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Towards dynamic randomized algorithms in computational geometry

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(1)Towards dynamic randomized algorithms in computational geometry Monique Teillaud. To cite this version: Monique Teillaud. Towards dynamic randomized algorithms in computational geometry. [Research Report] RR-1727, INRIA. 1992. �inria-00076966�. HAL Id: inria-00076966 https://hal.inria.fr/inria-00076966 Submitted on 29 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..

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(54)  K '*, XK_.983[$7  NB sb1A- %$wr(;1AQ($9Y2;3[‡O  K#K(.6Y: 35- F4(35|: M O A3[(/3[ *8D#TK‹.AQ82;34 0X B *( E\Ž#=_+* gGSH-C 243[n‡O X(|_ .N3[ /34 7$_ -.9A-(3/*1ˆ*=.` 0' >.{K35!*LGB €.?C‰"(;F>C M .24356x88.`0-3[9 >3*, % .10 M O?: -(? * K'(=I/# B * ^=(S[ %*,.9( x!  !* ]B (Y=(-.`. s‚ ƒB .`(3*$9 *) ]FH * M 3EK'(q= >.rfjd%htsYu@0KU(/3[\$NF4(#- GA-3[N >3[G243[p# B I/- M '*= >.?.1 lˆ: 243[K v3TK *(# $ M \$O d`efjd1g In: G: =$0 K_.b3[$C9 35Z-(- `A- 1A- ˆ3[*2;3[_x8(.<*,(3QS[ -..`(3#.j= ƒ243[y ,*=.  $ >3[wK(/3#S[(7~K(35-(3/* M (Q-  M F4(Q- *\=( M 8.9('* M G.5SˆC$bk. n„v q ¢l’ qAp h q tsx{n„v q=05q= o.1 ?EC- K_\3[- K '*_: wK(3[j *w‰!* $9(7-.`CJ*,0#A >3[= ˆ3*,   %-.yG: #(C'*m M %B $ * $ ,*g)_9 #- ,* M L1A zT

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(56)  L  E (E   E^. . 2%g ")(+C,")(!%

(57) 1

(58)  : l . 11'11111111111111111111'1111111'11111111111111111111'1111111'11111{v*x q h – m pPq x}¥„x}-v  11111'1111111'11111111111111111111'1111111'1111  ’5wytumozrxÄn p vWj5n„wyx

(59) h – zPm  x p vWmsh p  111111111111111'111111'11111111111111111111'1111111'1111111111{1 v•wµn‘ton{Ajl•hPzP’5w q  ~  ƒ 111111111111111111111'111111'11111111111111111111'1111111  ’8wytsm”zrx{n p zrmov q n p wyx  11111111'1111111'1111111'1111111111111'1111111'1111111111111²1 w}n{-zrm p n‘tum q Ÿ  h – n­vWx q ] •h„¢!~  ƒ 1111111111111'1111111'1111111'1111111111111'1111111'•1 jlhb¢5n{¢lmstum q Ÿ h – n p xi x prq  "! 111111'1111111111111'1111111'1  n q k`x  n q mow}n{tlx}|Pj5x{w q n q muh p h – n3‚n p zPh  „ n‘•m”n‘¢ltux

(60). (*)(-' A%$C)  & (')+*,.-/102 111^¤lm p m q n{tsmowµv 1'1111111111111'1111111'1111111'1111111111111ox}tux  x pPq v!h –3

(61) tux q•q x}-%v 4 (52(6798:1;< 1'11 11'11111111111111111111'1111111'11111²j5hbm pPq vAh =– > hbAh„¢ #*x{w q v ? (@A 111«¤lm p w}n{jlm q n‘t‡m q n‘tumow}v 111111111'1111111'111111RvWm  jltumowyx{v!hb4•x}¥„msh p vy¤l¢lm”wlw²tsx{v'111 B ¤ CE¤ D <¤ EA¤ 111411111111111111'1111111'1111111ivWx q vh – hb¢ #*xÄw q v²¤l•x}¥„msh p vy¤l¢lm”w lw²tsx{'v 111 #.

(62) rm. klx – hbtutsh Am p ¥ p h q n q muh p v Amstut@¢5xE’5vWx{z q k`•hb’`¥bklh„’ q q klmov q k`x{vWm”v \

(63) klx Amstut@¢5x zrx 5p x{zm p fixÄw q muh p e \" n p z  5k n‘j q x} \. 1 11111'1111111111111'1111111'1111111'1111111111111'1111111'1111}’ p m ix}‚vWx@h – h„¢ #*x{w q v 111'1111111111111'1111111'1111111'1111111111111'1111111'1111111{’ p mix}-v*x@h – •xµ¥bmsh p v B 11'1111111'11111111111111111111'111111'11111111111111111111PvWx q h – h„¢ #*x{w q v B B 1111111111111'1111111'1111111'1}1 v*x q h – n‘tut!vW’l¢5v*x q vAh – B h – w}n‘‚zrm p n{tsm q †  n q4 h v q

(64) D~ B ƒ 111'111111'11111111111111111111'1111111'111111-1 vWx q h – n{tst‡•xµ¥bmsh p vAzrx 8p x{z¢, B B ~ @ ƒ 1111'1111111'1111111111111111 v*x q h – n‘tst‡h„¢ #*x{w q vh – B m p wyh p. mow q Am q kg•xµ¥bmsh p @ D µ~ B ƒ 11111'11111111111111111111'1111111'111i1 v*x q h – n‘tut‡•x}¥„msh p vh – D~ B ƒh – Am”z q k D {~ B ƒ 1111111'111111'11111111111111111111 vWx q h – n‘tut‡•x}¥„msh p vh – D~ B ƒ"h – Amoz q k D  ~ B ƒ 1'1111111'1111111111111111{1 vWx q h – n{tst‡x}¥bmuh p vAh – D µ~ B ƒ<zrx 8p x{z ¢ * h„¢ #*x{w q v D  ~ B ƒ 1111111111111111'111111'1-1 vWx q h – n{tst‡•xµ¥bmsh p vh – D µ~ B ƒ<zrx 8p x{z ¢ * h„¢ #*x{w q v  {~ ' B ƒ 111111'111111111111111W1 x}|Pj5x{w q n q muh p h –  D ²~ C ƒ  – h„AC  B h – w}n‘‚zrm p n‘tsm q  '   ~ ' B ƒ 111111111111111111}1 xµ|rj5x{w q n q msh p h –  D  ~ C ƒ  – h„AC  B h – w}n‘‚zrm p n‘tsm q  '  ~ ') B ƒ#1111111'1111111'1111111111111'1111111'11111  n{|rm  ’  h –  ~ '  B ƒ – hb '  ' EA~ B ƒ 111111111111'1111111'1111111'1111111111111'111R1 vWx q h – n{tst‡¢lm”wl w²tsx{vzrx 8p x{z¢, B E µ~ B ƒ 1111111111111111'111111'1111111111111b1 v*x q h – n{tst ¢lmow` wytux{vCh – EA~ B ƒh – Am”z q k \\ 11'1111111111111}1 n p z h q klx} p h q n q msh p v – h„A¢lmow` wytux{vv*m  muton‘ q h q klx w}n„vWx3h – x}¥bmuh p v D. .

(65) 

(66)  .

(67) e. 

