High-Order Finite Difference Methods for Wave Equations - Applied

137

Transcript of High-Order Finite Difference Methods for Wave Equations - Applied

������������ ������������������������ �!�"�$#%��&'�(�!��)� $*,+-)��,.0/(1��24365�/7�!��)8�$*

9;:<>=@?BA8C;DEDFCHG$I�JKJMLNA�OB=FPRQ

S�TVU7T WYXNZ\[ ["]^W`_bacS�dBegf _bhidBegW^jRkRl7mnX W^o�_RpqkgW`e :sr�t�uvr ] r pqd�a r lw r!x ]^a _Rpblzyb{�{!|

wnTVU}T�W^XNS~dBegf(_bhidBegW^jRkRl7mnX�W`o�_RpqkgW`e :�r�t��8r ]`_ba r l�yb{�{��w�TVU7T"W^XN�$f : kqW^jRkRl m�X W`o�_RpqkgW^e :�r�t��8r ]`_ba r l�yb{�{��

Z�egf(_bkgW^k\k x(9 hiW^e�e�_bace r egf(_��d�j x ]`e :cr�t egf(_���p�d�a x dBe�_�U%j�f r;r ] r�t egf(_

mnX�W`o�_RpqkgW`e :�r�t$uvr ] r p�d�a r W^Xc[�dBpgegWYd�] tFx ]`�"]^]^h4_bX�er�t egf _�pg_b� x W`pg_bh4_bX�egk tFr p�egf(_�a(_R��pq_R_ r�t

� r j�e r p r�t ��f W^] r k r ["f :�n_R["dBpgegh4_bX�e r�t Z\[ ["]^W`_bacS�dBegf _bhidBegW^jRk

�B�����

� f W^k�egf(_bkgWYk�_bX�egW`eg]^_baz���W`�!f%�-��pqa _Rp��6W^X�W`e�_���W��7_Rpq_bX j�_�S�_Regf r a�k t@r p\��dbo�_¡ $� x dBegW r X k

¢ pqW`e�e�_bX 9;: S�W^j�f(_b]^]`_�£ : X�X,��f(pqW^kgef d�k 9 _R_bX,dB[ [ p r o�_ba tFr p�egf(_���_R[�dBpgegh4_bX�e r�t Zn[ [�]^W`_bacS~dBegf(_bhidBegW^jRk

wv_bX(��e\� r p�X 9 _Rpg�

U;e�_Ro�_�S�j uvr p�hiW^jg¤

��dBe�_

� f(_��"X�d�]7j r [ :¥r�t egf W^kvegf(_bkqW^k¦f d�k 9 _R_bXc_�§%d�h�W^X(_ba 9�: egf(_�kgW`�!X�dBe r pqW`_bkRl(d�X a ¢ _��"X a¥egf dBe9}r egfNegf _�j r X�e�_bX�end�X�aNegf(_ tFr pqh'h4_R_Re\d�jRj�_R[�egd 9 ]`_�[�pg_bk�_bX�egdBegW r X�k�egd�X a�dBpqa k r�t kgjqf r ]^dBpq] :

¢ r pg¤cW^Xcegf(_�d 9}r o�_�h4_bX�egW r X(_baNa W^kqjRW`[�]^W^X _�T

W^W^W

��f(p�W^k�eRl(S�WYjqf(_b]^]^_�£ : X X�¨E�$fzT���T`l7Z\[ ["]^W`_bacS�dBegf _bhidBegW^jRk�©��W`�!f%�-��pqa _Rp��KWYX W`e�_���W��7_Rpq_bX j�_�S�_Regf r a�k t@r p\��dbo�_¡ $� x dBegW r X k� f(_bkqW^k¦a W`pg_bj�e�_ba 9;: ��p r�t _bkgk r pnw�_bX ��e\� r pqX 9 _Rpg�

�ª_4f dbo�_4W^X�o�_bk�egW`�!dBe�_baHegf(_�o�_Rp : f�W`�!f�j r hi[ x egdBegW r X d�]K_�«sjRW^_bX j :�r�t f W^�!f%� r pqa(_Rp�"X W^e�_�a W��}_Rpg_bX j�_�h4_Regf r a kRl�_bk�[}_bjRW^d�]^] : d�k�egf(_ : W^X�j r pg[ r pqdBe�_ t _bdBe x pg_bk$k x jqfsd�k$W^h4["]^W^jRW`egX(_bkqk¨Ed�]^k r ¤%X r ¢ XNd�k¦j r h4[�d�j�egX(_bkgk\W^X¥egf(_�]^W`e�_RpqdBe x pq_¬©$d�X�as��p�W^ack�egdB����_RpqW^X(�(T$�­f WY]`_npq_bhid�W^X W^X �pg_b]^dBegW^o�_b] : j r h4[�d�j�eRl%egf(_bk�_�h4_Regf r a k$jRd�X¥dB[ [ p r d�j�f�egf _nk x [}_RpqW r p$d�jRj x pqd�j : d�X�ai_��}_bj�egW`o�_��X(_bkgk r�t k�[}_bj�e�pqd�]�hi_Regf r a�k ¢ f W^]^_�k�egW^]^]zd�]^] r ¢ W^X ��k r h4_ 97r!x X a dBp :�® _�§%W 9 W^]^W`e : T$¯°X�egf(_�[�d�k�eRl��pqW^a4kgegdB����_RpqW^X(��f d�k 9 _R_bX r�9 k�_Rpgo�_ba4e r�9 _ 9 _bX(_��"jRW^d�]%W^X4k r h4_�jRd�k�_bkn¨F_�T±�(T$egf(_�²�_R_\kgj�f(_bh4_tFr pnj r h4[ x egdBegW r X d�]³_b]^_bj�e�p r a : X d�h�W^jRk�©�l 9�x e�egf dBenWYa(_bdif d�k 9 _R_bX,kgf r ¢ X,f(_Rpg_�e r j r h 9 W^X(_t dbo r pqd 9 ] : ¢ W`egf 9}r egfNW^h4[�]^WYjRW`egX(_bkgkvd�X a�f W^�!f r pqa(_Rpqk r�t d�jRj x pqd�j : T

¯-Xsd�a a W`egW r Xzl ¢ _�f�dbo�_�_�§;["] r pg_baiegf _�X(_ ¢ W^a(_bd r�t ��pqW^ask�egdB����_RpqW^X � tFr p�egWYh4_�WYX�e�_����pqdBe r pqkbT�¯-X¥egf(_�W^hi[ r pqegd�X�e�dB[ [�]^WYjRdBegW r X r�t k r ]`o%W^X(��]^W^X(_bdBp ¢ do�_�_b� x dBegW r X k�¨F_�T±�(T$d�j r!x k�egW^jr pv_b]^d�k�egW^j ¢ do�_bk�_b� x dBegW r X kRl r p�S~d�§ ¢ _b]^]�´µk$_b� x dBegW r X k tFr p�_b]`_bj�e�p r hidB�!X(_RegW^jn��_b]^a�k�©�l�X(_bdBp�] :d�X r p�a(_Rp r�t hidB�!X W`e x a(_��!d�W^X�jRd�X x k x d�]^] :�9 _�d�jqf W^_Ro�_ba,W^X�d�jRj x pqd�j : ¨ t@r pnegf(_�kgd�hi_�j r h¡�[ x egdBegW r X d�]"j r kge�WYX 9}r egf r [}_RpqdBegW r X¥j r!x X�e�d�X acW^X�hi_bh r p : ©�j r h4["dBpg_ba¥e r jR]Yd�kgkgW^jRd�]z���� k r ]`o�_Rp�k4k x jqf¶d�k�Zna d�h�k r ps· x X(��_���¸ x e�egdHh4_Regf r a kRT�¯°X¶d�a a W^egW r Xzl r!x piX(_ ¢ k�egdB����_Rpq_bah4_Regf r a kvf dbo�_�k x [7_Rp�W r p$k�egd 9 WY]^W`e : [�p r [}_RpgegW`_bk�e r egf(_�jR]^d�kgkgWYjRd�]"h4_Regf r a kvW^X�egf(_�j r X�e�_�§%e r�tk r ]`o%W^X(� ¢ dbo�_�_b� x dBegW r X kRT��ª_�W^X�o�_bk�egW`�!dBe�_�egf _�d�jRj x pqd�j : d�X a,k�egd 9 W^]^W^e :�r�t egf(_bkg_�h4_Regf r a kd�X d�] : egW^jRd�]^] : l;_�§%[}_RpqW^h4_bX�egd�]^] : l%d�X acegf(p r!x �!fcegf(_ x k�_ r�t d¡X r o�_b]zp r�r e¦[ r pge�pqd�W^eve�_bj�f X W^� x _�T�ª_�d�]Yk r j r X kgW^a _Rp\k�_Ro�_Rpqd�]�egf(_ r pg_RegW^jRd�]8� x _bkgegW r X k�j r X j�_Rp�X W^X(�4egf(_bkg_�k�egdB����_Rpg_ba�egW^h4_�WYX�e�_����pqdBe r pqkbT

W`o

¹ #!º��$)�»�¼��� �����½­���8��*

¯ ¢ WYkgf�e r _�§;[ pq_bkgk�h : ��pg_bdBe$dB[�[ pg_bjRW^dBegW r X¡d�X a¡��p�dBegW`e x a(_¦e r j�_Rpgegd�WYX4W^X a W`o%W^a x d�]^kd�X a r pq�!d�X W`¾bdBegW r X k ¢ f r f(_b]`[}_bachidB¤�_�egf W^k�pg_bk�_bdBp�jqf�[ r kgkqW 9 ]`_�T

U x [ [ r pge t@r p¡egf W^k�pg_bkg_bdBpqjqf ¢ d�k¡[ p r o;W^a _ba 9;:�¿ Z�U(Z���£�_ ¢ W^k¡·�_bk�_bdBp�jqf u _bX�e�_Rpd�X aªegf _�mnX�W`o�_RpqkgW`e :�r�t\uvr ] r pqd�a r ��w r!x ]^a(_Rp�egf(p r!x �!f�d ¿ dBegW r X�d�]$�$f : kgW^jRd�]$U%jRW`_bX�j�_ uvr X%�k r pgegW x hÀ� _b]^] r ¢ kgf W`[Á¨ ¿ Z�U%ZÂ��pqd�X�e ¿ ��U u �-� u �¡y �!Ã�Ä w�©�d�X�a 9;: egf(_ ¿ dBegW r X d�]�U%jRW`_bX j�_� r!x X�a dBegW r X¶¨ ¿ U(�Åe�p�d�W^X(_R_bkgf W^[,��pqd�X�e���SHU��Æ{ ��Ä�Ç�Ã�Ã�Ä ©�T4¯�d�hÈ_bk�[}_bjRW^d�]^] : ��p�dBe�_ tFx ]Ke r ��W��pg_bj�e r p ¿ d�XHU%X r ¢ r�t�¿ �vU u­tFr pnf _Rp x X ¢ do�_RpqW^X(�sk x [ [ r pge�d�X a,e r S~kRT�w r X�X W`_�S~jRwvpqW^a(_r�t6¿ Z�U%Z\��£³_ ¢ W^k tFr p\f(_RpnW^X ®"x _bX�j�_�d�X ac¤%W^X a�X(_bkgkRT�Z�a a W`egW r X�d�] tEx X a WYX(� ¢ d�k¦[ p r o%W^a(_ba 9;:di� r p r egf : U;e�pqW 9 WYj t _b]^] r ¢ kgf W`[�T

¯ ¢ WYkgf,e r egf�d�X(¤�h : d�a(o%W^k r pl³��p r�t _bkgk r p�wv_bX(��e�� r p�X 9 _Rpg�(l tFr p�f W^k�]`_bd�a _Rpqkgf W`[�l_bX�egf x kqW^d�kghNlvk x [ [ r pgeRlvd�X aÉ[ pqd�j�egW^jRd�]YW`e : TÊ��W^kikg_bX k�_ r�t f x h r p�d�X a ¢ WY]^]^W^X(�!X _bkgk�e r _�§;�[�]^d�WYXÉegf W^X(�!k4d�k¥hid�X : egWYh4_bkid�k�X _R_ba(_ba ¢ _Rpg_,W^X�a W^k�[}_bX kgd 9 ]`_�T�¯4d�hËd�]^k r ��pqdBe�_ tEx ] tFr pegf(_¡W^X a WYk�[}_bX kgW 9 ]^_\f(_b]`[~egf dBe�[ r kge°��a r j���pbT �8r�9�: ��pqWYkgj r ]^]³[�p r o%W^a(_ba,egf(p r!x �!f�egf(_ : _bdBpqkRT��W^k¦j r h4[ x e�_Rp¦_�§%[}_RpgegW^k�_�d�X aNd 9 W^]^W`e : e r _�§;["]^d�W^Xcj r h4[�]`_�§cW^a(_bd�k¦W^XckgWYh4[�]`_�]^d�X(� x dB��_ ¢ d�kW^X�o�d�] x d 9 ]`_�T�S :st _b]^] r ¢ kgf W^[�h4_bX�e r pl���pbT�Z�X X(_�� r!x �!f(_Rpqe : l}a(_bk�_Rpgo�_bknh : ��pg_bdBendB[�[ pg_bjRW��dBegW r X t@r p¦f(_Rp�]`_bd�a(_Rp�kgf W`[³l�_�§(j�_b]^]`_bX�eve�_bd�jqf W^X �(l;["dBegW`_bX j�_�l(d�X a ¢ W^]^]^WYX(�!X(_bkgkKe r¡r �7_Rp¦d�a(o%W^j�_�T� f WYk ¢ r!x ]^a~f dbo�_ 9 _R_bXHdch x jqfªh r pg_4a W`«sj x ]`e�Ì r!x p�X(_ : ¢ W`egf r!x e�f(_Rp�d�kgkqW^k�egd�X j�_�T�¯�d�]^k regf d�X(¤��$p r�t _bkgk r p�wv_bX��n_Rp 9 k�e r�t U r!x egf�Z t pqWYjRd tFr pKf�W^k³� x WYa d�X j�_ r X�dn[ p r;r�t d�X a�egf�d�X(¤�egf(_pg_bk�e r�t h : j r hihiW`e�e�_R_�hi_bh 9 _Rpqk tFr p�egf(_bW^p\k x [ [ r pge�d�X a�f _b]`[³����p r�t _bkgk r p\ $]^]^_bX,Í ¢ _bW 9 _b]�l��p r�t _bkgk r pv�6dBe�pqW^jq¤4�ª_bW^a hid�X³l;�$p r�t _bkqk r p�U;e�_Ro�_�S~j uvr pqhiW^jq¤"l%d�X as��p r�t _bkgk r p�w r�9  �d�k�e r XzT

£�d�k�eg] : l�¯ r �7_Rp¡h : _�§%e�pg_bh4_s��pqdBegW`e x a _ie r h : f x k 9 d�X a�·nW^jqfzl ¢ W`egf r!x e ¢ f r hegf W^k ¢ r pg¤ ¢ r!x ]Ya�X r e�f dbo�_ 9 _R_bX¡[ r kgkgW 9 ]`_�l�d�X a�e r h : k r X4Z�dBp r Xzl tFr p�_bX a x pqW^X(��h : ¢ r pg¤7T

Π)8�������8�!*

Ï A8Ð Ñ8QC�O

Ò ¯°X�e�p r a x j�egW r X yyBT^y ¯°X�e�p r a x j�egW r X,T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T yyBT � ��] r kqkgdBp :¥r�t d 9�9 pg_Ro%W^dBegW r X k¦d�X a�e�_Rpqhik x kg_ba�W^Xcegf W^k�["dB[7_Rp�T�T�T�T�T�T�T�T �

Ó U;["dBegW^d�]z�6W^X W`e�_���W��}_Rpg_bX j�_�Zn[ [ p r §(W^hidBegW r X k tFr p\��do�_� �� x dBegW r X k Ç� T^y ¯°X�e�p r a x j�egW r X,T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ç� T � ¯°]^] x k�e�p�dBegW r X k r�t ��pqW^aNk�egdB����_RpqWYX(�cT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T {� T à Z�]`� r pqW`egf h t@r p¦�7X W`e�_�a W��}_Rpg_bX j�_ ¢ _bW`�!f�egk\d�X ac_�§(d�h4[�]`_bkÔT�T�T�T�T�T�T�T�T {� T±� � d 9 ]`_bk r�t k r hi_ ¢ _bW`�!f�egkbl"W^X jR] x a W^X(� tFr pqh x ]^dB_ t@r p ¢ _bW^�!f�egk�d�X a tFr pn]^WYhiW`egk

r�t W^X%�"X�W`e�_ r p�a(_RpÉT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T y Ç� T Ä  $� x W`oBd�]`_bX j�_ 9 _Re ¢ _R_bX¥WYh4[�]^W^jRW^e6d�X�a�_�§%[�]^W^jRW^e t@r p�h x ]YdB_nW^X�egf(_�jRd�kg_ r�t ]YW^h¡�

W`egW^X � r pqa(_Rp4T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ��Ã� T Ç ��[}_RpqdBegW r XNj r!x X�egkÊT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T � |� TV| uvr h4["dBpqW^k r X r�t d�jRj x pqd�jRW^_bk\d�X a�j r kge°��_��7_bj�egW`o�_bX _bkgkMT�T�T�T�T�T�T�T�T�T�T�T ��Õ� T Õ � _bk�e�[ p r�9 ]`_bh T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ã�Ã� TÖ{ uvr X jR] x kgW r X k­T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ã�Ä

× U;egdB����_Rpq_ba � WYh4_�¯-X�e�_R��pqdBe r pqk t@r p\��dbo�_¡ $� x dBegW r X k � yà T^y ¯°X�e�p r a x j�egW r X,T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T � yà T � ¯°]^] x k�e�p�dBegW r X k r�t ��pqW^aNk�egdB����_RpqWYX(� tFr p\]^W^X(_bdBp ¢ dbo�_�_b� x dBegW r X k0T�T�T�T�T�T�T � Ãà T à ��pq_b]^W^hiW^X�dBpqW`_bkØT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ��|

o;W

à T à T^y ��_��"X W^egW r X k T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ��|à T à T � S~d�§%WYh x h'¯-hidB�!WYX dBp : U;egd 9 W^]^W^e : w r!x X a�dBp : T�T�T�T�T�T�T�T�T�T�T�T ��{

à T±� U;egdB����_Rpg_ba~Z�a d�hik-Ù�w�d�kgf tFr pgegf�d�X�a 9 d�jg¤ ¢ dBpqa k\a�W��7_Rpq_bX�egW^dBegW r XNh4_Regf r a k ÄB�à T Ä U;egdB����_Rpg_ba t pg_R_�[�dBpqd�h4_Re�_Rp�h x ]`egW^k�e�_R[�h4_Regf r a k�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ä�Ç

à T Ä T^y � r!x pgegf r pqa _Rp t pq_R_�[�dBpqd�h4_Re�_Rp�h4_Regf r az��ÚÛ ��k�e�_R[³l r X _�[�dBpqd�h4_Re�_Rp,T Ä |à T Ä T � � r!x pgegf r pqa _Rp t pq_R_�[�dBpqd�h4_Re�_Rp�h4_Regf r az���B��k�e�_R[³l"e ¢ r [�dBpqd�h4_Re�_Rp�T Ä {

à T Ç � f(_ r pq_RegW^jRd�] uvr X kqW^a(_RpqdBegW r X�k�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ÇB�à T Ç T^y ¯°hidB�!W^X dBp : U;egd 9 W^]^W`e : w r!x X a dBp :�r�t Zna�d�hik-Ù�w�d�kgf tFr pgegf�h4_Regf r a k Ç yà T Ç T � U;egdB����_Rpq_ba�d�X d�] r � x _ r�t ��d�f�]^� x W^k�eR´µk¦�6W`pqk�enU%egd 9 W^]^W`e : w�dBpgpqW`_Rp4T�T�T Ç y

à TV| U;egdB����_Rpg_ba~��pq_ba W^j�e r p�� uvr pqpg_bj�e r p\S�_Regf r a�kÜT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ç yà T Õ U;egdB����_Rpg_ba~· x X(��_ÝÙ�¸ x e�egdihi_Regf r a�kÞT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ç��

à T Õ T^y Z�a(oBd�X jRW^X(�4ß~d�X aNàck�_R[�dBpqdBe�_b] : T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ç�Ãà T Õ T � Z�a(oBd�X jRW^X(�4ß~d�X aNà¥e r ��_Regf(_Rp�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ç |

à TÖ{ · r;r e�[ r pge�pqd�W^egk�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ç {à T^y � ¿�x h4_RpqW^jRd�]³_�§;[}_RpqW^hi_bX�egk�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T | �à T^y�y uvr X jR] x kgW r X k­T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Õ��

á uvr X�jR] x kgW r X�k Õ �

â4=FãKDE=Fä�å"O¬Ð Ñ6A7I Õ�Ç

æ Ñ8Ñ$C;J8çK=@è

æ  �§;[�]Yd�X dBegW r X r�t egf(_��6d�a�é_�d�]`� r p�W`egf hÂ�!W`o�_bX,W^X,U;_bj�egW r X�ê�ë@ì ízî

â ��_RpqW`oBdBegW r X r�t egf(_�]YW^hiW`e�_�§%[ pg_bkgkgW r X k¦W^X � d 9 ]`_ � T Õ { �

Ï uvr X�o�_RpqkgW r X k 9 _Re ¢ _R_bX,¸ r ["d�]�´µk�j r _�«sjRW`_bX�egk\d�X aNegf r k�_�W^X u f�dB[ e�_Rp � {��

ï U;egdB����_Rpq_ba�a W`�7_Rpg_bX�egW^dBegW r XNh�dBe�pqW�§ { Ç

o%W^W

ð ��_RpqW`oBdBegW r X r�t _b� x dBegW r X�¨ � TV|�© {�{ \T^yñ��_RpqW`oBdBegW r X r�t egf(_�_�§%[ pg_bkgkqW r X tFr p\ò�óôT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T {�{ \T �öõ _RpqW��7jRdBegW r X r�t egf(_�_�§%[ pg_bkgkqW r X t@r pnò�ó�� Ä ��a W^dB� r X d�]8jRd�k�_ËT�T�T�T�T�T�T�T�T÷y � y

ø ��_��"X WYX(�4egf(_�] r jRd�]ze�p x X�jRdBegW r XN_Rpgp r p r�t egW^hi_�W^X�e�_R��p�dBe r pqk y �!��vT^yö��W^kgj x kqkgW r XÁT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y �!��vT �  �§(d�h4[�]^_bkØT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y � �

�vT � T^y Z�a d�hik°��e : [}_�hi_Regf r a�k�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y � ��vT � T � w�d�jg¤ ¢ dBpqa k�a W��}_Rpg_bX�egWYdBegW r XNh4_Regf r a k�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y � ��vT � T à �(pq_R_��6dBpqd�h4_Re�_Rp�S,_Regf r a knT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y �!Ä

�vT Ã uvr X jR] x kgW r X k­T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y �!Ä

L ¿nr X k�egdB����_Rpg_ba t pg_R_�[�dBpqd�hi_Re�_Rpnh4_Regf r a k y �!Ç

ù �$p r�r�t"r�t pq_bk x ]`egk tFr!x X a4W^XiU;_bj�egW r X ׳ú^ûzú�Ò ?!ä7J�?!C;OBJ8=EJ8å�Q¬A8CiPRQÐ�ãK=EDE=@Q�IHä�O�çK=EJ8Ð(QC;Pä"ü æ â¥ý æ âsþ6ý�Ð�J�ç æ < ÿ�C�Q¬A8äzç8P Ò������T^yØ��p r�r�tKr�t�� f(_ r pg_bh'��T^yB��X r X k�egdB����_Rpg_ba�ZnwMh4_Regf r a k T�T�T�T�T�T�T�T�T�T÷y�y ���T � ��p r�r�tKr�t�� f(_ r pg_bh'��T � ��Z�w�Uch4_Regf r a k�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y�y����T à ��p r�r�tKr�t�� f(_ r pg_bh'��T à ��Z�S h4_Regf r a k T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y�y|

� �$p r�r�tKr�t egf(_�k�egdB����_Rpg_ba~d�X d�] r � x _ r�t ��d�f�]^� x W^k�eR´µkv��pqkge 9 dBpgpqW`_Rp y�yb{¯ÝT^y u d�k�_syB���Ødif d�] t ��W^X�e�_R��_Rp T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y � y¯ÝT � u d�k�_ � ���Ød�X,W^X�e�_R��_RpªT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y � �

�����85��!��*

ø =Få��8O�C� T^y U%j�f(_bhidBegW^j�WY]^] x k�e�p�dBegW r X r�t j r h4[ r kgW^e�_���pqW^a�j r X j�_R[�e T�T�T�T�T�T�T�T�T�T�T Õ� T � ¨Ed�©���¨ 9 ©�¯-]Y] x k�e�pqdBegW r X k r�t kg[�dBegW^d�]�k�egdB����_Rp�W^X(� tFr p�k r hi_�]^W^X(_bdBp ¢ dbo�_s_b� x d��

egW r X kb� r X(_���a WYh4_bX kgW r X�d�]$d�j r!x k�egWYj ¢ dbo�_,_b� x dBegW r X�d�X�a�e ¢ r ��a�W^h4_bX kgW r X d�]_b]^d�k�egWYj ¢ do�_�_b� x dBegW r X­T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T y�y

� T � ¨Ej©�¯°]^] x k�e�pqdBegW r X r�t kg[�dBegW^d�]�k�egdB����_Rp�W^X(� tFr p�egf(pg_R_���a WYh4_bX kgW r X�d�]KS~d�§ ¢ _b]^]�´µk_b� x dBegW r X kôT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T y �

� T à ¯°]^] x k�e�p�dBegW r X r�t X r egdBegW r X x kg_baNW^Xcegf(_��6d�avé_ ¢ _bW`�!f�e\d�]`� r pqW^egf h T�T�T�T�T�T y��� T±� ¿nr egdBegW r X x k�_baNe r WYX a(_�§c_bX�e�pqW^_bk\W^XNX r X�k�egdB����_Rpg_ba~d�X a�k�egdB����_Rpg_baHk�["dBegW^d�]

k�e�_bX jRWY]^k�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T y Ä� T Ä  $� x W`oBd�]`_bX�e ¢ _bW^�!f�egk�j r hi[�dBpqW^k r X T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ��Ç� T Ç � r!x p�W`_Rp\h x ]`egW`[�]YW^jRdBegW r X t d�j�e r p�k tFr p\a W��}_Rpg_bX�e�h4_Regf r a kÊT�T�T�T�T�T�T�T�T�T Ã��� TV| ��_Ro;WYdBegW r X r�t � r!x pqW`_Rp�h x ]`egW`[�]^WYjRdBegW r X t d�j�e r pqk t p r h>egf(_vWYa(_bd�]%k�e�pqd�W`�!f�eK]YW^X(_�l

j r h4[�dBpq_ba 9;:sr [}_RpqdBegW r X,j r!x X�e T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T à �� T Õ ·�_R� x ]^dBp���pqW^ack r ] x egW r X k�dBe��>y ��� x kgWYX(��a�W��7_Rpq_bX�e¦k�[�dBegWYd�]zdB[ [ p r §%W^h�dBegW r X k Ã�Ç� TÖ{ U%d�h4_�d�kK�KW^� x pg_ � T Õ l 9"x e x kqW^X(�\k�egdB����_Rpq_ba�dB[�[ p r §(W^hidBegW r X k tFr p8egf _vk�["dBegW^d�]

a(_RpqW^o�dBegW`o�_ T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T à |� T^y � U r ] x egW r X k t@r pikgegdB����_Rpg_baÞ��pqWYa�dBe��� �B����� ¢ W^egf���p�W^aÉkgW`¾R_bk4k�_b]`_bj�e�_baÞe r

hidB¤�_�j r h4[ x egdBegW r X�k¦_b� x d�]^] : egWYh4_���j r X k x h�W^X(�4W^X � ��� T�T�T�T�T�T�T�T�T�T Ã�Õ� T^y�yÞU r ] x egW r X k�dBe �� �B����� tFr psegf _~k�egdB����_Rpq_baM_�§;["]^W^jRW`e��� y�¨@²�_R_���e : [}_¬©

kgj�f(_bh4_ tFr pnW^X�j�pg_bd�kgW^X(�!] : �"X(_���pqWYa k T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T à {

W�§

à T^y ·�_R[�pg_bk�_bX�egdBegW`o�_ªkgd�h4[�]`_bk r�t o�dBp�W r!x k¥k�[�dBegW^d�]��¬egWYh4_���pqW^aÅ]^d :�r!x egk tFr p¥egf(_r X(_���a WYh4_bX kgW r X�d�] ¢ do�_�_b� x dBegW r X T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T � Ä

à T � ·�_R[�pg_bk�_bX�egdBegW`o�_�kgd�h4["]`_~kg[�dBegW^d�]���pqW^a­]^d :�r!x egk t@r pNegf _~e ¢ r ��a�W^h4_bX kgW r X d�]_b]^d�k�egWYj ¢ do�_�_b� x dBegW r X­T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T � Ç

à T à ·�_R[�pg_bk�_bX�egdBegW`o�_4kgd�h4[�]`_ r�t d�k�["dBegW^d�]���k�egdB����_Rpg_ba³l7egWYh4_���k�egdB����_Rpg_baH��pqWYa tFr pegf(_�e ¢ r ��a�W^h4_bX kgW r X d�]}_b]^d�k�egW^j ¢ dbo�_�_b� x dBegW r XÀT�T�T�T�T�T�T�T�T�T�T�T�T�T�T � Ç

à T±� � r!x pnpg_R[ pg_bkg_bX�egdBegW r X�k r�t Znw�U à T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ä yà T Ä � pqd�a(_�� r � 9 _Re ¢ _R_bXÊd�jRj x pqd�j : d�X aÉk�egd 9 W^]^W^e :�tFr p t@r!x pgegf r pqa(_Rp4k�egdB����_Rpg_ba

t pg_R_�[�dBpqd�hi_Re�_Rpnh4_Regf r aÁT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Ä�Õà T Ç U;egd 9 WY]^W`e : a r hid�W^X r�t h4_Regf r a�¨ à T^y|�© t@r p����� ��� y ��Ç T�T�T�T�T�T�T�T�T�T�T Ä�Õà TV| U;egd 9 WY]^W`e : a r hid�W^X k r�t egf(_ tFr!x pgegf r pqa(_Rp�kgegdB����_Rpg_ba t pg_R_�[�dBpqd�h4_Re�_Rp�kgjqf(_bhi_

¨ à T^y Õ ©÷T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ÇB�à T Õ U;egd 9 WY]^W`e : a r hid�W^X�k t@r p\kgegdB����_Rpg_ba�· x X(��_ÝÙ�¸ x e�egdih4_Regf r a k�T�T�T�T�T�T�T�T Ç�Õà TÖ{  �§(d�h4[�]^_ r�t d4p r�r e�[ r pge�p�d�W`enT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T |;yà T^y � · r;r e�[ r pge�pqd�W^egk t@r pnjR]^d�kgkgW^jRd�]zd�X�a�k�egdB����_Rpg_ba~h4_Regf r a k r�t a W��}_Rpg_bX�e r pqa(_Rpqk | Ãà T^y�yÞU%d�h4["]`_�p x X r�t Znw�U à x kgWYX(�iegf(_�[�f : kgW^jRd�]Y] : pq_b]`_Ro�d�X�e\p r�r e�d�X a��� à | Ä

tEx X j�egW r Xc_RoBd�] x dBegW r X�k T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T | Ç

��T^y � pqd�a(_�� r � 9 _Re ¢ _R_bX�d�jRj x p�d�j : d�X a�k�egd 9 WY]^W`e :�tFr p t@r!x pgegf r pqa(_Rp8X r X k�egdB����_Rpg_bat pg_R_�[�dBpqd�hi_Re�_Rpnh4_Regf r a�¨���T^y© T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T÷y �!Õ

��T � U;egd 9 WY]^W`e : a r hid�W^X r�t h4_Regf r a�¨��¡T^y© tFr p��� � ��� � y¶T�T�T�T�T�T�T�T�T�T�T�T÷y �!Õ

! /#"v¼���*

$ Ð ã6D@C� T^y  �§(d�h4[�]^_bk r�t �7X W`e�_�a W��}_Rpg_bX j�_�dB[ [�p r §(W^hidBegW r X�k T�T�T�T�T�T�T�T�T�T�T�T�T y �� T � �ª_bW`�!f�egk tFr p�_�§%[�]^W^jRW^eRl;pq_R� x ]^dBp���pqWYaN�K� tFr pqh x ]^dB_HT�T�T�T�T�T�T�T�T�T�T�T�T y|� T à �ª_bW`�!f�egk tFr p\W^hi[�]^W^jRW`e à ��a W^dB� r X d�]�l pg_R� x ]^dBp\��pqW^aN�6� t@r p�h x ]YdB_ T�T�T�T�T�T y Õ� T±� �ª_bW`�!f�egk tFr p\W^hi[�]^W^jRW`e Ä ��a W^dB� r X d�]�l pg_R� x ]^dBp\��pqW^aN�6� t@r p�h x ]YdB_ T�T�T�T�T�T yb{� T Ä �ª_bW`�!f�egk tFr p�_�§%[�]^W^jRW^eRl%kgegdB����_Rpg_ba,��p�W^aN�6� t@r pqh x ]^dB_ T�T�T�T�T�T�T�T�T�T�T yb{� T Ç �ª_bW`�!f�egk tFr p\W^hi[�]^W^jRW`e à ��a W^dB� r X d�]�l�k�egdB����_Rpg_ba���pqW^aN�6� tFr pqh x ]^dB_ T�T�T�T�T �B�� TV| �ª_bW`�!f�egk tFr p\W^hi[�]^W^jRW`e Ä ��a W^dB� r X d�]�l�k�egdB����_Rpg_ba���pqW^aN�6� tFr pqh x ]^dB_ T�T�T�T�T � y� T Õ £�WYhiW`egk r�t ¢ _bW^�!f�egk�d�k��&%(' T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ���� TÖ{ ��[}_RpqdBegW r XNj r!x X�e�e r jRd�]^j x ]^dBe�_*)#+}dBe r X(_���pqW^ac[ r W^X�e�T�T�T�T�T�T�T�T�T�T�T � {� T^y � uvr _�«sjRW`_bX�egk r�t ]`_bd�a WYX(��_Rpgp r p�e�_Rp�hik tFr p�a W`�7_Rpg_bX�e6��pqkge�a(_RpqW`oBdBegW`o�_\dB[ [�p r §;�

W^hidBegW r X kªT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T � {� T^y�yÉZn[ [ p r §%W^h�dBe�_�pqdBegW r�r�t ]`_bd�a WYX(��_Rpgp r p$j r _�«sjRW`_bX�egk��6k�egdB����_Rpg_base r X r X kgegdB�B�

��_Rpg_ba�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ÃB�

à T^y U;egdB����_Rpg_ba 9 d�jq¤ ¢ dBpqa kna W��}_Rpg_bX�egWYdBegW r XcegW^h4_�W^X�e�_R��pqdBe r pqkÈT�T�T�T�T�T�T�T�T Ä��à T � U;egdB����_Rpg_ba~Z�a d�hik°��w�d�kgf tFr pgegfNegWYh4_�W^X�e�_R��pqdBe r pqk T�T�T�T�T�T�T�T�T�T�T�T�T Ä�Ãà T à ¿nr X k�egdB����_Rpg_ba~Zna�d�hik°��w�d�kgf tFr pgegf�egWYh4_�W^X�e�_R��pqdBe r pqköT�T�T�T�T�T�T�T�T�T�T Ä �à T±�  �pqp r p��!W^o�_bX 9;: p x X X�W^X(�cegf(_ck�_bj r X a r pqa(_Rp�]^_bdB[ t p r ��h4_Regf r a x kgW^X(�,egf(_

p r;r e�[ r pge�pqd�W`e�e�_bj�f X W^� x _NT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T |�|

§%W

à T Ä  �pqp r p��!W`o�_bX 9;: p x X X WYX(�cegf W`pqa r p�a(_Rp�h4_Regf r a k x kgW^X ��egf(_�p r�r e�[ r pqe�pqd�W`ee�_bjqf�X W^� x _ T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T | Õ

à T Ç ¨Ed�©\ �pgp r pn�!W`o�_bX 9�: p x X�X W^X(� tFr!x pgegf r p�a(_RpnX r X�k�egdB����_Rpg_ba~h4_Regf r a k x kqW^X(�egf(_�p r�r e�[ r pge�p�d�W`e�e�_bjqf X WY� x _ T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T |B{

à T Ç ¨ 9 ©� $pgp r p¦�!W`o�_bX 9�: p x X X�W^X(� tFr!x pgegf r p�a(_Rp�k�egdB����_Rpg_ba~h4_Regf r a k x kgWYX(�¡egf(_p r;r e�[ r pge�pqd�W`e�e�_bj�f X W^� x _NT�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T ÕB�

à TV|  �pqp r p$�!W`o�_bX 9;: p x X X WYX(��k�_Ro�_bX�egf r pqa _Rpvh4_Regf r a k x kgW^X ��egf(_np r�r e�[ r pqe�pqd�W`ee�_bjqf�X W^� x _ T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Õ y

à T Õ  �pqp r pn�!W^o�_bX 9;: p x X X�W^X(�¡_bW`�!f�egf r pqa _Rpnh4_Regf r a k x kgW^X �4egf(_�p r;r e�[ r pqe�pqd�W`ee�_bjqf�X W^� x _ T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T�T Õ y

à TÖ{ uvr h4["dBpqW^k r X r�t%tFr!x pgegf r p�a(_Rp�egW^hi_�W^X�e�_R��p�dBe r pqkR�8X r X k�egdB����_Rpg_ba�o;kbT8k�egdB����_Rpg_ba Õ�Ã

�$/#,$��� � -

.��8�B��)6 �5$#;�!��)8�

� f W^kKegf(_bkqW^k�a r j x h4_bX�egk6e ¢ r pg_bk�_bdBp�jqf4[ p r Ì°_bj�egk ¢ f W^j�f�f�dbo�_ 9 _R_bXijRdBpgp�W`_ba r!x e�dBeegf(_�m�X W`o�_RpqkqW`e :�r�t³u�r ] r pqd�a r dBe�w r!x ]^a _Rp�W^X4j r ]^]^d 9}r pqdBegW r X ¢ W`egf4h : k x [}_Rpgo%W^k r plB�$p r�t _bkgk r pwv_bX(��e\� r p�X 9 _Rpg�(l�d�X�a ¿ U(�Á¨E]YdBe�_Rp ¿ U%�8� õ ¯g��·\ �©v[ r k�e°��a r j���pbT �8r�9 W^XNZ�T���pqW^kgj r ]^]�T

� f(_�e ¢ r [�p r Ì°_bj�egkndBpg_�a(_bkqj�pqW 9 _bacW^X u f dB[ e�_Rp�k � d�X a à �� TvU;["dBegW^d�]7�"X W`e�_�a W`�7_Rpg_bX�j�_�dB[ [ p r §%W^h�dBegW r X k tFr p ¢ dbo�_�_b� x dBegW r X�kà TvU;egdB����_Rpq_ba�egW^h4_�W^X�e�_R��p�dBe r pqk tFr p ¢ dbo�_�_b� x dBegW r X�kRT

Zn]^egf r!x �!fNW`e\WYk�a W�«sj x ]`e�e r W^a(_bX�egW tF: W^X a�W`o;WYa x d�]�j r X�e�pqW 9"x egW r X k�WYXNj r ]^]^d 9}r pqdBegW`o�_[ p r Ì�_bj�egkRl d�XNdBe�e�_bh4[�e ¢ W^]^] 9 _�hid�a _�W^X¥egf(_�W^X�e�p r a x j�egW r X r�t _bd�jqf,jqf dB[ e�_Rp\e r4r!x eg]^W^X(_�h :j r X�e�pqW 9�x egW r X k�e r _bd�jqf,[ p r Ì�_bj�eRT

- ë - .¬�8���!)� $5$#;�!��)��¯-X­hid�X : kgW`e x dBegW r X kRl¦�7X a W^X(��d�X­d�X�d�] : egWYj�k r ] x egW r XÅe r d�[�dBpgegWYd�]na W`�7_Rpg_bX�egW^d�]

_b� x dBegW r X r p¥d�k : kge�_bh r�t k x jqfÅ_b� x dBegW r X k¥W^k x X pg_bd�]^W^k�egWYj r ps_Ro�_bX­W^h4[ r kgkgW 9 ]`_0/�X x h4_Rp��W^jRd�]¦h4_Regf r a kiegf dBe x egW^]YW`¾R_Nj r h4[ x e�_Rp�d�]^� r pqW`egf hik4dBpq_Negf(_bX x k�_baÞe r �"X a¶dB[ [�p r §(W^hidBe�_k r ] x egW r X kRT � f _ tFr j x k r�t�r!x p�pg_bkg_bdBpqjqf�f�d�k 9 _R_bX~e r [ p r a x j�_�X(_ ¢ kgj�f(_bh4_bk tFr p�X x h4_RpqW��jRd�]^] : k r ]^o;W^X ��]^W^X(_bdBp ¢ do�_���e : [7_�_b� x dBegW r X k�¨Ek x j�fsd�kvS~d�§ ¢ _b]^]�´µk�_b� x dBegW r X kRl;d�j r!x k�egW^j ¢ do�__b� x dBegW r X kRl d�X�as_b]Yd�k�egW^j ¢ dbo�_�_b� x dBegW r X kÝ©�egf dBe�dBpg_�h r pg_�d�jRj x pqdBe�_�l�]`_bkgk¦j r hi[ x egdBegW r X d�]Y] :W^X�e�_bX kgW`o�_�l³d�X�a�� r p�_bd�kgW`_Rp�e r WYh4[�]`_bh4_bX�e�egf d�Xªj x pgpq_bX�eg] :~x k�_baHW^X a x k�e�p : k�egd�X�a dBpqa k�k x jqfd�k�egf(_�kg_bj r X a r p�a(_Rp¡¨EWYX 9}r egf,kg[�d�j�_�d�X�a,egW^hi_¬©v�"X W^e�_���a W��}_Rpg_bX j�_�²�_R_¡kgj�f(_bh4_�T uvr h4[ x �egdBegW r X d�]"j r k�e 9 _bj r h4_bk�_bk�[}_bjRW^d�]^] : W^h4[ r pgegd�X�e$d�k$egf(_nX x h 9 _Rp r�t _b� x dBegW r X�k$W^X4egf _nk : k�e�_bh

W^X j�pq_bd�k�_bkRT�6W^X W`e�_�a W`�7_Rpg_bX�j�_�h4_Regf r a k x egW^]^W`¾R_�]YW^X(_bdBp\j r h 9 W^X dBegW r X k r�t6tEx X j�egW r X,o�d�] x _bk r X

dNa W^kqj�pg_Re�_¡��pqW^a~e r dB[ [ p r §%WYhidBe�_ia(_RpqW`oBdBegW`o�_¡oBd�] x _bkRT � f(_bk�_4h4_Regf r a k�f do�_ 9 _R_bX~¤;X r ¢ XtFr p�hid�X :~: _bdBp�k�d�X a�kg_Ro�_Rpqd�]�X(_ ¢ _Rp�h4_Regf r a k�f�dbo�_ 9 _R_bX tFr!x X aªkqW^X j�_¡egf(_bXŨF_�T±�(T��"X W`e�__b]`_bh4_bX�egkRlzk�[}_bj�e�pqd�]�l}d�X a~[�k�_ x a r k�[}_bj�e�pqd�]�hi_Regf r a�k�©1/}egf x kbl r X _�hiW^�!f�e�� x _bk�egW r X ¢ f : ¢ _dBpg_�pg_Ro;WYkgW`egW^X(� ¢ f dBeie r k r h4_�h�W`�!f�e¥k�_R_bhËe r�9 _,d�X r!x ega dBe�_baÊ��_b]^azTÁ¯°XÞegf(_~j r X�e�_�§%er�t j r hi[ r kqW`e�_¡��pqW^a~h4_Regf r a kRlzf r ¢ _Ro�_Rpblz�7X W`e�_¡a W��}_Rpg_bX j�_¡h4_Regf r a k�[�]^d : d¥¤�_ : p r ]`_�T�� r p_�§(d�h4[�]`_�l�W^X r X(_�h r a _b]�l 9 ] r jq¤�[�k�_ x a r k�[}_bj�e�pqd�]�h4_Regf r a k2�yBl �43 dBpg_ x egW^]^W^¾R_ba r X 97r!x X a dBpqW`_bkd�X aÁW^X�e�_Rp t d�j�_bk�d�k ¢ _b]Y]nd�k�WYX r egf(_RpNpq_R�!W r X k r�t f�W`�!fÅd�j�egW^o;W`e : l ¢ f W^]`_��"X W`e�_Ha W��}_Rpg_bX j�_h4_Regf r a k�dBpg_ x kg_ba tFr p¦egf(_ 9 d�jq¤���p r!x X ac��pqW^a ¢ f WYjqf r o�_Rpq]^dB["k ¢ W`egf¥egf(_bk�_�[�kg_ x a r k�[}_bj�e�pqd�]k�e�pqW^[�kRT�U%W^h4[�]^_�l�pg_b]^dBegW^o�_b] : ] r ¢ ��j r k�ev�"X W`e�_�a W��}_Rpg_bX j�_�h4_Regf r a k�dBpq_ x kg_ba r Xsegf(_�hid¬Ì r pqW`e :r�t egf(_���pqWYazl [ p r a x jRWYX(��dsX r o�_b]8j r h4[ r kgW`e�_�hi_Regf r a,egf dBe\j r h 9 W^X(_bknf W`�!f�d�jRj x pqd�j : ¢ W`egf] r ¢ j r h4[ x egdBegW r X�d�]Kj r kge�egf dBe�W^k�k�egW^]^]KdB[ [�]YW^jRd 9 ]`_�e r j r h4[�]`_�§~��_ r h4_Re�pqW`_bkRT � f(_4k�[}_bjRW��"jtFr j x k r�t egf W^k\pg_bk�_bdBpqj�f ¢ d�k�e r _�§%[�] r pg_�d�X a,WYh4[ p r o�_�egf(_��"X W`e�_�a W��}_Rpg_bX j�_�h4_Regf r a knd�X aegW^h4_�kge�_R[ [�W^X(�4h4_Regf r a k�e ri9 _ x k�_ba tFr p�egf W^k 9 d�jg¤;��p r!x X aN��p�W^azT

� f(_~��pqkgeN� r d�] r�t egf W^kcpg_bkg_bdBpqjqf [ p r Ì�_bj�e ¢ d�k,e r W^X�o�_bk�egW`�!dBe�_�egf(_ªo�_Rp : f W`�!fj r h4[ x egdBegW r X d�]�_�«¥jRW`_bX j :ªr�t f W`�!f(� r pqa(_Rp��"X�W`e�_�a W��}_Rpg_bX j�_sh4_Regf r a kRlK_bk�[}_bjRW^d�]^] : d�k�egf _ :W^X j r pq[ r p�dBe�_ t _bdBe x pg_bk4k x jqfÉd�k4W^h4[�]YW^jRW`egX(_bkgk�d�X a���pqW^a�k�egdB����_RpqW^X(�(T u f dB[ e�_Rp � [ pg_bk�_bX�egkr!x p4d�X d�] : kgW^k r�t �7X W`e�_ca W��}_Rpg_bX j�_cdB[ [ p r §%W^h�dBegW r X k t@r p4egf(_¥��p�k�e�a(_Rp�W`o�dBegW^o�_cWYX�e�_Rpqh�k r�td�jRj x pqd�j : d�X�a�j r h4[ x egdBegW r X d�] j r k�eRl%j r X kgWYa(_RpqW^X(� 9}r egf4_�§%[�]^WYjRW`e�d�X a�W^hi[�]^W^jRW`e¦¨Ed�]^k r ¤;X r ¢ Xd�k�j r hi[�d�j�e�W^X�egf(_�]^W`e�_Rp�dBe x pg_¬©�kgj�f(_bh4_bk r Xªpg_R� x ]^dBp�d�X a�k�egdB����_Rpq_ba���pqWYa kRTi�Áf W^]`_ 9}r egfW^h4["]^W^jRW`e�k�e�_bX jRW^]^k¡d�X a¶kgegdB����_Rpg_baÞ��pqWYa k¡f dbo�_ 9 _R_bX¶j r X kqW^a(_Rpg_ba 9 _ tFr pg_�l�egf W^k4WYk¡egf(_¥��pqk�ek�e x a : e r j r h 9 W^X _�egf(_bkg_¡j r X�j�_R[ egk�d�X a~e r egf r p r!x �!f ] : d�X d�] : ¾R_�egf _bh0WYX,e�_Rpqh�k r�t j r h¡�[ x egdBegW r X d�]zj r k�eRT � f r!x �!fcegf(_�kgj�f(_bh4_bk�pq_bhid�W^Xcpg_b]^dBegW^o�_b] : j r h4["d�j�eRl egf(_ : jRd�X�dB[ [ p r d�j�fegf(_�k x [}_RpqW r p$d�jRj x pqd�j : d�X a�_��7_bj�egW^o�_bX(_bkgk r�t k�[}_bj�e�pqd�]7h4_Regf r a k ¢ f W^]`_�k�egWY]^] d�]^] r ¢ W^X(��k r h4_9}r!x X a dBp :i® _�§(W 9 W^]YW`e : T¦��pqW^a�k�egdB����_RpqW^X(�¥f d�k 9 _R_bX r�9 k�_Rpgo�_ba~W^XNegf(_�[�d�k�e�e r¥9 _ 9 _bX(_��"jRW^d�]W^XÉk r h4_�jRd�kg_bk,¨F_�T±�(T¶egf(_¥²�_R_,kgj�f(_bh4_ tFr p�j r h4[ x egdBegW r X d�]�_b]`_bj�e�p r hidB�!X _RegW^jRk�©�l 9�x e r!x p

¢ r pg¤�f�d�k$kgf r ¢ X4egf dBe�k�egdB����_RpqW^X(��j r h 9 WYX(_bk�� x W`e�_ t dbo r pqd 9 ] : ¢ W^egf 9}r egf4W^h4[�]^WYjRW`egX(_bkgkKd�X a

Ã

f W`�!f r pqa _Rpqk r�t d�jRj x p�d�j : l t _bdBe x pg_bk¡egf�dBeidBpg_�]^d�jg¤%W^X(�ªW^X�egf(_c²�_R_�kqjqf(_bh4_�d�X aÉW^XÉh r k�er egf(_Rpn[ pg_Ro%W r!x k�dB[ [�]^WYjRdBegW r X k r�t k�egdB����_Rpg_ba,��pqW^a kRT

� f(_�W^a _bd�e r d�]^k r�x k�_���p�W^aik�egdB����_RpqWYX(� tFr p$egW^hi_\W^X�e�_R��pqdBe r pqkRl;egf(_�e r [�WYj r�t�u f dB[(�e�_Rp à l�WYk�_bX�egW`pq_b] : X(_ ¢ T��ª_�f do�_i_�§%[�] r pg_baHoBdBpqW^dBegW r X�k r�t egf(_iZ�a d�hik°��w�d�kgf t@r pgegf³l 9 d�jg¤��

¢ dBpqa k�a W��}_Rpg_bX�egW^dBegW r Xzl;d�X ac· x X(��_���¸ x e�egd t d�hiWY]^W`_bk r�t egW^h4_�W^X�e�_R��p�dBe r pqk�e r k r ]`o�_�k : k�e�_bhikr�t ]YW^X(_bdBp ¢ do�_i_b� x dBegW r X k r X x X W tFr pqhNl7egW^h4_���kgegdB����_Rpg_baª��pqW^a�kRT�¯-X~egf(_4W^hi[ r pqegd�X�e�dB[ [�]^W`�jRdBegW r X r�t k r ]`o%W^X(�i]^WYX(_bdBp ¢ dbo�_¡_b� x dBegW r X k�¨F_�T±�(T�d�j r!x k�egW^j r pn_b]Yd�k�egW^j ¢ dbo�_bkRl r p�S�d�§ ¢ _b]^]�´µk_b� x dBegW r X k t@r pn_b]`_bj�e�p r hidB�!X(_RegWYjRk�©�l7X _bdBpq] : d�X r pqa _Rp r�t hidB�!X W`e x a(_��!d�W^X�jRd�X 9 _�d�jqf�W`_Ro�_baW^X�d�jRj x pqd�j : ¨ tFr p¡egf(_ckgd�h4_cj r h4[ x egdBegW r X�d�]�j r k�eRl�W^X 9}r egf r [7_Rp�dBegW r X�j r!x X�e4d�X a�h4_bh¡�r p : ©¦j r h4["dBpg_ba~e r jR]^d�kgkqW^jRd�]8X r X k�egdB����_Rpg_ba~egW^h4_�W^X�e�_R��pqdBe r pqkRT�¯°X~d�a a W`egW r X³l egf(_�kgegd 9 W^]^W`e :[ p r [}_RpgegW^_bk r�t egf _bk�_�X(_ ¢ k�egdB����_Rpg_ba­h4_Regf r a k�dBpg_�k x [}_RpqW r p¡e r egf _,jR]^d�kgkgWYjRd�]�h4_Regf r a kRT�ª_NW^X�o�_bk�egW`�!dBe�_¥egf(_¥d�jRj x pqd�j : d�X a�k�egd 9 W^]YW`e :Hr�t egf(_bkg_¥X(_ ¢ jR]^d�kgkg_bk r�t hi_Regf r a�k�d�X d�] : e°�W^jRd�]^] : l�_�§;[}_RpqW^hi_bX�egd�]^] : l6d�X�a�egf p r!x �!f�egf(_ x k�_ r�t dHX r o�_b]�p r�r e�[ r pge�pqd�W`e�e�_bjqf X�W^� x _�T~¯°Xd�a a W^egW r Xzl$k�_Ro�_Rp�d�]¦¤�_ : egf(_ r pg_RegW^jRd�]¦pq_bk x ]`egk4j r X j�_Rp�X W^X(��k�egdB����_Rpq_baÞegW^h4_�WYX�e�_R��pqdBe r p�kidBpg_�!W`o�_bXzl7W^X jR] x a W^X(�¡di��_bX(_Rp�d�]^W`¾bdBegW r X r�t ��d�f ]Y� x WYk�eR´µk��6W`pqk�e�U;egd 9 W^]^W^e : wvdBpqpqW`_Rp tFr pnk�egdB����_Rpq_bah4_Regf r a kRT

� x p�pg_bk x ]`egk¦f dbo�_�d�]`pg_bd�a : W^h4[�d�j�e�_bacegf(_��"_b]^a r�t ¢ dbo�_�j r h4[ x egdBegW r X�kRT$� r p�_�§;�d�h4[�]^_�l�k�_Ro�_Rpqd�]$pg_bk�_bdBpqj�f���p r!x ["k�¨F_�T±�(TsdBe�mn[ [�kqd�]^dNmnX�W`o�_RpqkgW`e : d�X�a�wvp r ¢ X�mnX W^o�_RpqkgW`e : ©j x pgpq_bX�eg] : _bh4[�] r¬:ir!x p�k�egdB����_Rpg_ba�egW^h4_�W^X�e�_R��p�dBe r pqk tFr p�hid¬Ì r p¦W^X�a x k�e�pqWYd�] _b]`_bj�e�p r h�dB�!X(_Re°�W^jRk�jRd�]^j x ]^dBegW r X�kRT�¯°X�d�a a�W`egW r Xzl³�ª_bWYa ]^W^X(��_Rp�Znkgk r jRW^dBe�_bkc¨EW^X�£ r k�Z�]`e r kRl u Z�©�f d�k�W^h4[�]`_��h4_bX�e�_ba r!x p�hi_Regf r a�k4e r kgW^h x ]^dBe�_c_��}_bj�egk�pq_b]`_Ro�d�X�e4e r h4_ba�W^jRd�] x ]`e�p�d�k r!x X azl ¢ W`egf r X(_] r X(�B��e�_Rp�h � r d�] 9 _bW^X(��e r pg_R["]^d�j�_�5n��pqd : k ¢ W`egf x ]`e�pqd�k r!x X aiW^X¥dBpg_bd�k�k x j�fsd�k�hid�h�h r ��pqd��[�f : T\Z�X r egf(_Rp�[ r e�_bX�egW^d�]KdB[ [�]^WYjRdBegW r X tFr p r!x p�kgj�f(_bh4_bk�W^k tFr p ¢ dBpqa~k�_bW^kghiWYj�h r a(_b]^W^X(� tFr pf : a(p r jRdBp 9}r Xc_�§%[�] r pqdBegW r XzT

- ë@ê 6 ¼�)�*B*¬/}�07�)³+�/8"9"��!�(1���/7�!��)8�$*N/z�$ ��� ��½­*,5$*��� �����!�$�Æ* ,$/8,¦� �wv_bjRd x k�_ ¢ _ x k�_~d�X x h 9 _Rp r�t d�j�p r X : hik ¢ f W^j�fÊhid :Ê9 _ x X t d�h�W^]^W^dBp4e r egf(_

pg_bd�a(_Rpl d4�!] r kgkgdBp :sr�t egf(_bk�_�d 9 9 pg_Ro%W^dBegW r X k¦WYk¦W^X jR] x a _ba¥f _Rpg_�TZ�w;: Zna�d�hik-Ù�w�d�kgf tFr pgegf�h4_Regf r a r�tKr pqa(_Rp�:Z�w¦U<: U;egdB����_Rpg_ba�Zna d�h�k-Ù�w�d�kgf tFr pgegf,h4_Regf r a r�t6r pqa(_Rp�:w��=: w�d�jg¤ ¢ dBpqa�k\a W��}_Rpg_bX�egW^dBegW r XNh4_Regf r a r�t6r pqa _Rp�:w���U4: U;egdB����_Rpg_ba 9 d�jg¤ ¢ dBp�a k\a W`�7_Rpg_bX�egW^dBegW r XNhi_Regf r a r�t8r pqa _Rp�:_Rpgp r pnj r X k�egd�X�e uvr _�«sjRW`_bX�e?>>egf dBe��!W^o�_bk\d�XN_bk�egWYhidBe�_ r�t ] r jRd�]}e�p x jRdBegW r X

_Rpgp r p\e ri9 _�_�§%[}_bj�e�_ba t p r h'dihi_Regf r a@/(egf(_�] r jRd�]e�p x X�jRdBegW r Xc_Rpgp r p\WYk¦�!W`o�_bX 9;: >*ACBED � )GF BED �IH ¨KJ!©�l¢ f(_Rpq_=:HW^k�egf(_ r p�a(_Rp r�t egf(_�h4_Regf r azT¨ �8rir�9 egd�W^X�d�X,d�a(_b� x dBe�_��!] r�9 d�]z_Rpqp r p�_bk�egW^h�dBe�_�l�X r pqhid�]YW`¾R_�egf(__Rpgp r pnj r X k�egd�X�e 9�:ML ¨°y© tFr p\h x ]`egW^kge�_R[�h4_Regf r a kRT �8rir�9 egd�W^Xd¡oBd�]^W^aNj r h4[�dBp�W^k r Xzl h x ]`egW`["] : egf(_�_Rpgp r p\j r X k�egd�X�e 9;: N BtFr p\d�X N ��k�egdB��_�h4_Regf r azTV©

_�§%[�]^W^jRW`e � r pnkg[�dBegW^d�]z�6� dB[ [ p r §%WYhidBegW r X kRl d�h4_Regf r a ¢ f(_Rpg_r X(_ x X ¤;X r ¢ XNa(_RpqW^o�dBegW`o�_�oBd�] x _�WYk��!W`o�_bX 9;: d�]^W^X(_bdBpj r h 9 W^X dBegW r X r�t ¤%X r ¢ X tFx X j�egW r XcoBd�] x _bkRT

� r pn�6�>egW^hi_�W^X�e�_R��p�dBe r pqkRl�dihi_Regf r a ¢ f(_Rpg_�egf(_ x X(¤;X r ¢ X¨ tEx e x pg_¬© tEx X j�egW r XcoBd�] x _�WYk��!W`o�_bX�W^XNe�_Rp�hik r�t ¤;X r ¢ XtEx X j�egW r XNd�X aNa _RpqW`oBdBegW`o�_�o�d�] x _bkRT

�6� �6W^X W`e�_�a W��}_Rpg_bX j�_�6� � � �6W^X W`e�_���a W`�7_Rpg_bX�j�_�egWYh4_���a r hid�W^X�¨Ekg_R_O2 � | 3 ©�6�vU4: U;egdB����_Rpg_ba t pg_R_�[�dBpqd�h4_Re�_Rp\hi_Regf r a r�tKr p�a(_Rp�:

Ä

W^h4["]^W^jRW`e ¯°X�k�[�dBegWYd�]z�K� dB[�[ p r §(W^hidBegW r X kRl d4h4_Regf r a ¢ f _Rpg_�]^W^X(_bdBpj r h 9 W^X�dBegW r X k r�t�x X(¤%X r ¢ XNa(_RpqW`oBdBegW`o�_�oBd�] x _bk¦dBpg_��!W^o�_bXWYXce�_Rpqhik r�t ]^W^X _bdBp�j r h 9 WYX dBegW r X k r�t ¤%X r ¢ X tEx X j�egW r XNo�d�] x _bkRT

� r pnegW^h4_�W^X�e�_R��pqdBe r pqkbl"d4�6� dB[ [ p r §%WYhidBegW r X ¢ f _Rpg_�egf(_ x X(¤%X r ¢ X¨ tEx e x pq_¬© tFx X�j�egW r Xco�d�] x _�W^X jR] x a(_bk�d4e�_Rpqh'W^X�o r ]`o%W^X(�4d�Xx X(¤;X r ¢ X�¨ tEx e x pg_¬©va _RpqW`oBdBegW`o�_�o�d�] x _�T

¯gU%w ¯°hidB�!W^X dBp : U;egd 9 W^]^W`e : w r!x X a dBp : �$egf(_�]YdBpg��_bk�e�¨Fpg_bd�]F©vo�d�] x _ r�t�P�Qk x jqfNegf�dBe�egf(_�W^X�e�_RpgoBd�]92R��S P QCTUS P Q 3 W^k¦j r X�egd�W^X(_ba�W^Xcegf(_kgegd 9 W^]^W`e : a r h�d�W^X r�t d¡egW^h4_���k�e�_R[ ["W^X(�ikgj�f(_bh4_�T¨E� r pnd�X N ��k�egdB��_�·n¸ h4_Regf r azl X r p�hid�]^W`¾R_�egf(_�¯gU%w 9;:MN TV©

����  ��p�a W^X dBp : a W��}_Rpg_bX�egWYd�]}_b� x dBegW r X�6d�a�é_ Zn[ [ p r §%WYhidBegW r X r�t d¡�!W`o�_bX tEx X j�egW r X 9�: d4pqdBegW r X�d�] tFx X�j�egW r X

¨ 9;: hidBegjqf�W^X(�id�k\h�d�X : a(_RpqW`oBdBegW`o�_bk�d�k�[ r kqkgW 9 ]`_�dBe\k r hi_�[ r W^X�e�©�$��  �6dBpgegW^d�]�a W��}_Rpg_bX�egWYd�]}_b� x dBegW r X�vU ��k�_ x a r k�[}_bj�e�pqd�]·\¸: · x X(��_ÝÙ�¸ x e�egd�h4_Regf r a r�t8r p�a(_Rp�:·\¸�U4: U;egdB����_Rpq_ba,· x X(��_ÝÙ�¸ x e�egdihi_Regf r a r�tKr p�a(_Rp�:U;egd 9 WY]^W`e : a r hid�W^X � r p�d4�!W`o�_bXNegWYh4_�W^X�e�_R��pqdBe r pbl�egf _�k�_Re r�t9V A

oBd�] x _bk\W^Xcegf(_�j r h4[�]^_�§¥[�]Yd�X(_�egf dBe��!W`o�_�k�egd 9 ]`_�k r ] x egW r X k tFr pegf _�[ p r�9 ]`_bhXWY+Z V WH¨[ANWYk�egf(_�k�e�_R[,kqW`¾R_¬©�T

�8r _R[�]YW`e�¾ Z ��r _R[�]^W^e�¾�hidBe�pqW�§NW^k¦j r X k�egd�X�end�] r X(�id�]^]za W^dB� r X�d�]^kRlW�T±_�T�egf(_Rpg_�_�§(W^k�e�X x h 9 _Rp�k\�]Z^ D � T_\9]Z^ D Û T �`�`� T_\GaCT �`�`� T_\b^c] �k x jqfNegf�dBe�d�ó4e fZg\Kó4]Zf tFr p?A#T_h;>yCT � T �`�`� Tgò �

Î �$/#,$��� � ê

i ,$/7�!��/z¼������$������������� �!����#%� ¹ ,=,$�!)�j���½­/7����)��$*c+°)³��. / 1��É2¡365$/"�!��)��$*

� f(_vkgW^h4[�]^_bk�e³�"X�W`e�_�a W`�7_Rpg_bX�j�_vdB[ [�p r §(W^hidBegW r X�k tFr p�k�[�dBegW^d�];a(_RpqW`oBdBegW`o�_bk6dBpg_�j�_bX%�e�_Rpg_baÞd�X�a¶_�§;["]^W^jRW`e¡d�X a¶dBpg_,dB[�[�]^W`_ba�e rlk pg_R� x ]YdBpb´�_b� x W^k�[�d�j�_baÉ��pqWYa kRT��ª_b]^]���_bk�egd 9 ]YW^kgf(_ba��_bX(_Rpqd�]YW`¾bdBegW r X knW^X jR] x a _�egf(_ x kg_ r�t W^h4[�]YW^jRW`e�¨Ej r h4[�d�j�e�©ndB[ [ p r §(W^hidBegW r X k\d�X a,k�egdB����_Rpq_ba��pqW^a�kRT ¯°XÁegf W^kcjqf�dB[ e�_Rpbl ¢ _H�7X a­egf dBeNegf(_�j r h 9 W^X dBegW r X r�t egf(_bk�_ªe ¢ r j r X j�_R[ egkRl�e r ���_Regf(_Rp ¢ W^egf�f W^�!f tFr pqhid�] r pqa(_Rp r�t d�jRj x pqd�j : lvWYk�o�_Rp : _��7_bj�egW^o�_ t@r p4dB[ [ p r §(W^hidBegW^X(�~egf(_��pqkge�a(_RpqW`oBdBegW`o�_bk¦W^XNk�["d�j�_�egf dBe r jRj x p\W^X,hid�X : ¢ dbo�_���e : [}_����� $kRT

ê�ë - .¬�8���!)� $5$#;�!��)��£�W^X _bdBp ¢ dbo�_�_b� x dBegW r X kRl�_bk�[}_bjRW^d�]^] : W^X­e ¢ rÞr p,h r pg_�a�W^h4_bX kgW r X kRl�dBpg_ r�t e�_bX

tFr pqh x ]^dBe�_baÞd�k4�"pqk�e r pqa(_Rpsk : kge�_bhikRTÅ�6W`p�k�e r pqa(_Rp tFr pqh x ]^dBegW r X�k4e�_bX a¶e r�9 _Re�e�_Rpspg_ ® _bj�eegf(_i["f : kgW^jRk r�t egf _i[ p r�9 ]^_bhØd�X a r�t e�_bX�d�]Y] r ¢ t@r p�_bd�kgW`_Rp�WYh4[�]`_bh4_bX�egdBegW r X r�t¦9}r!x X�a dBp :j r X a W^egW r X kRT8�ª_�dBpg_¦X r e�d ¢ dBpg_ r�t d�X : ]YW^X(_bdBp ¢ do�_�_b� x dBegW r X k ¢ f W^j�f¡jRd�X X r e 9 _vpq_ ¢ pqW`e�e�_bXd�k���pqkge r pqa _Rp�k : k�e�_bh�kRT � f x kRlzW^X~egf W^k�jqf�dB[ e�_Rpbl ¢ _ ¢ W^]^]8j r X kgW^a(_Rp r X ] : dB[ [ p r §%WYhidBegW r X kr�t ��pqk�e�a(_Rp�W`o�dBegW^o�_bkRT

� f(_�[�pqW^hidBp : pg_b� x W`pg_bh4_bX�egk tFr p�X x h4_Rp�W^jRd�]�dB[ [�p r §(W^hidBegW r X�k r�t k�[�dBegW^d�]���pqk�ea(_RpqW^o�dBegW`o�_bk\dBpg_

¨°y©�f W`�!fNd�jRj x pqd�j : l¨ � ©�] r ¢ r [}_RpqdBegW r X�j r!x X�eRl

d�X aNegf _ r o�_Rpqd�]^]�pg_bk x ]^egW^X(�¡h4_Regf r a�kgf r!x ]Ya t _bdBe x pq_

|

¨ à ©�j r h4[�dBegW 9 WY]^W`e : ¢ W`egfcj x pgo�_baNW^X�e�_Rp t d�j�_bk¦d�X acX r X%��pg_ ® _bj�egWYX(� t dBp���_b]^a 9}r!x X a(�dBp : j r X a W`egW r X kRT

U;_Ro�_Rpqd�]¦X x h4_RpqWYjRd�]�dB[ [�p r d�jqf(_bki_�§%j�_b]¦W^X r X(_ r pik r hi_RegW^h4_bk¡e ¢ r�r�t egf(_bk�_cpg_��k�[}_bj�egk`/ tFr p�_�§%d�h4["]`_�l}�"X W`e�_�_b]`_bh4_bX�e�h4_Regf r a k�f dbo�_4a W�«¥j x ]`e : d�j�f W`_Ro%W^X(�cf W`�!fHd�jRj x pqd�j :

¢ W`egf r!x e�d�]^dBpg��_ r [7_Rp�dBegW r X�j r!x X�eRl ¢ f WY]`_$k�[}_bj�e�pqd�]�d�X a�["k�_ x a r k�[}_bj�e�pqd�]�h4_Regf r a kKdBpg_ r�t e�_bXW^X j r hi[�dBegW 9 ]`_ ¢ W`egfNj x pgo�_ba,W^X�e�_Rp t d�j�_bkRT

�ª_�j r X kgW^a _Rp�egf(_ x k�_ r�t j r h4[ r kgW`e�_¦h4_Regf r a kRl ¢ f(_Rpg_¦f W`�!f%� r p�a(_Rp�W^X�e�_Rp t d�j�_¦e�_bj�f%�X W^� x _bk�dBpg_ x k�_ba¥d�] r X(�¡hidBe�_RpqW^d�]7a W^kgj r X�egW^X x W`egW`_bk�d�X a 97r!x X a dBpqW`_bkm2 Ç l | 3 d�X as�"X�W`e�_na W`�7_Rp��_bX j�_�h4_Regf r a k�¨ tFr p\_b� x W^k�[�d�j�_ba���pqW^a k�©vdBpq_ x k�_ba r X�egf(_�pq_bhid�W^X W^X �idBpg_bd�k r�t egf(_�j r h4[ x �egdBegW r X d�]6a r h�d�W^XzT � f W^knj r h 9 W^X dBegW r XHdB[ [ p r d�jqfªh4_R_Regk�d�]^]8egf(pg_R_�pg_b� x W`pg_bhi_bX�egk�d�X a~jRd�Xd�jqf�W`_Ro�_iX(_bdBp���k�[}_bj�e�pqd�]�d�jRj x pqd�j : pq_b� x W^pqW^X(� r X ] : d 9}r!x e��B� Ä [ r W^X�egk�[7_Rp ¢ dbo�_b]`_bX ��egf�d�X ad 9}r!x e Ç � Õ dBp�W`egf h4_RegW^j r [}_RpqdBegW r X k t@r p�_bd�j�fªk�[�dBegW^d�]Ka(_RpqW`oBdBegW`o�_�dBe�_bd�j�fH��pqW^a,[ r WYX�eRl ¢ W`egftEx ]^]�kg[7_bj�e�p�d�]Kd�jRj x pqd�j : h�d�W^X�egd�WYX(_ba�dBe�WYX�e�_Rp t d�j�_bkRT��6W`� x pg_ � T^y¡W^]Y] x k�e�pqdBe�_bk�kgj�f(_bhidBegW^jRd�]^] :f r ¢ dij r h4[ r kgW^e�_���pqW^a tFr p\egf WYk�dB[ [ p r d�j�f,jRd�X 9 _�kge�p x j�e x pg_ba,W^XNegf(_�jRd�kg_ r�t j r!x [�]^W^X � r�ta W��}_Rpg_bX�e�h4_ba W^d¡W^XNd � ��� jRd�]^j x ]^dBegW r X t@r p�S�d�§ ¢ _b]Y]�´µk¦_b� x dBegW r X kRT

� f W^k�jqf�dB[ e�_Rp tFr j x kg_bk r XHegf(_¡[ p r�9 ]`_bh r�t�r�9 egd�W^X W^X �¥f W^�!f~d�jRj x pqd�j : _bj r X r hiW��jRd�]^] :,r XHegf(_on 9 d�jg¤;��p r!x X aZps��p�W^a 9�: egf _ x k�_ r�t �"X W^e�_�a W��}_Rpg_bX j�_4h4_Regf r a kbT � f W^k 9 d�jg¤����p r!x X�a4��pqW^a r o�_Rpq]^dB["k�dBevW`egkn¨ x k x d�]^] : Ì�dB����_ba7©�_ba(��_bk ¢ W`egf�d�k�e�pqW^[ t@r ]Y] r ¢ WYX(��egf(_nWYX�e�_Rp t d�j�_r X ¢ f W^jqf ¢ _ip x X�d 9 ] r jg¤~[�k�_ x a r k�[}_bj�e�pqd�]�h4_Regf r azl t@r p�_�§%d�h4["]`_�T�·�_bk x ]`egk r X�j r h4[ x �egdBegW r X k ¢ W`egfÊegf W^kij r hi[ r kqW`e�_�k�_Re x [­dBpg_�pg_R[ r pge�_baÊWYXq2µ| 3 T ¿nr e�_�egf�dBe 9 _bjRd x k�_ r�t egf W^kW^X�e�_bX a(_ba x kgdB��_�l ¢ _¡a r X r e�a W^kgj x kqk�f(_Rpg_�egf(_�W^h4["]`_bh4_bX�egdBegW r X r�t e�pqd�a�W`egW r X d�] 9}r!x X�a dBp :j r X a W^egW r X kRT

� f(_�hid�W^X�e r [�W^jRk r�t egf(_�pg_bh�d�W^X W^X(�iU;_bj�egW r X�k � �Æ{idBpg_�d�k t@r ]Y] r ¢ kb�� T�¯°]^] x kge�pqdBegW r X k r�t ��pqW^a�k�egdB����_Rp�W^X(�à TvU%WYh4[�]`_�k : h 9}r ]^W^j�d�]`��_ 9 pqd4j r a _ t@r pnjRd�]^j x ]^dBegW^X � ¢ _bW`�!f�egk r�t �"X W^e�_�a�W��7_Rpq_bX j�_�k�e�_bX jRW^]Yk�(T � d 9 ]`_bk r�t ¢ _bW`�!f�egkr/ t@r p�h x ]YdB_ t@r p ¢ _bW`�!f�egkRl�WYX jR] x a WYX(��]^W^h�W`egk r�t WYX%�"X W`e�_ r pqa(_RpÄ Ti� 9 k�_RpgoBdBegW r XHegf dBe�WYX�egf _i]^W^hiW`e r�t WYX j�pg_bd�kgW^X � r pqa _Rpbl³W^h4[�]YW^jRW`e\d�X aH_�§%[�]^WYjRW`e tFr pqh x ]^dB_9 _bj r h4_�_b� x W`oBd�]`_bX�e�WYXNe�_Rpqhik r�t f r ¢ dia(_Rp�W`o�dBegW^o�_�oBd�] x _�a _R[7_bX�a k r X tEx X j�egW r XcoBd�] x _bk

Õ

Boundary simulating infinite domain

Non-reflecting boundary

Lossy (absorbent) media

Metallic object

Perfectconductor

Signalsource

�6W`� x pg_ � T^yB��s0tvuxw1y{zr|I}~tb}��R������|���zr|I}R�E�m�r��t��Ey{���<��}�|Iw��4�I}~��t��E��t�w��0|��#���x�R�0tv�����Iw����0�<���Yw1t_|I�vzr�������bsx�y{w_|�ux�0���G�4�x�R���Yw����x��}���|�uxw�t_�x���Ew�����|��I}R�o�0�Ey�zr}R�������xzE�Iuxw��&�4�I}~���{zE���oz ux}R�Eu0� �E�v�0w��m¡���}¢|�w�0}�£Yw1�Iw1��t_w¤��¥8¦§��ymw�|Iux�0�¨�b�E�x�~�©��w��I�x�¨}R�©|Iuxw��`�4w����RzE�x�x}R�x�mw1ª<�x}~����z4t_w��«��zEtv�C�E���E�x���¤�E��}~�O�����4��}~��E��}~���U�8¬[y{�x�Rw�y{w��<|�zr|I}R�E�¨�r����|I��}�������}�|Iu¨y{w1�x}Rzm}R�4|�w��I��zEt�w1��}~���0w1��t_��}��Yw1�©}R�M­ ®1¯ �¥x�4��|Iu�}R�«t�zE�IwE°b�bw�}�y�zr�4}���w����4���C}R�x�M±�z`²0�bw��R��³ ��w1ª<��zr|I}R�E���{}R�´zMt�z4��w���u�w���w�z ymw�|�zE���R}Rt¨�4�0µ�w1t_|��t��4zr|Iw1�¶��}�|Iu zr� zr���I�E���x}R�x�«y{w��0}���y��§}~��}R���R�xy{}���z`|Iw��O��}¢|�uOz©�vzE�xzE���I�E����t�wE�?�9�I�4�x���·|Iuxw{�4�0|Iw1��Y�E�x����zr��¸«}~�9���vzr����w���z*��|I��}��x�K�R}��4w��0�4y{zE}��·��ux}RtvuZ°YzE���4�x�¤}�|��=ym}~�x�0�RwE°��¹w�z`|��x�Iw��9z*��w1���¹w�tU|I�R¸¨�x�E�x���w_º�w�tU|I}R�x���Y�E�����xzr��¸{��w�|��Gw1w���|�uxw9y�zE}��*�x}�w1��w�tU|I��}~t��¹w4� ���8�cz4t_�x��y��Gzr���¤z���|I���E�x���I}R�E��zE��zr�����4�I�Yw����» uxw��4�I}~�¶�xw����I}¢|�}�w����¹w����Yw1t�}RzE���R¸·}R�·|�uxw*��|I��}����zr���E�x����|Iuxw��4�0µ�w1t_|�zr���·|Iu�w����4�x���xzE�I¸x�=�G�4�x�~�¶}R��Ew1�xw��vzr���Yw�t_�4����}~�0w1��zE�x��¸�u�}��4uxw���|�u�zr���Iux�`���¼�

{

Ç Tv��[}_RpqdBegW r XNj r!x X�egk|�T uvr hi[�dBpqW^k r X�k r�t d�jRj x p�d�j : d�X a�j r k�e°��_��}_bj�egW`o�_bX(_bkgkÕ T � _bk�e�_�§(d�h4[�]`_{;TvU x hihidBp :

� f(_�d x egf r p�hid�a(_�kqW`�!X W��"jRd�X�e\j r X�e�pqW 9�x egW r X k�e r k�_bj�egW r X�k\�cd�X a Ä T�U r h4_�j r X%�e�pqW 9"x egW r X k ¢ _Rpg_�hid�a(_�e r k�_bj�egW r X k Ç l7|�l�d�X a Õ T

ê�ë@ê .¬¼�¼Æ5$*¬���!/7�!��)���*s)�+��³���Æ *¬��/}�³�³� �������

S r kgec]YW^X(_bdBp ¢ dbo�_ª_b� x dBegW r X�k r�t ��_bX(_Rpqd�]�W^X�e�_Rpg_bk�eª¨EW^X­d�X : X x h 9 _Rp r�t k�[�d�j�_a W^hi_bX kgW r X kÝ©$f�dbo�_ r X�] : d t _ ¢ r�t d�]Y]z[ r kgkgW 9 ]^_�kg[�dBegW^d�]³a(_Rp�W`o�dBegW^o�_bk¦[ pg_bk�_bX�e`/�egf _bk�_�dB[ [}_bdBpW^Xik x jqfsd ¢ d : egf dBe�kg[�dBegW^d�](��pqWYaik�egdB����_RpqW^X � 9 _bj r h4_bkvk�e�pqd�W`�!f�e t@r p ¢ dBpqa³TK�ª_ r�9 k�_Rpgo�_negf dBeegf(_�k�e�p x j�e x pq_ r�t egf(_\� r o�_RpqX W^X(��_b� x dBegW r X k�e x pqX k r!x e�e r�9 _�[ pq_bjRW^k�_b] : k x j�f�egf dBevd x X�W^� x _d�X aªW^X�e�_RpqX d�]Y] : j r X ® W^j�e°� t pg_R_4k�egdB����_RpqWYX(��dBpgpqd�X(��_bhi_bX�e�W^k�[ r kgkqW 9 ]`_�l 9�x e ¢ _idBpq_ x X d ¢ dBpg_r�t d�X : a�W^kgj x kgkqW r X r�t egf�W^kiW^kgk x _�W^X¶egf(_�]^W`e�_RpqdBe x pq_�TÅ�6W`� x pg_bk � T � d���j,WY]^] x k�e�p�dBe�_�k�[�dBegW^d�]k�egdB����_RpqWYX(��W^X�egf(pq_R_vpq_R[ pg_bk�_bX�egdBegW`o�_¦jRd�k�_bkR��yÝ���Åd�j r!x k�egW^jBl � ���­_b]^d�k�egW^jBl�d�X a à ���­S�d�§ ¢ _b]^]�´µk_b� x dBegW r X kRT�¯-Xª_bd�j�f�jRd�kg_�l ¢ _�j r X�e�pqd�k�e�e ¢ r ��pqW^aª]Yd :�r!x egkRlKpg_R� x ]YdBp�o;kbTsk�egdB����_Rpg_ba³l 9}r egft _bdBe x pqW^X(�¥egf(_¡kgd�h4_4a(_bX kqW`e :�r�t ��pqW^a~a dBegd%T � f _�_bd�k�_ r�t j�pg_bdBegW^X(�Nk�egdB����_Rpg_ba�]^d :�r!x egk tFr pd�]^]"hid¬Ì r p�]^W^X _bdBp ¢ do�_�_b� x dBegW r X k�h�dB¤�_bk$egf(_�d�X d�] : kgW^k r�t egf W^k$j�f dB[ e�_Rp ¢ W^a _b] : dB[�[�]^W^jRd 9 ]^_�T

��X(_ijRd�X�d�]^k r k�egdB����_Rp4W^X�egW^h4_�l8d�k�W^k�a r X _�l tFr p�_�§(d�h4[�]`_�l6W^XHegf(_�²�_R_skgj�f(_bh4_tFr p4egW^h4_���a r hid�WYX¶j r h4[ x egdBegW r X�d�]�_b]`_bj�e�p r a : X�d�hiW^jRk½2 ��� l � |;l � { 3 T u f dB[ e�_Rp à a W^kqj x kgk�_bkf W`�!f _Rp�� r pqa(_Rp¦egW^hi_�k�egdB����_RpqW^X(�(T

ê�ë@ì ¹ ¼��³)³�����!�$½ +°)³��¾��$���B�É $����� �!����#%��»¥�������8�!*c/}�� >��j�/z½¿,v¼���*� d 9 ]`_ � T^y��!W`o�_bk�_�§(d�h4[�]`_bk r�t egf(_�kgW^hi[�]`_bk�e��"pqk�e�a(_RpqW`oBdBegW`o�_ndB[�[ p r §(W^hidBegW r X k tFr p

_bd�jqf r�t egf _ tFr!x p�kge�_bX jRW^]³e : [}_bk�j r X kgW^a _Rpg_ba,f(_Rpq_��¦_�§;[�]YW^jRW`e�d�X a~W^h4[�]YW^jRW`e¦dB[ [ p r §%WYhidBegW r X kr X�pg_R� x ]^dBp�d�X a�kgegdB����_Rpg_ba~��pqW^a kRT� �§;["]^W^jRW`e�dB[ [�p r §(W^hidBegW r X�k�pg_b]^dBe�_ r X(_¡a(_RpqW`oBdBegW`o�_�oBd�] x _

y �

ÀÂÁÃÄ¢ÅÆZÇÈ�ÉÊRËÁÌÍÄ¢ÅÎÏÐÑÒÓ Ô ÅÕ ÓÖ Å ×ÅÒØÅÁ ÍÍ×Ï ËÓÌÁÔÓÏ ÒÎÙ ÚÛ[ÜÒÏ ÒÎÔ ÁÝÝÅ ×ÅÕ#ÞÛ ÜÎÔ ÁÝÝÅ ×ÅÕß

à ááâã äå æçèå ã é

ê ëçìå éíî ç âç æëè ë âïð ã âñëå íòè ïó ëð ë âëéôëõ è ë éôåö áåôè ÷âë

ç éì íâåì

ê ã ñëïè ã âì ë âïè ë éôåöãð íå øë éè ùáë

ë ââã âè ë âæôãì ëú õ ëôèå ã éû�üûýþ çÿö ëú õ ëë�å í÷âëû�ü�ý

è ùáë

��� �

� äáöå ôå è�õ

� ú ý

�� ���� ��ú ��ý �� ��ú ��ý�� ��� �� ��ú ý ���ûû�üûú � ��ý�

� æáöå ôå è�õ� �� ú ��ý �� ��ú ý �� �� ú ��ý�� ���� ��ú ��ý �� ��ú ��ý��� ���� �� !� ú ý��ûûû�ü�ú � ��ý���

� äáöå ôå èõ

� ú ý

�� �"��# � �$ ��#%� �$�� � �� �� ��ú ý �� ���û�ü&ú � ��ý�

� æáöå ôå èõ� � � ú ��ý ��� ��� ú ý �� � � ú ��ý �� ����# � �$ ��#'� �$� ��( !(��� �� !� ú ý� �� �û�û�ü)ú � ��ý���

y�y

*,+*,- . *,/*,0*1/*,- . *,+*,0x

u,v u,v u,v u,v

u v u v u v u v

Nonstaggered grid

Staggered grid

¢ f(_Rpg_�ßGT�à½>o�_b] r jRW^e : l [ pq_bkgk x pg_

2 *,+*,- *"3*,054 *,6*,72 *,/*,- *,6*1084 *19*,7*:3*,- ¨ V 4 ��; © *1+*,054 V *,/*,7*,6*,- ; *,/*1084 ; *,+*,7*19*,- V *,+*,0 4 ¨ V 4 ��; © *,/*,7u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

y

x

y

x

Staggered grid

g

f,h u

v g

f,h u

v

g

f,h u

v

f,h u

gv

Nonstaggered grid

¢ f(_Rpg_ ß;T�འo�_b] r jRW`egW`_bk�WYX=<?>�d�X�a=@A>6a�W`pg_bj�egW r X k)#T%BZTDC�E<���j r hi[ pg_bkgkgW r Xzl kgf(_bdBpbl"d�X a=@%��j r h4[ pg_bkgkqW r X2 T V T ; >a(_bX�kgW`e : d�X ac_b]^d�kgegW^j�j r X k�egd�X�egk

�6W`� x pg_ � T � �c¯-]Y] x k�e�pqdBegW r X k r�t k�[�dBegW^d�]�k�egdB����_Rp�W^X(� t@r pik r h4_N]^W^X(_bdBp ¢ do�_�_b� x dBegW r X kR�ª¨Ed�©��X(_ÝÙ�a�W^h4_bX kgW r X d�]�d�j r!x k�egW^j ¢ dbo�_Þ_b� x dBegW r X d�X a'¨ 9 © � ¢ r Ù�a WYh4_bX kgW r X�d�]�_b]Yd�k�egW^j ¢ do�__b� x dBegW r XzT

y �

*:FHG*,- �I J *:KML*17 � *:KON*1PRQ*1F N*,- �ITS *:K G*1P � *:K L*10=U*1FVL*,- �I J *:KMN*,0 � *:KOG*,7 Q*:K G*1- �W J *1F N*:P � *:F L*17 Q*"KMN*1- �W S *1FHL*10 � *1FHG*1PXU*:K L*,- �W J *1F G*17 � *1FHN*,0 QYHZ\[^]_[ FHG e FVN e FVLa`cbed'fag1d'h [ hji_kHd%lmi Zn[o[epq[ bri ]_s but [^pqvKOG e KMN e KOLa`cbed'fag1d'h [ hji_kHd%lmi Zn[ fxw%y'h [ i s but [^pqvW e I `cg [^] f [ w%z sqpqs i|{j}\g [^] f [ i s ~ns i|{

Ez

Hx

Ez

Hy

Hx

Hy

HyHy Ez

Hx

Ez

Hx

Half-integer z-planes

Ex

Ex

EyHz

Hz Ey

Ey

Ey

Ex

Hz

Ex

Hz

Integer z-planes

y

x

Ex Ez

HyHx Hz

Ey Ex Ez

HyHx Hz

Ey

E x Ez

HyHx H z

E yEx Ez

HyHx Hz

Ey

Integer z-planes

Nonstaggered grid

y

x

Staggered grid

�6W`� x pg_ � T � �Á¨Ej©�¯°]^] x kge�pqdBegW r X r�t kg[�dBegW^d�]�k�egdB����_RpqW^X(� tFr pcegf(pg_R_ÝÙ�a W^hi_bX kgW r X d�]nS�d�§ ¢ _b]^]�´µk_b� x dBegW r X k

y Ã

e r ds]^W^X(_bdBpnj r h 9 WYX dBegW r X r�t�tEx X j�egW r X�o�d�] x _bkRl ¢ f WY]`_�W^h4[�]^WYjRW`e�_�§;[ pq_bkgkgW r X k�pg_b]^dBe�_�d�]^W^X(_bdBpj r h 9 W^X dBegW r X r�t a(_RpqW`oBdBegW`o�_�o�d�] x _bkie r d�]^W^X _bdBp�j r h 9 W^X dBegW r X r�t�tFx X�j�egW r XÞoBd�] x _bkRl�egf x kpg_b� x W`pqWYX(� r X _�e r k r ]`o�_�d�]^W^X(_bdBp�k : k�e�_bhÂe r �"X acegf(_�a _bkgW`pg_baNa(_Rp�W`o�dBegW^o�_�o�d�] x _bkRT

Znk�a W^kqj x kgk�_ba�WYX¿2�y�y 3 l6egf(_ ¢ _bW`�!f�egk¡W^X�d�X :�r�t egf(_¥k�e�_bX jRW^]^k ¢ _ca W^kqj x kgk�W^X�egf W^k[�dB[}_Rp�jRd�X 9 _�jRd�]^j x ]^dBe�_ba 9;: egf(_ � ��]^W^X(_�S~dBegf(_bhidBegW^jRdsd�]`� r pqW`egf h

�����������O�����"���1���:���������%�a�%�,�M�����^�M�����"����"���������� �¡� 1�:�����¢ ��,�£�_¤��:�¥���V ��m�"���"¦O�����u�e�����^�����:���¢ �¡� ,�:�����¢ ��\�£��§:¨:���:¦��:�m�"¦O�����o�^���m©\ªA�%���r p\W^XNS~dB[�]`_ 9�:

�£«^�:¬¥�����®­����"���"¯1��­���°��'���e�������¥�±�O�^����°H«¡:���"���²­%�"��¬m�:�m�²­³���1�¥�\��­���°�°H�e�M�j �° ´m ,��µM¶�¶r���¡:���"���²­%�"��¬m�:�m�²­e��¨1���"¦�­���°�°H�e�M�j �°:©1ª��'� ´m ,��µM¶�¶_�O�¯-X 9}r egf�jRd�k�_bkbl�d��6d�avé_c[�d�jg¤BdB��_�h x k�e 9 _s[ pg_���] r d�a(_ba@/�egf W^k�W^k�a r X _ ¢ W`egf�egf(_

j r hihid�X�a kc·�· ����¯m¡\¨¥¯1¨��V¸e�������o¸ r pX¹  \��ªº­e��¨:���:¬�¬�¦m�"��°»« pg_bkg[7_bj�egW^o�_b] : T�¯°XÉegf(_bk�_�]^WYX(_bk r�tj r a(_�l � a(_bX r e�_bk ¢ f WYjqf r pqa _Rp r�t a(_RpqW`oBdBegW`o�_ ¢ _ ¢ WYkgf¡e r dB[ [�p r §(W^hidBe�_�¨Fegf�W^k ¢ WY]^] 9 _ r X(_\W^Xd�]^](jRd�k�_bk$j r X kgW^a(_Rpq_ba4W^X¡egf W^kK[�dB[}_Rp 9�x e�jRd�Xzl;W^X���_bX(_Rpqd�]�l 9 _�d�X : X r X X(_R�!dBegW`o�_�WYX�e�_R��_Rpr/;egf(_jRd�k�_ ����µ ¢ WY]^]B��_bX(_RpqdBe�_¦W^X�e�_Rpg[ r ]^dBegW r X tFr pqh x ]^dB_¬©�T � f(_$pq_bhid�W^X W^X �¦egf(pg_R_�WYX([ x e}[�dBpqd�hi_Re�_Rpqk�V���o� d�X a � a(_bkgj�p�W 9 _�egf(_4kgf dB[}_ r�t egf(_4k�e�_bX jRW^]�l}d�k�W^]^] x k�e�pqdBe�_ba,WYX��6W`� x pq_ � T à ¨ � hid :�9 _d�X : pq_bd�]³X x h 9 _Rpr/ � d�X a � h x k�e 9 _�X r X%��X(_R�!dBegW^o�_�W^X�e�_R��_Rpqk�©�T

� r p6egf(_���pqk�e�a _RpqW`oBdBegW`o�_�¨EW�T±_�T�¼¾½À¿B©zd�X�a ¢ W^egf�egf(_�k�e�_bX jRW^]�kgf r ¢ X�WYX��6W`� x pg_ � T à legf(_�S~dBegf(_bhidBegW^jRd r!x e�[ x e 9 _bj r hi_bk

ÁÂÁ {ÕB� T

à y� � T

{ÕB�Äà T Á � y|

� � � C T`� Ç�ÃÕB� C T Ç�ÃÕB� C T y|

� � � C ÃTÃ � ¨ � T^y©

¨Ej t T�egf(_�jRd�k�_*�& � ]^W^kge�_baNW^X � d 9 ]`_ � T Ç ©�T¯-XNZn[ [}_bX a W`§sZ ¢ _�_�§%[�]^d�W^X ¢ f : egf(_�d 9}r o�_��Kd�avé_�d�]`� r pqW`egf�h ¢ r pg¤%kRT�\_Rpq_bd t e�_Rp\WYXcegf W^k�jqf dB[�e�_Rpbl ¢ _�j r X kgW^a(_Rp r X�] : ��p�k�eva _RpqW`oBdBegW`o�_�dB[ [ p r §%WYhidBegW r X kRl

d�X a ¢ _ x k�_��oTU��T³d�X a´A~e r a(_bX r e�_ik�e�_bX jRWY]6_bX�e�pqW^_bk�d�k�W^]^] x k�e�pqdBe�_ba~W^Xª�6W`� x pg_ � T±�(T ¿nr e�_

y��

egf dBeÆŽ � � 4 yBl ¢ f WY]`_ÂÇ� � � 4 y tFr pnX r X kgegdB����_Rpg_ba���pqWYa k¦d�X a=Ç� � � tFr p\k�egdB����_Rpq_ba��pqW^a�kRT

¯-X�d�a a W^egW r Xzl6X r e�_segf�dBe ¢ _cj r X kgW^a(_Rp r X ] : j�_bX�e�_Rpg_ba¶�6� dB[�[ p r §(W^hidBegW r X kRT,¯°X��_bX(_Rpqd�]�l!j�_bX�e�_Rpg_ba�kgjqf(_bhi_bk�f dbo�_ 9 _Re�e�_Rp�d�jRj x p�d�j : [ p r [7_RpqegW`_bk�egf�dBe�X r X j�_bX�e�_Rpg_ba4kgjqf _bh4_bk`/r X(_ x k x d�]^] :�r X ] : j r X�kgW^a(_Rpqk¦X r X j�_bX�e�_Rpq_ba,kgj�f(_bh4_bk ¢ f(_bX�j r X kgWYa(_RpqW^X(� 9}r!x X a dBp�W`_bkRT

ÈÉÈÈÉÈÊÊËÉËËÉËÌÉÌÌÉÌÍÉÍÍÉÍÎÉÎÎÉÎ ÏÉÏÏÉÏÐÉÐÐÉÐd

n

s

entries for

entries for

f

f

(m)

�6W`� x pg_ � T à ��U%jqf _bhidBegW^j\WY]^] x k�e�p�dBegW r X r�t egf(_�X r egdBegW r X x k�_basW^Xiegf(_��6d�a�é_ ¢ _bW`�!f�evd�]^� r pqW`egf htFr p�dck�egdB����_Rpq_ba�jRd�k�_0/�f(_Rpq_�l£Ñ �Û l�Å& � l³d�X aÒÇo à T¥¨EZn]^]Ka W^kgegd�X j�_bk5ÑMÓÔÅÕÓÖÇ~dBpg_4W^Xx X W^egk r�t egf(_ x X W`e¦k�e�_R[,]^_bX(��egfÔCzTV©� f(_4X r egdBegW r XªW^X~egf W^k�d�X aHk x(9 kg_b� x _bX�e�W^]^] x k�e�pqdBegW r X k r�t k�e�_bX�jRW^]^k t@r ]Y] r ¢ k�egf(_ij r X�o�_bX�egW r X¨Ed�k ¢ d�k\d�a r [ e�_ba tFr p�_�§%d�hi[�]`_�W^X´2�y �x3 ©��

���x�C�x�`���Ø×��C�x�`���Ù Ú ÚÜÛ �0w1�I}R�`z`|�}��4w§w1�<|I��¸Ú Ú �¹�x��tU|I}R�E�¨w1�4|��I¸

� f(_¦k : h 97r ]Yk�dBpg_ x X%�"]Y]`_ba r p6�7]^]`_ba¡a(_R[}_bX a W^X � r X ¢ f _Regf(_Rp�egf(_�j r pgpg_bkg[ r X�a W^X(��a(_RpqW`oBdBegW`o�_r p tEx X j�egW r X�o�d�] x _ ¢ r!x ]Ya 9 _ x X(¤%X r ¢ Xi¨EW�T±_�T8e rn9 _�k r ]`o�_ba tFr pÝ© r p�¤%X r ¢ X�W^X�egf _$d�X�egWYjRW`[�dBe�_badB[ [�]YW^jRdBegW r X r�t egf(_�k�e�_bX jRWY]�T

y Ä

¨Ed�© A· � à � � �Êy � y � Ã3,Ý ] [ hDi ]_sq[ kVÞ�ßà1á â3 ] [ hji ]±sq[ kVãrßà:á â ä ä ä å åß8æÂçeè%é�êjëíì�î�ï1ð%ëíìòñ órô�õòñ ó^ë�ëíç^õ|ìòñ ëíö�è%öòëíðîrçoëíôr÷|øMöùñ ð%ë¥î�ï1÷±ëíç^õ|ë±ìùú ñ ç³ë^ûø%ëíìòërü'ßXæþýrû â æÆÿ�ß á������:á � á������,á ß��à æÆçeè%é¢êDëíì�î�ï,ïqè%ç³÷íõ|ñ îrçuëíçeõ|ìùñ ëíö�è%öòëíðîrçoëíôr÷|øMöùñ ð%ë¥î�ï1÷±ëíç^õ|ë±ìùú ñ ç³ë^ûø%ëíìòërü à æ��³û â æÆÿ à1á������,á � á������,á à �

¨ 9 © A· � à � � �Êy � y � Ã3,Ý ] [ hDi ]_sq[ kVÞ�ßà1á â3 ] [ hji ]±sq[ kVã ßà:á â ä ä ä å åß5æÆöòôré?ë�ôrömôrêjî±ó^ëà æþçeè%é�êjëíì�î�ï1ë±ç^õ|ìòñ ë±ö�îrçoëíôr÷|ø�öòñ ð%ë¥î�ï÷íëíçeõ|ëíìòú ñ ç%ërû'ø%ëíìòërü à æ�³ûâ æÆÿ à� �� á������,á ÿ �� á��� á������,áíà ÿ �� �

�6W`� x pg_ � T±�(� ¿nr egdBegW r X x k�_baÉe r W^X�a(_�§�_bX�e�pqW`_bkiW^XÉX r X�k�egdB����_Rpg_baÊd�X�a¶k�egdB����_Rpg_ba­k�[�dBegW^d�]k�e�_bX jRWY]^kR��¨Ed�© ¿nr egdBegW r X tFr p\X r X�k�egdB����_Rpg_ba���pqW^azl³¨ 9 © ¿nr egdBegW r X t@r p\kgegdB����_Rpg_ba,��p�W^azT

y Ç

ê�ë�� ! /8"v¼���*�)³+n*�)�½­�~»¥�"�����8�!*��6�Æ�$#(¼Æ5$ $�Æ����+°)³��½Þ5�¼�/}��+°)³�¥»c�����8���!*�/}�� M+°)³�¼���½Á����*s)³+��Æ��¾��$������)³�� ����

� d 9 ]`_bk � T � � � TV|Þ[ p r o%W^a(_�X x h4_Rp�W^jRd�]�o�d�] x _bk�d�X a jR] r k�_ba%� tFr pqhö_�§%[ pg_bkgkgW r X k�¨EW^Xe�_Rpqhik r�t � d�X�agA © tFr pNegf(_ªj r _�«¥jRW`_bX�e ¢ _bW`�!f�egk r�t �"X�W`e�_�a W`�7_Rpg_bX�j�_Hkqjqf(_bh4_bk tFr pNegf(_jRd�k�_bk r�t hid�W^X,W^X�e�_Rpq_bk�eRT��(p r h0egf(_bk�_ t@r ]Y] r ¢ egf(_�� x(r e�_ba~]^W^hiW`egk tFr p�Ac� §%_ba,d�X a���% '­T� f(_bkg_ijR] r k�_ba%� tFr pqh _�§%[ pg_bkgkqW r X k�d�X a�]YW^hiW`egk ¢ _Rpg_ tFr!x X aª[ p�W^hidBpqW^] :N9�: egf(_�d x egf r p ¢ W`egfk r h4_¥d�kgkgW^kgegd�X j�_ t p r h wv_bX(��e�� r pqX 9 _Rpg�(T,�ª_¥X r e�_¥egf(_ x k�_ r�t ��d�]^]^W^kR´�[ p r a x j�e�W^X�egf W^k]^W^h�W`egW^X(��[ p r j�_ba x pg_��

]^W^hó���� A�� ¨ � A¨�Êy©����¨ � A ©������ Û y

�� `"!�# y� y¨ ��$ © Û&% y' ¨ � T � ©

¨�U;_R_¶2�y �C3 l t@r p\_�§%d�h4["]`_�TV©� f(_�]^WYhiW`egW^X(� ¢ _bW`�!f�egk�jRd�X�d�]^k r�9 _$a(_Rp�W`o�_ba t p r h dnh r pg_$��_bX _Rpqd�]�W^X�e�_R��pqd�] t@r pqh x �

]^dBegW r X³l ¢ f WYjqfiW^k��!W`o�_bX�W^X � d 9 ]^_ � T Õ T � f(_nW^X�e�_R��p�d�]^k��!W`o�_bX¥W^X4egf WYk�egd 9 ]`_\jRd�X 9 _�_RoBd�] x dBe�_ba_�§%[�]^W^jRW`eg] : T � f _�pg_R� x ]^dBpv��pqW^a�_�§;[�pg_bkgkgW r X�k�W^X � d 9 ]`_ � T Õ ¢ _Rpg_�a(_RpqW`o�_ba 9�: wv_bX(��e¦� r p�X 9 _Rpg�

¢ f WY]`_�egf(_�k�egdB����_Rpq_ba���p�W^a�_�§%[ pg_bkgkqW r X k ¢ _Rpg_�a _RpqW`o�_ba 9;: egf(_�d x egf r pbT�Zn[ [}_bX a W�§sw �!W`o�_bkd 9 p�W`_ t dBpg� x h4_bX�e�]^_bd�a W^X(�¡e r egf _�]^W^hiW`ev_�§%[ pg_bkgkgW r X k¦W^X � d 9 ]`_ � T Õ T

� f(_�]^W`e�_RpqdBe x pq_ r X 97r egf�pg_R� x ]YdBp�d�X a~k�egdB����_Rpg_baH��p�W^a,_�§%[�]^WYjRW`e¦�"X W^e�_�a W��}_Rpg_bX j�_kgj�f(_bh4_bk�W^k¦_�§%e�_bX kgW`o�_�TnU r hi_�kgjqf _bh4_bknf�dbo�_ 9 _R_bX,a(_bkgW`�!X(_ba ¢ W`egfNegf _�� r d�] r�t _bX�f d�X jRW^X(�egf(_¦d�jRj x pqd�j :�t@r p�j�_Rpgegd�WYX t pg_b� x _bX jRW^_bk�pqdBegf _RpKegf�d�X4hid�§%WYhiW`¾bW^X(�\egf(_ t@r pqh�d�] r pqa _Rp r�t d�jRj x �pqd�j : 2�y Ç l �B� l � � 3 T�¯-h4["]^W^jRW`en¨Ed�]Yk r ¤;X r ¢ Xcd�k¦j r h4[�d�j�e�W^Xsegf(_�]^W`e�_RpqdBe x pg_¬©�pq_R� x ]^dBp¦kgjqf _bh4_bkf do�_ 9 _R_bXÞa(_RpqW^o�_ba¶d�X aÊk�e x a W`_ba r XÞX x h4_Rp r!x k r jRjRd�kqW r X kRlv_�T±�(Tm2�y�l$�(l\y�� l\y Ä l ��à l ��Ä<3 T¸ r [�d�] 2 � y 3 [ pg_bkg_bX�egk~egd 9 ]`_bk ¢ f�W^jqf d�]^] r ¢ _bd�k : jRd�]^j x ]^dBegW r X r�t ¢ _bW`�!f�egkªW^X X x h4_Rp r!x kkgj�f(_bh4_bk ¢ f W^jqf,W^X jR] x a _�jRd�kg_bk\egf dBenj r h 9 WYX(_�k�egdB����_RpqWYX(� ¢ W^egfNW^h4[�]^WYjRW`egX(_bkgk�¨Ed�]^k r ¤;X r ¢ XW^X�egf(_N]^W`e�_RpqdBe x pg_¥d�k¡j r h4["d�j�egX(_bkgk�©1/�f r ¢ _Ro�_Rpl�f W^k�j r _�«sjRW`_bX�egk4dBpg_c[ pg_bk�_bX�e�_ba¶W^X�e�_Rpqhikr�t a W��}_Rpg_bX j�_ r [}_RpqdBe r pqk ¢ f(_Rpg_bd�k ¢ _i�!W`o�_i_�§%[�]^WYjRW`e�jR] r k�_ba%� tFr pqh _�§%[ pg_bkgkgW r X k t@r p�egf(_�j r �_�«sjRW`_bX�egk�d�X a�d�]^k r j r X kgW^a _Rp�]^W^h�W`egW^X(�cjRd�k�_bkN¨EW^X � d 9 ]`_bk � T � � � TV|�©�T�¨F¯°X�Zn[ [}_bX a W�§ u l ¢ _a(_bh r X�k�e�pqdBe�_�f r ¢ e r j r X�o�_Rpqe t p r h'¸ r ["d�]�´µk\j r _�«sjRW`_bX�egk\e rsr!x p\j r _�«sjRW`_bX�egkRTV©s� r ¢ _Ro�_Rpl

y|

� d 9 ]`_ � T � ���ª_bW`�!f�egk tFr p�_�§;["]^W^jRW`eRl%pg_R� x ]YdBp���pqW^aN�6� tFr pqh x ]^dB_�¨ r pqa(_Rp r�t d�jRj x p�d�j : � �8©�T

Y?[^s y Z i±k»ã �à1á â lùd ] 3( ó ` ]&) ]+* ]&, ] Û ] � a � Û , * )� ] ý- a ý-Û ýý - ] -� a -� ] ýý -, ] ý.�� �-�� ] �/ a �/ ] �-�� ý.��* ý-�0�� ] /ý �21 ý1 ] /1 a / 1 ] ý1 /ý �21 ] ý-�0��) ] ýý -�.�� 11�� / ] 10 / 1- ý ] 1. a 1. ] 1- ý 10 / ] 11�� / ýý -�.��3 d ] y [ h [^] w p ( eFó54Þ �à:á � ` � lùd ] w pqp ( ã �à1á â£`76889 88: a ó ` a; ÿ�ý=<?>A@ �â ; àCB < �; àD¥â < B ; à ÿ â < B óFE` aG s f s i?w%k ( �H�I4

Þ � J á � ` � ã � J á âO`K6889 88: a ó ` a; ÿ�ý=<L>M@ �â óFE` a

y Õ

� d 9 ]`_ � T à �$�ª_bW`�!f�egk tFr p�W^h4["]^W^jRW`e à ��a W^dB� r X d�]�l(pq_R� x ]^dBp¦��pqW^ac�6� tFr pqh x ]^dB_i¨ r pqa(_Rp r�t d�jRj x �pqd�j : � � 4 � ©�T

Y?[^s y Z i±kuÞ,ýà:á â Y?[^s y Z i±kuã³ýà1á âl d ] 3 Ý l d ] 3( ó ` ] � a � ]&) ]+* ]&, ] Û ] � a � Û , * )� ý. -� ý. ] ý- a ý-Û ý1 � 1 ý1 ] ý.�� ]ONý 1 a Ný 1 ý.��, �ý / / N �ý / ý0 / � ] ý� 1 ] -�11�. a -�11�. ý� 1 ] ý0 / �* -P 1P -P ] ýN 1�.�� ý� N 0 ] ý- N ] ýQ�� � a ýQ�� � ý- N ] ý� N 0 ýN 1�.��) 1-�- .ýrý 1-�- ý1�1 /�/ � ] ý- N�N - 1ý - � - ] ý �- �³ý ] ý /��� a ý /��� ý �- �³ý ] 1ý - � - ý- N�N - ] ý1�1 /�/ �3 d ] y [ h [^] w p ( e@óR4Þ ýà1á â `K6889 88: àD ý- àD ý ó ` aà- ; - à� ý=< ó `TS � ã ýà1á â ` 6888889 88888:

a ó ` aF ] �IH âU ý ; � à� ý=< ; àD - </ ; - à� ý=< ; àD ý=< ó `VS �; ÿ¢ý=< >; âW ý=< ; â < ; â ÿ¢ý=< ; àD ý=<; - àD ý=< ; àXB < �; à ÿ â < B ; àD¥â < BVY ó Y�Z ÛG s f s iAw%k ( �H�I4

Þ ýJ á âO`76889 88: ý- ó ` aý/ ó `TS � ã ýJ á âO` 6888889 88888:a ó ` a�0 k s y'h F ó H ó `TS �ý- ; ÿ�ý=< >; â ÿ�ý=< ; â < ; âW ý=< Y ó Y�Z Û

yb{

� d 9 ]`_ � T±�(�$�ª_bW`�!f�egk tFr p�W^h4["]^W^jRW`e Ä ��a W^dB� r X d�]�l(pq_R� x ]^dBp¦��pqW^ac�6� tFr pqh x ]^dB_i¨ r pqa(_Rp r�t d�jRj x �pqd�j : � � 4 ��©�T

[ ë±ñ \røeõòö^] �_C` > [ ëíñ \rø^õ|ö^a �_C` >ïqîrìcbed ïqîrì^bàÉâ æ ÿ - ÿ¢ý � ý - ÿ / ÿf� ÿ - ÿ�ý � ý - � /ý ÿ ��Qg�h �=ij h � jk h �Qij h ÿ ��Qg=h ÿ �� � ��- �i=h gk�l �Qgk�l gk=l �i=h ÿ lg=m ÿ g� � � g� � lg=m� �m � l� � �Qh� � l� � �m � ÿ �� �=n h ÿ �Qh��� ��n h ÿ g l��l=� � g l��l=� �Qh��� ��n h �� ��n h/ �k�k gk�k l��� gk=k �k�k �� i�i � h ÿ ���� l�l ÿ j �j�j h ÿ ��mm l � ��mm l j �j�j h ��=� l=l ÿ �� i=i � ho îrìp\rë±ç%ëíìòôrú à1á±â�q] �_C` > æsrtttttu tttttvk�Ow _ @ �Qx w _ @ � xw � _ @ �Qx w � _ @ k x â æ �_ w _ @ � xw � _ @ �Qx w � _ @ k x â æyAý_ w _�z �=xm w � _ @ �Qx w � _ @ k x â æy - a �_C` > æ rtttttttttu tttttttttv

� â æ �w z �=x >M@ � w _ @ � x w _ @ k x w l _ @ � xn w _ @ �=x w � _ @ �=x w � _ @ k x â æFyAýw z �Qx > w _ @ k x w ��l _ k @ ��k _ � z ��� _Cz g�xm�g w _ @ �=x w _ @ � x w � _ @ �Qx w � _ @ k x â æFy -w z �=x >w > z � x w > z �=x w > x w >A@ �=x w >M@ � x n w _ @ �=x w _ @ � xw � _ @ �Qx w � _ @ k x w _�{ x �w _Cz > x { w _ @|> x {~} â }e� -� ñ é?ñ õ�ôrö à�� J q] � � ` > æ rtttttu tttttvkg â æ ��m â æ�y?ý�� n â æ�y - a � � ` > æ rtttttttttu tttttttttv

� â æ �l� m öòñ \rç ; â < â æ�y?ý�=l� j�� öùñ \rç ; â < â æ�y -k� w z �Qx >A@ �w > z � x w > z �=x w > x w >A@ �Qx w >A@ � x } â }�� -� d 9 ]`_ � T Ä �s�ª_bW`�!f�egk tFr p¡_�§;[�]YW^jRW`eRl�k�egdB����_Rpg_ba¶��p�W^aÉ�K� tFr pqh x ]^dB_H¨ r p�a(_Rp r�t d�jRj x pqd�j : � �8©�T

Y?[^s y Z i±kVã �à:á â lùd ] 3( ó ` ] P - ]�N- ] 1- ] �- ] ý- ý- � - 1 - N- P -� ] � �Û ý- / ] P 0 P0 ] ý- /, ] �. / � -�1� 0 / ]�N 1. / N 1. / ] -�1� 0 / �. / �* 1N ý .�0 ] / P1 ý -�� - / 1� � N - ] ý -�-�1ý �2- / ý -�-�1ý �2- / ] - / 1� � N - / P1 ý -�� ] 1N ý .�0) ] � 1-�P / P ý - / �21-�-�P � N . ] 1�. N/ ��P�.�� N � 10 ý P2- ] ý P�0 / 1ý . � 0 / ý P�0 / 1ý . � 0 / ] N � 10 ý P2- 1�. N/ ��P�.�� ] / �21-�-�P � N . � 1-�P / P ý -3 d ] y [ h [^] w p ( eFó54Þ �à:á � ` � lùd ] w pqp ( ã �à1á â�` ; ÿ�ý=<?> z ��� �- â � � ; - à ÿ�ý=< B B � �; - à ÿ�ýrÿ - â < B B ; - à ÿ�ý - â < B BG s f s i?w%k ( ���I4Þ � J á � ` � ã � J á âO` ; ÿ�ý=< > z �=� �� â �

�B�

� d 9 ]`_ � T Ç �H�ª_bW`�!f�egk tFr psWYh4[�]^W^jRW^e à ��a WYdB� r X d�]�l�k�egdB����_Rpg_baÅ��pqW^aÊ�K� t@r pqh x ]^dB_�¨ r pqa(_Rp r�td�jRj x pqd�j : � � 4 � ©�T

[ ëíñ \rø^õ|öp] �_�` > ïqîrì^bed [ ëíñ \rø^õ|ö^a �_C` > ïqîrì^bà£â æÂÿ¢ý � ý ÿ j� ÿ i� ÿ l� ÿ k� ÿ �� �� k� l� i� j�ý �� m �=�� � �� m ÿ¢ý ý- jg�h k �m�h jg�h ÿ �=i� m�h ÿ n=kg=h n�kg�h �Qi� m�h� ��l� n g l=jgQm ��l� n g n �m�h k�� h ÿ j=��lg=h n m ÿ �=n i lm�h k�� �=n i lm�h k=� j=��lg�h n m ÿ n �m�h k�� h/ m j� g=g j=l��m=m m j� g=g ÿ m km k h=h�g=h k m k���Qh l�j=� ÿ i=g=g=m��l�l=��j�n h ÿ n m j��=l����h l�j=� n m j=��l�=�Qh l=j�� i=g=g=m2�l�l��=j�n h ÿ k m k����h l=j�� m km k h�h=g�h1 g��m�m�h � k=j��� h g��m�m�h ��� ���� i=h�g ��� m ÿ � l=j�l in=k h�iQg=m�h�h i=h=g � �� l i n=j�n h�h ÿ k�n m2��� j���=l�� g=h�h ÿ j�n=l i j�Qg=h ��� m j=n�l i j��g�h �=� m k�n m���� j�=��l=� g�h=h ÿ i=h=g � �� l i n�j=n h�h � l�j�l in�k h�i=gQm�h�h ÿ ��� ���� i=h=g ��� mo îrì^\rëíç%ëíìòôrú à:á±â�q] �_C` > æ rttu ttv m _ � @ g _Cz �m _ w � _ @ �=x â æ �w � _�z �=x �g _ w � _ @ �=x â æFyAý a �_C` > æ w z �=x >M@ ��� ��� w � _Cz �Qx { { � �g _ w � _ @ �=x w � _�z � z � > x { { w � _Cz � @ � > x { { w k > � z �=x w m _ � z �=x @ g _ w > � z �=x� w > z �=x w > x w >A@ �Qx � �� ñ é?ñ õ�ôrö à�� J q] �� ` > æ rttu ttv �� â æ ��m â æyAý a �� ` > æ w z �=x >M@ ��� ���� k > � z �� w > z �=x w > x w >A@ �Qx � �

� y

� d 9 ]`_ � TV|��H�ª_bW`�!f�egk tFr psWYh4[�]^W^jRW^e Ä ��a WYdB� r X d�]�l�k�egdB����_Rpg_baÅ��pqW^aÊ�K� t@r pqh x ]^dB_�¨ r pqa(_Rp r�td�jRj x pqd�j : � � 4 ��©�T

Y?[^s y Z i±kVÞ -à1á â l d ] 3 Ý Y?[^s y Z i_kVã -à:á â l d ] 3( ó ` a S � S Û ] 1- ] �- ] ý- ý- � - 1-� 0�. �P�.�� N�Ný /�/ � ] ý N1 N .�� ] � �Û � .�. N1 /�/ � � �21 Ný P�� / � ý 0 �N . ý .�� ] � . N-�021�. ] 1�021P21�- 1�021P21�- � . N-�021�., -�0�021�-�P/ P ý P�� / / 0 / -�1- / 1�P21�- ý � N 1ý ��P �³ý - ] .�P�� / Pý / N 1 N ý -�� ] 1��21 ý N 1-�P21 ý / - / ] .�0 � / -�1ý / N 1 N ý - .�0 � / -�1ý / N 1 N ý - 1��21 ý N 1-�P21 ý / - / .�P�� / Pý / N 1 N ý -��* ý / . ý N � ý- N - /�/ 0�� 0 N P / � �/ ��0�. N -�� 1 / ý / 1� -�.�P � N . ] ý P�. ý 0�.�.�Pý P�. ý .2-�1�.���� ] ý - / N � � P N ý.21 � 0 N 1�-���� ] -�.�P�0�. N 1N ýQ���³ý 0 / -�.�P�0�. N 1N ýQ���³ý 0 / ý - / N � � P N ý.21 � 0 N 1�-���� ý P�. ý 0�.�.�Pý P�. ý .2-�1�.����3 d ] y [ h [^] w p ( e@ó54Þ -à1á â£` 6888889 88888:

