Pions vs Magnons Diplomarbeit

"!$# % & %')(*+, -%./021340%'2 5067682+, -%. ;9 : <>=@?A?CBEDF=HGJILK 9NM*OQPR S PUT =@VC?CK PR ? MHWX =@?CYQVZ=H[]\*ÛD PR ^ P G _ R Da` P VZGCDa? :bMHWc.P V R X-M ` P K 9NP Ved@fHfhg *\ Y TNP VC`*DFG M Vi j+V MHWlk _ k mlnQkEo D P G P I R GA?CDa?CYQ? PeWpM V-qJB PUM V P ?CDFÛ=H[rjsB : GCDFÛGUtE_ R Da` P VZGCDa? :bMHWc.P V R DFD u0v]wUx7y{zE|Hx qJB P [ M7}~PRQP VC :OQ:*R =HKDFÛG MHWNT D MhR GD R gh 7 O DFK PR GCD MhR G= REO K=@ RQMhR GsD R dh 7 O DFK PR GCD MhR GUt } BEDF^ZBb=@V P ?CB PM [ O GA? MhRQP9NM G MhR G MHW ?CB P GA?AV MhR D R ? P VZ=H^)?CD MhR G.= REObMHW K=@ RQP ?CDFGCKt;V P G TNP ^)?CDa` P [ : t =@V P = R =H[ M M YEGD R K= R:} = : G k qJB PP [ P ^)?AV M7}.P =@D R ? P VZ=H^)?CD MhR G MHWT D MhR GV P GCYE[a? W V M Kh=HYQhD R = Rs dhl 7lG : KK P ?AV :} BEDF^ZBb?CB PR09 V P =@*G OQM7}-R ? M ?CB P 7lh=HYQ P G : KK P ?AV :MHW P [ P ^)?AV M K=@ RQP ?CDFGCK k qJB P-P [ P ^)?AV M K=@ RQP ?CDFêD R ? P VZ=H^)?CD MhR G MHW K=@ RQMhR G'=@V POQP GC^)VZD 9NPO9;: h=HYQhD R RQ M ? MhR [ : 7l 9 YQ?=H[FG M ?CB Ps dhLsG T D R V M ?C=@?CD MhR =H[QG : KK P ?AV :Hk qJB P'P [ P ^)?AV M K=@ RQP ?CDF^ P [ O G = REO = TETNP =@V-=HG RQMhR*m-9NP [FDF= R ` P ^)? M V TNM ? PR ?CDF=H[FG k I R ?CB P ?CB PUM V :MHW-T D MhR G = REO2T B M ? MhR G = M [ O GA? MhRQP)m o DF[F^)¡ P 2ÛYQVCV PR ? V PUT V P G PR ?CG?CB P¢9 =@V :HMhR R YEK 9NP V MHW \; : VZKD MhR G= REO hDa` P GVZDFG P ? M ?CB P£¥¤¦¨§©§2OQP Û= :Hkª Da PU} DFG P t¥D W+9 = 9;:m \; : VZKD MhR G BE=` P P [ P ^)?AV MhR~« YE= R ?CYEK R YEK 9NP VZGUtsK=@ RQMhR G } DF[F[^ M Y T [ P ? M ?CB P = R =H[ M hY PMHW = M [ O GA? MhRQP)m o DF[F^)¡ P ¬ÛYQVCV PR ? WpM V 9 = 9;:m \; : VZKD MhR G k qJBEDFG =H[FG M D R Û[FY OQP G=~` P VC? P)¬WpM V>?CB POQP Û= :MHW = K=@ RQMhR D R ? M ? }.MT B M ? MhR G k>R =H[ M M YEG? M = D MhR*m T B M ? MhR ^ MhR ` P VZGCD MhR D R =>GA?AV MhR K=@ RQP ?CDF^ P [ O tQK=@ RQMhR*m T B M ? MhR ^ MhR ` P VZGCD MhR DFG'=H[FG MTNM GCGCD 9 [ PHk ®s[ P ^)?AV M7}.P =@D R GA?C= R ? MhR GhDa` P VZDFG P ? M9 =@V :HMhRR YEK 9NP V`*D M [F=@?CD R T V M ^ P GCG P G Û=HYEG PO29;: ?CB P>¯ ? ° M;MHW ?= RQM K=H[ :Hk qJBEDFG T V M `*D OQP GJ= OQP Û= : ^ZBE= RERQP [ WpM Ve\; : VZKD MhR G k qJB P V P DFG RQM ^ M VCV P G TNMhREO D R OQP Û= : Û= RERQP [ WpM V 9 = 9;:m \; : VZKD MhR G k]c =@V :HMhR GK= : =H[FG MOQP Û= :> ?AVZ= R G WpM VZKD R ? M [ PUT ? MhR G±D R ?CB P T V P G PR ^ PMHW =K=@ RQP ?CDF^K MhRQMHTNM [ PHk qJB P = R =H[ M hY PMHW ?CB P K=@ RQP ?CDF^K MhRQMHTNM [ P D R K=@ RQP ?CDFGCK DFGJ= O DFGC^ZBE=@VChD R } DaV P ?CBE=@?J?CB P V PU9;: Û=HYEG P GJ?CB Pe9 = 9;:m \; : VZKD MhROQP Û= :Hk I R ?CB PT D MhR ?CB PUM V : ?CB PeR YEK 9NP V MHW³² =` M VZG'Û= R9NP D R ^)V P =HG PO V P GCYE[a?CD R D R = OEO Da?CD MhR =H[´K=HGCGC[ P GCG K P G MhR G k qJBEDFG-[ P = O G-? M ?CB P ? MHTNM [ M hDFÛ=H[ oµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZK·?CBE=@?^ MhR ?AVZD 9 YQ? P G? M ?CB P £¥¤¦,§©§¸OQP Û= : ^ZBE= RERQP [ k qJB P V P DFG¢=K=@?CB P K=@?CDFÛ=H[e= R =H[ M hY PWpM VK=@ RQMhR G } Da?CB¹[F=@VC P V G : KK P ?AV : HV M Y T G ks h=HD R = R = R =H[ M hY PMHW ?CB PoµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZKÛ= R9NPeWpM Y REO¥k I R ?CB PT D MhR ?CB PUM V : ?CB PT V PUW =H^)? M V MHW ?CB PoµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZKºDFG « YE= R ?CDa¡ PO = REOP« YE=H[ ? M ?CB PbR YEK 9NP V MHW« YE=@VC^ M [ M VZG k I R ?CB P K=@ RQMhR ?CB PUM V : t MhR ?CB PM ?CB P VBE= REO t¥?CB PT V PUW =H^)? M V V PUT V P G PR ?CG'?CB P = R:HMhR GA?C=@?CDFGA?CDFÛG T =@VZ=HK P ? P V»= REO DFG?CB;YEG RQM ? « YE= R ?CDa¡ PO¥k DFDFD Da` ¼ ½¨¾¿~ÀÁ¾¿¹Â u0v]wUx7y{zE|Hx ÃÄÃÄÃ ÅÇÆÈ x7y{É¥ÊË³|Hx{ÃpÉ È Å Ú ÌÎÍNÏ³Ð2ÐÑ x7y ÏÒ y{zEÓrÃ È³ÔrÕ+Ö zEww7× Ñ ww Ò É©wÉ È wbz È Ê¹Ø.É©Ù+É´×pÉ Ô Ãp|hz©× Í É´×ÄËrx{ÃpÉ È w d k Î\ TNMhR ?C= RQPUM YEG-\ : KK P ?AV :¢c V P =@*D R = REO ?CB P M [ O GA? MhRQP qJB PUM V P K kkekkkkekkÜÛ d k dÝ\ M [FDa? MhR G'= REO I R GA?C= R ? MhR G kkkekkkekkkkekkkekkkkekkkekkkekkkkekkÜÞ d k gßqJB PeX-MhR*mª D RQP =@V\*DahK=< M*OQP [ kkkekkkkekkkekkkkekkkekkkekkkkekk H à,áÑ y7x{Ë³y{v]zQx{Ããâ Ñ u0|Hx{ÃpÉ È É©äeå¢É´×pÊ]wUx7É È³Ñ>Ò É©wÉ È w Å;à g k ÎæçS8jsD MhR G kkkekkkkekkkekkkekkkkekkkekkkkekkkekkkekkkkekk g g k dß<>=@ RQMhR GJD R¢WpP VCV M K=@ RQP ?CG-= REO = R ?CD WpP VCV M K=@ RQP ?CG kkkkekkkekkkekkkkekk )è g k gß®é P ^)?CDa` P ®sYEÛ[FD OQP = R jsD MhR ^)?CD MhRkkekkkkekkkekkkkekkkekkkekkkkekk )è g k èÝ®é P ^)?CDa` P ®sYEÛ[FD OQP = R <>=@ RQMhR> ^)?CD MhRkkkkekkkekkkkekkkekkkekkkkekk Û g k è k <>=@ RQMhR G-D R = R ?CD WpP VCV M K=@ RQP ?CG kkkekkkekkkkekkkekkkekkkkekk Û g k è k dÜ<>=@ RQMhR G-D R¢WpP VCV M K=@ RQP ?CG kekkkkekkkekkkkekkkekkkekkkkekk ê ëßÍ Ó Ï y Ð ÃpÉ È wbz È Ê Ò zEv ÏNìUÍ Ó Ï y Ð ÃpÉ È w Å;í è k Î\; : VZKD MhR GD R æçS kkkekkkekkkekkkkekkkekkkkekkkekkkekkkkekk î è k d c = 9;:m \; : VZKD MhR G'D R¢WpP VCV M K=@ RQP ?CG-= REO = R ?CD WpP VCV M K=@ RQP ?CG kkkekkkekkkkekk d* Ú ÆÈ x7y{É¥ÊË³|Ã È³Ô2ï × Ñ |Hx7y{É Ð z Ô´È³Ñ x{Ãpw Ð ÌÚ Û;k ,jsD MhR G'= REO jsB M ? MhR G kkkekkkekkkekkkkekkkekkkkekkkekkkekkkkekk d Û Û;k k jsD MhR*m jsB M ? MhR ^ M Y T [FD R kkkekkkkekkkekkkkekkkekkkekkkkekk dhð Û;k dß<>=@ RQMhR GJ= REO jsB M ? MhR G kekkkekkkekkkkekkkekkkkekkkekkkekkkkekk dhð Û;k d k qJB P j=HYE[FD¥® « YE=@?CD MhR = REO ?CB Ps dhLG : KK P ?AV :"kkkekkkekkkkekk d Þ Û;k d k dÜ° M7}P [ P ^)?AV M K=@ RQP ?CDF^ P [ O GbK= R D WpP GA? PO ?CB P KG P [a` P G¢=HG RQMhR*m-9NP [FDF= R ` P ^)? M V TNM ? PR ?CDF=H[FG kkkekkkekkkkekkkekkkkekkkekkkekkkkekk dHî Û;k d k gÜ<>=@ RQMhR G-= REO> =HYQ Pñ D P [ O G kkkkekkkekkkkekkkekkkekkkkekk g@f Û;k d k è qJB P K=@ RQMhR¦ò§©§ ` P VC? P) kekkkkekkkekkkkekkkekkkekkkkekk g{è Û;k d k Û <>=@ RQMhR*m jsB M ? MhR ^ MhR ` P VZGCD MhR D R = RP) ? P V R =H[rK=@ RQP ?CDF^ P [ Okekkkkekk g Û óôÍ Ó Ï y Ð ÃpÉ È z È Ê Ò zEv ÏNìUÍ Ó Ï y Ð ÃpÉ È~õÑ |hz Ï à©í ê k Î\; : VZKD MhR S P Û= :3kkkkekkkekkkekkkkekkkekkkkekkkekkkekkkkekk gHî ê k k jsD MhR GUt´\; : VZKD MhR G= REO>ö÷mc.M G MhR G kekkkekkkkekkkekkkekkkkekk gHî ê k k dÜ<>=@ RQP ?CDF^< MhRQMHTNM [ P GJ= REOc =@V :HMhR S P Û= :/kkkkekkkekkkekkkkekk èHè ê k dÝçBE=@VC PO¢o DaV P GJ= REOc = 9;:m \; : VZKD MhROQP Û= :òkkkekkkkekkkekkkekkkkekk èê ` ÚÅ ø å Ñ*È³Ñ y{z©×ÄÃpùhzQx{ÃpÉ È x7É Í¥Ñ â Ñ y{z©×.ú-×pzâ´É©y{w ð k ,jsD MhR GUtQû= MhR GUtEü m < P G MhR G kkkekkkekkkkekkkekkkkekkkekkkekkkkekkýÛ ð k dß<>=@ RQMhR G } Da?CB>\ P ` P VZ=H[ ñ [F=` M VZG kkkekkkkekkkekkkkekkkekkkekkkkekkýÛ g ð k d k R ?CD WpP VCV M K=@ RQP ?CDFGCK kekkkekkkkekkkekkkkekkkekkkekkkkekkýÛ è ð k d k d ñQP VCV M K=@ RQP ?CDFGCK kkkekkkekkkkekkkekkkkekkkekkkekkkkekkýÛ è ð k g c = 9;:m \; : VZKD MhR G } Da?CB \ P ` P VZ=H[ ñ [F=` M VZG kkkekkkekkkkekkkekkkekkkkekkýÛ è ð k g k þ\;?C=@?CDFGA?CDFÛGJ= REO ?CB Po¶ó ? P VZK kkkekkkekkkkekkkekkkekkkkekkýÛ ê Úí ÿ,õ Ãpw|Ë³ww7ÃpÉ È z È Ê É È |×ÄË³w7ÃpÉ È u0|{Ó È É 0× Ñ Ê Ô´ÐÑ*È x7w ó©à u óÚ k ILK TNM VC?C= R ?\ T =H^ P G kkkkekkkekkkekkkkekkkekkkkekkkekkkekkkkekk ê Û k d =HYQhD R s dh kekkkkekkkekkkekkkkekkkekkkkekkkekkkekkkkekk ê Û k gç=H[FÛYE[F=@?CD R ?CB Po¶ó ? P VZK kekkkekkkkekkkekkkkekkkekkkekkkkekk êHê k è \*YEKK=@V :MHW ?CB P = R =H[ M hD P G MHW ?CB PT D MhR = REO K=@ RQMhR G'?CB PUM VZD P G kkkekkkkekk êhð øÅ Ò Ãpv×ÄÃpÉ Ô y{zEÙ Ï `*D ¾¿¹½8¿s½¨¾ I R ?CBEDFG }.M VC~?CB P = R =H[ M hD P G MHWT D MhR G0= REO K=@ RQMhR GUt?CB PM [ O GA? MhRQP9NM G MhR G MHW æçS = REO W V M K= R ?CD WpP VCV M K=@ RQP ?CG0= REO~WpP VCV M K=@ RQP ?CG0V P G TNP ^)?CDa` P [ : t } DF[F[ 9NPP)*P K T [FD PO¥k÷ GA? MhR DFGCBED R V P G P K 9 [F= R ^ P G P) DFGA? 9NPU:HMhREO>} BE=@? MhRQP KDahB?BE=` P P)*TNP ^)? PO¥k çBEDaVZ=H[ TNP VC?CYQV 9 =@?CD MhR ?CB PUM V : DFG YEG PO ? MbOQP GC^)VZD 9NP [ M7}PRQP VC : D R ? P VZ=H^)?CD MhR G MHW9NM ?CB¢?CB PUM VZD P G k q MHTNM [ M hDFÛ=H[ T V MHTNP VC?CD P G'B M7}.P ` P V =H[FG M D R Û[FY OQP]P) ?AVZ= M V O D R =@V : = R =H[ M hD P Gr?CBE=@?³=H[F[ M7}WpM V³= RQM K=H[ M YEG³^ MhR ?AVZD 9 YQ?CD MhR G¥D R9NM ?CB T =@VC?CDFÛ[ P T B : GCDFÛG³= REO G M [FD O GA?C=@? PT B : GCDFÛG k qJB P V P GCYE[a?CG M é P V PO =@V P.}.P [F[h RQM7}-RWpM V+æçS T D MhR G³= REO G P VC` P =HG=-hYED OQP = REO K=@?CB P K=@?CDFÛ=H[ W VZ=HK PU}.M VC WpM VD R ` P GA?CDah=@?CD R K=@ RQMhR GD R = R ?CD WpP VCV M K=@ RQP ?CG= REO WpP VCV M K=@ RQP ?CG k o B PR2MhR [ : ^ MhR ^ P V RQPO2} Da?CB[ M7}.P GA? PRQP VC : ^ MhR ?AVZD 9 YQ?CD MhR G?CB P¢OQ:*R =HKDFÛG MHW ?CB P [FDahB? P GA? T =@VC?CDFÛ[ P G } DF[F[ OQM KD R =@? P ?CB P ?CB PUM V : " ! k I R æçS ?CB P G P =@V P ?CB P ?CBQV PUPJT D MhR GUt } BEDF^ZBD R ^ M K T =@V m DFG MhR} Da?CB?CB P æçSGCÛ=H[ P Û= Rb9NP V P h=@V OQPO =HG.K=HGCGC[ P GCG T =@VC?CDFÛ[ P G k qJB PU: = TETNP =@V.=HG M [ O GA? MhRQP 9NM G MhR GUtQV P GCYE[a?CD R W V M K ?CB P G TNMhR ?C= RQPUM YEGJG : KK P ?AV :09 V P =@*D R MHW ?CB P ^ZBEDaVZ=H[¥G : KK P ?AV : HV M Y T s dhl¢ s dh$ #> 7$ %D R ? M ?CB P GCY 9 HV M Y T2s dhl' &(#> 7$ % gh mO DFK PR GCD MhR G± )d ! k qJB P-M [ O GA? MhRQP ?CB PUM V P K PR GCYQV P G]?CBE=@??CB P V P} DF[F[ 9NP ?CBQV PUP K=HGCGC[ P GCG P) ÛDa?C=@?CD MhR G Ä+£ *-,£¥)¤ ,+/£ . Zt V P GCYE[a?CD R W V M K G : KK P ?AV : ^ MhR GCD OQP VZ=@?CD MhR G MhR [ :Hk+M [ O GA? MhRQP'9NM G MhR G=@V P =H[ } = : GsK=HGCGC[ P GCGUthD W ?CB P G : KK P ?AV :>W V M K } BEDF^ZB?CB PU:M VZDahD R =@? P DFG P) =H^)? D R ?CB P æçSýÛ=HG P ?CBEDFGDFG RQM ??CB P Û=HG PbO Y P ? M ?CB P R Da? P K=HGCG MHW ?CB P¢« YE=@VC*GUt+B PR ^ P0T D MhR G=@V P0T G P Y OQM@mLM [ O GA? MhRQP09NM G MhR G= REO Û=@VCV : = GCK=H[F[K=HGCG± k I R = R ?CD WpP VCV M K=@ RQP ?CG= REO>WpP VCV M K=@ RQP ?CGe?CB P G TNMhR ?C= RQPUM YEGeG : KK P ?AV :9 V P =@*D R MHW ?CB P h[ MH9 =H[ s dhLG : KK P ?AV : D R ? M ?CB P GCY 9 HV M Y T 7L]V P GCYE[a?CG]D R ? }.M K=@ RQMhRTNM [F=@VZDa¡=@?CD MhR GA?C=@? P G pWpM Vdh O DFK PR GCD MhR G± 0g ! k qJB P G PP) ÛDa?C=@?CD MhR G } DF[F[D REOQPUPO>9NP K=HGCGC[ P GCGUtr=@h=HD RµMhR [ : D W ?CB P G : KK P ?AV : DFG P) =H^)? k ®+` PR =e^)V : GA?C=H[ } Da?CB M YQ?GA?AVZYE^)?CYQVZ=H[ OQPUWpP ^)?CG } DF[F[ PRQP VZ=H[F[ :RQM ?^ MhR ?C=HD R = R P) =H^)? s dhLG : KK P ?AV :Hk qJB P G PP é P ^)?CG } DF[F[ RQM ? 