Capacity of Multi-antenna Gaussian Channels DI

"!#!$% '&()*+!
-/, .0214365(785:9<;=>;3/?
8@ ACBED:FHGJIKD
L"MNPO/QRMESUTVNXWZY[TUM\TV]^M\_`SVMbaRcde_gfXTVNXhgfXMTUijYRO`SVdNPTUTVNPO^W2YRO`kKl%aRimiVMEn+MENXQoNPO^W2YRO/TUMEOÒ`YRS
cpaRi\SVNqO^WZfXM2_`SUMri\n+aZddb_Ò`NPnrY[TVNXaZOgSea%QRMriTV]^MYRk`k`NPTVNXQRM2stYR_gSVSVNPYRO(nj]gYROÒ^MEfuvNXTV](YRO`k
uvNXTV]âZ_`TwcxYRk`NPO`W^yeL"Mk`MrijNXQRM8cpaRide_`fqYRStcpaRizTV]`MnrY[hgYRnrNXTVNXMESzYROgk"MriViVaRimM+{ohCaZO^MEO6TVSzaRc
SV_`n]|n]`YROÒ^MEfPSE}vYRO`k~k^MESVn+ijNXCMn+aZd\hg_^TVY[TVNXaZOgYRfvhìja>n+MEk`_ìVMESTUa(MrQ[YRfP_`Y[TUMSV_`n]|caRiU
de_gfPYRSryL"MSj]âuTV]`Y[TzTV]^MhCaRTUMEO/TVNPYRfWZYRNPOgSmaRcSV_`nj]*de_`fPTVNYRO6TUMEOgO`YSUoSUTUMEdSza%QRMri
SVNPO^WZfPM+YRO6TUMEOÒgYeSUoSUTUMEdSNqS#iY[TV]^MrifPY[iVWRMt_Ò`k^MriNPOgk^MrhCMEO`k^MEO`n+MvYRSjSV_`d\h`TVNPaZO`ScaRiTV]^M
cYRk`MESYRO`kOâZNqSUMESY[Tvk`NX:MriVMEO/TiVMEn+MENXQoNPO^W\YRO/TUMEOÒ`YRSry
[bzb\wzb
|zp o¡:¢£: ¤¥)¢p¡C¦op¨§:¢ ¤2©¥/§C¢¢x¥>¡|rªH¥>¡C¡C%«zq¬+ª~§Cp¬®Cp2¬+¤+¥/¡C¢¨p¬¬+¡:¦¯¥>¡C£J°/>¤
¤% %p±g¡C¦¥>¡^¬ ¡C¡H¥/¢ ²$|zzpC£: ¡C>¬m¬+ªC¡`§C2³ ¤>´¬+¤+¥/¡C¢¨p¬¬+¡:¦\¥>¡^¬+%¡C¡H¥>¢v³^µ¶¥>¡C£¬+ª:
¡`§C2³ ¤\>´«¤% %p±g¡C¦¯¥/¡`¬ ¡C¡C¥>¢³^µ·K²|2zpE¸:%§C¢p±> pµ£C[¥/$zp¬+ª¥"p¡C ¥>¤b¨K£: $p¡
zªCprª*¬ªC¤ % q±o £*±o%%¬+>¤e¹»º½¼$¾£C%®%¡C£C¢b>¡¯¬ªC\¬+¤¥>¡C¢¨p¬¬+%£¯±> ¬+o¤¿Àº½¼$Á«±K¥
¹|ÂÃ(¿)Ä4Å
ÆjÇRÈ
zªC%¤ÃÉ¢m¥·2Ê¯¶w%o¨®CE¸"¥/¬+¤q¸¥>¡C£¯ÅËp¢mÌ %¤/ÍÎ ¥>¡" o¨®Cp¸*©¥>§C¢¢¥>¡"¡Cop¢8zp¬ª
¡:£C ® ¡C£: ¡^¬[ÏJ Ð`§H¥/Ñ±/¥>¤x¥>¡: ¤ ¥>Ñ¥>¡C£*¥>¦op¡H¥>¤µ¨®H¥/¤¬+¢%²v|¥>¢¢§C\ÒtÓÔÅzÅÕ<Ö×ÂØ ¾ ÏC¬+ªH¥6¬
¢%ÏÙ¬+ªC¡C>¢%¢ o¤¤§C®:¬¡C¦¬ªC£CpÚ ¤ ¡^¬¤% q±o%¤¢¥>¤p¡C£C ® ¡:£C ¡^¬[²ÛmªC¬¤+¥>¡C¢q¬¬ ¤8p¢
>¡C¢¬¤+¥>p¡C £*¡¯p¬¢t¬+>¬+¥>Ù®Rw%¤z¬¨Ü¨Ï
ÒwÓÝ¿ Õ ¿ÖÑÞßÜmà
áÐ`§Cp±/¥>p ¡^¬+qµoÏC¢¡C%¿ÕU¿~Ââ¬+¤[Æã¿¿ÕjÈÏH¥>¡:£)E¸:® ¬r¥/¬o¡)¥>¡C£"¬¤+¥>%%o¨2§:¬+/Ï
¬+¤[ÆäÒwÓÔ¿v¿ Õ ÖxÈtÞßÜzà
Æ<å>È
æjçè8égê%ëìÎí+îrï6ð^ñ`ò6ójôjõ ö÷gôóÎøZõZùúûùü%ýþôÿjð ×ôjúûúHñ /ù Eöãù <ýûôÿ
ð \ùòZõ ö Eýûõ %ôjõ[òZô%ð \ò Ñýûúûúpð 6ð
î [î+ï/ð"!#%$"&!%&'(%$*),+#-%!/.0+12
Ç
ÛmªCp¢¢ >¡C£À´äo¤ >´b¬ªC*®R« ¤%o¡C¢j¬+¤+¥/¡^¬zw®C¤R±o)>¤¯§C¢´ä§C¡»¬+ªC*§C® o¨¡:¦
£Cp¢ §:¢¢po¡Ù²
~\zpÙ%o¡C¢p£C ¤m¢%±> ¤+¥/#¢ ¡C¥>¤po¢m´äo¤t¬+ªC¥/¬+¤q¸Ã
Ço²ÃÉ¢m£:%¬+%¤¨¡Cp¢¬>²
åK²Ã ¢$¥¤+¥>¡:£Co ¥6¬+¤P¸Æä´äo¤ÑzªCprªww¢ªH¥>pK§:¢w¬ªCw¡C/¬r¥/¬o¡ ÈEÏ>rªC>¢ ¡¨¥>% o¤£C¡:¦
¬~¥®C¤>³H¥>³Cpp¬Uµ|£Cp¢¬+¤³C§K¬+>¡ÙÏv¥>¡C£ [¥>rª4§C¢*>´b¬ªC¯rªH¥>¡C¡: o¤¤ ¢®>¡C£C¢¬+|¥>¡
p¡C£C ® ¡:£C ¡^¬e¤[¥/Ì ¥/¬+po¡>´ ²
²ÃÉ¢z¥¤¥>¡C£Co'¥/¬¤P¸×ÏK³C§:¬¢ K¸:%£o¡: p¬zp¢mrªCo¢%¡Ù²
ÛmªC¥/¡´äg §C¢\/´«¬ªC¢8®C¥>®%¤\¡½o¡½¬ªCx¥>¢j¬8¬U«)>´¬ªC ¢¨ ¥>¢%¢ ²ÛmªC C¤¢¬ ¥>¢p¢
¡: §:£C £ ¢|¥>¢2¬ E¸K®o¢*¬ªC"¬+%rªC¡CÐ`§C%¢§:¢ £ ¡»¬ªC¯x¥/¬ ¤2 ¥>¢%¢p¡ ¥ö¤´¥>p¥>¤
>¡`¬¸g¬[² U¡»¬+ªC[¥>¢ ¢zªC ¡ ¢¤+¥>¡C£:o)Ï$«zpw¥/¢¢§:¬ªH¥/¬q¬+¢2%¡^¬+¤p ¢´ä>¤ ¥>¡
<²Ý<²Ý£Ù²`©¥>§C¢¢¥>¡ op ¬+po¡2zp¬ªÌ% ¤6ÍU¨[¥>¡ÙÏ^p¡C£C%®%¡C£C ¡^¬«¤ ¥>J¥>¡C£¨¥>¦op¡H¥>¤µ®H¥>¤j¬+¢%Ïg ¥>rª
zp¬ª|±/¥>¤x¥>¡C%)Ç oåK²*áÐg§:p±/¥>%¡^¬+pµ>Ï ¥>rª» ¡^¬+¤jµ >´ ªH¥>¢§C¡Cp´ä>¤É®CªH¥/¢¥/¡C£ ¥Rµgp ¦>ª
¥>¦o¡Cq¬+§C£C/²ÑÛmªC¢rªC> ¨K£: ¢Ù¥ "!$#%&#('$)+*#(,-#(.zq¬+ª ¡:o§C¦oª¢%®H¥>¤¥/¬+po¡
$.$%$#¬ªC¤ % q±Kp¡C¦¥/¡`¬ ¡C¡C¥>¢8¥>¡:£)¬+ª:¬+¤¥>¡C¢q¬¬+p¡C¦¥>¡^¬+%¡C¡H¥>¢e¢§Crª(¬ªH¥/¬¬+ªC´¥>£C%¢´ä>¤
[/ ¥/rª2¬+¤+¥/¡C¢¨p¬¬+¡:¦/ÍU¤ %p±g¡:¦z¥>¡^¬+ ¡:¡H¥b®H¥>p¤¥/¤wp¡C£C%®%¡C£C ¡^¬ ² U¡¥>pg ¥>¢%¢ Ï>«wzp`¥>¢¢§C¨
¬+ªC¥/¬¬ªC0 )+123.45*#¨/6´ p8¢ 7`¡CRz¡¬+¬+ªC«¤% q±o%¤ Ïô¤%Ï> Ð`§Cq±/¥>%¡`¬pµ>Ï/¬+ª:wrªH¥>¡:¡C C>§:¬+®C§K¬
>¡C¢p¢¬+¢z>´¬+ª:®C¥>¤Æä:¹ 9; ÈEÏJ¥>¡C£"¬+ªC< !=.4);4>@?A.45*#½>´ B¢ 7`¡CRz¡(¥6¬m¬+ªC\¬+¤¥>¡C¢q¬¬+%¤ ²
C D"F E:GI H)jF JbK EBL
M o¨®Cp¸½¤¥>¡C£C> ±o%%¬+>¤¿ º ¼ Np¢¢¥>£½¬*³©¥/§C¢¢x¥>¡p´¬ªC¤[¥/¤+¥>¡C£:o ±o%%¬o¤
¿O Qº PSR N >¡C¢p¢¬+p¡C¦">´q¬+¢8¤[¥>¥>¡C£¥>¦op¡H¥>¤µ®H¥>¤¬¢ Ï ¿ O Â T$]IUW^ V$XZX_Y\Y\[[2` ÏÙp¢\©¥>§C¢¢x¥>¡×²Ûmª`§C¢%Ï
¬+¢® q´ µ¬ªC8£Cp¢¬+¤³C§K¬+>¡>´¥%o¨®CE¸¯©¥>§C¢¢x¥/¡¤+¥>¡:£Co ±o ¬+o¤t¿zÏKp¬w¢w¡: %¢¢¥>¤µ¬
¢® %p´ µ¬ªÇK® %¬+¥/¬+po¡)¥>¡C£¯ R±/¥>¤¥>¡C%/´ ¿mO ÏC¡H¥/%pµoÏ
ÒtÓ ¿O ÖÑaº P R N ¥>¡:£ Ò bÆ d¿ O c ÒwÓ ¿O ÖxÈ Æ d¿ O c~ÒtÓ ¿O ÖxÈ 5Õ e fº P R N"g R N à
|zpÙ¢¥[µ"¬+ªH¥/¬e¥ >®Cp¸)©¥>§C¢¢¥>¡¯¤+¥>¡C£:o'±o%%¬o¤b¿4i¢ h$)+h?A);2j=\,j,-.4);5hp´¬+ª:
R±/¥>¤x¥>¡C%\>´¬ªC o¤¤%¢®o¡C£Cp¡C¦ ¿4O ªH¥>¢m¬ªC¢¬+¤§C%¬§C¤
ÒibÆ ¿O c~ÒmÓ ¿O ÖxÈ Æ ¿O c ÒwÓ ¿$O ÖxÈ Õke Â måÇ losvnqu¯p Æ44Æ rrÈÈ ctsvu"wÆÆwrr1ÈÈ y
Æ È
´äo¤¢>< ze%¤¨p¬+¥>¡½¡Co¡gÍU¡C%¦^¥/¬+q±o¨£C C¡Cp¬< rÉº ¼ N"g\NÙ|² {>¬+nx¬+ªCp ¥/¬¬ªC¨¤[¥/®H¥>¤¬>´t¥>¡
ze%¤¨p¬x¥>¡»¥/¬+¤q¸ ¢¢µg¨¬+¤*¥>¡C£ ¬+ªC*¥>¦op¡H¥>¤jµ|®C¥>¤¬¨>´8¥>}
¡ z ¤q¬+x¥/¡»¥/¬¤P¸ p¢
¥>¡^¬+PÍU¢jµK¨¨%¬+¤¥>¡C£¬ª`§C¢8¬+ªC¥/¬¤P¸)¥>®C®[¥>¤¡C¦¡ Æ Èp¢b¤ ¥>$¥/¡C£½¢µg¨¬+¤p>F² U¡(¬+ªCp¢
[¥/¢«Ò bäÆã~¿ cÒmÓÔ¿$Ö È%Æã~¿ cÒtÓÔ¿ÖxÈÕ e Â r¨Ï>¥>¡C£¬ª`§C¢ Ï^¥ p¤ §:x¥>¤pµ8¢jµg¨%¬¤v >®Cp¸©¥>§C¢¢¥>¡
¤+¥/¡C£Co'±> ¬+o¤¿Àp¢m¢® H £*³^µ¯®C¤%¢%¤³:¡C¦ÒwÓÝ¿$Ö¥>¡:£¯Ò bäÆã¿ c ÒtÓÔ¿$Ö È%Æã¿ c~ÒmÓÔ¿ÖxÈÕ e ²
å
Ho¤z¥>¡^µº(¼ N /¥ ¡C£ º½¼ N"g C£ H¡:
c svu"Æ\È à
O Â losvnqu"p ÆÆ^^ÈÈKy ¥>C¡ £ O Â losvnqu¯p ÆÆ\\ÈÈ t
Æ \ÈIy
nqp
O
!#"%$'&)(*,+ O Â T$]IUW^ V$X.X/-- [[2` $0,1+ Â T I]U ^ VX..X 22 [4[ 3 ]IU ^ V X/X/2v2v[[` )56789
:<;6=%=;> "?$'&@#A ; BCA 78"C(ED
F G
Â H IJ F O Â O H O
ÆK^¥^È
F L
Â MÄ H IJ F O Â O Ä H O
ÆKo³HÈ
F L
Â Õ IJ F O Â O Õ
ÆKo[È
F L
Â 3N IJ F O Â O 3N
ÆKo£HÈ
£C%¬6Æ \O ÈPÂ OV£:%¬ZÆ \QÈ O R Â£C¬ZÆ Õ È
ÆKo[È
G
Â RTÄ SUIJ O Â R2O Ä S O
ÆK>´rÈ
SL
Â RVIJ SO Â aO R O
ÆK>¦gÈ
Æ R Õ SCÈÂ R O Õ SO à
ÆKoªHÈ
nxp
W:)+**KYXÛmªC®C¤>®%¤¬+p ¢Æ K^¥^ÈÏÆ Ko³JÈt¥/¡C£ Æ KoRÈt¥/¤¨%£Cx¥6¬+>²wÆ K>£JÈw´äopZz¢«´ä¤o ÆK^¥^Èt¥/¡C£
¬+ª:´¥/%¬m¬+ªC¥/¬ Ø O N ÂØ R N ²eÆ KoRÈ«´äopRz¢t´ä¤>
£C¬6Æ 8O ÈÂ£C%¬ Z l Ø\ [ãØØ y O l Ø\ c[ãØØ y] Âß£C%¬ Z l svu" Æ8È^`\ _ y] Â£:%¬ZÆ \È:£C¬ZÆ\È _ à
Æ K/´ãÈEÏÆ Ko¦`Èt¥>¡C£~Æ K>ªJÈt¥>¤p¨ £C¥/¬+/²
acbed#befgf dih kj º(¼ N"g\N"?(mln$!"<7oAqp" : r$0 ; $ = ps" : j O f
º P R N g R N"%( ; AE78 ; $ ; Atu =<v
W:)+**KYX@jbCÕ jâÂâØ N IJ Æ j\O ÈjÕ jO Â Ø O N ÂØ R N ²
acbed#befgf dihxw y : r º½¼ N g\N "?(z$ ; ${8$9|&g'7"o5Q@0!C}!$'"o7~7C$( ; "?( r O f
º PSR N"g R N v
W:)+**KYXb©\p±o%
¡ R Â Ó R N 9[à[à[à 9R R N ÖÕbQº PSR N Ï×%¬ "ÂÓ R N Ä R NQ N 9[à à[@à 9R N Ä R R N ÖÕbº ¼ N ÏÙ¢
¬+ªC¥/z¬ R¯Â CO ²Ûmª: ¡³^µ~Æ K>¦`Èt¥>¡C£|Æ K>ªJÈ
R Õ rmO R"Â 8Æ Õ rm^È«
Â Õ rk \ à
nxp
ÛmªC®C¤o³H¥>³Cpq¬Uµ¯£C ¡C¢p¬Uµ»Æäzp¬ª(¤%¢® ¬\¬+¬+ª:2¢¬+¥>¡C£H¥>¤£ ³ ¢¦>§C ¥>¢§:¤2o¡¼NHÈ
>´v¥%¤ §C¥>¤qµ¯¢µg¨%¬¤p%o®:¸(©¥>§C¢¢x¥/¡zp¬ª( ¥>¡»¥/¡C£( R±/¥>¤x¥>¡C%r ¢b¦>p±o%¡
³^µ
ÆRÈÂ£C¬ZÆ rO È 3N R E¸K®
1c2Æ R|O c ÑO È Õ r O 3N Æ R-O c ÑO È
Â£C¬ZÆ rÈ 3N ¸K® c2Æ R|cÑÈ Õ r 3N Æ R|cÈ zªC%¤\¬+ªC¢ >¡C£)%Ð`§H¥>q¬Uµ´äopRz¢w´ä¤oÉÆ Ko£JÈ Æ KoªJÈr²ÛmªC£CpÚ ¤ ¡^¬+¥>×%¡^¬+¤>®`µ¯/´¥%oÍ
®Cp¸)©¥>§C¢¢x¥/¡)¿ zp¬ª*%R±>¥/¤x¥/¡C & r p¢m¦op±> ¡*³`µ
|Æ
ÈÂâÒ Ó c(po¦ Æã¿vÈVÖ
Âpo¦£C%¬RÆ rÈÄËÆäo
¦ ZÈKÒwÓÔ¿ Õ r 3N ¿$Ö
Âpo¦£C%¬RÆ rÈÄËÆäo
¦ ZÈK¬¤[Æ ÒmÓÔ¿¿ Õ Ö r 3N È
Âpo¦£C%¬RÆ rÈÄËÆäo
¦ ZÈK¬¤[ÆäØ:È
Âpo¦£C%¬RÆ rÈà
Ho¤§C¢ Ï¬+ªC2p®o¤j¬r¥>¡C%>´¬+ªC p¤ §:x¥>¤pµ"¢jµK¨¨%¬+¤ o¨®Cp¸(©¥/§C¢¢x¥>¡C¢e¢£C§C¬¬+ª:
´äopRz¡C¦ ¨v¥ %¤%§Cx¥/¤pµ¢µg¨¬+¤\ >®Cp¸¯©¥>§:¢¢¥>¡C¢z¥>¤ ¡^¬+¤o®^µ¯¥6¸KppÌ ¤¢ ²
w #lE! ; ( 78 ; k = ,AC$90 ; 5667 ; A¿ ºË¼ N "?(6CA ; {8s $$0(|'78"%(}|(
ÒwÓÝ¿¿Õ<ÖÂ r `" v v ÒtÓÝ"¿ !x¿ #_ ÖÂ r! # Ç Þ [I9q %
Þ $ v |$ 78 |$7A ; p ;6: ¿ (|'78"%(}|(
|Æã¿vÈwÞ po¦£C%¬6Æ rÈ > "<78&!l = "<7 p" : r$0 ; $ = p" :
¿ "?(z C"%A'6l = A = p(qp!s678At"() ; = * 'ln((t" $ > "<78
ÒwÓÝ¿¿ Õ ÖÂ r
W:)+**KYX%,¬ + ³¥>¡^µ(£C%¡C¢q¬Uµ(´ä§C¡C¬+>¡½¢+¥/¬¢´ µgp¡C.
