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epea oapa oaae eee poya ao-o p aax opeee o ocax poyo aoo acca. epea pecae coo opy eeoo oype p. aopa poyoo epea oy c a ypeee aeco oapa ee eo ypex xapaepc, a eee aeco - e, paep, yaoa, ycy, oope copooa eo poay.

epea poya ee eco o ex op, oa ca opee pacea pae oape ap aece ecoepex aeee. B opeeeo cce poyoa epea pecae coo cyey xapaepcy oee oyaee.

poyoa epea oe a peao, ae ce pa aece oapo, ooeoc pyx yoax xapaepcax, a aoo. B ocee cyae pa oapx apo oc cyyo e xapaep, a ce ee ea, yao, eeo a. K aoo epea oo oec pa aaax ca oapa, apep, oa poae oae-ceoo poya coye pece aa poa coeo oapa.

epea poya ee y a ocec p. Bo- epx, poyooe paoopae coae poy ac p, ocoy cea axoc oyae, oope oaac pepe poyy eo ao oapo ap ao p. Cooeceo, ec oyae paccapa pae oape ap a ecoepee cycy, pa oe o ey a co ocoe oap e ypo e oypeo e oep oyaee. Bo-opx, poyoa epea oa oyae. Koa pa xo a po c oo oapo apo, opee oya ee oee poyooe paoopae, oopoe cocoo ye cee cooecoa x peoe.
poyoa epea pac oooc opeecoo opa.

pee ceo, ae cee poyoo epea poc ce oapx apo, peaaex pa a pe, a ae oeaype ycaex oapo oo po o pepe ao-o opac.
e oee co oapx apo peaaec opee paax ooo poyooo acca e oee co oapo ycaec po ao opac, e e cee poyoo epea peeo aoy- o poyooy accy.

Cee poyoo epea oe epea a ocoe epepeco acoc cpoca. epepeca aoc oaae pea cpoca a a poy p ee e pyoo poya pyo oapo ap. e e epepeca acoc, e oee cycya c aax opeee pae oape ap e e cee poyoo epea. aoopo, cee poyoo epea ye e e, e e aee epepeco acoc cpoca.

Ee o oaaee cee poyoo epea cy ec po.

E = Z [qiln(1/qi)], i = 1, ..., n, e qi co aao, oopx opee oyae i- oap; n co oyaex oapo.

Ec E = 1, opee oya ce poy oo o e aae. poe epea ec aca. p E = 0 opee pacpee co oy paoepo ey ce aaa.
poe epea ec a.

,

Ha pax c epepoa poyo pa oaae opeeeo cee oooo ac, ooy ee yaa pa cpoca ye e opae ao. Bea aoa yao po cpoca
- eoa a-coc cpoca oeo p - ac o cee poo ac, oopo oaae pa. Ha o ocpoe o eco, oeax cee oooo ac p a pe oooceco oype, - ec Poa.

ec Poa cpoc a ocoe coocae aeco yo aoa po pooo cpoca aoo poyooo acca po yaoo cpoca p, ycae ay-o oapy apy oo acca:

R = tga/tgb, e R ec Poa; tga aec ya aoa po yaoo cpoca; tgb aec ya aoa po cooyo cpoca.

Ec pa e oaae poo ac, o ee ya cpoc e oaec o cooyoo pooo cpoca, oa ec Poa pae 1.
e oe poa ac p, e oe paa aeco, e oe ya- cpoc ooec o pooo, a a a ya cpoc cea oee ace, o ce eca paec y, , ceoaeo, aee eca ae ye pac y.

C pyo copo, ec apep xoa opac ocycy, o oocpoo epoe ooeca p p, ecyx a pe oooceco oype, a oaa .eep, ye paa y.
Ec p oya oo-ey p, oe p xo opac, yca ee oy paooc oapa, yeeec cooyoe peoee ee ae e a oap. Ec p ecy y, ac p paopc ye opac, yeeec cooyoe peoee oe e o eyooo ypo. Ta opao, a pe oooceco oype oocpooe paoece, oe p, ocaec a, e ea oapa oaaec pao cpe epa yca.

ocoy cpee ep yca e U-opay opy, o oa paeca e (aoo po yaoo cpoca) cpex oocpox epe pec a yc e ao eoo, paoo yy cpex oocpox epe. Ceoaeo, pa oooceco oype xapaepo ee X-eeoc - yc oapa e c ae epa.

peoo, opac ecy e p, ycae epepoa poy. Cpoc ao p ocaec a:

Qdi(Pi, Pj) = a - bPi + dPj, e Pi ea a oap ao p;

Pj ea a oap p-oypea; a, b, d - ooee apaep pa.

