Estimation of an O-D Matrix From Traffic Counts – a Review

8/12/2019 Estimation of an O-D Matrix From Traffic Counts a Review

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Zhivjrsitijs gd @jjas, Vcjddijà bha Ygrecttp;//jprihts.wcitjrgsj.bf.ue/

Ihstitutj gd Qrbhspgrt Vtuaijs

Zhivjrsity gd @jjas

Qcis is bh IQV ^greihn _bpjr prgaufja bha pumìscja my tcj Zhivjrsity gd@jjas. IQV ^greihn _bpjrs brj ihtjhaja tg prgviaj ihdgrlbtigh bha jhfgurbnjaisfussigh gh b tgpif ih bavbhfj gd dgrlb` pumìfbtigh. Qcjy rjprjsjht gh`y tcjvijws gd tcj butcgrs, bha ag hgt hjfjssbri`y rjd`jft tcj vijws gr bpprgvb` gd tcjspghsgrs.

^citj ]gsj ]jpgsitgry Z]@ dgr tcis pbpjr;

cttp;//jprihts.wcitjrgsj.bf.ue/=12:/

_umìscja pbpjr

î`ùlsjh, @.N. (29>3) Jstilbtigh gd bh G-A Lbtrix drgl Qrbddif Fguhts B]jvijw. Ihstitutj gd Qrbhspgrt Vtuaijs, Zhivjrsity gd @jjas, ^greihn _bpjr 99

^citj ]gsj Fghsgrtiul j_rihts ]jpgsitgryjprihtsOwcitjrgsj.bf.ue
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^greihn _bpjr 99

JVQILBQIGH GD BH ? A LBQ]ISD]GL Q]BDDIF FGZHQV B ]JTIJ^

@ î`ùrhsjh

Bunust 9>3

IQ V ^greihn _bpjrs brj ihtjhaja tg prgviaj ihdirl utigh bha jhfgurbnj aisfussighgh b tgpif h bavbh fj gd dgrlb` pumìfbtigh. Qcjy rjprjsjht gh`y tcj vijws gd tcjbutcgrs bha ag hgt hjfjssbri`y rjd`jft tcj vijws gr bpprgvb` gd tcj spghsgrs. Qc isrjvijw is pbrt gd b rjsjbrfc prgkjft gh tcj jstilbtigh gd trip lbtrifjs drgl t l d i ffguhts dihbhfja my tc j Vfijhfj ]jsjbrfc Fguhfi`.


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BMVQ]BFQ

Î@@Z;.JJH, @.N. 29>3) Jstilbtigh gd bh ?-A lbtrix drgl trbddif fguhtsb rjvijw. @jjas; Zhivjrsity gd @jjas, Ihst. Qrbhsp. Vtua., ^ 99

Dg``gwihn b rjvijw gd fghvjhtighb` ljtcgas,dgr jstilbtihn btrip lbtrix,tcj pgssimiìty gd usihn fcjbpjr ljtcgas mbsja gh trbddiffguhts is aisfussja. Qcrjj mrgba nrgups gd lgaj`s dgr sufc jstilbtighcbvj mjjh iajhtidija. Qcj dirst ghj bssuljs tcbt trips dg``gw b nrbvitytypj pbttjrh bha tcj prgm`jl is rjaufja tg fbìmrbtihn tcj pbrbljtjrsgd sufc b lgaj` drgl tcj gmsjrvja fguhts. Ajpjhaihn gh tcj bssuljadgrl gd tcj nrbvity lgaj` tcis tjfchiquj jbas tg ìhjbr gr hgh-ìhjbrrjnrjssigh sgùtighs.Qcj sjfgha nrgup gd lgaj`s bttjlpts tg jstilbtj tcj ?-A lbtrixtcrgunc b hjtwgre jquiìmriul bpprgbfc mbsja gh ^brargp s dirst prihfip`j.Qcj tcira nrgup dg``gws bh jhtrgpy lbxilisihn bpprgbfc ih wcifc tcj lgstìej`y trip lbtrix fglpbtim`j witc tcj gmsjrvja d`gws is sgunct.Dihb``y, tcj bavbhtbnjs gd jbfc bpprgbfc brj aisfussja bha tcjlgst prglisihn tjfchiquj bha brjbs gd bppìfbtigh brj iajhtidija.


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FGHQJHQV

Bmstrbft2 Qcj prgm`jl gd jstilbtihn b trip lbtrix

GmkjftivjsFghvjhtighb` ljtcgasMbsif fghfjpts bha ajdihitighsBssinhljht]jìbmiìty gd trbddif fguhtsJstilbmiìty gd b trip lbtrix drgl fguhtsFritjrib dgr sj`jftihn b ljtcga gd jstilbtighGvjrvijw gd trbddif fguht mbsja ljtcgas=. @ihjbr lgaj`s

=.2 Ihtrgauftigh=.= @gw s lgaj`=.=.2 Ajsfriptigh=.=.= Vfgpj bha bppìfbtighs=.=.6 Durtcjr ajvj`gpljhts

=.6 Gvjrnbbra s lgaj`=.6.2 Ajsfriptigh=.6.= Bppìfbtighs

=.1 @blbrrjd lgaj`= 1 2 Ajsfriptigh=.1.= ]jsu`ts

=.: .Fgllghwjb`tc Murjbu gd ]gbas lgaj`=.:.2 Ajsfriptigh=.:.= Bppìfbtigh

= 4 Abhisc ]gba Airjftgrbtj bpprgbfc=.4.2 Ajsfriptigh=.4.= Qcj itjrbtivj prgfjss=.4.6 Bppìfbtighs

6. Hgh-ìhjbr rjnrjssigh bpprgbfc6.2 Ihtrgauftigh6.= Cgnmjrn s lgaj`6.6 ]gmi``bra s lgaj`6.1 î`` s lgaj`6.1.2 Ajsfriptigh6.1.= Bppìfbtighs

1. Hjtwgre jquiìmriul bpprgbfc1 2 Ihtrgauftigh1.= Hnuyjh s ljtcga, fbsj I1.6 Hnuyjh s ljtcga, fbsj I2


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:. Jhtrgpy lbxilisihn bpprgbfc:.2 Mbfenrguha:.= Tbh [uy`jh s lgaj`

:.=.2 Ajsfriptigh:.=.= Ihfghsistjht fghstrbihts

:.6 Bh b`tjrhbtivj jhtrgpy lbxilisihn lgaj`:.6.2 Ajsfriptigh:.6.= Jxtjhsighs bha ìlitbtighs

4 Aisfussigh4 2 Ihtrgauftigh4.= Nrbvity typj bpprgbfcjs4.6 Jquiìmriul bssinhljht bpprgbfc4.1 Jhtrgpy lbxilisihn bpprgbfc4.: Jxtjhsighs tg ihfùaj fghnjstigh

>. ]jdjrjhfjs3 Bppjhaix 2 Hgtbtigh9 Bppjhaix = B `jbst squbrj jstilbtigh gd tcj tripdbftgr dgr tcj ] lgaj`

9 2 Ljtcga9.= Bppìfbtigh tg tcj ] lgaj`


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JVQILBQIGH GD H ?-A L Q ] I SD]GL Q]BDDIF FGZHQV ] J T I J ^

2 QC _]GM@JL GD JVQILBQIHN Q]I_. L Q]IS2 2 Gmkjftivjs

Qcis rjvijw i s pb rt gd b rjsjbrfc prgkjf t dihbhfja my tc j Vfijhfj]jsjbrfc Fguhfi` gh tc j jstilbtigh gd grini h aj stih bti gh t r i p lbtrifjsdrgl trbdd if fguhts .

Dgr b `br nj hulmjr gd bpp ìfbtig hs tcj jxistjhfj gd b r j` ib m `j bhar j ` b ti v j `y ihjxpjhsiv j ljtcga dg r js til btih n ?-A lb trifj s wguà mj vjryvb ùb m`j . Dgr jxblp`j;

lgaj`ìhn tr bh sp g rt ajlbha i h tgwhslg aj`` ihn bssjssljht bha ajsinh gd t r b d d i f lbhbnjljht sfcjljsi h ru rb ` bha urmbh brjbsfrgss-fcjf eihn gt cj r ljtcgasupa btihn g à ?-A lbtr ifj slgaj`ìhn r u r b ` gr ih tj r urmbh trbhspg rt ajlbha i h sp brsj` ypgpu`btja brjbs.lgaj`ìhn trb hs pg rt ajlbha wcjrj gtc jr a btb i s hgh jx is tj ht ,uh rj` ibm `j g r gut gd abtj b s pjrcbps ih ajvj`gpihn fgu htrij s.

t t c i s stb nj wj br j b`lgst j xfù sivj`y fghfjrhja witc kgurhjys my f br ,b s b rj b ` ` tc j ljtcgas rjvijwja cjrj. Qcj p`bh gd t c i s rjpg rt i s bs dg``gws;

Qcj rjlbihajrgd' ftigh ghj m r ij d ` y rjvijws fu rr jh t ljtcgag`gnijsd g r tc j jstil btigh gd ?-A lbtrifjs. Qcis i s dg``gwja my b aisfussigh gd sgljmbs if fghfjpts ` i e j t r i p njhjrbtigh , ai str im ut ig h bha bssinhljht lgaj`s. QcjVjftigh i s f`gsja witc b fglljht gh tcj prbftifb` bha tcjgrjtifb` prgm`jlsgd jstil btihn b t r i p lbtrix drgl fguhts.

Vjftigh twg rjvijws tcj i r s t nrgup gd tjfchiq ujs, hblj`y ì h j b rlgaj`s. Vjftigh tc rj j aisfussjs h jxtjhsigh gd tc js j i h tg hgh-ìhjbr lgaj`s.Vjf tigh dgu r aj sr im js ljtcgas mbsja gh tc j bssulptigh gd jq ui` imr iulbssinhljht bha Vjftigh divj aisfussjs jhtrgpy lbxilisihn lgaj`s.

Dihb ``y Vjftigh s i x fglpbrjs tc j tc jgr jt if b ` bha prb fti fb ` ilpìfbt ighsgd tcjs j d gu r nrgups gd lgaj`s-bha lbejs sglj rjfglljhabtighs dg r pr b f t i f b `bppìfbtighs. Bppjhaix I sullbrisjs tcj hgtbtigh usja ih t c i s pbpjr.

2


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2. = Fghvjhtighb` ljtcgasQcjrj b rj b hulmjr gd ljtcgas dg r jst il btihn bh gr in ih aj st i hb t ig h

t r i p l btr ix . B ` ` mut ghj gd tcjl ilp`y sblpìhn bha jvjh i d b ` ` t r i p s gh baby brj rjfgraja t c j prgm`jl gd s t b m i ` i t y gd tc j ? A l bt r i x gvj r t i l j s t i ` `rjlbihs. ]jb2 tri.p lbtrif js tcj h b r j hjvjr bv bi `b m` j5 wj gh `y cbvj lgrjgr `j s s r j ` ib m` j ljtcgas d gr jst ilbtihn tcjl.

Vglj gd t c j tjfchiqujs bvb i `bm `j b t prjsjht br j;( b ) ]gba s ia j ih t j rv ijws gd a r iv jrs , usub ` `y b t t cj jx i t g d b

fgraghja brjb. Vblpìhn dr b ft ig h s gd h lby mj fghsiajrjaty p if b` mut tcj y fj rtb ih` y ajpjha gh t r b d d i f `j v j` s bha lbhpgwjrbvb i ` bm ` j . Qcjy brj usub` `y bsyhfcrghif , t c b t i s t c jy b r jfb rr ija gut gh ai d djr jht abys mut b t s il i `b r t iljs. Qcjy tjhat g mj jxpjhsivj i h lbhpgwjr, aj`bys t g vjc if` js bha prgfjssihn.

(m ) Cglj ihtjrv ijw. B`tcgunc usu b``y hgt fghs iajrj a r j ` i b m ` j jhguncdg r b aj tbi `ja ajsinh g d , dg r jxblp`j, b t r b d d i f lbhbnjljhtsfcjlj, tc jy lby mj tcj r js u ` t gd b ` b r n w stuay bha mj bv bi `b m`jd g r frgss-fcj feihn. Qcj ljtcga i s jxpjhsivj gh lbhpgwjr bhatilj fghsulihn.

( f ) D`bnnihn ljtcgas. It i s pgss i m `j t g i ajh t i dy vjc i f ` j s b t fgraghbha ih tj rh b` pgihts my ljbhs gd rj ni s t rb t ig h hulmjrs, s t if ej rsgr my bse ihn ar ivj rs jh tj r ihn t b n iv jh p g i h t t g s w it fc t c j i r` i nc t s gh. Qci s ` b s t ljtcga cbs gh `y mjjh t r i j a d g r vjry slb``br j bs (rgu hab mgu ts), sj j d g r jxblp`j MjmJj (29: 9). Qcj hulmjrp `b t j ljtcga i s gd wiajr usbnj bha b`s g rjq uir js b ngga ajb `gd lbhpgwjr bha prgfjssihn jddgrt. Zsub` `y arivjrs ag hgtihfur jx t rb aj `bys .

( a ) Bj rib ` pcgtgnrbpcy. Qg b `b rn j jxtjh t t c i s ljtcga i s jxpjriljhtb`,it r jqu i r j s b ngga ajb ` g d p rgfjss ihn t g ia jh t i d y fb rs bha t rbf etcjl i h b fglputjr rj bab m`j dgrl. It i s gh ` y suffjs s du ` dg rslb` ` brjbs mut ilprgvjljhts i h tc j butglbtif ia jh t i d i fb t ig h gdvjcif ` js lby i hf rj b sj t c j i r b p p ` i f b m i ` i t y . I t i s t cj gh ` yljtcga wcifc agjs hgt hjfjssbri`y rjquirj sblpìhn.

( j ) Fbr dg``gwihn. Vunnjstja my ^rinct (29>>) bha t r i j a i h ^jstlihstjr,t c i s ljtcga cbs mjjh f`bilja t g mj fcjbpjr tc bh gtc jr ljtcgas.I t s bpp ` i fb t i gh i s p rg mb m`y r j s t r i f t j a t g t c j f j h t r b ` b r j b s gd` b r n j f i t i j s .


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Ih fgh t rbs t , wj br j ih tjr js tj a i h tc i s r jv ijw ih ljtcgas d grtcj js t ilbt igh gd ? A lbtrifjs mbsja gh b ajsfript igh gd tcj hjtwgrebha t r b d d i f fguht s . I h ba ai ti gh sglj gd tc j ljtcgas rj qu ir j sglj wiaj`ybv bi` bm `j zghb` ab tb, ` i e j pgpu`bt igh bha jlp`gyljht. Qrbd d if fguhts brjrj `b t iv j ` y s ilp`j t g gm tb ih bha du r tcj r prgnrjss i h bu tglbt if r jfgraihnbha f ` b s s i d i f b t i g h i s jhvisbnja. j suspjft tc b t hgt jhgunc usj i slbaj gd t c i s ihdgrlbtig h.

2.6 Mbsif fghfjpts bha aj d ih i t ig hsLgst gd t c j vgfbmu`bry i h tc i s rjvijw i s mgrrgwja drgl fghvjhtighb`

trbhspgrt ajlbha lgaj`s.Ih fghvjht ighb` t rbh spg r t lgaj` ìhn jxjrf isj tc j s tuay brjb i s

usu b``y aiviaj a ih tg zghjs wcifc br j fghsiajrja tc j nj hjrbtg rs bhab t t r b f t g r s gd t r i p s . Qcj lgaj`ìhn prgfjss us ub ``y prgfjjas i h b sjqujhfjgd dgur sumlgaj`s;

Qr ip n jhj rbtig h wcifc usjs zghb` ab tb t g lgaj` t c j hulmjrgd t r i p s mjihn njhjrbtja d rgl bha bt t r bf tj a t g jbfc zghj.Qr ip ais t r@mu t igh wcifc syhtcjs isjs . tcj gr inih-a js t ihbt ig h lbtr ix,t c b t i s t c j hulmjr gd t r i p s drgl jbfc zghj t g jbfc zghj. t i sfgllgh pr bf ti fj t g usj cjrj b nrb vity typj lgaj . Qcis , i hnjh jrb ` , bssuljs tc b t t c j hulmjr gd t r i p s mjtwjjh i bha k b r jprgpg r t ighb` t g tc j njhjrbt igh bha bt t rb ft ig h pgwjr gd jbfc zghjbha prgp gr t ighb ` t g sglj ajfrjbs ihn d uhft igh gd tc j fgs t ( i ht ilj, ais tb hf j g r lghjtbry tjrls) gd tr b v j `` ih n mjtwjjh tcjl.Qcis ajfrjbs ihn duhft igh i s usub` `y fb ` ` j a tcj aj tjr rjhfjduhft ig h gd tc j lgaj`.Lgab` s p ` i t i h wcifc t c j fcgifj g d lgaj lbaj my jbfc tr b v j ` `j ri s silu`btja. j s c b ` ` hgt mj fghfjrhja witc tc i s sumlgajì h t c i s rjvijw , b s wj r j s t r i f t g ur b t t j h t i g h t g f b r t r b d d i f .Bssinhljht , i h wcifc t c j rgu tj dg` `gwja my jbfc t r i p i slgaj``ja. Qcj gutput d r g l tc is s tbnj ihfùajs ` i h e d `gws bha

rjvisja ljbsurj gd tc j fgs ts gd t rb vj ` ` i hn mjtwjjh jbfc pb i rgd zghjs.


