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A.. yxoe (Bopoe) CCTEMHA HTEPPETA PETATOB ACCAOHHX AA Peya pee eoo acepoo aaa eppepyc cooec c ooe cceoo oxoa. B

paax opoo aaa pooc yee paox pacpeee, o ooe cea o o cceoc oea cceoa.

ee coa: eo ooepo acca, acep aa , cce aa, paoe pacpeee, oo pao oo oee, op aa.

Meooo cceoo oxoa, ooaeo coppo aac 70-x . XX ., acoee pe ye caec oe pao [1]. Oao cooae ooe cceoo aaa paecx aaax aco oc eapa xa paep, a peya aoo pee oo a peca e a aeceo (epao) ypoe.

aay acca epeo paccapa a aay cc eoo pecae oea cceoa. B o ae oe , o ooo aco ae ep acca ccea a yopec a co. Ha cao ee acca oe ccee pecae cocyecy ao o o py pya acoo aco, o pocxo epeo ceee accaox ccex eoo cceoa.

Ocoa e aeo cceoa aaec o, o oaa, o paax cceoo oxoa eec oooc Aece eope yxoe aa ooecx ay, oe Bopoeco o ocyapceoo apoyepcea.

Cooo: 4M. 2006. 22.

Cucmea umepnpemau peymamo accuuauox aa a ocee eoop aooepoc, ca c o ece oea oyex accaox pae, oope paac epe apaep paox pacpeee.

cooae po cceoo oxoa ec a eeo oepoa coao-ooecx poec co. Oao oppeoe peee ocox ooe cc eoo aaa eooo e peapeoo ycaoe eococ cce. oa y poey opypy a aay ee cce, opeee ee pa. O eoo pee o aa ec paccope oxo, ocoa a cceoa paox pae, oope o yac xoe ocpoe oo. B paax peoeoo oxoa yaec e oo oy coepaeo eppe pyee acca eeo cce, o pape o poc o eococ ce paccapaeo cooyoc.

Ha poe opo oo pooo ea pax oacx ay ocyecc epexo o exaceco cceo apae. Ocooe poopee aaoc ce aoooe ace eoo. Ae a ee e ac cooyoc oy aae exaucmuecoo, peyuoucmcoo noxoa. B poooooc ey ae a eoe xapaepe xocecoo cceoo a.

Bopo oxo aye po aa cce, a aa, oop apyec a ax ax, cce aao.

Coaco oy oxoy cyece coca cce c coca eoo, oop e oaae oa eo ace. Tae coca oa aoec ce ey oe ac. coca apyac, oa cc ea pacceaec a oee opoae ee.

A.. yxoe Mexaceca apaa coac yepe, o o coo ccee oeee ce cce a eoo oe ooc oceo a ocoe coc ee ace. B cceo oxoe pope ee eococ cce, a y ae paccapac ee cocae ee. Ccey e o oo ocpeco aaa ee ace. p cce o oxoe coca ace oy ee oo opa a eoo. Coca ace cce e c x y pe coca, o oy o occe oece ceo eoo. Cooeceo, cce aa a epye ae epy oepe a opaa oeca.

aaa acca, copypoaa a oeeope eco ypoe, paaec a aaa paee aaoo o eca oeo a aeceo oopoe py (acc) [2].

Cooyoc py, oyex peyae pee ac caox poeyp, po aa peymupyu paueue. B eoopx copeex ayx ocpoex oc ocy ec pecaee o acca a cc ee a, ae oopeeo cceoe pecaee oeo. acca paccapaec a aoe yopoe e oeca oeo, oopoe ooe ea ae ooceo ao, e coepaxc epo peca e x oeo.

Ho pe eca o cceoc paccapaeo cooy oc ee eoxooc p cec oo eca.

cceoae cceoc oea poec o, o oae oooc aeao, xo peo, oc a o oe eo cocae opae aopo e peex (pao).

Be, accaoa eococ cce, o e aopo [3, c. 69], opeeec a oooc ecec eoo oee acc apaee exc oeo. O oc x oeo coco a y x eo ppo, Cucmea umepnpemau peymamo accuuauox aa ooe ecece opao cooca ey coo oe opaoa x ececee acc. p ep ypee opaa ee cce a o e pa, oo papaa ccey cy a ooepa oeo, a ae ec ce ac oac ccea A.A. e.

cex poe, oax p cooa p o cceoo oxoa p ocpoe ooa, ae paoe opac oo epe paccopee oo ooo acea, caoo c cceoae oyaxc p acca paox pae [4].

o pao pacpeeee oa acoc c eoc, cooecye aoy eey, o eo paa p papoa eeo o ceoc. B paoax coao ooecoo xapaepa, a ae cax c oo ae, oo e yeec ooo a aay pey ao acca c o pe cceoa paox pac peee. Bece c e pacpeeee ceoce acco ocpoeo accaoo pae oe cy, a ye oaao e, eoop co oaaee eoc oc cce. Ocoeo ceye oepy, o o oaa e e ec eocpeceo ep, a oye pe yae opao epo opa, paec o ca co cpyyp ocoeoc ooepx ax poee x ocoeoce coo xapaepce o cpoeoo accaooo pae.

