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\usepackage{epsfig}


\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[]{inputenc}



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\providecommand{\selectlanguage}[1]{}%
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% !!! IMAGES START HERE !!!

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$x_i$%
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{\newpage\clearpage
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$i$%
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{\newpage\clearpage
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$y_i=c_i x_i$%
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{\newpage\clearpage
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$c_i=1+\alpha_i$%
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{\newpage\clearpage
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$\alpha_i>0$%
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$p_i=1-q_i$%
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{\newpage\clearpage
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$q_i$%
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{\newpage\clearpage
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$u(y)$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$y$%
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{\newpage\clearpage
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$U(x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline341}%
$x=(x_i,...,x_n), \ \sum_i=1,\ x_i \ge 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1298}%
$\displaystyle U(x)={\bf E} u(y) = \int_0^{\infty} u(y) p(y) dy.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline345}%
$p(y)$%
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{\newpage\clearpage
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$y=y^k,\ k=1,...,M$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1303}%
$\displaystyle U(x)=\sum_{k=1}^M u(y^k) p(y^k).$%
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{\newpage\clearpage
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$M$%
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{\newpage\clearpage
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$y^k$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline355}%
$p_x(y^k)$%
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{\newpage\clearpage
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$x$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1311}%
$\displaystyle \max_x U(x),$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1312}%
$\displaystyle \sum_{i=1}^n  x_i = 1,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1313}%
$\displaystyle x_i \ge 0.$%
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\stepcounter{section}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline363}%
$p(y^j)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline365}%
$y^j,\ j=1,2,....$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1319}%
$\displaystyle p(y^0)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1320}%
$\textstyle =$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1321}%
$\displaystyle \prod_{i} q_i,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1322}%
$\displaystyle p(y^1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1324}%
$\displaystyle p_1 \prod_{i \ne 1} q_i,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1325}%
$\displaystyle p(y^2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1327}%
$\displaystyle p_2
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1328}%
$\displaystyle .............$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1329}%
$\displaystyle ...................................$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1330}%
$\displaystyle p(y^n)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1332}%
$\displaystyle p_n
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1333}%
$\displaystyle p(y^{n+1})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1335}%
$\displaystyle p_1 p_2 \prod_{i
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1336}%
$\displaystyle p(y^{n+2})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1338}%
$\displaystyle p_1 p_3 \prod_{i
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1340}%
$\displaystyle ..................................................$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline367}%
$y^0=0,\ y^1=a_1 x_1,\ y^2=a_2 x_2,\ y^n= a_n x_n,\\y^{n+1}=a_1 x_1+a_2 x_2,\ y^{n+2}=a_1 x_1 + a_3 x_3$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1348}%
$\displaystyle U_K(x)= 1/K \sum_{k=1}^K u(y^k).$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1350}%
$\displaystyle y^k= \sum_{i=1}^n y_i^k ,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1352}%
$\displaystyle y_i^k=
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\begin{array}{ll}
c_i x_i, & \mbox{if $\eta_i^k \in [0,p_i]$} \\
0, & \mbox{otherwise}
\end{array}
\right.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline377}%
$K$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$\eta_i^k $%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1356}%
$\displaystyle U(x)= \lim_{K \to \infty} U_K(x).$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline381}%
$\alpha_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline383}%
$p_i,\ i=1,...,n$%
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{\newpage\clearpage
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$p_i,\  i=n+j, \ j=1,...,m$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline387}%
