スタイル検討のソースを表示

== 多段確率決定樹表(ツリーテーブル) (0053-a-e-03-1) ==


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Table 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}\footnotesize\renewcommand{\arraystretch}{0.91}
\begin{tabular}{|cr@{\hspace*{0.5mm}}|c|l|l|c|c|} \hline
\multicolumn{2}{|c|}{\makebox[62.6mm][c]{履歴}}&
\makebox[0.1mm][c]{加法} &
{経路} & 
\multicolumn{1}{|c|}{積} &
\multicolumn{1}{|c|}{部期} &
{全期}\\ \hline
\hline
&$s_1$ 0.3 & 2.0 & {\it 0.64} & 1.28  & & \\
&$s_2$ 1.0 & 2.7 & {\it 0.08} & 0.216 & \makebox[6mm][c]{1.696} & \\
&$s_3$ 0.8 & 2.5 & {\it 0.08} & 0.2   & & \\ \cline{3-5}
&$s_1$ 0.3 & 1.6 & {\it 0.08} & 0.128 & & \\
&$s_2$ 1.0 & 2.3 & {\it 0.72} & 1.656 & \makebox[6mm][c]{\bf 1.784} & \\
&$s_3$ 0.8 & 2.1 & {\it 0.0}  & 0     & & \\ \cline{3-6}
&$s_1$ 0.3 & 2.0 & {\it 0.0}  & 0     & & \\
&$s_2$ 1.0 & 2.7 & {\it 0.01} & 0.027 & \makebox[6mm][c]{\bf 0.252} & \\
&$s_3$ 0.8 & 2.5 & {\it 0.09} & 0.225 & & \makebox[6mm][c]{2.248} \\
 \cline{3-5}
&$s_1$ 0.3 & 1.6 & {\it 0.08} & 0.128 & & \\
&$s_2$ 1.0 & 2.3 & {\it 0.01} & 0.023 & \makebox[6mm][c]{0.172} & \\
&$s_3$ 0.8 & 2.1 & {\it 0.01} & 0.021 & & \\ \cline{3-6}
&$s_1$ 0.3 & 2.0 & {\it 0.08} & 0.16  & & \\
&$s_2$ 1.0 & 2.7 & {\it 0.01} & 0.027 & \makebox[6mm][c]{\bf 0.212} & \\
&$s_3$ 0.8 & 2.5 & {\it 0.01} & 0.025 & & \\ \cline{3-5}
&$s_1$ 0.3 & 1.6 & {\it 0.01} & 0.016 & & \\
&$s_2$ 1.0 & 2.3 & {\it 0.0}  & 0     & \makebox[6mm][c]{0.205} & \\
&$s_3$ 0.8 & 2.1 & {\it 0.09} & 0.189 & & \\ 
%\cline{3-7}
\hline
\end{tabular}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Figure 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% Nota. & Nume. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\put(1000,-5373){\makebox(0,0){$s_3$}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\end{picture}
\end{table}
%

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== 多段確率決定樹表(ツリーテーブル) (0053-a-e-03-2) ==

