• Keine Ergebnisse gefunden

Convex vNM-Stable Sets for linear production games

N/A
N/A
Protected

Academic year: 2022

Aktie "Convex vNM-Stable Sets for linear production games"

Copied!
9
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Volltext

(1)

!

/101012

354687:9<; 7>=@? ACB>D,EGFIHJ9 BK9LDNM

O 4!PRQST6U98EVPXWYPZ4>[]\U^LD_SJ46 `aEGbc9dM

ef g)hjilknm o_fqpsrjt mvu

w x'x

rjyzg t){Y|}rjt~g mknt_ilk€f‚ k€ƒ

„…Z†ˆ‡Š‰&‹ŒŽŒŒŽ‘’T“”‹•ŽŒŽ–—‹˜™

šœ›”—˜Ÿžn Ž¡£¢n¤”¤J¢n¥J¢

¥”¥Ž¦¤J¢£‰&‹ŒŽŒŒŽ‘‡¨§&ŒŽ–Ÿ©ªž“'™

ŒŽ©ªž”‹«¬‹©­®¯­‹­‹°±“”‹²´³”‹ŒŽŒŒŽ‘¨°‘Œ

¡'˜˜µ¶«·”·'­­­¸°­‹­‹°±“”‹²´³”‹ŒŽŒŒŽ‘¨°‘Œn·J¹n‹©­·Jšºžµ”ŒŽ–—·n—¡n›'­sµŽžµ”ŒŽ–°µJ¡µ”»n¥”¼”½

(2)

!#"$%& (') *+,-./"102345

687:98;=<?>A@CB7ED$FHG?@JI?KAKLFHMONP98G?QSRFHGETU98@#>AGWV*<?>YXZ7\[]>YXZ^H_a`

NZbcG?DXd>YXde*XfgI?Mihj9kXd<]FH@l9kXd>ADZ;=<]Fm>AMnXdDZ;=<9kfoXdDfp7EM$DZ;=<Ue?G]q

rG?>Y[EFHM$DZ>YXOskXiRP>LFHKLFtfpFHKAQ

uvnwxwxy]z\{|RP>LFHKLFtfpFHKAQ}]~iFHM$@l98GET

Fv€@l98>AK‚ƒ$Md„…a>Y…a>‚†‡e?G?>ˆv€‰?>LFHKLFtfpFHKAQ†‡Q]F

_=uaFHŠ98MnXd@|FHGEX78fŒ‹;t7EG]7E@#>A;ŽD

a98>Yf‚9|rG?>Y[EFHM$DZ>YX€T

h7Ee?GEXi‘98M$@|FHK‚}a98>Yf‚9|w]zH’x“E{*}/bcDZMZ9”FHK

Fv€@l98>AK‚•‰?>AGETU9E„iFH;t7EG†‡<98>Yf‚9]†–98;x†‡>AK

— “x“x˜

™›šEœž€Ÿ t¡Z

¢J£¥¤ž¦”§=¨c§=¤n©c£¨‚ª¬«£¥¤­®t¯£€°j¯\±&²a³k´Ž©ž§=µk¶¬£·´H£n©c¸%§=¤¤­¨‚¹kª¬®kº#©c­#¯­®

±»£¼k½§=®k®›§=®k¹²¾­¨‚º£®k¸g©c£¨‚®Œ¿L­¨:­¨g©c¦k­º­®”§=¶=¶¬ª¬®k£$§=¨EÀk¨‚­H¹k¼k¤n©cª¬­®ºt§=½£¸

Á

ª–©c¦¾§¤­®t©cª¬®Ž¼k¼k½Â­=¿?Àk¶ˆ§$㨂¸Ä

ÅƦk£P¨‚£¸‚¼k¶–©c¸&­=¿»ÇÈOÉ/§=¨‚£©c¦k£¨‚£µtø‚¼kµk¸g©ž§=®t©cªˆ§=¶¬¶–Ãiª¬½Àk¨‚­Z¯£¹:ě´Hª¬½P¼k¶‡Ê

©ž§=®k£­¼k¸‚¶–ÃËH©c¦kª¬¸ ª¬¸.§i̞ÍO΀΀ϖЎÑnÒxÓ=ÔHÕ¤­®k¤£¨‚®kª¬®kº©c¦k£•Àk¨‚­H­=¿U­=¿*§¶¬£½½§

ª¬®i­¼k¨Ö”¨‚¸g©»À”§=Àx£¨Ä

×pØ:ÙdÚÆۀÜZÝÞÙdßnàâá?ۀàÞÚ.ãäOåZÚgæZÝÞڂå›ÝÞߕç8èžÛ€äé$ÙdÚgêêëáAÙdڂۀà?ì‡ßnàÙOÛcè$ãädí•î=ßnãäÝÞڂå›ßnÜZÝ/ۀäÚgàÞàÞßnà?ãä›ÝÞÙdÚ

îdàÞÚgè$ãßnÜOá:îOۀî=Úgà‚ï

(3)

" #%$'&)(+*-,/./01&2*3$

¢Wª–©c¦kª¬®©c¦kª¬¸À”§=Àx£¨

Á

£¥Àk¨‚­Z¯£J§#º£®k£¨c§=¶¬ª¬«$§O©cª¬­®­=¿›©c¦k£½§=ª¬® ©c¦k£­¨‚£½ ª¬® ÇÈOÉÞË

©c¦k£ 4.¦”§=¨c§=¤n©c£¨‚ª¬«$§O©cª¬­®|ÅƦk£­¨‚£½ ¿L­¨P¤­®t¯£€°l¯\±&²a³k´Ž©ž§=µk¶¬£¾´H£n©c¸­=¿»®k­®Ž³\§O©c­½ª¬¤

­¨g©c¦k­º­®”§=¶¶¬ª¬®k£$§=¨&Àk¨‚­H¹k¼k¤n©cª¬­® ºt§=½£¸ÄP¢W¦kª¬¶¬£Pª¬®lÇÈOÉ

Á

£¸‚¦k­

Á

©c¦”§O©Œ£n¯£¨gÃ5”Í76987:

;

ÑcÓ=Î=<6¯\±&²a³k´Ž©ž§=µk¶¬£´H£n©ª¬¸•¸g©ž§=®k¹”§=¨‚¹:Ë

Á £ §=¨‚£P®k­

Á

ª¬®%©c¦k£Àx­¸‚ª–©cª¬­®¾©c­a­½ª–©»©c¦k£

>

¼”§=®t©cª–Ö”£¨@?pÀx­¶–ÃH¦k£¹k¨c§=¶BAžÄÅƦŽ¼k¸Ë

Á

£¸‚¦k­

Á

©c¦”§O©›£n¯£¨gÃJ¤­®t¯£€°J¯\±&²a³k´Ž©ž§=µk¶¬£a´H£n©

ª¬¸&¸g©ž§=®k¹”§=¨‚¹DCLªÞÄ£=ĖËE©c¦k£ ¤­®t¯£€°¦Ž¼k¶¬¶­=¿/֔®kª–©c£¶–Ã%½§=®tÃ%ª¬½Àk¼\©ž§O©cª¬­®k¸•¤­®k¤£®t©c¨c§O©c£¹

