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E.B. epeao (Moca) CTOXACTECOE OCAHE BOPOHOO METOA B cae paccopea c ey cya o oopa p cooa opooo eoa cooo. Hae cpoe co

ooe pacpeee, oop oec cya oop.

oaao, o pacpeeee ooo oopa ec oyco a pocae cyaoo, ocoy aeaece oa x pac peee coaa. peoe eo cacecoo oea aco cpeaeoc pao (coc) o cya opa.

ee coa: cpyyppoaa eepaa cooyoc, pepe ea oop, coxacecoe ocae, cacece oe, epeoepecoe pacpeeee, xooece epeee, cya a opa, oa opa.

O pyex caco XX . .. T ca:

epooc ( poex. Am.) ceye oocc ce peo oca ee ooe, ec pe o pee o o e oaac eoxo oe [1]. B cooo e ooo ae a pe oca oe cyaoc ooe.

o oycoeo e, o coae eoe e acoo co xapaep, o poc oo aex o ceoc py acee. Ceoaeo, couae cucme uem epomocmy npupoy, a x cepeaoe yee ooo oo eoa, ocoa a aco ecx cocax coxacecx cce.

Ee Bace epeao aa execx ay, a. aepo coao-ooecoo oecoo eeea Aae eeea oa. E-mail: e.cherep@gmail.com.

Cooo: 4M. 2007. 25.

E.B. epenao Bao oepy, o cyaocm epomocm a oe, oaee a yo ypoe o (a oe co, oa, yeo o ..). Tae o e opee, x oo oo oca. Hapep, epooc o ec aepeo oe ocaa cacec o P. M ecy [2] a ocoe eopeo-oeceo acoa A.H. ooopoa [3]. oaaeo, o epaype ( ae yeoo xapaepa) oo cpe paee onpeeeue epomocmu o ooopoy. o eoppeo, o pe e o onucauu epomocmu A.H. ooopo, o epe o ceao paoe [4] c oo oe epooco o pocpaca (acpaoo oeca c opeee a e ca-aepo epo, oppoao a ey). p e opoc o paax peoc coxacecoo opa a a peea ececeoayx poe cee epoc [5;

6].

C oea ooe pao cooo 30-x .

pooo ea ee eoooecy ocoy cocae o po eo [7]. Mc o eo cooa apyec a aoe ox ce ( ope . epy) [8], coaco oo poy opoa acoa cpeaeoc yaeoo paa cep eacx oo acoec (o oey op ) cxoc co acoe. Ho oae paa cooc: poe yco cyaoc ae x ea coc, eopea . epy peye x apopo oopooc [9]. Ho o coy cmpymypupoaoe, pe o o epee, oeco. p ooceo eox o eax op (cae, 2-3 c. cyao onpoex peco eo) pa cpyypax eepao cooyoc cyao op oy peo cop ooc oe ac o cpeaeoc ucceyeoo npuaa.

Cyecye a cocoa xoa o cya: 1) p paceax aeaec cpoo yec pa cpyypax Cmoxacmuecoe onucaue opooo emoa cyaoo opooo aca eepao cooyoc 2) ocpo omy opy, oopa o oco xapaepc a (o, opac, opaoae, aoaoc ..) a penpeemamua eepao cooyoc. ocoy 30-x .

XX . ceo ex e cyecoao, o y oepo pao cooo, oe-o, opa e o: pa c a ycoe epooc e a e, ye coaa oe op. oyo ae, o coae oo op oo eppop ae epocoe, pyoeoe opoo coee, a oaao, apep, M.C. ocoao [10].

Cea coax cceoa coco o, o p xoc paoa peyeceo c eco a, .e.

c epee, pae cax aax [5;

11], pe eo oop cao oe epee [12;

13] o ccy oaec o epe cx aax [14]. Oco a cax a c opoe oae a ( a aeoa) [11]. Ocooe eco coooec x cceoax aae pee cya a a eoa ye ( xooece) a [11], opoa ee ap ooe a oecax [16].

Cacec aa ecox ax ec ac ao coo aaeco aa, a opaoa paox epeex. B pax ax aaa oa peaec ceec opao, apep, a, a o peoeo ooeco aae [15]. Bece c e, cyecye a aox oxoa e acoc o o aaa.

Bo-epx, opoa cax epeex [17;

18]. Ho oeo oocoa ycee a epe pyo, a opo cyeceo peopeee ooe peya.

pe oe ycee a epe ec p o cae a ppoy ax-o ooex coc c ceyeo coao cce. ae paoa aea o poo a [19] paoo, ooa poo cepe E.B. epenao aa pecx ax [20;

21], e oe paccap ac a yepca eo. ocoy oeoe oeco oeo coao ppo c aa a e ooee cpooo opa xo aeo [16] eoopoy oo ecy aypaoo pa, o coe cy ocaec eco oeco.

Bo-opx, oxo, ocoa a xooa, .e. a ocaeuu cex nepeex o yeoo ypo c coomemcm yu yeueue paepocmu npocmpacma npuao.

e oxoa, oop apyec a aae cac ap oo ooe a oecax [22], coco o, o co oe oo c pepo pao opaoc oca eo co cx epeex, o co cax. a c a a O. ypo, oope o oo pa ea aa o acceco paae [23]. o O. yp o, oe cooe coco oea oe pecaeo a cyepo eo oee pocx coc. aoe x x oee pocx coc ec oae ee oee poc x .. ae oop, eec oooc eoo ecox coc oea o eoopoo eeapoo ypo . B oe oyae aop xooecx ( yex, apx) epeex, ocax, c yoeope ac ooc, yaey coxacecy ccey. p coca e oo opoca cey ye, yaa O. ypo, peay npuun uxomouauu opaoo oca cce yeoo coya. yee aceo epecyx poe o oc o oo eeapoo ypo oca, oop c aec ocao paecx oo. a ap a oea a opoc ae pecae coo yey epee y (a ao ae acpoa xooec pa, e acpoao eo ocyc). B oe opoc opeee apoe ooee a oecax pecoe pa (apa oeo).

Cmoxacmuecoe onucaue opooo emoa B o c c oe a coooo, a aeao, cax c oepo opaoo ax, opao cpoo paccope epoocy copoy opo oo eoa a oco pecx coooecx cceo a. aoe, peye oea opoc o o, acoo npao epo ucnooaue epomocmoo opaua a o x opax. O xo opaa ooepy cpyypy e epao cooyoc, o o caoy coey ocpoe c e noe cyau opa. ocy oea a o opoc ocea ca. poe oo, paoe a o xo opooy oea aco oe ecox pao p paoe co cya opa, oop oo e aumeo oc ooc peyao o cpae c pao eoa ooo oea. Oe, o o o xapaepcax pacpeee cyaoo oopa e poc e oaaec, x oo a oopa [24].

Cacece poeyp, a oopx apyec opo eo coooecx cceoax, ocoa a P [25], o epe oeecex ax, acoo o e co aopy, o oeeo epeoe . opea [7].

yc aaa eepaa cooyoc, pecaa coo aceee (paee, oyaee ..), cocoa N eoe (N >> 1). Cpe acee cyecye M eoe, o aax epecy ac pao (coco ao ap, copac y aoay, c ea ecooo oa, oyc cpaxoo ycyo). pooc cyaa opa pecoeo oea n. Bepooc oo co, o opy oay poo m , oaax yae xo oec pao (0 m n), aec opyo:

E.B. epenao - N M N - M Pr{m | n} hy(m | M, N;

n) = (1), n m n - m N N!

e co, Pr{} ooaae epooc co n (N - n)! n!

{}, a hy() caapoe ooaee P [26]. Maea ecoe oae P pao = n;

= M / N, 0 1, (2) N - n a eo cepc opeeec a Dm = n (1- ). (3) N - y pacpeee P opeeea e:

- m N M N - M Hy(m | M, N;

n) = (4) k n - k.

n k= Oe, o P oo aa aaa aeca ac coo poy [26]. Ho ceo ooepe ooe P oy pec oppeoo oca ox aa cooo apee opeecx po, aoc o ee, p oooe peax paex aa, oocoa poeo oepeo ece ayapx paceo cpaxoo ee.

pee a pocex pepa.

puep 1. yc cpe acee opoa c ceoc N cpaxoo oae o acpaxoao n ee. Coxacec ycoa epooc acye cpaxooo cya a aa epo pee paa = M / N, (0 << 1). aoa epo oc, o a o pe cpaxoo oa pec a e o poo m cpaxoa? Oe aec P epooce, aaae coooee (1).

puep 2. yc pa oeao oepe pae N. B o poe pacpocpaeo n oepex eo. Bepooc pa paa = M / N, (0 << 1). aoa epooc oo, o Cmoxacmuecoe onucaue opooo emoa opoe yeo poo m px eo? ec, oe o, oe aec P epooce, opeee cooo ee (1).

coy oe aa-y (-y) oo o y yooe ( popao peaa) paee ce ae P. ooex ecex x -y opeeea epao epa II poa [27;

28]:

+ x-1 x- (x) = e-tt dt = ( (5) -lnt) dt;

x.

0 Ha oece oecx ce z C -y peca a oyp epao ae [27;

28] e -z (z) = 2 -1 ett dt;

- argt ;

z C. (6) Bpaee (6) ae poe aaecoe pooee y (5) oecy oac. Ocoeoc y (z) a aac oax z = 1, 2, , e (z) ee poce oc.

ac ao, o cex aypax ce k o ec: (k +1) = k!, pe (0) = 1 = (1). o ooe pe ca P e:

- hy(m | N, M ;

n) = [(N - M + m - n +1)] (n +1) (M +1) (N - n +1) (N - M +1). (7) (m +1) (N +1) (n - m +1) (M - m +1) coy coco -y a (c. [27]) (z k) = k = (z) - l)-1, (7) ecoo oy: hy(m | N, M;

n) = (z l = m (M m - l +1)(n - l +1) 1+ M = 1- n - m. (8) N - n +1 l=1 N - l +1 l=1 l(N - n +1+ l) E.B. epenao o paee eceo oo oaec o pa ox pecae P ( cce eo cooa ax paceo), oope ocoa a pex c ex ecoex cy poee.

coy paee (3), oo oy poce oe apapoao ooc px oeo = m / n aco cpeae oc pao. Heapaepecoe pao pex c [9;

29], oe cepxy opeoc aco cpeaeoc e 3 D 3 (1- ) / n. (9) 2 n oo coooe eo oy apapoay o peoc oe aco cpeaeoc paa acoc o n. epeco opaoe: ao o oe op aax ypoe apapoao opeoc. pe opay epaeco (9), oyae: n. Cooecye ae pee a. 1.

Taua HEOXOME OEM BOP AAHHX POBHE APAHTPOBAHHO OPEHOCT 0,01 0,02 0,03 0,04 0,05 0, n 22 500 5 600 2 500 1 400 600 ae, o paox cooo oeo op opa 1,5-2 c. ae apapoaa ope oc aco paa pepo 3,5%.

Bao ae oe, o ec ac epecy cac ece o o eoopo eooceo aeop acee , o ceoc o aeop pepeeao ope oa coca (p ao payo opoe ooc 5%) e eee 600 (!) eoe. ae oecee opeoc Cmoxacmuecoe onucaue opooo emoa 10% a opeyec 225 yaao eooceo aeop. paec o epeayeo, ceoaeo, aa a cpyyp oeceoo e ceye opaoa oee cceoa ao ao aeop acee.

yc yaec ooee acee peoa, co e e oopoo pao N, eoopoy opocy, o o oopoy ce r oa pe, pe ao x oe pe r pepac M1, M2, , Mr j M N ee. Te M j ca, opeeec oaa aa, opoaa pae e ee a r + 1 eepeceaeec ooeco. oce ee x, ooc N M, coco , e ex o pe o yaeo poee.

oyc, o cpe acee poee cya opoc n ee, peyae eo ope acpoao m1, m2, , r mr m n , pepaxc ao ee mj j x oe pe. aoa epooc oo, o yy ac poa eo ae m1, m2, , mr? Oe a opoc ae c pacpeeee, oopoe aee ye aa MP.

Eo aaecoe paee eo oyaec cey x coopae. B, o yepoo cya hy2(m1, m m1 | M1, M M1, N;

n) = hy(m1 | M1, N;

n).

Oya, coy peypcoe paee a:

Pr(m1, m2, , mk | n) = Pr(mk | m1, , mk 1) Pr(m1, , mk 1 | n), ecoo oy paee r-epoo unepeoempu ecu pacnpeeeue (MP) epomocme ua:

E.B. epenao r -1 N - M j r H H M N H H j j hyr(m | M, N;

n) = r mj m, M. (10) r ;

n j n mj j Be apope aco: M / N;

j =1,r, (11) j j paee (10) oo peca e r -1 N(1- ) r M j N H H H H j j hyr(m |, N;

n) = r mj m,. (12) ;

nr j n mj j ae aeaecx oa ooe cyaoo eopa e :

H = (mj | N, ;

n) = n M / N = n ;

j = 1,r. (13) j j j ae x cepc opeee a n M (N - M )(N - n) H j j 2 = D(mj | N, ;

n) = = j N N - N - n = n (1- ) j = 1,r (14).

j j N - oapa ooe coxacecoo eopa, oe oo MP, ayc e N - n C Cov(mj,mk |,k, N;

n) = -nk ;

j k. (15) jk j j N - coooecx cceoa aee MP coco ceye. yc cpyeap opoca coepc o poc, opee eoopy oay ay. Hapep, a oo u auamo B aepe oocoam a npecmo ux opax peuema P?. Bapa oeo e :

1) a.A. aoa;

2) a .M. Xaaay;

r) a B.B. p Cmoxacmuecoe onucaue opooo emoa ocoo. a aoo aao (oyc, o a o ec o) aepe oocoa Nk, (k = 1,r) eoe, e N co paee. yc p cyao oope n pecoeo c a paee e cooeceo yepa pacpee r c a m1, m2, , mr, a n - 0 pecoeo e opee mk k c ope. Bepooc oo co cec pa ee (12).

yc a oece acee opeeeo paee a r eepeceaxc ooec, ooc oopx ooa r e N1, N2, , Nr;

j = N aaoe eoopo ao N, j aeoa. B aece ao oao a oy c ya pa, cpyee ococao: o, opac, pao poa, ypoe opaoa, yco poa .. Bao, o eepao cooyoc apop ec ceoc cooecyx py acee N1, N2, , Nr (, o aeo, ec aco 1, 2,..., r ):

r H = N / N, j = 1,r;

{1, 2,..., r};

1. (16) j j j j peoo, o yaec acoa cpeaeoc eomo poo npuaa (aepee oepa Ey Pocc a pe cox opax;

eae y op-oyc;

aepee oc ooac ycya cpaxoo oa MAC ..). yc a eco, o cpe eex aeop acee p r M N ao oaa poo M1, M2, , Mr;

M j paa.

j E.B. epenao Opee eop aco 1, 2,..., r e:

H = M / N = /, j = 1,r;

{1, 2,..., r}. (17) j j j j j r aco cooecy o , oaax a pao, yp ao eex aeop. yc po ee cya opoc. aoa epooc oo cocmaoo co, o cyay opy oea n (n << N) oae poo n1, n2, , nr pecaee eex py acee, pe poo m1, m2, , mr paa ao py yy oa a yae pao? Hecoo o, o paoepo coooee r H H H H H H Pr{m, n | M, N, n} = Pr{n | N} | n }. (18) Pr{m j j j= Oca ceye paee coo epooc, oo poe ye aa ooep cmpymypupoa unep eoempuecu pacnpeeeue (MCP):

- r H M N N - M H H H j j j Dyr(n, m |,, N;

n) = mj nj - mj (19).

n j Bpaee MCP oo ae peca e - r H N N( N - ) H H H j j j Dyr(n, m |,, N;

n) = mj nj - mj (20).

n j cooe aeaecoe oae ao ooe H eopa m = (m1, mk, , mr) opeec e:

n1 n2 nr H H H H H H mk (n) M (mk | n) =... mk Dyr(n, m |,, N;

n) = m1 =0 m2 =0 mr = - r N N nkk j = (21) nj.

k n j H coe cepc ao ooe eopa m ope ec a:

Cmoxacmuecoe onucaue opooo emoa n1 n2 nr H H H H H Dmk (n) =... mk Dyr(m, n |, ;

n) - mk 2 = m1 =0 m2 =0 mr = - r N N N - n j = nk (1- k ) (22) nj, N -1 n j a ee ycoo oapaoo ap ayc e:

H H Skj(n) Cov(mk, mj | n) = n1 n2 nr H H H H =... mk mj Dyr(m, n |, ;

n) - mk mj = m1 =0 m2 =0 mr = - r N N N - n j = -nk j n k, j = 1,r, k j. (23) ;

N -1 n j j Boae opoc: oya a ec ae M1, M2, , Mr ( aco 1, 2,..., r)? O a eec. peao aaa coooecoo cceoa ee epc xapa ep: a apop N eop 1, 2,..., r, opoca oyae ae eopo n1, n2, , nr m1, m2, , mr. o oea e eop M1, M2, , Mr ( ae aco 1, 2,..., r), a ae ce opeoc x oeo.

yc oa opa ocpoea o s epee, e oa ypoe epe, pe j- x ee rj paa. B o cyae eepaa cooyoc paaec s a r = eepeceaxc ooec ceoc rj j= N (k = 1,r). Cooeceo opo aca paaec j a r coxacec eacx oopo ceoc nj.

Bee ooaee n = nj j2... js ( j = 1,r;

j1 1,r1,..., js 1,rs ). To j a acoy cpeaeoc j- oo py ee E.B. epenao pao cooyoc ceye c a ey a s =.

j jk jk = Hapep, yc oa opa cpoc o pe epee : o (yco, ec), ypoe opaoa (eooe cpeee, cpeee, cee), opac (ooe, a cpeeo o paca (35-55 e), oe (cape 55 e)). Toa acoc o aax ae x epeex ea r = 2 3 3 = 18.

Coxpa cc cex ooae peyeo ya.

Toa, p oo oope, cya op oea n paa ec (cooeceo cy o) a r coxacec eac x oopo opo oea n ( j = 1,rH). Oya ceye, j o epooc oy eop ae m , cooec yx ee oa, oopx acpoa yae pa, paa:

r H H (m | n) = | N, N ;

n );

m. (24) hy(m j j j j r j= Haoe (24) pacnpeeeue omoo omopa. co, o mo pacnpeeeue e conaaem Hc epomocmu oapy eu ucupoaoo emopa m npu cyao omope n ae eepao cpyyppoao cooyoc:

r- n j n n-n n j= H H H H H Pr(m | n) =... Dyr(m, n |, ;

N, n) = n1 =m1 n2 =m2 nr =mr H H H H = hyr(m |,, N;

n) (m | n). (25) r Ececeo, epooc cooyoo oapye = m mj j= ae, oaax yae pao, oopa p oo oope paa Cmoxacmuecoe onucaue opooo emoa r- m j m m-m m j= H Pb(m | n) =... (m | n) = m1 =0 m2 =0 mr = m-m m = | N1, N1;

n1) | N2, N2;

n2 )...

hy(m1 hy(m m1 =0 m2 = r- m m j j=1 r -... | Nr-1, Nr-1;

nr -1) Hy(m - | Nr, Nr ;

nr ), (26) hy(mr -1 mj mr-1 =0 j= e coaae c aaoo epooc p noocm cy ao oope:

r- m m j m-m m j= H H H Pr(m | n) =... hyr(m |,, N;

n) = m1 =0 m2 =0 mr = r = hy(m | N, N;

n) Pb(m|n);

. (27) j j= Ceyem u u coomoeu (27) mom am, mo om onpoc eoppeme oeu acmom cmpeaeocmu a aoo npuaa ucceyeo eepao cooynocmu aceeu? Hem, e ceyem. Maeaecoe oae coxac eco epeeo m, oeo pacpeee ooo oopa (26), pao:

r r r nk Nk r m = M = n = n, (28) = = mk mk k Nk k = k =1 k =1 k = a ee cepc paa r r 1 k (1- k ), (29) Dm = D - mk k n N k =1 k = r e = M N =, j = 1,r;

= 1. (30) j j j j j j j j E.B. epenao Oya ceye, o oa opoa acoa oe yaeoo paa ec cocoeo oeo aco cpeaeoc yaeoo xooecoo paa:

m N -0 =.

nN n N oee oo, ecoo oaa, o a oea ec e ceeo acoec (o n) opao oeo c o aco cpeaeoc aoo paa.

Bee ey = mj / n;

j =1,r. Ee cepc, a ce j ye (24), paa j j 1-.

D (31) j n j C yeo eacoc ae m ( j = 1,r), cepc j oo oe aco r = (32) j j oo peo peca e:

r j D (1- ). (33) j n j j ae, o acy cec (33) ocaec p yco x = / 2;

( j = 1,r), o pay pex c ae:

j j r 3 =. (34) j 2 n 2 n j Cpa (34) c (9), ceae o o o, o apapoa a opeoc ooo oea aco cpeaeoc yaeoo paa peo aa e, a p po cyao opoce u ecmpymypupoao eepao coo yoc.

Oao ec yc. Bappy paee D, eo oo ye, o a ea eca ycmumea ae Cmoxacmuecoe onucaue opooo emoa eou opeoc p ocpoe o n. o a j1 j2... js poee xopoo eco copeeo cace poe ao op, oopa ocya po coa pa apae copeeo pao cac [6] eapa epecx poacx poeyp oea eoo aa a ax paax oe .. T.

Moo oy coo oe cacece oe ac o eocpeceo o cya opa. He oe aoee poco y ocpoe ax poeyp cacec oo oea, ooe oocoae oopoo ao cae [30].

B paoe [24] pee oee o eo pee o aa, coxpa cxoy e oxoa. a e ucuceu ycox epomocme cmamucmu uapoo omoe u a oecmax [22]. pe, o cy, oa e ee eo oeo c epeeae ae, a o payec p peoe ox opo.

yc yaec eepaa cooyoc acee, o oc oopo paa N, cpyeap cceoa e a a opoco, oope ycoo ooa a: coep aee, oee co apao oeo a oope pao p;

ocaee (ooa x co epe s), opeee a pope acca acee, o ae o epee ec ococae. yoca oe ye c xo ceyx ooae eco:

k oep apaa oea a coepae opoc, o ope ee oep cooecye xooeco epeeo, oep paa, cacecy oey oopoo xo oy;

i oep ocaeoo opoca, opeee i- apopy acca acee;

E.B. epenao j oep aeop acee i- acca.

p o = 1, p;

i = 1, s, j = 1,ri.

k Oe acee, ooceoc j- aeop i- acc a, ooa Nij. cex coyex apopx acc ri a cpaeo coooee a: o i 1, s : N =.

Nij j oeco , oaax k- pao, oopeeo oocc k j- aeop i- acca, ooa Nij. Oee co rj k k ee, oaax k- pao, pao N =.

Nij j oyc, o opoeo n (n << N) pecoeo. yc opy oao nij , oocxc j- aeop i- acc k a, pe k- yae pao oaa x.

nij Oee co pecoeo, ex k- pa, pao:

ri k i 1, s : nk =. Bee apope aco a ij Nij N, nij j a ae aco cpeaeoc k-o paa cpe peca k k ee j- aeop i- acca: ij Nij N. acoa ij cpeaeoc k-o paa o acee eo opeee k c e: k N N. p cooecyx peopaoax a acoa paaec e:

ri ri k k i 1, s : k = = ij. (35) Nij ij N j j pya oea aco cpeaeoc k-o yeoo p aa cpe j- aeop i- acca ee :

k k ~ ij = nij nij. (36) Hecoo oaa, o oea (36) ec cocoeo, e ceeo acoec (o n) opao oeo c k k o aco ij. Ho, a pao, ae nij oaac a, o oycaae oe opeoc oeo. ooy Cmoxacmuecoe onucaue opooo emoa oe coyc oo a cooaee opeee aco cpeaeoc. Opee oey a:

ri k ~ k (i) = ij. (37) ij j= C yeo oo, o k k k Dnij nij (nij - nij ) / nij (38) k k nij nil (l j) oapa e cec e 1 k (i) k k k k ;

C Cov(nij, nil ) -nij nil + l j, jl (39) nij nil cepc oe (37) opeeec e:

ri ij 2 ri - ijil (i) k Dk) = Ck = ( nij Dnij + 2 jl nijnil j=1 l< j ri ri - nij k ~ = nij -1ij~ij ~k 2 il 1+. (40) k(1- ij )- ij il nil j=1 l< j eo oaa cocoeoc eceeoc oeo k (i) (k = 1, p;

i = 1, s).

oe aco cpeaeoc coepaex epeex (pao) cooa oo oy ocaex epee x, co oopx s > 1. Ho ay s oeo a (37) oo paccapa a eoopoe uepeue coo aco cpeae oc k-o paa, ooc oopoo opeeea paee a (40). a c coya ee E.B. Maceoa .H. Tocoo [13] o o, o poo cce oe pecoe cceoae paoepo paoa a eoopoe uepeue yaeo coa o cce. ay oey a (37) oo oa a epe e e (35) paax i- apopo acca.

aao e oye ooo oe aco cpe aeoc yaeoo paa, xapaepyeo epecyee E.B. epenao ac coco coya, a acoaa aopo eop opao peyao cepeo e [31]. B o cy ae, oa eoopy ey eaco ep eco popa (c pao ooc), oooe aee e cec a ea cyepo oyex peyao c eca, oope opeec opeoc epe.

ye paccapa oyee ace oe aco ki) a epaomoe cmoxacmuecu eaucue (o ( paoepo c coepaeo o pe) uepeu c oo ae aco k. o ooe, a po aea eco cace [29], ooy oey aco k peca k e eo oa oeo (i):

s k k = (i). (41) i i B cy peoa eceeoc ooo oe eoxo s H o ycoe opae a eop a = 1. C yeo oo i i H peoa ae ooe eopa opee yco H Dk = min(). (42) a ecoo oaa, peee ocaeo aa opee ec e:

k 1 D(i) i = ;

(i =1,s).

s k- (43) ) (D( j) j= Toa coa ooa oea aco cpeaeoc k-o p aa paa:

k s ( j ) s k - k = ) (D( k (44) D( j ) j j), j - s - (Dki)). (45) a ee cepc cec e Dk = ( i Cmoxacmuecoe onucaue opooo emoa ae, o ce coooe pe peyaa omoo onpoca, ocoy o ac cya oeoo p aex nij = nij.

opy (45) ceye, o cepc ooo oe aco cpeaeoc ee, e aa cepc k acx oeo o aco a (i);

k = 1, p, i = 1, s. Ha pa e cepc (45) oo oaaec pao (a oa op oo) ee aoo ae cepc Dki). co ( oae oeoo eoa, oop ooe ocoy opaoo exoo [32], a poe oee 15 e pe ax cceoax coaoo, oooecoo apeooo xapaepa oaao, o p oeax op o pa 1 500 2 000 ae opeoc oeo k oo coca opa 0,0050,015.

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