Chapter 1 Parabolic partial differential equations ... - vscht.cz

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: ¶ Â ºK Ac= � » º K A _ � Ä » Ç � ¼ G

: ¶ " º K A Ã B#Å Ç.Ã ¼ Ã ÃD8 � ÇL�ÅµÆ ÃFÇ.Ã ÃDE � Ç5Ã 8�Ç.a ¼.¼ Pº 9A Å Bc8 B0: PwÃ B#Å Ç.Ã ¼ Ã ÃD8 � Ç5Ã 8�Ç.a ¼ �IPº K 9 Å Æ Ã º K < Å Æ Ã LlÅµÆ ÃhÇ(Ã ÃDE 8�Ç.a ¼ �pP

�dY º 8:°�A Ã ��K Pr/2OX<)`NDlO=+.-2L]<)/2+(G�+(Yr8�Ç(a0Ç �.PRyR/0<>`^<)`BD�/2GN/v<)/?&J-A1F+.GN@B/0<)/0+.G�8 Ç.avÇ �.Pr&JGN@�<)`ND*,+.LNGN@N&('=f�1F+.GB@N/0<>/2+.Gg8�Ç.avÇ %IP��J<)`BDFGl<)`BDcDF'='>+.'#+(Y;<)`NDtO>+.-0LB<)/0+.G�1H+.VT9BLB<)DH@�*pfg8�Ç(a ¼.¼ Pi�8 Ç.a ¼ �IPc&(GN@�8�Ç(a ¼ �IPt/2O � K A Å º 8:°�A Ã ��K P � º K A 8�Ç.a ¼ �.P�]/0VT/0-?&('=-0fr&(O Y:+.'�+.'>@N/0G;&('�fn@N/0CEDF'=DFGI<)/2&(-pDFKpL;&J<>/2+.GNOt8 $ 476zP�ytDq'>DFKpLN/0'>Dz<)`;&J<#VT&(�p/2GNS<>`NDUS.'=/2@�~NGNDF'H��/ a D(a :�� Æ Ã G�� Æ Ã#'=DFO>LB-0<)O�/2G � K A � Æ /2G�²�QSRUT �dYX<>`N/2O3/2O3<)`ND1F&(O>DUyqDuO)&hf�<)`;&e<l<)`NDUO>+.-0LB<)/0+.G�+(Y�8 Ç.a ¼.¼ Pi�}8�Ç.a ¼ �IP3&(GN@ 8 Ç.a ¼ �pP31H+.GI{.DF'=S.DFO�<>+^<)`NDD��N&J1H<cO=+.-2L]<)/2+(GT+(Y58�Ç.avÇ �IP��w8 Ç.avÇ �.P�&(GN@j8 Ç.avÇ %IPia.�d<c/0Oq+.*I{M/2+(LNOz<>`;&J<q/0YE<)`NDrGMLBVTDH'>/21F&(-O=+.-2LB<>/2+.Go@N+MDFOXGN+(<r1F+(Gp{(DF'=S.D�<)+�<)`BD�Di�B&(1i<�O=+.-2L]<)/2+(G_<>`NDFG_<)`ND�@N/0CEDF'=DFGN1HD�VWDH<>`N+]@/0OlLNO>DH-2DHO>OFa |}`NDo@N/vCwDH'>DHGN1FDo&(9B9N'>+h�]/2VT&J<)/0+.G 8 Ç.a ¼(¼ P�/2O�1F&(-2-0DF@�<>`NDuDi�]9N-0/21F/v<l<)`B'>DFD9,+./2GI<�@B/0CEDF'>DHGN1FDoO=1Q`NDFVWD(a�|}`N/0O�G;&(VWDU<)DH-2-2O�<)`;&J<�<>`NDu{J&(-2LND º K _ �A /2Ol1H+.VT9BLB<)DH@D��B9B-2/21H/0<>-0f�Y:'=+.V <>`NDz{J&(-0LNDFO º K Ac= � Ã º K A Ã º K A _ � |}`BDq'=DF-?&e<)/2+(GNOq8�Ç.a ¼.¼ P��N8 Ç.a ¼ �IPA&(GN@U8�Ç.a ¼ �pP&('=DT/v<)DH')&J<>DF@�ag|}`BDT{.DH1H<>+.'�� K Å 8 º K 9 Ã º K � Ã Ã º K < P7/2On1h&J-2-2DH@�<>`ND L \ <)`�9N'>+(~N-2D(a �¯G8 Ç.a ¼(¼ Pt<)`ND L \ <)`_9N'>+J~;-2D3/2OX1h&(-0-2DH@o<>`ND�+(-2@�8:<)`BD��pGN+�yRGxPX9B'>+(~;-0D(�,&(GN@_<)`ND L » ÇH\dO=<9N'=+(~;-0Du/2O�1h&(-0-2DH@ <>`NDoGNDHy 9B'>+(~;-0D(a | +�O=LNV LN9��t<>`NDoGNDHy«9N'>+(~N-2Do/2O�1H+.VT9BLB<)DH@9,+./2GI<�\dyR/2O=D�Y:'>+(V�<)`NDn+.-0@u9N'>+J~;-2DJa%

�� + 7��6��#��,+�� /2- +��%�� %N1?%� ) % � )�� %N "%��D�@NDFGB+(<)D�*If º K A <)`ND�D��N&J1H<nO>+(-2LB<>/2+.G�+JYz<>`ND�@N/vCwDH'>DFGB1FD�9N'=+.*N-2DHV 8 Ç.a ¼(¼ Pi��8�Ç.a ¼ �IP&(GB@½8 Ç.a ¼ �pP�&(GB@jyqDW@NDFGN+J<)D�*If��º K A <>`ND�GMLBVTDH'>/21F&(-2-vf_1F+.VW9NLB<>DF@jO>+.-0LB<)/0+.G�a�|}`NDFO=D@N/vCwDH't@NLBD�<)+l'=+.LNGN@M\¯+(CkDF'='>+.'=Oc/2GI<)'=+]@BLN1FDH@u/2GgDF&(1Qò&('>/v<)`NVWDH<>/21F&(-x+.9EDH')&J<>/2+.GT@N+.GND+.G�&g@N/0S./0<)&(- 1F+.VW9NLB<>DF'Fa ��D�yt&(GI<7<)`N/0O7'>+.LBGN@]\¯+JC�DF'='>+.'7GB+(<s<)+oS.'=+�y�<>+]+uVlLB1Q`/0Go<>`NDn1F+.LB'>O>Dn+(Y#1F+(VT9NL]<Q&J<>/2+.G�a ��D7yt&(GI<r<>`NDnDF'>'=+.'>O� K A Å º K A ��º K A 8�Ç.a ¼ %IP<>+TS.+�<)+ �FDH'>+U+('�&J<X-0Dh&(O�<X<>+UO�<Q&hfo*E+(LNGN@NDH@^Y:+.'R/2GN1H'>DF&(O>/0GNS L ac|}`B/2OX'>DFKpLN/0'>DHVTDHGp<9N'=DFO=DFGI<)O7<)`BD�O=<Q&J*N/2-0/0<¯fo1F+(GN@N/0<>/2+.G^+(Y�<)`ND�@B/0CEDF'>DHGN1FD�O=1Q`NDFVWD(a3|}`NDl<>+(<Q&(-#DF'='>+.'s+JY<>`NDnGMLBVTDH'>/21F&(-�O=+.-2LB<>/2+.Gu1F&(G_*EDnDFO�<)/0VU&J<>DF@o*If� � K A � » � � K A � Ã 8�Ç.a ¼ �.PyR`NDH'>D � � K A � /2O7O=VU&J-2-�&JGN@�GBDFS.-0/2S./0*N-2D31F+.VW9;&('=DF@[<)+u<>`ND�DF'>'=+.'7+(Yz<)`ND�VWDH<>`N+]@ � � K A �Y:+.'�O=<Q&J*N-2D�O=1Q`NDFVWDFOHa��XGNO=<)&(*N-0D�O>1Q`NDHVTDHO�&('=D�LNO>DH-2DHO>O7Y:+.'79N'>&(1H<>/21h&J-�1F+(VT9NL]<Q&J<>/2+.G*,DF1F&(LNO>DnyqD31F&(G_GNDH{(DF'X1F+.VW9NLB<>DnyR/v<)ò/2G]~;GN/0<>D7GpLNVl*,DF'R+(Y#@NDF1H/2VT&(-w@N/0S./0<>OFa

�ADH<uLBOgDi�]9N-2&(/2G½<>`ND�9N'=+.*N-0DFV +(Y3O=<)&(*N/2-0/0<¯f�Y:+.'W<)`NDÔ>1Q`NDHVTD®8 Ç.a ¼(¼ P�/0G VW+.'>D@NDi<Q&(/0- a �d<R/0O}Dh&(O�fu<)+�'>DiyR'>/v<)DT8�Ç.a ¼.¼ P��8�Ç(a ¼ �.Pc&(GN@�8�Ç.a ¼ �pPtLBO>/2GBSW9B'>+(~;-0DFOX&(O� K`_ � Å � � � K Ã� 9 Å � Æ Ã�Bc8 : P�Ã�Bc8 ¼ : PiÃ Ã�Bt8>8�8 �½ÇÈP : PiÃ Æ�� Ã 8�Ç.a ¼ �IP

yR`NDH'>Dn<)`NDnVT&J<)'=/v� � � /2Oc<)`B'>DFD�\¯@N/2&(S.+.GN&(-

� � Å��

Æ Æ� 8�Ç � ¼ � P �� 8�Ç � ¼ � P � Æa a a a a a a a aÆ � 8�Ç � ¼ � P �� 8�Ç � ¼ � P �Æ Æ

�! "Ã 8�Ç.a ¼ #IP

yR`NDH'>D � Å G: ¶ 8�Ç.a�� Æ P

XYZ<)DF' @NDHGN+(<)/0GNS �� K Å 8 º K � Ã º K ¶ Ã Ã º K <@= � PiÃe&(GN@�LNO>/0GNS º K 9 Å º K < Å Æ ÃÈyqDt1F&(Gl'=DHyR'>/v<)D8 Ç.a ¼ �IPc&(O�� K`_ � Å#� �� K Ã �� 9 Å � Bc8 : P�Ã�Bc8 ¼ : P�Ã Ã�Bc8=8�8 � ÇÈP : P � � Ã 8�Ç.a��BÇÈP�

yR`NDH'>Dn<)`NDnVT&J<)'=/v� � /0O}+(Y <¯f]9,DT8�8 � ÇÈP�< 8&8 � ÇÈPt·��Å

��8�Ç � ¼ � P �� 8 Ç � ¼ � P � Æa a a a a a a a a

Æ � 8�Ç � ¼ � P �� 8�Ç � ¼ � P� " 8�Ç.a�� ¼ P

+.GBO>/2@BDF'�GB+Èy�&_O>VT&(-2-5@NDi{]/2&J<)/0+.G�+(Y}<)`NDT/2GN/v<)/2&(-�1F+(GN@N/0<>/2+.G½8�/0GI<)'>+M@NLN1HDF@�*If�<)`ND'=+.LNGN@]\d+(C[DH'>'>+('QP �� 9 · �� 9 Å �� 9 � �� 9 8�Ç.a�� IP�XDF'>Dk<)`NDk9N'>/0VTD_@N+MDFOgGN+J<gVWDh&(G @BDF'>/v{J&J<)/v{.D(�}/v<��=LBO=<g@BDFGN+(<>DFOo&(GB+(<)`NDH'U9N'=+(~;-0D(a6�KpL;&J<>/2+.G�8�Ç(a��BÇ�PqyR/0<)ù<>`NDn/2GN/v<)/?&J-E1H+.GN@N/v<)/2+(G �� 9 *EDH1F+.VWDFO�� K _ � Å#� �� K Ã �� 9 Å �� 9 � �� 9 8�Ç.a�� pP|}`NDnDH'>'>+(' �� K Å �� K � �� K Di{.+.-v{.DFOr&(O�� K`_ � Å#� �� K Ã 8�Ç.a�� .PS./v{M/2GNS �� K Å#� K �� 9 8�Ç.a�� %IP|}`NDnGN+('>V«+(Y <)`BD3DiCwDH1H<r+(Y <)`NDn/2GB/0<)/2&(-x@NDH{M/2&J<)/0+.G �� 9 1h&JGk*,D7DFO�<)/2VT&J<>DF@o*If

� �� K �� K � �� 9 � Ã 8�Ç.a��+�.PyR`NDH'>Dn<)`NDnGN+('>VWO}1h&(G_*ED7@BDH~;GNDH@�8:O>DFD ��pP

�� Å VU&e�A � � A � Ã 8�Ç.a�� IP� � � Å VU&È�A <3= �

� � � � A � � 8�Ç.a�� #IP

|}`NDnDHO=<)/0VU&e<)DW8�Ç(a��+�(PtS./0{(DFOF·�dY

� � �� Ç5Ã 8�Ç.a�� Æ P<>`NDFG <)`BD[@NDH{M/?&e<)/2+(G �� 9 +JY�/0GN/0<>/?&(-}1H+.GN@N/v<)/0+.G @N+MDFOuGN+J<uS.'>+�y /2G <>`ND[1F+.LB'>O>D[+JY1H+.VT9BLB<Q&J<>/2+.Gwa�

