Rigorous results for mean field spin glasses: thermodynamic limit
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Rigorous results for mean field spin glasses: thermodynamic limit
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J +4gP q 7 $ v @ s L F F 5#1 72? z"6%'j";¥' 6z¨"6¿z%ª]¿'.%'"6Y×|z%' !"#$&% ')(*,+ -!./ 0,1-!-&% 2+43 - ^ à 5.HS* RfOO + K H R U5 Z )/+ O *#U¥) *#U¥) H-*#+ pc U 0 +¬,-+ O[b#T H O U5 HS*#+ NT d×U O H O[b ,-+ +4g RXO H-+Y5 K +AUphHS*#+ HS*#+ ,-d9Uz1 ` 5 d RLKTXR d R Hrh(UN,QHS*#+h(,-+ ++ 5#+Y,[] ` 5;1×h(U,QH-*#+],-U b 5#1 O H HS++Y5#+ ,-] `WK 5 c ++4g8H-+Y5#1#+ 1 HSUAM U HS*;+Y,×d×+ 5 3#+ T 1 O P R 5 ] T NO[O d9Uz1#+ TXO à 5 HS*;+36, O HÆP T MK + Z )/+ K 5 R d9d9+Y1 R H-+ T_` +4g8HS+ 5#1 HS*#+ Nc U 0 + P#P;,-U MK * HSU H-*#+65·+ ,-, R 1 87 V O P R 5$d9U1#+ TxR 5HS,[U1 b9K +Y1 R 5 e + K H R U5 M ÛMZ h(U,^+ 0 +Y5 7 e + K U5#1 T_`Z )x+ K 5 NTfT U¥) HS*#+ K U b P TfR 5#] O H-U c +¬5#U5zV:9 Nb#O-O[R 5 , 5;1#Ud 0 , R Nc#T + O Z P;,-U 0zR 1#+ 1 HS* H O-b#R H pc#T + c U b 5#1 O ,-+ R d9P\U O +Y1AUN 5 HS*;+ R ,id×UNd×+ 5H O > R 5 pTfT_`Z )x+ K U5 O-R 1#+Y,.d9U,-+]N+Y5#+ , NT d9U1#+ TfO Z )*#+ ,- + HS*;+ O P R 5 1#+ ],-+ + O UNhh(,-+ +Y1#UNd ,[+5#UhHa5#+ K + O[O , RfT_` HW)xUpV 0 NTXb +Y1 à O[R 5#] 0 , R pc#T + O w *#+ K UNi5 H-+Y5 H O Up h H-* RXOe + K H R U5 ,-+ c NO + 1U5,-+ O-b#T H O U c H NR 5#+ 1 R 5 K U TfT Nc U, H R UN5Q) R H-* > 9 b + ,-, R 5Ø JJÙZ Ø hopÙ E L = v B /?>A@h6CB5!'7 <; + L E ( F B F B E F E 5<% - È+H b ,-5Ê3#, O HUph NTfT HSUH-*#+D5·+Y,[, R 1 E7 V O P R 5d×Uz1#+ T#R 5H-,-Uz1 b0K + 1 R 5 e + K H R U5 M ²M;Z 5;1Ê)/+ K U5 O-R 1#+ , U5 T_` HS*#+ K pO +^UNhÌ+ 0 +Y5 7 O )x+Q1 R 1&h(U,HS*#+ e *#+ ,-, R 5#]MH-U5VGF R , S P HS, R@KTS d9U1#+ TZ )x+Q1#+4365#+[HS*#+ Nb g RXTfR , ` P ,(H R H R U5h b 5 K H R U5¨® B IH SZR 5 5 NT U] ` ) R H-* ²¯N¯ Zjcj`'JKb#O Hx,[+YP T MK R 5#][HS*;+HW)xUpV c Uz1 ` ° R 7 c ` R M K R ` M S R H X R 0 X R 0 ) H-* V Uz1 5HS+ , H U5 H 5#]WHS*;+ 1#+Y, H + Z )x+.3#5#1 h~H-+Y, R 5HS+Y]N, H R U5 cj` P ,'H O L B IH T q © H 7¬« 5® B © ( « @ ¯ K + L 798 8>= j: '8 < ? 7 N 7 s F :ML 8'?/q B L 7^? ?K= j: '8 < ? 7 q 7 kON Û³ u h(U, 7 + 0 + 5 Zc` SH *#+ O 9 d + K UN5 0 +4g R H ` ,-] b 9 d +Y5H NOÌc + h(U,[+ ZO[R 5 K +HS*;+yh b 5 K H R UN5 : n : L fR O:K U 5 0 l+ g à H RfO + NO[` H-U^,[+ NTXR@? +HS#* +,[+ NO U5×h(UN,QHS*#+ #P P+ , 5 K à 5h MK H Z (h U, 7 @ J Z + UNh H-*#+HS+ ,-d O N 7 )/+ K 5 ) , R H-+ L J 7 ? 8GP NONT ,-+ 1 ` FRE QTS PB +4gP T U R HS+ 1 R 5 qVU ? F @ u F QaE `b`b` QFdc 7 L G8 P PB C B F `bE `b` F c @ 7 L Ck k G 8 ? 7 EF S B qVU W H qVU ? ? F F Fc C vYvv W H C Yv vv H qVU 5#1 Z h(U, 8 k G w 5 HS*#+.UMH-*#+Y,* S W H H 7_^ Fec H ? F S @ W H H ? qYX : 8'?[Z Û³ 7]\tJ U5#+.* p O kN 7 @ Û³J qYX : L '8 ?[Z kON 7 v P !"