a5b c6bed#fhgjilkmfonefqprktsjuwvyx b...\i v lekts!fhghi=vjs dq rvtvyvjles f) tfhs sjkmftfq 0s...

31

Upload: others

Post on 23-Jan-2020

2 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

����������� � ��������������������������� �!�#"%$&�# '&(�)�#�* ���

+ �-, ���.���/(0����21435' �6(0�)���7"98%��(�;:%��������� <=��>�'&(0"@?

A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX�B Z\[�B^]R_^`QVLa/BEbcKM_Ed=VLa/BLe._LfhgHG-ijVX�BL]kf-lRm�FQnoFQILN�p#B q�BLr0gkNkgHG

p6stSJstFQG-f-l7p6shuYgHGJvcw6gLByxHzHzO{jZ|zL}~ FQIR_LFQG��&xQzOzO{

]Rst��K�ILFHG����_EGcqcIE�Hstm�FHILNRvJs#��FQvJlEst��FjvJKMPC�KMNE�HshI0�gOS�S�KTSJf-lLs!r0stf-lEILKMS�f-lEs#[6gkf-lLS�f-lR_E��s

X�[�Z\�HzO�Ox��y�_EG�KMf-l]Rm�K�vJ�tshG��MFHILN

���.�W���Y�6�-�h�W���������� ^���Y�W�W¡�¢��£��¢\¤���¢\¥����c¦t§©¨«ª­¬.¢\¤���¢\¥y®L�.�W¢¯¥±° �³²�°-´=µ¶�-�³���·�-¡j�-²t����¸�¦t�=¸h¹�����-��¡cº=�W��° �¥.�-�.�³���W�Q° �� �¢�¡c»)¼c½¶¾¿0¸t¨ÀE¾¶¦t¬y¸W¾«Á¬Â�-�W¡�Á«¦hÀ.®t�.�W¢¥£° ��²�°-´L¦t�|�)¥.�-»!�-�W¡��k°h¡W° �£¥.�-�.�³���W�Q° �� �¢�¡�»h¼§ÄÃ0Å��W¢\ ©¥£° ��²5Æ|DZ��¢��-²t���WÈ�É£° ����Ê�¢�Ët�  ©¼tÌ�°-´k ³��¢¶¿£É��W�W¡�¢��¯��° �h ��|�-�\ 0�t����»Q¢��0ïű¬¯Á¯ÍÎɱ�£ÍÄÏ Ð Ð Ï�ÍÄÐ Ð Ï Ñ Ò�¸W�-�W¡»)¼c ��W¢�¦h¥¯���³�.Àj¢�¡W¢��|�-Êk¾0Ó���¢´M° �0¦t����¢��W��¢��-�W¡Ô¿^¡W�W���� ³��° �!�W�W¡W¢��¯È �|�-�) Ç£ÇYÕ�Ð Ï�® Ð-ÖW×�ÑØ É±° �³��¢����Q° �W¡W���WÈ&�-�� ��W° ��¸«½� ¤t���³��° ��°-´�¨�W��Ê���¢�¡oª#�� ³�W¢��6�� ������J¸0DZ�³°�¥0�oÙ0�W� ¤)¢��³���  ©¼)¸0Å^�³°�¤���¡W¢��W��¢ ¸¶¬.§

Ð Ï Ú�×�Ï�¸HÙ«¦h¨�¸=Û�¢��6�-��ÊTÜ È ²WÝ¡W�-�Ô® »W�³°�¥0�O® ¢�¡��QÞß ½� ¤t���³��° �c°-´E¨�W��Ê���¢�¡!ª#�� ³��¢��6�� ������J¸WDZ�³°J¥¯�!Ù0�W� ¤)¢��³���  ©¼)¸WÅY��°J¤t��¡W¢��W��¢ ¸Q¬¯§±Ð Ï Ú�×�Ï�¸QÙ«¦t¨à ½¢��j�-�Π³��¢��) 0°-´^ɱ�W¢��������-Ê=¿^�WÈ ���W¢�¢��³���WÈW¸WÅY�³������¢\ �° �ÔÙ¯�W� ¤)¢��³�³�  ©¼)¸jÅ^�³���W��¢\ �° �=¸QÁá�Ð Ñ â-Ö ÖW¸HÙ«¦t¨ã-½¢��j�-�Π³��¢��) Ô°-´�¾��¢��-��¿Y��È ���W¢�¢������WÈW¸¶ª#�-���|�-�|�h�W��¢� Î ��#§©�W�� ��  ³�t ³¢�°-´��k¢��|�W�W° Ê�° È-¼)¸�É£�-��»��³��¡WÈ ¢ ¸¶ªÔ¨

Ð Ï�×�ä Ú�¸HÙ«¦h¨

Page 2: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

����������� ������������ ��������������������� "!#���$&%'�����()���

* �,+-���'���.%'����-/102$��3%������ 546� %�879���������;:<��=�$#% ×A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX�B Z\[�B^]R_^`QVLa/BEbcKM_Ed=VLa/BLe._LfhgHG-ijV

X�BL]kf-lRm�FQnoFQILN�p#B q�BLr0gkNkgHG]Rst��K�ILFHG����_EGcqcIE�Hstm�FHILNRvJs#��FQvJlEst��FjvJKMPC�KMNE�HshI0�gOS�S�KTSJf-lLs!r0stf-lEILKMS�f-lEs#[6gkf-lLS�f-lR_E��s

X�[�Z\�HzO�Ox��y�_EG�KMf-l]Rm�K�vJ�tshG��MFHILN

p�stSJstFHG�f-l�p�shuYgHGJvcw6g^B�xQzHz={WZ\zE} ~ FQIR_LFHGJ��xHzHzO{

>6?�@BADCFEHGIA]=v�gRf-l^FHS�vJKTfo�5gkNkst��KMIE� nR� NkKKJ±shG�shI=v�KMFH�csBL=_LFQvJKMgHILS�m�K�vJl G�FHILNkgH� K�IEuL_kv�S7KMS&GJsBM=KMshm�stN.B

p�s�f)shI=v�NksDMOsh�MgHuE��stIOv-S�KMIoNks)v�shG��5KMIEKTS�v�KMf!SJgH�M_kvJKMgHI�FQ�M�HgHG�K�vJlE��S�nLFHSJstN�gOI��OshIEstG�FH��KM�tFQvJKMgHILS�gQ�vJlLs5lLgH��gH�OshIEstgH_LS![6stGJ��K�vJs5N«gH�M�RIEgH��KTFQ�yX�lLFQg=S�O N�X�P�sRQkuLFHILSJK�gOILS!gQ��w B.S­K�stIEshG�FHILN�gOISJuLFQG-S�scvJstILS�gOG�uLGJgkNk_Lf)v�FHuEuEG�gQRKM��Fjv�K�gOILSygH�0S�u^FjvJKTFQ�±f)gOGJG�sh�TFjv�K�gOI��Ä_EILf)vJKMgHILS�KMI7uYshGJvJ_EG�nLFQvJKMgHIsRQkuLFHILSJK�gOILS�FHGJs!uEG�stSJshI=vJs�N£B¶��Fjv�lEsh��FQvJKTfhFQ�±KTSJSJ_Es�S�KMI&v�lEs!�ÄgHG�� _E�TFjv�K�gOI.VTN�X�NEKMS�f)G�s)v�K���FjvJKMgHI¯VFQI^N�IR_E��shG�KTfhFQ�.FHILFQ�M�kS�KTS�gQ��N�X2S�gO��_kv�K�gOI�FH���OgHG�K v�lE��S�FQG�sÔNEKMS�f)_LS�SJstN£B

U�V�W.XZY C[&@�\ N«gO���RIEgO��KMFH�«f-l^FQgOStV.gOG�v�lEgH�OgHILFH�uYgH�M�RIEgH��KTFQ�TShV¯G�FHILNkgH��K�IEuL_kv�StVNEKKJ±shG�shI=vJKTFQ�sBL=_LFQvJKMgHILStVkIEgOKMSJ��SJ�RS�vJst��ShVk_EI^f)shGJv�FHK�I=v��9L=_LFHI=vJK^]^fhFQvJKMgHI

_�`�?.a V GbA"ced,EH@'@Bf,g&G�ETABf Yih \kj {OX�xHzEV j {=X-lHzEV j {QwmlOz

���.�W���Y�6�-�h�W���������� ^���Y�W�W¡�¢��£��¢\¤���¢\¥����c¦t§©¨«ª­¬.¢\¤���¢\¥y®L�.�W¢¯¥±° �³²�°-´=µ¶�-�³���·�-¡j�-²t����¸�¦t�=¸h¹�����-��¡cº=�W��° �¥.�-�.�³���W�Q° �� �¢�¡c»)¼c½¶¾¿0¸t¨ÀE¾¶¦t¬y¸W¾«Á¬Â�-�W¡�Á«¦hÀ.®t�.�W¢¥£° ��²�°-´L¦t�|�)¥.�-»!�-�W¡��k°h¡W° �£¥.�-�.�³���W�Q° �� �¢�¡�»h¼§ÄÃ0Å��W¢\ ©¥£° ��²5Æ|DZ��¢��-²t���WÈ�É£° ����Ê�¢�Ët�  ©¼tÌ�°-´k ³��¢¶¿£É��W�W¡�¢��¯��° �h ��|�-�\ 0�t����»Q¢��0ïű¬¯Á¯ÍÎɱ�£ÍÄÏ Ð Ð Ï�ÍÄÐ Ð Ï Ñ Ò�¸W�-�W¡»)¼c ��W¢�¦h¥¯���³�.Àj¢�¡W¢��|�-Êk¾0Ó���¢´M° �0¦t����¢��W��¢��-�W¡Ô¿^¡W�W���� ³��° �!�W�W¡W¢��¯È �|�-�) Ç£ÇYÕ�Ð Ï�® Ð-ÖW×�ÑØ É±° �³��¢����Q° �W¡W���WÈ&�-�� ��W° ��¸«½� ¤t���³��° ��°-´�¨�W��Ê���¢�¡oª#�� ³�W¢��6�� ������J¸0DZ�³°�¥0�oÙ0�W� ¤)¢��³���  ©¼)¸0Å^�³°�¤���¡W¢��W��¢ ¸¶¬.§

Ð Ï Ú�×�Ï�¸HÙ«¦h¨�¸=Û�¢��6�-��ÊTÜ È ²WÝ¡W�-�Ô® »W�³°�¥0�O® ¢�¡��QÞß ½� ¤t���³��° �c°-´E¨�W��Ê���¢�¡!ª#�� ³��¢��6�� ������J¸WDZ�³°J¥¯�!Ù0�W� ¤)¢��³���  ©¼)¸WÅY��°J¤t��¡W¢��W��¢ ¸Q¬¯§±Ð Ï Ú�×�Ï�¸QÙ«¦t¨à ½¢��j�-�Π³��¢��) 0°-´^ɱ�W¢��������-Ê=¿^�WÈ ���W¢�¢��³���WÈW¸WÅY�³������¢\ �° �ÔÙ¯�W� ¤)¢��³�³�  ©¼)¸jÅ^�³���W��¢\ �° �=¸QÁá�Ð Ñ â-Ö ÖW¸HÙ«¦t¨ã-½¢��j�-�Π³��¢��) Ô°-´�¾��¢��-��¿Y��È ���W¢�¢������WÈW¸¶ª#�-���|�-�|�h�W��¢� Î ��#§©�W�� ��  ³�t ³¢�°-´��k¢��|�W�W° Ê�° È-¼)¸�É£�-��»��³��¡WÈ ¢ ¸¶ªÔ¨

Ð Ï�×�ä Ú�¸HÙ«¦h¨

Page 3: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

����� h ADC Y [&`#GbABf Y�h ����������� V�h&V V [� Y C @BA Y G � EH@BABf G @Bf � `&d,ETA'f Y�h @ � r�lEKMS�uLFQuYshG�FONENkG�stS�S�s�S�IR_E��stGJKTfhFH�

SJgH�M_kvJKMgHILS6gQ�yNkK^JYstGJstIOv�KMFH�.sBL=_LFQvJKMgHILS6m�K v�l�G�FHILNkgO� K�ILuE_kv�StB�r�lEs SJgH_EG-f)s#gH�¶G�FHILNkgH�%K�ILuE_kv�SKMILf)�M_LNks�S�_EILf)stG�v-FQKMI=v���K�IÂSJ�RS�vJst� uLFQG-FQ��shvJshG-StV=nYgH_LILNEFQG��&FQI^N�KMIEK�vJKTFQ�.f)gOILNkK�vJKMgHILStVk��Fjv�shG�KMFH�uEG�gHuYshGJvJKMstStVOSJgH_EG-f)s�FHILN�K�I=v�shG-FHf v�K�gOI5vJshG���ShVO�HstgH��s)v�GJ�OVQs)v-fQBy]R_Lf-l�v��RuYstS¶gH�±_LILf)stG�v-FQKMIOv��5FQG�s_EnEK L=_EK�vJgH_^S6KMI�stIE�HKMIEstshG�K�IE�&FHuEuE�MKMftFjv�K�gOILShV^FQILNoFQG�sÔgQ�©v�shIÂ��gkNksh�MstNÂFOS�G�FHILNkgO� ]Lsh�TNEStB�r�lLsf)�TFHS�SJKMftFQ�^FHuEuEG�gOFOf-l5KTS�vJg/�5gkNkst�Lv�lEs!G�FHILNkgH�9KMIEuE_kv-S�FOSy�Ä_LILf v�K�gOILFQ�TS�gH�¯KTNkstFH��KM�hs�N�uEG�gRfhstS�S�s�SSJ_Lf-l FHS S­KMshIEstG�uEG�gRfhstS�S�s�ShV&N«gHKTSJSJgHI uEG�gRfhstS�S�s�ShV¯s)v�fHB7r�lEKTS�FHuEuEG�gOFHf-l lLFHS���s�N v�gÂsh�Msh�=FQI=v��Fjv�lEsh��Fjv�KMftFQ�£FQI^FQ�M�RSJKTS�FQI^N�f)gOGJG�stSJuYgHILNkKMIE��IR_E��stGJKTfhFH�^��s)v�lEgkNES�nR��_LS�KMIE��S�v�gkf-lLFHS�vJKTfcftFQ��Zf)_L��K³V0FOS�sOB �^B�V��|vJgogHG ]=v�G�FQvJgOIEgFMRKMf-l ftFQ�Tf)_E�M_LS!�ÄgOG#gHG-NkK�I^FQG��oNEKKJ±shG�shI=vJKTFQ�¶s'L=_LFjv�K�gOILS#FQILN vJlLsS�vJgkf-lLFHS�vJKTfÔfhFH�Mfh_E��_^S�gQ�#MjFHGJKTFjv�K�gOILS�gQ�«��FQ�M��KTFMRK�I7�ÄgHG�u^FQGJvJKTFQ�.NkK^JYstGJstI=vJKTFQ�£sBL=_LFQvJKMgHILStBr�lEs¶G�stSJ_E��vJKMIE�6NkK^JYstGJstIOv�KMFH�QsBL=_LFQvJKMgHILS¯FQG�snLGJg=FHNk�M��vJstGJ��s�N��JS�vJgkf-lLFHS�vJKTfgHG-NkKMILFQG����WuLFHG�v�KMFH�

NkK^JYstGJstI=vJKTFQ�¯s'L=_LFjv�K�gOILS����LSJshsHVL�ÄgHG�sRQEFQ��uE�MsHV�� }W{RVYxE}QV±x��EV��^}��|B�p6stf)stI=vJ�M�HVY�5gOGJs#G�stSJstFHG�f-l�s)�©Z�ÄgHGJv�S�lLFMHsÂnYshstI NksBMHgQv�stN�vJg S�v�_LNk�RKMIE� uEG�gHnE�Msh��S�m�K�vJl �5gOGJs GJs�FQ�MKMS�vJKTfoG�FHILNkgO� KMIEuE_kv-ShVsHB �LBMVkf)gOGJG�sh�TFjv�stN�G-FQILNEgH� uEG�gRfhstS�S�s�S�O��JfhgH�MgHG�stN�IEgOKMSJs�� K�I7vJlLs��TFQIE�O_LFQ�OscgH�¯uElR�kS�KTfhS P�FHILN£VkKMIfhFOS�s�gQ�¯G-FQI^NkgH� uLFHG�FH�5shvJstG�StVH�Ä_L���M��f)gOGJG�sh�TFjv�stN�G-FQILNEgH� uEG�gRfhstS�S�s�ShV=K³B sOB�V ��!�"�#%$'&)('!'��*�!%+-,/.�0 B�\I�v�lEKTS!fhgHI=vJsDQRvtVYvJlEs�f)�TFHS�SJKMftFQ�0S�vJgkf-lLFOS�v�KMf/fhFH�Mfh_E��K«Nkg7IEgQvÔGJs�FHNkKM�M��FHuEuE�M��FQILNÂlLshILfhs/gHvJlEstGFQuLuEGJg=FHf-lEs�S�FHGJsÔG�sBL=_EKMGJs�N£B¶r�lEKTS�f)�TFHS�S�gQ�«uEGJgOnE�Msh��S�KMS�v�lEsÔ�Ägkf)_LS6gQ�¯v�lEKTS�uLFQuYshG�BC21&fhK�stIOv¶IR_E��shG�KTfhFQ�ESJgH�M_kv�K�gOI/gH�±NkK^J±shG�shI=vJKTFQ�ks'LO_^FjvJKMgHI^S«m�K v�l�S�vJgkf-lLFOS�v�KMf�KMIEuE_kv-S¶lLFOS¶NkK Z

G�stf v«KM�5u^FHf v¶gOI/SJK��/_E�MFQvJKMgHILS0gQ�^uElR�RSJKTfhFQ�kFHILN�nEKMgH�MgH�OKMftFQ�=uEG�gRfhstS�S�s�S¯KMI/FQv�MstFOS�vvJlLs��ÄgO���Mgjm�KMIE�vJlLGJstsÔFHGJs�FHS�3

}HB546I^f)shGJv�FHK�I=v��9L=_LFHI=vJK^]^fhFQvJKMgHI.VxkB6]=v-FQnEKM��K�v���gH�0IEgOKMSJ��SJ�kS�v�sh��ShVlEBcX�gOFHG�SJs)Z|�HG-FQKMIEs�N�FQILN�� _L� v�KMS�fhFH��sÔG�shuEG�stSJshI=v�FQvJKMgHI.B

�\I�vJlEsÔ�ÄgO���Mgjm�KMIE�LVRm�s#m�K��M�£sh�TFQnYgHG-Fjv�s!gOI7s�FHf-l�gQ�0vJlEs�S�s�FHGJs�FHStBr�lEstGJs6l^FHS�n^stshI�FHI&K�I^f)G�stFHSJKMIE�#K�I=v�shG�stS�v�G�stf)stI=vJ�M�/KMI�S�vJ_LNk�RKMIE�768":9;.-��<=!'*>"?< @BA�6�!'"?< * CD9;!'E

<F*�$'"!K�I5�MFHGJ�Os)Z\SJftFQ�Ms¶IR_E��shG�KMftFQ�RS�KM� _E�TFjv�K�gOILS0vJgÔFHS�S�s�SJS¯��gRNEsh�MK�IE�!_EILfhshGJv�FHK�I=v��HVQSJshsG� lH�kVR}HVR}'H��³B�\IoNks)v�shG��5KMIEKTS�v�KMf�IR_E��shG�KMftFQ�£SJK��/_E�MFQvJKMgHILS�m�s!ftFQI�ILgjm2GJgO_kvJKMIEst������gHILK v�gHG�FHftf)_EG-FHfh�/gH�¯vJlLsf)gO��uE_kvJs�N GJs�S�_E��v�S!nR�I!�JK$'0;<=.���*�$'��*«shG�GJgOG�nYgH_LILNES�FHILN�v�lR_LS#FHS�S�s�SJSÔNkKTS�f)G�s)vJKM�tFQvJKMgHI shG�GJgOG�StB�\I fhgHI=vJG-FHS�vtVL!J�$M0�<=.-��*�$���*.stS�vJKM��FjvJKMgHI gQ�5&�$N#O.�,P*>"RQS.-���T$'�;0 VYNE_Es�v�g�FHNkgOukvJKMgHIÂgH��S�KM��uE�MKK]Ls�Nm�gHG�P=KMIE�#��gkNksh�TS�FHS�nLFHSJKMSy�ÄgHG�IR_E��shG�KMftFQ�^SJKM� _E�TFjv�K�gOI.VOKTS�S�v�K��M�±Fjv�FHI&stFHGJ�M��S�v-FQ�HscgQ�¯NksBMHsh�MgHuEZ��shI=vtBVUc�©v�shI�vJlEstGJsÔFQG�s�NkKTS�f)G�shuLFHILf)KMstS�n^shv�m�stshI7fhgH��uE_kv-Fjv�K�gOILFQ�YGJs�S�_L� v-S�FHILN&sDQku^stGJKM��shI=v�FH�gHn^S�stG MjFjv�K�gOILStVQFQILN shG�GJgOG�S¯�ÄGJgO� FQIR��S�v�FH�Hs�gQ�Lv�lEs�IR_E��shG�KMftFQ�kSJK��/_E�MFQvJKMgHILS«ftFQI�f)gHI=v�GJKMnE_kv�s�v�gSJ_Lf-l5NEKMS�f)G�shuLFHILf)KMstStB0[cgjm�sBMHstGtVjK��Ym�s6FHS�SJ_E��s�v�lLFjv¶v�lEscNkKTSJfhGJshvJKM�tFQvJKMgHI/FHILN5��gRNEsh�MK�IE�ÔstGJG�gHG-SFQG�s�FQuEuLGJgOuEGJKTFjv�sh�M� f)gOI=vJG�gH�M��s�N"OÎm�lEKMf-l�ftFQI�n^s�FHf-lEKMsDMOstN �ÄgHGy��FQIR��uLGJgOnE��st��S¶gQ�±shIE�OK�ILshshG�KMIE�KMIOv�shG�stS�v P)V0v�lEshI v�lEs9MjFH��KTNkK�v�� gH��v�lEs�FONkgHukv�stN ��Fjv�lEsh��FQvJKTfhFQ���5gkNkst��V«sOB �^B�V¶FÂf)gOILS�vJK�vJ_kv�K^MOs�TFWm#V£n^s�f)gH��s�S!vJlEs��MstFHNEK�IE�ofhFH_LSJs/gH��vJlLs�NEKMS�f)G�shuLFHILf)KMstStB/r�lLs�MjFH��KTNkK�v���gQ�yv�lEs�_EILNEshG����RKMIE���Fjv�lEsh��Fjv�KMftFQ�«��gkNksh�yftFQI n^s�stS�v�FHnE�MKMSJlEstNW$'"?,P@�* Xc_LILf)stG�v-FQKMIOv��ÂKMI I=_L�5stGJKTfhFH�«uEGJs�NkKTf vJKMgHI^SNk_Es vJg�_EILf)stG�v-FQKMI­K�ILuE_kvÂNEFjv-F�OÄsOB �^B�V�v�G�FHILSJu^gOG�v7FHILN­��Fjv�shG�KMFH��fhg=s�1&f)KMshI=v�StVcSJgH_EG-f)s�FHILNKMIOv�shG-FHf)vJKMgHI7vJshG���ShVk�OshgO�5shvJG�KMf�KMGJG�sh�O_E�MFHGJK�vJKMstS�FOS�S�_EGJ�ÎFHfhsÔGJgO_E�HlEILstS�S P�fhFHI7nYs1L=_LFQI=vJK^]Ls�N£B

46I^f)shGJv�FHK�I=v�� LO_^FQI=vJK^]^fhFQvJKMgHI!GJs'L=_EK�G�stS£vJlEsyuLGJgOuLFQ�=FjvJKMgHI�gQ�R_EILfhshGJv�FQKMI=v��6v�lEGJgO_E�Hl#F��OK^MOshI��Fjv�lEsh��Fjv�KMftFQ�0�5gkNkst�0FHILNÂFFJ±stf)v�ScFH���S�v-FQ�OstS�gH�«IR_E��stGJKTfhFH�¯S�KM� _L�MFQvJKMgHI.B6]RuYstfhKK]^ftFQ�M���OV^u^FQGJZvJKTFQ�«NkK^JYstGJstI=vJKTFQ�«sBL=_LFQvJKMgHILScm�KMNkst���Â_^S�s�NovJg��ÄgHG�� _E�TFjv�s ��Fjv�lEsh��Fjv�KMftFQ���gRNEsh�TS�gH�yuElR�kS�KTfhFH�SJ�RS�vJst��S�� _LS�v6n^s GJsh�ÄgHG�� _E�TFjv�stN�FHS�S�vJgkf-lLFHS�vJKTf!uLFQGJvJKTFQ�.NEKKJ±shG�shI=vJKTFQ�¯sBL=_LFjv�K�gOILStByr�lEKMS6u^g=S�s�SIEstm f-lLFQ�M��stIE�Hs�SÔ�ÄgHG/��FjvJlLsh��Fjv�KMftS9OÄuL_EGJs�FQILN FHuEuE�MK�s�N FQ�MK�POs'P-35u^FQG-S�KM��gHIEKMgH_LSÔu^FQG-FQ��s)v�GJKTfNks�SJfhGJKMukvJKMgHI­gH� S�v�gkf-lLFHS�vJKTfÂKMIEuE_kvoNEFjv-F@FQI^N��5gkNkst�!ftFQ�MK�nLG�FQvJKMgHI­G�sBL=_EKMGJs�S���s)vJlLgRNLS&�ÄG�gH�S�v�Fjv�KMS�vJKTfhStVRm�lEKM��s!vJlLs!IR_E��stGJKTfhFH�YSJgH�M_kvJKMgHI7gQ�0S�vJgkf-lLFOS�v�KMf�uLFHG�v�KMFH�YNkK^J±shG�shI=vJKTFQ�±sBL=_LFQvJKMgHILS�m�KM���sBL=_LFH���M� KM��uLFHf)v�IR_E��stGJKTfhFH�6FQILFH���kSJKMS�FQI^N�S�f)KMshI=vJK^]^fof)gO��uE_kvJKMIE�^B2ac_Es�v�g ��KM��K v-FjvJKMgHI^S�gQ�SJuLFHfhsHVkKMI7v�lEs#uEG�stSJshI=v�uLFQuYshG�gOIE�M��S�gO��s!gH�0v�lEstSJsÔKMS�SJ_EstS�m�KM���¯n^s�FONENkG�stS�S�s�N£B

×

Page 4: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

x µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

� $�* 0�@ "�$�"�,P*>":.;!'� 0�@M0�<=.-&B0YFHGJs«shI^f)gH_LIOv�shG�stN!KMI#��FHIR�cFQuEuL��KTfhFQvJKMgHILStVh�ÄG�gH� vJlEs�ILFQIEg=SJftFQ�MsHVsHB �LB«KMI�SJsh���©Z\FHS�S�st� nE�M��uEG�gRfhstS�S�s�S � j l'�³VRv�g/v�lEsÔ��FHf)G�gOS�fhFH��sOVOsOB �^B«�MFHGJ�Os!SJ_LNENkstI�NEKMS�vJ_EG�nLFHILf)s�SKMI��Lgjm uLFOS�v�FQI FQKMG�fhG�FQ�©vtB���K��Ä_EG-fhFjv�K�gOILS5FQILN�f-lLFQgHvJKTf�vJG-FQILSJK�vJKMgHILS/K�I S�v�gkf-lLFHS�vJKTf�Nk�RILFH�5ZKTfhFQ��S��kS�vJsh��S/fhFQI nYs6MHstGJ� NkK^JYstGJstIOv �ÄGJgO��KMILS�v-FQnEKM�MK v�K�s�S�KMI Nks)v�shG��5KMIEKTS�v�KMf�Nk�RILFQ��KTfhFQ��S��kS�ZvJst��S5� {blM�³B«r�lEs�f)gO_EI=vJshGJZ|K�I=vJ_LK v�K^MOs�uElEstIEgH��stIEgHI/gQ�YS�vJgkf-lLFOS�v�KMf�GJs�S�gOILFQI^f)sy�ÄgOG0ILgHKTS���SJK��OILFQ�TStVm�lEstGJs�vJlEs6SJKM�HILFH� Z³vJgHZ³IEgOKMSJsyG-Fjv�K�gÔfhFHI/nYs�K���uEG�gFMHs�N�nR��KMILf)G�stFOS�KMIE�6v�lEs�IEgOKMSJs��MsDMOsh�³VQKTS«_EIEK LO_LsvJg7S�v�gRf-l^FHS�vJKTf#S��kS�vJsh��StB O�q6IÂsDQ=v�shILSJK MHs#G�sDMRK�stm4gOI�S�v�gkf-lLFHS�vJKTfÔGJs�S�gOILFQI^f)s#fhFHI�nYs��ÄgO_EILNoKMI��}��'�|B P5[cgjm sDQEFHf v����S.��%< ��*>"�0;*�9�S�vJgkf-lLFHS�vJKTf)K�v��5K�I=vJstG�FOf v-Sym�K�vJl *>"?< ��*>"�0�*�9�S�vJgkf-lLFOS�v�KMfhK v���fhFH_LSJstNnR�5vJlEs!S��kS�vJsh��S��HIEgOIE�MK�IEs�FQG�K�I=vJstG�FOf v�K�gOILS¶KTS�KMI=vJG�K��O_EK�IL� FQILN&�HshILshG-FQ�M���/IEgQv�m�st���^_EILNkstG�S�vJgRgkNFjv�uEG�stSJshI=v�B

�\I�L_LKMN�Lgjm6ShVO�ÄgHG�sRQEFH�5uL��sOV=FQv�lEKM�Hl�p6sh�RIEgH�TNES�IR_E� nYshG�m�lEshG�scF m�KMNks�G�FHIE�HscgQ�¯SJ��FH���S�fhFQ�MstS5sDQRKTS�v�S5vJlLs &�.;!'"��Lgjm S�stsh��S5vJg nYsovJgHv�FQ�M�M� _EILFIJYs�f vJs�N@sBMHstI�KMI vJlEsÂuEG�stSJshI^f)s�gQ�SJ_EnLS�v�FQI=v�KMFH��nLFOf-PR�HG�gH_EILN v�_EG�nE_E�MshILfhs � l j �|B �\I�fhgHI=vJG-FHS�vtV«�ÄgOG/gHvJlEstG��Lgjm SJ�kS�v�sh��S5Fjv���gjmp�st�=ILgH�TNES&IR_E�/n^stG�sDMOshI SJ��FQ�M��FH�5gO_EI=v�S�gQ�#IEgHKTSJs fhFHI2lLFMHs�F@NkG�FH��FjvJKTfÂsDJYs�f v7gOI­vJlLsS�vJG�_Lf v�_EGJsÔgH�¯vJlLs�& .;!'" �Lgjm#B �\I��K��O_EGJs�}OB�}!m�sÔuEG�stSJshI=v�FQI�sRQEFQ��uE�MsÔgQ�«S�_Lf-l�G�stSJu^gOILS�sOB¶q_EIEK��ÄgHG����Lgjm uLFOS�v«F6f)KMG�fh_E�TFQG0fh�R��KMILNkstG0g=SJfhK��M�MFQvJKMIE�6KMI�v�lEs�fhGJg=SJS��Lgjm NkK�G�stf)vJKMgHI�KTSf)gHI^S�KTNkshG�stN.Bq@SJ��FQ�M�OFH�5gO_EI=v.gQ�EIEgOKMSJs¶KTS0SJ_EuYshG�K���uYgOSJstNÔgHIÔv�lEsy_EILK �ÄgOGJ� K�I��Lgjm MHsh�Mgkf)K�v��HBL�\IÔvJlEs�FQnLSJshILfhsgQ�IEgHKTSJsHVEF�MHgOG�v�sRQ�S�vJG�shs)v�KTS��ÄgHG���stN7K�I�vJlLs!m�FQPOs!f-l^FQG-FHf v�shG�K��tstN�nR��v�lEs�SJlEstNENEK�IE��gH�¯vJlLGJstsMHgOG�v�KMfhstSuYshG�SJlEstNLNkK�IL�Ôfh�kf)�Ms��Ôv�lEs6SJgQZ\fhFQ�M�MstN O,N��Ô]3P¯u^Fjv�v�shG�I � j�j �³B«[6gjm�sDMOshG�Vjm�lEshI�IEgOKMSJs�KMSKMIOv�GJgkNk_^f)stN/v�lEs MHgOG�v�sRQ S�vJG�shshv50��2*><=9��K.-00v�g�FQIEgHvJlEstG�S�v-Fjv�s6FQnYgFMHs�FÔf)shGJv�FHK�I�IEgOKMSJs�vJlLGJs�S�lEgO�MN.Vf-lLFHG�FOf vJstGJKM�hs�N IEgjm n=� gOIE��� v�m�g MHgOG�v�KMfhstS u^stG5SJlEstNLNkK�IL� f)�kfh��sOV«FOS KMI v�lEs�S�v�FHILNEFHG�N MOgHID#FQG���FQI S�vJG�shshvÔ�ÄgHG#S�v-Fjv�K�gOILFQG���f)�R�MK�ILNEshG-S�O³xH] uLFjvJvJstGJIiP)B/r�lEKTSÔuElEstIEgH��stIEgHI KMS#NEKMS�f)_LS�SJstNKMIoNEs)v�FHK��£KMI � l�lM�0FHILN�K�ILNEshuYshILNkstI=v6sRQku^stGJKM��shI=v�FH�.MjFQ�MKMNEFQvJKMgHIofhFHI7nYsÔ�ÄgH_EI^N7KMI � �%�'�|B

x/d

y/d

0 5 10

-4

-2

0

2

4 (a)

P1

S1

III

x/d

y/d

0 5 10

-4

-2

0

2

4 (b)

P1

S1

III

������� �!��� ®#"%$'&)(�*'+-,/.0$214365�798:565;1=<25;795;+-&�,>1 ,>.079,/?A@B*-CA*'1D<A.07E$�?GFH*'.079,/?±��¢��-�I@B3BC),>1 .07E*'1 7E*'1D50$'J�.LK�$'+-79,/?;,>79MN 5;O <�,>1*IP'QR?;M'O ,>1D<25;+S8�*�T'54*'7A,/<!5�1 79,/?0*'OU79,>&V5�WYXZF[5�\B?�O 50*'1�]S8:*�T25^._FH$28%.`*#Û9acbed^Þ=._FH50<2<2,>1�f2gh&�$;<258iFH,>O 5#7>F[5j\h1D$',>.0MD]k8�*�T25#._FH$'8�.k*«Ï2d._FH50<2<',/1�f'gB&�$;<25A.0,>&�,>O *'+)79$l7/FH5#.079*21D<2*'+B<�K�$'1=mn*'+-&V*'1^K�$'+-7E5-ol.679+B505;7hWp ×�Ð2qr1D$',>.-5�O 5;K�5�OZ,>.A.0J�(�5;+-,>&)(�$'.-50<j7E$=7/FH5�J�1 , s-$'+-&t,>1;uv$'8�*'7:wL5;M'1D$'O <'.A1 JH&V365;+)xDy2y!W

r�lEs/vJlEKMG-N�FQG�stF�KMI�v�lEs�Fj�ÄgHG�sh��stIOv�K�gOIEstNo�MKTS�v#f)gOIOv-FQKMILScfhgH��uE�MsRQ�SJ�RS�vJst��Scm�K�vJl FQI sDQRZvJG�sh��st�����TFQG��Hs�IR_E�/n^stG#gQ��Nksh�OGJststS!gQ���ÄGJststNkgO�oV¯sHB �LBMV.��gkNksh�TS#gH��v�_EGJnL_E��stI=vz�Lgjm6S#Fjv MHstGJ�lEKM�Hl@p6sh�RIEgH�TNES I=_L� nYshG gOG/FQvJgH��KTS�v�KMf�S�KM� _E�TFjv�K�gOILS�gH�6��stSJgOS�f)gHuLKMf�SJK��ts�SJ�RS�vJst��ShB Uc�©v�shI.VF f)gOFHG�SJs)Z|�HG-FQKMIEs�N uEG�gkf)s�Nk_EG�s�KTS/st��uE��gj�OstN v�g G�sh��gFMOs�Nksh�OGJststS gQ�6�ÄG�shs�NkgH� ftFQG�GJ�RKMIE��G�sh��ZFjv�K^MOsh�M� SJ��FQ�M��fhgHI=vJG�K�nL_kvJKMgHILS�vJgÂv�lEs�gFMOshG-FQ�M��SJ�RS�vJst��� S shIEstGJ�O�HB�r�lEs7GJst�5gFMOstN Nkst�HG�shstS�gQ��ÄG�shstNEgH� FQG�s5_LS�_^FQ�M����FOfhf)gO_EI=vJs�No�ÄgHG#nR��S�vJgkf-lLFHS�vJKTf#v�shG���SÔK�I vJlEs�NkKM��shILSJK�gOILFQ�M�M�ÂGJs�Nk_Lf)s�N{ sRJ±stf v�K^MOs|�±gHG { _LuLSJftFQ�MstNL�YsBL=_LFQvJKMgHILStBj�EgHG!sRQEFH�5uL��sOVYKMI�v�lEs�NkKMS�SJK�uLFQvJK MHs/uLFQGJvJKTf)�Ms/Nk�RILFH��KMftS��s)v�lEgkN � }�zM�³V±f)g=FQG-S�shZ³�OG�FHK�ILK�IE�/gQ�vJlEs �5gO��s�f)_E�TFQG�Nk�RILFQ��KTfhS���s)v�lEgkNÂ�MstFHNLS�vJg&F&SJ�kS�v�sh�%gQ�S�vJgkf-lLFHS�vJKTf U!a!C�S¶v�lLFjv�IEshs�N5vJg�nYs�SJgH� MHs�N5s-1&f)KMshI=vJ�M�/�ÄgHG�F��MFHGJ�Os�I=_L� nYshG�gH�£uLFQGJvJKTf)�MstS � {E}��³B

���9} � _2ABETA'f,@BABf GbEHd#~ V CF@'`#@ h#Y�h�� @BABETA'f,@BABf,G�EHd�Ei�)�#C Y EHG � V @ � qcSy��stIOv�K�gOIEstN.VH�ÄG�gH�9vJlLs��Fjv�lEsh��Fjv�KMftFQ�RuYgHKMIOv¶gH�3MRK�stm m�s�IEststN vJg!GJsh�ÄgHG�� _E�TFjv�s���Fjv�lEsh��Fjv�KMftFQ�R��gkNksh�TS«FHS«S�v�gkf-lLFHS�vJKTfgHG-NkKMILFQG��5gHG�uLFQGJvJKTFQ�±NkK^JYstGJstIOv�KMFH�^s'L=_LFjv�K�gOILShVRm�lEKM�Msc�ÄG�gH�9vJlLs!fhgH��uE_kv-FjvJKMgHI^FQ�±u^gOK�I=v�gQ�2MRKMshmIEstm�s�1�fhK�stI=v�I=_L�5stGJKTfhFH�yS�gO��_EvJKMgHI ��s)vJlLgRNLS#� _LS�v�nYs&NksDMOsh�MgHuYstN£BY�LGJgO� vJlLs�u^stG�SJu^s�f v�K^MOs