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Table 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{table}[ht]
\caption{状態 $s_1$ からの２段確率決定樹表(続き)}
%\begin{center}
%図表1 : 状態 $s_1$ からの２段確率決定樹表
%\end{center}
\begin{center}\footnotesize\renewcommand{\arraystretch}{0.91}
\begin{tabular}{|cr@{\hspace*{0.5mm}}|c|l|l|c|c|} \hline
\multicolumn{2}{|c|}{\makebox[62.6mm][c]{履歴}}&
\makebox[0.1mm][c]{加法} &
{経路} & 
\multicolumn{1}{|c|}{積} &
\multicolumn{1}{|c|}{部期} &
{全期}\\ \hline
\hline
&$s_1$ 0.3 & 2.3 & {\it 0.08} & 0.184 & & \\
&$s_2$ 1.0 & 3.0 & {\it 0.01} & 0.03  & \makebox[6mm][c]{0.242} & \\
&$s_3$ 0.8 & 2.8 & {\it 0.01} & 0.028 & & \\ \cline{3-5}
&$s_1$ 0.3 & 1.9 & {\it 0.01} & 0.019 & & \\
&$s_2$ 1.0 & 2.6 & {\it 0.09} & 0.234 & \makebox[6mm][c]{\bf 0.253} & \\
&$s_3$ 0.8 & 2.4 & {\it 0.0}  & 0     & & \\ \cline{3-6}
&$s_1$ 0.3 & 2.3 & {\it 0.0}  & 0     & & \\
&$s_2$ 1.0 & 3.0 & {\it 0.09} & 0.27  & \makebox[6mm][c]{\bf 2.538} & \\
&$s_3$ 0.8 & 2.8 & {\it 0.81} & 2.268 & & \makebox[6mm][c]{\bf 2.791} \\
 \cline{3-5}
&$s_1$ 0.3 & 1.9 & {\it 0.72} & 1.368 & & \\
&$s_2$ 1.0 & 2.6 & {\it 0.09} & 0.234 & \makebox[6mm][c]{1.818} & \\
&$s_3$ 0.8 & 2.4 & {\it 0.09} & 0.216 & & \\ \cline{3-6}
&$s_1$ 0.3 & 2.3 & {\it 0.0}  & 0     & & \\
&$s_2$ 1.0 & 3.0 & {\it 0.0}  & 0     & \makebox[6mm][l]{\bf 0} & \\
&$s_3$ 0.8 & 2.8 & {\it 0.0}  & 0     & & \\ \cline{3-5}
&$s_1$ 0.3 & 1.9 & {\it 0.0}  & 0     & & \\
&$s_2$ 1.0 & 2.6 & {\it 0.0}  & 0     & \makebox[6mm][l]{\bf 0} & \\
&$s_3$ 0.8 & 2.4 & {\it 0.0}  & 0     & & \\ \hline
\end{tabular}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Figure 2　%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{-228mm}\hspace*{6mm}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u_0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% Nota. & Nume. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\put(1000,-5373){\makebox(0,0){$s_3$}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\put(400,-2507){\makebox(0,0){$a_1$}}
\put(400,-3507){\makebox(0,0){$a_2$}}
%\put(1400,-644.8){\makebox(0,0){$a_1$}}
%\put(1400,-949.6){\makebox(0,0){$a_2$}}
%\put(1400,-1559.2){\makebox(0,0){$a_1$}}
%\put(1400,-1864){\makebox(0,0){$a_2$}}
%\put(1400,-2473.6){\makebox(0,0){$a_1$}}
%\put(1400,-2778.4){\makebox(0,0){$a_2$}}
\put(1400,-3368){\makebox(0,0){$a_1$}}
\put(1400,-3672.8){\makebox(0,0){$a_2$}}
\put(1400,-4282.4){\makebox(0,0){$a_1$}}
\put(1400,-4587.2){\makebox(0,0){$a_2$}}
\put(1400,-5196.8){\makebox(0,0){$a_1$}}
\put(1400,-5501.6){\makebox(0,0){$a_2$}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\put(200,-2407){\makebox(0,0){\small 0.7}}
\put(200,-3607){\makebox(0,0){\small 1.0}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\put(700,-1021){\makebox(0,0){\small\it 0.8}}
%\put(800,-1535.4){\makebox(0,0){\small\it 0.1}}
%\put(700,-2249.8){\makebox(0,0){\small\it 0.1}}
\put(700,-3744.2){\makebox(0,0){\small\it 0.1}}
\put(800,-4258.6){\makebox(0,0){\small\it 0.9}}
\put(700,-4973){\makebox(0,0){\small\it 0.0}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\put(1200,-542.4){\makebox(0,0){\small 1.0}}
%\put(1300,-749.6){\makebox(0,0){\small 0.6}}
%\put(1200,-1456.8){\makebox(0,0){\small 1.0}}
%\put(1300,-1664){\makebox(0,0){\small 0.6}}
%\put(1200,-2371.2){\makebox(0,0){\small 1.0}}
%\put(1300,-2578.4){\makebox(0,0){\small 0.6}}
\put(1200,-3265.6){\makebox(0,0){\small 1.0}}
\put(1300,-3472.8){\makebox(0,0){\small 0.6}}
\put(1200,-4180){\makebox(0,0){\small 1.0}}
\put(1300,-4387.2){\makebox(0,0){\small 0.6}}
\put(1200,-5094.4){\makebox(0,0){\small 1.0}}
\put(1300,-5301.6){\makebox(0,0){\small 0.6}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\put(1900,-340){\makebox(0,0){\small\it 0.8}}
%\put(2100,-432.4){\makebox(0,0){\small\it 0.1}}
%\put(2100,-542.4){\makebox(0,0){\small\it 0.1}}
%\put(1900,-797.2){\makebox(0,0){\small\it 0.1}}
%\put(2100,-889.6){\makebox(0,0){\small\it 0.9}}
%\put(2100,-999.6){\makebox(0,0){\small\it 0.0}}
%\put(1900,-1244.4){\makebox(0,0){\small\it 0.0}}
%\put(2100,-1336.8){\makebox(0,0){\small\it 0.1}}
%\put(2100,-1446.8){\makebox(0,0){\small\it 0.9}}
%\put(1900,-1701.6){\makebox(0,0){\small\it 0.8}}
%\put(2100,-1794){\makebox(0,0){\small\it 0.1}}
%\put(2100,-1904){\makebox(0,0){\small\it 0.1}}
%\put(1900,-2153.8){\makebox(0,0){\small\it 0.8}}
%\put(2100,-2246.2){\makebox(0,0){\small\it 0.1}}
%\put(2100,-2356.2){\makebox(0,0){\small\it 0.1}}
%\put(1900,-2626){\makebox(0,0){\small\it 0.1}}
%\put(2100,-2703.4){\makebox(0,0){\small\it 0.0}}
%\put(2100,-2813.4){\makebox(0,0){\small\it 0.9}}
\put(1900,-3063.2){\makebox(0,0){\small\it 0.8}}
\put(2100,-3155.6){\makebox(0,0){\small\it 0.1}}
\put(2100,-3265.6){\makebox(0,0){\small\it 0.1}}
\put(1900,-3525.4){\makebox(0,0){\small\it 0.1}}
\put(2100,-3607.8){\makebox(0,0){\small\it 0.9}}
\put(2100,-3717.8){\makebox(0,0){\small\it 0.0}}
\put(1900,-3972.6){\makebox(0,0){\small\it 0.0}}
\put(2100,-4065){\makebox(0,0){\small\it 0.1}}
\put(2100,-4175){\makebox(0,0){\small\it 0.9}}
\put(1900,-4424.8){\makebox(0,0){\small\it 0.8}}
\put(2100,-4517.2){\makebox(0,0){\small\it 0.1}}
\put(2100,-4627.2){\makebox(0,0){\small\it 0.1}}
\put(1900,-4882){\makebox(0,0){\small\it 0.8}}
\put(2100,-4974.4){\makebox(0,0){\small\it 0.1}}
\put(2100,-5084.4){\makebox(0,0){\small\it 0.1}}
\put(1900,-5339.2){\makebox(0,0){\small\it 0.1}}
\put(2100,-5431.6){\makebox(0,0){\small\it 0.0}}
\put(2100,-5541.6){\makebox(0,0){\small\it 0.9}}
\end{picture}
\end{table}
\clearpage
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\begin{center}
 \begin{tabular}{cccc}
     $u_t=a_1$ & \hspace{30mm} &[[利用者:122.17.2.240|122.17.2.240]] 2007年7月12日 (木) 11:48 (JST)& $u_t=a_2$ \\
       \cline{1-1}\cline{4-4}
\end{tabular}
\end{center}
\begin{center}
 \begin{tabular}{ccccccccc}
      \cline{1-4}\cline{6-9}
  \multicolumn{1}{r|}{$x_t＼x_{t+1}$} & $s_1$ & $s_2$ & $s_3$ & 
2007年7月12日 (木) 11:48 (JST)[[利用者:122.17.2.240|122.17.2.240]] 2007年7月12日 (木) 11:48 (JST)& \multicolumn{1}{r|}{$x_t＼x_{t+1}$} & $s_1$ & $s_2$ & $s_3$ \\
  \cline{1-4}\cline{6-9} \\
  \noalign{\vskip-4.3mm}
 \multicolumn{1}{c|}{$s_1$} & {\it 0.8} & {\it 0.1} & {\it 0.1} & &
\multicolumn{1}{c|}{$s_1$} & {\it 0.1} & {\it 0.9} & {\it 0.0} \\
 \multicolumn{1}{c|}{$s_2$} & {\it 0.0} & {\it 0.1} & {\it 0.9} & &
\multicolumn{1}{c|}{$s_2$} & {\it 0.8} & {\it 0.1} & {\it 0.1} \\
 \multicolumn{1}{c|}{$s_3$} & {\it 0.8} & {\it 0.1} & {\it 0.1} & &
\multicolumn{1}{c|}{$s_3$} & {\it 0.1} & {\it 0.0} & {\it 0.9} \\
  \cline{1-4}\cline{6-9}
 \end{tabular}
\end{center}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


