Statistical model-based damage detection and localization: subspace-based residuals and damage-to-noise sensitivity ratios

HAL Id: inria-00071940

https://hal.inria.fr/inria-00071940

Submitted on 23 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents

Statistical model-based damage detection and localization: subspace-based residuals and

damage-to-noise sensitivity ratios

Michèle Basseville, Laurent Mevel, Maurice Goursat

To cite this version:

Michèle Basseville, Laurent Mevel, Maurice Goursat. Statistical model-based damage detection and localization: subspace-based residuals and damage-to-noise sensitivity ratios. [Research Report] RR- 4645, INRIA. 2002. �inria-00071940�

ISRN INRIA/RR--4645--FR+ENG

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Statistical model-based damage detection and localization: subspace-based residuals and

damage-to-noise sensitivity ratios

Michèle Basseville, Laurent Mevel, Maurice Goursat

N˚4645

Novembre 2002

THÈME 4

' (%*)+,-/.'01, 2%

!'345%"%6678:901

;=<?>A@$BDC?EGFHJIKILENM<?COC?EQPNRTSUHJV1WKENX Y;ZENM[ENC]\^R#;_HJV$WK<?>NEa`Gb[V$WKIcH5YAd

ef/gchGikjl m:noh-p qsrDt6nvuQwxictyuQz t6noh{nv|rDt6nvuQw

} i-|6~J|tgchGiA|AuQh{z qviK€[iA|

U‚uDƒ8ictm:no„3h…r3†

‡yrDz z1uQ‚6t } iˆ‚iAf/ic‚f/i‰wŠ3j5‹Dj5ŒlŽu^ich‘ ‚i†3’3’3†l“j5†zrD„iA|

”a•–A—^˜N™ š—3› ef/i:no‘ ‚rDt6nvuQw[œ‘rQ|i } |6t6‚6p/ct6p ‚rDq f/i^rDqot6f{hGuQw notuQ‚6now „kz ‚uQ‘ qvichžnv|Ur } } ‚iA||i }

rQ|-t6f/i } uQp ‘ qviGtrQ|Ÿ uD¡ } ictiAct6now „ } rDh…rD„iA|-hGu } icqvi } rQ|frDw „iA|now¢t6f/i…icno„icw/|6t6‚6p/ct6p ‚i

uD¡rqonow/i^rD‚ } ~:wrDh{nv|~J|6tich£ rDw } qvuJ^rDqono¤Anow „Gt6f/i } ictiActi }¥} rDh…rD„iA|¦§not6f nowZ¨©rª¬«U­®uD¡K¯

t6f/iGhGuQw notuQ‚i } |6t6‚6p/ct6p ‚i3°¥ef/i…z ‚uQz$u3|i }¢} rDh…rD„i } ictiAct6nvuQw±rDqo„uQ‚6not6f h²nv|-‘rQ|i } uQw³r

‚iA|n

}

prDqT„icw/ic‚rDti

}

¡?‚uQh´r|6tuJfrQ|t6nv|6p ‘/|6zrQAiKœ‘rQ|i

}

AuµQrD‚6nsrDw/AiKœ

}

‚6noicwxn

}

icw5t6n·¶^rDt6nvuQw

hGict6f/u } rDw } uQwxt6f/i|6trDt6nv|t6nv^rDq'qvuJ^rDq¬rDz z ‚urQf tu…t6f/i } iA|6no„3wxuD¡ } ictiAct6nvuQw rDqo„uQ‚6not6f hG|^°

ef nv|rDqo„uQ‚6not6f hž‘rQ|6nv^rDqoqo~AuQh{z p tiA|Ur„3qvuQ‘rDq[tiA|6t^£Q¦§f nvf{z$ic‚8¡©uQ‚6hG|r |icw/|not6no:not¸~rDwrDqo~J|nv|

uD¡ t6f/i‚iA|n

}

prDqv|#tut6f/i

}

rDh…rD„iA|^£D‚icqsrDt6noiUtu§p w/Aic‚6trDnow:t6nviA|UrDw

}

w/uQnv|iA|^°'¹yuµ¦Zt6f nv|#‚iA|n

}

prDq

‚icqsrDtiA|ktu|uQhGi‚iA|6n} prDqv|k¡]uQ‚ } rDh…rD„i{qvuJ^rDqono¤µrDt6nvuQw_rDw } hGu } icqUp z } rDt6now „nv| } nv|cp/||i } °

ºrDh…rD„i*qvuJ^rDqono¤µrDt6nvuQw+nv|{|6trDti } rQ|Gr } ictiAct6nvuQw+z ‚uQ‘ qvich°³ef nv|{z ‚uQ‘ qvichnv|Gr } } ‚iA||i }

‘:~»z qop „3„3now „¼rD„3„3‚ic„5rDti } |icw/|6not6noJnot6nviA|¥uD¡t6f/i hGu } iA|rDw } hGu } iKœ½|frDz$iA|¥¦k°‚^°t^°¾ª¬«U­

|t6‚6p/ct6p ‚rDqUzrD‚rDhGictic‚|know¿t6f/iGrD‘1u^iG|ict6t6now „/°{ef nv|‚iA|6p qot|now } no‚iAct6nvuQwrDqÀtiA|6t|^£1¦§f nvf

z1ic‚8¡©uQ‚6hÁt6f/i¿|rDhGi¿t½~Jz1i¿uD¡ } rDh…rD„iKœtuDœw/uQnv|i=|icw/|6not6noJnot½~2rDwrDqo~J|nv|¥uD¡t6f/i ‚iA|6n} prDqrQ|

¡©uQ‚

}

rDh…rD„i

}

ictiAct6nvuQw#°=¹u^¦Ât6f/i*|icw/|6not6noJnot½~³rD„3„3‚ic„5rDt6nvuQw+hGiAfrDw nv|h‚icqsrDtiA|{tu |6p ‘[œ

|t6‚6p/ct6p ‚6now „Gnv|uQp t6qonow/i } °ÃŽyp hGic‚6nv^rDq#‚iA|6p qot|yuQ‘ trDnow/i } uQwÄuQw/ikiK€/rDh{z qvi-rD‚iˆ‚icz1uQ‚6ti } °

ōÆÇ1ÈÉÊ

˜N˖3›

ºrDh…rD„i

}

ictiAct6nvuQw#£

}

rDh…rD„i§qvuJ^rDqono¤µrDt6nvuQw#£Jno‘ ‚rDt6nvuQwarDwrDqo~[|6nv|^£|6p ‘/|zrQAi

rDqo„uQ‚6not6f hG|µ£/|6trDt6nv|6t6nv^rDq#qvuJ^rDq'rDz z ‚urQf#£|icw/|6not6noJnot½~°

Ì·ÍÏθНÑ^ÒÎÀÓÏÔoНթÖA×

ØUٝÚ3ÛÝÜ8Þ:ßDàáÚ3ÜÏâãµä^åKåLæKçµèKéKéKæcê^èë^ècåLä ìOíKëDî

ï

ٝÚ3ÛÝÜ8Þ:ßNٝáÚ3Ûðވâ§ñ^äòAëAæó^ô/ìvõ^æKçAæAéLê^èëµècåä ìOícëDî

ö

ٝá5Ú3Û÷Þâõ^äò^ëµèKøLæ ì?ùAú6ò^ëµåLäKôcê^è6ó^ëµèä ìOícëDî

Unité de recherche INRIA Rennes

'$%& ½% !U%y)¿0, J9.

