Large © Dualities in Topological String Theory ... - Caltech THESIS

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Topological string theory is a yet another kind of string theory, which has a close relation- ship to type IIA3@ B string theories. As a CFT on the worldsheet, we ...
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g‰[ 2 GZN>[^]U| 2W/ } „>,.-y/ f[jG0]b[^L3Y€KQP V / P4kJN -0/ [^L 2W/1 [jGJN -0/ }Š[^LiP4k 13-0// N~L / P / |MKQGZN]b[^LdN -0/ NO[^gƒ[jPW[ ej2 fKQP™P¹KML eQ/Œº kUTUKQP 2 N 6 fKMG 5ƒ/ L / KQP 2 • / k K 1 N -0/`2 G0]bLiKML / k¨P 2 Y 2 N.[Q]+f / L3N‡K 2 G¨V / P4k¾N -0/ [^L 6 Y[yk / P 1 l0N -y/`e KMT e^/ kJP 2 G / KL 132We Y€KY [yk / P¢l‰KQG0k¨N -0/ žAKQGUkXKMTy¯«œ 2 G0• 5 T0L e Y[yk / P „ zd[ e T0L 2 KQGUk‹§ K]¿K 13- [} / k - [u}¸N -0/ kUTXKMP 2 N 6 [^]$œ)[Qg‰KMxyTUYKML.KQGUk#§ KM]¿K fKQG 5ƒ/ k / L 2 | / k 576 K¨k 6 GXKQY 2 fKMP e^/ G / L‡KN 2 [jGÊ[^] 5 [jTUGUkUKML 2W/1 [^G¤N -0/ f—PW[ 1O/ k 1 N3L 2 G e }Š[^LiP4k 13-0// N 1„ ¦/ } 2 P4P 5ƒ/ K 5 P / N3[ /—­ N / G0kN -0/ }%[^L3P4k 13-0// Nk / L 2 |QKN 2 [jGŒ[^]ƒN -y/ P¹KL e^/~º kUTXKQP 2 N 6 N3[:[^N -0/ L { ¯HY[7k / P 1 2 GJY[^L /:e^/ G / L‡KQP e^/ [jY / NOL 2W/1.5Z6 T 132 G e Y 2 L3LO[^L 1O6 YY / N3L 6j„+¦/ KMP 1 [ /­ N / GUk¨N -y/ k / L 2 |QKN 2 [jG¾NO[ ˜ ¯ Y[yk / P™P¹KML eQ/Œº kUTXKMP 2 N 2W/1„ { PW[jG e N -0/ }.K 6 l0} / TUGXf[| / L - [u}N -0/`2 GZN3L 2 fKN /:5 [jTUG0kXKML 6 f[jGUk 2 N 2 [jG 1 P 2 x / N -0/~¦¸2 P 1 [jG€P 2 G / fKMLOL 2W/ k 576 K c ¯ 5 LiKQG / KML / Y€KQG 2 ] /1 N / k[jG€N -0/ }%[QLiP4k 13-0// NN -0/ [^L 2W/1 [^]™fPW[ 13/ k 1 N3L 2 G ej1„ HF G€f - KgUN / L ç lQ} / } 2 P4P0k /1 f—L 2W5ƒ/ KN /1 N$[^]’Kf—P¹K 131 [^]ƒP¹KML e^/~º kUTXKQP 2 N 2W/1„ FHG N -U241 f—P¹K 131 [^]KML /2 G¨N -0/ P¹KML e^/º P 2 Y 2 N~fKMgUNiTyL / k 576 K m ¯Hk 2 Y / G 132 [jGXKQP 1 T0LO]¿K^f / fKQP4P / kÀN -y/ 1 g / fN3LiKQP~f—T0LO| /j„ žAKML eQ/(º k0TXKQP 2 N 6 gUL / k 2 f—N 1 KsgUL / f 241O/ L / P¹KMN 2 [jG 5ƒ/ N } // G€N -0/)1 g / f—NOL‡KQPƒfTyL3| / KQG0k®N -0/)eQ/ [^Y / N3L 62 G€} -U2 f - f—PW[ 1O/ k 1 N3L 2 G ej1 gULO[^g‰K e KN /j„A¦¤/ } 2 P4P‰f[jY gXT0N /~5 [^N - N -0/)1 g / f—NOL‡KQP‰f—T0L3| / [^]’N -y/ Y€KMN3L 2½­ Y [yk / PƒKQG0k€N -y/de^/ [jY / N3L 6 ]b[^L%f—PW[ 1O/ k 1 NOL 2 G e gULO[^g‰K e KN 2 [jG¤KQGUk¶f—[^G0VULiY N -0/ gUL / k 2 f—N 2 [jG „¨,.-U241 gULO[| 2 k /1 K a TXKQGjN 2 N‡KN 2 | / N /1 N`[^].N -0241 f—P¹K 131 [^] P¹KML e^/`º kUTXKQP 2 N 2W/1„ FHGªKÊL / f / GZN€k / | / PW[^gXY / GjNl N3[^g‰[jPW[ ej2 fKQP 1 N3L 2 G e N -y/ [QL 6- K 1€5ƒ// G›L / ]b[^L3YŒTUP¹KMN / k 2 G›N / LiY 1 [^] 1 N‡KMN 241 N 2 fKQPSY[yk / P 1„ FHGsf - KgUN / L ê lU} / } 2 P4PSgUL3[^g‰[ 1O/ KG / } 1 N‡KN 241 N 2 fKQPSY [yk / P™]b[^L~N -y/ NO[^gƒ[jPW[ e^2 fKMP { ¯HY [yk / P¦¤/ } 2 P4PSKQP 1 [ŒgUL /1O/ GZNK G / }"TUG 2 N‡KL 6 YKMN3L 2½­ ]b[^L3YŒTUP¹KMN 2 [jG®[^] N -y/ h -0/ LiG7¯«” 2 Y[jG 1 N -0/ [^L 6 [jGã Ä „ F¢N–} 2 P4PDN -y/ G 5ƒ/13- [}~GsN - KMNN -0/ fL 671 NiKQP@Y[yk / P 241 GXKMN3T0L‡KMP4P 6 k / L 2 | / k¨]bLO[jYÁN -y/ TUG 2 N‡KL 6 Y€KMNOL 2½­ Y[yk / P „ ¦¤/ } 2 P4P 1O// N - KMNdG0[jGy¯£f[jY g‰K^fN c ¯ 5 L‡KQG /1 K 1i1 [0f 2 KMN / k } 2 N - f / LON‡K 2 G‹xyG0[QN 2 GZ|MKML 2 KQGZN 1 fKQG 5ƒ/2 GXf[^LOgƒ[^LiKMN / k 2 GZN3[ N -0/ fL 671 NiKQP™KQG0k¨N -0/ Y€KMN3L 2½­ Y[7k / P 1„ ,\-U241 N -0/13241@241@5 K 1O/ kŒ[^GŒN -0/ KQT0N - [^L¡ 1 f[jGjN3L 2W5 T0N 2 [jG`NO[–N -0/.1 T 50‘ / fNlM} -U2 f - KgUg / KML / k 2 GŒgXKMg / L 1 - m . l - oç . lUKQGUk - ê .¢„ ‡‰ˆ,‡

