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!#$&% ')( *+, - u q j = p j 21C&*,+-I%'*%'19?+& S*#4&%'(*,:s.?=>1H=#G i p j.0*, v u q j = p j 21 &*#+I%'* %'19?+& `*#4&%'(*, w.?=>1h=#g i p j.0*, f H xw=(bf&1'.0*,%'>+f2 i (DE.F*#19w&*,+-I%r;19+f>8&2=>*,21' #+:s%'* %'19?+& &+&13Bf&>$(+?5 i F %3* d #4>+F& >+ 82(+*,+fw%'*`1'Jx#+-@h21'#+ ( H i 8-?&g2?v%'( >%3gBf& i F (DE.F*#19 %'* %'19?+& 5 i Bf&1Cx).F*#19s21 p ((p q) r) 8&>++&>+fE%'(I.0*,%'>&V #? (DE=(Bf&1'.0*,%'>+f2 p, q, r v, v, v v, f, v v, f, f Bf&w%r; (p#+:8 >v21'$ 8%919Ž>v>+ q r) q r) (p q r) (p r) (p q r) 8&&13)(+ 5 (p r) (p q) v}>~c<le } e/%'* +&?+:&+&13@A192=aw%3* d 5 ds$b/($#g ZK[ ŸF œl\v7 t$]?2!#$&%' *#%'@>&%_^e2?8-fd1921'#+&+>%exm=(bf&1'.ž*#%9(+f2 +&! #$%92#-s!#$ +&?2$ *,%'w@a#+;jx#+@a21'.##5 `baa~c9l? d:+e!<;:>9;?st c +S8-(v8&>+&2w%3* d s%3*m+=>?*,21' #+SAE+&1'>)%'w2=D%HV*0(5 c +S8-(d*,-221C@A?+D13=(2(/%'( G i = q 1... q n *ž.#(@ u q j = p j 21 &*,+-I%'* %'19?+& S*#4&%9*,:s.#=(2192=?G i p j.ž*# v u q j = p j 21C&*,+I%3*%'19?+& S*#4&%9*,:s.#=(2192=?G i p j.ž*# f G (Dw=(Bf&1'.ž*#%9(+f2 i x).f*#19s*, &*,+-I%r;19+f>8&2=>*,21' #+:w%'*%'19?+& 5 i %'* F #4&2>+F&m>+782(+*,+fd%3*@>#+LJx?+@h19?+7( G i 8-?&d2#-v%'( 2>%3gB? i F (D)J*,-22 %3* %91' #+ 5 i p ((p q) r) Bf&1g(DJ*,-22 21 8&>+&+>+f`%'(.ž*#%9(&V # # #? (D p, q, r v, v, f f, v, v f, v, f f, f, v f, f, f =(Bf&1'.0*,%'>+f2 ( p q r) (p q r) (p q r) (p q r) (p q r) Bf&w%r; #+:8 >v21'$ 8%919Ž>v>+ ( q r) (p q) (p q) 8&&13)(+ 5 ( q r) p E?+:&+&13@A192=aw%3* 5 ^ #&e$ >D2E+&)!#$%9E2# d? G#?+ 8 >&/19%'1'2>e%'*a&=>$ *,V@V &)@A?+x2-@h21'.#)82=@A=(&>+f2?G #+S8 >d*#d1 t u 2($ 8%'*?@A> 8*,)%3*m! #$&%'w=(bf&1'.ž*#%9(+f2 p q (p q) (q p) u 2($ 8%'*?@A> 8*,)%3*m! #$&%'w=(bf&1'.ž*#%9(+f2 p q p q u J*,1'2w(@A(+w%9I+&=> f*021' #+-/8-*,I%9!#$&%'()&w67#?*,+ Gf%'w8&%' %r;19+f=>19(&ew%'*m!?2$m&%9 u *,8&8&%'13B?> %3* 1'D21'4&21'.F1H= 8*# *#8&8 #2 *# Ge # % ;1'+F.#(2#G JxBfC; #4>+&1' %3*ƒ!#$ +& #$ *,%'g@v &(@V =>#5 p ((p q) r) p ( p n d gq q r) p ( ( p q) r) p ((p q) r) (p q) (p r) q p (p r) ( q r) (p ( q r) n

