wvwoipkq - pulsar.ca.astro.itpulsar.ca.astro.it/pulsar/tesi/bachetti/tesibachetti.pdf · ,fdf*}79*)...

50

Upload: vandung

Post on 12-Sep-2018

215 views

Category:

Documents


0 download

TRANSCRIPT

����������� ����������������������������� �"!#���$�$!#%�

&#')(�*)+-,/.103254(�2-6�798:61;<;�=#&>&?=A@ @B= C?*)DFEF*G092IH5')J3DF6%'K2L7M&�2-EF2-(%'

N OIPRQTS<PRU VWO XZYW[I\]U^S OI_ \]OI\G`MQba O cZOI_WU^SdOfe

OI[ XWSdg^cZ[hQia U VjQi[I[IU Pkgl_jmnQTS<a U

VjQiO PRUo_WVWOIVWUp`dO

qr6�EF25092�+s')J9Dt6%'1,uDt2L6:797A')+-6v092xw;<'y,t,u6:*�z?')(/{96:,t,u2

|�6:+s'y,F*}DF6yw~ Dt*)��=n@ 2-(�*}+-�K����� ��2-(�*

C?*���DF6:+s'y,F*}DF6yw09*),t,%=�� 7909DF6�'��r*}EFEt6�7�,u2

� 7979*G��(�(%'y096��G2L(:*��)�)���}�}�)�)�}�

�"_WVWOIPkQ

�:��� ���I�r�r�������r� �� � ��r�r� �$��� ���I���I�%����¡5� �¢ = ¢ ��'yDu')�G6:,FDF2I*}EtEF6�D¤£y'y,u2¥£2<=B=¦=B=¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦= ¢¢ =¨� H5'K��*)DF��')8�2-*}796©036�+L+-6 ~ J9+-Eu')Dl=¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦= ª¢ =�� HI6§��2-+L+L2-EF6:(�*}790 ~ J9+LEF')DFE =¦=B=¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦= «

¬ ­�® �I����¯$��� °²±A³´� ���#µ�³%��¶}±·�r�¸¯�¯��<¹º�$¯�¯��$³��¸¶}���r�º»��r¯$³:±9��¼��$�5±9����� ��½�= ¢ H5' ~ DF*¸(�6�03J9Du'K092�,F2L�G2L79¾16§+-6¿EFJ96 ~ *),u6:798�2L')+L2¥,/. =B=¦=B=§=¦=B=¦=¦=B=¦= ¢ ��=¨� � ~3~ +L2-(%')8:2L*}792�096�+-+s' ~ Dt*(:6�09J3Du'K096�+h,F2L�G2L79¾"'y+L+L6 ~ J9+LEF')Df')+h�G2L+-+L2-EF6�(:*}7909* ¢ ª

À �"¹Á��� �I�r�?�r�?����¶}�¸��¶}± ¬#¬�3= ¢ HI6¿��')EF2I096:+L+L'1DF2L(:6�Dt(%'l=¦=B=¦=B=¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=Â�}��3=¨� H5'GDt2L(:6�DF(�'"092 ~ J9+-Eu')D�2-7MEt2LE¤,u6��G2hÃ92-7A')Dt2 =¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=Â�)«

�3=¨�= ¢ |f2L(:6�Dt(%'"(�*¸6�Dt6�7�,u6¿=¦=B=¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=Â�}Ä�3=¨�=¨� |f2L(:6�Dt(%'"2L79(:*6:DF6:7�,F6 =¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=p�}�

Å Æ�Ç È9É}Ê�ËÌ9Í�Î�ÈÏ#Ç�Ê)Ð �Ñ��¯Ò¶}±A³:�k���ÒÓKÔ�ÕWÖ �¸×A½5�}Ø/¬I�¸À#½ À#¬ª9= ¢ Ù + ~ Dt*}Ã9+L6:�Ú'1036�+L+L'1(�*}7��6�DF��'"096�2I(�')79092-0A'y,F2Û=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=p���ª9=¨� 4¸,FDFJ3,t,uJ9DF'G092�Ü Ç%È9É}ʸËÌ3Í�Î�È3Ï#Ç�Ê)Ð =B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=p�}�ª9=�� Ù +I+s'%£)*}DF*KEt£)*}+-,F* =B=¦=¦=B=¦=B=¦=¦=B=§=¦=B=¦=B=¦=¦=B=¦=B=§=¦=B=¦=¦=B=¦=p�}«

ª9=��3= ¢ Ý ,u2-+L2L8:8�*1032�Ü Ç%È9É}Ê�Ë3Ì3Í�Î�ÈÏ�Ç�Ê)Ð 796�+I(�')EF*G092I�Þ43|àß ¢ á � ¢ �¤� ¢ �}� ª��� ����¶�¯���³������r� Å�¬â"��¼�¯����#ã#��±3µ�± Å�ÀÕ]���rã#��±9����±A¹Á�¸����� Å#Å

�"_ä`åSdgæVWYjçèOhgo_jQ

Ù + ~ DF2L�G*ÚDt2L+-6:£y')�G6�7�,u*�092>J97A' ~ J9+LEF')Dv'%£�£}6:79796G796�+ ¢ é «�Ä=§H5'�09*y,F,u*)Du')7909']ß)*(:6�+¥ê7z?6:+L+¿Et,u'%£)'REt,FJ9092L')7909*è(�*}7ë2L+¿EtJ9*èDF6�+L'y,u*)DF6Ñ�©7�,F{9*}7�êíì 6:îf2-EF{í2L+�ïñðA2L(/òy6�DF2-79¾yó²096�2EF6:¾}7A')+-2 ~ Dt* £}6�732L6�7�,F2>0A')2�ô¸J9')Eu')D:õIô�JA')7909*]Et2>2L��ÃA'y,F,Fö�2-7²J97A'�Et*}Dt,u'�092�DtJ9��*)DF61(/{96EF2ÒDF2 ~ 6´,u6:£y'<*)¾}792��y�<*}DF6Ú6å÷)«<�G2L7�J3,F2xõ�J37k¾}2L*}Dt79*<Et2L096:Du')+-6Ú6:Eu'y,t,u*9=·øvJ96:Et,%�ùJ9+¥,u2L�G*~ ')D¤,u2-(�*}+L')DF6M��')(�6´£)'k(�' ~ 2LDt6Ñ(/{96ú6�EtEF* ~ DF* £}6:792-£y'k0A')+-+x�ù6�Et,F6�Dt79*k096�+¿Et2LE¤,u6���'kEF*}+L')DF6y=�©79')+L2-8�8%'y7909* ô�J96:Et,u*�DFJ3��*}Dt6�(�2}Et2�')(:(�*}DtEF6n(/{96n6�EtEF*f6�DF'f2-7¿DF6�')+-,u. J97§EF6�¾)7A')+L6 ~ J9+LEF'y,u*'%£}6:7�,F6BJ37 ~ 6�Dt2L*¸09*"(�*)Et,/'y7�,F6§092 ¢ =��}��Ä�E:=ÒH��ù6�Et2LEt,F6�798�'G032IJ97åEF6�¾)7A')+L6¿(:*}Eñû ~ DF6�(:2LEt*G+-2~ *}Dt,F�G2-7dJ37 ~ Dt2L�G*K��*}�G6�7�,F*�'y0d2 ~ *),F2L8:8%')Dt6¿+s' ~ DF6:EF6:798%'Ú032IJ97<�G6�EtEu')¾}¾)2L*G')+L2-6�79*3=qrJ3,F,u' £¸2L'3õ ~ *(:*·,F6�� ~ *·09* ~ *ÁEt(�* ~ Dt2LDt*}79*·J97i')+¥,uDt*�Et6�¾}7A'y+L6d')7A')+-*}¾}*ú2L7èJ97h��')+-,FDF*~ J97�,F*�096:+5(�2L6:+L*9=nü�EtEF2�')797�J979(:2s')Dt*}79*K+s'"EF(:* ~ 6�Dt,u'G032Iô¸J36�Et,F2��G2LE¤,u6:DF2L*)EF2�*)¾}¾}6:,t,u2I(/{96J97M(�*}DtDF2-E ~ *}79096:7�,F6§EF(�2-6�7�,u2¥ýA(�*K096:+>þBÿ������������ ���tÿ���B(/{92s')�G����������ÿ������ ¢�� =

� ¾}¾}2�(�*)79*}EF(:2s')�G*å(�2-DF(%' ¢ ÷y�}� ~ J9+LEF')D¿6�0�2L+���6:79*}�G6�79*Mö�E¤,/'y,F*dE ~ 2L6:¾�'y,F*M*)DF��')22L7���*)+-,u2#EtJ9*}2�')E ~ 6:,t,u2xw�+L6 ~ J9+LEF')D?Et*}79*1E¤,u6�+-+L6 092�736�J3,FDF*}792�(/{96)õ309*),/'�,u6©032�J97](�')� ~ *��')¾}796´,u2L(:*]6�E¤,uDF6:�Ú'y��6:7�,F6�6:+L6´£)'�,u*9õI6:��6´,F,u*)79*dDF')092L')8�2-*}79616:+L6:,t,uDt*}�Ú'y¾}796:,F2L(�'�796�+-+L6*}79036MDF')092-*�'y+L+x�ù2L7�,F6�DF73*Ñ092�J97b(:*}79*·2L+ (:J92�')EFEt6döM+x��')EtEF6å�Ú'y¾}796:,F2L(:*9=T46å+x��')EFEt6dö2L73(�+L2-7A'y,F*ÚDF2-E ~ 6:,t,u*M')+L+$�¨'yEFEF6�092>DF*y,/')8:2L*}796yõh+s'�E¤,u6:+L+s'�Et2�(�*}� ~ *}Dt,u'Ú(�*}�G6"J97Ñ��')Dt*9= Ù ++L*)DF*fEF6:¾}7A')+-6Þ{9' J97 ~ 6:DF2L*¸09*fEt,u')Ã92-+L6)õ�2-7�')+-(�J9732�(%')Et2xõ�ô¸J9')7�,u*©2�73*}Et,FDF2���2-¾}+L2-*}DF2�*}Dt*}+L*}¾)2'y,F*}��2-(�2$õ�6K6�+L'�+L*}Dt*åEt,uDtJ3,F,FJ9Du'å2L7�,F6�DF79' ~ DF6�Et6�7�,/'M(%')DF'y,F,F6�Dt2LEt,F2L(/{96�ï�6�Et,FDF6:��6 ó"(�*)��6')0]6:EF6�� ~ 2-*"J97A'"096�73EF2-,u."�Ú')¾)¾}2L*}Dt6 032hô�J96�+-+s'1'y,F*}�G2L(%'õ3'%£}6:7909*GJ97A'"��')EFEF'1092hJ97A'£}*)+-,/'"6§�G6�8�8:*K+s'1��')EFEF'G096:+r4*}+-6¿(�*}79(:6�7�,uDF'y,/'K2L7åJ979'KE¤��6�DF'G092IDF')¾}¾}2-*"092 ¢ ���¿�M=

Ù 7Áô�J96:Et,u*<+s'%£}*}Dt* ~ ')DF+-6�DF�å096:+L+-6 ~ DF*}Ã9+-6���'y,u2-(/{96"(�*)79796�EtEF6�(:*}7·+s'åDF2L(:6�Dt(%'å096�+-+L62

2-2

~ J3+LEu'yD�õn6�0è2L7 ~ ')D¤,u2-(�*}+L')DF6�092 ~ J9+-Eu')D"(:*}7 ~ 6�Dt2L*¸092?2-73��6�Dt2L*}Dt2?'ú(�2-DF(�'ú�)�Ñ��E:õÒ096´,F,F6 ���������!�#"#$&%(')�(�*����ÿ�� =�H��ù2L7�,u6:DF6:EFEF6 ~ 6�D�6�EFEt6]£)'Ñ'y+?092Ò+s.<096:+L+-*<Et,FJ9092-*Ñ096�¾}+-2Ò*)¾}¾}6:,t,u22-7²EFöyw©+L6B��2-+L+-2LEF6:(�*}730 ~ J3+LEu'yD©Du' ~9~ DF6:EF6:7�,u')79*MJ97Ñ(%'y� ~ *�092 ~ DF* £y'�6�(:(�6�8:2L*}79')+L6 ~ 6�D,F6�*}Dt2L6K' ~9~ ')Dt,F6�796:7�,F2?'å092¥£}6�DtEF6GÃ9Du'y79(/{96Ú036�+L+L'�ýAEF2-(%'3õ50A')+-+s'�(:*}EF�G*}+L*)¾}2s']')+-+s'ÚýAEt2L(�'EtJ9Ã97�J9(�+-6%')Dt6)=,+·09J979ô�J96f796:(�6:EFEu'yDF2L*¿,FDF* £y')DF6 J37G¾)Du')7"7�J9�G6�Dt*¿0929ô�J96�E¤,u2A*}¾)¾}6:,t,u2 ~ 6�D~ *),u6:DF+-2E¤,uJ9092L')DF6f'©��*)7909*9=n4���*}Dt,FJ97A'y,u')��6:7�,u6)õ)(%' ~ ,u')DF6�2-+3Et6�¾}7A'y+L6�0929J37A' ~ J9+-Eu')D�79*)7ö"��')(:2L+L6"6GDF2-(/{92L6:096KJ97·092LE ~ 6:79092L*M79*),F6:£)*}+L6K092nEt,FDFJ9�G6�7�,F2Þ032�(%')+-(�*}+-*9=.-§+-2>2L� ~ J9+-EF2')DtDF2¥£)'y79*K')2h79*)Et,uDt2IDu')032L*),F6�+L6:EF(:* ~ 2h6:Et,uDt6���')�G6�7�,u6§092-Et,uJ3DFÃA'y,F2I6§092LE ~ 6:DFEF2I09')+I��6:8�8:*2-7�,F6�DtEt,u6:+L+L')DF6yõh*}+-,FDF61(/{36�Et{92-��,u'y,u2>2-7²��DF6:ô¸J36�798�'d0A')+-+x�ù6�/�6:,t,u*å�©* ~3~ +L6:D�õI6 ~ 6:D ~ *),F6�Dt+L2Dt2LEF*)+-£}6:DF6yõ5' ~ ')Dt,F6"2L7úDu'yDF2�(�')EF2$õIöK796�(:6�EFEF')DF2L']J97A']EF6:DF2L6K092�* ~ 6:Du')8:2L*}732�EFJ3+�EF6�¾)7A')+L6092�(�J92 ~ ')Dt+L6:DF�"2L7åEt6�¾}J92¥,u*9=

@ 6:+ ~ DF2L�G*R(%' ~ 2-,u*)+L*R0A')Dt�bô�JA')+-(/{96�(:6�7973* ~ DF6:+L2-��2-7A')DF6ÑEtJ9+ ~ DF*¸(�6:EFEt*i092§��*}D¤���')8�2-*}796¿096:+L+-6 ~ J9+LEF')Df6�096:+L+L6¿�G2L+-+L2-EF6�(:*}790 ~ J3+LEu'yD�õ#6BEtJ92r��6:(�(%'y792LEt��2I09256:��2-EFEF2-*}796096:+#EF6�¾)7A')+L610736�+#EF6:(�*}7903* ~ ')Dt+L6:DF�§096�+-+x�ù2L7�,u6:DF6:EFEF6 ')E¤,uDF*yýAEF2-(�* ~ 6:DÒ+-6���2-+L+L2-EF6:(�*}790 ~ J9+¥�EF')D�õ�2L7 ~ 'yDt,u2-(�*}+L')D>�G*03*¦ô�J96:+L+-6f��'y(�6�7�,F2 ~ ')Dt,F6�032�Et2LE¤,u6��G2AÃ92-7A')DF23Et,uDt6:,t,u2xõ¸')EtEF2-6��G6 'y0J979'§Ã3DF6:£)6f096�Et(�DF2-8�2-*}796�096:+L+L6 ~ DF*¸(�6:09J9DF6f092324� ��%*� (/{96fDu' ~9~ DF6:EF6:7�,u')79*¦+s'vÃA'yEF6�096:+L+s'Dt2L(�6:DF(�'Ú2�ô�J96:Et,u*](�')� ~ *50�796�+r,u6�Dt8�*9õ ~ ')DF+-6�Dt�Ú096:+L+s' ~ DF*¸(�6:09J9DF'�Et,/'y790A')Dt0Ñ092�Dt2L(�6:DF(�'092 ~ J9+LEF')D�=

øvJ96�E¤,/' ~ Dt*(:6�09J9DF'¦0329DF2-(�6�Dt(%'¿DF2-(/{92L6:096 E¤,uDFJ3��6:7�,F2A0929(�')+L(:*}+L*v�G*}+¥,u* ~ *),u6:7�,u2x=�H5'796:(�6:EFEF2¥,/.�092�,/')+-2}Et,FDFJ9�G6�7�,u2�{A' ~ *}Dt,u'y,u* ')+L+L' (�*}E¤,uDtJ98�2-*}796)õ ~ Dt6�EFEt*v+x� � EFEt6�Dt£y'y,F*}DF2-*f�©E¤�,FDF*}79*)��2-(�*�032IC ')¾}+-2s')Dt2xõ�092�J97å(�+LJ3Et,u6:D�092�ª}�KC � Ý = Ù +hEt2LEt,F6���'�* ~ 6�DF'y,u2¥£}*"2L73Et,/'y+L+s'�,u*ö�|f6�0�ì 'y,?H52-7�J�6 é =��3w�2#(:*}� ~ 2L+s'�,u*}Dt2¸��*}D¤,uDF')7 ~ 6�DÒHI2L7�J�6KEt*}79*B092-£)6�DFEt2#0A'Bô�J96:+L+L2 ~ 6�D+-6BîÒ*}DFò�Et,u'y,u2-*}7 Ý 73276dEFJú(�J32�2L+r(�*¸092-(�6�0328�!�Fÿ���"#�G6�DF' ~ DF6:(�6�036�7�,u6:��6:7�,F6�2-79Et,u')+L+L'y,u*3õ6:0Úö©E¤,/'y,F*B03J979ô�J96v796:(�6:EFEu'yDF2L*1')0A'y,t,/')Dt6�2-+#(�*¸092L(:6 'y+L+s'¿Et2L7�,/')EtEF2�096�+#7�J9* £}*"(:*}� ~ 2L+L'��,F*}DF6y=Þø¿J36�Et,F*Kö¿2L7]EF*)Et,/'y798%'"2L+�+s'%£}*)DF*"(/{96§2L*�{9*KEt£}*)+-,u*"03J9Du')7�,F6¿2L+�,F2LDt*(:2L792-* ~ Dt6�EFEt*+$� � EFEt6�D¤£)'�,u*}Dt2L*Ñ�©E¤,uDt*}79*}�G2L(:*·032�C ')¾}+L2L')DF2$wGï�,FDu')03J9DFDt6´ó]2-+ ~ Dt*}¾}Du'y����'²EF6:(�*}7903*Á+s'Et2L7�,/')EtEF2ÞDF2-(/{92L6:Et,/'d0A'd£y')DF2Þ(�*)� ~ 2-+s'y,F*}DF2 ~ 6:D1HI2L7�J�6�õ>6�(:*}73��Dt*}7�,/')Dt6Ú2ÞDF2LEtJ9+-,u'y,u2n79*)7Et*}+L*�(�*}7²ô�J96:+L+-2r*y,F,u6:7�J3,u2�EFJ9+-+s'"î?*}Dtò�Et,/'�,u2L*)7²�©+ ~ {A'3õ��Ú'�')79(/{96B,uDu'�ô¸J36�+L+-25*),F,F6�7�J3,u2

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

\�]?^�_7`Aacb�dfeg`h]�i 2L2-2

0A')2�092-£)6�DFEt25(�*}� ~ 2L+L'y,u*)DF2 ~ 6:DfH52-7�J�6�=@ 6:+¿ô¸J9')Dt,F*è(�' ~ 2¥,u*}+-* ~ ')DF+-6�Dt�kÃ9DF6´£}6��G6�7�,F6�096:+¿+s'%£}*)DF*REt£)*}+-,F*è6Ñ036�+L+-6 ~ DF2-79(�2 �

~ ')+-2Ò(�')Du'�,F,u6:DF2-Et,u2-(/{96Ú032ÞÜ Ç%ÈAÉ}Ê�ËÌ3Í�Î�ÈÏ#Ç�Ê}Ð = Ù 79*}+-,FDF6�E ~ 2-6�¾}{96:DF�Ñ2-7º(�*}EF'²(�*}73EF2LE¤,u6�2-+~ Dt*}Ã9+L6:�Ú'�096�+-+s'�(:*}73��6:DF��'�096�2>(�')79092-0A'y,F2�6�0Ñ2-+L+-J9Et,FDF6�Dt�ÚJ97úDt2LEFJ3+-,/'�,u*Ú6:�1Ã9+-6���'y,u2-(�*096:+L+x�ù2L� ~ *}Dt,u')798%'¦092IJ97M(�*¸092L(:6¿092I(�*)73��6�Dt�Ú'3=

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

n U^XZO�`Mgo[hg o

n Qi_W_WO OI_ä`MSMgæVWY `�`dO(p O

qsrtq uwvLxyvsz {j|;x~}����l�;{jx~��v�|l}R��}

HI6 ~ J9+LEF')D�õ�*}EtEF6:Dt£y'y,u6 ~ 6�D5+s' ~ Dt2L��'?£}*}+¥,/'�0A' ß)*(:6�+-ê¸7¦z?6:+L+�6�0¦�©7�,F*}7�ê¦ì 6:îf2-EF{��¨� � 796�+¢ é «}ÄõEt*}79*1036�+L+-6©Et*}DF¾}6:7�,u2�032�Et6�¾}7A'y+L2�DF')092-* ~ J9+-Eu'y,F2xõ�2L+�(�J32 ~ 6�DF2-*03*�092�DF2 ~ 6´,u2L8:2L*}736 ö~ Dt6:£}6:092LÃ32L+L6�2L7G¾}6:796�Dt6v(�*}7�Et,FDu')*}Dt092L79')DF2L' ~ DF6�(:2LEt2L*}796y= � ¾}¾}2#(�*)79*}EF(:2s')�G*¦(�2LDt(%' ¢ ÷)�}�~ J9+-Eu')D:õÒ+-6åô¸J9')+L2 ~ Dt6�Et6�7�,/')73* ~ 6�DF2-*032 (/{96d£y')7379*�09' ¢ õ¨÷²��EG'ú(�2-DF(%' ¢ �úEF6:(�*}79032xõ6�Et*}79*²(�')Du'y,t,u6:DF2L8:8%'y,F2Ò09'<J97A'²6:+L6:£y'y,u'dE¤,/')Ã92-+L2¥,/.3w1032?')+-(�J9736�092Þ6�EFEt6]EF2Ò(�*}79*)EF(�6]2-+~ 6�DF2-*03*"(�*}7MJ97h�ù2L79(:6�D¤,u6�8:8%'"��Du')8:2L*}79')DF2L'�092 10−15 õ ~ ')Du'y¾}*}7A')Ã32L+L6 (�*}7M+x��')(:(�J9DF'y,u6:8�8%'096:2I79*}Et,FDF2I�G2L¾}+-2L*}Dt2A*}DF*)+L*}¾}2�'y,u*)��2-(�2x=

Ý 7 ~ ')Du'y��6´,uDF*G(%'yDu'y,t,u6�Dt2LE¤,u2L(:*9õA6¦092�¾)Du')79036B2-� ~ *}Dt,u')798�' ~ 6�D�+s'"(:*}Et,FDFJ98:2L*}796B092J971�G*¸096�+-+L*f(�*¸6�Dt6�7�,u6ÒEFJ1ô�J96:Et,u2*}¾}¾}6´,F,F2xõ�ö?Du' ~9~ DF6:EF6:7�,u'y,u*¿09')+L+L'f036�DF2¥£y'y,/'f,u6�� ~ *}Du')+-6096:+ ~ 6�DF2-*03*9õ�* P = Ù +�¾)Du'yýA(:*�2L7dýA¾}J9DF' ¢ = ¢ Du' ~9~ DF6�Et6�7�,/']J97ú(�')� ~ 2L*}7A'yDF2L*K092�(�2-DF(%'Ä}÷)� ~ J9+-Eu')DÒ(�*}7]Dt6�+s'�,u2-£¸2A£y')+L*)DF2A092 P 6

Pw�(:*}�G6©EF2 ~ J9�"73*),/')Dt6)õ¸J97�£y')+L*)DF6f,u2 ~ 2L(�*B092

10−13÷10−17 0}Et6 ')EtEFJ9�G2s'y��*f(/{96 P EF2s'�(�*}E¤,/')7�,F6?6Þ(/{96?2-+ ~ 6:DF2L*¸09*�2L792-8�2L')+L6���*)EFEF6�G*}+-,F* ~ 2T�ÑÃ9DF6´£}6K092�ô�J96:+L+-*]'y,F,FJA')+-6)õh*),t,u6:792s')�G*Ú(:*}�G6��2���"Fÿ��tÿ�242h��R���24� "Fÿ P/2P ≈107 ')73792x=

Ý 7h��')+¥,uDu'�6:£¸2L096:798%'º*)EFEF6:Dt£y'y,F2-£y'ºö²2L+f��'y,t,u*º(/{96ÑEt*}+L*ÁJ97A' ~ 2-(�(�*)+s' ~ 'yDt,u6d096�+-+s'~ * ~ *)+s')8:2L*}796 092 ~ J3+LEu'yDs��ªV���Ò��' ~ ')D¤,u6§092hJ37MEt2LE¤,u6���'"Ã92L79')DF2-*9õ�G6�7�,FDF6¿,uDF'1+L6¿Et,F6�+-+L6

¢

� �h�g�h���R�5�V�5�,�1�*� \k����� �����H�&� \ � \

79*)DF��')+L2�+s' ~ 6�DF(:6�7�,uJ9')+L6nön092�(�2-DF(�'f2-+�÷)���]= Ù 79*}+¥,uDt6)õ�E ~ 6�EtEF*©+-6 ~ J9+-Eu')D5EF2���J9* £}*}79*f(:*}7£)6�+L*¸(�2¥,/. ~ 6:(�J9+-2s')Dt2A��*)+-,u*¦')+¥,u6yõ¸¾)6�796:Du')+-��6:7�,F6 EtJ ~ 6�DF2-*}DF2#092�J97�*)DF092-796 032�¾)Du')79036�8�8�'Dt2LE ~ 6:,t,u*¦')+-+L6?£)6�+L*¸(�2¥,/.¿096:+L+L6f'y+-,uDt6 Et,F6�+-+L6)= Ý 7h��')7A')+-2LEt23096´,F,/'y¾}+L2L'y,/'vDt2-£}6:+s'¿J979*§E ~ 6´,F,uDt*092¸£}6:+L*¸(�2-,u. ,uDF'¿�v6 ¢ �}�)�©ò����yEj��� � õ��G6�7�,uDt6 ~ 6:D�+L6ÒEt,u6:+L+-6?096:+L+s' EF6�ô�J96:798%' ~ Dt2L79(:2 ~ ')+-6?2£y')+-*}DF2�,u2 ~ 2L(:23EF*)79*¦,FDu' ¢ �¿6 ÷)�vò��Ú�yE�=�@�6�+A(�')EF*§096:+L+L6 ~ J9+LEF')Dn' ~9~ ')Dt,F6�796:7�,F2#'¿EF2LE¤,u6:��2Ã92-7A')Dt2xõ¸+L6v£}6:+L*¸(�2¥,/.1,u6:7909*}79*�')0å6�EtEF6:DF6¦2L7�,u6:DF�G6�092-6)õ92-7�,F*}DF73*�' ¢ �)�Kò��Ú�yE�=

Ù +���'y,F,F*d(/{36Ú+L6"£)6�+L*¸(�2¥,/. ~ 6�(�J3+L2s'yDF2>Et2s')79*M��')¾}¾}2-*}DF2 ~ 6:DB+-6 ~ J9+LEF')D§DF2LE ~ 6´,F,F*<')+-+L6')+¥,uDt6?Et,F6�+-+L6)õ)E ~ 2-6�¾�'¿')+-��6:79*©2-7 ~ ')D¤,u6 +L'©092LE¤,uDt2LÃ9J98:2L*}736?096:+L+L6 ~ J9+-Eu')D�'y+L+x�ù2L7�,F6�DF73*©096:+L+s'¾�'y+s')EtEF2s'w ~ 6�DG+L6 ~ J3+LEu'yD ~ 2��T£)6�(:(/{92L6yõ�2L73��'y,t,u2$õÞ+$�¨'y+-,u6:8�8�'ú,F2 ~ 2-(%'ÑDF2-E ~ 6:,F,F*Á'y+ ~ 2s')79*¾�'y+s'y,t,u2L(:*Kö ~ ')Dt2�'Ú(:2LDt(%'�÷y�}� ~ ()õ�(�2LDt(%' ¢ ��£}*}+¥,u6B�Ú')¾)¾}2L*}Dt6¿DF2-E ~ 6:,F,F*]'Úô�J96:+L+s'G096�+-+L6E¤,u6�+-+L6v(:*}�1J9732��ùª � =

-¿2s. ~ *¸(�*d09* ~ *d+L'MEt(�* ~ 6�D¤,/'M096�+-+s' ~ DF2-�Ú' ~ J9+-Eu')D§£}6:79796�6�+s'yÃ�*}DF'y,u*å2-+Þ�G*¸096�+-+L*')(:(�6´,F,/'�,u*¦')79(:*}Du'¿*}¾}¾)29EF6:(�*}7903*B(:J92A6�EtEF6fEF*}73*B+-6 Et,F6�+L+-6�0929796:J3,uDt*}792 ~ Dt6:£¸2LE¤,u6�� ~ *(:*09* ~ *·+s'ÑEF(:* ~ 6�Dt,u'�096:+f796�J3,FDF*}736d0A' ~ ')D¤,u6å092 C?{A')03îf2-(/òR796�+ ¢ é �}����796�+ ¢ é ���ú09'H5')7909')J§6�796�+ ¢ é �)ª�0A'fz '}')036�68��îf2L(/ò�ê}=�q�')+-2)E¤,u6�+-+L6>{9')7979*f092-��6:79EF2-*}792y,u')+L2y0A' ~ *y,u6�DDtJ9*),/'yDF6Ú(:*}7º£}6:+L*¸(�2¥,/.<'y79¾}*}+L')DF2�6:+L6:£y'y,F2LEtEF2L�G6��

104 Du')0#��E#�BEt6�798�'²092LEt¾}DF6:¾�')DFEt2x=<@ 6�+(�')EF*G2L7M(�J9256:EFEF6BEF2L')79*G09*),/'�,u6§0925J97<(�')� ~ *K��')¾}796´,u2L(:*KEFJ��G(�2-6�7�,u6:��6:7�,u6�6:+L6´£)'�,u*9õ(:*}��6 £}6�03DF6��G*"2L7]Et6�¾}J32-,u*3õ309J9DF')7�,u6¿+L'�DF*),u')8�2-*}796v6:EFEt6¿6��G6:,F,F*}79*"J97åEt6�¾}7A'y+L6vDF')092L*+-J979¾}*1(:*}792�2�(�J32h')EtEF2hJ9EtJA')+-��6:7�,F6vEF*)79*"2L79(:+L2-7A'y,u2#Dt2LE ~ 6:,t,u*"'y+L+x��')EtEF6©032hDF*),u')8�2-*}796yw�+L6E¤,u6�+-+L6v032I796�J3,FDF*}732IEF2I(�*)� ~ *}Dt,u')79*K(�*)��6¿096:2h��')DF2$=

46:(�*}7903*M2-+��G*036�+L+-*9õ�+L6 ~ J3+LEu'yDv096:£)*}79*d'%£}6�Dt6KJ97ú(%')� ~ *Ú�Ú')¾)796:,F2L(�*Ú6�Et,FDF6:�Ú'���G6�7�,u6M��*}Dt,F6)õf796:+L+x�ù*}Dt092L796å092

