This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
GQFAB K a ]B>N CQE>F^;XOFA=>E<\BAJaK E>WL EDN ` [<@DF K PJ<JL IfLI?EAYFDBXS O K?DED[<@F ` L I M>DC@A F>@C^cW;>[D;< K WXJ>DC@P K D@F< D @CJ P?AFc Y A;>F^;ABQ fM>CE>HF^;AD?E< D; E=QBD;CAJ JX[<@F L a ] >ICD D@CD@CJD;;AD A?EDMDFD; W>CDF^@CJ> 0 ;<[D;@JDEOQ;
/0"( %2 % #4k,$ $/%,h ,$$) %,# # ! g, $0$ & &7+%"% 7 ,/h #& 7 7 77 .$ & &.777 0 ,%( .*& ,h &. .& g(777 × .& " & & & / $ 4& & 6 5 2 2 !" (% !$&1 77.12 %1"( 6, #%)0/%%% 6k"/01 ! 7
. 1 #& "+#1 "& $) $#1 &
.241/
24
120 - 1203 24 120 )") * +,
&&.&& /$), %& && && && && && && && && && && && && $"), % & & & & & & & & & & && $")$/$), % & && $" (%)" ( & & & & & & 8 /24- 120 "(,)*+, & & & & & & & & & & & .&& ,%$ #,"(,h, $+h & & & && & & & & .&.& $ ",$/$ , % & & .&& $"),0") , % .&& $ ), %3, $+h & & .& & & 13 +,%$ "(,)*+,*& & & & &!& &&.&& "%,) "0%"(, +, ) ") && "%,)+,%$ "(,), % & & & & & /120/4/ %,$% & *& & & & &!& & & & & & & & ,,$ &&.&& 2 5%) $) +, !& & & & & & & && /$*/#"%,) && $") %!,+$ %*+,! && && && && && &&
7
.7 .. . .
8 . . .
1 131./101
& & 50%,h,,h %%",, & & & h & & & & & & & & & & & & & ! &.& ij!0,% & & & & . 1 ! && $#$ ,) $i3j 0/"( % & & &!& & & & & & & & & & & & & & && 5 "(/, &&&&&&&&&&&&&
2/1.- %0 1202/120/3 24 120/ ( & & & & & & & & & & & & & & & & & &&.&& , % & & & & & & & & & & & & & -",) && * * -", %,h ,$ " ( & & & & & & & & & & & & & & & && /$*/ % & & & & & & -",), && $0+%,) , % & & & && $),0"), % & && && && && && && && 24 2141 8 ,) $+"& & & & & & & & & & & & & & . &&.&& 2 "h%/h %%",, , & & & & & & & & & & & & & & & & & & & & & & & & & & & & &&&& 5-%)$%,) ",h, & & & & & & & & & & & & & & & & & && g$ +, % &&&&&&&&&&& & & , $+ 2 $0k$#3 & & & & & & & & & & & & & & & & & & && %)g$ k +, $0 $#3 2 + #$) ,) "%h & &k&$#30 & & & & & & & & & & 7 && $$ g$2+,$0 & & & & & & & & & & & & & & & & & & & 7
79 0 2
" ) 0
& & & & & & & & & & & & & & & & 7 &&.&& "(,) , ,%$ %% 6$h & & & & & & & & & & & & & && && && 7 &&
& & " *h, %%$$ & & & 5,+ ,)$ )%)""(,) 89 & & 0" & &$,#3$0", & & & & & & & & & & & & & & & & & & .7 &.& 2,)&g(i && 2,)g(i$,#3k +0, && && && && && && .. && %,) ",h& & & & & & & & & & . && 20"$%,,g(i$,# & & & & & & . && %+ $,, ",h & & & & & & & & & & .