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Bs tcis bssinhljht stbnj is vjry rj`jvbht tg gur prgm`jl wj wi`` aisfussit ih sglj ajtbi`.

2.1 BssinhljhtB rgba hjtwgre is usub``y ajsfrimja ih tjrls gd b fg``jftigh gd

pgihts, fb``ja lajs bha b fg``jftigh gd grajrja pbir gd lajs fb``ja' rjb ìhes" gr silp`y " ihes".. B ìhe is usub``y ajjlja tg rjprjsjhtb rjb` sjftigh gd b rgba, dgr jxblp`j drgl ghj ilpgrtbht ihtjrsjftigh tgbhgtcjr. Lgst gd tcj aj`bys ih urmbh brjbs gffur bt ihtjrsjftighs. Qcus,ih sglj fbsjs it is wgrtcwci`j tg ajdihj b hjtwgre ih sufc b wby tcbtfjrtbih ìhes rjprjsjht pbrtifu`br turhihn lgvjljhts bt bh ihtjrsjftigh.Dinurj 2.2 rjprjsjhts b wby ih wcifc bh ihtjrsjftigh fguà mj rjprjsjhtjamy ìhes rbtcjr tcbh lgajs.Dinurj 2.2 "HGAJ" BHA "@IHE" ]J_]JVJHQBQIGH G BH IHQJ]VJFQIGH

ihtjrsjftigh rjprjsjhtja ihtjrsjftigh rjprjsjhtjamy ghj hgaj. my 4 twg wby ìhes bha 1hgajs.Gd fgursj witc b "ìhe" rjprjsjhtbtigh tcj hulmjr gd hgajs bha ìhes

is nrjbt`y ihfrjbsja. Gh tcj gtcjr cbha, it is fustglbry tg fguht trbddifprjfisj`y bt ihtjrsjftighs rjfgraihn jbfc turhihn lgvjljht ihajpjhajht`y,tcus tcis rjprjsjhtbtigh is gd ihtjrjst.

Grinih bha Ajstihbtigh zghjs lby mj fghsiajrja bs b sum-hjt gd tcjhgajs, njhjrb``y rjdjrrja tg bs "fjhtrgias". Qcj brf ìheihn b "fjhtrgia"witc tcj "rjb` ìhe" hjtwgre is usub``y fb``ja b "fjhtrgia fghhjftgr".Jbfc ìhe cbs b trbvj` fgst bssgfibtja witc it (tilj, aistbhfj, lghjygr njhjrbìsja fgst) wcifc, auj tg fghnjstigh, ajpjhas gh tcj tgtb` d`gwgh tcbt ìhe jxprjssja bs

Fb fb(Tb) 2.2)


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( ~ b )wcjrj b i s b ` i h e

b i s b ` i he fgs tTb i s t c j t r b d d i f vg`ulj gh ` i h eImr b ngga aisfussigh gd t c j prgm`jl gd t r b d d i f bssinhljht t c j

rjbajr i s r j dj r rja t g Tbh T` i j t (29>4). Cjrj wj s c b ` ` gh` y ajs frim jmr i j d `y tc rjj b ` t j rhb t ivj bpprgbfcjs .

( b ) B``-gr-hgtcihn bssinhljht v ib t c j lihilul fg st rgu tj. dwj bssulj t c b t `` ar ivj rs tr b v j `` ih n mjtwjjh twg zghjs fcggsjtcj sblj rgutj it sjjls gh`y `g ni fb ` t g bssulj tcjy t r bv j`v ib tc j (bppbrjh t`y ) fcjbpjs t rgu tj ( b sjqujhfj gd ` i he s) .Ih t cj bmsjhfj g d fghnjst igh g r i d t c j r j b rj hg r j b `b ` t j r h b t i v j r g u tj s it i s pgss i m `j t g aj tj rl ihj t cj s j t g dlihilul fg st r gu tj s mj dg rj lbeihn bhy bssulptigh bmgut t c jhulmjr gd t r i p s us ihn tcjl.

(m ) _rgp grt ighb ` bssinhljht. d wj bffjpt t c b t hgt b ` ` a r i v j r sIpjrfjivj b rgu tj fgs t t g mj tc j sblj wj lust b` `gw ih tc jbss inhljht p rgfjss dg r tcjsj a i d dj rjhfjs . Ih t c i s fbsj tc jprgpgrt igh gd arivjrs fcggsihn jbfc gd b rjaufja s j t gd hjbrgptilul rgutjs w i ` ` mj ajtjrlihja my bssulja arivjrs bhargutj fc brb ftj r i s t if s . Qcjsj ljtcgas fur rjh t `y ag hgt fghsiajrfghnjst igh j d d jf t s sg tcjsj prgpgr tighs b r j t rj b t ja bsihajpjhajht gd ` i h e d`gw `j vj `s .Dg``gwihn ]gmi``bra (29>:) it i s p g ss im `j t g s t r i f t ` y a jd ih jprgp grt ighb ` bssinhljht b s b tjfchiquj i h wcifc;( i ) Qcj tgtb` . bssinhja d`gw gh b ` i h e jqub`s t c j sul gd

t c j bssinh ja d`gws gmtbihj a wcjh t c j ljtcga i s bpp` ijat g jbfc ?-A p b ir sjpbr btj`y.

( i i ) d b ` ` tc j jh t r ij s gd tc j ?-A lbtr ix brj lu` t ip` ijamy b fghstbht dbftgr b ` ` tcj bssinhja d`gws gh jbfc` i h e w i ` ` i hf rjb sj my t cb t d bf t g r .

F`jbr`y tcj sj fghai t ighs br j hgt rj b ` i s t i f wcjh fghnjst ighp`bys bh ilpgrtbht r g ` j ih bssinhljht. Gh t c j gt cj r cbha,tc j bavbhtbnj gd Kc js j bssulptighs i s t c b t it i s p g s si m `j t gbjtjrlihj tc j prgpgrt igh gd t cj t r i p s mjtwjjh i bha usihn


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b ` ih e mjdg rj bhy nujss i s lbaj bmgut t c j ? A lbtrix. Qcjsjprgpgrtighs ajpjha gh`y gh tcj hjtwgre bha tcj pbrbljtjrs gdtc j bssinhljht b`ngri tcl mut hgt gh d`gw `j v j `s b t jbfc ` ih e.

( f ) Jqui` imriul bssinhljht. ^cjrjvjr fghnjst igh jd dj ft s b r j tcgunctt g mj lgrj ilpgrtbh t tcbh t cj a i d dj rjhfjs i h pjrfj ivja t r bv j `fgsts b ai ddjrjht typj gd bssinhljht i s fghs i aj rja r jb ` i s t i f .Qci s typj t r i j s t g sb t i s dy ^brargp's d i r s t p r ihf i p `j wcifcfbh mj s t b t ja bs

Qrb dd if gh b hjtwgre ai s t r i mu tj s i t s j ` d i h sufc b wbyt c b t t cj t r bv j ` fgs t s gh b ` ` rgu t j s usja drgl bhy g r i n i h t gbhy ajst ihbt igh brj jqub` wci `j b ` ` uhusja rgutjs cbvj jqub`g r n rjb t j r fgs t s .I h g tc jr wgras bh bssinhljht i s sb ia t g cbvj rjbfcja jqui ` imr iulwcjh hg ar ivj r fbh rjaufj cis t r b v j ` fg st my swi tfcihn t g bhgtcjrrgu t j .

Ljtcgas mbsja gh mgtc cjuristif bha lbtcjlbtifb` prgnrbllihn tjfchiqujsbr j usjb t g gm tb ih tc i s typj gd bss inhljht. Ih t c i s fb sj t cj p rgpg rt igh gdt r i p s cjtwjjh bh ?-A p b i r usihn jbfc rg ut j ajpjhas gh t c j bf tu b ` d`gws ghjbfc ` ihe .

2 .: ] j ` i bm i ` i t y g d t r b d d i f fguht s.Qcjrj brj b hulmjr gd prgm`jls b ss gf ibt ja witc tr b d d i f fguhts bha wj

s c b ` ` rjvijw sglj gd tcjl.( b ) Ihajpjhajhfj. Hgt b ` ` t r b d d i f fguhts fgh tbih t c j sblj blguht

gd ' ihdgrlbtigh . Dgr jxblp`j ih Dinurj 2.= t r b d d i f ` i h e 6-1i s lbaj up gd t c j sul gd t r b d d i f gh ` i he s 2-6 bha =-6.Fguhtihn trbddif gh `ihe 6-1 i s tcjh rjauhabht bha gh`y twgfguhts tcj rj fbh mj s bi a t g mj ihajpjhajht.

Dinurj 2.= J_JH JHQ FGZHQV


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Ih lbtcjlbt ifb` tjrls t c i s fbh mj jxprjssja my wri t ihn dg r jbfc ` ih e i htcj hjtwgre;

Ajpjhajhfj i h tc j d`gws gffu rs wcjrj t i s pgss im `j t g jxprjss ghj gd tcjsjjqubt ighs bs b ` ih jb r fglmihbt igh gdsglj gd tc j gtcj r jqubt ighs.Qcis i s ` i e j ` y t g cbppjh i h s i t u b t i gh s sufc b s t c b t ajp if t ja i h

Dinurj 2.= wcjrj b d`gw fghtihuity jqubtigh bpp`ijs

Qcj jxis tjh fj gd b sgurfj g r s ihe gd d `gw fjh t rgia fghhjftgr) b t6 w i ` ` illjaibtj`y rjlgvj t c i s ajpjhajhfj.

m) Ihfg hsistjh fy. Fguhtihn j r r g rs bha bsyhfcrghgus fguh tihnbrj ` i e j ` y t g `j b a t g i h fg h s is t jh f ij s i h t c j d `g ws. I h g tc j rwgras, tc j jxpjftja fgh t ihu i ty rj `b t ig hsc ips w i ` ` hgt mj ljt.

s wj w i ` ` sj j sglj lgaj`s fbh rj ba i`y fgpj witc t c i s prgm`jlwci `j gtcjr s rjq ui rj tcj sj ih fghs is tjhfijs t g mj rjlgvjamjdgrjcbha.

f ) Fguhtihn pj rig as . Ajpjhaihn gh t c j fgu htih n ljtcga t i sp g s s im ` j t g g m tb i h t r b d d i f d`gw s d g r p j ri ga s b s s c g r t b s 2 :lihutjs gr s `ghn bs =1 cgurs. h ? A lbt r ix ajr ivja gh tc i sm b s i s w i ` ` g h `y mj r j ` j vb h t i d t c j t r i p t il j w it c ih t c j s tu ayb r j b i s s i nh i d i fb h t ` y scg r t j r t cbh t c j fguh ti hn pj ri ga. Dgri h t j r urmbh s t ua i j s t w i ` ` usub ` `y mj pgss i m ` j t g j s ti l b tjtc j bvjrbnj Bhhub` Abi `y Qrb d d i f L Q ) bha usj t i h t c jlgaj`s.


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a) Vylljtry. D`gws brj ih njhjrb` bsylljtrif, tcbt isT.. Tki. Ih lgst ihtjr urmbh bppìfbtighs, tcgunc,6it is pgssim`j tg bssulj sylljtry ih tcj fguhts bha ih tcj?-A lbtrix tcus rjaufihn tcj fglp`jxity gd tcj lgaj`s.

2.4. Jstilbmiìty gd b trip lbtrix drgl fguhts.b@jt Qik mj tcj hulmjr gd trips drgl zghj i tg zghj k bha pi k mj

tcj prgpgrtigh gd trips drgl i tg k trbvj`ìhn gh b ihe. Dgr jbfc ìhewj fbh hgw writj tcj jqubtigh

bwcjrj p is tcj prgpgrtigh gd trips drgl i tg usihn ihe b.i bIh b stuay brjb witc H fjhtgias zghjs) bha bssulihnJ.. tg mjKehgwh wj wguà hjja H ihajpjhajht jqubtighs gd tcj typj 2.6) tg uhiquj`y

ajdihj tcj wcg`j sjt gd @-~ik-i Id wj bssulj tcbt Qik < ? dgr i < k wjwguà gh`y hjja H H-2) qubtighs. Cgwjvjr, ih lgst fbsjs tcj hulmjr gdihajpjhajht ìhe fguhts wi`` mj `jss tcbh tcis dinurj. Qcj lgst ilpgrtbhtilpìfbtigh gd tcis is tcbt trbddif fguhts wi`` hgrlb``y mj ihsuddifijhttg uhiquj`y ajtjrlihj bh ?-A lbtrix @-~ik->. Qcus, ih grajr tg gmtbih bhjstilbtigh gd tcj ?-A lbtrix sglj bssulptigh wi`` cbvj tg mj lbaj bmguttrip lbeihn mjcbvigur.

Bs wj wi`` sjj wcjh rjvijwihn tcj prgpgsja lgaj`s, b drjqujhtbpprgbfc is tg bssulj sglj sgrt gd nrbvity typj mjcbvigur ih trip lbeihn.Ih tcis wby tcj bftub` hulmjr gd uhehgwhs is rjaufja tg tcj hulmjr gdpbrbljtjrs dgr fbìmrbtigh ih tcj bssulja lgaj`.

Id tcj hulmjr gd uhehgwhs is slb``jr tcbh tcj hulmjr gd ihajpjhajhtjqubtighs ìhe fguhts) jrrgrs cbvj tg mj bssulja ih tcj lgaj` gr tcjgmsjrvbtighs ih grajr tg sg`vj tcj systjl. Dgr jxblp`j

wcjrj n b i s bh jrrgr tjrl witc bssulja ljbh ?. Qcj sgùtigh is tcjh dguhamy-lihilisihn cj suppgsja jrrgrs, usub``y my ljbhs gd lu`tip`j ìhjbr


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gr gtcjrwisj) rjnrjss igh bhb`ys is .Lgst fglputjr ilp`jljhtbtighs ihfùa j sgdtwbrj t g sg `vj t c i s typ j

gd prgm`jl.

2 .> Fr i tj r ib dgr sj` jf t ih n b ljtcga gd js t ilbt igh.Dgr scg rt tjrl bp pì fb t ig hs, (wcjh tc j bssulptigh gd b d ix ja t r i p

lbtrix i s r j b ` i s t i f ) , t c j lbih f r i t j r i g h i s prgmbm`y bffurbfy.Ih grajr t g t j s t t c j bffurbfy gd b lgaj` tc j i aj b` fbsj wguà mj t g

fglpbrj tcj jstilbtja ?-A lbtrix wi tc tc j r jb ` ?-A lbtrix wcifc prgaufjatcj fguhts usja my tcj ljtcga. Cgwjvjr, wj aia hgt di h a bhy sufc t j s ti h tc j ` i t j rb tu rj , hg agumt mjfbusj b r jb ` ?-A lbtr ix i s a i d d i f u ` t t gfglj my. Ih st jb a , b lgrj fgllgh iha ifb tg r gd t c j bffurbfy gd b lgaj`,i s t g fglpbrj gmsjrvja bha prj aif tja ` ih e d`gws v i b , dg r jxblp`j

, ;]LV j r r g r < / GMVJ]TJA _]JAIFQJA // h-2(]ggt ljbh squb rj jr r g r ) //

jxprjssja j i t cj r i h bmsgù tj vb ùj g r bs b pjrfjhtbnj gd tc j bvjrbnjgmsjrvja vbùj. Qcis ljbsurj fguà b` sg mj usja t g t j s t tc j bffurbfyg d j bfc f j ` ` i h t c j ?-A lbtrix bha t c i s t j s t wguà mj lufc lgrj sin hid ifb ht .