Š

 $~ ‰‹ + € € ùA$%  &  $*

., -y/ Y[ 1 N 2 Ygƒ[^LON‡KQGjN€f[jG 1 N3L3TXfN 2 [jG¶[^])NO[^gƒ[jPW[ e^2 fKMP 1 NOL 2 G e N -0/ [^L 6¶2415 K 13/ kÀ[jGùKQGŒ ò p m B mjv G0[jG7¯HP 2 G / KML 132We Y€K`Y[yk / P‰} - [ 13/ NiKML e^/ N 1 gXK^f /–241 KŒf[jY gXP /—­#ç ¯Hk 2 Y / G 132 [jGXKQP h KQP¹K 5X2 ¯ÂŸŠKQT®Y€KMG 2 ]b[jP4k Ž „+,\-0/ G0[jG7¯HP 2 G / KML 132We YK Y[yk / P - K 1 Œ ò p m B mjv 1 T0g / L‡f[jG0]b[QLiY€KQP 136 YY / N3L 6 } 2 N -¾e^/ G / L‡KN3[^L 1 p

B`‘’“B”

v KQGUk pf • B ‘!• ’“B ” • v =

p r^„Wr^„Wr v

+

… / L /  241 N -0/#/ G / L e^6 Y[^Y / GZNiTUY N / G 1 [QLl ‘ ’ KML / N -0/‹1 T0g / L‡f—T0LOL / GZN 1 l+KMGUk ” 241 N -0/ 0 p r v _ ¯ f—T0L3L / GZN 2 G¤N -0/#- [jPW[jY[QL3g -U2 f 1O/ fNO[^L „(,\-0/ f[^LOL /1 gƒ[jGUk 2 G e(e^/ G / L‡KMNO[^L 1`2 GN -0/ KQGjN 2 ¯ - [jPW[^Y[^L3g -U2 f 1O/ f—NO[^L~KML / k / G0[^N / k¾} 2 N - K 5 KML „ ¦/ fKMG¨YKMx / N -0/ G0[jGy¯HP 2 G / KL 132We Y€KŒY[yk / P 2 GZN3[K N3[Qgƒ[jPW[ ej2 fKQPƒV / P4k‹N -0/ [^L 6#576 N£} 241 N 2 G eX¼ —–™˜rš7›?– a{œ

¼ò

í r m 

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r



• ”•

p r^„Wr^„ mjv

., -y/1O/ N } 241 N / k / G / L e^6 ¯HY[jY / GjNiTUY N / G 1 [^L 11 KMN 241 ] 6 N -0/¢¡ ò¸n § 2 LiK 1 [^L3[KMP e^/5 L‡K „D,\-0/ N£}%[f - [ 2 f /1 [^] 132We G P / KMk 1 NO[‹k 241 N 2 GXfNdN3[^g‰[jPW[ ej2 fKQPSV / P4k N -0/ [^L 2W/1„~,.-0/ N -y/ [QL 6 } 2 N - N -0/ J 132We G 241 fKQP4P / k¨N -0/ { ¯HY [yk / P¢ly} -02 P / N -y/ í 132We G¾P / KQk 1 N3[N -0/1 [Q¯£fKQP4P / k ˜ ¯HY[7k / P „ ” 2 GUf / } /¨- K| / N -0£/ ¡ òn § 2 LiK 1 [^L3[ÊKMP e^/5 L‡KUl@} / fKMGk / VUG / NO[^gƒ[jPW[ e^2 fKMP 1 NOL 2 G e N -0/ [^L 6¤576 KQGXKMPW[ e^6 } 2 N -‹5 [ 1 [jG 2 f 1 N3L 2 G e N -0/ [^L 6’¼ 1 g 2 G r ¼ 1 g 2G m ¼