Page 5: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ l

gQ��vJlEs�f)gO��uE_kv�FQvJKMgHILFH�¶SJfhK�stIOv�KMS�vtV±�ÎFH��K��MKMFHGJK�v��Âm�K�vJl sRQkKMS�vJKMIE�of)gOILf)stukv�SÔFHS!m�sh�M�¶FHS!uElR�kS�KTfhFH�KMIOv�shG�uEG�s)v�FQvJKMgHI FHILN�KM��uE�Msh��shI=v�FQvJKMgHI �ÄGJKMshILNE��KMIEstS�S!gQ�¶v�lEs�S�v�gRf-l^FHS�vJKTf���gkNksh�TS!gHnkv-FQKMIEstNÂnR�SJ_Lf-l G�s)�ÄgOGJ�/_E�MFQvJKMgHI�FHGJs�FQ�TS�g!K���uYgHGJv�FHIOv0�ÎFHf)vJgHG-StBk�EgOG¯v�lEs�IR_E��shG�KMftFQ�RS�gO��_kv�K�gOI gH�^S�v�gkf-lLFHS�vJKTfNkK^JYstGJstI=vJKTFQ�£sBL=_LFQvJKMgHILStVkm�s!nLGJg=FHNk�M��NkKTS�v�K�IL�H_EKTS�l 0�< !�< * 0�<F*�9;!',EFQI^N #%.-<=.-��&�*>"�* 0�<F*�9B&�.�<E��$�#'0 Br�lEs&S�v�FQvJKTS�v�KMftFQ�yFQuLuEGJg=FHf-l K�ILfh��_^NkstS�FH��gHIE�ogQv�lEshG-SÔ�ÂgHI=v�s7X�FQG���goS�KM� _L�MFQvJKMgHI.VS�v�G�FQvJK�Z

]Ls�N�SJFH��uE��KMIE�^V^e¯FQvJKMI�lR�Ru^stG�fh_En^s/SJFH�5uL��KMIE� O�f ��B ��}H}�� P B!]R_Lf-l S�v�FQvJKTS�v�KMftFQ�¯��shvJlEgkNES�K�I MOgH� MHsS�FQ��uE�MK�IE��FHILN/stS�vJKM��FQvJKMgHI�FQI^N/KMI���gOS�v�fhFOS�s�S¶FQG�s�S�vJG-FQKM�Hl=vJ�ÄgHG�m�FHG�NÔv�g�FQuEuL��� vJg#uLFHG�v�KMFH�ENkK �©Z�ÄshG�shI=v�KMFH�^s'LO_^FjvJKMgHI^SyK��¯s-1&f)KMshI=v�Nks)v�shG���K�IEKTS�vJKTf�N�a�C�S�gO�^MOshG-SyFQG�scFMjFQKM�MFHnE�MsHB«[6gjm�sDMHstGtV=S�KMILfhsvJlLs&FHfhfh_EG-FHf)�ÂgH��v�lEs&S�FQ��uE�MK�IE��v�stf-lEIEK L=_EstS#NEshuYshILNES gHI vJlEs&S�FQ��uE�Ms�S�KM�hsOV¯KMI FHfhfhgHG-NEFQI^f)sm�K�vJl5vJlEs { m�s�FQP#�TFWm@gH�^�TFQG��Hs�IR_E�/n^stG�S��MVHS�KM� _L�MFQvJKMgHILS«fhFHI/nYstfhgH��s�uEG�gHlEKMnEK�vJK MHsh�M��sDQRuYshI^S�K MHsOVstSJuYstf)KTFQ�M�M���ÄgOGcS��kS�vJst��S6vJlLFQv�FQG�s�FQ�MG�stFHNE�7f)gO��uE_kv�FQvJKMgHILFH���M�7fhgH��uE�MsRQosDMOshIoK�I�vJlEstK�G!Nks)v�shGJZ��K�ILKMS�vJKTf5MHstG�SJKMgHI.B �\I FONENkK�vJKMgHI.V«FjvJvJst�5uEvJKMIE�ovJg�G�stSJgH� MHs�lEKM�HlEZ³gOG�NkstGÔ�5gO��shI=v�S�FOSJSJgkf)KTFjv�stNm�K�vJlÂv�lEs/�Mgjm uEG�gHnLFHnEK��MK�v���NkgO��FQKMIÂgQ�¶vJlLs/S�vJgkf-lLFHS�vJKTf#G�stSJu^gOILSJs���FW�7G�sBL=_EKMGJs/F6MHstGJ�7�MFHGJ�OsIR_E� nYshG¶gH�^G�stFH��KM�tFQvJKMgHILStVjn^st�HgOILN�v�lEs���KM��K v-S¶gQ�YsDMOshI5��FOSJSJK MHsh�M�#uLFHG�FH���Msh�kf)gO��uE_kvJstG�StB0r0g#FHf)Zf)st��stG�FQvJs�fhgHI MHstGJ�OshILfhs¶gQ�ES�v�Fjv�KMS�vJKTfhFH�=SJKM� _E�TFjv�K�gOI#�5shvJlEgkNEStVQSJsDMHstG�FH�Q��gkNkKK]YfhFjv�K�gOILS0lLFMHsynYshstIKMIOv�GJgkNk_^f)stN.B S s5�5stI=vJKMgHI�lEstGJs5gHIL���Âe¯FQvJKMI�lR�Ru^stG�fh_En^s�S�FQ��uE�MK�IE� � lL}��|V±vJlEs���_LFHSJK�Z|�ÂgOI=vJsX�FQG��Mg O�!� X�P��5shvJlEgkN � }WxN�³V«v�lEs7� FQG�PHgFM X�lLFHK�I��ÂgHI=vJsÂX�FQG���gÂ��shvJlEgkN�O�� X�� X�P � lRH��³VFQI^N�vJlLs!p�s�S�uYgHI^S�sÔ]R_EGJ�ÎFHf)s!��s)v�lEgkN OÎp�]k� P � �R{N�|Byr�lEstSJsc��s)v�lEgkNES�K���uEG�gFMHscvJlEs!s-1&fhK�stILf)�gQ�.S�v�FQvJKTS�v�KMftFQ�³V { nEGJ_EvJs)Z³�ÄgHG-f)s �HS�FQ��uE�MK�IE� �5shvJlEgkNEStB«qcNENkK�vJKMgHI^FQ�YGJs�S�v�GJKTf v�K�gOILS«gHI�v�lEscS�v�Fjv�KMS�vJKTfhSgQ�cvJlEs�G�FHILNkgO� KMIEuE_Ev�FHGJs7K���uYgOSJstN£VyvJlR_LS5��KM��K v�K�IL� v�lEs��HshILshG-FQ�MK v�� FQI^N@FQuLuE��KTfhFHnEKM��K�v�� gQ�vJlLstSJs { FOfhf)st��stG�FQvJs�NL�kSJFH�5uL��KMIE����s)vJlLgRNLShBq6��vJstGJI^FjvJK MHst���OV£gHIEs�fhFHI NEsDMHst��gOu NkshvJshG���K�ILKMS�vJKTf5�5shvJlEgkNES!�ÄgOG#S�v�gRf-l^FHS�vJKTfeN�a�C�ShB r�lLs

��gOS�v�m�KTNksh�M��_^S�s�N��5shvJlEgkN­KTS�v�lEs�uYshGJvJ_EG�nLFQvJKMgHI­��s)v�lEgkN£V�m�lEshG�s�KMIEuE_kv�G�FHILNkgO� ]Lst�MNESFQG�scG�shuLGJs�S�stIOv�stN&FOS�K�IT]^IEK v�s�uYshGJvJ_LGJnLFQvJKMgHI7sRQkuLFQI^S�KMgHILS�gQ���L_Lf v�_LFjv�K�gOILS�FQG�gH_EI^N�vJlEstK�G���stFHI]Lst�MNEStB r�lEstSJs�u^stG�v�_EGJn^FjvJKMgHI@sRQkuLFQI^S�KMgHILS5FQG�s&v�GJ_LILfhFQvJstN@Fjv�F f)stG�v-FQKMI gHG-NkstG/KMI@gOG�NkstG�v�ggHnEv�FQKMI&f)gO_EuE�MstN�]LILK v�scS��kS�vJst��S�gQ�.NkK^JYstGJstI=vJKTFQ�Ls'L=_LFjv�K�gOILS«�ÄgHG�f)gHG�G�stSJu^gOILNkKMIE�ÔsRQkuLFQI^S�KMgHILSygQ�vJlLs/G-FQILNEgH� S�gO��_EvJKMgHI.B S s/st��uElLFHSJKM�hs/vJlLFQv ! J:��*�$'��*0vJG�_EILfhFQvJKMgHI�gH����gH��shI=vÔsRQkuLFHILS�KMgHI^SgQ�«G-FQILNkgO�%NEFQv�F�FHILNÂS�gO��_EvJKMgHILS�FH�5gO_EI=v�S #%.DX-!O9�< $#vJg�vJlLs�K���uYgOSJK v�K�gOIÂgQ� &�$�&�.�"�< 9�, $M0�68��.�R@TJ�$'<h�K.-0�.�0�gHIouYshGJvJ_EG�nLFQvJKMgHI�sRQkuLFQI^S�KMgHILStB

�\I uEG�FOf v�KMftFQ��FQuEuL��KTfhFQvJKMgHILStV�FQv���g=S�v�S�s�f)gOILNRZ|gHG-NkshG5sRQkuLFHILS�KMgHI^S5FHGJs�sh��uE�Mgj�Hs�N � vJlLsSJgQZ\fhFQ�M�MstN { C �;0�< E $���#O.�� E 0�.;9;$'"�# & $'& .-"?<!'"�!�,P@M0�* 0'� � xQ�'��v�lLFjv5lLFHS n^stshI _LSJstN sRQRvJstILS�K MHst���KMI�shIE�OK�ILshshG�KMIE�&FQuEuL��KTfhFQvJKMgHILSB� xblkVYxH�kV±{H�kV HM�'�|Bcr�lEKTS6KTS�NE_Es#vJg�vJlEs �ÄgH�M��gjm�KMIE��G�stFOS�gOILS�3 OÎF�P]LG-S�v5FQILN SJstfhgHILN ��gH��stIOv-S�gH�6G�FHILNkgH� S�gO��_EvJKMgHILS/FQG�s�gQ�6��FQKMI K�I=v�shG�stS�v K�I�FQuEuE�MKTfhFjv�K�gOILS��OÄn�P�vJlEs#SJ�RS�vJst� gQ�sBL=_LFjv�K�gOILS�GJs�S�_L� v�K�IE�/�ÄG�gH� vJG�_EILftFjv�K�gOILS�Fjv�lEKM�HlEstG�gOG�NEshG�n^s�f)gH��s�S LO_LK v�sf)gO��uE��KTfhFQvJs�N nYsh�OgHILN SJstfhgHILNRZ|gHG-NkstG��«FQILN O�fBP!v�lEs�NkKM��shILSJK�gOILFQ�MK�v�� gQ��vJlLs OÎNkshvJstGJ��KMIEKMS�vJKTfBPNkK^JYstGJstI=vJKTFQ�¯s'L=_LFjv�K�gOILS��ÄgHGcvJlEs/lEKM�HlEstG6gHG-NkshGc�5gO��shI=v�ScgQ�«vJlEs/G�FHILNkgO�%SJgH�M_kvJKMgHIÂKMILf)G�stFOS�s�Sm�K�vJl vJlLs�gHG-NkshG#gH��v�lEs���gH��shI=v�v�gÂn^s&fhgH��uE_kv�stN 3/K ��v�lEs�uElR�kS�KTfhFH�yuEG�gHnE�Msh� KMS#uYgOSJstN KMIF O�S�uLFOf)s�gOG�vJKM��s'P#NEgH��FQKMI� ������gQ�6NkKM��shILSJKMgHI��^V«vJlEs��RvJl ��gH��shI=v gH��vJlEs�G�FHILNkgH�SJgH�M_kvJKMgHI/K�I MHgO�^MOstS.vJlEs�S�gO��_EvJKMgHI gH�^F!Nks)v�shG��5KMIEKTS�v�KMf�uEG�gHnE�Msh� gOI�v�lEs�NEgH��FQKMI��������� � BqcIKMIElEshG�shI=v6�MK���K�v�FQvJKMgHIogQ�¶S�_^f-l"]^G�S�v�Z|gHG-NkshG�uYshGJvJ_EG�nLFQvJKMgHI��5shvJlEgkNES6KMS�v�lLFjv�v�lEs�_EI^f)shGJv�FHK�I=v�K�s�S� _^S�v�ILgQv�nYsÂvJgRg �TFQG��HsOV�K³B sHBMV�vJlEs �L_Lf v�_LFjv�K�gOILS�gH�!v�lEs G-FQI^NkgH� ]^sh�TNES�SJlEgH_L�MN�nYs SJ��FH���f)gO��uLFQG�stN7vJg&vJlEstK�G6��s�FQI�MjFQ�M_EstSeO©v��RuEKTfhFH���M���MstS�S�v�lEshI }�z���P B�r�lEKTS�G�sBL=_EKMGJst�5stI=v6IEshs�NES�v�gnYs�S�FjvJKTS ]LstN�IEgHv�gHIL���5nR� v�lEs�S�vJgkf-lLFOS�v�KMf�KMIEuE_kv-S�nL_kv�FH�MSJg�nR� v�lEscS�vJgkf-lLFOS�v�KMf�gO_kvJuL_kv�StB¶r�lEKMSKTSÔstSJu^s�f)KTFQ�M��� NEK 1&f)_L� v�v�g MHshG�K��Ä�I!�J:��*�$'��*�ÄgHG#IEgOIE�MK�IEs�FQG#uEG�gHnL��st��StV¯FOS#S���FQ�M�#�L_Lf)vJ_LFQvJKMgHILSKMI G-FQI^NkgH� KMIEuE_kv-S#��FW��G�stSJ_E� v#KMI �TFQG��Hs �L_Lf)vJ_LFQvJKMgHILS�K�I vJlEs&SJ�kS�v�sh��S��£GJs�S�uYgHILSJstS O�S�sts�FHIsRQEFH�5uL��sÔKMI � HQxM� P)Byq6�TS�g^VElEKM�HlEstG�gHG-NkshG�S�v�Fjv�KMS�vJKTfhS�gH�KMIEuE_EvcNEFjv-F5FHGJsÔIEgHv�GJs�FHNkKM���7FMWFHK��TFQnL��sOBq G�sh�TFjvJs�N FQuEuEG�gOFOf-l KTSÔnLFHSJstN gOI ��FQILK�uE_L�MFQvJKMgHI gQ��vJlEs&S�vJgkf-lLFOS�v�KMf5gOu^stG�FQvJgHG-StB�]k_Lf-l

��s)v�lEgkNES�K�ILfh��_^Nkscv�lEsÔw6sh_L��FHIEI&sDQRu^FQILSJK�gOI.V=m�lEKMf-l7KMS�nLFOS�s�N�gHI&sDQkuLFQILNEK�IE� vJlEs!KMI�MOshG-S�scgQ�vJlLs�S�vJgkf-lLFOS�v�KMf¶gOu^stG�FQvJgOG¯KMI/Fcwcsh_E��FHIEI SJshG�K�s�SV� {HxRVOHIlM�³VQFHILNÔv�lEs�m�shKM�Hl=v�stNÔKMIOv�sh�OG�FH�O��s)v�lEgkN

Page 6: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

� �EV±�EV.{H{N�|B#r�lEstSJs5�5shvJlEgkNES!lLFMOs��MK���K�v�Fjv�K�gOILS!gHIÂv�lEs/v��=uYs5gQ����gkNksh�«s'LO_^FjvJKMgHI^S6v�lEsh�ÂfhFHIFHNLNkGJs�SJStVQFQI^N£VjK �^vJG�_EILftFjvJs�N/FQ�©vJstG«SJstfhgHILN ��gH��shI=vvJshG���ShVQvJlEst��FQG�s�FH�MSJgcG�stS�vJG�KMf)vJs�N#vJgÔSJ��FH���_EILfhshGJv�FHK�I=vJKMstStB��\I v�lEs�uEG�stSJshI=v¶uLFQuYshG�VQm�s�SJPHshv�f-l.VQ�ÄgH�M��gjm�KMIE� � �=�kV'�O�'�³V=FQI5s-1&f)KMshI=v�FQuLuEGJg=FHf-l�ÄgHG�vJlLs�NkshvJshG���K�ILKMS�vJKTf�FHuEuEG�gQkK���Fjv�K�gOI�gQ�¯SJstf)gOILN&FHILN�lEKM�HlEstG�gOG�NEshG�SJuLFQvJKTFQ�^fhgHG�GJst�MFQvJKMgHILSygQ�G-FQILNkgO��SJgH�M_kvJKMgHI^ShV=nLFHSJstN�gOI&S�u^FQG-S�s�v�shILSJgHGyuLGJgkNk_Lf)v�S�gQ�.lEKMshG-FQG-f-lEKTf-]LIEK�vJs6st��st�5stI=v�SJuLFHfhstStB�|v6FQ�M��gjm6StVRK�IouEG�KMILf)KMuE�MsHVR�ÄgHG�v�lEsÔ�ÎFHS�v�sDMjFQ�M_LFjv�K�gOI�gH�0uYshGJvJ_EG�nLFjv�K�gOI7sDQkuLFQILSJKMgHILS�vJg�FHI=� ]3QRs�NgHG-NkstG!KMIW, $TQ�E=,P*>":.;!'�Ôf)gH��uE�MsRQkK�v���m�K�vJl GJs�S�uYstf)vÔvJg�� V.v�lEs�IR_E� nYshG#gH��Nkst�HG�shs�S�gH���ÄG�shs�NkgH�_LSJstN7vJg�FHuEuEG�gQRKM��Fjv�scv�lEs#��stFQI"]Lst�MN�uEG�gHnE�Msh� K�I�vJlLs#uElR�RSJKTfhFQ�.NEgH��FQKMI �Bq6ILgQvJlLshGyFQuLuEGJg=FHf-l#v�g#Nks)v�shG��5KMIEKTS�v�KMf�IR_E��shG�KTfhFQ�ESJgH�M_kv�K�gOI gQ�±S�v�gkf-lLFHS�vJKTfkN�a�C�S«KMS«n^FHSJstN

gHI7K�I=v�GJgkNk_LfhK�IL��Q .T$�&�.�<F��@�FQI^N 9;$�$���#'*>":!'<=.�0�KMI7vJlEs!uEG�gHnLFHnEK��MK�v���SJuLFOf)scgOI�m�lEKTf-l�KMIEuE_Ev�FHILNSJgH�M_kvJKMgHI�_EILfhshGJv�FQKMI=v���FQG�s!�5gkNkst��s�N£B2�|v6KTS�nLFHSJstN7gHI7v�m�g5gOnLSJshG MWFQvJKMgHILS�3

OÄK P�r�lEs�SJuLFHfhsÔgQ�«G�FHILNkgH� ]^sh�TNES�m�K�vJl ]LIEK�vJs SJstfhgHILN7��gH��shI=v-S�fhFQI�nYs#sBL=_EKMuEu^s�Nom�K v�lIEgOGJ��FHILN2KMIEIEstGJuEG�gkNk_Lf)vtV6v�lEshG�shnR��v�_EGJILK�IE� K�voKMI=vJg�F@[cK��Mn^stG�v�SJuLFHfhs FHILN FH���Mgjm�KMIE� �ÄgOG{ AÔFQ�MshG�P=KMI&uEG�g���s�f v�K�gOIv�OgH�¯F G-FQI^NkgH� ]Lsh�TN&gOI=vJg/F"OÎfhgH��uE_kv-FjvJKMgHI^FQ�M���&fhgHI MHstIEK�stI=v P�ÎFH�5KM�M��gQ�uLFHG�FH�5shvJG�KMf#FHuEuEG�gQkK���Fjv�K�gOILS�gQ�¶K�vS�9MHstGJ�7� _Lf-l�FHPRK�Iov�g�m�lLFjvcKTScNEgHIEs�KMIovJlLsZMjFQG�KMFQvJKMgHILFH��ÄgHG�� _L�MFQvJKMgHI�gQ��]^IEK v�s#sh�Msh��shI=v6��s)v�lEgkNES��ÄgOG6Nks)v�shG��5KMIEKTS�v�KMfÔuLGJgOnE��st��ShB

OÄKMK P#r�lEs�s-1&fhK�stILf)� gQ��vJlEKTS�FHuEuEG�gOFHf-l Nkstu^stILNES�fhGJ_LfhKMFH���M� gOI vJlEs���_LNEKMfhK�gO_LS f-lEgOKMfhs�gQ��JfhgRgHG-NkK�I^FjvJs�S���KMI&uEG�gHnLFHnEK��MK�v�� S�u^FHf)sOB«A!l^FQIEst�9FHILN&]RuLFHIEgOS¶KMIS� {'�'�YuEK�gOIEshstGJs�N/vJlEscfhgH��uE_kZv�FQvJKMgHILFH�«_LS�s5gQ��vJlEsBJ�$',P@'":$'&�*�!',V9��K!%$M0 O,N�X�P�sRQkuLFQI^S�KMgHI �5shvJlEgkN£V0FQILN lLFMHs�S�_^fhf)s�SJS��Ä_E�M���FQuLuE��KMstN/K�vv�g MWFHGJKMgH_^S¯uEG�gHnL��st��SKMI5SJgH�MKTN���stf-lLFHIEKTfhS � } j �|B&N�X sRQkuLFHILSJK�gOILS0FHGJs�nLFOS�s�N�gHI/vJlLslEgO�5gO�HstIEshgO_LS6f-lLFHgOS�v�lEshgOGJ�ogH��w�B�S­K�stIEshG�� j {N�¶FQILN FQG�s�stS�S�stI=vJKTFQ�M���ÂSJu^s�f vJG-FQ�0sRQkuLFHILS�KMgHI^SgQ�0AÔFH_LS�S�KTFQI�G-FQILNkgO� ]^sh�TNES�KMI=vJg [cshG���K v�scuYgH�M�=ILgH��KMFH�MStB�N�X@sRQkuLFHILS�KMgHI^SyFQ�M��gjm�lEKM�HlEZ³gOG�NkstGNkshvJshG���K�ILKMS�vJKTf FHuEuEG�gQRKM��Fjv�K�gOI�gH�¶G�FHILNkgH� ]Lst�MNES!FQI^NÂFQuEuYstFHG6vJg7sRQklEKMnEK�v!SJu^s�f vJG-FQ�f)gOI�MOshGJZ�HstILf)sÔKMIo��FHIR��fhFOS�s�S�FOS�m�s#m�KM�M�.S�lEgjm#BX��TFHS�S�KTfhFH��S­K�stIEshGJZ|[cshG���KMfhs N�X sDQkuLFQILSJKMgHILSÔFQG�s�nLFOS�s�N gOI v�lEs�� .���&�*>< .�u^gO���RIEgO��KMFH�

�Ä_EILf)vJKMgHILFH�MSKMI�v�shG���SgH��� !'6R0;0�*�!'"&G-FQILNEgH� MjFQG�KMFHnE��s�ShB��\I v�lEshgOGJ�OVWvJlEst��f)gHI MOshG��Hs¶v�g!FHI=� U�Ä_EILf)vJKMgHILFH�RgHI�v�lEs�G�FHILNkgH� SJuLFHfhs � j �|B[cgjm�sBMHstGtVWKMI uEG-FHf)vJKTf)syv�lEsh��fhgHI MHstGJ�Os�SJ��gjm��M�!�ÄgHG«IEgHIEZAÔFQ_^SJSJKMFHI�G�FHILNkgH� ]Lsh�TNES�FHILN�Nkg#IEgHv�FQuEuL��� vJg#G-FQILNkgO� ]Lst�MNLSym�K�vJl #'* 0�9���.�< .�NkKTS�v�GJKMnE_kv�K�gOILShBqcftf)gOG�NkKMIE�O���OVO�ÄgOG��ÎFHS�v�fhgHI MHstGJ�OshILfhs6K�I N�X�sRQkuLFQI^S�KMgHILS�FQI^N£VklEshI^f)sHV=�ÄgOG�fhgH��uE_kv-Fjv�K�gOILFQ�±s)�©Z]^fhK�stILf)�OVQvJlLs���f)gRgHG-NkKMILFjv�stSKMI5uLGJgOnLFQnEKM�MK v���SJuLFHfhs���K�I�m�lEKTf-l5N�X sRQkuLFQI^S�KMgHILSgH�LvJlLs�G�FHILNkgH�SJgH�M_kvJKMgHI FHGJs5S�gO_E�Hl=v#S�lLgH_E�TNÂnYs�FONEFQuEvJstNÂvJg7vJlEs�S�v�Fjv�KMS�vJKTfhS�gQ��vJlEs�KMIEuE_kv#NEFjv-F7FHILN�gH�yvJlLsG-FQILNkgO� SJgH�M_kvJKMgHI.B¶r�lEKTS6ftFQI�n^s�NkgOIEsÔK�IÂFQv��MstFOS�v�v�m�g5m�FW�kS�3

O�F�Pe���7st��uE��gj�RKMIE� Q .-":.-�T!',P*��N.;#� �� .��-JK!�"K0�*�$'"�0 OÎ��N�X2sDQkuLFQILSJKMgHILS P�vJl^Fjv�FHGJs�gOG�v�lEgH�HZgHI^FQ��m�K�vJl�GJs�S�uYstf)v v�g IEgOIkZ\AÔFH_LS�S�KTFQI uEG�gHnLFHnEKM��K�v�� ��s�FHSJ_EGJs�ShB ]R_Lf-l sDQRu^FQILSJK�gOILStVG�s)�ÄshG�G�stNov�goFOS { S­KMshIEstG�Z\qcSJPHst�U�Yf-lLFHgOS!sRQkuLFHILSJK�gOILScm�shG�se]LG�S�vÔsh��uE�Mgj�HstN K�I f)gO�5ZuE_kv-Fjv�K�gOILFQ�=FQ�M�HgHG�K�vJlE��S±KMI7� HQzM�|Vt�ÄgO���Mgjm�KMIE�6NksDMOsh�MgHuE��stIOv-S£KMI#uEGJgOnLFQnLK��MK v���K�I � �=zkV�� j �³VFQI^N�gOI�gOG�v�lEgH�OgHILFH�^uYgH�M�RIEgH��KTFQ�TS�K�I � xRV^xO{N�³B

OÄniPe���&gHuEvJKM��FH���M��SJshuLFHG�FQvJKMIE��Nks)v�shG��5KMIEKTS�v�KMf#FHILN�S�v�gRf-l^FHS�vJKTf!fhgH��uYgHIEstIOv-S�gQ�G�FHILNkgH�KMIEuE_kv�NEFjv-F#m�K v�l&uEG�stS�f)G�K�nYstN�SJuLFQvJKTFQ�^fhgHG�GJst�MFQvJKMgHI5vJlLGJgO_E�Hl�D#FQG�lR_EIEstIkZ|e¯g��sBMHs OÎD#e&PNks�f)gH��uYgOSJK v�K�gOI � lOzM�|B�q6uLFHG�v��ÄG�gH� nYshKMIE� Fov�lEshgOGJshvJKTfhFQ�yvJgRgH�³V«m�s�SJlEgjm9lEgjm D#eNks�f)gH��uYgOSJK v�K�gOILS�fhFHI7nYs#s-1&fhK�stIOv�����f)gO�5uL_kvJs�N7KMIo�HstIEshG-FQ�£NkgO��FHK�I^S �ÄgOGcF5m�KMNEsf)�TFHS�S�gQ��SJuLFjv�KMFH�fhgHG�GJst�MFQvJKMgHI��Ä_EILf)vJKMgHILS!nR�o�HshILshG-FQ�MK��tstNc�LFOS�v#�Â_E��vJKMuYgH�Ms5�ÂshvJlEgkNES�ÄgHG¶s�1&f)KMshI=vyf)gH��uE_Ev�Fjv�K�gOILFQ�ESJuYstf v�G�FH�kFQuEuEG�gQkK���FQvJKMgHI gH�Lv�lEs6f)gFMjFQG�KTFQILfhs�gHuYshG-Fjv�gHG�B

�\IÂ��N�X�VRvJlEs u^gO���RIEgO�5KTFQ�TS�FQG�s�f-lEg=S�stI��ÄG�gH� vJlEs�lR�RuYshG��HshgO��s)vJG�KTf�uYgH�M�RIEgH��KTFQ�TS�gQ�«vJlLs� 0��%.-@ X-!�&B*>,P@�m�lEstGJs5v�lEs�_EILNkstGJ�M�RK�IL��G-FQI^NkgH� MjFQG�KTFQnE�MstSÔFQG�s5IEgQv#G�stS�vJG�KMf)vJstN vJg�AÔFH_LSJSJKTFQIG-FQILNkgO� MjFQG�KMFHnE�MstStB��\I5�ÎFHf)vtVQv�lEshG�s�sRQkKTS�v-SyF!_EIEK LO_Ls6f)gHG�G�stSJu^gOILNkshI^f)s�n^shv�m�stshI5vJlEs�uLGJgOnLFQnEKM��ZK�v���NkKTS�v�GJKMnE_kv�K�gOI��Ä_EI^f vJKMgHI O N�a4��P�gH�¯v�lEs#S�v�gRf-l^FHS�vJKTfcKMIEuE_kvcFHILN�vJlEsÔm�shKM�Hl=vJKMIE�/�Ä_EILf v�K�gOIogQ�vJlLs�gHGJvJlEgO�HgOILFQ�£uYgH�M�RIEgH��KTFQ�TShB�r�lEs fhgHI MHstGJ�OshILfhsÔuEGJgOu^stG�v�K�s�S�gQ�yNkK^J±shG�shI=v6vJG�KTFQ�¯n^FHSJstS�m�shG�sS�vJ_LNkKMstN K�II� HQzM�yFQILNÂsDQku^gOIEshI=vJKTFQ�«f)gOI MHshG��HstILf)s#G-Fjv�s�m�FHScNEsh��gHILS�vJG-Fjv�stN�fhgH��uE_kv-Fjv�K�gOILFQ�M���

Page 7: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ {

�ÄgHG5��gkNksh��uEG�gHnE�Msh��StB r�lEs�Fj�ÄgHG�sh��stIOv�K�gOIEstN fhgHG�GJs�S�uYgHI^NkshILfhs&fhFHI n^s�sRQRv�shILNks�N vJg FQG�nEK�ZvJG-FQG�� N�a4�S/m�K�vJl v�lEs�gHGJvJlEgO�HgHI^FQ�¶uYgH�M�=ILgH��KMFH�MS5f)gOILS�vJG�_Lf v�stN gOIkZ�v�lEs)Z6�L�:�¶v�lEKMS5sDQ=v�shILSJKMgHIm�FHS¶uEG�stSJshI=v�stN�KMIS� j z'�|BL�\I&s�SJSJshI^f)sHVO��N�X@FHuEuEG�gQkK���Fjv�K�gOILS«gQ�£G-FQILNEgH� ]^sh�TNES�fhgHG�GJs�S�uYgHI^N�v�gvJlLsÔSJuYstf v�G�FH�>�jlEu&st��st�5stI=v���shvJlEgkN£VESJshs�� xOxRV8�RHN�³B¶a�shuYshILNkKMIE��gOI&vJlLs!S�vJgkf-lLFOS�v�KMf�GJst�H_E�TFQG�K�v��gQ�LvJlEs�G�FHILNkgO� ]^sh�TN£VQK�v«��FW�ÔnR��FHNTMjFHIOv-FQ�OshgH_^S±vJgÔf)gO� nEKMIEs��5s�S�l/GJsD]LIEst�5stI=vm�K�vJl/K�ILfhGJs�FHSJsgQ�¯vJlEs!u^gO���RIEgO��KMFH�YNkst�HG�shsOVO�MstFONkK�IL��vJg�FQI����LZ³�OshIEstG�FH��KM�tFQvJKMgHI�gQ�¯��N�X�FQuLuEGJgQkKM��FjvJKMgHI^ShV=S�sts� {Q�kV^x H=VK�'�|Br�lEs6u^FQuYshGyKTSygOGJ�=FQIEKM�hs�N/FOS«�ÄgH�M��gjm6S�3�S s ]LG-S�vyGJsBM=KMshm nLFOS�KTf�f)gOILf)stukv�SyFHILN5�ÄgHG�� _L�MFQvJKMgHI

gQ����N�X FQuLuEGJgQkKM��FjvJKMgHI^ScgH��S�vJgkf-lLFHS�vJKTf5NkKKJ±shG�shI=v�KMFH�¶sBL=_LFjv�K�gOILSÔKMI ]Rs�f v�K�gOI xEB�S s&NkKTSJfh_LS�SKMI@S�gO��s�Nks)v-FQKM��v�lEs�GJstuEGJs�S�stI=v�Fjv�K�gOI gQ�cS�vJgkf-lLFHS�vJKTf�KMIEuE_kv-S KMI �OshIEstG�FH��NkgO��FHK�I^S FQI^N m�K v�luEG�stS�f)G�K�nYstN�S�u^FjvJKTFQ��fhgHG�GJst�MFQvJKMgHI _LSJKMIE� � _E��vJKMu^gO��shZ³n^FHSJstN@D#FHGJlR_EILshIkZ\e.g��sDMOs�sRQkuLFQI^S�KMgHILS5KMI]Rs�f vJKMgHI lEB�\I ]Rs�f vJKMgHI^S �oFQI^N {�m�s5uEG�stSJshI=v���N�X SJgH�M_kv�K�gOILS�vJg�uEGJgHvJgHv��=uYs5gHG-NkK�I^FQG���FHILNuLFHG�v�KMFH�NkK^J±shG�shI=vJKTFQ�sBL=_LFQvJKMgHILStB#r�lEs/sDQku^g=S�K�vJKMgHI�gH�yvJlLs/��N�X�Z|nLFHSJstNo��s)v�lEgkNES!K�I ]Rstf)vJKMgHILSx�v�go{&KMSc�ÄgHG���FQ�³BG�\I ]Rs�f vJKMgHI j m�s/uEG�stSJshI=v�vJlEs5��FQKMI�KMNEstFHS�gHI f)gO� nEKMIEKMIE��uYshGJvJ_EG�nLFQvJKMgHIsRQkuLFHILSJK�gOILS¶FQILN�SJuLFQG-SJs��OGJKTNEStB)�KMILFQ�M�M�HVHKMI�]Rs�f vJKMgHI7H�m�s6FHNENEGJs�SJS¶SJgH��s�gH_Ev�S�v�FQI^NkK�IL�#��FQvJlkZsh��FQvJKTfhFQ�RFQI^N f)gO��uE_kv�FQvJKMgHILFH�RKMS�S�_LstSFHS�S�gkf)KTFjv�stN#m�K�vJl5S�v�gkf-lLFHS�vJKTfy��gkNksh�MKMIE��KMI �OshIEstG�FH��VjFHILNm�K�vJlo��N�X�nLFOS�s�N���s)v�lEgkNES�KMIouLFQGJvJKTf)_E�TFQG�B

} ��� V h&V CE3d,f�� V [�� Y d W2h#Y � f EHdic � E Y @ � ]RvJgkf-lLFHS�vJKTf«��Fjv�lEsh��Fjv�KMftFQ�Q��gkNkst�MS.FHGJs«nLFOS�s�NgHI&F J���$%+;!O+�*>,P*>< @�0FJ�!O9;. O��� ����eP¶m�lLshG�s� KMS�vJlLscsDMOshI=v�SJuLFHfhsHV� ���x��ÂK v-S��YZ\FQ�M�HstnEG-FEVHFHILN��K�v�S6uEGJgOnLFQnLK��MK v����5s�FHSJ_EG�sHBa!Fjv�FÔFHILN/SJgH�M_kv�K�gOILS«gQ�±S�v�gRf-l^FHS�vJKTf�NkK^J±shG�shI=vJKTFQ�ks'LO_^FjvJKMgHI^S¶FQG�s ��!�"�#%$'&WCV.�, #M0���O��kP)VQK�B sHB

��FQuEuLK�IE�=S�� 3��� �9�ÄGJgO� v�lEs uEG�gHn^FQnEKM��K�v��7SJuLFOf)s#KMIOv�g�F5�Ä_EILf)vJKMgHI SJuLFOf)s!��B �|�"�$# ��Vm�s�S�uYstFHP�gQ�¶G-FQILNEgH� MjFQG�KTFQnE�MstStVLFQI^N7K����9KTScF5�Ä_EILf)vJKMgHI�SJuLFHfhs#gFMHstG6F5vJKM�5s/FQILN?�jgHG6SJuLFHfhsKMIOv�shG MjFQ�³V0gH��G-FQILNEgH� ]^sh�TNES�gOG S�v�gkf-lLFHS�vJKTf�uEG�gRfhstS�S�s�ShB �EgHG5S�v�gkf-lLFHS�vJKTf5uLFQGJvJKTFQ��NEKKJ±shG�shI=vJKTFQ�sBL=_LFQvJKMgHILStV%� KMS�gQ�©v�shI F�S�uLFOf)s�gH�y�HstIEshG-FQ�MK��tstN7�Ä_EILf)vJKMgHILS!KMI F�uElR�kSJKMftFQ�0NEgH��FQKMI � ���HV�&#4x�� lEB

�\I&FQ�M�EsDQkFH��uE��s�Syf)gOILSJKMNkstGJs�N5lEshG�sHV�� KMS�F#[6KM��nYshGJv�SJuLFHfhs�m�K v�l�Nk_LFH�'�)(�V=IEgHG��+*-,"*�FHILNKMIEIEshG�uEG�gkNk_Lf v O�./�0. PD31�324�3� ��B«q�S5� KTS�NkstILSJsh�M��sh� nYstNLNkstN�KMI��!(ÎVRm�s!FHnE_LSJscIEgHv�FQvJKMgHIFQI^N7NkstIEgQv�s#nR� O�./�0. P�FQ�TSJg v�lEs!�627�!(.Nk_LFH��K�v���u^FQKMGJKMIE�LBq4G�FHILNkgH� ]Lst�MN8� 39:�;� KMS�F 0�.;9;$'":#'E $'�T#O.�� �T!'"�#%$'& CD.-,/# $'('.-�!� *>,/+T.���<20FJ�!O9;.<��V

K��= *>�?* U # = O@�A��� P�BDCE�

m�lEstGJs = NkshIEgHvJs�S�vJlEs#sDQRuYstf)v�FQvJKMgHIogQ�«F/G-FQI^NkgH� MjFHGJKTFQnE�MsGF6H ? OI�� ��P�NksD]LIEstN�nR�= FJ#LK1MON � F6O@�kP �1P5O��kP>Q

A!shILshG-FQ�MK��tstN�uYgH�M�=ILgH��KMFH�^f-lLFHgOS OÎ��N�X�P¶KTS�F���s�FQILS�gQ�.G�shuEG�stSJshI=vJKMIE��SJstfhgHILNRZ|gHG-NkstGyS�v�gRf-l^FHS�ZvJKTf�uEGJgkfhstS�S�s�SR��O@�kPyuLFHG�FH��s)vJG�KTfhFQ�M�M� v�lEGJgO_E�Hl7F SJs)v�gQ�¯G-FQILNEgH� MjFQG�KMFHnE��s�S�SUTWV�O��kPYXUZV�[ ? ���\H] �kv�lEGJgO_E�Hl7vJlLs#sDMHstI=v�S��^HA 3

��O��kPR#`_a� [%b-c ��d � O�e�O@�kP PYQ O�xEB�}P

[6stGJs�S d V O�e�O@�kP PWX5FQG�s#gHGJvJlEgO�HgHI^FQ�±u^gO���RIEgO��KMFH�MS�KMIovJstGJ��ScgQ�yF��hstGJgHZ³��stFHI7G-FQI^NkgH� MHstf)vJgOGe�3f#gShT V O@�kPWX ZV�[ ? VLS�Fjv�KMS��Ä�RK�IL�/v�lEs#gHGJvJlLgH�HgOILFQ�MK�v��5G�sh�TFjv�K�gOIi d5jkd VUl"# i d Uj lnm j V�� O�xEB x�P

Page 8: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

j µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

m�lEstGJs�m j V KMS�vJlLs!DÔG�gHIEs�f-PHstG�Nksh��v�F5FQI^N i ./�0.fl�NEshIEgHvJstS�vJlLs�stILS�st� nE�Ms�FMOshG-FQ�OsHB0r�lLscIR_E� nYshGgQ�«G-FQILNkgO� MjFQG�KMFHnE��s�S �\H ] KMS6K�Io�HstIEshG-FQ�±KMIT]LIEK�vJsOV^SJg�KMS�v�lEs#KMILNksRQ�K�I O³xkBM}'P B2�\IouEG-FHf)vJKTf)sOVlEgjm�sDMOshG�V�m�s�IEststN�v�g G�s)v�FHK�I2F ]LIEK�vJs S�shv�gQ��G-FQILNEgH� MWFHGJKTFQnL��s�ShV�K³B sOB�V�v�gDShTYV�X ZV�[ ? m�K v�l�\B:C2VLFQI^N�Fe]LILK v�s)Z³vJshG�� v�GJ_LILfhFQvJKMgHI�gQ�-O³xkBM}'P)Br�lEs�KMIEIEstGcuEG�gkNk_Lf)vcK�I O�xkB�xbP�KTS6KMIÂv�lEs [6KM�Mn^stG�vÔS�uLFOf)s�NkshvJstGJ��KMIEstNÂnR�7vJlEs �5s�FHSJ_EG�s#gQ�

vJlLs#G�FHILNkgH� MWFHGJKTFQnL��s�S

i�� O�eiP���O@eiPnlR# K MON � � O�eiP��.O�e3P �9P5O@�kP"# K � O�e3P��.O�eiP��ZO�e�P ��e O�xEB l�P

m�K�vJl��eO�e�P0NkshILgQvJKMIE�cvJlEs�NkshI^S�K�v��ÔgQ�Ev�lEs��TFWm �9P5O@�kP.m�K�vJl/GJs�S�uYstf)v0v�g6v�lEs�e¯shnYstSJ�H_Es���stFHSJ_EG�s��e�FQILN�m�K�vJl&KMI=vJst�HG-FjvJKMgHI5v-FQPHstI�gFMHstG�F�SJ_EK v-FQnE�MscNkgO��FQKMI.V=NEs)vJstGJ��KMIEstN&n=�/vJlLscG-FQIE�Os�gQ�£vJlLsG-FQILNkgO� MHs�f v�gHG5e.B

�\I�vJlEs�NEKMS�f)G�s)v�sÔftFHSJsHVRv�lEs�FQnYgFMHs!gHGJvJlEgO�HgOILFQ�YGJst�MFQvJKMgHI7v�FHPHstS�v�lEsÔ�ÄgHG��i�� O@eiP��.O�eiP�l"# a

� O�eiP���O@e3P��ZO@e�PYQ O�xEB � P

�\I sBL=_LFjv�K�gOI O³xkBM}'P V±v�lEshG�s�KMSÔF�gHILs)Z³vJgQZ|gHILs/f)gOGJG�stSJuYgHILNkstILf)s/n^shv�m�stshI vJlEs5v��Ru^s�gH��vJlLsgHGJvJlLgH�HgOILFQ�¶uYgH�M�RIEgH��KTFQ�TS S d X�FHILN vJlLs&�MFWm gH��v�lEs&G-FQILNEgH� MjFHGJKTFQnE�MstSGe±B�r�lLKMS KMS/Nks)v�shGJZ��K�ILstNÂnR�Âf-lEgRgOSJK�IL��vJlEs v��=uYs gH�¶gHGJvJlEgO�HgHI^FQ�.uYgH�M�RIEgH��KTFQ�TS S d X KMI SJ_Lf-l�F&m�FW�&v�lLFjv�vJlEstK�Gm�shKM�Hl=vJKMIE�5�Ä_EILf)vJKMgHI�ZO@e�P�KMI7v�lEs�gOG�v�lEgH�OgHILFH��K�v���GJst�MFQvJKMgHI O�xEB l�P�lLFHS�v�lEs S�FQ��sÔ�ÄgHG��%FOS�vJlLsuEG�gHnLFHnEKM��K�v��&NkKTS�v�GJKMnE_kv�K�gOI7�Ä_LILf v�K�gOI�gH�¯v�lEs#_EILNkstGJ�M�RK�IL�5G-FQI^NkgH� MjFHGJKTFQnE�MstS�e.B �LgHG�sRQEFQ��uE�MsHVvJlLs�m�stK��OlOv�K�IL�c�Ä_EI^f vJKMgHI�gH�Y[6stGJ��K�vJs�gHGJvJlLgH�HgOILFQ�=uYgH�M�=ILgH��KMFH�MSKTS ?

