# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/textstyleequiv;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="21" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$\textstyle \equiv$">|; 

$key = q/displaystyleDD{T}{t}=frac{RT}{c_p}left{DP{pi}{t}+frac{u}{acosvarphi}DP{pi}{lambda}+frac{v}{a}DP{pi}{varphi}+frac{dot{sigma}}{sigma}right};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$\displaystyle \DD{T}{t}
= \frac{R T}{c_p}
\left\{ \DP{\pi}{t}
+ \frac{u}{a \cos...
...\lambda}
+ \frac{v}{a} \DP{\pi}{\varphi}
+ \frac{\dot{\sigma}}{\sigma} \right\}$">|; 

$key = q/a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="img33.gif"
 ALT="$a$">|; 

$key = q/overline{k}_{R,i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img102.gif"
 ALT="$\overline{k}_{R,i}$">|; 

$key = q/displaystylerho_sbetaC_{E}|Dvect{v}_1|(q^*(T_g,p_s)-q_1),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img150.gif"
 ALT="$\displaystyle \rho_s \beta C_{E} \vert \Dvect{v}_1 \vert
(q^*(T_g, p_s) - q_1),$">|; 

$key = q/hat{q};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img80.gif"
 ALT="$\hat{q}$">|; 

$key = q/i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="7" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img98.gif"
 ALT="$i$">|; 

$key = q/L;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img37.gif"
 ALT="$L$">|; 

$key = q/F^{vdf}_q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img45.gif"
 ALT="$F^{vdf}_q$">|; 

$key = q/{displaymath}hat{q}>q^*(hat{T},p),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="20" BORDER="0"
 SRC="img78.gif"
 ALT="\begin{displaymath}
\hat{q} &gt; q^*(\hat{T},p),
\end{displaymath}">|; 

$key = q/F^{vdf}_T;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img44.gif"
 ALT="$F^{vdf}_T$">|; 

$key = q/displaystylefrac{dzeta}{dt}=frac{1}{acosvarphi}frac{partial}{partiallambda}{-(zeu-dot{sigma}DP{u}{sigma}-frac{RT'}{acosvarphi}DP{pi}{lambda}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$\displaystyle \frac{d \zeta}{d t}
= \frac{1}{a \cos \varphi}
\frac{\partial}{\p...
...- \dot{\sigma} \DP{u}{\sigma}
- \frac{RT'}{a \cos \varphi} \DP{\pi}{\lambda} \}$">|; 

$key = q/T,q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img56.gif"
 ALT="$T, q$">|; 

$key = q/q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img28.gif"
 ALT="$q$">|; 

$key = q/displaystyleC_H=C_E=left{array{{ll}C_{H0}left(1+15R_{iB}slashsqrt{1+5R_{iB}}righM0}}|R_{iB}|}right)^{-1}right]<col_mark>R_{iB}<0,array{right.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="478" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="img156.gif"
 ALT="$\displaystyle C_H = C_E = \left\{
\begin{array}{ll}
C_{H0} \left( 1 + 15 R_{iB}...
...M0}} \vert R_{iB}\vert }
\right)^{-1}
\right]
&amp; R_{iB} &lt; 0,
\end{array} \right.$">|; 

$key = q/displaystylebeta_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img130.gif"
 ALT="$\displaystyle \beta_1$">|; 

$key = q/T;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img27.gif"
 ALT="$T$">|; 

$key = q/displaystyleA_1[B_1(gamma_1-C_1)+6A_1+3A_2],;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img133.gif"
 ALT="$\displaystyle A_1 [ B_1 ( \gamma_1 - C_1 ) + 6 A_1 + 3 A_2 ],$">|; 

$key = q/displaystyle(F_{varphi})_{1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img146.gif"
 ALT="$\displaystyle (F_{\varphi})_{1/2}$">|; 

$key = q/displaystylefrac{partialPhi}{partialsigma}=-frac{RT}{sigma},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$\displaystyle \frac{\partial \Phi}{\partial \sigma} = - \frac{RT}{\sigma},$">|; 

$key = q/{displaymath}widetilde{S_H}=frac{alpha_1-alpha_2R_f}{1-R_f},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="38" BORDER="0"
 SRC="img121.gif"
 ALT="\begin{displaymath}
\widetilde{S_H} = \frac{ \alpha_1-\alpha_2 R_f }{ 1-R_f },
\end{displaymath}">|; 