! #$ %& ' ( ) * + E+K6# J W«(DE&+&a&1'Jx#+@A21'#+:s%'1H22=>V*,&KL5 c +`2V*ž.ž*#19%'%'>V*$ *,1'+f2(+*,+f)&+&13Bf&>$>+fv*ž.?(@g()@>%'*#D>5 k * 8& #821'=A=w& (;>K8&21'$ss%'*mJ*ihA #+:2&19.0*#+?t ZK[ ŸF œl\v7 :t ]W#g!#$&%'w(DE=(Bf&1'.ž*#%9(+f2 &+&a@a?+ljx#+-@h21'#+:s@a%3*,-d>5 c +S+&,>V* +`(+D($4&%'as@A%3*,-D) #+f)%'*@>#+ljx?+@h19?+`xe=b?19.0*,%'>+f C(F ) 5 F C((p q) = { p q, p q} E+ 1'+f2(28&=AV*019?+ «( r«5 & J @A?+f2V*#13@h#1'2gD1C>vD(&%'>$>+fED1 D1s>7D(&%9($>+f7D1s(%9%' 2*,213xJ*#1H 5)l+ 8*#D1'@>&%'19( F (DE&+&a*#+f21'%9? #1'#5 x C(F ) C(F ) F M,.-)_a\Ab YSb/, OIH X\A[ U TAXaR 8&9;:=<;:>9;?& t 4 1 (Dw+ %'1H22=(*#% C;&+@>%'*#2 G<?+ +&#2(* %3*:@A%3*,2#+fg2#-w%9w%919D=>V*,K u C C \ u 2 #+fe@a>&k` 2*# 5 C u (p q r) \ q = p r k *@>%'*#D (D)&+&sœ0ŸF«(! & & L )@A%3*,2( C Cy > Cz >;19% AK1'D2w&+:%'1H22=(*#% 2>%WB? u u (DI+S%'19D2=(*#%C u Cy G u (DE&+:%919D=>V*,%C u Cz G u C = (Cy \ u) (Cz \ u) { F}>~EL 9}h gt u A #++&>+f)%'*=(2#%'.0*,+f2 p r q r p q u A #+&+>+f p q r r s t q p q s t u A #+&+>+f A p0 q r p q s q r q s p r p s D2(+f21' #+CG(%9%'()+w&#+&+&(+fE &«r s u A #++&>+f p q p q u > #+&+>+f)%'*@a%3*,-dw.f1'&s+&,=> 5 p p E+v œž F W - œ21ÿf«- r J E%3*a@A%3*,-D F 8-*,221'/E% ;>+2>$m4&%9dv@A%3*,-D a@>%'*#d x/&+&v2&192ež-+&19 C C 1, C 2,...C n 2>%'%'(EBf&?`419(+ C i C C i (DE&+&s=(2 #%'.0*,+f2sa(K C j 8&=(=>+f(G&> 5 C n = F 8&9;:=<;:>9;? t C F {p, p q, q r} r >+:8&>+*#+? 3

!#$&% ')( *+, - G C 1 = p (DE&+&s=(2 G&*,+I% ;(+2>$4%9as=(8*,2(G C 2 = p #%'.ž*#+f2w q C 3 = q C 1 A C 2 G C 4 = q (DE&+&s=(2 G &*,+I% ;>+2>$m4&%9sa&=>8*#DG r #%'.ž*#+f2w C 5 = r C 3 A C 4 5 E+sœžŸV5 W ( J <;&+:>+2>$m4&%9sa@>%'*#2( (D)&+&s8&>.#sw%'*@>%'*#Dw.F13 C 8*,221'E 5 C 8&9;:=<;:>9;? t C v}>~c<le }gt 1'$8&%'1'Bf& $ *#1' +C;1'$ 8%913Bf&s «9L?3:e2} F}A~v '}wt C F G C C(F ) C C(F ) C F C = {p, q} F = p q { F}>~EL 9}?} e!a : <L:+>9L?:t n q n #q n q>n 3 q p q r p q s% ;(+2>$4%9sa@>%'*#D n.#q p q n?q?+`?421'>+fv2@>@>(d1'.