Paoe pacpeee eaco py o pya cceo ac pax ayx oacx. e oaaoc o, o p eca ox opaex, cax co coca cceoc paccapaex cooyoce, paoe pac peee oc ooy oy e y acoce.

B aoee poco ope a acoc oe peca ea epoo, ooy aeaeco cace ae A.. yxoe ao oy aae unepouecux aoo pacnpee eu. Maeaec a acoc oe paea cey opao:

C ni =, (1) i1+ e i = 1, 2, K pa acca;

C ocoa ea, oo paa oey aoeo (oaoo) acca (oo oa a C n1);

ni oe (ceoc, acoc) acca i-o pa a;

eoopa ocoa ooea ea, oo e peocxoa e.

pep paox pacpeee, pecaex yaa o e ope, oo a ooe, eopa, oo , ce, ayoep, opae, ooo o x pyx oacx. Cc a yaae a poc paoax [3;

5].

acoc yaaoo e a ooe oo a a aoo apeo, eopa aoo a, oo aoo ca, opae aoo peopa, ce aoo aMaepoa. Pa aa x opaa o a, o oye cayc p ecoo aoa acoc oye pa cceoa e eaco py o pya pax oacx. p o.. o epx, o e oo oapy o ee a peco ypoe oo aoa, o peo oc ee eo exaa oppoa [5]. ooy epaype pa oe pacpeee aoo a ae ceo aa uno u. ye pepac oo epa aee .

ao a a oeccea yepcaa xapaep a aooepoc p o ox oacx. Ta, ce o oaao, o aoex eco, opayx eoopy ececy ey ecyx ccoy apyy, oec ao a. aoopo, a oex paeax eca, a cooyoc pax eco, a aooepoc Cucmea umepnpemau peymamo accuuauox aa apyaec. Boee ooo pacpeee o co oao aece pep oe eococ eoopx capx eco. B ayoep o pepe a coppoaeoc ayoo apae peaaec ca oee ooo paooo pacpeee a cooyoc ya o eae oo ayoo apae. B oce ee pe o peoeo oea ypoe aca peyao opo o epe ooe pecaex o ao peyao o ooo pacpeee.

Cyecoae aooepoc, paaec oaoo aeaeco acoc co pax oace, ooo y peooee, o a acoc o e peca eoop oecce p, oee c cece oe aoo pa cce o cooyoc oeo. a eco, ce aye cce xapaepyc ae eoopx apa, pae x oo ope aoo coxpae. ao a, epe ca ope nii1+ = C, oo, oeo, eppepoa a eoop ao coxpae, peaye ao ccee.

ca, ae, o ao ope ao epoaao copypoa.

Ta opao, aece eoxooo opaoo p aa cceoc (eococ) cooyoc oeo a peaaec cooa ae ooo pacpeee a o cooyoc. Oeo, o o pa e ec e ce ocao, o, eycoo, oe oo e aece aao cceoopaye cooyoc.

ao a oo, oeo, paccapa aece a co eoopx eocx cce e ca opoc o exaax eo ooe. Ho ao oxo aeoo cao c eoeooec e oe peeoa a po oce oyex peyao. oee peae pe caec oxo, p oopo eec oooc oc A.. yxoe pecy aooepoc cxo ax-o oee ox ccex po. poe oo, xo opa a e a o, o a peaaec paccapa paoe pac peee, oope oyac peyae cceoa cpyyp ooepx ax eoa ooepo acc a, .e. paccapa paooe pacpeeee a eoo py xapaepcy cao ooepo cpyyp.

B aaax acca, a pao, e ooapac coca cceyex cooyoce, eepax o pox. Oo e yaaec, ec paccapaea cooyoc oeo oeco (ooepao), ooee oopoy opeeec ae y oea aoo-o ooo ecox coc, e paa cooyoc ec cceo, .e. cooyoc oeo, aoece oopx ae oee ox epax aec, e coce x oeo oea. a cece, e cceyc aee e coyc oe ccee (epe e) coca, opa o oopx oe oaac eca oeo p p pee.