#$&%'( £³ u > ,-UNd TXR d R H O w #* +rP#,[UUNh;UNh + ,-] ` P+Y, O[R H-+ F R , S P H-, @R KTS + o b NTfO | U5#+ 365#1 O Z NOR q 5 HS*#+&P#,[+ z0 R U b#OÆO + K H R U5 Z H-*#+&+4g XR O SH + 5 K +¬UNhH-*#+ R 5365 R HS+ 0 U XT b 9 d + pT d9U O H £³ £ ³NÞ = = ¸ B < L « lº @ ¸ < L « lº fT R d BIÜÝ = = = TfR d C B< L º C < L º @ q TXR d ¸ < L « º v BIÜÝ \ ÜÝ = O[b -, + K U5 0 +Y,-]N+Y5 K + Zc UMHS*^h(U,HS*;+rh(,[+Y+r+Y5#+ ,-] ` 5;12h(U,GHS*;+r]N,-U b 5;1 O H HS+r+Y5zV Z P#,-+ O + 5iH O 5;U 1;1 R H R UN5 NT 1 RpKYb#T H ` ) R H-*Æ,[+ O P\+ K H HSU5HS*;+ K NO +UNhHS*#+ e *#+Y,[, R 5#]MHSUN5V £J u d Uz1#+ T à 5¬h hK H Z h(UN, H-*#+ 7 V O P R 5d×Uz1#+ T H-*#+ K U 0 , R 5 K +Qd HS, R g1;+ 365#+ 1 R 5 9 F B H H @ J B 7 : LEUE J k 5;1 w *#+ U,-+ d J *#U T 1 O ) R H-* @ 5h(U,(H b 5 H-+ T_`Z U b ,P#,-UzUNh1#Uz+ O 5#UhH·+4g8H-+Y5#1A1 R ,-+ K H T_` H-URHS*#+ KNO +UNhUz1#1 7ZDO-R 5 K + R 5NHS* RXO KNO +pHS*#+9h b 5 K H R U5 : n : L RXO 5;UMH K U5 0 +lg Z h(UN,^5;+Y] H RX0 + 0FNTXb + O UNh : Y U¥)x+ 0 +Y,ÊU5;+¨+4gP+ K H O H-* H H-*#+·U 0 + , TB P c +UHW)/+ +Y5rHW)/U K U5;36] b , H R UN5 RfO 5;U5VW5;+Y] H RX0 +) R HS* P#,[U cNc#RXTXR H `w P#P#,[U MK * R 5#] U5;+ Z )*#+Y5 7 H-+Y5#1 O HSU R 5;365 R H ` w * RXO×RXOÊR 5 K U5HS, NO HQ) R H-*qH-*#+ KNO + UNh 7 + 0 +Y5 Z )*#+ ,-+RH-*#+ OK`O HS+ d RXOrR 5 0F , RB 5H b 5#1#+ ,x] T U cpT6O P R 5VV R P O[` d9d×+UHS, `Z 5#1pH-*#+1 RfO HS, Rfc#b H R U5¨UNh HS*#+U 0 + , TB P RXO OK` d9d9+OH-, R@K à H RXOR 5HS+ ,-+ O H R 5#]§H-* H w N TE ], 5;1P#,[U 0 +Y1 Ø ¯oÙ HS* H Z h(U,aUz1#1 7TB ,-]+.+ 5#U b ]* Z c;RfTXR H ` 1 RXO H-, RXc#b H R U5 UphHS*#+U 0 +Y, TE Pª* N O¨O[b P#PU,(H R 5 8 Ø u ? YÙ>Z|NO[` d9P9HSUhH R@KLNTXTX` h(U, 7 H-*#+¬P#,[U cN TB ,-]N+ Z. 5#1JH-*#+P;,-U cp c#RfTXR H ` H-* H K U b P T +·UNh K U5;3#] b , H R U5 O H * N O U 0 + , TB P :8'? u HS+ 5#1 O H ? 0 Z R Æ 0 ` K O f R X T I T b # b # c X T X R O S H-U + ,-U U,-+ U +Y, 5 + , ,-+ +Y5H H 5#P *#+ 1±)xU, Ø YÙ *#+Q]N+Y5#+ , N TXRL? +Y1 HS*;+Ê,-+ O-b#T H TXb +&UNh 7 > U, d9U,[+&P#,-+ KYRXO + O H HS+Yd9+ 5iH ZyO + + H-*#+ h(U,(H-* K UNd R 5#] c UzU S H-U ]+ 5#+Y, RLK U1;1 0FN Ø YÙ O K UN5 O + o b +Y5 K + Z d9Uz1 b#T U O Ud9+.d R 5#UN,HS+ K *;5 RLKN T d9U1 R 3 K H R U5 O Z HS*#+.+lg RXO H-+Y5 K +QUNhH-*#+ H-*#+Y,[d×Uz1 ` 5 d R@K&TfR d R Hh(U, HS*#+h(,[+Y+ +Y5;+Y,-] ` 5#1 ],[U b 5#1 O H H-+ +Y5#+ ,-] ` Uph H-*#+ 7 V O P R 5 d×Uz1#+ T h(U TXT U) O h(,[Ud £³ u Z p TfO U×h(U,aUz1#1 7 | n (O²-| ²(mT|<|(¬ n} L¨©,¦]] },|°MU m:U¬'}] (l } ,9|:m'¬!"]}hn # (©%$5U¬m&O' }(¬m Uc ' ¥ ® ' )(* ' ,+-*/. 10 :9¯; ®< =® < U } ¬| « |¬ | . 0 O « m . 6587R¦cm'}P| # <'¯ln²m(©0{~} l ' . ® * ± 0 > ®0 > 0 > 0 « '¬m {~}P|a « U:B%CM©GL¨©3]%U#DU > .