• Aucun résultat trouvé

Dynamic Changes in Concurrent Systems: Modelling and Verification

N/A
N/A
Protected

Academic year: 2021

Partager "Dynamic Changes in Concurrent Systems: Modelling and Verification"

Copied!
41
0
0

Texte intégral

(1)

HAL Id: inria-00072960

https://hal.inria.fr/inria-00072960

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

Dynamic Changes in Concurrent Systems: Modelling and Verification

Eric Badouel, Javier Oliver

To cite this version:

Eric Badouel, Javier Oliver. Dynamic Changes in Concurrent Systems: Modelling and Verification.

[Research Report] RR-3708, INRIA. 1999. �inria-00072960�

(2)

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

Dynamic Changes in Concurrent Systems:

Modelling and Verification

Eric Badouel and Javier Oliver

N ˚ 3708

June 1999

TH `EME 1

(3)
(4)

0-213 54.)6"

768:9<;>=@?BADCFEHGJILK?FMHAONP?RQ'9SGJ8.T.I<9UQPGV8W

XY[Z]\%^@_a`cb!d]ef^]gJhRi^j!efklemjfZ]\%^]e

npofqsrt^]j)nHgJofgVuJovgVw[Yl^

bLgJw[wFqJofjx[^om^:y5Yl^]ovy5Yl^z{}|~J€&`‚Jh[z[^%_:ƒVƒJƒ„`…{R|w†gsuV^:e

‡ˆ ‰]Š‹Œ[VŠVŽ zjvYl‘’eLw[gVwF^]o“)^„gVx[x[of^]eve)jfYl^„‘”evefhl^:eqs•D\0qlxl^]–—–’‘”zlugVz[x˜V^:om‘—™Fy]gsjm‘’qJzqs•DyqJz†yh[ovom^:z}j

efklemjf^]\@eLevh[šRrt^:yj!jfqxlklz[gJ\%‘’yy5Y†gVzluJ^]e!h[ef‘”zlunD^jvom‘ zl^jL•›qJov\@gs–’‘’ev\@eœ!že!•ŸgJoLgVeLjfYl^^i[w[of^]evem‘’˜R‘—j k

qV•¡jvYl^\%qlxl^–¢‘”e„yq}z[y^:ofz[^]x£g.š†hl‘—–’jt¤S‘”z¥gVz[x£xl^]y^]z}jfovgs–’‘’¦^]x£\%^]y5Y[gJzl‘”ef\§•›q}o„Y[gVz†xl–—‘”zlu>y5Y[gJzluV^:ea‘’e

–’qRqJ¨V^]x.•›qJo]œžjžjfYl^@evgV\%^jm‘”\%^0jvYl^0š†gVef‘’y0xl^]y‘’x[gJšl–’^0w[ofqJwF^]ofjm‘’^]eLqs•¢nD^jvom‘Dzl^jve©Un¢–”gVy^%ªqJh[z†xl^]xR¤

z[^]eve«b!^:gVy5Y[gJšl‘’–—‘’j kV«¬a^]gJxl–—qly5¨B«sgVz†x­®‘’˜V^:zl^]eve5¯'evYlqJh[–’x0om^:\%gV‘’z0xl^]y‘’x†gVšl–’^p•›q}o jfYl^^iljf^]z[xl^:x0\%qlxl^]–Uœ

XY[^0u}gs‘”z>‘”z°jf^]ov\%e6qV•¡\%qlxl^–’–—‘”zlu±wFq“¡^:oL‘”e„h[evh[gs–’–—k>w†gs‘”x°š}k°g–—q}efeaqs•)xl^]y‘’x[gJšl–’^@w†omq}w†^:omjf‘—^:eœ

jvofgJxl^¤Sqs²³zl^^:x[e0jmq°šF^•›q}h[z[x´šF^j “)^^:z¥^i[w[of^]evef‘—˜R‘’j kµgVz†x´yq}\%w†hljfgJšl‘—–’‘’j kVœ



z¶g°w[of^˜R‘’qJh[e0emjvh[xlk

“)^Y[g·˜J^„‘’z}jfofqlx[h[y^]x±g&y–”gVeve!qV•DY[‘—u}Y¸–—^]˜V^–nD^jfof‘z[^jfe]«Fy]gs–’–—^:x±om^:yq}zR™†uJh†ofgJšl–—^„zl^]jfe]«†jvY[gsjaygVz¸xlk}¤

z†gV\%‘’y]gs–’–—kµ\0qlxl‘—•›k°jvYl^‘”o„q“!z¹efjfovh[yjvh[om^&š}kµof^“!of‘’jm‘”zlu±emq}\0^@qV•)jvYl^‘”oyq}\@w†q}zl^]z}jfe]œXYl^:em^zl^]jfe

“)^]of^h[ef^]x>•›qJoa\%qRx[^–’–—‘”zlu¸yqJ\@w[h[jm^]oaevh[w[wFqJofjm^]x°yqRqJwF^]ovgsjf‘—˜J^“)qJov¨°© ºB»:º†¼¯LgJz[x>\%qJof^0w†om^:y‘”em^]–—k

“)qJov¨J½†q“3emklefjm^]\@e]œ  z>jfYl‘”e6emjvh[xlk¸“¡^%om^:emjvom‘”yjžqJh[ožgsjfjm^]z}jf‘—q}z±jmq.jfYl^%efh†šFy–’gJefežqs•pof^]yqJzR™†u}h[ovgVšl–’^

z[^jfe]«)jm^]ov\%^]x³of^˜V^:ofef‘”šl–—^J«¢“!Ylq}em^±efjfovh[yjvh[om^±\%qlxl‘—•›k}‘”zlu´ovhl–’^]e&gVof^.•›qJov\@gs–’–—k´‘”z}˜V^:ofef‘’š[–—^Jœ¿¾lh[y5YÀg

z[^j„\@g·k>š†^@˜R‘—^]“¡^:x°gJežjvYl^&ygJefy]gVxl^:x°yq}\@w†q}em‘’jm‘’qJz°qs•¡gJzµgJhljmq}\%gVjmq}z±“‘—jvYµg¸w[gJofgJ\%^jfof‘”ynD^jvom‘

z[^jÁ'gJz[x>h[z†xl^]oaemq}\%^0gVx†xl‘—jf‘—q}z[gs–DgVevevh[\@wljm‘’qJz±‘’ja‘’ež^]ÂRhl‘’˜gs–’^]z}jLjfqgefjfovgsjf‘ÙF^]x±nD^jvom‘Dzl^]jœ6n¢–”gVy^

šFqJh†z[xl^]x†zl^]eve«om^:gVy5Y[gJšl‘—–’‘’j kV«Äxl^]gJxl–’qRy5¨B«'gJz[x°–’‘’˜V^]z[^]eveagJom^@xl^:y‘”x[gVšl–’^&w[ofqJwF^]ofjm‘’^]eaqs•om^]˜V^]ovef‘’šl–’^0of^¤

yqJzR™FuJh[ovgVšl–’^„zl^jveœLÅFofqJ\Æg&w[ofgJyjf‘’y]gs–wFqV‘”z}j!qs•H˜R‘’^“ÇYlq“)^˜V^:ojfY[^y5YlqV‘”y^qs•¢gw[gJomjf‘’y]hl–’gJo!\%qlxl^–

©UnD^jfof‘Hzl^jve«Äef^–—•Ÿ\%qRx[‘Õ›kR‘”zluq}oLefjfovgsjf‘Ù†^:x±nD^jvom‘Hzl^]jfe]«Pof^]yqJzR™FuJh[ovgVšl–’^zl^]jfe0œ—œ’œÈ¯>xl^:w†^:z[x[e6efjfofqJzluJ–—k

q}zjvYl^z[gVjfh[of^6qs•DjfYl^w[ofqJš[–—^:\jmq&šF^\0qlxl^]–—‘’¦^:xĜ

ɸÊ}ËPÌvÍÎ ‹Ï ‰VŽ b!^:yq}zR™†uJh†ofgJšl–—^aÐL^]jfe]«[xlklz[gV\%‘”yžy5Y†gVzluJ^]e]«[ºP»:º†¼.«lÑ£qJov¨J½†q“Ò¾}klefjm^:\%e]«lªqJh[z†xl^]xR¤

z[^]eve«F¾}^]–ÕӤSÔ>qlxl‘—•›kR‘’zlu&nD^]jfof‘ÄÐL^jve

ÕÓÖÄ×fØSÙ]Ú×Û Ü’ØSÝSÞß

à'á:âäã'åPæ5çUè!å'éêã®ë·ì·í·îtç›ïSéêè5îtì„í·ë·çŸâäì·ðépñ:âäãUâï'æêòPó5étñ:âäîtç ô õäâñîmç'évïöÓçŸâäãSé:÷

øpùFú

éêâäõ”û

ù

çUâäü5÷ýÄéêí·æ5ë·îtõÃþ âäçŸâäãSé:÷ò—ç

ÿ

ùFú éêâäõ”ûŸæ5õäâñîtçSþ í·ãUâäü5÷ëñV÷îtã

Unit´e de recherche INRIA Rennes

(5)

¡0 !" (Ç&-/ 6" 0‚)" 54¸)6"

‰ Ž ОqJh[e)zlq}h[e¢‘”z}jmd]of^]evefqJz[e¢x†gVz[e)y^]jmjm^ždjvh[xl^žgJh&w[ofqJšl–’Z]\%^Lxl^ž–’g\0qlxld]–—‘”evgsjm‘’qJz@^]j¡xl^ž–’g

˜Jd]of‘ÙBygsjf‘—q}z±xl^@emklefjmZ]\%^:eayqJz[y]h[ovom^:zJjveLevh·rt^jvexl^:eay5Y†gVzluJ^]\%^]z}jfeaxlklz[gJ\0‘”ÂRhl^]e]œ6­®^0•›qJov\@gs–’‘’ev\%^

x[^0š[gJem^^:emjay^]–’hl‘Hxl^:eLofd]ef^]gJhRi¸x[^nD^jvom‘<œpzµy^%Â}h[‘ yqJz[y^]ovzl^efqJz±^ilw†om^:efef‘—˜R‘’jmdq}z±emq}h[Y[gV‘—jf^]ovgs‘’j

h†z.\%qlxlZ]–—^„g·kJgJz}j)h[z.\%d]y]gVzl‘”ef\%^„xl^w[of‘”em^6^]z.yq}\@wljm^xl^:ey5Y[gVz[uV^]\%^:zJjvexlklz[gV\%‘”Â}h[^]eÂRhl‘'efqV‘’j

–”g%•›qV‘”e!‘”z}jm^:ofzl^^j!–’qlygs–<œ)nDgJo!gs‘’–’–—^:h[ofe!–—^:eLw[ofqJw[of‘’djmd:e!xl^š†gVef^}jm^]–—–’^]e!–gVy]y^]evef‘’šl‘’–’‘—jfdV«†–’^y]gVovgVyjfZ]of^

šFqJovzldpxh[z[^¡wl–”gVy^V«·–—^)šl–’qRy]gsuJ^V«:–’g˜R‘’˜gVy‘’jmdaxl^]˜Rovgs‘’^]z}j®yqJz}jm‘”zRhl^]ojvom^)xl^]ew[ofqJw[of‘—d]jmd:e®xld:y‘”x[gVšl–’^]e

wFqJh†o„y^jfjm^&y–”gVevef^0d]jm^]z†x[hl^xl^&ofd]ef^]gVhli±x[^&n ^]jfof‘Uœ%¬q}ofxl‘”z[gV‘’of^0–’^@uJgV‘’zµ^]zµjm^:of\%^&x^i[w[of^]evem‘’˜R‘—jfd

ef^jvofgJx[hl‘’jLw[gVožh[zl^%w†^:omjf^^]z±jf^]ov\%^xl^w[ofqJw†om‘’djfdxld]y‘’x†gVšl–’^^jah[z±yq}\@w[omq}\%‘’ežxlqV‘’jjvom^jfofqJhl˜Jd

