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


$key = q/F_{IR,nu_{i}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$F_{IR,\nu_{i}}^{\uparrow}$">|; 

$key = q/theta,pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\theta, \pi $">|; 

$key = q/displaystylefrac{int_{0}^{infty}Q_{e,nu}pir^{2}DD{n(r)}{r}Ddr}{int_{0}^{infty}pir^{2}DD{n(r)}{r}Ddr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\displaystyle \frac{\int _{0}^{\infty}Q_{e,\nu}\pi r ^{2}\DD{n(r)}{r}\Dd r}
{\int _{0}^{\infty}\pi r ^{2}\DD{n(r)}{r} \Dd r},$">|; 

$key = q/displaystylesum_{i}Deltanu_{i}left{int_{z}^{infty}piB_{nu_{i},T}(z')DD{{calT}_{i}(z,z')}{z'}Ddz'right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle \sum _{i}\Delta \nu _{i}\left\{
\int _{z}^{\infty }\pi B_{\nu _{i},T}(z')\DD{{\cal T}_{i}(z,z')}{z'}\Dd z'
\right\},$">|; 

$key = q/dn(r)slashdr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$dn(r)/dr$">|; 

$key = q/displaystyleQ_{rad,IR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle Q_{rad,IR}$">|; 

$key = q/displaystyleI_{0}left(frac{r_{0}}{r}right)^{2}mu_{0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle I_{0}\left(\frac{r_{0}}{r}\right)^{2}\mu_{0},$">|; 

$key = q/Theta_{sfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\Theta_{sfc}$">|; 

$key = q/displaystyleDD{P_{0}}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle \DD{P_{0}}{z}$">|; 

$key = q/C_{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$C_{D}$">|; 

$key = q/displaystyleQ_{rad,dust,IR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\displaystyle Q_{rad,dust,IR}$">|; 

$key = q/{displaymath}W=-frac{4rho_{d}gr^{2}}{18eta}left(1+2frac{lambda_{r}}{r}frac{p_{r}}{P_{0}}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="\begin{displaymath}
W = - \frac{4\rho _{d}gr^{2}}{18\eta}
\left(1+2\frac{\lambda_{r}}{r}\frac{p_{r}}{P_{0}}\right).
\end{displaymath}">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$g$">|; 

$key = q/Q_{e,0.67mum};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$Q_{e,0.67 \mu m}$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$h$">|; 

$key = q/displaystyleDD{F_{IR,nu_{i}}^{downarrow}}{tau_{nu_{i}}^{*}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle \DD{F_{IR,\nu _{i}}^{\downarrow}}{\tau _{\nu _{i}}^{*}}$">|; 

$key = q/displaystylebeta_{s,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle \beta _{s,\nu}$">|; 

$key = q/displaystyleF_{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle F_{\theta }$">|; 

$key = q/lambda_{r}(p_{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\lambda_{r}(p_{r})$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\omega$">|; 

$key = q/e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$e$">|; 

$key = q/S_{nu_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$S_{\nu
_{i}}$">|; 

$key = q/displaystyle-rho_{0}g,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle - \rho _{0}g,$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\textstyle =$">|; 

$key = q/Q_{e,nu_{i}}slashQ_{e,0.67mum};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$Q_{e,\nu_{i}}/Q_{e,0.67\mu m}$">|; 

$key = q/u,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$u, v$">|; 

$key = q/mu_{0}=coszeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\mu _{0}=\cos \zeta$">|; 

$key = q/displaystyle-frac{1}{rho_{a}c_{p}}DD{}{z}left[sum_{nu_{i}}Deltanu_{i}left(F_{diff,nu_{i}}^{downarrow}-F_{dir,nu_{i}}^{downarrow}right)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle - \frac{1}{\rho _{a}c_{p}}\DD{}{z}
\left[\sum _{\nu _{i} } \Delta...
...w}-F_{dif,\nu _{i}}^{\downarrow}-
F_{dir,\nu _{i}}^{\downarrow}\right)
\right],$">|; 

$key = q/displaystylegamma_{2,nu_{i}}F_{dif,nu_{i}}^{uparrow}-gamma_{1,nu_{i}}F_{dif,nu_{mega}_{nu_{i}}^{*}S_{nu_{i}}e^{-tau_{nu_{i}}^{*}slashmu_{0}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle \gamma _{2,\nu _{i}}F_{dif,\nu _{i}}^{\uparrow} -
\gamma _{1,\nu ...
...}})
\tilde{\omega}_{\nu _{i}}^{*}S_{\nu _{i}}e^{-\tau _{\nu _{i}}^{*}/\mu_{0}}.$">|; 

$key = q/alpha_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\alpha _{i}$">|; 

$key = q/displaystylefrac{sigma_{s,nu}}{pir^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\displaystyle \frac{\sigma _{s,\nu}}{\pi r^{2}},$">|; 

$key = q/Q_{s,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$Q_{s,\nu}$">|; 

$key = q/times10{}^{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\times 10{}^{0}$">|; 

$key = q/displaystyleDD{theta}{t}+wDP{Theta_{0}}{z}=frac{Theta_{0}}{T_{0}}(Q_{rad}+Q_{dis})+D(theta+Theta_{0}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\displaystyle \DD{\theta }{t} + w\DP{\Theta _{0}}{z}
= \frac{\Theta _{0}}{T_{0}}(Q_{rad}+Q_{dis}) + D(\theta + \Theta _{0}) ,$">|; 

