 2 \Delta t \dot{\cal A}_{cnd}\left( \hat{\cal A}^{t+\Delta t} \right) .$">|; 

$key = q/displaystyle:quad時間[mathrm{s}].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle : \quad 時間 [\mathrm{s}].$">|; 

$key = q/L(mu_j)=f(mu_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="$ L(\mu_j) = f(\mu_j) $">|; 

$key = q/{displaystyleexp(imlambda_n)=expleft(frac{2piim(n-1)}{I}right)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="$ {\displaystyle \exp(i m \lambda_n)
= \exp \left( \frac{2\pi i m (n-1)}{I} \right) }$">|; 

$key = q/displaystyleq=hat{q}-frac{L}{C_p}DP{q^*}{T}frac{hat{q}-q^*(hat{T},p)}{displaystyle1+frac{L}{C_p}DP{q^*}{T}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="79" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$\displaystyle q = \hat{q} - \frac{L}{C_p} \DP{q^*}{T} \frac{ \hat{q} - q^*(\hat{T},p) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} } .$">|; 

$key = q/varphi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$ \varphi=0$">|; 

$key = q/P;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$ P$">|; 

$key = q/(T^a_{k+1},q^a_{k+1});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$ (T^a_{k+1}, q^a_{k+1})$">|; 

$key = q/{Y_n^m|n=0,1,2,cdots,m=-n,-n+1,cdots,n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="$ \{Y_n^m \vert n=0,1,2,\cdots, m= -n, -n+1,\cdots,n \}$">|; 

$key = q/displaystylequadsum_{i}sum_{j}f_{n'}^{m'}P_{n}^{m}(varphi_j)exp(imlambda_i)left.DD{P_{n'}^{m'}}{varphi}right|_jexp(-im'lambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="$\displaystyle \quad \sum_{i} \sum_{j} f_{n'}^{m'} P_{n}^{m}(\varphi_j) \exp(im \lambda_i) \left. \DD{P_{n'}^{m'}}{\varphi}\right\vert _j \exp(-im' \lambda_i) w_j$">|; 

$key = q/sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$ \sigma$">|; 

$key = q/displaystyleDP{q_k}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle \DP{q_k}{t}$">|; 

$key = q/displaystyle=(2n+1)(x-y)tilde{P}_n(x)tilde{P}_n(y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="$\displaystyle = (2n+1)(x-y)\tilde{P}_n(x)\tilde{P}_n(y)$">|; 

$key = q/displaystyle=imtilde{f}_n^m.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$\displaystyle = im \tilde{f}_n^m .$">|; 

$key = q/varphi_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="$ \varphi_j$">|; 

$key = q/displaystyle=-sigma_{k-1slash2}DP{pi}{t}-sum_{l=k}^{K}(D_l+Dvect{v}_lcdotnablapi)Deltasigma_l,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle = - \sigma_{k-1/2} \DP{\pi}{t} - \sum_{l=k}^{K} ( D_l + \Dvect{v}_l \cdot \nabla \pi ) \Delta \sigma_l,$">|; 

$key = q/displaystyle=frac{1}{rcos^2varphi_j}sum_{m,n}imtilde{f}_n^mY_n^m(lambda_i,varphi_j).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="$\displaystyle = \frac{1}{r \cos^2 \varphi_j} \sum_{m,n} im \tilde{f}_n^m Y_n^m (\lambda_i, \varphi_j) .$">|; 

$key = q/displaystyleepsilon_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle \epsilon_v$">|; 

$key = q/(lambda_i,varphi_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$ (\lambda_i,\varphi_j)$">|; 

$key = q/displaystyletilde{A}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle \tilde{A}_n^m$">|; 

$key = q/u_{ij},v_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="$ u_{ij},v_{ij}$">|; 

$key = q/displaystyle=T_{k-1}-hat{T}_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$\displaystyle = T_{k-1} - \hat{T}_{k-1}$">|; 

$key = q/(N_{tr}+1)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$ (N_{tr}+1)^2$">|; 

$key = q/displaystylelambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle \lambda$">|; 

$key = q/hat{T}_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="$ \hat{T}_{k}$">|; 

$key = q/displaystyleD^{t+Deltat}=2overline{Dvect{D}}^{t}-D^{t-Deltat};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$\displaystyle D^{t+\Delta t} = 2\overline{ \Dvect{D} }^{t} - D^{t-\Delta t}$">|; 

$key = q/K-J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="$ K-J$">|; 

$key = q/1leqkleqKMAX;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="$ 1 \leq k \leq KMAX$">|; 

$key = q/displaystyleunderline{h};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle \underline{h}$">|; 

$key = q/displaystyle:quad乾燥大気の大気定圧比熱[mathrm{Jkg}^{-1}mathrm{K}^{-1}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle : \quad 乾燥大気の大気定圧比熱 [\mathrm{J kg}^{-1} \mathrm{K}^{-1}],$">|; 

$key = q/displaystylefrac{partialDvect{D}}{partialt}=left(DP{Dvect{D}}{t}right)_{rmNG}-naa}(Dvect{Phi}_{S}+underline{W}Dvect{T}+Dvect{G}pi)+{calD}_MDvect{D},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle \frac{\partial \Dvect{D}}{\partial t} = \left( \DP{\Dvect{D}}{t} ...
...{\Phi}_{S} + \underline{W} \Dvect{T} + \Dvect{G} \pi ) + {\cal D}_M \Dvect{D} ,$">|; 

$key = q/i,j,m,m',n,n',I,J,M,N(m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$ i,j,m,m',n,n',I,J,M,N(m)$">|; 

$key = q/displaystyleg_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="$\displaystyle g_{ij}$">|; 

$key = q/{displaystylelambda_i=frac{2pi(i-1)}{I}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="$ {\displaystyle \lambda_i=\frac{2\pi(i-1)}{I} }$">|; 

$key = q/displaystyleS_{k-1slash2}>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$\displaystyle S_{k-1/2} &gt; 0$">|; 

$key = q/P_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ P_n^m$">|; 

$key = q/tilde{P}_n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="$ \tilde{P}_n$">|; 

$key = q/m=-M,cdots,M.quadn=|m|,cdots,N(m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$ m=-M,\cdots,M. \quad n=\vert m\vert,\cdots,N(m)$">|; 

$key = q/x=-1,beta_1,beta_2,1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="$ x=-1,\beta_1,\beta_2,1$">|; 

$key = q/{displaystyleP_n=frac{1}{2^nn!}DD[n]{}{mu}(mu^2-1)^n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$ {\displaystyle
P_n= \frac{1}{2^n n!}
\DD[n]{}{\mu} (\mu^2-1)^n }$">|; 