­® ©c¦k£ ¤$§=¨‚¨‚ª¬£¨‚¸&­=¿ ©c¦k£ ­¨g©c¦k­º­®”§=¶]½£$§=¸‚¼k¨‚£¸Œ¹k£n֔®kª¬®kºa©c¦k£ ºt§=½£E€Ä›ÅƦkª¬¸ª¬¸&¤£¨pÊ

©ž§=ª¬®k¶–à º­H­H¹®k£

Á

¸§=¸

Á

£•Àk¨‚­Z¯Hª¬¹k£•§›¤ž¦”§=¨c§=¤n©c£¨‚ª¬«$§O©cª¬­®ºª–¯£®©c¦k£

Á

£$§F=£¸g©ÆÀx­¸‚¸‚ª¬µk¶¬£

¤­®k¹kª–©cª¬­®k¸Ä

ÅƦk£¨‚£•ª¬¸.§=¶¬¸‚­›¶¬£¸‚¸ º­H­H¹®k£

Á

¸ÄHG»®\¿L­¨g©c¼k®”§O©c£¶–Ãˎ©c¦kª¬¸ À”§=Àx£¨.§=¶¬¸‚­›¦”§=¸ ©c­¸‚£¨g¯£&§=¸.§

̞ÍO΀΀ϖЎÑnÒxÓ=ÔHÕ Ä?ÅƦk£•Àk¨‚­H­=¿:­=¿E©c¦k£@I&¨g©c¦k­º­®”§=¶¬ª–©oÃÅƦk£­¨‚£½JCLÅƦk£­¨‚£½LKkÄM\Ī¬®¾ÇÈOÉNE

¤­®t©ž§=ª¬®k¸§=®£¨‚¨‚­¨§=®k¹¤$§=®k®k­=©µx£¸‚¼k¸g©ž§=ª¬®k£¹:Ä&¢W¦kª¬¶¬£›©c¦k£ÅƦk£­¨‚£½ ª¬¸»©c¨‚¼k£=ËE©c¦k£

§=ÀkÀk¨‚­t§=¤ž¦¤ž¦k­¸‚£®¤­¼k¶¬¹®k­=© µx£5¨‚£À”§=ª¬¨‚£¹§=®k¹§¤­½Àk¶¬£n©c£¶–ÃP¹kªPOE£¨‚£®t© ½£n©c¦k­H¹ ¿L­¨

©c¦k£ŒÀk¨‚­H­=¿?­=¿?­¼k¨Æ¨‚£¸‚¼k¶–©»¦”§=¹i©c­µx£¸‚¼kÀkÀk¶¬ª¬£¹:Ä

ÅƦk£JÀk¨‚­H­=¿

Á

£J§=¨‚£Àk¨‚£¸‚£®t©cª¬®kº ¦k£¨‚£¥ª¬¸i½­¨‚£ º£®k£¨c§=¶›§=®k¹WÃHª¬£¶¬¹k¸©c¦k£¥¹k£¸‚ª¬¨‚£¹

4.¦”§=¨c§=¤n©c£¨‚ª¬«$§O©cª¬­®%ÅƦk£­¨‚£½ ¹kª¬¨‚£¤n©c¶–ÃÄ»ÅƦk£¨‚£n¿L­¨‚£=Ë

Á £ ¦k­Àx£›©c¦”§O©•©c¦kª¬¸•À”§=Àx£¨•¤$§=®

µx£Œ¨‚£ºt§=¨‚¹k£¹%§=¸Æ©c­¸‚¼kÀkÀk¶–ý­¨‚£&©c¦”§=®3Q‚¼k¸g©•§¤­¨‚¨‚ª¬º£®k¹k¼k½¾Ä

¢J£ §=¨‚£›ª¬®k¹k£µ\©c£¹%©c­SRUTWV+XZY%[]\_^W^W`[]\V+aË_bg²i¢ ËxÅƦk£'G»®kª–¯£¨‚¸‚ª–©oþ­=¿1c.ª¬£¶¬£n¿L£¶¬¹:Ë

¿L­¨Æ¦”§$¯Hª¬®kºÀx­ª¬®t©c£¹i­¼\©Æ©c¦k£Œ£¨‚¨‚­¨Æ©c­¼k¸ÄdCÞ´H££›§=¶¬¸‚­¾ÇK=ÉNE€Ä

e fg*h&]ij&2*3$/klim$/,onJprq $s2t&2*3$/k

¢J£&¸‚¦k­¨g©c¶–è‚£Àx£$§O©¸‚­½£•­=¿U©c¦k£•®k­=©ž§O©cª¬­®k¸ ®k£¤£¸‚¸c§=¨gÿL­¨.­¼k¨ Àk¨‚£¸‚£®t©ž§O©cª¬­®:Ä/ÅƦk£

½­=©cª–¯=§O©cª¬­®k¸&§=¸

Á

£¶¬¶ §=¸­¨‚ª¬£®t©ž§O©cª¬­®¨‚£ºt§=¨‚¹kª¬®kº©c¦k£ £€°\ª¬¸g©cª¬®kºi¶¬ª–©c£¨c§O©c¼k¨‚£ª¬¸&¿L­¼k®k¹

ª¬®¥ÇÈOÉÞÄ

uwv_xy{z ª¬¸Œ§©c¨‚ª¬Àk¶¬£/|~}_ €@‚]ƒt:¸‚¼k¤ž¦©c¦”§O©j}%ª¬¸&¸‚­½£ ª¬®t©c£¨g¯=§=¶?ª¬®©c¦k£¨‚£$§=¶¬¸„CY©c¦k£

…+†

x‡ˆz‰Š

E€Ë € ©c¦k£{‹Œ5֔£¶¬¹ ­=¿ŽCc.­¨‚£¶NE¾½£$§=¸‚¼k¨c§=µk¶¬£J¸‚£n©c¸DCY©c¦k£·¤­t§=¶¬ª–©cª¬­®k¸Ei§=®k¹

 ‘ €“’•”„– §J¿L¼k®k¤n©cª¬­®W§=µk¸‚­¶¬¼\©c£¶–Ãl¤­®t©cª¬®Ž¼k­¼k¸

Á ĨĩS—U£µx£¸‚º¼k£ ½£$§=¸‚¼k¨‚£

˜ CY©c¦k£¤­t§=¶¬ª–©cª¬­®”§=¶U¿L¼k®k¤n©cª¬­®_E€Ä›¢J£¤$§=¶¬¶+Z™; ÑК<=ÕÑ §=¸

Á

£¶¬¶/§=¸&©c¦k£µ”§=¸‚ª¬¤ ¹”§O©ž§

Á

ª¬¶¬¶]®k­=©&¤ž¦”§=®kº£=Ä&¢J£¿L­H¤¼k¸•­®{6ÏYÒEт<=Λ5xÎcÍ$Ó=Ԕ̙AÏÞÍOÒК<=ÕѐœPº£®k£¨c§O©c£¹µtþ֔®kª–©c£¶–Ã