¦ -0/12+Æ R~È R3! R #5_ 4 R|Â r! # ÏÇÞ [19o(6Þ $²
%¬
Æ RÈÂ£C%¬RÆ rÈ 3N E¸:® c R Õ r 3N R à
7 ³C¢%¤±>¬+ªH¥6¬ - /1
Æ RqÈ R3! R9#_ 4 R»Â r! # Ï¥>¡C£¬+ªH¥6¬po¦ Æ RÈ8¢¥*p¡C ¥>¤\ >2³C¡C¥/¬+po¡½>´
¬+ª:¬ ¤z¢ R3!?R #_ ²Ûmª`§C¢8Ò 9#Ó o¦ Æã¿ÈUÖÂâ;Ò :gÓÔpo¦ Æã¿ÈUÖ<²ÛmªC%¡ÙÏ
~<Æ +È c=|Æ
ÈÂ c?> / 1 +Æ RÈ:o8¦ +Æ RÈ 4 R2@Ä > / 1 Æ RÈ:po¦ Æ RÈ 4 R
Â c > / 1 +Æ RÈ:o8¦ +Æ RÈ 4 R2Ä > / 1 +Æ RÈ:o¦ Æ RÈ 4 R
Â > / 1 +Æ RÈ:po¦ + Æ RÆ RÈ È 4 R
A
Þ \9
zp¬ª¯ Ð`§H¥>pp¬Uµ>¡Cpµp;´ +"Â ²vÛmª`§C)¢ |<Æ +JÈmBÞ |Æ È²
DC y : ¿Àº(¼ N "%( C"?AE6l = A = ps(qp's67A"(F ; k = * 'ln(t(" r$ 7C$( ; "?(w¹~G
Â 8¿
:<; A $np º½¼ Bg\N v
K
W:)+**KYXz|(¥[µ4¥>¢¢§C¨½¿
¹ O Â O ¿zO ÏC¥>¡C£
¢¨Ì %¤/ÍÎ ¥>¡Ù²x¬xr Â ÒwÓÔ¿¿ÕUÖã²ÛmªC%¡ ¹ p¢Ì% ¤6ÍU¨[¥>¡ÙÏ
ÒwÓ ¹ O ¹ O Õ ÖÂ (O ÒtÓ ¿ O ¿ O Õ Ö O Õ Â RN O r O O Õ Â RN O
zªC%¤ Â0rm Õ ²
4y : ¿,$90¹A "?$0!q |$0!|$7 |"?AE6l = A = pk(~p's67A" ; = * ln((t" $!(E9789C$
ÂË¿(Ä ¹ "?( C"%A'6l = A = pu(~p's67A" ; k = * 'ln(t(" r$ v
W:)+**KYX%¬ ÂâÒwÓÝ¿¿ÕÎÖ¥>¡C
£ H ÂâÒwÓÔ¹#¹ÕÎÖã²ÛmªC ¡*ÒwÓ O O Õ ÖÂ RN F O zp¬+ª F ÂGÀÄ H²
0E
Jm~ L(LK Je 0Jbe0 E:GßV # FE«ÉzJb~L E«ewz+b
|zp¢¬r¥/¤¬z³^µ"¤%p¡C£Cp¡C¦2o§C¤¢%p±o%¢¬ªC\[¥/¢>´£C%¬ ¤¨¡:¢¬\Ã|²ÛmªC¤ ¢§Cp¬¢z>´Ñ¬+ªCp¢
¢%%¬o¡*[¥>¡*³\¡:´ä%¤¤%£*´ä¤oÉÓXÇoÏ wªÙ² 6Ö
C
a n h
|zp C¤¢¬8£C ¤p±o2¥>¡½¸K®C¤ ¢¢o¡½´äo¤z¬+ª:2[¥>®C¥> q¬Uµ F ÆãÃq9rÜÈz>´¬+ª:¢brªC¥>¡C¡C%<²\Û¬+ªH¥6¬
¡:£ÙÏ^wzzp:¥6¸K¨Ì «¬+ªC¥[±o%¤+¥>¦oz2§K¬+§H¥>Hp¡:´äo¤¥/¬o¡"!\Æ¿$#+¹È³%¬U« %¡¬+ª:p¡C®C§:¬v¥/¡C£
¬+ª:>§:¬+®C§K¬e/´#¬ªCrªH¥>¡C¡C%ÑZ±> ¤m¬+ª:rª:o%/´¬+ª:£:¢¬¤p³C§:¬+po¡>´¿m²
%«µ¬+ªCv¢p¡C¦o§C¥>¤±/¥>§C£C% o¨®o¢q¬+>¡¬ªC >¤ *Ïo¥/¡`µ¥/¬+¤q¸\Ã º(¼ ;¾ g/Á [¥>¡³z¤q¬¬+%¡
¥>¢
Ã Â j'&)( Õ
zªC%¤z j º½¼ ¾ g/¾ ¥>¡C£ ( º(¼ wÁ g/Á ¥>¤§C¡:p¬r¥/¤µoÏ6¥>¡:*£ & fº P ¾ g/Á p¢¡Co¡KÍÎ¡C ¦o¥/¬+q±o¥>¡C££C¥>¦oo¡H¥/<²
U¡´¥/%¬[Ï`¬+ª:e£C¥>¦oo¡C¥>H ¡^¬+¤%¢w>´ &'¥>¤¬ªCe¡:o¡KÍU¡: ¦^¥/¬p±>e¢Ðg§C¥>¤e¤g>¬+¢v>´Ù¬ªCe%¦o%¡^±>¥/§C%¢
>´Ã(ÃÕÏK¬ªCb%o§C¨¡C¢«>´ j¥>¤¬+ªC8%¦o%¡^±o ¬+o¤¢m>´ÑÃ(ÃÕ¥>¡C£¬ªC8 >§C¨¡C¢v>+´ ( ¥>¤b¬+ª:
p¦o ¡^±> %¬o¤¢>´Ã(ÕUÃ~²Ûmª`§C¢%Ï«[¥>¡¯z¤q¬+¨ÆjÇRÈt¥>¢
¹ Â j'&)( Õ ¿(Ä Åà
%-¬ ¹~, x
Â jbÕV¹«.Ï ¿~, /Â (ÕU¿m$Ï Å , Â jbÕUÅ² {>¬+¬+ªH¥6¬ j¥>¡C0£ ( ¥/¤8p¡`±> ¤j¬+³:>1Ï Åß, ªH¥>¢v¬+ªC8¢¥>¨
£Cp¢¬+¤³C§K¬+>¡(¥>¢\Å ¥>¡C£ÙÏÙÒw2Ó ¿ , Õ ¿, ÖÂ ÒtÓÝ¿ Õ ¿$Öã²Ûmª`§C¢%ÏÑ¬ªC2o¤¦op¡H¥>rªH¥>¡C¡: $p¢8 Ð`§Cq±>¥/ ¡^¬8¬
¬+ª:rªC¥>¡C¡C%
¹ , 3Â &4¿, 5Ä Å ,
2Æ 6>È
zªC%¤7 Å , ¢Ì %¤/ÍÎ ¥>¡ÙÏ©¥>§C¢¢x¥/¡ÙÏzp¬+ª ¡:£C ® ¡C£: ¡^¬[Ï£C%¡^¬+ ¥>qµ£:¢¬¤p³C§:¬+%£|¤[¥>¥/¡C£
¥>¦op¡H¥>¤jµ|®C¥>¤¬¢¥/¡C£ ÒtÓ Å , Å , Õ Ö8Â Ø ¾ 7² 8Kp¡C *Ã ¢>é¤+¥/¡ 7 ¥/¬ö¢¬¨¡ 9Z· 9;¶ :`Ïw¥/¬¨R ö¢¬
¨<¡ 9Z· 9;¶ :~>´¬ªC ¢¡:¦o§Cx¥/¤±>¥/§C%¢)>´p¬*¥>¤|¡:o¡KÍUÌ% ¤C>
² =8 ¡:>¬+p¡C¦»¬+ªC%¢~³^3µ ? !N @Ï [½Â
Ç 9[à à[@à 9+¨¡ 9Z· 9;¶ :`Ï:« ¥>¡¯z¤p¬¨2Æ 6oÈw%o¨®o¡: ¡^¬Í<z¢/ÏC¬+¦o¬
S , !@
Â ? !N R R3, !KÄ $ , !o9 ÇGÞ [Þ p¡ 9Z· 9;¶ : 9
6
>¥ ¡C£¬+ª:v¤ ¢j¬>´g¬+ª:v%o¨®o¡: ¡^¬+¢Ñ>´ S, Æq´:¥/¡`µ:ÈÑ¥>¤%Ð`§H¥>^¬+z¬+ªC%o¤¤ ¢®o¡C£:¡C¦z >®o¡C%¡`¬¢
>´ $, ²#|¬+ª`§C¢¢ v¬+ªH¥6¬ S , !K´ä>¤[4p¡<9R¶;9+· :wp¢Ñ¡C£C%®%¡C£C%¡`¬>´:¬ªC¬+¤+¥/¡C¢¨p¬¬+ £¢p¦o¡H¥>`¥/¡C£
¬+ªC¥/¬ R3, !$´äo¤[Ëp¡9R¶;9+· :£Co¡Ý¬\®:x¥[µ(¥/¡`µ)¤>>²\Û"¥6¸K¨Ì \¬ªC22§:¬§H¥>#¡:´äo¤¥6¬+>¡ÙÏ
«¨¡: £ ¬+"rªCgo¢0 9 R3, !BÇ"Þ [bÞ ¨¡ 9Z· 9;¶ : :¬*³¡C£: ® ¡C£C%¡^¬[Ïzp¬ª ¥>rª R3, !«ªC¥R±gp¡C¦
¡:£C ® ¡C£: ¡^¬©¥>§C¢¢x¥/¡ÙÏ#Ì% ¤/ÍU¨[¥>¡ ¤ ¥>v¥>¡C£ ¥>¦op¡H¥>¤µ)®H¥>¤j¬+¢%²ÛmªC±/¥>¤x¥>¡: ¢¡C% £|¬
³rª:o¢%¡)±gx¥ jw¥/¬+%¤j5Í Hp¡C¦ 2¥>¢
ÒmÓ Æ R3, !È R ÖÂßÒtÓ svu"Æ R3, ! È R ÖÂ RN Æ xc4? !3N È
zªC%¤ 4p¢\rªCo¢%¡~¬+*¨ %nx¬p ¬ªC®R« ¤ o¡C¢j¬+¤¥>¡^¬[<² ze%¤/
Ï £C ¡C/¬+ ¢¥6¸ 9 \ 9 :`²ÛmªC
®Z« ¤eÜ ¥/¡C£*¬ªC¥Z¸:p¥/2§K¬+§H¥>p¡:´äo¤¥/¬o¡[¥>¡¯¬+ª`§C¢³\®H¥>¤+¥/¬+¤pÌ %£)¥/¢
ÜÆ ÑÈÂ ! xc ? !3N 9 F Æ ÑÈÂ ! p¡ÑÆ ?3!xÈ à
CA@C".#A ; C"<7 p v 8K¡C%v¬ªCw¡:o¡KÍUÌ% ¤b p¦o ¡^±/¥>p§C ¢>´JÃ(ÕUÃ ¥>¤¬+ª:w¢+¥/«¥>¢Ñ¬+ªCo¢
>´wÃ(Ã(Õ+ÏÙ«¢ ¬+ªH¥6¬\¬+ªC[¥/®H¥> q¬+p ¢\>´«rªH¥>¡C¡: ¢%o¤¤ ¢®o¡C£:¡C¦¯¬+*Ã ¥>¡C£ Ã(Õe¥>¤¬+ª:
¢+¥//²
2! = v Û#¥ 7>Ã ! # Â Ç\´äo¤z¥/ [I9qH²$~[¥/¡*z¤p¬+Ã ¥>¢
Ç /· "!