�]/0VT/0-?&('=-0f.�J&�@BDH{M/?&J<>/2+.G �� /0GW<>`ND L \ <)`W9N'>+J~;-2D�8�/0GNO=<>Dh&(@W+(Yw/2G�<)`NDR~;'>O�<t+(GND�P�1h&JG*,Dg<)'=Dh&J<>DF@ *If�1F+(GNO>/0@NDF'=/2GNS�<>`N/2O L \d<>`�9N'>+J~;-2Du&JOl<)`NDu/0GN/0<>/?&(-51F+(GN@N/0<>/2+.G�&(GN@�<)`ND1H+.GN1F-0LNO>/0+.GNO7&J'>Dl<)`BD�O)&(VWD(a �¯G�&g'>Dh&J-�1F+.VW9NLB<)&J<)/0+.G�'=+.LNGN@]\d+(C�DH'>'=+.'>On&(9B9EDF&('s/2GDF&(1Q`^9N'=+(~;-0D(ac|}`;&JGN�pOr<)+W<)`ND3-2/0GNDh&J'>/0<¯fU+(YR8 Ç.a��BÇÈPt<)`ND3<)+(<)&(-ADF'='>+.'XO=<)&hf]Or*E+(LNGN@NDH@/vYc8 Ç.a�� Æ Pt'>DHVU&J/2GNOc{J&(-0/2@�a�d<7/0O�Dh&JO=f^<>+uO>DHDl<)`;&J<�/0Y�<>`NDlDF-0DFVWDFGI<)O�/2G�<)`BDlVU&J/2G^@B/?&(S.+(G;&(-�+(Y5<)`ND�VU&J<>'>/ �� &('>DnGN+(G]\¯GNDHSI&J<>/0{.D7/ a�DJa�/0Y � � Ç¼ Ã 8�Ç.a��NÇÈP

<>`NDFGT@NLNDr<>+g8 Ç.a�� #IP�ytDr`;&h{.D � � � � � Å Ç.a�|}`MLBO78�Ç(a��NÇ�P�/0Oz&�O>L �T1H/2DHGp<t1F+.GB@N/0<>/2+.G�Y:+.'<>`NDnO=<Q&J*N/2-0/0<¯fT+(Y�VWDH<>`N+M@�8 Ç.a ¼.¼ Pia�ADH<RLNORO=DFD7yR`NDH<>`NDF'}<>`N/2O}1H+.GN@N/v<)/2+(Gg/2OR&(-0O>+�GNDH1FDHO>O)&J'=f.az|}`NDnGNDH1FDFO=O)&('�f_1F+.GN@B/v\<>/2+.GT'>DFKpLN/0'>DHOt<)`;&e<tY:+.'5<)`ND�-2Dh&JO=<cGB+.'>V +(Y�<>`NDsVT&J<)'=/v� � <>`NDsGN+(G]\¯DHKMLN&(-2/v<¯fk8�Ç.a�� Æ P`N+(-2@NOHa �O�Y:+.'z&(GIf�VT&J<)'=/v��GB+.'>V /v<5`N+.-0@NO � 8 � P Å VT&e� �� A � �� IyR`NDF'=D � Aw&('>D<>`NDnDF/2S(DFGI{J&(-2LNDHO}+(Y <)`NDnVT&J<)'=/v� � �N<)`NDnGNDH1FDFO=O)&('�fk&(GN@oO>L �W1H/2DFGI<r1F+.GB@N/0<>/2+.Gu/0O�� A � � Ç B#Å Ç.Ã ¼ Ã ÃD8 � Ç 8�Ç.a�� ¼ P|}`NDnVT&J<)'=/v�[8�Ç.a�� ¼ Pt`N&(ORDF/2S(DFGI{J&(-2LNDHO� A Å Ç � � � O=/2G ¶ B��¼ 8 Ã B#Å Ç(Ã ÃD8 � Ç5Ã

<>`NDFGo<)`NDn1H+.GN@N/v<)/2+(G�8�Ç.a�� ¼ Pt/0O}DFKpLN/0{J&(-0DFGI<}<)+�<)`BD31H+.GN@N/v<)/0+.G�8�Ç.a��NÇÈP�a�dY <)`NDn+.'=/2S./0G;&(-,DFKpL;&J<>/2+.G�8�Ç(a0Ç �.Pq`;&(ORGN+.GM\¯1F+(GNO=<)&(GI<r1H+]D��W1F/2DHGI<)O�8 &(O}Y:LNGB1H<)/0+.GNO+(Yr°EP�<>`NDFG®<)`NDk'>+�yROW+(Ys<)`BDkVT&J<)'=/v� � @N/vCwDH'Fa |}`NDHG½<)`BDkDH/2S.DHGp{J&(-0LNDFO�1F&(GNGN+(<*,D�D��]9N'>DHO>O>DH@�&(G;&(-vfM<>/21F&(-2-vf.�]<>`NDHf_VlLBO=<r*EDnY:+.LNGN@kGpLNVTDH'>/01h&(-0-0fj8:O>DHD�1Q`;&(9]<)DF' ��pPi�yR`N/01QÙ/0OqD��B9,DFGBO>/0{(D�Y:+.'5-?&J'>S.D 8�a�|}`NDFGg/v<z/2Oz*EDi<><)DH'z<>+�LNO=Dr<>`NDrO=L �W1F/0DFGI<cO�<Q&(*N/0-2/v<¯f1H+.GN@N/v<)/2+(G�8�Ç.a�� Æ PqyR`NDH'>D � � � /2O}@NDi~;GNDF@^&(1F1H+.'>@B/2GNS�<)+^8�Ç(a�� #.Pia�]+.VWDH<>/2VWDFOw<>`ND�O=<)&(*N/0-2/0<¯fX/0O�DFO�<)/2VT&J<>DF@7*Ifs<)`BD@x+(LN'>/0DF'�8Z{.+.G�brDHLNVT&(GNGxPwVWDH<>`N+]@wa��Du@NDFO=1F'=/2*,DU<)`N/0OlVWDH<)`B+]@�*N'=/2D��Nf�Y:+.'3<)`NDuD��]9N-2/01F/0<�@N/0CEDF'=DFGI<)/2&(-tO=1Q`NDFVWD�8�Ç(a ¼.¼ Pia|}`N/0OsVWDH<)`B+]@[/0S.GN+.'=DFOs*,+.LNGN@N&('=f^1F+.GN@B/0<)/0+.GNO�yR`B/21Q`j/2OsGB+u9N'>+.*B-2DFV /2G�+(LN'71h&(O=D(�O=/2GN1HDs<)`NDn*,+.LNGN@;&J'=fu1H+.GN@N/v<)/2+(GNOcO>9,DF1H/0YZf#�FDF'=+W{J&(-0LNDFO}+JY º &J<c<)`BD3*,+.LNGB@;&('>/0DFOHa �¯G1F&(O>DHORyR`BDF'>Dn<)`BD3*,+.LNGB@;&('=fU1F+.GB@N/0<>/2+.GNOt/2G��;LBDFGN1HDn<>`NDnO=<)&(*N/2-0/0<¯fW<)`N/0O}VTDi<)`N+M@u`;&(O&U-0/2VW/0<>DF@o{(&J-2/2@B/0<¯f.a $ G�<)`NDl+J<)`NDH's`;&(GN@�<>`NDlVWDH<>`N+]@^LNO>/0GNSU<)`BDlO>9,DF1i<)')&J-�')&(@B/2LNO+(Y <)`BD3VT&J<>'>/v�U/2O}O�<)/0-2-E{J&(-0/2@��B&(-0<>`N+.LNS(`_O=+.VWDH<)/0VTDHOc@N/ �T1HLN-0<}<>+W&(9N9N-vf.a�O=O>LNVWDl<)`N&J<s<)`BDlO>+.-0LB<)/0+.G�+(Y�<>`ND�@N/vCwDH'>DFGI<>/?&(- DFKpL;&J<>/2+.GBOs1h&(G[*,DlyR'>/v<><>DFG[&(Oº K A Å��

K ±@A ��&(GB@^-2Di<�LBO�1Q`N+M+.O>D�+.GND�`N&('>VW+.GN/01FO�� V Y:'=+.V�/0<>O @;+.LB'>/2DH'R'>DF9B'>DFO=DFGI<Q&È\<>/2+.G�a �XDF'>Dq/I/2O�<)`NDz/2VT&(S./0G;&('�f�LNGB/0< ' <)+r&h{.+./0@�1F+(GBY:LNO>/0+.GnytDq@NDFGN+J<)D5<)`NDz/2VT&(S./0G;&('=f#

LNGB/0<X*Ifk/AyR'=/0<><>DFGk/2G_+.'>@N/0G;&('�fgY:+.GI<ryR`B/2-2D7yqD�@NDHGN+(<>D�<)`BD�/0GN@NDi�k*If B yR'=/0<=<)DFG_/2GVT&J<)`BDFVT&J<)/01h&(-BY:+(Gp<Fa�|}`NDrO>+.-0LB<)/0+.GT+JY�<)`NDX@N/vCwDH'>DFGB1FD�DHKpL;&J<)/0+.GU/0Ot&JO>O>LBVTDH@g/2G�<)`NDY:+.'=V � [ �� V_&(GN@�yqDgyc&(GI<�<>+�~;GN@ 1F+.GB@N/0<>/2+.GNO3Y:+.'�<>`NDuDi�]9N'=DFO>O=/2+.G /0G � GB+(<l<)+S.'=+�y 8��ÀVT&hfu*ED71H+.VW9N-2D��;P�a��D39BLB< º K A Å � K�� A R 8�Ç.a�� IP/0Gp<>+k8�Ç.a ¼.¼ P�� Å;G > : ¶�·

� Q K`_ � T � �� A R Å 8�Ç � ¼ � P � K�� A R » � 8 � K�� Q Ac= � T R » � K�� Q A _ � T R P XYZ<)DF'}O=/2VW9N-2/v~;1h&e<)/2+(GUytDnS.Di<

� � Å Ç � � � O=/2G ¶ 8 Ç¼ � : PwÃ&(GB@o<>`NDn1F+.GB@N/0<>/2+.G � � � � � Ç3S(/0{.DHO � � �¶ |�&J*N-2D�Ç.a ¼ ·54s/vCwDH'>DFGB1FDnO>1Q`NDHVTDU8�Ç(a ¼.¼ Pi�NDH'>'>+('}9N'>+.9N&(SI&J<>/2+.GgY:+.' � Å �¶º K _ �A Å �¶ 8 º K Ac= � » º K A _ � P

LlÅ � � >]Ç % Æ � > � Æ � � > � Æ � > � Æ � >]Ç %LlÅ � Æ � > � Æ � � > � Æ � � > � Æ � > � ÆLlÅ ¼ Æ Æ � > � Æ � > ¼ Æ � > � Æ ÆLlÅ Ç Æ Æ Æ � > ¼ Æ � > ¼ Æ Æ ÆLlÅ Æ Æ Æ Æ Æ � Æ Æ Æ Æ|}`ND_DF'='>+.'�9N'=+.9;&(SI&e<)/2+(G�/2O�/2-0-2LNO�<)'>&J<)DH@�/2G |�&J*N-2DHO_Ç(a ¼ &(GN@ Ç.a��Ba |}`NDo/2GN/v<)/?&J-DH'>'>+('3/0G�&_O=/2GNS.-0D�GN+M@ND�/2O7@NDHGN+(<)DH@�*If � aT|}`BDW~;'=O=<31h&JO>DW/2O7Y:+.' � Å �¶ &(GN@j<)`ND@NDi{M/?&J<>/2+.Gu/0Oc@;&(VW9EDH@�a �¯Go<)`ND7+(<>`NDF'}1F&(O>D � Å Ç Æ &JGN@u<)`ND7DH'>'>+('}S.'>+�yRORKpLN/21Q�p-0f(abr+J<)Dc<)`N&J<�Y:+.'�<>`ND}O=<)&(*N/2-0/0<¯f3+(Yx<)`BD}@N/0CEDF'=DFGN1HDXO=1Q`NDFVWDR/0<�/2O�GNDH1FDFO=O)&('�f�<)`;&e<�<)`ND+.'=/2S./0G;&(-I@N/vCwDH'>DHGp<>/?&(-MDFKpL;&e<)/2+(GNO�&('=DcO=<)&(*N-2Dq/2G�&s1HDF'�<Q&(/0GlO>DHGNO>DJ�M/ a�DJa�&�O=VU&J-2-M1Q`;&(GNS.D/0Go<>`NDn/2GN/v<)/2&(-E1H+.GN@N/v<)/0+.Gu'>DHO>LN-v<)OX/2G_&�O>VT&(-2-E@NDH{M/?&e<)/2+(G_/0Gu<)`NDnDi�B&(1i<�O=+.-2L]<)/2+(G�a�|#+O=`N+�y�&JG^Di�B&(VW9N-0D3yR`NDH'>D�<>`N/2Or/2OXGN+(<r<)`ND�1h&(O=D(�w1H+.GNO=/2@NDH'r<)`BD�@N/vCwLNO=/2+.GkDFKpL;&J<>/2+.G/0G_*N&(1Q�Iyc&('=@k<>/2VWD ¹ º¹ � Å � ¹ ¶�º¹ ° ¶yR`N/01Q`�ytDuS(DH<lY:'=+.V 8 Ç.avÇ �IP3*If�1Q`;&(GNS./0GNS � <)+ � � a�br+�y <)`NDuVWDH<>`N+M@ 8�Ç.a ¼.¼ Pn/2OLNGBO=<Q&J*N-2D7Y:+.'R&(GIf � Æ &JGN@^&�O=/2VW/2-?&J'q'=DFO>LB-0<X`N+.-0@NOcY:+.'cY:LN'�<)`NDH'XVWDH<>`N+M@NOFa

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�� "!$#&% �� "!6#��)*�,+ - / 13 54 #�7�ADH<oLBOu@N/2O=1FLNO=Ok&�VW+.'=D�1F+.VW9N-0/21h&e<)DF@ÀY:+.'>V +(Yn<)`ND[@N/vCwDH'>DHGN1FD[Y:+.'=VlLN-?&�yR/0<)` &9;&J')&(VWDH<>DF'��

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K _ �A�= � � ¼ º K`_ �A » º K`_ �A _ �: ¶ » 8 Ç ��7P º K Ac= � � ¼ º K A » º K A _ �: ¶ 8�Ç.a�� %IP

