• Keine Ergebnisse gefunden

Practical Experiments with Regular Approximation of Context-Free Languages

N/A
N/A
Protected

Academic year: 2022

Aktie "Practical Experiments with Regular Approximation of Context-Free Languages"

Copied!
28
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Volltext

(1)

=>-%('-+%

?-@BADCFEHGI@BJLKNMOPM*ARQPSUTWV

X:Y[Z]\_^a`cbdYfeWYR^gZ]hjilk;YD`nm]Y[ZLoqpgZ0rsZWm]tvuwhDtx^ay

z`nm]Yfy{yxt{|!Yf`}hDY

~I[€g[W‚!ƒ„_f…q†}‡Dˆa‰;‚a]Šˆa‹q‰[Œ[‰j‰f]ˆŽ…q†1‚!…Œj‡g}‰H…‘HBŒ[…‚“’”w‹q…•d‚a}…•‡g„–‚!…•‡g—a‹˜€aHN‚Œj‡gw…•j™a…›šœ]]jž—aW‚a„–š

„–‚ajŸ ‹qUŒ[ƒ¡wˆa‹˜—2¢j‡a…q†„[…q†}‡Rˆa‰…q†1‚!…Šƒv]‚nˆ&…•‡N‰jw¢[‰f[…‘‰–‚a<ˆ…q†}‡g‰f…q†1‚!…Šƒ{W‚nˆ&…•‡£‰jR¤w[H‰f[…‘‰–‡¥œ¦…q†}

‡gH‹v—a‹˜<‚!ƒ;Œj‡gw…•j™a…›šœ]]jNƒ§‚a—gw‚R—nR¨;~I‡g„£‡¥œ…q†}[‰[„[…q†}‡Dˆa‰‡¥œª©g«¬U­¯®˜°w©2°w±P±¯©g²³¯´‘µ+°}¶·´˜²U¸.‚aj

<[¹“ŸŽ‚a<ˆ2‰f‡g„_‡a…q†}[H‰N‚a]¤<jH‰f[w…•]ˆº†}[]‹q»‚2„_‡g]N]‘’”U]ˆœf‡gH„l¹”‹q…q†]H‰¼¤wjŒf…:…•‡+j™g‹˜‰H…›š

‹˜—Nƒ¡‹q…•[W‚!…‘1]D¨½ W‚*Œf…‘‹›Œ]‚!ƒ¯j™j¤w[H‹˜„[w…‘‰Ž¹”‹‘…q†&…q†}ˆa‹¾s[][w…;„[…q†}‡Dˆa‰‡¥œª]•—g}ƒ§‚a‚H¤n¤<]‡R™g‹q„–‚!…‘‹¼‡g

‚a];¤w[‘œ[‡gH„]ˆŠœf‡gª‰›¤B‡·¿a[Bš•ƒ§‚a—a}‚R—*‹˜a¤<1…•ÀF†*Áj¤w‡a…q†}[‰fH‰“œ]j‡g„‚–‰¼¤wjjŒH†]jŒ]‡j—gw‹xÃD[‚a]”’žƒ…•[]]ˆ

…q†*]‡g!—g†&‚:’“w‹‘…•¦‚a1…•‡g„_‚!…•‡gU¨

ÄÅ

¸<¶D©g²FÆP­¯Ça¶·´˜²U¸

È*Y[ÉnY[Zj^ayI\_Y[m]i}pÊ}eŠpao¯Z]Yf|!Ë}y˜^·Zd^gÌ}Ì}Z]pRÍ1t{\^·m]txpa`£p!o¯hDpa`*m]Y[ÍmWμoxZ]YDYŽyx^a`}|!Ëw^a|aYDeÏiw^DÉnYªÐIYfYf`£Ì}Z]paÌUp!eWYfÊ

t{`m]i}Y;y{tvm]Y[Zj^gm]Ë1Z]Y!ÑDÒBpgZ”eWpa\_YaÓRm]i}YžZ]YD|!Ë}yx^gZPyx^a`}|!Ëw^a|!YÔt{e“^deWË1ÌUY[Z]eWYfmPp!o1m]iwYÔhfp!`nm]YfÍmWμoxZ]YDYžy˜^g`w|aËB^g|!Y!Ó

^g`wÊo˜paZ”pam]i}Y[Z]e”t{m“t{e”^ªeWË1ÐweWY[mDÑaÕYÏiw^DÉnYÏt{\–Ìwy{YD\–Yf`*m]Yfʦ^:yx^gZ]|!Y `*Ë}\ÐUY[Zžp!oB\–Y[m]iwp*ÊwefÓ!^g`wÊÖdi}YfZ]Y

`}YfYDÊ}YfÊ&Ö YZ]Y[uw`wYfÊ&m]i}YD\ÂÖdtvm]i^a`º^a`w^ayv×1eWt{edp!oPm]i}Y|gZj^a\_\_^gZDÑwÕY^ay{eWp–ÌwZ]pgÌIpaeWY¦^–`*Ë}\ÐIY[Z:p!o

`}Y[Ö0\_Y[m]i}pÊ}efÑ

Ø i}Yª^g`B^gy{×eWtxeÔt{eÔÐB^aeWYfÊNp!`N^eWË1Ù_hft{YD`nm hfp!`}Ê}t{m]t{p!`_oqpaZ;hfp!`nm]YfÍmWμoxZ]YDYd|aZj^a\–\^gZ]ežm]p|!Yf`}YfZj^·m]Y

Z]Yf|!Ë}yx^gZyx^a`}|!Ëw^a|!YfefÑPÒBpaZ¦^a`4^gZWÐwtvmWZj^gZW×+|aZj^g\_\_^gZDӏm]i}t{e¦^a`w^ayv×1eWt{et{ÊwYf`nm]tvuBYfeeWYfm]ep!o Z]Ë}yxYfem]iw^gm

`}YfYDÊ£m]pÐUYŽÌ}Z]phfYDeWeWYfÊ&tx`&^e¥ÌUYfhDtx^ayUÖÏ^D×£tx`paZ]Ê}Y[Zdm]p–paÐ}mj^at{`&^¦Z]YD|aËwyx^gZdyx^a`}|!Ëw^a|aY!Ñ Ø iwY`w^gm]Ë1Z]Y

pao m]i}txeŽÌ}Z]phDYfeWeWt{`}|ÊwtvÚUY[Z]eo˜paZm]i}Y_Z]Yfe¥ÌIYfh[m]t{É!Y^gÌ}Ì}Z]pRÍ1t{\_^gm]t{p!`\–Yfm]i}pÊ}efяÒwpaZ¦pam]i}Y[ZÌB^gZWm]ep!o

m]i}Y_|aZj^g\_\_^gZDӏ`}pe¥ÌUYfhDtx^ay“mWZ]YR^gm]\–Yf`*mt{e`wYfYfÊwYfÊ^a`}Ê+m]i}Y_|aZj^a\–\^gZZ]Ë}y{Yfe^gZ]Y–mWZj^a`}eWyx^gm]YfÊÛm]p

e¥mj^·m]YDed^a`}ÊmWZj^g`weWtvm]t{p!`}eÏp!o“^¦uw`wtvm]Y^gË}m]pa\^gm]pa`Ödtvm]i}p!Ë1md^gÚUYDh[m]t{`w|¦m]i}YŽyx^a`}|!Ëw^a|!YaÑ

ÒwYfÖ(p!o1m]iwYžÌwË1ÐBy{t{eWi}YDÊ^gZWm]t{hDy{Yfe¯p!`Z]YD|!Ë}yx^gZ“^gÌ}ÌwZ]pDÍ1t{\^gm]t{p!`iw^DÉnY;Ê}t{eWhDË}eWeWYfÊm]i}Y;^gÌ}ÌBy{t{hD^gm]t{p!`

t{`Ì}Zj^ahfm]t{hfY!Ñ z `&Ì<^·ZWm]txhfË}yx^gZDÓwyxtvmWm]y{Y^gmWm]YD`nm]t{p!`&iw^aedÐUYDYf`|!tvÉnYf`&m]p–m]i}Yoqpayxy{pRÖdt{`}|mÜÖ pNÝ*Ë}Yfe¥m]txpa`wefÑ

ÒPt{Z]e¥mDÓIÖdiw^gmiw^gÌ}ÌUYD`}eªÖdiwYf`^£hDp!`nm]Y[ÍmWμo˜Z]YfY|aZj^a\–\^·Z|aZ]pRÖdeŽt{`+eWt{ÞDY·ß¦Õiw^gmt{eªm]i}YD`2m]iwYt{`1Î

h[Z]YD^aeWY£p!oŠm]i}YNeWt{ÞDYfep!oÏm]i}Y£t{`nm]YfZ]\–YfÊwtx^gm]Y_Z]YfeWË}y{m]e^g`wÊ(m]i}Y£pgÐwmj^gtx`}YfÊ(\_t{`}t{\^ayÔÊ}Yfm]Y[Z]\–tx`}t{e¥m]t{h

^gË}m]pa\^gm]pa`UߣÈ*YDhfp!`}ÊIÓPiwpDÖáàWÌ}Z]YfhDt{eWYfâ2^gZ]Y_m]i}YN^gÌ}Ì}Z]pRÍ1t{\^·m]txpa`weHß Ø iw^gm¦t{efÓPi}pRÖ\Ëwhji(yx^gZ]|aYfZ

m]iw^a`2m]i}Y–pgZ]tx|atx`w^ayPhDp!`nm]Y[ÍmWμo˜Z]YfYyx^a`}|!Ëw^a|aY–t{eªm]i}Y–yx^a`}|!Ëw^a|aY–pgÐwmj^gtx`}YfÊ2Ð*×+^NeWË1ÌIY[Z]eWY[m^gÌ}Ì}Z]pRÍÎ

t{\_^gm]t{p!`IӔ^a`}Ê4i}pRÖã\Ëwhji4eW\^ay{y{Y[Ztxe¦m]i}Y£yx^a`}|!Ëw^a|!Y£paÐ}mj^at{`wYfÊ(Ð*×^2eWË1ÐweWY[m^gÌ}Ì}Z]pRÍ1t{\^·m]txpa`Uß

ä›å

pDÖÖ YŽ\–YR^aeWË1Z]Y:m]i}YNà]eWt{ÞDYfeWâp!o¯yx^a`}|!Ëw^a|aYDeÏt{`^Ì}Zj^ah[m]txhD^ayUeWY[mWm]t{`}|Ödtxy{y<ÐUYfhDpa\_Y:hDy{YD^gZŠt{`Nm]i}Y

eWYDÝ*Ë}Yfy¼Ñæ

È*p!\–Yºhfp!`}eWtxÊ}Y[Zj^gm]t{p!`}e_Ödtvm]içZ]Yf|n^gZ]Ê»m]pm]i}YfpaZ]Yfm]t{hD^aydË1Ì}ÌUYfZÐUp!Ë}`}Ê}e£p!`çm]i}YºeWt{ÞfYDep!oªm]i}Y

t{`nm]Y[Z]\_YfÊ}t˜^·m]Y–Z]YfeWË}y{m]e^a`}Êm]i}Y_uw`}tvm]Y^aË1m]p!\_^gmj^&iw^DÉnYN^ayvZ]YR^gÊ}×2ÐUYDYf`Êwt{eWhfË}eWeWYDÊÐ×+è:YDÊ}Y[Z]i}p!o

äWéDê!ênë æjÑ

z

`m]i}txež^·ZWm]txhfy{Y;Ö YÏÖdt{y{ymWZW×m]p^a`}e¥Ö Y[Zžm]i}Yd^gÐUpRÉnY mÜÖ pÝ*Ë}YDe¥m]t{p!`}e”t{`–^ªÌ}Zj^ah[m]t{hR^ay1eWY[mWm]t{`}|}Ó

Ë}eWt{`}|¦Ì}Zj^ah[m]t{hR^ay<yxt{`}|!Ë}t{e¥m]t{h:|aZj^g\_\_^gZ]eŠ^a`}Ê£eWYD`nm]Yf`whfYfeÏmj^gì!YD`£oxZ]p!\Â^e¥ÌIpgìnYD`1μyx^a`}|!Ëw^a|!YªhDpaZWÌwË}efÑ

Ø

i}Yse¥mWZ]Ë}hfm]Ë1Z]YspaoUm]iwt{ežÌB^gÌUY[Z t{e;^ae;oqpayxy{pRÖdefÑ

z

`È*Yfhfm]t{p!`NíªÖ YdZ]YfhD^ay{yBeWp!\–Yse¥mj^a`}Êw^gZ]ÊÊ}Yfuw`}tvÎ

îžï“ð}ñ”ò•óaôfõ¼ö·÷Rø¡ù›úHõ¼û¥ü¥ýR÷·ú[ö·ù‘þIü¥ÿDógï  ôDú[úö[ü¥ý!ó“üŠúHýŠú ¡ø"!·ýRü$#·ü%¼÷&')(#'*+ "#·ü

,

(2)

m]t{p!`}ežo˜Z]pa\ yx^a`}|!Ëw^a|!YÏm]iwYfpaZW×!Ñ}È*Yfhfm]t{p!`YXŽt{`nÉnYDe¥m]t{|n^·m]YDež^eWË1Ù_hftxYf`nm;hfp!`}Êwtvm]t{p!`–o˜paZ ^Žhfp!`nm]YfÍ*mWμo˜Z]YfY

|gZj^a\_\_^gZm]pÛ|!Yf`}YfZj^gm]Y^2Z]Yf|!Ë}yx^gZ–y˜^g`w|aËB^g|!Y!ÑPÕY&^ay{eWp2Ì}Z]YfeWYD`nm–m]i}YhDpa`we¥mWZ]Ë}h[m]t{p!`pao:^2uw`}tvm]Y

^gË}m]pa\^gm]pa`o˜Z]pa\ãeWË}hji^–|gZj^a\_\_^gZDÑ

z`NÈ*Yfhfm]t{p!`[Z}ÓaÖ YŠÊ}t{eWhDË}eWežeWY[ÉnY[Zj^ayw\–Yfm]i}pÊ}e“m]p^·ÌwÌ}Z]pRÍtx\_^gm]Y m]i}YŠyx^a`}|!Ëw^a|!YÏ|!Yf`}YfZj^gm]YfÊÐ*×^

|gZj^a\_\_^gZÏt{om]i}YªeWË1Ù_hftxYf`nmŠhfp!`}Êwtvm]t{p!`N\_Yf`nm]t{p!`}YDÊ£^gÐUpRÉnYŽt{eÏ`}pamÏe]^gm]t{e¥uBYfÊIÑ Ø i}YfeWYŽ\–Yfm]i}pÊ}eÏhD^a`

ÐUY–Yf`}iw^a`}hDYfÊÛÐ×Û^|aZj^a\–\^·ZŽmWZj^a`}eWoqpaZ]\_^gm]t{p!`2ÌwZ]YfeWYf`*m]YfÊ+t{`(È*YDh[m]t{p!`]\ÑPÈYfh[m]txpa`_^NhDpa\–ÌB^gZ]Yfe

m]i}YªZ]YDe¥ÌUYfhfm]tvÉnYª\_Y[m]i}pÊ}efÓ1Ödiwt{hjiyxYD^aÊ}eÏm]p–hfp!`}hDy{Ë}eWt{p!`}eŠt{`2È*Yfhfm]t{p!`

ë Ñ

`ba

©·«}®‘´qµ´‘¸°w©a´˜«dc

Ø i1Z]p!Ë}|!i}p!Ë1m&m]i}t{e£ÌB^gÌUYfZÖ Y+Ë}eWYe¥mj^g`wÊw^gZ]ÊLoqpaZ]\_^ayªyx^a`}|!Ëw^a|!YÛ`wpgmj^gm]t{p!`

ä

eWYfY+YaÑ|1Ñ

å

^gZWZ]t{eWp!`

äWéDênëfe

æWæjÑ z `m]i}t{eŠeWYfhfm]t{p!`NÖ YŽZ]YfhR^gyxyIeWp!\–YŽÐB^aeWt{hŽÊwY[uw`}t{m]t{p!`}efÑ

r Ç!²U¸<¶D«*³F¶gh›©g««–¬B©·°<µµ+°w©2i8t{ež^>ZaΛm]Ë1ÌwyxY

ä$jYkmlnkopkq

æjÓ·Ödi}YfZ]Y

j

^a`}Ê

l

^gZ]Y mÜÖ pªuw`}tvm]Y

Ê}t{esrWpatx`nmŠeWY[m]eŠp!om]Y[Z]\_t{`w^ay{eÏ^a`}Ê`wpa`*m]Y[Z]\–tx`w^ay{efÓZ]YDe¥ÌUYfhfm]tvÉnYfyv×nÓ qutvl t{e m]iwYªe¥mj^gZWmde¥×\ÐUp!y›Ów^a`}Ê

o t{es^¦uB`}tvm]YŽeWYfmdp!o¯Z]Ëwy{YfefÑw;^ahji&Z]Ë}y{Yiw^aeŠm]i}YoqpgZ]\yx{z}|Ödtvm]inx t~l ^a`}Ên| t€‚ Ó}Ödi}YfZ]Y

 Ê}Yf`}pam]YDe lyƒbj Ñ Ø

i}YZ]Yfyx^gm]t{p!`„z p!` l†…b‚ txe:YfÍ*m]YD`}Ê}YDÊm]p£^Z]Yfyx^gm]t{p!`ºpa` ‡ˆ…€‡ ^ae

Ë}eWËw^ay›Ñ

Ø

i}YŽmWZj^a`}eWtvm]tvÉnYŽ^a`}ÊZ]Y.‰BY[Í1tvÉnYŽhfy{p!eWË1Z]YpaoŠz t{eŠÊ}Yf`wpgm]YDÊ£Ð*׋z  Ñ

Ø

i}Yyx^a`}|!Ëw^a|!Y¦¬B«1¸«©·°}¶D«1Æ4Ð*×bit{eª|at{É!YD`ºÐ*×m]i}Y¦eWY[m[Œ+

tŽj[vFq

z 

‘nѓ’ ×Ê}Yfuw`}tvÎ

m]t{p!`IÓBeWË}hHiÛ^_eWY[mªt{e:^NÇ!²U¸<¶D«*³I¶+gh¼©·««yx^a`}|!Ëw^a|!YaÑF’ ×©g«1ÆP­¯Ça¶·´˜²U¸4paož^|gZj^a\_\_^gZsÖ Y\–YR^a`&m]i}Y