Coco cceoc cceyeo cooyoc oeo ao poec p ocpoe oo, xc, a eco, o cocoo oca cce. Paccopee o e (eepao) cooyoc accpyex oeo aece eoopo cce ee ac eo ceye oo, o ce yacye oe o oca o e e aopo pao, ocoeo o acaec aopo ac ca, coyx eoepec oxo (c., apep, [6, c. 148154]). pa p o o oaac cyec e, .e. a, o a x, oeoc, eoxo, a ce ece o ocao, o c x oo Cucmea umepnpemau peymamo accuuauox aa oo o o a oe o cex ocax o o eo copoe, oae oopo aec a ocoa aaa cceoa. B cyae ec oe oaa pa p aa, paccopee oc a aaee aope pa, ooe ye xoo a coc p ec ocae oeo eoy aopy pao. B o ye oo ycapa poee eoopoo oeo a a coo yoc oeo a oeca, oeeoo coco.

poea oppoa ox pacpeee o aco eo pee e ee ooaoo pee. Cyecy pa e oxo, ooe p ex x peooe x oya paoe pacpeee, cooecye (1). B epaype eco ecoo apao oce (a a aex oo) oo coooe.

aea ac oo epoecx pacpeee a oyea ye peeoo epexoa. ooy py, cooecyy coooe (1) oa paccapa a oy px ceeca pcoa (X IV o), oope oyac peyae peeoo epexoa epeoe pecoo pacpeee [5].

oa pacpeeee apeo paccapa a poe cya ea-pacpeee. Bo paooo pacpeee aco ocoac a oxoax, aaox e, oope cpeac epoae caceco e p o ca paoecoo pacpeee oey ae. Oe, o aoo poa oxo, a a , oxo cooocc c o e cceoc oeo, e ya pao oe oc ca eeo cce cya poopee c ae ccex ce ey oe eea. po ea oee cacecx peoco, oope p o coyc. Oao eoope ae ocoe oc yopoa cox cce ae oxo ooo xopoo opaa. B aece pepa paccop oppoae A.. yxoe pacpeee cyao e, oopa ocae poecc po ca ecoc eoopoo coa, pe cyecoa o opoo ec eoopo cyao eo.

yc eec eoop co, opoa oe, pe ecoc oo coa poopoaa ye ocyoy ypo ae e X. a eco, aoe peooee aeaec oo peca epe dX a ypaee = X. Ec aao aee e dt X0 = X(t0) aa oe pee t0, o, eppy, oy coooee X(t) = X0et.

Ec peoo, o pe cyecoa pao c oa ec cyao eo, ee coe aoe pacpeeee c apaepo , o ooc pacpeee pee coa ye opeec opyo p(t) = e-t. Toa, oo o a f(x) ooc pacpe ee cyao e X, pa aee t coooe 1 X X(t), paoe t = ln( ) oca paee X f (x) = p(t(x))tx.Ooaeo oy 1 X - ln( ) X X 1 1 X X 0 f (x) = e =, X X X X X 0 , ec ooa =, o oy xopoo ecoe pacpeeee apeo 1+ X f (x) =, X X oopoe p 0 < < 1 oo paccapa a epep aa o ooo pacpeee.

Cucmea umepnpemau peymamo accuuauox aa Paccope oxo exay oppoa epo ecoo pacpeee ao eocppye, o o e ec co eepcc, co coxacec, a pecae coo oeee x yx poooox ee. pe a eococ ayoc cce oe ae eepcca cocaa aoa, a coxaceca cocaa a aaaec a eepccy. o co co epoecx pacpeee oceee pe peae ocooe ae p aae paoo poa eex poecco.

B aece pyoo pepa paccop exa oppo a ooo pacpeee, oye a ocoe p a acao ccep, ya cep [3].

Haae pa cao c e, o aece oaae yo poeoc cooyoc oo epec po pacpee e o cooyoc, oopa, a eco, ocae coe o acaoo ae o cyae, oa ce coco coo yoc paoooe, .e. pacpeeee coco e c acao cep. aoopo, ooee o cepoc pacpeee ca c ae eoo po cpyyp, yopoeoc cooyoc. p o e o peoaaec, o yeee cep, o o e caoe, yeee ccep, ceecye o oe cpyyppoaoc paccapaeo cooyoc. ooe e poo coyc cepee, e oaaec, o xaoc oaae acao cepe.

ocypy p ya cep aece oe cceoo pa, oo, a ye oaao e, oy eoope cec, oope peca coo oece e xapaepc cceoc. Ta opao, oec oooc a pae poep oee oo ocyaa a peco aepae.

peoo, o eec cooyoc, cocoa N oeo, oopo ocpoeo accaooe paee, A.. yxoe cocoee x K eycx acco ceoc n1, n2,, nK, K pe = N. Toa aece ep cep oe c ni i= o peopaoa oeca ce, oopoe coxpae aoe paee. acca, coepaeo ni oeo, co ax peopaoa ye ni!, a ceo pae eo co peopaoa ye pao poee n1! n2!nK !.

Ec opee accaooe paee, cxo ya oo o ep cep, o ye oye p a peya: ni = 1 cex i = 1, 2, , N. ooy oope eo c paee paccopee oc copeoe ey L paee o e cooyoc m1, m2,, mL ( = N) a a mi i= aeoe opaee, oopoe opeeec cey opao:

1) acc ni mj epecee e e oee ooo eea;

2) oe ypyee acco opae coco e oaae;

3) ec epeceee acco ni mj e yco, o mj epecea ec c acco pae, co eeo oopoo e ee, e ni.

pep ocpoe opae oo peca, ec eec paoo pacpeee poec epae o oc, oope e acc cxooo pae, a opo ae acc opae. a ceye opeee, aoo pae cyecye oeco opae, oope oyac a ce epecao eeo ooo acca.