$key = q/displaystyleint_{-1}^1P_n^m(mu)P_{n'}^m(mu)dmu=2delta_{nn'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="$\displaystyle \int_{-1}^1 P_n^m(\mu) P_{n'}^m (\mu) d \mu = 2 \delta_{nn'} .$">|; 

$key = q/n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="$ n$">|; 

$key = q/I>M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="$ I &gt; M$">|; 

$key = q/displaystyleDP{pi}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle \DP{\pi}{t}$">|; 

$key = q/displaystyle=sum_{m=-M}^{M}frac{1}{2pi}g_mint_0^{2pi}exp(imlambda)dlambda=g_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="$\displaystyle = \sum_{m=-M}^{M} \frac{1}{2\pi} g_m \int_0^{2\pi} \exp(i m \lambda) d \lambda =g_0$">|; 

$key = q/w(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="$ w(\mu)$">|; 

$key = q/displaystyleleft{DeltaT_{k-1}+frac{L}{C_p}(q_{k-1}-hat{q}_{k-1})right}Deltap_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\displaystyle \left\{ \Delta T_{k-1} + \frac{L}{C_p} (q_{k-1} - \hat{q}_{k-1} ) \right\} \Delta p_{k-1}$">|; 

$key = q/displaystyle=Isum_{j=1}^{J}P_n^m(mu_j)P_{n'}^{m'}(mu_j)w_jdelta_{mm'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="$\displaystyle = I \sum_{j=1}^{J} P_n^m (\mu_j) P_{n'}^{m'} (\mu_j) w_j \delta_{mm'} .$">|; 

$key = q/displaystyle=int_{-1}^1L(mu)dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="$\displaystyle = \int_{-1}^1 L(\mu) d \mu$">|; 

$key = q/{calF}_lambda,{calF}_varphi,Q,S_q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$ {\cal F}_\lambda, {\cal F}_\varphi, Q, S_q$">|; 

$key = q/mu_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="$ \mu_j$">|; 

$key = q/A_{ins};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ A_{ins}$">|; 

$key = q/displaystyleC_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle C_p$">|; 

$key = q/w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$ w_j$">|; 

$key = q/nabla_H^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="$ \nabla_H^2$">|; 

$key = q/displaystyleu_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="$\displaystyle u_{ij}$">|; 

$key = q/displaystyleDeltaT_{k}equivhat{T}_{k}-T_{k}=S_{grst}(T_{Bk}-T_{k});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="$\displaystyle \Delta T_{k} \equiv \hat{T}_{k} - T_{k} = S_{grst} (T_{Bk} - T_{k})$">|; 

$key = q/displaystylehat{T}_{k}=T_{k}+S_{grst}(T_{Bk}-T_{k});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="$\displaystyle \hat{T}_{k} = T_{k} + S_{grst} (T_{Bk} - T_{k})$">|; 

$key = q/p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$ p$">|; 

$key = q/displaystyle(C_pT_{k-1}+Lq_{k-1})Deltap_{k-1}-(C_phat{T}_{k-1}+Lhat{q}_{k-1})Deltap_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$\displaystyle (C_p T_{k-1} + L q_{k-1}) \Delta p_{k-1} - (C_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}$">|; 

$key = q/Dvect{v}=(v_1,v_2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="$ \Dvect{v}=(v_1,v_2)$">|; 

$key = q/displaystyleT_{k}+S_{grst}(T_{Bk}-T_{k})-frac{sum^{k+1}_{k=k-1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{k+1}_{k=k-1}Deltap_{k}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="$\displaystyle T_{k} + S_{grst} (T_{Bk} - T_{k})
- \frac{
\sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{k+1}_{k=k-1} \Delta p_{k}
},$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}A_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J} A_{ij} Y_n^{m*} (\lambda_i,\varphi_j) w_j ,$">|; 

$key = q/int_0^{2pi}exp(imlambda)exp(-im'lambda)dlambda=2pidelta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="$ \int_0^{2 \pi} \exp(im\lambda) \exp(-im'\lambda)
d \lambda = 2 \pi \delta_{mm'}$">|; 

$key = q/displaystylequadhspace{1.5cm}timesleft.DD{}{varphi}left(cos^2varphiP_n^mright)right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="$\displaystyle \quad \hspace{1.5cm} \times \left. \DD{}{\varphi} \left( \cos^2\varphi P_n^m \right) \right\vert _j \exp(-im \lambda_i) w_j$">|; 

$key = q/displaystyleF_R(z)=left(piB(T_g)-piB(T_s)right){calT}^f(z,0)+piB(T(z_T)){calT}^f(z,z_T)-int_0^{z_T}DD{piB}{xi}{calT}^f(z,xi)dxi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="581" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$\displaystyle F_R(z) = \left( \pi B(T_g) - \pi B(T_s) \right) {\cal T}^f(z,0) +...
...(z_T)) {\cal T}^f(z,z_T) - \int_0^{z_T} \DD{\pi B}{\xi} {\cal T}^f(z,\xi) d \xi$">|; 

$key = q/J=65;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="$ J=65$">|; 

$key = q/b_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="$ b_i$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i,j}left(sum_{m',n'}tilde{f}_{n'}^{m'}left.DD{P_{n'}phi}right|_jexp(im'lambda_i)right)P_n^m(varphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i,j} \left( \sum_{m',n'} \tilde{f}_{n'}^{m'} ...
...t\vert _j \exp(i m' \lambda_i) \right) P_n^m(\varphi_j) \exp(-im \lambda_i) w_j$">|; 

$key = q/displaystyle{calD}(D)=-K_{HD}left[(-1)^{N_Dslash2}nabla^{N_D}-left(frac{2}{a^2}right)^{N_Dslash2}right]D,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$\displaystyle {\cal D}(D) = - K_{HD} \left[ (-1)^{N_D/2} \nabla^{N_D} - \left( \frac{2}{a^2} \right)^{N_D/2} \right] D ,$">|; 

$key = q/{displaystylesum_{m=-M}^{M}sum_{n=|m|}^{N}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="$ {\displaystyle \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} }$">|; 

$key = q/overline{Dvect{D}_n^m}^{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$ \overline{ \Dvect{D}_n^m }^{t}$">|; 

$key = q/displaystyle=frac{v^{2}_k+v^{2}_k}{2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle = \frac{v^{2}_k + v^{2}_k}{2}.$">|; 

$key = q/displaystyleqquadsum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}P_{n}^{m}(varphi_j)exp(imlambda_i)left.DD{P_{n'}^{m'}}{varphi}right|_jexp(-im'lambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="$\displaystyle \qquad \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} P_{n}^{m}(\varphi_j)...
...mbda_i) \left. \DD{P_{n'}^{m'}}{\varphi}\right\vert _j \exp(-im' \lambda_i) w_j$">|; 