(68)  .  h  jl’ q n q muh p n{t 4x}h  x q & n‘m  vCn q zrxÄvWms¥ p m p ¥Œn p zn p n{t }m p ¥3n{ts¥„hb•m q k  v – h„Av*hbt Pm p ¥ ¥„x}h  x q •m”wYjlhb¢ltux  v \`URq m”vYnŒ•x{w²x prq  x}tozh – q klx}h„•x q mow}n{t!wyh  jl’ q xµ4v•wymux p wyxi¤ q k5n q k8nbv £i’lmow Pt ­zrxixµtshbj5x{z†vWm p wyx

(69) m q  ‚v q n‘j`j xÄn‘•xÄz m p \ UÀ\ fik5n  hiv' q k`x{vWm”v  fik5n Š%$ ! m p "µ_ Š%$ \ klm”v zrx ixµtshbj  x pPq k5nbvn‘tsx{nbz;•x{n„wÀklxÄz n klmu¥bktuxix}t4h – v*hbjlk`mov q mow}n q muh p ¤ q k8n q v*h  x q m  xÄvAwyton{m  vAx ix p hbx    t  q klx q klx}hbx q m”w}n‘t nbvWj5x{w q h –Aq klx  x}toz (m p h„-zrxµ q hŒhb¢ q n‘m p n p h„j q m  n‘t wyh  jltux}|rm q b¤{m q< n Œ¢ x p xÄwyx{v•vn‘& q hŒzrx{v*ms¥ p ixµ ­wyh  jltsm”w}n q x{z n{ts¥bh„•m q k  v²¤r’5v*m p ¥†zln q n­v q ’5w q ’l•x{v Ak`hivWx m  j`tsx  x pPq n q m h p movAzrm )gwy’`t q}\ klh„’l¥bk q klxŒw²h pPq •mu¢l’ q msh p h – vW’5w-k x{vWx{n{-w-klx{vAmovY¢5x ih p zEn‘tut"£i’lx{v q muh p ¤5m q wµn p ¢5x ’5v*x – ’lt ¤ – •h  q m  x q h q m  xi¤ q h q nixn p m prq x}•x{v q m pO h„•xŒ•xÄn‘tsm”v q mow3n„vWj5x{w q v \:U q mov

(70) n‘tut q klx  h„•x q •’`xŒnbv4m q n‘tov*h Pmsx}t”zlvAn qq -n„w q m ix q klx}hbx q m”w}n‘t‡j`•hb¢`tsx  v²¤5n p z q klx  x q klhPz`v n{•xŒv q mutst‡•mu¥bh„•hb’8v \ klm”vYn{jljltumsx{v q h­-n p zrh  m }x{zgn{ts¥bh„•m q k  v²¤lm pPq hPzr’5wyx{zgm pq klx  x}t”z ¢ Œ\ "\  ton{ `vWh p m p "}_ $b‰   ton $„‰ ! \ k`xv q ’5,z Eh –4q klm”v rm p z h – £i’lx{v q msh p v@k5nbv

(71) jl•h Ž ¥„•x{vvWm ixµt m prq x}•x{v q x{z q klx3x{vWx{n{-w-klx}‚vy¤5m q x ix p -n{movWxÄz ’ljOn p m  jlx{v•v*m ix@x prq kr’5v*mon„v  n  h p ¥ q klx

(72) wyh  ’ p m q i¤‘’ prq mst(m q ¢5x{w}n  x4h p x

(73) h –:q k`x •klh q vW’l¢ #*xÄw q v4~RvWh  x q m  x{v q hih klh qYq h   q n„v q xi¤ q klh„’l¥bk-n„wym p ¥Œm”vYv q m  ’lt”n q m p ¥ «ƒh –"q klx

(74) ton„v q4q <h ix{n‘‚v \ X n p zrh  m Än q muh p n ihbmoz`v q klx­’5vWxh – wyh  jltumow}n q x{zEzln q nv q ’5w q ’l•x{v²¤!n p z m”v@¥bm Pm p ¥ jlhih – h – m q v3x )‹wymux p w i¤ – •h  q klxgj5hbm prq h – Pmsx

(75) Hh –@q klx}h„•x q mow}n{tAwyh  jltsxµ|rm q  nbv <x}tst n„v=j`-nbw q mowµn‘t!•x{v*’lt q v \‡URq4 ’5v q ¤5klh x ixµ}¤l¢5x p h q mowyxÄz q k5n q ¤(m p tsm q x}‚n q ’l•xi¤ q k`hb’l¥„k q klx x  jlk5nbv*mov3m”v h –q x p jl’ q h p jl‚nbw q mow}n{tYx )‹wymux p w i¤‡m q m”v h p t   x pPq muh p xÄz n p z;vWx}t”zrh  x}|Pj5x}•m  x pPq n{tst  q x{v q x{z \ & p;q klx wyh pPq ‚n‘& i¤ q klm”v 'x )gwymux p w OmovŒh p t  xµ|rj5x{w q x{z; n„vwyt”nbv•v*mow}n{t4n ix}-n{¥bx Ž w}nbv*x n p n‘t lv*movn„v•vW’  x{v­vWh  x jlhb¢5n{¢lmstumov q mowzrmov q •mu¢l’ q msh p h p zln q nP¤-n p zrh  m }x{zn p n{t `vWm”v n ix}‚n‘¥bxÄv q klxgw²h  jltux}|Pm q gh p n{tst<j h v•v*ms¢ltux ’ plp m p ¥iv3h –@q klxgn{ts¥bh„•m q k E\:URp – nbw q ¤ q klx ’ plp m p ¥gh –Aq klx­n‘tu¥bh„•m q k  k8nbv

(76) n-n p zrh  n„vWj5x{w q ¤(¢l’ q

(77) p x}m q klxµ q klx­wyh p ¥b’l‚n q msh p h – zln q nP¤ p h„ q k`xYx{vW’lt q h –‡q klx

(78) n{ts¥bh„•m q k  ¤ q k8n q x  n{m p vj`’l•x}t ­zrx q x}  m p mov q m”wCn p zŸ¥„m ix{v n p ’ p m”£ ’`x

(79) n p zgx}|`nbw q v*hbts’ q msh p‡\ X n p zrh  m µx{z n p n‘t lv*mov4%n ixµ-n‘¥„x{vYh p n‘tst!j5hivvWms¢`tsxŒ•’ plp m p ¥ivYh –q klxŒn{ts¥„hb•m q k  ¤ ¢l’ q v q ’5zrmux{v q klx <hb-v q•Ž w}nbv*xz`n q n \  h p vWx{£i’lx pPq t i¤lm q mov@n­•x{n{tsmov q m”w  hPzrx}t!h – n p n{t `vWm”v3 m p jl‚nbw q mowyx ¤ q klxm pPq x}x{v q m p ¥ zln q n n‘x h –q x p j5hbm prq v  x{n„vW’lx{z h p h„¢ #*x{w q v²¤n p z q k`x}ms zrm”v q •ms¢`’ q muh p m”v – n‘ – •h  ¢5x}m p ¥ klh  hb¥„x p x}h„’5vy¤h„ – •h  ix}•m – rm p ¥On p  jlhb¢5n{¢lmstum q  n„v•vW’  j q muh p m p v*j5nbw²x \ k`xŒj h„m pPq v Amstuth p t g¢5xŒn„v•vW’  x{z q h¢5x3m p zrx}j5x p zPx prq h p xŒh – n p h q klx} \<X n p zrh  m Än q muh p mov3m prq x}•xÄv q m p ¥ – •h  q k`movŒj h„m pPq h – Pmsx m –@q klmovŒx}|Pj xÄw q x{z wyh  jltux}|rm q  m”vŸ¢5x q•q x} q k8n pq klx <hb-v q•Ž w}nbv*xOwyh  jltsx}|Pm q Oh –°q klxE¢5x{v q zrx q x}  m p mov q m”w n{ts¥bh„•m q k  v  p h p ¤"hbŒm – xÄ£ ’5n{tR¤ Aklx p0q klxn‘ts¥„hbm q k  v

(80) n‘•xv*m  jltux}­~ Aklm”wÀk mo

(81) v ixµ  h –q x pgq k`x3wµnbvWx„ƒ \ URprq •hPzr’8wym p ¥v*h  x°£ ’5n prq m q msx{vA•x}j`•x{v*x prq m p ¥ q klx­wyh  jltux}|rm q Ÿh –q klxŒ•xÄvW’lt q m pEq klx pn n‘t lv*movm”v

(82) n‘tov*hEj5hiv•v*ms¢ltuxi¤!n p zOtsx{n„zlv q hEn‘tu¥bh„•m q k  v q k8n q n{•xh„’ q j`’ q•Ž vWx p vWm q m ix q hEn wyxµ q n{m p x}| q x pPq}\ . . .