9NP ^ MhR GCD OQP V PO t´GCD R ^ P K=HGCGC[ P GCG T =@VC?CDFÛ[ P G T V M `*D OQP =GCDFK T [ P VK M*OQP [ } Da?CB M YQ??CB P [ M GCG MHW D R ? P V P GA?CD R T B PRQM K PR = k I R æçS¹^ZBEDaVZ=H[ TNP VC?CYQV m 9 =@?CD MhR ?CB PUM V :} =HG OQP ` P [ MHTNPO ? MOQP ? P VZKD RQP ?CB POQ:*R =HKDFÛG MHW GCYE^ZB T =@VC?CDFÛ[ P G 1 ! t*GCD R ^ P D R9NM ?CB ?CB PUM VZD P G M [ O GA? MhRQP'9NM G MhR G=@V P ? Me9NP ^ MhR GCD OQP V PO Da?DFG RQM ?+GCYQV T VZDFGCD R -?CBE=@?+^ZBEDaVZ=H[ TNP VC?CYQV 9 =@?CD MhR ?CB PUM V : Û= R =H[FG M9NP = TET [FD PO ? M K=@ RQMhR GJD R = R ?CD WpP VCV M K=@ RQP ?CG-= REOWpP VCV M K=@ RQP ?CG k OEO Da?CD MhR =H[ t P) ?AVZ= M V O D R =@V : tH= R =H[ M hD P G P) DFGA? 9NPU:HMhREO} BE=@?]Û= R9NPsWpM Y REOW V M K TNP VC?CYQV 9 =@?CD MhR ?CB PUM V :Hk Il? } DF[F[ 9NP GCB M7}-R ?CBE=@?D R9NM ?CB?CB PUM VZD P Gs?CB P V P =@V P ? MHTNM [ M hDFÛ=H[F[ :RQMhR*m ?AVZDa`*DF=H[EG M [FYQ?CD MhR G k qJB P G P G M [FDa? MhR G OQP GC^)VZD 9NP B P =`*D P V T =@VC?CDFÛ[ P G RQM ?b=HÛ^ P GCGCD 9 [ P9;:TNP VC?CYQV 9 =@?CD MhR ?CB PUM V :Hk I R ?CB P æçSýÛ=HG PO Y P ? M ?CB P ^ MhR ?AVZD 9 YQ?CD MhR G MHW \; : VZK 2P èEt Û t³)ê !sDa?eDFG RQM7}-R t M V=@?[ P =HGA?e PRQP VZ=H[F[ : =HÛ^ PUT ? PO t¥?CBE=@??CB P \; : VZKD MhR GJÛ=@VCV :9 =@V :HMhR DF^^ZBE=@VC P tr= REO =@V P D REOQPUPO9 =@V :HMhR G-?CB P KG P [a` P G k qJB P9 =@V :HMhR ÛYQVCV PR ?Ut RQM7}-R =HG?CB PM [ O GA? MhRQP)m o DF[F^)¡ P ¹ÛYQVCV PR ?Ut PR ? P VZG?CB Pµª =@HVZ= R hDF= R t 3 46587)91:<;>=@?)A'B C1:D=FEHGJI8KD:$L EJC = REO ?CB P V PU9;: ^ M Y T [ P GJ?CB PRQP YQ?AVZ=H[ T D MhR ? M ?CB PP [ P ^)?AV M K=@ RQP ?CDF^ P [ O¥k qJBEDFG MhR [ : BE= TETNPR G MHW ^ M YQVZG PMhR ^ PP [ P ^)?AV M K=@ RQP ?CDFGCK BE=HG 9NPUPR h=HYQ PO k qJB P ? MHTNM [ M hDFÛ=H[? P VZK T V M `*D OQP G= OQP Û= : ^ZBE= RERQP [ WpM Ve?CB P = RQM K=H[ M YEG £¥¤¦§©§2OQP Û= :Hk I R =0? }.M G T =HÛDF=H[ O DFK PR GCD MhR =H[rK=@ RQMhR ?CB PUM V : ?CB P V P =@V P =H[FG M2RQMhR*m ?AVZDa`*DF=H[-B M K M ? MHT;: HV M Y T Gb?CBE=@?¢^ZBE=@VZ=H^)? P VZDa¡ P ?CB P ? MHTNM [ M hDFÛ=H[^ZBE=@VC PMHW G M [FDa? MhR G k Il?bK= :9NPO DFG T YQ? PO2} BE=@? T =@VC?CDFÛ[ P¢T V MHTNP VC? : ?CBEDFG^ZBE=@VC P V PUT V P G PR ?CG k Il? } DF[F[ 9NP =@VChY PO ?CBE=@??CB P9 = 9;:m \; : VZKD MhR G¢=@V P D REOQPUPO¹P [ P ^)?AV MhR G M V ^ MhR GA?AVZYE^)? PO ?CB P V PUMHW te= REO ?CB P ? MHTNM [ M hDFÛ=H[]^ZBE=@VC P ^ M VCV P G TNMhREO D R ?CBEDFG-Û=HG P ? M ?CB PP [ P ^)?AVZDF^^ZBE=@VC PHk ® *TNP VZDFK PR ?CG-GCB M YE[ O t´=@? [ P =HGA?bD RT VZD R ÛD T [ P t 9NP = 9 [ P ? M Û[F=@VZD Wp: ?CBEDFG « Y P GA?CD MhR¥k Il?BE=HG 9NPUPR GCB M7}-R9;:ñ )V M BE[FDF^ZB= REO \;?CY OQP V 0ð !.?CBE=@??CB P j=HYE[FD P« YE=@?CD MhR ^ MhR ?C=HD R G= BED OEOQPRs dhLG : KK P ?AV :Hk G=V P GCYE[a?UtD R M V OQP Ve? M D R Û[FY OQPP [ P ^)?AV M K=@ RQP ?CDFGCK D R ?CB P K=@ RQMhR ?CB PUM V : ?CB P0s dhLG : K K P ?AV : KYEGA? 9NP h=HYQ PO¥k qJB P V P GCYE[a? MHW GCYE^ZB0= G : KK P ?AV : DFGs?CBE=@?.?CB PP [ P ^)?AV M K=@ RQP ?CDF^- P [ O G = REO = TETNP =@V =HG RQMhR*m-9NP [FDF= R ` P ^)? M V TNM ? PR ?CDF=H[FG k qJBEDFG-DFGUt MHW ^ M YQVZG P t MhR [ :WpM Ve=0K=@?CB P K=@?CDFÛ=H[ OQP GC^)VZD T ?CD MhR G M ?CB P V P =@V PRQMµRQPU}OQP HV PUP G MHWW V PUPOQM K k qJB P = R =H[ M MHW ?CB P>M [ O GA? MhRQP)m o DF[F^)¡ P ÛYQVCV PR ? Û= R9NP ^ MhR GA?AVZYE^)? PO¥k h=HD R t¥Da?DFG?CBEDFG-? P VZK·?CBE=@? PR ? P VZG?CB P ª =@HVZ= R hDF= R = REO =H[F[ M7} G WpM V?CB P OQP Û= :MHW = RQP YQ?AVZ=H[K=@ RQMhR D R ? M ? }.MT B M ? MhR G k ® *TNP VZDFK PR ?C=H[F[ : Da?eK= :>9NP P =HGCD P Ve? MOQP ? P ^)? ?CB P ?AVZ= R G WpM VZK=@?CD MhRMHW =K=@ RQMhR D R ? M = T B M ? MhR t'=^ MhR ` P VZGCD MhR T V M ^ P GCG?CBE=@? } DF[F[ M ÛÛYQVbD W ?CB P K=@ RQP ?DFG T [F=H^ PO D R = RP) ? P V R =H['K=@ RQP ?CDF^b P [ O¥k qJBEDFG DFG = R =H[ M M YEG ? M ?CB P D RQW =HK M YEG T B M ? MhR*m = D MhR ^ MhR ` P VZGCD MhR K P ^ZBE= R DFGCK Þ ! t.=µK P ?CB M*OOQP ` P [ MHTNPO ? MOQP ? P ^)?= D MhR GUtsB M7}.P ` P V } Da?CB RQM¢TNM GCDa?CDa` P V P GCYE[a?CG? M ?CBEDFG O = :Hk q MHTNM [ M hDFÛ=H[^ MhR GCD OQP VZ=@?CD MhR G=H[FG MT V M `*D OQP D RQWpM VZK=@?CD MhR = 9NM YQ??CB P GA?C=@?CDFGA?CDFÛG MHW ?CB P \; : VZKD MhR G= REO 9 = 9;:m \; : VZKD MhR G k qJB P V P GCYE[a?DFG MH9 ?C=HD RQPO ?CBE=@??CB P \; : VZKD MhR G-D R æçS=@V PP Da?CB P V 9NM G MhR G M V WpP VZKD MhR GUt } BEDF[ P ?CB P9 = 9;:m \; : VZKD MhR G=@V P = R:HMhR GUt = REO B PR ^ P ?CB P DaV-GA?C=@?CDFGA?CDFÛG 9NP BE=`*D M V-DFG OQP ? P VZKD RQPO9;: = W V PUPT =@VZ=HK P ? P V»QtE?CB P = R:HMhR = R h[ P t ?CB PT V PUW =H^)? M V MHW ?CB P ° MHTEW ? P VZK k I R æçS?CB P V P =@V P ? }.M OQP Û= : K P ^ZBE= R DFGCKG WpM Ve?CB P \; : VZKD MhR t OQP G T Da? P ?CB P DaVe? MHTNM [ M hDFÛ=H[ GA?C= 9 DF[FDa? :Hk ®sDa?CB P V.= P [ P ^)?AV M7}.P =@0D R GA?C= R ? MhR `*D M [F=@? P G 9 =@V :HMhR0R YEK 9NP Vs`*DF=?CB P¯ ?° M;MHW ?= RQM K=H[ : )î ! t M V0D R = R¹s Û HVZ= REO Y R D PO ?CB PUM V : =K=@ RQP ?CDF^K MhRQMHTNM [ P} DF[F[^ZBE= R P ?CB P9 =@V :HMhR R YEK 9NP V MHW =ehDa` PR G : GA? P K UNf ! k I R ?CB P K=@ RQMhR ?CB PUM V : ?CB P V P DFG RQM = R =H[ M MHW ?CB PJP [ P ^)?AV M7}.P =@ D R GA?C= R ? MhR t@B M7}.P ` P V= R =H[ M M YEGr? M ?CB P K=@ RQP ?CDF^sK MhRQMHTNM [ P = O DFGC^ZBE=@VChD R } DaV P = TETNP =@VZGrÛ=HYEGCD R 9 = 9;:m \; : VZKD MhR>OQP Û= : ?CBEDFG?CDFK P D R ? }.M G T =H^ P)mO DFK PR GCD MhR G= REO>MhRQP ?CDFK P)mO DFK PR GCD MhR k qJB P } DaV PO DFGC^ZBE=@VC P G= REO ?CB P V PU9;: ^ZBE= R P G?CB P0R YEK 9NP V MHW ^ZBE=@VC P Û=@VCVZD P VZGD R ?CB P K=@ RQP ? k qJB P R YEK 9NP V MHW9 = 9;:m \; : VZKD MhR GUtV PUT V P G PR ?CD R >?CB P ^ZBE=@VC P Û=@VCVZD P VZGD R ?CB P K M*OQP [ t } DF[F[s?CB;YEG 9NP =H[a? P V PO¥k I R æçSÁ?CB P ^ZBEDaVZ=H['G : KK P ?AV : HV M Y T } =HGb^ZB M G PR ? M D R Û[FY OQP ?CB P ? }.M [FDahB? P GA? « YE=@VC*G k qJBEDFGÛ= R9NP'P)*T = REOQPO ? M = R =@V 9 Da?AVZ=@V :R YEK 9NP V MHW´² =` M VZG } B PR ^ MhR GCD OQP VZD R ?CB P h[ MH9 =H[E^ZBEDaVZ=H[ G : KK P ?AV : HV M Y T¢MHW ?CB PWpM VZK sP ORQ le sP ORQ $ # 7$ % } BEDF^ZB 9 V P =@*G.? M ?CB P GCY 9 HV M Y T sP ORQ l' &(# 7$ % P ORQ S gh k qJBEDFG[ P = O G? MRQPU} RQMhR*m ?AVZDa`*DF=H[]? MHTNM [ M hDFÛ=H[^ MhR ?AVZD 9 YQ?CD MhR GUt ?CBE=@?'=@V P =HÛ^ M Y R ? POWpM V'D R ?CB PoµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZK HHtNd*t¥)g ! k qJB PT V PUW =H^)? M V MHW ?CB P oµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZKòDFG?CB PbR YEK 9NP V MHW ^ M [ M VZG OUTe} BEDF^ZBDFG « YE= R ?CDa¡ PO¥k¢ª Da PU} DFG P ?CB P G : KK P ?AV : HV M Y TMHW ?CB P K=@ RQMhR ?CB PUM V : Û= R9NPeP)*T = REOQPO ? M ?CB P h[ MH9 =H[ sP ORQ .G : KK P ?AV : } BEDF^ZB0DFG 9 V M PR ? M0P ORQWV 7 P ORQRS gh k I R =æYE= R ?CYEK°=H[F[ WpP VCV M K=@ RQP ?'?CBEDFG.^ M VCV P G TNMhREO G ? M ?CB P [F= :HP VD REOQP)MHW ?CB P ? }.M@mO DFK PR GCD MhR =H[³[F=@?A?CDF^ P GA?AVZYE^)?CYQV XP )Hè ! k qJB P B M K M ? MHT;: HV M Y T GD R ?CB P K=@ RQMhR ?CB PUM V : ^ MhR ?AVZD 9 YQ? P D R = R = R =H[ M M YEGK= RERQP Vt } B P V ZP Y YEGA?-[FDa P D R ?CB P Û=HG PMHW ?CB P ° MHTEW ? P VZK WpM V s dhZt?CB P'T V PUW =H^)? M V+? M ?CB P'oµP GCG mL¶ YEKD RQM@m o Da?A? PR = R =H[ M hY P DFG RQM ? « YE= R ?CDa¡ PO¥k q }.M ? :;TNP G MHW K=@ RQP ?CGJ=@V P ^ MhR GCD OQP V PO0WpM V } BEDF^ZB¢GCYE^ZB= WpM VZK=H[FDFGCKýK= :bT V M `*D OQP D R GCDahB? k q }.M@mO DFK PR GCD MhR =H[s= R ?CD WpP VCV M K=@ RQP ?CG Û= R29NPbT V P ÛYQVZG M VZG? M BEDahB? P K TNP VZ=@?CYQV P GCY TNP VZ^ MhREO YE^ m [ ? M VZG = REO =@V P ?CB P V PUWpM V P0MHW HV P =@?D R ? P V P GA? Û tê)! k T BE=HG P0O DF=@HVZ=HK MHW GCYE^ZB2=>K=@? P VZDF=H[sDFG hDa` PR D R V PUWlkã k 7 k _ TNMhROQMHT D R Qt 9 = 9;:m \; : VZKD MhR G-Û=@VCV : D R 0= R>P [ P ^)?AVZDF^ ^ZBE=@VC P } DF[F[ OQP GA?AV M7: ?CB P = R ?CD WpP VCV M K=@ RQP ?CDF^GA?AVZYE^)?CYQV PMHW =K=@ RQP ? k qJB P V M [ P MHW ?CB P9 = 9;:m \; : VZKD MhR GD R ?CB P GCY m TNP VZ^ MhREO YE^)?CD R T BE=HG P DFG RQM ?Û[ P =@VtrB M7}.P ` P V?CB P DaVeD R*² Y PR ^ P DFG 9NP [FD P ` PO ? M9NP ^)VZYEÛDF=H[D R ?CB P WpM VZK=@?CD MhRMHW ç M;MHTNP V T =HDaVZG= REO B PR ^ P ?CB P K P ^ZBE= R DFGCK MHW BEDahB? P K TNP VZ=@?CYQV P GCY TNP VZ^ MhREO YE^ m ?CD MhR¥k <>YE[a?CD m [F= :HP V « YE= R ?CYEK°=H[F[ WpP VCV M K=@ RQP ?CG=@V P RQM7}-R ? M BE=@V 9NM V P [ P ^)?AV MhR G pM V W VZ=H^)?CD MhR G ?CB P V PUMHW =HG'? MHTNM [ M hDFÛ=H[ 9 = 9;:m \; : VZKD MhR G )è©tr7ð;tr Þ ! k qJBEDFG WpM VZK=H[FDFGCKýGCB M YE[ O ` P VZD Wp:0} BE=@?'DFG =H[aV P = OQ: RQM7}-R = 9NM YQ?J?CB P G P K=@? P VZDF=H[r= REOT V M `*D OQP = RMHTETNM VC?CY R Da? : ? M D R ` P GA?CDah=@? PWpP VCV M K=@ m RQP ?CDFêK=@ RQMhR G k T AF HTSC doping ñ DahYQV P k @i]\_^'`)a>bdcNef`>gHhD`Nij$kl`Nmn`NmpoPe k>b"h1hDjNi`>gHm6b8oPefqsrthubuq8v'hwa8jNhxj$kl`^yezgN^{o|b"i}r~b"hD`HoPv'hub" a1v0r~b"hDqwjNmtcNv~q>o<jNh Jq B P G P ?CY T¢MHW ?CBEDFG }.M VC0DFG.=HG WpM [F[ M7} G k çBE= T ? P VJd } DF[F[EhDa` P = 9 VZD PUW¥M ` P VC`*D PU}÷MHW ?CB P ?CB PUM V : ?CBE=@?DFG P GCG PR ?CDF=H[¥? M Y REOQP VZGA?C= REO ?CBEDFG }.M VC k qJBEDFG'D R Û[FY OQP G?CB PW Y REO =HK PR ?C=H[FG MHW G TNMhR ?C= RQPUM YEG G : KK P ?AV :9 V P =@*D R Qt?CB PM [ O GA? MhRQP ?CB PUM V P Kt?CB P °DaHhG0K P ^ZBE= R DFGCKº= REO ?CB P ? MHTNM [ M hDFÛ=H[ ^ MhR ?AVZD 9 YQ?CD MhR G MHW ?CB P G M [FDa? MhR G-= REO D R GA?C= R ? MhR G k qJB P M [ O GA? MhRQP9NM G MhR G-= REO ?CB P DaV[ M7}'m PRQP VC : OQ:*R =HKDFÛG³=@V P D R ?AV M*O YE^ PO D R ^ZBE= T ? P V+g k çBE= T ? P V³èDF[F[FYEGA?AVZ=@? P G¥?CB P.P K P VChD R B M K M ? MHT;: HV M Y T G = REO ?CB P DaVV P [ P `@= R ^ PµWpM V?CBEDFG }.M VC k ®s[ P ^)?AV M K=@ RQP ?CDF^ P [ O G=@V P D R Û[FY OQPO = REO ?CB POQP Û= : ^ZBE= RERQP [FG MHW ?CB PeT D MhR G= REO ?CB P K=@ RQMhR G'=@V P D R ` P GA?CDah=@? PO D R ^ZBE= T ? P V Û tE^ MhR Û[FY O D R } Da?CB0?CB P ^ MhR ` P VZGCD MhRMHW =K=@ RQMhR D R ? M = T B M ? MhR D R = RµP) ? P V R =H[+K=@ RQP ?CDF^ P [ O¥kñQM [F[ M7} D R ?CBEDFGeDFGe= O DFGCÛYEGCGCD MhR MHW ?CB POQP Û= :>MHW \; : VZKD MhR G= REO>9 = 9;:m \; : VZKD MhR G k \; : VZKD MhR G } DF[F[ OQP Û= :O Y P ? M ?CB P>¯ ? ° M;MHW ? = RQM K=H[ : = REO =>K=@ RQP ?CDF^0K MhRQMHTNM [ P t } B P V P ?CB P09 = 9;:m \; : VZKD MhR G OQP Û= :MhR [ : `*DF= = O DFGC^ZBE=@VChD R } DaV P t } BEDF^ZB0DFG.?CB P = R =H[ M hY PeMHW ?CB P K=@ RQP ?CDF^K MhRQMHTNM [ PHk qJB P [F=HGA?'