== 不変埋没原理 (0054-a-e-04-1) ==

\begin{eqnarray}
{\rm S}_{1}(x_{1}):\hspace{-2.21mm}& & \sum
 \hspace{0.3mm}\sum\hspace{0.3mm}\cdots\hspace{0.3mm}\sum
_{\hspace{-21.1mm}(x_{2}, x_{3}, \cdots , x_{N+1}) \in P_{1}(x_{1})}
\hspace{-1.9mm}\psi(g_{1}(x_{1},x_{2}) \circ \cdots \circ
 g_{N}(x_{N},x_{N+1}) \circ k(x_{N+1}))\  \nonumber \\[2.34mm]
& & \hspace*{0.8mm}( P_{1}(x_{1}) := \{(x_{2}, \cdots , x_{N+1})\, |\,
 x_{n+1} \in A_{n}(x_{n})~~1 \le n \le N \}) \nonumber
\end{eqnarray}



== 戦略形ゲーム (0071-a-g-03-1) ==

\[ \begin{array}{@{\  }c|ccc@{\  }}
           & 1             & \ldots   & n                \\  \hline
      1    & a_{11}, b_{11}    & \ldots   & a_{1n}, b_{1n}    \\
    \vdots & \vdots            & \ddots   & \vdots           \\
      m    & a_{m1}, b_{m1}    & \ldots   & a_{mn}, b_{mn}
    \end{array}
    \]



== 戦略形ゲーム (0071-a-g-03-2) ==

\[ \begin{array}{@{\  }c|ccc@{\  }}
           & c       & d                \\  \hline
      c    & 3, 3    & 0, 4    \\
      d    & 4, 0    & 1, 1
    \end{array}
    \ \ \ \ \ \ \ \ \ \ \ \ \ \
    \begin{array}{@{\  }c|ccc@{\  }}
           & a       & b                \\  \hline
      a    & 2, 1    & 0, 0    \\
      b    & 0, 0    & 1, 2
    \end{array}
    \]



== ゲームの解の計算 (0079-a-g-11-1) ==

\[
\begin{array}{c|ccc}
           & 1             & \ldots  & n                      \\ \hline
1         &  a_{11}    & \ldots  & a_{1n}  \\
\vdots &  \vdots    & \ddots  & \vdots             \\
m        &  a_{m1}  & \ldots  & a_{mn}
\end{array}
\]



== ゲームの解の計算 (0079-a-g-11-2) ==

\[ \begin{array}{c|cc}
      &  1  &  2 \\  \hline
     1  &  a_{11}, b_{11}   &   a_{12}, b_{12} \\
     2  &  a_{21}, b_{21}   & a_{22}, b_{22} \\
\end{array} \]



