% $BI=Bj(B: $BHs@5B'$K$J$i$J$$$h$&$K$9$k$?$a$K(B
%
% $BMzNr(B: 2002-08-04 $B?y;39L0lO/(B



\section{RAND $BK!$NE,MQ$G$-$J$$%1!<%9$H$=$N2r7hJ}K!(B}
\label{rand}

$BA0@a$^$G$G5DO@$7$?(B RAND $BK!$rE,MQ$G$-$J$$%1!<%9$,$$$/$D$+B8:_$9$k(B. 
$B$=$N$h$&$J%1!<%9$O<g$K9TNs$NHs@5B'@-$H$7$F8=$l$k(B. $BBeI=E*$J%1!<%9$H$7$F(B, 

\begin{itemize}
 \item $B$"$k(B 2 $B$D$NAj$KB8:_$9$k2=3X<o$,A4$/F1$8$J>l9g(B. 
       $BNc$($P(B, H$_2$O(l) $B$H(B H$_2$O(s) $B$,$=$l$>$lFHN)$K(B 1 $B$D$NAj$r(B
       $B7A@.$9$k>l9g$,$3$l$KAjEv$9$k(B. 
       $B$3$N:](B, $B78?t9TNs$N(B 2 $B$D$N9T$NMWAG$,A4$/F1$8$H$J$j(B, 
       $B9TNs<0$,Hs@5B'$H$J$k(B. 
 \item $B$"$kAj$KB8:_$9$kA4$F$NJ*<A$NB8:_NL$,(B 0 $B$K6aIU$$$?>l9g(B. 
       $B$3$N:](B, $B9TNs<0$,(B $0 x = 0$ $B$H$J$j2r$,ITDj$H$J$k(B.        
\end{itemize}

$B$,5s$2$i$l$k(B. $B0J2<$N@a$G$OHs@5B'$K$J$k>l9g$r<($7(B, $B$5$i$K$=$N(B
$B2r>CJ}K!$r=R$Y$k(B. 



\subsection{$B$"$k(B 2 $B$D$NAj$KB8:_$9$kJ*<A$,A4$/F1$8$J>l9g(B}
\label{same}

RAND $BK!$G$O(B, $BG.NO3X4X?t(B $G$ $B$N4X?t7A$OJ*<ANL$K4X$9$k(B 2 $B3,0J>e$N4X?t$G$"(B
$B$k$3$H$rA0Ds$H$7$F$$$k(B. $B$7$+$7(B, 1 $B@.J,(B 2 $BAj7O$NG.NO3X4X?t(B $G$ $B$N4X?t7A(B
$B$OJ*<ANL$K4X$9$k(B 1 $B<!J}Dx<0$G$"$k(B. $B$=$N$?$a(B RAND $BK!$G$O07$&$3$H$,$G$-$J(B
$B$$(B. $B$3$N%1!<%9$rHr$1$k$?$a$K$O(B, RAND $BK!$K$h$k7W;;$r;O$a$kA0(B($B29EY05NO$rM?(B
$B$($?CJ3,(B)$B$K$*$$$FB8:_$7F@$k2=3X<o$rM=$aH=Dj$9$kI,MW$,$"$k(B. 
$B3F2=3X<o$N2=3X%]%F%s%7%c%k$rHf3S$7(B, $B2=3X%]%F%s%7%c%k$NBg$-$$2=3X<o$r(B
$B:o=|$9$l$PNI$$(B. 
\bigskip

$B6qBNNc$H$7$F$^$:(B 1 $B@.J,(B 2 $BAj7O$N>l9g$r9M$($k(B. 
$BNc$H$7$F(B H$_2$O(l), H$_2$O(s) $B$+$i$J$k(B 1 $B@.J,(B 2 $BAj7O$r9M$($k(B. 
$B29EY!&05NO$rM?$($k$H(B, $BG.NO3X4X?t(B $G$ $B$O0J2<$N$h$&$K=q$1$k(B. 

\begin{eqnarray}
G &=& \sum_{\phi} \mu^{\phi} n^{\phi} \nonumber \\
  &=& \mu^{l} n^{l} + \mu^{s} n^{s}
\Deqlab{only-1}
\end{eqnarray}

$B$3$3$GE:;z(B $\phi$ $B$OAj$rI=$7(B, $l$ $B$O1UAj(B, $s$ $B$O8GAj$G$"$k(B. $\mu$ $B$O2=3X(B
$B%]%F%s%7%c%k(B, $n$ $B$O%b%k?t$G$"$k(B. $B$5$i$KJ*<A$NJ]B8B'$O0J2<$N$h$&$K=q$1$k(B. 