#($ (+f n?q n.?qanfq n,q q n #q>n fq p p n 3 q n?q nfqan #q r ^a\at>ỳ TVU O Ỳ b \A^ F -)_a\ab YSb, OIH X\A[ U TAXaR Cwœ0 œ0 JŸf (Ÿt0kW*v >?%9E=(2 #%'21'#+m(D «& J nj2#&+-qhg,@#;x2 1'2?22=D?%9.0*#+?ex@A?+D=Bf&>+@> 2=>$ *,+f213bf&s()@>%'*#2()?+?)(%9%'s(d)1'd#5 Xm œ0 J r &!œ0 tv]w #v@a%3*,2 =(&&1Hd<;&+ (+D($4&%' v@a%3*,-d8*,)=(2 #%'19?+ x@a#+-d=b?>+@> F C 2=>$ *,+f213bf&s 5 4 C 1 *,%'#V C F C = F Xm œ0 J r &!œ0 t v+s(+2>$4%9sa@>%'*#di*#$a2*#+?e+&w2=>!*,21' #+:(DE@A#+f*?1'@A2?19#5 4 1 *,%'#V C C = f D XmŠS\AOU [`YSb Ỳ b \A^ Š OUSX Ỳ b YSb, OIH X\A[ U TAXaR ZK[ ŸF œl\v7 St&k * $=A &s)=(2#%'21'#+`(d 6# 27 \f ( 8-?&I%'* =A!V*019?+CG@,;(DD 19#G21 >+-D($4&%'sa@A%3*,2(I@> #+f2v*#13@h#1'2?g*,%'#v/1'%c>kf13d2w&+&s=a!v*019?+s 5 (DI+ C C v}>~c<le }gt&l%'%9s+ ;xe8*?)@a?$ 8%9 >2w8-?&)%3* =(-@h21'#+ 5 {? eah ~cawt #+ * C F C = F C C( F ) C C( F ) = f v}>~c<le } t %3* $=A2 F&`x +& #+ =>2(2$1'+&1'D2?GW%'`2 &=( # >$19 Bf&`%'* 2=>!*,21'#+ >KF13D2#GW19%+&:19 8*?)@A #$$>+f)%3* 2#&.?>Gf+1CD1C%3* 2@V &>V@V &wdg>$ 1'+&?5 [Sb)\AŒ[`bIH H<U F ^wuwo)_at>bih!$#&%(')*,+-%(.0/%(#1+2*,+2354 c + +C;*#2?2132 %3*6)=(2 #%'19?+ BfC;>+f2 >&K @A%3*,2(s& #+fs%r;&+& xw 9ž > :+>87ž}nJ@,;(DD 1'2 +C;*:*,@>&+ %'1H22=>V*,%<+=>?*,219q v}>~c<le })t:9 %<;*a*, $?19+e&+&g@A%3*,2)8-fD1921'.#d&*,+e&+ (+D($4&%'E@A?+f2V*#13@h #1'2?5n 4 1'+&?+ %r;>+2>$m4&%' 2>V*,19)*01'DJ*,19)8*,)% ;19+f2(282=>*019?+ #LJx?&J*#D?5q = e!9v2e>a:=atk *>)=D?%9&21' #+S8-fD1921'.#w(DE@A?$ 8%9 >2s8 #&)%3* 2=>!*,21' #+C5

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q!#$&% ')( *+, - c +:1HvBf& &! 21rG8-?&I2?2a*?2219?+*019?+ G 5 I «( J«5 F σ F Iσ = v 4 1%'(g.0*,1'*#4&%'(d%91'4&(w 2 #+f F x 1 G x 2 G5'595 x n G<%'*! #$%9 x 1 x 2... x n (Ds@A%'?2m>wxs*,88-(%9=( F 6# r œ0 7! - fœ0«f r J 5 F E+w!#$&%'w(DI & J B 21C>%'%'gxv*01'DJ*,192w8*#I2?2s1'+f2>8&=AV*021'#+ 5 x(a(x) B(x)) A(a) B(a) d>ks! #$&%'( > 2 #+fvÿfª<! & & r f L F«n q)21 >vd(&%9($>+fd21 (Dv.0*,%'1'&#G@#;x2 F G F G 1'w21 8 #&I# AI2?2 G I σ F Iσ = G Iσ x(a(x) B(x)) xa(x) xb(x) 9L?3:e2} F}A~v '}wt A +&sd?