Yfy{t{\_t{`w^gm]t{p!`NoxZ]p!\

o

pao”^gyxyUZ]Ë}yxYfeTx{z•”ºeWËwhjim]iB^·m q z 

|x–„z—|˜”–„z



)Ê}pYfed`}pamdi}p!y{Ê

o˜paZs^a`n×v|

k – t‹‚

^a`}Ê~

tbj‡

Ñ

ÕY|!Yf`}YfZj^gyxyv×ÛË}eWY_e¥×1\ÐUp!y{e‚x

km™šk›>k+œœ+œ

m]p&Zj^a`}|!YpRÉnY[Z

l

ÓPe¥×\ÐUp!y{eˆ

kžkŸkœœ+œ

m]p&Zj^a`}|!Y

pDÉnYfZ

j

ÓRe¥×1\ÐUp!y{e˜ 

km¡¢k.£

m]pdZj^g`w|aY;pRÉnY[Z



Ó·e¥×1\ÐIpayxe|

k– k” k+œœ+œ

m]pŠZj^a`}|!Y;pDÉnYfZ

 

Óa^g`wÊe¥×1\ÐUp!y{e

¤ k  k¥Kkœ+œœ

m]p¦Zj^a`}|!YpDÉnYfZ j[

Ñ}ÕYªÖŠZ]tvm]Yˆ¦Ïm]pÊ}YD`}pam]Yªm]i}YYf\–Ì}mÜ×£e¥mWZ]t{`}|}Ñ

r-Z]Ë}y{YŽp!o¯m]i}YŽoqpaZ]\§x¨z

™

t{eŠhR^ay{y{YfÊ&^_­¯¸P´x¶Z]Ë}y{Y!Ñ

r ä

`wpa`wÊ}Y[m]YfZ]\–t{`}txe¥m]t{h·æR©”¸¯´x¶R«+°<­I¶R²Uµ+°1¶R²U¸_ª txeª^š\·Î›m]Ë1Ìwy{Y

ä«nk+j¬k­®k.¯fkm°

æjÓwÖdiwY[Z]Y

«

t{e

^uw`wtvm]Y¦eWY[mp!oRc[¶D°}¶D«dcaÓIp!oÔÖdi}t{hji

¯

t{e:m]i}Y´q¸P´x¶·´˜°<®že¥mj^gm]Y–^a`}Ê2m]i}p!eWY¦tx`

°²±³«

^·Z]Ym]i}Y‡©”¸°B®

e¥mj^·m]YDefÓ

j

t{e–m]i}Y&t{`1ÌwË}m^ayvÌwiw^gÐUYfmDÓÔ^a`}Êm]i}Y¶D©g°<¸KcR´x¶·´˜²U¸ ©g«}®x°}¶g´x²U¸

­

t{e_^Ûuw`}tvm]Y&eWË1ÐweWYfmp!o

«—…€j[>…~«

Ñ

ÕY Ê}Y[uB`}Y ^:Ç!²U¸K©P¬U­F©g°1¶g´˜²U¸£m]pdÐUYÏ^a`YfyxYf\–YD`nm“pao «´…>j[ Ñ·ÕY;Ê}Yfuw`}Y;m]i}Y;Ðwt{`B^·ZW×Z]Yfyx^gm]t{p!`

µ

ÐUYfmÜÖ YfYf`hfp!`1uw|!Ë1Zj^gm]t{p!`}e:^ge¶ ä·¸k

¤

Žæ

µ

ä·¹kŽæ t{o“^a`}Êp!`}y{×£t{o ä·¸k

¤

k·¹æ t€­ Ñ Ø

i}YmWZj^a`}eWtvm]tvÉnY

^g`wÊ£Z]Y‰wY[Í1tvÉnYŽhfyxpaeWË}Z]Yªp!o µ t{eŠÊ}YD`}pam]YfÊÐ*× µ  Ñ

È*p!\–YNt{`1ÌwË1m

¤

t{e©g«Ç!²B¬U¸P´ºn«1Æ8t{o ä¯k

¤ æ µ ä·¸k ¦jæjÓ¯oqpaZ¦eWp!\–Y ·]t»° Ñ Ø

i}YNyx^a`}|!Ëw^a|aYN°wÇfg

Ç!«*±¯¶D«1Æ(Ð*×vªãtxesÊ}Yfuw`}YfÊm]p_ÐUYm]i}YeWY[m:p!ož^ay{ye¥mWZ]t{`}|!e

¤

m]iB^·mª^gZ]YZ]YfhDpa|!`}txÞfYfÊFђ ×&Ê}Y[uB`}tvm]t{p!`IÓ

^¦y˜^g`w|aËB^g|!Y^ghDhfYfÌ}m]YfÊ£Ð×£^uw`}tvm]Y^aË1m]p!\_^gm]p!`t{eŠhR^ay{y{YfÊ^©g«*¬U­P®˜°w©yx^a`}|!Ëw^a|!YaÑ

¼„½

´‘¸¯´x¶R«b¾N­F¶D²Uµ+°}¶D°(´q¸»¾Y¿Àcf«}¸Ç!«º²FhMÁU«}®shgW«}µ‹¿”«1ÆPÆP´‘¸¬

ÕYŠÊ}Y[uB`}Yd^Mcf±”´‘¸F«¦t{`–^:Ì<^·Z]eWYŠmWZ]YfYÏm]pªÐUYd^:ÌB^gm]i–m]iw^gm”Z]Ë}`}ežo˜Z]p!\.m]i}YÏZ]ppamžÊ}pRÖd`m]peWpa\_YÏy{YR^ao•Ñ

ÂsË1Z \^gtx`_t{`nm]Y[Z]YDe¥m;t{`_e¥ÌBt{`}Yfe;yxt{YfeÔt{`_m]i}YseWYDÝ*Ë}YD`}hfYDe;paoI|aZj^a\–\^gZÔe¥×1\ÐUp!y{e;^gm;`wp*ÊwYfeÔÐUpaZ]Ê}YfZ]t{`}|

pa`&e¥Ìwtx`}YfefÑ

r4eWt{\ÌBy{Y”YfÍ}^g\–Ìwy{Yžt{eFm]iwYžeWY[mPpaoÌB^gZ]eWYžmWZ]YDYfeeWË}hji¦^gem]iwYžp!`}YÔt{`ғt{|!Ë1Z]Y

é

ÓRoqpaZP^Š|aZj^a\–\^gZp!o

ÌB^ay{t{`}Ê1Z]p!\_YfefÑ zmÔt{e”t{`nm]Ë}t{m]tvÉnYfyv×hDy{YD^gZ“m]iB^·m”m]iwYŠyx^a`}|!Ëw^a|aYŠt{e”`}pamžZ]Yf|!Ë}yx^gZ+¶am]i}YÏ|aZj^a\–\^·Zže¥×1\ÐUp!y{e

m]p–m]i}YyxYfo˜mdp!oPm]i}Ye¥Ìwt{`}YoxZ]p!\ãm]i}YZ]p*pamdm]pš¦–à]hfp!\–\¦Ë}`}t{hR^·m]YDâÖdtvm]im]i}p!eWYm]p–m]i}YZ]t{|!inmsp!oPm]i}Y

e¥Ìwt{`}Y!ÑúpaZ]Y_Ì}Z]YfhDt{eWYfy{×!ӏm]iwY_Ì}Z]Y[uwÍp!o m]i}Ytx`1ÌwË1mË1Ìm]pm]i}Y_ÌIpatx`nmÖdi}Y[Z]YNtvm\_YfYfm]em]iwY_uw`w^ay

`}pÊ}Y¬¦:paožm]i}Y¦e¥Ìwt{`}Y¦ÊwY[m]Y[Z]\_t{`}YDesm]i}YeWË1ٖÍ2^ao˜m]Y[Zªm]iw^gm:ÌUp!t{`nmDÓUt{`Û^_ÖÏ^D×m]iw^gmŽ^a`ºËw`nÐUp!Ë}`}Ê}YDÊ

ÝnËB^g`*m]tvmÜ×Np!o¯e¥×1\ÐUp!y{eŠoxZ]p!\>m]i}YŽÌ}Z]Y[u}Í`}YfYDÊ£m]pÐUYªmj^gìnYf`&t{`nm]p_^ahfhfp!Ë}`*mDÑ

ro˜paZ]\^gyÏYfÍ*ÌByx^a`w^gm]t{p!`4oqpgZ–Ödin×4m]i}Y|aZj^a\–\_^gZ–\^D×(`}pam_|!Yf`}YfZj^gm]Y^2Z]YD|!Ë}yx^gZ_yx^a`}|!Ëw^a|aY

Z]Yfy{t{YDeÏp!`£m]i}Yo˜p!y{yxpDÖdtx`}|¦ÊwY[uw`}t{m]t{p!`

ä

k;i}p!\_e¥ì*×nÓ éRê

\ ê ÐUæ¶

Ä «¸©”¸¯´x¶·´˜²U¸

(3)

S

S

S

a a

b b

ε a

S a

S

b b

ε S S S

͊Î)ÏdÐFÑÒ~Ó

Ô¢V%A<M<MA+VŠ;ÇF=9AD3B*C8ÅV%;<MLHP¸AC8Å[A>=9A+V%H%L0@V%LLÕ

r |aZj^a\–\_^gZ:t{e>cf«1®shgW«}µ‹¿ž«1ƯƓ´‘¸F¬+t{oPm]iwY[Z]Yt{e:eWp!\–Y‡x t€l

eWË}hHim]iw^gm>x³z



|Àx–ÔÓ<o˜paZªeWpa\_Y

|×Ö

Ø

¦d^a`}Êٖ»Ö

Ø

¦fÑ

zo^|aZj^g\_\_^gZÏt{e;`wpgmŠeWYfy{o˜Î¼Yf\ÐUYfÊ}Êwt{`}|}Ónm]iwt{e;\_YD^a`}e;m]iB^·m Ödi}YD`£^eWYfhfm]t{p!`Npao¯^e¥Ìwt{`}Yªt{`£^ÌB^gZ]eWY

mWZ]YfY Z]YfÌUYD^gm]e”tvm]eWYDy{oÜÓ·m]i}YD`YDtvm]i}YfZ”`}pŽ|aZj^a\–\_^gZže¥×1\ÐIpayxe”p*hDhfË1Z”m]pªm]i}YŠy{Yfo˜m”p!oBm]iw^gmžeWYfhfm]t{p!`¦p!oBm]i}Y

e¥Ìwt{`}Y!ÓFpaZ`}p&|aZj^a\–\_^gZe¥×\ÐUp!y{eŽphDhfË1Zm]p£m]iwY¦Z]tx|ai*mDÑ

Ø

i}t{eŽÌ}Z]YfÉ!YD`nm]em]i}YÛàWËw`nÐUp!Ë}`}Ê}YDÊhfp!\Î

\Ë}`}txhD^gm]t{p!`}âÐUY[mÜÖ YDYf`_m]i}YdmÜÖ peWt{Ê}YDe;p!oUm]i}Yse¥Ìwtx`}YsY[Í1Yf\–Ìwy{tvuwYDʖÐ*זm]i}YdÌB^ay{t{`}Ê}Z]pa\_Yd|aZj^a\–\_^gZDÑ

ÕYÔ`}pRÖÌwZ]pDÉnYÔm]iw^gm|aZj^a\–\^gZ]eFm]iw^gmP^gZ]Yž`wpgmPeWYfy{o˜Î¼Yf\ÐUYfÊwÊ}t{`}|d|!Yf`}YfZj^·m]YžZ]YD|aËwyx^gZy˜^g`w|aËB^g|!YDefÑ

ÒwpaZs^a`^gZWÐwtvmWZj^gZW×N|aZj^a\–\^·ZDÓ1Ö YÊ}Y[uB`}YŽm]i}YŽeWYfmdp!o¯©g«Ç*­©cR´Ú<«`}p!`nm]YfZ]\–t{`w^ay{ed^ae¶

l Ø

Œx

tÙlۏUÜ

| k

–pÝx¨z



|Àx–Kސ

ÕYdÊ}Yfm]Y[Z]\–tx`}YÏm]i}YŠÌB^gZWm]tvm]t{p!`‘ß p!o

l

hDpa`weWt{e¥m]t{`}|p!oUeWË}ÐweWY[m]e

lYà+kl[ákœœ+œkml[â

ÓnoqpaZ;eWpa\_Y2ãÙäŽå1Ó

pao”µÛ­F¶·­°B®‘®æ4©g«1Ç*­F©fcR´Ú<«`}p!`nm]Y[Z]\_t{`w^ay{e¶

ß Ø Œ l®à+kml[ákœ+œœkml[⠐

l®àÀƒšl‡áRƒnçç+烚l‡â

Ø l

èêé Ý l‚ë

Ö

بì

Þ¯^a`}Ê èêé kí

Ýé Ö

Ø

í‡îïl‚ëFðšlMñ

بì

Þ

Ü é Ýx

tvl‚ëdò‡™ótvl‚ë

Þyô Ü |

à+k

–

à+k

|

ák

– á Ýx¨z

 | à™

–

àõò‚™

z  | á x–

á Þk

oqpgZs^ay{yKx km™ót l

ÕY`}pRÖ Ê}Y[uw`wY&m]i}YoqË}`}hfm]t{p!`0]jŒH1H‰]‹q€aºoxZ]p!\ïß m]p+m]i}YeWYfmnŒ*ƒv›œj… k H‹v—g†… k ‰f[ƒœ k ŒHÁ*Œ[ƒ‹›ŒnÑÔÒBpaZ

å[ö é ö×ãF¶

j]Œ[H‰j‹q€g

äl‚ë

æ Ø

ƒv›œH…

k ‹œ ÷Šø¯‘œH…mùdHU[W‚!…‘‹˜—

äl‚ë

æ ò ú

‹v—g†…mùdHU[W‚!…‘‹q*—

äl‚ë

æ

Ø

H‹{—·†… k ‹œ ø¯‘œH…mùdHU[W‚!…‘‹˜— äl‚ë æ ò ÷ ú ‹v—g†…mùdHU[W‚!…‘‹q*— äl‚ë æ

Ø

‰ffƒœ k ‹œ ø¯‘œH…mùdHU[W‚!…‘‹˜— äl‚ë æ ò ú ‹v—g†…mùdHU[W‚!…‘‹q*— äl‚ë æ

Ø

Œ[ÁnŒfƒ¡‹¼Œ k ‹œ ÷Šø¯‘œH…mùdHU[W‚!…‘‹˜— äl‚ë æ ò ÷ ú ‹v—g†…mùdHU[W‚!…‘‹q*— äl‚ë æ

Ödi}Y[Z]Y

ø›œH…mùŠ[UH]‚!…‘‹˜—

äl‚ë

æ Ø

Ü<ä

x¨z}|

™

–žæ t~o

Ýx

t~lˆë5ò®™ót~lˆë5ò

|»Ö

Ø

¦%Þ

ú

‹{—g†…mùŠ[UH]‚!…‘‹˜—

äl‚ë

æ Ø

Ü<ä

x¨z}|

™

–žæ t~o

Ýx

t~lˆë5ò®™ót~lˆë5ò

–ûÖ

Ø

¦%Þ

Õ8i}YD`€üý

Ÿ.þ

ü ¯ é ¤ ý äl‚ë

æ Ø

ƒv›œj…[Ó l‚ë

hfp!`}eWtxe¥m]eªp!ožp!`}y{×y{YDoxmWΛZ]YDhfË1Z]eWtvÉnY`}p!`nm]YfZ]\–t{`w^ay{efÓUÖdi}t{hjiÛÊ}pYfe

`}pam&\–YR^g`tvm&hD^a`}`wpgm^ay{eWphfp!`nmj^at{`8Z]t{|!inmWΛZ]YDhfË1Z]eWt{É!YÛ`wpa`*m]Y[Z]\–tx`w^ay{efÓ ÐwË1mt{`8m]iw^gm&hD^aeWYÛZ]t{|!inm

Z]YfhfË}Z]eWt{p!`2^a\–p!Ë}`nm]e:m]p£^gÌ}Ìwyxt{hD^gm]t{p!`p!o”Ëw`}tvm:Z]Ë}y{YDefÑBÕi}YD`‹üý

Ÿþ

ü ¯ é¤ ý älˆë

æ Ø

ŒHÁ*Œfƒ¡‹›ŒaÓUtvmªt{e_‡gwƒÁ

eWË}hji&Ë}`}t{mŠZ]Ë}y{YfeÏm]iB^·mŠmj^gìnYªÌ<^·ZWmdtx`£m]i}YªZ]YfhDË1Z]eWt{p!`IÑ

Ø iw^gm¬üý

Ÿþ

ü ¯ é¤ ý äl‚ë

æ Ø

‰f[ƒœÓ”o˜paZ–eWpa\_Y é ӓt{e–^2eWË1Ù_hftxYf`nm_^a`}Ê4`}YDhfYDeWe]^·ZW×(hDp!`}Ê}tvm]t{p!`(o˜paZ

m]i}YŽ|aZj^a\–\^·ZŠm]p–ÐUYŽeWYDy{o˜Î¼Yf\ÐIYfÊ}Ê}tx`}|}Ñ Ø i}YfZ]YfoqpaZ]YaÓ}Ö Yiw^DÉ!Ym]pÌ}Z]pRÉnYŽm]iw^gmdt{o˜üý

Ÿþ

ü ¯ é¤ ý älˆë

æ t

Œnƒ{‘œH…

k

H‹{—g†…

k

Œ[ÁnŒfƒ¡‹¼ŒnÓ<o˜paZª^ay{y é Ó<m]i}Yf`m]i}Y|aZj^g\_\_^gZ:|!Yf`}YfZj^·m]YDe:^–Z]YD|!Ë}yx^gZ:yx^a`}|!Ëw^a|aY!ÑõÂsË1Z:Ì}Z]pp!o

(4)

Ê}tvÚUYfZ]eŠoxZ]p!\ã^a`Y[Í1t{e¥m]t{`w|¦Ì}Z]pp!o

ä

k;i}p!\–e¥ì×!Ó éRê

\ ê

^*æ;t{`£m]iw^gmdtvmŠt{eŠo˜Ëwy{yv×Nhfp!`}e¥mWZ]Ë}hfm]tvÉnYf¶}ғt{|!Ë1Z]Yí

Ì}Z]YfeWYD`nm]e“^a`¦^ay{|!paZ]tvm]i}\-oqpgZ“h[Z]YR^gm]t{`}|s^duw`wtvm]Y;^aË1m]p!\_^gm]p!`m]iw^gm”^ahfhfYfÌ}m]e¯m]i}Y;yx^a`}|!Ëw^a|!YÔ|!Yf`}YfZj^gm]YfÊ