$key = q/K_q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img106.gif"
 ALT="$K_q$">|; 

$key = q/displaystylealpha_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img126.gif"
 ALT="$\displaystyle \alpha_1$">|; 

$key = q/displaystyleleft(frac{kappa}{lnleft(frac{z_1}{z_{M0}}right)}right),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="img161.gif"
 ALT="$\displaystyle \left(
\frac{\kappa}
{\ln \left( \frac{z_1}{z_{M0}} \right)}
\right),$">|; 

$key = q/{displaymath}R_{iB}=frac{frac{g}{theta_s}(theta_1-theta_g)slashg}{(u_1slashz_1)^ac{T_1(p_sslashp_1)^{kappa}-T_g}{u^2_1slashz_1}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="41" BORDER="0"
 SRC="img157.gif"
 ALT="\begin{displaymath}
R_{iB} = \frac{\frac{g}{\theta_s} (\theta_1 - \theta_g)/g}
...
...{\theta_s}
\frac{T_1 (p_s/p_1)^{\kappa} - T_g}
{u^2_1/z_1}.
\end{displaymath}">|; 

$key = q/K_T;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img105.gif"
 ALT="$K_T$">|; 

$key = q/p_s;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img29.gif"
 ALT="$p_s$">|; 

$key = q/(Deltabullet);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img142.gif"
 ALT="$(\Delta \bullet)$">|; 

$key = q/displaystyleqquad-frac{1}{acosvarphi}DP{}{varphi}[{(zeta+f)v-dot{sigma}DP{u}{sigma}-frac{RT'}{a}DP{pi}{varphi}}cosvarphi]-F^{diff}_{zeta},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$\displaystyle \qquad - \frac{1}{a \cos \varphi}
\DP{}{\varphi}
[ \{ (\zeta + f)...
...{\sigma}
- \frac{RT'}{a} \DP{\pi}{\varphi} \} \cos \varphi]
- F^{diff}_{\zeta},$">|; 

$key = q/displaystyle0.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img61.gif"
 ALT="$\displaystyle 0.$">|; 

$key = q/64;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img51.gif"
 ALT="$64$">|; 

$key = q/l_0=300;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img113.gif"
 ALT="$l_0=300$">|; 

$key = q/l;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="7" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img111.gif"
 ALT="$l$">|; 

$key = q/{k-1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img141.gif"
 ALT="${k-1/2}$">|; 

$key = q/displaystyleq^*(hat{T}_{k-1},p_{k-1})+left.DP{q^*}{T}right|_{k-1}DeltaT_{k-1},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="img70.gif"
 ALT="$\displaystyle q^* (\hat{T}_{k-1},p_{k-1})
+ \left. \DP{q^*}{T} \right\vert _{k-1}
\Delta T_{k-1},$">|; 

$key = q/dot{sigma};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img26.gif"
 ALT="$\dot{\sigma}$">|; 

$key = q/{calT}^f(z_1,z_2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img90.gif"
 ALT="${\cal T}^f(z_1,z_2)$">|; 

$key = q/displaystylebeta_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img136.gif"
 ALT="$\displaystyle \beta_4$">|; 

$key = q/displaystyleq^*(hat{T}_{k},p_{k})+left.DP{q^*}{T}right|_{k}DeltaT_{k},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="img72.gif"
 ALT="$\displaystyle q^* (\hat{T}_{k},p_{k})
+ \left. \DP{q^*}{T} \right\vert _{k}
\Delta T_{k},$">|; 

$key = q/displaystyleDD{q}{t}=frac{g}{p_s}DP{F^{vdf}_q}{sigma}+F^{diff}_q+S^{cond}_q,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$\displaystyle \DD{q}{t}
= \frac{g}{p_s} \DP{F^{vdf}_q}{\sigma}
+ F^{diff}_q
+ S^{cond}_q,$">|; 

$key = q/displaystyleT_{k-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img64.gif"
 ALT="$\displaystyle T_{k-1}$">|; 

$key = q/displaystyleT_{k};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img67.gif"
 ALT="$\displaystyle T_{k}$">|; 

$key = q/displaystyle(F_{T})_{1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img147.gif"
 ALT="$\displaystyle (F_{T})_{1/2}$">|; 

$key = q/N_R;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img101.gif"
 ALT="$N_R$">|; 

