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: 18:25:21 12 2005
: 962 : 2 : 0 : 0 :    

, 30- 40- . XX ., . . .

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.

epea oapaoaae 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 ypexxapaepc, a eee aeco - e, paep, yaoa, ycy, oopecopooa eo poay.

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

poyoa epea oe a peao, ae ce pa aece oapo, ooeoc pyx yoaxxapaepcax, a aoo. B ocee cyaepa oapx apo oc cyyo e xapaep, a ce ee ea, yao, eeo a. K aoo epea oooec pa aaaxca oapa, apep, oa poae oae-ceoo poya coye pece aa poa coeo oapa.

epea poya ee y a ocec p. Bo-epx, poyooepaoopaecoae poy ac p, ocoy cea axoc oyae, oopeoaac pepe poyy eo ao oapo ap ao p. Cooeceo, ec oyae paccapa pae oape ap a ecoepeecycy, pa oe o ey aco ocoe oap eypo 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 ape, a ae oeaype ycaex oapo oo po o pepe ao-oopac. e oee co oapx apo peaaec opee paaxooo poyooo acca e oee co oapo ycaec po ao opac, e ecee poyoo epea peeo aoy-o poyooy accy.

Cee poyoo epea oe epea aocoe 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 ecee poyoo epea. aoopo, cee poyoo epea ye e e, e eaee epepeco acoc cpoca.

Eeo 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.

,

Hapaxc epepoa poyo paoaae opeeeo cee oooo ac, ooyee yaa pa cpoca ye e opae ao. Bea aoa yao po cpoca - eoa a-coc cpocaoeo p - ac o cee poo ac, oopo oaae pa. Ha o ocpoe o eco, oeaxcee oooo ac p ape oooceco oype, - ecPoa.

ecPoacpoc aocoecoocae aeco yo aoa po pooocpoca aoo poyooo acca po yaoocpoca p, ycae ay-o oapy apy oo acca:

R = tga/tgb,

eR ecPoa;

tga aec ya aoa po yaoo cpoca;

tgb aecya aoa po cooyocpoca.

Ec pa eoaae poo ac, oee ya cpoc eoaec o cooyoopooocpoca, oa ecPoapae 1. e oepoa ac p, e oepaa aeco, e oe ya- cpocooec 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 ape oooceco oype, a oaa .eep, ye paa y. Ec p oya oo-ey p, oe p xo opac, yca eeoypaooc oapa, yeeec cooyoe peoee ee ae e a oap. Ec p ecy y, ac p paopc ye opac, yeeec cooyoe peoee oe e o eyoooypo. Ta opao, ape oooceco oype oocpooepaoece, oe p, ocaec a, eea oapaoaaec pao cpe epa yca.

ocoycpee ep yca e U-opay opy, o oapaeca e (aoo po yaoocpoca) cpex oocpox epe pec a yc e ao eoo, paoo yycpex oocpox epe. Ceoaeo, pa oooceco oype xapaepo eeX-eeoc - yc oapa ec 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 cpocaa oap epo p;

a > c(b - d) - ec paycaaae ey aypoe peex epe c, oee yc ooee.

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

i = Qi(Pi - c).

epeyco aca p ao p ay ceye y pea:

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

Bycoxpaoec 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 oopaccapa c o pe cooyoc opeecxcoc, oope e axo opee. Ta, aoo ox opeee pecae epecc o pe ooc eo ae, pyeoea e epy oepe e , pex aoyoco ypae .. Cooeceo peoe opeee oooe oapy oy pae e ap px epa, e opocyecec ey y ( ec pe e o pocpace - N) eoxapaepca. 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 eeo oeoc.

peoo, epoaao a pe pcycye paoocoapa, A B, oeocoopx oaoaax opeee. opyapa ycaeoap D c a xapaepca, o eo oeocpeocxoa oeocpeyx apooapa:

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, poaaeepa pa, c o pe pee, eoxooo oca poya, yoeopeo xocoe peoa. e epoy ecoooe oyae e eeococa pac eae xapaepca opee, e e p poxpaxycox oeoc aoo oapa. Cooeceo e e a poyapacooe py pyy e oeecxo c xcoca, 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 aeoo eca poa oapa, o ece ooee pacope apa a oyypoya; ec opee oyae oapc eee eae coca, o oyae ey oeoc o eo opee. Haocoe x yx po ocpoe e ae oe pocpaceo epea poya oe Xoea oe Caoa. Paccop opoee .

peoo, o oape ap oac py o pya ooo oaaee -yaeoc o opee. yc opee pacooe paoepo o eceo y opoe. Ka opee pee cpoc aoyey oapa. e p poa o o e oap. Oa papacooea apacco a o ooo oay, pya apacco o pyooee oa (pc. 1). opee pa py, cxo pacopx epe: a oyae oapy 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.

xNya1

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

Ta opao, p cpoao ee ecopacooeepoao ooo oo e oapaoaaec cpoo eeppoa. o pocpaceoepaoece ec paoece oHy: a oo p opee coepaoecoeecopacooee, yoo 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.

caoeepox e p cpoao ecoooe p opeeec eo pacopxpacxoo.

