# LaTeX2HTML
# Associate images original text with physical files.


$key = q/varphi;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img3.png"
 ALT="$\varphi$">|; 

$key = q/U;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img75.png"
 ALT="$U$">|; 

$key = q/0.2;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img69.png"
 ALT="$0.2$">|; 

$key = q/g;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img11.png"
 ALT="$g$">|; 

$key = q/phi_{j}(t);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img47.png"
 ALT="$\phi_{j}(t)$">|; 

$key = q/t;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img5.png"
 ALT="$t$">|; 

$key = q/{displaymath}left{eqalign{varphi_1&=eta_1crvarphi_2&=eta_2crvarphi_3&=eta_3}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img63.png"
 ALT="\begin{displaymath}\left\{\eqalign{
\varphi _1 &amp;= \eta _1\cr
\varphi _2 &amp;= \eta _2\cr
\varphi _3 &amp;= \eta _3
}\right.\end{displaymath}">|; 

$key = q/R;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img60.png"
 ALT="$R$">|; 

$key = q/10^{-3};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img24.png"
 ALT="$10^{-3}$">|; 

$key = q/eta_i(t=0);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img48.png"
 ALT="$\eta_i(t=0)$">|; 

$key = q/{displaymath}partial_{varphi}g(eta(t),varphi(t));{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img26.png"
 ALT="\begin{displaymath}\partial_{\varphi} g(\eta(t),\varphi(t));
\end{displaymath}">|; 

$key = q/r_k;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img35.png"
 ALT="$r_k$">|; 

$key = q/2;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img68.png"
 ALT="$2$">|; 

$key = q/{displaymath}eqalign{partial_xf^g&=gf^{g-1}partial_xf+f^glogfpartial_xgcr&=f^{g-1}(gpartial_xf+fpartial_xg)cr}{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img39.png"
 ALT="\begin{displaymath}\eqalign{\partial_x f^g &amp;= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&amp;= f^{g-1}(g\partial_x f + f\partial_x g)\cr}\end{displaymath}">|; 

$key = q/k;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img30.png"
 ALT="$k$">|; 

$key = q/eta_{prey};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img19.png"
 ALT="$\eta_{prey}$">|; 

$key = q/eta_{pred};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img20.png"
 ALT="$\eta_{pred}$">|; 

$key = q/xslashDelta;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img40.png"
 ALT="$x/\Delta$">|; 

$key = q/psi;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img53.png"
 ALT="$\psi$">|; 

$key = q/{displaymath}partial_{eta}g(eta(t),varphi(t));{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img25.png"
 ALT="\begin{displaymath}\partial_{\eta} g(\eta(t),\varphi(t));
\end{displaymath}">|; 

$key = q/Q;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img58.png"
 ALT="$Q$">|; 

$key = q/{displaymath}left{eqalign{omega_1&=varphi_1+nu_1cromega_2&=eta_2+nu_2cromega_3&=eta_3+nu_3}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img64.png"
 ALT="\begin{displaymath}\left\{\eqalign{
\omega _1 &amp;= \varphi _1 + \nu_1\cr
\omega _2 &amp;= \eta _2 + \nu_2 \cr
\omega _3 &amp;= \eta _3 + \nu_3
}\right.\end{displaymath}">|; 

$key = q/{displaymath}left{eqalign{partial_teta_{k}^{pos}&=eta_{k}^{vel}crpartial_teta_{k+varphi_{k}^{dmp}-varphi_{k+1}^{dmp}),slashm_kcr}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img31.png"
 ALT="\begin{displaymath}\left\{\eqalign{\partial_t \eta _{k} ^{pos} &amp;= \eta _{k} ^{ve...
... + \varphi _{k} ^{dmp}-\varphi _{k+1} ^{dmp}) /m_k \cr}\right.\end{displaymath}">|; 

$key = q/{displaymath}left{eqalign{varphi_k^{spr}&=-k_k(eta_{k}^{pos}-eta_{k-1}^{pos})crvi_k^{spr}&=-d_k(eta_{k}^{vel}-eta_{k-1}^{vel})cr}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img32.png"
 ALT="\begin{displaymath}\left\{\eqalign{
\varphi_k ^{spr} &amp;= -k_k (\eta _{k} ^{pos}- ...
...spr} &amp;= -d_k (\eta _{k} ^{vel}- \eta _{k-1} ^{vel})
\cr}\right.\end{displaymath}">|; 