(83) a.   . . x <x}•xgj5n{ q mowy’lt”n‘t Om pPq x}x{v q x{z m p zrxÄvWms¥ p m p ¥ z, p n  mow­n‘tu¥bhbm q k  v m p jl-n„w Ž q mowyxi¤ q klx†zln q n h – n j`•hb¢`tsx  n{•x­h –q x p n„w}£ ’`ms•xÄz jl•h„¥b•xÄv•vWmix}t  \‡URq m”v@hb¢rmuhb’5v*t  p h q x{nbv*h p n{¢ltsx q hŒx{wyh  jl’ q x q klx Aklh„tsx

(84) •x{v*’lt q x{nbw-k q m  x4n p x zln q n m”vCm p vWx} q x{z \ kP’5v ~ vWx  m Ž ƒ z, p n  m”w"v•w-klx  x{v‡n‘x p x{wyx{vv•n{  \ x4v q ’5z, ¢ h q k q klxµhb•x q mowµn‘t`wyh  j`tsx}|Pm q n p z jl‚nbw q mow}n{tx )‹wymux p w Eh –@q klxgn‘tu¥bh„•m q k  v \ klm”v q k`x{vWm”vŒv  prq klx{vWm }x{v@hb’` <hb `v3m p q klm”v  xµtoz \ URp;q klx  -v q wÀk5n{j q xµ}¤ q klxOzrx 5p m q msh p vn p z  n‘m p jlhbj5x} q msx{v­h – wyton„v•v*mow}n{t

(85) v q •’5w Ž q ’l•x{v­m p  h  jl’ q n q muh p n{

(86) t 4x}h  x q & n‘•xEx{w}n{tstsxÄz(¤nbv <x}tstnbv†n – ’ p zln  x prq n‘t q hihbt zr’5n‘tum q  Aklh vWx

(87) jl•xÄvWx pPq n q msh p mov p x

(88)

(89) ¤5n p z Aklm”wÀk‹n‘tstuh 4v’5v q hŒjl@h ix x}tut  p h p x{vW’lt q v"m p n  n plp xµ q k5n q mov  h„•xAm pPq ’`m q m ix q k5n pq klx@’5v*’5n‘t5h p x \lZ tst p xÄwyx{v•vn‘& Œ¢5nbw  Ž ¥„•hb’ p z – h„ q klx

(90) ’ p zrx}‚v q n p zrm p ¥­h – h„’l4n‘tu¥bhbm q k  v Amstut(¢5x – hb’ p z m pgq klmovAw-k5n‘j q x} \ ] •x Pmsh„’5v‡•x{v*’lt q vÆh p -n p zrh  m }xÄz=m p wyx  x pPq n{tbn{ts¥„hb•m q k  v‡n‘•x<jl•xÄvWx pPq x{z@m p  k5n{j Ž q x}@e \ k`hivWx­n{ts¥„hb•m q k  vAn‘•x q klx h p xÄv q k5n q@ n‘ ixÄz q klx ¢5x}¥bm plp m p ¥Ÿh – x{vWxÄn‘-w-klx{vm p q klmov  x}t”z \ klx gn{•x°v q n q m”wb¤ q klhb’`¥bkEm p wy•x  x prq n‘t ¤b¢5x{w}n‘’8vWx q klx n‘tut  n ix’5vWx h –q klx  h ,p . mow q 4-n{jlk‡¤‡n­v q •’5w q ’lx q k8n q@p xµx{zlv q klx  p h Atsx{zr¥„x3h – n{tst!zln q nn„vYx{n{•t ‹nbv q klx m p m q mon‘tum {n q muh p v q x}j \:U q  ’8v q ¢5x p h q m”wyx{z q k5n q  \ "\  t”n‘ `vWh p n‘t”vWh <hb ixÄz ngtsh q h p zrm rm”zrx Ž n p z Ž wyh p £i’lx}Œn{ts¥„hb•m q k  vy¤ q k5n q w}n plp h q ¢ x†x}| q x p zrxÄz q hOn ,z  p n  mow­v•w-klx  xi¤ n p z q kP’5v Amstst p h q ¢ xzrx ixµtshbj5x{z3k`x}•x \ x@n{tov*h3jlx{vWx pPq v*x ix}-n{t  x q k`hPzlvh – n p n‘t lv*mov²¤ zr’`x q h Œ\ "\  ton‘ lv*h p ¤ Œ\ ’lt  ’`tsx °n p z X\ fix}mozPx}t \ klx  x}ton{’ p n  x}x

(91) movm prq •hPzr’5w²x{zm p  k8n‘j q x} aP\5URq m”vy¤‡~ j`•x Ž ƒ klmov q h„•mowµn‘tst i¤rh„’l  ‚v q vWx  m Ž z  p n  mowv q •’8w q ’lx 

(92) [ $bdP¤

(93) [ ! \iURq n‘tstuh 4v q klxwyh p v q ’5w q muh p h –‡q klx  x}t”n‘’ Ž p n  q •mon p ¥b’`ton q msh p h – ngvWx q h – j5hbm prq vWm q x{v²¤(m p n p OzPm  x p vWmsh p ¤ Am q k`hb’ q jlx}tsm  m p n{   p h Atsx{zP¥bx h – q klm”vŸv*x q}\ klx  x}ton{’ p n  x}x m”vŸwyh  j5n{•x{z q h n v*m  muton‘­v q ’5w q ’`•xi¤ p "µ_b_ cŒ¢  "\  \ 4’lmu¢5nbv²¤ 3\ A\ @p ’ q k‡¤5n p * jlhbj5hiv*x{z m # z \ fik5n‘ms \  k5n{j q x} Œv*klh 4vCklh q klx@¢5n„vWm”wm”zrx{n@h – q klx  x}t”n‘’ p n  •x}x4tsxÄnbzlv q h°zrx{v*ms¥ p m p ¥ n ix}& 3¥„x p x}‚n‘t v q •’5w q ’l•x ¤ q klx UR,p . ’lx p wy2x 4-n{jlk‡¤Pn‘tutsh Am p ¥ q klx@v*x  m Ž ,z  p n  mow"w²h p v q •’8w Ž q msh p h –p ’  x}•h„’5v@¥bx}h  x q mowŒv q •’8w q ’lx{v \ x‹w}n p hb’l¥„klt  v•n  q k5n q q klm”v3v q •’8w q ’lx n{jljltsmux{v q h q k`xŒv•n  x

(94) jl•h„¢ltsx  v – h„ Aklm”wÀk q klx  h ,p . m”w q Y‚n‘jlk An„vjlx Pmshb’8vWt †’5vWx{z ¤ ¢l’ q m q n‘tutsh 4vAm p v*x} q msh p v \ <h Pm p z`v h – wyh  jltsx}|Pm q On p n‘t lv*mov­n‘•xgjlx{vWx prq x{z(¤ Aklm”wÀk0klh„toz ’ p zrx}­,k Pj5h q klx{vWxÄv v*m  muton‘ q h q klhiv*xgv q n q x{z – hb°n p n{t }m p ¥En‘tu¥bh„•m q k  v@’5v*m p ¥ q klx  h ,p . m”w q 4-n{jlk \ klx j5hivvWmu¢lmstum q Ÿh – •x  @h rm p ¥ q klx{v*x wyh p zPm q muh p vAmovAn{tov*h­v q ’8zrmsx{z \ fix ix}-n{t(n{jljltumow}n q msh p vn{•xzrx ix}tuhbj5x{z \ klx’5vWx4h –!q klx UR,p . ’lx p wyx Y‚n‘jlk – hb4n p v xµ•m p ¥ x{£ ’`x{v q v Am q knŒ¥bhihPzEwyh  jltux}|rm q 3movAn{tov*hzrm”v•wy’8v•vWxÄz \  |Pj xµ•m  x prq n‘t5•xÄvW’lt q v – hb4w²h  jl’ q m p ¥Œwyh p ix}|ŒkP’ltutovm p zrm  x p vWmuh p v a n p z l¤5n p z  x Ž t”n‘’ p n  q mon p ¥b’lt”n q msh p vYm p zrm  x p v*msh p vAeŸn p z a ¤ vWklh q klx3j`-nbw q mowµn‘t‡x )‹wymsx p w ­h –q klx n{ts¥bh„•m q k  v \ URp  k5n‘j q x}4‰r¤ q klx

(95) mozrxÄnh – q klx  x}ton{’ p n  •x}x@m”vjlmow ix{zŒ’ljn‘¥ n‘m p ¤5n p zgx p ton{•¥„x{z q h¢5x­n‘jljltumsx{z q h q klxŒwµnbvWxŒh – klms¥„klx}4hb-zPx}-v ¦ h„•h p hbmzrm”n‘¥„-n  vy¤5m p n p  zrm  x p vWmuh p v \ . .

