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Bopooc. .

Maxoo . B.

epae C. H.

Cepee C. A.

EHETECE AOPTM, CCCTBEHHE HEPOHHE CET POEM BPTAHO PEAHOCT XAPOB OCHOBA 1997 32.815 519.7 B75 Peee:

o.ex.ay, po., e Haoaoo oea paco accoa o aoaecoy ypae . . Toope;

o.ex.ay, po. B. . peo.

Peoeoaa oyoa e coeo Xapoco ocyapceo aae opocoo xoca (pooo 6 o 28.02.97 .).

Bopooc.., p.

B75 eeece aop, cyccee epoe ce poe pyao peaoc /. . Bopooc, . B. Maxoo, C. H. epae, C. A. Cepee. X.: OCHOBA, 1997. 112 c.

ISBN 5776802938.

B oopa paccope opoc pee oox eoo a eaecoo oepoa, eeecx aopo cyccex epo x cee, pee oeca aa ypae aec oea, ocpoe aax eeyax cce ypae. Aop pe ex popapoa copooe peyaa cea epo yopo epoopoepo ecooo aecoo oea, oye aopa.

ayx paoo, acpao cyeo capx ypco, cea pyxc oac aaoo ypae aeaecoo oepoa.

1602110000 - B aaoe 32. 226 - ISBN 5776802938 Aop, PECOBE Hacoa popa oo o oe epoo aa ay oo poea peee oox eoo aeaecoo o epoa ypae oea epe, oeoo coe co Xapoc ocyapce oexec yepceo Xapoco T֗5 p oepe PocccoAepacoo o copya o eeec Aopa. poe aee a oc ox oeyax pee eeyao cce ypae cope e epoeeppy pepe, ep e eo a a pae a papaoy a ae eeecx aopo popaoo oecee cea epoceex ooe yye cce.

p peee oyoa oyee a poe 1995 96 . peya, oca epe coo e oec o pooo ae ee e pcece pe, coyee o oo oepoa, poeocppoa eoc ox cex exoo pee aa cycceoo eea.

Cpeee peeo pocoe aooc oe oyo ac cpyyppoa popy a e ac ocoo pae, aa eoece oco oxoo, poe, ee copee cpao xapaep. o ypoc ae epe a cao coeo oepoa cyccex epox cee, ca popy peyaa cea epoyopo epoopoepo ecooo aecoo oea, oca opoo poex cpyypy apaep cee.

oyc cyae, xoe pa aoapoc poeccopy py yay, peopy PocccoAepacoo ocopya o eeec Aopa, a eo ocooe ae a cceo a oac eeecx aopo ceepy opaoy ocyay oo ocyece poea.

Amop COEPAHE Cco ycox ooae copae Beee. O pax ooax epa eeyaoc ypae 1. eeece aop 1.1. pecaee eeeco opa 1.2. eeece oepaop 1.3. peyeceoe pao paoe cex 2. cyccee epoe ce 2.1. o o a cy epy eeoc 2.2. Caoee pae HC 3. A+HC = Hoa apaa ypae 4. A+HC = Hoa apaa oepoa 5. Coa o eeecx aopax 6. Bpyaa peaoc cycce ee aee Tepooec coap eo cco Cco epayp poee 1. Peya cea aa apaepeco yceoc epoopoepa poee 2. yop oeaeoo ea e ayxa poee 3. Peya cea aa apaepeco yceoc yopa oeaeoo ea c ayxae poee 4. yop oeaeoo ea c c ayxae poee 5. Bpya pa ypae a ae epoyopa poee 6. eeece aop cyccee epoe ce epee CCO COBHX OOHAEH COPAEH ai, bi ea paa pa oac oycx ae i-o e peeo poepoa;

=(A1 A2 A3 AL) xpoocoa;

(t)=( (t),..., (t)) eya oy eoo;

1 M c oopa epa aaoo y;

D eaee xo ce (xoo ao);

e oa a xoe ce;

E cpea, poocoa aao ccee;

H paep cpoo co ce;

I pea cpe, poocoe aao ccee;

J yoa aeca cce ypae;

k oe yce ocopa;

K oeco cpx coe ce;

L oeco eo xpoocoe;

M paep oy;

N paepoc pocpaca epeex poepoa, peca ex eeceo e;

piP epooc pee eeecx oepaopo;

Q paep pepoooo aopa aoo;

N ocooe pocpaco eecex ce;

S eea cya xox cao epoa;

s oepaop aaca;

t oaae pee (epep cpe);

T epo oea ocopa;

ur ca aa;

u ca ypae;

V paep xooo co ce;

wi caec ec epoa;

w0 ceee epoa;

W epeaoa y oea;

x=(x1,x2,xN) eop epeex poepoa;

x=(x,x ) epeee coco ypae aecoo oea 1 ypae;

~ x epeea coco epoyopa aecoo oea;

X=(X1, X2, , XV) eop xox cao ce;

X = (X1, X2,, XV ) xoo ao;

y xoo ca epoa;

Y = (Y1,Y2,...,YZ ) eop aecx ae xox cao ce;

Z paep xooo co ce;

epy, a oopo ocyecec peee aa oaop o oa;

oepaop aep;

epooa apa;

( t ) pcocoeoc oco;

(t) cpe o eyey ooe oy pcocoeoc ocoe;

j pa oa aaoo y j-oo epoa;

pepoy a Xoaa;

(t)=(1(t),...,M(t)) eop pcocoeoce ocoe oy;

i eeece oepaop;

pepoo aop aoo;

apaep ocopa;

AOP aop opaoo pacpocpae (o);

A eeec aop;

HC cyccea epoa ce;

H (NC) epoopoep (neurocontroller);

H (NE) epoyop (neuroemulator);

O oe ypae;

CA ccea aoaecoo ypae;

RBF-ce pexcoa epoa ce c paao-cepo a aoo ye epoo cpoo co;

XOR oeca y caee Ȼ.

BBEEHE. O PAHX TOOBAHX TEPMHA HTEETAHOCTܻ B PABEH B ocee o cpe ceaco oac eop aoae coo ypae aec oe oe epeca o epa o (o ec coppoac e pao acceco apa , apyec a aapae epo-epeaoo cce) oxoa, oee oe e eeyaa cce ypae. Haepoe, pyo ae epec ce e accao e pa, o oop oxo pac ey coo, o oo ocox pae pa ec o, o eo ooeo ocoy oe eeyaa opaoae a-o opao au eoea o oee ypae (O), o cocee eoey npue eu, ocpeco oopx o yae opya p oe eo co epeca.

epo pye oxoo oo oec, apep, eco eep poae cepe cce, a ae oee e cce ypae a ae eeo (a) o (fuzzy logic). Bopo oxo peay ec paax oox eoo oepoa, o oop opayeae eeece aop (A) cyccee epoe ce (HC).

HC ceo o e coo cooyoc acoax e pooo oee apaex cex cpyyp, coo apea op e o ppoe eea. Ec ep a caoe HC oo oxapaepoa a oy cepoa aopa cpa eo poco yopyx epoo eoopy yopoey cpyypy, cocoy o coe eee peopaoa xo-xo, o ceac, o epe oce ycexa pee aa ep oo aa, epe po cceoa epeeaec oac cxo o, ox ay. aaa acoeo oea coco o, o o, ae cepxcpyyp epoo a oy oepoa e eape a ceo eeoc, a ae oo p paoy cce ypae.

Mee eoea eooo e a. Bce e eeo pa a opaee e e aeop. Coa peca coo e poco aop yo, a a x co ae-o opee, o ocaoo oe pecae. ya p, o aaae op a, yopoae ee aee pocxo o, o cxoo aa oumu camue. pece a peopayc oa y acpay opy, yoy oeppoa, oopa, e e e ee, ece cee aoee ece ae paypce peaeo o paeco aa ep oea.

ocoy co, o poe epoo ax pyx oepaox e, yacyx opaoe opa, oe e, oo peoo, o a a pecaee, opao pa co o pe pae epoo ce oa. Coa opa oea ( coppepoa ye ec) oaae oa apepoa o pae a, o eo pea a oyee e oac o pea oea, ecx . p o ce oa ayc xpa o oe c oeo e e xpoooec o aoy o pyoy py yopoex oo, a e coceo cpyyp, o ec eocpeceo ocoo apxeyp c ca ecx ce ey epoa.

Moe , eo a ye y a caaec ype , cocea oo ey, apa pa, opa oopo ooa ocoa coe ooee pe, a ae poopoa ae xo co. eoe pepoceo popae ooe pooe po epye acoee a yyee e oo oa, oa pae axa.

a o pe, a opocy oop, pe o cocae ocoy up myao peaocmu, cyecye ae coa a opaee eeo pa. eo yee ceo ypoa p, oeppoa eo opaa ae a oooc apoa coe oeee, pe e co opepoac pocpace oeax o ooce.

To, o oac cea acoe paoe, o poeocp poa ceo co oea coea yx ce x exoo HC A pee aa cea eey ax cce ypae. C oo copo, a epec A oyco e x coo eocp pee aa oao o a ooe a oeao poeype pepo epoo ce, acoc. eceo, o ceo e opae, o oe poo ece ex pepo (Backpropagation, RBF-ce) c cyeceo oa co ce ea oca ocec , ooy o ooe A e ae oypeo. C pyo co po, py pecaec cao coeae A HC. Oa a pae oocc oooy oepoa a poca o eoa eop aoaecoo ypae, oea pe pa oe aa, e pea ae aoe o acceco a pa a epa, epea, aecoe eo . .

apyc a peex e ox paccyex, a yaoc cepoa epoceey oe cce ypae, oopa e oo yee cpo ypee pecae o ee pe, poo poa oeee oea ypae, o ae oaae cocooc eeppoa oaoe ypaee cooec c peoa a oo oe.

1. EHETECE AOPTM o coe cymu npoecc aanmauu mc onmuu auou npoeccau . Xoa, pecoe epoy (1975) a Adaptation in natural and artificial systems.

maam em o u paccmaum ce no cou ecma u oxaum n. Oao onpeu uu ao ap moy, ce ee axoy peucoue uau oa yuumeo yecm. Eucmeoe ueeue, o mopoe ec, mo ceam oee yapeue a coep ecmoauu u eee a onmuuauu. Paoma a o ee cou aanmuu cucmeau, anpuep, oo uecuu, yeua e, mo ux noeeue e onucaemc ma y xopoo mpaemopuu opy oax onmuy o. Haoopom, copeoaue ey onoemau cucme , anpaeoe a noaeue uaux oypemo, onpeeem oee noeeue.

