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\begin{document}
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\onecolumn

% !!! IMAGES START HERE !!!

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline145}%
$d(\svector{x}_i,\svector{x}^k,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline147}%
$t$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline149}%
$\svector{x}_i$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline151}%
$\svector{x}^k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline153}%
$\| \svector{x}_i - \svector{x}^k \|$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline155}%
$\| \svector{x}_i + \svector{x}^k \|/2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline157}%
$\Delta t_i$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline159}%
$\Delta t^k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay227}%
$\displaystyle
d(\svector{x}_i,\svector{x}^k,t)  \approx d(t - \Delta t_i - \Delta t^k ) 
~~\mbox{for}~~t_1 < t < t_2.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline161}%
$c_{ij}^{kl}(\tau)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay230}%
$\displaystyle c_{ij}^{kl}(\tau) \equiv  
c_{ji}^{lk}(-\tau) \equiv
\int_{t_1}^{t_2} 
d(\svector{x}_i,\svector{x}^k,t-\tau) ~
d(\svector{x}_j,\svector{x}^l,t) ~ d t  .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay232}%
$\displaystyle
\| \svector{x}_i - \svector{x}_j \| < x_{\max} ~,~
\| \svector{x}^k - \svector{x}^l \| < x^{\max} ~~ \mbox{and} ~~
\| (\svector{x}_i + \svector{x}^k)/2 -(\svector{x}_j + \svector{x}^l)/2 \| 
< x^{\raisebox{-4pt}{$\scriptstyle \max$}}~ .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay234}%
$\displaystyle \mbox{the lags} ~~ 
\tau_{ij}^{kl} \approx \Delta t_i - \Delta t_j + \Delta t^k - \Delta t^l
~~\mbox{will maximize}~~
c_{ij}^{kl}(\tau_{ij}^{kl}) .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline165}%
$\tau_{ij}^{kl}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay237}%
$\displaystyle \mbox{find}~ 
\Delta t_i ~\mbox{and}~ \Delta t^k 
~\mbox{to minimize}~
\sum_{ijkl} ( \tau_{ij}^{kl} - 
\Delta t_i + \Delta t_j - \Delta t^k + \Delta t^l )^2 .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay239}%
$\displaystyle
C_i^k (\tau) \equiv \sum_{jl} c_{ij}^{kl}(\tau) .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay241}%
$\displaystyle
C_i (\tau) \equiv \sum_{jkl} c_{ij}^{kl}(\tau) ~ ~\mbox{and} ~~
C^k (\tau) \equiv \sum_{ijl} c_{ij}^{kl}(\tau) 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay243}%
$\displaystyle
C_{ij} (\tau) \equiv \sum_{kl} c_{ij}^{kl}(\tau) ~ ~\mbox{and} ~~
C^{kl} (\tau) \equiv \sum_{ij} c_{ij}^{kl}(\tau) .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline167}%
$| \tau | < \tau_{\max}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay246}%
$\displaystyle \{ \tau_i^k , \tau_i , \tau^k , \tau_{ij} , \tau^{kl} \} 
~\mbox{maximize}~
 C_i^k (\tau_i^k ), C_i(\tau_i) , ~ C^k(\tau^k) , ~ C_{ij} (\tau_{ij}) , 
~\mbox{and} ~
 C^{kl} (\tau^{kl}) .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay250}%
$\displaystyle \min_{\Delta t_i \Delta t^k } ~~
\sum_{i,k} ( \tau_i^k - \Delta t_i - \Delta t^k )^2 +
\sum_i ( \tau_i - \Delta t_i )^2 +
\sum_k ( \tau^k - \Delta t^k )^2 +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay251}%
$\displaystyle \sum_{i,j} ( \tau_{ij} - \Delta t_i + \Delta t_j )^2 +
\sum_{k,l} ( \tau^{kl} - \Delta t^k + \Delta t^l )^2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay253}%
$\displaystyle \max_{\Delta t_i \Delta t^k }
\left [
C_i^k( \Delta t_i + \Delta t^k ) +
C_i( \Delta t_i ) +
C^k( \Delta t^k ) +
C_{ij}( \Delta t_i + \Delta t_j ) +
C^{kl}( \Delta t^k + \Delta t^l )
\right ]
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay255}%
$\displaystyle d(\svector{x}_i,\svector{x}^k,t )
\Leftarrow  d(\svector{x}_i,\svector{x}^k,t  - \Delta t_i - \Delta t^k ) .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay257}%
$\displaystyle c_{ij}^{kl}(\tau ) \Leftarrow 
c_{ij}^{kl}(\tau - \Delta t_i + \Delta t_j 
- \Delta t^k + \Delta t^l ) .
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}


\end{document}