(96) 

(97)  . klm”vAw}nbv*x zrhix{v p h q 5q m prq h q klx – -n  x

(98) h„ Œh – k5n{j q x} \5 |rj5x}m  x pPq n{tl•xÄvW’lt q vAn‘x. v*klh p‡\ klx p? k5n‘j q x}Ad 5p n{tst   n ix{v q klx An q h An{-zlv q klxz, p n  m {n q msh p h –‡q klx URp,. ’ Ž x p wy2x 4-n‘j`k \ klx4¥bx p x}-n{t5v•w-klx  x – h„zrx}tux q m p ¥

(99) n@zln q n@movwytux{n‘ \bURq AmutstP¢5x4vWx}x p h pŸq <h x}|`n  jltsx{v  x}ton{’ p n q mon p ¥b’lt”n q muh p h – j h„m pPq vWm q x{v

(100) n p zOn‘-n p ¥bx  x prq vYh – tsm p x­vWx}¥ Ž  x prq v m pq k`x@jlton p x q k5n q<q klx zrx q n‘mutovn{•xi¤Pklh xixµ}¤i-n q klx} q x{w-k p m”w}n‘t \ klmov<w}n plp h q ¢5x†%n ih„mozrxÄz(¤ ’ p tsx{vv@n q

(101) q klxŒjl•m”wyxŒh – x„nbv*m ix3h  movvWmuh p v \ klx q k`x}hbx q m”w}n‘t:wyh  jltsx}|Pm q  m”v p x ix} q klx}tux{v•vx}|`wyx}tstux pPq ¤in p z q klx n‘ts¥„hbm q k  mov ix}& Ÿ'x )gwymux pPq m p jl-n„w q m”wyx \ URp j8n‘-n{tstux}t q hghb’l h„ `vh p U p . ’lx p w²x Y‚n‘jlk ¤"ntsh q h – n‘’ q klhb‚vk5n ix†zrx{v*ms¥ p x{z v*x ix}-n{t5h q k`x}Av q •’8w q ’lx{v \PZ £ ’`mow 3jlx{vWx pPq n q muh p h –!q klx{v*x <hb lv²¤  h v q t  ix}& Œ•x{w²x prq ¤ p  k8n‘j q x}Š \ Amutst(¢5x – hb’ p zgm * . .

(102)  

(103)       

(104)  .

(105) d.    

(106) . 

(107) . . .   . RU p q klmov

(108) w-k5n‘j q x}}¤ <xjl•xÄvWx pPq

(109) q klxgzPx 5p m q msh p v

(110) n p z  n{m p jlhbj5x} q msxÄvh –A– ’ p zln  x prq n‘t v q •’8w q ’lx{v"m p4 h  j`’ q n q msh p n‘t 4x}h  x q &i¤ – hb Aklmow-k†n‘ts¥„hbm q k  vh – wyh p v q ’5w q msh p vn‘x jlx{vWx prq x{z m pq k`x – hbtutsh Am p ¥°wÀk8n‘j q x}-v \ k`x

(111) wyh  jltsx}|Pm q 

(112) h –!q klx@¢5x{v q  p h p zPx q x}  m p`Ž m”v q m”w

(113) n‘ts¥„hbm q k  vCm”vYn{tovWh­¥bmix p‡\ hiv q h –:q k`x3•xÄvW’lt q vAn‘x q n ix p‹– h    zrx%$ Ši¤ xµk $ `¤ ] f $„‰ ! ¤ Aklxµ•x  hbx­zrx q n{mst”vwµn p ¢ x – hb’ p z(¤‡x{vWj5x{w²mon‘tut  wyh p w²x} p m p ¥n‘tu¥bhbm q k  vy¤ q k8n q Amutst p h q ¢ x v q ’5zrmux{zklx}x \ rz x p h q x{v q klx bŽ zrm  x p v*msh p n‘t  ’5wytumozrx{n p v*j5nbw²xi¤ Am q k‹v•w}n{ton‘<jl•hPzP’5w q     ¤Pn p z  ’5wytumozrxÄn p zrm”v q n p wyx  \ x}  v@vW’5w-kOnbv &ix} q mow}n{t ¤ -n{¢5hix ¤ ¢ xµtsh ¤ Amstut¢5x­h –q x p ’5v*x{z q k`x

(114) ixµ q m”w}n‘t zrmsx{w q msh p m”vj5n{-n{tstsxµt q h q klx tonbv q n{|rm”vh –  ¤5n p z m q vh„ q k`hb¥bh p n‘t krj5x}jlton p x

(115) mov q kr’5vk`hb•m }h pPq n{t \ >. .  . . E . . . . . .  . klx ¿-ši± ‘žE¨`´!"! h – n 5p m q xvWx q. h – & j5h„m pPq vŒh –  ¤zrx p h q xÄz n„v ~ B ƒ-¤w}n p ¢5x x{£i’lmbn{tsx pPq t­zrx 5p x{zm pgq klx – h„tstsh Am p ¥ Angn„v # q klx v  n{tstux{v q wyh p ix}|†vWx q wyh prq n‘m p m p ¥ B ¤ # q klx

(116) m pPq x}‚vWx{w q msh p h – n‘tut!wyh p ix}|†vWx q vAwyh pPq n{m p m p ¥ B ¤ # q klx

(117) m pPq x}‚vWx{w q msh p h – n‘tut‡k5n‘t – vWj5n„wyx{v4wyh pPq n{m p m p ¥ B \ klx4w²h  jl’ q n q msh p h – q klxAwyh p ixµ|kP’ltutimov"n@w²x prq -n{trjlhb¢ltux  m p  h  jl’ q n q msh p n‘t 4x}h Ž x q  i¤„n p z m q k5nbv¢5x}x p „nbv q t °v q ’5zrmsxÄz(¤ p h q h p t  ¢5x{w}n‘’8vWx4h – m q v j`-nbw q mowµn‘t`n‘jljltumow}n q muh p v²¤ ¢l’ q n{tovWhŒ¢5x{wµn‘’5v*x3m q m”vAn3jl•xµtsm  m p n{  – hb4v*hbt rm p ¥n3tuh q h – h q klx}4£i’lx{v q msh p v \  ton„v•v*mow}n{t  n q k`x  n q mow}n{tYx{vW’`t q v – h„ w²h p ix}| j5hbt rk`x{zr-n0n{tstsh ’5v q h;v q n q x q klx – h„tstsh Am p ¥Œjl•h„j5x} q E~tsx q ’5vx{w}n{tst q k5n q n 0 Ž – n„wyx

(118) movAn – nbwyx

(119) h – zrm  x p v*msh p 0 ƒ4 B. ˜ ™šy¶ žÀ™À· ¹%$iÃ&$ klx p ’  ¢5x}­h – 0 Žo– nbwyx{vgn p z q klx p ’  ¢5x}Œh – m p wym”zrx p yw xÄv ¢5x q <x}x p 0 Žo– nbw²x{vŸn p z 0 ˆ "²Ž – n„wyx{vŒh – ~ B ƒ n‘x('*) &+-,/. ~02351 46 789 ƒ: ¤ – hb c  0  <;"b\ k`x{vWx

(120) ¢5hb’ p zlv@n‘x nbv   j q h q mow}n{tst  q ms¥„k qµ\ URp j5n‘ q m”wy’lton{}¤lm p ¢5h q kEzPm  x p vWmsh p veŒn p z a ¤ q klm”v p ’  ¢5x}<movtsm p x{n{ \ klx¢ xµk5n rmuhb’l­h –

(121) q klxwyh  jltsx}|Pm q Eh –> ~ B ƒ

(122) k5n„vn‘t”vWhO¢ xµx p v q ’5zrmux{z ’ p zrxµŸk Ž j5h q klx{v*x{v – h„ q klx­zrm”v q ms¢l’ q msh p v@h –q klxŒj5hbm prq v@h – B \ €lhb

(123) x}|`n  j`tsxi¤lm –q klx­j h„m pPq v

(124) n‘x w-klhiv*x p m p zrx}j5x p zPx prq t  – •h  n p hb  n‘t5zrm”v q •ms¢`’ q muh p ¤ q k`x pq k`xYx}|Pj5x{w q x{zŸv*m }x4h – ~ B ƒ m”=v '?>²~ tuhb¥ & ƒ 1A@C3EB D \.

(125) . 