$key = q/{displaymath}eqalign{partial_teta(t)&=g(eta(t),varphi(t))crvarphi(t)&=f(eta(t),varphi(t))cr}{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img13.png"
 ALT="\begin{displaymath}\eqalign{\partial_t \eta (t) &amp;= g(\eta(t),\varphi(t))\cr
\varphi(t) &amp;= f(\eta(t),\varphi(t))\cr
}\end{displaymath}">|; 

$key = q/{displaymath}left{eqalign{partial_teta_{prey}&=aeta_{prey}-avarphi_{meet}crpartial_teta_{pred}&=-ceta_{pred}+cvarphi_{meet}cr}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img14.png"
 ALT="\begin{displaymath}\left\{\eqalign{\partial_t \eta _{prey} &amp;= a \eta _{prey} - a...
... \eta _{pred} &amp;= -c \eta _{pred} + c \varphi _{meet}\cr}\right.\end{displaymath}">|; 

$key = q/mu;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img57.png"
 ALT="$\mu$">|; 

$key = q/A_{st}+A_{st}^dagger;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img73.png"
 ALT="$A_{st} + A_{st}^\dagger$">|; 

$key = q/t=s_i;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img56.png"
 ALT="$t=s_i$">|; 

$key = q/l;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img54.png"
 ALT="$l$">|; 

$key = q/{displaymath}varphi(t)=f(eta(t),varphi(t)){displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img4.png"
 ALT="\begin{displaymath}
\varphi(t) = f(\eta(t),\varphi(t))
\end{displaymath}">|; 

$key = q/{displaymath}partial_teta(t)=g(eta(t),varphi(t)){displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img1.png"
 ALT="\begin{displaymath}\partial_t \eta (t) = g(\eta(t),\varphi(t))\end{displaymath}">|; 

$key = q/varphi=f(eta(t-dt)+dvarphi;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img21.png"
 ALT="$\varphi=f(\eta(t-dt)+d\varphi$">|; 

$key = q/d_k;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img36.png"
 ALT="$d_k$">|; 

$key = q/h(t);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img49.png"
 ALT="$h(t)$">|; 

$key = q/tau;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img66.png"
 ALT="$\tau$">|; 

$key = q/V;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img77.png"
 ALT="$V$">|; 

$key = q/eta_1(t=0);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img45.png"
 ALT="$\eta_1(t=0)$">|; 

$key = q/nu;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img59.png"
 ALT="$\nu$">|; 

$key = q/h;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img42.png"
 ALT="$h$">|; 

$key = q/T;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img51.png"
 ALT="$T$">|; 

$key = q/{displaymath}J=psi[eta(T),varphi(T),h(T)]+int_0^T{l[eta(tau),varphi(tau),h(tau)]},dtau{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img52.png"
 ALT="\begin{displaymath}
J = \psi[\eta(T),\varphi(T) ,h(T)] + \int_0 ^T {l[\eta(\tau),\varphi(\tau),h(\tau)]}  d\tau
\end{displaymath}">|; 

$key = q/g(tau;t);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img67.png"
 ALT="$g(\tau;t)$">|; 

$key = q/Phi(t+deltat,t)=exp{A_{st}deltat};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img78.png"
 ALT="$\Phi(t+\delta t,t)=\exp{A_{st} \delta t}$">|; 

$key = q/omega;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img41.png"
 ALT="$\omega$">|; 

$key = q/eta;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img2.png"
 ALT="$\eta$">|; 

$key = q/{displaymath}pmatrix{A&Bcr-C^+&I-Dcr}pmatrix{deltaetacrdeltavarphicr}=pmatrix{GammacrOmegacr}{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img9.png"
 ALT="\begin{displaymath}\pmatrix{A &amp; B\cr
-C^+ &amp; I-D\cr} \pmatrix{\delta \eta\cr
\delta \varphi\cr} = \pmatrix{\Gamma\cr
\Omega\cr}\end{displaymath}">|; 

$key = q/g(tau);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img65.png"
 ALT="$g(\tau)$">|; 

$key = q/N+1;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img38.png"
 ALT="$N+1$">|; 

$key = q/g(t,tau);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img71.png"
 ALT="$g(t,\tau)$">|; 

$key = q/{displaymath}left{eqalign{partial_teta_1&=a_{11}eta_1+a_{12}varphi_2+a_{13}varpha_{32}varphi_2+a_{33}eta_3+W_{31}mu_1+W_{32}mu_2}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img62.png"
 ALT="\begin{displaymath}\left\{\eqalign{
\partial_t \eta_1 &amp;= a_{11} \eta_1 + a_{12} ...
...varphi_2 + a_{33} \eta_3 + W_{31} \mu_1 + W_{32} \mu_2
}\right.\end{displaymath}">|; 