� � U� ����sRQku�O�� ?U e�� eiP VHFHILN

KTS�vJlLs/S�FQ��s�FHS6vJlEs/uEGJgOnLFQnLK��MK v���NkshI^S�K�v����Ä_LILf v�K�gOI�gQ�«vJlLs ���6NkKM��shILSJKMgHILFH�0AÔFQ_LS�SJKMFHI�G-FQIEZNkgO� MWFHGJKTFQnL��s�SGe.B [6stILf)sOV¶vJlEsÂfh�MFOSJSJKMftFQ�kS­K�stIEshG�uYgH�M�=ILgH��KMFH��f-l^FQgOS KMS�FHI sRQkuLFHILS�KMgHI@gQ�[6stGJ��K�vJs�uYgH�M�=ILgH��KMFH�MS!KMI v�shG���S�gH��AÔFH_LSJSJKTFQI�G-FQILNEgH� MjFQG�KMFHnE�MstStB q f)gHG�G�stSJu^gOILNkshI^f)s nYs)Zv�m�shshIogOG�v�lEgH�OgHILFH�£u^gO���RIEgO�5KTFQ�TS6FHILNoG�FHILNkgO� MjFQG�KMFHnE��s�S�m�FHS�]LG-S�v6stS�v�FQnL��KTS�lLstNoKMI � �=zkV�� j �³B[6stGJsOV±m�s/��KTS�v#SJgH��s�v��RuYstS!gQ�y�OshIEstG�FH��KM�hs�Nou^gO���RIEgO�5KTFQ�«f-lLFHgOS!f)gHG�G�stSJu^gOILNkKMIE��vJg7vJlEs�f)gO�5Z��gHIE�M� PRIEgjm�I NkKTS�vJG�K�nE_EvJKMgHILS#KMI r0FHnE�Ms�xkBM}HB r�lEs �LsDQkK�nEKM�MK v�� gQ���HstIEshG-FQ�MK��tstN u^gO���RIEgO��KMFH�

���������! D���"%$'+-+B5;.9(�$'1D<!5�1D?05�$6sS7/FH5j79M-(H54$6s#"j,/5;1D5�+-g p ._T'5;M=(�$2O M'1D$'&�,/*2Ok?GFH*2$'.4*'1D< 7>F[5�,/+SJ�1D<!5�+-O M',>1�f +B*21D<2$'&

K�*'+-,/*!3�O 5�.�@%$'&�Ðz,>. * N 1 ,/7E5l,/1 795hf!5�+EC2W

¬¯�-�W¡W° �@¤ �-�³�·�-»�Ê�¢��)( Õ���¢��W¢���ÍT¨�³² ¢\¼c�|�j�-° �+*�,Û-(jÞ�. ¦t�W�W�Q° �Πɱ° �h ����h�W° �W� � �-�W�³���·�-� Ã0¢��³���  �¢\Í©�|�j�-° � Û0/2143�1&Þ

È)�-���6� ºk�-È �W¢����³¢\Í©�|�j�-° � 5 Ð63�1&Þ»Q¢\ ³� áh�-��° »W� ÍT�|�j�-° � 5 7�3�8�9�W�W� ´�° �³� ºR¢�È ¢��W¡W�³¢\Í©�³�j�-° � 5 7�3�8�9

½�������³¢\ ³¢ ÅE° ���³��° � ɱ�j�-�³Ê���¢��ÎÍ©�|�j�-° � *�Ð63�×:3³Ï63�;�;�;�.»W���W° ���·�-Ê µ«�³��¥. ��|�W° �W²)Í©�|�j�-° � *�Ð63�×:3<;�;�;�3�$!.

��¢�È)�� �� ¤)¢y»W���W° ���·�-Ê ªÔ¢�� Ë���¢��ÎÍ©�|�j�-° � *�Ð63�×:3³Ï63�;�;�;�.�)¼��Q¢��³È ¢�° ��¢\ ��³��� Ã�-�W��ÍT�|�j�-° � *�Ð63�×:3<;�;�;�3�$!.

f-lLFHgOS¯ftFQI/n^s�S�stshI�KMI �KM�H_EG�s�xEB�}OVWm�lEshG�s�m�s�_^S�s�[6shG���K v�s)Z\f-lLFQg=S£v�g!FHuEuEG�gQRKM��Fjv�s�F6_EILK �ÄgOGJ�G-FQILNkgO� MjFQG�KMFHnE��sOB�S s�gHnLSJshG MHs�vJlLFQv¶FH� v�lEgH_L�Hl�v�lEs6[6stGJ��K�vJshZ|f-lLFHgOSf)gOI�MOshG��Hs�S£vJg!v�lEs�v�FQG��HshvNkKTS�v�GJKMnE_kv�K�gOI�FHS�v�lEs#sRQkuLFHILSJK�gOI�gOG�NEshG�KMILf)G�stFOS�s�ShVRv�lEs FQuLuEGJgQkKM��FjvJKMgHI�KTS�IEgQv!FHfhfh_EG-FjvJs#FHILNSJ_TJYstG�S#�ÄGJgO� A!KMnEnLS�Z³�MK�POs�gOS�f)KM���TFjv�K�gOILShB�U�I v�lEs�gQv�lEshG lLFQILN.V.vJlLs&�HstIEshG-FQ�MK��tstN u^gO���RIEgO��KMFH�f-lLFHgOS¯fhgHG�GJs�S�uYgHI^NkK�IL��vJgÔF6_EILK �ÄgOGJ� NkKTS�vJG�K�nE_EvJKMgHI.VWv�lEs�e¯sh�OshILNkG�s)Z\f-lLFHgOS O�S�sts�rFQnE�Ms�xEB�}P VjfhFHIG�shuEG�stSJshI=v6_EIEK��ÄgHG�� G�FHILNkgO� MjFQG�KMFHnE�MstS�sDQkFOf v�����nR� ��_LS�vm]^G�S�v�Z|gHG-NkshGcsRQkuLFQI^S�KMgHILStB=�EgOGc��gHG�sNkshv�FQKM�TS�gHIoFQuEuEG�gQkK���FQvJKMgHI&gH�«FHI7FQG�nEK�vJG-FQG���G�FHILNkgO� MWFHGJKTFQnL��s MRKMF5�HstIEshG-FQ�MKM�hstN�u^gO���RIEgO��KMFH�f-lLFHgOStVRSJshs � HjzLV j zM�|B

Page 9: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ H

−1 −0.5 0 0.5 1 1.5 20

0.5

1

1.5exact 1st−order3rd−order5th−order

������� �>� ® p (2(D+B$�o',/&�*'79, $'1 .n$_sl*SJH1 , sG$'+-& <',>.079+-, 3�JH7 , $'1 3�M � 5;+-&�,>7E5�g�" FH*2$'.

r�lEs5sRQkuLFHILS�KMgHIÂKMI s'L=_LFjv�K�gOI�O�xEB�}PcftFQI�nYs v�GJ_LILfhFQvJstN�n=�ÂG�stNE_Lf)KMIE�&v�lEs5sRQkuLFQI^S�KMgHIov�gvJlLs�]LIEK�vJshZ|NkKM��shILSJKMgHILFH�6S�uLFOf)sOV�K³B sHBMV�sDQkuLFQILSJKMgHI gQ� ]LIEK�vJs)Z\NkKM��shILSJK�gOILFQ�cG�FHILNkgH� MWFHGJKTFQnL��s�Se.V�FOfhfhgHG-NkK�IL��vJg v�lEsoILFjv�_EGJsogH��G-FQILNkgO� K�ILuE_kv�S���m�s�FH�MSJg SJs)v�v�lEsolEK��OlEstS�v�gHG-NkshG�gH�cvJlLsuYgH�M�=ILgH��KMFH�MS"S d X�FHftf)gHG-NkKMIE��v�g!FOfhf)_LG�FOf)�!GJs'LO_LK�G�sh��shI=v-ShBr�lEs ]^IEK v�s)Z³vJstGJ� sDQRu^FQILSJK�gOI#v�FHPHs�SvJlLsÔ�ÄgHG��

��O@�kPR# �aV�[%b c V d V�O�e�O��kP PY� O�xEB {�P

m�lEstGJs�e4# O@T ? �h.0.0.%��T Z P � KTS�FQI ���6NkKM�5stILSJK�gOILFQ�±G-FQILNkgO� MHs�f vJgOG�m�K v�l�T j K�ILNEshuYshILNkstI=v6gQ�TWV6�ÄgOG�FH���}������#�� � B �|�.m�s�NkstIEgQv�s6vJlLsclEKM�HlEs�S�v�gHG-NkshG�gQ�.uYgH�M�RIEgH��KTFQ� S d X!FOS"P�V=vJlEstIvJlLsÔvJgQv-FQ�£IR_E�/n^stG6gQ�sRQkuLFQI^S�KMgHI7vJstGJ��S O � �2}'P�KTShVO�� �2}'PR# O � � P1P����TO �� P�� PYQ O�xEB j P

r�lEs��/_E��vJK�Z|NkKM��shILSJKMgHILFH�.�HstIEshG-FQ�MK��tstN�uYgH�M�=ILgH��KMFH�¯f-lLFHgOS�sRQkuLFHILSJK�gOI�KTScfhgHILS�vJG�_Lf)vJstNoFOS�vJlLsvJstILSJgHG.uEG�gkNk_Lf)v.gQ�=vJlEs�fhgHG�GJs�S�uYgHI^NkK�IL��gOIEs)Z\NkKM�5stILSJK�gOILFQ�jsDQRu^FQILSJK�gOI.B¯wcgQvJs�K�IÔgHILs)Z\NkK���stILS�KMgHI^FQ�sRQkuLFHILSJK�gOILS O � # }P V�� #EP�Be.shv&_LS&ILgjm%f)gOILSJKMNkstG�F �HstIEshG-FQ��SJs)vJvJKMIE� �ÄgHG7F NEKKJ±shG�shI=vJKTFQ�csBL=_LFjv�K�gOI�m�K v�l­G�FHILNkgH�

KMIEuE_kv-S� O�� ���Y��� ���.PR# � O�� �����n�kPY� � H O���PY��� H OÎz ����P>���?H �� O�xEB HbP

m�lEstGJs ��KMS5F�NkK^J±shG�shI=vJKTFQ��gHuYshG-Fjv�gHG�V O �-P�H ����O�� #�}���x � l�P#FÂnYgH_EILNEstN NkgO��FQKMI m�K v�lNkKTFQ��s)v�shG!�#" zLVjFQILN$�%"�zEBkOI��� 4�n�eP£KTS0FHI FQuLuEGJgOuEG�KMFQvJsh�M��NEsR]LIEs�N�f)gO��uE��shvJs�uEGJgOnLFQnLK��MK v��SJuLFHfhsHVLm�lLshG�s) '& x�� KTS�v�lEs&�YZ\FQ�M�HstnEG-F5FHILN�� vJlEs uEGJgOnLFQnLK��MK v��7��stFHSJ_EG�sO��� 3 #(�&O�� �����n�kPKTS!vJlEs�SJgH�M_kvJKMgHI FQILN � O�� �������kPcKMS!v�lEs�S�gO_EG�fhs v�shG��oB/r�lEs��HstIEshG-FQ�uEG�gkf)stNE_EGJs5gQ��FQuEuL���RKMIE�vJlLs#�HshILshG-FQ�MK��tstN&uYgH�M�RIEgH��KTFQ�.f-lLFHgOS�f)gOILSJKMS�v�S�gH�0v�lEsÔ�ÄgH�M��gjm�KMIE��S�v�shuLS�3

}HB�C�QkuEG�stS�S!vJlLs�G�FHILNkgH��K�IEuL_kv�S n=� F ]LIEK�vJs�IR_E�/n^stG�gQ��G�FHILNkgO� MjFQG�KMFHnE��s�S�e�O��kPG#ShT ? O��kP>�0./�nT Z O��kPYXOVLFHILN7GJstm�GJK�vJs!vJlLs�S�v�gRf-l^FHS�vJKTf�uLGJgOnE��st� uLFHG�FH�5shvJG�KMftFQ�M���&FOS� O�� ���Y�ne�����O�� �����neHP P"# � O�� �����ne3PYQ O�xEB ��P

Page 10: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

r�lEKTS�S�v�shu@KTS vJG�K^MRKTFQ��m�lEshI@vJlEs�G�FHILNkgO� KMIEuE_Ev�S�FQ�MG�stFHNE� v-FQPHs�vJlEs7�ÄgHG�� gQ�cG-FQIEZNkgO� MjFQG�KMFHnE��s�ShB S­lEstI@v�lEsÂG�FHILNkgO� K�IEuL_kv�S&FHGJs�G-FQILNkgO� ]Lsh�TNEStV�F Nks�f)gO�5uYgOSJK�ZvJKMgHI v�stf-lEILK L=_Es&KTS�ILshstNEstN£BSU�IEs&uYgHuE_L�MFHG f-lEgHKTf)s�gH�6S�_Lf-l NEstf)gO��u^g=S�K�vJKMgHI KTS#vJlLsD#FQG�lR_EIEstIkZ|e¯g��sBMHs6sDQkuLFQILSJKMgHI.VRm�lEKTf-lom�K��M�.nYs�NkKMS�f)_^SJSJstN7K�I�v�lEsÔ�ÄgH�M��gjm�KMIE��S�s�f v�K�gOI.B

xkB�q6uLuEGJgQkKM��FjvJs�vJlEs S�gO��_EvJKMgHI FHILN­KMIEuE_kv-S7nR� ]LIEK�vJshZ�v�shG�� u^gO���RIEgO�5KTFQ�Ôf-lLFHgOS&sDQRZuLFHILS�KMgHI^S O�xEB {�P V6FHILN­S�_LnLS�v�K v�_kvJs vJlLs sRQkuLFHILNks�N MWFHGJKTFQnL��s�S�K�I=v�g vJlLs MjFQG�KMFQvJKMgHILFH�sBL=_LFQvJKMgHI

��� � ���Y��e�O��kP-� �a j [%b � j d j O�e�O��kP��J# � O�� ������e�O@�kP PYQlEB N«shGJ�ÄgHG�� F�AÔFQ�MshG�PRK�I�uEG�g���stf)vJKMgHI7gHI=vJg�stFOf-l7gH�0v�lEs#uYgH�M�=ILgH��KMFH�£nLFHSJKTS�

� � � ���Y��e � �a j [%b � j d5j O@eiP � � d � O@eiP���# i�� � d � O�eiP�l%� �4# z �t}��0.h.0.-� � Qr�lEKTSuEGJgkfhstNk_EG�s�G�stSJ_E��v�SKMI/F!S�shvgH�#O � �o}'P #%.-<=.���&B*>"?* 0;<F*�9hVHKMI �HstIEshG-FQ�Rf)gO_EuE�MstN£VQNEKKJ±shG�shI=vJKTFQ�sBL=_LFQvJKMgHILScm�lEKTf-l�fhFQIÂnYs/SJgH� MHs�NonR��fhgHI MHstIOv�K�gOILFQ�0NkKMS�f)G�s)v�K���Fjv�K�gOI���shvJlEgkNEStB �\��u^gOG�v-FQI=vJ�M�HVvJlLKMS!S�_^fhf)s�SJSJK MHs AÔFQ�MshG�PRK�I�NEKMS�f)G�s)v�K���FjvJKMgHI �JK�IÂuLGJgOnLFQnEKM�MK v��8� OÎn=����N�X4FQuEuEG�gQkK���FQvJKMgHIiP�FHILN��KMI�uLl=�kSJKMftFQ�YS�uLFOf)sN�9OÄnR� ]LILK v�s!NkK^J±shG�shILfhstS�gHGk]LIEK�vJs!sh�Msh��shI=v-S P��RK�st�MNES��HstIEshG-FQ�M�M�5�TFQG��Hs�S��kS�ZvJst��S6gQ�yFH���OshnEG-FQKTf!sBL=_LFjv�K�gOILS�m�lEKTf-lÂfhFHGJG���F�v�shILSJgHG6uLGJgkNk_Lf)v6nE�MgRf-PoS�vJG�_Lf v�_EGJsOB��LgHG6�MKMIEstFHGuEG�gHnE�Msh��StVEv�lEs/S�vJG�_Lf v�_EG�s�gQ�«vJlLs uEG�gHnLFHnEKM��KTS�v�KMf�uLFQGJv6gQ�¶v�lEKMS!SJ�RS�vJst�%KTScNEs)vJstGJ��KMIEstN�n=�7vJlLsgHGJvJlLgH�HgOILFQ�^u^gO���RIEgO��KMFH�MS�_LSJstN�K�I7vJlEsÔ��N�X NkKTSJfhGJshvJKM�tFQvJKMgHI7FHILN&KTStVkK�I7uLFQGJvJKTf)_E�TFQG�VRK�I^NkshuYshIkZNkstIOv!gQ�¶v�lEs/NkK^J±shG�shI=vJKTFQ�gHuYshG-Fjv�gHG6_EI^NkshGÔf)gOILS�KTNkstG�FQvJKMgHI.B6r�lEKTS�gHnLSJshG MjFjvJKMgHIo_EI^NkshG���KMstScvJlLsFQuLuE��KTfhFQvJKMgHI gQ����N�X4v��RuYs���s)vJlLgRNLS#NkstS�f)G�K�nYstN KMI ]Rs�f v�K�gOILSG��FHILN {�FHlEstFON£B5e¯s)v#_LSÔIEsDQRvvJ_LGJI�vJg5v�lEs#uEG�gHnE�Msh� gH�u^FQG-FQ��s)v�GJKTfcG�shuLGJs�S�stIOv-Fjv�K�gOI�gQ�G�FHILNkgO� ]Lsh�TN�K�ILuE_kvcNEFQv�FEB���� V �#C V @ V h A'ETABf Yih Y "_.A Y G � E3@DA'f,G � h �&`#AB@�\ U ETC � ` h#V h��� Y �V ~ V�� � ��E h @Bf Yih �D#FQG�lR_EIEstIkZ|e¯g��sBMHs6O�D#e#P�sRQkuLFHILS�KMgHI KMS#F7m�FW�ÂgQ��G�shuEG�stSJshI=v�K�IE�oF7G�FHILNkgH� uLGJgkf)s�SJS�� lHzM�|B��|vKTS�n^FHSJstNÂgOI�vJlLs5SJu^s�f v�G�FH�sDQkuLFQILSJKMgHI�gH�¶vJlEs�f)gFMjFHGJKTFQILfhs#�Ä_EILf)vJKMgHI gQ�yv�lEs/uLGJgkf)s�SJStB#e.shv!_LSNkstIEgQv�scv�lEscuEG�gkf)s�SJS�FHS ��O�� �n�kP�FHILN�K�v�S�f)gFMjFQG�KTFQILfhs��Ä_EILf)vJKMgHI7FOS����iO�� ? ��� U P)Vkm�lEshG�s�� ? FHILN� U FHGJsÔSJuLFjv�KMFH�£gHG�vJst�5uYgHG-FQ�.fhgRgHG-NkK�I^FjvJs�ShB#����NksD]LIEK�vJKMgHI.Vkv�lEs#f)gFMjFQG�KTFQILfhs6�Ä_EILf)vJKMgHIoKTS�GJs�FQ�³VSJ�=����s)v�GJKTfÂFQI^N�uYgOSJK�vJK MHs)Z\NksD]LIEK�vJsHB �|v�lLFOS&FQI�gHGJvJlLgH�HgOILFQ��SJs)v�gH�!stK��OshIk�Ä_LILf v�K�gOILS�m�lEKTf-l�ÄgHG���S F�fhgH��uE�Ms)v�s&nLFHSJKTS���� j O���P�FQI^N�� j FQG�s�vJlLs&shKM�HstIk�Ä_EILf)vJKMgHILS5FQILN stK��OshI MjFQ�M_EstS�gQ��vJlLsf)gFMjFHGJKTFQILfhsc�Ä_LILf v�K�gOI.VEG�stSJu^s�f vJK MHst���OVkK�B sHBMV

K�� � O�� ? ��� U P�����O�� U P � � U #�� j ��� O�� ? P>� �+# }��-x��h.0.0.-Q O,lLB�}P

r�lEs ]LILK v�s)Z³vJshG�� D#FHGJlR_EIEstIkZ\e.g��sDMHscsRQkuLFQI^S�KMgHI7vJlEstI�v�FQPOstS�vJlLsÔ�ÄgH�M��gjm�KMIE�5�ÄgHG���3

� Z O�� �n�kP"#���#O���P��?��� Za� [ ?! � � � � O�� PkT � O@�kPY� O,lLB x�P

m�lEstGJs"���O���P�KMS�vJlLs���stFHI&gQ�¯vJlEs!G�FHILNkgO��uEG�gkf)s�SJStV1��� vJlEsÔS�v-FQILNLFQG-N&NksDMRKTFjv�K�gOI.V=FHILN4T � O@�kPF SJs)v�gH�#_EILf)gOGJG�sh�TFjv�stN�G�FHILNkgO� MjFQG�KMFHnE�MstS�m�K�vJl­�tshG�g �5s�FQI2FHILN�_EIEK�v9MjFQG�KMFHILf)sOB r�lLstSJsG-FQILNkgO� MjFQG�KMFHnE�MstS�FQG�s#Nks)v�shG��5KMIEs�N�nR�

T���O��kP�#�K �#O��Y�n�kP#��� O���P � � �$�+# }��-x��h.0.0.-Q O,lLB l�P

Page 11: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ �

������� � C Y � V C'A'f V @ Y U EHC � ` h&V�h���kY �V ~ V V � �&E h @'f Y�h � qc�5gOIE��gQvJlLshG!u^g=SJSJK�nL��s�Nks)Zf)gO��u^g=S�K�vJKMgHILS!gH��F7G�FHILNkgH� uLGJgkf)s�SJStV±vJlLs�D#FHGJlR_EILshIkZ\e.g��sDMOs#sRQkuLFQI^S�KMgHI�KTSÔgHuEvJKM��FH�¶K�I vJlLsSJshILSJs�vJlLFQvv�lEs���stFQIEZ|S L=_LFQG�s�stGJG�gHGgQ�^vJlEs-]LILK v�s)Z³vJshG�� G�shuLGJs�S�stIOv-Fjv�K�gOI&� Z O�� ���kPgH�LvJlLs�uLGJgHZf)s�SJS5��O�� �n�kP«KMS���K�ILK���KM�hstN � lOzM�³B¶r�lEs�f)gFMjFQG�KMFHILf)s��Ä_EI^f vJKMgHI � �iO�� ? ��� U P«uE�TFW�RS�F�f)stI=vJG-FQ�EG�gH�MsKMI D#FQG�lR_EIEstIkZ|e¯g��sBMHs!sRQkuLFHILS�KMgHI¯VYFOScK�v!KTScvJlEs5PHstGJIEst�¯�Ä_LILf v�K�gOI KMIÂvJlEs5shKM�HstI MWFH��_Ls uEG�gHnE�Msh�NksD]LIEstN&K�I O lEBM}'P B«r�lEs!NkstftFW� gQ�±v�lEscstK��OshI MjFQ�M_EstSyFHILN5vJlLs6GJst�H_E�TFQG�K�v�� gQ�±v�lEs6shKM�HstIk�Ä_EILf)vJKMgHILSNkstu^stILNÂS�v�GJgOIE�H�M�&gOI�v�lEs�G�sh�H_L�MFHGJK�v���gQ�vJlEs/f)gFMjFQG�KMFHILf)s!PHstGJILsh�±�Ä_EILf)vJKMgHI.BV�|v�fhFHI7nYs SJlEgjm�IvJl^FjvZOÎSJshs � {QzM�¯�ÄgHG�vJlLs#uEGJgRgH�ÎS P

� K������ KTS�uEK�s�f)stm�KMSJsÂFQILFH���=vJKTf�gHI ;2�ÂV�m�solLFMOs7sDQku^gOIEshI=vJKTFQ�6D#e stK��OshI MjFQ�M_EsNks�fhFW��FHILN7fhgHI MHstGJ�OshILfhscgH�0v�lEs�D#e sRQkuLFQI^S�KMgHI.B¶�ÂgOGJs!uEG�stfhKMSJsh�M�HV� � ��� ? sRQku2O���� U � ?�� � PY� ���� }�� O,lLB � Pm�lEstGJs� ? ��� U "�z�FQG�sÔfhgHILS�v�FHI=v�S�K�I^NkshuYshILNEshI=vcgQ� � �

� K�� � � KTS6uLK�s�f)shm�KTSJs � ��� b�� � ��� �U#m�K v�l � "2zEVEK³B sHBMV�� � lLFOS�]LIEK�vJs5NkKKJ±shG�shI=v�KMFQZnEKM��K�v��HVEvJlEstI � � ��� ` ��� � � � � � �� }9� O,lLB {�Pm�lEstGJs� ` "�z5KMS6F�fhgHILS�v�FHIOv�B

�EgOG/sDQEFQ��uE�MsHV«v�m�g gQ��v�lEs��5g=S�v�f)gO���5gOIE�M� _^S�s�N f)gFMjFQG�KTFQILfhs�PHshG�IEst�MS5FQG�s�vJlLs � !'6R0;0�*�!'"f)gFMjFHGJKTFQILfhsc�Ä_LILf v�K�gOI� � O�� ? ��� U P�#���� ����� � ��� � � �� � � O�� ? ��� U P5H O �-P�2 O �-P>� O,lLB j PFQI^N&v�lEs7.;�-J�$'":.-"?< *�!�,Ef)gFMjFQG�KMFHILf)sc�Ä_EILf)vJKMgHI� ��O�� ? ��� U PR#­sDQku�O��"! � ? � � U ! ��#2PY� O�� ? ��� U P5H O���P 2 O���PY� O,lLB HbPm�lEstGJs$# "%z KMS vJlEsÂfhgHG�GJst�MFQvJKMgHI �MshIE�HvJl.B r�lEsÂAÔFQ_^SJSJKMFHI PHstGJI^FQ� O,lEB j P KTS5FHILFQ�M�=vJKTfQVyFHILNF�SJlLFQG�uYshG s�S�v�K���FQvJs&gH�6shKM�HshI MjFQ�M_Es�NEstfhFW� vJlLFHI8O,lLB � P#fhFHI nYs�gHnEv�FQKMIEs�N£V«K�B sHBMV¶z B�� �%�£U� � ?��� �'& ��(*)�+ �, � b�- i � � (*) � V � �� }HVHm�lEshG�s/.�KTSvJlEs��=FQ����F6�Ä_EI^f vJKMgHI¯BL�\I �K��^B&lLB�}OVjm�s�SJlEgjm vJlLs�NEstfhFW�gQ�¶stK��OshI MjFQ�M_EstS��ÄgOG6vJlLs/AÔFQ_LS�SJKMFHI�POshG�IEsh�±�Ä_LILf v�K�gOI.B U�IovJlEs��Ms)�©v!gQ�A�K��^B�lLB�}OVkvJlLs NkstftFW��KMIF#v�lEG�shs)Z\NkKM��shILSJK�gOILFQ�&O�� # l�P�NkgO��FHK�I�KTS�S�lLgjm�I.V=FH��gOIE��m�K�vJl�vJlEscvJlEstgHG�s)vJKTfhFH�^s�S�v�K���FQvJsHV=�ÄgOG_Eu vJgÂx��JzOzHz�stK��OshI MjFQ�M_EstStB S s5gHn^S�stG MOs �HgRgkN�FH�HG�shsh��stIOv!n^shv�m�stshI vJlEs5stS�vJKM��FjvJs�FQI^NÂvJlLsFHf)vJ_LFH�.shKM�HstI MWFH��_LsÔNEstfhFW�OBVU�I�vJlEs�G�KM�Hl=v�gQ�A�0KM�LB-lEBM}HVRv�lEs ]LG-S�vcxE}#shKM�HshI MjFQ�M_Es�S�FQG�s!uL��gHv�vJs�N�ÄgHGyvJlEscAÔFH_LSJSJKTFQI�PHstGJIEst�kK�Io}�a VRxQa2FHILN lHa O � # }9��x � l�PSJuLFjv�KMFH�LNkgO��FHK�I^S ÂB&S s6gOnLSJshG MHssRQkuYgHIEstI=vJKTFQ�¯Nks�fhFW�7gQ�«shKM�HshI MjFQ�M_Es�S�K�I�FH���.vJlEG�shs ftFHSJstStVEm�K�vJl�SJ��FH���MshG�NkstftFW�&G�FQvJs�FQvclEKM�HlEstGNkKM��shILSJK�gOILStB«r�lLKMS�KMS�f)gOILS�KTS�vJshI=v�m�K�vJl&vJlEscvJlEstgHG�s)vJKTfhFH�Ls�S�v�K���Fjv�sHB �\I�K��^B�lEB�xkV=m�scSJlEgjm vJlLsNks�fhFW�!gQ�EshKM�HstI MWFH��_LstS£�ÄgOG¯v�lEs�f)gFMjFQG�KMFHILf)s¶POshG�IEsh�H�Ä_EILf)vJKMgHI"���!#2sRQku�O��"! � ? ��� U ! ?�021 P VHm�lEshG�sz �Em�B }�KMS�F�uLFQG-FQ��shvJshG6vJg�fhgHI=vJG�gH�£v�lEs NkK^J±shG�shI=vJKTFQnEKM�MK v���gQ�«vJlLs��Ä_EILf)vJKMgHI.B O�w6gQv�s m�lEstImG# }!m�s!gHnEv�FQKMI&v�lEs�AÔFQ_LS�SJKMFHI�PHstGJILsh�³B P/r�lEs�]LG�S�v#}��/shKM�HshI MjFQ�M_Es�S�FHGJs!S�lLgjm�I.VkFQ�MgHIE�5m�K v�lvJlLsÔvJlEstgHG�s)vJKTfhFH�.stS�vJKM��Fjv�sHVLFHILN��HgRgkN7FH�HG�shsh��stIOv�KTS�gHnEv�FQKMIEs�N£B�q6�TSJgLVk�ÄgOG6S���FQ�M�MshG MjFQ�M_EstS6gQ�mRVkv�lEs#shKM�HstI�MjFH��_Es�S�NkstftFW��S��Mgjm�shG�VRFOS�uEG�stNkKTf v�stN7n=�&vJlEs#s�S�v�K���Fjv�sHB

�\I�vJlLs�FQnYgFMHs�G�stSJ_E��v�StVOm�s�lLFMHs�_^S�s�N5vJlEs�IEgQv�K�gOILS¶gQ�5�JuEK�s�f)stm�KMSJs6FQILFH���=v�KMf��#FQILN �JuEK�s�f)shZm�KTS�s3� �4� b �LBY�EgOG�uEG�stf)KTSJs&NksR]LILK v�K�gOILS#gQ�6SJ_Lf-l vJstGJ��S�FHILN ��FQvJlEst��FjvJKTfhFH��FQI^FQ�M�RSJKTSÔgQ�6D#esRQkuLFHILSJK�gOILShVS�stsS� {HzM�|B7w6_L�5stGJKTfhFH��S�vJ_LNkKMstS gQ��vJlEs7f)gHI MOshG��HshI^f)s5gQ��vJG�_EILftFjvJs�N D#e�sRQkuLFQIEZSJK�gOILS«fhFQI5nYs��ÄgO_EILN/K�I ��}t�M�|B��\I5FHIEgQv�lEshG¶S�vJ_LNk�"O � l���� P VQvJlEs6fhgHI MHstGJ�OshILfhsyG�FQvJs�gQ�^vJlEs �oZ³vJstGJ�vJG�_EILftFjv�stN&D#FHGJlR_EIEstIkZ\e.g��sDMHs�sDQRu^FQILSJK�gOI��ÄgHG�vJlEs!sRQkuYgHIEstI=vJKTFQ�±f)gFMjFQG�KMFHILf)s��Ä_LILf v�K�gOI O,lLB HbP¶KMIgHILs)Z\NkK���stILS�KMgHI^FQ��O�� # }'P�SJuLFOf)s O���P�m�FHS�stS�vJKM��FjvJs�NoFHS

5 �i �LU�O��L���kPnl+� i �LUZ O��L���kPnli � U O��L���kPnl 6 z Q �=zO{Il � # }� Q O,lLB ��P

Page 12: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

}tz µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

0 200 400 600 800 1000 1200 1400 1600 1800 200010

−6

10−5

10−4

10−3

10−2

10−1

100

101

Largest 2000 Eigenvalues of Factorizable Kernel exp(−10|x−x′|2), x ∈ (−1,1)3

m

λ m

computed eigenvalues λm

estimated eigenvalues 1/ Γ(m1/3/2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2110

−14

10−12

10−10

10−8

10−6

10−4

10−2

100

102

Index

Eig

enva

lue

1D Gaussian kernel2D Gaussian kernel3D Gaussian kernel

���������D��� ®��v, f!5;1 K�*'O J[5A<250?6*2MLsG$'+)*21D*'O M'79, ?A?6$2K�*'+-, *'1D?05)T25�+-1D5;O W��Z5Es07����L, f25;1 K�*2O J[5�.k,>1�Q�<2$'&V*',/1j*21D<7/FH50$'+B5;79,/?0*'O�5;.679,/&�*'7E5��%w�, f�F�7�� �v, f!5�1 K�*'O JH5V<250?0*'M'. ,/1���Q��UP�Q��L*'1D<��Q <2$'&V*',>1 .GW

0 2 4 6 8 10 12 1410

−4

10−3

10−2

10−1

100

101

14 Largest Eigenvalues of exp(−|x−x′|1+δ), x∈ (−1,1)

δ=0.00, observedδ=0.00, predictedδ=0.25, observedδ=0.25, predictedδ=0.50, observedδ=0.50, predictedδ=0.75, observedδ=0.75, predicted