,[5. %68 0167

– › iˆz ‚uQ‘ qvgchGi } iqsr|6p ‚6icnoqoqsrDw/Ai } iqnow:tc„3‚6not } iˆ|6t6‚6p/ct6p ‚iA|icw*:no‘ ‚rDt6nvuQw/|

iA|t } AAuQh{z1u3|*icw } icp[€=tQf/iA| } i } ctiAct6nvuQw+ict } i qvu:^rDqonv|LrDt6nvuQw } icw } uQh{h…rD„ichGicw:t|^°

rÄz ‚ich{nvgc‚i¥iA|tt6‚rDnotAi¥AuQh{hGi*p w³z ‚uQ‘ qvgchGi } i } ctiAct6nvuQw } i*frDw „ichGicw5t| } rDw/|qsr

|t6‚6p/ct6p ‚iz ‚uQz ‚i } p w |6~[|6tgchGi } ~JwrDh{n:p/i3£§ict…qsr } icp[€[nvgchGix‚icz$u3|ix|6p ‚Gqp t6noqonv|rDt6nvuQw

} p wÄhGu } gcqvicqchGicw:t|§¶/w nv|^°

rDqo„uQ‚6not6f hGi } i } ctiAct6nvuQw } icw } uQh{h…rD„ichGicw5t|Gz ‚uQz1u3|aAuQh{z$uQ‚6ti…qvi…^rDqvcp q } p w

‚A|n

} p „cwc‚ ¼zrD‚6t6no‚

}

i_qsr¼h!ct6f/u

} i } n}

icw5t6n·¶^rDt6nvuQw zrD‚ |uQp/|8œ½iA|zrQAi"¼‘rQ|i } i

AuµQrD‚6nsrDw/AiA|µ£ict#c3rDqopxrDp¼hGuµ~icw } iÄqrDz z ‚u:f/ix|trDt6nv|6t6n5p/iÄqvu:^rDqvi } i¥qsr¢AuQw/Aicz t6nvuQw

} rDqo„uQ‚6not6f hGiA| } i } ctiAct6nvuQw#°%$4ict{rDqo„uQ‚6not6f hGiÄ^rDqvcp qvi iA||icw5t6nvicqoqvichGicw:tGp w³tiA|6t„3qvuQ‘rDq£

:p nÀi'&TiAct6p/i p w/i rDwrDqo~[|i

}

iA||icw/|6no‘ noqonotA|

}

p=‚A|n

}

p³rDp[€=icw

}

uQh{h…rD„ichGicw:t|^£U‚icqsrDt6noiKœ

hGicw:tÀrDp[€now/Aic‚6t6not6p } iA|ÃictÃrDp[€‘ ‚6p not|z ‚A|icw5t|Ã|6p ‚qvi§|6~[|6tgchGi3° iqonvicwGicw5t6‚iAi‚A|n} p…ict

} rDp t6‚iA|‚A|6n} p/|now:t6‚u } p not| } rDw/|'qsrqonot6tc‚rDt6p ‚i4z1uQp ‚'qsr qvuJ^rDqonv|rDt6nvuQw } icw } uQh{h…rD„ichGicw5t|

ict§qvik‚iA^rDqsrD„i

}

ihGu

}

gcqviA|iA|6t

}

nv|cp t3°

iz ‚uQ‘ qvgchGi } iˆqsr{qvu:^rDqonv|rDt6nvuQw } icw } uQh{h…rD„ichGicw5t|iA|6t§z1u3|AuQh{hGikp w¥z ‚uQ‘ qvgchGi

} i } ctiAct6nvuQw#£ict)(*+(kAuQh{hGiÀp w{z ‚uQ‘ qvgchGik¨?now:ic‚|iµ¯ } iA|6t6noh…rDt6nvuQw#°-,¸qJiA|trD‘1uQ‚ } .yqrDn} i

}

iA|Ã|icw/|6no‘ noqonotA|

}

iA|UhGu

}

iA|Uict

}

K¡]uQ‚6h!AiA|ÃhGu

}

rDqviA|Jnv|8œ/NœJnv|

}

iA|zrD‚rDhGgct6‚iA|4|6t6‚6p/ct6p ‚rDp[€

} p¿hGu } gcqvi0cqchGicw5t|k¶/w nv|^°rD‚Ai#5p/ituQp/|qviA|icw } uQh{h…rD„ichGicw:t|1cqchGicw5trDno‚iA|-icw::nv|6œ

rD„i^rD‘ qviA|Uw/iz$icp icw:tUzrQ|-2ct6‚i } nv|c‚6noh{nowA|UqvuQ‚| } p w/i |6p ‚6icnoqoqsrDw/Ai rAiAp w{z1ict6notw/uQh-‘ ‚i

} i^rDz ticp ‚|ictp wxz1ict6notˆw/uQh-‘ ‚i } i-hGu } iA|z ‚uQz ‚iA| } i-‚K¡3c‚icw/Ai3£TAiA|ˆ|icw/|6no‘ noqonotA|ˆ|uQw:t

rD„3„3‚c„AiA|)qrDn} i } p w/i h!ct6‚6n:p/i AuQfc‚icw:tirAiAqsrkh!ct6‚6n5p/i } p…tiA|6tÀ„3qvuQ‘rDq° iA|4|icw[œ

|no‘ noqonotA| rDnow/|6n'rD„3„3‚c„AiA|y|uQw5t icw/|p notinowQƒ8iActAiA| } rDw/|qvi¡©uQ‚6h…rDqonv|6hGi } itiA|6t§z ‚A4 } icw:t^°

5 Ê —^– È š76 › º8ctiAct6nvuQw } icw } uQh{h…rD„ichGicw:t|^£#qvuJ^rDqonv|rDt6nvuQw } icw } uQh{h…rD„ichGicw5t|^£rDwrDq·œ

~[|i } iA|ˆ:no‘ ‚rDt6nvuQw/|µ£#rDqo„uQ‚6not6f hGiA| } it½~Jz$i|uQp/|8œ½iA|zrQAi3£ÏrDz z ‚u:f/iGrQ|6~Jh{z tuQt6n5p/iqvuJ^rDqvi3£

|icw/|6no‘ noqonotA|^°

* *+( ( * * ( $

% &

%y01,Ï%

ºˆictiAct6now „arDw } qvuJ^rDqono¤Anow „ } rDh…rD„iA|§¡©uQ‚hGuQw notuQ‚6now „…t6f/iˆnow:tic„3‚6not½~¥uD¡|6t6‚6p/ct6p ‚rDqrDw } hGiKœ

frDw nv^rDqÃ|6~[|6tichG|nv|kratuQz nv{uD¡À„3‚u^¦§now „Änow5tic‚iA|6t^£

}

p/itu t6f/iGrD„3now „uD¡Ãh…rDw:~icw „3now/iAic‚8œ

now „¿AuQw/|6t6‚6p/ct6nvuQw/| rDw } h…rQf now/iA|…rDw } tunow/c‚i^rQ|i } |rN¡]ict¸~Zw/uQ‚6hG|^°(' p tuQh…rDt6nv„3qvuQ‘rDq

Jno‘ ‚rDt6nvuQw[œ‘rQ|i } hGuQw notuQ‚6now „¿tiAf w n5p/iA|t6p ‚6w±uQp ttuđ1iap/|iK¡?p qrDqotic‚6wrDt6noiA|tuJnv|6prDq

now/|z$iAct6nvuQw/|uQ‚-qvuJ^rDqUw/uQw

}

iA|6t6‚6p/ct6noi¨]i3°„/° p qot6‚rQ|uQw nvµ¯ic3rDqoprDt6nvuQw/|-z1ic‚8¡©uQ‚6hGi

}

h…rDw5p[œ

rDqoqo~°

¹yi^rDqot6f¥hGuQw notuQ‚6now „GtiAf w n5p/iA| ‘rQ|i } uQw*z ‚u:AiA||6now „{:no‘ ‚rDt6nvuQw¥hGi^rQ|p ‚ichGicw5t|y‘rQ|6n·œ

^rDqoqo~¥frDw } qvit¸¦Àuat½~Jz$iA|ˆuD¡ÃfrD‚rQctic‚6nv|t6nvA|)§t6f/i *+*,-,.+/-+ +0 ¨?h…rQ||^£|6t6n&$w/iA||^£

1

iK€[no‘ noqonot½~£ } rDh{z now „:¯rDw } t6f/i

*2

3/-+

+

¨?hGu } rDqU¡]‚i45p/icw/cnviA|µ£¬rDw } rQ||uJcnsrDti }

} rDh{z now „¿3rDqop/iA|GrDw } hGu } iKœ½|frDz$iA|L¯*4|iAi65873£†[£9$;: rDw } ‚iK¡]ic‚icw/AiA|t6f/ic‚icnow#°<' Aicw5t6‚rDq