$a_i$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline389}%
$L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline391}%
$a_i^l,\ l=1,...,L$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline393}%
$p_i^l,\  \sum_{l=1}^L  p_i^l=1,\  p_i^l  \ge  0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline395}%
$p(y^i)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline397}%
$y^i,\ i=1,...,n+m$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline399}%
$n=0$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline401}%
$L=2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1375}%
$\displaystyle p_1 p_1^1 \prod_{i \ne 1} q_i,$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1378}%
$\displaystyle p_1 p_1^2 \prod_{i \ne 1} q_i,$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1379}%
$\displaystyle p(y^3)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1381}%
$\displaystyle p_2 p_2^1 \prod_{i \ne 2} q_i,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1382}%
$\displaystyle p(y^4)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1384}%
$\displaystyle p_2 p_2^2 \prod_{i \ne 2} q_i,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1387}%
$\displaystyle p(y^{2n-1})$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1389}%
$\displaystyle p_n p_n^1 \prod_{i \ne n} q_i ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1390}%
$\displaystyle p(y^{2n})$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1392}%
$\displaystyle p_n p_n^2 \prod_{i \ne n} q_i ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1393}%
$\displaystyle p(y^{2n+1})$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1395}%
$\displaystyle p_1 p_1^1 p_2 p_2^1 \prod_{i
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1396}%
$\displaystyle p(y^{2n+2})$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1398}%
$\displaystyle p_1 p_1^2 p_2^p2^2 \prod_{i
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline403}%
$y^0=0,\  y^1=a_1^1  x_1,\  y^2=a_1^2  x_1,\ 
y^3=a_2^1 x_2, y^4=a_2^2 x_2,\\
\ y^{2n-1}= a_n^1 x_n,
\ y^{2n}= a_n^2 x_n,
\ y^{2n+1}=a_1^1 x_1+a_2^1 x_2,
\ y^{2n+2}=a_1^2 x_1+a_2^2 x_2$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline405}%
$p_i$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline407}%
$a_i^l$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline409}%
$p_i^l$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline411}%
$n=m=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline415}%
$p(y^k)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline417}%
$y^k,\ k=0,...,5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1412}%
$\displaystyle q_1  q_2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1415}%
$\displaystyle p_1  q_2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1418}%
$\displaystyle p_2 p_2^1 q_1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1421}%
$\displaystyle p_2 p_2^2 q_1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1424}%
$\displaystyle p_2 p_2^1  p_1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1425}%
$\displaystyle p(y^5)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1427}%
$\displaystyle p_2 p_2^2  p_1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline419}%
$y^0=0,\ y_1= a_1 x_1\  y^2=a_2^1  x_2,\  y^3=a_2^2 x_2, \\
y^4=a_1 x_1+ a_2^1 x_2,\  y^5=a_1 x_1+ a_2^2 x_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1432}%
$\displaystyle u(y)= c y.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline423}%
$p_ic_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1435}%
$\displaystyle u(y)=
\left\{
\begin{array}{ll}
0  & \mbox{if $0 \le y < a$} \\
1 & \mbox{if $a \le y \le c$}
\end{array}.
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline429}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline431}%
$c=\max_i c_i x_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline433}%
$a= 1/m\ min_i\   c_i x_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline435}%
$x_i^*=1/m,\ i=1,...,m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline437}%
$x=1/m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline439}%
$c_i x_i \ge
a,\ i=1,...,m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline441}%
$U(y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline443}%
$c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1447}%
$\displaystyle u(y)=
\left\{
\begin{array}{ll}
0  & \mbox{if $0 \le y < c$} \\
1 & \mbox{if $ y = c$}
\end{array}.
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline449}%
$x_i=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline451}%
$c_i=\max_j c_j=c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline453}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1452}%
$\displaystyle u(y) < y,\ if\  0 \le y < r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1453}%
$\displaystyle u(y)=y,\ if\  y= r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1454}%
$\displaystyle u(y) > y,\ if\  r < y  \le c.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1467}%
$\displaystyle U(x,a)=\sum_{k=1}^M  u(y^k) p(y^k),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline461}%
$u(y^k)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline465}%
$a=(a_i,\ i=1,...,m)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline469}%
$i=1,...,m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline471}%
$y^k=\sum_{i=1}^m  c_i (x_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1477}%
$\displaystyle c_i(x_i)=
\left\{
\begin{array}{ll}
z_i- a_i x_i & \mbox{if $\delta_i=1$}\\
(1-a_i)  x_i & \mbox{if  $\delta_i=0$}
\end{array}.