(126) . Š. "  . . . klx

(127) jlhb¢ltux  h – w²h  jl’ q m p ¥ q k`x

(128) wyh p ix}|­kr’`tst wyh p vWmov q vm p w²h  jl’ q m p ¥ q klx

(129) j5hbt Pklx Ž zrh pq k5n q m qC– hb  vy¤Pm \ x \rq klx wyh  j`tsx q x@zrxÄv•wymsj q msh p h – m q v¢5hb’ p zln‘& \. x q ’5v@v q n{ q Am q kOn  -v q hb¢5v*x} „n q msh p‡\!U pEq klx3j`ton p xi¤(m q movYx{n„v  q hvWx}x q k5n q

(130) q klm”v jlhb¢ltux  movAn q tux{nbv q nbvAwyh  jltux}|­nbv4vWh„ q m p ¥ & p ’  ¢5x}‚vA ltsx q ’5v q nix q klx

(131) j5hbm prq vh p n j5n{-n{¢ h„ton Am q ? k ix} q mow}n{t‡n‘|Pmov²¤ q klx p q klxŒw²h p ix}|ŸkP’ltut(mov q k`xj5h„t P¥bh p – h„  xÄzŸ¢, q klx{v*x & j5hbm prq vy¤ ©o±g· ¨5ž ši™¸rž²™@š œi¯Àªµ¿µ©«ª-ªµœrž-\5 nbw-k n{ts¥„hb•m q k  wyh  j`’ q m p ¥ q klx

(132) wyh p ix}|­kP’ltst h – & j5hbm pPq vk8nbv q kP’5vAn @~ & tsh„¥ & ƒ q m  x@wyh  jltux}|rm q  \ & j q m  n‘t v q n q m”w

(133) n‘ts¥„hbm q k  vCx}|Pmov q m p zrm  x p v*msh p vCe­n p z ar\ URp klms¥„klx}zPm  x p vWmsh p vy¤ X

(134) \ fixµmozrx}t  f x}m $ " ! k5nbv"¥bm ix p n p n{ts¥„hb•m q k  Aklhiv*x@w²h  jltux}| Ž m q  mov ' ) & tuhb¥ & ˆ & 0 1 3 B 4 : ¤ Aklm”wÀkŒm”v"hbj q m  n{t – h„Cx ix p zrm  x p vWmuh p e \ klxv q hb-n{¥bx m”v=m p ' ) & 0 31 4 : \ klxn{ts¥„hb•m q k  m”vYm p wy•x  x prq n‘t ¤l¢l’ q

(135) q klx†n p n‘t `vWm”v@mov

(136) n  h„ q m }x{zgh p q klx & m p vWx} q muh p v \ Z–q x}4vWx ixµ-n‘t ixÄn‘-vh – ’ p v*’5w}wyxÄv•v – ’`tx{vWx{n{-w-k5vh p 5p zrm p ¥†n p hbj q m  n‘t‡n{ts¥„hb•m q k  – h„@n p gzPm  x p vWmsh p vy¤ [@\  k5n}x}tutsx@k5n„vx{wyx pPq t Œ¥bm ix p vW’8wÀkn p n‘tu¥bhbm q k    k8n ,_ " ! \ ZYp n‘ts¥„hbm q k  Ak`hivWx°wyh  jltsx}|Pm q Œm”=v '3~ & ˆ  tshb¥ & ƒ‚¤ Aklx}•x  m”v q klx°vWm }x

(137) h –q klx h„’ q jl’ q ¤ q k5n q mov q k`x p ’  ¢5x}h –– n„wyx q vh –q k`x3w²h p ix}|ŸkP’ltutR¤rm”vAzrx{vwy•mu¢ xÄzŸm p  f x}m $„d ! \ URpEq klx jlton p xi¤ zrx q x}  m p mov q m”wYh plŽ tsm p xŒn{ts¥„hb•m q k  vYn{•x  p h p ¤ Am q kEh„j q m  n‘t!wyh Ž jltux}|Pm q  ' ~ tsh„¥ & ƒj5x}Am p vWx} q muh p ~Rv*x}x – hbAx}|`n  j`tsx  Z@ f $„‰ ! ƒ \ .

(138) . . . . . . . EE ^ %T . 9 5Ag 3'5 ²1ŒA-)8 - . klx ši™•ši±lši©4¸i©oœ}›i™œi h – nvWx q. !#". h – & j5hbm prq vy¤"wµn‘tstux{z ªµ©s·Wž•ª ¤!m p  m”vn ¥„x}h  x q mow v q •’8w q ’lx’5v*x{z q h=vWhbtix{z@jl•h{|Pm  m q @£i’lx}msx{v²¤{vW’5w-kŒn„v q klxwytsh vWx{v qp }x ms¥„kr¢5hb‚vh – nY¥„m ix p v*m q x ¤rhb q k`x3w²tshiv*x{v q j8n‘msAh – vWm q x{v \ klm”vv q ’5w q ’`•x­k5nbv

(139) ¢ xµx p j`tsx pPq m – ’ltst gv q ’5zrmsxÄz³m pEq klx­tsm q x}‚n q ’`•xi¤ n p z x­v q n‘ q x{z h„’l hb lv Am q k­m q}\ € \iZ ’l•x p k5n  x}‡•x{w²x prq t  zrx ih q x{zŒ2n ix}&  wyh  j`tsx q xv*’l ix  q h

(140) m q  Z ’l _" ! ¤‘m p Aklmow-k3klxA¥„m ix{v q k`x4n‘jljltumow}n q muh p v²¤ q klxAj`•hbj5x} q mux{vy¤„n p z­nYtuh q h – n‘tu¥bh„•m q k  v – h„@wyh  jl’ q m p ¥ q klx zrm”n‘¥„-n  \ €lhb4x{nbw-kvWm q x 4(¤ q klx ši™ši±lši©"¿yž !! ~ 45ƒh – 4mov q k`x3v*x q h – j h„m pPq vm p  q k5n q n‘x wytuhiv*x} q h 4 q k5n pq h†n p h q klx}4v*m q x

(141) h – B \ %$. B. ('. '. &$. ~ 4 ƒ. *),+.-0/.   5 1. /. B. #2. 4   +. 3. ~  45ƒ

(142) -. 54. . ~. 6-. +5. ƒ. 73.

(143) $ '.    

(144) . ~ 45ƒ<w}n p n‘tov*hŸ¢5x

(145) x}|Pjl•xÄv•vWxÄz n„v@ '. ~ 4 ƒ. *).  

(146) . 

(147) . . .   . ~ 4 (5 ƒ. Aklxµ•x ~ 4 (5 ƒmov q klxk8n‘t – v*j5nbw²x tum  m q x{zg¢, q k`x¢lmov*x{w q m p ¥k,Pj5x}•jlt”n p x†h – 4 n p z 5 ¤ wyh prq n‘m p  m p ¥ 4 \ klx ¦ h„•h p hbm<zrmon{¥b‚n  h – B mov q k`xŸj5n{ q m q muh p m p ¥ h – – hb  x{z ¢ q klx ¦ hbh p h„m wyxµtstovh –q klx vWm q x{v \ klx­j5hbm pPq v@h – B n{•x†nbv•v*’  x{z q hg¢ xŒm p ¥„x p x}‚n‘t"j5h vWm q msh p p h  ˆ ej h„m pPq v

(148) n‘x wyh vWjlk`x}•m”w}n‘t \iURpŒq klm”v"w}nbv*xi¤ q kl+x ixµ q m”wyx{v‡h – q klx4zrm”n‘¥„-n  n{•x q klx4w²x prq x}-v!h – q klxvWj`klx}•xÄv j5n„v•v*m p ¥ q klhb’l¥„k  ˆ eŸv*m q x{v \ ˜ ™šy¶ žÀ™À· ¹%$iÃ" klxOw²h  jltux}|Pm q Eh – q k`x ¦ h„•h p hbm

(149) zPmon‘¥„-n  h – n v*x q h – j5h„m pPq vAm p  m”v=' ) & 31  : \ &. URpgq klx a zrm  x p vWmuh p n{t w}nbv*xi¤ q klm”vAwyh  jltsx}|Pm q  movA£i’5nbzr‚n q mow \ klx °ž ! œi´P±lœi¹ ·R™²©oœi±b›i´! œb· ©oši± mov q klx†zr’5n{t¥b-n{jlk0h –q klx ¦ h„•h p hbm<zrmon{¥b‚n  q <h v*m q xÄvCh – B n{•x@tum p ix{z3¢†n p x{zP¥bx4h –!q k`x q mon p ¥b’lt”n q muh p m – n p zh p tŒm –‡q klx}mu•xÄvWj5x{w q m ix wyxµtstov4n‘xn„z#nbw²x prqµ\ klx  x}t”n‘’ p n q •m”n p ¥„’lton q muh p mov@nj5n{ q m q muh p h –  m p vWm  jltumowyx{v Aklh vW4 x ix} q mow²x{vYn{•x q klxgv*m q xÄv \‡URq vn q mov  x{v q klx – h„tstuh Am p ¥ j`•hbj5x} q i¤ Aklmow-k zPx 5p x{v@m q ’ p mo£i’lx}t  k`xv*jlklx}x{v@wymu-wy’  v•wyms¢lm p ¥ q klxv*m  j`tsmow²x{vCh –Aq k`x  x}ton{’ p n q •m”n p ¥„’lton Ž q msh p zPh p h q w²h pPq n‘m p n p gvWm q x