@? ; ® 0 * ; ® 0 ± ® |=|:$¯la m'}' ¨l©243c ® A µ ¨l©2IHl 0 ¥ ® ' )(E* F ® 0 * ' G+-* F 0 µ > > > J <'¯ln²|(}$Z,| K O¬ ' * F 0 c,}L|(¬|'U¬mZ | U¬ ' O « 3¬mM m Nh6 Ol |#Dc ,¬!M(}O © > ' /* z"6%'j";¥' 6z¨"6¿z%ª]¿'.%'"6Y×|z%' & @ 46969!' ! #G-4B5%'!(1=6 à 5 e + K H R UN5 M ¯#Z 5K UNd×P , RXO U59) NO d 1;+ c +OHW)x+Y+ 5 R 5;365 R HS+ 5;1×365 R H-+ K U5#5#+ K H RX0zR H ` d9+ 5×3#+ T 1 O P R 5] T NO-O d9U1#+ TfO Z 5#1 R H¿) NOIO H HS+Y1 H-* H<HS*#+ `yK 5 c + K * , MK HS+Y, RL? +Y1 ZjR 5P#,[U c Nc#RXTXRfO H R@K HS+ ,-d OYZ NO 9 pb#O-O[R 5 5#1 5#U5zV:9 Nb#O-O[R 5 P#,[U K + O[O + O U5 q k B Z ,-+ O P\+ K H RX0 + T_` à 5 HS*#+±P#,[+ O + 5H O + K H R U5 Z U5 H-*#+UhHS*#+ ,×* 5#1 Z )x+1#+ NT ) R HS* R 5;3#5 R H-+ K U5#5#+ K H RX0zR H ` d9Uz1#+ TXO + O-O +Y5H R NTXTX`NZ HS*#+ e *#+ ,-, R 5#M] H-U5GV F R , S P HS, @R KTS 5#1 7 V O P R 5 d9U1#+ TfO Z )*;+Y,-+HS*#+ K U b P TXR 5#] Oac +OHW)x+Y+Y5 O P R 5 O ,-+ D §§4'N , 5#1#Ud 0 , R Nc#T + O à q D A ^RfO NTXO U 5 HS* RXOWK NO + Z UNh K U b , O + Z HS*;+ Y d RfT HSUN5 R 5 B F H w à p # b O [ O R X R Y O Z 0 Z O K @ R K N c 0 O 5#U5V 9 5 * *#U¥)/+ + , 1#Uz+ 5#hU H U5HS, 1 H HS*#+ U + H HS+Yd9+ 5iH 5±h MK H Z h(U, 7 T ,-]+ Z B D A ¿RfO HS*;+ O[b d UNhd 5 ` h(UNQ J , HS*#+ e *#+ ,-, R 5#M] H-U5GV F R , S P HS, R@KTS d9U1#+ TZ 7 7 q R 5;1#+YP+YF 5#1;+Y5 H H R 1#+ 5 H @R K NTXTX` 1 RfO HS, Rfc#b HS+Y1, 5#1#Ud 0 , R Nc#T + O Z + MK *&* 0zR 5;] ÊO d NTXT )/+ R ]N*iH UNhGHS*#+ U,-1;+Y, 7 Z h(U5 , HS*;+ e *#+ ,-, R 5#h] HSU5GV F R , S P HS, LR KTS d9U1#+ T SZIO U HS* H B 7 * NO 9 Nb#O-O[R 5 F 1 RXO HS, Rfc;b H R U5 Z h(U, 7 ]U R 5#N ] H-U R 5;3#5 R H `NZ NO ] b , i5 H-+Y+ 1 cj` H-*#+ K + 5 HS, pTaTfR d R H H-*#+YU,[+Yd¨Ø ¥MÙ O )/+ O * NTXT¿O +Y+ Z HS*;+QP#,[+ KYRXO +QP#,-U c Nc#RXTfR H ` 1 RfO HS, RXc#b H R UN5 UNQ h HS*;+ K U b P TXR 5#] ORXOR 5#+ O[O +Y5 H R NT h(U, 7 T ,-]+ Z P#,[U 0zR 1#+Y1 H-* H K +Y', H NR 5 K U5#1 R H R U5 O Uph O[` d9d9O+ HS, ` 5;1|365 R HS+ 5#+ O[O UN h H-*#+¨d9Ud9+Y5 H O ,-+ F S O H RfO 36+Y1 w * H HS*;+aP#,-U c Nc#RXTfR H ` 1 RXO H-, RXc#b H R U59UNh H-*#+ K U b P TfR 5#] O A O *#U b#T 195#MU H R 95 V b + 5 K + H-*# + HS*#+ ,-d9UpV 1 ` 5 d @R KTfR d R HUNh HS*#+Qd×Uz1#+ T ) NO NT ,-+ 1 ` KYT + , HS§ U H-*#+ Nb H-*#U, O UNhØ ³ÙZ 5;1¬) pO , R ]U,[U b#O-F T_S ` P#,-U 0 +Y1 cj` w NT ], 5#1 Ø ÞNÅpÙ>ZrR q 5 H-*#+&P ', H @R KYb#T , K NO +&UN h HW)xUpV 0 pTfb + 1 o b + 5 K *#+ 1 0 , R Nc#T + O A Z )* @R K * pO-O-b d×+ H-*#+ 0 NTXb + O F S ) R H-* +Yo b NT P#,-U c Nc#RXTfR H ` NJ w h K U b , O + Z HS*#+P;,-U c pc#RfTXR H ` 1 RXO V RXO +lgP\+ K HS+ 1 HSU&* 0 + 5A+\+ K H2UN5 H-*#+Æ1 RfO U,-1#+ , V 0b K H b H R U5 O HS, Rfc#b H R U5|Uph HS*;+ K U b P TXR 5#] O A 0 R # b O z ` O R @ K N T b R UN h H-*#+ , U P#* o i5 H H R + OY( Z 5;1$U5365 R H-+ O-@R ? + K U,[,-+ K H R U5 O H-U HS*;J + HS*;+Y,-d9Uz1 ` 5 d @R K TfR d R H Y + ,-+ Z )x+^+48g HS+ 5#1 w NT ], 5;1 O ,-+ O-b#T HPH-UÆd9U,[+.]