I h ba ait igh , wj wguà ì e j t g ehgw cgw bffj ptb m`j i h jbfc fbsj b rjt c j bssulptighs il p` if it i h jbfc ljtcga. Dgr jxblp`j, i s t p g ss im ` j t gjxpjft b nr bv i t y typj g d t r b v j ` mjcbv igur7 s it s jhs i m ` j t g a i s r jnb rafghnjstigh j dd j f ts bha bssulj rgu tj fcgifj t g mj ihajpjhajht drgl d`gw` j v j ` s 7

Dih b` `y , i d wj b rj i htj rjs tja i h ljaiul t g `ghn tjrl ilp` ifbt ighswj wguà ` i e j t g ehgw i d t c j i lp ìf i t t r b v j ` ajlbha lgaj` i s s u d d i f i j h t ` ypg` i fy sj hs i t iv j dg r gur purpgsjs bha i d t i s pgss im `j t g cbvj b r j ` i b m ` jdgrj fbs t d in ur j d g r tc j p`bhhihn pbrbljtjrs i h tcj lgaj` (_gpu`bt igh,jlp`gyljht, jtf.

j s c b ` ` r j t u r h t g t c j sj f g hs ia j rb ti gh s i h s j f t i g h s i x .


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2 .3 Gvjrvijw gd t r b d d i f fguht mbsja ljtcgas.j cbvj gh`y dguha b rj s t r i ft ja hulmjr gd pum ` ifb t igh s i h tc j d i j` a .

j suspjf t , tcgunc, tc b t g tcjr rjsjbrfcjrs bha pr bf t i t ig hj rs cbvj ajvj`gpjabha usja s il i`b r ljtcgas witcgut rjp grt ih n tcjl i h tjf ch if b` kgurhb `s .

j cbvj nrgupja t c j prgpgsja ljtcgas ihtg tcrjj mrgba nrgups;Qcj d i r s t bssuljs tc b t b nrbvi ty lgaj` i s fbpbm`j gd jxp`bihihn

lgst gd tc j t rb v j ` mjcbvigur i h tc j s tuay brjb. Qcj uhajr `yihn nrbvi tylgaj` fbh mj prjsjhtja wi tc sj vjrb ` ajnrjjs gd sg pc is t i fb t ig h bha t c i scbs ` j a us t g fg hsiajr twg sum-nrgups;

- .Nrbvi ty lgaj`s ` jbaihn t g ` ih jb r jqubt ighs gh tc j ` ih e sNrbvi ty lgaj`s `jbaihn t g hgh- ìhjbr jqubt ighsgh t c j ` ih es .

Lgst g d t c j p rgpgsja ljtcgas bha n t c j bpp ` i fb t i ghs w i t c r jb à b tb d b ` ` i h t g tc i s -m r g b a d i r s t fbtjngry.

Qcj sjfgha nrgup gd lgaj`s bttjl pts t g j stil btj b h G A lbtrix tcrguncb hjtwgre jq ui` imr iu l bpprgbfc mbsja gh ^brargp s d i r s t pr ihfip`j . Qcjsjb r j ajs fr imja i h Vjf ti gh 1

Qcj t c i r a nrgup gd lgaj`s fghsiajrs ljtcgas dg r jst il btih n t c j ` i e j `yt r i p lb t r ix fglpbti m` j w it c t c j g ms j r vja t r b d d i f fguh ts . Qcjsj ljtcgasfgu à mj r j d j r r ja t g bs jhtrgpy lbxilisihn g r ihdgrl btigh l ihilisihn bpprgbfcjsbha br j ajsfrimja ih Vjf t igh :.

=. @IHJ ] LGAJ@V=.2 Iht rgauft igh

Qcj iaj b gd u sihn b sil pì dij a lgaj` d g r tr b v j ` ajlbha i s hgt hjw._rgmbm`y tcj d i r s t sufc lgaj` fb` imrbtja drgl ìhe d `gws w b s prgpgsja my@gw (29 >=) . Qcj m b s i f ia j b i s t g usj b s ilp`j ` ih jb r lgaj` gd tc j nrbvi tyt yp j ` i e j

wcjrj _i ,J k pgp u`b tigh , jlp`gyljht i h zghjs bha ka. ais tbhfj gr t r b v j ` t ilj mjtwjjh bha kK

pbrbljtjr dg r fb ` imrb t igh .


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Ih tcis lgaj` b p`bys b fglmihja rg`j, bs trip njhjrbtigh-bttrbftighpbrbljtjr. Qcjh, ih grajr tg fbìmrbtj b tcj lgaj``ja trips lust mjtrbhs`btja ihtg ihe d`gws tg fglpbrj tcjl witc gmsjrvja fguhts. Qcisilpìjs bh bssulptigh bmgut tcj typj gd trip bssinhljht fghsiajrja tg mjrjbìstif. Qcj silp`jst bssulptigh is tg bffjpt b``-gr-hgtcihn bssinhljht,tcbt is

id trips drgl i tg k ag hgt trbvj` gh ìhe b.b 2. d tcjy ag.Qcjh bTb < Q .p. - = b2~ `k < ~F.(_.J.~.. )pik

ik i.= 2Kih wcifc b`` pbrbljtjrs jxfjpt b brj ehgwh. It is tcjh hjfjssbry tg ajtjrlihj

ih sufc b wby tcbt tcj aiddjrjhfj (gr tcj sul gd tcj squbrjs gd tcjaiddjrjhfjs) mjtwjjh lgaj``ja bha gmsjrvja d`gws is lihilisjb. Qcis fbh mjbfcijvja cjrj usihn stbhabrb ihjbr rjnrjssigh tjfchiqujs.

Qcis fcbptjr rjvijws aiddjrjht ìhjbr lgaj`s bs sunnjstja my @gw,Gvjrnbbra, @blbrrj bha Kjhsjh jt b . Qcjy aiddjr lbih`y witc rjspjft tg;

- Qcj ihajpjhajht vbribm`js- Qcj ajtjrjhfj duhftigh- Qcj typj gd bssinhljht.Qcis is tcj dbli`y gd lgaj`s witc tcj nrjbtjst hulmjr gd bppìfbtighs,

lgst`y ih rurb` gr ihtjr-urmbh brjbs.

=.= A.J.@gw2s Lgaj`=.=.2 Ajsfriptigh. Qcj lbih gmkjftivj gd @gw's bpprgbfc is tg jddjftivj`y

fglmihj ihtg ghj prgfjss wcbt is usub``y cbha`ja ih b sjrijs gd tcrjjgr dgur sum lgaj`s, jbfc witc its gwh sjt gd jrrgrs. @G^ 29>=Bttjlpts tg ajvj`gp b lgaj` wcgsj airjft gutput is trbddif vgùljsbha wcjrj lgaj`ìhn jrrgrs,wcifc bppjbr ih tcj sblj tjrls, fbh mjjbsi`y ajsfrimja bha bssjssja.@gw sjjs cis lgaj` bs bppìfbm`j, ih prihfip`j, tg b `brnj rbhnj gdstuay brjbs mut jspjfib``y tg slb`` ghjs (brguha :?,??? ihcbmitbhts).

.


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2.3 Gvjrvijw gd t r b d d i f fguht mbsja ljtcgas.j cbvj gh `y dguha b r j s t r i f t ja hulmjr gd pu m` i fb t ighs i h tc j d i j à .

j susp jft , tcgunc, t c b t gtc jr rjsjbrfcjrs bha pr bf t i t ig hj rs cbvj ajvj`gpjabha usja sil i`b r ljtcgas witcgut rjp grt i hn tcjl i h tjf ch if b` kgurh b`s .

j cbvj nrgupja tc j prgpgsja ljtcgas i h tg t c rj j mrgba nrgups;Qcj d i r s t bssuljs t c b t b n rb vi ty lgaj` i s fbpbm`j gd jxp `bihihn

lgst gd t c j t r b v j ` mjcbvigur i h tc j s tuay brjb . Qcj uhajr`yihn nrbvitylgaj` fbh mj prjsjhtja wi tc sj vj rb` ajnrjjs gd sgp cis t ifb t igh bha t c i scbs ` j a us t g fghsiajr twg sum-nrgups;

- .Nrbvity lgaj`s ` jbaihn t g ` ih jb r jqubtighs gh tcj ` ih esR.bvity lgaj`s `jbaihn t g hgh-` ihjbr jqubt ighsgh tc j ` ih es .

Lgst g d t c j p rgp gsja ljtcgas bha s t c j p p ` if b t ig h s w i tc r j b àb t b d b ` ` i h t g t c i s m r gba d i r s t fbtjngry.

Qcj sjfgha nrgup gd lgaj`s bttj lp ts t g js til btj bh ?-A lbtr ix tcrguncb hjtwgre jqu i` imriul bpprgbfc mbsja gh ^brargp s d i r s t p rih fi p`j . Qcjsjb r j ajs f r imja i h Vjft igh 1

Qcj t c i r a nrgup gd lgaj`s fghsiaj rs ljtcgas dg r jst il btihn t c j ` i e j `yt r i p lbtr ix fglpbtim`j wi tc tcj gmsjrvja t r b d d i f fguhts . Qcjsj ljtcgasfguà mj rj dj rr ja t g bs jhtrgpy lbxilisihn g r ihdgrl btigh lihilisihn bpprgbfcjsbha br j ajsfr imja i h Vjf t igh :

=. @IHJB] LGAJ@V=.2 Ih t rgauft igh

Qcj iaj b gd usihn b sil p` id i ja lgaj` d g r tr b v j ` ajlbha i s hgt hjw._rgmbm`y tc j d i r s t sufc lgaj` fb ` im rb tja drgl ` ih e d `gws wbs prgpgsja my@gw (29>=). Qcj mbsif iajb i s t g usj b s ilp`j ` i h j b r lgaj` gd tc j nrbv i tyt yp j ` i e j

wcjrj _i,Jk < pg pu `bti gh , jlp`gyljht i h zghjs bha k.

a - . < ais tbh fj g r t r b v j ` t ilj mjtwjjh bha k6b < pbrbljtjr dgr fb ` imr b t ig h .


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C i s bpprgbfc fghs is ts gd tcrjj s tjps ;

( b ) Bssinhljht gd jx tjrhb ` t r i p s . Fur rjht jx tjrhb ` t r ip s bsgmtbih ja drgl jx tjr hb ` fgragh rgbasiaj ihtj rvijw s brjbss inhja t g t cj jx i s t ihn hjtwgre t g prgaufj js t ilbtjs gd

fur rjh t jx tj rh b` vgùljs tcrguncgut t c j hjtwgre.(m ) Jstilbtigh gd furrjht ih tj rh b` vgùljs . Qcj sg fb ``j a

furrjht i ht jr hb ` vgùljs brj tcjh gmtbihja drgl tcj bf tub `fguhtja d`gws ` j s s tc j bssinhja furrjh t j xt jrh b` vgùljs .Qcjsj furrjht ih tjr hj ` vgùljs brj tc j r j su ` t gd t r i p swcg` `y jxp`bihbm`j i h tjrls gd b rjb fcb rbf tjr is t i fs .

( f ) Ih tj rh b ` vgùlj dg rjf bst ihn lgaj`.i) Ih tj r zghb` t r i p gppgr tuhity lbt r ifjs gd tc j dgrl_k b r j ajvj`gpja. Dgr tc j kgurhjy t g wgre _gpu`bt igh

bha Jlp`gyljht b r j usja .( i i ) Jbfc j`jljht g d t c j t r i p gppgrt uh it y lb t r ix i s t cjh

ll u ` t ip ` ij a my b d r i f t i g h d b f t gr g d t c j t y pj Fi k I hnjhjrb` t ilj i s sunnjstja bs ljbsurj gd fg st . Qcj prgauft

222? A F . i s f b ` ` j a t c jh bh i h t j r z g hb ` t r i p p r g m b m i ` it y2 K 2Kd bf tg r bha tcj d u ` ` s j t g d d b f t g r s i s t cj t r i pp r gmbm i ` i t y lb t ri x . V j vj rb ` t r i p p r g m b m i ` i ty d b f t g r s ,sby d g r ai dd jr jh t kgurhjy purpgsjs bha pjrsgh ty pj s, lbymj sg ajvj`gpja.

lx < 2 . f2 K

^cjrj S < t r i p p r gmbm i ` i t y d bf t g r mjtwjjh i bha k d g rh i k pjrsgh tyq j g r kgurhjy purpgsj h.

( i i i ) Qr ip prgmb mi ` i ty lbt ri fjs b r j tcjh bs s inhja sjpbrb tj `yt g t c j f u rr j ht hjtwgre ( i h p r b f ti f j bh b``-gr-hgtcihnbss inhljht) kus t bs id tcjy wjrj t r ip s .


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Dgr b ì h e b

2 d tc j `j bs t fgst rgutj d rgl i t g kwcjrj p < pbssjs tcrgunc ìhe b? gtcjrwisj.iv ) . Lu`tip`j rjnrjssigh tjfchiqujs br j usja t g ajvj`gpjqubtighs gd tìj dg``gwihn dgrl

wcjrj s tcj ihtjrhb` trbddif vgùlj gh ìhe b bha mebr j tc j fghstbhts t g mj gmtbihja.

Q) @gw sunn jsts t c b t sjp brb tj jq ubtighs f bh mj ajvj`gpjadg r a i d djr jht typjs gd rgbas g r brjbs gr tcb t ba ai t ighb`pbrbljtjrs ajdihihn tc j fcb rb ft jr is tif s gd t c j ì h e lby mjihfùaja.

=.=.= Vfgpj bha bp pì fb tig hs . It s sunnjstja tcbt tcj lgaj` fguà mjusja dgr dgrjfbstihn purpgsjs bs wj`` bs rjpìfbtihn tcj prjsjhtp b t t j rh gd t r i p s . g tcis jha tcj vbùj gd tcj sgfig jfghglifpbrbljtjrs scguà mj gmtbihja dgr t c j ajsinh yjbr bs wj `` bs t cjb`tjrhbtivj hjtwgres tcbt wguà mj tjstja.@gw b` sg sunnjs ts tc b t lgrj s gp cis tif btj a vjrsigh sgd c i s lgaj`fbh mj ajvj`gpja, jspj fib``y i h rj` bt ig h t g tc j wby i h wcifc tc jt r i p p rgmbm i ` i ty lbtr ix i s gmtb ihja .Hg prgvis igh i s lbaj dgr pumìf t rbhspgr t t r i p s gr dgr lgab` s p ` i t .Qcj lgaj` wbs usja aurihn tcj Lghghnbìb Fguhty Qrbhspgrtbtigh Vtuayi h ^jst Ti rni hib i h 29>?->2. Fghvjhtighb` tjfc hiqu js wjrj usja i hp b r b ` ` j ` t g t c i s lgaj`.Qcj mbsif ihdgrlbtigh usja wbs

Mbsj yjbr pgpu`btigh bha jlp`gyljht my zghj := zghjs)Mbsj yjbr rgba t r b d d i f bssinhljht hjtwgreMbsj yjbr trbddif fguhtsMbsj yjbr jxtjrhb`-tr ips tbm`j


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Dihb``y, tjsts wjrj lbaj witc lu`tipbtc bssinhljht tjfchiqujstg sjj id it wbs pgssim`j tg ilprgvj tcj dit gd tcj lgaj`. Qcjlgaj` usja wbs tcj stbhabra ZLQ lu`tipbtc bssinhljht prgnrblZ]GBA. Gh`y lbrnihb` ilprgvjljhts wjrj gmtbihja witc tcisbpprgbfc.B fghvjhtighb` lgaj` wbs hgt bppìja tg tcj brjb sg it wbs hgtpgssim`j tg fglpbrj tcjir bffurbfijs. Hjvjrtcj`jss, tcj jvj`gd bffurbfy gd tcj IT lgaj` ih rjprgaufihn mbsj yjbr ìhevgùljs wbs fjrtbih`y witcih tcj ìlits gd fghvjhtighb` lgaj s.Qcis is tg sglj jxtjht surprisihn bs gh`y pgpu`btigh bha zghjtg zghj trbvj` tiljs brj ihfùaja ih tcj lgaj`. Qcj rjpgrtjaffrrtj btigh fgjddifijht wbs ?.3> bha tcj ] V vbùjs wjrj=?9 ih bmsgùtj tjrls bha :6% ih pjrfjhtbnj tjrls.Ih grajr tg jvbùbtj tcj dgrjfbstihn bmiìty gd tcj lgaj`jlpirifb``y tcj lgaj` wbs bppìja tg dgrjfbst 294? trbddifvgùljs usihn tcj 294? Dgha au @bf hjtwgre bha fjhsus abtb.Qcj rjsu`ts gd tcis jxjrfisj scgwja tcbt gvjrb``, tcj bmsgùtjjrrgr gd tcj 294? jstilbtj gd bssinhja vgSuljs wbs `jss tcbhtcbt gd tcj 29>? jstilbtjs.Qcj rjsjbrfcjrs, tcgunc dbvgurbm`y ilprjssja my tcj bffurbfygd tcj IS lgaj2,wjrj fritifb` gd its tcjgrjtifb` mbsis.Vlitc bha LfDbr`bhj pgihtja gut tcrjj mbsif lis-spjfidifbtighjrrgrs ih tcj lgaj .(b) Fcbhnjs ih tcj trip lbeihn prgpjhsity gd tcj stuay brjb

pgpu`btigh gvjr tilj fbhhgt mj fghsiajrja ih tcj lgaj`.Dgr ihstbhfj, tcj ilpbft gd fbr gwhjrscip is hgt rjd`jftjaih tcj lgaj`.