\begin{eqnarray}
n^{l} + n^{s} = n
\Deqlab{only-2}
\end{eqnarray}

$BJ*<A$OJ]B8$5$l$k$N$G(B $n$ $B$ODj?t$G$"$k(B. \Deqref{only-1} $B<0$K(B
\Deqref{only-2} $B<0$rBeF~$7(B, $B$5$i$K2=3X%]%F%s%7%c%k$rI8=`2=3X%]%F%s%7%c%k(B
$\mu^{\circ}$ $B$rMQ$$$F=q$-D>$9$H(B, 

\begin{eqnarray}
G &=& {\mu^{\circ}}^{l}(T) n^{l} + {\mu^{\circ}}^{s}(T) (n - n^{l})
  \nonumber \\
  &=& \{ {\mu^{\circ}}^{l}(T) - {\mu^{\circ}}^{s}(T) \} n^{l}
     + {\mu^{\circ}}^{s}(T) n
\Deqlab{only-3}
\end{eqnarray}

\Deqref{only-3} $B<0$h$j(B, 1 $B@.J,(B 2 $BAj7O$N(B $G$ $B$OJ*<ANL$K4X$9$k(B 1 $B<!4X?t$G(B
$B$"$k$3$H$,$o$+$k(B. \Deqref{only-3} $B<0$N:G>.CM$rM?$($k(B $n^{l}$ $B$O0J2<$N$h(B
$B$&$K7h$^$k(B:

\begin{eqnarray}
&&{\mu^{\circ}}^{l}(T) < {\mu^{\circ}}^{s}(T) $B$N>l9g(B \nonumber \\
&& \hspace{10mm}
 n^{l} = n \nonumber \\
&&{\mu^{\circ}}^{l}(T) > {\mu^{\circ}}^{s}(T) $B$N>l9g(B \nonumber \\
&& \hspace{10mm}
 n^{l} = 0 \nonumber \\
&&{\mu^{\circ}}^{l}(T) = {\mu^{\circ}}^{s}(T) $B$N>l9g(B ($BAjJ?9U$N>l9g(B)\nonumber \\
&& \hspace{10mm}
 0 \leq n^{l} \leq n \nonumber 
\end{eqnarray}

$B=>$C$FI8=`2=3X%]%F%s%7%c%k$NCM$+$i(B, $B$I$NAj$KB8:_$9$k$+H=Dj(B
$B$9$k$3$H$,$G$-$k(B. \bigskip


$B<!$KB?@.J,B?Aj7O$K$*$$$F$b(B, $B$"$k(B 2 $B$D$NAj$K4^$^$l$kJ*<A$,A4$/F1$8>l9g(B
$B$r9M$($k(B. $B7kO@$+$i8@$($P(B, $B$3$N>l9g$K$b(B 1 $B@.J,(B 2 $BAj7O$H(B
$BF1MM$NLdBj$,@8$8$k(B. $BNc$H$7$FB?@.J,7O$G$O$"$k$,(B, H$_2$O(l), H$_2$O(s) $B$,(B
$B$=$l$>$lC1FH$G(B 1 $B$D$NAj$r7A@.$9$k>l9g$r9M$($k(B. 
\Deqref{20010123-3} $B<0$r(B H$_2$O(l), H$_2$O(s) $B$K4X$9$k<0$KJQ7A$9$k$H(B, 

\begin{eqnarray}
\sum_{e} a_{{\rm H_2O},e}^{l} m_{{\rm H_2O}}^{l} \chi_{e} 
 &=& m_{{\rm H_2O}}^{l} \mu_{{\rm H_2O}}^{l} \nonumber \\
\sum_{e} a_{{\rm H_2O},e}^{s} m_{{\rm H_2O}}^{s} \chi_{e} 
 &=& m_{{\rm H_2O}}^{s} \mu_{{\rm H_2O}}^{s} \nonumber 
\end{eqnarray}

$BN>JU$rJ*<ANL$GDLJ,$9$k$H(B, 

\begin{eqnarray}
\sum_{e} a_{{\rm H_2O},e} \chi_{e}  &=& \mu_{{\rm H_2O}}^{l} \nonumber \\
\sum_{e} a_{{\rm H_2O},e} \chi_{e}  &=& \mu_{{\rm H_2O}}^{s}  
\Deqlab{only-6}
\end{eqnarray}

$B$3$3$G(B, $a_{{\rm H_2O},e}^{l} = a_{{\rm H_2O},e}^{s}$ $B$N4X78$rMQ$$$?(B. 
$BJ*<A$,F1$8$J$N$G(B, $BAj$,0[$J$C$F$b(B $a_{ie}$ $B$NCM$OJQ2=$7$J$$(B.
\Deqref{only-6} $B<0$r8+$k$H(B, $B:8JU$N78?t$OF1$8$G$"$k$,(B, $B1&JU$NCM$O0[$J$k$3(B
$B$H$,$o$+$k(B. $B$3$l$G$O(B $\chi_e$ $B$r5a$a$k9TNs<0$,Hs@5B'$H$J$j(B, $B2r$,5a$^$i$J$$(B. 
\bigskip

