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


$key = q/(x,y,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img27.svg"
 ALT="$(x,y,z)$">|; 

$key = q/(x_b,y_b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img68.svg"
 ALT="$(x_b, y_b)$">|; 

$key = q/N_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img11.svg"
 ALT="$N_b$">|; 

$key = q/P({svectorx});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1.svg"
 ALT="$P({\svector x})$">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.77ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img53.svg"
 ALT="$P$">|; 

$key = q/P_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3.svg"
 ALT="$P_i$">|; 

$key = q/R({svectorx},{{svectorx}_s});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img33.svg"
 ALT="$R ({\svector x}, {{\svector x}_s} )$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.77ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img35.svg"
 ALT="$R$">|; 

$key = q/T({svectorx},{{svectorx}_s});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img31.svg"
 ALT="$T ( {\svector x}, {{\svector x}_s} )$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.77ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img34.svg"
 ALT="$T$">|; 

$key = q/T_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.12ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img19.svg"
 ALT="$T_{bh}$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img14.svg"
 ALT="$a$">|; 

$key = q/a=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.68ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img17.svg"
 ALT="$a=0$">|; 

$key = q/a_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.54ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img18.svg"
 ALT="$a_{bh}$">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img10.svg"
 ALT="$b$">|; 

$key = q/bigl|d{svectorx}(a)slashdabigr|equiv1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img57.svg"
 ALT="$\bigl \Vert d {\svector x}(a) / da \bigr \Vert \equiv 1$">|; 

$key = q/displaystyle1slashv({svectorx})equivBigl|{svector{nabla}}_{{svector{scriptstylex}}}T[{svectorx},{svectorx}']Bigr|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.66ex; vertical-align: -1.26ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\displaystyle 1/v( {\svector x}) \equiv \Bigl \Vert {\svector {\nabla}}_{{\svector {\scriptstyle x}}} T [ {\svector x}, {\svector x}' ] \Bigr \Vert
$">|; 

$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 STYLE="height: 5.24ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img62.svg"
 ALT="$\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/displaystyle=int_{a_0}^{a}da'~P[{svectorx}(a')];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.84ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img63.svg"
 ALT="$\displaystyle = \int_{a_0}^{a} da'
&nbsp; P [ {\svector x}(a') ]$">|; 

$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 STYLE="height: 5.24ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img60.svg"
 ALT="$\displaystyle = \int_{a_0}^{a} da'
&nbsp; { d \over {da'} } T [ {\svector x}( a' ) , {\svector x}( a_0 ) ]$">|; 

$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 STYLE="height: 5.24ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img61.svg"
 ALT="$\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/displaystyleDeltahat{svectorx}_{cbh}={Deltat_{ch}({svectorx}_{bh})over2P({svectorx}_{bh})cos(theta_{cbh}slash2)}~{svectorq}_{bh}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.66ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img96.svg"
 ALT="$\displaystyle \Delta \hat {\svector x}_{cbh} =
{ \Delta t_{ch} ({\svector x}_{b...
...er
2 P ({\svector x}_{bh} ) \cos ( \theta_{cbh} / 2 ) }&nbsp; {\svector q}_{bh} .
$">|; 

$key = q/displaystyleDeltat_{ch}({svectorx}_{bh})equivt_{ch}({svectorx}_{bh}+Delta{svectoos(theta_{cbh}slash2){svectorq}_{bh}cdotDelta{svectorx}_{bh}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img95.svg"
 ALT="$\displaystyle \Delta t_{ch} ({\svector x}_{bh}) \equiv
t_{ch} ({\svector x}_{b...
...) \cos ( \theta_{cbh} / 2 ) {\svector q}_{bh} \cdot \Delta
{\svector x}_{bh} .
$">|; 

$key = q/displaystyleP({svectorx})equivBigl|{svectorp}[{svectorx},{svectorx}']Bigr|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.66ex; vertical-align: -1.26ex; " SRC="|."$dir".q|img54.svg"
 ALT="$\displaystyle P ({\svector x}) \equiv \Bigl \Vert {\svector p}[ {\svector x}, {\svector x}' ] \Bigr \Vert
$">|; 

$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 STYLE="height: 4.81ex; vertical-align: -2.60ex; " SRC="|."$dir".q|img7.svg"
 ALT="$\displaystyle P({\svector x}) \equiv \sum_{i}&nbsp; P_{i}&nbsp; w^{-1}&nbsp; g [ ( {\svector x}- {\svector x}_i ) / w ] ,$">|; 