^ZBE= T ? P V PR ?C=HDF[FG=^ M K T =@VZDFG MhRb9NP ? }.PUPR ?CB P [F=@VC P V R YEK 9NP V MHW¥² =` M VZG'D R æçS¬= REO =[F=@VC P V'G : KK P ?AV : HV M Y TWpM Vs?CB P K=@ RQMhR G } BEDF^ZB[ P = O G? MoµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZKG WpM V 9NM ?CBÛ=HG P G.= REO ?CB P DaV ^ M VCV P G TNMhREO D R T V PUW =H^)? M VZG k \ M [ P ?'?CB P VZD OQP9NP hD RkkUk 46587)91:<;>=@?)A'B C1:D=FEHGJI8KD:$L EJC Àý¿x '¾ Â~ÂsÀ·Â~Â ½Â½¨¾ Â $ ¾ Ý½ ½s½Z]4½W"¿s½¨¾ Â w U¡£¢£¤6¥¦¢R§-£¨R©ª¬«U®¯§¤6°6«²±°(§-¥W³µ´w¢R¶·¥¦¢R¸¤(¹R§»º¼£½u¸¾©~¤6£¢R§ ¿ ¹R§-}°(§À .c : îHê@f X =HK 9 Y = REOM [ O GA? MhRQPRQM ?CDF^ PO ?CB P GCDa R D ´Û= R ^ PsMHW G TNMhR ?C= RQPUM YEGG : KK P ?AV :9 V P =@*D R \E\ c eD R ^ MhREOQPR G PO K=@?A? P V T B : GCDFÛG g)! k qJB PbM ÛÛYQVCV PR ^ PbMHW \E\ c DFG P G TNP ÛDF=H[F[ :>P KD RQPR ?D R WpP VCV M@m = REO = R ?CD WpP VCV M K=@ RQP ?CG Äñ <t ñ kNX =HK 9 Y>=H[FG M V P ^ M R Da¡ PO ?CB P DFK TNM VC?C= R ^ PMHW \E\ c D R T =@VC?CDFÛ[ P'T B : GCDFÛG k I R îHê{è°DaHhGsD R ` P GA?CDah=@? 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M D R ?AV M*O YE^ P G TNMhR ?C= RQPUM YEG¢G : KK P ?AV : 9 V P =@*D R } Da?CB P) =HK T [ P G k ILK=@hD RQP = TNP V WpP ^)?^ MhRQP t 9 =H[F= R ^ PObMhR Da?CGs?CD Trk Il?DFG TNM GCGCD 9 [ P ?CBE=@??CB P ^ MhRQP ^ M YE[ O V P K=HD R D R ?CBEDFG TNM GCDa?CD MhR D REOQP R Da? P [ : t T V M `*D OQPO ?CBE=@?J?CB P V P =@V PRQMP) ? P V R =H[ WpM VZ^ P G } BE=@?CG M;P ` P V=H^)?CD R bY TNMhR Da? k Â P ?-= R D R R Da? P GCDFK=H[ O DFGA?CYQV 9 = R ^ P} DF[F[NÛ=HYEG P ?CB P ^ MhRQP ? MW =H[F[N? M Da?CGJGCD OQP © k d k 7 k qJB P V P =@V P ?CBQV PUP DFK TNM VC?C= R ?s?AVZ=HDa?CG.? M ?CBEDFG.GCDa?CYE=@?CD MhR i k qJB PM VZDahD R =H[©GCDa?CYE=@?CD MhR ^ MhR ?C=HD R G= TNP V WpP ^)?-G : KK P ?AV :µ V M ?C=@?CD MhR G-=@V M Y REO ?CB P ¡ m = DFG± k d k qJB P ^ MhRQP} DF[F[ W =H[F[rD R =hDa` PR O DaV P ^)?CD MhR D W Da? P)*TNP VZD PR ^ P G+= R D R R Da? P GCDFK=H[ O DFGA?CYQV 9 = R ^ PHk g k qJB P R =H[QGA?C=@? P DFG OQP PRQP VZ=@? P = REO ?CB P ^ MhRQP Û= R V M ?C=@? P D R ? M =H[F[ M ?CB P V-HV M Y REO GA?C=@? P G k R P) =HK T [ P K M V P V P [ P `@= R ?? M ?CBEDFG }.M VC^ M K P G W V M K ^ MhREOQPR G PO K=@?A? P V T B : GCDFÛG k ILK=@hD RQP =-^)V : GA?C=H[ k ®s=H^ZBD MhR D R ?CBEDFGr^)V : GA?C=H[;Û=@VCVZD P G³G T D R = REO ?CB P V PsP) DFGA?CG³=-GCK=H[F[^ M Y T [FD R 9NP ? }.PUPR ? }.M = )O Y =H^ PR ?G T D R G k qJBEDFGDFG } BE=@?BE= TETNPR GD R = WpP VCV M@m'M V= R ?CD WpP VCV M K=@ RQP ? } BEDF^ZB>=@V POQP GC^)VZD 9NPO 9;: ?CB P ° P DFG PR9NP VCK M*OQP [ } B P V P ?CB P °=HKDF[a? MhR DF= R ?C=@ P G-?CB PWpM VZK d k 7 ÃÅÄ VÆÈÇ ÊtÏ Í , É~ÊÌË Í8Î Ð 46587)91:<;>=t3yAJÑ)Ò)Ó¦ÓÀ;u:D= ÒUÔ6=z7)Õ8L C"Ö×ÙØ£7"Ú|ÚuÛ ;wÚ|Ú_ÔÙE0Ú|EJC"ÚÜ7)C8GÝ'EJ9>EJÛ E0ÖHL Kw7)Û)ÑNEJÛ I1:$L EJC"Ú Spontaneous Symmetry Breaking ñ DahYQV P d k @iWÞ-ßy`Ni}rtàábRj$k¬i`Jq8hDj)a8qwjwrtefqRa<rÙjNmpo<`Nm6bujNvaUa1âNiRiãb8oPh1â ä"hubu`)å)eÌmg } B P V P Ê DFG?CB P G T D RMHTNP VZ=@? M V= REOxÆ DFG=K=@? P VZDF=H[ T =@VZ=HK P ? P V?CBE=@? OQP ? P VZKD RQP G D W ?CB P ^)V : GA?C=H[DFG WpP VCV M@m'M V= R ?CD WpP VCV M K=@ RQP ?CDF^ 9NP [ M7} =^)VZDa?CDFÛ=H[]? P K TNP VZ=@?CYQV PHk ?BEDahB PRQM YQhB? P K m TNP VZ=@?CYQV P G¢?CB P ^ M Y T [FD R 9NP ^ M K P G RQP h[FDahD 9 [ P = REO ?CB P G T D R G TNM D R ?D R =@V 9 Da?AVZ=@V :~O DaV P ^)?CD MhR G k c.P [ M7} = ^)VZDa?CDFÛ=H[s? P K TNP VZ=@?CYQV P tB M7}.P ` P Vt?CB P ^ M Y T [FD R } DF[F[?C=@ P¢P é P ^)?= REO ?CB P V P0} DF[F[ 9NP = T V PUWpP VCV PO¢M VZD PR ?C=@?CD MhRMHW ?CB P G T D R G © k d k dh k Spontaneous Symmetry Breaking ñ DahYQV P d k d;i¦æHrÙjNmpo<`Nm6bujNvaµa1âNiRiãb8oPh1â ä"hubu`)å)eÌmg jNmç`XjNm6b"DcNeÌiãb"mÙa1efjNmt`Nà@àz`HofoPefq1b ª Da PU} DFG P ? M ?CB PT V P `*D M YEG P) =HK T [ P ?CB P V P =@V P ?CBQV PUP ?AVZ=HDa?CGUt©?CB P G : KK P ?AVZDFÛ=H[ ÄO DFG M V OQP V PO GA?C=@? P} BEDF^ZBDFG+?CB PRb9 V M PR ? M = R =H[ OQP PRQP VZ=@? PO GA?C=@? P t } BEDF^ZBÛ= R09NP ^ MhR ?CD R Y M YEGC[ : V M ?C=@? PO D R ? M =H[F[ M ?CB P V'HV M Y REO GA?C=@? P G k+o BEDF^ZBb R =H[NGA?C=@? P DFG.^ZB M G PR Û= RRQM ? 9NPT V PO DF^)? PO Y R [ P GCGs?CB P V P DFGe= RM YQ? P Ve P [ O>} BEDF^ZB P)*T [FDFÛDa?C[ :9 V P =@*G?CB P G : KK P ?AV :Hk I R ?CB P G M [FD O GA?C=@? P Û=HG P ?CB P V P DFGe= T BE=HG P ?AVZ= R GCDa?CD MhR¢} BEDF^ZBDFG'hDa` PR9;: =^)VZDa?CDFÛ=H[N? P K TNP VZ=@?CYQV PHk qJB P K M GA?^ M KK MhR tN= REO T V MH9 = 9 [ : GCDFK T [ P GA?'?CB PUM V P ?CDFÛ=H[ P) =HK T [ PMHW \E\ c DFG T V M `*D OQPO9;: ?CB P [FD RQP =@WV è m K M*OQP [ } B P V P ?CB Pª =@HVZ= R hDF= R ?C=@ P G-?CB P ®sYEÛ[FD OQP = R¢WpM VZK d*" ! é Ä /d êJëìtí)êJë'ìtí td î ï>ìtí0ìtí Èðè ìtí)ìtí ïNñ d k dh qJB P P [ O G ì í _t òóÈô , d , ñ8ñ8ñ Oçõ =@V P ?CB P ^ M K TNMhRQPR ?CG MHW = dR Om ^ M K TNMhRQPR ?V P =H['` P ^)? M V 3yA ?¦Ñ9>EJC1:|7)C";wEJI"ÚÜÑ)Ò)Ó¦ÓÀ;u:D= ÒUÔ6=F;17)Õ8L C"Ö7)C8G£:D5";£öpEJÛ G0Ú<:<EJC";ZÝÜ5";wEN=F;>Ó ÷ k qJB Pª =@HVZ= R hDF= R ^ MhR ?C=HD R G=µh[ MH9 =H[}ø PO G : KK P ?AV :Hk qJB P GCDFK T [ P GA? P) =HK T [ P DFG hDa` PR }ì B PRdO Ä d k qJBEDFG ^ M VCV P G TNMhREO G ? M = R ø dh¡ù 7 G : KK P ?AV :Hk I R ?CBEDFGÛ=HG P ì Û= R 9NP } VZDa?A? PR D R ?CB PWpM VZK ì Ä ì/ú û ì ï = REO ?CB P [F=@HVZ= R hDF= R KYEGA? 9NP V PU} VZDa?A? PR ÊFþ D R =^ M K T [ P) WpM VZK k qJBEDFG ª =@HVZ= R hDF= R DFGD R `@=@VZDF= R ? ? M ?CB P h[ MH9 =H['?AVZ= R G WpM VZK=@?CD MhR ìpü Ä®ý ì } B P V P ì DFG =^ M K T [ P) GCÛ=H[F=@V¢ P [ O¥k I WMhRQP ^ZB M;M G P G î ïdÿ f MhRQP REO G WpM V¢?CB P `@=HÛYEYEK P)*TNP ^)?C=@?CD MhR `@=H[FY P ì ï Ä V T Ä ï Fk c.: V PUT [F=HÛD R ¢?CB P ç=@VC? P GCDF= R ^ M;M V O D R =@? P G } Da?CB TNM [F=@Ve^ M;M V O D R =@? P GUt ì? }.Ä M K =HGC$ GCý DaÊ ` P P [íïO G V´¦ í= REO è RQM7} Q$ý9NÊ P ^ M K thDaP ?]G DFGMhRQ« P YEDFK^C*=H[ :GCGCGDa` PUPPR ?CP BE[ O =@? è } BE-=@? = T REV OP `*MhD RQM P YEGCK[ : =H[GCM;GCM[ P GCPG-O [FP Da [ O P » k qJB PeT B PRQM K Pì RQú MhR¢MHWRQì PUï } K=HGCGC[ P GCG T =@VC?CDFÛ[ P G'DFG P)*T [F=HD RQPO09;: ?CB P M [ O GA? MhRQP ?CB PUM V P K k qJB P¢M [ O GA? MhRQP ?CB PUM V P Kt WpM VZKYE[F=@? POµ9;:nQkM [ O GA? MhRQP D R îHêHd 0g ! tGA?C=@? P G?CBE=@? } B PR = ^ MhR ?CD R Y M YEG+h[ MH9 =H[EG : KK P ?AV : DFG+G TNMhR ?C= RQPUM YEGC[ :9 V M PR D R ? M =eV P K=HD R D R eGCY 9 HV M Y T Ã·?CB PR ?CB P V P =@V P K=HGCGC[ P GCG 9NM G MhR P [ O G?CBE=@?[FDa` P D R ?CB P ^ M G P ?G T =H^ P Ã k qJB PR YEK 9NP V MHW ?CB P G M Û=H[F[ PO0M [ O GA? MhRQPJ9NM G MhR GsDFGhDa` PR9;: ?CB P-O DFK PR GCD MhRMHW ?CB P ^ M G P ?.G T =H^ PO DFK ÃµÜ Ä O DFK m.O DFK Ãµ k qJB PM [ O GA? MhRQP ?CB PUM V P K } DF[F[ RQM7}89NP DF[F[FYEGA?AVZ=@? PO} Da?CB P) =HK T [ P G-V P [ P `@= R ?? M ?CB P K M*OQP [FG ^ MhR GCD OQP V PO D R [F=@? P V^ZBE= T ? P VZG ks PRQP VZ=H[ T V M;MHW Û= R9NPeWpM Y REO D çR g*t©dHd*t´d*Ht©dH)g ! k ñQM Vb?CB P K=@ RQMhR ?CB PUM V : ?CB P V P [ P `@= R ?h[ MH9 =H['G : KK P ?AV : HV M Y T DFG hDa` PR9;: Ä¯ø ghZt ^ M VCV P G TNMhREO D R ? XM O Ä8g k qJBEDFG-DFG-B M [ M K M V T BEDFê? M ?CB Ps dhLG : KK P ?AV :Hk qJB Pª =@HVZ= R hDF= R ?C=@ P G-?CB PWpM VZK é Ä d êJë'ì í êJë'ì í ! ì d k gh d k è; ! ì Ä ðè ì í ì í V ï ï d kÛ Ä ý , ý , ý" A ì ú qJB P `@=HÛYEYEKGA?C=@? P KD R DFKDa¡ P Gs?CB P [F=@HVZ= R hDF= R = REOï ?C=@ P G-?CB PWpM VZK d k êh ì Ä ì ¤ Ä f , f , Q qJBEDFG^ MhR ©hYQVZ=@?CD MhR DFG QR M [ MhR P V¾ø ghD R `@=@VZDF= R ?Ut 9 YQ??CB P V P DFG=V P K=HD R D R ø g V 7µÄ ø dh-ù 7+G : K K P ?AV : Ã k qJB P ^ M G P ?G T =H^ P-9NP ^ M K P G ÃÅÄ ï ù$#&% 7 k qJB P-O DFK PR GCD MhR MHW ?CB P ^ M G P ? G T =H^ P DFGd G M>MhRQP0P)*TNP ^)?CG? }.MM [ O GA? MhRQP09NM G MhR G ?CB P ? }.M K=HGCGC[ P GCGK=@ RQMhR OQP HV PUP G MHWW V PUPOQM K0 k Da` PR ?CB P `@=HÛYEYEKý P [ O¢} Da?CBGCK=H[F[ ² YE^)?CYE=@?CD MhR G ì Ä ì ¤ î ú , î ï , è AÀÄ î ú , î ï , è A D R G P CV ? PO D R ? M ?CB P [F=@HVZ= R hDF= R d k g=GCB M VC?JÛ=H[FÛYE[F=@?CD MhR G'V P ` P =H[FG d k ðH é Ä é ¤ ð ï è ï ' )î Ê( , î Êï è ï , î Êï è³ ñ d kÞ qJB P V P =@V P RQM¢« YE= O VZ=@?CDF^? P VZKG WpM V?CB P P [ O G t } B P V P ?CB P V P DFG-= « YE= O VZ=@?CDF^? P VZKÁD R è k qJBEDFGK P = R G?CBE=@?+?CB P è0 P [ O MH9 ?C=HD R G+=K=HGCGhDa` PRî 9;Ê : î ï Ä÷d ð ï = REO ?CB P V P =@V P ? }.M K=HGCGC[ P GCG 46587)91:<;>=t3yAJÑ)Ò)Ó¦ÓÀ;u:D= ÒUÔ6=z7)Õ8L C"Ö×ÙØ£7"Ú|ÚuÛ ;wÚ|Ú_ÔÙE0Ú|EJC"ÚÜ7)C8GÝ'EJ9>EJÛ E0ÖHL Kw7)Û)ÑNEJÛ I1:$L EJC"Ú * M [ O GA? MhRQPb9NM G MhR P [ O G k qJB P¢M [ O GA? MhRQPb9NM G MhR P [ O G[FDa` P D R ?CB P ^ M G P ? G T =H^ P ï k I R [F=@? P V ^ZBE= T ? P VZG ì } DF[F[ 9NP V PUT [F=H^ PO9;: ý } BEDF^ZBDFG RQM VZK=H[FDa¡ PO ? MMhRQPHk ñQM V¢?CB P>T D MhR ?CB PUM V : ?CB P V P [ P `@= R ?0G : KK P ?AV : HV M Y T DFGbhDa` PR~9;: ?CB P ^ZBEDaVZ=H[-G : KK P ?AV : Ä s dhlb s dh$# } BEDF^ZB DFGB M [ M K M V T BEDFê? M ø è; k qJBEDFG-K P = R G?CBE=@??CB P [FD RQP =@VGCDahK= K M*OQP [ } Da?CB O Ä¹è T V M `*D OQP GJ=K M*OQP [ WpM V-?CB PT D MhR G k+X-M7} ?CB P ^ M VCV P G TNMhREO D R P [ O ?C=@ P G-?CB P WpM VZK ì Ä+ ë Ä, ¤ , d k îh I R ?CBEDFG¢Û=HG P ?CB P h[ MH9 =H[eG : KK P ?AV : HV M Y T- DFG 9 V M PR D R ? M ?CB P V P K=HD R D R GCY 9 HV M Y T ÃÄ s dhl'&(# k qJB P ^ M G P ?G T =H^ P ÃÄ s dhDFG MHWO DFK PR GCD MhR g;t } B MQ¯ G PRQP VZ=@? M VZG WpM V ?CB P ?CBQV PUP K=HGCGC[ P GCG T D MhR P [ O G k qJB P G PeT D MhR P [ O G'=@V P ^ MhR ?C=HD RQPO D R ?CB P ` P ^)? M V ó s dh k ñQM V= R: hDa` PRsO Da?eÛ= R9NP OQP ? P VZKD RQPO ?CBE=@?e?CB P [F=@HVZ= R hDF= R>MHW ?CB P [FD RQP =@VGCDahK=¢K M*OQP [ ^ MhR ?C=HD R G-= h[ MH9 =H[+ø PO G : KK P ?AV :µ k qJB P `@=HÛYEYEKGA?C=@? P Û= R9NPeOQP RQPO =HG ì Ä ì ¤ Ä f , 8ñ ñ8ñ , f , Q ñ d k Uf qJBEDFGb^ MhR ©hYQVZ=@?CD MhR DFG RQM ?