Ã Â ²² # ·Z¶ T Ç6¶à[à[à Ç 6¶ `
Ç /· ¥>¡C£½«¬+ª`§C¢¢%¬ªH¥/¬p¡¬ªC¢p¡C ¦o§C¥>¤b±/¥>p§C2£C% o¨®>¢p¬o¡>´tÃ ¬ªC£Cx¥/¦oo¡H¥>¥/¬+¤q¸
& z×ªH¥[±oo¡Cpµo¡C¡Co¡KÍÎÌ %¤¨ ¡^¬+¤jµoÏ ·Z¶E²8Æ ~¥>p¢¢%¬ªH¥/¬z¬+ªC H¤¢¬ op§C¨¡*/´ j p¢
Ç /·KÓPÇ 9 à[à[@à 9 Ç ÖxÕ«¥>¡C£"¬+ª: C¤¢¬%o§C¨¡¯> ´ ( p¢ Ç Z¶%ÓPÇ 9 à[à[à 9[Ç ÖÕE²ûÈ2Ûmª`§C¢ Ï
F Âo¦HÆjÇ«Ä ·Z¶jÜÈEà
ÛmªC¿ËÂ ( ¿â, ¬ªH¥/¬¥>rªCp%±> ¢¬+ªCp¢ ¥>®H¥>%p¬Uµ½¢¥/¬+pI¢ H%¢ÒwÓ R3! R9#_ ÖvÂ Ü 6¶b´äo¤¥/B [I9qHÏ#ã²þ/²pÏ¬+ª:
¬+¤¥>¡C¢q¬¬+%¤¢¥/¤z¥>p:¢%¡C£Cp¡C¦¬ªCm¢+¥/m¢¦o¡H¥/<8² {e>¬t¬+ªH¥/¬ Ï^%±> ¡¬ªCo§C¦>ª¨ ¥>rª¬+¤+¥/¡C¢¨p¬¬+ ¤
¢¢ ¡:£C¡C¦¥8®Z« ¤>´Ü 6¶EÏ^¢¡C%z¬ªC p¤$¢p¦o¡H¥>p¢¥>£C£%oªC ¤ ¡^¬+qµ¥/¬$¬ªCm¤% %p±o%¤ Ï`¬+ªCm®Rw%¤
¤% %p±o%£¥/¬ ¥>rª¨¤ % q±o ¤p¢Ü¶E² 8K¡C%z[¥>rª¨¤% q±o%¤v¢ %¢v¬ªCz¢+¥>¨m¢p¦o¡H¥>H¥/¡C£¬+ªCz¡Cop¢%¢
¥/¬m¬ªC¤ % q±o ¤¢b¥/¤§C¡C%o¤¤ x¥6¬+ £¯¬+ª:R±> ¤+¥/Ù¢¦o¡H¥/×¬+¡Cop¢¤+¥6¬+p¢zÜ·Z¶E²
2! = %$ v Û#¥ 7>·Âß¶Â $ ¥>¡C£*Ã ÂØ N ²ÛmªC%¡
F Â $\o¦JÆVÇ«Ä4Ü $È
Ho¤t¿ ¬ªH¥/¬m¥/rªC±o ¢t¬ªC¢«[¥>®C¥> q¬UµÒwÓ R3! R #_ Ö'Â &E! # Ü $#Ï:ã²þ/Ïg¬ªC8 >®o¡C%¡`¬¢t>´¿ ¥>¤b<²Ý<²Ý£Ù²
zeR«%±> ¤ ÏHq¬wp¢wp¡C o¤¤%%¬w¬2¡K´ä ¤´ä¤o ¬+ª:¢w%o¡C%§C¢o¡¬ªH¥/¬«¬+2¥/rªC±o\[¥/®H¥> q¬Uµö¡C8ªH¥/¢
¬+£Cp¡C£C ® ¡:£C ¡^¬%K£Cp¡C¦)´ä>¤[¥/rª~¬+¤¥>¡C¢¨p¬¬+%¤ x² Î¬2p¢¬+¤§C¬ªH¥/¬¬+ªC[¥>®H¥/ p¬Uµ >´w¬+ªCp¢
(
rªH¥>¡:¡C [¥>¡³8¥/rªC±o £³`µ¢®:p¬¬+p¡C¦\¬+ªCe¡C%op¡C¦£H¥/¬+¥¢¬¤[¥/ p¡^¬+¶$¢¬+¤[¥>¨¢ ÏK g£C¡:¦
¥>¡C£)g£C§C¥/¬+p¡C¦¬+ªC%¢¢rªC%%¢8¢%®H¥>¤+¥6¬+ qµoÏ¥>¡C£¬ªC ¡¢ ¡:£C¡C¦¨¬+ªC¶m¨K£C§:x¥/¬ £*¢¦>¡H¥>¢
R±o%¤¬+ªC£CpÚ ¤ ¡^¬2¬+¤¥>¡C¢q¬¬+%¤¢%² %w§:¬ Ï¢§C®:®o¢ *¶³Cq¬+¢2¥/¤¦>o¡C¦*¬+(³¬¤+¥>¡C¢q¬¬ £ÙÏ
¥>¡C£¯«zpÙ%p¬+ª: ¤z¢%®H¥>¤+¥6¬+¬+ªC% ¡^¬+¶t¦>¤o§C®:¢/´ ³Cp¬¢m[¥>rª¥>¡C£*§C¢[¥>rª)¦o¤>§C®*¬
¢%%%¬\o¡:2>´wå ß¢¦>¡H¥>¢´äo¤b ¥>rª½¬+¤¥>¡C¢¨p¬¬+%¤ Ïo¤ Ï×«2zpÑ§C¢¥>p¥> *¶e³Cp¬¢e¬¢% ¬
o¡C>´å Á ¢p¦o¡H¥>×±> ¬+o¤¢ ²tÛmªC¢% o¡:£>´#¬+ªC%¢¥>p¬ ¤¡C¥/¬+q±o ¢mzp×µg%£*¥®C¤o³C¥>³Cpp¬Uµ>´
¤¤o¤2§:rª¢¥>p ¤¬ªH¥>¡¨¬+ªC H¤¢j¬[ÏK¥/¬¬+ªÇK® ¡C¢b>´×2§Crª¦>¤[¥6¬+ ¤%o®:¸Kq¬Uµo² U¡:£C %£ÙÏ
¬+ª:2o¦>´$¬+ª:2 ¤¤o¤e®C¤o³C¥>³Cpp¬Uµ"p¡)¬ªC¬U«[¥>¢ ¢8zpÑ£CpÚ ¤³^µ(¥¨´¥>%¬o¤b>´¶E²2Æ 8K%¬+ª:
¤¤o¤mE¸K®o¡: ¡^¬+¢e>´®C¥>¤+¥>p%×rªH¥>¡:¡C p¢p¡|ÓPÇoÏH®:®Ù²EÇ KJÇ 6 \ Öã²È
C
w f d
e
d b b 4
a n h
ÛmªC2§:¬§H¥>Ùp¡:´äo¤¥/¬o¡ !\Æ¿$#+¹Èw ¥>¡)³\z¤q¬¬+%¡*¥>¢
!\Æ¿$#+¹ÈvÂD~Æ¹È c |Æ¹ O ¿vÈÂ |Æ¹È c |ÆÅeÈ;9
¥>¡C£\¬ªg§:¢#¥6¸K¨Ì%¡C¦ !\Æ$¿ #+¹Èp¢Ù Ð`§Cq±/¥>%¡`¬¬z¥6¸KppÌ ¡:¦ |Æ¹È²8{e/¬+$¬+ªC¥/¬Ñp´K¿)¢¥/¬+p¢IH%¢
ÒwÓÝ¿ Õ ¿ÖÞ Ü¨Ïm¢ £CK%¢"¿ cÒtÓÝ¿$ÖãÏ¢ w½ ¥>¡ ¤%¢¬¤¬"o§C¤¥/¬¬ ¡^¬+po¡À¬+»Ì% ¤/ÍU¨[¥>¡ ¿z²
H§C¤¬ªC ¤>¤>Ï«p´b¿ ¢Ì% ¤6ÍU¨[¥>¡ zp¬ª4%Z±/¥>¤x¥>¡: ¯ÒtÓÔ¿¿Õ<ÖÂ rÏ«¬ªC ¡4¹ ¢Ì %¤/ÍÎ ¥>¡
zp¬ª R±/¥>¤¥>¡C 2ÒwÓ ¹¹#ÕÎÖÂ tÃ rÃ(ÕÑÄ Ø ¾ Ï¥>¡:£ ³^µ %¥¯å"¥>>¡C¦"¢§Crª ¹ ¬+ª:¨%¡^¬+¤>®`µ
¢x¥/¤¦o%¢¬bzª: ¡½¹ ¢b%¤ §C¥>¤qµ"¢µg¨¬+¤p%o¨®CE¸©¥>§:¢¢¥>¡ÙÏzªCrª(p¢e¬ªC ¥>¢zª: ¡
¿ß¢\ p¤%§Cx¥>¤pµ*¢µg¨¬+¤2%o®:¸½©¥>§C¢¢x¥>¡ Æ ¨¥>¢ ¥>¡C£ K`È² 8KCÏÙ«[¥>¡½´ä§C¤j¬+ªC%¤
¤%¢¬¤¬\o§C¤¥6¬¬+%¡^¬+>¡(¬+" p¤%§Cx¥>¤pµ¯¢jµK¨¨%¬+¤2%o¨®CE¸©¥>§C¢¢x¥/¡¿t² U¡½¬+ª:¢8 ¥>¢¬+ª:
2§:¬§H¥>Ùp¡:´äo¤¥/¬o¡¢m¦oq±o ¡¯³^µ
!8Æã¿ #+¹ÈÂpo¦£C%¬RÆØ ¾ Ä t
Ã rÃ Õ ÈÂ>¦v£:%¬ZÆäØ Á Ä rÃ Õ Ã½È
zªC%¤¬+ªC¢% o¡:£%Ðg§C¥>q¬Uµb´äopRz¢Ù´ä¤oâ¬+ªC£C¬+%¤¨¡H¥>¡^¬Ñp£C ¡^¬+q¬Uµ8£C¬ZÆäØC@Ä HÈvÂâ£:%¬6ÆäØCÄ
H8ÈÏ\¥>¡:£q¬¯o¡CpµÀ¤%¥>p¡C¢¬+ rªCgo¢
r ¬ ¥6¸K¨Ì%¬+ª:¢"Ð`§H¥>¡^¬+q¬Uµß¢§C³ %¬*¬+ ¬+ª:
>¡C¢¬¤+¥>p¡`¬¢m¬+¤R4Æ rÈmÞâÜ ¥>¡C£¯¬+ªH¥60¬ r p¢z¡Co¡KÍÎ¡C ¦^¥6¬+p±>£C H¡:p¬+/²«Ûmª:Ð`§H¥>¡^¬p¬Uµ¯>¦£C%¬6ÆäØ\Ä
tÃ rÃ Õ È«zpÙg §:¤m¡"¬+ªCp¢m£Cg §C¨ ¡^¬z´ä¤%Ðg§: ¡^¬+qµ¯ ¡Co§:¦oª*¬ªH¥/¬m«zp%¬
wÆ r 9rÃ½ÈÂpo¦£C%¬ZÆØ\Ä t
Ã rÃ Õ È
¬+)£C ¡:>¬+q¬[0² 8Kp¡C Ã Õ Ã pi¢ z ¤q¬+x¥/¡ q¬ ¥>¡ ³£C¥>¦oo¡C¥>pÌ £×Ï#Ã Õ Ã Â j Õ jÏ#zp¬ª
§C¡Cq¬r¥>¤j*µ jÀ¥>¡C£2¡C>¡KÍU¡C%¦^¥/¬p±ov£C¥>¦oo¡H¥/ Âß£Cx¥/¦J2Æ ? N 9[à[à[à 9 ? Á È² M ®C®CqµKp¡C¦e¬ªCv£C%¬ ¤¨¡C¥>¡^¬
£: ¡^¬+q¬Uµ"¥>¦^¥/¡"w¢ ¬+ªH¥/¬
£C%¬RÆØ ¾ Ä tÃ rÃ Õ ÈÂâ£C¬6ÆØ Á Ä N R j0r*j Õ N R ÈEà
7 ³C¢%¤±>8¬+ªH¥/¬ r , Â j0r jbÕ¢«¡Co¡KÍÎ¡C ¦^¥6¬+p±>b£C H¡Cq¬+bzªC%¡¯¥>¡C£"o¡:pµzªC%a
¡ r ¢%ÏC¥>¡:£¬+ªH¥6, ¬
,
¬+¤[Æ rÈÂ ¬¤RwÆ rÈ #«¬+ª`§C¢¬+ªC¯¥6¸K¨Ì[¥6¬+>¡|R±o%-¤ r [¥>¡ ³¯ ¥>¤¤ £ %Ðg§C¥>qµ|« pmZ±> ¤ r¨²
{e/¬+¥>¢2¬+ªH¥6¬´ä>¤z¥>¡^µ"¡Co¡KÍÎ¡C ¦o¥/¬+q±o\£CH¡Cp¬¥/¬¤P¸uÏH£C%¬6Æ\ÈwÞ ! £:%¬ZÆäØ ¾ Ä N R r , N R ÈtÞ ÆVÇ«Ä r , ! ! ? !äÈ
UÏ:¬ª`§C¢
!!
!
zp¬ª Ð`§H¥>pp¬Uµ*zªC ¡ r', ¢\£C¥>¦oo¡C¥><²Ûmª`§C¢w¢%¬+ªH¥/¬\¬ªC¥Z¸:ppÌ p¡C¦ r, p¢8£C¥>¦oo¡H¥/<Ï
¥>¡C£¯¬+ª:>®:¬+p¥>£C¥>¦oo¡H¥/Ù ¡^¬+¤%¢ ¥>¡*³8´äo§:¡C£*±g¥ Vt¥/¬ ¤VÍkHp¡:¦¬+³
r , ! !×Â xc ? !3N 9 [#Â Ç9[à[à[à 9¶
zªC%¤c ½¢trª:o¢%¡*¬¢+¥/¬¢´ µ ! r, ! !ÙÂÜ¨²$Ûmª:%o¤¤ ¢®o¡:£C¡C¦¥6¸K§C 2§:¬+§C¥>Ù¡K´äo¤jÍ
¥/¬+po¡"¢m¦oq±o%¡*³^µ
>¦JÆ ? !xÈ
!
¥>¢z³%´äo¤>²
C C
d d#bed + b \¡CRz¡C¦¯¬+ª:[¥/®H¥> q¬Uµ>´m¥*rªH¥>¡C¡: v¢¡C>¬¥>pw¥[µg¢¢§¨ %¡^¬[² 7 C¡ ¥[µ³¨¡^¬ ¤%¢¬ £
¡d7`¡CRz¡C¦(ª:Z ªC¥>¤£ q¬¢¬+(¦o¬%o¢¬)¬+ª:¢ ¥>®H¥>%p¬Uµ>²)á¤¤o¤¸K®>¡C ¡^¬+¢®C¤R±g£C¥
®H¥>¤j¬+¥>Ñ¥>¡C¢jw%¤e¬+¨¬+ªCp¢eÐ`§C%¢¬o¡(³^µ*¦oq±Kp¡C¦¨¥>¡§:®C®%¤b³o§C¡C£*¬+¨¬+ªC®C¤>³H¥>³Cpp¬Uµ>´%¤¤>¤
¥>rªCp%±/¥>³Cpe³^µ¨³CpK 7%K£C%¢t>´Ñ¥¦op±> ¡ ¡:¦>¬+ª$(¥>¡C£¤+¥/¬2²Ûmª:b§C®C® ¤«³>§C¡C£p¢:7`¡CRz¡
¥>¢m¬+ª:¤¥>¡C£C>' g£Cp¡C¦³o§:¡C£¥/¡C£)p¢m¦op±> ¡¯³^µ
Æ ¤¤o¤+ÈwÞß¸K®Æ c $ ¾ Æ ÈÈ 9
zªC%¤¬+ªC¤+¥/¡C£Co g£C¡C¦E¸:®o¡C%¡^¬ ¾ Æ Èmp¢m¦op±> ¡*³^µ
¾ Æ ÈÂ ¥Z ¸ Æ gÈ c9
N
zªC%¤>Ï¡"¬§C¤¡ÙÏ Æ gÈtp¢¦>p±o%¡)³^µ"¬ªC¢§C®C¤ 2§C R±> ¤e¥>Ùp¡C®C§:¬£Cp¢¬¤³:§:¬+po¡C¢ Y ¢+¥/¬¢jÍ
´ µg¡C¦¬ªC ¡C%¤¦>µ"%o¡C¢j¬+¤+¥/¡^¬>´
Æ (9 Y ÈÂ c(po¦ > l > Y Æ RÈ +Æ SO RÈ NIX N [ 4 R y N 4 Sà
U¡2o§:¤[¥/¢ +ÑÆ S4O RÈÂâ£:%¬6Æ Ø ¾ È 3N ¸K® cÆ S cmRÈÕÆ S8ckRÈ 8² Î´Hw«rªCgo¢! Y ¥>¢#¬ªCm©¥>§C¢¢¥>¡
£Cp¢¬+¤³C§K¬+>¡ «¦>%¬Æã¥/´ ¬ ¤m¢o¥/¦o%³C¤+¥^È
Æ (9+rÈ"
Â v>¦v£:%¬ZÆäØ ¾ ÄÆjÇ«#Ä gÈ 3N tÃ rÃ Õ È"Â ÆjÇ«#Ä gÈ 3N IÈ r 9rÃ à
ÛmªCz¥6¸K¨Ì[¥6¬+>¡>´ R±o%¤SrË¢$¬ªg§:¢v¢¥>¨m¢+¥>¨m®C¤>³C% ¥>¢¥6¸K¨Ì%¡C¦¬+ªCm2§K¬+§H¥>
¡K´äo¤¥/¬+po¡ÙÏg¥>¡C£¯«¦o¬ ÆgÈÂ F ÆãÜCÆjÇ«Ä gÈ9rÃ½ÈE²
Û#rªCgo¢ Y ¥>¢©¥>§C¢¢x¥>¡»p¢2¡C>¬2o®:¬+p¥/<Ï$¥/¡C£ ¥(£C¢j¬+¤³C§:¬o¡| o¡: ¡^¬¤+¥/¬ £ o¡ ¥
j¬ªC¡¢®:ªC ¤[¥/¢ªC% "zp¦>p±o³%¬¬+ ¤¤ ¢§:p¬+¢¥>¢p¡ÀÓXÇoÏ ² Ö ß¡C>¡C%¬ªC p ¢¢%Ï¬ªC¨¥>³Z±>
¸K®C¤ ¢¢>¡¢z¥%o¡^±o ¡: ¡^¬bRw%¤z³o§:¡C£"¬+ ¥>¡C£¯¬+ª`§C¢mµg%£C¢¥>¡¯§C®C® ¤z³o§C¡C£¯¬+¬+ª:
®C¤o³H¥>³Cpq¬Uµ>´# ¤¤o¤%²
0E
Jm~ L(LK Je 0JebF E G ßV" dJ ~G E« :Jb\V
8K§C®:®o¢\¡CRß¬+ªH¥/¬«¬+ªCb¥/¬¤P¸Ã ¢«¡C>¬ :¸K%£ÙÏC³C§:¬t¢t¥¤+¥>¡C£:o ¥/¬¤q¸ ¡:£C ® ¡C£: ¡^¬
>´³>¬+ª¯¿ ¥>¡C£¯Å²ÛmªC\¤ ¥>pÌ[¥/¬o¡>´#Ã >´ p¢m¥>¢¢§C¨ £"¬+³~ 7`¡CRz¡¥6¬t¬+ªC\¤ % p±> ¤%Ï
³C§:¬8¡C>¬¥/¬e¬+ªC¬+¤+¥/¡C¢¨p¬¬+ ¤%²\ÛmªC2rªH¥/¡C¡C ¢b¬ªg§:¢8zp¬+ª¡C®C§K¬\¿â¥>¡C£½o§:¬®C§:¬¨Æä:¹ 9 ÈzÂ
