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


$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$s$">|; 

$key = q/(x,y,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$(x,y,z)$">|; 

$key = q/{displaymath}{svectorp}[{svectorx},{svectorx}']equiv{svector{nabla}}_{{svector{scriptstylex}}}T[{svectorx},{svectorx}']{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="\begin{displaymath}
{\svector p}[ {\svector x}, {\svector x}' ] \equiv {\svector...
...{{\svector {\scriptstyle x}}} T[ {\svector x}, {\svector x}' ]
\end{displaymath}">|; 

$key = q/theta_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\theta_{bh}$">|; 

$key = q/{svectorx}_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="${\svector x}_b$">|; 

$key = q/{svectorp}({svectorx}_{bh},{svectorx}_c-{{svectorx}_h});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="${\svector p}( {\svector x}_{bh} , {\svector x}_c - {{\svector x}_h} )$">|; 

$key = q/{svectorx}(a_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="${\svector x}(a_0)$">|; 

$key = q/{displaymath}min_{P_{i}}=sum_{b}sum_{h}(e_{bh}-{1over{N_b}}sum_{h'}e_{bh'})^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="\begin{displaymath}\min_{P_{i}} = \sum_{b} \sum_{h} ( e_{bh} - {1 \over {N_b} }
\sum_{h'} e_{bh'} )^2 .
\end{displaymath}">|; 

$key = q/{displaymath}u(t,{{svectorx}_s},{{svectorx}_r})=intd{svectorx}~m({svectorx})~del_s})~R({svectorx},{{svectorx}_r})~mbox{gain}(t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="596" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="\begin{displaymath}
u (t, {{\svector x}_s} , {{\svector x}_r} ) = \int d {\svect...
..._s} )&nbsp; R( {\svector x}, {{\svector x}_r} )&nbsp; \mbox{gain}(t) .
\end{displaymath}">|; 

$key = q/R({svectorx},{{svectorx}_s});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$R ({\svector x}, {{\svector x}_s} )$">|; 

$key = q/{svector{nabla}}times{svectorp}={svector0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="${\svector {\nabla}}\times {\svector p}= {\svector 0}$">|; 

$key = q/{svectorx}_{bh}=[x_b,y_b,z_{bh}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="${\svector x}_{bh} = [x_b, y_b, z_{bh}]$">|; 

$key = q/P_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$P_i$">|; 

$key = q/{{svectorx}_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\{{\svector x}_{bh}$">|; 

$key = q/{svectorq}_{bh}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="${\svector q}_{bh}\}$">|; 

$key = q/{svectorx}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="${\svector x}'$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$a$">|; 

$key = q/{displaymath}e_{bh}=(t_{bh}-T_{bh})slashcos({theta}_{bh}slash2).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="\begin{displaymath}
e_{bh} = (t_{bh} - T_{bh} )/ \cos ({\theta}_{bh}/2) .
\end{displaymath}">|; 

$key = q/{svectorp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="${\svector p}$">|; 

$key = q/nabla^2T=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\nabla^2 T = 0$">|; 

$key = q/{displaymath}t_{ch}({svectorx}_{bh})=T({svectorx}_{bh},{{svectorx}_c}-{{svectorx({svectorx}_{bh},{{svectorx}_c}+{{svectorx}_h}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="\begin{displaymath}
t_{ch} ({\svector x}_{bh}) = T({\svector x}_{bh} , {{\svecto...
... T({\svector x}_{bh} , {{\svector x}_c} + {{\svector x}_h} ) .
\end{displaymath}">|; 

$key = q/(x_b,y_b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$(x_b, y_b)$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$h$">|; 

$key = q/{displaymath}hatm({{svectorx}_b})=sum_{s,r}intdt~dotu(t,{{svectorx}_s},{{svector~R({{svectorx}_b},{{svectorx}_r})~mbox{gain}(t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="650" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="\begin{displaymath}
\hat m ( {{\svector x}_b} ) =
\sum_{s,r} \int dt&nbsp; \dot u (t...
...&nbsp; R( {{\svector x}_b} , {{\svector x}_r} )&nbsp; \mbox{gain}(t)
.
\end{displaymath}">|; 

