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Properties of Random Direction Models

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(1)Properties of Random Direction Models Philippe Nain, Don Towsley, Benyuan Liu, Zhen Liu. To cite this version: Philippe Nain, Don Towsley, Benyuan Liu, Zhen Liu. Properties of Random Direction Models. RR5284, INRIA. 2004, pp.25. �inria-00070716�. HAL Id: inria-00070716 https://hal.inria.fr/inria-00070716 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Properties of Random Direction Models Philippe Nain — Don Towsley — Benyuan Liu — Zhen Liu. N° 5284 July 2004. ISSN 0249-6399. ISRN INRIA/RR--5284--FR+ENG. Thème COM. apport de recherche.

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(37)   ‡‰Š. TVUˆY/Xœlf~fYs‡fpqep~?YsoHgipqksrD‡mgwl=gwU?YV© vwrD}ryvwlDnˆoˆ~Xœlf~fYs‡ê±•giUˆYQlmo?‡c~fp :YsvwYsokYQšYBp‰o?޳giUr•g giU?YV~fpviYjk®gwp‰lmo Dl ›gwU?YXœlDšˆp‰‡Ype=viYB DYBvweiYB~Šr•›ÍgiYBv&U?p‰ghgwp‰o?ŽŠrœšlmn?oˆ~?rDvicm«P¾¸› giU?YXGlmš?p‡‰YU?p‰gwe³rœšlmn?oˆ~?rDvicr•g gwp‰XœY0>t± gwU?Ysof > 4w±?pžgte&~fpviYjk®gwp‰lmorygQgwp‰XœYE>t±?pqe&einˆktUŠgiUˆrygZfi7> 4d"™OLf >\O 4w« adpXœp‰‡qryv gwl=gwU?YV© vwrD}[rDvilmn?oˆ~Xœlf~fYB‡+±y©QYVrDewehn?XœY/giUˆryg giU?YVš2YsUˆr¡ dplDvly›ˆgwU?YVXœlDš?p‡‰YVpqeŽDl• DYBvioˆYB~ šdc$gwU?Y^Xœl• DYsXœYBomgV}ˆryghgiYBviQo !qC7 2\W2}r<4}D«5¹ Y^viYB}?vwYBeiYsoHg/gwU?Yezgtr•gwY§lD›KgwU?YXœlDš?p‡‰Y^pogwU?YXœlf~fYs‡ © p‰giU¢vwY¼ˆYjk®gwp‰lmoˆeVšdc$giU?Y mYBkgilD“v q–  7> 4

(38) 2}f   > 4

(39) 4i±© pžgwU –   > 4Pš2Yspo?ŽœgwU?Y‡‰lfkBr•giplDoly›giU?YXœlmš?p‰‡Yr•g gwp‰XœEY >) 1ˆ« #=l•©/YB DYsvj±yn?oˆ‡‰pªDY gwU?Y&© vtry}$ryvwlDnˆoˆ~Xœlf~fYB‡+±mgiU?YBviY³~fldYBe5o?lDgPY fpqezgQrehpXœ}?‡‰Y=Y f}?vwYBewehplDoG‡‰pªDD Y C+‚ F ›¥lm˜v f   > 4i« TVU?YPrD}?}?vwlmrmktU§©QY5© p‡‰‡m›¥lD‡‡‰l•©gil³klDXœ}?n?giY gwU?YPehgwrygiplDoˆrDvic§~fpehgivwpš?nfgiplDolDV› t–   > 4

(40) 2f  7> 44 © p‡‡VkslDoˆeipqezgj± ¶ˆvwehgB±Pp‰oŸYBehgwryšˆ‡‰pqehUˆp‰o?Ž r¦vwYs‡qr•gwp‰lmoˆeiU?p‰}­šYsgz©/YBYso¤gwU?Y© vwrD}­ryvwlDn?o~µXœld~?Ys‡ ryoˆ~¤giU?Y Xœlf~fYB‡§© p‰giURviYs¼ˆYBkgiplDoˆe C,eiYsY YBXGX$rº‚f'« &GF®±³ryoˆ~ giU?YBo<© p‡‰‡^nˆeiY7gwU?YvwYBein?‡‰gweŠlDšfgtrypo?YB~ ›¥lDvŠgiU?Y ›¥lmviXœYBvQXœlf~fYB@‡ C,eiYsYadYjk®gwp‰lmo  « ‚ F gwl$~fYs mYs‡lD}viYjehn?‡‰gweQ›¥lmvVgiU?Y‡qr•gigiYBv XGlf~fYB@‡ C,eiYsYafYBk®gwp‰lmo  «  F®« 6. 6. . zL{. }Š“ i‚˜FŠ‚ƒ4„d . „?ƒ‡)ˆSŠS‹†„=ŠH‹†ƒ H