Ta a poy p peca coo oap- cycy, o epepeca acoc cpoca ooea.
p o: d < b - poc e oox oapo ee copae cpoca a oap epo p; a > c(b - d) - ec pa ycaaae ey a ypoe peex epe c, o ee yc ooee.

yc peee ep p pa oco. Kaa pa cpec acpoa p:

i = Qi(Pi - c).

epe yco aca p ao p ay ceye y pea:

Ri = Pi = [a + dPj + bc]/2b.

B ycox paoec e yx p yy pa:

P* = (a + bc)/(2b - d).

Oya oyae p ao p:

* = P* - C = [a + c(b - d)]/(2b - d) > 0.

Ta opao, oyae, o ycox poyoo epea eoa oype ey pa po ooeo p ao p.

:

Toap oo paccapa c o pe cooyoc opeecx coc, oope e axo opee. Ta, aoo ox opeee pecae epec c o pe ooc eo ae, pye oea e epy oepe e , pex ao yoco ypae .. Cooeceo peoe opeee o ooe oapy oy pae e ap px epa, e op ocyecec ey y ( ec pe e o pocpace - N) eo xapaepca. y, poee aaa oopa, a epecee c ao-o po epa oaae ecoc ao xapaepc oape. e oy ecoc o ao xapaepce ee oap, e e eo oeoc.

peoo, epoaao a pe pcycy e paooc oapa, A B, oeoc oopx oao aax opeee.
opya pa ycae oap D c a xapaepca, o eo oeoc peocxoa oeoc peyx apo oapa:

U(D) > U(A);

U(D) > U(B).

opee epeac a oap opye p, ocae p ep cpoc.

Paccop eep pyo cya. opya pa aao pcycoaa a pe ycaa oap B. B peye oe peoaa, o apa px epa oaoa opye p, pox p pa, o ec opee o e e y cex p pa. Teep ee oee coy peocy o o, o peoe opeee paac. peoe opeee o-pye p eee ac, e peoe opeee p-aycaepo. aaa opye p aaec o, o ye poyoo epea epea opeee p-aycaepo, o oca a coo cex cox peyx eo (e oyc ea
caoopa). a e ocaec, ec oa apa oapa M, ycaea opye po, aae cooec co co xa- paepca poeyooe eco a poyoo pa, a o:

U(M) > U(A);

U(M) < U(B).

B o cyae opee, paee pepee opye pe, ocac e o, ocoy oeoc ooo oapa x e, e oeoc capoo poya; a opee p-aycaepo epexo opee poya o-pye p, a a oeoc oeeo x e.

opee oy oea oap, poaaee pa pa, c o pe pee, eoxooo oca poya, yoeopeo x ocoe peoa. e e poy ecoooe oyae e e eo coca pac eae xapaepca opee, e e p pox pax ycox oeoc aoo oapa.
Cooeceo e e a poya pacooe py pyy e oee cxo c x coca, e oee cycya o yy aax opeee. Ta opao, oap oy paccapac pocpaceo poyoo pocpace. C pyo copo, opee ae o-y paccapac pocpaceo poyoo pocpace: ec opee pacooe aeo o eca poa oapa, o ece ooee pacope apa a oyy poya; ec opee oyae oap c eee eae coca, o oyae ey oeoc o eo opee. Ha ocoe x yx po ocpoe e ae oe pocpaceo epea poya oe Xoea oe Caoa. Paccop opoee .

peoo, o oape ap oac py o pya oo o oaaee -yaeoc o opee. yc opee pacooe paoepo o eceo y opoe. Ka opee pee cpoc a oy ey oapa. e p poa o o e oap. Oa pa pacooea a pacco a o ooo oa y, pya a pacco o pyoo ee oa (pc. 1). opee pa py, cxo pacopx epe: a oyae oap y o p, oopa pacooea e eo oy.

yc opee N e a pacco x o p A (pacooeo a pacco a o ooo oa y) a pacco y o p
(pacooeo a pacco o pyoo oa y). Ec x > y, o opee ye peoa py . Ec x < y, o opee ye peoa py A. opee cea ye pa y py, oxo o oopo ye copooac oee pacop epa.

peoo, o e a oap oao y oox p. Toa p yco o pa ye pacooea a pacco o ooo oa y e oe cpo e coe ecopacooee, pa A epe aoe ecopacooee, p oopo ee p ye acao. oo pa A oa ae ooo oeo ca .
pa A ye pacooea eee p , a pacco a1 o pyoo oa y. Bce opee, ye a o oe y, yy oya oap y p A, a x oco. B co oepe pa , ocoy oa ye ec oep o pacooe p A, epeecc cey epo eoo eee p A, a o epexa opeee, yx a o oe y. o poecc ye pooac o ex op, oa oe p e oayc epe y: oa y x ye oaooe co oyaee, poo ooa o oeo x oeca. aoe paoece ye ca paoece, ocoy p ao pacooe y oo p e ye cyo epeac ay-o copoy, e coe pacooee - apaep coe eeoc.