$key = q/{displaymath}gamma_{1,nu_{i}}=frac{1}{4}[7-(4+3g_{nu_{i}}^{*})tilde{omega}_{nu_{_{3,nu_{i}}=frac{1}{4}(2-3g_{nu_{i}}^{*}mu_{0}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="631" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="\begin{displaymath}
\gamma _{1,\nu _{i}} =
\frac{1}{4}[7-(4+3g_{\nu _{i}}^{*}...
...amma _{3,\nu _{i}} = \frac{1}{4}(2-3g_{\nu _{i}}^{*}\mu_{0}),
\end{displaymath}">|; 

$key = q/displaystyleDD{w}{t}=-c_{p}Theta_{0}DP{pi}{z}+gfrac{theta}{Theta_{0}}+D(w),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle \DD{w}{t} = -c_{p}\Theta _{0}\DP{\pi }{z} +
g\frac{\theta }{\Theta _{0}} + D(w),$">|; 

$key = q/{displaymath}Piequivleft(frac{p}{P_{00}}right)^{kappa}=Pi_{0}+pi,quadPi_{0}=left(frac{P_{0}}{P_{00}}right)^{kappa}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="\begin{displaymath}
\Pi \equiv \left(\frac{p}{P_{00}}\right)^{\kappa } = \Pi _{...
..., \quad
\Pi_{0} = \left(\frac{P_{0}}{P_{00}}\right)^{\kappa }
\end{displaymath}">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$l$">|; 

$key = q/{displaymath}-kleft.DP{T}{z}right|_{z=0}=-F_{SR}(1-A)+F_{IR,net}+H,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="\begin{displaymath}
- k\left.\DP{T}{z}\right\vert _{z=0} = - F_{SR}(1-A) + F_{IR,net} + H ,
\end{displaymath}">|; 

$key = q/=2pitslashT-pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$= 2\pi t/T -\pi$">|; 

$key = q/{displaymath}tilde{omega}_{nu}=frac{beta_{s,nu}}{beta_{a,nu}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="\begin{displaymath}
\tilde{\omega}_{\nu} = \frac{\beta _{s,\nu}}{\beta _{a,\nu}}
\end{displaymath}">|; 

$key = q/nu_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\nu _{i}$">|; 

$key = q/displaystyleF_{NIR}^{downarrow}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle F_{NIR}^{\downarrow}(z)$">|; 

$key = q/{displaymath}tau_{nu}(z)=-int_{z_{t}}^{z}beta_{e,nu}(r)Ddz{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="\begin{displaymath}
\tau _{\nu}(z) = - \int _{z_{t}}^{z} \beta _{e,\nu}(r) \Dd z
\end{displaymath}">|; 

$key = q/sigma_{s,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\sigma_{s,\nu}$">|; 

$key = q/displaystylegamma_{1,nu_{i}}F_{IR,nu_{i}}^{uparrow}-gamma_{2,nu_{i}}F_{IR,nu_{i}i(1-tilde{omega}_{nu_{i}}^{*})B_{nu_{i},T}(tau_{nu_{i}}^{*}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle \gamma _{1,\nu _{i}}F_{IR,\nu _{i}}^{\uparrow} -
\gamma _{2,\nu _...
...}
-2\pi (1-\tilde{\omega}_{\nu _{i}}^{*})
B_{\nu _{i},T}(\tau _{\nu _{i}}^{*}),$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$q$">|; 

$key = q/displaystyleK=C_{m}sqrt{varepsilon}l.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle K=C_{m}\sqrt{\varepsilon }l.$">|; 

$key = q/w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$w$">|; 

$key = q/Q_{rad,NIR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$Q_{rad,NIR}$">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\delta$">|; 

$key = q/{displaymath}l=mbox{max}(Deltaz,z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="\begin{displaymath}
l =\mbox{max}(\Delta z,z).
\end{displaymath}">|; 

$key = q/tilde{omega}_{nu_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$\tilde{\omega}_{\nu _{i}}$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$t$">|; 

$key = q/{displaymath}B_{nu_{i},T}=frac{1}{nu_{2}-nu_{1}}int_{nu_{1}}^{nu_{2}}B_{nu,T}Ddnu.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="\begin{displaymath}
B_{\nu_{i},T} = \frac{1}{\nu _{2}-\nu _{1}}
\int _{\nu _{1}}^{\nu _{2}} B_{\nu ,T}\Dd \nu.
\end{displaymath}">|; 

$key = q/r_{eff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$r_{eff}$">|; 

$key = q/F_{IR,nu_{i}}^{downarrow}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$F_{IR,\nu_{i}}^{\downarrow}=0$">|; 

$key = q/F_{IR}^{uparrow},F_{IR}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$F_{IR}^{\uparrow}, F_{IR}^{\downarrow}$">|; 

$key = q/{}_{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="${}_{2}$">|; 

$key = q/rho_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\rho _{d}$">|; 

$key = q/displaystyleDD{F_{dif,nu_{i}}^{uparrow}}{tau_{nu_{i}}^{*}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle \DD{F_{dif,\nu _{i}}^{\uparrow}}{\tau _{\nu _{i}}^{*}}$">|; 

$key = q/times10{}^{1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\times 10{}^{1}$">|; 