½§=®tí¨g©c¦k­º­®”§=¶E½£$§=¸‚¼k¨‚£¸ ˜U ŸžŸžŸž  ˜+¡ ¯Hªˆ§

C£¢HÄð E 1|£¤Hƒ¥‘§¦ ¨-©«ªd¬ ˜+­ |£¤Hƒ¯®°'¦²±ŸžŸžŸž‚³´µ|£¤·¶ €¯ƒt

Á

¦kª¬¤ž¦¾ª¬¸

Á

¨‚ª–©‚©c£®

C£¢Hħ¢E ¦¹¸»º ˜U ŸžŸžŸž  ˜¡7¼ ž

¢J£ §=¸‚¸‚¼k½£P©c¦”§O©•©c¦k£ ˜­ §=¨‚£ §=µk¸‚­¶¬¼\©c£¶–þ¤­®t©cª¬®Ž¼k­¼k¸

Á

ª–©c¦ ¨‚£¸‚Àx£¤n©©c­s—U£µx£¸‚º¼k£

½£$§=¸‚¼k¨‚£¥CY©c¦k£J¨‚£n¿L£¨‚£®k¤£|½£$§=¸‚¼k¨‚£E€Ë›¹k£n֔®k£¹ ­®)¹kª¬¸NQ‚­ª¬®t©%ª¬®t©c£¨g¯=§=¶¬¸Ž½s­7¾|~°¿¦

±ŸžŸžŸž ‚³ƒ€Ë\©c¦k£Œ¼k®kª¬­®i­=¿ ¦kª¬¤ž¦¾ª¬¸›À?Ä

(4)

¢J£¼k¸‚£©c­ ¹k£®k­=©c£&©c¦k£

…

z‰Ÿx ª¬®a©c¦k£¶ˆ§O©‚©cª¬¤£»­=¿]¸‚£n©Æ¿L¼k®k¤n©cª¬­®k¸­® €

£ >

¼”§O©cª¬­®k¸@C£¢HÄð E/§=®k¹C£¢Hħ¢E?Àk¨‚­Z¯Hª¬¹k£5©c¦k£»¸g©ž§=®k¹”§=¨‚¹¼k¸c§=º£=Ä/ÅƦk£ x‰‰=z‰ ­=¿U§Œ½£$§dÊ

¸‚¼k¨‚£"!·ª¬¸*¹k£®k­=©c£¹Pµtà ½ |!¯ƒ€ËOª¬®Œ©c¦k£.¤­®t©c£€°H©­=¿”§»ºt§=½£ ºª–¯£®µtà C£¢Hħ¢Eg§=¤¤­¨‚¹kª¬®kº¶–Ã

Á

£¼k¸‚£.©c¦k£§=µkµk¨‚£n¯Hªˆ§O©cª¬­® ½/­D‘§¦ ½ | ˜­ ƒtž#5£¤$§=¶¬¶t©c¦k£.¤­®k¤£À\©/­=¿8§$&%('*)+ =x-,

† z

+ z& C~T/.X10m\243@V+X]X6587.a/9 \_X]`;:\_aX Ç<dÉNE€Ä

=?>&@BA4CEDFCHG-AJI6KLMKON*љd|~}_ €j‚]ƒQP€Ñ <aК<=ÕÑSRUT•Ò y

…WV

=x

Ï«œ <¾Õт<œnÔHÎcÑYX

Z

ÏN™ ; X]|~} ƒ ¦Z1|~} ƒ[R\T•ÒÏYÕd5xÔW™ <™AÏÞÍOÒ^]?_` y x‚zŠ <=ÒÏYÕd5xÔW™ <™AÏÞÍOÒ a

Z

R¬Î[R«™ ¤¾¶ €

ÏbcX|Ï«œ

zedsz

$ z

b$ÍOÎd¤+]ÏRLÑSRgf

C£¢HÄhšE ˜ |£¤Hƒ\ikj <=ÒxÓlX]|£¤Hƒ\m¥1|£¤Hƒ

<=ÒxÓÏb

C£¢HÄKE X]|En@ƒ\ia |En@ƒ |En ¶ €jonJpZ¤+ ˜ |En@ƒ\ikjšƒ

;

Í76–Óœ¯™A΀ԔÑ8f+™

;

<™?Ï«œ8f/Ñrq=ÑnÎt8jœnÔP€ÌžÍŸ<6ÏN™AÏÞÍOÒ¾ÍbU¤Js <6Õ͜™Ñrq=ÑnÎt8 5%6P<8tÑnÎ5ÏYÒ-¤tjœ™A΀ÏÞ̙698

ÏYÕd5xÎcÍq=ѐœ5ÏN™NœH5 <8tÍu <™Xvq=Ñn΂œnԚœwarž"xÑ

Z

΀ÏN™oÑyX{z|¨~}ya ™o͛ÏYÒxÓ=ÏÞ̂<™oÑ&ӎÍOÕ ÏYÒ%<™AÏÞÍOÒ-R

¢J£Œ§=¶¬¶¬­

Á

¹k­½ª¬®”§O©cª¬­®a§=¶¬¸‚­P©c­P©ž§F=£Àk¶ˆ§=¤£µx£n©

Á

££®¸‚¼kµkª¬½Àk¼\©ž§O©cª¬­®k¸[–Ë\ªÞÄ£=ĖË\½£$§dÊ

¸‚¼k¨‚£¸

Á

ª–©c¦©c­=©ž§=¶:½§=¸‚¸5¶¬£¸‚¸Æ©c¦”§=®/1|~} ƒtž

=?>&@BA4CEDFCHG-A1I6K€I6K"N*љP€Ñm<PК<=ÕÑSR\T²œZљW‚JÍb&ÏYÕd5xÔW™ <™AÏÞÍOÒ œŒÏ«œÌ‚<6N6¬ÑcÓ-<Q$&%('*)

+

=x-,

† z + z&

Ïb

ƒ ™; ÑnÎcÑ Ï«œÒEÍ 5 <=ÏYÎQX)8! ¶„‚ œnÔ”Ì ; ™; <™X{z|¨Q}\!