Oeo, o epa cep opae ye e ao e : m1! m2!... ml!. Toa oee co peopaoa, e ex cxooe paee, ye pac S = (n1! n2!... nK!) (m1! m2!... ml!), e ocoe e ee a ecoe oe ep cep.

Cucmea umepnpemau peymamo accuuauox aa Haa aaa ye eep aac axoe aoo pae, ceoc ae acco n1, n2, , nK oopx oca y S aoe aee p yco, o K = N.

ni i= a e S yoo epe ee oap y, ocaey aoo ae a e, e caa S.

poe oo, coy acoecy opyy Cpa ln(n!) n(ln n -1), oy K K L L ln S ln ni - + ln m -.

n n m m i j j i j i=1 i=1 j=1 j= eo ae, o pyea y S peca e coo c ooc o ocox caaex eey cy y po cxooo copeoo ey pae, .e.

eceo xapaepye cee yopoeoc oe ca, a oopo aao paee.

aeeo pee oaoo aa apo cpye ae ceoce acco ye y = y(x), p ae eocex oax ae, coaae c ni, a a mj pe accc oe c eoce opaa o e y. B peyae oo oy oooc a ca ceye pee paeca a K n ln ni ln ydx, i y i= c L m ln mj x ln xdy, j j= b a K L n = m = N.

i j ydx i=1 j= C yeo oyex paec eea y pe a d a ln S ln ydx + x ln xdy - ( + ) ydx.

y 1 c A.. yxoe Ceae aey epeeo o opo epae, ya o y = y(x), , ceoaeo, dy = y dx, a y(1) = d, y(a) = c. oce x peopaoa aaa coc axoe y y = y(x), pye ceyee paee a ln S ( ln y - xln x y - ( + )y)dx min y a p aao opae = N. aeeo pee ydx oyeo aa coye eo eopeeex oe e. y apaa oce peopaoa ye e :

a ( y ln y - x ln x y + y)dx min.

pee oyeo aa coye apao oxo ypaee epa. oaa F(x, y, y ) = y ln y - x ln x y + y, ae F = ln y + +, y F = -xln x, y d F - ln x -.

= dx y oca aee ae ypaee epa F d F - = 0, ooaeo oy lny + lnx + + + = 0.

y dx y Papea o ypaee ooceo coo y, ae y = Cx-, e =, a C = y(1).

Cucmea umepnpemau peymamo accuuauox aa oyea acoc ycaaae pey c paa acca x c y oeo oo acca. Hepyo ae, o a acoc cooecye aoy a.

Oe, o ao oxoe ce pa e paccap ac. o po oy, o oyeoe coooee xopo o ocae pacpeeee oeo oac ax pao opao xye oac ox pao, e aco cpyc acc, ee oaoy ceoc. Oao o eo e cae ae oyex xoe paccye oo. B acoc, peeoo paccye ceye, o c o pe peoeoo pa acao cepe cyae cpex e ye oaa paoepoe pacpeeee.

Ee oo coopaee oy oe paooo pac peee ope (1) poc a [7], e aaa ocpo e acca coc axoe pee caoap oo ypae peepa.

Oee peee eeoo paccopee ypae oe pecaeo e pa = n, , pa o a C n n e ycoe opooppoaoc cocex y aa, oo e, o (, * ) = Cn. o ooe eppepo n a oe Cn a ecoc acco, .e. e, poopoae x ceoc. Tpeoae oeoc y po oy, o p, cocae oeo, oe cxoc, , ceoaeo, Cn 0. Ec pe oo, o oe oo pa pocee cyae o pao poopoa opo oepa acco, .e. o 2 C ec coooee Cn =, e C, p eoope oca.

nP Toa cxooc pa, e oopoo aac a coo oee, oeo, oo oc peoae p > 1, o A.. yxoe aoaec po oy, o paooe pacpeeee c eoc acco oo oc epoec xapaep.

o-oy, oo ee a pye coopae oy o aooepoc, pec oapyeo o o x oacx ayo eeoc. Ho o cyae o o aae cpyyppoaoc oeca e oe ocaac e a p cceoa cox oeo, ocoeo paax cceoo oxoa. Ta, e cpyec oee coooe (1) a peco ypoe, ee cc ca poee pyx ccex aooepoce.