$key = q/D(cdot);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$D(\cdot )$">|; 

$key = q/displaystyleP_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle P_{0}$">|; 

$key = q/{displaymath}u(z,z')=int_{z}^{z'}1.67rho_{0}Ddzslashmu_{0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="\begin{displaymath}
u(z,z') = \int _{z}^{z'}1.67\rho _{0}\Dd z / \mu_{0},
\end{displaymath}">|; 

$key = q/C_{epsilon}=C_{m}=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$C_{\epsilon}=C_{m}=0.2$">|; 

$key = q/Theta_{z=z1},overline{Theta}_{z=z1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\Theta _{z=z1}, \overline{\Theta }_{z=z1}$">|; 

$key = q/=T_{sfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$=T_{sfc}$">|; 

$key = q/displaystyleF_{IR}^{downarrow}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle F_{IR}^{\downarrow}(z)$">|; 

$key = q/{}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="${}^{-3}$">|; 

$key = q/displaystyle-DP{}{x}left[rho_{0}left(uDP{u}{x}+wDP{u}{z}-D(u)right)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle - \DP{}{x}\left[ \rho _{0}\left
( u\DP{u}{x} + w\DP{u}{z} - D(u) \right) \right]$">|; 

$key = q/{displaymath}D(cdot)=DP{}{x}left[KDP{(cdot)}{x}right]+frac{1}{rho_{0}}DP{}{z}left[rho_{0}KDP{(cdot)}{z}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="\begin{displaymath}
D(\cdot ) = \DP{}{x}\left[ K\DP{(\cdot )}{x} \right] +
\f...
...}{\rho _{0}}\DP{}{z}\left[ \rho _{0}K\DP{(\cdot )}{z} \right].
\end{displaymath}">|; 

$key = q/displaystylefrac{sigma_{a,nu}}{pir^{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle \frac{\sigma _{a,\nu}}{\pi r^{2}}.$">|; 

$key = q/displaystylegamma_{2,nu_{i}}F_{IR,nu_{i}}^{uparrow}-gamma_{1,nu_{i}}F_{IR,nu_{i}i(1-tilde{omega}_{nu_{i}}^{*})B_{nu_{i},T}(tau_{nu_{i}}^{*}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle \gamma _{2,\nu _{i}}F_{IR,\nu _{i}}^{\uparrow} -
\gamma _{1,\nu _...
...w}
+2\pi (1-\tilde{\omega}_{\nu _{i}}^{*})B_{\nu _{i},T}(\tau _{\nu _{i}}^{*}).$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$T$">|; 

$key = q/{calT}_{i}(z,z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="${\cal T}_{i}(z,z')$">|; 

$key = q/displaystylec_{p}Theta_{0}left[rho_{0}DP[2]{pi}{x}+DP{}{z}left(rho_{0}DP{pi}{z}right)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle c_{p}\Theta_{0} \left[ \rho _{0}\DP[2]{\pi }{x} + \DP{}{z}
\left( \rho _{0}\DP{\pi }{z} \right) \right]$">|; 

$key = q/Q_{dis};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$Q_{dis}$">|; 

$key = q/T_{sol};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$T_{sol}$">|; 

$key = q/B_{nu_{i},T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$B_{\nu _{i},T}$">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\sigma $">|; 

$key = q/displaystyle-frac{1}{rho_{a}c_{p}}DD{}{z}left[sum_{nu_{i}}Deltanu_{i}left(F_{IR,nu_{i}}^{uparrow}-F_{IR,nu_{i}}^{downarrow}right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$\displaystyle -\frac{1}{\rho _{a}c_{p}}\DD{}{z}
\left[\sum _{\nu _{i} } \Delta ...
...}
\left(F_{IR,\nu _{i}}^{\uparrow}-F_{IR,\nu _{i}}^{\downarrow}\right)
\right].$">|; 

$key = q/F_{dir,nu_{i}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$F_{dir,\nu _{i}}^{\downarrow}$">|; 

$key = q/F_{NIR}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$F_{NIR}^{\downarrow}$">|; 

$key = q/displaystylefrac{overline{Q}_{e,nu}}{r_{eff}}frac{3rho_{a}q_{s}}{4pirho_{d}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle \frac{\overline{Q}_{e,\nu}}{r_{eff}}
\frac{3\rho _{a}q_{s}}{4\pi \rho _{d}},$">|; 

$key = q/times10{}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\times 10{}^{-3}$">|; 

$key = q/{displaymath}C_{D}=left{array{{lcl}C_{Dn}left(1-frac{displaystyleambox{Ri}_{B}}{{Ri}_{B})^{2}}&for&mbox{Ri}_{B}geq0,array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="93" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="\begin{displaymath}
C_{D} = \left\{
\begin{array}{lcl}
C_{Dn}\left( 1 -
\fra...
...Ri}_{B})^{2}}&amp; for &amp; \mbox{Ri}_{B} \geq 0,
\end{array}\right.
\end{displaymath}">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$\theta $">|; 

$key = q/displaystyleDD{}{t}=DP{}{t}+uDP{}{x}+wDP{}{z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle \DD{}{t} = \DP{}{t} + u\DP{}{x} + w\DP{}{z}.$">|; 

$key = q/r_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$r_{0}$">|; 