:p/iA|6t6nvuQw*¡©uQ‚§hGuQw notuQ‚6now „…nv|§tu{AuQh{z p ti *=. ( nowÄt6f/u3|ifrD‚rQctic‚6nv|6t6nvA|ˆrDw } tuGrQ||iA||

t6f/icno‚

*>

( ?@

(

c°ª/uQ‚ˆt6f/iBA

+

C

,

'(

£Ïc‚6p/cnsrDqnv||6p/iA|rD‚it6f/icwD)yf/u^¦ tu*AuQh{z p tit6f/i

frDw „iA|^£§tu³rQ||iA||…t6frDtat6f/ixfrDw „iA|rD‚ix|6no„3w n·¶^rDw5t^£ytu¢frDw } qvi * +*+ >* ( rDhGuQw „

now } noJn} prDqÃfrDw „iA|^°'‰‚icqsrDti } nv||6p/inv|f/uµ¦ tu¥AuQh{zrD‚iGt6f/i{frDw „iA|-now¿t6f/i¡]‚i4:p/icw[œ

cnviA|uQ‘ trDnow/i } ¡?‚uQh iK€[z$ic‚6nohGicw:trDq } rDtr ¦§not6f t6f/i{|icw/|6not6noJnot½~xuD¡4hGu } rDqzrD‚rDhGictic‚|-uQ‘[œ

trDnow/i } ¡]‚uQh rDwrDwrDqo~Jt6nv^rDqJhGu } icq°ª p ‚6t6f/ic‚6hGuQ‚i3£3not'frQ|ϑ1iAicw-¦§n} icqo~-rQŸ:w/uµ¦§qvi } „i } t6frDt^£

¦§f/ic‚i^rQ|ˆfrDw „iA|ynowx¡]‚i45p/icw/cnviA|‘1i^rD‚ p/|iK¡]p q'now[¡©uQ‚6h…rDt6nvuQwx¡]uQ‚ } rDh…rD„iEF * (£$now[¡©uQ‚8œ

h…rDt6nvuQw¢uQw¿frDw „iA|now¼¨?t6f/icp ‚6QrDt6p ‚i{uD¡K¯ hGu

}

iKœ½|6frDz$iA|ˆnv|ˆh…rDw

}

rDtuQ‚6~x¡©uQ‚z1ic‚8¡©uQ‚6h{now „

} rDh…rD„i * !#"G * (°{ef/icw#£#|6noh{noqsrD‚knv||p/iA|krD‚6nv|i¡]uQ‚t6f/i{AuQh{z p trDt6nvuQw³rDw } t6f/iG|6no„3w n·¡?œ

nv^rDw/AixuD¡kt6f/iÄfrDw „iA|^° ,¸w+zrD‚6t6nvcp qsrD‚^£yrQ||iA||6now „¢t6f/ix|6no„3w n·¶^rDw/AixuD¡…¨?p/|6prDqoqo~+|h…rDqoqO¯

frDw „iA| now¼t6f/ixhGu

}

iKœ½|6frDz1iA|^£rDw

}

frDw

}

qonow „_t6f/i_¨?p/|6prDqoqo~±f no„3f¯…AuQ‚6‚icqsrDt6nvuQw/|rDhGuQw „

now } noJn} prDq#hGu } iKœ½|6frDz1ikfrDw „iA|rD‚ik|6t6noqoq#AuQw/|6n} ic‚i } rQ|uQz$icw/i } 5p/iA|6t6nvuQw/|H5873£/† £I$[£[j:½°

$4uQw5t6‚uQqoqonow „{t6f/iˆAuQh{z p trDt6nvuQwrDq#AuQh{z qviK€Jnot¸~ uD¡#t6f/iz ‚uJAiA||6now „uD¡Ït6f/iˆAuQqoqviActi }*} rDtr

nv|§rDw/uQt6f/ic‚§|6trDw } rD‚ } hGuQw notuQ‚6now „{‚i4:p no‚ichGicw5t^£ ¦§f nvf now/cqop } iA|r-qonoh{noti } p/|iuD¡rDw¥rDwrNœ

qo~Jt6nv^rDq$hGu } icq1uD¡Ït6f/i|6t6‚6p/ct6p ‚i3°­xuQ‚iAuµic‚^£[t6f/i ‚i } p/ct6nvuQw ¡]‚uQh‰t6f/irDwrDqo~Jt6nv^rDqhGu } icq1tu

t6f/iiK€Jz1ic‚6nohGicw5trDqhGu } icq4¨?t6‚6p w/^rDti } hGu } rDq|6zrQAiµ¯4nv|yŸ:w/uµ¦§wÄtuGz qsr^~ÄrŸic~¥‚uQqviknowÄt6f/i

|p/AAiA||uD¡¬hGu

}

icq·œ‘rQ|i }Ä}

rDh…rD„i

}

ictiAct6nvuQwrDw

}

qvuJ^rDqono¤µrDt6nvuQw(5873£/Œ;:½°

ef/iˆz p ‚6z$u3|iuD¡t6f/iˆz ‚iA|icw5t zrDz$ic‚§nv|tu } iA|c‚6no‘1iˆt6f/i¡©uQp w } rDt6nvuQw/|yrDw } rDwrDqo~J¤^iˆt6f/i

z ‚uQz1ic‚6t6nviA|uD¡r } rDh…rD„i } ictiAct6nvuQwrDw } qvu:^rDqono¤µrDt6nvuQw¥hGict6f/u } °Uef nv|hGict6f/u } nv|‘rQ|i } uQw

rDwÄrDz z ‚urQf¦§f nvfrDnohG| rDt r } } ‚iA||6now „Gt6f/iˆnv||6p/iA|rDw } u^ic‚AuQh{now „ ¨]|uQhGiuD¡K¯Ãt6f/iˆqonohœ

notrDt6nvuQw/|rD‘1u^i3° ,½tynv|rQ||p hGi } t6frDtrG|6no„3wrDt6p ‚iuD¡Ut6f/i|t6‚6p/ct6p ‚i-nowxnot| w/uQh{nowrDq¨]|rN¡©iµ¯

|trDti…nv|{rA3rDnoqsrD‘ qvi3£t¸~:z nv^rDqoqo~³rhGu } ic‚rDti w5p h-‘1ic‚{uD¡ hGu } iA|rDw } rÄhGu } ic‚rDti w5p h‘$ic‚

uD¡AuQh{z1uQw/icw5t|uD¡UrQ||u:cnsrDti

}

hGu

}

iKœ½|6frDz1iA|^°Ãef nv|y|6no„3wrDt6p ‚iknv|p/|6prDqoqo~*n

}

icw5t6n·¶i

}

p/|now „

‚iK¡©ic‚icw/Ai } rDtr[£ z1u3||6no‘ qo~a‚iAAuQ‚ } i } p w } ic‚yrDwp w ŸJw/u^¦§wÄw/uQw[œ½|6trDt6nvuQwrD‚6~iK€[cnotrDt6nvuQw#°Ãef/i

z ‚uQz1u3|i } rDqo„uQ‚6not6f h‰z ‚u:AiA||iA|w/ic¦ } rDtrˆ‘5~¶/‚|6t„icw/ic‚rDt6now „r‚iA|6n} prDq£:rDw } AuQh{z p t6now „

not| |icw/|6not6noJnot½~¥¦k°‚^°t^°

}

rDh…rD„iA|^°Àef/ik‚iA|6n

}

prDqÏnv||f/u^¦§wÄtuG‘$i-rQ|~:h{z tuQt6nv^rDqoqo~KJrDp/||6nsrDw

j '( 6 *

p w } ic‚‘1uQt6faw/u } rDh…rD„irDw } |6h…rDqoq } rDh…rD„irQ||6p h{z t6nvuQw/|^°Uef nv|4‚iA|6p qot|4nowr-„3qvuQ‘rDqTtiA|6t^£

¦§f nvfxz1ic‚8¡©uQ‚6hG|r '( * rDwrDqo~J|nv|yuD¡Ut6f/i‚iA|6n} prDqÏtuat6f/i } rDh…rD„iA|µ£ + 8 *-p w[œ