$key = q/delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$ \delta$">|; 

$key = q/4pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="$ 4 \pi$">|; 

$key = q/displaystylefrac{1}{r}DP{Y_n^m}{varphi}=frac{1}{r}DP{}{varphi}left(P_n^m(sinvarplambda)right)=frac{sqrt{1-mu^2}}{r}DD{}{mu}P_n^{m}(mu)exp(imlambda).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="492" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="$\displaystyle \frac{1}{r} \DP{Y_n^m}{\varphi} = \frac{1}{r} \DP{}{\varphi} \lef...
...\right) = \frac{\sqrt{1-\mu^2} }{r} \DD{}{\mu} P_n^{m} (\mu) \exp(im \lambda) .$">|; 

$key = q/N_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$ N_S$">|; 

$key = q/displaystyle=frac{(2J-1)(1-sin^2varphi_j)}{(JP_{J-1}(sinvarphi_j))^2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="$\displaystyle = \frac{(2J-1)(1-\sin^2 \varphi_j)} {(J P_{J-1}(\sin \varphi_j))^2 } .$">|; 

$key = q/2J+2|m|-2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="$ 2J+2\vert m\vert-2$">|; 

$key = q/displaystyle(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle  (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystylefrac{1}{2pi}int_0^{2pi}g(lambda)dlambda=frac{1}{I}sum_{n=1}^{I}g(lambda_n),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="$\displaystyle \frac{1}{2\pi} \int_0^{2\pi} g(\lambda) d \lambda = \frac{1}{I} \sum_{n=1}^{I} g(\lambda_n) ,$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}A_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J} A_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j .$">|; 

$key = q/displaystyle=-frac{1}{I}sum_{i,j}left(sum_{m',n'}tilde{f}_{n'}^{m'}P_{n'}^{m'}(v(im'lambda_i)right)left.DD{P_n^m}{varphi}right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="455" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="$\displaystyle = - \frac{1}{I} \sum_{i,j} \left( \sum_{m',n'} \tilde{f}_{n'}^{m'...
...bda_i) \right) \left. \DD{P_n^m}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j$">|; 

$key = q/delta_S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$ \delta_S$">|; 

$key = q/lambda_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="$ \lambda_k$">|; 

$key = q/lambda_{subsolar};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$ \lambda_{subsolar}$">|; 

$key = q/M=N_{tr},N=N_{tr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$ M= N_{tr},  N =N_{tr}$">|; 

$key = q/displaystylenleft|{array}{ll}tilde{P}_n(x)&tilde{P}_{n-1}(x)tilde{P}_n(y)&tilde{P}_{n-1}(y){array}right|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="$\displaystyle n \left\vert \begin{array}{ll} \tilde{P}_n(x) &amp; \tilde{P}_{n-1}(x) \ \tilde{P}_n(y) &amp; \tilde{P}_{n-1}(y) \end{array} \right\vert$">|; 

$key = q/{displaystylesum_{m,n}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="$ {\displaystyle \sum_{m,n} }$">|; 

$key = q/m,n,n';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="$ m,n,n'$">|; 

$key = q/displaystyleequivT_v-overline{T},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\displaystyle \equiv T_v - \overline{T},$">|; 

$key = q/displaystylehspace{2em}+left(1+gamma_{k-1}-frac{R}{C_p}frac{Deltap_{k-1slash2}}{{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="595" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$\displaystyle \hspace{2em} + \left( 1 + \gamma_{k-1} - \frac{R}{C_p} \frac{\Del...
...1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}} \right)$">|; 

$key = q/displaystyle(T_{k}-T_{k-1})cdot(T_{k+1}-T_{k})geq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="$\displaystyle (T_{k} - T_{k-1}) \cdot (T_{k+1} - T_{k}) \geq 0$">|; 

$key = q/displaystyle=-(C_pT_{k}+Lq_{k})Deltap_{k}+(C_phat{T}_{k}+Lhat{q}_{k})Deltap_{k},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$\displaystyle = - (C_p T_{k} + L q_{k}) \Delta p_{k} + (C_p \hat{T}_{k} + L \hat{q}_{k}) \Delta p_{k},$">|; 

$key = q/mathaccentV{tilde}07E{P}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ \mathaccentV {tilde}07E{P}_n^m$">|; 

$key = q/m,m';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="$ m,m'$">|; 

$key = q/f(x)=(x-1)^n(x+1)^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="$ f(x)=(x-1)^n (x+1)^n$">|; 

$key = q/(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$ (\lambda, \varphi)$">|; 

$key = q/displaystyleequivTleft{1+left(epsilon_v^{-1}-1right)qright},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle \equiv T \left\{ 1 + \left(\epsilon_v^{-1} - 1\right) q \right\},$">|; 

$key = q/nabla_H^2equivfrac{1}{r^2}left[DP{}{varphi}left(cosvarphiDP{}{varphi}right)+frac{1}{cos^2varphi}DP[2]{}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="$ \nabla_H^2 \equiv
\frac{1}{r^2}
\left[ \DP{}{\varphi} \left( \cos \varphi \DP{}{\varphi} \right)
+ \frac{1}{\cos^2 \varphi} \DP[2]{}{\lambda}
\right]
$">|; 

$key = q/displaystyleoverline{seczeta}simeqfrac{1}{A_{zeta}+B_{zeta}cos^2varphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="$\displaystyle \overline{\sec \zeta} \simeq \frac{1}{A_{\zeta} + B_{\zeta} \cos^2 \varphi} .$">|; 

$key = q/{displaystyleMleleft[frac{I}{2}right],N(m)leJ-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="$ {\displaystyle M \le \left[ \frac{I}{2} \right] ,
N(m) \le J-1 }$">|; 

$key = q/f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$ f$">|; 

$key = q/displaystyle∴h_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="$\displaystyle ∴ h_{ij}$">|; 

$key = q/{align*}{split}DP{tilde{T}_n^m}{t}&=-frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}imu_{ijj=1}^{J}{calD}'_{ij}(Dvect{v})Y_n^{m*}(lambda_i,varphi_j)w_j.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="262" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{align*}\begin{split}\DP{\tilde{T}_n^m}{t} &amp; = - \frac{1}{I} \sum_{i=1}^{I...
...{ij}(\Dvect{v}) Y_n^{m *} ( \lambda_i, \varphi_j ) w_j . \end{split}\end{align*}">|; 

$key = q/Jge3N_{tr}+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$ J \ge 3N_{tr}+1$">|; 