+Y5#+ , N T K U5#1 R H R U5 O Z H-*#+Y,[+ cj` +48g HS+ 5#1 R 5#] O X T O X R O K X T R R KYb;T H ` HSp U HS*#+ +Êd9Uz1#+ HS*;+QP#,[UUNhIUNQ h H-*#+Q+lg H-+Y5 +9UNQ h HS*;+ d H Èt* RfT + H-* RXO P#,[+ O + 5 H O 5#U1 R p h(U , HS*;+2o b + 5 K *#+Y1h(,-+Y+.+ 5#+Y,[] `Z HS*;+^P;,-UzUNhIUph NT d9U O H O[b ,-+ K U5 0 +Y,-]N+Y5 K +Ê,-+ o b;R ,[+ O 5+l8g HS+Y5 O-R U5 ÛJJ SZ )* @R K * +lg;P;,-+ O[O + O +4gPU5#+Y5 H R NTO + T h¾V 0 +Y, ] R 5#]UpP UNh R 5#+ o b NTfR H ` h HS*;+h(,[+Y++Y5#+ ,-] ` 5#1 R @ K Z ¥ & ` R f R O O Z T O X T ` N ; b O O R f T O )* * HS*#+i) H H H-+Y1 *#U 1 U5 h(UN, 9 5d9U1#+ O R 7 O R T R @ K Z 7 J Z @ Ç/U5 1#+ P , HS*#+ V P 5¬d9U1;+ )* * h(UN, ,-+ 1 0b K + O HSW U HS*;+ e *#+ ,-, R 5#h] HSU5GV F R , S P HS, LR KTS Y T j c ` f R T R d9U1#+ 1#+4365#+ 1 HS*;+ d HSUN5 5 F `b`b` eF c F eF c F B _ 7 ^ F E E F a Q b ` b ` ` Q F e c < L = l C ÛM³ o v q º C vYvv B H º D @¹q J 7 L g 8 G8 P F H H ¦ 8 H P B G F `b`b` eF c C 5#1 O[b P#PU O + HS* HJHS*#+ K U b P TfR 5#] O C ,-+ R 5;1#+YP+Y5#1;+Y5 H R 1;+Y5 H @R K NTXT_` 1 RXO H-, RXc#b HS+ 1t, 5#1;Ud 0 , R Nc#T + O Z ) R H-* O[` d9d9O+ HS, LR K 1 RXO HS, Rfc;b H R U5 5#1&365 R HS+ih(U b ', HS*d×UNd×+ 5 H Z '¡'Y¡ Z F `b`b` dF c F `b`b` eF c F `bC `b` eF c @ q C Û³NÅ v o u C U¬< }²mU}$OlU} (,}( ¬m($ |, B E E E E ( ! B F B E w F L F B | v L B L L s E B ~ 8 E E E É E B E S F B + F B L ³ @¤´i(i0± h3 ³ @¤´m8'8| L¨©U $ n¬|c°,|¬mn'&Z |O}a,}i0,} m $° } O)(+* ,¬m }Ll'°M'} '}] « (¬|³=@¤´i(i n |!l'¬m¬|n}U |U}#"%Q l'}]mn( 1la m¬|#Olm y²" $m¬|a ¬,} M TD ,¬mnMO « | 9} | M'}]m(©,c# ,¬:¬| ,|nU}Z O¬<m .Q m²a,} DTU¬|a O | #U'¬=On¬! '¬ M(}O U<³ )- « a |'¬m$ U¬mm'} m5| M '}] ,</ « DT,¬ma,}' ³ @¤´i(i )0 © P !"#$&%'( B B UN,-+YU 0 +Y, Z )x+ pO-O-b d×+[HS*;+^1 fR O U ,-1#+ , 0 , R Nc#T + O HSU9* 0 + b 5 R H 0 , R 5 K + Z F `b`b` Fec ? C no @ NOR 5[HS*#+9 Nb#O-O[R 5 K NO + w * RXOT NO H NO-O[b d9P9H R U5 RfOCJKb#O H d H(HS+ ,Uph K U5 0 + 5iH R UN5 ZO-R 5 K + K * 5;]+ RR 5 HS*#+ 0 , R 5 K + RfO + o b#RX0 NT +Y5 HH-U yK * 5;]+ R J 5 HS*#+ O(K NT +iUNhGH-+Yd9P\+ , H b ,-+ O Ç/U5#1 R H R U5 OaO-R d RXT , Û³NÅ SZ no u * 0 + c + +Y5 NTXO U¬+4gP T U R H-+Y1 h(U, HS*#+ O H b 1 ` UNh HS*#+ e *#+Y,[, R 5#]MHSUN5V F R , S P H-, R@KTS H-U d9Uz1#+ T'Z H ? + ,-U×+48g HS+ ,-5 pT 3#+ T 1 5;1* R ]r * HS+ d×P+Y, H b ,-+ Z h(UN,a+4g d9P T + R 5$Ø Þ Ù 5#1Ø MMÙ O )/+ * 0 + O *#U¥)5 R 5 H-*#+ P#,[+ 0zR U b#O O + K H R U5 OYZR 5 HS+ ], H R UN5 c` P ', H O UN5 HS*#+*9 Nb#O[O-R 5 1 RXO UN,-1#+ , 'M ÛJ RXO &O[R d9P T + c#b H.