$key = q/beta_{nu,e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\beta _{\nu,e}$">|; 

$key = q/displaystyleoverline{Q}_{e,nu}int_{0}^{infty}pir^{2}DD{n(r)}{r}Ddr,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle \overline{Q}_{e,\nu}
\int _{0}^{\infty} \pi r^{2}\DD{n(r)}{r}\Dd r,$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\eta $">|; 

$key = q/H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="$H$">|; 

$key = q/times10{}^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\times 10{}^{2}$">|; 

$key = q/F_{IR,nu_{i}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$F_{IR,\nu_{i}}^{\downarrow}$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$K$">|; 

$key = q/displaystylecoszeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$\displaystyle \cos \zeta$">|; 

$key = q/F_{u},F_{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$F_{u}, F_{\theta }$">|; 

$key = q/{displaymath}Q_{e,nu}=frac{sigma_{e,nu}}{pir^{2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="\begin{displaymath}
Q_{e,\nu} = \frac{\sigma_{e,\nu}}{\pi r^{2}},
\end{displaymath}">|; 

$key = q/{}^{5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="${}^{5}$">|; 

$key = q/T_{sfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$T_{sfc}$">|; 

$key = q/s_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$s_{i}$">|; 

$key = q/{displaymath}rho_{g}c_{p,g}DP{T_{g}}{t}=k_{g}DP[2]{T_{g}}{z}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="\begin{displaymath}
\rho _{g}c_{p,g}\DP{T_{g}}{t} = k_{g}\DP[2]{T_{g}}{z}.
\end{displaymath}">|; 

$key = q/{displaymath}{calT}_{i}(z,z')=exp(-W_{i}slashDeltanu_{i}),quadW_{i}=frac{s_{i}u(z,z')}{sqrt{1+s_{i}u(z,z')slashalpha^{*}_{i}}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="61" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="\begin{displaymath}
{\cal T}_{i}(z,z') = \exp ( - W_{i}/\Delta \nu _{i}),
\qua...
...ac{s_{i} u(z,z')}
{\sqrt{ 1 + s_{i}u(z,z')/\alpha ^{*}_{i}}},
\end{displaymath}">|; 

$key = q/textstyleequiv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\textstyle \equiv$">|; 

$key = q/displaystyleB_{nu_{i},T_{sol}}left(frac{F_{s}}{sigmaT_{sol}^{4}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle B_{\nu _{i},T_{sol}}
\left(\frac{F_{s}}{\sigma T_{sol}^{4}}\right),$">|; 

$key = q/displaystylesinphisindelta+cosphicosdeltacosh,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$\displaystyle \sin \phi \sin \delta + \cos \phi \cos \delta \cos h,$">|; 

$key = q/piB_{nu,T_{sfc}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\pi B_{\nu,
T_{sfc}}$">|; 

$key = q/p_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$p_{r}$">|; 

$key = q/Q_{a,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$Q_{a,\nu}$">|; 

$key = q/tau_{m}geqtau_{mc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\tau_{m} \geq \tau _{mc}$">|; 

$key = q/tau_{mc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\tau _{mc}$">|; 

$key = q/times10{}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\times 10{}^{-2}$">|; 

$key = q/F_{SR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$F_{SR}$">|; 

$key = q/x,y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$x,y$">|; 

$key = q/r_{0}=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$r_{0}=a$">|; 

$key = q/k_{e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$k_{e}$">|; 

$key = q/Deltanu=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\Delta
\nu =$">|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\mu $">|; 

$key = q/{displaymath}F_{dir,nu_{i}}^{downarrow}=mu_{0}S_{nu_{i}}e^{-tau_{nu_{i}}slashmu_{0}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="\begin{displaymath}
F_{dir,\nu _{i}}^{\downarrow} = \mu _{0}S_{\nu _{i}}
e^{-\tau_{\nu _{i}}/\mu _{0}}
\end{displaymath}">|; 

$key = q/Q_{rad,IR},Q_{rad,NIR},Q_{rad,dust,SR},Q_{rad,dust,IR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$Q_{rad,IR}, Q_{rad,NIR}, Q_{rad,dust,SR}, Q_{rad,dust,IR}$">|; 

$key = q/displaystyle-frac{1}{rho_{0}c_{p}}DP{}{z}(F_{IR}^{uparrow}(z)-F_{IR}^{downarrow}(z)).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle -\frac{1}{\rho _{0}c_{p}}\DP{}{z}(F_{IR}^{\uparrow}(z) -
F_{IR}^{\downarrow}(z) ).$">|; 

$key = q/rho_{g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\rho _{g}$">|; 

$key = q/sigma_{e,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\sigma_{e,\nu}$">|; 

$key = q/displaystyleDD{F_{IR,nu_{i}}^{uparrow}}{tau_{nu_{i}}^{*}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle \DD{F_{IR,\nu _{i}}^{\uparrow}}{\tau _{\nu _{i}}^{*}}$">|; 

$key = q/{displaymath}C_{Dn}=left(frac{k}{ln(z_{1}slashz_{0})}right)^{2},quada=2b=9.4,quadotableft(frac{z_{1}}{z_{0}}right)^{frac{1}{2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="487" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="\begin{displaymath}
C_{Dn} = \left(\frac{k}{\ln (z_{1}/z_{0})}\right)^{2},
\qu...
... = 0.74\cdot ab\left(\frac{z_{1}}{z_{0}}\right)^{\frac{1}{2}},
\end{displaymath}">|; 