$key = q/displaystyleleft[DD{}{mu}left{(1-mu^2)DD{}{mu}right}+J(J+1)right]P_J(mu)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \left[
\DD{}{\mu}
\left\{ (1-\mu^2) \DD{}{\mu} \right\}
+ J(J+1) \right] P_J(\mu) = 0$">|; 

$key = q/displaystyleequivsum_{m=-M}^Msum_{n=|m|}^Nimtilde{f}_n^mY_n^m(lambda_i,varphi_j),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \equiv \sum_{m=-M}^M \sum_{n=\vert m\vert}^N im \tilde{f}_n^m Y_n^m (\lambda_i,\varphi_j) ,$">|; 

$key = q/displaystyleleft(-1-gamma_{k}-kappafrac{Deltap_{k-1slash2}}{2p_{k-1slash2}}right)DeltaT_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$\displaystyle \left( - 1 - \gamma_{k} - \kappa \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) \Delta T_{k}$">|; 

$key = q/kappa=RslashC_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="$ \kappa = R/C_p$">|; 

$key = q/(q,T);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$ (q, T)$">|; 

$key = q/n-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="$ n-1$">|; 

$key = q/-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="$ -1$">|; 

$key = q/f(mu_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="$ f(\mu_j)$">|; 

$key = q/displaystyleequivwidetilde{(BC)_n^m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="$\displaystyle \equiv \widetilde{(BC)_n^m}$">|; 

$key = q/P_n^m(mu)(n=|m|,|m+1,cdots);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="$ P_n^m(\mu)  (n=\vert m\vert,\vert m+1, \cdots)$">|; 

$key = q/displaystyletilde{A}_n^m=frac{1}{4pi}int_{-1}^1d(sinvarphi)int_0^{2pi}dlambdaA(lambda,varphi)Y_n^{m*}(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="$\displaystyle \tilde{A}_n^m = \frac{1}{4 \pi} \int_{-1}^1 d (\sin \varphi) \int_0^{2 \pi} d \lambda A(\lambda, \varphi) Y_n^{m*}(\lambda, \varphi)$">|; 

$key = q/displaystylelambda_n=frac{2pi(n-1)}{I}(n=1,2,cdots,I);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="$\displaystyle \lambda_n = \frac{2\pi (n-1)}{I}  (n=1,2,\cdots,I)$">|; 

$key = q/displaystyleq=q^*(T,p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$\displaystyle q = q^*( T,p )$">|; 

$key = q/DeltaT_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$ \Delta T_{k}$">|; 

$key = q/chi,psi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ \chi ,\psi $">|; 

$key = q/displaystyletilde{A}_n^m=frac{2n+1}{2}frac{(n-|m|)!}{(n+|m|)!}int_{-1}^1A(mu)tilde{P}_n^m(mu)dmu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="$\displaystyle \tilde{A}_n^m = \frac{2n+1}{2} \frac{(n-\vert m\vert)!}{(n+\vert m\vert)!} \int_{-1}^1 A(\mu) \tilde{P}_n^m(\mu) d \mu$">|; 

$key = q/m(n-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="$ m(n-1)$">|; 

$key = q/K+frac{1}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$ K+\frac{1}{2}$">|; 

$key = q/displaystyletilde{f}_{n'}^{m'}=-frac{n(n+1)}{r^2}tilde{h}_{n'}^{m'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="$\displaystyle \tilde{f}_{n'}^{m'} = -\frac{n(n+1)}{r^2} \tilde{h}_{n'}^{m'}$">|; 

$key = q/f(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="$ f(\mu)$">|; 

$key = q/g=DP{f}{lambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="$ g = \DP{f}{\lambda}$">|; 

$key = q/displaystyleh_{ij}=sum_{m,n}left.tilde{h}_n^mY_n^mright|_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="$\displaystyle h_{ij} = \sum_{m,n} \left. \tilde{h}_n^m Y_n^m \right\vert _{ij}$">|; 

$key = q/displaystyle=-left(1+gamma_{k}right)DeltaT_{k}Deltap_{k}+frac{L}{C_p}Deltahat{Q},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$\displaystyle = - \left( 1 + \gamma_{k} \right) \Delta T_{k} \Delta p_{k} + \frac{L}{C_p} \Delta \hat{Q},$">|; 

$key = q/nabla^2_Hf=-frac{n(n+1)}{r^2}f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="$ \nabla^2_H f = -\frac{n(n+1)}{r^2} f$">|; 

$key = q/f(lambda,varphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="$ f(\lambda,\varphi)$">|; 

$key = q/{align*}{split}nabla^2_Hf&equivfrac{1}{r^2}left[frac{1}{cosvarphi}DP{}{varphi}le{(1-mu^2)DP{}{mu}right}+frac{1}{1-mu^2}DP[2]{}{lambda}right]f{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="90" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="\begin{align*}\begin{split}\nabla^2_H f &amp;\equiv \frac{1}{r^2} \left[ \frac{1}{\c...
...\right\} + \frac{1}{1-\mu^2} \DP[2]{}{\lambda} \right] f \end{split}\end{align*}">|; 

$key = q/M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$ M$">|; 

$key = q/_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="$ _2$">|; 

$key = q/psi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="$ \psi$">|; 

$key = q/sigma_{SB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="$ \sigma_{SB}$">|; 

$key = q/displaystyletilde{calD}_{H,n}^m=-K_{HD}left(frac{-n(n+1)}{a^{2}}right)^{N_Dslash2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\displaystyle \tilde{\cal D}_{H,n}^m = - K_{HD} \left( \frac{-n(n+1)}{a^{2}} \right)^{N_D/2} .$">|; 

$key = q/{displaystylekappa=frac{R}{C_p}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$ {\displaystyle \kappa=\frac{R}{C_p} }$">|; 

$key = q/displaystyleleft[DP{}{mu}left((1-mu^2)DP{}{mu}right)+frac{1}{1-mu^2}DP[2]{}{lambda}+n(n+1)right]Y_n^m=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="$\displaystyle \left[ \DP{}{\mu} \left( (1-\mu^2) \DP{}{\mu} \right) + \frac{1}{1-\mu^2} \DP[2]{}{\lambda} + n(n+1) \right] Y_n^m =0$">|; 

$key = q/f_k（k=0,1,2,cdots,K-1）;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="$ f_k（k=0,1,2,\cdots,K-1）$">|; 

$key = q/A_{ij}^{even};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$ A_{ij}^{even}$">|; 

$key = q/A_{i,j}+A_{i,J-j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$ A_{i,j}+A_{i,J-j}$">|; 

$key = q/kappa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$ \kappa$">|; 

$key = q/displaystyle:qquad摩擦熱.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle : \qquad 摩擦熱.$">|; 