+ O[O + i5 H R pT H-UU T à 5 HS*;+P#,-+ O +Y5 H K NO + Z Ħo 'M ÛJ 5#U T U5#]+ , *#U T 1 O Z 5#1 R H O ,-U T + RfO P T ` +Y1 R 5 O HS+ 1 cj` H-*#+ih(U,-d b#T E B t v t F E B @ E q ¯ ? L B ? g L © ? q B B nojJ @ R K T O ` K O ` @ R K 0 R N # c T )* **;U 1 h(U, 5 d×d9+UHS, , 5#1#UNd , + 5#1±h(U, O-b)pKYR +Y5H TX` ,-+ ] b#T ,ih b 5 K H R UN5 O 9Z NO O-R d9P T +Q1 R ,[+ K H K NT@KYb#T H R U5 O *#U¥) O O[R d RXT ,·+4gP#,[+ O-O[R UN5A* NO·c +Y+Y5 +lgP T U R H-+Y1 R 5 Ø ÞÅÙ cj` w NT ], 5#1 Z h(U,HW)xUpV 0 NTXb + 1, 5#1#Ud 0 , R Nc#T + O @ = = 5·+Y5;MU HS+ NO ¸B < L « lº 5#1 ¸ B < L « lº H-*#+3#5 R H-+ 0 U Tfb d×+¬o b +Y5 K *#+ 1 h(,-+ +¬+Y5;+Y,-] R + O UNhH-*#+ 9 Nb#O[O-R 5 5#1&5#U5V 9 pb#O-O[R 5 7 V O P R 5d×Uz1#+ TZ ,[+ O P\+ K H R_0 + TX` w *#+ 5 Z HS*;+.h(U TfT U¥) R 5#]9,[+ O-b;T H*#U T 1 O S 2 B B ´ L B F 8 E F B N E B Q N>;§9 j¡ ¤l j¡l¤9NS·§YN'§(y- p q = ¸B < L « lº ¸ B< L = « º @ N 7 8 @ = ¸ B < L « lº fT R d B¿ÜÝ XT R d ¸ < L B¿ÜÝ « º @ = E E]f q q noN¯ 9§4>N94D4' no H D A noÞ = TfR d ¸ < L « lº v \ ÜÝ u à H O *#U b#T 1 c + KYT + , Zjcj` 5#U¥) Z HS* H B 5h(,-+ +a+Y5#+ ,-] R + O Z )x+5#+Y+ 1 HSU O-b;R H Nc#T_` E H R 5;] pb g RfTXRE , ` P ,(H R H R U5 h b 5 K H R U5 RXO @ @ T u 7 « 5® B ¬ ¸B < L T 7¬« 5® B ¸ B< L noM S¥¥¤ b#O H¦h(U, O-R d9P TXRLK R H `NZ )x+ K U5 O[R 1;+Y, HS*#+ K NO + º @ R 59U,-1#+ ,:HSU K Ud9P ,-+H-*#+ 9 Nb#O-O[R 5 5#1 HS*#+a5;U5V:9 Nb#O[O-R R 5 HS+Y,[P\U T H-+ c +UHW)/+ +Y5 HS*#+ d à 5NHS* RfO5K NO + Z HS*#+ R 5HS+Y,[P\U T ] R_0 + 5 cj` = D q « ® B H @ E +4gP q « H B < L F H e O[b0K * H-* H L v = ¸ < L « º À §4§¦2N6 « lº ¡ §4XN§4>N4¨46¦6X §¦.(6S = = = TXR d C B< L º @ TfR d C B< L º @ C < L >º @ q B¿ÜÝ BIÜÝ E g 7 4N4 (z§iÁ>§.(;Nr6^Á SÆ;Nl> XN6 B q « = = « v = H B< L F noj³ n o´o z"6%'j";¥' 6z¨"6¿z%ª]¿'.%'"6Y×|z%' F O ,-+ ] ,[1 O HS*#+ H 1;+Y, R_0 H _R 0 + Z U5#+.+ NO[RfT_` 365#1 O 7_^ F QaE `b`b` QFec T 5® B IH @ q q © ª H 7¬« J 7 J 7 L g 8 H G8 P C © « 7_^ F QaE `b`b` Q F c k q ¯ 7 L 8GP P C B B `b`b` F c F P B C F B ? F Fc F U W C v vv H H eF c U W C Yv vv H H F `b`b` Fec oÅ R 5 H-*#+ O + K U5#1 H-+Y,-d )*#+Y,[+2)x+ b;O +Y1/9 Nb;O-O-R 5 R 5HS+ ], H R U5 cj` P ,'H O U5 HS*#+ 0 , R Nc#T + O A C P#P TX`zR 5#]h(U,[d b#T ojJ Z U5;+ K 5 O +Y+WHS* H H-*#+936, O H H-+Y,-d R 5 HS*#+×, R ]*H^* 5#1 O-R 1#+ K 5 K + TXO 8 O K Z HS*#+ + UN5#1 P ,'Hah(,-UdHS+ ,-d O UphIU,[1#+Y, N 7 g L U,[+^P;,-+ K RfO + T_`Z ojJ ] RX0 + O F `b`b` eF c F dF c F Fec F `b`b` Fdc _ 7 ^ H ? ? 8>=É? C U W C vvv C U W C vYvv ²Å u @ « q kN 7 g-< L g 8 J 7 Lg H H H H ojJ SZ;O-R 5 K + H-*#+i1#+YP+Y5;1#+Y5 K + )*#+Y,[+5HS*#+.+Y,[,-U,H-+Y,[d , RfO + O h(,-UdHS*#+H-* R ,-11#+Y, RX0 H RX0 + F `b `b ` F c R 5 8>=É? w ° T ? f R ; c # c a O O [ O R T 0 R p # c T X R O UN h HS*#+ U H d 5;5:V 9 H HS+·UNR 5 HS*#+ 5;] + , + C UNhU,[1#+Y, 7 g6< L g 5#+·* NO NTXO W R o u 0 Z T `R O-R T R R ` U HSU9d MS + b#O +.UNF h NO[O-b Fdd9 c 9P H U5 F U,[+YU Fec + , +Yd9P U 5#]pHS*#+ d9P + 1#+Y5H H F `b`b` eF c ? ? ? c C U W C vvv @ U C vvYv W F eF c H H H F `b`b` eF c H c C ? ? s v Y v v k q U C C W H $ C G © H $ U5#+.