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¼ ºK`_ �A _ � Å �

¼ ºK Ac= � » 8 Ç � � P º K A » �

¼ ºK A _ � 8�Ç.a��+�IP

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¼ 8 Ç � ¼ �7P 8�Ç.a��+#IP@;+.'�� Å Æ <>`N/2ORS./v{.DHOr&JSI&(/2Gu1H+.GN@N/v<)/0+.G�8�Ç.a��NÇÈP�a�rGB-2/2�JD�<)`NDjD��B9B-2/21H/0<uVWDH<>`N+M@��XyR`BDF'>D�Dh&J1Q` {J&(-0LND[+(Yn<)`NDjGNDiy 9N'=+(~;-0D � K`_ �yt&(O}1F+(VT9NL]<)DF@oD��B9B-2/21H/0<>-0fW+.GNDn&JYZ<>DF'R&(GB+(<)`NDH'tY:'>+(V�<)`BD7+.-2@u9N'=+(~;-0D � K �B<>`ND7DFKpL;&e\<>/2+.G®8 Ç.a�� %IPXY:+.'�� Å Æ '=DF9N'=DFO>DHGI<)Ol&uO�f]O�<)DHV +(Yt-0/2GNDF&('�DHKpL;&J<)/0+.GNO7Y:+.'sLBGN�pGN+�yRGNOº K`_ �A Ã B#Å Ç.Ã ¼ Ã ÃD8 � Ç.Ã]yR`N/21Q`_VlLNO�<r*,DnO>+.-v{.DH@kO=/2VlLN-v<Q&(GBDF+.LNO=-0f(a

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6��]9N-2/01F/0<cVTDi<)`N+M@�8�Ç.a ¼.¼ P ')&(GB�I\¯br/01F+.-0O>+.G rG;&(-0fp<>/21VWDH<>`N+M@ O>+.-0LB<)/0+.G�8�Ç.a�� .P� Å �� 9 � Å �¶GWÅµÆ Æ.Æ Ç GWÅ Æ Æ.Æ � G�Å Æ Æ Ç� ÅµÆ Æ Ç Æ a � � %+� Æ a�� Æ.Æ(Æ Æ a�� % #]Ç Æ a�� ÅµÆ Æ ¼ Æ a�% � #BÇ Æ a�� Æ.Æ(Æ Æ a�% # ¼ Ç Æ a�% � Æ #� ÅµÆ Ç Æ Æ a�� Æ � % Æ a�� Æ �MÇ Æ a�� Æ % # Æ a�� Æ ¼ Ç|#&(*N-0D7Ç.a�%]· +.VW9;&('=/2O>+(GW+JYE<>`NDRDi�]9N-2/01F/v<5&(GN@�<)`ND ')&JGN�.\ br/01F+.-0O>+.G�VWDH<>`N+M@NOFa��z&J-v\LNDHOR/2Gu<)`NDn9,+./2GI<}° Å Æ ��&J'>D7O>`B+ÈyRG�8 :gÅ Æ ÇÈP

<>DFGg<)/0VTDHOcVW+.'>Dr9N'>+(~N-2DFOH�;&(-v<)`N+.LBS.Ù<)`BD71F+.VW9NLB<)&J<)/0+.GTyt&(ORDh&(O=/2DH'c*EDH1h&(LBO>D7/0<tyc&(OGN+J<gGNDH1FDFO=O)&('�f <)+�O>+.-v{.D�&�O=fMO=<>DFV +(Ys-2/2GBDh&('WDFKpL;&J<>/2+.GBOUyR/0<>` &�<)`B'>DFD�\¯@N/2&(S.+.GN&(-VT&J<)'=/v�Ea � `NDHGÀyqD^1F+(VT9;&J'>Dg<)`BDkGpLNVl*,DF'�+(Ys&('>/v<)`NVWDH<>/21g+(9EDH')&J<>/2+.GNOl<>`NDFG®<)`ND '>&(GN�.\ bX/21F+(-2O>+(G_VWDH<>`N+M@_/0O}VT+('>D7D �W1H/2DFGI<Fa�� C4 #&+ �� + %(! "%*+��/ � ��]+RY�&('H�eyqDt`;&h{(Dt1F+(GNO>/0@NDF'=DF@�<¯yq+J\¯9B'>+(~;-0D5VTDi<)`N+M@NO�<)`;&J< 1H+.GI<Q&(/0G � K &(GN@�� K`_ � +.GN-vf.a��D�`;&h{.D�GN+(<>DF@j<)`;&J<7<>`ND�@N/2O=1F'=DH<)/ �h&J<>/2+.G[/0G � `;&JOn<>`ND�S.'>DF&J<)DHO=<31F+(Gp<>'>/0*NLB<)/0+.G�<)+<>`ND�DF'='>+.'H��G;&(VWDF-vf a 8 G PiÃ�+.' a 8 G ¶ P�/2GÔ>9,DF1F/2&(-�VWDH<>`N+M@NOFa3|}`N/2O7VWDh&JGNO�yqD�VlLNO=<LNO=D3&WO=VU&(-0-E<>/2VWDsO=<>DF9 G &(GB@_<>`N/2O}'=DFKpLN/2'=DFOX&�-2+.GNS�1H+.VW9NLB<Q&e<)/2+(Gg<)/2VWD(a��GN+(<>`NDF'9,+.O>O=/2*N/0-2/v<¯fU/0O�8:O>/0VT/0-?&('=-0f�<)+ �@N&(VTO}Y:+.'=VlLN-2&(OF�NO=DFD31Q`;&(9B<>DF'&��pPi�;<)+T&(9N9N'=+h�B/0VU&e<)D<>`ND�@NDH'>/v{(&e<)/0{(D��

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¼ G Å º K`_ �Ac= � � ¼ º K`_ �A » º K`_ �A _ �: ¶ 8�Ç.a�� Æ P

|}`N/0OR1h&(Go*,D3'=DHyR'=/0<><>DFGo<)+� ¼ � º K`_ �Ac= � » 8 � » � � P º K _ �A � ¼ � º K`_ �A _ � Å � º K A � º K = �A 8�Ç.a��]ÇÈP�]/0VT/0-?&('=-0f�&�Y:+.LN' \¯9N'=+(~;-0Ds/2VW9N-2/01F/v<qY:+.'=VlLN-2&�/2O��% � º K _ �Ac= � » 8�Ç.Ç » Ç ¼ � P º K`_ �A � % � º K`_ �A _ � Å Ç � º K A � # º K = �A »À¼ º K = ¶A 8�Ç.a�� ¼ P&(GB@o~NG;&(-2-vfu&l~N{(Di\¯9B'>+(~;-0Dn/2VW9N-2/01F/0<zY:+.'=VlLN-?&�/2O�3Ç ¼ � º K _ �A�= � » 8 ¼ � »3¼ � � P º K`_ �A ��Ç ¼ � º K`_ �A _ � Å � � º K A � � % º K = �A » Ç % º K = ¶A � � º K = -A 8�Ç.a�� IP@;+.'=VlLN-?&JOR8�Ç.a��]ÇÈP��E8�Ç.a�� ¼ P�&(GB@[8�Ç(a � �.P�`;&h{.Dr<>`NDXDF'>'=+.' a 8 G ¶ » : ¶ PiÃ a 8 G - » : ¶ P�&(GB@� 8 G � » : ¶iP�'>DHO>9�a @;'=+.V <>`ND�1F+.VW9NLB<)&J<)/0+.G;&(- 9E+(/2GI<n+(Yz{]/0DHy<)`NDHO>D�Y:+.'>V�LN-?&(Os&('>DGN+J<�VlLN1Q`�VT+.'=Dq@B/ �W1FLN-v<#<>`;&(G�&rO>/2VW9N-0Dz/0VT9B-2/21H/0<�Y:+('>VlLN-2&�8 Ç.a�� .P ' <)`NDq'>/2S(`p<�\¯`;&JGN@]\O=/2@NDs+JYA<)`NDsO�fMO=<)DHV«+(Y -2/0GNDh&J't&(-0S.DF*B')&(/01rDHKMLN&J<)/0+.GNOtyR/v<)ò&�<>`N'>DHDi\¯@B/?&(S.+(G;&(-,VU&J<>'>/ �1H+.GI<Q&(/0G &[Y:Diy«VW+.'>DT<)DF'=VTOHa�| +�O�<Q&('�<�ytD_VlLNO�<�9N'>DH9;&('=Dg<)`N'=DFDo/2GN/v<)/2&(-q9B'>+(~;-0DFO8:*EDHO>/2@BDFOq<>`ND�/0GN/0<>/?&(-]1F+.GB@N/0<>/2+.GxP�LNO=/2GNS�&(GN+(<>`NDF'zVWDH<)`B+]@WyR/0<)Ù&�O=L �W1F/2DHGI<)-0fWO=VU&(-0-DH'>'>+('Fa|}`NDH'>D�D��]/2O=<s&(GN+(<>`NDF'XVlLN-v<)/ \¯O=<>DF9uY:+.'=VlLN-?&JORyR`BDF'>D3<)`ND�&(9N9N'=+h�B/0VU&e<)/2+(G_+JY � �

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yR`NDH'>D�nÅ ¿ - :¿ � : � ¿ ¶ Ã �

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¹ º¹ � Å � Â � Ã=°�Ã º Ã ¹ º¹ ° Ä ¹ ¶Qº¹ ° ¶ »��MÂ � Ã>°�Ã º Ã ¹ º¹ ° Ä ¹ º¹ ° » � Â � Ã=°�Ã º Ã ¹ º¹ ° Ä 8�Ç.a�% �IP8Z<)`ND�-?&(O�<X<¯yq+U<>DF'>VWO�1H+.LN-0@^*,D�yR'>/v<><>DFG�&JO�&UO=/2GNS(-2D7<)DH'>V_�E*NL]< � &(GN@ � &J'>D�+JYZ<)DFG/0GN@NDF9,DFGB@NDFGI<r+(Y ��

� V �NO=+W<>`N/2OcY:+.'=V�/0OXVW+.'=Ds1F+.GI{(DFGN/0DFGI<�P�a�]+.VWDs&JLB<)`N+('>OcLNO=Ds<)`NDX<)DH'>V KMLN&(O>/ \¯-2/0GNDh&J'zY:+.'qO=fMO=<>DFVWOcyR/0<>`g1F+MD �W1F/0DFGI<)Oc<>`;&J<@N+�GN+(<u@NDH9EDHGN@ +.G ~;'=O=<u@BDF'>/v{J&J<)/v{.DFO ' <)`BD^<)DH'>VW/2GN+.-0+.S(f�/0OUGN+J<gLNGN/vY:+.'>V_a �d<U/2O&(9B9N'>+.9B'>/?&e<)Dr<>+�O)&hfU<>`;&J<}LBGN-2/0�(Ds-0/2GNDF&('qDHKpL;&J<)/0+.GNOH�B<)`NDH'>D7/0OcGN+�S.DHGNDF'>&(-�&(9B9N'>+I&J1Q`<>+^GN+.GB-2/2GBDh&('n9;&('>&(*,+.-2/01�DFKpL;&J<>/2+.GNOHa_6z&J1Q`�GN+.GN-0/2GNDF&('nDFKpL;&J<>/2+.G 8�+.'�&kO�fMO=<)DHV +JY<>`NDFVUPr/2O�LNO>L;&J-2-0f^&gLNGN/0KpLND�9N'>+.*B-2DFV Y:+.'sGpLNVWDF'=/21F&(-�O=+.-2LB<>/2+.Gwa3|}`pLNOnyqD�@N/2O=1FLNO=O&(-0S.+.'=/0<)`BVTO�<>`;&J<q+(YZ<)DHGWyq+.'=�W/0GTDHGNS./0GNDFDH'>/2GBS�&(9B9N-2/01h&J<>/2+.GNOH�.<)`NDifT&('>DXGN+(<z`N+�yqDH{.DH''=DF-2/2&(*N-0D�'>DH1F/09EDHORY:+('R&(-2-�9B'>+.*N-0DFVWOFa�� c� �� "!$#&%�%(' !$#��)*�,+F "%*+��/ ��dY;yqDc'>DH9N-?&J1FDc&J-2-pO>9;&e<)/?&J-M@BDF'>/v{J&J<)/v{.DFO�&(GN@lGB+.GN-2/0GNDh&J' 1H+]D��W1F/2DHGI<)O�/2G3<)`NDq+.-2@�9N'>+J~;-2D/0G_DHKpL;&J<)/0+.G�8�Ç.a�% �IPqyqDnS.DH<R<>`ND3&(9N9N'=+��]/0VU&J<>/2+.G

º K _ �A � º K AG Å � ��K Ã>°�AdÃ º K A Ã º K A _ � � º K A�= �¼ : " º K Ac= � � ¼ º K A » º K A _ �: ¶ »

» � ��K Ã>°�A¯Ã º K A Ã º K A _ � � º K Ac= �¼ : " º K A _ � � º K Ac= �¼ : » 8�Ç.a�% #IP» � ��K Ã>°�AdÃ º K A Ã º K A _ � � º K Ac= �¼ : " Ã B#Å Ç.Ã ¼ Ã ÃD8 � Ç5Ã

yR`N/01QÙ/0O5Y:'=+.V�<>`ND�1H+.VT9BLB<Q&J<>/2+.GN&(-B9,+./2GI<z+(YE{]/0DHy O=/2VW/2-2&('�<)+n<)`BDrD��B9B-2/21H/0<5VWDH<>`N+]@8 Ç.a ¼(¼ Pia+@;'>+(V <)`NDk�pGN+�yRG½{J&(-2LNDHOU+(Y º K 9 Ã º K � Ã Ã º K < /0<W/0OT9,+.O>O=/2*N-0D_<>+�1H+.VT9BLB<)D<>`ND�'>/0S.Ì<s`;&(GB@�O=/2@ND�+(Y5<)`ND�&(9B9N'>+h�]/2VT&J<)/0+.G�8 Ç.a�% #IP�&(GB@j<>`NDFG[yqD�1h&(GjS.Di<7Dh&JO>/2-vfº K`_ �A Y:+.' BzÅ Ç.Ã ¼ Ã ÃD8 �µÇ |}`NDl9B'>+.*N-0DFV +(Y5&J9N9N'>+h�]/2VT&J<>/2+.G_+(Y�<)`BD�*,+.LNGN@;&J'=f1H+.GN@N/v<)/2+(Gu/2O}DFKpLN/v{J&(-2DHGp<}<>+W<>`;&J<}Y:+.'}-0/2GNDF&('cDHKMLN&J<)/0+.G�a¼ Ç