== カルマンフィルター (0098-b-h-05-1) ==

\begin{figure}[hbt]
\begin{center}
\unitlength=10pt
\begin{picture}(23,7.6)(0,0)
\put(0.5,4){\vector(1,0){3}} %  2.0
\put(1.3,4.5){\makebox(0,0)[b]{$w_t$}}
\put(3.5,3){\framebox(3,2){$B$}} % 4.0
\put(6.5,4){\vector(1,0){1.7}} %  1.2
\put(7.5,4.6){\makebox(0,0){\scriptsize $+$}}
\put(8.5,4){\circle{0.6}}  %8.5
\put(8.8,4){\vector(1,0){2.2}}
\put(9.8,4.7){\makebox(0,0)[b]{$x_{t+1}$}}
\put(11,3){\framebox(3,2){$z^{-1}$}}
\put(14,4){\vector(1,0){3}}
\put(15.5,4.5){\makebox(0,0)[b]{$x_t$}}
\put(15.5,4){\circle*{0.1}}
\put(17,3){\framebox(3,2){$C$}}
\put(20,4){\vector(1,0){2.2}}
\put(21.5,4.6){\makebox(0,0){\scriptsize $+$}}
\put(22.5,4){\circle{0.6}}
\put(22.8,4){\vector(1,0){3}}
\put(25,4.5){\makebox(0,0)[b]{$y_t$}}
\put(15.5,4){\line(0,-1){4}}
\put(15.5,0){\vector(-1,0){1.5}}
\put(11,-1){\framebox(3,2){$A$}}
\put(11,0){\line(-1,0){2.5}}
\put(8.5,0){\vector(0,1){3.7}}
\put(7.9,3){\makebox(0,0){$ \scriptstyle + $}}
\put(22.5,6.8){\vector(0,-1){2.5}}
\put(23,5){\makebox(0,0){$ \scriptstyle + $}}
\put(23.5,6.5){\makebox(0,0){$v_t$}}
\put(21,0){\makebox(0,0)[b]{$z^{-1}$: {\scriptsize 遅れ作用素}}}
\end{picture}
\end{center}
\caption{状態空間モデル} \label{B-H-05+KALMAN1}
\end{figure}


== カルマンフィルター (0098-b-h-05-2) ==
\begin{figure}[hbt]
\begin{center}
\unitlength=10pt
\begin{picture}(23,7.6)(0,0)
\put(0,4){\vector(1,0){2.5}}
\put(0.5,4.5){\makebox(0,0)[b]{$y_t$}}
\put(2,4.6){\makebox(0,0){$ \scriptstyle + $}}
\put(4,4.4){\makebox(0,0)[b]{$\nu_t$}}
\put(2.8,4){\circle{0.6}}
\put(2.8,0){\vector(0,1){3.7}}
\put(2.2,3.1){\makebox(0,0){$ \scriptstyle - $}}
\put(3.1,4){\vector(1,0){2.3}}
\put(5.4,3){\framebox(3,2){$K_t$}}
\put(8.4,4){\vector(1,0){2.1}}
\put(10.0,4.6){\makebox(0,0){$ \scriptstyle + $}}
\put(10.8,4){\circle{0.6}}
\put(12.5,4.5){\makebox(0,0)[b]{$\hat{x}_{t/t}$}}
\put(11.2,4){\vector(1,0){2.6}}
\put(13.8,3){\framebox(3,2){$z^{-1}$}}
\put(16.8,4){\vector(1,0){5}}
\put(19.5,4.5){\makebox(0,0)[b]{$\hat{x}_{t-1/t-1}$}}
\put(19.6,4){\circle*{0.1}}
\put(19.6,4){\line(0,-1){4}}
\put(19.6,0){\vector(-1,0){2.8}}
\put(13.8,-1){\framebox(3,2){$A$}}
\put(10.8,0){\circle*{0.1}}
\put(10.8,0){\vector(0,1){3.7}}
\put(10,3.1){\makebox(0,0){$ \scriptstyle + $}}
\put(5.4,-1){\framebox(3,2){$C$}}
\put(2.8,0){\line(1,0){2.6}}
\put(13.8,0){\vector(-1,0){5.4}}
\put(12,-1){\makebox(0,0)[b]{$\hat{x}_{t/t-1}$}}
\end{picture}
\end{center}
\caption{カルマンフィルターのブロック線図} \label{B-H-05+KALMAN2}
\end{figure}

== 待ち行列 (0112-b-a-01-1) ==

\[
  \rho = \frac{サービス要求量}{サービス処理能力}
\]


== 待ち行列 (0112-b-a-01-2) ==

\begin{figure}
\setlength{\unitlength}{.6mm}
\begin{center}
\begin{picture}(60, 35)(0, 5)
\thicklines
\put(10, 39){\line(1, 0){16}}
\put(26, 32){\oval(14, 14)[tr]}
\put(33, 32){\line(0, -1){4}}
\put(10, 34){\line(1, 0){14}}
\put(24, 31){\oval(6, 6)[tr]}
\put(27, 31){\line(0, -1){3}}
\put(23, 39){\line(0, 1){3}}
\put(21, 39){\line(0, 1){3}}
\put(22, 43.5){\oval(8, 3)}

\put(0, 15){\oval(8, 14)[tr]}
\put(14, 15){\oval(20, 14)[bl]}
\put(14, 5){\oval(24, 6)[tr]}
\put(60, 15){\oval(8, 14)[tl]}
\put(46, 15){\oval(20, 14)[br]}
\put(46, 5){\oval(24, 6)[tl]}

