28

Ö × & Ø ÙÛÚÜ J &Ý Ø - Nc State University...6 &Ø ~! #"%$'& (")$*" ×/ +.-, /, ý. @ *< , 9. \[9 ])^ _ [_ 9])^ [9])^ . [ 9])^

  • Upload
    others

  • View
    8

  • Download
    0

Embed Size (px)

Citation preview

������������� �������������� �����������������! "��#%$&�'�)(*������ +�����,�*-!.�#/���102#43

5�6�7�6�8:9;9+<=9;>+?A@�B�6DCE6�CF>HGJIDKA@DGJI�LMB�6�CE6D81GJIDNDOQP

7�9;ISR�9;>1TVUA>!W19&OX9&GJ>HY"Z\[=I]5^Y"[_9;I^RQ[a`bYc7�UAdceDfDRHGJRQ[_UAIg 9;e�GJ>"R�dh9;ISRUJTji�GJR�ZD9;d\GJRQ[kY;O

l UA>"R�Z�7mGJ>�Un<o[_I�Gp5ARHGJR�9Eq'IS[=rs9;>HOt[_RQuWGv<=9+[_wAZ�@ l 7�xSyvzA{s|

}�~����&�&���n�A�!� ISfDd��/9;>1UJTjY+UAdheDfDR+GJRQ[_UAI�G�<�dh9;R�ZDUDLDO�Z�G�rA9���9;9;I�eD>"UAe�U^OX9&L�[_I�R�ZD9'<a[=R"9;>HGJR�fD>�9ER"U�LS9&Ot[_wAIGJI�L�OQuSI^R�ZD9&O�[=�;9�T�9;9&LS��GsY�NMY+UAISR�>�Un<�O,�ZD9;I�R�ZD9EeS<kGJISR[kO1dhUDLS9+<_9&L��^u\IDUAIS<a[_ID9&GJ>�LSuSI�GJd�[kY;O;6:��R,[�O'IDUAR:[_dhdh9;�Ls[�GnR�9+<_u�Y"<_9&GJ>&@SZDUJ�19;rA9;>&@s�ZS[kY�Zc[kO�R"ZD9!�/9&OQR1dh9;R�ZDUDL�T�Us>mG�wJ[_rA9;I\eD>�UA�S<_9;dM�SR�ZS[kO:d�G�u�LS9;e/9;I�L\UAI\R�ZD9I�GJR�fD>"9UJT�R"ZD9�IDUAIS<a[=ID9&Gn>Q[_RQ[_9&O;@R�ZD9MO�[=�;9�UnT�R�ZD9MOXu�OQR"9;dM@��ZD9;R�ZD9;>cR�ZD9MGJdhUAfDISR�UJT�Y+UAISR�>�Un<,f�OX9&L�UA>hRQ[_dh9�ID9;9&LS9&LT�UA>�R�ZD9\dh9;R�ZDUDL�[�O�G�Y+UAI�Y+9;>�I�@:GJI�L�UAR�ZD9;>�T�GAY+R"UA>HO;6��tI�R�ZS[kO�e�GJe/9;>�G�Y+UAdceD>�9;ZD9;I�Ot[_rA9MY+UAdhe�Gn>Q[kOQUAI�OQR�f�LSuUJT`�rA9\dh9;R�ZDUDLDO�TVUA>�R�ZD9�OQu^ISR�ZD9&Ot[kO�UJTIDUAIS<a[_ID9&GJ>�Y+UAI^R">�UJ<mOQuDOQR�9;d�O�[kOhY;GJ>�>Q[_9&L]UAfDR&6MC,ZD9�e�9;>QTVUA>�d�GnI�Y+9�UJTR�ZD9Edh9;R�ZDUDLDO:UAI�OX9;rA9;>HG�<�R�9&OQR1eD>�Us�S<=9;d\OGJ>�9EOQR�f�Ls[_9&L�@�GJI�L�OXUAdh9�>�9&Y+UAdhdh9;I�LDGnRQ[_UAI�O1GJ>�9�d�GALS9�GAO:R�U��ZS[kY�ZT�9;9&LS��GAY"NMY+UAISR�>�UJ<�dh9;R"ZDU�Lc[kO'��9&OQRR"Uhf�OQ9EfDI�LS9;>�rvGJ>Q[_UAf�O�Y+UAI�Ls[_RQ[_UAI�O;6

�t�� �¡£¢�¤V¥Q¢V¥�¦�¤V§t �¨�¦"¢�¢V©&ª&ªJ«+¤V¬V¥Q­�¡£®�ªv¦"¤V¬�¯;°�¦±4²�±4³�´�µ^²�¶�·¹¸Eº4·�»�¼4¤�¦"®;¬�´�µS²�¶&·�µS½¿¾+À+ÁHÂXÃ�¾+ÄQÃ�ÅtÃ�Â"½H½;Æ�¦"®&­�¡£®�ªv¦"¤V¬�¯;°´jµS²�¶&·�¼4¤�¦�®;¬�µS½¿¾+À+ÁHÂXÃ�¾+ÀQÃ�ÅtÃ�Â+ÁH¾+Á�Ç_´4´j¶�È�·S��ÉÊ ¥tÃk˦X¡ÍÌ_Îb¢V§Q¯J¥Q¥�Ì£¥Q¤�Ï4¥Q«+¢QÐ ®&§Q¢V©sÐ ¥Q­&©ÑQ¥tÃk˦X¡ÍÌ_Îb¬V¤�¦"®vÏ4§Q«+®;¬V¤V«�Ì_Ð Ë,¦"¬V AÐ ®&§Q¢V©AÐ ¥Q­&©Ò ¥tÃk˦X¡ÍÌ_Îb ;¬V¯J¦�®�Ó;¢�Ï4¥�«+¢QÐ ®�§Q¢V©AÐ ¥Q­�©

Ô

Õ ��Ö�×��&��Ø�ÙÛÚÜ�J�&Ý�Ø�×

C1ZD9EUAeDRQ[_d�G�<�TV9;9&LS��GAY"N�Y+UAISR�>�UJ<�UJTjG�<a[_ID9&GJ>!OQuDOQR�9;dÞ[kOG�OQfD�DßQ9&Y+R1�ZS[kY�Z�Z�GsO1��9;9;I�9+àDR�9;I�Ot[_rA9+<_uMOQR�f�Ls[_9&Lá OQ9;9�9A6âw�6�ã Ô;ä GJI�L�R�ZD9�>�9+TV9;>�9;I�Y+9&O'R�ZD9;>�9+[_I�åH6'�VTmR"ZD9�Y+U^OQR,T�fDI�Y+RQ[_UAI�Gv<�[�O�æsf�GALS>HGJRQ[kY�[=I�R�ZD9�OQRHGJR"9�GJI�L�Y+UAI^R">�UJ<�@GJI�L��19hGAO�OQfDdh9�TVfS<a<,OQRHGnR�9�N^IDUJ�1<_9&LSwA9A@FR�ZD9;IçR�ZD9hUseDRQ[_d�G�<mY+UAISR�>�UJ<4[kO�Gc<a[_ID9&GJ>hOQRHGJR"9�TV9;9&LS��GAY"N�<kG��è�ZD9;>"9R�ZD9�Y+UAISR�>�UJ<�wSG�[_I�O�Gn>�9hUA�DRHGv[=ID9&L]�Su�OXUJ<_rA[_IDwçGMLs[aé�9;>�9;ISRQ[kG�<VêvG�<_wA9;�D>HG�[kY�W:[kY;Y;GJRX[,9&æsf�GJRQ[_UAI�6�C1ZD9�OQf�Y;Y+9&O�O�UJTR�ZS[kOE<a[_ID9&GJ>hæsf�GALS>HGJRQ[kY�>"9;wAfS<kGJR�UA> á�ë4ì W�å�eD>�UA�S<_9;dí[�O�LSfD9�R"U�R�ZD9�OXf�Y;Y+9&O�OtTVfS<,LS9;rA9+<_UAeDdh9;ISR�UJTm>"UA�Df�OQR�GnI�L9+î�Y"[_9;I^REG�<_wAUA>Q[_R�ZDd\O:T�Us>!OQUJ<_rs[=IDw\R�ZD9�W:[kY;Y;GJRX[j9&æsf�GJRQ[_UAI�6�B'UJ�19;rA9;>&@s[aT�R�ZD9EeS<kGJI^R'[kOLS9&O�Y+>Q[_�/9&L��^u\IDUAIS<a[_ID9&GJ>LSu^I�GJd�[�Y;O�@�R�ZD9;I�R�ZD9�UseDRQ[_d�G�<,OXRHGJR�9�TV9;9&LS��GAY"Nç<kG��ï[kO�wn[=rs9;Iç[_I�R�9;>�d�O�UJTR�ZD9�OQUJ<_fDRQ[_UAI�R�U�R�ZD9�B�GJd�[a<_R�UAID�ð GAY+UA�S[_��8:9+<a<=d\GJI á B ð 8'å�9&æsf�GJRQ[_UAI¹ãñx ä 6�C1ZD9�B ð 8ò9&æsf�GJRQ[_UAIMeD>"Uvrs[kLS9&O1R�ZD9�OQUJ<_fDRQ[_UAIMR"U�R"ZD9�UAeDRQ[_d�Gv<FY+UsI^R�>"UJ<eD>�UA�S<_9;dóT�Us>wA9;ID9;>HG�<�IDUAIS<a[_ID9&GJ>�OQuDOQR�9;d�O���ZDUJ�19;rA9;>&@S[_R'[kO'[=I�dhU^OQREY;GAOQ9&O,[_dhe�USO�Ot[_�S<_9hR�U�OQUn<=rs9�GnI�G�<_u^RQ[kY;G�<a<_uA6C1ZS[kO�Z�GsO�<_9&LcR�U�d\GJI^u�dh9;R"ZDU�LDO:��9+[_IDwheD>"UAe�U^OX9&L�[_I�R�ZD91<a[_R�9;>HGJR�fD>"9TVUA>��G�uDO�R�U�GJeDeD>�U�à^[_d�GnR�9+<_u�Us�DRHG�[_I�R"ZD9OQUJ<_fDRQ[_UAI�R�U\R�ZD9�B ð 8ô9&æAf�GJRX[=UsIõGAO'�19+<o<�GAO'UA�DRHG�[_IçG\OQfD��UAeDRX[=d\G�<�TV9;9&LS��GAY"NõY+UAISR�>�Un<bTVUA>�wA9;ID9;>HG�<�IDUAIS<a[_ID9&GJ>LSu^I�GJd�[�Y;Gv<jdhUDLS9+<kO;6

öID9he�U^O"Ot[_�S[o<a[_RQu�[kO�R�U�Y+UAI�OQR�>�f�Y+R�R�ZD9hY+UAISR�>�UJ<�GAO�Ghe/UJ�m9;>�OX9;>Q[_9&O;@�9+[_R�ZD9;>E�^u�OQ9;e�GJ>HGnRQ[_IDw�UAfDR!R"ZD9�IDUsID�<o[_ID9&GJ>X[=RX[=9&O�[_IõR"ZD9�OQuDOQR�9;d÷[_ISR�U�G�e�UJ�19;>�OX9;>Q[_9&O;@�Us>�^u\[_ISR�>�UDLSf�Y"[_IDwMGhR�9;dce�UA>HGn>�u�rJGJ>Q[kGJ�S<_9hGJI�L�9+àDe�GJI�Ls[_IDwGJ>�UAfDI�L�[_R&6õC,ZD9;I¹R�ZD9c`�>HOQR�T�9;�÷R�9;>"d�O�[_I�R�ZD9�OX9;>Q[_9&O�T�Us>�R�ZD9�Y+UsI^R�>"UJ<,GJ>"9�T�UsfDI�Lç�SuçrvGn>Q[_UAf�O�R�9&Y�ZDIS[kæsfD9&O;6C1ZS[kO'[�LS9&Gc[kO���GAOX9&L�UAIçY+UAI�Ot[kLS9;>Q[_IDw�R�ZD9�OQuDOQR�9;døGAO�Ghe/9;>�R�fD>���GnRQ[_UAIMUJTmG�<a[_ID9&GJ>�OQuDOQR�9;d�@D�1[_R�Z�R�ZD9�Y+UsI^R�>"UJ<��9+[_IDw�GnI�9+à�R�9;I�O�[=UsI�UJT�R�ZD9�<a[_ID9&GJ>EY+UAI^R">�UJ< á R�ZD9`�>+OQR1R�9;>�d*UJT4R�ZD9!e/UJ�m9;>OQ9;>X[=9&O,[kO1UA�DRHGv[=ID9&L\�Su�OQUJ<_rA[_IDwhR"ZD9W:[kY;Y;GJRQ[�9&æAf�GJRX[=UsI\T�UA>1R�ZD9�OQUJ<_fDRQ[_UAI�UJT�R�ZD9�<a[_ID9&GJ>Q[_�;9&L�OQuDOQR�9;d�åH6:C1ZD9&OQ9ERQu^e/9&O1UJT�dc9;R�ZDU�LDO�GJ>�9ELS9&O�Y+>Q[_�/9&L�[_Iã£ùD@Sú�@�|D@Dz ä 6

� IDUAR"ZD9;>�GneDeD>�U^GAY"Zç[kO�R"ZD>�UAfDwAZ�OQf�Y;Y+9&O�Ot[_rA9MGneDeD>�U�à^[_d�GJRX[=UsI�@��ZD9;>�9MGJI][_R�9;>HGJRX[=rs9�eD>�U�Y+9&O"OE[kO�f�OX9&L�R�U`�I�LçGMOQ9&æsfD9;I�Y+9hUJTGJeDeD>�U�àS[=d\GJRQ[_UAI�O�GneDeD>�U^GAY"ZS[_IDw�R�ZD9�OQUJ<_fDRQ[_UAI]UJTmR�ZD9\B ð 8%9&æsf�GJRQ[_UAI�6hC,ZS[�O�[kO�LSUAID9h�SuOQUJ<_rA[_IDwçGMOX9&æAfD9;I�Y+9\UJTmws9;ID9;>HG�<a[_�;9&L�B!GJd�[o<_R�UsID� ð GAY+UA�S[_��8:9+<a<=d\GJI á�û B ð 8å�9&æAf�GnRQ[_UAI�O;@�GnI�L�[kO�Ls[kO�Y+f�O"OQ9&L�[_Iãay^@^ü ä [_IMG�wA9;ID9;>HG�<�Y+UAISR�9+àDR&6 � dhUA>�9EY+UAI�Y+>�9;R"9!R�9&Y"ZDIS[kæAfD9�TVUA>:`�I�Ls[_IDwhR�ZD9ELS9&Ot[_>�9&LMOXUJ<_fDRQ[_UAI\[kOmLS9&O"Y+>Q[_��9&L\[_Iã£{D@ Ô&ýJä @S�ZD9;>"9�G û G�<_9;>�Ns[_I�eD>�U�Y+9&LSfD>"9E[kO1f�OQ9&LpR�U�`�I�LMG�ISfDdh9;>Q[kY;G�<�OQUJ<_fDRQ[_UAI�R�U�R�ZD9 û B ð 8þ9&æsf�GJRQ[_UAI�6

öR�ZD9;>!dc9;R�ZDU�LDO,[_I�Y"<_f�LS9hR�ZD9�OQRHGnR�9;��LS9;e�9;I�LS9;ISR�W:[kY;Y;GJRQ[�9&æAf�GnRQ[_UAI á 5 g W'ÿ1åH@D�'ZS[�Y"Z�[kOEGJI�9+àDR�9;I�Ot[_UAI�UJTR�ZD9�Wm[�Y;Y;GnRQ[�9&æsf�GJRQ[_UAI�R�U�IDUAIS<a[=ID9&Gn>�OQuDOQR�9;d\O!ã ÔAÔ @ Ô x^@ Ô ù ä 6�C1ZD9�Y+US9+î�Y"[_9;ISRHO:[_I�R�ZD9�5 g Wÿ GJ>"9TVfDI�Y+RQ[_UAI�O1UJTR�ZD9�OXRHGJR�91[_I�OQR"9&GAL\UJT��/9+[=IDw\Y+UAI�OQRHGJISR��VrJG�<_fD9&L�GAO4[_I�R�ZD9'<a[=ID9&Gn>!Y;GAOQ9A6�C,ZS[�O,d�GJNA9&OÛR�ZD9!9&æsf�GJRQ[_UAI�d�f�Y"Z�dcUA>�9Ls[oî�Y+fS<=R�R�U�OQUn<=rs9A6 � <kOQU�@ [_I�R�ZD9�IDUAIS<a[_ID9&GJ>�Y;GAOQ9ER�ZD9�>�9&OQfS<_RQ[_IDwMY+UAISR�>�Un<b[kO�UAIS<_uMOQfD�/UAeDRQ[_d�G�<�6�C1ZD9;>�9�[kO!G�<kOQUG�Y+UAISR�>�Un<�dh9;R�ZDUDL���GAOQ9&L�UsIõ>"9;eD>�9&OQ9;ISRQ[_IDw�R�ZD9hY+fD>�rs9�UJT�R�ZD9hOQuDOQR�9;d��£OOQUJ<_fDRQ[_UAIçGAO�G�<o[_ID9&GJ>EUse�9;>HGJR"UA>�GnI�LR�ZD9;I�[_ISrA9;>�RQ[_IDw�[_R�ã Ô ú ä @DGJI�LMGnI�9+à�eS<_UA>HGnRQ[_UAIMUJT4R�ZD9�f�OQ9EUnTjID9;fD>HGv<�ID9;RHO1R�U\OQUJ<_rA9ER�ZD9�B ð 8ò9&æsf�GJRQ[_UAI�ã Ô | ä 6

öe�9;ID� <_U^Use�Y+UAISR�>�Un<�O4Y;GJIhG�<kOQU���9:TVUAfDI�L��^u�GrJGJ>Q[_9;RQu�UJTbLs[aé�9;>�9;ISR�dh9;R�ZDUDLDO;6���ZS[a<_9UAe/9;ID� <_U^UAehY+UAISR�>�Un<�OGJ>�9Mws9;ID9;>HG�<a<_u IDUAR\f�OQ9+TVfS<!TVUA>\eD>HGAY+RQ[kY;G�<�GJeDeS<a[kY;GJRQ[_UAI�O;@'[_Rh[kO\e/U^O�Ot[_�S<_9çR�Uç9+àDR�9;I�LþR�ZD9;d [_I^R�U�Y"<_U^OQ9&LS� <_USUAeY+UAI^R">�UJ<kO;6�C,ZS[�O�Y;GnI���9LSUAID91�1[_R�Z�GJIE[_ISR�9;>�e/UJ<kGJRQ[_UAIhUJrA9;>�R"ZD9mOQRHGnR�9mOQe�GsY+9mGAO4LS9&O�Y+>Q[_��9&L�[=I�ã Ô z ä @;TVUA>49+à GJdceS<=9A6C1ZD91UAe�9;ID� <_USUAehY+UAI^R">�UJ<�Y;GJI���9:TVUAfDI�LE�Su�OQUn<=rs[_IDw�G1RQ�1UA�Ve�UJ[_ISR��/UAfDI�LDGJ>�uErJG�<_fD9 á C��:8���å�eD>"UA�S<_9;dM@A�ZS[kY"Z�[�OUA�DRHG�[_ID9&LcTV>�UAd÷R�ZD9�ID9&Y+9&O�O�GJ>�ucUAeDRQ[_d�G�<a[_RQu�Y+UAI�Ls[_RQ[_UAI�O�6��tR,Y;GnI��/9�OQUJ<_rA9&L\�Su�Ls[kO�Y+>�9;RQ[_�+[_IDw�GnI�L\R�ZD9;I�OXUJ<_rA[_IDw9+à GAY+RX<=u�ã Ô z ä @/UA>�9+<�OX9��SuMUsID9�UJTmOQ9;rs9;>HG�<4[=R"9;>HGJRQ[_rA9�dh9;R�ZDUDLDO á æAf�GsOt[a<o[_ID9&GJ>X[=�&GnRQ[_UAI�@4wA>HGALs[_9;ISR!dh9;R"ZDU�LDO;@�9;R+YJ6aåGAO:[_I¹ã Ô yn@ Ô üS@ Ô {D@Dx ý @/x Ô+ä 6

��R:[kOmGv<�OXUE[_dhe�Us>�RHGJISR�R�U�IDUAR�9R"Z�GJRmLs[aé�9;>�9;ISRmdc9;R�ZDU�LDO:GJ>�9EGJeDeS<a[kY;GJ�S<_9�R�U�Ls[aé�9;>�9;ISRmeD>"UA�S<_9;d�O;615AUAdc9!UJTR�ZD9�dh9;R"ZDU�LDO'R�Z�GJR�19��1[a<o<4[_I^rs9&OQRQ[_w^GJR�9�[_I�LS9;R+G�[a<ÛY;GJI���9�f�OQ9&L�UAIõG�dcUA>�9EwA9;ID9;>HGv<jeD>�Us�S<=9;dóR�Z�GJI�R�ZD9�UsID9�m9'�1[a<o<�Y+UAI�Ot[kLS9;>&@sT�Us>�9+à�GJdheS<_9A@S�1[_R�Z�G�IDUAIS<a[_ID9&GJ>1TVfDI�Y+RQ[_UAI�UJT�R�ZD9!Y+UAISR�>�Un<ÜGAOÛ�m9+<a<�GAO:R�ZD9!OQRHGnR�9A6�C1ZD9;>�9!GJ>"9G�<kOQU�dc9;R�ZDU�LDO��'ZS[�Y"ZçGJ>�9�LS9&Ot[_wAID9&LõT�UA>'UAR�ZD9;>EOQe�9&Y"[a`bY�eD>�Us�S<=9;d\O;@�OQf�Y"ZõGAO'R�ZD9��S[a<a[_ID9&GJ>hOQuDOQR�9;d �� ������� � á�� ������ å � 6�i�9;R�ZDU�LDOÛR�U�OQUJ<_rA9'R�ZS[kO�RQuSe�9UnTbeD>�UA�S<_9;d*GJ>�9Ls[kO�Y+f�O�OX9&Lc[=I�ã£xAxS@AxAù @AxJú�@AxA|D@Axsz ä 6 � IDUAR�ZD9;>

x

rvGJ>Q[kGJRX[=UsIçUAIMR"ZD9�IDUsIS<o[_ID9&GJ>hY+UAISR�>�Un<�eD>�UA�S<_9;dø[kOEGJI�fDI�Y+9;>�R+G�[_I¹OQuDOQR�9;dM@/�ZD9;>�9�fDIDNSIDUv�'Iõe�Gn>HGJdh9;R�9;>+O!GJ>"9[=ISrAUJ<_rA9&L�[_I¹R"ZD9h9&æAf�GnRQ[_UAI�@�GAOELs[kO�Y+f�O�OQ9&L][_Iòã£xSyA@�xAü ä 6 � dh9;R�ZDUDLçLS9&G�<a[_IDwõUsIS<=u]�1[_R�Z¹OQuDOQR�9;d�O��ZD9;>�9hR"ZD9I^fDd���9;>�UJTjOXRHGJR�9�GJI�L�Y+UsI^R�>"UJ<�rvGJ>Q[kGJ�S<_9&OEGJ>"9ER�ZD9�O�GJdh9�[kO1eD>"9&OQ9;I^R"9&L\[_I¹ã£xs{ ä 6

��I�R�ZS[kO�e�GJe/9;>�GçY+UAdceD>�9;ZD9;I�Ot[_rA9MY+UAdhe�Gn>Q[kOQUAI OQR�f�LSu�UJT`�rs9�UJT�R�ZD9�dh9;R�ZDUDLDOhLS9&O�Y+>Q[_�/9&L GJ�/Uvrs9��1[a<a<��9\e�9;>QTVUA>�dh9&L]UAI¹OX9;rA9;>HG�<1R�9&OQR�eD>"UA�S<_9;d�O;6��ç9\�1[a<a<!LS>HG�� OQUAdc9�Y+UAI�Y"<_f�Ot[_UAI�OhGAO�R�UM�'ZS[�Y"Z�dh9;R�ZDUDLDO�wn[=rs9R�ZD9��/9&OQRE>�9&OQfS<_RHO,T�Us>!Y+9;>�RHG�[_I�RQu^e/9&OUnTjeD>�Us�S<=9;d\O;@�GJI�LMGv<�OXU�Y+UAI�O�[�LS9;>EUsR�ZD9;>T�GAY+R�Us>HO1OQf�Y�ZçGAO,R�ZD9���9+à^[_�S[a<a[=RQuUJT�R�ZD9�dc9;R�ZDU�LDOEGnI�L�R�ZD9�Ls[oî�Y+fS<=RQuçGJI�LpRQ[_dh9�[=ISrAUJ<_rA9&Lp[_I�R�ZD9+[_>[_dheS<_9;dh9;ISRHGJRX[=UsI¹GJI�L�f�OX9A6�C,ZD9�e�GJe/9;>�[�OUA>�w^GJIS[_�;9&LhGsO�TVUJ<a<_Uv��O;6�C1ZD91eD>�UA�S<_9;d OQR+GJR�9;dh9;ISR�[kO�wJ[_rA9;I�[_I�5A9&Y+RQ[_UAI\xD6�C1ZD91dh9;R"ZDU�LDO4R�UE�/9Y+UAI�Ot[kLS9;>�9&L��1[a<a<��9�LS9&O�Y+>Q[_�/9&L\[_Iç5A9&Y+RQ[_UAIMù 6��tI�e�GJ>�RQ[kY+fS<kGJ>&@Ü5A9&Y+RQ[_UAIMùD6£ù�LS9&O�Y+>Q[_��9&O'R�ZD9�OQf�Y;Y+9&O�O�[=rs9�GJeDeD>�U�à^[_d�GnRQ[_UAI�dc9;R�ZDU�L�68�9&Y;Gnf�OQ9�R�ZD9;>�9M�GAOcGJI 9;>�>"UA>�[_IòUAID9MUJT�R"ZD9�TVUA>�d�fS<kGAO�[_IòR�ZD9MUA>X[=wn[=I�Gv<�e�GJe/9;>&@1R�ZS[kO�OQ9&Y+RQ[_UAIòY+UAISRHG�[_I�O�GLS9;RHG�[a<_9&LõLS9;>X[=rJGJRQ[_UAI�UJT�R�ZD9Edh9;R�ZDUDL�6�C1ZD9�e�9;>QTVUA>�d\GJI�Y+9EUJT�R�ZD9�dh9;R"ZDU�LDO1UsI�TVUAfD>19+à GJdceS<=9&OEGn>�9�Ls[kO�Y+f�O�OQ9&L[=I]5A9&Y+RQ[_UAIMú/@�GJI�L\UJrA9;>HG�<a<�Y+UAI�Y"<_f�Ot[_UAI�OEGJ>"9EwJ[_rA9;I�[_Iç5A9&Y+RX[=UsIõ|D6� �����&Ø�~! #"%$'&��;�D�(")$*"�×/�

7�UAI�Ot[kLS9;>EG�IDUAIS<a[_ID9&GJ>�OXu�OQR"9;d*UJT�R�ZD9ERQu^e/9+ á-, å � . á á-, å�å � ��� á á/, å�å á ý å � 1032 á Ô å