‘ U B`‘¤ ¥

”Q¦Q§©¨Xª«B Q” • ¦Q§©¨Xª

‘ L B`‘ ’ ¥

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ò

¼ ¬ ¡–¼ B ” • Z_®`¯ ›>– ò±J ¼ •¬ ¡–• ¼

p r^„Wr^„èç v p r^„Wr^„ ê v p r^„Wr^„ ojv

,.-y/2 k / GZN 2 V‰fKMN 2 [jG[^]SN -0/–_ ¯£f—T0LOL / GZN } 2 N - N -y/)ej- [ 1 N\f—T0LOL / GZN 2 G€N -0/ ¹P K 1 NŠP 2 G /)241 gƒ[ 13132W5 P /d5ƒ/ fKQT 1O/ N -y/6 KML / KQG0[jY€KMPW[jT 1.2 G¾N -0/1 KMY / }.K 6 } -0/ G¾N -0/ NiKML e^/ N 1 g‰K^f /:241 K h QK P¹K X5 2 ¯ÂŸŠKQT ç ¯¢]b[jP4k „ ,\-0/ N3[^gƒ[^PW[ ej2 fKQP 1 N3L 2 G e KQYgXP 2 N3TUk /1 KML / k / VXG / kJK 1 p v ¼ ò³²r´¶µ&·

Y T W

Ä ¸ T L Ä ²º ì ¹d

‘ L¼»¾½ ²fº ‘ • ’ » ½ • ¹Q¿ ¹

= –™˜rš7›?– a{œ

p r^„Wr^„èâ v

rn … / L / ½ ¹ BhÀ ò r B„=>=?=>B ç† J ç KML / N -y/˜Š/ PWNOL‡KQY 2 k 2W»ƒ/ L / GZN 2 KMP 1 [jG#N -0/–eQ/ GZT 1C®_2W/ Y€KQGUG 1 T0L3]¿K^f / l0KMGUk Á T 241 N -0/ Y[ykUT0P 2S1 g‰K^f / [^] eQ/ GZT 1G‹_~2W/ Y€KQG0G 1 T0LO]¿K^f /1„ p ¦/ L /1 N3L 2 f—N\[jT0L 1O/ PW| /1 NO[ ¶Â m „ v ,\-0/5 K 132 fŒgULO[^g / L3N 2W/1 [^] N3[^g‰[jPW[ ej2 fKQP 1 NOL 2 G e KQY gXP 2 NiTUk /1 KML / N -0/2 L 2 GUk / g / G0k / GXf / [jG - KMPW]Š[^] N -y/ Y[yk0TUP 2 [^] N -y/ h KMP¹K 5X2 ¯ÂŸŠKQT ç ¯¢]b[jP4k „`,.-0/ { ¯HY[yk / P+KMYgXP 2 NiT0k /1 k / g / GUks[jGUP 6 [^GN -0/ ‰K à - P / L Y[yk0TUP 2 ly} -02 P / N -0/`˜ ¯HY[7k / PAKQY gXP 2 NiTUk /1 k / g / GUk¾[jGUP 6 [jG¾N -0/ f—[^YgXP /—­‹1 N3L3TXfNiT0L / Y[ykUTUP 2¢„ ”Z[€]¿KL~} /`- K| /5ƒ// GJk 241 fT 1i132 G e f—PW[ 1O/ k¾N3[^g‰[jPW[ ej2 fKQP 1 NOL 2 G e N -0/ [^L 6j„ zdg / G¨N3[^g‰[jPW[ ej2 fKQP 1 NOL 2 G e N -y/ [QL 6#241 k / VXG / k 5Z6‹2 GZN3LO[ykUTXf 2 G e€c ¯ 5 L‡KMG /1„+c ¯ 5 L‡KQG /12 G‹[jT0L~f—[^GZN /—­ N~KML /1 T 5 YKQG 2 ]b[jP4k 1 [^]>N -0/ h KMP¹K 5X2 ¯ÂŸŠKQT[jG€} -U2 f - [^g / G 1 NOL 2 G e^1 fKQG / GUk „$,.-0/ f[jGUk 2 N 2 [jGN - KNŠN -0/˜\_ ” ,ª1O6 YY / N3L 2W/1 K 5 [| / 5ƒ/ gUL /1O/ L3| / k`L /a T 2 L /1 N - KMNDN -y/\1 T 5 Y€KMG 2 ]b[jP4k 1 KML / žAK e L‡KQG e^2 KQG 2 G`N -0/ { ¯HY[yk / P¢lMKQGUk - [jPW[jY[QL3g -U2 f 2 GÊN -y/#˜ ¯HY [yk / P¢lAL /1 g / fN 2 | / P 6Z„ zdg / G 1 NOL 2 G e KQYgUP 2 NiTUk /1 KL / k / VXG / k 2 GÊ}\K 6132 Y 2 P¹KL–N3[ fPW[ 13/ k 1 N3L 2 G ej1¼ Y

} -y/ L / ‡‰ˆÇ

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Thg R p W v ¼ ò

Ä

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ì

p r^„Wr^„ t v

241 N -y/ Y [ykUTUP 2S1 g‰K^f / [^] e^/ G7T 1G‹_2W/ Y€KQGUG 1 T0L3]¿KQf /1 } 2 N - H - [jP /1„ (}ɾ %Ê ŒÌË Í }‹Q sÎ  S*

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r^r

º c ¯ 5 LiKQG /1 [jG ã Ä

ãæ

(b)

(c)

ãæ

ãÄ

ãæ

ãÄ

(a)