�]/0VT/0-?&('=-0f^&(O�/0G�<>`NDU-0/2GNDF&('n1h&(O=D(��<)`BDUO=<>DF9NO : &JGN@ G /0G�<>`NDg&(9B9N'>+h�]/2VT&J<)/0+.G8 Ç.a�% #IP#1h&JGNGN+(<5*,D}1Q`N+.O=DFGT&('>*N/v<)'>&('>/0-0fn*,DF1h&JLNO>D}Y:+.'�O=+.VTDt1F+.Vl*B/2G;&J<>/2+.GBO�+(Y : &(GB@ G<>`NDR'>DF9B-?&(1HDFVWDFGI<�8�Ç.a�% #IP�/0OzLBGNO=<)&(*N-2DJa �rGB-2/2�JDc<)`NDX-2/0GNDh&J'�1h&(O=Dr/v<5/2O�GN+J<q9,+.O=O>/2*B-2Dc<)+S.Di<5O>/0VT9N-0Dc&(GN&(-0fp<)/01t1H+.GN@N/v<)/2+(G�+(Y,O=<Q&J*N/2-0/0<¯f.a |}`NDRO=<)&(*N/0-2/0<¯f3+(Y,GN+(GN-2/0GNDh&('#9N'>+(*N-2DHVTOVlLBO=<�*EDW<)DFO�<)DH@�Di�]9,DF'>/0VTDHGI<Q&(-0-0f.aU|}`N/2O�/2O3@N+.GNDW*If�1H+.VT9BLB<)/0GNS^&oY:DHy"O�<)DH9NO�Y:+.'{J&('=/2+.LNO3{J&(-2LNDHO�+(YR<)`NDuO�<)DH9 G �5<>`NDu/2GBO=<Q&J*N/2-0/0<¯fj1h&JG®*,DgO=DFDFG®1F-0Dh&('=-0f(a r-2O=+N��<)`ND1H+.GN@N/v<)/2+(G�+(YxO�<Q&(*N/0-2/v<¯f7VU&hfn{J&('=f3yR/0<>`�<)/0VTD � a @;+.'#DFKpL;&J<>/2+.Gu8�Ç.a�% #IP�<)`NDtGNDF1HDFO>O>&('=f1H+.GN@N/v<)/2+(G_+JY�O=<)&(*N/2-0/0<¯f[8 &(OR<)`ND3-2+�yqDF'X+.'>@BDF'R<)DF'=VTOX`;&h{.D�GN+UO=/2S.GB/0~;1F&(GI<r/0G��;LNDHGN1FD+.GoO�<Q&(*N/0-2/v<¯fNPz/2OG � Â ��K Ã>°�AdÃ º K A Ã \ X�� = \ X�� ¶ R Ä

: ¶ � Ç¼ 8�Ç.a�� Æ P

�¯G_8 Ç.a � Æ P <)`BDc*E+(LNGN@;&('�fl1H+.GN@N/v<)/2+(GNO�+(Yx<>`NDt~;'=O=<5�p/2GN@�&J'>Dc1H+.GNO>/0@NDF'=DF@ ' <>`ND}*E+(LNGN@]\&('�fU1H+.GN@N/v<)/0+.GNOtyR/v<)ù@NDH'>/0{J&J<>/0{(DFOcVT&hfU1Q`;&JGNS.Ds<)`BD71F+.GN@B/0<)/0+.GgO=LN*NO=<)&(GI<)/2&(-2-vf.a�|}`NDDHO=<)/0VU&e<)DU8�Ç.a�� Æ PcO>`B+ÈyROs<>`;&J<X<)`ND�&(1F1HDF9B<)&(*N-0D�O=<>DF9�O=/ �HD G VT&hfo/2GN@NDHDF@^{J&('�foyR/0<)`<>/2VWD � &(GB@o<>`N/2ORVlLBO=<R*,Dn<)&(�(DHG^/0Gp<>+�&(1F1H+.LNGI<habrD��M<h��yqD[LNO>D[<>`NDjDi�]9N-2/01F/v<gVWDH<)`B+]@8 Ç.a�% #IPWY:+.'o&�9N'=+.*N-0DFV yR/v<)` &��pGN+�yRG&(GN&(-0fp<)/01sO>+(-2LB<>/2+.G�a +.GNO>/0@NDF'}<>`NDn9;&('=<>/?&(-E@N/0CEDF'=DFGI<)/2&(-�DHKMLN&J<)/0+.G¹ º¹ � Å ¹ ¶�º¹ ° ¶ »

º¼ ¹º¹ ° » � º ¶ � = ¶ � � [ Â � O>/0G ¶ � ° » � � O>/0G ¼ � ° Ä 8�Ç.a��]ÇÈP

yR/v<)ù<)`NDn*,+.LNGN@N&('=fu1H+.GN@N/v<)/0+.Gº 8 Æ Ã � P Å º 8 Ç.Ã � P Å Æ 8�Ç.a�� ¼ P&(GB@o<>`NDn/2GN/v<)/2&(-E1H+.GN@N/v<)/0+.G º 8:°�Ã Æ P Å O>/0G � ° 8�Ç.a�� IP

�d<R/0OXDF&(O=fU<)+�1Q`NDF1Q�u<>`;&J<R<)`ND3&(GN&(-0fp<)/01sO>+(-2LB<>/2+.G�8ZY:+.'R&(GIf � P}/0Oº 8:°�Ã � P Å = � � [ O>/0G�° 8�Ç.a�� pP

|#&(*N-0D�Ç.a �lO=`N+�yROr'=DFO>LB-0<)OR1H+.VT9BLB<)DH@k*Ifu<)`BD3D��]9N-2/01F/0<cVTDi<)`N+M@�8:Y:+.' �}Å ÇÈPia�� c� �� %*+��/ � /2- � �� "!6#&% #�� %(7 13��*7 +?��/ |}`ND�D��B9B-2/21H/0<7VWDH<>`N+M@�/0OnDh&(O�f�<)+oLNO=D(� *NLB<3/0<n`;&JO�&uO�<)'>+(GNSkO�<Q&(*B/2-2/v<¯f^'=DFO�<)'>/01H<>/2+.GyR`N/01Q`j/2O7`NDH'>D�&uS.'>DF&J<)DH'7@N/2O>&(@B{J&(GI<Q&JS.Dl<)`;&JGjY:+('s-2/0GNDh&('�DFKpL;&J<>/2+.GNOH�A*EDH1h&(LBO>D�<)`NDDi{(&J-2L;&J<>/2+.G�+(Y�GN+.GN-0/2GNDF&('�Y:LNGN1H<>/2+.GBOq/0OqLNO=L;&(-0-0f�Di�]9,DFGNO=/0{(D(a ��Dr+(YZ<)DHGUO=9N-2/v<tGN+(GN-2/0G]\DF&('X<>DF'=VTOX/2GI<)+W<¯yt+U9;&('=<>OF·}&W-2/0GNDh&('}9N&('=<F�E1H+.GNO>/0@NDF'=DF@�+(Gk<)`BD�GNDiy 9N'>+(~N-2D�&(GN@�&

¼.¼

|#&(*N-0D�Ç.a��]· �XDHO>LN-v<)OUY:+('UDi�]9N-0/21H/0<TVTDi<)`N+M@ 8�Ç(a�% #.PT&(GN@½DFKpL;&J<>/2+.G8 Ç.a �MÇÈPi�c{J&(-0LNDFOº 8 Æ � ' � P Y:+.'c{J&('>/0+.LNOc{J&(-0LNDFO}+(Y : &(GB@ G:UÅ Æ Ç :gÅµÆ Æ � 6��B&(1H<rO>+(-2LB<>/2+.G�

GWÅµÆ Æ(Æ � GWÅµÆ Æ.Æ ¼ GTÅ Æ Æ.Æ Ç GWÅµÆ Æ.Æ Ç GWÅµÆ Æ.Æ.Æ � 8�DHKMLN&J<)/0+.G�8�Ç.a�� pP=PÆ a Æ Ç Æ a�# Æ � � Æ a�# Æ � # Æ a�# Æ % � Æ a�# Æ � � Æ a�# Æ % Æ Æ a�# Æ % ÆÆ a Æ � Æ a�% Æ � � Æ a�%]Ç Æ.Æ Æ a�%BÇ.Ç � Æ a�% Æ # % Æ a�%BÇ Æ � Æ a�%]Ç Æ �Æ a ¼ Æ avÇ � �NÇ Æ a0Ç � � � Æ avÇ � # # Æ avÇ � �BÇ Æ a0Ç � � � Æ a0Ç � � #Æ a�� Æ a Æ Ç � Æ Æ a Æ Ç # ¼ Æ a Æ Ç # % Æ a Æ Ç #BÇ Æ a Æ Ç # � Æ a Æ Ç # �GN+(GN-2/0GNDh&('R9;&J'=<�8:+.'s&T'>DFVT&(/0GN/2GNSW9;&('�<�P��E1H+.GNO>/0@NDF'=DF@[+.Gk<)`NDl+(-2@^9B'>+(~;-0D(ar6}a�SNa º,¶1F&(G�*EDRO>9B-2/0<�/2GI<)+ º K`_ � º K �IO>/0VT/0-?&('=-0f º - 1h&(G�*,D}O>9N-0/0<�/0GI<)+ º K`_ � 8 º K P ¶��I+.'X8 �� V P�¶51h&JG*,DRO>9N-0/0<�/0Gp<>+T8 ��

� V P K _ � 8 �� V P K Di<)1Ja��rDH'>DXO>LN9,DF'=O>1F'=/29B< ¼ +.'��nVTDF&(GNO�9,+�ytDH'F�pyR`N/2-0DcO>L]\9,DF'=O>1F'=/29B< L +.' L » ÇX@BDFGN+(<>DFO�@N/0O>1H'>DH<>/ �HDF@�<)/0VTDJa#|}`N/0O�<)'=/21Q�3/2O�1F&(-2-0DF@l-0/2GNDF&('>/ �h&J<>/2+.G�a|}`pLNOXDFKpL;&J<>/2+.G�8 Ç.a�% �IPt1h&(G_*,D�&J9N9N'>+h�]/2VT&J<>DF@u*Ifº K`_ �A � º K A

G Å � ��K Ã>°�A¯Ã º K A Ã º K A _ � � º K Ac= �¼ : " º K _ �Ac= � � ¼ º K`_ �A » º K _ �A _ �: ¶ »

» � ��K Ã>° K Ã º K A Ã º K A _ � � º K Ac= �¼ : " º K _ �A _ � � º K _ �A�= �¼ : » 8�Ç.a�� .P

» � ��K Ã=°�AdÃ º K A Ã º K A _ � � º K Ac= �¼ : " |}`NDq1F+MD �W1F/0DFGI<)O � Ã � Ã � &('>DzDH{J&(-0L;&J<)DH@�/0G3<>`NDt+.-0@�9B'>+(~;-0D L &(GN@�<>`NDq@BDF'>/v{J&J<)/v{.DFO � � � V �&(GB@ ��

� V &J'>Dz&(9N9N'=+h�B/0VU&e<)DF@n/0Gn<>`ND5GNDHy�9N'>+J~;-2D L » Ç.a�|}`NDz@N/0CEDF'=DFGN1HDzO=1Q`NDFVWD�8�Ç.a�� .P/0O�&J1H<)LN&(-2-vf[&(G�/2VW9N-2/01F/v<�O=1Q`NDFVWDg&(GB@�/v<�S(/0{.DHO�&oO=fMO�<)DFV +(Yt-2/0GNDh&('7DHKpL;&J<)/0+.GNO7Y:+.'LNGB�MGB+ÈyRGBO º K _ �9 Ã º K _ �� Ã Ã º K`_ �< 8�/0GN1F-0LN@N/0GNSk*,+.LNGB@;&('=f�1H+.GN@N/v<)/2+(G�'=DF9N-2&(1FDHVTDHGp<QPia|}`N/0On/2O3&o<>`N'>DHDi\d@N/?&(S(+.G;&(-�O�f]O�<)DHV &JGN@�/v<31h&(G�*EDWO>+(-0{.DH@�*If[Y�&(1i<)+.'=/ �h&e<)/2+(G�a �9]\9N'=+h�B/0VU&e<)/2+(GW8�Ç.a�� .P�/2OA/0VT9B-2/21H/0<EY:+.'�O>9;&J<>/?&(-I@BDF'>/v{J&J<)/v{.DFOHa r-0<>DF'>GN&J<)/v{.DF-vf � � � V � &(GB@ ��

� V1H+.LN-2@�*,DR&(9N9N'=+h�B/0VU&e<)DF@�*Ifl<>`NDX&�{(DF'>&(S.DR+(Y,<)`NDc{J&(-0LNDFO5/2Gl<>`NDR+.-2@�&JGN@�/2G�<)`NDRGNDiy9N'=+(~;-0DlO>/0VT/0-?&('=-0fu<)+u<>`ND ')&(GN�.\¯br/21H+.-2O=+.G[VWDH<)`B+]@�al6z&J1Q`�DHKMLN&J<)/0+.Gj1h&(GjLNO=L;&(-2-vf*,Dn-2/2GBDh&('=/ �FDH@u*Ifg{J&('>/0+.LNOcyt&�fMOH�x<>`NDnDi�]9,DF'>/0DFGN1HD�&JGN@k/0GI<)LN/v<)/2+(Gg/2O}/0VT9,+.'=<)&(GI<ha