1 N . à n ý P2-�� à l ý / 0�0 à m ÿ / -�0�0 à k ÿp�³ý 1�. à � P21�- à ÿ 0 ý0 ; - à < ; - à� ý=< ; - àD - < ; - à� �2< ; ý - à � ÿ�ý . àD ý=< ó ` a; - à ÿ�ý=< � ; / 0 à m ý -�0 à k ÿ�ý -�� à � ÿ�ý .�� à� - N </ ; - à < ; - à� ý=< ; - àD - < ; - à� �2< ; ý - à � ÿ�ý . àD ý=< ó `VS �; - à ÿ�ý=< � ; - à ÿf�2< � ; ý - à � 0 à ÿp�2<ý . ; - à < ; - à� ý=< ; - àD - < ; - à� �2< ; ý - à � ÿ�ý . àD ý=< ó `VS Ûã -à:á â ` ; ÿ�ý=< > z ��� � � ; - à ÿ�ý=< B B � �/ ; - à ÿ¢ýrÿ - â < B B ; - à ÿ�ý - â < B B � ; à1á â <; - à < ; - àD ý=< ; - à� - < ; - àD �2< ; ý - à � ÿ¢ý . àD ý=< � ; â ÿ - < ; â ÿ¢ý=< ; â < ; âW ý=< ; âW - < � �YHZ\[^]_[�� F�( e@ó H ` F ) ÚW� ( . ]�� �IH F )�ó / ] � )�ó - D * H D ,e�W* ( 1 F � )�ó / ]�)e��ó - D Û a H ]�*�� ( / F � a � ó / ] � Ú )�ó - ] � Û * H] � * ( � F � � ��ó / ] � )e,�ó - D Û � � H ] � Û ( - F ,e)�ó / ] Ú *�)�ó - D � a ) Û H D � (�F Û �e,�ó / ] �U� Û ��ó - D * ÚW� HG s f s iAw%k ( �H�I4Þ -J á â ` 6888889 88888:

�0 ó ` aý/ ó `VS �ýý . ó `VS Û ã -J á â ` ; ÿ¢ý=< > z ��� �- � � ; / ÿ¢ý 1 â � 1 â m <� ; â ÿ - < ; â ÿ¢ý=< ; â < ; âW ý=< ; âW - < � �

���

� d 9 ]`_ � T Õ �¥£�W^h�W`egk r�t ¢ _bW`�!f�egk�d�k©� % ' tFr p�kgj�f(_bh4_bk ¢ W^egf � � 4 y¥a W^dB� r X d�]YkRl�� � TbyCT � T������BT\¨�U;_R_�Zn[ [}_bX a W�§¥w t@r p\d 9 pqW`_ t a _RpqW`oBdBegW r X r�t egf(_�W^X�e�_R��pqd�] tFr pqhikRTV©

£�W^h�W`e ¯°X�e�_R��pqd�] tFr pqh  �§%[�]^WYjRW`e tFr pqh

2±·�_R� x ]^dBp���p�W^a~¨[AsW^X�e�_R��_RpÝ© 3

dc��¨e ó ���� �a j r kK¨[A��}© � j r k S 0 Û U�¡ Û � ò^� £¢¤¤¥ ¤¤¦�Û - ß F Û � H�§F � ]�ó H�§ F � D ó H�§"¨ A ¨�© �

� ¨ A ¨�ª �« � �©e ó ���� �a �>kgW^X�¨�A��z© � j r k S 0 Û U�¡ Û � òc� ¢¤¤¤¤¤¤¥ ¤¤¤¤¤¤¦

� A� �

F k s y'h ó H F Û � H�§�¬ } â }­ æ?ýrÿ } â } ý­ ßÛ - ß F � ]�ó H�§ F � D ó H�§ �V® ¨ A ¨�© �F ] �IH âW ß ý F Û � H�§Û - ß ¯ ß­ æ�ÿ�ß F ó D H ¨ A ¨ ª �

2ÖU;egdB����_Rpg_bac��p�W^a�¨[Asf d�] t ��WYX�e�_R��_RpÝ© 3

d � �¨e ó �� � �a j r kK¨[A��}©�� j r k S 0 Û U�¡ Û � ò^� ¢¤¤¥ ¤¤¦�Û - ß F Û � H�§° F � ]�ó D �IH ° F � D ó D �IH�¨ A ¨�© �

� ¨ A ¨�ª �« � �©e ó �� � �a �>kgW^X�¨�A��z© � j r k S 0 Û U�¡ Û � òc�© F k s y'h ó H F Û � H�§2¬ } â }­ æ?ýrÿ } â } ý­ ßÛ - ß ° F � ]�ó D �IH ° F � D ó D �IH

��Ã

¢ _�dBpg_�X r e�d ¢ dBpq_ r�t d�X : pg_ t _Rpg_bX j�_bk ¢ f W^j�fNd�X d�] : ¾R_�k x j�f�j r h 9 W^X(_baNkgj�f(_bh4_bkRT

ê�ë=± 2¡365���1}/}¼����$#%�&"¦�(�b»c� ��� �ƽ ,�¼��Æ#(����/}�� M��j�,�¼Æ��#(���¡+°)³��½Þ5$¼�/7�H���Å�!���ª#%/z*��)³+�¼��ƽÁ���!���$��)��� �� �

ZnX­_�§%[�]^W^jRW^e��"X�W`e�_~a�W��7_Rpq_bX j�_Þ¨E�K��©ckge�_bX jRW^]�a W`pg_bj�eg] : _�§;[�pg_bkgk�_bkNf r ¢ egf(_�dB[(�[ p r §%WYhidBegW r X r�t dNa(_RpqW`oBdBegW`o�_iW^k�WYX ®"x _bX j�_ba 9;: jqf d�X(��_bk�W^X tEx X j�egW r XHoBd�] x _bk�dBe�a�W��7_Rpq_bX�e] r jRdBegW r X kRTc� r p¡pg_R� x ]YdBp���pqW^a kbl8d�k�egf(_ r pqa _Rp r�t d�jRj x pqd�j : WYX j�pg_bd�k�_bk¥¨EW�T±_�TM�¿% 'Þ©�l6egf(_

¢ _bW`�!f�egkndB[ [ p r d�j�f « a �©e ó ¨���y© óA 4 y ¨[A³² � © ¨ � T à ©

¨Ej t T � d 9 ]`_ � T � l�d�]^k r 2�y �C3 l�[ [�T �B� � ��� ©�T � f(_�a(_RpqW`oBdBegW`o�_�dB[ [�p r §(W^hidBegW r Xiegf(_Rpg_ tFr pg_\a(_R[}_bX a kkgW`�!X�W��"jRd�X�eg] :�r X tEx X j�egW r XªoBd�] x _bk�� x W`e�_ t dBp�d ¢ d : ¨EW^X�j r X�e�p�d�k�e�e r egf(_s_�§%d�j�e¡a(_RpqW`oBdBegW`o�_9 _bW^X(�4dik�e�p�W^j�eg] : ] r jRd�]z[�p r [}_Rpge :sr�t d tFx X�j�egW r X"©�T

� r p�egf(_\e�p�W^a W^dB� r X d�]"W^h4[�]YW^jRW`e�k�e�_bX jRW^]�l�egf(_�a(_bjRd :�r�t egf(_ ¢ _bW`�!f�egk�WYk�h x jqf t d�k�e�_Rpb�

« ��©e ó y�

¨���y© ó¨[A��Êy©vAz¨[A 4 y© ¨ ¨ A ¨µ´ � © ¨ � T±��©

¨Ej t T � d 9 ]`_ � T à ©�T�U x [}_Rp��"jRW^d�]Y] : lbW`e8h�W`�!f�eKdB[ [}_bdBp�egf dBeKegf(_bk�_�dB[ [ p r §(W^hidBegW r X k�pg_bhid�W^X�h r pg_k ] r jRd�]�T`´c� r ¢ _Ro�_Rpbl�e r d�j�e x d�]^] :Hr�9 egd�WYX�a(_RpqW^o�dBegW`o�_idB[�[ p r §(W^hidBegW r X kRl ¢ _sX _R_ba�e r k r ]`o�_�de�pqW^a�W^dB� r X d�](k : k�e�_bhNT � f _¦_b� x W^o�d�]`_bX�e�_�§%[�]^W^jRW^e6kqjqf(_bh4_¡¨ r�9 egd�W^X(_baiegf(p r!x �!fsh x ]^egW`[�]^W^jRdBegW r X9;: egf(_¦W^X�o�_Rpqk�_ r�t egf W^k6W^X%�"X�W`e�_$e�pqWYa W^dB� r X d�];hidBe�pqW�§�©8W^k6d�k��!] r�9 d�]Y] : j r!x [�]^_ba�d�k6egf _ r pqW`�!W^X d�]_�§%[�]^W^jRW`e�kqjqf(_bh4_�T � f(_\kgd�h4_ ¢ W^]^](d�]Yk r f r ]Ya4e�p x _�W t ¢ _�f dbo�_ Ä r p�h r pg_na�W^dB� r X d�]^k`/;W^X t d�j�eRlW^Xsegf(_�]^W^hiW`e r�t W^X j�pg_bd�kqW^X(� r p�a(_Rpbl;egf(_bk�_�kgjqf _bh4_bk�d�]^] 9 _bj r h4_�W^a _bX�egW^jRd�]�l�d�k¦a(_bh r X�k�e�pqdBe�_ba]^dBe�_Rp\WYXcegf W^k�k�_bj�egW r XNegf(p r!x �!f,X x hi_RpqW^jRd�]zkgW^h x ]^dBegW r X kRT

¯-XÊegf(_�kgegdB����_Rpg_baÁjRd�k�_�l\d�]^]nW^h4[�]^WYjRW`e4kgjqf(_bhi_bk¥f�dbo�_HkgW^hiW^]YdBpq] : egf(_�_b� x W`o�d�]^_bX�e

� �

_�§%[�]^W^jRW`e¦kgj�f(_bh4_�]YW^hiW`e r�t

« �©e óm ¨���y© F ó4] �M¶ Û H' A Û � ¨ � T Ä ©

¨EZ'a(_Rp�W`o�dBegW r X r�t egf(_¥[}_RpqW r a W^j4k�egdB����_Rpq_baÉ[�k�_ x a r kg[7_bj�e�p�d�]$a W��}_Rpg_bX�egW^dBegW r X�hidBe�pqW�§ t p r hegf W^k¦]YW^hiW`e�jRd�X 9 _ tFr!x X aNW^XNZn[ [}_bX a W�§¥��TV©

¯-X�d�]^]KjRd�k�_bkU·Åpg_R� x ]^dBp�d�X�a�k�egdB����_Rpq_baH��pqW^a k r�t d�X :,r pqa(_RpW·Å_b� x W`oBd�]`_bX�e�_�§%[�]^W^jRW`ekgj�f(_bh4_bk\jRd�X 9 _ tFr!x X aNd�knW^]^] x k�e�pqdBe�_ba 9 _b] r ¢ �¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹º

» » » » » » » » »» » » » » » » » » » » »» » » » » » » » » » » » » » »» » » » » » » » » » » » » » »Þ ßà1á ÿ�ß ¼2¼A¼ Þ ßà:á � ¼2¼A¼ Þ ßà:á ß» » » » » » » » » » » » » » »» » » » » » » » » » » » » » »» » » » » » » » » » » » » » »» » » » » » » » » » » »» » » » » » » » »

½ ¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¿

ÿ¢ý ¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹º

»»»aaÀÀÀÀÀÀÀ aa »»»

½ ¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¿`

¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹º

»»»ÀÀÀÀÀÀÀÀÀÀÀ »»»

½ ¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¿Á Á ÁµÃ�Ä s ~ w pq[ hDiÅ {�faf [ i ]±s b»z,w%h vn[evÆ d [ g pqs i=Ç�fxw³i ]±s È ÉÂ[^s y Z i_k [�È g pqs b s iã à:á â Y?[^s y Z i_k

¨ � T Ç ©

� f(_¡_�§(d�j�e�W^X�o�_Rpqk�_ r�t d�XʨEW^X%�"X�W`e�_���a W^h4_bX�kgW r X d�]@©¦k : h�h4_Re�pqW^j 9 d�X a _ba ��r _R[�]^W`e�¾hidBe�pqW`§cW^k¦d�]Yk r k : hih4_Re�pqW^j�d�X�a ��r _R[�]^W^e�¾ ¢ W`egfc_bX�e�p�W`_bk\ò�ó�d�] r X �ia W^dB� r X d�];A7�

ò�ó� y'sÊ �a

j r k¨[A��z©d �( e a 4 �5Ë � ` � d �( e j r k¬¨ $ �}© òc� ¨ � TV|�©

tFr p��Ød�X aM�H� §%_bazT\¨E��_RpqW`oBdBegW r X r�t egf WYk¦W^k��!W`o�_bX,WYXNZ\[ [}_bX a�W�§s �TV©¯-X�egf(_�pg_R� x ]YdBp\��pqW^a�e�pqW^a W^dB� r X�d�]zjRd�k�_¥¨K� y©�l7egf(_ �8r _R[�]YW`e�¾�hidBe�pqW`§cf d�knj r _ t �

��Ä

�"jRW`_bX�egk

d �( e ó ¢¤¥ ¤¦ (CD �Û (0D � T A· �(Û F Û (CD �IH T¿A·ÍÌ¡y � ¨ � T Õ ©

Z t e�_Rp�k x 9 k�egW`e x egWYX(��egf W^k¥W^X�e r ¨ � TV|�©�l ¢ _ªkgW^h4[�]YW t@: e r �"X aÅegf dBeRl t@r pcegf(_ªX r X kgegdB����_Rpg_ba� >y�jRd�kg_�l

ò�ó{7Î � � 4 y Á ��y 4 y� S Î � � 4 y�Êy U à Y ó Y � ¨ � TÖ{!©

¯-XÉegf _�k�egdB����_Rpg_baÅ��pqW^aÉe�pqW^a�W^dB� r X d�]�jRd�k�_�¨K� y©�l�egf(_ �8r _R[�]YW`e�¾�hidBe�pqW�§Éf d�kj r _�«sjRW`_bX�egk

d �( e ó ¢¤¥ ¤¦* ( - D � ( ] �* (�F Û (0D �IH T¿A� �F Û ( ] �IH -� (�F Û (0D �IH T A�ÏÌ¡y � ¨ � T^y � ©

Z t e�_Rp�k x(9 k�egW^e x egW^X(�¡egf(_bk�_�W^X�e r ¨ � TV|�©�l ¢ _�kgWYh4[�]^W tF: e r �7X aNegf dBeRl7W^XNegf(_�kgegdB����_Rpg_ba�� yjRd�k�_�l

ò�ó{ÑÐ � �$¨ � � 4 y©Ç �M�Êy ¢¥ ¦ � S � Û 4 � �½� �* U 4ÍÒ � S � 4 �Û U ¨ Ç �M�Êy©

S �M� �Û U Û ÓÕÔÖ Y ó Y � ¨ � T^y�y©

�ª_�X r e�_�egf dBe\W^X 9}r egf�¨ � TÖ{!©\d�X a�¨ � T^y�y©�l7egf(_�� x d�X�egW^egW`_bk�W^X kqW^a(_�egf(_ 9 pqd�j�_bkndBpg_ 9}r!x X a(_ba9 _Re ¢ _R_bX´��y�d�X a�yBT � f x kRl egf(_�WYX�o�_Rpqkg_�hidBe�pqW�§�W^k ¢ _b]^]���a(_��7X(_ba 9 _bjRd x k�_�_b]`_bhi_bX�egk�a(_bjRd :d ¢ d :�t p r h'egf(_�hid�W^X,a�W^dB� r X d�]�T¦�ª_¡X r e�_�egf dBe tFr p?� ª yBl7W`e�W^k\h x j�f�h r pq_�a W�«¥j x ]`e¦e r_RoBd�] x dBe�_\egf _nW^X�e�_R��pqd�]�WYX,¨ � TV|�©�l k r ¢ _na r X r e$�!W^o�_\_�§%[�]^W^jRW`e�_�§%[ pg_bkqkgW r X k tFr p�ò�ó t@r p=� ª yBT

� f(_�d x egf r p8f d�k³X x h4_Rp�W^jRd�]^] : j r h4[ x e�_ba�_b� x W^o�d�]`_bX�e ¢ _bW`�!f�egk x kgW^X ��¨ � T Ç ©�l�egf(_$W^X%�o�_Rpqk�_¦hidBe�p�W�§��!W`o�_bX 9�: ¨ � TV|�©�l�d�X a�egf(_ ¢ _bW^�!f�egk�dµ�( e ó d�X a « �( e ó �!W`o�_bX¡W^X � d 9 ]`_bk � T à l � T±�(l � T Ç ld�X a � TV|�T��6W`� x pg_ � T Ä W^]^] x kge�pqdBe�_bk³��pqdB["f W^jRd�]^] : f r ¢ egf(_�_b� x W^o�d�]`_bX�e ¢ _bW`�!f�egk�j r h4[�dBpg_ tFr pK_�§;�[�]^WYjRW`eRl à ��a�W^dB� r X d�]�l d�X a Ä ��a�W^dB� r X d�]³kgj�f(_bh4_bkRl 9}r egfNX r X�k�egdB����_Rpg_ba,d�X�aNk�egdB����_Rpg_bazT � f(_bk�_

��Ç

-1/4

1/3

-1/2

11

-1

Value

weight

k

number)

of

point(Grid

2 4

3

1

(a)

4/(25 )

4/

1

Value

weightof

7/2

5/2-4/(9 )

1/2 3/2

-4/(49 )

-1/2

π

π

ππ

point(Grid

k

number)

(b)

=2

=1

=0(explicit)

=1(3-diagonal) (5-diagonal)

=2

1

0.5

=3

=10 =3 =2

=1

=1

=10

=2 =3

=10n

n

n

n nn

n

m m

n

m

nnn

n

1

Value ofequivalent

weight

(c) ×µØÚÙFØÕÛ�Ü�Ý�ÞÚßáà5Ý�â�ãåä7æ

�6W`� x pg_ � T Ä �,¨Ed�©� �� x W^o�d�]`_bX�e ¢ _bW`�!f�egk tFr p�egf _¥X r X�k�egdB����_Rpg_ba���pqW^a�jRd�kg_�T�¨ 9 ©� $� x W`oBd�]`_bX�e¢ _bW`�!f�egk tFr p�egf(_�k�egdB����_Rpg_baN��pqWYasjRd�k�_�T�¨Ej©$£�_R��_bX aª¨ t@r p¦egf _{A· ynjRd�k�_ r�t �KW^� x pg_ � T Ä ¨Ed�©�©�T¿nr e�_�egf dBe tFr p�_�§%[�]^W^jRW^evh4_Regf r a kbl ¢ _bW`�!f�egk\dBpq_ � tFr p�� ® A7T

� |

��� x pq_bk�a(_bh r X kge�pqdBe�_iegf dBe�d�]^]�X r X kgegdB����_Rpg_ba�W^hi[�]^W^jRW`e�kgj�f(_bh4_bk�f�dbo�_�egf _�kgd�h4_¥]^W^hiW`egWYX(�_b� x W`oBd�]`_bX�e ¢ _bW`�!f�egkRlvd�k¨� % '­l�d�kiegf(_N_�§;["]^W^jRW`e¡X r X k�egdB����_Rpq_baÊkgj�f(_bh4_�l�d�X aÉegf dBeid�]^]k�egdB����_Rpg_ba¶WYh4[�]^W^jRW^e�kgjqf(_bhi_bk�f�dbo�_cegf(_ckgd�h4_c]^W^hiW`egWYX(�c_b� x W^o�d�]`_bX�e ¢ _bW`�!f�egkRl�d�k©�g% '­ld�k�egf(_¥_�§;[�]YW^jRW`e�k�egdB����_Rpq_baÞkgjqf _bh4_�T � f x kRl6egf(_Rpg_cW^k�]YW`e�eg]`_sd�a o�d�X�egdB��_�W^X x kgW^X(�~W^h4[�]^WYjRW`ekgj�f(_bh4_bk t p r hÔegf(_Nk�egd�X a([ r W^X�e r�t ] r jRd�]^W`¾bdBegW r X@/$��pqW^aÉk�egdB����_Rp�W^X(��W^k¡k�_R_bXÉe r f do�_,h r pg__��}_bj�e�W^XHegf WYk�pg_bk�[}_bj�eRTi�ª_¥X r e�_iegf dBe�egf(_bk�_�]^WYhiW`egk4¨Ed�k¤� % 'Þ© tFr p 9}r egfªpg_R� x ]^dBp�d�X ak�egdB����_Rpg_ba,��pqW^a kbl;W t W^h4[�]`_bhi_bX�e�_ba r Xc[}_RpqW r a W^j�a�dBegd%l 9 _bj r h4_�W^a(_bX�egW^jRd�]7e r egf(_�pg_bk�[}_bj�egW`o�_[}_RpqW r a W^jn[�k�_ x a r k�[}_bj�e�pqd�]zh4_Regf r a k¤2±{%l³y �C3 T

ê�ë=ç M,¦���!/7����)��>#%)�5$�8�!*

·�_R�!dBpqa�W^X(�­egf(_ÞX x h 9 _Rp r�t dBp�W`egf h4_RegW^j r [}_RpqdBegW r X kHpq_b� x W^pg_ba e rMr�9 egd�W^X>egf(_a(_RpqW^o�dBegW`o�_�dBend4��pqW^ac[ r W^X�eRl ¢ _�X r e�_��è � f(_Rpg_~W^k�X r X(_R_baÅe r hidB¤�_Hd�X : a W^k�egW^X�j�egW r X 9 _Re ¢ _R_bX­pg_R� x ]^dBp¥d�X aÊk�egdB����_Rpq_ba

��pqW^a k`/%egf(_bW^p r [}_RpqdBegW r X�j r!x X�egk�dBpg_�W^a(_bX�egW^jRd�]�¨ ¢ f(_bXN_�§%[ pg_bkqk�_ba�W^X ��d�X a&A ©�Tè � r p�egf _\W^h4[�]YW^jRW`e6jRd�k�_bkRl%egf(_�é�ê t d�j�e r pqW`¾bdBegW r X r�t egf(_¦�"X�W`e�_�a W��}_Rpg_bX j�_\j r _�«sjRW`_bX�ehidBe�pqW�§ªjRd�X 9 _4k�e r pg_bazT � f _4_bX�e�pqW^_bk�W^X~egf(_bk�_�h�dBe�pqW^j�_bk�a r X r e�a(_R[}_bX a r Xªegf(_k : kge�_bh kgW^¾R_0/"W�T±_�T`l r X(_�j r [ : k x «sj�_bkn_Ro�_bX�W t egf(_�a r hid�W^X���_ r h4_Re�p : W^k\k x jqf,egf dBe

¢ _�f�dbo�_�e r k r ]`o�_�k : k�e�_bhik r�t a W`�7_Rpg_bX�e�kgW`¾R_bkbT

��X(_�_�§%d�hi[�]`_ r�t$r [}_RpqdBegW r XHj r!x X�e�k x «sj�_bk�e r W^]^] x k�e�pqdBe�_�egf(_¡��_bX(_Rpqd�]�j r!x X�egW^X(�[ p r j�_bkgkRT u�r X kgW^a(_Rp¦egf _ à ��a W^dB� r X d�]�pg_R� x ]^dBp¦��pqWYaNjRd�k�_ ¢ W^egf �&>yBl ¢ f WYjqfNf d�k ¢ _bW`�!f�egk� yÇ �

ÃyÇ � ) + � � y� � y

� � ) � ¨ � T^y � ©

��Õ

Z t e�_Rp ¢ p�W`egW^X(��egf W^k¦W^Xcegf _ t@r pqh�2�y���y 3 )#+¼ 2R� Ã4��Ã43 ¨Fe r ��_Re r X(_bk�dBe\egf(_�_ba(��_r�t egf(_«)#+}k�e�_bX jRW^]@©�l(egf _�éFê t d�j�e r pqW^¾bdBegW r X�egdB¤�_bk\egf(_ tFr pqhëììììììí \��yX\ Ûy T T T

T T T T T Ty \ïî

ðLññññññòëììììììí y¶���y � Ûy T T T

T T T �óî ] �y

ðLññññññòëììììììí ) +

ðLññññññò ëììììììí Ã� à Ã

� à T T TT T T Ã� Ã

ðLññññññòëììììììí )

ðLññññññò� f(_�j r k�e tFr p\_bd�jqf�_bX�e�p :N9 _bj r h4_bk�¨ ¢ W^egf n-��p%l�npô�p¥d�X a n��<psa(_bX r egW^X �iegf(_�e : [}_

r�tKr [7_Rp�dBegW r X"©��

·n��Us� yC�¤T�yõôm 9 d�jq¤ck x(9 k�egW`e x egW r X¥�vyC�¤T�yõô£ 9 d�jg¤Nk x 9 k�egW`e x egW r Xs�4yC�¤T�yXö �

w : k�e r p�W^X(� �÷pø W^X k�e�_bd�a r�t \ ! l%egf(_�a W^o;W^a _ 9 _bj r h4_bk¦d�]^k r d¡h x ]^egW`[�] : T � f(_�e r egd�] r [}_RpqdBegW r Xj r!x X�e 9 _bj r hi_bk Ç W^Xsegf W^k�jRd�k�_�l h�d�a(_ x [ r�t _b� x d�]Y] : hid�X : k x(9 e�pqd�j�egW r X kvd�X ach x ]`egW`[�]^WYjRd��egW r X kbT � f�W^k�jRd�k�_nWYk�k�_R_bX�W^X¡egf _ à ��a W^dB� r X d�]Z��>y¦_bX�e�p : W^X � d 9 ]`_ � TÖ{;T � f(_ r egf _Rp$_bX�e�pqW`_bkr�t egf W^k¦egd 9 ]^_�dBpg_ r�9 egd�W^X _ba�kgW^hiWY]^dBpq] : T uvr h4[�dBpqWYk r X k¦dBpg_��!W^o�_bX�W^Xcegf(_�X _�§;e�k�_bj�egW r XzT

ê�ë�ù Î )�½ ,$/}���Æ*¬)8� )³+�/z#(#(5��!/z#(���"*N/z�$ #%)�*¬���Ý� ����#;�!��1����$��*B*

� f(_�]`_bd�a W^X(��_Rpgp r p�j r _�«¥jRW`_bX�e�W^X~dskg[�dBegW^d�]z�7X W`e�_�a�W��7_Rpq_bX j�_ tFr pqh x ]^d�a r _bk�X r eX(_bj�_bkgkqdBpqW^] : �!W`o�_cd~o�_Rp : � r;r aÉW^hi[ pg_bkgkgW r X r�t egf(_ tFr pqh x ]^d%´µk�d�jRj x pqd�j :�r p r�t W`egk x egWY]^W`e : T¯°Xª[�dBpgegW^j x ]^dBpbl tFr p�f W`�!f _Rp�� r pqa(_Rp�h4_Regf r a kbl8W`e�hid : X r e�a r hiWYX dBe�_ tEx pgegf(_Rp�e�_Rpqh�kRTsZ�]^k r lW`e r �}_Rpqk�]^W`e�eg]`_sf(_b]`[�W^X�j r h4[�dBpqW^X �,h4_Regf r a k r�t a�W��7_Rpq_bX�e tFr pqhid�] r pqa(_RpqkbT ¿ _Ro�_Rpgegf(_b]^_bkgkRlW`e¡hid :�9 _ r�t WYX�e�_Rpg_bkge�e r X r e�_ t p r h � d 9 ]`_bk � T^y � d�X a � T^y�ycegf dBe4k�egdB����_RpqW^X(�ªW^k�d�] ¢ d : k9 _bX(_��"jRW^d�]�T � d 9 ]`_ � T^y � �!W`o�_bk�egf(_cj r _�«¥jRW`_bX�egk r�t ]^_bd�a W^X(��_Rpgp r p�e�_Rpqhik t@r p¡oBdBpqW r!x k���pqk�ea(_RpqW^o�dBegW`o�_idB[�[ p r §(W^hidBegW r X kRl ¢ f WY]`_ � d 9 ]`_ � T^y�yi�!W`o�_bk�egf(_idB[�[ p r §(W^hidBe�_�pqdBegW rNr�t ]`_bd�a W^X(�_Rpgp r pij r _�«sjRW`_bX�egk r�t k�egdB����_Rpg_baÅe r X r X kgegdB����_Rpg_ba tFr p4��pqkge¡a _RpqW`oBdBegW`o�_�dB[ [ p r §%WYhidBegW r X kRT� f(_id�a o�d�X�egdB��_ r�t k�egdB����_RpqWYX(�,W^k r�9 k�_Rpgo�_baªe r WYX j�pg_bd�k�_ ¢ W`egf r pqa(_Rp 9"x e�a(_bj�pg_bd�k�_bk ¢ W`egfegf(_�X x h 9 _Rp r�t a WYdB� r X d�]^k x kg_bazT

� {

� d 9 ]`_ � TÖ{;�N��[}_RpqdBegW r X�j r!x X�e¡e r jRd�]^j x ]^dBe�_M)#+$dBe r X(_¥��pqW^a�[ r WYX�e ¢ f(_bX x kgW^X(�,a�W��7_Rpq_bX�ekgj�f(_bh4_bkRTn¨ ¿nr e�_��vegf(_Rpg_�W^k�X r a W��}_Rpg_bX j�_ 9 _Re ¢ _R_bX�pg_R� x ]^dBp�d�X a�k�egdB����_Rpq_ba,��pqWYa kRTV©

��>y � à � �����÷��_bX _Rpqd�]�� �§%[�]^W^jRW`e � Ä Õ y�y ����� à �M�Êy

à ��a W^dB� r X�d�] Ç { y � y Ä ����� à � 4 ÃÄ ��a W^dB� r X�d�] y � y à y Ç yb{ ����� à � 4 |

TTT TTT TTT TTT TTT T T T TTTA¨��a W^dB� r X d�] � A � A 4 í� A 4 Ç­� A 4 {ú����� � A 4 à �M� Ã

� d 9 ]`_ � T^y � � u�r _�«sjRW^_bX�egk r�t ]`_bd�a�W^X(�c_Rpgp r p�e�_Rp�hik tFr p�a W��}_Rpg_bX�e���pqk�e�a(_Rp�W`o�dBegW^o�_idB[ [ p r §��W^hidBegW r X ki¨E �§%[ pg_bkgkqW r X k t@r p���_bX(_Rpqd�]�: tFr!x X a 9;: egf(_�d x egf r p�©�T��ÉWYk�egf(_4p r ¢ X x h 9 _Rp�W^X� d 9 ]`_bk � T � � � TV|�T

û ]_v\[^] d%l û ]±v\[^] Bw%b^b Ä ] w%br{ B ` Û * � � B s hxi [^] fak ]±] d ] l d ] f 9 - 3 ; �2< F 0 H 9 / 3 ; 1 < F 0 H 9 . 3 ; N < F 0 H 9 0 3 ; P < F 0 H 9�ü,3 ; ü ý=< F 0 H d%l (ýóþ 6D+ f Þ�ÿÂ È g pqs b s i ý. ] ý� � ýý / � ] ý. � � ; ÿ�ý=<�� � � @ ��� F � � H B � �; ü ý=< B Û (,8] vns w%y�� ] ý-�0�� ý- ý ��� ] ýý N . / � ; ÿ�ý=<�� � � z ��� F � � ÿ¢ý H B � � F � � H; ü ý=< B ; ü ÿ¢ý=< Û (�D Û)8] vns w%y�� ýý 1 ý - ] ý/�/ ý ��� ; ÿ¢ý=<�� � � z � . � F � � ÿ - H B � � F � � ÿ�ý H F � � H; ü ý=< B ; ü ÿf�2< ; ü ÿ�ý=< Û (�D * - Þj6j6 þ ÿ þ ^Â È g pqs b s i ý- / ] �. / � 1N ý .�0 ] � 1-�P / P ý - ; ÿ¢ý=<�� � � @ � ; ü < B- � � � F � � H B � � ; ü ý=< Û (,8] vns w%y�� ] ý N1 N .�� . ý� 1�0 / ��� ] - ý 1ý /�/ 1���.�0�0 ; ÿ�ý=<�� � � z � ; ü ÿp�2< ; � ü � ÿ P ü ý=<- � � z � F � � ÿ¢ý H B F � � H B ; ü ÿ�ý=< � ; ü ý=< Û (�D Û)8] vns w%y�� � . NP�. N .�0�� ] .�P�� / P. ý / ý 1 / - / ��� ; ÿ�ý=<�� � � z � ; ü ÿ 1 < B ; ü <- � � z m F � � H B F � � ý H B ; ü ÿp�2< � ; ü ÿ�ý=< � ; ü ý=< Û (�D *YHZ\[^]_[ ý F B H ` ; / 1 ü n ÿ P���� ü l .�0�P N ü m ÿ -�1 � � / ü k /�/ . �³ý ü � ÿp�³ýQ� P�. ü - ý 0 N <; � ü � ÿp� - ü 0 ý=<

ÃB�

� d 9 ]`_ � T^y�yB��Zn[ [ p r §%WYhidBe�_¡pqdBegW rNr�t ]`_bd�a W^X(�c_Rpgp r p�j r _�«sjRW^_bX�egk���kgegdB����_Rpg_ba�e r X r X k�egdB�B���_Rpg_ba

ZnjRj x p�d�j :Nr pqa(_Rp: � � Ç Õ y � y � y�� y Ç

 �§;[�]YW^jRW`e � T ��ÄB��� � T^y�� �!Ç � T � {!|�| � T � |¬� Õ � T �!ÇB�!Ç � T �!ÄB� { � T � � à { � T �!Ã�Õ�Çà ��a WYdB�(T � T Ä�à y à � T Ã�Ä |¬� � T ��Ç���Ä � T �B�!Ç�Ä � T^y| � y � T^y���� Ä � T^y ��Ä�ÇÄ ��a WYdB�(T � T Ä | à � � T±��{ Ä�Õ � T à {%y Ä � T à y| � � T ��Ç�Ä�Ç � T ����Õ y|��a WYdB�(T � T Ä {%y�� � T Ä�Ã�Ä�Ç � T±� Õ�à y � T±� �!Õ�à � T à � Õ�Ã{¬��a WYdB�(T � T ÇB� y�� � T Ä�Ä | Ä � T Ä y Ç�Ä � T±��| Ç�Çy�yÝ��a W^dB�(T � T ÇB� | Õ � T Ä |;y Ä � T Ä�à | Äy à ��a W^dB�(T � T Ç y ��� � T Ä�Õ y Ãy Ä ��a W^dB�(T � T Ç y Ä�Ä

à y

Z t pg_b� x _bX�eg] :,x k�_baHd�]`e�_RpqX�dBegW`o�_¡_Rpgp r p�j r h4[�dBp�W^k r XHdB[ [ p r d�j�fÞ¨F_�T±�(T 2 Õ l ��ÃC3 © tFr p¢ dbo�_�_b� x dBegW r Xid�X�d�] : kqW^k6j r X kgW^k�egk r�t W^X kg[7_bj�egWYX(��f r ¢ egf(_�a�W��7_Rpq_bX�e�a(_RpqW^o�dBegW`o�_¦dB[ [�p r §(W^hid��egW r X k\e�pg_bdBe�d�[ x pg_�� r!x p�W`_Rpnh r a(_�� !� ¥0 r X~di��pqWYa r o�_Rp�2R��yCTby 3 ¨ tFr pn_�§(d�h4[�]^_¬©�l ¢ W`egf,��pqW^ak�[�d�jRWYX(�8CzT � f(_\h r a(_bk�egf�dBe�jRd�X 9 _\pg_R[ pg_bk�_bX�e�_ba r X�egf(_\��pqW^a ¢ W^]^](kgdBegW^k t@: � ' ®�� C © ' /f W`�!f _Rp�h r a(_bk ¢ W^]^]7dB[ [}_bdBp¦_b� x W`o�d�]^_bX�e¦e r di] r ¢ _Rp r X(_ r XNegf(_���p�W^aca x _�e r d�]^W^d�kqW^X(�(T � f(__�§(d�j�ena(_RpqW^o�dBegW`o�_ r�t � !� ¥0 WYk ���������������� �"!�#$���%�&�'�(#)�*!+�������,� �*-x�%.0/4��ª_ ¢ W^kgfse r j r h4[�dBpg_�f r ¢M¢ _b]Y]"oBdBpqW r!x kv�6� dB[ [ p r §%WYhidBegW r X k�a r W^X¥dB[ [ p r §%WYhidBegW^X(��egf W^k_�§(d�j�e t d�j�e r p � T

Z\[�[�] : W^X(��e r � !� ¥0 egf(_n_�§%[�]^WYjRW`eRl�pg_R� x ]^dBp���p�W^azl�kg_bj r X a r pqa(_Rp��K� dB[ [ p r §(W^hidBegW r XtFr p�egf(_���p�k�e¦a(_RpqW`oBdBegW`o�_��!W`o�_bk.132 .- � �%�54��76980:<; .- � �%�=4%�,>?80:�@ �BA !DC � # 1 �1 �*!D� �%��� � �*-x�%.7E<�� f(_bk�_ t d�j�e r p�k�¨ � d�X�a k s h? ¢99 ©ndBpg_¡k�_R_bXªd�k�egf(_¡a W^dB� r X�d�]Kkge�pqd�W`�!f�e�]^WYX(_�d�X a~egf(_ 9}r e�e r hj x pgo�_4pq_bk�[}_bj�egW`o�_b] : WYXHegf(_4e r [�]`_ t e�k x(9 [�] r e r�t �6W`� x pg_ � T Ç T � f _ k s h F ¢9 H9 �\j x pqo�_iW^k�k�_R_bXe r¥9 _�dB[ [ p r §%WYhidBe�_b] : j r pgpg_bj�e r X ] :ctFr p�d¥kghid�]Y] t p�d�j�egW r X r�t egf(_�� r!x pqW`_Rp�h r a _bk\egf(_���pqW^ajRd�XÉpg_R[ pq_bk�_bX�e`/ x kqW^X(�HW`e�WYk�_�§%e�pg_bh4_b] : ¢ d�k�e�_ tEx ]�W^X�e�_Rpqhik r�t j r hi[ x egdBegW r X d�]�_�«¥jRW`_bX j : TZ�knegf _ r pqa _Rp r�t d�jRj x pqd�j : :�W^X�j�pg_bd�k�_bkRl}egf(_¡j r o�_RpqdB��_ r o�_Rp � 2 � T ' 3 jR]`_bdBpq] : W^h4[ p r o�_bkRT� f(_ r egf(_Rp���o�_ik x(9 ["] r egk�W^Xª�6W`� x pg_ � T Ç kgf r ¢ f r ¢ j r o�_RpqdB��_cW^k��!d�W^X _ba 97r egf 9;: d�a a W^X(�a W^dB� r X�d�]^k¦¨ x kgW^X(��W^X j�pg_bd�kqW^X(�!] : h r pq_�WYh4[�]^W^jRW^e�dB[ [ p r §%WYhidBegW r X k�©�d�X a 9;:�x kgW^X ��k�egdB����_Rp�W^X(�(T� f(_ t d�j�e�egf�dBe�egf(_�j x pgo�_bk t@r p�kgegdB����_Rpg_ba�dB[ [ p r §(W^hidBegW r X k�dBpg_4X r e tFr pqj�_ba~e rN9 _�¾R_Rp r dBe� ' ¨ 9�x e�W^X�k�e�_bd�a�f do�_s¾R_Rp r kg] r [}_iegf _Rpg_¬©�d�]^] r ¢ k�egf(_bhØe r [ p r o%W^a(_ 9 _Re�e�_Rp¡j r o�_Rp�dB��_d�j�p r kgk\egf(_�k�[}_bj�e�p x h�T

ZÀh�d¬Ì r p~d�a(o�d�X�egdB��_ r�t egf WYkNk�[}_bj�e�pqd�]�j r h4[�dBp�W^k r XMh4_Regf r a ¨Ed�k r [ [ r k�_baMe r] r;r ¤;WYX(��dBe�_Rpgp r p4j r _�«sjRW`_bX�egk�©�W^k�egf�dBe ¢ _NjRd�X�a�W`pg_bj�eg] : j r h4["dBpg_¥hi_Regf r a�k r�t a�W��7_Rpq_bX�er pqa(_Rp�k r�t d�jRj x pqd�j : T ��rN9 _Re�e�_Rp�k�_R_¡egf(_4a W`�7_Rpg_bX�j�_bk 9 _Re ¢ _R_bXHegf _¡hi_Regf r a�kRl ¢ _4kgf r ¢ W^X�6W`� x pg_ � TV|nf r ¢ egf(_�a W��}_Rpg_bX�eKj x pgo�_bk6W^X��KW^� x pg_ � T Ç a(_Ro%W^dBe�_ t p r h egf(_v_�§(d�j�eKpq_bk x ]`eRT8¯-X�egf W^k

��

0 1 2 30

0.5

1

1.5

2

2.5

3

Explicit, regular gridM

ultip

licat

ion

fact

or

ω

p=2

468

10

0 1 2 30

0.5

1

1.5

2

2.5

3

Explicit, staggered grid

Mul

tiplic

atio

n fa

ctor

ω

p=2

46810

0 1 2 30

0.5

1

1.5

2

2.5

3

3−diagonal, regular grid

Mul

tiplic

atio

n fa

ctor

ω

p=4

6810

12

0 1 2 30

0.5

1

1.5

2

2.5

3

3−diagonal, staggered grid

Mul

tiplic

atio

n fa

ctor

ω

p=4

681012

0 1 2 30

0.5

1

1.5

2

2.5

3

5−diagonal, regular grid

Mul

tiplic

atio

n fa

ctor

ω

p=6

810

1214

0 1 2 30

0.5

1

1.5

2

2.5

3

Mul

tiplic

atio

n fa

ctor

5−diagonal, staggered grid

ω

p=68

101214

�6W`� x pg_ � T Ç ��� r!x pqW^_Rpvh x ]`egW`["]^W^jRdBegW r X t d�j�e r pqk tFr pva W`�7_Rpg_bX�e�hi_Regf r a�kRl�a WYk�[�]^d : _ba�dB�!d�W^X kge � T� f(_�j x pgo�_bk�dBpg_�]Yd 9 _b]^_baNd�jRj r pqa W^X(�4e r egf(_ r pqa(_Rp r�t d�jRj x p�d�j : : r�t egf _�h4_Regf r a kRT

Ã�Ã

��� x pq_�l7egf _�j x pqo�_bk�dBpq_¡X r e�]^d 9 _b]`_ba~d�jRj r pqa WYX(�se r egf(_bW^p�d�jRj x p�d�j : l 9�x e�d�jRj r pqa W^X(�ce r egf(_j r h4[ x egdBegW r X d�]�j r kge�[}_Rp$��p�W^ai[ r W^X�eRl�d�kva W^k�["]^d : _basW^X � d 9 ]`_ � TÖ{;T��ª_�X r e�_�egf dBe t@r p�_bW`egf(_Rpe : [}_ r�t ��pqWYazl egf(_Rpg_�W^k\dskgW`�!X W`�"jRd�X�e�WYh4[ p r o�_bh4_bX�e�W^XN� r WYX(� t p r h'_�§%[�]^WYjRW`e¦e r à ��a�W^dB� r X d�]kgj�f(_bh4_bkRl 9"x e�e r [ p r j�_R_ba tFx pgegf(_Rp�e r Ä ��a W^dB� r X�d�]�a r _bk�X r e�W^h4[ p r o�_¡_�«sjRW`_bX j : h x jqfzl8W tdBe�d�]^]�T¥U;egdB����_RpqW^X �,W^k�dB�!d�W^X�k�_R_bX�e r jR]`_bdBpq] :�9 _sd�a(o�d�X�egdB��_ r!x k�W^Xªd�]^]�jRd�kg_bkRT � f _iegf(pg_R_kgj�f(_bh4_bk�egf dBe�dBpg_�f W^�!f ]^W`�!f�e�_ba�d�k�[�dBpqegW^j x ]^dBpq] : _��7_bj�egW`o�_�WYXs�6W`� x pq_ � TV|�dBpg_�d�]^]}k�egdB����_Rpq_bazld�X a�f�dbo�_�egf(_�k�e�_bX jRW^]^kF FGFHF FHFGFHFIF

��pqa(_Rp � ��pqa(_Rp Ç ��pqa(_Rp�y �

¢ f(_Rpq_ n p¶a(_bX r e�_bk,dÞ¤;X r ¢ X tEx X j�egW r XÁoBd�] x _�l�d�X a n ä pÞpg_R[ pg_bk�_bX�egk�d�X x X(¤;X r ¢ Xa(_RpqW^o�dBegW`o�_�oBd�] x _�_bX�e�p : T

ê�ë*J ! �"*�½,��!)@"v¼���½� f(_ ¢ r pg¤�W^X�egf�W^k�kg_bj�egW r X ¢ d�k4a r X _ 9;: wv_bX(��e4� r pqX 9 _Rpq�(THZ�k¡dHkgW^h4[�]^_ie�_bk�e

[ p r�9 ]`_bhNl ¢ _�j r X kgW^a(_Rp

ß - 4 ß 0 � T ¨ � T^y Ä ©

[}_RpqW r a W^j r o�_Rp¨2R��yCTby 3 l ¢ W^egf�W^X W`egWYd�]"j r X a�W`egW r X

ßK¨��;T � ©9 ¢¤¤¤¤¥ ¤¤¤¤¦�@y 4 j r k S � 0a � � ) UC¡ Û T ¨ � ¨�© ��� y Ä

� T ¨ � ¨�ª ��� y Ĩ � T^y Ç ©

� f W^k�_b� x dBegW r XcW^k�a W^kgj�pq_RegW`¾R_bacW^Xskg[�d�j�_�d�X acW`egk�k r ] x egW r Xsd�a(oBd�X j�_baNd�X d�] : egW^jRd�]Y] :W^X¶egWYh4_�¨Fegf x kiegf(_�[�] r egkiW^XÊ�KW^� x pg_bk � T Õ Ù � T^y�yHkgf r ¢ r X ] : k�["dBegW^d�]�_Rpgp r pqk�©�TÅ�6W`� x pg_ � T Õkgf r ¢ k�egf(_4X x h4_RpqW^jRd�]6d�X aH_�§(d�j�e�k r ] x egW r X k t@r p�dcpq_R� x ]^dBp���pqW^a x kgWYX(�¥a�W��7_Rpq_bX�e�h4_Regf r a kdBe�egW^h4_·�« y ��� l�d t e�_Rp�egf _s[ x ]^k�_�f d�k�e�pqdo�_Rpqk�_baÉegf(_¥a r hid�W^X ÄB� egWYh4_bkRT � f _sX x h 9 _Rpkgf r ¢ XiW^Xiegf(_ 9}r e�e r h ]`_ t e r�t _bd�jqf¥k x(9 ["] r e6e�_b]^]^k�egf(_nX x h 9 _Rp r�t k�[�dBegW^d�](��p�W^a4[ r W^X�egk x k�_ba�/

à �

2 5 8 11 14

6 9 12 15 18

10 13 16 19 22

2 5 8 11 14

6 9 12 15 18

0 0.5 1 1.5 2 2.5 3

10 13 16 19 22

ωπK)K)KK)K)KK)K)KK)K)KK)K)KL)LL)LL)LL)LL)L

Reg

ular

gri

dSt

agge

red

grid

Explicit

3-diag.

5.diag.

Explicit

3-diag.

5.diag.

8 50 20 10 5 3 2 PPW

π

�6W`� x pg_ � TV|�����_Ro;WYdBegW r X r�t egf(_c� r!x pqW`_Rp¡h x ]`egW`[�]YW^jRdBegW r X t d�j�e r pqk t p r h egf(_cW^a(_bd�]�k�e�pqd�W`�!f�e]^W^X _ t@r p�jRd�k�_bk�kgf r ¢ X�WYX,�6W`� x pg_ � T Ç T � f(_�f r pqW`¾ r X�egd�]Kd�§%W^knW^k�]^d 9 _b]`_ba�W^X 97r egf t pq_b� x _bX�j :� d�X�asW^X�[ r W^X�egk�[}_Rp ¢ dbo�_b]`_bX ��egf�¨E�$��� ©�T � f(_no�_RpgegW^jRd�]}d�§%WYk�W^X�_bd�jqfNk x 9 [�] r e�_�§%e�_bX a k�e r� T �!Ä T$Z�]^](j x pgo�_bk�dBpg_n]Yd 9 _b]^_ba4d�jRj r pqa W^X(��e r egf(_ r [}_RpqdBegW r Xij r!x X�e$[}_Rp���pqW^a¡[ r W^X�eRl�d�k$�!W`o�_bXW^X � d 9 ]`_ � TÖ{;T � f _ 9}r §%_ba,X x h 9 _Rpqk\hidBpg¤ckgjqf(_bhi_bk\egf dBe�dBpg_�[�dBpqegW^j x ]^dBpq] : d�a(oBd�X�egdB��_ r!x kW^Xce�_Rpqh�k r�t6r [7_Rp�dBegW r X�j r!x X�e\W^Xcegf(_bW^p¦pg_bk�[}_bj�egW`o�_�d�jRj x p�d�j : p�d�X(��_bkRT

Ã�Ä

egf W^k�X x h 9 _Rp ¢ d�k¡k�_b]^_bj�e�_ba¶k r egf�dBeRl 9 d�k�_ba r X�egf(_ r [}_RpqdBegW r X�j r!x X�egk4WYX � d 9 ]`_ � TÖ{;l�d�]^]jRd�k�_bk ¢ r!x ]^a 9 _n_b� x d�]^] : j r k�eg] : W t p x X¥W^X~yÝ����T �6W`� x pg_ � TÖ{�kqf r ¢ k�egf _�_b� x W`oBd�]`_bX�eva�dBegd tFr pk�egdB����_Rpg_ba¥��pqWYa kRT6Znk$_�§;[}_bj�e�_ba t p r h r!x p�d�X d�] : kgWYkRl�k�egdB����_RpqWYX(��W^k$d�a(o�d�X�egdB��_ r!x k�W^Xid�]Y] egf(_jRd�k�_bkRl 9�x e�]`_bkgk\k r4t@r pnegf(_�h r k�enW^h4[�]^WYjRW`e�kgj�f(_bh4_�T

�nW^�!f(_Rp�a�W^h4_bX kgW r X k�d�X a~] r X(��_Rp�egW^h4_�W^X�e�_R��pqdBegW r XHh r pg_¡k�e�p r X(�!] :Nt do r p�f W`�!f(_Rpr pqa(_Rp�h4_Regf r a k r o�_Rp�] r ¢ _Rp r pqa(_Rp r X(_bkbT��6W`� x pg_ � T^y � kgf r ¢ k�egf(_4kgd�h4_¡e�_bk�e�p x X�e r egW^h4_�= �B����� x kgW^X(�i��p�W^a�kgW`¾R_bk¡¨EW^X,_bd�jqfHk�[�dBegW^d�]�a W`pg_bj�egW r X7© ¢ f W^j�f ¢ r!x ]^aN[�p r o%W^a(_�_b� x d�]Kj r k�eW^X � ����T

¯-X,�KW^� x pg_ � T^y�yBl ¢ _�pq_��"X(_�egf(_�_�§%[�]^WYjRW`e��� y�kqjqf(_bh4_�k x jRj�_bkgkgW^o�_b] : T � f _�d�a a W��egW r X d�]zX x h 9 _Rp ¢ W`egf WYX�_bd�j�f�k x 9 [�] r e¦kgf r ¢ k¦egf(_�pq_b]^dBegW`o�_�j r h4[ x e�_Rp�egW^h4_�pq_b� x W^pg_ba�¨ ¢ W`egfp(y`p4j r pgpg_bkg[ r X�a W^X(��e r egf(_�j r k�e r�t _bd�j�f r�t egf _�jRd�kg_bk�W^X¥�KW^� x pg_ � T^y � ©�T$¯-e¦W^k�jR]`_bdBp¦egf dBe¦e rd�jqf�W`_Ro�_\d�jRj�_R[ egd 9 ]^_�¨Ekgd : l%d 9}r!x e¦y,Mi©6d�jRj x p�d�j : pq_b� x W^pg_bkK_�§ r p 9 W`egd�X�e�j r hi[ x egdBegW r X d�]�j r k�egkW^X 9}r egf4egWYh4_\d�X aihi_bh r p : T � f(_ 9}r e�e r h ]`_ t e�k x(9 [�] r e�W^X4�6W`� x pg_ � T^y�ynkgf r ¢ k$j r h4["dBpqd 9 ]`_d�jRj x pqd�j : e r egf(_ 97r e�e r h0pqW^�!f�e r X(_¡W^X��6W`� x pg_ � TÖ{~· dBe�d 9}r!x en�(l ����� egWYh4_bk�]^dBpg��_Rp�j r k�e¨EW^X à ����l egf W^k t d�j�e r p\W^X j�pq_bd�k�_bk�e r d 9}r!x e ��ÇB� l ����� ©�T � f(_�kgegdB����_Rpg_ba,k�_bj r X�a r pqa(_Rp�kgj�f(_bh4_W^X�egf W^k�j r hi[�dBpqW^k r X¡j r pgpq_bk�[ r X a k6e r egf(_�k�["dBegW^d�]%a W^kgj�pg_RegW^¾bdBegW r X r�t egf _�²�_R_���kgjqf(_bhi_�l ¢ f�W^jqf

¢ d�k¦[�W r X(_R_Rp�W^X(� ¢ r pg¤ ¢ f(_bX¥��p�k�e�[�p r [ r k�_ba t@r p¦egWYh4_���a(_R[}_bX a(_bX�evj r hi[ x egdBegW r X d�]³_b]`_bj�e�p r �hidB�!X(_RegWYjRk,¨ES�d�§ ¢ _b]^]�´µk4_b� x dBegW r X kÝ©�W^XMyb{ Ç�Ç 2 � { 3 T¶¯-eif d�k4kgW^X�j�_N_bX�Ì r¬: _baÞd�] r X �B��]^d�k�egW^X(�[ r [ x ]^dBp�W`e : ¨F_�T±�(T�2 ��� l � | 3 ©¦W^XNk�[�W`e�_ r�t W`egk�] r ¢ r pqa _Rp r�t d�jRj x pqd�j : T

ê�ë@í Î )��$#(¼Æ5$*B��)8�$*

uvr h 9 W^X WYX(�è f W`�!f r pqa(_Rp�k r�t d�jRj x pqd�j : ¨EW�T±_�T ¢ WYa(_Rp�k�e�_bX jRW^]Yk�©�lè W^h4[�]^WYjRW`egX(_bkgkRl;d�X aè k�egdB����_RpqW^X(�

]`_bd�a k�e r dcjR]^d�kqk r�t j r h4[ x egdBegW r X d�]^] : o�_Rp : j r k�e°��_��7_bj�egW^o�_i�"X W^e�_¡a�W��7_Rpq_bX j�_4kgjqf(_bhi_bkRT�Z�kegf(_bW`p r pqa _Rpqk r�t d�jRj x pqd�j : W^X j�pg_bd�kg_�l�egf(_bk�_�kgj�f(_bh4_bk�dB[ [ p r d�jqf4W^X�d�jRj x pqd�j : egf(_ ¢ _b]Y]���¤;X r ¢ X

Ã�Ç

��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

�6W`� x pg_ � T Õ �$·\_R� x ]^dBp¦��pqW^ack r ] x egW r X kvdBe�� y ��� x kgW^X(��a W��}_Rpg_bX�e�kg[�dBegW^d�]}dB[ [ p r §%WYhidBegW r X kRT� f(_¥��pqW^a�kgW`¾R_bkN¨Ekgf r ¢ XÉW^X�egf(_ 97r e�e r h ]^_ t e¡j r pqX(_Rp r�t _bd�j�fÞk x(9 ["] r e�© ¢ _Rpg_ck�_b]`_bj�e�_baÉe rhidB¤�_�_bd�j�f�jRd�kg_�_b� x d�]^] : j r kgeg] : W^XNj r h4[ x e�_Rp\egW^h4_�¨Ed�kgk x hiW^X(��yÝ����©�T

à |

��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

�6W`� x pg_ � TÖ{;��U%d�h4_¡d�k��6W`� x pg_ � T Õ l 9"x e x kqW^X(��k�egdB����_Rpq_baªdB[ [ p r §%W^h�dBegW r X k t@r p�egf(_¡k�[�dBegW^d�]a(_RpqW^o�dBegW`o�_�T � f(_�pg_ba x j�egW r X k6W^X�egf(_¦d�h4[�]YW`e x a(_bk r�t egf(_�a�W^k�[}_RpqkgW`o�_ ¢ do�_�e�pqd�W^X k¦¨Ej r h4["dBpg_bae r egf(_�pg_R� x ]^dBp6��pqWYa�jRd�k�_bk�WYX��6W`� x pg_ � T Õ ©KdBpq_v["dBpgegW^j x ]^dBp�] : X r egW^j�_bd 9 ]`_�W t r X _�j r hi[�dBpg_bk6egf(_¢ dbo�_bk�e�pqd�W^X k\d�k�egf(_ : ]`_bdo�_�egf(_�]`_ t e\_ba(��_ r�t egf(_�a r hid�W^X k�d�X�a�¨ 9 _bjRd x k�_ r�t [}_RpqW r a W^jRW^e : ©pg_bdB[ [}_bdBp\WYXcegf(_�pqW`�!f�e�f d�] tKr�t egf _�k x(9 ["] r egkRT

Ã�Õ

��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

�6W`� x pg_ � T^y � ��U r ] x egW r X k tFr p�kgegdB����_Rpg_ba¥��pqW^a4dBe9�� �B����� ¢ W`egf¡��pqWYaikgW`¾R_bk�k�_b]`_bj�e�_baie r hidB¤�_j r h4[ x egdBegW r X k�_b� x d�]Y] : egWYh4_���j r X k x h�W^X(��W^X � ����T³¨ � f _\h4_bh r p : pq_b� x W^pg_bh4_bX�egk$kgjRd�]`_ ¢ W`egfegf(_�Pb� x dBpg_ r�t egf _�X x h 9 _Rpqk��!W`o�_bX�WYXcegf(_ 9}r e�e r h ]`_ t e�j r pqX(_Rp�kRTV©

à {

��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

�6W`� x pg_ � T^y�yB�ÞU r ] x egW r X�k�dBeM�� �B����� tFr pcegf(_ªk�egdB����_Rpg_baÁ_�§%[�]^W^jRW^e·�X yHkgjqf(_bhi_ tFr pW^X j�pq_bd�kgW^X(�!] : �"X(_4��pqW^a�kRT � f(_4X x h 9 _Rpqk�WYXªegf(_ 9}r e�e r h ]`_ t e�j r pqX(_Rp�k�a(_bX r e�_�¨Ed�k�W^Xª�6W`�B�x pg_bk � T Õ � � T^y � ©segf(_�X x h 9 _Rp r�t ��pqW^aÊ[ r W^X�egksd�j�p r kgksegf(_,[}_RpqW r azT � f(_~X x h 9 _RpqkiWYXÞegf(_9}r e�e r h p�W`�!f�e�j r pqX(_Rpqk��!W`o�_�egf(_spg_b]^dBegW`o�_sj r k�e�WYX 9}r egf�j r h4[ x e�_Rp�egW^h4_sd�X a�h4_bh r p : l�W tW^h4["]`_bh4_bX�e�_baªW^X � ����l�j r h4[�dBpg_ba�e r egf(_ x X�W`ei¨°y©�j r k�e r�t d�]^]6egf(_sjRd�k�_bk�W^Xª�6W`� x pg_ � T^y � T� f(_�e r [�]`_ t evk x(9 [�] r e r�t �6W`� x pg_bk � T^y � d�X a � T^y�y�dBpg_�W^a _bX�egW^jRd�]�/ ¢ _�k�_R_�f(_Rpg_�f r ¢ j r k�eg] : W`eW^k�e r d�j�f W`_Ro�_�f W`�!fNd�jRj x pqd�j :N9;: pg_��"X W^X ��egf(_���pqW^a x kgWYX(�¡egf W^k¦kgj�f(_bh4_�T

� �

k�[}_bj�e�pqd�]nd�jRj x pqd�j :Þr�t [}_RpqW r a WYjBl$_�§%[�]^W^jRW`e�[�k�_ x a r kg[7_bj�e�p�d�]�kgjqf _bh4_bkRT � f(_,kgj�f(_bh4_bkca W^k°�j x kgkg_ba�W^XHegf W^k�jqf dB[ e�_Rp�dBpg_sa _��"X(_ba r X�_b� x W^kg[�d�j�_ba u dBpge�_bkqW^d�Xª��pqW^a�kRT4�­f _bX�j r h 9 W^X(_ba