$key = q/F_{dif,nu_{i}}^{uparrow}=F_{dif,nu}^{downarrow}timesA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$F_{dif,\nu_{i}}^{\uparrow}=
F_{dif,\nu}^{\downarrow}\times A$">|; 

$key = q/{displaymath}Q_{dis}=frac{C_{epsilon}}{lc_{p}}varepsilon^{3slash2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="\begin{displaymath}
Q_{dis} = \frac{C_{\epsilon }}{lc_{p}}\varepsilon ^{3/2}.
\end{displaymath}">|; 

$key = q/displaystyleQ_{a,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle Q_{a,\nu}$">|; 

$key = q/Deltanu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\Delta \nu$">|; 

$key = q/{displaymath}beta_{e,nu}=int_{0}^{infty}sigma_{e,nu}(r)DD{n(r)}{r}Ddr{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="\begin{displaymath}
\beta _{e,\nu} = \int _{0}^{\infty} \sigma_{e,\nu}(r)\DD{n(r)}{r}\Dd r
\end{displaymath}">|; 

$key = q/Q_{e,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$Q_{e,\nu}$">|; 

$key = q/{displaymath}F_{s}=I_{0}left(frac{1+ecos(L_{s}+omega_{0})}{1+e^{2}}right)^{2}lefcoshcosphisqrt{1-sin^{2}alphasin^{2}L_{s}}right]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="643" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="\begin{displaymath}
F_{s} = I_{0}\left(\frac{1+e\cos (L_{s}+\omega_{0})}{1+e^{2...
...s h \cos \phi \sqrt{1-\sin ^{2}\alpha \sin ^{2}L_{s}}
\right]
\end{displaymath}">|; 

$key = q/{displaymath}DD{n(r)}{r}=n_{0}r^{alpha}expleft[-left(frac{alpha}{gamma}right)left(frac{r}{r_{m}}right)^{gamma}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="\begin{displaymath}
\DD{n(r)}{r} = n_{0}r ^{\alpha} \exp
\left[ - \left(\frac{...
...gamma }\right)
\left(\frac{r}{r_{m}}\right)^{\gamma }\right].
\end{displaymath}">|; 

$key = q/times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$\times 10^{-2}$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$\phi $">|; 

$key = q/Q_{rad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$Q_{rad}$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$r$">|; 

$key = q/z,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$z,t$">|; 

$key = q/tau_{0.67mum}slashtau_{9mum};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$\tau
_{0.67 \mu m}/\tau _{9 \mu m}$">|; 

$key = q/2pitslashT-pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$2\pi t/T -\pi$">|; 

$key = q/displaystyleDD{F_{dif,nu_{i}}^{downarrow}}{tau_{nu_{i}}^{*}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle \DD{F_{dif,\nu _{i}}^{\downarrow}}{\tau _{\nu _{i}}^{*}}$">|; 

$key = q/zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\zeta $">|; 

$key = q/SP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$SP$">|; 

$key = q/I_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$I_{0}$">|; 

$key = q/{}^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="${}^{1/2}$">|; 

$key = q/{}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="${}^{-1}$">|; 

$key = q/{displaymath}rho_{a}q_{s}k_{e,nu}=int_{0}^{infty}sigma_{e,nu}(r)DD{n(r)}{r}Ddr{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="\begin{displaymath}
\rho _{a}q_{s}k_{e,\nu} =
\int _{0}^{\infty} \sigma_{e,\nu}(r)\DD{n(r)}{r}\Dd r
\end{displaymath}">|; 

$key = q/displaystyleS_{nu_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle S_{\nu _{i}}$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$a$">|; 

$key = q/x,y,z,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$x,y, z,t$">|; 

$key = q/q_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$q_{s}$">|; 

$key = q/tau_{nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$\tau _{\nu}$">|; 

$key = q/L_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$L_{s}$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$R$">|; 

$key = q/times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\times 10^{-6}$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\alpha $">|; 

$key = q/Iequivsqrt{rho_{g}c_{p,g}k_{g}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$I\equiv \sqrt{\rho
_{g}c_{p,g}k_{g}}$">|; 

$key = q/T=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$T=$">|; 

$key = q/{displaymath}Q_{rad}=Q_{rad,IR}+Q_{rad,NIR}+Q_{rad,dust,SR}+Q_{rad,dust,IR}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="435" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="\begin{displaymath}
Q_{rad}= Q_{rad,IR} + Q_{rad,NIR} + Q_{rad,dust,SR} + Q_{rad,dust,IR}.
\end{displaymath}">|; 

$key = q/overline{Q}_{e,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\overline{Q}_{e,\nu}$">|; 

$key = q/T_{sfc}=T_{g}|_{z=0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$T_{sfc} = T_{g}\vert _{z=0}$">|; 

$key = q/{displaymath}mbox{Ri}_{B}equivfrac{gz_{1}(Theta_{sfc}-Theta_{z=z1})}{overline{Theta}_{z=z1}u_{z=z1}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\begin{displaymath}
\mbox{Ri}_{B} \equiv \frac{gz_{1}(\Theta _{sfc}-\Theta _
{z=z1})}{\overline{\Theta }_{z=z1}u_{z=z1}},
\end{displaymath}">|; 