Aic‚6trDnow:t6nviA|nowat6f/iyhGu } rDq$iA|6t6noh…rDtiA|§rDw } w/uQnv|iA|4uQwat6f/iˆrA3rDnoqsrD‘ qvi } rDtr[°­xu } rDq } nsrD„3w/u3|6nv|

nv|y|6trDti

}

rQ|r

}

ictiAct6nvuQwz ‚uQ‘ qvich)

}

iAcn

}

i-¦§f nvf AuQh{z$uQw/icw:t|uD¡t6f/ihGu

}

rDqÏzrD‚rDhGictic‚

iActuQ‚kfr^iyfrDw „i } °Uef nv|Àz ‚uQ‘ qvich‰nv|À|uQqoi } ‘:~ } iA|6no„3w now „|6noh{noqsrD‚KœtiA|6t|¡©u:cp/||i }

uQw:tu*t6f/ihGu } rDqU|p ‘/|6zrQAiA|uD¡4now:tic‚iA|6t^°ºrDh…rD„iqvu:^rDqono¤µrDt6nvuQw¢nv||trDti } rQ|kr } ictiAct6nvuQw

z ‚uQ‘ qvich£/rDw

}

w/uQtrDw¢¨?p/|6prDqoqo~Gnoqoq·œz1u3|i

}

¯Ãnow5ic‚|iiA|t6noh…rDt6nvuQw¥z ‚uQ‘ qvich°Uef nv|4z ‚uQ‘ qvichÂnv|

r } } ‚iA||i } ‘5~ z qop „3„3now „ rD„3„3‚ic„5rDti } |icw/|6not6noJnot6nviA|uD¡t6f/iˆhGu } iA|rDw } hGu } iKœ½|frDz$iA| ¦k°‚^°t^°

ª¬«U­Á|t6‚6p/ct6p ‚rDqÀzrD‚rDhGictic‚|nowZt6f/i rD‘$uµia|ict6t6now „/°ef nv|-‚iA|p qot|-now } no‚iAct6nvuQwrDq4tiA|t|^£

¦§f nvfxz1ic‚8¡©uQ‚6h t6f/i-|rDhGi-t½~Jz$iuD¡

}

rDh…rD„iKœtuDœw/uQnv|i|icw/|6not6noJnot½~rDwrDqo~J|nv|yuD¡t6f/ik‚iA|n

}

prDq

rQ|k¡]uQ‚ } rDh…rD„i } ictiAct6nvuQw#°xef/i…AuQh{z p trDt6nvuQw#£t6f/i rDwrDqo~:t6nv^rDq·œtuDœ½iK€[z1ic‚6nohGicw5trDq§h…rDtf[œ

now „*rDw } t6f/irD„3„3‚ic„5rDt6nvuQw¿uD¡Ut6f/i-|icw/|6not6noJnot6nviA|ˆrD‚ikz1ic‚8¡]uQ‚6hGi } u &œqonow/irDtr } iA|6no„3wx|trD„i3£

¦§f/ic‚i^rQ| t6f/i

}

no‚iAct6nvuQwrDqÏtiA|6t|h…rA~*‘$iAuQh{z p ti

}

uQw[œ‘$urD‚

} °

ef/izrDz1ic‚nv|uQ‚6„5rDw no¤^i } rQ|y¡©uQqoqvu^¦|^° ,¸w |iAct6nvuQw †[£1¦4inow5t6‚u } p/Ait6f/ihGu } icqonow „rDw }

} nv|cp/||{|uQhGi Ÿic~ZzrD‚rDhGictic‚6no¤µrDt6nvuQw/|*rDw } |icw/|uQ‚t½~Jz1iA|nv||6p/iA|^°³mJiAct6nvuQw $nv| } icuQti }

tu*t6f/iGz ‚uQz$u3|i }Z} rDh…rD„i } ictiAct6nvuQwZhGict6f/u } £#‘rQ|i } uQw=r „icw/ic‚rDqÀ|trDt6nv|6t6nv^rDqUqvuJ^rDqÃrDz[œ

z ‚urQfZtu*t6f/i } ictiAct6nvuQw=uD¡|6h…rDqoq } ic:nsrDt6nvuQw/|-now¿t6f/i{zrD‚rDhGictic‚|-uD¡ } ~:wrDh{nv…|6~J|tichG|^£

rDw } uQw¢r |6tuJfrQ|6t6nv|6p ‘/|6zrQAiKœ‘rQ|i } Au^3rD‚6nsrDw/AiKœ} ‚6noicw¢hGu } rDqn} icw:t6n·¶^rDt6nvuQw¢hGict6f/u } °

ef/iˆu &$œqonow/iˆAuQh{z p trDt6nvuQwxrDw } t6f/iuQw[œ‘1urD‚ } rDwrDqo~[|6nv||6trD„irD‚i } nv|t6now „3p nv|6f/i } £/rDw } t6f/i

i'&TiAct*uD¡r¢t6‚6p w/^rDti } hGu } rDq|6zrQAixnv|a‘ ‚6nvi

1 ~ } nv|cp/||i } ° ,¸w |iAct6nvuQw j/£¦Ài } iA|c‚6no‘1i

t6f/ihGu } rDq } nsrD„3w/u3|6nv|…hGict6f/u } £4¦§f nvf¼frDw } qviA|G‚iA|n} prDq |icw/|6not6noJnot6nviA|{tu } rDh…rD„iA| rDw }

‚iA|n} prDqv|…p w/Aic‚6trDnow:t6nviA|^° ºrDh…rD„iÄqvuJ^rDqono¤µrDt6nvuQw¼nv| r } } ‚iA||i } now |iAct6nvuQw Œ[£4¦§f/ic‚iÄt6f/i

u &$œqonow/iAuQh{z p trDt6nvuQw=rDw } t6f/i{uQw[œ‘$urD‚ } rDwrDqo~[|6nv||6trD„i{rD‚i } nv|6t6now „3p nv|6f/i } rD„5rDnow#°¹yuµ¦

t6f/iz ‚uQz1u3|i } hGict6f/u } ‚icqsrDtiA|ktu¥uQt6f/ic‚¦4uQ‚6ŸJ|nv|kr } } ‚iA||i } now¢|iAct6nvuQwZ‹[£T¦§f/ic‚i‚iA|n} œ

prDq } iA|6no„3w¿rDw } |6t6‚6p/ct6p ‚rDqUrD„3„3‚ic„5rDt6nvuQwZrD‚i } nv|cp/||i } °yŽyp hGic‚6nv^rDq¬‚iA|6p qot|ˆuQ‘ trDnow/i } uQw

t¸¦Àu¥rDz z qonv^rDt6nvuQw¿iK€ rDh{z qviA|rD‚i‚icz$uQ‚6ti } now |iAct6nvuQwJ°ˆmJuQhGiAuQw/cqop/|6nvuQw/|rD‚i } ‚r^¦§w¿now

|iAct6nvuQw[°

%! %.§01 ¬01(%

¢i ¶/‚|6tÀ‚iA^rDqoqt6f/iyh…rDnow i4:prDt6nvuQw/|§rDw } zrD‚rDhGictic‚|§uD¡#t6f/iyhGu } icqv|æ4i p/|i3°-, } icw5t6n·¶rD‘ qvi

rDw } w/uQw_n} icw5t6n·¶rD‘ qvi*hGu } icqv|rD‚i } nv|6t6now „3p nv|6f/i } £ÀrDw } rÄp/|iK¡]p qÃnow53rD‚6nsrDw/Ai*z ‚uQz1ic‚6t½~ZuD¡

t6f/ihGu } rDqyzrD‚rDhGictic‚|nv| uQp t6qonow/i } °"ef/icw t6f/i i'&TiAct¥uD¡frDw „3now „±t6f/i |icw/|uQ‚ t½~Jz1iA|

nv| } nv|cp/||i } °*ªnowrDqoqo~£t6f/i } rDh…rD„i } ictiAct6nvuQw³rDw } qvu:^rDqono¤µrDt6nvuQw_z ‚uQ‘ qvichG|now5iA|6t6no„5rDti }

t6f ‚uQp „3f/uQp tˆrD‚ik|6trDti } °

* *+( ( * * ( Œ

!"# %$! &# '()