$key = q/dot{calA}_{adv};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$ \dot{\cal A}_{adv} $">|; 

$key = q/{calA}^{t+Deltat};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$ {\cal A}^{t+\Delta t} $">|; 

$key = q/displaystylehspace{-7em}=-left[1+frac{L}{C_p}left.DP{q^{*}}{T}right|_{k}right]Deap_{k}-frac{L}{C_p}left{q^{*}(hat{T}_{k})-hat{q}_{k}right}Deltap_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$\displaystyle \hspace{-7em} = - \left[ 1 + \frac{L}{C_p} \left. \DP{q^{*}}{T} \...
...- \frac{L}{C_p} \left\{ q^{*} (\hat{T}_{k}) - \hat{q}_{k} \right\} \Delta p_{k}$">|; 

$key = q/displaystyle)_k)+{calD}(D_k).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle )_k ) + {\cal D}(D_k).$">|; 

$key = q/displaystylesum^{KMAX}_{k=1}hat{T}_{k}Deltap_{k}=sum^{KMAX}_{k=1}left{S_{grst}(TT_{Bk}-T_{k})Deltap_{k}}{sum^{KMAX}_{k=1}Deltap_{k}}Deltap_{k}right};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="588" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="$\displaystyle \sum^{KMAX}_{k=1} \hat{T}_{k} \Delta p_{k}
= \sum^{KMAX}_{k=1}
\l...
...- T_{k}) \Delta p_{k}
}{
\sum^{KMAX}_{k=1} \Delta p_{k}
}
\Delta p_{k}
\right\}$">|; 

$key = q/N_{{rmmax}}=2M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="$ N_{{\rm max}}=2M$">|; 

$key = q/C_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$ C_p$">|; 

$key = q/v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$ v$">|; 

$key = q/{align*}{split}hat{H}_k&equivT_k'D_k-frac{1}{Deltasigma_k}[dot{sigma}_{k-1slash2vect{v}_lcdotnablapi)Deltasigma_lfrac{T_{v,k}}{Deltasigma_k},{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="339" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="\begin{align*}\begin{split}\hat{H}_k &amp; \equiv T_k' D_k - \frac{1}{\Delta \sigma_...
...a \pi ) \Delta \sigma_l \frac{T_{v,k}}{\Delta \sigma_k}, \end{split}\end{align*}">|; 

$key = q/{displaystylesum_{i,j}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="$ {\displaystyle \sum_{i,j} }$">|; 

$key = q/displaystyleequivfrac{1}{a^{2}cos^2varphi}DP[2]{}{lambda}+frac{1}{a^{2}cosvarphi}DP{}{varphi}left(cosvarphiDP{}{varphi}right),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \equiv \frac{1}{a^{2} \cos^2 \varphi} \DP[2]{}{\lambda} + \frac{1}{a^{2} \cos \varphi} \DP{}{\varphi} \left( \cos \varphi \DP{}{\varphi} \right),$">|; 

$key = q/h;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="$ h$">|; 

$key = q/bar{k}_{R,i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="$ \bar{k}_{R,i}$">|; 

$key = q/displaystyleq_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$\displaystyle q_{k-1}$">|; 

$key = q/delta_R=1.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="$ \delta_R = 1.5$">|; 

$key = q/displaystylesum_i^{N_S}a_ileft[(1-alpha_A)F_S^Iexpleft(-tau_{S,i}(z)seczetaright)right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\displaystyle \sum_i^{N_S} a_i
\left[
(1-\alpha_A) F_S^I
\exp \left( - \tau_{S,i}(z) \sec \zeta \right)
\right.$">|; 

$key = q/displaystyle=-frac{I}{2}int_{-1}^{1}f_{n'}^{m}P_{n'}^{m}(varphi)DD{P_n^m}{varphi}dvarphidelta_{mm'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="$\displaystyle = - \frac{I}{2} \int_{-1}^{1} f_{n'}^{m} P_{n'}^{m}(\varphi) \DD{P_n^m}{\varphi} d \varphi \delta_{m m'}$">|; 

$key = q/3slash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="$ 3/4$">|; 

$key = q/kleql;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$ k \leq l$">|; 

$key = q/dot{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$ \dot{\sigma}$">|; 

$key = q/{align*}{split}hat{kappa}_k&=frac{sigma_{k-1slash2}(sigma^{kappa}_{k-1slash2}-sima_{k-1slash2}alpha_k+sigma_{k+1slash2}beta_k}{Deltasigma_k},{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="92" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="\begin{align*}\begin{split}\hat{\kappa}_k &amp; = \frac{ \sigma_{k-1/2}( \sigma^{\ka...
...\alpha_k + \sigma_{k+1/2} \beta_k } { \Delta \sigma_k }, \end{split}\end{align*}">|; 

$key = q/J=63,N=42;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="$ J=63, N=42$">|; 

$key = q/displaystyle=sum_{m,n}left(-frac{1}{r}tilde{psi}_n^mleft.DD{P_n^m}{varphi}right|cosvarphi_j}imtilde{chi}_n^mP_n^m(sinvarphi_j)right)exp(imlambda_i).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="443" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="$\displaystyle = \sum_{m,n} \left( - \frac{1}{r} \tilde{\psi}_n^m \left. \DD{P_n...
...arphi_j} im \tilde{\chi}_n^m P_n^m(\sin \varphi_j) \right) \exp(im \lambda_i) .$">|; 

$key = q/t+Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$ t+\Delta t$">|; 

$key = q/displaystylesum_{m=-frac{I}{2}+1}^{frac{I}{2}}exp(imlambda_i)exp(-imlambda_{i'})=Idelta_{ii'};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$\displaystyle \sum_{m=-\frac{I}{2}+1}^{\frac{I}{2}} \exp(i m \lambda_i) \exp(-i m \lambda_{i'}) = I \delta_{ii'}$">|; 

$key = q/displaystyletilde{q}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="$\displaystyle \tilde{q}_n^m$">|; 

$key = q/g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="$ g$">|; 

$key = q/q_{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$ q_{k-1}$">|; 

$key = q/displaystyleb=left{{array}{ll}left(frac{1-langlembox{RH}rangle}{1-mbox{RH}_c}rig{RH}ranglegembox{RH}_c1&langlembox{RH}rangle<mbox{RH}_c{array}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$\displaystyle b = \left\{ \begin{array}{ll} \left( \frac{1-\langle \mbox{RH}\ra...
...mbox{RH}_c \ 1 &amp; \langle \mbox{RH}\rangle &lt; \mbox{RH}_c \ \end{array} \right.$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^Jimf_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J im f_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j .$">|; 

$key = q/(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$ (\varphi, \lambda, \sigma)$">|; 