$key = q/W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$W$">|; 

$key = q/displaystyleQ_{s,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle Q_{s,\nu}$">|; 

$key = q/p_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$p_{0}$">|; 

$key = q/F_{dif,nu_{i}}^{downarrow}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$F_{dif,\nu_{i}}^{\downarrow}=0$">|; 

$key = q/{eqnarraystar}r&=&frac{a(1-e^{2})}{1+ecosomega},sindelta&=&sinalphasin(omega-omega_{0}){eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="75" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="\begin{eqnarray*}
r &amp;=&amp; \frac{a(1-e^{2})}{1+e\cos \omega}, \\\\
\sin \delta &amp;=&amp; \sin \alpha \sin (\omega - \omega _{0})
\end{eqnarray*}">|; 

$key = q/displaystyleDD{u}{t}-fv=-c_{p}Theta_{0}DP{pi}{x}+D(u),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\displaystyle \DD{u}{t} -fv = -c_{p}\Theta _{0}\DP{\pi }{x} + D(u),$">|; 

$key = q/{displaymath}B_{nu_{i},T}=frac{2hc^{2}nu_{i}^{3}}{e^{hcnu_{i}slashkT}-1}=frac{1.mes10^{-8}nu_{i}^{3}}{e^{1.4387nu_{i}slashT}-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="\begin{displaymath}
B_{\nu _{i},T} = \frac{2hc^{2}\nu _{i}^{3}}{e^{hc\nu_{i}/kT...
... \frac{1.19\times 10^{-8}\nu _{i}^{3}}{e^{1.4387\nu_{i}/T}-1},
\end{displaymath}">|; 

$key = q/k_{g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$k_{g}$">|; 

$key = q/BP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$BP$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$A$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$i$">|; 

$key = q/displaystyleDD{v}{t}+fu=D(v),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle \DD{v}{t} + fu = D(v),$">|; 

$key = q/displaystyle2Kleft[left(DP{u}{x}right)^{2}+left(DP{w}{z}right)^{2}right]+frac{2}ft(DP{u}{z}+DP{w}{x}right)+Kleft(DP{u}{z}+DP{w}{x}right)^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="515" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle 2K\left[ \left(\DP{u}{x}\right)^{2} +
\left(\DP{w}{z}\right)^{2} ...
...eft( \DP{u}{z} + \DP{w}{x} \right)
+ K\left( \DP{u}{z} + \DP{w}{x} \right)^{2},$">|; 

$key = q/displaystylebeta_{e,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle \beta _{e,\nu}$">|; 

$key = q/F_{dif,nu_{i}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$F_{dif,\nu _{i}}^{\downarrow}$">|; 

$key = q/BP,SP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$BP, SP$">|; 

$key = q/displaystyleF_{IR}^{uparrow}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\displaystyle F_{IR}^{\uparrow}(z)$">|; 

$key = q/Pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\Pi$">|; 

$key = q/delta_{d}equivsqrt{k_{g}t_{d}slash(rho_{g}c_{p,g})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$\delta
_{d}\equiv\sqrt{k_{g}t_{d}/(\rho_{g}c_{p,g})}$">|; 

$key = q/g_{nu_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$g_{\nu_{i}}$">|; 

$key = q/z_{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$z_{t}$">|; 

$key = q/lambda_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\lambda _{r}$">|; 

$key = q/P_{00};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$P_{00}$">|; 

$key = q/Theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\Theta$">|; 

$key = q/{}^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="${}^{-4}$">|; 

$key = q/displaystyleSP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle SP$">|; 

$key = q/u_{z=z1},T_{z=z1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$u_{z=z1}, T_{z=z1}$">|; 

$key = q/sim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\sim $">|; 

$key = q/times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\times10^{-5}$">|; 

$key = q/z_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$z_{0}$">|; 

$key = q/Q_{rad,IR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$Q_{rad,IR}$">|; 

$key = q/times10{}^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\times 10{}^{-8}$">|; 

$key = q/Q_{rad,dust,SR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$Q_{rad,dust,SR}$">|; 

$key = q/Q_{rad,dust,IR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$Q_{rad,dust,IR}$">|; 

$key = q/mbox{Ri}_{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\mbox{Ri}_{B}$">|; 

$key = q/displaystylefrac{g}{Theta_{0}}DP{(rho_{0}theta)}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \frac{g}{\Theta_{0} }\DP{(\rho _{0}\theta )}{z}$">|; 

$key = q/displaystyleDP{(rho_{0}u)}{x}+DP{(rho_{0}w)}{z}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\displaystyle \DP{(\rho _{0}u)}{x} + \DP{(\rho _{0}w)}{z} = 0,$">|; 

$key = q/displaystyleBP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle BP$">|; 

$key = q/times10{}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\times 10{}^{-1}$">|; 

$key = q/displaystyler_{eff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle r_{eff}$">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$u$">|; 

$key = q/times10{}^{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\times 10{}^{3}$">|; 

$key = q/F_{dif,nu_{i}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$F_{dif,\nu_{i}}^{\uparrow}$">|; 

$key = q/T_{g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$T_{g}$">|; 

