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   \rho = \frac{サービス要求量}{サービス処理能力}
 
   \rho = \frac{サービス要求量}{サービス処理能力}
 
\]
 
\]
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== 戦略形ゲーム (0071-a-g-03-1) ==
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\[ \begin{array}{@{\  }c|ccc@{\  }}
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          & 1            & \ldots  & n                \\  \hline
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      1    & a_{11}, b_{11}    & \ldots  & a_{1n}, b_{1n}    \\
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    \vdots & \vdots            & \ddots  & \vdots          \\
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      m    & a_{m1}, b_{m1}    & \ldots  & a_{mn}, b_{mn}
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    \end{array}
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    \]
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== 戦略形ゲーム (0071-a-g-03-2) ==
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\[ \begin{array}{@{\  }c|ccc@{\  }}
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          & c      & d                \\  \hline
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      c    & 3, 3    & 0, 4    \\
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      d    & 4, 0    & 1, 1
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    \end{array}
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    \ \ \ \ \ \ \ \ \ \ \ \ \ \
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    \begin{array}{@{\  }c|ccc@{\  }}
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          & a      & b                \\  \hline
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      a    & 2, 1    & 0, 0    \\
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      b    & 0, 0    & 1, 2
 +
    \end{array}
 +
    \]

2007年7月12日 (木) 16:24時点における版

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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{-228mm}\hspace*{6mm} \setlength{\unitlength}{0.001in} %\setlength{\unitlength}{0.0001in} \begin{picture}(2300,5750)(0,0) \special{pn 8}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% p(x_2) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 492.4}% \special{pa 2270 340}% \special{fp}% \special{pa 1600 492.4}% \special{pa 2270 492.4}% \special{fp}% \special{pa 1600 492.4}% \special{pa 2270 644.8}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 949.6}% \special{pa 2270 797.2}% \special{fp}% \special{pa 1600 949.6}% \special{pa 2270 949.6}% \special{fp}% \special{pa 1600 949.6}% \special{pa 2270 1102}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 1406.8}% \special{pa 2270 1254.4}% \special{fp}% \special{pa 1600 1406.8}% \special{pa 2270 1406.8}% \special{fp}% \special{pa 1600 1406.8}% \special{pa 2270 1559.2}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 1864}% \special{pa 2270 1711.6}% \special{fp}% \special{pa 1600 1864}% \special{pa 2270 1864}% \special{fp}% \special{pa 1600 1864}% \special{pa 2270 2016.4}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 2321.2}% \special{pa 2270 2168.8}% \special{fp}% \special{pa 1600 2321.2}% \special{pa 2270 2321.2}% \special{fp}% \special{pa 1600 2321.2}% \special{pa 2270 2473.6}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 2778.4}% \special{pa 2270 2626}% \special{fp}% \special{pa 1600 2778.4}% \special{pa 2270 2778.4}% \special{fp}% \special{pa 1600 2778.4}% \special{pa 2270 