$key = q/displaystyleintg({svectorx})d{svectorx}=1,mbox{and}intg({svectorx})~|{svectorx}|^2~d{svectorx}approx1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle \int g ({\svector x}) d{\svector x}= 1, \mbox{ and }
\int g ({\svector x})&nbsp; \Vert {\svector x}\Vert^2&nbsp; d{\svector x}\approx 1 .$">|; 

$key = q/a=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$a=0$">|; 

$key = q/{svector{nabla}}_{{svector{scriptstylex}}_c}equiv({svector{nabla}}_{{svector{scrylex}}_s}+{svector{nabla}}_{{svector{scriptstylex}}_r})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="${\svector {\nabla}}_{{\svector {\scriptstyle x}}_c} \equiv ({\svector {\nabla}}...
... {\scriptstyle x}}_s} + {\svector {\nabla}}_{{\svector {\scriptstyle x}}_r})/2 $">|; 

$key = q/f(cdot);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$f(\cdot)$">|; 

$key = q/{{svectorx}_h}=({svectorx}_r-{svectorx}_s)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="${{\svector x}_h} = ({\svector x}_r - {\svector x}_s)/2$">|; 

$key = q/displaystylesum_{c}intdt~dotu(t,{{svectorx}_c}-{{svectorx}_h},{{svectorx}_c}+{{srx}_h})-T({{svectorx}_b},{{svectorx}_c}+{{svectorx}_h})]~cdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="563" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \sum_{c} \int dt&nbsp; \dot u (t, {{\svector x}_c} - {{\svector x}_h} ...
...x}_h} ) - T ({{\svector x}_b} , {{\svector x}_c} + {{\svector x}_h} ) ]
&nbsp; \cdot$">|; 

$key = q/{svectorx}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="${\svector x}_i$">|; 

$key = q/mbox{gain}(t)=t^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\mbox{gain}(t) = t^2$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$R$">|; 

$key = q/textstylehatu(t,{{svectorx}_c}-{{svectorx}_h},{{svectorx}_c}+{{svectorx}_h})=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\textstyle \hat u (t, {{\svector x}_c} - {{\svector x}_h} , {{\svector x}_c} + {{\svector x}_h} ) =$">|; 

$key = q/{displaymath}P({svectorx})equivBigl|{svectorp}[{svectorx},{svectorx}']Bigr|{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="\begin{displaymath}
P ({\svector x}) \equiv \Bigl \Vert {\svector p}[ {\svector x}, {\svector x}' ] \Bigr \Vert
\end{displaymath}">|; 

$key = q/{{svectorx}_h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="${{\svector x}_h} $">|; 

$key = q/displaystyle=int_{a_0}^{a}da'~{dover{da'}}T[{svectorx}(a'),{svectorx}(a_0)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle = \int_{a_0}^{a} da'
&nbsp; { d \over {da'} } T [ {\svector x}( a' ) , {\svector x}( a_0 ) ]$">|; 

$key = q/{displaymath}hatm_h({svectorx}_{b})approxf[({svectorx}_b-{svectorx}_{bh})cdot{svectorq}_{bh}]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="\begin{displaymath}
\hat m_h ( {\svector x}_{b} ) \approx f [ ( {\svector x}_b - {\svector x}_{bh} ) \cdot {\svector q}_{bh} ]
\end{displaymath}">|; 

$key = q/a_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$a_{bh}$">|; 

$key = q/t_{ch}({svectorx}_{bh});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$t_{ch} ({\svector x}_{bh})$">|; 

$key = q/T_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$T_{bh}$">|; 

$key = q/{svectorx}_{bh}(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="${\svector x}_{bh} (a) $">|; 