. Xoa. pecoe o opoy (1992) a Adaptation in natural and artificial systems.

Copeea opa o eeec aopa ao epe aa a 9000 aeoa pooae epepo yeac.

Oao, ecop a aoe oe epayp, ooo pyo oo copypoa, e eo o c ccee o ox epecpoe ppox oyx opao, yepca cpeco oca aaa oyx cyccex oeo, oo ocoo poeypo c pee a peee aa oa o oa.

M aepeo aa o pae c coocae yx aea . Xoaa o ooy aaa oa, ceax pe cox epoy opoy a eo aeo [1], oo e aao poeccy pacpocpae eeecx aopo a yx cooecax. paa, eeec o ca aac oee, a 1975 oy Xoa aa x pepoy aa (reproductive plan) paccapa pee ceo a aop aaa. Ho o ce ee aeo paoe o aanmau, o oopo o a co oop peco 1992 oa, oe oo, a a , epeae o cocoe aeaeca, oopoe oyae ceo, ac, c oo copo, a ocaoo oee epoopeoe o peeee aaa, a c pyo copo, papa o aaa oa, aaa o, aaa oye.

p aee oe ocox e A e ye pep ac c Xoaa, a ooe a poeype o ao onmuuauu. a, xo ecoo ypoea o cpae c xoaoco, paoa A aa c peoac epaype, a oaao pe, oe oocoao. o ooy cey, o a ece cceoa A a ecox oocpeax yx y a oaaeco eo o pa oyeca A, oca e oopo e x aec aae cocooc. * a, A apyc a eopeecx ocex ceeco eop o, yae poooece exa ace oa pao ppox cyccex oyx opao, a ae a aoeo eoeeco oe cee ox pace.

Meoooeca ocoa A ec a oee cee, oopa cao oe e oe copypoaa a: e e pco coeoc oco, e e epooc oo, o ooce, oye o c ee yace, pa, opeee pcocoeoc, yy pae ee cee. ocoy A e eo c oy oco o ceoc, ocoy ayaoc ec apae c oopo po e popeae oop a poae. Cpae poa, paa oe a opoc O ax ocoe oe eoeeo oaac? cocae e eee ay ooey copeex A, e cpae oopa poecy pyy. ae ceo oco, oa ae o pcocoeoc, e oo e yacy eepa ooo ooe, a pyc oy a eye cpeo ae (oxe) o.

Bpoe, caaoe cpaeo e oo A, a oo c eoo eoa oa. Caa e oaoc, a epo oe eo [3], pa ayy oo. Oao aeo e cea oa e cee oe o, co oe eoece pe oaoo poepoa e op ceeoo pae c pe po aeo e cea ocoaoo opaa ppoe.

* - Pc.1. oceoc aa cee, oycoea opaeoc ce oc oepyeo oy ec cpaeoc caaoo e pyo, ec oac y a poeypy ceo oa epe py oe cee (c. Pc.2).

a, ooeo poepoae aa c oppoa oc oo pocpace oac oycx ae epeex opa e eoopx pox oe.

aee epao o ceye ec. Caaa p o o aeaeco oe ycpoca poo oopaee oe ocooo pocpaca a pocpaco pepe, o ooe co ca pecaee o peee oepxoc pepe. ae a oco a oyeo opa cooec c pao ocoo cpaee ocyec eoope ay c oopaa oe pocpace epeex, aepaec eepae oopa ox pox oe.

Oepa ox coax y aoy ce eoy, oe o pae apae ey aoeo e eooe oca cpeya e, a peac ooe o coepa aa p poe, p aaa oy opao aopa opyae cpe .

Pc. 2. eca cpyypa poeyp ceo oa xapaepc poea oucmo pucmuecux noucox cmpameu npecmam coo ooo oeue ouecue peaue npaua, eee nyme ooeu peaoo uu yopumeoo onma oumau mpexepo npocmpacme. Hanpuep, npecmau cee, mo o a cmaa ac pacnox u a npecmoum e oapua uamc no nepe ceeo ecmocmu, anpuep, opamc a epuy noooo xo a. co, mo pyu nay u oyna e uaee opyeue, noyu mpeyey uopau o oao peee u ye uamc mo anpaeuu, omopo ecmocm noaemc, o e aoopom. pau op anpaeu ueu u euu aa apamupyem a cmp ycnex, ecu, oeo, noepxocm xoa aa, ae yxaucma.

eceo, paye coco oca execx oeo p oo eopo epeex poepoa opayeae c ooe opoae opa o oee. Beop epeex a e e epe, o ec a eo e a pa opoa, eo oo coca pecaee o oee. B opeeeo cce o o yepa, o aeop eop epeex poepoa pae exe y e po, o aeop eo oo. pypy ee apaep oea eop epeex, , o cyecy, p ae cayc eeeco opa. eo eeeco, ooy o, c oo copo, ee ocaoo, oo, o ocpo ca oe (oeec pac eo), a o-opx, oa cy cxo a epao p eepa eoo oeo ceyeo ooe.

Ae eo ao cc eoo ooo e oop a yoaxc ox pox oe. ooo oy, a ppoe cpeae opao ocyecec a eeeco ypoe, po eype oa oopa ox pox oe oyac a peya aypoa oopaa capx. pe, ec ep o pcycye oea cee aece poecx cea cya yue eoeco ooe, a e pooe o (oco) oy oeax pee, eyae e pee opaca a eye ae (oo ca, o o pa).

ec oxo, aoe, oy, o eo oae A a oe pyx cex eoo oa.

A acy oo:

o aapa;

e oemuoo oca cpeya p oo oy ocoe;

coco pecae eeeco opa;

coco epea eeeco opa epee ooe (eeece oepaop);

e o peyeceo paoe aoee pcocoex ocoe (pe e e o o, ac aa oco ooo, a o o, coo ye yee ooo).

1.1. pecaee eeeco opa ooo oy, a ppo xpooco aepa pecae coo ey oceoaeoc pax oa epex y eoo (A ae, o, T ya), eopa epeex A ae aca e eoe coo, coy yx-, pex- epexye aa. poco oe paccop cya apoo opoa, coye p oepo a o aox oy.

a, ye ca, o aa epeea xi opyec opeee paeo xpooco, coco cpoaoo oeca eo (c. pc. 3). Bce oyc xpooco ae o ec o o paea oe co a o, a ea. Po coe pae e oe py o pya a-o apepa, e e e ee, p eopoa xpooco eop epeex a poe ceo oepyeoo epoa o coyec oa a e aca appoa.

Pc. 3. pocea aca appoa xpooco, opeea a pacpeee aceceo opa o e xpooco Xo ocoo oop o eopoa, a cao ee, pa oepa, oaea a oepa opoa eopa epeex x xpoocoy, A e peec. Xpooco eeppyc cya opao, ye oceoaeoo aoe papo (eo), cpay apo e, ce oceye ee oy apa a caaa eeec ypoe, a oo oo aapyc eo ece ocec x ee, o oa e aoopo.

B pe, eopoa eeeco opa ap o op ecoy y oxo o oo-ec o, o oo cxo oo, o oa pecaea oe pe. Taa ocpoo oo oee poeypy eopoa paea xpooco poe eopa epeex xi.

Taa eopoae paeo xpooco poe eopa epeex o oo- ecoe a- Beeceoe ae pe ec o ee ca e oopa 0000 0000 0 ai 0001 0001 1 ai+1(bi-ai)/ 0011 0010 2 ai+2(bi-ai)/ 0010 0011 3 ai+3(bi-ai)/ 0110 0100 4 ai+4(bi-ai)/ 0111 0101 5 ai+5(bi-ai)/ 0101 0110 6 ai+6(bi-ai)/ 0100 0111 7 ai+7(bi-ai)/ 1100 1000 8 ai+8(bi-ai)/ 1101 1001 9 ai+9(bi-ai)/ 1111 1010 10 ai+10(bi-ai)/ 1110 1011 11 ai+11(bi-ai)/ 1010 1100 12 ai+12(bi-ai)/ 1011 1101 13 ai+13(bi-ai)/ 1001 1110 14 ai+14(bi-ai)/ 1000 1111 15 bi O oa pe epexo oo-ecoy oy, a o eo aypa e ca. Ooee oyeoo ca aca oy cy, ocyoy opoa a oeco papo paea (o ae 1 co 15) ae cooe aee ca e peeo ooceo eo pa ai oycoo aaoa ee e e, oppoaoo a py biai aaoa.

a xopoo o, oey o pe ee e peyec a o cpae c oo-ec oo, oop p eoopo cee ocoec opoae coeopae y ocooo poecca. B aece pepa paccop e p po coe cpo a 1, apep, opye c 4, 5 6 e.

peoo, pae xpooco, coe o cpoe o pye co 5, paea oaoy eopy, eyc pe ee eoopo aa, a ya oco eye oy coep pae xpooco cpo 4. Taa cya aopa oox oo. ocaoo o ceo oy oepa ae eepo pape paea 0 a 1 peee ye aeo. oee epec cya oyaec, ec ya oco coep pae cpo 6. oa pe a cya y e coee peye aea 0 a 1 pee pape o pee ycexy. B o e pe oo-ec o ca ac eoxooc o oceo aeo e oepa ae 1 a 0 pee pape 0 a 1 e epo. C ao x aa, peya e p ac pee (ep apa ae epeec ac eepy cpoy, a opo ooe cey). Ae o e ca xy pep pa oa c coea 3-4, 7-8, 11-12 . . cpo oo-eco oe ee coee. ae oop, ec pe eoepece eppe a, o pe apapye, o e cocee, paeae ooy pepy, ep epya L, a oopo ocyecec oc, cea eopyc e ae o pocpaca eecex ce N, ocoe py o pya a oy cpey ooc. oo ec o oo coco e oaae.

1.2. eeece oepaop Te exa epea aceceoc, oope ecy p poe, ypoea opa oopx ooea ocoy oo, o a ae eeec oepaopa, a cao ee, ceye paccapa a oeee, oepax epx apeo ooeoo ope a oypea ooax ecece oopo ao e epe, a ce, o ac opyae. Ceo oo, o eeece oe paop o acoa e oo poooecx c ceoa, o aaa ox e (ocaoo poaapo a oaope pc, peee eoeo p pee poccopo) opeaeco eeoc [4]. Ho o ceo;

a aa e aa yo o oaa eaoc . Xoaa, o oaac, a eppepoa p ec ooe cx exao pee aa aaa cyccex cce ax.