�ZD9;>�9 . á å�[kOEGcIDUAIS<a[_ID9&GJ>ETVfDI�Y+RQ[_UAI�UJT�R�ZD9�OQRHGJR�9 *46587:9�; @ �*< 58=>9@? [�O�R"ZD9�Y+UAISR�>�UJ<�@�GJI�L � [kO!GY+UAI�OQRHGJISR��VrJG�<_fD9&LBADCFE\d\GJR�>Q[aà�6 � <kOQU�Y+UAI�Ot[kLS9;>�GcY+U^OQR1TVfDI�Y+RQ[_UAI�G�<G á H0I2 � å �KJ*L0 M 1NPO�Q� � NP9 �1R�S ,�1[_R�Z�G'wJ[_rA9;I�Y+UAI�OQR+GJI^R"�VrvG�<_fD9&LTAUCVA÷OQuSdhdh9;R">Q[kY1e�U^O�[=RX[=rs9!OQ9;d�[_��LS9+`�IS[_R�9�d�GJR�>Q[aà O GJI�L�G@E�C@EhOQuSdhdh9;R">Q[kYe�U^Ot[_RQ[_rA9MLS9+`�IS[_R�9�d\GJR�>Q[aà 9 6MC1ZD9\UAeDRQ[_d�G�<Y+UAISR�>�UJ<�eD>�Us�S<=9;dí[kO�R�U�`�I�L�G�OQRHGJR"9�T�9;9&LS��GsY�N¹Y+UsI^R�>"UJ< �)W á å�ZS[kY�Z�d�[_IS[=d�[=�;9&O�R�ZD9�Y+U^OQR,T�UA>G�<a<�e/U^O�Ot[_�S<_9�[_IS[=RX[�Gv<mY+UAI�Ls[_RQ[_UAI�O H0 6X UA>�R�ZD9�Ot[_dheS<_9;>h<a[_ID9&GJ>\eD>�UA�S<_9;dM@��'ZD9;>�9 . á å �Y�Z0� @�R�ZD9�UseDRQ[_d�G�<�TV9;9&LS��GAY"N Y+UsI^R�>"UJ<�[kO�wJ[_rA9;I��Su� W á å �\[�9�])^ � N`_ @'�1[_R�Z _ ��9+[_IDw�R�ZD9çOQUJ<_fDRQ[_UAIòR�U�R�ZD9�d�GJR�>X[oà�Wm[�Y;Y;GnRQ[�9&æAf�GnRQ[_UAI _ ��0Q�:� N0 _ [_ � 9 ])^ � N _ �KOD� ý 6�C1ZD9cR�ZD9;UA>Q[_9&O�T�Us>ER�ZS[kOE<a[_ID9&GJ>hæsf�GALS>HGJRQ[kY�>"9;wAfS<kGJR�UA> á�ë4ì W�åEeD>�UA�S<_9;díZ�G&rs9h��9;9;I9&OQRHGJ�S<a[kOQZD9&L T�Us>h��UAR"Z R�ZD9p`�IS[=R"9õGJI�L [=IS`�IS[_R�9çLs[_dh9;I�Ot[_UAI�Gv<�eD>�UA�S<_9;d�O á OQ9;9M9A6âw�61ã£ù ý @mù ÔHä åH6���IòGALDLs[_RQ[_UAI�@OQRHGJ�S<_9hGJI�L�>�UA�Df�OQREG�<_wAUA>X[=R"ZDd�O'T�Us>�OQUn<=rs[_IDw�R�ZD9hW:[kY;Y;GJRQ[�9&æsf�GJRQ[_UAI�Z�G�rA9�Gv<=>"9&GALSuM�/9;9;I�LS9;rs9+<=Use�9&L�GJI�LMGJ>"9�m9+<a<jLSUDY+fDdh9;ISR�9&L\[_I�d�GJISu�eS<kGAY+9&O,[_IMR�ZD9�<o[_R�9;>+GJR�fD>�9�GJI�L�[_IMR�9+àDR���USUANDO;6X UA>R"ZD9EIDUAIS<a[=ID9&Gn>�Y;GAOQ9A@SR�ZD9�UseDRQ[_d�G�<�T�9;9&LS��GsY�NMY+UAISR�>�Un<b[kO'N^IDUJ�I�R"U��/9�UJT�R�ZD9�TVUA>�d� W á å � [ Ôx 9 ])^ � N�a)b á å 2�ZD9;>�9�R"ZD9�T�fDI�Y+RQ[_UAI a [�O,R�ZD9�OQUn<=fDRX[=UsIMR�U�R�ZD9�B�GJd�[a<_R�UAID� ð GsY+UA�S[_��8�9+<a<kd\GJIç9&æsf�GJRQ[_UAIa Nb á å . á å [ Ô

ú a Nb á å � 9 ])^ � N a b á å �c N O�d� ý1e á xSåC1ZD9õB ð 8Þ9&æAf�GnRQ[_UAI�[_RHOQ9+<aTE[kOcrA9;>�u�Ls[oî�Y+fS<=R\R�U¹OXUJ<_rA9MGJI�G�<_uSRQ[kY;G�<a<=u T�Us>�GJISu¹�DfDRhR"ZD9õOt[_dheS<_9&OQR\eD>�UA�S<_9;d�O;@ZDUv�19;rA9;>�6�C1ZSf�O�9+é�UA>�R+O4Z�G&rs9��9;9;I\d�GALS9R"UEI^fDdh9;>X[�Y;Gv<o<_u�GJeDeD>�U�àS[=d\GJR�91R�ZD9!OQUn<=fDRX[=UsI�UJT�R�ZD9�B ð 8�9&æsf�GJRQ[_UAI�@UA>R�UhOQUJ<_rA9�G�>�9+<kGJR�9&L\eD>"UA�S<_9;d eD>�UDLSf�Y"[_IDwMGhOQfD�/UAeDRQ[_d�G�<jY+UsI^R�>"UJ<�@^Us>R�Uhf�OQ9�OXUAdh9EUAR�ZD9;>'eD>�U�Y+9&O"O:[_IMUA>HLS9;>

ù

R�U�UA�DRHG�[_I�G�f�O"GJ�S<_9ETV9;9&LS��GAY�N\Y+UAI^R">�UJ<�6�C1ZD9'T�Un<o<_UJ�1[_IDw�OQ9&Y+RX[=UsI��1[a<o<4UAfDRQ<a[_ID9�OQUAdc9�OQf�Y"Z\dh9;R�ZDUDLDO1R�Z�GJR1Z�G�rA9��9;9;IMeD>"UAe�U^OX9&L\[_IMR�ZD9�<a[_R�9;>HGnR�fD>�9A6f ��gh"i"DÙ4~����3jlk�ØF×��&��Øm on8"S�3p�ØÜÙFØm �Ø)q�Ýr"D�ts�Ø��vupØ�×P kÝ�×w"^���x&my����(")$ç�f � Õ ����Ø1z{"D��&m"D�JÝr"D�h}�|�|���Ø1}�Ý~$��D�&Ý_ØF×

öID9�RQuSe�9�UJT�dh9;R�ZDUDL�UJT�UA�DRHGv[=IS[_IDwMGJI�GJeDeD>�U�àS[=d\GJR�9�OXUJ<_fDRQ[_UAIMR�U\R�ZD9�B ð 8 9&æAf�GJRX[=UsI á xSå�[kO�Su�f�Ot[_IDwG�e�UJ�19;>�OQ9;>Q[_9&OcR�U¹GJeDeD>"U&àS[_d�GJR�9 a á å+6 C1ZS[kO�[kOhLSUsID9M�Su û GJ>�>HGJ>+L�GJI�L�UAR�ZD9;>HO�[=I%ã£ùS@�ú�@�| ä 6ò7�UAI�O�[�LS9;>R�ZD9h>�9;eD>�9&OX9;I^RHGnRQ[_UAI a á å � � L�3� 0 a � á åH@��'ZD9;>�9h9&GAY"Z a � á å ��� á �3� ?�å+6 � <kOQUõOQ9;e�Gn>HGJR�9�R�ZD9hIDUAIS<a[_ID9&GJ>T�fDI�Y+RQ[_UAI . á å4[_I^R"Uhe�UJ�19;>HO:UJT GAO . á å �K�Z0��� � L�3� ? . � á å��1[_R�Z . � á å �K� á � åH6:5AfD��OQRX[=R"fDRQ[_IDw�R�ZD9&OX99+à�e�GJI�O�[=UsI�O1[_ISR�UhR�ZD9�B ð 8þ9&æsf�GJRQ[_UAI�>�9&OQfS<_RHO,[=I� L���� 0 á a � å Nbm� � ��0��� L���� ? . � á å � [ Ô

ú� L��3� 0 á a � å Nbw� � 9 ])^ � N � L��3� 0 á a � å b � ��HN!O�t� ý1e

8�u�OQ9;e�GJ>+GJRQ[_IDw�UsfDRm�Su�e�UJ�19;>HO:UJT �19EUA�DRHGv[=IMGcOQ9;>Q[_9&OUnTj9&æsf�GJRQ[_UAI�O <á a)0 å Nb �Z0�T[ Ô

ú á a%0 å Nb � 9 ])^ � N á a%0 å b���1N!O� � ý á ùSå

á a ^ å Nb ��0��[ Ôú á a ^ å Nb � 9 ])^ � N á a%0 å b@[ Ô

ú á a)0 å Nb � 9 ])^ � N á a ^ å b�� á a%0 å Nb . ? á å � ý á úDå

á a � å Nb ��0��[ Ôú��? � 0@� á a ? å Nb � 9 ])^ � N á a � ]H? å b3�o� � ])^�? � 0�� á a ? å Nb . �3� ^�]H? á å ��� ý 2 á |Så

�ZD9;>�9{� � x 2 ù 2 ú 2 erere�eÿ�æsf�GJRQ[_UAI á ùSå!Y;GJI��/9�OQUJ<_rA9&L��1[_R�Z a 0 á å �� N _ @��'ZD9;>�9�R�ZD9hOQu^dcdh9;R�>Q[kY�e/U^Ot[_RQ[_rA9�LS9+`�IS[_R�9hd\GJR�>Q[aà_ OXUJ<_rA9&O�R�ZD9hW:[kY;Y;GJRQ[�9&æsf�GJRQ[_UAI _ �Z0���� N0 _ [ _ � 9 ])^ � N _ ��O�� ý 6EC1ZS[kO�wJ[_rA9&O�R�ZD9hOQRHGJI�LDGn>HL\<a[_ID9&GJ>

Y+UAI^R">�UJ<�6�ÿ�æsf�GJRQ[_UAI�O á ú åÛGnI�L á |Så�Y;GJI���9�OXUJ<_rA9&L\TVUA> a � @1� � Ô 2 x 2 ù ere#e @J�Su\d�GJNs[=IDw a � GhO"Y;G�<kGJ>1e�UJ<_uSIDUAd�[kG�<Y+UAI^R+G�[_IS[=IDwhG�<a<�e�U^O�O�[=�S<_9EY+UAd��S[_I�GJRQ[_UAI�O:UJTbeD>"U�LSf�Y+RHOÛUJT�R�ZD9OQRHGJR"9m9+<_9;dh9;ISRHO:�1[_R�Z�G�R�UARHGv<�UA>+LS9;>�UJT!� � x @�GnI�LR�ZD9;IMOQfD��OQRQ[_R�fDRX[=IDwc[_R1[_I^R"UhR�ZD9E9&æsf�GJRQ[_UAIMGJI�L�OQUn<=rs[_IDw�TVUA>R�ZD9EY+U^9+î�Y"[=9;ISRHO;61C1ZS[kOY;GJI��/9�LSUAID9�TVUA>GAO1d\GJI^uR�9;>�d�OEGAO�LS9&Ot[_>�9&L�@4�DfDR�[_I¹wA9;ID9;>+G�<�R�ZS[kO�æsfS[kY�Ns<_uçwA9;RHO�rA9;>"u�Y+UsdheS<a[�Y;GnR�9&L�@49&OQe�9&Y"[kG�<a<_uçTVUA>EeD>�Us�S<=9;d\OE�1[_R�Z¹G<�Gn>�wA9hISfDd���9;>�UnT'OXRHGJR�9�rvGn>Q[kGJ�S<_9&O;6 � O�G\�G�uMUJT!G�rAUJ[kLs[_IDwMR�ZS[kO;@ û GJ>�>HGJ>+L�eD>�UAe/U^OQ9&O�G�dh9;R�ZDUDL�UJT1`�I�Ls[_IDwá a ^ å b dhUs>�9�Ot[_dheS<_uA@��'ZS[�Y"ZM>"9&OQfS<_RHO1[_I�G�rs9;>�u�9&GsOQu�dc9;R�ZDU�LpUJT�`�I�Ls[_IDwMGhæsf�GALS>HGJRX[�Y�RQuSe�9�Y+UAI^R">�UJ<jãñù ä 6��I�OQR�9&GsLEUJT�f�Ot[_IDw�R�ZD9�e/UJ<_u^IDUsd�[kG�<�>�9;eD>�9&OQ9;ISRHGJRX[=UsI�@&�19�d\G&uEY+UAI�Ot[kLS9;> á ú å GsO�[kO4GJI�LEf�OQ9:R�ZD9mOXfD��OQRQ[_R�fDRQ[_UAIá a%0 å b�� x _ á �'ZD9;>�9 _ [kOR�ZD9�OXUJ<_fDRQ[_UAIMR�UcR�ZD9�W:[kY;Y;GJRQ[�9&æAf�GnRQ[_UAI�å�R�UhUs�DRHG�[_I

á a ^ å Nb ��0��[ Ôú á a ^ å Nb � 9 ])^ � N á x _ å [ Ô

ú á x N _ å � 9 ])^ � N á a ^ å b�� á x N _ å . ? á å � ý1eW19&GJ>�>HGnIDwJ[_IDw�OQUsdh9ER�9;>�d�O�@^�19�`�I�L N � � N0 á a ^ å b@[ _ � 9 ])^ � N á a ^ å b�� x _ . ? á å ��� ý1eC1ZD9�æsf�GJI^RX[=RQup[=I�O�[�LS9\R�ZD9h�D>+GAY�Ns9;RHO1[kO��;9;>�U��ZD9;I á a ^ å b���[ x á � N0 [ _ � 9 ])^ � N å ])^ _ . ? á åH6�C1ZS[kO�G�<_UAIDw�1[_R�ZMR�ZD9 á a 0 å b R�9;>�d÷wJ[_rA9&O�Ghæsf�GALS>HGJRX[�Y'TV9;9&LS��GAY"NMY+UAISR�>�UJ<�<kG�� UJT�R�ZD9�T�Us>�d

ú

� á å � [�9 ])^ � N ã _ �[ á �ZN0 [ _ � 9 ])^ � N å ]H^ _ . ? á å ä-e á zSå�VT . ? á å � ý á R�Z�GJR�[kO;@F[aT!R�ZD9;>�9�GJ>�9cIDUõæsf�GALS>HGJRQ[kYcR�9;>�d�O¿åH@�R�ZD9;I á úDå1[kO�OQUJ<_rA9&L]R�>Q[_rs[kG�<a<=u��Su a ^ � ý 6

ÿ�æsf�GJRQ[_UAI á |SåÛT�UA>�� � x��1[a<o<�R�ZD9;I��/9�UJT�R�ZD9�TVUA>�dá a ? å Nb �Z0�T[ Ô

ú á a ? å Nb � 9 ])^ � N á a%0 å b@[ Ôú á a%0 å Nb � 9 ])^ � N á a ? å b�� á a)0 å Nb . K á å � ý1e

C1ZS[kO'[�O'9+à�GAY+RQ<_uMR�ZD9�O�GJdh9�TVUA>�døGAO á úDå�9+à�Y+9;eDRER�Z�GJRIDUJ� a ? [kO,[_IõR"ZD9�eS<kGAY+9�UJT a ^ GJI�L . K [�O,[_I�R�ZD9�eS<kGAY+9UJT . ? 6hC1ZSf�OER�ZD9\OQUJ<_fDRQ[_UAI�[kO�GnI�G�<_UAwAUAf�O�R�U�R"Z�GJREUJT á úDåH@��1[_R�Z á a ? å b���[ x á � N0 [ _ � 9 ])^ � N å ])^ _ . K á åH@>�9&OQfS<_RQ[_IDwh[_I�G�T�9;9&LS��GsY�NMY+UAISR�>�Un<ÜUnTjR�ZD9�TVUA>�d� á å � [�9 ])^ � N ã _ �[ á � N0 [ _ � 9 ])^ � N å ]H^ _ . K á å ä-e�VT . K � ý GAO��19+<a<�@DR�ZD9;I\R�ZD9>�9&OXfS<=RX[=IDw\Y+UAI^R">�UJ<��1[a<a<���9ER�ZD9!O"GJdh9�9+à Y+9;eDR:TVUA> . P [_I�R�ZD9eS<kGAY+9EUnT . K 64��I\UAR�ZD9;>�mUs>HLDO;@DR�ZD9�RQ�mUs�VR�9;>�d*Y+UAISR�>�UJ<jLS9&O"Y+>Q[_��9&L��Su û GJ>�>HGn>HLc[kO1TVUAfDI�L�f�Ot[_IDw�R"ZD9E<_UJ�m9&OXR��VUA>HLS9;>IDUsID�;9;>�U . � R�9;>"dM@�Z�GJR�9;rA9;>'R�Z�GJR1d�G�u��/9A6

C1ZS[kO�dc9;R�ZDU�L]Z�GAO�OQUAdc9�<a[=d�[=R+GJRQ[_UAI�O;6���R�[kO�IDUAR�e/U^O�Ot[_�S<_9MR�Up[_I�Y+>�9&GAOQ9\R�ZD9�GAY;Y+fD>HGAY+uçUnT,R"ZD9�GJeDeD>"U&àD�[=d\GJRQ[_UAI��Su GALDLs[_IDwçdcUA>�9�R�9;>�d\O�R"UõR"ZD9�e�UJ�19;>�OX9;>Q[_9&O��1[_R�ZDUAfDRhR"ZD9�R�9&Ls[_UAf�O�eD>�UDY+9&O�O�UJTEOQUJ<_rA[_IDw]T�Us>�R"ZD9e�UJ<_uSIDUAd�[kG�<�UJT�R�ZD9hGJeDeD>�UAeD>X[�GnR�9�UA>+LS9;>&6�öIS<_uMR�ZD9�`�>HOQR�R��1U�R�9;>�d\OUJT�R�ZD9hOQ9;>Q[_9&O�Y;GJIM�/9�T�UAfDI�Lp�^u�d\GJR�>Q[aàY;G�<kY+fS<�GnRQ[_UAI�O!GsOmLS9&O"Y+>Q[_��9&L�GJ��UJrA9A6 � <kOQU�@DR�ZD9ERQ�1UA�VR�9;>"d Y+UAISR�>�UJ<�UAIS<_u�Y+UsI�Ot[kLS9;>HOUsID9!UA>+LS9;>UJT�IDUAIS<a[_ID9&GJ>Q[_RQuA@GAO!OXZDUv�'I�[_I á zSå:�ZD9;>�9�UAIS<_u . ? [kO�f�OQ9&L�@/[_wAIDUs>Q[_IDwMGJI^u�ZS[_wAZD9;>EUs>HLS9;>!e�Gn>�RHO'UJT . 6!��TmG\eD>�UA�S<_9;døZ�GAO'��UAR"ZæAf�GALS>+GJRQ[kY�GJI�LçY+fD�S[kY�IDUAIS<a[_ID9&GJ>Q[_RQ[_9&O;@4TVUA>�9+à GndheS<_9A@�R�ZD9;IçR"ZD9�Y+fD�S[kYce�GJ>�R�UJTmR"ZD9�OXu�OQR"9;d �1[a<a<m�/9�[_wAIDUA>�9&L�68�9&Y;Gnf�OQ9�UJT4R�ZS[kO1eD>�UAe/9;>�RQuh[_R!OQ9;9;d\O1>�9&GAOQUsI�GJ�S<_9ER�U�UAIS<_u�f�OQ9ER�ZS[kO1dh9;R�ZDUDL\UAI�eD>�Us�S<=9;d\O�1[_R�Z�UsID9EUA>HLS9;>UJTIDUAIS<a[=ID9&Gn>Q[_R�u á �ZD9;R�ZD9;>�R�ZS[kO4UA>+LS9;>4[�O:æAf�GsLS>HGJRQ[kYJ@^Y+fD�S[kYJ@sUA>�ZS[_wAZD9;>;åH6�C1ZD9dc9;R�ZDU�L�LSUS9&O�Z�G�rA9:R�ZD9!GALSrJGJI^R+GJwA9R�Z�GJR1[_R1[kO'rA9;>�u\9&GAOQu\R�U�[=dceS<=9;dc9;I^R&@�GJI�L�[=R+OY;G�<kY+fS<kGJRQ[_UAI�OEY;GJI��/9�LSUAID9�rA9;>�u�æAfS[kY"NA<_uA6f � � ��&b�;�D�("����t"�|�"/×ÜÙh"/×����\Ý �A�J�D�&Ý����4Ú��D�&Ý�Ø�×

C1ZS[kO�dh9;R�ZDUDLMG�<kOQU\>�9&OQfS<_RHO,[_I�G�TV9;9&LS��GAY�NMY+UsI^R�>"UJ<�[_I�e�UJ�19;>�OQ9;>X[=9&O,TVUA>�dM@DR"ZDUAfDwAZ�[_RELSU^9&OEOXUhR�ZD>�UAfDwsZGhLs[aéÜ9;>"9;I^ReD>"U�Y+9&O�O�6���I�OQR"9&GAL\UJT�OQUJ<_rA[_IDw\R�ZD9�B ð 8þ9&æAf�GJRX[=UsI\[=R+OQ9+<aTX@/R�ZD9Ee�UJ�19;>OQ9;>Q[_9&O'9+à�e�GJI�O�[=UsI�[kOGJeDeS<a[_9&LR�U�R�ZD9h>�9+<kGJR"9&LçOQRHGJR"9;��LS9;e�9;I�LS9;ISR�W:[kY;Y;GJRQ[19&æAf�GnRQ[_UAI á 5 g Wÿ,åH6�C1ZD9�5 g Wÿôdh9;R�ZDUDL�[kO�Ls[kO�Y+f�O�OX9&L�[_I¹LS9;RHGv[o<�^u]7�<_UAfDRQ[_9;>&@ g �=5AUAfD�&G�GJI�L�i�>HGAY+9;N�[_I ã Ô ù ä @bGnI�L�R�ZD9�f�OQ9�UJTmR"ZD9�e/UJ�m9;>�OX9;>Q[_9&O�TVUA>!R"ZS[�O�9&æAf�GnRQ[_UAI�[�O�T�>"UAd�ç9;>�IS<a[ÛGnI�L�7�U^UsNõã ÔsÔHä 6

C1ZD9�[kLS9&G���9;ZS[_I�LçR"ZD9hdh9;R�ZDUDL�[kO�R�U�e�GJ>HG�<a<_9+<mR"ZD9hf�OQ9hUJT1R�ZD9�W:[kY;Y;GJRX[m9&æsf�GJRQ[_UAI�TVUA>E<a[_ID9&GJ>�eD>�UA�S<_9;d�O�^u�>�9;�'>Q[_RQ[_IDw�R�ZD9MIDUAIS<a[_ID9&GJ>pT�fDI�Y+RQ[_UAIòUJT [_I á Ô å�GsO . á å ��� á å 6 l UAR�9MR"Z�GJRhR�ZD9�Y�ZDUJ[kY+9çUnT � [�OIDUAREfDIS[kæAfD9A@4GJI�L�Ls[oé�9;>�9;ISR�Y"ZDUJ[kY+9&OE�1[a<a<m>�9&OXfS<=R�[_I¹Ls[aé�9;>�9;ISR�Y+UAISR�>�UJ<kO;6��þ[_R�Z . >�9;�'>Q[_R�R�9;I�[_IçR�ZS[kO��G&u�R"ZD9OQRHGJR�9;��LS9;e/9;I�LS9;I^REW:[kY;Y;GJRQ[�9&æsf�GJRQ[_UAI\[kOUnTjR�ZD9�TVUA>�d_ á å � á å ��� N á å _ á å [ _ á å � 9 ])^ � N _ á å ��O�� ý 2 á yAåGJI�L�R�ZD9EUseDRQ[_d�G�<�T�9;9&LS��GsY�NMY+UAISR�>�Un<b[kO'wJ[_rA9;I��Su� á å � [�9 ])^ � N _ á å e á üSå�ç9MIDUAR"9MR�Z�GJRcR�ZD9õW:[kY;Y;GJRX[�OQUn<=fDRX[=UsI _ á å�[�O\OQRHGnR�9;��LS9;e�9;I�LS9;ISRMGJI�L�[kO\IDUAR\GAOh9&GsOQu¹R"Uç`�I�LþGAO�TVUA>hR"ZD9Y+UAI�OQRHGJISR!Y+US9+î�Y"[_9;I^REY;GAOQ9A@ 9+à Y+9;eDR'T�Us>,O�[=dceS<=9�eD>�Us�S<=9;d\O�1[_R�Z�Y+9;>�RHG�[_IMOQR">�f�Y+R�fD>�9&O;6,öID9�eD>�UAe/U^OQ9&Lpdh9;R�ZDUDLT�UA>'R�ZD9EwA9;ID9;>HG�<�Y;GAOQ9�[kOR"U�f�OX9�R�ZD9Ee/Uv�19;>!OX9;>Q[_9&O9+àDe�GJI�Ot[_UAI�R�UhGJeDeD>�U�à^[_d�GnR�9ER�ZD9�OQUJ<_fDRQ[_UAI�6

|

�ç9�>�9;�>Q[_R�9 � [_I�R�9;>�d�O'UJT,G\Y+UAI�OQR+GJI^R'e�GJ>�REGJI�L�G�OQR+GJR�9;��LS9;e�9;I�LS9;ISR�e�Gn>�R�GsO � á å � � 0 �c �¡�� á å�ZD9;>�9   [kO!GcR�9;dhe/UA>HGJ>�ucrvGJ>Q[kGJ�S<_9�f�OQ9&L�T�UA>'R�ZD9�9+àDe�GJI�Ot[_UAI�R�Z�GJR�1[a<a<���9�OX9;RR�U Ô <kGJR"9;>&6o�]9�ID9+àDR�>Q[_R�9 _GAOG�e/Uv�19;>!OX9;>Q[_9&O:[_I   <

_ á h2�  å � _ á å�¢ £ � 0¤� _ £ á å�¢ £ � 0¥ Z� _ £-£ á å�¢ £ � 0   ?x � erere� L���� 0   �i¦ � á å 2 á {Så

�ZD9;>�9 _ [kO!OQuSdhdh9;R">Q[kYJ@bGJI�L�OQUh9&GAY"Z ¦ � [kO�OQuSdhdh9;R�>Q[kY�GAO1�19+<a<�6�5AfD��OXRQ[_R�fDRQ[_IDw�R�ZD9&OQ9�9+à�e�GJI�O�[=UsI�O1[_ISR�U�R"ZD9OQRHGJR�9;��LS9;e/9;I�LS9;I^REW:[kY;Y;GJRQ[�9&æsf�GJRQ[_UAI á yAå+@^�19�`�I�L� L���� 0   � ¦ � � á �Z0¤�� 3¡T� á å�å � M � N0 �6 �¡T� N á å R � L���� 0   � ¦ � �[ � L��3� 0   �1¦ � � � 9 ])^ � N � L��3� 0   �1¦ � � ��O � ý1el UJ� �Suhd�GnRHY�ZS[_IDw�R�9;>�d\O4[_I^rsUJ<_rA[_IDwhR�ZD9EO�GJdc9e�UJ�19;>HO�UnT   �19�UA�DRHG�[_I\R�ZD9'T�UJ<a<_UJ�1[_IDwhOQ9;R�UJT49&æAf�GJRX[=UsI�O�R"Z�GJRY;GJI���9�f�OQ9&L�R�U\LS9;R�9;>�d�[_ID9 ¦ � ¦ 0��Z0¤���ZN0 ¦ 0�[ ¦ 0 � 9 ])^ � N ¦ 0¤��O � ý á Ô�ý å¦ ^ M �Z0�[ � 9 ]H^ � N ¦ 0 R � M � N0 [ ¦ 0 � 9 ])^ � N R ¦ ^ � ¦ 0�¡T�§��¡T� N ¦ 0 � ý á ÔsÔ å¦ � M � 0 [ � 9 ])^ � N ¦ 0 R � M � N0 [ ¦ 0 � 9 ]H^ � N R ¦ � � ¦ � ])^ ¡T�§��¡T� N ¦ � ])^[ � ])^�? � ^ M ¦ ? � 9 ])^ � N ¦ � ])? R � ý1e á Ô xSå