¢D R `@=@VZDF= R ?bY REOQP Vb?AVZ= R G WpM VZK=@?CD MhR G W V M K t 9 YQ?0^ MhR ?C=HD R G0= R ÃÄÅø POV 7G : KK P ?AV :Hk qJB P M [ O GA? MhRQP¢9NM G MhR P [ O G [FDa` P D R ?CB P ^ M G P ?bG T =H^ .P ÃÄ ø PO ø PO V 7Zt } BEDF^ZBBE=HG O V O DFK PR GCD MhR G k qJB PM [ O GA? MhRQP ?CB PUM V P K T V M ` P GbhDa` PR = R: G : KK P ?AV : ^ MhR ©hYQVZ=@?CD MhR ?CBE=@?b?CB P>R YEK 9NP V MHW K=HGCGC[ P GCG- P [ O GDFGhDa` PR9;:>O DFK Ãµ Ä O DFK V O DFK ÃµZtr= REO ?CB PO DFK PR GCD MhR MHW ?CB P V P K=HD R D R µG : KK P ?AV : HV M Y T Ã hDa` P G?CB P KD R DFKYEK R YEK 9NP V MHW V P K=HD R D R µK=HGCGCDa` P P [ O G k qJBEDFG T VZD R ÛD T [ P DFG` P V : PRQP VZ=H[= REO}.M VC*GD R>9NM ?CB P) ?AV P K P GUieI R G M K P Û=HG P Ge?CB P V P K=HD R D R G : KK P ?AV : ÃDFG P« YE=H[´? M/ G M ?CB P ^ M G P ?JG T =H^ P ^ MhR ?C=HD R G MhR [ : ?CB P D OQPR ?CDa? :Hk I R ?CBEDFG.Û=HG P ?CB P V P =@V PeRQMbM [ O GA? MhRQP9NM G MhR G= REO =H[F[´?CB P P [ O G.K= :09NP K=HGCGCDa` PH1k 0R ?CB PM ?CB P V-BE= REO t MhRQP ^ M YE[ O ^ MhR ? P K T [F=@? P =?CB PUM V :0} B P V P ?CB P V P DFG RQM V P K=HD R D R G : KK P ?AV : G M Ã DFG?CB P D OQPR ?CDa? : = REO ?CB P ^ M G P ? G T =H^ P DFG P« YE=H[+? M2 k I R ?CBEDFGÛ=HG P ?CB P0R YEK 9NP V MHW K=HGCGC[ P GCG M [ O GA? MhRQPb9NM G MhR GDFG?CB P O DFK PR GCD MhR0MHW ?CB P G : KK P ?AV : HV M Y 3T k Il?.KYEGA? 9NPRQM ? PO ?CBE=@?.?CB P ?CB PUM V P K MhR [ : }.M VC*G } Da?CBb^ MhR ?CD R Y M YEG.G : KK P ?AVZD P GsGCYE^ZB0=HGs?CB P [FD RQP =@V V èK M*OQP [ RQM ?B M7}.P ` P V } Da?CB O DFGC^)V P ? P G : KK P ?AVZD P G k qJB PUM V P KÁ= REO Da?CG-V P GCYE[a?CG-=@V P ` P V : PRQP VZ=H[ t]= REOOQPUTNPREO>PR ?CDaV P [ :>MhR HV M Y T ?CB PUM V : ^ MhR GCD OQP VZ=@?CD MhR G k qJB PWpM VZK MHW ?CB PTNM ? PR ?CDF=H[ !DFGJDaVCV P [ P `@= R ? =HG[ MhR b=HGDa? W YE[ ´[F[FG.?CB P G : KK P ?AV : ^ MhREO Da?CD MhR G± k qJB P V M [ PMHW ?CB P M [ O GA? MhRQP ?CB PUM V P KD R¢P é P ^)?CDa` P P [ O ?CB PUM VZD P GJDFG'DF[F[FYEGA?AVZ=@? PO D çR 0d ! k $ µ£½w´$¤6£¢R© ¥¦¢R¸54~¢R©~¤6¥¦¢£¤6£¢R© I R ?CBEDFGG P ^)?CD MhR ?CB P ? P VZKGG M [FDa? MhR = REO D R GA?C= R ? MhR =@V P OQP RQPO¥k Il? } DF[F[ 9NPO DFGCÛYEGCG PO B M7} = REO } B P V P ?CB P G P ^ MhR ^ PUT ?CG PR ? P V.?CB P-WpM [F[ M7} D R }.M VC´t;= REO ?CB P ^ MhR G P« Y PR ^ P G.?CB P V PUMHWlk q M ^ MhR Û[FY OQP ?CBEDFG'D R ?AV M*O YE^)?CD MhR = WpPU} YEG PUW YE[NV PUWpP V PR ^ P GJ=@V P hDa` PR ?CBE=@?-D R Û[FY OQP = ?C= R hD 9 [ PP) =HK T [ Pã d{èH!³? M P)*P K T [FD Wp: D R¢} BE=@? } = : \; : VZKD MhR G'Û=@VCV :¢« YE= R ?CYEK R YEK 9NP VZG k 3yA 3ÑNEJÛ L :<EJC"Ú7)C8GRB C"Ú<:|7)C1:<EJC"Ú 6 \ M [FDa? MhR G= TETNP =@VJD R¢RQMhR*m [FD RQP =@V. P [ O ?CB PUM VZD P G'=HG RQMhR*m TNP VC?CYQV 9 =@?CDa` P GA?C= 9 [ P G M [FYQ?CD MhR G k qJB PU: @= V P =bV P GCYE[a? MHW ?CB P ? MHTNM [ M hDFÛ=H[ T V MHTNP VC?CD P G MHW ?CB P ?CB PUM V : = REO =@V PRQM ?GCDFK T [ : V P [F=@? PO ? M ?CB P « YE= R ?C= MHW ?CB PM VZDahD R =H[³ P [ O¥k X-MhR*m-9NP [FDF= R ?CB PUM VZD P G MHW ? PRW YE[ ´[F[r?CB P G P V P« YEDaV P K PR ?CGUtrB PR ^ P ?CB P G P G M [FYQ?CD MhR G-=@V PP)*TNP ^)? PO ? M = TETNP =@VD R T =@VC?CDFÛ[ PT B : GCDFÛG-= REO tN=HG } DF[F[ 9NP G PUPR D R ^ZBE= T ? P V è k d;t*=H[FG M D R ^ MhREOQPR G PO K=@?A? P V T B : GCDFÛG k \ M [FDa? MhR G WpM VZK } B PR ?CB P `@=HÛYEYEK GA?C=@? P DFG OQP PRQP VZ=@? P t =HG-DFG?CB P Û=HG P = W ? P VG TNMhR ?C= RQPUM YEGJG : KK P ?AV :09 V P =@*D R k I R ?CBEDFG'Û=HG P Da?'DFG TNM GCGCD 9 [ PWpM V-= hDa` PR P [ O ? M BE=` P R Da? P¢PRQP VC : = REO =@??CB P GC=HK P ?CDFK P ?CB P P [ O Û= R 9NP D RO D é P V PR ? TNM ? PR ?CDF=H[ KD R DFK==@?0G T =HÛDF=H[-D R R Da? :¹p} B P V P ?CB P PRQP VC : DFG RQM VZK=H[FDa¡ PO ? M ¡ P V M k qJBEDFGK P = R G?CBE=@? Da?eDFGeDFK TNM GCGCD 9 [ P ? M ^ MhR ?CD R Y M YEGC[ : OQPUWpM VZK=G M [FDa? MhR G M [FYQ?CD MhR D R ? M ?CB P `@=HÛYEYEKÁGA?C=@? P> =HGDa?eDFG TNM GCGCD 9 [ P0} Da?CB=H[F[. P [ O G D RTNP VC?CYQV 9 =@?CD MhR ?CB PUM V : ZtGCD R ^ P = R D R R Da? P =HK M Y R ? MHWPRQP VC :2} DF[F[ 9NP V P« YEDaV PO ? M GCBED W ?b?CB P P [ O Gb=@?¢G T =HÛDF=H[D R R Da? :W V M K MhRQP>TNM ? PR ?CDF=H[ }.P [F[-? M ?CB P>M ?CB P V k [a?CB M YQhBDa?eK= :>9NPP =HGCD P Ve? M `*DFGCYE=H[FDa¡ P = \; : VZKD MhR P K P VChD R W V M K= OQP PRQP VZ=@? P `@=HÛYEYEKt D R ?CBEDFG }.M VC¢?CB PU:¢} DF[F[ 9NPOQP VZDa` POW V M K T YQV P [ : ? MHTNM [ M hDFÛ=H[r^ MhR GCD OQP VZ=@?CD MhR G ^ZBE= T ? P V-è; k qJB P B M K M ? MHT;: HV M Y TOQP RQP GrB M7} K= R: ? MHTNM [ M hDFÛ=H[F[ :O D é P V PR ? 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M ?CB P `@=HÛYEYEK k qJB P j=HYE[FD T VZD R ÛD T [ P V P« YEDaV P G?CBE=@?+?CB P GCDa R ? P VZK PR ? P VZG+?CB PJT =@?CB D R ? P HVZ=H[ ko B P V P = 9NM G MhR t } Da?CB>= RP ` PRR YEK 9NP V MHW ^ M [ M VZGUt } DF[F[ RQP ` P V^ MhR ?AVZD 9 YQ? P } Da?CB ?CBEDFG ? P VZKt*= WpP VZKD MhR Û= R ^ MhR ?AVZD 9 YQ? P ? M ?CB P-T =@?CB0D R ? P HVZ=H[ } Da?CBb= RQP h=@?CDa` PT V PUW =H^)? M VtQB PR ^ P t*GCD R ^ P 9 =@V :HMhR GJ=@V PWpP VZKD MhR G OUT KYEGA? 9NPeM*OEO¢WpM V\; : VZKD MhR G k qJB P K=@ RQMhRT =@VC?CDa?CD MhReW Y R ^)?CD MhR D R Û[FY OQP GN?CB PsP é P ^)?CDa` P ®sYEÛ[FD OQP = R =H^)?CD MhR = REO ?CB P GA?C=@?CDFGA?CDFÛG W =H^)? M V } Da?CB?CB P GA?C=@?CDFGA?CDFÛG T =@VZ=HK P ? P V OUT)k I W ?CB P P [ O¹ OQP GC^)VZD 9NP G=\; : VZKD MhR} BEDF^ZB V M ?C=@? P G 9;: d £ ?CB PR \*Da @R !PÄ V k qJBEDFG'K P = R G'?CBE=@?\; : VZKD MhR GKYEGA?JBE=` P BE=H[ Wãm D R ? P P V-G T D R WpM V M*OEO OUT = REO D R ? P P VG T D R¢WpM V P ` PR OUT å Ä$çæ >P)*T] VW !ÄA\*Da R/ ! è±é ñ è k è; ¦U$ ±¥ëê «Kh~µ³«µ°/®ú£¢R© ´w¢>§-°(°(£¯¥W¶£¢R§¤6© ¥¦¢R¸¥¦¢£¤(Í>§-°(°(£¯¥W¶£¢R§¤6© o BE=@?BE=HG Y YEGA? 9NPUPRP)*T [F=HD RQPOWpM V]?CB P æçS Û=HG P Û= R9NP V PUTNP =@? PO D R = R = R =H[ M M YEG W =HGCBED MhRWpM V ?CB P K=@ RQMhR ?CB PUM VZD P G k I R ?CBEDFGÛ=HG P ?CB P ? MHTNM [ M hDFÛ=H[ P) ÛDa?C=@?CD MhR Ge=@V P Û=H[F[ PO 9 = 9;:m \; : VZKD MhR GUt } BEDF^ZB=H[FG M Û=@VCV : =-? MHTNM [ M hDFÛ=H[;^ZBE=@VC P¬ gHg)! k ?= R: hDa` PR ?CDFK P ?CB P B M K M ? MHT;: HV M Y TM ï !(Ä O PR GCYQV P G?CBE=@??CB P K=@ RQMhR P [ O ^ MhR ©hYQVZ=@?CD MhR G=@V P ^ZBE=@VZ=H^)? P VZDa¡ PO29;: = R D R ? P P V } ï D REO D R R YEK N9 P V è kÛ Ä @Þ £ ;Ã U ï Kß Ê Í ý Ï ê Ê ý¬ Á ê Í ý{ _óÕO ñ = REO ?CB P ^ M VCV P G TNMhREO D R ^ MhR G P VC` PO ? MHTNM [ M hDFÛ=H[rÛYQVCV PR ? è k êh Q ë Ä Þ@ £ ß ë£áâ ý Ï êá ý¬ Á êºâ ý{ ñ I R ?CB P æçS·Û=HG P ?CB P ? 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MHTNM [ M hDFÛ=H[³^ZBE=@VC P K= : D RW =H^)? 9NP ?CB PP [ P ^)?AVZDF^ 303 46587)91:<;>= AJÑÕuÒ)=ÌÓWL EJC"ÚÜ7)C8GRÔ~7£uÒa<ÑÕuÒ)=ÌÓWL EJC"Ú ^ZBE=@VC PHk qJBEDFG¥BE=HG OQP R D R JDFK T [FDFÛ=@?CD MhR G MhR ?CB P.R =@?CYQV P+MHW*9 = 9;:m \; : VZKD MhR G¥= REO ?CB P D R ? P VZ=H^)?CD MhR MHW K=@ RQMhR G } Da?CB P [ P ^)?AV M K=@ RQP ?CDFGCK=HG } DF[F[ 9NP G PUPR D R ^ZBE= T ? P V Û;k qJB P V PP) DFGA?CG= R = OEO Da?CD MhR =H[©DFK TNM VC?C= R ? RQMhR*m ?AVZDa`*DF=H[©B M K M ? MHT;: HV M Y T t } BEDF^ZB0^ZBE=@VZ=H^)? P VZDa¡ P G ?CB P9 VZ=HD O D R MHW]9 = 9;:m \; : VZKD MhR GD R ?CDFK P t M " ï !®Ä O ñ h=HD R t Y YEGA?s[FDa P D R ?CB P æçSÛ=HG P t*?CBEDFGsB M K M ? MHT;: HV M Y T D R Û[FY OQP G^ M K T =H^)?CD PO ?CDFK P = REO ^ZBE=@VZ=H^)? P VZDa¡ P G+?CB P GA?C=@?CDFGA?CDFÛ=H[ 9NP BE=`*D M V MHW´9 = 9;:m \; : VZKD MhR G k qJBEDFG[ P = O G? M ?CB P ° MHTEW ? P VZKÈÃ ý" ! } BEDF^ZB PR ? P VZGJ?CB PT =@VC?CDa?CD MhR¢W Y R ^)?CD MhR D R ?CB PeWpM VZK å Ä çæ ý P)*T] VW ý8 !Ä P)*T] û»JÃ ý8 !Ä ñ è k ðH } B P V P » ó V-£,C£ !DFG=K=@? P VZDF=H[ T V MHTNP VC? :ãY YEGA?[FDa P Å k qJB PT =@VZ=HK P ? P V »DFGÛ=H[F[ PO ?CB P = R:HMhR = R h[ P = REO Da? OQP ? P VZKD RQP G-?CB P GA?C=@?CDFGA?CDFÛG MHW ?CÊ B P9 = 9;:m \; : VZKD MhR g{èH! k qJB P `@=H[FY P » Ä¸f ^ M VCV P G TNMhREO G'? M9NM G MhR GJ= REO »UÄ £ ? MWpP VZKD MhR G ý Ä V ¦¨WpP VZKD MhR t~ý¤£Ä ¦¨9NM G MhR ks G } =HGG PUPR D R ?CB P æçS Û=HG P tN?CB P V P =@V PMhR [ :¢WpP VZKD MhR G M V 9NM G MhR G k I R ?CB P K=@ RQMhR ?CB PUM V : ?CB P ° MHTEW ? P VZKV PUT [F=H^ P G'\*Da R@ ! t*= REO ?CB P GA?C=@?CDFGA?CDFÛG T =@VZ=HK P ? P V OUTsWpM VJæçS¬DFG+V PUT [F=H^ PO0} Da?CB?CB P = R:HMhR = R h[ P » k qJBQV M YQhB¢?CBEDFGJDa?'DFG TNM GCGCD 9 [ P ? MbOQP RQP ?CB PWpP VZKD MhRR YEK 9NP ëV =HG è kÞ Ä £» ñ _ T Y R ?CDF[ RQM7} ?CB P =@VChYEK PR ?CGJBE=` Pe9NPUPR ^ M K T [ P ? 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M ?C=H[ P [ P ^)?AVZDF^^ZBE=@VC P MHW =µK=@ RQMhR P [ O ^ MhR ©hYQVZ=@?CD MhR¥k qJB P = R:HMhR = R h[ P =H[FG MOQP RQP G?CB P G T D R = REO GA?C=@?CDFGA?CDFÛG MHW+9 = 9;:m \; : VZKD MhR G-= REO ?CB P V PU9;: Da?CG WpP VZKD MhR>R YEK 9NP Vt } BEDF^ZB>DFG MHW ^ M YQVZG P ?CB P R YEK 9NP V MHWeP [ P ^)?AV MhR G0=hDa` PR~9 = 9;:m \; : VZKD MhR K= : ^ MhR ?C=HD R¥k I R = R = R =H[ M M YEG0K= RERQP V0? M ?CB P æçS Û=HG P ?CB PbP [ P ^)?AV MhR GK= :µ9NP ^ MhR RQPO D R GCD OQP = 9 = 9;:m \; : VZKD MhR¥k qJBEDFGeK P = R G?CBE=@? D R ?CB P [ M7}'m PRQP VC : = TET V M DFK=@?CD MhR ?CB PP [ P ^)?AV MhR G?CB P KG P [a` P G0=@V P>RQM ?b=HÛ^ P GCGCD 9 [ P D R GCD OQP ?CB P \; : VZKD MhR G k GCD R h[ P \; : VZKD MhR K= : ^ MhR ?C=HD R = R:¢W VZ=H^)?CD MhR =H[ R YEK 9NP V MHW]P [ P ^)?AV MhR G k qJBEDFG V P GCYE[a?DFG` P V : PRQP VZ=H[-= REO = TET [FD P G ? 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M ?CB P GCY TNP VZ^ MhREO YE^)?CD R T BE=HG P G PUP © k k 7=HG+DFG O DFGCÛYEGCG PO D R Û tg@fQt©ê)! k I R ?CB P Û=HG PJMHW¥« YE= R ?CYEK °=H[F[ WpP VCV M K=@ RQP ?CGsDa?+BE=HG 9NPUPR =@VChY PO ?CBE=@?J?CB Pe9 = 9;:m \; : VZKD MhR G=@V P tED R¢W =H^)?Ut « YE=HGCD T =@VC?CDFÛ[ P G } Da?CB « YE= R ?CYEK R YEK 9NP VZG MHW GCD R h[ PP [ P ^)?AV MhR G ghð;tg Þ tgH)î ! kR ?CD WpP VCV M K=@ RQP ?CG OQP GC^)VZD 9NPOµ9;: ?CB P ° P DFG PR9NP VC K M*OQP [s=@? BE=H[ Wãm ´[F[FD R b^ MhR ?C=HD Rµ9 = 9;:m \; : VZKD MhR G } BEDF^ZBµ= TETNP =@Ve? M9NP 9NM G MhR G g{èEt¥èhfN! k qJBEDFGK= : K P = R ?CBE=@?» Ä·f*tsD R2} BEDF^ZB2Û=HG P9 = 9;:m \; : VZKD MhR GÛ=@VCV :2RQM>P [ P ^)?AVZDF^¢^ZBE=@VC PHk ° M7}.P ` P V0Da?DFG=H[FG M TNM GCGCD 9 [ P ?CBE=@?sU» Ä÷d £ D R} BEDF^ZBÛ=HG P ?CB P V P =@V P ? }.MP [ P ^)?AV MhR Gs^ MhR RQPO D RP =H^ZB 9 = 9;:m \; : VZKD MhR ç M;MHTNP V T =HDaV)ZtrV P GCYE[a?CD R 0D R = RµP [ P ^)?AVZDF^ ^ZBE=@VC PMH£W V Hd ý k qJB P G P GCDa?CYE=@?CD MhR Ge=@V P DF[F[FYEGA?AVZ=@? PO D R © k è k d kñ V M KÁ?CBEDFGK M*OQP [Da?CG P [ W Da?DFG RQM ?e= TET =@V PR ? } B : \; : VZKD MhR G-D R = R ?CD WpP VCV M K=@ RQP ?CGe=@V P 9NM G MhR G k qJBEDFGV P GA?AVZDF^)?CD MhR DFG T YQV P [ :9 =HG POMhR ?CB P }.M VC*G MHW g{èEt¥èh)f ! t } B M =@V P =H[F[K M V P ?CBE= R ^ M K TNP ? PR ? T B : GCDFÛDFGA?CG k QCD Antiferromagnet B=1 q=0 Nc = 3 Quantum Hall Ferromanget q = −2e q = −e ñ DahYQV P è k d;i `íNîiBï æ~å)âNh1iRefjNm$ð$äu`Nh1âJjNmdi`Jcyb2j$kãoÌ^yhubwbñ8v~`Nhwå0a]í äeíò£`yä"âN|æ~å)âNh1iRefjNmdeÌmNó£m~ oPe k>b"h1hDjNi`>gHm6b8o¾qwjNmpo<`NeÌm~eÌmg2ô0b"hDj,ðãl» Ä £f í jNh oÏ?