# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/includegraphics[width=0.35paperwidth]{speex_analysis};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="127" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="\includegraphics[width=0.35\paperwidth]{speex_analysis}">|; 

$key = q/pm8000;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$ \pm8000$">|; 

$key = q/frac{partialE}{partiala_{i}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ \frac{\partial E}{\partial a_{i}}$">|; 

$key = q/displaystyleS'(z)=frac{Aleft(zslasha_{2}right)Aleft(zslasha_{3}right)}{Aleft(zright)Aleft(zslasha_{1}right)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle S'(z)=\frac{A\left(z/a_{2}\right)A\left(z/a_{3}\right)}{A\left(z\right)A\left(z/a_{1}\right)}$">|; 

$key = q/z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$ z$">|; 

$key = q/displaystyleR(m)=sum_{i=0}^{N-1}x[i]x[i-m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle R(m)=\sum_{i=0}^{N-1}x[i]x[i-m]$">|; 

$key = q/y[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ y[n]$">|; 

$key = q/1slashW(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$ 1/W(z)$">|; 

$key = q/p_{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$ p_{i}$">|; 

$key = q/R(0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$ R(0)$">|; 

$key = q/displaystyleW(z)=frac{A(zslashgamma_{1})}{A(zslashgamma_{2})};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle W(z)=\frac{A(z/\gamma_{1})}{A(z/\gamma_{2})}$">|; 

$key = q/T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$ T$">|; 

$key = q/displaystylemathbf{r}=left[{array}{c}R(1)R(2)vdotsR(N){array}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="103" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \mathbf{r}=\left[\begin{array}{c}
R(1)\\\\
R(2)\\\\
\vdots\\\\
R(N)\end{array}\right]$">|; 

$key = q/a_{1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$ a_{1}$">|; 

$key = q/g_{0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$ g_{0}$">|; 

$key = q/W(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$ W(z)$">|; 

$key = q/mathcal{O}left(N^{2}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$ \mathcal{O}\left(N^{2}\right)$">|; 

$key = q/mathbf{Ra}=mathbf{r};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ \mathbf{Ra}=\mathbf{r}$">|; 

$key = q/pm2^{15};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$ \pm2^{15}$">|; 

$key = q/includegraphics[width=0.45paperwidth,keepaspectratio]{celp_decoder};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="300" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="\includegraphics[width=0.45\paperwidth,keepaspectratio]{celp_decoder}">|; 

$key = q/left[17,144right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$ \left[17,144\right]$">|; 

$key = q/displaystylee_{a}[n]=g_{0}e[n-T-1]+g_{1}e[n-T]+g_{2}e[n-T+1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle e_{a}[n]=g_{0}e[n-T-1]+g_{1}e[n-T]+g_{2}e[n-T+1]$">|; 

$key = q/displaystyleX(z)=frac{C(z)}{A(z)left(1-betaz^{-T}right)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle X(z)=\frac{C(z)}{A(z)\left(1-\beta z^{-T}\right)}$">|; 

$key = q/x[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ x[n]$">|; 

$key = q/A(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$ A(z)$">|; 

$key = q/F_{s};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ F_{s}$">|; 

$key = q/F_{s}slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ F_{s}/2$">|; 

$key = q/e[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$ e[n]$">|; 

$key = q/20:mathrm{ms};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$ 20\:\mathrm{ms}$">|; 

$key = q/NtimesN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$ N\times N$">|; 

$key = q/p'_{i}=gammap_{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$ p'_{i}=\gamma p_{i}$">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ N$">|; 

$key = q/a_{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$ a_{2}$">|; 

$key = q/8:mathrm{kHz};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$ 8\:\mathrm{kHz}$">|; 

$key = q/displaystylee[n]=x[n]-y[n]=x[n]-sum_{i=1}^{N}a_{i}x[n-i];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\displaystyle e[n]=x[n]-y[n]=x[n]-\sum_{i=1}^{N}a_{i}x[n-i]$">|; 

$key = q/g_{frame};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$ g_{frame}$">|; 

$key = q/g_{1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$ g_{1}$">|; 

$key = q/mathbf{R};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$ \mathbf{R}$">|; 

$key = q/dagger;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ \dagger$">|; 

$key = q/R(m);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$ R(m)$">|; 