$key = q/F^{diff}_{zeta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img38.gif"
 ALT="$F^{diff}_{\zeta}$">|; 

$key = q/{displaymath}R_f=frac{1}{2beta_2}left[beta_1+beta_4R_{iB}-sqrt{(beta_1+beta_4R_{iB})^2-4beta_2beta_3R_{iB}}right],{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="37" BORDER="0"
 SRC="img124.gif"
 ALT="\begin{displaymath}
R_f = \frac{1}{2 \beta_2}
\left[ \beta_1 + \beta_4 R_{iB}
...
... \beta_4 R_{iB} )^2
- 4 \beta_2 \beta_3 R_{iB} }
\right] ,
\end{displaymath}">|; 

$key = q/{displaymath}R_{iB}=frac{displaystylefrac{q}{theta_s}frac{Deltatheta}{Deltaz}}{dtaz}right)^2+left(frac{Deltav}{Deltaz}right)^2}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="83" BORDER="0"
 SRC="img140.gif"
 ALT="\begin{displaymath}
R_{iB} = \frac{\displaystyle
\frac{q}{\theta_s} \frac{\De...
...\right)^2
+ \left( \frac{\Delta v}{\Delta z} \right)^2
}.
\end{displaymath}">|; 

$key = q/displaystyleA_2[B_1(gamma_1+gamma_2)-3A_1],;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img137.gif"
 ALT="$\displaystyle A_2 [ B_1 ( \gamma_1 + \gamma_2 ) - 3 A_1 ],$">|; 

$key = q/{displaymath}F_R(z)=left(piB(T_g)-piB(T_s)right){calT}^f(z,0)+piB(T(z_T)){calT}^(z,z_T)-int_0^{z_T}DD{piB}{xi}{calT}^f(z,xi)dxi,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="565" HEIGHT="38" BORDER="0"
 SRC="img89.gif"
 ALT="\begin{displaymath}
F_R(z) = \left( \pi B(T_g) - \pi B(T_s) \right) {\cal T}^f(...
..._T)
- \int_0^{z_T} \DD{\pi B}{\xi} {\cal T}^f(z,\xi) d \xi,
\end{displaymath}">|; 

$key = q/g;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img34.gif"
 ALT="$g$">|; 

$key = q/(lambda,varphi);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.gif"
 ALT="$(\lambda, \varphi)$">|; 

$key = q/k_{R,i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img96.gif"
 ALT="$k_{R,i}$">|; 

$key = q/{displaymath}{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).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="47" BORDER="0"
 SRC="img93.gif"
 ALT="\begin{displaymath}
{\cal T}^f(z_1,z_2)
= \sum_{i=1}^{N_R} b_i
\exp \left( ...
...ta_R \vert \tau_{R,i}(z_1) - \tau_{R,i}(z_2) \vert
\right).
\end{displaymath}">|; 

$key = q/{displaymath}P=frac{Deltap}{g}(hat{q}-q).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="38" BORDER="0"
 SRC="img87.gif"
 ALT="\begin{displaymath}
P = \frac{\Delta p}{g} (\hat{q} - q).
\end{displaymath}">|; 

$key = q/{displaymath}l=frac{kappaz}{1+kappazslashl_0},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="34" BORDER="0"
 SRC="img112.gif"
 ALT="\begin{displaymath}
l = \frac{\kappa z}{1+\kappa z/l_0},
\end{displaymath}">|; 

$key = q/{displaymath}P=sum^{K}_{k=1}(hat{q}_k-q_k)frac{Deltap_k}{g}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="47" BORDER="0"
 SRC="img77.gif"
 ALT="\begin{displaymath}
P = \sum^{K}_{k=1} (\hat{q}_k - q_k) \frac{\Delta p_k}{g}.
\end{displaymath}">|; 

$key = q/R;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img35.gif"
 ALT="$R$">|; 

$key = q/displaystylegz,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$\displaystyle gz,$">|; 

$key = q/textstyle>;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="22" ALIGN="MIDDLE" BORDER="0"
 SRC="img60.gif"
 ALT="$\textstyle &gt;$">|; 

$key = q/displaystylehat{T}+frac{L}{C_p}frac{hat{q}-q^*(hat{T},p)}{1+frac{L}{C_p}DP{q^*}{T}},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="img84.gif"
 ALT="$\displaystyle \hat{T}
+ \frac{L}{C_p}
\frac{\hat{q} - q^* (\hat{T},p)}
{1 + \frac{L}{C_p} \DP{q^*}{T}},$">|; 