¢ W`egf�egf(_�W^a(_bd r�t�r o�_Rpq]^dB[ ["W^X(�ik x(9 a r h�d�W^X kRl;egf(_�pq_b]^dBegW`o�_b] : X dBpgp r ¢ k�e�_bX�jRW^] ¢ W^a egf k¦hidB¤�_egf(_�kqjqf(_bh4_bk ¢ _b]Y]���k x W`e�_ba tFr p�j r h4[ x egdBegW r X k�W^Xªh4_ba W^d ¢ W`egfªj x pgo%W^]^W^X _bdBp�h�dBe�_RpqW^d�]�W^X�e�_Rp��t d�j�_bkRT � f(_�kgjqf _bh4_bk�jRd�X 9 _�dB[ [�]^W`_ba�e r h r k�ev]YW^X(_bdBp ¢ dbo�_���e : [}_����� $k r�t³9 p r d�a¥W^X�e�_Rpg_bk�eRT¯°X�egf(_s[�dBpgegW^j x ]YdBp�dB[ [�]^WYjRdBegW r X r�t egW^h4_���a r hid�W^X�j r hi[ x egdBegW r X d�]$_b]`_bj�e�p r hidB�!X _RegW^jRkN¨Ed�]^k r¤%X r ¢ XÅd�kc�K� � ��©�lvegf(_�jR]Yd�kgkgW^jRd�]�²�_R_~kgj�f(_bh4_ x k�_bk r X ] : egf(_~]^d�k�e r�t egf _,egf(pg_R_~f W`�!f%�]^W`�!f�e�_baHj r X j�_R[ egkRT��ª_¡�"X a~egf dBe�hid¬Ì r p�W^h4[ p r o�_bh4_bX�egk�W^XHd�jRj x pqd�j : d�X a~_�«sjRW`_bX j : jRd�X9 _\d�jqf�W`_Ro�_ba 9�: d�]^k r W^X j r pq[ r p�dBegW^X(��egf(_ r egf(_Rp�e ¢ r W^a(_bd�k r�t W^h4["]^W^jRW`egX(_bkqkKd�X�ask�egdB����_Rp�W^X(�(T

Î �$/#,$��� � ì

i ��/}�³�³� ���� ! �ƽ­� .¬�8��� �³��/"��)³��*N+°)³�~. /(1���24365�/7�!��)���*

¯-X�egf W^k�j�f dB[ e�_Rpbl ¢ _nj r X kqW^a(_Rp$oBdBpqW^dBegW r X k r�t egf(_�Zna�d�hik-Ù�w�d�kgf tFr pgegfzl 9 d�jg¤ ¢ dBp�a ka W��}_Rpg_bX�egW^dBegW r Xzl¦d�X a­· x X(��_ÝÙ�¸ x e�egd t d�hiWY]^W`_bk r�t egWYh4_�W^X�e�_R��pqdBe r pqk¥e r k r ]`o�_~k : kge�_bhik r�t]^W^X _bdBp ¢ do�_s_b� x dBegW r X k r X x X�W t@r p�hNl³egW^h4_���kgegdB����_Rpg_ba���p�W^a kRT � f(_bk�_�h4_Regf r a k�dBpg_ tFr!x X ae r f dbo�_�kqhid�]^]`_Rp¡] r jRd�]�e�p x X jRdBegW r X�_Rpgp r p�k�d�X�a�e r d�]^] r ¢ ]^dBpg��_Rpik�egd 9 ]`_segWYh4_¥kge�_R[�k¡egf d�Xe�pqd�a W^egW r X d�]³X r X�k�egdB����_Rpg_ba~o�_RpqkgW r X�k r�t _b� x W`oBd�]`_bX�e r pqa(_Rp�kRT¦�ª_�WYX�o�_bk�egW^�!dBe�_�egf(_¡d�jRj x pqd�j :d�X ask�egd 9 W^]^W^e :¡r�t egf(_bk�_�h4_Regf r a kvd�X d�] : egW^jRd�]^] : l!_�§%[}_RpqW^h4_bX�egd�]^] : l;d�X aiegf p r!x �!fsegf(_ x kg_ r�t dX r o�_b]6p r�r e�[ r pge�pqd�W`ene�_bjqf X�W^� x _�T�¯°X~d�a a W`egW r X³l ¢ _�d�a�a(pg_bkgk�k�_Ro�_Rpqd�]Kegf(_ r pq_RegW^jRd�]�� x _bk�egW r X kpg_R�!dBpqa�W^X(�4k�egdB����_Rpg_ba�egW^h4_�W^X�e�_R��pqdBe r pqkbT

ì�ë - .¬�8���!)� $5$#;�!��)���­f _bX ¢ dbo�_c_b� x dBegW r X k�dBpg_¥[ r kg_ba�d�k���pqkge r pqa(_Rp¡k : k�e�_bhik¡d�X a�a W^kgj�pg_RegW^¾R_ba�W^X

k�[�d�j�_�e r�: W`_b]^a�d�k : kge�_bh r�t"r pqa�W^X dBp : a W`�7_Rpg_bX�egW^d�]�_b� x dBegW r X k�¨����� $kÝ©�l!egf(_¦]^W^X(_bdBp�W`¾bdBegW r X r�tegf(_�pg_bk x ]`egW^X(�¡k : k�e�_bhÂf d�k¦d¡[ x pq_b] : W^hidB�!W^X�dBp : k�[}_bj�e�p x h�T � f W^k�j r pgpg_bk�[ r X a�k$e r egf(_ t d�j�eegf dBe r X�] : [�p r [�dB�!dBegW r X,egdB¤�_bkn["]^d�j�_�T�S~d�X : jR]^d�kqkgW^jRd�]³h4_Regf r a k t@r p����� $k\f�dbo�_�kgegd 9 W^]^W`e :pg_R�!W r X�k�egf dBe�W^X jR] x a(_¡d�X�W^X�e�_Rpgo�d�] r�t egf(_ tFr pqh 2R��S P QCTUS P Q 3 r XHegf _�W^hidB�!W^X�dBp : d�§(W^kRT4�ª_jRd�]^]}egf(_�]^dBpg��_bk�e�k x jqfNoBd�] x _ r�t�P Q�egf(_�=Eÿ�Ð å"=EJ8Ð OI¶PRQ¬Ð ãK=EDE=@Q�IÞã$ä��KJ�çKÐ O¬IBNU��þ}âPO r�t egf(_���� >W^X�e�_R��pqdBe r pbT�¯°X�egf(_¥j r X�e�_�§%e r�t d�kg_bhiW^a W^kqj�pg_Re�_ ¢ do�_c_b� x dBegW r Xzl6e ¢ r�t _bdBe x pg_bk�dBpg_a(_bkgW^pg_ba t@r pnd�X����� ÊW^X�e�_R��pqdBe r pb�

¨°y©�kghid�]^]z] r jRd�]ze�p x X jRdBegW r Xc_Rpgp r pnd�X a

� �

¨ � ©�]^dBpg��_�W^h�dB�!W^X dBp : k�egd 9 W^]^W^e :�9}r!x X�a dBp : ¨F¯gU%w�©�T

� f(_bkg_�e ¢ r [ p r [}_RpgegW^_bk¦dBpg_�e : [�W^jRd�]^] : W^X r [�[ r kqW`egW r X¥e rir X(_�d�X r egf(_RpbT¯-X u f dB[ e�_Rp � d�X a 2±{ 3 W^enf d�k 9 _R_bX�kgf r ¢ X,egf�dBe\egf(_ x k�_ r�t kgegdB����_Rpg_ba r p�W^X�e�_Rp��

]^d�j�_ba¥��pqW^a�k$W^Xsk�[�d�j�_�jRd�XcW^X j�pg_bd�k�_negf(_�d�jRj x pqd�j :�r�t �"X W`e�_�a W��}_Rpg_bX j�_nd�X�a�[�kg_ x a r k�[}_bj�e�pqd�]a W��}_Rpg_bX�egW^dBegW r X¡h4_Regf r a k ¢ f _bX x k�_ba tFr p�]^W^X(_bdBp ¢ dbo�_�_b� x dBegW r X kbT�U(W^hiW^]^dBp�] : legf(_ x X(¤;X r ¢ XoBdBpqW^d 9 ]`_bk r�t ]^W^X(_bdBp ¢ dbo�_�_b� x dBegW r X k�¨Ed�X aNk : k�e�_bhik r�t k x jqfc_b� x dBegW r X k�©vjRd�X 9 _�k�egdB����_Rpq_baW^X�egW^h4_\e r�: W`_b]^a 9 _bX(_��"egk$W^X 97r egf¥d�jRj x pqd�j : d�X askgegd 9 W^]^W`e : T6¯-Xsegf W^k�jqf dB[ e�_Rp ¢ _�WYX�e�p r a x j�_X r o�_b] t d�h�W^]^W`_bk r�t h x ]^egW^k�e�_R[Nd�X a�h x ]`egW^kgegdB��_�k�egdB����_Rpg_ba~���� ÅW^X�e�_R��pqdBe r pqkRT��ª_��"X a¥egf dBetFr p\h x ]`egW^k�e�_R[�h4_Regf r a k r�t egf(_�kqd�h4_ r pqa(_Rp r�t d�jRj x p�d�j : l"k�egdB����_RpqWYX(�sW^X¥egW^hi_ x k x d�]^] : W^h¡�[ p r o�_bk\d�jRj x p�d�j :N9�: d t d�j�e r p r�t d 9}r!x e\{4d�X a�WYX j�pg_bd�k�_bk¦egf _�¯�U%w 9;: d t d�j�e r p r�t � T±��Ù%|�T±�(l

¢ W`egf�egf(_ t d�j�e r p¡��p r ¢ W^X(�~d�k r p�a(_Rp�WYX j�pg_bd�k�_bkRT��ª_Nd�]^k r [�pg_bk�_bX�e�d t@r!x pqegf r pqa _Rp�h x ]`egW��k�egdB��_¡h4_Regf r a ¢ f WYjqfzl�j r hi[�dBpg_ba�e r jR]^d�kgkgWYjRd�] t@r!x pgegf r pqa _Rpn· x X(��_ÝÙ�¸ x e�egd%l7f d�k\d�X,_Rpgp r pj r X k�egd�X�enkqhid�]^]`_Rp 9;: d t d�j�e r p r�t y Ç d�X aNd�X�¯gU%wÁ]^dBpg��_Rp 9;: d t d�j�e r p r�t d 97r!x e¦e ¢ r T

�$: [�W^jRd�]Y] : egf _¥j r h4[ x egdBegW r X d�]vj r k�e r�t�x kgW^X �,d�XÉW^h4[�]^WYjRW`e�h4_Regf r a�W^k�Ì x k�egW���_bar X ] : W^X�egf _v[�pg_bk�_bX j�_ r�t k�egW`�}X(_bkqk�¨EX r e6d�X4WYkgk x _ t@r p�]^WYX(_bdBp ¢ dbo�_¦_b� x dBegW r X�k�© r p ¢ f(_bX�egf(_Rpg_W^k�dNpq_b]^dBegW`o�_b] : kghid�]^]6X x h 9 _Rp r�t _b� x dBegW r X k�W^XHegf(_ik : k�e�_bhNTi�ª_s_bX�o%W^kgW r X r!x p�h4_Regf r a k9 _bW^X(� x k�_ba~e r k r ]`o�_¡k : kge�_bhik ¢ W`egf~d¥o�_Rp : ]^dBpq��_�X x h 9 _Rp r�t _b� x dBegW r X�kRl}[ r kqkgW 9 ] : W^X~egf(_hiW^]Y]^W r X k�¨Ed�k�W^k�egf(_njRd�kg_ ¢ f(_bX � ��� r p à ��� ¢ dbo�_�_b� x dBegW r X kvdBpg_�k r ]`o�_ba ¢ W`egf�d�h4_Regf r a r�t]^W^X _bkvdB[�[ p r d�jqf7©�T$� r p\k x jqfNkgW`e x dBegW r X kRl%W`e¦W^k¦W^h4[�pqd�j�egW^jRd�]7e r ��_bX(_RpqdBe�_s¨Ed�X�aNk�e r pg_¬©�d�XN£8ma(_bj r h4[ r kgW^egW r XzT6�ª_�egf x k�j r X kqW^a(_Rp r X ] : _�§%[�]^W^jRW`e�h4_Regf r a k�WYXcegf W^k¦d�X d�] : kgW^kbT

Zn]^egf r!x �!f ¢ _ tFr j x k r!x p�a W^kgj x kgkgW r X r XN]^W^X(_bdBp ¢ dbo�_�_b� x dBegW r X kRl ]YW^X(_bdBpqW`e : W^k�X r ed�pg_b� x W`pg_bhi_bX�e�W^X¡d�X :�r�t7r!x p�[ p r [ r k�_ba¡kgj�f(_bh4_bkRT�Z�a a W`egW r X d�]^] : l r!x p�egW^hi_�WYX�e�_R��pqdBe r p�k�dBpg_a(_bkgW^�!X(_ba¥e r k r ]`o�_���pqk�e r pqa(_Rp¦k : k�e�_bhikRT�Zn]`egf r!x �!fsk : k�e�_bh�k r�t ¢ dbo�_�_b� x dBegW r X k�jRd�X r�t e�_bX9 _¦pg_ ¢ pqW^e�e�_bXid�k$k�_bj r X�a r pqa(_Rp�k : kge�_bhikRl!�"pqk�e r pqa(_Rp t@r pqh x ]^dBegW r X k�dBpg_���_bX _Rpqd�]^] : [ pg_ t _Rpgpg_baW^X,egf(_�]YW`e�_RpqdBe x pg_¥¨F_�T±�(T�S~d�§ ¢ _b]^]�´µk\_b� x dBegW r X kÝ©�l"[�dBpqeg] : a x _�e r _bd�kgW^_Rp�W^hi[�]`_bh4_bX�egdBegW r X r�t9}r!x X a dBp : j r X a�W`egW r X kRT¦¨F¯-evW^k$¤;X r ¢ X�egf dBevkgegdB����_Rpg_bac��pqW^a k$dBpg_ 9 _Re�e�_Rp t@r p�dB[ [ p r §(W^hidBegW^X(�r a a%� r pqa(_Rp8a(_RpqW`oBdBegW`o�_bk�d�X�a�X r X k�egdB����_Rpq_ba���pqWYa k³dBpg_ 9 _Re�e�_Rp t@r pKdB[ [ p r §%WYhidBegW^X(�¦_Ro�_bX%� r p�a(_Rpa(_RpqW^o�dBegW`o�_bk«2±{ 3 TV©

� Ã

� f(_�pg_bk�e r�t egf WYk�jqf dB[�e�_RpnW^k r pg�!d�X�W`¾R_ba,d�k tFr ]^] r ¢ kR�� T�¯°]^] x kge�pqdBegW r X k r�t ��pqW^a�k�egdB����_Rp�W^X(��W^XcegWYh4_ t@r pn]^W^X(_bdBp ¢ dbo�_�_b� x dBegW r X kà T$�$pg_b]^W^hiWYX dBpqW`_bk�(TvU;egdB����_Rpq_ba,Z�a d�hik°��w�d�kgf tFr pgegf�d�X a 9 d�jq¤ ¢ dBpqa k�a�W��7_Rpq_bX�egdBegW r X,h4_Regf r a kÄ TvU;egdB����_Rpq_ba t pg_R_�[�dBpqd�hi_Re�_Rpnh4_Regf r a kÇ T � f _ r pg_RegW^jRd�]³j r X kqW^a(_RpqdBegW r X�k|�TvU;egdB����_Rpq_ba�[ pg_ba�W^j�e r p���j r pgpg_bj�e r p�h4_Regf r a kÕ TvU;egdB����_Rpq_ba,· x X(��_ÝÙ�¸ x e�egdihi_Regf r a�k{;T$· r�r e�[ r pge�p�d�W`egky � T ¿�x h4_RpqWYjRd�]z_�§;[}_RpqWYh4_bX�egky�yBT uvr X�jR] x kgW r X�k

� f(_�d x egf r p�hid�a(_�kgW^�!X W��"jRd�X�e¦j r X�e�pqW 9�x egW r X k�e r k�_bj�egW r X k\�(l Ä l Ç l7|�l Õ l"d�X a�y � TU r h4_�j r X�e�pqW 9"x egW r X k ¢ _Rpg_�hid�a _�e r k�_bj�egW r X � T

wv_bjRd x k�_ ¢ _ x k�_~d�X x h 9 _Rp r�t d�j�p r X : hik ¢ f W^j�fÊhid :Ê9 _ x X t d�h�W^]^W^dBp4e r egf(_pg_bd�a(_Rpl d4�!] r kgkgdBp :sr�t egf(_bk�_�d 9 9 pg_Ro%W^dBegW r X k¦WYk¦W^X jR] x a _ba¥WYX,U;_bj�egW r X�yBT � T

ì�ë@ê .¬¼�¼Æ5$*¬���!/7�!��)���*s)�+��³���Æ *¬��/}�³�³� �������­+°)³�H¼����$� /}�,»c/(1�����365�/7�!��)8�$*

¨ ¿\r e�_��6egf WYk�k�_bj�egW r XiW^k�d�Xi_�§;e�_bX kqW r X r�t U;_bj�egW r X � T � T � f(_¦egWYh4_¦k�egdB����_RpqW^X(����pqW^a kW^Xcegf WYk¦k�_bj�egW r X ¢ _Rpg_�j�pq_bdBe�_ba�[�dBpgeg] :s9;: egf _�d x egf r pbTV©

U;egdB����_Rpg_ba,��pqW^ace�_bjqf�X W^� x _bk�dB[ [�] : e r ]YW^X(_bdBp¦f : [}_Rp 9}r ]^W^jn_b� x dBegW r X k ¢ f�W^jqf�f�dbo�_9 _R_bX ¢ pqW`e�e�_bXÉd�k���pqk�e r pqa(_Rp¡k : k�e�_bhikRT � f _�oBdBpqW^d 9 ]`_bk�W^X�egf(_ck : kge�_bh dBpg_¥kgegdB����_Rpg_baÞW^Xk x j�f�d ¢ d : egf dBe�egf _�] r jRdBegW r X k r�t o�d�] x _bk�d�X acegf(_bW^p\a(_RpqW`oBdBegW`o�_bk�dBpq_�W^X�e�_Rp�]^d�j�_bazT

�ª_4�!W`o�_4egf(pg_R_4_�§(d�h4[�]^_bk`/ r egf(_Rp�]YW^X(_bdBp ¢ do�_�_b� x dBegW r X k�jRd�X 9 _¡e�pg_bdBe�_ba�kgW^hiW��]^dBpq] : T��KW^� x pg_ à T^y¡�!W`o�_bk t@r!x p�a�W��7_Rpq_bX�e ¢ d : k�e r ]Yd :,r!x e�egf _���p�W^a r�t$x X(¤%X r ¢ X k�ß�d�X a~à

���

tFr p�egf(_ r X(_���a�W^h4_bX kgW r X d�]}d�j r!x k�egW^j ¢ dbo�_�_b� x dBegW r XQ ßQ � . Q àQ �Q àQ � . Q ßQ � � ¨ à T^y©

��X(_�jRd�X�jqf r;r k�_$e r�x egW^]^W^¾R_KegWYh4_�k�egdB����_RpqW^X �(lBkg[�d�j�_�k�egdB����_Rp�W^X(�(l 97r egf³l r pKX(_bW`egf(_RpbT¯°XH_Ro�_Rp : jRd�k�_iegf(_ikg[�d�j�_���egW^h4_�a _bX kgW`e :�r�t a dBegd�W^k�_�§(d�j�eg] : egf(_�kqd�h4_�T ¿nr e�_iegf dBe�W t�r X(_

¢ d�X�egk8e r W^X�j r pg[ r pqdBe�_�k�egdB����_RpqW^X �nW^X�egWYh4_�l¬egf _�o�dBp�W^d 9 ]`_bkzß¡d�X a�à�h x k�e³_�§(W^k�e r X�W^X�e�_Rpq]^d�j�_baegW^h4_�WYX�e�_RpgoBd�]^k\¨F_�T±�(T`l%ߥ_�§%WYk�egk r X�WYX�e�_R��_Rp�egW^h4_�]`_Ro�_b]^kbl ¢ f WY]`_�à¡_�§(W^k�egk r Xsf d�] t ��W^X�e�_R��_Rp�egW^h4_]`_Ro�_b]^kÝ©�T

�6W`� x pg_ à T � kqf r ¢ k�X r X k�egdB����_Rpg_ba�d�X a�k�egdB����_Rpq_ba�k�[�d�j�_$��pqW^a k tFr p³egf(_�e ¢ r ��a WYh4_bX kgW r X�d�]_b]^d�k�egWYj ¢ do�_�_b� x dBegW r X

2 Q ßQ � Q )Q � 4 Q BQ W2 Q àQ � Q BQ � 4 Q CQ WQ )Q � ¨ V 4 ��; © Q ßQ � 4 V Q àQ WQ BQ � ; Q àQ � 4 ; Q ßQ WQ CQ � V Q ßQ � 4 ¨ V 4 ��; © Q àQ W �¨ à T � ©

� f(_ik�["dBegW^d�]$k�egdB����_Rp�W^X(��]Yd :�r!x e��!W`o�_bX�W^X��6W`� x pg_ à T � W^k x X�W^� x _b] : a(_Re�_Rp�hiW^X(_bazT� r p6_�§(d�h4[�]`_�lBegf(_���pqk�e8_b� x dBegW r X�pq_b� x W^pg_bk³egf dBe6ß 9 _$pg_R[�pg_bk�_bX�e�_ba�f�d�] t ¢ d :�9 _Re ¢ _R_bX�oBd�] x _bkr�t )�W^Xsegf(_ ����a W`pg_bj�egW r Xsd�X acf d�] t ¢ d :i9 _Re ¢ _R_bXcoBd�] x _bk r�t B�W^Xsegf(_mW���a�W`pg_bj�egW r XzT6¯ t *16*,0 d�]^k rdB[ [}_bdBpg_baÞWYXÉegf(_c��pqk�e4_b� x dBegW r X³lvW`e ¢ r!x ]^a¶X r e 9 _N[ r kqkgW 9 ]`_¥e r k�egdB����_Rpck�[�dBegWYd�]^] : T¶�ª_r�9 k�_Rpqo�_�egf dBe tFr p�dc]^dBpq��_�X x h 9 _Rp r�t ]^W^X _bdBp ¢ dbo�_4_b� x dBegW r X k4¨F_�T±�(T�S�d�§ ¢ _b]^]�´µk�_b� x dBegW r X kW^X¥d�X : X x h 9 _Rp r�t a W^hi_bX kgW r X kÝ©�l�egf(_�k�e�p x j�e x pg_ r�t egf(_�� r o�_RpqX�W^X(�¡_b� x dBegW r X kve x pqX k r!x e�e r9 _¡[ pg_bjRW^k�_b] : k x j�fHegf dBe�d x X W^� x _¡d�X aªW^X�e�_RpqX d�]^] : j r X ® W^j�e°� t pg_R_ik�egdB����_RpqW^X ��dBpgpqd�X(��_bh4_bX�eW^k�[ r kgkgW 9 ]`_�l 9"x e ¢ _�dBpg_ x X d ¢ dBpq_ r�t d�X : a W^kgj x kgkgW r X r�t egf W^k¡W^X�egf(_N]^W`e�_Rp�dBe x pg_�Tª¯ t�r X(_d�]^k r ¢ d�X�egk\e r WYX j r pg[ r pqdBe�_�egW^h4_�kgegdB����_RpqW^X(� tFr p�egf WYk¦_b� x dBegW r X�¨ ¢ W`egf r p ¢ W`egf r!x e�k�[�dBegW^d�]

� Ä

k�egdB����_RpqWYX(��©�l ¢ _�h x k�e�dB�!d�W^X¡k�["]^W`e�egf _voBdBpqW^d 9 ]`_bk8WYX�e r e ¢ r ��p r!x [�kKegf dBe6_�§(W^k�e r X¡W^X�e�_Rpq]^d�j�_baegW^h4_¥W^X�e�_Rpgo�d�]Yks¨F_�T±�(TH߶d�X a�à r XÉW^X�e�_R��_Rp¡egW^h4_s]^_Ro�_b]^k�d�X�a )#T%BZT6d�X a C r X�f d�] t ��W^X�e�_R��_RpegW^h4_�]^_Ro�_b]^k�©�T$Z�X�W^]^] x k�e�pqdBegW r X r�t egf W^k¦dBpgp�d�X(��_bh4_bX�e\W^k¦�!W`o�_bX,W^XN�6W`� x pg_ à T à T

Znk�dN�"X�d�]�_�§%d�hi[�]`_�lKe r k�egdB����_Rp¡egf(_ à ��� S�d�§ ¢ _b]^]�´µk�_b� x dBegW r X�k��!W`o�_bX�W^X��6W`�B�x pg_ � T � ¨Ej©�W^XHegW^h4_�l r X(_ ¢ r!x ]^azl tFr p�_�§(d�h4[�]`_�l³pq_R[ pg_bk�_bX�e�egf(_i_b]`_bj�e�p�W^j���_b]^aªj r h4[ r X(_bX�egkR 0 l$R 7 l�d�X�a"R P r X�W^X�e�_R��_Rp�egW^hi_���]`_Ro�_b]^k�d�X aHegf _ihidB�!X(_RegW^j���_b]Yaªj r h4[ r X(_bX�egkTS 0 lUS 7 ld�X a"S P r X�WYX�e�_Rpq]Yd�jRW^X(�cf d�] t ��W^X�e�_R��_Rp�egW^h4_���]`_Ro�_b]^kbT � f�W^k�W^k�[ r kqkgW 9 ]`_ ¢ f(_Regf _Rp r p�X r e r X(_k�egdB����_Rpqk�W^XNk�["d�j�_�T

u,v u,v u,v u,v

u,vu,vu,v

u,v u,v u,v

u,v

u,v

u,vu,vu,vu,v

x

t

v v

v v v

v

vvv

u u u u

u

u

u

u

u

u

u

u

u u

u

u

v

v

v

v

v

v

v

x

t

u

v

u

v

v

u

v

u

v

u

u

v

x

t

u

v

u

vv

uu

v

u

v

u

v

v

u

v

u

v

u

u

v

x

t

u

u

u

v

u

v

v

u

v v

u

v v

u

v

uu

v

u

u

v

u

v

v

u

v

v

u

v

u

v

u

NO YES

SPACE STAGGERING

NO

YE

S

TIM

E S

TA

GG

ER

ING

�6W`� x pg_ à T^yB��·�_R[�pg_bk�_bX�egdBegW`o�_�kgd�hi[�]`_bk r�t oBdBpqW r!x k�kg[�dBegW^d�]��¬egW^hi_���pqW^a�]^d :�r!x egk tFr p\egf _ r X(_��a W^hi_bX kgW r X d�] ¢ dbo�_�_b� x dBegW r X�¨ à T^y©

� Ç

u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

u,vf,g,h

x

y

g

f,h u

v

g

f,h u

v g

f,h u

v

g

f,h u

v

g

f,h u

v

g

f,h u

v

g

f,h u

vg

f,h u

v

f,h u

gv

NONSTAGGERED SPACE GRID STAGGERED SPACE GRID

y

x

�6W`� x pg_ à T � �K·\_R[ pg_bk�_bX�egdBegW`o�_¦kgd�h4["]`_$k�[�dBegWYd�]���pqWYa�]^d :�r!x egk t@r p6egf(_�e ¢ r ��a W^h4_bX kqW r X d�]�_b]^d�k�egW^j¢ dbo�_�_b� x dBegW r X�¨ à T � ©

v

v

f,h

f,h

v

v

f,h

f,h

g

g

u

u

g

g

u

u

v

v

f,h

f,h

v

v

f,h

f,h

Spatial grid

g

g

u

u

g

g

u

u

Time

�6W`� x pg_ à T à ��·�_R[ pg_bkg_bX�egdBegW`o�_�kgd�h4["]`_ r�t d�kg[�dBegW^d�]���k�egdB����_Rpq_bazl�egWYh4_���k�egdB����_Rpg_bac��pqWYa t@r pvegf(_e ¢ r ��a W^hi_bX kgW r X d�]}_b]Yd�k�egW^j ¢ dbo�_�_b� x dBegW r X�¨ à T � ©

��|

ì�ë@ì V �!��¼Æ��½Á���$/}������*

×zú^׳úEÒ ïNCXW�JK=YQ�=@ä7J�PZnX½�c��k�e�_R[,]^W^X _bdBp�h x ]^egW^k�e�_R[�h4_Regf r a tFr p\k r ]`o%W^X(�¡egf(_����� 

ò�Wòx� )�¨K�1TUWz¨K�g©�© ¨ à T à ©

W^k¦dia�W��7_Rpq_bX j�_�_b� x dBegW r X r�t egf(_ tFr pqh

\ � W (0D � 4 \ � ] �_W (0D � ] � 4 �`�`� 4 \ a W ( Az¨K� � ) (CD � 4 �`�`� 4 � a ) ( © ¨ à T±��©

¢ f(_Rpq_MAÞW^k¡egf(_�k�e�_R[ÊkqW`¾R_�l§\ ! d�X a � ! dBpg_Npg_bd�]¦["dBpqd�h4_Re�_RpqkRl§� ! � a 4 SIA7l§W ! Wz¨K� ! ©�ld�X a´) ! �)�¨K� ! TUW ! ©�T � f _¡j r _�«sjRW`_bX�egk*\ ! d�X a�� ! jRd�X 9 _���_bX _RpqdBe�_ba 9;:~x kqW^X(�cdce ¢ r ��]^W^X(_S~dBegf(_bhidBegW^jRd r p�S~dB[�]`_�d�]`� r pqW^egf h 9 d�k�_ba r X��6d�a�é_\_�§%[�d�X kgW r X k�¨Ek�_R_©2�y�y 3 r p�U;_bj�egW r X � T±��©�TZ�X r egf(_Rp ¢ d :¥r�t pg_R[ pq_bk�_bX�egWYX(�¡egf(_�d 97r o�_���_bX(_Rpqd�]zh x ]`egW^kge�_R[chi_Regf r acW^kvegf(p r!x �!fcegf(_ x k�_r�t ��_bX(_RpqdBegW^X(��[ r ] : X r h�W^d�]^k

2 ¨DY�©� \ � Y � 4 \ � ] � Y � ] � 4 �`�`� 4 \GaL ¨DY�©�g� � Y � 4 � � ] �ZY � ] � 4 �`�`� 4 � a � ¨ à T Ä ©

�ª_nj r X�kgW^a(_Rp r X�] : _�§%[�]^WYjRW`e�h4_Regf r a kRl�W^X ¢ f W^j�fijRd�k�_�� � � T � f(_n] r jRd�] e�p x X jRdBegW r Xi_Rpgp r pr�t dih x ]`egW^k�e�_R[�h4_Regf r a r�t6r pqa _Rp�:~W^k x k x d�]^] : a _��"X(_baNd�k

é�¨KW�TU��T�A ©9 2 ¨\[�©IW}¨K�g©b� A L ¨\[�©IW + ¨K�g©� > B4D � A B4D � W F B4D �IH ¨K��© 4^] ¨[A BED Û ©1T ¨ à T Ç ©

¢ f(_Rpq__[>WYk\egf(_ tFr p ¢ dBpqa�kqf W t e r [}_RpqdBe r pr/zegf WYk\pg_bk x ]`egk t p r hÈd¥kgW^h4["]`_ � d : ] r p�_�§;["d�X kgW r XzT� f(_�j r X�k�egd�X�e{> BED �\W^k��!W`o�_bX 9;:

> BED � y¨�: 4 y©��'` �a !|` a \ ! S BED � �Ũ�: 4 y©

�a ! ` a � ! S B�b � ¨ à TV|�©

� Õ

� r ¢ _Ro�_Rpl�d�kia W^kgj x kgk�_baÉW^X¶Zn[ [}_bX a W�§��vlvegf W^k4j r X kgegd�X�e¥a r _bk�X r eid�jRj x pqdBe�_b] :pg_ ® _bj�esegf(_��!] r�9 d�]�_Rpgp r pse r�9 _�_�§%[7_bj�e�_ba ¢ f(_bX x kgW^X(��d�h4_Regf r azT � f(_�[ p r [}_RpiC;O¬O�ä�O?!ä7J�PRQ¬Ð�J7Q�W^k��!W^o�_bX 9�:

> > B4D �L ¨°y© � ¨ Ã T Õ ©

¯-enW^k\egf W^k\j r _�«sjRW`_bX�e¤> egf dBe ¢ _ x k�_ ¢ f(_bX�j r h4[�dBpqW^X ��egf(_�d�jRj x pqd�j :�r�t h4_Regf r a k r�t egf(_kgd�h4_ r pqa(_RpbT

U%W^hiWY]^dBpq] : l;d�XN_�§;["]^W^jRW`e N ��k�egdB��_�· x X(��_ÝÙ�¸ x e�egd4hi_Regf r a,jRd�X 9 _�pg_R[ pg_bkg_bX�e�_ba�d�k

W (0D �9gW ( 4 îa ` � « ò ¨ Ã TÖ{!©

¢ f(_Rpq_

ò¼�§ A�)�¨K� ( TUW ( ©ò Û A�)�¨K� ( 4 . Û A#TUW ( 4 d Û �qò¼�q©ò , A�)�¨K� ( 4 . , A#TUW ( 4 d , �qò¼� 4 d , Û ò Û ©TTT

ò î A�) ` � ( 4 . î A#TUW ( 4 î ] �a ! ` � d î ! ò ! b¨ Ã T^y � ©

� f(_i¨E]^W^X _bdBpÝ©�_Rpqp r p�j r X k�egd�X�e tFr p�k x jqf,d�hi_Regf r aNjRd�X 9 _ tFr!x X a 9;: j r X kqW^a(_RpqW^X �egf(_�]^WYX(_bdBp¦[ p r�9 ]^_bh

W + g)�¨K��TUW ©� V W ¨ à T^y�y©

d�X a � d : ] r p�_�§%[�d�X a�W^X(��¨KW (CD ���c�,d ó W ( ©�d 9}r!x e�A� � e r �"X a�>4�

Acef îa ` � « ò ,gh 4 ¨°y�c� d ó ©IW ( >i¨ V A © BED � 4^] ¨�¨ V A © B4D Û © � ¨ à T^y � ©

��{

� r p�h x ]^egW^k�egdB��_ih4_Regf r a kRl8W`e�W^k�dB[ [ p r [ pqW^dBe�_¡e r X r p�hid�]^W`¾R_¡egf(_�kgegd 9 W^]^W`e : a r h�d�W^X 9�: a W��o%W^a W^X(� 9;: egf _�X x h 9 _Rp r�t k�egdB��_bk N lKd�X aªe r X r p�hid�]^W`¾R_4egf(_�_Rpgp r p�j r X kgegd�X�e 9�: d t d�j�e r pN B�l ¢ f _Rpg_¨:­W^kiegf(_ r pqa(_Rp r�t egf _�h4_Regf r azT � f W^k¡_bX k x pg_bk4egf dBe ¢ _,dBpq_�j r h4[�dBp�W^X(��d�]^]egW^h4_���kge�_R[ [�W^X(�4h4_Regf r a k r XNegf(_ 9 d�kqW^k r�t _b� x d�] ¢ r pg¤7T

U;egd 9 W^]YW`e : a r h�d�W^X kKe�_b]^] ¢ f WYjqf�o�d�] x _bk r�t A V [ p r a x j�_�k�egd 9 ]`_¦k r ] x egW r X k6W^X¡k r ]`o%W^X(�egf(_�]^WYX(_bdBp6[ p r�9 ]`_bh WY+¼ V W tFr p�d��!W`o�_bX¡egW^h4_�WYX�e�_R��pqdBe r pT�� r p$]^W^X _bdBp�h x ]^egW^k�e�_R[4h4_Regf r a kRlegf(_ 9}r!x X a�dBp :�r�t egf(_�k�egd 9 W^]^W`e : a r hid�WYX J(¨Di;©vW^k tFr!x X a 9;: k r ]^o;W^X � tFr p�JiW^X

2 J � !kj Q �´J L J � !kj Q ��� ¨ à T^y à ©

×zú^׳ú^Ó < Ð(è�=Eÿo�8ÿ �bÿ�Ð å7=EJ�Ð O¬I­þ7Q¬Ð ãK=EDE=@Q�I¶â¡ä��KJ8ç8Ð O¬Il�_b]`egkqjqf d�X a ¿ _RoBd�X ]^W^X�X d 2�y Õ03 f dbo�_�kgf r ¢ XMegf dBe�egf _�X r pqhid�]^W^¾R_baÁ¯�U%w tFr p,d]^dBpg��_�jR]^d�kqk r�t kgjqf _bh4_bkRl W^X jR] x a W^X(��h x ]^egW^k�e�_R[cd�X ac·\¸ h4_Regf r a kRl(jRd�X X r ev_�§(j�_R_ba�y�W^X¥egf(_jR]^d�kgkqW^jRd�]K¨EX r X k�egdB����_Rpg_ba"©¦jRd�k�_�T � f WYk$]^W^h�W`e�W^kvd�jqf�W`_Ro�_ba 9�: egf(_�jR]^d�kgkgW^jRd�]}]`_bdB[ t p r �¡kgj�f(_bh4_

W (CD �= W ( ] � 4 � A�)�¨K� ( TUW ( © � ¨ à T^y���©

� f WYkvhi_Regf r a,f d�k�dik�egd 9 W^]^W`e : a r hid�WYX´2R��S_TUS 3 r XNegf(_�W^h�dB�!W^X dBp : d�§%W^kbT£³_bdB[ t p r �ijRd�X�d�]^k r49 _ x k�_ba�d�k\d4egW^h4_���k�egdB����_Rpq_ba�h4_Regf r azl X�d�h4_b] :

W (0D � W ( 4 A�) # � ( 4 A � TUW (0D ý- % � ¨ Ã T^y Ä ©

¯°X�egf�W^k6j r X�e�_�§%e�egf(_¦k�egd 9 WY]^W`e : a r hid�W^X¡W^k2R� � S_T � S 3 /;egf _v_�§%e�pqd t d�j�e r p r�t e ¢ r kgW^h4[�] : pq_ ® _bj�egkegf(_ t d�j�e\egf�dBe�egf(_�egW^hi_�]`_Ro�_b]^k�dBpq__mr��TU� 4 �Û TU� 4 y�n�pqdBegf(_Rp\egf d�X"mr�½�ÅyCTU��TU� 4 y�n!T�� r pk�egdB����_Rpg_baNh x ]`egWYk�e�_R[sd�X a¥·\¸ h4_Regf r a k$egf dBe ¢ _ ¢ W^]^] j r X�kgW^a(_Rpbl�egf W^k�W^h4[�]^W^_bk�d�h�d�§%W^h x hX r pqh�d�]^W`¾R_bac¯gU%w r�t � T

ÄB�

ì�ë�� i ��/}�³�³� �!�" ¹ �/z½Á*�oqpc/z*B��+°)³���!��/}�� "�/z#!ºK»¥/}�� �*� $����� �!���8�!��/7�!��)��ª½­�(�!���)6 �*

¨ � f W^kvk�_bj�egW r X,W^kvegf(_�d x egf r pb´µk ¢ r pg¤7l ¢ W`egf¥egf(_�j r h4[�dBp�W^k r X k�e r U;e,rr p�h4_Rp¦h4_Regf%�r a k�a r X(_ 9;:c��r�9;: �np�W^kgj r ]^]�TV©

��rix egW^]^W`¾R_�egf(_�h4_Regf r a k¦W^X�U;_bj�egW r X k à T±�4� à T Ç l ¢ _�pg_b� x W`pg_ r X ] : egf dBe¦ß~d�X a *,+*1-dBpg_ x kg_ba r XiW^X�e�_Rpq]^d�j�_ba¡egW^h4_�]^_Ro�_b]^kRT6� r ¢ _Ro�_Rpbl%d�k�X r e�_ba�W^X�U;_bj�egW r X à T � l;hid�X : ¨EW t X r e�d�]^]@©k : k�e�_bhik r�t ]^W^X _bdBp ¢ dbo�_s_b� x dBegW r X k�jRd�X 9 _¡pg_ ¢ p�W`e�e�_bXªW^XHegf(_ tFr pqh ß - )�¨K�1T�à}¨K��©�©1T�à - B7¨K��T�ßK¨K�g©�©\¨ ¢ f(_Rpg_¦ßsd�X�a4à�h�d :¡9 _¦o�_bj�e r pqk�©�T�¯°X4egf W^k$jRd�k�_�l 9;: f dbo%W^X(��ß r X r X(_�egWYh4_�]`_Ro�_b]d�X aªà r X�egf _ r egf(_Rp�WYX�e�_Rpq]Yd�j�_baªegW^h4_i]`_Ro�_b]�l r X(_�WYk�_��7_bj�egW^o�_b] : d 9 ]`_4e r a r!x(9 ]`_¡egf(_�¯�U%w�T¨�U;_bj�egW r X à T à T � a(_bh r X�k�e�pqdBe�_bk�egf W^k t@r pvegf(_n]^_bdB[ t p r ��h4_Regf r azTV©��ª_�_bX�o;W^kqW r X r!x pvh4_Regf r a k9 _bW^X(� x k�_ba tFr pnk x jqf�k : k�e�_bh�k r�t ¢ do�_�_b� x dBegW r X kRT

�ª_���p�k�e³j r X kgW^a _Rp8k�egdB����_Rpg_ba�o�_RpqkgW r X k r�t egf(_vZna d�h�k-Ù�w�d�kgf tFr pgegf�d�X a 9 d�jg¤ ¢ dBp�a ka W��}_Rpg_bX�egW^dBegW r X�egW^h4_¥W^X�e�_R��p�dBe r pqkRl$a(_bX r e�_ba�Z�w�U�d�X a�w���U�pg_bk�[}_bj�egW`o�_b] : T �8r WY]^] x k�e�p�dBe�_r!x p�X r egdBegW r Xzl ¢ _,kqf r ¢ WYX¶�KW^� x pg_ à T±� tFr!x p�a W`�7_Rpg_bX�e ¢ d : k r�t pg_R[ pg_bk�_bX�egW^X(�ªegf _�egf W`pqar pqa(_RpNZ�w�U­h4_Regf r a>¨EZ�w�U à ©��¶d�pg_R[ pg_bk�_bX�egdBegW`o�_�k�e�_bX�jRW^]�l�egf(_ªk�e�_bX�jRW^]nj r _�«sjRW`_bX�egkRl�egf(_[ r ] : X r hiW^d�]^k 2 ¨DY;©Kd�X a L ¨DY�©�l�d�X�a¡egf(_¦_�§;["]^W^jRW`e � d : ] r p t@r p�h x ]Yd%T ¿nr e�_¦egf dBe$d�]^]%j r _�«sjRW`_bX�egk]^W^kge�_baNW^Xcegf W^k�[�dB[}_Rp�jRd�X 9 _ tFr!x X aco%W^d4�6d�avé_�_�§%[�d�X kqW r X k�¨Ek�_R_¶2�y�y 3 r p�U;_bj�egW r X � T à ©�T

¯-X � d 9 ]`_ à T^y ¢ _��!W`o�_ tFr p�k�egd 9 ]`_�wv��U,h4_Regf r a k�egf _�kgf dB[}_�d�X a,j r _�«sjRW`_bX�egk r�tegf(_�k�e�_bX jRWY]�l�egf _�_Rpqp r p¦j r X k�egd�X�eRl d�["W^j�e x pg_ r�t egf(_�k�egd 9 WY]^W`e : a r hid�W^Xzl%d�X a¥egf(_�¯gU%w�T}¨ ¿nr e�_egf dBe 9;: k�egd 9 ]`_�l ¢ _�hi_bd�Xs¾R_Rp r ��k�egd 9 ]`_�l(W�T±_�T�egf dBe¦d�]^]"p r;r egk r�t 2 ¨DY�©�dBpg_�] r jRdBe�_ba ¢ W`egf WYXiegf(_x X W^e�a�W^k�¤7l ¢ W`egfHp r�r egk r X�egf(_ x X W`e�jRW`pqjR]^_ 9 _bWYX(�NkgW^h4[�]^_�TV© � d 9 ]`_bk à T � d�X a à T à �!W^o�_�egf(_kgd�h4_�W^X tFr pqhidBegW r X tFr p x k�_ tEx ]}Z�w¦U�d�X aNZ�wMh4_Regf r a k x [Ne rir p�a(_Rp Õ T

Ä y

|I}Rymws tttuvvvvvvvvvvvvwx y7z0{0y}|~ x ~ x { x yx {0y}|

� ����������������������3��� � ~ � -��� ������� ý- / � y7z � - ~ y �$� x � � ý*� -�X�����������)�����+�X� â- /�� y0z � Ý ���X� â - � ~ y � Ý �k� ~ â - � �_� Ý �k� ~ � â- ��� ������� / �

�6W`� x pg_ à T±�(��� r!x pcpg_R[ pg_bk�_bX�egdBegW r X k r�t Znw�U à ��kge�_bX jRW^]�kgf dB[}_�l\j r _�«sjRW`_bX�egkRl\��_bX(_Rp�dBegW^X(�[ r ] : X r hiW^d�]^k 2 ¨DY�©4d�X a L ¨DY�©�l�d�X a¶_�§%[�]^W^jRW^e � d : ] r p t@r pqh x ]^d%TÅ�\_Rpg_�l pg_R[�pg_bk�_bX�egk�d�Xx X(¤%X r ¢ X tFx X�j�egW r Xco�d�] x _�l ¢ f W^]^_ �

tk�egd�X a k tFr p�d4¤%X r ¢ X tFx X�j�egW r X���a(_RpqW^o�dBegW`o�_�oBd�] x _�T

��

� d 9 ]`_ à T^yB��U;egdB����_Rpg_ba 9 d�jg¤ ¢ dBpqa k¥a W��}_Rpg_bX�egWYdBegW r X¶egW^h4_�W^X�e�_R��p�dBe r pqkRT � f(_�X r p�hid�]^W`¾R_ba] r jRd�]$e�p x X jRdBegW r X�_Rpgp r p t@r p¡w���U<:¶WYk©>¤A B4D � ) F BED �IH ¨�� ©�l ¢ f(_Rpg_M>'WYk�egf(_s_Rpgp r p¡j r X k�egd�X�eRT��X ] : k�egd 9 ]^_�h4_Regf r a k¦dBpg_�kgf r ¢ XzT

¿ d�h4_ U;e�_bX�jRW^] uvr _�«sjRW`_bX�egk  $pgp r p U%egd 9 W^]^W`e : ¯gU%wuvr X k�egd�X�e � r hid�W^X

wv��U �� ÞÚàeÝZ���% \¡0¢ �t � . .; . � �

Û *-0.1 0.1

-2

-1

1

2

wv��U Ã

t ëììììí x - /- �~ - ý- �~ �- �ý- �ðLññññò �

Û * -0.2 0.2

-2

-1

1

2 ),T£ y �ÖÇ�Ç |

wv��U;�

t ëììììììí� ý -ýrý] ý N-�-] P-�-1-�-] ý-�-

ðLññññññò Ú �� � Û a -0.03 0.03

-1

1

y

Ä�Ã

� d 9 ]`_ à T � �vU%egdB����_Rpg_bacZna d�h�k°��w�d�kgf tFr pgegfiegW^hi_nW^X�e�_R��pqdBe r pqkRT � f(_nX r p�hid�]^W`¾R_bai] r jRd�]"e�p x X%�jRdBegW r Xc_Rpgp r p tFr p¦Znw�U4:�W^k>¤A B4D � ) F BED �IH ¨�� ©�l ¢ f(_Rpg_¤>�W^kvegf(_�_Rpgp r p¦j r X k�egd�X�eRT���X�] : h4_Regf%�r a k ¢ W`egfNX r X(¾R_Rp r ¯gU%w�k�dBpg_�kgf r ¢ X�¨ tFr p r pqa _Rpqk�: ® y � ©�T¤ Ý�ÙFà ¥�Û2à�¦�§WØÚÞ ¨©¡�à�ª�§WØÚà�¦�Û2â «¬ + \¡7  ¥CÛAÝZ­áØÚÞÚØÕÛ�® ¯D¥�°¥,±áÝ7�pà ¨©¡0¦|â�ÛAÝ7¦�Û ²q¡�Ù�Ý�Ø�¦³ °´¥ y� ÞÚàeÝ7�,�� \¡7¢ �

t µ . .; . ¶ ý- / -0.1 0.1

-2

-1

1

2 y³ °´¥�·

ttt uvvw � Û ) ¶ Û *] � ] �M¶1� Û�M¶ Û * � ��� ý- / -0.15 0.15

-1.5

1.5 ý -NP¸ x0¹ º�x |³ °´¥ |

tttt uvvvvvw � � , ¶1� Û] � ]&) ¶ Û *�M¶ �] �M¶ Û *� ������ -�- �1 N .�� -0.15 0.15

-1

1 /� ¸ x0¹ ·7·0·³ °´¥ º

tttttttuvvvvvvvvvwý ýrý 1�-�1 ýrý*� P�. N .�0��ÿ¢ý ÿ N P�.�P �%ý � N 1�-ýQ� / 0�0 ý*�'ý � N 1�-��ÿ -�P / .21�P � - / ý P2-��N .�P2- ý*�'ý � N 1�-��ÿ¢ý -�.2-�P � 1 � N .��� - ýrý P � P�. N .�0��

� ���������� ýrýrýrý� 1�0 / �-6.·10-6 6.·10-6

-0.3

0.3 � �2- / �0 ý / .�P ¸)» ¹ · º�x

³ °´¥�¼tttttttt

uvvvvvvvvvvvwý -�P21�.2- N � - / ý P2-��ÿ¢ý ÿ¢ý � � �2- ý*�'ý � N 1�-��ý �2- / � N � 1 � N .��ÿ -�-�-�021 �³ý*� P�. N .�0��- / ý P N �'ýQ� /�/ �ÿ P21�-�1 ý*�'ý � N 1�-��ý - ý � / P � / 0 � 0 / �ÿ�ýrýrýrý*�2� 1�0 / �

� ������������ ýQ� 1�-�0 � � ý/ . /�/ 0�. / ���-2.·10-8 2.·10-8

-0.2

0.2 / � -��-��2-���P ¸)» ¹ y x |

Ä �

� d 9 ]`_ à T à � ¿nr X k�egdB����_Rpq_ba�Z�a d�hik°��w�d�kgf t@r pgegf�egW^h4_iW^X�e�_R��pqdBe r pqkbT � f(_iX r p�hid�]^W`¾R_baª] r jRd�]e�p x X�jRdBegW r Xª_Rpgp r p t@r p�ZnwG:�WYk«>¤A BED � ) F BED �IH ¨�� ©�l ¢ f _Rpg_O>ÂWYk�egf(_i_Rpgp r p�j r X k�egd�X�eRT���egf(_Rpegf d�X�Z�w � l r X ] : h4_Regf r a k ¢ W`egfNX r X(¾R_Rp r ¯�U%w�k¦dBpg_�kgf r ¢ X�¨ t@r p r pqa(_Rpqk�: ® y � ©�T¤ Ý�ÙFà ¥CÛ2à�¦�§WØÚÞ ¨©¡�ཪ�§WØÚà�¦�Û2â «� + \¡Z  ¥CÛAÝZ­áØÚÞÚØÕÛ�® ¯+¥,°¥�±fÝZ�pà ¨©¡7¦áâ�ÛAÝZ¦CÛ ²q¡�Ù�Ý�Ø�¦³ ° y tt uvvw x~ x · {7y~ x {7y

� ��� 1ý --1 -0.5

-0.75

0.75 »³ °´· ttt uvvvvw �] � Û , ¶1� Û]+* ¶ ,) ¶1� Û

� ����� �0 -0.5-0.25 0.1

-0.8

-0.4

0.4

0.8 ý -1+¾ ýrý ¸)» ¹ º y}|³ ° |

tttt uvvvvvvvw �] � )e) ¶ Û *]&)e� ¶ Û *, Ú ¶ Û *]&, ¶ �� �������� -�1 ýN -�� -0.3 -0.15

-0.4

-0.2

0.2

0.4 1�-ý 1+¾ .21 ¸)» ¹ | · »

³ ° ºttttttt

uvvvvvvvvvvwýÿ¢ý ý P�0 N - ý*� .�� / 0��ÿ¢ý 0�. � N � -�1�-��- � 1 ý 0 �\� -�� ý .��ÿ¢ý � N 1 / � P / 1ýQ� 1 N ýQ�\� -�� ý .��ÿ 1�.�� �\� -�1�-��ý P���0 N � .�� / 0��

� ����������� 1�-�1 Ný N -�0�� -0.05-0.025

-0.06

-0.03

0.03

0.06 ¸)» ¹ » z ¼

³ °´¼tttttttt

uvvvvvvvvvvvvwýÿ�ý ý .���0 �\� /�/ 0��ÿ�ýrý 1�- ý .�P �%ý -���P�.��- / -�.21 �\�%ýQ� /�/ �ÿ -�P�.��21 �\�%ýQ� /�/ �- ý �2-�- / �\�%ý -���P�.��ÿ�ýrý 1 N / N �%ýQ� /�/ �� -�0�. �\�%ýQ� /�/ �ÿ 1�-�1 N �%ý N -�0��

� ������������� ý � N ��� ý N� .2-�0�0���� -0.025

-0.03

-0.015

0.015

0.03 ¸)» ¹ » yZ¿

Ä�Ä

� f(_�Z�w¦U�d�X a�w���Uch4_Regf r a k r�tKr pqa(_Rp � dBpg_ 9}r egfc_b� x W`oBd�]`_bX�e¦e r egf(_�]`_bdB[ t p r �h4_Regf r azT�Z�w¦U�d�X a¥w���Ush4_Regf r a k�dBpg_ 97r egfs_�§%[�]^W^jRW`e�¨ ¢ f(_Rpg_bd�kvX r X k�egdB����_Rpq_ba¥w���h4_Regf%�r a k�dBpg_�W^h4[�]YW^jRW`e�©�T8Z�wÁd�X acZnw�U¥h4_Regf r a k¦dBpq_�d�] ¢ d : k¦k�egd 9 ]`_0/ w���U¥hi_Regf r a�k¦dBpg_�k�egd 9 ]`_tFr p r pqa(_Rp�k x [�egf(p r!x �!fª��¨ ¢ f W^]`_4X r X kgegdB����_Rpg_ba�w��'hi_Regf r a�k�dBpg_skgegd 9 ]`_ tFr p r pqa(_Rp�k x [egf(p r!x �!f Ç ©�T ¿nr e�_�egf dBev_bW`egf(_Rp 2 ¨DY�© r p L ¨DY�©�f d�k�dÀY �M¶ Û t d�j�e r p 9 _bjRd x kg_ r�t egf _�k�egdB����_Rp�W^X(�k�_Re x [�T

U;egd 9 W^]YW`e : a r h�d�W^X k t@r p�kgegdB����_Rpg_ba h4_Regf r a kcdBpg_�k : hihi_Re�pqW^j ¢ W`egf­pg_bk�[}_bj�ece r9}r egf,j r;r pqa W^X�dBe�_�d�§%_bk`/ r X(_�jRd�X~k�_R_�egf W^k 9�: X r egWYX(��egf dBenegf(_Rpg_¡W^k\k : hihi_Re�p : d�j�p r kgk�egf(_� ��d�§(W^kH¨Fe�p x _ r�t d�]^]\k�egd 9 W^]^W`e : a r hid�W^X k 9 _bjRd x k�_�J ¨Di�© J ¨��Ái�©�©4d�k ¢ _b]^]nd�ksk : hih4_Re�p :d 9}r!x evegf(_ r p�W`�!W^XH¨ ¢ f W^j�fsj r h4_bk t p r h egf(_�k�e�p x j�e x pg_ r�t k�egdB����_Rpg_ba�h4_Regf r a kb�bJ�W^kvd�X r a atEx X j�egW r X r�tÁ Ã� !kj ©�T�wv_bjRd x kg_ r�t egf(_bkg_ck : hihi_Re�pqW`_bk¡d�X a 9 _bjRd x k�_Nk�egd 9 W^]YW`e : a r hid�W^X kh x k�e¦dB[ [ p r d�j�fMJ* � o�_RpgegW^jRd�]Y] : ¨EX(_bdBp�egf _ r p�W`�!W^Xzl�J ¨Di�©ÅÄ SÆi;©�l%kgegdB����_Rpg_ba,h4_Regf r a k¦f�dbo�_X r pg_bd�]¦d�§(W^k4j r o�_Rp�dB��_�T � f x kRl�egf(_bkg_�h4_Regf r a k4dBpg_ r X ] : dB[ [ p r [ p�W^dBe�_ t@r p4[ p r [�dB�!dBegW r X[ p r�9 ]`_bhikRTs¨E� r ¢ _Ro�_RpblKegf(p r!x �!fH_�§%[ r X(_bX�egW^d�]6egW^h4_���k�e�_R[�[�W^X(�o2 � | 3 l³egf(_ikqjqf(_bh4_bk�jRd�X�d�]^k r9 _�dB[�[�]^W`_base r [ p r�9 ]`_bh�k�k x jqfNd�k¦dBe�e�_bX x dBegW r X�W^X¥S~d�§ ¢ _b]^]�´µk�_b� x dBegW r X k tFr p�] r kgk : h4_ba W^d%TV©

� f(_¡_�§(d�j�e�¯gU%w�k�W^X � d 9 ]`_bk à T^yBl à T � lKd�X a à T à ¢ _Rpg_ tFr!x X a 9;: k r ]`o%W^X(� tFr pTiNW^Xegf(_�_b� x dBegW r X

·�_bd�]ÈÇ 2 S � !kj UL ¨+� !kj ©�É ��� ¨ à T^y Ç ©

� r p�kgegdB����_Rpg_ba�hi_Regf r a�kRlzegf(_4¯gU%w r jRj x pqk�dBeÊi � Û 9 _bjRd x k�_ r�t k�egd 9 WY]^W`e : a r hid�W^Xªk : h¡�h4_Re�pqW^_bkRT�� r p�Znw à l8egf(_¡¯�U%w r jRj x pqk�dBeÊi dBpqjRj r k S �� a U T�� r p�Znwv�(l�egf _4¯�U%w r jRj x pqk�dBeio'dBpqjRj r k S � * � U T � f(_s¯gU%w jRd�X 9 _ t@r!x X�a t p r h egf(_bk�_¥o�d�] x _bk 9;: k x(9 k�egW`e x egW^X �Ëi�WYX�e rÌ ¨ þ ø�Í ©Î ¨ þ ø�Í © T

Znk ¢ W^]^] 9 _�a WYkgj x kgk�_ba�W^Xik�_bj�egW r X à T Ç T^yBl ZnwÊh4_Regf r a k�f do�_�d�X r X%��¾R_Rp r ¯�U%w r X�] :tFr p$h4_Regf r a k r�t7r pqa(_Rp à l��(l4|�l Õ lsy�yBl7y � l�_RegjBT /%Znw�U¡hi_Regf r a�k�d�a a W`egW r X�d�]^] : W^X�jR] x a(_ r pqa(_Rp� T ¿nr e�_�egf dBenegf _�_Rpgp r p�j r X kgegd�X�egk tFr pnegf(_¡k�egdB����_Rpg_baHh4_Regf r a k�dBpg_�dB[ [ p r §%W^h�dBe�_b] : X W^X(_e r e�_bX�egW^h4_bk�kgh�d�]^]`_Rp�egf d�X4egf r k�_ r�t egf(_\X r X�k�egdB����_Rpg_ba�hi_Regf r a�k r�t _b� x W^o�d�]`_bX�e r pqa(_Rp�kRT8¯°X

Ä�Ç

d�a a W^egW r Xzl�kgegdB����_RpqW^X(�¡W^X j�pg_bd�kg_bk�egf _n¯gU%w 9;: d t d�j�e r p r�t � T±�B�-|�T±�(l ¢ W`egfsegf(_ t d�j�e r p¦��p r ¢ W^X(�d�k r p�a(_Rp�W^X j�pg_bd�kg_bkRT

�ª_NjRd�X�d�]Yk r j r hi[�dBpg_cegf(_ck�egdB����_Rpg_baÞh4_Regf r a k�e r U;e,rr pqh4_Rp4h4_Regf r a kM2�y Ã<3 W^Xegf r k�_NjRd�k�_bk tFr p ¢ f W^j�f�egf _¥[�p r�9 ]`_bh jRd�X 9 _¥pg_ tFr pqh x ]^dBe�_baÉd�k¡d~kg_bj r X a r pqa(_Rp4k : k�e�_bhNlß -|- ÐÏ�¨K��T�ß}©�l�à -|- ÒÑ�¨K�1T�à(©�T¶�­W^egf¶j r h4[�dBegW 9 ]^_ca _��"X W`egW r X�k ¢ _c�"X a�¯gU%w�k r�t dBp r!x X a� l\y � | à l�y � � yBl�y � y�yBl ���ÖÕ �(l ���ÖÇ�� l�d�X�a ��� � Ç tFr p r pqa(_Rpqk � Ù Õ T � f(_¥d�kqk r jRWYdBe�_baÉ_Rpgp r p4j r X%�k�egd�X�egk�dBpq_�dB[ [ p r §%WYhidBe�_b] : ���µ�!Õ�à l ���µ�!Õ�à l ���µ� |B{;l ���µ� | Ä l ���µ� |;yBl ���µ�!Ç�Õ l�d�X a ���µ�!Ç�Ç T � f x kegf(_�Z�w�U¥h4_Regf r a k¦j r h4[�dBpg_ t dbo r p�d 9 ] :¥t@r p r p�a(_Rpqk r�t d�jRj x pqd�j :ct@r!x p�d�X�aN]`_bkgkRl(d�X a x X t d��o r pqd 9 ] : egf(_Rpg_bd t e�_RpbT$� r ¢ _Ro�_Rpbl t@r pqh x ]^dBegWYX(� ¢ dbo�_�_b� x dBegW r X k x kgWYX(��e ¢ r egWYh4_�a(_RpqW`oBdBegW`o�_bkk r h4_RegWYh4_bk�j�pg_bdBe�_bk�a W�«sj x ]`egW`_bk�W^XNW^h4["]`_bh4_bX�egW^X(� 97r!x X a dBp : j r X a W`egW r X�kRT

