On nonlinear distributed parameter model predictive control strategy: On-line calculation time reduction and application to an experimental drying process

(1)

HAL Id: hal-00352371

https://hal.archives-ouvertes.fr/hal-00352371v2

Submitted on 21 Jan 2009

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

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

On nonlinear distributed parameter model predictive control strategy: On-line calculation time reduction and

application to an experimental drying process

Pascal Dufour, Youssoufi Touré, Denise Blanc, Pierre Laurent

To cite this version:

Pascal Dufour, Youssoufi Touré, Denise Blanc, Pierre Laurent. On nonlinear distributed parameter model predictive control strategy: On-line calculation time reduction and application to an experi- mental drying process. Computers & Chemical Engineering, Elsevier, 2003, 27 (11), pp.1533-1542.

�10.1016/S0098-1354(03)00099-1�. �hal-00352371v2�

(2)

This document must be cited according to its final version which is published in a journal as:

P. Dufour

¹

, Y. Touré

²

, D. Blanc

³

, P. Laurent

¹

"On nonlinear distributed parameter model predictive control strategy:

On-line calculation time reduction

and application to an experimental drying process", Computers and Chemical Engineering, ISSN: 0098-1354

27(11), pp. 1533-1542, 2003.

http://dx.doi.org/10.1016/S0098-1354(03)00099-1

All open archive documents of Pascal Dufour are available at:

http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008

The professional web page (Fr/En) of Pascal Dufour is:

http://www.lagep.univ-lyon1.fr/signatures/dufour.pascal

1

Université de Lyon, Lyon, F-69003, France; Université Lyon 1;

CNRS UMR 5007 LAGEP (Laboratoire d’Automatique et de GEnie des Procédés), 43 bd du 11 novembre, 69100 Villeurbanne, France

Tel +33 (0) 4 72 43 18 45 - Fax +33 (0) 4 72 43 16 99

http://www-lagep.univ-lyon1.fr/ http://www.univ-lyon1.fr http://www.cnrs.fr

2

Université d'Orléans,

UPRES EA 2078 LVR (Laboratoire de Vision et de Robotique ), 63 Av de Lattre de Tassigny, 18020 Bourges Cedex, France http://www.bourges.univ-orleans.fr/rech/lvr/

3

INSA de Lyon;

LAEPSI (Laboratoire d'Analyse Environnementale des Procedes et des Systemes Industriels);

Bâtiment Said Carnot, 9 rue de la Physique 69621 Villeurbanne cedex, France

http://laepsi.insa-lyon.fr/

(3)

!"$# !%&'()* +-,/.102 !34 !35)5

!"5 4 4 !%)$6 *

718 95 &:,; + !3 3<

=1>?A@B>C;DEGFIHKJLM@N>C*O

P1Q

EIRSLUTWVYXBZ[\=/EI]^XBZ_a`XB>C

P

Zcb;DEIF

dfehgikj(lmonBprqts uwvyxzqt{}|u4~B rGu%ouvzp veNI p5m3n~UUGI

r

mNU &I3s uwvu IG mIG5I¡ 2qt¢£uv¤¥ prp¦u)~kuyGu¥§mN¨¦v p©zu¤ª

«

e ¬Um%nhprqts uwvyxzqt{}|u¯®vz5|uf p}xymn°ljWj(g±²}¤

mcgUsGuoe{³{´v¥uGu-µ5xAxAq¶pr5m*²5²U v³¶·uzx)~kuyGu¥§mN¨¦v p©zu¤ª

¸Ae2gUj(l²¹ymB¹"gºecI p

U{»ªcI qo~c vAp¬{tm)vzruGu%¼¾½G5xAq³¿w¾umG5²\ qttuw²v¤¥prp¬u~ku¥·u¥§ mc¨¦v p©Aufª

À4ÁBÂwÃfÄ5ÅrÆÃ

ÇYÈÉ£ÊË}Ì$ÍSÎ¥Ï¤ÐÌÑIËrÉÒwÏ¤ÓWÈ¥ÔrÕ ÈÖÌÓ}Ï¤×¬ØrÎ¥Ï¤ÓrÉ£ÐÈ¥É£ÙÏoÐÌIË·ÈÎ¥ÌI×(Ú³Û6Ü*Ý9Þ*É£ÊÕË-É£Ë·ÈÏwÎ¥Ï¤ÊÈ¥É£Ë}ÑÕ×ÈÏwÎ¥ß

ËrÕ È¥É£ÙÏ9àtÌÎ(Î¥Ï¤Õ×áß»È¥ÉâÖÏ9ÐÌIË·ÈÎ¥ÌI×rÌàÉ£Ë¾ÓrãrÊÈÎyÉâÕ×·Ø¾Î¥Ì²ÐÏ¤ÊyÊÏ¤ÊwäIÇåËÈ¥Ô}ÏUÖÏ¤ÕËGÈ¥ÉâÖÏæ·ÊÌIÖÏØrÎ¥Ìç¾×£Ï¤ÖÊ

Ó}Ì1ÊÈ¥É£×£×Î¥Ï¤ÖÕÉ£ËÉ£ËØrÎyÌÑÎ¥Ï¤Ê¥ÊwèkàtÌÎÈ¥Ô}ÏwÌÎyÏwÈ¥É£ÐwÕ×éÕÊ¥Ø¬Ï¤ÐÈ¥Ê¤ækÈ¥Ô}ÏÕêØ¾ÎyÉÌÎyÉÑIãrÕ ÎAÕËGÈÏwÏ6ÌàUÈ¥ÔrÏ

ÊÈ¥Õ çÉ£×£ÉÈìë6ÕËrÓêàtÌÎ%È¥Ô}ÏØ¾ÎyÕÐÈ¥É£ÐwÕ×kÕÊØ¦Ï¤ÐÈ¥Êwæ2È¥Ô}ÏÑIãrÕ ÎyÕË·ÈÏwÏÌàÊ¥ã}í)ÐwÉÏ¤ËGÈ"È¥ÉâÖÏÈÌÊÌI×ÙÏÈÌ

ÌØrÈ¥ÉâÖÉÒ¤Õ È¥ÉÌIË6ØrÎ¥Ìç¾×£Ï¤ÖîÕ ÈoÏ¤ÕÐyÔêÊ¥ÕÖØ¾×Ï¤Ó6È¥É£ÖÏØ¬ÌIÊyÉÈ¥ÉÌIËrÊwä¾ÇYË6È¥ÔrÉ£ÊéØ¾Õ Ø¦ÏwÎ¤æ¾Í*Ï ØrÎ¥ÌØ¦ÌIÊÏÕ

ÑI×ÌçÕ×ÖÏwÈ¥Ô}ÌÓÈ¥ÔrÕ ÈÕÉ£ÖÊ ÈÌÎ¥Ï¤ÓrãrÐÏ-È¥ÔrÏ-ÌIËßï×£É£Ë}Ï-ÐwÕ×£Ðwã¾×£Õ È¥ÉÌIËÈ¥É£ÖÏWÓ¾ã}ÏÈÌÈ¥Ô}ÏÜðUñ

(4)

ÊëÊÈÏ¤ÖÊUË}ÌÈÙÏwÎyë-Ìà¢ÈÏ¤Ë ÊÈ¥ãrÓrÉ£Ï¤ÓWÉ£ËWÈ¥Ô¾É£ÊÐÌIË·ÈÏ²Èwè°ÊëÊÈÏ¤ÖÊéÓ}Ï¤Ê¥ÐÎyÉç¦Ï¤Ó-ç²ëØ¾Õ Î¥È¥É£Õ×hÓrÉ¦ÏwÎß

Ï¤Ë·È¥É£Õ×¦Ï ²ãrÕ È¥ÉÌIËrÊ%Ú´ÜðUñÊAÞÍ9ÔrÉâÐyÔ4Õ Î¥ÏærÉ£Ë4È¥Ô}ÏoØrÎ¥Ï¤ÊÏ¤Ë·ÈÐwÕÊÏærË}ÌIË¾×£É£Ë}Ï¤Õ ÎÕËrÓØ¾Õ ÎyÕ ç¦ÌI×£ÉâÐ äGÇåË

ÌÎyÓrÏwÎBÈÌ"Ó}Ï¤ÐÎyÏ¤ÕÊÏÈ¥Ô}Ï*ÐÌIÖØ¾ã}È¥Õ È¥ÉÌIËrÕ×²ç¾ãrÎyÓ}Ï¤Ë°æ$È¥Ô}Ï*ËrÌIËr×£É£Ë}Ï¤Õ ÎBÜ(ðoñêÊëÊÈÏ¤Ö É£ÊBÊÌI×ÙÏ¤ÓÌ¬ß

×£ÉâË}Ïä!ÔrÏ¤Ë°æ·Õ ×£É£ËrÏ¤Õ ÎyÉÒwÏ¤ÓÜðoñÖÌ²ÓrÏ¤×Õ Î¥ÌIã¾ËrÓÈ¥ÔrÏéØrÎyÏwÙ²ÉÌIã¾Ê(Ì¬ßï×£É£Ë}Ïéç¦Ï¤ÔrÕ¤ÙÉÌÎÉ£ÊãrÊÏ¤Ó)ÈÌ

