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MATEMATECOE MOEPOBAHE B.. yxa (Tep) HOPMAOHHA MOE COAHO HAM B cae oocoaec poyoc opaooo oxoa oepoa coax poecco

peaaec apoca op aoa oe pa coao cce. C oo ao o e cceyc opaoe aooepoc pax cpae coaoo pa.

ee coa: opao oxo, opa, po, opaooe paoopae, opaoee, coaa a, coaa ccea, apoc poecc, oe.

opaooe aoece eoeea y oo coaoo oea, e eee aa eo, e eaoeca y, oepaa eeceo-epe ec oe oea co cpeo. o opaooo oeca opaoo cac, oepo peo cycceoo eea, ceeoo coya ceeoo ea o oxo cooo, oco, ooo a e ececeo, a cepee pooo ea oe opa oo ececoae exy ooo cpo popeo oeay cayc. oe opa e eee yaea o, e o aep, ep coa. Teop opa Bap opco yxa oop ococx ay, poeccop Tepcoo ocyapceoo execoo yepcea. E-mail: guhman@yandex.ru.

Cooo: 4M. 2005. 20.

opauoa oe couao uauu ec o epepo paac aapao c ceoa, apa opeo ppoe opao x poecco ocee opa, ope coepa cao opa.

ooy ec ce ocoa cooa opao oo oxoa coao peaoc aece ooo a x cpyeo ee cceoa. o uopauo no xoo a caocoe ayo-ococ ocpyo opayeaec eoooec oec oa cyoc e, e poecco a ocoe o opa aoo epoce ee cyecoa. ococa oe opa ooo oxoa ae ooo eoea opa, o ceooece, paceooece acooece ace opaox poecco oa ypae [1;

2;

3;

4;

5;

6;

7]. B aye, acoc cooo, opao oxo ae oooc coaa poye oe cceyex e poecco c e e, apep, x a ey xaoco opo, e, a eco, opa o oec.

poea coaoo xaoca opa coco occe aooepoce oee cyax coax poecco paax opx cpae aapx ayp, eoc aceceoc, peoooc ocepaa .. a poea ayaa cea, a copeeo a ocoeoc. peaaea e oe, ecop a co poc oy oeecoc, yy peeo coepeo o o, a a , aece, ooe a yc oa ao poe, o cocae e cceoa.

B.. yxa oyae ooe coye e, ocoo, oceooec paceooec ace, cocee c opa eo coaeo eeoc. Oao eo e coy paec o e epe, ao o c cooeceo eeyao coao ccea, o eppepoac a ooece ae ec e cce, o o oeo oc ooec ec aoa cyecoa pa. Ta, eoey coyy e ea pex aa epoa, ecx aoo coxpae, ooecx aoo paoe, op a cyecoae, ececeoo oopa .. Ceoa eo, coooyax ooex, apy c opa opa oa ypae, eo pypye eee ea, o ooo e eee aa opa, coc ea ooecoy ecoy ypo eeeoc coya oaaa oe oyoe e a eo e e cpyyp, a coae exa poecc. o eee oy, cecya ooe, aoeae oxpao eppop, ocpooco caoopaae, co ae peyo oe ypa eca cxoe c caocoxpae, a, pooe poa ea co o oo, acaec o o ca, e eee, ocyapca ypaea. ce coae exa oac o coaex ao ypae coa poecca aco cpac a acao ocex. Ho o oe opyc, o oxopae, aao y coae, pay, a e oe c? a o o, coaee, aee o coao cceo ye opayea pae coya (o a o coaoo cya) coy eo.

opauoa oe couao uauu ce coae exa pyc op ae a oye yco o eeapaeo eeoc [8;

9].

a eco, ee cex cce eaco o x eeca coepa o e e ca apoe, caoe, pa, poea, caa, yaa, papye cep.