�%���%��� � ®:Q 50?0*'M`$6s 5;, f!5�1 K�*'O JH5;.A$_sl?6$2K�*'+-, *'1D?05�s0JH1D?�79, $'1 .A8%,/7>F4K�*'+-M',/1�f^<', �k5;+B5�1 79, *!3G,/O ,/79M!W

w6_L�5stGJKTfhFH�kS�KM� _E�TFjv�K�gOILS0�ÄgHGG�FHILNkgO� gOS�f)KM���TFjv�gHG-S.stS�v�FHnE�MKMSJlEstN�vJlLFQv«vJlEKTSK�ILNEshstN/KTSF�MHstGJ�SJlLFQG�u7stGJG�gHG�stS�vJKM��Fjv�s � lO�'�³B���9} � c � Y f G V @ Y �G Y ~HEHCf E h G V��iV C h#V d �` h GbABf Yih @ � r�lEs�PHshG�IEst�Q�Ä_EILf)vJKMgHI � ��KMI9O,lLB�}PKTS!vJlEs�f)gFMjFHGJKTFQILfhs��Ä_EI^f vJKMgHI gH��vJlLs5G-FQI^NkgH� uEG�gkf)s�SJSG�#O����n�kP V¯FHILN K v ftFQI nYs&f)gOILS�vJG�_Lf v�stN�ÄG�gH� GJstu^shvJK�vJK MHs gOnLSJshG MWFQvJKMgHILS&gQ�ÔvJlEs uEG�gRfhstS�ShB ]k_Lf-l2��stFOS�_EG�sh��stIOv7uEGJgkfhstNk_EG�s�fhFHI2nYsf)g=S�v����OVOFHILN5K�I�f)gO��uE_kv�FQvJKMgHILSym�s�gH�©vJshI&FOSJSJ_E��s�vJlEs6�ÄgHG�� gQ�YvJlLscf)gFMjFQG�KTFQILfhs��Ä_EI^f vJKMgHI¯B«r�lLs��gOS�v�fhgH����gHIE�M��_LSJstN�fhgFMjFQG�KMFHILf)s��Ä_EI^f vJKMgHI�KTS�v�lEs ��sRQkuYgHIEstI=vJKTFQ�YPHshG�IEst�/��NEsR]LIEs�N&KMI O lEBPHIP B]R_Lf-lÂF�f)gFMjFHGJKTFQILfhs6�Ä_EI^f vJKMgHIÂftFQIon^s#�OshIEstG�FQvJs�N�vJlLGJgO_E�HloFe]LG�S�v�Z|gHG-NkstG�� FQG�PHgFM�uEG�gRfhstS�S� j #�� � j � ? ��� T j ��� # � � ?��� ��� U ��� U # }9� O,lLB ��Pm�lEstGJs S � j X7FHGJs�NEKMS�f)G�s)v�s�uYgHKMIOv-S gOI@FÂ_EILK �ÄgOGJ� S�vJshI^f)KM��KMILNksDQRs�N nR� K�I=vJst�HstG�S ��V SUT j XoFQG�sK³B K³B N.B G-FQILNkgO� MjFHGJKTFQnE�MstS m�K v�l �hstGJg �5s�FQI MjFQ�M_Es�FQILN _LIEK v�MjFQG�KMFHILf)sOB w6gHvJs&v�lLFjv�S�_^f-l FuEG�gkf)stS�S�lLFOS�F/uLGJsh�ÄshG�shILfhs!KMIogHIEs#NkKMG�stf v�K�gOIÂFQILN7KMS6�5gOGJs#SJ_EK�v�FQnL��s!vJg���gkNkst�.G�FHILNkgO� vJKM��sSJshG�K�s�ShBS�LgHG0FJ�!'<F*�!',^G�FHILNkgH� uEG�gkf)stS�SJstStVLK�v�KTS6��gHG�s FQuLuEGJgOuEG�KMFQvJsÔvJg�v�FHPHs#KMIOv�g7FOfhf)gO_EI=v6vJlLsNkstu^stILNkshI^f)scgOI�FQ�M�^SJuLFQvJKTFQ�^NEK�G�stf)vJKMgHILStB«]ksDMHstG�FH�^f-lEgOKMfhstSyFHGJscuEGJs�S�stI=vJstN�KMI�rFQnE�Ms�lLB�}OVOFH��gOIE�m�K�vJl�vJlEs�fhgHG�GJs�S�uYgHI^NkK�IL�5fhgFMWFHGJKTFQI^f)s6�Ä_LILf v�K�gOILS��HstIEshG-Fjv�stN7nR��vJlEst�oB

Page 13: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ }O}����������D���

"%$'+-+B5;.9(�$'1D<!5�1D?05j$_s�+B*21D<2$'& (D+B$�?05;.0.05;.=*'1D<z7/FH5;,>+V?0$'K�*2+-,/*'1D?05)s-J�1D?;79,/$'1 .GW � 5;+B5���3�� 3��*'+B5`,>1 7E5hf25;+-. ���� � � / � Ø ,>.l7/FH5`<',>.07E*'1D?05`365�798:565;1 7 8:$V(�$',/1 79.n,/1 ��������3�� � ×:3�Ï63³ä �#*'1D< *�� .z*'+_5S, W�, W><!W=+B*21D<2$'&K�*'+-,/*!3�O 5�.#8%,/7/F���5;+B$=&V50*'1I*'1D<`J�1 ,/7�K�*'+-,/*21D?65�W�� � Û � Þ),/.#7>F[5 N +-.079gB$'+B<25;+A&V$�<', N 56<��k5�.0.-5;O�s0JH1D?;7 , $'1I$_s)7/FH5.-50?6$21D<=T',>1D<!W��i$'+ 7/FH5�� � äj?0*'.-5V36$'7/Fz7/FH5�(|O JH.l*'1D<`&n,/1 J�.A7E5;+-&n.�@B5�W f�W �"!$# �&% '�% ( C=._FH$'JHO <j365n,/1D?�O J[<250<!W

½����¢��W����° �)� ¬0�-�W¡�° � �W��°t��¢��³�*�RÛ �,+.- Þ É±°J¤ �-���·�-�W��¢«´M���W�\ ³��° �0/*1� � × � ! �32 � !.4 � b657� ! ¢\Ët�98:/ :;=<� � × � ! �?>Ø Û�� !@4 � b6� !BA � ÞZbC� ! ÛÎ×:b �ED�F Þt¢\Ë��RÛ0/ �GD�F Þ� � Ï � ! % ' �H>à ÛB� !B# �&% ' bI� ! % ' # � Þ bC� ! % ' :; � � 8 :;=<� � ä � ! % '�% ( � >J ÛB� !B# �&% '�% ( bI� ! % ' # �&% ( bI� ! % '�% ( # � Þ b6� ! % '�% ( ¢\Ët� 8 / :;=<� � ×:3³Ï63³ä Á�K�¨ ¢\Ët�RÛ�/ � Ø Þ�|v¶KMS«m�gHGJvJl5��shI=vJKMgHILK�IE��vJl^Fjv¶vJlLs�SJuLFQvJKTFQ�kuEG�gkf)stS�SJstS0m�K v�l�NEshuYshILNkstILf)s�KMIS!',>,jNkKMGJs�f vJKMgHI^S

KMI r0FHnE�Ms lEBM}�FQG�s¶gHnEv�FQKMIEs�N�FHS.SJgH�M_kv�K�gOILS£v�g�[6st����lEgO� v��ysBL=_LFQvJKMgHI6O�� j �LVBl={N� P B#�EgHG0sRQEFQ��uE�MsHVWKMIv�m�g�NEK���shI^S�KMgHILSZO��4#4x�P Vkv�lEs�uEG�gkf)s�SJS�m�K�vJl�fhgFMWFHGJKTFQI^f)s!PHshG�IEst�9L�M NPO ? LQM �N fhgHG�GJs�S�uYgHI^NESvJg5v�lEs#sBL=_LFQvJKMgHI RTS

US� U �

SUS UU �

}# UWV �#O�� � U P"#DTHO�� � U PYQ

U�I vJlEs gQv�lEshG&l^FQILN£V�v�lEs�sRQkuYgHIEstI=vJKTFQ�6POshG�IEsh�6sDQku�O���X ��#2P�KMI�v�m�g NEK���shI^S�KMgHILS O���# x�Pf)gOGJG�stSJuYgHILNES�v�g RYS

US� U �

SUS UU �

}# U=V ` � d �#O�� � U PR#DTHO�� � U P>Q

�|vÔKMS!NkK 1�fh_E��v�v�g9]LI^N F&uLl=�kSJKMftFQ�FQILFH��gO�&m�lEKTf-l m�gH_E�TNÂ�MstFHNÂvJg7SJ_Lf-l F�GJst�MFQvJKMgHI FH� v�lEgH_L�HlvJlLs#sRQku^gOIEshI=v�KMFH�£PHshG�IEst�£KMS�_LSJstN�KMI�vJlEs#�MK v�shG-Fjv�_EGJs!KMILNkKTSJfhGJKM��K�ILFQvJst���7K�IÂFQ�M�.NkKM��shILSJK�gOILStBr�lEs�FHuEuEG�gHuEG�KTFjvJs«G�sh�TFjv�K�gOILS�lLK�uÔnYs)v�m�shshI�SJ_Lf-l#POshG�IEsh�TS.FQI^N#NkKMS�f)G�s)v�syNk�RILFQ��KTfhFH�OSJ�RS�vJst��S

�ÄgHG!F5MjFQG�K�shv��7gH�yf)gHI^NkK v�K�gOILS6m�FHS�S�v�_LNkKMstNÂKMI � lO{N�|Bc[cshG�s�m�s �HK MHs F&SJuYstf)K^]^f#sDQEFQ��uE�Ms#�ÄgHG!FSJuLFjv�KMFH���M�&uYshG�K�gkNkKTfÔuEG�gRfhstS�S�gHI�gHIEshZ|NEK���shI^S�KMgHILFH�£sBL=_EKTNkKTS�v-FQI=v��HG�KMN7m�K v�l�S�u^FHf)KMIE�[Z �¯B�r�lLsNkKTSJfhGJshvJs#Nk�RILFH�5KTfhFH�.S��kS�vJst� KMS6�HK MHshI�nR�

� j # � x OI� j � ? �?� j 00? P�� � T j � � # }���x � l �0Q0QhQY�BO]\4� }'P

m�lEstGJs � ? # �_^�# z�FHILN`\ KTS�FHI�sDMOshI�KMI=vJsh�OshG�B�r�lEs5f)gOGJG�stSJu^gOILNkKMIE�&f)gOI=vJKMI=_LgH_LScuEGJgkfhstS�SS�FjvJKTS ]LstS OÎm�K v�lEK�Iba9O�Z �^UFP�FHuEuEG�gQRKM��Fjv�K�gOIiP¶v�lEsÔ�ÄgH�M�Mgjm�K�IE��[6st����lEgO� v��#sBL=_LFQvJKMgHIS

UU�S� U �

�# U #4x �Z � U T�Q

]RgO�^MRKMIE��FQI^FQ�M�Ov�KMftFQ�M����vJlEs5FQnYgFMHs#s'LO_^FjvJKMgHIÂm�K�vJl u^stGJKMgkNkKMf n^gO_EILNEFHGJ�of)gOILNkK�vJKMgHILScuEG�gRNE_Lf)s�SvJlLs�S�gO��_kv�K�gOI7�#O�� �nTbP��ÄG�gH� m�lEKMf-l7vJlLs�f)gFMjFQG�KMFHILf)sÔfhFHI�v�lEshIonYs�f)gO�5uL_kvJs�N£VLSJshs � l={N�|B��� ���Cc EH@DA G Y ���&`#ABETA'f Y�h Y U ETC � ` h&V hv� Y �V ~ V V � ��E h @Bf Yih � �\I gHIEs�SJuLFjv�KMFH�yNkK Z��shILSJKMgHI.V0vJlEs�shKM�HshI MjFQ�M_Es�uEG�gHnL��st� O,lLB�}P!m�K v�l vJlEs�sRQku^gOIEshI=v�KMFH��f)gFMjFHGJKTFQILfhs/POshG�IEsh�y�Ä_EILf ZvJKMgHI O,lEBPHIP�fhFQI nYs7SJgH� MHs�N FQILFH���=vJKTfhFH���M� O � {%H=V�} j � P B ]R_Lf-l FQI^FQ�M�Ov�KMftFQ��S�gO��_kv�K�gOILStV0lEgjm�sDMOshG�VFQG�s6IEgHv�FMjFQKM�TFQnE�Ms��ÄgHG���gOS�v�gQv�lEshG�fhFOS�s�ShVRFQILN&I=_L�5stGJKTfhFH�LuEG�gkf)s�Nk_EG�stSyFHGJs6G�sBL=_EKMG�stN5vJg5S�gO�^MOssBL=_LFQvJKMgHI�O lEBM}'P)B!wc_E��shG�KMftFQ��5shvJlEgkNESÔFHGJs#v��RuEKTfhFH���M�onLFHSJstN�gHI�uEG�g���s�f v�K�gOI���s)vJlLgRNLShV£SJ_Lf-lFHS/AÔFQ�MshG�P=KMI ��s)v�lEgkNES FHILN f)gO���MgkfhFjv�K�gOI �5shvJlEgkNES"OÎf)��B � {M� P)B �\I uEGJg ��stf)vJKMgHI ��s)vJlLgRNLShV«m�s

Page 14: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

}�x µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

f-lEgRgOSJs#F�S�s'LO_LshILfhs#gQ�&]LIEK�vJs)Z\NkKM��shILSJK�gOILFQ�.FHuEuEG�gQkK���Fjv�K�IL��SJ_EnLSJuLFOf)stS<� ^ & �UbO 9PY��\ � }HVm�K�vJl � ^ lLFMRKMIE��NEK���shI^S�KMgHI�� ^ # NkKM� OI� ^ PÔFQILN FoS�shvÔgH��nLFOS�KTS S�� � X�� �� [ ? B S s�v�lEshI SJshshP� ^� H � ^ �#� # }���x �0.h.0.�vJg&FQuLuEGJgQkKM��FjvJs�vJlLs#shKM�HshIE�Ä_EILf v�K�gOILS�KMI O lEBM}'P

� ^� O���P�# � �a� [ ? c � � � � � O���PY� � H �#� # }��-x��h.0.0.%Q

r�lEs AÔFH��stGJPRKMI7FQuLuEGJgQkKM��FjvJKMgHI7gQ� O,lLB�}P�G�stFONES�3#]^ILN � � �# z�FQILN � ^� HA� ^ SJ_Lf-l7vJlLFQvK����

���iO�� ? ��� U P�� ^� O�� U P��O���P � � � � U #�� � K�� ^� O���P���O���P � � � ����H7�_^%Q O,lEBM}tz�P

r�lEKTS�uEG�gHnE�Msh� KMS�F5��Fjv�GJK^Q�shKM�HstI MWFH��_Ls!uLGJgOnE��st�>~ #��� ~ � O,lEBM}H}P

m�lEstGJs/��FQvJG�KMfhstS > FHILN� �FQG�s S��R����s)v�GJKTf/FHILNÂuYgOSJK v�K^MOs/NksD]LIEK�vJsOV£m�K v�l� nYshKMIE�oNkKTFQ�HgHZILFH�0K��ym�s/f-lEgRgOSJs FQI �UIO�"P|Z|gHGJvJlEgO�HgHI^FQ�.nLFOS�KTStB 4cSJ_LFQ�M�M�HV%� ^�FHGJs1]LIEK�vJs st��st��shI=v!SJuLFHfhstScgQ�uEKMstfhshm�KTS�s!u^gO���RIEgO��KMFH�^�Ä_LILf v�K�gOILShBywcg�f)gHI=v�K�IR_EK�v���gQ���_^7KMS�G�sBL=_EKMGJs�N�SJK�ILfhscv�lEs#FQuEuLGJgQkKM��FQZvJKMgHI O,lEBM}H}P�KMS�KMI �UIO 9P B �\I � ��lM�|V±F&m�FMOsh�Ms)v�Z�AÔFQ�MshG�PRK�I���s)v�lEgkNÂm�K v�l�nYs)v�v�shG!GJs�S�gO��_EvJKMgHIoKMSuEG�stSJshI=vJs�N£Br�lEs�SJK��ts5gH��v�lEs���FjvJG�KTf)stS!KTS��_^ 2��_^±V0FQI^N K�v fhFHI nYs��MFHGJ�Os �ÄgOG#uEG�FOf v�KMftFQ�«uEG�gHnE�Msh��StV

stSJuYstf)KTFQ�M�M��KMIovJlEG�shshZ|NkKM��shILSJKMgHILFH�¯S�u^FHf)s6O ��# l�P BV�EgOG6sRQEFH�5uL��s�sBMHstIoF&�5gkNks�S�v!S�KM�hs#uEG�gHnEZ�Msh� m�K�vJl�FQnYgH_Ev7xQzHzLV zOzHz�NEsh�HG�shs�S5gQ�!�ÄGJststNkgO� GJs'L=_EK�G�stN�S�gO��_EvJKMgHI gHI­xH{ j uEG�gkf)stS�SJgHG-S KMI� j }��|B r0g�FMOgHKTNovJlEs�� O�� U^ P�f)gO��uE_kv�FQvJKMgHILFH�¶FQILN �5st��gHG���f)gOS�v!�ÄgHG�vJlEs&AÔFQ�MshG�PRK�I S�gO��_EvJKMgHIgQ�0vJlEs�D#e.Z³stK��OshI MjFQ�M_EscuLGJgOnE��st� O,lLB�}O}'P VESJsDMOshG-FQ�Y��s)vJlLgRNLS�lLFMHs!nYshshI�uEG�gHuYgOSJstN£B¶q PHstGJILsh��ZKMILNkshuYshI^NkshI=vl�LFOS�vy�Â_L� v�K�uYgH�Ms��Âs)v�lEgkN O_�«��� Pm�K�vJl�� O�� ^ ��gO��O�� ^ P PgHuYshG-FjvJKMgHI^S0FHILN ��st�/ZgHG���KMS�NEKMS�f)_LS�SJstN&KMI � {HzM�³BA�LgHG6AÔFQ_LS�SJKMFHI7f)gFMjFHGJKTFQILfhs6PHstGJILsh�TS ���5FHS�KMI O lEB j P VkKMI � j }-�¯F �^FHS�vAÔFQ_^SJS�r0G-FQILS��ÄgHG�� O_�0AÔr PÔm�K�vJl�� O�� ^iPÔgHuYshG-Fjv�K�gOILS#FQILN ��st�5gOGJ� f)gO�5uL��sDQRK�v�� KTS FHuEuE�MK�s�NFQI^N7SJlLFQG�u�stS�vJKM��FQvJs�S�gHI�vJlEs#stGJG�gHG�KMILNk_LfhstN�nR�&vJlLs AÔFQ_LS�S�r¯G-FQI^S��ÄgOGJ� KTS�uEG�stSJshI=vJs�N£B

�L��� CF[#f h ETC W�� f�� V C V h ABf,E3d ��� `&ETABf Yih @ � �\I vJlEKTS SJstf)vJKMgHI.Vm�s�K��M��_^S�v�G�FQvJs�vJlLs�S�gO��_EZvJKMgHI uEG�gRfhstNk_LGJs5gQ����N�X �ÄgOGÔF�SJK���uE�Ms/gOG�NEK�ILFHGJ�ÂNkK^J±shG�shI=vJKTFQ�«sBL=_LFQvJKMgHI.V£FHILN�uEG�stSJshI=vÔshG�GJgOGf)gOI MHshG��HstILf)s!nYgQvJlov�lEG�gH_E�Ol7IR_E��shG�KTfhFQ�¯sRQEFQ��uE�MstS�FHILN7vJlEstgHG�s)vJKTfhFH�.stS�vJKM��Fjv�stStB�r�lEs#��gkNksh�U!a!C�m�s#f)gOILS�KTNkstG�v�FQPOstS�v�lEsÔ�ÄgH�M��gjm�KMIE�/�ÄgHG��

U� �O��Y�n�kPR# � �2O��kP

U�

UO�z�PR#!

U����H O�z ��� PY� O �^B�}P

m�lEstGJs�v�lEsoNkstftFW� G-Fjv�s�f)gRs-1&fhK�stIOv �.O��kP�KMS5F�G-FQILNEgH� MWFHGJKTFQnL��s�m�K�vJl f)shGJv�FHK�I fhgHI=vJKMIR_EgH_^SNkKTS�v�GJKMnE_kv�K�gOI��Ä_EILf v�K�gOI � O �HP�FHILN��tshG�g/��s�FQI MjFQ�M_EsHByr�lEs#SJgH�M_kvJKMgHI7v�FHPHs�S�F5SJKM�5uL��sÔ�ÄgOGJ� gH�U

O��Y���kPR#!

U��� � �M�#" Q O �^B x�P

S s�FQuEuE�M��v�lEs#��N�X�sRQkuLFHILSJK�gOI O³xkB�{bP�vJg5vJlLs�S�gO��_kv�K�gOIUFQILN7G-FQILNkgO� KMIEuE_kv��U

O��Y���kPR# �a j [%bUj O�� P d5j O@THO@�kP PY� �.O@�kPR# �a j [%b � j d5j O@THO@�kP PYQ O �^B l�P

w6gHvJs/lEshG�s#vJlLs gHIL����G�FHILNkgO�%KMIEuE_kv!KMS �.O@�kP�FQILN F�gHIEshZ|NEK���shI^S�KMgHILFH�.��N�X KMS�IEshs�NkstN.V^K³B sOB�V� # }�K�I"O�xkB j P0FQI^N � #EP�Vjm�lEshG�s�P2KMS¯vJlEs�lEKM�HlEs�S�vgHG-NkshG0gQ�LsDQkuLFQILSJKMgHI.B�����SJ_EnLS�vJK�vJ_kv�K�IL�vJlLs#sRQkuLFQI^S�KMgHILS�KMI=vJg�vJlLs#�HgFMHstGJILK�IE�/sBL=_LFQvJKMgHI.Vkm�sÔgHnkv-FQKMI

�a j [%b�

Uj O�� P� � d j # �

�a j [%b�aV�[%b d j d V � j

UV O�� P>Q O �^B � P

Page 15: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ }'l

S s�v�lEshI/uEG�g���stf)v0v�lEs�FQnYgFMHs�s'L=_LFjv�K�gOI gHI=v�g6vJlLs�G-FQILNEgH� SJuLFHfhs�SJuLFQIEILstN�nR�Ôv�lEs�gOG�v�lEgH�OgHILFH�uYgH�M�=ILgH��KMFH�«nLFHSJKMS&S d j X�nR�ov�FQPRKMIE�7vJlEs�KMIEIEshG#uLGJgkNk_Lf)v#gQ�yv�lEs�sBL=_LFjv�K�gOI m�K�vJl stFOf-l nLFOS�KTStB���&_kv�K��MK��tK�IL��vJlEs#gOG�v�lEgH�OgHILFH��K�v���f)gHI^NkK v�K�gOI O�xkB�xbP)Vkm�sÔgOnkv�FHK�I 3

U� O�� P� �# � }i d U� l

�a j [%b�aV�[%b � j V � � j

UV�O�� PY� � #­z �h}9�0Q0QhQ>� � � O �^B {�P

m�lEstGJs � j V � # i d j d V d � l B�w6gHvJsÔv�lLFjv6v�lEs fhg=s�1&f)KMshI=v�S�FQG�sÔSJ��gRgQvJl�FHILN7vJlR_LS�FQIR�7S�v�FHILNEFQG-NU!a!C SJgH� MHstG�fhFQI�nYs#sh��uE�Mgj�HstN7lEstGJsOB�\II�K��O_EG�s �LBM}HVtvJlEs�f)gO�5uL_kv�FQvJKMgHILFH�HG�stSJ_E� v-S£gQ� ~ FHfhgHnEK�Z\f-lLFQg=S^sDQkuLFQILSJKMgHIÔKMS0S�lLgjm�I.VWm�lEshG�s

vJlLs#G�FHILNkgH� K�IEuL_kv��.O��kP�KTS�FHS�SJ_E��stN�vJg�lLFMOs!F +;.-<=!7#�* 0�< ��*�+�68< *�$�"&m�K�vJl�N�a4� gH�¯vJlLsÔ�ÄgHG��

� O �:� �"� �#P"# O�} � �HP��2O�}����3P��x � 0 � 00?�� O ���­}9� �Y�2}'P � �#} B � B4}�� �"� � " �#}9� O �^B j P

m�lEstGJs � O �"� �#P7KMS7vJlLs ��shv�F �Ä_LILf v�K�gOI NksD]LIEs�N FHS � O � ��IP # .kO ��P . O�IP�� . O �����IP B qcIKM�5uYgHGJv�FHI=v7S�uYstfhKMFH�cfhFOS�sÂKTS � # � # z m�lEshI�v�lEs NkKTS�vJG�K�nE_EvJKMgHI­nYstf)gO��stS�v�lEs�_EILK �ÄgOGJ�NkKTS�v�GJKMnE_kv�K�gOI­FQILN@vJlEs�fhgHG�GJs�S�uYgHI^NkK�IL� ~ FHf)gOnEK�Z|f-lLFHgOS/n^s�f)gO�5s�S5vJlEs�e¯sh�OshILNkG�s)Z\f-lLFHgOStB�S sgHn^S�stG MOscsRQkuYgHIEstI=vJKTFQ�.f)gOI MHshG��HstILf)scG�FQvJs!gQ�¯v�lEs#shG�G�gHG-SyKMI & .;!'"�FQI^NS('!'��*�!'":9;.�gHI�vJlEs#G�KM�Hl=vgQ�)�0KM�H_LGJs �LBM}HVRm�K v�l7NkK^J±shG�shI=v�SJs)v-S�gQ�¯uLFHG�FH��s)vJstGkMjFH��_Es�S � FHILN ��B��\I7uLFQGJvJKTf)_L�MFHGtVRm�sc��gQv�svJl^Fjv6v�lEs/FOS��R��ukvJgHvJKTf�f)gOI MHshG��HstILf)s!G-FjvJs/S�stsh��S�vJg�n^s vJlEs S�FQ��s#�ÄgOG�vJlLsZMjFQG�KMFHILf)s�FHILN�vJlLs��stFHI7_EIL��KMPHs#KMIÂ�ÂgHI=vJs X�FHGJ�Mg/��shvJlEgkNEStB

Time

So

lutio

n

0 0.25 0.5 0.75 1

-0.8

-0.4

0

0.4

0.8

1.2

y0 (mean)y1

y2

y3

y4

Deterministic

P

Err

or

0 1 2 3 4 510-11

10-9

10-7

10-5

10-3

10-1

Mean (α=0, β=0)Variance (α=0, β=0)Mean (α=1, β=3)Variance (α=1, β=3)

������� �D�>� ®�� $2O JH79,/$'18�,>7/F 365�7E*z+_*'1D<2$'& ,>1'(|J�7 3�MVx[7/F�g_$'+B<25;+���*!?6$�3G,/gG" FH*2$2. � � 59s-7 ��� $'O JH79,/$'1 $_sV50*2?GF&V$�<25I@ 2[� 5 � Ð � �Z5hf!5�1D<'+_5�gG"iFH*2$'.9C �kw�, f�FH7 � �v+-+B$'+=?0$'1 K�5�+9f25;1D?05`$_s�7/FH5S&�50*'1*'1D<j7/FH5`K�*'+-, *'1D?05S8�,>7/F<', ��5;+B5;1 7 2 *'1D< 5:W

�EgOG�vJlEKTS&SJK���uE�Ms U!a!C�m�sÂfhFHI�FH�MSJg u^stG��ÄgOGJ� stGJG�gHG�FHILFQ�M�kS�KTS5�ÄgHG&NkK^J±shG�shI=v�v��=uYstS&gQ�NkKTS�v�GJKMnE_kv�K�gOILStB�r0g�vJlEKTS6stILN£V^m�s�NksD]LIEs#v�lEs�G�sh�TFjv�K^MOs &�.;!'"?E 0�A-6�!���.B.�����$���FOS���� # i O U O�� P+�U � O�� P P�U l�� i U UbO�� Pnl)Vkm�lEshG�s U � O�� PyKTS�vJlEs�]LIEK�vJshZ�v�shG�� sRQkuLFQI^S�KMgHI O��LB l�P)B«r�lLs6�ÄgH�M�Mgjm�K�IE�/GJs�S�_L� v-SlLFMOs�nYshstI�gOnkv�FHK�ILstN�K�I � l��'� 3

� �|� �.O��kPKTS¶F � !'6R0;0�*�!'"#G-FQILNkgO� MjFQG�KMFHnE�Ms�m�K�vJl��hstGJgÔ��stFHI5FHILN�S�v-FQILNLFQG-N/NksBMRKMFQvJKMgHI� " z�FQI^N �B.-��&�*><=.-E 9��K!%$M0�KMS�_LSJstN.VkvJlEstI���� O�� � P�U � � 0? �

� ��� "�� � � } �O�P �2}'P��

R} � O� � P�UPt�2} V�� � ? Q O �^B HbP

Page 16: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

}�� µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

� �|� �.O@�kPyKTS�FQI .;�-J�$'"�.�"�<F*�!',OG�FHILNkgO� MjFHGJKTFQnE�Mscm�K�vJl7�hstGJg/�5s�FQI�FQILN7S�v-FQILNEFHG�N�NEsDMRK ZFjv�K�gOI�� " z5FHILN���!�Q�6�.�����.�E 9���!O$'0�KTS�_LSJstN£Vkv�lEshI

� � #R� �}n� � � V U � Q O �^B ��P

� �|� �.O@�kP#KTS/F 68"�* X-$���& nR� NkKTS�v�GJKMnE_kv�stN@G�FHILNkgH� MjFQG�KMFHnE�Ms�FQILN���. Q .-":#'��.�E 9���!O$'0 KMS_LSJstN£VIEg�sDQkuE��KTf)K�v��ÄgOGJ�/_E�MF��ÄgOG#vJlLs&shG�GJgOG#KMS/FMjFQKM�MFHnE��sOB7[cgjm�sBMHshG�V£v�lEs�stGJG�gHG#fhFHInYs�GJs�FHNkKM��� sDMjFQ�M_LFjv�stN MRKMF7v�lEs�vJlLGJsts)Z³vJshG�� G�stfh_EGJG�shI^f)s/�ÄgHG�� _E�TF�gQ��vJlEs&e¯sh�HstILNkG�suYgH�M�=ILgH��KMFH�MStB

�\I��K��O_EG�s��^B x�m�s�uE�MgQv�v�lEs�IR_E� nYshG O�P � }'P!gH�6e.sh�OshILNEGJs�sRQkuLFHILSJK�gOI v�shG���S#vJlLFQv KMSIEststNks�NovJg7shILSJ_EG�s�vJl^Fjvcv�lEs5shG�GJgOG6GJs�FHf-lEs�S6F&uLGJs�SJfhGJKMn^s�N�MjFQ�M_EsHB �\I�uLFHG�v�KMfh_E�MFHGtVYm�s1]HQovJlLsMjFQ�M_Es6Fjv � # }�z ��� BL�|v�fhFQI5nYscS�stshI5vJl^Fjv�FHS¶vJKM�5s�KMILfhGJs�FHSJstStVjvJlEs�IR_E�/n^stGygQ�YvJstGJ��S¶G�sBL=_EKMG�stN�HG�gjm6StVHFQILN�vJlEs�G�FQvJs6gH�¯S�_Lf-l��OGJgjm�v�l�KMS�NkK^JYstGJstIOv��ÄgHG�vJlEscvJlEG�shscftFHSJstS��Hv�lEs�e¯sh�OshILNkG�s)Z\f-lLFHgOSlLFOS!vJlEs�SJ�Mgjm�s�S�vÔ�HG�gjm�vJl G�FQvJs�FQI^N v�lEs&[6stGJ��K�vJshZ|f-lLFHgOS!v�lEs��ÎFHS�vJs�S�v�B�w6gHvJs�vJl^Fjv#vJlLs�vJKM��sFFQkKTS�KMS�SJftFQ�MstN7m�K v�lovJlEsZMWFHGJKTFQI^f)sG� �ÄgHG�stFOf-louEGJgkfhstS�ShB���gHG�s!IR_E��stGJKTfhFH�£sRQEFQ��uE�MstS��ÄgOG�vJlLs]LG-S�vJZ³gOG�NEshG U!a�C�S�fhFHI7nYsÔ�ÄgH_EI^N7KMI � HQz'�¯FQI^N�v�lEs�Nkshv�FQKM�MstN7shG�GJgOG�FHILFQ�M�kS�KTS�K�I � l��'�|B

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

σ t

P+

1

ε=1.0 × 10−7

Laguerre−Chaos/Exponential distributionHermite−Chaos/Gaussian distributionLegendre−Chaos/Uniform distribution

������� �D� ®��#JH&=3_5;+S$_sS50oG(�*'1 .0, $'17E5�+-&�.V1D5056<!56<�7E$j+B50*2?-F*=(D+B5;.-?�+-,93656< 5�+-+_$'+=O 5;K�5�OU$_s�� � ×�Ð 4�� WXZFH5j7/F�+_565�?�JH+-K�5;.`*'+_5 � 5;+-&�,>7E5�g_?-FH*!$'. � �Z*;f2JH5;+-+B5;gB?GFH*2$'. �V*21D<�� 5Ef!5;1D<'+B5;gB?-F[*2$'. �V?0$'+-+B5;.9(�$'1D<2,>1�f79$P�OÛ - Þ365�,/1�f� v*2J�.0.0,/*'1 ��5-o-(H$'1D5;1 7 , *'O �L*'1D<^JH1 , s-$2+-& +_*'1D<2$'&RK�*'+-, *!3GO 5;. �L+B5;.9(�50?�79,/K�5;O M!W

� � ��ETCABf EHd � f�� V C V h ABf EHd � � `#EHABf Y�h @ � �\I�vJlLKMS7S�s�f vJKMgHI¯V�m�s�uEG�stSJshI=v�FHuEuE�MKMftFjvJKMgHI^SgQ���HshILshG-FQ�MK��tstNÂuYgH�M�RIEgH��KTFQ�¶f-lLFQg=S6v�g�SJgH��s5uEG�gQvJgHv��Ru^s/uLFQGJvJKTFQ�¶NkK^JYstGJstI=vJKTFQ�«sBL=_LFQvJKMgHILStB �\IuLFHG�v�KMfh_E�MFHGtVRm�s!fhgHILSJKTNkshG�S�gO��s!ftFHSJstS��ÄgHG�m�lEKTf-l7FHILFQ�M�=vJKTfhFQ�±G�stSJ_E��v�S�fhFHI�nYsÔNEshG�K^MOstN�SJg/vJlLFQvSJ_Lf-l�ftFHSJstS�ftFQI�n^s#_LSJstN7�ÄgOG MHshG�K^]^fhFQvJKMgHI7S�vJ_^NkK�s�ShB

� ����� f h&V EHCZEH[k~ V GIA'f Y�h V � `&ETA'f Y�h � �K�G-S�v�VQm�s6f)gHI^S�KTNkshGv�lEs���KMIEs�FQGyFHNHMHstf)vJKMgHI5sBL=_LFQZvJKMgHIom�K�vJlo_EILfhshGJv�FHK�I7vJG-FQILSJuYgHGJv�MOsh�Mgkf)K�v�� ]Lsh�TN£VEK³B sOB�VS

�S�O��Y��� ���kP��?�6O��Y��� �n�kP

S�

S�#2z O��Y��� �n�kP5H � z ���5� 2 � �#}9�h}�� 27�� O�{EB�}P

m�K�vJl�KMIEK�vJKTFQ�£f)gOILNkK�vJKMgHI ��OÎz ����PR#2SJK�I�� �0VkFQILN�u^stGJKMgkNkKMfcn^gO_EILNEFHGJ��fhgHILNkK�vJKMgHI^ShB�S s!FOSJSJ_E��svJl^Fjv�vJlEs vJG-FQILSJu^gOG�v"MHsh�Mgkf)K�v��E�6O��Y��� �n�kP&KTS7F@�HK MHstI­G�FHILNkgH� uEG�gkf)stS�S&m�K�vJl4��stFQI8MWFH��_Ls��6O���P5# }#FQI^N9]^IEK v�s MjFQG�KMFHILf)sG�£U$"­zEB2�|�vJlLs#vJG-FQILSJuYgHGJv�MOsh�Mgkf)K�v�� � � �9O��Y�n�kP�K�I O³{kBM}'P�KMS

Page 17: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ }W{

IEgHv�F!�Ä_EILf)vJKMgHI�gQ�£SJuLFHfhsHVQv�lEs6KMIEK�vJKTFQ�3MjFH��_Es�uLGJgOnE��st��ftFQI�n^s�S�gO�^MOstN5sRQEFHf)vJ�M��nR� v�lEs6��s)v�lEgkNgQ�¶f-lLFHG�FOf vJstGJKTS�vJKTfhS OÎSJshs � xHzM� P B�r�lEsÔ��stFHIÂS�gO��_kv�K�gOI7KTS��HK MHstI7nR�

���O�� ��� P"#­SJKMI�� O�� �2} � ��$� P � � � �� � � � � U � O�{EB x�P

m�lEstGJs��of-lLFQG-FHf)vJshG�KM�hstS�v�lEs�f)gOGJG�sh�TFjv�K�gOI�S�v�GJ_^f vJ_LGJsÔgQ�R�6O��Y���kP�KMI7v�K���s� U # �� � ��U�� �Ä_E�M����f)gOGJG�sh�TFjv�stNO�

O�Z � P �Y� _LILf)gOGJG�sh�TFjv�stN-�x�# � � ��#�O�} � � � " �� P=�I� u^FQGJvJKTFQ�M����fhgHG�GJst�MFQvJs�N'� O�{EB l�P

m�lEstGJs #�KTS�vJlEs�fhgHG�GJst�MFQvJKMgHI&�MshIL�QvJlÂFHILN�Z ��NkshILgQvJs�S�vJlLs�SJFH�5uL��KMIE��K�I=v�shG MWFH��Br�lEs MjFQG�KTFQILfhs�gH�0v�lEs�S�gO��_EvJKMgHI �&O�� ��� P)VEm�lEstI �9O��Y�n�kP�KTS6F�AÔFQ_^SJSJKMFHI7G-FQI^NkgH� ]Lst�MN.VEKMS�3

� FQG'O���O�� ��� P P"# }x O�} � � � � � � � � P-��}n� fhgOSLx � O�� �2} � ��$� P � � � � �6� � � Q O�{EB � P

a�s)v�FHK��MstN�fhgH��uE_kv-Fjv�K�gOILFQ�EG�stSJ_E��v�S«�ÄgOGy�MK�IEs�FQG�FONTMHs�f v�K�gOI5s'L=_LFjv�K�gOILS¶fhFHI�n^s��ÄgO_EILN5KMIS� xHzM�F�=�ÄgOGFHNHMHstf)vJKMgHIkZ\NkK^JY_^S�KMgHI sBL=_LFjv�K�gOILStV.S�sts � j xN�|B�S s�IEgHvJs�lEshG�s/vJlLFQv#vJlEs�IR_E��shG�KMftFQ�¶SJgH�M_kvJKMgHI gQ�vJlLs ��N�X­s'L=_LFjv�K�gOILS6KTS6G-Fjv�lEshG�v�GJK MRKMFH�¯_LSJKMIE��S�v�FQI^NEFQG-NoNkKMS�f)G�s)v�K���Fjv�K�gOIÂ�5shvJlEgkNEStB6[6gjm�sDMOshG�V�ÄgH�M�Mgjm�K�IE� F@�ÂgHI=vJs X�FHGJ�Mg FQuLuEGJg=FHf-l�S�uYstfhKMFH��ftFQG�s�KTS&G�sBL=_EKMG�stN K�I lLFQILNE��KMIE� vJlLs SJuLFjv�KMFH�NkKTSJfhGJshvJKM�tFQvJKMgHI­KMI­vJlEs fhFOS�sÂv�lLFjv �6O�� ���Y�n�kP�KTS7F@S�v�gRf-l^FHS�vJKTfÂuEG�gRfhstS�S�Nkstu^stILNkKMIE�@gOI­vJlLsSJuLFjv�KMFH�£gHG�vJst��u^gOG�FH�.f)gRgHG-NkKMILFjv�sHB

