# LaTeX2HTML 2008 (1.71)
# Associate images original text with physical files.


$key = q/t({svectorx});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$t({\svector x})$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$s$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\epsilon$">|; 

$key = q/xapprox1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$x \approx 1$">|; 

$key = q/{svectorx}_{i,j}(s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="${\svector x}_{i,j} (s)$">|; 

$key = q/a'_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$a'_{i,j}$">|; 

$key = q/r_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$r_i$">|; 

$key = q/a_{i,j}slashr_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$a_{i,j}/r_i$">|; 

$key = q/log(x)approxx-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\log(x) \approx x -1$">|; 

$key = q/{displaymath}min_{mbox{t({{svectorx}{)}}sum_{i,j}left[r_ilog(a_{i,j}slashr_i)-r_i)right]^2+epsilonintt({svectorx})^2d{svectorx}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="\begin{displaymath}
\min_{\mbox{t(${\svector x}$)}}
\sum_{i,j} \left [ r_i \log ...
... \right ] ^2
+ \epsilon \int t( {\svector x})^2 d{\svector x}.
\end{displaymath}">|; 

$key = q/a_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$a_{i,j}$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$i$">|; 

$key = q/{displaymath}hata_{i,j}=r_iexpleft{intt[{svectorx}_{i,j}(s)]dsright}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="\begin{displaymath}
\hat a_{i,j} = r_i \exp \left \{ \int t[{\svector x}_{i,j}(s)] ds \right \} .
\end{displaymath}">|; 

$key = q/{hata}_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="${\hat a}_{i,j}$">|; 

$key = q/{displaymath}a'_{i,j}=a_{i,j}expleft{-intt[{svectorx}_{i,j}(s)]dsright}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="\begin{displaymath}
a'_{i,j} = a_{i,j} \exp \left \{ - \int t[{\svector x}_{i,j}(s)] ds \right \}.
\end{displaymath}">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$j$">|; 

$key = q/hata_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\hat a_{i,j}$">|; 

1;