
\vspace{0.5cm}
\noindent
{\bf 7. $B6X;_NN0h(B.}

$BD>8rI=<($G(B2$BK\$N6J@~(B$x=c$$B$H(B$X=c$$B$*$h$S$=$l$i$,7h$a$k3F<o$NNN0h$r9M$($h$&!%(B$X-c$$B$NId9f$,(B$x-c$$B$NId9f$HEy$7$$(B\underline{$B5vMFNN0h(B}$B$H!"$3$l$i(B2$B$D$NId9f$,0[$J$k(B\underline{$B6X;_NN0h(B}$B$r6hJL$7$h$&!%8e<T$K$O6J@~(B$X=x$$B$,F~$j9~$a$J$$!%(B$X=c$$B$N4pK\8I(B$HK$$B$H$=$l$K(B(5$B@a$N0UL#$G(B)$BD>@\J$$o$l$F$$$k8I$K4^$^$l$kNN0h$,5vMF$G$"$k$N$O!"(B$HK$$B$,5U$N$H$-$G!"(B$HK$$B$,=g$N$H$-$O6X;_$G$"$k!%(B

$B$3$&$7$?>e$G!"(B$S$$B$r$"$k6J@~(B$X=x$$B$N$"$kD:E@$H$9$k!%(B$x=c$$B$O$3$ND:E@$N2<$K0LCV$9$k?eJ?@~$G$"$C$F!"(B$X=x$$B$rD:E@$KHs>o$K6a$$(B2$BE@(B$A$$B$H(B$B$$B$G2#@Z$k$H$9$k!%(B$AMB$$B$O(B$A$$B$H(B$B$$B$r4^$`6J@~(B$X=c$$B$N4pK\8I$H$9$k!%$^$?(B$R$$B$O$3$N8I$H?eJ?@~(B$AB$$B$K64$^$l$kNN0h$H$9$k!%$3$N8I$,5U$J$i(B($B$9$J$o$A!"D:E@(B$S$$B$,5U$J$i(B)$B!"NN0h(B$R$$B$O5vMF$G$"$j!"NY@\$9$kNN0h$O6X;_$G$"$k$+$i!"6J@~(B$X=x$$B$N8I(B$ASB$$B$,$3$NNN0h$r2#@Z$k$O$:$G$"$j!"$3$NNN0h$O(B2$B$D$NItJ,NN0h(B$AMBS$$B$H(B$ASBA$$B$KJ,3d$5$l$k!%(B

\vspace{2.0cm}
\hspace*{5cm} $B?^(B2

\vspace{1.5cm}
$BBh0l$NNN0h>e$G(B$x>X>c$$B$G$"$j!"BhFs$NNN0h>e$G(B$X>x>c$$B$G$"$k!%$3$N$H$-NN0h(B$X>x$$B$r:8$K8B$kJ,;^(B$AS$$B$O6v?tHV9f$G$"$k!%$9$J$o$A!"D:E@(B$S$$B$NHV9f$b6v?t$G$"$k!%$7$?$,$C$F(B\underline{$B4q?t$N5UD:E@$O$"$jF@$J$$(B}$B!%$^$?F1MM$K(B\underline{$B6v?t$N5UDlE@$O$"$jF@$J$$(B}$B!%(B

$B0lJ}!"4JC1$K$o$+$k$h$&$K!"(B\underline{$B6J@~(B}$X=x$\underline{$B$N:G$b9b$$D:E@$O$D$M$K=g$G$"$k(B}$B!%:G$bDc$$DlE@$K$D$$$F$bF1$8$G$"$k!%(B