&& "+#$+)1 k$/+ij ,,h &
97 0
120/ 24 $#$) ,,)" & &$,,) & & & & & & & & & & & & & & & & & & 7&.&2,)g(i&$,#$#$) & & &!& & & 7&&$*, (%)")*+, 7&&g$)g$ #!0"h & & & & & & & && && 7&&$h0/"( %$g$ # 7 !*0"h & & & & & & & & & & & & & & & & & & & & & 7&& $ h$$h$,) %,$% & & & & & & & & & & & & & & & & & & &
2/
%,)*+,& & & & & &&.&&$%,$+$ $$)$%,$+$ ! & & & & & & & & & & & %,) * +, & && % & & & & & & &&$%,$+$ %,), &&$+#%0)$+$ & & & & & & & & & && && && . &&2,)g(i$,#$+$ %,) *+, & & & & & & & & & & & & & & & & & & & & &&' ,$+$ $+" %,)*+, & & & & & & &&6) " ( && , $ $ & & & & & & & & & & & . +,h$, & & & & & & & & & & & & &
00 . 0 -04 -04
$0"#h% +%,,i,#, , $""! 0"h"0+$ ,%1 $)" (%$%$/,)#0),, - $i%0h,# 5*+"(2& + /) "$, % ",h & g$h%)") j(i(i$%*+,! #0)1 #0,(i h%" (%7 ! k k)"$/$k,) $%) (i $%j , ) " $) & !! 7-#01 $0$/$k%k)",#" % ! g 0,/ /0" $,# ", !(i1 *+, "k$%) ") #0+, $,) & ,)1 $)$(,/)%i
(i1 ,"#(1k0h$,!%h- $$#$) )"0/,0/"( % $) +j %%,+,%$ "(,!,)g(i$,#& + ,%,) ,hh$%) "! "1#%$h ! k j $"#$% 0 ,) 1 5 %,,h%$#$ % $h & 60,/! !+"(+$,)! k" $ & !1 $, ! "( ,%" 1 "%#0+1*$+"$% #,hh % ) !" )#$(% $0 $, * $"(1+ +ij+i/,,i"( $+"$% ,hh,+$"(,# "& "+!1 ! %) /)%, %)#"h0 $+%",3 /k "0, 0 h"h) "h ,1 /0 $/" 0+ ) $0"#$ *" *%,1 $/"0+,, "#$ $/$) ,$/$ )1! ! $h ", %) ", "0, /,$"(,) %"# %kj%& /,"(,, h$ ", %) 2)! ", k"(h0"(,h& #-
k$(,$"(,),hh*) ))" ( ! k j $"#$%/"(,h,1 $h (,/ ",h($ )kj0, 0 "h&2),$0"#, "(,) $0 ! %$"(,)/,,!1 h$ ) %,,$) ,kh ,h1 +$%,( !+"(+$) * %1 +,h"0! %"(, 1, 5 " & 0h1 $%/,% $!"#$%0 %+0%"( % &"h 1/$0" !$ !h%"hi ! (/, % j h,$"( ,! (i !"#1 )+/)%, ,$)/0,,),$+ h/) ,#& & %$)"(/+i k h "+ "#0$( %# "0$ ,0$% , # " +"h 1 /)%,h$#%"h",, 1 1 )%) , 0$, ! ,#1 %$h,1 0% k"(! /,i& , 1 %$) $0#% * "(/%,)/ % & ! ! (% #!& j, $)!$"$0%$"(,) %$,,#,","& k6 $#,"$%#/0,h,#0#%", !$0$- 1 &&+%"%) k/#, !% %"( #%,%$h0"h%" $/0"( % %,, ( / k0$#," k) h +-"k $+& 9 $,h/00$ +# %$)$/,"(,) $%%%$!,#& h, ,h ! k"#0$h ,# "%/ ,) !1 $%/0, * * ,0+ +,0,"(,) + "0%, ! ,1 $) +#%$"%$%0( & & j%$/0, +0/h%+ $%",)/,,) & ,#",,) 0 k +%) %",, "( 1 /0 & $ kj(% k%-