Àjlb"àábuq>oPhDjNmÙaNðãl» Äòd £ í qcí.ò£`yä"âN|æ~å)âNh1iRefjNm eÌm îZv~`NmpoPv'i¯õµ`NàÌà±ö@b"h1hDjNi`>gHm6b8o¦qwjNmpo<`NeÌm~eÌmg2jNm6b¾b"àábuq>oPhDjNm ðãU» Ä £ í R = OEO Da?CD MhR =H[N^ MhR G P« Y PR ^ PWpM V-µ» Ä £µM Vd £ DFG'?CB P D R*² Y PR ^ PMHWOQMHT D R MhR ?CB P = R ?CD WpP VCV M@m K=@ RQP ? k I W ?CB P9 = 9;:m \; : VZKD MhR G=@V P D REOQPUPO V P [F=@? PO ? MP [ P ^)?AV MhR G'?CB PR¢9;:¢OQMHT D R = R = R ?CD WpP V m V M K=@ RQP ?= OEO Da?CD MhR =H[ 9 = 9;:m \; : VZKD MhR G-=@V P = OEOQPO ? M ?CB P G : GA? P K k qJB P¯ B PO P B M ¯ GA?AVZYE^)?CYQV P © k è k ghZtV P GCYE[a?CD R W V M Kò= RQMhR*m ?AVZDa`*DF=H[V M ?C=@?CD MhRMHW ?CB P G T D RµM VZD PR ?C=@?CD MhR GUt } DF[F[^ MhR*² DF^)? } Da?CB ?CB PM V OQP V PO M VZD PR ?C=@?CD MhR MHW ?CB P GA?C=@H P V PO K=@ RQP ?CDa¡=@?CD MhR>MHW ?CB P Y R*mOQMHTNPO = R ?CD WpP VCV M K=@ RQP ? k Il?DFGeD R ?CYEDa?CDa` P [ : Û[ P =@V?CBE=@?D WsPRQM YQhB 9 = 9;:m \; : VZKD MhR G=@V P = OEOQPO ? M ?CB P G : GA? P K ?CB PPR ?CDaV P = R ?CD WpP VCV M K=@ RQP ?CDF^GA?AVZYE^)?CYQV Pe} DF[F[N^ M [F[F= T G P g@fEtQèE" ! k ñQM VGC=@ PMHW ^ M K T =@VZDFG MhR¢} Da?CB¢?CB PeT D MhR ?CB PUM V : tQ?CB P K=@ RQMhRT =@VC?CDa?CD MhR0W Y R ^)?CD MhR ?C=@ P GJ?CB P WpM VZK åÄ$çæ ý P)*T³ VW ý8 !Ä P)*T û»JÃ ý" !Ä ñ è k Uf 3 46587)91:<;>= AJÑÕuÒ)=ÌÓWL EJC"ÚÜ7)C8GRÔ~7£uÒa<ÑÕuÒ)=ÌÓWL EJC"Ú The Quantum Hall Effect 71 Figure 1.26: Illustration of a skyrmion spin texture. The spin is down at the origin and gradually turns up at infinite radius. At intermediate distances, the XY components of the spin exhibit a vortex-like winding. Unlike a U (1) vortex, there is no singularity at the origin. Exercise 1.20 Derive eq. (1.231) from first principles by evaluating the loss of exchange energy when the Landau gauge ν = 1 ground state is distorted to make the spin tumble in the x direction Y θk θk (1.232) |ψi = cos c†k↑ + sin c†k↓ |0i 2 2 k ∂θ where θk = −γk`2 and γ = ∂x is the (constant) spin rotation angle gradient (since x = −k`2 in this gauge). 1.10.5 Topological Excitations So far we have studied neutral collective excitations that take the form of spin waves. They are neutral because as we have seen from eq. (1.197) they consist of a particle-hole pair. For very large momenta the spin-flipped particle is translated a large distance q~ × ẑ`2 away from its original position as discussed in appendix A. This looks locally like a charged excitation but it is very expensive because it loses all of its exchange energy. It is sensible to inquire if it is possible to make a cheaper charged excitation. This can indeed be done by taking into account the desire of the spins to be locally parallel and producing a smooth topological defect in the spin orientation [46, 50–56] known as a skyrmion by analogy with related objects in the Skyrme model of nuclear physics [57]. Such an object has the beautiful form exhibited in fig. (1.26). Rather than having a single spin suddenly flip over, this object gradually turns over the spins as the center is approached. 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PO D R © k Û;k d= REO GCB M YE[ O9NPP)*TNP VZDFK PR ?C=H[F[ : ` P VZD ´= 9 [ PHk I W.MH9 G P VC` PO Da? }.M YE[ Oµ9NP = RµP) ?AV P K P [ : DFK TNM VC?C= R ?-GA? PUT ? M0T V M `*D R ?CBE=@?-?CB P9 = 9;:m \; : VZKD MhR G OQM D REOQPUPO Û=@VCV :P [ P ^)?AVZDF^^ZBE=@VC PHk qJB P G TNMhR ?C= RQPUM YEG OQP Û= :¢MHW =GCD R h[ P K=@ RQMhR D R ? M ? }.MT B M ? MhR GJK :09NPP)*TNP VZDFK PR ?C=H[F[ :bO D0ÛYE[a?.? M ` P VZD Wp:Hko BE=@?KDahB? 9NP-P =HGCD P V.? MMH9 G P VC` P DFGs?CB P ^ MhR ` P VZGCD MhR0MHW =K=@ RQMhR D R ? M = T B M ? MhR D R = R P) ? P V R =H[rK=@ RQP ?CDF^ P [ O¥k qJBEDFG T V M ^ P GCGJDFG OQP GC^)VZD 9NPO D R ?CB PeWpM [F[ M7} D R G P ^)?CD MhR¥k ¤yA 3RØ£7"ÖJC"EJC"Ú7)C8Gp5"E>:<EJC"Ú [¤ γ m γ ñ DahYQV PÛ;k d;iç`>gHmtjNm~árp^'jHo<jNm~árp^'jHo<jNmNAHb"h"o|buß ©¨ Ë©¨P ¯®±°²v³²v³¸¹E³²;³²^¼¾½´@¶³²Z¶]²-®¸²Z¼Y}©¹E¼¾½²v® K ¿,®±°²v¼¹º¶&]1¼\&; u È z©×pÉ Ô É´Ë³wx7É2u³ÃpÉ È w J D MhR G'=@V PeT =@VC?CDFÛ[ P G?CBE=@?J= TETNP =@V-D R G M K P ?CB PUM V P ?CDFÛ=H[rK M*OQP [FGUt 9 YQ?'BE=` PRQM ? 9NPUPR D OQPR ?CD PO D RbP)*TNP VZDFK PR ?CG Þ t*è Û t*è)ê ! k+R DFK TNM VC?C= R ? T V MHTNP VC? :> =H[FG M WpM V'` P VZD ´Û=@?CD MhR0T YQV TNM G P G± MHW ?CB P G P = D MhR GJDFG'?CBE=@?J?CB PU: Û= R ^ MhR ` P VC?D R ? MT B M ? MhR G = REO9 =H^C=@h=HD R D R ?CB PeT V P G PR ^ PMHW =GA?C=@?CDF^@t P) ? P V R =H[K=@ RQP ?CDF^ P [ O¥k Il?Û= RP =HGCDF[ :9NP GCB M7}-R ?CBE=@?eK=@ RQMhR GD R = R = R ?CD WpP VCV M K=@ RQP ?CDF^ M V WpP VCV M K=@ RQP ?CDF^K=@? P VZDF=H[NÛ= R =H[FG MM GCÛDF[F[F=@? P D R ? MT B M ? MhR G k qJBEDFG.K= :b9NPP)*TNP VZDFK PR ?C=H[F[ : P =HGCD P V ? M ` P VZD Wp: ?CBE= R K=@ RQMhR ? M ? }.MT B M ? MhROQP Û= :Hk bË³z È x{Ë Ð z©×Ä×.ú Ñ y{y{É Ð z Ô´È³Ñ xbÃ È z Ö z Ô´È³Ñ x{Ãp|ú-Ã Ñ ×pÊ ç MhR GCD OQP VZD R P«©kã Û;k dHêh¢?CB P [F=HGA?¢? P VZK P«©kã Û;k èdhGCB M7} G0?CBE=@? WpM VGA?C=@?CDF^> P [ O Gb?CB P =H ^)?CD MhR DFG KD R DFKDa¡ PO D W ýe DFG T =@VZ=H[F[ P [´? M k _GCD R Û;k gHîh WpM V'?CB P K=@ RQMhR P [ O Da?'DFGÛ[ P =@V'?CBE=@? ÈÄ¹ ý =HG-Û= R9NP G PUPR D R ?CB PeWpM [F[ M7} D R P« YE=@?CD MhR î ý Ï ö Ä î T ý Ï È Ä î T ¾ ý ñ Û;k èdh ñQM VK=@ RQMhR ^ MhR ` P VZGCD MhR D R ? M = T B M ? MhR D R = RP) ? P V R =H[.K=@ RQP ?CDF^ P [ O ?CB P V P KYEGA? 9NP = OQP GC^)VZD T ?CD MhR¢MHW9NM ?CB=GA?C=@?CDF^ P) ? P V R =H[¥ P [ O = REO = ² YE^)?CYE=@?CD R P [ O¥k ç MhR GCD OQP VZD R =H[F[ TNM GCGCD 9 [ P ^ M K TNMhRQPR ?CG pP) ? P V R =H[ P [ O GUt ² YE^)?CYE=@?CD R 0 P [ O G= REO G MMhR K M GA?e? P VZKG } DF[F[³`@= R DFGCB k o BE=@? V P K=HD R GDFG.?CB P ?CB P ` P VC? 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M ?CB P K=@ RQP ?CDF^b P [ O¥k q MOQP ? P VZKD RQP ?CBEDFGDa? DFG RQP ^ P GCGC=@V : ? M G M [a` P ?CB P ®sYE[ P V mª =@HVZ= R PP« YE=@?CD MhR D R <>D R M7} GA*D©G T =H^ PHk q M [ P = O D R M V OQP Vt;?CB P M [ O GA? MhRQP)m o DF[F^)¡ P ? P VZK OQM;P G RQM ?^ MhR ?AVZD 9 YQ? P ? M ?CB P'P« YE=@?CD MhR G MHW K M ?CD MhR = REO DFG]?CB P V PUWpM V P'RQM [ MhR P VD R Û[FY OQPO¥k qJBEDFG]^ M K P G W V M K8^ MhR GCD OQP VZ=@?CD MhR G]D R ?CB P.TNM7}.P V+^ M Y R ?CD R eGC^ZB P K PHk qJB P h=HYQ P P [ O G'KYEGA? 9NP ^ M Y R ? PO D R ?CB P GC=HK P K= RERQP VJ=HG'?CB POQP VZDa`@=@?CDa` P G k+ GJ=V P GCYE[a??CB PM [ O GA? MhRQP)m o DF[F^)¡ P ? P VZKýDFG MHW BEDahB P V M V OQP V.?CBE= RbM ?CB P VD R Û[FY OQPO ? P VZKG k I W ?CB PM [ O GA? MhRQP)m o DF[F^)¡ P ? P VZK }.P V P ? M09NP D R Û[FY OQPO ?CB PR ?CB P V P K= :9NP K= R:M ?CB P VZGJ?CBE=@?^ MhR ?AVZD 9 YQ? P} Da?CB?CB P GC=HK PM V OQP V MHW K=@ R Da?CY OQPHk qJBEDFGsÛ=HG P} =HG RQM ?D R ` P GA?CDah=@? PO¥k qJB P V P [ P `@= R ? 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OQP GC^)VZD 9NP ?CB P9NP BE=`*D M V MHW©T D MhR G]= REO K=@ RQMhR GUt V P G TNP ^)?CDa` P [ :Hk q MHTNM [ M hDFÛ=H[s^ MhR GCD OQP VZ=@?CD MhR G=H[F[ M7} WpM V = } D OQP V= R =H[ : GCDFG MHW ?CB P K M*OQP [s= REO D R*m ?AV M*O YE^ PRQPU} T B PRQM K PR =¢?CBE=@?=@V PRQM ?=HÛ^ P GCGCD 9 [ P} Da?CB TNP VC?CYQV 9 =@?CD MhR ?CB PUM V : =H[ MhRQPHk I R ?CBEDFG V P G TNP ^)?s?CB P V P DFGs=GA?AV MhR ^ M VCV P G TNMhREOQPR ^ PJ9NP ? }.PUPR ?CB P ? }.M ?CB PUM VZD P GUt } B P V P æçS÷hDa` P GÛ[FY P G MHW} BE=@? MhRQP KDahB? P)*TNP ^)?J? M REO D R K=@ RQP ?CDFGCK k o B PR = ^ MhR ?CD R Y M YEG.h[ MH9 =H[´G : KK P ?AV : DFG.G TNMhR ?C= RQPUM YEGC[ :9 V M PR ? M = GCY 9 HV M Y T ?CB PM [ O*m GA? MhRQP ?CB PUM V P K T V PO DF^)?CGJ?CB P = TETNP =@VZ= R ^ PMHW K=HGCGC[ P GCG 9NM G MhR G k I R æçS D R gh mO DFK PR GCD MhR G± ?CB P h[ MH9 =H[Q^ZBEDaVZ=H[QG : KK P ?AV : HV M Y T Ä s dh$ # s dhl 7$ %µDFGG TNMhR ?C= RQPUM YEGC[ :9 V M PR t [ P =`*D R =V P K=HD R D R G : KK P ?AV : Ã Ä s dhl' &(# 7$ % k qJB PbM [ O GA? MhRQP9NM G MhR Ge=@V P ?CB P [FDahB? P GA? T =@VC?CDFÛ[ P G MHW æçSt } BEDF^ZB¢=@V P ?CD R ?CBEDFGÛ=HG P ?CB P ?CBQV PUPT D MhR G k qJB P G PM [ O GA? MhRQP9NM G MhR P [ O G'[FDa` P D R ?CB P ^ M G P ?G T =H^ P ÃÅÄ s dh k I R K=@ RQP ?CDFGCK D R dh mO DFK PR GCD MhR G±]?CB P V P DFGs=^ MhR ?CD R Y M YEGsh[ MH9 =H[©G : KK P ?AV : Ä s dhL } BEDF^ZBbDFG+?CB PR G TNMhR ?C= RQPUM YEGC[ : 9 V M PR ? M ?CB P GCY 9 HV M Y T ÃÅÄ 7ZtQD R ?CBEDFG+Û=HG P ?CB PeM [ O GA? MhRQP 9NM G MhR G=@V P ? }.M K=@ RQMhR2OQP HV PUP G MHW'W V PUPOQM Kò?CBE=@? [FDa` P D R ?CB P ^ M G P ?G T =H^ )P Ã Ä#&% 7 k M [ O GA? MhRQP09NM G MhR G=@V P K=HGCGC[ P GCG= REO} DF[F[+B PR ^ P¢OQM KD R =@? P ?CB P [ M7}'m PRQP VC :T B : GCDFÛG k çBEDaVZ=H[ TNP VC?CYQV 9 =@?CD MhR ?CB PUM V :bT V M `*D OQP Gs?CB PWpM VZK=H[FDFGCK WpM V'= OQP VZDa`@=@?CDa` PP)*T = R GCD MhR ?CBE=@?'DFG.YEG PO ? M REO ?CB P [ P = O D R M V OQP V³? P VZKG kR ?CD WpP VCV M K=@ RQP ?CDF^+K=@ RQMhR G]BE=` P =JV P [F=@?CDa`*DFGA?CDF^ O DFG TNP VZGCD MhR G´V P [F=@?CD MhR } BEDF[ PWpP VCV M K=@ RQP ?CDF^K=@ RQMhR G=@V PRQMhR*m V P [F=@?CDa`*DFGA?CDF^ k qJB PRQMhR*m V P [F=@?CDa`*DFGA?CDF^ =H^)?CD MhR ^ MhR ?C=HD R G= ? MHTNM [ M hDFÛ=H[r? P VZKt´V P GCYE[a?CD R D R ?CB P ^ MhR GA?AVZ=HD R ?-?CBE=@?-?CB P ? M ?C=H[]G T D R DFG « YE= R ?CDa¡ PO D R D R ? P P V M V BE=H[ W D R ? P P VY R Da?CG k qJB P = R =H[ M hD P G 9NP ? }.PUPR æçS·= REO K=@ RQP ?CDFGCK 9NP ^ M K P =H[F[.?CB P K M V PW =HGCÛD R =@?CD R } B PR ? MHTNM [ M hDFÛ=H[´^ MhR GCD OQP VZ=@?CD MhR G+=@V P D R Û[FY OQPO¥k I R æçS¹? MHTNM [ M hDFÛ=H[F[ :RQMhR*m ?AVZDa`*DF=H[ T D MhR P [ O G+Û=@VCV : =0? MHTNM [ M hDFÛ=H[^ZBE=@VC P ?CBE=@?BE=HG 9NPUPR D OQPR ?CD PO 9;: \; : VZK P ? M9NP ?CB P 9 =@V :HMhRµR YEK 9NP V k qJBEDFG K P = R G'?CBE=@?-= T D MhR P [ O t } BEDF^ZBÛ= RRQM ? 9NP ^ MhR ?CD R Y M YEGC[ :0OQPUWpM VZK PO D R ? M " ?CB P `@=HÛYEYEKÛ=@VCVZD P G 9 =@V :HMhR « YE= R ?CYEK R YEK 9NP VZG k+¸W YQVC?CB P VJB M K M ? MHT;: HV M Y .T M s dhÀ ù !