ÿ�æsf�GJRQ[_UAI á Ô&ý å�[kO1R"ZD9�OQRHGJI�LDGJ>+L�W:[kY;Y;GJRQ[�9&æsf�GJRQ[_UAIpT�UA>1R�ZD9�<a[_ID9&GJ>�e�GJ>�R � 0 6�ÿ�æsf�GJRQ[_UAI�O á ÔAÔ å�GJI�L á Ô x�åjd\G&u��9�OQUn<=rs9&L�@��DfDR�GAO��1[_R�Z�R�ZD9hB ð 8%e�UJ�19;>�OQ9;>Q[_9&O�9+à�e�GJI�O�[=UsI�[_REd�G�uM��9hG\R�9&Ls[_UAf�O�eD>�UDY+9&O�O'[aT,R"ZD9�TVfDI�Y+RQ[_UAI¡T� á å�[kO�Y+UAdheS<a[kY;GJR�9&L�6B'Uv�19;rA9;>�@S[_IõOQUAdc9�OQe�9&Y"[kG�<mY;GAOX9&O;@S[_R[kO'9&GAOt[_9;>�R�UhUA�DRHGv[=I�ZS[_wAZD9;>"�VUA>HLS9;>E>�9&OQfS<_RHO,TVUA>R�ZD9h5 g Wÿ 9+à�e�GJI�O�[=UsI�6 X Us>9+à GndheS<_9A@/[=I�R�ZD9�Y;GAOQ9�R�Z�GJRR�ZD9�IDUAIS<a[_ID9&GJ>�TVfDI�Y+RQ[_UAI . á å�[_I á Ô åÛ[�OEæsf�GALS>HGnRQ[kY[=I @SR�ZD9�T�fDI�Y+RX[=UsI ¡T� á å��1[a<a<���9�<a[_ID9&GJ>'[=I @DGJI�L�TV>�UAd á ÔsÔ å�R�ZD9 ¦ ^ R"9;>�d÷�1[a<o<4��9EUJT�Us>HLS9;> �ZS[kY�Z��1[a<a<eD>�U�LSf�Y+9hGJI�UA>HLS9;> ? Y+UAISR�>�Un<�@�GJI�L�OQU�UsI�61��IõY+Usdhe�GJ>Q[kOQUAI�R�UcR�ZD9�B ð 8ô9+à�e�GJI�O�[=UsI�@D[_RE>�9&æsfS[_>�9&OR"ZD9�UA>HLS9;> K R"9;>�d a ^ R�U�Us�DRHG�[_IçGJI�UA>HLS9;> ? Y+UAISR�>�UJ<��/R�Z^f�O'[_R�[kO�ID9&Y+9&O�O�Gn>�uMR�U�Y+UAI�Ot[kLS9;>�Gcd�f�Y�Z�<kGJ>�wA9;>EISfDd���9;>EUJTe�U^O�O�[=�S<_9hY+UAd��S[_I�GJRQ[_UAI�O'UJT�R�ZD9�OQRHGJR"9!rJGJ>Q[kGJ�S<_9&O'[_I 6

C1ZD9\5 g Wÿþdh9;R�ZDUDL�[kO�d�f�Y"ZM9&GAOt[_9;>ER�U�Y+UAI�Ot[kLS9;>�TVUA>EG�Y+9;>�R+G�[_IõY"<kGAO�O�UJT�IDUsIS<o[_ID9&GJ>X[=RQu�T�GAY+R�UA>Q[_�&GJRX[=UsI�O;@OQe�9&Y"[a`bY;G�<a<_uA@�R�ZDU^OQ9cT�Us>��'ZS[�Y"Z ¡�� Z�GAO�R�ZD9MO"GJdh9cT�fDI�Y+RQ[_UAI�UnT [_I�Gv<o<UJT�[_RHO�9+<_9;dh9;I^R+O;@mGnI�L�OQU¹Y;GJI���9�>Q[_R�R�9;I�GsO ¡T� á å �c¨ á å ¡T��© �,[=R"Z�GEY+UAI�OQRHGnI^R��VrJG�<_fD9&Lhd\GJR�>Q[aà ¡���© 64��IhR�ZS[kO:Y;GAOQ9A@A�Su�LS9+`�IS[_IDw ¦ � á å �¨ � á å á ¦ � å © @S�ZD9;>�9 á ¦ � å © [kO!GcY+UAI�OQRHGJISR1d�GJR�>X[oà�@D�19EUA�DRHGv[=I\TV>�UAd á Ô xSå

á ¦ � å © M �Z0�[ � 9 ])^ � N ¦ 0 R � M ��N0 [ ¦ 0 � 9 ])^ � N R á ¦ � å © � á ¦ � ])^ å © ¡T� © ��¡T��N© á ¦ � ])^ å ©[ � ])^�? � ^ M á ¦ ? å © � 9 ])^ � N á ¦ � ]H? å © R � ý1ez

C1ZS[kO1[kOÛß�f�OQR�GhY+UAI�OQRHGnI^R��VrJG�<_fD9&L�d�GnR�>Q[aà�9&æsf�GJRQ[_UAI�@ �ZS[kY�Z�Y;GJIM�/9�OQUJ<_rA9&L\9&GsOt[a<=uA61�tIMR�ZS[kO1�G�u�G�<kGJ>"wA9�Y"<kGAO�OUJT�5 g Wÿ eD>�UA�S<_9;d�OY;GJI��/9�OQUJ<_rA9&L\R�UhGAO:d�GnI^uhR"9;>�d�O:UJT�R�ZD9Ee/UJ�m9;>OQ9;>X[=9&O'GAO1LS9&Ot[_>�9&L�6öI�Y+9�GAO:d�GJISu ¦ �R�9;>�d�O1GAO:LS9&Ot[_>�9&L�Z�G�rA91TVUAfDI�L�@SR�ZD9�Y+UAISR�>�Un<D[�O,UA�DRHG�[_ID9&L\�Su�OQfD��OQRQ[_R�fDRX[=IDw�R�ZD9;d÷��GAY"N�[_ISR�U á {SåjGnI�L á üSå��,[=R"Z  OX9;RmR"U Ô 6

C1ZD9�5 g W'ÿ�dh9;R�ZDUDL�[kOmO�[=d�[o<kGJ>,[=Ic[_RHO�GsLSrvGJISRHGJwA9&O:GJI�L\Ls[�O"GALSrvGJISRHGJws9&O�R�U�R�ZD9!RQ�1UA�VR�9;>"d)B ð 8�dc9;R�ZDU�L�6C1ZD9;uh��UsR�Z�Y+UAI�Ot[kOQR1UJT�Y;G�<kY+fS<kGJRQ[_IDwhUAfDR:R�ZD91`�>HOQRÛT�9;�þR�9;>�d�OÛUJT�GEe/Uv�19;>1OQ9;>Q[_9&O;@DGJI�LhY;GJIc��UAR�Z\��9EY;G�<kY+fS<kGJR�9&LrA9;>�u�æsfS[kY�Ns<_uA6mB'UJ�m9;rs9;>&@DGAO:d�GJISu�R"9;>�d�O:UJT�R�ZD9�5 g W'ÿ�OQ9;>Q[_9&OGAO1LS9&Ot[_>�9&L�Y;GJI��/9�T�UsfDI�LcT�UA>1R�ZD9EY;GAOQ9E�'ZD9;I¡T�ª�«¨ á å ¡���© @�GAO�LS9&O�Y+>Q[_��9&LòGJ�/Uvrs9A@��'ZS[o<_9�R�ZD9�B ð 8÷GJeDeD>�USGAY�Z�G�<_�G�u�O�f�OQ9&O�UAIS<_u�R��1U�R�9;>�d�O;6çC,ZS[�OGAO�OQfDdheDRX[=UsI�UAIcR�ZD9TVUA>�dïUnT ¡�� LSU^9&Oj<a[=d�[=R'R�ZD9!eD>"UA�S<_9;d�OÛT�UA>��'ZS[�Y"Z�R�ZD9E5 g W'ÿ�GJeDeD>�U^GAY"Z�[kO:dhU^OQR�f�OX9+T�fS<�@ß�f�OQRGAOÛR�ZD9EB ð 8òGJeDeD>"U^GAY"Z�[kO1dhU^OQR:f�OQ9+TVfS<ÜUsIS<=u�T�UA>1eD>�Us�S<=9;d\O��,[=R"Z�UAIS<_u\UAID9'<=9;rs9+<ÜUnT�IDUAIS<a[_ID9&GJ>Q[_RQuA6mC1ZD9;>"9[�O:G�<kOQUER�ZD9LS>HG����GAY"NER�Z�GJR�R"ZD9!5 g W'ÿçdh9;R"ZDU�L�[kO�GJeDeD>"U&àS[_d�GJRQ[_IDwER�ZD9OQUn<=fDRX[=UsIhUJT�R�ZD9E5 g W'ÿ@J�ZS[kY"Zh�1UAfS<kLeD>�U�LSf�Y+9\UAIS<_uõG�OQfD��UseDRQ[_d�G�<mY+UAISR�>�UJ<�9;rA9;I�[aT!OQUJ<_rA9&L�9+à GAY+RX<=uA@F�ZS[a<_9�R�ZD9\B ð 8%dc9;R�ZDU�Lp[kO�GneDeD>�U�à^[_d�GJRX[=IDwR�ZD9�B ð 8ò9&æAf�GnRQ[_UAI�[_RHOQ9+<aT�6f � f ��&�Ú��A�3"D�&��Ýr¬w"*­��) #"D��jFÝV×�}�|�|4�&Ø1}4Ý®$��D�&Ý_ØF×

��I�OQR�9&GsL\UJTjR"ZD9E>�9;wAfS<kGJ>B ð 8ò9&æAf�GnRQ[_UAI á xSåH@SR�ZD9EOQf�Y;Y+9&O�O�[=rs9 û Gv<=9;>"NA[_IõGneDeD>�U�à^[_d�GJRX[=UsI á 5 û � å�dh9;R�ZDUDLá T�>"UAd 8:9&GJ>HL�@�5^GJ>X[�Ls[kO�GJI�L§�ç9;I�[_Iïã£{S@ Ô&ýnä å�f�OQ9&OcR�ZD9Mws9;ID9;>HG�<a[_�;9&L�B�GJd�[a<_R�UAID� ð GAY+UA�S[_��8:9+<o< d�GJI á�û B ð 8å9&æAf�GJRX[=UsI�6�8:9&Y;GJf�OQ9hR�ZD9;>"9E[kO�GJI�9;>�>�UA>�[_I�R�ZD9�e�GJe/9;>E�^u�8�9&Gn>HL�9;R�G�<�6hã Ô&ý�ä UAIMe�GJws9�z ý xD@/�m9�>�9&LS9;>Q[_rA9hR"ZD9eD>�UAe�USOQ9&L�dh9;R"ZDU�L\ZD9;>�9A6,7�UAI�Ot[kLS9;>�R�ZD9�Y+U^OQR1TVfDI�Y+RQ[_UAI�G�<a á 0 � � å � G á 0 2 � å � J*L0 á N O��� � N 9 � å S ,�ZD9;>�9 á-, å�O�GJRQ[kOt`�9&OÛR�ZD9IDUAIS<a[_ID9&GJ>LSu^I�Gnd�[kY;O�d�K. á å � ��� á åH@J�1[_R�Z\Y+UAI^R">�UJ< � á åjGJI�L�[_IS[_RQ[kG�<�Y+UAI�Ls[_RQ[_UAI10 6 g [aé�9;>�9;ISRQ[kGJRQ[_IDw a G�<_UAIDwhR�ZD9Ee�GnR�ZMUJT4R�ZD9�OQuDOQR�9;dÞ<_9&GALDO'R�UhR�ZD9 û B ð 8ò9&æAf�GnRQ[_UAI�@¯�° GP� ã a¤2 � ä1±Y²�³ a³ 10�´ N á . á 0 å � ��� á 0 å�å �� N0 O� 0 � � N á 0 å 9 � á 0 å � ýHe á Ô ùSå

C1ZS[kO�/9&Y+UAdh9&O'R�ZD9EIDUA>�d�Gv<FB ð 8ò9&æsf�GJRQ[_UAIp[aTjR�ZD9�T�Us>�d�fS<�G�TVUA>R�ZD9�Y+UsI^R�>"UJ<�@� á 10 å � [ Ôx 9 ])^ � N ³ a³ 0 á 10 å 2 á Ô úDå

[�O'f�OQ9&L�[=I á Ô ùSå+6���I�OXR�9&GAL�@�G�eD>"U�Y+9&O�O,[kO!OX9;RfDe�R�U�OQUn<=rs9 á Ô ùSå�GJI�L á Ô úDå�R�UAwA9;R�ZD9;>,[=I�GJI\[_R�9;>HGJRX[=rs9EeD>�U�Y+9&O"O;6�ç9:`�>HOQR�Y"ZDU^U^OX9,GnI�[_IS[_RQ[kG�<�Y+UAI^R">�UJ<ATVfDI�Y+RQ[_UAI �¶µ 0¥· á å á TVUA>49+à GJdceS<=9A@sR�ZD9:<a[=ID9&Gn>�UAeDRQ[_d�Gv< Y+UAISR�>�Un<�å+6jC,ZD9;I�m9Ef�OX9�R�ZD9 û B ð 8þ9&æsf�GJRQ[_UAI á �1[_R�Z�R�ZD9ErJGJ>Q[kGJ�S<_9 10 IDUJ� Y"Z�GJIDwA9&L\R�U å�R�U�`�I�L�¸º¹w»�¼-½¸ b �Su�OQUJ<_rA[_IDw� ³ a µ 0¥·³ � N M . á å � ��� µ 0¥· á å R �� N O�Q� á � µ 0¥· å N 9 � µ 0¾· � ý1e�ç9�<_9;R!R�ZD9EID9+àDREY+UAI^R">�UJ<�[_IMR�ZD9�OQ9&æsfD9;I�Y+9��/9� µ ^ · á å � [ Ôx 9 ])^ � N ³ a µ 0¥·³ á å e�ç9EeD>�UDY+9;9&L�R�Uhf�OX9�R�ZS[kO1R�U�`�I�L a µ ^ · GJI�L � µ ? · @�GJI�L�Y+UsI^RQ[_ISfD9E[_IMR"ZS[�O'�G�u�T�Us>!GAOÛ<_UAIDw�GsOLS9&Ot[_>�9&L�6

y

� û G�<_9;>�Ns[_I¹dc9;R�ZDU�L]Y;GJI¹�/9�f�OX9&LçR�U�GJeDeD>�U�àS[=d\GJR�9hR�ZD9 û B ð 8ï9&æsf�GJRQ[_UAI�OQUMR"Z�GJR�[_R�Y;GnI¹�/9�OQUn<=rs9&LI^fDdh9;>X[�Y;Gv<o<_uA61C�U�LSUER"ZS[�O�@A�19Y�ZDUSU^OQ9GEOQ9;R�UJT � ��GsOt[kOFT�fDI�Y+RQ[_UAI�OÀ¿�Á ��Â�Ã� � ^ GJI�L�LS9+`�ID9R�ZD9 ¦ ? [_IDID9;>1eD>�U�LSf�Y+RGAO Ä .%2ŨwÆ!� JIÇ . á å ¨ á å S P2�ZD9;>�9 5 [kO\GJI^u�Y+UAdhe�GsY+R�OXfD��OQ9;RhUJTER�ZD9�>�9;wJ[_UAIþUJT�GJR"R�>HGAY+RQ[_UAI�GAO�OXU�Y"[kGJR�9&L �1[_R�Z�R�ZD9�NSIDUJ�I OQRHGJ�S[a<a[_�+[_IDwY+UAI^R">�UJ< �wµ 0¥· á åH6�C1ZD9 û G�<_9;>�NA[_I�GJeDeD>�U�à^[_d�GnRQ[_UAI�UJT a µ�È · [kOwJ[_rA9;I��^ua µ�È ·Ã á å � Ã�� � ^1É µ�È ·� Á � á å 2�ZD9;>�9�R"ZD9�Y+U^9+î�Y"[_9;ISRHO É µÊÈ ·� O�GJRX[�O�T�u\R�ZD9E�19&GJNcT�UA>"d*UJT á Ô ùSå <Ä ¯�° G¶� ã Ã�� � ^)É µ�È ·� Á �Ë2 � µ�È ·Ã ä 2 Á � Æ`� ý á Ô |Så

T�UA>�� � Ô 2 ere#e 2¥� 6jC,ZD9E[_IS[_RQ[kG�<ÛY+UsI^R�>"UJ<�TVfDI�Y+RQ[_UAI � µ 0¥·Ã T�Us> á Ô |SåÛ[�O�Y"ZDU^OQ9;I�@�GJI�L\R�ZD9E<kGJR"9;>[_R�9;>HGnR�9&OGJ>�9�T�UsfDI�LGAO:TVUJ<a<=UJ�!O�6�ÿ�æsf�GJRQ[_UAI á Ô |Så�wJ[_rA9&O � 9&æAf�GnRQ[_UAI�OR"U�OXUJ<_rA9ETVUA>1R�ZD9 � fDIDN^IDUJ�I�O É µÊÈ ·� @3Ì � Ô 2 x 2 ere#e 2�� <Ã�� � ^%É µÊÈ ·�

Ä ² ³ Á �³ ´ N M .�� ��� µ�È ·Ã R 2 Á � Æh�Ä HN¶O�Q� á � µÊÈ ·Ã å N�9 � µ�È ·Ã 2 Á � Æ`� ý á Ô zSå

T�UA>�� � Ô 2 e#ere 2¥� 6�C1ZD9EID9+àDR�Y+UAISR�>�Un<ÜfDe�LDGJR�9E�/9&Y+UAdh9&O� µÊÈ � ^ ·Ã �8[ Ôx 9 ])^ � N Ã�� � ^ É µ�È ·� ²P³ Á �³ t´ e á Ô yAåX >�UAd á Ô z�åÜGJI�L á Ô yAå�R�ZD91eD>�UDY+9&O�O�Y;GJI���91�>X[=R"R�9;IhGAO�GnI�[_R�9;>+GJRQ[_rA91d�GJR�>X[oà�eD>"UA�S<_9;dM@A�1[_R�Z�R�ZD91ID9&Y+9&O�O"GJ>�u[=IDID9;>\eD>�UDLSf�Y+RHO\Y;G�<kY+fS<�GnR�9&Lþ��9+TVUA>�9;Z�GJI�L�6c�]9��1[a<o<Ef�OQ9�R�ZD9�IDUARHGJRX[=UsI�Í µ�È ·Ã � M É µ�È ·^ 2 erere 2 É µ�È ·Ã R N @ZÎ Ã á å �á Á ^ á å 2 erere 2 Á à á å�å N @1GJI�L�<_9;RvÏtÎ Ã LS9;IDUAR"9�R�ZD9 ð GsY+UA�S[kGJI UJT�Î Ã 6 � <kOQU�@:TVUA>hGJI^u�>�9&G�<_�VrJG�<_fD9&L�TVfDI�Y+RQ[_UAIÐ á åH@SLS9+`�ID9hG�rA9&Y+R�UA>1UJT4[_IDID9;>!eD>"U�LSf�Y+RHOÄ Ðw2 Î Ã Æ/Ñ@� á Ä Ðw2 Á ^ Æw2 ere#e 2 Ä Ðw2 Á Ã Æ å N 2GJI�L\TVUA>GJISu�rA9&Y+R"UA>��VrvGv<=fD9&L�T�fDI�Y+RX[=UsI Ð á å � á Ð ^ á å 2 erere 2¾Ð à á å"å N @�LS9+`�ID9hG�d\GJR�>Q[aà�UJT4[_IDID9;>!eD>"U�LSf�Y+RHOÄ Ðw2 Î Ã Æ ; �ÓÒÔÕ

Ä Ð ^ 2 Á ^ Æ ÖºÖ�Ö Ä Ð Ã 2 Á ^ Æ666 6 6 6 666Ä Ð ^ 2 Á Ã Æ'ÖºÖ�Ö Ä Ð Ã 2 Á Ã Æ@×ÙØÚ e

7�UAdheDfDR�9ER"ZD9�T�UJ<a<_UJ�1[_IDw ¦ ? [_IDID9;>!eD>�UDLSf�Y+RHO <ÛiÜ � Ýi N O�P2 Î Ã@Þ Ñ 2 Ûiß �8Ý á � µ 0¥· å N 9 � µ 0¾· 2 Î Ã@Þ Ñ 2 Û1à � Ä ÏtÎ Ã .%2 Î Ã Æ ; 2 á Ô üSåÛ�á � Ý Ï�Î Ã ��� µ 0¾· 2 Î Ã@Þ ; 2ºâ Û�á�ßmá? ã à ? � ^ �8âPÝ ÏtÎ Ã � 9 ])^ � N á ³ Á ?3ä ³ å 2 Î ÃZÞ ; ã à ? � ^ e á Ô {Så

ü

X >�UAd R�ZD9�Y�ZDUSOQ9;I\[_IS[=RX[�Gv<�[=R"9;>HGJR�9 � µ 0¥· OXUJ<_rA9 � É µ 0¥·Ã �æå32�ZD9;>�9 ��� Û à � Û á GnI�L å���[ Û Ü [ Û ß 6 û [_rA9;I�R�ZD9 á�ç åtR�Zh[_R�9;>+GJR�9A@/R�ZD9 á�ç � Ô åtR�Z\[_R�9;>HGJR�9�[kOR�ZD9�OQUJ<_fDRQ[_UAIR�UhR�ZD9E9&æsf�GJRQ[_UAI � É µÊÈ � ^ ·Ã �æå32�ZD9;>�9 �U� Û à [ ^ ? � à ? � ^ É µ�È ·? Û á�ßwá? GJI�L å�� [ Û Ü [ ^ P M � à ? � ^ É µÊÈ ·? Û á!ßwá? R Í µ�È ·Ã 6 á l UAR�9�R"ZD9 ^P [_I�R"ZD9�9+àDeD>�9&O�Ot[_UAIT�UA> å @D�ZS[kY�Z��GAO:[_I�Y+UA>�>�9&Y+RX<=u��>Q[_R�R�9;I�GAO ^? [_I�R�ZD9EUA>X[=wn[=I�Gv<je�GJe/9;>�ã Ô&ý�ä 6aå � R9&GAY"ZMOQR�9;e çoè ý @DR�ZD9�Y+UsI^R�>"UJ<[�O'wJ[_rA9;I��^u � µÊÈ � ^ ·Ã �é[ Ôx 9 ])^ � N Ï�Î NÃ Í µ�È ·Ã e

C1ZD9�OQf�Y;Y+9&O"Ot[_rA9 û G�<_9;>�NA[_I�GJeDeD>�U�à^[_d�GnRQ[_UAI�dh9;R�ZDUDL\[kO1dhUs>�9ERQ[_dh9;� [_I^R"9;I�Ot[_rA9�R�Z�GJI�R�ZD9�`�>HOXRRQ�mU�dh9;R"ZD�U�LDO�Ls[kO�Y+f�O�OQ9&L�6�C1ZD9�GsY+R�f�G�<�[_R�9;>+GJRQ[_UAI�eD>�U�Y+9&O"O�[kO�T�GAOXR&@��DfDR�R�ZD9hRX[=dc9�ID9;9&LS9&L�R�U�Y;G�<kY+fS<kGJR�9\R�ZD9h[_ISR�9;wA>HGv<�O[=I á Ô üSåmGJI�L á Ô {�åmY;GJI���9hOt[_wAIS[a`bY;GJISR&6EC1ZD9�dh9;R�ZDUDL�Z�GAO'R�ZD9hGALSrJGJI^R+GJwA9�R"Z�GJR1[_R�[kOEGJeDeS<a[�Y;Gn�S<=9\R�U�G�<kGJ>�wA9;>Y"<�GsO�OEUJTeD>�Us�S<=9;d\O;@��1[_R�ZDUsfDR�R�ZD9h>"9&OQR�>Q[kY+RQ[_UAI�O�[=dce�U^OQ9&L]�SuõR"ZD9�`�>HOQRERQ�1U�dc9;R�ZDU�LDO�6�B'Uv�19;rA9;>�@/[=R�Z�GAOER"ZD9Ls[�O"GALSrvGJISRHGJws9A@��/9+[_IDw�GnIM[_R�9;>+GJRQ[_rA9hdh9;R"ZDU�L�@4R�Z�GJR�[_R�[�O�LS9;e�9;I�LS9;ISRhUAI�R�ZD9�Y"ZDU^OQ9;I�[=IS[_RQ[kG�<1[_R�9;>HGnR�9 � µ 0¥· 6c�VTR�ZS[kO1[kO1IDUAR'�m9+<a<jY"ZDU^OQ9;I�@ R�ZD9;I�R�ZD9Edh9;R�ZDUDL�d\G&u\Y+UAI^rs9;>�wA9ErA9;>�u\Ot<_Uv�,<=uA@/UA>1d�G�u\9;rA9;I�IDUAR!Y+UAISrA9;>�ws9�GJR�G�<a<�6f ��ê���Ö�×��("��3|4Øw _�D�&Ý�Ø�× Ø%s�ë���ì�íî����Øb~� #")$ï&bØw VÚ��&Ý_ØF×Ü�

� rs9;>�uõLs[aé�9;>�9;ISR�GJeDeD>�USGAY�Z�R�U\`�I�Ls[_IDwçGcTV9;9&LS��GAY�NçY+UAISR�>�Un<�[kOEf�OX9&L�[_I¹R�ZD9�>�9;d\G�[_IS[=IDw�RQ�1U�dc9;R�ZDU�LDOR�Uh��9�Ls[kO�Y+f�O"OQ9&L�ID9+à�R&6:C1ZD9&OQ9Edh9;R�ZDUDLDO'f�OQ9ER�9&Y"ZDIS[�æsfD9&O'TVUA>:`�I�Ls[=IDw�GJI�UAe�9;ID� <_USUAeõY+UAISR�>�Un<bTVUA>1R�ZD9�OQu�OXR�9;d�1[_R�ZMGhY"ZDU^OQ9;I\[_IS[_RQ[kG�<ÛY+UsI�Ls[=RX[=UsI H0 6:C1ZS[kO1[kO1>�9;e/9&GJR�9&L�T�UA>1d�GnI^uhrJG�<_fD9&OUnT H0 6 � R9&GAY"Z�e�UJ[_ISR&@DR�ZD9�[_IS[_RQ[kG�<Y+UAI^R">�UJ< �wµ b ¼ · á-, � ý å�R"Z�GJR�[kO4TVUAfDI�L�[kOmY+UsI�Ot[kLS9;>�9&LhR"ZD9�Y+UAISR�>�Un<�rvG�<_fD9EGJR H0 6�C,ZD9;I�GJIc[=ISR�9;>�e/UJ<kGJRQ[_UAIc[kOmLSUsID9Uvrs9;>�Gv<o<R�ZD9&OX9h[_IS[_RQ[kG�<Ee�UJ[_ISRHO�R�U�T�UA>"d G�Y"<_U^OQ9&LS� <_USUAe á T�9;9&LS��GAY"N/å�Y+UsI^R�>"UJ< � á åH6�C1ZD9�UAe/9;ID� <_U^UAe Y+UsI^R�>"UJ<[�O,TVUAfDI�L��^u�OQUJ<_rs[=IDw�R"ZD9�B�GJd�[a<_R�UAIS[kGJIçOQuDOQR�9;d GJ>X[�O�[=IDwcTV>�UAd*R�ZD9�ID9&Y+9&O�O�GJ>"u�UAeDRQ[_d�G�<a[_RQuMY+UAI�Ls[_RQ[_UAI�O�ã Ô @ Ô y äwJ[_rA9;IM�Su + � . á å [ ^? � 9 ]H^ � N)ðð � [�. Nb á å ð [ x O� á x ý å

�1[_R�Z�[_IS[_RQ[kG�<�Y+UAI�Ls[_RQ[_UAI á ý å �ñH0 GJI�L `�I�G�<�Y+UAI�Ls[_RQ[_UAIþ<a[_d�òôó L ð á-, å � ý 6 X >�UAd R�ZS[kO;@1R"ZD9MUAe/9;ID� <=USUAeY+UAI^R">�UJ<�[kO!Y;G�<kY+fS<kGJR�9&L�GAO � á-, å � [ Ôx 9 ])^ � N ð á-, å e