$key = q/displaystylefrac{1}{acosvarphi}DP{u}{lambda}+frac{1}{acosvarphi}DP{}{varphi}(vcosvarphi),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$\displaystyle \frac{1}{a \cos \varphi} \DP{u}{\lambda}
+ \frac{1}{a \cos \varphi}
\DP{}{\varphi} (v \cos \varphi),$">|; 

$key = q/R_f;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img123.gif"
 ALT="$R_f$">|; 

$key = q/{displaymath}q=q^*(T,p){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="16" BORDER="0"
 SRC="img81.gif"
 ALT="\begin{displaymath}
q = q^*(T,p)
\end{displaymath}">|; 

$key = q/{displaymath}Deltahat{Q}=(hat{q}_{k-1}-q^*(hat{T}_{k-1},p_{k-1}))Deltap_{k-1}+(hat{q}_{k}-q^*(hat{T}_{k},p_{k}))Deltap_{k}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="20" BORDER="0"
 SRC="img76.gif"
 ALT="\begin{displaymath}
\Delta \hat{Q}
= (\hat{q}_{k-1} - q^*(\hat{T}_{k-1},p_{k-...
...k-1}
+ (\hat{q}_{k} - q^*(\hat{T}_{k},p_{k}) ) \Delta p_{k}.
\end{displaymath}">|; 

$key = q/displaystyleC_{H0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img162.gif"
 ALT="$\displaystyle C_{H0}$">|; 

$key = q/F^{diff}_{q};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img41.gif"
 ALT="$F^{diff}_{q}$">|; 

$key = q/{displaymath}Deqlab{ds瘦赂}sum^{k}_{l=k-1}(C_{p}T_l+Lq_l)Deltap_l=sum^{k}_{l=k-1}(C_{p}hat{T}_l+Lhat{q}_l)Deltap_l,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="48" BORDER="0"
 SRC="img54.gif"
 ALT="\begin{displaymath}
\Deqlab{ds 瘦赂}
\sum^{k}_{l=k-1} (C_{p} T_l + L q_l) \Del...
... \sum^{k}_{l=k-1} (C_{p} \hat{T}_l + L \hat{q}_l) \Delta p_l,
\end{displaymath}">|; 

$key = q/{displaymath}C_pT+Lq=C_phat{T}+Lhat{q}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="22" BORDER="0"
 SRC="img82.gif"
 ALT="\begin{displaymath}
C_p T + Lq = C_p \hat{T} + L \hat{q}.
\end{displaymath}">|; 

$key = q/n=8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img48.gif"
 ALT="$n=8$">|; 

$key = q/displaystylehat{T}_{k-1}+DeltaT_{k-1},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img66.gif"
 ALT="$\displaystyle \hat{T}_{k-1} + \Delta T_{k-1},$">|; 

$key = q/C_E;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img154.gif"
 ALT="$C_E$">|; 

$key = q/{displaymath}gamma_{k}=frac{L}{C_p}left.DP{q^*}{T}right|_{k},gamma_{k-1}=frac{L}{C_p}left.DP{q^*}{T}right|_{k-1},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="41" BORDER="0"
 SRC="img75.gif"
 ALT="\begin{displaymath}
\gamma_{k} = \frac{L}{C_p} \left. \DP{q^*}{T} \right\vert _...
...{k-1} = \frac{L}{C_p} \left. \DP{q^*}{T} \right\vert _{k-1},
\end{displaymath}">|; 

$key = q/hat{T};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="img79.gif"
 ALT="$\hat{T}$">|; 

$key = q/displaystyleC_M=left{array{{ll}C_{M0}left(1+10R_{iB}slashsqrt{1+5R_{iB}}right)^{M0}}|R_{iB}|}right)^{-1}right]<col_mark>R_{iB}<0,array{right.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="img155.gif"
 ALT="$\displaystyle C_M = \left\{
\begin{array}{ll}
C_{M0} \left( 1 + 10 R_{iB}/\sqrt...
...M0}} \vert R_{iB}\vert }
\right)^{-1}
\right]
&amp; R_{iB} &lt; 0,
\end{array} \right.$">|; 

$key = q/displaystyleD;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$\displaystyle D$">|; 

