# LaTeX2HTML 2019.2 (Released June 5, 2019)
# Associate images original text with physical files.


$key = q/a'_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.76ex; vertical-align: -0.97ex; " SRC="|."$dir".q|img16.svg"
 ALT="$a'_{i,j}$">|; 

$key = q/a_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.84ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img2.svg"
 ALT="$a_{i,j}$">|; 

$key = q/a_{i,j}slashr_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img7.svg"
 ALT="$a_{i,j}/r_i$">|; 

$key = q/displaystylea'_{i,j}=a_{i,j}expleft{-intt[{svectorx}_{i,j}(s)]dsright}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.82ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle a'_{i,j} = a_{i,j} \exp \left \{ - \int t[{\svector x}_{i,j}(s)] ds \right \}.
$">|; 

$key = q/displaystylehata_{i,j}=r_iexpleft{intt[{svectorx}_{i,j}(s)]dsright}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.82ex; vertical-align: -1.84ex; " SRC="|."$dir".q|img10.svg"
 ALT="$\displaystyle \hat a_{i,j} = r_i \exp \left \{ \int t[{\svector x}_{i,j}(s)] ds \right \} .
$">|; 

$key = q/displaystylemin_{mbox{t({{svectorx}{)}}sum_{i,j}left[r_ilog(a_{i,j}slashr_i)-r_i_{i,j}slashr_i)right]^2+epsilonintt({svectorx})^2d{svectorx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.74ex; vertical-align: -2.94ex; " SRC="|."$dir".q|img11.svg"
 ALT="$\displaystyle \min_{\mbox{t(${\svector x}$)}}
\sum_{i,j} \left [ r_i \log (a_{i...
...at a}_{i,j}/r_i) \right ] ^2
+ \epsilon \int t( {\svector x})^2 d{\svector x}.
$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img12.svg"
 ALT="$\epsilon$">|; 

$key = q/hata_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img9.svg"
 ALT="$\hat a_{i,j}$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.71ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1.svg"
 ALT="$i$">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.16ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3.svg"
 ALT="$j$">|; 

$key = q/log(x)approxx-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img14.svg"
 ALT="$\log(x) \approx x -1$">|; 

$key = q/r_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.54ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img6.svg"
 ALT="$r_i$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img5.svg"
 ALT="$s$">|; 

$key = q/t({svectorx});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img8.svg"
 ALT="$t({\svector x})$">|; 

$key = q/xapprox1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.68ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img15.svg"
 ALT="$x \approx 1$">|; 

$key = q/{hata}_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img13.svg"
 ALT="${\hat a}_{i,j}$">|; 

$key = q/{svectorx}_{i,j}(s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img4.svg"
 ALT="${\svector x}_{i,j} (s)$">|; 

1;