+fi8-*#i=(bf&1'.0*,%'>+f2 x(a(x) B(x)) xa(x) xb(x) D È XGFŠ [`\>bih F O)RSb bih E+d!?2$m&%' x) œžÿf C D1L>%'%'dx)w%'*a! #$ *ž.#@ *,+-/Bf*#+?1HŽ @>*0>& F Q 1 x 1 Q 2 x 2...Q n x n G G Av@V -*#Bf& Q i =AV*,+fvD?1H 2 #19 5 ZK[ ŸF œl\v7 :t ]W#g!#$&%'w(DE=(Bf&1'.ž*#%9(+f2 &+&w! #$%9w8&=>+&>K#5 `baa~c9l? d:+e!<;:>9;?ƒ@> #+D2@A21'.#S8*, &+:2&1927S*#+x!?2$ *,21'#+* ;?*#+f 8 #& >p >:8-?D(m# %'()Bf*,+f1HŽ-@(*0>&V %r;akf2=(21'>>e21'%'1'*,+fe%'(i8&#8&1'=a2=s2&1'.ž*#+f2((5 ^ #&g#m!?2$m&%' G #.0*#213*,4&%' Aw2?2!#$%9 &*#+w%'*?bf&>%'%9 +C;*`8-*#w<;F@(@A&>+@> F x G x %'194&#G&21 (DE&+ Bf*,+f219Ž-@(*02(&)B?>%3@A #+-B?g> % ;*#2sBf*,+f219Ž-@(*02(&G#+:*`t Q Q QxF Q x F QxF G Qx(F G) G QxF Qx(G F ) QxF G Qx(F G) G QxF Qx(G F ) G QxF Qx(G F ) n!(+`>p > QxF G Q x(f G) QxF G QxF G Q x F G Q x( F G) Q x(f G) v}>~c<le }gt,9 %C8 >E+s8*# ;*ž.?#1'/+&1'@>1h=#5 { F}>~EL 9}h gt xp 0 (x) yq(y) x y(p (x) Q(y)) y x(p (x) Q(y)) D>+f21' #+ +C;(DE8*?I>+: #=(+&=>V*,%L=(Bf&1'.0*,%'>+f2 x y(p (x, y)) y x(p (x, y)) xp (x) yq(y) x y(p (x) Q(y)) È XGFŠ [`\>bih R`XKF Š ^a\>bih E+ 6? J & «s(d&+&)13-jx?+@h19?+až+&1')!#$&%'( *,2#$13Bf&( #+&=> f*019?+!#$&%'( *0#$13B?((5 4 1 G<2*#+gB?-*,+f219Ž-@>*,2(&(Gxw&+&@A?+LJx#+-@h21'#+ Ž+&1' &m@a%3*,-d>gl*,%'#vv%3*! F?2$m&%' x 1 x 2... x n F (Dv192a2 # 5 -œ7 W -œl7 & J U6? - VM - $6,! - N OIQYX0Tž5 ZK[ ŸF œl\v7 :t ]W#g!#$&%'w(DE=(Bf&1'.ž*#%9(+f2 &+&w! #$%9w8&=>+&>Kw2#- 5 `baa~c9l? d:+e!<;:>9;?st21'%9132>)%'s2=d&%9*,e*,+*#%9? #&w *,%3@A&% ^e2?8-fd1921'#+&+>%<ae%'g2 &=(# >$w8&=(@a=>+f5

!#$&% ')( *+, - # g*,+%3* 8*,213B?#G #+š=>%'1'$ 1'+&:%'( A %'( G #+ J*,19 &(@A>+-2S%'(+&=(?*019?+(G?+š2&8&821'$`%'(?&4&%'(I+&=(?*019?+(G#+`J*,19E$?+f2>)%'()@>#+LJx?+@h19?+IA)%'(EBf*#+f219Ž-@>*,2>(5 ˆ axa\aoeš TH ^wuwt>xar c + V*LJx?2m*, %3*,+?*,?a&+& 1'+Ž+&192=@A#+-xV*,+f2v>(GL8-?&w@V *#Bf& G +&m1'+ž+1h= ;f$m4-?%9d& n! #+-@h21'#+-)<;*#2192= G*#8&8 >%'=>(I6? - «( ( & L f«aa 5 - $6, J W«0B - J V7 5 n E+s >œ0 & «5 -œ7 ( r - B - r 7 *#D@>19 &+&w!?2$m&%9w8&=>+akg@>%9fdss%3*m!