ãæ

ãÄ R 2We T0L /¨r^„èçU¼),.-y/1i2 G e TUP¹KML:f[jG 2 ]b[jP4k eQ/ [^Y / N3L 6 p K v fKQG 5ƒ/ k / ]b[^LiY / k(NO[ IÏ ã Ä p 5 v „:¦/ }LiKMg º c ¯ 5 L‡KQG /1 [jGã ÄÑÐ  Ï ã Ä l™[ 5 N‡K 2 G 2 G e KÒ0 p º ì v h 0- / L3Gy¯«” 2 Y[jG 1 N -0/ [^L 6 [jGã Ä „,.-y/ f[jG 2 ]b[jP4kfKQG KQP 1 [ 5ƒ/ L /1 [jPW| / kNO[¼Ó p J r vÔ Ó p J r Öv Õ ØÃ × p f v „$,\-U241%241 N -0/de^/ [jY / N3L 6 [jG€} -U2 f - f—PW[ 1O/ k 1 NOL 2 G e N -y/ [QL 6#241 k / VXG / k „ 1 [jPW| / k€f—[^G 2 ]b[jP4k 241 kUTUKQPXN3[ f—PW[ 1O/ kN3[^gƒ[^PW[ ej2 fKQP 1 NOL 2 G e N -y/ [QL 6 [^G€N -y/ k / ]b[^L3Y / k®f[jG 2 ]b[jP4k - o .¢„ qJ[^L / gUL / f 241O/ P 6 l‰[jG / f[jG 132 k / L 1º f[ 2 GXf 2 k / GZN c ¯ 5 L‡KQG /1 }L‡KgUg 2 G e ã Ä [^]+N -y/ k / ]b[^LiY / k(f—[^G 2 ]b[jP4k „d,.-0/ [^g / G 1 N3L 2 G e N -0/ [^L 6 P 2 | 2 G e [jGN -y/1O/¾c ¯ 5 L‡KQG /1 }\K 1Œ13- [}GN3[(L / kUTXf / N3[:0 p º v h -0/ L3Gy¯«” 2 Y[jG 1 e KQT e^/ N -y/ [QL 6 [jG¨ã Ä - oâ .¢„+,.-y/ k 2 fN 2 [jGXKML 6€241\1 TXf - N - KN\N -0/ ¡ N…~[7[Q]bN\gXKML‡KQY / N / L Oº241%2 k / GZN 2 V / k } 2 N - N -0/ f[jYgXP /—­02 V / k¾‰ K à - P / LY[ykUT0P4T 1 W ¼ Oº ò



p r^„ m „Wr v

W=

,\-0/ g‰KML3N 2 N 2 [jG#]ˆTUGXfN 2 [^G¾[Q]DN -0/ 0 p º v h -0/ LiGy¯«” 2 Y[jG 1 N -0/ [^L 6 KMNP / | / P À 42 1\ej2 | / G 576 ÙÖÚ ¨



BÀ—B 0

p º vOv†ò p À:í ºr ]v ÛÜ æ

m 31 2 àG À:ß[á í »,º â ÝÞ e ¸

=

p r^„ m „ mjv

rm … / L / m ßäã ä p Àí º v ò \241 N -y/`1 N3L 2 G e f[jT0gUP 2 G e f[jG 1 N‡KMGZNlXKQG0k¨N -0/ g0L3[ykUTUf—N 241 [| / LN -0/ gƒ[ 1i2 N 2 | / L3[Z[^N 1 [^])ãC0 p º v Ð 0 p º v l$} -U2 f - KML /‹ej2 | / G 576 á 4 6 ò D 4 J D 6%å Ã Û pçæ h KML3NiKQG 1 T 5 KMP e^/5 L‡K v ì ]b[^L ã$è5é „ â ò p r ä mjvê ÝQÞ e á òëê 4Û d ì p Û æU J ã v D 4 241 N -0/Œ¦/6 P@| / fN3[^L „ œ)[^gXKMxyTUY€KLKQG0ks§ KM]¿K 13- [} / k‹N - KMNN -U241 fKQG 5ƒ/ L / }L 2 N3N / G¨K 1 Ù

ò

p v

2 {ì D L“íjïhî ðoñ ïò3ó õ ïXïVö7÷ô =

p r^„ m „èç v

… / L / 2 3p ì +v òùø 6b d ì p r J ì 6 v 6 241 xyGy[}~GJK 1 N -0/ q(fq(K - [^G‹]ˆTUGXfN 2 [jG™lUKQG0k - ú . ò ì¾û Ü æ J ì L û Ü æ,B ì ò D L T]ü „šaƒ„ p rQ„ m „èç v 241 gUL / f 241O/ P 6 N -0/ g‰KMLON 2 N 2 [^G‹]ˆTUGXfN 2 [jG¾[^]>N -0/ L /1 [jPW| / k¾f[jG 2 ]b[jP4k „ ,\-0/ L / KML /:e^/ G / L‡KMP 2 •uKN 2 [jG 1 [^]>N -0/ N3[^gƒ[^PW[ ej2 fKQP 1 N3L 2 G e P¹KML e^/º kUTXKMP 2 N 6 NO[ { ¯HY[yk / P 1 [jG¾[QN -0/ L e^/ [jY / NOL 2W/1 KMGUkJKQP 1 [NO[ ˜ ¯HY[7k / P 1„

rç

Å

µ ³ÊÉ ´ Æ ´ÿþ  ²

ý

É É³ 

É ´ÿ'µ ³: ÆÈÇ

FHGN -0/ P¹KML e^/º kUTXKMP 2 N 2W/1–2 GsNO[^gƒ[jPW[ e^2 fKMP 1 NOL 2 G e N -0/ [^L 6 l’N -0/1 NOL 2 G e f[jT0gXP 2 G e f[jG 1 NiKQGZN )241 N -0/ 1 KQY / ]b[^L 5 [^N - [^g / G#KQG0k‹f—PW[ 1O/ k 1 N3L 2 G e132 k /1 l7KQGUkN -0/ ¡ N\…[7[^]bN%f[jTygXP 2 G ej1 [^]SN -0/ [^g / G 1 N3L 2 G e KML / 2 k / GZN 2 V / k} 2 N -e^/ [jY / N3L 2 f\Y [ykUTUP 2 [^][^]UN -0/ N‡KL e^/ N 1 g‰K^f / l 2 N 241 T 1O/ ]ˆT0P7NO[–k /1 f—L 2W5ƒ/ N -0/ }%[^L3P4k 13-0// N 576 N -0/ P 2 G / KML 132We Y€K€Y[7k / P „,\-0/ }Š[^LiP4k 13-0// NdN -y/ [QL 6 f—[^G 13241 N 1 [^]+]b[^T0L–f -02 L‡KQP 1 T0g / LOV / P4k ?1 > ì B > æ B > Ä B > ð