"

Ë¾Ó-È¥Ô}Ï%ÌØrÈ¥ÉâÖÕ×°Ù Õ ÎyÉ£Õ È¥ÉÌIËrÊà¢ÌÎéÈ¥Ô}Ï%ÌIËßï×£ÉâË}Ï"ØrÎ¥Ï¤ÓrÉâÐÈ¥ÉÙÏ%ÐÌIËGÈÎyÌI×³ä!ÔrÏ"Î¥Ï¤Õ×áß»È¥É£ÖÏÐÌIËGÈÎ¥ÌI×

Õ ØrØ×£É£ÐwÕ È¥ÉÌIËÑIÉÙÏ¤ËÉ£ÊÐÌIËrÐÏwÎyËrÏ¤Ó-Í9ÉÈ¥Ô-ÕÉâË}à¢ÎAÕ Î¥Ï¤ÓÓ}Î¥ëÉ£Ë}Ñ ØrÎ¥ÌÐÏ¤Ê¥ÊÌàBØ¾ÕÉ£Ë·È¥É£Ë}Ñ " ×£ÖWä

# uw%$( v5x&

ÛÌ²ÓrÏ¤×°ØrÎ¥Ï¤ÓrÉâÐÈ¥ÉÙÏ"ÐÌIËGÈÎ¥ÌI×»æ¾Ë}ÌIËr×£ÉâË}Ï¤Õ ÎØ¾Õ Î¥È¥É£Õ×°Ó¾É¬ÏwÎyÏ¤ËGÈ¥É£Õ×¦Ï ²ãrÕ È¥ÉÌIË¾ÊwærÉ£Ë·ÈÏwÎyËrÕ×°ÖÌÓ}Ï¤×

ÐÌIË·ÈÎ¥ÌI×³ærÎyÏ¤Õ×áß»È¥É£ÖÏ%ÐÌIË·ÈÎ¥ÌI×³æ¾ÓrÎ¥ë²ÉâË}Ñ ØrÎ¥ÌÐÏ¤Ê¥Êwä

' (*),+-/.10243+56.7)

8:9;=<>?A@CBEDGFH;*I*J?LKE;=BMNJO9?QPSRT>R,;*U?APVJBW;YXGJ;*@Z\[^]=_`JOBaPcbGPHJ;*<P<dBZ;*eQ;*ZfDgb%@B@h

eQ?A@;>US]jiCklPm/knK;@poq?LJ9fBE@eAbrBE@;=PORT>sJ?t>eEZ?Q<d;@NPO?QB@VuJ9N;PO;=PHbGPcJ;<dPn>UO;j@BJBMvJO;@

JUH;>JO;ZVuT;*POR7;I?Q>eQeLb?A@wJ9;%@B@eQ?A@;>UI>PH;m7x@;%9T>PyJOB\R,BE?A@gJ:BEzNJ:JO9T>Jq;>I9{JO?Q<d;

J9T>sJnR9;*@BE<d;@T>C>UO;J>|}?Q@~aRet>I;PHRT>JO?t>eAeAb%>@NZJ9T>JBE@;~E;BE<d;*JOUO?AI>e}Z?A<;*@PO?ABE@

>PW<BEUH;%?Q<dRT>I*JqJO9T>@^BJ9;*UOPrZNBuTJ9;f9gbR7BJO9;PH?QPrBMnz@?AZ?Q<d;@NPO?QB@T>eQ?LJbD7;I*BE<d;P

UO;>eQ?APHJ?AImlkXReA?QI?LJeLbEu4JOU>@NPOR7BEUHJdUO;>I*JO?QBE@R9;*@BE<d;@T>oq?AJO9PH?Q~E@?LTI>@}JdZ?LzNPO?AK;

>@ZIBE@gK;I*JO?AK;^R9;*@BE<d;@T>`>UH;JbGR?AI>eAeAbI9T>UO>I*JO;UO?A;*ZDgbPO;YKE;UH;@NBE@eQ?A@;>UO?Lh

J?A;Pa>@ZPHRT>J?Q>e1K>UO?Q>J?ABE@Pu>@Z>UH;@T>sJzUO>eQeLbZ;PHIUH?QD7;ZDgb{RT>UHJO?t>e1ZN?A,;UO;*@gJ?t>e

;}zT>JO?QBE@NPmnkXN><dReQ;*PpBMqPHzI9RUOBGI;*POPH;P\?Q@I*eQzZN;JzNDzet>UpUO;>I*JOBEUOP*uRT>I|;ZD7;Z

UO;>I*JOBEUOP*u>DPOBEUHRNJ?ABE@\IBEeAz<d@PugZUcbG?Q@~fBEUjIzUH?Q@~fRUHBI*;POPH;P*m8:9;Wet>UO~E;:@}z<D7;U=BM

UO;>e>RReA?QI>sJ?QB@PyJ9T>sJaUH;PHzeAJOPa?A@PHzI9]jiCk<BGZ;eAP:IBE@NPHJ?LJzNJO;PWJ9;f<BJ?AK>JO?QBE@

ÝÌÎ¥Î¥Ï¤ÊØ¦ÌIËrÓrÉâË}ÑÕã}È¥Ô}ÌÎfè¬Ï¤ÖÕÉ£×cÓrã}àtÌIã}ÎOo×âÕ ÑÏwØäãrËrÉÙ·ßï×ëÌIË äàtÎ¤æ}Ø¾ÔrÌIË}ÏWÚvIÞpsw

²æàtÕÚvIÞnpCs %

(5)

£@wIB@}JOUOBEeJ9N;BEUcbEuGZz;aJOBpJ9N;rIB<ReA;YX?AJb\BMVJ9;aRUOBDeQ;*<ugUH;et>sJ?AK;eLbM¢;*o¤PHJOzZ?A;P

>UO;Z;*KBJ;*ZJBwI*BE@gJUHBEe4BMlRUOBGI;*POPH;PC;YXReA?QI*?AJeLbI9T>UO>I*JO;UH?Q;*ZDgb>]=iCk¥<dBZN;e¦m

§=>UO?ABEzPa<;YJ9BGZP>UO;RUHBER7BEPO;*ZM¢BEUrI*BE@gJUOBeBMjPHzI9Z?QPcJUO?ADzNJO;ZRT>U><d;*JO;UrPcbGPch

J;*<PqDzNJWJ9N;UO;f?QPq@Bd~E;*@;UO>e1M¢U><d;*oBEUO|wb;*Jm,¨q;I*;@gJeLbEu,_9UH?QPHJOBTZ;*PrZ;YKE;*eQBER7;Z

BEUOZN;U=UO;ZNzI*JO?QBE@D}b\R>UHJO?AJ?ABE@?A@~J9;W;?A~E;@NPOR7;I*JOUOz<©BMJ9;WBER7;U>sJBEUjBM,J9;a]jiCk

PHbGPHJO;< ª¬«NuL ¡s® >@Z<;YJ9BGZPD>PO;*ZB@>RRUHBX?A<>JO;w?Q@N;UHJO?t>ej<>@?LM¢BEeQZ`M¢BEUPOR>sh

J?Q>elZ?QPHIUH;*J?A>JO?QBE@`BMyJO9;w]jiCk©ª°¯u¡s® m±²IBE<dRUO;*9;@NPO?AK;wPHJOzZNb`BM:9N?QP%oBEUH|I>@

D,;{M¢BEz@Z?Q@9N?QPD7BGBE|³ª°´

®

mxrJ9;*UoBEUO|}PM¢BEUdIB@}JOUOBEeAeQ;*UPcb@gJO9;PH?QPBMC@NBE@eQ?A@;>U

]jiCkPHbGPcJ;<dPW>UO;rDT>PO;*ZB@PHbG<<d;*JOUHb~EUOBEzNRPu?A@NT@?LJ;*PO?Q<>e~E;*@;UO>JBEUHPq>@Z?Q@Gh

K>UO?Q>@gJnIB@Z?AJO?QBE@NPqª

¡µ uA¶

®

mE_BE@I*;UO@N?Q@~ª·¸Nu

µ ®

usT@N?AJ;:ZN?Q<d;@PH?QBE@T>eI*BE@gJUOBeQeQ;*Un>UH;

BEDNJ>?Q@;*ZJ9UHBEz~E9`<BGZ;*eUO;*ZzIYJ?QB@DT>PO;Z`BE@K>UO?ABEzPC<d;*J9NBZP*¹VPO?A@~EzeQ>UrK>eAz;

Z;I*BE<dR,BEPH?AJO?QBE@Vujº%>UH9}z@;@Gh»1B4¼;*K;;YXRT>@PO?ABE@BEUd;?A~E;@M¢z@I*JO?QBE@<;YJ9BGZVmj£@½ªµ®u