2930.8}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 3235.6}% %\special{pa 2270 3083.2}% %\special{fp}% %\special{pa 1600 3235.6}% %\special{pa 2270 3235.6}% %\special{fp}% %\special{pa 1600 3235.6}% %\special{pa 2270 3388}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 3692.8}% %\special{pa 2270 3540.4}% %\special{fp}% %\special{pa 1600 3692.8}% %\special{pa 2270 3692.8}% %\special{fp}% %\special{pa 1600 3692.8}% %\special{pa 2270 3845.2}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 4150}% %\special{pa 2270 3997.6}% %\special{fp}% %\special{pa 1600 4150}% %\special{pa 2270 4150}% %\special{fp}% %\special{pa 1600 4150}% %\special{pa 2270 4302.4}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 4607.2}% %\special{pa 2270 4454.8}% %\special{fp}% %\special{pa 1600 4607.2}% %\special{pa 2270 4607.2}% %\special{fp}% %\special{pa 1600 4607.2}% %\special{pa 2270 4759.6}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 5064.4}% %\special{pa 2270 4912}% %\special{fp}% %\special{pa 1600 5064.4}% %\special{pa 2270 5064.4}% %\special{fp}% %\special{pa 1600 5064.4}% %\special{pa 2270 5216.8}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 5521.6}% %\special{pa 2270 5369.2}% %\special{fp}% %\special{pa 1600 5521.6}% %\special{pa 2270 5521.6}% %\special{fp}% %\special{pa 1600 5521.6}% %\special{pa 2270 5674}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u_1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1000 721}% \special{pa 1600 492.4}% \special{da 0.05}% \special{pa 1000 721}% \special{pa 1600 949.6}% \special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1000 1635.4}% \special{pa 1600 1406.8}% \special{da 0.05}% \special{pa 1000 1635.4}% \special{pa 1600 1864}% \special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1000 2549.8}% \special{pa 1600 2321.2}% \special{da 0.05}% \special{pa 1000 2549.8}% \special{pa 1600 2778.4}% \special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1000 3464.2}% %\special{pa 1600 3235.6}% %\special{da 0.05}% %\special{pa 1000 3464.2}% %\special{pa 1600 3692.8}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1000 4378.6}% %\special{pa 1600 4150}% %\special{fp}% %\special{pa 1000 4378.6}% %\special{pa 1600 4607.2}% %\special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1000 5293}% %\special{pa 1600 5064.4}% %\special{fp}% %\special{pa 1000 5293}% %\special{pa 1600 5521.6}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% p(x_1) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 500 1635.4}% \special{pa 1000 721}% \special{fp}% \special{pa 500 1635.4}% \special{pa 1000 1635.4}% \special{fp}% \special{pa 500 1635.4}% \special{pa 1000 2549.8}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 500 4378.6}% %\special{pa 1000 3464.2}% %\special{fp}% %\special{pa 500 4378.6}% %\special{pa 1000 4378.6}% %\special{fp}% %\special{pa 500 4378.6}% %\special{pa 1000 5293}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u_0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 180 3007}% \special{pa 500 1635.4}% \special{da 0.05}% %\special{pa 180 3007}% %\special{pa 500 4378.6}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%% Nota. & Nume. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \put(300,-2950){\makebox(0,0){$s_1$}} \put(1000,-621){\makebox(0,0){$s_1$}} \put(1000,-1735.4){\makebox(0,0){$s_2$}} \put(1000,-2649.8){\makebox(0,0){$s_3$}} %\put(1000,-3344.2){\makebox(0,0){$s_1$}} %\put(1000,-4458.6){\makebox(0,0){$s_2$}} %\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} %