rssrtquv1 wxtyrssrtquv 0$ 77 $ "$,,) tu ! 0$ 3 2!%1 .1"(!" (% ! %) $&1 k1 2 % ,$,$$)%,#$/%,hk& # 5, "#0$ $+0,% 1 )*0$) 1 $,% ! +0,% "# 0"(,hk"#0$, &,+ +1,0 ( 2 2 & + ,%, +," 1 !%$0%$"(,) ! ,$%" " %$,% !,#&
$#+,/,,+,h ,+$"(,) % ! "# $ h,/) %h! +j %+"#$ 1 !""#$ &1 1 !%)"hi j 1 ( • " ' $0",0"h,$#,+$"(, & ' #'1 "#$ ,%"% h,%0 ' & • " ' ,$0",1 "#$ , ,%"%h,%0'& 5 "(/,!%0+ #$0",h3
,h%)! $0"hh/0 (0"h& *+,k" ,) " (i$0",h$) h%"h & 5-h,$0,!%,+$"(,#$h0 $$1 ,#0,$0" ,,h *+,h%)#0/ " % & % ,0%/h($#$+1 $h% "% h 8&2,& k)"k)/,($0", /%3 1 , & k "#$ " ' ,$0", " ,1 h ,,#, k %"% h " ,%"% 1 1 % & 5 0" k),/," #,# ( #1 k) ,%"%( h1 ,#,,%1 "/"%( #$ h& k)(, 0%) 0"#$%#+ & " "(,+$"(,) " ,0%,) $ 1 7 "1 , %%"*% { ( } 1 $),+$"(,) k k "i ,) "0%"(, "%% j ) 1 #% k ) $h , $+%,) +,"#,) 1 & %)"! *k$/ ,$0"(,h 1 1 /,,h+, !0%+h,+$"(,)$#+, $ h%"hih$,"(,)"& 1
"h *+,!1 1 0! %"(,)$#+, /,,h,h%)" $k+ --
"(,#$0",h ( +h ",1$0&0 k ",h#+ )($/,) " 1 )%) 6 k *+,!#%$(, +0 "( & 1 -1 ,$$ ,+ $$/+,$0",%) " %)1 "1 *+,h1 $%,h− 1 7 $ 71 77 % %,,,& g, *+,$!k+ "(,#$0",h%) " ( k 1 $#+,$) h%"hih ,,) "!0, 0%"(, ,+" && ! 5 "(0 h" ,/0,h"#$ (i$k&%" "(,#$/ hk,,h& ! ! $,h#$, ( h ,,h% $%,, k (, +0 ,1 "# 1 "(+h k"i0( $ $&5% !,0 , (1k),$,h(/"#$1,h%"hh& $$ ,%$,#$ +0,h3 1% hh%)"h*+,hk ,+ $#+,/,,h !)($ $"(,) ! %)" ! * ,0% i0+$0" 0" ,, +, 3 N → N & 0"1 " %) "h h"#$%) "h*+,i1 &1 "0+ij!"#$ & 0i ' $0" j +i 3 " ,%"% h, 1 & & !$/+"(1 "7,,%"% h ! k ,'1 0!$/+"( % & $ +0, ! %,+$"(,) " ",/)% h k#+ 2, ! " +j %+"#$ $) "i 1 '$0"h $,0" 1 ",,,+$"(,+ 1 %+"& $+# "% "$/$ "#$%& "& !"%'() %* '+1 ',- '∈ "1 ./01023074 %)- "&
6%0,1 $ ,1 k0,,$/, ($/$), %$/$)& ik,, , %$/$& $/$ (, %$ ,"#,$0"hi " , ,+$"(,) 1 %$,"(,) "&&K AG>`
d@?AF^WAJ>;XF<JCABE>@@Q`MD;<
"1 ,,0"#/0+( "0+i% jk" k"(#$$)h ,( " % j k"(,#0,#,,( #0, %k+0,,)& !$+j %+,# %%",,) $0", "#, %& ,$)/,3 2, % $"!1 " , ( k" ( $0",h%)" *+,& ,! %$!*"1 ", (k" (/,. 2 , %)" +,& 2, % "$ "1 "# ,#0 "+$$ #%$h h *+,h $% ,h7, ",",$0"!,,h%,"11 %)-"& k)0/( %%",,#%# ( $0",!1 ' % "(/+h%/, (i ",,h"#$ + (& " $"hh ,$)"#$ && 1 "+$$ h*+,h,!%)",h( %"%)"& 0"1 "#$ "#%%) ' ,h%3"+%,%0 " 1 "#$&1 0h1 ,, " '&
7 "(, 0" %)0(,%) 0 /,( 1 $k5+&k k"!($0",h %)!$ 1 + ("%)( * " +, "h ,$)"#$ 1 "hh"#$ &3 & g#0"$ 7((.( 7 7((. 7((.( !