(108 ÷ 1013)-"w ~ 6�DG��')DF6dJ97 (�*}7��DF*}7�,u*3õ�2L+�(%')� ~ *

��')¾}796´,u2-(�*Á036�+¿4¸*}+L6dö²092¿� -K= 46Ñ')EtEFJ9�G2s')�G*Á(/{36²2L+�Du')+-+L6:7�,u')�G6�7�,u*�096�+-+L6 ~ J9+¥�EF')D¿*}EFEt6�D¤£)'�,u*MEF2s'�03*�£¸J3,F*dEt*}+L*å'y+L+x�ù6��G2LEtEF2-*}796�032>Du')032s')8:2L*}796�092>092 ~ *}+-*���')¾}796´,u2L(:*9õ~ *}EFEt2s')�G*¿J9¾}J9')¾}+L2L')DF6�+L'¿096�Dt2-£y'y,/'¿096:+L+$��6:796�Dt¾}2s'¿(�2-796:,F2L(�'§Dt*),/'y8�2L*)7A')+L6 dEk/dt ')+-+x�ù6�7�6:DF¾}2L'1092LEtEF2 ~ 'y,/' ~ 6�DfJ9792¥,/."092h,u6:� ~ *K0A'KJ97d032 ~ *}+L*"��')¾}796´,u2-(�*"2L036%')+-6¿2L7åDF*),u')8�2-*}796

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� �h� ¡ ��£�£ \�\ £*��� �5¤�¥ �V� \ � \ �

dEHD/dtõ9*y,F,u6:796�7309*

− 16π4B2R6sin2θ

6c3P 4=dEHDdt

≡ dEkdt

= −4π2IP

P 3

� ¢ = ¢ �

0A'"(�J32IEF25DF2-(%'%£y'1+s'"Et,F2L��'1096�+I(�')� ~ *"��')¾}796´,u2L(:*"EFJ ~ 6�D¤ýA(�2L')+L6

Bsinθ =1

2πR3

√6c3IP P ' 3.2 · 1019

√PP

-§')J9EtE � ¢ =¨���

09* £}6I� ≈ 1045 ¾ · (�� 2 ��ö"2L+>�G*}�G6�7�,u*]0h�ù2L736�DF8:2s'�096:+L+L' ~ J9+LEF')D�õ θ +$�¨'y79¾}*}+-*Ú,uDF'M'yEFEF6

��')¾}796´,u2L(:*Ú6"'yEFEF6"032>DF*),u')8�2-*}796yõR� ≈ 10

ò��¦�f2L+rDu')¾}¾)2L*Ú036�+L+L'ÚEt,F6�+-+s'�032�796:J3,uDt*}792x=øvJ96�E¤,/'vDt6�+s'y8�2L*)796Ò(:23092-(�6 (/{36)õ�' ~ 'yDF2-,u. 092 ~ 6:DF2-*09*3õ ~ J9+-Eu')D�'%£}6�7�,F23£y')+L*}Dt2�2L73��6:DF2L*)DF2�092P' £¸DF')7979* ~ Dt6�EFJ3��2-Ã92L+-��6:7�,F6�'y79(/{96"J97h�ù2L7�,F6�79Et2-,/.���2-79*}DF6B096�+�(%')� ~ *��Ú'y¾}796:,F2L(:*9=

+²2L+�(�')EF* 096�+-+L6 ~ J9+LEF')D5(�*}7 ~ 6:DF2L*¸09* ~ 2�� ~ 2-(�(�*)+L*�796�+¸092s'y¾}Du')�G��' P−P 2L7§ýA¾}J9DF' ¢ = ¢ =

§��7���*�tÿ©¨kª�¨k«­¬?®°¯±A²h®°¯*³f®�³´²hµ�¶�·l¸V¹c²A¶�®RºH® ¹�·�µ�»A¼kµ½º&¹c²c¶T¾tµ!³fµ�¸k¹�².¼�¯©¬?µ°¿�¸�¶�®°¯�¹Àº°¶m¬�¶�²h¬?µÁÂ&à ¸�¼1·K»�µ!²XÄy»A¶~¯�®!³´¶y¬?®°¿s¹m·[¹8¸�¼�·Å»#µ°²�¬?®°¯Æ¸k¹�²A¶�®RºH®.º°¶Ç²h®!³fµÈ#¶´®°¯5¹8¸�¶�É.¾t¹�·=®R¬A¹P¸�²?¹A»R¹c¯*³fµ°¯�®�¶T¯Ê ¹c¯5¹c²�µ!·�¹�µ°¯�¬cË�¹Ì¼�¯�µ�º1¹c²A¶�¾�µ!³fµ�¿�¶�¯�®°²?¹Ìº1¹c·�¸k¹c²c¶�®RºH®&Í

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

ª �h� Îc� ¢ ��Ï � �*�y��Ð \7� £�� ¤ � ¢°¢ ��� ¥�¢!� �5�

Ù +I�G6�(�(�')792-EF�G*G032I6��G2LEFEt2L*}736¿096�+-+L6¿*}79036¦DF')092-*G09' ~ 'yDt,u6§092IJ37A' ~ J9+LEF')D�ö¿��*}DFEt6+$�¨')E ~ 6´,F,F*kEFJ (�J92¿(:2vEF*)79*T�G6�73*k(�6�D¤,u6:8�8�6y= Ù +v(%')� ~ *k�Ú')¾)796:,F2L(�*Á6�Et,FDF6:�Ú')�G6�7�,F66:+L6:£y'y,F*<DtJ9*),/'d')+L+L'�£}6�+-*(:2-,u.d092ÞDF*),u')8�2-*}796G096�+-+s'åEt,F6�+L+L'3=ÒÑv2-(�2L73*<')2 ~ *}+L2n��')¾}796´,u2-(�2096:+L+L'�Et,F6�+L+L'�ö¿ô�J92L73092h2L7309*),F,F*"J97å(%')� ~ *"6�+L6´,F,FDF2L(:*À��03*�£¸J3,F*G')+L+-6 ��*}D¤,u2�£y')Dt2s')8:2L*}792#092B(%')J9EF'y,u6�0A')+-+s']DF*),u')8�2-*}796G096�2 ~ *}+L2´�©(%' ~ ')(�6�092Ò')(�(:6�+L6:Du')Dt6�+-6 ~ ')Dt,F2L(�6:+L+-6"(%')Dt2L(/{96yõ

2-7 ~ ')D¤,u2L(:*}+s'yDÚ�G*09*Á¾}+L2 6�+L6´,F,FDF*}792$õf'º£}6�+-*(:2-,u.ÁDF6:+s'y,F2-£¸2LE¤,u2L(/{36)=^43' ~9~ 2s')�G*º(/{96Ñ2-7,u')+L2f(�*)79092L8:2L*}732�+-6 ~ 'yDt,u2-(�6:+L+L6M(%'yDF2L(/{36<(�*)7�£)6�D¤,u*}79* ~ 'yDt,u6d096�+-+x�ù6�796:DF¾}2L'�(:2L796´,u2L(�'�2-7DF')092s'y8�2L*)796n6��G6:,F,F6�7903*©J971DF')¾}¾}2-*

γ=>46?+$��6:796�Dt¾}2s'fö?EtJ��G(�2-6�7�,u6yõ}2L+�Du'y¾}¾}2L*

γö?(�' ~ ')(:6

092n0A'yD¦+-J9*}¾}*M')+-+s' ~ Dt*09J38�2L*)796K092nJ97A'd(:* ~9~ 2L'M6:+L6´,F,uDt*}796 � ~ *}EF2¥,uDF*)796)õ5(/{96 ~ DF2-�Ú'�092')73792L(/{92-+s')DtEF2�£}6:79¾}*}73*ú'<+L*}Dt*d£)*}+-,u'²')(�(:6�+-6�Du'�,u2Þ0A')+?(�')� ~ *²��')¾}736:,u2-(�*M6��G6:,t,u6�7309*')+¥,uDt2)Du'y¾}¾}2

γõ�0A'y7909*f+LJ9*)¾}*f')0§J97A'�EF*)Dt,/'�092�(�')EF(�'y,/'=>;dJ3*�£)6�7903*}EF2�+LJ379¾}*�+L6�+-2L796:6>096:+

(�')� ~ *¦�Ú')¾)796:,F2L(�*3õ�+L6 ~ ')Dt,F2L(:6�+L+-6f(�*}Exû ~ Dt*03*),F,F6 6:��6´,F,u*)79*BDF')092L')8�2-*}796f092�(�J9D¤£)'�,uJ9DF'796:+L+L'G092-DF6:8�2L*)796B036�+r+L*}Dt*��G*),u*3w +x�ù6�/�6:,t,u*Ú(:*}� ~ +L6:EFEF2¥£}*�ö�+x�ù6��G2LEtEF2-*}796§092rDu')092L')8�2-*}796')+-+x�ù2L7�,u6:DF79*�092IJ97M(�*}79*K2-+h(�J925'yEFEF6¦ö¿+x��')EtEF6§�Ú'y¾}796:,F2L(:*"096�+-+s'1Et,F6�+-+s'3=

@ *)7�£}6:79¾}*}73*²*}EFEt6�D¤£)'�,u6G096�+-+L6 ~ J9+-Eu')D¦(�*}7�(%')� ~ 2���')¾}796´,u2-(�2�ÃA')EtEF2Þ6�0Á')+n(�*}7�,F6�� ~ * ~ 6:DF2-*092�6�+L6´£y'y,u2$=]øvJ96�E¤,u*M��'y,F,F* ~ J3�<6�EtEF6:DF6�E ~ 2L6:¾�'y,u*d'y,t,uDu'%£)6�DFEt*<J979'dEF6:�K�~ +-2L(:6�(�*}79Et2L096:Du')8:2L*}736)w ~ 6�Dt(/{5Ó©(:2AEF2L'¦6:��2-EFEF2-*}796�ö�796�(:6�EtEu')Dt2L*�(/{36 2-+A(%')� ~ *§6:+L6:,t,uDt2L(�*(/{96²')(�(:6�+L6:Du'Á+-6 ~ 'yDt,u2-(�6:+L+L6åEt2s'ÁEtJ��G(�2L6:7�,u6Ñ' ~ DF*¸09J9DFDt6²J97i¾)Du')7i7�J9�G6�Dt*º092 (�* ~ �~ 2-6�6�+-6:,t,uDF*)796´� ~ *}Et2-,FDF*}796y=�ø¿J36�Et,F*Ñ£J3*}+ 092-DF6�(/{96]+$��6/�6´,F,F*Ñ(�*}�1Ã32L7A'y,F*²092?£)6�+-*(:2-,/.')73¾}*}+s'yDF6Ú6:0R2L7�,u6:79EF2¥,/.²096:+ (%')� ~ *Ñ�Ú')¾)796:,F2L(�*<096:£)6M2-7909J9DtDF6�J37è(�')� ~ *Ñ6:+L6:,t,uDt2L(�*EtJ ~ 6:DF2-*}DF6 ')0ÚJ37Ú(�6:Dt,F*�£y')+L*}Dt6f092#EF*}¾}+-2s'3=>46�2�£y')+-*}DF2973*}7�EF*)79*�EtJ��G(�2L6:7�,u2xõ¸+s' ~ J9+-Eu')DEt2�E ~ 6:¾}796)õ�6�796:+�¾}DF'yýA(�* PP Et2�,uDt* £)'G796�+�(�*}Et2L09036:,F,F*À���tÿ�Ô���}ÿ��A'¦��"� ��2?���$t� õ�Et*),F,F*+L'À'*�Fÿ�2f�Õ����%3����ý9¾9= ¢ = ¢ �´=

qsr�Ö × v Ø&��xyz v�Ùj}�ÛÚÒ{ÝÜÒ{YÞÞ�{àß�áÒÞ��lv�x

Ù ~ DF*¸(�6:EFEF2n(/{96 ~ *}EFEt*}79*M(�*}7903J9DFDt6Ú')+-+s'Ú��*}Dt�Ú'y8�2L*)7961096:+L+s' ~ J3+LEu'yD¿EF*}79*MEF*)Et,/'y798�2L')+¥��G6�7�,u6§09J36Gw

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� �h� ¡ ��£�£ \�\ £*��� �5¤�¥ �V� \ � \ ÷

• �¸³�»�¯���³������r���r�I³%�r»������5�¡9±Ú����� ��»���� �yw�2L7Bô�J96�E¤,u2 ~ DF*¸(�6�EtEF2¸J97A'©E¤,u6:+L+s'�'%£}6:7�,F6J979'§��')EtEu'vEFJ ~ 6:DF2L*)DF6f' 8M�

')+-+s'�ý9796f096�+-+s'©EtJA'¿6:£}*)+LJ98:2L*}796�6:E ~ +-*036�+s')Et(�2s'y7�09*©(�*}�G6?Dt6�Et,F23J979'©7�J9Ã�6?092¾}')E>6 ~ *}+¥£}6�Dt26?J97A'©E¤,u6�+-+s'�092736�J3,FDF*}792(/{96)õ ~ 6�D�+s'(:*}79EF6:Dt£y')8:2L*}796¦096:+��G*}�G6�7�,u*�')79¾}*)+s')Dt6)õ ~ J9��' £)6�Dt6�J97 ~ 6�Dt2L*¸09*K092rDF*),u')8�2-*}796,FDu'd�)�M6 ¢ �}�]�GE�õr6 ~ 6�D§+L'M(:*}79EF6:Dt£y')8:2L*}796G096:+nð9J9EFEt*<��')¾}796´,u2L(:* ~ J9�²'%£)6�DF6J97d(%')� ~ *���')¾}796´,u2-(�*KEFJ ~ 6�D¤ýA(�2L')+L6¦092 (1012 ÷ 1014)

-â09£y')+L*)DF2h,/'y7�,F*�6:+L6´£)'�,u2092�(%'y� ~ *B��')¾}736:,u2-(�*¦6 £)6�+L*¸(�2¥,/.¦092�Dt*),/'y8�2L*)796fEF*}79*�EFJ��G(�2-6�7�,u2 ~ 6:D?0A'yDÒ+-J9*}¾}*')+-+x�ù6��G2LEtEF2L*)796 DF')092-*GEt* ~ DF'K036�EF(:DF2¥,F,/'õA*}DF2-¾}2L7A'y7909*1J979' ~ J3+LEu'yD�=

• ã ¶�¶}�����������ä���r�r��¶}�¸� � ��¯�¯�±9»�³:��wú2-7iô�J96�E¤,u* ~ DF*¸(�6:EFEt*9õ +L'Á��')EFEF'º092©J979'7A'y7A'<Ã92L')79(%'M£2-6�796 ~ *}D¤,/'y,u'<'d£y')+-*}DF2ÞEFJ ~ 6:DF2L*)DF2Ò')+Ò+-2L�G2-,F6"092�C?{A'y7909Du'yEF6�ò�')D0A'å��6�79*)��6:792n092Þ')(�(:DF6�Et(�2-��6:7�,F*²092n��'y,u6:DF2s']0A' ~ ')D¤,u6G092nJ97A'<(:*}� ~ ')¾}7A'å2L7J97ÑEt2LE¤,u6���'ÚÃ92-7A')Dt2L*9=v4J ~ 6�Du'�,u*�,/'y+L6�+-2L�G2-,F6)õ#+s'G7A')7A'�Ã92L')79(�'ÚEF2�(�*}7�,uDF')61ýA79*']092¥£}6�7�,u')DF6KJ97A'åEt,F6�+-+s'�092�796:J3,uDt*}792$õI6G736�+L+L'�(�*}7�,FDu')8:2L*}796"2-+>EFJ3* ~ 6�Dt2L*¸09*]092Dt*),/')8:2L*}736§')J9�G6�7�,/'K79*),F6:£}*)+L�G6�7�,u6���J9EF')7909*�+s'"(�*)79EF6:Dt£y')8�2-*}796¦096�+5�G*}�G6�7�,u*')73¾}*}+s'yDF6�6�£y')+L*}Dt23,u2 ~ 2L(:29092#��')EFEF'¦6 ~ 6:DF2-*09*3õ}EF2#*),t,u2L6:796fJ97�'yJ9��6:7�,u*¦092A(�2-DF(%'�}÷y�}�}�}�B£)*}+-,F6!�?6¿+-*"Et,u6:EFEt*�£y')+L6 ~ 6:D�2L+�(�')� ~ *"��')¾}796´,u2-(�*"EFJ ~ 6:DtýA(:2s')+-6)=n4*y,F,u*+-6¿(�*}79032L8�2-*}792�096:,t,u6§EF* ~ Du'3õA+L'KE¤,u6:+L+s'1032I796�J3,FDF*}732 ~ J9�K092-£)6�7�,/'yDF6¦J97A' ~ J9+-Eu')D:=

HI6¿6:£¸2L096:798�6¿*)EFEF6:Dt£y'y,F2-£}6¿(:2 ~ *}Dt,u')79*"'12 ~ *),F2L8:8%')Dt6 (/{96§2-+���6:79*}�G6�79* ~ Dt6 ~ *}79096:D¤�')7�,u6 EF2L'B2L+ ~ Dt2L�G*9= Ù 737A')798:2-,uJ,F,u*3õ2-+ é ÷��l096�+-+L6 ~ J9+-Eu')DÒEF*}79*�*}¾}¾}6´,F,u2#2-EF*}+L'y,u2$õ���6:7�,FDF6(�2-DF(�'�+s'Ú�G6:,u.�096�+-+L61E¤,u6�+-+L61(:*}�1J9732>' ~9~ ')Dt,F6�79¾}*)79*M'�EF2LE¤,u6:��2��1J9+-,F2 ~ +-2 0�2L+�(/{96"(�2���'~ 6�79EF')DF6 (/{96vEF6 6�EtEF6v{A'y7979*���'y,t,u* ~ ')D¤,u6©032�Et2LEt,F6��G2#Ã92L7A'yDF2xõ�6:EFEt2�EF*)79*1Et,u'y,u2#092-Et,FDFJ3,t,u20A']J97h�ù6�E ~ +L*)EF2L*)796K092�EFJ ~ 6�Dt79* £y'3=�C?2L�åöK(�*}73��6:DF��'y,u*]09')+L+-6"')+-,F61£}6:+L*¸(�2-,u. ~ 6:(�J9+-2s')Dt2092Þ(�J92Ò')Ã9Ã32s')�G* ~ ')DF+L'y,u* ~ DF6:(�6:096�7�,u6:��6:7�,u6)w�EF6�J37º6:£)6�7�,u*Ñ092ÞEFJ ~ 6:DF79* £y'²ö�')Et2L�"��G6:,uDt2L(:*���(�*}�G6¦79*}7<ö¦0927��(:2L+-6¿(/{961')(:(%')09'�2L7MJ97dEF2LE¤,u6:�Ú'KÃ92L79')DF2-*"2L7M(�J92r+s'1��*}Dt�Ú'096:+L+s' Et,u6:+L+L'©¾}2L¾}')7�,u6 ~ J9�¿6�EtEF6�Dt6�')+-,F6�Du'�,/'©0A'y+L+x��'y,t,uDu'y8�2L*)796Ò¾)Du'%£¸2-,/'y8�2L*)7A')+L6n096:+L+L'©(�*}�"�~ ')¾)7A'k�´õ�+L'¦796:*}7A'y,u'BE¤,u6�+-+s'§092�796�J3,FDF*}732�Dt2L(:6:£}6 J97A'�E ~ 2L7�,u'B(/{96 +x��')(�(:6�+L6:Du'¦'¦£)6�+L*¸(�2¥,/.�G*}+-,F*�'y+-,u6yõ#')79(/{96 ¢ �}�}�Gò����yE:= Ù 79*}+¥,uDt6)õ#EF6B6�/�6:,F,F2-£y')�G6�7�,u6¦+x�ù� Ù C ~ DF*¸09J9(:6�EFEt61J97A'

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

« �h� äc� ¢ ��� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5� �

��6´,F,/'MDF2-+L6:£y')7�,F6G036�+L+-6 ~ J9+LEF')D�õr09* £¸DF6��G�G*d£}6:096�Dt6�096:2ÒEt2LEt,F6��G2nÃ92L7A'yDF2n(�*}� ~ *}Et,F2Þ09'~ J3+LEu'yD�¾)2L* £y')7925')EtEF2L6:��6¦'GEt,u6:+L+-6§£)6�(:(/{92L6yõh')0d6�EF6:� ~ 2L*G7A')796¦Ã92s'y79(/{96)=�q�')+-2IEF2LE¤,u6:��279*)7MEt*}79*G�Ú'y2hEt,u'y,u2h*)EFEF6:Dt£y'y,F2x=

qsrAå ×æ{àz }�ÞÞ}t�;{èçP��ÚÀÜ ßÕáÒÞ��ÇvLxé�

@�6�+I¾}DF'yýA(�*K2-7åý9¾}J9Du' ¢ = ¢ EF2 ~ J3��6´£2-096�738�2s'yDF6§+s' ~ Dt6�Et6�798�'�092I09J36 ~ * ~ *}+s'y8�2L*)792�032LE¤�,F2L7�,u61032 ~ J9+-Eu')D:w©J979'åDF' ~9~ Dt6�Et6�7�,/']+s'���')¾}¾)2L*}DF')798%'K096:+L+L6 ~ J9+LEF')D�õ�(�*}7Ñ£y')+L*)DF2r092 PEt* ~ Du']2n÷y����E¿6"092 P 796:+L+x�ù2L7�,F6�Dt£y')+-+L*

10−13 ÷ 10−17 =�Hr']Et6�(�*)790A' ~ * ~ *}+L')8�2-*}796¦öDF' ~9~ Dt6�EF6:7�,/'y,u'M796:+�¾}Du'�ýA(�*M2L7ÑÃA'yEFEF*<']EF2L732LEt,FDu'3w©+L6"(%'yDu'y,t,u6�Dt2LE¤,u2L(/{36 ~ 6:(�J9+-2s')Dt2>EF*}73*~ 6�Dt2L*¸0925092�Dt*),/'y8�2L*)796B6:Et,FDF6���')�G6�7�,u6�Ã9DF6´£2$õ�2-73��6�Dt2L*}Dt25']�)�Ú�GE�õ�6B£y')+L*)DF25092 P 2-73��6´�Dt2L*}Dt2>'

10−17 w§0A')+-+x�ù6�ô�JA')8:2L*}736 ¢ =¨�å(:2n')E ~ 6:,t,u2s'y��* ~ 6�Dt(�2L�å(/{96G6�EtEF6�')Ã9Ã92L')79*]£y')+L*)DF2096:+A(%')� ~ *¿�Ú')¾)796:,F2L(�*©DF6�+L'y,u2¥£y')��6:7�,u6 ÃA'yEFEF2$õ�796�+-+x�ù*}DF032L796 032 109 -�0)6�EFEt6 ~ DF6:EF6�7�,u')79*J97���6´,/.¿(%')DF'y,F,F6�Dt2LEt,F2L(�'v796�+-+x�ù*}DF092-796 096:2

108÷109 ê)õ�EF*}73*Bô�J92-790929096:¾}+L23*}¾}¾}6´,F,u23��*}+¥,u*£)6�(�(/{32x=føvJ96:Et,u25*}¾)¾}6:,t,u2h£}6:79¾}*}73*Ú(/{92L')�Ú'�,u2 ���������!�#"#$&%('L�(�*����ÿ�� � =�46:(�*}7309*Ú2-+h��*¸0�6:+L+L*å6:E ~ *}Et,F*²796�+èê ¢ = �dJ37h��6:E ~ +-*}EF2-*}796G092ÞEFJ ~ 6�Dt79* £)'d79*}7 ~ *),FDF6�Ã3Ã�6�0A')D¦+LJ9*}¾)*<')+-+s'��*}Dt�Ú'y8�2L*)796v092IJ979'��G2L+L+-2LEt6�(�*)790 ~ J3+LEu'yD�=Òz?2LEt*}¾}7A' ~ 6�DF(:2L�G2L79032-£¸2L09J9')DF6vJ37 ~ Dt*(:6�EFEt*(�' ~ ')(:6¦032IE ~ 2-6�¾�')Dt6¿+x�ù6�Et2LEt,F6�798�'G032Iô¸J36�Et,F2I*}¾}¾}6´,F,F2IEF2L73¾}*}+s'yDF2x=

�v')+-+L*vE¤,uJ9032L*§096�+ ~ DF*}Ã9+-6���'©096:29,uDF6�(:*}D ~ 2AEF6�� ~ +-2-ýA(�'y,u*���09J96f(�*)D ~ 2hõ�796:+9EF2-Et,F6���'092ÒDF2¥��6�DF2-��6:7�,u*<036�+?(:6�7�,uDt*ú092?��')EFEF'3õ�(�*)7k2L+n,u6�Dt8�*Ñ(:*}D ~ *Ñ092?032L�G6�79Et2L*}792n,uDF')EF(:J9D¤�')Ã32L+L2´�©Eu' ~3~ 2s')�G*M(/{96�+L6GEFJ ~ 6:DtýA(:2?6�ô�J92 ~ *y,u6�738�2s'y+L2n2L7�,u*)DF79*<')0ÁJ97kEt2LE¤,u6���'dÃ32L7A')Dt2L*096:EF(:DF2-£)*}79*KJ97M+L*}Ã�*9õ¸096:,t,u*¦ël$�ì$.'��~íè$!"#���´õ92-+�(�J32 ~ J97�,u*G092h(:*}7�,/'y,t,u*Kö¿096´,F,u*Æ�(�*%�î2h$¦�¥ÿ!���tÿ�%*����ÿ�%3$�õA6B(�*}DtDF2LE ~ *)790961'y+ ~ J97�,u*]+LJ379¾}*G+s'�(:*}79¾}2-J979¾}6:7�,u6�036�2r09J96�(:*}D ~ 2�2-7(:J92�+$�¨'�,F,uDF')8�2-*}796¿¾}DF'%£2¥,/')8:2L*}79')+L6¿EtJ²J97 ~ J37�,F*���'y,u6:DF2s'y+L6v0A' ~ ')Dt,F6B036�+L+-6§09J96�E¤,u6:+L+L6öGJ9¾}JA'y+L6G2L7Á�G*¸09J9+L*å6�092LDt6�8�2-*}796K��'d* ~9~ *}E¤,u*<2-7�£)6�DFEt*9=<ø¿J9')7909*d2L7ÁJ37ÁEF2-Et,F6���'ïAð WJ°ñ>AJHòX:�WJ&BGKOj>AJ�M >PI4:�:�J&C!:=<XBL<?W�G5M4>A@4Oj:�JH>YOj:KG�GK:=I4>A<?W�J&C�UHEHG=I4B@,EHJ&BmUHEHG=I4B@�<?W�JÛU�>X@ :�W°CHW�CH:@4WM BòX:�WJH>;:�J!Z[>X@ :�W@ >lBR:kóRô,OYIAõ�:�G�CH:�I <?W�@ I4W�<�öH>~I4>X÷�EH>ÇI4:1BUHUHG�:�<AByM4E!M4M B�ñ°:=B8BRJ1<�öH>ÇB,UHE&G�I BR@UH:Kø�GK>AJ�M >OYB�<�öH>�UH@4>cIN>AJtM BRJ&WèGK>PIfM >AI IN>P<XB@ BRMNM4>A@4:=INM4:=<�öH>�C!:

P ù >jútEH:KJ1C!:�CH:�>XM û�>�<XBOjU1WÌOjB÷JH>XM4:=<?W°ülC!>AGKG�>Oj:KG�GK:=I4>A<?W�J&CÌUHEHG=I4B@Aý9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� �h� ¡ ��£�£ \�\ £*��� �5¤�¥ �V� \ � \ Ä

Ã92-7A')DF2-*]J97A'å096�+-+L6"09J36�E¤,u6�+-+L6"Et2Þ6´£}*}+¥£}6G2L7úJ97A'å¾}2-¾�')7�,u6yõr6:EFEF'dDF2-6�� ~ 2L6 ~ DF2-�Ú'Ú,FJ3,t�,u*Ú2L+rEFJ9*]+-*}Ã�*�092>|f*¸(/{96)õh03* ~ *¸092-(/{5Ó�2-792L8:2s'G'Kï�,FDu'%£y')Eu')Dt6´óB��'y,u6:DF2s'�')+L+$��2-7�,u6�Dt79*G096�++L*)Ã�*�092>|f*(/{361096�+-+s'G(�*}� ~ ')¾}79'3=§øvJ96�E¤,/'���'y,u6:DF2L'�79*}7 ~ J9�](%')036�DF6�092LDt6:,F,u')�G6�7�,u6EFJ3+L+s'B(�*}� ~ ')¾}79'3õ ~ 6�D £¸2s'1036�+h�G*}�G6�7�,u*"'y79¾}*}+L')DF6 096�+IEt2LEt,F6���'�(/{96§+s'1(:*}Et,FDF2-79¾}6¿')0*}DtÃ92-,u')DF6©'y,F,F*}DF79*K'y0]6�EFEF'3=Ò42���*}Dt�Ú'B(�*}Exû�J97þ'����!"#$)'���ÿ*"#"�#�#�!"� �%�2h$�=>@�6�+h032LEF(:*"EF2(�Dt6%')73*���*}Dt8�6�032�'�,F,uDt2-,F*G£¸2LEt(�*}Et*Ú(/{96§ï���DF6:7A')79*�ó§2L+I��'y,u6:DF2L')+L6¿6¦+L*K��')7979*�Du')+-+L6:7�,u')DF6yw092h(:*}79Et6�¾}J96:798%'õ�2-+h��'y,u6:DF2s'y+L6©Et2I'%£�£2-(�2-7A'"E ~ 2-Du')+-6�¾}¾}2L')7909*1')+L+L'�Et,F6�+L+L'�ýA79*G'"(%')036�DF6EFJ3+L+s'BEFJA'1EtJ ~ 6:DtýA(:2L6y=?4¸6¿+s'�E¤,u6�+-+s'�2-7�,u*}Dt79*"')+-+s'Bô�JA'y+L6vEt2���*}Dt�Ú'�2-+�032LEF(:*"092I')(:(�Dt6�EF(:2¥��G6�7�,u*·öd03*),/'y,u'·032�J37b��*}Dt,F6å(%')� ~ *·��')¾}796´,u2L(:*9õÞ2L+��G6�(�(�')792-EF�G*·öM+L6:¾}¾}6:DF�G6�7�,u6092¥£}6�DtEF*9=]42�096:ý9792LEt(�6Ú��±9ã#ã���� ��� ã ¯fÿx¡��¸�

rA+s']092-Et,/'y798%'M0A')+L+L'�Et,F6�+L+L'å')+L+L'�ô¸J9')+L6

EF2f6:ô¸J32-£y')+L¾)*}79*Ñ+s'ú096:79EF2¥,/.ú092�6�796:DF¾}2L'·��')¾}736:,u2-(%'um = B2/8π

6M+L'Ñ096�79Et2-,u.�0926�736�DF¾)2s'"(�2-796:,F2L(%'

uK = 12ρv2 =Ò42 ~ J9��032L�G*}Et,FDu')Dt6v(/{96

rA =

(B4sR

12

2GMM2

) 17 � ¢ =��k�

09* £}6Bs

öÑ2L+©(�')� ~ *k��')¾}796´,u2-(�*k')+-+s'ÁEtJ ~ 6�Dtý9(�2L6Ñ036�+L+L' ~ J9+-Eu')D:õ M öÑ2L+�,/')EtEF*è092')(:(�DF6:EF(:2L�G6�7�,u*å092��Ú')EtEu'3õ

Rö12-+�DF')¾}¾}2-*Ú096:+L+s' ~ J9+-Eu')D:=�4¸*}Et,F2-,uJ36�7909*å2r£)'y+L*}Dt2r,F2 ~ 2-(�2

Bs = 1012 -"õR = 10

ò��dõM = 1.4M�

õM = 1017 ¾��yE:õ�*),t,u6:792s')�G*å(/{96 rA =

3.09× 108 (��M=Ù +©��'y,u6:DF2L')+L6å096:+©092-EF(�*Á092v')(:(�Dt6�EF(:2L�G6�7�,u*3õ�J37A'�£}*)+-,/'�Du')¾}¾)2LJ97�,u*�2L+fDu'y¾}¾}2L*�092