$key = q/g({svectorx});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$g ({\svector x})$">|; 

$key = q/{svectorx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="${\svector x}$">|; 

$key = q/{displaymath}{doverda}{svectorp}[{svectorx}(a),{svectorx}(a_0)]={svector{nabla}}_{{svector{scriptstylex}}}P[{svectorx}(a)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="\begin{displaymath}
{d \over da} {\svector p}[ {\svector x}(a) , {\svector x}(a_...
...\nabla}}_{{\svector {\scriptstyle x}}} P [ {\svector x}(a) ]
.
\end{displaymath}">|; 

$key = q/{displaymath}{dover{da}}{svectorx}(a)equiv{svectorp}[{svectorx}(a),{svectorx}(a_0)]slashP[{svectorx}(a)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="\begin{displaymath}
{d \over {da}} {\svector x}(a) \equiv
{\svector p}[ {\svector x}(a) , {\svector x}( a_0 ) ] /
P [ {\svector x}(a) ] .
\end{displaymath}">|; 

$key = q/{{svectorx}_r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="${{\svector x}_r} $">|; 

$key = q/{svectorx}(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="${\svector x}(a)$">|; 

$key = q/{svectorx}_c=({svectorx}_r+{svectorx}_s)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="${\svector x}_c = ({\svector x}_r + {\svector x}_s)/2$">|; 

$key = q/displaystyle=int_{a_0}^{a}da'~Bigl|{svectorp}[{svectorx}(a'),{svectorx}(a_0)]Bigr|~Bigl|{dover{da'}}{svectorx}(a')Bigr|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle = \int_{a_0}^{a} da'
&nbsp; \Bigl \Vert {\svector p}[ {\svector x}(a')...
... ) ] \Bigr \Vert
&nbsp; \Bigl \Vert { d \over {da'} } {\svector x}( a' ) \Bigr \Vert$">|; 

$key = q/textstylembox{where};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\textstyle \mbox{ where }$">|; 

$key = q/{displaymath}e_{cbh}equiv{Deltat_{ch}({svectorx}_{bh})overcos(theta_{cbh}slash2)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="\begin{displaymath}
e_{cbh} \equiv
{ \Delta t_{ch} ({\svector x}_{bh}) \over
\cos ( \theta_{cbh} / 2 ) } .
\end{displaymath}">|; 

$key = q/{{svectorx}_h}equiv({{svectorx}_r}-{{svectorx}_s})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$ {{\svector x}_h} \equiv ({{\svector x}_r} - {{\svector x}_s} )/2 $">|; 

$key = q/{displaymath}Deltat_{ch}({svectorx}_{bh})equivt_{ch}({svectorx}_{bh}+Delta{svect}slash2){svectorq}_{bh}cdotDelta{svectorx}_{bh}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="\begin{displaymath}
\Delta t_{ch} ({\svector x}_{bh}) \equiv
t_{ch} ({\svector ...
...{cbh} / 2 ) {\svector q}_{bh} \cdot \Delta
{\svector x}_{bh} .
\end{displaymath}">|; 

$key = q/hatm_h({svectorx}_b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\hat m_h ({\svector x}_b)$">|; 

$key = q/displaystyle=int_{a_0}^{a}da'~P[{svectorx}(a')];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle = \int_{a_0}^{a} da'
&nbsp; P [ {\svector x}(a') ]$">|; 

$key = q/P({svectorx});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$P({\svector x})$">|; 

$key = q/{displaymath}T[{svectorx},{svectorx}']=int_{{svector{scriptstylex}}'}^{{svector{orp}[{svectorx}'',{svectorx}']cdotd{svectorx}'',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{displaymath}
T[ {\svector x}, {\svector x}' ] =
\int_{{\svector {\scripts...
... p}[ {\svector x}'' , {\svector x}' ] \cdot d {\svector x}'' ,
\end{displaymath}">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$P$">|; 

$key = q/{svectorx}_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="${\svector x}_{bh}$">|; 