$key = q/overline{seczeta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="$ \overline{\sec \zeta}$">|; 

$key = q/displaystyle:quadコリオリパラメータ[mathrm{s}^{-1}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle : \quad コリオリパラメータ [\mathrm{s}^{-1}],$">|; 

$key = q/displaystyleint_{-1}^1Y_n^m(lambda,varphi)Y_{n'}^{m'*}(lambda,varphi)d(sinvarphi)dlambda=4pidelta_{mm'}delta_{nn'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="$\displaystyle \int_{-1}^1 Y_n^m(\lambda, \varphi) Y_{n'}^{m'*} (\lambda, \varphi) d (\sin \varphi) d \lambda = 4 \pi \delta_{mm'} \delta_{nn'} .$">|; 

$key = q/displaystylehat{T}_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="$\displaystyle \hat{T}_{k}$">|; 

$key = q/displaystylecoszeta=sinvarphisindelta+cosvarphicdotsqrt{1-sin^2delta}cdotcosH;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$\displaystyle \cos \zeta = \sin \varphi \sin \delta
+ \cos \varphi \cdot \sqrt{1 - \sin^2 \delta} \cdot
\cos H$">|; 

$key = q/displaystyleDP{pi}{t}=-int_{0}^{1}Dvect{v}_{H}cdotnabla_{sigma}pidsigma-int_{0}^{1}Ddsigma,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$\displaystyle \DP{\pi}{t} = - \int_{0}^{1} \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma - \int_{0}^{1} D d \sigma ,$">|; 

$key = q/rho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="$ \rho$">|; 

$key = q/lambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ \lambda$">|; 

$key = q/{displaystylefrac{1}{rcosvarphi}DP{f}{lambda}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="$ {\displaystyle \frac{1}{r \cos \varphi} \DP{f}{\lambda} }$">|; 

$key = q/displaystylehat{T}_{k+2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="$\displaystyle \hat{T}_{k+2}$">|; 

$key = q/seczeta_0=1.66;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$ \sec \zeta_0 = 1.66$">|; 

$key = q/displaystyle:quad比湿[mathrm{kg}mathrm{kg}^{-1}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle : \quad 比湿 [\mathrm{kg} \mathrm{kg}^{-1}],$">|; 

$key = q/overline{coszeta};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="$ \overline{\cos \zeta}$">|; 

$key = q/{align*}{split}DP{tilde{zeta}_n^m}{t}&=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}im(v_c{w_j}{acosvarphi_j}&quad+tilde{calD}_{M,n}^mtilde{zeta}_n^m,{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="146" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="\begin{align*}\begin{split}\DP{\tilde{\zeta}_n^m}{t} &amp; = \frac{1}{I} \sum_{i=1}^...
... \ &amp; \quad + \tilde{\cal D}_{M,n}^m \tilde{\zeta}_n^m , \end{split}\end{align*}">|; 

$key = q/K=J+M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="$ K=J+M$">|; 

$key = q/displaystyleq(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle q (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystyle:quad惑星半径[mathrm{m}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle : \quad 惑星半径 [\mathrm{m}],$">|; 

$key = q/w_j=w(mu_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="$ w_j=w(\mu_j)$">|; 

$key = q/displaystylelambda_i=frac{2pi(i-1)}{I}(i=1,2,cdots,I);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle \lambda_i = \frac{2 \pi (i-1)}{I}  \
(i=1,2,\cdots,I)$">|; 

$key = q/displaystyleT^a_{k+1}leftarrowT^a_{k+1}+frac{L}{C_p}frac{q^a_{k+1}-q^*(T^a_{k+1},p_{k+1})}{displaystyle1+frac{L}{C_p}DP{q^*}{T}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="79" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$\displaystyle T^a_{k+1} \leftarrow T^a_{k+1} + \frac{L}{C_p} \frac{ q^a_{k+1} - q^*( T^a_{k+1},p_{k+1}) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} }$">|; 

$key = q/displaystyleC_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$\displaystyle C_{k}$">|; 

$key = q/L=f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$ L=f$">|; 

$key = q/-;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="$ -$">|; 

$key = q/displaystylesum^{I}_{n=1}expleft{imfrac{2pi(n-1)}{I}right}=frac{1-left(e^{frac{i)^I}{1-e^{frac{im2pi}{I}}}=frac{1-e^{im2pi}}{1-e^{frac{im2pi}{I}}}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="$\displaystyle \sum^{I}_{n=1} \exp \left\{ im \frac{2 \pi (n-1)}{I} \right\} = \...
...im 2 \pi}{I} } } = \frac{1 - e^{im 2 \pi} } {1 - e^{ \frac{im 2 \pi}{I} } } = 0$">|; 

$key = q/displaystylev;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="$\displaystyle v$">|; 

$key = q/T^a_{k+1},q^a_{k+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="$ T^a_{k+1}, q^a_{k+1} $">|; 

$key = q/displaystyletau_{S,i}(z)=int_z^inftyk_{S,i}rhoqdz+int_z^inftybar{k}_{S,i}rhodz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="$\displaystyle \tau_{S,i}(z) = \int_z^\infty k_{S,i} \rho q dz + \int_z^\infty \bar{k}_{S,i} \rho dz$">|; 

$key = q/displaystylewidetilde{left(DP{f}{lambda}right)}_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \widetilde{ \left( \DP{f}{\lambda} \right) }_n^m$">|; 

$key = q/displaystyle=-frac{1}{I}sum_{i=1}^Isum_{j=1}^Jf_{ij}left.DD{P_n^m}{varphi}right|_jexp(-imlambda_i)w_j.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\displaystyle = - \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J f_{ij} \left. \DD{P_n^m}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j .$">|; 

$key = q/2J-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="$ 2J-1$">|; 

$key = q/displaystyle=beta_kleft[left(frac{sigma_k}{sigma_{k+1}}right)^{kappa}-1right]^{-1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle = \beta_k \left[ \left( \frac{ \sigma_k }{ \sigma_{k+1} } \right)^{\kappa} - 1 \right]^{-1} .$">|; 

$key = q/1+(2times1+1)+cdots+(2times42+1)=43^2=1849;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="$ 1+ (2 \times1 +1) + \cdots
+ (2 \times 42 +1) = 43^2 = 1849$">|; 

$key = q/displaystyle=q^*(T_{k-1},p_{k-1}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$\displaystyle = q^* (T_{k-1}, p_{k-1}),$">|; 

$key = q/displaystyle=sum_{m=0}^{M}sum_{n=m}^{N}Retilde{A}_n^mY_n^m(lambda_i,varphi_j),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle = \sum_{m=0}^{M} \sum_{n=m}^{N} \Re \tilde{A}_n^m Y_n^m(\lambda_i, \varphi_j),$">|; 