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

Oao e aepacooe opee o oo p e e pyo pe, e caeeoaaec ooooe oece epo p acpoc, e cee ye poc cee eoo oype ey . Eeoa 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 acoxceeaxpa py-oceoae a yx ceeaxcceopo oypexaoec poeye.

. 2.

1 2


1

2

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

a oe oaae ooe epoca pacopxapo a ooee p: coo copo, yeee apo ee cye oax pa pa pocypoo ac poaa apeoao pe, ac pyo copo, copaaec aeecoco cpoc.

Moe Xoea oaae aecoca eoo oype oooco. Ec ape oae eoa oype, opaoece eppaa ooo oo p oopooc oapa. Bcyae eoopooc oapa, apep, pocpaceo epea, p oy aaa pae e, pe ce e yy e peex epe.

co p, ecyx apec epepoa poyo, po poopoao pacop pacxoa opao poopoao ee ocox epe. ea oapa opacae p poce pacopxpacxoo yee ocox epe.

Paccop eep oeecoy cya, oa p pa aae ecopacooee, a oo oopeeoaaa e - oe 'Acpeoa aea - Tcce.

peoo, ape ecy e p, aa oopx ycae o epepoaoo oapa. Kaa pa pae o ae, a opao op ecooe ee aaaoae e e oo aee y cpoca, o acee eoo oype ey pa.

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

Kaa pacpec epeecc eo, ec oa epoaao apacooeaceao pyo p, pao, ec oa epoaao apacooeacpaao pyo p. ooypaoece oe 'Acpeoa aea - Tcceoaae acay yaeoc poao py o pya - acay cee poyoo epea.

Ta opao, poca, cxoa oe opoao epea oapa ae coeopoa acoe paoece eo opoe. Ec p coo ope oooooapaepacoeo oee o ecoooe, o e, o oyae ypaa paoec peya: poa opacoaac e py pyy (aa cee poyoo epea), o aaa oaoe e cyeo pacopx epe. Ec e p oy appoa ecoooee e, paoecoecocoeoaae acay yaeoc poao py o pya, oopa ec cece cpaeecoo ea - ea, aaaea oo po, oaae e acpoc pyo p.

. . , . .

, :

dC(U)/dU >> 0,

C(U) ;

U ;

d ,

. , , , , , .

, . , , , . . .

( ) . , , . , , , . , . , . . - , .

ocx op paccapa poyoy epea c o pe opee - co oapx apo, oopeec ape 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 aocaeoac pooca - pacpee poyoo , o pye eopaecep - pacpee pocpaceo cep p. Ec epca pocxo ecaecoco pooco cep eeoc, ooa oc aae ooeppoa, acaa pa ao cyae ye aac ooepao. Ka pao, ooepaepacpe eeoc p xapaep epex, caoxc po. Haoee aco cpeac eoa pexpo c ce epcaoe ee pooca ca p.

epca ee pocy ca poyox , ocyaexoo po, o epe ypeeepacpee pooco ox oapx apo ox oapo, o o-cpeco c ooe. Boae opoc, oey oxcyax peoaae epxcoco epca, a pyx opo? cceoa oa oaa, o opp ca c ao eoo aopac. B oo pacye opac p oea epce poca ooeo (ocec), ooyo cpec yee poocex ooce. o epepocaopac yee ca oapx apo, peaaex po, pepaaec pacpeecpoca, ooeoe co aeoa oapa eee cyeceoyyee o p ape, copaaec o p ooceo eecoopaoc ypeeopoca. Ha ae peoc opac pye acoopee p yy epcpoa pooco ye c ooe c e pooe a pyep. ec e epca oe paccapac a coco yxoacpa , o pae epe, oecee ao a epoo ea.

epe cee epca p coy ec epca, opaoa aocoe ecaXep-aXpaa:

d = 1/[∑zi2], i=1, ..., n,

ezi - o oea poa p, pxoac ai- 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 aopeococ, ax a: aeco, ecoooee poaaooceo opeee, pe poa, ooeoc, opaoa ocyoc eococ opeee, ooeeycy, peocaee o pe oce poa .. Kaoe xcoc oe cya aece aopa poyoo epea.

Bycoxcoepeo oypeoopa poy oopo, aa pa poae oap e oapy, oop peaae a pya papa. eoc oypex oapo ae ce oaooc cexca poyoo eo, o pooca oyco poa ocepoaooocya. ooyy p e cyo oy, o pepa ae-oocoeyc ca oapa, oype po peocae ao pe oooc poaa oe oeco oapa o oypeo ee e ooexpacxoo yc. Oe ca yao p ac ooo ee exooecx apaepo - coooe pxcpex peex epe. oo ycox ecoepeo oype pa eecoopaopepa yc apoc oea poa. Koapo eec ooco oype, pa oe pe ocoecpae ycaoe ee oooo ac a oyae.

B ooecyecy p, a oopx p ocaoo oo ce poao oyaee p oaa ce eopeeeo ac cepeycaoe e. Taep aac pa oooceco oype, a a o oe ep a oype - e ooo caoyaee poao, coooo xoa xoa p opac, a ooo - eopeeeoo oec aey oapa, a ocpoc a poy ao p pecae coo py copae aoo. Poy ac a oapo ae pe epea poya.

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


1) ., ., , , 1998.

2) ., ., , , 2000.

3) ., ., , , 1997.

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