^:z}jfof^^ilw†om^:efef‘—˜R‘’jmd.^jy]gs–”yhl–”gVšl‘’–’‘—jfdVœ¶¬6gVz†e&h[zl^±djvh[xl^±w[ofd]yd]xl^:zJjf^V«)zlqJh[e@g·˜JqJz[e%‘”zJjvomqlx[h[‘—j&h[zl^

y–’gJefef^>xl^£omd:em^:gVhRi³xl^°nD^jvom‘axl^µY†gVhlj.zl‘—˜J^]gJhÄ«!gVw[wF^–’d]eomd:em^:gVhRi³om^:yq}zR™†uJh†ofgJšl–—^:e«ÂRhl‘6w†^:hl˜V^:zJj

y5Y†gVzluJ^]oDxlklz[gV\%‘”ÂRhl^]\%^]z}jD–’^]h[o¢w†omq}w[om^efjfovh[yjvh[om^^:z@omd]d]yof‘’˜·gJz}j y^]ofjfgs‘”z%xl^–—^:h[oHyq}\@w†q}efgJzJjveœ! ¡^]e

ofd]ef^]gJhRiw†^:hl˜V^:z}jef^]of˜R‘’o"%\0qlxld]–—‘”ef^]o)–—^:ey5Y[gVz[uV^]\%^:zJjve¡x[^6\%qlxl^:e¡q}w†d:ofgVjmqJ‘’of^]e)x[gVz†e¡–’^]eefklemjfZ]\%^]e

x[^jvofg·˜gs‘’–yqRqJwFd]ovgsjf‘Õ!^]j%wl–”h[e&evw†d:y‘—™FÂRhl^]\%^:zJj@x[gJz[e–’^]e@efklemjfZ]\%^]e#±½FqVjfe@xl^.j%$Jy5Yl^]e]œ¹¬agJz[e%–’g

w†omd:em^:zJjf^d]jfh[xl^%qJzµem^@of^]efjfof^‘”zJj–”gefqJh†eay–’gJefef^0x[^]eaomd:em^:gVhRi>of^]yq}zR™†u}h[ofgJšl–’^]e]«Bxl‘’jfe6ofd˜J^]ovem‘”šl–’^]e]«

wFqJh†o–—^:efÂRhl^]–’ey5Y[gJÂ}h[^6ofZuJ–—^6xl^\%qlxl‘—™FygVjm‘’qJz.emjvofh[yjfh[of^–’–’^awF^]hlj]jfof^a•›qJov\0^]–—–’^]\%^:zJj‘”z}˜V^]ovefd^Vœ&žz

jf^–Pomd:em^:gVh&wF^]hlj"jvom^ž˜lhyq}\%\%^ah[zl^žyqJ\@wFqJef‘—jf‘—q}z&^]zy]gVevygJxl^Lxh[zgJhljmq}\%gVjm^ž^j¡xh[zomd:em^:gVh&xl^

nD^]jfof‘Dw†gVovgV\%djvomdJ«B^]jaefqJh†eay^]ofjfgV‘’zl^:ežY}klwFqVjfY[Z]ef^]ež^]efjad:ÂRhl‘—˜gV–—^:zJjh†zµofd]ef^]gJh>xl^%n ^]jfof‘HemjvofgVjm‘—™†dVœ

nHgJogs‘’–—–’^]h†ofejmqJh[jm^]e–—^:ew[ofqJw†om‘’djfd]e\%^]z}jf‘—q}z[zld^:ey‘ä xl^]evevh[eefqJz}jxld:y‘”x[gVšl–’^]ew†q}h[o–’^]eomd:em^:gVhRi

of^]yqJzR™FuJh[ovgVšl–’^]e®omd]˜V^]ovef‘’šl–’^]e]œ'¬h†z0wFqV‘”z}j xl^˜lhl^w[ovgsjm‘”ÂRhl^¡y^]wF^]z[x†gVz}j y'^:emjD–”gLz[gVjfh[of^w[gVofjm‘”yhl–’‘’Z]of^

x[^)y5Y[gJÂRhl^pw[ofqJšl–’Z]\%^)Â}h[‘Rx[djm^:of\%‘”zl^)–—^y5YlqV‘—i„xh†z0\%qlxlZ–’^¡w†gVofjm‘”yhl–’‘—^:op©<omd:em^:gVhRixl^¡nD^jfof‘<«somd:em^:gVhRi

gJhljmq}\%qRx[‘ÙFgJz}jfe)qJh¸efjfovgsjm‘—™†^:e«[ofd]ef^]gJhRiom^:yq}zR™†uJh†ofgJšl–—^:eLœ’œ’œä¯5œ

( Î Š:‰ Ì ') Ž b!d:em^:gVhRi±of^]yq}zR™†u}h[ofgJšl–’^]e]«[y5Y[gVzluJ^]\%^]z}jve!xlklz[gV\%‘”ÂRhl^]e]«PºP»:º[¼¸«PemklefjmZ:\0^:e@½FqVjLxl^

j*$Vy5Yl^:e«[y]gVovgVyjmZ]of^žšFqJovzldJ«[omd:em^:gVhRixl^„nD^]jfof‘®gVhljfqJ\%qlxl‘—™FgVz}jfe

(6)

' (

" &-¸p"

 zom^:y^:zJj)kV^:gVove¡\@gJzJkefjfh†xl‘—^:eY[g·˜V^ayqJz†em‘”xl^]of^]xh[em‘”zlu%nD^jfof‘'zl^]jfe¡•›qJo\%qlxl^–’–—‘”zlu)$+*,!-./#%*,0

*!-213$42*. !5 6)78 9@© ºB»:º†¼¯/:Ã_%;R«†€%<Sœ¡XY[^]ef^6gJw[wl–’‘’y]gsjf‘—q}z[e«Fgs–”emq@ygV–—–’^]x3= %*>? LgVw[wl–’‘”yg¤

jf‘—q}z[e]«ByqJz[y^]ovz±xl‘’efjfof‘”š[hljm^:x>gVyjm‘’˜R‘—jf‘—^:eœLXY[^k¸‘’z}˜JqV–’˜V^efkRefjm^:\@e!qs•pgVuV^:zJjve©<yqJ\@w[h[jm^]oaefkRefjm^:\@e!qJo

YRh[\@gJz[eꯓ!Yl‘’y5Y±yqRqJwF^]ovgsjm^„“‘’jfY[‘’z>gJz±Yl^jf^]ofqVuJ^]zl^]qJh[egJz[x¸uV^]qVuJovgVw†Yl‘’y]gs–’–—kx[‘’efjfof‘’š†hljm^:x±^]z}˜R‘’ofqJzl¤

\%^:zJj]œ!XYl^ef‘’\@wl–’^]efj!‘”z[efjfgVz†y^]eLqs•¢yqRq}w†^:ofgVjm‘’˜V^6“¡q}of¨gVof^„jfYl^78 9A@B>DC)EFG.,!H#%!&5œ

XY[^]ef^žefkRefjm^:\@e)evh[w[wFqJofjpjvYl^6om^:gs–’‘—¦:gsjm‘’qJzqs•®“)qJov¨0w†omqly^:x[h[of^]e)š}k%u}omq}h[w[epqs•yqV–’–’gJš†q}ofgVjm‘”zlugsuJ^]z}jfe

š}kyqRqJovxl‘’z†gsjm‘”zlu%jfYl^6½Fq“+qs•DjfgJef¨Re)“‘’jfYl‘”z¸jfYl^„xl‘”efjfof‘’š[h[jm^]x¸efklemjf^]\.œ

XYl^xl^:em‘’uJz„qV•PºP»]º†¼ efklemjf^]\@eovgs‘”ef^]e®efqJ\%^¡‘’\@wFqJofjfgVz}j \0qlxl^]–—–’‘”zluž‘”evefhl^:e®–’‘”¨s^¡x[kRz†gV\%‘’y¡y5Y[gVz[uV^]e

qV•¢gVyjf‘—˜R‘’jm‘’^]e]«FjvgVev¨\%‘’uJovgsjf‘—q}zÄ«Fevh[wF^]of‘’\@wFqJef‘—jf‘—q}z¸qs•pxl‘—²B^:om^:z}j!–—^]˜V^]–’eLqs•pgVyjm‘’˜R‘—jf‘—^:eLgVz†x¸jfYl^%zlqVjf‘—q}z

qV•'\hl–’jm‘”wl–’^LqJwF^]ovgsjf‘’z[u\%qRx[^]e]œ XYl^žnD^jfof‘Pzl^jp•›qJov\%gV–—‘”ev\xlqR^]e¡zlqVj¡qs²P^]o¡gxl‘”om^:yjp“g·kjfqgVx†x[om^:efe

jvYl^]ef^•›^:gsjvh[om^:eLgJz[x¸•›qJoLjfY[gVjžof^]gJemq}z.\%qlxl^]–—–’‘’z[ugVz}k¸om^:gs–’‘’efjm‘”y0ºP»:º[¼efklemjf^]\§xl‘”om^:yjm–’k¸“‘—jvY±nD^jvom‘

z[^j\@g·k°šF^g¸xl‘JIy]hl–—jjfgVev¨K



j„‘’ejfYl^:om^•›qJof^%jf^]\@wljf‘’zlu°jmq¸‘’z}jvomqlx[h[y^&^iljm^:z[ef‘—q}z[e6qs•nD^jfof‘pzl^]jfe

^:efwF^]y‘’gV–—–’k¹xl^]ef‘—u}zl^]x¥efq°gJejmq£gs–’–—q“•›qJo0gVz¥^:gVefk°•›q}of\@gV–—‘’¦]gVjm‘’qJz£qs•Levh[y5Y¹qJo0efh†y5Y£•›^]gsjvh[of^Vœ°XYl^

u}gs‘”z%‘’z@jf^]ov\qV•P\%qlxl^–’–’‘’zlu0w†q“)^]oH‘”e¢h[evh[gV–—–’k%w†gs‘”x%š}k@g6–—q}efe¢qs•'xl^]y‘’x†gVšl–’^!w[ofqJwF^]ofjm‘’^]e]œ  jvofgJxl^¤Sqs²

z[^^]x†ejmqšF^6•›qJh[z[x.šF^j “)^^]z.^ilw†om^:efef‘—˜R‘’j kgVz[x.yq}\@w[hljfgJšl‘’–—‘’j kVœ

 zµjfYl‘”e6w[gVwF^]oa“)^0gJx[x[of^]eveLjvYl^0‘”evefhl^:eaqs•LGE1F.MMJ &gJz[xN6. OP2!Q ¸qs•¡yqJz[y]h[ovom^:zJjžemklefjm^]\@e

evh[šRrt^:yjjmqx[kRz†gV\%‘’y6y5Y[gJzluV^:eœ

že„gs–”om^:gVxlk¸\%^]z}jm‘’qJz[z[^]xÄ«'\@gV¨}‘”zlu¸yqJz†yh[ovom^:z}jLemklefjm^:\%e6gJx[gVwljvgVšl–’^jfq.y5Y†gVzluJ^]ež‘’eaqJz[^0qV•pjfYl^

\@gV‘’z¸y5Y[gV–—–’^]zluJ^„‘’z>ºP»:º[¼efklemjf^]\@e!xl^:em‘’uJzĜ j!‘”e‘’\@wFqJofjfgJzJjjvY[gsjLjfYl^\%^:y5Y[gVzl‘”ev\•›qJoLy5Y[gVzluJ^š†^