(m) Qcj uhfghstrbihja hbturj gd tcj lgaj`. Id pgpu`btigh isagum`ja trbddif d`gws wi`` mj lu`tipìja my b dbftgr gddgur ihstjba gd kust agumìhn bs wguà mj jxpjftja. Qcisfritifisl bppìjs lbih`y tg tcj lgaj` usja ih tcjdgrjfbstihn lgaj. Qcis gmkjftigh is jbsi`y gvjrfglj mytcj ihfùsigh gd b hgrlbìsihn dbftgr jqub` tg2 ih jqubtigh =.6).

k


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(f) Qcj aiddjrjht ljbsurjs gd tcj trip prgmbmiìty dbftgrsbrj ìej`y tg mj fg-ìhjbr ih wcifc fbsj gh`y ghjprgmbmiìty dbftgr scguà mj ihfùaja ih tcj jqubtigh.

Qcj rjsjbrfcjrs fghsiajrja sjvjrb` pgssim`j ilprgvjljhts tg tcjlgaj`, sglj gd wcifc brj ajsfrimja `btjr ih tcis wgreihn pbpjrbs tcjy bppjbr ih tcj ìtjrbturj. Qcjy dihb``y fghfùaja tcbttcj ihfùsigh gd tcjsj ilprgvjljhts wguà prgmbm`y lbaj tcjITD lgaj` dbr tgg sili`br tg fghvjhtighb` tjfchiqujs bha itsgrinihb` bttrbftivjhjss wguà mj `gst.

=.6 Gvjrnbbra's Lgaj`=.6.2.Ajsfriptigh Gvjrnbbra's,@gw`s bha tcj Abhisc ]gba Airjftgrbtj ljtcgas

wjrj aisfussja ih tcj GJFA ]jpgrt gh pgssimiìtijs dgr tcj silpìdifbtighgd urmbh trbddif lgaj`s GJFA (29>1).Gvjrnbbra's lgaj`, tcgunc prgmbm`y ajvj`gpja ihajpjhajht`y, fbh mjfghsiajrja bs bh ilprgvja vjrsigh gd @gw's bpprgbfc. Bs it ihfùajsb p rgw ljbsurj dgr trip lbeihn prgpjhsity it ngjs sglj w y tg bhswjrsglj gd tcj fritifisls gd Vlitc bha LfDbr`bhj. Qcis lgaj` cbs mjjhbppìja tg Vièjmgrn, b Abhisc tgwh gd 11,??? ihcbmitbhts.Jxtjrhb` trips brj gmtbihja ih tcj sblj wby bs ih @gw's ljtcga. Qcjlbih fcbhnj is rjnbraihn trip njhjrbtigh;Fbr gwhjrscip jvj`s wjrj ehgwh dgr Vièjmgrn sg tcbt trip njhjrbtighjqubtighs wjrj stbtja ih tjrls gd trips pjr fbr pjr aby (It cbs tg mjrjljlmjrja tcjsj ljtcgas brj gh`y fghfjrhja witc fbr lgvjljhts).Durtcjrlgrj, bs b prgxy dgr sgfig jfghglif jvj`, tcj typj gd awj`ìhn( sihn`j dbli`y cgusj gr bpbrtljht ) wbs b`sg ihtrgaufja ih tcjtrip njhjrbtigh tjrl.Qcj njhjrb` trip njhjrbtigh (bha bttrbftigh) tjrl wbs tcjh jxprjssjaih tcj dgrl

wcjrj ?. njhjrbtigh/bttrbftigh dgrfj ih zghj iJ i jlp`gyljht bha pgpu`btigh ih zghj i.4i. pjrfjhtbnj gd pgpu`btigh ih ghj dbli`y cgusjs


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Qcis t r i p njhjrbt igh lgaj` w b s fb` i mrb tja ihajpjhajht `y b t twgaiddjrjht zghjs.Qcj gt cj r lbih aid dj rj hf j witc @gw's bpprgbfc i s tcbt Gvjrnbbrausjs twg a i d d j rj h t aj tj r rjhfj duhf t ighs dg r lgtgri sja t r i p s g d` j s s bha lgrj tcbh 9? sjfghas gd aurb tigh.

=.6.= Bppìfbtighs. cjh t c i s lgaj` wbs b pp ìj a i h Vi èj mgr n t wbs dguhat c b tm` < 2.>: -tr ips pj r wgrep`bfj->m= < ?.> -trips pjr ihcbmitbht->m6 < ?.??3 trips pjr ihcbm itbh ts i h ghj dbli`y cgusjsnbvj t c j mjs t r j su ` t s .B`sg, bh jxpghjht gd -2.3 d g r t r b v j ` t ilj w b s f b ` im r b t ja d g r t r i p swi tc t 8 9? sj fs . Qcj 'cffurbfy gd tc j lgaj` i h tjrls gd t c jfglpbrisgh gd gmsjrvja bha prj ai ft ja ì h e d`gws wbs ljbsurja my bh] V (pjrfjhtbnj) jr rg r . Qcis wbs dguha t g m j brguha =?% bha m j t t j rdgr cincjr d `gws.

=.1 @bl brrj's Lgaj .= . 1 . 2 . ~ j s f r i ~ t i g h . h n j h jr b ` ` i h j b r lgaj`s b r j r j s t r i f t j a i h tj rl s gd t c j

hulmjr gd pbrbljtjrs dg r fb ` im rb t ig h. Dgr jxblp`j, t c j fb` i mr bt i ghg d t c j t r i p n jh jr bt ig h - bttrbft igh bha aistbhfj jxpghjht pbrbljtjrsi s lbaj i h s t jps . su i t b m ` j , bha sguhajr, b` tj rh bt iv j ljtcgawguà mj t g usj b hgh-` ihjbr rjnrjssigh tjfchiquj bs wj sc b `` sj ji h V j ft ig h 6.@blbrrj (29>>) ajvj`gpja bha tj s t j a b silp`j ì h j b r lgaj` ihfgrgp grbtihnfb ì mr bt bm `j pbrbljtjrs bdd jf t ih n sgfig-jfghglif ha t r b v j ` t il jiha ifb tgr s. @blbrrj ajvj`gpja twg b` tj rh b t i v j dgrlu`bt ighs. Qcjd i r s t g hj i s bh ?-A mbsja dgr lu `btig h bs dg` `gws

Q i k < mg m`(Gi Gk ) m= ik (=.3)bha


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= : Fgllghwjb tc Murjbu gd ]gbas lgaj`

=.:.2 Ajsfript igh. Qcis bpprgbfc wbs ajvj`gpja d g r t c j Fgllghwjb`tc Murjbugd ]gbas (fM]) i h B u st rb ì b my Vylghs, î`sgh bha _btj rsg h (29 >4 ).Qcj gm kjf tiv j gd tc j jxj rfis j wbs tg ajvisj b rin gr gu s ljtcgag`gnydg r a isbnn rjnbtih n tc j Bu strb` ibh Hbtighb` Vystjl gd Zrmbh Fjhtrjsih tg ai s t ih ft zghjs gd jfghglif bf t iv i ty 5 t c jh , t g u s j , t c i s z g h b ti g ht gfghst ru ft b lgaj` gd t r b d d if njhjrbt igh dgr tcj Hbtighb` CincwbyVystjl . Qcis bpprgbfc i s gh` y bpp ì fbm ` j t g i h t j r - f i t y t r bv j ` .Qcj lbih ihhgvbt ighs gd t c i s bpprgbfc rjsiaj s b t tc j t r i p njhjrbtighs tbnj . B r j ` b t i g h s c i p i s bssulja mjtwjjh trbddif njhjrbt igh bha tcjurmbh cijrbrfcy wcifc i s ajtjrlihja my tc j prgvisigh gd sjr vifj s tg`j ss j r urmbh fjht rjs . c ijrbrfcy gd urmbh fjh t rjs i s prgaufja usihnFjhtrb` _`bfj Qcjgry fghsiajrbt ighs bha it i s bssulja tcb t t r ips w i ` `mj njhjrbtja drgl b `gw grajr fjh trj t g b cincjr gr ajr fj htr j gh`y.Qcj t r i p njhjrbt igh rb tj s pjr cjba gd pgpu`bt igh br j jxpjftja t g vbrydrgl ` j v j ` t g ` j v j ` . Jbfc gd t c j Bustrb` ibh urmbh fj htr js wbs tcjhbssinhja t g ghj gd sjvjh mrgba rbhes usihn pgpu`btigh bha jlp`gyljhtt yp j s t b t i s t i f s . B s jxp`bhbtgry vbribm`js mgtc pgpu`bt igh bha brj fr jb t ig hb ` bt t r bf t iv jh js s ihajx wjrj usja. Qcj lgaj` fguà tcj h mjjxprjssja bs b nrgup gd sum lgaj`s.Qr ip _urpgsj Du hfti ghb ` Dgrl (Dr)Vjjeihn ` jv j ` > sj rv ifjsVjjeihn `jvj` 4 sjrv ifjsVjjeihn ` j vj ` : sj rv i fj sVjjeihn `jvj` 1 sjrv ifjs]jfrjbt ighIh t j r - fbp i t b `

^cjrj _i _gp u`b tigh urmbh fj ht rj i]i ]jfrjbt ighb` ihajx urmbh fjhtrj i

-eF Ajtjrjhfj duhftigh.K

-eik

_. Fik -e-e_i Fik

_. F -e2

_. ] F -e2 K_. _. F -eK i k

D Duhf tighb` dgrl d g r kgurhjy purpgsj r .r . ..


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Qcj njhjrb` lgaj` is tcjh

bbha Tb < Q _ik I K 2Ktcbt is bm D_' = r r ` k~ r

wcjrj jqubtighs (=.2=) fbh mj usja tg ajtjrlihj tcj fbìmrbtighpbrbljtjrs m dgr jbfc kgurhjy purpgsj. Gd fgursj bh ilpìfitrbssulptigh ih tcis lgaj` is tcbt rgutj fcgifj agjs hgt ajpjha ghkgurhjy purpgsj bha tcbt prgpgrtighb` bssinhljht is suddifijht`yrjbìstif.Ih grajr tg silpìdy fb`fu`btighs gh`y trips mjtwjjh Vtbtj fbpitb`sbha trips mjtwjjh b fjhtrj bha tcj hgajs ih its lbrejt brjb wjrjfghsiajrja. It wbs dj`t tcbt tcis sjt gd trips wguà fbpturj tcjmuè gd ihtjr urmbh trbddif.

= : = Bppìfbtigh. Ih tcj Bustrbìbh fbsj bssinhljht wbs pjrdgrlja lbhub``ybha lu`tip`j ihjbr rjnrjssigh tjfchiqujs wjrj usja tg fbìmrbtj tcjlgaj`. Ih baaitigh aiddjrjht jxpghjhts e dgr tcj ajtjrrjhfj duhftighdgr jbfc kgurhjy purpgsj wjrj tjstja bha tcgsj nivihn mjst dit wjrjbagptja. Qcjy dguha tcbt tcj slb``jst jxpghjht wbs tcbt gd trips tg`jvj` : bha sunnjstja tcbt pjrcbps tcj lgst jssjhtib` bha irrjp`bfjbm`jnggas bha sjrvifjs wjrj suppìja my tcjsj fjhtrjs. Qcj rjsjbrfcjrsb`sg dguha b cinc jxpghjht dgr ihtjr-fbpitb` trips. Qcjy jxp`bihjatcis my tcj ilpbft gd fglpjtitigh drgl gtcjr lgajs (bir bha rbi` sjrvifjs).Vylghs jt b fghfùaja tcbt tcj lgaj` wbs tg mj gd nrjbt ihtjrjst tgVtbtj Cincwby Butcgritijs dgr it ihaifbtjs cgw lufc ihdgrlbtigh lby mjjxtrbftja drgl fjhsus ihdgrlbtigh bha rgba fguhts. Qcjy wjrj sbtisdijatcbt tcj rjsu`ts wjrj jhfgurbnihn bha stbtistifb``y sguha. Qcjyjhvisbnja hg fghfjptub` aiddifu`tijs ih trbhsdgrlihn tcj lgaj` ihtg brgmust prjaiftivj tgg` . Qcj rjsjbrfcjrs ljhtighja b hulmjr gd ajsirbm`jilprgvjljhts ih tcbt airjftigh lbih`y ih tjrls gd butglbtihn prgfjssjswitcih tcj lgaj`.


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=.4 Abhisc ]gba A ir jf tg rb tj bpprgbfc.=.4.2.Ajsfriptigh. Qcis i s prgmbm`y tcj ljtcga witc tcj nrjbtjst hulmjr

gd rjpgr tja bpp ` ifb t igh s. B t ` j bs t twg d u ` ` sfb ` j bpp ` ifb t ighs i hr u r b ` b r j b s, jhs jh @Hij`sjh (29>6) .la Cg`l j t b 2 (29> 4), cbvjmjjh rjpgrtja i h Jhnìsc. Qcj ljtcga cbs mjjh ilprgvja s ih fj i t sd i r s t fghfjpt igh mut gh`y tc j vjrsigh ajsfr imja my Cg`l j t b (29>4)w i ` ` mj aisfussja cjrj.Ih njhjrb` tcj ljtcga i s bnbih sjjh bs b wby gd a i r j f t `y f b ` imr b t ihnb tr ip-njhjrbt igh-aistr imutigh-bssinhljht lgaj` drgl t r b d d i f fguhts._rgmbm`y tc j lbih pgiht gd ih tj rj st i s t cj usj g d bh i t j r b t i v jbssinhljht tjfchiquj ihstj ba gd tc j silp`jr b` `-gr-hgtcihn vi blihilul fgst pbtc bpprgbfc gd prjvigus rjsjbrfcjrs.Ih njhjrb` jxtjrhb ` t r ip s br j hgt gmtbihja ihajpjhajht`y mut bsb r j su ` t gd tc j usj gd tcj lgaj`. Ih j d dj f t , t c j jx tjrhb ` zghjsb r j fgaja i h t c j sblj wby bs t cj 'd ih tjrhadghjs bha t jb tja i h tc jsblj wby.Qcj mbs if t r i p njhj rbt igh-ais tr imutigh lgaj` i s ;

wcjrj m i s t c j t r i p n j h jr bt ig h d b f t gr .Qcj prgm`jl i s t cjh t g ajtjrlihj b vb ùj d g r fghs i s t jh t w i tc t cji t j r b t i v j bssinhljht bha wcifc lihilisjs tc j aid djr jh fj mjtwjjhgmsjrvja bha lgaj``ja ì h e d`gws.Bh i t j r b t i v j bssinhljht cbs mjjh fcgsjh, cgpj du``y fghvjrnihn

btgwbras b ^brargp's jquiìmriul, bha fghsjqujht `y tc j p. . vbùjs2 Kfcbhnj b t jbfc i t j rb t igh . Qcj Abhisc ]gba Airjftgrbtj fcgsjVlgfe's (2943) i t j r b t i v j b`ngritcl dgr bssinhljht bha ajvj`gpjab ljtcga dg r f b`f u`b t ih n m bs pbr t gd t c j i t j r b t i v j pr gfjss .