��I�R"ZD9�rA9;>HO�[=UsIEUJT�R"ZS[�OFdh9;R�ZDUDL�LS9&O"Y+>Q[_��9&L��^u���R"U!GJI�L�5^Y"ZD>�US9;R�9;>�ã Ô z ä @&R�ZS[kOFeD>�UA�S<_9;dô[�O4OQUJ<_rA9&LEGsO/T�Un<o<_UJ�!O;6X [=>+OQRR�ZD9'`�I�G�<�RQ[_dh9�[kOY"Z�GJIDwA9&LcTV>�UAdÞ[_IS`�IS[_RQu�R�UhGhY�ZDUSOQ9;I\`�IS[_R�9@õ�@DR�ZD9;I�R"ZD9ER��1UA�Ve/UJ[_I^R1�/UAfDI�LDGJ>�u\rvG�<_fD9á C���8���å�eD>�UA�S<_9;d [kOLs[kO�Y+>�9;RQ[_�;9&L�I^fDdc9;>Q[kY;G�<a<=u�TVUA> , 4 ã ý 2 õ ä 6�C1ZD9�Ls[kO�Y+>"9;R�9�C��:8��ïeD>�UA�S<_9;d*[kO1wn[=rs9;IM�Su+ ^ö ò á ? [÷ ?ø]H^ å � ^? á . á ? å ��. á ?ø])^ å�å [ ^? � 9�])^ � N ð ?^ö ò á ð ? � ^ [ ð ? å � [ ^? . Nb á ? å á ð ? � ð ? � ^ å [ x O� ? á x Ô å

{

�ZD9;>�9{E � Ô 2 erere 2¥�«[ Ô @DGJI�L � [�O�G�eD>�9&O"Y+>Q[_��9&L�I^fDd��/9;>UJT�Ls[�O"Y+>�9;RQ[_�&GJRQ[_UAIp[=ISR�9;>�rJG�<kO;@�OQUhR�Z�GJR ¡ , � õ ä � 6B9;>�9 10 [kOR�ZD9�Y"ZDU^OQ9;Ip[_IS[=RX[�Gv<ÛY+UAI�Ls[_RQ[_UAI�@�GJI�L ð à � ý 6ë 9;R�RQ[_IDw�ù � á ^ 2 ere#e 2¥ à ])^ 2 ð ^ 2 ere 2 ð à ])^ åmGJI�L\>"9;�>Q[_RQ[_IDw á x Ô å�GAOú á ù å � � ^ö ò á ? [� ?(])^ å [ ^? á . á ? å ��. á ?ø])^ å�å � ^? � 9 ])^ � Nwð ?^ö ò á ð ? � ^ [ ð ? å � ^? . Nb á ? å á ð ? � ð ? � ^ å � x O� ? � ? � ^¾ûýüýüýüýû à ])^ � ý á xsxSå

>�9&OQfS<_RHO'[_IõG\xIA á �D[ Ô åmLs[_dh9;I�Ot[_UAI�G�<mOQuDOQR�9;dóUJT�IDUAIS<a[_ID9&GJ>�9&æsf�GJRQ[_UAI�O á �ZD9;>�9QAó[kO�R�ZD9�I^fDd���9;>�UJTmOQR+GJR�9rvGJ>Q[kGJ�S<_9&O+å1�ZS[kY"ZõY;GJI���9�OXUJ<_rA9&L\f�Ot[_IDw l 9;�R�UsIP�£O1dh9;R�ZDUDL�6�C1ZD9 l 9;�R�UsIP�£O1dh9;R�ZDUDLc[_R�9;>HGJR"9�[�Où � � ù3þ [ ãÙÏ ú á ù3þ"å ä N ú á ù�þ¿å 2�ZD9;>�9{Ï ú [�O'R�ZD9 ð GsY+UA�S[kGJIMUJT ú GnI�L\Z�GAO1R�ZD9�TVUJ<a<_Uv�,[=IDw�OQR�>"f�Y+R�fD>�9 <Ï ú � � � Íÿ [�� N � eC1ZD9!d\GJR�>Q[aà � [�O:�S<_UDY�N�<_UJ�19;>��S[_��Ls[kGJwAUAI�Gv<FGnI�L�R�ZD9�d�GJR�>Q[kY+9&O�Í GJI�L ÿ GJ>�9�S<_UDY�N\Ls[�GnwAUAI�G�<�@^Gv<o<��1[_R�Zc�S<=UDY"NOt[_�;9{A�6�C1ZD9ErJG�<_fD9&O�UJT�R�ZD9E�S<_U�Y"N�O�GJ>�9�GsO�TVUJ<a<_UJ�!O á f�Ot[_IDw Û ; GsOGJIBADCBA [kLS9;I^RX[=RQu�d�GnR�>Q[aàbå <

� ?øû ? � Ô¡ , Û ; [ Ôx .ºb á ? å 2� ? � ^�û ? � [ Ô¡ , Û ; [ Ôx .ºb á ? å 2Í ?øû ? � Ô

x � 9 ])^ � N¤2ÿ ?øû ? � Ôx . Nb(b á ? å á ð ? � ð ? � ^ å � x O e�ç9çZ�G�rA9¹Y;GJ>">Q[_9&LòUAfDR�R�ZD9ç>"9&æAfS[_>�9&L [_I^R�9;>"e�UJ<kGJRQ[_UAI�O�@ETVUJ<a<_Uv�,[=IDwþ��R�UòGJI�L%5^Y"ZD>�US9;R�9;>��£O�Y"ZDUJ[kY+9A@��,[=R"Z

û >�9;9;IP�£OÜTVfDI�Y+RQ[_UAI�O4UJTDR�uSe�9¤¯ á h2�� å � ¢ �[�� ¢ ��GJI�L�G�Y�ZDUn[�Y+91UJT�� � ù e y�TVUA>�R�ZD9:9+à�e/UAID9;I^R�6jC,ZD9mY"<_U^OQ9&LS� <_USUAeY+UAI^R">�UJ<�[kOR�ZD9;I�wn[=rs9;IM�Su � á å � �� È � ^ Ð È ¯ á h2 á H0 å È å 2�ZD9;>�96¿ Ð È Â GJ>�9MR"ZD9õY+US9+î�Y"[_9;I^RHO\UnT�R�ZD9p[_I^R�9;>"e�UJ<kGJRQ[_UAI GJI�LU¿ á 10 å È Â GJ>�9MR"ZD9�� [_IS[_RQ[kG�<�e�UJ[_ISRHOcf�OQ9&LþR�U[=ISR�9;>�e/UJ<kGJR�9�Uvrs9;>hR�ZD9�>�9;wJ[_UAI 5 6 C1ZD9õY+US9+î�Y"[_9;ISRHO�Gn>�9MY�ZDUSOQ9;I OQUçR�Z�GnRhR�ZD9MY+UAISR�>�UJ<1`�RHO�9+à GAY+RX<=u�GJRhR"ZD9[=ISR�9;>�e/UJ<kGJRQ[_UAI�e�UJ[_ISRHO;@�OQUhR�Z�GJR� á�á 10 å � å � ��È � ^ Ð È ¯ áQá 10 å ��2 á 10 å È å � ��� á/, � ý 2 á H0 å � åT�UA>�G�<a<�Ì � Ô 2 erere 2 �Þ6�B'9;>�9 � �� á/, � ý 2 á H0 å � åE[kO\R�ZD9�UAe�9;ID� <_USUAe Y+UAI^R">�UJ<TVUA>c[=IS[_RQ[kG�<hY+UAI�Ls[_RQ[_UAI á 10 å � @9;rvG�<_f�GJR�9&L]GJR , � ý 6EC1ZD9hY+U^9+î�Y"[_9;ISRHOQ¿ Ð È Â R�Z�GJR��1[a<a<,GAY"ZS[_9;rA9�R�ZS[kO�9+à GsY+R�`�R�GJR!R"ZD9�[_ISR�9;>�e/UJ<kGJRQ[_UAIçe/UJ[_I^RHOGJ>�9�TVUAfDI�L��Su�OXUJ<_rA[_IDw\R�ZD9�x�� Ls[=dc9;I�Ot[_UAI�G�<4<o[_ID9&GJ>�OXu�OQR"9;d

Ô�ý

ÒÔÕ Û�� ¯ á�á 0 å ^ 2 á 0 å ^ å ÖºÖ�Ö Û�� ¯ á�á 0 å ^ 2 á 0 å � å666 6 6 6 666Û � ¯ á�á H0 å � 2 á 10 å ^ å ÖºÖ�Ö Û � ¯ á�á 10 å � 2 á 10 å � å ×ÙØÚ ÒÔÕ Ð ^666Ð � ×ÙØÚ � ÒÔÕ � �� á-, � ý 2 á 0 å ^ å666� �� á-, � ý 2 á 10 å � å ×ÙØÚ 2�ZD9;>�9 Û � [kO�GJI�[kLS9;ISRQ[_R�u�d�GnR�>Q[aà�UJT�Ls[_dh9;I�Ot[_UAI���@JR�ZD9ISfDd���9;>�UnTÜY+UAISR�>�UJ<DrvGn>Q[kGJ�S<_9&O;6 l UAR�9R�Z�GnR�R�ZD9'rvG�<_fD9&OUAI�R�ZD9�Ls[kGJwsUAI�G�<�GJ>�9�G�<a<��;9;>"U�T�Us>R�ZD9�Y"ZDU^OQ9;I�TVfDI�Y+RQ[_UAI*¯h6

C1ZD9Ef�OQ9�UnT�R�ZD9�[_I^R"9;>�e�UJ<kGJRX[=UsIMd�GJNs9&O�R"ZS[�O'dh9;R�ZDUDL\rA9;>�ucRQ[_dh9;��Y+UAI�OQfDd�[_IDw�@/wJ[_rA9;I�R�Z�GJR1R�ZD9EUAe/9;ID� <=USUAeY+UAI^R">�UJ<md�f�OQR��/9\T�UAfDI�L]TVUA>�d�GJISuçLs[aéÜ9;>"9;I^R�[_IS[_RQ[kG�<�OXRHGJR�9&O;6çC,ZS[�O�[�O�9&OQe�9&Y"[kG�<a<_u R�>"fD9hTVUA>�eD>�UA�S<_9;d�O��,[=R"Z<�Gn>�wA9;>hISfDd���9;>HOcUJT�OQR+GJR�9�rvGn>Q[kGJ�S<_9&O;�R�ZS[kO�[_I�Y+>�9&GAOQ9&OcR�ZD9�RQ[_dh9�ID9;9&LS9&L���UsR�Z��^u�d\GJNA[_IDwçR"ZD9MLs[�O"Y+>�9;RQ[_�;9&LC���8�� eD>�Us�S<=9;d d�f�Y"Zc<�Gn>�wA9;>!GJI�Lc�Su�[_I�Y+>�9&GAOt[_IDw\R�ZD9!ISfDd���9;>1UJT�[_ISR�9;>�e/UJ<kGJRQ[_UAI�e�Un[=ISRHO1ID9;9&LS9&L�LSfD9!R"U�R"ZD9<�Gn>�wA9;>�Ls[_dh9;I�Ot[_UAI�6:��R4[kO�IDUsRjG�rA9;>"u�Y+UAdheS<a[kY;GJR�9&LceD>�UDY+9&O�O;@JZDUJ�19;rA9;>&@AGJI�L�G�<a<�UJT�R�ZD919+à�e/9;I�Ot[_rA9EY+UAdheDfDRHGJRX[=UsI[�OcLSUAID9�UJé�� <a[=ID9A@OXUõR"ZD9MGAY+R�f�G�<!Y+UAISR�>�UJ<1UJT!R�ZD9MOXu�OQR"9;d Y;GnI OQRQ[a<a<!��9�LSUAID9�rA9;>�u¹æsfS[kY�Ns<_uA6 C1ZD9;>�9MGn>�9�IDU>�9&OQR�>Q[kY+RQ[_UAI�O�UAI�R�ZD9�RQu^e/9&OEUJT�eD>�Us�S<=9;díR�Z�GJR�Y;GJI��/9�OQUJ<_rA9&L�6hC1ZD9�eD>�UDY+9&O�O�UJT�[_I�Y+>�9&GAOt[_IDw�R�ZD9hGAY;Y+fD>HGAY+u�UJTR�ZD9�Y+UAISR�>�UJ<��Su�GALDLs[_IDw\dhUA>�9�[_ISR�9;>�e/UJ<kGJRQ[_UAI�e�UJ[_ISRHO:[kO�G�<kOQU�OQR�>+G�[_wAZ^RXT�UA>"�,Gn>HL�6f ���b��Ö�×��("��3|4Øw _�D�&Ý�Ø�× Ø%s!Ö+�("D�&�D�&Ý#¬w"÷&bØw VÚ��&Ý_ØF×Ü�

� O�[=I]R�ZD9heD>�9;rs[_UAf�OEdh9;R"ZDU�L�@FR�ZS[kOER�9&Y"ZDIS[kæAfD9�G�<kOQUMf�OX9&O�[_I^R"9;>�e�UJ<kGJRX[=UsI¹UJrA9;>EG�ISfDd���9;>�UnTmUAe/9;ID� <=USUAeY+UAI^R">�UJ<�OQUJ<_fDRQ[_UAI�O;@ �DfDRmR"ZD9Edh9;R�ZDUDL\UJT�UA�DRHGv[=IS[_IDw\R�ZD9&OQ9EOQUJ<_fDRQ[_UAI�O,[kOLs[aéÜ9;>"9;I^R&6Û��I�R�ZS[kO1dh9;R"ZDU�L�@DeD>"UAe�U^OX9&L�^u�i�GJ>"N^d�GnI�GJI�L��EGJR���ã£x ý @^x Ô�ä @AR�ZD9EB�GJd�[a<_R�UAIS[kGJIMOQuDOQR�9;dÞ[kO1OQUJ<_rA9&LcIDUARGAO�UAID9'<kGJ>�wA9ELs[kO�Y+>�9;RQ[_�;9&L�C���8��eD>�UA�S<_9;d wn[=rs9;IM�Su á xsxSåH@A�DfDR�R�ZD>�UsfDwAZMGJI\[_R�9;>HGJRX[=UsI�eD>�U�Y+9&O"O1<_9&GALs[_IDw\R�UhR�ZD9�LS9&Ot[_>�9&L�Y+UAISR�>�Un<�6�ç9�GJw^G�[_I�Y�ZDUSU^OQ9�G�`�I�Gv<�RQ[_dh9@õ�@�GnI�L\�1[_R�Z�[_R!LS9+`�ID9hG�Ls[kOQRHGJI�Y+9�TVfDI�Y+RQ[_UAIú á õ 2 ð 0 å ���( á õ�� 0 2 ð 0 å � ? ��� ð á õ�� 0 2 ð 0 å � ? ����� á õ�� � 0 å � ? eB9;>�9 ��� á P2 ð å N [kO4f�OQ9&LER"U�Ot[_dheS<a[aTVu�IDUsRHGJRQ[_UAI�@AGJI�L � á õ�� �(0 å�[kO4R�ZD91OQUJ<_fDRQ[_UAIhGJR4RQ[_dh9oõ�UnT�R�ZD9mB�GJd�[a<_R�UAIS[kGJIOQu�OXR�9;d á x ý åOQRHGn>�RQ[_IDwMGJR �(0 á GnI�L á õ�� 1032 ð 0 å!GnI�L ð á õ�� 10�2 ð 0 å!GJ>�9�R�ZD9hOQRHGJR"9�GnI�LçY+U^OQRHGnR�9�e�GJ>"RHO�UJTmR"ZS[�OOQUJ<_fDRQ[_UAI�åH6 ú [kO1G�dh9&GAOQfD>"9;dh9;I^R1UJT�ZDUJ� Y"<_U^OQ9ER�U��;9;>�U�R�ZD9�OXu�OQR"9;d �,[o<a<���9�GnRmRX[=dc9�õ�@SwJ[_rA9;I�G�rvG�<_fD9EUJT ð 0 6C1Z^f�O:R�ZD9�UAe/9;ID� <=USUAeMY+UAISR�>�Un<D[�OÛTVUAfDI�L\�Su�OXUJ<_rA[_IDw�[_IST�� ¼ ú á õ 2 ð 0 å�R�U�`�I�LcR�ZD9!rJG�<_fD9EUJT ð 0 �ZS[kY"Z�d�[_IS[_d�[_�;9&Oú á GJI�LhOXU�LS>Q[_rA9&O�R�ZD9�OQu�OXR�9;dèY"<_U^OQ9&OQR:R�UE�;9;>�U�GnR�RQ[_dh9�õEåH6�C1ZD9'd�[_IS[=d�[=�&GnRQ[_UAIh[kO1LSUAID9�Su�G û GJf�O"OQ� l 9;�'R�UAIdh9;R�ZDUDL�61öID9�OQR+GJ>�RHO:�1[_R�Z�GhY�ZDUSOQ9;I ð µ 0¥·0 @�GJI�Lc[_R�9;>HGnR�9&OGAO:TVUJ<a<_UJ�!O <

M ð µ � � ^ ·0 R N � M ð µ ��·0 R N [ M Ï ú á ð µ � ·0 å R N M Ï ? ú á ð µ � ·0 å R ])^ 2 á xsùSå�ZD9;>�9{Ï ú GJI�LBÏ ? ú Gn>�9ER�ZD9EwA>HGsLs[=9;ISR!GJI�L�B9&O"Ot[kGJI�UJT ú �1[_R�Z�>�9&OXe�9&Y+R�R�U ð 0 GJI�LMGn>�9EwJ[_rA9;I��Su

Ï ú á õ 2 ð µ � ·0 å � ²T³ �³ ð 0 á õ 2 ð µ ��·0 å ´ N � á õ 2 ð µ ��·0 å 2Ï ? ú á õ 2 ð µ � ·0 å � ²T³ �³ ð 0 á õ 2 ð µ ��·0 å ´ N ²T³ �³ ð 0 á õ 2 ð µ ��·0 å ´ ��� N á õ 2 ð µ � ·0 å ³ ? �³ ð ?0 á õ 2 ð µ ��·0 å eX UA>!G�OQfSî�Y"[=9;ISRQ<_uõY"<_U^OX9�[=IS[_RQ[kG�<�[_R�9;>+GJR�9A@SR�ZD9ER�9;>�d ³ ? � ä ³ ð ?0 [kOGsO�OQfDdh9&L\rA9;>"u�OQd\G�<a<�@�OQU�[_R[kO:[_wAIDUs>�9&L�6mC,ZS[�Odh9&GJI�O1R�Z�GnR á xAùSå��/9&Y+UAdh9&O

ÔsÔ

M ð µ � � ^ ·0 R N � M ð µ ��·0 R N [�� N ³ �³ ð 0 � ³ � N³ ð 0 ³ �³ ð 0 � ])^ eC1ZS[kO�[_R�9;>HGJRX[=UsIçeD>�UDY+9&O�OE>�9&æsfS[_>�9&OE�/UAR�Z � GnI�L ³ � ä ³ ð 0 GnRER�ZD9�`�I�G�<�RQ[_dh9�õ�6hC1ZD9�rvG�<_fD9\UJT � Y;GJI���9T�UAfDI�L�Ot[_dheS<_u��Su�OQUJ<_rs[_IDw�R�ZD9B�GJd�[a<_R�UAIS[kGJI�OQuDOQR�9;d á x ý å�TVUA>��GJ>HL�R"U@õ�@AOQRHGJ>"RQ[_IDwTV>�UAd%R�ZD9:[_IS[=RX[�Gv<ÜY+UAI�Ls[_RQ[_UAI�(0@� á 1032 ð 0 å N 6�C1ZD9Ee�GJ>�RQ[kG�<�LS9;>Q[_rvGJRX[=rs9&OY;GJI\��9�TVUAfDI�Lc[_I�R�ZD9�TVUJ<a<_UJ�1[_IDw��G�uA64�VT�R"ZD9�B�GJd�[a<_R�UAIS[kGJI�OQu�OXR�9;d

[�O �Q� ° ����� á � å+@^�,[=R"Z �(0�� á 10I2 ð 0 å N @SR�ZD9;I�Ls[oé�9;>�9;ISRQ[kGJRQ[_IDw\�1[_R�Z�>�9&OQe/9&Y+R!R"U ð 0 eD>�U�LSf�Y+9&O� ! " ## ò ¸%$¸ � ¼ � M ° � ¸'&¸�$ á � å R ¸�$¸ � ¼¸%$¸ � ¼ á ý å � � ýÛ � e� L�ßQUJ[_IS[_IDw�R�ZS[kO:R�U�R�ZD9EB!Gnd�[a<=R"UAIS[kGJIMOQuDOQR�9;d÷>�9&OQfS<_RHOÛ[_IMG�xIA á A � Ô åjLs[_dh9;I�Ot[_UAI�G�<�OQuDOQR�9;dÞUJT�ö g ÿ�O:R�U���9OQUJ<_rA9&L�UsIçã ý 2 õ ä 6

��IçR�ZD9cdh9;R�ZDUDL�UJT,i�GJ>"N^d�GnI�GnI�L��EGnR��hR�ZD9hd�[=IS[_d�[_�&GJRX[=UsI¹UJT ú á õ 2 ð 0 åUvrs9;> ð 0 [�O�GAY+R�f�G�<a<_u¹Y;GJ>">Q[_9&LUAfDR�T�Us>�G\OQ9&æsfD9;I�Y+9hUJTmRX[=dc9�rJG�<_fD9&O@õô[_I�Y+>�9&GAOt[_IDwMR"Uv�GJ>+L\[_IS`�IS[_R�uA6�C1ZS[kO�>�9&OQfS<_RHO'[_I¹G�OX9&æAfD9;I�Y+9hUnT�rvG�<_fD9&OT�UA> ð 0 �ZS[kY�Z�Y+UAISrA9;>�wA9EUAI�R"ZD9�`�I�G�<�rvGv<=fD9hGAO,R�ZD9�`�IS[_R�9;�VRQ[_dh9�eD>�UA�S<_9;d�O'wA9;R!Y"<_U^OQ9;>�R�U�R�ZD9�GAY+R�f�G�<�[_IS`�IS[_R�9;�RQ[_dh9�eD>�UA�S<_9;dM6!C,ZD9�OQUJ<_fDRQ[_UAI�UJT�R"ZD9�B�GJd�[a<_R�UAIS[kGJIçOQuDOQR�9;dówA9;ID9;>HGJR�9&Lp�^u�R"ZD9�`�I�Gv< ð 0 [_I�R�ZD9�OQ9&æAfD9;I�Y+9�[�OR�ZD9;Içf�OQ9&L]R�U�UA�DRHGv[=I]R�ZD9�LS9&Ot[_>�9&L�Y+UAISR�>�UJ< � á-, åH6hC1ZS[kO�eD>�UDY+9&O�O�[kO�[_dhe/UA>�RHGnI^RE�/9&Y;GJf�OQ9\rvG�<_fD9&O�UJT ð 0 9&GJ>Q<_u[=I�R"ZD9MOQ9&æAfD9;I�Y+9�d\G&u]IDUAR���9�rA9;>�u]wAU^UDL�@�GJI�L�d\G&uçY;GJf�OX9�R�ZD9�OXu�OQR"9;d R"Uõ�S<_UJ�÷fDe�[aTVõÞ[kOhY"ZDU^OQ9;I�R�USU<�Gn>�wA9A6�5AR+GJ>�RQ[_IDw��1[_R�Z GçOQd\G�<a<Àõ*GJI�L][_I�Y+>�9&GsOt[_IDwç[_R�TV>�UAd R�ZD9;>�9\ZD9+<_e�OhR"U�G�rAUn[�L]R�ZS[kO;6���R�[kOhG�<kOQU]f�OQ9+T�fS<[=I�OQZDUJ�1[_IDwMR"Z�GJR�R�ZD9crvG�<_fD9&O�UJT ð 0 �ZS[kY"Z Gn>�9�T�UAfDI�L�GAY+R�f�Gv<o<_u¹Gn>�9�Y+UAISrA9;>�wJ[_IDw�GAO�õ = ( 6�C1ZD9\C���8��dh9;R�ZDUDLçLS9&O�Y+>Q[_��9&L][_Iþ5A9&Y+RQ[_UAI�ùD6ÍúMLSUS9&O�IDUsREID9;9&LçR�U���9�OXUJ<_rA9&L�TVUA>�G�OQ9&æAfD9;I�Y+9\UJT1`�I�G�<�RQ[_dh9&O�@��/9&Y;GJf�OQ9R�ZD9;>�9E[kO1IDU\R�ZD>�9&GnRmUnTjR�ZD9�eD>�UA�S<_9;dó�S<=UJ�1[_IDw\fDe�6mB'UJ�19;rA9;>&@s[_R!Y+UAfS<kL���9�f�OX9+T�fS< á R�ZDUAfDwAZ�RQ[_dh9;��Y+UsI�OQfDd�[_IDwDåR�U�LSU�R�ZS[kO:R�U�d\GJNA9EY+9;>�RHG�[_I\R�Z�GJRoõþZ�GAO:IDUAR��/9;9;IMY�ZDUSOQ9;I�R"U^U�OQd�G�<a<�R�U�wn[=rs9�G�wAU^UDL\GJeDeD>�U�à^[_d�GnRQ[_UAI�UnTÜR"ZD9[=IS`�IS[_R�9;�VRX[=dc9heD>�UA�S<_9;dM6

C1ZD9�[_IS[_RQ[kG�<ErvG�<_fD9�UJT ð 0 Y;GnI ��9MY"ZDU^OQ9;I T�>"UAd R�ZD9�<a[_ID9&GJ>�æAf�GALS>+GJRQ[kY�>�9;wsfS<�GnR�UA>heD>�Us�S<=9;d�6 C1Z�GJR�[kO;@ð µ 0¾·0 � x _ H0 �'ZD9;>�9 _ [kO�R�ZD9hOQUJ<_fDRQ[_UAIçR�U\R�ZD9hG�<_wA9;�D>HGv[�Y�W:[kY;Y;GJRX[m9&æsf�GJRQ[_UAI�6 X UA>�OXfD��OQ9&æAfD9;ISR�rJG�<_fD9&OEUJToõ[=I]R�ZD9�OQ9&æsfD9;I�Y+9hR�ZD9heD>"9;rA[_UAf�O�`�I�G�<�[_R�9;>HGJR�9hY;GJI��/9hf�OQ9&LçGAO�R"ZD9�ID9;� [_IS[=RX[�Gv<�[_R�9;>HGJR"9A6�C1ZD9�[=ISR�9;>�e/UJ<kGJRQ[_UAIUJTmR�ZD9�UAe/9;ID� <_U^UAe�Y+UAISR�>�UJ<kOEY;GJI]��9�Y;GJ>">Q[_9&LMUsfDR�[=I]R�ZD9�O�GJdc9��G�uMGAOELS9&O�Y+>X[=�/9&L�[_IçR"ZD9heD>�9;rs[=Usf�O�OQ9&Y+RQ[_UAI�@f�Ot[_IDw�R�ZD9�OXe�9&Y"[a`�9&L û >"9;9;IP�£O:TVfDI�Y+RQ[_UAI�O�,[=R"Z)� � ù e y^6