B aecme npuepa ocpoe oo coao-o oecx cceoax peaaec paccope peya , oyee aopo coeco c B.M. aco cye coooecx cceoa 19771978 . Paoa a o ea a aepaax cceoa, poeeoo ypco ACCP.

o cceoae o cao c yee cpyyp yo xc c poex pep c e e ac co pao, oaax pa a pyoo o oc. o o pyoo ooc oa cooy oc peaoo peoaaeoo e pyococooo acee ey peoa cpa, oopoe ec cyece ao cooyoc pecoeo. ee a ocox a oee, cooecyx oey cceo a: eppopaa caoc (yoec epexo a pye pep peeax aceex yo) epp opaa ooc (yoec ea pye aceee y). O o e oee oe coce cooyoc acco, a oopx oee pyy pecoeo co cxo oc xapaepca.

Cucmea umepnpemau peymamo accuuauox aa B aece pao, opayx pocpaco, oopo pooac acca, pa ae epeee a opac, opaoae, eoc poa pecoea ao aceeo ye, a ae ypoe paoax poe, oye opaoa, peoaaeoo cee. P pyx oaaee, ae, apep, a ca pa o a pep, cooac oo a ca ep pea accaox pae.

Bxoo opae ocpoe acca ocy ae aeoo opoca yoxc c poe x pep . a-e, poeeoo 1977 . ceo oea yoxc a opaoaa cyaa opa, cocaa 5% oea eepao cooyoc.

Bec acc cxox ax peapeo pa a e py. epa pya xapaepoaac eppopa o caoc. B ee coca o ae ex, o epexo a pye pep peeax opoa. Bopy pyy coca ae pecoeo, oope copac exa opo a a-e yaa pao ooo cee. a pya xa paepoaac eppopao ooc. Ae cop poax a opao py opaaac epoaa o oeo.

p ocpoe oo a cooaa cooyoc aopo ooepo acca cooec c pe oeo a eoo [8, c. 3941]. Ta, a epo ae p ec aop epaoo eoa acca op.

aee ypaeo apaepa, payca epcep, paoc cxo coepaex oeo oyex pae.

B ae cyae o pac a, o p e ec aeceo pae pa acco.

Ha ceye ae pee epapxec aoe pa aop, paoa o py aeo coce a. yoca cpae peyao, oyex pa A.. yxoe aopa, a cooaa oa oo eoa, oo a oya oo paee a aao ypoe coc.

Tpe a cceoa acca ooepx ax a ac pee aopa, coyeo oe e ex oec. B aece y paeoc paoc co oe epcepe paoo payca. Peya pao oo aopa cooac yoe ooc pac peee oe o oex acco.

oye cx a pao ypoe acco a e epo ae pec aop oaoo aaa, co y paey poeypy. o aop, a pey , ocpoe accaooo pae cyeceo coye y paeoc, yc ae cy ae oeo ooc pacpeee. Peya pao oo aopa coca ocoy peypyeo accao oo pae. peee eoo ooepo acca ooo e cocae epo py 9 acco, a cocae opo 11 acco pax oeo.

Haoee ooce cex acco ec acc 1, oop ooc coco ecx ypoee. Cpe opac pecaee oo acca axoc epae 23-25 e. pe cae oo acca ao e eca pao, o e ce ecye ocyce ao oppe ey opaco ca e pao. B eo, cpe ecx ypoee, epepacpee xc cpe pep opoa, ypoe opaoa 8-10 acco pcy oo o pye. Ocyce acca yoxc aa oo ceoc opacax ce 25 e ooe peoo , o o epe poce a pya pacceaec, aco pe paac cae ap pep aco epexo pye acc, oopx xapaepo paooe oeee.

acc 2 coca ece ypoe, eae py e opoa c oee co ypoe , o pe a oe ee ecx ypoee, cocax acc 3, pa Cucmea umepnpemau peymamo accuuauox aa ae opoa oce yp. o-oy, ec po ec ece ax-o ooex, e yex a a opo. Ceye oe, o cpe acco, cocaex ecx ypoee, epepacpeexc peeax opoa, e x py epae 19-22 oa. yoec c pep ooe c oce cpe opaoa e o opaco epae xapaepa aeopoc p pee o ea opoa, e oac ycpoc a pyoe pepe. Cpe oo ea o acce ao ye ec e e a yey, oo y ocooe apaee pa pye opoa Cp aeo Bocoa.

yoxc ecx ypoee c ooceo ypoe opaoa ec paooe o eee cpex opacax 30-33 e (acc 6). oo acca xapaepa eca coa ecoc eyec, o e c eecye ae ao oppeoo c ey eoc poa opoe cae pao. oc ax acco c a ypoe opaoa ec eppopaa caoc. ecx ypoee, oy x cpeee ceaoe cee opaoae, paooe oeee ec aoee epo opaco epae 26-30 e (acc 4), ocax xapaepo epepacpee ee ey pep peeax opoa (acc 5 6).