\thinlines
\put(4, 18){\line(1, 0){52}}
\multiput(27.5, 29)(1, 0){6}{\line(0, -1){5}}
\multiput(26.5, 4)(1, 0){8}{\line(0, -1){4}}
\end{picture}
\end{center}
\caption{流体近似 : 水道のイメージ} \label{B-A-01+suidou}
\end{figure}

== 待ち行列 (0112-b-a-01-3) ==

\begin{figure}
\setlength{\unitlength}{1mm}
\begin{center}
\thicklines
\begin{picture}(65, 20)(0, 7)
\put(10, 15){\vector(1, 0){7.5}}
\put(45, 15){\vector(1, 0){7.5}}
\put(20, 12.5){\line(1, 0){15}}
\put(20, 17.5){\line(1, 0){15}}
\put(25, 12.5){\line(0, 1){5}}
\put(30, 12.5){\line(0, 1){5}}
\put(35, 12.5){\line(0, 1){5}}
\put(37.5, 10){\line(0, 1){10}}
\put(42.5, 10){\line(0, 1){10}}
\put(37.5, 10){\line(1, 0){5}}
\put(37.5, 15){\line(1, 0){5}}
\put(37.5, 20){\line(1, 0){5}}
\put(32.5, 15){\circle{4}}
\put(40, 12.5){\circle{4}}
\put(40, 17.5){\circle{4}}

\put(0, 15){\makebox(0, 0){客の到着}}
\put(25.5, 7){\makebox(0, 0){待ち行列}}
\put(40, 4){\makebox(0, 0){窓口}}
\put(57.5, 15){\makebox(0, 0){退去}}
%\put(27.5, 23){\makebox(0, 0){待ち時間}}
%\put(40, 27.5){\makebox(0, 0){サービス時間}}
\end{picture}
\end{center}
\caption{待ち行列のイメージ図} \label{B-A-01+queue1}
\end{figure}


== 待ち行列モデルの標準形 (0113-b-a-02-1) ==

\begin{figure}[htb]
\unitlength 1mm
\thicklines
\begin{center}
\begin{picture}(130, 60)(0, 10)
\put(0, 40){\vector(1, 0){20}}
\put(105, 40){\vector(1, 0){20}}
%
\multiput(25, 32)(0, 16){2}{\line(1, 0){45}}
\multiput(25, 32)(10, 0){2}{\line(0, 1){16}}
\multiput(50, 32)(10, 0){3}{\line(0, 1){16}}
\put(70, 40){\line(1, 0){15}}
\put(85, 20){\line(0, 1){40}}
\put(85, 20){\line(1, 0){5}}
\put(85, 45){\line(1, 0){5}}
\put(85, 60){\line(1, 0){5}}
%
\put(95, 20){\circle{10}}
\put(95, 45){\circle{10}}
\put(95, 60){\circle{10}}
%
\put(10, 45){\makebox(0, 0){客の到着}}
\put(10, 35){\makebox(0, 0){到着過程}}
\put(30, 40){\makebox(0, 0){$N$}}
\multiput(38.75, 40)(3.75, 0){3}{\circle*{.7}}
\put(55, 40){\makebox(0, 0){$c$+2}}
\put(65, 40){\makebox(0, 0){$c$+1}}
\put(47.5, 53){\makebox(0, 0){待合室}}
\put(95, 70){\makebox(0, 0){窓口}}
\put(95, 60){\makebox(0, 0){1}}
\put(95, 45){\makebox(0, 0){2}}
\multiput(95, 28.75)(0, 3.75){3}{\circle*{.7}}
\put(95, 20){\makebox(0, 0){$c$}}
\put(95, 10){\makebox(0, 0){サービス時間分布}}
\put(115, 45){\makebox(0, 0){客の退去}}
%
\put(77.5, 48){\makebox(0, 0){\shortstack{サ\\\rule{.6pt}{7pt}\\ビ\\ス}}}
\put(77.5, 35){\makebox(0, 0){\shortstack{規\\律}}}
%
\end{picture}
\end{center}
\caption{待ち行列の標準形 */*/{\it c}/{\it N}}
\end{figure}




== 待ち行列ネットワーク (0123-b-b-01-1) ==

\begin{figure}[htbp]
\begin{center}
%\includegraphics[bbllx=0, bblly=210mm, bburx=230mm, bbury=260mm, 
%height=40mm]{. . /b-b/tandem.eps}
\setlength{\unitlength}{1mm}
\begin{picture}(108, 20)(0, -10)
\thicklines
\put(0, 0){\vector(1, 0){8}}
\multiput(9, -2.5)(0, 5){2}{\line(1, 0){7}}
\put(16, -2.5){\line(0, 1){5}}
\put(16, 0){\line(1, 0){2}}
\put(21, 0){\circle{6}}
\put(24, 0){\vector(1, 0){8}}
\multiput(33, -2.5)(0, 5){2}{\line(1, 0){7}}
\put(40, -2.5){\line(0, 1){5}}
\put(40, 0){\vector(2, 3){4}}
\put(40, 0){\vector(2, -3){4}}
\put(47, 7.5){\circle{6}}
\put(47, -7.5){\circle{6}}
\put(47, 0){\makebox(0, 1.2){$\vdots$}}
\put(50, 6){\vector(2, -3){4}}
\put(50, -6){\vector(2, 3){4}}
\multiput(55, -2.5)(0, 5){2}{\line(1, 0){7}}
\put(62, -2.5){\line(0, 1){5}}
\put(62, 0){\line(1, 0){2}}
\put(67, 0){\circle{6}}
\put(70, 0){\vector(1, 0){5}}
\put(80, 0){\makebox(0, 0){$\cdots$}}
\multiput(84, -2.5)(0, 5){2}{\line(1, 0){7}}
\put(91, -2.5){\line(0, 1){5}}
\put(91, 0){\line(1, 0){2}}
\put(96, 0){\circle{6}}
\put(99, 0){\vector(1, 0){9}}
\end{picture}
\end{center}
\caption{直列型待ち行列} \label{B-B-01+tandem-model}
\end{figure}