� �9} � � d,d fh�&ABf,G V � `&ETA'f Y�h � w6sDQ=v�Vkm�sÔf)gOILSJKMNkstG�NkKKJ±_LSJK�gOI7uLGJgOnE��st��S�m�K�vJl�G�FHILNkgO� NkK �©Z�Ä_LSJK^MRK�v�� �#O�� �n�kP�m�lEKMf-loFQG�s!uEGJgHvJgHv��=uYs!sBL=_LFjv�K�gOILS��ÄgHG6SJ_EnLSJ_EGJ�ÎFHf)s^�Lgjm2uLGJgOnE��st��S�FHILN7lEstFQvf)gOILNk_Lf)vJKMgHI 3 �

�3. � �#O�� ���kP� ��O�� ���kP=�-# � O�� �n�kPY� O�� ���kP�H 2 ��O�� �n�kPR# �.O�� ���kP>� O�� ���kP�H

S 2 O�{EB {�P

[6stGJs KTScF�nYgH_LILNkstNÂNEgH��FQKMIoK�I ���9O���# }���x � l�P�FHILNA KMS�F�uEGJgOnLFQnLK��MK v���S�u^FHf)sOVLFQI^N � V� FHILN � FQG�s ��Z�MWFH��_LstSÔ�Ä_EI^f vJKMgHI^S�gHI \2 !Bor�lEKTS�FQ�TSJg�fhFQI nYs�f)gOILSJKMNkstGJs�N FHS�Fo��gkNksh�gQ��S�vJs�FHNk�ÂS�v�FQvJs/NEKKJ±_LSJK�gOI uEG�gHnE�Msh��S�S�_En ��stf v!vJg7K�I=v�shG�ILFQ��OÎNkK^J±_LS�K MRK v�� ��P6FHILN?�jgHGcsDQRvJshG�ILFH�OÎSJgH_LG�fhscv�shG�� � FHILN?�WgOG�acKMGJKTf-lE�Ms)v�nYgH_EILNLFQG��&f)gHI^NkK v�K�gOI �HP�_EILfhshGJv�FQKMI=vJKMstStBA�EgHG�v�lEshgOGJshvJKTfhFH�FQI^FQ�M�RSJKTS�gOI�v�lEs#f)gOI�MOshG��HstILf)s�gQ�0uYgH�M�RIEgH��KTFQ�£f-lLFHgOS�sRQkuLFHILS�KMgHI^S��ÄgOG�sh�M��KMukvJKTfÔuEG�gHnE�Msh��StVkS�sts� �LV8�O�'�³B

�\I gHG-NkstGÔvJg�Nkst�5gOILS�vJG-FjvJs�IR_E��shG�KTfhFQ�M�M��vJlLs�f)gOI�MOshG��HstILf)s/gQ���HstIEshG-FQ�MK��tstN u^gO���RIEgO��KMFH�f-lLFHgOStV=m�s#f)gOILS�KTNkstG�vJlEsÔ�ÄgO���Mgjm�K�IL��SJKM�5uL��sÔnYshILf-lE��FHGJP&uLGJgOnE��st�

� ����O�� �n�kP � �

� �O�� ���kP � # z � �&O�z �n�kP #2z � �&O�}��n�kP # }�Q O�{EB j P

r�lEs#G-FQILNEgH� NkK^JY_^S�K MRK v��7lLFHS�v�lEsÔ�ÄgHG��

��O�� ���kP�# }n� �'O@�kP � � O�{EB HbP

m�lEstGJs �'O@�kPyKTS�F�G-FQILNkgO� MWFHGJKTFQnL��sOV=FHILN �#O�� �n�kP " zLB¶r�lEscsDQkFOf v�S�gO��_kv�K�gOI�vJg/vJlLKMS�uEG�gHnE�Msh�KTS

� �O�� �n�kP"#��MI� }n� �O��kP �K� ���I ��}n� �O@�kP �9� �ÄgHG��O��kP �# z �� � �ÄgHG��O��kPR# z � O�{EB ��P

Page 18: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

} j µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

FQI^N�m�syf)gO��uE_kvJsyvJlEs { ��stFQIEZ|S L=_LFQG�s|� stGJG�gHG£NksD]LIEstN#FOS2� U O���P"# L = � � � O�� �n�kP � � �O�� ���kP=� U N ?�� U �m�lEstGJs � � O�� �n�kP«KTS«vJlEs<P ��v�l�gHG-NkshG«��N�X SJgH�M_kvJKMgHI¯Br�lEs _ ILgHG�� KMSysh��uE�Mgj�HstN/KMI�ftFQukv�_EGJZKMIE��stGJG�gHG-ScNk_Ls v�g7SJuLFjv�KMFH�NkKTS�f)G�s)vJKM�tFQvJKMgHI.VYm�lEKTf-l KTS�NEgHIEs5_LSJK�IE��vJlEs�SJu^s�f vJG-FQ� ������st��st�5stI=v��s)v�lEgkN � xHxM�³B

�\IY�KM�H_EG�s�{kBM}HVOvJlLs�f)gOI MHshG��HstILf)s�gH�±vJlEs!��stFQIEZ|S L=_LFQG�s�shG�GJgOGygQ� ~ FHfhgHnEK�Z|f-l^FQgOS«KTS�S�lEgjm�I¯Vm�lEstGJs7m�soFHS�S�_L�5s �O��kP4# �-THO@�kP KMI@s'L=_LFjv�K�gOI8O�{EB HbP�KTS�F � � � c G�FHILNkgO� MjFHGJKTFQnE�MsHB [cshG�s�'" z ��stFHSJ_EG�stS5v�lEs���FQ�OIEK v�_LNks�gH�#K�IEuL_kv�_EILfhshGJv�FHK�I=v���FHILN:THO��kP�KMS7F S�v-FQILNEFHG�N nYs)v-FG-FQILNkgO� MjFQG�KMFHnE�Ms�KMI O��#}��t}'P�m�K v�l�N�a4�8O �^B j P B2�|v6fhFHIon^s#SJshshIogOI�v�lEs�0�.-&�*>E=, $TQ#SJftFQ�Ms!vJlLFQvvJlLs ~ FOf)gOnEK Z\f-lLFHgOS«S�gO��_EvJKMgHI.V=K�I^f)�M_LNkKMIE�#vJlLsce.st�HshI^NkGJshZ|f-l^FQgOS0�ÄgOGy_EIEK��ÄgHG���G-FQI^NkgH� MWFHGJKTFQnL��s�SO �E# �D#9z�P)V¯f)gOI�MOshG��Hs�S6sRQkuYgHIEstI=vJKTFQ�M���Â�ÎFOS�v�FOS!vJlEs�sRQkuLFHILSJK�gOI gHG-NkstG P K�I^f)G�stFHSJstStB/r�lLssRQkuYgHIEstI=vJKTFQ�0fhgHI MHstGJ�OshILfhs�G-Fjv�s�KTS6G�s)v�FHK�ILstN7�ÄgHG��MFHGJ�Os!KMIEuE_Ev�_EILfhshGJv�FHK�I=v��oS�_Lf-lÂFOS � # z Q �LVm�lEKTf-l KTS�fh��g=S�s vJg�vJlEs��MK���K�v!gH�yvJlEs5sRQkKTS�v�shILfhs gH�¶vJlEs�SJgH�M_kvJKMgHI�O�^B }'P)B#r�lEKMS!KTScKMI NEK�G�stf)vf)gOI=vJG-FHS�v�v�g�vJlEs#uYshGJvJ_EG�nLFQvJKMgHIkZ|nLFHSJstN���s)vJlLgRN�m�lEKTf-l7v��=uLKMftFQ�M���&m�gHG�PkS��ÄgHG<� B z Q�}OB

p

L 2er

ror

0 1 2 3 4 5 6 7 810-13

10-11

10-9

10-7

10-5

10-3

10-1

σ=0.1 (α=0, β=0)σ=0.5 (α=0, β=0)σ=0.9 (α=0, β=0)σ=0.1 (α=1, β=3)σ=0.5 (α=1, β=3)σ=0.9 (α=1, β=3)

�%���%��� ��� ® "%$'1 K�5�+9f25;1D?05n$_s ��*!?6$�3G,/gB?-F[*2$'.UsG$'+A7/FH5V$'1D5;gB<',>&V5;1 .6, $'1D*'O�5;O>O , (D79, ?l&V$�<25;O (D+B$�3GO 5�&=W

�EgOG�I=_L�5stGJKTfhFH��sRQEFQ��uE�MstS�m�K�vJl gQv�lEshG�v��RuYstS�gQ�!G�FHILNkgO� K�IEuL_kv�StV��/_E��vJK�Z|NkKM��shILSJKMgHILFH�FQuLuE��KTfhFQvJKMgHILS�m�K�vJlÂG-FQI^NkgH� ]^sh�TNEShVYFQILNoFHI�s�1&f)KMshI=v6nE�MgRf-P=Z ~ FOf)gOnEK±K v�shG-FjvJKMgHIÂSJgH� MHstG��ÄgOG�vJlLsG�stSJ_E� v�K�IL�5s'L=_LFjv�K�gOILShVESJshs � j �M�|B

� �9} ������� V ETA V � `&ETABf Yih � S s!IEgjm­f)gHI^S�KTNkshG�vJlEs!_EILS�vJs�FHNk��S�vJgkf-lLFOS�v�KMf�lLstFjv�sBL=_LFQvJKMgHIKMIoF�SJuLFjv�KMFH���M�6MjFQG��RK�IL�/��stNEK�_E�oV^K�B sHBMV

�bO�� �n�kPS�S�O��Y��� �n�kPR# .%� �.O�� ���kP �5�i� � O��Y��� �n�kP O��Y��� ���kP5H OÎz �WC P52 +2 O�{EB ��P

SJ_En ��stf)vJs�N�v�g5vJlEsÔ�ÄgO���Mgjm�K�IL�5KMIEK�vJKTFQ�¯FHILN7n^gO_EILNEFHGJ��fhgHILNEK v�K�gOILS�ZO�z ��� ���kP # �Ob�O�� �n�kPY� O�{kBM}tz�P

�ZO��Y��� ���kPR# ���>� �AHS ? � � �

S�S \ O��Y��� ���kPR# ���0� �AH S U Q O�{kBM}H}P

r�lEs#v�sh��uYshG-FjvJ_LGJs ]Lst�MN �eO��Y��� ���kP�FHILN�lEstFQv�SJgH_EG-f)s � O��Y��� �n�kP�FQG�s ��Z�MjFH��_Es�N7�Ä_EILf v�K�gOILS6gOI� z �WC P 2 2�!B«r�lLscKMIEK v�KMFH�£f)gHI^NkK v�K�gOI �-bHV=vJlLsmMHgO��_L�5shvJG�KMfclEstFQv�ftFQuLFOf)K�v��/gH�.vJlEs���stNkKM_E�

Page 19: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ }'H

�jVkFQI^N�vJlLs!fhgHILNk_^f vJK MRK v�����FQG�s ��Z�MjFQ�M_EstN&�Ä_EILf v�K�gOILS�gHI� 2�!BS ? FQILN

S U NkshILgQvJs�vJlLsSJ_EnLSJs)v�S�gH�0v�lEs#nYgH_EILNLFQG��&m�K v�l ]HQkstN�vJsh��uYshG-Fjv�_EGJs�FHILN7lEstFQv=�L_TQ£VkGJs�S�uYstf)vJK MHst���OB

[6stGJs�m�s�f)gOILS�KTNkstG.vJlLs�lEs�Fjv«f)gHI^Nk_Lf v�K�gOI�KMI/FQI sh�Mstf v�GJgOIEKTf�f-lEKMu SJ_En ��stf)v0v�gc_EI^f)shGJv�FHK�I=v�K�s�SKMI lEstFQv f)gHI^Nk_Lf v�K^MRK�v�� FHILN fhFHuLFHfhK v�� OÎSJshs�sBL=_LFQvJKMgHI O�{EB ��P P)B�r�lEs7f)gH��uE_Ev�Fjv�K�gOILFQ�yNEgH��FQKMI KTS�SJlEgjm�I�K�IR�KM�H_EG�s {kB�x FQ�MgHIL� m�K v�l�vJlEs SJuLFQvJKTFQ��NEKMS�f)G�s)v�K���FjvJKMgHI¯B r�lEs n^gO_EILNEFHGJ��gQ�vJlLs/NkgO��FHK�I f)gHI^S�KTS�v-S6gH�¶�ÄgH_EG!S�st�H��shI=v�S�3�vJlEs/vJgOu�. � VLv�lEs/nYgQvJvJgO� .��6V^vJlEs v�m�g�S�KTNks�S .��FQI^N�vJlEs/n^gO_EILNEFHGJKMstScgQ�«vJlEs5fhFMRK�v��$.��6V^m�lEKTf-lÂlLFOScF&NkstukvJl gQ��z Q j B�q�NkKMFHnLFjv�KMf n^gO_EILNEFHGJ�f)gOILNkK�vJKMgHILS�FQG�sÂuEGJs�SJfhGJKMnYstN�gHI�.�� FQILN�.��.B r�lEs fhFMRK v���n^gO_EILNEFHGJ� .�� KTS&sDQRuYgOSJstN�v�glEs�Fjvj�L_TQ ����! ,�� #%}OB�r�m�g7v��=uYstS�gQ��fhgHILNEK v�K�gOILSÔgHI vJlEs�v�gHu . � FHGJs�f)gOILS�KTNkstGJs�N 3�gOIEs�KMS��FQKMI=v�FQKMIEs�N�FjvÔf)gHI^S�v-FQI=v6vJst��u^stG�FQvJ_EG�s � # z O�fhFOS�s7}'P6FHILNov�lEs/gHvJlEstGcKTS�FONkKTFQnLFQvJKTf9OÎftFHSJsxbP)Byac_Ls�v�g�IEgHIEZ³�tshG�g IEshv6lEstFQv��^_TQ7KMI=vJg5vJlEs#NkgO��FQKMI.VRvJlEstGJsÔKTS�IEg�S�vJstFONk�&S�v�Fjv�sÔK�IÂfhFOS�s#xkBr�lEs�KMIEK v�KMFH�kf)gHI^NkK v�K�gOI KTS«�hstGJg�sDMHstGJ�Rm�lEstGJsOB0]RK^Q G�s)�ÄshG�shI^f)s�uYgHKMI=v�S«FQG�s�uE�MFOf)s�N FjvvJlLs-MOshGJvJKTf)s�SgQ�«S�gO��sÔf-lLgOSJshI�sh�Msh��shI=v�S�KMI�vJlEs�NEgH��FQKMI.VEFHS�SJlEgjm�I�K�I��K��O_EG�s#{EB xEB�S s�FHGJsÔKMIOv�shG�stS�vJs�N�KMIvJlLs�S�v�gRf-l^FHS�vJKTf!SJgH�M_kv�K�gOI�FQv�v�lEstSJs#uYgHKMIOv-S�FQILN7v�lEshKMG6f)G�gOS�S�Z\f)gOGJG�sh�TFjv�K�gOI&f)gRs-1&fhK�stIOv-ShB

x

y

-3 -2 -1 0 1 2 3

-0.5

0

0.5

1

1.5

ΓT

ΓSΓS

ΓBΓB

ΓCΓC ΓC

A

B C D

E

F

������� � � ®�� ?GFH5;&�*27 , ?`$_s=7/FH5�f!50$'&�5;79+-Mz$_s�7/FH5`5;O 56?;79+B$'1 , ?^?GF�, (ZWXZFH5`&�5;._F ?0$'1 .0,>.079.V$6s ��4.9(�50?;79+B*'O5;O 5;&�5;1 79.A$_s $2+B<25;+Ò� �I@� #(H$',>1 79.A,>1 56*!?-Fz<',>+B50?;79,/$'1'C2W

r�lEs/_EILf)stG�v-FQKMI�lEs�Fjv!fhgHILNE_Lf v�K^MRK�v��oFHILN�ftFQuLFOf)K�v��7gH�¶vJlEs/�5s�NkKM_E� FQG�s�G-FQILNkgO� ]^sh�TNEShVm�K�vJl ��stFQI ]Lst�MNES ��2O�� � U ���kP # }�� ��FO�� � U ���kP # }HV¯FHILN m�K v�l fhgHG�GJst�MFQvJKMgHI �Ä_EILf v�K�gOILSÔgQ��vJlLs�ÄgHG���� O]XFP # M O ? L M �N V�FOS�NksR]LILstN K�I2]Rs�f v�K�gOI lLB xEB­r�lEs�D#FQG�lR_EIEshIEZ|e¯g��sBMHs O�D#e#P5Nks)Zf)gO��u^g=S�K�vJKMgHI O,lLB x�PcKTSÔsh��uE�Mgj�Hs�N�v�gÂNkstfhgH��u^g=S�s5v�lEs�K�IEuL_kv G-FQILNkgO� ]Lsh�TN£B �\I �K��O_EGJs&{EB lLVvJlLs�f)G�gOS�S�Z\f)gOGJG�sh�TFjv�K�gOI f)gRs�1�fhK�stI=v n^shv�m�stshI uYgHKMI=v/q FHILN �!V0FQI^N q%FQILN@X�VFQG�s�uE�MgQv�v�stN£VFQ�MgHIL�#m�K v�l�vJlEs6G�stSJ_E��v�Sy�ÄGJgO���ÂgOIOv�s!X�FQG��MgÔSJKM� _E�TFjv�K�gOI.B«A!gRgkN�FQ�OGJstsh��shI=vyKTSySJshshI�nYs)v�m�shstIvJlLs�v�m�gÂFQuLuEGJg=FHf-lEs�ShB�r�lEs&e¯sh�OshILNkG�s)Z\f-lLFHgOS�KMSG�HZ|NkKM��shILSJKMgHILFH� O � # ��PÔFHILN vJlEKMG�NkZ³gOG�NkstGO�P3#8l�P Vkm�lLKMf-l7GJs�S�_E��v�S�KMI O�� � }PR# l={#v�shG���S�sDQRu^FQILSJK�gOI O�S�sts!s'L=_LFjv�K�gOI O�xEB j P P)B U�I7vJlLsgQv�lEshG!lLFHILN£V±m�s/_kvJKM�MK��ts�xHz �JzOzHz�FHILN }W{Qz ��zHzOz/G�stFH��KM�tFQvJKMgHILS6�ÄgHG�vJlEs�S�vJstFONk�ouEG�gHnE�Msh� OÎftFHSJs}'P!FHILNÂv�lEs�_EILS�vJstFONk��uEG�gHnL��st� OÎfhFOS�s�xbP)V.G�stSJu^s�f vJK MHst���OB/�ÂgOGJs5FQuEuL��KTfhFQvJKMgHILS!gQ��S�v�gkf-lLFHS�vJKTflEs�Fjv6f)gOILNk_Lf)vJKMgHIÂfhFHI7nYsÔ�ÄgH_EI^N7KMI � Hk}��|B

� � ����� `�C�� V C@�� V � `&ETA'f Y�h � [6stGJs#m�s#f)gHI^S�KTNkshG�v�lEs MRKMS�f)gO_LS=��_EGJ�OshG-S!�Rs'LO_^FjvJKMgHI¯V�� " ���� � #�� � ��� � � H � �#}9�h}��I���O��#}'P # }n� m�� ��O�}'PR# �#}�� O�{kBM}�x�P

m�lEstGJs�m " z�KTS/F S���FQ�M��uYshGJvJ_LGJnLFQvJKMgHI v�g�v�lEs��Ms)�©v�n^gO_EILNEFHGJ� f)gOILNkK�vJKMgHI8O���# �#}'P#FHILN� " z KMS�v�lEs�MRKTSJfhgOSJK v��OBr�lLs�uEG�stSJshI^f)scgH��MRKMS�f)g=S�K�v���S���gRgQv�lEstS�gH_Ev�v�lEs!SJlEgkf-P�NkKTSJfhgHI=vJKMIR_EK v��m�lEKTf-l m�K��M��NksDMOsh�MgHu gQv�lEshG�m�KTS�sOBor�lR_LStVvJlEs�S�gO��_EvJKMgHI lLFOS Fov�G�FHILS�K�vJKMgHI �TFW�HstGtVm�lEKTf-l KMS/FG�sh�HKMgHIogH�yG�FHuEKMN MjFHGJKTFjv�K�gOIoFHILNosRQRv�shILNES�gFMHstG6F&NkKTS�v-FQILfhs � O��HPcFOS����5zLB6r�lEs��MgRftFjv�K�gOIÂgQ�

Page 20: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

}t� µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

0 1 2 3 4 5 6−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

time

Cro

ss c

orre

latio

n

ρAB

: MCSρ

AB: Chaos

ρAC

: MCSρ

AC: Chaos

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

time

CO

V

A: MCSA: ChaosD: MCSD: Chaos

������� � � � ®4"�$'&k(H*'+-,>.-$'1 $_sn+B5;.6JHO 7 .V$!3�7E*',>1D50<z3GM���$'1 7E5z"%*'+-O $j.0,>&�J�O *'79,/$21Y@��" �!C4*'1D<`f�� " 5-o-(H*'1 g.0,/$'1|W �Z5Es07vgA?0*'.-5 � �V5;K�$2O JH79,/$'1 $_s�?;+B$'.0.0gB?0$'+-+B5;O *'79, $'1?0$�5��?;,/5;1 79.n*'7k+B59sG5�+_5�1D?05A(H$',>1 79.UsG$'+=?0*'.-5 ��@EPHy �Ey2y+B50*'O , �;*'79,/$21 .ks-$'+��" �!C �vw�, f�F�7#gB?0*'.-5`P �`5;K�$'O JH79,/$'1$6s4"��i.=*'7)+B5Es-5;+B5�1D?05n(�$',/1 79.`@ � ��y �Ey2y!yI+B50*'O , �;*'79, $'1 .s-$2+��" �!C2WvJlLsÔvJG-FQILSJK v�K�gOI��TFW�HstG��^VkNksR]^IEstNoFHS�v�lEsÔ�hstGJg5gQ�0vJlEs�SJgH�M_kvJKMgHI�uEG�gI]L�Ms �&O���PR#2zEVTMjFQG�K�s�S�m�K v�lvJKM��sHVEFHILN&K�v�S�sBMHshI=v�_LFQ�Y��gkftFjvJKMgHI�Fjv�S�v�stFONk�&S�v-Fjv�s�KTS�sRQRvJG�sh��sh�M�&SJshILSJK v�K^MOscv�g v�lEsÔn^gO_EILNEFHGJ�NEFQv�FEB«r�lEKTS«uElEstIEgH��shILgHI.Vjv�shG���stN 0�6NJK.��;0�.-"�0;*><F*>(N*>< @�K�IS#%.-<=.-��&�*>"�* 0�<F*�9¶FHSJ�R��ukvJgHvJKTf�FHILFQ�M�kS�KTStVm�FHS�]LG-S�v�gHnLSJshG MHs�N5n=��e.gOGJstI=vJ�� lOxN�|B �\I�vJlEKTS�S�s�f vJKMgHI¯VHm�s6m�K��M�YuEGJs�S�stI=vyI=_L�5stGJKTfhFH�^SJgH�M_kvJKMgHI^SvJl^Fjv�sDQklEK�nLK v�S�_EuYshG-SJshILSJK v�K^MRK�v��/_LILNkshG�G�FHILNkgO��uYshGJvJ_EG�nLFQvJKMgHILS¶gOI�vJlLs6n^gO_EILNEFHGJ��f)gOILNkK�vJKMgHI.B�\I�uLFQGJvJKTf)_L�MFHGtV�m�sÂf)gOILSJKMNkstG4m 6�� OÎz ��<P KTS&F _EIEK��ÄgHG�� G-FQILNEgH� MjFQG�KTFQnE�Ms7KMI OÎz ���<P5m�K v�l��� � O�}'P)B

�\I�rFQnE�Ms�{EB�}OVHv�lEsc��stFHI&�MgRftFjv�K�gOI�gQ�£vJlLs6vJG-FQI^S�K�vJKMgHI��TFW�HstGmO ���P�FHILN�K v-S�S�v�FHILNEFHG�N�NksBMRKMFQZvJKMgHI O����FP�FQG�scS�lLgjm�I.Br�lLsh��FQG�s6gHnEv�FQKMIEs�N�nR�5FOSJSJ_E��K�IL�!m 6�� O�z �Jz Q�}P¶FQI^N ��#­z Q zO{EBr�lLsG�stSJ_E� v-SygH�¯S�sBMHshG-FQ�L�5shvJlEgkNES�FQG�scSJlEgjm�I.V=FQ�MgHIE��m�K�vJl&vJlEstK�G�f)gO�5uL_kv�FQvJKMgHILFH�^f)g=S�v�IEgHG���FQ�MK��tstNnR��vJlEs5f)gOS�v�gH�ygHIEs/Nks)v�shG��5KMIEKTS�v�KMf5SJK��/_E�MFQvJKMgHI.B!]Ru^s�f)K^]^fhFH���M�HV±KMI=vJshG MjFQ�FQILFH���kSJKMS�NkstFH�MS�m�K v�lvJlLs���FFQkKM��FQ�YgH_kv�uE_kv�n^gO_EILNEStVEFQILN&KMS�S�vJG-FQKM�Hl=v��ÄgOGJm�FQG-N/vJg/FHuEuE�M��vJg vJlEKTS�uEGJgOnE�Msh� ? B¶[cgjm�ZsDMOshG�VRK v6NkgRstS�ILgQv�uEGJgFMRKTNksÔFQIR�&S�v-Fjv�KMS�vJKTfhFH�YKMIk�ÄgOGJ��Fjv�K�gOI�gH�¯vJlLsÔSJgH�M_kv�K�gOI.B¶r�lEsÔGJs�S�_E��v�S��ÄG�gH�uYshGJvJ_EG�nLFjv�K�gOI���s)vJlLgRNLS�FHGJs�ILgQvJKTf)s�FQnE�M��NkK^JYstGJstIOv��ÄGJgO� v�lEsÔFHfhfh_EG-FjvJs6SJgH�M_kv�K�gOI&gHnkv-FQKMIEstN�nR��ÂgOIOv�s�X�FHGJ�Mg�SJK��/_E�TFjvJKMgHI m�K v�l�}�z ��zHzHz�G�stFH��KM�tFQvJKMgHILStBG�\I FONENkK�vJKMgHI.V±v�lEs �ÄgO_EGJvJlkZ|gHG-NkshG�u^stG�ZvJ_LGJnLFQvJKMgHIo��s)v�lEgkN�NEg=s�S�IEgHv6�=KMsh�TNÂFQIR�&KM��uEG�gFMHsh��stIOv�gFMOshG�vJlEs1]LG�S�v�Z|gHG-NkstG���shvJlEgkN£B�r�lEKMSSJ_E�H�OstS�v�SvJl^Fjv¶vJlLs�u^stG�v�_EGJn^FjvJKMgHI5��s)v�lEgkN�f)gHI MOshG��HstSSJ��gjm��M�HVQK��£Fjv�FQ�M�³Br�lEs6e¯sh�OshILNkG�s)Z\f-lLFHgOS��s)v�lEgkN FHftf)_EG-Fjv�sh�M�7G�stSJgH� MHs�S�v�lEs5SJgH�M_kv�K�gOI S�v-Fjv�KMS�vJKTfhStB!q�v!�ÄgH_LG�v�lkZ³gOG�NEshG�V^K�v�SÔf)g=S�v!KMS!FQnYgH_EvvJlLs/S�FQ��s/FOS�vJlLs �ÄgO_EG�v�lkZ|gHG-NkshG6uYshGJvJ_LGJnLFQvJKMgHIÂ��s)v�lEgkN FHILNÂKTS &�6�9��S, .-0;0�vJlLFHIÂvJlEs5�ÂgHI=v�sX�FQG��Mg��5shvJlEgkN£B U�IÂvJlLs �Ms)�©v�gH�l�K��O_EGJs5{kB �LVEv�lEs/SJgH�M_kv�K�gOI�uEG�gI]L�MstS�gH�y��stFQI FQILNÂS�v�FHILNEFQG-NNksBM=KTFjv�K�gOI FQG�s�uE�MgQv�v�stN ��gHI vJlLs&GJKM�Hl=v/FHGJs�v�lEs7SJgH�M_kv�K�gOI N�a4�S/Fjv �:# z Q HÂFQILN �^#%z Q �LVgHnEv�FQKMIEs�N�n=� vJlEs!e.st�HshI^NkGJshZ|f-l^FQgOS«FHILN��ÂgHI=vJsÔX�FQG���g#SJK��/_E�MFQvJKMgHI�m�K�vJlÂ}�zEV zHzHz!G�stFH��KM�tFQvJKMgHILStBS s&gHnLSJshG MHs5�HgRgkN FQ�OGJstsh��shI=v#n^shv�m�stshI vJlLs�e.st�HshI^NkGJshZ|f-l^FQgOS!SJgH�M_kvJKMgHI FQI^N ��gHI=vJs7X�FHGJ�MgSJgH�M_kvJKMgHI.B��ÂgOGJs�NEs)v�FHK��TS6gH�yf)gH��uE_Ev�Fjv�K�gOILS�gH�¶S�vJgkf-lLFOS�v�KMf���_LGJ�OshG-S!�ks'LO_^FjvJKMgHI�ftFQIonYs��ÄgH_LILNKMI � HQxN�|VHm�lLshG�s�lEKM�Hl5G�stSJgH�M_kvJKMgHI5IR_E��shG�KMftFQ�kS�gO��_EvJKMgHILS«f)gOI MHshG��HstI=v¯vJgÔ_Eu/vJg#SJsDMOshI�S�KM�HIEK^]^ftFQI=vNkKM�HK�v�S�FHGJsÔuEG�stSJshI=vJs�N£B

��� � V C'A'`�C?�ETABf Yih � � ��E h @'f Y�h E h [�_v�&EHC@ V � CFf,[&@ � �|v�lLFHS�nYshshI���shI=vJKMgHILstN�vJlLFQvKMIoSJ_EnLSJ_EGJ�ÎFHfhs`�Lgjm4��gRNEsh�TS�u^stG�v�_EGJn^FjvJKMgHI�sRQkuLFHILSJK�gOILS�FQG�s!gH�©vJstI�_^S�s�N&v�g5gOnkv�FHK�IoS�v�Fjv�KMS�vJKTfhS� Àj° �Y ��W���±�W��° »WÊ�¢��Ô¸ ¥£¢¯° �WÊ ¼��W¢�¢�¡� ³°y��° �W¡W���� .° ��¢�³�����WÊ·�� ���° ����° �³�³¢����H° ��¡W���Wȶ ³°y ��W¢�6��Ët�����W� ���W�W�t 

°-´�� � Ð6;�×6 �°/¡W¢\ �¢��³�����W¢� ��W¢!�6��Ët�����W� ° �� ��W�� �®&§©��È ¢��W¢��|�-ÊT¸±��°J¥£¢\¤)¢��J¸Y�³�W�|����° ��°- ³° �W���c¡W¢��Q¢��W¡W¢��W��¢»Q¢\ ©¥£¢�¢��/���W�W�� ��-��¡/° �� ��W�� �¡W°h¢��y�W°- y¢\Ë����ΠJ¸R�-�W¡5�c��¼t�� �¢��6�� ³�����³¢��-�³�|� ���# ³��¢����W�W�� y�³�-�WÈ ¢����«��¢�¢�¡W¢�¡  ³°Ê�°h�J�� �¢¶ ³��¢¶�6��Ë������W� �³¢��³�Q° �W��¢)®

Page 21: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ }��

�Âs)v�lEgkN O ��LV � � P X�gOS�v1OÄ_EILK v<P�\I=vJshG MjFQ�.FHILFQ�M�kS�KTS wG�jq � x

�K�G-S�vJZ³gOG�NEshG�u^stG�v�_EG�nLFjv�K�gOI7��s)v�lEgkN O�z Q �OxIl �Jz Q lO�O��P 6 x�EgO_EG�v�lkZ|gHG-NkshG�u^stG�v�_EG�nLFjv�K�gOI���shvJlEgkN O�z Q �Ox'�'�Jz Q l=xQ��P 6 {�EgH_LG�v�lkZ³gOG�NEshG�e.st�HshI^NkGJshZ|f-l^FQgOS O�z Q �E}��'�Jz Q �^}���P 6 {�ÂgHI=v�s/X�FQG���g�S�KM� _L�MFQvJKMgHI O�z Q �E}��'�Jz Q �^}���P 6 }tz �JzOzHz��������� �D����|7E$�?GFH*'.079,/? .0$2O JH79,/$'1 .z*'1D<?0$'&)(DJH7E*'79,/$'1D*'OA?0$'.07V$_sz<', �k5�+B5;1 7l&V5;7>F[$�<'.nsG$'+9��J�+ f!5;+-.��U5 � J[*'79,/$'1c8�,>7/FJH1D?65;+-7E*',>1 3_$2J�1D<2*2+-M`?0$'1D<',>79, $'1|Wn@ �L1D5lJH1 ,>7L$_s ?0$'.07v?6$2+-+B5�.9(H$'1D<'.l7E$=7/FH5�?0$'.07v$_sA$21D5n<25;7E5�+-&�,>1 ,/.07 , ?l.0,/&nJHgO *'79,/$'1|W C

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

mean solutionstandard deviationupper boundlower bound

−1 −0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5Legendre−chao: x=0.7Monte Carlo: x=0.7Legendre−chaos: x=0.8Monte Carlo: x=0.8

������� �D� � ® �|79$;?-F[*'.07 , ?.-$'O J�79,/$21 . 3GM �Z5hf25;1D<'+B5;gB?GFH*2$'. 8%,>7/F ������ÛTÐ63³Ð6;�×JÞ *'1D<�� � Ð6; Ð â W��Z5Es07��� $'O J�79, $'1=(D+B$ N O 5;.#$6s)&�50*'1z*'1D<SK�*'+-, *'1D?05�W�XZF[5 J�(2(�5;+ *'1D<=O $'8�5;+ 36$'J�1D<2.#*2+B5 7/FH5n<25�7E5;+-&n,/1 ,>.079,/?A.-$'O JH7 , $'1 .?0$'+-+B5;.9(�$'1D<',/1�f`79$�7/FH5�3_$2J�1D<'.#$_s)7/FH5 +B*'1D<2$'&t,/1'(DJ�79. � � � Ð6;�×�*21D< � � Ð ��+_5�.9(�50?;79,>K�5�O M!Wvw�, f�F�7�� �v+B$!36*!3�,>O ,>79M<25;1 .0,>79Mks0JH1D?�79, $'1 . *'7 � � Ð6; j*'1D< � � Ð6; Ñ WgQ��v�lEs�G-FQILNEgH� S�gO��_kv�K�gOI.BÂr�lEstSJs&v�stf-lEILK L=_Es�S FQG�s&NkK^JYstGJstI=v �ÄG�gH� ��N�X FQuLuEGJg=FHf-lEs�S#S�KMILfhsvJlLsh��m�gHG�P5MRKMF & $'& .-"?<�0�gQ�vJlEs#G-FQILNEgH� SJgH�M_kvJKMgHI�30�ÄgOG

��O�� ���kPD3 +2 ^� �m�sÔNEsR]LIEsÔv�lEs & $'& .-"?<D$ XB$'��#%.-����nR�

�� 3 � # 2 +2 .0.h. 2 � � �� O�� ? ��� U �hQ0Q0Qh��� � PD3f# K � ��O�� ? �n�kP ��O�� U ���kP-.h.0.��&O�� � �n�kP �9P5O@�kP

qcS�SJ_E��K�IE�/K�I O�{EB {�P«vJlLs�f)gRs�1�fhK�stI=v �&vJg5n^s!Nks)v�shG��5KMIEKTS�v�KMf!FQI^N�vJlEs!S�gO_EG-f)s�v�shG�� � O�� �n�kP«v�gnYs�S�v�gRf-l^FHS�vJKTfQVkm�s!l^FMHsÔFS#O.�< .���&B*>"?* 0�< *�9�uLGJgOnE��st� gQ�«gHG-NkstG�x ���ÄgOG� �� 3r0g�NEsR]LIEs#K�vtVLm�sÔG�sBL=_EKMGJs !'"?* 0�$'<F��$TJ:*�9� $O+;$',/.-(�0FJK!%9;.�0�gQ��5K^QkstN�lEKM�HlEs�S�v6NkstGJK MjFjv�K^MOstS�3

���O � P 3f# ���O 9P � ���O�9P � .h.0. � ���O 9P ���)H �-�#}��YC ����b O� � P 3f# � ?b O�9P � � ?b O�9P � .0.h. � � ?b O 9P

sHB �LB ��� O &U'P�� S���O�� �UP�H �U�O� 2 "P ! � �'� �� �'� � ���� H �U X5FHILN�NksD]LIEs gOIÂvJlLstSJs

SJuLFHfhstS�vJlLsÔ�ÄgH�M��gjm�KMIE�5uEGJgkNk_^f v6�MK�IEs�FQG�gOu^stG�FQvJgHG-SZ�3 #­NEK^M�O�� PD3 � ?b O�"P"� � � ? O�"PY�

Page 22: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

xQz µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬Z�� Z

�� .0.h. � Z

�3 � �b O� � PR� � � � O� � P>Q

r�lEstI.VLF�Nks)v�shG���K�IEKTS�vJKTfÔsBL=_LFjv�K�gOI��ÄgOG� �� KMI7v�shG���S�gQ� �� KMSO��#}P � O�Z

�� Z

�� .h.0. � Z

�P ��# �� K�I � � � O� � P

r�lEKTSÔNks)v�shG��5KMIEKTS�v�KMf/uEG�gHnE�Msh� �ÄgOGcv�lEs �RvJl ��gO�5stI=v!gH� � KMI�v�shG���S!gH�¶vJlEs �=vJl ��gH��shI=vÔgQ�� SJlEgjm6S�vJlLFQv�m�s!ftFQI�vJG-FHNksOVRFOS�KMI���N�X�V=G-FQILNkgO��IEstS�S�KMI&v�lEsÔn^gO_EILNEFHGJ� MjFQ�M_EsÔuEG�gHnE�Msh� FQvvJlLs#sRQku^stILSJs!gH�0lEKM�HlÂNkKM��shILSJKMgHI�K�I7vJlEs#uLGJgOnE��st� NkgO��FHK�I¯B��\I � �O�kV8�=�M�|VEK v6m�FHS�SJlEgjm�I7vJlLFQv0FJK!��;0�. QO��*�#M0�ftFQI&nYsÔ_LS�s�N�vJg�SJgH� MHs6v�lEs!lEK��Ol7NkKM��shILSJKMgHILFH� �=v�l���gH��stIOv�uEG�gHnE�Msh��S�K�I7m�gOGJPstS�SJshI=vJKTFQ�M����uEGJgOu^gOG�v�K�gOILFQ�^vJg�v�lLFjv6gH�¯v�lEs#��stFQI ]Lst�MN�s'LO_^FjvJKMgHI¯VkK�B sHB«�ÄgOG � # }HBr�lEs��ÎFHS�v0IR_E��shG�KTfhFQ�RSJgH�M_kvJKMgHI�gH�EvJlLs �=v�l ��gH��shI=v«sBL=_LFQvJKMgHILS0m�K v�l/FHI=� � "4}�nR�ÔSJuLFHG�SJs