�©+¥��£�Ó:7hõ£¸2L6:796¿(�*)7�£)*}¾}+-2s'y,F*B£}6:DFEt*G2 ~ *)+L2#�Ú'y¾}796:,F2L(:2�096:+L+L'�@v4�=9�©J9DF')7�,u6¿ô�J96:Et,u* ~ Dt*y�(�6:EFEt*<£}6:79¾}*}79*<6��G6�EFEt2?J979'd¾}DF')7Áô�JA')7�,F2-,/.å092ÞDu')¾)¾}2��1õr6�0�ö ~ Dt*�£y'y,F*<(/{96Ú')+L(:J9796096:+L+L6 ~ 2T����*}D¤,u2�EF*}Dt¾}6�7�,u2�092�Du')¾)¾}2�� (�*}73*}EF(:2LJ3,F6©EF*)79*1EF2-Et,F6��G2�Ã92-7A')Dt2�2-7Ú(:J92�+L'¦E¤,u6�+-+s''y,t,u*}Dt79*G')+L+L'1ô¸J9')+L6§(�J32rEt2I��*}DF��'12L+I092-EF(:*�ö§J97A'KEt,F6�+-+s'"0925796�J,uDF*)792xõAE ~ 6:EFEF*G£¸2LEF2-Ã92L+-6(�*)��6 ~ J3+LEu'yD���= Ù 7Áô�J96:Et,F6�Et*}DF¾}6:7�,u2�EF2 ~ J3�å£)6�096:DF6�(/{96�2-+ ~ 6�DF2-*03*]096�+-+s'�Et,F6�+-+s']092796:J3,uDt*}792I2L7å¾}6:796�DF')+L6¿032L�G2L7�J92LEt(�6v(:*}+ ~ ')EtEu')Dt6§096�+h,F6�� ~ *9=

HI6 ~ Dt*(:6�09J9Dt610925,u2-��2-79¾KEFJ²(:J92��G25EF*�/�6�Dt��6:DF�Ú2-7<Et6�¾}J92¥,u*�(�2�032L(�*)79*Ú(/{96B(�2-DF(%'+x� á �k� 096�+-+L6f��2-+L+-2LEF6:(�*}730 ~ J9+LEF')DFE?' ~9~ 'yDt,u2-6�796 '§EF2LE¤,u6:��2#Ã92-7A')DF2$=�øvJ96:Et,u*B��'y,F,F*BDt6�79096

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

á �h� äc� ¢ ��� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5� �

~ +L')J9Et2LÃ92-+L6 ~ 6�79EF')DF6 (/{96v+L6��G2L+L+-2LEt6�(�*)790 ~ J9+LEF')DÞEF2�EF2s'y79*B��*}Dt�Ú'�,u6 ~ DF* ~ DF2-*1'y,t,uDu'%£)6�DFEt*J97k��6:79*}�G6�79*ú092f')(:(�Dt6�EF(:2L�G6�7�,u*3=RHr'ÑDt6�(�6:7�,u6MEF(�* ~ 6:Dt,/'Ñ092�÷²Et*}DF¾}6:7�,u2�Ã92-7A')DF2-6Ú2-7')(:(�Dt6�EF(:2L�G6�7�,u*¦+s'v(:J92AEt,F6�+-+s'¿29796:J3,uDt*}792#DFJ9*y,/'¿(�*}7 ~ 6�DF2-*03*¿092 ~ *¸(/{92A�G2L+-+L2LEt6�(:*}79092 �¨÷ �DF' ~9~ Dt6�EF6:7�,/']J97h�ùJ9+-,F6�Dt2L*}Dt61(�*}7��6�DF��'Ú096:+L+L'�£y')+L2-092-,u.G092�,/')+-6�2 ~ *),F6�EF2$=§| 'y(�(�*)¾}+L2-6�7909*+-6²2L73��*)DF��')8�2-*}792fýA79*}DF'R032LEF(:J9EFEt6)õ ~ *}EFEt2s')�G*º,uDF')(�(:2s')Dt6²2L+©EF6�¾)J96�73,F6�ô�JA'y09DF*R096:+L+s'��*}Dt�Ú'y8�2L*)796©092IJ37A'G�G2L+-+L2-EF6�(:*}790 ~ J9+LEF')D�w2x=�J97A']@©4²EF2���*)DF��'Ú2L7²J37·Et2LE¤,u6���'ÚÃ92-7A')Dt2L*�'�,F,uDF'%£}6�DtEF*åJ97h�ù6�E ~ +L*)EF2L*)7961092�EFJ ~ 6�D��79* £y'3=MH5'<�Ú'yEFEu'M6�E ~ J9+LEF'<0A')+nEt2LEt,F6���'d09J3Du')7�,u6�+s'MEFJ ~ 6�Dt79* £)'d79*}7ÁöG,/')+-6�09'092-Et,uDtJ9¾}¾}6:DF+-*9õ#6�0²25£y')+L*}Dt25092 ~ 6�Dt2L*¸09*G6�(%'y� ~ *Ú��')¾}796´,u2-(�*Ú036�+L+L'�@©4dEF*)79*Ú,/'y+L20A'G')(�(:6�79036�DF+L'"6:£}6:7�,uJA')+-��6:7�,u6¦(�*}�G6 ~ J9+-Eu')D�0

2L2$= +s'å@©4úEt2�6:£}*)+-£}610 ~ 6�D§2>��6�79*)��6:792�EF* ~ Du'å096�Et(�DF2¥,F,F2�2L+>EtJ9* ~ 6�Dt2L*¸09*å')J9�G6�7�,u'3õ56+s'"092-EFEt2 ~ ')8:2L*}736¿092I6�796:DF¾}2L'GDt*),/'y8�2L*)7A')+L6 ~ DF*}Et6�¾}J36¦ýA73(/{5ÓB+L'K@v4]79*}7MEFJ ~ 6�DF'�+s'ï�+-2L796�'v096�+-+s'¿�G*}Dt,F6´ó�*¸(�(:J ~ ')7309*BJ37A' ~ *}Et2L8�2-*}796�796:+���Fÿ�Ô���)ÿ��A'�096:+L+L'©ýA¾}J9DF' ¢ = ¢ 0

2-2L2$= '3=f+s'B(�*}� ~ ')¾}79'1EF2I6:£)*}+-£)6¿2L7]J979'K¾)2L¾�')7�,F6)w>Et6¦+L'1EFJA'"��')EFEF'179*}7åö¿EFJ���(:2L6:7�,F6~ 6�DÚ09')DÚ+-J9*}¾}*Á')0iJ97A'ºEtJ ~ 6�DF73*�£y'3õf+$��6´£}*}+-J98�2-*}796<ö<')Ã9ÃA'yEt,/'y798%'º+-6�7�,/'Á09'~ 6�DF�G6:,t,u6:DF6²(/{96<6�79*}Dt��2 ô�JA')7�,u2¥,/.Á092 �Ú'�,u6�Dt2s')+-6åEF2©Dt2-£)6�DFEt2L79*Á796�+ +L*}Ã�*Á092|f*(/{96Ò096�+-+s' @v4�õ�0A')7903*v+LJ9*)¾}*v')+ ~ Dt*(:6�EFEt*¿092¸E ~ 2-7¸J ~ = Ý 79' £}*}+¥,/'f��*}DF��'y,/'yEF2+s' ~ J9+LEF')D ~ J9�Ñ2-7k(�6:Dt,u2�(�')EF2?6:£y' ~ *}Du')Dt6�+s'²(:*}� ~ ')¾}7A'wÚ2L7kô�J96:Et,F2�(%')Et2 096�+EF2-Et,F6���'åDt2L��')7961Et*}+L*]J37A' ~ J9+LEF')D¿2LEt*}+s'y,u'3=�� +-,FDF2L�G6�7�,F2xõ�2-+>EF2-Et,F6���'ÚýA7A')+-6"ö(�*)� ~ *}Et,F*K0A'"J97A' ~ J9+LEF')D�6�0MJ97A'"7A'y7A'GÃ32s')79(�'�0

Ãh=fEF6§+L'K(:*}� ~ ')¾}7A'"6´£}*}+¥£}6¦6�E ~ +L*¸096�7903*G(:*}�G6¦EtJ ~ 6�DF73*�£y'K6B032-£}6:7�,/'G')79(/{h�ù6�EtEu'J97A']@©4�õ�2-+�Et2LE¤,u6���'�0927��(:2L+-��6:7�,F6BDt2L��')796B+L6�¾}'y,u*9wfô�J96:Et,u*å(:2�£¸2L6:796"(�*}7��6�D¤���'y,u*]0A'y+���'y,F,F*å(/{96�2�EF2LE¤,u6:��2>Ã32L7A')Dt2>(�*)� ~ *}Et,F2>0A'å09J96KEt,F6�+-+L61092�736�J3,FDF*}792EF*)79*K6�Et,FDF6:�Ú')�G6�7�,F6¿Du')Dt2x=�@�6¿EF*}79*KE¤,/'y,F2h2L79032-£¸2L09J9'y,u2�ýA79*}DF'1EF*}+-*"EF6�2$õ96�0å2-7796:EFEFJ37<(%'yEF*G(�*}� ~ *)Et,u2�0A'"09J96 ~ J9+LEF')D�=

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� �h� ¡ ��£�£ \�\ £*��� �5¤�¥ �V� \ � \ é

§��7���*�tÿ ¨kª��*«���¬�Ë�¹c¿�µÀº&¹c·�·�®¦»�¬A¹c¯�µ°²c¶´®�º°¶j¹�¾�®°·�¼!È#¶´®°¯5¹)º&¹�·T·[¹Ì¸�¼�·K»�µ°²�¹�º&¹�¶8»c¶7»�³N¹c¿�¶c¶�¯�µ°²c¶º&¹A»#¬�²c¶�³�³f®ÆºHµ°·�¿�®Rº1¹c·T·�®

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

n U^XZO�`ågl[hg �

� }Y `dOI[IO�`�� Uo\G`MSMg�� \]OIPRU VjQi[I[hQ

a OI[I[IOI\�QiPkgo_WV XZYW[I\]U S cZOI_WU^SdOhQ

HI6"�G2L+L+-2LEt6�(�*)790 ~ J3+LEu'yDvÃ92L79')DF2-61EF*}73*M*)¾}¾}6:,t,u2�092>6�73*}DF�G6"2L7�,u6:DF6:EFEF6G')E¤,uDt*)ýAEF2-(�*9=�HI6+-*}DF* (%')DF'y,F,F6�DF2-Et,F2L(/{96 ~ 6:(�J9+-2s')Dt2 ~ 6�Dt��6´,F,u*)79*v2L7��'y,F,F2¸+L' £}6:DF2¥ýA(%'v092J97A'vEt6�DF2-6 092 ~ DF6:092¥�8:2L*}792�,F6�*}Dt2L(/{96d2L7iE¤£)'yDF2s'�,u2f(%')� ~ 2f096:+L+s'úýAEF2-(%'3õ�09')+L+L'·(:*}EF�G*}+L*)¾}2s'²ýA79*º')+L+L'úýAEt2L(�'7�J9(:+L6%'yDF6)=ú� +ÒýA796]032?(�*)� ~ 2-6�Dt6Úô�J96�E¤,u6]£}6:DF2¥ýA(/{96)õÞ')Ã3Ã92s')�G*<Ã32LEF*)¾}79*Ñ092Ò��2-EFJ9DF')DF6(:*}7 ~ Dt6�(�2-EF2-*}796G2Þ,F6�� ~ 2Ò032?')DtDF2¥£}*<036�¾}+-2Ò2-� ~ J3+LEF2$õ ~ 6:D ~ *),u6:DB£y')+LJ,/')Dt6�Et2s'd2n£y')+L*)DF2092 ~ 6�Dt2L*¸09*9õn£}6�+-*(:2-,u. ~ 6�(:J9+L2L')DF6yõ?6�(:()= 096:+L+L' ~ J9+LEF')D�õ Et2s'ú¾}+L2�6´£}6:7�,FJA')+-2 ~ 'yDu')�G6:,FDF2*}DtÃ92-,u')+L2$=

@ 6:2 ~ ')DF')¾}Du'�ýTEt6�¾}J36�7�,u2 ~ ')Dt+L6:DF�ú096�+-+s'<,F6�(�732L(%'ú096:+ ,u2L�G2L73¾²(/{96)õ?'y,F,FDu'%£}6:DFEt*Á+s'�G2LEtJ9Du')8:2L*}736�096�+-+x��')DFDt2-£)*·036�¾}+-2�2L� ~ J9+LEt2xõ ~ 6�Dt��6´,F,u6M092�(:*}� ~ 2L6�Dt6å+L6å��2-EFJ9Dt6]092f(�J92')Ã3Ã92s')�G*MÃ92LEt*}¾}79*9= Ù 79*}+¥,uDF6yõ�(:2-,u6:DF�Ñ'y+L(�J3792Ò036�¾}+-2Ò'yDF¾}*}�G6�7�,F2Ò092ÞDF2-(�6:DF(%' ~ 6:D1(�J92Þ+L6�G2L+-+L2LEt6�(:*}790 ~ J9+LEF')D�Ã92L79')DF2-6vDu' ~3~ DF6:EF6�7�,u')79*ÚJ37d*),t,u2-��*1(�')� ~ *K092 ~ Dt* £)'=

Ö�rtq × vÝßÒxé�)çP{èÜÀá¦xév ÜÒ}½|l}tz }�Ú�� { Þ�{ �láÒ{ ß���|l{èÚÒÙj}tv�Þ}|��H��ù*}EFEt6�Dt£y')8:2L*}736�096:+ÒEt6�¾}79')+L6G092nJ97A' ~ J9+LEF')D§ö)õ>2-7�¾}6:796�Dt6)õ>73*}7ÁÃA'y7A')+L6y= Ù +ÞEF6�¾)7A')+L6(/{96"Dt2L(:6:£¸2s')�G*�ö"DF')Du')�G6�7�,F61EF* ~ Du'�2L+�+L2¥£}6�+-+L*�092�DtJ9��*)DF6)õ ~ 6:DF(�2-�å')Ã9Ã92L')�G*�Ã92LEt*}¾}79*

¢ �

¡ �5� \ � ��¢!� Îc� ¢�� ¥ � \�¢t\ ����� � �*� � Ï \7�X\ ¡ � ¤ � ¢°¢ �è� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5��� \ £���� \ � ¢}¢

§��7���*�tÿ��*ª�¨k«�����¹�³�³f®âµ!·T·[¹�º°¶�¾t¹c²A»#¹é±c²h¹ ��¼k¹�¯�ȹ�»A¼�·F»#¹ Ê ¯�µ°·[¹LºHµè¸�µ°²�³N¹Lº&¹�·T·�µâº°¶T»f¸k¹c²A»A¶�®°¯�¹Í"!A¯hµt»A»�®$#)²A¶Å¸�®°²�³fµ!³f®�¶�·3¸�²�®&%l·=®�¬cËk¹¦µA¸H¸�µ°²?¹¦ºHµ°·�·�µÀ»R¹c²c¶�¹.³N¹c¿�¸�®°²hµ°·[¹¦º&¹hº°¶T»f¸V¹c²X»#µ('�»R¹â¯�®°¯þ»c¶¸�²hµ!³´¶�¬?µt»X»R¹Ì·=µÛº&¹hº!¶7»N¸k¹c²A»A¶�®°¯�¹*)é¯�¹c·�·=µ�»#¹c²c¶f¹�³N¹�¿8¸k®°²�µ!·�¹Ì· + ¶�¿�¸�¼�·Å»#®�¯�®!¯)»#µ°²h¹,-?¹m²c¶7»#®°·=³f®&Í

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

¢ � Îc�g�h� ¢ �s�1� � ¡ � ¤5¥ �V� ¤�\ � \ � \ £/.�� ¢ � �c¥ �è� � �*��£�Ð \ � ¢t\ ���092 ~ Du'y,F2L(%'yDF6"J97A' ~ Dt*(:6�09J9DF'M03210°$&�7'���%*�)õI796�+-+s'�ô�JA')+-6K£)6�79¾)*}79*MEF*}�G�Ú'�,u2�J37�(:6�Dt,F*7�J9�G6�Dt*²092?2-� ~ J9+LEt2 ~ 6�D1' £)6�Dt6�J97A'<��*}Dt�Ú'M0h�ù*}790A' ��096:,t,/' ~ Dt*)ýA+-*²2L7�,u6:¾}Du'�,u*V�¿Ã�6:7096´ýA792¥,/'�Et* ~ DF'Á2L+f+L2¥£}6:+L+L*ú092�DFJ3��*}Dt6)= � +-,FDF6d')+ ~ DF*}Ã9+-6���'·036�+L+L' ~ 2L(�(:*}+s'·')� ~ 2L6:8´�8�'å036�+�EF6:¾}7A')+-6)õ56�Et2LE¤,u6KJ97·')+-,FDF*���'y,t,u*}Dt6"2L� ~ *)Dt,/'y7�,F61092>(:J92�Ã92-EF*}¾}79'],F6�796:DF6K(�*)7�,F*~ 6�D ~ DF*¸09J9DFDt61J97úÃ9J9*)7 ~ DF*)ý9+L*]2L7�,F6�¾}DF'y,u*9wf+L'�����³�»�����³%�����5�#w©2-7²¾}6�736�Du'y+L6)õ�+x�ù2L79092-(�6092fDt2-��Du'y8�2L*)796å092 J37i��6:8�8:*Áöd��J3798�2-*}796<036�+L+L'ú��Dt6�ô�J96:798%'�0 ~ 6:D�ô�J96:Et,u*k�G*),F2-£}*3õ?+L6(:*}� ~ *}796:7�,u2Þ2L7���Dt6�ô�J96:798%'Ñ092ÞJ97kEF6:¾}7A')+-6Ú(/{96�£2L')¾}¾}2L'M736�+?�G6�8:8�*²2-7�,u6�DtEt,F6�+L+L')DF6GEF2�1J3*�£)*}79*1(:*}7Ú£)6�+L*¸(�2¥,/.¦092-£)6�DFEF'3õ36v')DFDt2-£y')79*B'�79*}2�(�*)7�J97A'1(:6�Dt,u'�0927/�6:DF6�738%'�092#��')Et6Dt6�(�2 ~ DF*¸(%'=�46f(/{92L')��2L')�G*32�����*�tÿâ'��hþ����h������� $&%3��4$þ5276 +$��2-7�,u6�¾)Du')+-6 +LJ973¾}*§+s'v+L2-796%'(/{96å(:*}+L+-6�¾�'²79*)2�')+L+L'<Et,F6�+-+s'²096:+L+s'²036�79Et2-,/.ú092 6:+L6´,F,uDt*}792 +-2LÃ�6�Dt2 � ' £¸Dt6��G*·(/{36d+L'²092-�s���6:DF6�738%'B036�2#,u6�� ~ 2A092�')DtDF2-£)*B032�J37Ú0A'y,F*�2-� ~ J3+LEF*¦'§09J96���DF6�ô�J96:798�6©EF6 ~ ')Du'y,F6 09' ∆νö§0A'y,F*K0A'

∆t ≈ 8, 3 · 103 ∆νMHz

ν3MHz

DMEF6:(,

�x�¸= ¢ �09* £)6

νMHz

ö<+s'·��Dt6�ô�J96:798%'k�G6�092L'·��Du'�+L6<03J96���6:E ~ Dt6�EFEF'k2L7 ;<ì�8!��6 ∆νMHz

+s'0927/�6:DF6:798%'1,uDF'"+L6¿09J96yõ#EF6�� ~ Dt6¦2-7M;<ì 8y=

46]79*)2Ò£}*)¾}+L2L')��*M*}EtEF6�D¤£y')DF6åJ97A' ~ J9+LEF')D�õn')Ã3Ã92s')�G*<Ã32LEF*)¾}79*Ñ092ÒJ3,u2-+L2L8:8%')Dt6ÚJ979'ÃA'y790A'¿0923��Dt6�ô�J96�738�6�+s')Dt¾�'v2L7"�G*03*¿0A'§' £)6�Dt6 J97KDF' ~9~ *}Dt,F*¿EF6�¾)7A')+L6 ��DtJ9��*)DF6 Et*09032LE¤���')(:6�7�,u610 ~ 6:D ~ *),F6�D5(�*}� ~ 2-6�DF6ÞJ97h�ù*}EtEF6�D¤£y')8�2-*}796)õ)')Ã9Ã92L')�G*�ô�J92-79092�Ã92-EF*}¾}73* 092¸* £�£2L')DF6'§ô�J96�E¤,u6©032T/�6�DF6:798�6�796:2#,F6�� ~ 2A092�')DtDF2-£)*B036�¾}+-2A2L� ~ J9+LEt2xõ)'y,F,FDu'%£}6:DFEF*B+s' ~ DF*¸(�6:09J9DF'¦092'*�c'����h������� $&%3�´=�ünEtEu'1(:*}79EF2-Et,F6©796:+L+s'§EFJ309092-£¸2-EF2L*)796 036�+L+L'¦Ã9')790A'§,u*),u')+L6

∆ν2L7�(%')79')+L2

092��DF6�ô�J96:798%'δν << ∆ν

6f796�+-+x��' ~9~ +-2L(%'y8�2L*)796?'y2A092-£)6�DFEt2A(%')79')+L290329J97A'§092T/�6�Dt6�798�'¿092��')Et6 * ~9~ *)Dt,uJ37A'3õ�(/{96 ~ 6�Dt��6´,F,u6f092�EF*)����')DF6f2-7G��')Et6 +$��2-� ~ J9+LEt*§')+L+-6f£y')Dt2L6���DF6:ô�J96�798:66§092I'yJ9��6:7�,/')Dt6¦(:*}Eñû>2-+hDu' ~9~ *)Dt,u*"Et6�¾}79')+L6%�yDFJ9�G*}Dt6)=

Ý 79'R£)*}+-,u'è6:EF6�¾)J92-,F6·(:*}DFDt6:,t,/')�G6�7�,u6ú,uJ,F,u6ú+-6·* ~ 6:Du')8:2L*}792©092§096�092-E ~ 6�DtEF2L*)796ú6ï98 >�<�öH:=BROj:�BOjWPCmG=BPCH:�INM BJHòAB�M4@�BPJHW:k>,G=BjIfM >XG�G�B(:

DM =

∫ d

0

nedl

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� Îc� ¢�� ¥ � \�¢t\ ����� � �*� � Ï \7�X\ ¡ � ¤ � ¢°¢ �è� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5��� \ £���� \ � ¢ �

��*}+-092L79¾d096�+?EF6�¾)7A')+L6yõnô¸J36�+L+-*²(/{96å*),t,u6�732s')�G*²ö�J97 ~ Dt*)ýA+-*Ñ2L7�,u6:¾}Du'y,F*9õ>(/{96 ~ J3�·6:E¤�EF6:DF6"(:*}79EF2-096�DF'y,u*å(:*}��6�J97h�ù2L� ~ DF*}7�,u'Ú092L¾)2-,/'y+L6¦096�+-+s' ~ J3+LEu'yD�=¦@ *}73*}Et,u')7�,u6K2L73��'�,F,u2r2EF2-79¾}*}+-2h2L� ~ J9+-EF2�£y')Dt2L79*K79*y,u6:£)*}+L�G6�7�,F6¦,FDu'K+L*}Dt*9õA2L+ ~ DF*)ýA+-*�2-7�,u6�¾)Du'y,F*G{9'�J97A'"��*}Dt�Ú'*}+¥,uDF6:��*¸09*1Dt6�¾}*)+s')Dt6¿6¿Et,/'yÃ92L+-6)=

Ý 7A'·£}*}+¥,/' ~ Dt*03*),F,F*Á2L+ ~ Dt*)ýA+-*Á2L7�,F6�¾}DF'y,u*�092©J979'Á0A'y,u'�*}EtEF6�D¤£y')8�2-*}796)õfEt2 ~ J9�096´,u6�Dt��2-7A')Dt612L+�(�*}Et2L09096´,F,F*]q�2L�G6 � �?� DFDF2¥£y')+j��*åq � �L�©036�+L+$��2-� ~ J9+LEt*�2-7Ñ6�EFEt*d(:*}7�,u6:7�J3,u*9õ¸6�E ~ DF6:EFEt*1(�*}�G6fEF*}�G��'§036�+A,u6:� ~ *B032A2L792-8�2L*¿036�+L+$��*)EFEF6:Dt£y')8:2L*}796f6�096�+A,F6�� ~ *(�*)DFDF2-E ~ *}79096:7�,u6v'y+L+s'v032T/�6�DF6:798%'¦092#��')EF6f,uDF'B+s'v��')Et6fï�8�6�Dt*yóf096:+ ~ DF*)ýA+-*B2-7�,u6�¾)Du'y,F*B6�+s'��')Et6K'�(�J92>Et2>Et,u')¾}+-2s'�+$��2-� ~ J9+LEt*9=¿H���J3792-,u.�092��G2LEtJ9Du'ÚJ,u2L+-2L8:8%'y,u'�ö"+x�¨;²ß}��õ�*]¾}2L*)DF79*¾}2-J9+L2L')79*G��*¸092-ý9(%'y,F*9õ�(/{36G(:*}DFDt2LE ~ *}73096"')0ÑJ97ú(:*}7�,u6�¾)¾}2L*�036�2>¾}2-*}DF732�(/{96 ~ 'yDt,u6�0A')+�G6�8�8:*}¾}2-*}DF79*"036�+ ¢ Ä"@ * £)6��1Ã9Dt6 ¢%á ÷ á =

øvJA')7909*ÚJ97A' ~ J3+LEu'yD £¸2L6:796�2-79092-£¸2-09JA'y,u' ~ 6�D +s' ~ DF2L��'"£}*}+¥,/'3õ#£¸2L6�73612L79Et6�Dt2-,/'G2L7J97d0A'y,/'yÃA')EF6B'�(:J92�'y,F,F2L79¾}*)79*K2rDF')092-*),u6:+L6�Et(�* ~ 2I092I,uJ3,t,u*Ú2-+I��*)7909*9=�ü�EtEF2r6�EF6:¾}J9*}73*J97A'åEF6:DF2-6G032�096:,F6�DF�G2L79')8�2-*}792�036�2nq � �Û'å(�J92>£¸2L6:796 ~ *}2>' ~9~ +-2L(%'�,u*]2L+5ï��G*096:+L+-*�092,u2-��2-79¾yóu=�ü�EFEt*d,F2L6�736"(�*}7�,u*M092�,FJ3,F,F2�¾}+L2�6�/�6:,t,u2�(/{96G2L7ú+L2-796%'�032 ~ DF2-79(�2 ~ 2L* ~ *}EtEF*}79*2L7ðAJ96�738%')Dt6¦2h,F6�� ~ 2h0925'yDFDF2¥£}*"096:+5EF6�¾)7A')+L6 ~ J9+LEF'y,u*K096:+L+s'1Et*}DF¾)6�7�,u6yw

• �r��³�»����y³������5�(0

• ¹��#�%�]096�+-+s'BEt*}DF¾)6�7�,u6¿Dt2LE ~ 6:,t,u*"'y+L+x�ù*}EtEF6�D¤£y'y,u*}Dt6)õ�(/{96 ~ J3�"6�EFEt6�Dt6¿*}DF2-¾}2L7A'�,u*¦EF2s'0A'y+L+s'<£)6�+-*(:2-,/. ~ 6�(:J9+L2L')DF6]036�+L+$��*)¾}¾}6:,t,u*9õnEt2s'Ñ0A'ú��*),F2 *}DtÃ92-,u')+L2Ò096�+-+s'²qr6�DFDF'�6096:+L+$��*}¾)¾}6:,t,u*50

• »���³%���������5�G096�+-+x�ù*}¾}¾}6´,F,u*3=��6:D�J97 'yEFEF6:¾}7A'y,F*ºEF6´,�092 ~ ')DF')�G6:,uDt2xõÒ2L+f��*¸096:+L+L* ~ Dt6�092-(�6d2�,F6�� ~ 2f092©'yDFDF2¥£}*�096�+EF6:¾}7A')+-6 ~ J9+-Eu'y,F*9=Þ�v')+L+$�¨'y790A')�G6�7�,u*�096�+-+L6¿0927/�6:DF6�738�6)õ#096´,F,F6)���#��N'��*��õ3,uDF'K,F6�� ~ 2 ~ Dt6´�096´,F,u2I6v,F6�� ~ 2h0h��')DtDF2-£)*K*}EFEt6�Dt£y'y,F2xõ9ö ~ *}EFEt2LÃ92-+L6 (�*}DtDF6�¾)¾}6�Dt6¦2 ~ ')Du'y��6´,uDF2�096�+I�G*036�+L+-*EF6:(�*}7309*�J37A' ~ DF*¸(�6�03J9Du'K2-,F6�Du'�,u2-£y'�0328ì�#�2�;�2N0#')0å6�Et6�� ~ 2L*9w• Et6§EF*),t,u*}E¤,u2L�G2s'y��*B2L+�»��������I�r�d+x��')790A'y��6:7�,F*"096�2IDt6�Et2L09J92IEF')Du.K¯��$�5��±9���<¶}���¸³ Ø

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

¢ ª Îc� Îc�è�5�1� ¢°\ ¡ �5Ð \7� £ \�¤ � ¢°¢ ���1� � ¡ � ¤5¥ �*� ¤ � ¢ � \ � \ £/.s� ¢°¢ ��� ¥*¢H� ����� ¢ � \�¢t¢°\7� � ¡ � £ ¤��¶}�¸���%��=��©7A')+-*}¾�')�G6�7�,F6)õ¸EF6vEt*),F,F*}Et,F2L�G2s')�G*

Põ+x��')790A'y��6:7�,F*�096:2�Dt6�EF2-09J92�Eu')DF.