Cpe pao, pox eppopay ca oc, oye acc 7, 8, 9. acc 7 coca pa ce opoo c oee ypoe , e x acoee eco pea. pecaee oo acca xapaepo o, o oco x ye e eco eca o pea yp. B acc 8 o pa, pexae a-e pyx pyx opoo. pe, ec pecae acca 7 aoy oey ye yce oe ecoo pa eco eca, o oe o x A.. yxoe pecaee acca 8 a cea eca eca ec epo. acc 9 pecae cec paa, pexa ce Bocoo Cp . a-e opace 20- e poe xopoy paeoc. Ooceo coe oaae x poa opoe oceeo cee a ocoa peoaa, o pecae oo acca yy po eppopay caoc epce e. Oeo, o o ax aopo, cax paoy ooc, ec ypoe x opaoa.

Cpe caocoex pao, yoxc c pe p opoa eax a eo pee, oo e acco. Mooe oeee o, opaoax acc 7, po aa opao pae. B e ya cy ypoe ce Bocoo Cp, oopx a-e ep py opoo x cee. Ocyce eoxo x yco , ae oopx ec ae , oyo x epyc eca poe. o oe e oy pooe pacpocpaee. Bopaa pa xapaepa ae yoxc, oex acc 10, oop cocae ceaco, oyx cpeee ce aoe opaoae eax, ocoo, eca poe cea Bocoo Cp. Ceec oeee oac pa, xo ce, opaoae acc 8, oope, e yce pc opoe, ea a yey pye opoa Cp. o ee oyo aae yeo pa. acc 9 xapaepye paooe oeee ypoee ce Pocc, oope, oao, pexa a-e ye pyx pyx opo o, ex oee co ypoe . Cee ypo oycoo x peee exa a pee a-e a pae pyx pyx opoo. acc 7-10 cocae a opao ooceo, oope, e pc opoe o pa pa, ea a eo pee. Maoce e c acc 11, oop o pao opace 30-40 e co Cucmea umepnpemau peymamo accuuauox aa cpe cea opaoae. x xapaepo p e pee o ee oce eoo poa opoe.

peee oca acco, oyex peyae p ee eoo acepoo aaa, oaa, o a acc oaae xapaep, pcy oo ey ocoeoc . Bea cpyypa py yoxc oapyae e oxooc epepoaoo oxoa p ye p oo poee paoo o. oee opooe o cae peyao oo a yax (c., apep [9]).

ocpoea oo yoxc e cae opoca o eococ ce cooyoc: oo paccapa y coo yoc a eoopy ccey co ce ea oca ocec, paccopea cooyoc pecae coo oee, eaco yopye py. Ec paccopea cooyoc pecae coo ac ao-o oee poo cce, oa p p ypaeecx pe e ceye ya e pyx aopo, e ye x cceoae. oeo a ocaee opoc epee cceoa paox pacpeee oyex accaox pae.

ocpoe paox pacpeee a a co oaa ccea Statistica. Paoe pacpeee, cooecy e peyaa acca, pecae a pc. 1 2.

Ocoo oe, p ocpoe paox pacpeee a e ye e oecee ae acc oe, oaa e ya xapaepca cooecoae e oy paooy oee. poe oo, o pacco peo paooe pacpeeee, ocpoeoe o cey accy A.. yxoe cxox ax. Oe, o acc, cooecye pa a ooc xoe pae peypy e pae, e oy oee cy oo, o epa ee pao pax acco pa.

poepa oe aoa a a paccapaeo oece e ec ao y poco aae, a oe o aac a ep . a poea poo ocyaac epaype, o o cx op ocaec ayao. Ca poco , a oe oaac, o coco coc ocpoe pepeccoo acoc a oapecx o opaax. oo oappy paee (1) oya eoe ooceo cex epeex ypaee ln(ni ) = ln C + ln(i), (2) e = -(1 + ).

Oe, o ocoae oapa p o e ee aoo ae opeee e apaepa. ae caap cocoo pooc oea apaepo pepec cooo ypae.

Oao, a pao, ao oxo e ae eaeoo pey aa: yao cpyec aeoe ooee o ep oecoo ooo pacpeee, a ypaee pepecc c eecye o o, o cooece oe peeoe, ypa ee pepecc ao a caapo ypoe, oe a o peae ey, oe eepa eca o ee. Coac cya pocec oce po ep oe yco eope aycca-Mapoa, oopa o aae, o o ce yco oaac apye. Ta, o ceye oe epy oepe, papoae acco o x ceoc oc cyecey acoc ca a e. Pe o eacoc oo (ooe) e oe . B o eo yec, ccey oca c oo pe p apa-ocoa. Aooppe ocao, oca pa poo oeo, o cea aa a cao cpoo ypoe.

