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


$key = q/df(x)slashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$d f(x) / d x$">|; 

$key = q/displaystyledeltax_k^{m,N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \delta x_k^{m,N}$">|; 

$key = q/stensor{W}^n+alphaDeltastensor{W}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\stensor{W}^n + \alpha \Delta \stensor{W}^n$">|; 

$key = q/displaystylesum_mdeltax_i^{m,n}f_j^n(svector{x}^{m,n-1}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle \sum_m \delta x_i^{m,n} f_j^n ( \svector{x}^{m,n-1} ),$">|; 

$key = q/displaystylesvector{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle \svector{0}$">|; 

$key = q/displaystylex_i^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle x_i^{m,n}$">|; 

$key = q/Deltastensor{W}^n=(stensor{G}^{m,n})^{*}cdot(svector{p}^m-svector{x}^{m,N});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\Delta \stensor{W}^n = ( \stensor{G}^{m,n} )^{*} \cdot ( \svector{p}^m - \svector{x}^{m,N} )$">|; 

$key = q/displaystylesvector{x}^{m,0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \svector{x}^{m,0} .$">|; 

$key = q/displaystylesvector{x}^{m,N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle \svector{x}^{m,N}$">|; 

$key = q/stensor{w}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\stensor{w}^n$">|; 

$key = q/displaystyledeltaF(stensor{W}^1,ldots,stensor{W}^N);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle \delta F(\stensor{W}^1,\ldots,\stensor{W}^N)$">|; 

$key = q/stensor{W}^n+stensor{w}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\stensor{W}^n + \stensor{w}^n$">|; 

$key = q/sum_{m,k},[p_k^m-x_k^{m,N}(svector{d}^m,stensor{W}^1,ldots,stensor{W}^N)-sum_{n,i,j}G_{kij}^{m,n}w_{ij}^n]^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\sum_{m,k}   [ p_k^m - x_k^{m,N} ( \svector{d}^m , \stensor{W}^1,\ldots,\stensor{W}^N)
- \sum_{n,i,j} G_{kij}^{m,n} w_{ij}^n ]^2$">|; 

$key = q/displaystylesum_{j},deltaW_{ij}^ncdotf_j^n(svector{x}^{m,n-1})+sum_jW_{ij}^nsum_artial}{partialx_k}f_j^n(svector{x}^{m,n-1})deltax_k^{m,n-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle \sum_{j}   \delta W_{ij}^n \cdot f_j^n (\svector{x}^{m,n-1}) +
...
... \frac{\partial}{\partial x_k} f_j^n (\svector{x}^{m,n-1}) \delta x_k^{m,n-1} ,$">|; 

$key = q/Deltastensor{W}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\Delta \stensor{W}^n $">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\epsilon$">|; 

$key = q/displaystyle-(svector{p}^m-svector{x}^{m,N})deltaF;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle - (\svector{p}^m - \svector{x}^{m,N} ) \delta F$">|; 

$key = q/svector{f}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\svector{f}^n$">|; 

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

$key = q/Deltasvector{x}^{m,N}=sum_nstensor{G}^{m,n}:Deltastensor{W}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\Delta \svector{x}^{m,N} = \sum_n \stensor{G}^{m,n} : \Delta \stensor{W}^n$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\textstyle =$">|; 

$key = q/displaystylesvector{p}^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle \svector{p}^m$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\alpha$">|; 

$key = q/DeltaW_{ij}^n=sum_{m,k}G_{kij}^{m,n}[p_k^m-x_k^{m,N}(svector{d}^m,stensor{W}^1,ldots,stensor{W}^N)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\Delta W_{ij}^n
= \sum_{m,k} G_{kij}^{m,n} [ p_k^m - x_k^{m,N} ( \svector{d}^m , \stensor{W}^1,\ldots,\stensor{W}^N) ],$">|; 

$key = q/stensor{G}^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\stensor{G}^{m,n}$">|; 

$key = q/svector{x}^{m,n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\svector{x}^{m,n-1}$">|; 

$key = q/svector{d}^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\svector{d}^m$">|; 

$key = q/displaystylembox{where}~deltasvector{x}^{m,N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \mbox{where}&nbsp; \delta \svector{x}^{m,N}$">|; 

$key = q/0leqf(x)<f(x')leq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$0 \leq f(x ) &lt; f(x' ) \leq 1$">|; 

