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


$key = q/L^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$L^2$">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$u$">|; 

$key = q/displaystyleG(v,b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle G ( v, b)$">|; 

$key = q/{displaymath}G(v,b)approxleft|{dtoverdtau}(b)right|^{-1}~Fleft{u=vcdotleft[{dtoverdtau}(b)right]^{-1},~a=t(b)right}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="\begin{displaymath}
G(v,b) \approx
\left \vert {dt \over d\tau} ( b ) \right \v...
... {dt \over d\tau} ( b ) \right ]^{-1} ,&nbsp; a = t(b) \right \} .
\end{displaymath}">|; 

$key = q/displaystylet(tau_0)+(tau-tau_0)cdot{dtoverdtau}(tau_0)~~~~{{rm{and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle t(\tau_0 ) + (\tau - \tau_0 )
\cdot {dt \over d\tau} ( \tau_0 )&nbsp;&nbsp;&nbsp;&nbsp;{\rm and }$">|; 

$key = q/srightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$s \rightarrow 0$">|; 

$key = q/(s,u);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$(s,u)$">|; 

$key = q/displaystyleleft{int{1over|u'|}tildew(u')du'right}cdotleft{inte^{i2pis't}ds'right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \left \{ \int {1 \over \vert u'\vert} \tilde w ( u' ) du' \right \} \cdot
\left \{ \int e^{i 2 \pi s' t } ds' \right \}$">|; 

$key = q/{displaymath}F(u,a)=intw[u(a-t)]f(t)dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="\begin{displaymath}
F(u,a) = \int w[u(a - t)] f(t) dt .
\end{displaymath}">|; 

$key = q/g(tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$g(\tau)$">|; 

$key = q/displaystyleb+[t'-t(b)]cdotleft[{dtoverdtau}(b)right]^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle b + [ t' - t(b) ]
\cdot \left [ {dt \over d\tau} ( b ) \right ]^{-1} .$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$a$">|; 

$key = q/displaystylet';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle t'$">|; 

$key = q/displaystyleC_w^{-1}intC_wdelta(t-t')f(t')dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle C_w^{-1} \int C_w \delta(t-t') f(t') dt'$">|; 

$key = q/{displaymath}g(tau)=f[t(tau)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="\begin{displaymath}
g(\tau) = f[t(\tau)].
\end{displaymath}">|; 

$key = q/{displaymath}C_w=int{1over|s|}tildew(s)ds.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{displaymath}
C_w = \int { 1 \over \vert s\vert } \tilde w (s) ds .
\end{displaymath}">|; 

$key = q/displaystyleintintleft|{u'overs'}right|tildew(u')e^{i2pis't}left|{s'overu'^2}right|ds'du';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle \int \int \left \vert {u' \over s'} \right \vert \tilde w ( u' ) e^{i 2 \pi s' t }
\left \vert { s' \over u'^2 } \right \vert ds' du'$">|; 

$key = q/displaystyleinte^{i2pist}tildew(s)ds.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\displaystyle \int e^{i 2 \pi s t } \tilde w (s) ds .$">|; 

$key = q/w(t)={{rm{cos}(2pit)(e^{-pit^2slashc^2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$w(t) = {\rm cos}(2\pi t) (e^{- \pi t^2 / c^2} )$">|; 

$key = q/displaystyle{{bf{Proof:~}G(v,b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle {\bf Proof:&nbsp;}
G ( v, b)$">|; 

$key = q/displaystylet(tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle t(\tau)$">|; 

$key = q/partial(s,u)slashpartial(s',u')=|s'slashu'^2|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\partial (s,u) / \partial (s',u') = \vert s'/u'^2\vert$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\textstyle =$">|; 

$key = q/tildew(s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\tilde w (s)$">|; 

$key = q/displaystyleinte^{-i2pist}w(t)dt{{rm{~and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle \int e^{-i 2 \pi s t } w(t) dt {\rm&nbsp;and}$">|; 

$key = q/displaystylew(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle w(t)$">|; 

$key = q/u^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$u^{-1}$">|; 

$key = q/G(v,b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$G(v, b)$">|; 

$key = q/displaystyleintw(ut)du;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle \int w(ut) du$">|; 

$key = q/F(u,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$F(u,a)$">|; 

$key = q/textstyleapprox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\textstyle \approx$">|; 

$key = q/displaystyleC_wcdotdelta(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle C_w \cdot \delta (t) .$">|; 

$key = q/textstyleequiv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\textstyle \equiv$">|; 

$key = q/{displaymath}G(v,b)=intw[v(b-tau)]g(tau)dtau~~~~{{rm{and}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{displaymath}
G(v, b ) = \int w [ v ( b - \tau ) ] g (\tau) d\tau&nbsp;&nbsp;&nbsp;&nbsp; {\rm and}
\end{displaymath}">|; 

$key = q/displaystyletildew(s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\displaystyle \tilde w (s)$">|; 

$key = q/displaystyleleft|{dtoverdtau}(b)right|^{-1}intwleft{vleft[{dtoverdtau}(b)right]^{-1}cdot[t(b)-t']right}cdotf(t')dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="77" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle \left \vert {dt \over d\tau} ( b ) \right \vert^{-1}
\int w \left...
...t \over d\tau} ( b ) \right ]^{-1}
\cdot [t(b) - t']
\right \} \cdot f(t') d t'$">|; 

$key = q/{displaymath}{{bf{Proof:~}intw(ut)du=intleft{int{1over|u|}tildew({soveru})e^{i2pist}dsright}duldots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="\begin{displaymath}
{\bf Proof:&nbsp;} \int w(ut) du
= \int \left \{ \int {1 \over \...
...e w ( { s \over u } )
e^{i 2 \pi s t } ds \right \} du \ldots
\end{displaymath}">|; 

$key = q/2^u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$2^u$">|; 

$key = q/{displaymath}w(t)=w(-t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="\begin{displaymath}
w(t) = w(-t) .
\end{displaymath}">|; 

$key = q/displaystyleintwleft{vcdot[t(b)-t']cdotleft[{dtoverdtau}(b)right]^{-1}right}cdotf(t')cdotleft|{dtoverdtau}(b)right|^{-1}~dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="434" HEIGHT="77" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle \int w \left \{ v \cdot [t(b) - t'] \cdot
\left [ {dt \over d\tau...
...\} \cdot f(t')
\cdot \left \vert {dt \over d\tau} ( b ) \right \vert^{-1}&nbsp; dt'$">|; 

$key = q/displaystyleintw[v(b-tau)]cdotfleft[t(b)+(tau-b)cdot{dtoverdtau}(b)right]dtauldots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \int w [ v(b-\tau)] \cdot f \left [ t(b) + (\tau-b)
\cdot {dt \over d\tau} ( b ) \right ] d\tau \ldots$">|; 

$key = q/displaystylet(b)+(tau-b)cdot{dtoverdtau}(b)~~~~{{rm{and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle t(b) + (\tau-b) \cdot {dt \over d\tau} ( b )
&nbsp;&nbsp;&nbsp;&nbsp; {\rm and}$">|; 

$key = q/(s'=s,u'=sslashu);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$(s'=s,u'=s/u)$">|; 

$key = q/{displaymath}f(t)=C_w^{-1}intF(u,a=t)du.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="\begin{displaymath}
f(t) = C_w^{-1} \int F(u, a=t) du .
\end{displaymath}">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$c$">|; 

$key = q/tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\tau$">|; 

$key = q/displaystyleintint{1over|u'|}tildew(u')e^{i2pis't}ds'du';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle \int \int {1 \over \vert u'\vert} \tilde w ( u' ) e^{i 2 \pi s' t } ds' du'$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$t$">|; 

$key = q/displaystyleleft|{dtoverdtau}(b)right|^{-1}~Fleft{u=vcdotleft[{dtoverdtau}(b)right]^{-1},~a=t(b)right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="77" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \left \vert {dt \over d\tau} ( b ) \right \vert^{-1}
&nbsp; F \left \{ u=v \cdot
\left [ {dt \over d\tau} ( b ) \right ]^{-1} ,&nbsp; a = t(b) \right \} .$">|; 

$key = q/displaystyle{{bf{Proof:~}C_w^{-1}intF(u,a=t)du;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle {\bf Proof:&nbsp;}
C_w^{-1} \int F(u,a=t) du$">|; 

$key = q/displaystylef(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle f(t).$">|; 

$key = q/displaystyletau_0+[t-t(tau_0)]cdotleft[{dtoverdtau}(tau_0)right]^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \tau_0 + [ t - t (\tau_0 ) ]
\cdot \left [ {dt \over d\tau} ( \tau_0 ) \right ]^{-1} .$">|; 

$key = q/t(tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$t(\tau)$">|; 

$key = q/displaystyleC_w^{-1}intleft{intw[u(t-t')]duright}f(t')dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle C_w^{-1} \int \left \{ \int w[u(t - t' )] du \right \} f(t') dt'$">|; 

$key = q/{displaymath}intw(ut)du=C_wcdotdelta(t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\begin{displaymath}
\int w(ut) du = C_w \cdot \delta (t) .
\end{displaymath}">|; 

$key = q/displaystyleintw[v(b-tau)]cdotf[t(tau)]dtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \int w[v(b-\tau)] \cdot f[t(\tau)] d \tau$">|; 

$key = q/f(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$f(t)$">|; 

$key = q/displaystyleC_w^{-1}intleft{intw[u(t-t')]f(t')dt'right}du;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle C_w^{-1} \int \left \{ \int w[u(t - t' )] f(t') dt' \right \} du$">|; 

$key = q/w(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$w(t)$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$t=0$">|; 

$key = q/rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\rightarrow 0 $">|; 

$key = q/displaystyletau(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle \tau(t)$">|; 

$key = q/epsilon>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\epsilon &gt; 0 $">|; 

$key = q/tildew(s)slash|s|^epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\tilde w (s) / \vert s\vert^\epsilon $">|; 

$key = q/displaystyletau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle \tau$">|; 

$key = q/{displaymath}g(tau)=C_w^{-1}intG(v,b=tau)dv.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="\begin{displaymath}
g(\tau) = C_w^{-1} \int G(v, b = \tau ) dv.
\end{displaymath}">|; 

1;