$key = q/displaystyleT[{svectorx},{svectorx}']=int_{{svector{scriptstylex}}'}^{{svector{sylex}}}{svectorp}[{svectorx}'',{svectorx}']cdotd{svectorx}'',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.65ex; vertical-align: -1.76ex; " SRC="|."$dir".q|img51.svg"
 ALT="$\displaystyle T[ {\svector x}, {\svector x}' ] =
\int_{{\svector {\scriptstyle ...
... x}}}
{\svector p}[ {\svector x}'' , {\svector x}' ] \cdot d {\svector x}'' ,
$">|; 

$key = q/displaystyleT_{bh}=int_{0}^{a_{bh}}P[{svectorx}_{bh}(a)]da.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.63ex; vertical-align: -1.76ex; " SRC="|."$dir".q|img15.svg"
 ALT="$\displaystyle T_{bh} = \int_{0}^{a_{bh}} P [ {\svector x}_{bh} (a) ] d a.
$">|; 

$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 STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img44.svg"
 ALT="$\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/displaystylee_{bh}=(t_{bh}-T_{bh})slashcos({theta}_{bh}slash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img21.svg"
 ALT="$\displaystyle e_{bh} = (t_{bh} - T_{bh} )/ \cos ({\theta}_{bh}/2) .
$">|; 

$key = q/displaystylee_{cbh}equiv{Deltat_{ch}({svectorx}_{bh})overcos(theta_{cbh}slash2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.66ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img97.svg"
 ALT="$\displaystyle e_{cbh} \equiv
{ \Delta t_{ch} ({\svector x}_{bh}) \over
\cos ( \theta_{cbh} / 2 ) } .
$">|; 

$key = q/displaystylehatm({{svectorx}_b})=sum_{s,r}intdt~dotu(t,{{svectorx}_s},{{svectorxsvectorx}_s})~R({{svectorx}_b},{{svectorx}_r})~mbox{gain}(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.53ex; vertical-align: -2.72ex; " SRC="|."$dir".q|img39.svg"
 ALT="$\displaystyle \hat m ( {{\svector x}_b} ) =
\sum_{s,r} \int dt&nbsp; \dot u (t, {{\...
...\svector x}_s} )&nbsp; R( {{\svector x}_b} , {{\svector x}_r} )&nbsp; \mbox{gain}(t)
.
$">|; 

$key = q/displaystylehatm_h({svectorx}_{b})approxf[({svectorx}_b-{svectorx}_{bh})cdot{svectorq}_{bh}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img72.svg"
 ALT="$\displaystyle \hat m_h ( {\svector x}_{b} ) \approx f [ ( {\svector x}_b - {\svector x}_{bh} ) \cdot {\svector q}_{bh} ]
$">|; 

$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 STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img9.svg"
 ALT="$\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/displaystylemax_{{svector{scriptstylex}}_c}~Bigl|[{svectorp}({svectorx}_{bh},{{s_{bh},{{svectorx}_c}+{{svectorx}_h})]cdot{svectorq}_{bh}Bigr|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.05ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img82.svg"
 ALT="$\displaystyle \max_{{\svector {\scriptstyle x}}_c}
&nbsp; \Bigl \Vert
[{\svector p}(...
... , {{\svector x}_c} + {{\svector x}_h} )]
\cdot {\svector q}_{bh}
\Bigr \Vert
$">|; 

$key = q/displaystylemax_{{svector{scriptstylex}}_{bh}}~Bigl|[{svectorp}({{svectorx}_c}-{}_c}+{{svectorx}_h},{svectorx}_{bh})]cdot{svectorp}_{ch}Bigr|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.13ex; vertical-align: -1.72ex; " SRC="|."$dir".q|img91.svg"
 ALT="$\displaystyle \max_{{\svector {\scriptstyle x}}_{bh}}
&nbsp; \Bigl \Vert
[ {\svecto...
... {{\svector x}_h} , {\svector x}_{bh} ) ]
\cdot {\svector p}_{ch}
\Bigr \Vert
$">|; 

$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 STYLE="height: 2.72ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img84.svg"
 ALT="$\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/displaystylemin_{P_{i}}=sum_{b}sum_{h}(e_{bh}-{1over{N_b}}sum_{h'}e_{bh'})^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.81ex; vertical-align: -2.67ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle \min_{P_{i}} = \sum_{b} \sum_{h} ( e_{bh} - {1 \over {N_b} }
\sum_{h'} e_{bh'} )^2 .
$">|; 

$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 STYLE="height: 4.86ex; vertical-align: -2.66ex; " SRC="|."$dir".q|img46.svg"
 ALT="$\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/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 STYLE="height: 5.23ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img43.svg"
 ALT="$\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/displaystylet_{ch}({svectorx}_{bh})=T({svectorx}_{bh},{{svectorx}_c}-{{svectorx}_h})+T({svectorx}_{bh},{{svectorx}_c}+{{svectorx}_h}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img86.svg"
 ALT="$\displaystyle t_{ch} ({\svector x}_{bh}) = T({\svector x}_{bh} , {{\svector x}_...
...vector x}_h} ) + T({\svector x}_{bh} , {{\svector x}_c} + {{\svector x}_h} ) .
$">|; 