(41) }‡‰Š†Œ]‡P‹SFŽ. TVUˆY[vwYBein?‡‰g^š2Ys‡l•©™Yjezgtryš?‡peiU?Yje³r¢eip‰Xœ}?‡Y[}r•giUd© pqehYGvwYs‡qr•giplDoehU?p}¦š2Ygz©QYsYBo7gwU?Yœ© vwrD}ryvwlDnˆoˆ~7ryo~ vwY¼YBk®gwp‰lmoŠXœlf~fYB‡eB« ” !#"%$ '&#(!)   ’ ÅÂdÂ(ºÅ “•” *£”?“ Æ ( Ç ” ( Ç“ Â,+ –D’ &¥Æ-( Æ Ç Â ,‘/. / ° . . . F. 0 N )  4

(42) qy +=)  4   `t–  7> 4

(43) 2}f  7> 44} ! )*+1 +#1 >>ix( 59+ &(%+C+   `tC   2\W  2}r   4}& % +1  )*,)*+=)    & ' W U,243  ' +=hN +4 ! '& %(0 4   `t–65‰ > 4

(44) 2f5P > 4

(45) 4} ! )*+#1 +1  : 4x  : ,+ &(%+C+   !tC 5 2\W7 5 2r

(46)  5 4}& % +#1  )*9)*+C) <  & ' W85U hN 91 +#1(+@&3+1! )  K  5 " K  W85 " W  ; # : r- 5 "lr   %     3 % W85U "]W U ; # 2=<  +1  >!#  : +#1 >>ix( 59+ &(%+C+    `tC 5 2$W85 2}r- 5 4   `tC   2\W  2}r   4}  %

(47) ;&(%+#1 ! ) 8)  ,+=) '  ?>  &9+ +1<+ +1   &> +1 .4A@)   )* +#1  

(48) qy +=)  > )    !#$(+=! )  +1 E=&'  8+1  4A@)   )* +1  ! '& i(>4 2 < 8+#1 

(49) ?%+C) % –   > 4 " B ## –63L)5 O€ > –64 2 )5  > 4

(50) 4

(51) 2 13 ; B”#j–6B )5  > 4‰G 3 ; # C F f   > 4 " B fOLp5 f  5 > 4

(52)  >2 4

(53) 2 1

(54) 3 ; B”#–6BD)5 –  5> 4, > G 4,G 3 ; #3 2 C7J<F 1( ?. +. =" >. ËËÖ LNMHOHPQ. 1. +1.  . +1. . $C1<<? % .   >@? 1. 2. D.

(55) ,%!$H $ )   ) . . %)*.       4 2 : ÀHnˆr•gwp‰lmoˆe5C F^ryoˆ~AC7JF³givwp‰ dpqry‡‡‰c¦U?lD‡q~7›¥lmvry‡‡@>E? 1Šp‰›VgiU?YBc7U?lm‡~°r•g " ¢1 ›¥vwlDX giU?Y~?Y¶ˆo?p‰giplDoµlD› YBrDktUµXœlf~fYB‡/ryo~ ›¥vilmXgwU?YrDewein?Xœ}fgiplDo giUr•ggwU?YAXœlDšˆp‰‡YApoµgiU?Y. >. vwY¼YBk®gwp‰lmoŠXœlf~fYB‡ ry‡©Qr¡cfeQXœl• DYBe/gz© pqkYrmeP›,rmezg=rmeQgiU?YXœlmš?p‰‡Y^p‰ogwU?Y© vwrD}rDvilmn?oˆ~XGlf~fYB‡+« zL{.  ` „?Œ] mŽ  S„  † Sƒ‡, “Fƒ. ¹ YA›¥lfksnˆelmo°giU?Y›¥lD‡‡‰l•© po?Ž7ÀHn?YBehgiplDo 8[n?o~fYsv[© Uˆr•gœklDo~fpžgwp‰lmoˆepo¤Ysp‰giUˆYsvgwU?Y© vtry}¤rDvilmn?oˆ~ lDv vwY¼YBk®gwp‰lmo¦Xœlf~fYs‡5pqe³giU?Y$Xœlmš?p‰‡YGYBÀHnˆry‡‡c{‡‰pªDYB‡‰c¢gwlš2Y$r•gryodc{}2lmeipžgwp‰lmo¦pAo / 12;3<4