$key = q/displaystylesvector{x}^{m,N}(svector{d}^m,stensor{W}^1,ldots,stensor{W}^N)=svector{x}^{m,N}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \svector{x}^{m,N}(\svector{d}^m ,\stensor{W}^1,\ldots,\stensor{W}^N) = \svector{x}^{m,N}.$">|; 

$key = q/displaystylembox{or}~delta{stensor{W}}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \mbox{or}&nbsp;
\delta {\stensor{W}}^n$">|; 

$key = q/displaystylembox{and}~deltax_k^{m,n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \mbox{and}&nbsp; \delta x_k^{m,n-1}$">|; 

$key = q/stensor{W}^n+epsilonDeltastensor{W}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\stensor{W}^n + \epsilon \Delta \stensor{W}^n$">|; 

$key = q/textstyleapprox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\textstyle \approx$">|; 

$key = q/{stensor{w}^1,ldots,stensor{w}^N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\{\stensor{w}^1,\ldots,\stensor{w}^N\}$">|; 

$key = q/displaystylembox{fromdata}~svector{d}^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle \mbox{from data}&nbsp; \svector{d}^m$">|; 

$key = q/delta{stensor{W}}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\delta {\stensor{W}}^n$">|; 

$key = q/stensor{W}^N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\stensor{W}^N$">|; 

$key = q/stensor{W}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\stensor{W}^n$">|; 

$key = q/displaystylestensor{W}^ncdotsvector{f}^n(svector{x}^{m,n-1})~mbox{(invectornotation).};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle \stensor{W}^n \cdot \svector{f}^n (\svector{x}^{m,n-1})
&nbsp; \mbox{(in vector notation).}$">|; 

$key = q/svector{x}^{m,N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\svector{x}^{m,N}$">|; 

$key = q/displaystyle[stensor{nabla}svector{f}^n(svector{x}^{m,n-1})]^{*}cdot(stensor{W}^n)^{*}cdotdeltasvector{x}^{m,n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle [ \stensor{\nabla} \svector{f}^n ( \svector{x}^{m,n-1} )]^{*}
\cdot (\stensor{W}^n)^{*} \cdot \delta \svector{x}^{m,n} .$">|; 

$key = q/displaystyle(stensor{G}^{m,n})^{*}cdotdelta{svector{x}}^{m,N}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle ( \stensor{G}^{m,n} )^{*} \cdot \delta {\svector{x}}^{m,N} .$">|; 

$key = q/0leqx<x'leq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$0 \leq x &lt; x' \leq 1$">|; 

$key = q/sum_{m,k},[p_k^m-alphaDeltax_k^{m,N}]^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\sum_{m,k}   [ p_k^m - \alpha \Delta x_k^{m,N} ]^2$">|; 

$key = q/displaystylembox{and}~deltax_i^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \mbox{and}&nbsp; \delta x_i^{m,n}$">|; 

$key = q/displaystylesum_{m,k},[p_k^m-x_k^{m,N}(svector{d}^m,stensor{W}^1,ldots,stensor{W}^N)]^2=sum_m,|svector{p}^m-svector{x}^{m,N}|^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="463" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \sum_{m,k}   [ p_k^m - x_k^{m,N} ( \svector{d}^m, \stensor{W}^1,...
...tensor{W}^N) ]^2
= \sum_m   \Vert \svector{p}^m - \svector{x}^{m,N} \Vert^2 .$">|; 

$key = q/displaystyle-sum_{m,k},(p_k^m-x_k^{m,N})deltax_k^{m,N}=-sum_{m},(svector{p}^m-svector{x}^{m,N})cdotdeltasvector{x}^{m,N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle - \sum_{m,k}   ( p_k^m - x_k^{m,N} ) \delta x_k^{m,N}
= - \sum_{m}   ( \svector{p}^m - \svector{x}^{m,N} ) \cdot \delta \svector{x}^{m,N} ,$">|; 

$key = q/displaystylesum_{n,i,j}G_{kij}^{m,n}deltaW_{ij}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \sum_{n,i,j} G_{kij}^{m,n} \delta W_{ij}^n$">|; 

$key = q/displaystyledeltaW_{ij}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle \delta W_{ij}^n$">|; 