$B<B:]!"(B$R$$B$O6J@~(B$X=x$$B$,6I=jE*$J0UL#$GJD$8$F$$$k$J$i$3$N6J@~$K$h$C$F0O$^$l$kNN0h$H$7!"$=$&$G$J$1$l$P$3$N6J@~$H?eJ?@~(B$x=b$($B$3$l$O1_I=<($GFbB&$N6-3&1_$KBP1~$9$k(B)$B$K64$^$l$kNN0h$H$9$k!%(B$R'$$B$r(B$R$$B$NA|$H$9$k!%(B$S$$B$O$o$l$o$l$N6J@~$N:G$b9b$$D:E@$H$9$k!%$=$NA|(B$S'$$B$O(B$R'$$B$r8B$k6J@~(B$(X)=x$$B$N:G$b9b$$D:E@$G$"$k!%(B$M$$B$O(B$R$$B$N%3%s%H%"$r(B$R$$B$r1&$K8+$J$,$iF0$/E@$H$9$k!%$=$NA|(B$M'$$B$O(B$R'$$B$N%3%s%H%"$r(B$R$$B$r1&$K8+$J$,$iF0$/!%(B$M$$B$,(B$S$$B$KC#$7$?$H$-!"$3$l$O:8$+$i1&$KF0$/!%$J$<$J$i(B$S$$B$O(B$R$$B$N%3%s%H%"$N:G$b9b$$E@$G$"$k$+$i!%$3$N=V4V$K(B$M'$$B$O(B$S'$$B$KC#$7$F$*$j!"F1$8M}M3$G:8$+$i1&$KF0$/!%$3$N(B2$B$D$NF0E@$OF1$8J}8~$KF0$$$F$$$k$H8@$($k!%$9$J$o$AD:E@$O=g$G$"$k!%(B\hfill C.Q.F.D.

\vspace{0.5cm}
\noindent
{\bf 8. $B2DG=>r7o(B.}

$BJQ49(B$T$$B$O0J2<$N%G!<%?$K$h$C$FFCD'$E$1$i$l$k$3$H$,!"D>8rI=<($G$O4JC1$KJ,$+$k!%(B

$1^{\circ}$ $B6J@~(B$X=x$$B$N(B\underline{$B7A(B}$B!"$=$N3F!9$NJ,;^$NHV9f$H0LCV!"0[$J$kD:E@$dDlE@$NAjBPE*$J9b$5!%$3$l$i$N6J@~$N7A$,M?$($i$l$k$H!"3FJ,;^$N(B\underline{$B@J<!(B}$B$O7h$^$k!%$H$$$&$N$O!"$3$l$O$3$l$i$NJ,;^$KAjBPE*$J4v2?3XE*0LCV$N$_$K$7$+0MB8$7$J$$$+$i$G$"$k!%(B

$2^{\circ}$ $B3FJ,;^$N(B\underline{$BHV9f(B}$B!%(B

$3^{\circ}$ $B6J@~(B$X=x$$B$N$=$l$>$l$N(B\underline{$BId9f(B}$B!%$3$l$O(B4$B@a$N0UL#$G@5$^$?$OIi$G$"$jF@$k!%(B

$B$7$+$7$J$,$i$3$l$i$N%G!<%?$OG$0U$KA*$V$3$H$O$G$-$J$$!%$3$l$i$O0J2<$G=R$Y$k$"$k?t$N>r7o$rK~$?$9I,MW$,$"$k!%(B

$1^{\circ}$ $B$$$^9M$($F$$$k6J@~(B$X=x$$B$r?eJ?@~(B$x=c$$B$G@Z$C$?$H$9$k!%$3$N?eJ?@~$O$3$N6J@~$N$9$Y$F$NJ,;^$r2#@Z$k$3$H$O$G$-$J$$!%$7$+$7!"2#@Z$kJ,;^$NHV9f$r=P2q$&=gHV$K!"$^$?$OF1$8$3$H$@$,!"$=$N@J<!$N=g$r=q$1$PL58BNs$rF@$k!%(B