Z

R¬Î[R«™…R¿œZÍOÕѥ̞͟<6ÏN™AÏÞÍOÒ

¤·¶ €j

ƒ

b$ÍOλÑrq=ÑnÎt8&ÏYÕd5xÔW™ <™AÏÞÍOÒaJ†¶‚ ™ ; ÑnÎcѕш‡Ï«œ™NœWXS¶‰‚ œnÔ”Ì ; ™ ; <™EfŠb$ÍOÎHœZÍOÕÑH¤¾¶ €

™; ћÎcÑ6P<™AÏÞÍOÒ~Xoz|¨Q}ya)Ï«œ@œŸ<™AÏ«œH‹ÑcÓ&R

¢J£J¨‚£¸g©c¨‚ª¬¤n©¾©c¦k£¥¹kª¬¸‚¤¼k¸‚¸‚ª¬­®j©c­l¯\±&²a³k´Ž©ž§=µk¶¬£·´H£n©c¸%¤­®t©ž§=ª¬®kª¬®kºl½£$§=¸‚¼k¨‚£¸%­®k¶–Ã

Á

¦kª¬¤ž¦i©c¦”§O©•§=¨‚£Œ§=µk¸‚­¶¬¼\©c£¶–Ãa¤­®t©cª¬®Ž¼k­¼k¸

Á Ĩĩ$Ä/©c¦k£d?p¨‚£n¿L£¨‚£®k¤£›½£$§=¸‚¼k¨‚£tA

C£¢HčŒE ˜Ž ‘§¦

¡



­ˆ‘%

˜­ ž

ÅƦk£»§=¸‚¸‚¼k½À\©cª¬­®P­=¿E§=® ¼k®k¹k£¨‚¶–ÃHª¬®kº¨‚£n¿L£¨‚£®k¤£5½£$§=¸‚¼k¨‚£Æ§=®k¹£€°\ª¬¸g©cª¬®kº&¹k£®k¸‚ª–©cª¬£¸¿L­¨

©c¦k£Œ½£½Pµx£¨‚¸5­=¿§P¯\±&²a³k´Ž©ž§=µk¶¬£´H£n©»ª¬¸]Q‚¼k¸g©cª–Ö”£¹iª¬®¥ÇÈOÉÞÄ

u

¶¬ª¬®k£$§=¨Àk¨‚­H¹k¼k¤n©cª¬­®iºt§=½£&½§$õx£®k­¨‚½§=¶¬ª¬«£¹a©c­ ÃHª¬£¶¬¹

C£¢HÄȚE ±d¦Z1|~} ƒ ¦ ˜U |~} ƒ\m ˜+­ |~} ƒ²|~°'¦²±ŸžŸžŸž ‚³ƒtž

Ä

=?>&@BA4CEDFCHG-AI6K€’6KwN*љˆ ¦ º ˜U ŸžŸžŸž ˜¡7¼ P€Ñ@<ÒEÍO΀Õ-<6ϔ“dÑcÓ ÍOÎt™; ÍcЎÍOÒ%<66ÏYÒEт<=Î

5xÎcÍ$Ó=Ԕ̙AÏÞÍOÒ Ðš<=Õћ<=ÒxÓj6¬Ñ™!



ŸžŸžŸž 8!

¡

P€Ñ+5xÎcÍP<&PÏN6ÏN™AÏÞѐœHœnÔ”Ì ; ™ ; <™!

­{•

˜­ –—&˜

–™

˜ m

±°'¦±ŸžŸžŸž ‚³ ; Í76–ÓœH™A΀ԔÑSR^š ; ÑnÒ ™; Ñwq[›oœvž_™ <&P 6¬Ñyž:љ‚¦ ŸYW$& Ž¬!



ŸžŸžŸž 8!

¡ ´

Ï«œ ̂<6N6¬ÑcÓ <

Š=x

_

_ Š

R

(5)

1 & t

sp ih2 $sp *h(+p */ij(im01&pr(+2 ij&2*3$

ÅƦk£ ֔¨‚¸g©Œª¬½Àx­¨g©ž§=®t©&¨‚£¸‚¼k¶–©ª¬®#ÇÈOÉ/¸g©ž§O©c£¸&©c¦”§O©›§a¸g©ž§=®k¹”§=¨‚¹¸‚­¶¬¼\©cª¬­®ª¬¸ª¬®k¹k££¹§

¯\±&²a³k´Ž©ž§=µk¶¬£´H£n©$Ä ÅƦk£¨‚£n¯£¨‚¸‚£¨‚£¸‚¼k¶–©›§=¤¤­¨‚¹kª¬®kº©c­

Á

¦kª¬¤ž¦¥£n¯£¨gà ¯\±&²a³k´Ž©ž§=µk¶¬£

´H£n©.ª¬¸ ¸g©ž§=®k¹”§=¨‚¹ª¬¸ µ”§=¸‚£¹­®¸‚£n¯£¨c§=¶E¶¬£½½§O©ž§'CL®”§=½£¹©c¦k£•£®k¸‚ª–©oà —U£½½§\Ë©c¦k£

bo®k¦k£¨‚ª–©ž§=®k¤£r—U£½½§Æ£n©c¤=ħE

Á

¦kª¬¤ž¦

Á

£.¹k­•®k­=©?¨‚£Àx£$§O©?¦k£¨‚£=Ä u ¸ Á

£.¦”§$¯£½£®t©cª¬­®k£¹

§=µx­Z¯£=Ë]©c¦k£Àk¨‚­H­=¿.­=¿.©c¦k£ I&¨g©c¦k­º­®”§=¶¬ª–©oÃ%ÅƦk£­¨‚£½ ¤$§=®k®k­=©›µx£¸‚¼k¸g©ž§=ª¬®k£¹Jª¬® ©c¦k£

º£®k£¨c§=¶ ¤$§=¸‚£CLª–©›ª¬¸›§=¤n©c¼”§=¶¬¶–ä­¨‚¨‚£¤n©›¿L­¨Œ©

Á

­%£€°H©c¨‚£½§=¶¬¸E€ÄÅƦk£¿L­¶¬¶¬­

Á

ª¬®kºÀk¨‚­H­=¿

¨‚£Àk¶ˆ§=¤£¸*©c¦k£/¿A§=¼k¶–©oÃ&¯£¨‚¸‚ª¬­®§=®k¹›£€°H©c£®k¹k¸?ª–©c¸U¨‚£¸‚¼k¶–©$ËO®k­=©?§=¸‚¸‚¼k½ª¬®kºÆ©c¦k£ Àx­¶–ÃH¦k£¹k¨c§=¶

¸‚¦”§=Àx£.­=¿”©c¦k£ ¸‚­¶¬¼\©cª¬­®:Ä]ÅƦkª¬¸]¤­®k¹kª–©cª¬­®

Á

§=¸ª¬®t©c¨‚­H¹k¼k¤£¹ª¬®aÇÈOÉHª¬®­¨‚¹k£¨]©c­•Àk¨‚­Z¯Hª¬¹k£

£€°H©c¨‚£½§=¶¬¸Ä u ¸ Á

£&¸‚££&µx£¶¬­

Á

ËH®k­®k£&­=¿:©c¦k£¸‚£Œ§=¸‚¸‚¼k½À\©cª¬­®k¸ ª¬¸.®k£¤£¸‚¸c§=¨gÃÄ ¢J£ Q‚¼k¸g©

®k££¹%¤­®t¯£€°\ª–©oÃÄ

>ŠGF>! ’6KLMK{N*љB‚P€Ñ <̞ÍOÒMq=ш‡~q[›oœvž_™ <&P 6¬Ñž:љ…RUš ; ÑnÒ ‚¥Ï«œjœ™ <=ÒxӚ<=΂Ó&R