(150) m pgq k`x}ms<m pPq x}mshb \ klm”vYjl•h„j5x} q En{tstuh 4v4’5v q h‹zrx{vWmu¥ p n ixµ vWm  jltsx

(151) m p wy•x  x pPq n‘t n{ts¥bh„•m q k E\ klm”v n{ts¥bh„•m q k  mov@zr’`x q h 4•x}x p n p z fimu¢5vWh p  f`@Š $ ! – hb q klx q hgzrm  x p v*msh p n‘t:w}nbv*xi¤ n p z m q k8nbv3¢5x}x p ¥bx p x}-n{tsm µx{z q hEn p Ozrm  x p v*msh p v  [ h $ " ! \!Z v  n p  m p wyx  x pPq n{t"n{ts¥bh Ž m q k  vy¤im q mov p h q x )‹wymsx pPq m p q klx <hb-v q w}nbv*x­ rm q vAwyh  jltsx}|Pm q 

(152) mov ' ~ & ƒm p†q klx@j`ton p n‘ w}n„vWx n p ? z ' ) & 31  89 : m p zrm  x p vWmuh p l\ k`xOn‘’ q klhb‚v vWk`h q k5n qgq klxOwyh  jltsx}|Pm q  w}n p ¢5x

(153) m  jl@h ix{z q h­n p x}|Pj5x{w q x{zŸw²hiv q h – '?> & 9 8 B1 D – h„klh  hb¥„x p x}h„’5vzrm”v q •ms¢`’ q muh p v \  h <x ix}}¤ q klx

(154) jlhih – mov p h q •x{n{tst  – h„  n{tR¤ q k`x k Pj h q klxÄvWx{v4n‘x p h q ix} ­jlx{wymov*x n p z q klxŸj5x} – hb  n p w²x{v q x p z q h¢5xj5hihb•xµ – hb°zrx}¥„x p x}‚n q x†zrm”v q ms¢l’ q msh p v

(155) vW’5w-k nbvj5h„m pPq v h p vW’` – nbw²x{v \ klxgn{ts¥„hb•m q k  wyh p vWm”v q v

(156) m p m p vWxµ q m p ¥ q klx†j h„m pPq v

(157) m p q ’l p ¤!n p z m p ’lj zln q m p ¥ q klx q  movŸm p vWx} q x{z ¤ q klx vWm  jltumowyx{v v q •’8w q ’lx n –q x}†x{nbw-k m p vWxµ q muh p‡\ klx p n p x

(158) j h„m pP  r p q p    q Aklh vWx­wymu-wy’ v•wyms¢5x{zv*jlklx}xŒwyh n‘m v ’8v ¢5xŒ•x  h ixÄz(¤ q klx zrh p h q ¢5x}tuh p ¥ q h q klx q •m”n p ¥„’lton q msh p n p   hbx \ klxŸ’ p msh p h –Aq klx{v*xv*m  jltumowyxÄvmov@ngvWm  jlt gwyh p`p x{w q x{z .

(159) . 

(160) . _. "  . . . x}¥bmuh p ~  ƒ \‡U – @ ~  ƒzrx p h q x{v q klx­v*x q h –– n„wyx q v4h –<q klxŒ¢5h„’ p zln{ Eh – ~  ƒ‚¤ q k`x p x

(161) v*m  jltumowyxÄv@n‘x h„¢ q n{m p xÄz ¢Otsm p rm p ¥  q h q klxx}tux  x pPq vYh – @ ~  ƒŒ~ €ms¥„’l•x "„\ " ƒ \ klm”v n{ts¥bh„•m q k  m”v ix} †vWm  jltuxi¤Pn p zn‘tstuh 4v’5v q hŒjl•h„¥bx{v•v*m ix}tn„w}£ ’`ms•x p x zln q nP¤ Aklm”wÀk m”v3h – ¥„•x{n q jl‚nbw q mow}n{tm prq x}•x{v q}\ hOm p w²•x{n„vWxm q vŒx)gw²msx p w'i¤‡nOzln q n v q •’8w q ’lxg¥bm Pm p ¥ £i’lmow Pt  q klx­vWx q ~  ƒAk8nbv q h¢5x – h„’ p z \ klm”vYjl•h„¢ltsx  k8nbv@¢5x}x pEq k`xŒv q n‘ q m p ¥ j5h„m pPq h – hb’lAx{vWxÄn‘-w-klx{v@~  k5n‘j q x} a ƒ \. .  . .   . . €ms¥„’l•x "„\ " URp vWxµ q m p ¥­n­vWm q x@m pgq klx  x}ton{’ p n q •mon p ¥b’`ton q msh p V ’  }x •h„’5vhbj q m  n‘t5n{ts¥bh„•m q k  v:n‘•x p h Ÿp – bh  q k`xYjlt”n p n{<w}nbv*x \ klxYx{wyx pPq n{ts¥bh Ž m q k  ¢  [@\ k5n}x}tutsxi¤ – h„ q klxŒwyh  jl’ q n q msh p h – ²w h p ix}|kP’ltst”vy¤ p h &¥„m ix{v¢zr’5n‘tum q .

(162) "c.    

(163) . 

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(165) n – ’ p w q muh p h –q klx vWm }x h –q k`x3zPmon‘¥„-n E\ klm”vk5nbvA¢5x}x p vWh„t ix{zm p q klx

(166) j5n‘ q m”wy’lton{4w}nbv*x Aklxµ•x q klx

(167) j5hbm prq vtumsx@m pgq <hŒjlton p x{v  [ hbm $ $r¤ [   A_ " ! \  '+";5

(168) " 9 5A@Ag 3'5,.  .  =    ; . . zrx p h q xÄv@ngvWx q h – & vWm q x{v4m p ¥bx p x}-n{t"j5hiv*m q muh p m pEq klxŒjlton p x \ 4mix p n v*’l¢5v*x q h – j5hbm prq vh – B ¤ q klx

(169) ¥„x p x}‚n‘tsm }x{z ¦ h„•h p hbm!j h„t P¥bh p h – mov4zrx 5p xÄz n„v@ ~  ƒ 4    B    ~ 4 

(170) ƒ  ~ 4 

(171) ƒ ~  ƒ<mov q klx3tuhPwy’5vAh – n j5h„m pPq 4 q k5n q m”v@wytsh vWx} q hx{n„wÀk vWm q x

(172) h –  q k8n pEq h‹n p  h q klxµ j5hbm prq m p B g\ klx

(173) h„-zrx} 0 ¦ hb•h p hbm!zPmon‘¥„-n  h – B mov@~  zrx p h q x{vAwµn‘-zPm p n{tsm q 5ƒ  ' ~ B ƒ ~  ƒ   B    0 7. x q 4 9  4  4Œ¢5x q klx}xgvWm q x{v3h – B ¤  q klx}muŒwymu-wy’  wyx pPq x²} ¤ ~ 4 9  4  4yƒ q klx}ms hbj5x p wymu-wy’  zrmov  \ fim p wyx q k`x j5hbm prq vn‘x m p ¥„x p x}‚n‘t4j h vWm q msh p ¤ q klx}ms­w²ms-w²’  wymu-w-tsx†zrh p h q j5n„v•v q k`•hb’`¥bkOn p gh q klx}

(174) v*m q x \ x q ¢5x q klxŒv*x q h – vWm q x{vA¢ xµtsh p ¥bm p ¥ q  h ~ 4 9  4  4yƒ \ U –   0 ¤ q klx p ­movAn ix} q x}|­h –  ' 78 9 ~ B ƒ<n p z  ' 78 ~ B ƒ4 B. '. ). 1. +. 1. /. /. #2. 4. 3. '. #2. '. ). +. '. ). 3. . . '. ). . '. . 

(175) m”v q k`x4wyh  h p j5hbm pPq"q hx}¥bmuh p v ~  4 bƒ-¤ ~  4 bƒÆn p z ~  4  bƒ m p  ' 789 ~ B ƒ \ 

(176) m”v"w}n‘tutsx{z n ¿ ! š‘ª{ž R·R¹-¶5ž {ž²™À·*ž 9 m pŒq klmov"zPmon‘¥„-n  ~Rv*x}x4€mu¥b’lx "b\ e ƒ \ 0m”v q k`xEwyh  h p j5hbm prq†q h x}¥bmuh p v ~  4 9  4 bƒ‚¤ ~  4  4 bƒ°n p z ~  4  4 9 bƒm p  ' 78 ~ B ƒ \  m”vŒn µœi™  ·R¹-¶ ž ‘žÀ™À·*ž m p q k`mov3zPmon‘¥„-n  ~Rv*x}x €!ms¥b’`•x "b\ e ƒ \ #. '. +. '. 3. +. #. '. 3. +. 3. . 0'. '. '. +. '. 3. . +. 3. '. +. . 3. . . h v*’  n{•m }xi¤"n p  q mon p ¥btsx Aklhiv*x ixµ q m”wyx{vŒn{•xOvWm q x{v­h –. n p z Aklh vWxOhbj5x p wymu-wy’  zrmov 

(177) wyh prq ‘n m p v vWm q x{v"w²hb•x{vWj5h p zlv q hŒ~ ©«ª¸i´Pœ!l· š ƒ!n2ix} q x}|@h – ¢5h q k  ' 789 ~ B ƒ n p z  ' 78 ~ B ƒ \  h p ix}‚vWx}t i¤bn p !ix} q x}|

(178) h –  ' 7 ~ B ƒ‡m”v"zr’5n{t q h n q mon p ¥btsx Ak`hivWxhbj5x p wyms‚wy’  zrm”v  wyh prq n‘m p v 0 ; " h„ 0 ; eŒvWm q x{vm p m q vm prq x}•muhb \ 0. B. '. '. . '.

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(187) jlx{wyx{zPm p ¥Œx{vW’lt q vAw}n p ¢ x x}| q x p zPx{z q h­klmu¥bklx}4zPm  x p Wv msh p v \ klx

(188) hb‚zrx} 0 ¦ hbh p h„m!zrmon{¥b-n  wyh p v*mov q vm p wyx}tst”vCh – zrm  x p v*msh p vc  111  l\lq k`x

(189) ixµ Ž. q mowyx{vh –­q klx zrmon{¥b‚n  n‘•x zr’5n{t q h;vWm  jltumowyx{v Ak`hivWx ix} q m”wyx{v­n‘•x vWm q x{vh – B \ x q 4  4  111  4  ¢5x  ˆ " v*m q xÄv h – B ¤ ~ 4  111  4  bƒ q klx}muŒhbj5x p wyms‚wy’  ¢5n‘tutR¤  m q 9 vwyx prq x}n p 8z 9 C q klxOvW’l¢8vWx q h – j5hbm prq vh – 9 B wyh pPq n{8 m 9 p x{z m p ~ 4 9  111  4  89 bƒ \U –  C  EDR¤ q klx p Œmov<n ix} q x}|Œh – n‘tut ¦ hbh p h„m‡zrm”n‘¥„-n  v  ' ~ B ƒ – h„FDiˆ "  0 GDiˆ l\ 7 "  111   ˆ " m p # †mov q klx wyh  h p j h„m pPqAq h q klx

(190) x}¥bmuh p v ~ C  4  bƒ – hb *  '+H ~ B ƒ4 5nbvAm pgq klx

(191) jlton p n‘4w}n„vWxi¤ †movAw}n{tstux{zn­wytsh vWx Žq rj5x2ix} q x}| \ 8 9 # URp  ' H 8JI ~ B ƒ-¤ Œm”v q k`x@wyh  h p j5hbm prqq h q klxA•x}¥„msh p v ~ C LK ƒ Ak`x}•x K n ¢5x†n p Ev*’l¢5vWx q h – v*m }Nx MEh – 4 9  111  4  89 CO gmov@m p wymozrx prq4q hO~ 1 B ƒ4•x}¥„msh p v \‡U – I " PM  <x w}n‘tut n Ÿž¸i©o´P R·R¹-¶5ž ‘ž²™-·*ž {\ 4  bƒ – hb * # gm”v q k`xŒwyh  h p j5hbm prqq h q klx3x}¥bmuh p v ~ C  4 9  111  4  89 "  111   ˆ " 3m p  '+H 8  ~ B ƒ4 5n„vm p zPm  x p vWmsh p eP¤ m”vAn – n{ Žq Pj5x ix} q x}| \ h­vW’  n‘•m }xi¤{nŒwytuhiv*x Ž q Pj5x ix} q x}| h – n3klmu¥bklxµhb‚zrx} ¦ h„•h p hbm zrmon{¥b-n  x  n{m p v pm  vW’5w}w²x{v•v*m ix†zrmon{¥b-n  v \ hbx ¥„x p x}‚n‘tut i¤:Q n M Žo– nbwyxg•x  n‘m p v@m p  ; M0vW’8w}wyx{vvWm ix zrm”n‘¥„-n  v \ +. 3. . +. 3. '. ). '. +. 3. /#+. 3. '. '. '. +. 4. 3. 4. '. +. 6. 3. '. +. 3. 2. +. 3. /.

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(195) zrx{n{t Am q k 0 wytsh vWx{v q j5hbm prq vj`•hb¢`tsx  v \ x}x  x}x@$„e ! ¥„m ix{v q klx – hbtstuh Am p ¥Œx{vW’lt q ˜™šy¶ žÀ™À· ¹%$iÃuÅ URpgq klx

(196) jlt”n p x ¤ q klx vWm }x

(197) h –:q klx hb‚zrx} 0 ¦ h„•h p hbm!zrm”n‘¥b‚n  mov ' ~ 0 ~ & ; 0 ƒ•ƒ \ k`x

(198) vWm }xYh – h„-zrx}‚v

(199)  0 ¦ hbh p h„m‡zrm”n‘¥„-n  v m”v q kP’5v ' ~ & 0 ƒ \ . klx†-n p zrh  vn  j`tsm p ¥ q x{w-k p mo£i’lxg~*fix{w q msh p e \^aP\ " ƒ

(200) vWk`h 4v q klx – hbtstuh Am p ¥ hb‚v qŽ w}n„vWx. x{vW’lt q m p zrm  x p v*msh p.  . f$ _ ! . ˜ ™šy¶ žÀ™À· ¹%$ià   RU p zPm  x p vWmsh p    er¤ q klx°vWm µx3h – n{tst ¦ h„•h p hbm:zrmon{¥b‚n  vYh – h„-zrxµ-v "@q h 0 ”m v=' ) 0  1 3 B  & 0 1 3 B 4 : \ 6. 6. x}x4k5n„vn‘t”vWh ¥bm ix pŸq klx  -v q n{ts¥bh„•m q k Hq hŒwyh  jl’ q Ax klms¥„klx}hb‚zrx}-v ¦ hb•h p hbm zrm”n‘¥„-n  v – h„ & vWm q x{vCm pq k`xj`ton p x \ klxhb-zPx} 0 zrmon{¥b-n  mov<wyh p v q ’5w q x{z – •h  q k`x@hb‚zrx} 0 ; " zrm”n‘¥„-n  m p ' ~ 0 ~ & ; 0 ƒituhb¥ & ƒ q m  x \ klx4hb‚zrx}-v 0 zrm”n‘¥„-n  vCn{•x q kP’5vwyh p v q ’5w q x{z m p ' ~ 0 & tsh„¥ & ƒ q m  x \  Z  f`f$ _ ! ¥bm i x=n q ms¥bk q xµ¢5hb’ p z h – '3~ & tsh„¥ & ˆ 0 & ƒ \ [@\  k5n}x}tstuxn p z 3\ zrxµtovW¢`•’ plp x}  <  b$ ‰ ! k5ni xEzPxi x}tsh„j5x{z q <h i x}-v*msh p v h – n ¢5x qq x}<n‘tu¥bh„•m q k  – hb<ton{•¥bx 0 \ klx  -v q h p xYk8nbvn ' ~ & tuhb¥ & ˆ 0 ~ & ; 0 ƒituhb¥ & ƒ q m  x wyh  jltux}|rm q i ¤ Am q kn ' ~ 0 ~ & ; 0 ƒ•ƒ v q h„-n‘¥„xi¤ Aklmstux q klxvWx{w²h p z h p x •’ p v m p '3~ & ˆ 0 ~ & ; 0 ƒitsh„¥ & ƒ q m  x Am q k ' ~ & ƒv q hb-n{¥bx \ 3\‡ zrx}t”vW¢l’ plp x}µ¤  \ &  X h„’l ix°n p z X

(201) \ fixµmozrx}t   & f„$ d ! ’5vWx

(202) zP’5n‘tum q g  ~WfixÄw q muh p?b" \ Pƒ q h­wyh p v q ’5w q n{tst5hb‚zrx}‚v  & ; " zrm”n‘¥„-n  v m p ' ~ &  89 ƒ q m  x@n p z v*j5nbwyx°wyh  jltsx}|Pm q  \ . . . . . . . . 9  5Ag 3'5  ³%--& l"',C<)5 B p h zrx p h q x{v4nŸv*x q h –ši¯ {ž¿²· ª 5j h„m pPq vAhb4tsm p x vWx}¥  x pPq vy¤lm p ’8wytsm”zrx{n p vWj5n„wyx \ klx ¦ h„•h p hbmzrm”n‘¥„-n  h – B mov4zrx 5p x{z m pq klx­vn  x Anlvnbv q klxŒjl•xÄwyx{zrm p ¥wµnbvWx ¤ m q m”v q klx q xÄv•vWxµton q msh p h –q k`xj`ton p xm prq h­wyx}tutov

(203) ~ iƒ<nbvvWhPwym”n q xÄz Am q kvWx}¥  x pPq v B   B    ~  ƒ  ~   ƒ

(204) ~ iƒ €mu¥b’lx "b\^a v*klh 4vŸn p x}|ln  jltux \ x q ’5v p h ,zrx q n{mst q klxv q •’5w q ’lx h –@q klxzrmon{¥b‚n  ¤ Aklm”wÀk Amutst(¢5x

(205) ’5v*x – ’lt – hb

(206) fix{w q msh p \ ar\ ar\ "„\ klx  n‘|Pm  n{t5x  j q †wyms‚wytsx

(207) w²x prq x}•xÄz n q n ix} q x}|Ÿh –q k`xŒzrm”n‘¥b‚n  q hb’8wÀklxÄv q klx}x h„¢ #*x{w q v²¤5n p z q klx  n{|rm  n{t5x  j q ­wymu-wytux@wyx prq x}•x{z­h p n p x{zr¥bx q hb’5w-klx{v q h­hb¢ #*xÄw q v \ ZYp x{zr¥„x  h –q klm”v@zrm”n‘¥b‚n  m”vYj5n‘ q h –Aq klxŒ¢lm”vWx{w q m p ¥†tsm p xŒh –<q hghb¢ #*x{w q v 4 n p z 5 ¤n p z0m q v q <hEx}| q •x  m q msx{v@n{•xx{£ ’`mozrm”v q n prq

(208) – •h  4 ¤ 5 n p z 6 n p z – •h  4 ¤ 5 n p z . . . '. '. ). +.-0/. . 1. /. #2. +. /. 3. 6-. 4. 6-. 73.

(209) . 

(210) . "}a. "  . . . €mu¥b’lx "b\^a ¦ h„•h p hbm:zrmon{¥b-n  h – tsm p x

(211) vWx}¥  x pPq v. . . . . €!ms¥b’`•x "b\ g  zP¥bx~ 4. 52(62. iƒ.

(212) ".    

(213) . 

(214) . . .   . {•x{v*j5x{w q mix}t  \  movAzPx 5p x{z¢ – hb’`@v*x}¥  x prq vn p z zrx p h q xÄz n„v~ 4 52(62 iƒ \PURq wyh p v*mov q v h – j5hb q muh p vAh – tsm p x{vn p zgj5n‘‚n‘¢5hbt”nbv \ h­zrx{vwy•mu¢ x q klx w}n„vWx@h – m p 5p m q x@x{zP¥bx{v²¤ x=nbzlz q klxv   ¢5hbt \ klx­•xµ¥bmsh p ~ 4 52(62 ;ƒwyhb•x{v*j h p zlv q h n p ’ p ¢5hb’ p zPx{z j5n{ q h –Aq klx ¢lm”vWx{w q m p ¥tsm p x3h – 4 n p z 5 ~R€mu¥b’lx "b\ ‰ ƒ \ hb•xµhixµ}¤ q hx p vW’lx­wyh plp x{w q mrm q i¤ x°nbzlz x{zP¥bx{vAn q m p 5p m q i¤ q k5n q Amutst ¢ h„’ p zg’ p ¢5h„’ p zrx{zgwyxµtstov4 q klx

(215) x{zr¥bx­~ 4 (62 iƒ!m p €mu¥b’lx "„\ ‰ mov q klx‹vWx q h – wyx pPq xµ-vŒ~Rn q m p 5p m q  ƒ4h –4q klxgw²ms-w²tsx{vŒ~ Am q k m p 5p m q x­-n„zrms’5v²¤ q k5n q m”v tum p x{v-ƒ q k5n qq hb’5w-k 4(¤„n p z m q m”vtsm  m q x{zY¢  q k`x4wyms‚wytsx{v q k5n q x{vWj5x{w q m ix}t q hb’5w-k 6 n p z \ URp €!ms¥b’`•x{v "„\ gn p z "„\ ‰r¤ q k`xŒvWk8nbzrh xÄz j5n{ q v4n‘x q klx3m prq x}•muhb-vh –q k`x3x  j q ­w²ms-w²tsx{v. . . . . . . $$$  . $  ).  . . 6 6

(216) .  , $1# : ' /, . . , ' ). $$$  . $  ). 

(217) =6 6 . . . €ms¥„’l•x "„\ ‰g URp 5p m q x@x{zP¥bx{v. wyx prq x}•x{z­h p xÄzr¥bx  \ URp v*h  xn  ¢lmu¥b’lh„’5v"w}n„vWx{v²¤rton{¢5x}t‡~ 4 52(67 ƒ  n%°zrx p h q x q h zrm x}x pPq x{zr¥„x{vy¤ q k8n q AmutstP¢ x4zPmov q m p ¥„’lmov*klx{z3m p3q k`x – hbtstuh Am p ¥ nŸ `~ 4 57(62 iƒ 8 n p z ~ 4 52(62 iƒ†~R€mu¥b’lx "b\ d ƒ \. klxŒ¥„x}h  x q •m”w

(218) zr’5n‘th –q klx ¦ hbh p h„mzrmon{¥b‚n  h – tum p x°vWx}¥  x pPq vmov q klxŒx{zP¥bx  x Ž p ”t n‘’ n  q •m”n p ¥„’lton q msh p‡\ 4\ Œ\ 'n{j  '<n‘j $iŠ ! ¥bm ixÄv3n p hbj q m  n{t<n‘ts¥„hbm q k  •’ p`p m p ¥Em p ' ~ & tshb¥ & ƒ q h­wyh  jl’ q x q k`x ¦ h„•h p hbm:zrmon{¥b-n  h – tsm p x{vn p z j5hb q muh p vYh – w²ms-w²tsx{v \.

(219) "‰.      C   . 

(220) =6 6 . . .  . . 6 6

(221) @.  . . 6 6 . . . . . . . . 6 6 . .  . . 6 6

(222) . . 

(223) =6 6 . . . €!ms¥b’`•x "b\ d ZY ¢`ms¥b’`hb’5vton‘¢5x}t~ 4  . 52(62. iƒ.  %T  . . YZ p n‘•‚n p ¥„x  x pPq m”v q k`x@j5n‘ q m q msh p h – j5hb q muh p vYh – kPj xµ-vW’` – nbw²x{v \. . . m p zr’8wyx{zŒ¢,†n 5p m q xvWx q h – kPj xµ-vW’` – nbw²x{v"hb. #55'C,C<)5 ; E+1Œ"513%@: B m”vn v*x q h – k rj5x}jlton p vŸm p  \

(224) klxE¥„x p x}‚n‘t4j h vWm q msh p w²h p zrm q muh p vWx q v q k5n q n p   ˆ " k,Pj5x}•jlt”n p xÄvk5n ix­x  j q gm pPq x}‚vWx{w q msh p ¤‡v*hEnixµ q xµ| h –4q klxgn{•-n p ¥bx  x pPq ¢5x Ž tuh p ¥ v q h x}|`nbw q t   k rj5x}jlton p x{v \ klx

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