Ea e a oo o eepeooo epoa cceo a cax A cao oae pepaco ao oeapo c pa eeecx oepaopo poccoep ya epc.

Boecy c eoopo epooc a eo poecx ocoe, a x, c oo copo, oeceae epeay oocy eo ax pao, a c pyo oepae a poe o oo aoo epoa ocaoo co ypoe eo e oc. Beee ooce ox, ox o poecx, eo ecx pao opae oy ooee oo oc aaa, o ec cococye coxpae e ocoo co cooc.

a, oepaop ya (c. pc. 4), ooo oe ya ppoe, eppepyec a aea cyecyeo aeoo co co oeoo ea xpoocoe a poooooe (e a o aoopo). Oeo, o acoc o oo, ao pape paea, opyeo epeey, pooe ya, ac e a pacco, oeeo ooa o poe (pe e e o x Pc. 4. Tpaa eeecx oepaopo cex mpex onepamopo ecmo npuoeu, noeeoe ao, upaemc cyao oo pocpace L, e o paccoe pao 1, a o pocpace eecex ce N). epc po apye opa ce oa paeo xpooco y ooa o cpae c poeco xpoocoo. Haoe, poccoep, oca exa aeoeea ox oyx opao pece Xoao oe poae o aox oy, po oy, o xpoo coa ooa ae a paea, o oopx paea pa ee, ycoo oop, ooco xpoocoe, a pyo aepco.

eo aoap a poccoepx oeo oco oy o eac ey coo eeeco opae, o ec oc p opeae eceo oe xapaep.

oa, oop o pae eeecx oepaopo, oepa co cooc poccoepa epc oaoy ocy, o pe a y a ooec co cpeca oao acpo pee, oo e ooy po. Taoe pacpeeee poe pecaec cop, a a ya oe opo ooa aeo a peea oaoo cpeya, oopo axoc poe, c pyo copo, poccoep, poee a aea poee, pacooex oe cpey e, aepa opo ooo o e cpeye. Bao pyoe poccoep, ya e opac poecce eeppoa ooa a ae oaoo peea oepxoc eeo y. B o cce x oo ca oa.

1.3. peyeceoe pao paoe cex C e, p oo, co oaec o ex ecoo e. B oo eae ee, ao o oo cce acyae a, cyae oy, a e oea oco. O o, acoo oy aapoaa cpee, a coo aooyo oa paaec, cy o ae ee ceoc.

He co epeco, ca poa y oee ecee, ao, o p poc ceoc caa ooe. ouuem paoeu, ycpee o oy, paccapaec a ece yep ca pep pcocoeoc oy yco oa [5].

C pyo copo, yaa pcocoeoc oco oaa e poe e a yyee oy. e oe ooo ao oco oe o pepoyoo opaca, e oee co eo oy yyeo ooe ye ec ee ae. pcocoe oc, paccapaea a epa eoa a yyee, e Xoa [1], pecae e, oey o ce cepe poe aaa. Xopo coco paccope y e oee poo o ece, o paccapa ecpoae eoo a poeypy op poa opo (o opo sample Xoa opayeae e yy oy p.a.). pocpaco opo o cyae pecae coo aop cex eoo, a peyao oea ao cpyyp caoc pcocoeoc E cooecyeo eoa. O opoc, ca c pcocoeoc, y a:

B ao cee oea E( ) ao-o cpyyp oaae e ee a oppoa oo op? Oa c aa copee e epe, caaec c py aoca opoco: a cop peyao ecpoa peyx opo oaae e a ey a oppoa ox? Oe a opoc yxo aeo opeee oo, o cocae ocoy oo aaoo poecca. M ye e, pooae Xoa, o oe a ep o poc, o acaec eeecx cce, coco o, o yyee e ao oco po poopoao oee pcocoe oc E( ). Booe, o ooee e oaeo cyecye oo pax poeyp oa, aeaecoo oye p., e ooee ey oeo aeca yy cpyypa oo o pyoe. Te e eee, ocnpouocmo nponopuu ocmuymoy aecmy ec ao ee, oopa oe ooea c e, o cea a oppoa opo penpoymue na pe o aae aaa腻 Ta opao, a , oeo epo pepoyx ao Xoaa ec pao oee pcocoex a oee oeco ooo.

onmo, o npu ycouu eueo uceocmu nonyuu (a onmepo oeupoauu ouu mo ycoue eooo uopu poam) npueeue npuuna npeuyecmeoo paoeu oee npucnocoex npuoum ecoo eouaoy peymamy nonyuu paoamc a e cau ocou, ae. o cyecmy, mo uaemo noueu ypo paccompeu cucme: onepupye e ocou, a eau. e opmc py c pyo a uaue, cue mecm u eooa nonyuu cax.

poco pepoy a ae e oopec poey p. B eee epo x ooee o eoopx ocoe, oaax pcocoeoc e cpeeo o oy ypo, oac eye oy (t), o pe a eoope oco c o pcocoeoc pyc. oee oo, aa oco oyae oooc ca poee c epooc, poopoa o ee pcocoeoc. B eee opo poeyp eeece oepaop oecy a eo ooo, opy aop a ee a, o c eoc ooo poee. B pe yae oyaec oa oy (t+1). poecc epao oo pec, eeppy oceoaeoc ooe eoo.

ae, o oece ecaaoo oy ee aoe e ooee poeccy aaa, a oe coco aoa epeaoo y eop aoao. ae cocaa ey e oy ooe opee cpyypy ceyeo ooe, e opaac peyey. Ooe oepaopo, o peopaoae (t) (t+1) ec pepoy a. Mo py eo eeec oepaopa i paax ooo ce, opaex cpyypo, pepoy a eeppye oe oco, oee pcocoee cpee E. Ooa epe I(t)= E( t ) pea cpe, poocoe aao ccee, Xoa ae ce yee coecoe opeeee pepoyoy ay : I (1) Pc. 5. peopaoae aceceo opa A Pepoy a Xoaa a 1. aa aao oy Bec oy ocea ox t=0 apoa cya o-.

pao M eoo ocoe coppoa x aay oy (0)=( (0),..., (0)). Bc 1 M pcocoeoc ocoe oy (0)=(1(0),...,M(0)), a ae cpe pcocoeoc o oy M (0) = (0) / M.

h h= a 2. Bop poee cpea e oep ox a ey t=t+1. Opee cyay epeey Randt a oece M={1,, M}, aa epo oc ae oo h M poopoao h (t) /(t).

Cea oo cae Randt c peya i(t), oo p opee oep epoo poe (t). oop c i(t) ae opee oep opoo poe i (t).

a 3. oppoae eoa ooa C epooc Pc poec a eoa pax po ee poccoep. Bpa c epooc 0,5 ooo peya o coxpa eo a (t). oceoaeo pe (t) oepaop epc (c epooc Pi), a ae ya (c epooc Pm). oye eo ooa coxpa a (t).

a 4. Oop oco a poae aea ee ooo C pao epooc 1/ M cex h M opee cya opao oep j(t) oco oy, oopy aec o oo. Oo eyy oy (t) ye ae (t) i(t) a (t).

a 5. Opeeee pcocoeoc ooa Bc pcocoeoc ooa E( (t)). Oo a ee cpee pcocoeoc (t) eop pcocoeo ce (t).

a 6. epe ay 2.

peee a ocex yx cpaax coopae c ocaoo o, o e opaa ay ay c opooa e pax cpae oopa a cpeae poae, opo opa ecoc oec eeecx oepaopo. a ocee 10 e o ce pe oe opo oe cceoa o apae, ye pae oa pc, a a e oe oxo, ycoepecye ocoy cocooc A.

ocoy aaece eo cceoa yco copoc cxooc aaac o oac a cepee poe, a papaoaa ea ccea ecox aa (benchmark), peaaex oocey eoc pax epc aopa. Ha x e o ocyeceo cpaee A c py exa oaaa yaoc eo cocooce pee aa oao oa . Oao oe cceoae oepa, o p ce ee pocoe aca A pey aex yc p acpoe o opey aay, ae o cpae c o yxy o o eoa (a aae oo cpae). Ba cpoe yac, pee ceo, epooc pee eeecx oepaopo, oaae cyeceoe e a caacpoaoc poecco oopa eoc. Heoope pyooca peoey apopo pa e x cpaeecx apaepo a ypoe Pc = 0,9;

Pi =0,01;

Pm =0,1.

o-oy, ceoao oop e o cooc pee A ooe, a o aeaoc ypoe cooc aopa peaeo a a. e poe aaa, e eccceee caoc pae yx pe c opoo eoo, acpoo epooce . . B peee, ec eea y ee ece cpey cceyeo o ac, peee A epe c cc, a a o oa e o ae peee cpee poe ac. C pyo copo, e caa, o e ao aa, oopy e o e pe c oo A. coae, ax aa ocaoo, p o-y oe a ce ceoc pecaa, oa o cepac.

e e poxo ceo paa payo cooc aa? Haep oe, ce opeeec e, a pecypca pacoaae epco ao PC386 pacepo T64000. aco aa oee opee e pep aaa oa peea a oy o pao oepa ypo Pentium-100.

a o, a ceo e A peao poy epe pa ax cex oooce. poeypo paoy oo eo cpo cxoxc epc oo pocppoa o-cxeo, pecaeo a pc. 6.

Pc. 6. Pepoy a Xoaa Ha epo ae cya opao eeppye cxoy oy apx xpooco. eopye ae epeex ooo eeceoy y.

p oo aeaeco oe opeee ec pcoco eoc aoo pee acoc o eo e yopoa e oy. Bce cpe o oy pcocoeoc.

Opac a ee, aaae epooc, c ao aa oco, oaa a pcocoeoc e cpeeo ypo, oe ca poee.

p o aoo poe ec e oooc - o poco copoa ceyee ooee, o oepyc oec eeecx oepaopo poecce eeppoa xpooco ooa.

aee oeae pcocoeoc ooa, , ecy aao opao, oceeo aoe oy ceyeo ooe.

epe M ao ooe ooee oaaec coppoa. co, o ocoy oo oyeo o yx poee, o eo pcocoeoc oa ae coo. He ae coe, o, opy cao pcocoe oco oooc ca poee a ooco, yeae , o pae epe, e yeae cpe o oy pcocoeoc.