»r±9��±9¼���¯��$¶}��¶}���³�¶}���� �#=

• Ý 7�6:DFDF*)DF6v796:+L+L'B096´,u6�Dt��2-7A')8:2L*}796�096:+L+L6 ¶}�h�#�������5±3� ���$')Et(�6:79EF2-*}796¿DF6´,F,u'�6v096 �(:+L2-7A')8�2-*}796°� ~ *}D¤,/'�'y0�J97]')730A')�G6�7�,u*"³��$�h�r³������r±A¯��"096:2�DF6:EF2-09J92xõ¸(�*)7 ~ 6:DF2-*09*'y797�JA')+L6y=ÛøvJ96�E¤,/' ~ ')Dt,F2L(:*}+s')Dt2-,u.Á(�2¿ö·')EtEu')2¿J3,F2L+-6 ~ 6:Då096:,F6�DF�G2L79')DF6Ñ+L' ~ *y�Et2L8:2L*}796?096�+-+s' ~ J9+-Eu')D�(:*}7K6�+-6:£y'y,u2-EFEt2L��' ~ DF6:(�2-EF2L*)796)õ�* £�£¸2s')7903*�')+-+s'©Et(%')DtEF2-EFEF2-�Ú'Et6�79Et2LÃ92-+L2¥,/.1')73¾}*}+s'yDF6v096:2IDu')032L*),F6�+L6:EF(:* ~ 2 0

• Hn�ù6�DtDF*}Dt6Ò736�+L+L'�036:,u6:DF�G2L7A'y8�2L*)796n096�+¸¹Á�A� ��»����#»������1096:+L+s' ~ J9+-Eu')D ~ *}Dt,u' ')0BJ97'y790A')�G6�7�,u*G³%���h�r³����$�5±A¯���032I±A¹Á»���������±·¶}���³�¶}���� �Ú(:*}7 ~ 6�Dt2L*¸09*K')797�JA'y+L6)=

Ö�r�Ö < ßÀßÀÞ}tçjv�Ùj}�ÛÚÒ} ÜÒ{YÞÞtv ßÀx~�)çP{èÜÀá¦xyv ÜÀ{YÞ½|l}�z }tÚ�� vsÞÞ�{ßÕáÀÞ��lv�x v�Þ z }�ÞÞ}t�;{èçP��ÚÀÜÀ�

HI6G��2-+L+L2-EF6:(�*}790 ~ J9+LEF')D§Ã92L7A'yDF2L6KEt*}79*²'y+�(�6�7�,FDF*²092nDt2L(�6:DF(/{96�2L7·092-£)6�DtEF2Þ(%')� ~ 2x=ÚHI*E¤,/'y,F*�092�')¾}¾)DF6�¾}')8�2-*}796>096:+L+L'?�Ú'�,u6�Dt2s'3õ�2}��*y,u2)032}DF*),u')8�2-*}796>6�Dt2-£)*}+LJ98:2L*}736�£}6:+L*¸(�2-EFEF2-��2$õ+L'�Et,FDu')*}Dt092L79')DF2L' ~ Dt6�(�2-EF2-*}796©(:*}7å(�J92�,/')+-2��G*),u2 ~ *}EFEt*}79*"6�EtEF6:DF6§Et,FJ9092s'�,u2�+-6©Dt6�7909*)79*(�')� ~ 2�092 ~ DF* £y'�2-� ~ *}Dt,u')7�,u2#092�,u6�*)DF2L6 DF6:+s'y,F2-£¸2LE¤,u2L(/{36 6 ~ ')Dt,F2L(�6:+L+L')DF2$= Ù 7 ~ 'yDt,u2-(�*}+L')DF6yõ+L'·Et(�* ~ 6�D¤,/'Á092�6:£)6�7�,uJ9')+L2 EF2LE¤,u6:��2f(�*)� ~ *}Et,F2f0A'Á09J96 ~ J9+-Eu')D���ýA73*}Du'3õ�736�2�EF2LE¤,u6:��2Ã92-7A')Dt2r032>@v4MEF(�* ~ 6:Dt,u2$õ�J973*]EF*}+-*Ú096:2�09J96�*}¾}¾}6´,F,u2rö1J979' ~ J9+-Eu')D���*�0A'�J37A' ~ J9+-Eu')D6:0bJ97iÃ3J9(�*º736�DF* ~ *y,uDF6:Ã9Ã�6�DF*Á6�EFEt6�Dt6<��*}7�,u6M092���*}+¥,u6å(�*)73��6�Dt��6M*ÁEt��6:7�,F2-,F6<')+-+s'|f6�+L'y,u2¥£2¥,/.Û-§6:796�DF')+L6¿6¦')+-+L6©,F6�*}Dt2L6¿(�*)79(�*}DtDF6:7�,F2x=

Ô�� ���5�����r��±ú�5�¸¯$¯��º³�»r±9����� Ø � �¸¹Á»��46:(�*}7309*d+L'å|�6:+s'y,F2-£¸2-,u.¦-¿6�796:Du')+-6)õ5+s' ~ Dt6�Et6�798�'<092>J979'M��')EFEF']096:��*}Dt�Ú']+-*ME ~ ')8:2L*y�,F6�� ~ *9õ�610A.�+-J9*}¾}* ~ 6:DF(�2-�å'���6�73*}��6:792�2-79E ~ 2L6�¾}')Ã92L+-2I2L7ÑJ979'�(�*}79(:6�8:2L*}796§ï�(�+L')EFEt2L(�'�ó096:+L+L'ÚýAEF2-(%'3= Ý 7A'M' ~9~ +L2L(�')8�2-*}7961Dt2L¾}J9')DF0A']2��G*),u2�*}DFÃ92¥,/')+-2�096:2nEF2LE¤,u6:��2�Ã92-7A')Dt2xõh(:*}7+L' ~ DF6:092L8:2L*}796<092¿��*y,u2©032 ~ DF6:(�6�EtEF2-*}796ú096�+ ~ 6�Dt2s')E¤,uDt*50§J97 ��6�79*}�G6�73*èEt2L�G2L+-6<EF2©ö

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� Îc� ¢�� ¥ � \�¢t\ ����� � �*� � Ï \7�X\ ¡ � ¤ � ¢°¢ �è� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5��� \ £���� \ � ¢ ÷

*}EtEF6�D¤£y'y,u*]796:+�Et2LE¤,u6���'ÚEt*}+s')Dt6B736�+�(�')EF*]032>;d6:DF(:J9DF2-*�09* ~ *�(/{96"ü�2-79Et,F6�2L7<(�*}� ~ +L6´,u�+s'§EFJ9'¦,u6:*}DF2L'¦036�+L+L'B|f6�+L'y,u2¥£¸2-,/.�-¿6�736�Du'y+L6)= Ù 7�ô�J96�+�(%')Et*9õ¸+s' ~ DF6:(�6�EtEF2-*}796v096:+ ~ 2s')796´,/'~ Dt6:£¸2LE¤,/'�0A')+-+L6B+L6�¾)¾}2�736:î�,u*)792s')736���*}DF732-£y'ÚJ97A'�E¤,u2-�Ú'Ú2-73��6�Dt2L*}Dt6B032 43′′

0h�¨'yDF(�*]*)¾}792EF6:(�*}+-*©Dt2LE ~ 6:,t,u*©')+09'y,u* *}EFEt6�Dt£y'y,F2-£)*v092 574′′

=>H���'%£)'y798%')�G6�7�,F*v096�+-+s'f+L*}73¾}2-,FJ9092L736�096�+~ 6�DF2L')Et,FDF*v£¸2L6:796�2L73092L(�'y,u*¿(:*}7 ω 6:0Kö�J379*§096�29(:*}EF2-09096´,F,u2��3ÿ��tÿ �2N�R����$!�24î>=k�h�(����R��ÿ�%��096:+L+x�ù*}DtÃ92-,u'3w

• ω 0

• Pbõ12L+�096�(�')092L�G6�7�,F*ë036�+ ~ 6�DF2-*03*i*}DFÃ32-,/'y+L6º09* £¸J3,F* ')+-+x�ù6��G2LEtEF2L*)796�0321*}79096

¾}DF'%£2¥,/')8:2L*}79')+L240

• γ õ9+$��6/�6´,F,F*�� * ~9~ +-6�D�,uDF')Et£)6�DFEt*Ú*KDF6:09EF{32-��,f¾}DF' £¸2¥,/')8:2L*}7A'y+L6�0

• r 6�0 s õ3(/{96§Et*}79*"2�03J96 ~ ')DF')��6´,uDt2,�X�tÿ�%*�*�Þ6Û�#�3ÿ���ÞDt2LE ~ ==�1(/{96§(%'yDu'y,t,u6�Dt2L8:8%')79*2-+IDF2-,u')DF03*�092�4{9' ~ 2LDt*9õ#(%')J3Eu'y,F*�0A')+-+x��')8�2-*}796¿EFJ32�Et6�¾}7A'y+L250A' ~ ')Dt,F6B096:+�(�')� ~ *¾}DF'%£2¥,/')8:2L*}79')+L6y=

HI6�ô�JA'y7�,F2-,u.ω6γ ~ *}EtEF*}73*T6:EFEF6:DF6º�G2LEtJ9Du'�,u6)õ 6�+L'k+L*}Dt*è(:*}�1Ã92-7A')8:2L*}796Ñ(:2¿��*}D¤�

792-EF(�6¿J37A'"Et,u2-�Ú'1�G*}+¥,u* ~ DF6�(:2LEF'K036�+L+L'1�Ú'yEFEu'1036�2I09J96§*}¾)¾}6:,t,u2�036�+IEF2-Et,F6���'1Ã92L7A'yDF2L*3=C?*}79*)EF(�2-J3,u6å+-6��Ú'yEFEF6yõÒEt2 ~ J9� ~ DF6´£}6:096�Dt6d+$�¨')730A')�G6�7�,u*Ñ096:¾}+L2 ')+-,FDF2Ò,FDF6 ~ ')DF')�G6:,uDt2~ *}Et,¤��ò)6 ~ +L6:DF2L')792xwKô�J96:Et,/'úö�+L'<ÃA')Et6]096�+-+s'd£)6�DF2¥ýA(%'Ñ096:+L+L'd£y')+L2-092-,u.M096:+L+L'²|�6:+s'y,F2-£¸2-,u.-¿6�796:Du')+-6�6"096:+L+L6¦,u6:*}DF2-6�(�*)79(�*}DtDF6:7�,F2x=¦@ 6:+ ¢ é)é ��ì J3+LEF6���« � 61q�'%ê+-*}D°��Ä � {A')7979*]Dt2L(:6´�£¸J3,u*Ñ2-+ ~ DF6:��2-*²@ *)Ã�6:+ ~ 6�D�2Þ+L*)DF*<E¤,uJ9032 (/{96�{A'y7979* ~ *}Dt,u'y,u*²')+L+L'M(:*}73��6�Dt�Ú'M096�+-+s'£y')+L2-092-,u.M036�+L+-6 ~ Dt6:£¸2LEt2L*}732Ò096:+L+L'²|�6:+s'y,F2-£¸2-,u.�-¿6�736�Du'y+L6ÚEtJ9+ Pb 096�+-+s' ~ J9+LEF')D1796:+?EF2-E¤�,u6:�Ú'²Ã32L7A')Dt2L*<z ¢ é3¢ �@? ¢ «3õ>(�*)7èJ37h��2-79(�6:Dt,F6�8�8�'ÑDF6�+L'y,u2¥£y'<096�+-+L*<�3=�ªk� ��£)6�092ÒýA¾9=¨�= ���´=øvJ96�E¤,u*"096:(%')032L�G6�7�,u*1036�+ ~ 6�Dt2L*¸09*�*)DFÃ92¥,/')+-6)õ�EF6:(�*}7903*"+s'Æ-§| öv0A'y,F*10A')+-+x�ù6��G2LEFEt2L*}7360925*}79036�¾}DF' £¸2¥,/')8:2L*}7A'y+L2xõ¸6�DF' ~9~ Dt6�Et6�7�,/'Úô�J92-790925J97A'G(�*}7��6�DF��'�2-79092-DF6:,t,/'"096:+L+s'"+-*}DF*6�Et2LE¤,u6�738%'3=

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

¢ « Îc� Îc�è�5�1� ¢°\ ¡ �5Ð \7� £ \�¤ � ¢°¢ ���1� � ¡ � ¤5¥ �*� ¤ � ¢ � \ � \ £/.s� ¢°¢ ��� ¥*¢H� ����� ¢ � \�¢t¢°\7� � ¡ � £ ¤��

§��7���*�tÿA�*ª��*«CB;®!¯R±A²h®°¯*³f®¦³´²hµ�¸�²?¹hº°¶[È�¶�®°¯�¹â³N¹h®°²c¶´¬?µ�º&¹c·�·=µED�¹c·�µ!³´¶T¾¶�³GF$H8¹�¯�¹c²hµ°·�¹JIf·�¶T¯5¹hµÀ¬?®°¯LK³´¶T¯*¼�µNM ¹�º&µ!³´¶�®t»A»#¹c²c¾�µ!³´¶�¾R¶Y¸V¹c²O��¼kµ°¯*³f® ²c¶ Ê ¼�µ!²�ºHµ ¶T·Ìº1¹h¬?µHº°¶�¿s¹c¯*³f® º1¹c·,¸k¹�²A¶�®RºH® ®!²Pc¶´³fµ°·[¹If¿�®t»�³´²�µ!³f®Ûµ!³�³´²hµ°¾t¹c²A»�®Û· + µ°¯*³´¶�¬�¶ ¸k®�¯�¹�·�¸�µt»A»�µ ÊRÊ ¶´®Æµ°·�¸V¹c²A¶�µt»�³´²�®NM�¯5¹c·(¬?µt»#®âº°¶RQTS�UVSXWZY[S]\_^�`-a

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� Îc� ¢�� ¥ � \�¢t\ ����� � �*� � Ï \7�X\ ¡ � ¤ � ¢°¢ �è� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5��� \ £���� \ � ¢ Ä

­ ±�����¶}�¸��¶}±ú�r�?�����5�²ã#��±�¡5���%±9�������5±A¯��

�©6:+L+x�ù6�Et2LE¤,u6�738%'b096:+L+-6Á*}79036º¾}Du'%£¸2-,u')8�2-*}7A')+-2¿79*}7ÂEt2�{A')7379*i(�*)73��6�Dt��6º032LDF6´,F,F6)õ¦�Ú'EF*)+L*Á*)EFEF6:Dt£y')8:2L*}792�2L73092LDt6:,F,F6d(:*}�G6dô�J96:+L+s'·EF* ~ Du'Á096:EF(:DF2-,t,/'Á736�+�(%')Et*º096�+-+s' ~ J9+-Eu')Dz ¢ é¢ �Z? ¢ «3=n4¸*}79* ~ 6�DF�K2-7]Et,uJ3092L*"096:2I��6´,u*¸092�032LDF6´,F,F2�092hDt2-£)6�+s'y8�2L*)796v092h*)79096¿¾}DF' £��2-,u')8�2-*}7A')+-2xõ�')+L(:J9792 096:2�ô�JA')+L2Ò��')7979* ~ ')D¤,u6]092�6:E ~ 6�DF2-��6:7�,u2�(�*)� ~ 2-J3,u2ÒEFJ9+f��2L')796:,u'3õ')+¥,uDF2�2L7�£}6:(�6¦DF2-¾}JA')Dt0A')79*"+$��*}EtEF6:Dt£y')8�2-*}796§')E¤,uDt*}79*}�G2L(�'3=

HI6d�G2L+-+L2LEt6�(:*}790 ~ J9+-Eu')D ~ *}EFEt*}79*Á6:EFEt6�DF6<(�*}79Et2L096:Du'y,F6d036�¾}+-2�*)DF*}+-*}¾}2 2-79(�Dt6�092-Ã92L+ ��G6�7�,u6 ~ DF6:(�2LEt2xõ�EFJÑ(�J32�£y')+LJ,/')Dt6B6´£}6�7�,FJA')+L2�6�/�6:,t,u2�032�*}730961¾}DF' £¸2¥,/')8:2L*}7A'y+L2x=�� + ~ ')E¤�Eu'y¾}¾}2L*�032�J97A' ,/')+-6�*}790A'õ�03*�£¸Dt6��G��*f6�EtEF6:DF6Þ2L7§¾}Du'y09*f092�6:£¸2L036�798:2s')Dt6�J97A'�£)'yDF2s'y8�2L*)796796:2>,u6�� ~ 2>032n')DFDt2-£}*]036�2�EF6:¾}7A')+-2�092>J979' ~ J3+LEu'yD�="�r*),uDt6�Ã9Ã�6�6:EFEt6�DF6GJ97h�ù2L� ~ *}Dt,u')7�,u6(�*)73��6�Dt�Ú'v096:+L+$��6:EF2LE¤,u6:798%'¿0929J37A'¿Du')092L')8�2-*}796 ¾)Du'%£¸2-,/'y8�2L*)7A')+L6Þ0929��*}7309*)� -5bëzY�´õ)*}DF2-¾y�2L79'y,/'f')+-+x�ù6 ~ *(�'f036�+¸z?2L¾ z ')73¾9= Ù 7�ô¸J36�Et,F*v(%'yEF*9õ�,uJ3,t,u2�¾}+-2�*}¾}¾}6´,F,u2�(:6�+-6�Et,F203*�£¸Dt6�Ã9Ã�6�Dt*6�EtEF6:DF6"EF*)¾}¾}6:,t,u2�'Úô�J96�E¤,/']Du')032s')8:2L*}796¦092r��*}7909*9w ~ 6�Dt(�2L�Úô¸J36�+L+-*�(/{96K'y,t,uJA'y+L�G6�7�,u6¦EF2Et,u'](�6�Dt(%')7309*dö"+L' ~ DF6:EF6:798%'3õr796:+L+x��')7909')��6:7�,u*�096:2�DF6:EF2L03J92>092>J37·(:6�D¤,u*M7¸J3��6:DF*å092~ J9+-Eu')D:õ?J97T')7909')��6:7�,u*·(�*}�1J3796d(/{36 ~ *),uDt6�Ã9Ã�6å6�EFEt6�Dt6²09* £¸J3,u* ~ DF* ~ DF2L*·')+-+s' ~ Dt6´�EF6:798%'M092>,/'y+L2�*)79096)=�&�2-79*}Du'�73*}7�Et2nöGDt2LJ9Et(�2¥,u2�'�,uDt* £)'yDF6KJ97ú,/')+-6K')790A')�G6�7�,F*9õ5�Ú'')� ~ +L2L')7909*©2L+97�J9�G6�Dt*¦��6�+L'¿092LE¤,uDF2-Ã9J98:2L*}796?E ~ ')8:2s')+-6!��096:+L+-6���2-+L+L2-EF6:(�*}790 ~ J9+LEF')D�EF*y,F,u**}EtEF6�D¤£y')8�2-*}796)õrEu'yDu. ~ *}EtEF2-Ã92L+-6"')J9�G6�7�,/'yDF6K+s'�Et6�79Et2LÃ92-+L2-,u.ÚýA79*d'MDt6�79036�DF+L'å')096�¾)JA'y,/'')0åJ97A'K�G2LEFJ3Du'3=

­ �ѳ%�5¼�¹º��¯�¯$��³��¸¶}�����k»���¯�³�±9�

�©+5ýA796B092 ~ *y,u6�D 096�Et(�Dt2-£}6:DF612r(�*)� ~ +-6�EtEF25��6:(�(�')792LEt��25(/{96BDF6:¾}*}+s'y79*�+L'G��*}Dt�Ú'y8�2L*)7966K+x�ù6�ô�J92-+L2LÃ3DF2L*Ú096�+-+L6"Et,F6�+-+L6K092�796:J3,uDt*}792xõrEF*)79*dE¤,/'y,F6�E¤,uJ9032s'y,F6G032-£}6:DFEt6�6:ô¸J9')8�2-*}792n092Et,u'y,u*3=íü�EtEF6Ñ{A')7379*Á2-+�(:*}� ~ 2-,F*�092�096:EF(�Dt2-£)6�DF6<+L6M�Ú')732-��6�E¤,/')8:2L*}732��Ú')(:DF*}Et(�* ~ 2L(/{96096:+L+L6M2L7�,F6�Du'y8�2L*)792f096�+-+L6 ~ ')D¤,u2L(:6�+-+L6å(/{96²(:*}� ~ *}79¾)*}79*Á+L'·E¤,u6:+L+s'õ 2L7è��J9798�2-*}796d096�+-+L6£y')DF2L')Ã92-+L2�,F6�Dt��*¸092L79')��2-(/{96)õI(:*}� ~ *}Et2L8:2L*}796yõ ~ DF6:EFEF2-*}796yõ�096:79EF2¥,/.d6:0º6:£)6�7�,uJ9')+L�G6�7�,u6096:+L+s'",u6:� ~ 6�DF'y,uJ3Du'3= øvJ96�E¤,u616:ô�JA')8�2-*}792 ~ *}79¾}*}73*Ú096:2�+-2L�G2-,u2�796�25£y')+L*}Dt25')EFEtJ97�,u2�0A')2

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

¢ á Îc� Îc�è�5�1� ¢°\ ¡ �5Ð \7� £ \�¤ � ¢°¢ ���1� � ¡ � ¤5¥ �*� ¤ � ¢ � \ � \ £/.s� ¢°¢ ��� ¥*¢H� ����� ¢ � \�¢t¢°\7� � ¡ � £ ¤��~ 'yDu')�G6:,FDF2f096�+-+L6MEt,F6�+L+-6)õ�'y0i6�Et6�� ~ 2L*º+L'���')EFEF'3õ�2L+ ~ 6�Dt2L*¸09*�032©DF*y,/')8:2L*}796yõ 6�(:()=¥õf6~ 6�Dt(�2L�B+s'§EF(:* ~ 6:Dt,u'�092�6:£}6:7�,uJA')+-2�*}¾)¾}6:,t,u2#(/{96vEtJ ~ 6:Du')73*�,/')+-2A+L2-��2¥,u2 ~ J9�16�Et(�+-J9096�Dt6v+s'£y')+-2L092¥,/.B0325')+L(:J9796¿6�ô�JA'y8�2L*)792x= Ù 7 ~ ')D¤,u2L(:*}+s'yDF6)õ6�Et2LEt,F*}79*K09J96§(:+s')EtEF2I092I6:ô¸J9')8�2-*}792h092E¤,/'y,F* ~ 6�D¦+s'å�Ú'�,u6�Dt2s'�796:J3,uDt*}792-(%'dJ3+-,uDF')096:79Eu'3w¦+L6K6:ô¸J9')8�2-*}792j�24� cfõr(/{96 ~ DF6´£}6�03*}79*J97å£y')+L*)DF6v�G2L792-��* ~ 6:Df2L+hDF')¾}¾}2-*"092IJ97A'"Et,F6�+-+s'"092h796:J3,uDt*}79252L7�,F*}DF79*K'y2 ¢ «"ò¸�Mõ96§+L66:ô¸J9')8�2-*}792�!$ 0R2�õ�(/{96 ~ DF6´£}6�03*}79*�J37K£y')+-*}DF6?2L7�,u*}Dt79*¦')2 é ò��d=>øvJ96�E¤,u2#+L2-��2¥,u2 ~ *}79¾}*}73** £�£¸2s')�G6�7�,u6§J979'G+-2L�G2-,/'y8�2L*)796�')2 ~ *)EFEF2-Ã92L+-2�£y')+-*}DF2�')EFEtJ97�,u250A')+ ~ 6�Dt2L*¸09*K092IDF*),u')8�2-*}796092nJ979'<@v4�wrEt6�')0�6�Et6�� ~ 2L*MEF2n,uDt*�£y')EtEF6:DF* ~ J3+LEu'yD¦(:*}7 ~ 6�Dt2L*¸092�2L7��6�DF2-*}DF2n'M�3= á �GE�õ+-6¿6�ô�JA')8:2L*}792é�2N� cfõ9ýA79*)Du'KDF2-,F6�7�J3,F6 ~ +L')J9Et2LÃ92-+L2xõ�£)6�DFDt6�Ã9Ã�6�Dt*Ú092-��*)Et,uDF'y,u6¿2-7A')096:¾}JA'y,F6)=Ù 79*)+-,uDt6KDF6�(:6�7�,u2ÒEt,FJ9092�� á&� 2L73092L(�')79*å(/{96�+$��2-79092-£¸2-09JA')8:2L*}796�092 ~ J9+LEF')D¦(�*}7 ~ 6:DF2L*¸092�092Dt*),/')8:2L*}736G2-73��6�Dt2L*}Dt2�'<�= ÷]��E¦(�*)73��6�Dt��6:DF6�Ã3Ã�6G+x�ù6�Et2LEt,F6�798�'d092ÞEt,F6�+-+L6K(�*}� ~ *}Et,F6�79*)7~ 2T�K0A'B��'y,u6:DF2L'v*}DF092-7A')Dt2s'v��'§Ã�6�73EñûI0A'BJ37�2-79EF2-6��G6�092#ô¸J9')DFò#õ�,uDu'§(�J32�'y79(/{96�ô¸J9')DFòd 2N�tÿ�%*�*�´õ ~ 2�� ~ 6�EF')7�,u2I092�e5�]61þÆ$(f,%���(/{36¦(:*}� ~ *}73¾}*}79*K+s'1��'y,F6�DF2L'1*}DF032L7A')Dt2s'k� =

­ �º³:� ���r���Á�r��ã�¯��Ò±A¹º¹�±A³%³%�?ã�¯��#¼��r¯�±3�y�C?2-DF(%'G+s'G��6´,/.�036�+L+-6B�G2L+-+L2-EF6�(:*}790 ~ J3+LEu'yD©(�*)79*}EF(:2LJ3,F6�Et*}79*�+-*(�')+L2-8�8%'�,u6§2L7<')����')EtEF2¾}+-*}Ã9J9+L')DF2$=�Hn��')+¥,/'Ú096:79EF2¥,/.ÚE¤,u6:+L+s'yDF6�(�')Du'�,F,u6:DF2-Et,u2-(%'G092�,u')+L2�')�G�Ú')EtEF2$õ�J3792-,u'�')+���'�,F,u*(/{96Ò¾}6�736�Du'y+L�G6�7�,u6nEF*)79*©*}¾)¾}6:,t,u2���*)+-,u* £)6�(:(/{92 Î õ)DF' ~9~ Dt6�Et6�7�,/'©J37A' (:*}79092-8�2L*)796n2L096�')+L6~ 6�Dn+s'v��*}Dt�Ú'y8�2L*)796 092#EF2-Et,F6��G2AÃ92L7A'yDF2l��796�2#ô�JA')+-2#')Ã9Ã92L')��*v£¸2-Et,u*¦(/{96 ~ J9�B'%£¸£)6�792-DF6 2L+~ Dt*(:6�EtEF*"092�E ~ 2-7�J ~ (/{96 ~ *}Dt,u'1')+-+s'¿��*}DF��')8�2-*}796f092���2-+L+L2-EF6:(�*}790 ~ J3+LEu'yD#�´õ'y,t,uDu'%£)6�DFEt*092¥£}6:DFEF2h��6:79*}�G6�792I032h(�J92I2 ~ 2��å2L� ~ *)Dt,/'y7�,F2�Et*}79*9w

• +s'K¶}±3�%���5��±Á¹�±9���¸±9¯��#õA2L7å(:J925J97A'�E¤,u6:+L+s'1£¸2L6:796§(%'y,t,uJ9DF'y,/'K0A')+5(�')� ~ *K¾}Du'%£¸2¥�,u')8�2-*}7A')+-6©092IJ37A'GE¤,u6:+L+s'1032I796�J3,FDF*}732I6�0M2L792-8�2s'�')0å*}DFÃ92¥,/')Dt6¿2L7�,u*)DF79*K')0M6�EtEu'�0

• +L*G³%¶}±A¹Ñ¼����5õ#2L7M(�J925J979'�Et,F6�+-+s'"092r796�J3,FDF*}7325£¸2-6�796¦(%'y,t,uJ9DF'y,/'K0A'GJ97<Et2LEt,F6���'g_h EH>AINM4WmZ7B#M4M4WL@ :�I4EHGKM BmU&BGK>cIN>YI4:�BLCHBGKG=B�<?W�OPU�W�I4:�òX:�WJH>jU�W#ñ>X@�BmC!:FOj>?M�BRG�GK:�:VM :KUH:=<XBLCH>XG�GK>èINM4>AGKG�>UH:�øþñ>c<X<�öH:�>,:�G�B�<?WtIN:=CHC!>XMNM BÕU1W�U1W�G�BòX:�WJH>7iji&:y>ACþ:KJHW�GÅM @4>�CHBRG�G�k BJ&BRG�:�I4:�CH>XGYC!:=BR÷@�BROjOYBÀ<XWG�W@ > lOYBR÷J&:ÅM E&C!:�JH>lJH>AG�útE&BGK>ÇI4WJ&W�BI IN>AJ�M :&G�>ÇINM4>XG�G�>ÇOYBI IN:�ñ>;J&>XG�G�B�I4>AútEH>AJHòAB�UH@4:�J&<X:KU&BGK>Ç>ACj:�Jtñ�>A<X>ÇINW�JHWJ°EHOj>X@ W�I4>~G�>�IfM >XG�GK>y÷�:K÷tBRJtM4:�:HIN>A÷JHWjC!:VE&JHWYIfM�BC!:�WYB�ñ�BJHòABRM4WjC!>XG�G�k >AñWG�EHòA:KW�JH>éCH:*útEH>AINM4:*I4:=IfM >XOj:nmpo9q9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� Îc� ¢�� ¥ � \�¢t\ ����� � �*� � Ï \7�X\ ¡ � ¤ � ¢°¢ �è� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5��� \ £���� \ � ¢ é

Ã92-7A')Dt2L*Ñ092fEt,F6�+-+L6](�*)�1J9792$õ?(�*)7T+L'ú(:*}79Et6�¾}J96:7�,u6<��*}Dt�Ú'y8�2L*)796�092fJ97TEF2LE¤,u6:�Ú',FDF2 ~ +L*10A'K(�J32h£2-6�796§6:E ~ J9+-EF*G+x�ù*}¾}¾}6´,F,F* ~ 2��å+L6:¾}¾}6:DF*9=

Ù 79*}+¥,uDt6)õÞö<')+¥,/'²+L' ~ DF*}ÃA'yÃ92L+-2-,/.<')79(/{96d096�+ ~ Dt*(:6�EFEt*Á2-7�£)6�DtEF*9õÒ2L7è(�J92f+x�ù2L7�,F6�Du'y8�2L*)796¾}DF' £¸2¥,/')8:2L*}7A'y+L6K(�*}7R'y+-,uDt2n*}¾}¾}6´,F,u2ÞEF+-6�¾�'M2L+ÞEF2-Et,u6:�Ú'dÃ92L7A'yDF2L*3= Ù Et2LEt,F6��G2Ò(/{36]{A')7979*��')¾}¾}2-*}DF2 ~ *}EFEt2LÃ92-+L2¥,/.]092?Et* ~ DF' £�£¸2-£)6�Dt6]EF*}79*Ñô�J96:+L+-2 ~ 2��º+-6�¾�'y,F2xõ ~ 6:D�79*}2 ~ 2��Á2L7�,u6:D¤�6�EtEu')7�,F2x=æü�0p6/�6´,F,u2¥£y')��6:7�,u6ú(�2-�T(/{96�EF2§*}EtEF6�D¤£y'bö�(/{36�2§EF2-Et,F6��G2¦Ã32L7A')Dt2¿EF2¥,uJA'y,F2796:¾}+L2A'y����')EFEt2A¾}+L*)Ã9J9+s'yDF23036�79Et2�{9')7979* ~ 6:DF2-*0923*}DFÃ92¥,/')+-23�G*}+-,F*¿(�*}D¤,u2A6�*}DFÃ32-,u6��G*}+¥,u*Et,FDF6´,F,u6y=

H5'¦E¤,uDFJ,F,uJ3Du'§096�¾}+-2A')�G�Ú'yEFEF23¾}+L*}Ã3J9+s')Dt23ö�,/'y+L6�(/{96�+L6�E¤,u6�+-+L6 ~ 2T�G��')EtEF2-£)6)õ�,uDF'¿(�J92* £�£2L')�G6�7�,u6f+L6�E¤,u6:+L+L6�032A796�J3,FDF*}732xõ�EF2L')79* ~ *)EF2L8:2L*}79'y,u6?£¸2-(�2L73*B'y+A(�6�7�,FDF*¦096�+-+x��')����')E��EF*3=?øvJ96:Et,F*G��6:79*}�G6�79*9õA036:,F,F*K096�+-+s'��!� ����� ��ÿ�rt� $&%3�s'�� ÿ&�#��ÿ)õ9ö§09* £¸J3,F*Ú')+h��'�,F,u*K(/{962L7�J97]')�G��')EFEt*B2-7Ú6�ô�J92-+L2-Ã9DF2-*§,FJ3,F,F6©+-6 ~ * ~ *}+s')8:2L*}732AEt,u6:+L+L')DF2A096´£}*}73*K' £)6�Dt6v+s'¦Et,u6:EFEF'6�736�DF¾)2s'§(�2L736:,u2-(%'§��6:092s'õ�6 ~ 6�Dt(�2L�¦+L6fE¤,u6�+-+L6 ~ 2T����')EFEt2-£)6 096´£}*}73*1'%£}6:DF6©J37A'¦£)6�+L*¸(�2¥,/.�G6�092L'v2L73��6:DF2L*)DF6)õ)DF2L��')796:7909*¿(:*}Eñû ~ 2T�"£2-(�2-796f')+9(:6�7�,uDt*�096:+L+x��')�G�Ú'yEFEF*3õ)09* £}6f+L'§036�7�EF2¥,/.GEt,u6:+L+L')DF6Bö ~ 2T�Ñ')+-,u'G6�+s' ~ DF*}ÃA'yÃ92L+-2-,/."096:+L+L'G��*}Dt�Ú')8:2L*}736¦032�J97²Et2LE¤,u6���'ÚÃ92-7A')Dt2L*ö ~ 2��å6:+L6:£y'y,u'3=