== 待ち行列ネットワーク (0123-b-b-01-2) ==

\begin{figure}[htbp]
\begin{center}
%\includegraphics[bbllx=0, bblly=210mm, bburx=230mm, bbury=260mm, 
%height=40mm]{. . /b-b/central.eps}
\setlength{\unitlength}{1mm}
\begin{picture}(72, 33)(0, -13)
\thicklines
\put(0, -1){\vector(1, 0){10}}
\put(0, -1){\line(0, 1){21}}
\put(0, 20){\line(1, 0){72}}
\put(72, 0){\line(0, 1){20}}
\put(62, 0){\line(1, 0){10}}
\put(6, 1){\vector(1, 0){4}}
\put(6, 1){\line(0, 1){7}}
\put(6, 8){\line(1, 0){23}}
\put(29, 0){\vector(0, 1){8}}
\multiput(11, -2.5)(0, 5){2}{\line(1, 0){7}}
\put(18, -2.5){\line(0, 1){5}}
\put(18, 0){\line(1, 0){2}}
\put(23, 0){\circle{6}}
\put(26, 0){\line(1, 0){12}}
\put(38, -10){\line(0, 1){20}}
\put(38, 10){\vector(1, 0){5}}
\multiput(44, 7.5)(0, 5){2}{\line(1, 0){7}}
\put(51, 7.5){\line(0, 1){5}}
\put(51, 10){\line(1, 0){2}}
\put(56, 10){\circle{6}}
\put(59, 10){\line(1, 0){3}}
\put(38, -10){\vector(1, 0){5}}
\multiput(44, -7.5)(0, -5){2}{\line(1, 0){7}}
\put(51, -7.5){\line(0, -1){5}}
\put(51, -10){\line(1, 0){2}}
\put(56, -10){\circle{6}}
\put(59, -10){\line(1, 0){3}}
\put(62, -10){\line(0, 1){20}}
\put(48, 0){\makebox(0, 1.2){\Huge $\vdots$}}
\end{picture}
\caption{セントラルサーバモデル}\label{B-B-01+central-server-model}
\end{center}
\end{figure}



== 待ち行列の生産システムへの応用 (0131-b-c-03-1) ==


\begin{figure}[hb]
\begin{center}
%\includegraphics[bbllx=0mm, bblly=0mm, bburx=500mm, 
%bbury=300mm]{BC03ZU. eps}
\setlength{\unitlength}{1mm}
\begin{picture}(121, 15)(0, -4.5)
\thicklines
\put(5, 0){\vector(1, 0){8}}
\multiput(5, -4)(0, 8){2}{\line(1, 0){26}}
\multiput(15, -4)(8, 0){3}{\line(0, 1){8}}
\put(35.5, 0){\circle{9}}
\put(35.5, 0){\makebox(0, 0){\Large $s_1$}}
\put(40, 0){\vector(1, 0){5}}
\multiput(45, -4)(0, 8){2}{\line(1, 0){20}}
\multiput(45, -4)(10, 0){3}{\line(0, 1){8}}
\put(69.5, 0){\circle{9}}
\put(69.5, 0){\makebox(0, 0){\Large $s_2$}}
\put(74, 0){\vector(1, 0){3}}
\put(81.5, 0){\circle{9}}
\put(81.5, 0){\makebox(0, 0){\Large $s_3$}}
\put(86, 0){\vector(1, 0){3}}
\put(93, 0){\makebox(0, 0){\Large $\cdots$}}
\put(97, 0){\vector(1, 0){3}}
\multiput(100, -4)(0, 8){2}{\line(1, 0){9}}
\multiput(100, -4)(9, 0){2}{\line(0, 1){8}}
\put(113.5, 0){\circle{9}}
\put(113.5, 0){\makebox(0, 0){\Large $s_N$}}
\put(118, 0){\vector(1, 0){3}}
\put(0, 2.1){\makebox(0, 0){需}}
\put(0, -2.1){\makebox(0, 0){要}}
\put(19, 8){\makebox(0, 0){バッファ}}
\put(55, 8){\makebox(0, 0){バッファ}}
\put(104.5, 8){\makebox(0, 0){バッファ}}
\end{picture}
\caption{直列生産ライン} \label{fig:line}
\end{center}
\end{figure}