rut

} 2 N - f - KML e^/1\ej2 | / G 576 

ò pr Br BJ r BJ rvB

p m „Wr^„Wr v

KQGUk¤K e KQT eQ/ YŒTUPWN 2 gXP / Nf—[^T0gXP / kÊN3[ „ R0[jP4PW[} 2 G e - Úo. lA} / L / KML3LiKQG e^/ N -0/€e KQT eQ/ YŒTUPWN 2 gXP / N 2 GZN3[ KN } 241 N / k(f -U2 L‡KMP>YŒTUPWN 2 gXP / N@ „.¦¸-0/ G W 241 G0[jGy¯¢• / L3[Xl‰N -0/ L /Œ241 Kgƒ[^N / GZN 2 KQP™]b[^LdN -0/Œ1 fKMP¹KML~V / P4kBA$l } -02 f -241 N -0/ PW[} /1 Nf[jY gƒ[jG / GZN+[^]@ÀKQGUkN -0/ P 2 G / KML 1i2We Y€KY[yk / PfU[} 1 NO[:N -0/ G0[jG7¯HP 2 G / KML 132We YK Y[yk / P™} 2 N - N -0/ L /1 [^PW| / k f—[^G 2 ]b[jP4kJK 1 N -0/ N‡KML e^/ N 1 g‰K^f /j„ FHG N -U241 k /1 fL 2 gUN 2 [jG™lUN -0/132 G e TUP¹KML 2 N 6 KMN W ò¸n 241 f - KML‡K^fN / L 2 • / k 5Z6 N -0/ ]¿K^fN.N - KMN.N -0/ gƒ[QN / GZN 2 KMPS]b[^C L Ask 241 KMgUg / KML 1~2 G‹N -0/ P 2 Y 2 NKQGUk 2 N~fKQG 5ƒ/ f[jY /#2 GUk / VXG 2 N / P 6 P¹KML e^/ } 2 N - [jTyN f[ 1 N 2 G e N -0/ }Š[^LiP4k 1i-y// NŒK^fN 2 [jG  K G / } G0[jG7¯£f—[^Yg‰K^fN KMGUk G0[jG7¯ e^/ [jY / N3L 2 f–g - K 1O// Y / L e^/1 [jGJN -0/ }Š[^LiP4k 13-0// N - oÚ .¢„d,\-0/Œ2 k / K[^]+N -0/ k / L 2 |MKMN 2 [jG¨[Q]+N -0/ P¹KML e^/ º kUTXKMP 2 N 6 l‰KQky|^[0fKMN / k 2 G - o . KQGUk a TXKQGZN 2 V / k 2 G - ­t . l 241 NO[®L /e KMLikJk0[^Y€K 2 G 1~2 G¨N -U241 G / }g - K 1O/ K 1 - [jP /1 [jG¾N -y/ }Š[^LiP4k 1i-y// NlUKMGUk¨g - K 1O/:5 [jTUGUkUKML 2W/1 K 1 L / gUL /1O/ GZN 2 G ec ¯ 5 L‡KQG /1„ ,\-0/ k / L 2 |MKMN 2 [^G¨[^] - t¾. fKQG 5ƒ/ 1 NOL / KQYP 2 G / k 576 T 132 G e N -0/ Y 2 LOL3[^L~[^]$N -0/ P 2 G / KML 132We Y€K€Y [yk / P¢l } -02 f -241 ]b[jT0GUk 576 g / L3]b[QLiY 2 G e N -0/  ¯HkUTXKQPXNOL‡KQG 1 ]b[^L3Y€KMN 2 [jG [jGg - K 1O/ LO[^N‡KN 2 [jG 1 [^] > 6 ljx // g 2 G e @ K 1 K 1 g / fN‡KN3[^L - rQr/.¢„,\-0/  ¯HkUTXKQPS[Q] > 6 KL / N } 241 N / k¨f -U2 LiKQP 1 Tyg / L3V / P4k 1D 6 } 2 N - g / L 2 [yk 2 f 2 N 6ED 6 9 D 6 í m „ h [jY 5X2 G / k} 2 N - @l^N -y/ Y 2 LOL3[^L 241 K`žAKQGUkUKQTy¯«œ 2 G0• 5 TyL e Y[yk / PX} 2 N - N -0/d1 T0g / L3g‰[^N / GZN 2 KQP ßäã F e^2 | / G 5Z6 F

ò @ pD ì í D æ

J D

Ä

ð

v

J D EJ W J c

ð

6d ì

D LHGJI =

p m „Wr^„ mjv

[QN / N - KMNl i1 2 GUf / N -0/ [^L 2We^2 GXKQP@Y [yk / P 241 { ¢¯ N } 241 N / k™l’N -0/ Y 2 L3LO[^L:žAKQGUkUKQTy¯«œ 2 G0• 5 TyL e Y[yk / P 241:˜ ¯ N } 241 N / k „ F¢N 42 1/ K 136 N3[Jf -0/ fix N - KMNl’} -0/ G W 42 1 G0[QN /a TXKQPDN3[¾• / LO[‰lN -0/132We Y€KŒY[yk / P’]b[^L.N -0/ f[jG 2 ]b[^P4k „ { N W ò¸n lyN -0/1 T0g / LOgƒ[^N / GZN 2 KQP’L / YK 2 G 1 XKMN]b[^L ì ò K æ ò°J WP [ e A í B K Ä ò K ðò°J WP [ e A K