= 4 = Qcj i t j r b t iv j prgfjss . Qcj fgst- d`gw rj` bt i gh sc ip dg r b ` ih eb i s bssulja t g mj

Qcjh b ` ` g r pb r t g d tc j t r b d d i f mjtwjjh jbfc pb i r gd zghjs i sbssinhja dgr rgutjs i h sufc b wby t c b t , dg r jbfc ` ih e, tc j d `gwb t i t j r b t i g h h i s


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wcjrj T b < trbddif vgùlj rjsu`tihn drgl b``-gr-hgtcihnbssinh lj hts t g t c j ` i h e b d t j r t c j h t c i t j r b t i g h .

j fbh hgw fr jb tj bh bu xi ìb ry vbri bm `j S ( b ha g n gu s t gb@gw's Sb) sufc t c b t

. -l bSb < 2 ? i G . . F ~ K p . .i k K 2 Kbwcjrj pik < prgpgr tigh gd t r b d d if Q wcifc usjs ` ih e b .26

B t tcj sblj tilj2 2vbh < mxbh < m(2- - xbh-' mSbh (=.24)

my lbeihn

B t t c i s s t b n j , it wguà mj pgs sim ` j t g fb ` fu ` b t j , b d t j r jbfc i t j r b t i gh ,t c j vbùj gd m usihn ` i h jb r rjnrjssigh, bha wj fguà bffjpt tc btfghvjrnjhfj cb s mjjh bfcijvja wcjh t c j js ti l bt ig hs gd ag hgta i d d j r s i nh i d i fb h t `y i h twg fghsjfu tivj i t j r b t i g hs .Qcj Abhisc ]gba Airjftgrbtj cgwjvjr prjdjrrja b lbxilul ` iej ` icgga..ljtcga. t i s bssulja t c b t t c j gmsjrvja d`gws Tb b r j lutub``yihajpjhajht, hgrlb``y ais tr im ut ja vbr ibm` js w itc ljbh vbh, t c b t i s

T b < vbh b =..23)w c j r j . n b i s b hgrlb``y a i s t r im u tja vbr ibm `j=i tc ljbh bha vbr ib hf j U(Tbhdg -/ t

t < g ljbhs t c b t t cj s tbhabra ajvib t igh i s ihajpjhajhtdrgl tc j ljbh.d 2 ljbhs t c b t ljbh bha vbribh fj br j i h prgp grtigh.y < =ljbhs tcbt bvjrbnj d`gw bha stbhabra ajvibtigh brjprgpgrt ighb` .


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Zsihn t c j lbxilul ` ie j ì c gga ljtcga it i s p g s si m `j t g d i h at cj mjs t j s t ilb t g r d g r m bs

bha b`sg

Qcj ajr ivbt i gh gd tc js j rj`b t igh scip s i s scgwh i h Bppjhaix 22Qcj b`ngritc l ajvj`gpja my tc j A]A fbh mj sulhbrisja bs;Vtjp < Fb`fu`b tj d r jj d `gw t r b vj ` t iljs .Vtjp = < Ajtjrlihj lihilul fgs t rg utj s d g r b ` ` ? A pb i r s .V tjp < Bssinh dg``gwihn Vlgfe s b`ngritc l, t c j S . < I d m* m s hgt fghvjrnja prgfjja t g s tj p = ,

gtcjrwisj stgp.Qcis b`ngr i tcl i s t j s t ja wi tc a i d d j rjh t vb ùjs gd t c j jxpghjhtbha i h lbhhjr si l i` br t g Vlitc bha LfDbr`bhj (29>3).Qcj lgaj` i s ihtjha ja lbih`y b s b rjp`bfjljht d g r lgrjsg pc ist ifb tja bha jxpjhsivj d grjf bst ih n lgaj`s.

=.4.6 Bppìfbt ighs. Qcj lgaj` cbs mjjh bppìja, i h s ` i n c t` y aid djr jh tvjr s ighs , i h tcj Bbrcus bha i h tc j Vgutc [jb`bha r u rb ` b rj bs i hAjhlbre. I h t c i s ` s t fbsj tc j abtb usja fghsistja gd b rgbahjtwgre, wi tc sjvjh typ js gd rgbas (bha spjja-d`gw rj `b tig hs ci ps )pbrisc pgpu`bt ighs bha bmgut 1 fguhtihn pgihts. Qcj hjtwgre


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ihfùaja >6 zghjs bha 661 ìhes. It wbs dguha tcbt bhal 6.=: nbvj tcj mjst dit.Qcj rjsjbrfcjrs dguha tcbt tcj lgaj` tjhaja tg gvjr jstilbtj`brnj d`gws bha uhajr jstilbtj slb`` vgùljs. Qcis is fjrtbih`yhgt vjry ajsirbm`j drgl b p`bhhihn vijw pgiht. Qcjy tcgunct tcjsgurfj gd tcis jrrgr wbs tcj dbft tcbt ihtrbzghb` trips wjrj hgtfghsiajrja my tcj lgaj`.Qcj rjsjbrfcjrs jstilbtja tcj pjrfjhtbnj jrrgr ih d`gws gh tcjìhes -nbs brguha 2> bha tcbt tcis aia hgt ajtjrigrbtj lufc wcjhtcj lgaj` wbs fbìmrbtja witc gh`y cb`d tcj fguhts.Qcj rjsjbrfcjrs b`sg prjpbrja fghdiajhfj ihtjrvb`s dgr tcj furvjs.Qcjy dguha tcbt tcj cb`d-wiatc gd tcj 9: fghdiajhfj ihtjrvb`wbs, dgr jxblp`j, :=?? pfu/aby bt 2?.??? pfu/aby bha bmgut 6???pfu/aby bt :.??? pfu/aby `jvj`s. Qcjy fghfùaja tcbt tcis bffurbfywbs hg wgrsj tcbh tcbt gmtbihja tcrgunc tcj usj gd lgrj jxpjhsivjtrbaitighb` lgajs.Ih b pjrsghb` fglluhifbtigh ghj gd tcj rjsjbrfcjrs ihvg`vjaihdgrlja tcj butcgr tcbt tcj Abhisc ]gba Airjftgrbtj wbs hgwwgreihn gh b hgh-ìhjbr rjnrjssigh bpprgbfc, sili`br tg tcgsjajsfrimja ih tcj hjxt sjftigh.

6. HGH-@IHJB] ]JN]JVVIGH B__]GBFC

6.2 Ihtrgauftigh.Vjvjrb` tjfchiqujs dgr sg`vihn hgh-ìhjbr rjnrjssigh prgm`jls

brj bvbi`bm`j bha ilp`jljhtja ih lgst fglputjrs. B hgh ìhjbr rjnrjssighprgm`jl hgrlb``y tbejs ghnjr tg sg`vj tcbh b ìhjbr ghj witc tcj sbljhulmjr gd vbribm`js. Cgwjvjr, tcj hgh ìhjbr rjnrjssigh bpprgbfc, b``gwstcj usj gd lgrj rjbìstif bha njhjrb``y bffjptja ilpìfit nrbvity lgaj`sih tcj jstilbtigh gd Grinih-Ajstihbtigh lbtrifjs.


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j w i ` ` ais fu ss cjr j tc rj j sufc ljtcgas. Qcj d i r s t ghj my Cgnmjrn(29>4) bssuljs t c b t bh b``-gr-hgtcihn lihilul fg st bssinhljht i s rj b ` i s t i fjhgunc mut ihfgrpgrbtjs b vjry njhjrb` ajtjrrjhfj duhf t igh bha up t gtcr jj kgurhjy purpgsjs ih tc j nrbvi ty typj ai s t r i mu t i gh lgaj`. Qcjsjfgha bpprgbfc my ]g mi` `bra (29> :), usjs b n jhjr b` izja nr bv ity lgaj`bha bffjpts prgp grt igh b` bssinhljht bs rj b ` i s t i f . Qcj tc i r a lgaj` cbsmjjh ajvj`gpja my i ` ` s (29>>) bha b`sg ihfùajs b njhjrb` izja nrbvi tylgaj` mut gd b ai dd jr jh t eiha.

It i s pgss im`j t g jxtjha b ` ` ` ih jb r bha hgh-ìhjbr lgaj`s (Vjft ighs= bha 6 i h t c i s wgre) t g tcj prgpgrt ighb` bssinhljht f bsj mut jvjh tcjhtcjy d b i ` t g fghs iajr fghnjs tigh bs bh ilpgr tbht db f tg r i h rgu tj fcgifj .Qcis sjjls t g iha ifbt j t cb t tcj sj ljtcgas fguà mj lgrj bp prgp ribtj t gr u rb ` g r uhfghnjstja urmbh brj bs.

6.= Cgnmjrn's Lgaj`Cgnmjrn bssuljs tc b t tc j kgi ht njh jrbt igh -aistrim utigh lgaj` s

gd t c j dgrl2 2 2 2 = = = = =Q i k < m ?. B A d ( f . . . + m ?. B A d ( f 5 . + m G i Bi A. d ( f . .

2 2 2 K 2 K = K K 6 K 26(6.2)wcjrj

=gi` bha ? . b r j a i d dj r jh t typjs gd t r i p njhjrb tigh pbrbljtjrs=A . ~ha A . b r j a i d d j rjh t t ypjs gd t r i p b t t r bf t i gh s pbrbl j tj rsK K

2B bha B br j mb`bhfihn d bf tg rs gd tc j dgrl B.


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Dgr b su msjt gd ì h e s wj fbh tcjh fglpbrj tc j gmsjrvja witc tc jlgaj``ja d`gws bha lihilisj tcj squbrj gd tcj aiddjrjhfj.

b( v b ` . p ik Q i k )

Cgnmjrn fb rr ij a gut b ajse stua y gd c i s ljtcga gh b s yh tc jt if hjtwgrewi tc 24 lgajs bha == twg wby ìhes usihn pgpu`btigh bha jlp`gyljht bsGis bha A .s . Cj bssulja tc j tc rj j j`jljhts i h tc j a is tr im u ti gh lgaj`stgg a d g r cglj-wgre, cglj-cglj bha wgre-wgre t r i p s . Cgnmjrn tcjh usjabh b`ngritcl d g r hgh-ìhjbr rjn rjs sig h sunnjstja my Lbrqubht (2946)bha drgl b syhtcjtif G A lbtrix cj sblp`ja d`gws drgl cb `d gd t c j ` i he s.Bdtjr iht rgaufihn bh b r t i d i f i b ` jrr gr fglpghjht cj usja t c i s sblp`j t ggm tb ih b lihilul squbrja ai dd jr jh fj mjtwjjh gm sjrvj a bha lgaj``jat r b d d if . Cj tcjh fglpbrja tc j d`gws prjaiftja dgr tc j r j s t gd tcj ==` i h e s bha dguha tc j lgaj` bffjptbm`j .

Cgnmjrn (29>:) cbs fb rr ij a gut sglj tc j g rj ti f b ` wgre gh t c jfghtr imutigh gd jbfc ` i h e t g t c j bffurbfy gd tc j lgaj`. Cj dguha

tc b t bD tj r tc j ihf ùs ighs gd b djw ` ihe s i h tc j ~~~~~~~~~~~~~tcjrj wbs` i t t ` j nb ih ih tc j bffurbfy gd tc j lgaj`. Ih b pjrsghb` fglluhifbtight g t c i s butcgr L r Cgnmjrn cbs fghdirlja tcbt prbft ifb` bppìfbt ighsbr j mjir nf br rij a gut i h Vwjajh witc t c i s lgaj` mut tc jy cbvj hgt yj tmjjh rjpgrtj a i h Jhn` isc.

6.6 ]g mi `` br a` s Lgaj`]gmi` `b ra (29>:) bssuljs b njhjr b` izja nrb vit y lgaj` `jbaih n t g

wcjrj Jb i s bh j rr gr tjrl bha6 s . br j tc j pbrbljtjrs t g mj jst ilbtja my tc j hgh-ìhjbr

rjnrjssigh bpprgbfc.d ( F . . ) s b ehgwh fgst d'uhftigh.


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It is hgtja tcbt tcj jstilbtigh gd ]i bha V. hjja hgt mj uhiquj5 wcbtlbttjrs is tcbt tcjir prgauft is. It is b`wbys pgssim`j tg sg`vj tcisprgm`jl sg tcbt tcj ]i. bha V brj pgsitivj.k

]gmi``bra ihaifbtjs tcbt tcj ljtcga sunnjstja my @bwtgh bhaVy`vjstjr 29>2) bh mj usja tg sg`vj tcis lgaj` ih grajr tg lihilisjtcj aiddjrjhfj mjtwjjh gmsjrvja bha syhtcjsizja d`gws. Gd fgursj tcjhulmjr gd ihajpjhajht ihes witc trbddif fguhts bvbi`bm`j scguà mjnrjbtjr tcbh tcj hulmjr gd tcj vbribm`js ]. bha V5. Ih tjrls gdCgnmjrn s prjvigus jxblp`j it ljbhs tcbt bt `jbst 66 gd tcj 11 ghj wbyìhes scguà mj sblp`ja. Qcj prgm`jl gd lihilisihn

fbh mj sg`vja my rjp`bfihn tcj V s my tcjir ìhjbr rjnrjssigh sgùtighih tjrls gd tcj ] s bha tcjh sg`vj my tcj ] s gh`y. Gd fgursj gtcjrb`ngritcls brj b`sg pgssim`j mut it is f`bilja tcbt tcis bpprgbfc scguàrjaufj fglputjr tilj. It is ihtjrjstihn tg hgtj tcis ljtcga agjs hgtrjquirj bhy ihdgrlbtigh rjnbraihn pgpu`btigh gr gtcjr trip njhjrbtihnpbrbljtjr. Qcjsj brj b`` jlmgaija ih tcj ] s bha V s. Qcj lgaj` is,ih jddjft, gh`y b njhjrbìsja nrbvity lgaj`. Ghj fbh fglpbrj tcjstbhabra agum`y fghstrbihja nrbvity lgaj`.

Q G.B.A.M. d(F..i k < ~ ~Kwitc

Qik < ].V. d(f..K

tg diha . tcj jquivb`jhfjs]. < G.B.V. < A.M.

It lust mj ljhtighja tcbt ]gmi` bra s ljtcga is bppìfbm`j gh`ywcjrj p. .b is ehgwh, tcbt is wcjh tcjrj brj hg fghnjstigh jddjfts. Ih

Kgtcjr wgras tcj bppìfbtighs gd tcis lgaj` brj rjstriftja tg fbsjs ihwcifc b prgpgrtighb` bssindijht tjfchiquj is fghsiajrja rjbìstif.


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6.1 ^ i ` ` s t Lgaj`.

6.1.2. Ajsfript igh Bh b` t jr hb t iv j hgh-` ihjbr lgaj` dg r t c j jst ilbt ighgd bh ?-A lb trix i h i h t j r urmbh fbs js cbs mjjh prgpgsja my ^ i ` ` s (29>>).

C i s s t b r t i hn pgih t i s b njhjrb ` isja nrbvi ty lgaj` gd tc j dgrl.

wcjrj e t cB < Qcj e vbr ibm `j fgr rjspghaihn t g g r in ih idg r jxblp`j pgpu`bt igh b t i.

bha m ---m pbrbljtjrs dg r fb ` im rb t ig h drgl t r b d d i f fguhts.eBs usub` tcjs j t r ip s b rj t r bhs `b t j a ih tg lgaj``ja ` i h e d`gws bs

Qcj pbrbljtjrs m Pr j fb ` i m r b t ja sg b s t g l ihilisj

Qcjrj b rj sj vj rb ` b`ngri tcls wcifc fgu`a mj usja t g lihilisj6 . 9 ) . ^i``s i h d b f t usja b qubsi-Hjwtgh gptil izihn ljtcga auj t g

D`j tfcjr bha g tcjr s .Qcj lbih ihh gvb tigh i h ^ i ` ` s bpprgbfc i s t c j wiaj rbhnj gd vbr ibm `js

tc b t fbh mj ih t rgaufja ih t c i s lgaj`. Cj t r i j a , d g r jxblp`j, tcr jjnrgups gd vbr ibm`js dgr bh i h tj r urmbh systjl;

Vgfig jfghglif vb ri bm `j s ` i e j pgpu`btigh bha jlp`gyljhtBffjssimi ` i ty vbr ibm`js5 cj usja b fjht rb` i ty ihajx bssulihntc b t tgwhs i h tcj pjr ipcjry w i ` ` cbvj b a i d d j rjh t prgpjhs i tyt g njhj rb t j t r i p s t cbh t cgsj hjb r t cj fjht rj .Vjpbrb t igh , t ilj gr a i s t bhfj , vbr i bm `js .