��r W^h4["]`_bh4_bX�e r X(_ r�t egf(_vegW^h4_���k�egdB����_Rpq_ba4h4_Regf r a kRl r X(_�X(_R_ba kKe r�r�9 egd�W^X�k�egdBpge°�W^X(��oBd�] x _bk tFr p�k�_Ro�_Rpqd�]zegW^hi_�]^_Ro�_b]^k¦d t e�_Rp\egf(_�W^X W`egW^d�]7j r X a W^egW r XzT�� r p\X r X�k�egdB����_Rpg_ba�h x ]`egW��k�e�_R[ªh4_Regf r a kRl"egf W^k�W^k x k x d�]^] : d�jRj r h4["]^W^kgf(_ba ¢ W`egf�ds· x X(��_ÝÙ�¸ x e�egd¥h4_Regf r azT�� r p�k�egdB�B���_Rpg_bacegW^hi_�W^X�e�_R��pqdBe r pqkbl r X(_�kgf r!x ]^a r�9 egd�W^Xcd�k�hid�X : ¨Ef d�] t ��W^X�e�_R��_RpÝ©�]`_Ro�_b]^k r�t ß,d�X a¥àid�kX(_R_ba(_ba x kgW^X ��d�X r X k�egdB����_Rpg_ba¥· x X(��_ÝÙ�¸ x e�egd�h4_Regf r aid�X a4egf(_bXsk�_b]`_bj�e r!x e$egf r k�_nX(_R_ba(_bae r W^X�e�_Rpq]^d�j�_�ßHd�X aNà¥dB[ [ p r [�pqW^dBe�_b] : T

ì�ë=± i ��/}�³�³� �!�" >+-��� � ,�/}�!/z½Å� �B���H½Ê5$¼��!�Æ*���¼, ½­�(�!��)� $*

¨ � f W^k�k�_bj�egW r X,W^k�egf(_�d x egf r pb´µk ¢ r pg¤7TV©�ª_¥f�dbo�_Na(_Ro�_b] r [}_ba�h x ]^egW^k�e�_R[�hi_Regf r a�k�egf dBe¡d�]^] r ¢ t pg_R_s[�dBpqd�h4_Re�_Rpqk¡a x _�e r

k x(9}r [ egWYhiW`¾bdBegW r X r�t�r pqa _RpbT � f(_bk�_ t pg_R_�[�dBpqd�h4_Re�_Rpqk�hid :N9 _ x k�_ba�e r a(_bj�pg_bd�kg_�egf(_�_Rpgp r pj r X k�egd�X�eRl�W^X j�pg_bd�kg_~egf _ª¯�U%w�l r p r�t e�_bX 9}r egfzT ¯°XÁegf W^kck�_bj�egW r Xzl ¢ _�a W^kgj x kqksk�egdB����_Rpq_bat pg_R_ª[�dBpqd�h4_Re�_Rp~kgjqf _bh4_bk�d�X a r �}_Rp�e ¢ r _�§%d�h4["]`_bk r�t k x jqf hi_Regf r a�k�d�k�W^]^] x k�e�pqdBegW r X�kr�t�r [ [ r pge x X W`egW^_bksdo�d�W^]Yd 9 ]`_�W^X­egf W^kNdBpq_bd%T'Z\[ [}_bX a�W�§­�Ôa W^kqj x kgk�_bkNX r X�k�egdB����_Rpg_ba t pg_R_[�dBpqd�hi_Re�_Rpnkgj�f(_bh4_bkRT

Ä |

×zú�ÓzúEÒ ø ä#��O¬Q¬AÅä�O�ç8C;Ocü�O�C�C�Ñ8Ð O�Ð�ÿ�C�Q¬C�O�ÿ�C�Q¬A�äzçÕÔ,ÚÛ�Ö PRQC;Ñ�ý6ä7J�C~ÑKÐ O¬Ð"ÿ�C�QC;O

�ª_�j r X kgWYa(_Rp�h4_Regf r a k ¢ W^egfNk�e�_bX jRW^]^k r�t egf(_ tFr ]^] r ¢ W^X(� tFr pqhN�ttttëìììììí x × �Ø - × -Ø ý × ý× �

ðLñññññò�Áf W^]`_�W^e�W^k�[ r kqkgW 9 ]`_4e r �"X a�d�� t egf r pqa(_Rp¡h4_Regf r a r�t egf WYk tFr pqhNl�W`e�WYk�X r e¡k�egd 9 ]`_H¨Ek�_R_U;_bj�egW r X à T Ç T � ©�T �ª_�W^X k�e�_bd�a kg_bdBpqjqf t@r p tFr!x pgegf r pqa(_Rp,h4_Regf r a k,j r X�egd�W^X�W^X(� r X(_ t pg_R_[�dBpqd�hi_Re�_RpbT � f�W^k��!W`o�_bk\d�]^W^X(_bdBp�k : k�e�_bh r�t _b� x dBegW r X k ¢ f W^j�fNf d�k¦egf(_ t@r ]^] r ¢ W^X �¡k r ] x egW r X

¢ W`egfc["dBpqd�h4_Re�_Rp�� � T ëìììììí x × ý � ýrýý -y}| × ý ~ z y7y × ý ~ �³ý0~ y}| × ý � | × ý~ ý- /ðLñññññò ¨ à T^y|�©

� f WYkvhi_Regf r a,W^k�k�egd 9 ]^_ t@r p��@�'Ù S �� T )Û * ¡ T��ª_�X r e�_�egf dBe tFr p����§ �� l ¢ _�pq_bj r o�_Rp�Znw�U;�(T� f W^k�hi_Regf r a³´µk�_Rpgp r pvj r X k�egd�X�evWYk§> � Ú ] � , ��Ú ý) ÚW� a F � Ú ý ] �IH T�Znk9� � % �� l;egf(_\¯gU%w r�t egf(_

h4_Regf r a�dB[�[ p r d�jqf _bk�ÄÈy � |;y�� 9�x e�egf(_�_Rpgp r p�j r X k�egd�X�e 9 _bj r hi_bk x X 9}r!x X a(_bazT��ª_segf x kr�9 k�_Rpqo�_vdne�pqd�a(_�� r � 9 _Re ¢ _R_bX¡d�jRj x pqd�j : d�X a�k�egd 9 W^]^W^e :�t@r pKegf W^k8h4_Regf r azT � f W^k8W^k�W^]Y] x k�e�pqdBe�_baW^X��KW^� x pg_ à T Ä T^yBT�¯ t�r X(_¡W^k ¢ W^]^]^WYX(�4e r kqd�j�pqW��"j�_¡k r h4_¡d�jRj x pqd�j : e r �!d�W^XHW^X�k�egd 9 W^]YW`e : l7egf W^kh4_Regf r a ¢ r!x ]^ac[ p r o%W^a(_�egf(_�h4_bd�X�k¦e r a r k r T

Znk�d�X�_�§(d�h4[�]^_�l ¢ _��!W`o�_�egf(_�k�egd 9 W^]^W^e : a r hid�W^X r�t egf(_�hi_Regf r a,egf dBe�f d�k�������� y ��Ç W^X,�6W`� x pg_ à T Ä T^yBT � f W^k�hi_Regf r a�f d�k�d�X,¯gU%w r�t Ä y � | �!Õ d�X a�d�X�_Rpgp r p�j r X k�egd�X�e r�tÄ �Y� � Õ T

Ä�Õ

0.5 1 1.5 2ISB

0.25

0.5

0.75

1

Error Constant

�6W`� x pg_ à T Ä � � pqd�a(_�� r � 9 _Re ¢ _R_bX>d�jRj x pqd�j : ¨F_Rpqp r p~j r X�k�egd�X�e�©�d�X a k�egd 9 WY]^W`e : ¨F¯gU%w�© tFr ph4_Regf r a�¨ à T^y|�©

-0.2 -0.15 -0.1 -0.05 0.05 0.1 0.15 0.2

-2

-1.5

-1

-0.5

0.5

1

1.5

2

�6W`� x pg_ à T Ç ��U;egd 9 W^]^W`e : a r hid�WYX r�t hi_Regf r a�¨ à T^y|�© tFr p����§ ��� y ��Ç

Ä {

×zú�Ózú^Ó ø ä#��O¬Q¬AÅä�O�ç8C;Ocü�O�C�C�Ñ8Ð O�Ð�ÿ�C�Q¬C�O�ÿ�C�Q¬A�äzçÕÔ�� Ö PRQC;Ñ�ýKQ0Û¡ä�ÑKÐ O¬Ð"ÿ�C�QC;O

�ª_�j r X kgWYa(_Rp�h4_Regf r a k ¢ W^egfNk�e�_bX jRW^]^k r�t egf(_ tFr ]^] r ¢ W^X(� tFr pqhN�ttt ëììììììí x × �Ø � × -Ø - × ýØ ýØ �ðLññññññò

�ª_ªk�_bdBpqj�f t@r p tFr!x pgegf r pqa(_RpNh4_Regf r a k¥j r X�egd�W^X�W^X(��e ¢ r�t pg_R_~[�dBpqd�h4_Re�_Rp�kRT � f(_~]^W^X(_bdBpk : k�e�_bh r�t _b� x dBegW r X k¦e ri9 _�k r ]^o�_bac�!W`o�_bk�egf(_ tFr ]^] r ¢ W^X(�4k r ] x egW r X ¢ W`egfc[�dBp�d�h4_Re�_Rpqk N d�X a�ÝT ëìììììììí

x ý -ýrý � ý-�-�Ü~ ý N-�- � 1 N�N1�-�0,Ü ~ ý- / � Üÿ P-�- ~ -�� ýý N .,Ü � P 0 � �1-�- � Pý N .,Ü ~ P0 �ý-�- ~ ý1�-�0,Ü � ý- / �ðLñññññññò ¨ à T^y Õ ©

¿nr e�_vegf�dBe tFr p N � d�X a*�� � l ¢ _�pq_bj r o�_Rp�w���U;�(T � f(_$k�_Re r�t ¨ N TU��©���oBd�] x _bk tFr p ¢ f W^jqf�egf W^kkgj�f(_bh4_�WYk�k�egd 9 ]^_$W^k³p r!x �!f ] : d�e�pqWYd�X(�!]`_$W^X�egf(_�¨ N TU��©���["]^d�X(_ ¢ W^egf�o�_RpgegW^j�_bkKdBe8dB[�[ p r §(W^hidBe�_b] :¨���y � { Õ Tby �µ��� y Ç ©�l$¨�� ���Öà T`� ���ÖÕ ©�l}d�X�a�¨°y �ÖÄ Tby � y Ç ©�T

� f(_�_Rpgp r pnj r X k�egd�X�e r�t egf W^k¦kgj�f(_bh4_�WYk

> ¨°y| � �*�Êy � | N �Êyb{ Õ �g©yb{ �B� ¨ � � 4 ��à N 4 ��� �g© � ¨ à T^yb{!©

w : jqf r�r kgWYX(��oBdBpqW r!x k$o�d�] x _bk r�t egf(_\[�dBp�d�h4_Re�_Rpqk t@r p ¢ f WYjqfsegf(_nh4_Regf r a¥W^k$kgegd 9 ]`_�l ¢ _�jRd�Xjqf�d�X(��_iegf(_4_Rpgp r p�j r X k�egd�X�e�d�X aHegf(_�¯�U%w r�t egf(_ih4_Regf r azT4Znk�egf(_4¯�U(w dB[�[ p r d�jqf _bk�egf(_egf(_ r pg_RegWYjRd�]³]^W^hiW^e r�t � ¨ N d�X a �vdB[ [ p r d�j�fNegf(_ x [ [}_Rp¦]`_ t e°��f d�X acj r pqX(_Rp r�t egf(_�e�pqW^d�X �!]`_ r�tk�egd 9 WY]^W`e : ©�l!egf(_n_Rpgp r pvj r X k�egd�X�e 9 _bj r h4_bk x X 9}r!x X�a(_bazT³�ª_�egf x k$dB�!d�W^X r�9 k�_Rpgo�_�d�e�pqd�a(_�� r �9 _Re ¢ _R_bX,d�jRj x p�d�j : d�X�a�k�egd 9 W^]YW`e : T

�ª_��!W`o�_�egf pg_R_�_�§(d�h4[�]`_bk r�t W^X�e�_Rpg_bk�eR�

ÇB�è N ��yBlY��>y �µ� � Ä T�¯�U%wÝÄ>y �ÖÕ�Õ���� l _Rpgp r p�j r X�k�egd�X�e�>ÞÄ ���µ�!Ã�Ä���Ç T��Áf W^]^_\egf(_�_Rp��p r p�j r X k�egd�X�e�W^k8j r hi[�dBpqd 9 ]`_ve r egf dBe r�t Z�w�U;�(l�egf(_Rpg_¦W^k6d�a(pqd�hidBegW^jvW^h4[�p r o�_bh4_bX�eW^Xcegf(_�¯gU%w�T(�ª_�kgf r ¢ egf(_�kgegd 9 W^]^W`e : a r h�d�W^X r�t egf W^k¦h4_Regf r a�W^XN�6W`� x pg_ à TV|%¨Ed�©�Tè N ��� |¬�(l���>y � y � yBT$¯gU%wßÄ>y �ÖÃ�à |�l�>ÞÄ ���µ� y�y � T � f W^k�h4_Regf r asW^h4[ p r o�_bk r Xsegf(_d�jRj x pqd�j :Nr�t Znw�U;� 9�: d 9}r!x e�d t d�j�e r p r�t à ¢ f W^]^_�h�d�W^X�egd�WYX W^X(�4d 9}r!x e�egf(_�kgd�h4_¯�U%w�Tè N ��y � { Ä l��OËy �µ��� y Ä�Ä l�¯�U%wàÄôy � {�{ Ä lm>áÄ Ã��Y�Öà �(T � f W^k4h4_Regf r aÊf�d�k�d�X¯�U%w­o�_Rp : jR] r kg_�e r � l egf(_�egf(_ r pg_RegW^jRd�]³]YW^hiW`eRT$U;_R_��6W`� x pg_ à TV|%¨ 9 © tFr p�egf(_�kgegd 9 W^]^W`e :a r hid�W^X r�t egf W^k¦hi_Regf r a³T

¿\r e�_cegf dBe¡egf(_bkg_ t pg_R_c[�dBpqd�hi_Re�_Rpih4_Regf r a k�pg_b� x W`pg_sX r h r pq_ tEx X j�egW r X�_RoBd�] x �dBegW r X k�egf d�X�Z�w�U;��/�d�]^]�h x ]`egWYk�e�_R[�h4_Regf r a k�pq_b� x W^pg_ r X ] :Hr X(_ tEx X j�egW r Xª_Ro�d�] x dBegW r X�[}_RpegW^h4_�k�e�_R[³T�Znk ¢ _�f do�_4X r en_�§%[�] r pq_ba,egf(_�[ p r [}_RpgegW`_bk r�t egf(_bk�_ t pg_R_�["dBpqd�h4_Re�_Rp�kgjqf _bh4_bkW^XNd�X : ��pg_bdBe\a(_Regd�W^]�l ¢ _�_�§(jR] x a _�egf(_bh t p r h tEx pgegf(_Rp�d�X d�] : kgWYkRT

-0.0002 0.0002

-2

-1.5

-1

-0.5

0.5

1

1.5

2

-0.0004 0.0004

-2

-1.5

-1

-0.5

0.5

1

1.5

2

�6W`� x pg_ à TV|��4U;egd 9 W^]^W^e : a r h�d�W^X k r�t egf(_ t@r!x pgegf r pqa(_Rp�kgegdB����_Rpg_ba t pg_R_4[�dBpqd�hi_Re�_Rp�kgj�f(_bh4_¨ à T^y Õ ©���¨Ed�©v¯�U(wâÄ y �ÖÕ�Õ���� l�>ÞÄ ���µ�!Ã�Ä�à ¨ 9 ©�¯�U%wBÄ y � {�{ Ä l@>BÄ Ã��Y�Öà �

ì�ë=ç ! �$� )³�!�(�!�Æ#%/}¼ Î )���*��Æ �� ��/"�!��)��$*

¨E��p r;r�t$r�t egf(_���pqkge�pq_bk x ]`e ¢ d�k�a r X(_ 9;: wv_bX(��e�� r p�X 9 _Rpg��d�X a 9;: egf _id x egf r pbl

¢ f WY]`_n[�p r�r�tKr�t egf(_�k�_bj r X a�pg_bk x ]`e ¢ d�k�a r X _ 9�: egf(_�d x egf r pbTV©

Ç y

×zú^û³úEÒ �bÿ�Ð�å"=EJ�Ð�OI­þ}QÐ ã6=FDE=@QÝIÞâ�ä#�8J8çKÐ OIÞä"ü æ çKÐ�ÿ�P�ã}â¡Ð PA8ü�ä"OQ¬A­ÿ�C�Q¬A8äzçKP

Zna�d�hik-Ù�w�d�kgf tFr pgegf�h4_Regf r a kzf�dbo�_�X r X%��¾R_Rp r ¯gU%w�k r X ] :nt@r p r pqa(_Rpqk à T���T�|�T Õ T�y�yCTby � l_RegjBT�U;egdB����_Rpg_ba�Znw h4_Regf r a k�d�a a W`egW r X�d�]^] : W^X�jR] x a(_ r pqa(_Rp � ¨E]`_bdB[ t p r ��©�T ¿nr X k�egdB����_Rpq_baZ�a d�hik°��S r!x ]`e r X4h4_Regf r a k¦¨EW^hi[�]^W^jRW`e8o�_RpqkgW r X�k r�t Zna�d�hik°��w�d�kgf tFr pgegf4h4_Regf r a k�©8f do�_�X r X%�¾R_Rp r ¯gU%w�k r X ] :,t@r p r p�a(_Rpqk yCT � T Ä T Ç T�{YTby � lK_RegjBTi��p r�r�t k r�t egf _bk�_4pg_bk x ]^egk�dBpq_4�!W`o�_bX�W^XZn[ [}_bX a W�§s��T

×zú^û³ú^Ó þ7Q¬Ð å�å"C�O�C�ç­Ð�J8Ð�DFä�å#��C~ä�ünïNÐ�A8D�ä@�K=FPRQ�å`P ø =FO�PRQcþ}QÐ ã6=FDE=@QÝIÞâ�Ð�O¬OB=FC�O

��d�f ]^� x W^k�eR´µk¡�6W`pqk�esU%egd 9 W^]^W`e : w�dBpgpqW`_Rp t@r pih x ]`egW^kge�_R[Þh4_Regf r a kik�egdBe�_bk�egf dBeiegf(_r pqa(_Rpb: r�t d�Xc_�§%[�]^W^jRW^e$k�egd 9 ]`_m�c��k�e�_R[�h4_Regf r ach x k�e�kgdBegW^k tF: : © � 2 Ä<3 T � f _�d�X d�] r � x _ r�tegf W^k�egf _ r pg_bh tFr p\k�egdB����_Rpg_ba~h x ]`egW^k�e�_R[�hi_Regf r a�k�W^kR�

� f(_ r pqa(_Rp�: r�t d�XN_�§;["]^W^jRW`e¦k�egd 9 ]^_��c��k�e�_R[�k�egdB����_Rpq_ba,h4_Regf r a�kgdBegWYk°��_bk

: © ¢¤¤¤¤¤¤¥ ¤¤¤¤¤¤¦� l �Ød�XN_Ro�_bX~W^X�e�_R��_Rp

� 4 �Û l �Ødif d�] t ��W^X�e�_R��_Rp

� 4 y l �Ød�X r a a�W^X�e�_R��_Rp

¨ Ã T �B� ©

� x p�[ p r;r�t³r�t egf W^kvegf(_ r pg_bh tFr ]^] r ¢ kvegf r k�_ r�t l�_b]`egkgj�f�d�X a ¿ _Ro�d�X ]YW^X X d 2�yb{ 3 d�X a��d�f ]^� x W^k�e¤2 Ä<3 d�X�a�W^k��!W`o�_bX�W^XNZ\[�[7_bX�a W�§i¯ÝT

ì�ë�ù i ��/}�³�³� �!�" V �!�� ���#;��)³�B� Î )³�!����#;��)³��&Â�(�!��)� �*

�ª_¦f dbo�_�W^X�o�_bk�egW`�!dBe�_ba4kgegdB����_Rpg_ba4[ pg_ba�W^j�e r p���j r pgpg_bj�e r p�hi_Regf r a�k8d�X a tFr!x X a�egf dBeegf(_bk�_�h4_Regf r a kKa r X r eKf r ]Ya�d�k6h x jqf�[ p r hiWYk�_$d�k6k�egdB����_Rpg_ba4h x ]`egW^kge�_R[�d�X a�· x X ��_ÝÙ�¸ x e�egdh4_Regf r a kRT��ª_�a W^kgj x kgk r!x p�pg_bk x ]`egk¦f(_Rpg_�T

� x p�� r d�] ¢ d�k�e r �7X aHdNk�egdB����_Rpg_ba�[ pg_ba W^j�e r pg��j r pgpg_bj�e r p�h4_Regf r a ¢ W`egfHd�]^dBpg��_¯gU%w�T\�(p r h U;_bj�egW r X à T à T � l ¢ _�¤%X r ¢ egf dBe 9 _bjRd x k�_�[ pq_ba W^j�e r p���j r pgpq_bj�e r pHhi_Regf r a�kNpg_��� x W`pg_�e ¢ r¥tEx X j�egW r X,_Ro�d�] x dBegW r X kn[7_RpnegW^h4_�k�e�_R[³l7egf(_�]^dBpq��_bk�en[ r kgkqW 9 ]`_�¯gU%w tFr p�k�egdB����_Rpq_ba[ pg_ba�W^j�e r p���j r pgpg_bj�e r p�h4_Regf r a k�W^k��(T��ª_ij r X�kgW^a(_Rpg_baHoBdBpqW r!x k�j r h 9 W^X�dBegW r X k r�t Z�w�U~d�X a

��

Z�SHU¥h4_Regf r a k¦d�k ¢ _b]^]}d�k r egf _Rp�h4_Regf r a kRT � f(_�hid�§(W^h x h [ r kgkgW 9 ]^_\¯gU%wÊegf�dBe ¢ _ tFr!x X a

¢ d�kËÄ yBl ¢ f W^j�f ¢ d�k t@r p�Z�w�U;� ¨F[ pg_ba WYj�e r pÝ©U��ZnSªU;� ¨Ej r pgpg_bj�e r p�©�T Z t e�_Rp�X r p�hid�]^W`¾bW^X �egf W^k t@r p�j r h4[�dBp�W^k r Xie r h x ]`egW^k�e�_R[¥h4_Regf r a kRl ¢ _n�"X a4egf�dBevW`evW^k t dBp�W^X t _RpqW r p�e r Znw�U;��d�X aw���U;�(T6�ª_ 9 _b]^W^_Ro�_�egf dBeKegf(_bk�_¦kgj�f(_bh4_bk�a r X r e6f r ]^a�[ p r hiWYk�_ 9 _bjRd x k�_�W^h4["]^W^jRW`e³k�egdB����_Rpq_bah x ]`egW^k�e�_R[ch4_Regf r a k�dBpg_�e r;r WYh4[�]^W^jRW^e�e r49 _ r�t [ p�d�j�egW^jRd�] x k�_4¨EW�T±_�T 9 _bjRd x k�_ r�t k�egdB����_Rp�W^X(�(lW (0D ��a _R[7_bX�a k�W^h4[�]YW^jRW`eg] :�r X¶) (0D Û pqdBegf(_Rp�egf�d�X·) (CD ��©�T6�ª_\egf x k�a�W^a4X r e tEx pgegf(_Rp�j r X�kgW^a(_Rpk�egdB����_Rpg_ba�[ pg_ba�W^j�e r p���j r pgpg_bj�e r p�h4_Regf r a kRT

ì�ë*J i ��/}�³�³� �!�" çæH5����³�?oqè�5��B�B/ŽÅ� ���$)� $*

¨ � f(_~��pqkgeck x(9 k�_bj�egW r X ¢ d�kNpg_bkg_bdBpqjqf(_ba 9�:Á��r�9;: �np�W^kgj r ]^] ¢ f WY]`_�egf _�k�_bj r X ak x(9 k�_bj�egW r X ¢ d�k�pg_bk�_bdBp�jqf(_ba 9�: egf(_�d x egf r pbTV©

S x ]`egW^k�egdB��_�hi_Regf r a�k,jRd�X d�]^k rÊ9 _ª[ x e,W^X�e r dÊkgegdB����_RpqW^X(� t pqd�hi_ ¢ r pg¤7T �ª_pg_ ¢ p�W`e�_�egf(_ r pqa WYX dBp : a�W��7_Rpq_bX�egW^d�]}_b� x dBegW r X,W^Xcegf(_ tFr pqh

ß + )�¨K�1T�à}¨K��©�©à + B7¨K�1T�ß6¨K��©�© � ¨ à T � y©

� f(_�k�[�]^W`e�egWYX(�4W^X�e r ߪd�X a�à�¨F_bd�jqfHj r!x ]Ya 9 _�dio�_bj�e r pÝ©nd�]^] r ¢ kn� x d�X�egW`egW`_bk\e r�9 _��!W`o�_bX~dBer �zk�_Re�egWYh4_\]`_Ro�_b]^kbl�d�kvk x ����_bk�e�_bacW^Xikg_bj�egW r X à T � T � f(_nk�["]^W`e�egW^X(��W^X�e r )�d�X aØB¡pg_ ® _bj�egk�egf dBeoBd�] x _bk r�t ßZ+�¨ r p\à�+`©¦dBpg_��!W`o�_bX�dBe\egW^h4_�]`_Ro�_b]^k\k�egdB����_Rpg_ba ¢ W`egfcpg_bk�[}_bj�e¦e r ߶¨ r p�à(©�T

Ç�Ã

×zú�é³úEÒ æ ç$ê(Ð�J8?�=EJ�å�ß�Ð"J�çÅà�PbC;ÑKÐ O¬Ð QC;D@I

��X(_ tFr pqh tFr pnd4k�egdB����_Rpg_ba~· x X(��_ÝÙ�¸ x e�egd,¨E·n¸�U ©vh4_Regf r a�WYk

ò��§ A�)�¨K� (0D ý ¶ - T�à (CD ý ¶ - ©ò Û A¢B}¨K� ( 4 . Û A#T�ß ( 4 d Û �qò���©ò , A�)�¨K� (0D ý ¶ - 4 . , A#T�à (CD ý ¶ - 4 d , Û ò Û ©ò * A¢B}¨K� ( 4 . * A#T�ß ( 4 d * �qò�� 4 d *�, ò , ©TTT

ò�î= A�)�¨K� (0D ý ¶ - 4 .�î1A#T�à (0D ý ¶ - 4 d î Û ò Û 4 ����� 4 d î e î ] ��òµî ] �Ý©ß (CD �=­ß ( 4 « �qò¼� 4 «�, ò , 4 ����� 4 « îqòµî`T

¨ à T ��� ©

W t�N W^k r a a³T\¨F¯ t�N WYk¦_Ro�_bXzl egf(_���pqk�e�k�egdB��_�kgf r!x ]Ya 9 _�d�X,_Ro�d�] x dBegW r X r�t B¥dBe\egWYh4_�� ( l d�X aegf(_�k�egdB��_bk x k�_base r d�a o�d�X j�_ t p r h ß ( e r ß (CD �vdBpg_negf _n_Ro�_bX%��X x h 9 _Rpg_ba r X _bkRTV© � f(_�kgd�h4_tFr pqh x ]^d�jRd�Xcegf _bX 9 _ x k�_bace r d�a(oBd�X j�_�à"l r X j�_�pg_ t _Rpq_bX j�_bk¦e r )~d�X a BsdBpg_�k ¢ W`egj�f(_bacd�X aegW^h4_¡]`_Ro�_b]^k�dBpg_4kgf�W t e�_ba tFr p ¢ dBpqa 9�: �Û T¡� 9 k�_Rpgo�_�egf dBe�d�a(oBd�X jRW^X � 9}r egf�ß�d�X a~à 9;:�r X(_k�e�_R[�pg_b� x W`pg_bk N _Ro�d�] x dBegW r X k�_bd�j�f r�t )¶d�X aÉB�T � f _ tFr pqh r�t egf _�� r o�_Rp�X W^X(�~_b� x dBegW r X kW^XM¨ à T � y©4k x ����_bk�egk4egf dBeid�XÉ_RoBd�] x dBegW r X r�tn9}r egf )Åd�X a B�kgf r!x ]^aÉj r!x X�eid�k r X _�k�egdB��_�lk r ¨ à T ��� ©�W^k�d�X N ��k�egdB��_�h4_Regf r azT

� f(_~j r _�«sjRW^_bX�egkcW^XÅk x jqf­d t@r pqh x ]^d�jRd�X 9 _~a(_RpqW`o�_ba 9�: kge�pqd�W`�!f�e t@r p ¢ dBpqazlnW t]^d 9}r pqW r!x kRl � d : ] r pn_�§;[�d�X�kgW r X r�t69}r egfcegf(_�_�§(d�j�ena W��}_Rpg_bX j�_

ß�¨ �� Az¨K� 4 y©�©���ß�¨K�� AY�8©

d�X aNegf _�·\¸�UcdB[�[ p r §(W^hidBegW r X

« ��ò¼� 4 ����� « î�ò�î �� f(_�_�§%[�d�X kgW r X�k�h x k�e 9 _¡hid�a(_4k r egf dBe�à�¨Ed�X aHj r X kg_b� x _bX�eg] : )³©\WYkn_RoBd�] x dBe�_ba r X�] : dBe

Ç �

� (CD ý ¶ - l�d�X a�ß�¨Ef(_bX j�_=B%©�W^k�_RoBd�] x dBe�_baÉdBe�� ( Tª¯ t h r pg_cegf d�XÉd t _ ¢ k�egdB��_bkidBpq_ca _bkgW`pg_bazld�k : h 9}r ]^W^j�j r h4[ x egdBegW r X d�]n[�d�jg¤BdB��_ªW^k x k�_ tFx ] 9}r egf tFr ps��_bX _RpqdBegW^X(��egf(_bk�_~_�§;[�d�X�kgW r X kd�X a t@r p�k r ]`o%W^X(�Negf(_�k : k�e�_bh r�t X r X ]^WYX(_bdBp�_b� x dBegW r X k�egf dBe�pg_bk x ]`egk t p r h _b� x dBegW^X(��egf(_bW`pj r _�«sjRW`_bX�egkRT

U;egd 9 W^]YW`e : d�X�d�] : kqW^k t@r ]Y] r ¢ k�egf(_ x k x d�]}["dBe�e�_RpqXzT � f _�h r a _b]}[ p r�9 ]`_bhÂWYk¦]^W^X(_bdBpb�

Ç ßà É + Ç � VV � É Ç ß à É �

¨Em�kgW^X(��a�W��7_Rpq_bX�e¥kgjRd�]^dBpqksW^XÞegf(_ r �"��a�W^dB� r X d�]n_bX�e�pqW^_bk r�t egf(_~hidBe�pqW�§Þa r _bk�X r e¥j�f d�X(��_d�X : egf WYX(�¶_bkgk�_bX�egW^d�] 9 _bjRd x k�_�egf(_ª_bW`��_bX�o�d�] x _bk,a(_R[}_bX a r X ] :­r X egf _ª[ p r a x j�e r�t egf r k�__bX�e�pqW`_bkRTV©�¯°XNdB[ [�] : W^X ��egf _�·\¸�Uchi_Regf r ace r egf(_�h r a(_b]}[ p r�9 ]`_bhNl r X(_��"X�a k�egf dBe

ß (CD � �v¨[A V ©và (0D ý ¶ - 4 \�¨[A V ©vß (à (0D � ¶ - �v¨[A V ©vß (CD � 4 \�¨[A V ©�à (CD ý ¶ - T

¢ f(_Rpq_���d�X a½\ÉdBpg_�[ r ] : X r hiWYd�]^k�WYX½A V T��ª_�jRd�XNegf x k ¢ pqW^e�_

Ç ß (CD �à (0D � ¶ - É áÇ y �

���0y É ] � Ç \ �� \ É Ç ß (à (CD ý ¶ - É áÇ \ �

\;� \ 4 � Û É Ç ß (à (0D ý ¶ - É ìë�¨[A V ©íÇ ß (

à (CD ý ¶ - É �� f(_�kgegd 9 W^]^W`e : pg_R�!W r X�j r X kgW^kgegk r�t d�]^]}o�d�] x _bk r�t A V�tFr p ¢ f�W^jqf 9}r egfN_bW`��_bX�oBd�] x _bk r�t ëi¨[A V ©dBpg_�W^X kqW^a(_\egf _ x X W`e�jRW^pqjR]`_�l r p�kgW^h4["]`_nd�X a r Xcegf(_ x X�W`evjRW^pqjR]`_�T�Z t e�_Rp�d4kgf r pqevjRd�]^j x ]^dBegW r Xzlr X(_��7X a kvegf dBe«2�y�î 3kï W^k�d�X�_bW`��_bX�o�_bj�e r p�W t d�X a r X ] : W t

î Û ��¨[A V ©½î 4 \�¨[A V ©1T ¨ à T ��à ©

d�X aÁegf(_�j r pqpg_bk�[ r X a W^X ��_bW`��_bX�o�d�] x _�W^kðî Û T ¨ � f WYk¥WYkcegf(_�kgd�h4_ª_b� x dBegW r XÁegf dBe�dBp�W^k�_bk

¢ f(_bX x kqW^X(��egf _¡d�X�kgdBe�¾¡ß ( çî Û ( lzà (CD ý ¶ - ñî Û (0D � TV© � f _�e ¢ r p r;r egkíî r�t ¨ à T ��à ©�egf x ka(_Re�_Rpqh�W^X(_�egf(_�k�egd 9 W^]^W`e : pg_R�!W r X³T

Ç�Ä

Znk ¢ d�k¦h4_bX�egW r X(_basWYX�k�_bj�egW r X à T à T^yBl ¢ _�X r pqhid�]^W^¾R_\egf(_�k�egd 9 W^]YW`e : pg_R�!W r X 9;: egf(_X x h 9 _Rp r�t kgegdB��_bkvWYX r pqa(_Rp�e r hidB¤�_�d t d�W`p�j r hi[�dBpqW^k r X�e r�r X(_���kgegdB��_�hi_Regf r a�kRT�ZnX�_Rpgp r pj r X k�egd�X�e�jRd�X�d�]^k r�9 _4a(_��"X(_ba 9�: ] r;r ¤;W^X �cdBe�egf(_4��pqkge�_Rpqp r p�e�_RpqhÀW^XHegf(_�dB[ [�p r §(W^hidBe�_k r ] x egW r X r�t egf(_�]YW^X(_bdBp\h r a(_b]z[�p r�9 ]`_bhNT � f W^k�e r�r kgf r!x ]^a 9 _�X r pqhid�]^W`¾R_ba 9�: d t d�j�e r p N�BtFr p\d{: - 9 r pqa _Rp\h4_Regf r azT

�ª_¡pg_bj r �!X W`¾R_4]`_bdB[ t p r �cd�k�d�yÝ��kgegdB��_�·\¸�U,h4_Regf r a r�t�r pqa(_Rp � T uvr hi[ x egdBegW r Xr�t egf(_4_�§;["d�X kgW r X k tFr p � ��k�egdB��_¥d�X a à ��k�egdB��_¥h4_Regf r a k�pg_Ro�_bd�]^k�egf�dBe�X(_bW`egf(_Rp�f d�k�_bX r!x �!fd�a a W^egW r X d�] t pg_R_c[�dBp�d�h4_Re�_Rpqk¡e r W^h4[�p r o�_ x [ r X�egf(_ r pqa(_Rp r�t ]`_bdB[ t p r �(T��­f�W^]`_��B��kgegdB��_�legf W`p�a r pqa(_Rp�h4_Regf r a k�a r _�§%WYk�eRl8egf _ : a r X r e�k�_R_bhÀe r W^hi[ p r o�_ r X�egf(_bW^p�X r X kgegdB����_Rpg_baj r!x X�e�_Rpg[�dBpgegkbT

� f(_¥��pqkge¡WYX�e�_Rpg_bkgegW^X(��f W`�!f _Rp r p�a(_Rp�h4_Regf r a¶W^k4egf _c��o�_���k�egdB��_�·n¸�U�h4_Regf r azT�n_Rpg_¦egf(_Rpg_�dBpg_�y à j r X k�egd�X�egk�e r�9 _¦a(_Re�_RpqhiW^X _ba�WYX�egf _ t@r pqh x ]^d%T �8r d�jqf W`_Ro�_ t@r!x pqegf r pqa(_Rpd�jRj x pqd�j : l � y¦j r X a W`egW r X kv¨Eh r k�e r�t ¢ f�W^jqf¡dBpg_¦X r X ]YW^X(_bdBpÝ©³h x kge 9 _�kgdBegW^k°�"_bazTK·\_bhidBpg¤Bd 9 ] : legf(_Rpg_�W^k\d t d�h�W^] :¥r�t k r ] x egW r X�k¦[�dBpqd�h4_Re�_Rp�W`¾R_ba 9;:s«�) T¦�­W^egf)ò� ¨ Ç «�) © ] �M¶ Û l7egf(_�egd 9 ]`_bd xtFr p�egf(_���_bX(_Rp�d�]³k r ] x egW r XNW^k

��* ¨ � �"òz© �* ¨ � �(òz©� �Û ò � �Û ò�* ¨ � 4 òz© �* ¨ � 4 òz© ��Û ò � �

Û òy� � «�) «�) «�)

¨ à T � ��©

¨E $X�e�pqW`_bk ¢ f W^jqfHdBpg_ 9 ]^d�X(¤,dBpg_4¾R_Rp rNt@r p�k�e�p x j�e x pqd�]6pg_bd�k r X kRTV© � f(_4k�egd 9 W^]YW`e : pq_R�!W r Xªd�X a_Rpgp r p�j r X�k�egd�X�e�dBpg_�W^X a(_R[}_bX a _bX�e r�t egf(_�j�f r W^j�_ r�t egf(_ t pg_R_¦[�dBpqd�h4_Re�_RpT � f(_¦h r k�e�dB[ [}_bd�]��W^X(�ch4_bh 9 _Rp r�t egf(_ t d�hiW^] : l ¢ f�W^jqf ¢ _ijRd�]^]6·\¸�U;�(l³WYkn�!W^o�_bX ¢ W`egf «�) ÂyXö � ��d�X aªf(_bX j�_

Ç�ÇòM � �

ò¼�§ A�)�¨K� (CD ý ¶ - T�à (0D ý ¶ - ©ò Û A¢B7¨K� ( T�ß ( ©ò , A�)�¨K� (CD ý ¶ - � A#T�à (CD ý ¶ - ��ò Û ©

ò * A¢B7¨K� ( 4 A#T�ß ( 4 ò��Ý©ò ) A�)�¨K� (CD ý ¶ - 4 A#T�à (CD ý ¶ - 4 ò * ©

ß (0D �=­ß ( 4 �U�� Û ò¼� 4 �Û * ò , 4 �Û * ò ) �¨ à T ��Ä ©

� 9 kg_Rpgo�_�egf�dBe ¢ f W^]`_ Ä kgegdB��_bk�dBpg_¡pg_b� x W`pg_bazl7egf(_4k�egdB��_iò¼��W^k�d�j�e x d�]Y] : _b� x W`oBd�]`_bX�e�e r egf(_tEx e x pg_�k�egdB��_�ò Û tFr p�egf(_�d�a(oBd�X j�_ r�t à t p r h egWYh4_�]`_Ro�_b]#� 4 �Û e r � 4 ,

Û T��\_bX�j�_ r X ] :itFr!x p_RoBd�] x dBegW r X k�_bd�jqf r�t )~d�X aÖBcdBpg_�X(_R_ba _baNe r d�a(oBd�X j�_ 9}r egfNß~d�X aNà r X(_�egW^h4_�kge�_R[³l d�X a

¢ _�j r X kgW^a(_Rp�egf WYk�e r49 _�d tFr!x p���k�egdB��_�hi_Regf r a tFr p¦[ x pq[ r kg_bk r�t X r pqh�d�]^W`¾bdBegW r X r�t egf _�¯�U%wd�X a r�t egf(_�_Rpqp r p\j r X k�egd�X�eRT

·\¸�U%�cf�d�k�d¥kqW^h4[�]`_¡W^X�e�_Rpg[ pg_RegdBegW r XzT¡��W^o�_bXHegf(_ r pqW`�!W^X�d�]Ka�dBegdcß ( d�X aHà (0D ý ¶ - l]`_bdB[ t p r �,WYk x k�_baªpq_R[7_bdBe�_ba�] : e r _bk�egW^hidBe�_sà ( ] ý ¶ - l�ß (0D �bl8d�X�a�à (CD � ¶ - W^X�k x jRj�_bkgkgW r XzT � f(_egf(pg_R_�_bk�egWYhidBe�_bk r�t à�o�d�] x _bk¦dBpg_�egf(_bXNj r h 9 W^X(_bacd�jRj r pqa W^X ��e r d��"X�W`e�_�a�W��7_Rpq_bX j�_�k�e�_bX jRW^]¨EZ�SHU;��©�e r pq_b]^dBe�_�ß ( e r egf _�X _ ¢ o�d�] x _ r�t ß (0D �RT � f(_�h4_Regf r aNW^k t@r!x pgegf r pqa(_Rp�a x _�e r dk : hih4_Re�p : ¢ f WYjqfc[ p r a x j�_bk¦jRd�X�j�_b]^]^dBegW r X�WYXcegf(_�]`_bdB[ t p r �4_Rpgp r pqkRT

� f(_4k�egd 9 WY]^W`e : pg_R�!W r X r�t ·\¸�U;�NW^k�dNkg_R�!h4_bX�e r�t egf(_iWYhidB�!W^X dBp : d�§%W^kbl³d�X aªegf(_X r pqh�d�]^W`¾R_bas¯�U%w r�t egf�W^k�h4_Regf r a¥WYkvd 9}r!x e�y � � ��Ä ¨Ekg_R_��KW^� x pg_ à T Õ ¨Ed�©�©�T��n_bX j�_ tFr p¦_b� x W^o�d��]`_bX�e\d�h r!x X�egk r�t ¢ r pg¤c[7_Rpnk�e�_R[³l egW^hi_�k�e�_R[�k\d 9}r!x e\e ¢ W^j�_�d�k\]^dBpg��_�d�k¦egf r k�_ r�t kgegd�X a dBpqa·\¸��¥dBpg_¡[ r kgkgW 9 ]`_�T � f(_�_Rpgp r p�j r X�k�egd�X�e�WYk�yXö;yb{ �B� lKj r h4[�dBpg_ba~e r yXö;y �B� tFr p�·n¸��(Ti¨EZ t �e�_Rp�X r pqh�d�]^W`¾bdBegW r X tFr p�j r h4[�dBpqW^k r X�e r�r X _���k�egdB��_\h4_Regf r a kRl�egf _bk�_¦j r X k�egd�X�egk 9 _bj r h4_ � ö;y Äd�X a Ã�� ö;y Ä pq_bk�[}_bj�egW`o�_b] : TV©�Znk ¢ W`egf¡h x ]`egW^k�e�_R[4h4_Regf r a kRl�egf _v[�p r�9 ]`_bh>hid : W^X¡hid�X : jRd�k�_bk9 _ ¢ pqW`e�e�_bX¥d�k¦d�k�_bj r X�a r pqa(_Rp�k : kge�_bhÂW^X�egWYh4_�T � f(_negf(pg_R_���k�egdB��_�l tFr!x pgegf r pqa _Rp ¿n: k�e�p�rr hh4_Regf r a�[�pg_bk�_bX�e�_ba�W^X¿2�y Ã<3 f d�k�d�X�_b� x W`oBd�]`_bX�e�X r p�hid�]^W`¾R_baª¯gU%w r�t d 9}r!x e ���ÖÕ�Ç l t dBp�]`_bkgkegf d�XNegf�dBe r�t ·\¸�U;�(T

Ç |

¿\r egWYj�_�egf dBe\k�egdB��_bkn�sd�X�a Ä dBpg_�WYX a(_R[}_bX a(_bX�e r�t k�egdB��_bk � d�X a à T � f(_�kge r pqdB��_pg_b� x W`pg_bhi_bX�egk6jRd�X4egf(_Rpq_ t@r pg_ 9 _�¤�_R[ e�] r ¢ T6¯-X�egf(_ tFr ]^] r ¢ W^X(��[ p r j�_ba x pq_�l�egW^h4_¦a(_R[}_bX a(_bX j�_d�X aªk x 9 kgj�pqW`[�egk r X�ß�d�X aHà~dBpg_ r hiW`e�e�_ba tFr p�jR]^dBp�W`e : lKd�X a"Y0��W^k�d�kqk x h4_baHe r kgegdBpge ¢ W`egfegf(_�oBd�] x _*A¢B7¨Fßz©�l r�9 egd�WYX(_ba t p r hÂegf(_�[�pg_Ro;W r!x k¦d�a(oBd�X j�_ r�t à�T

Yx�Èó à«�ôYx�Yx�Èó A�)�¨DY0�Ý©Y Û ó A�)�¨Fà%©Y , ó ß 4 Y ÛY , ó A¢B7¨DY , ©Y , ó à 4 Y ,Y , ó A�)�¨DY , ©ß)ó ß 4 Yx��ö � � 4 y�y�Y Û ö;y � 4 Y , ö � � �

Z�e�egf(_4_bX�a r�t egf WYkn[�p r j�_ba x pg_�lõY Û f r ]^a k�egf(_4oBd�] x _¡egf dBe�k�_Rpqo�_bk�d�k�k�egdB��_ � r�t egf(_iX _�§;ed�a(oBd�X j�_ r�t à�T~��X�] : egf pg_R_�e�_bh4[ r pqdBp : o�dBpqWYd 9 ]`_bk�dBpg_cX(_R_ba(_ba³T� $d�jqfÉX(_R_ba�k�e r f dbo�_cd�khid�X : j r hi[ r X _bX�egk¦d�k¦egf _�]^dBpg��_Rp r�t ß�d�X acà"T�¯-X¥egf(_�j r h�h r X�kgW`e x dBegW r X ¢ f(_Rpg_�ß,d�X�acà_bd�jqf~f r ]^a,f d�] t�r�t egf(_�o�dBpqWYd 9 ]`_bk r�t egf(_�k : k�e�_bh�l egf(_�d�a�a W`egW r X d�]}k�e r p�dB��_�W^k�_b� x W^o�d�]`_bX�e¦e rà ö � r�t egf(_4e r egd�]�X x h 9 _Rp r�t�x X(¤%X r ¢ X�kRT�¯°X~kgegd�X a dBpqa tFr!x pgegf r pqa(_Rp�· x X(��_ÝÙ�¸ x e�egd%l�egf(_9 _bk�e¦e�_bh4[ r pqdBp : k�e r pqdB��_�W^k�e ¢ W^j�_�egf(_�X x h 9 _Rp r�tKx X ¤;X r ¢ X kRT

×zú�é³ú^Ó æ ç$ê(Ð�J8?�=EJ�å�ß�Ð"J�çÅà,Qä"å�C�Q¬A8C�O

� f(_�·n¸�U4h4_Regf r ask x ����_bk�e�_ba¥d 9}r o�_\_RoBd�] x dBe�_bkvd�X x h 9 _Rp r�t k�egdB��_bkve r d�a(oBd�X j�_ß�l%egf(_bX¥d¡X(_ ¢ k�_Re r�t W^X a(_R[}_bX a _bX�e$kgegdB��_bk�e r d�a o�d�X j�_�à,¨Ed�]`egf r!x �!fc·\¸�U;��jRd�Xcpg_ x k�_ r X(_k�egdB��_¬©�T�Z�X�d�]`e�_RpqX�dBegW`o�_$W^kze rnx k�_$dKÌ r W^X�e�k�_Re r�t k�egdB��_bk8e r d�a o�d�X j�_$ß�d�X a�à�kgWYh x ]^egd�X(_ r!x kg] : T�Áf W^]`_�k�egWY]^] x kgW^X ��egf(_\kgd�h4_�X x h 9 _Rp � N�r�t W^X a W^o;W^a x d�]�)Nd�X�aXB�_RoBd�] x dBegW r X k�[}_Rp�egW^hi_\k�e�_R[d�k³egf _ r egf(_Rp N ��k�egdB��_vk�egdB����_Rpg_ba¡h4_Regf r a kRl�d�[ r e�_bX�egW^d�]!d�a(oBd�X�egdB��_�f(_Rpg_�W^kzegf dBe8egf(_$X x h 9 _Rp

Ç�Õ

−0.04 −0.02 0 0.02 0.04−1.5

−1

−0.5

0

0.5

1

1.5

−0.04 −0.02 0 0.02 0.04−1.5

−1

−0.5

0

0.5

1

1.5

�6W`� x pg_ à T Õ �$U;egd 9 W^]^W`e : a r hid�WYX k tFr p$k�egdB����_Rpg_ba¥· x X ��_ÝÙ�¸ x e�egd�h4_Regf r a kb��¨Ed�© r p�a(_Rp��s¨F_b�;XzT¨ à T ��Ä ©�©�¨ 9 © r pqa(_Rp à ¨F_b��XzT�¨ à T ��Ç ©�©

r�tKt pg_R_�j r X k�egd�X�egk���p r ¢ k\h r pq_�� x W^jg¤%] : ¢ W`egf N T�ª_�f�dbo�_�_�§;[�] r pg_ba�egf W^pqa r pqa(_Rp�h4_Regf r a knegf dBe x kg_ Ç ¨Ef�d�] t �-©-kgegdB��_bkne r d�a(oBd�X j�_

9}r egf�ßÊd�X a�à�T � f(_Rpg_NdBpg_ªy Ç ¨Eh r k�eg] : ©�X r X ]^WYX(_bdBp�_b� x dBegW r X k4WYX �B� oBdBpqW^d 9 ]^_bk tFr p4egf W^kjRd�k�_�TN�ª_¥f dbo�_ t@r!x X aªegf(pg_R_ t d�h�W^]^W`_bk r�t k r ] x egW r X k�e r egf(_bk�_s_b� x dBegW r X kRl ¢ W`egfªegf(_sh r k�eW^X�e�_Rpg_bk�egW^X ��jRd�k�_�f�dbo%W^X(�$Ì x kge r X(_ t pg_R_�[�dBpqd�h4_Re�_RpT � f W^k8egf W`pqa r pqa(_Rpbl�egf pg_R_���k�egdB��_�h4_Regf r aW^k��!W`o�_bX�f(_Rpg_��

ò��§ A�)�¨K� (CD ý ¶ - T�à (0D ý ¶ - ©ò Û A¢B7¨K� ( T�ß ( ©ò , A�)�¨K� (CD ý ¶ - � �Û A#T�à (CD ý ¶ - � �Û ò Û ©ò * A¢B7¨K� ( 4 � ,� Û A#T�ß ( 4 � ,� Û ò��Ý©ò ) A�)�¨K� (CD ý ¶ - 4 �Û A#T�à (CD ý ¶ - 4 ÚÛ � ò Û 4 ,� , ò * ©ò � A¢B7¨K� ( 4 � ,� Û A#T�ß ( 4 ¨ � �Ú Û � � ò³©-ò�� 4 ¨�� � ,Ú Û 4 òz©-ò , 4 ò}ò ) ©

ß (0D � ­ß ( 4 Û, ò � 4 �� ò , 4 �� ò )à (0D � ¶ - ­à (0D ý ¶ - 4 �� , ò Û 4 �� , ò * 4 �� , ò � �

¨ à T ��Ç ©

Ç {

�n_Rpg_íò�W^k¦d4j r X kgegd�X�e�egf�dBe�d��7_bj�egk\egf(_�d�jRj x pqd�j : d�X aNk�egd 9 WY]^W`e :�r�t egf(_�h4_Regf r azT � f(_�¯�U%wW^k�dB[ [�p r §(W^hidBe�_b] :�r [ egW^hiW^¾R_baªW t ò y � �µö;y Õ yBTs� r p�egf W^k�j�f r W^j�_�l�egf _iX r pqhid�]^W^¾R_ba�¯gU%w>W^kÄ>y �µ� ���cd�X aNegf(_�X r pqhid�]^W^¾R_bac_Rpgp r pnj r X�k�egd�X�e�W^k � |,ò�ö � �_Ä ���ÖÇ � Ç �(T � f(_�k�egd 9 W^]YW`e : pg_R�!W r XW^k�a W^kg[�]^d : _baHW^XH�6W`� x pq_ à T Õ ¨ 9 ©�T4� r p�j r h4[�dBpqW^k r XzlzjR]^d�kgkgW^jRd�]�·n¸ à f d�k�dcX r pqhid�]YW`¾R_ba~¯�U%wr�t yXöcÎ Ã Ä ���ÖÄ |�|id�X a�X r p�hid�]^W`¾R_bac_Rpgp r p\j r X k�egd�X�e r�t {^ö Õ >y � y ��Ä T

�ª_�f dbo�_ 9�: X r hi_bd�X k$_�§(f d x kge�_basegf _n[ r kgkgW 9 W^]^W`egW^_bk tFr p�_bW`egf(_Rpve : [}_ r�t kgegdB����_Rp��W^X(��W^X¡· x X(��_ÝÙ�¸ x e�egd�hi_Regf r a�k`/ r!x p�W^X�e�_bX�e�f d�k 9 _R_bX�e r a(_bh r X kge�pqdBe�_¦egf dBe�k x j�f4h4_Regf r a ka r _�§(W^k�e�d�X a,jRd�X,W^h4[�p r o�_ r XNegf _bW`p\X r X kgegdB����_Rpg_ba,j r!x X�e�_Rpg[�dBpqegkRT

ì�ë@í æ~)6)z�½,¦)������!/z���!*¨ � f(_ ¢ r pg¤�W^X�egf WYk�kg_bj�egW r X ¢ d�k4a r X(_c[ pqW^h�dBpqW^] :H9;:��8r�9�: ��pqW^kgj r ]^]�d t e�_Rpiegf(_

j r X j�_R[ e ¢ d�knW^X�e�p r a x j�_ba 9�: wv_bX(��e\� r pqX 9 _Rpg�(TV©U%W^X j�_ r!x pi� r d�]\W^k¡e r [}_Rp tFr pqh egW^h4_���k�e�_R[ ["W^X(� t@r p ¢ dbo�_�_b� x dBegW r X kRlvW`e4W^k4W^]^] x �

hiW^X�dBegW^X(�Ne r j r hi[�dBpg_�h4_Regf r a k 9 d�k�_ba r X�egf(_bW`p�[7_Rp t@r pqh�d�X j�_ r X�egf _ r X(_���a W^hi_bX kgW r X d�]kgjRd�]^dBp ¢ do�_�_b� x dBegW r Xzl

ß - ­à 0à - ­ß 0 � ¨ à T � |�©

�ª_�egf W^X(¤ r�t egf(_�k�[�dBegW^d�]8a r hid�W^X�d�k x X 9}r!x X a(_baNd�X�a,k�[�dBegWYd�]�a(_RpqW^o�dBegW`o�_bk�d�kn_�§%d�j�eRT�� r pd~� r!x pqW`_Rp4h r a(_ ¢ f r k�_ck�[�dBegWYd�]�a(_R[}_bX a _bX j�_sW^k�� !� ¥0 l�egf _ ¢ dbo�_N_b� x dBegW r X 9 _bj r h4_bk¡egf(_���� Êk : k�e�_bh ëìí ß

à

ðLñò - ëìí� S �S � �

ðLñò ëìí ßà

ðLñò � ¨ à T ��Õ ©

� f(_bkg_i_b� x dBegW r X k�d�]Y] r ¢ ]`_ t e�� r WYX(�,d�X aªp�W`�!f�e�� r WYX(�,h r a(_bkRT¥�­f _bX�d,h r a(_iWYk�d�a(oBd�X j�_baW^X�egW^h4_ 9�: d�X~d�h r!x X�e�A7lzegf(_¡k r ] x egW r X�W^k�h x ]`egW`[�]YW`_ba 9;: d t d�j�e r pT� S"! ó l ¢ W`egf,egf(_4kgW`�!Xa(_Re�_Rpqh�W^X W^X(� r X ] : a W`pq_bj�egW r X r�t e�p�dbo�_b]�T

| �

� r p4jR]^d�kgkgWYjRd�]�h x ]`egW^kge�_R[�h4_Regf r a kblKegf _¥d�X d�] : kgWYk�pg_ba x j�_bk�e r egf(_ckgW`e x dBegW r X t d��hiW^]YW^dBp t p r hË]^W^X(_bdBpikgegd 9 W^]^W`e : T � f _�X x hi_RpqW^jRd�]�k r ] x egW r XÞW^k�jRdB[�d 9 ]`_ r�t e�pqdo�_b]nWYXÉ_bW`egf(_Rpa W`pq_bj�egW r Xzl8d�X�a�e r d�a o�d�X j�_¥d,h r a(_ 9;: egW^h4_¶A�egf(_�k r ] x egW r X�W^k�h x ]`egW`[�]^W^_ba 9;: d t d�j�e r pY�¨KSIA � ©�T�� r p�]YW^X(_bdBp�h x ]`egW^kge�_R[�h4_Regf r a kRlqY,WYk�d�p r�r e r�t egf(_sj�f dBpqd�j�e�_RpqW^kgegW^ji[ r ] : X r hiW^d�]_b� x dBegW r X

2 ¨DY;©b�´SIA � L ¨DY�©= ��� ¨ à T � {!©

�Áf(_bX&A � � l"d�k�egd 9 ]`_�hi_Regf r a�f d�k�_�§(d�j�eg] :Nr X(_�p r�r e�dBeöY¨ yBT�Znk�SIA � e�p�dbo�_b]^k�d�] r X(�egf(_iW^h�dB�!W^X dBp : d�§%WYkRl³egf W^k�p r�r e�dB[�[ p r §(W^hidBe�_bk�egf(_i_�§(d�j�e t d�j�e r p÷� ! ó ¨ r p�W^egk�j r X�Ì x �!dBe�_¬©9�x e�_Ro�_bX�e x d�]^] :ª9 _bj r h4_bk�X r egW^j�_bd 9 ] : a�W��7_Rpq_bX�eRT � f(_ r egf(_Rp¡p r;r egk r�t egf(_sj�f dBpqd�j�e�_RpqWYk�egW^j[ r ] : X r hiW^d�]!dBpq_v["f : kgW^jRd�]^] : W^pgpg_b]`_RoBd�X�e�¨Ed�k�] r X(��d�kKegf(_ : dBpg_�W^X kqW^a(_�egf(_ x X W^e8jRW`pqjR]^_¬©�T8�Áf(_bXA � W^k�]YdBpg��_Rp�egf d�XNegf _�¯�U%w r�t egf(_�h4_Regf r azl k r h4_�p r;r e\W^k r!x egkqW^a(_�egf(_ x X�W`e¦a W^k�¤¥d�X aNegf(_h4_Regf r a 9 _bj r h4_bk x X k�egd 9 ]`_�T

��r o;WYk x d�]^W`¾R_�egf�W^k�[ p r j�_bkgkbl ¢ _�a(p�d ¢ d n°p r;r en[ r pge�p�d�W`e_piegf dBe�e�pqd�j�_bk�egf(_�[�f : kgW��jRd�]^] : pq_b]`_Ro�d�X�e�p r;r evd�k�A � egdB¤�_bk r Xcd�]^]"kgegd 9 ]`_�o�d�] x _bkRT�ZnXs_�§(d�h4[�]`_ t@r p¦Z�w à WYkvkqf r ¢ X¥W^X�6W`� x pg_ à TÖ{;T