�©+-+x�ù2L7�,u6:DF79*�092©J97 'y����')EFEt*º¾}+-*}Ã9J9+L')DF6 ~ J9�R'%£�£}6:792LDt6ÑJ97 ')+-,FDF*���6:(�(%'y792LEt��*096´,F,u*�"#$&����"#$&���¥ÿ���!�Þ796�+hô�JA'y+L6v2-+�7�J9(:+L6�*KEt2�(�*)7�,FDu')6yõ ~ 6:D?£¸2s'�036�+L+L' ~ 6�DF032-,/'B092hEt,F6�+-+L60A')+-+x��')�G�Ú')EtEF*9= Ù 7�ô�J96:Et,F* ~ Dt*(:6�EtEF*<032�(�*}7�,uDF')8�2-*}796"+-6GE¤,u6:+L+L6�096�+n7�J9(�+-6�*M79*}7ú(�*)+¥�+s'yEFEu'y79*���'ÑÃ�6:79Eñû¿��*}Dt�Ú')73*·036�2fEF2-Et,u6:��2�Ã32L7A')Dt2���*)+-,u*ÑE¤,uDt6:,F,F2xwM2L79(:*}7�,uDF')7909*ú,/')+-2EF2-Et,F6��G2xõ9J97å,u6:DF8:*�*}¾)¾}6:,t,u*K79*}7MEF2I+-6�¾�'"��'G'y(�ô�J92LE¤,/'K6�796:DF¾}2L'"(�2L736:,u2-(%'K'"E ~ 6�Et6�096:+¥�+x�ù6�736�DF¾)2s'ú¾}Du'%£¸2-,u')8�2-*}7A')+-6M036�+�EF2LE¤,u6:�Ú'3=ëq�')+L6<')J9�G6�7�,u*�092©6:796�Dt¾}2s'·(�2L736:,u2-(%'·096�+-+L6Et,F6�+-+L6Ú+-2LÃ�6�Dt6�+-2L�G2-,/']+L'd(�*)7�,FDu')8:2L*}736�096�+-+x��')�G�Ú')EtEF*M6:£¸2-,u')7909*<2L+Þ(�*}+-+s')EtEF*9= Ù +?DF2-EFJ9+ �,/'�,u*Ú032�ô�J96�E¤,/'�(:*}7�,uDu'y8�2L*)796�öB+s'�(:*}� ~ ')DFEF'Ú092rJ97²7�J9(:+L6�*](:6�7�,uDF')+L6B��*)+-,u*G096:79EF*]6(�*)� ~ '�,F,u*3õ3(/{96§��'%£}*}Dt2LEF(:6§+x�ù*(:(�*}DtDF6�738%'"092I2L7�,F6�Du'y8�2L*)792�,uDF'K@v4�6§EF2LE¤,u6:��2IÃ92-7A')Dt2x=

q�J,F,u2I2���6:(�(%'y792LEt��2�ýA79*}DF'K036�EF(:DF2¥,F,u2IDt6�7903*}79*K¾}+L2�')�G�Ú')EtEF2�¾}+L*}Ã3J9+s')Dt2�6:Et,FDF6���'���G6�7�,u6¦2L7�,u6:DF6:EFEu'y7�,F2xõ#*}+¥,uDF6¿(/{36�(�*)��6§*}¾}¾)6:,F,F2I2L7MEFöyõ�'y79(/{96 ~ 6�Dfô�JA')7�,F*ÚDF2-¾}JA')Dt0A'"+s'DF2-(�6:DF(%'å092 ~ J3+LEu'yD¦Ã32L7A')Dt2L6"�G*}+-,F*]Et,FDF6:,t,u6yõ�EFJ·(�J32Þ(:*}� ~ 2L6:DF6K¾}+L2�Et,uJ3092n096�Et(�DF2¥,F,F2�796�+

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

�)� Îc� Îc�è�5�1� ¢°\ ¡ �5Ð \7� £ \�¤ � ¢°¢ ���1� � ¡ � ¤5¥ �*� ¤ � ¢ � \ � \ £/.s� ¢°¢ ��� ¥*¢H� ����� ¢ � \�¢t¢°\7� � ¡ � £ ¤��ê/�= �¸õ9*}+-,FDF6¿'y0M*)¾}¾}6:,t,u2 ~ 2��Úï�6:EF*),F2L(:2¥ó (�*}�G6¿EF2-Et,F6��G2�Ã92-7A')DF2�(�*}� ~ *)Et,u2�0A'"J97A' ~ J9+-Eu')D6§J97åÃ9J9(:*�736�DF*�� ÿ!��� "m�P�*����ÿ����c�´õ9EtJ9Ã9�G2L+-+L2LEt6�(:*}790 ~ J9+-Eu')D�6¿(:*}Eñû>£¸2s'=

Ù 79*}+¥,uDt6©+L6 ��2-+L+-2LEF6:(�*}730 ~ J9+LEF')D?Et(�* ~ 6�D¤,u6 ~ *}EFEt*}79*16:EFEF6:DF6§J3,F2L+L2-8�8�'y,u6 ~ 6�D E¤,uJ9092L')DF6+-6�(�')Du'�,F,u6:DF2-Et,u2-(/{96�096�+-+x��')����')EtEF*¿Et,F6�EtEF*9=Ò4 ~ 6�EtEF*9õ09J9Du'y7�,F6 +$��*)EFEF6:Dt£y')8:2L*}796�092 ~ J9+-Eu')D' ~3~ ')Dt,F6�796:7�,u2 ')0i')�G��')EFEt2�¾}+L*}Ã3J9+s')Dt2xõnEF2f,uDt* £)'y79*ÁDt2LEFJ3+-,/'�,u2 2-7A')E ~ 6:,t,/'y,F2f(�*}�G6<'y06:EF6�� ~ 2-*d£y')+L*)DF2n796�¾}'y,u2¥£2Þ092 P =Ñø¿J36�Et,F2?0A'�,u2ÞEF2 ~ *}EtEF*}79*<E ~ 2-6�¾�')Dt6 ~ 6�79EF')7909*Ñ79*)7(/{96�2L+ ~ 6:DF2-*09*§096:+L+-6 ~ J9+-Eu')Dn092-��2-7¸J32LEF(�'3õ)��'¿(/{96�EF6�� ~ +-2L(�6:��6:7�,u6�79*}2A+-*¿*}EFEt6�D¤£2L')�G*092-��2-7�J92LDt6 ~ 6:DB6/�6´,F,F*<096:+L+x��')(:(�6�+-6�DF')8�2-*}796"096:+L+s' ~ J9+-Eu')D§796:+n(%')� ~ *M¾}DF' £¸2¥,/')8:2L*}7A'y+L6096:+L+$�¨')�G��')EFEt*9= Ù ~ *),F2L8:8%')7903* ����*}7909'y,/')�G6�7�,F6!�Ú(/{96ú+s'Á£)6�+-*(:2-,/.Á,FDu')E¤£}6:DFEu'y+L6Ñ096:+L+s'~ J3+LEu'yD ~ *}EtEu'K6�EtEF6�Dt6¦,FDu')Et(�J9DF'y,/'G'%£¸DF6��G*9õ92-7å¾}6�796:Du')+-6)õ

˙PobsPobs

=˙Pintr

Pintr+alc

�x�¸= ���

0A'"(:J92∣∣∣∣∣

˙PobsPobs

∣∣∣∣∣ c < |al|�x�¸=¨�k�

H��¨'y(�(�6:+L6:Du')8:2L*}796§+-J979¾}*K+s'"+-2L796�'1092h£¸2LEt,u' ~ J9��6:EFEt6�DF6B��6:EFEF'G2-7dDt6�+s'y8�2L*)796¿(�*}7M+s'092-Et,u')798%' ~ Dt*}2L6´,F,u'y,/'Ñ096:+L+s' ~ J9+LEF')D"0A')+�(:6�7�,uDt*Á096:+L+x��')�G�Ú'yEFEF* R⊥ õ?+L'²�Ú'yEFEu' Mint(:*}7�,u6�7�J3,u'd796:+L+L'�Et��6�DF'<'%£}6:7�,u6G(�*}�G6KDu')¾}¾)2L*]+s']092-Et,u')798%'],uDF']+s' ~ J9+-Eu')D§6K2L+>(:6�7�,uDt*096:+L+$�¨')�G��')EFEt*�6"+$�¨')73¾}*}+L*

θ,FDu'�+s'�092LDt6�8�2-*}796B096�+-+x��')(�(:6�+L6:Du')8:2L*}736�096:+L+s' ~ J9+-Eu')Dv6:0ú2L+

~ 2L')79*"096:+I(�2-6�+L*3wal = −GMint

R2⊥

cos2 θ sin θ�x�¸=�ªV�

0A'1(:J92xõ3J3,u2-+L2L8:8%')7309*1J97A'"E¤,u2L��'1' ~3~ DF*}EtEF2-�Ú'y,u'1092 Mint

õ9Et2h*),F,F2L6:796¿J97A'"Et,F2L��'�096:+L+s'�5�¸��³%��� °·¶}�¸��� ��±A¯��Ú096:+L+$�¨')�G��')EFEt*�� é°� w

ρ(0) =

∣∣∣∣alR⊥

4πk2G sin 2θ

∣∣∣∣ >∣∣∣∣alR⊥

4πk2G

∣∣∣∣ =

∣∣∣∣∣9cR⊥ ˙Pobs

4πk2Gr2cPobs

∣∣∣∣∣�x�¸= ÷��

09* £)6rcöG2L+nDF')¾}¾}2-*M036�+�"#$&���§096�+-+x��')�G�Ú')EtEF*9=�C?*}79*}Et(�6:DF6Ú+L'M036�79Et2-,/.M(�6:7�,FDu')+-6Ú096:+¥�

+$�¨')�G��')EFEt*�(:2 0A.�2L� ~ *}D¤,/')7�,F2�2L73��*}Dt�Ú'y8�2L*)792 EFJ3+L+s' ~ DF*y��*}79092¥,/.ú096�+-+s'�EtJA'ÁÃ9J3(%'Á0929;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� Îc� ¢�� ¥ � \�¢t\ ����� � �*� � Ï \7�X\ ¡ � ¤ � ¢°¢ �è� \�¢°¢°\7� � ¡ � £ ¤ � ¥�¢H� �5��� \ £���� \ � � ¢

~ *),u6:798�2L')+L6y=�v'f092LEt(�*}DtEF2¸')7A')+-*}¾}{92y092 ~ J9� *),F,F6�796:DF6nJ97A'fEt,F2L��'�096�+���±9»r»��#���%��¹Á±A³�³�±Rs3¯$�r¹º� Ø

�5��³���� °Ñ036�+L+$�¨'y����')EFEt*9õ�2-+�(:J92>(�*)73��DF*}7�,F*M(:*}7ú+s'�E¤,u2L��'Ú096:+L+L'Ú�Ú'yEFEu'](/{96 ~ *}EtEF2s'y��**),t,u6�736�DF6]09')+?7�J9�G6�Dt*·032?Et,F6�+-+L6�(/{96]*)EFEF6:Dt£¸2s'y��*Ñ796:+L+L'<ÃA')7909'²*),F,F2L(%'d(�2 ~ J3�·09')DF6J97h�ù2L036%'dEtJ9+L+L' ~ DF6�Et6�798�'²092Þ*}¾}¾}6´,F,u2�73*}7Á£¸2LEt2LÃ92-+L2xõI(:*}�G6Ú@©4·*²zÒJ9(/{92 @�6�Dt2x=åü�E ~ Dt2¥��G6�7909*

R⊥(�*}�G6

θ⊥Dõ?03*�£)6

DöM+s'Ñ092LE¤,/')738%'ú096�+-+s' ~ J9+-Eu')DK0A')+�Ã9')DF2-(�6�7�,FDF*·096�+

EF2-Et,F6���'ÁEF*}+L')DF6yõ 6θ⊥

+L'Á092-Et,/'y798%'k')73¾}*}+s'yDF6²' ~9~ ')Dt6�7�,u6Ñ096:+L+L' ~ J9+-Eu')D�09')+©(:6�7�,uDt*096:+L+x��')�G�Ú'yEFEF*3õA6�0²2-7�,FDF*¸09J9(:6�7909*Ú+s'KÃ9DF2-+L+s'y798%'KEFJ ~ 6�D¤ýA(�2L')+L6 ä �G6�092L'�796:+L+L'GÃA'y790A'.Ñ')+-+x�ù2L7�,u6:DF79*1036�+L+L'1+L2-796%'1092h£¸2-Et,/'"Et*),F,F6�Eu'K0A'

θ⊥õΣV,θ⊥

õAEt2I*),F,F2L6�736�� ¢ � � w∣∣∣∣∣

˙PobsPobs

(θ⊥)

∣∣∣∣∣ c < 5.1× 10−18MLV

[ΣV,θ⊥

104LV,�

] �x�=�«k�

Ý 7h�ùJ9+¥,u2L��' 2-73��*}Dt�Ú')8:2L*}736Ò2-� ~ *}Dt,u')7�,u6ÒDF2L¾)JA')DF09'v+s' ~ Dt6�Et6�798�'¦092 ~ +s')Et�Ú' 2L*}792-8�8�'��,u*K796:¾}+L25'y����')EFEt2 0+s'1�G2LEFJ3Du'"092I092-E ~ 6�DFEt2L*}736���£�=èê/�= ¢ � 096�2IEt6�¾}7A'y+L2 ~ Dt*�£)6�792-6�7�,u250A'~ J9+-Eu')DnEt2-,uJ9'y,u6f2L7�')�G�Ú'yEFEF2A¾)+L*}Ã9J3+s')Dt29092 ~ 6�73096 +-2L796�')DF�G6�7�,F6�0A')+L+L'v+L*}Dt*B032LEt,u')798�'¦0A'79*}2$w�ô�J96�E¤,u*���' ~ 6�79EF')DF6§(/{96¦+s'"092-E ~ 6�DtEF2L*)796¿09* £¸J3,/'G')+I�G6�8�8:*�2-7�,u6�DtEt,F6�+L+L')DF6©092-£)6�7�,u2,uDF')EF(:J9Du'yÃ92L+-61DF2-E ~ 6:,F,F*å']ô¸J36�+L+L'Ú09* £¸J3,/'M')+ ~ +s')Et�Ú' ~ DF6�Et6�7�,u6G796:+L+x��')�G�Ú'yEFEF*3õ�+s'�(�J92096:79EF2¥,/.dEt2 ~ J9�²Et,F2L��')DF6K(:*}��6GDu' ~9~ *)Dt,u*M,uDF'd+s']£y')DF2L')798�'d096:+L+L6K�G2LEtJ9DF6G092Þ092LE ~ 6:D¤�EF2-*}796v6¿+L'�£y')DF2L')798%'1036�+L+-6©092-Et,u')798�6¿036�+L+-6 ~ J9+-Eu')DL��ö¿796:(�6�EtEu')Dt2L*G(/{96§EF6¿796¿*)EFEF6:Dt£¸2L73*')+-��6:79*å����ª3õ ~ 6:DF(/{5ÓG+L6�Et,u2-��6K'yÃ9Ã92s'y��*Ú£y')+-6�798�']Et,/'�,u2LE¤,u2-(%'k� *)EFEF6:Dt£y'y,F6G2-7úJ97ú0A'y,u*')�G�Ú'yEFEF*3=

t 8 :(C!>9u&JH:=I4<X>wv9x&y{z{zp|P}�~N|5�&�N�]�9x��R�9y�|Pz���C!:�EHJÆW�÷÷>XMNM WÌ<?>AGK>cIfM >jG�BmOYBR÷�JH:ÅM E&C!:�JH>jñ°:�I4E&BRG�>jOj>AC!:=B�C!:EHJ�k BR@ >AB�U&B@4:VB�C�EHJLI4>A<XWJ&C!WYCZk BR@�<?WjútE&BCH@ BRM4W9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

n U^XZO�`ågl[hg �

� a QR`Mg VWO VWO S<OIPkQTS<PRU

å.rtq ×æ{ Ø�vs�;} ÜÒ{YÞ�Þ�v xé}�çP{jxéçjv

H5'úDF2L(:6�Dt(%'ú096�+-+L6 ~ J9+-Eu')DG79*}7 ~ J9��6�EtEF6�Dt6<6:EF6�¾)J92-,u'·2-7è,F6�� ~ *·DF6�')+L6yõÒ��'·Dt2L(/{92-6�096J97<+LJ979¾)*�+s'%£}*)DF*Ú032>')7A'y+L2LEt25096�2�0A'y,u2rDF6:¾}2LE¤,uDF'y,u2r0A')2rDu')032L*),F6�+L6:EF(:* ~ 2x= H5' ~ Dt*(:6�09J9DF'E¤,/')7909')DF0d'y,F,FJA'"+L6¿Et6�¾}J96:7�,u25* ~ 6�Du'y8�2L*)792,��EF(/{96:�Ú'y,F2L8:8%'y,F6¦2-7]ýA¾}J9DF'G�= ¢ � w

• ����ã���³:� ��±9�������5�M�r�¸� ³:�¸ã��5±A¯��

• �r�¸�r�$³�»�����³%�����r�

• � ±9³:� � ���5���������Ò��±9��³tÿx����¹• ÿñ��¯$�r�$�5ã

• ³��#��� �$�5ã@�6�2 ~ ')DF')¾}Du'�ýÚEt6�¾}J96:7�,u2�0A')DF�¦J97A'¦Ã9DF6´£}6v036�EF(:DF2-8�2L*)796f092#ô¸J36�Et,F2 ~ ')EFEF')¾}¾}2$õ¸6:0Ú2-79*}+-,FDF6096:+L+-6 ~ DF*)Ã9+L6:�Ú'y,F2L(/{96©+L6�¾}'y,u6§')+I�G*),F*"*}DFÃ92¥,/')+-6©096:¾}+L2�*}¾}¾}6´,F,u2�*}EFEt6�Dt£y'y,F2x=

­ ±�����ã��$³´� ��±9�������5�<�5�¸�?³���ã��5±A¯$�Ù Du')092-*),u6:+L6:EF(�* ~ 2�6�Et6�¾}J9*)79* ~ 6�Dt2L*¸092L(�')��6:7�,u6"096:+L+L6���*�RÔ���K796�+-+L6"ô�JA')+-2�DF6�¾)2LEt,FDu')73*d2Et6�¾}7A'y+L2IDu'y092L* ~ Dt*�£)6�792-6�7�,u2r0A'GJ97A'KEF6�+-6�8:2L*}7A'�,/'KDF6�¾)2L*}796§096:+5(�2L6:+L*9= Ù +IEF6:¾}7A')+-6BDF')092L*

�)�

¡ �5� \ � ��¢!� äc� \ �,�&� �5¤�\�¤�\ � \ ¡ ��� ¡ � �)�

§��7���*�tÿ��Vª�¨k«m»�¬cË�¹�¿LµÆº&¹�¶5¸�µt»A»�µ ÊRÊ ¶éº°¶~¬#¼1¶�#̬X®°¿�¸�®t»c³fµÛ¼�¯�µè¸�²h®R¬X¹hº!¼1²hµ.º!¶�� �-�w� � �ÍT�F®°¯�³N¹-'I�^�`Pa�M

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

�yª äc�g�h� ¢ �YÏc� �A\k¤ � ¢°¢ ��� \ ¡ �1� ¡ �

(�' ~ ,/'�,u*ú0A'ÑJ97RDu')032L*),F6�+L6:EF(:* ~ 2L*²£¸2-6�796](�')� ~ 2L*}7A'�,u*ÑEF6:(�*}7309*�2-7�,u6�D¤£y')+L+-2Ò092 ,F6�� ~ *Dt6�¾}*}+L')DF2$õ3EtJdJ97d(�6:Dt,u*G7�J9�G6�DF*G092I(�')7A')+-2h*}¾}7�J979*G096:2rô�JA'y+L2I(�*)DFDF2-E ~ *}79096§'y0dJ97d096´�,F6�DF�G2L79'y,u*"2-7�,F6�D¤£)'y+L+L*�092I��DF6�ô�J96:798�6y=�H5'"DF6�¾)2LEt,FDu')8:2L*}736§' £�£¸2L6:796¦2L7å��*}DF��'y,u*"Ã32L7A')Dt2L*EtJ�7A'yEt,uDt2��Ú'y¾}796:,F2L(:2xõh2�(:J92�0A'y,F2>£}6�73¾}*}79*dEu')+¥£)'�,u2>EtJ�092-EF(:*dDt2L¾}2-09*]')+��G*}�G6�7�,u*]0926/�6´,F,uJ9')DF6§+x��')7A'y+L2LEt2x=

H5'²EF6:79EF2-Ã92L+-2-,/.å096:+ Du')032L*),F6�+L6:EF(:* ~ 2L*3õ�096´ýA792-,u'²(�*}�G6�096:79EF2¥,/.²092ÞðAJ9EtEF*ú��2-792L��'Dt2L+L6´£y')Ã92L+-6 09')+L+$�¨')7�,F6�797A'õ9ö¿096:ý9792-,u'G0A'�� éH� w

Smin 'S/N · TsysG√n∆ντ

(W

P −W) 1

2 �$�= ¢ �

09* £)6S/N

öÞ2L+)Du' ~9~ *}D¤,u*fEF6:¾}7A')+-6´��DtJ9�G*}DF6��G2L792-��*?')(�(:6:,t,/')Ã92-+L6yõ Tsys öÒ+L' ,u6�� ~ 6�Du'�,uJ�DF'¦092#DtJ9��*)DF6f096�+�EF2-Et,F6���'3õGö 2-+A¾}JA')0A'y¾}79*¦096�+-+x��')7�,u6�737A'¦2-7��¦�}ßyê)õ

n2L+A7�J9�G6�Dt*B032

~ *}+s'yDF2L8:8%')8:2L*}732xõ τ 2-+�,F6�� ~ * 09232-7�,u6�¾)Du')8:2L*}796Þ2L7BEF6:(�*}79032xõ W +L' +s'yDF¾}{96:8�8�'©096�+EF6:¾}7A')+-6*}EtEF6:Dt£y'y,u*3õ)(/{96Ò092 ~ 6�79036�Du.f0A'f,uJ3,t,u2�¾}+L2�6/�6´,F,F2¸032¸036:,u6:DF2-*}Du')�G6�7�,F* 096:+�EF6�¾)7A')+L6Þ09* £¸J3,u2')+��G6�8�8:*"2L7�,u6:DFE¤,u6�+-+s')Dt6)õ¸(�*}�G6©+-*�Et(%'y,t,u6�Dt2L79¾Õ�

∆tscatt�n6v+s'B092LE ~ 6:DFEF2-*}796�� ∆tDM �´õ096´�Et(�DF2¥,F,F2 ~ 2��¦'%£y')7�,u2$õ�09')+),u6:� ~ *f092�(%'y� ~ 2-*}7A')�G6�7�,F* tsamp 6n0A')+-+s'?+L')DF¾){96�8:8%'�2L7�,uDt2L79Et6�(�'096:+IEF6:¾}7A')+-6

Wint

Et6�(:*}7909*�+s'1DF6:+s')8:2L*}736

W 2 = W 2int + t2samp + ∆t2DM + ∆t2scatt

�$�= ���

­ ±Á�5�¸����³�»�����³%�����5�

� ~ ')Dt,F6 2L7"DF')DF2(%')Et29796�23ô¸J9')+L2¸+s'v�G2LEtJ9Du'©0323092-E ~ 6�DFEt2L*}736 ö�79*),u'â�$')0K6:EF6�� ~ 2-*9õ}ô�JA')7�09* ~ J97�,u2L')�G*G+$�¨'y7�,F6�7979'G£}6:DFEt*�J97²'y����')EFEt*�¾)+L*}Ã9J3+s')Dt6¿+s'K(�J925092-Et,/'y798%'GöB(:*}79*}Et(�2¥�J3,u'k�?2L+h£y')+-*}DF6 £)'K(�6:DF(�'y,u* ~ 6:Df,F6�7�,/'�,u2-£¸2$=?4¸25' ~9~ +-2L(%'"'Kô�J96�E¤,u* ~ J97�,u*�+s' ~ Dt*(:6�09J9DF'096:EF(:DF2-,t,/'f796�+�ê/�= ¢ õ}' ~9~ +L2L(�')7909*fJ979' 0927/�6:DF6�738%'f092���')EF6Þ* ~9~ *}Dt,FJ97A'���Dt6�+s'�,u2-£y'f'f092-£)6�D¤�Et2�£y')+L*)DF2#092��¿;��?')+-+L6�EF6:DF2L6 ,u6�� ~ *}Du')+-2A096�2�092-£)6�DtEF2�(�')7A')+-2�032���Dt6�ô�J96�738%'3=Þ�©* ~ *K'%£}6:D' ~3~ +L2-(%'y,F*B+-*�Et��'yEu')�G6�7�,u*3õ+-6©EF6:DF2-6 ,u6:� ~ *}DF')+L2ADt6�+s'�,u2-£)6©'y2�£y')Dt2�(�')7A')+-2#£)6�79¾)*}79*"EF*)�K���'y,u6 ~ 6�D ~ Dt*03J9DFDt6GJ37h��J3792L(�'åEt6�Dt2L6",u6:� ~ *}Du'y+L6�052-+ ~ DF*¸(�6:092L�G6�7�,F*壸2-6�796�' ~9~ +-2L(�'y,u*

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� äc� \ �,�&� �5¤�\�¤�\ � \ ¡ ��� ¡ � �}÷

~ 6�Df092-£)6�DtEF2h£y')+L*)DF2�032 ~ DF* £y'"096�+r�¿;�=

­f® ±9�r±A¯���³%�?�r� � ���r�����¸�� ¾}7925EF6:DF2-6B,u6:� ~ *}DF')+L6§096:092LE ~ 6:DFEu'Ú£¸2-6�796BEF*),t,u* ~ *}Et,u'Ú')0<J97h��')7A')+-2LEF2I032�&A*}J9Dt2L6:D ~ 6�D096´,u6�Dt��2-7A')Dt6G+$��6:EF2-Et,u6:798%'M092 ~ 6:DF2-*092-(�2¥,/.3= Ù 7ÁEt*}Et,u')798%'õ>EF2n* ~ 6�DF'dJ97A'å,uDF')Et��*}Dt�Ú'�,/'£}6:+L*¸(�6K092�&A*}J3DF2L6:D�� ��� �Û� ~ 6:D¦2-79092¥£2-09JA')Dt61+L6"(:*}� ~ *}736�7�,u2>032n&#*)J9DF2-6�Dv796:+L+L'�EF6�Dt2L66�EF')�G2L7A'y,u'3=¦øvJA')+-*}Du'GJ97ú2L� ~ J9+LEt*Kï�DF6%'y+L6´óB09* £¸J3,F*å')0ÑJ97A' ~ J9+-Eu')D©EF2s' ~ DF6:EF6�7�,F6)õ5+s'EFJ9'ú��*}Dt�Ú'Ñ79*)7TöåEF2-7�J9EF*}2-0A')+-6)õ ~ 6:DF(:2L��' £¸Dt6��G*·+L'Ñ(�*}� ~ ')DtEu'Ñ092fJ97A'úEF6:DF2L6å092f'yD¤��G*}792L(/{36)õ5+s'�(:J92Þ')� ~ 2L6�8:8%']Eu'yDu.],/')7�,u*M��')¾}¾}2-*}DF6Bô¸J9')7�,u*<�G2L73*}DF61öG2L+Y'���2N�½"�k"���´õ(�2-*öK+L' ~ 6�Dt(�6�7�,FJA')+L6�096�+ ~ 6�DF2-*03*d092ÞDF*y,/')8:2L*}796K796:+L+L'Mô�JA')+-6�ö ~ Dt6�EF6:7�,u6]+x�ù2L� ~ J9+-EF*9=��6:Dvô�J96�E¤,u*å�G*),u2¥£}*�Et2�6�Et6�¾}J36"J97A' ~ Dt*(:6�09J9DF'�092R0°$&�7'���%*�åÿ�� $&%�� "#$�wf2L7 ~ Du'y,F2L(%'GEF2EF*)����')79*M')+-+s'���DF6:ô¸J36�798�' ~ DF2-79(�2 ~ ')+L6"2n(:*}7�,uDF2-Ã9J3,F2Þ03*�£¸J3,F2?'y+L+L6G')Dt��*)792L(/{96K092nEt6�(´�*}7903*9õ�ô�JA')D¤,u*9õ�6�(:()=å*}DF032L796y= Ù 7ºô�J96�E¤,u*²�G*03*dö ~ *)EFEF2-Ã92L+-6K2L79092¥£¸2L09JA'yDF6K��6:¾}+L2-*]+s'~ Dt6�EF6:798%'§0923')+L(:J9796?��Dt6�ô�J96�738�6f(/{96 ~ *y,uDF6:Ã9Ã�6�DF*¿6:EFEt6�DF6f(:*}DFDt2LE ~ *}79036�7�,u23')+L+L'���DF6:ô�J96�7�8%'B092�Dt*),/')8:2L*}736 092�J97A' ~ J9+LEF')D�=éÑ©2L6:796v')+-+s'¿ýA796v(:*}� ~ 2L+L'y,u*¦J97�6:+L6�73(�*"092#��DF6:ô¸J36�798:6(%'y79092L09'y,u6yõ¸(:*}DFDt2LE ~ *}73096�7�,u6 ')2 ~ 2-(�(/{92#796:¾}+L2AE ~ 6´,F,FDF2#092�&A*}J9DF2-6�D�Dt6�+s'�,u2-£¸2A'y29£)'yDF2#Et,u')092096:+h��*}+L092-79¾"')Dt��*)792L(:*9=

�:¯�ÿñ��¯������rã� ô�J96�E¤,u* ~ J97�,u*9õÒ6�7�,uDF'·2-7R¾}2L*¸(�*Ñ+L' ~ DF*¸(�6�03J9Du'ú092 ��*}+-092L79¾<(/{96)õ 2-7RÃA')EF6M')+-+L6�2-7���*}Dt�Ú')8:2L*}73290A'y,F6©0A')+-+x��')7A')+-2LEt23092�&A*}J9Dt2L6�D:õ�DF2 ~ 2L6�¾}'§2-+#EF6�¾)7A')+L6�096:092LE ~ 6:DFEF*Ò��(�*)7�,F6�7�J3,F*796:+L+s'fEF6:DF2-6Þ,F6�� ~ *}DF')+L6�Dt6�+L'y,u2¥£)'�')0BJ97�(:6�Dt,F*¿�¿;��r'�,FJ3,F,F2¸2�£y')+-*}DF2�096:+ ~ 6�Dt2L*¸09*�(%')79032¥�0A'y,F2

PDMcand

DF6:+s'y,F2-£¸2�'1ô�J96�+��¿;�=#46:(�*}7309*K+s'BE¤,/'y,F2LE¤,u2L(�'�092���*}2-EFEF*)7hõ309J3Du')7�,u6¿ô�J96:Et,u'* ~ 6�DF')8�2-*}796"2L+�+L2¥£}6�+-+L*�032�DFJ9�G*}DF6"(:DF6:EF(�6 ~ Dt* ~ *)DF8�2-*}7A')+-��6:7�,u6"')+-+s'ÚDF')092-(�6"ô�JA')09DF'y,/'096:+L+x��')� ~ 2L6:8�8�'G096:+>7�J9�G6�DF*Ú092�Dt2 ~ 2-6�¾�')�G6�7�,F2P��(�2-*öB096�+�7¸J3��6:DF*]092�(�2L(:+L25092 ~ 6:DF2L*¸09*PDMcand

796:+L+L'¦Et6�DF2-6�,F6�� ~ *)Du')+-6�*)DF2L¾)2L7A')+-6!� õ)�G6�7�,uDt6©J97�6:£}6:7�,uJA')+-6vEF6:¾}7A')+-6 Dt6%')+-6f(�DF6:EF(:6+L2-796%'yDF�G6�7�,u6y=

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

�)« äc� Îc� ¢ ��� \ ¡ �1� ¡ � ¤�\ � ¥�¢!� �5� \ £ �A\7� �*��� \ � \ £��5� \�:¯?³��#� �����rãÙ 7ÑJ9Et(�2¥,/'�0A')+���*}+L092-79¾9õ�*),F,F6�792L')�G*9õ ~ 6�D¿*)¾}792�£y')+-*}DF6B092��¿; 6

PDMcand

õh03J961ýA+L6�(�*}7�,F6�796:7�,F2>DF2-E ~ 6:,t,u2-£y')�G6�7�,F6�J97ú*}J3, ~ J3,¿¾)Du'yýA(:*]6�0úJ97²ýA+-6���*}Dt�Ú'y,t,/'y,F*Ú(:*}7�,u6�736�7�,u6K+L62-73��*}DF��')8:2L*}792nEF')+L2-6�7�,u2 ô�JA'y+L2 DF' ~9~ *}Dt,F*ÑEF6�¾)7A')+L6 ��DtJ9��*)DF6)õÞ�¿;·õ ~ 6:DF2L*¸09*9=ÁH���J9+¥,u2-�Ú'~ Dt*(:6�09J3Du'§+L6�¾)¾}6f29ýA+L6���*}Dt�Ú'y,t,/'y,F296�+L29*}Dt092L79'.��0A'Bô�J92 �!$&�R2N��%*�!��2-7KÃA')EF6 ')+#Du' ~9~ *)Dt,u*Et6�¾}7A'y+L6 ��DFJ9�G*}DF6y= Ù ýA+L6 ~ 2T�º2L7�,u6:DF6:EFEu'y7�,F2ÒEF')Du'y7979* ~ Dt6�EtJ9��2-Ã92L+-��6:7�,u6Kô�J96�+-+L2n(�*}7Á2L+~ 2T�M')+-,F*"Du' ~9~ *}D¤,u*"EF6:¾}7A')+-6 �yDtJ9�G*}DF6yw�6�EFEt2I£}6�73¾}*}79*K£¸2LEF2-*}7A'y,F2�J973* ~ 6�DfJ979*3=