1 )+ ,%" %%",, ( 0,# && "%"($$0",h$0",h ! %0,,,"#$k (,$#+,) !$-1 /,%$ + $/+"() ,$) 1 !k" ( k)1 "+ h"#$ $ "hi j 1 ! 6 ! k * /,, +,& " (j + 0( h1!% h k $ ", % ( " (/,, %)"!*+, , 0"( ,$$ & 1 1 3+ ( " (k" ($0",h%) "!*+,1%)!,$)"#$&&g#0" (k" ( "h /,,!*+, ( "&/,%$k+,( ( ,$0",%$%, "+ )"hi 1 j! +*+,i"#$0!k%+ &1 ,"(% )"#$ $/+"($ ! &%)0 i%0 & 0, %%",,$0",$"# j!%3, , k "$!"1 ","!k+! %,+$"(,) " (, %/,, % i1 "!*+,0$+# "% 0+$0" ,, %) 1 # ",) ,$ " (%%) "+i " 0%"(, (& 0" %" 1 + ($ 1 -&1 ,+", ! ! /( %, $ "h"#$ & &g$($ $+i% i0+$!!- ", k)"#$*+,i3 ",'-#$ 0" ,,+i & h%"hh"1 " ' " ' & 2)$0,#,h%"hh1 " k)"#$ "#1 ,0,,#$ h%( h"(0, " %$%, "+$ k+,0$/k(,k""#& 1 & $ +0,,, $+%, h"#$ 1 ),/,(1 + "$"h, %",&
$ ,k0,,$") 1
, %$")& "0,,$ " $ "hih"#$ & 1 k "hh"#$ $)!! 1 & # % $"""(,%)&",h i $ ,,,# ",1
$/+"()$k)&& ,0,"%( kj#(&%$h( 0$+# EAJDM
AG>`
,) "$ ",+$"(,) % "#0" & ", $"- ,, 0, %% )1 &$/$& ,"#$ (",& %+ & "$,0" ,$%$(,$) 1 #0"-,,$")3,0$0$%$h($,0 ⊂N ⊂N × ⊂ N×N
", ("&7((.( (/, 1$) & ,$,0" $,0" " $) 1 "+, ("#$ $ &0$+#+i $,+3 1 0$+#! "#$1 $"hij! "hij! &1 & 0",, 1 0"h%) h ,,h$,0", /0,,#"'&,0/+ (k)/, "#$ ' 0( 0,/,, 1 & 1 $,"/0,$%,0,/, 0" ! "#$ )+/, ' $% 0"" " " 1 1 %&&1 *,/) % $"&& %i&$$,
6 ,#%$1 $/$) % $ "), % $")0",,h& 5$% "), %,$0"( 1 $ 3 $/$/$ ) 1
,+$"(,) "$ 2, %1#0,h%"h "#0"(#0 h$!,$#$/$ #, % $,+$"( $h"+h1 "$ %(,) ",,)3 & ∈ ⇔ ∃h(i ∈ & $%) k %$$h"i "#, $"hi#$ ! "#$0" ," " j (+0"h( 1 $h$/$#, ",)$ %$) k"$ 5% " & $%1 "&$", %1 $ "h"#$ 1, #, %1 hj #/%($h$/$ $ ' ( h i1 k #%$ )" ' h%"h h%,$%) #$&& %! %1 %0,1 $/$& ! !%,$", 2)%0"1$ * 0"(%$,%) ") +, &2,1 !*+,,$$ k" ($0",h%) " 0k$3 "(, 1
,+$"(,)$#+, +,h /,,h%) "#0"(#01 #0!