* NO F Fc F Fc F `b`b` F c ? ? ? 8>= C U W C vvv ²Å @ U W C vvv k N 7 g6< L g v H H H H b H H R 5#]¬Ä¦o O noÅ Z ²Å u ÛÅ noM ¨e H H-+Yd9+Y 5;1 HSU]U+ HS*#+ , Z U5#+9365 NTXT_` U c H pR 5 O 5 HO oN¯ o c z 0 R # b O K O b K O O o M Û ³ Û N ³ Þ S Z R 5;1 ,[+2U U U5 +Yo +Y5 + UNhÌĦo 5#1 V ,-+4h(+Y,[, 5#§ ] HSU ' HS*#1 + 9 Nb#O[O-R 5 7 V O P R 5d9U1#+ T O )/++lg;P T NR 5#+ 1 R 5 e + K H R U5 ²¯ ¯#Z h(U,Id×Uz1#+ TfO ) R HS* 9 pb#O-O[R 5 K U b P TXR 5#] O pT d9U O H O-b ,[+ K U5V 0 + ,-]+ 5 K +UN h H-*#+h(,[+Y++Y5#+ ,-] ` 5#1¨],[U b 5#1 O H HS++Y5;+Y,-] ` P\+ , O[R H-+h(U TXT U) O h(,-UNd HS*#+ K UN5 0 +Y,[]+Y5 K + UN h HS*#+o b +Y5 K *#+Y1 ¥0 +Y, ]+ 5#1h(,-Ud ° U,[+ T VKÇ 5 HS+ TfTXRT + d9d Z P;,-U 0zR 1#+ J 1 H-* H 59+ O H R d HS+UN h HS*#+ `H P\+ £JJ *#U T 1 O w *;++lug H-+Y5 O[R UN5¨UNh ÛJJ HS5 N # b [ O O R K N O X R O R _ T ` _ R U HS*#+5#UN5:V 9 5 + 5#MU H+Y5 H ,[+ HS, 0zR pT > U, R 5 O H 5 K + Z w *#+YUN,-+Yd J UNhÊØ bF Þ S YÙ NTXT U¥) O HSUA+48 g F HSS + 5#1 R HWHSU HS*;+ K NO + )*#+ ,-r + HS*#+P#,-U c Nc#RXTfR H ` R1 XO HS, Rfc;b H R U5&UN 0 R N # c T O 0 X R O O T N O N O N O p y O R 5 H-*# h HS*#+ , + 5 *#+ h(U, n H + H h H + 9 Nb#O-O[R 5 K NO + h(U, R 5 O H 5 K + Z HS* RfOiR 5 KYTXb 1#+ O HS*#+ K NO +9UNh c U b 5#1#+ 1|, 5#1#UNd 0 , R Nc;T + O Zc#b H·)/+ ,[+5#M U H O K U5 K +Y,[5 R 5;] K UN5 K + i5 H-, H R UN5¬UNhId×+ NO-b ,-+ R 5#+ o b NTXR H R + O h(U, ) ,[+2UphÌd 9b K *¬d9U,-+^]+ 5#+Y, NT ,-+ O-b#T H h b 5 K H R U5 O UNhId 5 ` 5;U5:V 9 Nb#O[O-R 5, 5#1;Ud 0 , R Nc#T + O Y +Y,[+ Z )x+2P;,-U 0 [ + HS*#+ih(U TXT U) R 5#] B c B ~ F B J F B F F E 2 J J B E L E B F E q « 7 B <n\ = » T 5® B « lºD $ ! & s « hC g ²ÅjJ $ $ $ $ $ ¶I64S « §§¥¨.;§4>N6'¶Iz>¨ zW64 §i6Á96464[N S iN ×&(6· N§¥[ z4 N§4l' >¡ $ «7 T 5® B « lºD E E ´ z ·6 4D6- ×Nl'jY§§YN'§(l¨ N'>;§9 j¡ ¤¥/ j¡l¤¥Ì642i6 7 q §W ¨Y z4NlSÊ4D4' " $ P !"#$&%'( { 3 S¥¥¤ È|+] RX0 + JKb#O H c , R + h O S +UH K *ÊUphuH-*#+xP;,-UzUNh ZO-R 5 K + HS*#+ O HS, HS+Y] `iRfO H-*#+ O d9+¦)/+h(U TXT U¥)x+Y1 H-U P#,[U 0 + w *;+YU,[+Yd JZ P ,(Hh(,-UNd O Ud9+=HS+ K *;5 RLK NT + O H R d H-+ OYZ )* RLK ** ¥0 + NT ,-+ 1 `^c +Y+Y52+Yd9P T U ` +Y1 H-U×P;,-U 0 + w *#+YUN,-+Yd ³ ÛJNÞ SZ 5 Nb g RfTXR , ` P ,(H R H R U5±h b 5 K H R U5® B IH SZ 1;+YP+Y5#1 R 5#] È|+×1;+ 365#+ ZIR 5 5 NT U] ` ) R HS* 8>= ?K= U5 HS*#+ R i5 H-+Y,[P\U T H R 5#]¬P , d×+UHS+ , uAs H s 5#1|U5 HW)xU R 5#1#+YP+Y5;1#+Y5HÊh d RXTfR + O/ < < UNh R 5#1#+ P\+ 5#1#+Y5 H R 1#+Y5 H LR K NTfT_` 1 RfO HS, RXc#b H-+Y1±, 5#1#Ud 0 , R Nc#T + O Z ) R HS*NHS*;+ O d×+Q1 RfO HS, Rfc#b H R U5 NO H-*#+ U, R ] R 5 pT 1 RXO U,[1#+Y, 1 