pa oy oepoe ao cceo a ecoo (ec yoo, eaecoo) pocxoe. p o ce e auoecmu cce, a coae cce (cocoe a o-xeco ypoe opaec oo eeca), ocyecc epe ece o, coep ae coy (epeecy) opaoy coca e. ecoe oe e acoc o coeo xapaepa epe cea coep ey opa o coe c oe, eo coa cocaa ec e oce e, ocpeco oopoo aa opa epeaec poc pace o coa o oea aoec. Too ae oapyaeo coo ooe ooe a ocoa eppepoa ecoe oe a ocoy opy aep. C pa ocoae eo oo paoa a ocoy (coy, y) opy opa. B ecx aax eeeanpaeoo npuueu pcycye opa oo a e, a o ee eco o ppoe aax eeanpaeoo ynpaeu1. oee oo, y ac e ocoa aoec yepe o o, o coa coca a ecoo o e ypaec opae, ae ec pe e e o eeapaeo ec, a o pe ec. Tae e ocoa yepa, o a coa pay peecpyee coae a e oaae o ypaee pee oac, cooeceo, eeapaeoe eeeapaeoe ee coco cce oea ypae pe.

B.. yxa c eeaa epapx opaox ooe yp o aep o o aooo ypo [10].

Copeee a oo aac a poe a, ea paceeae eae eoe coa, opa, a, opaooo o peea coeo cceoa [11;

12;

13]. ece, ooece oac ococe poe e, e e eee, poe ooee cooo, o ypee ee aoec co ax cce oc a , a e xapaep, o ae ppo ex aoec, ypee ee opa coye oo cyeceo oe oa e ox coax e poecco, ocoe oopx e eyce o p opa. Te ca o (oceooec) oxo, poo oe apce a cpec coooecoo cceoa [14], oe acy po paax oee oe oe opaooo oxoa.

oeo, opao oxo p ce eo oopaoc e ceoy, o ooe cceoa opao cpe coao peaoc e peeye a oaoc.

Te e eee, paax opaooo oxoa ooo oc aoo aeaoe cceoae coax exao, o cpoee coepaex opax oee coax e poecco.

poecc ee (pa, epaa) oo coa oo paa o opeee ecaoape , apy c pe o (peypo ooeo, ee eyeo pae o pee), coep cyay ooey, oycoey e eex cyax aopo. Hae pea oaae, o ey ocaoo o pee ocea ecao apoo poecca cyecye aooppe, ocoe oopo exa namu. He a e oppe, e oppe e pea, e pea e ee. Ocaec oo cyaa opauoa oe couao uauu ooea caoap poecc (ooo pe)1. B a oe coeo pa2 ccea aoap a cocoa ya xpay opa o pox cocox, poo oe pee eyx poe coeo cyecoa. Ta opao, a o opao aop pa cc e pooo ppo. B coao ccee o cou aa nam.

Teeooec pae opo cce oaaec e cya co copo eo cpe oa. oc e oecye a ccey oopc / o cya, a oee (ae, aae) pea (ypae) cce. Haoe oeco cyo oeco pea (ypae) cooeceo paoopaue cpe paoopaue cucme3. oce ee cyecoa cce paoopae eo cpe oo oec poac (appoac) paoopae cce (ao eo xooo paoopa .P. [15]). coa, pocy paoopa cpe oe cooecoa poc paoopa cce, aoopo, c yeee paoopa cpe ccea oem yea coe paoopae4. Ta opao, coco oc cce yea coe paoopae (oeco pea , ypae) ec o aopo ee pa, e Beee pea poecca pooc, a pao, c opopyeo oo. ooy cyaa ooea oe coepa ocaoy aoop pe, oopa, poe, cyeceo ee, e pee.

ec aee ye paccapa poecc pa.

Paoopae opaooe oe;

opaoc cce (cpe) oooo ac o paoopa ee coco, epo oopoo ec o oc oeca coco. opaooe paoopae xapaepye co oc cce (cpe), o cce opa aco opee a epy cooc.

Moaoc oe, oem opaa o a, o ao aea ec opaae paoopae cce cy, o e cepxy.