_rgv isigh fbh b` sg mj lbaj dg r b hgh-sylljtrif vj rs ig h gd t c jlgaj`. Qcis tb ej s tc j dgrl

rjp`bf ihn jqubtigh (6 .4) .


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6.1.= Bppìfbtighs Qwg bpp ìf bt ig hs gd t c i s lgaj` br j ehgwh t g tc i sbutcgr . Qcj d i r s t ghj my ^ i ` ` s t g b rgba hjtwgre i h M r i t i sc Fgùlmibihfùaihn 6> fjh trgias bha gh`y 6 pbrbljtjrs. Bs t r b d d i f fguhts dg rsjvj rb ` yjbr s wjrj bvb i ` bm `j t wbs p gss im`j t g fglpbrj tc j pjrdgrlbhfjgd tc j lgaj` i h t c j dgrjf bs t ihn lgaj.

Qcj sjfgha bp p` if bt ig h cbs mjjh fb rr ij a gut my @blbrrj (29>>)us ihn ^ i ` ` s fglputjr prgnrbls. Qcis jxjr fi sj wbs bilja b t fglpbrihnt c j pjrdgrlbhfj gd ^ i ` ` s hgh-ìhjbr lgaj` witc @blbrhj's ` ih j b r ghj.B s r jpgr tja i h =.1 î ` ` s ' lgaj` nbvj b mj t t j r d i t .

Ih mg tc fb sjs t c j fglpbrisghs wjrj lbaj bn bi hs t gmsjrvja d`gwsbha hgt bnb ihs t rjb ` ?-A lbtrifjs . Ih mgtc fbsjs tc j prj aif t igh sgd t c j lgaj` wjrj dguha sbt i sdb ftg ry . Ih tc j M ri t i s c Fgùlmib fbsj=bh ] gd brguha ?.3= wbs rj pg rtj a. @blbrhj rj p g rt s bh ]~ gd ?.33 dg r^ i ` ` s lgaj` bnbihst bh ] gd ?.>= dg r tc j ` ih j b r bpprgbfc.

1 HJQ G]E JRZI@IM]IZL B__]GBFC

1 2 Ih t rgauft ighîtc tc j s g `j jxfjptigh gd tc j Abhisc ]gba A irj ftg rb tj ljtcga

` ` gtcjr bpprgbfcjs ajsfr imja sg dbr b r j r j s t r i f t j a t g t c j p rg pg rt ig h b`bss inhljht fbsj, tcbt i s wcjrj pik i s ihajpjhajht drgl

Qcis bssulptigh lby mj ngga dg r b ` br nj hulmjr gd bp p` if bt ig hs ,js pj fib ` `y wcjrj t c j hulmjr gd b` tj rh bt iv j rgutjs mjtwjjh twg pgihtsi s sl `` bha wcjrj fghnjstigh agjs hgtney h i lpgr tbht r g ` j i h r gu t jfcgifj. Lgst i h t j r urmbh trb hs pg rt hjtwgres prgmbm`y s tisdy t c j s jfghai t ighs .

Vbhn ~ n y y j i 29>>) cbs jxtjhaja sglj gd ] gm i ` `br a 's iajbs dg r tc jjqu i` imriul bssinhljht fbsj wcifc i s lgrj rj`j vbh t t g urmbh brjbs .Hnuyjhsunnjsts twg ljtcgas. Qcj d i r s t ghj i s d g r t cj fbs j i h wcifcf g h s i st j h t t r b d d i f f g u ht s b r j b v b i `b m ` j d g r b ` ` ` i h e s . Qcj sjfg haljtcga rjq ui rjs gh`y f gs ts d g r b ` ` ?-A p b ir s t g mj ehgwh bha agjsh g t j x p ` i f i t ` y b s e d g r t r b d d i f fguh ts b t b ` ` .


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1.= Hnuyjh s ljtcga, f bsj IBffgraihn t g H l j h (29>>) tc j d i r s t ljtcga fbh mj ajsfr imja bs

dg``gws ;. @jt Ta gmsjrvja d`gws ` i h e b bha f . . tc j gmsjrvja fgs ts gdIKt r bv j `` ih n mjtwjjh bha k my bhy usja rg u tj . Dgr jbfc ?-A p b i r

gh` y ghj f i k w i ` ` jx i s t s i hfj T i s bssulja t g mj i h ^brargp sjqui` imriul. Qcj fgst-d `gw rj`b t ig hsc ip i h hy ` i h e i s Fb(vb).

.I d Q i k i s t c j t r i p l b tr ix f grrjsp gh aih n t g t c j T . tcjh tcj jqui ` imr iuli ~s t b t j i s jxpr js sja my

Cjhfj tc j hjfjssbry fghai tighs dg r b t r i p lbt r ix @rQi k/ t g mj iajh t i fb `.. Wt g W Qik / b r jbha ..m ) F . . < F . . d g r b ` ` ?-A p b i r s

2 K 2 K 2i s bss inhja ghtg t c j hjtwgre bffgraihn t g ^brargp s d i r s t pr i hfip `j .

Hnuyjh ngjs gh tcjh t g prgvj t cb t t c j Qi k lbt r ix s b t i s j i h n (1.=)bha (1.6) fbh mj gmtbih ja my sg` vih n _2 wcjrj_2)lih D ( v ~ ) < e ` T b ~ b ( x ) a x (1.1)

s u mk j ft t gQ i - p i g d g r ` i ktpi8g dgr b ` ` p , i kf.

I Q . 8g dgr b ` ` i k2bha


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^cjrj < d`gw gh rgutj p fghhjftihn i witc k_`

Zsihn Euch bha Qufejr f gh aitig hs Hnuyjh (29>>) j s tb m `i sc j s tc jjquivb`jhfj mjtwjjh _I bha jqubtighs 1 . = ) bha 1 . 6 ) . Hnuyjb tcjhajs frim js bh b`ngritc l t g sg`vj _2.

Qcj prgm`jl _2 witcg ut tc j fg hs trb ih t F= cb s t c j sblj st ru ft ur jb s b hjtwgre jqui`imriul prgm`jl. Bffgraihn`y, t c j dg``gwih n b`ngri tcli s sunn jstja my Hnuyjh.V tj p V j ` jf t bh i h i t i b ` d j b s i m ` j -- ~ i k-

.dgr jxblp`j Q i k < E/rkfik wcjrjE ~ b ( ~ b ) T b .jtjrlihj bh i h i t i b ` d `gw pb t t j rh Tb us ihn Qi kb

Vtj p = Ajtjrlihj tc j scg rtj st rgutj mjtwjjh jbfc ?-A p b ir bha ` j tF . . mj tcj t r bv j ` fgs t gh tc i s rgutj .K

Vtjp 6 - Diha t c j ?-A p b ir r s dg r wcifcFrs/ < lihrs i , k F i k / F ;

bha `gba ghtg tc j scg r tjs t rgutj drgl r t g si

@jt --vb j t cj r j s u ` t i hn t r b d d i f pb t t j r h .

V t jp 1 Qjst fghvjrnjhfj.

t c j s g ` u t i g h i s gptilb` bha stgp.Vtjp : Diha bh gptilul fglmihbtigh mjtwjjh p rjv igu s d`gw p b tt j rh bha t c j

hjw ghj. Ajtjrlihj B lihilisihnD(Tb S ( 5b-~b))

sum kjf t t g g0B02.Vtjp 4 ]jvisj tc j t r i p lbtr ix bha d `gws bs dg` `gws

. .

Q . . < Q . . B Q . . d g r b ` ` i k r sK K


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]jturh t g s t j p =.

1 6 Hpyjh ' s ; ljtcga, Fbsj 22.Qcj Fbsj I ljtcga i s gh`y suitbm`j wcjrj it i s p g s s im ` j t g g m tb i h

t r b d d i f fgu hts d g r b ` ` ` i h e s . Q cis wguà r j s t r i f t i t s b p p ` i f b t i g ht g slb`` hjtwgres. I h b a ai t ig h , t c j b `n gr it cl i s ` i e j ` y t g m j s `gwdg r b `b rn j hulmjr gd ? A pbirs. Hnuyjh tcjh prgpgsja b sjfgha ljtcgawcifc rjaufjs tcj abtb rjquirjljhts.

Cj s t b r t s my prgvihn tc b t tc j sg ù t igh t g tc j dg ` `gwihn prgm`jl_= b ` s g i s b s g ` u ti g h t g t c j i h i t i b ` lgaj`.

s um kj ft t gt . . < d g r b ` ` i kik p ` k

Q p i k 8 d g r b ` ` p , i , k ( 1 . 2 4 )2 Q i k 8 d g r b ` ` i k

.It fbh mj hgtja tcbt cjrj gh`y tcj gmsjrvja fgsts i k brj rjqu i rja

bha h g t t c j t r b d d i f f g uh ts .It scgu à b ` s g mj hg tja tc b t _= cbs tcj sblj dgrl bs b dgrlu`btigh

gd b t r b d d i f bssinhljht prgm`jl witc j` bs ti f ajlbha. My bhb`gl Hnuyjhfghsiajrs tc b t t cj ihfrjbs j gd tc j ajlbha duhft igh d gr bh ? A p b i r i ki s f g h s tb h t bha j qu b ` t g Fik Cj tcjh sunnjsts t c b t bh b`ngritcl b s tc jghj s t b t j a i h Hnunjh (29>4) fguà mj usja t g sg `vj t c j prgm`jl.

j dguha gh` y ghj t j s t gd mgtc ljtcgas gh b sy ht cj ti f hjtwgrewitc 1 fjh trg ias bha 23 ghj wby ` ih es b s i h Dinurj 1 2 Qcis i s bsystjl wit c 1 Q t g js t ilbtj drgl 23 jqubtighs. Qcj jr rg rs gmtbih ja` kwjrj gd bmgut 24 d g r t c j Q fj``s , bha bmgut 6 gh ì h e d`gws. Mgtc2 Kljtcgas nbvj bh bhswjr i h tìis fbsj w itc bpprgxilbtj`y t c j sbljprjf is igh .


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Hgaj > Fjhtrgia

Dinurj 1.2 HNZYJHV QJVQ _]GM@JL HJQ G]E


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t i s ih t j rj s t i hn t g hg tj tcb t Hnuyju cbs gh `y iaj h t i d ij a tc jhjfjssbry fghai t ighs t g sg`vj tcj prgm`jl bha hgt t c j s ud d if ij ht ghjs.Qcbt i s , t c j s gù tigh s dguha witc ci s ljtcga ljjt tc j jqu iìmriu lfghait ighs mut tcjy w i ` ` hgt mj hgrlb``y uhiquj sg ù tig hs . Qcis issujw i ` ` m j du r tc j r a i s f u s s j a ` b t j r .

: JHQ]G_Y LBSILIVIHN B__]GBNC

: 2 Mbfenrguha

Qcj fghfjpt gd jhtrgpy gri nih btja ih pcysifs. Ih b f`gsja pcysifb `systjl i t s j`jljhts tjha t g bh brrbhnjljht wcifc fbh mj grnbh isja ih bslbhy wbys b s pg ssi m`j fglpbtim`j wi tc t c j systjl fg h st rb ih ts (jhjrny,lbss, j t f ) . Qcis brrbhnjljht i s tcj lgst ` i ej `y ghj bha b ` sg tc b t gdtc j n rj b tjs t a isg raj r .

Qcj ia jb gd jhtrgpy i s b `sg ` iheja t g tc b t g d ihdgrlbt igh .t fbh mj sjjh ih tu i t iv j ` y b t ` jb s t , tc b t b s t b t j gd lbxilul aisgrajr, /

i s b`sg ghj fghtbihihn b lihilul gd ihdgrlbtigh. Qcj pgtjht ib ` ihdgrlbtighfghtjht gd b ljssbnj nrgws bs tcj sjqujhfj gd sylmg`s ajpbrts drgl bpurj`y rbhagl (cinc aisgrajr) sjqujhfj.

Qcj usj gd tcj fghfjpt gd jhtrgpy (gr ihdgrlbtigh) cbs dguha sjvjrb`bpp ` ifb t igh s i h t rb hs pg rt , urmbh bha rjnighb` systjls, sjj d gr jxblp`jî`sgh (29>?). I t s mj st ehgwh bp p` ifb tig h i s i h t c j a j r i vb t i g h g d bdu ` `y fghstrb ihja nrbvi ty lgaj` .

Qcj i aj b mjciha t c j usj gd bh jhtrgpy lbxilisihn (gr ihdgrlbtighlihilisihn) bpprgbfc t g gur prgm`jl fbh mj ajsfri mja b s dg ``gws ;

j wguà ` i e j t g d ih a tcj lgst ` ie j ` y g r in ih - a j s t ih b t i g h l b t r ixfglpbtim`j witc tcj b vbi `bm` j s j t gd ` i he fguhts . Ih g tc jr wgras ,wj wguà ` i e j t g jxp `g it b ` ` tc j ihdgrlbt igh fgh tb ihja i h tc jgmsjrvja ` i h e d`gws t g ajtjrlihj tc j lgst ` i e j `y ?-A lbtrix fglpbtim`jwitc tcjl.

î`sgh bha LbfNi`` (29>>) cbvj gmsjrvja tc b t t c j jh trg py lihilisihnljtcga i s pb rt if u` br `y su i tj a L.tcis typj gd systjl (systjls witc `br njhulmjrs gd fglpghjhts witc bppbrjht aisgrnbhizja fglp`jxity).

.


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It is pgssim`j tg brnuj tcbt wcjh ghj is bssulihn bh uhajr`yihntrbhspgrt ajlbha lgaj` (i.j. nrbvity typj) bha sjjes tg fbìmrbtj itdrgl trbddif fguhts ghj is prgmbm`y hgt du``y usihn tcj ihdgrlbtighfghtjht gd tcj d`gws. Qcis is tg sglj jxtjht fghdirlja my b tcjgrjtifb`stuay my ]gnmjrn 29>:). ]j stuaija tcj fghtrimutigh gd jbfc jxtrbìhe fguht gh tcj bffurbfy gd cis hgh- ihjbr lgaj` (dgr cis 24 hgajs

ghj wby ìhes hjtwgre). Cj gmsjrvja tcbt bdtjr ihfùaihn tcjlgst ilpgrtbht ghj wby ìhes tcj nbih ih prjfisigh is vjry slb` .

Qwg vjry sili`br jhtrgpy lbxilisihn lgaj`s wi`` mj aisfussjacjrj. Qcj dirst ghj put dgrwbra my vbh [uy`jh 29>>) sjs b pbrtifu`srljbsurj gd ihdgrlbtigh my Mri``guih. Tbh [uy`jh b`sg jxtjhaja cissgùtigh tg tcj ihfghsistjht d`gws fbsj. Qcj sjfgha ghj my tcj butcgrgd tcis pbpjr dg``gws b lgrj trbaitighb` bpprgbfc mut rjbfcjs b vjrysili`br dgrlb` sgùtigh. Qcis ghj is b`sg jxtjhaja dgr tcj ihfglp`jtjfguhts fbsj.

:.= Tbh [u.y jhts lgaj`

:.=.2 Ajsfriptigh. Tbh [uy`jh 29>>) pprgbfcjs tcj prgm`jl drgltcj ihdgrlbtigh lihilisihn vijw pgiht. Cj is tryihn tg ajvj`gpbh b`ngritcl tg gmtbih tcj trip lbtrix witcgut `gsihn lgrjihdgrlbtigh tcbh hjfjssbry.Blghn tcj sjvjrb` ihdgrlbtigh ljbsurjs aisfussja my b`sc bha^jmjr 29>>) j fcggsjs Mri `guih's ajdihitigh. Qcis bssuljstcbt bh b prigri sgùtigh t is ehgwh. Gh`y b mrijd sullbryikgd vbh [uy jh's bhb`ysis wi`` mj nivjh cjrj. B lgrj fglp`jtjajsfriptigh bppjbrs ih vbh [uy`jh 29>>).Id wj cbvj b sjt gd gmsjrvja d`gws Tb tcj lgaidija Mri` guih'sljbsurj gd ihdgrlbtigh dgr jbfc fguhtja ìhe is nivjh my;

usihn Vtjr ihn's bpprgxilbtigh


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` gnj S - S ` gn S S `gn) bha :.:) b r j fbsj gd t c j lu`t ip rgpg rt ighb `prgm`jls bs aisfussja my Lurfc`bha 29>>). C j cbs scgwh t c b t tc i slgaj` fghvjrnjs t g uhiquj sg `ut ig h bha cb s ajvj`gpja b silp`jb `ngr i tcl dgr it


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:.=.= Ihfghsistjht fghstrbihts. Ih tcj ihfghsistjht fghstrbihts fbsjtcj d`gw jqubtighs fbh mj rjbrrbhnja bs

wcjrj &b is bh jrrgr tjrl dgr jbfc ìhe. Tbh ~ N j hcjh sunnjststcbt tcj b`ngritcl scguà hgw mj lgaidija sg tcbt tcj Sb dbftgrsdgr jqubtigh (:.>) lust mj sufc tcbt lihilizj tcj sul gd squbrjs

Qcis is b prgm`jl gd lgrj aiddifu`t sgùtigh.Ih b rjfjht pbpjr Tbh [uy`jh (29>3) sunnjsts tcbt b mjttjr bpprgbfcwguà mj tg rjlgvj ihfghsistjhfijs ih tcj fguhts dirst bha tcjhtg sg`vj tcj prgm`jl usihn Lurfc`bha`s b`ngritcl. Cj usja blbxilul ìejìcgga ljtcga bs babptja my Cbljrs`bn bha Cuislbh29>3) tg rjlgvj ihfghsistjhfijs ih tcj gmsjrvja d`gws ih bslb`` jxblp`j. Tbh [uy`jh dguha tcjh tcbt tcj qubìty gd tcjsgùtigh ajpjhaja b nrjbt ajb` gh cgw ngga tcj b prigrijstilbtigh gd tcj trip lbtrix @-tik\ wbs. ]j fghfùaja cis ljtcgawguà mj iajb` tg upabtj bh gà Grinih-Ajstihbtigh lbtrix.