B ® B IH @ E e Ecf H F >8 `b= `b` Fdc <C k £J Z U5;+^1;+ 365#+ O B I H @ T 5 u @ q ( eF c F F ?K`b= `b` Fec F B E F <C v k « º C vvv H H 8 H Ì G H IH 8 +lg;P ? T 5 ® B « = L < T ÛÅM q 5 ® B B B « º v I +4g8H Z U5;+ K Ud9P b H-+ ONOb#O-bpT HS*#+ H 1#+Y, RX0F H RX0 +2UNh B IH 5#1 Zt h~HS+ , O Ud9+ NT ]+ c , ;Z U5#+i365;1 O ? B IH s « 7 ÛÅN¯ k R 5 5 NT UN] ` ) R HS* ÛJNÅ Y + ,-+ 5#1 R 5 HS*#+ih(U TXT U) R 5#] Z « 1#+Y5;UMHS+ OO UNd×+^PU O-R H R_0 + K U5 O H 5H Z )* R@K * 5#+Y+ 1 O 5#UMH c +§HS*;+ O( d9+ H+ MK * U KOKYb ,[,-+ 5 K + w *#+ 1#+UH NRXT +Y1 P#,-UzUNhUNhĦo ÛÅp¯iRXO , HS*#+ , T +Y5;]MHS* `ZIc#b H K U5 K +YP9H bNTXTX`|O H-, NR ]*H-h(UN,[) ,-1 Z¿O-R 5 K + R H2,-+ TfR + O U5 T_` U5|h(U,[d b#TB ojJ Z 5;1AUN5 + O H R d H-+ O UNh HS*#+ SR 5#1 ²Å u SZ ²Å S Z )* R@K * O[R d9P T_` +4gP#,[+ O[O H-*#+Ê)/+ MS 1#+ P\+ 5#1#+ 5 K + UNhHS*#+49 Rfc;c#OÆO H H-+ h(,-Ud 5 ` R 5#1 R_0zR 1 bNTK U b P TfR 5#] 0 , RBNc#T + > UN,9h b ,(HS*;+Y,91#+OH NRXTfO ZyO + + H-*#+ h(U,'HS* K Ud R 5;] P P+Y,Ø Þj³Ù 5I UMH R@K +yH-* H R 5NHS*;+QP#,[+ O + 5H KNO + Z ) R HS* ,-+ O P+ K H5HSU £ JpÅ Z HS*#+ ,-+ RXO NTXO U×1#+ P\+ 5#1#+Y5 K +QUN5rH-*#+5HS+ d×P+Y, H b ,-+ R 5 HS*;+ c U b 5;1 Û Åp¯ + KNTfTXR 5#]¨Ä¦o ² ÅM S Z )x+^365;1 ® < L = « lºD q ® < L = « lºD $ & s « C B <n\ = » v " 7 $ 4 + g P $ 7« B $ 7¬« B $ $ $ $ HHS* RfO PU R 5H Z U5#+.P#,-U K + +Y1 OTXRLS + h~HS+Y,Ħo ² M u 5;1 H-*#+5HS*#+ U,-+ d RfO P#,[U 0 +Y1 ' q F B O[b0K * H-* H B 7^ E « J 7 Lg 8 +lgP ÄIg MK H TX` pOR 5Äo T5 = T 5® B < L « º 4 + g P « c à 5 K U5 K Tfb;O-R U5 Z NO O-R d×P T + K U5 O +Yo b + 5 K +QUNh w *;+YU,[+Yd ´ 7 4N4# z4^§§ '>;§× j¡ ¤l j¡l¤¥I(64S À §4(6^Á§ q N o;Z )x+^* 0 + @ = @ C < L >º = XT R d T 5® B < L « l ºD B¿ÜÝ 7« = fT R d C B< L >ºD BIÜÝ = ¸ < L « l º q v C v q v C v ÛÅ ÛÅÞ "6%j" z ¨ " z %].%'" z% µ S¥ w *#+i36, O H O H HS+ d×+ 5H O[R d9P T_` h(U TXT U¥) O h(,-Ud ° U,-+ T VÇ 5HS+ TfTXRT + d×d ²ÅjJ 5#1 O h(U, HS*#+]N,-U b 5;1 O H HS++ 5#+Y,[] ` ,[+ K pTfT H-* H ZÌR 5 H-*#+29 Nb#O-O[R 5 K NO + Z HS*#+¨,-+ O[b#T H O-R d×P TX` X T T h(U U¥) O h(,[Ud HS*#+xh MK HZHS* H C B ºD A RfO HS*#+ ? +Y,[UpVH-+Yd9P\+ , H b ,-+ TfR d R HÌUNh0HS*;+y1 RXO U,[1#+Y,Ì1;+YP+Y5#1#+ 5H h(,-+ +i+Y5#+ ,-] ` P+Y, O[R H-+ P ,(Hyh(,[Ud d R 5 b;OO[R ]5 Z 5;1&h(,[Ud"H-*#+ T MKTS UNh « VW1#+ P\+ 5#1#+ 5 K +^UNhHS*#+ à 5 h MK H Z HS*#+ TfR d R H « n R 5XHS*#+ ÛJJ , R ]* H* 5#1 O[R 1#+¬UN h HS*;+¬+4gPU5#+ 5iH R pT + O H R d HS+ ²ÞÅ Ã 5 HS*;+QP#,[+ O + 5H +4gPU5#+Y5 H R NT¿R 5;+Yo b NTXR H ` K 5 c [ + HS*;+Y5 H MS + 5 ) R H-*#U b HP#,-U c;T + d O Z NOR 5 K NO + Z 1 b + HSU HS*;+ « 1#+ P\+ 5#1#+ 5 K +^UN h HS*#+, R ]*H* 5#1 O-R 1#+iUNh ÛÅJ Z HS*#+iP#,[UUph RXO 5#UMH O U91 R ,-+ K H Z f T R O ` 5#1 , HS*#+ ,a,-+ + U5 H-*#+Y,[d×Uz1 5 d @R K5K U5 O-R 1#+Y, H R U5 O Zc NO + 1UN5 K U5 0 +lg R H ` P#,[UP+Y,(H R + O UNhHS*#+ ²Þ u SZ H-U]O+ H-*#+Y,) R HS* ÛÞjJ ÌR d9P TfR + O Z h(U, 5 ` 7 « lºZ h(,-+ ++Y5;+Y,-] ` à 5#1#+ +Y1 Z HS*#+ R 5#+ o b NTXR H ` = = T 5® B < L « G º D º D s C B< L > 7¬« L 5#1 E L L E E L B S Z H-* 5 SO HSUWHS*;+ pT d9U O H O-b ,[+2+lg RXO H-+Y5 K +QUNh<HS*;+ TXR d R Hh(U,HS*;+.h(,[+Y+.