ZM[ r W^X�e=SIA � r Xcegf(_�W^h�dB�!W^X dBp : d�§(W^k�kgf r!x ]^asWYa(_bd�]^] : hidB[ce r � S"! ó r Xcegf(_ x X W`ejRW`pqjR]^_�l�d�k�egf(_\egW^jg¤ihidBpq¤;k r!x egkgW^a(_¦egf(_ x X W`e�jRW`p�jR]`_�k x ����_bk�eRT � f(_¦[�f : kgWYjRd�]^] : pq_b]`_Ro�d�X�e�p r;r eRld�k�a(_Re�_RpqhiWYX(_ba 9;: egf(_¡jqf dBp�d�j�e�_RpqW^k�egW^j�[ r ] : X r hiW^d�]�l�W^kn[7_Rp t _bj�e�dBe�egf _ r pqW^�!W^X,d�X aHds� r�r adB[ [ p r §(W^hidBegW r X�X(_bdBp 9;: l 9�x e�_Ro�_bX�e x d�]^] : egf(_�[�dBegf r�t egf(_�p r;r ena�W`o�_Rpg��_bk t p r h egf(_�jRW`pqjR]`_�T�Áf(_bX·S�A � _bX j r!x X�e�_Rpqk�egf(_ 9}r!x X�a dBp :�r�t egf(_nkgegd 9 W^]^W`e : pq_R�!W r Xzl r X(_ r�t egf(_�[�dBpqd�kqW`egW^j¦p r;r egkX r e\kqf r ¢ XNWYkKÌ x k�e�j�p r kgkgWYX(�¡egf(_ x X W^e�jRW^pqjR]`_ r X,W`egk ¢ d : e r j�pg_bdBegW^X(�iegWYh4_�W^X k�egd 9 W^]^W`e : T

Z kgWYhiW^]^dBp�d�X d�] : kgW^k�jRd�X 9 _�hid�a _ tFr p�jR]^d�kgkqW^jRd�]6· x X(��_ÝÙ�¸ x e�egdch4_Regf r a kRT��n_Rpg_egf(_cjqf dBp�d�j�e�_RpqW^k�egW^js[ r ] : X r hiW^d�]�WYk�]^WYX(_bdBp�W^XøY(l 9�x e�egf(_Rpg_cW^k�d,[ r ] : X r hiWYd�]�a(_R[}_bX a(_bX j�_r X SIA � TM¨E� r p r pqa _Rpqkm:Ê]`_bkgk�egf d�X���o�_�l�egf W^k�[ r ] : X r hiW^d�]vW^k\Ì x k�e¡egf(_©: - 9 r pqa(_Rp � d : ] r p[ r ] : X r hiW^d�] tFr p'� ! ó TV©¡Z�]^k r l;egf(_�kgegd 9 W^]^W`e : pg_R�!W r Xch x k�e 9 _�X r pqhid�]YW`¾R_ba 9;: egf(_�X x h 9 _Rp Nr�t k�egdB��_bk¦WYXiegf(_�h4_Regf r azl%d�X a�egf _ N - 9 p r;r e r�t Y¡h x kge 9 _\egdB¤�_bXNW^Xsd�jRj r pqa d�X j�_�T�w�_bjRd x k�_

|;y

−1 −0.5 0 0.5−1

−0.5

0

0.5

1

ikω

−1 0 1−1

0

1 z

�6W`� x pg_ à TÖ{;�� �§(d�h4[�]`_ r�t d n°p r;r en[ r pge�pqd�W^eRT p � f(_�[ r pgegW r X r�t egf(_�W^h�dB�!W^X dBp : d�§(W^k ¢ f�W^jqf]^W`_bk�W^X kgW^a _segf(_~k�egd 9 W^]YW`e : pg_R�!W r X r�t Z�w à W^kshidB[ [}_baÉe r egf(_,[�f : kgW^jRd�]Y] : pg_b]^_Ro�d�X�e�p r;r egkW^X kqW^a(_¥egf(_ x X W`e4jRW`p�jR]`_�Tɯ-a(_bd�]Y] : l$egf(_,_Ro�_bX ] : k�[�d�j�_ba¶egW^jq¤�h�dBpg¤;k�d�] r X(�ªegf(_ x X W`e¡jRW`pqjR]`_kgf r!x ]^aª]^W^X(_ x [ ¢ W`egfHegf(_iegWYjg¤ªhidBpg¤%k�d�] r X �Negf(_ip r;r e�[�dBegf³l 9�x e�egf�W^k�W^k�e�p x _ r X ] : X(_bdBpegf(_ r pqW^�!W^XzT

| �

egf(_Rpg_�WYk r X ] :sr X(_�p r;r eRl egf(_�["f : kgW^jRd�]^] : pg_b]`_RoBd�X�e\p r�r e�d�]Yk r a(_Re�_Rpqh�W^X(_bk¦k�egd 9 WY]^W`e : T� r p�k�egdB����_Rpg_ba4h x ]`egWYk�e�_R[�kqjqf(_bh4_bkbl�egf(_¦jqf dBpqd�j�e�_Rp�W^k�egW^jv_b� x dBegW r X¡W^kKdB�!d�W^XN¨ à T � {!©RT

� f WYkKWYk�X r ¢ d�[ r ] : X r hiWYd�]�W^X_Y �M¶ Û l�d�X a4egf(_¦p r�r egk�dBpq_¦_bd�kgW^] :�t@r!x X�azTKZn�!d�W^X r X ] :�r X(_¦p r;r e[}_Rp�a�W`pg_bj�egW r X r�t e�pqdo�_b]�W^kn[�f : kgW^jRd�]Y] : pg_b]`_RoBd�X�eRT�� r p�kgegdB����_Rpg_baª· x X ��_ÝÙ�¸ x e�egdch4_Regf r a kRlegf(_4k�egd 9 WY]^W`e : d�X�d�] : kqW^k�W^X�kg_bj�egW r X Ä dB[ [�]^W^_bk`/zW^X t d�j�eRl$Y �M¶ Û W^k$Ì x k�e�egf(_¡o�dBp�W^d 9 ]`_÷î W^X~egf(_jqf�dBpqd�j�e�_RpqW^k�egWYj�_b� x dBegW r X�¨ à T ��à ©bl d�X a V W^k¦[ x pq_b] : W^hidB�!WYX dBp : WYXcegf dBe tFr pqh x ]^d%T

�6W`� x pg_ à T^y � a W^k�[�]Yd : k}egf(_�p r;r e³[ r pge�pqd�W`egk t@r pKjR]^d�kgkgW^jRd�]�d�X a�k�egdB����_Rpg_ba�h4_Regf r a k r�tr pqa(_Rp�k � l à l!�(l�d�X a�|�T�Z�k�egf(_ r pqa(_Rp r�t d�h4_Regf r a4W^X j�pq_bd�k�_bkRl!W^X X _Rp6d�X�a r!x e�_Rp�egW^jg¤%k�hidBegj�fx [�h r pq_�d�jRj x pqdBe�_b] : X(_bdBpöY©>yBT � f(_�k�egd 9 W^]YW`e : pg_bk�e�pqW^j�egW r X�W^k¦hid�a(_�jR]`_bdBp 9;: ¢ f(_Rpg_�egf(_egW^jq¤,hidBpg¤%k r X~egf(_ x X W^e\jRW`pqjR]`_�_bX azT � f(_�Znw � d�X a~·\¸ � h4_Regf r a k�dBpg_�kgegd 9 ]`_ 9"x e�f�dbo�_¾R_Rp r ¯gU%w�T � f _�Znw�U � l;wv��U � l;d�X ai·n¸�U � h4_Regf r a k�dBpq_\d�]^]%_b� x W`oBd�]`_bX�e�e r ]`_bdB[ t p r �(l ¢ f�W^jqff d�k�egf(_�hid�§(W^h x hÈ[ r kgkgW 9 ]^_�¯gU%w r�t � T�¯°X�_Ro�_Rp : jRd�kg_�l6kgegdB����_Rpg_ba�kqjqf(_bh4_bk�dBpg_�kg_R_bX�e rf do�_�k�egd 9 WY]^W`e : d�X aNd�jRj x pqd�j : [�p r [}_RpgegW`_bk¦k x [}_RpqW r pve r egf(_bW`p�X r X kgegdB����_Rpg_ba,j r!x X�e�_Rpg[�dBpqegkRT

ZnX r egf(_Rp ¢ d : e r o;W`_ ¢ egf(_�p r;r ev[ r pge�p�d�W`egk$W^kvW^Xse�_Rpqhik r�t X x h4_RpqWYjRd�]"a WYkgkgW`[�dBegW r Xd�X a�a W^k�[}_RpqkqW r XzTcw�_bjRd x k�_ ¢ _¥f dbo�_c_b]^W^h�W^X dBe�_baªegf(_ck�[�dBegWYd�]$a W^kqj�pg_RegW`¾bdBegW r X�_Rpgp r pqkbl8p r;r e[ r pge�pqd�W`egk�jR]`_bdBpq] : kgf r ¢ egf(_�_Rpgp r pqk³k r ]`_b] : a x _�e r egf(_�egWYh4_�k�e�_R[ [�WYX(��kgjqf _bh4_bkRT � f(_�d�h r!x X�er�t X x h4_RpqW^jRd�]¦a WYkgkgW`[�dBegW r X¶W^X¶d�kgj�f(_bh4_,WYkikgf r ¢ X 9;: f r ¢ jR] r k�_�egf(_�[�dBegf r�t egf(_�p r;r e[ r pge�pqd�W`e�kgegd : k\e r egf(_ x X�W`e�jRW`pqjR]`_�l ¢ f(_Rpg_bd�k\egf(_�d�h r!x X�e r�t a�W^k�[}_RpqkgW r XcW^k\kgf r ¢ X 9;: f r ¢¢ _b]^](egf(_�W^X X(_Rp�egWYjg¤%k r X�egf(_\p r;r e$[ r pge�p�d�W`e�[�dBegf¥hidBegjqf x [ie r egf(_ r!x e�_RpvegW^jq¤;k r Xiegf(_ x X W`ejRW`pqjR]^_�Tc� r p�_�§(d�h4[�]^_�lKZ�w�U � ��w���U � ��·\¸�U � ¨E]`_bdB[ t p r ��©�d�X a�·n¸�U;�,f�dbo�_cX r a WYkgkgW`[�dBegW r X9 _bjRd x k�_�d�]^] p r;r egkvk�egd :4r Xsegf(_ x X W`e$jRW`p�jR]`_ 9�x e�f dbo�_�kgW`�!X W`�"jRd�X�e�a W^k�[}_RpqkgW r X�X _bdBp�egf(_n_ba(��_r�t egf(_�k�egd 9 WY]^W`e : a r hid�W^X 9 _bjRd x kg_�egf(_�W^X X _Rp�d�X a r!x e�_Rp�egWYjg¤%k\a r X r enhidBegjqf ¢ _b]^]}egf _Rpg_�T

ì�ë - î ù 5�½­� ����#%/z¼\��j�,¦� ����½­���8�!*

¨ � f(_ ¢ r pg¤cW^Xcegf W^k�kg_bj�egW r X ¢ d�k\a r X(_ 9;: egf(_�d x egf r pTV©� f(_�p r;r e�[ r pqe�pqd�W`e�a dBegdNjRd�X 9 _ x k�_ba~e r _�§;[}_RpqW^hi_bX�egd�]^] : j r h4[�dBpg_iZ�w�l}Z�w�U7l

w���U7l�·n¸4l�d�X a­·\¸�UÉegW^h4_~W^X�e�_R��pqdBe r pqk t@r p ¢ do�_H[ p r [�dB�!dBegW r X³T Znk¥a W^kqj x kgk�_baÞWYXÞegf(_[ pg_Ro%W r!x kNkg_bj�egW r Xzl ¢ f(_bXMk r ]^o;W^X ��_b� x dBegW r X ¨ à T � |�©�l r X(_�jRd�X h r a(_b]�egf _�_��7_bj�e�egf dBe�d

| Ã

unstable

?RKS

BDS

ABS

RK

AB

p=2 p=3 p=4 p=7

�6W`� x pg_ à T^y � ��· r;r e�[ r pge�p�d�W`egk tFr p�jR]^d�kgkgWYjRd�]Kd�X�a�k�egdB����_Rpq_ba�h4_Regf r a k r�t a W��}_Rpg_bX�e r p�a(_RpqkRTU;egd 9 WY]^W`e :cr�t egf _�h4_Regf r a k tFr pnegf _ ¢ dbo�_¡_b� x dBegW r XHW^knpg_ ® _bj�e�_ba 9;: egf(_¡]`_bX(��egf r�t egf(_¡dBpqjhid�a(_ 9;: egf(_¡egW^jq¤�hidBpq¤;k r XHegf(_ x X�W`e�jRW^pqjR]`_�T�Z�jRj x pqd�j : W^k$Ì x a ��_ba 9;: egf _¡h�dBegjqf W^X � r�tW^X X _Rp�d�X a r!x e�_Rp�egW^jq¤;k�d�] r X(��egf(_�p r�r e�[�dBegf k¥¨Ek r ]^W^a�]YW^X(_bk�©�Tc¯°X�egf(_¥jRd�k�_ r�t ·n¸�U;�(l6egf(_p r;r e�[�dBegf�a r!x 9 ]`_bk 9 d�jg¤ r Xªegf _ x X W`e�jRW`pqjR]`_4W^XHegf _ ¢ p r X(�Na W`pq_bj�egW r X�/³egf r kg_iegW^jg¤HhidBpg¤%kdBpg_ r hiW^e�e�_ba t@r p�jR]YdBpqW`e : T � f(_¡_�§(W^k�e�_bX j�_ r�t d�Xª·\¸�U | t@r pqh x ]^dcW^k x X(¤;X r ¢ Xzlzd�X a ¢ _ia rX r e : _Renf dbo�_�d x k�_ tEx ]z·\¸�U à h4_Regf r a t@r p ¢ f W^j�fcegf W^k¦d�X d�] : kgW^k¦WYk�dB[ [ p r [�pqW^dBe�_�T

|¬�

[�dBpgegWYj x ]^dBp6X x hi_RpqW^jRd�];egW^h4_�W^X�e�_R��pqdBe r p$f d�k r X¡d�[�dBpgegWYj x ]^dBp6� r!x pqW`_Rp�h r a(_'� !� ¥0 9;: k r ]`o%W^X(�_b� x dBegW r X�¨ à T � {!© tFr p$egf(_n[�f : kgW^jRd�]%p r�r eÈY�¨KSIA � ©�T��ª_�jqf r;r k�_\egf _�[�f : kgWYjRd�](p r;r e$k r egf�dBe$egf(_k r ] x egW r X�h r o�_bknk�e�p�W^j�eg] : e r egf(_�p�W`�!f�eRT � f(_bX�egf(_�k r ] x egW r XNdBe\egf _*� - 9 egW^h4_�k�e�_R[~WYk¦�!W`o�_bX9;:

ß6¨K�� AY�8©�ÝY ( � !� ¥0à}¨K�� AY�8©� �ÁY ( � !� ¥0 � ¨ à T ÃB� ©

�ª_ x k�_�egf _�W^X W`egWYd�]"j r X a�W`egW r X

ßK¨��;T � ©= ¢¤¥ ¤¦ S y 4 j r k S 0a � � ) U"U Û T ¨ � ¨ ®Ê��� y Ä� T ¨ � ¨µ´ ��� y Ä ¨ à T à y©

d�X a¥d�a(oBd�X j�_�egf(_�k r ] x egW r Xse r �"X d�] egWYh4_Áú Ç ' l(k r egf dBe�egf _�_�§(d�j�ev�"X d�]7k r ] x egW r X�W^kvegf(_kgd�h4_�d�kvegf(_�W^X W`egWYd�]�j r X a W^egW r XzTK�ª_�a(_��"X(_m� e r¡9 _�egf(_�X x h 9 _Rp r�t³tFx X j�egW r Xs_Ro�d�] x dBegW r X kx k�_ba~e r d�a(oBd�X j�_¡egf(_4k r ] x egW r X t p r hûú � e r ú Ç ' l³W�T±_�T�egf _¡X x h 9 _Rp r�t egW^h4_¡k�e�_R[�kegdB¤�_bXMh x ]`egW`[�]YW`_ba 9;: egf(_HX x h 9 _Rp r�t k�egdB��_bk r�t egf(_HegW^h4_HW^X�e�_R��p�dBegW^X(�Éh4_Regf r azT � f W^k[ p r o;WYa(_bk�d�]`_R�!W^egW^hidBe�_\j r h4["dBpqW^k r X 9 _Re ¢ _R_bX r X(_���k�e�_R[shi_Regf r a�k$]^W`¤�_�Z�w�l�Z�w¦U}l�d�X aiw���Ud�X a�h x ]`egWYk�egdB��_�h4_Regf r a k�]^W^¤�_�·n¸ d�X a�·n¸�U7T

� f(_4k�egd 9 WY]^W`e : pg_bk�e�pqWYj�egW r X tFr p�egf W^k�[ p r�9 ]`_bhÈW^k*A � � Þj0 ®ýü Pqþ l ¢ f(_Rpg_·Ao � �ÿd�X a � � ÞD0 �� Û T � f x k ¢ _�f dbo�_

� ª à '��ü Pqþ � ¨ à T Ã�� ©

�ª_ x kg_ba � Ç � tFr p�egf(_�_�§%[7_Rp�W^h4_bX�egk�W^Xcegf W^k¦kg_bj�egW r XzT�6W`� x pg_ à T^y�y4kgf r ¢ kndckgd�h4["]`_�p x X r�t egf�W^k\h4_Regf r a tFr p�egf�W`pqa r p�a(_Rp�Z�w�U x kgW^X(�

� à | Ä ��egf(_4W^X W`egW^d�]8j r X a W`egW r X�¨Ed�X a~_�§(d�j�e�k r ] x egW r X�dBe�egW^hi_Tú Ç ' ©�lzegf(_4X x h4_RpqW^jRd�]k r ] x egW r X�dBeqú Ç ' l!d�X a�egf(_�_Rpgp r p�W^X�egf(_¦X x h4_RpqW^jRd�];k r ] x egW r XzT�¯°X r!x p�j r h4[�dBpqWYk r X�egd 9 ]`_bk�!W`o�_bXs]^dBe�_Rpbl ¢ _\kgf r ¢ r X�] : egf _�_Rpgp r p$WYX4egf(_\X x h4_RpqWYjRd�](k r ] x egW r X³T8¯°X r pqa(_Rp$e r d�a a(pq_bkgk�egf(_

| Ä

X x h4_RpqW^jRd�]}a WYkgkgW`[�dBegW r X r�t egf(_�kgjqf(_bhi_bkRl ¢ _�f�dbo�_�W^X�jR] x a(_ba�egf(_�pg_b]^dBegW`o�_�] r kqk r�t _bX(_Rpg� : W^Xegf(_�a WYkgj�pg_Re�_ é Û ��X r pqh'W^Xcegf(_ x [ [}_Rp���pqW`�!f�e¦j r pqX(_Rp r�t egf(_�_Rpgp r p�[�] r egkRT

� d 9 ]`_ à T±��kgf r ¢ k�egf(_¦_Rpqp r p$W^X�p x X�X W^X(��egf(_�k�_bj r X a r pqa(_Rp�]`_bdB[ t p r ��¨EZ�w�U � l�w���U � l�·n¸�U � ©h4_Regf r a t@r p�� ÄB��� d�X a � y ����� T � d 9 ]^_ à T Ä j r h4["dBpg_bk4egf(_c_Rpgp r p�k r�9 egd�W^X(_ba 9;:p x X�X W^X(�4Z�w à lzZ�w�U à lzd�X a,w���U à t@r p{�� ÄB��� d�X�a&�� y ����� l ¢ f�W^]`_ � d 9 ]`_ à T Ç kgf r ¢ kegf(_�_Rpqp r pqk�pq_bk x ]`egW^X � t p r h p x X X�W^X(�¡Znwv�(l}·\¸��(l7Znw�U;�(l7wv��U;�(l7d�X a,·n¸�U;� tFr p?� ÕB���d�X a¤� >y ÇB��� T��6W^X d�]^] : l � d 9 ]`_ à TV|�j r h4[�dBpq_bk³egf(_�_Rpqp r pqk³W^X�Z�w�|�d�X a�Z�w�U | tFr p;� �B�����d�X a � ­� ����� l ¢ f WY]`_ � d 9 ]`_ à T Õ j r h4[�dBpg_bk�egf _�_Rpqp r pqk�W^X¥Znw Õ d�X acZ�w¦U Õ tFr p�� ÃB�����d�X a½� ÇB����� T

¯-X�d�]^]�jRd�k�_bkRlvk�egdB����_Rpg_baÞhi_Regf r a�k�dBpg_Nk x [7_Rp�W r p�e r X r X�k�egdB����_Rpg_ba¶h4_Regf r a k¡W^Xe�_Rpqhik r�t d�jRj x pqd�j : d�X a�k�egd 9 W^]^W^e : T$�Áf W^]^_�egf _�pg_b]^dBegW^o�_�d�jRj x pqd�j :Nr�t X r X kgegdB����_Rpg_ba,o�_Rp�k x kk�egdB����_Rpg_baÉh4_Regf r a k�a r _bk�X r e�j�f d�X(��_ ¢ W`egf r pqa(_Rpl8egf(_sW^h4[ p r o�_bh4_bX�e�W^Xªk�egd 9 W^]^W`e :�t p r hx kgWYX(��kgegdB����_Rpg_ba,h4_Regf r a k¦j r X�egW^X x _bk¦e r W^hi[ p r o�_�d�k r p�a(_Rp�W^X j�pg_bd�kg_bkRT�¯Æe�WYk¦d�]^k r W^X�e�_Rpg_bk�e°�W^X(�ce r X r e�_iegf dBe�egf(_s·\¸�U;��hi_Regf r a�W^k�W^X t _RpqW r p�e r Z�w�U;�,d�X a�w���U;�,WYXªd�jRj x pqd�j :H9�x ehidBpg�!WYX d�]^] :i9 _Re�e�_Rp�W^XNk�egd 9 W^]YW`e : l ¢ f(_Rpq_bd�k\W`e�W^hi[ p r o�_bk r X�·\¸��iWYX 97r egf�pg_bk�[}_bj�egkRT

¿\r egWYj�_¥egf�dBe�egf _Rpg_¥WYk�d~a W��}_Rpg_bX�e�j�f dBpqd�j�e�_Rpie r egf(_¥_Rpgp r p¡egf d�XÉW^k¡j x kge r hidBp : T��: [�WYjRd�]^] : l%_Rpgp r p�e�p�d�W^X k¦dBpg_ r X _���kgW^a(_ba�a x _�e r k�[�dBegWYd�]za W^kgj�pg_RegW^¾bdBegW r Xc_Rpgp r pbT�� r ¢ _Ro�_Rpbl7d�kX r e�_ba�W^X�egf(_�[�pg_Ro;W r!x k³k�_bj�egW r X³l ¢ _�f do�_$_b]^WYhiW^X dBe�_ba�kg[�dBegW^d�]!a WYkgj�pg_RegW`¾bdBegW r X�_Rpgp r pqkzegf p r!x �!fegf(_ x k�_ r�t egf(_�p r�r en[ r pqe�pqd�W`e¦e�_bjqf�X W^� x _�T � f x kRl(egf(_�_Rpqp r pqk\kqf r ¢ X,W^XNegf(_bk�_�[�W^j�e x pq_bk�dBpg_k r ]`_b] : egW^h4_�a�W^kgj�pg_RegW`¾bdBegW r X�_Rpgp r pqkRT � f(_bk�_v_Rpgp r pKe�pqd�W^X kKdBpg_�d�]^h r k�eKk : h�h4_Re�pqW^j$pqdBegf(_Rp6egf d�Xr X(_���kgWYa(_baskqW^X j�_\egf _�kgj�f(_bh4_bk¦dBpg_�d�]^h r kgeva WYk�[}_RpqkgW r X%� t pg_R_�T � f(_nd�h r!x X�e r�t a�W^kgkgW`["dBegW r XiW^kr X¥egf(_ r pqa(_Rp r�t hid�j�f W^X(_�[ pg_bjRW^kqW r X tFr p¦]`_bdB[ t p r ��d�X ac·n¸�U;��d�X�a¥WYk$pg_bd�k r X d 9 ] : kgh�d�]^] tFr pegf(_ r egf(_Rp�kgjqf _bh4_bkRT

| Ç

0

2

4

−π 0 π

0

2

4

−π 0 π

−1

0

1

−π 0 π

−0.085976

�6W`� x pg_ à T^y�yB�iU%d�h4["]`_4p x X r�t Z�w¦U à x kgW^X �¥egf _i[�f : kgWYjRd�]^] : pg_b]^_Ro�d�X�e�p r;r e�d�X a � à | ÄtEx X j�egW r X�_Ro�d�] x dBegW r X kRT¥¨Ed�©n¯-X W^egW^d�]8j r X�a W`egW r XɨEd�X aH_�§(d�j�e��"X d�]6k r ] x egW r X"©�T ¿\r e�_4egf�dBe ¢ _[�W^jq¤�egf _,[�f : kqW^jRd�]�p r;r esk r egf�dBeiegf(_�f x h4[Þh r o�_bk¥e r egf(_�pqW`�!f�eRTn¨ 9 © ¿�x h4_RpqWYjRd�]¦k r ] x �egW r X�dBe��"X d�]$egW^h4__ú Ç ' TܨEj©� �pgp r p�W^X�egf _�X x h4_RpqW^jRd�]�k r ] x egW r X³T � f _ipg_b]^dBegW`o�_s] r kgkJ�� + b ø à ]�� � -� + ø à ø�?ø ]� � - �Åy Q W^k¦kgf r ¢ X�W^Xcegf(_ x [ [}_Rp�pqW`�!f�e°��f d�X aNj r pqX(_Rp r�t egf _�_Rpgp r p�["] r eRT

|�|

� d 9 ]`_ à T±�(�� $pgp r p\�!W^o�_bX 9;: p x X X WYX(�¡egf(_�k�_bj r X�a r pqa(_Rp�]`_bdB[ t p r ��hi_Regf r a x kgW^X �iegf(_�p r;r e[ r pge�pqd�W`e4e�_bj�f X W^� x _�T­£³_bdB[ t p r ��W^kiegf(_ r X ] : jR]^d�kgkqW^jRd�]�k�_bj r X a r pqa(_Rp¥h x ]^egW^k�e�_R[Þh4_Regf r aegf dBeif d�k�dªX r X%��¾R_Rp r ¯gU%w�T ¿\r e�_,egf dBe4o�_RpgegW^jRd�]�kqjRd�]`_bkia W��}_Rp 9�: � a, T � f(_Npg_b]YdBegW`o�_N] r kgkJ � + b ø à ]�� � -� + ø à ø�?ø ]� � - �Åy Q WYkvkqf r ¢ XNWYXsegf _ x [ [}_Rp�pqW^�!f�e°��f d�X�a¥j r p�X(_Rp r�t egf _�_Rpqp r p¦[�] r egkRT��ÀW^k�egf(_X x h 9 _Rp r�t6tEx X j�egW r Xc_RoBd�] x dBegW r X�k x k�_baNe r pq_bd�jqf�egf _��"X d�]}egW^hi_íúg Ç ' TS�_Regf r a  �pgp r p�dBe?� ÄB���  �pqp r p\dBe�� >y �����

£�_bdB[ t p r �

¨EZ�w�U � ©

−1.6

0

1.6

−π 0 π

4.2188e−15

−0.48

0

0.48

−π 0 π

−1.6875e−14

¨Ew���U � ©¨E·\¸�U � ©

| Õ

� d 9 ]`_ à T Ä �$ �pqp r p��!W`o�_bX 9�: p x X�X W^X(��egf�W`pqa r pqa(_Rp�h4_Regf r a k x kqW^X(��egf _�p r�r e�[ r pge�pqd�W^e�e�_bj�f%�X W^� x _�T~� 9 k�_Rpgo�_segf dBe�egf _so�_RpgegWYjRd�]�kgjRd�]^_bk�dBpq_segf(_¥kgd�h4_cW^X�d�]^]$jRd�k�_bk¡d�X a�egf dBe¡Znw à W^kX r e�k�egd 9 ]`_ x X�egW^]�� ª Õ�à �(T � f _4pg_b]^dBegW`o�_i] r kqk J�� + b ø à ]�� � -� + ø à ø�?ø ]�� � - �Êy Q W^k�kgf r ¢ XªW^XHegf(_ x [�[7_RppqW`�!f�e°��f d�X aHj r pqX _Rp r�t egf(_¡_Rpgp r p�[�] r egkRT¤�ñW^k�egf(_4X x h 9 _Rp r�t�tFx X�j�egW r X,_RoBd�] x dBegW r X k x k�_bae r pg_bd�j�f�egf(_��"X d�]}egW^h4_íú Ç ' TS�_Regf r a  $pgp r p\dBe?� ÄB���  �pqp r p�dBe�� >y �����

Z�w à m�X k�egd 9 ]`_

−0.6

0

0.6

−π 0 π

−0.053874

Z�w�U Ã

−0.6

0

0.6

−π 0 π

−0.049417

−0.6

0

0.6

−π 0 π

−0.0087588

w���U Ã

−0.6

0

0.6

−π 0 π

−0.049146

−0.6

0

0.6

−π 0 π

−0.0087353

|B{

� d 9 ]`_ à T Ç ��¨Ed�©¦ �pgp r p\�!W`o�_bX 9;: p x X X W^X � tFr!x pgegf r pqa _Rp\X r X k�egdB����_Rpq_ba,h4_Regf r a k x kgW^X(�¡egf(_p r;r e�[ r pqe�pqd�W`e\e�_bj�f X W^� x _�T ¿nr e�_4egf dBe�egf(_�o�_RpqegW^jRd�]�kgjRd�]`_bk�dBpg_¡egf(_¡kgd�h4_4W^X~d�]^]KjRd�k�_bk�d�X aegf dBe�Z�w��NW^k�X r e�k�egd 9 ]^_ x X�egW^]G� ª y�� �!à d�X�a�·n¸��¥WYk�X r e�k�egd 9 ]`_ x X�egW^]G� ª Õ�Ä �(T*� W^kegf(_\X x h 9 _Rp r�t7tEx X j�egW r X4_Ro�d�] x dBegW r X k x k�_ba4e r pg_bd�j�f�egf _¦�"X d�]%egW^hi_�úg Ç ' T � f(_\pg_b]^dBegW`o�_] r kgk J�� + b ø à ]�� � -� + ø à ø�?ø ]�� � - �Þy Q W^k¦kqf r ¢ X,W^Xcegf(_ x [ [}_Rp¦pqW^�!f�e°��f d�X�aNj r pqX(_Rp r�t egf(_�_Rpgp r p�[�] r egkRT

S,_Regf r a  �pgp r pndBe�� ÕB���  �pgp r p�dBe�� >y ÇB���

Znwv� m�X k�egd 9 ]`_

−0.25

0

0.25

−π 0 π

−0.0004525

·\¸�� m�X k�egd 9 ]`_

−0.25

0

0.25

−π 0 π

−0.0051758

ÕB�

� d 9 ]`_ à T Ç ��¨ 9 ©� �pgp r p$�!W`o�_bX 9;: p x X X WYX(� tFr!x pgegf r pqa(_Rp$kgegdB����_Rpg_bach4_Regf r a k x kgWYX(��egf(_�p r;r e[ r pge�pqd�W`e¦e�_bj�f X W^� x _�T ¿nr e�_�egf dBenegf(_�o�_RpqegW^jRd�]8kqjRd�]`_bk\dBpg_�egf(_�kqd�h4_�W^X,d�]^]�jRd�k�_bkbT�� WYk�egf(_X x h 9 _Rp r�t�tEx X j�egW r X�_Ro�d�] x dBegW r X k x kg_ba�e r pq_bd�jqf�egf _i�"X d�]�egW^h4_�úX Ç ' T � f(_�pg_b]^dBegW`o�_] r kgk J�� + b ø à ]�� � -� + ø à ø�?ø ]�� � - �Þy Q W^k¦kqf r ¢ X,W^Xcegf(_ x [ [}_Rp¦pqW^�!f�e°��f d�X�aNj r pqX(_Rp r�t egf(_�_Rpgp r p�[�] r egkRT

S�_Regf r a  �pqp r p\dBe�� ÕB���  �pgp r p�dBem� y ÇB���

Z�w�U;�

−0.25

0

0.25

−π 0 π

−0.0010809

−0.25

0

0.25

−π 0 π

−3.5431e−05

w���U;�

−0.25

0

0.25

−π 0 π

−0.0010738

−0.25

0

0.25

−π 0 π

−3.537e−05

·\¸�U;�

−0.25

0

0.25

−π 0 π

4.4409e−16

−0.25

0

0.25

−π 0 π

5.9952e−15

Õ y

� d 9 ]`_ à TV|��c $pgp r p¡�!W`o�_bX 9;: p x X X W^X(��k�_Ro�_bX�egf r pqa(_Rpih4_Regf r a k x kgWYX(�,egf(_cp r;r e4[ r pge�pqd�W`ee�_bjqf�X W^� x _�T¥Z�w�|�WYk�X r e�kgegd 9 ]`_ x X�egW^]�� ª y �!Ã�Õ �(T ¿nr e�_segf�dBe�o�_RpgegW^jRd�]�kgjRd�]`_bk�a W��}_Rp 9;:y ��� T � f(_�pq_b]^dBegW`o�_c] r kgk J�� + b ø à ]�� � -� + ø à ø�?ø ]�� � - �Êy Q WYk�kgf r ¢ X�W^X�egf _ x [ [}_Rp�pqW`�!f�e°��f d�X a�j r p�X(_Rp r�tegf(_�_Rpgp r p�[�] r egkbT�� W^k�egf(_�X x h 9 _Rp r�t³tEx X j�egW r Xs_Ro�d�] x dBegW r X k x k�_base r pg_bd�jqf¥egf(_n�"X d�]"egW^h4_úg Ç ' TS�_Regf r a  �pqp r p�dBe�� �B�����  �pqp r p�dBe�� ­� �����

Z�w�| m�X k�egd 9 ]`_ m�X k�egd 9 ]`_

Z�w�U |

−7

0

7

−π 0 π

−1.0724e−07× 10−6

−7

0

7

−π 0 π

−8.7562e−10× 10−8

� d 9 ]`_ à T Õ �� �pgp r ps�!W`o�_bX 9;: p x X�X W^X(�ª_bW`�!f�egf r pqa(_Rpch4_Regf r a k x kgW^X(��egf(_Hp r�r e¥[ r pge�pqd�W`ee�_bjqf�X W^� x _�T¥Z�w Õ WYk�X r e�kgegd 9 ]`_ x X�egW^]�� ª �B� � Ä�Ä T ¿nr e�_segf�dBe�o�_RpgegW^jRd�]�kgjRd�]`_bk�a W��}_Rp 9;:�B����� T � f(_¡pg_b]^dBegW^o�_¡] r kgk J�� + b ø à ]�� � -� + ø à ø�?ø ]�� � - �Êy Q W^k�kgf r ¢ XªW^X~egf(_ x [ [}_Rp�pqW`�!f�e°��f d�X aHj r pqX(_Rp r�tegf(_�_Rpgp r p�[�] r egkRT

S�_Regf r a  �pqp r p�dBe�� ÃB�����  �pqp r p�dBe�� ÇB�����

Z�w Õ m�X k�egd 9 ]`_ m�X k�egd 9 ]`_

Z�w�U Õ

−6

0

6

−π 0 π

−1.3782e−10× 10−8

−3

0

3

−π 0 π

−4.9727e−13× 10−10

��

ì�ë -@- Î )���#(¼�5$*B��)��$*

�ª_�f dbo�_�WYX�e�p r a x j�_back�egdB����_Rpq_ba�egW^h4_�W^X�e�_R��pqdBe r pqk tFr p�k r ]`o%W^X(�¡k : k�e�_bhik r�t ¢ do�__b� x dBegW r X kRT¦�ª_��"X a�egf dBe\egf(_�k�egdB����_Rpg_ba~o�_RpqkgW r X k r�t Z�a d�hik���wvd�kqf t@r pqegf,d�X a 9 d�jg¤ ¢ dBp�a ka W��}_Rpg_bX�egW^dBegW r Xihi_Regf r a�k$f do�_�kgW^�!X W��"jRd�X�eg] : kghid�]^]`_Rp�] r jRd�]�e�p x X jRdBegW r Xi_Rpgp r p�k$d�X a���pg_bdBe�_Rp¯gU%w�k�egf d�X�egf _bW`p�X r X k�egdB����_Rpq_ba�j r!x X�e�_Rpg[�dBpqegkRT�¯°X�d�a a W^egW r Xzl³k�egdB����_Rpg_ba�kgj�f(_bh4_bk�dBpg_�X rh r pg_ca W�«¥j x ]`e�e r W^h4["]`_bh4_bX�e�egf d�XÉX r X kgegdB����_Rpg_ba¶kgjqf _bh4_bkRTH�ª_�f dbo�_Nd�]^k r j r X kqW^a(_Rpg_bat pg_R_\[�dBp�d�h4_Re�_Rpvh x ]`egWYk�e�_R[sh4_Regf r a k$egf dBe�d�]Y] r ¢ t@r pvd�a a W`egW r X d�] W^h4[�p r o�_bh4_bX�e�WYXiegf(_n¯�U%w�TU;egdB����_Rpg_ba¥· x X(��_ÝÙ�¸ x e�egd�h4_Regf r a k�d�]^k r kgf r ¢ [ p r hiWYk�_ t@r p�e�pg_bdBegW^X(��f : [}_Rp 9}r ]^W^jvk : kge�_bhikRT�ª_�f dbo�_�W^X�e�p r a x j�_baid�] r ¢ ��kge r pqdB��_ tFr!x pgegf r pqa(_Rp�h4_Regf r aiegf dBevf d�k�e ¢ W^j�_negf(_�¯�U%w¶d�X�a�dh x jqf�kghid�]^]`_Rp�_Rpgp r p8j r X�k�egd�X�e8egf d�X�egf _�jR]^d�kgkqW^jRd�] tFr!x pgegf r pqa _Rp8· x X(��_ÝÙ�¸ x e�egdnh4_Regf r a�d�X ad¡egf W`p�a r pqa _Rp�h4_Regf r a ¢ W`egf ÕB� M ]^dBpg��_Rp\¯�U%w­d�X a¥� à MÂkqhid�]^]"_Rpgp r p\j r X kgegd�X�e¦egf d�XN·n¸ à T� d 9 ]`_ à TÖ{ªk x hihidBpqW`¾R_bk r!x p�pg_bk x ]`egk4j r X�j�_RpqX W^X(�ªk�egdB����_Rpq_ba tFr!x pgegf r pqa _Rpih4_Regf r a k4d�X aj r h4[�dBpq_bknegf _bh e r k r hi_�_�§%[�]^W^jRW^e\X r X k�egdB����_Rpq_ba t@r!x pqegf r pqa _Rp�hi_Regf r a�kRTn �§;[}_RpqW^hi_bX�egd�]pg_bk x ]`egk�o�_RpqW tF: egf(_ t _bd�kgW 9 W^]^W`e :Nr�t egf(_bk�_iX(_ ¢ hi_Regf r a�kRT¡¯-Xªd�a a�W`egW r Xzl ¢ _if dbo�_s[ pg_bk�_bX�e�_bak�_Ro�_Rpqd�]�egf(_ r pg_RegW^jRd�]�j r X kgW^a(_Rp�dBegW r X k�j r X j�_Rp�X W^X(�4k�egdB����_Rpg_ba�egW^h4_�WYX�e�_R��pqdBe r p�kRT

Õ�Ã

� d 9 ]`_ à TÖ{;� uvr h4["dBpqW^k r X r�tztFr!x pgegf r pqa(_Rp$egWYh4_�W^X�e�_R��pqdBe r pqkR��X r X�k�egdB����_Rpg_baso;kRT�k�egdB����_Rpq_bazT� f(_�X r pqhid�]^W`¾R_ba4] r jRd�]%e�p x X jRdBegW r X4_Rpgp r p$W^k9>¤A ) ) F ) H ¨�� ©�l ¢ f _Rpg_?>ÁW^k�egf _�X r pqhid�]^W^¾R_ba¡_Rpgp r pj r X k�egd�X�eRT

¿nr X k�egdB����_Rpg_ba U;egdB����_Rpg_ba¿nr pqhid�]^W`¾R_ba ¿\r p�hid�]^W`¾R_ba ¿nr pqhid�]^W^¾R_ba ¿nr pqhid�]^W^¾R_ba

¿ d�h4_ U;e�_bX jRWY] ¯gU%w _Rpgp r p ¿ d�h4_ U;e�_bX�jRW^] ¯�U%w _Rpgp r pj r X�k�egd�X�e j r X k�egd�X�e

¨Ewv���¥W^h4[�]^WYjRW`e�© w���U;�

ty �µ����� Ä ���µ�!à | �

Znwv�

tttt Ä ��� � ÃB� Ä ���Öà � Õ�Ç Znw�U;�

tttt Ä>y �ÖÃ�Ã�Ã Ä ���µ�!Ã�Õ |

·n¸��t Ä ��� | � | Ä �Y� y Ã�Ã�à ·\¸�U;�

t Ä>y � � ��Ä Ä ��� y Ã�Ã�Ã

Î �$/#,$��� � �Î )���#(¼�5�*���)��$*

¯-X¥egf WYk¦a W^kgk�_RpqegdBegW r Xzl ¢ _�f do�_�W^X�o�_bk�egW`�!dBe�_ba�f�W`�!f%� r pqa(_Rpv�"X�W`e�_�a W��}_Rpg_bX j�_�h4_Regf%�r a knd�X�a,k�egdB����_Rpg_baHegWYh4_�W^X�e�_R��pqdBe r pqk tFr p�]^W^X(_bdBp ¢ do�_�_b� x dBegW r X�kRT\Z j r h4[ r kgW^e�_�h4_Regf r aj r h 9 W^X(_bk�dcf W`�!f�] : d�jRj x pqdBe�_�¨F_�T±�(T 9 ] r jg¤�[�k�_ x a r k�[}_bj�e�pqd�]@©\h4_Regf r a r X 97r!x X a dBpqW`_bknd�X aX(_bdBp�W^X�e�_Rp t d�j�_bk ¢ W`egf�d�] r ¢ j r h4[ x egdBegW r X d�]}j r k�e�h4_Regf r a x k�_ba r Xcd 9 d�jg¤;��p r!x X as��pqW^a r Xegf(_spg_bk�e r�t egf _sj r h4[ x egdBegW r X d�]$a r hid�W^XzTc�ª_¥_bX�o%W^kgW r X�egf(_sh4_Regf r a k�a W^kgj x kgk�_ba�W^X�egf W^k[�dB[}_Rp 9 _bW^X(� x k�_ba t@r p\k x jqf�d 9 d�jg¤;��p r!x X a���pqW^azT

�ª_��"X acegf�dBe\j r h 9 W^X W^X(�è f W`�!f r pqa(_Rp�k r�t d�jRj x pqd�j : lè W^h4[�]^WYjRW`egX(_bkgkRl;d�X aè k�egdB����_RpqW^X(�

]`_bd�a k�e r d�jR]Yd�kgk r�t j r h4[ x egdBegW r X d�]^] : o�_Rp : j r k�e°��_��7_bj�egW^o�_c�"X W`e�_¥a W��}_Rpg_bX j�_ckgjqf(_bhi_bk tFr p_b� x W^k�[�d�j�_ba u dBpge�_bkgWYd�XN��pqW^a kbTvZ�k�egf(_bW^p r pqa(_Rp�k r�t d�jRj x pqd�j : WYX j�pg_bd�k�_�l"egf(_bk�_�kqjqf(_bh4_bk�dB[(�[ p r d�j�f�egf _ ¢ _b]^]���¤%X r ¢ X�k�[}_bj�e�pqd�]�d�jRj x p�d�j :�r�t [}_RpqW r a W^jBlb_�§%[�]^W^jRW^ez[�k�_ x a r kg[7_bj�e�p�d�]!kgjqf _bh4_bkRT�Áf(_bX ¢ _�j r h 9 W^X _�egf W^k ¢ W`egfNegf(_�W^a(_bd r�t�r o�_Rpq]^dB[ ["W^X(��k x 9 a r hid�W^X k�¨Ed�k�W^X,dsj r h4[ r kgW`e�_h4_Regf r a"©�l;egf(_�pg_b]^dBegW`o�_b] : X�dBpgp r ¢ k�e�_bX jRWY] ¢ W^a egf k$hidB¤�_�egf(_�kgjqf _bh4_bk ¢ _b]^]`��k x W`e�_ba t@r p�j r h¡�[ x egdBegW r X k�WYX�h4_ba WYd ¢ W`egfsj x pgo%W^]^W^X _bdBp$hidBe�_RpqW^d�]7W^X�e�_Rp t d�j�_bkRT � f(_�kgjqf _bh4_bk�jRd�X 9 _�dB[ [�]^W`_bae r h r k�e�]YW^X(_bdBp ¢ dbo�_���e : [}_��$�� �k r�t¦9 p r d�a�W^X�e�_Rpg_bk�eRT�¯°X�egf _�[�dBpgegWYj x ]^dBp�dB[ ["]^W^jRdBegW r X r�tegW^h4_���a r hid�W^X�j r hi[ x egdBegW r X d�]�_b]`_bj�e�p r h�dB�!X(_RegW^jRkN¨Ed�]^k r ¤;X r ¢ X�d�k��6� � ��©�lKegf(_¥jR]Yd�kgkgW^jRd�]

Õ�Ä

²�_R_ikgj�f(_bh4_ x k�_bk r X�] : egf(_i]^d�kge r�t egf(_¡egf(pg_R_if W^�!f ]^W`�!f�e�_ba�j r X�j�_R[ egkRT��ª_¡�"X a~egf dBe�hid��Ì r p�W^h4[ p r o�_bh4_bX�egk�W^Xªd�jRj x p�d�j : d�X�aH_�«sjRW`_bX j : jRd�X 9 _id�jqf W^_Ro�_ba 9;: d�]^k r WYX j r pg[ r pqdBegW^X(�W^h4["]^W^jRW`egX(_bkqk�d�X a,f W`�!f r pqa(_Rp�k r�t d�jRj x pqd�j : T

�ª_4f dbo�_4d�]^k r W^X�e�p r a x j�_ba�k�egdB����_Rpg_baªegW^hi_�W^X�e�_R��pqdBe r pqk tFr p�k r ]`o%W^X(�sk : k�e�_bh�k r�t]^W^X _bdBp ¢ dbo�_�_b� x dBegW r X�kRT��ª_��"X asegf dBe¦egf(_�k�egdB����_Rpg_ba�o�_RpqkgW r X k r�t Zna�d�hik°��w�d�kgf tFr pgegfcd�X a9 d�jq¤ ¢ dBpqa k�a W��}_Rpg_bX�egW^dBegW r X�h4_Regf r a knf dbo�_�kgW`�!X W`�"jRd�X�eg] : kgh�d�]^]`_Rp\] r jRd�]³e�p x X jRdBegW r XN_Rpqp r pqkd�X aÊ��pg_bdBe�_Rp¥WYhidB�!W^X dBp : k�egd 9 WY]^W`e :�9}r!x X a dBp�W`_bk¡egf d�XÞegf _bW`p�X r X kgegdB����_Rpg_baÅj r!x X�e�_Rpg["dBpgegkRT¯°XÊd�a a W^egW r Xzl�kgegdB����_Rpg_baÁkgjqf(_bhi_bksdBpg_~X r h r pq_,a W�«sj x ]`e4e r W^hi[�]`_bh4_bX�e4egf d�XÊX r X k�egdB�B���_Rpg_baMkgj�f(_bh4_bkRT �ª_�f�dbo�_�d�]^k r j r X kgWYa(_Rpg_ba t pq_R_�[�dBp�d�h4_Re�_Rp�h x ]`egW^k�e�_R[Áh4_Regf r a k¥egf dBed�]^] r ¢ t@r pid�a�a W`egW r X d�]�W^hi[ p r o�_bhi_bX�eiW^X�egf(_�WYhidB�!W^X dBp : k�egd 9 W^]^W^e :�9}r!x X�a dBp : TÉU%egdB����_Rpg_ba· x X(��_ÝÙ�¸ x e�egdihi_Regf r a�k�d�]^k r kqf r ¢ [ p r hiW^kg_ tFr p\e�pq_bdBegW^X(��f : [}_Rp 9}r ]^WYjnk : k�e�_bhikbT$�ª_�f�dbo�_W^X�e�p r a x j�_ba­d�] r ¢ ��k�e r p�dB��_ t@r!x pqegf r pqa _Rpchi_Regf r a­egf dBeNf d�k¥e ¢ W^j�_Hegf(_ªW^hidB�!W^X�dBp : k�egd��9 W^]YW`e :�97r!x X a dBp : d�X a�d�h x jqf�kghid�]^]`_Rp�_Rpgp r p�j r X�k�egd�X�e�egf d�X�egf(_sjR]^d�kqkgW^jRd�] tFr!x pgegf r pqa(_Rp· x X(��_ÝÙ�¸ x e�egd�h4_Regf r asd�X asd�egf W^pqa r pqa(_Rp�h4_Regf r a ¢ W`egf ÕB� M ]^dBpg��_Rp�W^hidB�!W^X�dBp : kgegd 9 W^]^W`e :9}r!x X a dBp : d�X a�� à M0kghid�]Y]³_Rpgp r p�j r X k�egd�X�e�egf d�X~·\¸ à Tn¯-X~d�a a W`egW r Xzl ¢ _�f�dbo�_¡[ pg_bk�_bX�e�_bak�_Ro�_Rpqd�]}egf _ r pg_RegW^jRd�]³j r X kqW^a(_RpqdBegW r X�kvj r X�j�_RpqX W^X(�4k�egdB����_Rpq_baNegW^h4_�W^X�e�_R��pqdBe r pqkRl"W^X jR] x a�W^X(��d��_bX(_Rpqd�]YW`¾bdBegW r X r�t ��d�f ]^� x W^k�eR´µk¦�6W`p�k�e\U;egd 9 W^]^W^e : w�dBpgp�W`_Rp�e r k�egdB����_Rpq_ba,kgj�f(_bh4_bkRT

pN��"�¼���)³�³�!/8,v�;7

2�y 3 ²¡TBZn��Z�S�l �nW`�!f�] : d�jRj x pqdBe�_ j r h4[�d�j�e W^h4["]^W^jRW`e h4_Regf r a k d�X a 9}r!x X a dBp : j r X a�W`egW r X k�ll T uvr h4[ x eRT �$f : kRT`l � �H¨°yb{!|�|�©�l"[�[³Tzy � � ��� T

2 �43 ¸iT¬Z � ¸�¯ ¿ U � ¿ l Z�X ¯°X�e�p r a x j�egW r X e r ¿�x h4_RpqWYjRd�] Z�X d�] : kgW^k¬l�l r f X��ÁW^]`_ : l ¿ _ ¢ ² r pg¤7lyb{ Õ {;T

2 Ã43 ·�Tw�mn·n��  ¿ d�X a÷l(T�%Zn¯-·n vU7l ¿�x h4_Rp�W^jRd�] Z�X d�] : kgW^kRl � - 9 _bazTElb��� U���¸�  ¿n� lw r k�e r Xzlyb{ Õ {;T

2 � 3 £$T u ��£�£8Z � ÍKl � f(_ ¿nx h4_RpqW^jRd�] � pg_bdBegh4_bX�e r�t ��W��}_Rpg_bX�egWYd�]  �� x dBegW r X kBl6U%[ pqW^X(��_Rpg�õ _Rp�]^dB�(l�wv_Rpq]^W^X³l}yb{ ÇB� T

2 Ä43 �¡T���Zn��£� �m\¯gU � l uvr X�o�_Rpg��_bX j�_ d�X a k�egd 9 WY]^W`e : W^X egf(_ X x h4_RpqW^jRd�] W^X�e�_R��pqdBegW r X r�tr p�a W^X dBp : a W��}_Rpg_bX�egWYd�] _b� x dBegW r X k�l;S~dBegfzT7U%jRd�X�azT`l(��¨°yb{ Ä�Ç ©�l7[ [³T Ã�à � Ä�à T

2 Ç43 � T�Z�Tv��·�¯gU u ��£�£ d�X aÊw�T��8��· ¿ w� $·���l Z 9 ] r jq¤ ["k�_ x a r k�[}_bj�e�pqd�] h4_Regf r a tFr pS~d�§ ¢ _b]^]�´µk _b� x dBegW r X kR� ¯�T ��X(_���a W^hi_bX kgW r X d�]�l a W^kqj r X�egW^X x(r!x k���j r _�«sjRW^_bX�egk jRd�kg_ lTl(Tu�r h4[ x eRT ��f : kRT`l³y�� � ¨°yb{�{ Õ ©�l7[ [³TzyÝ�qyb{;T

2µ| 3 � T�Z�T���·�¯gU u ��£8£Âd�X a>wnT��K��· ¿ w� $·���l w�] r jg¤ [�k�_ x a r kg[7_bj�e�p�d�] hi_Regf r a�k tFr pS~d�§ ¢ _b]^]�´µk _b� x dBegW r X kb� ¯q¯�T � ¢ r ��a�W^h4_bX kgW r X d�]�l a W^kgj r X�egW^X x(r!x k°��j r _�«sjRW`_bX�egk jRd�kg_�l�e rdB[�[7_bdBpnW^X,U;¯°ZnS l(T"U%jRW�T uvr h4[ x eRT

2 Õ43 w�TN�8��· ¿ w� �·¦�¡l ��X d � r!x pqW`_Rp hi_Regf r a tFr p egf(_ W^X�e�_R��pqdBegW r X r�t f : [}_Rp 9}r ]^WYj_b� x dBegW r X�kRl"U;¯°ZnS l(T ¿�x h4_RpT ZnX d�]�T`l³y � ¨°yb{!| Ä ©�l"[�[³T ÄB� {¬� Ä���Õ T

2±{ 3 w�TK�8��· ¿ w� $·���l ��W`�!f%� r pqa(_Rp �"X W`e�_ a W��}_Rpg_bX j�_bk d�X�a egf(_ [�k�_ x a r k�[}_bj�e�pqd�] h4_Regf r ar X k�egdB����_Rpg_ba ��pqW^a kl(U;¯°Z�S l T ¿nx hNT ZnX�d�]�T`l � |N¨°yb{�{ � ©�l7[ [³T�{ � �B�Æ{%y Õ T

2�y �<3 w�T¦�8��· ¿ w� �·¦�¡l Z �$pqd�j�egW^jRd�] � x WYa(_ e r ��k�_ x a r kg[7_bj�e�p�d�] S�_Regf r a k�l u d�h 9 pqW^a(��_m�X W`o�_Rp�kgW`e : ��pg_bkqkRl u d�h 9 pqW^a ��_�l%m�¸4l�yb{�{ Ç T

2�y�y 3 w�T(�8��· ¿ w� �·¦�¡l u d�]^j x ]^dBegW r X r�t ¢ _bW`�!f�egk W^X �7X W`e�_ a�W��7_Rpq_bX j�_ tFr pqh x ]^d�k�l!U;¯°ZnS ·�_��o%W`_ ¢ l(� � lK¨°yb{�{ Õ ©�l"[ [�T Ç�Õ�Ä � Ç {%yBT

2�y �43 ¯ÝTVU7Tz��·\Z���U%� �  �² ¿ d�X a�¯�TµS�T}·�²�Í}�n¯-¸il6¨EZ�]^d�X(l�_��}pg_ : lz_bazTV© � d 9 ]^_ r�t ¯°X�e�_R��p�d�]^kRlU%_RpqW`_bkRl d�X a �$p r a x j�egkRl Ä - 9 _ba³T�l!ZnjRd�a _bhiW^j���pq_bkgkRl(¯°X jBT`l7U%d�X���W`_R� r l u Z�l8yb{�{��(T

Õ |

2�y Ã43  \T���Z\¯°·\ �·�l U7Tµ�KT ¿�� ·�U(  ��� l;d�X a¥�¡T��HZ ¿�¿  $·�l U r ]^o;W^X � ��pqa W^X�dBp : ��W��}_Rpg_bX�egW^d�] �� x dBegW r X k ¯Ýl�U;[ pqWYX(��_Rp�� õ _Rpq]^dB�(l(wv_Rpq]^WYXzlzyb{�{%yBT

2�y�� 3 ·�TvU7Tv�\¯°·�U u ��l ��W`�!f(_Rpg� r pqa(_Rp d�jRj x pqdBe�_ a�W��7_Rpq_bX j�_ k r ] x egW r X k r�t ®"x WYa h4_bjqf�d�X W^jRk[�p r�9 ]`_bhik 9;: d j r h4[�d�j�e a W`�7_Rpg_bX�jRW^X(� e�_bjqf X WY� x _�lUl(T u�r h4[ x eRT��$f : kRT`l�yb{ʨ°yb{!| Ä ©�l[�[³T { � �qy � {;T

2�y Ä43 ·�T\U7T¦�\¯°·�U u ��l �nW^�!f%� r pqa(_Rp dB[ [ p r §(W^hidBegW r X k WYX ®"x WYa h4_bj�f d�X W^jRk�l õ ¸�¯�£�_bj�e x pg_U%_RpqW`_bk�yb{ Õ�à � � �(l õ r X,¸�dBp�hid�Xc¯-X�k�eRT t@r p��6] x W^ac� : X³T`l�wvp x kgk�_b]YkRlzyb{ Õ�à T

2�y Ç43 �¡T ����£8w� $·���l uvr hi[ x egdBegW r X d�] d�kg[7_bj�egk r�t egf(_ jqf r WYj�_ r�t r [7_Rp�dBe r p d�X akqd�h4[�]^W^X � W^X�e�_RpgoBd�] t@r p X x h4_Rp�W^jRd�] a W��}_Rpg_bX�egWYdBegW r X W^X ]^dBpg��_���kgjRd�]^_ kgW^h x ]^dBegW r X r�t ¢ do�_["f(_bX r h4_bX d%l"��_ r [�f : kRT��$p r k�[}_bj�egW^X(�(l Ã�Ä ¨°yb{ Õ |�©�l"[ [�T Ç�� {¬� Ç�Ä�Ä T

2�y| 3 Z�TH¯�U( $·\£8 vU7l Z �6W`p�k�e uvr!x pqk�_ W^X egf(_ ¿�x h4_RpqWYjRd�] Z�X d�] : kgW^k r�t ��W��}_Rpg_bX�egW^d�] �� x dBegW r X kRl u d�h 9 pqWYa(��_�mnX W^o�_RpqkgW`e : �$pg_bkgkRl u d�h 9 pqWYa(��_�lzyb{�{ Ç T

2�y Õ43 ·�Tõl! $£ � U u � d�X a���T ¿   õ Z ¿ £�¯ ¿�¿ Z�l U;egd 9 W^]^W`e : r�t _�§%[�]^W^jRW`e egW^h4_ a W^kgj�pq_RegW`¾bdBegW r X ktFr p k r ]^o;W^X � WYX W`egW^d�] oBd�] x _ [ p r�9 ]^_bhikBl ¿nx h4_RpbT S~dBegfzT`l à |N¨°yb{ Õ y©�l7[ [³T Ç yÝ�Æ{%yBT

2�yb{ 3 ·�T l! $£ � U u �'d�X aÊ��T ¿   õ Z ¿ £�¯ ¿�¿ Z�l ��d�f ]^� x W^k�eR´µk ��p�k�e 9 dBpgpqW`_Rp tFr p h x ]`egW^k�egdB��_h x ]`egWYk�e�_R[ t@r p�h x ]Yd�kbl(wv¯ � l � �~¨°yb{ Õ ��©�l"[ [�T Ä�Ã�Õ � Ä�Ä�Ä T

2 �B�<3 S�T(¸�¯ ¿ �� $£8Z ¿ l%Z�T(¸�Z�S� �£�l(Z ¿ � �KT U���mnZ�ͳÍ} �·���l ��X egf(_ j r X k�e�p x j�egW r X d�X a_�«¥jRW`_bX j : r�t k�egdB����_Rpq_ba X x h4_RpqW^jRd�] a W`�7_Rpg_bX�egW^dBe r pqk t@r p egf(_ ¢ dbo�_ _b� x dBegW r X�l¦��_ r �["f : kgW^jRkRl Ä�Ä ¨°yb{�{ � ©�l7[ [³T³y � |�qy�y � T