$key = q/displaystylehat{q}_{k-1}>q^*(hat{T}_{k-1},p_{k-1}),hat{q}_{k}>q^*(hat{T}_{k},p_{k}).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img62.gif"
 ALT="$\displaystyle \hat{q}_{k-1} &gt; q^*(\hat{T}_{k-1},p_{k-1}), \ \
\hat{q}_{k} &gt; q^*(\hat{T}_{k} ,p_{k}).$">|; 

$key = q/{displaymath}tau_{R,i}(z)=int_z^inftyk_{R,i}rhoqdz+int_z^inftybar{k}_{R,i}rhodz,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="38" BORDER="0"
 SRC="img95.gif"
 ALT="\begin{displaymath}
\tau_{R,i}(z) = \int_z^\infty k_{R,i} \rho q dz
+ \int_z^\infty \bar{k}_{R,i} \rho dz,
\end{displaymath}">|; 

$key = q/displaystyleqquad-nabla^2(Phi+Roverline{T}pi+E)-F^{diff}_{D},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$\displaystyle \qquad - \nabla^2 (\Phi + R \overline{T} \pi + E )
- F^{diff}_{D},$">|; 

$key = q/C_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img152.gif"
 ALT="$C_M$">|; 

$key = q/displaystyleDD{}{t};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$\displaystyle \DD{}{t}$">|; 

$key = q/R_{iB};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img125.gif"
 ALT="$R_{iB}$">|; 

$key = q/displaystylebeta_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img132.gif"
 ALT="$\displaystyle \beta_2$">|; 

$key = q/(T_k,q_k);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img63.gif"
 ALT="$(T_k, q_k)$">|; 

$key = q/K_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img104.gif"
 ALT="$K_M$">|; 

$key = q/displaystyleA_2B_1,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img135.gif"
 ALT="$\displaystyle A_2 B_1,$">|; 

$key = q/displaystyleDP{}{t}+frac{u}{acosvarphi}DP{}{lambda}+frac{v}{a}DP{}{varphi}+dot{sigma}DP{}{sigma},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$\displaystyle \DP{}{t}
+ \frac{u}{a \cos \varphi} \DP{}{\lambda}
+ \frac{v}{a} \DP{}{\varphi}
+ \dot{\sigma} \DP{}{\sigma},$">|; 

$key = q/displaystylefrac{1}{acosvarphi}DP{v}{lambda}-frac{1}{acosvarphi}DP{}{varphi}(ucosvarphi),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$\displaystyle \frac{1}{a \cos \varphi} \DP{v}{\lambda}
- \frac{1}{a \cos \varphi}
\DP{}{\varphi} (u \cos \varphi),$">|; 

$key = q/displaystyleq;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img85.gif"
 ALT="$\displaystyle q$">|; 

$key = q/{displaymath}(A_1,B_1,A_2,B_2,C_1)=(0.92,16.6,0.74,10.1,0.08),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="16" BORDER="0"
 SRC="img138.gif"
 ALT="\begin{displaymath}
(A_1, B_1, A_2, B_2, C_1 ) = ( 0.92, 16.6, 0.74, 10.1, 0.08 ) ,
\end{displaymath}">|; 

$key = q/displaystyleA_1B_1(gamma_1-C_1),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img131.gif"
 ALT="$\displaystyle A_1 B_1 ( \gamma_1 - C_1 ),$">|; 

$key = q/128;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img50.gif"
 ALT="$128$">|; 

$key = q/displaystyleT;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img83.gif"
 ALT="$\displaystyle T$">|; 

$key = q/S^{cond}_q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img46.gif"
 ALT="$S^{cond}_q$">|; 

$key = q/tau_i(z);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img94.gif"
 ALT="$\tau_i(z)$">|; 

$key = q/displaystyleC_{M0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img160.gif"
 ALT="$\displaystyle C_{M0}$">|; 

$key = q/displaystylealpha_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img128.gif"
 ALT="$\displaystyle \alpha_2$">|; 

$key = q/displaystylehat{T}_k-hat{T}_{k-1}+frac{L}{C_p}left(q^*(hat{T}_{k},p_{k})-q^*(hattap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_k+hat{T}_{k-1}}{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="img59.gif"
 ALT="$\displaystyle \hat{T}_k - \hat{T}_{k-1}
+ \frac{L}{C_p}
\left( q^*(\hat{T}_{k},...
...{R}{C_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{\hat{T}_k + \hat{T}_{k-1}}{2}$">|; 

