Closed loop observers bundle for uncertain ... · Closed loop observers bundle for uncertain...

26
Closed loop observers bundle for uncertain biotechnological models Olivier Bernard, Jean-Luc Gouz´ e To cite this version: Olivier Bernard, Jean-Luc Gouz´ e. Closed loop observers bundle for uncertain biotechnological models. RR-4905, INRIA. 2003. <inria-00071676> HAL Id: inria-00071676 https://hal.inria.fr/inria-00071676 Submitted on 23 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es.

Transcript of Closed loop observers bundle for uncertain ... · Closed loop observers bundle for uncertain...

Closed loop observers bundle for uncertain

biotechnological models

Olivier Bernard, Jean-Luc Gouze

To cite this version:

Olivier Bernard, Jean-Luc Gouze. Closed loop observers bundle for uncertain biotechnologicalmodels. RR-4905, INRIA. 2003. <inria-00071676>

HAL Id: inria-00071676

https://hal.inria.fr/inria-00071676

Submitted on 23 May 2006

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

ISS

N 0

249-

6399

ISR

N IN

RIA

/RR

--49

05--

FR

+E

NG

ap por t de r ech er ch e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Closed loop observers bundle for uncertain

biotechnological models

Olivier BERNARD — Jean-Luc GOUZÉ

N° 4905

Août 2003

Unité de recherche INRIA Sophia Antipolis

2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France)Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65

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

/103254�23687�9;:�<>=�?$<>@BADCE6GFEH�I%JKMLONO/1P�QSR

TSUWV�X;Y&Z"[]\G^_X)`Wacb�de^gfih�Y�d.fkjlde^gX;^cmnbodn^_fkhp Y&mrqlmrdnVsXtYumv%fiXtjwagY�xGYum

y(zefo{|Y�d~}�fkX;fkzeY

�.bojwj�fizrd p Y&zeYsv�UWYszev�UwY�hE��Zi�i�i��[��Sfi�ld~�o�i�k��[��k�"jwbo�iYsm

�>���s�����W�o�i��� Y�jWzefkjEfimnY.hWfihWag^_hWYuboz�fk�wmnY�ze�kYszemD�5fkzSb"v�a_bimnm�fo���w^gfkdnYsv�UwhWfka_fk�i^_vsboawjwznflv%YumnmnYsms��TSUwYsmnY~fi�wmrYszn�iY�z�mDbozeY~bkhY%xGdeY�hwmn^gfih>fk��dnUWY&bimrqGX;jldnfkdn^cv�fi�wmnY�ze�kY�z�m� 3fk�wmnY�ze�kYszem¢¡^£deU�`whW¤GhWf�¡h>^_hWjW`ld�me¥ p Ys�kfkdnY p dnft�W^_fodnYuv�UWhWfiagfi�k^cv�boa¦mnqGmrdnYsX�m�5fkz~¡UW^cv�U§mrfiXtY&j�bozndem.fk�MdnUWY�X;f p Ysa�bozeY�`Whw¤8hwf�¡h�� � Y&d�bo¤iY&��YshWY%¨Wd©fo�MdnUwY"b pwp ^£de^gfihwboa�fk`ldejW`ldem~¡UW^cv�U§bozeYª 5hWfiha_^ghWYuboz«¥~�5`Whwv%dn^_fkhwm)fo��dnUWY>mrdebodnY�def p Ysmn^_�kh¬b1v%a_fimnY p a_f8fij,fk�wmnY�ze�kYszs�>TSUwYª�ka_fk�wbkaDv%fih8�iY�ze�kYshwv%Ytfo�SdnUwYsmnY�hWfkhWa_^_hWYsbkzfk��mrYszn�iY�z�m­^_m�jWzef��kYsh�� � Y�`wmnYDdeUWY�h)dnUWYumrY�fk�wmnY�ze�kYszem­dnf p Ysmn^g�ih�^gh8deY�ze�®bkai��bkmnY p fi�wmrYszn�iY�z�m­¡UW^cv�U�jWzeY p ^cv«d�dnUWY�^_hideY�ze��boacm^_h�¡Uw^_v�U�dnUwY)m|d�b�deY©^cma_qG^ghW��� � Y&zn`Wh$^_h1jwboz�boa_a_Y�a­b;�Wzefib p mnY%d.fo�M^_hideY�ze��boa­fk��mrYszn�iY�z�m�bkh p ¡�Y�mnY�a_Ysv%ddnUWY&�EYsmrd�fkhwYsms�TSUWY�X;Y%deUWf p ^cm�^ga_ag`�m|dezebodnY p ¡^£deU�b"X;f p Y�a p Yumnv�zn^_�W^_hW��deUWY��W^_fGv�fkhG�kYszemn^_fkh�fo�Mb"mn`W�wmrdnz�b�deY~`�mr^_hW�tXt^cv%zefGfkze�ibkhW^_mnX�mD^_hbt�W^_fkzeYsbkv%dnfizs�¯1°8±¦²n³)´ ��µ��i� hWfihWag^_hWYubozSfk�wmnY�ze�kYszems¶8`WhW¤GhWf�¡h>^_hWjW`Wdems¶WX�bkmem���boacbohwv�Y~X;f p Y�acms¶l�W^gfijWzefGv�YsmemrYum�¶Gzefk�W`�m|dehWYsmem�¶G�W`wh p a_Yfo�Mfk��mrYszn�iY�z�m��

� ������!��w����������© ����.����� O�)��� ����+-����.���� �$!%������M'����)�%��*"!����>�� +B )�����)���;�>�

�� �� � � ��� fi`wmtv%fkh�m|dezn`W^cmnfkhwm p Ysm"fk�wmnY�ze��b�dnYs`Wz�m&j�fi`Wz p Ysm"jWznflv�� p �um��W^_fodeYsv�UWhWfiagfi�k^��8`WYsms�O}�Y>mnfkh8d p Yum�Y�x8deY�h��mn^gfihwm p Yum�fi�wmnY�ze�®bodnYs`Wzem�bkmnq8X;jldefode^��8`WYum) 5Ysh��Efk`wv�agY"fk`W�iY�zndnY®¥«¶��i`w^�jEY�zeX;Y%drdeY�h8d p�� Yum|de^gX;Y�z©a � ��deb�d p Y)X;f p VsagYum p fih8dv%Yszrd�bo^_hWYsm"jwbkzrde^gYum"mnfkh8d"^_hwv�fkhWhG`WYum�� � fi`wm"`ldn^_ag^cmnfkhwm p Yum"mnfkzndn^_Ysmtmr`wjWjWa���X;Y�h8debk^gzeYsm)j�fi`Wz�v%fihwm|dezn`w^gzeY p Yum"fi�wmnY�ze�®b��dnYs`Wz�m&hWfkhwag^_h��sbk^gzeYsm�Ysh,��fi`wv%a_Y;�5Y�zeX���Yk��y(`W^cm�hWfi`wm�v�fkh8dnze`W^cmrfihwm p Ysm&fi�wmnY�ze�®bodnYs`Wzem&mn^_Xt^_acbo^_znYum�¶�X�bk^_m��$^_h8dnYszn��boa_a_Ysms¶�8`W^ p fihWhWY�h8d&`WhWY;Yum|de^gX�b�de^gfihO�8boz�boh8dn^_Yk�;}�Y�acb�hwfk`wm©jEY�zeXtY�d p Y�a_bkhwv%Ysz�`WhOYshwmnY�X)�wagY p�� fk�wmnY�ze��b�deY�`Wz�m~mn^_X)`Wagdebkh���Y��X;Y�h8ds¶ij�fi`WzDboX��sag^_fkzeY�z�agYum(jEY�zn�5fkzeX;bkhwv%Yum�� � fk`�m p fkhWhwfkhwmMa � Y�xlY�X;jWa_Y p�� `Wh;X;f p V�a_Y p �uv%ze^g��boh8d(acb~�w^gflv%fihG�kY�z�mn^gfih p�� `Whmn`W�wmrdnz�b�djwboz p YsmSX;^_v�znfGfizn�8bohW^cmrX;Yum¢Ysh��w^gfiz �ubkv«deY�`Wzu�!�´ �s� ² �#" � ��� fk�wmnY�ze��b�dnYs`Wz�m�hwfkh�ag^_h��sbk^gzeYsms¶GY�h8dnz$��YumS^gh�v%fkhwh8`wYsms¶l�W^gfijWzefGv�� p �um�¶GX"`Wa£de^�fk��mrYszn��b�deY�`Wz�ms�

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

, � ���%�

/103254�23687�9;:�<>=�?$<>@ A¢CE68FEH�I%JKMLON�/1P$QSR-�/�. /1<>:�A'/%=�< /«? A

91032�4�A65�7�2�598;:=<�>�?M2 FwI«?�H9@®2A>B<¦032ACD-t6FEM6HG�A"I(7®FEH�L86I¢FJGLK�M�4�4;N92�8O4QP9R;P9SQP

:©IUT F�2 0AC�K�<¦03234�23687FVXW¢687sH(FE7YE'Z123HM7s2 F[V]\|78AQ^�68FEH�I�0 KML_VX`Q<¦K�a86bZ$2 HM7s2 FcVd\|7

e f �)����������D�M!%�)�

TSUWY��W^_fodeYsv�UWhwfka_fk�k^cv�bka�jwznflv%YumnmnYsm©^_h mrdn^_zeznY p d�bohW¤§zeYsbiv«defkz�m©vsboh ��Y�X;f p YsagY p �Gq§hWfihWa_^ghWYuboz p ^Xg¦Y�zeY�h8dn^cboa(Y �i`�b�dn^_fkh�m^_h8�ifka_�G^ghW�1hwfkhWa_^ghwYsboz)�W^gfiagfi�k^cv�bkaD¤G^ghWY�dn^cv�m� 5Yk� �w�§v�Y�a_ag`wa_bkz��kzef�¡SdnU,z�b�dnYi¶��w^gfijWznf p `�v«dn^_fkh¬z�b�deYk¶��g�_� ¥«��h(YsznqOfo� dnYsh�¶MdnUwYjWzeYsv�^_mnY��5fiznX"`Wacb�dn^_fkh>fo��deUWYsmnY©¤8^_hWY�dn^cv�mS^cm�hwfod¡�Ysaga¦¤GhWf�¡h�¶lbkh p zefk`w�kU>bkjWjWzef®xG^_X�b�de^gfihwm¢bkh p UGqGjEfodnUwYsmnYsmSbozeY�X�b p Ydnf�¡ze^gdnY�dnUwY�X;f p Y�a �Bi�Y�d�`wm.mn`WjWjEfimnY&hWf�¡ dnUwbod�¡�Y�bozeY�bk�Wa_Y�dnf�X;Ysbimr`WzeY&¡^gdnUWfi`ld.hWfk^cmnY�mrfiXtY&fi`ldnjw`ldems¶�bkh p dnUwbod¡�Y"¡Sboh8d�def$�W`W^_a p boh�fi�wmnY�ze�kY�z�dnf�Ysmrdn^_X�b�dnYtdeUWYtmrdebodnYt��boze^_bk�WagYum��)\lfkX;Y"z�b�deUWY�z©�kYshWY�z�boa�X;Y%deUWf p fka_fk�i^gYum�Y�xG^cmrd~�5fizhWfihWag^_hWYuboz�mnqlm|deY�X�m$j �l¶_kml�boh p ^_h1jwbkzrde^_v�`Wa_bkz�5fkz��W^gfiagfi�k^cv�bka�mrqlmrdnY�Xnj �ol ¶��W`ld.deUWY�X;f p Y�a�Uwbkmdnfª�EY�Y%xWbiv«dna_q>¤GhWf�¡h��p�Ysvsbo`wmnY&fo��dnUWY"�wb p �8`wbkag^gd|q>fk��deUWY�X;f p Y�acm.^_h1�W^_fodeYsv�UWhWfiagfi�kqi¶l^£d©^_mfk� dnYsh1jWznY��5Y�z�bo�Wa_Y�dnf>�W`W^_a p b p ^Xg¦Y�zeY�h8d�¤G^gh p fo�fk��mrYszn�iY�z� 5fo� deY�h$v�bkaga_Y p bkmnqGXtjWdnfode^_v~fk��mrYszn�iY�z«¥«¶GhWfod`wmn^_hW�)deUWY&`WhW¤GhWf�¡h�jwbozndem& 3�W^_fka_fk�k^cv�bka�¤G^_hWY%de^_vsme¥�fk��dnUwY&Xtf p Ysa �q h$dnUwY)v%fi`Wh8dnY�zejwbkzrddeUWYsmnY�fk��mrYszn�iY�z�m�U�b®�kY&¡�Ysbo¤iY�zjWzefkjEY�zndn^_Ysm�v%fkh�v%Y�zehW^_hW�w¶W�5fkz.Y�xlbkX;jWagYi¶WdeUWY)z�b�deY&fo�Dv%fih8�iY�ze�kYshwv%Yjsrk¶­�Yl �©TSUWYsmnY�fi�wmrYszn�iY�z�m&jXr�lMbkznY&��bkmnY p fih1X;bimnm � �wboacbohwv�Y�v%fihwmr^ p Yszebodn^_fkhwms¶wboh p mr^_hwv%Y)dnUWYsq1bozeY�^gh1fij�Ysh�� agfGfkj�¶wdeUWY�qbozeY&hWfkd.�kY�zeq>zefk�w`wm|ddefªY�zezefkz�m�fih$dnUWY)Ysmrdn^_X;bodn^_fkh$fo�MdeUWY�^_hutw`WYshid~X;bimnmnYsms� � Y��iY�zndnUWYsagYumnm�deUWYsmnY�fi�wmrYszn�iY�z�m�znY �i`w^gzeYdnUwYtX;Yubkmn`WznYsX;Y�h8dem~fo��mnfkX;Yt�ibimrYsfk`wmvtwf�¡�z�b�dnYum��$q h�dnUW^cm�jwbkj�Ysz©¡�Y"debo¤iY)�EY�hWY�¨Wd&fo��dnUWYumrYtfk`ldejW`ld�m©bkh p fk��fkdnUWYszX;Ysbimr`WzeY�X;Yshid�m.z�b�deUWY�z~Ysbkmnq�dnf>jEY�zn�5fkzeX�^gh§jwzebiv«dn^cv%Y� 5jxw)¶Ev�fkh p `wv«de^g�G^gd|qk¶M�g�_� ¥«��TSUWYsmnY�fk`WdnjW`ld�m©znYum|d�fih§jWUGqlmr^cv�bka�fizv�UWYsXt^cv�bkaDacb®¡.m�dnUwbod"bozeY�¡�Y�a_aD¤GhWf�¡h�¶Mboh p jWzef��G^ p Y;deUWY�zeY%�5fiznY;zeY�a_^_bk�Wa_Y§ 5hWfihWag^_hWYuboz«¥�znYsa_bodn^_fkhwmnUW^_jwm�¡^gdnU,dnUwY>m|d�b�deY��boze^_bk�Wa_Ysms�cyWfiaga_f�¡^_hW��dnUWY�^ p Yub&jWzeYsmnY�h8dnY p ^gh�j Zml ¶i¡�Y`wmnYdnUwYsmnY.fk`ldejW`ld�m(dnf)�W`W^_a p b&v�agf8mrY p � agfGfkjthWfihWag^_hWYubozDfi�wmrYszn�iY�zu¶dnU�b�d p f8Yum)hwfod"`�mrY�deUWY>`whW¤GhWf�¡h ¤G^ghwY%dn^cv�ms¶M�W`ldtdebk¤kYsm"b p ��bkhid�bo�iY�fo�dnUwY�b pwp ^£de^gfihwboa�fk`ldejW`ld�m�defObkv�Uw^gYs�kYª�EY%dndnY�zjWzefkjEY�zndn^_YsmSfk��zefk�W`wmrdnhwYsmem�bkh p v%fih8�iY�ze�kYshwv%Y~zebodnYk�

TSUW^cm¢jwznfi�WagYsX ^_m�zeY�acb�deY p ¡^gdnU>dnUWY�a_^ghWYuboz�dnUWYsfkzeq;fo��zeY|{|Yuv«dn^_fkh�fo��`whW¤GhWf�¡hª^_hWjW`ld�m&jXru�l¶�ru�G¶xzYl ¶G�W`ld¡�Y©bkznY~UWY�zeY^_h$b;hwfkhWa_^ghwYsbozS�5z�boX;Ys¡�fizn¤¦�"{$fiznYsf��kY�zu¶8¡�Y&`wmnY�mnfkX;Y&mrjEYsv�^£¨�v�^£de^gYumfo�MdeUWY&�W^_fka_fk�k^cv�bka¦Xtf p Ysa_mdnUwbod�¡�Y�v�fkhwmn^ p Y�zu�'q hjwbkzrde^_v�`Wa_bkzs¶idnUwY©v�a_bimnmnYsm�fo��mnqlm|deY�X dnU�b�d¡�Y©v%fihwmr^ p Ysz© 3¡UWY�zeY�deUWY©¤8^_hWY�dn^cv�mSbozeY~v�fkhwmn^ p Y�zeY p bim¢`Whw¤8hwf�¡hª^ghwjW`ldem�¥�bozeY�kYshWY�z�boa_a_q>hWfkd�fk�wmnY�ze��bo�Wa_Y� 5�W`Wd p Y�dnYsv%debk�WagY®¥«¶¦mrfªdnUwbod.dnUWY"v%acbkmemr^cv�bka�X;Y%dnUwf p m�5fkz~fk�wmnY�ze�kYszem�¡^gdnU§`whW¤GhWf�¡h1^ghwjW`ldemv�bkhWhWfkdS�EY�bojwjWag^_Y p �

TSUWYsh�¡�Y&^_Xtjwznf��iY~deUWY&jWzefkjEfimnY p fk��mrYszn�iY�z�m¢�Gq>`�mr^_hW�;dnUwY�^_z�jWzefkjEY�zndn^_YsmSa_^ghw¤kY p def p ^dg¦Y�zeY�h8de^_bka�^ghwY �8`wboa_^gdn^_Ysm.bkh pjEfimn^£de^g�G^gd|q1dnf p Yumr^_�khO^gh8dnYszn��bka�fi�wmnY�ze�kY�z�m*jXrFro¶6rs�ol(dnUwbod&vsboh p Ysbka(¡^£deUO`whwv%Yszrd�bo^_hide^gYum�¶�mn`wv�U,bkm©^_XtjwznYuv%^cmr^_fkhO^gh dnUwY

|=|3}m~u�%�����

^_hutw`WYshid.v�fkhwv�Y�h8dnz�b�de^gfih>X;Ysbimr`WzeY�X;Yshidu��TSUwY©^ p Yub"fk��^_h8dnY�ze��boa¦fk��mrYszn�iY�z�mD^cm�dnf;jWzefkjEfimnY~boh�Ysmrdn^_X�b�deY©fk��dnUwY&^gh8dnYszn��bka^_h�¡Uw^_v�U�dnUWY�mrdebodnY&^cmmr`wznY©dnf;a_^gYi�

� hWY�¡ dnzeY�h p ^ghOdnUwY p Ysmn^g�ih�fk��fk��mrYszn�iY�z�m.^cm©dnUWY;^ p Ysb>dnf$^_hW^£de^_bkag^���Y�mn^gX"`WagdebohwY�fk`�mra_q1mrYs�kY�z�boa�fk��mrYszn�iY�z�m~bkh p defdebk¤kY~��YshWY%¨WdSfo��bkaga�dnUwYsmnY�Ysmrdn^_X�b�deYsm�^gh�fkz p Y�z¢dnf)^_X;jWzef��kYdeUWY~mrdebodnY�Yum|de^gX�bodn^_fkh�j �ol � � Y©Y%xljWa_fk^gd¢deUW^_m�^ p Ysb�UWY�zeY~bkh pdnUwY"de`WhW^_hW�1jEfimemr^_�W^_ag^gd|q1fo��dnUWY;fk��mrYszn�iY�z�m�¡UW^cv�U,boa_a��i`wboz�boh8deY�Y"b��Efk`Wh p ^ghw��fk�¢deUWY;znYuboa�dnz�b�{|Yuv«dnfizn^_Ysms��p�Ysvsbo`wmnYtfo�dnUwY.^gh8deY�ze�®bkal�5z�boX;Y�¡�fkze¤¦¶o¡�Y~bozeYSbk�Wa_Ydnf&d�bo¤iYSdnUWY.�EYsmrd�mnX�boa_agYum|d¢YshG�kY�a_fkjEYfo�EdnUw^_m��W`Wh p agY.fk�­fk�wmnY�ze�kYszems¶®dnf�^_X;jWzef��kYdnUwY&Ysmrdn^_X;bodn^_fkh�^gh1b;mrdnze^g¤G^_hW�;¡�b®qi�

TSUWYSjwbkj�Ysz(^_mMfizn�8bohW^���Y p bkm��5fiaga_f�¡.m���b�� dnYszDmrfiX;Y p Y%¨whW^gdn^_fkh�m�¶i¡�YSzeYsv�bkaga8deUWYhWfode^gfih"fk���nbkmnqGXtjWdnfode^_v�fk��mrYszn�iY�z�m��¢^_hfkjEY�h�agfGfij� 3mnYsv%dn^_fkh��i¥«¶8dnUwY�h��k^_�kY�btv%a_fimnY p a_fGfkjªfi�wmnY�ze�kY�z© �mnYsv%dn^_fkh��i¥Dbkh p mnUWf�¡ acb�deY�z�dnUwbod�deUW^_mSfi�wmnY�ze�kY�z¢^_m�X;fkzeYzefk�W`wmrd¢def"Ysznzefkz�mD^_h�dnUWY©^ghwjW`ldem&  mrYuv«de^gfih>Z8¥%�(TSUWY�h�¡�Y�mrUwf�¡ UWf�¡ dnf p Yumr^_�kh>bkh>^_h8dnY�ze��boa¦fk��mrYszn�iY�zD¡UW^cv�U>Yum|de^gX�bodnYsm�Efk`Wh p m�5fkz�dnUWY"m|d�b�dnY)�®bkzn^cbo�wagYum� 3mnYsv%dn^_fkh��k¥%��}�fkX)�w^ghW^_hW�ªbªmnY%d~fo�Dmr`�v�U1fk�wmnY�ze�kYszems¶l¡�Y"mrUWf�¡ UWf�¡ dnfª^_X;jWzef��kY�dnUwYmrdeb�deY.Ysmrdn^_X�b�deYk� � Y.Ysh p `Wjª^_hªmnYsv«de^gfih�&�Gq"boh�Y�xWboX;jWa_Y¡UWY�zeY�b�X;f p Y�a�fo�­�W^_fkjWzeflv%YsmemM^cm¢mn^gX"`Wa_bodnY p bkh p b&�W`wh p a_Yfo�Mfk��mrYszn�iY�z�m¢^cmSjWzefkjEfimnY p �5fizdnUw^_mSX;f p Y�a�boh p v%fiXtj�bozeY p ¡^£deU�deUWY&X;fkzeY&v%acbkmemr^cv�bkaEfij�Ysh�a_fGfkj�^gh8deY�ze�®bka­fk�wmnY�ze�kYszs�

� ���� &��!%�)��� )��#�� �$��!���!��)���

� �W^_fkjWzeflv%Ysmem©^gh,b�m|de^gzeznY p d�bohW¤§�w^gfiznYubkv«defkz�v�bkh��EY p Ysmev%ze^g�EY p �Gq�b$mrY�d©fk� �Ov%fk`wjWagY p X;^cv%zef�� �W^_fka_fk�k^cv�bka�bkh p �w^gf �v�UWYsXt^cv�bka­znYubkv%dn^_fkhwm�¡UW^cv�U�debo¤iY�jWa_biv%Y�^_h�deUWY�zeYsbiv«dnfizboh p ^ghG�ifka_�kY�b�mrY�dSfk��� �W^_fka_fk�i^_vsboa¦fkz.v�UWYsX;^_vsboa�mnj�Yuv%^_Ysmmn`wv�UbkmSX;^cv%zef�� fkze�ibkhW^_mnX�m�¶8mr`w�wm|dezebodnYum�¶lX;Y%d�bo�Efka_^£deYsms¶lY�h��sqGXtYum��_�_�

TSUWY p q8h�boX;^_vsboaW�EY�U�b®�8^_fkz¢fo��b�v%fih8dn^_h8`wfk`wmnagqtm|de^gzezeY p debkhW¤t�W^gfiznYubkv%dnfkz.  }S\lT��¥D^_m¢fo� dnYsh p Yumnv�zn^_��Y p �Gqtb&�iY�hWYszebkaX�bkmem � �wbka_bkhwv%Y©X;f p Y�a­fo��dnUwY��5fka_agf�¡^_hW�"�5fkzeX  3mnY�Y&Yi� ���Ljsrk¶E�Yl ¥��

����������������! "�$#%�&�(') *�&#%�&�,+.-/�$#%�0�213�����   r®¥q htdnUW^cm(X;f p Y�a ¶odeUWY�kYuv«defkz �!�4���65879��:;7�<,<�<�7=��->�;? ^_m�deUWY�kYuv«defkz(fo�EdnUwY.v%fkh�v%Y�h8dezebodn^_fkhwm�fo�EdnUwY�®bkzn^_fk`�m(mrjEYsv�^gYumM^gh��

mn^ p Y¢dnUWY�ag^��8`W^ p X;Y p ^_`WX$��TSUwYD¨wz�m|d�dnYsznX �@������� fkh�deUWY�zn^_�kU8d � Uwbkh p mr^ p Y¢zeY�jwznYumrYshid�m¦dnUwY��W^_fka_fk�i^_vsboakbkh p �W^_flv�UWY�X;^cv�bkav%fihG�kY�z�mn^gfihwm­^_h)deUWY�zeYsbiv«defkz� 3j�YszM`WhW^gdMfk�Wdn^_X;Yu¥�bkvsv%fiz p ^_hW�def�deUWY�`Wh p Yszna_qG^ghW�~znYubkv%dn^_fkh�hWY�d|¡�fizn¤¦��TSUwY � �BA(� � X;bodnze^£x� ^cm.b�v%fihwm|d�boh8d� 3mrdnfi^_v�UW^_fkX;Y�dnze^_v�� a_^g¤iYu¥�qG^gYsa p v�f8Y�Cªv%^_Y�h8d.X�b�dnze^gx¦��TSUWY&�kYuv«defkz �������3�D���E5E�&���=7=�,:F�����=7,<�<,<,7=�6G��&���9�;? ^_mb��kYuv«defkzDfk� � ° �W�o�6H ´JI ���l� ° �  5fkz�v%fkhG�iY�z�mr^_fkh"zebodnYsm�¥«�MTSUWY^_hutw`WYsh8dD�5Y�Y p ^ghw�)v%fihwv%Yshidezebodn^_fkht^_m¢znYsjWzeYsmnY�h8dnY p �Gq � +.- �$#%� ¶boh p" "�&#%� ¶�deUWY p ^_a_`ldn^_fkh§z�b�deY�^cmdnUwY)z�b�dn^_f�fo�MdeUWY)^_hutw`WYsh8d twf�¡ z�b�dnY&f��iY�zdeUWY��ifka_`WX;Y�fo�MdnUwY��5Y�zeX;Y�h8dnYszs�vywfkz�mebo¤iYfo��WzeY��G^gd|q§deUWY�dn^_X;Y p Ysj�Ysh p Y�h�v%Yª¡^_aga���Y>fkX;^£dndnY p ^gh,deUWY��5`lde`WznYi��TSUwYªa_bim|d&deY�zeX 1����� zeY�jWzeYsmnY�h8d�m©dnUWYª�8bkmnY�fi`wmY%xWv�UwbkhW�kY©¡^gdnU�dnUWY&fi`ldemn^ p Y�fo��dnUWY��5YsznX;Y�h8deY�zu�

q h§deUWY;mrY �i`wY�a�dnUWY;X�bojWjw^ghW�8m ���&���=7K1����� bozeY"bkmemn`WX;Y p def��EYML 5 fkh�dnUWY;v%fihwmr^ p YsznY p hWfkhwhWY��8b�dn^_�kY p fkX�bk^ghON©�TSUWY�mnfka_`ldn^_fkh�m�fk��deUWY&fkz p ^_hwbozeq p ^XgEYsznYsh8dn^cboa­Y �8`wbodn^_fkhwmbkznY©¡�Y�a_a p Y%¨whwY p boh p `Whw^��8`WYi�

P$±RQD´ �6S ° �,H5�UTWVYX[Z]\_^3`�acbdb]egf3`�h�igaEhjh�ig`kh&l%a�m�`dn�h�oEl]p�`�b[orqKb]scb]ht`�fuVrZd\vaEl%`Vtw.oExy`�l[aEzJ{3ec|;|�`�lt\v}%oEegzJ{;`d{vo8z N q�o8l~ p��c`�z!}%oEegzJ{;`d{p�z;|�egh&b�� +.- a8z>{� DaEzJ{ ~ p��c`�zv|�ocb]p�h$p��c`�p�z�p�h&p�a8w�ndoEzJ{Ep�h$p�oEz�b��

TSUW^cmjWzefkjEY�znd|q�^_mS�iY�hWYszebkaga_q��kYszn^g¨wY p �5fizX;bimnmS��boacbohwv�Y�mnqlm|deY�X�m&j � l �� Yªbkmemr`WX;Y;deUwb�d"b$j�boznd �65 fo��dnUwY>m|d�b�deY � vsboh,�EYªX;Ysbkmn`WzeY p fkh�� a_^ghWYi��TSUWY>jwboznd�fo��dnUWY�m|d�b�dnY�¡Uw^_v�U¬^cm&hWfkd

X;Ysbimr`WzeY p ¶ ��: ¶�^cm.fk� p ^gX;Y�h�mr^_fkhv��� � Y�U�b®�kY�dnUG`wm �����&�65E7=��:E�$? � � Ytbkmemr`WX;Y&X;fkzeY�f��iY�zSdeUwb�d.deUWY)fi`ldnjw`ld���fo�MdnUwY

�Y�[|R���

mnqGmrdnYsX  5^ � Yk�(deUWY&mrY�d.fo�MXtYubkmn`WzeY�X;Y�h8dem�¥�v�boh��EY�mrjWa_^gd.^gh8dnfª�tjwbkzrd�m��

� ������ 5�;:���

�����   �i¥

¡^gdnUR�

� 5 � �65�� -� ��  3�8¥� : � 13�������� -  5ZG¥� � � �R�&�65E7=��:E������   �i¥

q h�fkdnUWYsz~¡�fkz p m~¡�Ytmr`wjWj�f8mrY"dnU�b�d�¡�Ytv�bohOX;Ysbkmn`WzeY&dnUwY"�8bkmnY�fk`�mtwf�¡�z�b�deYsm 13����� boh p boacmrf�b>mnY%d�fo�D�5`whwv«de^gfihwm©fo�dnUwY"mrdeb�deY �0��� 5 79� : � �~TSUWY�q1v�bkh1��Y"jWUGqlmr^cv�bka���boze^_bk�Wa_Ysm� 3jxw�¶Ejwbozndn^cboa�jWzeYsmemr`WzeY&fo�¢bª�ibkms¶wY�devk� ¥$zeY�acb�deY p def�dnUWYtm|d�b�deY� �(��m�^gd�¡^_aga¦�EY�^_aga_`wmrdnz�b�dnY p ^_hªdnUwY.�5fka_a_f�¡^ghW��¶i^_h�deUWY~�iY�hWYszebka�vsbkmnYdnUWYsznY p fGYsm�hWfod�Y%xl^cm|dSbohGq;^gh�{|Yuv«de^g�iY�zeY�acb�dn^_fkh�mrUW^_j�EY%d|¡�Y�Y�h"�$boh p"� �q h p YsY p deUWY��kYuv«defkz�m��;:)bkh p ����bkznYi¶w^_h§X�bohGq>zeYsbkag^cmrdn^cv�v�bimrYum�¶�X;bk^ghwagq$v%fiXtjEfimnY p fk� ��Y�zefims¶wbkh pdnUwY�hWfkh��$�sY�zef)deY�zeX;m~v�bkh��EY)v%fiX;jWag^cv�bodnY p bkh p hWfkh�� ^_h�{|Ysv%dn^_�kY&Y�xGjwznYumnmn^gfihwmSfo��dnUwY�¡UWfka_Y�mrdeb�deYk� � Y�U�b®�kY©dnUWYsznY��5fkzeYdnf;Yum|de^gX�b�deY�dnUWY&��bkzn^cbo�Wa_Ysm�¡^gdnU1boh�fk��mrYszn�iY�zu�

��� � � Q " °��.��agfihW��deUWY)jwbkj�Ysz�¡�Y�¡^_aga�^ga_ag`�m|dezebodnY�fi`Wz�X;Y%deUWf p ¡^gdnU�b��iY�zeq�mn^gX;jWa_Y��W^_fodeYsv�UWhwfka_fk�k^cv�bka�Y%xWbkXtjwagYi�� Y~bkmemn`WX;YdnUwbod�b)�wbkv%dnY�ze^cboaW�W^_fkX�bimnm~ ��O¥D^_m��kzef�¡^ghw�©^_h>b;}S\lT�&�GTSUWY�X;^cv%zef�� fkze�ibohw^_mnX�m�v�fkhwmn`WX;Y.deUWY~mn`W�wmrdnz�b�deY� bkh p jWznf p `�v%YSb�jWzef p `wv%d��;����mMX;fimrd(fo�WdeUWY�dn^_X;Y�^_ht�W^gfkdnYuv�UWhWfka_fk�iqk¶udnUwY���bkv«deY�ze^_bkaG�kzef�¡SdnU�z�b�deY ������� ^cmMb�v%fkX;jWa_Y%x�5`Whwv%dn^_fkh$fo��dnUwY�m|d�b�dnY�¡UW^cv�U�^_m�iY�hWYszebkaga_q�jEf8fizna_qª¤GhWf�¡h���q h�dnUWY�mnY �8`WYsa�¡�Y�bimnmn`WX;Y©dnUwbod � �&��� ^cmS`WhW¤GhWf�¡h��

TSUWY�X;f p Y�a�bimnmnflv%^cb�deY p ¡^gdnU�deUW^_m.Y%xWboX;jWa_Y�^_m�deU8`�mSdnUWY��5fiaga_f�¡^_hW� ���� ��!

�� � ���&�����! ���_� �#" 5 �������R') "�$� +�- �%�j��� �&" : �������/' "� ��+�- � � �  ��8¥

¡UWYsznY �J+�- boh p � +.- bkznY�deUWY.^_hutw`WYshid�mr`W��m|dezebodnY.boh p jwznf p `wv%d¢v%fihwv%Yshidezebodn^_fkhwms¶kbkh p'",5 boh p("�: bozeYSq8^_Y�a p v%fGY�C�v�^gYsh8dems�TSUW^cmX;f p Y�a­Uwbim�dnUWY��5fiznX jWznYumrYsh8dnY p ^_h,  ru¥�¡^gdnUR�

�u� �*)F7��#",567+"�:E� ? 7 ��+�-� �-, 7.�J+�-J7 � +�-J� ? 7y13�&��� �@�/,�70, 70,�� ?   zk¥

� Y�bimnmn`WX;Y©dnUwboddnUWY&��bkv«deY�ze^_bka¦�W^gfiX�bkmemv�boh��EY&XtYubkmn`WzeY p �'{$fkzeY�f��iY�z�¡�Y&mn`WjWjEfimnY©dnUwbod.¡�Y&v�bkh�Yum|de^gX�bodnY�dnUwYjWzefkjEfkzndn^_fkh�fo� � ^gh�dnUwY�X;Y p ^_`WX ¡^gdnU1zeYsmnjEYsv«ddef1�;�¢TSUWYumrY&zeY�acb�de^g�iY©X;Yubkmn`WznYsX;Y�h8dembkznY�fo� deY�h$X)`�v�U�Yubkmn^gYsz� 3bkh pboacmnf"a_YsmemY%xljEY�hwmn^_�kYu¥¢deftfi�ldebk^gh�dnU�boh�dnUWY�bk�wmnfka_`ldnY���boa_`WYsms�

� Y©U�b®�kY©dnUWYsznY��5fkzeY;�

� 5 � �  Ak8¥� : � �-,�7+,�7+,g� ?  3�8¥��� � ��U' �   rs�8¥

2 `Wzbo^_X ^cm�dnf�Yum|de^gX�bodnY � boh p �;¶l¡^£deUWfk`Wd.`wmr^_hW�;deUWY&`WhW¤GhWf�¡h�¤G^ghWY�dn^cv�m ������� �

|=|3}m~u�%�����

TSUW^cm)Y�xWboX;jWa_Y>^cm)�iY�hWYszn^cvo¶(boh p ^gh Xtf8m|d;fo�deUWY�vsbkmnYsm � v%fi`Wa p ��Y>dnUWY�f®xlqG�kY�h bkh p ��deUWY���� : �,TSUWYsh dnUwY�ibimrYsfk`wm�Y�xlv�U�bohW�iYsm�¡^£deU§b�dnX;f8mrjWUwY�zeY~Uwb®�iY�def���Y�d�bo¤iY�h�^gh8dnf�biv�v%fi`Wh8ds�

w.YsznY�¡�Y�¡^ga_aGv%fkh�mr^ p Y�z�dnUwY�bohwf®xG^cv p Y�hW^gdnze^£¨Ev�b�de^gfih��Gq p Y�hW^gdnze^g�5q8^_hW�~�wbkv%dnY�ze^cbW��TSUWYsh�deUWY�mn`W�wmrdnz�b�deY�\�v�fkzeznYumrjEfkh p mdnf;hW^gdnz�b�deY�boh p dnUwY&jWznf p `�v«d�y dnf;hW^gdnze^£deYk�DTSUWY&^_hutw`wY�h8d.^_mb;�wagYsh p fo��hw^£dezebodnY&boh p hW^gdnze^gdnYk�

q hwmrdnYub p fo��X;Yubkmn`Wzn^_hW��dnUWY���� ��bkh p ���(:;v�fkhwv�Y�h8dnz�b�de^gfih�¶�^gd�^_m&mn^gX;jWa_Y�z�def1X;Ysbkmn`WzeY)deUWY�z�b�dn^_f�� ����� Y��kYshO^g�mnf)�3bkzSdnUWY&`wmn`wbka¦v�fka_fkze^gX;Y�dnze^_v©mrYshwmnfkz�m�bka_mnf"jwznf��G^ p Y�deUWY&Ysmrdn^_X�b�deY©fk��deUWY&v%fkh�v%Y�h8dezebodn^_fkhwmSb�� deY�zb;v�bkag^_�Wz�b�dn^_fkh�m|deY�j��2 hWY>v�fkhwmnY �8`WYshwv%Y�fk��fi`Wz"mrdn` p q v�fk`Wa p ��Y>dnf�mrdn^_X)`wa_bodnY�deUWY p Ys�kY�a_fkjwXtYsh8d�fo�SdnUWYumrY�mr^_X;jWagYsz �8`wbkag^gdebodn^_�kYªmnY�hwmnfkz�m¡UW^cv�U�jwznf��G^ p Y&boh$bkv�v�`Wz�b�dnY©^_hl�5fkzeX�b�dn^_fkh$b�� deY�z.v�fk`WjWa_^_hW�;¡^£deU$bkh$fk�wmnY�ze�kYszs�

����� ������������� �"!#�$��%'&)(+*)�-,��".��/,102%3�54-61��47%yWfiz p Y�debo^_acm�dnUWY>znYub p Ysz&X;b®q v%fihwmr`wa£d jsr�l � � Y>mnY�jwbkzebodnYtdnUWY>XtYubkmn`WzeY p m|d�b�dnY���bkzn^cbo�Wa_Ysm �65 boh p deUWYª`WhwXtYubkmn`WzeY pmrdeb�deY��®bkzn^cbo�wagYum ��: � � Y&znYs¡zn^gdnY&mnqlm|deY�X   ru¥Sbkm��5fiaga_f�¡.m,�

��65 ��� 5d���������_ v�65 ' ��+�-F5 �21[56�&���   rHr®¥�� : ��� : ���������_ v� : ' � +�-8: �21 : �&���   ru�i¥

¡UWYsznY �&�U5c7=� :E� ¶ ����+�-F5879��+�-8:;� boh pO�$1[58�����%7%1B:;�����=� bozeY�deUWY&^_h p `wv�Y p jwbozndn^gdn^_fkh�fo� �*7g�,+.- boh pU13�&��� znYumrjEYsv%dn^_�kYsagqi�� Y�mrdebodnY&hWf�¡ boh�UGq8jEfodeUWYsmn^cmSfkh�dnUWY&z�bohW¤>fo��deUWY&X�b�dezn^gx � 5 �

P$±RQD´ �6S ° �,H5��8 VYX�9�\�:Rig`[� � � � � A � �9x p�h&i � � � � �<; � �(faEh$l]p>=M� 5�i�aEbyqdegw�wRl=a8z"?8�yWzefkX� Aw~�i¥«¶wmn^_hwv%Y�^gd.Uwbkm��5`Wa_a�z�bohW¤¦¶ � 5 b p X;^£d�m.btagY�� d.^ghG�kYszemnY�y��

� � 5 �@ G   rs�8¥

¡UWYsznY @ G p YshWfodeYsm�dnUwY&^ p Ysh8dn^gd|q>X�b�dezn^gx>fo� � G � � f�¡ ^g��¡�Y p Y�hwfodnYA�BDCFE� � � : �   r�ZG¥

¡�Y�v�fkhwmn^ p Y�zSdeUWY�h�dnUwY��5fka_agf�¡^_hW�tag^_hWYsbkz.v�Uwbohw�kY©fo�(v%fGfkz p ^_hwb�deYsm,�G,5 � �c5   ru�i¥G�: � A �65 ')��:   r,�8¥

dnUw^_m.v�U�bohW�iY~fk����boze^cbo�Wa_Ysm�dnz�boh�m|�5fiznX�m�  rFru¥�boh p   ru�k¥�^_h8dnf ��G�5 � � 5d� �IH2G����_ G�5 ' JG]+�-F5 �21[5c�IH2G��   r zk¥�G]: � � "�FG]:��KG]+�-8:8�R� � A 1[58�LH2Gg�>' 1B:;�LH2Gg�9�   r�k8¥

¡^gdnU

H BDCFE�NM @�-� �� ,;- �PO �� A @ � Q 7KR B�CFE�TS A @ �VU   rs�8¥

boh p G]+.-;:��WR �,+.-   �o�8¥

�Y�[|R���

TSUWY�Y �8`wbodn^_fkh�fo� r�ktv�bkh��EY&znYs¡zn^gdrdeY�h$`wmn^ghw�"deUWY&fk`WdnjW`ld � : ��G : � � "�FG : �KG +�-8: ��� R �;:   �ur®¥

�>° �,�l���(� q d.^cm¡�fkzndnU>hwfodn^_hW�;deUwb�d.mnqGmrdnYsX�  �uru¥�^cmb;ag^_hWYubozmrqlmrdnYsX `Wj�dnf�bkh�fi`ldnjW`Wd.^gh�{|Yuv«de^gfih��

P$±RQD´ �6S ° �,H5��� VYX���\�:/ig`y|goEbdp�h$p��E`�b�nda8w.aEl p�z;|�egh��vVth.\Bp b |g`�ldb]p bdh�`�z h$w s[` =�n�p�h&p�z ~ p���`,�(h�ig`�l%`K` =Fp b]h�b |�ocb]p�h&p��E`BndoEz bdh�aEz�h�b aEz>{��bde n�i h&i�a8h , � ���� ?����?

"���J�����yWfizDmnbk¤kYSfo�¦mr^_X;jWa_^_v�^£d|q"¡�Y¡^_aga�bkmemr`WX;YS^_h;dnUWYjWzefGfo��dnUwbodDdnUWY p ^ga_`ldn^_fkh;z�b�deY ^cmDb©jEfimn^£de^g�iY.v%fkh�m|d�boh8ds�[w.f�¡�Y��kYsz

boa_a¦dnUwY&znYumr`WagdembkjWjWa_qª¡^gdnU§bt��bozeq8^_hW� "�&#%� meb�de^_mr�5qG^ghw�$  w��8¥«�

�¢° � �,� T���Z��! �z>{;`�lKiFsd|�oEh&i�`�b]p b VYX��]\�" h&i�`�b�oEw egh$p�oEz�#� : o9qBh�ig`yq�o8w�w.oEx p�z ~ od|�`�z%$�w.o6od|)oF}]b�`�l]�E`�l'&�#G : � � "�(#G : �KG +�-8: ��� R �;:#� : �)#G : � A � 5   �k�i¥

ndoEz��c`�l ~ `]b[acb]sEf�|�h�oEh$p�ndaEw�w s hto8xyaEl={ h�ig`kb�oEw egh&p�o8z ��: orqkh&i�`[l=`d{Ee nd`d{3b]scb]ht`�f VrZ 9�\;�* � ´�´,+ � q d.^cmSYsbkmnq�deft�iY�ze^£�5qªdnUwboddnUWY&Yum|de^gX�b�de^gfih�Ysznzefkz.-c: B�CFE�/#� : �_� : �)#G : �KG :�meb�dn^cmr¨wYsm,�

�- :(� � - :;<   �o�8¥

boh p v�fkhG�kYszn�iYsm�bkmnq8X;jldefode^_vsboa_agq�def�¡�bkz p � :o��>° �,�l���(� q d�^cm¢¡�fkzndnU�hwfodn^_hW�)dnUwbod�deUWY�a_^ghwYsboz�mrqlmrdnYsX   �ur®¥(^cm¢hWfkd�fi�wmrYszn��bk�WagY.�5fkzSbohGq"a_^_hWYsbkz¢fk`WdnjW`ld � � � G �

q h p YsY p ^gd.^_mb;mnY%d.fo�J� p Ysv�fk`WjwagY p ¨wz�mrd.fkz p Y�zSY �8`wbodn^_fkhwms���� � � Q " ° � �5fkzSdeUWY�bo�Ef��kY©X;Y�h8dn^_fkhwY p Y%xWboX;jWa_Y�¡�Y�Uwb®�iY� 5¡^gdnU �65 � � 79��:(� � � 7 � � ¥��H � ���

�) , ,",5 ) ,�#" : , )

�����   ��ZG¥

a_Ysb p ^ghW�tdef"deUWY��5fka_a_f�¡^ghW�;fij�Ysh�a_fGfkj�fk�wmnY�ze�kYsz,��#0 5 � � "� #0 5 � 0 +�-F5 �   �k�i¥�#0 : � � "� #0 : � 0 +�-8: �   �8�8¥#� � #0 5 � � 5",5   �Fzk¥#� � #0 :y' � 5" :   �mk8¥

¡^gdnU 0 +.-F5(� �J+�- bkh p 0 +.-8:(� � +.- �TSUW^cm&fk��mrYszn�iY�z�Uwbkm�hWY��iY�zndnUWYsagYumnm&mnY��iY�z�boa p Y%�5Yuv«d�m��Dq d)^cm&^gh,fij�Ysh¬agfGfkj¬bkh p dnUWYsznY��5fkzeYt^gd)^cm�bkmemn`WX;Y p dnUwbod�dnUwY

X;f p Y�a­ 5Y�xWv%Y�jWd�deUWYS`WhW¤GhWf�¡h�zeYsbiv«dn^_fkh)zebodnYsm�¥�^_m�j�Yszr�5Yuv«deagq�¤GhWf�¡h"boh p dnUwbod�deUWY�zeY�^cm�hWf©Y�zeznfiz�^_h�dnUwY�X;Ysbimr`wznYsXtYsh8dems¶^_h�dnUWY~Ysmrdn^_X�b�dn^_fkh�mDfo�­deUWY.�5YsY p ^_hW��^_hWjW`Wdem�boh p ^_h�deUWY�Yum|de^gX�b�deYsm¢fo�­dnUwY�qG^gYsa p v�fGY�Cªv%^_Y�h8d�X�bodnze^£x � �'{$fkzeY�f��iY�zMdeUW^_mbkmnqGX;jldnfkdn^cv~fi�wmnY�ze�kY�z p fGYsm.hWfodSdebk¤kY��EY�hWY�¨Wd.fo�(boa_a¦dnUWY�b®��bk^gacbo�Wa_Y©^ghl�5fiznX�bodn^_fkh, Y�;:&bkh p � �s¥«�

|=|3}m~u�%�����

� ��������� �%���� #+- )��� �� "�% )����� ���������������

����� � ,��". 6 � �". ,��TSUWY�bimrqGX;jldnfkdn^cv�fk�wmnY�ze�kYszemSbkznY��wbimrY p fih$X;bimnm.�wboacbohwv�Y&v%fkh�mr^ p Y�z�b�de^gfihwms¶l�W`ld�^_h§mrfiX;Y�vsbkmnYsmSdeUWY&Y%xWbiv«d.X�bkmem twf�¡z�b�dnY ��+�- Y�h8dnYszn^_hW�~^gh)dnUWYSmrqlmrdnYsX ^cm�hWfodM¡�Ysaga8¤GhWf�¡h���TSUW^_m�^cm��5fiz�Y�xWboX;jWa_YDdnUwY�vsbkmnYD�5fkz�¡SbkmrdnYD¡Sb�deY�z�dnzeYsb�deX;Y�h8d�¡UWYshdnUwY&Y%xWbkv%dSX�bimnm�fo�MjEfka_ag`lde^ghw�;mn`W�wmrdnz�b�deY�^gh�dnUWY&^_hutw`wY�h8d.^_mShwfod.X;Ysbimr`WzeY p �cq h�dnU�b�d�v�bimrY©fo�Mv%fiznze`WjldeY p ^ghl�5fiznX�bodn^_fkhfkh deUWY>mnqGmrdnYsX ^_hWjW`ld�m�¶�dnUwY�jWznY p ^cv«dn^_fkh�m&fo��dnUWY>X;bimnm���boacbohwv�Y�¡^ga_aD�EYª�W^cbkmnY p � q d�^cm�¡�fkzndnU hWfkdn^_hW�$dnUwbods¶ p `WY;defdnUwY�^_z©mnj�Yuv%^g¨�v)v�fkhwmrdnze`wv%dn^_fkhwms¶WdeUWYsmnY)fi�wmrYszn�iY�z�m.bozeY�^_h§fkjEY�h�agfGfkj��vq h p YsY p deUWY"jwznY p ^_v%dn^_fkhwm�fo�(deUWYsmnY)fi�wmrYszn�iY�z�mbozeYhWfkdtv%fiX;jwbozeY p ¡^gdnU bkh8q X;Ysbimr`WzeY�X;Yshid�m�^_h fkz p Ysz&dnf v%fkzezeYsv«d&deUWY>Yum|de^gX�bodn^_fkhwms��q h¬deUWYª�5fiaga_f�¡^ghw�§¡�Y>¡^ga_a�mnUWf�¡dnU�b�d&mr`wv�UOb>v%fiznzeYsv%dn^_fkh1^cm�jEfimemn^g�Wa_Y)¡UwY�hObkh§fkhwag^_hWY)X;Yubkmn`WznYsX;Y�h8d~^cm~bª�5`Whwv%dn^_fkh�fk�(dnUWY;mrdeb�deY"��bkzn^cbo�Wa_Ysms�~TSUw^_m~^_m�5fkz�Y%xWboX;jWa_Y�dnUWY"v�bkmnY��5fkz.dnUWY��8bkmLtwf�¡ z�b�dnYum¡UW^cv�U1bozeY&�kY�hwY�z�boa_agq>b;a_^_hWYsbkz�5`Whwv%dn^_fkh1fo��dnUwY)v%fihwv%Yshidezebodn^_fkh�fo�MdnUwYv%fiX;j�fi`Wh p mS^_h�dnUWY p ^cmemrfiag�iY p jwUwbkmnYk�"{1bkhGqªfodeUWY�z.b pWp ^gdn^_fkhwbkaM 3ag^_hWYuboz.fiz�hwfkhWa_^ghwYsboz«¥�fk`ldejW`ld�m.bozeY~jEfimemn^g�Wa_Yk�

���I� ��4 .��#� .�*2���� Y�mr`Wjwj�f8mrY�UWYsznY©dnU�b�d � � �� �MdnUwY&X;bkjWjW^_hW� � ^cm�dnUG`wm p Y�¨whWY p bim��5fka_agf�¡.m,�

��� ���65879��:8� _�/� - � A � � � � � �(� �0���65879��:;����� Y�bimnmn`WX;Y©dnUwbod � meb�dn^cmr¨wYsm�dnUwY��5fka_agf�¡^_hW�;UGq8jEfodeUWYsmnYsm& 3�Gq>v%fih8�iY�h8dn^_fkh�¶��� ��� � ^cm.btag^_hWY&�iYsv«defkz«¥]�

P$±RQD´ �6S ° �,H5��� VYX��8\�:Rig`[fad|F|�p�z ~ iUp bBf3o8z>oEh�oEzJ`�x p�h&i l%`]bt|�`%n�h htok�,:(" p���`6���� ��� � p b[orq�� =�`%{3bdp ~ z�b[o8z N ���� � � Q " ° � ^_h�fi`WzY%xWbkXtjwagYi¶ �65 � � boh p �,:(� �$��7 � � ¶ldnUWYsh �R� � 7.��7 � ��� �� ��� ¶Wboh p dnUG`wm,�� �� � : ��� �

� � ' � � : � �� �"' � � :��   �o�8¥

¡UW^cv�U�^cmSfo��¨WxlY p mn^g�ihwm�fkh � : � � MS�� I�!E°1´%+ I�´ �s�l�6H ´>I �i� T�f;ag^_�kU8dnYsh>deUWY�hWfod�b�de^gfih�¶l¡�Y©¡^_aga p YshWfodeY 0 �G :i¶Wmnf)deUwb�ddeUWY�znYuboa­mrqlmrdnYsX mnbodn^cm|¨�Ysm,�

�0 �@� "� 0 � 0 +�->�0�KR � :��:�� 0 � A � 5   �k�8¥

* � ´�Q¢´ �6H �,H ´>I T#"�`�h%$��� � }%`Ka�ndoEz�b]h�aEz�h�egz�p�h0�E`%n�h�oEl�V�&'$(& � )�\�"0x i�oEb�`(b]p ~ z�b�aEl%`�n�i�oEb�`�z bde n�i3h�igaEh%$ + �� ��� �*) ; ,V q�oEl ) �,+ � � \�".-*p b[a"V�|�ocbdb]p&}]w s h&p�f`��EaEl]sEp�z ~ \B|�ocb]p�h$p��c`[b�ndaEw.a8l " aEzJ{ 0 +�-�WR ��+�-0� :/ig`yq�o8w�w.oEx p�z ~ b]scbdh�`�f�#0 �@� "� #0 � 0 +�- �0�KR �F: �/-0$R� �R� � 5 7 #0 � A � 5 �R� ��� �   �Jr®¥

p b[aEz!oF}]b�`�l]�E`�l�o9qkh�ig`�l%`%{8e nd`%{b]scbdh�`�f V �21]\8��>° �,�l��� �deUWYt^ghWY �8`wboa_^£d|q $ + �� ��� �3) ; , Uwbkm~def>�EYtmeb�de^_mr¨wY p �5fkz~dnUWY;mrdeb�deY � ¶­�W`Wd&bka_mnf��5fiz�deUWY;Ysmrdn^_X;bodnY p m|d�b�deY

��� 5 7 #� : � �D��mSb)v�fkhwmnY �8`WYshwv%Yi¶8^gdSX)`wmrd��EY�v�UWYsv�¤iY p ¡UWY�dnUWYsz �R� � 5 7 #� : � znYsX�bo^_hwm¢X;fihWfodefkhWY~¡UWY�h #� :©^_m�fk`Wdemn^ p YkN �'q �dnUw^_m©jWzefkjEY�znd|q p f8Yum�hwfod�UWfka p ¶ � X"`wmrd©�EY"jwznfiagfihW�ibodnY p ^_h1deUWY"hwY��ibodn^_�kY p fkX�bo^_h1def�meb�dn^cmr�5q�deUWYt�kfGf p jWzefkjEY�zndn^_Ysms�TSUW^cm^cmS^ga_ag`�m|dezebodnY p ^_h�fi`WzS¨whwbka­Y%xWboX;jWa_Yk�

T�ftjwznf��iY�deUW^_mSzeYsmn`Wagds¶W¡�Y©¨wz�m|d.mnUWf�¡ deUWY��5fka_agf�¡^_hW�1i�YsXtX�bw�

�Y�[|R���

�¢° � �,� 8��Yq�h�ig`kh&l%a�m�`dn�h�oEl]p�`�bko9q�bdscb]h�`�f VrZ]\3aEl%`[}%oEegz>{F`d{Mh�ig`�z h&i�`kh$l=a�m�`dn�hto8l]p�`]b�orq�h&i�`�o }db�`�l]�c`�l ~ p��E`�zO}�s�bdscb]h�`�fV �FZ]\va8l=`3}=o8egz>{F`%{F�* � ´�´,+´%+ �cS ° �¢° � �,�­� TSUWY&Y �i`�b�dn^_fkh�Y�zezefkz�^_m� 3¡^£deU - B�CFE� #0 � 0 ¥��

�- � � - � -2$R� �R� � 5;7 #0 � A � 5c�0� �R� � 5c7 0 � A � 56�=�   �i�i¥� Y�v�fkhwmn^ p Y�z��Y5 7,<�<�<07 � � /5 �� � bkh�fizrdeUWfkhwfkzeX;bka���bkmn^_mSfk��deUWY&�kYuv«dnfizn^cboa­mn`W�wmnjwbkv�Y~fizrdeUWfk�ifkhwbkaEdnf $ �i�Y�d`wm p YshWfodeY©�Gq��-�dnUWY&Ysznzefkz�^_h�deUWY&hWYs¡ �wbimr^cmS�k^_�kYsh>�GqO ��Y5 7,<�<�</7 � � /5 7 $ ¥%�TSUWY&v%fiX;j�fihWY�h8dembkagfihW��� +r¶ldeUWY +�� �kYsv%dnfiz�  + � );7�<,<�<�7 � � ) ¥�fo��dnUWY&��bkmn^_m�^cm�k^_�kYsh��Gq

�- +�� � ?+ -\G^_hwv%Y�deUWY�� +(bozeY©fkzndnUWfi�kfkh�boaEdnf $ ¶W^£d.^cm.v�agYuboz��5znfiX  3�8�k¥�deUwb�d6�

��- +�� � �- +q d��Yuv%fiXtYumSdnUwY�h1v%a_Ysbkz�deUwb�ddeUWYª  � � ) ¥�¨�zemrd.v%fkX;jEfkhWYsh8dembozeY���fi`Wh p Y p �

�� �� �-, 7 �-c+ �/,g�9� � �-c+ ������� �/,�7 �-c+ �-,g�� f�¡ �5fkzSdeUWY�v%fiXtjEfkhwY�h8d��- � bkmemrflv%^cb�deY p dnf $  ��- ��� $ ? -®¥��

��- �k� � �- ���/-�� �R� � 587 #0 � A � 5E�R� �0� � 5c7 0 � A � 56�=�   �k�8¥i�Y�d�`wm�zeY�X;^_h p deUwb�d�dnUWY©fkze^_�k^_hwboaEmrqlmrdnY�X   ru¥¢^_m��Efk`Wh p Y p   w�r®¥��G^£d��5fka_a_f�¡.mDdeUwb�d 0 � A ��5^cm���fi`Wh p Y p boh p mr^_hwv�Y� ^cm.v%fih8dn^_h8`wfk`wm�¡^gdnU1zeYsmnj�Yuv«dSdnf ��: ¶WdeUWY�zeY�Y%xl^_mrdem�� � bkh p ����^gh � �   p Ysj�Ysh p ^_hW��fkh�dnUwY&^ghW^gdn^cboa�v%fkh p ^£de^gfihwm^_h 0

boh p #0 ¥Smr`�v�U>deUwb�d6��R� � 5c7 � � � � �R� � 5c7 0 � A � 56�=� � �0� � 5c7 ��� �

q h dnUwY�mnbkX;Y§¡�b®qi¶�dnUWYsznY§Y�xl^_mrdemªd|¡�f¬�Efk`Wh p m�� � boh p � � ^gh � � mn`wv�U dnU�b�d>deUWY1deY�zeX �0� � 5 7 #0 � A ��5 � ��0� � 5 7 0 ' - � A � 5 � v�bkh��EY&��fi`Wh p Y p ��R� � 5c7 � � ' � � ' $ �- � � � �R� � 5c7 0 � A � 5 ' � /5

�+ �05

� + �- +�' $ �- � � � �0� � 5E7 ��� ' ��� ' $ �- � �   �oZG¥

� Y©U�b®�kY©dnUWYsh

�* �- �y'/-�� �R� � 5E7 � � ' � � ' $ �- � �>� �0� � 5E7 ��� �=� � ��- � � � �- �j' -��/�0� � 587 ��� ' ��� ' $ �- ����� �0� � 5E7 � � �=�   �i�i¥� Y©zeY�¡ze^gdnY©dnUWY�deY�zeX �0� � 5E7 � � ' � � '�$ �- �F��� �0� � 5E7 � � ' � � � `wmn^_hW��b"�iY�hWYszebkag^���Y p T�b®qGagfiz¢�5fiznX"`Wacb��

�R� � 5 7 � � ' � � ' $ �- � �R� �R� � 5 7 � � ' � � ��� ��!�� � � ' � � 7 $ �- � 7 ��5 � $ �- �   �;�8¥¡^gdnU !0� � � ' � � 7 $ �- ��7 � 5c� �#" 5$ �� � � � � � 5c7 � � ' � � ' $ � �- �g� � � �ªTSUwY;meboX;YtY%xljWzeYsmemr^_fkhOUWfka p m©�5fiz~deUWY�`WjWjEY�z

�Efk`Wh p m%�W^gd.a_Ysb p mS`wm�dnf;deUWY��5fka_agf�¡^_hW�tY%xljWzeYsmemr^_fkh0�� �& ' -&!�� � � ' � � 7 �- � 7 � 5 � $/� �-�� ' -��/�0� � 5 7 � � ' � � �0� �0� � 5 7 � � �=�   ��zk¥

� ��- � �   �Hk8¥�B�& ' -'!0� ��� ' ��� 7 �- � 7 � 5,� $R� �- �(' - �/�0� � 587 ��� ' ��� �R� �0� � 5E7 � � �=�   �k�8¥

|=|3}m~u�%�����

\G^_hwv%Y&¡�Y&Uwb®�iY�v�UWfimnY�h$b $ mn`wv�U�dnU�b�d $�+ �� ��� �3) ; , ¶w^£d�^_X;jWa_^gYum�¶��8q�^_hideY��izebodn^_fkh�¶GdeUwb�d !�� � � ' � � 7 �- ��7 � 5c� $�;&,boh p !�� ��� ' ��� 7 �- ��7 � 5c� $ ; , ¶Wbkh p Y�hwmn`WzeYsm�dnUwY&��fi`Wh p Y p hWYsmemSfo� �- � �

* � ´�´,+�´%+�* � ´>QD´ �,H5�,H ´JI � � f�¡�deUWY;jWzef8fk��fk�¢dnUwY�jWznfij�f8mr^gdn^_fkh��5fka_agf�¡.ms�1y�^_z�m|du¶�agY�d�`wm�zeY�¡ze^£deY)deUWY�Y �8`wbodn^_fkhY�zezefkz& 3�i�i¥¢�5fkzSdeUWY�v%fiXtjEfkhwY�h8d��-��G¶W¡UWYsh �-6+ � , �5fkz + � �����~mr^_hW��bo�8bo^_hªdeUWY&�kYshWY�z�boa_^.�sY p T�b®qGa_fkz��5fkzeX)`Wacb��

��- �B� �B�& ' -&!�� #0 7 0 7 � 56� $R� �- �  3Zi�8¥¡^gdnU !�� #0 7 0 7 � 5,��� " 5$ �� ��� � � � 5E7�� #0 '��*)�� �J� 0 � A � 56� � � �\G^_hwv%Y !�� #0 7 0 7 � 5,� $ ; , ¶8^£dSjWzef��kYsm(dnUwbod¢dnUwY�Y�zezefkz¢bkagfihW� $ v%fih8�iY�ze�kYumM�ka_fk�wbkaga_q)Y�xGjEfkhwY�h8dn^cboa_agq;¡^gdnU>b)zebodnY.acboze�kYsz

fkzY �8`wboa¦def �\GqlmrdnY�X� 3�i�i¥�v�boh$hWf�¡ ��Y�zeY�¡ze^£dndnYsh$bim��5fka_agf�¡.m� �� p Y�hwfodnYum�dnUWY � � � )8� ¨wz�m|d��- + ¶�� � �- � ¥]�

���(� �� ����$#d7 � ��� � ���&#d7 � 7 � �  3Zxr®¥

¡UWYsznY�� � , ^cm�b.�ka_fk�wbkaga_q~Y�xlj�fihWY�h8dn^cboa_a_q~mrdebo�wagY�Y �8`W^_ag^_�Wze^g`WX fo� �� ��>�&#d7 � � ¶obkh p � � , ^cm�b�iagfi�wboa_agq©bkmnqGXtjWdnfode^_vsboa_agqmrdebo�wagY)¨WxlY p jEfk^_hid~�5fkz �� �����&#d7 � 7+,g� � � YtUwb®�kY&jwznf��iY p dnUWYt�Efk`Wh p Y p hWYumnm�fo�(deUWY�dezebo{|Ysv«defkze^gYumfo��  �i�i¥«¶¦boh p deUG`wm�¶�5zefkX jsr,� l ¶ , ^cm.bt�ka_fk�wbkaga_qªbkmnqGXtjWdnfode^_vsboa_agq�m|d�bo�Wa_Y©¨WxlY p j�fi^gh8d�5fkz.mnqlm|deY�X   �i�i¥«�

* � ´�Q¢´ �6H �,H ´>I 8���ec|F|goEb�`�foEl=`do8�c`�l�h&i�aEh ! $)p bBw.o8xy`�l3}=o8egz>{F`%{U}]s aB|goEb]p�h&p��E`�l=`daEw�� � +�- &, ������� � � !�� #0 7 0 7 � 5,� $07���� #0 7 0 7 � 5,�  3Z8�i¥

h&i�`�z�h&i�`[ndo8z �E`�l ~ `�z>nd`�l%aEh�`�o9q �- � p b ~ l%`%a8ht`�lBh&i�aEzO�& ' -�� � +�-J�d� �]h ndaEz!}%`Ma;{rm]e�bdh�`d{e�b]p�z ~ -��

��� � � Q " ° ��� Y p Yumr^_�kh>dnUWY&v�agf8mrY p agfGfij>X�bkmem¢��boacbohwv�Y~fi�wmrYszn�iY�z¢�5fkz�dnUWY&v%fihwmn^ p YsznY p �W^_fodeYsv�UWhWfiagfi�k^cv�bkawjWzeflv%Ysmem,�

����� ����!�#0 5 � *� 0 +.- 5 � #0 5 �R�/-0$ 5 ������ � �� � ��� ��#0 :(�� "� 0 +.-8: � #0 :E���/-2$�:F� ���� � �� � � �E�#�!� #0 5 ��� �! �#� � #0 :j'"� �! �

 3Zi�8¥

TSUWYªv�fkhG�kYszn�iY�hwv�Y"fk��deUW^_m)fk�wmnY�ze�kYsz�^_m�b1v�fkhwmnY �8`WYshwv%Y;fk�Sy(zefkjEfimn^gdn^_fkh r�^£�¡�Y�v�UWfGfimnY $>5$# ,  3meboX;Yªmr^_�kh¬bim�% � ���'& � ¥Sboh p�$�: � ,   mnbkX;Y�mn^_�kh1bkm � �% � ���'& � ¥«��>° �,�l��� ��dnUWY�meboX;YzeY�X�boze¤)bimMdnUWY�fkhWY.bo� dnY�z¢dnUWY~y(znfij�f8mr^gdn^_fkhDr.v�bkh���Y�X;b p YUWYsznYF��fk`Wdemn^ p Y.dnUWY.hwfkhWhWYs�ibodn^_�kY

p fiX;bk^gh�¶GdnUWY��5`Wh�v«dn^_fkh � U�bkm�dnf;�EY&jWzefka_fkhW�8b�dnY p �( ) ���$�>���������� ��� ��'�� ���������������� #+- ���� �� )�� )����� �������������

p�Y%�5fiznY�boa_a ¶(hWfkdnY>dnUwbod"deUWY�v�agf8mrY p agfGfij v%fiznzeYsv%dn^_fkh p fGYsm"hWfkd;biv�v%YsagYszebodnY�deUWY�v�fkhG�kYszn�iY�hwv�Y�zebodnY�fo�dnUwY�fi�wmrYszn�iY�zu¶Y%xWv�Y�jld�^gh fkhwY p ^_zeYsv«de^gfih��)TSUW^cm�v�bkh��EYtYubkmn^ga_q§mnY�Y�hOfkh�dnUWY;Y �8`wbodn^_fkh  3Zi�8¥«�)TSUW^cm�^cm�deUWY�v%fihwmrY �8`WY�hwv�Y)fk�DdnUWY;hWfihfk��mrYszn��bo�w^ga_^£d|q�fk�Mmnqlm|deY�X   �ur®¥��l¡�Y�vsbohWhwfod.Y%xljEYsv%d�def;dn`WhwY��5znYsY�a_q�dnUWY�v�fkhG�kYszn�iY�hwv�Y�z�b�deYk�

q h¬�3biv«d $ ^cmtboacmrf b§zefk�W`wmrdn^g¨�vsb�dn^_fkh¬j�boz�boX;Y%deY�z)�iYsv%dnfkzu� q h¬dnUWY��5fka_a_f�¡^ghW�O¡�Y�¡^ga_amrYsY>UWf�¡ deUWY$v%a_fimnY p a_fGfkjmnqGmrdnYsX ^gX;jWzef��kYum&dnUwY�Ysznzefkz�m&fkh dnUWY�Ysmrdn^_X�b�dnYum p `WY>def§deUWY�X;f p Ysag^_hW��Ysznzefkz�m)mn`wv�U bim"b��wb p Ysmrdn^_X;bodn^_fkh fk�.dnUwY^_hutw`WYshid�v�fkhwv�Y�h8dnz�b�de^gfih��

�Y�[|R���

i�Y�d~`wm©Y�xlbkX;^ghWY)dnUWY;mrdnYsb p q$m|d�b�dnYtjWzeY p ^cv«de^gfihwm~fo�(dnUwY"fi�wmrYszn�iY�z.�i^g�iY�h§�Gq¬  �i�k¥.¡UWY�h�dnUWYt^ghW�5fkzeX;bodn^_fkh§fih1dnUwY^_hutw`WYshid�v�fkhwv�Y�h8dnz�b�de^gfih§^_m��w^_bimrY p � � Y;¡^ga_aDv%fihwmr^ p Ysz~^_h�deUWYt�5fka_agf�¡^_hW��dnUWY�vsbkmnY"¡UWYsh§deUWY;^ghWjw`ldem&fk�DdnUwY;mnqlm|deY�X  p ^ga_`ldn^_fkhOzebodnY)bkh p ^_hutw`WYsh8d�v�fkhwv�Y�h8dnz�b�de^gfihwme¥.bozeY)bkmnqGXtjWdnfode^_vsboa_agq$v%fihwmrdeboh8du�+i�Y�d©`�m p YshWfodeY -c+�- BDCFE� �0 +.- � 0 +�-$dnUwYY�zezefkz¢�EY%d|¡�Y�YshªdeUWY©bimnmn`WX;Y p ^ghJtw`WY�h8dv%fihwv%Yshidezebodn^_fkh§ %�0 +�-w¥�boh p dnUWY�bkv%dn`wbka¦fkhWYt  0 +.-�¥«�DTSUWY©Y�zeznfiz¢�EY%d|¡�Y�Ysh #0 boh p 0b�d^_hl¨whW^gd|q>^cm p YshWfodeY p -����

TSUWY�Y �8`wbodn^_fkh�fo��dnUWY&fij�Ysh�a_fGfkj�fk�wmnY�ze�kYsz&  �k�i¥�mrUWf�¡ p ^gzeYsv%dna_qªdeUwb�du¶wb�dY �8`W^_a_^g�Wze^_`WX �

- �W� - +�-  3ZkZG¥

TSUWY&Ysznzefkz�fkh�dnUWY�mrdebodnY&^cmSY%xWbkv%dna_q�dnUwY&Y�zeznfiz�fih>deUWY&X�bkmemS�wboacboh�v%Yk�� Y©¡^_a_a�mrUwf�¡ dnU�b�ddnUw^_mYsznzefkz�^cmznY p `wv�Y p �5fkzSdnUwY�v%a_fimnY p agfGfkj�fk��mrYszn�iY�zu�� fkdnY�¨wz�m|d(deUwb�d(deUWYjWzefk�Wa_Y�X�b�d¢mrdnYsb p q)mrdebodnY^cm(b�ag^_hWYsbkz(jWzefk�Wa_Y�X mn^_hwv%Y !��W��� �� ?�� � ���

�(� � v�bkht�EY.v%fiX;jW`ldnY p 5`�mr^_hW�tdnUWY�v�fkhG�kYszn�iY�hwv�Y�fk��deUWY&fk�wmnY�ze�kYsz��i^g�iY�h��Gq>y(zefkjEfimn^£de^gfih r®¥]�

!�� � � �� � : � � 5E7 #0 � � A � 5c�  3Z8�i¥

¡UWYsznY #0 � �� �� ?�� � � #0 �� � ?�� � � 0 �� Y�v%fkh�mr^ p Y�zhwf�¡ dnU�b�ddnUwY�^ghJtw`WY�h8d�v�fkhwv�Y�h8dnz�b�de^gfihwmSbozeY©�w^_bimrY p bkh p ¡�Y�¡^_aga�v%fkX;jW`WdnY&deUWY�m|deYsb p q>mrdeb�deY&Y�zeznfiz-���� � Ytm|de^ga_a�bimnmn`WX;Y�dnUwbod ! � ^_m�¤GhWf�¡h1¡UW^cv�U1^_m�^gh p Y�Y p bt¨�zemrd�fkz p Ysz�bojWjwznf®xl^_X;bodn^_fkh�� � fkdnY&deUwb�d�^gd~^cm.Y�xWbkv«deagq

¤GhWf�¡h�^£� � ^_m.ag^_hWYsbkzs�y�^gz�mrds¶l^gd�5fka_agf�¡.m��5zefkX   �Jr®¥DdeUwb�ddeUWY&Y �8`wbodn^_fkh�Y�zeznfiz�^cm�i^g�iY�h>�GqJ�

�& @ � ' -2$ !�� � - ����  3ZF�8¥¡UWYsznY �)p Ysmn^g�ihwm�dnUWY&X;f p Ysag^_hW�;Y�zeznfizS�kYsv%dnfizs�[q ��deUWY&fkhwagq�`WhW¤GhWf�¡h�^_m�deUWY&^ghJtw`WY�h8d - +�- deUWY�h �B�� - +�- �

* � ´�Q¢´ �6H �,H ´>I ���Yqkxy`Mn�i�o6ocb�`$ � !�? �

& !�� &  3Zbzk¥h&i�`�z " q�oElMaEz sk|�ocb]p�h$p��c` ~ aEp�z - "yh&i�`[`�l]l=o8l�{Ee `�hto � p bkl%`%{8e nd`%{U}]sh&i�`[l=o }]e�b]h aEb]sEf(|>hto8h&p�n3oF}]b�`�l]�E`�l'&

& - ��& � & - $ � &  3ZFk8¥

x i�`�l=` - $ � ����p b�h&i�`M`�l]l=o8l[oF}�hta8p�z>`d{ }]sh&i�`Macb]sEf�|�h�oEh$p�nMo }db�`�l]�c`�l�p�z!od|�`�zOw.o,o]| Vth&i�`[z>o8l]f &E< &Mp bBh&i�`�� e n�w p�{;`daEz

z>o8l]f(\;�

Q � ´�´%+ � � fodnY.¨wzemrdDdeUwb�d $ !�� ^cm¢b�z�bohW¤tfkhWYX�bodnze^£x­� � ^£deUªfk`Wz�v�UWfk^cv%Yfk� $ � ��� �� � � �¶8^£d�^_m�b�mrqGX;X;Y%dezn^cvX�b�dezn^gx­�

� Y�v�boh p ^cbo�ifkhwbkag^���Y©^£d.^_h1boh�fkzndnUWfihWfkzeX�boaE�wbkmnYk�TSUWY�hWfih�dezn^_�G^_bka¦Y�^_�kY�hG��boa_`WY�^cm ! � $ # , bimnmnflv%^cb�deY p ¡^gdnU�deUWYª 5`Whw^£d�bozeql¥�Ys^g�iY�hG�kYuv«dnfiz $ ¶W^_h p YsY p �

$ !�� $ � ��!�� $R� $

q d.^cmSYsbkmnq�def;mnY�Y�deUwb�dSdeUWY�zeY&Y%xl^cm|d�mboh�fkzndnUWfi�kfkh�boaEX;bodnze^£x ��mn`wv�U�dnUwbod

� ? �& @ � ' -2$ ! � � � �-�� � ��  3Zi�8¥

|=|3}m~u�%�����

�k^_�G^ghw�t^_h�dnUWY�hWYs¡ ��bkmn^_m�deUWY&Y �8`wbodn^_fkh,  dnUwY�dn^_a p Y p Y�hWfkdnYsm�deUWY&hWYs¡ �wbimr^cm�¥]�

� �-�� � ��   �o�8¥

¡^gdnUR�

� �

�����������

' -'! � $ , <�<,< ,, � � �

� � � � � � ������ ,, <�<,< ,

� ����������

  �ur®¥

dnUwY�zeY%�5fkzeY�-�� � �

R5 ��   �k�i¥TSUW^cmSjWzef��kYsm�deUwb�d6�

& -�� &�� & �-�� & � & �� & � & � &

  �o�8¥

�>° �,�l���(� dnUwY&¨wz�m|d�v�fkX;j�fihWY�h8d.fk���-�� ^_m p Ysv%zeYsbimrY p �Gq�b;zebodnY��3bkv%dnfiz �� ��� � ��� �"q � - ^_m�a_bkzn�iYk¶GdnUw^_mS�3biv«defkz.v�bkh�EY.X�b p Y�bim¢mnX�boa_awbkm p Ysmn^gzeY p ��TSUW^cm¢v�fkX;jEfkhWYshidD^cm¢bimnmnflv%^cb�deY p dnf&deUWY p ^_zeYsv«de^gfih $ �6{$fiznYsf��kYszs¶�^g��X;fkzeY^ghl�5fiznX�bodn^_fkh

^cmb®�®bk^gacbo�wagY�fkh�dnUwY&^ghut�`WY�h8d.Y�zezefkzu¶8fkdnUWYsz.v�UWfk^cv%Yum��5fkz $ vsboh���Y p fihWYk�

� f �)������~ )�¬�)������������� )��#�$����$�%� ��� ���������������

��mt¡�Y>Uwb®�iY>mnY�Y�h bo�Ef��kYk¶(^gd;^_m"�kYsznqO�5znY �8`WY�h8dtdnUwbod"deUWY>^_hutw`WYsh8d;v�fkhwv�Y�h8dnz�b�de^gfihwm�¶M^ � Yi� dnUWY � +�-­¶¢bozeYªhWfkdtY�xWbkv«deagq¤GhWf�¡h�� � Y;Uwb®�kY;mnY�Y�h�dnUwbod�dnUWY�v%a_fimnY p agfGfij�fk��mrYszn�iY�z�^_X;jWzef��kYsm�dnUwYtzefk�w`wm|dehWYsmem©fo�DdeUWY;fkjEY�h agfGfij�fk��mrYszn�iY�z��GqjWzef��G^ p ^_hW�;bt��Y�drdnYsz�bkmnqGX;jldnfkdn^cv~Ysznzefkzu�

� Y�¡^_a_awmr`wjWj�f8mrYS^_h)deUW^cmDmrYuv«de^gfih)deUwb�d(¡�Y�¤GhWf�¡ `WjWjEY�zDbkh p a_f�¡�Y�zM��fi`Wh p mMfih)deUWY^_hWjW`ld�m�¶8boh p ¡�YS�W`w^ga p ^gh8dnYszn��bkafk��mrYszn�iY�z�m�¶8�k^_�G^ghW�t�k`�boz�boh8dnYsY p �Efk`Wh p mSfkh�dnUWY�Yum|de^gX�b�deY p m|d�b�deY;  boh�^gh8deznf p `wv%dn^_fkh�dnf;^_hideY�ze��boa¦fk�wmnY�ze�kYsz�^cmS�k^_�kYsh>^_hjsrs� l ¶�b$X;fiznY�Ysa_bk��fizebodnY p jWzeYsmnY�h8d�b�dn^_fkh ^cm&^gh jsr�Zml ¥%� 2 `Wz�¨wzemrd"bk^gX�^_m�def§fk�Wdebo^_h,��fi`Wh p m)fkh dnUwYªYsmrdn^_X�b�dnYum��(fk`wzmnYsv%fih p bo^_X ^cm�dnf1�W`w^ga p hWfod�fihWa_q�fkhwY�fk�wmnY�ze�kYszs¶­�W`Wd"b�¡UWfka_YªmrY�d�fo�Sfk�wmnY�ze�kYszem;  v�boa_a_Y p b$�W`Wh p agY�fk��fi�wmrYszn�iY�z�me¥%¶dnf���Y�bo�Wa_Y�dnf§debo¤iY;dnUWY�^gh8deY�z�mrYuv«dn^_fkh,fk�dnUWYª�Efk`wh p m"fo�Ysbiv�U fi�wmnY�ze�kY�zu¶�bkh p mnf1dnf§^_X;jWzef��kYªmn^gX"`Wa£d�bohWYsfk`wmna_q§dnUwYv%fihG�kY�ze�kYshwv%Y~zebodnY&boh p deUWY�bkmnqGXtjWdnfode^_v©�Efk`Wh p mfkh�dnUwY&Ysmrdn^_X;bodnYum��

����� �2���-�54-6 ��� ,102%3�54-61��4� Y�mr`Wjwj�f8mrY©dnU�b�d.¡�Y©¤GhWf�¡ dnUWY&`wjWj�Ysz�boh p a_f�¡�YszS��fi`Wh p mfih>deUWY&^_hWjW`ld�m�¶wmnftdnUwbod.¡�Y&vsboh�¡zn^gdnYF�

0 +�- �&#%� ��0 +.-J�$#%� � 0 �+�- �&#%�   ��ZG¥

T�f"mn^gX;jWa_^£�5q;deUWY©jWznYumrYsh8deb�de^gfih�¶8¡�Y©v%fkh�mr^ p Y�z¢dnUWY�v�bimrY�¡^£deU 0 � � 0 5 7 0 : � ^_h p ^gX;Y�h�mr^_fkh�d|¡�fw¶8�W`ld�dnUwY~zeYsmn`Wagd�boh p dnUwYjWzefGfo�3m©bozeY&dnUWY;meboX;Y)^_h p ^_X;Y�hwmn^gfih ��� � Ytbka_mnf>mn^gX;jWa_^g�5q$dnUWYthWfod�b�de^gfih �R� � 5 7 0 � A � 5 � � �R� 0 � ¶­boh p debo¤iY��;: � , 5zeY�X;YsX)�EY�zMdnU�b�d �;: p ^cmnbkjWjEYsboz�m(bohGqG¡Sb®q©¡UwY�h;¡�Yv�fkX;jW`ldeY�deUWYY �8`wbodn^_fkhtY�zeznfiz�¥%�cywfkz(mnbk¤kYSfo�¦v%acboze^£d|qi¶�dnUwYS�5`Whwv«de^gfih

�Y�[|R���

� ^_m©mr`wjWj�f8mrY p dnf���Yt^_hwv%zeYsbimr^_hW��¡^gdnU�zeYsmnjEYsv«d~dnf>dnUWY)¨wzemrd©v�fkX;jEfkhWYshid©fo� 0 boh p�p Ysv�znYubkmn^ghW��¡^gdnUOznYumrjEYsv%d�defªdnUwYmnYsv%fih p fkhWYi¶WbkmS^_h�deUWY&Y%xWbkXtjwagYi�MTSUwY&�kYsv%dnfiz $ Uwbkmmn^g�ihwmbkmS^_h$jWzefkjEfimn^£de^gfih rk¶GdeUWY�zeY%�5fiznY $J5 ; , 7 $�: � , �* � ´�Q¢´ �6H �,H ´>I � :Ri�` q�oEw�w�oEx p�z ~ b]scb]h�`�f p b[aEz*p�z�ht`�l]�ca8w�o }db�`�l]�c`�lyq�oElBh&i�`[�EaEl]p�aF}�w.`�b 0 �&#%� b�oEw egh&p�o8z_orqvV �01d\

�0 �5 � 0 �+�-F5 �&#%�0�! 0 �5 � -2$J5E� �R� 0 �5 7 0 �: �0� � �E�   �k�i¥�0 �: � 0 �+�-8: �&#%�0�! 0 �: � -2$ : � �R� 0 �5 7 0 �: �0� ��� �   �8�8¥�0 5 � 0 +�-F5 �&#%�0�! 0 5 � -2$ 5 � �R� 0 5 7 0 : �0� � � �   �Fzk¥�0 : � 0 +�-8: �&#%�0�! 0 : � -2$ : � �R� 0 5 7 0 : �0� � � �   �mk8¥

p���`6� "jp q�aEh h$p�f3`��6`�l=o 0 �-,�� � 0 �-,�� � 0 � �-,g�h&i�`�z�q�oEl |�ocb]p�h$p��c`�h$p�f3` 0 �$#%� � 0 �&#%� ��0 � �$#%�Vth�ig`�p�zJ`���e a8w p�h&p�`�bM}%`�p�z ~ h�aP?8`�zOoEz!`%aFn]i*ndoEf�|go8z>`�z h.\;�* � ´�´,+ �)� Y�mrdeboznd&mr`wv�U�dnUwbod 0 �/,g� � 0 �-,�� � 0 �y�/,g� ��q �|¶��5fiz&mrfiXtY"dn^_X;Y # $ ¶­deUWYsmnY;^ghWY �8`wboa_^£de^gYum�bozeY"hWfkd~dezn`wY

bohGqGX;fkzeYk¶u^£d(^_X;jWag^_Ysm�dnU�b�d(b�dMagYubkmrd�fkhwY�fk�ldnUWYsX ^_mMboh)Y �8`wboa_^gd|qk�ci�Y%dM`wmMmr`wjWj�f8mrY¢dnUwbods¶��5fiz�Y�xWboX;jWa_Yk¶ 0 5c�&# $ ��� 0 �5 �&# $ � ¶dnUwY�h$¡�Y&vsboacv%`Wacb�deY;�

�0 �5 � �0 5�� *� 0 �+.- 5 �$# $ �0� 0 +.-F58�&# $ �9�0� -2$J5E� �R� 0 �5 7 0 �: �0� �0� 0 5c7 0 :8�9�TSUW^cm p Yszn^_��b�de^g�iY �0 �5 � �0 5 ^cm.X�b p Y"fo�Md|¡�f�dnYsznX�m,�¢deUWY�¨wz�mrd�^_m�j�f8mr^gdn^_�kY)��Yuv�bo`�mrY�fk�MdnUWY"��fi`Wh p m~fkh$deUWY)^_hWjW`ld�m�¶

boh p deUWY�mrYuv%fih p fihWY�^_m�mr`wv�U�dnU�b�d�¶wbod�de^gX;Y # $ ��0� 0 �5 7 0 �: �0� �0� 0 5E7 0 :E��� �R� 0 �5 7 0 �: �0� �R� 0 �5 7 0 :c� � ,

�EYsv�bk`wmnY�dnUWY��5`Whwv%dn^_fkh � ^cm p Yuv%zeYsbkmn^_hW�1¡^£deU zeYsmnj�Yuv«d�def§deUWY�mnYsv�fkh p ��boze^cbo�Wa_Y>boh p 0 �: ; 0 :o�OTSUWY p Yszn^_��b�de^g�iYª^_mdnUwY�zeY%�5fkzeY;hWfkhwhWY��8b�dn^_�kYi¶�boh p deUWY�zeY%�5fiznYt�5fiz # 5 # # $ ¶ 0 5 �&# 5 � � 0 �5 �&# 5 � � y�^_hwboa_a_qk¶�¡�Y�fk�Wdebo^_hOdnUWYª^_hWY �i`�boa_^£de^gYum��>��agadnUwYsmnY�boze�k`WX;Y�h8d�m�bkznY�v%acbkmemn^_vsboa¦^gh�deUWY�¨wY�a p fo�MX;fkhWfkdnfkhwY©mnqlm|deY�X�mboh p$p ^Xg¦Y�zeY�h8dn^cboa­^_hWY �8`wbkag^gdn^_Ysm&jsru� l �

{$fiznYsf��kY�zu¶­deUWY�meboX;YªjWzefGfo�.bkm�dnUWY>fkhWY�fo�vi�YsXtX�b��1jWznf��iYsm�deUwb�d"dnUWY�X�b�xl^gX�bkaDY�zeznfiz��kYuv«defkz�- � 0 �)� 0 zeY�X�bo^_hwmS�Efk`Wh p Y p �

���I� ��� ���#��� ,�.����-�54-6 ��� ,<0 %'��4-61�547%� Y§Uwb®�kY1fi�ldebk^ghwY p �k`�boz�boh8dnYsY p ��fi`Wh p m>fkh dnUWYOYsmrdn^_X�b�dn^_fkh fk�©deUWY 0 ¶S�k^_�kYsh �Efk`wh p mªfih dnUWY�^ghWjw`ldems� TSUW^_m>^_m^_hideY�zeYsmrdn^_hW�>�Gq$^gdemnY�ag�|¶E�w`ld©^_h§deUWY)hwY%xGd©j�boz�bo�kz�bojwU�¡�Y"v�fkhwmn^ p Y�z©mr^_X)`WagdebkhWY�fi`wmnagq$mrYs�kYszebka�^_hideY�ze��boa�fk�wmnY�ze�kYszem& 3¡^£deUp ^XgEYsznYsh8d;v�fk`WjWa_Ysm � $07�-�� ¥«¶Sboh p ¶(��Yuv�bk`wmrY�¡�Y>fk�Wdebo^_h �i`wboz�boh8dnYsY p �Efk`Wh p m"�5fkz;Ysbiv�U fk�wmnY�ze�kYszs¶�¡�Y�vsboh¬d�bo¤kY>dnUWYs^gz^_hideY�z�mrYuv«de^gfih�¶k^ � Yi��debo¤iYSdnUWY~mrX�boa_a_Y�zDYsh8�iY�a_fkjEYfo�¦dnUwY~mnY%d¢fk�EYum|de^gX�b�de^gfihwms�MTSUwY.^ p Ysb�^cm(dnU�b�ds¶8^_h;dnUW^cm�mnY%d�fo�­fk�wmnY�ze�kYszems¶mnfkX;Y"bkznY��ifk^_hW��def>�EY"�iY�zeq��if8f p bod�deUWY"�EY��i^ghwhW^ghw�>fo�(deUWYtYsmrdn^_X;bodn^_fkhwmt  �5fiz�deUWY�dezebkhwmn^£defkze^gYume¥%¶�fkdnUWYsz~¡^_aga��k^_�kY"b�EY%drdeY�z�¨whwbkaiYsznzefkzu¶8�g�_�[i�Y%d�`wm�znYsX;bkzn¤~dnU�b�ds¶�^_h&deUW^_mMbkjWjWzefibkv�U�¶ubkh8q�fi�wmrYszn�iY�z�vsboh�fihWa_q©^_X;jWzef��kY(deUWY�mnX�boa_agYsz�Ysh8�iY�a_fkjEYfo�MYsmrdn^_X�b�de^gfih�¶l^£�M^gd.^_m.bkh�^_h8dnYszn��boa­fi�wmnY�ze�kY�zu�(\G`wv�U1boh$bojWjwznf8bkv�U>^cmhWfkdj�f8mnmn^g�wagY&¡^gdnU1v%acbkmemn^_vsboa¦fk�wmnY�ze�kYszem© 5Ys�kYsh�^g�dnUwY.^ghwjW`ldem¢¡�YsznYSjEY�zn�5Ysv%dna_q"¤GhWf�¡h�¥��EYsvsbo`wmnYSdnUwY�zeY^_m(hwf&hWfode^gfihwm(fo�¦a_f�¡�YszDboh p `WjWjEY�z�Ysmrdn^_X�b�dnYum�¶8v%fiXt^_hW�&UWYsznY��5zefkXdnUwY&U8qGjEfodeUWYsmnYsmSfk��X;fkhWfkdnfih8qO  p ^XgEYsznYsh8dn^cboa­^_hWY �8`wbkag^gdn^_Ysm�¥Sboh p fo��dnUwY&^ghW^gdn^cboa­Yum|de^gX�bodn^_fkh 0 �/,g� ��0 �/,g� ��0 �j�-,�� �

|=|3}m~u�%�����

yMboz�boX;Y�dnY�z ",5 "�: �/+.- � +.- ��5 ��: ���hDbkag`WY �W� � � �k�����i������� �&#���� � rk� � �w� � ru���hW^£d�m � � � �®a � ��a ��� � /5 ���®a � �®aT�bk�Wa_Y rF� yMboz�boX;Y�dnY�z�m���boa_`WY&`wmnY p �5fkzSdnUwY�mr^_X)`Wacb�de^gfih�fk��X;f p YsaD  �o�8¥«�

* � ´�Q¢´ �6H �,H ´>I�� "�`�h3e�b � = h&i�`_p�z�p�h&p�a8wkndoEzJ{Ep�h$p�oEz b 0 �-,g� � 0 �-,�� � 0 �j�-,���" a8z>{ ndoEz�b]p�{F`�l!a)b�`�h Vr}�egz>{gw.`�\ o9qoF}]b�`�l]�E`�ldbkq�o8l b�`��E`�l=a8w(ndoEec|�w�`]b � $07�-g�&\ Vtp�zJn�w e {8p�z ~ - � ,8\�x i�oEb�`"b]p ~ z�b �E`�l]p qds2h�ig`�ndoEzJ{Ep�h$p�oEz o9q�� l=od|�ocb]p�h$p�oEz ZF�:Ri�`�z�h&i�`[w.oExy`�l�`�z �E`�w�od|�` 0 orqBh&i�`[ec|;|�`�l[`]b]h$p�f3a8ht`�b 0 � "jaEzJ{h&i�`[ec|;|�`�l[`�z �E`�w.od|�` 0 orq�h�ig`�w.o8xy`�lM`]b]h$p�f3a8ht`�b 0 p baEw b�oUa"V9}%`�h&h�`�lt\ ~ e aEl=a8z h�`%`d{v`�b]h&p�faEh$p�oEz2orq 0 " p�z>n�w e {8p�z ~ aEz>{vp�f(|>l=oE�6p�z ~ h&i�`Mod|�`�zOw.o6od|)`]b]h$p�f3a8h&p�o8z>�TSUWY�Y%xWbkXtjwagY&^_h�dnUWY&hWY�xGd�mrYuv«dn^_fkh�¡^_aga�^_a_ag`wmrdnz�b�deY©dnUWY&jWzefkjEfimn^gdn^_fkh��(TSUWYsfkzeY%dn^cv�bka­¡�fizn¤�zeY�X�bk^ghwm�def;��Y p fkhWYi¶lfo�

v%fi`Wz�mrYi¶idef�fk�ld�bo^_h�X;fiznY&boh�boa_qide^_vsboa¦zeYsmn`Wa£d�m�¶l^g�Mj�f8mnmn^g�wagYi�

���3� ��� ���#��� ,�.����-�54-6 ��� ,<0 %'��4-61�547%�� . �"! 4"��. �#. �-.�����.�� � �". , ���m"^gdt¡^_aga��EY�X�b p Y�v%a_Ysbkz��5zefkX�dnUWY$mn^gX"`Wa_bodn^_fkhwm)��Ysagf�¡&¶(^_h X�bohGq¬v�bimrYum�^gd"^cm"b p ��boh8debk�kYsfk`wm�def�zeY�^_hW^gdn^cboa_^.�sYªdnUwY^_hideY�ze��boawfi�wmnY�ze�kY�z�mDbod�zeY��k`wa_bkz(dn^_X;Ysms¶i�EYsvsbo`wmnY�^gd�^_X;jWznf��iYsmDmrdn^_a_a�deUWY~mnX�boa_agYum|d�Y�hG�kYsagfij�Y.fk�­dnUWY©Ysmrdn^_X�b�deYsms�cq dSX;Ysboh�mdnU�b�ds¶Wbod�zeY��i`WacbozDde^gX;Yum�¶l¡�Y�zeYsmrdebkzrd�dnUWY�¡UWfiagY©�W`Wh p agY©fo��fi�wmnY�ze�kY�z�m(�5zefkX deUWY©��Yum|dYsmrdn^_X�b�de^gfihªfo��deUWY&m|d�b�deY©bod�deUW^_mdn^_X;Yk�DTSUWY�b p ��boh8debk�kYum�fk��zeY�^_hW^gdn^cboa_^.�sY~deUWY&fk��mrYszn�iY�z�m¢^cm¡�Y�a_a­¤8hwf�¡h j � l �

� � ���������� )�#���ª )+B ����

T�f ^_aga_`wmrdnz�b�deY fi`Wz$X;Y%dnUwf p fka_fk�kq fih b hWfkh8dezn^_�G^_bka©Y�xWboX;jWa_YO¡�Y debo¤iY�deUWY,X;f p Y�a��5fkz p YshW^gdnze^£¨�vsb�de^gfih jWzeYsmnY�h8deY pdnUwznfi`W�kUWfi`ld(dnUwY�jwbkj�Yszs��yWfizDdnUwY�mr^_X)`wa_bodn^_fkh�jW`WzejEfimnYk¶k¡�Y.hWYsY p bkhªbohwbkagq8dn^cv�bkaWY%xljWzeYsmemn^gfih"�5fizDdeUWY.�wbiv«dnYszn^cboaw�kzef�¡SdnUz�b�dnYi�(TSUW^_m��iznf�¡SdeUªzebodnY; 5¡UW^cv�U>^cmSfo��v%fk`wzemnY~mn`WjWjEfimnY p dnft��Y�hWfkd�¤GhWf�¡h�¥¢^cmb"meb�de`WzebodnY p �5`Whwv%dn^_fkh�fo� ��� � boh p ^_m^_hWUW^_�W^£deY p �Gq ����:� 5hw^£dezn^gdnY&^cmS¤GhWf�¡h>def���Y�def®xl^_v��5fkz.�iznf�¡SdeU�¥«�MTSUW^cma_Ysb p m�dnftdnUWY��5fiaga_f�¡^_hW��mrqlmrdnY�X �

��� ��!�� ��� 5 �� ��� � � �� � � � � �! ���_� �#",5 ��5 �� �!� � � �� � ��� � ' "� �/+.-M�%�j��� � "�:"��5 �� �!� � � �� � ��� � ' "� � +.-3� � �   �o�8¥

TSUWY���boa_`WYsm��5fizSdnUWY&j�boz�boX;Y%deY�z�m�vsboh���Y��5fi`Wh p ^gh$T�bo�Wa_Y1rk¶GdnUwY&Y��kfiag`Wdn^_fkh�fo� *�&#%� boh p �J+�-/�$#%� bozeY~zeY�jWzeYsmnY�h8deY pfkh y�^g���rk�

� Y�bkmemr`WX;Y�hWf�¡ dnUwbod.dnUWY�b®��bk^gacbo�Wa_Y�fk`ldejW`ld�m.bozeY©dnUWY&�W^_fkX�bimnm& �� 5 � �O¥Sboh p deUWY&j�Yszev�Y�h8debk�kY�fo�(mn`W�wmrdnz�b�dnY�^_hdnUwY&XtY p ^_`WX �

��� � ��U' �  &�k�8¥��m©¡�Y;Uwb®�kY;boa_znYub p q1mnY�Ysh�¶R� � ^_m&b�X;fkhwfodnfihWY"�5`Whwv«de^gfihOfk� � boh p �;� w�f�¡�Ys�kYszs¶E�5fkz�hWYs�ibodn^_�kYt�®bkag`wYsm©fo� #� ¶�^gd

�EYsv%fiX;Ysm�^gh�v%zeYsbkmn^_hW�~¡^gdnUtzeYsmnj�Yuv«dMdnf #�;¶kboh p �5fiz�hwY��ibodn^_�kY���boa_`WYsm�fo� #�;¶o^gdM^cm(b p Ysv�znYubkmn^ghW�~�5`Whwv%dn^_fkhtfo� #� ��TSUWYsznY��5fkzeY¡�YUwb®�kY�dnf)Y%xGdnYsh p1� ^_h;dnUWY.hwY��ibodn^_�kY p fiX;bk^gh1 5�5fkz(deUWY.fk��mrYszn�iY�z«¥«�cywznfiX�deUWY.Y �8`wbodn^_fkh;fo� � ^gh1  �o�i¥%¶8mn^_hwv%Y#��+.- # ,^gd.^_mv�agYubozSdnU�b�ddnUwY�zeY©Y�xl^_mrdemb;jEfimn^£de^g�iY mr`�v�U>deUwb�d � �$#%��# �5fiz�boa_a­jEfimn^£de^g�iY~de^gX;Yª 3jWznf��G^ p Y p dnU�b�d � �-,���# ¥«�

� Y©jwznfij�f8mrY©dnUwY��5fka_agf�¡^_hW�tjWznfiagfihW�ibodn^_fkh$#�/� #� 7 #� � �

�Y�[|R���

� q � #��� , ¶GdnUWYsh #�0�%#� 7 #� ��� ,� q � #� ; , boh p #� � ¶ldeUWY�h #�R�,#� 7 #� ��� ���� ���� q � #� ; , boh p #� ; ¶ldeUWY�h #�R� #� 7 #� ��� �0� #� 7 #� �

q d�^cmDYubkmnq)def��kYszn^g�5q"dnUwbod #� v%fk^_hwv�^ p YumD¡^gdnU � fkh�� #�K; ,�7 #� ; �� bkh p Uwbim(dnUwY~meboX;YdnzeY�h p fkh � � bim � fkh � � � �TSUWY�^_hW^£de^_bka�v%fih p ^gdn^_fkhwm��5fiz � bkh p � bkznY�zeYsmnj�Yuv«dn^_�kYsagqªbimnmn`WX;Y p dnf�a_^_Y©^_h�dnUWY&^_h8dnYszn��boacm � ,���, � boh p � ,�� , � �{$fiznYsf��kY�zu¶k¡�Y©¤8hwf�¡ ��fi`Wh p m��5fizSdnUWY�^_hutw`WYsh8dv�fkhwv�Y�h8dnz�b�de^gfihwm,� � +�- � � '� ����� �&#���� � '� ����� �&#���� � bkh p� +.- � �< g< � �� f�¡ ¡�Y&vsboh p Ysmn^g�ih>deUWY&hWfihWag^_hWYubozfk��mrYszn�iY�z�jWznfij�f8mrY p ^_h§\GYsv%dn^_fkh§�)�5fkz.mnqGmrdnYsX   �k�i¥%�

��������������� ��������������!

�0 �5 � "� 0 �+�-F5 � 0 �5 �0�/-0$>58�#�0� � � 7 � �j�0� � �c��0 �: � "� 0 �+�-8: � 0 �: �0�/-0$ :F�#�0� � � 7 � �j�0� � �c��0 5 � "� 0 +.-F5 � 0 5 �0� -2$J5E� #�R�$� 7 � ��� � �8��0 : � "� 0 +.-8: � 0 : �0� -2$�:;� #�R�$� 7 � ��� � �8�� �_� 0 �5 ��� �! �� �!� 0 �: '�� �! �� � 0 5 ��� �! �� � 0 : '"� �! �

 &�Jr®¥

T�ft�i`wboz�boh8d|qtdnUwY�v%fkhG�iY�ze�kY�h�v%Y�fk��deUW^cmSfk�wmnY�ze�kYszs¶G¡�Y©hwY�Y p   bkv�v�fkz p ^_hW�)def�y(znfij�f8mr^gdn^_fkh ru¥ $J5 ; , bkh p�$ : � , �� Y�U�b®�kY>ze`Wh mr`�v�U fk��mrYszn�iY�z�m&�5fkz>�i�1��boa_`WYum;fo� $ ¶�bkh p ¡�Y�Uwb®�kY�boacmrf ze`Wh deUWY1mr^_X;jWa_Y$bimrqGX;jldefodn^cv�^gh8dnYszn��bka

fk��mrYszn�iY�z� 3v%fiznzeYsmnjEfkh p ^_hW�"dnf $ � , ¥%�TSUWY�znYumr`Wagdem"fo�deUWYsmnY>fi�wmnY�ze�kY�z�m�bkznYªjwznYumrYshideY p fih y�^g�i`WzeY��l�,��m"^£d�v�bkh �EY�mnY�Y�h�¶MdnUWY��ibk^gh biv�v%YsagYszebodnYum&dnUwY

v%fihG�kY�ze�k^_hW�,z�b�dnY�fo�)mnfkX;Y§fk��mrYszn�iY�z�m;^gh deUWY§dezebkhwmn^£defkzeq jWUwbimrY boh p �5fiz�mnfkX;Y�fk��dnUWYOfk�wmnY�ze�kYszem�^gd�zeY p `wv%Yum�dnUwYbkmnqGX;jldnfkdn^cv&Y�zeznfizs�.�~m~b�v%fihwmrY �8`WY�hwv�Yk¶�dnUWY"��Yum|d©Ysmrdn^_X�b�dnY"�k^_�kYsh1�8q�deUWY)a_f�¡�Ysz�Ysh8�iY�a_fkjEY�fo�(deUWY)`wjWj�Ysz©bkh p a_f�¡�Yszfk��mrYszn�iY�z�m�W`Wh p agY�v�bkh§�EYtmnY�Ysh�fkh y�^_�k`wznY;�W�&q d�^_m©¡�fkzndnU§hWfkdn^_hW�ªdeUwb�d©dnUwY"Yum|de^gX�b�deYsm©fo� � ^_m�mrdnzefkhW�iagq�^_Xtjwznf��iY p^_h$dnUWYtmrYshwmrY�deUwb�d~dnUWY)`Whwv%Yszrd�bo^_h8d|q>^_hideY�ze��boa�^cm p zebim|de^_vsboa_agqªh�bozeznf�¡�Y p v%fiXtj�bozeY p dnf�deUWY�fij�Ysh1agfGfkj1fi�wmnY�ze�kY�zu��TSUwYYsmrdn^_X�b�de^gfih�fk� ��v%fkhG�iY�ze�kYsm�X)`�v�U�X;fiznY©zebkjW^ p agqi�

� f�¡ y�^_�k`WzeY.Z)jwznYumrYshid�m(deUWY~zeYsmn`Wagdem¢fk�ld�bo^_hWY p bo� dnYsz¢zeY�^_hW^£de^_bkag^���^_hW�tboa_aWdnUwY~fi�wmrYszn�iY�z�mM�Gq"deUWY�mrX�boa_a_Ysmrd¢Ysmrdn^_X�b�dnY p^_hideY�ze��boa �.��d�dnUwY���Ys�k^_hWhW^_hW�ªdeUWY)zeY�^_hW^gdn^cboa_^.�ub�de^gfih�¡Sbkm.�kY�zeq��5znY �i`wY�h8d" 5Yubkv�U§�w� �;UWfi`Wz«¥boh p dnUWYsh1dnUWY)^ghW^gdn^cboa_^��sb�de^gfih�5zeY �8`WY�h�v%q�^_m p Ysv�znYubkmnY p �.TSUwY���Yum|d�Ysmrdn^_X�b�deY��k^_�kYsh1�8q�dnUwY)Y�hG�iY�a_fkjEY�fo�(deUWY)`Wjwj�Ysz©bkh p agf�¡�Y�z�fk�wmnY�ze�kYszemhwY%d|¡�fkze¤^cm¢jWzeYsmnY�h8deY p fkh y�^_�k`WzeY~�W��TSUWY~znYs^ghw^£de^_bkag^��sbodn^_fkh;jWzefGv�Ysmem¢v�fkh8dnze^g�w`ldnYum(dnf"m|deznfihW�ka_q)^_hwv%zeYsbimrY.dnUWY©v%fkhG�iY�ze�k^_hW��zebodnY�5fiz�EfodnU$��boze^cbo�Wa_Ysms¶lboh p fk�G�G^_fk`wmnagq;deUWY�mrdnYsb p q � mrdebodnY©^gh8deY�ze�®bka­Ysmrdn^_X�b�dnY�^cm`Whwv�U�bohW�iY p �

� � �"�>�S������!��)�

TSUWYumrY©znYumr`wa£d�m�^_a_ag`wmrdnz�b�deY�deUWY�znfi�W`wmrd�jwznfij�Yszrde^gYum�fk��deUWYsmnY~hwfkhWa_^ghwYsbozSfi�wmrYszn�iY�z�m(deUwb�d p fGYsm�hWfkdhWY pWp dnUwY~¤GhWf�¡a_Y p �iYfo��bkaga�dnUwY�X;f p Y�a�  deUWY�¤8^_hWY�dn^cv�m"dnYsznX�mtbozeY>mrYsY�h bim)bkh `WhW¤GhWf�¡h ^_hWjW`Wd�¥tboh p ¡UW^_v�U v�boh p Ysbka�¡^gdnU jwboz�boX;Y%dezn^cv`Whwv�Y�zndebk^gh8dn^_Ysms� � Yt^gh�mr^cm|d�fkh§dnUWY"�3bkv%d~deUwb�d~dnUWY;v%fih8�iY�ze�kYshwv%Y&jWzefkjEY�zndn^_Ysm~jWzeYsmnY�h8dnY p UWYsznYtbozeY)�ka_fk��boa �~TSUWYt`Whwv�Y�z �debk^gh8de^gYum&dnU�b�d)Uwb®�iY;��YsY�h v%fihwmn^ p YsznY p ^gh,deUW^_m)jwbojEY�ztbozeY;�kY�zeq�acboze�kYi¶��W`Wd�dnUWYsq bkznY�zeYsbkag^cmrdn^cvt�5fkz��W^_fodeYsv�UWhwfka_fk�k^cv�bkajWzeflv%YsmemnYsms�

|=|3}m~u�%�����

0 10 200

0.2

0.4

0.6

D

0 10 2020

40

60

80

Sin

timey�^_�k`WzeY1r;�DTSUWY�^_hWjW`ld�m boh p��J+�- �

�Y�[|R���

0 2 4 6 8 10 12 14 16 18 20

0

10

20

30

40

50

60

70

80

S

time

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50

P

time

y�^g�i`WzeY"�g�.\GY�d~fo�Dfi�wmnY�ze�kY�z�m��5fkz~��fi`Wh p Y p `Whwv�Y�zndebk^gh8dn^_Ysm�^gh � +.-1bkh p ��+.-���TSUWY)`wjWj�Ysz~��bkag`WYum�bkznY p bkmnUWY p bkh p dnUwYa_f�¡�Ysz���bkag`WY&bkznY p fkdrdnY p �DTSUWY�biv«dn`�boa­��boa_`WYsmbkznY©^_h$v�fkh8dn^_hG`Wfk`�mSag^_hWYsms�

|=|3}m~u�%�����

0 2 4 6 8 10 12 14 16 18 20

0

10

20

30

40

50

60

70

80

S

time

open loop observer real state

closed loop observer

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50

P

time

open loop observer (lower bound)

open loop observer (upper bound)

closed loop observer

real state

closed loop observer (lower bound)

y�^g�i`WzeY"��� i�f�¡�Y�z~Y�hG�kYsagfij�Y"fo�DdeUWY;Ysmrdn^_X;bodnYum~�i^g�iY�h§�Gq$deUWYtmnY%d�fo��fk�wmnY�ze�kYszems¶w�5fiz~`whwv%Yszrd�bo^_hide^gYum©^gh � +.-Oboh p ��+�- �TSUWY�bkv%dn`wbka���boa_`WYum�bkznY~^gh�v%fkh8de^ghG`Wfi`wmDa_^ghwYsms�MTSUwY~Yum|de^gX�b�deY~fk�­dnUWY©fkjEY�h�agfGfijª^gh8deY�ze�®bka�fi�wmnY�ze�kY�z�^_m�jWa_fodndnY p ^gh p fod�m��

�Y�[|R���

0 2 4 6 8 10 12 14 16 18 20

0

10

20

30

40

50

60

70

80

S

time

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50

P

time

y�^g�i`WzeY�Z���\GY%d�fo��fk�wmnY�ze�kYszem)�5fkz��Efk`Wh p Y p `Wh�v%Y�zndebk^gh8de^gYum;^gh � +�- boh p ��+�-­� TSUwY1fk�wmnY�ze�kYszem;bozeY$znYs^ghw^£de^_bkag^���Y p def^_Xtjwznf��iY�dnUWYt�ka_fk�wbka�v%fihG�kY�ze�kYshwv%Y�z�b�deY)fo�MdeUWY)Ysh8�iY�a_fkjEYk��TSUwY)`WjWjEY�z©��boa_`WYsm~bozeY p bimrUWY p boh p dnUWY"agf�¡�Y�z.��bkag`WYtbozeYp fkdrdnY p �DTSUWY�biv«dn`�boa­��boa_`WYsmbkznY©^_h$v�fkh8dn^_hG`Wfk`�mSag^_hWYsms�

|=|3}m~u�%�����

0 2 4 6 8 10 12 14 16 18 20

0

10

20

30

40

50

60

70

80

S

time

open loop observer real state

closed loop observer

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50

P

time

open loop observer (lower bound)

open loop observer (upper bound)

closed loop observer

real state

closed loop observer (lower bound)

y�^g�i`WzeY"�g���(hG�iY�a_fkjEY)fo�(deUWY)Yum|de^gX�bodnYsm~�k^_�kYsh1�Gq�deUWY"mnY%d©fo�DzeY�^_hW^gdn^cboa_^.�sY p fi�wmrYszn�iY�z�m�¶W�5fkz©`Whwv%Yszrd�bo^_h8dn^_Ysm.^_h � +.-1bkh p��+.-1�DTSUwY~bkv%dn`wbka���bkag`WYum�bkznY�^gh�v%fkh8de^ghG`Wfi`wmDa_^ghwYsms�MTSUwY�Ysmrdn^_X�b�deY~fk�­dnUWY©fkjEY�hªa_fGfkjª^_h8dnYszn��boaEfk��mrYszn�iY�zD^cm¢jwagfkdrdnY p ^_hp fkdems�

�Y�[|R���

� fkdnYdeUwb�d¢dnUWY�v�fkhG�kYszn�i^ghw�©z�b�deYfo�­Ysbiv�U;fo�¦dnUWYumrY~fk�wmnY�ze�kYszemMvsboh��kYshWY�z�boa_a_q�hWfod���Y�dn`WhWY p ��q dDdn`wznhwm¢fk`ld¢dnUwbod¢dnUwYmnagf�¡�Ysmrd~Ys^g�iY�hG��boa_`WY)^cm&boa_¡�b®qlm ��p�q§v%fihwmr^ p Yszn^_hW��b��W`Wh p agY;fk�¢fk�wmnY�ze�kYszems¶E¡�Y;bozeY)hWYs�kYszrdeUWY�a_Ysmem~bk�Wa_Y)def�^_X;jWzef��kYdnUwY&zebodnY�fo�Mv%fkhG�iY�ze�kY�h�v%Y~bkh p dnUWY�bimrqGX;jldefodn^cv©��fi`Wh p ms� 2 ��v�fk`Wz�mnYk¶Wb pwp ^£de^gfihwboa¦deUWY�fiznY�dn^cv�bkaE¡�fkze¤�^cmSdnf;�EY p fkhWYi�

TSUWY&meboX;Y�jWzn^_hwv�^gjWa_Y�bojwjWag^_Ysm��5fiz`Whwv�Y�zndebo^_h8dn^_YsmS^_h>deUWY&qG^gYsa p v�f8Y�Cªv%^_Y�h8demSfiz��fi`Wh p Y p hwfk^cmrY�fkh�dnUwY&fk`ldejW`ldems�

�;� � I�´G³ " ° µ ! � °gI �s�i� TSUWYObk`ldnUWfizem>¡^_mnU def¬dnUwbkhW¤ dnUWY�d|¡�f znYs�8^_Y�¡�Y�z�m;�5fizªdnUwY�^_z�bodrdnYsh8dn^_�kY§zeYsb p ^ghw�imªbkh pjEY�zndn^_hWY�h8d�mn`W�k�iYsmrdn^_fkhwms��TSUwY�q>biv�¤8hwf�¡agY p �kY~dnUWY�mn`WjWjEfkzndfo��dnUWY&biv«dn^_fkh$�MTy¢�o���t\lT qn} fo�D} � ��\­�

TSUW^cm©¡�fizn¤$Uwbim~�EY�YshOvsbozeznqG^_hW�>fi`ld©¡^gdnUOdnUwYtmn`WjWjEfkznd&jWznf��G^ p Y p �8q$deUWY �(`WzefkjEYsbkhOv%fiX;Xt^cmemr^_fkh�¶�q hl�5fiznX�bodn^_fkh\Gflv%^_Y%d|q"T�Yuv�UWhWfka_fk�i^gYum�jWznfi�kz�boX$¶���Y�q"bkv«de^gfih*q(\GqlmrdnY�X�m�� \GY�ze�G^_v�Ysm��5fizMdnUWY~}�^gdn^���Ysh�¶iv�fkh8dnz�bkv%d(T �"i �"{1��} hG`WX)�EY�zqr\lT �|�o�i�k� �&�mk8�k�8�w� TSUW^cm;^ghW�5fkzeX;bodn^_fkh ^_m;jWzef��G^ p Y p `Wh p Y�z;deUWY1mrfiagY$zeYsmnj�fihwmr^_�W^_ag^gd|q¬fo�~dnUWY1bk`ldnUWfiz�boh p p fGYsmthWfkdhWYuv%Ysmemeboze^ga_q�zeY�jWzeYsmnY�h8d�deUWY>fijW^_hW^gfih¬fo�deUWY �(`wznfij�Yuboh }�fkX;X;^cmnmn^gfih�¶M¡UW^cv�U ^_m)hWfodtznYumrjEfkh�mr^_�Wa_Y��5fkztbohGqO`�mrY>dnUwbodX;^g�iU8dS�EY&X�b p Y&fk��^gds�

) �������.������

jsr%l��t�JpSbkmrdn^_h1boh p�� � � flv�Uwbk^gh�� 2 h�� a_^_hWY Ysmrdn^_X;bodn^_fkh boh p b p bojlde^g�iY v�fkh8dnzefka fo� �W^_fkzeYsbiv«defkz�m®� �(a_mnY��G^_Y�zu¶9rs�i�k�W�j � l��t� pSbim|de^gh-boh p �;hDbohxq XtjEYk� � fihWag^_hWYuboz boh p b p bojWdn^_�kY v%fihideznfia ^gh �W^_fodeYsv�UWhwfka_fk�kqJ� b dn`Wdnfkze^cboa �

�(`wznfij�Yuboh fi`Wznh�boa¦fo�D}�fkh8dnzefka ¶9ri  ru¥]�sr��l��zl¶_ru�k�i�W�j �ol 2 �6p�Y�zehwbkz p � {1bkmem;�wbka_bkhwv%Y�X;f p Y�a_ag^_hW�,fo���W^_fkjWzeflv%YsmemnYsms� q h ��� �.�kz�bkv�UwY��¦¶DY p ^£defkzu¶ {1bodnUWYsX�b�dn^cv�bka v%fkh8deznfia

deUWY�fiznq¦¶Gjwbo�iYsm z8�k� �ukJr®�l�Hqn}�Ty a_Ysv%dn`WzeY�hWfodeYsms¶��o�i�i�l�j Zml 2 � p�Y�zehwboz p ¶����ow�b p { �|\lb p fi¤¦¶®bkh p� � � i¢���©fi`����i� 2 �wmrYszn�iY�z�m¦�5fkz�deUWY��w^gfkdnYsv�UwhWfka_fk�i^_vsboakjwznflv%YumnmnYsm�¡^gdnUt`WhW¤GhWf�¡h

¤G^_hWY%de^_vsm��WbkjWjWa_^_vsb�dn^_fkh�dnf;¡SbkmrdnYs¡�bodnY�z�deznYub�dnX;Yshidu��q h yDznflv%YsY p ^_hW�8m fo� } � } �o�k�i�w�l\Gq p hWYsqk¶w��`wmrdnz�boa_^_bw¶l�k�k�i�W�j � l 2 �op�Y�zehwboz p ¶��t�o\lboa_a_Y%ds¶obkh p �)�k\lv%^cboh p zebw� � fkhWa_^_hWYsbkz�fi�wmnY�ze�kY�z�m¦�5fizMb©v%acbkmem�fo�w�W^_fka_fk�i^_vsboa8mrqlmrdnY�X�ms���.jWjWa_^cv�b�de^gfih

deft��bkag^ p b�de^gfih�fk�MbtjWUGq8dnfijWacbohW¤8dnfihW^cv��iznf�¡SdeU�X;f p Y�a � q � � � T�z�bohwms� �.`ldefkX$� }�fkh8dezs� ¶8Zi� �Xru�i�8���Qru�;�i�W¶urs�i�HkW�j �ol ��up�`wmn�kYsaga_Y�boh p� ����bo`WdnUW^_Y�zu�=w.^_�kU�� �8bo^_hªboh p hwfkh�� UW^_�kU�� �ibk^gh�fi�wmrYszn�iY�z�mM�5fkz�hWfihWag^_hWYuboz�mnqlm|deY�X�ms�9q h��.h �sboa p f �

{$YshWYsmnYsms¶��)�g¶�p�fkhWh�boz p ¶xp©� ��bk`ldnUw^gYszs¶ � y�� �9{$fkhwznf�q � y �sznY,�k¶Jy��_¶�Y p ^£defkzu¶ }�fihideY�X;jEfkz�bozeq dnzeY�h p m ^gh hWfkhWa_^_hWYsbkz�iY�fkX;Y�dnze^_v v%fkh8deznfia deUWY�fiznq bkh p ^£d�m bojWjWa_^cv�b�de^gfihwms� q h8deY�zehwb�de^gfihwboa v%fihl�5Y�zeY�hwv�Yk¶ { �%xl^cv%f }�^£d|qi¶ { ��xG^cv%f�� � fizna p\lv�^gYsh8dn^g¨�vo¶w�k�k�i�W�

j]zYl�{,� � bkznfi`wbkv�U�¶ {,���¦bimnb p ��^_hwmn¤G^ ¶�boh p \¦� � ����`�� yW`waga � fiz p Y�z�fk��mrYszn�iY�z�m��5fiz�ag^_hWYsbkz>mnqGmrdnYsX�m;¡^£deU `WhW¤GhWf�¡h^_hWjW`ld�m�� q � � � T�z�boh�m�� ��`ldnfiX�� }�fkh8ds� ¶G�k�� 3�i¥��Xru�;�Fk �Qru��zk�l¶urs�i�oZ��

j kol�y�� � Y,�sbW¶ ��'p�`�mr�iY�a_agYi¶ ����bo`ldeUW^_Y�zu¶Dboh p�� �(�.bo¤ifodefkjwbkzebw� w.^_�kU �8bo^_h Ysmrdn^_X�b�de^gfih¬�5fkzthWfkhwag^_hWYsbkztmnqlm|deY�X�ms�\GqlmrdnYsX boh p v�fkh8dnzefka a_Y%drdeY�z�m®¶_rYk�� �o�8���l�k�k�w¶xrs�i�i�W�

j �ol �ly�����bk`ldnUw^gYszs¶uw��Jw~boX;X;fk`Wze^ ¶Gbkh p \¦� 2 dnUWX�boh���� mn^gX;jWa_Y~fi�wmnY�ze�kY�z��5fkz�hWfihWag^_hWYubozmrqlmrdnYsX;mSbkjWjWa_^_vsb�dn^_fkh�mDdef�W^_fkzeYsbiv«defkz�m�� q � � � T�zebkhwm�� ��`ldnfiX$� }�fkh8dnzu� ¶G��z�� k�zk���ukHkk�w¶Jrs�i�i�W�

jsrs�ol �"iD���©fk`�� �k¶�����.bojwbkj�fizrdu¶�bkh p ���"w~b p { �|\lb p fk¤¦� q h8dnYszn��boafi�wmnY�ze�kY�z�m"�5fkzª`whwv%Yszrd�bo^_h �w^gfiagfi�k^cv�boa.mnqlm|deY�X�ms��Dv�fka_fk�i^_vsboa X;f p Y�a_ag^_hW�E¶Qru�k� � ZG���l�;�W¶G�o�k�i�W�

|=|3}m~u�%�����

jsrHr%l�{,� �M�=w�b p { � \Wb p fi¤§boh p ��i¢� �©fk` ���k� �Dmrdn^_X�b�de^gfihOfk��`Wh�v%Y�zndebk^gh X;f p Y�acm�fo�Sbkv«de^g��bodnY p mnag` p �kYtjWzefGv�Ysmem�¡^£deU^_h8dnY�ze��boa­fi�wmrYszn�iY�z�m�� fi`Wzehwboa fk� y(zefGv�Ysmem }�fkh8dnzefka ¶QrHr8 3�8¥]� �o�k���G�xrs�W¶8�o�k�xrk�

jsru� l�{,�6w�fk` boh p y��B{ � aga_Y�zu� � Yumr^_�kh fo�©fk�wmnY�ze�kYszem)�5fkz�a_^ghwYsbozªmnqlm|deY�X�m;¡^gdnU `WhW¤GhWf�¡h ^ghwjW`ldems� q � � � T�zebkhwms���`ldnfiX�� }�fkh8dnzu�c¶8��} � ��zW ��i¥�� kbzbr �bk�zk�l¶Jru�k�xrk�

jsrs�ol�y�� ��` p ��bW¶ � �xh�^cmn¡�bkhwb p U�boX$¶Wboh p �)���.bkX;bk¤Gzn^cmrUwhwbW� 2 ��mrYszn�iY�z�mD�5fiz.ag^_hWYuboz�mnqlm|deY�X�m¡^gdnU1`WhW¤GhWf�¡h$^_hWjW`ld�m��q � � � T�z�bohwms�l�.`ldefkX$�E}�fihidezs�_¶W��} �|�k�W  ru¥��XrFrs� ��rHr®�l¶Jru�Hkk�w�

jsr�Zml��)�¦��bojwbkj�fizrd�boh p � � i¢� �©fi`����i��yMboz�boa_agYsagfkdnfkjw^_v�bkh p jWz�bkv%dn^cv�bka�fi�wmrYszn�iY�z�m�5fiz~hWfihWa_^ghWYuboz©`Whwv�Y�zndebo^_hOmnqlm|deY�X�ms�q h8ds� fk`wznhwbka � }�fih8dnzefka ¶uz8�w  �i¥]� �o�bz �W�k�uri¶i�o�i�k�w�

jsru� l�w)��i¢��\GX;^£deU��t\lqGmrdnYsX�m~fk��fiz p ^_hwbkznq p ^XgEYsznYshide^_bka(Y �8`wbodn^_fkhwm~¡UW^cv�U��kYshWY�z�b�deYsm©bohOfkz p Y�z�jWzeYsmnY�ze�G^ghW� twf�¡ ���mn`Wze�kY�q�fk��zeYsmn`Wagdems� \bq|�+{ �Ys�8^_Y�¡)¶G�i��� k�z��QrHru�W¶_rs�HkFkW�

jsr,�ol�{,�uh~^ p qibkmebo�8bozu� � fkhWa_^ghwYsboz \lqGmrdnYsX�m �.hwbkagqlmn^_ms�(y(zeY�h8dn^cv%Y�� w~boa_a ¶ �(hw�ka_Y�¡�f8f p }�ag^Xg­m�¶ � Y�¡ YszemnY�qi¶9rs�k�i�W�

�Y�[|R���

Unité de recherche INRIA Sophia Antipolis

2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)

Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes

4, rue Jacques Monod - 91893 ORSAY Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique

615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)

Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France)

Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

Éditeur

INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)��������� ���� ���������� ��� ���

ISSN 0249-6399