"FG6G#%$¢J£Ö\°j¸‚­½££¶¬£½£®t©(a ¶ ‚xÄ ¢Wª–©c¦kª¬®©c¦k£ ֔¨‚¸g©vŒ|¸g©c£Àk¸

Á

£¥¸‚¦k­

Á

£¸‚¸‚£®t©cªˆ§=¶¬¶–Í©c¦”§O©Wa¾ª¬¸?§5¤­®t¯£€°P¤­½Pµkª¬®”§O©cª¬­®Œ­=¿”¤£¨g©ž§=ª¬®›ª¬½Àk¼\©ž§O©cª¬­®k¸Uª¬®^‚©c¦”§O©§=¨‚£

¤­®k¤£®t©c¨c§O©c£¹J­®©c¦k£ ¤$§=¨‚¨‚ª¬£¨‚¸Œ­=¿ ©c¦k£ º£®k£¨c§O©cª¬®kºi½£$§=¸‚¼k¨‚£¸ ˜­ |~° ¦l±ŸžŸžŸž ‚³ƒ€Ä

ÅƦk£©c¦k£­¨‚£½ ©c¦k£®|¿L­¶¬¶¬­

Á

¸ª¬½½£¹kªˆ§O©c£¶–ÿL¨‚­½ § ¨‚£¸‚¼k¶–© ª¬®WÇÈdÉmCY©c¦k£¸‚ª‡°H©c¦|¸g©c£À

µx£¶¬­

Á

Eۀ

bo®¾¹k£n©ž§=ª¬¶

Á

£›Àk¨‚­H¤££¹%§=¸Æ¿L­¶¬¶¬­

Á

¸Ä

&('*),+.-/10

‘

—U£n©oa¾¶‰‚µx£›§=®¾§=¨‚µkª–©c¨c§=¨gÃa£¶¬£½£®t©5­=¿?­¼k¨Æ¸‚­¶¬¼\©cª¬­®:Ä

2 ­

‘§¦ a |£½s­Ÿƒ»° ¶ ¬±ŸžŸžŸž‚³´

§=®k¹¾¶¬£n© 3 Ž

‘§¦o¬°

2 ­ ¦ jW´ p¹¬±ŸžŸžŸž=³´

3 – ‘§¦o¬‹

2,4 ij/

a 576

2,4

¶‰‚_´ p ¬±ŸžŸžŸž ³´

3 8

‘§¦o¬:9

2<;

ijs

a 5>=

2<;

†¶‰‚_´ p ¬±ŸžŸžŸž ³´

¸‚¼k¤ž¦¾©c¦”§O©



­<?A@1B(C@ED 2 ­

¦±

¦k­¶¬¹k¸Æ©c¨‚¼k£=Ä

F”­¨ ‹ ¶ 3 – ¶¬£n©

GIH 4KJ

‘§¦

a 576

2,4

¶‰‚%ž

±»­

Á

Ë8ª–¿]ª–©©c¼k¨‚®k¸»­¼\©Æ©c¦”§O©

3 8

¦MLkËk©c¦k£®

Á

£›¦”§$¯£

Ch\Äð E 

­<?A@1B 2 ­

GIH

­ J ¦ 

­<?A@1B

a 5 ˜ ¦ aU

(6)

©c¦”§O© ª¬¸Ë&aª¬¸ §¤­®t¯£€°¤­½Pµkª¬®”§O©cª¬­® ­=¿E­¨g©c¦k­º­®”§=¶\£¶¬£½£®t©c¸ ­=¿ ‚xÄÅƦk£5ÅƦk£­¨‚£½

©c¦k£®¥¿L­¶¬¶¬­

Á

¸Œ§O©›­®k¤£§=¸

Á

ª¬¶¬¶µx££€°\Àk¶ˆ§=ª¬®k£¹¥ª¬® ©c¦k£7¤Wn ÄÅƦk£¨‚£n¿L­¨‚£=Ë]ª–©›ª¬¸

­¼k¨»§=ª¬½©c­Àk¨‚­Z¯£©c¦k£Œ£½À\©oÃH®k£¸‚¸•­=¿

3 8 Ä

+.-/10

‘

4.­®k¸‚£

>

¼k£®t©c¶–ÃË

Á £ Á ª¬¶¬¶Ž®k­

Á

¤­®t©cª¬®Ž¼k£¼k®k¹k£¨?©c¦k£Æ§=¸‚¸‚¼k½À\©cª¬­®›©c¦”§O©

3

8

¦ L žOÅƦkª¬¸

Á

ª¬¶¬¶:¶¬£$§=¹a©c­§ ¤­®t©c¨c§=¹kª¬¤n©cª¬­®:Ä

±»­

Á

˔¿L­¨ 9S¶

3 8

Àkª¬¤F GIH

;,J

¶‰‚§=®k¹

H

;,J

¸‚¼k¤ž¦¾©c¦”§O©

GIH

;,J

z|¨

= a 5 =

2<;

ž

ÅƦ”§O©»ª¬¸Ë\¿L­¨ 9 ¶

3 8 Ë Á

£›¦”§$¯£

Ch\ħ¢E

GIH

;,J

i a 5>=

2<;

­®

H

;,J

§=®k¹ GIH

;,J

|

H

;,J

ƒ"m 1|

H

;,J

ƒ@ž

¢J£Œª¬®t©c¨‚­H¹k¼k¤£©c¦k£Œ®k­=©ž§O©cª¬­®

H

;,J

¦ H

;,J

H

;,J

žŸžŸž

¡H

;,J

Á

¦k£¨‚£

­H

;,J

¦

H

;,J

½s­•¿L­¨ °'¦±ŸžŸžŸž ‚³ §=¸Æ¼k¸‚¼”§=¶ÞÄ ÅƦk£®

Á

£›¨‚£

Á

¨‚ª–©c£-Ch\ħ¢E

Ch\ÄhšE

2<;

GIH

;,J

i1a 5>=

H

;,J

|*9S¶

3 8 ƒ

§=®k¹

Ch\ÄKE

2<;

GIH

;,J

|

H

;,J

ƒ\m

2<;

1|

H

;,J

ƒ |*9S¶

3 8 ƒ

ÅƦk£¨‚£›ª¬¸Æ®k­¦”§=¨‚½ ª¬®¾§=¸‚¸‚¼k½ª¬®kº ¿L­¨ 9S¶

3 8

Ch\čŒE

1|

H

;,J

ƒD¦ ˜1 |

H

;,J

ƒH¦ ˜U |m

H

;,J

ƒ

¦ ˜

|

H

;,J

ƒH¦

˜

|

H

;,J

ƒ

¦ žŸžŸž

¦ ˜+¡ |

H

;,J

ƒ ¦ ˜¡ |

¡H

;,J

ƒdž

²¾­¨‚£­Z¯£¨ËxµtÃ%§=ÀkÀk¶–ÃHª¬®kº-—U£½½§ KkčŒSCLÅƦk£3bo®k¦k£¨‚ª–©ž§=®k¤£m—U£½½§šE.ª¬®JÇÈdÉÞË

Á

£›½§$Ã

¹k£¤¨‚£$§=¸‚£i¸‚­½£­=¿Æ©c¦k£!