$key = q/displaystylesum_mdelta{svector{x}}^{m,n}[svector{f}^n(svector{x}^{m,n-1})]^{*}~~mbox{(outerproduct),};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \sum_m \delta {\svector{x}}^{m,n} [ \svector{f}^n (\svector{x}^{m,n-1} ) ]^{*}&nbsp;&nbsp;
\mbox{(outer product),}$">|; 

$key = q/displaystylembox{or}~delta{svector{x}}^{m,N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \mbox{or}&nbsp;
\delta {\svector{x}}^{m,N}$">|; 

$key = q/alpha=(sum_{m,k},p_k^mDeltax_k^{m,N})slashsum_{m,k}Deltax_k^{m,N}Deltax_k^{m,N}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\alpha = (\sum_{m,k}   p_k^m \Delta x_k^{m,N} ) /
\sum_{m,k} \Delta x_k^{m,N} \Delta x_k^{m,N} ) .$">|; 

$key = q/svector{f}^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="23" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\svector{f}^1$">|; 

$key = q/displaystylembox{or}~delta{svector{x}}^{m,n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle \mbox{or}&nbsp;
\delta {\svector{x}}^{m,n-1}$">|; 

$key = q/displaystylembox{where}~delta{svector{x}}^{m,0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle \mbox{where}&nbsp; \delta {\svector{x}}^{m,0}$">|; 

$key = q/displaystyledelta{stensor{W}}^ncdotsvector{f}^n(svector{x}^{m,n-1})+stensor{W}^nvector{f}^n(svector{x}^{m,n-1})cdotdelta{svector{x}}^{m,n-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle \delta {\stensor{W}}^n \cdot \svector{f}^n ( \svector{x}^{m,n-1} ...
...bla} \svector{f}^n ( \svector{x}^{m,n-1} ) \cdot \delta {\svector{x}}^{m,n-1} .$">|; 

$key = q/svector{x}^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\svector{x}^{m,n}$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$m$">|; 

$key = q/delta{svector{x}}^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\delta {\svector{x}}^{m,n}$">|; 

$key = q/deltaF;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\delta F$">|; 

$key = q/svector{x}^{m,0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\svector{x}^{m,0}$">|; 

$key = q/displaystylesum_nstensor{G}^{m,n}:delta{stensor{W}}^n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle \sum_n \stensor{G}^{m,n} : \delta {\stensor{W}}^n .$">|; 

$key = q/displaystylemin_{{W_{ij}^n}},F(stensor{W}^1,ldots,stensor{W}^N);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle \min_{\{W_{ij}^n\}}
  F(\stensor{W}^1,\ldots,\stensor{W}^N)$">|; 

$key = q/displaystylembox{or}~svector{x}^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle \mbox{or}&nbsp; \svector{x}^{m,n}$">|; 

$key = q/svector{p}^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\svector{p}^m$">|; 

$key = q/displaystylesum_{m,k}G_{kij}^{m,n}deltax_k^{m,N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \sum_{m,k} G_{kij}^{m,n} \delta x_k^{m,N} ,$">|; 

$key = q/sum_{m,k},[p_k^m-x_k^{m,N}(svector{d}^m,stensor{W}^1+alphaDeltastensor{W}^1,ldots,stensor{W}^N+alphaDeltastensor{W}^N)]^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\sum_{m,k}   [ p_k^m - x_k^{m,N}(\svector{d}^m ,
\stensor{W}^1 + \alpha \Delta \stensor{W}^1 , \ldots ,
\stensor{W}^N + \alpha \Delta \stensor{W}^N )]^2$">|; 

$key = q/displaystylesum_jW_{ij}^nf_j^n(svector{x}^{m,n-1}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle \sum_j W_{ij}^n f_j^n ( \svector{x}^{m,n-1} ),$">|; 

$key = q/displaystylembox{or}~delta{svector{x}}^{m,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle \mbox{or}&nbsp;
\delta {\svector{x}}^{m,n}$">|; 

$key = q/displaystylembox{Findparameters}~svector{p}^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle \mbox{Find parameters }&nbsp; \svector{p}^m$">|; 

$key = q/deltastensor{W}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\delta \stensor{W}^n$">|; 

$key = q/displaystylesum_jfrac{partial}{partialx_k}f_j^n(svector{x}^{m,n-1})sum_iW_{ij}^ndeltax_i^{m,n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle \sum_j
\frac{\partial}{\partial x_k} f_j^n (\svector{x}^{m,n-1})
\sum_i W_{ij}^n \delta x_i^{m,n} ,$">|; 

1;