^i[wl–—‘”y‘’jm–’kof^]w[of^]ef^]z}jf^]x„‘”z}jmq6jfYl^\%qlxl^–[efqajfY[gVjDgVjD^]gVy5Y0emjvgsuJ^¡qV•Fw[ofqRx†h[yjHxl^]˜V^–’qJw†\0^:z}j«sxl^:em‘’uJzl^:ofe

y]gVz.^i[wF^]of‘’\%^:zJjjvYl^^²B^:yj!qV•Hefjfovh[yjfh[ovgs–®y5Y†gVzluJ^]e]«l^Vœu†œšJk.h[ef‘’zluw†omqJjmqVj klwF^]e]œ¡XYl‘”eL\%^:gVz[ejvY[gsj

efjfovh[yjfh[ovgs–ly5Y[gJzluV^:egJom^)jfgJ¨s^]z‘’z}jfqagJyyq}h[z}j®•ŸofqJ\3jvYl^˜V^:omkšF^uJ‘’zl‘”zluaqs•BjfYl^xl^:em‘’uJz%w[ofqRy^]eveovgsjvYl^]o

jvY[gVz°Y[gVz[x[–—^:x°š}k±gVz±^iRjf^]ovz[gs– gVz[x°uV–’qJš[gV–efklemjf^]\.«P^Vœu†œ6emq}\0^^i[y^:wljm‘’qJz>Y†gVz[xl–’‘”zlu\%^]y5Y†gVzl‘”ef\.«

x[^]ef‘—u}zl^]x.gVz[x¸gJx[xl^]x.jfq%jvYl^\%qlxl^–xl^]evyof‘’š[‘’zlu%jfY[^emklefjm^:\ zlqJov\@gs–'šF^]Y[g·˜R‘’qJh[o]œ¢XYRh[e“)^6•Ÿg·˜VqJh†o

gJzR "!-.SMsgVz†xT .G"!-Mq˜V^:oHgVz3VU=!-MsgJz[xR" W.Oxl^:efy]om‘”wljm‘’qJz%qV•Äy5Y†gVzluJ^]e]«VgVz[x&gXMYE2M

q˜J^]oHg=MZF[VMVY[gJz[xl–’‘’zluqs•'y5Y[gVz[uV^]e]œXY[‘’e¡gVw[w[ofqJgJy5Y‘”epyqJ\@w[gVjm‘”šl–—^L“‘—jvY@jfYl^LšFqVjfjmq}\¤ h[w\%qlx[hl–”gVo

efklz}jfYl^:em‘”eqV•LnD^jvom‘zl^jve%“!Yl^]of^g£yq}\%w[–—^i¥efklemjf^]\‘”e%x[^]of‘—˜J^]x¹•ŸofqJ\ evh[yy^]evem‘’˜V^.om^™Fzl^]\%^:zJjveqV•

w[–’gJy^]eq}o)jfovgVz[ef‘—jf‘—q}z[eš}kevh[šR¤ emklefjm^]\@e]œ

\¢gV–’¨ †ef^–—•Ó¤S\%qlxl‘—•›kR‘’zluz[^jfe:Ã_%]R«'_E^<®‘’egJz.^]gVof–’kgsjfjm^]\@wljqV•DgJz.^iljm^:z[em‘’qJzqs•DnD^jvom‘®z[^j!\%qlxl^–

“‘’jfY0gLš[h[‘—–’jt¤S‘’z%\%^]y5Y[gJzl‘”ef\O•›qJo Y[gJz[xl–’‘’zluay5Y[gVz[uV^]e]œ j ‘’eD\%qJof^q˜J^]o'ÂRhl‘’jm^gLz†gsjfh†ofgV–JuJ^]zl^:ofgV–—‘’¦]gVjm‘’qJz

qV•BnD^]jfof‘[zl^jveœ z@yq}zJjvofgJemj “‘’jfY@nD^jvom‘[zl^]j«}jfYl^!w†om^¤SyqJz[xl‘’jm‘’qJz%gVz†x0wFqJefjt¤ yq}z[xl‘’jm‘’qJz0qs•Äg6jfovgVz[ef‘—jf‘—q}z

_

gJom^!zlqJj¢uV‘’˜V^:z@gVeH˜J^]yjfqJoveHš[hlj)gVe¢\@gsjvom‘”y^:eH`

_ab_

`dc=egfeihkjl„œHXovgVz†em‘’jm‘’qJz

_

‘’epjfYl^:z@^]z[gJšl–’^]x@‘”z

\@gJof¨}‘”zlu8monTjlLp´‘—• gJz[xq}zl–—k‘Õ•›qJo)^]gJy5Ywl–”gVy^Pq,r jvYl^„yqJz†xl‘—jf‘—q}zsmutJq,r&vPwDxzy ` _ t{qr

aq y v mut{q

y v

‘”e„evgsjm‘”em™†^]xĜ%Ñ¿Yl^:zµ^:z[gVš[–—^:x°jvYl‘’e6jvofgJz[ef‘—jf‘—q}z°ygJz>™Bom^&gVz†xµw[ofqlx[h[y^%jvYl^&zl^“ \@gVov¨J‘”zlu3mi|Hefh†y5Y

jvY[gsj$mi|5t{q rv?}~mut{q rv x y ` _ t{q r aq y

vbmutJq

y

v%€ x y _ ` t{q r aq y vbmutJq

y

v5«JjfY[gVj‘”eDjmq6evg·kmi|,}Ddt

_

v=‚ƒm

“!Y[^]of^¡jvYl^/!5 ƒW.![\%gVjfof‘Ãi¹‘”eDuV‘’˜V^:zš}kdt{q r aq y v?}D„ rƒ…

y  ` _

t{q r aq y

_ ` t{q r aq y

v “‘—jvY„ rƒ…

y

}‡†)‘—•

ˆ }Š‰&gJz[xR„

y

}~‹%‘Õ ˆŒ}‰†œHXYl^z[qVjm‘’qJzqs•Demklefjm^]\@eqV• of^]wl–”gVy^]\%^]z}j2Žs\hl–’jm‘”wl–’‘’y]gsjf‘—q}zqs•D\@gsjfof‘”y^]e

jvgV¨V^]eHjvYl^Lwl–”gVy^!qs•ÄjfY[^LzlqVjf‘—q}z@qs•'efkRefjm^:\@eHqs•'of^]wl–”gVy^]\%^]z}j2ŽsgVx[x[‘—jf‘—q}z0qV•Ä˜V^]yjmq}ofeDjvY[gsjpy5Y†gVovgVyjf^]of‘—¦]^

nD^]jfof‘'zl^jveœ

&aefh[gV–—–’k½Fq“+om^]–’gVjm‘’qJz[ex[^]wF^]z[x[e!qJzl–’kh[wFqJz¸g%–—‘”\%‘—jf^]x¸zRh[\šF^]oqV•Dw[–’gJy^]ejvY[gsj“)^„efY†gs–’–Äjm^]ov\

2"!Q M*,MY=25œ%XYl^%yqJz}jm^:z}jžqV•pjfYl^:em^@wl–”gVy^]ea‘’z°jfh[ovz°gJom^@g²P^]yjm^:x>qJz[–—k>š}k±y^:omjvgs‘”z>jfovgVz†em‘’jm‘’qJz[e

(7)

jf^]ov\%^]xŠ2 AWX2EO V!Q ¸šJk±yqJz}jfovgVefj!jmq.jfY[^0qJjfYl^:o8 1 SjvofgJz[ef‘—jf‘—q}z[eœaÑ ‘’jfY>^]˜V^:omk

\@gJof¨}‘”zlu8m‚‘”egVevemqly‘’gVjm^]xgnD^jvom‘Äzl^]j } te aLa ` t5v

a t5v `

v¡qJšljvgs‘”zl^]xš}k&^˜gs–”h[gsjf‘—q}z&qs• jfYl^

½Fq“ of^–”gsjf‘—q}z[e„‘”z´\@gVov¨J‘”zlu m

` _ t{qrQv}

` _ t{qr a LvP‚Fm gVz[x

` _ t{q,r&v}

` _ t{q,r a LvP‚m œ¸XY[‘’e

nD^]jfof‘Pz[^j ‘”e)jfYl^ 24O= !Q @qV•®jfYl^„ef^–—•Ó¤S\%qlxl‘—•›kR‘’zlu&zl^]j$‘”z\@gVov¨}‘’z[u8m œ¢Le)–’qJzlu@gVezlq

yqJz}jfofqV–Bwl–”gVy^:epgJom^a\0qlxl‘—™†^:x&jfYl^6ef^–—•Ó¤S\%qlxl‘—•›k}‘”zlu%zl^jš†^:Y[g·˜V^:epgJep‘’jfe)yh[ovof^]z}jpyq}zR™†u}h[ofgVjm‘’qJzĜ¢¾}^]–ÕӤ

\%qlxl‘—•›kR‘’zlu0zl^jve¡gJom^!jvYl^]of^•›q}om^“)^–’–FgJx[gVw[jm^]x%•›q}opef‘—jvh[gsjf‘—q}z[e¢‘”z&“!Yl‘”y5Yef^˜J^]ovgs–[\%qlxl^]e¡qs•ÄqJwF^]ovgsjf‘—q}z

yqR^il‘’efjœ

že‘”z[xl‘”ygVjm^:x‘”z„ÅD‘—uFœ}_¡nD^jfof‘Rzl^j “‘—jvY‘”z[Yl‘”šl‘’jmqJoveDgVovyeygVzš†^)‘’\@wl–’^]\%^:zJjf^]x0šJk„ef^–—•Ó¤S\%qlxl‘—•›kR‘’zlu

z[^jfe]œXY[‘’eP•›q}of\@gV–—‘”ef\¿‘’e®jfYRh[e'X h[of‘’zlu!wFq“)^]om•Ÿhl–sgVz[x6jvYl^]of^H‘”e'zlq!Ylq}w†^Hjfq!qJšljvgs‘”zauV^]z[^]ovgs–sgVh[jmqJ\@gVjm‘”y

˜J^]of‘ÙBygsjf‘—q}z¶jfqRqV–”e@•›qJo&jvYl^±•Ÿhl–’–6y–”gVeve&qs•„em^]–ÕӤ \%qlxl‘Õ›kR‘”zlu¶zl^]jfe]œOÔ°qJof^q˜V^:o%‘—jef^^:\@exl‘ZIyhl–’jjmq

™Bz[x£‘’z}jm^:om^:emjf‘’z[u>efh[šl¤Sy–’gJefef^]eaqs•!ef^–—•Ó¤S\%qlxl‘—•›kR‘’zlu>z[^jfe“‘—jvY¥xl^]y‘’x[gJšl–’^w[omq}w†^:omjf‘—^:e@©UšFqJh[z†xl^]x[z[^]eve«

–’‘’˜V^]z[^]eve«Hof^]gVy5Y†gVšl‘’–—‘’j kV«œ’œ—œÈ¯3^i[y^]w[j•›qJo2!/MW20-GE1 W2 S.!5 :Ã_%]4<“!Yl^]of^gV–—–w[of^]yq}z[xl‘’jm‘’qJz[e

gJom^yqJz[efjfgJz}jœ z[xl^^:xÄ«D¬ahl•›qJh[ovx¹^j%gs–<œ :—_]~<)w[ofq˜V^@jfY†gsj0šFqJh†z[xl^]x†zl^]eve‘”egs–”of^]gVx[kµh[z[x[^]y‘”x[gJšl–—^

•›q}onD^]jfof‘)zl^]jfe0“‘—jvYg ..! :—_.<S«H“!Yl‘”y5Y¥‘”e0gµem‘”\@wl–—^.ygJem^qs•Lef^–—•Ó¤S\%qlxl‘—™FygVjm‘’qJz ©<em^]^ÅD‘—uFœ¡_¯êœ

žzlqVjvYl^]o&ef‘”\%w[–—^±ygJem^¸qV•aef^–—•Ó¤S\%qlxl‘—™FygVjm‘’qJzÀ‘’eof^–”gsjf^]x¶jmq¥jfovgVz†et•›^:omj@gVovyeT:ä|4<Sœ z :—_]~%<ž¬ahR•›q}h[ovx