Paoy aopa pepaae p oce oye coco aaa, epyeoy o ca pa oy caaa ooe oao, a ae - oy. poccoep a exa eoc epe ax ycox co cy - p cpea ex po ee ooo e e ye oac o ooo x. Mya epc yy o-peey opoa ooco, ecpy ce oe oe o ocooo pocpaca, o eyceo - ye aeoo pee e, oo e coy ae cyc po eoe po.

coae, o oa (a cee aaec co cpypoax ecox aa) e oe c yepeoc yepa, o aeoe peee pecae coo oa cpey. eo ecoe eoecoe poee oy ec eoxo , o e ocao pao yceoc oca. Oo oo c eecye, o aoo cpey ae, o eo e oop o o, ao eo xapaep. Te e eee, a e ocaec eo pyoo, a oocoac ocy peyao. B poo cyae ye oopo ayc aay aee a oee aopoe pae co , e a ya o coeo oy. o eoopa p oo coea cyax aopo peee oe oaac o ee peae.

2. CCCTBEHHE HEPOHHE CET Ce epoo, opaya eoeec o, pecae coo cooey oecy, cyeceo apaey ccey opao opa. Oa cocoa opaoa co epo a opao, o peaoa ocpe opaa, eo pacoae o oo pa cpee, e aa yy pee ca copee o epa. Ta pacoae aooo a pocxo oe eoea a 100120 c, o pe a oepy oo eoxo y ae ac.

Ceo, a 40 e aa, ecoeo o, o o paoae oee eo pao py opao, e a cea aa, coaa eoeo. eo o a ee cox e oyae apae pao yex o coa cceoa c yccex epox cee.

2.1. o o a cy epy eeoc Bopoc, ec o opa e-o poe a, epe o payc ocoo aeao Pee eapo (15961650). eap epo oea exa, oa eep a e pcy papaoe e o e eecx e. Paa o oe a eoea Bceey oya oa oo ep oo. o oo ap pecae, o ao ppo, aa o ae ae aaa ee ae, c ee ee. Bceea pecaac a opaa oopaee co acaa acoo exa, coa pee ee Be Topo. Ha oo ypoe pecae axo ooee exaecx eeyax, coaaex oaee aox oo Epo. ac c yyo, oa aex, o ae oceee, cyao acyx a cpy pyy pa e e o oc c ec eoea oxox exa cecx epax?

o eapy, ce ec, a y eoea, a y ox, c oeo a co eeo pa. Be papae oyae o opao yc. Boyee epeaec o, oop apa e eo a cooecye ycy. Ta opao, oyee opa o yc po copae ycy, o ec pa pea a e papae. ep papae a opaaec opao epo cceo epe ycy ooo. Tep peec (o a. re flex opaee, oce, oec) epe aao eo x paccye x eapa.

popecc oa exao ax pea ocy e coo oee a oax c o, y oopx yae o.

Ooo 1750 oa oac ye B oaa, o ae e opopyc c oo. O oapy, o oeaea ya oepae o o ya, o ec ya y ee oopeeo ooo co o, oa epecae peapoa a yo.

ae oo ye eycox peeco oye o pe payco Peo. ep aa, py pa eoopx ee epo, cceoa, coxpaec coae oce opoa.

O pe oy, o e, o cyopo oeaeoo ea c copee peeop ec. pae cceoa pooe ee cceoaee Teoopo oo, oop o cep cepeo a ooa aex pecyo. a e ocaoo ce oye e poo aoo ea eee epo y oce oeaa.

accece ycoe peec ep oca aae XX ea .. ao, cpay e ycope x pocey opy oyeu, aoap oopo accopyc a co. p acceco yco o peece cxoo ee papae, aae yco , oopo coeaec c cooe papaee, a ae eyco. Baae yco papae ae ca oe ooe aoo;

eyco papae poo pye ypy pea e aoo o o peapeoo oye . B peyae pao ycooo peeca yco papae popeae cocooc a o c, o o oe. oo, o opaoaac ycoa c, o ec pooo oyee, yc o papae oe oppepoa c eyco, peecy ey a eoop pec poeyo pee.

o aaa eyeo coe oco epoooo epo, o appy peeca poeae epe cyeceo epepe epo a. oe caca, e ey epoa, ocpeco oopo o o aoecoa, ec cpaeo o.

cceoa, ycaaae ae caca eo po epo aoc, oe a pyee eo ac ooo cpo apo eppoo (18571952). Paoa eppoa apa aa oeeec ypoe, a e epoooec. Te e e ee, aaa peeopx ec coa, oe oe o cye paaa ocoe p pao caca.

ep oa pacp cepe aaoeco opaa oa oo oec cceoa Cao Pao--axa (1911). p e eo opac epoo co cepepa, papaoa paee a o o (cepepo paeo poae epo, o e po ae pye e oa), axa ye, o o ee eoy apxeypy. poe epoo coca oa xo paoopae ae e, oe oope y yacye peapa ox poeccax. axa oca epo a opoae e, oope oya ca co paee opoca, oy aae epo, a oca opa epaee opoca, aa acoa (c. pc. 7).

Pc. 7. Aca epx eo oooo oa eoea Opaae o o ooo opooe paoopae epoo o ope ea, paeeoc epo ac e aco a. axa pa ey ea c opo acoa, a oecy c coce epoa, ea c aco a, poepyc pye yac oa.

Hecop a pa cpoe, ce epo poo opa oaoo. opa epeaec o acoa e opox ep ecx yco, a aaex oeao ec, aya o opx cocae ooo 100 B, a eoc 1 c. Booee yco ca c ee ooeo apex oo ap epe oepxocy eoy epay eeoo oc yp e, ee oay.

oepa ap eeoo pocpace pepo 10 pa oe eo ypeoo oepa. B coco oo oep aec pacepaa paoc oeao ooo 70 B. p o o ap poa ey eeo, a a ocy ya x opae coca epa. eca xeca cy , eopya epay, yeae ee poaeoc oo ap. oo ap yp e ee cee eopye epay, ea ee ce oee poaeo.

oa ocaec eoopoe pecoe aee oeaa, a aeoe opoo, ooea opaa c po peeepa ca, peyae oopx a paoc oeao e ec a poooo, o ec ypeee coepoe e cao c ape ooeo o ooe ee cpee. p eo epe 1 c poaeoc epa ap aae pacepa oea opaaec coey ae coco oo 70 B. oce aoo aoo pa epo ocaec a e coo cey pepa, o ec apea poaeoc e pa o epo e oe ec. o ae pee acoe e epa yco e oee 200 pa ceyy.

Xo aco oxo a pooa, yc o poo ae. x aee xapaepc eae: copoee o oc co eo, a epaoe copoee co ao. ooe a p pacceaec ye epe 12 . o peooea pacco, co cae oa ecoo caepo, yc o peeep poac. Heoxooc oopo yca o opaae ac ay copoc pacpocpae epoo yca o acoy o /c.

C ey epoa oocpeyc xec epeaa epoeaopa ec ooa opoco epoo cacax. oa oea ec ocae ooa acoa, oe y eaopa xo ypeox aex ypo, e o xpac, caecy e pocpaco po 20 e y epaa pecaeco occaeco eo. oa oyee ocae a, aaec ooppoaoe eee oey epoeaopa.

Bcooec oey epoeaopa cac c peeo pa occaeco epae, o ee ee poaeoc. e ye oya, ec eee apa pae epa oea opoy eeppoa yca. Ec e epaa ca pyec a ypoe oeaa oo, e ye opo.

a cac ae eae e a aoc aco a epoa. o ycaoac ecoc xoa, a epo oe epepo eppoa o 1000 caecx xoo.

Ee aae ea epoooa caa ca ceo aa po caco oye. Ca oa, poxo epe x, oy pa o cee ycac ocac. Opaae a ce ae ao a. Mo oopoeoo o pocoo eoea coepa pepo oaooe oeco epoo. Ho oo o pocoo e oea oaec yopoeoc eepox caecx c e. o-oy, oyee oa ec poecc ee apxeyp epoo ce, copooae acpoo caco.

2.2. Caoee pae HC Haoee e pecaec ceyee opeeee HC a aao a, aoe [6]:

cyccmea epoa cem mo cyecmeo napa eo pacnpeee npoeccop, omop oaaem cnocoo cm coxpaeu u penpeemauu onmoo au. Oa cxoa c oo yx acnemax:

1. aue npuopemaemc cem npoecce oyeu;

2. coxpaeu au ucnoymc cu eepox co eueu, aaee mae cuanmuecuu ecau.

cop HC aaec 1943, oa Maao c peo oe opoooo oecoo epoa oaa, o a y, oopa oe cea a epoo-ceo ae, oe ae cea ce epoo [7]. Ca xi, o cyae a xo epoa, yoac a ecoe oe wi (caece eca). aee o cypyc, peypy ca, cy a ey cee w n S = xi + w0, (2) w i i= oaec a xo oa, peayeo aaoy y epoa.

Pc. 8. Moe epoa Tpaoo aaoa y ee cyea , o ec ca a xoe epoa y oec oa, oa cyapoe xooe oece peae eoopoe pecoe aee.

Pc. 9. T aaox y epoo Xe [8], ya eoe exa eeoc oa, copy poa pao oye, oopoe yeae cy c ey pe- occaec epoa, ec aoc oox coaae o pe e.

pya oe oye paax oee pao apxeyp ce , aao epepoo, a peoea yceo peea oepoa pao peoo paa Poeao [9].

B coe cao poco epc ooco epepo (c. pc. 10) pecae coo ce c o xo, o xo o oee ype , a oop, cp co epoo. Oe epo cex oocox epepoo ec poapae oc ce, xapaepyac epeae opa o xooo co epe K cpx coe xooy co. B caapo ooo, ye ( i coe k, (k=1,...,K+1) coeec ocpeco eco wijk ) co ce j y a peyeo co k1. ec k=0 k=K+1 ooaa, cooece o, xoo xoo co.

Pc. 10. Cxea poapaeo coo HC Mopoae epc oy e pe c ey ece co, c peeax ooo co, xaoe c ey co eco peypx.