$key = q/S_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img115.gif"
 ALT="$S_M$">|; 

$key = q/F_{R,i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img88.gif"
 ALT="$F_{R,i}$">|; 

$key = q/{displaymath}widetilde{S_M}=frac{beta_1-beta_2R_f}{beta_3-beta_4R_f}widetilde{S_H}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="39" BORDER="0"
 SRC="img122.gif"
 ALT="\begin{displaymath}
\widetilde{S_M} = \frac{ \beta_1-\beta_2 R_f }
{ \beta_3-\beta_4 R_f }
\widetilde{S_H}.
\end{displaymath}">|; 

$key = q/displaystylehat{q}-frac{L}{C_p}DP{q^*}{T}frac{hat{q}-q^*(hat{T},p)}{1+frac{L}{C_p}DP{q^*}{T}}.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="img86.gif"
 ALT="$\displaystyle \hat{q}
- \frac{L}{C_p} \DP{q^*}{T}
\frac{\hat{q} - q^* (\hat{T},p)}
{1 + \frac{L}{C_p} \DP{q^*}{T}}.$">|; 

$key = q/displaystyleqquad+frac{1}{acosvarphi}DP{}{varphi}[{(zeta+f)v-dot{sigma}DP{u}{sigma}-frac{RT'}{a}DP{pi}{varphi}}cosvarphi];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$\displaystyle \qquad + \frac{1}{a \cos \varphi} \DP{}{\varphi}
[ \{ (\zeta + f)...
... \dot{\sigma} \DP{u}{\sigma}
- \frac{RT'}{a} \DP{\pi}{\varphi} \} \cos \varphi]$">|; 

$key = q/C_H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img153.gif"
 ALT="$C_H$">|; 

$key = q/b_i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img99.gif"
 ALT="$b_i$">|; 

$key = q/displaystyle3A_2gamma_1,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img127.gif"
 ALT="$\displaystyle 3 A_2 \gamma_1,$">|; 

$key = q/5.0times10^{-5};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img103.gif"
 ALT="$5.0 \times 10^{-5}$">|; 

$key = q/F^{vdf}_u;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img42.gif"
 ALT="$F^{vdf}_u$">|; 

$key = q/C_{H0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img159.gif"
 ALT="$C_{H0}$">|; 

$key = q/{displaymath}DeltaT_{k-1}=-frac{(1+gamma_{k})Deltap_{k}}{(1+gamma_{k-1})Deltap_{gamma_{k-1})Deltap_{k-1}}frac{L}{C_p}DeltaT_{k},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="429" HEIGHT="39" BORDER="0"
 SRC="img74.gif"
 ALT="\begin{displaymath}
\Delta T_{k-1}
= - \frac{ (1 + \gamma_{k}) \Delta p_{k}
...
... \gamma_{k-1}) \Delta p_{k-1} }
\frac{L}{C_p}
\Delta T_{k},
\end{displaymath}">|; 

$key = q/u;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="img24.gif"
 ALT="$u$">|; 

$key = q/displaystylerho_sC_{p}C_{H}|Dvect{v}_1|(T_g-(frac{T}{Pi}_1)),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="img148.gif"
 ALT="$\displaystyle \rho_s C_{p} C_{H} \vert \Dvect{v}_1 \vert
(T_g - (\frac{T}{\Pi}_1)),$">|; 

$key = q/displaystyleleft(frac{kappa}{lnleft(frac{z_1}{z_{H0}}right)}right),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="img163.gif"
 ALT="$\displaystyle \left(
\frac{\kappa}
{\ln \left( \frac{z_1}{z_{H0}} \right)}
\right),$">|; 

$key = q/S_H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img116.gif"
 ALT="$S_H$">|; 

$key = q/sigma_k;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="19" ALIGN="MIDDLE" BORDER="0"
 SRC="img53.gif"
 ALT="$\sigma_k$">|; 

$key = q/displaystyleB_1^{1slash2}(1-R_f)^{1slash2}widetilde{S_M}^{3slash2},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="img118.gif"
 ALT="$\displaystyle B_1^{1/2} ( 1- R_f )^{1/2}
\widetilde{S_M}^{3/2},$">|; 

$key = q/kappa=0.4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img114.gif"
 ALT="$\kappa=0.4$">|; 