$B$3$&$7$F2#@Z$i$l$k3FJ,;^$K(B$X=c$$B$H(B$x=c$$B$H$N8rE@$,BP1~$9$k!%$3$NJ,;^$NHV9f$O$3$N8rE@$NHV9f$H$O0lHL$K0lCW$7$J$$!%$J$<$J$iJ,;^$NHV9f$NNs$K$O!"(B$x=c$$B$K$h$C$F2#@Z$i$l$J$$J,;^$KBP1~$9$k7d4V$,$"$jF@$k0lJ}!"8rE@$NHV9fNs$K$O7d4V$O$J$$$+$i$G$"$k!%$7$+$7$3$N(B2$B$D$NHV9fNs$OF1$8=g=x$GJB$s$G$$$k(B($B$=$N$?$aJRJ}$+$i$b$&0lJ}$X$O!VBbNs$r$D$a$k!W$d$jJ}$G0\$l$k(B)$B!%$7$?$,$C$F$3$l$i$N$&$ABh0l$NNs$OBhFs$NNs$HF1MM(B5$B@a$N>r7o$rK~$?$9!%$=$l$O$U$?$?$S<!$N$h$&$K=R$Y$k$3$H$,$G$-$k!%(B

$B6v?t$H4q?t$,8r8_$KJB$V$3$NHV9fNs$r9M$($h$&!%AjB3$/HV9f$N(B2$B$D$NAH$r6hJL$9$k!%$?$@$73FAH$G:G=i$NHV9f$,6v?t$GFsHVL\$,4q?t$G$"$k$h$&$K$H$k!%$3$N(B2$B$D$NAH$O(B5$B@a$N0UL#$G0lJ}$,$b$&0lJ}$N>e$K8Y$k$3$H$O$J$$!%$^$?$3$l$O:G=i$,4q?t$GFsHVL\$,6v?t$NAjB3$/HV9f$N(B2$BAH$K$D$$$F$bF1$8$G$"$k!%(B

$2^{\circ}$ $BD:E@$^$?$ODlE@$G$D$J$,$C$F$$$k(B2$BK\$NJ,;^$NHV9f$H@J<!$O!"(B6$B@a$N0UL#$G$3$ND:E@$^$?$ODlE@$HF1$89b$5$G(B\underline{$BAjB3$$$F$$$k(B}$B$O$:$G$"$k!%(B

$3^{\circ}$ \underline{$B6v?t5UDlE@(B}$B$b(B\underline{$B4q?t5UD:E@(B}$B$b$"$jF@$J$$!%(B

$4^{\circ}$ $B6-3&?eJ?@~(B$x=a$$B$*$h$S(B$x=b$$B$N6a$/$G$O!"$$$m$$$m$JJ,;^$NHV9f$O!"$=$N@J<!$HF1$8=g=x$GJB$s$G$$$k$O$:$G$"$k!%$^$?<B:]!"$?$H$($P(B$X=a$$B$O(B$x=a$$B$H0lCW$9$k!%$7$?$,$C$F(B$c$$B$,(B$a$$B$N6a$/$K$"$l$P!"(B$X=c$$B$O(B$x=c$$B$H$[$s$N>/$7$@$1N%$l$F$*$j!"(B$X=c$$B$X$N@\@~$O?eJ?@~(B$x=c$$B$H$$$D$bHs>o$K>.$5$J3QEY$r$J$7!"$^$?(B2$B$D$NJD6J@~$O8_$$$K>/$7$7$+N%$l$F$$$J$$$+$i!"$3$l$i$N8rE@$NJ,I[$O(B5$B@a$N0UL#$G@55,$G$"$k!%(B

$5^{\circ}$ $BF10l$N6J@~$KB0$9$k(B2$BK\$NJ,;^!"$^$?FC$KF10l$ND:E@$^$?$OF10l$NDlE@$G$D$J$,$C$F$$$k(B2$BK\$NJ,;^$O(B\underline{$BF1Id9f(B}$B$N$O$:$G$"$k!%(B