#$ x 1 x 2... x n xf %3*!?2$m&%' x 1 x 2... x n F (x f(x 1, x 2,..., x n )) F (x f(x 1, x 2,..., x n )) (D:%'*! #$&%'?42(+F& 8*#D19: >+ 2($ 8%'*ih>*,+f`2#&2(S%'(S@>@>&2(+@A`& 8*#`%' >$ F x f(x 1, x 2,..., x n ) (DE&+&s+ #&.?>%'%9d!#+@A21'#+ #%'>$ <;*,192= 5 f 4 n <ž <Le:+>f >J}ewt&%3*!?2$m&%' xf (D)2V*,+-x!?2$=>g>+ Bf&1 (De%'*a! F (x c)#$&%'e?42(+f 8*#D19/ (+ 2($8&%'*ih>*#+? #(/%9l@>@>&>+@>(e& 8-*,e%3*a@> #+D*#+? F x 4 #%'>$ 5 c c + *,8&8 >%'%9 «- JŸV7 r«(ÿf & &+&S! #$%9S&+&1'.#(2>%'%9S#4&2>+F&:(+š*#8&8&%'1'Bf*#+?192=>V*019.?>$>+f ( F 2V*,+-x!?2$ *019?+I 4?%9($ JxBfC; abfc;1'%c+c; ;`*,19)8&%'E 5 &%3*m!#$&%' (Dv x y z u vp (x, y, z, u, v) #%'=>$13D=(d(+ y up A D (c,?+f)&(! y, f(y), #+-@h21' u, g(y, #+-) u))?%9($<;*,1h=(i(28-@h19.?( A).mA &+&s@> #+D*#+?s f g 4 4?%9($:5 c v}>~c<le }h dt,9 %<+C; ;`* 8*#I+&1'@>1H=sAE%3* #%'=>$1'2=> <;&+&w!?+@h19?+ 67*#1' (DE@A #+-D=B?>+@>w2=>$ *#+?1'Bf&s n +&s%'&1cxe8*?i=(bf&1'.0*,%'>+f2?5 F qe>e #+ * F 5 F {F } {F } = F = F F xp (x) yq(y) 2w?%9=($1'2w>+ y(p (a) Q(y)) #S>+ Bf&1C+&w%'&1 2 y(p (f(y)) #+f)8*#i=bf&19.0*#%9(+?((5 Q(y)) 67*#1'I?+S* %' ZK[ ŸF œl\v7 ƒt 4?19(+? &+ >+2>$m4&%9!?2$m&%'(g8&=>+&>KFs@A%'?2(gA ;<?42(+f >+?%9=($ 13*,+fd%'( Σ Σ! #$%9) 5 0 %'#V (Dv*0213DJ*,132*#4&%9n!(28C5&@> #+f2v*#13@h#1'2žqe21c>)2>%9($ (+fvd1 %r;(d(5 Σ Σ Σ {/ >3 >} #} a>~09;?& :+e!<l:+>9l?7t 4 1C+&s19+f>8&2=>*,21' #+ 2*,213xJ*#1H G&>%'%9s*01'DJ*,19v*,21 5 4 I Σ Σ 1C+&s19+f>8&2=>*,21' #+ 2*,213xJ*#1H G& #+:@A?+D2&1H)&+s19+f2(282=>*019?+ Bf&1 *01'DJ*,19 5 I Σ I Σ

!#$&% ')( *+, -. PR`ThQ ^wuwtaxar E+`2&4D219219?+ (D&+&S*,8&8%913@>*,21' #+ % ;>+2>$m4&%9`(.ž*#213*,4%9a&*,+-a% ;(+D($4&%'(m(2(2$ σ 2(%9%'dBf& (D/=(?*#%9 σ 5 %r;13>+f2192=w*,c8 #&&+&d+&#$m4&)ž+&1<d.ž*#213*,4%9 {x 1, x 2,...x n A2>V*s+& #2=( } (x 1 t 1, x 2 t 2,..., x n t n ) c +S8&2?%9?+& #g>+:&+a*,8&8&%'13@>*019?+`s% ;>+2>$m4&%9sI2(2$sn!8&&13E!#$&%'(Vq&*,+-)>KF $0/>$#5 *ž.?