^]j„gs–<œ@w†omq˜J^0jvY[gsj„wl–”gVy^¤ š†q}h[z[xl^:x[zl^]eve6‘”e„h[z[xl^:y‘”x[gVšl–’^%•›qJo6nD^jvom‘¢z[^jfe“‘—jvYµjvofgJz[em•›^]ofjagJofy]ež^]˜V^:z

jvYlqJh[uJY¹š†q}h[z[xl^:x[zl^:efe‘’e0xl^]y‘’x[gJšl–’^&•›qJo„jvY[gsj0y–”gVeveœLq“)^˜J^]o]«®‘”z¹qJovxl^]o„jfq±–—^:efef^]z¹q}h[ow[of^˜R‘’qJh[e

gJefef^]ofjm‘’qJz'«]q}zl^pevYlqJhl–”x\%^]z}jf‘—q}z„jfY[gVj ¡q˜J^]ovgVšl‘’–—‘’j kžgJz[xX^]ov\%‘’z[gVjm‘’qJz6“!Yl‘”y5YgJom^pšFqVjvYh[z[x[^]y‘”x[gJšl–—^

w†omq}w†^:omjf‘—^:e6qs•!em^]–ÕӤ \%qlxl‘Õ›kR‘”zlu>zl^]jfegJom^&xl^:y‘”x[gVš[–—^šFqVjvY£•›qJo„nD^jvom‘)zl^jve„“‘’jfY¥of^]ef^jgVovye„gJz[xµ•›qJo

nD^]jfof‘'zl^jve“‘—jvY.jfovgVz[em•›^]ofjgVovye]œ

!"$#%'&(

)+*-,.*0/12435,

!6"$#%'&(

798;:;<>=;<?/4@A2B12435,

CD!E6"GF%H&I"GF4%;JK"$#%

LM241C8N,9OP*52./12435,

Q4R

R S R

S R R S T

R # #

S S

R T

S

R

ÅD‘—u}h[of^%_;H‘’\@wl–’^]\%^:zJjvgsjf‘—q}zqV• ‘”z[Yl‘”šl‘’jmqJo]«[of^]ef^j«[gJz[x.jfovgVz[em•›^]ofjgVovye)‘”z.ef^–—•Ó¤ \0qlxl‘—•›kR‘’z[u@z[^jfe

XYl^:om^H‘”e'Ylq“)^˜J^]oÄg)uJgJw6š†^]j “¡^]^]za“!Y[gsj®‘’eÄjvYl^q}om^]jm‘”ygV–—–’k!^i[w[of^]evef‘’šl–’^D‘’z6jf^]ov\@eÄqs•lem^]–ÕӤ \%qlxl‘Õ›kR‘”zlu

nD^]jfof‘Dz[^jfe„gJz[xµjfYl^&\@gVz[z[^]oa‘’zµ“!Yl‘”y5Y>“)^@‘’z}jm^:z[xµjmq¸h[em^@jvYl‘’e„\%qlxl^]–D•›qJo6\%qRx[^–’–—‘”zlu¸yqJz†yh[ovom^:z}j

efklemjf^]\@eagVx[gJwljfgJšl–—^jmqy5Y†gVzluJ‘’zluem‘’jfh[gVjm‘’qJz[e]œp˜V^]z°jfYlq}hluJY>jfYl^%h[em^%qs•pof^]ef^jagVovyežgVz[x±jvofgJz[em•›^]ofj

gJofy]egJom‘”em^:eÂRhl‘’jm^¸z[gsjvh[ovgs–’–—k£‘’z¶jfY[gVj%yqJz}jm^ilj‘’j0‘”e0wFqJevef‘’šl–’^gJe“)^evY[gV–—–em^]^evYlqJofjm–’k¹jmqµqJšljvgs‘”z

\0h[y5Y±\%qJof^jfovgVyjfgJšl–—^0\0qlxl^]–’eL“‘—jvY±˜V^:omk¸ef‘’\%‘’–’gJo•›^]gVjfh[of^]e]œ!Leaefjfgsjf^]x±gJš†q˜J^V«†“)^‘”z}jm^:z[x±jmqh[em^

ef^–—•Ó¤ \0qlxl‘—•›kR‘’z[u£zl^]jfe%•›q}o%\%qlxl^]–—–’‘’z[u£g£emklefjm^:\ yqJz†em‘”emjf‘’z[uµqV•žgµš†h[z[y5YÀqs•LnD^jvom‘!z[^jfe]«¡y]gs–’–—^:x´‘’jfe

2EO= !5 †«pjfqVuJ^jfY[^]o%“‘—jvY³emq}\0^¸\%^]y5Y[gJzl‘”ef\ ©<h[ef‘’zlu¹jvYl^±emqV¤Sy]gs–’–—^:x¶yq}z}jfofqV–wl–’gJy^:e&gVz[xÀjfYl^

y5Y†gVzluJ^]ežqs•¡yqJzR™†u}h[ovgsjm‘’qJzB¯gs–’–’q“‘’zlujfYl^&efklemjf^]\§jmq¸^]˜VqV–’˜V^•Ÿomq}\§qJzl^@yq}zR™†u}h[ofgVjm‘’qJz±jfq.gJzlqVjvYl^]o

q}zl^žh†z[xl^]o)y^:omjvgs‘”z&y‘”ofy]h[\@emjvgVz[y^]e]œ zqJovxl^]opjmq™†jp‘”z\%qJof^Lefjfovgs‘’uJY}jt•›q}om“gVovxl–’k“‘’jfYjvYl‘”e)\@gJz[zl^]o

qV•Fxl^:efy]om‘”šl‘”zluLevh[y5Yefklemjf^]\@e®“)^)‘’z}jfofqlx[h[y^pjfY[^)\%qlxl^–RqV•VU+!&X!& V"!Q MMYV1 !5 l!5D©9W'ºYX[Z

‘”z¥evYlqJofjê¯5œ¸žz\W'ºMXHZ ‘’e0g>w[gJofgJ\0^]jfof‘’y%•ŸgJ\%‘—–’kµqV•n ^]jfof‘¡zl^]jfe]«D“!Yl‘’y5Y¥\%^:gVz[e0g±nD^jfof‘¡z[^j“!Y[qJef^

(8)

½Fq“3gJofy6‘”z[evyof‘’w[jm‘’qJz[ežgVof^–—‘”zl^:gVo•Ÿh[z†yjm‘’qJz†eLqV•py^]ofjfgV‘’z¸w[gJofgJ\%^jm^:ofe]«†jfqVuJ^jfY[^]o“‘’jfY>efqJ\%^yqJz}jfofqV–

uJ‘—˜J^]zšJkg™Bzl‘—jf^„gVhljfqJ\@gsjfqJz“!YlqJef^aefjfgVjm^:exl^jf^]ov\0‘”zl^6jfY[^6y]h[ovom^:zJj˜gs–”hl^:e¡qV• jvYl^]ef^„w[gVovgV\%^]jm^]ove]œ



jž‘’ežjfY[^]of^•›qJof^jvYl^0y]gVevygVx[^]x±yq}\@w†q}em‘’jm‘’qJz¹©UqJoLef^]\%‘Dxl‘”om^:yjLw[ofqlx[h[yjê¯!qs•¢g>©<yqJz}jvomqJ–Ó¯gJhljmq}\@gsjmq}z

“‘’jfY.g%w[gVovgV\%^jvom‘”yžn ^]jfof‘Äzl^j]œ  zjvY[gsjof^]evw†^:yj‘—j‘”eÂ}h[‘—jf^6ef‘”\0‘’–”gVo)jmq&g\H^]yjfqJožx[xl‘’jm‘’qJz±¾}klemjf^]\

“‘’jfY´¾}jvgsjf^]e&© W»:»]¯ž“!Yl‘”y5Y£‘’e„g±x[‘’of^]yj6w†omqlx[h[yj„qs•gVz¹gVhljfqJ\@gsjfqJzµ“‘—jvY¹gnD^]jfof‘pzl^j]œ&ѵ^evY[gV–—–

‘”z[xl^]^]x¹šF^gVšl–’^@jmq>gJefefqly‘”gsjm^@^:gVy5Y WĺMXHZÀ“‘’jfY¥efqJ\%^@“¡^:gV¨}–’k>^]ÂRhl‘’˜gs–’^]z}j W»:»œXYl‘’ezlqVjf‘—q}zµqV•

“)^]gJ¨%^]ÂRhl‘’˜·gV–—^:z[y^6‘”e)^]zlq}hluJYjmq@^]z[evh[of^žjvY[gsjšFqVjvY\%qlxl^–”egVof^a^]ÂRhl‘’˜·gV–—^:z}j¡“‘’jfY.om^:efwF^]yjjmq&emq}\%^

•Ÿh†z[x[gV\%^:zJjvgs–¢w[ofqJwF^]ofjm‘’^]e6gJe6n¢–’gJy^@ªqJh[z†xl^]x[z[^]eve«Äb!^:gVy5Y[gJšl‘’–—‘’j kV«'gJz[x°­‘—˜J^]zl^:efe]œ¾}‘’z†y^&gs–’–HjfYl^:em^

w†omq}w†^:omjf‘—^:e)gJom^„xl^:y‘”x[gVš[–—^a•›qJo;W»]»6jfYl^]kgVof^6gs–”emq&xl^:y‘”x[gVšl–’^a•›qJoW'ºMXHZDœ

¢˜J^]z¥jvYlqJh[uJY\W'ºMXHZ Y[g·˜J^g>xl^™Fzl‘’jm^¸gVxl˜gJzJjvgsuJ^&q˜V^]ojfYl^.em^]–ÕӤ \%qRx[‘Õ›kR‘”zluµzl^]jfe0‘’z´jm^]ov\@eqV•

6MJ 1=!Q qs• w†omq}w†^:omjf‘—^:epjvYl^kY†g·˜V^6em^:om‘’qJh[e)x[ovg·“!š[gVy5¨Re¢•Ÿomq}\ gG41=MM{ „efjfgJz[x[wFqV‘”z}jœ¢Lyjfh[gV–—–’k

jvYl^žY†gVz[xl–’‘”zluqV•y5Y[gVz[uV^]e¢qs•yqJzR™†u}h[ovgsjm‘’qJz†eH‘’e)xl^:efy]om‘”š†^:x&uV–’qJš†gs–’–—k@gVz[x^iljm^:ofz[gV–—–’k&š}k%jvYl^žyqJz}jfofqV–

gJhljmq}\@gsjmq}z.“!Yl^]of^„qJz¸jvYl^0yqJz}jfovgVofk‘’j!“)gJeuV‘’˜V^:z.–—qlygV–—–’k¸gVz[x.‘”zJjf^]ovz[gs–’–’k‘”z±em^]–ÕӤ \%qlxl‘Õ›kR‘”zluzl^]jfe

“!Y[^]of^6yqJz}jfofqV–Äwl–”gVy^]egVz†xy5Y[gJzluV^:e)qs• yqJzR™FuJh[ovgsjf‘—q}z[ea©Ÿ“!Yl‘”y5YgJom^„of^]evw†^:yjf‘—˜J^–’kwl–’gJy^:egVz[xjfovgVzR¤

ef‘’jm‘’qJz[e%qs•žjfYl^±efkRefjm^:\¯gJom^¸h[ef^]xĜ¶XY[‘’e@\%^]gJz[e%jfY[gVj@\%qlxl^]–—–’‘’z[uµ“‘’jfY W'ºYX[Z¿ygJz[zlqJj%gV–—–’q“ •›qJo

jvYl^\%qlx[hl–”gVo0š†qJjmjmq}\0¤Sh[w¶emklz}jfYl^:em‘”e„jf^]y5Y[zl‘”ÂRhl^Vœ>XY[‘’e%\%qRx[^–p“‘’–’–¡jvYl^]of^•›q}om^šF^‘”z[gVx[^]ÂRh[gsjf^@•›qJo