(56) <TVU?YG›¥lm‡‰‡l•© p‰oˆŽ ‡YsXœX$r$ehgwr•gwYBeVgwUˆr•g&p‰› giU?YXœlmš?p‰‡Ypqe YBÀHnˆrD‡‰‡c‡p‰ªmYs‡cAgwl$šYrDoHcd© U?YBviY^po / 1N23<4Pry g >," 1ˆ±fgiUˆYso Xœl• mYsXœYsoHgV}ˆr•gigiYsvw€o C  2$W  2}r    }?vwYBeiYsvw DYBePgiUˆpe&ryg >@?A1?« ” !  $ ^“  ‘  “ ?”f’ &¥

(57) Æ ( Æ  (&¸Æ “ Ç & ‘B’s“ &  ’ &¥-Æ ( ‘ . / ° 9$. . . %.   h(5;+#1(+0+#1 ;)*,)*+=)    & ' W U  #+#1 ;>,@ )  B) > ' % +#1 ;>ix( : ,+ &3+=+=   C7<2$W2}ri )   +  )*,)  +=) 2 <  t–w71 4,GD2 2}f4 1 4d" f 4?"s2 ; #  <  2 X  1N23 0 f X !O 3 23i : +1   2  t– > 4,GD2 2}f4 > 4?" f 4d" # D %    2 X 712;3 : f X !O 3 23 % >@? 1 2. TVU?Y³}?vwlHlD› ly› KYsXœX$r[‚f«Ø‚^vwYs‡p‰Yje lmo$giU?Y=›¥lD‡‡‰l•© po?ŽgwYBktU?oˆpkBry‡2‡‰YBXGX$rˆ±mgwUˆr•gQ©/Y³© p‰‡‡2nˆehY§ehYB DYBvwrD‡ gwp‰XœYje p‰oŠgiUˆY^›¥lD‡‡‰l•© po?Žˆ« ¾¸gte }?vwlHlD›pqeVŽDp DYBoŠpogiU?Y ˜ }?}YBoˆ~fp I« ” ! $ ^“ Æ *  “j’ ÃÆ  ’   +Æ Æ “  ( –D’ &¥-Æ ( . / ° . ?6. . . .  <. . 2 X. . / 1N23. 0.  X OH[ 2h[A4 : E U ‘4 !

(58) gw O 0!

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(60) 2f 144Kpqe n?oˆpž›¥lmviXœ‡cG~fpqehgivwp‰š?n?giYB~œl• mYs v / 12;3<4&%A !O 3 2\gD3iH±•©/YV¶oˆ~œ›¥vwlDX C,„ F5rDoˆ~ YBXœXœr[‚f«  gwUˆr•g E 3 2  . . 4. . 4.  t–w7> 4,G”2 }2 f7> 4?" f 4?" # U ‘7 '!jgwf!W U >dO™0!

(61) gwf!W U >-3GD2˜(")!o" #. C* F. ›¥lmvE1€B >jG C E Z/lDoˆeipq~fYsvo?l•© giUˆYA~fpehgivwpš?nfgiplDo°lD›mq–wtC E 4 2}fqC E 4

(62) 4i«afp‰oˆksYAftC E 4H" f71 4qr E šdc ~?Y¶ˆo?p‰giplDo°lD›PgiUˆY$© vwrD} rDvilmn?oˆ~XGlf~fYB‡+±©/Y$eiYsYG›¥vwlDX C,„ F=giUr•g–wqC E 4Z" –w 14FgMf 14qr E W E C E O 0 –w 14’g—f4 1 4-r E W E C E 3H«7Z/lmoˆ~fp‰giplDo?po?Ž7lmM o t–w71 4