. 1.

x N y a1

a, p eoooc ee ypo e, ecopacooee yx p ye cy cpaeeco epeeo ooao opeec epo oac ocya. Ta, cceoa oape p pyx opoo, aeae, o aoa ooc aao eceo pxoc a ep opoo.

Ta opao, p cpoao ee ecopacooee poao ooo oo e oapa oaaec cpoo eeppoa. o pocpaceoe paoece ec paoece o Hy: a oo p opee coe paoecoe ecopacooee, y oo p e cyo e eo, ocoy o e pee pocy ca oyaee.

Booa pya eppea ao oe. Ec ecopacooee p cpoao (apep, p ex a opeeeoe cooae eex yaco eoc), cpoo eeppoa oaec ypoe e. ao cyae ae eooe paoece oaec paoece o Hy: aa pa ye aaa ey, pay ee oypea c opao a ey pacopx pacxoo.

caoee pox e p cpoao ecoooe p opeeec eo pacopx pacxoo.

Ec p pacooe a pao pacco o opee, aa pa oe aa oee coy ey a co oap, e e eee aoe-o co opeee ye eo oya, e opee, oope peoy yoco pacooe- pacop epa o ee.
ooy yoo pacooea pa oaae opeeeo poo ac, o ooe e aaa y oee coe e.

Oao e ae pacooe opee o oo p e e pyo pe, e caee oaaec ooooe oece epo p a cpoc, e cee ye poc cee eoo oype ey . Ee oa yaeoc opee o epo p yeae aoc pac pacxoo oc pyo p eo, a o o epe oo, a opee yaec o epo p, opacae oooa ac opo p.

Ta opao, pocpacea epea oapa aoap a pacopx epe ee paee pa a p ceea: cee oooo ac epo p, cee eoo oype cee oooo ac opo p (pc. 2).

Ta a e cea epooc poa oapa yaeo pe, aa pa ye peca coo e ooo, a opyy py a cox ceeax pa py-oceoae a yx ceeax c ceopo oypex aoec poeye.

. 2.

1 2

1 2

eee pacopx pacxoo ee cy cpoca e eca pacooe p, a o oac eoo oype copaaec, a oac ooooo ao p opaca, xo p o ypoe e, oopy opee oo a a oap, copaaec.

a oe oaae ooe e poca pacopx apo a ooee p: c oo copo, yeee apo ee cye oax pa pa pocy poo ac poaa a peoao pe, a c pyo copo, copaaec aeecoco cpoc.

Moe Xoea oaae ae coca eoo oype oooco. Ec a pe oae eoa oype, o paoece
eppaa ooo oo p oopooc oapa. B cyae eoopooc oapa, apep, pocpaceo epea, p oy aaa pae e, pe ce e yy e peex epe.

co p, ecyx a pe c epepoa poyo, po poopoao pacop pacxoa opao poopoao ee ocox epe. ea oapa opacae p poce pacopx pacxoo yee ocox epe.

Paccop eep oee coy cya, oa p pa aae ecopacooee, a oo oopeeo aaa e - oe
'Acpeoa aea - Tcce.

peoo, a pe ecy e p, aa oopx ycae o epepoaoo oapa. Kaa pa pae o ae, a opao op ecooe ee aaa oae e e oo a ee y cpoca, o a cee eoo oype ey pa.

ecoooee poaa p pocpaceo epea oaae ooe oece a p p. C oo copo, ecye e cpoca - poe e ecoooe a oe cpoca. C pyo copo, oae cpaeec e - oceoe oece ecoooe ooo poaa a ey, oopy ycaaae pyo poae.

Kaa pa cpec epeecc eo, ec oa epoaao a pacooea cea o pyo p, pao, ec oa epoaao a pacooea cpaa o pyo p. ooy paoece oe
'Acpeoa aea - Tcce oaae acay yaeoc poao py o pya - acay cee poyoo epea.