$key = q/displaystyleu(t,{{svectorx}_s},{{svectorx}_r})=intd{svectorx}~m({svectorx})~delt},{{svectorx}_s})~R({svectorx},{{svectorx}_r})~mbox{gain}(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.48ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img37.svg"
 ALT="$\displaystyle u (t, {{\svector x}_s} , {{\svector x}_r} ) = \int d {\svector x}...
...}, {{\svector x}_s} )&nbsp; R( {\svector x}, {{\svector x}_r} )&nbsp; \mbox{gain}(t) .
$">|; 

$key = q/displaystyle{doverda}{svectorp}[{svectorx}(a),{svectorx}(a_0)]={svector{nabla}}_{{svector{scriptstylex}}}P[{svectorx}(a)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.95ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img66.svg"
 ALT="$\displaystyle {d \over da} {\svector p}[ {\svector x}(a) , {\svector x}(a_0) ] = {\svector {\nabla}}_{{\svector {\scriptstyle x}}} P [ {\svector x}(a) ]
.
$">|; 

$key = q/displaystyle{dover{da}}{svectorx}(a)equiv{svectorp}[{svectorx}(a),{svectorx}(a_0)]slashP[{svectorx}(a)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.95ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img58.svg"
 ALT="$\displaystyle {d \over {da}} {\svector x}(a) \equiv
{\svector p}[ {\svector x}(a) , {\svector x}( a_0 ) ] /
P [ {\svector x}(a) ] .
$">|; 

$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 STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img83.svg"
 ALT="$\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/displaystyle{svectorp}[{svectorx},{svectorx}']equiv{svector{nabla}}_{{svector{scriptstylex}}}T[{svectorx},{svectorx}'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img50.svg"
 ALT="$\displaystyle {\svector p}[ {\svector x}, {\svector x}' ] \equiv {\svector {\nabla}}_{{\svector {\scriptstyle x}}} T[ {\svector x}, {\svector x}' ]
$">|; 

$key = q/f(cdot);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img73.svg"
 ALT="$f(\cdot)$">|; 

$key = q/g({svectorx});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img4.svg"
 ALT="$g ({\svector x})$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img13.svg"
 ALT="$h$">|; 

$key = q/hatm_h({svectorx}_b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img47.svg"
 ALT="$\hat m_h ({\svector x}_b)$">|; 

$key = q/mbox{gain}(t)=t^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.61ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img38.svg"
 ALT="$\mbox{gain}(t) = t^2$">|; 

$key = q/nabla^2T=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img55.svg"
 ALT="$\nabla^2 T = 0$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img26.svg"
 ALT="$r$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img25.svg"
 ALT="$s$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.62ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img24.svg"
 ALT="$t$">|; 

$key = q/t_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.96ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img12.svg"
 ALT="$t_{bh}$">|; 

$key = q/t_{ch}({svectorx}_{bh});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img94.svg"
 ALT="$t_{ch} ({\svector x}_{bh})$">|; 

$key = q/t_{ch};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.96ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img88.svg"
 ALT="$t_{ch}$">|; 

$key = q/textstyleT[{svectorx}(a),{svectorx}(a_0)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img59.svg"
 ALT="$\textstyle T [ {\svector x}(a) , {\svector x}(a_0 ) ]$">|; 

$key = q/textstylehatm_h({{svectorx}_b})=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img42.svg"
 ALT="$\textstyle \hat m_h ( {{\svector x}_b} ) =$">|; 

$key = q/textstylehatu(t,{{svectorx}_c}-{{svectorx}_h},{{svectorx}_c}+{{svectorx}_h})=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img45.svg"
 ALT="$\textstyle \hat u (t, {{\svector x}_c} - {{\svector x}_h} , {{\svector x}_c} + {{\svector x}_h} ) =$">|; 

$key = q/textstylembox{where};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img8.svg"
 ALT="$\textstyle \mbox{ where }$">|; 

$key = q/theta_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.15ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img20.svg"
 ALT="$\theta_{bh}$">|; 

$key = q/theta_{cbh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.15ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img85.svg"
 ALT="$\theta_{cbh}$">|; 

$key = q/u(t,{{svectorx}_s},{{svectorx}_r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img23.svg"
 ALT="$u(t, {{\svector x}_s} , {{\svector x}_r} )$">|; 

$key = q/w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img6.svg"
 ALT="$w$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img28.svg"
 ALT="$z$">|; 

$key = q/z_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.54ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img69.svg"
 ALT="$z_{bh}$">|; 