:.6 Bh b`tjrhbtivj jhtrgpy lbxilisihn lgaj .

:.6.2 Ajsfriptigh. Qcj butcgr cbs ajvj`gpja b lgaj` sili`br tg tcbt gdTbh [uy`jh, mut wcifc agjs hgt rjquirj bh b prigri jstilbtighgd tcj Grinih-Ajstihbtigh lbtrix. Bs tcis ajrivbtigh cbs hgtmjjh pumìscja it wi`` mj ajsfrimja h sglj ajtbi` cjrj.Bffgraihn tg tcj usub` jhtrypy bssulptigh, tcj lgst prgmbm`ybrrbhnjljht gd trips -~ik-i is dgrlja my tcj fghdinurbtighwitc tcj nrjbtjst hulmjr gd stbtjs bssgfibtja witc it. Qcjhulmjr gd wbys ih wcifc ihaiviaub` trips fbh mj bssinhja tgb pbrtifu`br trip lbtrix is


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w Q i \ < - Q . .~ ~Qcj lgst ` i ej `y t r i p lbt rix w i ` ` mj tcbt lbxilisihnw(Q i k ) . Vihfj w(Qi k ) i s i h vb ri bh t witc b lghgtghifri@`yihfrjb s ihn t rbhsdgrlbt igh, tc j prgm`jl fbh mj ajsfr imja bs

lbx ` g n w ( Q i k ) < ` g n KkQik) - , k `gn Qibha usihn V ti r ` ih n s bpprgxilbtigh

lb ; `gn ^(Q .. < ` g n 2 ;. .).. - 2 Q;. . g n Q . . . - Q. . .)2K ~ k K ~Vihfj `gn 2 . ) i s b fghs tbht ajpjhajht gh`y gh tcj t g t b `

` k 2K hulmjr gd t r i p s , it hjja hgt mj fghsiajrjai h t c j l bxilisbtigh prgm`jl.

Qcjh tc j prgm`jl t g mj sg`vja i s t g lbxilisj` g n j ^ (Q.. < - ` g n d - Q...)

IK j i k2,K 26s um k jf t t g t cj ` i h e d `gw fghs t r b i h t s

d g r ` ` fguhtja ` ihes b .Qcis i s jb si `y gmtbihja my ljbhs gd tc j @bnrbhnjbh


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Qbeihn tc j ajr ivb t ivjs wi tc rjspjf t t g Q i k wj cbvj

4@ b4 Q i

` g n Q i k cb p~k

my lbeihn j B xbtc j dgrlb` lgaj` i s dguha t g mj

9Q i k r xb&kb (:.29)

wcjrj bnb ih tcj Sb b rj fb `fu `b t ja d r gl tc j rj s t r i f t ig hs

t fbh mj sjjh t c i s s vbh [uy`jh's lgaj` id wj lbej b ` ` ci sI b pr ig r i js t ilbt ighs @ t i k jqub` t g 2

:.6.= Jxtjhsighs bha ` ili tbt ighs. t cbs hg t mjjh yj t pgss i m ` j t g d i habh bajqub tj i h t j rp rj t b t i gh t g t cj vb r i bm ` j s Sb. Qcjy brj fjrtbil`ybssgf ib t ja wi tc tc j fght r imu t igh tc j d `gw gh jbfc fguhtja ` ih elbejs t g jxp`b ih jbfc pb r t i fu `b r ? A p b i r .Qcj fg hvj htighb ` n rb vi ty lgaj` fbh mj ajr ivj a my lbxilisihn(:.21 ) sum k jf t t g

(: .=2) bha (:.==) mj ihn tc j gr in ih bha ajs t ihb t igh fgh s t rb ih t sbha (:.=6 ) t c j t g t b ` fg s t fghs t r b i h t . I d i h gur lgaj` wj fguht


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t r b d d i f g h b ` ` ` i he s, ihfùaihn fjh trgia fghhjftgrs, wj br jdg rf i hn gu r sg ` u t i gh t g ljjt b t ` j b s t t c j fghs t r b i h t s (:.=2 )bha (:.==) bs wj`` . Ih b fgraghja urmbh b rj b t c i s wguà ilp`yfguht ihn t r b d d i f b t f br pbres bha gtcjr lbkgr sgurfjs bhaajs t i hb t i ghs g d t r i p s .I d i h baai tigh , ghj bssuljs tcb t b ` ` t rbhspgr t fgs t s b rjgh`y t r i p jha bha ` ih e fg sts ( tcis jxfùajs tci hn s ` i e j lgab`pj hb `t i js g r pbreihn fgs ts wcifc ajpjha gh tc j `jhn tc gd tc jstby dgr jxblp`j) it fbh mj s b ia tc b t t c j fgs t fghs t rb ih t (:.=6)i s b `s g ljt my t c j lgaj`. Mut it lust mj rjljlmjrja tcbt tcjrjbrj gh`y =h fg hs trb iht s dg r tc j nrb vit y lgaj` , wcjh h i st c j hulmjr gd zghjs. u r lgaj` cbs bs l hy fghs t r b i h t s b sihajpjhajht fguh ts, jbfc ghj ihfr jbs ihn tc j ihdgrlbtigh fghtjhtg d t c j sg ` u t igh .

cjh gh`y b p b r t i b ` s j t gd t r b d d i f f g uh ts i s b v b i ` b m ` j t c jlgaj` i s ` i ej `y t g uhajrjst ilbtj t cj t g t b ` hulmjr gd t r ip s .I d ghj cbs bh ihajpjhajht jst ilbtj gd t c i s hulmjr tc j sg ùt ighfbh mj ilprgvja. Ih j dd jf t , it i s p g ss im `j t g ih fù aj b hjwfg hs trb iht t g tc j lgaj` ilpgsihn

wcjrj i s t cj t g t b ` hulmjr g d t r i p s .Lbxilisihn (:.` )i ) s umkj ft t g (:.2:) bha (:.=1) `jb as t g tc jsg ` u t i gh

wcjrj i s tc j @bnrbhnj lu ` t ip ` ijr d gr fg hst r biht (: .=1).Qcis lby mj i ht jr pr jt ja bs t c j ihf ùs igh gd bh jx t rb ( hg t ighb ` )` i h e wcifc b ` ` t r i p s usj bha wcgsj d`gw jqu b`s tc j t g t b ` hulmjrg d t r i p s .

t t cj t ilj gd wr i t ihn tcj bu tcgr i s jxpjriljhtihn witc t c i s lgaj`gh b syhtcjtif hjtwgre gh wcifc jhfgurbnihn rjsu`ts cbvj mjjhgmtbihja. Qcjsj wi ` .mj rjpgrtja `b tj r .


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bD i hb ` ` y , it i s wgrtc h gtihn tc b t mgtc lgaj`s bssulj p. . t gm j f g hs tb ht t c us r j s t r i f t i h n t c j i r b p p ` if b ti g hs t g t c jprgpgrtighb` bssinhljht fbsj.

4 AIVFZVVIGH

4 2 Ih t rgauft ighQcj lbih bavbhtbnjs bha aisbavbhtbnjs gd jbfc nrgup gd lgaj`s w i ` `

mj aisfussj a cjrj. j w i ` ` fghsiajr bpp` i fb t ighs i h tc rj j typjs gdb r jbs

Ih tjr urmbh gr rub ` b rjbsDrjj stbha ihn urmbh brj bsVum gr ihhjr brjbs ihsiaj bh urmbh brjb.

j s c b `` ai sf us s jbfc nrgup gd lgaj`s i h tjrl mu t wj lust balit,drgl t c j gu t s j t , t c b t ` i t t ` j fbh mj sb i a bmgut t c j r j ` b t i vj bffurbfy gdt c j prgpgsja ljtcgas gd jst ilbtihn b t r i p lbtrix. Ih j d djf t , vjry d jwt j s t s cbvj mjjh lbaj witc rj b ` abtb bha i h tcjsj fbsjs b`` fglpbrisghscbvj mjjh lbaj bnb ihst gmsjrvja ` i h e d `gws bha hgt bnb ihs t rjb ` /gmsjrvja ?-A lbt rix .

Hjv jrtcj`js s, sgljtcihn fbh mj s b ia bmgut t c j lgst prglisihnlgaj`s bha brjbs gd bpp` ifbt igh d rgl tcjgrjt ifb` fghsiajrbt ighs. I hpb r t i fu `b r wj s c b ` ` aisfuss jbfc lgaj` i h tjrls gd

tc j fghai t ighs uhajr wcifc tc j bssulptighs b rj ` i e j `y t g mjbffjptbm`jtc j blguht gd jx t rb ab tb ( i h baai tigh t g t r b d d i f fguht s) r jquirjaih tjrhb ` fghs i s t jhfytc j i r jvjhtub ` usj dgr dgrjfbs t ihn purpgsjs bha hgt kus t scgr tt j rl js t ilbtigh gd b t r i p lbt r ix .t c j i r d ` j x i m i ` i t y d g r i hfg r pgr bt ihn ih dg rlb ti gh b ` r jbaybv bi` bm `j bmgut t r i p lbeihn mjcbvigur.

4.= .Nrbv ity ty pj bpprgbfcjsQcis nrgup ihf`uajs t c j lgaj`s rjvijwja i h fcb ptjr s = bha 6

t lust mj sb ia tcb t lgst p `bhhjrs b rj d bli ` i b r wi tc tc j iajb tc b tt r b v j ` ajlbha lby dg``g w b nrb vit y typ j gd mjcbvigur. Qcis bssulptigh


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i s lgrj ` i e j ` y t g mj v b ` i a i h ` b r n j b rj b s , w cjrj t r i p f g s t g r t r i p`jhn tc i s bh ilpgrtbht db ftg r i h tc j dgrlbtigh gd b t r b v j ` ajlbhap b t t j rh .

Gd t c i s nrgup, vjry njhj rb` bpprgbfcjs ` i e j tc j ghjs sunnjstjamy Cgnmjrn bha ^ i ` ` s br j i h njhjr b` lgrj tc jg rj ti fb `` y sguha. Ghtc j g tcj r cbha, tcjy tjha t g rjqu i rj lgrj ab tb bha n rjb tj r j d dg r t i hf b ` i m r b t i g h . I d wj bssulj cjrj tcb t lisp jfid ifb t igh j rr gr s a isqu b` i dyt c j u sj gd b lgaj` d g r ljaiul tjrl p`bh hihn wj w ` ` cbvj t g bffjpttc j s j j x t r b f g s t s bs b r j b sg h bm `j p r i f j t g pby i h t c i s f bs j .

Qcj j xt rb ab tb usja i h tc j lgaj` w ` ` ajpjha gh t c j typ j gdab tb rjba i `y bvb i `bm `j g r gm tb ihbm `j wi tc rjbsghbm`j j d dg r t . ]gm i ` `b ra ' slgaj`, dg r jxblp`j, pbssjs lgst spj fid i fb t i gh tj s t s , rjq uirj s hgjx trb abtb , mut ilpìjs b vjry `b rn j fb ` im rb t ig h j ddg r t (Qcj lihilulhulmjr gd pbrbl jtjrs t g ajtjrl ihj my lihilul squb rjs tj fc hiqu jsi s twi fj tc j hulmjr gd zghjs p` us ghj ).

t i s hgt my fcbhfj tc b t lgst bpp ìfb tigh s gd t c i s bpprgbfc cbvjmjjh ih i h tj r urmbh b rjbs . Qcj ljtcga sjjls i a jb `` y su it bm `j d grprgm`jls wcjrj jbfc tgwh rjprjsjhts b sihn`j zghj.

Bppìfb tighs t g d rj j s tbhaihn tgwhs w ` ` usub``y ilp`y b lgrjaj tb i` ja zghihn systjl bha bh ihajpjhajht rgbasi aj ihtj rvijw t gajtjrlihj jxt jrhb ` tr ip s . Lgrjgvjr, f gh nj st ig h j d d j f t s b r j ` i e j `y t gmj lgrj ilpgrtbht i h tc i s fbsj bha h b``-gr-hgtcihn bssinhljhtw ` ` hg t su d d ifj .

j ag h gt t c ih e t c i s bp prgb fc t g m j b p p rg pr i b t j t g i h h j r f i t ybr jbs . Qcjrj sjjls t g mj twg rjbsghs d g r tc is . Ghj i s t c j s c gr tt r i p `jhn tcs ihvg`vja bha tcj g tcj r tcj db f t t c b t p rgmbm `y lgst g db t r i p w ` ` tbe j p `bfj guts iaj t c j s tuay brjb . Cjhfj, b n rb v i ty t y p jgd t r i p lbeihn mjcbvigur i s h gt ` i e j ` y t g mj b sj hs im` j bssulptigh.

Dih b` `y , t c i s typj gd lgaj` fbh fgpj pjrdjf t `y wj` ` witcih f g h si s t j hf i j s i h t c j t r b d d i f f gu ht s.

4 6 Jquiìmriul bssinhljht bpprgbfcj cbvj b`r jb ay ljhtighja t c b t wj tc ih e mgtc Hnuyjh's ljtcgas

w ` ` ajtjrlihj b t r i p lb t r ix mu t , wi tc tc j jxfjp tigh g d pjf u ` ib rf irfulstbhfjs , tc j sg ù t i gh .g d dj r ja w ` ` hgt mj uhiquj. t w ` `


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bftub``y ajpjha gh tcj ihitib`, djbsim`j, sgùtigh bssulja ih jbfc fbsj.Hjvjrtcj`jss, Hnuyjh cbs rinct`y pgihtja gut tcj ilpgrtbhfj gd

ihtrgaufihn bh b``gwbhfa dgr fghnjstigh jddjfts ih bssinhljht. ^jwi`` aisfuss ih sjftigh 4.: sglj gd tcj wbys ih wcifc tcis linct mjbfcijvja.

4 1 Jhtrgpy lbxilisihn bpprgbfcQcis bpprgbfc bppjbrs bs tcj ghj gd nrjbtjr njhjrbìty sg dbr.

Ih prihfip`j it fguà mj bppìja tg tcj tcrjj brjbs gd ihtjrjstljhtighja mjdgrj. ^j cbvj b`rjbay pgihtja gut, tcgunc, tcbt tcj lgaj`bppjbrs sjhsitivj tg tcj tgtb` hulmjr gd trips, b vbribm`j usub``yhgt bvbi`bm`j ih lgst fbsjs. Dbiìhn tcis,fguhts gh ìhes tg lbkgr tripprgauftighs gr bttrbftighs brj rjquirja bha tcjsj brj lgrj ìej`y tgmj bvbi`bm`j ih urmbh brjbs (fbr pbres, rgbas rjprjsjhtihn gh`y ìheswitc lbkgr rjsiajhtib` brjbs, jtf).

Durtcjrlgrj, tcis bpprgbfc, mjihn ihajpjhajht gd p`bhhihnpbrbljtjrs ìej pgpu`btigh bha fbr gwhjrscip, agjs hgt sjjl suitbm`jdgr ljaiul tg `ghn tjrl p`bhhihn bppìfbtighs.