(Ä·OµÜV P GA?AVZDF^)?CG'?CB P GA?C=@?CDFGA?CDFÛG MHW ?CB P \; : VZKD MhR ? M ?CBE=@? MHW9NM G MhR G M V WpP VZKD MhR G ( } Da?CB?CB PR YEK 9NP V MHW ^ M [ M VZG OUT =HG =GA?C=@?CDFGA?CDFÛG T =@VZ=HK P ? P Vt } B P V PM*OE¡O OUT ^ M VCV P G TNMhREO Gs? MWpP VZKD MhR G.= REObP ` P2R OUT ^ M VCV P G TNMhREO Gs? M 9NM G MhR G k Il?sDFG RQM7} W V M K ?CB P KDF^)V M GC^ MHT DF^æçS¹?CB PUM V : ?CBE=@?.D RR =@?CYQV }P OUT Ä÷ge^ M VCV P G TNMhREO D R ? M ?CB P ?CBQV PUP« YE=@VC¢^ M [ M VZG k ÐF 46587)91:<;>=Ý*yAY¢@L Ú K8I"Ú|ÚDL EJC¦7)C8Gµ4ÙEJC8K8Û I"ÚDL EJC ? MHTNM [ M hDFÛ=H[+^ZBE=@VC P} Da?CBµ=^ M VCV P G TNMhREO D R ^ MhR G P VC` PO ? MHTNM [ M hDFÛ=H[+ÛYQVCV PR ?Û= R =H[FG M9NP OQP RQPO D R ?CB P K=@ RQMhR ?CB PUM V :Hk qJB P ^ M VCV P G TNMhREO D R RQPU} ? MHTNM [ M hDFÛ=H[G M [FDa? MhR G=@V P RQM7}-R =HG 9 = 9;:m \; : VZKD MhR G k Il?DFG RQM ? PR ?CDaV P [ : Û[ P =@V } BE=@? « YE= R ?CYEK R YEK 9NP VZG-GCYE^ZB MH9'YAP ^)?CGeK= : Û=@VCV :Hk h=HD R =KDF^)V M GC^ MHT DF^?CB PUM V : Û= RµT V M `*D OQP G M K P D R GCDahB? k I R ?CB P æçSÛ=HG PbRQMhR*m ?AVZDa`*DF=H[ T D MhR P [ O G p} B P V PbT D MhR G^ MhR GCDFGA? MHWJ« YE=@VC*G±ZtV P GCYE[a?CGD R9 =@V :HMhR G?CBE=@?Ut MHW ^ M YQVZG P t=H[FG M ^ MhR GCDFGA? MHW « YE=@VC*G k qJB P K=@ RQMhR Gs=@V P ^)V P =@? PO ?CBQV M YQhBG TNP ÛDF=H[E^ MhR ©hYQVZ=@?CD MhR G MHWNP [ P ^)?AV MhR G k qJB P V PUWpM V P Da? DFG RQM ?-?CBE=@? W =@V WpP ?C^ZB PO ?CBE=@?-?CB P9 = 9;:m \; : VZKD MhR G'=@V P V P [F=@? PO ? M ?CB PP [ P ^)?AV MhR G k I R « YE= R ?CYEK °=H[F[ WpP VCV M K=@ RQP ?CGeDa?DFG- RQM7}-R ?CBE=@??CB P P [ P ^)?AV MhR ^ZBE=@VC P DFGD R>OQPUPO ?CB P ? MHTNM [ M hDFÛ=H[^ZBE=@VC PHk qJB P V P K= :9NP = OEO Da?CD MhR =H[¥`@=@VZDF=@?CD MhR G MHWWpP VCV M K=@ RQP ?CG= REO =H[FG M = R ?CD WpP VCV M K=@ RQP ?CG } B P V P ?CB P ? MHTNM [ M hDFÛ=H[;^ZBE=@VC P DFG¥V P [F=@? PO ? M ?CB PsP [ P ^)?AVZDF^+^ZBE=@VC PHk qJB PsR YEK 9NP V MHWQP [ P ^)?AV MhR G³?CBE=@?^ MhR ?AVZD 9 YQ? P ? MP =H^ZB 9 = 9;:m \; : VZKD MhR DFG OQP RQPO ?CBQV M YQhB= T =@VZ=HK P ? P V+» } BEDF^ZBDFGK=@? P VZDF=H[ mOQPUTNPREOQPR ? k qJB P = OEO Da?CD MhR =H[B M K M ? MHT;: HV M Y 2T M " !ÀÄ O^ZBE=@VZ=H^)? P VZDa¡ P G?CB P9 VZ=HD O D R MHW9 = 9;:m \; : VZKD MhR GD R ?CDFK PHk qJB P V P =@V P =2^ MhR ?CD R Y M YEGb`@=@ï VZD P ? : MHW GA?C=@?CDFGA?CDFÛGUtJY R [FDa P D R ?CB P æçSòÛ=HG P>} B P V P ?CB P ^ M VCV P G TNMhREO D R B M K M ? MHT;: HV M Y T OµÜ;tE=H[F[ M7} G WpM VJ?CB P P [ O ^ MhR ©hYQVZ=@?CD MhR G? M9NP Û[F=HGCGCD PO D R ? M P Da?CB P V.?AVZDa`*DF=H[ f M V RQMhR*m ?AVZDa`*DF=H[ 7sj MhR ?AV : =@hD R Û[F=HGCG P G k ° PR ^ P ?CB PMhR [ : GA?C=@?CDFGA?CDFÛG=H[F[ M7}.PO D R ?CB P æçS K M*OQP [rDFG P Da?CB P V 9NM G MhR DF^ M V WpP VZKD MhR DF^ k qJB P9 = 9;:m \; : VZKD MhR GJÛ= R 9NP« YE= R ?CDa¡ PO =HG = R:HMhR G } Da?CB?CB P ^ M VCV P G TNMhREO D R = R:HMhR = R h[ P » T =@VZ=HK P ? P V k qJB P9 = 9;:m \; : VZKD MhR GJÛ= R Û=@VCV : W VZ=H^)?CD MhR =H[ P [ P ^)?AV MhR« YE= R ?CYEK R YEK 9NP VZG k Il?BE=HG 9NPUPR =@VChY PO ?CBE=@?D R = R ?CD WpP VCV M K=@ RQP ?CDFGCK 9 = 9;:m \; : VZKD MhR G =@V P9NM G MhR GUt.D R} BEDF^ZBÛ=HG P »µDFG= R D R ? P P VbKYE[a?CD T [ P0MHW d £k I R ?CBEDFGÛ=HG P ?CB P ? MHTNM [ M hDFÛ=H[^ZBE=@VC P DFG= R>P ` PR KYE[a?CD T [ PMHW ý pM V¡ P V M kñQP VCV M K=@ RQP ?CDF^ 9 = 9;:m \; : VZKD MhR G =@V P RQM7}-R ? M09NPWpP VZKD MhR GJ=HGDFGJ?CB P Û=HG PMHW+« YE= R ?CYEK·°=H[F[ WpP VCV M K=@ RQP ?CGUt } B P V P ?CB PU: Û=@VCV : ?CB P ^ZBE=@VC P ý k 0RQP K= : `*D PU} ?CB PP [ P ^)?AV MhR GUt]D R =[ M7}'m PRQP VC : = TET V M DFK=@?CD MhR tr=HG ¯ ^ MhR RQPO¥¯ D R GCD OQP ?CB P9 = 9;:m \; : VZKD MhR G k qJBEDFG³`*D PU}TNM D R ?K=@ P G+K M GA?G PR G PWpM V?CB P Û=HG P'} B P V P ?CB P9 = 9;:m \; : VZKD MhR G^ MhR ?C=HD R ? }.MP [ P ^)?AV MhR G k qJBEDFG]V PUT V P G PR ?CG=ç M;MHTNP V T =HDaVt } BEDF^ZBY TNMhR ^ MhREOQPR GC=@?CD MhR ^ M YE[ O [ P = O ? M GCY TNP VZ^ MhREO YE^)?CDa`*Da? : t.=HGbDa?DFG?CB P Û=HG P } Da?CB^ P VC?C=HD R~OQMHTNPO = R ?CD WpP VCV M K=@ RQP ?CG k S MHT D R b= R ?CD WpP VCV M K=@ RQP ?CG P ` PR ?CYE=H[F[ :OQP GA?AV M7: GJ?CB P GA?C=@H P V PO K=@ RQP ?CDa¡=@?CD MhR GA?AVZYE^)?CYQV PHk qJB P 9 = 9;:m \; : VZKD MhR Gr= TETNP =@V=HG=-B PO P B M GA?AVZYE^)?CYQV P D R ?CB P G T D RM VZD PR ?C=@?CD MhR¥k I W = OEO D R P [ P ^)?AV MhR G K P = R G]D R ^)V P =HGCD R '?CB P.R YEK 9NP V MHWQ9 = 9;:m \; : VZKD MhR G¥?CB PR Da?]DFG RQM ?]GCYQV T VZDFGCD R ?CBE=@?³?CB P B PO P B M GA?AVZYE^)?CYQV Pe} DF[F[ P ` PR ?CYE=H[F[ :¢OQP GA?AV M7: ?CB P = R ?CD WpP VCV M K=@ RQP ?CDFêGA?AVZYE^)?CYQV PHk ®s[ P ^)?AV M K=@ RQP ?CDFGCK DFG+D R Û[FY OQPO D R æçS 9;: V PUT [F=HÛD R e?CB P-OQP VZDa`@=@?CDa` P G } Da?CB 7^ M `@=@VZDF= R ? OQP VZDa`@=@?CDa` P G k qJB P ? MHTNM [ M hDFÛ=H[©ÛYQVCV PR ?+KYEGA?+=H[FG Me9NP = O = T ? PO G M ?CBE=@?sDa?+DFGh=HYQ P D R `@=@VZDF= R ?+= REO ^ MhR G P VC` PO¥k \*D R ^ P =@??CB P KDF^)V M GC^ MHT DF^-[ P ` P [´?CB P ^ZBE=@VC PMHW ?CB P \; : VZKD MhR DFGs?CD PO ? M ?CB P9 =@V :HMhR R YEK 9NP Vt³?CB P V P DFG= ^ M Y T [FD R 9NP ? }.PUPR ?CB P0RQP YQ?AVZ=H[ T D MhR P [ O = REOP [ P ^)?AV M K=@ RQP ?CDFGCK k qJBEDFG K P ^ZBE= R DFGCK } BEDF^ZB>DFG-V P =H[FDa¡ PO ?CBQV M YQhB>?CB PM [ O GA? MhRQP)m o DF[F^)¡ P >ÛYQVCV PR ?=H[F[ M7} G WpM Ve= RQP YQ?AVZ=H[ T D MhR ? MbOQP Û= : D R ? M ? }.MbT B M ? MhR G Ä£¥¤-¦ò§©§ k Il? } =HGGCB M7}-R ?CBE=@?Y T ? M ?CB PM V OQP V ú Þ$ ?CB P j=HYE[FD P« YE=@?CD MhR ^ MhR ?C=HD R G= Rbs dhLG : KK P ?AV :Hk qJB P j=HYE[FD P« YE=@?CD MhR Û= R9NP `*D PU}.PO =HG?CB P KDF^)V M GC^ MHT DF^ ?CB PUM V :WpM VK=@ RQMhR G= R =H[ M MHW ?CB P \;?C= REO =@V O < M*OQP [ } BEDF^ZBDFG+?CB P KDF^)V M GC^ MHT DF^'?CB PUM V :WpM V T D MhR G k [F[EG : KK P ?AVZD P G MHW ?CB P Y REOQP VZ[ :m D R KDF^)V M GC^ MHT DF^?CB PUM V : KYEGA? 9NP V P =H[FDa¡ PO D R ?CB PP é P ^)?CDa` P ?CB PUM V :Hk I R ?CB P j=HYE[FD P« YE=@?CD MhR ?CB P P [ P ^)?AVZDF^= REO K=@ RQP ?CDF^ P [ O G= TETNP =@V=HG RQMhR*m-9NP [FDF= R ` P ^)? M V TNM ? PR ?CDF=H[FG k q M D R Û[FY OQPP [ P ^)?AV M@m K=@ RQP ?CDFGCKD R ?CB P K=@ RQMhR ?CB PUM V : Da?JDFG RQP ^ P GCGC=@V :RQM ? MhR [ : ? M h=HYQ P ?CB P 7l G : KK P ?AV : 9 YQ?e=H[FG M s dhL k I W ?CB P ? MHTNM [ M hDFÛ=H[^ZBE=@VC P DFGV P [F=@? PO ? M ?CB PP [ P ^)?AVZDF^ ^ZBE=@VC P ?CB PR ?CB PRQPU} s dhLh=HYQ P D R `@=@VZDF= R ? M [ O GA? MhRQP)m o DF[F^)¡ P bÛYQVCV PR ?[ P = O Gs? M = ^ M Y T [FD R MHW K=@ RQMhR G p} BEDF^ZB =@V PbRQP YQ?AVZ=H[p-? M ?CB PP [ P ^)?AV M K=@ RQP ?CDF^ P [ O¥k qJBEDFG[ P = O ? M ?CB POQP Û= : ` P VC? P) î ¦ §©§]k < M GA? [FDa P [ : Da?.DFG P)*TNP VZDFK PR ?C=H[F[ : P =HGCD P V? M OQP ? P ^)?'?CB P ^ MhR ` P VZGCD MhR0MHW =K=@ RQMhR D R ? M = T B M ? MhR¥k qJBEDFG ÐJ? M GCÛDF[F[F=@?CD MhRbT V M ^ P GCG } DF[F[ M ÛÛYQVJD R ?CB PT V P G PR ^ PMHW = R0P) ? P V R =H[¥GA?C=@?CDF^K=@ RQP ?CDF^- P [ O t*D R0} BEDF^ZB Û=HG P ?CB P K=@ RQMhR GJ=H^ « YEDaV P =K=HGCG T V MHTNM VC?CD MhR =H[©? M ?CB P K=@ RQP ?CDF^ P [ O¥k qJBEDFG.DFG'= R =H[ M M YEG'? M ?CB P = D MhR*m T B M ? MhR ^ MhR ` P VZGCD MhRT V M ^ P GCGUt P)*TNP VZDFK PR ?C=H[F[ : G M YQhB?-= W ? P V k Il? } =HG W YQVC?CB P VD R ` P GA?CDah=@? PO} BE=@? OQP Û= :T V M ^ P GCG P G P) DFGA? WpM V ?CB P \; : VZKD MhR G= REO9 = 9;:m \; : VZKD MhR G k I R ?CB P GA?C= REO =@V O K M*OQP [©= 9 =@V :HMhR0R YEK 9NP V R YEK 9NP V+`*D M [F=@?CD R P [ P ^)?AV M7}.P =@0D R GA?C= R*m ? MhR =H[F[ M7} G WpM V+?CB POQP Û= :MHW = 9 =@V :HMhR¥k qJBEDFG+DFG?CB P V P GCYE[a? MHW¯ ?s° M;MHW ? ¯ Gsh[ MH9 =H[©= RQM K=H[ : Û=HYEG PO } B PRs dhl DFGh=HYQ PO¥kµ G= V P GCYE[a?Ut?CB PM [ O GA? MhRQP)m o DF[F^)¡ P ÛYQVCV PR ? DFGh=HYQ P D R `@=@VZDF= R ? 9 YQ? RQM [ MhR P Ve^ MhR G P VC` PO¥k qJB P V P DFG RQM = R =H[ M : ? M ?CBEDFG WpM V?CB P K=@ RQMhR K M*OQP [ k Il? } =HG=H[FG M GCB M7}-R t?CBE=@? D R ?CB PbT V P G PR ^ PbMHW =>K=@ RQP ?CDF^bK MhRQMHTNM [ P t 9 =@V :HMhR GÛ= R ^ MhR ` P VC?D R ? M [ PUT ? MhR G k \*YE^ZBbK=@ RQP ?CDF^JK MhRQMHTNM [ P Gs= TETNP =@VsD R0s Û _q ?CB PUM VZD P G k qJB P K MhRQMHTNM [ P DFG+[ M Û=@? PO =@?s?CB P G T =HÛDF=H[ PREO¢MHW =SDaVZ=HêGA?AVZD R = REO = TETNP =@VZGJ=HGJ=G M [FDa? MhR¥k I R ?CB P K=@ RQMhR ?CB PUM V : t } Da?CB MhRQP G T =HÛDF=H[ O DFK PR GCD MhR [ P GCGUtNDa?Û= R9NP GCB M7}-R ?CBE=@?e=0SDaVZ=H^ GA?AVZD R = R =H[ M >V PUT V P G PR ?CG= ^ZBE=@VC PO2} DaV PHkO DFGC^ZBE=@VChD R } DaV P Û=@?C=H[ : ¡ P G= 9 = 9;:m \; : VZKD MhR OQP Û= :Hk I R ?CBEDFGÛ=HG P ?CB P'P ` PR ?.V PUT V P G PR ?CG+= R D R GA?C= R ? MhR¥ko BE=@?s=H^)?CYE=H[F[ : BE= TETNPR GDFGUt MHW ^ M YQVZG P t RQM ?³= R =H^)?CYE=H[ OQP Û= :MHW = 9 = 9;:m \; : VZKD MhR t } BEDF^ZB }.M YE[ O V P GCYE[a?¥D R = RP [ P ^)?AV MhRR YEK 9NP V¥`*D M [F=@?CD R T V M ^ P GCG k qJB P9 = 9;:m \; : VZKD MhR¯ OQP Û= :´¯ DFG Y YEGA?.= R¢P [ P ^)?AV MhR [ P =`*D R ?CB P ? }.M@mO DFK PR GCD MhR =H[ T [F= RQP MHW ?CB P K=@ RQP ?J`*DF==^ZBE=@VC P Û=@VCV : D R } DaV PHk Il?]DFG¥ RQM7}-R ?CBE=@?]?CB P V P =@V P K M V P ?CBE= ZR Y YEGA?r? }.M« YE=@VC ² =` M VZG k qJB P h[ MH9 =H[^ZBEDaVZ=H[G : KK P ?AV : HV M Y T Û= Rb9NPJP)*T = REOQPO ? M D R Û[FY OQP =H[F[ « YE=@VC*G k qJB P G : KK P ?AV : Ä sP ORQ $ # sP ORQ l 7$ %¬?CB PR9 V P =@*G? M Ã Ä sP ORQ l' &(# 7$ % kñQM V ORQ Äg?CBEDFGV P GCYE[a?CGD R ?CB P ?CBQV PUP T D MhR GUt-?CB PWpM YQV@= MhR G= REO ?CB P ü m K P G MhR G k \*D R ^ P ?CB Pµ« YE=@VC*G } Da?CB ² =` M V M ?CB P V?CBE= R Y T M V OQM7}-R BE=` P = RQMhR*mRQP h[FDahD 9 [ P K=HGCGe?CB P = TET V M DFK=@?CD MhRMHW K=HGCGC[ P GCGK P G MhR G 9NP ^ M K P G[ P GCG = TET V MHT VZDF=@? PHk qJBEDFG.DFG 9NP Û=HYEG P ?CB P h[ MH9 =H[¥G : KK P ?AV : DFG RQM [ MhR P VJ= ` P V : =HÛÛYQVZ=@? P G : KK P ?AV :Hk ñQM V ORQãS gb?CB P V P [ P `@= R ?B M K M ? MHT;: HV M Y T G^ZBE= R PHk \*D R ^ P M sP ORQ < !Ä¸fb?CB P B M K M ? MHT;: HV M Y .T MÔèH sP ORQ < !