\%qlxl^]–—–’‘’z[u–’gJomuJ^„emklefjm^]\@e]«Bš†hljL\@g·k.šF^h[ef^]x±gJeLg&jvgVofuV^]j•›qJov\%gV–—‘”ev\ qJz¸“!Y[‘’y5Y¸˜J^]of‘ÙFy]gsjf‘—q}z.\@g·k

šF^wF^]om•›qJov\0^:xĜ¢XYl‘”e!ef‘—jvh[gsjf‘—q}z‘”eÂRhl‘’jm^ef‘’\%‘’–’gJojmq&nD^jvom‘®z[^jfe!“!Yl^]of^„g@n ^]jfof‘®zl^]j‘’eh[ef^]x•›q}ojfYl^

\%qlx[hl–”gVo)efkRz}jvYl^]ef‘’e)qV•g0yqJz[y]h[ovom^:zJj¡emklefjm^]\ “!Y[‘—–’^6˜V^]of‘—™FygVjm‘’qJz@‘”e)wF^]om•›qJov\%^]xqJz‘’jfeefjfgVjm^auJovgVw[YĜ

 z¸q}ofxl^:ojmq&q}šljfgV‘’z¸g%–—qly]gs–®xl^:efy]om‘”wljf‘—q}zqV• jvYl^y5Y[gJzluV^:eqs•HyqJzl™†uJh[ovgsjf‘—q}z[eqJz[^\%g·kyqJz†em‘”xl^]o

\%qlxl^]–—–’‘’z[uLjfY[^)yqJz}jfofqV–}gVhljfqJ\@gsjfqJz6‘’jfef^–—•FgVe g©<efg·k6qJz[^¤ efgs•›^·¯BnD^jvom‘lzl^]j®jvY}h†eq}šljfgV‘’z[‘’zluag!j “)qs¤S–—^]˜V^]–

efjfovgsjf‘ÙF^]x¸nD^jvom‘ zl^j]œž¾}jfovgsjf‘Ù†^:x¸nD^jfof‘z[^jfe: < gJom^ef^–—•Ó¤S\%qlxl‘—•›kR‘’zluzl^jve!“!Ylq}em^w[–’gJy^]e$q

aa q

\@g·k>šF^@uV‘’˜V^]z°‘’z£gVz°qJovxl^]o6evh[y5Y>jvY[gsj6jvYl^%½†q“of^–”gsjm‘’qJz°‘’z†efy]om‘”wljm‘’qJz†ežqV•¡jvYl^&gVovye6yq}z[zl^]yjm^:x>jmq

w[–’gJy^ q,rD‘”z}˜VqV–’˜V^aqJz[–—kjfYl^wl–”gVy^]e q y

©Y‰ ˆ¯¡“!Y[‘’y5Y.gVw[wF^]gJoemjvom‘”yjf–—k.š†^•›qJof^ q,rtœ¡XYl‘’e\%^:gVz[ejvY[gsj

jvYl^jvofgJz[et•›^:omj\@gsjvom‘—iqV•Dg&efjfovgsjf‘ÙF^]x.nD^jfof‘z[^j‘”eLg@–’q“¡^:o¡jvom‘”gVz[uJhl–”gVo\@gsjvom‘—i“‘’jfY£_yq}^Iy‘’^]z}jfe

q}z¸jfYl^0xl‘’gVuVq}z[gs–<œ emjvofgVjm‘—™†^]x¸nD^]jfof‘zl^]jžygJz±š†^˜}‘’^“)^]x±gJe!jvYl^ygJefy]gVxl^:x¸yqJ\@wFqJef‘—jf‘—q}z¸qs•HnD^jvom‘

z[^jfe]Á®gJz[x°gJyjfh†gs–’–—k±jvYl^&\%gJof¨}‘”zluu}ofgJw[Y±qV•¡gefjfovgsjf‘ÙF^]x>nD^]jfof‘Dz[^j6‘’eajvYl^&ygVevygJxl^]x°yqJ\@wFqJef‘—jf‘—q}z

qV•pjfY[^@\@gJof¨}‘”zluu}ofgJw[Y[eaqs•pnD^]jfof‘¢zl^jveœ j6“gVe6evYlq“!z>‘”zŠ: <¢jvY[gsj6emjvofgVjm‘—™†^]xµnD^jvom‘Hzl^]jfe„\@g·k>š†^

efklz}jfYl^:em‘’¦^:x±•ŸofqJ\§jfY[^‘”o„\%gJof¨}‘”zluu}ofgJw[Y°h†em‘”zlu.jfYl^&of^uV‘’qJz>jm^]y5Y†zl‘’ÂRhl^Jœ0žea•ŸgVo6gVea˜V^:om‘—™Fy]gsjm‘’qJz>‘’e

yqJz[y^]ovzl^]x±Y[q“¡^]˜V^]oLemjvofgVjm‘—™†^]x±nD^]jfof‘ zl^]jfeaefhl²B^:o!•ŸofqJ\ÆjfY[^0evgV\%^–’‘’\%‘’jfgVjm‘’qJz[eagVežjfYl^0“!YlqV–’^0y–’gJefe

qV• ef^–—•Ó¤S\%qlxl‘—•›kR‘’zlu&nD^]jfof‘'zl^jveœ

 z±g&w[of^˜R‘’qJh[eefjfh†xlk :]%<®“)^Y[g·˜J^„‘’z}jfofqlx[h[y^]x¸g&y–”gVeveqs•HYl‘’uJY.–—^]˜V^]–'nD^jfof‘z[^jfe]«†y]gs–’–—^:x.of^]yqJzR¤

™FuJh[ovgVšl–’^zl^]jfe]«†jfY†gsjLy]gVz±xlklz[gJ\0‘”ygV–—–’k\%qlxl‘—•›kjvYl^‘”o!q“!z±efjfovh[yjfh[of^š}k.of^“!of‘—jf‘’z[uemq}\0^„qV•HjfYl^]‘’o

yqJ\@wFqJzl^:zJjveœ¡ om^:yq}zR™†uJh†ofgJšl–—^anD^jvom‘®z[^j!‘”e!g@nD^jvom‘ zl^j“‘’jfY¸–’qlygs–emjvofh[yjfh[ovgs–'\%qlxl‘—•›kR‘’zluofhl–’^]e

wF^]om•›qJov\%‘’z[u„jfYl^Lof^]w[–’gJy^]\%^:zJjDqV•Pq}zl^qs•Ä‘’jfe¡efh[š†zl^jvepš}k0gJzlqVjvYl^]o¢evh[š[z[^jœHXYl^LjmqJ¨V^]z[eD‘”z&gxl^]–—^]jm^:x

w[–’gJy^„gVof^6jfovgVz[em•›^]of^]xjmqg@yof^]gVjm^]xqJz[^Vœ¢XYl^:em^„zl^]jfe“)^]of^„h[em^:x•›q}o\%qRx[^–’–—‘”zluxlklz[gJ\0‘”y6y5Y[gVz[uV^]e

“‘’jfY[‘’z¸“)qJov¨J½†q“Oefklemjf^]\@e!gVeL‘’z :—_V_.<<œ j!“gVe!evYlq“!z.jfY†gsjžšFqJh†z[xl^]x†zl^]eveqs•¢gof^]yqJzR™FuJh[ovgVšl–’^„zl^j

y]gVz³šF^>xl^]y‘’xl^:x š}kÀyq}z[efjfovh[yjf‘’zlu¥g¥ef‘’\@wl–’‘—™†^]xÀ•›qJov\ qV•gJofw³gJz[x Ô>‘—–’–’^]oe&yq˜V^]ovgVš[‘—–’‘—j k¥jvom^]^V«

Y[q“¡^]˜V^]o¡jfY[‘’e!yqJz[efjfovh[yjm‘’qJz.xl‘’x¸zlqJj!gs–’–—q“+jmqxl^:y‘”xl^6“!Yl^jvYl^]o!g%uJ‘—˜J^]z.wl–’gJy^6qs• jfYl^0zl^j‘”eš†q}h[zR¤

x[^]xĜLXY[^jm^:y5Y[zl‘”ÂRhl^0h[ef^]x±š}k¸˜gVz±xl^:ožžgs–”emj:;<•›q}o!˜V^:om‘—•›kR‘’z[uemq}h[z[x[zl^:efeLqs•¢“)qJov¨J½†q“Òz[^jfežygJz

šF^%uV^]z[^]ovgs–’‘—¦]^]x±jfqof^]yq}zR™†u}h[ofgJšl–’^zl^jveœ„ÅD‘”z[gs–’–’k>gjfovgVz†em–”gsjf‘—q}z±qs•¡g.of^]yq}zR™†u}h[ofgJšl–’^zl^j6‘”zJjfqgJz

^:ÂRhl‘—˜gV–—^:zJj!ef^–—•Ó¤ \0qlxl‘—•›kR‘’z[uzl^j!“gVeLgs–”emq&w[of^]ef^]z}jm^:xĜ¡XY[^y–”gVeveqs•¢of^]yq}zR™†u}h[ofgJšl–’^azl^]jfeLjfYl^:om^•›qJof^

(9)

gJw[wF^]gVoveHgVeHg„evh[šBy–”gVeveDqs•Äem^]–ÕӤ \%qlxl‘Õ›kR‘”zluzl^]jfeH•›q}oD“!Yl‘”y5Y%šFqJh†z[xl^]x†zl^]eve¢ygJz@š†^!xl^:y‘”xl^]x'œ žq“¡^]˜V^:o

jvYl‘”eLjvofgJz[em–”gsjf‘—q}z¸h[em^:e!•›^:gsjvh[om^:e!–’‘’¨V^of^]ef^jžgJofy]e“!Yl^:om^:gVeLšFqJh†z[xl^]x†zl^]eve!qV•¢jfYl^%y–”gVeve!qs•¢nD^]jfof‘ zl^]jfe

“‘’jfYom^:em^]j¡gVovye¢‘’e)h[z[xl^:y‘”x[gVš[–—^JœDXY[‘’e)efh[uVuV^:emjveHjfY†gsjgem‘”\@wl–’^]o¡jfovgVz[ef–’gVjm‘’qJz@\%‘—u}Y}j¡šF^awFqJevem‘”šl–’^Lgsj