Bxoo co epepoa cy pea pepac xox cao a epo cpoo co. B cpx cox pocxo ocooe eeoe peopaoae opa, a xoo co ocyece cyepo eex cao oceeo cpx coe. B aece eeoc y cpoo co coy e pepyee coae y f (S)= (3) 1+ e-S o oyee epepoa oa eeapae poecc ee ae eco ecox caecx ce, epao oope o ex op, oa ce e popee eoxoe coca.

B ocoe oye e cooae pepoox ax, oe ex ao (c. pc. 11).

Pc. 11. opopyeoe oyee HC a ao X,D ae ce eop ecx xox cao ce X = (X1, X2,, XV ) cooecy ey eop eae x xox cao D=(D1,D2,,DZ). B poecce oye a xo HC oceoaeo oac ae pepoooo aopa a oo ={X,D,q = 1,Q}, oce eo cec oa ey ae q c Y = (Y1,Y2,...,YZ ) eae xoa ce e = Yq - Dq. (4) ec o opo oo oa eoo paccoe ey e opa Y D.

aee, c oo opeeeoo paa aopa pocxo aa oa acpoex apaepo ce, o a oa yeaac. poecc oopec o oce ce cocooc o eae peopaoa xo-xo, aaoo e o e pepoo aopo aoo.

aoap oye ce popeae cocooc pao pea poa e oo a ao, peee poecce pepo, o ae xopoo cpac c py aopa ax oycoo pocpaca xoo, oope oa oa e ea paee. B o cce oop, o HC oaae coco ooe (generalization).

Oa ooe, cea ea eco a xoe ce, ee e cocae. epa x oycoea eocao aeco apoca, oeo ce oex paepo. Bopa aa eooo opa, peeo ce poecce oye, -a opaeoo oea oyae op.

Poeaa ca ecox caecx ce eac acoc o oo, acoo oo xo epepoa coaa c xo aoo, cooec co cey pao oye. Be ca ce yeuuamc, ecu xoo cua, copupoa npuu au epoo, cuo ca, u yeamc, ecu o cuo co u. Oao, o pocoe pao a o peo o o poapae ce e cpx coe.

Hecoo oe Mc eep o yo aa ceo ooc oocooo epepoa.

e x coeco epcepo [10], peaaeo ec ocpy a eop epox cee, ox oecypaa pe ypae epeca epo ce. aa oc, o ec ce e oy peaoa ae XOR-y (oeca y caee Ȼ, oya c eo py aopo [10] cayc eca p cceoa cpaeo eoc pepoo Aop opaoo pacpocpae o a 1. aa eco cee.

( k Beca wijk ) cee wi(0 ) o cex cox aac cya opa o a aee e, apep, epae o 1 o +1.

a 2. pecaee ooo xooo eopa X cooecyeo eaeoo xooo eopa D.

a 3. po poxo: pace aecoo xoa.

Bcee xoa Yi(k ) i-o ya k- cpo coe, k=1,...,K, Yi xoo coe:

Hk- k ( Yi(k ) = f wi(0 ) + wijk )Yj(k -1)(k = 1,..., K), e Yj(0) = X, j j= H K K +1) Yi = f wi0 + w( Yj(K ).

ij j= ec Hk oeco yo k- cpo coe.

a 4. Opa poxo: aaa eco opoo.

cooae peypcoo aopa, aaeoc a xo x yax opaaeoc epoy cpoy co:

( ( ( wijk )(t +1)= wijk )(t)+ ik )Yj(k -1)(k = 1,..., K +1) ( k=K+1 e ik ), oca oy, ece:

(K i +1) = (Di -Yi )Yi(1-Yi ) eo oo peypco oca cex pyx cyae:

( k ik ) = Yi(k )(1-Yi(k ))(jk +1)w(ji +1)(k = 1,..., K).

j Oe, o e Yi(k )(1-Yi(k )) ec pooo coa o y ooceo ee apyea. Ec coyec pya opooa y, o e eoxoo e. Oya apaep oo paec epae o 0 o +1.

a 5. oopee o aa 2.

x poeyp), x cee cocooc co opae.

Bxo oo ooe oaee cpx coe c ee epoa ece oa, oao e o coc, a acpo eca y ao ce.

Haco popecc ocy oce oo, a Pyexap, Xo Bc 1986 oceoaeo epeop Aop Opa oo Pacpocpae o (AOP) [11, 12], epe oca Bepo co 1974 oy [13].

eco ae co pao oocpcx yex [14,15], ea co oopeeo c Pyexapo peox oe AOP Aop oceoo yopoa oye epo o ce.Xo AOP pacce ecc o oooc oye oocox cee, o, e e eee, e ca cpyeo, oop oo pe opeo opoc cea epox cee oay oa cpyyp apaepo ce. aa aax apaepo ce ocyecec ec cya opao, a ca AOP, ec cace a eo coxaceco apoca , ec o coe cy e oee e oa eoo cy oo e apapye ooa poecca oye oe oaoo cpeya. Bece c e, e ae coe, o oa (4), coyea oe aeca HC, ec oocpeao ye apaepo ce, ooy oca ee ya peyec, cooeceo, oa eo.

Te e eee, c oee AOP epec epo ce coa opoc. He oppoa o a, o oy 80-x oo oa cya pe ay cyeceo eac o cpae c 60- popecc papaoe epcoax oepo cyece o pay pa ceoo cepepoa, aaac pa cex eoo oepoa. cyccee epoe ce ca oc acco yeee epe cox ooo poa cae pae aye c.

ocee 10 e oaeoac y co, e oo ee ee aeo cceoa. epoe x oee RBF-cee, oaxc oe poco, e coepae peypc, a cpoe [16]. Bopoe peee A pepo ce pooo apxeyp, coepae e oa aaox y epoo cpoo co [17].

ooe ae yeoc ae oaaecy yepcaoc epox cee pee aa apoca pooo y c o cee ooc. B [1819] o ceao cee epe pooo a c coa aao y, [20] RBF-cee.

Paccop poeypy pepo RBF-ce (c. Pc.12), ocyec e apoca y, aao eo e aopo a oo, a oa ocaa [16].

yc V oeco xoo ce, H oeco epoo cpo o co, Z oeco xoo ce.

peoo, o paep Q aopa pepoox aoo e co e o ao paee ocaoo papeeo po cpace xox cao ce X=(X1, X2, , XV).

Pc. 12. acceca RBF-ce Cem xapamepuyemc mpe ocoeocmu: 1) eucme cpm co;

2) moo epo cpmoo co uem euey amuauoy yu;

3) cuanmuecue eca cex epoo cp moo co pa euue.

Bee ceye ooae:

c = (c1,c2,...,cV ) eop oopa epa aaoo y e poa cpoo co;

pa oa aaoo y j-o epoa cpoo co;

j V (X - -c ) 2 j j j= f (X,c)= e- X-c 2 = e paao-cepa aa oa y epoa cpoo co;

wij ec c ey i- epoo xooo co j- epoo cp oo co.

Ce oyee ce ae ce p aa, oeee ce y aopo.

Aop cea RBF-ce 1. Bepe paep cpoo co H pa oecy pepoo x aoo Q. Caece eca epoo cpoo co p e pa 1.

2. Paec ep aaox y epoo cpoo co oax pocpaca xox cao ce, omope xom aop mpeupoox aoo : c = X, j = 1, H.

j j 3. Bepe p oo aaox y epoo cpoo co, j = 1, H ocmamoo o, o a, o o e aa j ac py a pya pocpace xox cao ce.

4. Opee eca epoo xooo co ce wij, i=1, Z j = 1, H.

oo pe ce ec aop pepoox aoo. B xo i-o epoa xooo co p-o aoa ye pae:

Yi = wi1 f (X,c1)+ wi2 f (X,c2)+... + wiH f (X,cH )= p p p (5) = wi1 f (X,X1)+ wi2 f (X,X2)+... + wiH f (X,XH )= Di.

p p p Pacca o ypaee cex xoo ce cex aoo, o y ceyee ypaee apo ope:

wT = D, (6) f11... f1H f21... f2H e = epooa apa,.....

fH1... fHH fij = f (Xi,X );

j w11... w1Z w =... apa xox caecx eco;

wH1... wHZ D11... D1Z D =... apa xox aoo.

DH1... DHZ Peee wT = -1D (7) ac a coe ae xox caecx eco, oece ae poxoee epooo oepxoc epe pe pooe ao pocpace xox cao ce.

Oa apoca oax xooo pocpaca, e coa ax c epa aaox y, ac o oo, acoo yao pa p oo, aeao oeco pepoox aoo cooc yoaoo peopaoa.

coae, poeypa acpo caecx eco ec a eo e eceo e ocee poeo, cpeaec p oy e ce. ya a oee co opoco ocaec oppoae aopa pepoox aoo, aeao ocaeo paccap aeoe yoaoe peopaoae. o poee ee epe c ceyx paeax.

3. A+HC = HOBA APAMA B PABEH accece eo cea cce ypae apyc a xopo o pao aapae epo-epeaoo cce, coa o Hoo ooo pexco e aa. Hepoe ce peca coo aepaoe, cyecyee ceo ecoo e, apaee eop aoaecoo ypae, peaaee o coco opae peopaoa eceoc, oopo oo oapy cxoe, pae ep c acceco apao.

pooee epeax ypae eop aoae coo peypoa ca c ea . . Macea (18311879) . A. Bepacoo (18311895) [21]. eo o, o c oea o cpoe . ao apoo a c epoe peyopo copo c pae (1784) o cepe opo oo pooo ea a a-o eop peypoa poco ocycoaa. Oao, c poco ooc apox a yacc aap, ae ox aec o peypoa. o Mace Bepac o oopee o eaco py o pya c a eopeec aa o cc e. Oa cooa eop ax oea, epyy aao o . . apaa*. aca ypae apaa apoo a pa x aoe epeee epe oye ooceo eoo px paoecx ae, Mace Bepac eapoa ypae ooceo oye cceoa yco ycooc coco paoec.

Ta aac ep a pa eop aoaecoo ypae , a pacea accecx eoo aaa. pooac o o oo oo o 40-x oo aeo ea, o coepaeo ooe e oac o paoopae oxoo. cceoae yco oc, a ae aeca epexox poecco pooa ocaac oco aaa ceo oo epoa.