B.. yxa e oo cpyypo-yoay, o opaoy p poy. opa pye ypaee, aca ccey epe ee coee opa epe ooo coco pyoe, aeaoe cyy cpe. B o cce paoopae cce xapaepye ae ooe pa ey ee o o coco cao oeco x coco, .e.

opooecoe coepae ypee opa cce ee opa o ccee.

epexo coco cocoe peeax aoeoo cceo paoopa ocyecc, oe cyae, c pa epooc. Ec coco oee peoee epooco cce, ec eee peoee aoe poe. ae x epooce ooe pe op aoe ep (opaoy po, oeco op a p.) epe opa, eeppyeo poec ce pa cce. p o eycoa po cce xapaepye ee opaoc (ype opa), a oeco opa e opa o ccee o cpee. eeppoae opa (uopauoee [16]) po cxo c pa c poco paoopa cce, poe ycoe ee eeoo cocaa ce ey e ea cce. coee eeoo cocaa pocxo peyae eaoecx poecco caoopaa cc e. Hapaae ce ec cece caoopaa caooye, xoe oopoo ccea yc cooa ycoee eao opaoo aoec co cpeo. B poecce oo aoec pocxo pac opooecx oo paoopa cpe opooece o paoopa cce. Caoopaa caooyee peopay aoee opooece o paoopa oee ee cacece o ae (ao), coyex cax oyax ooex, , aoe, aoee ee ceaece o cco (oeo), aeaex opauoa oe couao uauu a. p epaa cce pocxo poecc, opa opaoeey, uccunau (paccee) ypee opa, .e. peopaoae oee ex opaox oo eee ee, yeee paoopa. Ta opa o, opaoee pe opao aop pa cce.

ecx aecx oee [17;

18;

19;

20], co yx oocoae e opaoe aop a, paoopae, opaoee (oe oeoo oee aoao, oe oca, apoce oe p.), pac cop apocy oe coao a. e oe poa ee opaox aooepoce pax cpae oeceoo pa.

Paccop opy coay ccey, eaoec opaoo aoecyy co cpeo. Ccea pa aec, .e. o e cpe ee oeco coco c co (popecc) c yco (pepecc), oac e co eo cyecoa c oo oeca oex pea e epoocx epexoo ey coco. epexo cy oeecee ypccee ypae, aeee a ocoee eeoo oeca coco, oaee .

Ca cocmou (cape oe, popeee xoe pa ) peca coo cpe X1,Xj,Xn e pa x eopo cpyypo-yoax opaox coc cce. Coco oceoaeoc (pee) epe xoo py pya cae oppepoa ey coo.

oppe oe oxaa ec pe eo ac. Ec cocoe a eye ae pea peepeo cao oppe poao c coco a peecyx aax, caec, o B.. yxa ccea e ee a, a a oa e o ooo po oo coco, ae aeo o pee. Peae (e aoo) cce e a, .e. o, a y, peyee cocoe ecoo ax coco. o- oy, oo oo cocoe pee oe eac o peecyx caoe epoe (apopoe) o p yco , o oo e ac o coco peyeo pea, ec aoo . Anpuopa epomocm oe aoo coco, cooeceo, eycoa. aoe ocax coco pee oe cyae ac o peyx, cooeceo epooc eyeo coco ycoa ooceo cex po x coco.

Ha pc. 1 aece pepa oaa ooao pa e pexoo yx coco (n = 2 o eo epec pao opae cce) pee o q (k oep aa: k = 1, 2,q).

ec P11, P12, P21, P22 ycoe epooc ooaox e pexoo cooeceo 1-o coco 1-e, 1-o o 2-e, 2-o 1-e, 2-o o 2-e. Cooecya ooaoa apa epexoa ee :

X1 X P11 P12 X P(1) = (1) P P X 21 o yco oppo epooce x cya ao cpo e ap oa pac 1 ( =1). B poecce pa Pij j ea paoopa n yeaec, cooeceo ye aec opo ap (1), , a cece, ce ee epooc e ee o epeopeee p cpoo o e yco oppo epooce.

opauoa oe couao uauu m p e c o c m o u (0) (1) (2) (k) (q) . .

p a n e p e x o o ( ( ( ( ( X10) X11) X12) . X1k) . X1q) P11 P11 P11 P . .

P P P P 12 12 12 P21 P21 P21 P . .

P22 P22 P22 P X(0) X(1) X(2) . X(k) . X(q) 2 2 2 2 Puc. 1. pa nepexoo yx cocmou Poc paoopa cce, coco yee o eca ee coco, ec eoxo, o eocao ycoe pa. o oc e pa, ooeo eoopx oyax, opoox aex, ycooc eo ax apaepo, ccea yaec ooaoo e epexoo o pee coco cocoe o oce o e. py coa, ccea oa acpo (aa poa) coe oeee c e, o ee pea ca ae a cya cpe. Hacpoa aaaec epexoo oepeo apaop, .e. caoap, yco pe cce o o ceyeo ee n, a eo oopee ocax oepa, a o oa eoo a cce. poecc aaa yaao cce oe coepoa a apoc poecc.

Ha pc. 1 oaaa oopoa e Mapoa, oopo oo aoa apa P(1) e ac o oepa aa. p o a cxo k-o aa oaae e cxo oo (k 1)-o aa B.. yxa e oaa cxo (k 2)-o, (k 3)-o, 1-o ao (ooca e Mapoa)1.

Aepaec c oo paa pc. 1 eo oaa, o apa epexoa a a aa paa P(2) = [P(1)]2, e a n ee ap P(2) pae Pij (2) = Pim Pmj, e i, j = 1n. Aa m= n oo a p aa P(3) = [P(1)]3, e Pij (3) = Pim Pmj (2). e m= cy o y, oy ooeoe cece ypae ooopoa-eea2 ap epexoa a k ao i-o coco j-e:

P(k) = [P(1)]k. (2) a ee ap P(k) pae n Pij (k) = Pmj (k -1), e i, j = 1n. (3) Pim m= B (3) Pim ee ap epexoa i-o coco m-e cocoe a epo ae;

Pmj (k -1) ee ap epe xoa m-o coco j-e cocoe a oceyx (k 1) aax3. Coooe (2), (3) coye oepoa poecca aaa cce.

B aece pepa aa ce ooaox ap epe xoa n = 2 (a. 1) poee x coepae aa, cxo e cceoa.

ec aee paccapaec pocea oe e cpeo o pee oopoo ooco e Mapoa. cpe (a) apocoo poecca cy oce o pee. oee coe oe (c epep peee p.) c. [20].

Coaco oy ypae apa epexoa a k ao paa poee ap epexoa a s ao a apy epexoa a (k s) ao (p s < k):

P(k) = P(s)P(k s).

B (3) (k 1) e oume, a uec aa.

opauoa oe couao uauu Taua CXOHE OHOAOBE MATP EPEXOA M1 M2 M3 M4 M M5 () M7 (P) (/) (A) (O/) (A) (/p) 0,7 0,3 0,5 0,5 1 0 0,7 0,3 1 0 0,3 0,7 0 0,4 0,6 0,5 0,5 0 1 0,6 0,4 1 0 0,6 0,4 1 B ape M1 aoe cocoe c oe epooc epexo cao ce, a e pyoe, o ceecye o oeo caeco (ocepao) cpae pa cce. Oao ee coco, xo c e epooc, o o o, o coceo opooy ocepamuy (/), e yoy coax oa. ocoy epooc epexoa epoo coco o opoe opao o o y, oa aec, o ccea ee cooauec coco.

B ape M2 ce epexo paoepo, o coceo aapxuecoy (A) pa. B ao ccee ap xaoc.

Mapa M3, a M1, xapaepye oeocaecy ccey, oao y-epooc ee coco ce ecy o opmoocao ocepamue (O/) cce M3, eco apopapoao a oepae cxoo aa x nooaux coco (epooc P11 = P22 = 1 coc e ocoep epexoa coco cax ce).

Ccea, ocaea ape M4, opepoaa a o poae ooo yx oox coco, a eo, epoo.

Taoe aocypoae ooo oaoo coco c co xpaee eopyx eopo pa coceo a opaecoy pae ope amopumapua (A).

B ccee, cooecye ape M5, aocy ep oo coco oeea o paoc, a a oo ooaee Apeayp ap oce e.

B.. yxa (opoe cocoe ooe apeeo). o pa aopa ope umamyp ().

Mapa M6 xapaepa e, o epexo coco cocoe opy o cpae c aocoxpaee x coco, xo e apea oceee. o coceo o aoo oe coax peop cee ypca, epecpoe, apxamo peouu (/p).

Haoe, ccea, ocaea ape M7, opepoaa a eycoy, eopay oy ocepax pa, o xapaepo coaoo epeopoa, (apx)peouo o (P) cce c eco apopapoa opae pooo pa yyeo.

eo oaa, o p oepoa poecca o cooo e (2), (3) ooaoe ap epexoa oop oo aoe ap M2, M3, M4 oo k (k ), .e. coo ecye coae cce e coco aapoac ee cpe (pc. 2). Ccea, cooecya ape M7, ea, oao a eoc ecoea o pee, e coc ycooy coco a ao ae poecca popeae pooooy opoc ooceo pey eo aa. Ccea a pocaec peooo ope a opoocao-ocepay opao (a. 2, pc. 2).

Taua MHOOAOB POECC B CCTEME PEBO߻ k = 1 k = 2 k = 3 k = 4 k = 5 k = 6 k 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 opauoa oe couao uauu Opooca Aapx ocepa P11=P22= P12=P21= a (k) a (k) Peo aypa a (k) a (k) Puc. 2. Mooao npoecc eaanmux cucmeax B o e pe ooaoe ap cce, cxoo oc aex ooao apa M1, M4, M6, ec a ao ae poecca, cpec ua apa epe P = xoa lim P(k) const coaco eopee Mapoa (ooa k oa apa epexoa cooaxc coco cpec ycooy peey) (a. 3, p ypc, ooc o 4-o aa;

pc. 3).

epooc epooc epooc epooc B.. yxa Taua HAMA MAPOBCOO POECCA B AATBHX CCTEMAX opo apxa a k A op ap o cepa peo 0,7 0,3 0,7 0, 0,3 0, 0,4 0,6 0,6 0, 0,6 0, 0,61 0,39 0,67 0, 0,51 0, 0,52 0,48 0,66 0, 0,42 0, 0,583 0,417 0,667 0, 0,447 0, 0,556 0,444 0,666 0, 0,474 0, 0,575 0,425 0,667 0, 0,466 0, 0,567 0,433 0,667 0, 0,458 0, 0,572 0,428 0,667 0, 0,46 0, 0,57 0,43 0,667 0, 0,463 0, 0,572 0,428 M= 0,462 0, 0,571 0, 0,461 0, 0,572 0, 0,461 0, 0,571 0, 0,462 0, 0,571 0,429 M= 0,462 0, 0,571 0, 0,462 0, 0,571 0, 0,462 0, 0,571 0, 0,462 0, eycoa epooc j-o coco a k- ae poecca opeeec, cxo eopa apopx epooce coco P(0) = {P1(0), P2(0), Pn(0)} ycoo epooc (3):

opauoa oe couao uauu n Pj (k) = (0)Pij (k), e j =1...n. (4) Pi i= Cooeceo apopa po cce paa:

n H (0) = - (0) log Pi (0), (5) Pi i= a oa po cce a k- ae apocoo poecca paa {- log[Pi (0)Pij (k)]} aeaecoy oa e [21]:

n n H (k) = - (0) (k) log[Pi (0)Pij (k)]. (6) Pi Pij i=1 j = opo ocepa Aopap a (k) a (k) apxaa peo Puc. 3. Mooao apocu npoecc aanmux cucmeax a (k) p ocoa oapa, pao 2, po epec ax.

epooc epooc epooc B.. yxa Ec ccea cocoa aaa, o coaco eopee Mapoa poee pacea (a. 3, pc. 3) ycoe e pooc epexoa (3) cxoc a ae k = M eyco a epooc Pj:

Pij(M) Pj(M) = Pj, e i, j = 1n. (7) Cooeceo po (6) aae oe ac o k, a aa c k = M capyec caoc pao coey aoy ae:

n H (M) = - Pj log Pj. (8) j= B eaax cceax apoc poecc, cpoo oop, e ee eca, a a ycoe epooc epexoa, oa po e oaa ao, coceo a po ecca. oa po p o k > 0 o coxpaec pa o apopo po (opooca ocepa, peo ), o, ec a epo ae, aee e eec o pee (aapx, aypa).

Peya paceo po o opya (5), (8) cee a. 4.

Cpaa apopy ay po, oo oe xapaep opaoeea. Ec paoc I = H(0) H(M) oo ea, a, poecce aaa cce ceeppoaa opa a epa opaoaoc (yopoeoc) cc e. p I < 0 opa ccpoaa (poa ee ), o paoao eopaa (payopoeoc) cc e. p I = 0 opaoee ocycye (opaa cc e e oepea ee). Peya aaa peca e a. 5.

opauoa oe couao uauu Taua HAMA HTPO CCTEM B POECCE AATA (B TAX) n = 2 a a o a po H(M) P1(0);

H(0) P2(0) / A O/ A /p P 0,5;

0,5 1 0,985 1 1 0,918 0 0,996 0,7;

0,3 0,881 0,985 1 0,881 0,918 0 0,996 0, 0,4;

0,6 0,971 0,985 1 0,971 0,918 0 0,996 0, 1;

0 0 0,985 1 0 0,918 0 0,996 Taua XAPATEPCT HOPMAOEHEA P1(0);

/ A O/ A /p P P2(0) 0,5;

0,5 0 0 0,7;

0,3 0 0,4;

0,6 0 1;

0 0 0 peae: Ȼ eepa opa, ݻ cca opa, 0 opaoee ocycye.

poaapye ee. C poco paoopa (n > 2) ec a opo apax ap M1 M7 a. 1, a x ee (c coee yco oppo epooce).

eea ea oo opa. p n = 2 acaa po H = 1 , o cooecye opaoo pocee ccee (n = 1 H = 0).

B a. 4 aa cpaea ee opaoeea cce o pee, a e opee ae po ex ax, a po ca o epx poex.

B.. yxa Oao, a oaa pace, p eeoc cpae cce, oopaaex apa, ee opao eea, peee a. 5, ocac oe ee.

Ta, aapx e acoc o apopoo coco cc e opepye ee a acay po xaoca, a aypa a acay opa ecoo opa. Ca o cee po oeco opa a aeaece acpa e ecy ooao apy ococ eoc ao. po xapaepye ype opaoc cce a oea ee pa (opo poaec xaoca).

B o cce yepea po a epa cca op a ece a cee ea oeoc aaoo yepeo cca eaoo paaec opae. B co oepe, oeco opa xapaepye e o yay y cce, apaey a opaa ypaeo cce, ee pecayeoc. B ao o ece peea pooc aapxeco cce a e pea, a peea opaoaoc (aopaoa oc) oaapa, o aapx e cpec opa opa, a aypa e cocoa oeo ccpoa op a oy po. B peyae aapxeca, oa apa cce e oo e oo peooe pee x pa coeo pooo (aapx) opaooo ( aypa) cyecoa, o ocyc oy poo oooo, poyoo eopa pa. cce e coco opaoo paac.

p ce aooc coax o opooca oo ocepaa peo ( ee opoocao ope ec p o ocoa, a ae셻) opaoo o co, o opaoee oaoo e coce. Ec o cepaa coxpaoc apopo po (a poee epaa peeceoc) oca ae yo, e oee eoao oy ao e peya peo opauoa oe couao uauu (c ee epao eoc) a coeopay opao y eppea eeecoo ooo opa. Bpoe, a. 3 e ae ocoa ycoc paoc aoo peyaa. B ae xoceco oe eococ pa, oocepo apa opaoa cep coax opooc pooooo opoc e oa a ye, o ooa cep cocea ce ppoe, ac oopo ec coy. ppoa e ep cao, e e pocxo poecc c ecoe paeo ec x e. ppoe eoea coya peooe ca x pooececeoc ae poooaa, opa ooe ecoe peo, ee oeeapa cep c opooca ocepao oy oaaeco. a e cce oe e coco opaooy pa.

Aae cce oy eeppoa a opa (ec apop coy e xaopoa), a po (p e cxoo yopoeoc oeca). p o cce a opo ocepa xapaepe a (e poco) poecc aaa, eo e caa o apxao peo (pc. 3). coa, ae cce coco coa pay opao aac coya, oepa e, c oo copo, oopoc yopoe oo, pecayeoo opaooo cyecoa , c py o copo, opec (po) oea pa.

o acaec aopapo cce, epo ee aaa oo opoe, e y pyx aax cce ae ce a opoae ox coco o cpae c py. Ec ae ap cex aax cce a. 3 cpa c cxoo ooaoo ape aopapa M4, oapyc cxoco, cocoee oeo opoa ooo coco eaco o a cce. o po yoae , o oe epexooo epoa (epecpo) y aay ccey e aopapa coaa opea, B.. yxa c oopo ccea cyae caoap epo coeo cy ecoa (o ceye epecpo, cao c poco pa oopa coco).

B oeo oece e ee paa ea aeo ye coae o cyyo opao oe, o cpoeo a ycox oeax pocex ap epexoa.

Oao poee aa ooe a, o pae epe, c oae oecc aye o oceeoc epop (M.E. Cao-ep. cop ooo opoa).

B caoapo coco cce opaoee ocyc ye. Oaae o, o pae cce aepo? He, o eo, o ee ypee eaoece poecc, e oxoe oepa eeeoc cce, po oac. p o o epe ee ex yco eeeoc ooc cey cao paoopa cce c oopee ocaoo e ooaooo ao pa. B eo e paaec cce pe cae coo epepo-ocyae poecc, aop ec ocae cceo oex o, co oo px xo eaa aaao [10, c. 148149;

11, c. 149150]. p o oa pooeoc aaa epoopoao cpo yeaec c poco paoopa coco cce.

Ho o oo acpao-aeaeca epxya ac epa. opeoe coepae aopa pa coao cce cao co caceco ppoo ee epooco oe, .e. c accooc ypccex aoec.

Moe oe aoea paaec cco, ec eco epooce coco cooa x cacece aao e oocex aco a peyao cooo ecx opoco. Too p coe epoocoo aoa ox ce, .e. p ocaoo oo oee cac oo oeppoa epooc epexoo (ypae, pea).

opauoa oe couao uauu Teep peca cee peay popecco paayc coay ccey c epee opo paoopae coco, pea cpoece aaaooo exaa (a ecoo opo e, e y copeex oe po), pooe caoapoc, e pey pa , eee ac eeo cce pepeccy, oe, oey pae coax cce peye oo pe e, co oo o cpae c epea cpoa, o ope oo aea coae apxeop.

Caec, o ccea c ocoo (o aa ay) oo aoo ape epexoa ee ocoy a. ocoy c a eee paoopa cce a apa e ec, a paaec cce oe cyae epe ea. po ae ca, o ocoy eyee coco e cpeoo oocoo apocoo poecca ac o cxoa oo ooo (oceeo) aa e ac o cxoo ocax ao, ccea o oo oo oceee o pee cocoe ee a ( aax), cooeceo, paa ee. Taa ayaa eppea a oaaa cpaeoc ypae ooopoa-eea [c. cocy a cp. 106] oo yx cocex ao eo epaooco cooc ocax ao, yaex a o epa, o oe e eco poex cyax, o e p cooaxc cocox accecoo apocoo poecca.

ayaa acoc A o B paoaa ecoy B a A. Ho a copee opaooe, ee ecoe oe, ca a pee ceo oa apoac a opaoo oxoe.

B.. yxa oppe ey eco, a e oo coce a a poecca pyec eopeo Mapoa, oopo ce ye, o aa c eoopoo aa k M, epec epo oca acoc poecca e oo o ce eo pec op, o ae o oceeo peecyeo aa. B o cce a cce p n = const paa M, .e. oepy aa, aa c oopoo oc yco eacoc (7), o cooecye pae ey epexo caoap epo a apocoo poecca. peca pep oe a (7) e oeco a, cpaeo epoo k ( pa k = 1, 2, 3 ), p oopo oec ycoe cxooc eycox ycox epooce c oyco oo cex coco (i, j = 1n):

{i,j[|Pij(k) Pj(k)| ]} > M = min(k), e k=1, 2, 3. (9) B a. 6 pee oe a cceyex cce o opye (9).

Taua AMT CCTEM ( = 0,0001;

n = 2) C c ea / A O/ A /p P a (M) 8 1 4 1 Oe M a y o n (n = 3, 4, 5) oaa, o y cce co cpae opooo ocepaa, aopa pa apxao peo a c poco paoopa coco eec peeo epeeo ac oc o xapaepa pacpeee ycox epooce o oaox apax epexoa. ocax cce aa a ocycye a eycea n.

Ec p cpae opooo ocepaa ycaec oeocaeca ee, a cce eeo cpo opauoa oe couao uauu pace peee (p epepoe opooo ocepaa opooca) cpec ecoeoc. Haoopo, p oc ae oeocaa, oa epooc coxpae coco ecyeceo pea epooc epexoa ey , a cce caee, cpec aoy peey M = 1, coceoy aapxeco ccee.

Aaoe ee xapaep ccee a ap xaa peo, ec oa, opoc peepea oo po oceeoc epop, popeae co oc ooo epa apxpeoooc (M ) , acy epe pyoc peop, ycae x a aapxec caoe (M 1).

Ec aopap c poco paoopa coco cpe c co pee opa aype aapx, ey cocea epeea aa coao a (M 1).

B ye cyae, oa oopee opyx coco e eae x ooa, a aopapo cce oe paec cao, o oa peeo.

Ta opao, coaa a paaxc cce pecae coo oey aecy cpyypy xpae opa, coa opao poecc epeoca opa o pee. Bece c e, coax cceax c opooca cpae pa eoc coao a oepea eeapaeoy aypoa, poey aooec opa ecoeo (oaeco) a ecaca.

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B.. yxa 4. Lash S. Critique of Information. London;

Thousand Oaks (Ca): Sage Publications, 2002.

5. yxa B.. oco opaooo oxoa. Tep: TT, 2000.

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TT, 1998.

7. yxa B.. opaoe ace caopa, aoa aooa yyp // oco oeco. 2003. 2(31). C. 150168.

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9. Buep H. epea oeco. M.: , 1958.

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11. mua P. ey pa a. M.: ae, 1986.

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13. epacu .C. Cepea opa (aeca eop opa). M.: PCC, 2004.

14. omucu .M. Moe coax poecco. M.: ooc, 2001.

15. u .P. Beee epey. M.: , 1959.

16. oepu A.H., aep .. opaoee opoc eo oa.

Hoocpc: Haya, 1977.

17. Rapoport A. Mathematical Models in the Social and Behavioral Science.

N.Y.: Wiley, 1983.

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20. eeu ., Ce . oee e Mapoa. M.: Haya, 1970.

21. umpue B.. paa eop opa. M.: Bca oa, 1989.




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