¢iGrQ||6p hGit6frDtt6f/i‘$icfr^:nvuQ‚-uD¡4t6f/ihGiAfrDw nv^rDq4|6~J|tich^rDw¿‘1i

}

iA|c‚6no‘1i

}

‘5~¿r*|6trNœ

t6nvuQwrD‚6~Zqonow/i^rD‚ } ~JwrDh{nv^rDq§|6~J|tich£¬rDw } t6frDt^£¬now=t6f/i…¡]‚i45p/icw/c~¿‚rDw „i*uD¡now5tic‚iA|t^£¬t6f/i

now z p t¡]uQ‚AiA|^rDwđ$iˆhGu } icqvi } rQ| rw/uQw[œ½|6trDt6nvuQwrD‚6~¥¦§f notikw/uQnv|i3°Uef nv|§‚iA|6p qot|nowD)

* +,.-0/21436587,.-0/213:9,;-0/<16= >4-0/<1@?BA;-0/216=DCE,.-0/21 ¨7µ¯

¦§f/ic‚iF/ } icw/uQtiA|ˆAuQw5t6now:p/uQp/|t6nohGi3£G*B?@5H?29 rD‚ikt6f/ih…rQ||^£ } rDh{z now „rDw } |6t6n&1w/iA|| h…rNœ

t6‚6nvAiA|*‚iA|z$iAct6noicqo~£¨?f no„3f } nohGicw/|nvuQwrDqO¯aiActuQ‚I,AuQqoqviAct|*t6f/i } nv|6z qsrQAichGicw5t|uD¡t6f/i

} ic„3‚iAiA|yuD¡'¡]‚iAi } uQh´uD¡¬t6f/i|6t6‚6p/ct6p ‚i4/t6f/iiK€[tic‚6wrDqÀ¨?w/uQwhGi^rQ|p ‚i } ¯4¡©uQ‚AiJ>*nv|§hGu } icqvi }

rQ|Àrw/uQw[œ½|6trDt6nvuQwrD‚6~{¦§f notiw/uQnv|i¦§not6f…t6nohGiKœQrD‚6~Jnow „AuµQrD‚6nsrDw/Ai h…rDt6‚6n·€LKJM"-0/21K£hGi^rQ|p ‚iKœ

hGicw:t|§rD‚iyAuQqoqviActi } now t6f/i¨]uD¡]ticw#£Jqvu^¦ } nohGicw/|6nvuQwrDqO¯ÀiActuQ‚EA £[rDw } h…rDt6‚6n·€.C³now } nv^rDtiA|

¦§f nvfAuQh{z1uQw/icw5t|uD¡Ut6f/i|6trDtikiActuQ‚rD‚irQct6prDqoqo~hGi^rQ|6p ‚i } ¨?¦§f/ic‚i-t6f/i|icw/|uQ‚|rD‚i

qvuJ^rDti } ¯K°

ef/ihGu } iA|uQ‚Uicno„icw[¡]‚i45p/icw/cnviA| } icw/uQti } „icw/ic‚6nv^rDqoqo~‘5~ONU£t6f/i§icno„icw5iActuQ‚|!PGQ$£rDw }

t6f/iˆhGu } iKœ½|6frDz1iA| } icw/uQti } „icw/ic‚6nv^rDqoqo~¥‘:~.R Q £/rD‚ik|uQqop t6nvuQw/| uD¡)

SUTWV -0N *X3YNZ5[3:9\1=^]?_-0N *`3YNZ5'3:9\1aP

Q

=^]?bR

Q

=^C'P

Q

¨©†¯

ef/i¡?‚i4:p/icw/c~arDw }a} rDh{z now „AuJidc…cnvicw5t§rD‚iy‚iAAu^ic‚i } ¡?‚uQh¾r * ( ( , * , icno„icw53rDqop/iHN

t6f ‚uQp „3fD)

ª/‚i45p/icw/c~feg= h

i)j

?ĺrDh{z now „lkm=on p

q p 3 h

?¦§f/ic‚i)

p

=srJ-0Nt1@?

h

=buJ-0Nt1 ¨$¯

'Âqvu:^rDq } rDh…rD„i*now_t6f/i |t6‚6p/ct6p ‚ia‚i } p/AiA|t6f/i*|6t6n&1w/iA||{rDw } now/c‚i^rQ|iA|t6f/i } rDh{z[œ

now „/°=ef5p/|h…rDw:~ } rDh…rD„i } ictiAct6nvuQw+tiAf w n5p/iA|GfrAi*‘1iAicw_z ‚uQz1u3|i } ¦§f nvf¼hGuQw notuQ‚

t6f/i|6t6n&1w/iA||h…rDt6‚6n·€I9³°¹yuµ¦Àicic‚^£$hGuQw notuQ‚6now „*not|now:ic‚|iF9Zvw^£/wrDhGicqo~Ät6f/i

1

iK€[no‘ noqonot½~

h…rDt6‚6n·€T£'frQ|-z ‚uµicw=hGuQ‚i…t6‚rQctrD‘ qvi rDw } AuQh{z p trDt6nvuQwrDqoqo~¢¡©i^rQ|6no‘ qvi587£Tj/£Œ;:½° ,½w_|uQhGi

^rQ|iA|^£[uQt6f/ic‚|t6‚6p/ct6p ‚rDqTzrD‚rDhGictic‚6no¤µrDt6nvuQw/| |6p/fÄrQ|ÀuQqop h{nvˆh…rQ||rDw }Lx uQp w „GicqsrQ|t6nvcnot½~

hGu } p qop/|h…rA~¢‘1iaz ‚iK¡]ic‚rD‘ qvi 5‹ £ 7:½°mJicic‚rDqhGict6f/u } |now_t6f/i…qonotic‚rDt6p ‚i¥rD‚ia‘rQ|i } uQw

rGt6‚rDw/|6h{nv||6no‘ noqonot¸~h…rDt6‚6n·€(5$[£ 2:½£¦§f nvfxnow:uQqoiA|ˆt6f/ikz ‚uJAiA||6now „*uD¡Unow z p t8œ½uQp t6z p t } rDtr[°

¹u^¦4icic‚^£ now¥t6f/i^rQ|iuD¡w/uQw¥hGi^rQ|6p ‚i } now z p tiK€ cnotrDt6nvuQw#£ z ‚u:AiA||6now „GuQp t6z p t8œ½uQw qo~ } rDtr

nv|h…rDw

}

rDtuQ‚6~ 5 £)y;:½°zywt6f/iuQt6f/ic‚frDw

}

£ry‚i

}

p/Ai

}

|6t6n&1w/iA||rDw

}

rDwnow/c‚i^rQ|i }}

rDh{z now „

‚iA|p qotynow } iAc‚i^rQ|i } wrDt6p ‚rDq¬¡?‚i4:p/icw/cnviA|rDw } hGu } n·¶i } hGu } iKœ½|frDz$iA|„iAuQhGict6‚6~°­uQw n·œ

tuQ‚6now „-t6f/i§hGu } rDqzrD‚rDhGictic‚|Ãnv|Ut6f5p/|U‚icqvic3rDw5t^£[rDtUqvi^rQ|6tU¡]uQ‚ } rDh…rD„i } ictiAct6nvuQw#°UºrDh…rD„i

qvuJ^rDqono¤µrDt6nvuQw#£f/u^¦Àicic‚^£1‚i4:p no‚iA|¨©rDtyqvi^rQ|6t zrD‚6t6nsrDqO¯ŸJw/u^¦§qvi

}

„iuD¡Ã|6t6‚6p/ct6p ‚rDqÏzrD‚rDhGictic‚|

rDw } „iAuQhGict6‚6~°

ef/i…z ‚uQz1u3|i }_} rDh…rD„i } ictiAct6nvuQw³hGict6f/u } frDw } qviA|t6f/iahGu } rDq4zrD‚rDhGictic‚|^£¬¦§f nvf

icwQƒ6u^~krp/|iK¡?p q3now:QrD‚6nsrDw/AiÀz ‚uQz$ic‚6t¸~£3rQ|#iK€Jz qsrDnow/i

}

w/iK€Jt^°'­xuQ‚iAuµic‚^£Qt6f/iz ‚uQz1u3|i

}

hGict6f/u

}

‹ '( 6 *

} uJiA| (*

h…rDŸi¥p/|iuD¡krDw5~³hGu } rDqzrD‚rDhGictic‚|aiK€[t6‚rQcti } ¡]‚uQh rDw»rDwrDqo~Jt6nv^rDqhGu } icq£