Ð*×Nm]i}Y|aZj^g\_\_^gZDÑ

Ø i}YŠÌwZ]p*hDYfeWe;t{eÔt{`}tvm]tx^gm]YDʖ^gmÔm]i}Yde¥mj^gZWm;e¥×1\ÐUp!y›Ó^a`}Ê_o˜Z]p!\ m]i}YfZ]YŠm]i}YŠÌ}Z]phDYfeWeÔÊwYfeWhfYD`}Ê}eÔm]i}Y

|gZj^a\_\_^gZtx`^ay{yžÖÏ^f×1eË}`nm]txy”m]Y[Z]\_t{`w^ay{e^gZ]Y_Yf`}hDp!Ë}`nm]Y[Z]YDÊIÓP^a`}Êm]i}Yf`+mWZj^a`}eWtvm]txpa`we^gZ]Yh[Z]YD^gm]YDÊ

yx^gÐUYfy{yxYfÊÖdt{m]i£m]i}p!eWYªm]YfZ]\–t{`w^ay{efÑUÿªYfeWhDYf`}Êwt{`}|m]i}YŽ|aZj^a\–\^gZdt{eŠe¥mWZj^at{|!inm]o˜paZWÖÏ^gZ]Êt{`m]i}YŽhR^geWYp!o

Z]Ë}y{YfespaoPÖdi}txhji&m]i}Yy{Yfo˜mWμiw^a`}Ê&eWt{Ê}Yt{ed`}pam:^Z]YDhfË1Z]eWtvÉnY`}p!`nm]Y[Z]\_t{`w^ay¶}m]iwYeWË1Ð<^gË}m]pa\^gmj^–oqp!Ë}`}Ê

Z]YfhfË}Z]eWtvÉnYfyvזo˜paZ \_Yf\ÐIY[Z]e;t{`_m]iwYŠZ]tx|ai*mWμiw^a`}ÊNeWt{Ê}YdÖdtxy{ywÐUYshDp!`}`}Yfhfm]YfÊIÑ

z

`_m]i}Y:hD^aeWY:p!oUZ]YDhfË1Z]eWt{É!Y

`}p!`nm]Y[Z]\_t{`w^ay{efӓm]iwY£ÌwZ]p*hDYfeWe_Ê}YfÌUYf`wÊ}e_p!`Ödi}Y[m]iwY[Z_m]i}Y&`}p!`nm]YfZ]\–t{`w^ay{e–t{`m]i}Y&hfpaZWZ]YDe¥ÌUp!`}Ê}t{`}|

eWY[m:oxZ]p!\ ß ^·Z]Y\Ë1m]Ëw^ay{y{×NyxYfo˜mWΛZ]YfhfË}Z]eWtvÉnYpgZsZ]t{|!inmWΛZ]YDhfË1Z]eWt{É!Y

t{o¯m]i}Yf×&^·Z]YÐUpam]iIÓwÖdi}txhji&\_YD^a`}e

m]i}Y[×N^·Z]Yªh[×1hDy{t{haÓnm]iwYf`NYDtvm]i}YfZ eWË1Ð}Ì}Z]phfYDeWeÏhR^g`ÐUYŽ^gÌ}Ìwy{txYfÊ

tx`_m]iwY:hfpÊ}Yªt{`NÒPtx|aË}Z]YŽíh[×1hfy{txh:^a`}Ê

Z]t{|!inmWΛZ]YfhDË1Z]eWtvÉnYŽeWË1ÐweWY[m]e lˆë

^gZ]YªmWZ]YR^·m]YDÊË}`}txo˜paZ]\–y{×!Ñ

ÕY–Ê}t{eWhDË}eWeŽm]i}Y–hD^aeWY–m]iw^gmªm]iwY`wpa`*m]Y[Z]\–tx`w^ay{e^gZ]Y–y{Yfo˜mWΛZ]YfhDË1Z]eWtvÉnYaјÂ:`}Y–`}YfÖ e¥mj^gm]Y–t{eŽhfZ]Y[Î

^·m]YDÊ&oqpaZsYR^ahji&`wpa`*m]Y[Z]\–tx`w^ayFtx`m]i}YeWYfmDÑ

Ø

i}YmWZj^a`}eWtvm]t{p!`}eŠm]iw^gm:^gZ]YhfZ]YD^gm]YfÊo˜paZdm]YfZ]\–t{`w^ay{es^a`}Ê

`}p!`nm]Y[Z]\_t{`w^ay{e `}pamÏtx`

l‚ë

^·Z]YŽhfp!`}`}YDh[m]YfÊ£t{`£^ÖÏ^D×_m]iB^·mŠt{e;Z]Yf\_t{`}t{eWhDYf`nmÏp!oFm]i}Y:hDp!`}e¥mWZ]Ë}h[m]txpa`£p!o

y{Yfo˜mWμhfpaZ]`}YfZžÌB^gZ]eWY[Z]e

ä

bdp!eWYD`1ìZj^g`*m]Þs^a`}ʏY[Ödtxe zWz Ó éRê!ë

å*æjÓ^a`}Êe¥ÌUYfhDtvuwhD^ay{y{צp!oIp!`}Yshfp!`}e¥mWZ]Ë}hfm]t{p!`

m]iw^gmdo˜phfËweWYfeŠp!`&eWY[m]edpaoP\Ë}m]Ëw^ay{yv×Z]YfhfË}Z]eWtvÉnYª`wpa`*m]Y[Z]\–tx`w^ay{e

ä

è:YDÊ}Y[Z]i}p!oÜÓ éRê!ê

Z}ÓUÈ*Yfhfm]t{p!`~\Ñ

e

æjÑ

r:`4Y[Í}^a\ÌwyxYtxe¦|at{É!YD`4t{`(ғt{|!Ë1Z]Y~XѓÒwp!Ë1Z_e¥mj^·m]YDe¦iB^fÉnYNÐUYDYf`4yx^gÐUYDy{y{YfÊ(^ahDhfpaZ]Ê}t{`}|2m]pºm]i}Y

`w^a\–Yfeªm]i}Yf×2^gZ]Y|!tvÉnYf`2tx`ºÌ}Z]phfYDÊ}Ë1Z]Y£„_‚g¿! œH‚BÑ Ø i}Y[Z]Y–^gZ]Y¦mÜÖ pe¥mj^gm]Yfe:m]iB^·m^gZ]Yyx^gÐUYfy{yxYfÊ

·

Ñ

Ø i}t{eÏhD^a`NÐUYªYfÍÌwyx^at{`}YDÊ_Ð×_m]i}YŽoq^ah[mÏm]iw^gmÏ`wpa`*m]Y[Z]\–tx`w^ay

™

hR^g`NÐIYsZ]YR^ghHi}YfÊ£Ð*×NÊ}YfeWhDYf`}Êwt{`}|¦m]i}Y

|gZj^a\_\_^gZŠo˜Z]p!\

q

t{`£mÜÖ p–YDeWeWYf`nm]t˜^gyxyv×Êwt{e¥m]t{`}hfm ÖÏ^D×1efÑ

Ø i}YhfpÊ}Y¦t{`2ғt{|!Ë1Z]Y–íÊ}t{ÚUY[Z]eªoxZ]p!\m]i}Y–^ah[m]Ëw^ayPtx\Ìwy{YD\–YD`nmj^gm]t{p!`t{`ºm]iw^gmªeWp!\–Yfm]t{\–YDe:o˜paZ

^Û`}p!`nm]Y[Z]\_t{`w^ayŠ^+eWYfÌB^gZj^·m]Yuw`wtvm]Y&^aË1m]p!\_^gm]p!`t{e–hDp!`}e¥mWZ]Ë}h[m]YDÊIӔÉ1t{Þaўo˜paZ_m]i}p!eWY`wpa`*m]Y[Z]\–tx`w^ay{e

m]iw^gmp*hDhfË1Z¦^aeˆx tx`Ûm]i}Y_hfpÊ}Y!ÑFrmWZj^a`}eWtvm]t{p!`+t{`+eWË}hHi^&eWË1ÐB^aË1m]p!\_^gm]p!`\_^D×2ÐUY_yx^gÐUYfyxy{YfÊ2Ð*×

^g`wpgm]iwY[Z¦`wpa`*m]Y[Z]\–tx`w^ay ™ ÓPÖdi}t{hjim]i}YD`Z]Y[Ì}Z]YDeWYf`nm]em]iwYeWË}ÐB^aË1m]p!\_^gm]p!`(hfpaZWZ]Yfe¥ÌIpa`wÊ}t{`}|m]p ™ Ñ

Ø

i}YªZ]YfeWË}yvm]tx`}|Z]YfÌ}Z]YfeWYD`nmj^gm]t{p!`£t{eÏeWtx\–t{yx^gZ m]pY[Ím]YD`}Ê}YfÊ£hDp!`nm]Y[ÍmWμo˜Z]YfYª|aZj^a\–\^·Z]e ä

Ë1Z]Ê}p!\ã^a`}Ê

’;Z]pRÖd`IÓ éRêfe1é

æjÓUÖdtvm]iºm]i}Y¦Y[Í1hDY[Ì}m]t{p!`ºm]iw^gmŽt{`2p!Ë1ZhD^aeWY¦Z]YfhDË1Z]eWt{p!`2hR^g`w`}pamŽphfhfË}ZDÓ<Ð×É1tvZWm]Ë}Y¦p!o

m]i}YŽhDpa`we¥mWZ]Ë}h[m]t{p!`IÑ

Ø

i}Y–Z]Y[Ì}Z]YDeWYf`nmj^gm]t{p!`+oqpaZm]i}YZ]Ë}`w`}t{`}|&Y[Í}^a\ÌBy{Yt{et{`wÊ}t{hD^gm]YDÊ2Ð*×Ûғt{|!Ë1Z]YYZ1ÓFÖdi}t{hHi+eWi}pRÖde

mÜÖ p:eWË1ÐB^aË1m]p!\_^gmj^1Ógyx^gÐUYfy{yxYfÊ

q

^a`}Ê

™ Ñ Ø i}Y;p!`}Y yx^gÐUYfyxy{YfÊ

q

t{em]iwY ^gË}m]pa\^gm]pa`p!`m]iwYÔm]pa̦y{Y[ÉnYDy›Ó

^g`wÊhDpa`*mj^gtx`}emÜÖ pmWZj^a`}eWtvm]txpa`weyx^gÐUYfyxy{YfÊ

™

ӏÖdi}txhjiZ]YfoqY[Zm]p&m]i}YNpgm]iwY[Z¦eWË1ÐB^aË1m]p!\_^gm]p!`IÑPè:pgm]Y

m]iw^gmPm]i}t{e¯Z]YfÌ}Z]YfeWYD`nmj^gm]t{p!`t{e“\–paZ]Y;hDp!\ÌB^ah[mPm]iw^a`m]i}Y p!`}Y;o˜Z]p!\)ғt{|!Ë1Z]YXÓgeWt{`whfY;m]i}YÔmWZj^a`}eWt{m]t{p!`}e

m]iw^gmÏ^gZ]Y:t{`nÉnp!yvÉnYfÊNt{`Z]Y[Ì}Z]YDeWYf`nm]t{`w|m]i}Y:eWË1Ðwyx^a`}|!Ëw^a|!Yªpaoe¥mWZ]t{`}|!e;|!YD`}Y[Zj^gm]YfÊÐ*×`wpa`*m]Y[Z]\–tx`w^ay

™

^·Z]Yt{`}hDy{Ë}Ê}YDÊ£p!`}yv×£p!`}hDYaÑ

Ø i}YhDp!\ÌB^ah[mŽZ]Y[Ì}Z]YDeWYf`nmj^gm]t{p!`2hDp!`}eWt{e¥m]t{`}|£p!o;eWË1ÐB^aË1m]p!\_^gmj^£hD^a`2ÐUY¦m]Ë1Z]`wYfÊÛt{`nm]p^£eWt{`}|!y{Y

uw`}tvm]Y¦^aË1m]p!\_^gm]p!`&Ð*×eWË1Ðwe¥m]tvm]Ë}m]t{`}|eWË1Ð<^gË}m]pa\^gmj^®x.oqpaZ:mWZj^g`weWtvm]t{p!`}esyx^gÐUYfyxy{Yfʋx.t{`ºpam]i}Y[ZŽ^gË}Î

m]pa\^gmj^Ñ

Ø

iwt{e–hDpa\_Yfe_Ê}pRÖd`m]p+Z]YD|aËwyx^gZ_eWË1Ðwe¥m]t{m]Ë1m]t{p!`tx`4m]i}YeWYf`}eWYp!o2’ÏY[Z]e¥m]YDy äWéRênëaê æjÑ

Ø

i}Y

^gÊ}Éa^a`nmj^a|!Y£paodm]i}t{e¦ÖÏ^f×(p!odpaÐ}mj^at{`wt{`}|Û^uw`wtvm]Y^aË1m]p!\_^gm]p!`(pRÉ!YfZ_^ºÊwtvZ]Yfhfmhfp!`}e¥mWZ]Ë}hfm]t{p!`(p!os^

`}p!`}Ê}Y[m]YfZ]\–t{`wt{e¥m]t{h_^aË1m]p!\_^gm]p!`+txeŽm]iw^gmeWË}ÐB^aË1m]p!\_^gmj^\^f×ÛÐIY_Ê}Y[m]YfZ]\–t{`}txÞfYfÊ^a`}Ê\–tx`}t{\–txÞfYfÊ

ÐUYfoqpaZ]Ym]i}Yf׺^gZ]YeWË1ÐBe¥m]tvm]Ë1m]YfÊÛt{`nm]p£yx^gZ]|aYfZŽeWË1ÐB^aË1m]p!\^·mj^1ѯÈ*t{`whfYt{`2\^g`*׺hD^aeWYfeŽÊ}Yfm]Y[Z]\–tx`}t{ÞfYDÊ

^g`wÊ\_t{`}t{\_t{ÞfYDÊ^aË1m]p!\_^gmj^_^gZ]Y\¦Ë}hjieW\^gyxy{Y[ZDÓ}m]iwt{edÌ}Z]phfYfeWe:^DÉnp!t{Ê}es\¦Ë}hjip!o“m]i}Yhfp!\Ðwt{`w^gm]paÎ

Z]tx^aywY[ÍÌwyxpaeWtxpa`–m]iw^gmÔmj^·ìnYDe”ÌByx^ahfYdË1ÌIpa`_`B^gt{É!Yshfp!`}e¥mWZ]Ë}hfm]t{p!`_paoF^ŽeWtx`}|!y{Yd`}p!`}Ê}Yfm]Y[Z]\_t{`}t{e¥m]t{hÏuw`}tvm]Y

^gË}m]pa\^gm]pa`FÑ

r:eWeWË}\_YÏÖ YŠiw^DÉnYs^Žy{t{e¥mžp!oUeWË1ÐB^aË1m]p!\_^gmj^Mx à+kœ+œœk

x m]iB^·m;t{e”paZ]Ê}YfZ]YfÊ_oxZ]p!\ y{pRÖ Y[ZÔy{YfÉ!YDym]p

i}t{|!i}Y[ZPyxY[ÉnYfy*^aË1m]p!\_^gmj^

t›ÑYaÑRt{o}^a`¦^aË1m]p!\_^gm]p!`ˆxsp*hDhfË1Z]eP^aePyx^gÐUYfynp!ow^ŠmWZj^g`weWtvm]t{p!`p!ow^aË1m]p!\_^gm]p!`

÷RüÀ¼ü%6¼ü¥ù›ü¥ýfõ¼újõ 1&Hý M&H÷ *úHý#}ü%¼ü% ¼úF ¡ùü[ü¥ý>p&¼üÀ%&.06gú.õUõ¼÷·úHý>&[ö+¼ùK'*&ÿ¼úÏú¼ù<õ¼÷·úHõ

ú¼ü“ý&Hõù¼üø1'*xü$¢!ü$## ¡ýRÿ&WþIü[ü%¥ó ý:õ¼÷·ü”ù›üfö·ü¥ønþUü”ú¼ü“ÿ.&. ý·ÿ;õ&Ïö·ù›ü &[öõ¼ü%6¼ü¥ù¼ü¥ý[õ¼úHõ &[ýsú[ù

¡ý[õ¼ü%Ïü$# úHõ¼ü¼ü¥ù›ö·øõ˜ ýªú66& + 1ÏúHõ ý·ÿ ú[ý:ö·ý+¼ü¥ù›õ õ¼ü$#2$&Hýfõ¼ü Dõ'*¼ü¥ü“ÿ¼úÏú¥ófþ˜ õ¼÷sõ¼÷·ü!gýRú[ø9&#"›ü$õ [ü

&.'¸&·õ¼ú ¡ý ý·ÿÏú ù ý·ÿ[øü ý ŠúHø8#Rüõ¼ü%p ¡ý ù›õ “ú[öRõ&Šújõ&[ý8Rð&Fõ¼÷ ¡ùõ6gö6&Hù¼üHóRõ¼÷·üÀ¼ü%6¼ü¥ù›ü¥ý[õ¼úHõ &[ýT+

M&H÷ *úHý#}ü%¼ü$ ¼ú$F&&%!ü%¼ùFø1 õ›õ¼ø¡ü”ú#'júHýfõ¼úHÿ[ü

(5)