–’^]gJemj)•›q}ow[gVofjm‘”yhl–”gVoevh[šBy–”gVevem^:eqs• of^]yqJzR™FuJh[ovgVšl–’^6zl^jveœ

 z jfY[‘’e&efjfh[x[k´“¡^±of^]efjfof‘’yj0q}h[o@gsjfjm^]z}jf‘—q}z¶jfq£jvYl^±efh†šFy–’gJefe@qV•aof^]yq}zR™†u}h[ofgJšl–’^zl^jve«)jm^:of\%^:x

of^˜J^]ovem‘”šl–’^V«s“!Y[qJef^!emjvofh[yjfh[of^L\%qlxl‘—•›k}‘”zluovhl–’^]e¢gJom^!•›qJov\%gV–—–’k‘”z}˜V^:ofef‘’š[–—^JœXYl‘”epgJefevh[\@wljm‘’qJz@‘”epÂRhl‘’jm^

z†gsjfh†ofgV–¡ef‘’z[y^jfY[^efkRefjm^:\ jvY[gsj0“¡^‘’z}jm^:z[x¥jfqµ\%qlxl^–’‘—¦]^‘”e0evh[w[wFqJef^]x¹jfq°ofh†z¹•›qJof^˜J^]ogJz[x¹jfYRh[e

evYlq}hl–’x z[qVjY[g·˜J^>xl^u}ofgJxl^]x³šF^]Y[g·˜R‘’qJh[o]œ¾Rh[y5Y g´z[^j\@g·k³š†^°˜}‘’^“)^]x gJejvYl^µy]gVevygVx[^]x³yq}\¤

wFqJef‘’jm‘’qJz¸qs•¢gJz±gVhljfqJ\@gsjfqJz¸“‘’jfY±gw[gJofgJ\%^jfof‘”y6n ^]jfof‘ z[^j«B‘<œ^Jœ!gVeLgJz W'ºYX[ZD«†jvY}h†eLªqJh†z[xl^]x†zl^]eve«

bL^]gVy5Y†gVšl‘’–—‘’j k6gVz[x­®‘’˜V^]z[^]evegJom^px[^]y‘”x[gJšl–—^¡•›qJo of^˜V^:ofef‘”šl–—^¡om^:yqJzl™†uJh[ovgVš[–—^¢zl^]jœ ÅD‘’z[gV–—–’kh[z[x[^]oDemq}\%^

gJx[xl‘’jm‘’qJz[gV–lgVevefh[\@wljf‘—q}zgaom^]˜V^:ofef‘’š[–—^)om^:yqJzl™†uJh[ovgVš[–—^pz[^jD‘’eHevYlq“!z^]ÂRhl‘’˜·gV–—^:z}jjfq6gaefjfovgsjm‘—™†^:xnD^jvom‘

z[^jœ

XYl^6of^]\@gs‘”z[xl^:o¢qs•'jvYl^6w[gVwF^]o¡‘’e¡qJofuJgJzl‘’¦^]x&gJeH•›qJ–—–’q“!eœ z.¾R^]yjf‘—q}z;„“)^L‘”z}jfofqlx[h[y^žjfYl^6\%qlxl^–

qV•MU+!&X!&T"!Q MMYV1D.!Q l!H©W'ºMXHZ®¯5œÑ£^¡evYlq“¹jfY†gsjDgVz}k W'ºMXHZ&\@g·k6š†^gVevefqRy‘’gVjm^:xž“‘’jfY

efqJ\%^@“)^]gV¨}–’k±^]ÂRhl‘’˜gs–’^]z}j,2.!-KU+1=1 !5 N#,%!-. > ! #,!-!-0© W»:»:¯agVz[x£jfY†gsjyq}z[ef^]ÂRhl^]z}jf–—k

w[–’gJy^¤ šFqJh[z[x[^]x[zl^:efe]«lom^:gVy5Y[gJšl‘’–—‘’j kV«Rxl^]gJxl–’qRy5¨&gJz[x–—‘’˜V^:zl^]evegVof^axl^:y‘”x[gVš[–—^6w[ofqJwF^]ofjm‘’^]e)qs•WĺMXHZHœ z

¾R^]yjf‘—q}z„{“)^pom^:ygV–—–sjvYl^¡x[^™Fzl‘’jm‘’qJzqs•L224O= =[MZ l!ÄgVz†x„yqJz†em‘”xl^]o®‘—jve®evh[šBy–”gVeve'qs•+.6.2 [MZ

+2VEO F[.MYsl.!5•›q}o“!Yl‘”y5Y g¹•Ÿh[z[x†gV\%^]z}jfgV–aw†omq}w†^:omj kÀ‘’e^]efjfgVš[–—‘”efY[^]xĜ XYl‘”e&•Ÿh†z[x[gV\%^:zJjvgs–

w†omq}w†^:omj k@‘”eh[em^:x‘”z±¾}^]yjm‘’qJz jfq@w†omq˜J^LjfY†gsjjfYl^„\@gVov¨}‘’z[uuJovgVw†Yqs•Dg0of^˜J^]ovem‘”šl–’^žof^]yqJzR™†u}h[ovgVšl–’^

z[^jH‘”e¢^]ÂRhl‘’˜gs–’^]z}jHjmq„jvYl^L\@gVov¨}‘’z[uau}ofgJw[Y0qs•Äemq}\0^W'ºMXHZDœDXYRh[e¢wl–”gVy^¤ š†q}h[z[xl^:x[zl^:efe]«Jof^]gJy5Y[gVšl‘’–’‘—j kJ«

x[^]gVx[–—qly5¨°gJz[x¥–’‘—˜J^]zl^:efegVof^gs–”emq>x[^]y‘”x[gJšl–—^.w[ofqJwF^]ofjm‘’^]e„qV•Lom^]˜V^]ovef‘’šl–’^of^]yq}zR™†u}h[ofgJšl–’^@z[^jfe]œ°XYl^

•Ÿh†z[x[gV\%^:zJjvgs–w[ofqJwF^]ofj kµqV•Lom^]˜V^]ovef‘’šl–’^of^]yq}zR™†u}h[ofgJšl–’^zl^jve‘”e0h†em^:x´‘”zÀ¾}^]yjm‘’qJzŠ]>jmqµ^]efjfgVš[–—‘”efY¥g

jvofgJz[ef–’gVjm‘’qJzqs•Hemq}\0^of^˜J^]ovem‘”šl–’^aof^]yqJzR™FuJh[ovgVšl–’^„zl^jve‘”zJjfqemjvofgVjm‘—™†^]x.nD^jvom‘zl^jveœ z>¾}^]yjm‘’qJzT^@“¡^

uJ‘—˜J^pefqJ\%^¢^i[gJ\%w[–—^:e'qs•†yqJz[y]h[ovom^:zJjemklefjm^]\@eefh[šlrt^]yjjmqaxlklz[gV\%‘”y¢y5Y[gVz[uV^]e]œ®XYl^]k„gVof^pom^:efwF^]yjm‘’˜V^]–—k

\%qlxl^]–—‘’¦^:x.h†em‘”zluof^˜V^:ofef‘”šl–—^6of^]yq}zR™†u}h[ofgJšl–’^azl^]jfe]«†nD^jvom‘zl^jve«BgVz[x¸efjfovgsjm‘—™†^:xnD^]jfof‘®zl^jve!evYlq“‘’z[u

jvY[gsj%jfY[^.y5YlqJ‘’y^qV•žgµw†gVofjm‘”yhl–”gVo0\0qlxl^]–\h[y5YÀxl^]wF^]z[x†e0q}z´jvYl^.z†gsjfh†om^qs•LjvYl^.w†omq}šl–—^:\ jmq¹š†^

\%qlxl^]–—‘’¦^:xĜ

&"06"0 0" //-+)" )"

 z´jfYl‘”e¾}^]yjm‘’qJz¥jvYl^.z[qVjm‘’qJz´qs•LLh[jmqJ\@gVjmqJz ¡qJz}jfofqV–’–—^:x¥nD^jvom‘)ÐL^]j©< ¡n¢Ð6¯‘’e%‘”z}jfofqRx†h[y^:xĜ£

“)^]gJ¨@^]ÂRhl‘’˜gs–’^]z[y^6šF^j “)^^:z ¡npОe!gJz[x\H^:yjfqJoLx†xl‘—jf‘—q}z>¾}klemjf^]\@e“‘—jvY>¾}jfgVjm^]e6©5\ 6¾[¾ :Ã_ <Ÿ¯¡‘’e

‘”z[xl‘”ygVjm^:x6•Ÿomq}\+“!Y[‘’y5Y„‘’j•›qV–’–—q“!e®jfY[gVj®n¢–”gVy^¤ š†q}h[z[xl^:x[zl^]eve]«:bL^]gVy5Y†gVšl‘’–—‘’j kV«:¬a^]gVx[–—qly5¨agVz[x„­‘—˜J^]zl^:efe

gJom^!x[^]y‘”x[gJšl–—^žw[omq}w†^:omjf‘—^:eHqs•' ¡n¢ÐaeœDÑ£^L‘”z[xl‘”ygVjm^!‘”zw[gJomjf‘’y]hl–’gJoHgxl^™Fzl‘’jm‘’qJz&qV•PjvYl^Lyq˜V^]ovgVš[‘—–’‘—j k

jvom^]^6qs•HgVz. ¡n¢ÐǓ!Yl‘”y5Y‘”ejfY[^yqJh†zJjf^]ovw[gVofj)qs•DjfYl^yq˜V^]ovgVš[‘—–’‘—j k@jvom^]^aqV• jvYl^„gVevemqly‘’gVjm^]xs\Da¾[¾Bœ

Ê

Š

ŸÎ

Œl‹Œ Ê

Š‹



Š‹

¸Ê

Š

U * G.!Q !Q S.!X Š!Q".!Q t a e a

e"!$# a e&%(' _a m (4v > ) e 1 T* > .1 +* ,!+O?" !- .!5 >.Š.MZG.,!)

V&*V!Q 6%M{!-.G21P* X!&2 *MZ=2. S16%"!5 e"!$# ae&%(' _ c=eNf h jl,D L .&*2!5 6.MJ

!-X21/!ƒ$*, ..!X!5 JU8S1 *%!5.!G!Q JU

m ( n3jlp !ƒ " !Q M,X 9

jƒW >?LMZ.!

`  a  ` c

jl-,)h t5e‡f

h jlLv[VL 6.)[.

`

+t/. vt{q

a

#v?}ge"!$# t{q

a

#v‚0.

`

t. v.tJq

a

#v?}~e&%('

_

t{q

a

#v ‚0.

W.&. nzjl,

#sn

1 qŠnŠe21L!ƒ8*VG.!Q EL.!Q !+G,!8!& W.8 M{ AW !Q

(10)

S.!5 } te a a ` +t/. v a ` t/. v v S1=VU V1s[. .ŠnTjl , PO? GV.MZ!5 L= 6% [.

m#$. Lm | qRn3e

tˆ v mut{qvPw e"!$# t{q

a

#v ‚ .

tˆ&ˆ v mi|5tJqv?}~mut{qv)e"!$# t{q

a

#v ‚ .T€Ne&%('

_

t{q

a

#v ‚ .

ʊ ŸÎ ‡Š Î ÀŒ[Š Î0Î Š]‹ Î ))Ê Ï Š‹ ¸Ê Š U+ !-G!-iV"!Q MMYV1 !5 S.!

GR!5 *MZ } t

asa

vG> } t

aGa a

'C(4v8 G/O$, !& 1F.!- , 2!Q !&X!& > !

!HAWd!-!-

.! AW 6%"!5

!5 !Q 3 MZ!Q

f

f

1G " !Q M !-!- ' ( n

} t

a e aGa

e"!$#

a

e&%('

_a

m ( vX 8* G!5 !5 !> !ƒ !ƒG.XG.!+bW .6"!5G8!ƒ

!&X!&

c h jl ,

!-.G21T!"G!-!-241 W2!Q

6G!ƒ "!-.ƒW.FVR[2.!Q>?2.

!ƒd2,!5 M*!"!&!"d!&X!&#S1!ƒ/2,!5VMMZ21*!$!&!ƒ?* G!5 !5 !%# U+!5"MM{

2)[22!5"21s% !"?W. MJRAW! V"!Q MMYV1s[.!"!&X!&& G 9

bW' V !ƒP* 2/t5m

a

'%v n3jlp f( S18 !d!5 !Q 3 MZ!Q [2!5>?2TX 9 / = 6% [

tQm

a

'%v*)h tQm |a ' |v +-,

.