�HG�KTN�v�stf-lEIEK L=_EstS�KMS�FH�MSJg�SJK��OIEKK]YfhFQI=vÔ�ÄgHG uEGJgOnE�Msh��SÔm�K v�l S�v�gkf-lLFHS�vJKTf�f)gRs-1&f)KMshI=v �#O�� ���kPÔKMIvJlLs&f)gHI=v�sRQRv!gH��F�uYshGJvJ_EG�nLFjv�K�gOI FHuEuEG�gOFOf-l.B r�lEs�f)gO��uE_kv�FQvJKMgHI uEG�gRfhshs�NES!K�I vJstGJ��SÔgH��vJlLs��gH��shI=v-S gH�6vJlEsoNEFQv�F O�� � � P�FHILN �OK^MOstS/NkK�G�stf)vJ�M� vJlEs���gH��shI=v-S/gH��vJlEsoSJgH�M_kvJKMgHI��0B S suEG�stSJshI=v�lEshG�s!vJlEs#��s�FQI"]Lsh�TNof)gH��uE_Ev�Fjv�K�gOIÂFQ�M�HgHG�K�vJlE� O�S�sts#sHB �LB5� { j �.�ÄgOG��5gOGJs#Nkshv�FHK��TS P)Br�lEs�KTNks�F�KMS6IEgjm#V^FOS�K�I�vJlEs�m�KTNkst����_LSJstN ]LG-S�v6gOG�NEshG�Z�S�s�f)gHI^N7��gO�5stI=v�FQuEuLGJg=FHf-l.VRv�g

_LSJs#F�NkstfhgH��u^g=S�K�vJKMgHI�#O�� ���kP"# � O���P)�TXTO�� ���kP�# { Nks)v�shG���K�IEKTS�vJKTfÔsRQku^s�f v-FjvJKMgHI��H� { G-FQILNkgO� �L_Lf)vJ_LFQvJKMgHIv� �

m�lEstGJs!vJlLsj�L_Lf v�_LFjv�K�gOIoKMS�FOSJSJ_E��stN�vJg�nYs�S���FH���MshG�vJl^FQI�vJlEs#sDQku^s�f v�FQvJKMgHI.V

z B *GX�*���� � ��� ���KMIk� � N � � O���P B4}9�FQI^N FHILFQ�M�=vJKTf5K�I vJlLs�uElR�RSJKTfhFQ�yNEgH��FQKMI �)�-�#}��t}-� � O©vJlLKMS�fhgHILNEK v�K�gOI ftFQI n^s�GJst�MFIQRs�NÂv�ggHIL���5]^IEK v�s ]RgHnYgH�MsDM�GJst�H_E�TFQG�K v��HP)V X H� 9O �-�#}��h}�� � �� _ O P PYQr�lEsoFQILFH���=v�KMfhK v�� FOSJSJ_E��ukvJKMgHI OÄm�lEKTf-l@KTS�S�FjvJKTS ]LstN@sHB �LB K��cvJlLsofhgFMjFQG�KMFHILf)s&gH� � KTS�AÔFH_LS�ZSJKMFHIiP�shI^S�_EG�stS�vJlEs�sDQkKMS�vJstILf)s�gH�yF �L_Lf v�_LFjv�K�gOIÂGJstuEG�stSJshI=v�FQvJKMgHIÂFHS6F5�ÎFOS�v!f)gHI MOshG��HshI=v6SJshG�K�s�SSJshuLFHG�FQvJKMIE� v�lEs�NkshvJshG���K�ILKMS�vJKTf#FQILN�S�vJgkf-lLFHS�vJKTf MjFQG�KMFHnE��s�ShVXTO�� �n�kP"# a� N � + � � O���P�� � O��kP>� *�� � � � � *���� � ��� ��� % ����� � � � (*) � Qw6gHvJsÔv�lLFjvcSJ_Lf-lÂF�GJstuEG�stSJshI=v�FQvJKMgHI�KTS�gH�«fhgH_EG-S�sÔIEgHv6_EIEK L=_EsO�L�ÄgHG�sRQEFH�5uL��sOVEgHIEs�ftFQIof-lEgRgOSJssHB �LB¯vJlEs�D#FHGJlR_EIEstIkZ\e.g��sDMHs«sDQRu^FQILSJK�gOI�gQ�_X=VHgHG�O � � P � N � + vJg!n^s�vJlLs�e¯sh�HstILNkG�s�uYgH�M�RIEgH��KTFQ�TSKMI �-�#}��t}-� �QB��\I/nYgQv�l5ftFHSJstS0vJlLs6Nks)v�shG��5KMIEKTS�v�KMf�uLFHG�v O � � P � N � + ftFQI/n^s6fhgH��uE_kv�stN/sRQkuE�MKMfhK v����FQI^N2S�v-Fjv�KMS�vJKTfhFH��KMIk�ÄgHG���Fjv�K�gOI2gHI­v�lEs S�v�gRf-l^FHS�vJKTf�uLFHG�v O@� � P � N � + �ÄgO���Mgjm6S�nR� vJs�S�v�K�IL� XFQ�=FQKMILS�v O � � P � N � + V

� � O@�kPR# K � X O�� �n�kP#� � O���P �9P5O@�kPYQX�lEgRgOSJKMIE�7F�vJG�_EILftFjvJKMgHI gHG-NkshG$� �ÄgHG�vJlLs��L_^f vJ_^FjvJKMgHI SJshG�K�s�SeO]X � NkstIEgQv�stS�vJlEs/vJG�_EIkZfhFQvJs�N��L_Lf)vJ_LFQvJKMgHIiPcFQILNÂF6]LIEK�vJs st��st��shI=v�O_�C-P6NkKTS�f)G�s)vJKM�tFQvJKMgHIÂ�MsDMOsh� OÎf)gOGJG�stSJuYgHILNkKMIE��v�g

vJlLs �«C SJuLFHfhs � � gH�cNkK���stILS�KMgHI � � P V«m�s�NksR]^IEs�G�stfh_EG�SJK MHsh�M�HV0m�K v�lZ �8#%NkK M2O'� P V«vJlLsSJsBL=_EshI^f)s5O�� � � � P#� N � nR�

� Z � �Ob � � On. �n�kP # � On. �n�kP� Z � � � � � On. �n�kP # NEK^M2O]X � O�./���kP � � � ? � � O�./���kP P ���� }

KMI7�� � P!Z\FEB sHB��:H7�Q

Page 23: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ xE}

r�lEsÔw6st_E��FQIEI�S�stGJKMstS�� � N � � � � � KTS�vJlEstI�stFOS�KM�M��SJlEgjm�I�v�g/fhgHI MHstGJ�Os6_EIEK��ÄgHG�������KMI�� �MK�POsF��OshgH��shvJG�KMf�SJshG�KMstStB6�ÂgHG�shgFMOshG�VEFHS�S�_E��KMIE��v�lEs/NEFQv�F � v�g�nYs/SJ_81&f)KMshI=vJ�M�7G�sh�O_E�TFQG6KMI FOSvJg�stILS�_LGJsz�«C­f)gOI�MOshG��HstILf)s�G�FQvJs d O � � P�_LIEK �ÄgOGJ���M��KMI��^H !VEm�s!l^FMHs

* ?� � ^aV�[%b ?����� � *�� � � � � % � � � � � �( )� � d O � � P�� � ��� � ^ � Q

�\I�gOG�NkstG6v�g&nLFQ�TFQI^f)s�v�lEs/fhgHI=vJG�KMnE_kvJKMgHI^S6gQ�¶v�lEs�v�lEG�shs/NEKMS�f)G�s)v�K���FjvJKMgHI�S�vJstuLSZOÄvJG�_EILftFjvJKMgHI gQ��L_Lf)vJ_LFQvJKMgHI S�stGJKMstStVL�C K�I ÂV±vJG�_EILftFjv�K�gOI�gQ��wcsh_E��FHIEI SJshG�K�s�S PcFQILN FHf-lEKMsDMOs FQI FHftf)_EG-FHfh�gQ�«gHG-NkstG 5 "�z5m�s�f-lEgRgOSJs

� 6 !���gO� 5 ! � � �ShB vtB d O � � P � 5 � \ 6 !���gO� 5 ! Q[6gjm�sDMOshG�VkvJlLs/f)gO��uE_kv�FQvJKMgHI�gH� ?���� � �ÄgHG�z �� � \ KTS�IEgQv�FHI�gHn MRKMgH_LS�v-FHSJP±B5�|v!fhFHI�nYsSJlEgjm�I�vJlLFQv ? O�� V � � P�fhFQI�n^sÔf)gO�5uL_kvJs�N .;�R!%9-<F,P@6_LSJKMIE�/FHI=��NkshvJshG���K�ILKMS�vJKTf�SJgH� MHstGyKMI� FQv�«C�NkKMS�f)G�s)v�K���Fjv�K�gOI7�MsDMOsh� 6VES�v�FHG�v�K�IL�/�ÄG�gH� vJlEs &�*>�R.T# &�$�&�.�"�<

� V � ? �M�� � � O�� ����P 3 # K � X � O�� ? ���kP X � O�� U �n�kP-.0.h. X � O���V9�n�kP � O�� ���kP �9P5O@�kP � H V ��� H MRKMF�F&f)gO�5uYgOSJK�vJKMgHIÂgQ� O j�4}P�nYgH_EILNEstNÂgOu^stG�FQvJgHG-S�NksD]LIEstN�K�IÂv�shG���S6gQ��NEK^M%� �V^vJlLs�vJG-FHfhsgHuYshG-Fjv�gHG�gHI�vJlLs�NkKMFH�HgOILFQ��SJs)v&KMI 2 FHILN v�lEs �«C S�gO��_EvJKMgHI gHuYshG-FjvJgOG6Z � ?� � � gQ�!vJlLsNkK^JY_^S�KMgHIouEG�gHnE�Msh� m�K v�lofhgRs-1&f)KMshI=v�� FQv��MsDMOsh� cV

9O� V � � � ? O�9P P �� � ����� ����������

� � �� � � � � � � � � ��� 6O V �W� � P � 9O� V � ? �W� � P � .0.0. � � � � V � ? �M�� � � �� � ����� � �������

�� � �� � � � � � � � � ��� � V � ? �M�� � � � � � � V � ? � ? �M�� � � � � � � .0.0. � ?���� �

r�lEs�FH� v�shG�ILFjv�K^MOs�G�shuEG�stSJshI=v-FjvJKMgHI7gQ�0vJlEs6O ��t}'P���K^QRs�N��5gO��shI=v6gQ��O.X � � � P V � V � ? �M�� � � # a

��� &! � ���� � �

RK � � � � O@�kP-.0.h.n� � � O@�kP � O�� ���kP �9P5O@�kP V" #�$ %H � � ? O 9P

��� � � .h.0. � ��� �" #&$ %H _ O V PKTSclEstGJs uEGJgkfhstS�S�s�NÂFQILNov�G�FHILS��ÄgHG��5s�NoK�I=v�g ?����� � FjvÔF&f)g=S�v!m�lEKTf-l�KMS�stS�SJshI=vJKTFQ�M����sBL=_LFH�.v�gvJlLs/f)gO��uE_kv�FQvJKMgHILFH�¯sDJYgOG�vcILshstNEstNov�g&GJ_LIÂvJlEsZ]LG-S�v�S�vJstuÂ�ÄgHG �# \�OÎNEsR]LIEK�vJKMgHI gQ�¶vJlLs�vJlLs�ÄgH�M�Mgjm�K�IE��ÂgOu^stG�FQvJgOG�S�K�I v�lEs&NkKTFQ�HG-FQ� FHn^gFMOs v�lR_LS#gH��K�v�v�stN3P)B&r0FHP=KMIE�oKMIOv�gÂFHfhfhgH_EI=vÔvJlLs��gH��shI=vcSJ�R�5��shvJG��HVkv�lEs#GJs�S�_L� v�K�IE�&FH���OgHG�K v�lE� fhgHILSJKMS�v�S�v�lEshG�s)�ÄgOGJsÔKMI�S�gO�^MRKMIE��FHS���FQIR��NkK �©Z�Ä_LSJK�gOI�uEGJgOnE�Msh��SyFjvl�«C NkKTS�f)G�s)vJKM�tFQvJKMgHI5��sBMHst�� FHS«v�shG���SyK�I5vJlLscFQ��vJstGJILFQvJK MHs�G�shuEG�stSJshI=v�FQvJKMgHIgQ�vJlLs#�5K^QkstN7��gH��shI=v6gQ��O.X � � � P VRv�lLFjv6KTStV� ^ � \ � 6 5 � � � ? � !\�MgH� 5 ! � ��� � � ? ��'�( )�*,+-' � Nks)v�shG���K�IEKTS�vJKTfÔuEGJgOnE�Msh��S�K�I %m�K v�l�FHftf)_EG-FHfh� 5 Qr�lEKTS¶S�_Lu^stG�Z\FQ�M�HstnEG�FHKMf�f)gO�5uL��sDQRK�v��9OÎm�lEKMf-l�G�shILNEshG-S¯v�lEs6FQ�M�HgOGJK�vJlL� K�IEs�1&f)KMshI=vtV=f)gH��uLFHGJs�N#v�gFcS�v�FHILNEFHG�N#�ÂgOI=vJs�X�FHGJ�MgcSJK��/_E�TFjvJKMgHI¯VWSJshs�NkKTSJfh_LSJSJKMgHI#nYsh�MgjmmP.fhFHI�nYs�SJ_EnLS�v�FHIOv�KMFH���M�!GJs�Nk_Lf)s�NnR�ÂIEgQv�K�IL��v�lLFjv#IEgHv .��R!O9�<¶nE_kv#gHIE�M� !TJ%J���$��%*>&�!�< .hV 5 �6FHftf)_EG-Fjv�s PRIEgjm��MstNk�Os gH� ?����� � �ÄgOGz � �H\ KTS�GJs'L=_EK�G�stN.B���FHSJstNogOI�vJlEs �ÎFHS�vcNkstftFW��gQ�«v�lEsI�L_^f vJ_^FjvJKMgHI�SJshG�KMstStVE��FQIR�&v�shG���SKMI vJlEs7FQ��vJshG�ILFQvJK MHs�G�shuEG�stSJshI=v�FQvJKMgHI gQ��v�lEs���K^QRs�N ��gH��shI=v/gH�1O.X � � � P#fhFHI n^s�NkKMS�fhFHG�NEstNm�K�vJlEgO_kv�FFJ±stf v�K�IL��v�lEs5fhgH��uE_kv-Fjv�K�gOI FHftf)_EG-FHfh�HBz����NkgHKMIE�oS�g�vJlEs�fhgH��uE�MsRQkK v��oKTS!GJs�Nk_Lf)s�NvJg�F�":.T!���,P@7$TJ:< *>& !',kgOIEsHVRv�lLFjv6KTS�v�g�SJgH� MRK�IL�

6 !\�MgH� 5 ! � � '.( )�*,+-')�( � ) + � � � % 5 �0/ � ? � Nks)v�shG���K�IEKTS�vJKTfÔuEGJgOnE�Msh��S�K�I %m�K v�lÂFHfhfh_EG-FHf)� 5 Q

Page 24: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

xHx µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

w6gHvJs�v�lEs6lEKM�HlEstGys-1&fhK�stILf)�/gQ�YvJlEs6uYshGJvJ_LGJnLFQvJKMgHI�FQ�M�HgOGJK�vJlL� FHSyfhgHI=vJG-FHS�vJs�N m�K�vJl�v�lEs�� $'"?< .� !'��, $#�5shvJlEgkN£B�]EFQ��uE�MK�IE� � � � GJs'LO_LK�G�stS�PRIEgjm��MstNk�Os�gH�¯v�lEs�NEFjv-F�NkKMS�vJG�KMnE_kvJKMgHI .�(M.���@ �k�K.���.*>" FHILN�S�gO�^MRKMIE� �ÄgHG&s�FHf-l­S�FQ��uE�MsovJlEs NEKKJ±_LSJK�gOI­uEGJgOnE�Msh� FQv7NkKTSJfhGJshvJKM�tFQvJKMgHI ��sBMHsh� uEG�gkNk_Lf)s�S�FQI

FHfhfh_EG-FHf)� 6 d O � � P�� }

! b ! �m�lEstGJs� b NkshILgQvJs�S¶v�lEseO ]LIEK�vJs'P�SJFH��uE��s!S�shvtB«r�lEs�fhgH��uE�MsRQkK�v��/gH�Yv�lEs���gHI=vJs!X�FHGJ�Mg���s)v�lEgkNKTS�vJlEstGJsh�ÄgHG�sÔFOS�lEKM�HlÂFHS�v�lLFjv�gQ�¶SJgH� M=KMIE�

6 5 � U NEs)vJstGJ��KMIEKTS�v�KMf!uEG�gHnE�Msh��S�KMI %m�K�vJlÂFOfhf)_LG�FOf)� 5 Qr�lEs 0FJ�!'<F*�!',V��. Q�68, !���*>< @�gH��v�lEs&G-FQILNEgH� �^_Lf v�_LFjv�K�gOI ftFQI nYs�vJlLshG�s)�ÄgHG�s�_LSJstN vJg f)gHI^S�v�GJ_Lf)vFQ��vJstGJI^FjvJK MHsÔFQ�M�HgOGJK�vJlL��S�m�lLKMf-l�u^stG��ÄgOGJ� n^shv�vJstG�vJl^FQI�vJlEs�� $�"�<=.�� !'��,/$#S�KM� _L�MFQvJKMgHI.B

S s�fhgHILfh��_LNEs�nR�ÔIEgQv�K�IE�cvJlLFQv0v�lEs�uYshGJvJ_LGJnLFQvJKMgHI FH���OgHG�K v�lE� uEG�stSJshI=vJs�N#FQnYgFMHs�fhgH� nLK�IEs�Nm�K�vJl vJlEs�SJuLFQG-SJs/�OGJKTN SJgH�M_kv�K�gOI FQ�M�HgOGJK�vJlL� �ÄgHGÔvJlLs�lEK��OlEshGÔgOG�NkstGÔ�5gO��shI=v#uEGJgOnE�Msh� ��FQPOsuYgOS�S�KMnE�Ms&FQ�TS�gov�lEs�f)gO��uE_kv�FQvJKMgHI gQ�� �� �ÄgOG���� x�KMI "�.;!���,P@ $TJ:< *>& !',4f)gH��uE�MsRQkK�v��HB��EgOGNkshv�FQKM�TShVkm�s#GJsh�ÄshG�v�g�� { j �³B

� ��� � V h � @B@'` V @ �� ����� EHA � V ��ETABf GbEHd �CFEK� V�XZY C � � ]kg �ÎFHGtVkm�scuEG�stSJshI=v�stN�v�lEs MjFQG�KMFQvJKMgHILFH�E�ÄgHG�� _L�MFQZ

vJKMgHIÂ_LILNkshG��M�=KMIE��S�vJgkf-lLFOS�v�KMf�AÔFH��stGJPRKMIÂuEG�g���stf)vJKMgHILS X-$'��& !',>,[email protected]�IÂu^FQGJvJKTf)_E�TFQGB!'0;0;68&�*>" QvJlLs!sDQkKMS�vJstILf)s!gQ�0F/uEG�gHnLFHnEKM��K�v��&S�u^FHf)s�O�� 4���eP�gHI�vJlEs!�Ä_EI^f vJKMgHIoSJuLFHfhstS � KMI�m�lLKMf-loNEFjv-FFQI^N?�WgOG«SJgH�M_kv�K�gOILS¶FQG�s�S�gO_E�Hl=vtBqcS¶KTS«m�sh�M�EPRIEgjm�I5SJKMILf)s�vJlLs�uEK�gOIEshstGJKMIE�Ôm�gHG�P#gQ�£w�BIS­KMshIEstGtVlEgjm�sDMOshG�V¶vJlEs�fhgHILS�vJG�_Lf)vJKMgHI gQ�#F uLGJgOnLFQnEKM�MK v�� ��s�FHSJ_EGJs�� gHI�F �Ä_EILf v�K�gOI­S�uLFOf)soKTS�IEgHIEZvJG�K M=KTFQ�³B7U�IEs�m�FW��vJgonE_EKM�MN SJ_Lf-l �5s�FHSJ_EG�stSÔKTS M=KTFoDÔgH�M��gH�HgOGJgbJ=� S!f)gOILS�v�GJ_^f vJKMgHI m�lEstGJstn=�� KTS�gHnkv-FQKMIEstN�FHS�SJ_EK�v�FQnL��sÔ�MK���K�v�gH�0uEG�gkNk_Lf)v���s�FHSJ_EGJs�S�gOI�fh�R��KMILNkstG�S�gQ�K�I^f)G�stFHSJKMIE�/NkKM��shIkZSJK�gOI.BDÔgO����gO�HgHG�gIJ=� S«f)gHI^S�v�GJ_Lf)vJKMgHI�KTS¶K���uYgHGJv�FHIOvyKMI�vJlLscf)gOIOv�sRQRvygQ�±��N�X NEKMS�f)G�s)v�K���FjvJKMgHI^S«gQ�S�vJgkf-lLFHS�vJKTf N�a!C6VkS�KMILfhs!F/��N�X�NkKTSJfhGJshvJKM�tFjv�K�gOI&KTShVkKMI�F5SJshILSJsHV=vJlLsÔfhgHI MHstG�SJs�v�g/v�lEsÔ��KM��K v�K�IL�uEG�gkf)stS�S�K�IÂDÔgO����gH�OgHG�gIJ=� S�fhgHILS�vJG�_Lf)vJKMgHI.B

�\IoF/SJshG�K�s�S�gH�0uLFHu^stG�StVi��FQnE_��S�PjF5FHILN&lLKMS�fhgQZ|m�gOGJPOshG-S � ���.�OFMHs!F ��FQvJlEst��FQvJKTfhFH�^�ÄG-FQ��shZm�gHG�P7�ÄgOG���N�X FHuEuEG�gQkK���Fjv�K�gOIÂgQ�yv�lEs5sh�M��KMukvJKTf5n^gO_EILNEFHGJ��MjFH��_Es5uEG�gHnE�Msh� m�K�vJl S�v�gkf-lLFHS�vJKTff)gRs�1�fhK�stI=v�StVES�sts ]Rstf)vJKMgHIÂ{kB�xkVR�ÄgHG�lLgH��gH�OshIEstgH_LS�nYgH_EILNLFQG���f)gOILNkK�vJKMgHILStB¶r�lEs�NkK^JY_LSJKMgHIÂf)gHZs-1&fhK�stIOv-S#FQG�s G�shuEG�stSJshI=v�stN�nR��F7vJG�_EILftFjv�stN D#e�sRQkuLFHILSJK�gOI Fjv�SJ_81&f)KMshI=vJ�M�ÂlEKM�HlkZ|gHG-NkstG�� Br�lEsÔshG�G�gHG�K�ILfh_EG�GJs�N&KMI�v�GJ_EI^fhFjv�K�IL��D#e sRQkuLFHILSJK�gOILS�gQ�0KMIEuE_Ev�NLFjv�F5gOI&vJlLs�FHfhfh_EG-FHf)��gH�¯vJlLsSJgH�M_kvJKMgHILS!gH��S�vJgkf-lLFHS�vJKTf5sh�M��KMukv�KMf5sBL=_LFQvJKMgHILS#ftFQI n^s�s�S�v�K���Fjv�stN _LSJK�IE�ÂS�v�FHILNEFQG-N�IR_E��stGJKTfhFH�FQI^FQ�M�RSJKTS�gQ��sh�M��KMukvJKTf7n^gO_EILNEFHGJ� MjFQ�M_Es�uEGJgOnE�Msh��ShV¶KMI@u^FQGJvJKTf)_E�TFQG�V«vJlEsÂ]=v�G�FHIE� e¯sh����FEB �\IFHftf)gOG�NEFHILf)sÔm�K�vJlÂv�lEs G�sh��FHGJPkS���FHNEs Fjv�vJlEs�stILNÂgH��]Rstf)vJKMgHI xkV±FQI^NÂFHS6KM�M��_LS�vJG-Fjv�stNoKMIÂvJlLssRQEFH�5uL��s�S�K�I ]kstf v�K�gOILS5�&FHILNÂ{kVL��N�X NkKTSJfhGJshvJKM�tFjv�K�gOI7KTS��ÎFHK�G��M��KMILNkshuYshI^NkshI=vcgH�0v�lEs#v��Ru^s gQ�NkK^JYstGJstI=vJKTFQ�sBL=_LFjv�K�gOI�_EILNEshGÔf)gHI^S�KTNkshG-Fjv�K�gOI.BÔX�gO� nEKMIEKMIE�7fhgHI=vJKMIR_EgH_^S�Nkstu^stILNkstILf)s5GJs�S�_L� v-SgQ�±S�gO��_EvJKMgHILS«gOI v�lEs6f)gRs-1&fhK�stIOv-SgQ�±uLFQG-FQnYgH�MKMf�FQI^N lR�Ru^stGJnYgH�MKTf-N�a�C�Sm�K v�l�NEstfhFW�#s�S�v�K���FQvJstSgHI D#e@sDQkuLFQILSJKMgHILS!S�lLgH_E�TNovJlLshG�s)�ÄgHG�s�FQ�M��gjm ��_LS�vJK^]^ftFjvJKMgHI gQ�yv�lEs���N�X FQuEuEG�gQkK���FQvJKMgHILScgQ�,P*>":.T!���NEKKJ±shG�shI=vJKTFQ�¯sBL=_LFjv�K�gOILS�uEG�stSJshI=vJs�N&KMI�]Rstf)vJKMgHILS5��FHILN�{5FHn^gFMOsHB

� �9} � _2A Y G � EH@BABf,G C V �i`&d,ETCFf,A W E h [ @ � Y CA G Y CC V d ETABf Yih d V h �3A � � q POsh��S�v�shu­KMIvJlLs�shG�GJgOG6FQILFH���kSJKMScFQILN�v�lEs�_EILNEshG-S�v-FQILNkKMIE��gH�v�lEs�uYshGJ�ÄgHG���FQILfhs#gQ�¶��N�X2FHuEuEG�gQRKM��Fjv�K�gOILSgQ�!S�v�gRf-l^FHS�vJKTf7NkK^J±shG�shI=vJKTFQ��sBL=_LFQvJKMgHILS/KTS v�lEs 0�< $N9���!M0�<F*�9���. Q�68,/!'��*><F@�gQ�cvJlEsÂSJgH�M_kvJKMgHI.B r�lLsuEG�K�I^f)KMuE��sc_EILNkstGJ�M�RK�IE�#s�1&f)KMshILfh�/gH�Y��N�X@FQuEuEG�gQkK���FQvJKMgHILS�ÄgOG ,P*>"�.;!��«S�vJgkf-lLFOS�v�KMf�NEKKJ±shG�shI=vJKTFQ�sBL=_LFQvJKMgHILS5KTS5vJlLFQv�vJlEKTS&Nkstu^stILNkshI^f)sogHI^T KTSS!'":!',P@'<F*�9-�cvJlEKTStV�KMI�v�_EG�I.V�KM��uE��KMstS&sRQku^gOIEshIEZvJKTFQ�yfhgHI MHstGJ�OshILfhs G-Fjv�stS!sRQku�O�� � P1P�m�lEshG�s � " z7FHILN P NkstIEgQv�stS!vJlLs�NEsh�HG�shs5gQ��vJlLs5��N�XFQuLuEGJgQkKM��FjvJKMgHI¯B

Page 25: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ xbl

C MOshIÂm�K�vJl�sDQku^gOIEshI=vJKTFQ�f)gOI�MOshG��HstILf)sOVE��N�X­KTS�fhgH��uE_kv-Fjv�K�gOILFQ�M����sRJ±stf)vJK MHs�gOIE�M��K��¶vJlLsIR_E� nYshG � gH��G�FHILNkgH� MWFHGJKTFQnL��s�S T _^S�s�N KMI vJlEs7f)gH��uE_Ev�Fjv�K�gOI KMS�SJ��FQ�M� 3��ÄgHG�sDQkFH��uE��sOV0K��F�v�shILSJgHG!uEG�gkNk_Lf v!��N�X S�uLFOf)s/KMS�_LSJstN£V±v�lEs/IR_E�/n^stG�� gH��NkshvJshG���K�ILKMS�vJKTf�uEG�gHnL��st��ScvJg�nYsSJgH� MHstN7Fj�©v�shG���N�X�NkKTSJfhGJshvJKM�tFQvJKMgHI�KTS �`# � O�P Z P�FQI^N&v�lEs#sRQkuYgHIEstIOv�KMFH�±��N�X2f)gOI�MOshG��HstILf)ssRQkuEG�stS�SJstN&KMI�vJstGJ��S�gH�!� KTS � OÎsRQku#O�� � � ?�� Z P P)B�]R��FQ�M��ILstS�S�gQ� � KTShVRv�lEshG�s)�ÄgOGJsOVkstS�S�stI=vJKTFQ�F�_EIk�ÄgOG�v�_EILFQvJsh�M�HV=v�lEs�SJK��tscgH� � IEs�f)stS�S�FQG����ÄgHG��HgRgkN&FHuEuEG�gQRKM��Fjv�K�gOI5gH�£vJlEsÔS�vJgkf-lLFHS�vJKTf�KMIEuE_kvNEFQv�F KTSof)�MgOSJsh�M��GJst�MFQvJstN­vJg�vJlEs NkstftFW��gQ�#vJlLs stK��OshI MjFQ�M_EstS�gQ��v�lEs f)gFMjFQG�KMFHILf)s gHuYshG-FjvJgOG�ÄgHG�v�lEsoK�ILuE_kv�NEFQv�FK��m�solLFMHs��HK MHstI@KMI�]kstf v�K�gOI l SJgH��s�vJlEstgHG�s)v�KMftFQ��stS�vJKM��FjvJs�S5�ÄgHG�v�lEKMSshKM�HstI MWFH��_Ls5Nks�fhFW�e�ÂK�I uLFHG�v�KMfh_E�MFHGtV±�ÄgOGÔ��FHIR��f)gFMjFQG�KMFHILf)s�ScsDQku^gOIEshI=vJKTFQ�«stK��OshI MjFQ�M_Es5NEstfhFW�fhFHI7nYs�FHf-lLK�sBMHstN.BX�gH��uE_Ev�Fjv�K�gOILFQ�«uEG-FHf)vJKTf)s/lLFHSÔSJlEgjm�I.V±K�I FHftf)gOG�NEFHILf)s m�K v�l v�lEs�FQnYgFMHs lLsh_EG�KMS�vJKTf5f)gHIEZ

SJKMNkstG�FQvJKMgHILStV=sDMHstI�sDQRuYgHILshI=vJKTFQ�Y��N�X f)gHI MOshG��HshI^f)s6G-Fjv�stS�vJg5n^s!_LSJsh�MstS�S�K��.v�lEs!NEstfhFW��G-Fjv�s�KMIvJlLs�D#e sRQkuLFQI^S�KMgHI7gQ�vJlEs#KMIEuE_kv!NEFjv-F/KTS�v�g=g�SJ��FQ�M��B�]R�Mgjm D#e stK��OshI MjFQ�M_Es#NkstftFW�&gkfhfh_EG�S�K��vJlLs&S�uLFQvJKTFQ�yfhgHG�GJst�MFQvJKMgHI��MshIE�HvJl gQ��K�ILuE_kv NEFQv�FoFQILN SJgH�M_kvJKMgHI FQG�s�S���FQ�M�yf)gO��uLFQG�stN�vJgovJlLsNkKTFQ��s)v�shG�� gH��vJlEs�uElR�kS�KTfhFH��NEgH��FQKMI�ÂB r�lEKTS KM��uE��KMstS�FHI sRQEf)s�SJSJK MHsh�M� lEK��Ol@NkKM��shILSJK�gOI� gQ��v�lEs9MOstf v�gHG)ToKMI vJlLs&��N�X NEKMS�f)G�s)v�K���FjvJKMgHI FHILN£V«lEshI^f)sHV«gH��v�lEs���N�X f)gO�5uL_kv�FQvJKMgHILFH�NkgO��FHK�I¯B

U�IEs L=_EstS�vJKMgHI gQ��S�vJgkf-lLFOS�v�KMf/G�sh�H_L�MFHGJK�v��7uYshGJvJKMIEstIOvÔv�g7v�lEs�s-1&f)KMshI^f)�ÂgQ����N�X FQuEuEG�gQRZKM��FQvJKMgHI�KTStV^v�lEshG�s)�ÄgOGJsOVLlEgjm v�lEs/fhgHG�GJst�MFQvJKMgHIo�MshIE�HvJl gH�¶vJlEs/K�ILuE_kv#NEFjv-F&KMIi�L_EstILf)s�S6v�lLFjv!gQ�vJlLsÔSJgH�M_kv�K�gOI �RK v6FQuLu^s�FQG-S�v�lLFjv6FQv��MstFOS�v��ÄgHG��MK�IEs�FQG�uEG�gHnE�Msh��StVkFQnLSJshILfhs�gH�SJ��FQ�M�±fhgHG�GJst�MFQvJKMgHI�MshIE�HvJl�KMI�K�IEuL_kv6NEFjv-F stILS�_LGJs�S�v�lEKTS�KMI7vJlEsÔG-FQILNkgO� S�gO��_kv�K�gOI.BA�EgOG�ILgHIE�MK�ILstFQG�uEG�gHnE�Msh��S�vJlLs��stf-lLFHIEKTS���S#m�lEKTf-l uEG�gkNk_Lfhs&S�KMIE�H_L�MFHGJK�vJKMstS6O�FHStV«sHB �LBMVSJlEgkf-PkShV«S�KMIE�O_E�MFHGJK�vJKMstStVs)v�fHB P4KMI vJlLsNkshvJshG���K�ILKMS�vJKTf�ftFHSJs�FHuEu^s�FQG«FQ�TS�gcvJg!�HstIEshG-Fjv�s�G-FQILNkgO� S�gO��_kv�K�gOILS0m�K v�l/SJ��FH���kSJuLFjv�KMFH�=fhgHG�GJst�MFQZvJKMgHI��MshIL�QvJl¯VOsBMHshI�K��£vJlLscKMIEuE_kv�G�FHILNkgH� ]Lsh�TNES�FQG�s�IEgQv�gQ�±vJlEKTS�v��=uYsZO�S�stsB��}t�M�^�ÄgHG�IR_E��stGJKTfhFH�G�stSJ_E� v-S6KMIÂvJlLKMS!NkKMGJs�f vJKMgHI�P B6r�lEKTS5J:��$O+�, .�& $ X0�&�!�,>,29;$�����.-,/!'<F*�$'" , .�" QO<E� *>" *>"'J:68<5#%!'<=!�!'"�#0�$',P68<F*�$'"/KMStVkFjv�uLGJs�S�stIOv�V=F ��F ��gHG�n^gHv�vJ�MshILstf-P�K�I&vJlEsÔNksDMOsh�MgHuE��stIOv�gQ�.G�gHnE_LS�v�FHILN��HstIEshG-FQ�M�M�FQuLuE��KTfhFHnE�Ms!��N�X�Z|nLFHSJstN7Nks)v�shG���K�IEKTS�vJKTf#S�gO�^MOshG-Sy�ÄgOG6S�v�gRf-l^FHS�vJKTf!NEKKJ±shG�shI=vJKTFQ�£s'L=_LFjv�K�gOILShB

��FHSJstNogOIovJlEs5FQnYgFMHs�NkKTSJfh_LS�S�KMgHI.V^m�s5S�sts#v�m�g&FQuEuEG�gOFOf-lEstS�vJg�v-FHf-PR��s�vJlEs5S���FQ�M�0fhgHG�GJshZ�TFjvJKMgHI��MshIE�HvJlouEG�gHnE�Msh��3

O�F�P { f)gOFHG�SJshILK�IE���0gH��v�lEs�vJstILS�gOG�uEG�gRNE_Lf v���N�X SJ_EnLSJuLFHfhstS���v�lEsÂ��gOS�v&NkK�G�stf)v�m�FW� v�gFHf-lLK�sBMHs vJlEKTSÂKTSÂv�g2FQ�M��gjm��ÄgHG ('!'��*�!%+-, . 0�<=$�9��K!'0;<F*�9 JK$�,P@'"�$�&B*�!�,�#O. QO��.;.�0 P j ��� #}��hQ0QhQ>��� B�r�lEKTS�m�FOS5_LS�s�N@sOB �^B�KMI � }'lM�cFQILN FQ�TSJg KMI � ���cFHILN FQ�M��gjm6S vJg lLFHILNk�MsOÄgOI7u^FQG-FQ�M��st�±FHG�f-lLK v�stf v�_EG�stS PysDQRu^FQILSJK�gOI�gOG�NkstG�S�_Eu�vJg � #2{HzEB¶w6_L�5stGJKTfhFH�£sRQkuYshGJZKM�5stI=v�S#FQuLu^s�FQG!vJgoKMILNkKTfhFjv�sHV.lLgjm�sBMHshG�V±vJl^Fjv#sDMOshI uLGJgkNk_Lf)v�S�uLFOf)s�SÔm�K v�l MjFQG�KTFQnE�MsuYgH�M�=ILgH��KMFH�!NEsh�HG�shs�S&FQG�s { vJgRg��HshILshG�gH_LS�� �!K��/FQILN2lEgjm �Ä_EG�v�lEshGoS�FM=KMIE�=S�fhFHI2nYsG�stFQ�MKM�hstN7KTS�vJlEsÔv�gHuEKTfÔgQ�gHIE�OgHKMIE�/m�gHG�P±B

OÄniP�FQn^FQILNkgOIEKMIE� v�lEs�D#e£Z³v��Ru^sÔSJshuLFHG�FQvJKMgHI�gH�S�vJgkf-lLFOS�v�KMf!FQILN�NkshvJshG���K�ILKMS�vJKTf MWFHGJKTFQnL��s�S� v�lEKMS�KTSyG-FjvJlLshG�SJuYstf)_L�MFQvJK MHs6Fjv�uEG�stSJshI=v�FQI^N���FW�5nYscf)gO�5uL_kv�FQvJKMgHILFH���M�/KMIk�Äs�FHSJK�nE�MsHB

q6��vJlLgH_E�OloFHILFQ�M�kS�KTS�gQ�¶��N�X �ÄgOG6�MK�IEs�FQG6st���MKMukvJKTfÔuEG�gHnE�Msh��S�KTS ��G�sh�TFjv�K^MOsh�M�8�/fhgH��uE�Ms)vJsOVLKMIvJlLs&S�stILS�s�v�lLFjv�sDQku^gOIEshI=vJKTFQ��f)gHI MOshG��HshI^f)s5_EILNkstG S�_K1�fhK�stI=v S���gRgQv�lEIEstS�S#FHS�SJ_E��ukvJKMgHI lLFOSnYshshIouEG�gFMHs�N£VR� _Lf-loG�sh��FQKMILS�vJg�nYs�NkgOIEs!�ÄgHG�IEgOIE��KMIEs�FQG�uEG�gHnE�Msh��StB