(63) 2f 144w± ryoˆ~ nˆeip‰oˆŽ¦ryŽHrypogwU?Yrmeiein?Xœ}fgiplDo°gwUˆr•g gwU?pqeŠ}rypvŠlD›vi feŠpen?o?p‰›¥lDvwXœ‡‰c ~?pehgivwp‰šˆnfgiYj~ l• DYB"v / 12;3<4$% !O 3 2\gD3m±V©/Y¦¶ˆoˆ~I±^eip‰Xœp‡rDvi‡³gilŸgiU?Y ~?Ysvwp‰ •r•gwp‰lmoŠlD%› C * F®±?giUˆryg  t–wqC˜EG4‰G2 2}fqC˜E 4d" f 4?"M2 ; #?« É¥ÊË ÉÍÌ.

(64) '& +=)  % )*

(65)  +C) %. J. . TVU?pqeeiU?l•©&e³giUˆrygRt–w7 > 4

(66) 2f > 4

(67) 4&pe^n?oˆpž›¥lmviXœ‡c~fpqezgwvipš?nfgwYB~l• DYBv5/ 12;3<4 %— !O 3 2\Dg 3 ›¥lDvrD‡‰‡ 1 B TB C E «¤TVU?Y}?vwldly›&pqe[kslDoˆks‡‰nˆ~?YB~µgwU?vwlDn?ŽmUµgiU?YŠ›¥lD‡‡l•© p‰o?Žp‰o~fnˆk®gwp‰lmoŸrDviŽmn?XœYsoHg;8rmeiein?XœYAgwUˆr•g gwU?Ynˆo?pž›¥lmviX ~fpqehgivwp‰š?n?giplDoµU?lm‡~?e›¥lDv 1—B >B CVb=rDoˆ~°‡‰Ysg[nˆeGeiU?l•© giUˆryg[p‰gGehgip‡‰‡QU?lD‡q~?e›¥lDv 1—B >QB C b N E•« adpoˆkY”t–wqC b 4

(68) 2ftC b 44œpen?o?p‰›¥lDvwXG‡c£~fpqezgwvipš?nfgwYB~£l• mYsvK/ 1234 % !O 32hgD3i¢›¥vwlDX giU?Y poˆ~fnk®giplDoUHcd}2lygwU?YBeipe/ryoˆ~ehpoˆkYHftC b N GE 4="MfqC b 4qr b N E šdc$~fYs¶ˆo?p‰giplDoAlD›IgiU?Y³© vwrD}AryvwlDn?oˆ~œXœlf~fYB‡+± ©QYksrDovwYs}ˆvilf~fnˆksY=gwU?Yryory‡cdeipqeVp‰o)C* F/gil$eiU?l•© gwUˆr•gq–w > 4 2}f7 > 44Ppqe n?o?p‰›¥lDvwXœ‡‰c~fpqezgwvipš?nfgwYB~l• DYBv / 12;3<4 %M !O 32hD g 3iŠ ›¥lDvrD‡‰‡ > X / C b 2}C b N E ¸«<TVU?YsvwY›¥lmviYm±PgwU?Y7n?oˆpž›¥lmviX ~fpehgivwpš?nfgiplDoU?lm‡~ˆeœ›¥lDvArD‡‰‡ > X / 1N2}C b N E ¸±?© U?pqktUkslDXœ}?‡YgiYjeQgiU?Y}ˆvildly›z« >. ¹ YUˆr¡ DY§gwU?Y^›¥lD‡‡‰l•© po?Žœklmvilm‡‰‡qryvwc 8 Æ “ Æ ,”f“ à !#" <  @ A@  

(69) S  FF. .  )  $ (9)  . .

(70) ". 4 ). >.  ) ,  + +=)      +  $  )  += ) @ (+ '  %. h. +1. 1. . :.  &. L. hx. &.  (,) % D $ )  +C )@ (+    +#1  (,)*+)*,+    / 1N23<4 ! )*+#15 ,   $ 0 )  +1  $ > ( )*0 &   9+  $  ' 1 +1   : +1   +1  $ %  