‘ p t…p/|iA|{n} icw5t6n·¶i } hGu } rDqzrD‚rDhGictic‚|…now/|ti^r } °»ef/i¥z ‚uQz1u3|i }+} rDh…rD„iÄqvu:^rDqono¤µrDt6nvuQw

hGict6f/u } frDw } qviA| ‘$uQt6fhGu } rDq'rDw } |t6‚6p/ct6p ‚rDq#zrD‚rDhGictic‚|^£/p/|now „arDwÄuQ‚6no„3nowrDq'|t6‚6p/ct6p ‚rDq

rD„3„3‚ic„5rDt6nvuQwxhGiAfrDw nv|6h°

GW $ 6 &! ! H$ &# U( U # t

m[rDh{z qonow „ÄhGu } icq ¨7µ¯ˆrDt‚rDti  ~Jnvicq} |t6f/i } nv|c‚ictit6nohGihGu } icqnow¢|6trDti{|6zrQAi¡©uQ‚6h

587^’[£ 77*: )

w =

3

w

A =

¨?j:¯

¦§f/ic‚ikt6f/ik|6trDtikrDw

}

t6f/ikuQp t6z p trD‚i)

=

,;-1

7

,;-1

? A

=^A -1@? ¨©Œ¯

t6f/i|trDtit6‚rDw/|6not6nvuQwxrDw } uQ‘/|ic‚6QrDt6nvuQwh…rDt6‚6nvAiA|rD‚i)

B= ! ;?#" =

] $

n* vw 9 n%* vw 5

rDw

} =&% C ](' ¨©‹¯

,¸w¥¨?j:¯K£3t6f/i , ( 0,.+ |6trDtiÀw/uQnv|i)

w

nv|¬rQ||6p hGi } tuy‘1i JrDp/||6nsrDw#£Q¤^ic‚uDœhGi^rDw#£5¦§f noti3£

¦§not6fxAu^3rD‚6nsrDw/Aikh…rDt6‚6n·€)

K

w+*-,.

=0/f-

w

21

w

1=4365

w87

:9<;KL-= 1> @?:9 k!=

¦§f/ic‚iA/f-CB1 } icw/uQtiA|t6f/iiK€[z$iActrDt6nvuQwuQz$ic‚rDtuQ‚yrDw }

;

K -=)1= ] ]

] * vw K M -=)1 * v 1

ef/iˆ¦§f noticw/iA|| rQ||6p h{z t6nvuQwÄuQw¥t6f/i|trDtiˆw/uQnv|ikrDw

}

t6f/ikrD‘/|icw/AiuD¡¬hGi^rQ|6p ‚ichGicw5tw/uQnv|i

now³¨?j:¯rD‚i } nv|cp/||i } now(587^† :½°.,¸tnv||6t6‚iA||i } t6frDtˆ|6now:p/|uQn} rDquQ‚AuQqvuQ‚i } w/uQnv|i-iK€ cnotrDt6nvuQw

^rDw ‘1iicw/AuQh{zrQ||i } rQ|ˆ¦Àicqoq°{m:trDti

rDw } uQ‘/|ic‚6i } uQp t6z p tJA´frAi } nohGicw/|nvuQw/| iD

rDw }FE

‚iA|6z1iAct6noicqo~£/¦§not6f

E

¨]uD¡]ticwh-p/f¯§|6h…rDqoqvic‚ t6frDw iD nowz ‚rQct6nvAi3°

* *+( ( * * (

ictF-4? P"14‘$iˆt6f/iicno„icw/|t6‚6p/ct6p ‚i-uD¡¬t6f/ik|6trDtit6‚rDw/|6not6nvuQwÄh…rDt6‚6n·€…£[wrDhGicqo~)

S(TWV - sn $"1=s]?g- bn $"1aPF=s] ¨3¯

ef/ihGu } rDq1zrD‚rDhGictic‚|F-0N?<R Q1Ãnow¢¨©†¯À^rDw¥‘$i } i } p/Ai } ¡]‚uQh t6f/i -4? P 1'|now¢¨3¯Up/|now „I)

Q

=4? R Q =

*-,.

= P ¨¯

ef/i…¡]‚i45p/icw/c~³rDw }=} rDh{z now „¢AuJidc…cnvicw5t…rD‚ia‚iAAu^ic‚i } ¡]‚uQh r } nv|c‚icti*icno„icw:QrDqop/i

t6f ‚uQp „3fD)

ª ‚i4$°.=

p

i)j

? ºrDh{z now „ = h

q p 3 h

?¦§f/ic‚i)

p

=

V

ul-G1

rJ-G1 ? h

=

¨y¯

«Uno„icw5iActuQ‚|rD‚i‚i^rDq#n·¡5m=t*o3 9³£[t6f/ik|noh{z qviA|6t§¡©uQ‚6h´uD¡z ‚uQz1uQ‚6t6nvuQwrDq } rDh{z now „/°

iA^rDp/|i{uD¡4t6f/i|6t6‚6p/ct6p ‚i{uD¡Àt6f/i{|6trDtinow+¨©Œ¯K£Tt6f/i |krDw } |krD‚izrDno‚6¦§nv|i{AuQh{z qviK€

AuQwQƒ8p „5rDti3°

,½tt6p ‚6w/|ˆuQp tyt6frDtyt6f/iAuQqoqviAct6nvuQwuD¡UhGu } iA| -4? 1K£¦§f nvfx¡]uQ‚6hr{ic‚6~¥wrDt6p ‚rDqzrNœ

‚rDhGictic‚6no¤µrDt6nvuQw¡©uQ‚'|t6‚6p/ct6p ‚rDq[rDwrDqo~[|6nv|^£3rDqv|uyicwQƒ8uµ~r§w nvAiÀnow53rD‚6nsrDw/Ai4z ‚uQz$ic‚6t¸~° '§ct6prDqoqo~£

not4^rDw i^rQ|noqo~G‘$iy|6f/u^¦§w*tu-‘$iynow53rD‚6nsrDw5t¦k°‚^°t^°frDw „iA|now t6f/i|6trDti ‘rQ|nv|ÀuD¡Ï|6~[|6tich¨?j:¯K°

,¸w…uQt6f/ic‚À¦ÀuQ‚ } |^£:t6f/iF-4?"1'|¡©uQ‚6h‰r-^rDw/uQw nv^rDqzrD‚rDhGictic‚6no¤µrDt6nvuQw¥uD¡Tt6f/i icno„icw/|6t6‚6p/ct6p ‚i

¨]uQ‚i45p no3rDqvicw5t6qo~¢t6f/i…z$uQqviGzrD‚6tL¯uD¡§t6frDt|6~[|6tich° ict-t6f/i -? 1'|‘1iG|6trQŸi } now5tu r

-E 3 1 D œ } nohGicw/|nvuQwrDqϐiActuQ‚ I)

*-,.