H

;,J

¸‚¼k¤ž¦|©c¦”§O©£n¯£®t©c¼”§=¶¬¶–à 1|

H

;,J

ƒ'¦ 1|

H

;#"J

ƒs|*9  9%$¯¶

3 8

ƒ§=®k¹¥¦k£®k¤£©c¦k£

>

¼”§=®t©cª–©cª¬£¸Œª¬®DCh\čŒE•¤­ª¬®k¤ª¬¹k£P¿L­¨&¯=§=¨gÃHª¬®kº 9·¶

3 8 Ä u

¶¬¸‚­kË

®k­=©c£©c¦”§O©

Ch\ÄȚE GIH

;,J

ª¬¸ÆÀx­¸‚ª–©cª–¯£­®&

H

;,J

|*9S¶

3 8

ƒdž

')(*!+.-/10

‘

±»­

ÁSÁ

£›¹k£n֔®k£

G

‘§¦



4

2,4 GIH

4KJ

ž

(7)

1 & t

F”¼k¨g©c¦k£¨‚½­¨‚£=Ë

Á £ Á

ª¬¶¬¶:¹k£n֔®k£P§½£$§=¸‚¼k¨c§=µk¶¬£Œ¸‚£n©h¤ ¦ ¤ 

žŸžŸž

¤ ¡ Á

¦kª¬¤ž¦

Á

ª¬¶¬¶

¸‚£¨g¯£›¿L­¨Æ¹k­½ª¬®”§O©cª¬­®­=¿Ba#£n¯£®t©c¼”§=¶¬¶–ÃÄ

F?ª¬¨‚¸g©5­=¿§=¶¬¶ÞËH¿L­¨ 9S¶

3 8 Á

£›Àk¼\©

Ch\č<E ¤ ;

‘§¦ ;H

;,J

ž

±»£€°H©$˔¿L­¨ ‹ ¶ 3 – Á

£Œ¤ž¦k­H­¸‚£ ¤ 4 pZ½

4

¸‚¼k¤ž¦¾©c¦”§O©{a

} 6

ikj§=®k¹

Ch\ÄMšE 4

|£¤

4

ƒH¦

4

|£¤

½ 4

ƒD¦µ1|

H

;,J

ƒ |*9S¶

3 8

ƒtž

ÅƦk£•¤­½½­® ¯=§=¶¬¼k£»­®©c¦k£•¨‚ª¬º¦t© ¦”§=®k¹a¸‚ª¬¹k£5­=¿@Ch\ÄMšEª¬¸/©c¦k£»­®k£»¹k£n֔®k£¹ª¬®ŽCh\čŒEžË

¸‚­·©c¦”§O©a®k­

Á

§=¶¬¶Æ©c¦k£

>

¼”§=®t©cª–©cª¬£¸ª¬®Ch\čŒE§=®k¹Ch\ÄMšE§=ºt§=ª¬®l¤­ª¬®k¤ª¬¹k£=Ä u ¸ a ª¬¸

Àx­¸‚ª–©cª–¯£ ­®À”§=¨g©c¸­=¿ ½ 4

ËU©c¦kª¬¸¤$§=®µx£§=¤ž¦kª¬£n¯£¹Jµtà —WQc§=Àx­¼k®k­OE¸ÅƦk£­¨‚£½ §=®k¹

©c¦k£@bo®k¦k£¨‚ª–©ž§=®k¤£h—U£½½§›ª¬® ÇÈdÉÞÄ ±»­=©c£•©c¦”§O©.©c¦k£E•£®k¸‚ª–©oà —U£½½§sC—U£½½§mKkÄ

ð

ª¬®

ÇÈOÉ+E.£®k¸‚¼k¨‚£¸

Ch\ĚE

GIH­ J

|£¤+­ ƒD¦

a |£¤

­ ƒ

2 ­ m

˜­

|£¤+­ ƒH¦Z1|

H

;,J

ƒ

¿L­¨ ° ¶ 3

–+ 9S¶

3 8 Ä

F?ª¬®”§=¶¬¶–ÃË

Á

£›¤ž¦k­H­¸‚£Œ¸‚­½£&Ö\°\£¹9S¶

3 8

§=®k¹iÀk¼\©5¿L­¨ ° ¶ 3 Ž

¤ ­ ‘§¦ ­

H

;J

ž

ÅƦkª¬¸

Á

§$Ã

Á

£Œ¦”§$¯£›®k­

Á

ª¬®k¹k££¹¾¹k£n֔®k£¹§ ¸‚£n©

¤ ‘§¦ ¤1

¤ žŸžŸž

¤+¡

¸c§O©cª¬¸g¿YÃHª¬®kº

Ch\Äð E 1|£¤HƒD¦ ¨-©«ª_¬

˜­

|£¤+­ ƒ´ ¦µ1|

H

;,J

ƒ |*9S¶

3 8

ƒtž

ÅƦkª¬¸5¦k­¶¬¹k¸©c¨‚¼k£›§=¸Æ©c¦k£

>

¼”§=®t©cª–©cª¬£¸Æª¬® Ch\čŒE§=®k¹ Ch\ÄMšE§=¨‚£›§=¶¬¶E£

>

¼”§=¶ÞÄ

) +.-/10 ‘

±»­

ÁSÁ

£›Àk¨‚­Z¯£Œ©c¦”§O© G £€°\¤££¹k¸Oa#­® ¤Ä

F?ª¬¨‚¸g©5­=¿§=¶¬¶E¤­®k¸‚ª¬¹k£¨ 9S¶

3 8

Ä/¢J£Œ¦”§$¯£

Ch\Ä

ðð

E G } = ¦ G =

= 2<;

G ; =

= ia

=

=

¦ a } =

µtà Ch\ÄhšE€Ä

±»£€°H©$Ë8¤­®k¸‚ª¬¹k£¨›° ¶ 3

–?Ä F”­¨9S¶

3 8 Á

£›¦”§$¯£

Ch\Ä

ð

¢E G ‘§¦



4

?A@1B C@ED 2,4

GIH 4KJ

2 ­ G ­ 2

;

G

; ž

#5£¤$§=¶¬¶ ©c¦”§O© GIH

;J

¶ ‚·ª¬¸PÀx­¸‚ª–©cª–¯£­® ­H

;,J

p ½s­CL¸‚££ Ch\ÄȚE=E€Ä u ¶¬¸‚­kˏaL¶ ‚·ª¬¸

Àx­¸‚ª–©cª–¯£¸‚­½£ ¦k£¨‚£Œ­® ½s­OÄ»£®k¤£=˔µtÃa©c¦k£´H¼kÀkÀx­¨g©5ÅƦk£­¨‚£½ŽC~KkÄÈ ­=¿ÇÈdÉNE.µx­=©c¦