(Ä·O DFGJYEG PO ? M V P GA? M V P ?CB POQP GCDaV PO GA?C=@?CDFGA?C(DF^ 9NP BE=`*D M V MHW ?CB P \; : VZKD MhR G k ñQM V?CBEDFGJ= RP) ÛYQVZGCD MhR DFGJK= OQP D R ? M = W ?CB O DFK PR GCD MhR YEGCD R = OQPUWpM VZK=@?CD MhRT =@VZ=HK P ? P V k qJB P oµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZKÛ= R ?CB PR9NP D R Û[FY OQPO D R ?CB P ?CB PUM V :Hk I RM V OQP V WpM VJ?CB POQ:*R =HKDFÛG MHW ?CB P K P G MhR G³? M9NP ={é P ^)? PO MhR [ :e9;: ?CB P.T B : GCDFÛ=H[ T D MhR P [ O ?CB P D R ? P P V T V PUW =H^)? M V OUT KYEGA? 9NP D R ?AV M*O YE^ PO¥k qJB P oµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZK PR GCYQV P G?CBE=@?=H[F[ T =@VZDa? : G : KK P ?AV : T V MHTNP VC?CD P G T V P G PR ?+D R æçS¹=H[FG M B M [ O D R ?CB P'P é P ^)?CDa` P ?CB PUM V :Hk qJBEDFG? P VZK =H[FG M ^ MhR ?AVZD 9 YQ? P G? M ?CB P-£ ¦ò§©§ OQP Û= :Hk ñQM V?CB P K=@ RQMhR ?CB PUM V : ?CB P G : KK P ?AV : HV M Y T Û= R 9NPP)*T = REOQPO ? M Ä sP ORQ } BEDF^ZB ?CB PR9 V P =@*GG TNMhR ?C= RQPUM YEGC[ : ? M ÃÄ P ORQ¾V 7 k qJB PM [ O GA? MhRQP¢9NM G MhR P [ O G[FDa` P D R ?CB P ^ M G P ?G T =H^ P Ã Ä #&% P ORQµV 7 kbñQM V « YE= R ?CYEK°=H[F[ WpP VCV M K=@ RQP ?CGe?CBEDFGe^ M VCV P G TNMhREO G? M = [F= :HP VD REOQP)Nk ñQM [F[ M7} D R ?CB P K=@?CB P K=@?CDFÛ=H[ T V M ^ PO YQV P G MHW ?CB P æçSÛ=HG P ts= oµP GCG mL¶ YEKD RQM@m o Da?A? PR = R =H[ M Û= R9NP'OQP RQPO = REO ^ MhR GA?AVZYE^)? POW V M K8?CB P B M K M ? MHT;: HV M Y T M #&% P OV 7< !(Ä ô7f õ D R = R sP ORQ D R `@=@VZDF= R ? WpM VZK k~ñQM V ORQ Ä d?CBEDFGV PO YE^ P G? M ?CB P ° MHTE( W ? P VZK p9NPUWpM V P h=HYQhD R ; k q M D R Û[FY OQPsP [ P ^)?AV M K=@ RQP ?CDFGCK Da?DFG MhR [ :RQP ^ P GCGC=@V : ? M h=HYQ Ps dhLt=eGCY 9 HV M Y TMHW sP O Q*k qJBEDFG oµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZK =H[FG M ={é P ^)?CG+?CB P GA?C=@?CDFGA?CDFÛG MHW ?CB P'9 = 9;:m \; : VZKD MhR G = REO ^ MhR ?AVZD 9 YQ? P G]? M ?CB P î ¦ò§©§0OQP Û= :Hk \*D R ^ P ?CB P B M K M ? MHT;: HV M Y T V P G TNMhR GCD 9 [ P+WpM V?CB PoµP GCG m ¶ YEKD RQM@m o Da?A? PR ? P VZKDFG?AVZDa`*DF=H[ t;?CB P V P DFG RQM« YE= R ?CDa¡=@?CD MhR ^ MhREO Da?CD MhR¢MhR ?CB PeT V PUW =H^)? M Vt } BEDF^ZB DFG RQM7} ?CB P = R:HMhR GA?C=@?CDFGA?CDFÛGJ= R h[ P » k qJB P V P GCYE[a?CG T V P G PR ? PO D R ?CBEDFG }.M VC =@V P ^ MhREOQPR G PO D R = T = TNP V 9;: _ }.P)mlnHPR G o D P G P t 0 [FDa` P V c =@M V= REO <>=@?A?CBEDF=HGJILK 9NM*OQPsR è;0ð ! k Ð03 46587)91:<;>=Ý*yAY¢@L Ú K8I"Ú|ÚDL EJC¦7)C8Gµ4ÙEJC8K8Û I"ÚDL EJC \ M t } BE=@?DFG[ PUW ? WpM V?CB PW YQ?CYQV PõX-M7} ?CBE=@??CB PWpM VZK=H[FDFGCKBE=HG 9NPUPROQP ` P [ MHTNPO Da? }.M YE[ O 9NP D R ? P V P GA?CD R ? M G PUP} BE=@?-Da?-Û= R ? P [F[rYEG-= 9NM YQ?-K=@ RQMhR G k qJBEDFGJK M*OQP [rK=@ P GDa? TNM GCGCD 9 [ P ? M D R ` P GA?CDah=@? P K=@ RQMhR = REO9 = 9;:m \; : VZKD MhR D R ? P VZ=H^)?CD MhR G-D R = RQPU}¸} = :Hk Il?K= :9NPTNM GCGCD 9 [ P ? M ^ MhR GA?AVZYE^)?=K P ^ZBE= R DFGCK WpM V 9 = 9;:m \; : VZKD MhR ^ M Y T [FD R k I R ?CB P« YE= R ?CYEK8°=H[F[ WpP VCV M K=@ RQP ??CBEDFG }.M YE[ O ^ M VCV P G TNMhREO ? M ç M;MHTNP V T =HDaV WpM VZK=@?CD MhR¥k+ñQM V-` P VZD ´Û=@?CD MhR ?CBE=@?'?CB Pe9 = 9;:m \; : VZKD MhR G OQM D REOQPUPO Û=@VCV :P [ P ^)?AVZDF^-^ZBE=@VC PP)*TNP VZDFK PR ?CG.K= :9NPRQP ^ P GCGC=@V :Hk qJB P-MH9 G P VC`@=@?CD MhRbMHW =K=@ RQMhR*m T B M ? MhR ^ MhR ` P VZGCD MhR }.M YE[ O9NP =GA?AV MhR ` P VZD ´Û=@?CD MhR MHW ?CB P P [ P ^)?AV MhR DF^ R =@?CYQV PMHW ?CB P9 = 9;:m \; : VZKD MhR G k \ M K P V P GCYE[a?CG MH9 ?C=HD RQPO2WpM V?CB P K=@ RQMhR G= REO29 = 9;:m \; : VZKD MhR GD R K=@ RQP ?CDFGCK =@V P = R =H[ M hY P G OQP VZDa` POW V M K } BE=@?DFGe=H[aV P = OQ: RQM7}-R = 9NM YQ? T D MhR Ge= REO \; : VZKD MhR GD R æçS k ~ P ` P VZG P [ : t } BE=@?DFGb RQM7}-R D R K=@ RQP ?CDFGCKK= : B P [ T P)*T [F=HD R t M V=@?[ P =HGA?K=@?CB P K=@?CDFÛ=H[F[ : OQP GC^)VZD 9NP t } BE=@?eDFGeBE= TETNPR D R 0D R>T =@VC?CDFÛ[ PT B : GCDFÛG kñQM V P) =HK T [ P Da? } =HG WpM Y REO t¥?CBE=@?e?CB P V P DFG = R = R =H[ M hY P09NP ? }.PUPR ?CB P¢R YEK 9NP V MHW² =` M VZG pM V 9NP ?A? P V « YE=@VC m [ PUT ? MhR PRQP VZ=@?CD MhR2R YEK 9NP V) D R>T =@VC?CDFÛ[ PT B : GCDFÛG= REO ?CB P D REOQP)>R YEK 9NP V MHW =¢KYE[a?CD m [F= :HP V « YE= R ?CYEKÁ°=H[F[ WpP VCV M K=@ RQP ? k Il? DFGÛ[ P =@V } BE=@??CB P [F= :HP VD REOQP) K P = R G WpM V= « YE= R ?CYEK°=H[F[ WpP VCV M K=@ RQP ?Ut } B P V P =HG?CB P M VZDahD R MHW ?CB P PRQP VZ=@?CD MhRR YEK 9NP VD RµT =@VC?CDFÛ[ PT B : GCDFÛGDFGGA?CDF[F[= K : GA? P V :Hk Il?DFG 9NP [FD P ` PO ?CBE=@??CB P V P DFG-GA?CDF[F[¥KYE^ZB ? Mb9NP [ P =@V RQPOW V M K?CB P V P [F=@?CD MhR GCBED T G 9NP ? }.PUPR T =@VC?CDFÛ[ P = REO ^ MhREOQPR G PO K=@?A? P V T B : GCDFÛG k w ¾ ½÷ö sÀ ÀÁ¾¿¹Â Jq BEDFG }.M VCBE=HG 9NPUPR K= OQPeTNM GCGCD 9 [ P ?CBQV M YQhB?CB P ^ MhR ?CD R Y M YEGJGCY TETNM VC? MHW K : GCY TNP VC`*DFG M Vj+V M@m WpP GCG M Ve_ }.P)mlnHPR G o D P G PHk j+V MHWpP GCG M V o D P G P BE=HG MhRQP ? M HV P =@?e[ PR H?CBEG? M¢T V M `*D OQP =HGCGCDFGA?C= R ^ P t PR ^ M YQVZ=@ P K PR ?= REO hYED O = R ^ P ?CBQV M YQhB M YQ?'?CB P:HP =@V k I=HKHVZ=@? PUW YE[ WpM V-BEDFG PREO [ P GCG T =@?CD PR ^ PHk ° P =H[ } = : Gb? M;M ?CB P>RQP ^ P GCGC=@V : ?CDFK P ? MP)*T [F=HD R ?CB P K M GA?0D R ?AVZDFÛ=@? P>OQP ?C=HDF[FG k ° P T V M `*D OQPO ?CB P GA?CDFKYE[F=@?CD MhR = REO GCY TETNM VC? WpM VK :OQP GCDaV P ? M ^ MhR ?CD R Y P ? MbP)*T [ M V P ?CB P V P =H[FK MHW ?CB PUM V P ?CDFÛ=H[ T B : GCDFÛG k Ð 46587)91:<;>=Ý*yAY¢@L Ú K8I"Ú|ÚDL EJC¦7)C8Gµ4ÙEJC8K8Û I"ÚDL EJC ø w ®jùûú÷üDý ø 4~®¡}°t¤6¥¦¢£¤]UR¥RÜ§-© ñQM V¢=µ? }.M² =` M VæçSÁ?CB PUM V : = REO ?CB P ^ M VCV P G TNMhREO D R GCD R h[ P)m [F= :HP V PO K=@ RQMhR ?CB PUM V : ?CB P HV M Y T G Ä s dhlb s dh$# 7l÷= REO2 Ä s dhLtNV P G TNP ^)?CDa` P [ : =@V P 9 V M PR ? M ?CB P GCY 9 HV M Y T GÃ Ä s dh$#t&N¢ 7l¬= REO Ã Ä 7L k q MOQP ? P VZKD RQP} BE=@?BE= TETNPR G } B PR ?CB P V P =@V P K M V P ?CBE= R ? }.M² =` M VZG }.P ^ MhR GCD OQP V'?CB PWpM [F[ M7} D R G T =H^ P G } Da?CB ORQRS g k ñQM V-?CB P æçS P é P ^)?CDa` P P [ O ?CB PUM V :¢}.P BE=` P Ä sP ORQ l sP ORQ $ # 7$ % , Äk 7 Äk dh Ã Ä sP ORQ $ #t&N 7$ % , Ã Ä sP ORQ ñ Äk gh o BEDF[ P D R ?CB P K=@ RQMhRP é P ^)?CDa` P ?CB PUM V : s PORQ , ÃÅÄ PORQ V 7 , ÃÅÄ$#&% PORQ V 7 , Ä k è; } B P V P #&% PORQ£V 7DFG OQP RQPO =HG è " " #&% PORQ V 7-Ä sP ORQ PORV Q 7 Ä ï è+þ * ú è+þï è+* þ" * ñ8 ñ8ñ Ä ï è+þ * ú ñ Ä k Û ñ8ñ8ñ ú ú ï ñQM V P) =HK T [ PeMhRQP BE=HG è " è s h g Ï #&% dhù dh Ä " Ä "Ï ú ú s h d #&% 7 ù 7 Ä Ä ï Ä $ º¼¥¦¨R¶£´w¢R¶ ÿ ú qJB P V P =@V P GA?C= REO =@V O T V M ^ PO YQV P G WpM Ve^ MhR GA?AVZYE^)?CD R ¢=0h=HYQ P ?CB PUM V :Hk \ M K P OQP ?C=HDF[FG MHW h=HYQhD R = R>s dh'G : KK P ?AV : =@V P DF[F[FYEGA?AVZ=@? PO09NP [ M7}k Ð0Ð 46587)91:<;>=¾-A qJB P ^ M `@=@VZDF= R ? 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P VZKòÛ=H[F[ PO ?CB P P [ O GA?AV PR H?CB k \*D R ^ P0ö ë FD G= RQMhR*m-9NP [FDF= R h=HYQ P P [ O t*?CB P ^ M VCV P G TNMhREO D R P [ O GA?AV PR H?CB?C=@ P G-?CB PWpM VZK ed ö ë£á Ä Jê ë ö á V ê á ö ë ö ë ,±ö á ! ñ | ¥¦½I-¨¾½u¥_¤(´w¢R¶¯¤(¹R§ Û Äk îh Û ¤6§-°/ \ M K P = OEO Da?CD MhR =H[*D RQWpM VZK=@?CD MhR DFGhDa` PR B P V P ? M Û[F=@VZD Wp: ?CB P Û=H[FÛYE[F=@?CD MhR GYEG PO ? M REO ?CB P h=HYQ P `@=@VZDF=@?CD MhRMHW ?CB Po¶ó ? P VZK= REO ?CB P ^ M VCV P G TNMhREO D R ^ M Y R ? P V-? P VZK WpM VJ?CB P K=@ RQMhR ?CB PUM V :Hk qJB P h=HYQ P `@=@VZDF=@?CD MhR÷ éº % ü ! V÷ éº % ! t% ¦ % ü ÄûX %nXQV P GCYE[a?CG D RÞ ¢? P VZKG ?CBE=@?'Û= R0P ` PR ?CYE=H[F[ :9NP GCDFK T [FD PO ? M ? PR ? P VZKG k qJB P G P Û= R¢9NP-} VZDa?A? PR =HG=? M ?C=H[ O Da` P VC PR ^ P G M ?CB P D R ? P HVZ=@?CD MhR M ` P V?CB P B P KDFG T B P V P Ã DFG'V PO YE^ PO ? M ?CB P9NM Y REO =@V :0MHW ?CB P B P KDFG T B P V P } BEDF^ZBDFG " tE?CB P GCYQV W =H^ PeMHW = WpM YQV mO DFK PR GCD Mh( R =H[´B :;TNP VZG T B P V PHk q M REO ?CB P ^ M Y R ? P V? P VZK$Da? } =HG RQP ^ P GCGC=@V : ? M ?AV :M YQ? `@=@VZD M YEG? P VZKG^ MhR ?C=HD R D R MhR [ : ?CB P K=@ RQMhR P [ O %¸= REO ?CB P h=HYQ PTNM ? PR ?CDF=H[ ö ë = REO 7M V^ M VCV P G TNMhREO D R OQP VZDa`@=@?CDa` P Gs?CB P V PUMHWlk qJB PRQPU} ? P VZKG= OEOQPO KYEGA?BE=` P ?CB P GC=HK P h=HYQ P `@=@VZDF=@?CD MhR =HG?CB PM VZDahD R =H[ oµP GCG mL¶ YEKD RQM@m o Da?A? PR ? P VZK k qJB P G P ? P VZKGÛ= R ?CB PR09NP GCY 9 ?AVZ=H^)? PO tQK=@*D R ?CB PPR ?CDaV P ^ MhR h[ M K P VZ=@? P h=HYQ P D R `@=@VZDF= R ? k ° P V P =@V P G M K P YEG PUW YE[ WpM VZKYE[F=HGUi Ä X % êá X<X êá % êá ö % ü Ü Ä X ö â V X êºâ X pX üö Ü â X V ü ÄÜ ê áX<X;±â á X<X êá ö ê Ä ê á X<X; êºâ X<X; êá êºâ â V êá X<X pX ö 0â êá X<X êºâ X<X êá X<X pX Äk Uf Äk H7 Äk dh Äk gh -A ÑI)Ó¦Ó_7>= Ò}Ep:D5";¦7)C87)Û E0ÖHL ;wÚ@Et:D5";£90L EJC}7)C8GUÓ_7"ÖJC"EJC"Ú+:D5";wEN= L ;wÚ Ð0÷ o B PR ?CB PeO YEGA?G P ?A?C[ P GUtQ?CB P h=HYQ P `@=@VZDF=@?CD MhR0MHW ?CB P ^ M Y R ? P V'? P VZK } DF[F[©Û= R ^ P [r=H[F[©? P VZKG MHW ?CB P h=HYQ P `@=@VZDF=@?CD MhR MHW ?CB Po¶ó ? P VZK k qJB P V P =@V P = OEO Da?CD MhR =H[¥? P VZKG?CBE=@?e= TETNP =@VtNG M K PMHW ?CB P K Û= R ^ P [s= } = : =@h=HD R t]G M K P V P K=HD R¥k Il?Û= Rµ9NP GCB M7}-R ?CBE=@?e?CB P V P K=HD R D R 0? P VZKG ?CBE=@? GCB M YE[ O `@= R DFGCBD R =eh=HYQ P D R `@=@VZDF= R ??CB PUM V : WpM VZK =? M ?C=H[ O Da` P VC PR ^ PHk \*D R ^ P ?CB P ^ M Y R ? P Vs? P VZK DFGs= R D R ? P HVZ=H[ M ` P V'= 9NM Y REO =@V : ?CB P-9NM Y REO =@V :MHW = WpM YQV mO DFK PR GCD MhR =H[QB :;TNP VZG T B P V P ³?CB P ? M ?C=H[ O Da` P VC PR ^ P BE=HG RQM ^ MhR ?AVZD 9 YQ?CD MhR¥k ;ÃºÞ U " ±ß áâDãêá V % êºâ X<X;% ö ã Ä ;ÃºÞ U " ±ß áâDã % êá X<X êºâ % ö ã V êá % ºê â X<X % ö ã Äk )è; K% êá X<X;I% êºâ ö ã V % êá X<X; êºâ X<X;I% ö ã U¨¾®¯¥W°6« ¤(¹R§¥¦¢R¥¦½u}¶£ú§-© ¤(¹R§ª¾ú£¢ ¦¥ ¢R¸ ¯¥W¶£¢R£¢R© fÄ ¦ ¤(¹R§-}°/ú§-© æ_ X q'ILqZÂ < -X&0X \ j+I 0X \ [ MH9 =H[rG : KK P ?AV : ø ghLZÃ ù s dhL s dhl s dh$# 7$% ø dh ù 7L s dhl'&(# " _ R9 V M PR GCY 9 HV M Y T ° M [ O GA? MhRQP9NM G MhR P [ O D R. Ã ý Àó ï , %Èó3#&% 7 Àó £´mOQP Û= : ^ MhR GA?C= R ? ç M Y T [FD R GA?AV PR H?CB G T D R GA?CD é RQP GCG j+V MHT =@h=@?CD MhR G TNPUPO G T D R0} =` P ` P [ M ÛÅ Da? : ` P [ M ÛDa? :¢MHW [FDahB? 9 = 9;:m \; : VZKD MhR q MHTNM [ M hDFÛ=H[rG M [FDa? MhR \; : VZKD MhR M ï !6Ä·O M " " !(Ä·O \ M [FDa? MhR B M K M ? MHT;: P [ P ^)?AVZï DFê^ZBE=@VC P 9 =@V :HMhRR YEK 9NP VJ q MHTNM [ M hDFÛ=H[r^ZBE=@VC P 9NM G MhR G M " V WpP VZKD MhR G \ M [FDa? MhR GA?C=@?CDFGA?CDFÛG = R:HMhR G M " !6Ä·O M !(Ä·O \;?C=@?CDFGA?CDFÛGJB M K M ? MHT;: ( ! è±é ï P)*T] ûï»JÃ ý8 !