#$* {h(i | $0",$%,} h%"h h $"), %$,+$"(,) "& %)!k"& g#0 +j %+"#$1 + ( ! $ "hij " ($0",h1 (ij!% 1 ,$) $0", & "$(0"h ! 0#/%)"h(j /,, 1 ! , "+"#$ j % & ! 1 $"hi 5$%1 " h"#$ $ "hij 1 1 *+,h!h%",h% %)"hh"#$3h, $)1 $%)!",$! %0''10 $%, "(h$h%" (1 ! !",,$k+& %$ + ( ,h*+,h ,+$"(,) $#+& ,/,,h # , % $ & "' 0"h$)$0 & ' "h h, %% 1 ∈ # , %&$ $0 '$0",& $$ "hh, %%& '1$$)'$0",$,0" & k$/$"#, k!$/ 1
$ %$%) " *+,$ ")& k 0" $/ $ $ "# ,1 !*+,,"+(3 %&$%) " %/h(#$*& 1 $ (# $"), $$%(,$%+i$0,+ % × +N0,0"h k$/%,"#,1 "($0,-& ),hi h & Q@C^ ?DED[<@F
i∈
0
⊂
0
⊂
0
∪
0
∪
QE>J;D;
DC K[CABA`;A>F=AE
! ! ) $$$$"#,$ *k+0 %1 ,h%"hij# h$/$)& "(,h "(/%( h,/) %h+,%$ +,h& %$h1 *+,h %0%+ ,+$"(,) $#+ ,%h%"h ) "# $ 0"h" %) ") h *+,!0,#$#+,1 "0"h0#'*+,h 3 7→ '( , *+, $ *$%,,' h%"hh ! "% %)") *+, 0,# %) " $#+, $0 % $i h & 5,1 , *+,h ,%)") *+,0,#$#+, ,kh/,)1k)(% i0+$0"!,,)& ,"#,$0",,0(0"h0$+# 3,$$1 *+,"% *+,!0,#$#+, !0"h" k h% 0%+$#+,% +0+,%$ "(, ! i0+$0"! ,,)%)") *+,! 0,# %$#+, ,h h%"hih% i0+$01 " "!,,)%) ")**+,h0,#$#+, +,&k6%0, $) %i % +,%$%"(1" ! * ,) +, +j %+i 0"h"i ) ,) & "(0"h,
"i%+i$"(% $/0"#$!*3 +j %+ %)"h! *+,h!0%+ 1
$#+,% h%"hijh h +,%$ "(, *+, 0"h " %)1 ")*+,!0,#$#+,&* % $#$)1 %)"hij +, 0,# $#+, %)"+i "0%"(, ( 1 %%$h0%/$ (( ,$$ ,h0",) 1 $/+"(+$ k)-! $!-& " ( $%,) #$),%0 & g#0 *+,h k+0
"(,!! *+,!&!, !k+%)"! +,%$ ! * & 0%)" +,! + "h $#$ 1 %) * "#$ %) "hi j +,i ( +j %+,$$$0"h 1 1 $#$-"(/+#h/) $%,h ,$,h$%)!!$#+,%$+ 1 & " 0 %($#$+ ,$ V@D@D[D;
% $,+$"(,)"1 +,%$ "(,0"h" " ") , %,+$"(,) & ! 6 k $ " ( $0",h +,%$ "(, *+, & , k+0+,%$ "(,)$") , %k1 "(+% h$", %! ! %)" h%"h h " (i$0",h,$ *+, & :>G?A@CEA
$0)0+j$/0") $"+,%$!"(,+i *+,i0"h" % %)") *+, 0,#
$#+,& 2 ," 0"( 0"h" ! % i0+$0" ,,)%)")*+,!6/)%h1 ,& 5 ! % i0+$1 +j %+%)" ! 0"h 0"!,,!*+,0%+$#+,% +,%$ 1 !,,)"(, ! *+, % %)")% i0+$0" " 0,#$#+, & h 0#,"(,! , $+! "(/+ 0/)%h,k !!, , (, %% k ,,)0 h,)0$ !& + (*$/%"(i0+$0" ,,h *+,h0%+$ ,h%)"h% ' $0#,"(,+i #+,% +,i & '('& 6%0,1 ,$#+,'*+,h %0!1 *+,h''"h *+, g ! & k$/1 %)"h% i0+$0" ,,h ! *+,h " , ' h% + 1 *+,h,h%"hh+,%$ "(,!& + $ + 0,,$00"h" % "% %)")*+,!% " ,) kh/, /,, ' '(' $(, 1 "( h/,,h ' '('1k, k #+ )(,$0",)& g,,1 ($ +0,h !h% "& +j %+%)"h*+,h!,1