2 � y 3 Í6T ¸����}Z�£�l ¿�x h4_Rp�W^jRd�] ZnX�d�] : kqW^k�¨ � ( ^  $azTV©�l u f�dB[�hid�XNd�X a���d�]^]�l £ r X a r Xzl³yb{ Ç yBT2 ���43 ¸iT�U7TK¸�m ¿ ÍÅZ ¿ �0·�TÅl(T6£�m�w�wv �·�U7l � f(_ �6W^X W`e�_ ��W��7_Rpq_bX j�_ � W^h4_ � r hid�WYX tFr p

 �]`_bj�e�p r hidB�!X _RegW^jRkbl u · u �$pg_bkgkRl w r jRd�·ndBe r Xzl��6£�l�yb{�{ à T2 ��Ã43 U}Tµ¸4T7£8 $£8 �l uvr h4[�d�j�e �"X�W`e�_ a�W��7_Rpq_bX j�_ kqjqf(_bh4_bk ¢ W`egf k�[}_bj�e�pqd�]���]^W`¤�_ pg_bk r ] x egW r X�l�l(T

u�r h4[ x eRT ��f : kRT`l³y �!à ¨°yb{�{ � ©�l7[ [³Tzy Ç ��� � T2 � � 3 ·�T;S�¯ ���   � l%��T;����£8w� $·���l(w�T;Z�· ¿ U �   ¿ l%Z ¿ � £$T;Z�S~m ¿ ��U%  ¿ l � d�k�e �"X W`e�_

a�W��7_Rpq_bX j�_ h r a(_b]^W^X � r�t egf _ à ��� _b]Yd�k�egW^j ¢ dbo�_ _b� x dBegW r X�l�U r jRW`_Re :¶r�t  �§;["] r pqdBegW r X��_ r [�f : kgW^jRk\ �§%[�d�X a(_baNZ 9 k�e�pqd�j�egkbl�y�¨°yb{ Õ�Õ ©�l7[ [³T³y ÃB�!Õ �qy à y�yBT

2 ��Ä43 U}T�Z�T ��·�U Í}Z\� Z ¿ � S�T ¯gU%·\Z� $£�¯�l ¿nx h4_RpqW^jRd�] kgW^h x ]^dBegW r X r�t o;WYkgj r!x kWYX j r h4[ pg_bkqkgW 9 ]`_ ®�r ¢ kl(Z�X XzT(·�_Ro7T��6] x W^acS�_bjqfzT`l Ç ¨°yb{!|¬��©�l7[ [³T ��Õ yÝ� à y Õ T

2 ��Ç43 l TzU � �� $·>d�X aH·�T7w�m�£³¯°·�U u ��l ¯-X�e�p r a x j�egW r X e r ¿nx hi_RpqW^jRd�] ZnX d�] : kgWYkl7U%[ pqW^X(��_Rpg�õ _Rp�]^dB�(l ¿ _ ¢ ² r pg¤7l�yb{ ÕB� T

2 � | 3 Z�T � Z��6£K� õ  \l u�r h4[ x egdBegW r X�d�]  $]^_bj�e�p r a : X d�h�W^jRkR� � f(_ �6W^X W`e�_�����W��}_Rpg_bX j�_� W^h4_���� r hid�W^X S�_Regf r a8l%Znpge�_bjqf�� r!x kg_�l�w r k�e r Xzl8yb{�{ Ä T

2 ��Õ43 ·�T õ ¯ u � ¿   õ   � U%¸�²ÔZ ¿ � l(T�w�T�w����­£8 vU7l � r!x pqW`_Rp Z�X d�] : kgW^k r�t ¿nx h4_RpqW^jRd�]Zn[ [ p r §(W^hidBegW r X k r�t � : [}_Rp 9}r ]^WYj  $� x dBegW r X�k¬l6U;e x a W`_bk�W^X�Z\[�[�]^W`_ba�S�dBegf _bhidBegW^jRk Ä lU%¯-Z�S�l ��f W^]^d�a _b]`[�f W^d%l;�}Z�l�yb{ Õ�� T

Õ�Õ

2 � { 3 ¸iTVU7T¦²� $ �l ¿nx hi_RpqW^jRd�] k r ] x egW r X r�t W^X�W`egW^d�] 9}r!x X a dBp : oBd�] x _ [ p r�9 ]`_bhik WYX�o r ]`o%W^X(�S~d�§ ¢ _b]^]�´µk _b� x dBegW r X k WYX W^k r e�p r [�WYj h4_ba WYd"l}¯° $ �  � pqd�X kbT8Z�X�e�_bX X�d�k�d�X�a��$p r [�dB�!d��egW r Xzl³y���¨°yb{ Ç�Ç ©�l7[ [³T ÃB�!� � ÃB� |�T

Õ {

æ���� ð�� ïM� Ï ð þZ�T� �§%[�]^d�X dBegW r X r�t egf(_��Kd�avé_�d�]`� r pqW`egf�h �!W`o�_bX�W^X,U;_bj�egW r X � T Ãw�T���_RpqW`oBdBegW r X r�t egf(_�]^WYhiW`ev_�§;[ pq_bkgkgW r X k¦WYX � d 9 ]^_ � T Õu T uvr X�o�_RpqkgW r X k 9 _Re ¢ _R_bX,¸ r ["d�]�´µk��6� j r _�«¥jRW`_bX�egknd�X aNegf r kg_��!W`o�_bX�W^X u f dB[ e�_Rp ���T7U;egdB����_Rpg_ba�a W��}_Rpg_bX�egW^dBegW r XNhidBe�pqW`§ �T ��_RpqW^o�dBegW r X r�t _b� x dBegW r X�¨ � TV|�©�vT���_��"X W^X ��egf _�] r jRd�]}e�p x X jRdBegW r X�_Rpgp r p��T ¿nr X k�egdB����_Rpq_ba t pg_R_�[�dBpqd�hi_Re�_Rpnh4_Regf r a k��T���p r;r�t6r�t egf(_�pg_bk x ]`e tFr!x X aNW^X�U%_bj�egW r X à T Ç T^y�j r X j�_RpqX WYX(�i¯gU%w�k r�t Znw�l�Z�w�U7l"d�X�a�ZnSh4_Regf r a k¯ÝT ��p r;r�t8r�t egf(_�kgegdB����_Rpg_ba�d�X�d�] r � x _ r�t ��d�f ]^� x W^k�eR´µkv�"pqk�e 9 dBpgpqW^_Rp

� f(_¥d x egf r p¡hid�a(_ckgW`�!X W��7jRd�X�e�j r X�e�pqW 9�x egW r X k�e r Zn[ [}_bX a WYj�_bk u lK��l6 �l6�vlK��ld�X aɯÝT$U r h4_�j r X�e�pqW 9�x egW r X k ¢ _Rpg_Nhid�a _Ne r Z\[ [}_bX a�W�§���T�Zn[ [}_bX a W^j�_bk�Z d�X�a¶w ¢ _Rpg_tFr pqh x ]^dBe�_ba 9;: wv_bX(��e\� r pqX 9 _Rpg�(T

¹ ,=,¦���$ ��[j ¹

2©j�,�¼�/z�$/"�!��)�� )�+��!��� V /} ���É/}¼��³)³�����!�$½ ����18���>��� i ��#;�!��)�� ê6ë@ì

¯-X,egf W^kndB[ [}_bX a W�§}l ¢ _�_�§%[�]^d�W^X ¢ f : egf(_¡�6d�a�é_4d�]`� r pqW`egf h ¢ r pq¤;k�W^X�egf _�k�[}_bjRW^d�]jRd�k�_ª�!W`o�_bX W^X U;_bj�egW r X � T à T �ª_ tFr ]^] r ¢ egf _HdBpq� x h4_bX�e�W^X 2�y�y 3 l ¢ f W^j�f­jRd�X _bd�kgW^] :Þ9 _��_bX(_Rpqd�]YW`¾R_baNe rir egf(_Rpno�d�] x _bk r�t ¼ÄÓ ÑOÓ Å¥d�X a Ç}T

�ª_�k�_bdBpqj�f tFr p\j r _�«sjRW`_bX�egk « ! d�X aÒ. ! k r egf dBe« a ) + ¨��O� C"© 4 « �_) + ¨��}© 4 « Û ) + ¨�� 4 C"©Ä . a ) # �¶� Ã� C % 4 .4��) # �·� y

� C % 4 . Û ) # � 4 y� C % 4 . , ) # � 4 Ã

� C % ¨EZ�T^y©

9 _bj r h4_bk�_�§(d�j�e t@r p�d�k\f W`�!f¥a(_R��pg_R_�[ r ] : X r hiW^d�]^k�)�¨��}©�d�k�[ r kgkgW 9 ]`_�T�U x(9 k�egW^e x egW^X(�¨)�¨��}©�� !� ¥0 WYX�e r ¨EZ�T^y©��!W`o�_bk

S ��� « a � ] !� ¢9 4 « � 4 « Û � !� ¢9�� � !� ¥0Ä � .ca�� ] � - !� ¢9 4 . � � ] ý- !� ¢9 4 . Û � ý- !� ¢9 4 . , � � - !� ¢9 � � !� ¥0 ¨EZ�T � ©

¢ W`egfHegf _�X(_ ¢ � r d�] 9 _bWYX(�ce r hidB¤�_iegf(_�pg_b]^dBegW r Xªd�k�d�jRj x pqdBe�_sd�k�[ r kgkgW 9 ]^_�W t ] r jRd�]^] : _�§;�[�d�X a _ba¶dBp r!x X a � � ¨Ej t T?2 ��Õ<3 l�[ [³T � �B� ��Ç ©�TÁZ t e�_RpsjRd�X�j�_b]^]^W^X(�Hegf(_ t d�j�e r p)� !� ¥0 d�X ak x(9 k�egW`e x egW^X ��� !% �9 J%l ¢ _���_Re

J ý- ]YX�JC Ä .�a 4 . � J 4 . Û J Û 4 . , J ,« a 4 « �UJ 4 « Û J Û ¨EZ�T Ã ©

� f WYk�X(_R_ba�k�e r49 _�d�k¦d�jRj x p�dBe�_�d�k�[ r kgkgW 9 ]^_�¨Eh4_bd�X WYX(�4d�k�f W`�!f r pqa(_Rp�d�k¦[ r kgkqW 9 ]`_¬©�dBp r!x X a

{%y

J*>yBT��6d�a�é_�_�§;[�d�X�kgW r X r�t egf(_�]^_ t e°��f d�X�a�kgW^a _ndBp r!x X�a�J*>yne r�r pqa _Rp{2 à l �43 [ p r a x j�_bk�egf(_a(_bkgW^pg_baNj r _�«¥jRW`_bX�egkb�

J ý- ]^X�JC Ä yC ¨KJ��Êy© 4 ¨KJm�Åy© Û 4 � ÚÛ * a ¨KJ��Êy© ,y 4 ¨KJ��Åy© 4 �� a ¨KJ��Êy© Û

S � � ÚÛ * a �Ï� ,� a J 4 � ,� a J Û 4 � ÚÛ * a J , U �9S �� a 4 , �* a J 4 �� a J Û U ¨EZ�T±��©

� f(_�X r egdBegW r X,d 9}r o�_�W^Xcegf(_�a _bkgj�pqW`[ egW r X r�t egf(_ ¢ _bW`�!f�egk\d�]^� r pqW`egf h ¢ d�k\j�f r k�_bX�e r dB��pg_R_

¢ W`egfo2�y�y 3 T$¯Æe¦W^k¦X r e�_ba�egf(_Rpg_�egf dBe¦egf(_�_�§%[�]^W^jRW^evjRd�k�_�¨�Å ½��;©�jRd�X 9 _�f d�X a�]`_ba�_Ro�_bX�h r pg__bd�kgW^] :�9�: k x(9 k�egW`e x egW^X �nd � d : ] r p�_�§;["d�X kgW r X tFr p�egf(_��6d�a�é_�_�§;["d�X kgW r X x k�_ba¡f(_Rpq_�¨EkgW^X j�_�egf(_a(_bX r h�W^X dBe r p�W^XN¨EZ�T à ©6W^kKegf(_bX r X(_¬©�T ¿nr e�_�egf dBe�egf WYkKdBpq� x h4_bX�e�jRd�X4_bd�kgW^] :�9 _���_bX(_Rp�d�]^W`¾R_bae rir egf(_Rpno�d�] x _bk r�t ¼ÄÓ ÑOÓ Ç Ó d�X aÒÅ��

¹ ,9,¦���� $��j p�ª������1}/7����)�� )�+��!���ɼ��ƽ­���¥�¼j�,��!��*B*B��)���*,�Æ� ! /8"�¼�� ê�ë*J

�ª_ r �}_Rp�d 9 p�W`_ t dBpq� x h4_bX�enegf dBe�]`_bd�a k\e r egf _�]^W^h�W`e¦_�§;[�pg_bkgkgW r X�k\W^X � d 9 ]^_ � T Õ T��X(_�jRd�k�_4W^k�k x «sjRW`_bX�e\e r W^]Y] x k�e�pqdBe�_�egf(_���_bX _Rpqd�]6dBpg� x h4_bX�eRTn�ª_4j r X kqW^a(_Rp�egf(_ tFr ]^] r ¢ W^X(�e�pqW^a�W^dB� r X d�]�¨ à ��a W^dB� r X�d�]@©vpg_R� x ]YdBp¦��pqW^a�jRd�k�_��

Þ ÿ�ý Þ � Þ ýF F F�����C�����X����� �����X�����C�����ã ÿ N ã ÿ . ã ÿ 1 ã ÿ / ã ÿf� ã ÿ - ã ÿ�ý ã � ã ý ã - ã � ã / ã 1 ã . ã Nó %ZnkKegf(_bW^p ¢ WYa(egf k@�¥W^X j�pg_bd�kg_�l�egf(_$�7X W`e�_���kgW`¾R_ba�k�e�_bX jRWY]^k8dBpq_�_�§(d�j�e t@r p6[ r ] : X r hiW^d�]Yk

r�t W^X j�pg_bd�kgWYX(�!] : f W^�!f(_Rp r pqa(_RpqkbT � f(_¦W^X%�"X W^e�_�� ¢ W^a(egf�k�e�_bX jRW^] ¢ W^]^];egf(_bX4d�]^k r�9 _�_�§(d�j�e tFr p$d�]^]e�pqW`� r X r h4_Re�pqW^jih r a(_bk�kgW^X³¨ � �}©�l ¢ f WYjqfªf do�_¥a(_Rp�W`o�dBegW^o�_ � j r k¬¨ � �}©�T¥�Áf(_bX�egf(_sW^X%�"X W^e�_��

¢ W^a egf�k�e�_bX jRWY]vWYk�dB[ ["]^W`_ba�e r d~[�dBpgegWYj x ]^dBp�h r a(_cdBeT� � ¢ W`egf�kge�_R[ÞkgW`¾R_ C ÀyBl�egf W^k�!W`o�_bk

� 2 d ] � j r k�¨�� � © 4 d a j r k¬¨ ��� © 4 dZ��j r k¨ � © 3 � 2 « � kgW^X³¨ � © 4 « Û kgW^X³¨ ��� © 4 «�, kqW^X³¨ Ã�� © 4 � � � 3 ¨Ew�T^y©

¢ f WYjqf¥f r ]^a k t@r p¦d�]^] � Ù ��Tn¨ ¿nr e�_�egf dBe ¢ _�f do�_ x k�_basegf dBe « ] � « TV©��ª_�X(_�§%e¦hidB¤�_egf(_�o�_Rp : pg_bd�k r X d 9 ]`_�d�kgk x h4[ egW r X�k�egf dBe

¨°y©Negf(_$a(_bkgW^pg_ba�]^W^hiW^e7pq_R[ pg_bk�_bX�egkzegf(_$h r k�e�d�jRj x pqdBe�_�a(_RpqW^o�dBegW`o�_�dB[�[ p r §(W^hidBegW r X�dboBd�W^]��d 9 ]`_ r�t egf(_�a(_bkgW^pg_ba t@r p�hNl d�X a

{ Ã

¨ � ©Negf(_�a(_RpqW`oBdBegW`o�_�l 9 _bW^X �~dª] r jRd�]�[ p r [}_Rpge :�r�t d tFx X�j�egW r Xzl$W^k 9 _bk�e4dB[ [ p r §(W^hidBe�_ba

¢ f(_bXªegf(_sj r _�«sjRW^_bX�egk « ósa(_bjRd : e r ¾R_Rp r d�k t d�k�e�d�k�[ r kgkgW 9 ]^_c¨Ek x 9 Ì°_bj�e�e r ¨Ew�T^y©f r ]^a W^X ��e�p x _¬©�T

� f(_¦]`_ t e°��f d�X a¡kgW^a _ r�t ¨Ew�T^y©6W^k�d�[ p r a x j�e r�t egf(_¦k�e�_R[ tEx X j�egW r X � ¨ ¢ f�W^jqf\Ì x h4[�kdBe � ÏÌ '�¢ f(_bXi[}_RpqW r a WYjRd�]^] : _�§%e�_bX a(_ba7©�d�X a¥d�[7_Rp�W r a�W^j tEx X j�egW r X¶d a 4 � dZ��j r k � ¨EkgW^X j�_9;: k : hih4_Re�p : d ] � gd � ©�T � f(_�a(_bjRd : pqdBe�_ r�t egf(_�� r!x pqW^_Rpvj r _�«sjRW`_bX�egk r�t egf WYk$[ p r a x j�e�W^khid�§(W^hid�]8W t egf(_¡£���U�W^knd�k�kgh r;r egf~d�k�[ r kgkgW 9 ]`_�dBe � Ì ' l7W�T±_�T ¢ f(_bXɨ d a 4 � dZ��j r k � ©f d�k�d�¾R_Rp r egf(_Rpg_ r�t d�k�f W`�!f�a(_R��pq_R_sd�k�[ r kqkgW 9 ]`_�T � f W^k r jRj x pqk ¢ f(_bX d a � dZ�bl ¢ f�W^jqf¢ f(_bXNj r h 9 W^X _ba ¢ W`egfcegf(_�pq_bk�e�pqW^j�egW r Xcegf�dBe Ë d yBl��!W`o�_bk�d a �Û d�X a½dZ�= �* T��ÁW`egfegf(_bk�_�o�d�] x _bkRl

d a 4 � d¼��j r k � J j r k � � Q Û � ¨Ew�T � ©

w : W^X�e�_R��pqdBegW^X(�¥_b� x dBegW r X k¡¨EwnT � ©\d�X aɨEw�T^y©\dB�!d�WYX k�enj r kK¨ � A ©¦d�X�a�kgWYX�¨ � A ©�pg_bk�[}_bj�egW`o�_b] :¨Ed�X a~k x(9 kgegW`e x egW^X(�~¨EwnT � ©nW^X�e r ¨EwnT^y©�©�l ¢ _�egf x k�¨EW^X�egf(_�e�pqW^a WYdB� r X d�]�jRd�k�_¨� y© r�9 egd�W^Xegf(_�W^X(�"X W`e�_�� r pqa _Rp�j r _�«sjRW`_bX�egk t p r hبEw�T^y©\d�k

d;ó y' Ê �a j r k¬¨ � A © J j r k � � Q Û ò �« ó y'sÊ �a � kgW^X³¨ � A © J j r k � � Q Û ò � ¨Ew�T à ©

� f(_�jRd�k�_ r�t ��_bX(_Rpqd�]G� tFr ]^] r ¢ k\j r h4["]`_Re�_b] : d�X d�] r � r!x kq] : d�X a,]^_bd�a k�e r egf(_�_�§%[ pg_bkqkgW r X k]^W^kge�_baNW^X � d 9 ]`_ � T Õ T

¹ ,9,¦���� $�[j Î

Î )��81�����*B��)���*M"¦�(�b»c� ���ýè�)@,$/z¼"!Y*�#%)6�$#M#(�����8�!*N/z�$ >�!�$)�*����Æ� Î ��/8,���� � ê

¯-XM2 � y 3 l�¸ r [�d�];�!W`o�_bk�egd 9 ]`_bk r�t j r _�«sjRW`_bX�egk$WYX�e�_Rp�hik r�t egf _�a W��}_Rpg_bX j�_ r [}_RpqdBe r pqk% d�X a'& ¢ f(_Rpg_

% ¨KW ( ©�(W (CD �M¶ Û � W ( ] �M¶ Û&�¨KW ( ©�(W ( �´W ( ] � � ¨ u T^y©

¯-X�egf W^k8dB[ [}_bX a W�§}l ¢ _vf _b]`[�hidB¤�_�jR]`_bdBp6egf(_vj r X X(_bj�egW r X 9 _Re ¢ _R_bX�egf _vj r _�«sjRW`_bX�egk�!W`o�_bX�WYX u f dB[ e�_Rp � d�X aNegf r k�_�]^W^k�e�_bacW^X�Zn[ [}_bX a W`§i¯g¯ r�t ¸ r [�d�]�T

��X(_HjRd�X x k�_ª¸ r ["d�]�´µk � d 9 ]^_bk � T^yªd�X a � T � e r �"X a­egf(_ª�6�Ôj r _�«sjRW^_bX�egk tFr pX r X kgegdB����_Rpg_basdB[�[ p r §(W^hidBegW r X k r�t ��pqk�e�d�X a�k�_bj r X a�a _RpqW`oBdBegW`o�_bkRl!pg_bkg[7_bj�egW^o�_b] : T � d 9 ]^_bk � T±�d�X a � T Ä r�t ¸ r ["d�]zjRd�X 9 _ x k�_bace r �"X�asegf _�j r _�«sjRW^_bX�egk r�t k�egdB����_Rpq_ba�dB[ [�p r §(W^hidBegW r X�k r�t��pqkge�d�X aNk�_bj r X a�a(_RpqW`oBdBegW`o�_bkRl(pg_bkg[7_bj�egW^o�_b] : T

� r pi_�§%[�]^W^jRW^e�kgj�f(_bh4_bkiWYX¶¸ r [�d�]�l r X _,kgf r!x ]Ya�j r X kqW^a(_Rp ÿ ; � <­( ; ­ <� T¶� r p à ��a�W^dB� r X d�]

kgj�f(_bh4_bkRl r X(_ ¢ d�X�egk ÿ ; ý=<­( ; ­ <ý TÞ� r p Ä ��a�W^dB� r X d�]�kgj�f(_bh4_bkRl r X(_,kqf r!x ]^aÉj r X kgWYa(_Rp ÿ ; - <­( ; ­ <- T¶�ª_r �}_Rp r X(_s_�§%d�hi[�]`_�l6egf(_skqW�§;egf r pqa(_Rp�k�egdB����_Rpg_ba à ��a W^dB� r X d�]vdB[ [ p r §(W^hidBegW r X�e r egf(_���pqk�e

{ Ä

a(_RpqW^o�dBegW`o�_�T�m�kgW^X � � d 9 ]^_ � T±� r�t ¸ r [�d�]zd�X a $ >yBl ¢ _��"X�acegf dBe

) F �IH� ) +ó Ä % � F �IH� )BóÇ y 4 {Ä # %� % Û É ) +ó Ä % �°y 4 y|

� � � % Û � )Bó) +ó 4 {

ÕB� S ) +ó4] � � � ) +ó 4 ) +ó D � U Ä % � )Bó 4 y|� � � ¨�)Bó4] � � � )Bó 4 )Bó D � © �

{ÕB� ) +ó4] � 4 Ã y

� � ) +ó 4 {ÕB� ) +ó D � Ä � �?) ó4] �M¶ Û 4 ) ó D �M¶ Û

4 y|� � � S �?) ó4]&, ¶ Û 4 Ã ) ó4] �M¶ Û � Ã ) ó D �M¶ Û 4 ) ó D , ¶ Û U �

{ÕB� ) +ó4] � 4 Ã y

� � ) +ó 4 {ÕB� ) +ó D � Ä � y|

� � � ) ó4]&, ¶ Û � Ç�ÃÕB� ) óE] �M¶ Û 4 Ç�Ã

ÕB� ) ó D �M¶ Û 4 y|� � � ) ó D , ¶ Û

¨ u T � ©

¿nr e�_\egf dBe�egf�W^k�hidBegjqf _bk$egf(_��& � jRd�k�_nWYX � d 9 ]^_ � TV|�Tv��egf(_Rp$j r _�«sjRW`_bX�egk$jRd�X 9 _�a(_RpqW`o�_baW^Xcegf(_�kgd�h4_�hid�X X _RpbT

Zn]^egf r!x �!f�X r e8a W^kqj x kgk�_ba�f _Rpg_�l r X(_�jRd�X x k�_ r egf(_RpKj r h 9 W^X�dBegW r X k r�t ��´µkKd�X a�)�´µkt p r h ¸ r [�d�]�´µk�egd 9 ]^_bk�egf d�XHegf r k�_ia WYkgj x kgk�_ba~d 9}r o�_4e r �"X�a~j r _�«sjRW`_bX�egk tFr p�X r X j�_bX�e�_Rpg_bakgj�f(_bh4_bkRT

¹ ,=,¦���$ ��[j �

i ��/}�³�³� ���� $����� �!���8�!��/7�!��)���½­/"������j

Z>a W��}_Rpg_bX�egWYdBegW r X�hidBe�pqW`§NWYk�d�hidBe�p�W�§ ¢ f W^jqf³l ¢ f(_bX�h x ]`egW^[�]^W`_ba 9;: d�o�_bj�e r p r�ttEx X j�egW r X~oBd�] x _bk�dBe�a W^kqj�pg_Re�_¡��pqW^a([ r W^X�egkRl7�!W`o�_bk�¨F[�k�_ x a r k�[}_bj�e�pqd�]@©na(_RpqW^o�dBegW`o�_¡oBd�] x _bk�dBe�dk�_Re r�t a W^kqj�pg_Re�_�_b� x W^k�[�d�j�_ba�] r jRdBegW r X�kRT

ZnX,_�§%d�hi[�]`_�WYk��!W`o�_bX~W^X 2�y �C3 T\¯ t�r X(_�d�kgk x hi_bk�egf dBe�egf(_�a�dBegdsW^k\[}_RpqW r a W^j ¢ W`egf[}_RpqW r a � l�W`e�W^k�[ r kgkgW 9 ]`_�e r �"X aNdih�dBe�pqW�§+*) k x jqfNegf dBeëììììììììììììí

à�+�¨�� � ©TTT

à�+E¨�� ©TTT

à + ¨�� ÿ ©

ðLññññññññññññò

ëììììììììììììí *)ðLññññññññññññò

ëììììììììììììíà}¨�� � ©TTT

à7¨�� ©TTT

à7¨�� ÿ ©

ðLññññññññññññò¨E��T^y©

� f W^k�¨F[}_RpqW r a W^j©�X r X kgegdB����_Rpg_ba�["k�_ x a r k�[}_bj�pqd�]Ba W`�7_Rpg_bX�egW^dBegW r X�h�dBe�pqW�§�*)�W^kzj : jR]^W^jd�X a�WYk��!W`o�_bX 9;:

*) ! e ¢¤¥ ¤¦ � F ] �IH ø ÿ ­Û k s h � � F ! ] HQ¶ ÿ � S�² $� S� $ ¨E��T � ©

U%W^hiWY]^dBpq] : l r X(_�jRd�X��"X aªegf _�k�egdB����_Rpg_ba�[�k�_ x a r k�[}_bj�egd�]�a W��}_Rpg_bX�egW^dBegW r XªhidBe�pqW`§

{!|

)Ô¨Ed�kgk x hiWYX(�¡egf(_�a dBegdif�d�k¦[}_RpqW r a � ©�egf dBe\kgdBegW^k���_bkëìììììììììíà�+�¨�� �M¶ Û ©TTTà�+�¨�� ] �M¶ Û ©TTTà�+E¨�� ÿ ] �M¶ Û ©

ðLñññññññññò ëìììììììììí )

ðLñññññññññòëìììììììììíà}¨��@��©TTT

à7¨�� ©TTT

à7¨�� ÿ ©ðLñññññññññò ¨E��T à ©

� f W^k�hidBe�p�W�§�)0W^k¦j : jR]^W^j�d�X a��!W`o�_bX 9;:

) ! e ' ¨���y© ! ] ] �� �

j r e�� S S;� $ � �Û U �ÿ ¡kqW^X � S S;� $ � �Û U �ÿ ¡ � ¨E��T±��©

¯ t8r X(_�W^X�k�e�_bd�a�a(_bkgW^pg_bacegf(_�a W��}_Rpg_bX�egW^dBegW r XNhidBe�p�W�§ tFr p� à + ¨�� , ¶ Û © �`�`� à + ¨�� D �M¶ Û © �`�`� à + ¨�� ÿ D �M¶ Û © � l(egf W^k ¢ r!x ]^a 9 _��!W`o�_bX 9�:

) ! e ' ¨���y© ! ] � �

j r e � S S;� $ 4 �Û U �ÿ ¡kqW^X � S S;� $ 4 �Û U �ÿ ¡ � ¨E��T Ä ©

��X(_�jRd�X,[ p r o�_�egf W^k 9;:stFr ]^] r ¢ W^X(�¡egf(_�a(_RpqW`oBdBegW r X tFr p *) �!W^o�_bX�W^X´2�y �03 l d�k t@r ]Y] r ¢ kbT�ª_ 9 _R�!W^X ¢ W`egf¡egf(_�]YW^hiW`egW^X ��¨EW^X%�7X W`e�_ ¢ W^a(egf"©8k�egdB����_Rpq_ba��6�Mk�e�_bX jRW^] t p r h>_b� x d��

egW r X�¨ � T Ä ©�¨ ¢ W`egfÒC � ö��ª©

« �¨e óm �ɨ���y© F ó4] ý- H' A Û ¨E��T Ç ©

Z�kgk x hiWYX(� ¢ _�f dbo�_¡a dBegd ¢ W`egf�[}_RpqW r a � l ¢ _�jRd�X�d�a�a�e r ��_Regf(_Rp�[}_RpqW r a%� ¢ W^a _�kg_bj�egW r X k r�tegf(_�kge�_bX jRW^]�e r j�pg_bdBe�_¥d�X�_b� x W`o�d�]^_bX�e�kge�_bX jRW^]�egf dBe�j r o�_Rpqk r X ] :Hr X(_�[7_Rp�W r a r�t egf(_¥a dBegd%T

{ Õ

� f(_bkg_ ¢ _bW`�!f�egk\dBpq_��!W`o�_bX 9;:

òµ�©e ó ��¨���y© óE] �M¶ Û� ' �a ` ]ó� ¨���y© ' ¨[A 4 $ �H© Û

¨���y© ó4] �M¶ Û� ' � �a ` ]ó� ¨���y©

¨ $ 4 A+ö��ª© Û

' ¨���y© ó4] �M¶ Û� �

j r eK¨[A ' ö��ª©kgW^X�¨[A ' ö��ª© ¨E��TV|�©

�ª_n¤%X r ¢ egf dBevegf W^k�a W��}_Rpg_bX�egW^dBegW r X¥hidBe�pqW�§iW^kvj : jR]YW^j ¢ W`egf~¨KS_T $ ©Æegf�_b]`_bh4_bX�e,) ! e �!W`o�_bX 9�: ò �©e ! ] ] �M¶ Û tFr p�egf(_i��p�k�e�jRd�k�_¥�!W`o�_bX�d 9}r o�_cd�X a��!W`o�_bX 9;: ò �©e ! ] D �M¶ Û t@r p�egf(_k�_bj r X a,jRd�k�_��!W`o�_bX,d 97r o�_�T

�ª_�egf x k��"X acegf�dBe t@r p\egf(_�jRd�k�_��!W^o�_bX�W^X�¨E��T à ©�l

) ! e ' ¨���y© ! ] ] �� �

j r e � S S;� $ � �Û U �ÿ ¡kgW^X �E¨KS;� $ �ÊyXö � © �ÿ ¡ � ¨E��T Õ ©

� f(_�k�_bj r X aªjRd�k�_4kgW^hi[�] : jqf d�X ��_bk�egf(_ � �Û e r �Û T�� r p�a�dBegd ¢ W`egf,[}_RpqW r a r egf(_Rpegf d�X � l r X(_�h x k�e�kgjRd�]`_�dB[ [ p r [ p�W^dBe�_b] : T

¹ ,=,¦���$ ��[j 2

��� ����1}/7�!��)���)³+���365$/"�!��)���- ê6ë�ù/.� f W^k�a(_RpqW`oBdBegW r X ¢ d�k¥a r X(_ 9;: egf(_~d x egf r p ¢ W`egfÞegf _~f(_b]^[ r�t ��p r�t _bkgk r p¥wv_bX

�n_Rp 9 k�eRT

2 ë - �ª� ����1}/"�!��)�� )�+��!���É��j�,$�!�"*�*B��)��>+°)³�10 ó� x ps� r d�]�W^k�e r k r ]^o�_32 � « l ¢ f _Rpg_12 W^kcd�X­WYX%�"X W`e�_ 9 d�X a(_ba­k : h�h4_Re�pqW^j

�8r _R[�]YW`e�¾�h�dBe�pqW�§�d�X a « W^k�d�o�_bj�e r p\j r X�egd�W^X WYX(��egf _�j r _�«sjRW`_bX�egk « �( e ó T ¢ f(_Rpg_m�Èd�X�a·�HdBpg_� §%_bazT� $� x W`oBd�]`_bX�eg] : l ¢ _ ¢ W^kgfce r k r ]`o�_¤d�4��M « l ¢ f _Rpg_d � ����� � d ] � d ] � D � �����od ] ��d a dZ� ������d � ] �od � � ����� � T� mX� n � ` ]ó� Td�X a« � B ¨Fegf(_�o�_bj�e r p�j r X kgWYk�egW^X(� r�t d�]Y]z¾R_Rp r k�_�§(j�_R[ e tFr p\d r X _�W^Xcegf(_�: - 9 [ r kqW`egW r X"© ��ª_~egdB¤�_�egf(_~a W^kgj�pq_Re�_,� r!x pqW^_Rpse�pqd�X�k t@r p�hik r�t d�Te�;T�d�X a « d�X a x k�_�egf(_ t d�j�e�egf dBe¥egf(_r pqW`�!WYX d�]}hidBe�pqW�§NW^k 9 d�X�a(_baNd�X a�k : hih4_Re�p�W^j�e rir�9 egd�W^X

y ���

5d7¨Di;©´ Ë � ` ]ó� d � ! j Ë � ` ] � d � ! j(d a 4 �5Ë � ` � d j r k¬¨ $ �}©1T5�K¨Di�©& Ë � ` ]ó� � � ! j T

d�X a5« ¨Di�© Ë � ` ]ó� « � ! j � ! B j �

¨E �T^y©

U%W^X�j�_©d�4��´ « l t p r h egf _¡� r!x pqW`_Rp�j r X�o r ] x egW r XHegf _ r pg_bh ¢ _4f do�_35d}¨Di�©65�K¨Di�©� 5« ¨Di�©�lzk regf dBe75�6¨Di�©� 5« ¨Di�©eö85d}¨Di�©�T � dB¤;WYX(�4egf(_�W^X�o�_Rpqk�_�� r!x pqW`_Rp�e�p�d�X k tFr pqh e r k r ]^o�_ t@r p��~�!W`o�_bk

� �Û � � �] � 5�K¨Di�©�� ] ! j òXi �Û ��� �] �:9ã F j H9; F j H � ] ! j òXi �Û ��� �] � þ ø ; ü ÿ ­ < jÞ � D Û ¬ ß< æ�ý Þ < b^d'k F>= 0 H ò i �Û ��� �] � b^d'k F�F B ] H 0 H D !jk s h F�F B ] H 0 HÞ � D Û ¬ ß< æ?ý Þ < b^d'k F>= 0 H ò5i ¨E �T � ©

�ª_�egf(_bX�pg_bj r �!X W`¾R_�egf dBe 9 _bjRd x k�_ ¢ _ r X�] : ¢ d�X�e�e r h4_bd�k x pg_�[ r kgW`egW r Xcpg_b]^dBegW`o�_e r egf _�j�_bX�e�_Rp�[ r kgW`egW r X³l;egf _�pg_b]`_RoBd�X�enW^X a(_�§¥o�dBpqWYd 9 ]`_�W^k�A@? :·� $0� ¯°X�d�a a W^egW r Xzl 9 _bjRd x k�_egf(_va(_bX r hiW^X�dBe r p r�t egf(_$WYX�e�_R��pqd�X�a�W^k³_Ro�_bXzl r!x p8WYX�e�_R��pqd�X�a�W^k�egf(_�k x h r�t d�X�_Ro�_bX tEx X j�egW r Xd�X aid�X r a a tEx X j�egW r X�/�d t e�_Rp$W^X�e�_R��pqdBegW r Xzl r X ] : egf _¦��pqk�e6[�dBpqe�pg_bhid�W^X kbT8�ª_negf x k�j r X�jR] x a(_egf dBe�egf(_¦W^X�o�_Rpqk�_¦hidBe�p�W�§ r�t d�k : hihi_Re�pqW^j 9 d�X a(_ba �8r _R[�]YW`e�¾vh�dBe�pqW�§�WYkKd�]Yk r k : h�h4_Re�pqW^jvd�X a�8r _R[�]YW`e�¾ ¢ W`egfN_bX�e�pqW`_bk�ò�ó�d�] r X(�ia W^dB� r X d�]GA7�

ò�ó� y'sÊ �a

j r k¬¨[A��}©d �( e a 4 �5Ë � ` � d �( e j r k�¨ $ �z© ò^� � ¨E �T à ©

y � y

A�BDC EGF8HJILK�MONQP6ISRUTVR/W�PYXZF:F8[]\,H6F_^�^�ISR`TaWR/Hb0$cJd ±fehg ISNji/RUTkN�l�MONj^mFnporqts$u6v$w6sbx�yGzYyh{"|r}D~3qts$y�� c }�uY{"��v_or��u6�8o�~3}�uY{�qts$y������8|r��wYu6�8�Yo��h�Y��yb�������6���u6�$y��h�Y� y��Y�t|ro�~�wYy��$yh{"�Yor|r�hy�qts$y���{tw6v8��y���q�w6|rzYy��7}DuY{p�Y��~7�h�Y��yY�2 |r�,���Uu�yh�_or|�q�������q�{"| ��uY}/¡f�Y�8�$x¢|r�8qtsG���Y�_� 2�£�¤ |¥�Zqts$y��UuJyh�_o¥|�q��p����q�{�| ��x¢|�qtsy��Jq�{"|�y���� c �Yo�u6�8wG�8|r��wYu6�8�Yo/¦Q�,§,y��h�Yv_��y 2 £�¤ 2 � ü �8x�y��hor�Y|r�¨qts_��q� c £_©«ª £_©Z¬ � c £�¤tª £�¤�¬ � c ª�­ ¬ � ch® ¤tª ¤�¬ � ch® ©«ª © � ¯°²±G³ ¦���´´ ¦1µ��´�¶ �¸·��²¹J�

x¢s$yh{"y ªJº � ª ©»J¼ º �]½by¾�tv$¡_�tqt|�qtv$q�y,� c }D{"u6�+�¸·¢�¿6�����Y�8��qts$yÀo�yh}Dq��s_�Y�8���"|r�$yZuY}��¸·��²¹J�`¡jy��«u6�Áy��ÂÃGÄ ÅÆÈÇJÉ�Ê8Ë"Ì�Í8Î�ÏpÐ�Ñ�ÒLÓ�Ô'ÇJÉ$ÕOË"Ì�Í8Î�Ï�Ð Â ÒLÓpÔ'Ç Æ ËtÌ�ÍJÏ�Ó�Ô'ÇYÕ$ËtÌ�Í_ÎDÏ�Ô Â ÒLÓpÔ'Ç�Ê8ËtÌmÍ8ÎDÏ�ÔÖÑ×ÒSÓÎ¥Ç Æ ÔÖÑ�Ç6Õ�ËtÌmÍYÓ�ÔÖÑ�Ç�Ê8Ë"Ì�Í�Ñ�Ó�Ò Ø ÓÙ ÂÃGÄ ÅÆ Ç Æ ËtÌ�ÍJÏ�ÓpÔ'Ñ×Ç Õ ËtÌmÍ�Ï�ÓZË"Ì�ÍYÓ�ÔÖÑ�Ç Ê Ë"Ì�Í�Ï�Ó,ËtÌ�ÍJÑhÓÇ Æ ÔÖÑ�Ç�Ú�Û Õ�ËtÌmÍYÓ�ÔÖÑ�Ç�Ê8Ë"Ì�Í�Ñ�Ó Ø ÓÙ Âà Ä'ÅÆ ËtÌ�ÍJÏ�Ó Ø ÓÙ ÜÝ Þ Â Ï Ùbßß ÏGàÙbß�á Î¥âZã ä�Òx¢s$yh{"y�x,y�s_��zYy�v_��y�� ª £ º � ª º �Y�8�7q�{"|�wYu6�8u6�Áyhq�{"|r��|r�8y���qt|�qt|ry��h�

å \Z\¾F_T g IS[ æçbF$KÀTZIèTkiéPYXZFêl�RëMONjl¢PYH�ìZT,MONQPYI�R`TíF8H6H6R`HÖR/W�P6I�îïFðI�TUPYF8i/H�NfPYR/HJ^

�¸��s$y�x�uY{tñ�|r��qts$y���y��«qt|ru6�7x��Y�p�$u6�$y�¡�~7�`uY¡�~�ò�{"|¥�t�«u6oro��Y�8�7qts8y��Yv$qts$uY{��ó��`{��Y�8|�qt|�u6�8�Yo¥o�~Y��o�u��h�Yokq�{"v8�8�h��qt|�u6�ôyh{t{tuY{�}�uY{�� o¥|r�$y���{���v8o�qt|r��q�yh�ô��v8�Áyh{�|r�h�Yo]qt|r�Áy|r�Jq�yhwY{"��q�uY{�s8�Y��¡jyhy��'�8y«õf�$y�� |r�'q�yh{"���¢uY}k�U�×~�o�uY{py«���f�Y�8�t|�u6�8����n�o�qts$u6v$w6s'qts8|r���8y«õf�8|�qt|�u6�w6|�zYy���qts8y��«uY{t{ty��«q�uY{"�8yh{�uY},�Y�h�hv${"�Y�«~3}�uY{��7�t��s$y��ÁyY�/uY}�q�y��ô|�q��$u�y����$uYq�w6|�zYyÁqts8y��«uY{t{ty��«q�«u�y«ö@�h|�y��JqZ��v_o�qt|��_o�~O|r�$w¢qts$y¾yh{t{tuY{ëq�yh{"� �]�¢s$yÀ�8{tuY�jyh{k�$y«õf�8|rqt|�u6��uY}jo�uO�h�YoOq�{"v8�8�h��qt|ru6�÷yh{t{tuY{|r�p�$y«õf�$y�� |¥� q�yh{"���¢uY}kø]�Y�,ùy�y«�O�_�Y�8�"|�u6�8�h�À½by�w6|�zYy�y«�$�Y�Á�_o�y��¢uY}k�t�"s8y��Áy��¢}�uY{�x¢s8|r��s qts$y�$y«õf�_|�qt|�u6�8�À�«u6|r�8�h|¥�$y��Y�8� �t��s$y��Áy���}�uY{�x¢s_|r�"s�qts$yh~7�8|�úQyh{��æ÷Bèû çðI�^�M$ìZ^�^�ISR`T

ü �÷wYy��8yh{"�YoL��qts8yh{ty¢��{ty�qts8{tyhy��8| újyh{ty��Jqëx��×~��Zq�u��$y«õf�8y�qts8y¢o�uO�h�Yo$q�{"v8�8�h��qt|ru6�'�¸�8|r���«{tyhqt|�����qt|ru6�f��yh{t{tuY{¢uY}]��ýfþrÿÁuY{"�$yh{¢��v8o�qt|¥��q�yh� �t�"s8y��Áy��� ³ � �U�×~�o�uY{py«���f�Y�8�t|�u6��uY}�qts$y���q�y��_�h|ro���¡ju6v$q¢¦G��´��²���Q¿��f�������� �����j�� t���:¦��k�������S�� ��ë��� ¤ ¦�� ® ¤ ��� � ® ¤�� ����� ¬�� �L¦�� ® © ��L�6� �U�×~�o�uY{py«���f�Y�8�t|�u6� ��¡ju6v$q Y � ³ � ³ � ���¸�Yorqts$u6v$w6s'�tyhy�qts$y�}�u�uYqt�$uYq�y�u6�'�/� � �Á{tyh}�yh{��{"|r�$w÷q�uG�$y«õQ�8|�qt|�u6�7¿6�!�� � Y ���"�k� Y ��or� Y ��� © � Y � ³ � � ® ¤ ¬#� ��� Y � ³ � � ® © �

³ ´6¿�L¿6� ø��Y��ùy�y«���f�Y�8�t|�u6�8�¾��¡ju6v$q Y � ³ � ³ ¿����$ �&% �' �(% � �ðo¥�/� Y �k���*)6� Y � ³ ��� ® ¤ ¬�� ��� Y � ³ ��� ® © �

x¢s$yh{"y+�|¥�Àqts$y�}�uY{tx���{��7�ts8|�}�q¾uY�jyh{"��q�uY{��ò�y«õf�8|�qt|�u6�_� ³ �Y�8��� ��{tyðy-,Jv8|rzm�Yo�y��Jqð��¡jy��h�Yv8��yôqts8yô�8| újyh{ty���qt|¥��qt|�u6��uY�jyh{"��q�uY{. � ¤c or�/����]¡_v$q��$y«õf�8|�qt|ru6�ð¿'ory��Y�8��q�u3�8| újyh{ty��Jq�o�y��Y�_|r�$w yh{t{"uY{��«u�y«ö@�h|�y��Jqt��}DuY{÷���Y�J~�Áyhqts$uO�8�¾¡jy��h�Yv8�ty � ¤ �0� © �0�k� ³ �1� )2 uY{@�tqt�Y�8�8��{"�énp�8�Y�G���§À�Y�ts$}�uY{tqts �Y�8� np�8�Y�G��43'u6v_o�q�u6� �t��s$y��Áy��h�5�k� ³ ��� ³ ��Y�8��qts$yh{ty¾|r�]�$u��8| újyh{ty��8�«y�¡jyhq�x�yhy��6� ¤ �Y�_�7� ) �98pu×x�yhzYyh{��J}�uY{]¡_�Y�tñ�xÀ��{"�8�ë�8| újyh{ty��Jqt|r��qt|�u6��Y�8�buYqts8yh{��t��s$y��Áy��h��� ¤ �Y�8�"�*)Á�8|�úQyh{��@·ë�O�Qyh{�|r�Áy��Jqt�Yo]{ty��tv8o�qt��w6|�z�|¥�$w�qts$y�w6o�uY¡_�Yokyh{t{tuY{��q�{tu6�8w6o�~ |r�8�8|¥�h��q�y�qts8��q��$y«õf�8|�qt|ru6�'¿G|¥��qts$y÷���8�8{tuY�_{"|r��q�y��$y«õQ�8|�qt|�u6���;:��$y��h�Y�1�Yor��u��«u6�Áyq�u qts8|¥���«u6�8�horv8�"|�u6�3¡J~3y«�$�Y��|r�8|¥�$w7� ���jy��h|r�Yok�h�Y��yY�=<�u6�8�"|r�$yh{��'��v8o�qt|r�tq�yh�ô�Áyhqts$uO�bqts8��q�$yh�jy��8�8��u6�8o�~êu6� �8{"yhz�|�u6v_�Á}�v_�8�«qt|�u6� z��Yorv$y��@�Y�8� �$uYq@u6�é�8yh{"|�z���qt|�zYy z��Yorv$y��h� 2 uY{�qts8|r��h�Y��yY�>�k� Y �¢� ´�}�uY{��Yoro Y �/�Y�8�3qts$yÁ�8|�úQyh{ty��Jqt|r�YoUy-,Jv_��qt|�u6�3�_or�×~����$u�{tu6o�yY�/�tu�qts8y÷�tu6orv$qt|�u6��h�Y�8�$uYq¢¡Qy��«u6�JzYyh{twYy��Jqh�Àò�y«õf�_|�qt|�u6�8� ³ �Y�8�Ö�÷�«u6v8or� �$yhzYyh{"qts$y�o�y��t��|¥�8�8|r�h��q�y���s8|rw6s7�$yhwY{tyhyuY}`�Y�h�hv${��Y�«~@|�}�qts$y��8| újyh{ty��8�«y��t��s$y��Áy�|r�,�Y��y«�Oq�{"���ju6or��qt|�u6���Áyhqts$uO���?:��@qts$y�uYqts$yh{�s8�Y�8����$y«õf�_|�qt|�u6�7¿÷x�u6v8or�7�«uY{t{ty��«qtor~�{"yA@_y��«q¢�Y� |r�$õf�8|�q�y�yh{t{tuY{��¸�"|r�8�«yB�k� ³ �Z� ´÷}DuY{pqts8|r�¾�h�Y��y����3'uY{"yGwYy��$yh{"�Yo¥o�~Y� � � ³ ���+´Ö�Y�8� � �¸� ³ ���C�k� ³ ��}DuY{÷�Y��~b�«u6�8�"|r��q�y��Jq��Áyhqts$uO��� ü }�k� ³ �U|r���t���YoroL�mqts$y�� ³ |¥�U�$y���{�o�~��p�8u6v$¡_o�yk{"uJuYq]uY}$qts$yÀ�8| újyh{ty��8�«y�y-,Jv_��qt|�u6���Y�_��qts$yÀ�Áyhqts$uO�|r�¾�$y���{�o�~�v_�8��qt��¡_o�yY�½byÀqtsJv8�]�«u6�8�ho¥v8�$y�qts8��qUqts8yÀ�«uY{"{ty��«që�$y«õf�8|�qt|ru6��uY}foru��h�YoJq�{"v8�8�h��qt|ru6��yh{"{tuY{ë�ts$u6v8or�¡jy¢¡_�Y�ty��Gu6��ø]�Y�,ùy�y«���_�Y�_�t|�u6�8���¸�$y«õf�8|�qt|ru6�G¿6�,�Y�8�@�8uYqZu6���U�×~�oruY{,y«�O�_�Y�8�t|ru6�1�¸�$y«õQ�8|�qt|�u6�8�³ �Y�8� �6���

³ ´�¹æ÷B�C A�[ëN�îï\,lSFf^DFEHGIEKJ LNM�OQP"RASUTWVYX�Z[P"Z\T�]>^_M�Rnpo¥o6np�_�Y�����§À�Y�ts$}�uY{tqts÷�Y�8��n��8�Y�����43'u6v8orq�u6���Áyhqts8u��8����{ty��«u6�8�t|r��q�y��Jq]�Y�8��s_��zYy� � Y �Z� Y�` � Ya` £�¤ �À��s$y����Q�k� Y � ³ ��� � � � Y � ³ �����b�����b� ³ �,� ³ ¶Ic |r�8�«yB�k� ³ ��� ³ �����~Oo�uY{¢y«�O�_�Y�8�t|ru6�8�¾�Y�8�7ø]�Y�,ùy�y«�O�_�Y�8�t|ru6�8�¾��{ty�y-,�v8|�z��Yo�y��Jq¾}DuY{�qts8y���y��Áyhqts$uO�8�h�

:��$y�y«�$�Y�Á�_o�y�|¥�Àqts$y�}�u6v${tqts�uY{"�$yh{pnp�8�Y�G���§À�Y�ts$}�uY{tqts �t��s$y��ÁyY�_xps8|r�"s7s_�Y�� � Y �k� Yad � Y )�e �k� Y �,� �Y��m¹ Y ) � ��f�m¹ Y © ¬ ¿ ��m¹ Y � ¿g ¶ � 2 � ³ �

��s$y�yh{"{tuY{¢�«u6�8��qt�Y�Jq¢|r�!���+©1h ¤i © ­ ���s$y�qts8|�{���uY{"�$yh{¢n��8�Y����43Öu6v8o�q�u6�'�t�"s$y���y�s8�Y�

� � Y �k� Y © � Y e �k� Y �,� �³ � Y © ¬ � ¿ Y � ³³ � ¶ � 2 ��6���s$y�yh{"{tuY{¢�«u6�8��qt�Y�Jq¢|r�!���j� ¤© d �DFEHGIEHG klOQmonIpqOsr�MtRuM9vxw?Z�roZ�yzTov�O{Tov�^�y|P"Z\To]t^_M�R��s$y�}�u6v${tqts7uY{"�8yh{�¡_�Y�tñ�xÀ��{"�8���8|�úQyh{ty��Jqt|r��qt|�u6�'�t�"s$y���y�s8�Y�

� � Y �Z� Y d � ¹ g�Y� Y ) ¬ ¿���Y� Y © � ³ ��Y� Y ¬ ¿�Y� e �k� Y �k� ³ ��Y� Y d ¶ � 2 �¿6�} �t|r�$w��U�×~�oruY{Z�$y«õf�8|rqt|�u6�8�h�mqts$yÀyh{t{tuY{k�«u6�8�tqt�Y��qZ|¥�~� ¤�©¤�©1h xps$yh{ty��Y�]qts$y�ø]�Y��ùy¢�$y«õQ�8|�qt|�u6��w6|�zYy���Y�7yh{t{"uY{¢�«u6�8��qt�Y�Jq¢uY}����j� ¤h �

³ ´6���s$y�qts8|�{���uY{"�$yh{¢��qt��wYwYyh{"y��'¡_�Y�"ñJxÀ��{"�8�¢�8| újyh{ty���qt|¥��qt|�u6�7�t�"s8y��Áy�s8�Y�

� � Y �k� Y ) � � ³�Y¿ Y © � ¿�Y¿ Y ¬ ³�Y¿ e �k� Y �,� �m¹�Y¿ Y>�� ¶ � 2 �²¹J���s$y�yh{t{"uY{¢�«u6�8��qt�Y�Jq¢v8�t|¥�$wÁ�U�×~�o�uY{p�$y«õf�8|�qt|ru6�8�À|r� ¤© ) �$x¢s8|rorypqts$y��«uY{t{ty��«q�yh{t{"uY{��«u6�8��qt�Y�Jqp|r���� ¤© d �DFEHGIE�� D>r�Z�Z��;OQroOQP"Z�T Z�rN��Z�To]t^_MtRnp���8|¥�t�hv8�t��y��é|r� c y��«qt|�u6� ¿�����¢x�ybs8��zYyb�$yhzYy�o�uY�jy�����v8o�qt|r��q�yh���Áyhqts$uO�8�@qts8��q�Yoro�u�x }DuY{¢}D{tyhy��_��{"�Y�Áyhq�yh{"�¢�8v$y�q�uG�tv$¡juY�8qt|¥��|�����qt|�u6��uY}�uY{"�$yh{��kní�$u6�8��qt��wYwYyh{"y�� y«�$�Y�Á�_o�yuY}]�tv8�"sÖ�Á�Áyhqts$uO�ð��x¢s8|¥�"s |r�¾�_|r�t�hv8�t�ty���|¥� c y��«qt|�u6�����À|r�¾�Á}�u6v${tqts�uY{"�8yh{¢�t�"s8y��Áy�x¢|�qts

� � Y �Ö� Y�d ¬ � g �ð�m¹\��� Y ) ¬ �L�m¹\�/��f6� Y ©�k� Y �3� � ³ �¿ ��f�� � Y ) ¬ � ³ ¹¿ � ³ f�� � Y © ¬ � ³¿ ¬ ��� � Y �"� � 2 ��6�x¢s$yh{"y/��|r�k��}�{tyhy��f��{"�Y�Áyhq�yh{�� ü �ÁuY{"�$yh{ëq�u�s_��zYyp����qt��¡_o�y��Áyhqts8u�����x,y���v8��qks8�×zYy ¤)q� ���h¤�© �ë�U�×~�oruY{ky«���f�Y�8�t|�u6�8�]w6|rzYy¾qts$y�yh{t{tuY{k�«u6�_��qt�Y��q,�Y� � ¤ ­ ® h i1� �� ­ �6x¢s8|rory�ø]�Y��ùy¢y«�O�_�Y�8�"|�u6�8��w6|�zYy��� � ¤ ­ ® h i1� �¤4� ­ � h £�¤�© � � ��x¢s$yh{ty��k� ³ �Z� � �L� ³ �Z� ³ ´��G�m¹\�����¢uYq�y�qts_��qk}DuY{ Y �$y���{ ³ ���Y�*�;� h¤�© �6u6v${�Áyhqts$uO�ô¡jy��«u6�Áy����Y�ôy«�Oq�{"���ju6or��qt|�u6�:�Áyhqts$uO���`x¢|rqtsbqts$yGø]�Y��ùy�yh{t{tuY{��«u6�_��qt�Y��q��«uY{t{ty��«qto�~{tyA@_y��«qt|¥�$wÁqts8|r�h�æ÷B�� ��R`TZM$lèìZ^�ISR`T,^� uO�h�Yo�q�{�v8�8�h��qt|�u6��yh{t{tuY{�}�uY{]��or|r�8y���{U��v8o�qt|r��q�yh�÷�Áyhqts$uO���h�Y��¡jyÀ�$y«õf�$y���|r��q�yh{"���uY}]�U�×~�o�uY{¢y«���_�Y�_�t|�u6�8��uY{¢ø]�Y��ùy�y«�O�_�Y�8�t|ru6�8�h�ë§�uYqts w6|�zYy�qts$y��"�Y�Áy�uY{"�$yh{¾uY}]�Y�h�hv${"�Y�«~�¡_v$quY}�q�y��7w6|�zYy��8| újyh{ty��JqÀyh{t{tuY{��«u6�8��qt�Y�Jqt�h� 2 uY{¢n��8�Y����Sqè~J�jy��Áyhqts$uO�8�h�Oqts$yh{"y�|r�¾�$uÁ�8| újyh{ty��8�«y¡jyhq�x�yhy��'qts8y��$y«õf�_|�qt|�u6�8�h�_¡_v$q�}�uY{p�Áu6�tqpuYqts$yh{��t��s$y��Áy��h�Qqts$y��8y«õf�8|�qt|�u6�_�¾�8| újyh{�� ü �'uY{"�$yh{q�uGuY¡_qt�Y|r�Ö�G{ty��Yor|r�tqt|r��y���qt|r����q�y�uY}]qts$y�w6oruY¡_�Yo/yh{t{"uY{pq�u@¡Qy�y«���jy��«q�y��Ö}D{tu6� �G�t��s$y��ÁyY�Qu6�$y�ts$u6v_or��v8��y����$y«õQ�8|�qt|�u6��uY}]yh{t{tuY{¢�«u6�_��qt�Y��q¢¡_�Y��y��7u6�Öø��Y��ùy�y«���f�Y�8�t|�u6�8���

å \Z\¾FfT g IS[ ��ðRUTZ^�PYNQi`i/F8H6F g WH6F_F:\,NQH�NjîïF$PYF8HbîïF$P6XkR g ^�¸��s$y�x�uY{tñ�|r��qts8|r�����_�Qy��_�8| �GxÀ�Y���$u6�$y�¡�~�qts$y��Yv$qts$uY{×�ó�2 {tyhy÷�_��{"�Y��yhq�yh{��Áyhqts$uO�8����{tyÁ��v8orqt|r��q�yh�3�t�"s$y���y����«u6��qt�Y|¥�8|r�$w��}D{"yhy-�@�f��{"�Y�Áy«�q�yh{"�p�8v$y�q�u��tv$¡juY�8qt|r��|r����qt|�u6��uY}]uY{"�$yh{��À��s$y�}�{tyhy��f��{"�Y�Áyhq�yh{"������~7¡jy�v8�ty�� q�u@�8y��«{ty��Y��yqts$y@yh{t{tuY{÷�«u6�8��qt�Y�Jqh�Z|r�8�«{ty��Y�tyGqts$y ü c §p�UuY{÷uY}Dq�y��:¡juYqts�� ü �:�Y�8�_|�qt|�u6�ôq�u3��qtv8�8~�|r�8w ��qt��w��wYyh{ty��ï}�{tyhyÖ�f��{"�Y�Áyhq�yh{7�Áyhqts$uO�8�3�¸�8|r�t�hv8�"��y�� |r� c y��«qt|�u6� ¿���6���¢x�y3s8��zYyb�Yor��uêy«�$�Y��|r�$y����u6�Áy��$u6�_��qt��wYwYyh{ty���}�{tyhy��_��{"�Y�Áyhq�yh{��Áyhqts8u��8���Y�8���8|r�"�hv8�t�,u6�$y��tv8�"s��Áyhqts8u���s$yh{ty��Y�¾�Y�|roro¥orv8��q�{"��qt|ru6�'uY}�uY�8�juY{tqtv8�8|rqt|�y���|r�3qts8|r����{ty��O� ½by@�«u6�8�"|r�$yh{��Áyhqts$uO�8��x¢|rqtsb��q�y��8�h|ror��uY}qts$y�}�u6oro�u�x¢|r�$w÷}�uY{"���

���� ¡¡¡¡¡¡¢¤£¥{¦ §�¦¥ � § �§�¨§�©

ª(««««««¬½ïs_|ro�y�|�qZ|¥�ë�ju6�t�t|�¡_ory�q�u�õf�8�Á��õ_}�qts�uY{"�$yh{��Áyhqts$uO��uY}jqts8|r�Z}DuY{��7�J|�q,|r�k�$uYq���qt��¡_o�y�¸��yhy c y��«qt|�u6�Ö¿��­����6���¢½by�|r�_��q�y��Y�'��y���{��"sÖ}DuY{p}Du6v${"qts7uY{"�$yh{��Áyhqts$uO�8�¢�«u6�Jqt�Y|r�8|r�8w�u6�$y�}�{tyhy�_��{"�Y��yhq�yh{��@��s8y�or|r�$y���{���~O��q�y�� uY}�y-,�v8��qt|�u6�_��q�u ¡jy���u6o�zYy��:s8�Y��qts$yG}Du6ororu×x¢|r�8w��tu6orv$qt|�u6�

³ ´ �x¢|�qts��f��{"�Y�Áyhq�yh{/ �  ¡¡¡¡¡¡¢ £®>¯u°²±²³ ¨x´¦ ¯uµ²³¶ µ ¶ °²±²³ ¨H·¦ ¯uµ²³¶ ¨¦ ¶q¸ ³³

ª(««««««¬ ���� ³ ���s8|¥����yhqts$u��7|¥�¾��qt��¡_o�y�}�uY{� ~¹|º1�»h¤�© e �7¤)a¼ �k½by��8uYq�y�qts8��q�}�uY{5 ë�½� )� �8x,y�{"y��«u×zYyh{�np§�¹$���s8|r�ë��yhqts$u��Y¾ �kyh{t{tuY{À�«u6�8��qt�Y�JqÀ|r�~��� ¤ ­ £Qh i þ¤4� ­ � h ® ¤�© þ � �ënp�~ ��¿�|h¤�© ��qts$y ü c § uY}�qts$y�Áyhqts$uO�ð���_�8{tu6�Y�"s8y��qÀ+´ ¶ � � � ¡_v$q�qts$yGyh{t{"uY{��«u6�8��qt�Y�Jq�¡Qy��«u6��y���v8�J¡ju6v8�8�$y����G½by@qts�v8�uY¡_��yh{"zYy��pq�{"�Y�$y«�Su�úG¡jyhqèx,yhy��÷�Y�h�hv${"�Y�«~��Y�8����qt��¡_|ror|rq�~�}DuY{�qts8|r�U�Áyhqts$uO���]��s8|r�U|r�`|ro¥orv8��q�{"��q�y��|r� 2 |�w6v${"yN��� ³ � ü },u6�$y@|r��x¢|roro¥|r�$wGq�uÖ�t�Y�«{"| õf�«y@��u6�Áy��Y�h�hv${"�Y�«~bq�u'w6�Y|r�ô|r�b��qt��¡f|ror|�qè~Y�/qts8|r��Áyhqts$uO�7x�u6v8or���8{"u×zO|r�$y�qts$y��Áy��Y�_�¾q�uG�$uG�tu$�np���Y�ôy«�$�Y�Á�_o�yY�Ux,y@w6|�zYy�qts$yG�tqt��¡_|ror|�qè~1�8u6���Y|r�3uY}Àqts$yG�Áyhqts8u��ðqts8��q�s8�Y�� ���¢´ ¶ ¹ ³ |r� 2 |�w6v${"yl������¢��s_|r���Áyhqts$uO�'s_�Y�¢�Y� ü c §�uY}~À�´ ¶ � g ´O�/�Y�8�Ö�Y� yh{t{tuY{��«u6�8��qt�Y�Jq�uY}À � ¶ ¿ ³ � �À��s$y���qt��¡_|¥or|�q�~��$u6���Y|¥��y«��q�y��8�_�¾q�uÁÀj�¢´ ¶ ��´afY�Gu6�7qts$y��$yhw6��qt|�zYy�{ty��Yo`�m�O|r���

³ ´ g

0.2 0.4 0.6 0.8ISB

1

2

3

4

Error Constant

2 |�w6v${tyÂ��� ³ �é�`{"�Y�8y«�Su�úa¡jyhqèx,yhy�� �Y�h�hv${"�Y�«~ ��yh{t{tuY{'�«u6�_��qt�Y��q�� �Y�8� ��qt��¡_|¥or|�q�~a� ü c §¾�@}�uY{�Áyhqts$uO�ð���� ³ �

-0.5 -0.4 -0.3 -0.2 -0.1 0.1

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1

2 |�w6v${"y+������ c qt��¡_|¥or|�q�~��$u6���Y|r��uY}ë�Áyhqts8u��ð��÷� ³ �À}�uY{5 ë�½�¢´ ¶ ¹ ³

å \Z\¾FfT g IS[ ÃÄGH6R]R/W�R/W�H6F_^�ì,lLP6^7WR`ìZT g I�TÆÅ�FfM�PYI�R`T �_E�Ç_EKJ[ma^�ytmaZ�r�y�vÈy>É�To]tZ�RÊToOsË�vÈÌÈvxTÍV^Qr�M9v�ytO{T Z�Ru^�Î;LÁkÁÏÐLÁkNÑ9Ï�OQy>M|LÒ� PÂZ�To]t^_MtR

½by�x¢|r�"s�q�u�y���qt��¡_or|¥�ts�qts8��qÓl]>Z�^Qr�Z�PÕÔÖEKJ n�§ �Áyhqts$uO�8��s_��zYy��8u6�$�hyh{tu ü c §À�¾u6�8o�~�}DuY{¢uY{"�$yh{"��ý��V¿ e ¹ e � e g e ¶h¶h¶ �Ól]>Z�^Qr�Z�PÕÔÖEHG n�§ c �Áyhqts$uO�8�÷s8��zYy �8u6�$�hyh{tu ü c §���u6�8or~ô}DuY{÷uY{"�8yh{"�pýï� � e ¿ e ¹ e � e g e³Y³ e ³ � e ¶h¶h¶ �Ól]>Z�^Qr�Z�PÕÔÖE�� n!3 ��yhqts$u��_�1s_��zYy �$u6�$�hyh{tu ü c §À�Öu6�_o�~ }DuY{3uY{"�8yh{"�@ý � ³ e � e � e � ef e ³ ´ e ¶h¶h¶ ���s$yhuY{"y��¤8�� ³ xÀ�Y���8{tu×zYy��Ö¡�~ §,y��8wYq 2 uY{���¡jyh{tw$�Q�Y�8�'qts8y��Yv$qts$uY{py«��q�y��_�$y��Ös_|r���8{"uJuY}]q�u��s$yhuY{"y����58���Á�Y�8�=8��¿��× Z�P�PÂOØÔÂE&Ù|Ú1kqZ�ytÉsTuDt^Qr�yIË�Z�roÉYÛ ��|�zYy��lÜë��Ýj����o�yhq$ý » ��Ýj�Q¡jykqts8yk�ju6o�~��8u6��|r�YomuY}$�$yhwY{tyhyÞ qts8��q¢|¥��q�yh{t�ju6or��q�y��5Üë��Ý��À��q5Ý7��´ e �p¦ e ���Y¦ e ¶h¶h¶ e � Þ ¦Q�k�¢s$y����Üë��Ýj�t�7ý » ��Ýj��ßÝ���Ý ¬ ¦8� ¶h¶h¶ ��Ý ¬ Þ ¦8�áà Üt� » ® ¤�� �¸´��� Þ ¬ ³ �Íâ ¬ Üt� » ® ©U� �¸´��� Þ ¬ �6�Íâ � ÝN� Þ � Þ ¬ ³ �� ¦ � ¬ ¶h¶h¶1ã �È8�� ³ �

³Y³ ´� {tu�uY}��� ³ � øZ|r�"ñ6äQ��Ý��¾�tv_�"s7qts8��qÜë��Ý��t�7ý » ��Ý��k�å� Ý]��Ý ¬ ¦8� ¶h¶h¶ ��Ý ¬ Þ ¦8�4� äQ��Ýj� ¶ �È8���6�§,~ � ��wY{"�Y�$wYy�¾ �¾|¥��q�yh{t�ju6or��qt|ru6��}�uY{"��v_or�O�×ý » ��Ýj�Z�$yh�jy��8�8�,or|r�$y���{�o�~÷u6�ÒÜë��Ý����ë��s$y�����KÜë��Ýj���7ý » ��Ýj���`��v_��qU�Yor�tup�$yh�jy��8��o¥|r�$y���{"o�~pu6�lÜë��Ý����Y�8��qtsJv_�/¡�~�y-,Jv8��qt|ru6���È8���6���äQ��Ýj����v8�tq��Yor��u��$yh�jy��8�7or|¥�$y���{"o�~�u6�[Üë��Ýj����L�6� ü }tÜë��Ý��ë�|Ý ` }�uY{À� ��´ e ¶h¶h¶ e Þ �Oqts$y��NäQ��Ýj�?æ�´�¡Qy��h�Yv_��yáÜë��Ý��ë�:ý » ��Ý��Z}DuY{¾�Yoro�Qu6or~��$u6�G|r�Yor��uY}��8yhwY{tyhy�o�y��t��qts8�Y�7uY{�y-,�v8�Yo�q�u Þ ��L¿6� ü }ÐÜë��Ýj�ë�|Ý » ® ¤ �8qts8y��ÒäQ��Ýj�?æ ³ �:��$y��h�Y�7��yhy�qts8|r�,¡jy��h�Yv8��y ç-èAé ¨ £ � è � ç �ç � ç ®jc �Kêëêëê � ç ® » c � �ìäQ��Ýj����v8��qÀ¡jy��Á�«u6�8��qt�Y�Jq��t|r�8�«y�qts$y�Jv8��yh{"��q�uY{¢�Y�8�7�$y��8u6��|r�8��q�uY{�s8�×zYy�qts$y��t�Y�Áy��8yhwY{tyhy��Y�8��qts$y��"�Y�Áy�{tu�uYqt�h�k��s$yo�y��Y�8|r�$w3�«u�y«ö@�h|�y��Jqt�÷uY}¢qts$y7��v8�Áyh{"��q�uY{Á�Y�8� �$y��8u6��|r�8��q�uY{÷��{ty7¡juYqts ³ ����u3qts8|r��«u6�8��qt�Y�Jqp��v8��q¾¡jy ³ ���¹J� ü }ÐÜë��Ýj�ë�|Ý » ® © �8qts8y��ÒäQ��Ýj�Z�|ÝN� » � » ® ¤��© ¦Q�<�u6�8�t|r�8yh{ ç-èAé � £ � è � ç �ç � ç ®jc �Èêëêëê � ç ® » c � æìäQ��Ý����,��s8|¥�,|r�¾�÷or|¥�$y���{À}�v8�_�«qt|�u6��x¢|�qts�o�y��Y�8|r�8w��«u�y«ö���h|�y���q ³ ��¡J~@qts$y��t�Y�Áy�{ty��Y��u6�8|¥�$w��Y���L¿6�����,��sJv_�h�\äj��Ýj�Z�»Ý ¬�í �?3Öv_o�qt|��_o�~O|r�$w$�Yx�yõf�8� Ý » ® © � ý » ��Ý��ë� ��Ý ¬�í �I� Ý���Ý ¬ ¦8� ¶h¶h¶ ��Ý ¬ Þ ¦8�4� ¶ �È8��¿6�c |r�8�«y�qts$y�oryh}Dq��s8�Y�_� �t|r�$y�|r�¾�G|r�t�t|r�8w�qts8yFÝ » ® ¤ q�yh{"�7�8qts$y��"v8�¨uY}]|�qt�¾{tu�uYqt�¢��v8��qy-,Jv8�Yo`´O� } �"|r�$wÁqts8|r�Àu6� qts$y�{"|�w6sJq��s8�Y�8�7�"|r�$y�w6|�zYy���¢´B�ð¦q�:�Y¦q� ¶h¶h¶ � Þ ¦l� í ��´ ¶ �È8��²¹J���sJv_�h� í �j� » � » ® ¤��© ¦Q�_w6|�z�|¥�$w÷qts$y��$y��t|r{ty���{ty��tv8orqh�

³Y³Y³�L�6� � yhq!Üë��Ý��,�jî0ïðWñ ­ ª ð Ý ð �¾½by�õ_{"��qp�$uYq�y�qts_��q ª ð �¤ò�ó ôöõ � ­ �ð-÷ ¡J~ ����~Oo�uY{�y«���f�Y�8�t|�u6�����s$y����$x�y�s8�×zYy Üë��Ýj�t�7ý » ��Ýj�� ïøðÍñ ­ ª ð Ý ð ��ý » ��Ý���ù����Ýj�«��Ý ¬ ¦8� ¶h¶h¶ ��Ý ¬ Þ ¦8�4�-äQ��Ý�� �È8���6���sJv_�h�$¡J~�|�q�y������L¿6�À�Y�8�ð��¹J���fx,y�õQ�8�äj��Ýj�1� ª » ® ¤U¬ ª » ® © � Ý6� Þ � Þ ¬ ³ �� ¦ � ¬ ¶h¶h¶� Üt� » ® ¤�� �¸´��� Þ ¬ ³ �Íâ ¬ Üt� » ® ©U� �¸´��� Þ ¬ �6�Íâ � Ý6� Þ � Þ ¬ ³ �� ¦ � ¬ ¶�¶�¶ �È8��­�6���sJv_�h� � y����G�78��²¹G|¥�¾�8{tu�zYy����

½by��8{"u��«yhy��'x¢|�qts��8{tu�z�|¥�$wÁ��s$yhuY{ty����/8�� ³ �z8�����_�Y�_�=8��¿��½ïs8y�� ��u6o�zO|r�$w1qts$y or|r�$y���{��8{tuY¡fo�y��ûú1üú þ �þý{� ��x¢|�qts��ð� ¦sýQ���,qts$y7y��8wYy7uY}p���qt��¡_|¥or|�q�~��$u6���Y|r�7|¥���$y��t�«{"|r¡Qy���¡�~@qts8y�{tu�uYq��ÁuY}Uqts$y�y-,Jv8��qt|ru6�� ��ÿ����Ö���k��ÿ��ë��´

x¢s$y��lÿ�q�{"��zYy�o¥�ë��{tu6v8�8��qts$y�v8�_|�qU�h|�{��ho�y���ÿ���� º�� ����½�s$y��Á�«u6�8�"|r�$yh{"|r�8w¢x¢s$yhqts8yh{k���tqt��¡_|ror|�qè~�$u6���Y|¥�Ö�h�Y�bs8�×zYy�|r����w6|r�_��{t~ �m�O|¥���«u�zYyh{"��wYyGuY{��8uYqh��x,y÷x¢|r�"s q�u �$y��t�«{�|�¡jy�qts$y÷¡jy�s8��zO|�uY{uY}�qts$y���qt��¡_|¥or|�q�~��$u6���Y|r��¡ju6v8�_�8��{t~@�8y���{5����´O�2 uY{p�Y� y«�O�Y�«q��Áyhqts$uO���$x,y�x,u6v8o¥��wYyhq�8���J�ë�����

³Y³ �¡jy��h�Yv8��y ��� � ��ÿ���k��ÿ�� �ïor� ÿ���o¥��� º�� � ����� ¶ �È8�� � �

n ��v8�Áyh{�|r�h�Yo��t�"s8y��Áy�uY}]uY{"�$yh{]ý1x¢|roroQ|r�8��q�y��Y�'o�y��Y�7q�u�8���J�ë����� ¬�� � �����J� � ® ¤ ¬ � � �����J� � ® © ¬ ¶h¶h¶ �È8�� g ���s$y��"|�w6�buY}�qts$yÁõ_{"�tq roZ�OQÌ q�yh{"� uY}Àqts8|¥��y«���f�Y�8�t|�u6�3x¢|¥oro]�8|r�«qt��q�y�x¢s8yhqts$yh{�qts$yG�tqt��¡_|ror|�qè~�$u6���Y|¥��¡Qu6v_�8�8��{t~��$y���{�qts$y�uY{"|rw6|r�7��x¢|r�8w6�Àq�u�qts$y�{"|rw6s�q¾uY{�q�uGqts$y�o�yh}�q¾uY}]qts$y�|r����w6|r�_��{t~�m�$|r�h�ÃéB�û ÄGH6R]R/W�R/W���XkF8R`H6F_î ÃéB�û�dGTZR`TZ^�PYNji/i/F8H�F g å�� îïF$P6XkR g ^2 uY{Ànp§é�Áyhqts$uO�8�h��x�ypõf�8�Áqts8��q � ��� ´��Y�_�@� � � ´@��q�u�¡jyp�ts$u�x¢��¡jy�o�u�x����ë��s$y�_��q�q�yh{"�ô}DuY{�xps8|r�"sb��yhqts$u��_��s8��zYyG�8u6�$�hyh{tu ü c §À��qts$y��b}�u6oro�u�x¢��}D{"u6� qts$yÁ�ju×x�yh{"��uY}Àqts$y|r����w6|¥�8��{t~�v_�8|�që|r�'�È8�� g � � 2 uY{�y«�O�Y�Á�fo�yY�6}�uY{�ý�� ¿���qts$y��Áqts$y�õ_{"��që{ty��Yo8q�yh{"� |r�Áqts8y¢��¡ju×zYyy«�O�_�Y�8�t|�u6�ð|r��w6|�zYy��ð¡J~ � ) �����J� d � � ) � d ��§,y��h�Yv_��y@qts_|r��q�yh{"� |r���ju6�t|�qt|�zYyY�Uqts$yG¡ju6v8�_�8��{t~uY}kqts$yÁ��qt��¡f|ror|�qè~ �$u6���Y|r�1��x¢|r�8w6�¢q�u�qts$y÷{"|�w6sJq�uY}kqts$yÁ|r����w6|r�_��{t~ �m�O|¥���Y�_�Öqts�v8��x�y÷s_��zYy�ð�8u6�$�hyh{tu ü c §+}�uY{@qts_|r���Áyhqts$uO��� 2 uY{�ýí� ���¾qts$y'õ_{"��q�{"y��Yo�q�yh{"� |r� qts$yÖy«���f�Y�8�t|�u6�|r�����Y�����J� � �¨���6���J� � �7§�y��h�Yv8��y�qts8|r��q�yh{�� |r���$yhw6��qt|�zYyY�]qts$y@�tqt��¡_|ror|�qè~1�8u6���Y|r�ô¡ju6v8�_�8��{t~��x¢|¥�$w6�Àq�u�qts$y�o�yh}�q�uY}�qts$y�|r�G��w6|r�8��{t~��m�O|r�¢�Y�8��qts$y ü c §ïuY}Uqts_|r���Áyhqts$uO� |r�À�hyh{"u$��`uGõf�8�'qts$y�z��Yorv$y��¢uY} � � �Y�8�1� � |r� qts8y��h�Y��y�uY}k�$u6�8�tqt��wYwYyh{ty��bnp§Uýb�Áyhqts$uO�8�h�x�y��$uYq�y�qts8��q¢qts$y���y��t��s$y��Áy��h�_x¢s$y��7���8�_o¥|�y���q�uu� � ��ýs�b��x¢|�qts�ý��|����¦8���8qt��ñYy�qts8y�}DuY{������ ë�V¦8��� �j�� Z��´��Z� �¦�� c­ �óý » �� t�����a �È8��­f6�x¢s$yh{"yÀý » �� t��|r�¾qts$y�|¥��q�yh{t�ju6or��qt|¥�$w÷�Qu6or~��$u6�G|r�YoQuY}t��u×zYyh{! ë� �(���óý6� ³ �¦ e ´��S�

³Y³ ¿�¢u�x��8¡�~ � y������u8��²¹$��j�� t���7ý » �� ��k�» «�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8� à ��� » ® ¤�� �¸´��� Þ ¬ ³ �Íâ ¬ ��� » ® ©U� �¸´��� Þ ¬ �6�Íâ �{ �� Þ � Þ ¬ ³ �� ¦�� ¬ ¶h¶h¶ ã�È8�� ³ ´����u�qts_��q�j�L¦8���Â�j�¸´��� �¦���� c­ ���� �� �\ ¬ � c­ �óý » �� t�t�Ö�j�� t���O�\ ��� � �¦�� c­ «�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8�áà ��� » ® ¤�� �¸´��� Þ ¬ ³ �Íâ ¬ ��� » ® ©U� �¸´��� Þ ¬ �6�Íâ � �� Þ � Þ ¬ ³ �� ¦ � ¬ ¶h¶h¶1ã �a ¬ �¦�� c­ �j�� t� �a ¶ �È8�� ³Y³ �

½�s$y��1x,yÁ�tv$¡f��qt|�qtv$q�yl�j�� t��� � º�� þ"! c |r�Jq�ub�È8�� ³Y³ �Á�¸�8uYqt|r�$w�qts8��qá� � » ® ¤�� �¸´��¢� º�º#�c%$ » ® ¤ �Y�8���� » ® ©U� �¸´��k�bº º��c&$ » ® © ���8x�y�õf�_�� º�� � ³ � ���� � º�� � ³ � �Ö� ª » ¦ » ® ©� Þ ¬ ³ �Íâ � ���¦ � » ® ¤ �Ö� ¦(' è » ® )� Þ ¬ �6�Íâ � ���¦ � » ® © � ¶h¶h¶ �È8�� ³ �6�x¢s$yh{"y

ª » � ³¦ » ® © � c­ h�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8� �a � � ¤­ ���K� ¬ ³ � ¶h¶h¶ �K� ¬ Þ � ���) » � ³¦ » ® ) � c­ h�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8� � �� Þ � Þ ¬ ³ �� ¦ � �a � � ¤­ ���K� ¬ ³ � ¶h¶h¶ �K� ¬ Þ � � �/� Þ � Þ ¬ ³ �� � ��� �È8�� ³ ¿6�

½by�qts$y��ð��u6o�zYyÁ}�uY{B�8���J��|r� �È8�� ³ �6���Y�8�ô�$u �Y�ð�Y��~����8q�uYqt|r�÷y«�O�_�Y�8�t|�u6�b��¡ju6v$q*��� � ´�q�uõf�8�

³Y³ ¹

�8���J�?À���� ¬ ª »� Þ ¬ ³ �Íâ �����J� » ® © ¬ ³�$� Þ ¬ �6�Íâ �S� ) » � ª » � Þ ¬ �6���/�����J� » ® ) ¬ ¶h¶h¶ �È8�� ³ ¹J�§�~��$uYqt|¥�$wÁqts8��q¾qts$y�uY{��$yh{]ý�� Þ ¬ ³ �8x�y�qts�v8�Àõf�8��u6v8{��«uJy«ö@�h|ry���qt� � � �Y�_� � �}�{tu6�¨y-,�v8��qt|�u6�=8�� g q�u�¡jy

� � � � ¤­ � Ý ¬ ý6� ³ý � �aÝ e � � �½� � ¤­ � Ý ¬ ý6� ³ý � ý © ¬ ³ �:��Ý�$�óý ¬ ³ � �aÝ �È8�� ³ �6�§�y��h�Yv8��y�¡juYqtsô|¥��q�yhwY{"�Y�_�8����{tyG�$u6�_�$yhw6��qt|�zYyÁ}�uY{¾ý�+ ³ �Ux,yÁqts�v8��s_��zYy�qts8��q � � � ´7�Y�8�� � ��´O�ê��s8|r��y���qt��¡for|r�ts$y���u6v${Á{ty��"v8o�q�qts8��q��$u6�8��qt��wYwYyh{"y�� np�8�Y�G���§À�Y�ts$}�uY{tqts �Áyhqts$uO�8�s8�×zYy �$u6�$�hyh{tu3��qt��¡_|ro¥|�q�~buY{"�_|r�8��q�y�u6�8o�~ô}�uY{÷uY{"�$yh{"�pýé� ¿ e ¹ e � e g e ³Y³ e ³ � e ¶h¶h¶ �Y�8�êqts�v8���s$yhuY{"y�� 8�� ³ |r�¾�8{tu�zYy����ÃéB-, ÄGH6R]R/W�R/W���XkF8R`H6F_î ÃéB-,]d å�� Å�îïF$P6XkR g ^2 uY{¾qts$y���qt��wYwYyh{ty��'�h�Y��yY�$x,y��_{tu��«yhy����t|¥��|ror��{"or~�q�uÁqts$y���¡ju×zYy��h�Y�tyY�8�$uYqt|r�$w�qts8��qx�y÷��{"y��$u×x v8�"|r�$w�qts$y÷�Qu6or~��$u6�G|r�Yo`���8�_{tu��$|r����qt|�u6�1uY}*�j�� t�¢u6�Ø á¹|� Þ ¦ e ´��kq�u ��q�yh�b}�{tu6� k�j� c © q�u6 k� c© |¥�8��q�y��Y�7uY}�}D{"u6�b ë� ´Áq�uu k� ¦Q�Z��s�v8�h�$y-,�v8��qt|�u6�ð�È8�� ³Y³ �À¡jy��«u6�Áy���Ò� ¦ � ���Ö���_� ¦ � �ï� �¦ à � c ! ©£ c ! © �j�� t� �a ¬ � c ! ©£ c ! © � ý » �� t���Ö���� t�4���a ã �È8�� ³ �6�np}Dq�yh{�v8�t|r�$w � y��G���u8��²¹G�Y�8� �tv8¡_��qt|�qtv$qt|¥�$w+���� t�k�.� º�� þ"! c �8x�y�s8��zYy� º�� ! © �/� £ º�� ! ©� �¦10 � � c ! ©£ c ! © «�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8�áà ��� » ® ¤�� �¸´��� Þ ¬ ³ �Íâ ¬ � � » ® ©U� �¸´�� � �� Þ � Þ ¬ ³ �� ¦ � ¬ ¶h¶h¶1ã �a

¬ � c ! ©£ c ! © � º�� þ"! c �a 32 �È8�� ³ � �

³Y³ �np}Dq�yh{���u6o�zO|r�$w÷}DuY{/�÷�Y�_� �$u6|r�$wÁ�Y�Ö�Y��~����8q�uYqt|r��y«�O�_�Y�8�t|�u6�7��¡ju6v$q4������´O�8x�y�õf�8���À���� ¬ � »� Þ ¬ ³ �Íâ �����J� » ® ¤ ¬ � »� Þ ¬ �6�Íâ �����J� » ® ) �È8�� ³ g �x¢s$yh{"y

� » � ³¦ » ® © � c ! ©£ c ! © «�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8� �\ � » � ³¦ » ® ) � c ! ©£ c ! © «�� ¬ ¦8� ¶h¶h¶ �� ¬ Þ ¦8� � �� Þ � Þ ¬ ³ �� ¦ � �\ �È8�� ³ f6�

n¢}�q�yh{÷�tv$¡_��qt|rqtv$qt|r�$w�ý � Þ ¬ ³ �Y�8�ôq�{��Y�8��}�uY{"��|r�$w'u6v${�|r�Jq�yhwY{"�Yor���Ux�y�õf�_�bu6v${�«u�y«ö@�h|�y��Jqt� � � �Y�8� � � }D{tu6��y-,Jv8��qt|ru6�:�È8�� g ��q�uG¡jy� � � � ¤ ! ©£�¤ ! © � Ý ¬ ý6� ³ý �'�\Ý e � � �j� � ¤ ! ©£�¤ ! © � Ý ¬ ý6� ³ý � ý]�óý6� ³ ���:��Ý�$�óý ¬ ³ � �aÝ �È8����´��n�o�qts$u6v$w6s1qts$y�|r�Jq�yhwY{"�Y�8�_�p}�uY{�¡juYqts � � �Y�_�b� � ��{tyÁ�$u o�u6�$wYyh{�uY}À�«u6�8��qt�Y�Jq��t|�w6����x�yÁ�h�Y���w6�Y|r�7y��tqt��¡_or|r�ts�qts_��q � ��� ´��Y�8� � � � ´'��}�uY{ëý � �6�À¡J~7|r�8�_v8�«qt|�u6���O�Y�¢�ts8u×x¢��¡jy�o�u�x��× Z�P�PÂOØÔÂE65

� ¤ ! ©£�¤ ! © � £�¤7�öñ ­ �K� ¬ Ýj� �\Ý � ´ 8�ý9+é� �È8��� ³ �� {tu�uY}]¡J~�|r�8�_v8�«qt|�u6�_�: �óý�� �6�Í�

� ¤ ! ©£�¤ ! © Ý�� ³ ¬ Ý�� �aÝ � ³³ � �È8���Y�6�

³Y³ �: np�t�"v8�ÁyG�È8��� ³ �¾|r�¾q�{�v$y�}DuY{ký�� ¦Q�_��uÁqts_��q� ¤ ! ©£�¤ ! © c £�¤7�öñ ­ �K� ¬ Ý�� �aÝ � ´ �È8���Y¿6�

: c s$u×x�qts8��q�y-,�v8��qt|�u6�ð�È8��� ³ ��|¥�Àq�{"v$y�}�uY{ëý�� ¦ ¬ ³ �� ¤ ! ©£�¤ ! © c7�öñ ­ �K� ¬ Ýj� �aÝ � � ¤ ! ©£�¤ ! © �L¦ ¬ Ý�� c £�¤7��ñ ­ �K� ¬ Ý�� �aÝ��¦ � ¤ ! ©£�¤ ! © c £�¤7��ñ ­ �K� ¬ Ýj� �\Ý ¬ � ¤ ! ©£�¤ ! © Ý © c £�¤7�öñ ¤ �K� ¬ Ý�� �aÝ�È8���m¹J�

��s$y�õf{"��q�q�yh{"�+|r�k�ju6�t|�qt|rzYy¢¡�~Ö�È8���Y¿6���f�Y�8�Gqts8y���y��«u6�_�@q�yh{�� |¥�Z�ju6�t|�qt|rzYy¢¡jy��h�Yv8��yqts$y@|r�Jq�yhwY{"�Y�8�:|r���ju6�t|rqt|�zYy�u6�<;x�7¤© e ¤© ¼ �]��u'x�y@s8�×zYy@qts_��q � � � ´'}DuY{pý=++�7¡�~|r�8�8v8�«qt|ru6���× Z�P�PÂOØÔÂE Ç� ¤ ! ©£�¤ ! © º ý © � ý6�:��Ý $ � £�¤7�öñ ­ �K� ¬ Ýj� �\Ý � ´ 8�ý>+é¿ �È8���Y�6�� {tu�uY}U¡�~�|r�8�8v8�«qt|ru6�_�

: 2 uY{ký��V¿��8x,y�s8��zYy� ¤ ! ©£�¤ ! © �Kfá�:¿!�ê��Ýj� ) £�¤7�öñ ­ �K� ¬ Ý�� �aÝ�� ³ ¿ �³ ��´ ¶ �È8�����6�

: np�t�"v8�Áy�qts8��q�y-,�v8��qt|�u6�:�È8���Y�6�¢|r�Àq�{"v$y�}�uY{ëý��V¦7��uÁqts8��q� ¤ ! ©£�¤ ! © º ¦ © �ê¦l�:��Ý $ c £�¤7�öñ ­ �K� ¬ Ý�� �aÝ � ´ �È8��� � �

³Y³ �: c s$u×x�qts8��q��È8���Y�6�¾|r�¾q�{�v$y�}DuY{ký�� ¦ ¬ ³ �� ¤ ! ©£�¤ ! © ;¸�L¦ ¬ ³ � © �é�L¦ ¬ ³ ���:��Ý ¼ c7�öñ ­ �K� ¬ Ý�� �aÝ��¦ � ¤ ! ©£�¤ ! © º ¦ © �ê¦q�ð��Ý $ c £�¤7�öñ ­ �K� ¬ Ý�� �aÝ

¬ � ¤ ! ©£�¤ ! © ºè�Y¦ © ¬ ÝQ¦��L¦ ¬ ³ ���:��Ý © $ c £�¤7�öñ ­ �K� ¬ Ý�� �aÝ��¦ � ¤ ! ©£�¤ ! © º ¦ © �ê¦q�ð��Ý $ c £�¤7�öñ ­ �K� ¬ Ý�� �aÝ ¬ �Y¦ © � ¤ ! ©£�¤ ! © c £�¤7��ñ ­ �K� ¬ Ýj� �aÝ

¬ � ¤ ! ©£�¤ ! © Ý © �L¦��L¦ ¬ ³ ���ê��Ýj� c £�¤7��ñ ¤ �K� ¬ Ýj� �\Ý �È8��� g ���s$y�õ_{���q¾q�yh{"� |r�¾�ju6�t|�qt|�zYy�¡�~ô�È8��� � ���p��s$y���y��«u6�8�1|r�¾�ju6�t|rqt|�zYy�¡J~ � y������68������Y�8��qts8y,qts8|r{"��q�yh{"�a|r�U�ju6�t|�qt|�zYyZ¡Qy��h�Yv_��y,qts8y�|r�Jq�yhwY{"�Y�8��|r�U�ju6�t|�qt|�zYy,u6�Á�(� ³ ��� e ³ ���o�}DuY{p¦?+é¿����s�v8�h�`� � � ´7}DuY{¢ý@+ ¿�¡�~3|¥�8�8v8�«qt|�u6�b�tu qts8��q�n�§ c �Áyhqts$uO�8��s_��zYy@�8u6�$�hyh{tuü c §À�Àu6�8o�~�}DuY{¾uY{"�8yh{"�]ý�� � e ¿ e ¹ e � e g e ³Y³ e ³ � e ¶h¶h¶ �¢� � y����_}D{tuYw$�6ý�� ���_|r�¾�Á�t�Qy��h|¥�Yo��h�Y��yY�ó�ÃéBx� ÄGH6R]R/W�R/W���XkF8R`H6F_î ÃéBx�]d å�A îïF$P6XkR g ^2 uY{�qts8|r���h�Y��yY�`x,y÷x¢|r�"s'q�u7��q�yh� � }�{tu6� ��C�p¦'q�u� ¢�a´�v8�t|r�8w@|r�Jq�yh{t�ju6or��qt|r�$w�8��qt�7��qF ¢� ´ e ��¦ e ¶h¶h¶ e ��� Þ ¬ ³ �¦Q���È�puYq�y�qts8��q�qts8|r��|r��y-,�v8|�z��Yo�y��Jq�q�u7��q�yh�_�_|r�$wÁ�'}�{tu6� �� ´7q�u= p� ¦3v8�t|¥�$w7|r��q�yh{"�Qu6o¥��qt|r�$w��8��qt� ��qF �� ¦ e ´l� ¦ e ¶h¶h¶ e � Þ ¦Q�/xps8|r�"sb|¥��s$u×x x�yv8�tv_�Yoro�~@|¥��q�yh{t�_{tyhq¢n��8�Y����43Öu6v8o�q�u6�Ö�Áyhqts$uO�8�h�ó� 2 u6oro�u�x¢|r�$w�qts8y��t�Y�Áy��8{tuO�«y��8v${ty��Y���$u6�$y|r��qts$y��8{tyhzO|�u6v8��q�x�u@�h�Y��y����¸�Y�8�'�8uYqt|r�$w÷qts8��qëý�� Þ ¬ �6���8x�y�õf�8��qts8��q��À���� ¬ ª �ý>â �����J� � ¬ ) ��$�óý ¬ ³ �Íâ �����J� � ® ¤ ¬ ¶h¶h¶ �È8����f6�

³Y³ gx¢s$yh{"y

ª � � � ¤­ � £_©7��ñ £�¤ �K� ¬ Ýj� �\Ý) � � � ¤­ º ��Ý6�ï�óýN� ³ � © $ � £_©7��ñ £�¤ �K� ¬ Ýj� �\Ý �È8��¿�´��§�y��h�Yv8��y�qts$y�|r�Jq�yhwY{"�Y�8�8����{"y�uY}��«u6�_��qt�Y��q��t|�w6��u6��� ´ e ³ �S� ª � � ´��Y�8� ) � � ´O�·ë�$�Y��|r�8|¥�$w¾qts$y,�"|�w6��uY}$qts$yZõ_{"��q`{ty��Yo�q�yh{�� |r���È8����f6�`�Yoro�u�x¢��v8�/q�u��«u6�8�horv8�8ykqts8��qn��8�Y����43Öu6v8o�q�u6�÷�Áyhqts$uO�8��s8��zYy¾�$u6�8�hyh{tu ü c §À�Uu6�8o�~�}�uY{�uY{"�$yh{"�fý�� ³ e � e � e � e f e ³ ´ e ¶h¶h¶ ��¸§À�Y�tñ�x���{��8�p·,v8o�yh{��óý�� ³ �À�Y�8� n!31�'�óý7� �6�À��{"y����jy��h|r�Yo��h�Y��y��h�ó�

å \Z\¾F_T g IL[ BÄGH6R]R/W�R/W�P6XkF ^�PYNQi`i/F8H6F g N�TZNjl�R/i`ìZF R/W�çbN�XZl�C]ìZI�^�PED¥^�K�H�^�P>FZNjH6HJISF8H�¸��s$y�x�uY{tñ�|r��qts8|r�����_�Qy��_�8| �GxÀ�Y���$u6�$y�¡�~�qts$y��Yv$qts$uY{×�ó�Ól]>Z�^Qr�Z�PHG�EKJ ��s$y�uY{��$yh{ëý'uY}ë�Y�7y«�O�_or|r�h|rqÀ�tqt��¡_o�y�������q�yh�'�tqt��wYwYyh{ty��Ö��yhqts$u��'�t��qt|r�õ_y��

ý � ¯IIIII° IIIII±� � � �Y�7yhzYy��1|r�Jq�yhwYyh{� ¬ ¤© � � ��s8�Yor}¥��|r�Jq�yhwYyh{� ¬ ³ � � �Y�7uO�8� |r�Jq�yhwYyh{ � ü � ³ �

:�v${��8{tu�uY}¢uY}pqts8|r��qts$yhuY{ty�� }�u6oro�u�x¢��qts$u6��y �$u6�$y�¡�~KJYy�orqt�t�"s �Y�8���pyhzm�Y�_or|r�8�8��� ³ f����Y�8�ò��Ys8o�,�v8|r��qB�²���/}�uY{¢�$u6�_��qt��wYwYyh{ty��1�Áyhqts$uO�8�h�× Z�P�PÂO1G�EHG �¢s$y��Y��~O�Á�8q�uYqt|r��y«�O�_�Y�8�"|�u6��uY}YL ³ � Y © o�uYw�¤ ® %¤�£ % � ïøðWñ ­ � ð Y ð � ü ��6��t��qt|r��õ_y���� © ð ® ¤ ��´��Y�8�'� © ð � ´O�� {tu�uY}��

:��$yÁ�h�Y�ô��yhyGqts8��q�� ­ � ¤© ¡J~3�«u6�8�t|r�8yh{"|r�$w�qts$y�or|r�G|�qpuY}�qts$yGoryh}Dq��s8�Y�_�b�t|r�$y÷�Y�Y � ´O�'n�or��u$�]� © ð ® ¤ �¨´'¡jy��h�Yv8��yGx�y�s8��zYy��Y�ðyhzYy��:}¸v8�8�«qt|�u6���7½by��8|�zO|r�$yÁ¡juYqts:�t|r�$y��uY}�y-,Jv_��qt|�u6� � ü ��6�÷¡�~ Y �Y�8� qts8y�� q�{"�Y�8�t}DuY{"� Y � ¤M � ½by1��{ty'qts$y�� �«u6�8�t|r�$yh{�|r�$wbqts$y

³ ��´y«�O�_�Y�8�t|�u6� N

L N © � ³ oruYwO�¤ ® MM £�¤ � �N� ¬ ïøðWñ ­QP © ð ® ¤

N£ � © ð ® ¤�� � ü �¿6�

x¢s$yh{"y P © ð ® ¤ ��� © ð ® © �k§�~�<À�Yv8��s�~z¾ � ü ��q�yhwY{��Yo 2 uY{"��v8or�P © ð ® ¤ � ³�3RQ�&SET N © ð

NL N © � ³ o�uYw j¤ ® MM £�¤ � �

N� ³�3RQ�&SET

N© ð ® ¤VU M ® ¤M £�¤�

N¬ ³ ��o�uYw M ® ¤M £�¤ � �

N� ü �²¹J�

x¢s$yh{"y+� |r�¾�Y� ��{"¡_|�q�{"��{t~��hv${tzYy�y��_�ho�u6�t|r�$w �ö� ³ e ³ �¾u6� qts$y�{"y��Yo/�m�O|¥�h�§�~@qt��ñO|r�$w�u6v8{¾¡8{"�Y�8��s �hv$q�u6�ð�ö� ³ e ³ �ÀuY}]qts$y�{ty��Yo/�m�$|r�h�$x�y�qts�v8�Àõf�_��qts8��qW ÊYX�ZfÕ Ù ÂÑ ÃE[�\]Ä ÕÉ8Õ Ó Ê^X�ZfÕ`_ ÕYZbaÕÉ(a Î [ ÒÎrÓ�Ô Â Òdc [�à Ô9eóÌ`fgc Õ�ZhaÕÉ(aji(i Ø Ó�Ð Ä ÕÉ$Õ Ó ÊYX�ZfÕk_ Õ�ZhaÕ�Éla ÎSÐ [ ÒÎ¥Ó�Ô Â Òdc�Ð [¸Ã Ô9e>Ìkf*c Õ�ZhaÕ�Élali(i

mnØ ÓÙ ÂÃGÄ ÕÉ8Õ Ó Ê^X�ZfÕ eóÌ`f c Õ�ZhaÕ�Éla io  Ð@Ó Ê c Ã Ê Ô9eóÌ`f Ê c Õ�ZhaÕ�Éla iEi Ø Ó Î"p�ã ä�Ò

§�y��h�Yv8��y¢qts8y¢|r�Jq�yhwY{"�Y�8��|r�Z�$u6�O���$yhw6��qt|�zYypu6�'�ö� ³ e ³ ���Ox�y�qtsJv_�ëõf�8�÷qts_��q P © � ® ¤ �´��Y�8��qts�v8�¾qts_��q¢� © � � ´�|r�ô� ü ��6���_qts�v8�¾�8{tu�z�|¥�$w � y������ ü ����× Z�P�PÂO1G�E�� ü �7qts$y��Y�t~��Á�_q�uYqt|r��y«�O�_�Y�8�t|�u6�Y U ¤ ® %¤�£ %o�uYwO�¤ ® %¤�£ % � � ïøðWñ ­rq ð Y ð � ü �­�6�x�y�s8��zYy q ð � ´O�

³ � ³øk{"uJuY}ö�

½by��$uYq�y�qts_��qY U ¤ ® %¤�£ %o�uYwO�¤ ® %¤�£ % � � � ³ ¬ Y � YL ³ � Y © o�uYwOj¤ ® %¤�£ % � � � ³ ¬ Y � ïøðÍñ ­ � © ð Y © ð � ü � � ���s$y��/�$¡J~ � y����G� ü ���� q © ð � q © ð ® ¤ � � © ð � ´O�8qtsJv_�¾�8{tu�z�|r�8w � y������ ü �¿��× Z�P�PÂO1G�E Ù#ÚtsÒZ�r�P�u�y>M�v�OQ]�Ì-wxu�v�RÊT�Û ü } � � Y �7� î `ðWñ ­ ª ð Y ð }�uY{��:��qt��¡_o�y1��v_o�qt|r��q�yh��Áyhqts$uO���$qts$y��'�Yoro��«uJy«ö��h|�y���qt� ª ð s8��zYy�qts$y��t�Y�Áy��t|�w6���øk{"uJuY}�uY}Uqts_|r��o�y����G�Á�h�Y�7¡jy�}Du6v8�_�7|r�Ö�²���S�½by��8{tuO�«yhy��7x¢|rqts�qts$y��8{tu�uY}�uY}���s8yhuY{ty�� ü � ³ �BJB�û �@N�^�F û�dzy NïXkN�lSW e IèTUP�F_i/F8H

½bykõ_{���q`�«u6�8�t|¥�$yh{`qts$y,�h�Y��y,uY}$� �¢s8�Yo�}D��|r�Jq�yhwYyh{�� 2 uY{�qts_|r�/�h�Y��yY�Yx�y,�h�Y��{tyh�8{ty��ty���qqts$y�wYy��$yh{���qt|r�$w��ju6o�~O�$u6��|r�Yo¥���Y�� �^{J�1�|{ ¤ ! ©~}6� ­ ¬ � ¤ { ¬ ¶h¶h¶ ¬ � ` £�¤ ! © { ` £�¤ ! ©t��k�^{J�1� } í_­Z¬�í ¤ { ¬ ¶h¶h¶ ¬�í ` £�¤ ! © { ` £�¤ ! © � � ü � g �

½by@����ñYyGqts$yÁ��{tyhyhñJ����u6�G�Y�ðq�{"�Y�_��}DuY{�����qt|�u6�/{ � ¤ ® %¤�£ % �Y�8�ô�$y«õQ�$yÁqts$y�}¸v8�8� �qt|�u6�8�

³ �Y�

ÿ8� Y �[æ � ³ � Y� � ` £�¤ ! © � � ³ ¬ Y³ � Y �� ³� ` £�¤ ! ©�� ³ ¬ Y³ � Y }6� ­ � ³ � Y � ` £�¤ ! © ¬ � ¤ � ³ � Y � ` £ ) ! © � ³ ¬ Y � ¬¶h¶h¶ ¬ � ` £�¤ ! © � ³ ¬ Y � ` £�¤ ! ©��æ � ³ ¬ Y³ � Y ` £�¤ ! ©ø º ñ ¤ ª º Y º � ü �­f6��Y�8���� Y �æ � ³ � Y� � ` £�¤ ! © � � ³ ¬ Y³ � Y �� ³� ` £�¤ ! © } í ­ � ³ � Y � ` £�¤ ! © ¬�í�¤ � ³ � Y � ` £ ) ! © � ³ ¬ Y � ¬ ¶h¶h¶ ¬�í ` £�¤ ! © � ³ ¬ Y � ` £�¤ ! ©��æ ` £�¤ ! ©ø º ñ ­ ) º Y º ¶ � ü � ³ ´��½by �$uYq�y�qts8��q÷¡jy��h�Yv8��y � �^{ð� ³ �Á� ´ �¸�«u6�8�t|r�tq�y��8�«~$���Zx,y7s8�×zYy�ÿ$� Y � ´��Á� ´O�ð��s�v8�h�ª�­ ��´O� §�y��h�Yv8��y¾x�y¢s8��zYy����tqt��¡_o�y��Áyhqts$uO���6�YoroO{"uJuYqt��{�uY} � �^{�����v_��q]¡Qy¾|r�_�t|r�$y,qts$y�v8�8|�q�8|r�tñf�Yx¢|rqts÷{tuJuYqt�ku6�Áqts$y�v8�8|rq]�h|r{"�ho�y¾�t|r�Á�fo�yY� c u$�J�YoroO{tu�uYqt� Y uY}zÿ8� Y �]��v8��qkor|�y¾|r�÷qts8y��ho�u6��y��o�yh}�q��s8�Y�8�Ö�_or�Y�$yY�jx¢|rqts'{tu�uYqt��u6�3qts$y÷|r����w6|r�8��{"~ �m�O|r���t|¥�Á�_o�yY����s$y����Q¡�~ � y����G� ü �²¹$�/�Yoro�«u�y«ö@�h|�y��Jqt� ªJº qts_��q¢��{ty��$u6�$�hyh{"uG��v_��q�s8��zYy�qts$y��t�Y�Áy��t|�w6��� c |¥�8�«y

ª ¤ �|ÿ � � Y ��´��k� � ) ! © £ ` � ´ e � ü � ³Y³ �x�y�s8��zYy�qts8��q

ª ð +é´ 8(�O+ ³ ¶ � ü � ³ �6�

³ �Y¿��s$y��«u6�8�8|rqt|�u6��}DuY{��Á��v_o�qt|r��q�yh� �Áyhqts8u��7q�uG¡Qy�uY}]uY{"�8yh{]ýÖ�h�Y� ¡jy�x�{"|rq�q�y��7�Y�� �^{J�o�uYw�{ �Â�k�^{��k� � � ® ¤ �^{F� ³ � � ¬#� ;¸�^{F� ³ � � ® ¤ ¼ � ü � ³ ¿6�

��}�uY{¢��u6�Áy � � ® ¤ µ� ´����Z��s8|r�¾�h�Y� ¡Qy�{"yhx�{"|�q�q�y��7|r� q�yh{"���¾uY} Y �sÿ8� Y ���_�Y�_���J� Y �À�Y�ÿ8� Y �Y U ¤ ® %¤�£ %  ¢ Y U ¤ ® %¤�£ %o�uYw�j¤ ® %¤�£ % � ª¬ �"��� Y �k�V� � £ ` ® ¤ ! © � � ® ¤ Y � ¬�� � Y � ® ¤ � ¶ � ü � ³ ¹J�½by��$y«õf�8y Y�U ¤ ® %¤�£ %o�uYwO�¤ ® %¤�£ % � æ ïøðWñ ­rq ð Y ð � ü � ³ �6�

x¢s$yh{"y�x,y�ñO�$u�xVqts8��q q ð � ´ 8E��¡�~ � y������ ü �¿����s�v8�h�Oqts$y�uY{"�8yh{¢�«u6�8�8|�qt|ru6��¡Qy��«u6��y���� ` £�¤ ! ©ø º ñ ¤ ª�º Y º £�¤��� �� ïøðWñ ­rq ð Y ð �� � ` £�¤ ! ©ø º ñ ­ ) º Y º/�V� � £ ` ® ¤ ! © � � ® ¤ Y � ¬�� � Y � ® ¤ � ¶ � ü � ³ �6���s$y¾õf{"��qZq�yh{�� |r�Gqts$y�y«���_�Y�_�t|�u6��uY}�qts8yp�8{"u��8v_�«qkuY}/��yh{"|�y���|r�1� ü � ³ �kqts8��qÀ�h�Y�8�$uYq�ju6�t�t|�¡fo�~Ö¡jy��h�Y�8�«y�oro�y��ê¡�~ð�Öq�yh{"� |r�:qts$y��tyh{"|�y���}DuY{u��� Y ��|r��qts$y Y ` ® ¤ ! © q�yh{"�7�3½by o�yhqýð� � ¬ ³ ��� �Y�8�b�«u6�8�"|r�$yh{�qts$y��«u�y«ö@�h|�y��Jqt��uY}�qts$y Y ` ® ¤ ! © q�yh{�� u6�b¡juYqtsb�t|r�$y���uY}�qts$yy-,�v8��qt|�u6�7q�uÁõQ�8� ` £�¤ ! ©øðÍñ ¤ ª ð q ` ® ) ! © £ ð � � � ` ® ) ! © ¶ � ü � ³ � ���s$y����O¡jy��h�Yv8��y q ð � ´G�Y�8� ª ð + ´÷}�uY{p�Yoroh� � ´O�8x�y�s8�×zYy� ` ® ) ! © � ³� ` £�¤ ! ©øðWñ ¤ ª ð q ` ® ) ! © £ ð + ³� ª ¤ q ` ® ¤ ! © � ´ ¶ � ü � ³ g �

³ �m¹c |r�8�«y � ` ® ) ! © µ� ´O�/x,y�õf�_�'qts8��q�ýð�h�Y�8�8uYq�y-,�v8�Yo¾��uY{�¡jy÷or��{twYyh{�qts8�Y�f�¢� ¬ )© ���s�v8�h�¾qts$y1uY{"�$yh{�ý�uY}��Y�ï������q�yh� �Áyhqts$uO���¾x¢s$yh{ty1� |¥�@�ês8�Yo�}D��|r�Jq�yhwYyh{��¢��v8��q@�"��qt|r��}�~ý � � ¬ ¤© �k½by��$uYq�y�qts_��q¢np§ c ý1�Áyhqts$uO�8��s8�×zYy¾ý��ï� ¬ ¤© �Y�8�7qts�v8���Y�"s_|�yhzYy�y-,�v8�Yor|�qè~}�uY{�qts8|r�¾�h�Y��yY�BJB-, �@N�^�F@,]dzy N�T I�TUPYF8i/F_H½ïs8y��7� |r�¾�Y�'|¥��q�yhwYyh{��_x,y��h�Y�'{tyh�8{ty���y��Jq¾u6v${�wYy��8yh{"��qt|r�$w��ju6o�~O�$u6��|¥�Yor�À�Y�

� �^{J�1�Õ� � ­ ¬ � ¤ { ¬ ¶h¶h¶ ¬ � ` { ` ��k�^{J�1��{ ¤ ! © ; í ­ ¬�í/¤ { ¬ ¶h¶h¶ ¬�í ` £�¤ { ` £�¤ ¼ ¶ � ü � ³ f6�np}Dq�yh{�����ñ�|¥�$w÷qts$y�q�{"�Y�8�t}DuY{"�G��qt|�u6�>{�� ¤ ® %¤�£ % �$x,y��8y«õf�$y�qts$y�}¸v8�8�«qt|ru6�8�ÿ8� Y ��æ � ³ � Y� � ` � � ³ ¬ Y³ � Y �� ³� ` ; � ­ � ³ � Y � ` ¬ � ¤ � ³ � Y � ` £�¤ � ³ ¬ Y � ¬ ¶h¶h¶ ¬ � ` � ³ ¬ Y � ` ¼æ `ø º ñ ¤ ª�º Y º � ü ���´���Y�8���� Y ��æ � ³ � Y� � ` �Ö� ³ ¬ Y³ � Y �� ³� `1� ³ � Y © ; í ­ � ³ � Y � ` ¬�í�¤ � ³ � Y � ` £�¤ � ³ ¬ Y � ¬ ¶h¶h¶ ¬�í ` £�¤ � ³ ¬ Y � ` £�¤ ¼æ � ³ � Y © ` £�¤ø º ñ ­ ) º Y º ¶ � ü �� ³ �

n¢w6�Y|¥���ëx,y�s8�×zYy ªJ­ �È´1}�uY{Á�«u6�8�t|r��q�y��_�«~ð�Y�8� ª ð +¨´ 8(��+ ³ }�uY{÷�tqt��¡_|ror|�qè~�¸�$uYqt|r�8wÁqts8��q ª ¤ � � ¤�£ ` � ´��À¡J~ � y��G��� ü �²¹$�

³ �Y���s$y�uY{"�$yh{p�«u6�8�8|�qt|�u6�ô� ü � ³ ¿6�À¡jy��«u6�Áy��ÿ8� Y �Y � YL ³ � Y © o�uYwÒ� ³ ¬ Y³ � Y ���q� �J� Y �L ³ � Y © � � � £ ` � � ® ¤ Y � ¬#� � Y � ® ¤ � � ü ��Y�6�x¢s8|r��s��$v8�t|r�8w7� ü ��6���f�h�Y� ¡Qy�{"yhx�{"|�q�q�y��7�Y�� `ø º ñ ¤ ªJº Y º £�¤�� �� ïøðÍñ ­ � ð Y ð �� � ` £�¤ø º ñ ­ ) º Y º/� � � £ ` � � ® ¤ Y � ¬#� � Y � ® ¤ � ¶ � ü ��Y¿6�½by�ñO�$u×xV}�{tu6� � y������ ü ��÷qts8��q�� © ð � ´Á�Y�8�7� © ð ® ¤ � ´O�Z��s$y���qts$yh{"y���{ty�q�x�u�h�Y��y��Ê�

� ³ �7� yhzYy��ü },� |¥��yhzYy����/qts$y��b� ` � ´O�÷��s$y�õ_{"��q�q�yh{"� |¥�3qts$y÷�8{tuO�8v8�«q�uY},qts$yÁqèx,u �tyh{"|�y��|r�:� ü ��Y¿6�¾qts_��q��h�Y�8�8uYq¢¡jy��h�Y�8�«y�orory��'¡�~7��q�yh{"� |r� qts8y���yh{"|ry���}�uY{á��� Y �¾|¥��qts$y Y `q�yh{"�7�k½by�oryhqëý��ï� �Y�8�'�«u6�8�t|r�$yh{¾qts8y��«uJy«ö@�h|ry���qt�puY}Uqts8y Y�` q�yh{����h�$w6|�zO|r�$w� ` ® ¤ � `ø º ñ ¤ ªJº � ` £ º ® ¤ + ª ¤ � ` � ´ � ü ��m¹J�

�¸v8�t|r�$w'qts$y@}¸�Y�«q�qts8��q ªJº + ´����1��s�v8�h��qts8|r��q�yh{�� �h�Y�8�8uYq�y-,�v8�YoZ´1�Y�8�:x,yGõf�8�qts8��qZ�tv8��s����Áyhqts8u����h�Y�_�$uYqZs8�×zYy¢uY{"�$yh{Z� ¬ ³ ��uY{,s_|�w6s$yh{ ���]��s�v8�h�6x�y�s8��zYypqts8��qý � � }�uY{�� yhzYy�����L�6�7� u��8�ü }�� |r�ZuO�8���Jqts$y���� ` � ´�¡_v8q,� ` ® ¤ � ´O�k��s$y¢õ_{"��q,q�yh{"�+|r��qts8yp�8{"u��8v_�«qkuY}/qts$yq�x�u@��yh{"|ry��¾|r�ô� ü ��Y¿6�¾qts8��q¢�h�Y�8�8uYq�¡jy��h�Y�8�«y�oro�y��7¡�~��Áq�yh{"��|r��qts8y���yh{"|�y��¾}�uY{;��� Y �|r�Zqts8y Y ` ® ¤ q�yh{"�7�ë½by�qts$y���o�yhqUý��ï� ¬ ³ �Y�8���«u6�8�t|r�8yh{,qts$y��«u�y«ö@�h|�y��Jqt�ÀuY}`qts$yY�` ® ¤ q�yh{"�G�h�8w6|�zO|r�$w� ` ® © � ³� `ø º ñ ¤ ªJº � ` £ º ® © + ³� ª ¤ � ` ® ¤ � ´ � ü ��Y�6�

³ ����¸v8�t|r�$w�qts$y�}��Y�«q�qts8��q ª�º � ´O�k��s�v8�h��qts8|r�Zq�yh{"�+�h�Y�8�$uYq�y-,Jv_�YoQ´��Y�8�@x,ypõf�8�Gqts8��q�tv8�"s:� �Áyhqts$uO�ð�h�Y�_�$uYq�s8�×zYyGuY{"�8yh{�� ¬ �ð��uY{�s_|�w6s$yh{ ������sJv_�h�`x�y@��v8��q�s_��zYyqts8��qëý � � ¬ ³ }DuY{¢� u��8�/���s8|r�À�«u6�Á�fo�yhq�y���qts$y��_{tuJuY}�uY}ë��s$yhuY{ty�� ü � ³ �½by��8uYq�y�qts8��q�§Àò c ý3��yhqts$u��_�ps8�×zYy�ý'��� �Y�8�'qts�v8���Y�"s8|ryhzYy�y-,�v8�Yor|rq�~7}�uY{p�yhzYy���� 2 uY{¢� uO�8���Ox�y�or|r��q¾�Á}�yhxVy«�$�Y�Á�_o�y���uY}��Áyhqts8u��8��qts8��q¢�Y�"s_|�yhzYy�y-,�v8�Yor|�qè~Y�: � � ³ �Zo�y����8}�{tuYw � » ® ¤ �»� » ¬ ¦{Ü » ® ¤ ! © � ü ����6���s$y���qt��¡_|ror|rq�~G�$u6�G�Y|r�GuY}Uqts8|r����y��«u6�8��uY{"�8yh{À�"�"s$y��Áy�y«�Oq�y��8�8�À}�{tu6� �p�V�ëq�uG�V�ëu6�qts$y�|r����w6|¥�8��{t~@�m�$|r�h�: � � ¿�� � » ® ¤`¬ �ö�p� � ¬ �m¹� ���� » �é�ö�p� � ¬ �m¹� ���� » £�¤ �Ö� » £_©� ¦7ºK 1Ü » ® ¤ ! © ¬ �ö�p�m¹ ¬ �Y�� �� Ü » £�¤ ! © ¬ 1Ü » £ ) ! © $ � ü �� � ���s8|r��}�u6v${tqtsêuY{"�$yh{��t��s$y��Áy7x¢|rqts:�f��{"�Y�Áyhq�yh{u �|r�÷��qt��¡_o�y�}�uY{7 N¹ � ³ e � ���6�Áx¢|�qts��qt��¡_|ror|rq�~@�8u6���Y|r�8�¾�«u6�8�"|r��qt|r�$w÷uY}]u6�8o�~@qts$y�uY{"|rw6|r���