®x«*¶

«

Ø´ì Ó ¯ Ø

œj][‰]† ‰H…¼‚!…•!Ó)(

Ø

œj][‰]† ‰H…¼‚!…•!Ó

° Ø

Œ*(“

„–‚g¿! œ[‚

ä¯fkqk

(IæjÑ

±¯©g²FÇ!«Æ“­©·«„–‚g¿! œ[‚

ä·'+k

|

km·à

æ¶

´shT|

Ø ¦

¶-,F«}¸»®˜«*¶

­ Ø ­ ƒ Œ

ä·'+k

¦

km·fà

æ

«}®scf«}´hT|

Ø

<Óêcf²Uµ+«n t€j

¶-,F«}¸»®˜«*¶ ­ Ø ­ ƒ Œ ä·'+k  k·fà æ

«}®scf«}´hT|

Ø

 v–;Óêcf²Uµ+«n  t‹ Ód– t‹‚ cR­¯Ç*,¶,°}¶ – /. å

¶-,F«}¸»®˜«*¶ · Ø

œ]jH‰]† ‰H…¼‚!…•

„_‚g¿! œ[‚ ä·'+k  km· æ

„_‚g¿! œ[‚

ä·¸k

–

k·fà

æ

«}®scf«2®˜«*¶Yx

Ø | ä10

|(\Ë}e¥mdhDpa`weWt{e¥mdp!oP^–eWt{`}|!y{YŽ`}p!`nm]Y[Z]\_t{`w^ay 0 æ

´sh϶-,F«©g««n³P´sc[¶c é cR­Ç*,¶,°1¶‚x tvlˆë

¶-,F«}¸×h›²B©N«°BÇ*,

™ótvl‚ë

Ə²4®˜«n¶

·

Ø

œj]H‰]† ‰H…¼‚!…•«}¸Æ

´h]jŒH1H‰]‹q€a

äl‚ë

æ Ø

ƒv›œj…

¶,«1¸×h¼²B©N«°BÇ*, ä›

zï  àõçç+ç

 2æ t~o

cR­¯Ç*,¶,°1¶

›„tpl‚ë5ò

 

à+kœœ+œk  243tlˆë

Ư²ç„_‚g¿! œ[‚

ä·'+k

 

àõç+çç

 2 k·'5

æ

«}¸¯Æ

h¼²B©N«°BÇ*, ä›

z76Y  àõçç+ç

 8æ tvo

cR­¯Ç*,¶,°}¶

›>k

6

t~lˆë5ò

 

à+kœœ+œk  293tvl‚ë

Ư²ç„_‚g¿! œ[‚

ä·:2k

 

àõçç+ç

 8 km·5

æ

«}¸¯Æ

®˜«*¶ ­ Ø ­ ƒ Œ ä·';¢k ¦ k·fà æ

«1®scf« ä10 ]jŒH1H‰]‹q€a äl‚ëæ t ŒnH‹{—·†… k Œ[ÁnŒfƒ¡‹¼Œ 0 æ

h¼²B©«°BÇ*, ä›

zï  àõç+çç

 2æ t~o

cR­¯Ç*,¶,°1¶

›„tpl‚ëFò

 

àkœ+œœk

 2<3 tpl‚ë

Ə²»„_‚g¿! œH‚

ä·5Rk

 

àõçç+ç

 2 km·fà

æ

«}¸Æ

h¼²B©«°BÇ*, ä›

zï  àõç+çç

 26£æ t~o

cR­¯Ç*,¶,°}¶

›>k

6

tvl‚ë5ò

 

àkœ+œœ+k  293t~lˆë

Ə²»„_‚g¿! œH‚

ä·5Rk

 

àõçç+ç

 2 km·':

æ

«}¸Æ

®˜«n¶

­ Ø ­ ƒ Œ

ä·#+k

¦

km·;

æ

«1¸¯Æ

«}®scf«€h›²B©N«°BÇ*,

ä

x¨z –žæ

t~o

Ư²ç„_‚g¿! œ[‚

ä·'+fk

–

km·à

æ;«}¸¯Æ ä10

x-t{eŠ`}pamŠZ]YfhDË1Z]eWtvÉnY 0 æ

«}¸¯Æ

«}¸¯Æ

«1¸¯ÆÔÑ

±¯©g²FÇ!«Æ“­©·«Nœ]][‰]† ‰H…¼‚!…•

ä

æ¶

hfZ]YD^gm]YŽeWpa\_YŽpaÐdr¥YDh[m

·

eWË}hHim]iw^gm

· 3t~«

®˜«*¶

« Ø « ƒ Œ · 

©g«n¶g­F©!¸

·

«1¸¯ÆÔÑ

͊Î)ÏdÐFÑÒ>=

? V%AC8HÇ);V%<>A@%B*;C‚Ç"V%;< A2GV%A<M<>AVA@CB<DFEHGFIJGKLGMONK@%Æ8A@ÀB3H C8;+@ HLD*ÇQPL<TSULÅ8Å8B3C8G>B3C@%;>AC‚L&Rf?8BTSAD3LC@

U C8B1@%LA?@%;<MA+@%;CWVXB<DZYJG&EHG[\G]'G^NmÕ

(6)

q z _d‚

x z ~a`

x z `:¢

™ z `:Œ

™ z b l Ø Œ

qk

x

km™



ß Ø Œ

lYà+kl[á



lYà

Ø Œ qk

x‘]jŒH1H‰]‹q€a

äl®à

æ Ø

ƒ{‘œH…

l‡á

Ø Œ ™  ]jŒH1H‰]‹q€a

äl[á

æ Ø

ƒ{‘œH…

d b a d

c c

ε

ε

q q

ε q B

q

B S

A

͊Î)ÏdÐFÑÒc

Ì¢=8=9D*B*IA+@%B*;CY;ÇF@%Æ8LpI;fÅ8LÇ"V%;<ed“B*G?V%L N2;C[AMH<MAD3DG+V%A<M<MA+VÕ

b a

ε q q

S

B A

B

d c

ε q B

B S

͊Î)ÏdÐFÑÒJf

? Æ8LA?@%;<>A@%;C‡Ç"V%;<gd“B*G?V%Lh2B3C[AMI;<2=9AIm@ŠV%L=8V%LHLC@%A+@%B*;CÕ

xigÓnm]iwYf`kjml

·

x\Ëwe¥mÔÐUYdm]i}Yde¥mj^gZWm e¥×\ÐUp!y

q Ñ Ø iwt{eÔpaZ]Ê}YfZ;t{e;^`w^gm]Ë1Zj^aywZ]YDeWË}yvm;p!oUm]i}YdÖÏ^f×

m]iw^gm”eWË1ÐB^aË1m]p!\^·mj^Ž^·Z]YÏhDpa`we¥mWZ]Ë}h[m]YDʦÊ}Ë}Z]t{`}|ªp!Ë1ZžÊ}YfÌ}m]i1Λu}Z]e¥m”mWZj^DÉnY[Z]e]^ay}p!owm]i}YÏ|gZj^a\_\_^gZDÓ·Ödi}txhji

t{e ^ahfm]Ëw^ay{yvז±ž²Fc[¶D²B©aƏ«©t{`m]i}Y:eWYf`}eWY:m]iw^gmŠ^eWË1ÐB^aË1m]p!\_^gm]p!`Nt{e;p!Ë1mWÌBË1mŠ^aoxm]YfZÏ^ay{y<eWË1ÐB^aË1m]p!\^·mj^

p*hDhfË1ZWZ]tx`}|–^gmdtvm]eÏmWZj^a`}eWtvm]t{p!`}eŠiw^DÉnYŽÐUYfYD`p!Ë1mWÌwË1mDÑ

ÂsË}Z;t{\–Ìwy{Yf\_Yf`nmj^gm]t{p!`hfp!`}e¥mWZ]Ë}hfm]e;^\–t{`wt{\_^ay}Ê}Yfm]Y[Z]\_t{`}t{e¥m]t{hd^aË1m]p!\_^gm]p!`–Ð*צZ]YfÌUYD^gm]t{`w|Žm]i}Y

o˜p!y{y{pRÖdt{`w|¦oqpaZLj

Ø

ék+œœ+œ.kon ¶

é

ÑÃÛ^·ìnY^hfpaÌ*×£p!oÀx1ÑUÿŽY[m]Y[Z]\_t{`}t{ÞDYª^a`}Ê&\_t{`}t{\_t{ÞfYsm]i}YhfpaÌ*×nÑ zo¯t{mŠiw^aedo˜YfÖ Y[Z

mWZj^a`}eWt{m]t{p!`}eÏyx^gÐUYDy{y{YDÊÐ*×`}p!`nm]Y[Z]\_t{`w^ay{e m]iB^g`m]i}YŽpaZ]t{|!t{`w^ay›Ó1m]iwYf`£Z]YfÌwyx^ahfY‘x¦Ð*×£tvm]e

hDpaÌ*×!Ñ

íÑgbsY[Ìwyx^ahDYªYR^ahjimWZj^a`}eWtvm]t{p!`t{`~xpao¯m]i}Yo˜paZ]\

ä·¸k

xp km· ¹

æÔÐ*×

ä

^¦hDpaÌ*×£p!ojæ ^aË1m]p!\_^gm]p!`

xpŽt{`^¦e¥mWZj^at{|!inm]oqpaZWÖÏ^gZ]Ê£ÖÏ^D×!Ñ Ø i}txeŠ\_YD^a`}eÏm]iw^gmd`}YfÖ³¦Î›mWZj^a`}eWtvm]t{p!`}eŠhDpa`w`}Yfhfm

·

m]p

m]iwYŽe¥mj^gZWmde¥mj^gm]YŽp!oxp^a`}Êm]i}YŽuw`w^ayFe¥mj^gm]YfeŠp!oÀxpªm]p · ¹Ñ

XÑgr:|n^at{`Ê}Y[m]YfZ]\–t{`wt{ÞfYŽ^a`}Ê&\–t{`}tx\–t{ÞDY>x–^a`}Ê&e¥m]pgZ]Yt{mŠoqpgZdy˜^·m]YfZÏZ]YDo˜YfZ]Yf`}hDYaÑ

Ø i}Y^aË1m]p!\_^gm]p!`paÐ}mj^at{`}YDÊ£oqpaZ x.^ao˜m]Y[Zde¥m]Yf̋X¦t{eÏm]iwYŽÊ}YDeWtvZ]YfÊ£Z]YDeWË}yvmDÑ

qsr «n¶-,F²FÆc–²Fhut«¬U­¯®˜°w©v¾_±P±¯©g²³¯´‘µ+°}¶·´˜²U¸

Ø i}t{eªeWYfh[m]txpa`2Ê}YDeWh[Z]tvÐIYfeŽ^`*Ë}\ÐUY[ZpaoÔ\_Y[m]i}pÊ}e:oqpaZ^gÌ}Ì}Z]pRÍ1t{\_^gm]t{`}|£^Nhfp!`nm]Y[ÍmWμo˜Z]YfY¦|gZj^a\_\_^gZ

Ð*×\–YR^g`wePp!ow^duB`}tvm]YÏ^gË}m]pa\^gm]pa`FÑ!È*p!\–YÔÌwË}Ðwy{t{eWi}YDÊ\_Y[m]i}pÊ}ePÊwt{Ê`}pam“\_Yf`nm]txpa`eWYfy{o˜Î¼Yf\ÐUYfÊ}Êwt{`}|

(7)

Y[ÍÌwy{t{hDtvm]yv×^aeŽÌUpam]Yf`nm]tx^ay“eWp!Ë1Z]hfY–p!oÔ`wpa`}ΛZ]Yf|!Ë}yx^gZ]tvmÜ×2p!ožm]i}Yy˜^g`w|aËB^g|!Y!ÓF^a`}Ê+eWË}|!|aYDe¥m]YfÊÛm]iw^gm^·ÌwÎ

Ì}Z]pRÍtx\_^gm]t{p!`}eeWi}p!Ë}y{ÊÐIYN^gÌ}ÌBy{t{YfÊ(|!y{paÐB^ay{yv×+o˜paZ¦m]i}YNhfp!\–Ìwy{Y[m]Y|aZj^a\–\_^gZDѯÕi}Y[Z]Ym]i}txet{em]i}Y

hD^aeWYaÓPÖ Y^aÊw^gÌ}m¦m]iwYN\–Yfm]i}pÊ(eWpºm]iB^·mt{m¦t{e¦\_pgZ]Y£eWYfy{YDh[m]tvÉnYN^a`}Ê4Ê}YR^ay{eÖdtvm]i(eWYfy{o˜Î¼Yf\ÐUYfÊ}Êwt{`}|

y{phD^ay{yv×nÑ

Ø i}Y ^gÌ}Ì}Z]pRÍ1t{\^·m]txpa`weP^·Z]Y;tx`nm]Yf|aZj^gm]YfÊt{`nm]pdm]i}Y;hDp!`}e¥mWZ]Ë}h[m]txpa`p!o1m]i}YÔuB`}tvm]Y;^aË1m]p!\^·m]p!`o˜Z]pa\

m]i}Ys|aZj^a\–\^·ZDÓnÖdi}t{hHi_ÖÏ^ae;Ê}YDeWh[Z]tvÐIYfÊt{`_m]i}YdÌ}Z]YfÉtxpaËwe;eWYfh[m]txpa`FÑ*reWY[Ì<^·Zj^gm]Y:t{`}hD^gZ]`w^gm]t{p!`p!oUm]i}Y

^·ÌwÌ}Z]pRÍtx\_^gm]t{p!`NÌwZ]p*hDYfeWedtxed^ah[m]t{Éa^gm]YfÊË1ÌUp!`uB`}Ê}t{`}|^–`}p!`nm]Y[Z]\_t{`w^ayKx-eWË}hHi&m]iw^gm x tvl‚ë

^a`}Ê

]jŒH1H‰]‹q€a äl‚ë æ Ø

‰ffƒœÓ<oqpgZªeWp!\–Y

é Ñ Ø

i}t{estx`}hD^gZ]`w^gm]t{p!`&m]i}YD`p!`}yv×ÌUYfZWmj^gtx`}edm]p_m]i}YeWY[mªpao“Z]Ëwy{Yfe

paožm]i}YoqpaZ]\ ™ z |ÔÓ<Ödi}YfZ]Y ™ tbl‚ëÑ z

`2pgm]iwY[ZªÖ pgZ]ÊwefÓU`wpa`*m]Y[Z]\–tx`w^ay{es`}pamŽt{` l‚ë ^gZ]YmWZ]YD^gm]YDÊ

Ð*×Nm]i}txeÏt{`}hR^gZ]`w^gm]t{p!`£p!o¯m]i}Y^gÌ}Ì}Z]pRÍ1t{\^·m]txpa`£Ì}Z]phfYDeWed^aeŠt{o¯m]i}Yf×Ö Y[Z]YŽm]Y[Z]\–tx`w^ay{efÑ

qwvqÄ

Á­±”«©cf«*¶–°w±P±¯©g²³¯´‘µ+°}¶·´˜²U¸Ž¿¯°êcf«1Æ»²U¸<tHx\y~c

Ø

i}Y_o˜p!y{yxpDÖdtx`}|^gÌ}ÌwZ]pDÍ1t{\^gm]t{p!`2ÖÏ^aeÌ}Z]paÌUp!eWYfÊ+Ð*×Ûè:YDÊ}Y[Z]iwpao äWéRê!ê!ë

æjÑ

Ø

i}Y–Ì}Z]YDeWYf`nmj^gm]t{p!`+i}YfZ]Y

i}pRÖ Y[ÉnY[ZsÊwtvÚUY[Z]edeWË1Ðwe¥mj^a`nm]t˜^gyxyv×No˜Z]pa\Âm]iwYYD^gZ]y{t{YfZÏÌwË1ÐBy{t{hD^gm]t{p!`IÓ1Ödiwt{hjimWZ]YD^gm]YDÊ£m]iwY^·ÌwÌ}Z]pRÍtx\_^gÎ

m]t{p!`ÛÌ}Z]phfYDeWeYD`nm]tvZ]Yfy{׺p!`+m]iwY–y{YfÉ!YDy”p!o hfp!`nm]YfÍ*mWμo˜Z]YfY_|aZj^g\_\_^gZ]e¶¯^eWYfyxoxμYD\ÐUYDÊ}Ê}t{`}|&|gZj^a\_\_^gZ

ÖÏ^gesmWZj^a`}eWo˜paZ]\_YfÊ&tx`eWË}hji2^ÖÏ^D×m]iw^gm:tvmŠÖÏ^ae:`}py{p!`}|!Y[Z:eWYfy{o˜Î¼Yf\ÐUYfÊ}Êwt{`}|}ÑBr)uw`}tvm]Y^aË1m]p!\_^gmj^

ÖÏ^geŠm]i}YD`paÐ}mj^at{`}YfÊ&oxZ]p!\>m]i}YŽ|aZj^a\–\^gZŠÐ*×Nm]i}Y^ay{|!paZ]tvm]i}\>Êwt{eWhfË}eWeWYDÊ^·ÐIpDÉnY!Ñ

Ø i}YÌ}Z]YfeWYD`nmj^gm]t{p!`»i}Y[Z]Yºt{e_ÐB^aeWYDÊ pa`»Z]YfhDË1Z]eWtvÉnY&mWZj^a`}eWtvm]t{p!`»`}Y[mÜÖ paZWì1e

äb Ø è:eHæ

ä

Õpp*ÊwefÓ

éDênë

å*æjÑ;ÕY2hR^a` eWYDYÛ^(hfp!`nm]YfÍ*mWμo˜Z]YfY2|gZj^a\_\_^gZ^ae^a`8b Ø è^ae£oqpayxy{pRÖdefÑ;ÕY2t{`nmWZ]pÊ}Ë}hDYmÜÖ p

e¥mj^·m]YDe

·;

^a`}Ê

· ¹;

o˜paZ£YR^ahji8`}p!`nm]YfZ]\–t{`B^gy>xÓÏ^a`}Ê

n{z é

e¥mj^gm]Yfe

·#+fkœœ+œkm·

loqpgZ£YR^ghHi Z]Ë}y{Y

x¨zï  àõçç+ç

 2Ñ Ø i}Yªe¥mj^gm]Yfe oqpaZÏ^Z]Ëwy{Y>x¨z— 

àKççç

 2-^gZ]Y:hDpa`w`}Yfhfm]YfÊÖdt{m]iYR^ahjiNpam]i}YfZŠ^a`}Ê

m]pŠm]iwYÔe¥mj^gm]YfePo˜paZ¯m]i}Y;y{Yfo˜mWμiw^a`}ÊeWtxÊ}YRx(Ð*×p!`}YÔmWZj^a`}eWtvm]t{p!`

ä·';¢k

¦

km·'+

æjÓ·^dmWZj^g`weWtvm]t{p!`

ä·+ë|Kà+k

 

ë%k·ë

æ

o˜paZYR^ahji

é

eWËwhji+m]iw^gm é ö é ö n Ó¯^a`}Ê+p!`}YmWZj^a`}eWt{m]t{p!` ä· k ¦ k· ¹

;

æjÑ är:h[m]Ëw^ay{y{×!ÓIeWp!\–Y–Y[ÌweWtxy{p!`

mWZj^g`weWtvm]t{p!`}eŽ^·Z]Y_^fÉnp!t{Ê}YDÊ2t{`Ûp!Ë1Zt{\ÌwyxYf\–YD`nmj^gm]t{p!`IÓBÐwË1mŽÖ Y¦Ödt{y{yP`wpgmŽÐUYhfp!`}hDY[Z]`}YDʺÖdtvm]iÛeWË}hji

pgÌwm]t{\–t{ÞR^gm]t{p!`}e i}YfZ]Yaѧæ

z

`£m]i}t{e ÖÏ^D×!Ó}Ö YªpaÐ}mj^at{`^¦uw`}tvm]YŽ^aË1m]p!\^·m]p!`NÖdtvm]i£t{`}tvm]t˜^gyUe¥mj^·m]Y

·;

^a`}ÊNuB`w^ayIe¥mj^gm]Y

· ¹; o˜paZ

YD^ahjiº`}p!`nm]Y[Z]\_t{`w^ay˜x ^a`}ʺtvm]esÊ}Y[uB`}t{`}|_Z]Ëwy{Yfe2x³z† 

àõç+çç

 8Ñ

Ø

iwt{e:^aË1m]p!\_^gm]p!`&hR^a`&ÐUYeWYDYf`

^gepa`wY_hDpa\–ÌUp!`}Yf`*mp!o m]i}Y_b

Ø

èÑ

Ø

i}Y_hfp!\ÌBy{Y[m]Y_b

Ø

è>t{epaÐ}mj^at{`wYfÊ+Ð*×Ûm]i}Y_hDpayxy{Yfhfm]t{p!`ÛpaoŠ^ay{y

eWË}hjiuw`}t{m]Y^aË1m]p!\_^gmj^¦oqpaZdÊ}tvÚUYfZ]Yf`nmd`}p!`nm]YfZ]\–t{`B^gyxefÑ

r:`2^gÌ}Ì}Z]pRÍ1t{\^·m]txpa``wpDÖ.Z]YfeWËwyvm]e:t{o“Ö YrWp!t{`2^ay{ym]i}Y¦hfp!\ÌIpa`wYf`nm]e:t{`2pa`wYÐwt{|£^aË1m]p!\_^gm]p!`IÓ

^g`wÊt{oŠÖ Y&^·ÌwÌ}Z]pRÍtx\_^gm]YNm]i}YË}eWËw^ayÏ\_YfhjiB^g`wt{eW\ p!odZ]YfhDË1Z]eWt{p!`(Ð×Z]Y[Ìwyx^ahDt{`}|2YR^ahji4mWZj^a`}eWtvm]t{p!`

ä·¸k

x

km·¹

æÐ×(mÜÖ p+mWZj^a`}eWtvm]txpa`we ä·¸k

¦

km·;

æ^g`wÊ ä·¹

; k ¦ km·¹

æjÑ Ø i}Y&hDpa`we¥mWZ]Ë}h[m]t{p!`çt{e_t{y{yxË}e¥mWZj^gm]YfÊ4tx`

ÒPtx|aË}Z]Yˆ\Ñ

z`+m]YfZ]\–ep!o m]i}YpaZ]t{|!t{`w^ayž|aZj^a\–\_^gZDÓFm]iwt{e^gÌ}Ì}Z]pRÍ1t{\_^gm]t{p!`hD^a`ÐUY_tx`}o˜paZ]\^gyxyv×2Y[ÍÌwy˜^gtx`}YfÊ

^ge:o˜p!y{yxpDÖdefÑIÈ*Ë}Ì}ÌUp!eWYÖ YiB^fÉnYm]i}Z]YfYZ]Ë}yxYfe

™ z |x–;Ó

™ ¹ z | ¹

¹

Ó<^a`}ʀx³z}”¯Ñ Ø paÌ}μÊ}pRÖd`

y{Yfo˜mWΛm]paΛZ]t{|!inmPÌB^gZ]eWt{`}|ªÖ paËwy{ÊÌwZ]p*hDYfYDʦo˜paZ”YfÍ}^g\–Ìwy{YÔÐ*×Z]YDhfp!|!`}t{Þftx`}|>|&t{`¦m]i}Y;u}Z]e¥m”Z]Ë}y{Y

t{mPÖ p!Ë}y{Ê

m]i}Yf`ÊwYfeWhfYD`}ÊNt{`nm]pZ]Ë}y{Y>x¨zÓ1^a`}ÊZ]Yfhfp!|!`}t{ÞDYT”

tvm;Ö p!Ë}yxÊ_m]i}Yf`Z]Y[m]Ë1Z]`m]pm]i}YduwZ]e¥m;Z]Ë}yxY:^a`}Ê

eWË1ÐweWYDÝ*Ë}YD`nm]yv×+Ì}Z]phfYDeWeM–;Ñ

z

`m]i}YN^gÌ}Ì}Z]pRÍ1t{\_^gm]t{p!`i}pRÖ Y[ÉnY[ZDÓ¯m]iwY–uw`wtvm]Y^aË1m]p!\^·m]p!`Là]o˜paZ]|!Y[m]eWâ

Ödi}t{hji8Z]Ë}yxY2tvmhD^a\–YÛoxZ]p!\ Ödi}YD`8t{m£e¥mj^gZWm]e£m]p(Z]YfhDpa|!`}txÞfY‹”¯ÓŠeWp4m]iw^gmtvm\_^D× eWË1ÐweWYRÝnËwYf`nm]yv×

Z]Yfhfp!|!`}t{ÞDY2– ¹ t{`Nm]iwYŽeWYfhDp!`}ÊZ]Ë}y{YaÑ

ÒwpaZ m]i}Y:e]^gìnY:paoFÌ}Z]YfeWYD`nmj^gm]t{p!`w^ay<hfp!`nÉnYf`wt{Yf`}hDYaÓ*m]i}Yª^gÐUpRÉnY:Ê}YfeWhfZ]tvÐUYfeÏ^hDp!`}e¥mWZ]Ë}h[m]txpa`Ö pgZWìÎ

t{`}|+p!`m]i}Y&hDpa\–Ìwy{Yfm]Y£|aZj^a\–\^·ZDÑ

å

pRÖ Y[ÉnY[ZDÓÔp!Ë1Zt{\ÌBy{Yf\_Yf`nmj^gm]t{p!`4^gÌ}Ìwyxt{Yfe–m]i}Y&hfp!`}e¥mWZ]Ë}hfm]t{p!`

eWY[ÌB^gZj^gm]Yfyv×&oqpgZªYD^ahji2`}p!`nm]Y[Z]\_t{`w^ay¯t{`2^_eWY[m lˆë

eWËwhjiºm]iw^gm]jŒ[H‰j‹q€g

älˆë

æ Ø

‰ffƒœÓBÖdi}txhjiºy{YD^aÊ}e

m]p–^eWYfÌB^gZj^·m]YeWË}ÐB^aË1m]p!\_^gm]p!`p!om]i}Yhfp!\Ì<^ghfmÏZ]YfÌ}Z]YfeWYD`nmj^gm]t{p!`

ä

È*Yfhfm]t{p!`~XnæjÑ

È*YDYªè:YfÊ}YfZ]i}p!o äWéDê!êe

æÔo˜paZd^É!^gZ]tx^a`nmÏp!oFm]i}txeÏ^gÌ}Ì}Z]pRÍ1t{\_^gm]t{p!`m]iw^gmŠhfp!`}e¥mWZ]Ë}hfm]e;uB`}tvm]Y:mWZj^g`we¥Î

Ê}Ë}hfYfZ]eÏZj^gm]i}YfZŠm]iw^a`£uw`}t{m]Y^aË1m]p!\_^gmj^1Ñ

ÕY_iw^DÉ!Y_oqË1ZWm]i}YfZt{\ÌBy{Yf\_Yf`nm]YDÊ+^£ÌB^gZj^a\–Yfm]Y[Z]t{ÞDYfÊ2ÉnY[Z]eWt{p!`p!oÔm]iwY–b Ø è>^gÌ}ÌwZ]pDÍ1t{\^gm]t{p!`IÑ

r e¥mj^gm]Y¦p!ožm]i}Y`}p!`}Ê}Y[m]YfZ]\–t{`wt{e¥m]t{h¦^aË1m]p!\_^gm]p!`2t{eª`wpDÖ ^ay{eWp^aeWeWphftx^gm]YDʺm]p^Ny{t{e¥mH}6p!oÔy{YD`}|am]i

} 

e¥mWZ]t{hfm]yv׺eW\^ay{y{Y[Zm]iw^a`^`Ë}\ÐUYfZ\bBÓFÖdi}txhji+t{em]i}Y–ÌB^gZj^g\_Y[m]YfZŽm]pm]iwY–\–Yfm]i}pÊIÑ Ø i}t{ey{t{e¥m

Z]Y[Ì}Z]YDeWYf`nm]eª^_i}t{e¥m]paZW×&pao“Z]Ëwy{YÌUp!eWtvm]t{p!`}edm]iw^gmdÖ YfZ]YYf`}hDpaËw`nm]Y[Z]YDÊt{`&m]iwYhfp!\ÌBË1mj^gm]t{p!`&y{YR^gÊwt{`}|

m]p¦m]iwYªÌ}Z]YDeWYf`nmse¥mj^gm]YaÑ

(8)

q A

q B

q A

q B

b

ε a ε

ε A

B

c

q A

d A e

ε

ε

b ε a

ε

ε

c

q A

d e

f f

ε

ε ε

ε

ε

ε ε

ε

ε ε

ε

ε ε

ε b

B a

A c

e A d f

(b)

(c) (a)

q B

q B A

A B B

͊Î)ÏdÐFÑÒ>~

Ì¢=8=9D*B*IA+@%B*;CY;ÇF@%Æ8LpË ? QŽ<ML@%Æ8;Å[Ç;+V @%Æ8LG+V%A<M<MA+V¢A+@uDA*NmÕ ? Æ8LË ? QuB*H¢GB SLC[A+@DSNmPAC8ŀDIN

=8V%LH%LC@%HŠ@%Æ8LA+=8=8V%;.ÉfB*<MA+@%B3C8G

U

C8B1@%LTA?@%;<MA+@%;CՂvLAHH%?8<ML„ƒuB*HŠ@%Æ8LpH@%A+V@¢HF…<TSU;DAC8Ň@%Æ8LV%LÇ);+V%L

†‡

SdLI;<MLH¢B*C8B*@%B*ADFH@%A+@%LpAC8Å

†$ˆ‡

SdLI;<MLH

U

C8ADêH@%A@%LpB*C‡@%Æ8LA=8=8V%;ÉB*<MA+@%B*C8G‘A?@%;<MA+@%;CÕ

úpaZ]Y”Ì}Z]YDhft{eWYDyv×!ÓfÖ YžÊwY[uw`}Y;^a`´x¶D«}µÂm]pÏÐUYÔ^a`pgÐdrWYfh[m¯p!o*m]iwYžo˜paZ]\óÝx{z—|Š‰–˜Þ¼ÓfÖdi}YfZ]Y¢x{z

|õ–txeÏ^¦Z]Ë}y{Yªo˜Z]p!\ m]i}YŽ|gZj^a\_\_^gZDÑ Ø i}YDeWY^·Z]Yªm]i}Yªe]^a\–YŽpaиrWYfhfm]eŠ^geÏm]i}YNà]Ê}pamWm]YfÊwâÌ}Z]pÊ}Ëwh[m]t{p!`}e

oxZ]p!\ w;^·Z]yxY[× äWéRênë ånæjÑ

Ø

i}YÊ}pamdt{`wÊ}t{hD^gm]YDeÏ^ÌUp!eWtvm]t{p!`t{`Nm]iwYªZ]t{|!inmWμiw^a`}Ê&eWt{ÊwYaÑ

Ø

i}YªËw`1ÌB^gZj^a\–Y[m]YfZ]t{ÞfYDÊNb

Ø

è-\–Yfm]i}pÊNiw^aÊpa`wYªe¥mj^gm]Y ·#‹ oqpaZÏYR^ahjitvm]Yf\ŒBÓw^a`}ÊNmÜÖ pe¥mj^gm]Yfe

·'; ^g`wÊ · ¹;

o˜paZŽYR^ghHiÛ`}p!`nm]Y[Z]\_t{`w^ay xÑ

Ø

i}Y¦ÌB^gZj^a\–Yfm]Y[Z]t{ÞDYfÊ2b

Ø è \–Yfm]i}pÊ2iw^aeŽp!`}Ye¥mj^gm]Y ·-Ž

o˜paZYD^ahHiçtvm]Yf\‘Œ(^a`}Ê»YD^ahHiçy{t{e¥m_p!o:t{m]Yf\–e2}7m]iB^·m_Z]Y[Ì}Z]YDeWYf`nm]eN^ÛÉa^ay{t{Êiwt{e¥m]paZW×4oqpaZ–Z]YR^ghHi}t{`}|

ŒwÓP^a`}Ê+mÜÖ pe¥mj^gm]YDe

·’O

^a`}Ê

·

¹’O o˜paZYR^ghHi`}p!`nm]Y[Z]\_t{`w^ay¢x>^g`wÊYD^ahHiy{t{e¥mp!oÏtvm]YD\–ek} m]iw^gm

Z]Y[Ì}Z]YDeWYf`nm]e^NÉa^ay{t{ʺiwt{e¥m]paZW×oqpgZŽZ]YD^ahji}tx`}|vxѯÈ*Ë}hji^Éa^ay{txʺi}t{e¥m]paZW׺t{eªÊwY[uw`}YDÊ2m]pNÐUY–^Ny{t{e¥mH}

Ödtvm]iuå×ö

} 

l9bm]iB^·m–Z]YfÌ}Z]YfeWYD`nm]e^2eWYfZ]t{Yfe_p!odÌUp!eWtvm]t{p!`}e–t{`4Z]Ëwy{Yfem]iw^gm_hfp!Ë}y{ÊiB^fÉnYÐUYDYf`

t{`nÉnpaì!YDÊÐUYfoqpaZ]YsZ]YD^ahji}tx`}|“Œ–paZxÓ*Z]YDe¥ÌUYfhfm]tvÉnYfyv×nÑ9úpaZ]YsÌ}Z]YfhDt{eWYfyv×nÓ*txoIÖ Y:eWY[m}

Ø Œ àõç+çç

Œ$”UÓ*m]iwYf`

YD^ahjimŒ

äWé

ö n

ö<•¯æ eWi}p!Ë}y{Ê&ÐUYp!o¯m]iwYo˜paZ]\—Ýx z}|–g‰

™ –—2ÞP^g`wÊo˜paZ é ö n

l<•ÛÖ Y

eWi}p!Ë}y{Êiw^DÉnY2x

Ø ™ u˜

à

Ñ*ÒBË1ZWm]i}Y[Z]\_paZ]YaÓo˜paZÏ^e¥mj^gm]Y

·-Ž

Ödtvm]iJŒ

Ø Ýx¨z}|™‰T–˜ÞBÖ YsÊ}YD\_^a`}Ê

x Ø

™‡à

t{ow•

.

å1Ñ}ÒwpaZd^¦e¥mj^gm]Y

·'’w

Ö YŽÊ}YD\_^a`}Ê~x

Ø

™‡à

txoO•

.

å1Ñ

ä

ÈnmWZ]t{hfm]yv×_e¥ÌUYR^gìtx`}|}Ó1e¥mj^gm]Yfe

·'’w

^a`}Ê

·Ž

ÓBÖdt{m]i

} 

lšb8›

é

^a`}ʜŒ

Ø Ýx³z |‰2–˜Þ›ÓBÖdtxy{yFp!`}yv×ÐUY`}YDYfÊ}YDÊt{o xWžŸžwt{edm]i}Y

e¥mj^·ZWmde¥×1\ÐUp!yIt{`m]i}YŽhR^geWY

}

 .

å1ÓwpaZdt{ox-txe m]i}Ye¥mj^·ZWmde¥×1\ÐUp!yFt{`£m]i}YŽhR^geWYk}

Ø

¦[ѧæ

Ø i}YžmWZj^a`}eWtvm]t{p!`}ep!o*m]iwYÔ^aË1m]p!\^·m]p!`Žm]iw^gm¯ÌUY[ZWmj^at{`Žm]pŠm]Y[Z]\_t{`w^ay{eFt{`ŽZ]tx|ai*mWμiw^a`}ÊeWtxÊ}Yfe¯p!o*Z]Ëwy{Yfe

^·Z]YÏÉnYfZWצeWt{\_t{yx^gZ“m]pªm]i}p!eWYdt{`¦m]i}YŠhR^geWYdp!oBm]i}YŠË}`}ÌB^gZj^g\_Y[m]YfZ]t{ÞfYDʦ\_Y[m]i}pʓ¶!ÒBpaZ;^ªe¥mj^gm]Y

·Ž

Ödt{m]i

(9)

Œ¦paoUm]iwYdo˜paZ]\ Ýx{z—|Š‰2–˜Þ¼Ó!Ö Ysh[Z]YR^gm]Ys^ŽmWZj^a`}eWtvm]t{p!`

ä·-Ž¡‘k



k·#‹¢Ÿ

æjÓ!Ödtvm]iJŒ

¹ Ø Ýx{z—|˜J‰–˜Þ¼Ñ

È*t{\_t{yx^gZ]yv×nÓwÖ YhfZ]YD^gm]Y¦Y[ÌweWtxy{p!`ºmWZj^a`}eWtvm]t{p!`}e:m]iw^gmŽhDpa`w`}Yfhfmªy{YDoxmWμiB^g`wÊ2eWt{Ê}YDe^g`wÊ2Z]t{|!inmWμiw^a`}Ê

eWt{Ê}YfepaoÏZ]Ë}y{YDe¶ÒBpaZYR^ahjie¥mj^gm]Y

·'’w

m]i}YfZ]Y_txe^mWZj^a`}eWtvm]t{p!`

ä·'’wMk

¦

k·Ž

æªoqpaZYD^ahHitvm]YD\{Œ

Ø

Ýx{z£‰2|KÞ¼Ó1oqpaZÏeWp!\–YM|ÔÓ}^g`wÊ£o˜paZÏYR^ghHi£e¥mj^gm]Y:p!oFm]i}Yªo˜paZ]\

·Ž¢¤

ÓÖdtvm]iŒ

¹ Ø Ýx{z—|Š‰+Þ¼Óm]iwY[Z]Y:t{e

^mWZj^a`}eWt{m]t{p!`

ä·-Ž&¢¤‘k

¦

k· ¹

’w

æjÑ

ÒwpaZ;mWZj^g`weWtvm]t{p!`}ežm]iB^·mÔÌUYfZWmj^at{`–m]p`wpa`*m]Y[Z]\–tx`w^ay{eÔt{`–m]iwYŠZ]t{|!inmWμiw^a`}ÊeWtxÊ}Yfe;paoUZ]Ëwy{YfefÓnÖ Ys`}YDYfÊ

m]p\^a`}tvÌwË}y˜^·m]Yªm]i}YŽi}txe¥m]pgZ]txYfefÑwÒwpaZs^–e¥mj^gm]Y

·Ž

Ödtvm]i€Œp!o¯m]i}YŽoqpaZ]\ïÝx{z}|™‰

™

–˜Þ›Ó}Ö Yh[Z]YR^·m]Y

mÜÖ psY[ÌBeWt{y{p!`ŽmWZj^a`}eWt{m]t{p!`}efÑfÂs`}Y;txe ䷎Mk ¦ k·¥—¦¢æjÓRÖdi}YfZ]Y§} ¹ txe¯Ê}Y[uw`wYfÊm]pdÐUY¨© t{o ¨o©  lªbBÓg^a`}Ê

m]pÐIYŠm]iwYdu}Z]e¥m¦bu› é tvm]Yf\_eÔp!o–¨©ãpam]i}Y[ZWÖdtxeWYaÑ

z

`}oqpaZ]\_^ay{yv×nÓ!Ö YsYfÍm]Yf`}Ê_m]i}Ysiwt{e¥m]paZW×Ð*זm]iwYdt{m]Yf\

Œ¦Z]YfÌ}Z]YfeWYD`nm]t{`}|m]i}Y:Z]Ë}y{YsÌUp!eWtvm]t{p!`_m]iB^·mÏÖ Y:iw^DÉnY¢r¥Ë}e¥mŠhfp!\–Y:o˜Z]p!\Ó*ÐwË}m m]i}Y:p!y{Ê}YDe¥mÏt{`}oqpaZ]\_^gm]t{p!`

t{`»m]i}Y2i}t{e¥m]paZW×»t{eNÊ}t{eWhD^gZ]Ê}YDÊ txoªm]i}Yºiwt{e¥m]paZW×ÐUYDhfp!\–YDem]p*p(y{p!`}|}Ñ

Ø

i}Y2eWYfhDp!`}Ê»mWZj^a`}eWt{m]t{p!`»t{e

ä·

¹ Ÿ ¢k ¦ k·Ž¢¤

æjÓ1Ödt{m]i>Œ ¹ Ø Ýx{z—|

™

‰T–KÞ¼Ñ

zoÏm]i}Ye¥mj^gZWme¥×\ÐUp!y;t{e

q

Ó¯m]i}YNt{`}tvm]tx^ayže¥mj^gm]YNt{e

·«

^a`}Êm]i}Yuw`B^gy e¥mj^gm]Yt{e

· ¹« ä

^aoxm]YfZm]i}Y

e¥×\ÐUp!y

q

tx`–m]i}YseWË1ÐBeWh[Z]tvÌ}m]eÔÖ Yduw`wÊN^a`Yf\–Ì}mÜ×yxt{e¥m]eÔp!oItvm]YD\–eHæjÑnè:pam]YŠm]iw^gmÔm]i}YdÌB^gZj^a\–Yfm]Y[Z]t{ÞDYfÊ

\–Y[m]iwp*ÊÛÖdtvm]iŠb

Ø é

hfp!`}hDË1Z]eŽÖdt{m]i2m]i}Y_Ë}`1ÌB^gZj^a\–Yfm]Y[Z]t{ÞDYfÊ+\–Yfm]i}pÊIÓFeWt{`}hDYm]i}Y_y{t{e¥m]ep!o;t{m]Yf\–e

m]i}Yf`£Z]YD\_^at{`Yf\–Ì}mÜ×!Ñ

r:`4Y[Í}^a\ÌwyxY_Ödt{m]iÌB^gZj^a\–Yfm]Y[Z8b

Ø

íºt{e¦|!tvÉnYD`(t{`4ғt{|!Ë1Z]Yv^ѓÒBpgZ–m]i}Y£Ë}`1ÌB^gZj^a\–Yfm]Y[Z]t{ÞDYfÊ

\–Y[m]iwp*ÊFÓUYD^ahji™Œ

Ø Ýx z |<‰‚–˜Þ“hDpaZWZ]Yfe¥ÌUp!`}Ê}YDÊ2m]p£p!`}Y¦e¥mj^gm]Y

ä

ғt{|!Ë1Z]Y¬\næjѯÈ*t{`whfYZ]YD^ahHi}t{`}|vx

hD^a`&iw^DÉ!Ym]i1Z]YDYÊ}tvÚUYfZ]Yf`nmsi}t{e¥m]paZ]t{YDeŠpao“y{Yf`}|am]i&eWi}paZWm]Y[Zsm]iw^a`í

ä

m]iwYŽYf\–Ì}mÜ×£iwt{e¥m]paZW×!ÓweWt{`whfY‘x)t{e

e¥mj^·ZWm“e¥×1\ÐUp!y

m]i}Y;i}t{e¥m]paZW×p!owhfp!\_t{`}|soxZ]p!\-m]i}YÔZ]Ëwy{YÔÌUp!eWtvm]t{p!`|!tvÉnYf`Ð*×t{m]Yf\ Ýx{z

Ÿ

‰2xTÞ

^a`}ÊIÓ

m]i}Ysi}txe¥m]pgZW×_paoFhfp!\_t{`}|o˜Z]p!\ m]i}YdZ]Ë}y{YsÌUp!eWtvm]t{p!`|at{É!YD`–Ð×_tvm]YD\ ݙ

z7b8‰>x>ý.ޑæjÓ*t{`NÒPtx|aË}Z]Y>^ŽÖ Y

`}pRÖ.iw^DÉ!Ym]i1Z]YDYe¥mj^gm]Yfe:pao“m]iwYoqpaZ]\

·Ž

oqpaZ:YD^ahHimŒ

Ø Ýx³z |‰>–˜Þ¼ÓU^gesÖ YDy{y¯^aesm]i1Z]YDYe¥mj^gm]Yfe

pao¯m]i}Yo˜paZ]\ ·’O ^a`}Ê · ¹’w Ñ

Ø

i}Y–i}t{|!i}YfZÖ Y–hji}pp!eWY2bBÓIm]iwY–\–paZ]YÌ}Z]YDhft{eWY¦m]iwY_^gÌ}Ì}Z]pRÍ1t{\_^gm]t{p!`Ût{efÓFeWtx`}hfYm]i}Y–i}t{e¥m]paZ]t{YDe

^gyxy{pRÖ m]i}Y^aË1m]p!\_^gm]p!`Ûm]peWt{\Ëwyx^gm]Y¦Ì<^·ZWm¦pao m]i}Y_\–YDhjiw^a`}t{eW\p!o;Z]YfhDË1Z]eWt{p!`o˜Z]p!\cm]i}Y_paZ]t{|!t{`w^ay

|gZj^a\_\_^gZDÓw^a`}Ê&m]i}Y\_^gÍ1t{\¦Ë}\Ây{Yf`}|am]ip!o¯m]iwYi}t{e¥m]paZ]t{YfedhfpaZWZ]YDe¥ÌUp!`}Ê}eŠm]p–m]i}Y`*Ë}\ÐUY[Zsp!oPyxY[ÉnYfy{e

pao¯Z]YfhDË1Z]eWt{p!`£m]iw^gmdhR^g`ÐUYŽeWt{\¦Ë}yx^gm]YfÊ&^ahfhDË1Zj^gm]Yfyv×nÑ

qwv` t«¸©”¸F«}µ+«}¸B¶²FhtHx\y cR­±”«©cf«*¶_°w±¯±P©·²³P´‘µ+°}¶·´˜²U¸

ÕYNZ]Y[Ìwi}Zj^geWYNm]iwY£\–Y[m]iwp*Ê(Ð*×çXsZ]t{\–yxY[×]w”É!^a`}e äWéRê!ênë æ^aeo˜p!y{y{pRÖdefѓғtvZ]e¥mDÓPÖ Yhfp!`}e¥mWZ]Ë}hfm¦m]i}Y

^·ÌwÌ}Z]pRÍtx\_^gm]t{`}|–uw`wtvm]Y^aË1m]p!\^·m]p!`º^ahfhDpaZ]Ê}t{`}|_m]p–m]iwYËw`1ÌB^gZj^a\–Y[m]YfZ]t{ÞfYDÊ&b

Ø è \–Yfm]i}pʺ^·ÐIpDÉnY!Ñ

Ø

i}Yf`2^a`2^aÊ}Êwtvm]t{p!`w^ay¯\–YDhjiw^a`}t{eW\t{e:t{`nmWZ]pÊ}Ë}hDYfÊm]iw^gm:YD`}eWË1Z]YfeªoqpgZªYR^ahjiZ]Ë}yxY‚x z   àõç+çç 2

eWY[ÌB^gZj^gm]Yfyvצm]iB^·mÔm]i}Ydy{t{e¥mÔp!o<É1t{eWtvm]e”m]pm]i}YŠe¥mj^gm]YDe ·'+fkœ+œœkm· e]^gm]t{e¥uwYDežeWp!\_YŠZ]YD^aeWp!`w^gÐwy{Ydh[Z]tvm]YfZ]tx^d¶

^ÉtxeWtvmŠm]p

·+ë

ÓwÖdtvm]i~å®ö é l n

ÓBeWi}p!Ë}yxÊÐUYo˜p!y{yxpDÖ YDÊ£Ð*×p!`}Ym]p

·ë

˜ à paZ

·'+

Ñ Ø

iwYyx^gmWm]YfZdpgÌwm]t{p!`

^g\_p!Ë}`nm]ePm]pª^:`}YDe¥m]Yfʦt{`}hR^gZ]`w^gm]t{p!`p!owm]i}YÔZ]Ëwy{YaÑ

Ø

i}Y[Z]Y t{e”^shDp!\Ìwy{YD\–YD`nmj^gZW׎hDp!`}Ê}tvm]t{p!`¦o˜paZPÖdiw^gm

eWi}p!Ë}y{ÊÌ}Z]YfhDYfÊ}Y^¦ÉtxeWtvmÏm]p

·+ë

Ó}Ödtvm]i~å2l é ö n Ñ

È*t{`whfYpa`wyv×£ÌB^atvZ]esp!o”hfp!`}eWYfhDË1m]tvÉnYÉtxeWtvm]eÏm]pe¥mj^gm]Yfeso˜Z]pa\ m]i}YeWY[mˆŒ

·#+fkœ+œœkm·

ˆ^gZ]YhDp!`}eWt{Ê1Î

Y[Z]YfÊFÓFuB`}tvm]Y[μe¥mj^gm]Y–m]YDhji}`}t˜ÝnËwYfeeWË1Ù_hfY_m]pt{\–Ìwy{YD\–Yf`*meWË}hHihfp!`}Ê}tvm]txpa`wefÑ Ø i}t{ehR^a`+ÐUY_Z]YD^ay{t{ÞDYfÊ

Ð*×4^gmWmj^ahjiwt{`}|Ûi}t{e¥m]paZ]t{YDe¦m]p2m]i}Ye¥mj^gm]YDe–^ae–t{`4m]i}YhD^aeWYp!osm]i}Y£ÌB^gZj^a\–Yfm]Y[Z]t{ÞDYfÊ(b Ø è\–Yfm]i}pÊ

^·ÐIpDÉnY!ӓÐwË1m_`}pRÖÂYR^ahjii}t{e¥m]paZW×(t{e_^2eWY[mZj^gm]i}YfZm]iB^g`ç^2yxt{e¥mDӔ^a`}ÊhD^a`hfp!`nmj^at{`^gm–\_p!e¥m–p!`}Y

tvm]Yf\ÛÝx z |¬‰~–˜ÞŠoqpgZ–YD^ahHi4Z]Ë}y{Yvx z |K–Ôєr:e¦Z]YfÌUpaZWm]YfÊ(Ð*×çXsZ]t{\_y{Y[×_wžÉa^a`}e äWéDê!ênë

æ^a`}Ê

hfp!`1u}Z]\_YfÊÐ×p!Ë1ZspRÖd`YfÍ*ÌIY[Z]t{\_Yf`nm]efÓ}m]iwY`}p!`}Ê}Y[m]YfZ]\–t{`wt{e¥m]t{hªuB`}tvm]Y^aË1m]p!\_^gmj^¦Z]YDeWË}yvm]t{`w|–o˜Z]pa\

m]i}t{eª\_Y[m]i}pÊ2\^D×ÐUYÝ*Ë}t{m]Y¦yx^gZ]|aY!ÓIY[ÉnYf`Ûo˜paZeW\_^ay{y“|aZj^a\–\_^gZ]efÑ Ø i}YY[ÍÌwyx^a`w^gm]t{p!`2t{e:m]iB^·mŽm]i}Y

`*Ë}\ÐIY[ZspaoPeWË}hHiiwt{e¥m]paZ]t{YfeŠt{eŠY[ÍÌUp!`}YD`nm]tx^ayItx`Nm]i}Y`*Ë}\ÐUY[Zsp!oZ]Ë}yxYfefÑ

ÕYsiw^DÉnYsZ]Y[uw`wYfÊ_m]i}Y:\–Yfm]i}pʖÖdtvm]i_Z]Yfe¥ÌIYfh[m;m]pm]i}YspaZ]t{|!t{`w^aywÌwË}Ðwy{t{hR^·m]txpa`–Ð*×^gÌ}ÌByv×1t{`}|m]i}Y

hfp!`}e¥mWZ]Ë}hfm]t{p!`£eWYfÌB^gZj^·m]YDyv×£o˜paZdYR^ghHi`}p!`nm]YfZ]\–t{`w^ayFt{`&^eWY[m l‚ë eWË}hji&m]iw^gmŽ]jŒ[H‰j‹q€g älˆë æ Ø

‰[fƒœÑ

qwv)¼ Á­K¿cf«*¶_°w±¯±P©·²³P´‘µ+°1¶g´˜²U¸u¿õæ(¶D©g°<¸Kc+h¼²B©aµ´‘¸¬+¶-,F«º¬B©·°<µµ+°w©

Ë}mWm]t{`}|ŽZ]Yfe¥mWZ]txh[m]t{p!`}ežp!`e¥Ìwt{`}YDe;t{e;^a`}pam]i}Y[Z;ÖÏ^fזm]ppaÐ}mj^at{`^ŽZ]YD|!Ë}yx^gZ;yx^a`}|!Ëw^a|aY!Ñ1È*YfÉnY[Zj^ayB\–Yfm]i1Î

p*ÊwehD^a`ÐUY_Ê}Yfuw`}YDÊIÑ Ø i}Y_u}Z]e¥m¦\–Yfm]i}pÊ+Ö Y–Ì}Z]YDeWYf`nm¦t{`*É!YDe¥m]t{|n^gm]Yfee¥Ìwt{`wYfet{`^ÉnY[ZW×+Ê}Yfmj^gtxy{YfÊ

ÖÏ^f×nÑ zmYfyxt{\–t{`B^·m]YDeŽoxZ]p!\cm]i}Y_yx^a`}|!Ëw^a|!Y–p!`}yv×2m]i}p!eWY_eWYf`nm]YD`}hfYDeoqpaZÖdi}txhji^&eWË1ÐUÊ}YfZ]tvÉa^gm]t{p!`Ût{e

(10)

e A d

f B B

ε H =

d e

f

q BH b

a

c ε

ε ε

b a

c ε

b ε a

c

q ε

ε

q BH

ε ε

ε

ε

ε ε

ε ε

ε ε

ε

ε ε

ε ε

ε ε

ε ε

ε ε

ε H = [B d A e]

H = [A a B b]

ε H = [A c A]

q AH

q AH

q AH q

AH q AH

AH

b B a

A c A A

͊Î)ÏdÐFÑÒ­

Ì¢=8=9D*B*IA+@%B*;CY;ÇF@%Æ8L0=9A+V%A<>L@%LV%B ®LÅ¬Ë ? Qu<ML@%Æ8;fŇʊB*@%Æ2¯B NfÕ°vLpAGAB*C[AH%H%?8<>Luƒ B3H @%Æ8LH@%AV@

HF…<TSU;DÕ ±@%A@%LH

†²Q³

Æ8ASLC8;+@ŠSdLLC[D*A+SULD*D*LÅYB*C[;+V%Å8LVŠ@%;MAS;B3ŇID*?@@%LV%B*C8GM@%Æ8Lp=9B*I@%?V%LÕ

Z]YDÝ*Ë}tvZ]YDÊ£paom]iwYªoqpaZ]\

™ z  | ™

–;Ó}o˜paZdeWpa\_Y‘|×Ö

Ø

¦d^g`wʚ–»Ö

Ø

¦[Ñ Ø i}YŽ\–pam]tvÉ!^gm]t{p!`t{e m]iB^·mdeWË}hji

eWYf`nm]YD`}hfYDe;Ê}p`}pam phfhDË1Z o˜Z]YDÝ*Ë}Yf`*m]yvזt{`_Ì}Zj^ah[m]t{hDYaÓ*eWt{`whfYdm]iwYfeWYseWË}ÐUÊ}Y[Z]t{Éa^gm]t{p!`}eÔ\^gì!Y:tvm;ÊwtvÙ_hfË}yvm

o˜paZÔÌIYfpaÌwy{YŠm]phfp!\–Ì}Z]Yfi}YD`}Ê_m]i}Yf\

ä

bsYfeW`}tvìUÓ éDê!ê

ínæjÑ Ø i}Yft{ZÔYfÍ1hfy{Ë}eWtxpa`–Ödt{y{y}m]i}YfZ]YfoqpgZ]Ys`}pam;y{YR^gʖm]p

\Ë}hHiyxpaeWeŠp!oPhfpRÉnY[Zj^a|!Yp!omÜ×Ìwt{hR^ayIeWYf`nm]YD`}hfYDefÓwYfe¥ÌUYDhftx^ay{y{×o˜paZdeWt{\–Ìwy{Y^gÌ}Ìwy{t{hR^gm]t{p!`£Ê}p!\_^at{`}efÑ