$key = q/N;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img37.png"
 ALT="$N$">|; 

$key = q/deltavarphi;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img8.png"
 ALT="$\delta \varphi$">|; 

$key = q/t+deltat;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img6.png"
 ALT="$t + \delta t$">|; 

$key = q/J;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img50.png"
 ALT="$J$">|; 

$key = q/W;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img61.png"
 ALT="$W$">|; 

$key = q/Phi(t,0);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img80.png"
 ALT="$\Phi(t,0)$">|; 

$key = q/c;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img17.png"
 ALT="$c$">|; 

$key = q/{displaymath}varphi_{meet}=eta_{prey}eta_{pred}{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img15.png"
 ALT="\begin{displaymath}\varphi _{meet} = \eta _{prey}\eta _{pred}\end{displaymath}">|; 

$key = q/{displaymath}left{eqalign{eta^{pos}_{0}&=0creta^{vel}_{0}&=0crvarphi^{spr}_{N+1}&=0crvarphi^{dmp}_{N+1}&=0cr}right.{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img33.png"
 ALT="\begin{displaymath}\left\{\eqalign{\eta ^{pos}_{0} &amp;= 0\cr
\eta ^{vel}_{0} &amp;= 0\...
...arphi ^{spr}_{N+1} &amp;= 0\cr
\varphi ^{dmp}_{N+1} &amp;= 0\cr}\right.\end{displaymath}">|; 

$key = q/(I-D);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img29.png"
 ALT="$(I-D)$">|; 

$key = q/w;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img76.png"
 ALT="$w$">|; 

$key = q/a;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img16.png"
 ALT="$a$">|; 

$key = q/{displaymath}UwV^dagger{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="22" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img74.png"
 ALT="\begin{displaymath}
U w V^\dagger
\end{displaymath}">|; 

$key = q/A_{st};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img72.png"
 ALT="$A_{st}$">|; 

$key = q/deltaeta;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img7.png"
 ALT="$\delta \eta$">|; 

$key = q/dvarphi;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img22.png"
 ALT="$d\varphi$">|; 

$key = q/{displaymath}eqalign{partial_teta(t)&=g(eta(t),varphi(t))+W(t)mucrvarphi(t)&=f(eta(t),varphi(t))cromega(t)&=h(eta(t),varphi(t))+nucr}{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img55.png"
 ALT="\begin{displaymath}\eqalign{
\partial_t \eta (t) &amp;= g(\eta(t),\varphi(t)) + W(t)...
...varphi(t))\cr
\omega(t) &amp;= h ( \eta(t) , \varphi(t)) + \nu\cr
}\end{displaymath}">|; 

$key = q/eta_1(t);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img44.png"
 ALT="$\eta_1(t)$">|; 

$key = q/deltat;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img12.png"
 ALT="$\delta t$">|; 

$key = q/t=0;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="12" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img46.png"
 ALT="$t=0$">|; 

$key = q/varphi=f(eta),varphi);MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img23.png"
 ALT="$\varphi=f(\eta),\varphi)$">|; 

$key = q/sqrt{sqrt{2}};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img70.png"
 ALT="$\sqrt{\sqrt{2}}$">|; 

$key = q/f;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img10.png"
 ALT="$f$">|; 

$key = q/varphi_{meet};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img18.png"
 ALT="$\varphi_{meet}$">|; 

$key = q/{displaymath}omega=h(eta,varphi){displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img43.png"
 ALT="\begin{displaymath}
\omega = h ( \eta , \varphi)
\end{displaymath}">|; 

$key = q/{displaymath}partial_{eta}f(eta(t),varphi(t));{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img27.png"
 ALT="\begin{displaymath}\partial_{\eta} f(\eta(t),\varphi(t));
\end{displaymath}">|; 

$key = q/m_k;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img34.png"
 ALT="$m_k$">|; 

$key = q/{displaymath}partial_{varphi}f(eta(t),varphi(t));{displaymath};MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img28.png"
 ALT="\begin{displaymath}\partial_{\varphi} f(\eta(t),\varphi(t));
\end{displaymath}">|; 

$key = q/Phi;MSF=1.5;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|mini_ker_l2h_img79.png"
 ALT="$\Phi$">|; 

1;