=

T

¨7^’¯

¦§f/ic‚i

nv|t6f/iiActuQ‚ˆ¦§f/u3|iicqvichGicw5t|krD‚it6f/iicno„icw:QrDqop/iA|#£

nv|yt6f/ih…rDt6‚6n·€Ä¦§f/u3|i

AuQqop h{w/|krD‚it6f/ihGu } iKœ½|frDz$iA||^£1rDw } T

nv|t6f/iAuQqop h{w¿|6trQŸJnow „¥uQz$ic‚rDtuQ‚^°ª/‚uQh

w/uµ¦ uQw#£ iActuQ‚ nv| AuQw/|6n} ic‚i } rQ|§t6f/i|~J|6tichÂzrD‚rDhGictic‚^°

¢i |t6‚iA||_t6frDt±¦Ài } u w/uQt³w/iAi } tu ¡rAuQ‚+r zrD‚6t6nvcp qsrD‚+w/uQ‚6h…rDqono¤µrDt6nvuQw´uD¡xt6f/i

hGu } iKœ½|6frDz1iA|sP Q | rDw } t6f5p/| uD¡¢t6f/i |^£¢rQ| uQz z$u3|noti tu‰t6f/i h…rQ||»w/uQ‚6h…rDqono¤^i }

hGu } iA|) P 1Q * P Q =$ p/|i } now i3°„/° 5Œ;:½°B'|yiK€[z qsrDnow/i } ‘$icqvuµ¦k£t6f/iz ‚uQz1u3|i }x} rDh…rD„iKœ

tuDœw/uQnv|iG|icw/|6not6noJnot½~ ‚rDt6nvu3|rD‚i{now53rD‚6nsrDw5t¦k°‚^°t^°a|p/f¢w/uQ‚6h…rDqono¤µrDt6nvuQw/|^°*¹u^¦4icic‚^£|uQhGi

^rD‚i |6f/uQp q} ‘1i§trDŸicw{¡©uQ‚ } rDh…rD„iyqvu:^rDqono¤µrDt6nvuQw#£:¦§f noqvih…rDtf now „n} icw:t6n·¶i } hGu } iKœ½|6frDz1iA|

¦§not6frDwrDqo~:t6nv^rDqÏuQw/iA|yrQ| } nv|cp/||i } nowČ[°†[°$[°

"! $# (#G I ! 4 $

ef/i hGi^rQ|6p ‚ichGicw5t§i4:prDt6nvuQwanow¿¨?j:¯¬¦§not6f rQ|Unow¿¨©‹¯¬noh{z qonvcnot6qo~ rQ||6p hGiA|Àt6frDtÃt6f/iˆrA3rDnoq·œ

rD‘ qvi |icw/|uQ‚|hGi^rQ|6p ‚iat6f/i¨?‚icqsrDt6noiµ¯

}

nv|6z qsrQAichGicw:t|{uD¡t6f/i

}

ic„3‚iAiA|uD¡¡]‚iAi

}

uQh t6f/ichœ

'( 6 *

|icqoiA|^£$wrDhGicqo~ rD‚iAuQw/|6t6‚rDnow:tk„5rDp „iA|^°,½¡ÀAuQw/|6t6‚rDnow:tk„5rDp „iA|^£1icqvuJcnot½~ |icw/|uQ‚|rDw } rQKœ

Aicqvic‚uQhGictic‚|ˆrD‚ikrA3rDnoqsrD‘ qvi3£/t6f/ikhGi^rQ|6p ‚ichGicw5ti45prDt6nvuQwnow_¨7µ¯4|6f/uQp q} ¦§‚6noti)

A -0/21=

C!,;-0/21

7,;-0/21

+,;-0/<1

¦§not6f C ? ? žh…r } ikuD¡] |yrDw } +|^£/rDw } |6~J|tich²¨©Œ¯4|6f/uQp q} ‘1iˆp w } ic‚|6tu:u } ¦§not6f )

= C ]

]

nJ* vw 9 nJ* vw 5

$4uQw/|i45p/icw:t6qo~£|trDti…|6zrQAi{hGu } icq¨?j:¯k^rDw_rDqo¦rA~[|-‘1iGicw[¡©uQ‚Ai } £'¦§frDticic‚t6f/i…|icw/|uQ‚|

rD‚i3°Ãef/iˆwrDt6p ‚i-uD¡¬t6f/i|icw/|uQ‚|§p/|i } uQw qo~anow 1 p/icw/AiA| t6f/ikuQ‘/|ic‚63rDt6nvuQwh…rDt6‚6n·€F=°

& 4 ()G" B &! U G# b$!#!^

,¸w t6f nv|ÀzrDz1ic‚^£ } rDh…rD„i } ictiAct6nvuQw¥nv||6trDti } rQ|Àt6f/iz ‚uQ‘ qvich uD¡ } ictiAct6now „GfrDw „iA|§now t6f/i

^rDw/uQw nv^rDq1zrD‚rDhGictic‚§iActuQ‚ } iK¶/w/i } now ¨7^’¯K°-,¸tÀnv|§rQ||p hGi } t6frDtr-‚iK¡]ic‚icw/Ai3rDqop/i

nv|ˆrA3rDnoqsrD‘ qvi3° Jˆicw/ic‚rDqoqo~£1|6p/f¿r{‚iK¡©ic‚icw/AizrD‚rDhGictic‚ynv|yn} icw5t6n·¶i } p/|6now „ } rDtrG‚iAAuQ‚ } i }

uQwat6f/i p w } rDh…rD„i } |6~[|6tich°z ¡ÏAuQp ‚|i3£J¦§f/icw t6f/ihGuQw notuQ‚i } |6~[|6tich"nv|4|6p ‘[ƒ6iActÀtu-w/uQw[œ

|trDt6nvuQwrD‚6~ now z p tiK€[cnotrDt6nvuQw#£t6f/i‚iK¡©ic‚icw/Aik3rDqop/i |6f/uQp q} ‘1in} icw5t6n·¶i } uQwqvuQw „ } rDtr

|LrDh{z qviA|AuQw:trDnow now „=rQ|h…rDw5~=uD¡yt6f/iA|i w5p nv|rDw/Ai*frDw „iA|arQ|z1u3||6no‘ qvi3° ¹u^¦4icic‚^£Unotnv|

noh{z1uQ‚6trDw5t-tu¥w/uQtit6frDt^£#¦§not6f¢t6f/iGz ‚uQz$u3|i } hGict6f/u } £#t6f/i } ictiAct6nvuQw=z ‚uQ‘ qvich h…rA~ ‘1i

|uQqoi } uQwt6f/i‘rQ|6nv|uD¡ } rDtr{|rDh{z qviA| uD¡hp/fx|h…rDqoqvic‚ |6no¤^i3°

Jnoicw#£3uQwuQw/i4frDw

}

£3r‚iK¡©ic‚icw/Ai4QrDqop/i ÀuD¡/t6f/iÃhGu

}

icqJzrD‚rDhGictic‚rDw

}

£3uQwt6f/i4uQt6f/ic‚

frDw } £1r{w/ic¦ } rDtrG|rDh{z qvi3£t6f/i } ictiAct6nvuQwz ‚uQ‘ qvich nv| tu } iAcn} i-¦§f/ict6f/ic‚t6f/ikw/ic¦ } rDtr

rD‚iy|6t6noqoq/¦4icqoq } iA|c‚6no‘1i } ‘:~{t6f nv|ÃzrD‚rDhGictic‚43rDqop/i uQ‚Ãw/uQt^°¬ef/i hGu } rDq } nsrD„3w/u3|6nv|Ãz ‚uQ‘ qvich

nv| tu

}

iAcn

}

ik¦§f nvfAuQh{z1uQw/icw5t|uD¡t6f/ikhGu

}

rDqÏzrD‚rDhGictic‚yiActuQ‚ {fr^i-frDw „i

}

°§ef/i

} rDh…rD„i4qvuJ^rDqono¤µrDt6nvuQw{z ‚uQ‘ qvich nv|'tu } iAcn} i¦§f nvfzrD‚6t|uD¡t6f/i4|6t6‚6p/ct6p ‚i4frAi‘1iAicw } rDhœ

rD„i } £uQ‚ i45p no3rDqvicw5t6qo~¥tu } iAcn} i-¦§f nvficqvichGicw5t|uD¡t6f/ik|t6‚6p/ct6p ‚rDqÏzrD‚rDhGictic‚ h…rDt6‚6nvAiA|

fr^ikfrDw „i } °

4iA^rDp/|i§|6t6‚6p/ct6p ‚rDq/n} icw5t6n·¶^rDt6nvuQwanv|UrˆAuQh{z qviK€Ä¨©rDw } „icw/ic‚rDqoqo~w/uQt¬¡]p qoqo~rDp tuQh…rDt6nvµ¯

z ‚uJAiA||^£3rDw } ‘1iA^rDp/|iÀnotnv|now:ticw } i } tu } iA|6no„3wGr } rDh…rD„i } ictiAct6nvuQw…rDqo„uQ‚6not6f hž¦§f nvfG^rDw