Tep epoypaee epe oc paoax Bepoca ye 1976 oy, oao peay po o epe HC cepy ypae * ecx aa cpa pao Hapep c coaopa (1989), acoc, [22].

a, cceax ypae HC oy pec e:

epoopoepo;

epoyopo, pyx aecoe oeee oea ypae eo ocax eo oee xapaepc , pyo oaec aeaecoy oepoa (ap ep, poe e . .).

epoe, o oac cea caocoeo, ce e poopoepa a ae pexcoo poapaeo ce [23].

B aece oea ypae pa epooe oeae oe eo opoo opa c epeaoo ye a k W =, (8) T s2 + 2Ts + a aece e ypae oaee oeaeoc oea p cyeao xoo oec (ae ocox oeo k=1;

T=0,5;

=0,1 ypae (8) oopa a, o oeae e coca y oea pae ocaoo oeo - c.

pc. 13).

a) ) Pc. 13. epexoa xapaepca (a) AX () ecooo aecoo oea ypae Oacac peepoo paaa a aao ae cceoa ( cce oaa o paox cxeoexecx pee -peyopo), oa a xo epoopoepa ca o, a ae eo pooy epa, aec, o ce ae ee e ee oe x a caaex.

Pc. 14. ep o c epoopoepo, apocpy oe -peyopa Cmpymypa epoompoepa: mpu pempacupyux ya o xo o coe, empe cpmx ya c cuouau amuauou yuu u ou xoo. Ha xoe epo noaemc paocm ey xo oecmue ur u xoo oema x1, ee umepa u npouoa, a a xoe cemu opupyemc ynpaee oecm ue u.

B aece poeyp pepo ce cooa A. A op opaoo pacpocpae o ae ooe o e, o o peye opa o oe a eopo coe HC.

oye ao opa cxee oye eoxoo pey cope opae epoyop oea, po oopoo coc peopaoa o a xoe oea xoo ca a xoe epoopoepa, o cyeceo ycoe poeypy pepo.

Pc. 15. peee A acpo apaepo epoopoepa eeec e aop acpaae apaep epoopoepa e o oe ypae u, a o oe xoe oea, cpaa eo c xoo aoo oe. oce ooae cee a pe cae o eaeo oee oea, o ec pae peo y e po, o oea pepoox aoo poeype pe po.

cxoa oy 100 xpooco eeppoaac cya o pao. a 21 acpoex apaepo ce opoac ec a, a opao, xpoocoa, opya epoopoep e o, pecaa coo 210-papy oceoaeoc oe e . p o, o aao ee aoo apaepo pocpa ce 21 p o 1 o 1, ecpapoe opoae oecea o cpeoc ee apaepa e xye 0,002.

oce eopoa xpooco eopa epeex oeaac cocooc aoo apaa ce ceoa aoo oe. poep a ocyecac ye oceoaeo oa a ypa xo epoopoepa eoo ooeoo, yeoo eoo opaeoo xooo oec ce cpeeapao o xoo oopa oea a peeo epae o 10 ce y. peapeo epeaoa y oea ypae peo paoaac ccey ooex epeax ypae ope o x1 = x2;

(9) = (- 2Tx2 - x1 + kU )/ T.

x eppoae cce ocyecoc c oco ao, pa 0,01 ce. Cyapa oa o ce pe epexo poecca paac aece ep eyaoc ocpy cooaac aee aece oeceoo eca papoa ocoe o y.

pe epexox poecco yeo apaa oy a pax aax oca pecae a pc. 16.

Pc. 16. ye eocppyex oye epoopoepo epexoe poecc a xoe oea ypae pae o e pao A (aae ea cyea): pa 1 a aa oy, 2 oce 2000 ooe, 3 oce 4000 oo e, 4 oce 5000 ooe.

a o oo pcya, o epe pao aopa pee epe po yyac. Beop epeex, ae 5000 ooe, oeceae oe yoeopeoe peee ocaeo aa.

Pc. 17 cppye oeee oea e oo a pepoox aoax, o p poeyox aex ay xooo aa , oopoe oepae yepcaoc apocpyx coc epox cee.

Pc. 17. epexoe poecc CA c oye epoopoepo p a yax xooo aa 1, 0,5;

0;

0,5;

1 (cy epx) Booyec ocy peyao, yco aay. Ha xo opoepa ca oaa e ca o, eo pooy epa, a poco xoy oopay oea a eye pey e aax (eo a aepa ca - c. pc. 18).

Pc. 18. Hoa cxea opaa opax ce o [22] oepac ee aoa oe, oopy coppoa eep a peoae AX aaa ypae [24]. Bo pe a ca oe oaae AX c oeo pae peoac o p acoe 0,32 , epoopoep oe ayc, c oo copo, o paa peoace oea oea, a c pyo copo, yc a ayy yex oea pe- ocpeoaco oac x, e oc p o c a ey xo xo oea , a ae oa oea oea p acoax, peax acoy cpea eaeo AX (pa 2 a pc. 19).

Ha o pa opoepa o a paa pexcoa ce 3-10-1, . e. c oeco epoo cpo coe pa 10. ope ee pooc ce a ee xo oaac cpoa cep apoecx oea pao ay ( aaoe 0,1-1) c acoa 0,16;

0,48;

0,80;

1,11 1,59 .

epaa oa o ce eco epexo poecca, po oeoc oopx, a paee, cocaa 10 cey, paac aece ep yceoc ypae.

Peya cea oaac ya. opoep, apaep oo poo pecae poe 1, cpac c ooe a eo aaa.

aeca AX epoceeo cce ypae pecaea a pc. 19. Oa ocpoea ye a epepo cepe aco, ae aco pepoox cao. o-oy, -a eocaooo paepa cpoo co ce, cepoaa AX a yace 0,61 aeo oaec o aoo. Oao oe, oyee pe ya ceecye, o cocooc ce ooe oe c ooac p cee epoopoepa acoo oac.

Pc. 19. Cepoaa (pa 1) eaea (pa 2) AX cce ypae pecaee pep yeeo oaa cocooc o a yx ox cex exoo eeecx Ao po cyccex Hepox Cee caocoeo pea a ay ypae aec oeo paax ooo apa . oeo, a oy opa, cocac a pyoc cep epoa eocpeceo c oeo p acpoe caecx eco epoopoepa, o p coe ooc e aea eco oe oea, a a, e acoa oce o oco apa. Te oee, o pecaee pep poe ceecy oy oo ooa. Oao o e a, ceye paee poeocppye, o e e exoo coco cao coeo cepoa aeaecy oe aecoo oea oo a ocoa a eo epexox xapaepc.

4. A+HC = HOBA APAMA B MOEPOBAH uua npecmaem coo pauayc oue cy cucmey eu, oco omopo oo noyum e eeue ux auu-uo uymuu emoau u nepeumx onmo, a u coo co. Ooco aue (ucmuocm) cucme ocoao a oaamecme npueuocmu meaux u ee meope oacmu y cmeoo onma, npue coomoeu ey noceuu u nepu oo nom u umyumuo. ou npoucxoum anpaeuu ce yeuuaec npocmom ouecux oco. oe moo, mo npuuumc mo eu, o peumc npuam, mo oueca oc oa ce oe u oe yaemc om ax onma, u ce nym om oco meau u ux meopea, oppeupyu c ycmeu onmau, cmaoumc ce oee mpy u u.

A. e. a peaoc.

Hepoe ce epeae ypae oocc pa e oepoa, ec a p yaea.

epa e, p, ocxo paoa Apcoe eoapo a B, opa, yaea, oaa co poee ae, aeyc peaoa oepoa eooece pecae aoa o pe e yee o ye. epeae ypae o ca yy oea, o pe a epoa ce oaaec co co ao, a oo ocpoec aecoe oeee o ea cyax, oope e ec. Aaeca opa pecae a e eocya, oa cocoa ao oo oo opee pece acoc, xo pe ec e, oeo, e o aoa ax ao e.

acceco apa xapaepo o, o cey aeae co oe oea poecca oaeo peecye aa aa a, eee oopo poecc yopeo eoopyec a ee ape e, aoe oopx oepaec ae aeoy c ceoa. Caaa cea apyec oe cepe, oopo cceyea cocaa poecca oocoec o ocax, a ae, o epe peax oooce, o cepe oec. a peya, aec peeo poca, ooeo ea, oe e c ece oco oeo, oopoo o yco poee cepea, o ax-o pex yco opaec popaa eca eppea. Ec ay-o cocay co e y e yaec, a ee epeo poco apa aa. Haoe, ocyec ce oo oe, caa acx ex oee a po ey ap y poecca, paa, c ooopo, o oe, eceo c, oy ee.

pepo ax poeyp oo pec oeco, e pea ae opac o peeo poc papo aape o ecaopo a ayy c oy cepeo.

a eco, poecc papa ocaec epea ypa ee t di L + iR + (10) idt = U dt C Xo e copaa ceo yx yo aape ay, eo ypae p. Bce o coepa ocoe oe.

oe p oe R, ec a aoe copoee ay , pecae coo e o oe, a oe poopoao c ey apee a aye oo, p yco oo, oeo, o aya aaa o coa nocmooo ape (oe cepe 1). oe p pooo oa L cocea yoc ay ee ooee pyoy cepey: ec aa ayy o coa apouecu ueeoc ape ocaoo coo aco (oe cepe 2), o po eee pyoo aco oea coceo yoc a y o ac a oe poopoaoc ey ay a oa ape a aax ay. Haoe, eoc oeca opa C oe yaec opeee oec oa a oe, o-a, aoo-o oeoo cepea 3, cpaeo c oa ape a oaax oecaopa.

Co ayac, acoo ay peooe ooe ococa cex x oeo. M ap aa a ypee eoee pooe, yco oxae ay, oep epe oecaopa. epee eyex aopo pacpc, ec oe ayy c ee cepeo, oop e oo coe a yoc, o opoe ooee oooc yee eox oep ccee (o xpex oo, a epeaae . .).

Heo oo oe (10) e. Bc pa, o yec o o aop, a pec ocpypoa o cepe, peaa o e e, opee eppepoa ee apaep. p ocyc oe e coe oca e, ceoaeo, ao ypae u, ocaeo poecc, yem aeoo eno.

Te e eee, o e eae a o ea o oe, oopa y ac ec. paa, oo a ce pao npuemc o cepe co ce e, oce eo oopa ae o eo a, o opeoc pecaa oee oa a ao. He ao, acoo oo aee ae o eo coay c e, o oyc acx cceoa.