� O:�1[_R�Z�R�ZD9�eD>�9;rs[_UAf�O1dh9;R�ZDUDL�@DR�ZD9'[_I^R"9;>�e�UJ<kGJRX[=UsI�d�GJNA9&O:R�ZD9EY;G�<kY+fS<kGJRQ[_UAIMUnT�R�ZS[kO:TV9;9&LS��GAY�N\Y+UAI^R">�UJ<ÜGrA9;>�uhRQ[_dh9;��Y+UsI�OQfDd�[_IDwheD>�UDY+9&O�O;6�B'Uv�19;rA9;>�@AR�ZD9'[_R�9;>HGJRQ[_rA9�dh9;R�ZDUDLcUJT�`�I�Ls[=IDwcR�ZD9!Use�9;ID� <_U^UseMY+UAI^R">�UJ<bOQZDUAfS<kL��9�OXUAdh9;�Z�GJR:T�GAOQR�9;>1R�Z�GnI�R�ZD9�Ls[kO�Y+>�9;RQ[_�;9&L�C���8��%eD>�UA�S<_9;døGAO1R�ZD9EeD>�Us�S<=9;døLs[_dh9;I�Ot[_UAIp[=I�Y+>"9&GAOQ9&O;6:��R!Y;GnIG�<kOQUh��9E>"9+`�ID9&L��Su�GALDLs[_IDwhdcUA>�9�[_I^R"9;>�e�UJ<kGJRX[=UsI�e�UJ[_ISRHO1[_I�R�ZD9�O"GJdh9��,G�u�GsO1R�ZD9�eD>�9;rA[_UAf�O'dh9;R�ZDUDL�6�C1ZD9;>"9[�O,IDU�OQR�>X[�Y+R:<a[_d�[_RUAI\R�ZD9�R�uSe�9&O:UJT�eD>�Us�S<=9;d R�U��ZS[kY"Z\[_R,Y;GnI��/9�GJeDeS<a[_9&L�@/�DfDR,GsO��,[=R"Z�R�ZD9�5 û � dh9;R"ZDU�L\UJT5A9&Y+RQ[_UAIõùD6ñùD@SR�ZD9�e/9;>QT�Us>�d�GJI�Y+9EUJT�R�ZS[kO'dh9;R�ZDUDLMLS9;e�9;I�LDO'[_I�GJI�9&O�OQ9;ISRQ[kG�<��G�u�UsI�R�ZD9�Y�ZDUn[�Y+9�UJT�R�ZD9�[_IS[_RQ[kG�<[=R"9;>HGJR�9A6ê���}�|�|! Ý �J�D�&Ý_ØF×��;Øcë�"����T����Øb~� r"%$ç�

��IçR�ZS[kOEOQ9&Y+RX[=UsIç�19��,[o<a<mY+UAdce�GJ>�9�R�ZD9�e�9;>QTVUA>�d\GJI�Y+9hUJT�R�ZD9�`�rA9cdh9;R�ZDUDLDOELs[�O"Y+f�O�OQ9&L�[_IçR�ZD9�eD>�9;rs[_UAf�OOQ9&Y+RQ[_UAIhUAIhOQ9;rs9;>HG�<�R�9&OQR49+à�GJdheS<_9&O;6`�ç91�1[a<a<ÜY+UsI�Ot[kLS9;>�R�ZD9+[_>mY+UsI^R�>"UJ< GnfDR�ZDUA>Q[_RQu á [�6Í9A6�@JR�ZD9GJ�S[a<o[_RQuhR�UELS>Q[_rA9R"ZD9OQRHGJR�9&O,R�Uh�;9;>�UDå+@DR�ZD9�GndhUAfDISRUJT�Y+UAI^R">�UJ<�f�OQ9&L�@/R�ZD9EUJrA9;>HGv<o<�Y+U^OQRUJT�R"ZD9Edh9;R�ZDUDLDO;@bGnI�L�R�ZD9�Y+UAdheDfDRHGJRX[=UsI�G�<

Ô x

RQ[_dh9�GJI�L���UAe�O á ��U^GJRQ[_IDw\e�UJ[_ISR!Use�9;>HGJRX[=UsI�O+åmf�OX9&L�6 � <o<�Y+UAdheDfDR+GJRQ[_UAI�O1�19;>�9�LSUAID9�f�Ot[_IDwMY+UDLS9&O�'>Q[_R�R�9;I�[_Ii � C ë � 8�@S[_dheS<_9;dh9;ISR�9&L�UAI�Gh5AfDI�q1<_R�>+Gh|D6

��Ic[=dceS<=9;dc9;I^RQ[_IDwh�tR�U�GJI�Lp5^Y�ZD>"U^9;R�9;>º�£O�C���8��òeD>�UA�S<_9;d÷dh9;R�ZDUDL�@AR"ZD91[_R�9;>HGJRQ[_UAIceD>�U�Y+9&O"O��GAO4>"fDIhfDI^RX[o<� ú �+* Ô�ý ]-, 6�C,ZD9�i�GJ>�NSd�GJI�GJI�L��EGJR���[_R�9;>HGJRQ[_rA9Edc9;R�ZDU�L\�GAO'Y+fDRUJéç�ZD9;I ��� È á õ�å [.� È ])^ á õEå �/* Ô&ý ]-, @T�UA>19&GAY"Ztõ�@�GJI�L ��� á õ � å [�� á õ � ])^ å �/* Ô&ý ]-, [_IMR�ZD9EOQ9&æsfD9;I�Y+9�UJT!õòrJG�<_fD9&O;6mC,ZD9Ee�GJ>�RQ[kY+fS<kGJ>!OQ9&æsfD9;I�Y+9EUJT!õrvG�<_fD9&O:f�OQ9&L�rvGJ>X[=9&O:GJdhUAIDwER"ZD9mR"9&OQR�eD>�UA�S<_9;d�O;@SGAO�LSUER�ZD9!Ls[kO�Y+>"9;RQ[_�&GJRQ[_UAI�[_ISR�9;>�rvGv< ¡ , GnI�L�`�I�G�<�RQ[_dh9¤õ f�OX9&L[=I�R�ZD9�C���8��ïeD>�Us�S<=9;dódh9;R�ZDUDL�6 � IDUAR�ZD9;>�e�GJ>HGJdh9;R"9;>R�Z�GJR�rvGJ>X[=9&O,[kO�R�ZD9�>"9;wJ[_UAI 5 UJrA9;>'�ZS[kY�Z�R�ZD9c5 û �dh9;R�ZDUDL�[_ISR�9;wA>HGJR"9&O�GJI�L]R�ZD9�C���8��*GJI�L]��R�9;>HGnRQ[_rA9hdh9;R�ZDUDLDO�[_I^R�9;>"e�UJ<kGJR�9 á R�ZD9hISfDd��/9;>�UJT1[=ISR�9;>�e/UJ<kGJRQ[_UAIe�UJ[_ISRHOf�OX9&L�rvGn>Q[_9&OGAO1�19+<a<VåH6ê�� Õ ����}��w$6|� r" Õ

C1ZD9`�>+OQR19+à GJdceS<=9�[kOLS9&O"Y+>Q[_��9&L��Su�7�<_UAfDRX[=9;>�@ g �=5AUAfD�&GD@DGJI�L\iM>+GAY+9;N�[=IçãñùAx ä @DGJI�L�Y+UsI^RHGv[=I�O:RQ�1U�OQR+GJR�9rvGJ>Q[kGJ�S<_9&OEGJI�LpRQ�mUhY+UAISR�>�Un<ÜrJGJ>Q[kGJ�S<_9&O;6�C1ZD9�OQuDOQR�9;d�@D�ZS[kY�Z�Z�GAO�Y+fD�S[�Y�IDUAIS<a[_ID9&GJ>Q[_RQ[_9&O�[=I�9&GAY"ZM9&æsf�GJRQ[_UAI�@ [�OwJ[_rA9;IM�Su 0 ^ ?�1 �

0 ^ [6 K ^ �� ? ^ �c ?^ ? [� ?21 �0Ô ýý Ô 1

0 � ^� ?�1 e�ç9�T�GsY+R�UA>R�ZD9EIDUsIS<o[_ID9&GJ>�TVfDI�Y+RQ[_UAI . á å �K� á å �^u. á å � 0Ô [� ?^ ÔÔ ?^ [ Ô 1

0 ^ ? 1T�UA>\R�ZD9�5 g Wÿ÷dc9;R�ZDU�L�6 X UA>\R�ZD9�eD>�UA�S<_9;dM@'�m9�f�OQ9&LþR�ZD9�[_IS[_RQ[kG�<�Y+UsI�Ls[=RX[=UsI 10c� á Ô 2 Ô å N 6èC,ZD9�Y+USOQRT�fDI�Y+RQ[_UAI�Gv<jR�U��/9�d�[_IS[_d�[_�;9&L�[kOG á 10I2 � å � J*L0 � 1N 0 ^ ? ý

ý ^ ? 1 Q� � N0Ô ýý Ô 1 � � S , eX UA>hR"ZD9õC��:8o�ødc9;R�ZDU�L�@1UsfD>�Y;G�<kY+fS<kGJRQ[_UAI�Opf�OQ9&L ¡ , � ý1e£ý |çGJI�L�R"ZD9�`�I�G�<!RX[=dc9Fõ � | e xA|D6 X UA>hR"ZD9

[=R"9;>HGJRQ[_rA9�dh9;R�ZDUDL�@DR�ZD9�OX9&æAfD9;I�Y+9�UJT`õ rvGv<=fD9&O��GAO'OQRHGJ>�R"9&L�GJRZõ 0�� ÔIe£ý GnI�L\[_I�Y+>�9&GAOQ9&Lp�^u�9&æsf�G�<a<_uõOQe�GsY+9&LRQ[_dh9�[=ISR�9;>�rJG�<kOEUJT ¡ õ � ý1e xA| 6�C,ZD9�>�9;wJ[_UAI 58� ã [ Ô 2 Ô;ä C ã [ Ô 2 Ô;ä @�GJI�L Ô�ýAý � Ô&ý C Ô&ý >�9;wAfS<kGJ>X<=uçOQe�GsY+9&L[=ISR�9;>�e/UJ<kGJRQ[_UAI�e�UJ[_ISRHO�19;>�9Ef�OX9&L�6X [=wsfD>�9 Ô OQZDUJ�!O �(3� T�Us>�R�ZD9�`�rA9�TV9;9&LS��GAY"N Y+UAI^R">�UJ<kO�LS9&O�Y+>Q[_��9&L%9&Gn>Q<a[=9;>�@�GJI�L G�<kOQU T�Us>�R�ZD9�UAe�9;ID�<=USUAeçY+UAISR�>�UJ<FT�UAfDI�Lpf�Ot[_IDw�R�ZD9hLs[kO�Y+>�9;RQ[_�;9&L�RQ�1Uhe�Un[=ISR���UAfDI�LDGJ>"uMrvGv<=fD9�eD>�Us�S<=9;d GneDeD>�U^GAY"Z�TVUA>�R�ZD9E[_IS[_RQ[kG�<Y+UAI�Ls[_RQ[_UAI 10 6 � <a<�UJT�R�ZD9&OQ9�>�9&OQfS<_RHOEGn>�9�9+à�R�>"9;dh9+<_uõY"<_U^OQ9�R�U\9&GAY"ZõUsR�ZD9;>&@/�1[_R�Z�R�ZD9hC���8��è��GsOQ9&L�dh9;R�ZDUDLe�9;>QTVUA>�d�[_IDw�Ot<a[=wsZ^RQ<_uh�/9;R�R�9;>&@AGnI�L�R�ZD9E5 û � dh9;R�ZDUDL�e/9;>QT�Us>�d�[_IDw�Ot<a[_wAZSRQ<_uh�1UA>HOQ9A64C1ZD9IDUA>"d�O4UJTbR"ZD9,Y+UsI^R�>"UJ<� � � GJ>�9�OQZDUJ�I�[=I X [_wAfD>�9�x�T�Us>�G�<a<�`�rs9hdh9;R�ZDUDLDO;6�C1ZD9;>�9�GJ>�9hUsIS<=uçOQd\G�<a<,Ls[aé�9;>�9;I�Y+9&O���9;RQ�19;9;IçdhUSOQR�UJTR�ZD9�dh9;R"ZDU�LDO;@ �1[_R�ZMR�ZD9�Y"<_9&GJ>!9+à�Y+9;eDRQ[_UAI���9+[_IDw�R�ZD9h5 û � dc9;R�ZDU�L�@/�ZS[kY"ZM>�9&æsfS[_>�9&OID9&Gn>Q<_u�R��,[�Y+9�GAO1d�f�Y"ZY+UAI^R">�UJ<�[_IS[=RX[�Gv<o<_uA6

C1ZD9hRQ[_dh9�GnI�L���UAe�OE>"9&æAfS[_>�9&L�T�Us>E9&GAY�Z�T�9;9&LS��GAY"NçY+UAISR�>�UJ<�@�Gv<=UsIDw��1[_R�Z¹9&GsY�Z�UJTR�ZD9+[_>�rJG�<_fD9&O�T�UA>ER"ZD9Y+U^OQR:T�fDI�Y+RX[=UsI�G�< G á 10I2 � åH@SGJ>�9'<o[kOQR"9&Lc[=I�C�Gn�S<=9 Ô 6jCFUhY+UAdhe�GJ>"9A@^R"ZD9EUAe�9;ID� <_USUAeõY+UAISR�>�Un<ÜY+U^OQR:[kO1ú�6=yv{AzA|D@AGnI�LR�ZD9<a[_ID9&GJ>Y+UAISR�>�UJ< á �ZS[kY�Z�G�<kOQUhOQf�Y;Y+9;9&LDOÛ[_IMLS>Q[_rA[_IDw�R�ZD9�eD>�UA�S<_9;d÷R�U��;9;>�U�[_I�R�ZS[kO�9+à�GJdheS<_9Jå�Y+U^OQR�[kO:ú�6ayJü Ô&ý 6C1ZD9!Y+U^OQR+O�GJ>�9!G�<a<�rA9;>�u�O�[=d�[o<kGJ> á 9+à�Y+9;eDR5 û � å+@JrvGJ>�us[_IDw��^u�UAIS<_uhGJ��UsfDR ý 6£|54 GJdcUAIDw�R�ZD9;d\OQ9+<_rA9&O;@^GnR�GJ��UAfDR|64ï<_9&O�O�R�Z�GJI�R"ZD9E<a[_ID9&GJ>�Y+UAISR�>�UJ<�61C1ZD9�Y+UAdceDfDRHGJRQ[_UAI�G�<4RQ[_dh9ETVUA>!C��:8��èGJI�L��tR�9;>&@ [=ISrAUJ<_rs[_IDw�R�ZD9�OQUJ<_fDRQ[_UAI

Ô ù

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

Time

Nor

m(x

)

HJB SDRE SGA TPBV IterativeOpen−Loop

X [_wAfD>�9 Ô < 7:UAdhe�GJ>Q[kOQUsI�UJTjR"ZD9EIDUA>�d�O1UnT�TV9;9&LS��GAY"NMY+UAI^R">�UJ<a<_9&L�R�>HGnß�9&Y+R"UA>Q[_9&OÛ[=I�ÿ4à�GJdheS<_9 Ô 6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

Time

Nor

m(u

)

HJB SDRE SGA TPBV IterativeOpen−Loop

X [_wAfD>�9�x < 7:UAdhe�GJ>Q[kOQUsI�UJTjR"ZD9EIDUA>�d�O1UnT�TV9;9&LS��GAY"N�Y+UAISR�>�Un<�Om[=I�ÿ4à�GJdheS<_9 Ô 6UJTjd\GJI^u\UAe/9;ID� <=USUAe�eD>�UA�S<_9;d�O;@ [kOd�f�Y"Z\<�Gn>�wA9;>R�Z�GnI�R�Z�GJRUJT�B ð 8òGJI�L�5 g Wÿ'6�C1ZD9c5 û � Y+UAdheDfDRHGJRX[=UsI�G�<RQ[_dh9�[�O'[_I���9;RQ�19;9;I�R�ZD9&OQ9�9+àDR�>�9;dh9&O;@/�DfDR�[kOEOQRQ[a<a<�d�f�Y�Z�<_9&O�O�R�Z�GJI�R�ZD9�[_I^R�9;>"e�UJ<kGJRQ[_UAI�dh9;R"ZDU�LDO;6EB'UJ�m9;rs9;>&@R�ZD9!9+àDe�9;I�O�[=rs9�Y+UAdheDfDR+GJRQ[_UAI�O�UnT�5 û � @^C��:8�� GJI�Lc��R�9;>GJ>�9�G�<a<FLSUsID9!UJé�� <a[_ID9A@�OQU�R�ZD9;u�Y+UsfS<�Lc��9E>"fDI�GJwSG�[_IrA9;>�u�æsfS[�Y"Ns<=u��1[_R�ZhG�Ls[aéÜ9;>"9;I^R H0 [aTÜOQUELS9&Ot[_>�9&L�6 X UA>4R�ZS[kO4eD>�UA�S<_9;dïR�ZD9��/9&OQR�Y"ZDUJ[kY+9mUnTbdh9;R�ZDUDLSUJ<_UAwAu�GneDe�9&GJ>HO

Ô ú

7¤��q%C:[_dh9 á OX9&YJ6aå X <=Use�O 7�USOQRB ð 8 ý 6 Ô | ú e y Ô C Ô&ý P ú�6ñzA{AüA|5 g W'ÿ ý 6£x Ô ú e üA{�C Ô&ý P ú�6ñzA{AxA{5 û � Ô 6£|Ax ÔIe zA{�C Ô&ý87 Ô yS6£|Aù ý {CZ��8�� úsú^üD6Íú^z ÔIe zAx�C Ô&ý ^ 0 ú�6ñzAü ý {�tR�9;> {�y&ú�6£üA{ x e xAü�C Ô&ý89 ú�6ñzSyvzAü

C�Gn�S<=9 Ô <�l fDdh9;>Q[kY;G�<jY+Usdhe�GJ>Q[kOQUAI�UJT�TV9;9&LS��GAY"NMY+UAI^R">�UJ<�dh9;R�ZDUDLSUJ<_UAwJ[_9&O,[=I�ÿ4à�GJdheS<_9 Ô 6R�UM�/9�B ð 8ïUs>h5 g Wÿ < R"ZD9;u�GsY�ZS[_9;rA9\>�9&OQfS<_RHO�rs[=>"R�f�G�<a<_u GAO�wAUSU�LçGsO�GJISu�UAR�ZD9;>�dh9;R�ZDUDL�@�GJI�LçLSUçOQUM�,[=R"Zd�[_IS[=d\G�<ÛY+UsdheDfDRHGJRQ[_UAI�6ê�� � ����}��w$6|� r" �

C1ZD9�OQ9&Y+UAI�L]9+à�GJdheS<_9��19�Y"ZDU^OQ9cR�U�R�9&OQRER�ZD9\rvGn>Q[_UAf�O�TV9;9&LS��GAY"N�Y+UsI^R�>"UJ<�dh9;R�ZDUDLDO�[kO�T�>"UAd i�GJ>�NSd�GJIGJI�L:�EGJR���ã£x ýJä 6E��REZ�GAO�RQ�1U�OQRHGJR�9�rvGJ>X[�Gn�S<=9&O�GJI�L�UAID9hY+UAISR�>�Un<jrJGJ>Q[kGJ�S<_9A@�GJI�L�Z�GAOEG�Y+fD�S[kYcIDUAIS<a[_ID9&GJ>Q[_RQuM[_IR�ZD9�OQuDOQR�9;dM@D�'ZS[�Y"Z�[kO�LS9+`�ID9&L��Su 0 ^ ?21 �

0 ? K ^ 1 �0ýÔ 1 � e

C1ZD9ETVfDI�Y+RQ[_UAI . á å4[�O'>�9;�>X[=R"R�9;IMGAO . á å � 0ý Ô ?^ ý 1

0 ^ ?21T�UA>1R�ZD9�5 g W'ÿ�dh9;R�ZDUDL�6�C1ZD9�[_IS[_RQ[kG�<�Y+UAI�Ls[_RQ[_UAI�[kO 0 � á Ô 2 ý å N GnI�L\R�ZD9�Y+U^OQR:TVfDI�Y+RQ[_UAI�G�<�R�U��/9�d�[_IS[_d�[_�;9&L[�O G á 10I2 � å � J L0 � N 0 ^ ? ý

ý ^? 1 Q� Ôx � ? � S , eX UA>R"ZS[�O,9+à GJdceS<=9A@ [_IMR�ZD9�CZ��8�� dc9;R�ZDU�L\�19Ef�OQ9&L ¡ , � ýHe£ý |�GJI�Ltõ � y e | ý 6 X UA>'R�ZD9�[_R�9;>HGJRQ[_rA9Edc9;R�ZDU�L�@õ 0d� ÔIe£ý GnI�L ¡ õ � ý1e |D6�C1ZD9MO�GJdh9c>�9;wJ[_UAI 5 � ã [ Ô 2 Ô;ä C ã [ Ô 2 Ô;ä GAO�[_I ÿ4à�GJdheS<_9 Ô �GAO�f�OQ9&L�@��,[=R"Z

Ô&ýAý � Ô&ý C Ô&ý [_I^R"9;>�e�UJ<kGJRX[=UsIMe�Un[=ISRHO;6X [=wsfD>�9hùhLS9;eS[kY+RHOER�ZD9�OQRHGJR"9 ^ GnI�L X [_wAfD>"9�ú�Ls[�OXeS<�G�uDO�R�ZD9�Y+UsI^R�>"UJ< � T�Us>�G�<a<4`�rA9�Y+UsI^R�>"UJ<�dh9;R�ZDUDLDO;6C1ZD9h5 û � dh9;R�ZDUDL�[_R�9;>+GJRQ[_UAI�O'ID9;rA9;>�GsY+R�f�G�<a<_uõY+UAISrA9;>�wA9&LpR�U�G�`�I�G�<jY+UAISR�>�Un<��/R�ZD9�UAID9�OQZDUJ�I�ZD9;>�9 á �ZS[kY"ZLSU^9&O'TVUA>HY+9�R�ZD9�OQu�OXR�9;døR�U\�;9;>�UDå:[�O�R+GJNA9;IõGvT�R�9;>EGJI�[_R�9;>HGJRX[=UsIõISfDd���9;>ER�>"fDI�Y;GJRQ[_UAI�6���R�Y;GJI��/9�OX9;9;I�[_IõR"ZD9`�wAfD>�9&O'R�Z�GJR�R�ZD9E[_ISR�9;>�e�Un<�GnRQ[_UAI�dh9;R�ZDUDLDOELS>Q[_rA9�R�ZD9�OQRHGJR"9&OR�Uc�;9;>�U�O�<o[_wAZSRQ<_uMdcUA>�9�O�<=UJ�1<_u�R�Z�GJIMR"ZD9h5 g WÿGJI�LMB ð 8þdh9;R�ZDUDLDO;@D�DfDR�R�ZD9�5 g WÿþGJI�LMB ð 8òdh9;R"ZDU�LDO1>"9&æAfS[_>�9�dhUA>�9�Y+UAISR�>�Un<ÜR"U�GsY�ZS[_9;rA9�R�ZS[kO;6

C�GJ�S<_9Mx�Y+UAI^R+G�[_I�O�R"ZD9hRQ[_dh9�GJI�L*��Use�O�>"9&æAfS[_>�9&L�GJI�L�Y+U^OQRETVUA>�9&GAY�Z�Y+UAISR�>�UJ<�dc9;R�ZDU�L�6�C�UçY+UAdhe�Gn>�9A@R�ZD9hUAe/9;ID� <=USUAe Y+UAISR�>�Un<mY+U^OQR�[kO Ô 6£|AzAxnú�6 X UA>�R"ZS[�O�9+à GndheS<_9�R�ZD9�<o[_ID9&GJ>\Y+UAI^R">�UJ<4T�G�[a<kO�R�UM�D>X[=IDw�R�ZD9�OQu�OXR�9;dR�U��;9;>�U�6�C,ZD9�Y+USOQRHO�GJ>�9hOt[_d�[a<kGJ> á Gnw^G�[_I��1[_R�Z�R�ZD9�9+à Y+9;eDRQ[_UAI�UJT5 û � åH@/�DfDR�IDUsR�GAOEY"<_U^OX9�GAO,T�UA>�ÿjà GndheS<_9Ô 6�C,ZD9;uõrJGJ>�u��^u�GJ��UAfDR�|54 GJdhUAIDw�R�ZD9;d\OQ9+<_rA9&O;@�GnI�LõGn>�9�9+éÜ9&Y+RX[=rs9h�ZD9;IçR�ZD9�<a[_ID9&GJ>hY+UAISR�>�UJ<4T�Gv[o<kO;6hC,ZD9

Ô |

0 1 2 3 4 5 6 7 8 9 10−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time

Sta

te x

1

HJB SDRE SGA TPBV IterativeOpen−Loop

X [_wAfD>�9�ù < 7�UAdhe�GJ>X[�OXUAI�UJT4T�9;9&LS��GAY"NMY+UAISR�>�UJ<a<_9&LMOXRHGJR�9&O ^ [_I�ÿ4à�GJdheS<_9�xD6

0 1 2 3 4 5 6 7 8 9 10−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

Time

Con

trol

u

HJB SDRE SGA TPBV IterativeOpen−LoopX [_wAfD>"9Eú < 7�UAdce�GJ>Q[kOQUAI\UJT4T�9;9&LS��GAY"NMY+UAISR�>�UJ<kO:[_I�ÿ4à�GJdheS<_9�xD6

Ô z

7 �:q Cm[=dc9 á OQ9&YJ6aå X <_UAe�O 7�U^OQRB ð 8 ý 6ñxA| ü e úSù�C Ô&ý P Ô 6£| ý xsü5 g Wÿ ý 6ñù ý { e xsz�C Ô&ý P Ô 6£|AzAxs{5 û � xD6 Ô { x e_Ô�ý C Ô&ý87 |D6£|A{Aùs|C��:8�� Ô ú Ô ùD6£ù ú e { ý C Ô&ý ^ 0 Ô 6Íú^üAz�y�tR�9;> Ô&ý zA|D6£{ x e ú yVC Ô&ý89 Ô 6Íú^üJúSx

C�Gn�S<=9�x <�l fDdh9;>Q[kY;G�<jY+Usdhe�GJ>Q[kOQUAI�UJT�TV9;9&LS��GAY"NMY+UAI^R">�UJ<�dh9;R�ZDUDLSUJ<_UAwJ[_9&O,[=I�ÿ4à�GJdheS<_9�x 6Y+UAdheDfDRHGJRX[=UsI�G�<bRQ[_dh9&O:GJ>�9rs9;>�u�d�f�Y"Z�<a[_NA9ER�ZDU^OX91[_I�ÿjà GJdceS<=9 Ô @A�1[_R�Z\R�ZD9RX[=dc9&O�TVUA>�C��:8�� GnI�Lh�tR�9;>mGJwSG�[_Id�f�Y"Z�<kGJ>�wA9;>ER�Z�GnIMR�ZDU^OX9�TVUA>EB ð 8ïGJI�L]5 g Wÿ@�GJI�L]5 û � [=I]��9;RQ�19;9;I�6�C1ZD9���9&OQR�Y"ZDUJ[kY+9hUJTmY+UsI^R�>"UJ<jZD9;>"9d�[_wAZ^R:��9EB ð 8 < [_RHO�e/9;>QT�Us>�d�GJI�Y+91[kO:G�<_dhU^OQR1GAO4wAUSU�LhGsO�R�ZD91[_ISR�9;>�e/UJ<kGJRQ[_UAI\dh9;R�ZDUDLDO;@A�1[_R�ZDUsfDR�R�ZD91[_ISR�9;I�Ot[_rA9Y+UAdheDfDRHGJRX[=UsI�O;@�GJI�Lc[_RHO�Y+U^OQR:[kO1<_9&O�O'R�Z�GJI�R"Z�GJR1UJTm5 g W'ÿ6� [_R�Z\R�ZS[kO:9+à GndheS<_9E�m9�G�<kOQU�R�>Q[_9&Lhf�O�[=IDw\Ls[oé�9;>�9;ISR:[_IS[=RX[�Gv<jY+UAI�Ls[_RQ[_UAI�O1R�U�OQ9;9�ZDUv�þR�ZD9�rvGJ>Q[_UAf�O1Y+UAISR�>�Un<�O�mUsfS<�L]e�9;>XT�UA>"d �,[=R"Z OQR+GJ>�RQ[_IDw�e�UJ[_ISRHO�T�Gn>�R�ZD9;>�G��G�u�T�>�Usd R�ZD9\UA>Q[_wJ[_I�6��ç9�R"9&OQR���UAR�Z 10d� á x 2 ý å N GnI�L10�� á ú 2 ý å N 6 l UsR�9�R�Z�GnR��UAR"ZõUnTjR�ZD9&OX9�e/UJ[_I^R+O!GJ>"9�UAfDRHO�[�LS9�R�ZD9�>�9;wJ[_UAI 5 f�OQ9&LpTVUA>R�ZD9�[_I^R�9;>"e�UJ<kGJRQ[_UAI�O'[_IC���8���GnI�L��tR�9;>�GJI�L�R�ZD91[_ISR�9;wA>HGnRQ[_UAI�O�[_I�5 û � 6AC,Z^f�O;@AOXUAdh9:<_U^O�O4UJT�9+é�9&Y+RQ[_rA9;ID9&O�Oj[_IhR�ZD9&OQ91dh9;R�ZDUDLDO�OQZDUAfS<kL��919+à�e/9&Y+R�9&L�6�C1ZD9B ð 8�GJI�L�5 g Wÿ�dh9;R�ZDUDLDO�OQZDUAfS<kL�G�<kOQU�OXfSéÜ9;>�@AOt[_I�Y+9mR"ZD9+[=>�e/UJ�m9;>�OQ9;>Q[_9&O�GJeDeD>"U&àS[_d�GJRQ[_UAI�O�1[a<o<���9�<_9&O�O!GsY;Y+fD>HGJR�9�T�GJ>�R�ZD9;>G��G�u�T�>"UAd÷R�ZD9�9+àDe�GJI�Ot[_UAI�e�UJ[_ISRUJT�R�ZD9EUA>Q[_wJ[_I�6