‘1i‚6p wuQw[œ‘$urD‚ } £$uQp ‚rDz z ‚urQf } uJiA|(* z$ic‚8¡©uQ‚6h rGw/ic¦ zrD‚rDhGictic‚ˆiA|6t6noh…rDt6nvuQwÄp/|now „

t6f/ikw/ic¦ } rDtr{|rDh{z qvi3° ,½w/|6ti^r } £/t6f/i } rDh…rD„i } ictiAct6nvuQw rDw } hGu } rDq } nsrD„3w/u3|6nv|z ‚uQ‘ qvichG|

rD‚i|uQqoi } t6f ‚uQp „3f t6f/iuQw[œ‘$urD‚ } AuQh{z p trDt6nvuQwZrDw } rDwrDqo~J|nv|uD¡rG‚iA|6n} prDq°-m:noh{noqsrD‚6qo~£

* *+( ( * * ( y

‘1iA^rDp/|iU|t6‚6p/ct6p ‚rDq5hGu } icq5p z } rDt6now „ nv|'rAuQh{z p trDt6nvuQwrDqoqo~know5uQqoi } z ‚u:Ai } p ‚i3£Dt6f/i } rDhœ

rD„i qvu:^rDqono¤µrDt6nvuQw z ‚uQ‘ qvich¾nv|Uw/uQt§r } } ‚iA||i } rQ|4rDw ¨?p/|6prDqoqo~{noqoq·œz$u3|i } now5ic‚|iµ¯ÃiA|t6noh…rDt6nvuQw

z ‚uQ‘ qvich£[‘ p t rQ|rDw¥ic3rDqoprDt6nvuQwuD¡'t6f/iˆAuQ‚6‚icqsrDt6nvuQw/| uD¡t6f nv|‚iA|6n} prDq1¦§not6f|6z1iAcn·¶|t6‚6p/Kœ

t6p ‚rDqÏzrD‚rDhGictic‚y|6p ‘/|6zrQAiA|µ°ef nv|nv|§iK€[z qsrDnow/i

}

now¥t6f/iw/iK€[t§t6f ‚iAik|iAct6nvuQw/|^°

! "#$%

ef/i

}

iA|6no„3w¢uD¡4t6f/iGz ‚uQz$u3|i }Z}

rDh…rD„i

}

ictiAct6nvuQw_rDqo„uQ‚6not6f h®nv|‘rQ|i

}

uQw=r „icw/ic‚rDq4|6trNœ

t6nv|t6nv^rDqyrDz z ‚urQf#£§¦§f nvf rDnohG| rDtGt6‚rDw/|8¡©uQ‚6h{now „³rqsrD‚6„ixcqsrQ||…uD¡ } ictiAct6nvuQw»z ‚uQ‘ qvichG|

AuQw/Aic‚6w now „{rˆzrD‚rDhGictic‚6no¤^i } * * *=. @/+ * now:tu-t6f/i§p w noic‚|LrDqz ‚uQ‘ qvich uD¡1hGuQw notuQ‚8œ

now „¥t6f/ihGi^rDw¢uD¡r JrDp/||6nsrDw +

(7*

* +

587cj:½°ef nv|rDz z ‚urQfZ‘rQ|nv^rDqoqo~ r } } ‚iA||iA|

t6f/i…i^rD‚6qo~x¦rD‚6w now „xuD¡ 0 F *+( uD¡t6f/iG|6~[|6tichzrD‚rDhGictic‚^° ef/iŸic~n} i^r¥nv|tu

} iK¶/w/iˆrAuQw5icw nvicw5t§‚iA|n} prDq£:t6no„3f:t6qo~arQ||uJcnsrDti } ¦§not6f*r-‚icqvicQrDw:tÀzrD‚rDhGictic‚iA|t6noh…rDt6nvuQw

hGict6f/u } £rDw } tuÄAuQh{z p tiat6f/i…|icw/|6not6no:not¸~¿uD¡t6f/i…‚iA|6n} prDqæk°‚^°t^° } rDh…rD„iA|*¨?Jnvic¦Ài } rQ|

frDw „iA|now¥t6f/izrD‚rDhGictic‚yiActuQ‚L¯§rDw } t6f/ip w/Aic‚6trDnow:t½~¥nowt6f/iˆ‚iA|6n} prDq } p/ituz ‚u:AiA||

w/uQnv|irDw } iA|6t6noh…rDt6nvuQw ic‚6‚uQ‚|^° ­uQ‚iAu^ic‚^£ t6f/iĂiA|n} prDqˆ^rDw ‘1iÄ|6f/uµ¦§w»tu=‘$i rQ|6~Jh{z[œ

tuQt6nv^rDqoqo~ JrDp/||6nsrDw#°¹icw/Aiat6f/i*rDwrDqo~[|6nv|uD¡t6f/ia‚iA|n} prDqv||icw/|6not6no:not¸~¢tut6f/i } rDh…rD„iA|

‚icqsrDt6noiytukp w/Aic‚6trDnow:t6nviA|rDw } w/uQnv|iA|Ànv|Ãi^rQ|~)¬rk|uQp w }a} iAcnv|6nvuQw ‚6p qvi ^rDw ‘$i } iA|no„3w/i } ¡©uQ‚

rQ||iA||6now „¦§f/ict6f/ic‚ t6f/ik‚iA|6n} prDq#frQ| *> ( ?@ ( } icJnsrDti } ¡]‚uQh¤^ic‚uGuQ‚w/uQt^°

ª/uQ‚À|6t6‚6p/ct6p ‚rDq:no‘ ‚rDt6nvuQw…hGuQw notuQ‚6now „rDw }G}

rDh…rD„i

}

ictiAct6nvuQw#£:t6f/i§h…rDnow…nv||p/i§nv|t6f5p/|

t6f/i } iK¶/w not6nvuQw_uD¡§r zrD‚rDhGictic‚iA|6t6noh…rDt6now „¥¡]p w/ct6nvuQw=rQ||uJcnsrDti } ¦§not6f=r hGu } rDqUn} icw5t6n·¶ œ

^rDt6nvuQw¢rDqo„uQ‚6not6f h°ef/ip/|iuD¡§rDwuQp t6z p t8œ½uQw qo~¿rDw } Au^3rD‚6nsrDw/AiKœ} ‚6noicw=|6p ‘/|6zrQAiKœ‘rQ|i }

|tu:frQ|6t6nvn

}

icw5t6n·¶^rDt6nvuQw=frQ|ˆ‘$iAicwZr

}

uJ^rDti

} 5y[£ 7^† :½°ef/i‚iA|6n

}

prDqUAuQ‚6‚iA|6z1uQw

}

now „tu

t6f nv|yhGict6f/u } nv| now5t6‚u } p/Ai } now6$[°873° ef/i-frDw } qonow „*uD¡t6f/i‚iA|6n} prDq¬|icw/|6not6noJnot6nviA|rDw } p w[œ

Aic‚6trDnow:t½~¢nv|r } } ‚iA||i } now<$[°†[£¬rDw } t6f/icno‚u &œqonow/iaAuQh{z p trDt6nvuQw } iA|c‚6no‘1i } now $[°$[°*ef/i

‚iA|n

}

prDqÀrDwrDqo~J|nv|-rDw

}

t6f/i{‚iA|6p qot6now „xuQw[œ‘$urD‚

}¢}

rDh…rD„i

}

ictiAct6nvuQw=rDqo„uQ‚6not6f h rD‚iG„3noicw

now $[°j/°

! ) U B #Z ! $ 6t#a G#

ef/iŸic~|6ticz/|UuD¡$t6f/i|6p ‘/|6zrQAi§|t6‚6p/ct6p ‚rDq/n} icw5t6n·¶^rDt6nvuQw hGict6f/u } rD‚i‘ ‚6nvi 1 ~‚iA^rDqoqvi } °9'

frD‚rQctic‚6no¤µrDt6nvuQw{uD¡[t6f/iÃhGu } rDq5zrD‚rDhGictic‚'now*¨7^’¯1nv|#iK€[f no‘ noti } £D¡?‚uQh ¦§f nvft6f/iz ‚uQz$u3|i }

‚iA|n} prDqÏ^rDw‘1i } iK¶/w/i } °UªnowrDqoqo~£ t6f/iki'&TiAct uD¡rt6‚6p w/^rDti } hGu } rDq#|zrQAinv| } nv|cp/||i } °