$key = q/displaystylegamma_{1,nu_{i}}F_{dif,nu_{i}}^{uparrow}-gamma_{2,nu_{i}}F_{dif,nu_{mega}_{nu_{i}}^{*}S_{nu_{i}}e^{-tau_{nu_{i}}^{*}slashmu_{0}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle \gamma _{1,\nu _{i}}F_{dif,\nu _{i}}^{\uparrow} -
\gamma _{2,\nu ...
...i}}
\tilde{\omega}_{\nu _{i}}^{*}S_{\nu _{i}}e^{-\tau _{\nu _{i}}^{*}/\mu_{0}},$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$k$">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\pi$">|; 

$key = q/tau_{5-11.6mum};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$\tau _{5-11.6 \mu m}$">|; 

$key = q/displaystyleI_{0}left(frac{r_{0}}{r}right)^{2}coszeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$\displaystyle I_{0}\left(\frac{r_{0}}{r}\right)^{2}\cos \zeta,$">|; 

$key = q/tau_{m}equiv|F_{u}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\tau _{m}\equiv\vert F_{u}\vert$">|; 

$key = q/c_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$c_{p}$">|; 

$key = q/varepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\varepsilon $">|; 

$key = q/omega_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\omega _{0}$">|; 

$key = q/{}^{circ};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="${}^{\circ}$">|; 

$key = q/t_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$t_{d}$">|; 

$key = q/F_{q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$F_{q}$">|; 

$key = q/F_{dif,nu}^{downarrow}timesA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$F_{dif,\nu}^{\downarrow}\times A$">|; 

$key = q/displaystyle-frac{g}{Theta_{0}}KDP{(theta+Theta_{0})}{z},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle -\frac{g}{\Theta _{0}}K\DP{(\theta +\Theta _{0})}{z},$">|; 

$key = q/{displaymath}tau_{nu_{i}}^{*}=(1-tilde{omega}_{nu_{i}}g_{nu_{i}}^{2})tau_{nu_{i}adg_{nu_{i}}^{*}=frac{g_{nu_{i}}}{1+g_{nu_{i}}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="\begin{displaymath}
\tau _{\nu _{i}}^{*}=(1-\tilde{\omega}_{\nu _{i}}g_{\nu _{i...
...quad
g_{\nu _{i}}^{*} = \frac{g_{\nu _{i}}}{1+g_{\nu _{i}}},
\end{displaymath}">|; 

$key = q/times10{}^{4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\times 10{}^{4}$">|; 

$key = q/displaystyleint_{0}^{infty}sigma_{s,nu}(r)DD{n(r)}{r}Ddr,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle \int _{0}^{\infty} \sigma_{s,\nu}(r)\DD{n(r)}{r}\Dd r,$">|; 

$key = q/F_{IR,net};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$F_{IR,net}$">|; 

$key = q/displaystyleF_{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle F_{u}$">|; 

$key = q/rho_{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\rho _{a}$">|; 

$key = q/displaystyleDD{varepsilon}{t}=BP+SP+D(varepsilon)-frac{C_{epsilon}}{l}varepsilon^{3slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \DD{\varepsilon }{t} = BP + SP + D(\varepsilon )
- \frac{C_{\epsilon }}{l}\varepsilon ^{3/2},$">|; 

$key = q/displaystyleoverline{Q}_{e,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\displaystyle \overline{Q}_{e,\nu}$">|; 

$key = q/Deltanu_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\Delta \nu _{i}$">|; 

$key = q/F_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$F_{s}$">|; 

$key = q/displaystyleQ_{rad,dust,SR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle Q_{rad,dust,SR}$">|; 

$key = q/displaystylerho_{0}RT_{0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle \rho _{0}RT_{0}.$">|; 

$key = q/r_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$r_{m}$">|; 

$key = q/sigma_{a,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\sigma_{a,\nu}$">|; 

$key = q/gamma_{1,nu_{i}},gamma_{2,nu_{i}},gamma_{3,nu_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\gamma _{1,\nu _{i}},\gamma _{2,\nu _{i}},\gamma _{3,\nu _{i}}$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$p$">|; 

$key = q/{displaymath}tau_{nu}=-int_{z_{t}}^{z}frac{overline{Q}_{e,nu}}{r_{eff}}frac{3rho_{a}q_{s}}{4pirho_{s}}Ddz,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="\begin{displaymath}
\tau _{\nu} = -\int _{z_{t}}^{z} \frac{\overline{Q}_{e,\nu}}{r_{eff}}
\frac{3\rho _{a}q_{s}}{4\pi \rho _{s}} \Dd z,
\end{displaymath}">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$y$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$f$">|; 

$key = q/tilde{omega}_{nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\tilde{\omega}_{\nu}$">|; 

$key = q/displaystylefrac{1}{rho_{0}}DP{F_{IR}^{downarrow}(z)}{z},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle \frac{1}{\rho _{0}}\DP{F_{IR}^{\downarrow}(z)}{z},$">|; 

$key = q/coszeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$\cos \zeta $">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$c$">|; 

$key = q/displaystylerho_{0}C_{D}|u_{z=z1}|(T_{sfc}-T_{z=z1}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \rho _{0}C_{D}\vert u_{z=z1}\vert(T_{sfc}-T_{z=z1}).$">|; 

$key = q/displaystylefrac{int_{0}^{infty}r^{3}DD{n(r)}{r}Ddr}{int_{0}^{infty}r^{2}DD{n(r)}{r}Ddr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle \frac{\int _{0}^{\infty}r ^{3}\DD{n(r)}{r}\Dd r}
{\int _{0}^{\infty}r ^{2}\DD{n(r)}{r} \Dd r},$">|; 