Ä \;?C=@?CDFGA?CDFÛG W =H^)? M V R YEK 9NP V MHW ^ M [ M VZG OUT \;?C=@?CDFGA?CDFÛG T =@VZ=HK P ? P V = R:HMhR = R h[ P » T D MhR ¦ §©§ ®s[ P ^)?AV M K=@ RQP ?CDF^ OQP Û= : K=@ RQMhR¦ò§©§ \ M [FDa? MhROQP Û= : Û=@?C=H[ : ¡ P V ^ZBE=@VC PO} DaV P K=@ RQP ?CDFêK MhRQMHTNM [ P q]= 9 [ Pk @ió£mt`NàzjugHe<b1aRäwb8oÏ?_bwb"mãrtefjNmÙaR`Nmtc¡i`>gHmtjNmÙa Ð* 46587)91:<;>=¾-A ORQ < -&X 0X ñª³ 8 0 ~\ j+I 0X \´tEû 0X \´tE= REO ü m <>®\ 0X \ æ_ X q'ILqZÂ [ MH9 =H[¥G : KK P ?AV : sPORQ sPORQ l sPORQ $# PORQ V 7 sPORQ l'&(# _ R9 V M PR GCY 9 HV M Y T Ã M [ O GA? MhRQP P [ O D .R Ã % _ó3#&% PORQ V 7 _ó sPORQ OEO Da?CD MhR =H[N[F= 9NP [ [F= :HP VD REOQP) PRQP VZ=@?CD MhR D REOQP) M #&% PORQ£V 7<!/Ä·O M " sPORQ <!(Ä$O \ M [FDa? MhR B M K M ? MHT;: ï = R:HMhR G 9NM G MhR G M V WpP VZKD MhR G \ M [FDa? MhR GA?C=@?CDFGA?CDFÛG M sPORQ <!(Ä ô7f õ \;?C=@?CDFGA?CDFÛGJB M K M ? MHT;: M " #&% PORQ V 7<!(Ä ô7f õ o¶ó ? P VZK P)*T] û» éº % !Ä P)*T]( d £ û OUT± éº !Ä o¶ó B M K M ? MHT;: M #&% PORQ V 7<!(Ä ô7f õ MÔèJ sPORQ <!(Ä$O ( Y RE« YE= R ?CDa¡ PO » « YE= R ?CDa¡ PO OUT \;?C=@?CDFGA?CDFÛG T =@VZ=HK P ? P V q]= 9 [ Pk d;vi ó£mt`NàzjugHe<b1a}äwb8oÏ?_bwb"m¬rtefjNmC(åH`JjNmC`NmtcJüt iãb1a8jNm¬rp^yâ)a1efq"a}`NmtcµoÌ^Ùb+rp^yâ)a1efq"a}j$kZi`>gHmtjNmÙa ?ÜePoÌ^2a>b AHb"hD`NàºùW`@ANjNhwa_= 1s Ws½ 1!° k©ªrP YQ? }J: [ P V k+X-MhR V P [F=@?CDa`*DFGA?CDF^ P é P ^)?CDa` P [F=@HVZ= R hDF= R G k \_^yâ)a_=¦b A@=ïtQèî;i g@fhgHg;t îHî{è; k d0! ° k©ªrP YQ? }J: [ P V k.M [ O GA? MhRQPe9NM G MhR G k `Nh¬e Az^Ùb|rtárp^_ü _ü ht îHî{è; k g0! k \*=H[F=HK nQk]M [ O GA? MhRQP = REO \ kroµP D R9NP VC kc V M PR G : KK P ?AVZD P G k \_^yâ)a_=!¦b A@=Ft.dhði îHê Û t îHêHdh k èN!q k ° k ~ k \; : VZK PHk> Y R D PO P [ O ?CB P V M7:MHW K P G MhR G= REO9 =@V :HMhR G k#" v~q8àábu`Nh\_^yâ)a1efq"a±t g*@i ÛHÛ ê;t îHêHdh k Û !q k ° k ~ k \; : VZK PHk qJB PeM VZDahD R G MHW GA : VZKD MhR G k%$ mpo=&=+çj>cº=@\_^yâ)a_=Ft g;i dhð7è Û t î ÞHÞ k 0ê !¬Â k j k ~ :;9 =@ M &` 8 k k <>=@*BE= R M `= REO 8 k I k \*= R: *Y k >/^ÙbÀæ~å)âNh1iãb6çj>cyb"à k \ T VZD R P V m 8 P VZ[F=@Qt îHîHgh k >ð ! nQkEñ V M;P [FDF^ZB = REO _ k < k \;?CY OQP V k. =HYQ P D R `@=@VZDF= R ^ P = REO ÛYQVCV PR ?J=H[a PU9 VZ=D RRQMhR V P =@?CDa`*DFGA?CDF^ K= R:m 9NM*OQ: ?CB PUM V :Hk ¦b A0e<b ?aUj$knçj>cyb"h1m \_^Ja1efq"a±t´ê Û i ð@gHg;t îHîHgh k Þ !\ kQoµP D R9NP VC ks¸RQPU} [FDahB? 9NM G MhºR õ \_^yâ)a_=¦b A@='@b8ofo=FtEèhf*i dHdHg;t îhð Þ k 0î ! k.¯ ?° M;MHW ? k \ : KK P ?AV :9 V P =@*D R ?CBQV M YQhB 9NP [F[ Fm Y =H^C*D } = RQM K=H[FD P G k \_^yâ)a_=(¦b A0e=('@b8ofo=Ft ghði Þ t îhð@êh k U)f ! n V k ç kNk ç=H[F[F= R = REO ® k©o Da?A? PR¥k < MhRQMHTNM [ P Û=@?C=H[ : GCDFG MHW GA : KD MhR OQP Û= :H)k " v~q8à =+\_^yâ)a_=Ft c iFê*@t î Þ è; k H1 ! nQkóµP GCGe= REOck³¶ YEKD RQMQk ç MhR G P« Y PR ^ P G MHW = RQM K=H[ M YEG } =@V O D OQPR ?CDa?CD P G k \_^yâ)a1efq"a*'@b8ofo=Ft ghð c i î Û t îhð;7 k 0d ! ® kQo Da?A? PR¥k [ MH9 =H[r=HG TNP ^)?CG MHW ÛYQVCV PR ?J=H[a PU9 VZ= +k " v~q8àábu`Nh \_^yâ)a1efq"a±t c dHdHg;i èdHd;t î Þ gh k 0g ! ® kJo Da?A? PR¥k çYQVCV PR ?=H[a PU9 VZ=*t 9 =@V :HMhR GUte= REO¬« YE=@VC¹^ MhR RQP K PR ? , k " v~q8àábu`Nh \_^yâ)a1efq"a±t c dHdHg;i ègHg;t î Þ gh k )Nè !\ k < k¥ DaVC`*D R¥k >/^ÙbîZv~`NmpoPv'igõµ`NàÌà6Þ- buq>o. " j@AHb"àtÞ-ßyq8ePo<`HoPefjNmÙaR`Nmtcò¦hDj)åJb"m æpâNiRiãb8oPh1e<b1a k ? M9NPeT Y 9 [FDFGCB PO> \ T VZD R P RV 8 P VZ[F=@;Zt îHî Þ k Û ! ® k ç k <>=@VZD RQMQk æYE= R ?CYEKÁGA : VZKD MhR = REO ?CB POQP GA?AVZYE^)?CD MhR>MHW = R ?CD WpP VCV M K=@ RQP ?CDF^ M V OQP VD R BEDahB m ? P K TNP VZ=@?CYQV P GCY TNP VZ^ MhREO ^)? M VZG k `Nh¬e AÌqwjNmtcN i`Ho /01231 @A@û@t îHî Þ k ÷F Ô(B Ô¸bHB 4-ö65kÈ798 ê0! q k < M VZD R =@VZD k < P ^ZBE= R DFGCK MHW Y R ^ MhR ` PR ?CD MhR =H[+GCY TNP VZ^ MhREO YE^)?CDa`*Da? : D REO YE^ PO9;: GA : VZKD MhR P) ÛDa?C=@?CD MhR G D R ? }.M@mO DFK PR GCD MhR =H[.GA?AV MhR h[ : ^ M VCV P [F=@? POP [ P ^)?AV MhR G : GA? P KG k \_^yâ)a_=(¦b A@=òJt ê Û t d@fHfhdh k 7ð>! ° k kñQP VC?CDa\ k < k DaVC`*D R < k]-9NM [ W =@?CB¥t nQk nQk j=H[F=HÛD M G = REOk ° k <>=HÛS MhR =H[ O¥k ç.VZDa?CDFÛ=H[ ^ M K T =@VZDFG MhRMHW Û[F=HGCGCDFÛ=H[¥ P [ O ?CB PUM V : = REO KDF^)V M GC^ MHT DF^ } =` PW Y R ^)?CD MhR G WpM VGA : VZKD MhR GJD R « YE= R ?CYEKBE=H[F[ WpP VCV M K=@ RQP ?CG k \_^yâ)a_=¦b A@=òJt Û ê;i êhð@î Û t îHîhðH k Þ ! ª+k¶ B PR k ° k <>=HÛS MhR =H[ O \ k < k DaVC`*D R S k Â M GCBED M @=>û k Âs= R Qtû k < M;MhR = REO \*B M Y m çB PR ¶ BE= R k æYE= R ?CYEK WpP VCV M K=@ RQP ?CDFGCK·= REO T BE=HG P ?AVZ= R GCDa?CD MhR GD R OQM Y 9 [ m [F= :HP V « YE= R*m ?CYEKBE=H[F[¥G : GA? P KG k \_^yâ)a_=¦b A@='@b8ofo=FtNð@d;i ð@gHd;t îHî{è; k î0! j kó¸k °DaHhG k-c V M PR G : KK P ?AVZD P G= REO ?CB P K=HGCG P G MHW h=HYQ P9NM G MhR G k \_^yâ)a_=6¦b A@='@b8ofo=Ft g;i Û f Þ t îHê{è; k d@f)! k¥¯ ?-° M;MHW ? k ~ PRQM VZK=H[FDa¡=@?CD MhR¢MHW K=HGCGC[ P GCG : = R m KDF[F[FGs P [ O G !k " v~q8à =/\_^yâ)a_=Ft c gHg;t îhð;7 k d*1! < k ® k j P GCBQ*D R = REO S k 8 k \*^ZBQV M;POQP V k ó£m $ mpoPhDj>cNv~q>oPefjNm o<jtîZv~`NmpoPv'i ö-e<b"àzc·>/^ÙbujNh1â k o =HGA?A`*D PU} j+V P GCGUt îHî Û k dHd0! ª+k ° k ~ :*OQP V k îZv~`NmpoPv'i¯ö-e<b"àzcÕ>/^ÙbujNh1â k ç=HK 9 VZD O P _ R Da` P VZGCDa? : j+V P GCGUt îHîHêh k dHg0!\ kQoµP D R9NP VC k >/^Ùb/îZv~`NmpoPv'i >/^ÙbujNh1â j$kö-e<b"àzc)aDC:2~jNà v'iãb $Zk ç=HK 9 VZD O P t îHî Û k d{Nè ! nQkrM [ O GA? MhRQP = REO>ñ.kNo DF[F^)¡ P kñ VZ=H^)?CD MhR =H[ « YE= R ?CYEK R YEK 9NP VZG MhR G M [FDa? MhR G k \_^yâ)a_=áà:¦b A@= '@b8ofo=FtEè;ði î Þ ê;t î Þ 7 k d Û ! nQk ~ k ç[ P Ký= REO < k o¸k ç M é PU:Hk 8DFGC^ M YEG ² Y K M ?CD MhR D R = YAM G PUT BEG MhR*m ^ M Y T [ PO [F= :HP VJK M*OQP [ MHW BEDahB m G$T GCY TNP VZ^ MhREO YE^)? M VZG k \_^yâ)a_=¦b A@=òJtQèd;i êHd@fhî;t îHî@f k dH0ê ! j kQk < k SDaVZ=H^ k æY R =@?CDa¡ PO GCD R hYE[F=@VZDa?CD P G+D R ?CB PP [ P ^)?AV M K=@ RQP ?CDF^- P [ O¥k \ZhDj>q=;WjNâº=@æ6j>q=Ft gHg;i ê@f*t îHg*7 k dh>ð !ç k ª+kr =@V OERQP Ve= REOµnQk k °=@VC` PU:Hk \;?C= 9 [ P HVZ= REO*m Y R D PO K MhRQMHTNM [ P G } Da?CB>KYE[a?CD T [ PO DaVZ=H^ ^ZBE=@VC PHk \_^yâ)a_=¦b A@=:'@b8ofo=Ft Û d;i Þ ð@î;t î Þ è; k d Þ !~ k ~-= Y =@VZ=HK= R¥k æ6jNà ePo<jNmÙa¾`Nmtc $ mÙa"o<`Nmpo<jNmÙa kX-M VC?CB m ° M [F[F= REO t î Þ dh k dH0î ! nQk© =HGCG P V k ç M [F= R P [ M = REO ° kQªrP YQ? }J: [ P V k qJB PT D T D´G m } =` P GCÛ=@?A? P VZD R [ PR H?CBEG k \_^yâ)a_= '@b8ofo=Ft c è ÞHÞ i dHê*@t d@fHfHf k g@)f ! ® k ç k <>=@VZD RQM = REO < k ck \*DF[a`*DF= X-P ? MQk æYE= R ?CYEK GA : VZKD MhR G= REO ?CB POQP GA?AVZYE^)?CD MhR÷MHW [ MhR m VZ= R P = R ?CD WpP VCV M K=@ RQP ?CDF^ M V OQP VD R ?CB P BEDahB m G$T GCY TNP VZ^ MhREO YE^)? M VZ=G <Pò * > À Æ Â ? = REO ï ( @ ò ï Æ ÂÝ"? . k \_^yâ)a_=¦b A@=òJt´ê{èQt d@fHfQ7 k g*1 !çB k j k ° MHW K= RER¥k \ T D R*m } =` P GCÛ=@?A? P VZD R D R ?CB P P é P ^)?CDa` P [F=@HVZ= R hDF= R>TNP VZG TNP ^)?CDa` PHk \_^yâ)a_= ¦b A@=òJt©ê@f*i g ÞHÞ t îHîHîh k gH0d !çB k j k ° MHW K= RER¥k'ñQP VCV M K=@ RQP ?CG= REO = R ?CD WpP VCV M K=@ RQP ?CGD R ?CB PP é P ^)?CDa` P [F=@HVZ= R hDF= RTNP V m G TNP ^)?CDa` PHk `Nh¬e AÌqwjNmtcN i`Ho ;ABAkû 12EA@û@t d@fHfhdh k gH0g ! ñ.kó DF[F^)¡ P = REO kr¶´PUPHk-ª D R *D R R YEK 9NP VZGUt´G T D R = REO GA?C=@?CDFGA?CDFÛG MHW G M [FDa? MhR G k \_^yâ)a_=6¦b A@= '@b8ofo=Ft Û @i dHd Û f*t î Þ gh k Ô(B Ô¸bHB 4-ö65kÈ798 ÷J? g{èN!DC k koµPR = REOk+¶´PUPHk \ T D R} =` P G= REO ? MHTNM [ M hDFÛ=H[.? P VZKG D R ?CB P K P = R*m P [ O ?CB PUM V : MHW ? }.M@mO DFK PR GCD MhR =H[ WpP VCV M K=@ RQP ?CGb= REO = R ?CD WpP VCV M K= R P ?CG k \_^yâ)a_==¦b A@=='@b8ofo=FtJê*@iFUfhd Û t î ÞHÞ k g Û ! j k ck'o D P hK= RER¥k \*Y TNP VZ^ MhREO YE^)?CDa`*Da? : D R GA?AV MhR h[ : ^ M VCV P [F=@? PO¹P [ P ^)?AV MhR DF^G : GA? P KG= REO ^ MhR RQP K PR ?J` P VZGCYEG OQP ^ MhR RQP K PR ? T B PRQM K PRQMhR¥k \_^yâ)a_=:¦b A@='@b8ofo=Ft´ê@f*i Þ d*@t î ÞHÞ k gHê0! j k 8 M VZYQh= R ?CD¥= REO \ k S MhR DF=H^ZB kñQP VZKD MhR G= REO G M [FDa? MhR GD R ?CB PM© gh RQMhR [FD RQP =@V_èK M*OQP [´D R dh G T =H^ P ?CDFK P)mO DFK PR GCD MhR G k \_^yâ)a_=¦b A@=:'@b8ofo=FtEèhf*i dHdHg;t îhð Þ k ghð>! û k < M;MhR = REO û k <>YE[F[ PR¥kr ÛÛYQVZ=@? PeP é P ^)?CDa` P =HÛD MhR0WpM V « YE= R ?CYEKBE=H[F[´GA : VZKD MhR G k \_^yâ)a_= ¦b A@=òJt Û ðiF)è Þ gHg;t îHî Þ k g Þ ! k 8 kNñQP VCV P Ve= REO>k 0k ç=H[ OQP DaVZ= k \; : VZKD MhR OQ:*R =HKDFÛG-D R>« YE= R YEKBE=H[F[ WpP VCV M K=@ RQP ?CG k \_^yâ)a_=¦b A@=òJt©ê*@t d@fHfHf k gHî0! ® k S ¯ ° M P Ve= REO ® k©ñ =@VZBED k qJB POQP Û= :¢MHW ?CB P GA : VZKD MhR¥k \_^yâ)a_='@b8ofo=Ft³ê{è c i Þ ê;t î Þ è; k èhf)! ® krñ VZ= O *D R = REO < k \;? MhRQPHk q MHTNM [ M hDFÛ=H[? P VZKGeD R>MhRQP)m = REO ? }.M@mO DFK PR GCD MhR =H[ « YE= R ?CYEK B P DFG PR9NP VZG'= R ?CD WpP VCV M K=@ RQP ?CG k \_^yâ)a_=¦b A@=Ftrg{è c i ð@d* Û t î ÞHÞ k èE1!\ k SBE=@V ck¥c =HGCYµ= REO j k¥c = REOQ:HMHT = O B : = :Hk °DahB>? T GCY TNP VZ^ MhREO YE^)?CDa`*Da? : tNGA : VZKD MhR G= REO 9NP VCV :bT BE=HG PHk `Nh¬e AÌqwjNmtcN i`Ho ;2013E ü £A@û@t d@fHfhgh k è0d ! nQk³R = REO = R¥k ®s[ P ^)?AV M K= R P ?CDF^ P é P ^)?CGD R ?CB Pb« YE= R ?CYEK D R ? P V WpP V PR ^ PbMHW'O D TNM [ P G k \_^yâ)a_= '@b8ofo=óetrg Þ i g{è;ðt î Þ îh k è0g ! _ k < k \;?CY OQP V nQk ñ V M;P [FDF^ZBý= REO ® k qJBEDaVZ= R¥k æYE= R ?CYEK ?CB PUM V : MHW [F=@VC P G : GA? P KG MHW RQMhR¥k V P [F=@?CDa`*DFGA?CDF^K=@?A? P V k `Nh¬e AÌqwjNmtcN i`Ho 13/0 EAht d@fHfhdh k èHNè ! _ k mlnQkEo D P G PHk qJB P GA?AVZ= REO =@V O K M*OQP [ k \*^)VZD T ?CYEKt d@fHfhdh k è Û !ç k °=@hK= RER û k `@= Rc D 9E9NP V'° k <>YQVZ= : =HK=*t k k ~-={é P [a?J= REOª+k nQk ~ M G PR9NP VC k+J D MhR G = REOM ?CB P V` P V : [FDahB? 9NM G MhR GUtE?CB PUM V : tN=HGA?AV MHT B : GCDFÛ=H[³^ MhR GA?AVZ=HDa?CG= REOP)*TNP DFK PR ?C=H[r[FDFKDa?CG k mtjHo(rtvpä"à e aw^Ùbuc@t d@fHfHf k è0ê ! S k m \ kQªrPUP = REO û k m o¸kQX k jsB M ? MhR¢T V M*O YE^)?CD MhRMHW = D MhR DF^^ M [ O¢O =@VCbK=@?A? P V k \_^yâ)a_=;¦b A@= ït©ê*@t d@fHfHf k è;>ð ! < k ILK 9NM*OQPR 0k{c = P V= REO _ k mlnQk{o D P G PHk ®s[ P ^)?AV M K=@ RQP ?CDFGCK¸=@?[ M7}2PRQP VChD P GUi]jsD MhR Gr` P VZGCYEG K=@ RQMhR G k `Nh¬e AÌqwjNmtcN i`Ho ;2û32312EA@û@t d@fHfhgh k

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