+$"(,)$#+,/,,h ,1$ % i0+"( h%)k!"h*+,h , ! ! ! * h30"h"i %) " +, , 0 h '' "0,$%, %,h"'1 kk/,,h'',$% )k"1" k 0",)1" $0",)$%,) & ! +j %+% + /,3%0#,"(,h *+,h ''('/0 (%)"h*+,h ") 1+,%$ "(,h0"h" & ikh%)%) *0%+$#+,% * +,! 0,#$#+, "h +, ' ' ' h ( $,$ + '(''&
9+j!%+%)"h*+,h1,1
,h ijh%gi0+$0" ,,#%) "#$0" & * % ' ' ,$$ +,h #0 1 1 1 *+,h/$0)0+j !$)& 0"1"ik! ! ,% i0+" % i0+$0" ,,$0" h * * $0", % #0 +,h +,h 1 , *+,,0,+ k"(1 +"ik$0" "! h* 1 #0 ,$0", "ikh 1 % i0+$0" ,,h +,h"h & AG>`
0
0
K I CDAEDBX;D
1
, %& $*$+"$%3 +j %+$ & ", 0",, % ,$ ") * $%) "+i +,i 1 ,i ! ! ,h i0+$0" j +i% ,,#%) "#$0" k+0 ), %&& k" ($0",h 0,+/$0",!-0"1 $ " $" & "k)k)"$/$1 *+,h ( " 7 ( ∈ ( ( "∈ ! k)"k)%)")% i0+$0" ,,)$0", * +, $%) ) ,"$%$h ", 1""%1 ""1 %)"h& "/,$ "0( ,,, %%# /" ($")1,$/$)&#,h( $0-1 ' ' , % '1 $$) ( ", "% ,(, $+i*+, ,&% '1 $$) '-h$#$1 k,%"%h,'& +,#0#%$h1 $ "
$, $, $#$) %+ ,$+ ,$/$& k" ($0 i0!"0+ 1 1 ! ",h% +,%$ "(, *+, h%"h h$ k ,$/$ , ") ) %$ " )$ & k"%)h ,,h$, $#$)$/%"( ! ! k k ,+$#+,+ ) " )$/$ ,) 1 k k)" k) "+! $, ($#$) $/$ & k" %,,+i1 %)h +k"kj+i ,%h ,, $, 1 /0+ +/,( ,/)1%i "0,,h$#$,0,,%0 ,#0 %"$k"! ,%& 2,# "+"+$#$/ #$"#$%,h, %,,) g(i$,#"-,) "%$k" ,%0"h , k)%% ! "(,& #$ ,$/$10/ Q@C^?DED[<@F
E>WEDN
RA`;AF
@F
i∈
}
⊂ N×N
{h
i|
h
i∈
h
i∈
P
}
−
)%$,! h%)")0! %"(,)" 2 %/0 & ! 5k"(h0*h$ +0,h/%"h0!%)$)3 /(+ ",0/,,
8 +j %+%) *+,h1 $1
"h 7 ,i j!h"(/,,h ,i jh% i0+ $0" ,h ,,#%) "#$0" & ,$ $( * +, *+,i ( 7( 7( " ( "7 h%%0+1 ,$0",1 " , &g#0"ik% i0+$0"!,,$0"$0", h% i,*+, kk+0-$,+"( 0++, +0%)")&
$/+"(,$% ,h/)$ "), %&%$h10%,$ ijh,%0$ " $&#' &"', %1 ", h 0$+#& % 1 0,/,,$
ijh+j %+i 0%,$ % " 1 $),0"hi $"), h , ,$/$ ) % 0"1+ (%)&"h*+,h1$ h"(/,,h 7 ,ijh% i0+ ,i j ! $0",,#%) "#$0",h& + ( " {| } {| 7} &#%0(1 + (,0"hi , % " $") h & k $/$), % +0 ( 1 0$ ",$ h9 ",k$1 $!& g#0$$ h*+,h !0",,i 0, % $%,h %,+$7%,,# $0" & "%+%$0, %%,$ 1 $/+"(+ +j "#,$/$#,0
00
00
00