$key = q/nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$\nu$">|; 

$key = q/nu_{1},nu_{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\nu_{1},\nu_{2}$">|; 

$key = q/w=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$w=0$">|; 

$key = q/displaystyleint_{0}^{infty}sigma_{a,nu}(r)DD{n(r)}{r}Ddr,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\displaystyle \int _{0}^{\infty} \sigma_{a,\nu}(r)\DD{n(r)}{r}\Dd r,$">|; 

$key = q/{displaymath}u(z,z')=int_{z}^{z'}1.67rho_{0}Ddz,quadalpha^{*}_{i}=alpha_{i}overl_{0},quadoverline{p}=int_{z}^{z'}P_{0}Dduslashu.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="471" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="\begin{displaymath}
u(z,z') = \int _{z}^{z'}1.67\rho _{0}\Dd z,
\quad
\alpha ...
.../p_{0},
\quad
\overline{p} = \int _{z}^{z'}P_{0} \Dd u / u.
\end{displaymath}">|; 

$key = q/P_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$P_{0}$">|; 

$key = q/beta_{e,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$\beta _{e,\nu}$">|; 

$key = q/{displaymath}DD{q}{t}+frac{1}{rho_{0}}DP{}{z}(rho_{0}Wq)=D(q).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="\begin{displaymath}
\DD{q}{t} + \frac{1}{\rho _{0}}\DP{}{z}(\rho _{0}Wq) = D(q).
\end{displaymath}">|; 

$key = q/displaystyle-rho_{0}C_{D}|u_{z=z1}|u_{z=z_{1}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle - \rho _{0}C_{D}\vert u_{z=z1}\vert u_{z=z_{1}},$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$x$">|; 

$key = q/alpha^{*}_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\alpha ^{*}_{i}$">|; 

$key = q/displaystylefrac{overline{Q}_{e,nu}}{r_{eff}}int_{0}^{infty}pir^{3}DD{n(r)}{r}Ddr,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle \frac{\overline{Q}_{e,\nu}}{r_{eff}}
\int _{0}^{\infty} \pi r^{3}\DD{n(r)}{r}\Dd r,$">|; 

$key = q/tau_{nu_{i}},tilde{omega}_{nu_{i}},g_{nu_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\tau _{\nu _{i}}, \tilde{\omega}_{\nu _{i}}, g_{\nu _{i}}$">|; 

$key = q/z_{1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$z_{1}$">|; 

$key = q/rho_{0},Theta_{0},T_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\rho
_{0}, \Theta _{0}, T_{0}$">|; 

$key = q/displaystylebeta_{a,nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle \beta _{a,\nu}$">|; 

$key = q/c_{p,g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$c_{p,g}$">|; 

$key = q/displaystyleQ_{rad,NIR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle Q_{rad,NIR}$">|; 

$key = q/displaystyleF_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle F_{s}$">|; 

$key = q/tau_{nu_{i}}^{*},tilde{omega}_{nu_{i}}^{*},g_{nu_{i}}^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\tau _{\nu _{i}}^{*}, \tilde{\omega}_{\nu _{i}}^{*},
g_{\nu _{i}}^{*}$">|; 

$key = q/displaystylesum_{i}Deltanu_{i}left{piB_{nu_{i},T}(z=0){calT}_{i}(0,z)+int_{0}^{z}piB_{nu_{i},T}(z')DD{{calT}_{i}(z,z')}{z'}Ddz'right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="499" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$\displaystyle \sum _{i}\Delta \nu _{i}\left\{
\pi B_{\nu _{i},T}(z=0){\cal T}_{...
...\int _{0}^{z}\pi B_{\nu _{i},T}(z')\DD{{\cal T }_{i}(z,z')}{z'}\Dd z'
\right\},$">|; 

$key = q/displaystyle-DP{}{z}left[rho_{0}left(uDP{w}{x}+wDP{w}{z}-D(w)right)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle - \DP{}{z}\left[ \rho _{0}\left
( u\DP{w}{x} + w\DP{w}{z} - D(w) \right) \right].$">|; 

$key = q/L_{s}equivomega-omega_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$L_{s}\equiv \omega - \omega _{0}$">|; 

$key = q/tau_{5-1.6mum};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$\tau _{5-1.6 \mu m}$">|; 

$key = q/kappa=Rslashc_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\kappa = R/c_{p}$">|; 

$key = q/displaystylesum_{i}Deltanu_{i}left{S_{nu_{i}}{calT}_{i}(infty,z)mu_{0}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \sum _{i}\Delta \nu _{i}\left\{
S_{\nu _{i}}{\cal T}_{i}(\infty,z)\mu_{0}
\right\},$">|; 

$key = q/{}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="${}^{-2}$">|; 

$key = q/{displaymath}ThetaequivTPi^{-1}=Theta_{0}+theta,quadTheta_{0}=T_{0}Pi_{0}^{-1}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="\begin{displaymath}
\Theta \equiv T\Pi^{-1} = \Theta _{0} + \theta, \quad
\Theta _{0} = T_{0}\Pi_{0}^{-1}
\end{displaymath}">|; 

$key = q/times10{}^{5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\times 10{}^{5}$">|; 

1;