$key = q/displaystyleK_T=K_q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img109.gif"
 ALT="$\displaystyle K_T = K_q$">|; 

$key = q/displaystyleK_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img107.gif"
 ALT="$\displaystyle K_M$">|; 

$key = q/bullet_{k}-bullet_{k-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="22" ALIGN="MIDDLE" BORDER="0"
 SRC="img143.gif"
 ALT="$\bullet_{k}
- \bullet_{k-1}$">|; 

$key = q/displaystylel^2frac{Delta|Dvect{v}|}{Deltaz}S_M,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="img108.gif"
 ALT="$\displaystyle l^2 \frac{\Delta \vert\Dvect{v}\vert}{\Delta z} S_M,$">|; 

$key = q/displaystyleS_M;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img117.gif"
 ALT="$\displaystyle S_M$">|; 

$key = q/displaystyleqquadqquadmbox{}+frac{1}{c_p}left(frac{g}{p_s}DP{F^{vdf}_T}{sigma}+fg}{p_s}DP{F^{rad}_{T}}{sigma}right)+F^{diff}_{T}+LS^{cond}_q.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$\displaystyle \qquad \qquad \mbox{} + \frac{1}{c_p} \left(
\frac{g}{p_s} \DP{F^...
...+ \frac{g}{p_s} \DP{F^{rad}_{T}}{\sigma} \right)
+ F^{diff}_{T} + L S^{cond}_q.$">|; 

$key = q/K;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img49.gif"
 ALT="$K$">|; 

$key = q/F^{diff}_{D};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img39.gif"
 ALT="$F^{diff}_{D}$">|; 

$key = q/(k,k-1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img57.gif"
 ALT="$(k,k-1)$">|; 

$key = q/displaystyle-rho_sC_{M}|Dvect{v}_1|u_1,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img145.gif"
 ALT="$\displaystyle - \rho_s C_{M} \vert \Dvect{v}_1 \vert u_1,$">|; 

$key = q/bar{k}_{R,i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img97.gif"
 ALT="$\bar{k}_{R,i}$">|; 

$key = q/C_{M0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img158.gif"
 ALT="$C_{M0}$">|; 

$key = q/{displaymath}DeltaT_{k}=frac{(1+gamma_{k-1})Deltap_{k-1}S_{k-1slash2}+[1+gamma_{{k-1}-(1+gamma_{k})Deltap_{k}]}raisebox{-5mm}{,}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="600" HEIGHT="57" BORDER="0"
 SRC="img73.gif"
 ALT="\begin{displaymath}
\Delta T_{k}
= \frac{
(1 + \gamma_{k-1}) \Delta p_{k-1} ...
...k-1}
- (1 + \gamma_{k}) \Delta p_{k}]
} \raisebox{-5mm}{,}
\end{displaymath}">|; 

$key = q/displaystyleq_{k};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img71.gif"
 ALT="$\displaystyle q_{k}$">|; 

$key = q/displaystyleST_{k-1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img58.gif"
 ALT="$\displaystyle ST_{k-1/2}$">|; 

$key = q/hat{T},hat{q};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img55.gif"
 ALT="$\hat{T}, \hat{q}$">|; 

$key = q/displaystyle(F_{q})_{1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img149.gif"
 ALT="$\displaystyle (F_{q})_{1/2}$">|; 

$key = q/1slash2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img151.gif"
 ALT="$1/2$">|; 

$key = q/displaystylepi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="19" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$\displaystyle \pi$">|; 

$key = q/F^{diff}_{T};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img40.gif"
 ALT="$F^{diff}_{T}$">|; 

$key = q/displaystyleS_H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img119.gif"
 ALT="$\displaystyle S_H$">|; 

$key = q/Phi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img31.gif"
 ALT="$\Phi$">|; 

$key = q/{displaymath}F^{diff}=-(-1)^nKnabla^{2n}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="19" BORDER="0"
 SRC="img47.gif"
 ALT="\begin{displaymath}
F^{diff} = - (-1)^n K \nabla^{2n}
\end{displaymath}">|; 

$key = q/z_{H0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img165.gif"
 ALT="$z_{H0}$">|; 

$key = q/k;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img52.gif"
 ALT="$k$">|; 

$key = q/c_p;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img36.gif"
 ALT="$c_p$">|; 

$key = q/displaystylebeta_3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img134.gif"
 ALT="$\displaystyle \beta_3$">|; 