Ta opao, poca, cxoa oe opoao epea oapa ae coeo poa acoe paoece eo opoe. Ec p coo ope oo ooo apaepa coeo oee o ecoooe, o e, o oyae ypaa paoec peya: poa o pacoaac e py pyy (aa cee poyoo epea), o aaa oaoe e c yeo pacopx epe. Ec e p oy appoa ecoooee e, paoecoe cocoe oaae acay yaeoc poao py o pya, oopa ec cece cpaeecoo ea - ea, aaaea oo po, oaae e a cpoc pyo p.


. . , . .

, : dC(U)/dU >> 0, C(U) ;

U ; d , . , , , , , .

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o cx op paccapa poyoy epea c o pe opee - co oapx apo, oope ec a pe ocy oyae. Teep cae opoc, oo yca ooe co oapx aeoa cao pe. C o pe p poea poyoo epea popeae epca pooca.

epca oaae poee p oe aocae oac pooca - pacpee poyoo , o pye eopaece p - pacpee pocpaceo cep p. Ec epca pocxo e cae c oco pooco cep eeoc, o oa oc aae ooeppoa, a caa pa ao cyae ye aac ooepao. Ka pao, ooepae pacpe eeoc p xapaep epex, caoxc po.
Haoee aco cpeac eoa pex po c ce epcaoe ee pooca ca p.

epca ee pocy ca poyox , ocyaex oo po, o epe ypeee pacpee pooco ox oapx apo ox oapo, o o-cpeco c ooe.
Boae opoc, oey ox cyax peoaae epx coco epca, a pyx opo? cceoa oa oaa, o op p ca c ao eoo a opac. B oo pacye opac p oea epce poca ooeo (ocec), ooy o cpec yee poocex ooce. o epe poca opac yee ca oapx apo, peaaex po, pepaaec pacpee cpoca, ooeoe co aeoa oapa e ee cyeceoy yee o p a pe, copaaec o p ooceo eecoopaoc ypeeo poca. Ha ae peoc opac pye acoo pee p yy epcpoa pooco ye c ooe c e pooe a pye p. ec e epca oe paccapac a coco yxoa c pa , o pae epe, oecee ao a epoo ea.

epe cee epca p coy ec epca, opaoa a ocoe eca Xep-aXpaa: d = 1/[Szi2], i=1, ..., n, e zi - o oea poa p, pxoac a i- eeoc; n - oee co o eeoc, oopx aa pa.

Ec pa ecye oo oo cepe, o d = 1. Ec pa ecye 10 poyox x, a ay oopx pxoc 10% oea poa, o ec epca cocae 10. Co oa o, pxoac a o eeoc, p o o a pye pxoc eaea ac yca, ye aa ae eca epca, e ee.

poy oe xapaepoac epe aop eo coc, ax a: aeco, ecoooee poaa ooceo opeee, pe poa, ooeoc, opaoa ocyoc eo coc opeee, ooee ycy, peocaee o pe oce poa ..
Kaoe x coc oe cya aece aopa poyoo epea.

B ycox coepeo oypeoo pa poy oopo, aa pa poae oap e oapy, oop peaae a pya pa pa. eoc oypex oapo ae ce oaooc cex ca poyoo eo, o pooca o yco poa ocepoaoo ocya. ooy y p e cyo oy, o pepa ae-o ocoe yc ca oapa, oype po peocae ao pe oooc poaa oe oeco oapa o oypeo ee e ooex pacxoo yc. Oe ca yao p ac oo o ee exooecx apaepo - coooe px cpex peex epe. oo ycox ecoepeo oype pa eecoopao pepa yc a poc oea poa. Koa po e ec ooco oype, pa oe pe ocoe cpae ycaoe ee oooo ac a oyae.

B ooe cyecy p, a oopx p ocaoo oo ce poao oyaee p oaa ce e opeeeo ac cepe ycaoe e. Tae p aac pa oooceco oype, a a o oe ep a oype - e ooo ca oyaee poao, coooo xoa xoa p opac, a ooo - e opeeeoo oec a ey oapa, a o cpoc a poy ao p pecae coo py c opae aoo. Poy ac a oapo ae pe epea poya.

cceoa poyoo epea oaa cooc opeee oapa aax opeee. Paoec a pax ooocecoo poya oy po o co oo, o e ao cee epea oapa. o e oee a, ec pa o ae, o pea poy oe epepoa cpay ecox opoao, epao.

1) ., ., , ,

1998.

2) ., ., , ,

2000.

3) ., ., , , 1997.


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