� � ����� A � V C V � �&E h @'f Y�h ?&EH@'f,@ � r�lEs���N�X sDQkuLFQILSJKMgHI KMS#F �LZ�v��RuYs5sDQkuLFQILSJKMgHI vJlLFQvshI���gj�RS!�ÎFOS�v fhgHI MHstGJ�OshILfhs/m�lLshIEsBMHshGÔv�lEs�SJgH�M_kvJKMgHI KTS�S���gRgQv�l.B7[cgjm�sBMHstGtV±�ÄgOG S�gO��s�FHuEuE�MK ZfhFQvJKMgHILStVEv�lEs uLGJgOnLFQnEKM�MK v����Ä_EILf v�K�gOI gH�v�lEs/SJgH�M_kv�K�gOIÂ��FW�7IEgQv!lLFMHs�SJ_81&f)KMshI=vÔS���gRgQv�lEIEstS�StB]R_En^S�s'LO_LshI=vJ�M�HV±v�lEs5fhgHI MHstGJ�OshILfhs�gQ�¶v�lEs �EZ³v��Ru^s/sRQkuLFQI^S�KMgHI NEs)vJstGJKMgHG-Fjv�stStVYFOS!K vÔKMSÔF��H�MgHnLFH�uYgH�M�=ILgH��KMFH�6FQuEuLGJgQkKM��FQvJKMgHI KMI�vJlEsÂG-FQILNEgH� SJuLFHfhsHB�r¯g f)KMG-f)_E�eMHshI=v5vJlEsÂNkK 1&f)_E��v��HV�gHILsf)gO_E�TN _LSJs&uEKMstf)stm�KMSJs�uYgH�M�RIEgH��KTFQ�TShB ]k_Lf-l@FQuLuEGJg=FHf-l.V0vJstGJ��s�N FHS �=Z�v��RuYs&sRQkuLFHILSJK�gOI.V«m�FOS]LG-S�v«uEG�gHuYgOSJstN#KMI � ���|B«q�SJK���KM�MFHG0��shvJlEgkN£VHFH�MSJgcn^FHSJstN�gOI#vJlLs�KTNks�FcgH�L��gkftFQ�RFQuEuEG�gQkK���FQvJKMgHILStVKTScuEG�stSJshI=v�stNÂKMI � x%H��|V±m�lEshG�s/F�m�FMOsh�Ms)vcnLFOS�KTS6KTSÔFQILFH���R�tstN£Bcqc�MSJgLV±KMII� {Q�M�¶F&�/_E��vJK�Z³st��st�5stI=v

Page 26: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

x'� µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

Nks�f)gH��uYgOSJK v�K�gOI gH��v�lEs�G�FHILNkgO� S�uLFOf)s�KTS#NksDMOsh�MgHuYstN FQILN ��N�X sRQkuLFHILSJK�gOILSÔFQG�s/st�5uL��gj�OstNgHI7stFOf-l&sh�Msh��shI=v�Byq6I�sDQRvJshI^S�KMgHI7gQ�.v�lEs�S­KMshILshGJZ|q�S�POsh��sRQkuLFHILS�KMgHI^Syv�g�!���+-*><F��!'��@�uYNk�ÎS�m�FOSuEG�stSJshI=vJs�N�KMI � j zM�¯m�lEstGJs#gOG�v�lEgH�OgHILFH�^uYgH�M�RIEgH��KTFQ�TS�m�stGJs#fhgHILS�vJG�_Lf v�stN7gHIkZ³vJlLs)Z6�L�&v�g5G�shuLGJshZSJshI=v gHuEvJKM��FH���M� FQI FQG�nEK�vJG-FQG���uEG�gHnLFHnEKM��K�v�� NkKTS�vJG�K�nE_EvJKMgHI.B�r�lEKTS�sDQRvJshI^S�KMgHI.V«KMI �ÎFHf)vtV¶KTS#vJlLsPHst��v�g#� _E��vJK�Z|NEgH��FQKMI�G�FHILNkgH�9NkstfhgH��uYgOSJK v�K�gOI.VQgQv�lEshG�m�KTS�s�m�s6FQG�s�gHIE�M� �MKM�5K�vJs�N5vJg#_EILK �ÄgOGJ�u±NR�ÎS�FHILN�f)gOGJG�stSJuYgHILNkKMIE�O��� e¯sh�OshILNkG�s6uYgH�M�RIEgH��KTFQ�TShB«q6IEgHvJlEstG�fhgHILS�vJG�_Lf v�K�gOI�gQ�£nLFHSJKTSym�gHGJvJl��shI=vJKMgHILK�IE�ÂKTSÔv�lEs �JNEgH_EnE�Ms)Z|gHGJvJlLgH�HgOILFQ� ��nLFOS�KTS�NkKTS�f)_LS�S�s�N K�I � �'�|B9S­lEstI G�FHILNkgH� K�ILuE_kv�SFQG�s�GJstuEG�stSJshI=vJs�N FOS�D#e�sRQkuLFHILS�KMgHI^ShV£v�lEs�NkgO_EnE�Ms)Z|gHGJvJlEgO�HgOILFQ�«nLFOS�KTS#fhFHI sDJYs�f v�K^MOsh�M� NkKTFQ�HZgHI^FQ�MK��ts�vJlLs/��Fjv�GJK^Q�G�stSJ_E� v�K�IL�&�ÄG�gH� vJlLs5S�vJgkf-lLFOS�v�KMf5AÔFQ�MshG�P=KMI�uEG�g���s�f v�K�gOI.B#r�lEs/��FQvJG�KKQ�KMINkgO_EnE�M��gHGJvJlEgO�HgHI^FQ�Ln^FHSJKMS�m�KM���£nYsÔnE��gkf-P&NkKTFQ�OgHILFH�YFHILN�ftFQI7n^s#SJgH� MHstN&K�IoSJFH��s!fhgH��uE�MsRQkK v��FHS���gHI=vJs X�FQG��Mg/��s)v�lEgkNEStB

� � �L� c Y d,d Y GbETA'f Y�h � V A � Y [&@ � �\I FHNENEK v�K�gOIÂvJg�vJlEs�AÔFQ�MshG�P=KMIÂ��s)v�lEgkNES�NEKMS�f)_LS�SJstNÂKMIvJlLKMS�uLFHu^stGtV�gHIEsofhFHI FONkgHuEv�F f)gO���MgkfhFjv�K�gOI�FHuEuEG�gOFHf-l¯B�]R_Lf-l FQI�FQuEuEG�gOFOf-l v��RuEKTfhFQ�M�M� GJshZL=_EKMGJs�ScG�shuYs)v�K v�K^MOs G�_EILS�gQ��F�NEs)vJstGJ��KMIEKTS�v�KMf/S�gO�^MOshGcgOI F�SJs)v!gQ��uLGJs�SJfhGJKMn^s�N OÎNkshvJstGJ��KMIEKMS�vJKTfBPIEgkNEFH�uYgHKMI=v�S#FHILN G�stSJ_E��v�S!KMI Fof)gO��uE��shvJst���Â_EI^f)gH_LuE��s�N SJ�kS�v�sh� gH��sBL=_LFQvJKMgHILStB/[cshILfhsHV.K�v�SKM�5uL��st�5stI=v�Fjv�K�gOI�KTS6v�GJK MRKMFH�0FQI^NÂKMScuLFQG-FQ�M�Msh�MK���FjvJKMgHIÂKTS6G-Fjv�lEshG!S�v�G�FHK��Ol=v��ÄgHG�m�FQG-N£B�r�lEs/f-lEgOKMfhsgQ�±IEgkNEFH�LuYgHKMIOv-S¶KTS�f)G�K�vJKTfhFQ�F�OFH� v�lEgH_L�Hl�K�I�gOIEs6G-FQILNkgO� NkKM��shILSJK�gOI O � # }PvJlLshG�s6FQG�s�FHnE_EIkZNEFHIOv�f-lEgOKMfhstStV.sHB �LBMV�L=_LFONkG�FQvJ_EG�s5u^gOK�I=v�SÔgH��gOG�v�lEgH�OgHILFH�0uYgH�M�RIEgH��KTFQ�TS5O � lH�kVLHQzM� P)V.v�lEs&fhFOS�s�SgQ��� _E��vJK�Z\NkK���stILS�KMgHI^FQ�«G�FHILNkgO� S�uLFOf)s�S�O ��� }'P!FQG�s ��gHG�s�NkK 1&fh_E� v�B��\I � j �M�|V.lEKM�HlEZ³gOG�NkstGf)gO���MgkfhFQvJKMgHI&��s)v�lEgkNES�FQG�scuLGJgOu^g=S�s�N&FQILN7FQILFH���R�tstN£B �|v�KMS�SJlEgjm�I�v�lLFjv�vJlLs�IEgkNEFH�£S�shv�n^FHSJstNgHI5v�shILSJgHGyuLGJgkNk_Lf)v�S¶gH�£gHIEshZ|NkKM��shILSJKMgHILFH�kIEgkNEFQ�LSJs)v-SyKTS¶KMILFQuEuLGJgOuEGJKTFjv�s�K�I�lEKM�HlEZ|NkKM��shILSJKMgHILFH�G-FQILNkgO� S�uLFOf)s�S OÎNE_Es�vJgcK�v�S0�ÎFOS�v«�HG�gjm�vJl#gH�EvJgHv�FQ�=IR_E� nYshGgQ�^u^gOK�I=v�S P VQFHILN#v�lEs�S�shv�S0nLFHSJstN#gOI]R��gH�M�OFHP&S�u^FQG-S�s��HG�KMN7FQILN�]=vJG�gH_LNv� S�fh_EG MjFQvJ_EG�s!FHGJs�� _Lf-l���gHG�s�s�1&f)KMshI=vtB¶r�lEs#f)gO���MgkfhFQvJKMgHI��s)v�lEgkNÂnLFHSJstNogOIovJlEs�]R��gH�M�OFHP�SJuLFQG-SJs#�HG�KMNoKTScFHnE��s�vJg7FOf-lEKMsDMHs#lLK��OlkZ³gOG�NEshG6f)gOI MHshG��HstILf)sOBq6��vJlLgH_E�Ol/K�v�S0vJgHv�FH�=IR_E�/n^stG¶gQ�LILgRNLFQ�Ru^gOK�I=v-S«KMSlEKM�HlEstGvJlLFHI�vJlLs�IR_E�/n^stG¶gQ�Ln^FHSJKMS0�Ä_EILf)vJKMgHILSgQ��F���N�X sDQkuLFQILSJKMgHI.VYvJlLs�SJuLFHG�SJs/�OGJKTN fhgH�M��gkftFjvJKMgHI �5shvJlEgkN S�lLgH_E�TN nYs�K�I MOstS�vJKM�OFjv�stN�FOSÔFuYgQvJstI=vJKTFQ�¯FH� v�shG�ILFjv�K^MOscv�g�AÔFH��stGJPRKMI7��shvJlEgkNEStB

� � � ���� V�� � E3f,d,@�� � r�lLs�FOSJSJ_E��ukvJKMgHI vJlLFQvG-FQI^NkgH� KMIEuE_kv-S¯�ÄgO���Mgjm FÔAÔFQ_LS�S�KTFQI/NkKMS�vJG�K�ZnE_kv�K�gOI�KMS¶st��uE��gj�OstN5KMI5��FHI=�5FQuEuL��KTfhFQvJKMgHILStVQnE_kv�K vyKTS¶gHn MRKMgH_LSJ��� K�ILFHuEuEG�gHuEG�KTFjvJs��ÄgHG�G�FHILNkgH�]Lst�MNES5m�lEKTf-l@sDQklEK�nLK v&SJK��OIEKK]YfhFQI=v�S�POshm�IEs�SJStB �EgHG�sDQkFH��uE��sOV«vJlEsÂfhg=s�1&f)KMshI=v5KMI v�lEsÂNkK^JY_kZSJK�gOI&sBL=_LFQvJKMgHI&��FW�5�ÄgH�M��gjm2F7, $TQ�":$'��& !',RNkKMS�vJG�KMnE_kvJKMgHI¯B¶]kK��OI�uEG�gHuYshGJvJKMstS�gQ�.KMIEuE_kv6NEFQv�F�vJlLFQvFQG�s#f)G�_Lf)KTFQ�Y�ÄgOG6m�st����Z|u^g=S�s�NkIEstS�S�gQ�«n^gO_EILNEFHGJ�5MjFH��_Es#uLGJgOnE��st��S���FW��n^s#�MgOS�v�K�I�vJlLs#uEGJgkfhstS�SgQ�yD#e v�GJ_LILfhFQvJKMgHI.V^GJs�S�_E��vJKMIE�&KMIÂKM����Z³uYgOSJstNEIEstS�S6gH�v�lEs/NEs)vJstGJ��KMIEKTS�v�KMf#uLGJgOnE��st��S6m�K�vJl�SJ��FH���uEG�gHnLFHnEKM��K�v�� KMI ��N�X�FQuEuLGJgQkKM��FQvJKMgHI.Bc�LgHG sDQEFQ��uE�MsHV«_EILSJgH� MjFQnEKM��K�v�� gQ�6SJ�RS�vJst��S G�stSJ_E��vJKMIE��ÄG�gH� [6shG���K v�s)Z\f-lLFQg=S�sRQkuLFHILS�KMgHI��ÄgOG6gHG-NkshG<P9gH�«sDQkuLFQILSJKMgHILS�lLK��OlEshG�v�lLFQI�F�fhGJK�vJKTfhFH�.gHG-NkstGm�FHS6gOnLSJshG MHstN�KMI�IR_E��shG�KMftFQ�0sRQku^stGJKM��shI=v�S�� j H��|B�q GJst�5s�Nk��uEGJgOu^g=S�s�NoK�II� j H��m�FHS6vJlEs/_LSJsgQ�.F���vJG�_EILfhFQvJs�NK��AÔFQ_LS�SJKMFHI�NEKMS�vJG�K�nL_kvJKMgHI.By]R_^f-l&FÔ�5gkNkst�LKTSynLFOS�s�N�gHI�FÔv�GJ_EI^fhFjv�stN ~ FHfhgHnEK�Zf-lLFHgOSsRQkuLFHILS�KMgHI¯BL�|v-SyNkKTS�v�GJKMnE_kv�K�gOI�FHuEuEG�gQkK���Fjv�stS«F#AÔFQ_LS�SJKMFHI5fh��g=S�st���OVHFHS¶SJlEgjm�I�K�I�KM�H_EG�sHRBM}HV=FQILN�K�v�l^FHSynYgH_LILNkstN�SJ_EuEuYgHGJvtVOvJlLshG�shnR�5FH���Mgjm�KMIE��f)gOIOv�GJgO�EgQ�±v�lEsc_EI^NkshG-S�lLg=gHvJKMIE�#m�lEKTf-lfhFH_LSJstS�KM����Z³uYgOSJstNEIEstS�ShB

�|v&lLFOS�FQ�TS�g nYshshI­SJlEgjm�I�vJlLFQv�vJlEs�D#FHGJlR_EIEstIkZ\e.g��sDMHs�sDQkuLFQILSJKMgHI ��FW��NksDMOsh�MgHu ��gOIE�v�FHK��TSÔFHS!gHILs KMILf)G�stFOS�s�S6v�lEs�I=_L� nYshGÔgQ�yv�shG���ShV£sBMHshI vJlEgO_E�Hl FQ�M�vJlEs�G-FQILNkgO� MWFHGJKTFQnL��s�ScKMIvJlLs5sDQkuLFQILSJKMgHI l^FMHs5n^gO_EILNks�N SJ_EuEuYgHGJvtB5r�lEKTSÔm�K��M��fhFH_LSJs v�lEs�_EILNkstGJ�M�RK�IE�ouEG�gHnL��st��V£sOB �^B�Vsh�M�MK�ukv�KMf sBL=_LFQvJKMgHI.VLvJg�nYs SJK�IL�H_E�TFQG����7u^stG�v�_EG�n^s�N£V£S�sts7� l'�³B �|v!KMSc�Hshvc_EILfh��s�FQGclLgjm4v�g&G�stSJgH� MHsvJlLKMS!KTSJSJ_Es��ÄG�gH� F���FjvJlLsh��Fjv�KMftFQ�u^gOK�I=vÔgQ� MRKMshm#V£FQ��vJlEgO_E�Hl¯VYKMI uLG�FOf vJKTf)sOV±gHIEs5fhFQI f)gHI=v�GJgO�vJlLs�I=_L� nYshG¶gQ�±sRQkuLFHILSJK�gOI�vJstGJ��S«v�gÔPHshstu v�lEs6f)gOILS�vJG�_Lf v�stN/G�FHILNkgH� uEGJgkfhstS�S0m�sh�M�EnYgH_EI^NkstN£B

� � ��� kYih � � A V C'� f h A V �iCEHABf Y�h � r�lEs GJs�S�_E��v�S6K�I ]Rs�f v�K�gOI ��S�lLgjm6S�vJlLFQv6vJlEs shG�GJgOG�gQ��HstIEshG-FQ�MKM�hstN7uYgH�M�=ILgH��KMFH�.f-lLFQg=S���FW�&�HG�gjm­�ÄgHGc��gOIE�QZ³vJstGJ� KMI=vJst�HG-FjvJKMgHI^ShBy]R_Lf-lÂgOnLSJshG MWFQvJKMgHI

Page 27: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ xO{

−4 −3 −2 −1 0 1 2 3 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45exact 1st−order3rd−order5th−order

−4 −3 −2 −1 0 1 2 3 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45exact 1st−order3rd−order5th−order

���������[��� ® p (2(D+_$;o',/&�*27950< v*2J�.0.0,/*'1+_*'1D<2$'&�K�*2+-,/*!3�O 5;.�3�M ��*2?0$!3�,>gB?GFH*2$2. � �Z5Es07�� 2[� 5 � Ñ �Lw�, f�F�7��20� 5 � ×�Ð WuEG�stSJshI=v�S F�f-lLFQ�M�MshIE�Os5gOI vJlEs�f)gOIOv�GJgO�¶gQ��shG�G�gHGÔ�ÄgHG vJKM��s)Z\NkshuYshILNEshI=v uEG�gHnE�Msh��StBÂq u^g=SJSJK�ZnE�M�7G�sh��s�Nk�7��FW�7n^s vJg�G�sh�H_L�MFHGJ�M�7f-lLFHIE�Hs!v�lEs uLFHG�FH��s)vJstG�S T�KMIovJstGJ��ScgQ�¶m�lEKTf-lovJlEs���N�XFQuLuEGJgQkKM��FjvJKMgHI7KMS�S�gO_E�Hl=v�B�r�lEKTS6f-lLFQIL�HsÔgQ�¶uLFHG�FH�5shvJstG�S�fhFHIon^s FOf-lEKMsDMHs�N�s�1&f)KMshI=vJ�M�&�ÄG�gH�FQI�s�S�v�K���Fjv�stN­fhgFMWFHGJKTFQI^f)soPHstGJIEst� ��� nR� v�lEsÂ�ÎFHS�v7FHuEuEG�gQRKM��Fjv�K�gOI�gH�!v�lEs D#e stK��OshI MjFQ��Z_Es�ShB�r�lEs���gOIE�QZ³vJstGJ� KMI=vJst�HG-FjvJKMgHI KMS�SJ_Es�lLFHS!nYshshI FONENkG�stS�S�s�N�KMI � {Q�M�|V¯m�lLshG�s5FHI FONEFQukv�K^MOs� _L� v�K Z\NkgH��FHK�I���N�X FHuEuEG�gOFHf-lÔm�FHSNksDMOsh�MgHuYstN �QSJuYstf)K^]^ftFQ�M���OVj�5gOGJs�sh�Msh��shI=v�S«FHGJsyKMI=vJG�gkNk_Lf)s�NSJsh�Mstf v�K^MOsh�M�ÂK�I gHG-NkshG!v�g�SJ_EuEuEG�stS�S�vJlEs/�ÎFHS�v#�HG�gjm�vJl�gH��stGJG�gHG!FHS�vJlEs�KMI=vJshG MjFQ�«gQ��vJKM�5s�KMI=vJs)Z�HG-Fjv�K�gOI�KMILf)G�stFOS�s�ShB

� � � � _2A Y G � EH@BABf,G [&f,@'G Y�h ABf h `&f A'f V @ � �|vÔKMS�m�sh�M�PRIEgjm�I�vJlLFQv�uYgH�M�=ILgH��KMFH�f-l^FQgOS6�ÎFQKM�MSKMI�F&S�lLgHGJv6vJKM��s#�ÄgHGcvJlEs SJgQZ\fhFH���MstNoDÔG-FQKTf-lEILFHIkZ U�G-SJ�tFQ� vJlEG�shshZ³��gkNks#uEG�gHnL��st��V±f)gOILS�vJG�_Lf v�stNFHS�F�S�KM��uE�MKK]Ls�N���gRNEsh�Ev�g�G�shuEG�stSJshI=v«vJ_EG�nE_E�MshI^f)s6KMI=vJshG-FHf)vJKMgHILS � �RxN�³B �|v�KTSyF#ILgHIE�MK�ILstFQGyvJlEG�shshZNkKM��shILSJK�gOILFQ�LU!a!C�S��kS�vJst� 3

� � ?� �##� U � ` � � � U

� �# � ? � ` � � � `

� �# �cx � ? � U

SJ_En ��stf)v v�g S�vJgkf-lLFHS�vJKTf�KMIEK�vJKTFQ��f)gOILNkK�vJKMgHILStB ]=v-FQILNLFQG-N u^gO���RIEgO�5KTFQ��f-lLFHgOSÔ�ÎFHK��TS�v�g uEG�stNEKMf)vvJlLs5SJgH�M_kvJKMgHI¯V.FQILN K�I �ÎFHf v!vJG�_EILftFjv�stN�sDQkuLFQILSJKMgHILS���FW�ofhgHI MHstGJ�Os#vJg�shG�G�gHIEstgH_LS�S�gO��_kv�K�gOILStBr�lEs���FQKMI G�stFHSJgHI �ÄgHG�vJlEKTS#KTS#vJl^Fjv#vJlLs��ÄGJs'L=_EshILfh� gH��v�lEs&SJgH�M_kvJKMgHI Nkstu^stILNES�gOI vJlEs&G-FQIEZNkgO� MjFQG�KTFQnE�Ms&FQILN FH�MSJgovJl^Fjv�v�lEshG�s&KTS F�NkKTS�f)gHI=v�K�IR_EK�v�� KMI vJlLs&K�ILK v�KMFH��f)gOILNkK�vJKMgHILStB 4cSJK�IL�FQI FHNLFQukv�K^MOs/�/_E� v�K Z|sh�Msh��stIOv���N�X FHuEuEG�gOFOf-l.V£lEgjm�sDMHstGtV±nLFOS�s�N gOI v�lEs��MgRftFQ��MjFQG�KMFHILf)s�fhFHIsRJ±stf)vJK MHst���7GJs�S�gO�^MOs�v�lEKTS6uEG�gHnE�Msh�oVLSJshs � {Q�'�³BV�\I ]L�H_EG�s HRB�xHOÎ��sh�©v P V^m�s�SJlEgjm4vJlEs sDMHgO��_EvJKMgHI�gQ�vJlLs-MjFHGJKTFQILfhsygQ� � ? _LSJK�IL�6vJlLKMS«�/_E� v�K Z|sh�Msh��stIOv¶FQuLuEGJg=FHf-lÔ�ÄgOG«NEKKJ±shG�shI=v�MWFH��_LstSgQ�^FHI/FONEFQukv�K^MOsvJlLGJs�S�lEgO�MN�� ? B �EgOG�f)gH��uLFHGJKTSJgHI�m�s�K�ILfh��_^Nks5vJlEs�G�stSJ_E� v-SÔ�HK MHstI nR����N�X m�K�vJl u^gO���RIEgO��KMFH�gHG-NkstG � #�lOzEBL�|v�fhFHI�n^s!S�stshI�v�lLFjv�f)gH��uLFHGJKMIE�Ôv�g#vJlEs�GJs�S�_L� v-Sy�HK MHstI�n=���ÂgOIOv�sÔX�FHGJ�Mg#m�K v�l}���zHzOz �JzOzHz7GJs�FQ�MK���Fjv�K�gOILShV«��N�X m�K v�l uYgH�M�=ILgH��KMFH��gOG�NEshG<�E# lHzÂnYsh�OK�I^S�v�g���g=S�s�FHftf)_EG-FHfh�Fjv���� � FHILN �ÎFHK��TS5n^st�HgOILN v�lEKMS�uYgHKMI=v5m�lLK��Ms�v�lEso� _E��vJK�Z|sh�Msh��shI=v���N�X f)gHI MOshG��HstS FHS�� ?Nks�f)G�stFHSJstStB��\I ]^�H_EG�s HRB�xHOÎGJKM�Hl=v<P VHm�scSJlEgjm�vJlEs!f)gHG�G�stSJu^gOILNkKMIE�#FHNEFHukvJK MHs���stSJl.B�S s�fhFHI�S�stsvJl^Fjv/FHGJgO_EILN vJlEs&uYgHKMI=v)T # zoK�I G-FQI^NkgH��SJuLFOf)s�gQ� TkV«m�lEshG�s5vJlEs7NkKMS�f)gOI=vJKMI=_LK v�� gRftf)_EG-StVvJlLs!G-FQI^NkgH� st��st�5stI=v�S�FQG�s�SJ��FQ�M��s�S�vN�RvJlEKTS���stFHILS�vJlLFQv�vJlEs#NkKTSJfhgHI=vJKMIR_EK�v��&fhFQI7n^s�ftFQukv�_EG�stNsRJ±stf)vJK MHst��� n=� S���FH���yG-FQI^NkgH� st��st��shI=v�StB�r�lEs�S�s�G�stSJ_E��v�SÔlEgO�MN �ÄgHG�vJlEs&DÔG-FQKTf-lEILFHIkZ U�G-SJ�tFQ�uEG�gHnE�Msh��m�K v�l FoNkKTS�f)gHI=v�K�IR_EK�v���KMI gOIE��� gHIEs MjFQG�KMFHnE�MsHV.ILFH��sh�M� � ? B��\I v�lEG�shs)Z\NkKM��shILSJK�gOILStVlEgjm�sDMOshG�V.vJlLs�IR_E� nYshG/gQ��sh�Msh��stIOv-S G�sBL=_EKMG�stN vJg fhgHI=vJG�gH��FHfhfh_EG-FHf)� KMSeL=_EK v�s�lEKM�Hl SJgÂv�lEKMS� _L� v�K Z|sh�Msh��shI=v6FHNLFQukv�K^MOs!G�sR]^IEsh��shI=v�FQuEuLGJg=FHf-l�nYstfhgH��stS�fhgH��uE_kv-FjvJKMgHI^FQ�M���&sDQku^stILS�K MHsOVkS�sts� {Q�M�|B

Page 28: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

x j µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

t

Var

ianc

e of

y1

MC: 1,000,000ME−GPC: N=46, p=3, θ

1=10−2

ME−GPC: N=106, p=3, θ1=10−3

GPC: p=30

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

ξ

Leng

th o

f Ele

men

ts������� � � ® ������� ������ ��������������� ������������� �!�� �"!���� $#�&%'���(�)����*'�� +�,��� -&%.�/�0"0��12��&���3*'��,�%4������#5%$ ��6

7���89 :��*-�� +9�;�<�)�$��,��� '&%+���<��#����� =���>���$ 2"?&%+�/"��&,)�<�� .��� +�$���@06!ACBED'�)����� ,F������� +������#G�/H)�$9�0"I��12������JK��L�ACBEDM���� +������#G��,N�O��,�P6!��D9�����P��,<@=�Q�(R/���0��� ���� $#TSK�� 0�

� �&U�� c Y � �&`#ABEHABf Y�h EHd2G Y � ��d V � f A W � A!shILshG-FQ�MK��tstN�uYgH�M�RIEgH��KTFQ�kf-lLFHgOS«fhFHI nYs�gHG-NkshG-SgQ�«��FQ�OIEK v�_LNks#��gHG�sÔs-1&f)KMshI=v�v�lLFQIÂS�FQ��uE�MK�IE����shvJlEgkNES6SJ_Lf-lÂFHS���gHI=vJs/X�FHGJ�Mg/��shvJlEgkN£B�qf)gO��uLFQG�KMSJgHI gQ�Ev�lEstSJs�v�m�gÔFQuEuEG�gOFOf-lEstS.�ÄgHG«F�SJstfhgHILNkZ³gOG�NkstG¯g=SJfhK��M�MFQvJgOG0KTS«S�lEgjm�I K�I�r0FHnE�Ms5HkB�}OBq S�KM��K��TFQG�f)gO�5u^FQG�KMSJgHI�KTS�FH�MSJg/SJlEgjm�I�KMI7rFQnE�MsGHkB xEVRm�lEshG�scm�scuEG�stSJshI=v�vJlEsÔf)gO�5uL_kv�FQvJKMgHILFH�f)g=S�vÔ�ÄgOG�F�v�m�gHZ|NkKM��shILSJKMgHILFH�«NEKKJ±_LSJK�gOI s'L=_LFjv�K�gOI m�K�vJl �ÄgH_LG�Z\NkKM�5stILSJK�gOILFQ�¶G-FQILNEgH� KMIEuE_kv-ShBr�lEs FHuEuEG�gHuEG�KTFjvJsÔ��N�X2nLFHSJKMS6KMScsh��uE�Mgj�HstNoFOfhf)gOG�NEK�IE�5v�g�vJlEs v��=uYs�gH�«KMIEuE_Ev�NkKTS�v�GJKMnE_kv�K�gOILShVFQI^N�FQ�M�O��N�X sDQRu^FQILSJK�gOILS.l^FMHs � ��} # lO{�vJstGJ��SFjv¯v�lEKMG�NRZ|gHG-NkstG � #W�'��P #8lEBw6gHvJs�lEshG�svJlLKMS/f)gH��uLFHGJKTSJgHI KMS/FQuEuLGJgQkKM��FQvJs�nYstfhFH_LSJs�vJlEs�I=_L� nYshG gH��GJs�FQ�MK���FjvJKMgHI^SÔK�I@��gHI=vJs7X�FHGJ�MgSJK��/_E�MFQvJKMgHILS!KTSÔNks)v�shG��5KMIEs�N�KMI SJ_Lf-l F7m�FW�7v�lLFjvÔv�lEshKMG#S�gO��_kv�K�gOILSÔFQG�s G�stFOS�gOILFQnE�M�Âf)�MgOSJs�v�gvJlLs#��N�X2S�gO��_EvJKMgHILStBA�EgHG6NEs)v�FHK��TS�gQ�vJlLs�f)gH��uE_Ev�Fjv�K�gOILFQ�£G�stSJ_E��v�StVES�sts � j �M�³Bq6��vJlLgH_E�Ol/��N�X ftFQI5n^s L=_EK�vJs�s-1&fhK�stIOv�VHK�v¶KMS¶S�vJKM���LgHG-NkshG-S¯gH�^��FQ�OIEK�vJ_LNks���gHG�s�sRQkuYshILSJK^MOs

vJl^FQI���shvJlEgkNES��ÄgHG�Nks)v�shG���K�IEKTS�vJKTfcuEG�gHnL��st��StB«��FHS�S�K MHst���5uLFHG�FH���Msh�±S�gO��_EvJKMgHI�FHuEuEG�gOFHf-lLstSyFHGJsOVvJlLshG�s)�ÄgHG�sHV±IEs�f)s�SJS�FQG��ÂFQILN��Ä_kvJ_EG�s5�Ägkf)_LSÔSJlEgH_E�TN n^s5gHI NksDMOsh�MgHuE��shI=vÔgQ�y�ÎFOS�v�FHILN�s�1�fhK�stI=vSJgH� MHshG-StB q6I K���uYgHGJv�FQI=v�SJfhK�stI=vJK^]^fof)gH��uE_EvJKMIE� KTS�S�_Es�KMI@v�lEKMS�fhgHI=vJsDQRv5KTS5vJlR_LS/vJlLsofh��sBMHstGf-lEgOKMfhs¶gQ�RnLFHSJKMS£�Ä_EILf v�K�gOILS.KMIÔvJlLsy��N�X�NkKTS�f)G�s)vJKM�tFQvJKMgHI.B0r�lEsyNkgH_LnE���!gHGJvJlLgH�HgOILFQ�WuYgH�M�RIEgH��KTFQ�TSKMI � lM�ym�lEKTf-l uYshGJ�ÄgHG�� MHstGJ�om�sh�M�0�ÄgOGÔ��KMIEstFHG�uLGJgOnE��st��ShV±v�lEs�uLS�st_LNkg=S�uYstf)vJG-FQ�0vJstf-lLIEK L=_Es�S!gQ�� HN�«vJg7sDMjFQ�M_LFjv�s/s�1&f)KMshI=vJ�M�ÂIEgHIL��KMIEstFHGc�Ä_LILf v�K�gOILFQ�TS!gQ�y��N�X4sRQkuLFHILS�KMgHI^ShV£FQI^NÂvJlLs5FONEFQukv�K^MOs� _L� v�K Z|sh�Msh��shI=v«FQuEuEG�gOFOf-lEstS±KMI7� x j Vj{Q�'�RFHGJs�FQv�v�sh��ukv�S¯vJgcGJs�Nk_Lf)s�f)gO�5uL_kv�FQvJKMgHILFH�Of)gO��uE��sDQkK v��OB

¬.¿YÀE¿±¬.¿±ÁÉ£¿±¦5 ×�9jQl50?�,/.0,/$'1 &V*�T',>1�fYJH1D<25�+ J�1D?05;+-7E*',>1 79M ¸0����¦t¢��³��¢��JÜ5�.�W¢/§ÄªÔ¨WVY° Ê�����¢��c���oª#�� ��W¢��6�� ������Ô�-�W¡o�  ��

¨0�W�WÊ������� ���° �W�J¸HÉ® � �³¢�¢��WÈ)�-�³¡#�-��¡!¨�®W¬¯���QX��<X�¼t�W��²t�T¸j¢�¡W��®�¸�¤)° ÊT®R×�Ï Ñ�¸Q¦t�W�³����È ¢��ÎÍ�V^¢���Ê·�-ÈW¸WÏ Ð Ð Ï�®5 Ï�9�Y �GZ\[�] �5^ �$_$`'a|�0b � �;[>c$_ ¸ � $'&V5n36*'.0,/?AF�M-(�5;+ f!50$'&�5;79+-,/?�(�$'O M'1D$'&�,/*'O .A7/FH*'7�f25;1D5�+_*'O , �;5 ��*!?6$�3G,D(H$'O M'g

1D$'&n, *'O .³¸HªÔ¢���° �����£¨��¢��J®tª#�� ��=®H¦t°h� ®�¸j¨«ª�¦Q¸�Å^�³°J¤t��¡W¢��W��¢�¬¯§|¸Wä�×�Ú!Û�×�Ú Ñ â)Þ|®5 ä�9�d �.e ���0f2g[�] ���$_`�h)��ikj���lGm;�on<�_$l�� ���o`D� [ ¸ �L1I.-$'O K;,/1�f45�O/O , (D79,/?�.07E$�?GFH*'.079,/?A(H*'+-79,/*'O%<2, �k5�+_5�1 79,/*2O�5 � J[*'g7 , $'1 .|¸Hɱ° ���W�t J®WªÔ¢� ��W°h¡W�¯¨�W�WÊT®WªÔ¢��|�=®j¿^�WÈ �³ÈW®�¸O×�Ú�×�ÛTÏ Ð Ð Ï)Þ|¸H�W�=®�Ö)Ð Ú ä�phÖW×�Ï Ï�®5 Ö�9�d ��e ���0f2g[�] �rq Y � � ��stnIc$_��.q �_$`vuV�(w.cf$x �$x � [ ¸ v*2O 5;+6T�,/1 N 1 ,>7E5Y5;O 5�&V5�1 7j*-(2(|+B$;o2,>&V*'79,/$'1 .Y$6s

.67E$;?-FH*2.679, ?=5�O/O , (D79,/?�<', �k5;+B5�1 79, *'Oi5 � J[*'79,/$'1 .|¸j�k¢��|�=®j¬¯¢��Q° �� 0Ð Ï�ÍÄä Ñ�¸j�.§Îɱ¨«ª5¸WÏ Ð Ð Ï�®

Page 29: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ x H

_v� V V [ � `�� �EHGbA Y C@�ÂgOI=vJs)Z�X�FQG��Mg�3 A!stIEshG-FQ�MK��tstN N«gH�M�RIEgH��KTFQ�.X�lLFQg=S�3��� ����� � ��� � _

x�� lO{Hz { j j Q xO{AÔFQ_^SJSJKMFHI z Q ��� x��t}�{Hz }�xHz }t�

z Q�x � lbl ��xQzOz xHxHz }�{E}z Q�x � }Bl �JzHzOz }�z }Bl �JzHzOz

46IEK��ÄgHG�� z Q zE}t� � }��-{Q�Hz �JzOzHz xHz Hj� �JzHzOzz Q zHzE} � j }tz �JzOzHz ��zHzOz l={ }MH�����lOz �JzOzHz

��������� � ����!(�5050<'ghJ�(AsG*2?;79$2+-. 36*'.-50<n$'1=+_5�O *'79,>K�5^��¢J�-�45;+-+B$'+ ���� �����$_s�f25;1D5;+B*'O , �;50< ��$'O M'1D$2&n, *'Oi" FH*2$2.#@ÄÛ a=bc×JÞ7E5�+-&�.9C=K�5;+-.0J�. ��$'1 7E5;gG"%*'+-O $S.0,>&�JHO *'79, $'1 .V@%$ 5�K�5�1 79.9C�s-$'+ � �-���³�³�·�-�*'1D<�Ù0�W� ´�° �³��<2,>.079+-, 3�J�79,/$21 .-W

KMIEuE_Ev�NkKTS�v�GJKMnE_kv�K�gOILS _EILK �ÄgOGJ� AÔFQ_^SJSJKMFHI N«gHKTS�S�gOI nEKMIEgH��KTFQ�� z Q � z Q x z Q�x z Q�x�ÂgHI=v�s�X�FHGJ�Mg {Hz �JzOzHz xHz ��zHzHz }tzHz �JzOzHz {Qz �JzHzOz

��������� � � "%$'.07�?0$'&)(�*'+-,/.-$'1$_s *^798�$'g_<',>&V5�1 .0, $'1D*'OU@$� � Ï�C^<', ��JH.6, $'1 5 � JH*27 , $'1�8�,>7/F sG$'JH+-gB<',>&V5;1 .6, $'1D*'OU@%$ �Ö�C4+B*'1D<2$'&�,>1'(|J�79.�8%,>7/F�<', ��5;+B5;1 7�79M-(�5;.n$6sV<',>.079+-, 3�JH7 , $'1 .GW�f � "eJH.0,>1�f�'+B<'gB$2+B<25;+S50oG(�*'1 .0, $'1 @>a � ä�Cj$'+

5 � JH,>K�*'O 5�1 79O M�� b�× � ä âz5-o-(H*'1 .0,/$'1 7E5�+-&�.GW

5 â�9 iA�re �$] ��x ¸#XZFH5^1 J�&V5�+-, ?0*'OU7 +_56*27 &V5;1 7#$6sV,>1 7E5hf2+B*'OU5 � J[*'79,/$'1 .|¸L¾0Ëh´M° ��¡5Ù¯�W� ¤)¢��³���  ©¼�ÅY�³¢����J¸Rº=° �W¡W° �=¸×�Ú t®5 Ò�9�Y �+i �.s ��xGc$_ �$_$` b���� �$x5l[�o_ ¸�X FH5V$'+-7/FH$6f!$'1D*'O�<25;K�5�O $-(D&V5�1 7v$6sA1D$'1 O ,>1D50*'+Us0JH1D?�79,/$21D*'O .A,/1z.-5�+-, 5�.