$6^{\circ}$ $B$9$G$K8+$?$H$*$j!"J,;^(B$X=x$$B$,@5$J$i$=$NJQ496J@~(B$(X)=x$$B$O$=$N1&$K0LCV$9$k$O$:$G$"$k!%$=$3$G(B$A$$B$H(B$B$$B$r(B$X=x$$B$N(B2$B$D$NJ,;^$H$9$k!%$3$l$i$O!V$"$Y$3$Y!W$G$"$k$H$9$k!%$9$J$o$A!"(B$A$$B$NHV9f$O(B$B$$B$NHV9f$h$jBg$-$/!"(B$A$$B$N@J<!$O(B$B$$B$N@J<!$h$j>.$5$$$H$9$k!%$=$N>e$3$l$i$O5U$NId9f$r;}$C$F$$$k$H$9$k!%$3$N$H$-!"(B$A$$B$,@5$G(B$B$$B$,Ii$G$J$1$l$P$J$i$J$$!%(B$A$$B$,Ii$G(B$B$$B$,@5$G$"$k$3$H$O$G$-$J$$!%<B:](B$A$$B$,Ii$G(B$B$$B$,@5$G$"$k$H$9$k$H!"(B$A$$B$OA|(B$A'$$B$N1&$K$"$j!"(B$B$$B$OA|(B$B'$$B$N:8$K$"$k!%$3$l$OIT2DG=$G$"$k!%$H$$$&$N$O!"(B$A$$B$O@J<!$,>.$5$$$+$i(B$B$$B$N:8$K$"$j!"(B$A$$B$NHV9f$NJ}$,Bg$-$$$+$i!"(B$A'$$B$O(B$B'$$B$N1&$K$"$k$+$i$G$"$k!%(B

\vspace{0.5cm}
\noindent
{\bf 9. $B@5Ii$N8I(B.}

$B$5$i$K?J$`$?$a$K?7$7$$35G0$rF3F~$7$h$&!%JD$8$?%3%s%H%"(B$C$$B$r9M$(!"$=$N>e$r7h$^$C$?J}8~$KF0$-$^$o$kE@(B$P$$B$H$"$kE@(B$M$$B$r9M$($k!%%3%s%H%"$N(B\underline{$B78?t(B}$B$H$O!"(B$P$$B$,$3$N%3%s%H%"$r0l<~$7$?$H$-$K%Y%/%H%k(B$MP$$B$N3QEY$,$"$k8GDjJ}8~$+$iB,$C$F(B$2m \pi$$BA}$($?$H$-$N?t(B$m$$B$N$3$H$G$"$k!%3QEY$O4v2?3XE*$JJ}8~$H$O5U$K7W;;$9$k!%J?LL$NG$0U$NE@$K4X$9$k$3$N%3%s%H%"$N78?t$,$D$M$K@5$^$?$O%<%m$N$H$-!"$3$N%3%s%H%"$O@5$H8@$o$l$k!%$3$N%3%s%H%"$N78?t$,$D$M$KIi$^$?$O%<%m$N$H$-!"%3%s%H%"$OIi$H8@$o$l$k!%%3%s%H%"$,@5$^$?$OIi$N$H$-!"%3%s%H%"$O(B\underline{$B3NDjE*(B}$B$H8@$o$l$k!%(B

$ABCDA$$B$H(B$ECBFE$$B$r(B2$B$D$NJD%3%s%H%"$H$9$k!%$3$N(B2$B$D$r7k9g$7$F?7$7$$%3%s%H%"(B$ABFECDA$$B$r:n$l$k!%$=$N:]!"$b$H$N(B2$B$D$N%3%s%H%"$NItJ,$N$&$A!"H?BPJ}8~$K=d$k6&DL$N(B$BC$$B$H(B$CB$$B$r>JN,$9$k!%$3$N$H$-<!$N$h$&$K=q$1$k!%(B
$$
  ABCDA + ECBFE = ABFECDA
$$
$B$^$?$O(B
$$
  ABCDA = ABFECDA - ECBFE.
$$

$B$3$&$7$F(B2$B$D$N%3%s%H%"$N(B\underline{$BOB(B}$B$*$h$S(B\underline{$B:9(B}$B$,Dj5A$G$-$k!%(B2$B$D$h$jB?$$%3%s%H%"$K$D$$$F$b$*$J$8$h$&$KOB$H:9$rDj5A$9$k!%L@$i$+$K!"%3%s%H%"$,J#?t8D$N%3%s%H%"$NOB$J$i!"G$0U$NE@(B$M$$B$K4X$9$k$=$N78?t$O@.J,%3%s%H%"$N78?t$NOB$G$"$k!%(B