5Æ ¿4Ä Å 9; È² ~(zpb¥>¢¢§C(¬ªH¥/¬"¬ªC½ ¡^¬+¤%¢">j´ ¥>¤½¡C£C%®%¡C£C%¡`¬)¥>¡:£â ¥>rª
¡^¬¤µ*¢mÌ% ¤6ÍU¨[¥>¡ÙÏ©¥>§C¢¢x¥/¡ÙÏCzp¬ª)p¡C£C ® ¡:£C ¡^¬e¤[¥/#¥/¡C£)p¥/¦o¡H¥/¤µ®H¥>¤¬¢ ÏJ[¥/rª)zp¬ª
±/¥>¤¥>¡C% Ç oåK² áÐ`§Cq±>¥/ ¡^¬pµoÏ«[¥>rªÀ ¡^¬+¤jµ4/´ ªH¥/¢§C¡:p´äo¤qµ £Cp¢¬+¤³C§K¬+ £ ®CªH¥/¢(¥/¡C£
¥Rµgp ¦>ª£Cp¢¬¤³:§:¬+%£¥>¦o¡Cq¬+§C£:>ÏRzp¬ª¸K® ¬+ £¥>¦o¡:p¬+§:£C¢Ð`§H¥>¤w%Ðg§C¥>g¬e§:¡Cp¬Uµ>²ÛmªCp¢
¢p¡^¬+ ¡:£C £¬+g£C oF¥ ¥[µKp p¦oª\´¥>£C¡:¦mrªH¥>¡C¡C%gzq¬+ª ¡:o§C¦oª®Cª^µK¢ ¥>`¢ ®C¥>¤+¥/¬o¡\zq¬+ªCp¡
¬+ª:¬¤+¥>¡C¢q¬¬¡C¦¥>¡C£¨¬+ªC¤% %p±g¡C¦¥>¡^¬+%¡C¡H¥>¢v¬+2¥/rªC±obp¡C£C%®%¡C£C ¡: bp¡¬ªCe%¡^¬+¤p ¢v>´
²~8zp H¤¢¬¢ª:ZË¬+ªH¥/¬z¢§Crª(¥/f¡ ¢m¡^±/¥>¤x¥>¡^¬m§C¡:£C ¤§C¡Cq¬r¥>¤jµ¬+¤¥>¡C¢j´äo¤¥/¬+po¡C¢%²
##lE! ; ( º½¼ ¾ g/Á "?( ; = * 'ln(t(" $u'78At" > "<78u"%$0!~BC$90!C$97 "0!C${
78" =%= p0i"%(E78At" 'l'7~ 0 |$978A"C(E9 sC$978Aqp > "o7"%$0!q |$0!C$97 A = $90*"%ur&"?$Aqp` A 78( > "o7
r|A ; { $ $0, &'l) = 5 A" $ Y v C$ :<; Ak$npMln$!"<7oAqp j ºÀ¼ ;¾ g/¾ B$0 (ÉºÀ¼ kÁ g/Á 789
0i"%(E78At" 'l'78" ; $ ;6: j( Õ "?(c789`(|s@r(c78c0i"%(E78At" 'l'78" ; $q v
W:)+**KYXÎ¬«¢§ ¨ %¢w¬+¢ªCR ¬ªH¥/¬ Â j ªH¥>¢¬+ªCe¢+¥>¨z£C¢j¬+¤p³C§:¬o¡¨¥>¢ ²$ÛmªCbp ¨¥
¬+ª: ¡"´äopRz¢v´ä¤o'¥/¡¯¥>®C®Cp[¥6¬+>¡>´Ñ¬ªC¢v¬+ Õ ² 8Kp¡C b op§C¡:¢w>´ ¥>¤8p¡C£C%®%¡C£C ¡^¬ Ï
¬+ª:)%o§C¨¡C¢>´ ¥>¤¯¡:£C ® ¡C£: ¡^¬"¥>p¢Cm² Î¬¨¤%¥/¡C¢2¬|rªC% 7»¬+ªH¥/¬¨ ¥>rªÀ%o§C¨¡ >´
ªC¥>¢¬+ª:¢+¥>¨£:¢¬¤p³C§:¬+po¡|¥>¢¬ªH¥/¬2/F´ ² 8K¡: ¬ªC%o§C¨¡C¢>´ ¥>¤ ¤ §C¥>¤qµ
¢µg¨¬+¤%o®:¸ ©¥/§C¢¢x¥>¡ ±> %¬o¤¢%Ïw¢|¥/¤¬+ª:o¢">´ ² Î´ # ¥>¡C£ # ¥>¤¬+ªC
>§C¨¡">´ ¥/¡Ct£ ¤ ¢®%%¬p±o%pµ>ÏC¬+ªC%¡
ÒtÓ # #Õ ÖÂ jÒmÓ # #Õ Ö j Õ Â ÒmÓ # #Õ Ö
zªC%¤z¬+ªCzx¥/¢¬ Ð`§H¥/p¬Uµ2ªCo£:¢³%[¥>§C¢ÒtÓ # #Õ ÖJp¢¥§Cp¬®Cpw>´¬+ªCzp£C ¡^¬+q¬Uµ¥/¬+¤q¸²
U¡ ¬ªC¢¢ ¬+po¡»w"zpt¥>¢¢§C¨¬+ªC¥/¬¬+ªC¯rªH¥/¡C¡C mp¢2¨ ö¤µg%¢¢ ´äo¤[¥/rª §:¢¯>´
¬+ª:rªH¥/¡C¡C ¥>¡p¡C£C%®%¡C£C ¡^¬b¤[¥/Ì ¥/¬+po¡">S´ p¢z£C¤+¥[z¡Ù² U¡)¬ªC¢[¥/¢«2¥/¤o¡*´¥/pqÍ
x¥/¤¦>¤o§C¡:£(¥>¡C£)¬+ªC[¥>®C¥> q¬Uµ) ¥>¡³%o¨®C§:¬+%£(¥>¢¬+ªC¥6¸K2§C'2§:¬+§C¥>Ñ¡:´äo¤¥6¬+>¡Ù²
zeR«%±> ¤ Ï¬+ªC¤%¢§Cq¬+¢z¬+ªH¥6¬´ä>RË¥>¤\±/¥>p£"±o%¤³H¥/¬´äo¤zrªH¥/¡C¡C p¢´ä>¤zzª:rª ¢z¦o ¡gÍ
¤¥/¬+%£³^µ¥/¡ ¤¦og£C®C¤g %¢¢ ¥>¢wpo¡C¦¥>¢«¬ªCb¤ %p±> ¤w>³C¢%¤±o%¢t¬+ªC ®C¤g %¢¢w>¡Cpµ¬+ª:
H¤¢¬o¤£: ¤z¢¬+¥/¬+p¢¬+p ¢z¥>¤\¡C %£C £)¬+£C%¬ ¤p¡C\rªH¥>¡C¡: Ñ[¥>®C¥> q¬Uµo²
!
"
"
"
4 a n h
8Kp¡C w¬ªCt¤ %p±> ¤7`¡CRz¢¬+ªCw¤[¥/Ì ¥/¬+po¡>´6
>Ï ¬+ªCwrªH¥>¡C¡C%Co§:¬®C§:¬p¢#¬ªCt®H¥>p¤tÆä¹ 9; ÈÂ
Æ5 ¿Ä Å 9; È²ÛmªC2§:¬§H¥>Ùp¡:´äo¤¥/¬o¡³¬Uw% ¡(p¡C®C§:¬¥/¡C£)>§:¬+®C§K¬z¢t¬+ª: ¡
! ¿ #ZÆä¹:9 È Â4!bÆ¿ # ÈÄ !bÆã¿ #+¹ O È
Â4!bÆ¿ #¹ O È
ÂâÒ Ó !8Æã$¿ #+¹ O ÂËÃ½ÈVÖãà
| 7g¡:Z ´ä¤o ¬+ª:"®C¤±Kpo§C¢¢%%¬o¡ ¬ªH¥/¬p´¿ ¢2%o¡C¢j¬+¤+¥/¡C%£ ¬½ªH¥[±o¯ R±/¥>¤x¥>¡C%xr¨Ï
¬+ª:rªCop >´¿ ¬+ªH¥6¬b¥6¸K¨Ì% ¢ !bÆã¿ #+¹ O Â Ã½Èm¢¬+ªC p¤ §:x¥>¤pµ"¢jµK¨¨%¬+¤ >®Cp¸
©¥>§C¢¢x¥>¡>´v R±/¥>¤¥>¡C ir¨ÏÙ¥>¡C£ wÆ r 9rÃ½ÈmÂ po¦£C%¬ZÆØ ¾ Ä tÃ rÃ(ÕVÈep¢e¬+ª:2 o¤¤%¢®o¡C£Cp¡C¦
¥6¸K¥>§:¬+§H¥/¡:´äo¤¥6¬+>¡Ù²|\¬+ª`§C¢¡C %£*¬¥6¸KppÌ
wÆ rÈÂâÒtÓ wÆ r 9; ÈUÖÂâiÒ bPpo¦£C%¬ZÆØ ¾ Ä ri Õ È e
R±o%¤¬ªCrªCo%>´¡:o¡KÍU¡: ¦^¥/¬p±>\£C H¡:p¬+& r ¢§C³ ¬e¬¬+¤R4Æ rÈtÞßÜ²
8K¡: F r¢¡Co¡KÍÎ¡C ¦o¥/¬+q±oz£C C¡Cp¬>Ï^w[¥/¡z¤q¬+zp¬v¥/:¢ r Â j &j8ÕzªC ¤m jâ¢§:¡Cp¬+¥>¤µ
¥>¡C£ & ¢m¡C>¡KÍU¡C%¦^¥/¬p±o¥/¡C£)£:x¥>¦o>¡H¥><²ßp¬ª¯¬ªC¢m¢§C³C¢j¬+p¬§:¬+po¡
wÆ rÈÂßÒ bo¦£C¬ Ø ¾ Ä5Æ j8È &½wÆ Uj8È Õ e
%«µ ¨¥ 6*¬+ª:£C¢j¬+¤³C§:¬o¡ >F´ j'¢¬+ªC¢¥>¨¥>¢¬+ªH¥/¬>F´ Ï¥>¡C£|¬+ª`§C¢ wÆ rÈÂ
Æ &"ÈE²½~ ¥>¡ ¬+ª`§C¢¤ ¢¬¤p%¬o§:¤¥/¬¬ ¡^¬+po¡~¬½¡Co¡KÍÎ¡C ¦^¥6¬+p±>£C¥>¦oo¡H¥/ r²|©q±o ¡ ¥/¡`µ
¢§:r
ª r ¥>¡C£ ¥/¡`µ|® ¤§:¬r¥/¬o¡|¥6¬+¤P¸ Ï$%o¡C¢£C%j¤ r Â FreÕr² 8K¡: 'ªC¥>¢¬+ª:
¢+¥/¨£C¢j¬+¤³C§:¬o¡¥/¢ Ï ¨4Æ rÙÈÂ wÆ rÈ² {>¬+¬+ªC¥/¬´ä>¤¥/¡`µ Ã|Ï¬ªC¥>®C®:¡Cq¦ r
+
Ø ¾ Ä tÃ rÃ(Õm¢8p¡C ¥>¤b¥/¡C£®C¤%¢ ¤j±o%¢®o¢q¬+q±o£: H¡Cq¬+%¡C ¢¢ -² 8Kp¡C o¦£C¬\¢8%o¡C ¥R±>o¡
¬+ª:\¢%¬z/´#®o¢p¬+q±o8£: H¡Cq¬+\¥/¬+¤% ¢ vÏ r+ 4Æ r 9rÃ(ÈÂo¦£:%¬6ÆäØ ¾ Ä»tÃ rÃ Õ È«p¢t >¡C[¥[±o/²
Î¬z¬+ªC%¡*´ä>Rz¢w¬ªH¥/¬r+ ¨Æ4rÈwp¢m o¡:[¥[±o/²wÛmª`§C¢
r , Â ¶Ç r ¢+¥6¬+¢ H ¢ Æ r, `È wÆ rÈe¥>¡:£)¬+¤[Æ r, ÈtÂ ¬¤R4Æ rÈEF² {>¬+¬+ªH¥6¬ r , ¢e¥2§Cq¬+p®C\>´¬+ªC£C%¡`¬p¬Uµ
¥/¬+¤q¸¯¥/¡C£)«%o¡C%§C£C¬+ªC¥/¬e¬ªCo®:¬+p¥/W r 2§C¢j¬b³>´¬ªC´ä>¤
#ØJS² Î¬bp¢z ¥>¤m¬+ªH¥6¬
¬+ª:8¥Z¸:p2§C p¢t¥>rª:%±> £zªC%¡ p¢«¬+ª:8x¥>¤¦o ¢j¬w®o¢¢³:>Ïg¡H¥>¨ qµ¨Ü 6¶E²Û#¢§C¨¥/¤Ì%>Ï
«ªH¥[±>¢ªCRz¡*¬ªC\´äopZzp¡C¦
4
b d ) C"o7 p ;6: 7, $'$ = "?( !"Q56 0 > C$¿ "%( |"?AE6l = A = p (qp!s67<{
A" ; k = * 'l((" $ > "<78 6CA ; {8s $$0 ; 5YrA" r$ ÆãÜ 6¶ÈjØ Á v 9 Y C"<7 p "?(&"o56|$
p¯Ò b po¦£C%¬ Ø ¾ ÄËÆÜ 6¶1È Õ e v
{e>¬¬ªH¥/¬´äo¤ K¸:%£½·KÏ³^µ¯¬+ªCx¥[ >´¥>¤¦>¡`§C2³ ¤¢ NÁ Õ + Ø ¾ ¥>p>¢¬¢§C¤ qµ¥/¢
Ç\
¶t¦>%¬+¢z¥>¤¦o/²$Ûmª`§C¢ ÏH¬ªC[¥>®H¥/ p¬Uµ¡"¬+ªCp¨p¬«>´¥>¤¦>8¶w%Ðg§C¥>¢
·po¦JÆjÇ«Ä ÜÈEà
4 w
' f b b 4
a n h
Æ( È
q ¬+ªC>§C¦oª(¬+ª:¸K®%%¬+¥/¬+po¡½Ò b >¦£C%¬ Ø ¾ Ä ÆãÜ6¶ÈI Õ e p¢8[¥/¢µ¬¯%±/¥>§C¥/¬+´ä>¤8 q¬+ªC%¤
·Â Ço¤z¶«Â Ç>Ïq¬+¢%±/¥>p§H¥/¬+po¡¯¦o%¬¢b¤¥/¬+ªC%¤ep¡^±ooq±o £*´äo¤·¥/¡C£)¶m¥>¤¦> ¤m¬+ªH¥/¡~Ço²t|zp
¡CR¢ªCR ªCRË¬£C¨¬ªC¢m±/¥>§H¥6¬+>¡Ù²{e/¬+\¬+ªH¥6¬
£C%¬ <Ø ¾ ÄËÆFÜ Z¶1È Õ bÂ£C¬ ÎØ Á ÄËÆFÜ Z¶1È Õ ¥>¡C£*£C H¡C
Õ · À¶
Â
Õ *· ;¶ 9
$)Ââ¥6
¸ 9Z· 9;¶ :¥>¡C£ Â¨¡ 9Z· 9;¶ :`²ÛmªC%¡ ¢$¥/¡ ËÊ ¤¥>¡C£C> ¡C>¡KÍU¡C%¦^¥/¬p±o«£C C¡Cp¬
¥/¬+¤q¸ ¥>¡C£»¬+ª`§C¢¨ªH¥>¢¤ ¥><Ï¡C>¡KÍU¡C%¦^¥/¬p±o"%¦o%¡^±>¥/§C%¢ ² |* ¥>¡ z¤p¬¬+ªC¯ ¥>®H¥>%p¬Uµ»p¡
¬+%¤¨¢z>´#¬ªC p¦o ¡^±/¥>§: ¢ N 9[à[à[à 9 >´ Ò l ! >¦ ÇwÄÆãÜ 6¶È "! y
Æ È
N
ÛmªC¨£C¢j¬+¤³C§:¬o¡x¥[ >
´ ¢[¥>p%£(¬+ªC = v).0!=.4)4>@?%.45*# / $. v)I,-.o)+= $
¥>¡C£»¬ªC o¡^¬£C%¡C¢q¬Uµ»>´z¬+ª:*>¤£C%¤ £ %¦o%¡`±/¥>p§C ¢pj¢ 7`¡CRz¡ ¬ ³ Æ¢ ¯>²Ý¦C²zÓÝå6Öm>¤*Ó Ï
®Ù² Ö È
+
2Æ ? N 9[à[à[à 9 ? È/
Â 3N N 3!#"%$ " ! ? N! 3 !& 2Æ ? ! c ? # È R 9 ? N (')')'! ? \
#
zªC%¤ N p¢w¥¡Co¤¥>pÌ p¡C¦8´¥>¬+o¤%²$ÛmªCb§:¡Co¤£: ¤%£ p¦o ¡^±/¥>p§C ¢¬+ªC%¡ªH¥[±o¬+ªCe£C ¡:¢p¬Uµ
+*×Æ ? 9[à[à[à 9 ? ÈÂ Æ N È 3N 3!#"$ " ! ? N! 3 !& 2Æ ? ! c4? # È R à
N
#
ÛmªÇK® %¬+¥/¬+po¡"wz¢ª*¬ o¨®C§:¬
Ò l ! o8¦ ÇwÄÆãÜ 6¶È ! y Â ! Ò b >¦ +ÇwÄÆãÜ 6¶È "! e
N
Â âNiÒ bXo¦ Ç«ÄÆãÜ 6¶%È N e
+
M
ÇoÇ
C£ %®%¡C£C¢2o¡:pµo¡ ¬+ªC£C¢j¬+¤p³C§:¬o¡>´m>¡C>´w¬+ªC¨§C¡Co¤£C ¤ £»%¦o%¡`±/¥>p§C ¢%²¯Û#) o¨®C§:¬
¬+ª:£: ¡C¢p¬Uµ¯>´! N «>¡Cpµ¡C %£)¬+p¡`¬ ¦o¤¥/¬+\>§:¬z¬+ªC? R 9[à[à[à 9 ? +Æ2? ÈÂ > ')')' > +×2Æ ? 9[à à[@à 9 ? È ? ')')' ? à
4 R 4 N
N
Û¨¬ªH¥/¬z ¡:£ÙÏH¡C>¬¬ªH¥/¬ !& # Æ ?3! c4? # Èmp¢t¬+ªC£C¬+%¤¨¡H¥>¡^¬z>´¥ v¥>¡C£C%¤ö¡C£C¥/¬+¤q¸
Ç à[à[à Ç "!!!