Fglputbtighb``y spj ihn tcj b`ngritcl dgr sg`vihn tcis typjgd prgm`jl bppjbrs dbstjr bha lgrj fghvjhijht tcbh tcj fgrrjspghaihnljtcgas dgr sg`vihn hgh ihjbr rjnrjssigh lgaj s. Hjvjrtcj`jss,ihfghsistjhfijs ih tcj trbddif fguhts lust mj rjlgvja prjvigus tg bhbppìfbtigh gd tcj b`ngritcl.

4.: Jxtjhsighs tg ihfùaj fghnjstigh^j cbvj sjjh tcbt mgtc nrbvity typj bha jhtrgpy lbxilisihn

lgaj`s fbh mj sg`vja dgr tcj prgpgrtighb` bssinhljht fbsj. Qcjrj brjqbsjs ih wcifc fghnjstigh jddjfts brj uhilpgrtbht fglpbrja witcaiddjrjhfjs ih arivjr's pjrfjivja rgutj fgsts.

Qcj Abhisc ]gba Airjftgrbtj c s ajvj`gpja tcjir nrbvity lgaj`sg tcbt it fbh ihtrgaufj sglj fghnjstigh jddjfts vib Vlgfe's itjrbtivjbpprgbfc. It is pgssim`j tg jxtjha tcis typj gd bpprgbfc tg b`` tcjgtcjr ljtcgas bs wj`` (witc tcj gmvigus jxfjptigh gd Hnuyjh's lgaj`s).


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Qcj dg``gwihn njhjrbìsja b`ngritcl linct mj usja

Vtjp 2. Bssulj trbddif vgùljs ih tcj hjtwgre tg mj zjrgbha fb`fu`btj trbvj` fgsts dgr b`` ? A pbirs.

Vtjp =. Diha tcj sjt gd lihilul fgst rgutjs il7 ifit ybrgaufihn b hjw sjt gd p. .b,@ . . /. Vjt h < h+`.2 K 2K. btjp 6. Fglmihj tcis @ pik / witc tcj prjvigus ghjb h-2 -@ _ik ih tcj dg``gwihn wby

Vtjp 1. Jstilbtj bh ?-A lbtrix uhajr prgpgrtighb` bssinhljhtbssulptighs (usihn @-p. b> ha bhy sj`jftja bpprgbfc.26

Vtjp :. Bssinh @-Q~-Q usihn /-p. . / bha diha hjw rgutj fgsts.2KVtjp 4. Qjst dgr fghvjrnjhfj usihn b suitbm`j fghvjrnjhfj

fritjrigh. Dgr jxblp`j tjst id 2 f.. is suddifijht`yh 2 2sili`br tg /-f.. / . Id b`ngritc cbs fghvjrnja stgp,2Kgtcjrwisj prgfjja tg stjp =.

Qcj lbih prgm`jl witc tcis bpprgbfc is tcbt tcjrj is hg nubrbhtjjgd bfcijvihn fghvjrnjhfj. Gtcjr bpprgbfcjs brj pgssim`j mut tcjirbhb`ysis jsfbpj tcj purpgsj gd tcis rjpgrt.

Qcjrj is b`sg bh jxtrb fgst bssgfibtja witc hy ljtcga ihfgrpgrbtihnfghnjstigh jddjfts. B`` gd tcjl rjquirj ngga d`gw-fgst rj`btighscipsdgr tcj ihes. Qcjsj brj hgt jbsy tg gmtbih bha lby ihvg`vj fghsiajrbm`jba cgf abtb fg``jftigh. Qcjrj brj twg gtcjr b`tjrhbtivj sgurfjs;

Qcj stbhabra AQp spjja d`gw furvjs wcifc fbh gh`y fbtjr dgrvjry fgbrsj typjs gd ìhes mut lby prgviaj b silp`j bhaihjxpjhsivj b``gwbhfj dgr fghnjstigh jddjfts. Qcjy brjprgmbm`y quitj ngga dgr ihtjr urmbh brjbs.


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Dgr urmbh brjbs lgst aj`bys gffur bt ihtjrsjftighs bhacjhfj bhy lgaj` nivihn b ngga jstilbtj gd aj`bys uhajraiddjrjht fghaitighs tcjrj fguà mj babptja. Qypifb`jxblp`js wguà mj lgaj`s ìej Q]BHVYQ gr V B ^ Mg``bhajt b 29>>).


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>. ]jdjrjhfjs

2 MJMJJ L.B. (29:9) Hgvj` t r b d d if survjy ljtcga u t i ` i s j sv j c i f `j ` i n c t s . Mu``jtih gd tcj Cincwby ]jsjbrfc Mgbra ==1.

=. MG@@BHA K . CB@@ L . TBH T@IJQ, A . I@@ZLVJH, @., (29>>)B lgaj` d gr tc j silu`b tigh gd t r b d d i f lbhbnjljht sfcjljs_Q]F Vulljr Bhhub` Ljjtihn, ^brwife.

6 I^J]V@BN, ]. ha CZIVLBH E .F . 29>3) Mir ,b i rj Fb` imrbt ijTjrejjrs Euhaj 244-243.1. CGNMJ]N _. (29>:) _`bhhihn gd t r b dd if fguhts . Zhivjrsi ty gdNgtjmgrn, Ajpbrtljht gd V t b t i s t i f s ]jsjbrfc ]jpgrt 29>:;6

:; CGNMJ]N _. (29>4) Jstilbtigh gd pbrbljtjrs i h lgaj`s d g rt r b d d i f prjaif t igh; b hgh-ìhjbr rjnrjs sigh bpprgbfc.Qrbh spgrtb t igh ]jsjbrfc Tg`.2?, pp. =46-=4:.

4. CG@L K . KJHVJH, Q;, HIJ@VJH, V.,FC]IVQJHVJH, B. KGCHVJH, M.]GHMY N (29>4) Fbìmrbtihn t r b d d i f lgaj`s gh t r b d d i f fjhsusrj su ` t s gh ` y . Qrbddif Jhnihjjrihn bha Fghtrg`, Tg2.2>,Bpri` 29>4.> KJHVJH Q. HIJ@VJH, V. (29>6) Fb ìmrb t ihn n rb vi ty lgaj`s bhajst ilbt ihn tc j i r pbrbljtjrs usihn t r b d d i f vgùlj fguhts .:tc Fghdjrjhfj gd Zhivjrsi t ijs Qrbhspgrt Vtuay gup. @ghagh.

3, @BLB]]J @. (29>>) Zhj ljtcgaj ` ih j b i r j silp`j a'j sti lb tig h aj` b l b t ri fj ajs g r i n i hjs j t ajs aj s t i hb t i ghs b p b r t i r a jfglptbnjs sur ` j s ` ij h s a uh rjsjbu; uhj bppìfbt=?hbu rjsjbu rgutijr au Rujmjf. Fjhtrj aj ]jfcjrfcj Vur @jsQrb hsp grt , Zhivj rsitj aj Lghtrjb`, _u mì fb tig h Hg. >4.

n @G^ A. (29>=) B hjw bpprgbfc t g trb hs pg rt bt ig h systjls lgaj`ìhn.Qr bd di f R ub rt jr `y , Tg`. =4, 692-1?1.

2? ^K]FJ@BHA Q ._. (29>>) Qcj l u` ti pr gp gr tig hb ` prgm`jl. @ghagh;Zh ivj rsity Fg``jnj, @ghagh, Q rbhspgrt Vtu aij s Nrgup,Hgtjs KA^46 (uhpumìscja).


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22. HNZYJH, V. 29>4) _rgfjaurjs dgr jquiìmriul trbddif bssinhljhtwitc j`bstif ajlbha. Fjhtrj aj ]jfcjrfcj sur js Qrbhspgrts,Zhivjrsitj aj Lghtrjb`, _umìfbtigh Hg. 69.

2=. HNZYJH, V. 29>>) Jstilbtihn bh ?-A lbtrix drgl hjtwgre abtb;b hjtwgre jquiìmriul bpprgbfc. Fjhtrj aj ]jfcjrfcj sur`js Qrbhspgrts, Zhivjrsitj aj Lghtrjb`, _umìfbtigh Hg. 3>.26. GJFA ]gba ]jsjbrfc Nrgup 29>1) Zrmbh Qrbddif Lgaj`s; _gssimiìtijsdgr Vilpìdifbtigh _bris5 GJFA.

21. ]GMI@@B]A, _. 29>:) Jstilbtihn bh ?-A lbtrix drgl gmsjrvja ihevgùljs. Qrbhspgrtbtigh ]jsjbrfc 9, 2=6-2=3.

2:. VLIQC, ]., LfDB]@BHJ, . 29>3) xblihbtigh gd b silpìdija trbvjàjlbha lgaj` Qrbhspgrtbtigh Jhnihjjrihn Kgurhb` gd BVFJ 2?1, QJ2)

24. VLGFE, ]. 294=) Bh itjrbtivj bssinhljht bpprgbfc tg fbpbfityrjstrbiht gh brtjrib` hjtwgres. Cincwby ]jsjbrfc Mgbra Mu``jtihHG. 61>, 4?-44.2>. VYLGHV, K., Î@VGH, ]. bha _BQJ]VGH, K. 29>4)B lgaj` gd ihtjr-fitylgtgr trbvj` jstilbtja my ìhe vg uljs. Bustrbìbh ]gba ]jsjbrfcMgbra _rgfjjaihns, Tg2.3 Vjssigh =?.

23. TBH T@IJQ, 29>4) ]gba bssinhljht5 pbrts I, 22 bhaQrbhspgrtbtigh ]jsjbrfc 2?, pp. 26>-216.29. TBH [ l J H , C. . 29>>) Vglj rjlbres gh tcj ihdgrlbtigh lihilisihnljtcga Yjrejjrsb.ebajlij, Qi`murn, Liljgnrbpcja hgtjs, Gft.29>6.

=? TBH [ZY@JH, C.K. 29>3) B ljtcga tg jstilbtj b trip lbtrix drgltrbddif vgùlj fguhts _Q]F Vulljr Bhhub` Ljjtihn, Zhivjrsitygd ^brwife, Ku`y 29>3. @ghagh; _Q] Jaufbtigh ]jsjbrfcVjrijs @ta. uhpumìscja)

=2. ^B@VC, K., ^JMMJ], L. 29>>) Ihdgrlbtigh tcjgry; sglj fghfjptsbha ljbsurjs. Jhvirghljht bha _`bhhihn, B.9, 69:-12>.

==. Î@@V, L. 29>>) Mgh ìhjbr jstilbtigh gd grinih-ajstihbtigh d`gwsbha nrbvity lgaj` pbrbljtjrs drgl trbddif fguhts gh ìhes.Ajpbrtljht gd Njgnrbpcy, Zhivjrsity gd Mritisc Fgùlmibliljgnrbpcja hgtjs.


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=6. Î@VGH, B.N. 29>?) Jhtrgpy ih Zrmbh bha ]jnighb` Lgaj`ìhn@ghagh _igh.

=1 Î@VGH, B.N., LbfNI@@, V.L. 29>>) B systjls bhb`ytifb` drbljwgredgr fglprjcjhsivj urmbh bha rjnighb` lgaj` muiàihn. @jjas;Zhivjrsity gd @jjas, Vfcgg` gd Njgnrbpcy ^greihn _bpjr Hg. =?9.

=:. ^]INCQ, F. GII]GL, C. 29>4) Qcj ^jstlihstjr rgutj fcgifj survjy;b hjw tjfchiquj dgr trbddif stuaijs. Qrbddif Jhnihjjrihn bhaFghtrg` 2>. 329).


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Hgtbtigh.j cbvj t r i j a t g ejjp hgtb t ig h uhidgrl tcrguncgut t c i s pbpjr .

Hjv jrtcj` jss, sglj ih jv it bm `j mut lihgr aj pbr turj s drgl t c i s hgrl w i ` `mj bppbrjh t t g tc j rjbajr.

I h n j h jrb `Q i k t r ips mjtwjjh i bha k , wcjrj i bha k brj g r in ih -ajs t ihb t igh

p g i h t s , t c b t i s zghj fjhtrgias.*2-~i\ < Qcj wcg`j t r i p lbtrix-b b ` i h eTb t g t b ` d `gw gh ` i h e -Fb(Tb) Fgst d `gw rj`b tig hs ci p gh `ih e b

i t r i p jha f c b r b f t j ri s t i f d g r t g h j i i h p b r t if u ` b r_ J _b rt if u` br pg pu`btig h bha jlp`gyljht b t i bha k .ki k < fg st gd t rb vj ` ` ih n mjtwjjh i bha kr i k < b rgu tj gr pbtc drgl i t g k ajdihja my

i d ` i h e b i s hgt gh r . .cb-.. -K2 k ( 2 i d ` i h e b gh r t c b t i s r i k u sj s ` i h e b .i k

t r i < hulmjr gd t r i p s drgl i t g k gh pb tc r i k i h n j hj rb ` Q < [ t .IK r tikb < hulmjr gd t r i p s drgl i t g k gh pbtc r i k l i h nt r i ` i h e b

b_ i k < ztr ik IQik< prgpgrtigh gd t r i p s mjtwjjh i bha ku s i h n ` i h e bi h n jh jr b` . 0 2 bha tcj jxtrjlj vb`ujs brji ktbejh wcjh tcjrj i s gh`y ghj pbtc mjtwjjh i bha k .

j ag hgt a id dj rj ht ib tj mjtwjjh pjrsgh bha fb r t r i p s i h tcj uhajrstbhaihnt c b t b lu `ti p` ifb tig h my bh ihajx fgrrjspghaihn t g bh bvjrbnj f br gffupbhfyr b t j i s tc j gh `y gpjrb ti sl rjqu i rja t g fghvjrt ghj i h t g t cj g tcj r .


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.B bs ih ~ b ) s usja tg rjprjsjht gmsjrvja abtb d`gws)B bs ih rikh) is usja tg rjprjsjht bh gptilul dinurj

`iej gptilul pbtc mjtwjjh i bha k)


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9. B__JHAIS =.

` j b s t s qu br j j st il b ti gh gd t c j t r i p d b f t g r d g r t c j ] lgaj`

9.2 LjtcgaQcj ljtcga i s f `gsj `y ` iheja t g tcj hgrlb` a i s t r imu t ig h . I h d b f t ,

dg r tc j hgrlb` a is tr im ut ig h tc j lbxilul `iej` icg ga s g` ut ig h i s dguhawcjh tcj vbribhfj i s lihilisja.

I d wj lbej J S ljbh it i s pgss im `j t g rjp rjsjh t tcj hgrlb`a i s t r i m u t ig h my

= =-J / = td ~ ) 5-j . h i h f= =


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^cjrj @ i s tc j ` ie j`i cg ga duhftigh. Qcj lbxilul `ie j` ic gg a i s gmtbihja=d g r 2 p < lihilul.

wcjrj p i s hgrlb``y fb `` ja wjinct .9.= Bpp` ifb ti gh t g t c j ADSK lgaj`

Qcj lgaj` jstil btjs t c j d`gw gh b ` i h e bs

b < m S b + s wcjrj` bb < K g G F p - w i tc l ehgwh2 Ki k

ra tc j j r r gr t jrl . sb i s hgrlb``y a ist r im ut ja witc ljbh zjrg bha vbribhfj

Dgr jxblp`j y < ljbhs tc b t ljbh bha vbribh fj b rj i h prgp grt igh bhay < = ljbhs tc b t t c j s t bhabra ajvib t ighs gd tc j j r rg r i s

pr gpgrt i ghb` t g t r b d d i f d`gw .y w i ` ` mj fcgsjh ihajpjhajht`y gd tcj ljtcga.

Ih t cj bmsjhfj gd m jt tj r ihdgrlbtigh bh i h i t i b ` nujss fbh mj lbajr jnb r ai hn y bha t c b t ilprgvja my t r i b ` bha j r r g r i h g r aj r t g gm t b i h t c jm js t d i t .

Ih gu r fb sj wj lby aj di hj

Ibha p b b witc s i d ( ~ , ( m ~ x ~ - ~ )Sb


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Hgw, gur mj st uhmibsja ` i h j b r js til btj wgu`a mj t c b t wcifc lihilisjsfpJ=Ih gur fbsj

I b-m 'b

wj fglputj (yi-m) pi F p ~

Lbeihn tcj d i r s t a j r iv b t iv j jqub ` zj rg .

mut gur wjincts wjrj pi- 4 s(m% -B)

wcifc agjs fg ihfia j witc Al's sg `u t igh .

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