$key = q/displaystyleDD{D}{t}=frac{1}{acosvarphi}DP{}{lambda}{(zeta+f)v-dot{sigma}DP{u}{sigma}-xfrac{RT'}{a}DP{pi}{varphi}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$\displaystyle \DD{D}{t}
= \frac{1}{a \cos \varphi} \DP{}{\lambda}
\{ (\zeta + f) v - \dot{\sigma} \DP{u}{\sigma}
- x\frac{RT'}{a} \DP{\pi}{\varphi} \}$">|; 

$key = q/z=z_1,z_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img91.gif"
 ALT="$z=z_1,z_2$">|; 

$key = q/delta_R;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img100.gif"
 ALT="$\delta_R$">|; 

$key = q/displaystyleDD{pi}{t}=-frac{1}{acosvarphi}DP{u}{lambda}-frac{1}{acosvarphi}DP{}{varphi}(vcosvarphi)-frac{partialdot{sigma}}{partialsigma},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$\displaystyle \DD{\pi}{t}
= - \frac{1}{a \cos \varphi} \DP{u}{\lambda}
- \frac{...
...P{}{\varphi} ( v \cos \varphi)
- \frac{\partial \dot{\sigma}}{\partial \sigma},$">|; 

$key = q/displaystyle3A_2(gamma_1+gamma_2),;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img129.gif"
 ALT="$\displaystyle 3 A_2 (\gamma_1+\gamma_2),$">|; 

$key = q/displaystylel^2frac{Delta|Dvect{v}|}{Deltaz}S_H.;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="img110.gif"
 ALT="$\displaystyle l^2 \frac{\Delta \vert\Dvect{v}\vert}{\Delta z} S_H.$">|; 

$key = q/displaystyleB_1^{1slash2}(1-R_f)^{1slash2}widetilde{S_M}^{1slash2}widetilde{S_H},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="img120.gif"
 ALT="$\displaystyle B_1^{1/2} ( 1- R_f )^{1/2}
\widetilde{S_M}^{1/2} \widetilde{S_H},$">|; 

$key = q/f;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img32.gif"
 ALT="$f$">|; 

$key = q/piBequivsigma_{SB}T^4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img92.gif"
 ALT="$\pi B \equiv \sigma_{SB} T^4$">|; 

$key = q/displaystylePhi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$\displaystyle \Phi$">|; 

$key = q/displaystylehat{T}_{k}+DeltaT_{k},;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img68.gif"
 ALT="$\displaystyle \hat{T}_{k} + \Delta T_{k},$">|; 

$key = q/displaystyle(F_{lambda})_{1slash2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img144.gif"
 ALT="$\displaystyle (F_{\lambda})_{1/2}$">|; 

$key = q/z_{M0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img164.gif"
 ALT="$z_{M0}$">|; 

$key = q/displaystylelnp_s,;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.gif"
 ALT="$\displaystyle \ln p_s,$">|; 

$key = q/sigma;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="11" ALIGN="BOTTOM" BORDER="0"
 SRC="img23.gif"
 ALT="$\sigma$">|; 

$key = q/F^{vdf}_v;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img43.gif"
 ALT="$F^{vdf}_v$">|; 

$key = q/textstyle=;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="18" ALIGN="MIDDLE" BORDER="0"
 SRC="img65.gif"
 ALT="$\textstyle =$">|; 

$key = q/v;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="img25.gif"
 ALT="$v$">|; 

$key = q/displaystyleq_{k-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="20" ALIGN="MIDDLE" BORDER="0"
 SRC="img69.gif"
 ALT="$\displaystyle q_{k-1}$">|; 

$key = q/{displaymath}gamma_1=frac{1}{3}-frac{2A_1}{B_1},,,,,gamma_2=frac{B_2}{B_1}+6frac{A_1}{B_1},{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="36" BORDER="0"
 SRC="img139.gif"
 ALT="\begin{displaymath}
\gamma_1 = \frac{1}{3} - \frac{2 A_1}{B_1}\, , \, \, \,
\gamma_2 = \frac{B_2}{B_1} + 6\frac{A_1}{B_1},
\end{displaymath}">|; 

$key = q/10^{-4};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img166.gif"
 ALT="$10^{-4}$">|; 

$key = q/T_g;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img30.gif"
 ALT="$T_g$">|; 

$key = q/displaystylezeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$\displaystyle \zeta$">|; 

1;