å.r�Ö × v x~}�çP{jxyçPv ÜÒ} ßÕáÒÞ��ÇvLx }tÚ �;}t� |l{èz }��À}tÚÀvLxé}H5' ~ DF*¸(�6�03J9Du'úýA79*º'y0b*}DF'�096:EF(�Dt2-,t,/'�Dt2L¾}J9')DF0A'ú+s'úDF2-(�6:DF(%'·092 ~ J9+-Eu')DGEF*}+-2-,u')DF2-6)õÞ2L+(:J92?�G*),u* ~ DF* ~ DF2L* ~ J9�Ñ(�')J9Eu'yDF6å')+ ~ 2��º+$��*)EFEF6:Dt£y')8:2L*}796Ú092?J97 ~ 6�Dt2L*¸09*<032-£}6:DFEt*·09'ô�J96:+L+L*KDt6%')+-6 ~ 6�Df£¸2s'K096�+-+x�ù6�/�6:,t,u*��©* ~9~ +-6�D:õ���'K2L7M*}¾}792I(�')EF*�2L+ ~ 6�DF2-*03*�ö¦(�*}E¤,/')7�,F6796:2>,u6:� ~ 2�092�2L7�,u6:¾}Du'y8�2L*)7961J9EF'y,u2 � =KH5'MDt2L(�6:DF(�'å032 ~ J9+LEF')D¿2L7ÑEt2LE¤,u6��G2>Ã92-7A')Dt2xõh6:0�2-7~ 'yDt,u2-(�*}+L')D¦��*¸09*Ñ796:2�EF2LE¤,u6:��2 Ã32L7A')Dt2?E¤,uDF6´,F,F2xõnö](�*}� ~ +-2L(%'�,/'<0A'y+?��'y,F,F*Ñ(/{96åE ~ 6�EtEF*2-+ ~ 6�Dt2L*¸09*²*}DtÃ92-,u')+L6Gö]6�E¤,uDF6:�Ú'y��6:7�,F6�(�*)Dt,u*3õÞ6:0k2L+ ~ 6:DF2L*¸09*²032?DF*y,/')8:2L*}796�*}EFEt6�D¤£)'��,F* ~ J9��£y')Dt2s')Dt6B(:*}79EF2-096�Dt6:£)*}+L�G6�7�,u6yõI'�(%'yJ9Eu'�096:+L+$��6/�6´,F,u*Ú�©* ~9~ +L6�D:õI')+-+x�ù2L7�,u6:DF79*G096�2,F6�� ~ 2 092�2-7�,F6�¾}DF')8�2-*}796yõÒ(�')J9Eu'y7909*·J97b'y+L+s'yDF¾�')�G6�7�,F*²096�+-+x�ù2L� ~ J9+-EF*²2-7�,F6�¾}DF'y,u*©��*),t�,F6�7�J3,u*�ï�DF2 ~ 2L6�¾}')7909*yó�2�0A'y,u2h' ~ 6:DF2L*¸09*"(:*}Et,u')7�,u6!� (/{96§Et2hDF2 ~ 6:DF(�J3*),u6v736�¾�'y,F2-£y')�G6�7�,u6EtJ9+nDu' ~9~ *}D¤,u*<Et6�¾}79')+L6%�yDFJ9�G*}Dt6)õ5��')(�6:7909*<(:*}EñûfJ9Et(�2LDt6�2-+�ï�(�')79092-0A'y,u*�óK0A')+-+s']+L2-Et,/'�ý3�7A'y+L6§096�2r(%'y79092L09'y,u25EF*y,F,u* ~ *}E¤,u2r')0d2LE ~ 6�8:2L*}736¦£¸2LEtJA')+-6���£�=fý9¾9=��= �1�´=f�r£)6�7903*�E ~ 6�EtEF*Ã92-EF*}¾)79*1092h*)EFEF6:Dt£y')8:2L*}796¿(:*}7],u6:� ~ 2�092�2-7�,u6�¾)Du')8:2L*}796©6�+L6´£y'y,u2y�$')0]6:EF6�� ~ 2-*9õ3ô�JA')7309*E¤,u2s'y��*¿6:EF6�¾)J96�7903*"J97A'§DF2L(:6�Dt(%'§2L7GJ97�')�G��')EFEt*¦¾)+L*}Ã9J3+s')Dt6�+L*}7�,/'y79*V�´õ�+$�¨'y+L+s'yDF¾�')�G6�7¸�,F*"096�+-+x�ù2L� ~ J9+LEt* ~ J3�G2-7]DF6�')+-,u.�6�EtEF6�Df,/'y+L6v0A'1(�')79(:6�+L+L')DF6©(�*}� ~ +L6´,/')�G6�7�,F6v+s'17A'�,uJ9DF'2-� ~ J3+LEF2¥£y'B096:+IEF6�¾)7A')+L6y=

�©+#ýA796 092�*�£�£¸2s'yDF6v'Bô¸J36�Et,F2 ~ Dt*}Ã9+-6��G2�Et*}79*1E¤,/'y,F2#Et£¸2L+-J ~9~ 'y,F2�E¤£y')DF2L'y,u2A�G6:,F*092#092ï � >XGF<ABI4WmCH>X÷G�:�BROjOYBI IN:5÷�GKW�QHEHG=BR@ :�:�G�k :�J��&EH>AJHòAB�C!>AG�OjWRM4W�C!>AGKG�>jUHEHG=I4B@yI4WG�:KM BR@ :�>8JH>AGF<XBROjU�W÷@�B�ñ°:ÅM�BRòX:�WJ1BRG�>(C!>XG�G�k BOPOYB�I4I4WéI4:!@ :KU�>X@�<?EHWM4> INE&:HU&BR@�BROj>XM4@ :tWtI4I4>X@ ñ#B#M :�:#<?W�Oj>3:�G

P:ROYBéG�>3ñ#B@4:=BRòA:KW�JH:INW�JHWjBRQHQ&B�IfM�BRJHòcB8G�>XJtM >�CHBPJHWJ�<?W�OPU&@4W�OP>XMNM >X@ >éG=BPOj:�I4EH@�B

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� äc� \ �,�&� �5¤�\�¤�\ � \ ¡ ��� ¡ � �}Ä

DF2-(�6:DF(%'§096:+�Et6�¾}79')+L6?ï¤'y(�(�6:+L6:Du'y,F*yóf0A')+A�G*),F*¦*)DFÃ92¥,/')+-6)õ�(�+L')EFEt2-ýA(�')Ã92-+L232-7�03J96 (�'y,u6:¾}*}Dt2L6~ Dt2L79(:2 ~ ')+-2xw�DF2L(:6�Dt(%'©¶}���¸���¸��� �#õy(/{96 ~ Dt6�EF6:Dt£y'©+-6Ò2-73��*}DF��')8:2L*}792)EFJ9+-+s'���')EF6Ò096�+¸EF6:¾}7A')+-6)õ6§DF2-(�6�Dt(%'K����¶}�h�����¸��� �#õ9(/{96§79*)7d+-6 ~ DF6:EF6�D¤£y'3=

���¡ �9¢ £¥¤ ¦¨§1©�¦¨ª«¦¨¬�§1©�§®­T¯°§� ,F,FDu'%£}6:DFEt*²ô�J96�E¤,u* ~ Dt*(:6�092-��6:7�,u*9õrEF*),t,u*M* ~9~ *}Dt,FJ9796G2 ~ *),u6:EF2$õrö ~ *}EFEt2LÃ92-+L61,uDF')Et��*)D¤���')DF6¿+L'GEt6�DF2-6¿,u6�� ~ *}Du')+-6v0925J97A' ~ J9+-Eu')DfÃ92-7A')Dt2s'1796:+L+s'"Et6�DF2-6¦,F6�� ~ *)Du')+-6v(�*}DtDF2-E ~ *}7�096:7�,F6�')0"J979' ~ J9+-Eu')D�EF2L73¾}*}+s'=�H��ù2 ~ *),u6:EF2 ~ DF2-79(�2 ~ ')+-6ÞEtJ"(�J92EF2ÃA')Eu' ô¸J36�Et,F*¿��6´,u*¸09*vö(/{96§796:2�,u6:� ~ 2�092h2-7�,F6�¾}DF')8�2-*}796 +x��')(�(:6�+L6:Du')8:2L*}736©*}DtÃ92-,u')+L6 EF2s'1(:*}Et,u')7�,u6y=Ò�r*}Et,u'"ô¸J36�E¤�,/'²(:*}79092-8�2-*}796)õ�Et2�' ~9~ +L2L(�'<')+-+s'MEF6�Dt2L6�,F6�� ~ *}DF')+L6GJ97A'dï�096:��*}Dt�Ú'y8�2L*)796´óG096:+L+L'<EF(�')+s'096:2 ,u6�� ~ 2$õÒ'�,F,uDF'%£}6�DtEF*·J97èDF2L(�')� ~ 2L*}79')��6:7�,u*²096:+�EF6:¾}7A')+-6)õÞ(/{96M��'ÑExûv(/{96d2-+ ~ 6�Dt2¥�*¸09*Ñ096�+-+x�ù2L� ~ J9+-EF*²' ~9~ ')2L'<(�*}E¤,/')7�,F6)õ ~ 6�D ~ *),F6�D ~ DF'y,u2-(%')Dt6]2 ~ Dt*(:6�092-��6:7�,F2ÒýA7Rô�J92096:EF(�Dt2-,t,u2x=

Ù + ~ 6�Dt2L*¸09*M*}EFEt6�Dt£y'y,F*Ñ096�+-+s' ~ J9+-Eu')D P (t) ~ J9�²6:EFEF6:DF6�6:E ~ Dt6�EtEF*ú2L7·��J9798�2-*}796G096�+~ 6�DF2-*03*"796�+IEt2LEt,F6���'"092IDF2¥��6�DF2-��6:7�,u*1096:+L+L' ~ J9+LEF')D P0

EF6:(�*}7309*Ú+L'���*}DF�1J3+s'3w

P (t) = P0 ·[1 +

v(t)

c

]−1 �$�3=��k�

�©J9DF')7�,u6�2-+ÒDt2L(�')� ~ 2L*}7A'y��6:7�,F*å096�+ÒEF6�¾)7A')+L6Ú09* £Dt6��G*<��')Dt6Ú2L7Á��*¸09*<(/{36�2L+Þ79*}E¤,uDF*,u6:� ~ *ºEt(�*}DtDu'k' ~9~ DF*}EtEF2L��'y,F2-£y')�G6�7�,u6M(�*}�G6²2-+�,F6�� ~ *º736�+vEt2LEt,F6���'Á092 DF2-��6:DF2-��6:7�,u*ú096:+L+L' ~ J9+LEF')D�õn2-7è�G*¸09*Ñ(/{96M2L+?7�J9�G6�Dt*�032 (%')� ~ 2-*}7A')�G6�7�,u2Ò2L7RJ97 ~ 6:DF2-*09*ÑEt2s'(�*)Et,/'y7�,F6)w"2-+�7¸J3*�£)*Ñ2L7�,u6:Dt£y')+-+L*å092n(%')� ~ 2-*}7A')�G6�7�,u* tnew EF2Þ*),F,F2L6:796�09')+L+L'M�=¨�3õ�(�*}7+x��')EtEFJ9798:2L*}736G(/{36�+$�¨')(:(�6:+L6�DF')8�2-*}796"*}DtÃ92-,u')+L6"Et2s'](�*)Et,/'y7�,F6���79*}7·Eu' ~3~ 2s')�G*åô�JA')+x�ùöK+s'£}6:+L*¸(�2¥,/.�+LJ379¾}*å+s'�+-2L796�'�092>£¸2LEt,u']096�+-+s' ~ J9+-Eu')D:õ509*}Ã9Ã92L')�G*]2 ~ *),u2-8�8%'yDF61(/{96 v = at

õ(�*)7

a09'�096:,F6�Dt��2-7A')DFEt2 ~ 6�D ~ DF* £}6¿EtJ9(�(:6�EtEF2-£)6!� õ�2-7��G*09*�(/{96v+x�ù2L7�,F6�Dt£y')+-+L*¦092�,F6�� ~ *

096:+(�')� ~ 2L*}7A'y��6:7�,F*f*}DF2-¾}2L7A'y+L6 tsamp EF2L' J9¾)JA')+L6Þ'�ô¸J36�+L+-* 736�+�EF2-Et,u6:�Ú'�092�DF2¥��6�DF2-��6:7�,u*9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

� á äc� Îc� ¢ ��� \ ¡ �1� ¡ � ¤�\ � ¥�¢!� �5� \ £ �A\7� �*��� \ � \ £��5� \

§��7���*�tÿ±�Vª��*«³²é»X»#¹�²A¾�µ�È�¶�®°¯�¹Àº1¹c·T·�µ.¸�¼�·K»�µ°²´QTS�UVSXWZY[S]\þºHµ.¸�µ°²�³N¹Àº1¹c·�²hµHº°¶�®!³N¹c·[¹A»#¬?®A¸�¶�®æº!¶µ ²h¹?¬�¶¶?®('�¶�· Ê ²hµ¡%~¬?®�¶T¯ µ°·=³f®�¿L®°»c³´²hµÕ· + ¹���¹�³�³f®�º&¹c·�¿�®!³f®�®°²P�¶�³fµ°·[¹)»A¼�·�·=µ�±#µt»#¹�º&¹c·8»#¹ Ê ¯�µ°·[¹If·�µ�»�¬?µ!·=µ·#m¯�®°²c¿�µ°·K¶[ÈXȵ!³fµÛ¶�¯Ò¿L®ºH®âºHµÆ¶Å¸�®!³´¶[ÈXȵ°²h¹�¸k¹c²c¶´®Rº&®)¬?®t»�³fµ°¯*³N¹�M)¹¸��¼�¶�¯�º°¶l»c¼1·*¸�²h®¡%l·�®¶T¯�³N¹ Ê ²hµ!³f®7If»�®!³�³f®_MÄ;¶T· Ê ²hµ¡%~¬X®s¶�¯�?µt»X»#®�²hµA¸H¸�²?¹A»R¹c¯*³fµ�¶T¯*¾t¹h¬X¹Ì¶�·�»#¹ Ê ¯�µ°·�¹�²c¶ ¸�¼1·�¶�³f®�ºHµ Ê ·�¶~¹���¹�³�³´¶®°²-c¶�³fµ!·K¶�)é¹hº�¶T·�²?¹c·�µ!³´¶�¾�®�¸�²h®¡%l·�®�¶�¯*³N¹ Ê ²hµ!³f®&Í

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� äc� \ �,�&� �5¤�\�¤�\ � \ ¡ ��� ¡ � � é

096:+L+s' ~ J9+LEF')D t0 '"�G6:,u.K036�+h,u6:� ~ *K092I2L7�,F6�¾}DF')8�2-*}796 T õA*),t,u6�736�7909*

tnew =tsamp

1 + aT/2c

�$�3=ùªV�

øvJA')7909*¦Et,F2s')�G*v6/�6´,F,uJ9')7909*¦J97A'§DF2-(�6�Dt(%'¿092 ~ J3+LEu'yD�õ�79*}7GEu' ~9~ 2s'y��*¿ô�JA')+-6�EF2L'§2-+£y')+L*)DF6�036�+x��')(:(�6�+-6�DF')8�2-*}796�*)DFÃ92¥,/')+-6)õ ~ 6:DF(:2L��09*)Ã9Ã92s'y��*�6�/�6:,F,FJA')Dt6"096�2r,u6�7�,u'y,u2¥£2�(�*}7£y')+L*)DF2�092 ~ DF* £y'3=�C?2-� ~ *}Dt,u'v'©096:2 ~ Dt*}Ã9+L6:��2�092DF2-EF*}DtEF6?0323(%'y+L(�*)+L*�2L71ô�JA')7�,F*¿EF2,FDu'y,t,/'092�')7A')+-2L8�8�')DF6 092-£)6�DtEF2h¾}2-¾�')Ã�ê�,u6 092�0A'�,u2xõ(�*}7]032-£}6:DFEt2h(�2-(�+L2�(�*)DFDF2-E ~ *}79096:7�,u2h'y2�092¥£}6�DtEF2£y')+L*)DF2�0929'y(�(�6:+L6:Du')8:2L*}796yõ}*}¾}7�J973*v096�2ô�JA')+L2¸096´£��ù6�EtEF6:DF6 ~ DF*¸(�6:EFEu'�,u* ~ 6�D>092¥£}6:DFEF2¸£y')+L*}Dt2092r�¿;�=�øvJ96�E¤,u* ~ DF*¸(�6:092L�G6�7�,u*GDF2-(/{92L6:096�Dt6�Ã9Ã�6B,F6�� ~ 2I796:+L+x�ù*}Dt092L796¿032rJ37²��6:EF6�� ~ 6�DJ97A'ÑEt*}+s'Ñ*}EtEF6�D¤£y')8�2-*}796!�"')73(/{96 ~ 6:D"J97T(:+LJ9E¤,u6:DG032f�yª�C � Ý 032���6:092L*Ñ+-2-£}6:+L+-*�� ¢)¢R� =Ù 79*}+¥,uDt6)õ9+$�¨')EtEFJ9738�2L*)796§(/{96B+$�¨'y(�(�6:+L6:Du')8:2L*}796¿Et2s'"(�*)Et,/'y7�,F6§796�+I,u6:� ~ *K092I2L7�,F6�¾}DF')8�2-*}796~ J9�]73*}7Ñ6�EtEF6�Dt6"(�*}DtDF6´,F,/'w©')0Ñ6:EF6:� ~ 2-*9õ�736�+>(�')EF*]2-7²(�J92�EF2>(:6�Dt(%')79*]Et2LE¤,u6��G2�Ã32L7A')Dt2+L*)7�,u')792$õ�2-7<(:J92�2-+5EF6�¾)7A')+L6B096�+-+s' ~ J9+-Eu')D ö ~ Dt*}ÃA')Ã92-+L�G6�7�,u6§096:Ã�*)+L6¦61DF2-(/{92L6:096¦,F6�� ~ 2092h2-7�,u6�¾)Du')8:2L*}796©+LJ979¾){92xõ+x��')(�(:6�+L6:Du')8:2L*}736 ~ J9�"£y')Dt2s')Dt6v79*),F6:£}*)+L�G6�7�,u610A+L*1E¤,u6�EtEF*G£)'y+L6796:2?(%'yEF2 2-7º(�J92?2L+ÞEF2LE¤,u6:�Ú'<Ã32L7A')Dt2L*dö]��*}+¥,u*MEt,FDF6:,t,u*©��6Úô¸J32L79092 ~ 2��Á2L7�,u6:DF6�EtEu')7�,F6!�´=C?2L��DF2L(/{32L6�036©096:+L+L6 ��*¸092¥ýA(/{96v'y+L+s' ~ Dt*(:6�09J9DF'1(/{96 ~ 6�DF�G6:,t,/')73*1092�* £�£¸2s')Dt6¿'�ô�J96:Et,u2~ Dt*}Ã9+L6:��2$=

�:¯?¹Á��� �I�5�º�r�?Õ�±9��³���¹º¹ �¸¬�»øvJ96�E¤,u*"�G6:,F*09*�EF2�Ã9')Eu'1EtJ9+���'y,t,u*1(/{36¿2L+#��*y,u*1*}DtÃ92-,u')+L6f�G*03J9+s'¦2L+ ~ 6:DF2L*¸09*BDF2L(:6:£¸J�,u*Ú096�+>Et6�¾}79')+L6y=¦46"79*}2�')7A')+-2L8:8�2s'y��*G+L*�E ~ 6:,F,FDF*]092 ~ *),F6�798�'�096�+�EF6:¾}7A')+-61DF2-(�6:£¸J3,F*9õ6�EtEF* ~ Dt6�EF6:7�,u6�DF.G03J96v��DF6:ô¸J36�798:6¦+-2L�G2-,F6)õ�(�*}DtDF2-E ~ *}79096:7�,F2h')+��Ú')EtEF2-��*B6¿��2-792L�G*¦£y')+ �*}Dt6B'yEFEFJ37�,F*Ú0A'y+L+s'1��Dt6�ô�J96�738%'�032rDt*),/'y8�2L*)796¿096�+-+s' ~ J9+-Eu')D:õ#')+L+-6vô�JA')+-2I(�*}DtDF2LE ~ *)79096§+s'��')EFEt2L��' ~ *),u6:798%'3=Þ4¸2 ~ J9�"032L�G*}Et,FDu')Dt6©(/{96¿+L'B�G*09J3+s')8:2L*}796�096:+L+s'§��')EF6¿036�+�Et6�¾}79')+L609* £¸J3,/'G'"ô�J96�E¤,u*���6:79*}�G6�79*Kö ~ ')Dt2I'

Φorb = 2πxorbfspin =2πxorbPspin

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

�}� äc� Îc� ¢ ��� \ ¡ �1� ¡ � ¤�\ � ¥�¢!� �5� \ £ �A\7� �*��� \ � \ £��5� \09* £)6

xorbö]2L+ÒEF6��G2s'yEFEF6Ú�Ú')¾)¾}2L*}Dt6�73*}7 ~ DF*}2-6:,t,/'y,F*<096:+ EF2-Et,u6:�Ú'²Ã32L7A')Dt2L*9=Ñ� ~ ')D¤�

,F2LDF6¿09')+L+-*GE¤,uJ9032L*G092Iô�J96�E¤,/'Ú�G*03J9+s')8:2L*}736v092h��')Et6)õ ~ *)EFEF2L')�G*GDt2LEF')+L2-DF6¿')2 ~ 'yDu')�G6:,FDF2òy6 ~ +-6�DF2L')792h036�+L+$��*)DFÃ92¥,/'3=

Ù + ~ Dt*}Ã9+-6���' 092}ô�J96�E¤,u*���6´,u*¸09*�DF2-EF2-6�096�796:+L+L'?796�(:6�EtEF2-,u.3õ)736�+}(�')EF*�2L7¿(:J92�2L+yEF6�¾)7A')+L6Et2s'¦,FDF* ~3~ *1036�Ã�*}+L6yõ3092�6�EF6:¾}J92-DF6vJ97]¾)Du')7�7�J9�G6�Dt*1092�,uDu'yEt��*}Dt�Ú'y,F6 032h&A*}J9Dt2L6�D:õ2-+�(/{36(:*}� ~ *}D¤,/']J97º'yJ9��6:7�,u*M096�2�,u6:� ~ 2�092n(%')+-(�*}+-*]79*),u6´£}*}+-6)= Ù 73*}+-,FDF6"6�EtEF*²öG6��G(:2L6�7�,F6Et*}+L*BEF6v2-+�,F6�� ~ *B092�2-7�,u6�¾)Du')8:2L*}796 ö ~ 'yDF2h'y+L�G6�79*B' ¢ =¨÷¦£}*)+-,u6 2L+ ~ 6:DF2-*09*B*}DFÃ32-,/'y+L6�� é!� =

���> ��>  £¥¤ ¦R§1©/¦¨ª¼¤ ­½¦R¬�§1©/§®­T¯°§Ô�� ±A¶]¾iÔh��±9��¶(¿46M79*}2�EFJ309092-£¸2-092s')�G*ú+s'úEF6:DF2L6å,u6:� ~ *}DF')+L6]2-7bJ97T(�6�D¤,u*º7�J9�G6�Dt*Á092 ~ ')D¤,u2$õ?6�0T6�E��6:¾}J92s'y��*�EtJ�*)¾}7�J97A']092�6�EtEF6GJ97A'�,uDF')Et��*)DF��'y,/'Ú032n&#*)J9DF2-6�D�õ�EF2s'y��*]2-7Ѿ}Du')03*M032>6�E��6:¾}J92LDt6?J979'vDF2L(:6�Dt(%'v092¸��DF6�ô�J96:798�6f(�')79092-0A'y,u6 ~ *¸(�*v2-73ðAJ96:798%'�,/'v0A')+-+x�ù6�/�6:,t,u*¿�©* ~9~ +L6:D�=�©* ~ *¸092L(/{�ÓÒEt2¸Et*}�G�Ú')73* 2-7B��')792-6�Du'f2L73(�*¸6�DF6:7�,u6m��(�2-*öyõyEt6�798�'©,u6:796�Dr(�*}7�,F*v096�+-+s' ��')Et6096:+IEF6:¾}7A')+-6!�?2 ~ 2-(�(/{92I096:+L+-*"E ~ 6:,F,FDF*G092 ~ *),u6:798%'=

øvJ96�E¤,u*1�G6:,F*03*�öv'yEFEu'y2�J3,F2L+-6�736�2�(�')EF2�2L7�(�J92�EF2�J3,F2L+L2-8�8:2L79*§*}EtEF6�D¤£y')8�2-*}792�+LJ979¾){96)õ796:+L+-6©ô�JA')+-2�2�,F6�� ~ 2�092�(%')+-(�*}+-*1(�*}7å¾}+-2�'y+-,uDt2��G6:,F*032�Eu'yDF6�Ã3Ã�6:DF* ~ DF*)2LÃ92¥,u2-£¸2$= Ù + ~ DF*}Ã�+-6���'¦��*}7909')��6:7�,/')+-6©ö¿(/{96¿+L'�EF*}�G��'�2L79(:*6:DF6:7�,F6)õ9J3792-,u'"')¾}+L2#6/�6´,F,u2�EF6 ~ J9D��G2L732L�G2096:+L+$��6/�6´,F,u*K� * ~9~ +-6�D�õ ~ *}D¤,/'K')+L+L' ~ 6�DF032-,/'1032IEF6�73EF2LÃ32L+L2¥,/.�036�+I�G6:,u*¸09*9=

Ôh¹Á�h�A�]¿r�$�5ã�³�»����%� ��±A¯��øvJ96:Et,u*d��6´,u*¸09*åEF2ÞÃA')EF'MEtJ9+L+$�¨' ~3~ +L2-(%')8:2L*}796�092nJ97A'd(:*}7�£}*}+-J98�2-*}796KEFJ3+L+L*ME ~ 6:,t,uDt*d092~ *),u6:798%'å(�*)7ÁJ97A']��J9798:2L*}736�092>ý9+-,uDt*9õr')+L+-*]EF(:* ~ *d092�6�EF')+-,u')DF6K6´£}6�7�,FJA')+L2n��DF6:ô�J96�798:6(�')79092-0A'y,u6y= Ù +�ýA+¥,uDt*1£2-6�796§' ~9~ +L2-(%'y,F*�EtJå£y')Dt2 ~ J97�,F2h096�+-+L*1E ~ 6´,F,FDF*K092 ~ *),u6:798%'w�6�EFEt*6:Eu')+¥,/'<6´£}6�7�,FJA')+L2 ~ 2L(:(/{92?Et�1J9EtEu'y,F2 0A')+-+x�ù6�/�6:,F,F*²�©* ~9~ +L6:D�õ>�G6�7�,FDF6Ú,F6�79096å'y0k'y,F,F6�7�JA'yDF6"2L+�EF6:¾}7A')+-6"EF61£¸2L6:796"(�6:7�,FDu'y,F*dEtJúJ97Ñ��DF6�ô�J96:798%'MEFJ9+-+s'Úô�JA'y+L6"()�ùö"EF*)+L*]DFJ3��*}Dt6)=

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!� äc� \ �,�&� �5¤�\�¤�\ � \ ¡ ��� ¡ � � ¢

42�*),t,u2-6�796]+L'ú��')EtEF2L��'Ñ')� ~ 2L6:8�8�'ú036�+fEF6:¾}7A')+-6Mô�JA'y7909*·2L+?ýA+¥,uDt*·öå(:6�7�,uDF'y,u*·EFJ9+-+s'��DF6:ô�J96�798�'�092IDt*),/'y8�2L*)796v096:+L+s' ~ J9+LEF')D�=

C?*}7²ô�J96:Et,u*å�G6:,F*09*3õ�Et2�Dt2L6�Et(�6�')0²*),t,u6�736�DF6BJ97A'�+-2LEt,u'G032r��Dt6�ô�J96�738%'�(%'y79092L09'y,u66�Et6�¾}J36�7909*·EF*)+L*²J979'²EF2L73¾}+L*�'<&>&�qäEFJR*}¾}732?EF6:DF2-6Ú,u6:� ~ *}Du'y+L6Ú036�092-E ~ 6�DFEF'3õn(�*}7RJ97796´,F,u*úDt2LE ~ ')DF�G2L*²032�DF2LEt*}DFEt6å(�*}� ~ J3,u')8�2-*}7A')+-2ÒDt2LE ~ 6:,t,u*·')+ �G6:,F*03*²,uDu'y092L8:2L*}7A'y+L6)õ�2-+ô�JA')+-6 ~ DF6´£}6�036�J97A'K&>&�q ~ 6�D�*}¾}732h£)'y+L*}Dt6v092 ~ Dt*�£y'"096:+L+x��')(:(�6�+-6�DF')8�2-*}796v*}DtÃ92-,u')+L6y=

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

n U^XZO�`ågl[hg À

ÁÃÂ�ÄÆÅÈDZÉËÊÍÌÏÎÐÄÒÑÃÂCÇÔÓ Q OI[ PRU^\�g VWO Õ ÖæN

× oÈØ�Ù oÔÚ´� oº�ÍÙ

Ý 7A' ~ ')Dt,F6¦2-� ~ *}D¤,/')7�,u6©096�+-+s' ~ Dt*(:6�09J9DF'G032,�!�Fÿ���"#��DF2-¾}JA')Dt0A'1+s'"(�*)73��6�Dt�Ú'"096:2rEt6�¾y�7A'y+L2hï�(%'y79092L09'y,u2 ó/= Ý 7·6:EF6:� ~ 2-*�092>(:*032L(�6�(/{96"6�Et6�¾}J96Kô�J96:Et,u* ~ 'yEFEu'y¾}¾}2L*Úö"Du' ~9~ DF6´�Et6�7�,/'y,F*K0A'�Ü Ç%È9É}Ê�Ë3Ì3Í�Î�ÈÏ�Ç�Ê)Ð õ�2-79Et,u')+L+L'y,u*BEFJ9+I7�J9* £}*G(�+-J9Et,F6�D ;<')73¾}J9Et,u'3õ9(:*}Et,F2-,uJ32-,u*0A'úª��·C � Ý õÞ096�+-+x� � EFEF6:Dt£y'y,F*}DF2-*Ñ�©Et,FDF*}73*}��2-(�*ú092�C ')¾)+L2s'yDF2x=º�©J9Du'y7�,F6<2-+?,u2-DF*¸(�2L732L*{9*å+L' £)*}Du'�,u*å')+-+s'���')Et6"092é��$&�R24��%*�1092�Ü Ç%È9É}ʸËÌ3Í�Î�È3Ï#Ç�Ê)Ð 0A')+L+L'ÚEFJ9' ~ Dt6�(:6�096:7�,F6G£)6�D��Et2L*}796yõ)Et(�DF2¥,F,u' 2L7¦��*}Dt,FDu')71Ä}Äõy2L79E¤,/')+-+s'y,u' EFJ9+-+s'�î?*}Dtò�Et,/'�,u2L*)71�©+ ~ {A'©&�&�q�Äõ}'y+L+s'�7�J9* £y'£)6�DFEt2L*}736¦2-7]��*}Dt,FDu')7 é �"2L73Et,/'y+L+s'�,/'BEtJ²;d')79¾}J9E¤,/'3=