$key = q/displaystylemathbf{R}=left[{array}{cccc}R(0)&R(1)&cdots&R(N-1)R(1)&R(0)&cdots&R(N-2)vdots&vdots&ddots&vdotsR(N-1)&R(N-2)&cdots&R(0){array}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="103" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle \mathbf{R}=\left[\begin{array}{cccc}
R(0) &amp; R(1) &amp; \cdots &amp; R(N-1...
...&amp; \vdots &amp; \ddots &amp; \vdots\\\\
R(N-1) &amp; R(N-2) &amp; \cdots &amp; R(0)\end{array}\right]$">|; 

$key = q/gamma_{2}=0.6;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$ \gamma_{2}=0.6$">|; 

$key = q/includegraphics[width=0.4paperwidth]{speex_abs};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="548" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="\includegraphics[width=0.4\paperwidth]{speex_abs}">|; 

$key = q/gamma_{1}=0.9;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$ \gamma_{1}=0.9$">|; 

$key = q/mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ \mu$">|; 

$key = q/includegraphics[width=10cm]{echo_path};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="242" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="\includegraphics[width=10cm]{echo_path}">|; 

$key = q/A(zslashgamma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$ A(z/\gamma)$">|; 

$key = q/displaystylee[n]simeqp[n]=betae[n-T];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle e[n]\simeq p[n]=\beta e[n-T]$">|; 

$key = q/X(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$ X(z)$">|; 

$key = q/e_{a}[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$ e_{a}[n]$">|; 

$key = q/1slashA(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$ 1/A(z)$">|; 

$key = q/g_{subf};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$ g_{subf}$">|; 

$key = q/displaystylee[n]=p[n]+c[n]=betae[n-T]+c[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle e[n]=p[n]+c[n]=\beta e[n-T]+c[n]$">|; 

$key = q/n-2T+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$ n-2T+1$">|; 

$key = q/g_{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$ g_{2}$">|; 

$key = q/pm1.0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$ \pm1.0$">|; 

$key = q/includegraphics[width=0.45paperwidth,keepaspectratio]{ref_shaping};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="301" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="\includegraphics[width=0.45\paperwidth,keepaspectratio]{ref_shaping}">|; 

$key = q/S(z)=1slashA(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$ S(z)=1/A(z)$">|; 

$key = q/r=.9;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$ r=.9$">|; 

$key = q/e[n-T];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$ e[n-T]$">|; 

$key = q/a_{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ a_{i}$">|; 

$key = q/c[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$ c[n]$">|; 

$key = q/a_{3}=frac{1}{r}left(1-frac{1-ra_{1}}{1-ra_{2}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$ a_{3}=\frac{1}{r}\left(1-\frac{1-ra_{1}}{1-ra_{2}}\right)$">|; 

$key = q/displaystylefrac{partialE}{partiala_{i}}=frac{partial}{partiala_{i}}sum_{n=0}^{L-1}left[x[n]-sum_{i=1}^{N}a_{i}x[n-i]right]^{2}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle \frac{\partial E}{\partial a_{i}}=\frac{\partial}{\partial a_{i}}\sum_{n=0}^{L-1}\left[x[n]-\sum_{i=1}^{N}a_{i}x[n-i]\right]^{2}=0$">|; 

$key = q/TggN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$ T\gg N$">|; 

$key = q/n-T+1geq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$ n-T+1\geq0$">|; 

$key = q/displaystyleE=sum_{n=0}^{L-1}left[e[n]right]^{2}=sum_{n=0}^{L-1}left[x[n]-sum_{i=1}^{N}a_{i}x[n-i]right]^{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle E=\sum_{n=0}^{L-1}\left[e[n]\right]^{2}=\sum_{n=0}^{L-1}\left[x[n]-\sum_{i=1}^{N}a_{i}x[n-i]\right]^{2}$">|; 

$key = q/hat{A}(z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$ \hat{A}(z)$">|; 

$key = q/4^{th};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$ 4^{th}$">|; 

$key = q/beta_{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$ \beta_{i}$">|; 

$key = q/displaystyley[n]=sum_{i=1}^{N}a_{i}x[n-i];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle y[n]=\sum_{i=1}^{N}a_{i}x[n-i]$">|; 

$key = q/mathcal{O}left(N^{3}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$ \mathcal{O}\left(N^{3}\right)$">|; 

$key = q/beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$ \beta$">|; 

1;