(@ G σ = (x a, y f(x)) R(f(x), f(y)) σ = R(f(a), f(f(x))) kcw8&&19 τ σ &w&>k:d&4-x1h21' #+ σ > τ xe%3*d&4-x1h21' #+: #4&2>+F&w(+:*#8&8&%'1'@(*,+f σ 8&1' τ 5 21 σ = (y f(x)) A τ = (x a) G R(f(x), f(y)) τ σ = R(f(a), f(f(a))) R(f(x), f(y)) σ τ = R(f(a), f(f(x))) 5 σ(l 1 ) = σ(l 2 ) =... = σ(l n ) E+:(+D($4&%'ss%'1H22=>V*,&K xe W,@ r >;1'%CAK13xg+&aD4x1H21' #+ 2>%'%'aB? (Dv*,8&8 >%'=w&+&19ž-@>*,2>e {l 1, l 2,...l n } 5 σ σ {l 1, l 2,..., l n } E+`&+&19Ž-@>*,2(& (D œ0 J $6# J & WD1 #)*,2d&+&19Ž-@>*,2(&/x)g%'*a!#$ σ τ 8 #&I&+g2&4D219219?+ @A?+F.#>+-*,4&%' 5-kCs=(2&%HV*0Ew% ;*#8&8&%'1'@(*021' σ #+:<;&+S2(%C&+&19Ž-@>*,2(&E(DE*,8&8 >%'=K5,6, F œf5 τ x)&+&19ž-*#4&%9s8-*, {R(x, g(x)), R(f(z), y), R(x, u)} G&&+1HŽ-@(*0>&)+&?+:8&21'+@>198*#% τ = (x f(f(c)), y g(f(f(c))), z f(c), u g(f(f(c)))) nwj*#@a2> q R(f(f(c)), g(f(f(c)))) AE8-*, σ nwj*#@a2> GF&+1HŽ-@(*0>&E821'+@A1'8*#%r5 = (x f(z), y g(f(z)), u g(f(z)))) c q R(f(z), g(f(z))) +:* 5 τ = (z f(c) σ = e!9v2e>a:=atkl;&+&19ž-@(*02(&)8&19+-@a1'8*,% G&>;1'%CAK13x#G(DE&+&13Bf& &+ @V *,+&?>$>+fes.0*,13*,4&%'(8& ((5 1- -œ0! [ 7 B 9 W $6? ( r - a&>k%'19d2=(*#k l 1 > l 2 t c + @V &(@V &?G/&*#+ + 8*,V@A?&V 8&=AŽ&K#G/%'* 8-fD1921' #+ & 8&>$19(` ;F$4 #%' Bf&1d+ ;xs8*#%9 $b/($ &*#+I%9)>&K`%'1H22=>V*,&KL5 u 4 1,%'(C(Ks;F$4 #%'(<@>#2D8 #+-&*,+fl2#+f C@A?+xV*,+f2L#sC;F$m4-?%9L!#+@A21'#+&+>%3lnJ19pL=>>+fVqhG 19% ;S*m=@V &(@#5 u 4 19+ #+S%r;&+ *,S$#1'+)(D)&+&s.0*,13*,4&%' 5 x 4 #19 %'g2>$a@a?$ $(+ h>*#+? t @A>Ds8-fD1921'#+:&*,+-I%r;*,2w%'1H22=(*#%r5 5 4 1 *,8&8*#*#1H)&*#+ G&1'% ;`**,21<=(@V &@ n V(D)C;@>@>&>+@> >qag x t 5E219+ #+ #+ @A#+-D13 >a%3*2&4d219219?+ Aw #+ 2=(1H >a%9m8&f@>(d-v*ž.#@ A σ = (x t) σ(l 1 ) σ(l 2 ) JxBfC; @>sb?s%r;#+s#419(+&+&a(k%'1h22=(*#k`13>+f1'bf&>5 c +S #=>+=>V*,%'1'2vJ*?@A1'%9($>+f &+:>+2>$m4&%9ss8%9)&a>KS%919D=>V*,K<5 ZK[ ŸF œl\v7 t kl;*,%' ##192 &$ <;&+&19Ž-@>*,21'#+ D 2>$19+ Am@>#+1HGW21l#+ƒ% ;*#8&8&%'1'Bf& &>Kƒ%919D=>V*,K &+&19Ž-*#4&%9>G +&ad1haad4x1h21' #+- σ 1, σ 2,..., σ k #+f)%'s8&21h 5'595 σ k σ 1 (DI+S+&1HŽ @>*0>& 8&19+-@A1'8*,%<>E%9a(2+19(%'19D2=(*#%C #4&2>+FS&+SJ*#@A2>E(I%'1H22=(*#K`1'+&19213*,K<5