¼ �

�� c� �� ' + 1?7 ! / #�7 +?��/ + %N) � 6�� 4�%��ADH<XLNO}<>'=fg<>+W'=DF9N-2&(1FD7DHKpL;&J<)/0+.G�8�Ç.a�% �IPt/0Gu9NLN'>D3/2VW9N-0/21F/v<5yc&hf.�x/ a�DJa

º K`_ �A � º K AG Å � K _ �A º K`_ �Ac= � � ¼ º K _ �A » º K`_ �A _ �

: ¶ »�� K _ �A º K`_ �A _ � � º K`_ �Ac= �¼ : » � K _ �A Ã

B�Å Ç.Ã ¼ Ã ÃD8#� Ç 8�Ç.a�� %IP|}`NDn1H+]D��T1H/2DHGp<>O � Ã � Ã � &J'>DsY:LNGN1i<)/0+.GNOR+(Y <)`NDnLNGN�pGN+�yRGNO � K _ � �;D(a SNa

� K _ �A Å � ��K _ � Ã>°�A¯Ã º K _ �A Ã º K _ �A _ � � º K`_ �Ac= �¼ : " 8�Ç.a�� .P

�MfMO=<>DFV 8�Ç(a � %.P�1F&(GW*EDXO>+.-v{.DH@g&(Oz&nO>DH<q+(YwGN+.GN-0/2GNDF&('�DFKpL;&J<>/2+.GBOF�pyR`N/21Q`�yR/2-0-N*ED@N/0O>1HLNO>O=DF@_-?&J<>DF'Fa��rDF'=DsytDs<>'=fT<)+�9N'=DF@N/01H<c<>`NDs{J&(-2LNDHOc+(Y � K`_ �A Ã � K _ �A Ã � K`_ �A *N&(O>DH@k+.G<>`NDl�pGN+�[email protected]�+(Yz&UY:Diy�-2&(O=<s9N'>+(~N-2DFOHa&�O=O>LNVW/2GNS º 8Z°�Ã � PiÃ � Ã � Ã � &('=DlO>L �W1H/2DFGI<>-0fO=VT+M+(<)`�Y:LNGN1i<)/0+.GNO5ytDr1h&(GTDi�M<)'>&(9E+(-?&J<>DX<>`NDX{J&(-0LNDFOz+(Y � K _ �A Ã � K`_ �A Ã � K _ �A -0/2GNDF&('>-vf�Y:+.'O=VU&(-0-E<>/2VWDsO=<>DF9 G Y:'=+.V�<)`BD3�pGN+�yRGk9N'>+(~N-2DFO L &(GN@�8 L � ÇÈPc&(1F1H+.'>@B/2GNS�<)+� K`_ �A � ¼ � K A � � K = �A 8�Ç.a�� IP

8�&(GN@ O>/0VT/0-?&('=-0f�Y:+.' � &(GN@ � Pia ��Du1h&JGÀD��]<>')&(9,+.-2&J<)DUY:'=+.V�VT+.'=Dg<)`;&JG �=LBO=<�<¯yq+9N'=+(~;-0DFOF�BD(a SNa5KMLN&(@N')&e<)/217D��M<)')&J9E+.-2&J<)/0+.GuS./v{.DFO� K`_ �A Å � K = ¶A � � � K = �A » � � K A 8�Ç.a�� #IP

r9N9N'>+h�]/2VT&J<>/2+.GU8�Ç.a�� %IP�/2O#/2VW9N-2/01F/0<F�h<)`pLNO�<>`NDcO�<Q&(*N/0-2/v<¯fn'>DFO�<)'=/21H<>/2+.G�/2O GN+(<�O=+sO>Di{.DF'=D8:/0Yq&(GIfBPn&JOnY:+('7Di�]9N-2/01F/v<7+.GNDJaW|}`BDWDH'>'=+.'7/2GI<)'=+]@BLN1FDH@�*IfjDi�M<>')&(9,+.-?&e<)/2+(G�/2O7VlLB1QÒ=VU&(-0-2DH'�<)`;&JG�<)`BDWDH'>'=+.'�+JYt-0/2GNDF&('>/ �h&J<>/2+.G[&JO�@N/0O>1HLNO>O=DF@�/0G�<>`NDT9B'>DH{M/0+.LNOnO>DH1H<)/0+.G�a�]+[yR`;&e<�/2Ol<)`BD_@B/2O)&J@B{J&(GI<Q&(S.Du+JYr<>`N/2O�&(9B9N'>+I&J1Q` � �d<�/2O�&[VlLB-0<)/ \¯O�<)DF9�VTDi<)`N+M@��VWDh&(GB/2GNSo<)`NDW~;'>O�<l+.GBDU+.'n<¯yt+[O�<)DH9NOlVlLNO�<�*,DU1H+.VW9NLB<)DH@�*If�&(GN+(<>`NDF'�VTDi<)`N+M@��DJa�SNa�*If_&(1i<)L;&J-AO>+.-v{]/0GNSl<)`BD3GB+.GN-2/0GNDh&J'cDFKpL;&J<>/2+.GBO�8 Ç.a�� %IPia�� c� �� 1?%��6��)�+ /21 � ) /21?1?%N)�+ /21 + %N)�� 4 %�¯GU<>`ND�-2&(O=<qO>DH1H<>/2+.GUyqDs@N/0O>1HLNO>O=DF@u<)`NDr9N'>DH@N/21i<)/0+.GU+(Yw<)`NDr1F+MD �W1F/0DFGI<)O � Ã � Ã � /2GW<)`ND9N'=+(~;-0D�8 L » ÇÈPia�|}`NDF'=D7/2Oc&JGN+(<)`BDF'tyt&hfE·�<>+l9N'>DH@N/21i<t<>`ND�{J&(-2LBDFOc+(Y �� K`_ � LBO>/2GBS�<)`NDD��B9B-2/21H/0<�VWDH<>`N+M@^8 Ç.a�% #IPi�.yR`BDF'>D º K`_ �A Å �º K _ �A Ã B#Å Ç.Ã ¼ Ã ÃD8 ��Ç |}`B/2O59N'>DH@N/21i<)DH@�� K`_ �A 1h&(G_*,D7O>LN*NO�<)/v<)LB<>DF@^/0GI<)+�<)`NDn1H+]D��T1H/2DHGp<>O � Ã � Ã � /2GoDFKpL;&J<>/2+.G�8 Ç.a � %IPi�NDJa�SBa�� K _ �A Å � ��K _ � Ã>°�A¯Ã �º K _ �A Ã �º K _ �A _ � � �º K`_ �Ac= �

¼ : " 8�Ç.a�� Æ P¼ �

|}`NDHG�8 Ç.a�� %IPt*,DF1F+(VTDHOº K`_ �A � º K A

G Å �� K _ �A º K`_ �Ac= � � ¼ º K _ �A » º K`_ �A _ �: ¶ » �

�K _ �A º K`_ �A _ � � º K`_ �Ac= �

¼ : » �� K _ �A ÃB�Å Ç.Ã ¼ Ã ÃD8#� ÇzÃ 8�Ç.a��BÇÈP

yR`N/01Q`j/2O7&gO�f]O�<)DHV /2G[-2/0GNDh&J'�DFKpL;&e<)/2+(GNOW8�/0GN1F-0LN@N/2GBSU*,+.LNGN@;&J'=f�1H+.GN@N/v<)/0+.GNOQPRyR/0<)`&l<)`B'>DFDn@N/2&(S.+.GN&(-�VT&J<)'=/v� ' <>`NDnO>+.-0LB<)/0+.Gu*EDH/2GNS�O=/2VW/2-?&J't&(OR/0Gg<)`NDn-2/0GNDh&J'c1h&(O=D(a� `;&J<k&(@]{(&JGp<)&(S.DHO^&(GB@µ@N/0O)&(@]{(&JGp<)&(S.DHOk`;&JOo<>`N/2OoVWDH<>`N+]@µ&(Oo1F+(VT9;&J'>DF@ <)+D��]<>')&(9,+.-2&J<)/0+.GgVWDH<)`B+]@NO78:yR`N/01Q`k1F&(Go*ED7'=DFSI&('=@NDF@_&(OR&�O=9EDH1F/?&J-�1h&(O=D7+(Y#9N'>DH@N/21i<)+.'\ 1H+.'>'=DF1H<>+.'5VTDi<)`N+M@NO)P � �d<z/0OzGB+(<5GNDF1HDFO=O)&('�fT<>+3O�<Q&('�<5yR/0<)`T&n@N/0CEDF'=DFGI<zVTDi<)`N+M@�/ a D(a<>`ND71F+.VW9NLB<)&J<)/0+.Gg1F&(GuO=<)&('=<}yR/v<)`g<)`BD7�MGB+ÈyR-0DF@NS(D3+JY <>`ND7/2GB/0<)/2&(-;1F+(GN@N/0<>/2+.Gg&(-2+.GBD(a�]+(VTDi<)/2VWDFOr<)`ND�VWDFVW+.'=fk'>DHKpLN/2'=DFVWDFGI<)O3&('=DlytDF&(�(DH'Fa �On+.9N9,+.O=DF@j<)+u<)`ND�-0/2GNDF&('D��]<>')&(9,+.-2&J<)/0+.GT<>`N/2Oq9N'>DH@N/21i<)/2+(Gg/2OcLBO>L;&(-0-0fW*,DH<><>DF'n8:DH{(DFGo<)`N+.LBS.`g<)`NDifU*,+(<>ò&('>Ds+JY+.'=@NDF' a 8 G P>P $ G�<>`NDg+(<>`NDF'l`N&(GN@�<>`NDg1F+(VT9NL]<Q&J<>/2+.G�<)/2VWDW1h&(G�S.'=+�yna �rO=/2GNS[&-2&('>S.DnO�<)DF9Ô>/ �HD G 8:Y:'=+.V�<)`BD�9,+./2GI<X+(Y�{M/2Diy +(Y�O=<Q&J*N/2-0/0<¯fu+(Y#<)`ND�Di�]9N-0/21F/v<RVTDi<)`N+M@xP/0O}GN+�9N'>+.*B-2DFV�*EDH1h&(LNO=D3<>`NDn/2VW9N-2/01F/v<qVWDH<>`N+M@�8 Ç.a��BÇÈPtDF-0/2VW/2G;&e<)DFOz<)`N/0OR/2G��;LBDFGN1HD(a�d<s/0Or1H-2DF&('r<>`;&J<XyR`NDFG[LNO=/2GNST<)`ND ')&(GN�.\¯br/21H+.-2O=+.G^VWDH<>`N+M@^/2GBO=<)DF&(@�+(YR8�Ç.a��BÇÈPyqDUVlLBO=<lDi{J&(-2L;&e<)D �� K _ �� ¶A Ã � � K`_ �� ¶A Ã �� K _ �� ¶A Ã yR`B/21Q`�1F&(G�*,DU@N+.GBDULNO=/2GNS^&(G�Di�]9N-0/21H/0<VWDH<>`N+]@jyR/0<>`�<>`NDUO�<)DH9�O>/ �FD G � Å G > ¼ � `NDHG�LNO=/2GNSo<)`N/0On9N'>DH@N/21i<)+.'7\r1F+.'='>DF1i<)+.'VWDH<>`N+]@kytD�1F&(G[1F+.VW9;&('=D �º K`_ �A &(GN@ º K`_ �A 8:9N'>DH@N/21i<)DH@�&JGN@[1F+.VW9NLB<>DF@�{J&(-0LNDFO)PX/2GDF&(1Q`�9B'>+(~;-0D(a ��D�yt&(GI<3<)`NDHO>D�{(&J-2LNDHOs<)+_*ED�1F-0+.O>DJa �dYq<>`NDHfj@N/vCwDH'7VlLN1Q`�ytD�1h&JGO=LN*NO=<>/0<>LB<)D º K`_ �A Y:+(' �º K`_ �A &(GN@ '=DF9,Dh&J<u<>`ND[1F+.VW9NLB<)&J<)/0+.G &(1H1F+.'=@N/2GBS�<)+ 8�Ç(a��BÇ�Pia|}`N/0O�VTDF&(GNO�yqDX'=DF9,Dh&J<�<>`NDR1F+.'='>DH1H<)+('zO�<)DH9��pO>/2VW/2-2&('>-vf3&(O�Y:+.'�+.'=@N/2GN&('=f�@N/0CEDF'=DFGI<)/2&(-DHKMLN&J<)/0+.GNOn8:O>DFD�� MP�a �d<cyt+(LN-2@u*,Ds<)+M+l@N/ �T1HLN-0<q<)+�9N'=+�{.Ds<)`BD71F+.GI{.DH'>S.DHGN1FDn+(Y�<>`N/2OVWDH<>`N+]@lY:+('�S.DFGBDF')&J- � Ã � Ã � &(GN@�&J'>*N/v<)')&J'=f�*E+.LBGN@;&('�fl1F+(GN@N/0<>/2+.GBOFa�|}`BD}Di�]9EDH'>/0DFGN1HD<>DF-2-0OcLNO}<)`N&J<R<)`N/0OR&(9N9N'=+I&(1Q`_LNO>L;&J-2-0fU1F+.GI{(DF'>S(DFOrY:+('}O>L �W1F/0DFGI<)-vfuO>VT&(-0- G a