ßäã

B

p m „Wr^„èç v

} 2 N - A 5ƒ/2 G e KML 5U2 N3L‡KL 6j„ … / L / K 4 241 N -0/ PW[} /1 N~f[jYg‰[jG / GZN 1 fKQP¹KML.V / P4k 2 G D 4 „ RU[jP4PW[} 2 G e - t­. lU} / ì fKQP4P’N -U241 ‰KN~k 2 L / fN 2 [jG‹N -0/  g - K 1O/Z„ FHG - t¾. l 2 N–}.K 1 KML e T / kN - KMN:N -0/. g - K 1O/€241 k /1 fL 2W5ƒ/ k 576 K¨žAKQGUkXKQT7¯«œ 2 G0• 5 T0L e Y[7k / P$]b[^LK 132 G e P / |MKML 2 K 5 P / Ž } 2 N - KQG /»ƒ/ fN 2 | /:1 T0g / LOgƒ[^N / GjN 2 KQP W

= F OMLL ò±J Ž

p m „Wr^„ ê v

F¢N 241Œ1 N3L‡K 2Wej- N3]b[QL3}.KLikN3[k / L 2 | / N -U241 ]bL3[jY N -y/¨˜ ¯HY [yk / P „ ¦¸-0/ GNA 241 P¹KML e^/ l@N -0/ g‰[^N / GZN 2 KQP ]b[^L D 4 5‰/ f[jY /1)1 N // gÊKQGUk } / fKMG 2 GZN /e L‡KMN / N -0/ Y [jTyN–T 1i2 G e N -0/ œ–KQT 1i132 KQGsKMgUg0L3[ ­02 YKMN 2 [jG „ ” 2 GXf / N -y/ Y 2 L3LO[^Ldž>KMGUkXKQTy¯«œ 2 G0• 5 T0L e Y [yk / P 241)˜ ¯¢N£} 241 N / k™l 2 N 241~1 TPO®f 2W/ GZNN3[#f[jG 132 k / L)KMG 2 GZN /e L‡KQPS[| / L f[jG 1 N‡KMGZNY€KMg 1 l r æ /—­ g p W @ v = ì p m „Wr^„ ojv ²RQ D Q D æ Q D Ä Q D ð /—­ g p J F v 9 @ ., -y/ g0L / ¯¢]¿K^fN3[^L r ä @ æ ^e 2 | /1 KGy[jGy¯£fKQG0[jG 2 fKMPƒY / K 1 T0L / ]b[^LS@ „>¦/ fKQG#K 5X1 [^L 5#2 N 576 f - KMG ej2 G e N -0/ ì |MKML 2 K 5 P / @ Õ Ž ò @ L €„ ,\-U241–ej2 | /1 N -0//»¦¤/~- K| / G0[^N 6Q/ N 13- [}~G [jG} -02 f -c ¯ 5 L‡KMG /1 [Qg / G 1 N3L 2 G ej1 KML // G0k 2 G e‰„ { ff[^L3k 2 G e N3[ N -y/ f[jG ‘ / fNiTyL /d2 G - o . lZN -0/c ¯ 5 LiKQG /1Š13- [^TUP4k 5ƒ/ }.L‡KMg0g 2 G e N -0/d5 K 13/ ã Ä [^] 4 V / P4k 1@2 GN -0/\132We Y€KdY[7k / P 5ƒ/ f[jY / Y€K 13132 | /j„D,\- T 1 l > 4 Õ n K 1 } / KMgUg0L3[ZK^f - N -y / •O- [jP —/ – [jG N -y/ f—PW[ 1O/ k 1 NOL 2 G e }%[^L3P4k 13-0// NljKMGUk 2 N 241 L3[^T ej- P 6 } -y/ L / N -0/5 K 1O/ ã Ä 241 PW[0fKMN / k „@_./ gUL3[yk0TXf 2 G e N -0/ gUL / f 241O/:5 [jTUGUkXKL 6 f[jGUk 2 N 2 [jG‹]b[^L c ¯ 5 LiKQG /1 }LiKMgUg 2 G e ã Ä  ]b[^L /—­ KMYgXP / lUk / L 2 | 2 G e N -y / ~/ TUY€KMGUG 5 [jT0GUkXKML 6 f—[^GUk 2 N 2 [^GJKMPW[jG e ã )Ä ˜ 241 k 2 O€fT0PWN 2 G¨N -U241 KMgUgULO[ZK^f -¨132 GXf / N -0/ P 2 G / KL 1i2We Y€K Y[yk / P™k0[ /1 G0[^Nk /1 f—L 2W5ƒ/ N -0/:e^/ [jY / N3L 6 [^]>N -y/ k / ]b[QLiY / k¨f[jG 2 ]b[jP4k#} 2 N - VXG 2 N / ã Ä „ { WP N - [jT ej- L / gUL3[yk0TXf 2 G e Kg0L / f 2413/5 [^TUGUkXKML 6 f[jGUk 2 N 2 [jG:]b[QL / K^f -`c ¯ 5 L‡KQG / Y€K 65ƒ/ k 2 O®f—TUPWNl[jG / Y€K 6 K 1 x 2 ]>} / fKQG¨k 241 N 2 G e T 2413- k 2W»=>=?B ê } 2 N - N£}%[ 1O/ N 1 [^]@f - KML e^/1 l  

ì ò p Jm B r B r B n B nZv B æ ò p Jm B n B n B r B r v B

p m „Wr^„èÚ v

KQGUkN }Š[ e KMT e^/ YTUPWN 2 gXP / N 1 f—[^T0gXP / k N3[N -0/13/ f - KML e^/1„ ” 2 GXf /1 ì J  æ ò p n B r B r B J r B J r v l 1 [jPW| 2 G e N -y/~c N / LiY f[jG 1 NOL‡K 2 GjN+KQGUk k 2 | 2 k 2 G e5Z6 N -0/ 0 p r v e KQT e^/.1O6 YY / N3L 6 f—[^T0gXP / kŒN3[N -U241 f—[^Y 5X2 GXKMN 2 [jG