!#$&% ')( *+, - %'19D2=(*#K 2&4D219219?+ > R(x, g(c, z)) R(f(y), g(y, k(x)) (x f(y)) A R(f(y), g(c, z)) R(f(y), g(y, k(f(y))) (y c) A R(f(c), g(c, z)) R(f(c), g(c, k(f(c))) (z k(f(c))) R(f(c), J*?@h2(&)8&19+-@A1'8*,% g(c, k(f(c)))) (x f(c)), &+1HŽ-@(*0>&E821'+@A1'8*#% (y c), (z k(f(c))) :+e2}a} f}>~v 9}wt %'19D2=(*#K 2&4D219219?+ > R(x, f(x)) R(f(y), y) (x f(y)) A =@V &(@ n!2xv<;@>@>&2(+@ažq R(f(y), f(f(y))) R(f(y), y) :+e2}a} f}>~v 9}wt %'19D2=(*#K > =@V &(@n xe&+a@a #+-xv*,+f2žq P (f(x)) P (c) c

! % & & / % / & M,.-)_a\Ab YSb/, OIH X\A[ U TAXaR c +*.f`b?e2?2v!#$&%'e&+19.?>vd(%9%'e(d/=bf&19.0*#%9(+? &+&E!?2$m&%' @V *?B? x 1 x 2... x n (F 1... F k ) F i (DE&+&a&1'Jx #+@A21'#+:a@A%3*,-D>5 A22w!?2$m&%9wxE*,-221<=(Bf&1'.0*,%'>+f2 x 1 x 2... x n F 1... x 1 x 2... x n F n 5 c + 2($ 8%'*?@A>V*`&+ƒ>+2>$m4&%9!?2$m&%'(w@A%'?2(w&+19.?>VD(%9%'(g8*#s&+ƒ>+2>$m4&%9 @>%'*#2(g 19%e(D 1'$ 8%913@A192aBf&s%'(I.0*,13*,4&%'(I2 #+feb?-*,+f219ž=>i&+&1'.#(2>%'%9($>+f(5 8&9;:=<;:>9;?& gt 4 1 (DE&+ D?D (+D($4&%'ws%r;>+-D($4&%'a(I%'19D2=(*#KS&s%'*@A%3*,-D G& #+:+&#2(* S C C \ S %3* @>%'*#2w&#+f)%9)%919D=>V*,KSD?+?E@>>K`& *, %9)=>%'=>$(+?V) 5 C S P (x) Q(y) R(x, y) T (z) \ {Q(y), T (z)} = P (x) R(x, y) 4 1 (DE&+:>+-D($4&%'ss%919D=>V*,K<G?+`+&#2(* % ;>+2>$m4&%9 5 S S { l l S} {Q(y), T (z)} = { Q(y), T (z)} k * @A%3*,2 (D&+& œžÿf«- J & & L ( š@a%3*,-d C Cy A Cz (;1'%v>K1'D2 &(@>%'*#2( C y > C z G( >+-D($4&%'()s%'19D2=(*#K Sy > Sz AE&+aD&4-x1H21' #+ 2>%3EBf& σ u C y > C z 2 #+fl(.0*,13*,+f2 & Cy > Cz Bf&1+C;?+f 8-*# I.0*,1'*#4&%9>+ @>#$$&+:n!+&i.ž*#213*,+f <;+&g! #$&%'w(de&+&w!#$%9sbf&1<%'&1c(de13>+f213bf& &+:2(+& #$$ *,?g&(i.0*,1'*#4&%'(8& (Vq u Sy A Sz 2 #+fe()2#-x >+2>$m4&%'(I(I(+2>$4%9)s%919D=>V*,KS C y > C z 2D8 (@A21'.#>$(+? u Sy Sz (DE&+&19Ž-*,4&%'wA >+:(D)&+:&+&19Ž-@>*,2(&E8&19+-@A1'8*,% σ u C = σ((c y \ Sy ) (C z \ Sz )) { F}>~EL 9}h gt P (x) Q(x) A P (a) x)&+a@a #+-xv*,+f2?g&#+&+&(+fi%3*=(2#%'.ž*#+f2 a Q(a) P (f(x), y) Q(x, y) A?+&+&>+f 2=(=(@A19I(+ P (x, f(y)) R(x, y) P (x, f(y )) R(x, y ) Q(x, f(y )) R(f(x), y ) *ž.#@ σ = (x f(x), y f(y )) 3