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline477}%
$a_i x_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline481}%
$x_i \le z_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline485}%
$z_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline489}%
$\delta_i=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline493}%
$\delta_i=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline495}%
$p_i=P\{\delta_i=1\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline499}%
$p(y^1)=p_1 \prod_{i \neq 1} (1-p_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline501}%
$y^1=c_1( x_1)+\sum_{i=2}^m c_i(x_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline503}%
$c_1(x_1)= z_1-a_1 x_1,\\
 c_i(x_i)=(1-a_i)x_i, \ i=2,...,m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1495}%
$\displaystyle U(x,a)=\sum_{y}  u(y) p(y),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline515}%
$y=  c (x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1503}%
$\displaystyle c(x)=
\left\{
\begin{array}{ll}
z- a x & \mbox{if $\delta=1$}\\
(1-a)  x & \mbox{if  $\delta=0$}
\end{array}.
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline521}%
$z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline523}%
$a x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline525}%
$x \le z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline527}%
$\delta=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline529}%
$\delta=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline531}%
$p=P\{\delta=1\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1511}%
$\displaystyle V(x,a)=\sum_{y}  v(y) p(y),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline537}%
$v(y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline541}%
$y=  d (x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1518}%
$\displaystyle d(x)=
\left\{
\begin{array}{ll}
a x, &  \mbox{if $\delta=1$} \\
-(1-a)  x & \mbox{if  $\delta=0$}
\end{array}.
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline555}%
$(x^0,a^0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline557}%
$(x^1,a^1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline559}%
$U(x,a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline561}%
$V(x,a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline563}%
$(x^0,a^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1530}%
$\displaystyle x^1 = arg \max_{x}
U(x, a^0),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1531}%
$\displaystyle a^1 = arg \max_{a}
V(x^0, a_),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline565}%
$w^n=(x^n,a^n) \in B ,\
n=0,1,2,...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline567}%
$w^{n+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline569}%
$T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1536}%
$\displaystyle w^{n+1} = T(w^n),\ n=0,1,2,...$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline571}%
$w^n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1539}%
$\displaystyle w^{n} = T(w^n).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline575}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1544}%
$\displaystyle \min_{w \in B} \parallel w - T(w) \parallel^2.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline581}%
$x_i=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline583}%
$x_i=z_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline587}%
$n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline589}%
$x=\sum_{i=1}^n x_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline591}%
$n \le m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline593}%
$s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline595}%
$k=m-n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline597}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1561}%
$\displaystyle x_i=z_i=1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline605}%
$u_i(y_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1567}%
$\displaystyle U(x,a)=\sum_y  u(y) p(y),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1572}%
$\displaystyle c(x)=
(1-a)n+l,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline613}%
$x=n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline617}%
$p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline619}%
$z=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline621}%
$x=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline623}%
$x=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline625}%
$\lambda =qk$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline627}%
$q=1-p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline631}%
$k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline633}%
$k-l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1587}%
$\displaystyle p(k,l,q)=e^{-\lambda} \frac {\lambda^l}{l!}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline637}%
$y=(1-a)n+l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1591}%
$\displaystyle p(y)=p(k,l,q)=P\{y=(1-a)n+l\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1595}%
$\displaystyle V(x,a)=\sum_y  v(y) p(y),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1602}%
$\displaystyle d(x)=
a n-(1-a)(n-s),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline659}%
$y=an-(1-a)(n-s)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1608}%
$\displaystyle p(y)=p(n,s,q)=P\{y=sa-(1-a)(n-s)\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline683}%
$V_j(x,a_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline685}%
$j=1,2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1624}%
$\displaystyle V_j(x,a)=\sum_{y_j}  v_j(y_j) p(y_j),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline687}%
$p(y_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline689}%