== 間接費管理 (0157-c-j-07-1) ==

%        　図表1　　製品のコスト・利益・価格
%                                               ┌───┬───┐     
%                                               │ 利益 │      │     
%                                 ┌──────┼───┤      │     
%                            　 　│ 一般管理費 │      │      │     
%                                 ├──────┤      │      │     
%                            　 　│ 　販売費   │      │  価  │     
%             ┌─────┬───┼──────┤  総  │      │     
%             │間接経費  │　間  │            │      │      │     
%             ├─────┤      │            │      │      │     
%             │間接労務費│  接  │            │  コ  │      │     
%             ├─────┤      │            │      │      │     
%             │間接材料費│  費  │            │  ス  │  格  │     
% ┌─────┼─────┴───┤　製造原価  │      │      │     
% │直接経費  │　　　　　  　直  │            │  ト  │      │     
% ├─────┼─────┐      │            │      │      │     
% │直接労務費│　素　　　│　接  │            │      │      │     
% ├─────┤          │      │            │      │      │     
% │直接材料費│　価　 　 │　費　│            │      │      │     
% │          │          │      │            │      │      │     
% └─────┴─────┴───┴──────┴───┴───┘
%

\renewcommand{\arraystretch}{1.5}
{\small 
\begin{table} 
\caption{製品のコスト・利益・価格}\label{c-j-07-hyou1}
\begin{center}
\begin{tabular}{|l|l|c|c|c|c|}
\cline{5-6}
\multicolumn{4}{c|}{}                                   &利益&    \\
 \cline{4-5}
\multicolumn{3}{c|}{}                  & 一般管理費     &    &    \\
 \cline{4-4}
\multicolumn{3}{c|}{}                  & 販売費         &    & 価 \\
 \cline{2-4}
\multicolumn{1}{c|}{}& 間接経費   & 間 &                & 総 &    \\
 \cline{2-2}
\multicolumn{1}{c|}{}& 間接労務費 & 接 &                & コ &    \\
 \cline{2-2}
\multicolumn{1}{c|}{}& 間接材料費 & 費 &                & ス & 格 \\
 \cline{1-3}
直接経費            &\multicolumn{1}{c}{}  &直&製造原価& ト &    \\
 \cline{1-2}
直接労務費          &\multicolumn{1}{c|}{素}&接&        &    &    \\
 \cline{1-1}
直接材料費          &\multicolumn{1}{c|}{価}&費&        &    &    \\ \hline
\end{tabular}
\end{center}
\end{table}
}



== 研究開発 (0178-c-j-14-1) ==

\[研究開発効率(ROI)＝\frac{事業収益}{研究開発費}\]




== 産業連関分析 (0204-c-d-07-1) ==

\begin{table}[h]
\caption{産業連関表}\label{C-D-07+hyou1}
\vspace{0.3cm}

% \footnotesize

\normalsize
\def\pbox[#1]{\parbox[t]{1zw}{#1}}

$\begin{array}{|c|p{2.5cm}|cccc|cccccc|c|c|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{4}{|c|}{中間部門} & \multicolumn{6}{c|
}{最終需要} & &  \\
\cline{3-12}
\multicolumn{2}{|c|}{} & & \pbox[産業1] & \pbox[産業2] & \pbox[産業n] & 
\pbox[民間消費] & \pbox[政府消費] & \pbox[民間設備投資] & \pbox[政府設備投資] 
& \pbox[在庫調整] & \pbox[輸出] & \pbox[輸入] & \pbox[合計] \\
\hline
中 & 産業1 & & X_{11} & X_{12} & X_{1n} & C_{1} & G_{1} & IP_{1} & IG_{1} & 
J_{1} & E_{1} &  M_{1} & X_{1} \\
間 & 産業2 & & X_{21} & X_{22} & X_{2n} & C_{2} & G_{2} & IP_{2} & IG_{2} &
 J_{2} & E_{2} & M_{2} & X_{2} \\
部 & ... &  & . & . & . & . & . & . & . & . & . & . & . \\ 
門 & 産業ｎ & & X_{n1} & X_{n2} & X_{nn} & C_{n} & G_{n} & IP_{n} & IG_{n} &
 J_{n} & E_{n} & M_{n} & X_{n} \\
\hline
総 & 家計外消費支出 & & N_{1} & N_{2} & N_{n}    & & & & & & & & N \\
付 & 雇用者所得     & & Y_{1} & Y_{2} & Y_{n}    & & & & & & & & Y \\
加 & 営業余剰       & & O_{1} & O_{2} & O_{n}    & & & & & & & & O \\
価 & 資本減耗引当   & & D_{1} & D_{2} & D_{n}    & & & & & & & & D \\
値 & 間接税補助金   & & T_{1} & T_{2} & T_{n}    & & & & & & & & T \\
\hline
 \multicolumn{2}{|c|}{合計} & & X_{1} & X_{2} & X_{n} & C & G & IP & IG & J 
& E & M &  \\
\hline
\end{array}$