$B<!$K8I(B$X=x$$B$^$?$O8I(B$X=c$$B$NId9f$rDj5A$7$h$&!%8I(B$X=x$$B$,(B\underline{$B@5(B}$B$H$$$o$l$k$N$O!">e>:$9$k$H$-$K@5$G$"$kJ,;^$KB0$9$k$+!"2<9_$9$k$H$-$KIi$NJ,;^$KB0$9$k$H$-$G$"$k!%$3$l$,(B\underline{$BIi(B}$B$H$$$o$l$k$N$O!"EP$k$H$-$KIi$G$"$kJ,;^$KB0$9$k$+!"2<$k$H$-$K@5$NJ,;^$KB0$9$k$H$-$G$"$k!%$7$?$,$C$F@5$H$$$&8l$O!"J,;^$N>l9g$H8I$N>l9g$H$G0UL#$,0[$J$k!%$J$<$J$i!"J,;^$N>l9g(B(4$B@a;2>H(B)$B!"Id9f$OF0$/J}8~$K$O0MB8$7$J$+$C$?!%(B

\vspace{2cm}
\hspace*{5cm} $B?^(B3.

\vspace{2cm}
$AB$$B$O@5$NJ,;^(B$X=x$$B$KB0$9$k@5$N8I$G$"$C$F!"?^$NLp0u$G<($5$l$k$h$&$K>e>:$9$kJ}8~$K=d$k$H$9$k!%$7$?$,$C$F$=$NA|(B$A'B'$$B$O$=$N1&$K$"$k!%?eJ?@~(B$BB'$$B$H(B$A'A$($B$3$l$OD>8rI=<($G$N?eJ?@~$G!"(B$x={\rm const.}$$B$J$k<0$GI=$o$5$l$k(B)$B$r0z$$$F%3%s%H%"(B$ABB'A'A$$B$r9=@.$9$k!%$3$N$h$&$KDj5A$5$l$?%3%s%H%"$O(B\underline{$B@5(B}$B$G$"$k$3$H$,J,$+$k!%$3$l$O8I$,@5$G$"$k$H$$$&L>>N$r@5Ev2=$7$F$$$k!%(B

$B$3$l$r0lHL2=$7$F(B$X=x$$B$N8I$,@5$^$?$OIi$"$k$3$H$r(B\underline{$BAj;&K!(B}$B$K$h$jF3F~$G$-$k!%(B

$B8I(B$DCBA$$B$O@5$N6J@~(B$X=x$$B$KB0$9$k$H$7!"(B\underline{$B5U(B}$BD:E@(B$C$$B$H(B\underline{$B5U(B}$BDlE@(B$B$$B$r;}$D$H$7!"(B$A$$B$O(B$D$$B$N>e$K$"$j!"0lJ}(B$C$$B$H(B$B$$B$,Cf4V$N9b$5$K$"$k$H$9$k!%$3$N8I$rLp0u$NJ}8~$K=d$k!%$3$N$H$-JQ498e$N8I(B$D'C'B'A'$$B$G?^$K<($5$l$k$b$N$r9=@.$G$-!"?eJ?@~(B$AA'$$B$H(B$D'D$$B$K$h$C$FN><T$rJD$8$k$3$H$,$G$-$k!%$3$N$H$-L@$i$+$K%3%s%H%"(B$DCBAA'B'C'D'D$$B$O@5$G!"8I(B$DCBA$$B$O(B\underline{$BAj;&K!$K$h$C$F@5(B}$B$H8@$o$l$k!%$7$+$70J2<$G$OAj;&K!$K$h$k@5$N8I$H$$$&$h$&$J;H$$J}$O$7$J$$!%(B

$B8I(B$X=c$$B$K0\$m$&!%(B$AMB$$B$O$3$l$i$N8I$N(B1$B$D$G(B$AMB$$B$NJ}8~$K=d$k8I$G$"$k$H$9$k!%(B

\vspace{2.5cm}
\hspace*{5cm} $B?^(B4.