(71) D  > ? 1 2 (,)*+#)*9+=    ! )*+ 1 ,   $  )  $% )9+ %+C) %    . . ix. hx. ¾¿o¢gwU?Yo?Y Hg§ehYjk®giplDo¢©QY}?vwl• Hpq~fYklmoˆ~fp‰giplDoˆe&n?oˆ~fYBv&© U?pqktU¢giU?Y xzlmp‰oHg=~fpqehgivwp‰š?n?giplDo{ly› }2lmeipžgwp‰lmo rDoˆ~~fp‰vwYBkgiplDoly›5rGXGlmš?p‡‰Y^pqe n?o?p‰›¥lDvwX l• DYBvE/ 1N23<4 rDoˆ~k `O 32hgD3im«   ^ 

(72) sŠF 6b¢

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(83) 2 . X *, . 4

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(85)  +1  ' &(+C) x +Cix(#+=)*5H K E 2}K 6 %&%&%    %ix     ! 1   \" % X  +1 

(86) +1 +=x #+=)*: K\ )  +     '  . \ K    K %  4    KhQ" E K\% 4‘’ h" % 4 2 3 K\i% 4}& : :

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(88)  j(+-, 0  $45)*0 $  &   9+@ &N  : )*  &0 ,+B   +1 ( hh(x;: Wh+#1(2ri+ 2 \i 2 3 :\( +#1  (h(: +1<%+ +1  &N    \i % W2rii& 

(89) 

(90) (+-,   $ )* &0 ,+ 2 !1 :?+=+ >(h( &+C) % : +   +1   ! )*+1 (h( &+C) %  : )* &+ ) +1<%+     0 W  2}r    %

(91)  @%+#1  %ixK 91()*N 2   +  % &% , 4m"   $N ER" % ,  " % 4 : %"2&% , X  @  +1   

(92)  +  &   -W 2}r + %o r ,  4d" -W $N E X +,2r $N EZ" &A@,@ )  )*+=$>+C )*+=)   .+1   %: r , W  "]W 2}r  " r 4 : + X *, Y 4 : W Xx Y 91(: ,r )*2} r , X `O 32hDg  3i : +#1 8&9A@A@)  )*+=$ +C % )*+=)  <  # +1 E %x 1<)* W  2}r    2 ! 1   : +#1  &9A@A@)  )*+=$ +C% )*+=) !<      2D4   +1   %ix 1<%)*      !  )*+ H7  !#"#"   D4d% " $ & . )54  -W 2}r + %Q r ,  4   % % , 4 C&j‚F r 2&% 4 X  :  * " ) %#+ %^ r ,  %s % ,  ! )*+1  ) 2+ 4 X *, / 12hA [ 4 % Y 4: % <   " qK 2$W 2}, r , X !O 3 2\Dg 3i 2 <  +1 @&(% +C) & ?0 '  ! 1    " 3 +#1 +=i(x +=)*: K\ %

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(94)  : + 2 <     )*,  ) " 0  )   # ++#1   )*+ ,+=)  ! 1  @+1  +@ ) ?,@H' =&'(B)  ' (,+ A@  2  (:@+#1(+ +1   N  .   & '( 0 

(95) /+=) (%)*

(96)  +=) N 

(97) . (+ ,<  $)*0 &   9+$ % 1<%)* : ! )*+1 &A@A @)  )*+=$ +=N )*+C) % <  .0/  , 4 + #1  , 4 : 

(98)  &  +C)  $ 2 !1  

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(101)  q  W \W qr r  D4d"%$ &  )54 .2/ -W$W , 4  #1 qrr , 4  % &% 0 ™"#) % W ,  %Q r ,  %Q % ,  X *,  4 2 x. ,. i. x.  h. . ix. 4. 3è QíÑ¡Ü+ì¡Ð®Ùõ¡×+ÔtÓØÑ¡õ¡Ö¡ÙØÓØï¡ÓØÙØÝhÓÞz×ÍÔw܍ë§×ê×+Ó éí Ò¡ÞÞÞhÝzÔtÔtЮÚ+ÚêÖ¡ì¡ÚêìjÚ+Ü+×êÞ í Ôt×+ÖsÑjÐ ×0×ê?¸ÓØÞFЮß:EjÖjÌ7ÓØÚÚ,×GÑ¡ÚêìAD ÙÕÔt@VÝzÓØÚ ÞzÝhï ÓØ×+ÞzҕÖЮÔwÖ× ×Ýz46×êЮ58Ò¡Ö¡7:Þzï¡90Ü,7ÓÞ/×+ÓØîIÞFЮEBÖ³ÞÓØÚ+Ôtæ‰×+Ð®ÙØÚÜ+Ü:ÞhÔ/Ôt×êÒ¡ïjÑDÓØëQÞ¿Ú ×+ôBí Ó ×êÖjÞPÞhÐiÔtîÚêÚêÞ¿ìj×I×êÜ+ҕÞH<J8ÔwKj×+×2ÐQÎ•Ó ×2ÑHõyÒ¡ßLÞCÔtJB¡Ú:OAÖ¡Ô5JFÓ Mf×êì¡ÞCÚêÖ¡ìjD <Ó Ý¸;sÒ§Ôtì¡Ö¡Þ ×+ï&Ò•ÓØÖsÔw×êét×Ò¡ÔtÞz×+Ü+Ü,Ò¡ÓÕÞ¿ÔtÞ æÖЮÞF×IÜ,EjÞ5í ÑyæÞzЮÞhÝ¿ÔtÜ ×êÚêÞzÔtìjïÖ=Ü+>Þ Ü,ÓØÖsÞz=‰×+ì¡étì¡ÔtÑVÜ,Ü+Ö^ÓÕ×êÔtÐPÖ×êÐÔ× ×êÒ¡ÓØÚ ÑyÞ¿×êÓ ×+Þ ÚêÞ¿×KÓØÚ ì¡Ö¡Ó æ‰Ð®Ü+í Ù ë&õyЮì¡Ö¡ïjÞhï+H<J8KjΡø Ò¡ÞzЮÜ+ÞzíNJ8Kjß Kjß<J®ÎjÑHß OPOPKMÍß. É¥ÊË ÉÍÌ.

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(104) O % +1<%+ +1   

(105) (+q,<  $ )*  &0 ,+ " ,)*+ 

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(107) 'N )H@ ' 0  &   ) ) 2 !1  

(108) %

(109)  : ' 91  +1  1 )*+ R(,)&N )*7x % ) ,+@%) '+= ) @ (+C) % :  0+  @ $ . :   0 : 

(110) H & +=) x( $ 2   8+#1 H (h( &+C) % : +#1   %x <1 %)*     )   &   )  %) : L

(111) )* 

(112) 'N )@H  0 %  )    &( 

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(116) Y " 0 2  W     )*) ) B% )* ) )   &0N!  + 1   D h)*;x +-, : +=! ) )*+# 15! %1  

(117) 4 +1 E&9,+;@,@  )   )*& +C$ '%()   +C )@) (+C0) % 

(118) 'i(%,+  A#@ , )*+   >h&(5 + 8+=+#)1( + )* '( +1   + Y ) )*'#,)*+  2 3  &+? 7+#1   5 (h( &+C) % % +#1  +Cix(D+C)*5 :  ?%+C) x  %)*

(119)  +=)  0  4 x )*9: ,+@&N   H( )* =) " ,@ix( 2 : !1   +1 0 %x 1<%)*      ) >'& ) ) : L

(120) )* 

(121) 'N )@H 4% %  )  

(122)  &( 

(123) 9+ : % 1<  R(,)&N )*7x % ) ,+&A@A@)  )*+=$ 5'(h(  

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(125)  ) 4

(126)  +%4   tr 4   % 4 [ 4

(127) 4 : W X *‰ Y 4 : r X `O 32\Dg 3 : % X  2  %

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(129) 2}f4 > 4

(130) 2T7> 44 gtryªdpo?Ž¢ ¡rD‡‰nˆYBepo giU?YeiYg  " / 12;3<4 %w `O 32\gD3 %±© UˆYsvwYT > 4  "†  7> 4

(131) 2+P > 4

(132) 2r17> 4

(133) 2  > 44w« |&YBksrD‡‰‡ygiUˆryg˜–w > 4ˆpqe:gwU?Y }2lmeipžgwp‰lmo§lD›mgwU?Y XœlDšˆp‰‡YPr•gIgwp‰XœY@>,C¥Žmp‰ mYso^po C¥„ F

(134) FIryo~Hf4 > 4ˆpqeIgwU?Y5lDvwp‰YBoHgwr•gwp‰lmo lD›KgwU?YXœlDš?p‡‰YrygVgipXGYE> C,eiYsY5Cê‚FF«Q\³šˆeiYsvw DY=giUˆryg“   > 4}  pqe&r$]{ryvwªDl• œ}?vwlfkYBeweB«. ËËÖ LNMHOHPQ.

(135) j‹. ,%!$H $ )   ) . &. %)*. ³Y¶ˆoˆY   " “qC4<4=giU?YehgwrygiYAlD›VgiU?YeicfezgwYsX r•ggwp‰XœTY C7y± oˆryXœYB‡‰cm± o"q2 2f&2 <4i«{TVU?Y oˆY dg&viYjehnˆ‡žg&eiU?l•©&e/giUˆryg giU?Y}?vwlfkYjeieH po?U?Ysvwp‰gweQgiUˆY]{ryvwªDl• dpqryoehgivwnˆk®gwn?vwY§lD›‰ iy« / °”  #"%$ ^“ Æ ”? & & ’ à ’B“•” ( ‘ & ’ &¥

(136) Æ ( )Â “ (K Æ “  . A. . 6. . . . F. F. &9+=)    & ) 5 %ix 91()*    X *,  4 : %) x  @ $   / E4d" ‘Z 2

(137) g—f`W&KAO™0 2jgwf!WK+3 r 2&% 4 :  " %   a" q2 2}fN2& 4 X "! )*+1 €" tK 2\W 2}, 

(138) 2) 2+%4 X *,/ 1N234 % / 12hA [ 4 % Y 4 : r , X `O 32hDg 3i : %.    (h(   4 : X :. . . :. ! )*+1. &9,@,@ )  *) +C$. +C% )*+=) . < . . C&  F X

(139) 2f , "sfir ,    D4

(140) %w f ,q % ) % + %w r ,t % %-,  ! )*+#1 , X  :  ™"#) % + % r ,  % % ,  2 D. TVUˆY§}ˆvildly›ly› YBXGX$r  «'&^peVŽmp‰ mYsop‰ogwU?Y ˜ }?}2Yso~fp I« TVU?Y¢vwYBehg$ly›&gwU?pe$eiYBkgiplDoºpeœ~fYB DlDgiYB~­gilgiUˆY7klDXœ}?n?gwr•gwp‰lmo­lD›=giUˆY‡pXGp‰gipo?޵~fpqezgwvipš?nfgwp‰lmoŸlD› i “7> 4}  « !QYs‡l•©<pqeQgiUˆYXœrDp‰o¢vwYBein?‡‰gVlD›KgwU?pe=ehYjk®giplDo 8 ^“ Æ * Æ ‘ & ’ &¥-Æ ( !" $  & & ’ &#( Ç & ‘s’B“ &  K’ &,

(141) Æ (£Æ  i “7> 4}  . .   h(5. iN )@ . L

(142) )* 

(143) '. ). . #,)*+  2 . + +. !1   :. . . +#1 K %ixI 91()*     ix K  " U  

(144) 3PO + / 12

(145) > 4 % Y % `O 32\gD3 %  4" >. \. +1<%+ =) "   ( &9+=) N-  1( ? :  )*) " : 0- )*)*) " + 1 0 > &  +=' C+  (+=)*:. +1 E )* )*+C)*  % ) 1)  @ $. :. . 6. x. h. )  =+  )@ (+=) . i “7> 4}.  .  +#1 D  &; . ?>)  + . . ). '& ) ). %. s„. C& F. : )8  )* &0. ,+ .+#1. . . )*,)*+=) . !  & % r ,  %Q % ,  44 " > C&jF        > 4 X  4?" # K U 3LO + / 12

(146) > 4 % + Q %    J" / 12 ! 4 %j f ,  %:/ 12K , 4 % + %j r ,  %j % ,  : ! )*+1 f , 2r , X ` O 32\gD3 : % , X  : ! X  12;3 D : K , ? 1 : + X *, Y 4 2. ˜ ~fpviYjk®g klmoˆeiYBÀHn?YsokYQly›u5vwlD}2lmeip‰giplDo « &QpqegiUˆryg poœezgwYBrD~?cm·¿ehgwr•gwY gwU?YVXGlmš?p‡‰YVpqeYjÀHnˆry‡‡‰c‡pªDYs‡c gwlœšYrDoHcd© U?YBviY§po)/ 12;3<4w±f© pžgwUYjÀHnˆry‡‡‰c‡‰pªD YB‡‰cAlmvipYsoHgtr•giplDoes«5]¢lDvwY^}?vwYBkpqeiYs‡c 8 ^“ Æ * Æ ‘ & ’ &¥-Æ ( ! $ (&¸Æ “ Ç & ‘s’B“ &  K’ &¥-Æ ( Æ  Æ –m”f’ &,