\normalsize

\end{table}



== 軍事モデル (0206-c-d-06-1) ==

%\vskip30pt
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{table}[h]\label{C-D-06+boukuu}
\begin{center}
\begin{tabular}{cccc}
\cline{4-4}
& & \multicolumn{1}{c|}{} & 監視管制機能\\
\cline{4-4}
& &  \multicolumn{1}{c|}{レーダー監視}& 整備補給機能\\
\cline{3-3}
\cline{4-4}
& \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & 基地業務機能\\
\cline{4-4}
& \multicolumn{1}{c|}{警戒監視} & 代替監視 & 移動警戒機能\\
\cline{2-2}
\cline{3-3}
\cline{4-4}
\multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & 自動管制 & 防空管制機能\\
\cline{3-3}
\cline{4-4}
\multicolumn{1}{c|}{}&&&\\
\cline{4-4}
\multicolumn{1}{c|}{防空}& & \multicolumn{1}{c|}{} &飛行機能\\
\cline{1-1}
\cline{4-4}
\multicolumn{1}{c|}{}& & \multicolumn{1}{c|}{戦闘機部隊} & 整備補給機能\\
\cline{3-3}
\cline{4-4}
\multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & 
基地業務機能\\
\cline{4-4}
\multicolumn{1}{c|}{} & \multicolumn{1}{c|}{要撃} & & \\
\cline{2-2}
\cline{4-4}
& \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & 射撃機能\\
\cline{4-4}
& \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{高射部隊}& 整備補給機能\\
\cline{3-3}
\cline{4-4}
& & \multicolumn{1}{c|}{} & 指揮運用機能\\
\cline{4-4}


\end{tabular}
\end{center}
\end{table}
                                 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


== 積分幾何学 (0207-c-e-01-1) ==

%\begin{figure}[h]
%\begin{center}
%%\vspace*{40mm}
%%%%%%%%%%%%%%%%%%%%%%%%%%
%\includegraphics{C-E-01f+2.eps}
%\caption{直線に下ろした垂線} \label{fig:C-E-01+2}
%\end{center}
%\end{figure}

\begin{figure}[h]
\begin{center}
\begin{picture}(300,170)(-50,-20)
%\put(-50,-20){\framebox(300,170)}
\put(0,0){\vector(1,0){220}} \put(220,0){\makebox(0,0)[l]{\large  $ x $ }}
\put(0,0){\vector(0,1){130}} \put(0,130){\makebox(0,0)[b]{\large  $ y $ }}
\put(0,0){\line(1,2){50}}
\put(-10,100){\line(2,-1){220}}
\put(140,30){\makebox(0,0)[bl]{\large  $ g $ }}
\put(22,71){\line(2,-1){11}}
\put(22,71){\line(1,2){5}}
\put(20,50){\makebox(0,0)[tr]{\large  $ p $ }}
\put(0,0){\makebox(0,0)[tr]{O}}
\put(5,0){\oval(15,20)[tr]}
\put(15,15){\makebox(0,0)[l]{\large  $ \theta $ }}
\end{picture}
\vspace{-10mm}
\caption{直線に下ろした垂線} \label{fig:C-E-01+2}
\end{center}
\end{figure}


== 積分幾何学 (0207-c-e-01-2) ==

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}[p]
%\begin{center}
%\vspace*{40mm}
%\includegraphics{C-E-01+4.eps}
%\caption{曲線と直線} \label{fig:C-E-01+4}
%\end{center}
%\end{figure} 

\begin{figure}[h]
\begin{center}
\begin{picture}(300,170)(-50,-20)
%\put(-50,-20){\framebox(300,170)}
\put(0,0){\vector(1,0){220}} \put(220,0){\makebox(0,0)[l]{\large  $ x $ }}
\put(0,0){\vector(0,1){130}} \put(0,130){\makebox(0,0)[b]{\large  $ y $ }}
\put(0,0){\line(2,1){150}}
\put(100,-10){\line(-1,2){70}}
\put(90,10){\makebox(0,0)[bl]{\large  $ g $ }}
\put(71,22){\line(-1,2){5}}
\put(71,22){\line(2,1){11}}
\put(40,30){\makebox(0,0)[tr]{\large  $ p $ }}
\put(0,0){\makebox(0,0)[tr]{O}}
\put(15,0){\oval(11,15)[tr]}
\put(30,10){\makebox(0,0)[tl]{\large  $ \theta $ }}
\put(30,110){\oval(60,80)[br]}
\put(56.2,77.6){\vector(2,3){40}}
\put(56.6,85.5){\oval(9,8)[t]}
\put(56,89.5){\makebox(0,0)[b]{\large  $ \varphi $ }}
\put(55.5,72){\makebox(0,0)[t]{\large P}}
\put(30,70){\makebox(0,0)[r]{\large A}}
\put(60,115){\makebox(0,0)[b]{\large B}}
\end{picture}
\vspace{-5mm}
\caption{曲線と直線} \label{fig:C-E-01+4}
\end{center}
\end{figure} 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

== 積分幾何学 (0207-c-e-01-3) ==

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
                
%\begin{figure}[p]
%\begin{center}
%\vspace*{40mm}
%\includegraphics{C-E-01+5.eps}
%\caption{ $ C $ と交わる確率} \label{fig:C-E-01+5}
%\end{center}
%\end{figure}  

\begin{figure}[h]
\begin{center}
\begin{picture}(300,140)(-50,-10)
% \put(-50,-10){\framebox(300,140)}
\put(-10,130){\line(2,-1){220}}
\put(-30,130){\line(1,-1){130}}
\put(40,50){\circle{80}}
\put(90,60){\oval(200,100)}
\put(150,90){\makebox(0,0)[bl]{\large  $ C_0 $ }}
\put(60,60){\makebox(0,0)[l]{\large  $ C $ }}
\end{picture}
\vspace{-5mm}
\caption{ $ C $ と交わる確率} \label{fig:C-E-01+5}
\end{center}
\end{figure}            
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%