��R�R"fD>�I�O�UAfDR:R�Z�GJR�R�ZD9�5 g Wÿ¹GnI�L\5 � û dh9;R�ZDUDLDO���UsR�Z�T�G�[a<bR�U�OQR+GJ�S[a<o[_�;9ER�ZD9�OQu�OXR�9;dM@JTVUA>�9&GAY"ZhUJT�R�ZD9&OX9[=IS[_RQ[kG�<�Y+UAI�Ls[_RQ[_UAI�O;6�C1ZD9�rvGv<=fD9EUnTÜR"ZD9�Y+U^OXR�TVfDI�Y+RQ[_UAI�G�< G TVUA>�R�ZD9�UAR�ZD9;>:R�ZD>�9;9�dh9;R�ZDUDLDO á GJI�L�R�ZD9�UAe/9;ID� <=USUAeY+UAI^R">�UJ<mY;G�<kY+fS<kGJR�9&L]R�ZD>�UAfDwsZõR"ZD9�C���8��÷eD>�UA�S<_9;d�å+@�TVUA>E��UAR"Z�[_IS[=RX[�Gv<'Y+UsI�Ls[=RX[=UsI�O;@�GJ>�9�Ls[kOQeS<kG�uA9&L�[=I�C�GJ�S<_9ùD6MC1ZD9�OQRHGJR"9 ^ GnI�L¹Y+UAISR�>�Un< � T�UA> 0 � á ú 2 ý å N GJ>�9hws>HGJeDZD9&L�[=I X [_wAfD>�9&O�|�GJI�LçzD6 C1ZD9\>�9&OQfS<_RHO�TVUA>

7:U^OQR:T�Us> á x 2 ý å N 7�U^OXR1T�Us> á ú 2 ý å NB ð 8 xsüD6 Ô { Ô ùJú ýC���8�� xs|D6ayvù x Ô y ý��R�9;> xszD6£{A| |Syvx ýöe�9;ID� ë USUAe x�y^6£zAz {AüAx

C4GJ�S<_9�ù <�X 9;9&LS��GAY"N�Y+UsI^R�>"UJ<�dh9;R�ZDUDLSUJ<_UAwJ[_9&O1[_I�ÿ4à�GJdheS<_9�x��,[=R"ZMGhLs[kOQRHGJISR1[_IS[_RQ[kG�<ÛOXRHGJR�9A6 0 � á x 2 ý å N GJ>"9IDUAR�R"U^U�Ls[oé�9;>�9;ISR:T�>"UAdïR�ZDU^OQ9'TVUA> 0 � á Ô 2 ý å N @SGJR�<_9&GAOQR:TVUA>�R"ZDU^OQ9dh9;R"ZDU�LDO:R�Z�GJR�Gn>�9�OXRQ[a<o<9+éÜ9&Y+RX[=rs9 < R�ZD9�Y+U^OQRLs[aé�9;>�9;I�Y+9&O'��9;RQ�19;9;I�R�ZD9ER�ZD>�9;9�TV9;9&LS��GAY"N�Y+UAISR�>�Un<�O'GJI�L\R�ZD9EUAe/9;ID� <=USUAe�Y+UAI^R">�UJ<b9+àDe�GJI�LOQUAdh9;�Z�GnR&@AfDe\R�U�ID9&GJ>Q<_u�G Ô&ý 4èLs[aéÜ9;>"9;I�Y+9E��9;RQ�19;9;I�R�ZD9;d�@^GJI�L\R�ZD9'UAe�9;ID� <_USUAeõY+UAISR�>�Un<D[�O,>�9+<kGJRQ[_rA9+<_u�dcUA>�99+éÜ9&Y+RX[=rs9mR"Z�GJI���9+TVUA>�9A6�BUJ�19;rA9;>&@�TVUA> H0@� á ú 2 ý å N R�ZD9;>"9,Gn>�9LS>HGJd�GJRX[�Y:Ls[aéÜ9;>"9;I�Y+9&O;6�C1ZD91UAe/9;ID� <=USUAe�Y+UsI^R�>"UJ<[�O�d�f�Y"Z¹dhUs>�9h9+é�9&Y+RQ[_rA9A@��ZS[kY"Zç[kO�9+àDe�9&Y+R�9&L�Ot[_I�Y+9\[_R�[kO��/9+[_IDw¹OQUJ<_rA9&L�T�Us>�R�ZS[kO�e�UJ[_ISRhOQe�9&Y"[a`bY;G�<a<_u >HGnR�ZD9;>R�Z�GJIçLS9;e�9;I�Ls[_IDw�UAIçGJI�[_I^R�9;>"e�UJ<kGJRQ[_UAI]>�9;wJ[_UAIçUA>�e�UJ�19;>�OQ9;>Q[_9&O�9+à�e�GJI�O�[=UsIõe/UJ[_I^R��ZS[kY�Z�[�O'T�GJ>�G��G�uA6�C,ZD9B ð 8 dh9;R�ZDUDLc[�O�G�<kOQU�OXZDUv�'I�R�Uc��9�d�f�Y"Z���9;R�R"9;>R�Z�GJIMC��:8�� á �'ZS[�Y"Z\[kO1[_I�R�fD>�I�d�f�Y�Z��/9;R�R�9;>R"Z�GJI���R�9;>�åH@[=I]R�9;>�d�O�UJTOQRHGJ�S[a<a[_�&GJRQ[_UAI�@�GJdhUsfDI^REUJTmY+UsI^R�>"UJ<�@�GJI�L�Y+U^OQR�6 X UA>!R"ZS[�O�9+à GndheS<_9�GJR�<_9&GAOQR&@FR�ZD9hB ð 8%dh9;R�ZDUDLeD>�U�LSf�Y+9&O'R�ZD9�TV9;9&LS��GAY"NMY+UAI^R">�UJ<�<_9&GAOQR!G�é�9&Y+R�9&L\�Su\R�ZD9�Y"ZDUJ[kY+9�UJT�GJI\[_IS[_RQ[kG�<�OQRHGJR�9EG��G&u�T�>�Usd R"ZD9�UA>Q[_wJ[_I�6

5J[=I�Y+9�R�ZD9ERQ�1UA�VR�9;>"d B ð 8òdh9;R�ZDUDL\e�9;>XT�UA>"dh9&L�rA9;>"uh�19+<o<4TVUA>1R�ZS[kO9+à�GJdheS<_9A@D�19�G�<kOQU�Y;Gv<�Y+fS<kGJR"9&LMdcUA>�9R�9;>�d�OÜ[_I�R"ZD9�e�UJ�19;>�OQ9;>Q[_9&O4R�U!OQ9;91ZDUJ�çd�f�Y"Z�[kOÜ<_U^OQR4�^u�>�9&OQR�>Q[kY+RQ[_IDw'[_R�R�URQ�1UR�9;>�d�O�6�C1ZS[kOF[kO�Y+UAdheS<a[kY;GJR�9&L�@SGAO

Ô y

0 1 2 3 4 5 6 7 8 9 10−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time

Sta

te x

1

HJB TPBV IterativeOpen−Loop

X [_wAfD>�9�| <`X 9;9&LS��GAY"NMY+UAISR�>�UJ<a<_9&LMOXRHGJR�9&O ^ [_I�ÿ4à�GJdheS<_9�x��,[=R"ZMGhLs[kOQRHGJISR1[_IS[_RQ[kG�<ÛOXRHGJR�9A6

0 1 2 3 4 5 6 7 8 9 10−160

−140

−120

−100

−80

−60

−40

−20

0

20

Time

Con

trol

u

HJB TPBV IterativeOpen−LoopX [_wAfD>�9�z <`X 9;9&LS��GAY"NMY+UAISR�>�UJ<kO:[_I�ÿ4à�GJdheS<_9�x��1[_R�Z�GhLs[kOQRHGJISR1[_IS[_RQ[kG�<ÛOXRHGJR�9A6

Ô ü

dh9;I^RX[=UsID9&L�[_I�5A9&Y+RQ[_UAIMùD6 Ô @J�DfDR:<_9&O�O1OQU�T�UA>�R"ZS[�O:9+à�GJdheS<_9EOt[_I�Y+9ER�ZD9!OQuDOQR�9;d [�O:>�9+<kGJRX[=rs9+<=u�Ot[_dheS<_9A6 X [aTVR�Z�GnI�LOQ9;rA9;ISR�ZMUA>+LS9;>!R�9;>"d�O�19;>�9�GALDLS9&L�R�U\R�ZD9E`�>HOXR�GJI�L�R�ZS[_>HLpUA>HLS9;>�R�9;>�d�O�G�<_>�9&GALSupT�UsfDI�L�@bGJI�L�R�ZD9�>�9&OQfS<_RQ[_IDwY+UAI^R">�UJ<��GAO'f�OQ9&L�UAI�R�ZD9�9+à GndheS<_9��,[=R"ZM[_IS[_RQ[kG�<Y+UAI�Ls[_RQ[_UAI 10Q� á Ô 2 ý å N 6�C1ZD9�>"9&OQfS<_R��GAOOt<a[_wAZSRQ<_u���9;R�R�9;>R�Z�GJI�R�ZD9\RQ�mUs�VR�9;>�d Y+UsI^R�>"UJ<1[=I�[_RHO�9+éÜ9&Y+R�UAI�R"ZD9�OQR+GJR�9\rvGJ>Q[kGJ�S<_9&O;@1�DfDRcf�OQ9&L�Ot<a[_wAZ^RX<=u�dhUA>"9MY+UAI^R">�UJ<,GnI�L>�9&OQfS<_R�9&L\[_I�G�Y+USOQR1UJT Ô e | ý z ý Y+UAdhe�GJ>"9&L\R�U�R�ZD9ERQ�mUs�VR�9;>�d Y+UsI^R�>"UJ<-�£O1Y+U^OQR1UJT ÔIe | ý xsüD6 X UA>1R�ZS[kO19+à GndheS<_9A@D�19Y;GJIMY+UAI�Y"<_f�LS9�R�Z�GJRrA9;>"uh<a[_R�RQ<_9E[kO,<_U^OQR�Su�R"ZD9�>�9&OQR">Q[kY+RQ[_UAI�R�UhRQ�1U�R�9;>�d�O;6ê�� f ����}��w$6|� r" f

C1ZD9�R�ZS[_>HL�9+à�GJdheS<_9��19�OQR�f�Ls[_9&L�[kO�GhdcU�LS9+<�UJT�R�ZD9��D[=wsZ^R�LSuSI�GJd�[kY;O�UJT�GhZS[_wAZD�Ve/9;>QTVUA>�d�GJI�Y+9\G�[_>HY+>HG�TVRRHGJNA9;I�TV>�UAd û Gn>�>HGJ>HL�@�ÿÛIDI�O�GJI�Lþ5AID9+<a<hã£| ä 6�C1ZS[kO�[kO�G�ZS[_wAZD9;>�Ls[_dh9;I�Ot[_UAIòeD>�UA�S<_9;d R�Z�GnI�R�ZD9\`�>HOQRhRQ�1U�@Y+UAI^R+G�[_IS[=IDw�`�rA9MOQRHGJR"9hrvGJ>X[�Gn�S<=9&O\GJI�L�UAID9�Y+UAISR�>�UJ<rJGJ>Q[kGJ�S<_9A6ç�tRhZ�GAO�æAf�GsLS>HGJRQ[kY\IDUAIS<a[_ID9&GJ>Q[_RQ[_9&O\UAIS<_uA66�]9Z�G&rs9!Y�Z�GnIDwA9&LhR"ZD9!eD>�Us�S<=9;dÞTV>�UAdïR�ZD9ELS9&O�Y+>Q[_eDRQ[_UAI\[_I\R�ZD9�e�GJe�9;>1�Su�O"Y;G�<a[=IDwcR�ZD9rvGn>Q[kGJ�S<_9&OOQU�R"Z�GJR�R�ZD9;uhGJ>"9Y"<=USOQ9;>�R�UER"ZD9,O"GJdh9UA>+LS9;>&6�C1ZS[kOÛ�,GsO�LSUAID9�Su�Y+UAISrA9;>�RQ[_IDw�T�>�Usd)LS9;wA>"9;9&O�R�UE>HGsLs[�GnI�O4[_I , GJI�L � [_I�UA>+LS9;>�R�Ud�GJRHY"Z�R�ZD9EfDIS[_RHO1UJT�R�ZD9EUAR"ZD9;>mrJGJ>Q[kGJ�S<_9&O;@�GJI�L\�Su�Y"Z�GJIDwJ[_IDw ^ T�>�Usd dpêvO1R�U á Ô&ýsý d�å�êvO�6P�ç9�G�<kOQU\Y�Z�GJIDws9&LR�ZD9�Y+U^OQR1TVfDI�Y+RQ[_UAI�G�<�R�U�UAID9EUJT�R�ZD9�TVUA>�d*�19�GJ>"9�Y+UAI�Ot[kLS9;>Q[_IDw á æAf�GALS>+GJRQ[kY�[_IMR"ZD9�OQRHGJR�9EGJI�L�Y+UAI^R">�UJ<VåH6

C1ZD9mOQR+GJR�9�rvGn>Q[kGJ�S<_9&O4[_I�R�ZS[kO�dhUDLS9+<D>�9;eD>�9&OQ9;ISR�R"ZD9`�D[_wAZSRjY+UAI�Ls[_RQ[_UAI�O4UnT�R�ZD9mG�[_>HY+>+G�T�R < ^ [kOFR�ZD9mLS9;rs[kGJRQ[_UAIUJTmR�ZD9�rA9+<_UDY"[_R�u�TV>�UAdóR�ZD9�<_9;rA9+<`�D[_wAZ^RER">Q[_dørvG�<_fD9\UJT Ô á Ô&ýsý d�å�êvO á wJ[_rA9;I�[_IçfDIS[_RHOEUJT á Ô&ýAý d�å"êvO+åH@ ? [�O�R"ZD9LS9;rA[kGJRQ[_UAI]UJTmR�ZD9hGJIDwn<=9�UJTGJR�RHGsY�N á R�ZD9hGJIDwJ<_9�UJT1R�ZD9hG�[_>HY+>HG�TVR!�,[=IDw��,[=R"Zç>�9&OQe/9&Y+RER�U�R"ZD9�Ls[_>�9&Y+RX[=UsI¹UJT�R"ZD9rA9+<_U�Y"[_RQu�å'T�>"UAd R"ZD9hR�>Q[_dørvGv<=fD9\UJT�ú e x á<; ä Ô ü ý å�>HGsLs[�GnI�O;@ K [kOER�ZD9�eS[_RHY"Zç>HGJR"9 á R�ZD9�>HGJR�9�UJTY�Z�GJIDws9�[_IçR"ZD9GJIDwJ<_9�UnT,R"ZD9�G�[_>HY+>+G�T�RE�,[=R"Z¹>�9&OXe�9&Y+R�R�UMZDUs>Q[_�;UAI^R+G�<Vå[_I�>HGAL/êvO�@ P [�O�R�ZD9��D[_wAZSR�e�GJR�Z�GJIDwJ<_9 á R�ZD9�GnIDwJ<_9�UJTR�ZD9�rA9+<_U�Y"[_RQuM�1[_R�Z�>�9&OXe�9&Y+RER�U\ZDUA>Q[_�;UAISRHG�<Vå1[_I�>HGALs[kGJI�O;@�GJI�L , [kO�R�ZD9hLS9;rA[kGJRX[=UsIõUnTmR�ZD9�Y;GJI�GJ>HL�LS9¾��9&Y+RQ[_UAIGJIDwJ<_9[_I\>HGALs[kGJI�OÛTV>�UAdïR�ZD9�R�>Q[_dèrJG�<_fD9A@S�ZS[kY�Z\[kO�IDUsR�wJ[_rA9;I�6�C,ZD9�Y+UAISR�>�Un< � [kO:R�ZD91[_IDeDfDR!Y;GJI�Gn>HLhLS9¾��9&Y+RQ[_UAI[=I]>HGALs[kGJI�O;6EC1ZD9hY;GJI�GJ>+LDOEGJ>�9�Y+UsI^R�>"UJ<P�bGJe�O��ZS[kY"Z¹Y;GJIçLS9¾��9&Y+R�LSUJ�IS�,Gn>HL��Su�fDe�R�U�{ ý á<; ä Ô ü ý å�>HGALs[kGJI�O;6C1ZD9;>�9'[�O1G�<�Gnw�[_I\R�ZD9'[=IDeDfDR'wJ[_rA9;I�R"U�R�ZD9;d [=I�Y"<_f�LS9&L�[=I�R"ZD9dhUDLS9+<�61C1ZD91[_IS[_RQ[kG�<jY+UsI�Ls[=RX[=UsIMY�ZDU^OX9;IhTVUA>�R"ZS[�O9+à GJdceS<=9�[kO!G�ZS[_wAZõGnIDwJ<_9�UJTjGnR�RHGAY"N á ? å��,[=R"Z�UAR�ZD9;>��1[kOQ9�R�>Q[_d*rJG�<_fD9&O;�DR�ZD9�Y+UAISR�>�Un<Üdc9;R�ZDU�LDO,�1[a<o<�GJR�R"9;dheDRR�UçOQRHGJ�S[a<a[_�;9õR"ZD9MG�[_>HY+>HG�TVR��^u�LS>Q[_rA[_IDw�G�<a<R�ZD9�rvGJ>X[�Gn�S<=9&OcR�U�R�ZD9�R�>X[=d Y+UAI�Ls[_RQ[_UAI�O;6 á C,ZD9�dh9&GnIS[=IDw�UJT!R"ZD9dhU�LS9+<F[�O�LS9&O�Y+>Q[_�/9&L�[_I�dhUA>�9�LS9;RHGv[o<F[=I�ã£| ä TVUA>1[_I^R"9;>�9&OQR�9&Lp>�9&GALS9;>HO;6=å

C1ZD9�OQuDOQR�9;dÞ[kO'wJ[_rA9;IM�Su t� á ��0¤�� ? � à � å Q� ��� 2�ZD9;>�9�R"ZD9Ed�GJR�>Q[kY+9&O � 0 @ � à � GJI�L � GJ>�9�Gv<o<�Y+UAI�OQRHGJISR��VrJG�<_fD9&L�@�GJI�LMGn>�9EwJ[_rA9;I��Su <

�Z0 � ÒÔÔÔÔÔÕ[ ý1eñý úAú^ù ÔIe_Ô xAü ý ýHe£ý [ ý1eñý {Aü Ô ý1eñý[ ý1eñý ú^{ ý [ x e |AùA{ ý Ô e£ý ý1e£ý [ ýHe£ý üA|Jú[ ý1eñý yvù ý Ô { e ùAx ýAý [ x e x�y ýAý ý1e£ý xAx e zsüAùJúýHe£ý ú^{ ý x e |AùA{ ý ýHe£ý ý1e£ý ý1eñý üA|Júý1e£ý ý1eñý ýHe£ý ý1e£ý x ý1e£ý ×ÙØØØØØÚ 2

� Ã � � ÒÔÔÔÔÔÕ[ ý1e xAù Ô y ý1eñý ý1eñý ý1e£ý ý1e£ý[ ÔIe xSyvz ý [ ýHe yv{AxAx ý1eñý ý1e£ý ý1eñý x ý zýHe_Ô&ý x ý zJú e xA{Jú ý [ Ô ù e {Sy Ô&ý ý1e£ý [ | e ú Ô zSyÔ e xSyvz ý ý1e yv{Axsx ý1eñý ý1e£ý [ ý1e£ý x ý zý1e£ý ý1eñý ý1eñý ý1e£ý ý1e£ý ×ÙØØØØØÚ 2� � � ý1e£ý ý1e£ý ý1e£ý ý1e£ý x ý1e£ý � N e

Ô {

C1ZD9E[_IS[_RQ[kG�<�Y+UAI�Ls[_RQ[_UAI�[kO 0 � á ý 2 xA| á<; ä Ô ü ý å 2 ý 2 ý 2 ý å N 6�C1ZD9�Y+USOQR:T�fDI�Y+RQ[_UAI�Gv<jR�U��/9�d�[_IS[_d�[_�;9&L�[kOG á 0 2 � å � J*L0 M N á Û , å Q� Ô&ýAý � ? R S , 2�ZD9;>�9�R�ZD9¹d\GJR�>Q[aà O � Û , [kOõGò|*C | [�LS9;ISRQ[_RQu d\GJR�>Q[aà�6 X UA>�R�ZS[kO�9+à�GJdheS<_9A@��19�f�OQ9&L ¡ , � ý1e�Ô |GJI�L8õ � Ô | e£ýAý @�GJI�L:õ 0 � ý1e | GnI�L ¡ õ � ýHe xA|D6 C1ZD9�>�9;wJ[_UAIïf�OX9&L%ZD9;>�9�[kO 5 � ã [ ý1e ù 2 ý1e ù ä Cã [ xA| á<; ä Ô ü ý å 2 xJ| á<; ä Ô ü ý å ä P @D�,[=R"Z Ô&ý xnú � ú , [=ISR�9;>�e/UJ<kGJRQ[_UAI�e�UJ[_ISRHO;6C1ZS[kO�9+à GJdceS<=9hGJeDe/9&GJ>HO�R�Uc��9�d�f�Y�Z�dhUA>"9�Ls[aî�Y+fS<_R�R�U\OQUJ<_rA9�R�Z�GJI�R�ZD9�eD>�9;rs[_UAf�O�UAID9&O;6EC1ZS[kO�d�G�u\��9Y;GJf�OQ9&L��SuçR�ZD9\<kGJ>�wA9;>hLs[_dh9;I�Ot[_UAIþUJT!R�ZD9\eD>�UA�S<_9;dM@:UA>���9&Y;GJf�OQ9�R�ZD9�OQu�OXR�9;d LSu^I�GJd�[�Y;OcGJ>�9\dhUA>�9\ZS[_wAZS<_ufDI�OQRHGJ�S<_9�R�Z�GJI\R�ZD9eD>�9;rs[_UAf�O19+à�GJdheS<_9&O;@SUA>��/9&Y;GJf�OQ9�R�ZD9'[=IS[_RQ[kG�<�OQR+GJR�9�19!Y"ZDU^OQ9��GAOFT�Gn>�9;IDUAfDwAZ�G��G&u�T�>"UAd�;9;>�U�R�U�d�GJNA9'R�ZD9eD>�UA�S<_9;d÷rA9;>�uhLs[aî�Y+fS<_R&61C1ZD9E5 û � dh9;R�ZDUDLhLSUS9&O�IDUsRmY+UAISrA9;>�wA9A6�C1ZD9'��R�9;>1G�<_wAUA>Q[_R�ZDdÞTVUA>`�I�Ls[=IDw�R"ZD9EUAe�9;ID� <_USUAeõY+UAISR�>�Un<bTVUA>!G�wJ[_rA9;I\[_IS[=RX[�Gv<�e�UJ[_ISR1T�Gv[o<kO'R�U�Y+UAISrA9;>�ws9TVUA>d�GnI^u\UJT�R�ZD9Ee/UJ[_I^R+O1[_IMR"ZD9[=ISR�9;>�e/UJ<kGJRQ[_UAIçLSUAd�Gv[=I�6C,ZD9�C��:8o�ïdc9;R�ZDU�L�LSU^9&O,`�I�L�R"ZD9�UAe/9;ID� <=USUAeçY+UAISR�>�UJ<kO:TVUA>!Gv<o<�R�ZD9�[=ISR�9;>�e/UJ<kGJRQ[_UAIe�UJ[_ISRHO;@D�DfDR�R�ZD9�TV9;9&LS��GAY�NMY+UsI^R�>"UJ<�Y+>�9&GJR�9&L\�Su�R"ZD9�[=ISR�9;>�e/UJ<kGJRQ[_UAIpT�G�[a<kO'R�U�LS>Q[_rA9�R�ZD9�OQuDOQR�9;d*R�U��;9;>�U/6X [=wsfD>�9�y!LS9;eS[�Y+R+O�R�ZD9OQRHGnR�9 ? @J�ZS[kY�Z�[kO4R�ZD91eD>Q[_d�Gn>�u�rJGJ>Q[kGJ�S<_9!�19:�,GnI^R4R�UEY+UAI^R">�UJ<�GJI�L�R�ZD91UAID91�ZS[kY�Z[�O�[_IS[=RX[�Gv<o<_uçIDUsID�;9;>�U�6 X [=wsfD>�9hü�Ls[�OXeS<�G�uDOER�ZD9�IDUA>"døUJTmR�ZD9�9;ISRQ[_>�9hOQRHGJR"9�rA9&Y+R�Us>&@ �(=� @�R�U�eD>"Uvrs[kLS9hG\��9;R�R�9;>

0 5 10 15−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time

Sta

te x

2

HJB SDRE Linear Open−Loop

X [_wAfD>�9cy < 7�UAdhe�GJ>X[�OXUAI�UJT4T�9;9&LS��GAY"NMY+UAISR�>�UJ<a<_9&LMOXRHGJR�9&O ? [_I�ÿ4à�GJdheS<_9�ùD6rA[_9;�òUJTbR"ZD9UJrA9;>HG�<a<�9+é�9&Y+R�UJT�R�ZD9!Y+UAISR�>�Un<�dh9;R�ZDUDLDO�UAIhR"ZD9!OQuDOQR�9;dM6 X [=wsfD>�9!{�LS9;eS[kY+RHO:R�ZD9�Y+UAI^R">�UJ< � 6�C1ZD9&OX9wA>HGJeDZ�O4GJ>�9�G�<a<�LSUAID9:T�Us>�B ð 8!@s5 g Wÿ'@&R�ZD9:UAe�9;ID� <_USUAehY+UAISR�>�UJ<ATVUAfDI�L��^uER�ZD91C���8���eD>�Us�S<=9;dèLs[kO�Y+>"9;RQ[_�&GJRQ[_UAI�@GJI�L�R�ZD9�<a[_ID9&GJ>�Y+UsI^R�>"UJ<�@�G�<a<mUnTm�ZS[kY"Z OQf�Y;Y+9&O"OtT�fS<a<_u�OQRHGJ�S[a<a[_�;9&L�R�ZD9�OQuDOQR�9;dM6\C1ZD9�B ð 8%dc9;R�ZDU�L�e�9;>QTVUA>�d�O��9;R�R�9;>�UAI���UAR"ZçR�ZD9�OQR+GJR�9 ? GJI�L�R�ZD9hIDUs>�d �(=� UJrA9;>+G�<a<�6\5 g W'ÿ e/9;>QT�Us>�d�OEOQUAdc9;�Z�GJRE��9;R"R�9;>�R�Z�GnIõR"ZD9UAe�9;ID� <_USUAe Y+UAISR�>�UJ<��1[_R�Z �¥3� �DfDR�Ot<a[=wsZ^RQ<_uç�1UA>+OQ9��1[_R�Z ? 6 � <a<R�ZD>�9;9cdh9;R�ZDUDLDO�GJ>�9�dhUs>�9h9+é�9&Y+RQ[_rA9hR�Z�GnIR�ZD9�<o[_ID9&GJ>�Y+UAISR�>�UJ<�[_IçR"9;>�d�O'UJT,OQR+GJ�S[a<o[_�&GJRX[=UsI�6��tI�Y+Usdhe�GJ>Q[kOQUAI�@�R"ZD9�Y+UsI^R�>"UJ<�f�OQ9&L��Su�R�ZD9hB ð 8%dh9;R�ZDUDLp[�O<�Gn>�wA9;>ER�Z�GJI�5 g Wÿ TVUA>!R"ZD9�[_IS[=RX[�Gv<m�DfD>HOQRE�DfDRER"ZD9;I�<_Uv�19;>�G�TVR�9;>EGJ��UsfDR ý1e |D6�5J[_d�[a<kGJ>Q<_uA@15 g W'ÿòf�OQ9&OEdcUA>�9

x ý

0 5 10 150

0.2

0.4

0.6

0.8

1

1.2

1.4

Time

Nor

m(x

)