^m m [^]Šf - KML e^/1 L / kUTXf /1©¨ ì B„=>=?=>B ¨ ð N3[#N -0/ L /1 [^PW| / ksf[jG 2 ]b[jP4k „ HF GsN -0/ f[jG / ª ì è n B ª ì J ª æ è n l 132 GXf / ¨ e ò¸ « n lj} / fKMG#T 13/ N -0/ L / Y€K 2 G 2 G e  ì e KQT eQ/)136 YY / N3L 6 3N [V ­ N -0/ g - K 1O/ [^] ¨ e „+,\-U241 P / K| /1 [jTyN K L /132 kUTUKQP åæ e KQT e^/:136 YY / N3L 6 K^fN 2 G e K 1 p ¨ e B ¨ ì B ¨ æ B ¨ Ä B ¨ ðvÕ p ¨ e B J ¨ ì B J ¨ æ B ¨ Ä B ¨ ðv =

p m „Wr^„A+ v

,.- T 1 } / VUGUk¨N -0/ åæ a T0[^N 2W/ GjN.[^]>N -y/ L /1 [^PW| / k¨f[jG 2 ]b[jP4k¾K 1 N -0/ N‡KML e^/ N 1 g‰K^f /j„ { )1 2 GJN -0/ gUL / | 2 [jT 1d1 T 5X1O/ fN 2 [jGSl‰} / L / KMLOL‡KQG e^/ N -0/`e KQT eQ/ YŒTUPWN 2 gUP / N 1d2 GjN3[®N£} 241 N / k f -02 L‡KQP 1 Ty¯ g / L3V / P4k 1 l¬@ ì KQGUk­@ æ l^KQGUkg / L3]b[^L3Y N -y/  ¯HkUTUKQPyNOL‡KQG 1 ]b[^L3Y€KMN 2 [jGKQPW[jG e g - K 1O/ L3[^NiKMN 2 [^G 1 [^]XN -0/ VU| / f -U2 L‡KMP 1 T0g / LOV / P4k 1 NO[ŒKML3L 2 | / KN N -0/)˜ ¯¢N } 241 N / k®žAKQGUkUKQTy¯«œ 2 G0• 5 TyL e Y[yk / PX} 2 N - N -0/d1 T0g / L3g‰[^N / GZN 2 KQP F

ò @ ì p Jm D e í D ì í D æ

J W

ì v í @ æ p Jm D e í D í D &ð J W æ v Ä

p m „4r^„Wr nZv

J c ® D LHG¯ B 4 dfe

} -y/ L / N -0/ N }Š[€‰K à - P / LY[7kUTUP 2 l W ì KQGUk W æ lUKML / P 2 G / KML3P 6 f—[^T0gXP / k‹N3[N -0/:e KQT e^/ YŒTUPWN 2 gXP / N 1„

VXGUk

ž / NT 1/—­ KQY 2 G / } -0/ G¤N -U241`1 T0g / L3gƒ[QN / GZN 2 KMP - K 1 X KMNŒk 2 L / f—N 2 [jG 1„ ”Z[jPW| 2 G e PW[ e p m A ì í m A æ v B ò J PW[ e p J A ì v B K æ ± ò J PW[ e p J A æ v = K ð±



F

ä  K 4 ò©n lD} /

ò J Ke ± K

ìò

K

Äò

p m „4r^„Wr^r v

mç ˜Š6‹1 T 5U1 N 2 NiT0N 2 G e N -U2412 GZNO[N -0/ L / Y€K 2 G 2 G e/a TXKMN 2 [jG 1 l 

F

A  

ò°Jm K e í

K

í

ì W KU J 

ò¸n p ò r B mjv B

p m „4r^„Wr mjv

} / VXGUk DŽ ñ D Ž÷

æ A æ í ò ê.°Ar A Xì ± æ A ì í ò ê °r Aæ± =

B

p m „4r^„Wrç v

” 2 GXf /:5 [^N - W ì MK GUk W æ k / g / G0k¨[jGUP 6 [jG‹N -0/ LiKMN 2 [ A ì ä A æ l0N -0241~241 gƒ[ 13132W5 P / [jGUP 6#2 ]DN -y/6#1 KN 241 ] 6 N -0/ L / P¹KMN 2 [jG ² p m „4r^„Wr—ê v ò râ p D L Ž ñ J D L Ž ÷ v æ J Ú p D L Ž ñ í D L Ž ÷ v í r ò¸n B } 0- 2 f -‹241 [ 5 N‡K 2 G / k 576®/ P 2 Y 2 GXKMN 2 G e ² A ì ä A æ ]bL3[^Y N -0/ N£}%[ /a TUKMN 2 [jG 1.2 G p m „Wr^„Wrç v „$,.-y/:1 T 5X1 g‰K^f / [^] N -y/ ‰K à - ² P / L\Y[yk0TUP 2B ) J r v „d¦/ }Š[jTUP4k(P 2 x / NO[ 1O//Œ- [} N -0/6 KML /Œ2 k / GZN 2 V / k } 2 N -) k 2W»ƒ/ L / GZN  g - K 13/12 G¾N -0/ fPW[ 13/ k 1 NOL 2 G e kUTUKQP „ ,\-0/ }%[^L3P4k 13-0// N[Q]\N -0/ fPW[ 13/ k 1 N3L 2 G e [jGÊN -0/ å™é a T0[^N 2W/ GZN:[^]%N -0/ L /1 [jPW| / kÊf—[^G 2 ]b[jP4kfKMG 5ƒ/ k /1 fL 2W5ƒ/ k 576 N -0/ P 2 G / KML 132We YK#Y[yk / P@} 2 N - p ) í ç v f -U2 LiKQP@V / P4k 1 > e B > ì B„=>=?=>B > é UXæ f—[^T0gXP / ksN3[ )

m+

e KQT e^/ V / P4k 1 } 2 N - N -0/ ]b[jP4PW[u} 2 G e f - KML eQ/ | / f—NO[^L 1 - oç .¢¼ > ìB > æB