+0/1 m#

t'4v2Lm |

j.! G 9 X= 2* !ƒX!&X!&

1F.S!-V1E43657

F[.!- SV1T[ .!5 !5 !5!Q "2 !Q

V.MZ!5 !-G!ƒ.! AW G 9 2=2=[MZ W2 !ƒ " !Q MX 9 tQm ( a

'C(4v

žzµgJhljmq}\@gsjmq}zµyqJz}jfofqV–’–’^]x>nD^]jfof‘¢zl^j6jfY[^]z¹yq}z[em‘”efjfeaqs•j “¡q¸efkRefjm^:\@e„yqJ\@wFqJef^]x°‘’z¹ygJefy]gVxl^;žgJz

gJhljmq}\@gsjmq}z8+gVz†x&gw[gVovgV\%^]jfof‘’ynD^jvom‘Bzl^j¥œDXYl^L‘”z}jm^]om•ŸgVy^!š†^]j “¡^]^]z&jvYl^!j “)qefkRefjm^:\@e¢‘”e¢uV‘’˜V^:z

š}kjfYl^efjfgVjm^^:z[yqlxl‘”zlu@•Ÿh[z†yjm‘’qJz¸jvY[gsjž\%g·k.š†^0w[om^:em^:z}jm^]x.‘”z±\@gsjfof‘—i•›qJov\

c9zf) h jl„œÑµ^

gJš[š[of^˜R‘”gsjm^ :365ÒjmqI:3&3“!Yl^:z

‘”egR!5 64 M[efjfgVjm^6^]z†yqlxl‘”zlu†«l‘<œ^JœD“!Yl^]z; } ÇgJz[x

‘’e

jvYl^%‘’xl^:z}jm‘’j k>\%gVjfof‘ÃiĜ„Lh[jmqJ\@gVjmqJz ¡qJz}jfofqV–’–’^]x¸nD^jvom‘Hzl^]jfe6gVof^˜J^]ofk.ef‘’\%‘’–’gJoLjfqs\H^:yjfqJoaLx[xl‘’jm‘’qJz

¾RkRefjm^:\“‘’jfY>¾}jfgVjm^:eœ

ʊ ŸÎ=< ?>„Ê VŠ Î ‹‡ÏÏ Š ŸÎA@'Ë ‰Š Ê Í ŠCB @ Š]Œ[Š Ê ‰ D> ‡ @'@ U ,2!& UL1F1 !Q 8#,%0

!- > !N#,!-!-.stE a !GF ' a?H v32 !5RAWTXO$, !&3 .,!&213= 2*7I } tJE a -!KF '%v "!-&F

L w † 1) X* H c !GF 'ThNMMPO Ud#,#Š sD "!-21s= 2*ŠMZ=[2MMZ21 *MMQO U

G 9 s /* 8t5m a2R vXF1=XAW6V!- > !ƒ3S"0-S&F!5 6"!Q .mon jlO S1s 6%!&VU

R

nE S S!-!Q 8TU-VXWZY\[

.

TU /VXW /YX2"?!ƒ!^]X B VSW2

R

!-

R | 1Bmi|,}~m € H

t]v

"G 9 st5mi|

a?R

|v/ /. 1 !- [2 VVFV"=[MZ W2 G 9 st5m

a?R

v W_TU-VXWZY

ø

.

TU /VDW /Y+>

ø

. !"s @BVUF 6%RS1 !Q !5 6R.MZ TAWG!ƒs MZ!Q DAWRS.0&!--*z 2=2=[ M{ !QT= 6.D[.7`

TUaVXWZY

.

TU

/

VbW

/Y c ] nd TU-VXWZY [

.

TU

/

VXW

/Y jƒW Ud#,#i2G e *=*21z> !gG

, !5 MHG 9 tQm (

a2R

( v ! G 9 3= *Š !"X *Š>RMZ=[2MMZ21 .s s!ƒs!Q *,MZ.

TUaVXWZY([

.

TU

/

VbW

/

YX> TtQm

a?R

v!AS1 ! GtQmi|

a2R

|vX# sG 9 2=2F[.MZW2 !ƒR " !Q M

G 9

¡–’^]gJom–’k°gJz¥ ¡n¢Ðf } t

aga

v„“!Y[^]of^I ‘’eg3*, 6nD^]jfof‘¡zl^]j‘’e^]ÂRhl‘’˜gs–’^]z}jjmq±jvYl^ \Da¾[¾

ih} tE

a

-!KF '

a?H

vL“!Y[qJef^˜V^:omjf‘’y^]eagVof^jvYl^&emjvgsjm^:eaqs•$KjE }k gJz[x>q}zl^%Y†gVeaqJzl^%gVovy‘”zl !KF '

•ŸofqJ\ '„jmq '4|Ė”gVšF^–’–—^:x¸šJkjfYl^„˜J^]yjfqJomE t/#

a

'%vPnlMM uV‘’˜V^:zš}k

Et#

a

'%vtˆv$}ne&%('

_

t{qr

a

#%v  e"!$# t{q,r

a

#vXo"‚

t/'%v

(11)

,

,

,

,

,

ÅD‘—u}h[of^ ;HD•Ÿomq}\‘”\%w†h[om^„zl^]jjmqw[h†om^„zl^]j

“!Y[^]of^ei} q

aa

q !‘”epefqJ\%^™[il^]x@^:zRh[\%^]ovgsjm‘’qJz0qs•ÄjvYl^Lef^j¢qV•Äw[–’gJy^]e¢qs•¥œDLyjvh[gs–’–’kj gVz†x

ihY[g·˜V^6jvYl^evgV\%^\@gVov¨J‘”zlu}e!gVz[x7TUaV + Y ,

.

TU /V

+0/

Yp‘’z¸jvYl^\@gVov¨}‘’zlu&u}ofgJw[Yqs• …‘Õ¢gVz†xq}zl–’k‘—•

TUaV

+

Y!

,

.

TU /V

+g/

Y¢‘”z.jfYl^\@gVov¨}‘’z[u0u}ofgJw[YqV• ihVœ

¾Rh†w[w†q}em^)jfY†gsjDzl^j ‘”e®‘”\@w[h[of^¡“!Y[‘’y5Y0\0^:gVz[ejfY†gsjDš†qJjfYe"!$# t{q

a

#v‚

t/'%vgVz[xe&%('

_

tJq

a

#%v‚

t'4v

gJom^„zlq}z¸¦^:omq%•›qJoLemq}\0^w[–’gJy^Bq®«F^˜J^]z}j-#gJz[x±emjvgsjf^ 'V«FqVjvYl^]of“‘’ef^„emjvgsjf^]x¸jfY[^yq}zR™†uJh†ofgVjm‘’qJzqs•

gJefefqly‘”gsjf^]x¸“‘’jfY£emjvgsjm^ 5 "% ¯L‘’e6gJz±‘’\@w[h†om^%nD^jfof‘Hzl^j]œ„ÐLq“ q}zl^0y]gVz°^]gVef‘’–—k¸jfovgVz†et•›q}of\§gVz}k

nD^]jfof‘}zl^]j®‘”z}jmqžgžw[h[of^pnD^jvom‘Rzl^]jš}k„efwl–’‘’jmjm‘”zluž‘—jve®^]˜V^]z}jveœ XYl‘’ejfovgVz†et•›q}of\@gsjf‘—q}za“!Yl‘’y5Y‘’e‘—–’–”h[emjvofgVjm^:x

‘”z¹jfY[^–—^•›jqV•)ÅD‘’u†œ ;¸yqJz[ef‘”emjve„‘’z¥evwl–’‘—jfjm‘”zlu>^:gVy5Y£^˜J^]z}j #‘”z}jmq>j “)q±^˜J^]z}jfe]«®jvYl^#"fšF^uV‘”zl‘”zlu±qs•-#%$

x[^]zlqJjm^]x # J

«pgVz[x¶jfYl^&"m^]z[x¶qs• #%$xl^:zlqVjf^]x #('¡œ pgVy5Y¶‘’z†w[hlj@wl–’gJy^.qs•L^]˜V^:zJj #¸‘”z´jfY[^.q}om‘’uV‘”z[gV–

z[^j„‘”egVz£‘”z[w[hljw[–’gJy^@qs•-#

J

“‘’jfY¹jvYl^evgV\%^@“¡^]‘—u}YJj]œ.¾}‘”\%‘—–”gVof–—k°^]gVy5YµqJh[jfw[hlj0wl–’gJy^&qV•)^]˜V^]z}j&#

‘”zµjfYl^@qJof‘’uV‘”z[gs–Dzl^j6‘”e6gVzµqJhljvw[hlj„wl–”gVy^%qs• #)'À“‘’jfYµjfYl^&evgV\%^0“)^‘’uJY}j]œÅD‘’z[gV–—–’k>“)^%Y†g·˜V^%‘’zµjfYl^

evwl–’‘—j6zl^]jagJz>^iljvofgwl–’gJy^•›qJož^]gVy5Y>^˜V^:z}jLqs•¡jfYl^%qJof‘—uJ‘’z†gs–Dzl^j%©UšF^]gJom‘”zlu•›q}ožef‘”\%w[–—‘”y‘’j k±jfYl^@z[gJ\0^

qV•jfY[gVj^˜J^]z}jê¯6jfYl‘”e0w[–’gJy^‘”egJz¹qJhljvw[hlj0w[–’gJy^&•›q}o # J

gVz[x¥gJz¹‘’z†w[hlj0w[–’gJy^&•›q}o #)'+“‘’jfY´ef‘’z[uV–’^

“)^‘’uJY}jve«·‘’jfeDyq}zJjf^]z}j uV‘’˜V^]e®jfYl^zRh[\0š†^:o®qV•†‘’z†emjvgVz[y^]eqs•†^]˜V^]z}j #)jfY[gVjDgJom^¡yh[ovom^:z}jm–’ka^il^]yh[jm^]x'œ XYl^

evwl–’‘—j„zl^]jžuJ‘—˜J^]e6g™Fzl^]o6xl^:efy]om‘”wljf‘—q}z>qs•¡jfYl^&w[Yl^:zlqJ\%^:zlqJzµš†^]‘’zlu¸\%qlxl^–’‘—¦]^]xµ‘’zµjfY†gsj6šJk>š†om^:gV¨}‘’z[u

jvYl^&gsjfqJ\%‘’y‘—j k±qV•¡^]˜V^]z}jvež‘’j„gs–’–—q“!ež•›q}oagJz°^i[wl–—‘”y‘’j„xl^]evyof‘”wljm‘’qJz°qs•¡jvYl^&yqV¤<qlyy]h[ovom^:z[y^0qs•¡^]˜V^:zJjveœ

žq“¡^]˜V^:o‘Õ¢q}zl^‘”eLzlqJj!‘’z}jf^]of^]efjm^]x¸‘”z±jvYl^‘”z[xl^]wF^]z†xl^]z[y^qV•D^]˜V^:zJjve«F“!Yl‘”y5Y±‘’eLjfYl^0ygVef^“!Yl^:z¸qJzl^

“gVz}jjmq&y5Yl^:y5¨w[ofqJwF^]ofjm‘’^]e–’‘’¨V^„om^:gVy5Y[gJšl‘—–’‘’j kV«lš†q}h[z[xl^:x[zl^:efe]«[–’‘—˜J^]zl^:efeq}oxl^]gJxl–—qly5¨B«RjfYl^:z¸jfYl^evwl–’‘—j

z[^j‘”e^:Â}h[‘—˜gs–’^]z}jjfq>jfY[^qJof‘—uJ‘’z†gs–pzl^]j©Uef^^ :{%<Ÿ¯êœ+*az[^\@g·k°jfY[‘’z[¨£jfq°gVw[w[–—kµjfYl‘”eq}w†^:ofgVjm‘’qJz°•›qJo

^:gVy5Y±yqJzR™†u}h[ovgsjm‘’qJz.qV• gVz[x±jfqh[ef^jvYl^0yqJz[efjfovh[yjf‘—q}z¸uV‘’˜V^:z.gJš†q˜J^„•›qJožw[h[of^ ¡n¢Ð0œMžq“¡^]˜V^:o

jvYl^gsjfqJ\%‘”y‘’j k±qs•^˜V^:z}jfe6om^:ÂRhl‘’of^%jfY[gVj„^]gVy5Y°™Fof‘’z[uqV•gJz°^]˜V^]z}j6jfgJ¨s^:eaw[–’gJy^@‘’z¹efqJ\%^@w[gVofjm‘”yhl–”gVo

yqJzR™FuJh[ovgsjf‘—q}zqV• jvYl^0efklemjf^]\.«†gVz†x¸jfYl‘”eLw[ofqJwF^]ofj k‘”eLzlqJjLw[of^]ef^]of˜V^:xš}kevwl–’‘—jfjm‘”zluqV•D^]˜V^:zJjve«Fem‘”z[y^