(8)

¦”§$¯£©c¦k£¸c§=½£¤$§=¨‚¨‚ª¬£¨ª¬®k¸‚ª¬¹k£&­=¿½s­

Á

¦kª¬¤ž¦i®k£¤£¸‚¸c§=¨‚ª¬¶–Ãaª¬®k¤¶¬¼k¹k£¸¯¤

­

Ä/ÅƦk£¨‚£n¿L­¨‚£=Ë

Ch\Äð ¢E.½§$Ãaµx£Œ¤­®t©cª¬®Ž¼k£¹¾­®Ž¤

­

©c­ª¬½Àk¶–Ã

Ch\Ä

ð

hšE G 2 ­ G ­

2

;

G

; ¦ a 2

;

G

;

i1a ­® ¤ ­

F?ª¬®”§=¶¬¶–ÃË

Á

£›¦”§$¯£Œ¿L­¨ ° ¶ 3 Ž

Ch\Ä

ð

KE G } ˜ ¦ G ˜

=

2

;

G

; ˜

=

ij3¦a

} ˜ ž

!) +.-/10

‘

4.­½Pµkª¬®kª¬®kº Ch\Äð KE€ËCh\Äð hšE€Ë”§=®k¹ Ch\Äðð EžË

Á

£Œ­µ\©ž§=ª¬®

Ch\Ä

ð

ŒE G ia ­®´ž

±»­

Á

­µk¸‚£¨g¯£›©c¦”§O©

Ch\Äð ȚE

1|£¤HƒD¦



4

?A@ B C@

8

2,4

1|£¤Hƒ=ƒ

¦ 

4

?A@ B 2,4

1|

H

;J

ƒ 

;

?A@ED 2<;

1|

H

;,J

ƒ



4

?A@ B a›|£¤

4 ƒ 

;

?A@ED 2<;

G ;

|

H

;,J

ƒ µtà Ch\ĚEžË]Ch\ÄKE

i 

4

?A@ B a›|£¤

4 ƒ 

;

?A@ED a |

H

;,J

ƒ µtà Ch\ÄhšE



4

?A@ B a›|£¤

4 ƒ 

;

?A@ED a |£¤

; ƒ µtà Ch\č<E

a |

4

?A@ B(C@ED

¤ 4 ƒ

a |£¤Hƒtž

»£®k¤£=˔¿L­¨Æ¸‚¼¤ª¬£®t©c¶–ø‚½§=¶¬¶^ikjP©c¦k£Œª¬½Àk¼\©ž§O©cª¬­®

G ‘§¦ | ±›Œƒa G ¶‰‚

£€°\¤££¹k¸Oa#­®´i§=®k¹i¸g©cª¬¶¬¶E¸c§O©cª¬¸g֔£¸ G |£¤HƒD1|£¤Hƒ€Ë\©c¦”§O©»ª¬¸Ë\ÃHª¬£¶¬¹k¸

G

z|¨Q}wa¥ž

ÅƦkª¬¸Àk¨‚­Z¯£¸©c¦”§O©©c¦k£%§=¸‚¸‚¼k½À\©cª¬­®l½§=¹k£¾§O©©c¦k£¾µx£ºª¬®k®kª¬®kº­=¿•©c¦k£

–

¤Wn

¶¬£$§=¹k¸Æ©c­§ ¤­®t©c¨c§=¹kª¬¤n©cª¬­®:ËkªÞÄ£=ĖË

Á

£Œ¦”§$¯£

3 8 ¦ LkÄ

) +.-/10

‘8±»­

Á Ë a ¦ 

4

2,4 GIH

4KJ

(9)

ª¬¸§•¤­®t¯£€°¤­½Pµkª¬®”§O©cª¬­®›­=¿8£¶¬£½£®t©c¸­=¿`‚Œ©c¦”§O©/§=¨‚£.¤­®k¤£®t©c¨c§O©c£¹­®P©c¦k£.¤$§=¨‚¨‚ª¬£¨‚¸

½/­ |~°{¶

3

–)ƒ€Ä%±»£¤£¸‚¸c§=¨‚ª¬¶–ÃË]¿L­¨£n¯£¨gà ° ¦ ±ŸžŸžŸž ‚³©c¦k£¨‚£ª¬¸P§=®J£¶¬£½£®t©P­=¿

‚¥©c¦”§O©Pª¬¸Àx­¸‚ª–©cª–¯£­®·½s­dÄ c Ã¥©c¦k£§=µx­Z¯£Àk¨‚­H¤£¹k¼k¨‚£=Ë

Á

£a֔®k¹·¿L­¨£n¯£¨gà °¥§=®

£¶¬£½£®t©­=¿W‚©c¦”§O©ª¬¸.¤­®k¤£®t©c¨c§O©c£¹i­®/½s­OÄ»£®k¤£=ËkµtÃ/4.­¨‚­¶¬¶ˆ§=¨gÃ'Kkħ¢HÄ­=¿ ÇÈOÉÞËH©c¦k£

ÅƦk£­¨‚£½ ª¬¸¯£¨‚ª–Ö”£¹:Ä

Kg>KyK

>! 1’6K€I6K.ÅƦk£­¨‚£½ È\Ä

ð Ä ­=¿ÇÈOÉU¤$§=®¾µx£Œª¬½Àk¨‚­Z¯£¹¾¼kÀx­®¾§=¤¤­¨‚¹kª¬®kº¶–ÃÄ/ÅƦ”§O©

ª¬¸Ëtª–¿`‚

Ž

ª¬¸ §&¤­®t¯£€°¯\±&²a³k´Ž©ž§=µk¶¬£5´H£n© ¿L­¨/§&¶¬ª¬®k£$§=¨?Àk¨‚­H¹k¼k¤n©cª¬­® ºt§=½£¤­®k¸g©c¨‚¼k¤n©c£¹

µtÛ­¨g©c¦k­º­®”§=¶t¼k®kª–¿L­¨‚½)¹kª¬¸g©c¨‚ª¬µk¼\©cª¬­®k¸U­®P§Æ֔®kª–©c£ Àk¶ˆ§$ã¨]¸‚£n©$ËO©c¦k£® ‚

Ž

ª¬¸]¸g©ž§=®k¹”§=¨‚¹:Ä

F”­¨©c¦k£ÆÀk¨‚­H­=¿pË

Á

£5¹k­Œ®k­=© ¦”§$¯£5©c­Œ§=¸‚¸‚¼k½£Æ©c¦”§O©\‚

Ž

ª¬¸Àx­¶–ÃH¦k£¹k¨c§=¶ÞÄ I•¿x¤­¼k¨‚¸‚£=ˎ©c¦k£

¨‚£n¯£¨‚¸‚£&¸g©ž§O©c£½£®t©Æ§=¸‚¸‚£¨g©cª¬®kºŒ©c¦”§O©§=®tøg©ž§=®k¹”§=¨‚¹¸‚£n©.ª¬¸.§¯\±&²a³H¸‚­¶¬¼\©cª¬­®Àk¨‚£n¯=§=ª¬¶¬¸