$key = q/t_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$t_{bh}$">|; 

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

$key = q/{{svectorx}_s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="${{\svector x}_s} $">|; 

$key = q/displaystyle{svectorp}({svectorx}_{bh},{{svectorx}_c}-{{svectorx}_h})+{svectorp}=2~P({svectorx}_{bh})~cos(theta_{cbh}slash2)~{svectorq}_{bh},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="501" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle {\svector p}( {\svector x}_{bh} , {{\svector x}_c} - {{\svector x...
... )
= 2&nbsp; P ({\svector x}_{bh})&nbsp; \cos ( \theta_{cbh} / 2)&nbsp;
{\svector q}_{bh} ,$">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$b$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$t$">|; 

$key = q/|{svectorq}_{bh}|equiv1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\Vert {\svector q}_{bh} \Vert \equiv 1$">|; 

$key = q/{displaymath}max_{{svector{scriptstylex}}_{bh}}~Bigl|[{svectorp}({{svectorx}_c}-rx}_h},{svectorx}_{bh})]cdot{svectorp}_{ch}Bigr|{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="\begin{displaymath}
\max_{{\svector {\scriptstyle x}}_{bh}}
&nbsp; \Bigl \Vert
[ {\s...
...} , {\svector x}_{bh} ) ]
\cdot {\svector p}_{ch}
\Bigr \Vert
\end{displaymath}">|; 

$key = q/displaystyleP({svectorx})equivsum_{i}~P_{i}~w^{-1}~g[({svectorx}-{svectorx}_i)slashw],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\displaystyle P({\svector x}) \equiv \sum_{i}&nbsp; P_{i}&nbsp; w^{-1}&nbsp; g [ ( {\svector x}- {\svector x}_i ) / w ] ,$">|; 

$key = q/N_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$N_b$">|; 

$key = q/{t_{ch},{svectorp}_{ch}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\{t_{ch},{\svector p}_{ch}\}$">|; 

$key = q/displaystylesum_{b}hatm_h({{svectorx}_b})~delta[t-T({{svectorx}_b},{{svectorx}_crx}_h})-T({{svectorx}_b},{{svectorx}_c}+{{svectorx}_h})]~cdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="410" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle \sum_{b} \hat m_h ( {{\svector x}_b} )
&nbsp; \delta [ t - T ( {{\svec...
...x}_h} ) - T ({{\svector x}_b} , {{\svector x}_c} + {{\svector x}_h} ) ]
&nbsp; \cdot$">|; 

$key = q/{{svectorx}_c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="${{\svector x}_c} $">|; 

$key = q/textstyleT[{svectorx}(a),{svectorx}(a_0)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\textstyle T [ {\svector x}(a) , {\svector x}(a_0 ) ]$">|; 

$key = q/theta_{cbh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\theta_{cbh}$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$z$">|; 

$key = q/{svectorp}(a_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="${\svector p}(a_0)$">|; 

$key = q/{displaymath}Deltahat{svectorx}_{cbh}={Deltat_{ch}({svectorx}_{bh})over2P({svectx}_{bh})cos(theta_{cbh}slash2)}~{svectorq}_{bh}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="\begin{displaymath}
\Delta \hat {\svector x}_{cbh} =
{ \Delta t_{ch} ({\svector ...
...or x}_{bh} ) \cos ( \theta_{cbh} / 2 ) }&nbsp; {\svector q}_{bh} .
\end{displaymath}">|; 

$key = q/displaystyle=int_{a_0}^{a}da'~{svector{nabla}}T[{svectorx}(a'),{svectorx}(a_0)]cdot{dover{da'}}{svectorx}(a');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle = \int_{a_0}^{a} da'
&nbsp; {\svector {\nabla}}T [ {\svector x}(a') , {\svector x}( a_0 ) ] \cdot { d \over {da'} } {\svector x}( a' )$">|; 