M e oe oa, o o coay e, pcycye aoe, o a ce a ocycyx. a cece, a e oeo oya eoope ppae, ace, o oy, ee o oo, apep, ao aaoe oo pooc cepe co ce e. co, o epoaa oe y e ocoepa oo o aaoe, o p oe aec, o p pyx oax apaep oe ocayc pe.

B e e coco o epoceeoo oxoa? a, oay, oo o, o o aao e opayeae a aaa p ocpoe oe. Hepoe ce o cyeceo cumemuecu, a e aa ec oxo. oeo, ec ocaec oe aoa, ec c e oe coc apaepeco oa aoa, coc pypoaoo o acy aaox y epoo. Ho ec oo e epecye, aoy oeecoy oee oea cooe cye aoc ooo epoo ao ec cc po pea o cyae caece eca. aaa opypyec ce ce eo. cxo oo oe cceyec cpay eo, e oex cyax, a ex peax, oope ac epecy pa eco, yapo ooe.

Xo oe peoo, o epoa ce oe o co yoo cooe peopaoae xo-xo, apaee eooo pecaa, aa apxeypa ce (o ec aoa) oaec a ye pee epecye ac aa. ao aaox y epoo oe pa? aa cooc ce coo epoo ao cpo coe oecea peyey opaoy eoc ce? He oee opoc o oece opax ce, oxa ax ce, a e e x oeee ce e coe ca a .

a o, ceoe cepepoae ec a ceo e ece ae eoo oca oeo a o caee opoc.

Ceye oe, o epoceee oe, ce-a, co oa c o oo, o oo oa o aeaeco oe. He p ooy x aa yopa, o py aece xapa epc oea e oee oo. Cyecye x pyoe aa e peop (o acoo aoa to predict pecaa) oo oe e ecoeo, a a epoceee oe opepoa a o, o ye o eyey eco pey eopa coco oea pecaa eo ceye coco. B acoc o y pecaa paa ooaoe paocpoe pe op.

Ocooe oe ey coco o, o ooao pe op (c. pc. 20,a) oyae opa o eye coco oea o caoo oea, o ec o eco pa oey. ocoy p ao oxoe oa pecaa oae oo peeax ey eo aa, a e aaaec ae a yx ax aax, o cye ceo oae peoae ooc pecaa, e ypoae aay cea.

) a) Pc. 20. Oyee ooaooo (a) paocpooo () peopo o xo xo a oea aeo ox yc peye ce a aaeoo pao cpooo peopa (c. pc. 20,), oop oe pecaa oe ee oea a 1001000 ao oop oaaec pooe aoo oceyeo aa o coceoo pooa peyeo aa.

co, o ae ec oa pecaa a oo ae cpo o, a 100 ao oa oe opac o aoo peea, a oop ep ec aoe-o cxoco oee yopa c oeee oea ex e ycox.

Coxpa epoc paoy py ecoa paax o oo apa ee coce cpeca, oo po ee cea epoceex oee aecx oeo, oopy c xopoo apeoeoa ce ax aax coeae A+HC. o coxpa ey peeceoc c paee oye peyaa, coxpa aece aecoo oea epo oe eo opoo opa c e e ae oeo, o paee c epoopoepo.

Ha ep o [25], aepoe, e aa yopo. o cy ecy, ac ocpo epoy ce, oopa apocpo aa pae ac cce ypae (9). opeeeoc p, o ce ye pexcoo c oypae 3-8-2 (. e. c pe epoa o xoo coe, oce epoa cpo coe y cypy epoa xoo coe). Ha xo ce oaac xoo ca u, xoo ca a peye ae x1 eo po oa x2. Ha xoe ce oppoac epa opa pooa xooo caa x1 x2 (c. pc. 21).

Pc. 21. ep o cea yopa Cyece oe o opoepa o o, o aece a aox y epoo cpoo co e y cey eo a:

n - wi xi +w i= y = e, (11) oopa ac e po coao paao cepo y.

Ocoaa a ceo A pepooa poeypa aa ce paec e e a, o p cee epoopoepa. oy cocoa 100 apx xpooco. aa xpoocoa coepaa eo opoaa 50 apaepo ce. pooc aoo apa o ce poa pea oea a oyee oeaac ye oa a xo ce oceoaeo yx cao: eo cye , a ae yeoo caa. poeppoae ca c eop oo co HC cpaac c peyaa pee epeaoo ypae (9) ex e cyae. opeoc pao HC oeaac ye eppoa oo (4) oox cyae a epae pee [0, 10 c] oceyeo x cypoa.

Pc. 22 cppye peya y oa ce, ocy e 5000-y ooe.

Heocao yopa o o, o o xopoo e ce oo p ex oyex, p oopx poooc oyee. p oae a eo xo caa c poeyoo ayo (ey 0 1) eo oee e cyeceo oaoc o oee oea. oeo, oo o , ocaac paax pee eoo oye, aca eo ao oeee oea p x aex ay, o o y oaac a co cec. ooy opac eo e oye RBF-ce, pecaeo a cpae 38, paccope ee a oeaoo peeea a po oaoo ycope A.

) a) Pc. 22. epexoa y oea ypae o oopaa x1 (a) x2 () (coa pa) ee y ce (yp) Caa o cee, eoa xopoa e, o ooe oe cpo pe aay pepo ce xo epo pe. Bece c e, ee opaeoc ae pocaec aa.

Bo-epx, oa peye ooo oeca o aaec pyoo pya, ae ec pocpaco xox cao oaae o paep oc, a oeco xox aoo ao. Bce pao, o poaapoa, acoo aeo ao pacooe py o pya, o e oc c opo p oo aaox y.

Bo-opx, cya caoc oecypaae, ec aoo y ac co oo (cae, oee 1000 10000). Ha pae oe pyo caa apriori, ae eo o aoec c oeo oy ca coo xopox aoo ocpoe epoceeo oe oea. co oo oo - cya, oa ae o oee ao, aeoo xye, e oa ae oo.

oeo, paoa c ce, coepae 10000 epoo cpo coe, oo, o p yoo. a pyo pacca a cpoe pe ee ypae (7). Boae opoc a eceo y ce ao? Moe , cpe x ec ae, oope ocaoo oo xapaepy oe c oop oo co paoa? Ho a oa x opoa? Moo poco oaac o ac aoo, o paep ce ca yooap, o oa pcye oep ay opa o oee oy eoopoe eca eooe peee ocaeo aa.

oo, o c, ae ao c eceo e oa a oea, a ae oopeeo o ce epoyopa c ao cpyypo cpoo co, copoa eoy acpo caecx eco RBF-ce c A.

B papaoao poeype [26,27] a ao epa oca A ca ocoeo pae, ax oax pocpaca xox cao ce paec ep aaox y epoo cpoo co, aaae ao x py oa. Cooeceo, oe o peyeo cya ceoo oca, xpooco coepa eep o o opa o apaepax epoo cpoo co ce, o e o ca ecx ecax epoo xooo co.

Cxea opo xpooco pecaea a pc. 23.

Pc. 23. opoa apaepo cpoo co RBFce xpoocoe p eopoa xpooco eop epeex oopeeo c eo acpoex apaepo opepyec caa cpyypa cpoo co ce.

pc. 23 o, o aca paep cpoo co opae oeco oox ceeo, opayx xpoocoy. B ec eoc e, cy oo, o ye opopoa ey acpoex apaepo, o cea oyaec ecoo e.

Ha epo ae poepec pa oa aaox y epoo. Ec aoo-o x oa oaaec ee eoopo o opoooo ae (poo ax cepeax pa 0,01), o ao epo oycaec.

poe oo, o oo o ocooac eoo acpo caecx eco, pecaeo a cpae 38, eoxoo, o ep aaox y coaa c pepoo aoa pocpace xox cao ce. ooy e oe -opecoc opy aoo pepoooo aoa, pay 0,1. Ec ep, aopoa eye ceee xpooco, xo oy ax opecoce, o p aee acpoe ce coyec coo ecy pepoo ao. B poo cyae c opa , xpaac eye ceee, oppyec, aac cpo coe, apeeppoaa epoa c e e oepo, ocaec op o.

ce, coppoao peyae aaa eopa acpoex apaepo cpoo co, ucmc o (7) (a e opac, a p ceo oce) caece eca xox epoo.

Pepeeaoc aecoax oye ce aoo, o ec x cocooc aea coo ec ec o aoec c oeo, oeaec ye pee ce cex ecx aoo cypoae o y o cey peeoy aopy. oce, a pae, coyec p papoa oy oeax pee, oope ocoe a poae po ecy pyy oceyeo cpea.

Aop poeyp cea pecae a pc. 24.

poep eo ocooac peye ecoo a ae. Caaa ae oe oeo pepoox aoo, ceeppoa ee ocpeco pee cce ypae (9) p pa x coeax aax yco o xoo oopae oea ee pooo, a ae p pax aex ypaeo oec u. ae opeccpoa oey, c ee o pac ooee coaae ao. Ec e cea oo, p pee apoo ypae (7) oy oy poe -a oo, o epooa apa ye a ocoeo. Haoe, pcy cey, eo ceeppoa oy 100 apx xpoo co o o 1200 aa.

Pc. 24. opoaa poeypa pepo RBF-ce B peyae oa cpyyp apaepo HC a yaoc ocpo paocpo peop oea (eo apaep cpyypa oca poe 3), oop a epae o 30 cey (p e pepoooo epaa 10 c) eca oo pecaa oeee oea p apoecx ypax oecx aaoe ac o o 0 o 1,6 aye u o 1 o 1. eo, o cp co ce coepa ceo 8 (!) epoo, eo, pooa a pe e paccye, oo a, o 12000 aoo, oca x a cepe o ye pea oea, oo 8 oaa c a.

o ea peya, ooo, popae aecy a aa e, e o, o cyecy, peaae exa, oc e ooo ca, o oopo oop cxoo. O aac o opooo ca oo aoec c oeo, oy oe oay cpyypy, oopa oeppye o o oppye opa oea, oop oo cooa pee a a cycceoo eea acca oeo, aoc x coco, poopoa oee p pax cpaex ypae a aee.

oeo, ceye oe, o ce co coepeoo peopa a ooo oo pee ooo 50000 epa, o, copee, o opao, e eopao, a a yoae ocoeoc p pooo eea, ao ceye oec eoe pe oy e, e oy e epe cycceoy eey.

oy py co oy poeypy cea epoyopo, e co yepac o coaa poep a oa ooc eo ppo e a oeyao oe eeyao cce ypae. Bcox cepeax c e ac a ce oe a ceye opoc.