PHJ>D?QeA?AJbIBE@NZ?AJO?QBE@P4M¢BEUnIeABEPO;*ZeABBRIBE@gJOUOBEeTBM7eA?Q@;>Ul]jiCk`oq?LJ9T@?LJ;:Z?A<;*@PO?ABE@

IBE@gJOUOBEeAeQ;U=>UH;r~E?LKE;*@w?Q@dJ?Q<d;qZBE<>?Q@>@ZdM¢UO;*GzN;@IYbwZBE<>?A@dJO9UOBEzN~E9wPO;*<?A~EUOBzR

>@T>eLbGPO?QP*m

8:9;¾M¢U><;YoBEUH|¿RUH;PH;@gJ;*ZÀ9;*UO;>ZZNUO;PHPJ9;ÁD7BEz@Z>UHbÂIBE@gJOUOBEeBM@NBE@eQ?A@;>U

RT>UO>D,BeQ?QI]=iCklPPHbGPHJO;<dPI9T>U>IYJ;UH?Q*;Z¾DgbIB<ReA;YX@NBE@eQ?A@;>UO?AJO?Q;*P?Q@J9;dPOR>sh

J?Q>elZBE<>?Q@>@Z¾>JJO9;D7BEz@NZT>UHb>Pfo;*eQeÃm[{BEUO;*B/K;U*u4J9N?QPfPHJUO>J;*~b`9T>PfJB^D7;

>DeA;dJOB^D7;?A<ReA;<d;@gJ>DeQ;M¢BEUfBE@heQ?A@;IBE@gJOUOBEeÃuSJ>|}?Q@~{?Q@gJOB>I*IBEz@gJpBM:@T>JOzU>e

R9gbGPO?QI>eTeQ?A<?LJ>JO?QBE@NPBUnPOR7;I*?ATI>J?ABE@PWÄ6I*BE@PcJU>?Q@gJPÅ?Q@9;*UO;*@}JjJOBf<>@gbRNUOBGI;PHPO;*Pm

±r@>ZNK>@I*;Zw<dBZN;eTDT>PH;ZwI*BE@gJUHBEePHJUO>J;*~bEuGZ;YKE;eABER7;ZM¢BEUjBEUHZ?Q@>UHbZN?A,;UO;*@gJ?t>e

;}zT>JO?QBE@PcbGPHJ;*<P*uV?QPWo;*eQe4Z;Z?AI>JO;ZJOBPOBEeLKE;pJO9?QPI*BE@PcJU>?Q@;*ZRUOBEDNeQ;<{¹<BGZ;*e

RUO;*Z?QIYJ?LKE;qIBE@gJOUOBEeÃmG[^]=_BEUjUO;*I;ZN?Q@~f9BEUH?QB@I*BE@gJUOBeTUO;*M¢;*UOPjJB>CIet>POP=BMI*BE@gJUHBEe

>eQ~BEUO?LJ9<dP?A@oq9?AI9>Zb@><?AIRUHBI*;POP:<dBGZ;e,?QPyzPH;ZJBRNUO;ZN?QI*J:>@ZBERNJO?Q<d?Q;

RUOBGI;*POPWR,;*UHM¢BEUH<>@I;mT8:9;?AZ;>\?QPyJOBPHBEeAK;u7>Jq;>I9^PO><RNeQ;CJ?A<;u>@{BER7;@heQBGBER

BERNJO?Q<d?Q>sJ?QB@RUHBEDeA;<½BKE;U=>a@?AJO;yRUO;*Z?QIYJ?ABE@9BEUH?Q*BE@?Q@BUOZ;*UJBT@NZ\JO9;K>eAz;

(6)

?AJO;U>sJ;ZÆ>JfJ9;@;YXGJPO><dReQ;J?A<;oq?LJ9JO9;zNR,ZT>sJ;dBM:RUHBI*;POPp<;>POzUH;<d;@gJP*m

84BGZT>bEu[^]=_¿9T>PaD,;*IBE<d;>@>ZK>@I;*ZIBE@gJUHBEeSPHJOU>JO;~boq?QZN;eAbzNPO;Z?A@?A@ZzPh

JUcbEmG£@Z;;*ZVuT[]_?AP=o;eAe,PHz?AJO;ZM¢BU9?A~E9R7;UcM¢BEUO<>@I*;aI*BE@gJUHBEe,PH?Q@I*;rI*BE@PHJOU>?A@gJP

I>@D,;; XNRNeQ?QI*?AJOeAb¾?A@IBUOR7BEU>JO;Z?Q@gJBJ9N;M¢BUO<zeQ>J?ABE@ÁBMaJ9;{IBE@gJOUOBEeqRUHBEDeQ;*<m

8:9;UH;*M¢BEUH;uS?AJ%?AP%@BJ>{PHzUORNUO?QPH;JB{PO;;\J9>Jf?AJ%?QP%>@?A<R7BEUHJ>@gJCJBGBEeM¢BEUCI*BE@gJUHBEe

;@~?Q@;*;UOPWoq9;UH;ReQ>@gJrD7;?A@~I*BE@gJUOBeQeQ;*Z>UH;PHzNÇdI?A;@gJeLb^PHeQBoÈM¢BEUW?AJOPa?A<ReA;<d;@h

J>JO?QBE@¹V?Q@ZN;;ZuB@;9>PfJOBD7;d>DeA;\JOBPHBEeAK;>@BE@GheQ?A@;BERNJO?Q<d?Q>J?ABE@RUHBEDeQ;*<m

[BEUH;{ZN;*J>?QeQP\>@ZUO;*M¢;*UO;*@I;*PBE@[^]=_²I>@D7;M¢BEz@Z?Q@Âª·Eu

¡

EuL´Nu

¡

¯u

¡ ¸ ® mnÉTUOBE<

>RU>IYJ?AI>eR,BE?A@gJBMWK?A;*o%uJO9;ZU>oqDT>I|¾BM[^]=_²?QPJ9;IB<RzJ>JO?QBE@T>e=JO?Q<d;

>POR7;IYJm£@NZ;;*ZVuJ9;r<BGZ;e>?Q<dPJOBRUO;*Z?QIYJyJ9N;rM¢zNJzNUO;CZNbG@T><d?QIrD,;*9T>K?ABEUyBM1JO9;

RUOBGI;*POPBEzJRzNJB/K;U>^@?AJO;RUH;Z?AI*J?ABE@¾9BUO?Q*BE@¾>@ZÁ9T>PpJOBD7;wPOBEeLKE;*ZÁZzUO?A@~

J9;%BE@GheQ?A@;I*BE@PHJOU>?A@;Z{BERNJO?Q<d?Q>J?ABE@RUHBEDeA;<ÊUH;PHBEeQzNJO?QBE@m

8:9;%IBE@gJOUO?QDNzNJ?ABE@BMSJ9?AP:RT>R7;Uq?QPyJOBdRNUOBKG?QZ;%>d[^]=_³M¢UO><;YoBUO|M¢BU:POzI9]jiCk

PHbGPHJO;<dPyJBUH;ZzNI;J9N;CBE@heA?Q@;qUH;POBeQzNJO?QBE@JO?Q<d;r>sJ

µ

eQ;YKE;*eQPuN>Py>RReQ?A;Zw?A@ª·Ë

®

M¢BEU

J9;dIB@}JOUOBEejBMy>{I>J>eAb}J?AIUO;*K;UHPO;ÌTBoÍUH;>IYJBEU*mSÉ?QUHPHJuVJ9;dIBE@gJOUOBEelPcJUOzNI*JzNUO;?AP

>@>ZT>RNJ>J?ABE@\BMV[^]=_oq?AJO9?A@}JO;UH@T>eT<dBZ;*eIB@}JOUOBEe4Ä¢£c[_:ÅjPcJUHzI*JOzUO;qoq9;UH;WJO9;

@BE@eA?Q@;>Ua]=iCk³PHbGPHJO;<ÎÄ6POBeAKE;*ZB7heQ?A@;Å:>@Z>weA?Q@;>UO?A;*Z]jiCk³PcbGPHJ;*< Ä6PHBEeAK;Z

ZzUH?Q@~wJO9;BE@heQ?Q@N;pBERNJO?Q<d?Q>J?ABE@J>PO|Å>UH;D,BJO9zPO;*Z?A@BEUOZN;UJBZ;*IUH;>PH;\JO9;

IBE<dRzNJ>J?ABE@T>e,DzUHZ;@Vm±a<BE@N~BJO9;U:JO9?Q@~PuzPH;BMn£c[_ÂPcJUHzI*JOzUO;fR,;*UO<d?AJOPyJB

zPO;\@}z<d;UH?QI>eUO;*POBEeAzNJ?ABE@<d;*J9NBZPreQ;PHPf>II*zU>JO;J9T>@`<d;*JO9BGZPC?Q@BJO9;Uf[]_

M¢BEUO<pzet>JO?QBE@NPmÏ;*IBE@NZeAbu7JO9;pI*BE@gJUOBe4PcJU>sJ;~b?APaI*BE@I*;UO@N;Zoq?AJO9^BE@heQ?A@;CUO;*POBEeAzh

J?ABE@J9T>J>?A<PaJB{IBEUHUO;IYJfB7heQ?A@;PHJOUOzIYJzUH;UH;PHzeAJOPm1£@JO9;J9?AUOZRT>UcJuVM¢BEUJO9;

IeQ>POP:BM4IB@PHJOU>?A@}JOP:IBE@NPO?QZN;UO;*Z9N;UO;uT<;YJ9BGZPyBM4JOU>@PcM¢BEUO<>JO?QBE@>@ZR,;*@T>eQ?A>sh

J?ABE@\>UO;qRUHBER7BEPO;*ZVug9;@NI;W>eQeABoq?Q@~rJO9;qzPO;qBM,BERNJO?Q<d?Q>J?ABE@>eA~EBEUH?AJ9N<½M6>PHJ;*U=>@Z

eQ;*POPUO;*PHJOUO?QIYJ?A@~^J9>@ÁBJ9N;UOP*mlÉ?A@T>eQeLbEu1J9N;et>PcJRT>UcJBMqJ9N;RT>R7;U?APIBE@NI;UH@;Z

oq?AJO9wJ9;; XR,;*UO?Q<d;@gJ>e£c[_=h[^]=_¤M¢BEU?Q@NM¢UO>UO;*ZwZUHbG?A@~RUOBGI;*POP:BMSR>?Q@gJ?A@~pTeA<m

(7)

ÜGÝvÞ ßnàLásââãäåãsæTç6èvæTéãségâ%ç6èvêëfêãìGëYà4åãsæNâYè6ìGëYíëOì

8:9;ÁIeQ>POP^BMdPO?Q@N~EeQ;?Q@RzJPO?A@~EeQ;BEzNJORzNJÄÃÏ£cÏx%ÅBE@;ÁZN?Q<d;@PH?QBE@T>ef@NBE@eQ?A@;>U

RT>UO>D,BeQ?QIr]jiCkjPqoq?AJO9D,BEzN@ZT>UcbIBE@gJOUOBEe1I*BE@PO?AZ;UH;Z{?QP*¹

Ä¢îïðTÅ

ñòòòòòòòòòòòòòòòòòò

óòòòòòòòòòòòòòòòòòòô õö ÷ùøúûLü

õû ý³þ4ÿ

Ä Ä

ÅOÅ

Ë

þ Ä Ä

Å

Ä

ÅOÅ

ý

Ë

Ä

ËgÅ

ý

! "

#%$

Ä Å

ý'&

Ä

Å(! "

Ë

Ä/Å

oq9;UH;)p?QP=J9;r?Q@Z;*R,;*@Z;*@}JyPORT>I*;K>UO?Q>DeQ;u*¥?QPJO9;rPHRT>JO?t>e7ZBE<>?Q@>@Z+¥?AJOP

D,Bz@ZT>UcbEu

?APjJO9;W?Q@Z;*R,;*@Z;*@}JJ?A<;yK>UH?t>DeA;m, ?QPlJ9;WPHJ>J;qKE;*I*JOBEU?A@>.-a?AeQD7;UcJ

ÏRT>I*;u

?QPJ9N;dI*BE@gJUHBEenBEU%<>@?QRNzet>JO;Z^K>UH?t>DNeQ;ÄÃ[{§%År?A@/Wu

#0$

?QPrJO9;\<BGZ;*e

BEzNJORzNJq?Q@1/Wm

þÿ

>@NZ

þ2

>UO;@B@eQ?A@;>UBER,;*U>JOBEU%ª

Ð ®m &

?QPy>eQ?Q@N;>UyBR,;*U>JOBEU%ª

¡ Ð ® m

35464

2Ù87S+/56.7)Â':9<;

ëdâãsà·éGç6è¦ãsæäãsí Ä¢îïðTÅ èQâéGæTè=éëáæ7ììGë?>TëYæ7ìsâåãsæTçÃèvæTéTãségâYàA@

ãsæç; ëCèvæTèvçÃè6áàCBsáà·éTëÝ

[BEUH;BKE;*UuJO9;wIB@}JOUOBEeBMWRUOBGI;*POPZ;*POI*UO?QD7;ZÁDgbÆPOzI9<dBZ;*e?APpPH?Q<zeLJ>@N;BEzPHeAb

POzD}FH;I*JWJBN¹

D

I*BE@PHJOU>?A@gJPqBE@J9;%<>~E@?LJzZN;C>@ZKE;*eQBGI?AJbBMJO9;[{§¹

(8)

òòòòòò

óòòòòòòô

FECGIHKJ(

Ä Å

J(FE dML

Ë

N

$ PO

J N

Ä Å J N

$RQ

ö

Ë Ä ¡ Å

DTS

~E;*@;UO>eCRUHBI*;POPBEzJRzNJI*BE@PcJU>?Q@gJPBE@¥J9N;IBE@gJUHBEeQeA;Z¥K>UO?Q>DeA;ÁÄ¦_§CÅ

#VU

UH;et>sJ;ZJOBdBR,;*U>JO?Q@~I*BE@Z?LJ?QB@PuPO>M¢;*JbuGz>eQ?LJb,¹

W Ä

#VU Ä Å

Ä

ÅHÅ

J Ë

X Ë

ZY[]\

O

ý_^

)`a`b`a Sc

Ä µ Å

35464

2Ù87S+/56.7)Ñd9<; ëYíëaëfeEèQâYç¢â

Ä Å ý g

Ä Å

àQëOágìèvæihCçã%ç; ë>Náí çÃè¦åYéGàLáíyíë?>7íëâëYæTçá,j

çÃè¦ãsæ Ävî

g Å ãä Ävîï4ðNÅ ìGëâåYí èkYëOìlkV@Wç; ë=ç6í èm>7àQëYç

^ Ä Å ý g Ä Å

Ä

f

Å ý g

Ä

Å

#%$

Ä Å ý

# g Ä Å c Ý

§=>UO?Q>J?ABE@P:>UOBEz@NZJO9?QPyJOUO?AReQ;YJq>UO;%~E?LKE;*@Dgb7¹

ñòòòòòòòòòòòò

óòòòòòòòòòòòòô Ä Å ý g Ä

Å2npo

Ä Å

Ä Å ý qÄ

ÅCnTor Ä Å

#%$

Ä Å ý # g Ä ÅCnpo

#%$

Ä Å ÄÐ Å

oq9;UH;:POzNÇdI*?Q;@gJOeAbPH<>eQe}K>UO?t>sJ?QB@P>UO;yZ;*POI*UO?QD7;Z\DgbpJO9;yJ?A<; hK>Ucb?A@~WeQ?Q@N;>UH?Q;*Z

<BGZ;*ejÄ¢î<sutðÅyBEDNJ>?Q@N;Z{>D7BEzNJÄ¢î

g

ÅY¹

Ä¢î<sutðÅ

ñòòòòòòòòòòòòòòòòòò

óòòòòòòòòòòòòòòòòòòô

õwvö ÷ùøúûLü

õû ýyxrÿ

Ä Åfor Ä

Å

Ë

x ö Ä Åzo{ Ä

Å|n

x}

Ä Åfo

Ä Å ý Ë

Ë

or Ä

ËgÅ

ý Ë ! ~

o

#%$

Ä Å

ýy&

or Ä

f

Å !

Ë

ÄÃ¶EÅ

oq9;UH;J9;JO?Q<d;YhK>UcbG?Q@~eQ?Q@N;>UWBER7;U>sJBEUHP

xrÿ Ä

Å u

x ö Ä År>@NZ

x } Ä

Å>UH;BEDNJ>?Q@N;Z

(9)

g

35464

2Ù87S+/56.7)d9<; ëCâãsà·éç6è¦ãsæäãsí

Ävî<stðNÅ

èQâéæTè=éTëáæ7ììGë?>TëYæ7ìsâåãsæTçÃèvæTéTãségâYàA@

ãsæç; ëCèvæTèvçÃè6áàCBsáà·éTëÝ

ÜGÝQÜ %èQâåYíëYçë%çÃèvêëK~rß^äãsí êéàLáç6è¦ãsæ

x@;yBMJ9N;:>ZNK>@gJ>~E;:BM,[^]=_¾M¢BEUO<zNet>JO?QBE@>Pj>rI*BE@PHJOU>?A@;Z\BERJ?Q<d?Q>J?ABE@%RUOBDh

eQ;*<Í?QPjJ9T>J>eQ>UO~;a@}z<D7;U=BM1I*BE@gJUHBEe,RNUOBEDeA;<dPI>@D7;rPcJ>JO;ZVmG£JIBKE;*UOPyJUO>/FH;I h

JBEUcbJOU>I|}?Q@N~M¢BEU:>\_§uT<d?Q@N?Q<d?Q>sJ?QB@BM4>@gb;I*BE@BE<d?QIWM¢z@I*JO?QBE@u<?A@?Q<d?Q>J?ABE@

BMq;@N;UO~b¾POzNRReAbÆz@Z;*UJ;*I9@?QI>ePHR,;*I?LTI>JO?QBE@NPu;YJIª·E ® m8:9N;UO;YM¢BEUO;unBE@;I>@

IBE@NPO?QZN;UjJ9;qM¢BEeQeABoq?Q@~C~E;*@;UO>eTJ>PH|BMV<d?Q@N?Q<d?Q?A@~u/z@ZN;UPHBE<d;WI*BE@PcJU>?Q@gJP*u}JO9;

IBEPcJqM¢z@I*JO?QBE@ÄÃ>eQPOB@><;*ZR7;UcM¢BEUO<>@I*;C?Q@ZN;YXÅY¹

Y S

}

jÄ

Å ýf

W Ä

#0?