$_s*�i$'J�+-, 5�+-g � 5;+-&n,/7E5Us-J�1D?;79,/$'1D*'O .|¸j¨0�W�=®Qª#�� ��=®�¸�Ö)Ñ�Û�×�Ú-Ö� Þ|¸Q�W�=®jä Ñ â�ptä Ú Ï�®5 <9 eA��� � �0f[>[��Ij���x �.q������ ���QsFq$h)�h � �6��^rq����� �_|� c:q Y �+uFj �$_���sFq��$_`!����" �#� �D�ol0x � ¸ �AJH&�5;+-,/?0*'O

?-FH*2O>O 5�1�f!5�.�,>1 7/FH5VJH.05`$_sk(�$'O M'1D$'&�,/*'OL?GFH*2$'.�+B5_(D+B5;.-5�1 7E*'79,/$21 .LsG$'+n.07E$�?GFH*'.079,/?l(D+B$;?65;.0.-5�.|¸E¦h§©¨«ªá ° �W���j�-ÊR°-´Y¦t����¢��h �� $j��ɱ° ���W�� ����WÈW¸� �°��-�W�Q¢��-�yÛTÏ Ð Ð â)Þ|®

5 Ñ�9 u=�%� ��c` ��l[� [ ¸!"j5;, f�F�7E50<,>1 7E5hf2+B*'O)&�5;7/FH$�<!W'& �A.07E$�?GFH*'.079,/? .07 , ��1D5�.0.j&�*27 +-, o ¸áW®£¿^�WÈW®.ªÔ¢��|�=®�¸y× × ÛÎ×�Ú Ú�×JÞ|¸O���=®=×�Ñ â�×�pQ×�Ñ Ò-ÖW®

5 Ú�9 u=��� ��c` ��l[� [+�$_`(� �*)IjD�o_c.m�f$] � ¸ "j5;, f�F�7E56<^,>1 7E5hf2+B*'Oi&V5�7/FH$;<!W&+& �%+_5�.9(�$21 .05`K�*2+-,/*!3�,>O ,>79M`*'1D<^+B5;O ,/g*!3G,/O ,/79M ¸WáW®W¿Y��ÈW®QªÔ¢��|�=®�¸=× × �ÛÎ×�Ú Ú�×JÞ|¸Q�W�=®=×�Ñ Ò â�pQ×�Ñ t®

5 ×�Ð�9 h)�-, [�n��$_c �+�$_$` h)��b �$xGx ��_ ¸ �|7E*'79,>.079,/?0*'O &V50?-F[*'1 ,/?;.k$_s)<2,>.0.0, (�*27 ,/K�5v(�*'+-79,/?;O 5 <'M'1D*'&�,/?;.|¸h¿^�W�³° �W�)¼t�J®º=¢� Î �®�¸Hä Ð�Û�×�Ú Ú â)Þ|¸Q�W�=®O×�Ú�×�pQ×�Ú Ò�®5 × ×�9 u=���%� [�js �$_ ¸ �I$21 795 "%*'+-O $ �A"%$21D?65_(D79. � p O f!$'+-,>7/F�&�. �i*21D< p (2(|O , ?6*27 , $'1 .|¸h¦h�W�³���WÈ ¢��ÎÍ�VY¢���Ê·�-È.Á0¢\¥��^° �³²Q¸§©���)®�¸=×�Ú Ú Ò�®5 ×�Ï�9 eA� ��c-. ¸ �|7 +_*'7E5Ef2,/5;.�s-$2+0/LJH*2.6,/g���$'1 7E5`"�*'+-O $)¸jµ«Ê��h¥£¢��.¨���-¡W¢������¶Å^�W»=®�¸=×�Ú Ú Ú�®5 ×�ä�9 h)���:x �Gf ��_�1 � �O`���x�q iA�2)-�Ij43 ���2q��$_$` Y � �9c`c$x ¸ �:,/1 ,>7E5`5;O 5;&V5�1 7)&�5;7/FH$�<2.ks-$'+=5;O>O , (D79,/?l(D+B$!3�O 5�&

8%,>7/Fj.67E$;?-FH*2.679, ?=?6$;5��Y?;,/5;1 7 .|¸Qɱ° ���W�� �®jªÔ¢\ ��=®j¨0�W�WÊT®jªÔ¢��|�O®W¿Y��È �J®�¸W���c�W��¢�����ÛMÏ Ð Ð-ÖhÞ|®5 ×�Ö�9 "U��u �.sks �D�olGc$_D��qOh)��� �$_ � � ��q;hk�5a�f$_|� q��$_$`V�v�5� �$x4�Ij���[>c_D� ¸ �|7E$;?-FH*2.679, ?v+B5;.-$'1D*'1D?05�¸ ¬.¢�¤H®JªÔ°t¡�¢����Å^�h¼t�J®�¸ -Ð�Û�×�Ú Ú Ñ)Þ|¸Q�W�=®WÏ Ï ä�ptÏ Ñ Ñ�®5 ×�â�9 iA��u �$xG`D�o_ ��x ¸ � *'1D<�3_$;$�Tn$_sL.67E$;?-FH*2.679, ?�&V5�7/FH$;<'.��ZsG$'+i([F�M'.0, ?�. �%?-F[5�&�,>.079+-MA*'1D< 7/FH5�1D*'79J�+B*2O .0?;,/5;1D?05�.|¸¦h�W�³���WÈ ¢��ÎÍ�VY¢���Ê·�-ÈW¸jÏ-�W¡�¢�¡O®�¸R×�Ú Ñ â�®5 ×�Ò�9 Y �0u�j��$_��Is �_$`?h)�-)In��$_c.[ ¸ �|79$;?-F[*'.07 , ?Q�:,>1 ,/7E5 �vO 5�&V5�1 79.��k* �!(H56?;79+B*'O p (2(D+_$�*2?GFt¸W¦t�W�³����È ¢��ÎÍ�V^¢���Ê·�-ÈW¸×�Ú Ú�× ®5 × <9 a|�9u ��� sks �$_`6�V�%)Ij �$xGn ¸�L+_56<2,/?;7 , $'1c*'1D< 7/FH5 � JH*21 7 , N ?0*'79,/$'1c$_s4JH1D?05�+-7E*',/1 79M ¸YÅY�)¼��������/½�¸.×�ä ä

ÛÎ×�Ú Ú Ú)Þ|¸O���=®=×�â Ï�pQ× -Ð�®5 ×�Ñ�9 �l���Fc$f:q����7 A� sFqeA� Y cm)c-8.[�]|�>��q �$_`����+wjc$f ¸)"4, 5�1D5;+l?GFH*2$'. 5-o-(H*'1 .0,/$'1 .n*'1D<`1 JH&V5�+-, ?6*2OZ.-$'O JHg

7 , $'1 . $_s +B*'1D<2$2&nO M#sG$'+B?050<^5 � JH*'79, $'1 .l$_s:uUJH,/<`&�50?GFH*'1 ,/?;.|¸jÅ^�³¢��W�����h �¸=ÛMÏ Ð Ð-ÖhÞ\®5 ×�Ú�9 )Z�9�\f��_|�rq�)Z�;:\f���]rq �$_$`< =�Ch jc.c$_ ¸="%$21 K�5;+ f!5�1D?05I.079J[<'M$_sj7/FH5z79+-JH1D?0*'7E56< mn*'+6F�JH1D5�1 g � $�5;K�5

50oG(�*'1 .0, $'1=sG$'+l.0,/&nJHO *27 , $'1 $6s .07E$�?GFH*'.079,/?#(|+B$�?05;.6.-5;.|¸H§©�) J®HáW®QÁ¯�W��¢��J®WªÔ¢� ��=®Q¿^�WÈ �WÈW®�¸Qâ Ï!ÛMÏ Ð Ð�×JÞ\¸���=®R×�Ð Ï Ú�pQ×�Ð-Ö)ä�®

5 Ï Ð�9 � �3a �$xG` �$] qEiA� =>���?)If:q �$_$` uV�@ +�$xG_|� �$` �$]|� [ ¸��!(H50?�79+B*'O#(H$'O M'1D$2&n, *'O=?-FH*!$'. .0$2O JH79,/$'1 .$_s 7/FH5.67E$;?-FH*2.679, ?=*2<'K�56?;79,/$'1 5 � J[*'79,/$'1j¸QáW®Q¦t���T®jÉ£° ������ J®�¸O× cÛMÏ Ð Ð Ï)Þ\¸Q�W�O®Qä�×�Ú�ptä ä Ñ�®

5 Ï�×�9 d �- �$x ��lGm<�[ �_$`�)Z��)Ij$x �58 � ¸ ��+B$'8�1 ,/*'1�&�$'79, $'1z*'1D<=.07E$�?GFH*'.079,/?l?0*'O ?;J�O J�.|¸Q¦t���³���WÈ ¢���Í&VY¢��³Ê·�-ÈW¸Q×�Ú Ñ Ñ�®

Page 30: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

xQ� µ«¨¬0Á¯§©¨«½.¨«µ«§Î¦H¸ ¦�Ùy¸ ¹§ÄÙy¸ ºkÙ«É.¾«¬¶¸W¦�É.Ã.Õ#¨«Ç¸W¨«Á½��0¾«½¶¾«¬

5 Ï Ï�9 u=�� +�$xG_|� �$` �$]|� [ �$_$` )Z� )0j���x 3 �o_ ¸ �!(H56?;79+B*'O � F;( �LO 5�&V5;1 7 ��5�7/FH$;<'.UsG$'+^",�%Qy¸O¾0Ëh´�° �³¡#Ù¯�W� ¤)¢��³�³�  ©¼Å^�³¢��³��¸=×�Ú Ú Ú�®

5 Ï ä�9 � � +���!� ����x �$_$` �l� �)� ��_ ¸�XZFH5#.07E$�?GFH*'.079,/? N 1 ,/7E5)5;O 5�&V5�1 7%&�5;7/FH$�< ¸�á ° �W��Õ7��Ê�¢\¼��o¦t° �W�YºO ³¡=¸Q×�Ú Ú Ï�®5 Ï-Ö�9 h)�4 +�;c���`���_ �$_`#,)�$h ����l���_ ¸ �#JH&�5;+-,/?0*'O .-$'O JH79,/$'1I$6sk.67E$;?-FH*2.679, ?n<', �k5�+B5;1 79,/*'O 5 � J[*'79,/$'1 .|¸Q¦h�W�³���WÈ ¢��ÎÍV^¢��³Ê·�-ÈW¸R×�Ú Ú Ú�®5 Ï â�9 Y �2 Fc ��]c ��] �$_$` Y �9)�3 �$x5l0lGc$f�3 ¸lXZFH5 p ._T'5;M'gh.-?-F[5�&V5j$_s=F�M-(�5;+ f!56$2&�5;79+-,/?I$'+-7/FH$0f2$21D*'O%(H$'O M'1D$2g

&n, *'O .�*'1D<4,>79. � gB*'1D*'O $6f2J[5�¸H�k¢��³�=®O¬¯¢��Q° �� «Ú Ñ�Í|× t¸H½¢��j�-�� ���¢��h °-´Y�k¢��|���W�����-Ê^ª#�� ��W¢��6�� �������-�W¡§©�t´M° ���6�� ³�����J¸W½¢�Ê ´� ¯Ù¯�W� ¤)¢��³���  ©¼�°-´E�k¢��|���W° Ê�° È-¼)¸k×�Ú Ú Ñ�®5 Ï Ò�9 ����" � � �D�ol0x �q ���� �_D� crq������ ���QsFq �_$` Y �+uFj��_���s ¸ p .079$;?-F[*'.07 , ?)(D+B$���56?;79,/$'1�&�5;7/FH$�<#s-$'+:uLJ�, <

uL$'8 � 36*'.0,/?vs-$'+-&�JHO *'79, $'1j¸HáW®Qɱ° ���W�t J®�ÅY�)¼���®�¸=× -ä�ÛMÏ Ð Ð�×JÞ\¸H�W�O®WÖ)Ñ�×�ptâ�× × ®5 Ï <9 ¸���1D?05�+-7E*',/1 79Mv(D+B$-(H*;f!*'79,/$'1zJH.0,>1�f "4, 5�1D5;+-g � *2*'+k5-oG(�*'1 .0,/$21 .³¸�áW®tɱ° ���W�� �® Å^�h¼t�J®�¸j×�Ú �ÛMÏ Ð Ð-ÖhÞ\¸���=®QÏ Ñ�ptâ t®5 Ï Ñ�9 h)� =>"U�" �of#�$_$`4Z��*� ��x A�of$x ���.jD� �$_ ¸ �:,>1 ,/795`5�O 5�&V5;1 7v+B5;O , *!3G,/O ,/79M4$_sAf!50$'&V5�79+-,/?0*'O/O Mj1D$'1 O ,>1D50*'+VJH1 g

?65;+-7E*',>1�.679+-J[?�79JH+B5;.³¸jáW®j¿Y��ÈW®jªÔ¢��|�=®�¸R× × 6Û�×�Ú Ú�×JÞ|¸Q�W�=®R×�Ñ Ð Ò�pQ×�Ñ Ï â�®5 Ï Ú�9 b��4" �of:q � �Ge � ��^.l0[��Ij$].c:q��$_$`-Z��-� �$_D� ¸ p (2(DO ,/?0*'79,/$'1 .A$_s�(|+B$!36*!3�,>O ,>.079,/? N 1 ,/7E5 5�O 5;&�5;1 7�&V5�7/FH$;<'.#,>1

5�O *'.079,/? � (DO *'.07 , ?=<'M'1D*'&�,/?;.|¸jáj®�¿Y�WÈ ��ÈW®j§©�W¡=®�¸�¨¶¦�ªÔ¿¯¸=×�Ð Ú�ÛÎ×�Ú Ñ Þ|¸Q�W�=®QÏ�ptÑ�®5 ä Ð�9 � ��"�c���58 � ¸ �L+B$�3_*�3G,/O ,/7 M XZFH50$'+-M � � $'JH+-7/Fj50<',>79, $'1j¸H¦h�W�³���WÈ ¢��ÎÍ�VY¢���Ê·�-ÈW¸O×�Ú t®5 ä�×�9 b���"�c$j ¸ �L1� *'79,>1jF�M-(H5�+_?�J 365n.-*'&)(DO ,>1�f)¸Q¨0�W�=®Q¦) |�� �®�¸QÏ-Ö!ÛÎ×�Ú Ú Ò)Þ\¸Q���=®QÏ Ð â Ñ�ptÏ Ð Ñ Ð�®5 ä Ï�9 a|��"�cx ��_$lGm ¸ �A$'1 O ,>1D50*'+ .0,>1�f2J�O *'+�(H5�+-79JH+�36*'79,/$'1�(D+B$!3�O 5;&�. *'1D<�7/FH5 �v1�f � JH,>.079g �L._FH5;+Y<', �k5;+B5;1D?65

.0?GFH5;&�5J¸j�k¢��|�=®j¬¯¢��Q° �� 0Ñ�× ×�â�¸HÙ0��� ¤)¢����³�  ©¼6°-´LÁ¯� ���¢�È ¢��=¸jÁ¯� ���¢�È ¢��=¸t�.�W¢yÁ0¢\ ��W¢��³Ê·�-�W¡W��¸R×�Ú Ñ�× ®5 ä ä�9 �V� "2f��0c$x �$_$` uV� +�$xG_D� �$` �]|� [ ¸ � $',>.0M`,/1;uL$'8�.n?0*'JH.-5S*`._FH50<2<2,>1�f2gh&�$;<25^.68�,>7E?GF�,>1�f^,/1VuL$28(�*'.07

*'1 $'.-?;,>O/O *'79,/1�fS?;M'O ,/1D<25;+\¸�ÅY�)¼���®Q¬.¢�¤H®Wº=¢� Î �®�¸QÚ Ï�Û�×�â)Þ¶ÛTÏ Ð Ð-ÖhÞ|¸Q�=®O×�â-Ö)â Ð�× ®5 ä-Ö�9 �V�7"2f��0c$x�qri#� =>���)If:q �$_$`=u=�� +�xG_D� �$` �$] � [ ¸ v5�1D5;+B*'O , �;50<�(�$'O M'1D$'&�,/*'O:?-FH*!$'.n*'1D<^+B*'1D<!$'&r$'.-?;,>O g

O *'7E$'+-.|¸Q§©�h �®QáW®jÁ¯�W��¢��J®�ªÔ¢\ ³�=®W¿Y�WÈ �WÈW®�¸jÒ Ð�ÛTÏ Ð Ð-ÖhÞ|¸Q�W�=®Wâ t×�ptâ Ú Ò�®5 ä â�9 ¸Lmn*'+6F�JH1D5�1 g � $�5;K�54+B5_(D+B5;.-5�1 7E*'79,/$21e$_s (�5;+-,/$;<',/?I.050?0$'1D<'g_$'+B<25;+4*2J�7E$'gh+_5Ef2+B5;.0.6,/K�5V(|+B$�?05;.6.-5;.|¸Y���

Å^�³°h��¢�¢�¡W����È �!°-´�§©�h �¢��³�j�� ���° �j�-Ê�ɱ° ��´�¢���¢��W��¢ ° �ÂÉ£° ������ |�� ���° �j�-Êy¦h����¢��W��¢ ¸¶á �W��¢/Ò�Í©Ú�¸µ«�³�-² °J¥y¸ÅE° Ê·�-�W¡O¸QÏ Ð Ð-ÖW®

5 ä Ò�9 h)�7� ����� ����� 33[�]|� �$_$` Y �*�-c�151���l ¸ � 50*'7L79+B*'1 .>s-5;+l8�,>7/FjK�5;+-MVF�, f�Fns0+B505;gh.07 +_56*2& 7 JH+�3�J�O 5�1D?05�W �v*'+-7 &g �:o-(H5�+-,/&�5;1 7E*'Oi<2*'7E* ¸Qá ° �W���j�-ÊR°-´^Ã0¢��� ¯�k�|�-�W�δM¢���¸O× ×�ÖÔÛÎ×�Ú Ú Ï)Þ\¸Q���=®QÑ Ï �ptÑ ä ä�®

5 ä <9 ���*� �$`$x �[ ¸ �Z50?�79JH+B5�.�$'1 �I$21 795I"%*'+-O $^&V5;7>F[$�<'.|¸R¨0��¢��³�����-�#ª#�� ��W¢��6�� ³�����-Ê^¦t°h����¢\ ©¼)¸OÅY�³°�¤���¡�¢�����¢ ¸¬.§|¸QÏ Ð Ð Ï�®

5 ä Ñ�9 "U� � ��l0j�� ���o_ �$_$` �� �\f[>[��D�o_D� ¸ p .07E$�?GFH*'.079,/?z?0$'O/O $;?6*27 , $'1�*'O f!$'+-,/7>FH& s-$'+^J�1D?05;+-79*2,>1 79MI*'1D*'O M'.0,>.|¸�k¢��|�O®H¬¯¢��Q° �� 0Á0¨«¦t¨ K É£¬£ÍÄÏ Ð Ð ä�ÍÄÏ�×�Ï�×�â ä�¸HÁ¯¨¶¦t¨�ºk�-�WÈ Ê�¢\¼!¬¯¢���¢J�-���|�#ɱ¢��) ³¢��J¸jÏ Ð Ð ä�®

5 ä Ú�9 b��;� ����xG] �stn 1$q)�l�)�Cx0f��6�$_crq)�$_$` iA� �k�ox$[��Ij ¸ |5;+-, N ?0*'79,/$'1 �VK�*2O , <2*'79,/$'1 �S*'1D<j(D+_56<2,/?;7 ,/K�5 ?0*'g(�*!3�,>O ,>79M`,/1 ?0$'&)(DJH79*27 , $'1D*'O:5�1�f2,>1D505;+-,>1�f^*'1D<�([F�M'.0,/?;.|¸Q�k¢��|�=®H¬.¢��Q° �� y¦h¨«Á½Ï Ð Ð ä�ÍÄä -Ò Ú�¸=¦��-�W¡W�·�Á0�� ³��° �W�-Êkºk�-»Q° �|�� �° �³��¢��J¸WÏ Ð Ð ä�®

5 Ö)Ð�9 ��� �A�f$x � ¸��L+-7>F[$6f!$'1D*'OZs-J�1D?;79,/$'1D*'O .`$_s`7/FH5 ��$',>.0.-$'1�(|+B$�?05;.6.|¸±§©¿^¿Y¿ �k�³�-�W�J®R§©��´M°W®E�.�W¢�° �μh¸^§©�£Í|×�ÑÛÎ×�Ú -Ï)Þ|¸O���=®WÖ�-ä�phÖ)Ñ�× ®

5 ÖW×�9 eA� �\].[���_$` ��� ¸ �|7E$�?GFH*'.079,/?j<', ��5;+B5;1 79,/*'OL5 � J[*'79,/$21 .-W p 1,/1 79+B$�<'J[?;7 , $'1Y8�,>7/F *G(2(DO ,/?0*'79,/$'1 .|¸£¦h�W�³���WÈ ¢��ÎÍV^¢��³Ê·�-ÈW¸-$�´� ��!¢�¡=®�¸O×�Ú Ú Ñ�®

5 Ö)Ï�9 )Z� �Fx$[>m��D� �$_$` "U� eL� [>[>c$_$_ ��l0l�� ¸UQ M'1D*'&�,/?0*'O (D+B$G(�5;+-7 , 5�.S$6s=79+-JH1D?6*27950< "4,/5;1D5�+-g � 5;+-&n,/7E5`5-o-(H*'1 g.6, $'1 .|¸jÅ^�h¼t�J®WÀLÊ�����¡W�J¸H×�Ð�ÛÎ×�Ú Ò Þ\¸H�W�=®WÏ Ò Ð ä�ptÏ Ò�×�ä�®

5 Ö)ä�9 =�$h jc.c$_:q )Z���\f��$_|� q �$_$`!)Z��:Ff���] ¸4&-&k(DO 5;&�5;1 7E*'79,/$'1�$6skmn*'+6F�JH1D5;1 g �Z$�5;K�5n5-o-(H*'1 .0,/$'1=s-$'+A.0,/&nJHgO *'79, $'1�JH.0,>1�f`*S8�*2K�5;O 5;79g v*'O 5�+6T',>1�.0?GFH5;&�5J¸WÅ^�³° »=®�¿Y�WÈW®jªÔ¢��³�=®�¸=× cÛMÏ Ð Ð Ï)Þ|¸Q�W�=®QÏ Ú ä�ptä Ð ä�®

5 Ö Ö�9 �l�+htc$l0l�� ���Gfs ¸vX FH5=+B5;O *27 , $'1 ._F�, (Y365;798�505�1 1D50*'+-gh8�*�T'5=.079+-J[?�79JH+B5S*'1D<`FH50*'7k7 +_*'1 .>s-5;+LsG$'+�*21 $'.-?;,>O gO *'79,/1�f`?;M'O ,>1D<25;+A,>1�?;+B$'.0.0g uv$'8L¸jÅY�W½  ��W¢��³���J¸jÉ£�-Ê�� ´M° ���W�·��§©�W�Π³�  ��� �¢y°-´E�k¢��³�W�W° Ê�° È-¼)¸OÏ Ð Ð ä�®

5 Ö)â�9 � � Y �����[��Ij���].j��$x4�$_$` eA�;, �����o_|��3�cc$` ¸ p 1D5;8�O $;$�T*'7n7/FH5�+B5;. (H$'1 .-5�.0JH+/s-*2?05 *-(2(D+_$�*2?GF�sG$'++B5�O ,/*�3G,/O ,/7 M^*'1D*'O M'.6,/.|¸Q¦h ³���W� ®H¦���´�¢\ ©¼h¸=×�Ï ä�Û�×�Ú Ú ä)Þ|¸H�W�=®WÏ Ð â�ptÏ Ï Ð�®

5 Ö)Ò�9 b��7)-�Ijcf$l���_[ ¸ �|7E$�?GFH*'.079,/?#(D+B$;?05�.0.-5�.l,>1I7/FH5 p ._T25�M=.-?GFH5;&�5J¸�ÅY�j½� ³�W¢������J¸jµ�® Ùy®WºR¢���¤)¢��=¸=×�Ú Ú Ú�®5 Ö�<9 iA�7)-�Ij43 ��� ¸�(|g�*'1D<SF;(DgB�:,/1 ,>7E5 �LO 5�&V5;1 7 �I5;7/FH$�<2.³¸H¾0Ët´�° �³¡!¦t����¢��W��¢yÅY�W»WÊ������� ���° �W�J¸=×�Ú Ú Ñ�®5 Ö)Ñ�9 iA�)4��j�3 � ���$_$` Y ���9c`c$x ¸ �!(�*2+-.05 N 1 ,>7E5`5;O 5�&V5�1 79.Ls-$'+=5;O>O , (D79,/? (D+B$!3�O 5;&�.�8�,>7/F�.07E$�?GFH*'.079,/?`<!*'7E* ¸

Á¯�W��¢��J®�ª#�� ³�O®�¸QÚ â�ÛMÏ Ð Ð ä)Þ\¸Q�W�O® -Ð �p -ä-ÖW®5 Ö)Ú�9 ¸ �!(�*'+-.-5 N 1 ,/795�5;O 5;&�5;1 79.%s-$'+A.07E$�?GFH*'.079,/?V5;O>O , (D79,/?k(D+B$�3GO 5�&�.0g9F�, f�FH5;+n$2+B<25;+ &�$2&�5;1 79.³¸Hɱ° ���W�� ÎÍ����ÈW¸ t×�ÛMÏ Ð Ð ä)Þ\¸Q�W�O®WÖ)ä�ptÒ ä�®5 â Ð�9 ¸ mn*'+6F�JH1D5�1 g � $�5;K�5 *G(2(D+B$;o2,>&V*'79,/$21�$_s)+B*21D<2$'& N 5�O <'.A3GMAf25;1D5�+_*'O , �;56<)s-*'.07%&�JHO 79, (H$'O 5l&V5�7/FH$;<'.|¸�����W�³¢��j�-�³�� ³��° �O¸RÛTÏ Ð Ð-ÖhÞ|®5 â�×�9 �l�2)Ij��$xG` �Oc43 ¸ �!(|O ,/7 79,/1�fls-$2+S<',>.0.0, (H*'79,>K�5n(H*'+-79,/?;O 54<'M'1D*'&�,/?;.|¸^¦t§©¨ª9áW®E¦h���T®kɱ° ���W�� �®�¸EÏ-Ö/ÛMÏ Ð Ð ä)Þ\¸

���=®R×�Ï Ò �pQ×�Ï Ñ Ï�®5 â Ï�9 � ��)0jD�o_cm�f$] � �$_$`Ku=��� ��c` ��l[� [ ¸Dwv5;. (H$'1 .-5VK�*2+-,/*!3�,>O ,>79M=$_s .67E$;?-FH*2.679, ? N 1 ,/7E5n5;O 5;&V5�1 7:.0M'.67E5;&n.|¸jáW®¿^�WÈW®QªÔ¢��|�=®�¸O× ×�ÖÔÛ�×�Ú Ñ Ñ)Þ|¸Q�W�=®�Ö)Ú Ú�ptâ�×�Ú�®5 â ä�9 ,)�2)H� sU�of ¸�" FH*!$'79,/? X +B*'1 .0,/7 , $'1,>1 Ql5;795;+-&�,>1 ,>.079,/?^*'1D< �|7E$�?GFH*'.079,/? �|M'.07E5�&�.|¸=ÅY�³������¢\ �° ��Ù¯�W� ¤)¢��³�³�  ©¼

Å^�³¢��³��¸jÏ Ð Ð Ï�®

Page 31: A5B C6BED#FHGJILKMFONEFQPRKTSJUWVYX B...\I v lEKTS!fhgHI=vJs DQ RvtVYvJlEs f) TFHS SJKMftFQ 0S vJgkf-lLFOS v KMf/fhFH Mfh_E K«Nkg7IEgQvÔGJs FHNkKM M FHuEuE M FQILNÂlLshILfhs/gHvJlEstG

� ¿±Á0¿Y¬¯¨0ºR§��H¿Y½ ű¾º��¶Á¾«ªÔ§©¨º5É£Ã0¨0¾¶¦cÀE¾«¬Â½0§©ÀLÀE¿Y¬¯¿YÁ0�.§©¨º/¿��«Ù0¨L�.§Î¾«Á«¦ xH�

5 â-Ö�9 h)�2)In��$_c.[ �$_$` Y �tu�j��$_��Is ¸ �|7E$;?-FH*2.679, ? N 1 ,/7E5^5;O 5;&V5�1 7A5-o-(H*'1 .0,/$'1zs-$'+S+_*'1D<2$'& &V50<',/* ¸YáW®k¿^�WÈW®ªÔ¢��|�O®�¸R× ×�â�ÛÎ×�Ú Ñ Ú)Þ\¸Q�W�O®R×�Ð ä â�pQ×�Ð â ä�®

5 â â�9 �l�����$] �` � ¸ "z5�, f�F�7E50<=,/1 795hf2+B*'OZ&�5;7/FH$�<`,>1z.07E$�?GFH*'.079,/? N 1 ,>7E5l5;O 5�&V5�1 7L*'1D*2O M'.0,>.|¸WÅ^�³° »=®t¿Y�WÈW®WªÔ¢��|�=®�¸âcÛ�×�Ú Ú Ð)Þ|¸Q�W�=®R×�Ö)Ò�pQ×�â Ò�®5 â Ò�9 Y � Z�� �9c`c$x ¸ �#JH&V5�+-, ?6*2Ov*'1D*'O M'.6,/.`$_s v*'O 5�+6T',>1C� � � sG$'+S.07E$�?GFH*'.079,/?z5;O>O , (D79, ? �UQ �L.|¸LÅY�j½  ³�W¢������J¸

¿^�¯Ã �E¸W�����W��¢��j�-�|�� ���° �=®5 â <9 ����8 �$_ �9x � ��[ ¸iQ 5;7E50?�79,/$21 �v5;.079,>&V*'79,/$'1 *'1D<4&�$;<'J�O *'79,/$217>F[56$2+-M �%(�*'+-7 � ¸jÕ7��Ê�¢\¼ÔÅY��¢��³�J¸HÁ¯¢\¥ �^° �³²Q¸

×�Ú Ò Ñ�®5 â Ñ�9 ,)��� �_s �$x4�I] � �$_`�� �+uFx ���+c$x �of ¸ �|7E$�?GFH*'.079,/? N 1 ,>7E5�5�O 5;&�5;1 7:*21D*'O M'.0,/.l$_s#.0,/&k(DO 5=3656*2&n.|¸QáW®W¿^�WÈW®

ªÔ¢��|�O¸R×�Ð Ú!Û�×�Ú Ñ ä)Þ|¸Q�W�=®O×�Ï Ð ä�pQ×�Ï�×�ÖW®5 â Ú�9�� �;b �$_ �_$`�uV�5 +�xG_D� �$` �$] � [ ¸ p 1S*!<2*-(D79,>K�5)&nJHO 7 ,/gB5;O 5;&�5;1 7|f25;1D5;+B*'O , �;50<v(�$2O M'1D$'&�,/*2OD?-FH*!$'.v&V5�7/FH$;<

s-$'+ .07E$�?GFH*'.079,/?=<2, �k5�+_5�1 79,/*2OZ5 � JH*'79, $'1 .|¸jáj®QÉ£° ������ J®�ÅY�)¼���®�¸W���W»W���  Î ³¢�¡/ÛMÏ Ð Ð-ÖhÞ|®5 Ò Ð�9 ¸ �k5�M2$'1D< "4, 5�1D5;+-g p ._T'5;Mn5-o-(H*'1 .0,/$'1 .�� � *'1D<[O ,>1�fV*'+�3�,>79+B*2+-M��UQ �:.|¸táW®�¦t���T®Wɱ° ���W�t J®�¸)���W»W���  ÎÍ �¢�¡5ÛMÏ Ð Ð-ÖhÞ\®5 Ò�×�9 ¸ p s-*'.07 v*2J�.0.l79+B*21 .�sG$'+-& � f25;1D5;+B*'O , �;50<S(�$2O M'1D$'&�,/*2O:?GFH*2$'.�.-$'O K�5;+LsG$'+ �Q +B*21D<2$'&r<2, ��J�.0, $'1

8%,>7/F^F�, f�F�gB<',/&�5;1 .0,/$'1D*2O�.079$;?-F[*'.07 , ?V?6$;5��Y?;,/5;1 7M¸jáW®Qɱ° ���W�� �®WÅ^�h¼t�J®�¸��³�W»����  � �¢�¡/ÛMÏ Ð Ð-ÖhÞ\®5 Ò Ï�9�� �;b �$_:q��V� � �ofrq �$_$`?u=�5 +�$xG_D� �$` �]|� [ ¸ �|79$;?-F[*'.07 , ?�.-$'O JH7 , $'1 . s-$2+L7>F[5�798�$2gB<',>&V5;1 .6, $'1D*'O *2<'K�50?�79, $'1 g

<', ��JH.6, $'1 5 � JH*27 , $'1j¸H¦t§©¨ª áW®H¦t���T®jÉ£° ������ J®�¸��������³¢��³�¶ÛMÏ Ð Ð-ÖhÞ\®5 Ò ä�9 u=�5b j|�ol6�I[0�o`���[2�$_$`�eA�0u�x$m<^ �Gc-33[�] � ¸ � 5�O s0g_*'.0.05;&=3GO Ml*'7�*'O/O .-?6*2O 5;.|¸t¦h����¢��W��¢ ¸tÏ Ú â�ÛTÏ Ð Ð Ï)Þ|¸t�W�=®)Ï-ÖW×�Ñ�pÏ-Ö)Ï�× ®

5 Ò-Ö�9 h)�$b jD�ol0l���� ¸ �L1z.67E*'79, $'1D*'+-M (D+_$�?05�.0.-5;.l,>1z7/FH5)(DO *'1D5J¸QDZ��° ��¢\ ��³��²���¸�ÖW×�ÛÎ×�Ú â-ÖhÞ|¸Q�W�=®jÖ)ä-Ö)phÖ Ö)Ú�®5 Ò â�9 ���$be� ��_���x ¸:X FH5lFH$'&V$6f!5�1D50$'JH.n?GFH*2$'.|¸Q¨��¢��J®táW®Qª#�� ��=®�¸jÒ ÐcÛ�×�Ú ä Ñ)Þ|¸Q�W�=®QÑ Ú �ptÚ ä Ò�®5 Ò Ò�9 iA�+be� ����� �sk[>c$_ �$_`=Z�� Y c.[�j$]c ¸�|$'+-7E50o sG$'+-&V*'79,/$'1 ,>1 7/FH5=8:*�T25`$_sV*21 $2.0?;,>O/O *27 ,/1�fj?;M'O ,/1D<25�+\¸RáW®

ÀEÊ��W��¡!ªÔ¢��|�=®�¸jÏcÛ�×�Ú Ñ Ñ)Þ|¸Q�W�=®Wä â â�ptä Ñ�× ®5 Ò <9 �V� � �of ¸� v5;1D5�+B*2O , ��50<I@�"4,/5;1D5�+-g p ._T25�M-C)(�$'O M'1D$'&�,/*'O�?-FH*!$'.|¸QÅ^�j½Â ³�W¢������J¸QDZ��°J¥¯�!Ù¯�W� ¤)¢��³���  ©¼h¸WÏ Ð Ð-ÖW®5 Ò Ñ�9 �V� � �of �$_$` aD� � ��[�l0j���8 ��_ ¸ � , f�F�$'+_<25�+ ?0$'O>O $�?0*'79,/$21�&V5�7/FH$;<'.VsG$'+�<', �k5�+B5;1 79,/*'O 5 � JH*27 , $'1 .I8�,>7/F

+B*'1D<2$'& ,>1'(DJH79.³¸H¦t§©¨«ª4áW®H¦t���T®Qɱ° ���W�� �®�¸W���W»W���  Î ³¢�¡�ÛTÏ Ð Ð-ÖhÞ|®5 Ò Ú�9 �V� � �of �$_$` u=�% +�$xG_D� �` �$]|� [ ¸���$;<25�O ,>1�fYJH1D?05�+-7E*',/1 7 M,/1c.07950*2<2M.079*2795 <', �vJH.0,/$'1Y(D+B$!3�O 5;&�.IK;, *

f25;1D5�+_*'O , �;56<�(�$'O M'1D$'&�,/*'OD?GFH*2$2.³¸hɱ° ���W�� �®-ªÔ¢\ ��W°t¡��L¨0�W�WÊT®Jª#�� ��=®-¿^�WÈ �³ÈW®�¸t×�Ú�×0ÛMÏ Ð Ð Ï)Þ\¸)���=®-Ö)Ú Ï �pÖ)Ú-Ö)Ñ�®

5 -Ð�9 ¸�XZFH5 "4,/5;1D5�+-g p ._T25�Mk(�$'O M'1D$'&�,/*'Oi?GFH*2$'.�sG$'+#.67E$;?-FH*2.679, ?n<', �k5�+B5;1 79,/*'OZ5 � J[*'79,/$'1 .|¸Q¦t§©¨ª4áW®�¦t���T®É±° ���W�t J®�¸WÏ-Ö!ÛTÏ Ð Ð Ï)Þ|¸Q�W�=®jÒ�×�Ú�ptÒ-Ö ÖW®5 t×�9 ¸ p 1D5�8 .079$;?-F[*'.07 , ? *G(2(D+B$;*2?-Fc7E$79+B*'1 .0,/5;1 7nFH50*'7=?0$'1D<'J[?�79,/$21c&�$;<25�O ,>1�fY8�,>7/F JH1D?65;+-7E*',>1 79M ¸

§©�) �¢���®HáW®jÃ0¢��� 0ª#�-�³�¯�k�|�-���J®�¸t�����W��¢��³�yÛTÏ Ð Ð ä)Þ|®5 -Ï�9 ¸ �|J�(�5;+-.-5�1 .0,/7 ,/K;,/79M�<'J[5A7E$�J�1D?05;+-7E*',>1z36$'J�1D<!*'+-M=?6$21D<',>79,/$21 .³¸�§©�) J®�áW®hÁ0�W��¢���®)ªÔ¢\ ³�=®h¿^�WÈ �WÈW®�¸h���

���³¢��³�yÛTÏ Ð Ð-ÖhÞ|®5 -ä�9 b��Gwj$frq��V� Y ��_:q��$_$` b���b f ¸ �|7E$�?GFH*'.079,/?�� � � 36*'.-50<=$'1^O $�?0*'O *'K�5�+_*;f25l$_sk+B*'1D<2$2& K�50?�7E$'+ N 5�O <'.|¸áW®j¿^�WÈW®jªÔ¢��|�O®�¸R× ×�Ñ�ÛÎ×�Ú Ú Ï)Þ\¸Q�W�O®jÖ)Ú Ò�ptâ�× × ®5 �Ö�9 b��rw$jf �$_`Kb��2b f ¸ p .07E$�?GFH*'.079,/? N 1 ,/7E5=5�O 5�&V5;1 7�&V5�7/FH$;<ls-$'+�+B50*'O�5;, f!5;1 K�*'O J[5A(D+B$!3�O 5�&�.|¸OÅY��° »=®¿^�WÈW®QªÔ¢��|�=®�¸WÒ�ÛÎ×�Ú Ú�×JÞ\¸Q�W�O®QÏ Ï Ñ�ptÏ ä Ï�®