D!#$&% ')( *+, - P (f(x), y) Q(x, y) P (z, z) A =>=(@>219 P (x, f(y)) R(x, y) P (z, z) P (x, f(y )) R(x, y ) P (z, z )?+&+&>+f Q(x, f(x)) R(f(x), x) *ž.#@ σ = (x f(x), y f(x), z f(x), y x, z f(x)) c +?=>+&=(*#%9132m*, *,%3@A&%^l2=13@>*0Vg%9d+,21'#+-g& œ0 F Awœ0Ÿ5 W ( J.F&(w&*#+g%9 *,%3@A&% 8& #8?21H19?+&+&(%r5 ^a\at>ỳ TVU O bu /XŠ:\AOUW[SYSb c + *%9I$0/>$()=(2&%9*,EBf&a&*#+I%' *,%3@A&%<82?8-fD1921'#+&+>%t%3* $=A2 F& )=D?%919?+:(Dv«( & r W A 6? 37 \? 8-?&E%3*m=A!&*019?+S*,+I%' *,%3@A&%C&( ^l=(13@>*,(5 ^ #& a>~c9l? :+e2}e%3* @>#$8&%'=A2-#G 8*,221' <;+ >+-D($4&%'S@> #+f2v*#&1'@a2#1':@a%3*,2( *,%3@A&%I( 8&=(13@>*,C&g82($ 1'> #V2?Gh#+s@A?+D2&1HC+g(+2>$4%9l@>#+f2V*#13@h#1'2l@>%'*#2(< *#%'@>&%;^l#8?21h19?+&+&(% Bf&1-*w+&E=A!V*021' #+ 8*#D19/E%3*#Bf&>%'%') #+ @A?+x21Hl&+E2=>!*,21'#+ E% ;>+2>$m4&%9v19+&19213*,%-v@A%3*,-D # #@> &+S &=>?2 ($ s@>#+&+f:d?i%9w+&?$ A%9($ $as>%' >.?>$>+f 05 ˆ U F ^wuwo)_at>bih c +=>Ž+&19(G@A?$$ g&*,+-l%' *,%3@A%-8&#8?21921'#+&+&(%rG?%9/D2V*0=>?19l8?21H19.?#Gf+&=> f*021'.#?g#%'19+=(*,1'#g#%'1'+&=(*#19 8*#)>+f2=>?G&w%r;>+2>$m4&%'aD&88-?D5 c +:* %'(I$0/>$)2=D%HV*0Ia@> #$8&%'=A#5 S\>T/^sUWTAXaR H ^ #&)$?+?2(EBfC;+&g! #$&%' F x).0*,%'1'&#g&?+s@v &(@V >V*&+g=A!&*019?+ C( F ) 5 l+:aplaat F.0*#%913 C( F ) @A?+f2V*#13@h #1'2 C( F ) 4?1H F = x(a(x) B(x)) x(b(x) C(x)) x(a(x) C(x)) $1'2a2 #/!#$w8&2=(+&akt #%'=>$132*,21'#+ t x)&+a@a #+-xv*,+f2s 4 #%'>$:5 a n q A(x) B(x) @A%3*,-Dwt n.#q B(y) C(y) n?q A(a) n 3 q C(a) =A!V*021'#+S8?21H19.?g>E%91'+&=*,1'2w8*#)>+f2=>t F x(a(x) B(x)) x(b(x) C(x)) x(a(x) C(x)) F z x y((a(x) B(x)) (B(y) C(y)) A(z) C(z)) x y((a(x) B(x)) (B(y) C(y)) A(a) C(a)) =A!V*021' #+S+&=(?*019.?wA)%91'+&=*,1'2w8*#)>+f2=>t n?q n q>nfq n fq B(a) n.#q>n?q C(a) n #q n 3 qan fq n &;q n+.#qaan 3 q n ;q B(a) n qaan ; q A(a) n ;q n?q>an &; q

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