$key = q/1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img636.png"
 ALT="$ 1$">|; 

$key = q/A_{ij}=A(lambda_i,varphi_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$ A_{ij}=A(\lambda_i,\varphi_j)$">|; 

$key = q/{displaystyleM=left[frac{I-1}{3}right]};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="$ {\displaystyle M= \left[ \frac{I-1}{3} \right] }$">|; 

$key = q/0le|m|,|m'|leM,|m|lenleN,|m'|len'leN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="$ 0 \le \vert m\vert,\vert m'\vert \le M, \vert m\vert \le n \le N, \vert m'\vert \le n' \le N$">|; 

$key = q/epsilon_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="$ \epsilon_v$">|; 

$key = q/Depsf[10cm]{spectralslashspl-spherical-harmonics-imagesslashlegendre1.ps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="275" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="\Depsf[10cm]{spectral/spl-spherical-harmonics-images/legendre1.ps}">|; 

$key = q/displaystyle=delta_{nn'},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle = \delta_{nn'},$">|; 

$key = q/displaystyleQ(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle Q  (\varphi, \lambda, \sigma)$">|; 

$key = q/displaystylep_{ij}=sum_{m,n}tilde{f}_n^mleft.DD{P_n^m}{varphi}right|_jexp(imlambda_i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="$\displaystyle p_{ij} = \sum_{m,n} \tilde{f}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _j \exp(im \lambda_i)$">|; 

$key = q/displaystyle=dot{sigma}_{K+1slash2}=0.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$\displaystyle = \dot{\sigma}_{K+1/2} = 0.$">|; 

$key = q/displaystylef(mu)-L(mu)=tilde{P}_J(mu)S(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="$\displaystyle f(\mu) - L(\mu) = \tilde{P}_J(\mu) S(\mu)$">|; 

$key = q/displaystylet;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle t$">|; 

$key = q/displaystyleequivfrac{u^{2}+v^{2}}{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle \equiv \frac{u^{2}+v^{2}}{2 }$">|; 

$key = q/dot{calA}_{dis};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$ \dot{\cal A}_{dis} $">|; 

$key = q/displaystyleleft(DP{T_{k}}{t}right)^{rmNG}=-frac{1}{a(1-mu^{2})}DP{U_kT'_k}{lambc{1}{a}DP{V_kT'_k}{mu}+H_{k}+{calD}(T_{k})+{calD}^{prime}(Dvect{v}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$\displaystyle \left( \DP{T_{k}}{t} \right)^{\rm NG} = - \frac{1}{a(1-\mu^{2})} ...
...} \DP{V_k T'_k}{\mu} + H_{k} + {\cal D}(T_{k}) + {\cal D}^{\prime}(\Dvect{v}) ,$">|; 

$key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^Jleft(sum_{m'=-M}^{M}sum_{n'=|m'|}^Nvarphi_j)exp(im'lambda)right)P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="575" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="$\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J \left( \sum_{m'=-M}^{M} \...
...hi_j) \exp(im' \lambda) \right) P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$">|; 

$key = q/displaystylehat{hat{T}}_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="$\displaystyle \hat{\hat{T}}_{k}$">|; 

$key = q/displaystyleint_{-1}^1tilde{P}_n^m(mu)tilde{P}_{n'}^m(mu)dmu=frac{2}{2n+1}frac{(n+|m|)!}{(n-|m|)!}delta_{nn'}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="$\displaystyle \int_{-1}^1 \tilde{P}_n^m(\mu) \tilde{P}_{n'}^m (\mu) d \mu = \frac{2}{2n+1} \frac{(n+\vert m\vert)!}{(n-\vert m\vert)!} \delta_{nn'} .$">|; 

$key = q/{figure}center{picture{(300,170)(10,-20)put(20,10){vector(1,0){85}}put(30,0){vec0){shortstack{平方四辺形切断}}{par{picture{center{{{{figure};MSF=1.6;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="218" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="\begin{figure}\begin{center}
\begin{picture}(300,170)(10,-20)
\put(20 , 10){\v...
...20) \{ shortstack\{平方四辺形切断\}\}
\par
\end{picture}\end{center}\end{figure}">|; 

$key = q/displaystyle=2sum_{j=1}^{J}f(mu_j)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$\displaystyle = 2 \sum_{j=1}^{J} f(\mu_j) w_j$">|; 

$key = q/A,B,C;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="$ A,B,C$">|; 

$key = q/hat{p_s};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$ \hat{p_s}$">|; 

$key = q/N_{tr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ N_{tr}$">|; 

$key = q/{align*}{split}{v_A}_{,k}&=-(zeta_k+f)u_k-frac{1}{2Deltasigma_k}[dot{sigma}_{k-1ac{C_{p}hat{kappa}_kT_{v,k}'}{a}DP{pi}{mu}+{calF}_{varphi,k},{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="86" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="\begin{align*}\begin{split}{v_A}_{,k} &amp; = - ( \zeta_k + f ) u_k - \frac{1}{2 \De...
...a}_k T_{v,k}'}{a} \DP{\pi}{\mu} + {\cal F}_{\varphi, k}, \end{split}\end{align*}">|; 

$key = q/0le|m|len-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="$ 0\le \vert m\vert \le n-1$">|; 

$key = q/Depsf[][7cm]{spectralslashspl-spherical-harmonics-imagesslashlegendre2.ps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="450" HEIGHT="317" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="\Depsf[][7cm]{spectral/spl-spherical-harmonics-images/legendre2.ps}">|; 

$key = q/displaystyleG_{k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle G_{k}$">|; 

$key = q/A_n^m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$ A_n^m$">|; 

$key = q/{align*}{split}Phi_{1}&=Phi_{s}+C_{p}(sigma_{1}^{-kappa}-1)T_{v,1}&=Phi_{s}+C_{p}alpha_{1}T_{v,1}.{split}{align*};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="59" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="\begin{align*}\begin{split}\Phi_{1} &amp; = \Phi_{s} + C_{p} ( \sigma_{1}^{-\kappa} - 1 ) T_{v,1} \ &amp; = \Phi_{s} + C_{p} \alpha_{1} T_{v,1}. \end{split}\end{align*}">|; 

$key = q/(lambda',varphi');MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="$ (\lambda', \varphi')$">|; 

$key = q/displaystyle=C_{p}alpha_{l}delta_{kgeql}+C_{p}beta_{l}delta_{k-1geql},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$\displaystyle = C_{p} \alpha_{l} \delta_{k \geq l} + C_{p} \beta_{l} \delta_{k-1 \geq l} ,$">|; 