+Y5;+Y,-] ` ²Å SZ = = TXR d O-b P C B< L ºGD s q ¸ < L « lº q v v F BIÜÝ F F = = o SZ )/+^]+UH Ç/*#UzU O-R 5#] 9O +Yo b + 5 K + « < ) R HS* TfR d ÜÝ « < @ 5; 1 ,[+ K pTfTXR 5;]¨Ä¦o = = TfR d O[b P C B< L > º D s C < L >º q v v B¿ÜÝ w 5JHS*;+UMH-*#+Y, L O-R 1#+ Z;O-R 5 K +HS*;+h b 5 K H R U5 « n T 5® B « ¿ RXO-K U5 0 +4g R 5 « Z h(UN, 5 `« = = T 5® B < L « lºD T 5® B < L « lºD « q « = s T 5® < L « lºD k « O UWHS* H #Z T O+ H(H R 5#] « n « ) R H-* « 3;g+Y1 Z = C B< L ºD « F s <L T \ 5® B 7 = B « lºD \ { \ « )x+* 0 + « 7 v ²Åj³ F = = = Ç/*#UzU O-R 5#] O +Yo b + 5 K + « < )* R@K * ]Uz+ O H-U R 5;3#5 R H ` 5#1 O-b0K * HS* H s \ ¸ < L « < lº +4g RXO H OYZ )/+ * 0 + Z#R 5 H-*#+ R ;5 3#5 R -H + 0 U XT b 9 d + TXR d R H F = = = TXR d R 5h C B< L > º D s  < L « < º q v v ²Å´o \ BIÜÝ G ' mT3mG }$|nU} ±G "' !$#&% @m´ua$O} DO$¯=n}OU} -|, $O} DO$¯ } m O} a-l('´'¬m'}]|aO O²G OD n' ¬m « '¬m*)T ¦,+ | |, aG},< °¬mMO | 9} m ¬|C ¬m P| C '}h$*-( ! ( %/. © $ U¬m'4OD '¬ h nQc} « }0) , ¦,+3|hT(,U #UD '} P| C (}$1- ' ; . ,$O} DO$¯}$|nU} « n $O} DO'¬!U G| K G }$|nU} ' ´; 3#25 4 ' ; O¬,}c [ ; mT '6 ;$¯la 'cm'}5 | ' 6 ;7 ' 6 ;´ µ J a@O Gn ² n}1B%CM©L¨© 8:9] « '}P| n}:9} m UD K n,U(}n}P| ¬m#U]G,} |#U© P : " = Ç/U5 0 +4g R H ` UNh  < L « l º &% ) R H-*,[+ O P+ K HH-U « R d×P fT R + O HS* H = =  < L « lº q  < L u lº « = RXO2R 5 K -, + pO-R 5#] R 5 « w * RfO Z HSUN]+OH-*#+Y,.) R -H * -H *#+×h hK [ H HS* H  < L « lº « 1#+ K ,-+ NO + O ) R HS* « 'O Y+ + ²Þ u rR d9P TXR + O H-* H Ħo = = < L « º < L u º   s " s & st;u v q \ « ? « w *#+ ,-+4h(U,-+ Z F F = = TXR d s  < L « < l º \ ÜÝ 5;1 )* R@K * Z HSUN]+OH-*#+Y,a) R HS* m F F F = = = L « F < l º TXR d s « <  < « < = ÜÝ \ @ F L = « F < = l º TfR d  < « < = ÜÝ = = TXR d R 5h C B< L >ºD C < L >º q v BIÜÝ ²Åj³ S0Z K Ud9P T +OH-+ O HS*#+.P#,[UUphIUNh<HS*;+[H-*#+YUN,-+Yd [<%$7[!'6u-353 5<%$6.! )0/ F = @ C < L >º ÛÅÅ uu @ 69!(1 ' )´ y B 26CB5!'6 F à 5 NTXT SH *#+^d9U1#+ TfO F )x+2* 0 + K U5 O-R 1#+ ,-+Y1 O UÆh , Z H-*#+ c NO-R@K 1;+Y],[+Y+ O UNh¿h(,-+Y+ 1#Ud ,[+5HW)/UpV 0 NTfb +Y1 à O[R 5#] 0 , R Nc;T + O à 5 HS* RXO.O + K H R U5 Z )x+ K U5 O-R 1#+Y, d9U,-+Ê]N+Y5#+ , NT K T NO[O UNhxd×+ 5 36+ T 1 @ H O P R 59] T NO[O d9U1#+ TfO Z )*#U O + O P R 591#+Y],[+Y+ O UNhh(,-+Y+ 1#Ud d ¥`NZjR 5]N+Y5#+ , NT'Z * 0 +ad 5 ` K Ud9P\UN5#+Y5H O Z w * RfO ]+ 5#+Y, NTfR@? 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