ÄaGÅ

#U ÄbGÅ

ÄaC/ÅHÅ[u]

ï

ý^%

n

K`a`b`a n

U,c Ä6¸gÅ

oq9;UH;

?QPrJO9;\>I*JOzT>enZN?QPOI*UO;YJ;J?A<;?Q@ZN;YX,uF?APrJ9N;Z?QPHIUO;YJ;JO?Q<d;p?Q@NZ;YX,uC

U

?AP

J9;:UH;I*;Z?A@~C9BEUH?QB@>@Z

ï

?APJ9N;M¢zNJzNUO;:Z?APOIUH;*JO;yJ?Q<d;joq?Q@ZBo%m

#0?

I*BE@gJ>?A@P

J9;dZ;*POIUH?QRNJO?QBE@BMUO;YM¢;UO;*@I;D,;*9T>KG?QBEU*u

?QPCJ9N;dPHBEz~E9gJPO;*GzN;@I*;wBMJO9;M¢zNJzNUO;

[{§

BMJ9N;fRNUOBGI;PHPWJO9T>Jq?AP:Iet>POPO?AI>eAeAbdJz@N;Z>P:M¢BEeQeAB/o%¹

ý ª

`b`a`F ÄbGÅ

`b`a`

®s

u]

ï

g

ý^% )`b`a`b

np2

c

ÄÃ¯EÅ

oq9;UH; .?APyJ9;%I*BE@gJUOBe19BEUO?ABE@{>@NZ{oq9;*UO;¹

ÄbGÅ

ý Ä

np2¥/Å[u]

ï

ý¡^%

np

)`b`a`a

nT

U

¥

c

Ä6«gÅ

8:9?QPpBERNJ?A<?A>JO?QBE@RUHBEDeA;< 9T>P>eAPOB^JOB>I*IBEz@gJM¢BUZ?QPHIUH;*J;J?Q<d;\KE;UHPO?ABE@PBM

J9;%I*BE@gJ?Q@}zBzP:J?Q<d;KE;*UOPH?QBE@{IBE@NPHJUO>?Q@gJOPpÄ

¡

Åy>@ZÄ

µ

ÅY¹

(10)

D ñòòòòòò

óòòòòòòô

FECGIHKJ(

ÄbGÅ

J(FE dML

u

ï

g

ý¡^%

)`a`b`a

nT

U

¥

c

o

FECGIHKJ¢

ÄbGÅ

Äb)¥/Å

J o FE

dML

u]

ï

g

Ä6´gÅ

DTS

~E;*@;UO>e1BEzNJORzNJWIB@PHJOU>?A@}JOP:M¢BEUyJ9;_§p¹

£ Ä

#%?M

ÄbGÅ

#VU ÄaÅ

Äb)¥/ÅOÅ

J Ë u]

ï

ZY[1\

O

ÄcËgÅ

£@pJ9N;R7;UHM¢BUO<>@I;=?Q@NZ;YXf~E?LKE;*@?Q@wÄÃ¸gÅS>@Z?Q@JO9;BzNJRzJI*BE@PHJOU>?A@gJP4M¢BUO<zeQ>J;*Z

?Q@ ÄËgÅYu=BE@;@N;;ZNPuq>JwJO9;IzNUOUO;*@gJZ?QPHIUO;YJ;JO?Q<d;

u=J9;K>eAz;BM%J9N;^M¢zNJzNUO;

<;>POzNUO;<d;@gJOP

#U

BK;U\J9;RUH;Z?AI*J?ABE@Á9BEUH?Q*BE@p

U

mn8:9?AP\?Q<dR,BEPHPO?AD?QeA?AJbI>@D7;

9T>@ZNeQ;ZzNPO?Q@N~JO9;?Q@gJO;UO@>e<dBZN;eI*BE@gJUHBEeqÄ6£c[^_:ÅrPHJUHzI*JOzUO;ª

¡

ËNu

¡ ´ ®

oq?AJO9Æ[]_

>PfZ;R?AI*JO;Z¾É4?Q~mlEm1£@`J9?AP%PHJUHzI*JOzUO;uJO9;[§Ê?AP>RReQ?A;ZJB{D,BJ9J9;dRUOBGI;*POP

>@ZJ9;%<dBZN;e¦m

£@{JO9?QP:I*BE@gJUHBEe1PHJOUOzIYJzUH;I*BE<D?A@;Z?Q@JO9;[^]=_ÂPHJOUOzIYJzUH;uTJ9;%;*UOUOBU¤?QP*¹

¤}ÄbGÅ

ý

#U ÄbGÅR

#%$

ÄaÅ Äc/Å

£@BEzUr>RRUHBg>I9Vu7J9;ZN?A,;UO;*@I;r¤\D7;*Jo;;*@RNUOBGI;PHPC>@Z<dBGZ;e_§Í?QPWM¢;ZDT>I|

?Q@gJBaJ9;:I*BE@gJUOBeQeQ;*UusDzNJj>eQPOBr?QPJO9;y<dBZ;*eT_§pm8yoB%M¢;*;ZD>I|eQBGBERP>UO;J9;*UO;*M¢BUO;

zPO;*Z¥?Q@J9?AP£c[_=h[^]=_ØPcJUHzI*JOzUO;^JOBÁ>ZsFHzNPHJwRNUOBGI;PHPwR7;UHM¢BUO<>@I;*P¹=@BJBE@eAb

zPO?A@~JO9;I*et>PHPO?QI>e:M¢;;*ZDT>I|;UHUOBEUDzNJ>eQPOB`oq?AJO9J9N;IBEUHUO;*I*J?ABE@BMC<BGZ;*eQ?Q@N~

;UHUOBEUHPW?A@gJUOBGZzI*;Z{?Q@J9N;f<dBGZ;ehDT>PH;ZBE@GheQ?A@;BERJ?Q<d?Q*;U*m

35464

2Ù87S+/56.7)p¥¡¦ Þ¨§%©6Üuª«1¬rçëOáGå ; âáê>7àQëç6èvêë

©pç ; ëëYí íãsí

¤}ÄaÅ

kYëYç®ëëYæ³ç ; ë

>7íãåëââãséGç¯>7éGçáæ7ìç

;

ëêãìGëYàCãséçA>7éGçdíëYêdáèvæNâ^ç

;

ëâáêëã0BëYí^ç

;

ë>7íëOìè¦åYç6è¦ãsæ

; ãsí èa°sãsæ U Ý 9<; ëëYí íãsí)Bsáà·éëCèQâfé±>NìgáçëOìwáçWëOáGå ; çÃèvêë

Ý

8:9?QP>POPHz<RJ?QB@>@ZklmWÄcE/Åf>eQeABoÍJB?Q@gJOUOBGZzI;J9;<dBZN;erÄ¢îï4ðÅp>@Z¾JO9;

(11)

ñòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò

óòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòô Y S

}

jÄ

Å ý ³

w´VµC¶

· W Ä

#0?

ÄbGÅ

#0$

ÄbGÅ

Äa.¥/Å

¤}Ä

ÅOÅ

ý ª

`a`b`F ÄbGÅ

`a`b`

®s

u

ïF

g

ÄaGÅ

ý Ä

nT./Å u]

ï

ECGIHlJ(

ÄaGÅ

J(E dML

u]

ï

g

o

FECGIHKJ(

ÄaÅ2

ÄaÅ

J o FE

dML

u

ï

g

£ Ä

#%

ÄaÅ

#%$

ÄaÅ

Äb)¥/Å

¤}Ä

ÅHÅ

J Ë u

ïu

ZY[]\

O

>@ZPOzD}FH;I*JWJB\J9N;fUH;PHBEeQzNJO?QBE@BM4JO9;%<BGZ;elÄ¢îï4ðÅYm

Äc ¡ Å

¸1¹ ÙÆÛ-±ºÑ<»Ã'

#0$

ÄbGÅ èQâç; ëâáê>7àQëOì+Bsáà·éëã,kçáèvæëOìfä íãsê ç ; ë\íëâãsà·éGçÃè¦ãsæãäç; ë

åãsæTçÃèvæTéTãségâfêãìGëYà Ä¢îïðÅ Ý

ÜGÝ½¼ ¾À¿jà·èvæëáæ7ìãsæFjà·èvæëÁÂ¾ßÃjMrßâYç6í éåYç6éíëâ

x@heA?Q@;WIBE<dRzNJ>J?ABE@T>eTJO?Q<d;r?QPZ;>eQ?Q@N~poq?AJO9J9;CUH;PHBEeQzNJO?QBE@BMSJ9;rBERNJ?A<?A>JO?QBE@

RUOBDeQ;*<²JO9T>J:?A@IeAzZ;PyJO9;C<dBZ;*e,UH;PHBEeQzNJO?QBE@mi?QPHIUH;*J?A>JO?QBE@BMSJ9;%]jiCk<BGZ;*e

I>@eQ;>ZÁJB`>et>UH~E;><dBEz@gJ\BMr>eA~E;DUO>?QIZ?A,;UH;@gJ?Q>e;*Gz>J?ABE@PÄÃiq±k=ÏÅpJ9>J

?Q@I*UO;>PO;*PyJ9;I*BE<dRzNJ>sJ?QB@T>eDzUHZ;@VuN;POR7;I*?t>eAeAbd?Q@J9;@NBE@eQ?A@;>UI>PO;m£@BEUOZ;*U

JB%UO;*ZzI*;WJO9;aB@heA?Q@;IBE<dRzNJ>J?ABE@T>eGJ?Q<d;uJ9;q£c[_=h[^]=_PHJOUOzIYJzUH;a?AP=zNPO;ZBh

eQ?A@;M¢BEUnJO9;:PHbGPcJ;< Ävîï4ðNÅYmE±aPlRUO;YKG?QBEzPHeAbpZ;PHIUO?AD,;*ZVuE~E?LKE;*@dPH<>eQeN?A@RzNJK>UO?t>sJ?QB@

o

ugPH<>eQePcJ>JO;qK>UH?t>JO?QBE@NPÄor >@ZdPO<>eQeNBEzNJRNzNJjK>UO?t>sJ?QB@{o

#%$

>D7BEzNJaÄÅ

g

ÅI>@

D,;`UO;*RUO;*PO;*@}JO;ZÈJO9UOBEzN~E9ÂJO9;`JO?Q<d;Yh¦K>UHbG?Q@~ÁeA?Q@;>UO?A;*Z³<dBGZ;edÄvî<stðNÅYmqÉ?A@T>eQeLbEu

(12)

g

eQ?A@;>UH?Q*;Z<dBZN;eSÄÅstTðÅ4UO;*Ret>I*;yJ9;q?A@?AJO?t>e}@BE@NeQ?Q@N;>Un<dBGZ;eVÄ¢îï4ðÅ4?Q@JO9;:£c[_=h

[^]=_ÂPHJOUOzIYJzUH;p>P:Z;R?AI*JO;ZÉ4?Q~m

¡ m

8:9;IBE@gJOUOBEeBDGFH;IYJ?AK;?QP@Bo JBÁT@Z¥J9N;K>UH?t>JO?QBE@o

BM%J9N;`<>@?ARzeQ>J;*Z

K>UO?Q>DeQ;

>D,BEzJ>WI9BEPH;@pJOU>/FH;*I*JBUHb

g

eA;>Z?A@~qJBa>aD7;*JOJO;UBE@heQ?Q@N;lBERNJ?A<?A>JO?QBE@

UO;*POzeLJml±rI*IBEUHZ?Q@N~`JOB`JO9;J?Q<d;Yh¦K>UHbG?Q@N~eQ?Q@N;>UH?Q;*ZÁ£c[_ PcJUOzNI*JzNUO;ujJ9N;{I*BE@gJUHBEe

RUOBDeQ;*<²?AP@Bo³;}z?LK>eQ;*@}JJBpJO9;aM¢BEeAeQBoq?Q@N~I*BE@PHJOU>?A@;ZBRNJ?A<?A>JO?QBE@\RUHBEDeQ;*<¹

ñòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò

óòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòô Y S

}

jÄ

Å ý ³

w´Vµ ¶

· W Ä

#0?

ÄbGÅ

o

#0$

ÄaGÅ

o

Äb./Å

¤}Ä

ÅHÅ

o

ý ª

`b`a`

o ÄbGÅ

`b`a`

®s

u]

ï

g

o ÄaÅ

ý o Ä

nT2¥/Å u]

ï

ECGIH

g ÄbGÅ

J o

ÄbGÅ

J(E dML

g

ÄaÅ u]

ï

g

o

FÆ

ECGIH

J o

ÄbGÅRÇo

Äb.¥/Å

J o FÆ

E

dML

u]

ïÈ

g

o

FÆ

ECGIH ý o

ECGIH

³Ä

g ÄbGÅR

g

Äa¥/ÅHÅ u]

ï

g

o ÆE

dML ý o

FE dML

¤Ä

g ÄbGÅR

g

Äb./ÅOÅ u

ïu

g

£ Ä

#%

ÄaÅ

o

#%$

ÄbGÅ

o

Äa.¥Å

¤}Ä

ÅOÅ

J Ë u]

ï

ZYÉ]\

O

>@ZPOzD}FH;I*JWJB\J9N;fUH;PHBEeQzNJO?QBE@BM4JO9;%<BGZ;elÄ¢î<sut7ðNÅYm

Äc µ Å

8:9;q@;YXGJ=PHJO;Rd@BoZN;*KE;*eQBER7;Zd?QPlI*BE@I*;UO@N;Z\oq?AJ9\<d;*JO9BZNPnJB%9T>@ZNeQ;yI*BE@PHJOU>?A@gJP

ZzUH?Q@~J9N;fB@heA?Q@;BRNJ?A<?A>JO?QBE@RUOBEDNeQ;< UO;*POBEeAzNJ?ABE@Vm

(13)

8yoB{Z?L;*UO;@gJ%|}?Q@NZ`BMI*BE@PHJOU>?A@gJPf>UO;JOBD,;\>I*IBEzN@}JO;ZM¢BEU¹IBE@PcJUO>?Q@gJPf>IYJ?A@~

BE@eLbwBE@^[{§ >@ZIB@PHJOU>?A@}JOPW>I*JO?Q@~\BE@_§ ÄÃ>@Z;YKE;@gJOzT>eQeLbBE@^[{§ >eQPHB}ÅYm

ÜGÝmÊ7ÝvÞ ÁYæ,>7éGç:åãsæNâYçÃíHáèvæTçvâ ; áæ7ìNà·èvæih

84UO>@PcM¢BEUO<>J?ABE@Æ<d;*JO9BGZÆM¢BEUK>UH?t>DNeQ;Pp>eQeABoqPfJOBJU>@POeQ>J;;YXReQ?AI?LJpI*BE@PHJOU>?A@gJP

BE@\J9;qBERNJO?Q<d?Q>J?ABE@>UH~Ez<d;@gJ

ÄÃ>@ZB@eAbJO9;qBERNJO?Q<d?Q>sJ?QB@>UO~z<;*@gJ Ån>P=@;*o

;}zT>JO?QBE@NP=M¢BEUj@;Yo¤z@I*BE@PHJOU>?A@;Z>UO~z<;*@gJËª µs® m*-W;UO;uGo;rRNUOBER7BEPO;qJBf;@Net>UH~E;

J9?AP%<;YJ9BGZ`JOBI*BKE;U<>~E@?AJOzZ;\IB@PHJOU>?A@}JOPp>@Z`K;eABI*?AJbIB@PHJOU>?A@}JOPp>P%o;eAe

ÄÃ>I*I;*eQ;UO>J?ABE@%U>JO;lIBE@NPHJUO>?Q@gJOP<>b%>eAPOB:D7;>IIBz@gJ;ZfM¢BEUÅ m£@BUOZ;*UVJBWD,;jzPH;Zf?Q@

J9;qBERJ?Q<d?Q>J?ABE@>eQ~EBEUH?AJO9<usPOzNI9w>JUO>@PHM¢BUO<>J?ABE@<zPcJ=9T>KE;a>CUOPHJ=Z;*UO?LK>sJ?AK;

Z?A,;UH;@gJwM¢UHBE< *;UHB>@Z<zNPHJD7;?Q@gK;UHJO?QDeA;m=8:9?QPeQ;>ZPJB¾>ÆJU>@PHM¢BEUH<>sJ?QB@

;}zT>JO?QBE@Ä6É?Q~m

µ

ÅyeQ?A|;J9N;%JOU>@NPHM¢BEUH<>JO?QBE@zPO;*Z^?Q@`ª

¡ ¶ ® ¹

oq9;UH;¹

ñòòòòòò

óòòòòòòô ÄaGÅ

ý'Ì ÄAËÄbGÅOÅ

ý'Ì

ECÍÎ n Ì d

ECÏ J>@9Ð

U ÷ ü

ÑÓÒbÔ

MÕÖÑÓ× Ø

u]

ï

g

ËÄbGÅ"/ u]

ï

g

Äc Ð Å

oq?AJO9JO9;CJ?A<; hK>UHbG?A@~IBG;*ÇdI*?Q;@gJOP

Ì

ECÍÎ

>@Z

Ì d

ECÏ

zR7ZT>J;*Z^>sJq;>I9{J?Q<d;

¹

(14)

òòòòòòòòòòòòòòòòòò

óòòòòòòòòòòòòòòòòòòô Ì ECÍÎ

ý

MÑÓÕ½ÙÚF

ÑÓÛÜ

Ý

Ì d

ECÏ ý ÑÓÕ½Ù

ÑÓÛÜ

Ý

Ì ECGIH ý

<>sXCÄ

FECGIH0

Äb)¥/ÅCnTo

FECGIH

Å u

ïF

g

Ì E dML ý

<?A@fÄ

FE dML

Äa/ÅCnpo

E dML

Å u]