?
à[à[à ? ²
&(2Æ ? N 9[à[à[à 9;? ÈÂ ² N
²
² #
? N 3N à[à[à ? 3N
¥>¡C£¯« ¥>¡¯z¤p¬ +¯¥>¢
+×2Æ ? 9[à[à[à 9 ? ÈÂ Æ N È 3N £C¬ &½2Æ ? N à[à[Wà 9;? È R ! ? N! 3 3 $ " à
N
ßp¬ª¯¤Ro® ¤¥/¬+po¡C¢t«[¥>¡¯¬+¤¥>¡C¢´ä>¤>
&½Æ ? N 9[à[à[à 9 ? Èwp¡`¬
N 2Æ ? N È à[à[à N 2Æ ? È !
²²
&½, Æ ? N 9[à[à[à 9 ? ÈÂ ²²
#
2Æ ? N È à[à[à 2Æ ? È
zªC%¤ N 9 à[à[Wà 9 p¢«¬+ª:8¤%¢§Cq¬t>´¥>®:®Cpµg¡:¦¬+ª:©¤¥> 8KrªC¨£:¬vo¤j¬+ªC>¦oo¡H¥>pÌ ¥/¬+po¡®C¤/Í
%£C§C¤¬¬ªC¢%Ðg§: ¡C%
Ç 9? 9? R 9Ñà[à[Wà 9<? 3N
¡"¬ªC¢®H¥>%>´$¤[¥>×±/¥>p§C £"´ä§C¡:%¬+po¡C¢mzp¬ª¯¡C¡C%¤z®C¤g£C§C¬
9
vÂ > 2Æ ?È ×2Æ ?È ? N 3 3 $ ?Ñà
4
Ûmª`§C¢ - !VÆ ?È # 2Æ ?È ? N 3 3 $ 4 ? Â &E! # ²¯ÛmªC£C%¬ ¤p¡H¥>¡^¬/´ & ¬ªC ¡| Ð`§H¥>p¢"Æ¨g£C§C,
2§Cq¬+p®Cp[¥/¬p±o o¡C¢j¬r¥>¡^¬¢®Cp 7> £»§:®|´ä¤> ¬+ªC¤R o® ¤+¥6¬+>¡C¢rÈb¬+ª:£C¬+ ¤p¡H¥>¡^¬>´ &Ï
zªCprª)p¡¯¬§C¤¡×ÏH³`µ¬+ªC£C H¡Cp¬o¡¯>´¬+ª:£:%¬+%¤¨¡H¥/¡`¬ ÏC Ð`§H¥/¢
£C¬ &½, 2Æ ? N 9[à à[@à 9 ? È Â Æ cÇZÈ X [ ! & , " !×Â Æ cÇZÈ X [ ! " Æ ?3! È
ÇZå
zªC%¤"¬+ªC¯¢§C¥/¬o¡ p¢R±o ¤¨¥>pw® ¤2§:¬r¥6¬+>¡C¢>´ 9`Ç 9[à[à[à9 :`Ïv¥>¡C£ ® ¤RÆ $Èp¢ \ o¤"Ç
£C%®%¡C£C¡:¦o¡"¬ªC®%¤2§:¬+¥/¬+po¡ »³%¡C¦±o ¡)o¤mg£C£Ù²Ûmª`§C¢
+×2Æ ? 9[à[à[à 9;? ÈÂ F
N ÆKcÇRÈ X [ X [ ! " Æ ?3! È " Æ ?3! È ? !N 3 3 $ " à
N
U¡^¬+%¦o¤+¥/¬¡C¦R±o%¤ ? R 9[à à[@à 9 ? «¦o%¬
+ 2Æ ? ÈÂ F
N KÆ cÇZÈ X [ X [ 2Æ ? N È 2Æ ? N È ? NN 3 3 $ ! & " "
N
R
Â F N Æ c ÇRÈ ! !U2Æ ? N È R ? NN 3 3 $
N
Ç
Â ! !VÆ ? N È R ? NN 3 3 $
N
zªC%¤8¬+ª:b¢% o¡:£*%Ð`§H¥>q¬Uµ´äopZz¢´ä¤> ¬ªCb´¥>¬w¬ªH¥/¬mq´ !×Â !Ù´äo¤ [ âå¬ªC ¡ N Â N
¥>p¢Æä¢p¡C «³>¬ª *¥>¡C£ ¯¥/¤v®%¤2§:¬+¥/¬+po¡C¢>´ 9`Ç 9 à[à[Wà 9 :/ÈÑ¥>¡C£¬+ª`§C¢ Â vÏ>¥>¡C£¬ªCw¥>¢¬
Ð`§H¥/p¬Uµ´äopZz¢#´ä¤o ¬ªCm´¥>%¬¬ªH¥/¬ !VÆ ? N È R ? NN 3 3 $ p¡`¬ ¦o¤¥/¬+%¢¬+§C¡Cq¬Uµ¥>¡C£¬+ª`§C¢ F N
2§C¢j¬ Ð`§H¥>Ç p² 7 ³C¢%¤±>¡CR¬+ªH¥/¬z¬ªC©¤¥> 8KrªC¨£:¬wo¤¬ªCo¡Co¤¥/Ì ¥/¬+po¡µKp p£C¢
N R N 3 2Æ ?È 9 ¨Â \ 9[à[à[à 9 c Ç
N 2Æ ?ÈÂ T vN X 3 [`
zªC%¤ N 3 Æ RÈtÂ N ER 3 N (Æ 3 ER(N 3 Èz¢m¬+ª:2¥>¢¢g x¥6¬+ £ Ñ¥>¦o§C%¤¤®>pµg¡Co¨x¥>>´
o¤£C ¤ ²Æ 8K Ó KKÏ :² \ Ï :² Öã²È
Û#¨¢§:¥>¤pÌ \
¶ 78A|$!(t"<77~|A( $90"*· A |"o5QCA(ln$0!|A
4
b d w |"o7 p ;Q: 789 $!$ = > "<78¯@
;n> CA ; $!(E7AC"%$7Ü &'l) = (
> o¦HÆjÇ«Ä4
Ü
?6Z¶È 3N vN b N 3 2Æ ?È e R ? N 3 3 $ 4 ?
Æ oÈ
3 [
X
> |A # Ââ¨¡ 9Z· 9;¶ : r$0 $)Âß¥6¸ 9Z· 9;¶ : r$0 #! rA k789@r(( ; C" '7~Y0 r&lgCAtA ;6= p'$ ; {
" = ( v
¦>§C¤Ç¢ª:Zz¢z¬+ª:±/¥>p§C\>´¬+ªCp¡`¬ ¦o¤¥>Ùp¡~Æ ^È«´äo¤\ÇÞ · 9¶tÞâå \ ¥>¡:£Ü Âå \ £ %e²
2! = v wo¡C¢£C%¤¶Â Ço8² U¡¬ªC¢ ¥>¢
Â Çe¥>¡C£ $)Ââ·g² {e/¬+¡:¦¬ªH¥/¬ N 3 2Æ ?ÈÂ ÇoÏ
¥>¡*¥>®C®: ¥/¬+po¡>´Æ ^È«µg%£C¢t¬ªC[¥>®H¥/ p¬Uµ"¥>¢
Ç > po¦JÆVÇwÄ *Ü ?È ? ¾ 3N 3 $ à
Æ oÈ
4
«Æä·oÈ Ç
F
\
(
\
(\
²K
6 \ ²
å K6 ² ÇZåK² 6\
K\
\
å\
Ç\
\ \
\
Ç\·
Ç
6
Ç6 å\
å\
#¦o§C¤Ç t¥>®H¥/ p¬UµÆ¡"¡C¥/¬+¢+Èt±g¢%²·2¥>¡C£¯¶«´äo¤zÜ Âå \ £ %
ÛmªC±/¥>p§C ¢>´¬ªC¢¡^¬+%¦o¤+¥/#¥/¤¬+¥>³C§C¥/¬+%£p¡Û#¥>³C¨Ç´äo¤ÇÞ·Þ Ç \ ¥/¡C£(Ü ´ä¤> \ £ %
¬+ 66£ % ¡ 6/£ % ¡: ¤%%¡^¬+¢ 1² 8K%¥>¢ ¦o§:¤åK² {>¬+8¬ªH¥/¬e¥>¢m·2¦o¬+¢zx¥/¤¦o/Ï:¢¨£Cg ¢m¬+ª:
[¥/®H¥> q¬Uµo² Ho¤vx¥>¤¦ob·gÏ`¬+ªC8 ¥>®H¥>%p¬Uµ¨¢w¥>¢µg¨®:¬+/¬+¬+2po¦JÆVÇÄ Ü·>ÈÏg¡¬+ªCe¢ ¡:¢8¬+ªC¥/¬t¬+ª:
£CqÚ×%¤ ¡: ¦og ¢m¬+Ì %¤C²
2! = v wo¡C¢£C%¤·»Â Ço² M ¢p¡ ¬ªC*®C¤±Kpo§C¢¨¸:¥>¨®C/Ïm¥>®C®:pµg¡C¦ Æ ^Èµg%£C¢¬+ª:
[¥/®H¥> q¬Uµ¯¥>¢
Ç > o¦ Ç«Ä4Ü? 6¶ ? Á 3N 3 $ à
ÆjÇ \ È
4
«Æ ¶È M ¢«¡C>¬ £"¡(Æ ( ÈrÏK¬ªCb ¥>®H¥>%p¬Uµ¥>®C®:¤^¥>rª: ¢tpo¦JÆjÇ#Ä ÜÈ¥>¢v¶¦o%¬¢wx¥/¤¦o/²$ÛmªCe±/¥>p§C ¢«>´¬+ª:
[¥/®H¥> q¬Uµ¯¥>¤\¢ªCRz¡p¡¯Û¥>³:å2´äo¤t±/¥>¤po§C¢w±/¥>p§C ¢z>´¶m¥>¡:£Ü.² 8K%¥>p¢ p¦o§C¤ ²
2! = v wo¡C¢£C%¤z·Ââ¶E² U¡*¬ªC¢z ¥>¢
$)Â Ââ·KÏH¥/¡C£¥/¡¥>®:®Cp[¥/¬o¡/´Æ ^È«µgp £:¢
¬+ª: ¥>®H¥>%p¬Uµ¯¥/¢
¾
> >¦JÆjÇ«Ä4
Ü
? /·oÈ 3N 2Æ ?È R 3 $ 4 ? 9
ÆjÇoÇZÈ
zªC%¤ Â p¢t¬+ªCm Ñ¥>¦o§C%¤¤®oqµK¡:o¥>>´>¤£C%¤ ²
¦>§C¤ K*¢ªCRz¢¬ªC¢ ¥>®H¥>%p¬Uµ½´äo¤\±/¥>¤po§C¢\±/¥>§: ¢>´t·¯¥/¡C£ Ü-² Î¬¢%[¥/¤´ä¤o ¬+ª:
H¦o§:¤¬ªH¥/¬¬+ªC[¥/®H¥> q¬Uµ*¢z±o ¤jµ)« p¥>®C®C¤R¸Kp¥/¬ £)³`µ)¥¨¡:[¥>¤m´ä§C¡C¬+po¡)/´·KB² U¡:£C %£ÙÏ
ÇEK
6
6
¶Ç\
·Ü
Ç
å
\£%
K
(
6
Ç\
6/£ %
Ç\£%
Ç 6/£ %
%
%
%
%
%
$
10 .
,6
/ .
87
å\£%
"
å 6/£ %
\ £ %
!
#$
$
!
6/£ %
!
]& ]^M8MnrhgY[Y[hgTVYR] nrNXWZTãYRNqO NPOciVOàZY[d TVStTVaR]^cMY2TUdbiYR_Ò`fXSVTVdNXhgNXfPTUMzTUMriVMEin+TUMEa½NXQRMrYRiEO6}J½SjNPiVO^MEWZn+fXMEMeNPQRTUMriji2YRO`]gSVYRdSNPTU_`TUOgMriwNXcpaRcxYRik`d NPO`hgW]`njYR]gSVYRMO`YROÔ`MEfk y
^
'vY>fXMENPWZ]¯YRd\hgfPNPTV_`k^M8aRc_gO`NXTmd\MEYRO*S(/_`Y[ijMRy & ]^M\WZYRNPOgSmTUak`NX:MriVMEO/TmiVMEn+MENXQRMriSY[iVM
NPO`k^MrhCMEO`k`MEO6Try & ]^MzO>_`de:MriaRcÙiVMEn+MENPQRMrijSvNPS*)o}`YRO`k,+ßNPSTV]^MzSjNXWZO`YRfCTUaOâZNqSUMmijY[TVNXa^y
Û#¥>³CÇ v¥/§C%¢m>´#¬ªC¡^¬+%¦o¤+¥/Ù¡|Æ oÈ
&
0/
01.
4
3
2
/
.
F
.
-.
2.
96;:7
5.
·
PN O ]^5 MkQ[<»YRfP_^NPOgMn+aRiVMEcCd\TV]^MEM«O/TVnrSrY[y hgYRnrNXT xNqOO`Y[TVS ÙYRScpaZ_gO`k\ciVaZd Q>Sry )mcaRi . k <>=>+?= -5 k <
p¦o§C¤Aå t¥>®H¥/ p¬Uµ±K¢%²J·´äo¤t¶Â Ç¥/¡C£"±>¥/¤>§C¢t±/¥>§C%¢z>´$Ü²
&
Ç6
¶Ü
Ç
å
\£%
K
(
6
Ç\
6/£ %
Ç\£%
Ç 6/£ %
#
$!
å\£%
å 6/£ %
$
$
\ £ %
6/£ %
]& ]^M8MnrhgY[Y[hgTVYR] nrNXWZTãYRNqO NPOciVOàZY[d TVStYRaRO6cY2TUdbiYR_Ò`fXTVSVNXdhgfPNXMzTUTUTUMrijiYRO`TUaSVdTVNX]^TUM¨TUMriEiV}HMEn+SVMENPO^NPQRWZMrfPi2MiV]gMEYRn+SMENX_`QRMrOgimNXcpaRcxYRik`d NPO`hgW]`njYR]gSVYRMO`YROÔ`MEfk y
^
'vY>fXMENPWZ]YRdhgfPNXTV_`k`MuvNXTV](_Ò`NPTed\MEYRO(S(>_`Y[iVMRy & ]`McxYRk^MES8caRibMEYRn]½hgY[TV]WZYRNPO(NPS
NPO`k^MrhCMEO`k`MEO6Try & ]^MO>_`dCMriaRc:TUijYRO`SVdNXTUTUMrijSÑNPSYRO`k +4NPSÙTV]^MvSjNXWZO`YRfoTUaOâZNqSUMijY[TVNXa^y
Û¥>³:Aå v¥>p§C ¢m>´¬+ª:p¡^¬+ ¦>¤+¥>Ùp¡|ÆjÇ \ ÈE²
&
F
4
3
2
/
.
.
/
2
3
4
01.
0/
¶
PN O ]^5 MkQ <»YRfq_^NPOgM#n+aRiVMEcgd\TV]^MEMO/TVnrSrY[y hgYRnrNXT 6xNPObO`Y[TVS87YRSÙcaZ_Ò`kecpiVaZd 6 01. 7QoSry JcpaRi . k <>=>+?= -5 k <
p¦o§C¤ t¥>®H¥/ p¬Uµ±K¢%²H¶w´äo¤m·Â Ç¥/¡C£"±>¥/¤>§C¢t±/¥>§C%¢z>´$Ü²
&
Ç(
F
02.
0 /.
01..
4.
3.
2.
/.
.
.
5
01.
05
6 00 7
·
/.