$y_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline691}%
$v_j(y_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline695}%
$y_j=  d (x_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1631}%
$\displaystyle d(x_j)=
a_j s_j-(1-a_j)(n_j-s_j),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline697}%
$x_j=n_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline699}%
$j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline701}%
$s_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline705}%
$y_j=s_j a_j-(1-a_j)(n_j-s_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1638}%
$\displaystyle p(y_j)=p(n_j,s_j,q)=P\{y=s_j a_j-(1-a_j)(n_j-s_j)\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline707}%
$V_j(x_j,a_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline711}%
$x_j, \ j=1,2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline713}%
$n_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline717}%
$a_j, \ j=1,2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline719}%
$x_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline721}%
$a_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline723}%
$(x_j^0,a_j^0,\ j=1,2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline725}%
$(x_j^1,a_j^1,\ j=1,2)$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline727}%
$U(x_j,a_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline731}%
$(x_j^0,a_j^0,\ j=1.2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1654}%
$\displaystyle (x_1^1,x_2^1) = arg \max_{x_1,x_2}
U(x_1,x_2, a_1^0,a_2^0),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1655}%
$\displaystyle a_j^1 = arg \max_{a_j}
V_j(x_j^0, a_j,a_l^0,\ l \ne j),\ j=1,2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline733}%
$w^n=(x_j^n,a_j^n,\ j=1,2) \in B ,\
n=0,1,2,...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline749}%
$N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline751}%
$(x_1,x_2,a_1,a_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline753}%
$(x_1,x_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline755}%
$(a_1,a_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline759}%
$L(A,B,p)=\{pA+(1-p)B\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline763}%
$A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline765}%
$(1-p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline769}%
$C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline777}%
$p(C)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1690}%
$\displaystyle L(A,B,C,p(C))=[C \approx \{p(C) A + (1-p(C)) B\}].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline781}%
$\approx$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline783}%
$u(A)=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline785}%
$u(B)=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline789}%
$u(C)=p(C)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline793}%
$y=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline797}%
$y=2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline801}%
$y=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline803}%
$p(1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline805}%
$u(1)= u(0)+p(1)(u(2)-u(0))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline807}%
$u(0)=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline809}%
$u(2)=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline811}%
$u(1)=p(1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline813}%
$y=0,\ y=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline819}%
$y=0.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline821}%
$y=1.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline823}%
$p(0.5)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline825}%
$p(1.5)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1715}%
$\displaystyle L(1.0,0.0,0.5,p(0.5))=$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1716}%
$\displaystyle [(y=0.5) \approx  \{p(0.5)(y=1) +(1-p(0.5))(y= 0) \}] \nonumber$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1718}%
$\displaystyle L(2.0,1.0,1.5,p(1.5))=$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1719}%
$\displaystyle [(y=1.0) \approx  \{p(1.5)(y=2.0) +(1-p(1.5))(y=1) \}]. \nonumber$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline827}%
$u(0)=0,\ u(0.5)=p(0.5),
\  u(1)=p(1),\  u(1.5)=u(1) + p(1.5) (u(2)-u(1))\  u(2)=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1722}%
$\displaystyle u(y)=u(y_i) + p(y_i) (u(y_{i+1}) - u(y_i)),\  \  y_i \le y
<y_{i+1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1723}%
$\displaystyle i=0,1,...,4.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline829}%
$r_{prudent} < r_{average} < r_{rich} <r_{risky}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure301}%
\begin{figure}\centerline{
 \epsfig{file=flexible.crop2.in.eps,width=12.0cm}
}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure306}%
\begin{figure}\centerline{
 \epsfig{file=flexible.crop.out.eps,width=12.0cm}
}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline831}%
$yk[i]=0.25*i,\
i=0,...,8$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline833}%
$f[0]=0.0,\ f[1]=0.3,\ f[2]=0.5,\ f[3]=0.7,\ 
f[4]=0.8,\ f[5]=0.85,\ f[6]=0.9,\ f[7]=0.95,\ f[8]=1.0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline835}%
$f[0]=0.0,\ f[1]=0.1,\ f[2]=0.2,\ f[3]=0.25,\ 
f[4]=0.3,\ f[5]=0.4,\ f[6]=0.7,\  f[7]=0.9,\ f[8]=1.0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline837}%
$f[0]=0.0,\ f[1]=0.125,\ f[2]=0.25,\ f[3]=0.325,\ 
f[4]=0.5,\ f[5]=0.625,\ f[6]=0.75,\  f[7]=0.875,\ f[8]=1.0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline839}%
$f[0]=0.0,\ f[1]=0.1,\ f[2]=0.2,\ f[3]=0.25,\ 
f[4]=0.5,\ f[5]=0.7,\ f[6]=0.85,\  f[7]=0.95,\ f[8]=1.0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
