# LaTeX2HTML 2023 (Released January 1, 2023)
# Associate images original text with physical files.


$key = q//;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 22.64ex; " SRC="|."$dir".q|img25.svg"
 ALT="\begin{eqnarray*}
\tau(v_i+p_2) &amp;=&amp; p_4 \cdot r_i\qquad (\rm assumption  A4)\\\\...
...p_4 r_i}\right)\\\\
T_{\rm ant}(v_i+p_2) &amp;\approx&amp; p_1 \cdot r_i
\end{eqnarray*}">|; 

$key = q/0.1-30;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.30ex; " SRC="|."$dir".q|img33.svg"
 ALT="$0.1-30$">|; 

$key = q/10^6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img36.svg"
 ALT="$10^6$">|; 

$key = q/4'';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.99ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img37.svg"
 ALT="$4''$">|; 

$key = q/<30;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img38.svg"
 ALT="$&lt; 30$">|; 

$key = q/<40;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img39.svg"
 ALT="$&lt; 40$">|; 

$key = q/=3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.70ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img59.svg"
 ALT="$= 3$">|; 

$key = q/=5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.70ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img58.svg"
 ALT="$= 5$">|; 

$key = q/H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img44.svg"
 ALT="$H$">|; 

$key = q/H=-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.99ex; vertical-align: -0.30ex; " SRC="|."$dir".q|img54.svg"
 ALT="$H=-1$">|; 

$key = q/H=5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img53.svg"
 ALT="$H=5$">|; 

$key = q/HPBW;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img7.svg"
 ALT="$HPBW$">|; 

$key = q/N;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img12.svg"
 ALT="$N$">|; 

$key = q/N=7;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img14.svg"
 ALT="$N=7$">|; 

$key = q/S;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img27.svg"
 ALT="$S$">|; 

$key = q/S=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img28.svg"
 ALT="$S=1$">|; 

$key = q/S=27;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img15.svg"
 ALT="$S=27$">|; 

$key = q/S=sum{ensuremath{r_i}{;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.33ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img13.svg"
 ALT="$S=\sum\ensuremath{r_i}$">|; 

$key = q/^+;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.07ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img9.svg"
 ALT="$^+$">|; 

$key = q/^{-1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img60.svg"
 ALT="$^{-1}$">|; 

$key = q/^{1,2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2.svg"
 ALT="$^{1,2}$">|; 

$key = q/^{1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1.svg"
 ALT="$^{1}$">|; 

$key = q/^{3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3.svg"
 ALT="$^{3}$">|; 

$key = q/^{4};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4.svg"
 ALT="$^{4}$">|; 

$key = q/_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.30ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img8.svg"
 ALT="$_2$">|; 

$key = q/backslash;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.53ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img56.svg"
 ALT="$\backslash$">|; 

$key = q/displaystyleT_{{rm{ant}(v)=T_A^*(v)=frac{B_{{rm{eff}}{F_{{rm{eff}}[T_{{rm{ex}-T_{{rm{bg}](1-e^{-tau(v)});MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.32ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img31.svg"
 ALT="$\displaystyle T_{\rm ant}(v) = T_A^*(v) = \frac{B_{\rm eff}}{F_{\rm eff}}
[T_{\rm ex} - T_{\rm bg}] (1-e^{-\tau(v)})
$">|; 

$key = q/displaystyleT_{{rm{ant}(v)=frac{p_1}{p_4}left(1-e^{-tau(v)}right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.81ex; vertical-align: -2.15ex; " SRC="|."$dir".q|img24.svg"
 ALT="$\displaystyle T_{\rm ant}(v) = \frac{p_1}{p_4}
\left(
1 - e^{-\tau(v)}
\right)
$">|; 

$key = q/displaystyleT_{{rm{ex}=T_{{rm{bg}+frac{F_{{rm{eff}}{B_{{rm{eff}}frac{p_1}{p_4};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.40ex; vertical-align: -2.15ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\displaystyle T_{\rm ex} = T_{\rm bg} + \frac{F_{\rm eff}}{B_{\rm eff}} \frac{p_1}{p_4}
$">|; 

$key = q/displaystylef(nu)=frac{{ensuremath{{calA}}{}{{ensuremath{Deltanu}{},frac{1+4H,[(nu-nu_0)slash{ensuremath{Deltanu}{]^2}{1+Hslash3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.87ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img40.svg"
 ALT="$\displaystyle f(\nu) = \frac{\ensuremath{{\cal A}}}{\ensuremath{\Delta \nu}} 
\frac{1+4H [(\nu-\nu_0)/\ensuremath{\Delta \nu}]^2}{1+H/3}
$">|; 

$key = q/displaystylefrac{f({ensuremath{Deltanu}{slash2)}{f(0)}=1+H;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.68ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img47.svg"
 ALT="$\displaystyle \frac{f(\ensuremath{\Delta \nu}/2)}{f(0)} = 1 + H$">|; 