$key = q/{svectorp}(a_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img65.svg"
 ALT="${\svector p}(a_0)$">|; 

$key = q/{svectorp}({svectorx}_{bh},{svectorx}_c+{{svectorx}_h});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img80.svg"
 ALT="${\svector p}( {\svector x}_{bh} , {\svector x}_c + {{\svector x}_h} )$">|; 

$key = q/{svectorp}({svectorx}_{bh},{svectorx}_c-{{svectorx}_h});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img81.svg"
 ALT="${\svector p}( {\svector x}_{bh} , {\svector x}_c - {{\svector x}_h} )$">|; 

$key = q/{svectorp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img49.svg"
 ALT="${\svector p}$">|; 

$key = q/{svectorp}_{ch}={svector{nabla}}_{{svector{scriptstylex}}_c}t_{ch};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img89.svg"
 ALT="${\svector p}_{ch} = {\svector {\nabla}}_{{\svector {\scriptstyle x}}_c} t_{ch} $">|; 

$key = q/{svectorq}_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.77ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img70.svg"
 ALT="${\svector q}_{bh}$">|; 

$key = q/{svectorq}_{bh}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img75.svg"
 ALT="${\svector q}_{bh}\}$">|; 

$key = q/{svectorx}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.89ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img36.svg"
 ALT="${\svector x}'$">|; 

$key = q/{svectorx}(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img56.svg"
 ALT="${\svector x}(a)$">|; 

$key = q/{svectorx}(a_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img64.svg"
 ALT="${\svector x}(a_0)$">|; 

$key = q/{svectorx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.22ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2.svg"
 ALT="${\svector x}$">|; 

$key = q/{svectorx}_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img76.svg"
 ALT="${\svector x}_b$">|; 

$key = q/{svectorx}_c=({svectorx}_r+{svectorx}_s)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img79.svg"
 ALT="${\svector x}_c = ({\svector x}_r + {\svector x}_s)/2$">|; 

$key = q/{svectorx}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img5.svg"
 ALT="${\svector x}_i$">|; 

$key = q/{svectorx}_{bh}(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img16.svg"
 ALT="${\svector x}_{bh} (a) $">|; 

$key = q/{svectorx}_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img77.svg"
 ALT="${\svector x}_{bh}$">|; 

$key = q/{svectorx}_{bh}=[x_b,y_b,z_{bh}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img67.svg"
 ALT="${\svector x}_{bh} = [x_b, y_b, z_{bh}]$">|; 

$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 STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img90.svg"
 ALT="${\svector {\nabla}}_{{\svector {\scriptstyle x}}_c} \equiv ({\svector {\nabla}}...
... {\scriptstyle x}}_s} + {\svector {\nabla}}_{{\svector {\scriptstyle x}}_r})/2 $">|; 

$key = q/{svector{nabla}}times{svectorp}={svector0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img52.svg"
 ALT="${\svector {\nabla}}\times {\svector p}= {\svector 0}$">|; 

$key = q/{t_{ch},{svectorp}_{ch}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img92.svg"
 ALT="$\{t_{ch},{\svector p}_{ch}\}$">|; 

$key = q/{{svectorx}_c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img87.svg"
 ALT="${{\svector x}_c} $">|; 

$key = q/{{svectorx}_c}equiv({{svectorx}_r}+{{svectorx}_s})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img40.svg"
 ALT="${{\svector x}_c} \equiv ( {{\svector x}_r} + {{\svector x}_s} )/2$">|; 

$key = q/{{svectorx}_h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img48.svg"
 ALT="${{\svector x}_h} $">|; 

$key = q/{{svectorx}_h}=({svectorx}_r-{svectorx}_s)slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img78.svg"
 ALT="${{\svector x}_h} = ({\svector x}_r - {\svector x}_s)/2$">|; 

$key = q/{{svectorx}_h}equiv({{svectorx}_r}-{{svectorx}_s})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img41.svg"
 ALT="${{\svector x}_h} \equiv ({{\svector x}_r} - {{\svector x}_s} )/2 $">|; 

$key = q/{{svectorx}_r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img30.svg"
 ALT="${{\svector x}_r} $">|; 

$key = q/{{svectorx}_s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img29.svg"
 ALT="${{\svector x}_s} $">|; 

$key = q/{{svectorx}_{bh},{svectorq}_{bh}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img93.svg"
 ALT="$\{{\svector x}_{bh}, {\svector q}_{bh}\}$">|; 

$key = q/{{svectorx}_{bh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img74.svg"
 ALT="$\{{\svector x}_{bh}$">|; 

$key = q/|{svectorq}_{bh}|equiv1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img71.svg"
 ALT="$\Vert {\svector q}_{bh} \Vert \equiv 1$">|; 

1;