> eB

 e  6  éL

ò p ò p

ì ò p

J

> ÄB

> ð B > B =„=,=„B > ð U 6 B ,» »,» B > é UXæ ®

rB rB J rB J rB nB B n B nB nB nB é rB rB nB nB nB

nB pé í r v B

J ) B ) J

=„=,=„B =„=,=„B =„=,=„B

nB rB nB

=„=„=,B =„=„=,B =„=„=,B

njv B njv B njv B

p m „4r^„ m^mjv

} y- / L / é ò r B »,»„» B ) Jùm „ ž / N)T 1)13- [} N - KMNdN - KNdN -U241d2 GUk // k(k /1 fL 2W5‰/1 N -0/ å™é a Ty[^N 2W/ GZN~[^]$N -0/ L /1 [jPW| / k¾f—[^G 2 ]b[jP4k 2 G‹N -0/ f—[^G / l ªe

nB

ì nB è í r ì ªéL ª6 í é n pr è )

ªéL J

è

Ú é

Ú ) Jmjv =

p m „4r^„ m ç v

¦/ } L 2 N / 0 p r v  ]b[^L®N -0/ 0 p r v e^/ G / L‡KN / k 576}  lKQGUkùN -0/ f[^L3L /1 g‰[jGUk 2 G e¶c N / LiY 241í  ¼ ò ê 4   4^î ¨ 4^î æ J ª  pg ò r B,=>=>=?B ) J r v „ F¢] ª e n láï í e ò¸nÊð ä 0 p r v e k /1 fL 2W5ƒ/1 N -y/ L /1 [^PW| / k®f—[^G 2 ]b[jP4k „ è ì ì F¢] ª é L è n l í é L ò©n k0[ /1 G0[QN KQP4PW[} ¨ e N3[ |QKMG 2413-™„(,.- T 1 l@} / fKQGT 1O/ N -0/ 0 p r v é L ì e KQT eQ/ 1O6 YY / NOL 6 NO[€V ­ N -0/ g - K 1O/ [^] ¨ e „ ” 2 GUf /¨ e fKML3L 2W/1 p J ) v TUG 2 N 1 [^]  é L ì l0N -0/ L /241 K å™é L /132 kUTUKQP e KQT e^/1O6 YY / NOL 6 [^E] 0 p r v é L ì ej2 | / G 576 p ¨ e B ¨ ì B ¨ æ B ¨ ·Ä ñ 4 ñ é L ì vÕ p ¨ e B D L

ì

æ Ä é ìv=

÷óò ¯ ¨ B D ÷ óò ¯ ¨ B ¨ ^ñ 4 ñ L

p m „4r^„ m ê v

çn 6U ì ì í 6 6 p zdN -0/ L e KQT e^/Œe LO[jT0g 1 0 r v ñ ñ é L æ KL / f[jYgUP / N / P 6 V ­y/ k 2 ] J ª é ª é L ì è n 132 GXf / n®ò í 6 J 6U ì 6 éU ì 6U ì 6U ì ì ì æ % æ í æ í 6 6 L é í é L ò “ é ” î ¨ î J é î ¨ æ î î ¨ ð U î J ª é ª é L ì L /a T 2 L /1 ¨ ð U 6 NO[ 5ƒ/ G0[jG7¯¢• / LO[ „ ,.- T 1 lD} / [ 5 N‡K 2 GÊN -0/ å™é a T0[QN 2W/ GZN[^].N -0/ L /1 [^PW| / k¤f—[^G 2 ]b[jP4k¤K 1 K 1 g‰KQf / [^] 1 [jP4T0N 2 [jG 1 NO[(N -0/‹c N / L3Y©f[jG 1 NOL‡K 2 GjN 1 T0g¨N3[ e KQT e^/ NOL‡KQG 1 ]b[^L3Y€KMN 2 [jG 1„ ,\-0/ Y 2 L3LO[^L~žAKQG0kXKQTy¯«œ 2 Gy• 5 T0L e Y[yk / P - K 1 N -0/1 Tyg / L3gƒ[^N / GZN 2 KQP F

ò

@ e D
k 2 L / f—N 2 [jG 1 [^]yN -0/ g‰[^N / GZN 2 KQP „ ”Z[jPW| 2 G e p ã ò¸n B„=„=„=,B ) í mjv e^2 | /1 éi L ì í B K e ò J PW[ e c 6 ì p é r v A 6 k d ì é L ì i B K ò J PW[ e J A e J c 6 ì é A 6 k d ì B K æ ò J PW[ e p J A e J A é v K

J W6 @

ò

J J

PW[ e A e B PW[ e A e B PW[ e p J A 4 v B p ã ò r B„=,=„=,B ) ÀJ mjv =

ò n B,=„=„=,B ) J r v e^2 | /1Ì) L / P¹KMN 2 [jG 1 [^]DN -0/ ]b[^LiY ä  A  ò¸n p  "

p m „4r^„ m â v

çUr DŽÐô DŽäõ DŽ ó ñ ó

A eæ ì í L vpA e í rvA 6v ê 6 A 6

B ò pA e í A é 6 ê ì6 A v é ¹U B p J ê 6 p ò A p A e íé v¹ ¹ é í p A 4vé r Jê 6 p v ò pA e í A é ì v pAée í ê 6 A 6 vé L ì B L é

p m „4r^„ m t v

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