#)'µy]gVz&qly]yh[o¡‘’zgxl‘—²P^]of^]z}j)yqJzR™FuJh[ovgsjf‘—q}z0jvY[gVzjfYl^6yq}ofof^]evwFqJz[xl‘”zlu # J œ zq}ofxl^:o¢jfq0^:efy]gVwF^LjfY[‘’e

w†omq}šl–—^:\$“)^efY†gs–’–¢^]zR•›q}ofy^&^˜J^]z}j # J

jfq±qRy]yh[o‘’\@\%^]xl‘”gsjf^–’k£gs•›jm^:o #)'pœ  z¹jvYl‘’e“)g·k°“¡^&jfqVjfgV–—–’k

–’qRqJef^gVz}k‘’zR•›q}of\@gVjm‘’qJz±gVšFqJh[jLjfY[^0yq}z[yh†ofof^]z[ykqV•¢^˜V^:z}jfe]«Fš[hljagVeL“¡^%gs–”om^:gVxlk.\0^:z}jm‘’qJz[zl^:x±jfY[‘’e

Y†gVezlq°^²P^]yjqJz¹jfY[^w[ofqJwF^]ofjm‘’^]e„“)^gVof^&‘’z}jf^]of^]efjm^]x£‘”zĜ±XYRh[e^:gVy5Y¹ ¡n¢Ð } t

asa v„‘’e

gJefefqly‘”gsjf^]x¸“‘’jfY°g\ 6¾[¾8ih} tE

a !KF ' aDH

vL“‘—jvY°yq}\@w†q}zl^]z}jfeagVeL•›qV–’–’q“!eœ+\H^]ofjm‘”y^]eagVof^^]‘—jvYl^]o

efjfgVjm^:e„qs•jfY[^ ¡n¢Ð q}ow[gV‘’ove t/'

a

#%v\%gJxl^qV•g±efjfgVjm^gJz[x¹qs•!gJz¹^˜V^:z}j„^]z[gJšl–—^:x¹‘’z¹jvYl‘”eefjfgsjf^

E } -,+t ' a

#vBnlzf

/.

c

'4| n +a,

. + /

}œ¡ÅFqJo!^:gVy5Y.jfovgVz†em‘’jm‘’qJz +-,

. + /

“)^Y[g·˜J^„j “¡qgJofy]e‘”z

jvYl^ \Da¾[¾MFqJzl^a•ŸofqJ\ ˜V^]ofjm^i '„jfq&˜V^:omjf^i t' a

#v)–’gJš†^]–—–’^]x;E t/#

J a

'%vgVz[x¸gJzlqVjvYl^]oq}zl^a•Ÿomq}\ ˜V^:omjf^i

t' a

#v„jfq°˜V^:omjf^i'E|¡–”gVšF^–’–—^:x*E t/#('

a

'%v„“!Yl^:om^E t/#

J a

'%vgVz†xaE t#)'

a

'%vgVof^jvYl^˜J^]yjfqJoveqV•jMM J10

(12)

uJ‘—˜J^]zšJk

E t/#

J a '%v.tˆvH}

e"!$# t{q r a #v ‚ t'%v ‘—• † ˆ

† ‘—•

ˆ

gVz[x #d} #%r

'

‹ ‘—•

ˆ

gVz[x # Œ} #%r

'

gVz†x

E t/#)'

a

'%v.tˆv?}

e&%('

_

tJq,r

a

#v ‚

t/'%v ‘Õ † ˆ

 † ‘Õ ˆ gVz†x #/} #%r

'

‹ ‘Õ ˆ gVz†x # Œ} #%r

'

“!Y[^]of^se } q

a.a

q ±gVz[x

} #

aEa

# 0 ±gVof^efqJ\%^™†iR^:x´^:z}h†\0^:ofgVjm‘’qJz[eqs•LjvYl^±em^]j0qV•

w[–’gJy^]e&gJz[x ^˜J^]z}jfe@qV•žjfY[^° ¡n¢Ðœ¡XYl^]z jfY[^°\@gVov¨J‘”zlu}e0qV• gVof^±gs–”emq¥\@gVov¨}‘’z[uJe%qs•mih¸gVz†x

TUaV + Y ,

.

TU /V + /

Y'‘’z%jfY[^!\%gJof¨}‘”zluauJovgVw[Yqs• ‘—•PgJz[x%qJzl–’k‘—•B“)^Y[g·˜V^)jfYl^!ef^]ÂRhl^:z[y^qV•FjfovgVz†em‘’jm‘’qJz[e

TUaV

+ Y ,

.

TU

//

V + Y ,

.

TU /V+ /

Y)‘”z>jvYl^&\@gVov¨J‘”zluu}ofgJw[Y±qV•'ih“!Yl^]of^Xmi||ceuh jl„œ

Ô°qJof^q˜V^:o TUaV

+

Y!

,

.

TU

//

V+

Y¢‘”ejvYl^qJz[–—kjfovgVz[ef‘—jf‘—q}z–’^]gJxl‘”zlu&jmq\@gVov¨}‘’z[uTtQmi||), #)

a

'%v

gJz[xATU

//

V + Y ,

.

TU /V + /

YL‘”ejvYl^q}zl–’kµjvofgJz[em‘’jm‘’qJzµ•ŸofqJ\jfYl‘”e\@gJof¨}‘”zlu>š†^:ygJh[em^ E t#

J a

'4v

“!Y[‘’y5Y£gVx[xµqJz[^&jmqJ¨V^]z°jmq>wl–”gVy^ #gVz[x E t/#('

a

'%va“!Yl‘”y5Yµof^]\%q˜V^%qJz[^%jfqJ¨V^]z°•Ÿomq}\jfYl‘”ewl–”gVy^&gVof^

jvYl^%qJzl–’k¸˜V^]yjmq}ofeLjfY[gVja\%qlxl‘—•›k±jfYl^%˜gs–”hl^qV•¡wl–”gVy^2#}œ •¡“¡^%om^:emjvom‘”yjagsjmjf^]z}jm‘’qJz>jmqjvYl^@\%gJof¨}‘”zluJe

of^]gJy5Y[gVš[–—^D•ŸofqJ\Òemq}\%^¢‘’z[‘—jf‘’gV–}\@gVov¨}‘’z[ut5m ( a

'C(4v n3jl p fm.‘—j®•›qV–’–—q“!e®jfY[gVj®jfY[^¡of^]gVy5Y†gVšl–’^H\%gJof¨}‘”zluJe

qV• ihgJom^¡jfYl^of^]gVy5Y†gVšl–’^¡\@gVov¨}‘’z[uJeqs• jmqJuV^jvYl^]o “‘’jfY%emq}\%^)\@gVov¨}‘’z[uLqs•BjfYl^)•›q}of\ tQmi||, #)

a

'%v

“!Y[^]of^ m || c e h jl„«"#in

«6gVz[x' n œ XYRh[e.jvYl^¥ ¡n¢Ð gVz[x+‘—jve.gJefefqly‘”gsjf^]xD\Da¾[¾

gJom^&^:ÂRhl‘—˜gV–—^:zJj0“‘—jvY´of^]evw†^:yjjfq°jfY[^•›qV–’–’q“‘’zluµw[omq}w†^:omjf‘—^:e%n¢–”gVy^¤Sª)q}h[z[xl^:x[zl^:efe]«bL^]gVy5Y†gVšl‘’–—‘’j kV«

¬a^]gJxl–’qRy5¨gVz[x­®‘’˜V^:zl^]eve«[ef‘”z[y^6jfY[^]ef^6w†omq}w†^:omjf‘—^:egVof^6x[^]y‘”x[gJšl–—^a•›q}o \ 6¾[¾°©Uef^^ :—_ <Ÿ¯êœ

‹ ÎpÎ ‰ Š ŸÎ BMZ=20 1=21.V

+VFV"=[ M{ !Q

2=1MZE29 1$ 6%.2/V1=2 1==[MZ*, 0

*!5 .$W. U$l

 z@w[gJomjf‘’y]hl–”gVo qJzl^y]gVz%xl^]y‘’xl^!w[–’gJy^š†q}h[z[xl^:x[zl^:efeDqV•PgJz0 ¡n¢Ð¿š}k%yqJz†emjvofh[yjm‘”zluajfYl^!yq˜V^]ovgVš[‘—–’‘—j k

jvom^]^qs•‘’jfe0gVevemqly‘”gsjf^]x)\Da¾[¾Bœ Ñ£^ygJz¥em‘”\@wl–’‘Õ›k¹jfY[^yq}z[emjvofh†yjm‘’qJz¹qV•jfYl‘”eyq˜V^]ovgVš[‘—–’‘—j k°jfof^^š}k

gJ\@gs–’uJgV\@gVjm‘”zlu0jvYl^evh[yy^]evem‘’˜V^gJofy]egVevemqly‘’gVjm^]x“‘’jfYlEt#

J a

'%vgVz†xE t#)'

a

'%v5œ)ѵ^yqJz[y–’h†xl^jfY[‘’e

ef^]yjm‘’qJz.š}kg@xl^]evyof‘’w[jm‘’qJzqs•DjfYl‘”e!yq˜J^]ovgVšl‘’–’‘—j k@jfof^^Jœ

Ñ£^xl^™Bzl^gVzqJovxl^]oof^–”gsjf‘—q}zšF^j “)^^:z.\@gJof¨}‘”zluJe)qs•DgVz. ¡n¢Ðš}k–’^jfjm‘”zlu

t5m

a

'4vit5m

|a ' |v t'+} ' |v 1 t

qTnReumut{qSvzm

|

t{qv v

¾R‘’\%‘’–’gJojmq&“!Y[gVj)‘”e!xlq}zl^a•›qJonD^jvom‘zl^jve«†g0™Fz[‘—jf^gVw[w†omq·il‘”\%gVjm‘’qJz&qV• jvYl^of^]gVy5Y†gVšl‘’–—‘’j k&jfof^^„y]gs–’–—^:x

jvYl^°yq˜V^]ovgVš[‘—–’‘—j k¶jfof^^>ygJz š†^µyqJz†emjvofh[yjm^:xĜ3ņqJojfY[gVjw[h[ovwFqJef^>g´zl^“§˜gs–”hl^>xl^:zlqVjf^]x gVz†x

of^]w†om^:em^:zJjf‘’z[u "mgJz>gVovšl‘’jfovgVofk–”gVofuV^ $„‘”z}jm^]uV^]ož‘”ežgJx[xl^]x>jmq.jfYl^@em^]jLqV•Pjl qV•pzlqJzl¤Szl^]uJgVjm‘’˜V^‘”z}jm^uJ^]oveÁ

“‘’jfYÀjfY[^±qJovxl^]o%om^]–’gVjm‘’qJz gVz[x¶jfYl^>gJx[xl‘’jm‘’qJz gVz[x evh[š[efjfovgVyjf‘—q}z´q}w†^:ofgVjm‘’qJz´^iljm^]z†xl^]x š}k´–—^]jmjf‘’zlu

n3jl a €3} €Š} €N}

a

) }

a

gVz†x R!À‘”e!h[z[xl^™Fzl^:xĜ

ʊ ŸÎ#" %$.Ê Ê ‹Œ )'&VÊ Ï ÀŒ[‹)( /+* ‰$ U F MJ -,E21 X 9 AWG U$l XX*

t/.m a

'%v/>". 0.m GG2*1.m ce hkjl , s1 ' n X!-!-

Références

Documents relatifs

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST