# LaTeX2HTML 99.2beta8 (1.42)
# Associate images original text with physical files.


$key = q/x+y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.gif"
 ALT="$ x + y$">|; 

$key = q/eta<pislashN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.gif"
 ALT="$ \eta &lt; \pi/N$">|; 

$key = q/displaystylevarepsilon=30deg;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.gif"
 ALT="$\displaystyle \varepsilon = 30 deg$">|; 

$key = q/displaystylecos{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.gif"
 ALT="$\displaystyle \cos{\eta}$">|; 

$key = q/displaystyletan{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.gif"
 ALT="$\displaystyle \tan{\eta}$">|; 

$key = q/a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.gif"
 ALT="$ a$">|; 

$key = q/displaystyleeta=33.53deg;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.gif"
 ALT="$\displaystyle \eta = 33.53 deg$">|; 

$key = q/displaystyle=frac{b}{y};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.gif"
 ALT="$\displaystyle = \frac{b}{y}$">|; 

$key = q/(r_1+w_x)a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.gif"
 ALT="$ (r_1+w_x)a$">|; 

$key = q/includegraphics[height=5in]{imgslashstarL.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="529" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.gif"
 ALT="\includegraphics[height=5in]{img/starL.ps}">|; 

$key = q/displaystylefrac{deltaS}{deltaw_x}=2Nleft[frac{pi}{N}-varepsilon+a-frac{pi}{2}+etaright];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.gif"
 ALT="$\displaystyle \frac{\delta S}{\delta w_x} = 2N\left[ \frac{\pi}{N} - \varepsilon + a - \frac{\pi}{2} + \eta \right]$">|; 

$key = q/displaystylea=frac{pi}{2}-eta+varepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.gif"
 ALT="$\displaystyle a = \frac{\pi}{2} - \eta + \varepsilon$">|; 

$key = q/displaystyleeta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.gif"
 ALT="$\displaystyle \eta$">|; 

$key = q/displaystyle=(r_1+w_x)tan{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.gif"
 ALT="$\displaystyle = (r_1+w_x)\tan{\eta}$">|; 

$key = q/displaystyleN=6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.gif"
 ALT="$\displaystyle N = 6$">|; 

$key = q/includegraphics[height=3in]{imgslasharc.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="283" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img37.gif"
 ALT="\includegraphics[height=3in]{img/arc.ps}">|; 

$key = q/displaystylex;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.gif"
 ALT="$\displaystyle x$">|; 

$key = q/eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.gif"
 ALT="$ \eta$">|; 

$key = q/L;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.gif"
 ALT="$ L$">|; 

$key = q/N=6;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img64.gif"
 ALT="$ N=6$">|; 

$key = q/displaystyleY*=(R-w-r_1)frac{sin{varepsilon}}{cos{eta}}-r_1=w;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.gif"
 ALT="$\displaystyle Y* = (R-w-r_1)\frac{\sin{\varepsilon}}{\cos{\eta}} - r_1 = w$">|; 

$key = q/displaystyleR;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.gif"
 ALT="$\displaystyle R$">|; 

$key = q/varepsilon<pislashN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.gif"
 ALT="$ \varepsilon &lt; \pi/N$">|; 

$key = q/displaystyleb+z;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.gif"
 ALT="$\displaystyle b + z$">|; 

$key = q/displaystyler_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.gif"
 ALT="$\displaystyle r_2$">|; 

$key = q/includegraphics[height=5in]{imgslashvariable.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="498" HEIGHT="401" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.gif"
 ALT="\includegraphics[height=5in]{img/variable.ps}">|; 

$key = q/displaystylefrac{S}{2N}=(R-w+w_x)(frac{pi}{N}-varepsilon)+(r_1+w_x)left[varepsilon+arcsin{(frac{R-w-r_1}{r_1+w_x}sin{varepsilon}})right];MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="550" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.gif"
 ALT="$\displaystyle \frac{S}{2N} = (R-w+w_x)(\frac{\pi}{N}-\varepsilon) + (r_1+w_x)\left[ \varepsilon + \arcsin{(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}}) \right]$">|; 

$key = q/varepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img49.gif"
 ALT="$ \varepsilon$">|; 

$key = q/includegraphics[height=4in]{imgslashmainstar.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="516" HEIGHT="392" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.gif"
 ALT="\includegraphics[height=4in]{img/mainstar.ps}">|; 

$key = q/r_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.gif"
 ALT="$ r_2$">|; 