$key = q/mneq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="$ m \neq 0$">|; 

$key = q/displaystyleDP{pi}{t}=left(frac{partialpi}{partialt}right)_{rmNG}-Dvect{C}cdotDvect{D},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle \DP{\pi}{t} = \left( \frac{\partial \pi}{\partial t} \right)_{\rm NG} - \Dvect{C} \cdot \Dvect{D} ,$">|; 

$key = q/P^m_n(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="$ P^m_n(\mu)$">|; 

$key = q/displaystyle=frac{displaystyleS_{k-1slash2}+left(1+gamma_{k-1}-kappafrac{Deltap_ight)frac{1+gamma_{k}}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="480" HEIGHT="100" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle = \frac{ \displaystyle S_{k-1/2} + \left( 1 + \gamma_{k-1} - \kap...
...frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}} \frac{\Delta p_{k}}{\Delta p_{k-1}} }$">|; 

$key = q/displaystyleequivDinv{acosvarphi}left{DP{u}{lambda}+DP{(vcosvarphi)}{varphi}right}:quad発散[mathrm{s}^{-1}].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \equiv \Dinv{a \cos \varphi} \left\{ \DP{u}{\lambda} + \DP{(v \cos \varphi)}{\varphi} \right\} : \quad 発散 [\mathrm{s}^{-1}].$">|; 

$key = q/{displaystyletilde{P}_{J-1}=sqrt{frac{1}{2(mbox{J}-1)+1}}P_{J-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="$ {\displaystyle
\tilde{P}_{J-1}
=\sqrt{ \frac{1}{2(\mbox{J}-1)+1} } P_{J-1}
}$">|; 

$key = q/M=32;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="$ M=32$">|; 

$key = q/displaystylefrac{hat{p_{s}}sigma}{RT}hat{q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="$\displaystyle \frac{\hat{p_{s}} \sigma}{RT} \hat{q}$">|; 

$key = q/displaystylehat{calA}^{t+Deltat}=bar{calA}^{t-Deltat}+2Deltatdot{calA}_{adv}leftDeltat}right)+2Deltatdot{calA}_{phy}left(bar{calA}^{t-Deltat}right).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$\displaystyle \hat{\cal A}^{t+\Delta t} = \bar{\cal A}^{t-\Delta t} + 2 \Delta ...
...ight) + 2 \Delta t \dot{\cal A}_{phy}\left( \bar{\cal A}^{t-\Delta t} \right) .$">|; 

$key = q/A_{ij};(i=1,2,cdots,I,;j=1,2,cdots,J);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="$ A_{ij} \; (i=1,2,\cdots,I, \; j=1,2,\cdots,J)$">|; 

$key = q/displaystyleT^a_{k+1}=T^a_kleft(frac{p_{k+1}}{p_k}right)^{kappa};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="$\displaystyle T^a_{k+1} = T^a_k \left( \frac{p_{k+1}}{p_k} \right)^{\kappa}$">|; 

$key = q/displaystyleR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle R$">|; 

$key = q/displaystyle=frac{1}{rcosvarphi}DP{psi}{lambda}+frac{1}{r}DP{chi}{varphi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="$\displaystyle = \frac{1}{r\cos\varphi} \DP{\psi}{\lambda} + \frac{1}{r} \DP{\chi}{\varphi}$">|; 

$key = q/displaystyleDvect{v}cdotnablapi=frac{u}{acosvarphi}DP{pi}{lambda}+frac{v}{a}DP{pi}{varphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\displaystyle \Dvect{v} \cdot \nabla \pi = \frac{u}{a \cos \varphi} \DP{\pi}{\lambda} + \frac{v}{a} \DP{\pi}{\varphi}.$">|; 

$key = q/displaystylehat{T}_{k}+S_{grst}(T_{Bk}-hat{T}_{k})-frac{sum^{k+2}_{k=k}S_{grst}(T_{Bk}-hat{T}_{k})Deltap_{k}}{sum^{k+2}_{k=k}Deltap_{k}},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="$\displaystyle \hat{T}_{k} + S_{grst} (T_{Bk} - \hat{T}_{k})
- \frac{
\sum^{k+2}...
..._{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k}
}{
\sum^{k+2}_{k=k} \Delta p_{k}
},$">|; 

$key = q/displaystyleT^c_k<hat{T}_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="$\displaystyle T^c_k &lt; \hat{T}_k$">|; 

$key = q/0leKleJ-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="$ 0 \le K \le J-1$">|; 

$key = q/displaystyle=-frac{1}{I}sum_{i,j}f_{ij}left.DD{P_n^m}{varphi}right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="$\displaystyle = - \frac{1}{I} \sum_{i,j} f_{ij} \left. \DD{P_n^m}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j$">|; 

$key = q/L(mu);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="$ L(\mu)$">|; 

$key = q/displaystyle)+{calD}(D).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\displaystyle ) + {\cal D}(D).$">|; 

$key = q/Ige3N_{tr}+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$ I \ge 3N_{tr}+1$">|; 

$key = q/(hat{q},hat{T});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$ (\hat{q}, \hat{T})$">|; 

$key = q/t-Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$ t-\Delta t$">|; 

$key = q/displaystylezeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="$\displaystyle \zeta$">|; 

$key = q/displaystyleleft(-1-gamma_{k}-frac{R}{C_p}frac{Deltap_{k-1slash2}}{2p_{k-1slash2Deltap_{k-1slash2}}{2p_{k-1slash2}}right)DeltaT_{k-1}=-S_{k-1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$\displaystyle \left( - 1 - \gamma_{k} - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{2...
...{C_p} \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) \Delta T_{k-1} = - S_{k-1/2}$">|; 

$key = q/displaystyle{calF}_lambda(varphi,lambda,sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle {\cal F}_\lambda  (\varphi, \lambda, \sigma)$">|; 

$key = q/64times64=4096;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="$ 64 \times 64 = 4096 $">|; 

$key = q/n+n';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="$ n+n'$">|; 

$key = q/2M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$ 2M$">|; 

$key = q/displaystyleA=BC,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="$\displaystyle A= BC ,$">|; 

$key = q/displaystyle=frac{1-mu_j^2}{(Jtilde{P}_{J-1}(mu_j))^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="$\displaystyle = \frac{1-\mu_j^2}{(J \tilde{P}_{J-1}(\mu_j))^2 }$">|; 

$key = q/displaystyleu=-frac{1}{r}DP{psi}{varphi}+frac{1}{rcosvarphi}DP{chi}{lambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="$\displaystyle u = - \frac{1}{r} \DP{\psi}{\varphi} + \frac{1}{r\cos\varphi} \DP{\chi}{\lambda}$">|; 

1;