$key = q/displaystyletau(v)=p_4displaystylesum_{i=1}^{N}r_icdotexpleft[-4ln{2}left(frac{v-v_i-p_2}{p_3}right)^2right];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.06ex; vertical-align: -2.91ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle \tau(v) = p_4 \displaystyle\sum_{i=1}^{N}
r_i\cdot\exp\left[
-4\ln{2}\left(
\frac{v-v_i-p_2}{p_3}
\right)^2
\right]
$">|; 

$key = q/displaystyletau_i(v)=tau_icdotexpleft[-4ln{2}left(frac{v-v_{0,i}}{p_3}right)^2right];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.55ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle \tau_i(v) = \tau_i\cdot\exp\left[
-4\ln{2}\left(
\frac{v-v_{0,i}}{p_3}
\right)^2
\right]
$">|; 

$key = q/displaystylev_{{rm{exp}=c,frac{{ensuremath{Deltanu}{slash2}{nu_0};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.45ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img48.svg"
 ALT="$\displaystyle v_{\rm exp} = c \frac{\ensuremath{\Delta \nu}/2}{\nu_0}
$">|; 

$key = q/ensuremath{Deltanu};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img43.svg"
 ALT="\ensuremath{\Delta \nu}">|; 

$key = q/ensuremath{^{-1}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.14ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img52.svg"
 ALT="\ensuremath{^{-1}}">|; 

$key = q/ensuremath{r_i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img11.svg"
 ALT="\ensuremath{r_i}">|; 

$key = q/ensuremath{v_i};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img10.svg"
 ALT="\ensuremath{v_i}">|; 

$key = q/ensuremath{{calA}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img41.svg"
 ALT="\ensuremath{{\cal A}}">|; 

$key = q/exp(-tau)ll1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.53ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img34.svg"
 ALT="$\exp(-\tau)\ll 1$">|; 

$key = q/f(nu_0)=frac{{ensuremath{{calA}}{}{{ensuremath{Deltanu}{}frac{1}{1+Hslash3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.52ex; vertical-align: -1.35ex; " SRC="|."$dir".q|img45.svg"
 ALT="$f(\nu_0) = \frac{\ensuremath{{\cal A}}}{\ensuremath{\Delta \nu}}\frac{1}{1+H/3}$">|; 

$key = q/f(nu_0+{ensuremath{Deltanu}{slash2)=frac{{ensuremath{{calA}}{}{{ensuremath{Deltanu}{}frac{1+H}{1+Hslash3};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.52ex; vertical-align: -1.35ex; " SRC="|."$dir".q|img46.svg"
 ALT="$f(\nu_0+\ensuremath{\Delta \nu}/2) =
\frac{\ensuremath{{\cal A}}}{\ensuremath{\Delta \nu}}\frac{1+H}{1+H/3}$">|; 

$key = q/ge;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.00ex; vertical-align: -0.42ex; " SRC="|."$dir".q|img57.svg"
 ALT="$\ge$">|; 

$key = q/i;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.74ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img16.svg"
 ALT="$i$">|; 

$key = q/includegraphics[width=0.6textwidth,angle=-90]{class-hfs};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 58.54ex; vertical-align: -58.65ex; " SRC="|."$dir".q|img35.svg"
 ALT="\includegraphics[width=0.6\textwidth,angle=-90]{class-hfs}">|; 

$key = q/lambda<3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.91ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img30.svg"
 ALT="$\lambda&lt;3$">|; 

$key = q/nu_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img42.svg"
 ALT="$\nu_0$">|; 

$key = q/p_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.66ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img29.svg"
 ALT="$p_1$">|; 

$key = q/p_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.66ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img20.svg"
 ALT="$p_2$">|; 

$key = q/p_3;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.66ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img18.svg"
 ALT="$p_3$">|; 

$key = q/p_4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.66ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img26.svg"
 ALT="$p_4$">|; 

$key = q/tau(v);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.53ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\tau(v)$">|; 

$key = q/v_i=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.05ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img21.svg"
 ALT="$v_i=0$">|; 

$key = q/v_{0,i}=v_i+p_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.24ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img19.svg"
 ALT="$v_{0,i}=v_i+p_2$">|; 

$key = q/v_{rmexp}=2.49;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.38ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img55.svg"
 ALT="$v_{\rm exp}=2.49$">|; 

$key = q/v_{{rm{exp}=2.49;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.38ex; vertical-align: -0.78ex; " SRC="|."$dir".q|img51.svg"
 ALT="$v_{\rm exp}=2.49$">|; 

$key = q/w_i=DeltatDeltanuslashT_{{rm{sys}^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.04ex; vertical-align: -1.01ex; " SRC="|."$dir".q|img5.svg"
 ALT="$w_i=\Delta t\Delta
\nu/T_{\rm sys}^2$">|; 

$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.21ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img6.svg"
 ALT="$x$">|; 

$key = q/{ensuremath{Deltanu}{=3.83;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img50.svg"
 ALT="$\ensuremath{\Delta \nu}=3.83$">|; 

$key = q/{ensuremath{{calA}}{=5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.79ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img49.svg"
 ALT="$\ensuremath{{\cal A}}=5$">|; 

1;