ÛÒrtq Ü(Þ ßÀx~�Ý�ÕÞ{èz v ÜÒ{YÞ�Þ�v çP�ÛÚÒØ&{jxyz v ÜÀ{Y} çjv�ÚÀÜÒ}�ÜÕvL|l}

H5' ~ Dt*(:6�09J9DF'M032��!�Fÿ���"#�¸õI(�*}�G6K')Ã9Ã92L')�G*Ú£¸2LEt,F*9õIDF2-(/{92L6:096"J97ú¾}Dt*}EFEt*M032LE ~ 6�73092L*]092�G6�8:8�2I(�*)� ~ J,/')8:2L*}7A'y+L2x=>øvJA')7909*KEt2r6:EF6:¾}J96¦J97A'¦����RÔ���¿E ~ 6�EtEF*�79*}7Mö¦(:*}7�£}6:792L6:7�,F6~ Dt*(:6�EtEu')Dt6Ñ092LDt6:,F,u')�G6�7�,u6²2-+©Et6�¾}7A'y+L6²2-7i��*¸09*º(:*}� ~ +L6´,u*·ï�')+L+L'�(�2-6�(�'�ó/=^42©,F6�790362-7�£)6�(:61')0d6�EF6:¾}J92-DF6�J37A'�Dt2L(�6:DF(�'��G6�79*Ú' ~9~ Dt*)��*}79092¥,/'3õA��' ~ 2��dEF796:+L+s'K0A')+ ~ J37�,F*Ú092£¸2LE¤,/']096:2Þ�G6�8:8�2n092�(�')+L(:*}+L*]2-� ~ 2-6�¾�'�,u2xõ�(/{96G2L79092¥£¸2L09J92�096�2�ï�(�')79092-0A'y,F2¥ó/õ�*�£�£)6�DF*d096�2Et6�¾}7A'y+L2Þ(/{96 ~ *y,uDF6:Ã9Ã�6�DF*Ñ79')EF(:*}79096:DF6]¾}+-2Þ2-� ~ J9+LEt2Þ032?J97A' ~ J9+LEF')D�õ���')¾�')Dt2Þ')+-,F6�Du'�,u2

�}�

¡ �5� \ � ��¢!�ÝÞ ��ß_àGá&â¡ã&ä*å¡æ ç>á¡èPà¶ã&éé� \�¢ ¡ � ����¤�\ � � ��ê��jë&ìc�¶í[Îc�Nä&ì �}�

0A')+5�G*),u*G*}DtÃ92-,u')+L6y=f�©2�ô�J96:Et,F2�(%'y79092L09'y,u2IEt2�{A'�J97A'�E¤,u2-�Ú'K096�+��¿; 6B096�+ ~ 6�DF2-*03*9õ(/{96§£}6:79¾}*}79*GDF6:¾}2LE¤,uDF'y,u2 ~ 6�D�(:*}7�,uDt*}+L+-2�EFJ3(�(�6:EFEt2-£¸2 ~ 2��M')(�(:J9Du'�,u2x=

Ù ����')¾}2-792s'y��*d092©'%£)6�D�,FDF* £y'y,u*3õ 'y,t,uDu'%£)6�DFEt*ÁJ979'�ô�JA')+-J979ô�J96<036�+L+-6 ~ DF*¸(�6:09J9DF6092��!�Fÿ���"#�úEF* ~ Du'·6�E ~ *}E¤,u6)õ�J37A'��G2L+-+L2LEt6�(:*}790 ~ J9+-Eu')D"��')(:6�7�,u6 ~ ')Dt,F6<092fJ97bEF2LE¤,u6:�Ú'Ã92-7A')DF2-*9õ�*·J97T*)¾}¾}6:,t,u*ú(/{96 ~ *y,uDF6:Ã9Ã�6M6:EFEt6�DF+-*9= Ù 7b¾}6:796�DF')+L6yõÒ+L' ~ DF2L��'<£}*)+-,/'Ñ(/{96£¸2L6:796f*}EFEt6�Dt£y'y,u'¦J37A' ~ J9+LEF')D�2L7KJ97KEF2-Et,F6���'§Ã32L7A')Dt2L*9õ)79*}7GEF2AEu'§792-6�7�,u6�EtJ9+L+L'§EtJA'¿��')EF6*}DtÃ92-,u')+L610�092�(�*}79Et6�¾}J36�798�'M79*)7ÑEu' ~9~ 2s')�G*�ô�JA')7�,u*å2-+r£y')+-*}DF6B096�+ ~ 6�Dt2L*¸09*Ú*)EFEF6:Dt£y'y,F*~ *}EFEF'�6�EtEF6�Dt6¿2L73ð9J96�798�'y,u*B0A')+-+x�ù6�/�6:,F,F*1�©* ~9~ +L6:DÒ*)DFÃ92¥,/')+-6)=>@�6�+�(%')Et*"2L7�(�J92�EF2�*}EFEt6�D¤£22L7�£)6�(�6GJ97·EF6:¾}7A')+-6"(/{96 ~ *),FDF6�Ã3Ã�6 ~ Dt*�£)6�792-DF6K0A'åJ97A' ~ J9+-Eu')D:õ5')Ã9Ã92L')��*]Ã32LEF*)¾}79*å0926�Et6�¾}J32LDF6Ú096�+-+L6 ~ DF*¸(�6:09J9Du'²032Ò(:*}73��6�Dt�Ú'd(/{96 ~ *)EFEu'y79*²6:£)6�7�,uJ9')+L�G6�7�,u6]6´£¸2L096:798�2L')DF62L7å��')792-6�Du'12-796�ô�J92¥£}*¸(%')Ã32L+L6 +s' ~ Dt6�EF6:798%'G092IJ97A' ~ J3+LEu'yD�=

��6:D ~ *y,u6�DG6�Et6�¾}J32LDF6d��2-EFJ9DF')8�2-*}792�EtJ9(�(:6�EFEt2-£)6ÑEF6�738%'º09* £}6:D�DF2-��6´,F,F6�DF6å2-7b�G*),u*096:+L+L6G+LJ379¾}{96 ~ DF*¸(�6:09J9DF6Ú092?(�')+L(:*}+L*9õrEF6:Dt£)6M+-*<E¤,uJ9092-*²092ÞJ97k�G6:,u*¸09* ~ 6:D16�Et6�¾}J92-DF6+s'"Dt2L(�6:DF(�'G0925*}¾)¾}6:,t,u2I¾}2L. ~ DF6�(:6�096:7�,u6��G6�7�,F612L79032-£¸2L09J9'y,u2$õ3Et��DtJ3,F,u')7909*�+s' ~ *}EFEt2LÃ92-+L2-,u.092Þï�¾}JA')09')¾}7A')Dt6´óÚDF2-EF*}DtEF6](�*)� ~ J,/')8:2L*}7A'y+L2Ò'y,F,FDu'%£}6:DFEF*·+s'²E¤,u2-�Ú'²2-792L8:2s')+-6�092 ')+L(:J9792~ ')DF')�G6:,uDt2Ò(/{36M6´£¸2-,/'²032?09* £}6:DK6�EF6:¾}J92-DF6�,uDt* ~9~ 2Þ,u6:7�,u'y,u2¥£¸2�'<£¸J9*),u*3=ºC?*}�G6�E¤,u2L�G62L732L8�2L')+L2#096:2 ~ ')DF')��6´,uDt2�£}6:79¾}*}79*GJ3,F2L+L2-8�8�'y,u2�2�£y')+L*}Dt2�096:+L+-6 ~ DF6:(�6�036�7�,u2r*}EFEt6�D¤£)'y8�2L*)792x=

ÛÒr�Ö î)|;xéá¦|;|Çá¦xyv ÜÒ}Ðï7ðòñÝó�ô"õ3ö¸÷ø[ñ½ùúðûô[üÙ +�(�*¸092L(:6 ö�(�*}� ~ *}Et,F*�0A'¦(�2LDt(%'B�}�¦,FDu' ~ DF*}¾}DF')�G��296 EFJ9Ã3DF*}J3,F2L796yõ+L'B(:J92�6:EF6:(�J98:2L*}7962L7REt6�ô�J96�738%'Áöå*}Dt092L7A'�,/'²0A'ÑJ979*·EF(:DF2 ~ ,%=TøvJ96�E¤,u2 ~ Dt*}¾}Du'y���G2Ò6åEt*),F,F* ~ DF*)¾}Du')�G�G2+L6:¾}¾}*}73*¿+x�ù{96%')036�Dn096�29ý9+L6�0A'¦')7A')+-2L8:8%')Dt6)õ}(:*}73��DF*)7�,u')79*¦(�*}7G6:£)6�7�,uJ9')+L2A0A'�,u2A6�Et2LE¤,u6�7�,F2xõ6�Et6�¾}J3*}79*è+L6 ~ Dt*(:6�09J9Dt6ú092¿096�032LE ~ 6�DtEF2-*}796)õ©')(�(:6�+-6�Du'y8�2L*)796)õ���*}+L092-79¾9õf6Ñ��*}DF732LEF(:*}79*(�*)��6�*}J3, ~ J3,"¾}DF'yýA(�*<J97A'²EF(/{36�DF��'y,u'²092Tý°þ@ýnÿ Î�� 796�+-+s'dô�JA'y+L6ÚEt*}79*Ñ(:*}7�,u6�7�J3,F6å+L62L7��*}DF��')8�2-*}792�Eu')+-2L6�7�,F2r036�+L+-6§��2-¾}+L2-*}DF2�(%')73092L0A'�,u6)õ�+L6§ô�JA')+-2I£}6�73¾}*}79*�Et(�6:+-,u6 ~ 6:D *)¾}7922L7�,F6�Dt£y')+-+L*1032 ~ 6:DF2L*¸092�092 ~ DF* £y'"2L7åÃA')Et6�'y+hDu' ~3~ *}D¤,u*KEF6:¾}7A')+-6´�ñDFJ9�G*}DF6y=

Ù 0A'y,F25DF2L(:6:£¸J3,F2�0A'y2rEt2L79¾)*}+L2I(�')7A')+-2I096�2rDu')032L*),F6�+L6:EF(:* ~ 28��*)¾}7�J979*Ú036�2rô¸J9')+L2I(:* ~ DF69;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

�)ª Þ � Îc� � ��� ¥ �V� ¥ �*� ¤�\ ß_àGá&â¡ã&ä*å¡æ ç>á¡èPà¶ã&éJ97¦(�6:Dt,F* 2-7�,F6�D¤£)'y+L+L*?092}��DF6:ô¸J36�798:6!�5£)6�79¾)*}79*�DF6�¾)2LEt,FDu'y,F2}EFJ¦J97¦7A')E¤,uDF*���')¾}796´,u2L(:*9=r��6:D2-792L8:2s')Dt6?+x��')7A'y+L2LEt2xõ�2A0A'y,F23£}6:7909*}79*BEu')+¥£y'y,u2EFJG092LEt(�*¦2L71��*}Dt�Ú'y,F*¿Ã92L79')DF2-*¿+L6�¾)¾}2LÃ92-+L6Þ0A')+Et2LEt,F6���'"* ~ 6:Du'y,F2-£)*"2L7åJ9EF*�'y,t,uDu'%£)6�DFEt*�2-+h(�*)�Ú')7309*�� Í)Ì���� � ¢ � � =

� ÿ�� É���� �#Ç ���Ù + ~ DF*}¾}DF')�G�Ú' Í�Ê���É�����Ì��3É ÜÚ(:DF6�'¦J979'¿,u')Ã�6�+L+L'v0923£y')+-*}DF2092 ~ DF* £y'¿092#�¿;�=�� ,t,uDF' £)6�D��Et*Ú2 ~ DF*)¾}Du')�G�G2�� � ���yÈ9É�Ð�� õ�� ��� ý É�ÊÉ�Ð ��6�� � ����� � ��� ��Ü Ç%È�Í�Î�ÈÏ £}6:79¾}*}73*�6�E¤,uDu' ~ *y�+L'y,u2>09')+�ýA+L6G+L6K2L7��*}DF��')8�2-*}792>032 ~ ')Dt,F6�798�' ~ 6�D¦6�EF6:¾}J92-DF6Ú+L'M036�092-E ~ 6�DFEt2L*}736)õ�,FDu'å(�J92+$��6:EF2LE¤,u6:798%'�092�J97A'Ú,/'yÃ�6:+L+s'G092�£y')+-*}DF2r092 ~ DF* £y'å032>�¿; ��£)6�DF2¥ýA(%'�036�+���J9738�2L*)7A')�G6�7�,F*²092 Í�Ê���É ����Ì��3É Ü5� õÒ79*)��6�036�+L+L'<EF*)DF¾}6:7�,F6]6 ~ ')DF')�G6:,uDt2Ò*)EFEF6:Dt£y'y,F2-£¸2x=·�©* ~ *¸092L(/{5Ó� ÿ�� É���� �#Ç ����6�EF6:¾}J96v+L'¦036�092-E ~ 6�DFEt2L*}736©6 ~ 6�DÞ*}¾}7�J973*1092#ô�J96�E¤,u2�£y')+-*}DF2A032��¿; (�DF6�'J97dýA+L6¦092r0A'y,u2579*)7<��*}DF��'y,t,/'y,F2I096�092-E ~ 6�DtEF2x= Ù + ~ DF*)¾}Du')�G��'KDt2L(/{92L')��'G092¥£}6:DFEF6BEFJ9ø�Dt*}J3,u2-796)õA+-6Bô�JA'y+L2I6�Et6�¾}J3*}79*�25092¥£}6�DtEF2 ~ ')EtEu')¾}¾)25,FDu'K(�J92r+s'K+L6´,F,FJ9Du'K096�+-+x�ù{96%'y096�D:õ�6¦+s'096:092LE ~ 6:DFEt2L*}796y=

� ÿ�� É� � � � ��Î�È�����ÏAÎ ÿ �øvJ96:Et,/'vö�+L' ~ ')D¤,u6�096:+3(:*092-(�6�(/{96�6:EF6:¾}J96f2L+���*}+L032L79¾9=rü�EFEt*�'y7A')+L2-8�8�' 290A'�,u23036�092-E ~ 6�D¤�Et2xõ}6:0K'y,F,FDu'%£}6:DFEF*§+-6?2L7��*}DF��')8�2-*}792�0A'�,u6�0A')+-+x��')7A')+-2LEt2}092A&A*}J9Dt2L6:D�6:EF6�¾)J96f+s' Dt2L(:6�DF(�'v096�+~ 6�Dt2L*¸09*G,FDu'Ú2I£y')Dt2�(�')79092-0A'y,u2$=�Hr'GDF2-(�6�Dt(%'�£¸2-6�796B6�EF6:¾}J92¥,/'ÚEtJ²2L7�,u6:Dt£y')+-+L2I092 ~ 6:DF2-*09*')+-+x�ù2L7�,u6:DF79*K096:2�ô�JA'y+L2xõ9,FDu'K,uJ3,t,u252r£y')+-*}DF2I032 ~ DF* £y'3õ�£)6�79¾)*}79*�Et(�6�+¥,u2rô�J96�+-+L2 ~ 6�D©(:J92r2L+DF' ~9~ *}Dt,F*¿EF6�¾)7A')+L6%�yDFJ3��*}Dt6�ö ~ 2��G')+¥,u*9=�H���*}J, ~ J3,nöfEtJ�09J36fý9+L6 ~ 6�D�*}¾}7329£)'y+L*}Dt6 EF(:6�+¥�,F*9w�J973*�(�*)7�+x�ù6�E¤,u6�73EF2L*)796���� �}Ê õ3(/{96©��*)DF792-EF(�6 ')+-(�J9796�2L7��*}DF��')8�2-*}792 ~ DF2-79(�2 ~ ')+L23ô¸J9')+L2DF' ~9~ *}Dt,F*]EF6�¾)7A')+L6%�yDFJ3��*}Dt6)õ56 ~ *¸(%']096�+-+x�ù*}EFEt6�D¤£)'y8�2L*)796)õ ~ 6�Dt2L*¸09*å*}EFEt6�Dt£y'y,F*9õ ~ 6:DF2-*09*ÃA'yDF2L(:6�7�,uDt2L(:*9õh�G2LEFJ3Du'Ú092�092LE ~ 6:DFEF2-*}79610r+$�¨'y+-,uDt*�(�*)7·+$��6:Et,F6�79Et2L*}796������ Ç õr(/{36K��*)DF792-EF(�6+-6�2-73��*}DF��')8:2L*}792�796�(:6�EFEF')DF2-6 ~ 6:D�+$��*}J, ~ J3,B¾}DF'yýA(�*<EFJÐý°þ@ý ÿ Î�� õ�(/{96Ú£¸2L6:796�6:EF6�¾)J92-,F*0A'y+ ~ DF*)¾}Du')�G��' � ÿ�� É�Ì � ÿ Î��3Ì ��� Ç =

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!�ÝÞ ��ß_àGá&â¡ã&ä*å¡æ ç>á¡èPà¶ã&éé� \�¢ ¡ � ����¤�\ � � ��ê��jë&ìc�¶í[Îc�Nä&ì ��÷

­f® ���I� »��5�Gµ>�5±A¯��HI*úEF(�Dt2 ~ ,G'y7A')+L2-8�8�'²2 ýA+L6 ��� �}Ê õÒ+L2 *)DF092-7A'²2L7RÃA')Et6M')+ Du' ~9~ *)Dt,u*úEt6�¾}7A'y+L6 ��DFJ9�G*}DF6yõ09* ~ *¸092L(/{5Ó§' ~ DF6§(�*)7<�8-§�n+-*),f2L+�ýA+L6!����� Ç (�*}DtDF2LE ~ *)79096�7�,F6B'y+��"� �}Ê (�*)7d2-+h�Ú'y¾}¾}2L*)DDu' ~9~ *)Dt,u*úEt6�¾}7A'y+L6 ��DFJ9�G*}DF6y= Ù 7è,/')+-6�ýA+L6åEt*}79*·DF2s'yEFEFJ37�,F2f2�DF2LEtJ9+-,u'y,u2?Eu')+-2L6�7�,F2 096�+-+s'DF2-(�6:DF(%'w

• 2-73��*}Dt�Ú')8:2L*}732�£y')DF2-6�Dt2L¾}JA'yDF0A')7�,F2Ò2-+ný9+L6���7A')E¤,uDF*3õ>7�J9��6:DF*²036�+Òý9+L6)õ�Ã9+L*¸(�(:*²092~ 'yDt,u6:798%'õA0A'y,/'"2-7å��*)DF��'y,u*"'y79¾}+L*)Eu')EtEF*}796¿ê�ê¸���G090hõ3*}Du' Ý q�CY�R0

• ,F6�� ~ *úEt2L096:Du')+-6]+L*¸(%')+-6�096�+-+x�ù*}EFEt6�D¤£)'y8�2L*)796�0�'yEF(�6:79EF2-*}796MDF6´,F,/'ú6å096�(:+L2-7A')8�2-*}796Dt2 ~ *}Dt,u'y,u6¿'y+L+x�ù6�ô�J92-79*}8:2L*1096:+r�)�}�}��0

• 73*}��6Ú096�+-+s'²EF*)DF¾}6:7�,F6)õn��DF6:ô¸J36�798�'�EFJ ~ 6:DF2L*)DF6]2L7è;dì 8)õÞ7�J9�G6�DF*ú092?(%')7A'y+L2 ×')� ~ 2-6�8�8�'1092IÃA')730A'G032I*}¾}792h(�')7A')+-6)õ3,F6�� ~ *K092�(%')� ~ 2L*)7A')�G6�7�,u*50

• 7�J9�G6�Dt*K092h(%'y� ~ 2-*}7A')�G6�7�,F2xõ�6 ~ *(�'"(�6�7�,FDu')+-6¿096�+-+x�ù*}EFEt6�Dt£y')8:2L*}736¿2L7M;²ß}��õA7�J��G6�Dt*G032hEF*),t,u*}2-7�,u6�¾)Du')8:2L*}792$õ3�G2L¾}+-2L*}DnE¤,u2L��'1096:+5�¿;æ0

• �G2L¾)+L2L*)D�DF' ~9~ *}Dt,F*¦Et6�¾}79')+L6%�yDFJ9�G*}Dt6)õ ~ 6:DF2-*09*¿*)EFEF6:Dt£y'y,F*�6�ÃA')DF2-(�6:7�,FDF2-(�*.��* £�£}6 �Dt*9õ3Dt2-��6�Dt2-,F*1')+�ÃA')Dt2L(�6:7�,uDF*"036�+542-Et,F6���'"4*}+L')DF6°�´õ')(�(:6�+L6:Du')8:2L*}736v+LJ973¾}*1+s'¦+L2-796%'092h£¸2-Et,/'õ96:£)6�7�,uJA'y+L6§£)'yDF2s'y8�2L*)796©092Iô�J96:Et,���J9+¥,u2-�Ú'"796:+h,u6�� ~ *"092I2L7�,u6:¾}Du'y8�2L*)796�0

• ô�JA'�,F,uDt*K¾}Du'yý9(�2I2L7å(:J92IEF*}73*G�G*}E¤,uDu'�,u2xw

'3=f'y790A')�G6�7�,u* 036�+L+L'è��')Et6º096:+1EF6:¾}7A')+-6Á096:092LE ~ 6:DFEF* ��(�*}7Â2-+B�G2L¾}+-2L*}D�£y')+ �*)DF6²092v�¿;���2 ~ *),F2L8:8%')7903*k')(�(:6�+-6�Du'y8�2L*)796<7�J9+-+s'­��+s'�Et(%')+L'º096�+-+s'ú��')EF6Ñö73*}DF��')+L2-8�8�'y,/'�2-7å��*¸09*"0A' ~ *y,u6�D�(:*}79Et2L096:Du')Dt6¦(:*}Et,u')7�,u6§2L+ ~ 6:DF2L*¸09*V�R0

Ã�=f��'yEF6·096�+¦EF6:¾}7A')+-6·036�092-E ~ 6�DFEt*i09* ~ *è+x��' ~9~ +-2L(%'y8�2L*)796²096:+ ~ ')Du')�G6:,FDF*è092'y(�(�6:+L6:Du')8:2L*}79610

(y=��G2L¾)+L2L*)DGE¤,u2-�Ú'Á036�+ ~ Dt*)ýA+-*º2L7�,u6:¾}Du'�,u*9õf*),t,u6�7�J3,u'k'y,F,FDu'%£}6:DFEt*è2©��2-¾}+L2-*}DF2£y')+-*}DF2�092I')(:(�6�+-6�DF')8�2-*}796§6§�¿;æ0

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

�}« Þ � äc� \�¢P¢ �°� � � ��� � ��¢ � �0h=�')790A')�G6�7�,F*M036�+�Du' ~9~ *)Dt,u*åEt6�¾}7A'y+L6 ��DFJ9�G*}DF6�2L7úÃA')Et6�'y2�£y')+L*}Dt2�092 ~ DF* £y'J3,u2-+L2L8:8%'y,F2 ~ 6�Dr2L+ ~ ')DF')�G6:,uDt* 032'y(�(�6:+L6:Du')8:2L*}796Þ6�0B2L+ ~ 6�DF2-*03*�032Dt*),/')8:2L*}736)=

§��7���*�tÿ$#(ª�¨k«�²y¼�³K¸�¼�³ Ê ²hµ¡%~¬?®½%ǯ�µ°·[¹�º!¶&%�')(�*,+.- / 0�1,(�2�')+3½¯�¹c·~¬?µ°»�®¦º&¹c·�·=µ�¸�¼�·K»�µ°²�4@S,5 à SXK6 SXW Ã

ÛÒrAå Ü(Þ Þtvè�Æ��xé� � �Æ�sÞ|l�

H��ù*}Ã92L6´,F,F2-£}* ~ DF2-79(�2 ~ ')+-6�096:+?�G2L*d+s'%£}*}Dt*9õ>2-7 ~ ')D¤,u6�738%'3õ�6:Du'd��')D�')(�(:6:,t,/')Dt6]2L+ ~ DF2-��*Ã9+-*(:(�*�092�Ü Ç È9É}Ê�ËÌ9Í�Î�ÈÏ#Ç�Ê)Ð õ�* £�£}6�Dt* 2-+ ~ Dt*}¾}DF')����'Ò032}096�032LE ~ 6�DtEF2-*}796 � ÿ�� É����� ��Ç ����õ0A'y+�(�*}� ~ 2L+L'y,u*)DF6>¾�Ä)Äf2-79Et,u')+L+L'y,u* EtJ�J979' 096:+L+L6���')(:(/{92L796nE¤,/')790¸��')+-*}796n096�+-+x�ù*}EFEt6�D¤£)'�,u*y�Dt2L*9õ¸C ')E¤,u6:+L+L*3õ�EFJÚ(:J92#öf2L79E¤,/')+-+s'y,F*¿J97�Et2LE¤,u6���'§* ~ 6:Du'y,F2-£)*�HI2L7�J�6K�©6�Ã92L')7��x;<')73¾}J9Et,u'6:Du'¿')79(:*}Du'v2-71(�*)Et,uDtJ98�2-*}796yõ�6 09J979ô�J96f79*)7K' £)6:£)*B+L' ~ *)EFEF2-Ã92L+-2-,u.�092+s'%£}*)Du')Dt6 092LDt6:,t,/'��

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!�ÝÞ ��ß_àGá&â¡ã&ä*å¡æ ç>á¡èPà¶ã&éé� \�¢ ¡ � ����¤�\ � � ��ê��jë&ìc�¶í[Îc�Nä&ì ��Ä

�G6�7�,u6BEFJ9+�(�+LJ3Et,u6:D#� =¿�©* ~ *032L(/{5ÓB09* £}6:£)*å(�*}73��Dt*}7�,/')Dt6�+-6 ~ Dt6�Et,u')8�2-*}792r6�0²2�DF2-EFJ9+¥,/'y,F2096:¾}+L2f6�Et6�¾}J32LÃ92-+L2�(�Dt6%'y,F2©0A'·¾�Ä}Äú(�*}7iô�J96:+L+-6<096:¾}+L2f6�Et6�¾}J32LÃ92-+L2�(�Dt6%'y,F2 EtJ &>&�q�Äú0A')+(�*)� ~ 2-+s'y,F*}DF6Ò� é � � = Ù +#+L' £)*}DF*¦79*}7�ö E¤,/'y,F*B+-J979¾}{32LEFEt2L�G*9õ}6�09* ~ *�Dt6�+s'�,u2-£y')�G6�7�,F6 ~ *¸(�*,u6:� ~ *<{3* ~ *),FJ3,u*d£}6�Dt2-ýA(�')DF6Ú(/{96�2?Dt2LEtJ9+-,u'y,u2�*),t,u6:7¸J,u2?09')2 ~ Dt*}¾}DF')���G2xõ5(:2L*¸öÚ2nýA+L6096:092LE ~ 6:DFEF2$õ96�DF')79*G2L096:7�,u2L(:2x=

�©J9DF')7�,u6ú+s'Á£¸2LEt2-,u'º096�+ ~ DF*)��=^�©7909Dt6:îj&�'yJ9+Lò�796:D]096�+-+x� Ý 792¥£}6�DtEF2¥,/.Á092¿;<')79(/{�6�E¤,u6:D�õ�öKE¤,/'y,F*<2L73Et,/'y+L+s'�,u* � ÿ�� É���� �#Ç ���Á6�+L']DF6�E¤,/')7�,F6 ~ 'yDt,u6G092�Ü Ç%È9É�Ê�ËÌ3Í�Î�ÈÏ#Ç�Ê)ÐEFJ ;<')79¾}J3Et,/'=Â�©2�(�*}79Et6�¾}J36�798�'3õ 2-+f+s'%£}*}Dt*Á(:*}7 (�J92�EF*)79* ~ ')D¤,u2¥,u*Á6:Du'Á¾)2LJ97�,u*Á')+,u6:DF�G2L796y=G��6�Dt�9õ�Dt2L��')796´£)'�2-+>09J9Ã3Ã92L*MEF6G¾�Ä}ÄÚ��*}EtEF6G6�/�6:,F,F2-£y')�G6�7�,u6KJ979'MEt(�6�+¥,/'d' ~ �~ Dt* ~ DF2L'y,/'=^� 2v(�*}73EF6�¾)J96�798�'3õvJ979'Á£}*}+¥,/'º(/{96úö²E¤,/'y,F*è2-79Et,u')+L+L'y,u*·+x� Ù 7�,u6:+¿&A*}Dt,FDu')7C?*}� ~ 2L+-6�D¿EtJR;<')79¾)J9Et,u'3õ�Et*}79* ~ 'yEFEu'�,u*²'y+L+s']Dt2LEF(:DF2¥,F,uJ3Du'å092>Ü Ç%È9É}Ê�Ë3Ì3Í�Î�ÈÏ�Ç�Ê)Ð ~ 6�D')0A'�,F,/'yDF+L*1')+L+-6©6�Et2L¾}6:798�6§092�ô¸J36�Et,F*�(:*}� ~ 2L+L'y,u*}Dt6)=r�©+h(:*}7�,uDF')DF2-*"092�� é �3õ(/{96§(�*}� ~ 2-+s'

��*)Et,/'y8�2L*)796 &>&�q�Ä ;<')73¾}J9Et,u'C?*}� ~ 2-+s'y,F*}DF6 � é � ¾}(�( ��¾�Ä)Ä Ù &rC&A*}Dt�Ú'y,F*1ýA+L6 = � = � = � é �

&#*)DF��'y,u*"Ã92-7A')Dt2L* Ã92L¾K6:79092s'y7 +L2¥,F,F+L6©6:79092L')7 +L2¥,F,F+L6©6:79092L')7

q�')Ã�6:+L+L'iª9= ¢ w^q�'%£}*}+L'ë096:+L+-6 ~ DF2-79(�2 ~ ')+L2B(%')DF'y,F,F6�Dt2LEt,F2L(/{96R096:+L+-6º£)'yDF2L6k£)6�DFEt2L*}732"096�2~ Dt*}¾}Du'y���G2

EF6:798%'�092T�G(�*)+-,/.²ýA+-6dEt(�Dt2-,F,F2�(�*}7b+s'ÑEF2-7�,u')EFEt2 036�+f��*}Dt,FDu')7bÄ}ÄÑ�Ú'ú(�*}7b')+L(:J9796å��J97�8�2-*}792Ò2L7�,uDt2L79Et6�(/{96 ~ 2��kDF6:(�6:7�,F2xõ Ù &rCä73*}7k{A'²ô�J96�E¤,u*ú¾}DF')09*Ñ092Ò(�*}� ~ 'y,F2LÃ92-+L2-,u.3=dHr'~ Dt6�EF6:798%'M2L7²Ü Ç%ÈAÉ}Ê�ËÌ3Í�Î�ÈÏ#Ç�Ê}Ð 092n')+-(�J97961��J3798�2-*}792�2L7�,FDF2L73EF6�(/{36G036�+���*}Dt,FDu')7 é �]{A'DF6:EF*1736�(�6:EFEF')DF2-*1,uDu'yEt��*}Dt�Ú')Dt6�,FJ3,F,F*�2-+�(:*032L(�6 (�*}7Ú+s'BEt2L7�,/'yEFEF2�096�+#��*}D¤,uDu'y7 é �3=nøvJ96:E¤�,/'M,uDu'yEt��*}Dt�Ú')8:2L*}736�Dt2L¾}JA'yDF0A'MEF2s'd+x�ù6�Et,F6�79Et2L*}736�096�2ÞýA+L6��$')738�2L(/{�Ó7� Ï õ8� Ï�9�: � õ�EF2L'<+s'092-(/{92s')DF')8�2-*}796K096:+L+L6K£y')DF2L')Ã92-+L2xõI2Þ(�*)���G6�7�,u2n6:0º2Ò(�')Du'�,F,u6:DF2Þ092Þ(�*}7�,u2-7�JA')8�2-*}796�096�+-+L6DF2-¾}{96M092�(�*}��')7909*3= Ý 79'�£}*}+¥,/'·6�EF6:¾}J92¥,/'Á+L'²ïñ,uDu'yEt��*}Dt�Ú')8:2L*}736´ó/õÒJ9792¥,/'Á'y0 ')+L(:J9796ï<; k E&I4WèC!>XG�<?WOjUH:�G=B#M4W�@4>éZ>=�ôYU1>A@lUH@ W÷�@ BOPOj:VI <?@ :ÅM4M4:�:KJmZ[W@4M4@�BRJ�?@?BA,UH:K>AJ&BROj>AJ�M >�÷:�E&INM4:pu1<XBRM4WCHBGKG=BY<XB@ BRMNM4>A@4:=INM4:=<XBjC!>XG�<?WOjUH:�G=B#M4W�@4>�CH:*>AI I4>X@ >y<XWOjU&BRM4:�QH:KG�>8<XWJmM4E!M4M4>�GK>,ñ�>X@�IN:�WJH:*UH@4>c<?>cC!>XJtM4:�C!:Z[W@4M4@�BRJ