]NPO ^5 M#kQ <»YRfP_`NPOgMn+aRiVMEc`d\TV]^MEM$O/nrTVSrY[yhgYRnrNXTã x6 NPOeO`Y[TVS87YRS×cpaZ_gO`kzciVaZd JQoSry )caRi . k<>=>+?= -5 k<
&
p¦o§C¤`K t ¥>®H¥>%p¬Uµ±g¢%²·´äo¤m·Ââ¶t¥>¡C£"±/¥>¤po§C¢t±/¥>§: ¢z>´Ü¨²
H¤¢¬¤z¤p¬Æ Èt¥>¢
F Â Ò > >¦ ^Ç«Ä Ü
¶ 4 Æ È
zªC%¤ 2 Æ RÈ¢z¬+ª: ¨®Cp¤ ¥>£Cp¢¬+¤³C§K¬+>¡)>´¬+ªC ¦> ¡^±/¥>§C%¢b>´¥>¡ ÉÊ z ¤¨p¬x¥>¡
¥/¬+¤q¸ i
¬+ª:¡`§C³%¤/´%¦o%¡`±/¥>p§C ¢z>é %¢¢m¬+ªH¥/¡R à
2 Æ RÈÂ
M ±> ¤µ¦o ¡: ¤+¥/×¤%¢§Cq¬t´ä¤> ¬ªCb¬ªC o¤jµ/´#¤¥>¡C£C> ¥/¬¤% ¢8Æ¢%>ÏC/²þ¦:²pÏÙÓ 66ÖxÈ«¢¥Rµg¢t¬ªH¥/¬w´ä>¤
£C H¡C%£»¥>¢2¥/³R±o/Ï¥>¢ $ Â'¥6¸ 9Z· 9;¶ :¯¥/¡C£ Â ¨¡ 9Z· 9;¶ :¯¥>¤p¡C ¤[¥>¢ £~zq¬+ª $W ¥>®C®:¤^¥>rª:¡C¦¨¥pq¬ ÇoÏ
Æ È RN c Ç Ç c ´ä>¤ º Ó 3 9 Ö
4 +
ÆjÇZåoÈ
/¬+ªC%¤z¢>Ï
\
4
zp¬ª Â Æ ËÇZÈ R[²Ûmª`§C¢%Ïp¡¬+ªCpq¬w/´¥>¤¦ob·¥>¡C£¯¶EÏ
F
Ç > o¦ ÇwÄ Ü +
å
¶ c Ç Ç c! 3 4 à
Ç
ÆjÇ È
Ho¤t¬+ª: ¥>¢§C¡:£C ¤ o¡:¢£: ¤+¥6¬+>¡ÙÏ Â $)Ââ·Âß¶EÏC´ä>¤tzªCrª 3 Â \ Ï ÂKCÏH¥>¡C£
F · > po¦JÆVÇvÄ4Ü È Ç Ç c KÇ 4 zªCprª)p¢m¡:[¥>¤tp¡¯·¥>¢zo³C¢ ¤±> £(³%´ä>¤8´ä¤> ¬+ª: C¦o§C¤/²
CA $ v ÛmªCb¤ ¢§:p¬´ä¤o ¬ªCz¬+ªC%o¤µ¨>´×¤+¥>¡C£:o ¥6¬+¤p %¢«§C¢ £p¡á¸:¥>¨®C 6¥>®C®Cp ¢
¬+¤+¥>¡C£:o ¥6¬+¤p %¢v¬ªH¥/¬m¥/¤b¡:>¬t¡C% %¢¢+¥/¤qµ©¥>§:¢¢¥>¡Ù² Ho¤v Ð`§H¥6¬+>¡ÆjÇ È¬2ªCop£p¬vp¢
¢§ %%¡`¬´äo¤ ¬+¨ªH¥[±o<²Ý<²Ý£Ù²C%¡`¬¤p ¢z>´#§C¡Cp¬m±/¥>¤x¥>¡: >²
CA v ÛmªC¤ %®C¤K%p¬Uµ½®:¤o® ¤j¬Uµ(¬+ªH¥6¬\wö³C¢ ¤±> £~´ä>¤\£C%¬ ¤¨¡:¢¬Ã £Cg ¢¡C/¬
ªCop£~´äo¤¤+¥>¡C£:o Ã wo®C¥>¤"á¸:¥>¨®C%¢ ¥/¡C£ KzªC%¤¬+ª: o¤¤%¢®o¡C£Cp¡C¦½Ã Ý¢¥>¤
¬+¤¥>¡C¢®o¢ ¢\>´$[¥>rª>¬ªC ¤%² U¡½á¸:¥>®: Ï×[¥/®H¥> q¬Uµ*¡C%¤[¥/¢ ¢8zq¬+ªC>§:¬b³o§C¡:£¥>¢8·¦o%¬¢
x¥/¤¦o/Ï:zªC ¤[¥>¢¡¯á¸:¥>¨®Cc K¬+ª: ¥>®H¥>%p¬Uµ"p¢m³>§C¡C£C%£*´ä¤o¥>³R±o/²
{eo¡:%¬+ª: %¢¢%Ï$¡^¬+%¤rªH¥/¡C¦o¡:¦)·¯¥>¡:£ ¶\£:K%¢¡C/¬rªH¥/¡C¦o¬+ªC¨¥6¬+¤P¸ Ï#¥>¡C£¬+ªC¨[¥ZÍ
®H¥>%p¬Uµ£C%®%¡C£C¢«o¡Cpµ2o¡Ü 6¶¥>¡C£¬+ªC p¦o ¡^±/¥>§: ¢v>´ ²$Ûmª`§C¢%Ï:q´ F Æ· 9;¶ 9rÜÈ$£C ¡:>¬+%¢«¬+ª:
[¥/®H¥> q¬Uµ>´¥rªH¥>¡C¡: zp¬ª*·¤% q±o%¤¢ ÏH¶«¬+¤+¥/¡C¢¨p¬¬+ ¤¢m¥>¡C£¯¬+/¬r¥>¬+¤+¥/¡C¢¨p¬¬+ ¤w®R« ¤Ü¨Ï
¬+ª: ¡
F Æ (99rÜ %ÈÂ F Æ 9 9+Ü gÈà
CA v U¡¬+ª:w >®C§K¬r¥/¬o¡®C¤% %£C¡C¦eÛmªC >¤ åz«w>³:¬r¥>p¡C £¬+ª:w£C%¡C¢q¬Uµ/´Ho¡Cv>´
¬+ª:§:¡Co¤£: ¤%£%¦o%¡^±>¥/§C%¢>´¬ªCm >®Cp¸ß¢ªC¥>¤¬¥/¬+¤q¸ ² ¢¡:¦¬ªCm£: ¡^¬+q¬Uµ)ÆjÇ ^È
¡¬+ª:w¥>®:®%¡C£Cq¸«v[¥>&¡ H¡C£¬ªC o¡^¬£C ¡:¢p¬Uµ/´H¥>¡^µ¡`§C2³ ¤ >´:§C¡Co¤£C ¤ £2%¦o%¡^±>¥/§C%¢
>´ Æ c CÈ £C¬ & 2Æ ? 9[à[à[à 9 ? È Õ & 2Æ ? 9[à[à @à 9 ? È ? !N 3 3 $ "
+ Æ ? 9[à[à[à 9 ? ÈÂ
N
N
N
!
N
zªC%¤
N Æ2? N È à[à à N Æ2? È !
²² à
& 2Æ ? N 9[à à[@à 9 ? ÈvÂ ²²
#
Æ ? N È à[à à Æ ? È
4 C
d d#bed + b e¢ w2£:£(p¡¬+ªC[¥>¢>´£C¬+%¤¨¡Cp¢¬+pÃ w2 ¥>¡½ >®C§K¬+¬ªC2%¤¤>¤b¸K®o¡C%¡`¬p¡¬+ª:
[¥/¢>´´¥/£C¡C¦rªC¥>¡C¡C%<²Û#¬ªH¥/¬ ¡C£×ÏH¡C>¬+~H¤¢¬z¬+ªC¥/¬
Æ (9 Y ÈÂ c(po¦ > > l > Y Æ RÈ +Æ S 9rMÃ O RÈ NIX N [ 4 R y N 4 S 4 Ã)à
M
Ç
8Kp¡C
{e/¬+\¬+ªH¥6¬
p¢m¡C£: ® ¡C£C%¡^¬b>´¿mÏ +ÆS 9rÃMO RÈ$Â + ÆãÃ(È+ÆSO R 9rÃ½È«¥/¡C£*¬ª`§C¢
Æ (9 Y ÈÂ c(o¦$Ò l > l > Y ÆRÈ+ÆS4O R 9 È NIX N [ 4 R y N 4 S y à
ÆSO R 9rÃ½È$Âß£C%¬6ÆØ ¾ È 3N E¸:® cÆSc ÃRÈ Õ ÆS c ÃRÈ à
¥>¡C£´ä>¤! Y Â ÏK¬ªC©¥/§C¢¢x¥>¡£:¢¬¤p³C§:¬+po¡zq¬+ª"%Z±/¥>¤x¥>¡: ~rÏ:«\[¥>¡"§C¢8¬+ªC\¤ ¢§Cp¬¢
´äo¤t¬ªC£C%¬ ¤¨¡:¢¬\ÃÉ ¥>¢\¬+¨ >¡C p§C£C
Æ (9 ÈvÂ c(>¦Ò b £C%¬ZÆØ ¾ ÄÆjÇvÄ gÈ 3N ri Õ È 3 e à
{e/¬+¡:¦2¬+ªH¥/¬ L+ £C%¬RÆ 8È 3 ¢z¥ o¡^±>¸¯´ä§C¡C¬+po¡ÙÏ:¬ªC¥>¤¦>§C%¡^¬mw§C¢ £*®C¤±Kpo§C¢pµ¬
¢ª:Z ¬ªH¥/¬0r Â ÆFÜ Z¶ÈjØ Á ¥Z¸:ppÌ %¢z¬ªC2§:¬+§C¥>Ñ¡:´äo¤¥6¬+>¡"¥>®C®Cp%¢z¬¥6¸K¨Ì%¡C¦ ¥>¢m« ãÏH¥>¡C£"«>³:¬r¥>p¡
ÆjEÇ K`È
Æ gÈvÂ c(>¦Ò l £C%¬ Z Ø ¾ Ä ¶%ÆjÇ«Ü Ä#gÈ Õ ] 3 y à
Û# %%¡`¬pµ o¨®C§:¬ ÏCo¡Cb«o§Cp£"¤%®C¤%¢ ¡^¬z¬+ª:8ß¢ªC¥>¤¬m%¦o%¡^±>¥/§C8£: ¡C¢p¬Uµ"¥/¢
¥ v¥>¡:£C ¤o¡:£C£C¬+ ¤p¡H¥>¡^¬[ÏmÆ §C¢j¬¥>¢2p¡|¬+ª:®C¤±go§C¢¢ ¬+po¡JÈÏ¥/¡C£»o¤¬ªCo¡C>¤¥>pÌ
¬+ª:ö¡C>¥>¢Ç 9 ? 9 ? R 9[à[à[à 9 ?! 3N ÏKzp¬+ª*¤%¢® ¬e¬¬ªC¡C¡: ¤m®C¤K£C§:%¬
3 3 $ ?Ñà
9
vÂ > 2Æ ?È ×2Æ ?È ? N 3 oÇ«Ä
?
ÁXN [ 4
ÛmªC2§Cq¬+p®Cp[¥/¬p±o"´¥>¬+o¤"®: 7>%£§:®âp¡ ¬+ªC½>¤¬+ª:o¡Co¤¥>pÌ ¥/¬+po¡4p¢¬+ª:±/¥>p§C(>´¬+ª:
¸K® ¬r¥/¬o¡*¡ ÆVEÇ K`È²
M ¢\³%´äo¤>Ï¬+ªC¤ ¢¬¤p%¬+po¡(>´ Y ¬+*©¥>§C¢¢x¥>¡£C¢j¬+¤p³C§:¬o¡C¢e¢e¢§C³o®:¬¥><ÏJ³C§:¬b¬+ªCp¢
rªCop ¥>£C¢t¬¢¨®C%¤t¸K®C¤ ¢¢o¡:¢ ²
b Ev 8\ 0Jeb0
E:G8L
|eªH¥/£¤%¥/1¤ 7>%£"¥/¬¬+ª:e³ ¦op¡C¡Cp¡C¦/´×¬+ª:e®C¤%±g>§C¢w¢ %¬o¡¨¬+ªH¥6¬v¬ªCb¥6¸K§C 2§K¬+§H¥>
¡K´äo¤¥/¬+po¡ªH¥/¢¬ªC¨[¥/¡C¡C¦>´[¥>®C¥> q¬UµzªC ¡)¬+ªCrªH¥>¡C¡: Ñ¢z¨ ö¤µg%¢¢%Ïã²þ/²pÏCzª: ¡
[¥/rª»§C¢/´m¬+ªCrªH¥>¡C¡C%t ¨®CpZµg¢¥>¡ ¡:£C ® ¡C£: ¡^¬¤ ¥>pÌ[¥/¬o¡ >´ ²(Ûmª:¢p¢¡C/¬¬+ª:
o¡Cqµ¯[¥>¢zªC%¡(¬+ªC¥Z¸:p2§C§:¬+§H¥/p¡:´äo¤¥/¬o¡"p¢¬ªC ¥>®H¥>%p¬Uµ¯>´¬+ªCrªH¥>¡C¡C%<² U¡
®H¥>¤j¬+p §C¥>¤ ÏKp´Ñ¬+ªC\®:¤g ¢¢¬ªH¥/¬z¦o%¡C ¤¥/¬+%F¢ ¢t%¤¦og£Cp>Ï:¬ªC ¡¯¬+gCÏK«[¥>¡*¥>rªCp%±>¤¥/¬+%¢
¥>¤³Cp¬¤+¥>¤pµ¨%o¢8¬+¬+ªC¥6¸K2§C 2§:¬§H¥>Ùp¡:´äo¤¥/¬o¡×²
U¡%o¡^¬+¤+¥/¢¬[Ï6´äo¤¬+ªCv[¥/¢v¡zªCrª ¢ÑrªCo¢ ¡2¤¥>¡C£C>qµ\¥/¬Ñ¬+ª:«³ ¦op¡C¡Cp¡C¦z>´H¥>p>¬+p
¥>¡C£¢ª: &£ :¸K £´äo¤#¥>^¬ªCw§C¢ ¢>´:¬+ªCtrªC¥>¡C¡C%<Ï>¬ªCw¥6¸K2§: 2§:¬+§C¥>`¡:´äo¤¥6¬+>¡p¢p¡
+
Ç
o¦ %¡C ¤¥>¡:>¬w%Ð`§H¥>J¬+¬ªCbrªC¥>¡C¡C%×[¥/®H¥> q¬Uµo²U¡¬+ªCp¢«¢ %¬o¡¨wzpC´äK%§C¢wo¡¢§Crª¯¥[¥>¢
zªC%¡(¬+ªC ¡^¬+¤ ¢e>´: ¥>¤<²Ý<²Ý£Ù²qÏJÌ ¤/ÍU¨[¥/¡( p¤ §:x¥>¤pµ"¢jµK¨¨%¬+¤ o¨®Cp¸©¥>§C¢¢x¥>¡:¢
zp¬ª"ÒmÓ O 2! # O R ÖJÂ ÇoÏ:¬ªC¢+¥>¨£C¢j¬+¤p³C§:¬o¡«ªH¥[±o¥>¡H¥>qµKÌ% £*¡¬ªC®C¤±Kpo§C¢¢%%¬+po¡Ù²
# a n h
U¡~¬ªC ¥>¢£C ¢ ¤p³%£»¥>³R±o>Ï#¬+ªC 8KªH¥>¡C¡:o¡ [¥/®H¥> q¬Uµ >´w¬ªCrªH¥/¡C¡C «¢Ì %¤ ªCR«%±> ¤
¢¥>p¬ªC¤¥/¬+¨w¥/¬¬ ¨®:¬¬( >2§:¡C ¥/¬+¥/¬[Ï¬+ªC%¤p¢¥)¡Co¡KÍÎÌ ¤(®C¤o³H¥>³Cpq¬Uµ(¬+ªH¥6¬
¬+ª:¤ ¥>pÌ £Q ¢p¡C[¥/®H¥>³Cp>´z¢§C®C®o¤¬¡C¦)p¬¡C(¥/¬¬ ¤ªCR po¡C¦¯w¬+¥7>o§C¤%K£:
%¡C¦>¬ªÙ² 7 ¡¬ªC>¬ªC ¤bªH¥>¡C£(>¡C2[¥/¡¬r¥> ¯7 ¥>³o§:¬\¥¨¬+¤+¥/£C >Ú|³%¬U« ¡ *?%.k%
)+*> ">@$2$.w
¥>¡C£¯¢§C®C®o¤¬+¥>³Cb¤+¥/¬>² b{ ¥/%pµoÏK¦op±> ¡¯¥¤+¥6¬+ 2ÏH¥/¡C£¯®R« ¤zÜÏ:o¡C\ ¥>¡ H ¡C£*Ü Ær9 ÜÈ
¢ §:rª*¬ªH¥/¬m´äo¤m¥/¡`µ¤+¥/¬8%¢¢t¬+ªC¥>¡ ¥>¡:£)¥/¡`µ &¬+ª: ¤E¸:p¢¬¢z¥%K£:\¢+¥/¬¢´ µgp¡C¦2¬+ªC\®Rw%¤
>¡C¢¬¤+¥>p¡`¬wÜË´äo¤zªCprª¬+ª:e%¤¤>¤«®C¤o³H¥>³:q¬Uµp¢«p ¢¢v¬ªH¥>¡ &\´ä>¤«¥/H³C§:¬w¥¢%¬«>´ÑÃ zªCo¢
¬+/¬r¥>Ù®:¤o³H¥/³Cpp¬Uµ¢m%¢¢m¬+ªC¥>¡*Ü Æ9rÜÈ
Ü Æ 9rÜÈ$Â ¡:´ 4Æ r 9; È ÆjÇ 6oÈ
X [
zªC%¤
wÆ r 9; ÈvÂßo¦£C¬6ÆØ ¾ }
Ä r Õ ÈEà
ÛmªCp¢e¥/®C®C¤o¥>rª)p¢t¬r¥ 7/ ¡*¡|Ó ( ÖÑ¡¯¥¢ppx¥>¤v®C¤>³C%)²
U¡â¬ªC¢¯¢ %¬o¡×Ï\¥>¢¯¡ ¬+ª: ®:¤%±gpo§C¢¯¢%%¬+po¡ßwzpb¬r¥ 7/½¬+ªC £C¢j¬+¤³C§:¬o¡ /j´ ¬+½³¢§Crª»¬+ªH¥/¬¬+ªC%¡^¬+¤p ¢>0´ ¥>¤¡C£C%®%¡C£C%¡`¬Ì% ¤/ÍU¨[¥>¡»©¥>§:¢¢¥>¡C¢%Ï[¥>rª»zp¬ª
¡:£C ® ¡C£: ¡^¬b¤[¥>Ù¥>¡C£*¥>¦o¡C¥>¤µ¨®H¥>¤j¬+¢mzp¬ª"±>¥/¤x¥/¡C Ç >åK²
2! = v wo¡C¢£C%¤e¶wÂ Ço² U¡¬+ª:¢[¥>¢>Ï×q¬¢ ¥>¤z¬+ªH¥/¬¬+ª:
r Â Ü ¢o®:¬¥><²«ÛmªC
o§:¬+¥>¦o\®C¤o³H¥>³:q¬Uµp¢t¬+ªC%¡
>¦v£:%¬6ÆäØ ¾ }Ä Ü Õ È Â o¦HÆjÇ«Ä4Ü Õ È 8Kp¡C Õ ¢¥ Rb¤+¥/¡C£Co'±/¥>¤x¥>³:8zp¬ª)å/·£C ¦>¤ %¢e/´´ä¤% £C> ¥>¡C£* ¥>¡)·gÏC« ¥>¡
>®C§K¬+\¬+ªCo§K¬r¥>¦o\®:¤o³H¥/³Cpp¬Uµ¥>¢
Ü Æ 9rÜÈÂ Î· 9RÆ «|Æäc·oÈ ÇZIÈ >Ü 9
ÆjÇ ( È
zªC%¤ Æ (9RÈ¢¬ªCp¡C o¨®Cp%¬+¨¦^¥>¨¥¯´ä§C¡:%¬+po¡ - 3N 3 4 ² %¬ 8ÆÜ 9 rÈ³¬+ª:
±/¥>§:\>´ ¬+ªH¥6¬z¢+¥/¬I¢ C ¢
"Æ ¨ÆBÜ 9; ÈwÞ ÈvÂ à
ÆjÇ È
p¦o§C¤ 62¢ªCRz¢ bÆãBÜ 9 rÈt¥/¢e¥2´ä§C¡:%¬+po¡¯>´#·´äo¤m±/¥>¤po§C¢w±/¥>p§C ¢z>´ e¥/¡C£Ü²
å\
/
/ 5
/
0 5
0
0 5
0
. 5
.