ÕYŠY[ÍÌ}Z]YfeWežm]i}YŠ\–Yfm]i}pʦt{`m]YfZ]\–e”p!oU^ª|aZj^a\–\^gZ”mWZj^g`weWo˜paZ]\_^gm]t{p!`t{`–Ò“t{|!Ë1Z]Y ë Ñ Ø

i}YŠYfÚUYfhfm

paoUm]i}t{ežmWZj^a`}eWoqpgZ]\^gm]t{p!`–t{ežm]iw^gm ^`}p!`nm]YfZ]\–t{`w^ayêx8t{ežmj^a|a|!YDʖÖdtvm]i^ŽeWYfm;p!o<Ì<^gt{Z]e 䙚k&´ æjÓ!Ödi}YfZ]Y

™ t{e–^2`}p!`nm]YfZ]\–t{`w^ay phDhfË1ZWZ]t{`w|2i}t{|!i}YfZtx`m]iwY£e¥Ìwt{`}Y

oqpaZ|!tvÉnYD` ™ Ӟ^·m_\–p!e¥mp!`}YeWË}hHi4ÌB^atvZ

䙮k&´

æ“hR^a`_ÐIYdhDp!`nmj^at{`}YfÊNt{`–m]iwYseWY[mDÑ

Ø

i}Y:eWY[m

´

\_^D×_hfp!`nmj^at{`_m]i}YsYDy{Yf\_Yf`nm¦µIm]pt{`}Ê}t{hR^gm]YŠm]iw^gm

eWpa\_Y[m]i}tx`}|:m]pªm]i}YÏyxYfo˜m“p!oBm]i}Y Ì<^·ZWmžp!oBm]i}YÏe¥ÌBt{`}YÏo˜Z]p!\

™

m]pMxçÖÏ^ae”|!Yf`wY[Zj^gm]YfÊIÑÈ*t{\_t{yx^gZ]yv×nÓü tœ´

t{`}Ê}t{hR^gm]Yfe“m]iw^gmÔeWp!\–Yfm]i}t{`}|Žm]pªm]i}YŠZ]t{|!inmžÖÏ^aež|!YD`}Y[Zj^gm]YfÊFÑ z o ´ Ø

ε

k

ü9nÓam]iwYf`Ö Ydiw^DÉnYdpaÐ}mj^at{`}YDÊ

^–Ê}Y[Z]tvÉ!^gm]t{p!`

™ z 

|Àx–ÔÓBoqpaZseWp!\–Y‚|¨Ö

Ø

¦s^a`}Êv–¨Ö

Ø

¦[Ó<^a`}ÊoqË1ZWm]i}YfZsphfhDË1ZWZ]Yf`}hDYfedp!o

™

ÐUYDy{pRÖ

x-eWi}p!Ë}y{ÊÐUYªÐBy{ph]ìnYfÊt{`paZ]Ê}YfZŠm]p–^DÉnp!t{Ê&^–Ê}Y[Z]tvÉ!^gm]t{p!`NÖdtvm]i£eWYDy{o˜Î¼Yf\ÐIYfÊ}Ê}tx`}|}Ñ

r:`+YfÍ1^a\–Ìwy{Yt{e|!tvÉnYf`+t{`+ғt{|!Ë1Z]Y

e Ñ Ø i}Y–paZ]t{|!t{`B^gy”|aZj^g\_\_^gZtxet{\Ìwyxt{hftvmªtx`Ûm]i}Y–Ê}Y[ÌBt{h[m]YDÊ

ÌB^gZ]eWY&mWZ]YfY&p!`m]iwY&y{YDoxmDÓÔ^g`wÊçhDp!`nmj^at{`}e^gmy{YD^ae¥m_m]i}Y&Z]Ë}y{YDe

q z x²<ÓRxïz

žÙ™

Ó ™ z ›

^g`wÊ

› z q Ñ Ø i}t{es|aZj^a\–\^·Z:t{edeWYfyxoxμYD\ÐUYDÊ}Ê}t{`}|}ÓBeWt{`}hDYÖ Yiw^DÉnY^_eWË1ÐUÊ}YfZ]tvÉa^gm]t{p!`

q z  žq

<Ñ

ÕYY[ÍÌwy˜^gtx`ºiwpDÖ

°L

t{eŽpgÐwmj^gtx`}YfÊÛoxZ]p!\

°L;

tx`2m]i}YZ]Ëwy{Y¬x¶°· z

žˆ™

¶°¸”ÑIÕY¦u}Z]e¥mhDpa`we¥mWZ]Ë}h[m

° ¹ Ø Œ äqk

Œü9gæ kRä

x k ì 搎o˜Z]pa\

°L;

Ø Œ äqk

Œü9a搎Ð*×^aÊ}Ê}tx`}|

äx k ì

æjÓ}eWtx`}hfY`}p–pgm]iwY[ZŠÌB^atvZdp!o¯m]i}Y

o˜paZ]\

äx k´

æÏÖÏ^aeª^ayvZ]YR^gÊ}×Ì}Z]YfeWYD`nmDÑ Ø pm]i}Y¦y{Yfo˜m:p!o”m]i}YphDhfË1ZWZ]YD`}hfY¦pao

™

t{`m]iwYpaZ]t{|!t{`w^ayZ]Ë}y{Y

é

(11)

ÕYª^gZ]Yª|!tvÉnYf`£^|aZj^a\–\^gZi

Ø

ä$jYkmlnkopkq

æjÑ Ø i}Yªoqpayxy{pRÖdt{`}|t{e;m]pÐUY:ÌUYfZ]o˜paZ]\–YDÊNo˜paZŠYD^ahji£eWY[m

lˆë¢t

ß eWËwhjim]iw^gm]jŒH1H‰j‹˜€a

äl‚ë

æ Ø

‰[fƒœÑ

é

ÑfÒBpgZ YR^ahjišx tvl‚ë

^g`wÊ_YR^ghHi

° t

í ¹¤º–»o¼ á½F¾Q¿ÀÁÂ

Ó^aÊ}Ê_m]i}Yso˜p!y{yxpDÖdtx`}|Ž`}p!`nm]YfZ]\–t{`B^gywm]p l Ñ

‰ x¶;Ñ

íÑgÒBpaZdYR^ghHinx tvl‚ë ÓB^aÊ}Êm]i}YŽoqp!y{y{pRÖdt{`}|¦Z]Ë}y{YŽm]p o Ñ

‰ x¨z—xÃgÑ

XÑgÒBpaZdYR^ghHi

ä

x¨z—|

+ x à | à x áçç+ç

|Kà

x>|–æ tvo

eWËwhjim]iB^·m x k x àkœœ+œk

x tvl‚ë

^a`}Ê&`}p–e¥×1\ÐIpayxeŠoxZ]p!\§|

+fk+œœ+œ.k

|w ^·Z]Y\–YD\ÐUYfZ]eÏp!o l‚ë

ÓB^a`}Ê&YD^ahji

°

eWË}hji&m]iw^gm

äx k

Œµ k ü9aæ3t~°

ÓB^aÊ}Ê£m]i}Yo˜p!y{y{pRÖdt{`w|¦Z]Ë}y{Yªm]p o Ñ

‰ x¶„z—|

+ x

¶°Ä

à | àõçç+ç

x¶‚Å

|–¦Ó1Ödi}YfZ]YaÓwoqpaZ

é ö í ö n Ó

Æ

°Kñ

Ø Œ 䙚k&´»ƒ>´

ñÇ

ƒ>´

ñp æ B䙚k&´ æ t~° ¹

Æ ° ¹ Ø

°»ƒ Œ äx k ì

æt{o ÷ Ü´ Ýäx k´ æ t~° ޛÓB^a`}Ê ° ¹ Ø ° pam]i}YfZWÖdt{eWY

Æ ´ ñÇ Ø¨ì

txo| + x à | àõç+çç x ñ$|Kà| ñ$|Kà

Ø

¦[ÓB^g`wÊ ´ ñÇ

Ø

Œµpgm]iwY[ZWÖdt{eWY

Æ ´ ñp بì

t{oÀ| ñ x ñ ˜ à | ñ ˜ àõçç+çx>|–

Ø

¦[ÓB^a`}Ê ´ ñp Ø

Œü9pam]i}Y[ZWÖdtxeWYaÑ

Z}ÑgbsYf\–pRÉnYŽo˜Z]p!\

o

m]i}Yp!y{ÊNZ]Ëwy{YfeŠp!o¯m]i}YŽoqpaZ]\§x{z—|ÔÓ}Ödi}Y[Z]Yˆx tvl‚ë

Ñ

\ÑgbsYfÊ}Ë}hDYŽm]i}YŽ|aZj^g\_\_^gZDÑ

͊Î)ÏdÐFÑÒ>È

±f?S9HL@¢A+=8=8V%;.ÉB*<MA+@%B*;C[S-…ˆ@V%AC8HÇ);V%<>B3C8G>@%Æ8LpGV%A<M<>AVÕ

x z

žM™

Ö YuB`}ʺ^_`}p!`1μYD\Ì}mÜ×&e¥mWZ]t{`}|

ž Ñ Ø iwt{es\–YD^a`}esm]iw^gmdÖ Yiw^DÉnYm]pN^aÊ}ÊɵPm]pN^ay{yeWYfhfp!`}Ê

hfp!\ÌUp!`}YD`nm]eŠp!oÌ<^gt{Z]eŠt{`

°‘¹

Ó}Ödi}t{hHi|!tvÉnYfeŠË}e

°L

Ø Œ äqÀk

ε

k

ü9aæ kDä

x k

Œ'µaænÑ

z`m]iwYÏmWZj^g`weWo˜paZ]\–YDʖ|aZj^a\–\^·ZDÓam]i}Ydy{pRÖ Y[ZÔphfhfË}ZWZ]Yf`}hDYŠpao

q

t{`m]i}YŠmWZ]YfYŠt{e”mj^a|!|aYDÊÖdtvm]im]i}Y

eWY[m®Œ

äqk

ε

k

ü9aæ kDä

x k

Œµaæ kD䙚k

ì æ kDä›>k

ì

æ!Ñ Ø iwY\_YD^a`}t{`w|ºt{em]iB^·mi}t{|!i}YfZ¦Ë1Ì4tx`m]i}YNe¥Ìwtx`}YaÓPÖ Y

Ödt{y{yIuw`}Êm]iwY`}p!`nm]Y[Z]\_t{`w^ay{e

q

ÓêxÓ

™

^g`wÊ

› Ñ Ø i}YŽÌB^atvZ äx k

Œµaæ;t{`}Ê}t{hR^gm]Yfe m]iB^·mseWt{`}hDYŽÖ Ye]^DÖ

x»p!`–m]i}YŠe¥Ìwtx`}YaÓneWp!\–Yfm]i}t{`}|Žm]pŽm]i}YŠy{Yfo˜mžiw^aežÐUYfYD`–|!Yf`wY[Zj^gm]YfÊIÓ!ÉtxÞaÑ

ž Ñ Ø i}YÏÌ<^gt{Z 䙚k

ì

æPt{`}Êwt{hD^gm]Yfe

m]iw^gm“`wpgm]iwt{`}|ªYftvm]i}YfZ¯m]p:m]i}Y yxYfo˜m“paZPm]p:m]i}Y;Z]tx|ai*m“iB^ge“ÐUYfYD`¦|!Yf`}YfZj^·m]YDʦeWt{`}hDY;Ö Y e]^DÖ ™ Ñ Ø i}Y ÌB^atvZ

äqk Œµ kü9aæ;t{`}Êwt{hD^gm]YfeÏm]iB^·msÐUpam]i£m]p–m]iwYy{Yfo˜ms^a`}Ê&m]p–m]i}YŽZ]t{|!inmseWp!\–Y[m]iwt{`}|–iB^gedÐUYDYf`&|!Yf`}YfZj^gm]YfÊ

äÉtxÞaÑ ž pa`m]i}YŠy{Yfo˜mž^a`}ʬp!`¦m]iwY Z]t{|!inm[æjÑÈ*t{`}hDY m]i}t{e”t{`}Êwt{hD^gm]Yfe“m]iw^gmž^a`–paÚUYf`}Êwt{`}|ŽeWË1ÐUÊ}YfZ]tvÉa^gm]t{p!`

q z  | q –iw^aeÐUYfYD`o˜p!Ë}`}ÊFӏoqË1ZWm]i}YfZhDp!\Ìwy{Yfm]t{p!`Ûp!o;m]i}Y–ÌB^gZ]eWY_mWZ]YfY_t{eÐwy{ph]ìnYDʓ¶Im]iwY–mWZj^g`we¥Î

o˜paZ]\–YDÊ&|gZj^a\_\_^gZŠÖdt{y{yF`}pamdiB^fÉnY^a`n×£Z]Ë}y{YDeÏÖdtvm]i&y{YDoxmWμiB^g`wÊeWtxÊ}Y q§Ê

¹

«°Ë

Ê ÇË pÌ

ÂFË

¹

;–Ë

Ê ÇÌ ÂÍË

¹

Ã

ÂÍË

¹

5OË

à ÂÌ Ñ

z`oq^ahfmDÓ!^go˜m]Y[Z”m]i}YÏ|aZj^a\–\^gZ“txe“Z]YfÊ}Ë}hDYfÊIÓn^a`n×ÌB^gZ]eWYÏmWZ]YfY m]iw^gm”txe“hfp!`}e¥mWZ]Ëwh[m]YfʖhD^a`}`}pamžY[ÉnYD`hfp!`1Î

mj^gtx`&^a`n×yxpa`w|aYfZ:^–`}pÊ}Yyx^gÐUYfyxy{YfÊ£Ð*×

q§Ê

¹

«°Ë

Ê ÇËpÌ ÂÍË

¹

;–Ë

Ê ÇÌ ÂÍË

¹

Ã

ÂÍË

¹

5ÎË

à ÂÌ

ÓBpgZ‚awÁN`}pÊ}YDedÖdtvm]i&yx^gÐUYfy{e

pao¯m]i}Yo˜paZ]\§x¶(eWËwhjim]iw^gm äx k

ε

k

ü9aæ t~°

Ñ

Âs`wY¦hDpaËwy{Ê2|!Yf`wY[Zj^ay{t{ÞDYm]i}t{eŽ^gÌ}Ì}Z]pRÍ1t{\_^gm]t{p!`2t{`2eWË}hHi+^ÖÏ^D×m]iw^gmŽ`}pam^ay{y“eWYfy{o˜Î¼Yf\ÐUYfÊ}Êwt{`}|

t{eÐwyxp*hjìnYfÊIÓ;ÐwË}m£p!`}yv×»eWYfy{o˜Î¼Yf\ÐUYfÊwÊ}t{`}|(phfhfË}ZWZ]t{`}|}Ó e]^D×!Ó mÜÖdt{hfYºtx`8^Z]pRÖÓÏt{` m]i}Y2eWYf`}eWYÛpao^

eWË1ÐUÊ}YfZ]tvÉa^gm]t{p!`Np!om]i}YŽoqpaZ]\ x¨z

 | à

à z  | à | á

á – à

Ñ1ÕY:Ödtxy{yU`}pamdÊ}peWp–i}Y[Z]Y!Ó1ÐUYfhR^aË}eWY

^gy{Z]YD^aÊ1×NoqpaZŠm]i}YªÐB^aeWt{hhR^aeWY^gÐUpRÉnYaÓ}m]i}YŽmWZj^a`}eWo˜paZ]\_YfÊ|aZj^a\–\^·ZdhD^a`£ÐUYiË}|!YÊ}Ë}Yªm]pm]i}Yi}t{|!i

`*Ë}\ÐIY[Z“p!ow`}p!`nm]Y[Z]\_t{`w^ay{e¯p!o}m]i}Y;oqpgZ]\´x¶&m]iw^gmP\^f×Z]YDeWË}yvm

m]iwY;`*Ë}\ÐIY[Z”p!o}eWË}hji¦`wpa`*m]Y[Z]\–tx`w^ay{e

t{eŠY[ÍÌUp!`}YD`nm]tx^ayIt{`£m]i}YeWt{ÞfYŽp!o lˆë

Ñ

ÕYm]i}YfZ]YfoqpgZ]YÌ}Z]YfeWYD`nmDӞtx`ÒPtx|aË}Z]Y

ê

ÓÔ^a`»^ayvm]YfZ]`w^gm]tvÉnY^·ÌwÌ}Z]pRÍtx\_^gm]t{p!`4m]iw^gm_iw^ae^Ûy{pRÖ Y[Z

(12)

A S

a

b B

C

S (a)

A S

a

b B

C

S

C

S

(b) F

F

F

F

F S

B A

S

°A«

Ø ì

°L;

Ø Œ

äqk

Œü9gæ

°L

Ø Œ

äqk

ε

k

ü9aæ kDä

x k

Œµaæ

°L5

Ø Œ äqk Œµk ü9aæ kDäx k ŒµaækD䙚k

ì

æ

° ¹

« Ø Œ äqk Œµk ü9aæ kDäx k ŒµaækD䙚k

ì æ kDä›>k

ì

æ

͊Î)ÏdÐFÑÒÏ

Ì =9A+V%H%Lp@V%LLpB*C¬A>H%LD*ÇQPL<TSdLÅ8Å8B*C8G‚G+V%A<M<MA+VuDA-NmP8AC8ł@%Æ8LI;+VV%LH=d;C8Å8B*C8GM=9AV%HLp@V%LLB3C‡@%Æ8L

@V%AC8HÇ;+V%<MLÅ[G+V%A<M<MA+VDSNmP8Ç);+VŠ@%Æ8Lp@V%AC8HÇ;+V%<MA+@%B*;C[Ç"V%;<gd“B*G?V%LÐfÕ/d9;+VŠ@%Æ8L<>;<>LC@ Ê LpB*GC8;V%L

H@%L=ÒÑ ;Ǘd“B3G?V%LÐPBsÕLÕ8V%LÅ8?8I@%B*;C¬;ÇF@%Æ8L0@V%AC8HÇ);V%<>LÅ[G+V%A<M<MA+VÕ

hfp!\ÌwyxY[Í1tvmÜ×!ъ’ ×ÌB^gZj^g\_Y[m]YfZÒbBÓ;tvm_Z]YDe¥mWZ]t{h[m]e_m]i}Yº`*Ë}\ÐUY[ZNp!oªZ]Ë}y{YDeN^ay{p!`}|^e¥ÌBt{`}Ym]iw^gmN\_^D×

|aYD`}Y[Zj^gm]Y£eWp!\–Yfm]i}t{`}|ºm]p2m]i}Y£y{Yfo˜m–^a`}Ê(m]p2m]i}YNZ]t{|!inmDÑPÕY£Ê}pÛi}pRÖ Y[ÉnY[Z_`}pam¦Z]YDe¥mWZ]t{h[m¦ÌwË}Z]Y£y{YDoxm