"0%, %, 0")$/$) % , %1 ,0,/,,$/$& :>GA?<@>C^?A@CEAD;;XD?DED[<@F
& 5/%!, % )
1 ", k ,0$k ,,)$")0,,1 ,,$ %& ",6 %,/)%i$"& 1 "#0",,+,, & %0,1, % k)($/$ , ) & , % +j %+$
& 1 5,+,1k)$", % "+,,0",,
/,1 0", ( hk"ik)k&,,) $"),$ %&' )#$,$%( "/,0"h 01%( ! k #$"#, % 0 # hk)0"hk ,,) & $ , ",% k( h1k)%, " (k ,,0/ ,# ",%& k,#$,$%( "0k1 "( ",) ,$$1 /,%"h(0 , k %,$ 0 !.& %"h("(0, ",1 $ k "( 6kh ,, $+i0$k,& + (+,%$ "(, $" ,$ % $1 $0 , ,!$#% $i h% ") $-"& +0,/) %,+$"(,) %( , %,$ $ $/,),$ ") & % %%(0, , % $, %$ {h (i | ∈ .} &
, %$ " $ , $/
%{h(i | .}& $ $ #, "hh#1 ! k+0 k$ )%($) +$) $%) ",+ 1 h ,$ $" % $"h $,& 6, 0, % ⊂ & $$($" , % %$)",%$1 %0hj % & k k , %$ h "i ) ,,)
k %& 0" " $"), 1 k ,, "1 "( .1 + 1 ,%0$ ", %$!1/, ($) $%) 1 & ! k $)/ +0"(%k1 % & ", 0$+#! $,)1 , %" ,, 0",,1 "(+ $0 7 0 .'− ( +'$/",) "#+$,0" !/$%) 90, '%$"! "1 %% k k "(.'&D@CJA % "(,) +0++ Y AG>`
0
0
0
!! 6%0,1/h0%+%)")*+,!%)$ +%$0,h **%! " & % )"1 $#$0%+ *+, ,) ,"#$ "+($#$+ k+0/ $/+,h/) $#$$%,h, & h(/0%+0$#$ % %+ij0%+ 1 ! * 0,%) ") +,h #"%, $#$) 1 l|& ! $!utmvuy %,, 60,)#%$(,$#$ k),%0%( $#$$%,h 1 !& "h #+, *+,h%0"h/) , $0 ,$ ( % &"* "(,h %) , % hh+,%$ +,h 0"h" 1 )*+,!0,#$#+,/0!*,+$i 3 #" " 'h%"hh,$ +, 3 7→ ' 7→ (kj& )* % k" ,1 &)# $% ) %F ,/) * !%,,$/%"(,#, %i % i0+ k k $0" , $ 3 " (/, N → F1 !$# (% ! , % , F & " ' 1 gk$/1 " '*,/) %i $$k !&,+$i, %$#" hh +,h0%+$#+,%/0 ! * 0,#$#+, +, h%"h h !0"h #" & "(, +,%$ 5"( *$+"$%(0/(+ %$ 0,3 $,$) "%h,,+$i%) ! +j+ ! * ") +, %+"#$ $) 1 k)!0%+,$%)") *+,! 0!,"i $) ,$/&k $ #)$ +1kk)+,%$!"(,h g*+,h10% /0i h,+$i j ) "%) " 1 & 6 ,+$,/)%ik ! "# k & 0, k# +"%h"3,$ +h ),+$h )"1 #%$h1 # $%#$%1 &
+ ( 0%+ ,h %)"h+,%$ "(,h *+,h *+, 0, 0"h " ,) %) ") ! * * /, $, -!,h +,h +,h ! $#+,% % #
$ ,/) %i +,%$ & k!0%+ ,!%)"!"(, *+,!1 "0"h"i * +, -! * i0+$0" +j %+% ,,h%) "h +, h 1 0"h$! ( ( $%, $% %, h1 k),"1k% k k ) /,,h,$0",) " " 1 & 1 $0",)$%,) $+# "%1 !*1 (*!+,h0!! *-,$+,$ +,,$) -,$ 1 +, & +j %+#"%,h+,%$ "(,h*+,