$key = q/{svectorp}({svectorx}_{bh},{svectorx}_c+{{svectorx}_h});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="${\svector p}( {\svector x}_{bh} , {\svector x}_c + {{\svector x}_h} )$">|; 

$key = q/u(t,{{svectorx}_s},{{svectorx}_r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$u(t, {{\svector x}_s} , {{\svector x}_r} )$">|; 

$key = q/{{svectorx}_{bh},{svectorq}_{bh}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\{{\svector x}_{bh}, {\svector q}_{bh}\}$">|; 

$key = q/{{svectorx}_c}equiv({{svectorx}_r}+{{svectorx}_s})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="${{\svector x}_c} \equiv ( {{\svector x}_r} + {{\svector x}_s} )/2$">|; 

$key = q/displaystylecdot~R({{svectorx}_b},{{svectorx}_c}-{{svectorx}_h})~R({{svectorx}_b},{{svectorx}_c}+{{svectorx}_h})~mbox{gain}(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \cdot&nbsp; R( {{\svector x}_b} , {{\svector x}_c} -{{\svector x}_h} )&nbsp; R( {{\svector x}_b} , {{\svector x}_c} + {{\svector x}_h} )&nbsp; \mbox{gain}(t) .$">|; 

$key = q/{displaymath}T_{bh}=int_{0}^{a_{bh}}P[{svectorx}_{bh}(a)]da.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\begin{displaymath}
T_{bh} = \int_{0}^{a_{bh}} P [ {\svector x}_{bh} (a) ] d a.
\end{displaymath}">|; 

$key = q/displaystylembox{where}cos(theta_{cbh})equiv[{svectorp}({svectorx}_{bh},{{svectobh},{{svectorx}_c}+{{svectorx}_h})]slashP({svectorx}_{bh})^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="507" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle \mbox { where } \cos ( \theta_{cbh} ) \equiv
[ {\svector p}( {\sv...
...x}_{bh} , {{\svector x}_c} + {{\svector x}_h} ) ] / P ( {\svector x}_{bh} )^2 .$">|; 

$key = q/{displaymath}max_{{svector{scriptstylex}}_c}~Bigl|[{svectorp}({svectorx}_{bh},{{orx}_c}+{{svectorx}_h})]cdot{svectorq}_{bh}Bigr|{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="\begin{displaymath}
\max_{{\svector {\scriptstyle x}}_c}
&nbsp; \Bigl \Vert
[{\svecto...
..._c} + {{\svector x}_h} )]
\cdot {\svector q}_{bh}
\Bigr \Vert
\end{displaymath}">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$r$">|; 

$key = q/t_{ch};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$t_{ch}$">|; 

$key = q/{displaymath}1slashv({svectorx})equivBigl|{svector{nabla}}_{{svector{scriptstylex}}}T[{svectorx},{svectorx}']Bigr|{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\begin{displaymath}
1/v( {\svector x}) \equiv \Bigl \Vert {\svector {\nabla}}_{{...
...criptstyle x}}} T [ {\svector x}, {\svector x}' ] \Bigr \Vert
\end{displaymath}">|; 

$key = q/{svectorp}_{ch}={svector{nabla}}_{{svector{scriptstylex}}_c}t_{ch};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="${\svector p}_{ch} = {\svector {\nabla}}_{{\svector {\scriptstyle x}}_c} t_{ch} $">|; 

$key = q/bigl|d{svectorx}(a)slashdabigr|equiv1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\bigl \Vert d {\svector x}(a) / da \bigr \Vert \equiv 1$">|; 

$key = q/textstylehatm_h({{svectorx}_b})=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\textstyle \hat m_h ( {{\svector x}_b} ) =$">|; 

$key = q/T({svectorx},{{svectorx}_s});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$T ( {\svector x}, {{\svector x}_s} )$">|; 

$key = q/{svectorq}_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="${\svector q}_{bh}$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$T$">|; 

$key = q/z_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$z_{bh}$">|; 

1;