HJB SDRE Linear Open−Loop

X [_wAfD>�9�ü < 7:UAdhe�GJ>Q[kOQUsI�UJTjR"ZD9EIDUA>�d�O1UnT�TV9;9&LS��GAY"NMY+UAI^R">�UJ<a<_9&L�R�>HGnß�9&Y+R"UA>Q[_9&OÛ[=I�ÿ4à�GJdheS<_9�ùD6

0 5 10 15−2

−1

0

1

2

3

4

5

6

Time

Con

trol

u

HJB SDRE Linear Open−Loop

X [_wAfD>"9�{ < 7�UAdce�GJ>Q[kOQUAI\UJT4T�9;9&LS��GAY"NMY+UAISR�>�UJ<kO:[_I�ÿ4à�GJdheS<_9�ùD6x Ô

Y+UAI^R">�UJ<�R�Z�GnIMR�ZD9�<a[_ID9&GJ>�Y+UAISR�>�UJ<4[_IõR"ZD9E[_IS[_RQ[kG�<m�DfD>HOXR!�DfDR'[kO'<=UJ�19;>�R�ZD9;>�9&G�TVR�9;>&6�C1ZD9�UAe�9;ID� <_USUAe¹Y+UAISR�>�UJ<F[�OrA9;>�u�<kGJ>"wA9�[=IS[_RQ[kG�<a<_u���9+TVUA>�9�LS>�UseDeS[=IDw�LSUJ�I�R�U�R�ZD9�<_9;rA9+<�UJTmR"ZD9hUAR�ZD9;>EY+UAISR�>�UJ<kO;6�C1ZS[kOEd�G�u�9+àDeS<kG�[_I¹�ZSuR�ZD91[_I^R"9;>�e�UJ<kGJRX[=UsIhUJTbR"ZD9&OQ9UAe/9;ID� <=USUAe�C���8��òY+UAI^R">�UJ<kOFT�Gv[o<_9&LcR�U�eD>�U�LSf�Y+9EGJI�9+é�9&Y+RQ[_rA9!Y"<_U^OQ9&LS� <_USUAe�Y+UAI^R">�UJ<�6C1ZD9�[_I^R�9;>"e�UJ<kGJRQ[_UAI�[kOY;GJ>">Q[_9&L�UAfDR1UAI�R�ZD9�[_IS[_RQ[kG�<�Y+UAISR�>�UJ<�@D�ZS[kY"Z�[_I�R�ZS[kO�Y;GAOQ9�[kO1rA9;>�uc<kGJ>�wA9�[_I�Y+UAdhe�GJ>Q[kOQUsIR�UhR�ZD9�TV9;9&LS��GAY"NMY+UAI^R">�UJ<kOGJI�Lp9;rA9;I�R�ZD9�Use�9;ID� <_U^Use�Y+UsI^R�>"UJ<�<�GnR�9;>1[_IMRQ[_dh9A61C1ZS[kO'd�G�uhd�GJNA9�[_RELs[aî�Y+fS<_RER�U9+à�R�9;I�L]�1[_R�Z¹GnI�[_I^R�9;>"e�UJ<kGJRQ[_UAI�@49&OQe/9&Y"[kG�<a<=u��'ZD9;Iç[_RE[kO�LSUAID9�OXU�>�UAfDwAZS<_u á �,[=R"ZçUAIS<_u�T�UAfD>�e�UJ[_ISRHO�[_I�9&GAY"ZLs[=dc9;I�Ot[_UAI�åH6

C1ZD9�RQ[_dh9GJI�LV��UAe�OF>�9&æAfS[_>�9&L�GJI�L�Y+U^OXR�T�fDI�Y+RX[=UsI�G�< G á 0 2 � åST�UA>4R�ZD9:R��1U!OXf�Y;Y+9&O�OtTVfS<�IDUAIS<a[_ID9&GJ>ÛT�9;9&LS��GAY"NY+UAI^R">�UJ<kOhGJ>�9p<a[�OXR�9&L�[_I C�Gn�S<=9�ú�6òC1ZD9MUAe/9;ID� <_U^UAe Y+UAISR�>�Un<'Y+USOQR�TVUA>hR�ZS[kOceD>�UA�S<_9;d [kO Ô&ý y^6ñ|AüD@�rA9;>"uç<kGJ>�ws9

7 ��q%C:[_dh9 á OQ9&YJ6aå X <_UAe�O 7:U^OQRB ð 8 ý 6£üAü ÔIe úsú{C Ô�ý 7 Ô ùD6ayv{Aüsù5 g Wÿ Ô 6 Ô&ý ÔIe£ý {�C Ô�ý 7 ÔsÔ 6£ù Ô yJ|

C�Gn�S<=9�ú <�l fDdh9;>Q[kY;G�<jY+Usdhe�GJ>Q[kOQUAI�UJT�TV9;9&LS��GAY"NMY+UAI^R">�UJ<�dh9;R�ZDUDLSUJ<_UAwJ[_9&O,[=I�ÿ4à�GJdheS<_9�ù 6Y+UAdhe�GJ>�9&Lþ�1[_R�ZòR�ZD9]UAR�ZD9;>HO\LSfD9çR�U�R�ZD9�<kGJ>�wA9�[_IS[_RQ[kG�<�Y+UAISR�>�Un<��ZS[kY"Zò[kO\�19+[=wsZ^R�9&L ZD9&G&rs[a<_u [_I R"ZD9�Y+USOQRT�fDI�Y+RQ[_UAI�Gv<�6���ISR�9;>�9&OXRQ[_IDwJ<_uA@�R"ZD9�<a[_ID9&GJ>�Y+UAI^R">�UJ<4T�UA>�R�ZS[kO�9+à�GJdheS<_9hZ�GAOEG�Y+U^OXR!UJT�UsIS<=u Ô&ý 6£x ýDÔ ù @�GJeDe�GJ>�9;ISRQ<_u��9&Y;GJf�OQ9\[_RhZ�GsOErA9;>�u�<o[_R�RX<=9�UJTR�ZD9�ZD9&G�rA[a<_uS�V�m9+[_wAZSR�9&L�Y+UAISR�>�Un<,Y+UAdhe�Gn>�9&Lç�,[=R"Z¹R�ZD9�UsR�ZD9;>�dh9;R"ZDU�LDO;6çC,ZD9OQRHGJ�S[a<a[_�&GJRQ[_UAI 9+é�9&Y+R�UJT!R"ZD9h<a[_ID9&GJ>�Y+UAI^R">�UJ<�[kO�OQd�Gv<o<_9;>�Y+Usdhe�GJ>�9&L��1[_R�Z�R�ZD9�UAR"ZD9;>�dh9;R�ZDUDLDO;@�ZDUJ�19;rA9;>&@:GAOOQZDUJ�I\[_I X [_wAfD>�9&O�y�GJI�LMüD6

g 9;R�9;>�d�[_IS[_IDw��ZS[kY�Zçdc9;R�ZDU�Lõ[�O���9&OQR�[kO�dhUA>�9hLs[aî�Y+fS<_R�ZD9;>�9hR�Z�GJI�T�UA>ER"ZD9�`�>+OQRERQ�mU\9+à�GJdheS<_9&O;6�C,ZD95 g WÿèGJI�L <a[=ID9&Gn>�Y+UAISR�>�Un<,Z�G�rA9c<_UJ�m9;>\Y+U^OQRHO��DfDR�<_9&O�Oc9+é�9&Y+RQ[_rA9;ID9&O�O�[=IòOQRHGJ�S[a<a[_�+[_IDw�R�ZD9MOQRHGJR"9�rJGJ>Q[kGJ�S<_9&O;@�ZS[a<=9ER"ZD9�B ð 8 Y+UsI^R�>"UJ<bGJeDe�9&Gn>HO:��9;R�R�9;>:[_I\R�9;>�d�OÛUJT�OQRHGJR�9�OQRHGJ�S[a<a[_�&GJRQ[_UAI��DfDR1>�9&OQfS<_RHOÛ[_I�G�ZS[_wAZD9;>Y+U^OQR�6jC,ZD9<�Gn>�wA9;>E�19+[_wAZ^REUsIõR"ZD9�Y+UsI^R�>"UJ<�[_IçR"ZD9�Y+USOQR�T�fDI�Y+RX[=UsI�G�<mY;GJf�OQ9&O�R�ZS[kO�ZS[=wsZD9;>�Y+U^OQR�@��SuçGJdheS<a[aT�us[_IDwMR�ZD9hOQd�Gv<o<Ls[oé�9;>�9;I�Y+9&O,[_I�R�ZD9�Y+UAISR�>�UJ<kO1OQ9;9;I\[_I X [_wAfD>�9�{�[_I^R"U�<kGJ>�wA9EY+U^OQRLs[aé�9;>�9;I�Y+9&O;61C1ZD9�Y�ZDUn[�Y+9EUnT�R�ZD9�<kGJ>�wA9��19+[_wAZ^R[=I\R�ZD9!Y+USOQR�TVfDI�Y+RQ[_UAI�G�<��,GsO4d�GALS9R�U�G�rAUJ[kL�IDUAIDeDZ^uDOt[kY;G�<�>�9&OQfS<_RHO:OQf�Y"Z�GAO4R"ZD9!ZSfDwA91[_IS[_RQ[kG�<�OQeS[_NA9EOQ9;9;I�[_I�R"ZD9UAe�9;ID� <_USUAeõY+UAISR�>�Un<�6�C1ZS[kO1�GAO1OQf�Y;Y+9&O"OtT�fS<FT�UA>1R�ZD9�UAR�ZD9;>1dh9;R"ZDU�LDO;@ �DfDR�[_R!Gv<�OXU�>"9&OQfS<_RHO:[_I�R�ZD9�B ð 8þdh9;R�ZDUDLZ�G&rs[_IDw�G�ZS[_wAZD9;>Y+U^OQR�9;rs9;IhR�ZDUAfDwAZ�[_R�f�OX9&O�UAIS<_uhOt<a[_wAZ^RX<=u�dhUs>�9!Y+UAISR�>�UJ<�6Û5AU�9;rA9;IhR"ZDUAfDwAZ�R�ZD91<a[_ID9&GJ>mY+UsI^R�>"UJ<Z�GAO�R�ZD9h<_UJ�19&OQR�Y+USOQR&@4R�ZD9�B ð 8÷Y+UAfS<kL��19+<o<1��9MY+UAI�O�[�LS9;>"9&L�R�ZD9��/9&OQRhY�ZDUn[�Y+9\TVUA>�R�ZS[kO�9+à�GJdheS<_9A@���GsOQ9&LçUsI[=R+OE9+é�9&Y+REUAI�R�ZD9hOQRHGJR"9&O;6�C,ZS[�O�[kO�fDIS<o[_NA9c[_I ÿjà GndheS<_9 Ô @��ZD9;>�9�R�ZD9\Y+U^OQREGJI�L�R�ZD9hOQRHGnR�9���9;Z�G�rA[_UA>�d�GJRHY"ZfDeM�19+<a<�@�GnI�L\[_Içÿ4à�GJdheS<_9�xD@ �ZD9;>�9�R"ZD9�9+é�9&Y+R!UsIMR�ZD9�Y+U^OQR1TVfDI�Y+RQ[_UAI�G�<4T�>"UAd*R�ZD9�Y+UAI^R">�UJ<��GAO1��GsOQ9&L�UAIMGwA>�9&GJR�9;>Ls[aé�9;>�9;I�Y+9���9;RQ�19;9;I�R�ZD9�dc9;R�ZDU�LDO�6ê���ê�����}��w$6|� r"*ê

C1ZS[kO19+à GndheS<_9[kO1RHGnNA9;I�TV>�UAd û GJ>">HGJ>HL�GJI�L ð UA>HLDGnIõãÍú ä @^GJI�L�[kOG�Ls[aé�9;>�9;ISR1dhU�LS9+<�UJTh�D[=wsZ^RY+UAISR�>�UJ<�64��RZ�GAO:UAIS<_u�R�ZD>"9;9�OQRHGJR�9'rvGJ>Q[kGJ�S<_9&O,[_I�OQR�9&GAL\UJTF`�rA9E�DfDRY+UAI^R+G�[_I�O1��UAR"Z�æsf�GALS>HGJRX[�YEGnI�L�Y+fD�S[kYEIDUsIS<o[_ID9&GJ>�R�9;>�d\O;6��I�R�ZS[kOEdhUDLS9+<�R�ZD9hOQRHGJR�9�rvGJ>X[�Gn�S<=9&O�GJ>�9�GAO1TVUJ<a<_UJ�!O < ^ [�O�R"ZD9�LS9;rs[kGJRQ[_UAI�UJT1R�ZD9�GJIDwn<=9�UJTGJR�RHGsY�NcT�>"UAd R"ZD9R�>Q[_d÷rvG�<_fD9�UnT ý1e£ý úsú�>HGALs[kGJI�O�@ ? [kO1R"ZD9��D[=wsZ^R1e�GJR�ZMGnIDwJ<_9[_IM>+GALs[kGJI�O;@DGJI�L K [kO1R�ZD9�>HGJR�9�UJTjY"Z�GJIDwA9�UJT�R"ZD9�D[=wsZ^Re�GnR�Z�GnIDwJ<_9�[=I�>+GAL/êvO;6�C1ZD9EY+UAISR�>�UJ< � [kO:R�ZD9�LS9;rA[kGJRX[=UsI�UJT�R�ZD9�RHG�[a<�LS9¾��9&Y+RQ[_UAIõGnIDwJ<_9 á �1[_R�Z\>�9&OQe�9&Y+R'R�UR�ZD9��1[_IDwMLs[_>�9&Y+RQ[_UAI�å1TV>�UAdóR�ZD9�R�>Q[_d rJG�<_fD9�UJT [ ý1e£ýAý {�>HGALs[kGJI�O;6'��I�R�ZD9�G�[_>HY+>HG�TVR�LS9&O"Y+>Q[_��9&L��Su�R�ZS[kO�dhUDLS9+<�@R�ZD9�9;I^RQ[_>�9�RHGv[o<�Y;GJI�>�UARHGJR"9ER�U�Y+UsI^R�>"UJ<�[_RHOZ�D[_wAZSR&6 � O,[_IõR"ZD9�eD>"9;rA[_UAf�O�9+à�GJdheS<_9A@�R�ZD9hY+UAISR�>�UJ<4dh9;R�ZDUDLDO!GJ>"9wJ[_rA9;IMGJIc[=IS[_RQ[kG�<�Y+UAI�Ls[_RQ[_UAI�UJTjG�ZS[_wAZMGJIDwJ<_9�UJTjGJR"RHGAY"N á ^ åj�DfDR1UAR"ZD9;>��1[kOQ9�R�>Q[_d*Y+UAI�Ls[_RQ[_UAI�O;@�GJI�L�Gn>�9!GAOQNs9&L

xsx

R�U�OQRHGn�S[o<a[_�;9�R�ZD9�OQuDOQR�9;dM6 á C,ZD9E[_I^R"9;>�9&OQR�9&L\>�9&GsLS9;>!Y;GJI�`�I�LpdhUA>�9'[_IST�Us>�d�GJRQ[_UAI�UAI�R�ZS[kO'dhU�LS9+<F[=I�ãÍú ä 6aåC1ZD9�OQuDOQR�9;dÞ[kO'�>Q[_R�R�9;IMGAO

ÒÔÕ ^ ? K × ØÚ �ÓÒÔÕ [ ý1e üSyAy ^ �� K � ýHe úDy ?^ [ ý1eñý üAü ^ K [ ý1eñýDÔ { ?? � ù e üJú^z K ^ [6 ?^ K K[ ú e x ý ü ^ [ ý1e ùA{Az K [ ý1e úDy ?^ [ ù e |AzJú K ^ × ØÚ �ªÒÔÕ [ ý1e x Ô |ý1e£ý[ x ý1e {szSy × ØÚ ��1[_R�ZMGJI\[_IS[_RQ[kG�<jY+UAI�Ls[_RQ[_UAI�UJT 10�� á xA| á>; ä Ô ü ý å 2 ý 2 ý å N 6 X UA>1R�ZD9�5 g W'ÿ�dh9;R�ZDUDL\R�ZD9�IDUAIS<a[_ID9&GJ>TVfDI�Y+RQ[_UAIp[�O>�9;�>Q[_R�R�9;IMGsO

. á å � ÒÔÕ [ ý1e üSysy � ý1e úDy ^ � ù e üJú^z ?^ [ ý1e£ý Ô { ? Ô [ ý1e£ý üAü ^ [÷ ?^ý ý Ô[ ú e x ý ü [ ý1e úDy ^ [ ù e |AzJú ?^ ý [ ýHe ùA{Az × ØÚ ÒÔÕ ^ ? K × ØÚ eC1ZD9�Y+U^OXR�TVfDI�Y+RQ[_UAI�G�<4[kO G á 10I2 � å �æJFL0 ² HN ² Ôú Û K ´ �� � ? ´ S , eX UA>:R�ZS[kO�9+à�GJdheS<_9A@s[_I�R�ZD9EC���8��òdh9;R�ZDUDLh�19f�OX9&L ¡ , � ý1e�Ô GJI�L�õ � Ô x eñý @AGJI�L�[=I�R"ZD9��R�9;>+GJRQ[_rA9�dh9;R�ZDUDLõ 0�� ýHe |�GJI�L ¡ õ � ýHe xA|D64C1ZD9E>�9;wJ[_UAI 5l� ã [ xA| á<; ä Ô ü ý å 2 xJ| á>; ä Ô ü ý å ä K �GAOÛf�OQ9&L�GnI�LhR�ZD9;>"9�GJ>"9 Ô xs| � | K[=ISR�9;>�e/UJ<kGJRQ[_UAI�e�UJ[_ISRHO;6

� O'�1[_R�ZMR"ZD9EUAR�ZD9;>Z�D[=wsZ^ReD>"UA�S<_9;dó[=I�ÿ4à�GJdheS<_9�ù @DID9+[_R�ZD9;>EUJT�R�ZD9E[_R�9;>HGnRQ[_rA9�dh9;R"ZDU�LDOY+UsI^rA9;>"wA9A6mC,ZD9C���8��èdc9;R�ZDU�L�@F�ZS[kY�Z�T�G�[a<_9&L�TVUA>�R�Z�GJREeD>�UA�S<_9;dM@4LSU^9&O��1UA>"N�ZD9;>�9A6 X [_wAfD>"9 Ô�ý LS9;eS[�Y+R+OER�ZD9hOQRHGnR�9 ^ GnI�LX [=wsfD>�9 ÔsÔ Ls[kOQeS<kG�u�O�R�ZD9�Y+UAISR�>�UJ< � T�Us>�B ð 8�@�5 g W'ÿ@�CZ��8���@4GJI�L]R�ZD9hUAe/9;ID� <=USUAe Y+UAISR�>�Un<�T�UAfDI�L]�SuõR"ZD9C���8��÷eD>�UA�S<_9;d Ls[kO�Y+>"9;RQ[_�&GJRQ[_UAI�6 C1ZD9�C��:8o�÷dh9;R"ZDU�L�[kO�Y"<=9&Gn>Q<_uõR"ZD9h��9&OQR�GJR�Y+UAISR�>�UJ<a<a[_IDw ^ @��1[_R�ZçR"ZD9UAe�9;ID� <_USUAe�Y+UAISR�>�UJ<^G�Y"<_U^OQ9mOX9&Y+UAI�L�6�8�UsR�Z�UJT�R"ZD9&OQ9�Z�G�rA9�G,<kGJ>�wA9Û[=IS[_RQ[kG�<bY+UsI^R�>"UJ<^�ZS[kY"Z�æsfS[kY�Ns<_u��/9&Y+UAdh9&OFrA9;>�uOQd�G�<a<�6��tI¹Y+UAISR�>HGAOXR&@�R"ZD9�5 g W'ÿ GJI�L�B ð 8%dh9;R�ZDUDLDO�f�OQ9�dhUA>�9hY+UAI�OQR+GJI^REY+UAISR�>�UJ<�@��1[_R�Z�<_9&O�O�Y+UAI^R">�UJ<�R�Z�GnIR�ZD9�UAR"ZD9;>!dh9;R"ZDU�LDO�GJR1`�>HOXR!�DfDR�dhUA>�9�GvT�R�9;> ý 6£|�UA>EOQU�6C,ZD9;uMGJ>�9�G�<kOQU�Ot[_wAIS[a`bY;GJISRQ<_uõ�1UA>+OQ9�GJR!Y+UAISR�>�Un<o<a[_IDw ^ @��1[_R�Z�R"ZD9MB ð 8 dh9;R�ZDUDL�R�ZD9��1UA>+OQR�UJT!R�ZD9\TVUAfD>&6�C1ZS[kO�OQZDUsfS<�L��/9M9+àDe�9&Y+R�9&L�@O�[=I�Y+9�R�ZS[kO�[kO�UAfD>�`�>HOQR9+à GJdceS<=9c�1[_R�ZçGh>�9+<kGJRX[=rs9+<=uçY+UAdceS<o[kY;GJR"9&L�IDUAIS<a[_ID9&GJ>�OQR">�f�Y+R�fD>�9A6�C,ZD9�RQ�1UA�VR�9;>"d B ð 8 dh9;R"ZDU�Lp[_wAIDUA>�9&O�R"ZD9Y+fD�S[�Y\R"9;>�d�O�[_I�R�ZD9�OQu�OXR�9;dM@�GsOE9+àDeS<�Gv[=ID9&L [_I 5A9&Y+RQ[_UAI ù 6 Ô @�UAIS<_uçf�Ot[_IDwçR"ZD9�<a[=ID9&Gn>�GJI�Lçæsf�GALS>HGJRX[�Yce�GJ>�R+O;6C1ZD9EIDUAIS<a[_ID9&GJ>Ee�GJ>�RUnT�R�ZD9�OQuDOQR�9;d Y;GnIDIDUAR��9�>�9;�>Q[_R�R"9;I\T�UA>1R�ZD9c5 g Wÿ�dc9;R�ZDU�L�GsO ¡T�U�c¨ á å ¡���© á GAOLS9&O�Y+>Q[_��9&Lc[_I�5A9&Y+RQ[_UAI�ùD6£x�åH@AOQUER�ZD9e/UJ�m9;>�OX9;>Q[_9&O�[kO:Ls[oî�Y+fS<=R'R�U�Y+UAdheDfDR�9,T�UA>�R"Z�GJR�dh9;R�ZDUDL�6:öIS<=ucR��1UER�9;>"d�O�m9;>"9hf�OQ9&L�[=I�R�ZS[kOE9+à�GJdheS<_9A@�Y+UAdhe�Gn>�9&Lç�,[=R"Z�`�rA9hR�9;>"d�O�TVUA>ER�ZD9hUsR�ZD9;>�eD>�Us�S<=9;d\O;6�C1ZD9�CZ��8��÷dh9;R�ZDUDLLSU^9&OÛIDUAR�Z�G�rA9OQf�Y�Z\OQR�>�UAIDw�LS>+G&�'��GAY�NDOF�1[_R�ZhR�ZS[kO�RQuSe�9UnTbeD>�UA�S<_9;dM@SOQU�[_R�[kO�I�GnR�fD>HG�<a<_u�d�f�Y"ZhdhUs>�919+éÜ9&Y+RX[=rs9R�Z�GJI�R�ZD9�UAR�ZD9;>:T�9;9&LS��GsY�NMY+UAISR�>�Un<�O�6

C1ZD9�RQ[_dh9A@H��UAe�O�GJI�L�rJG�<_fD9�UJT�R�ZD9�Y+USOQR1TVfDI�Y+RQ[_UAI�G�< G á H0I2 � å�T�Us>9&GAY"ZõY+UAISR�>�UJ<�dh9;R"ZDU�L�GJ>�9�Ls[kOQeS<kG�uA9&L[=IçC4GJ�S<_9h|D6!C1ZD9�UAe/9;ID� <_U^UAeçY+UAISR�>�Un<�Z�GAO�G�Y+U^OXR!UJT ý 6 ý ú^üAù @�GnI�LMR"ZD9E<a[_ID9&GJ>�Y+UAISR�>�Un<�Z�GAO�G�Y+U^OXRUJT ý 6 ý |SyvzD6

7 �:q Cm[=dc9 á OQ9&YJ6aå X <_UAe�O 7�U^OQRB ð 8 ý 6âú^x x e xs{�C Ô&ý , ý 6 ý üA|sz5 g Wÿ ý 6âú Ô ÔIe üs|�C Ô&ý , ý 6 ý |SyJüC��:8�� z ý Ô ú x e_Ô ú{C Ô&ý ^�^ ý 6 ý ú^ùs|

C�Gn�S<=9�| <�l fDdh9;>Q[kY;G�<jY+Usdhe�GJ>Q[kOQUAI�UJT�TV9;9&LS��GAY"NMY+UAI^R">�UJ<�dh9;R�ZDUDLSUJ<_UAwJ[_9&O,[=I�ÿ4à�GJdheS<_9�ú/6xsù

0 2 4 6 8 10 120

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time

Sta

te x

1

HJB SDRE TPBV Open−Loop

X [=wsfD>�9 Ô&ý < 7:UAdhe�GJ>Q[kOQUsI�UJT�TV9;9&LS��GAY�NMY+UsI^R�>"UJ<a<=9&L�OQRHGJR"9&O ^ [_Iõÿ4à�GJdheS<_9�ú�6

0 2 4 6 8 10 12−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time

Con

trol

u

HJB SDRE TPBV Open−Loop

X [=wsfD>�9 ÔAÔ < 7:UAdhe�GJ>Q[kOQUsI�UJT�TV9;9&LS��GAY"N�Y+UsI^R�>"UJ<kO:[_Iõÿ4à�GJdheS<_9�ú�6xnú

C1ZD9&OQ91d�GJRHY"Z�R"ZD9m>"9&OQfS<_RHO�OQ9;9;I�[_I X [_wAfD>"9&O Ô&ý GnI�L ÔsÔ @&�,[=R"Z�R"ZD9,CZ��8���Ot<a[_wAZSRQ<_u��/9;R�R�9;>�R�Z�GJI�R�ZD91UAe�9;ID� <_USUAe�@�1[_R�ZM5 g W'ÿ¹Ot[_wAIS[a`bY;GJISRQ<_uc<=9&O"O�9+é�9&Y+RQ[_rA9�GJI�L�B ð 8þY"<=9&Gn>Q<_u�<kGAOQR�[_I\e�9;>QTVUA>�d\GJI�Y+9A6�C1ZD9�CZ��8��þ[=ISR�9;>�e/UJ<kGJRQ[_UAIdh9;R�ZDUDL�RHGJNs9&OG�rA9;>�u\<_UAIDw\RQ[_dh9�R�U�LSU�G�<a<�R�ZD9�Use�9;ID� <_U^Use�Y;Gv<�Y+fS<kGJRX[=UsI�O'[=R�ID9;9&LDO;@/�DfDRTVUA>R"ZS[�O'9+à�GJdheS<_9�[=R[�O'�19+<a<��1UA>�R�Z\R�ZD9E9+é�UA>�R!O�[=I�Y+9�[_ReD>�UDLSf�Y+9&Od�f�Y"ZM��9;R"R�9;>>�9&OQfS<_RHO,R�Z�GJI�R�ZD9�UAR�ZD9;>1TV9;9&LS��GAY"N�Y+UAISR�>�Un<�O�6�b�Qk�ØF×Ü� VÚ��&Ý�Ø�×��

��I�Y+Usdhe�GJ>Q[_IDw¹OQ9;rs9;>HG�<TV9;9&LS��GAY"N Y+UAISR�>�Un<,dc9;R�ZDU�LDO�T�UA>cIDUAIS<a[=ID9&Gn>�OQuDOQR�9;d\O;@��19�Z�G�rA9MOQ9;9;I�R"Z�GJR�TVUA>d�GJISuMeD>�UA�S<_9;d�O�[_R�GJeDe/9&GJ>HOER"Z�GJR�G�O�[=dceS<=9\dh9;R�ZDUDL�[kOER"ZD9��/9&OQR�Y"ZDUJ[kY+9A6�C,ZD9�dc9;R�ZDU�L�UJT û GJ>�>HGJ>+L�f�Ot[_IDwUAIS<_uMRQ�1Uhe�UJ�19;>�OX9;>Q[_9&O�R�9;>�d�O,[kOrA9;>"u�9+éÜ9&Y+RX[=rs9�TVUA>�eD>�UA�S<_9;d�O��1[_R�Z�UAID9�<_9;rA9+<jUnT�IDUAIS<a[=ID9&Gn>Q[_R�uA@4G�Y;GnR�9;wAUA>�u[=I�Y"<_f�Ls[_IDw�d�GJISuMeD>�UA�S<_9;d�O�UJT1wA>�9&GJR�[_ISR�9;>�9&OQR�6 X Us>�ÿ4à�GJdheS<_9&O Ô ��ùD@��'ZS[�Y"Z�GJ>�9hG�<a<mUJTR�ZS[kO�R�uSe�9A@FR�ZD9hRQ�1UA�R�9;>�dèB ð 8çdc9;R�ZDU�L�eD>�U�LSf�Y+9&L�>�9&OQfS<_RHO4ID9&GJ>Q<_uhGAO4wAUSUDLEUA>��/9;R�R�9;>�R�Z�GJI�R�ZD91UAR"ZD9;>4T�9;9&LS��GAY"N�Y+UsI^R�>"UJ<�dc9;R�ZDU�LDO9+à GJd�[=ID9&L�6\�tR�[�O�rA9;>"uM9&GAOQu�R�U\[_dheS<_9;dh9;ISRhGJI�LçLSUS9&OEIDUARE>"9&æAfS[_>�9\R�ZD9�d�f�Y�Z�<kGJ>"wA9;>�Y+UAdceDfDRHGJRQ[_UAI�G�<�RX[=dc9OQUAdh9�UJT�R�ZD9EUsR�ZD9;>1dh9;R�ZDUDLDO�ID9;9&L�6:��RG�<kOQUceD>�UJrA9&LhdcUA>�9�9+éÜ9&Y+RX[=rs9�[=IMÿjà GndheS<_9�xETVUA>:[_IS[_RQ[kG�<jOQRHGnR�9&OÛT�GJ>"R�ZD9;>G&�G�u�TV>�UAd*R"ZD9�UA>Q[_wJ[_I�6 X UA>eD>�UA�S<_9;d�O'�1[_R�Z�dhUA>�9�Y+UAdceS<=9+àMIDUsIS<o[_ID9&GJ>X[=RX[=9&O�@�OQf�Y"ZõGAO'ÿ4à�GJdheS<_9�ú�@DR�ZD9ERQ�1UA�R�9;>�d B ð 8 dh9;R�ZDUDL�[kO�IDUsR�rA9;>�u�9+é�9&Y+RQ[_rA9A@SOQU�G�<=9&O"O�>"9&OQR�>Q[kY+R�9&Lcdh9;R�ZDUDL�[kO1GE��9;R"R�9;>mY"ZDUJ[kY+9A6���I\R�ZS[kO1Y;GAOQ9R"ZD9C���8���[_ISR�9;>�e/UJ<kGJRQ[_UAIhdh9;R"ZDU�L�eD>"U�LSf�Y+9&L�wsU^UDL�>�9&OQfS<_RHO;@AG�<_R�ZDUsfDwAZ�>�9&æAfS[_>Q[_IDwhG'wA>�9&GJR�LS9&G�<�UJT�Y+UAdheDfDRHGJRX[=UsI�G�<RQ[_dh9A6õC,ZD9hdhUA>�9�Y+UAdheS<a[kY;GJR�9&L][_R�9;>+GJRQ[_rA9hdh9;R"ZDU�LDO�Z�GAL�Ls[aî�Y+fS<_RQ[_9&Oh�1[_R�Z�OQUAdc9hUJTR�ZD9\9+à GJdceS<=9&O�@4T�Gv[o<a[_IDwR�U�Y+UsI^rA9;>"wA9���9&Y;GJf�OQ9cUJT�[_I�GALS9&æAf�GnR�9�[_IS[_RQ[kG�<�[_R�9;>HGnR�9&O;6�7�UsI^rA9;>"wA9;I�Y+9�>�9&OXfS<=R+O�GJ>�9�wJ[_rA9;I�[_I�ã Ô&ý @�x Ô+ä TVUA>!R"ZD9[=R"9;>HGJRQ[_rA9dc9;R�ZDU�LDO�@A�DfDR�R"ZD9&OQ9!>"9&æAfS[_>�9>"9&OQR�>Q[kY+RQ[_UAI�O;@sTVUA>�9+à�GJdheS<_9!UsI�R"ZD91[_IS[=RX[�Gv<b[_R�9;>+GJR�9A@A�'ZS[�Y"Z�LSU�IDUAR�ZDUJ<kLT�UA>'UAfD>9+à�GJdheS<_9&O;6

xs|

?�$&����1������#

ã Ô;ä � I�LS9;>HOQUAI�@D8�6 g 6 ö�6_@DGJI�L\iMUSUA>�9A@ ð 6^8�6_@3@3A�BDC�EGF�H3IKJ�LMBDN<JOHQPSRTC�L-UVF�N+WYX6F�Z�N>F�BDC�[+\:U]B�^_J'Z8`¿@DÿÛIDwJ<_9;�mUSUDL7�<a[aé�O;@ l 9;� ð 9;>HOX9;u < �Û>�9;ISRQ[kY+9;��B!G�<a<�@ Ô {A{ ý 6

ã£x ä ë 9;�,[�O�@ X 6 ë 6_@/GJI�L�5Au^>"dhU^O;@���6 ë 6_@a@3AbBDCcEGF�HaIdJ�L-BDN>J�Ha@ l 9;�fe�UA>�N < �þ[o<_9;uA@ Ô {A{A| 6ã£ù ä û GJ>�>HGJ>+L�@!�ï6 ë 6_@Sg�5AfD��UAeDRQ[_d�Gv< X 9;9&LS��GAY"Nò7�UAISR�>�Un<�TVUA> l UAIS<a[=ID9&Gn>M5AuDOQR�9;d�O�@hg � fDR�UAd\GJRQ[kY;GD@`��UJ<EüD@

eDe�x Ô {J��xAx Ô á Ô {�yvxSåH6ãÍú ä û GJ>�>HGJ>+L�@1�ï6 ë 6_@�GJI�L ð UA>HLDGnI�@ ð 6�i�6_@bg g 9&Ot[_wAIMUnT l UAIS<a[_ID9&GJ> � fDR�Usd�GJRQ[kY X <a[_wAZSR�7:UAI^R">�UJ<�5AuDOQR�9;d�O�@hg

� fDR�UAd�GnRQ[kY;GD@���UJ< Ô ùD@SeDeDú^{�y&��| ý | á Ô {�yAyAåH6ã£| ä û GJ>�>HGJ>+L�@I�ï6 ë 6�@�ÿÛIDI�O;@ g 6 X 6_@SGJI�L�5AID9+<a<�@F5�6 � 6�@5g l UAIS<a[_ID9&GJ> X 9;9&LS��GAY"N�7�UsI^R�>"UJ<bUJT�B1[_wAZS<_uMi�GJIDUS9;fD�

rS>HGJ�S<_9 � [=>+Y+>HG�TVR&@hg��tI^R�9;>"I�GJRQ[_UAI�G�< ð UAfD>�I�G�<�UJT17�UAISR�>�UJ<�@���UJ<j|szD@SeDe�yv{A{J��ü Ô x á Ô {A{sxSåH6ã£z ä l [kOQZS[_NvG��GD@6e�6_@ 5^GJIDIDUAd�[_u^G @ l 6_@DGJI�L���R+GJN^fD>+GD@^B�6_@_g � i�9;R�ZDU�L�T�UA>'5AfD��UAeDRX[=d\G�< g 9&Ot[_wAI�UnT l UAIS<a[_ID9&GJ>X 9;9&LS��GAY�N�5AuDOQR�9;d�O;@ig � fDR"UAd�GJRQ[kY;GD@���UJ<:y^@SeDe�y ý ùJ�Qy Ô x á Ô {Sy Ô å+6ãay ä ë 9&GnNA9A@bW�6 ð 6�GJI�L ë [_f�@�WE6%�ï6_@-gS7�UsI�OQR�>�f�Y+RQ[_UAI�UJT5AfD��UseDRQ[_d�G�<17�UAISR�>�UJ<�5A9&æsfD9;I�Y+9&O;@hg�5A� � i ð UAfD>�I�G�<

UAI�7:UAI^R">�UJ<ÜGnI�L�öeDRQ[_d�[_�&GJRQ[_UAI�@%��UJ<j| @^eDe�|núA��zAù á Ô {AzSyAåH6ã£ü ä 5^GJ>X[�Ls[kO;@ û 6 l 6_@DGJI�L ë 9;9A@Ü7!6D5�6 û 6_@_g � I � eDeD>"U&àS[_d�GJRQ[_UAIMC,ZD9;UA>�uhUJT:öeDRQ[_d�G�<�7�UsI^R�>"UJ<DT�Us>,CF>HG�[_I�GJ�S<_9

i�GJIS[_eDfS<kGJR�UA>+O;@hg���ÿ:ÿ�ÿ�C�>+GJI�O�GAY+RQ[_UAI�O4UsI�5AuDOQR�9;d\O;@^i�GJI�@AGJI�L�7�u^�/9;>�ID9;RQ[kY;O;@���UJ<b{D@JeDe Ô |AxJ� Ô |A{ á Ô {�yv{SåH6ã£{ ä 8:9&GJ>HL�@1WE6`�ï6_@,5^GJ>Q[kLs[kO;@ û 6 l 6_@1GJI�L÷�ç9;I�@ ð 6:CE6_@Kg û G�<_9;>�Ns[=I � eDeD>"U&àS[_d�GJRQ[_UAI�UnT�R�ZD9 û 9;ID9;>HG�<a[_�;9&L

B�GJd�[a<_R�UAID� ð GsY+UA�S[_��8�9+<a<_d�GJI�ÿ�æsf�GJRQ[_UAI�@hg � fDR�UAd\GJRQ[kY;GD@���UJ<jùAù @^eDe�x Ô |A{J��x Ô yAy á Ô {A{SysåH6ã Ô&ýJä 8:9&GJ>HL�@4WE6w�ï6_@45^GJ>Q[kLs[kO;@ û 6 l 6_@4GJI�L*�ç9;I�@ ð 6�CE6_@3g � eDeD>"U&àS[_d�GJR�9\5AUJ<_fDRQ[_UAI�O�R�U�R�ZD9�Cm[=dc9;�V��ISrvGJ>Q[kGJISR

B�GJd�[a<_R�UAID� ð GsY+UA�S[_��8�9+<a<_d�GJIMÿ:æAf�GnRQ[_UAI�@hg ð UAfD>�I�G�<�UJT4öeDRQ[_d�[_�&GJRQ[_UAI�C1ZD9;UA>�uhGJI�L � eDeS<a[�Y;GnRQ[_UAI�O;@1��UJ<b{szD@eDe�|Aüs{J��zAxAz á Ô {s{AüSåH6

ã ÔAÔ;ä �ç9;>"IS<o[�@ � 6&GnI�Lh7:U^UAN�@ û 6_@8gS5AfD��UseDRQ[_d�G�<�7�UAISR�>�UJ<JTVUA>�R"ZD9 l UAIS<a[=ID9&Gn> ì f�GALS>HGJRQ[kY1W19;wAfS<kGJR"UA> �Û>�UA�S<_9;dM@hg� fDR�UAd�GnRQ[kY;GD@���UJ< ÔAÔ @SeDe�yv|n��üJú á Ô {�yv|SåH6

ã Ô x ä ��>Q[_NA9+<a[kO;@ l 6 ð 6bGnI�L��'[=>X[�GnNA[kLs[kO;@���6/�H6_@-g�öeDRQ[_d�G�< X 9;9&LS��GAY�N�7�UAISR�>�Un<ÜUnT l UAID� <a[_ID9&GJ>�5AuDOQR�9;d\O;@hg��tI^R�9;>"�I�GJRX[=UsI�G�< ð UAfD>�I�G�<4UJTm5AuDOQR�9;d\O�5^Y"[_9;I�Y+9A@w��UJ<jxAùD@SeDe�x Ô ú Ô ��x Ô |sù á Ô {s{AxSåH6

ã Ô ù ä 7�<_UAfDRX[=9;>�@ ð 6bW�6_@ g �a5AUAfD�&GD@F7!6 l 6�@bGJI�L�i�>HGAY+9;N�@F7!6m�46_@bg l UAIS<a[_ID9&GJ>�W19;wsfS<�GnRQ[_UAIçGJI�L l UAIS<a[_ID9&GJ>Q° L7�UsI^R�>"UJ<m�'[kG�R�ZD9�5ARHGJR�9;� g 9;e/9;I�LS9;I^R!Wm[�Y;Y;GnRQ[jÿ�æsf�GJRQ[_UAIMCF9&Y"ZDIS[�æsfD9 < ��GJ>�R Ô 6DC1ZD9;UA>�uA@ig{�Û>�UDY+9;9&Ls[=IDwSOUJTR�ZD9 X [_>HOQR1��ISR�9;>�I�GnRQ[_UAI�G�<�7�UsIST�9;>�9;I�Y+9EUsI l UAIS<a[_ID9&GJ>V�Û>�UA�S<_9;d�O:[_I � rA[kGJRX[=UsIMGJI�L � 9;>"U^OQe�GAY+9A@ g G�uSR�UAI�G8:9&GAY"Z�@ X ë @�i�G�u Ô {s{AzD6

ã Ô ú ä B�G�<_dh9A@ � 6_@4GJI�LçB�GJd�G�<kG�[_ID9;I�@�WE6��46_@=gSöI]R�ZD9 l UAIS<a[=ID9&Gn>�W,9;wAfS<kGJR�UA>T��>"UA�S<_9;dM@hg ð UAfD>�I�G�<1UJT!öeDRQ[_�d�[_�&GJRX[=UsIMC1ZD9;UA>�u�GJI�L � eDeS<a[kY;GJRQ[_UAI�O;@w��UJ< Ô z @DeDe�xA|A|J��x�yv| á Ô {Syv|�åH6

ã Ô | ä û UAZ�@�7!6 ð 6_@3gSöI¹R"ZD9 l UsIS<o[_ID9&GJ>pöeDRQ[_d�G�<,W,9;wAfS<kGJR�UA>Q��>�UA�S<_9;dM@ig � fDR�UAd\GJRQ[kY;GD@P��Un<,xA{D@FeDe�yv| Ô �QyJ|Azá Ô {A{AùSåH6

xsz

ã Ô z ä �tR�U�@a��6�GJI�L 5^Y"ZD>�U^9;R"9;>&@ ð 6 g 6_@agAW19&LSf�Y+9&Lþö>HLS9;> X 9;9&LS��GsY�N�5AuSISR�ZD9&Ot[kO�T�UA>��[kO�Y+Usf�O���I�Y+UAdceD>�9&O�Ot[_�S<_9X <_UJ�!O;@hg'C�9&Y"ZDIS[kY;G�<ÜW19;e/UA>�R:7mW�5D7���C'W{AüJ�Vú Ô @S7�9;I^R"9;>�TVUA>�W19&OX9&GJ>HY"Z�[_I\5^Y"[_9;I^RX[o`bY�7�UAdheDfDRHGnRQ[_UAI�@ l Us>�R�Z7mGn>�UJ<a[_I�G\5ARHGJR�9�q'IS[_rA9;>HOt[_RQu á Ô {s{AüSåH6

ã Ô y ä �'[_>�N�@ g 6�ÿ'6_@3@3A�BDCcEGF�HjIKJ�L-BDN>J�Hlk�^_UVJ�N�mJ@Dÿ�IDwn<=9;�1USU�L�7�<a[aéFO�@ l 9;� ð 9;>HOX9;u < �Û>�9;ISRQ[kY+9;��B!G�<a<�@ Ô {Sy ý 6ã Ô ü ä 5^GJws9A@ � 6P�46_@bGnI�LB�òZS[_R�9A@47!6F7!6_@/�Q�Q�H@Y@3AbBDCcEGX6Eon�m'`�BDU]Ep`qIdJ�L-BDN>J�HirSsOL-Z�tSZOCcBDC�J�L�@�ÿÛIDwJ<_9;�1U^UDL]7�<a[oé�O;@

l 9;� ð 9;>HOX9;u < �Û>�9;ISRQ[kY+9;��B!G�<a<�@ Ô {Sysy^6ã Ô { ä 8:U^O�Gn>�wA9A@��ï6jÿ'6_@ ð UAZDI�OQUsI�@ö�6 û 6�@ji�Y���IS[_wAZSR&@1WE6:5�6_@�GJI�L�C:[_d�<kGJNs9A@`�ï6 �46_@dgAC1ZD9�W:[_R��;� û G�<_9;>�Ns[_I�Û>�U�Y+9&LSfD>"9MTVUA> l UsIS<o[_ID9&GJ>�7�UsI^R�>"UJ<V��>"UA�S<_9;d�O;@hg 5A� � i ð UsfD>�I�G�<�UAI l fDdh9;>Q[kY;G�< � I�G�<_u�Ot[kO;@���UJ< Ô�ý @

eDe�{Jús� ÔAÔ&ý á Ô {SyJùSåH6ã£x ýJä i�GJ>�NSd�GJI�@ ð 6�GnI�Lu�EGJR��A@S�H6 l 6�@_g � I��tR�9;>HGJRX[=rs9 � <_wAUs>Q[_R�ZDdÞT�UA>'5AUJ<_rA[_IDw�B�GJd�[a<_R�UAI ð GAY+Us�S[ÜC:u^e/9�ÿ:æAf�Gn�

RQ[_UAI�O�@hg�IDUARuA9;ReDfD�S<a[kOQZD9&L�6ã£x Ô;ä i�GJ>�NSd�GJI�@ ð 6:GJI�Lv�EGJR"�A@��H6 l 6_@wgS7�UAISrA9;>�ws9;I�Y+9�UJT�GJI��tR�9;>HGJRQ[_rA9 � <_wAUA>Q[_R�ZDd T�UA>\5AUJ<_rs[_IDw B!GJd�[o<_R�UsI

ð GsY+UA�S[jC:u^e/9�ÿ�æsf�GJRQ[_UAI�O;@ig�IDUAR1uA9;ReDfD�S<a[kOQZD9&L�6ã£xAx ä B'UJTV9;>&@ÿ6¤�46GJI�L C:[_�DNA9;I�@E8�6_@/g � Iò�tR�9;>HGJRQ[_rA9�i�9;R�ZDU�L TVUA>\R�ZD9 X [=IS[_R�9;��Cm[=dc9¹8Û[o<a[_ID9&GJ> ì f�GALS>HGnRQ[kY

7�UsI^R�>"UJ<H�Û>�UA�S<_9;dM@hg ð UAfD>�I�Gv<�UJT�öeDRQ[_d�[_�&GJRQ[_UAI�C1ZD9;UA>�uhGJI�L � eDeS<a[kY;GJRQ[_UAI�O;@1��Un<b|Sy^@JeDeDú ÔAÔ �Vú^xSy á Ô {süAüSåH6ã£xAù ä � w^GJIDUJrs[�YJ@ x�6AGJI�L û GJßt[kYJ@x�6_@�gsC1ZD9E5Af�Y;Y+9&O�Ot[_rA9 � eDeD>�U�àS[=d\GJRQ[_UAIv�Û>�U�Y+9&LSfD>"9TVUA> X [_IS[_R�9;��C:[_dh9�öeDRQ[_d�G�<

7�UsI^R�>"UJ<�UJT8�[a<a[_ID9&GJ>�5AuDOQR�9;d�O�@hg\��ÿ:ÿ�ÿ%C�>HGnI�O�GAY+RQ[_UAI�O�UAI � fDR�UAd�GnRQ[kY\7�UAISR�>�UJ<�@w��UJ<mxs{D@�eDe Ô {AùAxn� Ô {AùA|á Ô {A{JúDåH6

ã£xJú ä 7�9;�DfDZ�Gn>&@¤�ï6 � 6mGnI�L 7:U^OQRHGJID�&G @o��6_@yg � eDeD>�U�àS[_d�GJRQ[_UAIæ��>�UDY+9&LSfD>�9&OcTVUA>�R"ZD9çöeDRQ[_d�G�<h7:UAI^R">�UJ<!UJT8Û[a<a[=ID9&Gn>�GJI�L l UAIS<a[_ID9&GJ>�5Au�OQR"9;d�O;@hg ð UAfD>�I�G�<UJT�öeDRX[=d�[=�&GnRQ[_UAI�C1ZD9;Us>�u GnI�L � eDeS<a[kY;GJRQ[_UAI�O;@¤��Un<,úSùD@eDe�z Ô |J��zAxSy á Ô {süJúDåH6

ã£xA| ä W1uSGJI�@Dÿ61�46_@gSöeDRQ[_d�G�< X 9;9&LS��GsY�N�7�UAISR�>�UJ<�UJTj8Û[a<a[=ID9&Gn>�5AuDOQR�9;d�O�@hg ð UAfD>�I�G�<�UJT:öeDRQ[_d�[_�&GJRQ[_UAIõC,ZD9;UA>�uGJI�L � eDeS<a[kY;GJRQ[_UAI�O;@w��UJ<4úAú�@SeDe�ùAùAùJ��ùszAx á Ô {AüJú åH6

ã£xAz ä C1�&GsOtT�9&OXRHGAO;@45�6 û 6_@ � I�GJwsIDU^OQR�UAf�@3��6�ÿ'6_@�GJI�L �4[_dh9;IS[kLS9&O;@�CE6 û 6_@�g�5ARHGJ�S[a<a[=�+[_IDwþöeDRQ[_d�G�<�7�UAISR�>�UJ<�UJT8Û[a<a[=ID9&Gn>�5AuDOQR�9;d�O,�1[_R�ZMG û 9;ID9;>+G�<a[=�;9&L�7�U^OQR�@hg�öeDRQ[_d�Gv<�7�UAISR�>�UJ< � eDeS<a[kY;GJRQ[_UAI�OEGnI�L�iM9;R"ZDU�LDO;@���UJ<�|D@eDe ÔAÔsÔ � ÔAÔ y á Ô {süJúDåH6

ã£xSy ä �ç9;>"ID9;>&@AWE6 � 6AGJI�Lc7�>�fD�A@ ð 6A8!6�@�g X 9;9&LS��GAY"Nh7:UAI^R">�UJ<1��ZS[kY"ZT��>�9&OQ9;>"rA9&O:öeDRQ[_d�G�<a[_RQu�TVUA>15AuDOQR�9;d�O4�,[=R"Zq'IDN^IDUJ�IB��Gn>HGJdh9;R�9;>+O;@hgE�Qÿ�ÿ:ÿ CF>HGJI�O�GAY+RX[=UsI�O1UAI � fDR�UAd\GJRQ[kY�7�UAISR�>�UJ<�@���UJ< Ô ùD@SeDe�zAx Ô ��zAxs{ á Ô {AzAüSå+6

ã£xAü ä ì f�@3x�6�@�gAW1UA�Df�OQR�7:UAI^R">�UJ<�UJT l UsIS<o[_ID9&GJ>hq'I�Y+9;>�RHG�[_I�5AuDOQR�9;d�O��1[_R�ZDUsfDR û 9;ID9;>HG�<a[_�;9&L�iõGnRHY�ZS[_IDw�7�UsID�Ls[_RQ[_UAI�O;@ig���ÿ:ÿ�ÿòC�>+GJI�O�GAY+RQ[_UAI�O,UAI � fDR"UAd�GJRQ[kY�7�UsI^R�>"UJ<�@i��Un<�ú ý @SeDe Ô ú^|sùJ� Ô ú^z ý á Ô {A{A|SåH6

ã£xA{ ä 8:UAfD>HLDGsY�ZD9;�Q5J[_wAfD9;>HLs[kL�ß�GJID9A@�B�6�GJI�L X <a[=9&O"O;@�i¹6�@�gSöeDRQ[_d�G�<7�UsI^R�>"UJ<�UJT l UAID� <a[_ID9&GJ>\5AuDOQR�9;d�O;@ig � fDR�Us�d�GnRQ[kY;GD@���UJ<jxAùD@SeDe�ùSyJùJ��ùSyv{ á Ô {süSyAåH6

ã£ù ýJä 81GJIDNDO;@�B�6�CE6_@�5Ad�[=R"Z�@�WE647!6�@�GJI�L��¹GJIDw/@be�6_@jn�EGF�NVBw\�FOBDU]NVCcF�Hjn�BDNVX_['BDX_N>U%`%Pz\�J'Z�U]H{C�L_|8rdtK`�BDCcEGF�BDC�J�LF�LMZ)IdJ�L-BDN>J�Ha@/7�ZS[kY�ZD9&OXR�9;>&@�ÿÛIDwJ<kGJI�L < �þ[a<_9;uA@ Ô {A{AzD6ã£ù Ô;ä ë GsOt[_9&Y�NJGD@��H6�GJI�LMCF>Q[_wAwJ[kGJIS[�@�WE6�@�}+C ~/U]N>U]LMBDCcF�H3F�LMZu�+H�|�U��%N>F�Cc[p�YC�[�[VF�BDCatw�]X6F�BDC�J�L`G�aCcB�^q�lA�A�H{C�[�F�BDC�J�L.BDJ� J�X6L-Z�FON�mV��wJ�CcLMB/IKJ�L-BDN>J�HM�wN<J6��H{U]Ep`;@ l 9;��e�UA>"N < 5AeD>X[=IDws9;>��®��9;>Q<kGJw�@ Ô {A{ Ô 6

x�y

ã£ùAx ä 7�<_UAfDRX[=9;>�@ ð 6bW�6_@ g �a5AUAfD�&GD@F7!6 l 6�@bGJI�L�i�>HGAY+9;N�@F7!6m�46_@bg l UAIS<a[_ID9&GJ>�W19;wsfS<�GnRQ[_UAIçGJI�L l UAIS<a[_ID9&GJ>Q° L7�UsI^R�>"UJ<)�[kG�R"ZD9�5ARHGJR�9;� g 9;e/9;I�LS9;I^R!Wm[�Y;Y;GnRQ[jÿ�æsf�GJRQ[_UAI�CF9&Y�ZDIS[kæsfD9 < ��GJ>�Rmx 6�ÿjà GndheS<_9&O;@hgQ��>�UDY+9;9&Ls[_IDw^OUJTSR�ZD9 X [_>HOQRF��ISR�9;>�I�GJRQ[_UAI�Gv<�7:UAIST�9;>"9;I�Y+9�UAI l UAIS<a[_ID9&GJ>o��>�Us�S<=9;d\O/[_I � rA[kGJRQ[_UAI�GJI�L � 9;>�U^OXe�GAY+9A@ g G�uSR�UAI�G8:9&GAY"Z�@ X ë @�i�G�u Ô {s{AzD6

xsü