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

� á Þ � äc� \�¢P¢ �°� � � ��� � ��¢ � �

Ù &�C -¦Ä}Äqr6�� ~ *���Et6�(:*}79092´� q�6:� ~ *���Et6�(�*)79092��(�Dt6%'y,F6�C�,/')à é õ¨÷}� á õ á}é

£¸+LEF'�Cf096�092-E ~ ¢ �õ¨��Ä �}÷õ¨Ä)�Ñv+-Eu'��ñEF6�¾���*}796 �ñ��*}+-0

¢ « é õ ¢ é Ä}÷õ ¢ á� « é õ ¢ é Ä}÷õ ¢ Ä� « é õ ¢ é Ä}÷õ¨�)�ª « é õ ¢ é Ä}÷õ¨�}�÷ « é õ ¢ á Ä}÷õ ¢ á« « é õ ¢ á Ä}÷õ¨�)�Ä « é õ ¢ á Ä}÷õ¨�)�á « é õ ¢ é Ä}÷õ ¢ Äé « é õ ¢ á Ä}÷õ ¢ é¢ � « é õ ¢ á Ä}÷õ ¢ é¢)¢ « é õ ¢ Ä Ä}÷õ ¢ ᢠ� « é õ ¢ Ä Ä}÷õ¨� ¢¢ � « é õ ¢ « Ä}÷õ ¢ «¢ ª « é õ ¢ á Ä}÷õ ¢ Ä¢%á « é õ ¢ é Ä}÷õ ¢ Ä¢%é « é õ ¢ á Ä}÷õ��}��y� « é õ �}Ä Ä}÷õ ¢ é� ¢ « é õ ¢ é Ä}÷õ¨� ¢�)� « é õ �}Ä Ä}÷õ¨�)��y� « é õ �)� Ä}÷õ¨�)«��ª « é õ �)� Ä}÷õ ¢ é�)÷ « á õ é ÷ Ä}÷õ¨�)��y« « é õ ¢ á Ä}÷õ ¢ «�)Ä « é õ ¢ á Ä}÷õ¨� á� á « é õ ¢ á Ä}÷õ¨� ¢� é « é õ ¢ á Ä}÷õ ¢ Ä�)� « é õ ¢ é Ä}÷õ ¢ Ä� ¢ « é õ ¢ á Ä}÷õ ¢ á�}� « é õ ¢ Ä Ä}÷õ��}��)� « é õ ¢ á Ä}÷õ ¢ á�yª « é õ ¢ é Ä}÷õ¨�)��}÷ « é õ �}÷ Ä}÷õ ¢ é�)« « é õ ¢ é Ä}÷õ¨�)��}Ä « é õ ¢ á Ä}÷õ ¢ é

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!�ÝÞ ��ß_àGá&â¡ã&ä*å¡æ ç>á¡èPà¶ã&éé� \�¢ ¡ � ����¤�\ � � ��ê��jë&ìc�¶í[Îc�Nä&ì � é

� á « é õ¨�}� Ä}÷õ ¢ Ä� é « é õ ¢ á Ä}÷õ¨� ¢ª�� « é õ ¢ é Ä}÷õ¨�)�ª ¢ « é õ¨�)� Ä}÷õ¨�)�ª�� « é õ ¢ é Ä}÷õ¨�)�ª�� « é õ ¢ á Ä}÷õ ¢ «ª}ª « é õ ¢ é Ä}÷õ¨�}�ª�÷ « é õ ¢ á Ä}÷õ ¢ éª�« « é õ ¢ á Ä}÷õ¨�}�ª�Ä « é õ ¢ é Ä}÷õ¨�)�ª á « é õ ¢ á Ä}÷õ ¢ áª é « é õ ¢ é Ä}÷õ ¢ é÷)� « é õ ¢ á Ä}÷õ¨� ¢÷ ¢ « é õ ¢ Ä Ä}÷õ¨� ¢÷}� « é õ ¢ é Ä}÷õ¨�)�÷)� « é õ ¢ á Ä}÷õ ¢ á÷yª « é õ ¢ á Ä}÷õ ¢ é÷}÷ « é õ ¢ Ä Ä}÷õ ¢ «÷)« « é õ ¢ á Ä}÷õ ¢ é÷}Ä « é õ¨�)� Ä}÷õ¨�)�÷ á « é õ¨�}� Ä}÷õ¨�)�÷ é « é õ ¢ á Ä}÷õ ¢ Ä«}� « é õ ¢ á Ä}÷õ¨� ¢« ¢ « é õ ¢ á Ä}÷õ¨� ¢«�� « é õ ¢ « Ä}÷õ ¢ á«}� « é õ ¢ Ä Ä}÷õ¨�)�«)ª « é õ ¢ é Ä}÷õ ¢ Ä«�÷ « é õ ¢ Ä Ä}÷õ ¢ é«}« « é õ ¢ á Ä}÷õ ¢ é

qr6�� ~ *G�G6�032L*Õ��Et6�(:*}79092´� qr6�� ~ *K�G6�092-*F��Et6�(�*)79092��« é õ ¢ á Ä}÷õ¨�)�q�')Ã�6�+-+s'©ª3= �wr(�*)73��DF*}7�,F*v��Du'v2,F6�� ~ 232-� ~ 2L6�¾}'y,u2�0A')+-+L6Þ£}6�DtEF2-*}792092�Ü Ç È9É}Ê�ËÌ9Í�Î�ÈÏ#Ç�Ê)Ð 2L73Et,/'y+L+s'�,u6�EtJº;d')79¾}J9E¤,/' ~ 6�D§6�Et6�¾}J92-DF6+L6 ~ Dt*(:6�09J9Dt6

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

ª�� Þ � äc� \�¢P¢ �°� � � ��� � ��¢ � �£y')Dt2s')8:2L*}792#796:+L+-6©ð#')¾}E�032h(�*}� ~ 2-+s')8:2L*}796�6¿+x��')¾}¾)2L*}Dt7A')�G6�7�,u*B092I')+-(�J9796©+L2LÃ3DF6�Dt2L6yõ Ù &rC{A'"(:*}� ~ 2L+s'�,u*1(:*}DFDt6:,F,u')�G6�7�,u6§2 ~ Dt*}¾}DF')���G2x=

H���J3+-,u2-�Ú'Ú��'yEF6G096�+Þ+s'%£}*)DF*Mö�(:*}79EF2-Et,F2-,/'å796:+Þ(:*}73��Dt*}7�,u*d,FDu'å+L6 ~ Dt6�Et,u')8�2-*}792n096:¾}+L26:EF6�¾)J92LÃ92-+L2$=�øvJ96:Et,u*d(�*}7��DF*}7�,u*dDF2-¾}JA')Dt0A']EF2s'å2nDF2-EFJ9+¥,/'y,F2>£}6�Dt2Ò6 ~ Dt* ~ DF2$õ5(�2L*¸öG+x�ù2L79092 �£¸2L03JA')8�2-*}796G096�¾)+L2ÞEt,u6:EFEt2?£y')+L*}Dt2n092Þ,FJ3,F,F2?2 ~ ')DF')��6´,uDt2xõrEF2s'dJ97º(�Dt*}79*}�G6:,FDu')¾)¾}2L*M096�2,F6�� ~ 2n2L� ~ 2L6:¾�'y,u2 ~ 6:D�'%£}6:DF6�2nDt2LEFJ3+-,/'�,u2x= Ù +Þ,F6�� ~ *M2L� ~ 2L6:¾�'y,F*M09')+L+L']£)6�DtEF2L*)796 Ù &rCö1036�(�2-Eu')�G6�7�,F6"2L73��6:DF2L*)DF6�Dt2LE ~ 6´,F,u*å'y+L+s'K£}6:DFEF2-*}796"¾�Ä)Äw 2-7 ~ ')D¤,u2L(:*}+s'yDF6)õ�+s'Ú036�092-E ~ 6�D¤�Et2L*}796K£¸2L6:796 ~ DF'y,u2-(%'y,u'M2-7��G6�73*<096:+L+s'å�G6:,/.M096�+n,u6:� ~ *9õr��6:7�,uDF6�796�+n��*}+-092L79¾ Ù &rC2-� ~ 2-6�¾�'"2-+ ¢ ���æ032r,F6�� ~ *�2L7²�G6�79*3=vH5' ~ 6�Dt(�6�7�,FJA')+L6�092�C � Ý J3,F2L2-8�8%'�,/'3õ#2L7�£)6�(�6�ö~ DF'y,u2-(%')�G6�7�,F6B2-096�7�,u2-(%'���(�2-DF(�'�2L+ é}é �)� õ�2-+5(/{96���' ~ 6�73Eu')Dt61(/{961¾}+-256�EF6:¾}J92-Ã92L+-2I(�DF6�'y,u20A' Ù &rC E¤��DFJ3,t,u2-79*]��6:¾}+L2-*Ú+-6"DF2LEt*}DFEt6"096�+ ~ DF*¸(�6�EtEF*}Dt6)õr(%')DF'y,F,F6�Dt2LEt,F2L(�'�6�EFEt6�798:2s')+-6"796�+�G*}�G6�7�,u*�2L7²(:J92�Et2�£}*}¾)+L2L*)79*�6:EF6:¾}J92LDt6"(%')+-(�*}+-25��*}+¥,u*G+LJ973¾}{92r(�*}7ÑJ97Ñ(:+LJ9E¤,u6:Dv092�ª}�C � Ý (�*}�G6¦;<')73¾}J9Et,u'3=

D �j���9¢ Eº¯°¤GF ¤<HIHR¬KJ ¤MLBN�OQPIR&SUTWV�XYO[Z\N�RY]Ë­½§&FJ¦¨ª_^L¬`J½¤Macb�£ d5¢fe_g�¢Ih ¢ �\g

Ý 79*v096:23ýA+L6?')7A')+-2L8:8%'y,F2¸03J9Du')7�,F6 2L+¸+s'%£}*)DF*vDt2L¾}JA'yDF0A'%£y'vß ¢ á � ¢ �¤� ¢ �}�3õ�J97A'v�G2L+-+L2LEt6�(:*}790~ J3+LEu'yDÒ2-7�J97�Et2LEt,F6���'BÃ92-7A')Dt2L*�(:*}7�J97��¨')+¥,uDF'�@v4�=3H��ù*}EFEt6�Dt£y')8:2L*}736v092�ô¸J36�Et,F*"*}¾}¾}6´,F,F*öú')EtEu')2¿(:*}� ~ +L2-(%'y,u' ~ 6:D�£¸2s'º096:+L+x��')+¥,u*Á£y')+-*}DF6²032§')(�(:6�+L6:Du')8:2L*}736²*}DFÃ32-,/'y+L6)= Ù 7 J97(�')EF*�(�*}�G6Bô�J96:Et,F*9õ�+$��J3,F2L+-2L8�8:*"092rÃ92L7A'yDtêYCf(�*}73ý9DF�æEF2rö�Dt2-£)6�+s'�,u*K2L79032LE ~ 6�73Eu')Ã92-+L6y= Ù 7ýA¾)J9Du'Rª9=¨�RöúDF2 ~ *)Dt,/'�,u*R+x�ù*}J3, ~ J3,å¾}DF'yýA(�*è092¸ý°þ@ý ÿ Î�� (�*}DtDF2-E ~ *}79096:7�,F6·')+¿ýA+L6Ñ(:*}72-+?�G2L¾}+-2L*}D§Du' ~9~ *)Dt,u*úEt6�¾}7A'y+L6 ��DFJ9�G*}DF6y=k42 ~ J9�ú79*),/'yDF6](�*)��6yõÒ796:+�¾}Du'�ýA(�*ú2L7R'y+-,u*'ÁEt2L792-Et,FDu'3õ 2-+ Et6�¾}79')+L6d79*}7 ')(:(�6:+L6�DF'y,u* ~ DF6:EF6�7�,u'3õ 736�2©(:2L(:+L2�092���*)+L092-79¾�EtJ9(�(:6�EtEF2-£¸2$õJ979'd0927/�6:DF6�738%'d032Þ��')Et6�,u')+L6K(/{96�+$��2-� ~ J9+LEt*]2L7�,u6:¾}Du'y,F*<EF')DF6:Ã9Ã�6G,/')7�,F*åï¤' ~9~ 2s'�,F,u2¥,u*yó0A'º73*}7 6�EtEF6�Dt6úDF2L(:*}79*}Et(�2-Ã92L+-6d(:*}��6<2L� ~ J9+LEt*9=ÂH���' ~9~ +-2L(%'y8�2L*)796<096:+ ~ 'yDu')�G6:,FDF*º092')(:(�6:+L6�DF')8�2-*}796�ï¤')+-+L2L736%'�ón+L' ��')Et6 096�+-+x�ù2L� ~ J9+-EF*�796�+-+L6?032-£}6:DFEt6�EF*),t,u*}2-7�,F6�¾}DF')8�2-*}7923��(:*}��6Et2 ~ J9�Ñ£}6:096�Dt6d736�+L+$��2-����')¾}2-796"796:+�¾}Du'yý9(�*·'²EF2-792LE¤,uDu'Ñ'y+ (�6:7�,FDF*V� ~ 6�Dt��6´,F,F6�7909*ú092

9;:=<?>A@ <AB�C!:*DFEHG=I4B@;:KJLI4:�INM4>AOP:*QH:KJ1BR@ :TS5:�GVUH@ WQHG�>XOYBPC!>XG�G�BY<XWJ!Z[>A@4OYBPC!>X:�<XBRJ1C!:�C&B#M4:

¡ �5� \ � ��¢!�ÝÞ ��ß_àGá&â¡ã&ä*å¡æ ç>á¡èPà¶ã&éé� \�¢ ¡ � ����¤�\ � � ��ê��jë&ìc�¶í[Îc�Nä&ì ª ¢

,uDF')(�(:2s')Dt6©J97]2-� ~ J9+LEt*1')Ã9Ã9')Et,u')798%'1Ã�6�7å096´ýA792¥,u*À��2L7�ÃA'yEFEF*G'�Et2L792-Et,FDu'k� =�@ 6:+�¾}DF'yýA(�*¾}DF')79096"Et2�79*),/']+$��2-7�,F6�D¤£)'y+L+L*G092>£y')+-*}DF2�092 ~ 6�DF2-*03*]6K')(�(:6�+L6:Du')8:2L*}736 ~ 6:D¿(�J92�Et2�EF*}79**),t,u6�7�J3,F2IDu' ~3~ *}D¤,u2hEt6�¾}79')+L6%�yDFJ9�G*}Dt6 ~ 2��M')+¥,u2x=

9;:=<?>A@ <ABjC!:kDFEHG=I4B@l:�JmI4:�INM4>AOj:VQH:�J&BR@ :TS5:�GVUH@ WQHG�>XOYBjC!>AGKG=Bj<?WJHZ[>X@ OjBPC!>A:*<XBJ&C!:=CHB#M :

n gl_WPR[IYW\]Ohgo_WO

Ù 7�ô�J96:Et,F*G+L'%£}*}Dt*�{9*"(:6�DF(�'y,u*�092�2-+L+LJ3Et,uDF')DF6f�G6�¾}+-2L* ~ *)EFEF2-Ã92L+-6f+L6 ~ DF*}Ã9+-6���'y,u2-(/{96�(�*}7�796:EFEt6v(�*}7�+s'§DF2-(�6�Dt(%'¦096�+-+L6 ~ J9+LEF')D�õ�6:0�2L7 ~ ')Dt,F2L(:*}+s')Dt6�096�+-+L6���2-+L+-2LEF6:(�*}730 ~ J9+LEF')D�=�q�DF'ô�J96:Et,u6 ~ DF*}Ã3+L6���'y,F2L(/{96KE ~ 2L(�(�'d2-+n��'�,F,u*M092Þ09* £}6:DB£}6:DF2¥ýA(%')Dt6Ú*}EtEF6:Dt£y')8�2-*}792Þ09J9Ã9Ã32L6G*2-79(�*}� ~ +-6:,u6yõ#2L7 ~ DF'y,u2-(%'G+s'�(:*}73��6:DF��'Ú096�2�(%')73092L0A'�,u2x= Ù +�(:*032L(�6BEFJÑ(:J92�{3*]+s'%£}*}DF'y,u*Et2>ö1092-��*}E¤,uDF'y,u*�6:EFEt6�798:2s')+-6"2L7²ô�J96:Et,u*MEF6:79EF*å6 ~ 6�Dt��6´,F,u6�092>*),t,u6�736�DF6"036�2>Dt2LEFJ3+-,/'�,u20A'%£�£}6:DF*�096�¾}732I092I79*),u'3õ9(�*)��6¿796:+I(%')Et*�032rß ¢ á � ¢ ��� ¢ �}�

Ý 7 ~ ')EFEt*GEtJ9(�(:6�EtEF2-£)*Ú09* £¸DF6:Ã9Ã�6¿6�EFEt6�Dt6)õ�'1��2-* ~ 'yDF6�Dt6)õ92-+ ~ *}Dt,F2L79¾BEFJd;<')73¾}J9Et,u'096:+fDF6�E¤,u*º036�+�(�*¸092L(:6)õ 6:0b2L7TEF6:¾}J92-,F*Á+L'²ï ~ J9+L2¥,uJ9DF'�óÚ096�+�(�*¸092L(:6d09'·,uJ,F,u6d+L6],uDF')(´�(:6 ��EFJ9Ã3DF*}J3,F2L796M2L7R092-EFJ9Et*9õ?* ~ 6:Du')8:2L*}792nï�(�*)���G6�7�,/'�,u6´ó�6�(:()=�� +s')Et(�2L'y,u6]0A'y+L+L6�£y')Dt2L6~ 6�DtEF*}796<(/{96Ñ(�2 {A')7979*k+L'%£}*}DF'y,u*50 (�*}7�,F6�� ~ *}DF')796�')��6:7�,u6)õfEF')DF6:Ã9Ã�6Ñ* ~9~ *)Dt,uJ37A'Á+s'Et(�DF2¥,F,FJ9Du'À��')79(/{96¦')+-+x�ù2L7�,u6:DF79*1036�2 ~ Dt*}¾}DF')���G2�Et,u6:EFEt2xõAEF*y,F,u*"��*}Dt�Ú'B092h(�*)���G6�7�,u2´�Þ092J979'<¾}J92-0A'<')+-+L6K£y')DF2-6 ~ 'yDt,u2Þ096:+?(�*¸092-(�6Ú2-7Á�G*03*d,/'y+L6Ú09'd��')(�2-+L2¥,/')Dt6"2L+n+s'%£}*)DF*Ñ')¾)+L2E¤£2-+LJ ~3~ 'y,u*)DF2�036�+L+-6 ~ DF*)EFEF2-��6v£)6�DtEF2L*)792I096�+I(:*032L(�6y=

ª��

i OhcZ[IOhgkjoSdU � U

� ¢t� �v')+-6 �B= � E¤,u+-2L6 z?Du'y09+L6´ê bà=iC ')DtDF*}+$= lm%nm%�2N�#$t'���"2N� $&% 2h$ 2þ$t'*��R%lm�24��$#���*�!�� "#�´=Þ��03092LEt*}7�¡b�6�Et+L6´ê}õ ¢ é}é «3=

��� � ì 6´îf2LEt{<6:,�'y+x= � Ã9Et6�Dt£y'y,F2L*}73E�*y�>'"Du' ~ 2L09+¥ê ~ J3+LEu'�,u2L73¾"Du')092-*"EF*}J3DF(�6y=�ù� � ��=#|§=#HI*}DF2-��6:D ��=F-"=AHhê¸796)=po¿ÿ�24�*���´õÇ�$�}« é �´õ ¢ é)é ª9=� ª � �©J973(%')7 |§=·H5*)DF2L�G6�D:= z?2-7A')D¤ê ')790 �G2L+-+L2LEt6�(:*}790 ~ J9+-Eu')DtEo'�,^,F{96 796´î

�G2L+L+-6�79732LJ9�M=yëé��Ô!��%*�)íè�Ô!� �,fé����%�í���¥ÿ�2N��Ô!��2N�yõAªF�$÷��´õ3¾}2LJ9¾)79*G�)�}� ¢ =��÷ � £y')7M096�D��¿+L2-Ef;�=/b 2rqt79')7909E:õA|¦=so¿ÿ�2N�����´õ~�$� é ªV�´w��)ª}ª9õ ¢ é}é}á =�ù« � |fJ9EFEt6�+A��=}ì J9+-EF6)=Aq�{36�032LEF(:* £}6�D¤ê"*)�#,u{36�Ã92L7A'yDtê ~ J9+LEF')D�=Ios$�ì���ël�#"2N�����#�´õ ¢ é}é �3=��Ä � ß)*}Et6 ~ {dìB=q�'%ê¸+L*}D:=>z?2-7A')D¤ê ~ J9+LEF')DFE�'y790åDF6�+L'y,u2¥£¸2LEt,F2L(f¾}DF' £¸2¥,�ê}=\os$�ì��ël�#"2N�����#�´õ¢ é}é �3=� á1� �v2L')* ~ 2-79¾²6´,K')+x=Ñ� 7è')Et,FDF*}79*)��2-(%')+n6:£¸2-096�79(:6å*)�f662LE¤,u6:79(�6å*)��ô�JA')DtòÁ��'y,F,F6�D')790å,u{36 ~ DF6�032L(:,F2L*}7]��*}D�EtJ9Ã9�G2L+-+L2LEt6�(:*}790 ~ J3+LEu'yDFE�=� é1� �©7�,F*}796�+-+s'vH5'y,F6�Dt8%'3=9qr6�Et29092+s')J9Dt6%'3õyDu')EtEF6:¾}7A'v096:2 ~ DF2-79(�2 ~ ')+-2���6´,u*¸0920323DF2-(�6:DF(%'092 ~ J3+LEu'yDFEn2L7KEF2-Et,F6��G29Ã92L79')DF2$wrE¤£¸2L+LJ ~9~ *§092AJ37A'B'y�1Ã92L6:7�,u6 ~ 6�Dn+x�ù*),F,F2L�G2L8:8%')8:2L*}796096:2I(�*¸092L(:2xõ#�)�)���=� ¢ � � ü�= 4�=���{92-79796´ê}=� ¢}¢t� £y')7·4¸,FDu'y,F6�7 bà=hzÒDu')2-+L6�Ev;�=hü�03î?')Dt09E�õr|§=�q¿=§�lEt6%')Dt(/{ú��*)DvEFJ9ø���G2L+L+-2LEt6�(�*)790

~ J9+-Eu')DtE�= ÿ&�2N�#$&î�����t&u�¨�u�vV��w@�}õ3�)�}� ¢ =� ¢ � � 4�= C©=?|�')79Et*}�d=í&#')Et,�EF6�')DF(/{i,F6�(/{9732Lô�J96�E���*)DÚ{92-¾}{b6:796�Dt¾)ê ~ J9+LEF')DFE:=lÿ&�2N��$&î

����t&u�¨k¨���u�u�v�=� ¢ � � �*2N2[�3«xt�t�f�f�f8ª�ÿ�2N%X0�ªN"#�����$�ª�ÿ��t(���#�!�Fÿ���"#��tk�(������ÿ��yt��!$ 0R2jfÞÿ����zt(��%('*�|{Vª7�*2 � =

ª��

N OI_}j^S<U çTOIU^a Qi_ä`dO

Ù 7 ~ Dt2L�G*Ú+-J9*}¾}*9õ#£}*)DFDF6:2>DF2-79¾}DF')8�2L')DF6 ~ DF*y��=§@ 2L(:*}+L�Ú���ù�©�G2L(�*Ú6109*),t,%=¿�©7309DF6�']��*}E��Et6�7�,u2 ~ 6�Df'%£)6�DF�G2h0A'�,u*"+s' ~ *}EtEF2-Ã92L+-2-,/.§092h+L'%£}*}DF')DF6¿'1ô�J96:Et,u'",F6�Et2xõ96vEt* ~ DF'y,F,FJ3,F,F* ~ 6�D'%£}6:DF�G2IEF6:¾}J92-,F*K09J9Du'y7�,F6§+L6v£y')DF2-6v��')EF2�096�+I+L' £)*}DF*K(:*}7<�"ò ~ ( 3 032 ~ ')8�2-6�798�'3=|f2L79¾}DF')8�2-*<'y79(/{96Ú,FJ3,F,F*²2L+ ~ 6:DFEt*}7A')+-6Ú096:+L+x� � EFEt6�Dt£y'y,F*}DF2-*9w�,FJ3,F,F2Ò�G2Ò{9')7979*Ñ'y2LJ�,u'y,u*ú09J9DF')7�,u6d2L+ +L' £)*}DF*·(�*)7b¾}DF')79096M(�*}� ~ 6:,u6:798%'ú��'·Et* ~ Du'�,F,uJ,F,u*·092-E ~ *}792LÃ32L+L2¥,/.3=|f2L79¾)Du')8:2L*v� 7�,F*}796:+L+s'õ�|�*)EF2-,u'3õ}� +L6�EtEu')7309DF*9õ�� 7909Dt6%'§q¿=�6f��=¥õ3C?+L')J9092-*9õ�C ')Dt+L*9õ�;<'y,t�,F6�*9õI��2-79*9õÇ-§')Ã9DF2-6�+-6)õ�� 7�,u*}792-*9õI|f6�7A'�,/'�6�(:()= ~ 6�D§'%£)6�DF�G2���'y,t,u*]Et6�7�,u2-DF6"0A'%£�£}6:DF*d'(�')Eu'3=

|f2L79¾}DF')8�2-*Ú,uJ,F,u2�2��G2L6:2���')�G2L+-2s')Dt2xõA£¸2L(:2L792>6"+-*}7�,/')732x="|f2L79¾)Du')8:2L*]2>�G2L6:2>¾}6�732-,u*)DF2(/{96���2n{A'y7979*<Et6�� ~ DF6�EF*}E¤,u6:7¸J,u*Ñ(�*)7k')�G*}DF6yõ�2-7Á*}¾}732Þ�G*}�G6�7�,u*3õ�')73(/{96Úô�JA')7309*79*)7ºEF*}73*²Et,u'y,u*²J37º��*)Et,uDt*<092Þ*}Dt092L796�2L7�(%')EF' ��(:2L*¸ö)õ�09'<(�2-DF(%'<�}�<')73792?'dô¸J36�Et,u'~ 'yDt,u6y=-=¥=��´õ?6 ~ 6�D",uJ,F,u*ú+$�¨')2-J3,u*Ñ09'y,u*}�G2 *}¾)792 £}*}+¥,/'Ñ(/{96M796M'%£}6:£)*ºÃ92-EF*}¾}73*9= Ù DF6�736~ 6�Dt(/{5Óv*}+¥,uDF6©')0�6:EFEF6:DF6§+s'¦��2L'BEt*}DF6:+L+s' ~ Dt6:��6�Dt2-,u'�ö¿')79(/{36¿092�J37A'109*}+-(�6�8:8%'12-7A')J9092¥,/'��ô¸J9')7909*M79*}7�EF2�DF2¥ýAJ3,u'M092>��'yDF6K2�(�*}� ~ 2¥,u2"~��´= Ù 79*}79792�� 7�,u*}792-*d6 Ù 796:E�õ�ün�G2L+-2L*½��,u2Dt2L(�*)DF096:DF�kEF6:� ~ DF6!�Ú6þ-¿2L79' ~ 6:DF(/{5Óú�G2©Et*}79*REF6:� ~ Dt6úEt,/'�,u2 £¸2-(�2L732©2L73EF6�¾)7A')7909*)��2J97���2-73ýA792¥,/."092r(�*}Et6B6B0A')7909*)��2I¾}DF')7909256:EF6�� ~ 2r092I£¸2-,/'= q�J,F,u25¾}+-2I8�2-2I6�+L6§8:2L6 ~ 6:D 2,u')7�,u25(�*}73EF2L¾)+L2xõ32L7å,uJ3,t,u2I25(%')� ~ 2$õA*}¾}7�J979*�EF6�(:*}7909*Ú+s'"EFJA'�6�E ~ 6�Dt2L6:798%'3õ�*}¾}7�J973*�(:*}72-+�EFJ3* ~ 'yDt,u2-(�*}+L')DF6©¾}6�792-*9=|f2L79¾}DF')8�2-*Ò,FJ3,F,F2}2}�G2L6�2y')�G2L(:2 ~ 6�Dh+$��2-79(�*}DF')¾}¾}2L')�G6�7�,u*Ò2L7©,FJ3,F,F2}ô�J96�E¤,u2�')79732xw5')79(/{36ô�JA')7309*©6:DF*�(�*}7�£¸2L7�,u* 092�79*}7 ~ *),F6�D5Du'y¾}¾}2LJ379¾}6�Dt6n(�6�D¤,u2�DF2-EFJ9+¥,/'y,F2xõ +-*}DF*�6�DF')79*�(�*}7�£¸2L7�,u2096:+>(�*)7�,FDu')Dt2L*9õ�6"(�*}+�+L*}Dt*�EF*}E¤,u6:¾}79*å+L2r{9*åDu')¾)¾}2LJ97�,F2x=§|f2L79¾}DF')8�2-*Ú2�-¿6�7Ñ6"¾)+L2�4(�*}J,(/{96���2r{A')7973*���'y,F,F*�(�Dt6�EF(:6�Dt6G2-7²J97ú')��Ã92L6:7�,F6�6:Et,uDt6���')�G6�7�,u61EF')+LJ,/')Dt6)õ�(/{32�2L7<J97�G*03*¦6 (/{92�2L7GJ97]')+¥,uDF*3=>|f2L79¾}DF')8�2-*§+s'§��2L'§��')6:Et,uDF'3õ�6 ,FJ3,F,F2�ô�J96:2 ~ DF*)��6:EFEF*)DF2�(/{96)õ3',FJ3,F,F2�2�+-2-£)6�+L+-2xõ�2-7�ô�JA')+L(/{36¿��*¸09*1{A'y7979*"(�*)7�,FDF2-Ã9J92-,F*1')+-+s'¦��2L'¦��*}Dt�Ú')8:2L*}736©79*}7]Et*}+L*Et(�*}+L')Et,F2L(%'õI')79(/{96Kô�JA')7309*d+-61+L*)DF*]��'y,u6:DF2L6�79*}7ú��2�6�DF')79*å(�*}73¾}6�792L')+L2$=BqrJ3,t,u2�ô�J96�2(:*}� ~ ')¾}792I092rEF(:J9*}+L'�6¦092�J3792-£)6�DFEt2-,u.�(/{96B{A')7979*ÚEu' ~ J,u*Ú6:EFEt6�DF6 ~ 2��d(/{96�(:*}� ~ ')¾}7926§(�*)+L+L6:¾}{92$=

|f2L79¾}DF')8�2-*ú;<')J3DF2L8:2L*Ñ6dC?*}DtDu')09* ~ 6�DK+s'²¾)Du')79036 ~ ')8�2-6�798�'·6 ~ 6�DK'%£}6:DF�G2�0A'y,F*J979'K¾)Du')79036 ~ *}EtEF2LÃ32L+L2¥,/.¦(/{96B73*}7d{3*GEF' ~ J3,F*�E¤��DFJ3,t,/')Dt6)=ëhÿ&�2Lìt�*2�%3$&2����Fÿ&�2�õ�Dt2L79¾}DF')8�2-*d;<')Dt,u'3=M��6:D1ô�J96�E¤,u2?03J96�')73792Ò6 ~ ')EtEu' ~ 2-6�792n092¾}2-*}2s'õ ~ 6:Dv2���')792-(%')Dt6:,F,F2xõ ~ 6�Dv2-+r,FJ9*�Et*}DFDt2LEF*3õ ~ 6�D©+$�¨'y��*}Dt6B(/{36"{A')2rDF2-£)6�DtEu'y,F*�EFJÑ092�G6¿2L7å*}¾}732h��*)��6:7�,F*9=>� 79(/{96¦ô¸J9')7909*GDF*}� ~ 2$=>q�25')�G*9=

ª)ª