ï

g

Äc¶EÅ

[BEUH;BKE;*UurPHzI9¿JO?Q<d;YhK>UcbG?Q@~IBG;*ÇdI*?Q;@gJOP

Ì E dML

;YJ

Ì ECGIH

;@PHzUO;ÆJO9T>J{J9;TUHPHJ

Z;UH?AK>JO?AKE;\?APf;*}zT>ejJB{BE@;d?QPCJ9;d<d?QZZeA;BMJO9;dIBE@PcJUO>?Q@;*ZÆUO>@~E;m18:9;UH;*M¢BEUH;u

?Q@wJO9?QPy*BE@;uJ9;CBERJ?Q<d?Q>J?ABE@dRUOBGI;*ZzUO;%?APy@BJqZ?APHJOzUOD7;ZDgbJO9;%PO;@NPO?AJO?AKG?AJbBM

J9;CJOU>@PcM¢BEUO<>JO?QBE@VuGoq9?QI9{?QP:@NBJ:J9;%I>PO;f@;>UyJ9;%IB@PHJOU>?A@}JOPqD,BEzN@ZVm

ÜGÝmÊ7ÝQÜ ¾yéGç¯>7éGçWåãsæNâYç6íHáèvæTç¢â ; áæ7ìNà·èvæih

£@^BEUHZ;UqJBdJ>|;>I*IBEzN@}JaM¢BEUqBEzNJORzNJaIBE@PcJUO>?Q@gJPa>PaPOBMvJWIB@PHJOU>?A@}JOPÄvM¢BEU:oq9?QI9

KG?QBEeQ>J?ABE@<>bfD,;:>eQeQBo;Zª

¡ ¸ ®

ÅYu/o;q>ZBERNJ4J9;;YXGJ;*UO?QBUnR,;*@T>eLJb<d;*JO9BGZª

µ®

zNPO;Z

?Q@@NBE@eQ?A@;>UaRUHBE~EUO><<d?Q@N~\oq9N;UO;\>R,BEPH?AJO?AKE;Z;*@;Zo;?Q~9}JO;ZR7;@T>eLJbJ;UH< ?AP

>ZZ;*Z{JOBdJO9;%?Q@?LJ?Q>eIBEPcJWM¢zN@I*JO?QBE@n¹

ñòòòòòòò

óòòòòòòòô ûq û ý

n¢

öû

ý ³

Â´6µ ¶

· Þ ³

´ß,à

·Vá

+â

Ý

Ä6Ë

£ Ä

#%?M

ÄbGÅ

o

#0$

ÄbGÅ

o

Äb)¥/Å

¤}Ä

ÅHÅOÅ?ã Äc¸gÅ

oq9;UH;

á

?QPq>@>Z>RNJ?LKE;CR7BEPO?LJ?LKE;CZ;YT@;Zo;?Q~9}J¹T?AJ:?A@IUH;>PH;P:oq9;*@{JO9;CUO;*et>JO;Z

IBE@NPHJUO>?Q@gJWJ;*@ZPaJOBD7;I9N;I|;*ZVu1BJO9;Ucoq?QPO;f?AJWZ;*IUH;>PH;PmV¨WBEzN~E9eAbwPOR7;>|}?Q@N~uTM¢BEU

>@gbIBE@NPHJUO>?Q@gJ

£

@NBJWI9;I|;ZÄ6?Ãm;oq9N;@

£ Ä

#%?M

ÄbGÅ

o

#0$

ÄbGÅ

o

Äb.¥/Å

¤}Ä

ÅHÅ

ËgÅYu>R,BPO?AJO?AK;J;*UO< R,;*@T>eQ?A;JO9;:<d?Q@?A<?A>JO?QBE@J>PO|mE8:9?APn;@M¢BEUOI*;PlJ9;:BRNJ?A<?A;U

JB<d?Q@?A<?A;{

öû

>@Z9;@I*;JB;@M¢BEUOI*;J9;KG?QBet>JO;ZI*BE@PHJOU>?A@gJCJBD7;I9;I|;ZVm

(15)

POzDNPHJ?LJzNJO?Q@~>R,;*@T>eLJbwM¢z@IYJ?QB@{M¢BEUyJO9;fIBE@PcJUO>?Q@gJmT8:9N;UO;YM¢BEUO;uTJ9;%IB@PHJOU>?A@;Z

POBEeAzNJ?ABE@<d?Q~9}JD,;>RRUHBg>I9;*ZM¢UHBE<ÍJ9;CzN@NM¢;>PH?QDeA;rPH?QZ;BM1J9;CI*BE@PHJOU>?A@gJP¹GJ9?AP

UO;*et>JO?AKE;pZU>oqDT>I|^I>@D7;\>@>ZNK>@gJ>~E;?A@J9;I>PO;oq9;*UO;uVPOBE<d;*JO?Q<d;P*u@BPHBh

eQzNJO?QBE@M¢BEUJ9N;IBE@PcJUO>?Q@;*Z¤RUOBEDNeQ;< ;YX?QPcJP`ª·Ë ® >@Z¤IBE@PcJUO>?Q@gJwKG?QBet>JO?QBE@9T>P

J9;*UO;YM¢BEUO;CJB\D7;f>eQeAB/o;Zm

ÜGÝÖä åjèvæ7áà>TëYæ7áà·èa°sëOìãÂ>7çÃèvêèa°áç6è¦ãsæ>7íã,kàQëYê

É?Q@>eQeLbEuGIBE<DN?Q@?A@~J9;CJOU>@PcM¢BEUO<>JO?QBE@w<d;*JO9BGZM¢BUqJO9;%IBE@NPHJUO>?Q@gJOPWB@JO9;[{§

>@Z³J9;`;YXGJ;*UO?ABEUR,;*@T>eAJb¤<d;*JO9BGZ³M¢BEUJO9;I*BE@PcJU>?Q@gJP{BE@¤J9;Æ_§u:J9N;`T@>e

R,;*@T>eA?Q;*ZBERNJ?A<?A>JO?QBE@RUOBDeQ;*< JBdD7;CPOBEeLKE;Z{BE@heQ?A@;?QPyJO9;CM¢BEeQeABoq?Q@~B@;¹

ñòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò

óòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòô Y S v

U ûq û Äo8ËÅ

ý ³

w´Vµ ¶

· W Ä

#0?

ÄbGÅ

o

#0$

ÄaGÅ

olËÄa¥/Å

¤}Ä

ÅHÅn

³

Â´6µ ¶

·

Þ!æ

´ß,à

· á

+â

Ý

Ä6Ë

£ Ä

#%?M

ÄbGÅ

o

#0$

ÄaGÅ

olËÄa.¥/Å

¤}Ä

ÅOÅã

o8Ë ý ª

`a`b`

Ì Äo

ÄbGÅOÅ

`a`b`

®s

u] ïz

g

oKËSÄbGÅ

ý

olËÄ

np2¥/Å[u]

ïÈ

ï

o ÄaÅ

ý

ÄbGÅR

g ÄbGÅ

ýÌ ÄAË

g

ÄaÅCnpolËÄbGÅOÅR

Ì

Ä¯Ë

g

ÄbGÅOÅçu]

ï

g

Ë g ÄbGÅ

ýÌ

Ä

g

ÄaÅHÅ[u]

ïz

g

>@ZPOzD}FH;I*JWJB\J9N;fUH;PHBEeQzNJO?QBE@BM4JO9;%<BGZ;elÄ¢î<sut7ðNÅYm

Äc¯EÅ

8:9?QP=R7;@T>eA?Q*;ZdRUOBEDNeQ;<ÀI>@@Bo¤D,;WPOBEeLKE;*ZDgbd>@gbdz@IB@PHJOU>?A@;ZBERNJ?A<?A>JO?QBE@

>eQ~BEUO?LJ9<{m

(16)

ê¤?QZ;*eAbÆ|G@NB/oq@M¢BEU?LJPUOBDzPHJO@;PHP>@ZIBE@gKE;*UO~E;*@I;RUOBR,;*UHJ?A;P*uo;zPH;BMaJO9;

o;*eQeh|}@Boq@»1;*K;@}D,;*UO~h[^>UHGz>UOZNJVëPq>eQ~EBEUH?AJO9< ugoq9;UH;rJ9N;>UH~Ez<d;@gJXo8Ëw?APZ; h