2
.
/
3
Æã¥^ÈtÜ Â \ £ %
4
01.
2
/
/
2
.
3
3
-
/
/
2
.
3
4
4
.
/
.
/
.
/
2
3
Æ£HÈzÜÂ Ç 6/£ %
4
01.
Æ ´rÈtÜ ÂËå 6/£ %
2
3
4
01.
2
3
4
01.
4
3
2
.
0
.
01.
Æ[ÈmÜ Âå \ £ %
Æ³HÈtÜ Â@6/£ %
01.
-
0
.
4
5
2
/
3
3
5
2
2
0
.
01.
Æ[ÈmÜ Â Ç \ £ %
4
/
-
0
.
.
5
/
2
. 5
.
2
3
/
.
2
/
3
4
01.
.
/
äÆ ¦`ÈtÜ Â \ £ %
ÆªHÈzÜÂ 6/£ %
6 + 7vQ>Sry )Y[T
0 cpaRitQ[Y[ijNXaZ_`SwQ[YRfP_^MES«aRc +YRO`k ry 'MEnrYRfPf×TV]`Y[T 6 + 87wNPS«TV]^M
]`n+aRNXWZiViV]^MEMESUSVhCTaZijO`Y[kTUMzTUacaRTViv]ûvM]`+4NqnjNP]2O`k`TV]^NqnrMzY[TUaZME_`k\TVY[CWRMEMfXahù iVaRNPKTry×Y[gL NPfPNXNXTVTã]`NqO8NPSMEfPYRMEnjSVS]2TVSU]`MrYRTÑO TV]ÊMwy nr#_^YRiVnjQR]¨MES#SVMrn+aRTiVaRiVcMESUnrhC_âZiVO`QRMEkHS }
NPOk^MESVn+MEOgk`NPO^W8aRijk^Mri}^TUa 01. 3N } 01. 3 R } 01. 3 } 01. 3 y
p¦o§C¤ 6AÛmªC jÍU ¥>®H¥>%p¬Uµ´ä>¤t¶Â Ç¥>¢z£C H¡C%£³^µ|ÆjÇ È²
åKÇ
{e>¬«¬ªH¥/¬#³`µ ¨¥ 6z¬ªCw£:¢¬¤p³C§:¬+po¡>´ j4¢Ñ¬+ªC«¢+¥>¨t¥>¢Ñ¬+ªC¥/¬$>´ j²Ûmªg§:¢ ÏHw[¥/¡)%o¡C p§C£C\¬+ªC¥/¬
´äo¤#§:¡Cp¬+¥>¤µ
Æqj0r j Õ ;9 È
ªH¥>¢¬+ªC«¢+¥>¨w£:¢¬¤p³C§:¬+po¡¥>¢ Æ4r 9; ÈE² %«µrªCgo¢p¡C¦kj ¬+e£Cx¥/¦oo¡H¥>pÌ% rß«t[¥/¡2¤%¢¬+¤¬
o§C¤z¥6¬¬+%¡^¬+>¡¯¬£:x¥>¦o>¡H¥>Wr²
ÛmªC¢µg¨%¬¤µ"p¡¬+ªC®C¤o³Cp ¢§C¦o¦o%¢¬+¢z¬+ª:´ä>Rzp¡C¦2 >¡ ¬+§C¤>²
acb 4d 4 ; B7"? = rU"%( ;6: 7 :<; A
Ü £C¥>¦JÆjÇ9[à[à[à 9[Ç 9 \ 9[à[à[à 9 \ È
Á 3 :<; A ( ; Â Ç9[à[à[à9¶ v `5 = lg ;6: 0!~BC$0)( ; $7 AC'7q6D!"%&)9CAz7 AC'7q ? " v v i!" &)|A
789 ; l!7or& #A ; n " = "o7 p !( =?= CA`78 v
M ¢t>¡Cb¢ªH¥>¤%¢«¬ªC8®Z« ¤« Ð`§H¥>ppµ³%¬U« %¡*ö¤¬¤+¥>¡C¢q¬¬ ¤¢%Ïg¬ªCbE¸K®%%¬r¥6¬+>¡>´ ¡: ¤ ¥>¢%¢ Ï³C§K¬\¬+ªC2¬+¥>p¢b>´vp¬¢8£Cp¢¬+¤³C§K¬+>¡£C%[¥[µ(´¥>¢j¬+ ¤%²Û¯p¡C¨Ì%\¬+ªC®C¤o³H¥>³:q¬Uµ
>´Ño§K¬r¥>¦o/Ï:o¡:bªH¥>¢«¬+2¥6¸K¨Ì%z¬ªC8®C¤o³H¥>³:q¬Uµ¥/¢¢w/´ ¬ªH¥/¬mp%¢v¬¬+ªCb¤¦>ª`¬w>´¬+ª:
¤+¥6¬+\>´¡^¬+%¤ ¢j¬[² Î´#o¡C¢mp¡`¬ ¤ ¢¬ £*¡*¥>rªCp%±g¡:¦¨¤¥/¬+%¢zªC¦oª: ¤t¬+ªC¥>¡*¬ªÇK® %¬+¥/¬+po¡¯>´
2 Ïo¬+ªC%¡q¬¥\7> ¢¢ ¡C¢¬§:¢e¥¢¥/:¡`§C³%¤v/´¬¤+¥>¡C¢q¬¬ ¤¢$¬\¬r¥7/e¥/£:±/¥>¡^¬r¥>¦oz>´¬+ª:
¢pR £C ¥[µ¯>´¬ªC¬+¥>p¢m>´¬ªC£C¢j¬+¤p³C§:¬o¡¯>´ ² 7 ´$ >§C¤¢>ÏJ¬+ªC o¤¤%¢®o¡C£Cp¡C¦>§:¬r¥>¦>
®C¤o³H¥>³Cpq¬Uµzp×¢j¬+p×³x¥>¤¦oÆäx¥>¤¦o ¤t¬ªH¥>¡ RN ÏH¢+¥[µ:È²
2! = v wo¡C¢£C%¤(· Â Ç>² ßp¬ªË¬+ªC~ o¡ %%¬§C¤ ¥>³R±o/Ïp¬)¢§ % ¢½¬+À o¨®C§:¬
ÆãÜ6¶ÈVØ Á 9 ´ä>¤«¥/K±/¥>p§C ¢>´¶ #gp´¬+ªC¥>¬+§H¥>H¡`§C³%¤v/´×¬+¤¥>¡C¢q¬¬+%¤¢p¢ Ï^¢+¥[µ>Ï
ÙÏR¬ªC ¡¬+ªC>§:¬r¥>¦>$®C¤>³H¥>³Cpp¬Uµzzp>³$¬+ª:p¡C2§: >´`¬+ªC®C¤o³H¥>³Cpq¬+%¢H´äo¤Ù¶Â Ç 9[à[à[à 9Ù²
M ¢\p¡½á¸:¥>®: ( «¢%2¬+ªH¥/¬ Õ ¢b¥ R¢j¬r¥/¬¢¬zp¬+ª åZ¶e£: ¦o¤ ¢\/´v´ä¤ %£Co ¥/¡C£
¨[¥>¡"¶EÏC¬+ª`§C¢
EÆãÜ 6¶ÈjØ Á 9; Þ 8Â Æä¶;9¶%Æ( v|Æä¶c È ÇZÈ1/ÜÈ à
p¦o§C¤ ( ¢ªCRz¢¬ªC¢£Cp¢¬+¤³C§K¬+>¡ ´äo¤\±/¥>¤o§C¢±/¥>§: ¢>´w¶¥>¡:£ Ü|² Î¬p¢% ¥>¤´ä¤o ¬+ª:
H¦o§:¤e¬ªH¥/¬«x¥>¤¦oz¶®%¤´äo¤¢v³¬¬ ¤t¥6¬wpZ ¥>¡C£¢¥/H¶® ¤´ä>¤¨¢«³%¬¬+ ¤w¥/¬tª:¦oª 2Ï:p¡
7>% ®Cp¡C¦zq¬+ª¬+ªC >¡ ¬+§C¤>² M ¢v¡á¸:¥>®: Ï`¬ 8ÆÜ 9 rÈ$³z¬+ªCz±/¥>§:/´ Ë¢¥/¬+p¢´ µg¡:¦
ÆãÜ 6¶ÈjØ Á 9; Þ Â à
ÆjÇ ^È
p¦o§C¤ ¢ªCRz¢ 8ÆBÜ 9 rÈ±g¢ ²#¶´äo¤±>¥/¤>§C¢±/¥>p§C ¢>éÜ ¥>¡C£ ² J>¤¬+ª:"¢¥> 2±>¥/§C%¢
>¡C¢p£C ¤ £¡(¬ªC H¦o§C¤>ÏÙ§:¢¡:¦)¥/#¥R±/¥>px¥>³:¬+¤+¥/¡C¢¨p¬¬+ ¤¢bp¢\¥>pw¥[µg¢\³¬¬+%¤8¬+ªH¥/¡½§C¢p¡C¦
¥¢§C³:¢%¬ ²
åoå
01.
01.
01.
3N
01.
3N
01.
3R
01.
3
.
3R
01.
3
3R
01.
3
.
. 5
0
0 5
/
/ 5
ÆäRÈmÜ Â Ç \ £ %
-
.
0
/
-
ÆäRÈmÜ Âå \ £ %
2
5
01.
3
/
2
3
4
. 5
0
Æ³JÈtÜ Â/6/£ %
.
0
0 5
/
3N
01.
3R
01.
3
/
Æ£JÈmÜ Â Ç 6/£ %
2
-
3N
01.
3R
01.
3
.
0
01. 01.
.
.
01. 3
3N
3R
3
01.
01. 01.
01.
01. 3N
01.
3R
01.
01. 01.
. 4
3N
01.
01.
. 3
Æã¥oÈtÜ Â \ £ %
01. 01.
. 2
. /
01.
/
2
-
Æä´+ÈtÜ Âå 66£ %
5
3
3N
01.
3R
01.
3
.
2
/
3
4
01.
Æ ¦`ÈtÜÂ \ £ %
ÆªJÈmÜ Â 6/£ %
+ 7 Á =eQ>SryßcaRitQ Y[ijNPaZ_`SQ[YRfP_^MES«aRc+YROgk y #YRnj]SUMrT«aRc#nr_îVQRMES
n+NPO2aRiVTViV]^MEMzSUhCaRaZiO`k^kgMrSCiTUaRacTVNP]Ô`Mn+iV+|MEYRNPSVO`NqO^k`W\NPnrY[SV]`TUMEY[ktiVhgCO`MEMEfXa%SVu*Sr}oNXTUTra yL~NXTV]g} NPOw}MEYRnj}]b2^SU} MrTr} }[TV]^} MÑ/nr} _îV}QR:>ME} Sn+aRiVYRiVO`MESUk hCaZO`kHy }
0 / -
5 3
4
¦o§:¤ ( .=8p¢¬+¤³C§K¬+>¡>´ ÆÜFZ¶ÈjØ Á 9; ´äo¤m·Â Ço²
å
01.
01..
0
. 4
. 2
. -
. 3
. 2
. /
. 0
.
/
2
.
3
4
/
Æã¥^ÈtÜ Â \ £ %
01.
.
/
2
3
4
Æ[ÈmÜ Â Ç \ £ %
01.
. 5
.
2
/
/
2
.
3
4
01.
.
/
2
3
4
01.
.
/
2
3
4
.
01.
/
Æ ´rÈtÜ ÂËå 6/£ %
2
3
4
01.
.
/
2
3
4
01.
/
0
.
5
2
-
Æ£HÈzÜÂ Ç 6/£ %
3
5
.
Æ³HÈtÜ Â@6/£ %
4
0
.
01.
Æ[ÈmÜ Âå \ £ %
3
/
3
-
0
2
2
5
.
/
/ 5
/
0 5
0
. 5
.
/
.
-
0 5
0
2
. /
.
0
äÆ ¦`ÈtÜ Â \ £ %
ÆªHÈzÜÂ 6/£ %
6 + 7tQoSry tcaRizQ[Y[ijNXaZ_`SQ YRfP_`MESmaRc + YRO`k ry 'MEnrYRfPfTV]`Y[T 6 + 87zNPSmTV]^M]`NXWZ]^MESUT
ijn+Y[aRTUiVMiVMEcSUaRhCizaZOùvkg]`SJNqnjTU]atTVTV]^]^M*M+~aZ_^NqTVO`Y[k`WRNPMnrY[h`TUiVMEaRkegCY[MEgfXNqafPu(NXT¨NXTriVy×MEL~dYRNXTVNPO`]gSmNPOzfPMEMESVYRStn]\TV]`SUYRMrTÙO TVE]^y M#nr_`YRiVnjQR])MESÙSUMrn+TzaRiVaRiVc$MESUnrhC_âZiVO`QRMEkHS }
NPOk^MESVn+MEOgk`NPO^W8aRijk^Mri}^TUa 01. 3N } 01. 3 R } 01. 3 } 01. 3 y
p¦o§C¤ ÛmªC jÍU ¥>®H¥>%p¬Uµ´ä>¤m·Â ÇoÏJ¥>¢z£C H¡C%£³^µ ÆjÇ ^È²
åK
'GgKJez EBL(L
wo¡C¢£C%¤\¡CR
0Jbe0E:G8L
"¥ ¡`§C2³ ¤\/´v¬¤+¥>¡:¢¨p¬¬ ¤¢ ÏÙ¢¥Rµ ÏÑ[¥>rª½zq¬+ª½¶z¬+¤+¥/¡C¢¨p¬¬+¡:¦"¥>¡^¬+%¡C¡H¥>¢%Ï
¥>¡C£[¥>rª"¢§C³ ¬m¬+¥®R« ¤t%o¡C¢¬¤+¥>p¡^¬mÜ²$ÛmªC ¤8¢w¥¢p¡C¦ope¤ %p±> ¤wzq¬+ª·¥>¡^¬+%¡C¡H¥>¢%²
ÛmªC¤% q±o%£)¢¦o¡H¥/Ù¹»¢m¦oq±o%¡)³^µ
¿ ² N "!