�� c� �� % � + / �� %(+ � / � +.GBO>/2@BDF'n<)`NDWO=fMO=<>DFV 8�Ç.a�� %IPs/0GN1F-0LN@N/2GBSo<>`NDW*E+.LBGN@;&('�f�{J&(-0LND�'>DH9N-?&(1HDFVWDFGI<�&(O�&O�f]O�<)DHV�+(Y�GB+.GN-2/0GNDh&J'}DFKpL;&J<>/2+.GNO� K`_ �A º K`_ �Ac= � � ¼ º K`_ �A » º K _ �A _ �

: ¶ »�� K _ �A º K`_ �A _ � � º K`_ �Ac= �¼ : » � K`_ �A � º K _ �A

G » º K AG ÅµÆ Ã�8�Ç.a�� ¼ P

<>`MLBO� A 8 º K _ �Ac= � Ã º K`_ �A Ã º K`_ �A _ � P Å Æ Ã B#Å Ç.Ã ¼ Ã ÃD8 � Ç5Ã 8�Ç.a�� IP

¼ �

&(GB@_9,+.O=O>/2*B-2D7*,+.LNGN@;&J'=fu1H+.GN@N/v<)/2+(GNOº K _ �9 Å º K`_ �< Å Æ Ã 8�Ç.a�� pP

<>`;&J<n&(-0-2+�y£<>+uDF-2/0VT/0G;&J<>D º K _ �9 &(GN@ º K`_ �< Y:'=+.V DFKpL;&J<>/2+.G®8 Ç.a�� ¼ Pia rYZ<>DF's1Q`B+]+.O=/2GNS<>`ND�/0GN/0<>/?&(-r&(9N9B'>+h�]/2VT&J<)/0+.G º K _ � Z 9� Ã º K _ � Z 9¶ Ã Ã º K _ � Z 9<3= � �s<)`BD�GBDi�M<[&(9B9N'>+h�]/2VT&J<)/0+.G1F&(Gk*,D71F+(VT9NL]<)DF@_*Ifu<)`NDn/v<)DF'>&J<)/0+.G��8 � K _ � Z � P�� K`_ � Z � Å ��X8 � K`_ � Z � PwÃ 8�Ç.a�� .P

� K _ � Z � _ � Å � K _ � Z � » � � K`_ � Z � Ã 8�Ç.a�� %IPyR`NDH'>D

� Å��

¹ � �¹ º K`_ �� ¹ � �¹ º K`_ �¶ ��¹ � �¹ º K _ �<3= �aaa aaa

¹ � <@= �¹ º K`_ �� ¹ � <@= �¹ º K`_ �¶ ��¹ � <3= �¹ º K _ �<3= �

� "Ã � K`_ � Å

��º K`_ ��º K`_ �¶ aaaº K`_ �<@= �

�! " Ã � Å��

� �� ¶aaa� <@= �

� " @;'>+(V 8�Ç.a�� IP�yqD^1h&JG O>DHDk<)`N&J<T<>`ND!�.&J1F+.*N/RVT&J<)'=/v�� /2O�<>`N'>DHD^@N/2&(S.+.G;&J- a |}`NDbXDHy}<)+(G��O VWDH<)`B+]@n1F+(Gp{(DF'=S.DFO�&(-2VW+.O=<A&(-0yt&hf]O�/0G�&cY:Diy�/0<>DF'>&J<)/0+.GNOA*,DF1h&JLNO>D5ytD5`;&h{(D&n{.DF'�fUS(+]+M@T/0GN/0<>/?&(-B&(9N9N'=+h�B/0VU&e<)/2+(G º K A Ã B#Å Ç.Ã ¼ Ã ÃD8&��Ç |}`ND�@N/0O)&(@]{(&JGp<)&(S.DX/2O<>`NDnGNDFDH@_<>+TDi{(&J-2L;&J<>Ds<)`ND �.&(1H+.*N/AVT&J<)'=/v�Ea�r9[<>+_GB+Èy�ytD�1H+.GNO>/0@NDF'=DF@�+.GND�GN+(GN-2/0GNDh&('�9;&('=<>/?&(- @N/vCwDH'>DFGI<>/?&(-�DHKpL;&J<)/0+.G�a �¯GVW+.O=<�1h&JO>DFO�ytDT`;&h{.Du&_O=fMO=<>DFV +JY}9;&('�<)/?&J-�@N/0CEDF'=DFGI<)/2&(-5DFKpL;&J<>/2+.GNO�&(GN@�<)`NDHG�<)`ND�.&(1H+.*N/�VT&J<)'=/v�^Y:+.'7<)`NDTbrDiy}<)+.G� O3VTDi<)`N+M@�/0OnGN+k-0+.GNS.DH's<)`N'=DFDW@N/?&JS.+.G;&(- �A/0<nO�<)/2-0-`;&JO�&o*;&(GN@�O=<>'>LN1i<)LN'=D(a#��DU&J'>D�S.+./0GNSu<)+Ô=`N+�y"`N+�y &(9B9N'>+.9B'>/?&e<)D�-2/0GNDh&('=/ �F&J<)/0+.G8:O>+.VWDH<>/2VWDFOX1h&(-0-2DF@^KMLN&(O>/ \¯-2/0GNDh&J'>/ �F&J<)/0+.GxPq1F&(G[*,DlLNO>DH@[<)+U<)&(�(D�<>`ND�&(@]{(&JGp<)&(S.Dl+JY&l<)`B'>DFDn@N/2&(S.+.GN&(-�VT&J<)'=/v�Ea +.GNO=/2@NDH'X&�O�fMO=<)DHV +(Y#<¯yq+WDFKpL;&J<>/2+.GNO

¹ º�¹ � Å ¹ ¶ º�¹ ° ¶ » � 8 º � Ã º ¶ PwÃ � Å Ç.Ã ¼ �XO>/2GBS�<>`ND ')&(GB�I\¯br/01F+.-0O>+.GoVWDH<)`B+]@uyqD3S(DH<RY:+.' � Å Ç.Ã ¼º K`_ � Z A � º K Z AG Å Ç

¼ Âº K _ � Z Ac= � � ¼ º K`_ � Z A » º K _ � Z A _ �

: ¶ » ºK Z Ac= � � ¼ º K Z A » º K Z A _ �

: ¶ Ä » �K`_ �� Z A 8�Ç.a��+�.P

¼ %

�dY ytD3'>DH9N-?&J1FD7<)`NDnGN+(GN-2/0GNDh&('q<)DF'=V«*Ifg<)`BD3|#&hfM-2+.'}D��B9N&(GNO>/0+.G�K _ �� Z A Å � 8 � K A P » ¹ � 8 � K A P¹ º � º K`_ �� Z A � º K � Z A¼ » ¹ � 8 � K A P¹ º ¶

º K`_ �¶ Z A � º K ¶ Z A¼ Ã � Å Ç.Ã ¼ ÃyqDgS.Di<�&(1i<)L;&(-0-0f[<>`NDubrDiy}<)+.G ��OlVWDH<>`N+M@ 8:yR'=/0<><>DFG�/0G�&^@B/0CEDF'>DHGI<lyc&hfBP�&(GB@�<)`ND�.&(1H+.*N/qVU&J<>'>/ ��yR/0-2-q`;&h{.Do&�*;&(GB@®O�<)'=LN1H<>LN'>DuyR/0<>`�~N{.Do@N/2&(S.+.GN&(-2OU8:yR/v<)` &(9N9B'>+J\9N'=/?&J<>DU+.'=@NDF'=/2GNSk+(Y}<)`BDgLNGN�pGN+�yRGNOW&(GN@�<)`NDgDHKpL;&J<)/0+.GNO)Piaj4s+./0GNS^+.GB-0f�&^9;&('�<)/2&(--0/2GNDF&('>/ �h&J<>/2+.G

�K _ �� Z A Å � � 8 � K A P » ¹ � � 8 � K A P¹ º � º K`_ �� Z A � º K � Z A¼ 8�Ç.a�� IP

�K _ ��¶ Z A Å � ¶ 8 � K A P » ¹ � ¶ 8 � K A P¹ º ¶

º K`_ �¶ Z A � º K ¶ Z A¼ Ã<>`NDnO=fMO=<>DFV +(Y#DFKpL;&J<>/2+.GNO�8 Ç.a�� .PcO>9N-0/0<)O}/0GI<)+�<¯yt+W/2GB@NDF9,DFGN@BDFGI<�O=LN*NO�f]O�<)DHVTOH�wDh&J1Q`+.GBDRyR/v<)`T&s<)`N'=DFDX@N/?&(S(+.G;&(-NVT&J<>'>/v�Ea |}`NDr&(-2S.+('>/0<>`NV1h&(GW*EDRY:LN'�<)`NDH'z/0VT9B'>+�{.DH@T*IfLNO=/2GNS º K`_ �� Z A Y:+.'5<)`NDX1F+.VW9NLB<)&J<)/0+.G�+(Y � K`_ �� ¶¶ Z A &JGN@T<>+l&(-v<)DF'=G;&J<>DR<>`NDX+.'>@NDH'q+JY58�Ç(a�� .Pia�� ! #"?��")'A*��-,#�/%|}`NDWVWDH<)`B+]@�+(Yc-0/2GNDHOn/2OnO>+.VWDH<>/2VWDFOn1h&J-2-2DH@[<)`NDW@N/0CEDF'=DFGI<)/2&(-�@N/vCwDH'>DFGB1FDWVTDi<)`N+M@�a|}`N/0O�G;&JVTDq'>D �NDF1H<>O�<)`NDzY�&(1H<#<)`;&e<�yqDc'>DH9N-?&(1HDc9;&('�<)/2&(-p@NDF'=/0{J&J<)/v{.DHO�/2G�+.GNDc@B/2'>DH1H<>/2+.G*IfÀ@N/0CEDF'=DFGN1HD^Y:+.'>V�LN-?&(O�yR`N/0-2DkyqD[9N'=DFO>DH'={(Dj<>`NDFV /2GÀ<)`NDk+(<)`NDH'g@N/0'>DF1i<)/0+.G &(GB@1H+.GNO>/0@NDF'#<)`NDHV &(O�+.'=@N/2GN&('=f3@NDH'>/0{J&J<>/0{(DFOFa ��DcD��]9N-?&(/0Gl<)`ND}VWDH<>`N+M@lLNO>/0GNSn&sO>/0VT9B-2DKpL;&(O=/v\d-2/2GBDh&('qDFKpL;&J<>/2+.G

¹ º¹ � Å ¹ ¶�º¹ ° ¶7» ´�8 º P 8�Ç.a�� #IPyR/v<)ò*E+(LNGN@;&('�fu1F+(GN@N/0<>/2+.GBO}+(Y#<>`ND7~;'>O�<X�M/0GN@

º 8 Æ Ã � P Å º 8�Ç.Ã � P Å Æ Ã � Æ Ã 8�Ç.a�# Æ P&(GB@o<>`NDn/2GN/v<)/2&(-E1H+.GN@N/v<)/0+.Gº 8Z°�Ã Æ P Å Bc8Z°EPwÃ ° � 8 Æ ÃFÇÈP 8�Ç.a�#BÇÈP��D3'=DF9N-2&(1FD7<>`NDnO>9;&J<>/?&(-w@NDF'=/0{J&J<)/v{.D7LNO=/2GNSW&�@N/vCwDH'>DFGB1FD7Y:+.'>V�LN-?&

¹ ¶ º¹ ° ¶�� V VYX �

º 8Z°�Ac= � Ã � P � ¼ º 8Z°�AdÃ � P » º 8:°�A _ � Ã � P: ¶ Ã B#Å Ç.Ã ¼ Ã ÃD8 � Ç5Ã 8�Ç.a�# ¼ P

¼ �

yR`NDH'>Dn°�A Å BI: Ã B#Å Æ ÃhÇ.Ã ¼ Ã ÃD8 ��Dn@NDHGN+(<>Dº 8:°�AdÃ � P Å º A 8 � P 8�Ç.a�# �IPr-2+.GNSl{(DF'�<)/21F&(-A-2/0GNDFO38:O>DHD @#/2SNacÇ(a�%IPtyqDnS.DH<X@N/vCwDH'>DFGI<>/?&(-�DHKpL;&J<)/0+.GNO@ º Ad8 � P@ � Å º Ac= � 8 � P � ¼ º A 8 � P » º A _ � 8 � P

: ¶ » ´ Â º A¯8 � P Ä Ã B#Å Ç.Ã ¼ Ã ÃD8 ��Ç5Ã�8�Ç.a�# �pP*If�O=LN*NO�<)/0<>LB<)/0GNSu/2GI<>+uDFKpL;&J<>/2+.G®8 Ç.a�� #IPia3|#+uO>&J<)/0O=YZf^*E+.LBGN@;&('�f�DFKpL;&e<)/2+(GNO�8�Ç(a�# Æ Pi�/v<}/2O}DF&(O=fu<>+WO=DFDn<)`;&e<R/0<RVlLNO�<X*EDº 9È8 � P Å Æ Ã º <B8 � P Å Æ 8�Ç.a�# �.P

� � � � � QW[�T �^QW[�T � Q [�T �`QW[�T

� �V V � V � V�� V�� V �� °

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: ¶ " Ã B#Å Ç.Ã ¼ Ã ÃD8 � Ç 8�Ç.a�# �IP|}`NDH'>D_/2O�GN+�9N'>/0GN1F/09;&(-c@N/vCwDH'>DHGN1FD_*EDi<¯ytDHDFG O�fMO=<)DHV 8 Ç.a�# �pPl&(GN@ÀO=fMO=<>DFV 8�Ç(a�# �.Pia|}`NDoVWDH<>`N+]@ +(YX-0/2GNDHO�/2O�&[S.DFGBDF')&J-}&(9N9N'=+I&(1Q`®*E+J<)`�Y:+.'�-2/0GNDh&J'l&(GN@ Y:+.'�GN+(GN-2/0G]\DF&('�9N&(')&(*,+.-0/21�DFKpL;&J<>/2+.GBO�/2G�<¯yt+k{(&J'>/?&J*N-2DHOFa �O�fMO=<)DHV +JY}+.'>@B/2G;&('�fj@N/0CEDF'=DFGI<)/2&(-¼ �

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¼ #

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: ¶ 8 Ç.a0Ç Æ ¼ P��Dn@NDFGN+J<)D7<)`ND7{J&(-0LND7+(Y <)`NDnGpLNVWDF'>/01h&(-wO>+.-0LB<)/0+.Go&J<r&�S.'>/0@u9E+./0GI<º A Z K � º 8:°�A¯Ã>± K Ã � P Å º 8 B0: Ã L : Ã � G P 8 Ç.a0Ç Æ �IP

� Æ

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¶�

º A Z K Å º A Z K _ � � ¼ º A Z K » º A Z K = � 8 Ç.a0Ç Æ �pP|}`NDnO=/2VW9N-2DsD��]9N-2/01F/0<tY:+.'>VlLB-?&�<)`BDFG_*EDH1F+.VWDFO� _ � Å 8�Ç » � 8 � ¶V » � ¶� P=P � » a 8 G ¶ » G : ¶ PwÃ 8 Ç.a0Ç Æ �.P+.'}/0Go@NDH<)&(/2-0O

º _ �A Z K Å º A Z K » � 8 º Ac= � Z K � ¼ º A Z K » º A _ � Z K » º A Z K = � � ¼ º A Z K » º A Z K`_ � P 8 Ç.a0Ç Æ %IP|}`NDo+.'=@NDF'�+(YX<)`B/2O�VWDH<)`B+]@ /2O�1H-2DF&('>-vf a 8 G » : ¶iPl&JGN@ÀDF&(1Q`®9E+./0GI<�/2G�<)`NDoGNDiy9N'=+(~;-0Dr/0Ot1F+(VT9NL]<)DF@TY:'>+.V ~N{(D79E+(/2GI<)Oz/2GW<)`NDs+(-2@U9B'>+(~;-0D(a �d<t/2Oz9E+(O>O>/0*N-2DR<)+�@NDF'=/0{.D&�O>/0VT/0-?&('5Y:+.'=VlLN-?&� _ � Å 8�Ç » � � ¶V PH8�Ç » � � ¶� P � » a 8 G ¶ » G : ¶ PwÃ 8 Ç.a0Ç Æ �.P<>`;&J<XLNO>DHO #W9E+./0GI<)OR/2Go<)`ND3+.-0@_9B'>+(~;-0D3&(GN@k<>`;&J<X`;&(OR<)`BD�O>&(VTD3+.'=@NDF'r&(O}Y:+.'>V�LN-?&8 Ç.a0Ç Æ �.Pia�|}`NDq'>DF&(@NDF' /2O�/0Gp{M/v<)DF@3<)+X'>DiyR'>/0<>Ds8 Ç.avÇ Æ �.Pw/0G3<>`NDzY:+('>V O>/0VT/0-?&(',<)+�8�Ç.avÇ Æ %.Pia6�KpL;&J<)/0+.G�8�Ç.avÇ Æ %.Pt1h&(G_*ED7yR'=/0<><>DFGo*Ifu<)`NDnO=1Q`NDFVWD�

� 8 Ç � � � P ��&(GB@_O=/2VW/2-2&('>-vf�DFKpL;&J<>/2+.G�8�Ç.avÇ Æ �(Pq*Ifu<)`NDnO>1Q`BDFVWD� ¶

� ¶

� 8 Ç � ¼ � P� 8�Ç � ¼ � P 8�Ç � ¼ � P ¶ � 8 Ç � ¼ � P

� 8 Ç � ¼ � P

� ¶

� ¶�BÇ

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yR`N/0-2D�<>`ND #�9,+./0Gp<}Y:+('>VlLN-2&u8�Ç(a0Ç Æ �.Pt/2O}O�<Q&(*N-0DsY:+.'� � Ç

¼ 8 Ç.a0Ç Æ #IP�dYzytD�<Q&(�JD � Å �

�Ã�<)`ND�+('>@NDH'3/0GN1F'=Dh&(O=DFO7<)+ a 8 G ¶ » : � P7&(GN@[<>`N/2OsY:+.'=VlLN-2&U/2O&(9B9N'>+.9B'>/?&e<)D�Y:+.'�9N'>DH9;&('>/0GNSu9N'=DF1F/0O>D�O=<)&('=<>/2GNSu9B'>+(~;-0DFO�Y:+('7VlLN-0<>/#9B'>+(~;-0D�VTDi<)`N+M@NO8Z<)`N/0Ot/2Oz<)'=LNDsY:+.'tDHKpL;&J<)/0+.Gj8 Ç.a�# #IPz+.GB-0fBPia��M<>'>/01H<cO�<Q&(*B/2-2/v<¯f�1F+.GB@N/0<>/2+.GNOs8�Ç.avÇ Æ �.Pz&(GB@8 Ç.a0Ç Æ #IP7'>DFKpLN/0'>DgO=VU&J-2-�<)DHVT9,+.')&J-qO�<)DF9�O=/ �HD G '>DHO>LN-v<)/0GNS�/2G�&^-2+.GBS^1F+(VT9NL]<Q&J<>/2+.G<>/2VWD5yR`B/21Q`l/0G�<)LB'>G�-0/2VW/0<>O�<)`NDqLNO)&(*B/2-2/v<¯f7+(Y;D��]9N-2/01F/0< VWDH<>`N+]@BOc8 Ç.a0Ç Æ �.P�&(GN@o8 Ç.a0Ç Æ �.PY:+.'rGpLNVTDH'>/01h&(-#O>+.-0LB<)/0+.G^+(Y�<>`N'>DHD�@N/2VWDFGBO>/2+(G;&(- 9N'>+.*B-2DFVWOFa#@x+('�Y:+.LN'r@N/2VWDFGNO=/2+.GN&(-9N'=+.*N-0DFVWO�<)`NDzO=<)&(*N/2-0/0<¯f�'>DFO�<)'=/21H<>/2+.GBO#&J'>D5DH{(DFGlO�<)'>+(GNS.DF'Ha $ Gn<)`NDz+(<)`BDF'�`;&(GN@w�.&R*N/2S&(@]{(&JGp<)&(S.D7+(Y#Di�]9N-0/21H/0<}VWDH<>`N+]@BO}/2Oc<)`BDF/2'}S(DFGNDH')&(-0/0<¯fu&JGN@oDh&(O=D3+JY�LNO=DT8�DH{J&(-0L;&J<>/2+.G+(Y#'>DH1FLN'='>DHGp<XY:+.'=VlLN-?&JOQPia

@�/2S(LN'>DTÇ.a �M· �¯-2-0LNO=<>')&J<>/2+.Gk+(YzDi�]9N-2/01F/v<sY:+.'>V�L]\-?&(O38 Ç.avÇ Æ %IPt&JGN@�8 Ç.avÇ Æ �.P4sL @;+.'=<�&(GN@ @;')&(GN�JDF-N@BDF'>/v{.DH@U&sO�<Q&(*N-0D}Di�]9N-0/21F/v<�VWDH<>`N+]@�*If�<Q&(�p/2GBSW8�O>/0VT/0-?&('=-0f&(O}Y:+.'R&�O=/2GNS.-0DsO>9N&J<)/2&(-�1F+M+.'=@N/2G;&e<)D�Pq<>`NDnLNGNO�<Q&(*N-0D �X/01Q`;&('>@BO>+.GuY:+.'=VlLN-?&

º _ �A Z K Å º = �A Z K »À¼ � 8 � ¶V » � ¶� P º A Z K 8 Ç.a0Ç(Ç Æ P|}`NDifo'>DH9N-?&(1HDF@ º A Z K *Ifg<>`ND3&('>/v<)`NVWDH<>/21sVWDh&(G �¶ 8 º = �A Z K » º _ �A Z K Pc&(GN@o<)`NDifuS.+(<8 Ç » � � P º _ �A Z K Å 8�Ç�� P º = �A Z K »�¼ � 8 º Ac= � Z K » º A _ � Z K » º A Z K = � » º A Z K`_ � P 8 Ç.a0Ç(Ç.ÇÈP|}`N/0O�DHKMLN&J<)/0+.Gl/2O <)`NDc4sL @;+.'=< \ @;'>&(GN�(DH-BVWDH<>`N+]@wa�|}`NDcGBDF1FDHO>O>&('=f�O=<Q&J'=<)/0GNS�{J&(-0LNDFOVlLBO=<q*EDX1F+.VW9NLB<>DF@T*pfT&(GB+(<)`NDH'tVWDH<>`N+]@wa�|}`NDr1F+.GI{.DH'>S.DHGN1FD7/0OqS(L;&(')&JGp<>DFDH@U/0YE<)`ND

� ¼

9;&J')&(VWDH<>DF'>On+(Yt<)`NDWS.'>/0@jO)&J<>/2O=YZfj1HDF'�<Q&(/0G�&(@B@N/0<>/2+.G;&J-�1F+.GB@N/0<>/2+.G��DJa�SNa G > : � Æ a|}`NDHO>D31F+.GB@N/0<>/2+.GNO}@BDF1F'=Dh&(O=D3<>`ND7{J&(-2LND7+JY#<>`N/2O}VWDH<>`N+]@wa�]/0VT/0-?&('=-0f3<)+�<>`NDs1h&JO>Ds+(Y &�O>/2GBS.-2DXO>9;&e<)/?&J-x{J&('=/?&(*B-2DX/0<q/2Oz9E+.O=O>/0*N-2DX<)+l@NDH'>/v{.D7&(GD��B9B-2/21H/0<t\z/0VT9B-2/21H/0<qVTDi<)`N+M@uyR`NDF'=D7<)`NDnGNDiy 9N'>+J~;-2D7/0O}1F+.VW9NLB<>DF@_*pfº _ �A Z K Å 8�Ç » � 8 � ¶V » � ¶� P=P º A Z K Ã � » B » L DH{(DFG�Ã 8 Ç.a0Ç(Ç ¼ P8 Ç � � 8 � ¶V » � ¶� P>P º _ �A Z K Å º A Z K Ã � » B » L +]@B@ 8 Ç.a0Ç(Ç �IP

@;+.'>V�LN-?&�8�Ç(a0Ç.Ç ¼ Ps/2O3&(G�D��]9N-2/01F/0<n+(GNDT/0G�<>`NDTY:+('>V +(Y78�Ç.avÇ Æ %.Pn&JGN@ 8 Ç.a0Ç(Ç �IPs/2O/0VT9N-0/21H/0<h�NyR`BDF'>DlyqD�`;&h{.D�&(-0- <>`NDl{J&(-2LBDFO º _ �Ac= � Z K Ã º _ �A _ � Z K Ã º _ �A Z K = � Ã º _ �A Z K`_ � /0G^<)`ND_8 � »ÇÈPd\d<>`½9N'=+(~;-2D_1F+(VT9NL]<)DF@½*pf£8�Ç(a0Ç.Ç ¼ Pi�t<>`pLNO[8 Ç.a0Ç(Ç �IP�1h&(G *,D^LBO>DF@ Y:+('T'=DF1FLB'>'>DHGI<Di{(&J-2L;&J<>/2+.Gwa�|}`N/0O�&J-2S.+.'=/0<>`NV /2O7/2-0-2LNO�<)'>&J<)DH@[/2G @�/0SNagÇ.a��Ba �d<31h&(Gj*,D�O>`N+�yRG�<>`;&J<<>`N/2O5VWDH<)`B+]@W/2O�{.DH'=fWO>/0VT/0-?&(' <)+n<)`NDr4sL @x+('=<�\�@x'>&(GN�JDF-xVTDi<)`N+M@��pO>+3DH{(DFGg`BDF'>DXytDGNDHDF@ G > : � Æ a@;+.'RDi�]9N-0/21F/v<RVTDi<)`N+M@u<)`NDn<)DHVT9,+.'>&(-AO=<>DF9Ô=/ �HD G /2OR*,+.LNGN@NDH@^*Ifu<)`BD�O�<Q&(*N/0-2/v<¯f1H+.GN@N/v<)/2+(Gl+.'�*Ifl<)`BD}1F+.GN@B/0<)/0+.G G > : � Æ |}`MLBOz/0VT9B-2/21H/0< VWDH<)`B+]@NO5&J'>D}+(YZ<>DFG�LNO>DH@/0GNO=<>Dh&(@�a � `NDFG�LBO>DF@�Y:+.'n9N'>+.*B-2DFVWOn@NDFO=1F'=/2*,DF@�*If½8�Ç(a�# #.P�\l8 Ç.a0Ç Æ ÇÈP�ytDTGNDFDH@�<)+O=+.-0{(DU&_O=fMO=<>DFV�+(Y}-2/0GNDh&J'n&(-2S.DH*N')&J/21�DFKpL;&J<>/2+.GBO3Y:+.'U8�8!� ÇÈP ¶ LNGN�pGN+�yRGNOl/0G�Dh&J1QÒ�<)DF9wau|}`NDU9N'=DF1H/2O>D�Y:+.'=V +(Yt<>`N/2O3O=fMO=<>DFV @NDH9EDHGN@NOlO�<)'>+(GNS.-0f�+.G�<>`NDW<¯fM9,DU+(Yq<)`ND9N'=+.*N-0DFV &JGN@T+(GW<>`NDRVTDi<)`N+M@TLBO>DF@ ' S.DHGNDF'>&(-2-vf�<>`NDFO=DrO�f]O�<)DHVTOq&('>DRO=9;&('>O=Dr*,DF1F&(LNO=D/0G�Dh&(1Q`jDHKMLN&J<)/0+.G[+.GN-vf�&gO=VU&(-0-#GpLNV�*EDH's+(YzLNGN�pGN+�yRGNO3&(9N9,Dh&J'>OFa&�]+gY:+.'r-?&('=S.D 8/v<q/0OqLBGN'>DF&(O>+.GN&(*N-2DR<)+�LNO>DX~;GN/v<)DXVTDi<)`N+M@NO�8�D(a SNa�<>`ND��n&(LNO=OqDH-2/2VW/2GN&J<)/0+.GxP *,DF1F&(LNO=D+(Y#VWDFVW+.'=fg&(GN@o1F+.VW9NLB<)&J<)/0+.Gg<)/0VTD�@NDFVT&(GN@NOHa�d<�/0O�9,+.O>O=/2*N-0Dz<>+s9N'=DF9;&('=D}&rO=9EDH1F/2&(-B&J-2S.+.'=/0<>`NV yR/0<>`�&r~;GB/0<)DzVWDH<)`B+]@�Y:+('�&�9N&('�\<>/21FLB-?&('}9N'=+.*N-0DFV_�;*NLB<r/0<)OX&(9B9N-2/01h&(*N/0-2/v<¯fT/0OR'>DFO�<)'=/21H<>DF@_<)+T<>`N/2OR9;&J'=<)/01FLN-2&('}9N'=+.*N-2DHVO=+T/v<}/2O}GN+J<Xyq+.'�<)ò<)`NDnDHCE+.'�<ha$ YZ<)DHG�<)`NDlVWDH<>`N+M@�1h&(-0-2DH@�&(-v<)DF'=G;&J<>/2GNST@N/2'=DF1H<>/2+.Gk/2VW9N-2/01F/v<�8 s4 ��PR/2OrLNO>DH@�/0G]\{(+.-0{M/2GBSg<¯yt+oO>+(-2LB<>/2+.GNO�+(Yq&u<>`N'>DHD�@N/?&JS.+.G;&(-#O=fMO=<>DFV +(Y�8&8 � Ç�PrDFKpL;&J<>/2+.GBOFal|}`NDLNO>&(S.D3/2OXO>/0VT/0-?&('t<>+ �4 �tY:+.'RDF-0-2/29]<)/2179B'>+.*N-0DFVWORO>DFD�1Q`;&(9B<>DF' � �;aR�XDF'>DJ�E`B+ÈyqDH{(DF'H�<>`NDl*N-0+]1Q�_'>DH-?&e�B&J<>/2+.G s4 �R/2OsGB+(<s@N+(GNDlY:+.'r<>`ND�O)&JVTD3<)/2VWD�-0DH{(DF- a $ '�<>`NDl9,+./2GI<'=DF-?&È�N&e<)/2+(G 8:LN9N9,DF'QP3VTDi<)`N+M@�1h&JG�*EDTLNO>DH@ yR/v<)`�+.GN-0f�&kY:Diy�8�LNO=L;&(-2-vf �=LNO=<�+.GND�P'=DF-?&È�N&e<)/2+(Gu1HfM1F-0DnY:+('}Dh&(1Qò<)/0VTD7-0DH{.DH- a$ Y#Y:LBGN@;&(VWDFGI<Q&J-�VTDF&(GN/0GNSl/2Oc<>`ND ')&JGN�.\ br/01F+.-0O>+.GoVWDH<>`N+]@�8ZyR`N/21Qò/0OR&(-0yt&hf]OO�<Q&(*N-0DsY:+.'}9N'=+.*N-2DHVTO38 Ç.a�# #IPz\�8�Ç(a0Ç Æ ÇÈP>PzyR/v<)`k&l~N{.D39E+(/2GI<}O>1Q`BDFVWD Ç � �

¼ 8 � ¶V » � ¶� P " � _ � Å Ç » �¼ 8 � ¶V » � ¶� P " � »ba 8 G - » G : ¶ P 8 Ç.a0Ç(Ç �pP� �

A 9 � ¶ - � �

�¶-K �

=��

A 9 � ¶ - � �

�¶-K �

=��@#/2S.LN'=D�Ç.a��B·56��B9B-2/21H/0<}/0VT9B-2/21H/0<zVWDH<)`B+]@��\5{J&(-2LBDFOR1F+.VW9NLB<>DF@_*If�8�Ç.avÇ.Ç ¼ P� \5{J&(-2LBDFOR1F+.VW9NLB<>DF@_*If�8�Ç.avÇ.Ç �.P+.'cY:'=+.V«*,+.LNGN@;&J'=fu1H+.GN@N/v<)/2+(G

+.'R&�GN/0GNDn9E+(/2GI<}O>1Q`BDFVWD Ç � � ¼ � ¶V " Ç � � ¼ � ¶� " � _ � Å Ç » � ¼ � ¶V " Ç » � ¼ � ¶� " � » a 8 G - » G : ¶ P 8 Ç.a0Ç(Ç �.P|}`NDifn*E+(<>`�&J'>D5+(Y]+.'>@NDH' a 8 G ¶ » : ¶iPia ��D5S.DH<�<>`NDs4 �wVWDH<>`N+M@3*Ifn/0Gp<>'>+M@NLN1H/2GNS&(@B@N/0<>/2+.G;&J-E9N'=+(~;-0D � _ &(GN@o*If_&(9N9N'=+.9N'>/2&J<)D�O>9N-0/0<><>/2GNS�<)`ND7Y:+.'=VlLN-?&o8 Ç.avÇ.Ç �pP�a�|}`N/2Oyt&hfuytDnS.Di<X<>`ND3%#DF&(1FDHVU&(GM\ �X&(1Q`BY:+.'=@kVWDH<>`N+]@

Ç � �¼ � ¶V " � _ Å Ç » �

¼ � ¶� " � Ã 8 Ç.a0Ç(Ç %IP Ç � �

¼ � ¶� " � _ � Å Ç » �¼ � ¶V " � _ 8 Ç.a0Ç(Ç �.P

�dY�yqD�DH-2/2VW/2GN&J<)Dt<>`NDX9N'>+(~N-2D � _ ÃIY:'>+(V 8�Ç.avÇ.Ç %.P5&JGN@[8 Ç.a0Ç(Ç �.P�*IfTO=/2VW9N-2DRVT&(GN/09]\LN-2&J<)/0+.GUyqD�S(DH<�8�Ç.avÇ.Ç �IPia0@�/0SNacÇ.a�#�/2-0-2LNO�<)')&e<)DFOq<)`ND3%#DF&(1FDHVU&JG]\ �X&(1Q`BY:+.'=@kVWDH<>`N+M@�a|}`NDH'>D_&('>Du+J<)`NDH'�VTDi<)`N+M@NO�LNO=/2GNS�&(-v<)DF'=G;&J<>/2GNS�@B/2'>DH1H<>/2+.GNOu8 4��>&(�J+.G VTDi<)`N+M@��4s+.LBS.-?&(O \ �X&(1Q`BY:+.'=@^VWDH<>`N+]@^DH<)1Ja P�an|}`NDl/2GI<>DF'>DHO=<>DF@j'>DF&(@NDF'�/2Os/0Gp{M/v<)DF@k<)+gLNO=Dl<)`ND+.'=/2S./0G;&(-,-2/v<)DF'>&J<)LB'>D(a

@�/2S.LB'>D�Ç.a�#B·5%#DF&(1FDHVU&JG]\ �X&(1Q`BY:+.'=@kVWDH<>`N+M@�l\z�pGN+�yRGk{J&(-0LNDFOH�� \zLNGB�MGB+ÈyRGk{(&J-2LNDHO

�O�<)`BD^GpLNVl*,DF'W+(YsLBGN�pGN+�yRGNOu&(GN@®<)`ND_GpLNVl*,DF'W+(YsDHKpL;&J<)/0+.GNO�Y:+.'�/2VW9N-2/01F/v<VWDH<>`N+]@BOW@BDF9,DFGN@NOU`NDh&h{M/2-vf�+.G 8#�tG;&JVTDH-0f &(O^8�8 ��Ç�P�¶hÃ�yqDk<)'�f�<)+�'>DH@NLN1FD_<)`NDGpLNVl*,DF'W+(Y7GB+]@NDHOTyR`N/0-2Do�(DHDF9N/0GNS�<>`ND�&(1H1FLN'>&(1Hf(aµ|}`B/2OW1h&(G *,D_@N+.GNDk*pf®LNO=/2GNSVW+.'>D7GB+]@NDHO}<)+W&(9N9N'=+h�B/0VU&e<)Ds<)`BD3O=9;&J<>/?&(-�@BDF'>/v{J&J<)/v{.DFO}DJa�SBa¹ ¶ º¹ ° ¶

�� A Z K �� º Ac= ¶ Z K » Ç % º Ac= � Z K � � Æ º A Z K » Ç % º A _ � Z K � º A _ ¶ Z KÇ ¼ : ¶ 8 Ç.a0Ç(Ç �IP

� �

+.'R&e<}<)`NDn*,+.LNGN@;&J'=f¹ ¶ º¹ ° ¶

�� Z K �Ç.Ç º 9 Z K � ¼ Æ º � Z K » % º ¶ Z K » � º - Z K � º � Z KÇ ¼ : ¶ 8 Ç.a0Ç(Ç #IP

|}`N/0O#VWDH<>`N+M@�/2O /2-0-2LNO�<)'>&J<)DH@3/0G @�/0SNa5Ç.avÇ Æ Y:+.' *,+(<)`�Di�]9N-2/01F/v<�&JGN@�/0VT9N-0/21H/0<AVWDH<>`N+]@BOFa|}`ND7+('>@NDH'c/2Gg°k&(GN@u±T/2O a 8 : � P��N&(S.&(/2G '>&(GN�.\ bX/21H+.-2O=+.Go&h{.DF'>&(S./0GNSl1h&JG_*,DsLNO=DF@�a4s/vCwDH'>DFGB1FDnY:+.'>VlLB-?&(OR+(Y5&�{.DH'=fk`N/2S.`k+.'>@BDF'X1h&(G�*,D31F+.GNO�<)'=LN1H<>DF@��LBO>/2GBSULN9^<>+g&(-0-8&8 � ÇÈPt{(&J-2LNDHO}+(Y º O>+�<)`;&J<XDi{.DFGkY:+.'}O>VT&(-2- 8�&�S.+M+M@k&J1F1FLB')&(1ifo1h&(G_*EDn'=Dh&(1Q`NDH@/0G_1HDF'�<Q&(/0G_1F&(O>DHOFa@�/2S.LB'>D7Ç.avÇ Æ ·�6��]9N-0/21H/0<z&(GN@W/2VW9N-0/21F/v<�Y:+.'=VlLN-2&+(Y�`B/2S.`NDH'}+.'>@BDF'�l\z�pGN+�yRGk{J&(-0LNDFOH�� \zLNGB�MGB+ÈyRGk{(&J-2LNDHO

�]+.-0LB<)/0+.Gl+(YxGB+.GN-2/0GNDh&J'�9;&('>&(*,+.-2/01tDFKpL;&e<)/2+(GNO�/2Gl<>`N'>DHD}@N/2VWDFGBO>/2+(GNO�/0O�O>/0VT/0-?&('A<)+<¯yq+o@N/2VWDFGNO=/2+.GN&(-�9N'>+.*B-2DFVWOF�,<)`ND�'=DFO=LN-0<>/2GNSg/0VT9B-2/21H/0<R-0/2GNDF&('�9N'=+.*N-0DFVWOs&('=DlO>+.-v{.DH@*IfuO=+.VTDnVWDH<>`N+]@oS./v{.DHGk&J*E+�{.DJ�xD(a SNa5LN9N9,DF'R'>DH-?&e�B&J<>/2+.Gu+.' �4 �Qa�]/0VT/0-?&('=-0fj&(OlY:+('�<¯yt+�/2GB@NDF9,DFGN@BDFGI<�{(&J'>/?&J*N-2DHOF��<)`BDuVTDi<)`N+M@�+(YX-2/0GNDFOl1F&(G *EDLNO=DF@�a +.GBO>/2@BDF'X&WKpL;&JO>/v\d-2/0GNDh&('qDFKpL;&J<>/2+.G¹ º¹ � Å ¹ ¶ º¹ ° ¶ » ¹ ¶ º¹ ± ¶ » ´�8 º PyR/v<)`½/0GN/0<>/?&(-t&(GN@ *,+.LNGB@;&('=f®1H+.GN@N/v<)/2+(GNOk8�Ç.avÇ Æ.Æ P��78 Ç.a0Ç Æ ÇÈPia 4sDHGN+(<>/2GNS º A Z K 8 � P Åº 8:°�A Ã)± K Ã � P�Ã;&(GN@_LNO=/2GNS�<)`BD3O=/2VW9N-2DHO=<c<>`N'>DHD�9,+./0Gp<}Y:+('>VlLN-2&(OtyqDnS.DH<

@ º A Z K@ � Å º A�= � Z K � ¼ º A Z K » º A _ � Z K: ¶ » º A Z K = � � ¼ º A Z K » º A Z K _ �

: ¶ » ´�8 º A Z K PwÃº A Z K 8 Æ P Å Bc8:°�A¯Ã>± K PwÃ B#Å Ç(Ã ÃD8 � Ç5Ã L�Å Ç.Ã Ã`8 � Ç |}`NDWGpLNVl*,DF'n+(Yc+('>@N/0G;&('=f^@N/0CEDF'=DFGI<)/2&(-�DHKMLN&J<)/0+.GNOn/2On/2G[<>`N/2O71F&(O>DW-?&('=S.D(�A9B'>+J\9,+.'=<>/2+.GN&(-E<>+ 8 ¶ a�|}`ND�&(@B{J&(GI<Q&(S(D7+(Y#<>`N/2OX&(9B9N'>+I&J1Q`k/0Oc<)`;&J<R/v<R/2O}DF&(O=f(a� � �

@;+.'cY:LN'�<)`NDH'}O=<>LN@BfoO>DHD 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : � 9 � : a� �

Chapter 1 Parabolic partial differential equations ... - vscht.cz

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