Cucmea umepnpemau peymamo accuuauox aa Puc. 1. Paooe pacnpeeeue accuuauooo paueu Puc. 2. Paooe pacnpeeeue accuuauooo paueu A.. yxoe Hapye epooc paooo pacpeee ac o xopoo ae yao, o c o pyo cpy c a ypoe oecex oaaee. Ta, ec poaa poa paecoe pecaee peyao, oyex p cceoa pyoo ooc (c. pc. 1 pc. 2), o e o yec yao (a aeceo ypoe), o aoe paox pacpeee, ocpoex oeo o cooyoc yoxc, oaax pa a pyoo ooc, aeo oaec o ox. Oao aa pepeccox ypae, ocpoex a oap ecx oopaax, e oepae oo. Ec ooa e pe Y ae oapo ceoce acco, a epe X a e oapo cooecyx pao, o ax ep o py, poe eppopay caoc, oc poeoe ypaee pepecc ye e Y = 3,116 1,395X (R2 = 0,88), a ax opo py Y = 2,641 1,053X (R2 = 0,83).

Oa peex pepeccox ypae a a caap o 5%-o ypoe. paee pepecc, ocpoeoe o o ee a, ae ao ee Y = 3,348 1,107X (R2 = 0,87). a , cpaee peyao pepeccooo aaa e ooe oe a opoc o a pacpeee a , ceoaeo, o eococ cce. Bce o ec cece apye yco eope aycca-Mapoa ao cyae po eoppeoc paooo aaa.

oxo, peaae a, ocoa a poepe yep e, o oyeoe pacpeeee eceo ec o, .e. oaec o cyao coppoaoo pa oepoo paooo pacpeee. Cpaee c paoep pacpeeee, oopoe paec ao cyae ae ce pacpeee yeo oe, cao c e, o, a eco, eo o pacpeeee ocae acy po, y, xapaepye cee yopoeoc paccapaeoo oeca.

Cucmea umepnpemau peymamo accuuauox aa poep oo peooe cooa eo cacecx ca, oop aac o, o c o o aa cyax ce cpooc paee oe ca a apaee aaoe co acco, ceoc oopx pacpeee cooec c paoep pacpeeee.

Oe acco, paee poeax, papoac, a a e o oyeoy a opao paooy pacpeee pooac oea apaepa. a poeypa oopac opeeeoe, ocaoo ooe co pa, apep 1000.

ae apaepo aee paccapac a cya e e. Ha ocoa oyeo cepee co pa oo oopa y pacpeee ooc.

C oo ypo aoc oeac epa, oopo axoc epecy ac apaep paooo pacpeee c aao epooc. , py coa, opeeec peca oac poepeo oe.

aea poepa oe o o, o ocpoeoe paooe pacpeeee eceo oo o cyaoo, pooc caap cocoo. Ec paccae a ocoa pec x ax apaep paox pacpeee cooecy a e, oye ao cocoo, .e. oaa o ac p yeo oe, o o oaae, o e ocao x p oo, o oaac o yeo oe. py coa, oe pecoo paooo pacpeee o pao epoo e ec a, a oc cya xapaep.

aoopo, ec pece ae apaepo paox pac peee oaa pecy oac, o o ceecye o o, o paccapaeoe paooe pacpeeee p oo pa cya. ae oop, oyeoe paooe pac peeee ceye pa o c aa ypoe ae oc. oceee ee a coo p oeecx cec, yaax e, oco oopx ec yepee o eococ cce.

A.. yxoe peaa oo oxoa a a cocaea popa a cpee MathCAD, ooa aaoo ca acco cpo paoe pacpeee, oopx ceoc ac co oc paoepoy pacpeee. oyex peyae cepea ax a oapeco acae cpooc ypaee apo pepecc cooec c (2). Paccae o a ae oeo pepec c paccapac a ae cyao e. Ha ocoa oyex a opao ax aee cpoc oepee epa, ooe c aa ypoe a eoc oe aee apaepa paooo pacpeee.

B xoe cepea o ycaoeo, o p cpaeo eox oeax oope ( peeax o 100 o 200) oy eoe pacpeeee xopoo apocpyec opa pacpeeee. Xapaep cya pecae a pc. 3.

B o cyae pa oac p yeo oe o peec a ocoe ooc opaoo pacpeee c coo ecy apaepa, oe oopx oye xoe cepea. Peya cepeo pecae a. 1.

B o cyae, oa co ca peao 1000, aa oc oe oyeoo pacpeee o opaoo. T cya oo e a pc. 4, e pecaeo pacpeeee apa epa, oyeoe xoe 100000 cacecx ca.

B o cyae ocpoee peco oac poooc ocpeco opeee cooecyx poee pecoo pacpeee. O peyao aoo cep ea pecae a. 1.

Cucmea umepnpemau peymamo accuuauox aa Oe op 100;

pacnpeeee: opaoe pep ooopoa-Cpoa: d = 0,0281992, p = n.s.