\newpage
\subsection{$B$"$kAj$K4^$^$l$kJ*<A$NB8:_NL$,(B 0 $B$K6aIU$/>l9g(B}
\label{sou}


$B$"$kAj$KB8:_$9$kA4$F$NJ*<AB8:_NL$,(B 0 $B$K6aIU$/$H(B, \Deqref{20010123-3} $B<0$O(B

\begin{eqnarray}
0 \cdot \chi_{e} = 0
\end{eqnarray}

$B$H$J$j(B, $\chi_{e}$ $B$OITDj$H$J$k(B. $B$3$N%1!<%9$rHr$1$k$?$a$K$O(B, $BEv3:29EY05(B
$BNO>r7o$K$*$$$FB8:_$G$-$J$$2=3X<o$r!V?dDj!W$7(B, $B7O$+$i<h$j=|$/$H$$$&:n6H$,(B
$BI,MW$H$J$k(B. $B7P83>e(B, $BC1=c$KAj$KB8:_$9(B
$B$kA4$F$NJ*<A$NB8:_NL$,(B 0 $B$K6aIU$$$?>l9g$K$=$NAj$,B8:_$7$J$$$b$N$H$7$F7W(B
$B;;$r?J$a$k$H(B, $BB8:_$9$k$O$:$N2=3X<o$^$G7O$+$i<h$j=|$$$F$7$^$&2DG=@-$,$"$k(B.
\bigskip


$BJ?9U>r7o$+$iB8:_$7$J$$2=3X<o$r?dDj$9$k(B. $B2=3X<o$N5$Aj$N%b%kHf$O$@$$$?$$J](B
$BB8$5$l$k$H2>Dj$7$?;~$K(B, $B5$Aj$H6E=LAj$NJ?9U>r7o$rK~$?$9$?$a$KI,MW$J6E=LAj(B
$B$N%b%kHf$r7W;;$7(B, $B$=$NCM$H<B:]$N6E=LAj$N%b%kHf$rHf3S$9$k(B. $B$=$7$F6E=LAj$N(B
$B%b%kHf$,<B:]$N%b%kHf$h$j$bCx$7$/>.$5$/$J$C$F$$$k2=3X<o$rB8:_$7$J$$$b$N$H(B
$B$9$k(B. 
\bigskip

$B9TNs$,Hs@5B'$K$J$C$?$H$-$N$"$k2=3X<o$N5$Aj$N%b%kHf$r(B $x^{g}$, $B6E=LAj$N%b(B
$B%kHf$r(B $x^{l}$ $B$H$9$k(B. $B%b%kHf$r(B $x^{g}$ $B$N5$Aj$HJ?9U$9$k6E=LAj$N%b%kHf(B
${x^{l}}^{'}$ $B$O0J2<$N$h$&$K5a$^$k(B. 
%
\begin{eqnarray}
 \mu_{0}^{g} + R T \ln{x^{g}} + RT \ln{(p/p_{ref})} 
  &=& \mu_{0}^{l} + R T \ln{{x^{l}}^{'}} \\
 \frac{(\mu_{0}^{g} + RT \ln{(p/p_{ref})}) - \mu_{0}^{l}}{RT}
  &=& \ln{{x^{l}}^{'} / x^{g}} \\
 {x^{l}}^{'} &=& \exp{\left(
  \frac{(\mu_{0}^{g} + RT \ln{(p/p_{ref})}) - \mu_{0}^{l}}{RT}
  \right)}  x^{g}
\end{eqnarray}
%
$BC"$7(B $R$ $B$O5$BNDj?t(B, $T$ $B$O29EY(B, $p$ $B$O05NO(B, $p_{ref}$ $B$OI8=`05NO(B,
$\mu_{0}$ $B$OI8=`2=3X%]%F%s%7%c%k$G$"$k(B. $B0J>e$h$j5a$a$?(B ${x^{l}}^{'}$ $B$H(B
$B<B:]$N6E=LAj$N%b%kHf(B $x^{l}$ $B$H$NHf$r<h$j(B, $B:G$bCM$,>.$5$$$b$N(B, $B$9$J$o$A(B
$BJ?9U$9$k$?$a$K$O%b%kHf$,Cx$7$/8:>/$;$M$P$J$i$J$$$b$N(B, $B$rB8:_$7$($J$$2=3X(B
$B<o$G$"$k$H!V?dDj!W$9$k(B. 