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

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} \setlength{\unitlength}{0.001in} %\setlength{\unitlength}{0.0001in} \begin{picture}(2300,5750)(0,-2700) \special{pn 8}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% p(x_2) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 492.4}% %\special{pa 2270 340}% %\special{fp}% %\special{pa 1600 492.4}% %\special{pa 2270 492.4}% %\special{fp}% %\special{pa 1600 492.4}% %\special{pa 2270 644.8}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 949.6}% %\special{pa 2270 797.2}% %\special{fp}% %\special{pa 1600 949.6}% %\special{pa 2270 949.6}% %\special{fp}% %\special{pa 1600 949.6}% %\special{pa 2270 1102}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 1406.8}% %\special{pa 2270 1254.4}% %\special{fp}% %\special{pa 1600 1406.8}% %\special{pa 2270 1406.8}% %\special{fp}% %\special{pa 1600 1406.8}% %\special{pa 2270 1559.2}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 1864}% %\special{pa 2270 1711.6}% %\special{fp}% %\special{pa 1600 1864}% %\special{pa 2270 1864}% %\special{fp}% %\special{pa 1600 1864}% %\special{pa 2270 2016.4}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 2321.2}% %\special{pa 2270 2168.8}% %\special{fp}% %\special{pa 1600 2321.2}% %\special{pa 2270 2321.2}% %\special{fp}% %\special{pa 1600 2321.2}% %\special{pa 2270 2473.6}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1600 2778.4}% %\special{pa 2270 2626}% %\special{fp}% %\special{pa 1600 2778.4}% %\special{pa 2270 2778.4}% %\special{fp}% %\special{pa 1600 2778.4}% %\special{pa 2270 2930.8}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 3235.6}% \special{pa 2270 3083.2}% \special{fp}% \special{pa 1600 3235.6}% \special{pa 2270 3235.6}% \special{fp}% \special{pa 1600 3235.6}% \special{pa 2270 3388}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 3692.8}% \special{pa 2270 3540.4}% \special{fp}% \special{pa 1600 3692.8}% \special{pa 2270 3692.8}% \special{fp}% \special{pa 1600 3692.8}% \special{pa 2270 3845.2}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 4150}% \special{pa 2270 3997.6}% \special{fp}% \special{pa 1600 4150}% \special{pa 2270 4150}% \special{fp}% \special{pa 1600 4150}% \special{pa 2270 4302.4}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 4607.2}% \special{pa 2270 4454.8}% \special{fp}% \special{pa 1600 4607.2}% \special{pa 2270 4607.2}% \special{fp}% \special{pa 1600 4607.2}% \special{pa 2270 4759.6}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 5064.4}% \special{pa 2270 4912}% \special{fp}% \special{pa 1600 5064.4}% \special{pa 2270 5064.4}% \special{fp}% \special{pa 1600 5064.4}% \special{pa 2270 5216.8}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1600 5521.6}% \special{pa 2270 5369.2}% \special{fp}% \special{pa 1600 5521.6}% \special{pa 2270 5521.6}% \special{fp}% \special{pa 1600 5521.6}% \special{pa 2270 5674}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u_1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1000 721}% %\special{pa 1600 492.4}% %\special{da 0.05}% %\special{pa 1000 721}% %\special{pa 1600 949.6}% %\special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1000 1635.4}% %\special{pa 1600 1406.8}% %\special{da 0.05}% %\special{pa 1000 1635.4}% %\special{pa 1600 1864}% %\special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 1000 2549.8}% %\special{pa 1600 2321.2}% %\special{da 0.05}% %\special{pa 1000 2549.8}% %\special{pa 1600 2778.4}% %\special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1000 3464.2}% \special{pa 1600 3235.6}% \special{da 0.05}% \special{pa 1000 3464.2}% \special{pa 1600 3692.8}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1000 4378.6}% \special{pa 1600 4150}% \special{fp}% \special{pa 1000 4378.6}% \special{pa 1600 4607.2}% \special{da 0.05}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 1000 5293}% \special{pa 1600 5064.4}% \special{fp}% \special{pa 1000 5293}% \special{pa 1600 5521.6}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% p(x_1) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 500 1635.4}% %\special{pa 1000 721}% %\special{fp}% %\special{pa 500 1635.4}% %\special{pa 1000 1635.4}% %\special{fp}% %\special{pa 500 1635.4}% %\special{pa 1000 2549.8}% %\special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \special{pa 500 4378.6}% \special{pa 1000 3464.2}% \special{fp}% \special{pa 500 4378.6}% \special{pa 1000 4378.6}% \special{fp}% \special{pa 500 4378.6}% \special{pa 1000 5293}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u_0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\special{pa 180 3007}% %\special{pa 500 1635.4}% %\special{da 0.05}% \special{pa 180 3007}% \special{pa 500 4378.6}% \special{fp}% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%% Nota. & Nume. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \put(300,-3067){\makebox(0,0){$s_1$}} %\put(1000,-621){\makebox(0,0){$s_1$}} %\put(1000,-1735.4){\makebox(0,0){$s_2$}} %\put(1000,-2649.8){\makebox(0,0){$s_3$}} \put(1000,-3344.2){\makebox(0,0){$s_1$}} \put(1000,-4458.6){\makebox(0,0){$s_2$}} \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} &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)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}

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}

\]


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}
   \]
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