ª¬®©c¦k£Ö”®kª–©c£¤$§=¸‚£

Á

ª–©c¦i¼k®kª–¿L­¨‚½ ¹kª¬¸g©c¨‚ª¬µk¼\©cª¬­®k¸Æ§=¸ÆÀk¨‚£n¯Hª¬­¼k¸‚¶–ÃÄ

p 7pr(+p›$/0Up›k

Çð ÉN^W^W\_a)V "!$#%!]V+X'&)(jV]V+XV+X* #%!,+- ÍOÎcѐœ Íb››ÍOÒ: <™oÍOÕ ÏÞÌYN?ÏYÒEт<=Î/..ÎcÍ7:

Ó=Ԕ̙AÏÞÍOÒ10›<=ÕѐœSR.²%§O©c¦k£½§O©cª¬¤¸­=¿hI&Àx£¨c§O©cª¬­®k¸U#5£¸‚£$§=¨‚¤ž¦È\ËjC

ð

M

ð

E€Ë ÀkÀ:Ä

K¢ ³ K¢h\Ä

Ç¢dÉ'R"NX32" R4+,65.^7Š3@V+X*6(8!, 7.X'&+\_a\_a96:;!,WV+X'&ŽY%['¡:/. T$¡:<7=>?!,+- ÍOÎcÑ

<=ÒxӞ_™ <&P 6¬Ñ{ž:љNœÍb"N)<=ÎÞЎÑ?0›<=Õѐœ"T•Î€Ï«œnÏYÒHЛÏYÒA@5̞ÍOÒEÍOÕ ÏÞ̐œSRB=­¼k¨‚®”§=¶k­=¿3C/¤­OÊ

®k­½ª¬¤&ÅƦk£­¨gþÈM\ËC ð ȚE€Ë\ÀkÀŽ¢ Êr¢ ðð Ä

ÇhOÉ5hV+a :9hY'!,+ED]ÍO΀Õ-<™AÏÞÍOÒWÍbE-H<=Ît™oÑ6œ¾ÏYÒ N)<=ÎÞÐŽÑ œ <=ÎGFtљNœSRB=­¼k¨‚®”§=¶5­=¿/C/¤­OÊ

®k­½ª¬¤&ÅƦk£­¨gà <HËC

ð

&<7KE€ËkÀkÀ:ÄKŠŒh›Ê KtÈÈ\Ä

ÇK=ɄY%[]\_^W^W`[]\V+a9R4!,+"q[›oœvž_™ <&P 6¬Ñ"ž:љNœ6b$ÍOÎwN?ÏYÒEт<=Î*..ÎcÍ$Ó=Ԕ̙AÏÞÍOÒH0›<=Õѐœ

Z

ÏN™ ;

I

Ît™

;

ÍcЎÍOÒ%<6J0»ÍZÍ$ÓLKŒÏ«œ™A΀ÏPÔW™AÏÞÍOÒ œÄ.•ª¬Àk¶¬­½§aÅƦk£¸‚ª¬¸ËrC£¢ ŒE€Ë)bo®k¸g©cª–©c¼\©c£­=¿

²%§O©c¦k£½§O©cª¬¤$§=¶3C/¤­®k­½ª¬¤¸ËG»®kª–¯£¨‚¸‚ª–©oÃi­=¿c.ª¬£¶¬£n¿L£¶¬¹:Ä

njdɏ2'M V+`=NO!QP!,+SR8ÍOÒ ››ÑnÔHÕ-<=ҔÒ: œ¥ÍOÎÞЎÑnÒ œ™oÑnÎ€Ò ž_™ <&P 6¬ÑOž:љNœSR •§=®k¹kµx­H­F­=¿

T

§=½£ÅƦk£­¨gÃ

Á

ª–©c¦UC/¤­®k­½ª¬¤

u

ÀkÀk¶¬ª¬¤$§O©cª¬­®k¸Ë=V ­¶ÞÄ ð Ë)4.¦”§=À\©c£¨ ð <HË6#ŒÄQB\Ä

u ¼k½§=®k®¾§=®k¹´xÄ •§=¨g©C/¹k¸Ä–Ë]C 𠚢E€ËkÀkÀ:Ä-Œ7K&hÊ"Œ Ä

ÇÈOÉ(O.`\_X434W]^W^W\_a9<#%!,)V+X'& Y%['¡:/. T$¡:<7=<?+-TX- ; <=Î=<ŽÌ™oÑn΀ϔ“<™AÏÞÍOÒÍbYq[›oœŽ:

ž_™ <&P 6¬Ñž:љNœ b$ÍOΉN?ÏYÒEт<=ÎE..ÎcÍ$Ó=Ԕ̙AÏÞÍOÒO0›<=ÕѐœSR@bo®t©c£¨‚®”§O©cª¬­®”§=¶8B=­¼k¨‚®”§=¶P­=¿

T §=½£&ÅƦk£­¨gà ¢ \ËC£¢ E€ËkÀkÀ:Äh Ê.È ð Ä

Ç<dÉmT/.X 0m\243@V+X]X*Y# .[]X §=®k¹„7.a`9 \_X]`;:\_aX*YZ `[+V+a9+ š ; ўÍOÎt8 Íb

0›<=Õѐœ·<=ÒxÓ\@5̞ÍOÒEÍOÕ ÏÞÌ^]&Ñ ; <qZÏÞÍOÎ[R4_/¨‚ª¬®k¤£n©c­® G»®kª–¯£¨‚¸‚ª–©oÃ`_/¨‚£¸‚¸ C ð KKkË

ð

KŠ<HË

ð

&ŒhšE€ËkÈK

ð

ÀkÀ:Äx´ c± È ð Ê K ð MhdÊ

Referenzen

ÄHNLICHE DOKUMENTE

Later, Erdo˝s also posed the problem of determining the maximum number g( k) of points in general position in the plane so that no k points form the vertex set of an empty

• The adjoint ODE approach, see [6], is advantageous compared to the sensitivity ODE approach if the number of nonlinear constraints is less than the number of variables in

The basic dierences of our approach to other existing embeddings are that there are no equivalence classes (as in [13], [15]) and secondly, that dierences of directed convex sets in R

[r]

Key words: Noncooperative constrained games, Nash equilibrium, subgradient projec- tion, proximal point algorithm, partial regularization, saddle points, Ky Fan

Furthermore, the cumulative distribution function P {ξ ≤ x } of a max-stable random vector ξ with unit Fréchet marginals is determined by the norm of the inverse to x, where

Theorem: A language L over X is regular if and only if L can be generated by a finite number of iterated applications of the operations union, product and Kleene-closure ∗ starting

In convex geometry, where one strives to avoid a priori smoothness as- sumptions different from those already implied by convexity itself, curva- ture measures of arbitrary