X-apa pep: 5,594137, df = 8, p = 0,6925856 (copp. a co c. c.) Puc. 3. ucmopaa ouuema paooo pacnpeeeu 30 acco ope oeo 100 euu Oe op 100000;

pacnpeeee: opaoe pep ooopoa-Cpoa: d = 0,0419926, p < 0, X-apa pep: 1029,452, df = 14, p = 0, Puc. 4. ucmopaa ouuema paooo pacnpee eu 16 acco ope oeo 100000 euu Taua PETAT OEHBAH HAEH APAMETPA PAHOBOO PACPEEEH (HOPMAHA APOCMA) Hopaa apoca (n = 100) Pace oe ceoc aee acco Cpeee C aap oe ea paa apae pa aee o oee paa paa 1 16 1,395 0,889 0,267 1,412 0, 2 30 1,053 0,845 0,167 1,172 0, 3 46 1,107 0,748 0,112 0,968 0, A.. yxoe Taua PETAT OEHBAH HAEH APAMETPA PAHOBOO PACPEEEH (METO CTATCTECX CTAH) Maa (coa) apoca (n = 100000) Pace oe ceoc aee acco Cpeee C aap oe ea paa apae pa aee o oee paa paa 1 16 1,395 0,893 0,247 1,441 0, 2 30 1,053 0,844 0,167 1,241 0, 3 46 1,107 0,813 0,124 1,036 0, Cucmea umepnpemau peymamo accuuauox aa A.. yxoe Aa pecaex peyao oaae, o ec eoc paooe pacpeeee, ocpoeoe oeoc o a ao py, e pa o, a a o eao oac o cyax pacpeee, ce oc acco oopx e paoepoe pacpeeee. o o ceye oo, o ae cooecyx apae po pacpeee e xo a pa oac p y eo oe. B a. 1 oo e, o aee 1,395 p ae epay (1,412;

0,367), a aee 1,053 epa y (1,172;

0,518). B a. 2 ocpoee epa (1,441;

0,481) (1,241;

0,569) ae a ce ae. paec o oaae, o cooyoc pao p co pac capa a eoce aye cce. py coa, poeee paoo o oo ooe oo x py e yea epeco pyo py e ec ee coopa, a paccopee oeoc pecaee pa x py pa e ooe coca pecaee o ce cooyoc a eo eo.

C pyo copo, oe ae oy cooyoc, oo oy cce oe, oopoo xapaep ec eococ (cceoc). Bo o oe ao a a a coeco paoo pacpeee oo cea oo, o aee paceoo oea, paoe 1,107, e pae epay (0,968;

0,529) a. 1, epa y (1,036;

0,551) a. 2. a, ceye pa, o pao oe pacpeeee, ocpoeoe o ce cceyeo cooyo c, ec o. o oaae, o oo c cceye a cooyoc oe pecaea a ccea, a o ee ee ac coco e oaa.

Ta opao, a o ycaoeo p cceoa paox pacpeee, p coeco paccope ce coo yoc e ceye oxo a eoopo coec e oco ccee, yopoae oopo aeo cee Cucmea umepnpemau peymamo accuuauox aa opeeec ec yco aoece oex ee cocax. oyee o cooa pa eco eeoc o poee eopaeco pa oo o paoax Cp aeo Bocoa.

*** pe pee o ypae cce oeo o o oaeo ya ocoeoc eo yopoa.

Ta, apep, o cec oe ooo pac peee ec ae ooo ca aocex acco. o ooee ceye e y, ec pepa c po cceoo oxoa. oppoae oo cec po, a pao, apye eococ cce e ae opaoy ee yopoa. ocaoo, apep, co ooaee peya oa o ypye ceco xocex pep coecoe pe. , c o o pe, oac oe eao pe ocyapceo yo opa eepa ao O oecx apx, coaco oop aa ceoc oecx ap Pocc opaaec cy 50 c. eo.

TEPATPA 1. yxoe A.. pep cceoc coao-ooecx oeo // Maeaece eo coooecx cceoax / A.. yxoe, A.C. Cooe.

M.: C AH CCCP, 1984. C. 2836.

2. yxoe A.. acep aa a eo pee accaoo aa // Bec ayea pao aea exa. Bopoe: B, 2000. C. 248253. B. 2.

3. peep .A. Cce oe / .A. peep, A.A. apo. M.:

Pao c, 1982.

4. yxoe A.. cooae paox pacpeee p eppea peyao acepoo aaa // Meo coooecx cceoa. 3- Bcecoa oepe / A.. yxoe, A.C. Cooe. M., 1989.

5. ocu A.. Maeaece oe cceoa ay. M.: Haya, 1986.

A.. yxoe 6. Too acca coooecx cceoax. M.: Haya, 1982.

7. yxoe A.. O oo oxoe aae acca // Cooo:

eooo, eo, aeaece oe. 2004. 18. C. 82105.

8. yxoe A.. oceoaeoe peee aopo ooepo acca // Mooep aa coooecx ax (eoece yaa, aop oca popa). M.: C AH CCCP, 1981. C. 2473.

9. yxoe A.. yee pyoo ooc eoa ooepo acca // poe ocpooca pa acee / A.. yxoe, B.M. aco. M.: C AH CCCP, 1981. C. 215228.




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