Z]YfhfË}Z]eWt{p!`»^a`}ÊçÌwË1Z]Y&Z]t{|!inm_Z]YfhfË}Z]eWt{p!`IÑ¢’ÏY[mÜÖ YDYf`mÜÖ pphfhDË1ZWZ]Yf`}hDYfe_p!oŽ^g` ^gZWÐwtvmWZj^gZW×(Z]Ëwy{YaӞ֠Y

^gyxy{pRÖyxYfo˜m Z]YfhDË1Z]eWt{p!`£oqp!y{y{pRÖ YfÊNÐ×Z]t{|!inmÏZ]YDhfË1Z]eWtxpa`

ä

Ödi}t{hHi£y{YD^aÊ}eÏm]pmj^a|[ü¦o˜p!y{yxpDÖ YDÊNÐ*×mj^a|£[ƒ›æjÓ

pgZŠZ]tx|ai*mŠZ]YfhfË}Z]eWt{p!`o˜p!y{yxpDÖ YDÊNÐ×£y{YDoxmŠZ]YfhfË}Z]eWt{p!`

ä

Ödi}t{hHi£y{YR^aÊ}eÏm]pmj^g|JµPoqpayxy{pRÖ YfÊ£Ð*×Nmj^a|&ƒ¡næjÑ

r:`ºYfÍ1^a\–Ìwy{Yt{e:|!tvÉnYf`ºtx`ºÒ“t{|!Ë1Z]Y

é

å1Ñ<r:e:ÐUYDo˜paZ]YaÓ<m]i}YZ]Ë}y{Yfe:p!o”m]iwY|aZj^a\–\_^gZŽ^·Z]Y¦tx\Ìwy{txhftvm

t{`+m]i}Y_ÊwY[Ìwt{hfm]YfÊ+ÌB^gZ]eWY_mWZ]YfYaѯrÏmm]i}Y_m]pgÌp!o m]i}YÊ}Y[Z]tvÉ!^gm]t{p!`2Ö Y_uw`}Ê

q Ñ z `m]i}Y–mWZj^a`}eWo˜paZ]\_YfÊ

|gZj^a\_\_^gZDÓwÖ Yu}Z]e¥mªiw^DÉ!Ym]pN^gÌ}ÌByv×

q z q§Ó

Ë+ Ñ Ø iwYÊwY[Z]tvÉ!^·m]txpa`&e¥mj^gZWm]edÖdt{m]iº^–Z]Ë}y{Y

q z x´<Ó

Ödi}t{hji|aYD`}Y[Zj^gm]YDe^£e¥mWZ]tx`}|

ä

ÉtxÞaѓwæsm]p£m]iwYZ]t{|!inmpaoÏ^`}p!`nm]Y[Z]\_t{`w^ay

ä

ÉtxÞaÑõxŽæjÑK’ÏYfoqpaZ]Y¦Ö Y_hD^a`

^·ÌwÌwyv×çÞfYfZ]ppaZN\–paZ]YºpaoŽeWË}hHi»Z]Ë}y{YDefÓÔÖ Yu}Z]e¥m£iw^DÉ!Yºm]p(^·ÌwÌwyv×ç^Ë}`}t{m_Z]Ë}yxY

q Ó Ë+ z q p Ë+

tx`

m]i}YªmWZj^g`weWo˜paZ]\–YDÊ£|aZj^a\–\^gZDÑ}ÒwpaZdÞfYfZ]ppaZŠ\–paZ]YªZ]Ë}y{YDe m]iw^gmdeWË1ÐweWYDÝ*Ë}YD`nm]yv×N|!YD`}Y[Zj^gm]YŽeWp!\–Y[m]iwt{`}|

pa`çm]i}Y&y{Yfo˜mDӞeWË}hji ^gešxïz

žÙ™

Ӟ֠Y&iw^DÉnY&m]p+paÐ}mj^at{`»^+eWË1ÌUY[Z]eWhfZ]tvÌ}mhfp!`nmj^at{`}t{`w|[ƒ¡Ó;^g`wÊçtx`

m]i}YY[Í}^a\ÌBy{Ym]i}t{eŽt{eŽÊ}p!`}YÐ*×Û^gÌ}ÌByv×1t{`}|vx

p Ë+ z x p ÇË+

ÑIè:pRÖ Ö Y_^·Z]Yuw`}t{eWi}YDÊ2Ödt{m]iºÌwË1Z]Y–y{YDoxm

Z]YfhfË}Z]eWt{p!`£^a`}ÊNÌwË1Z]Y:Z]t{|!inm Z]YDhfË1Z]eWtxpa`FÓ1^a`}Ê^gÌ}ÌByv×

™ p ÇË+ z

™JÔ

Ë+ Ñ Ø i}txeÏ^ay{y{pRÖde Ë}e m]p¦^gÌ}ÌByv×p!`}Y

Ë}`}hfp!`}e¥mWZj^at{`wYfÊ£Z]Ë}yxYaÓ}Ödi}t{hji^·ÌwÌUYD^gZ]edt{`£m]i}YŽmWZj^g`weWo˜paZ]\–YDÊ|aZj^a\–\_^gZs^ge ™ Ô Ë+ z ŸMq§Ó Ë1à

bBÑ

è:pRÖ m]i}Yhfp!Ë}`nm]YfZ2((iw^aeÐUYDYf`tx`}h[Z]YR^geWYDÊo˜Z]p!\ïå^·mm]i}Y_e¥mj^gZWmp!o m]i}YeWË1ÐUÊ}YfZ]tvÉa^gm]t{p!`Ûm]p

é ^gmsm]i}YYD`}ÊIÑ5ÿªY[ÌIYf`}Ê}tx`}|_p!`m]i}YÉa^ay{Ë}Y\b£m]iw^gmdÖ YhHi}ppaeWY!ÓBÖ YhR^g`w`}pamsÐwË}txy{ÊÊ}Y[Z]t{Éa^gm]t{p!`}eŠÐ*×

Z]Y[ÌUYR^·m]tx`}|ŽeWË1ÐUÊ}YfZ]tvÉa^gm]t{p!` q z 

žpŸq b‚¦^a`_Ë}`}y{t{\_tvm]Yfʦ`Ë}\ÐUYfZÔp!oBm]t{\_Yfe¶n^·mÔeWp!\–YÏÌUp!t{`*m”m]i}Y

hfp!Ë}`nm]YfZ Ödt{y{y<YfÍ1hfYfYDÊbwÑ z oIÖ YŽhji}pp!eWYb

Ø

å1Óm]iwYf`£^ayvZ]YR^aÊ1זm]i}YªÊ}YfZ]tvÉa^gm]t{p!`N^gmÏғt{|!Ë1Z]Y é å ä

ÐUæžt{e

`}pamdÌIpaeWeWt{Ðwy{Y^a`n×1\–paZ]Y!Ó<eWt{`}hfY`}p`}p!`nm]YfZ]\–t{`w^ay¯t{`&m]i}YmWZj^a`}eWoqpaZ]\–YfÊ|aZj^a\–\^gZdÖ p!Ë}yxÊhDpa`*mj^gtx`

é

tx`tvm]eŠeWË1ÌUYfZ]eWh[Z]tvÌwmDÑ

’ÏYfhR^gËweWYp!oPm]i}YÊ}Yf\_pa`we¥mWZj^·m]YDÊ&t{`}h[Z]YR^aeWYp!oPm]i}Yhfp!Ë}`*m]Y[Zk(FÓwm]i}t{edmWZj^g`weWo˜paZ]\_^gm]t{p!`&t{ed|!Ëw^gZWÎ

^g`*m]YfYfÊm]p&Z]Yf\_pDÉnYeWYfy{o˜Î¼Yf\ÐUYfÊwÊ}t{`}|oxZ]p!\m]i}Y_|aZj^a\–\^gZDÑ

å

pRÖ Y[ÉnY[ZDÓ¯tvmtxe`}pam^aeeWYfy{YDh[m]tvÉnY_^ae

m]i}YÏmWZj^a`}eWoqpaZ]\_^gm]t{p!`¦Ö Yde]^DÖçÐIYfoqpgZ]Y!Ó!t{`–m]i}YŠeWYf`}eWYdm]iw^gmžtvmÔ\_^Dז^gyxeWpŽÐwy{ph]ìeWË1ÐUÊ}YfZ]tvÉa^gm]t{p!`}e”m]iw^gm

^·Z]Y`}pamŠp!o¯m]i}YŽoqpaZ]\ x¨z



|x–;Ñ<k;p!`}eWt{Ê}YfZdo˜paZdY[Í}^a\ÌBy{Y:m]i}YŽeWË1ÐUÊwY[Z]tvÉ!^·m]txpa`£o˜Z]p!\ÂÒPtx|aË}Z]Y

é

å1Ó

ÐwË1mZ]YfÌwyx^ahftx`}|&m]iwYyxpDÖ YfZ¦phfhDË1ZWZ]Yf`whfYp!o

q

Ð*×^a`n×pam]i}Y[Z`}p!`nm]Y[Z]\_t{`w^ay

›

m]iw^gm¦t{e¦\Ë1m]Ëw^ay{y{×

Z]YfhfË}Z]eWtvÉnYŽÖdtvm]i

q

Óêx.^a`}Ê

™

ÑIÈ*Ë}hHiº^eWË1ÐIÊ}Y[Z]tvÉ!^gm]t{p!`

q z

ž>Ÿˆ›

b®NÖ paËwy{Ê^ay{eWp–ÐUYŽÐwy{ph]ìnYDÊ

Ð*×hHi}pp!eWt{`}|Jb

Ø

åÑ z`|!Yf`wY[Zj^ay›ÓBt{`}hfZ]YD^aeWt{`}|Jb£^ay{y{pRÖded\_pgZ]Yp!o“eWË}hjiºÊ}Y[Z]t{Éa^gm]t{p!`}eŠm]iw^gm:^gZ]Y`}pam

pao¯m]i}Yo˜paZ]\§x¨z



|x–ÐwË}ms^gyxeWp–^ay{yxpDÖdeŠ\_paZ]YŽÊ}YfZ]tvÉa^gm]t{p!`}e m]iw^gms^gZ]YŽp!o¯m]iw^gmdo˜paZ]\Ñ

é

(13)

ÕYª^gZ]Yª|!tvÉnYf`£^|aZj^a\–\^gZi

Ø

ä$jYkmlnkopkq

æjÑ Ø i}Yªoqpayxy{pRÖdt{`}|t{e;m]pÐUY:ÌUYfZ]o˜paZ]\–YDÊNo˜paZŠYD^ahji£eWY[m

lˆë¢t

ß eWË}hjim]iw^gmŽ]jŒ[H‰j‹˜€a

äl‚ë

æ Ø

‰f[ƒœ¯Ñ Ø i}YªÉ!^gyxË}Yb_e¥mj^a`}Ê}edo˜paZŠm]i}YŽ\_^gÍ1t{\Ë}\>`*Ë}\ÐUY[Zdp!o

Ë}`}hfp!`}e¥mWZj^at{`wYfÊZ]Ë}y{YDe ^gyxpa`w|^e¥Ìwt{`}Y!Ó*ÌUp!eWeWtvÐwy{×_^ayvm]Y[Z]`w^gm]YDÊ_Ödtvm]iN^eWY[Z]txYfe;p!oFy{YDoxmWΛZ]YDhfË1Z]eWtvÉnYŠZ]Ëwy{Yfe

o˜p!y{y{pRÖ YDÊNÐ*×&^eWY[Z]t{YDeŠpao¯Z]t{|!inmWΛZ]YDhfË1Z]eWtvÉnYŽZ]Ë}y{YfefÓwpaZŠÉ1t{hfYªÉnY[Z]e]^1Ñ

é

ÑgÒBpaZdYR^ghHinx tvl‚ë

ÓwYD^ahji

´ t

Œ-Õ k µ k ü k

ƒ

k

[ƒ

nÓw^a`}Ê&YR^ghHiœ(eWË}hHi£m]iB^·m å¬öš(nöªbBÓ

^aÊ}Êm]i}Yo˜p!y{yxpDÖdtx`}|¦`wpa`*m]Y[Z]\–tx`w^ay{e m]p l Ñ

‰ x×

ËØ Ñ

íÑgÒBpaZdYR^ghHinx tvl‚ë ÓB^aÊ}Êm]i}YŽoqp!y{y{pRÖdt{`}|¦Z]Ë}y{YŽm]p o Ñ

‰ x¨z—x

Ó Ë+ Ñ

XÑgÒBpaZdYR^ghHinx tvl‚ë

^a`}ÊÉ(&eWËwhjim]iB^·m å¬öš(nöªbBÓB^aÊ}Êm]i}YŽoqpayxy{pRÖdt{`}|¦Z]Ë}yxYfeÏm]p o Ñ

‰ x Ó ËØ z—x

ÇËØ Ñ

‰ x Ó ËØ z—x

p ËØ Ñ

‰ x ÇËØ

z—xkÙÚ ËØ Ñ

‰ x p ËØ z—x ÚÙ

ËØ Ñ

‰ x ÙÚ ËØ z}x

Ô ËØ Ñ

‰ x ÚFÙ ËØ

z—x Ô ËØ Ñ

Z}ÑgÒBpaZdYR^ghHi äx¨z ™ |”æ t~o eWË}hHim]iw^gm x km™ótvlˆë ^a`}Ê&`}p–e¥×1\ÐUp!y{eŠoxZ]p!\§|(^gZ]Y

\_Yf\ÐUY[Z]eŠpao l‚ë ÓwYD^ahHiœ(eWËwhjim]iw^gm å[öš(‹öªbwÓ<^g`wÊYR^ahji ´ t Œ+ü k ƒ¡9nÓB^aÊ}Êm]i}Y

oqp!y{y{pRÖdt{`}|¦Z]Ë}y{Yªm]p o Ñ

‰ x×

ËØ z ™ × ËØ

|ÔÑ

\ÑgÒBpaZdYR^ghHi

ä

x¨z—|

™ æ t~o

eWË}hHim]iw^gm x

km™ótvlˆë

^a`}Ê&`}p–e¥×1\ÐUp!y{eŠoxZ]p!\§|(^gZ]Y

\_Yf\ÐUY[Z]eŠpao l‚ë

ÓwYD^ahHiœ(eWËwhjim]iw^gm å[öš(‹öªbwÓ<^g`wÊYR^ahji

´ t

Œ'µ

k

[ƒ!ÓB^aÊ}Êm]i}Y

oqp!y{y{pRÖdt{`}|¦Z]Ë}y{Yªm]p o Ñ

‰ x×

ËØ

z—|

™ × ËØ Ñ

^ÑgÒBpaZdYR^ghHi

ä

x¨z—|

+ x à | à x áçç+ç

|Kà

x>|–æ tvo

eWËwhjim]iB^·m x k x àkœœ+œk

x tvl‚ë

^a`}Ê&`}p–e¥×1\ÐIpayxeŠoxZ]p!\§|

+fk+œœ+œ.k

|w ^·Z]Y\–YD\ÐUYfZ]eÏp!o l‚ë

ÓB^a`}Ê&YD^ahjiÉ(eWË}hjim]iw^gm

å¬öš(nöªbBÓB^aÊ}Ê£m]iwYŽoqpayxy{pRÖdt{`}|¦Z]Ë}y{Yªm]p

o

Ó}Ì}Z]pRÉ1t{Ê}YfÊ n Ø

åÛÜ(mlªbwÑ

‰ x Ô ËØ

z—| + x Ó ËØ ˜ à

à | àõç+çç x Ó ËØ ˜ à

|–¦Ñ

ë ÑgbsYf\–pRÉnYŽo˜Z]p!\ o m]i}Yp!y{ÊNZ]Ëwy{YfeŠp!o¯m]i}YŽoqpaZ]\§x{z—|ÔÓ}Ödi}Y[Z]Yˆx tvl‚ë Ñ

e ÑgbsYfÊ}Ë}hDYŽm]i}YŽ|aZj^g\_\_^gZDÑ

͊Î)ÏdÐFÑÒÝ

Ìu<M;+V%LH%B*<>=9D*LH%?S9HL@¢A+=8=8V%;.ÉfB*<MA+@%B3;C[S-…ˆ@V%AC8HÇ);V%<>B3C8G2@%Æ8LGV%A<M<>AVÕ

Ø i}YŠZ]YD^aeWp!`_oqpaZÔhfp!`}eWtxÊ}Y[Z]t{`w|Žm]i}t{e”mWZj^a`}eWoqpaZ]\_^gm]t{p!`Zj^gm]i}YfZžm]iw^a`^a`n×pam]i}YfZžm]iw^gmÔYDy{t{\–tx`w^gm]Yfe

eWYfy{o˜Î¼Yf\ÐUYfÊ}Êwt{`}|t{e:ÌwË1Z]YDyv×&Ì}Zj^a|!\_^gm]t{hf¶<p!o”m]i}Y¦\_^a`n×&É!^·Z]t˜^g`*m]esÖ Y¦iw^DÉ!Y¦mWZ]t{YDÊ&m]iw^gm:×1t{YDy{Ê`wpa`}Î

mWZ]tvÉ1tx^ay<eWË1ÐweWYfms^·ÌwÌ}Z]pRÍtx\_^gm]t{p!`}efÓm]iwt{e mWZj^g`weWo˜paZ]\_^gm]t{p!`£iw^aeÏm]i}Yªy{pRÖ Yfe¥mdhfp!\ÌBy{Y[Í1tvmÜ×_t{`Nm]YfZ]\–eÏp!o

é

Referenzen

ÄHNLICHE DOKUMENTE

The measure which corresponds to the state complexity is the number of nonterminals (if one restricts to regular grammars with rules of the form A → aB or A → λ, where A and B

[r]

[r]

Picture courtesy of imagerymajestic / FreeDigitalPhotos.net Gabriele R¨ oger (University of Basel) Theory of Computer Science March 31, 2021 4 / 26... Closure under

Pumping lemma: use a necessary property that holds for all regular languages. Picture courtesy of imagerymajestic

C3.1 Regular Expressions C3.2 Pumping Lemma C3.3 Summary.!. C3.1

The word problem, emptiness problem and finiteness problem for the class of context-free languages are decidable. The equivalence problem and intersection problem for the class

Picture courtesy of imagerymajestic / FreeDigitalPhotos.net Gabriele R¨ oger (University of Basel) Theory of Computer Science April 3, 2019 5 /