(147) Æ ( ” ( Ç Ç & “  –y’ &¥

(148) Æ ( .   h(5. iN )@ . L

(149) )* 

(150) '. !1   :. % . . . . +#1 K %iI x 91()*   K ix  %) x   )*   "#" )  ,)*+  2 !     t–w7> 4,G !,2}f7> 4?"Mf 4=" # f X `O 32\Dg 3 :  %,$4)*,)*+=)  ,&(  )*+C) % % %)*

(151)  +=)  2. \. +1<%+ =) "   ( &9+=) N-  1( ? :  )*) " : 0- )*)*) " + 1 0 > &  +=' C+  (+=)*:. ! X 712;3. %. F. ). . '& ) ). %. C&; F. D. É¥ÊË ÉÍÌ.

(152) '& +=)  % )*

(153)  +C) %.   . . '&3( )*+=) . . 2. *. & &. . ˆlDv&ry‡‡ ! X  1N23¸± f X !O 32hgD3iH±D©QYUˆr¡ DY³›¥vilmX C &¡F -. !       t– > 4,G !,2}f4 > 4?"sf 4 " # K. .   

(154)  . !. U 

(155) 3LO+/ 1N2

(156) > 4 % Y %Q r1 % %  44 " >. " # K U  3LO +  / 12

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(167) '& +=)  % )*

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(169)  3LO+/ 1N2

(170) > 4 % + % r ,  % % ,  4

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(172)   ‡‰ŠŒ]‡L‹ZFŽ. Z/lmoˆeip~fYBvGr¦viYs¼ˆYBkgiplDo¤Xœlf~fYB‡Q© p‰giUŸgiUˆYŠXœl• DYBXœYsoHg[ mYBk®gwlDvT  " tK  2$W  2r  2  4Š© p‰giUºezgtr•giY ie }ˆrmkY   " / 12\[ 4 % Y %Q `O 32hgD3i % «V¹YGrDewehn?XœY^gwUˆr•gj   ew r•gipqeh ¶ˆYBe³ rDew ehn?Xœ}fgwp‰lmoˆe 6" « KYg  7> 4"†q–  7> 4

(173) 2}f   > 4 2  qC 4

(174) 2  7> 4

(175) 2}r  7> 4

(176) 2   > 4

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(178) 5 2 5 4}  © p‰giU[ezgtr•giYQeh}rDkY 5 '" / 12\[ 4 % Y ; #(%S `O 32\gD3 % ¬© U?pqktUeirygipqez¶ˆYjermeiei n?Xœ}fgwp‰lm oˆe 6  " rD oˆ~ ehnktU gwUˆr•g³}ˆr•gwUH© pqei“Y K  5 "JK   ’± W85 " W  ; #?± r- 5 "Jr   ryoˆ~  5 "   ›¥lmv=ry‡’‡ o 3 C,einˆktU7r$kslDoˆehgivwnˆk®gwp‰lmo pqerD‡‰©Vr¡cfe=}2lmewehpš?‡GY F« Ysg  5 š2YœgiU?YœgwU?YApoH •rDvipqryoHg^}?vilmšˆryšˆp‰‡pžgzc¦XGYjrDein?vwYGlD›/gwU?Y]{rDviªml• ¢ktUrypo  5 &•« KYg K 5 " U  

(179) 3LO 5  / 12 > 4 %€3 ; # 4 Y % `O 32\gD3 % 4

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(181) Æ ( ”f“ Ã Æ  &  ‘œ  )”  &,Æ “ . . . . . . . +. . . . .  -. . &. . . . . 6. . . . .   h(5. . . . F. A5  . ) 7 &   )  %) % L

(182) )* 

(183) 'N  )@  :  +1 K?> & +   ix(+=)*: K !1   : !  Cꂕ„ F         > 4 X  4=" # K 5 U 

(184) 3LO 5 / 1N2

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