\vspace{2.5cm}
$BD>8rI=<($G$3$N8I$N89(B$BA$$B$r9M$($k$H!"$o$l$o$l$,2>Dj$9$k$H$*$jN>C<E@(B$A$$B$H(B$B$$B$,(B$X=c$$B$H(B$x=c$$B$N8rE@$J$i!"$3$l$O?eJ?@~(B$x=c$$B$KB0$9$k!%$3$N8I$H$=$N89$+$i9=@.$5$l$k%3%s%H%"(B$AMBA$$B$r9M$($h$&!%$3$N%3%s%H%"<+?H$,3NDjE*$G!"@5$^$?$OIi$N$H$-!"8I$O(B\underline{$B3NDjE*(B}$B$G!"(B\underline{$B@5(B}$B$^$?$O(B\underline{$BIi(B}$B$H8F$P$l$k!%(B

$B4pK\8I$O>o$K3NDjE*$G$"$k!%8I(B$AMB$$B$NId9f$O@Q(B
$$
 \alpha \beta \gamma
$$
$B$NId9f$HF1$8$G$"$k!%$3$3$G(B

$A$$B$NHV9f$H@J<!$,4q?t$J$i(B$\alpha = +1$$B$G$"$j!"6v?t$J$i(B$-1$$B$G$"$k!%(B

$A$$B$N@J<!$,(B$B$$B$N@J<!$h$j>.$5$1$l$P(B$\beta = +1$$B$G$"$j!"5U$J$i(B$-1$$B$G$"$k!%(B

$A$$B$NHV9f$,(B$B$$B$NHV9f$h$j>.$5$1$l$P(B$\gamma = +1$$B$G$"$j!"5U$J$i(B$-1$$B$G$"$k!%$^$?<B:]!"(B$\beta=+1$$B$J$i8I(B$AMB$$B$O:8$+$i1&$K=d$j!"(B$\alpha \gamma=+1$$B$J$i8I$O89$N>e$K$"$k!%(B

$BBhFs$NNc$H$7$F!"$$$^9M$($F$$$k9b$5$G(B$A$$B$H(B$B$$B$N@J<!$,AjB3$$$F$$$k$h$&$K8I(B$AMB$$B$r<h$k!%F1MM$N8I$O$D$M$K3NDjE*$G$"$k!%$=$NId9f$O$d$O$j@Q(B$\alpha \beta \gamma$$B$NId9f$HF1$8$G$"$k!%(B

\vspace{0.5cm}
\noindent
{\bf 10. $B%3%s%H%"(B $C$.}

$BBg0hE*$J0UL#$GJD$8$F$$$k%3%s%H%"(B$C$$B$r9M$($k!%$?$@$7$3$l$O(B$X=x$$B$N8I$H(B$X=c$$B$N8I$N$_$+$i$G$-$F$$$F!"8I$O(B\underline{$B$9$Y$F@5(B}$B$G$"$k$+(B\underline{$B$9$Y$FIi(B}$B$G$"$k$H$9$k!%(B$C$$B$r=d$kJ}8~$OM?$($i$l$F$$$k$H$9$k!%(B$C'$$B$O(B$C$$B$NJQ496J@~$H$9$k!%$3$l$O(B$(X)=x$$B$N8I$H(B$x=c$$B$N8I$+$i$G$-$F$$$k!%(B

\vspace{0.3cm}
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$$
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$$
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$$
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$$
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$$ \begin{array}{rl}
 C - C' = & 
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& + B_2M_2A_3A'_3M'_2B'_2B_2 + \cdots + B_nM_nA_1A'_1M'_nB'_nB_n.
   \end{array}
$$

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$$ \begin{array}{cc}
I(C) = \Sigma N_k I(R_k), & I(C') = \Sigma N'_k I(R_k).
   \end{array}
$$
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$$
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$$

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$$
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$$
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