$key = q/pislashN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.gif"
 ALT="$ \pi/N$">|; 

$key = q/eta>pislashN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.gif"
 ALT="$ \eta &gt;
\pi/N$">|; 

$key = q/0<w_x<r_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.gif"
 ALT="$ 0 &lt; w_x &lt; r_2$">|; 

$key = q/includegraphics[]{imgslashres.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="348" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img71.gif"
 ALT="\includegraphics[]{img/res.ps}">|; 

$key = q/{displaymath}split{frac{deltaS}{deltaw_x}<col_mark>=2Nleft[frac{pi}{N}-varepsilo{N}-tan{(frac{pi}{2}-eta)}right]<row_mark>split{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="83" BORDER="0"
 SRC="|."$dir".q|img46.gif"
 ALT="\begin{displaymath}\begin{split}\frac{\delta S}{\delta w_x} &amp;= 2N\left[ \frac{\p...
...c{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)} \right]\  \end{split}\end{displaymath}">|; 

$key = q/w;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img60.gif"
 ALT="$ w$">|; 

$key = q/displaystylevarepsilon;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.gif"
 ALT="$\displaystyle \varepsilon$">|; 

$key = q/displaystyle=;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.gif"
 ALT="$\displaystyle =$">|; 

$key = q/(R-w+w_x)(pislashN-varepsilon);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.gif"
 ALT="$ (R-w+w_x)(\pi/N - \varepsilon)$">|; 

$key = q/displaystyle=(R-w-r_1)sin{varepsilon};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.gif"
 ALT="$\displaystyle = (R-w-r_1)\sin{\varepsilon}$">|; 

$key = q/displaystylex=frac{r_2-wx}{tan{eta}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.gif"
 ALT="$\displaystyle x = \frac{r_2-wx}{\tan{\eta}}$">|; 

$key = q/displaystylesin{varepsilon}=frac{w+r_1}{R-w-r_1}cos{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.gif"
 ALT="$\displaystyle \sin{\varepsilon} = \frac{w+r_1}{R-w-r_1}\cos{\eta}$">|; 

$key = q/3inch;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img63.gif"
 ALT="$ 3 inch$">|; 

$key = q/displaystylew;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.gif"
 ALT="$\displaystyle w$">|; 

$key = q/N;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.gif"
 ALT="$ N$">|; 

$key = q/{displaymath}split{frac{deltaS}{deltaw_x}<col_mark>=2Nbiggl[frac{pi}{N}+arcsin{barepsilon}}{(r_1+w_x)^2}}}biggr]<row_mark>split{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="110" BORDER="0"
 SRC="|."$dir".q|img57.gif"
 ALT="\begin{displaymath}\begin{split}\frac{\delta S}{\delta w_x} &amp;= 2N \biggl[ \frac{...
..._1)^2\sin^2{\varepsilon}}{(r_1+w_x)^2}}} \biggr]\  \end{split}\end{displaymath}">|; 

$key = q/displaystyleL=y+x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.gif"
 ALT="$\displaystyle L = y + x$">|; 

$key = q/displaystyle=frac{1}{tan{(frac{pi}{2}-eta)}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.gif"
 ALT="$\displaystyle = \frac{1}{\tan{(\frac{\pi}{2}-\eta)}}$">|; 

$key = q/displaystylefrac{deltaS}{deltaw_x}=2pi;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.gif"
 ALT="$\displaystyle \frac{\delta S}{\delta w_x} = 2\pi$">|; 

$key = q/displaystyleN;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.gif"
 ALT="$\displaystyle N$">|; 

$key = q/r_1=1slash16in;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.gif"
 ALT="$ r_1 = 1/16 in$">|; 

$key = q/displaystyler_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.gif"
 ALT="$\displaystyle r_1$">|; 

$key = q/displaystyle=(R-w-r_1)frac{sin{varepsilon}}{sin{eta}}-frac{r_1+w_x}{cos{eta}sin{eta}}+(r_1+w_x)tan{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.gif"
 ALT="$\displaystyle = (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} - \frac{r_1+w_x}{\cos{\eta}\sin{\eta}} + (r_1+w_x)\tan{\eta}$">|; 

$key = q/displaystylesin{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.gif"
 ALT="$\displaystyle \sin{\eta}$">|; 

$key = q/displaystylesin^2{eta}-1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.gif"
 ALT="$\displaystyle \sin^2{\eta} -1$">|; 

$key = q/includegraphics[height=4in]{imgslashperimeter.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="628" HEIGHT="447" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.gif"
 ALT="\includegraphics[height=4in]{img/perimeter.ps}">|; 