J;*UO<d?Q@;*Z>sJq;>I9P><dReQ;r?Q@PcJ>@gJ

D}bJO9;%?AJO;U>sJ?QB@wRUOBGI;*ZzUH;¹

o8Ë O Ú ý o8Ë O

³Äì Ý O

ûq û níFîÅ

ì

O

ûq û

Äc«gÅ

oq9;UH; ì

O

ûq û

>@NZ"ì Ý O

ûq û

>UO;rJO9;CIUH?AJ;*UO?Q>~EUO>Z?Q;*@gJ:>@ZwJO9;I*UO?AJO;UH?t>p9;*POPH?t>@woq?LJ9

UO;*POR7;I*J:JOBo8Ë O

>JJ9;r?AJ;*U>JO?QBE@

S

mì

O

ûq û

?QP;YXReA?QI?LJeLb\RUOBKG?QZ;*Z?Q@gJBJ9;I*BE@gJUHBEe

>eQ~BEUO?LJ9<²>@ZJ9N;fI*et>PHPO?AI>e|ï%>zPHPVë°Pr>RRUOBX?Q<>JO?QBE@M¢BUì Ý O

ûq û

>Pyo;eQeÃm

8:9?QPp£c[_=hc[^]=_ÍUO;*POBEeAzNJ?ABE@Á>eA~EBEUO?LJ9< ?APp@Bo²?Q<dReA;<d;@gJ;*ZÆM¢BEUpI*BE@gJUHBEeBM:JO9;

ZUHbG?A@~\RUOBGI;*POPa>@Z{;YXR,;*UO?A<;*@}J>eVUH;POzNeAJPW>UH;%~E?AK;@{?Q@@; XJaPO;*I*JO?QBE@Vm

ðñ<7 ¹ -s56Ù ¹ ),+ÛTÚ3E.7),+-/.7Ú=.×WÛÆ0S-óòS5Ã)|ô87-/.13 ¹ 464

8:9;\>?A< BMjJO9?QPPH;IYJ?QB@`?APrJB;YK>eQzT>sJ;pJO9;£c[_=hc[]_ÖM¢BEUO<pzet>JO?QBE@M¢BEUI*BE@gJUHBEe

BMq>{ZUHbG?Q@N~RUHBI*;PHPm8:9N;ZUcb?A@~^RNUOBGI;ZNzUO;?QP%TUOPcJpZ;*POI*UO?QD7;Z¾>@ZÆJO9;I*BE@gJUHBEe

RUOBDeQ;*< ?QPr?Q@gJUHBZzNI;ZmV8:9;@u1;YXR,;*UO?A<;*@}J>enUH;POzNeAJPCJOB?QeQeAzPHJOU>JO;JO9;RUOBR,BEPH;Z

£c[_=hc[]_³PHJUHzI*JOzUO;>UH;fPH9Boq@>@NZ{ZN?QPOI*zPOPH;ZVm

¼}ÝvÞ ÁYæTç6íãìéåYç6è¦ãsæ

¨W;>I*JO?AK;RT>?Q@gJO?Q@~ZUcbG?Q@~?AP%>@?Q<dR,BEUcJ>@gJr?Q@ZzNPHJUH?t>e4RUOBDeQ;*< JO9UOBEzN~E9?AJPC?A<\h

RT>IYJCM¢BEUrJ9N;d}zT>eQ?AJbBMjJ9N;T@T>el>POR7;I*JfBM=RUHBZNzI*JOPf?A@<>@}b?Q@NZzPHJOUO?A;PdÄ6I>UOP*u

RUO;*~Eet>POP=Ret>?A@gJPH9;;YJP*uNI>@Pu;*JImÅ m8:9N;r<>?Q@dZ?AÇdI*zeAJb\;*@IBEzN@}JO;UH;ZZzUH?Q@~fJ9?AP

BER7;U>sJ?QB@Á?QPpJO9;;*K>I*zT>J?ABE@BMqJ9;PHBEeAK;@gJ\D,;YM¢BEUO;wJO9;;@ZBMaR7BEeAbG<d;UO?A>JO?QBE@

(17)

JBd;@PHzUO;J9;%TeQ<ÊR,BEeLbG<;*UO?Q>J?ABE@DzNJaBE@;fPO9NBEzeQZ>KEBE?AZJOBdJOU>R?AJq?Q@J9N;fT@>e

ZUO?A;ZRUHBZzNI*Jm<õa@gJ?Aen@Bo%uVJ9;\zPH;\BMKBEet>sJ?QeA;pBEUH~g>@?AIIB<R7BEz@ZNPdÄ¢§ax%_PÅC>eh

eQBo;ZJ9;CI*BE@gJUHBEeVBMSJ9N?QPy;YK>IzT>JO?QBE@ZNzUO?A@~J9;CR7BEeLb<d;UH?Q>J?ABE@UH;>IYJ?QB@PmFözNJ

J9;;@NM¢BUOI;*ZUO;*~Ezet>sJ?QB@PqIBE@I*;UH@?Q@~;@gKG?QUOB@<;*@gJeQ;>Z^@NB/oÖJOBwUO;*Ret>I;JO9;pzNPO;

BMj§ax%_PCD}bJ9;pzPO;BMjo>J;*UCDT>PH;ZPOBeAKE;*@gJmC-WB/o;*K;U*uI*BE<dRT>UO;*Zoq?AJO9^§ax%_Pu

J9;Yb;*K>I*zT>JO;WeA;PHP=UO>R?AZeAbp>@Zd>Jj9?A~E9;*UnJ;<dR7;U>sJzUH;Pmg8B%BKE;UHIBE<d;:J9?APlRUOBDh

eQ;*<uT?A@NM¢U>UH;Z{ZUHbG?A@~9>PaD7;;*@^oq?QZN;eAbwZ;*K;eQBR,;*Z?Q@{?Q@ZNzPHJOUO?t>eVRUOBGI;*POPH;PmVÏBE<d;

PHJOzZ?Q;*Pª

¡E¡

u¡

«Nu

µ Ë ®

Z;>e1oq?LJ9{Z?A,zPO?ABE@RUOBDeQ;*<Pyoq?LJ9{D,BJO9?A@NM¢U>UO;Z{ZUcb?A@~>@Z

oy>sJ;UqzPH;Z^>PqPOBEeLKE;@gJm

ê¤?AJO9?Q@\J9;WM¢U><d;*oBEUH|BMS>RNUO;*KG?ABEzP=PHJzNZNbª¬¸

®

uG>@; XNR7;UH?Q<d;@gJ>e,ZUcbG?Q@~fRUOBGI;*POP

9T>PfD,;*;@¾DNz?QeLJmV£J>eAeQBoqPCJB{ZUHb>RT>?Q@gJO?Q@~TeA< P><dReA;dI*Bg>JO;ZÆB@¾>I>Uf?QUHBE@

POzRNR,BEUcJDgb{POzRNReAbBMl>@^?A@NM¢U>UH;Z{ÌTBo%m,8:9;;YXR7;UO?A<;*@gJ>eSReQ>@gJa?APaUH;RUH;PH;@gJ;*Z

É?Q~Nm Ð oq?LJ9J9;%?A@NM¢U>UH;Z{RT>UcJr>@Z{oq?LJ9J9;f?Q@NPHJUHz<d;@gJ>JO?QBE@RT>UHJmT8:9N;PH;@PHBEUOP

>UO;¹E>CRgbGUOBE<d;*JO;UJO9T>J=>eAeQBoqP4JO9;:BE@heQ?Q@N;=JO;<dR,;*U>JOzUO;y<d;>POzUH;<d;@gJjBMJ9;:PO><h

ReQ;p>JrJO9;pzNRR,;*UPOzNUHM6>I*;>@Z>dRUO;*I?QPH?QBE@^DT>et>@I;fJ9T>J>eQeABoqPWJO9;pM¢BEeAeQBoyhzR{BM

J9;qPO><RNeQ;q>@ZdPOzNRR,BUHJjPO;YJ<>PHPmE8:9;WRT>?A@gJ?Q@N~TeQ< P><dReQ;:<>PHPl?QPlJ9;qPHz< BM

J9;CI*BE@PcJ>@gJ:T@T>eZUH?Q;Z<>PHPyBMSJ9;rP><dReQ;Woq?AJO9wJ9;JO?Q<d;WK>Ucb?A@~o>J;*U:<>PHP

?Q@wJO9;CP><dReA;mN£@NZ;;*ZVuTZzUH?Q@~JO9;CZUHbG?A@~z@Z;*U:?Q@NM¢UO>UO;*ZwÌTBo%uNJ9N?QPo>J;*Uq<>PHP

Z;I*UO;>PO;*P:PO?Q@NI;aJO9;ao>JO;UyI*BE@gJ>?A@;Z?Q@JO9;rR>?Q@gJ?A@~eQ<ÍP><ReA;a<d?Q~U>JO;PlM¢UOBE<

?Q@PH?QZ;JOBJ9;%zRR7;UqPHzUHM6>I*;p>@ZK>R,BEUH?Q*;PW>J:J9N?QP:POzNUHM6>I*;m

¼}ÝQÜ ßãsæTç6íãsàã,k÷ëåYç6èÖBë

£@J;*UO< BMCT@T>ea}zT>eQ?LJbBM%J9;^eQ<{u=R>?Q@gJ?A@~M¢BUO<zeQ>J?ABE@¿ÄÃ>@Z¥R>UHJO?QIzNet>UHeAb

J9;PHBEeAK;@gJ ÅpZNB;*P@BJd>eABE@;weA;>Z¾JOBIBER7;woq?AJO9¾J9;Z;*eQ?AI>JO;wDT>eQ>@I;RUOBEDNeQ;<