¹ Â Ó N à[à[à Ö% ² # Ä Å
¿ zªC%¤¿ p¢¬ªC¢¦o¡C¥>¬+¤+¥/¡C¢¨p¬¬+ £ ³^µ¬+ªC ¬+¤¥>¡C¢¨p¬¬+%¤ ÏÅ ¢©¥/§C¢¢x¥>¡|¡Co¢¥/¢
¡ÆVÇZÈEÏ/¥>¡Ci£ Ï Â Ç 9[à[à à 9 ¥>¤v·×Ê«¶Ù%o¨®CE¸\¥/¬+¤ %¢ ²|«¥/¢¢§:¬+ªC¥/¬Ñ¬+ªC¤% %p±o%¤
7`¡CRz¢\¥>pÑ¬ªCi Ý¢ ÏÙ¥/¡C£)¬ªH¥/¬b¬ªC ¢ªH¥[±>2¡C£: ® ¡C£C%¡^¬\ p¤ §:x¥>¤pµ"¢jµK¨¨%¬+¤ >®Cp¸
©¥>§C¢¢x¥>¡ ¡^¬¤%¢/´8Ì %¤| ¥>¡À¥/¡C£4§:¡Cp¬±/¥>¤¥>¡C%>²ÀÛmª:)2§:p¬+p§C¢%¤[¥>®H¥/ p¬Uµ~´äo¤¬+ªCp¢
>2§:¡C ¥/¬+po¡8¢% ¡H¥/¤z ¥>¡³%±/¥>p§H¥/¬ £[¥>¢qµb³^µ\E¸:®:>¬¡C¦t¬ªC¡H¥/¬+§:¤>´g¬+ªC¢o§K¬+>¡
¬+ ¬+ªC)¢p¡C¦o¯§C¢ ¤¢ %¡H¥>¤p~£Cp¢%§C¢¢ £ß¥>³R±o>² {b¥/%pµoÏw¢¡: )¬ªC ¥>®H¥>%p¬Uµ ¥>rª:%±gp¡C¦
£Cp¢¬+¤³C§K¬+>¡´ä>¤¬ªC¢¡:¦oz§C¢ ¤w¢ %¡H¥>¤pµg%£C¢v¥>¡<²Ý<²Ý£Ù²o¢o§:¬o¡´äo¤[¥/rª"¥>¡^¬+%¡C¡H¥:Ï`¬+ªH¥6¬
¬+ª:)§C¢ ¤¢¡ ¬+ª:)2§:p¬+p§C¢%¤¢% ¡H¥>¤ [¥>¡:¡C>¬ go®%¤+¥/¬¯³% o¨ ¢¨¨¥6¬+ ¤x¥>ã² M ¤+¥/¬
±o%%¬o¤2Æ N 9[à à[@à 9È«zpÙ³¥>rª:%±/¥>³:\p´
!×Þ F Æ· 9;¶ 9%¯Ü;È 9 ´ä>¤z¥> Â Ç 9[à à[à 9
!
N
zªC%¤Æ N 9[à[à @à 9
PÈvp¢«¬+ª:8o¤£: ¤p¡C¦/´¬+ªC8¤¥/¬+±o%%¬+>¤w´ä¤o ¬ªC8x¥/¤¦o%¢¬v¬+¬ªC8¢¥>pqÍ
¢j¬[Ï¥>¡:£ F Æ (99rÜÈ¢¬+ªC¢¡:¦o¨§C¢%¤ ¤ % q±o ¤ ¬¤+¥>¡C¢q¬¬ ¤[¥>®H¥/ p¬Uµ §C¡:£C ¤2®Rw%¤
>¡C¢¬¤+¥>p¡`¬Ü²
8\ GÑ~ LK8
ÛmªC§C¢ /´2§:p¬+p®C¥>¡^¬+%¡C¡H¥>¢"zpb¦o¤[¥/¬pµ4¡C%¤ ¥>¢½¬+ª:|¥/rªC±>¥/³C(¤¥/¬+%¢¯o¡ ´¥>£C¡:¦
rªH¥>¡:¡C p¢\p´$¬ªCrªH¥>¡C¡: $®H¥/¤+¥>¨%¬ ¤¢b[¥>¡½³2 ¢j¬+p¥/¬ £½¥6¬8¬+ªC¤ % q±o ¤¥/¡C£½p´¬ªC2®H¥/¬ª
¦^¥>p¡C¢¨³¬Uw% ¡ß£CpÚ ¤ ¡^¬"¥/¡`¬ ¡C¡C¥ ®H¥>¤¢³ ªC¥R±>½¡C£: ® ¡C£C%¡^¬+pµ>²ËÛmªC¢ %o¡C£ >´\¬ªC ¢
¤%Ð`§C¤ ¨ ¡^¬+¢«[¥>¡³¬«zq¬+ª¨¤%x¥/¬p±o[¥/¢8¥/¡C£p¢v¢o¨%zªH¥/¬«¬+%rªC¡C ¥>J¡¨¡H¥/¬§C¤/²ÛmªC
H¤¢¬m¤ Ð`§C¤ ¨ ¡^¬tp¢t¥¤¥/¬+ª: ¤«¬+¥>Jo¤£C ¤%ÏC¥>¡:£"[¥>¡³ §C¢j¬+ H £p¡ %¤¬+¥>¡ o¨2§C¡Cp[¥/¬o¡
¢% ¡H¥/¤>¢t¥>¡C£¡C>¬w¡¨>¬+ªC%¤¢%² 8g¡C%¬ªCbo¤¦op¡H¥>:z¤p¬¡C¦>´Ù¬ªC¢v>¡Co¦o¤¥>®Cªp¡¥/¬+Ç K
¥>¡C£[¥>¤pµ¯Ç 6KÏ`¬+ªC%¤bªC¥>¢w³ %¡¢o¨zwoI¤ 7¡zª:rª¬ªCb¥/¢¢§:®:¬o¡>´Ù¬ªC8¥[±/¥>¥>³Cpp¬Uµ
>´rªH¥>¡C¡: ¢¬+¥/¬+½p¡:´äo¤¥/¬o¡ p¢"¤%®Cx¥>% £ zp¬ª ¬+ªC ¥>¢¢§C¨®:¬+po¡ß>´¥ ¢Rzpµ4±/¥>¤µg¡:¦
rªH¥>¡:¡C ãÏH¢ >²Ý¦C²qÏÓ Ö<²
å6
E«e\ 4
b d * * o" 5QC$
: ln$;678" ; $!( N 9 à[à[à@9 ; AE7 ; $ ; Atu = > "o7A C(< 67 7 ; " v v >
UÆ2?È # Æ2?È 4 Æ ?ÈÂ'&'! # 9
!
= Q7
Æ2v ? N È à[à[à N Æ2v ? È "!
N
& Æ2? N 9[à[à[à 9 ? ÈÂ v
v #
Æ2? N È à[à[à Æ2? È
$0 Æ2? N 9[à[à à@9 ? ÈÂ3& Æ2? N [9 à[à à@9 ? È Õ & Æ2? N 9[à à[à@9 ? È v C$
> £C¬ Æ2? [9 à[à à@9 ? È Æ2? ÈÂ Æ c ÄßÇZÈ:£C%¬ Æ 3N Æ2? N 9[à[à à 9 ? 3 N È à ÆjÇ ^È
4
N
W:)+**KYX%¬\Æ ?ÈÂ Ó N Æ ?È;9[à[à[à 9 Æ2?ÈVÖÕ+²ÛmªC%¡¯¬ªCÆ1[ 9qg ÈV¬ª p ¨ ¡^¬m>´4 Æ ? N 9 à[à[à@9;? Èvp¢
\Æ2? !äÈjÕ\Æ2? ÈE²|{e/¬+¬+ªH¥/¬-\Æ2?ÈÕ\Æ2?È Æ ?È\Â ¥>¡C£ -\Æ2?È\Æ ?ÈjÕ 4 Æ2?È\Â Ø ² %«µ
¬+ª:£: H¡Cq¬+# po¡¯>´#¬ªC£C%¬ ¤p¡H¥>¡^¬ 4
:£ %¬ZÆ Æ2? N 9[à[à[à 9;? ÈÈÂ Æ cÇZÈ X [ ! N \Æ2? !È Õ \Æ ? " È
zªC%¤«¬ªCv¢§C ¢ÑR±o%¤$¥>po® ¤§:¬r¥/¬o¡:¢">´ 9`Ç 9[à[à[à9 :`²e%¬#§C¢¢ ®C¥>¤+¥/¬«¬ªC«¢§C¨¥/¬o¡
R±o%¤ p¡`¬ ¢§C¥/¬o¡C¢%Ï×¬+ª:o¢´äo¤8zªCprª # Â 9Ï (Â Ç 9[à[à à 9 Ï#¥/¡C£|%o¡C¢£C%¤ ¥>rª
¢§: p¡|¬§C¤¡Ù²Ho¤¬+ªC ¢§C*Ï Â Ç 9[à[à @à 9 |cÇoÏ # Â ´ä>`¤
Â ² Ho¤¢§Crª ¥>¡ «[¥>¡|£C C¡C ß¥>¢ !zÂ 8!w´äom¤ [Â 9 Ï$¥>¡C£ # Â q² {>¬+¨¬+ªH¥/¬ ¤+¥/¡C¦o ¢R±o ¤2¥>
® ¤§:¬r¥/¬o¡:¢m>1´ 9`Ç 9[à[à[à 9 c Ç :¥>¡C£¯¬+ªH¥/¬z® ¤[Æ #Èw£CqÚ×%¤¢m´ä¤o ®%¤RÆ $Èw³^µÇo²
Æ cÇZÈ X [ ! \Æ ?3!È Õ \2Æ ? " È
N
Â KÆ cÇRÈ X [ ! # \Æ ?3! È Õ \Æ ? " È \Æ ? # È Õ \Æ ? È \Æ ? È Õ \2Æ ? È
Â c Æ cÇZÈ X [ ! # \Æ ?3! È Õ \2Æ ? " È \Æ ? # È Õ \Æ ? È \Æ ? È Õ \2Æ ? Èà
U¡^¬+%¦o¤+¥/¬¡C¦R±o%¤ ? ÏJ¥>¡C£¯¤%[¥>p¡:¦ -\2Æ ?È \Æ ?ÈjÕ 4 2Æ ?ÈÂØ Ï
>
KÆ cÇZÈ X [ ! \Æ ?3! È Õ \2Æ ? " È 4 Æ ? ÈÂ c Æ cÇZÈ X [ ! 3N \Æ ?3!äÈ Õ \2Æ ? " È
N
N
Â c(£:%¬6Æ 3N Æ ? N 9[à[à[à 9 ? 3N ÈÈ
å(
8KCÏ6¬+ªCw o¡^¬+¤³C§K¬+>¡>Ć¬ªC H¤¢¬ cÇw¢§:¢¬e¬ªCt¡^¬ ¦o¤¥>`¡"ÆVÇ ^ÈÑ¢Sc2Æ cÇZÈ:£C%¬RÆ 3N È²
Ho¤m¬+ªCx¥/¢¬¢§C Â ²$=8 H¡C »¥>¢ !ÑÂ8!#´äo¤ [ Â ² M ¢³´äo¤ ¤¥>¡C¦o%¢bR±o%¤e¬+ª:
® ¤§:¬r¥/¬o¡:¢m>´1`9 Ç9[à[à[à9 c Ç `: ÏC³C§K¬e¡:ZË®%¤RÆ ÈÂâ®%¤RÆ È²
KÆ cÇRÈ X [ ! N \Æ2? !È Õ \Æ ? " ÈÂ ÆKcÇZÈ X [ ! 3N N \Æ ?3!È Õ \Æ2? " È \Æ ? È Õ \Æ2? ÈEà
U¡^¬+%¦o¤+¥/¬¡C¦R±o%¤ ? ÏJ¥>¡C£¯¤%[¥>p¡:¦ - \Æ2?È Õ \Æ ?È 4 Æ2?ÈÂ ½Ï
>
KÆ cÇRÈ X [ ! N \Æ2? !äÈ Õ \Æ ? " È 4 Æ ? ÈÂ+ ÆKcÇZÈ X [ ! 3N N \Æ2? !È Õ \Æ2? " È
Â â£C¬6Æ 3N Æ ? N 9[à à[à@9 ? 3N ÈÈ
+
M ¡:£(¢CÏH¬ªC%o¡^¬+¤p³C§:¬o¡*>´$¬ªC¥>¢¬e¢§: ¬¬ªCp¡^¬+ ¦>¤+¥>Ñ¡~ÆjÇ ^Èzp¢ â£C¬ZÆ 3N ÈE²mÛmªC
¤%¢§Cq¬¡CRË´äopRz¢t³^µ*¥>£C£Cp¡C¦2¬+ª:¬U«%o¡^¬+¤³C§:¬o¡:¢ ²
$ G Ev E HfEvb0 L
×«o§Cp£p 7>¬¬ªH¥>¡ 7 8² ze¥>¡Cpµ>Ï b² ¥/Rz¢%Ï :² ¥/Ì CÏ M ² 7 ¤q¬+I¢ 7`µ>Ï =2²RÛm¢w¥/¡C£ M ²Z µg¡C%¤
´äo¤mªC%®:´ä§:Ù o¨¨ ¡^¬+¢¥>¡C£*£Cp¢ §:¢¢po¡C¢%²
dE8E« E«\ EBL
ÓXÇ Ö ²w©²w©¥>¥>¦o ¤%Ï ;# *), .45*#
W( *);# !d 24">@:*,j,j?A#(5h1.45*#H² {%
voI¤ 7
>oªC¡¯ß
µ 8Ko¡C¢%ÏÇ ( :²
ÓÝå6Ö M ²zÛ\² o¥>%¢ Ï =8¢¬¤p³C§:¬+po¡C¢">´¥6¬+¤P¸ ±/¥>¤x¥/¬ ¢*¥>¡C£âx¥/¬ ¡^¬)¤g>¬+¢¯£C%¤p±> £â´ä¤o
¡Co¤¥>¢+¥>¨®C%¢ Ï 0#(# Z=*K .$(, .45h1 .k.4=.45h =ÏC±ooã² 6KÏC®:®Ù² K 60 6 \ ÇoÏÇ ( KC²
Ó Ö M ²zá£C p¥/¡ÙÏ :%#('2? = # !:*# !$.45*#0?A, >)+=Q*Kf# !%*, .4)5h =² ª =
¬+ªC%¢¢%Ï =8%®H¥>¤j¬+¨ ¡^¬v>´ ¥/¬ªC ¥/¬ ¢%Ï ¥>¢¢¥>rª`§C¢¬¬B¢ U¡C¢¬p¬+§K¬+>´ÙÛ rªC¡:oo¦/µoÏ t¥>Í
³C¤p£C¦o>!Ï M ÏÇ :²
Ó K>&Ö r² 8²J©\¤+¥/£C¢ª^¬+µg¡¥>¡:q£ r"² |(² mµgÌ ªC 7#Ï ">@i*K$#(.o5)1Z= %W);5 = S# ! W:)+*@!?(h. =² {%
vo1¤ 7 M ¥>£C%p&
¤ ¢¢ Ï o¤¤ ¬+%£¥>¡:£)%¡Cx¥>¤¦o £¯%£Ù²pÏÑÇ \ ²
Ó 66'Ö :²` ² 8Kpp±o%¤¢j¬+ p¡Ù
Ï 8g¬+¤o¡C¦ wo¡^±o ¤¦o ¡: >´Ù¬ªC8á¨®C¤[¥/ =8¢j¬+¤p³C§:¬o¡>´Ñáp¦o ¡^±/¥>qÍ
§C ¢>´ Ñ¥>¤¦> =8p%¡C¢po¡H¥> ¥>¡C£:o(
¥/¬+¤% ¢ Ï *)(*?A);# *K+t?%2.4$')4.o+0# 2 ==Ï
±ooã² 6 6KÏC®:® Ç%Í :Ï×Ç 6K²
å
Ó ( Ök²\z² 7 Ì[¥>¤ZÏ 8² 8KªC¥>¥/<Ïo¥/¡C£ M ² =2²6 µg¡C%¤ Ï IU¡:´ä>¤¥/¬+po¡¬ªC >¤%¬« o¡C¢£C%¤+¥/¬o¡:¢
´äo¤ p§C¥>¤8ö³Cp2¤¥>£C:Ï v)I#v=@%h.w5*#v=<*# %5h?A) 6 h %# **16ÏÙ±o><² K Ï
®C®Ù² 60 :Ï"¥[µ½Ç KC²
Ó Ö %b² zegrª^t¥>p£~¥/¡C£|Û\4² ² ¥/¤Ì ¬¬+¥:Ï t¥>®H¥>%p¬Uµ½/´m¥">³Cp22§Cq¬+®:ÍU¥>¡^¬+%¡C¡H¥%oÍ
2§C¡Cp[¥/¬o¡2p¡ 7¡¥ ¥[µKp p¦oªJ¥/¬jÍÎ´¥>£Cp¡C¦\ ¡^±g¤o¡C¨ ¡^¬[Ï ¬+¥>®C®[¥>¤p¡ )I#v=
%h.w5*#v=*# # *);, .w5*# W( *)6²
å

Download Report

Capacity of Multi-antenna Gaussian Channels DI

Paperzz.com

Your Paperzz