h& $%)! k ,,%0 & & 1$,+,%$ "(,! /"( %$) *+,0!#"%,+i+,%$ "(,+i*+,i& 5,1 )$"h"% $#$)((( # %,,#h/)$#$$%,h% - ,h0","#" '( $%,)$h0%/$ $/+"(+$,,h$#$) %0+ & + ( * $( (h "h +,h 0%+ -0$+#h%)k 5,0"i $#+,% +,+$"(,+ & *+, *1 ( *+, "+($#$+ 1 -! / $#+ $h"+ h "% $%($%) 1 %k"(,,$%,) &,1+i$#$+ "+("# ,0 %h/) %$#$$%,h ! /,($%) $#+, "(%$#$0"h ""(/%($#$+ ,$0",, ,) !$#$ % 0"h % %0$#$) ,%, 1 *k$%,,) $%)$#+,& %)/) %( ! 5 $ & "(, h%0" ! *,,%0%( % $,h+,%$ +, "(/%( h "(*! +j %%,h& 1
*+, "(,h0"h" ," +j %+%) "h 1 ! h$ $#+,% 1 +,%$ (h%) *+,*!0%+$#+,% * ") +, -1 * $%#$#+, $0 h! 1$ +, ( '(( % $i h% %) ") *+,0%+$#+,% & $( $+ g+i*+,i, & (%),$+i%) "+i,+$i$ 1 % "%/,0,/,, % h(i ↔ ( $h( %+ij"$( N×N N "( 1 % i1 )k0+ +0,/) %(,$ !"(,h $) & *+,h0"h%) 0%+ ,h%) "h+,%$ -!1 %) * * ") 0, ,) +, "h +, ! *$+"! '(('((*1k+$0" h ,,h 1 ! "(, 0"h%) 0+,%$ ")0%+ ,) +,!& 0" + ( "1 $/%"(,h%) *+,h0%+$#+,% h $%) "+i & ! *+,i 0, $0" ,, ,+i ,,+i"(, 1 !0! ( ( & "(+ +,%$ , 1 & "h '1 0"h$# '( h $% '%) ' #" ",,)$%, % '(( ( ( ( (1 + '- , *+, %0 & 1 +,%$ "(,h*+,h$!$#+,% $,& ! +,g$( ! "(/+ 0"h$0",h#"%, ! 5 * * $"(, %$ "(,)%+, 0%+$#+,% & 0$+#%) #%$h $%,+$( % ") 1 *+,0%+$#+,% ) ,#"% 1 ' ' ,!&$"(,#%$h " 1 k+0#"%, ( !( ikh%) ( (* $%$ +,h 1 & **+,h 0%+$#+,%% "h $ h$0 ! ! , ' +, 3 ,, 1 ( g #0 ' ' +,h *($+ ( ( 0"h% & $0" ( !,,h (* 0"h% + 1 k%,h/$0! '!(1 +0%"%$h$ " ",h#"%, +,%$ "(,!*+,& 5+$1 % %+ij #"%,)+,%$ "(
# & *+,h1 ,/)%i# 1 " ,)g$(+ ! ,0/(,) %$,+%$0,h $#)," 1 + ( 0%+ & ,h #"%,h +,1 *+,hg0"h " %)") *+,!! "(,h %$ 0,#$#+, ,& #0 +j %+% i0+$0" * ,h +,h $h,$ 0%+ *+,1 !,$ /3 !0,#$#+,0 (/h◦ 1 (( (((( 0"h%1$0%+ & "+i*+,i 1 ( ! (( ,+i%) 0"h$ (& $0",i !+,%$ "(,!*+,1 ,!0!hh% i0+ #"%, *+,h $0" ,h%) "h 1 (!,,h0, (0"h% g #0 & ( ( ! ( ( +*+,h 1 $0" ,,h ((1 k+0!& , 6$0, *$"(, %$!0/"( %, & ! k k) * "(, ",#"%, +,%$ +,$ + 1 k 0"h"i#0$+##h/) $#$$%,h -11 0"h ! $# h%) ") ,$$$ +j % k)%)")!$, "h$$#$ #h/) %" %$#$)h/)& "h$ ),$/" $% $#$),$$ " * -$#$+ +, & g$($ $,%)! k$#$$%,h 1 ! k $$$ h%"h h$#$ ( i /*+,! h-$#$ & +"%i1 $#$) ,"#$ $,"$%(% k %" -$#$) $ (0/( & +%$ik),11%$,k$,$ 0,3 Q@C^ MJQBD@C;>P JX[<@FP Q;<JDE@>F^;>P \Q;GH
\Q;GH