$key = q/r_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.gif"
 ALT="$ r_1$">|; 

$key = q/displaystyle=frac{r_1+w_x}{z};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.gif"
 ALT="$\displaystyle = \frac{r_1+w_x}{z}$">|; 

$key = q/R-w+w_x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.gif"
 ALT="$ R-w+w_x$">|; 

$key = q/displaystyle=-cos^2{eta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.gif"
 ALT="$\displaystyle = -\cos^2{\eta}$">|; 

$key = q/displaystyle=(r_2-wx)(frac{pi}{2}-eta);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.gif"
 ALT="$\displaystyle = (r_2-wx)(\frac{\pi}{2}-\eta)$">|; 

$key = q/displaystyleeta=frac{pi}{N}-tan{(frac{pi}{2}-eta)}+frac{pi}{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.gif"
 ALT="$\displaystyle \eta = \frac{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)} + \frac{\pi}{2}$">|; 

$key = q/displaystylec^2=a^2+b^2-2abcos{theta};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.gif"
 ALT="$\displaystyle c^2 = a^2 + b^2 - 2ab\cos{\theta}$">|; 

$key = q/displaystylefrac{deltaS}{deltaw_x}=0=frac{pi}{2}-eta+frac{pi}{N}-tan{(frac{pi}{2}-eta)};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.gif"
 ALT="$\displaystyle \frac{\delta S}{\delta w_x} = 0 = \frac{\pi}{2} - \eta + \frac{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)}$">|; 

$key = q/{displaymath}split{L<col_mark>=(R-w-r_1)frac{sin{varepsilon}}{sin{eta}}+(r_1+w_x-(r_1+w_x)tan{(frac{pi}{2}-eta)}<row_mark>split{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="191" BORDER="0"
 SRC="|."$dir".q|img36.gif"
 ALT="\begin{displaymath}\begin{split}L &amp;= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta...
...sin{\eta}} - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\  \end{split}\end{displaymath}">|; 

$key = q/{displaymath}split{frac{S}{2N}<col_mark>=(R-w+w_x)(frac{pi}{N}-varepsilon)+(r_1+eta)}+(r_2-w_x)(frac{pi}{2}-eta)<row_mark>split{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="204" BORDER="0"
 SRC="|."$dir".q|img41.gif"
 ALT="\begin{displaymath}\begin{split}\frac{S}{2N} &amp;= (R-w+w_x)(\frac{\pi}{N} - \varep...
...c{\pi}{2}-\eta)} + (r_2-w_x)(\frac{\pi}{2}-\eta)\  \end{split}\end{displaymath}">|; 

$key = q/displaystyle=frac{(R-w-r_1)sin{varepsilon}-frac{r_1+w_x}{cos{eta}}}{y};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.gif"
 ALT="$\displaystyle = \frac{(R-w-r_1)\sin{\varepsilon} - \frac{r_1+w_x}{\cos{\eta}}}{y}$">|; 

$key = q/{displaymath}split{frac{S}{2N}=(r_1+w_x)biggl[<col_mark>varepsilon+arcsin{biggl((r_1+w_x)(R-r_1-w)}biggr)}biggr]<row_mark>split{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="501" HEIGHT="98" BORDER="0"
 SRC="|."$dir".q|img62.gif"
 ALT="\begin{displaymath}\begin{split}\frac{S}{2N} = (r_1+w_x) \biggl[ &amp; \varepsilon +...
...1-w)^2-R^2}{2(r_1+w_x)(R-r_1-w)}\biggr)} \biggr]\  \end{split}\end{displaymath}">|; 

$key = q/{displaymath}split{frac{S}{2N}<col_mark>=(R-w+w_x)(frac{pi}{N}-varepsilon)+(r_1+-(r_1+w_x)tan{(frac{pi}{2}-eta)}<row_mark>split{{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="83" BORDER="0"
 SRC="|."$dir".q|img45.gif"
 ALT="\begin{displaymath}\begin{split}\frac{S}{2N} &amp;= (R-w+w_x)(\frac{\pi}{N} - \varep...
...  &amp; \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\  \end{split}\end{displaymath}">|; 

$key = q/displaystylew=0.500;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.gif"
 ALT="$\displaystyle w = 0.500$">|; 

$key = q/w_x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.gif"
 ALT="$ w_x$">|; 

$key = q/w_x=Y*;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.gif"
 ALT="$ w_x = Y*$">|; 

1;