1. peoo, epoyop eceo ec e opao, cyecy paax ycooo coa, opo eoo cycce eeo. Ec o a, o epoo poep, ceo apepoa ye cepepo a c opaee eeo pa, oe ye ypa ca aec oeo. Ocyeco o?

2. Moo a aope pax pecae ocpo aay ccey, oopa caocoeo oa ya a ee oee, epecpaa co ypee pe cae, a oeo oe, paaa oy oa y cpae oec a eo?

3. ec coeae A+HC acoo o c eo ae, o oece eceo aae coca cce ypae ycox, oa xapaepc oea ec c eee pee ca epee opao?

pex opoco aoee co ac c pe, ooy o, e cye oe a eo yepeo, e co a ope ee oe a opo opoc.

oeae pyoc pee aa aaa c, pe e ceo, o, o aaa, xo e ec coo oa , eca e oaox ocaoo, a poecc oa oe cxoc co ce ea oca ocec . o ce eo o eo e opaec poecce oca cpeya a oy oeax pee, a oopo ocyecec oop. Ho oa cpey ae, oy oaaec poeo. Pee caoc oxo py a pya a e a o, ececeoe paoopae coaec oy epe oeay cocooc ocea ee cpee.

O pe, oop peec occaoe ocoo cocooc o oa peeepa oy (ec o ac y peeepa, coxpa xo ecoo ocoe capo oy , o, ye oaa eoxo pcocoeoc, cpa a oe oxo pcocoex ox eo po cepxo , ooo apaopa, py epe cox ooo c oy cee), o eo cycceoc oea, poe oo, e co, a ccea oa oaac, oa eo ceye eo pe.

a aec, a yaoc, ec e acea peooe y pyoc, o, o pae epe, cyeceo pay pa eo pao oox eoo. Bxo ae e ox eeecx oepaopax, a epo acceco ay ope pecae eeeco opa a eo, ope, acoao y ox opao.

5. CHOBA O EHETECX AOPTMAX oa oop e o aeoc o eo oo eop epeex aeae, ceoao ooop, o a aeoc ee cc oo oa, oa pe e o a ox opaax, o ec o opaax, oaax oap a opo xpooco. ao oocc aep, oopoc oe py e pocee opa, aae e cye oooo pa. Meoae, acoc, eoe, c o opaa. B pe ao e aoo ac (a cee oox eo cepaooo eeo oope c a o) ope coepc oo aop 23 xpooco. O oe ocac a, a eco, o oa, a pyo o aep. B oox oeax cyecy a aaee oooe xpooco, opye o e e eoece pa oaae, pe, oaoo cpyypo. Ta, ooco, aepco xpoocoax ee pae opy e a. Te e eee, e a peea ac o oo, ao ooe opoa e y ea poee. Oo, a peypyc ppoe ooe o aoc peeccoc ey ooo ea poe cx xpooco, y ooo e eoo e eep. Papaoa pa e eoeooece oe, o oopx peoaa e xa ooo opoa, cae aoc ea, axo eoc peecco coco. pye oe oyca, o oa ea oy po aoc oopeeo, o pao cee (o opoae).

ac o e a ao. B oe oo, e e ca epe co o aay occoa aooepoce, ecyx ppoe. M oe ycaaa co cocee ao, ooy o caa o y ac cyccea e ax ocox opae a o, a ax ox oyx yy oopoa ooe o aoc peeccoc eax ooca. Cyeceo pyoe, a eo ca p, a epeaec o acecy a eopyec eoece pa eeeca opa ocoe.

M p oy, o ao-y poe ocaec oo eceo oo pocpaca epeex, oopo ooao cooecye o-a oa oa pocpaca pepe. o p ypoe cooc pecae cooecye cocoy xpae eeeco opa y aox opao. o x opao ce aeee epecee oco opeeea a a yx oax oopeeo (ooca aepca xpooco), xo o ape cooecye o-peey oa oa pocpaca e oo. B poecce pao coe ooo e aa yxoea oco eeppye pe oy, oopa coep cee acy opa o oex poecx xpoocoax. Ho a oep oa ee e popeae cayc oco. Oco oae oo oa, oa c e y oy c pyo ao e oepe oo c pcy o ape eo, p o ae cocoe aoc ooo x eo oex xpoocoax pape o ey cyae eoxooc.

ae e ooe peyeca ae ooc? Haepoe, ax peyec ecoo, o ocaoc oo a oo, oco eo ao ac. poco aox oy eomunue coe poeue ocoe nomu eueo oaaem u eomunuecoe poeue (xo c ao epooc, pae peo cpeaec pae oepoa, oo peoo, o ooy oao y eoy oy cooecoa pae eo). Bo e pe, ox ocoe o pao e ec oae, o ec eo ecoe poee oy, ececeo aaeec co co aaa, o e ceecye o ypae e eeeco o paoopa.

o ee o oo ee 20-x oax ocao C. C. eepo, peo oe eeecoo pya, o oaeo oy opae, xpaec peeccx eax [28]. aco oy oy cpaa c acepo, oo ep xya oopoo, accopyea c ea, poc eoe, a a oo. oa e ac acepa cpa o aeo opa. Ho ocaoo cya ec, a acepa ec: o oep ec py oo, o e yoe.

Tpyo yepa, o pecaea e epc o o o oy oo ceye ooec eop, o c ee oo oc ocox epax oo, eo xoe [29,30].

aaa e epexye aa {RrDd}, oopo R r ooaa peeccy 1 peecc 0, a D d oay oa 0. Oopeeo copypoa paa ooo opoa p opeee cpecc eo o opaoao oco, pecaee a pc. 25 e a papee oo.

a oo, ap ooox eo eoe poec o, o oaae oee c pao aoc. e c pao a oc oa (D d), aoy poe o paee p aea, oae o e c pao peecc (R r), o ec eo eo coepae pa (1 0) paec o a e poecce eopoa ooo eoa oco caaa Pc. 25. Taa papee oo pao ape ooox eo Bxoau mauy mc oa u ee eoo cmoa uoa u ee epxe cmpou, a xoo - aeue eu, cmoe a nepe ceeuu cmpou, omopo npuaeum nepa u ynouauxc ee, u cmoa, omopoy npuaeum mopa apy cpoy, a ae epe o pe (c. ay 1) eop epee x. Oao, ooa cya, oa oa ea e oao p a aoc, o ecy pay opa. ec y ap o ooo D-d R-r (apaee e). Bo cyae ee p a aoc ooo x c e, o ea eooaoc p opeee eoa oco (cyecye ae cooecya eo p eeecx pepo aoa Mao, ocaa o exa opoa).

cooaoe a pao papee oa pao e coo oaec o oo, o peo Xoa 1971 [31] Bo 1995 [32]. B oe o x pa o ae cee ooceo pcocoeoc poee, ae ocac pac capaeo oco, ape ax oooo coxpa a e oee pcocoeoo poe, a ape accx oca ac c e eee yceoo a.

Pc.26. pep cooa a papee oo onpeeeocmu npumo, mo aema A npuaeaa pou me c oee cou ueco npucnocoeocmu oeo, aa ooopa ec eoopo ycyo aapy, opaeoy copeeo oyoo eeo. ae ec eoc e coepa opa o cee pcocoeoc poe . oce ec peoco oo, o e ao oco pooa coe cyecoae ooce. Ho, a ye oop, ycox cycceo o ooeo ce, a a ceecy a cepe, peoeoe pao papee oo o ca ycope cxooc A.

Pc. 27. poecc opaoa o ooa o o poee o acaec pa eeecx oepaopo, o o, coxpa e e aa, pope ooe coepae, oee peoe cxo ooec eppea. poccoep ox oyx oecye a eo e yx ocoe (o opeee Xoaa), a a oooe xpooco oo oco. epc ocaac ae oca oe pee, o e acaec ya, o oa ee eyee ae oe cocoe ea ae a oe pyoe, papeeoe aao. Ta, ya oe oaac epao, o ec e caaec eo e ooa, ec oa e ee cocoe aoc peeccoo ea (r-R aoopo). Oao o e a, o oa oa e po c yye ooce. ocaoo ypoaoy a opao ey cpec c peecc oooo, o paea paee eee pcocoeo oco, a o cpeccpyec eoe.

Ee oo ycoepecoae, o oopo oa o eo e o caao, acaoc opa oppoa aao oy. M o cya a: caaa eeppoa oy a aoy, a ae ypoa xpooco ocoe, opay oe eo (o cyecy, ocyec eoy ya). B ao cyae aa e ooe opoa e pa ao po, a a ooo e e ape xpooco oaa oaoo aoc ec ey coepaey opa. oce epoo e papoa oy o pcocoeoc ye ooac pecae o e ae papee oo oca.

oo, o poeocppoa e peyeca oo oy a aoo cocooc occaaa eeecoe paoopae ocyec oc exc ycox, oca cey ce cepe.

peoo, o aa oe paccapaeoo a epoa o coa c ea eee peea eeo y.

peoo ae, o peecy epo ca a coo e, o oe oy (a aoa, a o a) poc a eoec, a eoec opy aaa oopa pocpace oca 10. aoo oy o o aae, o o cex papax ao xpooco co o (c. pc 28).

Pc. 28. oy aox eoo, poac aae oopa Bo pe a oo o e peooee oe oeo, ec o cex ooox apax eo yy ouupoam o , eaco o oo, ay opa ecy peecce e (c.

pc 29).

Pc. 29. Bpoac oa oy a, eao eea y popeae ( ) f (x)= xi sin xi, - 500 xi 500. (12) i= o oa poo ecx ecox y, peoex eee. Oa ee oee 10 oo oax cpeyo, o a e y o ao oopa e oe xi = 420,9687, i = 1...10. (13) Pc. 30 cppye poecc oca cpeya oo a oo oy o y ep oopaa eopa epeex.

B aa oe pee t=0 oe oy ea aae oop a. Ec cxo coo eeecoo paoopa y po eo aoo oy ec ya, a epc poccoep oo yca ocec ee oec, o oo oy ep e a cpea po oe ecox o ax e eoe ooa. E eac a ce pe eccx oao eooa, aoap ey oy oe c po papacae ooo o cey ocooy pocpacy cceye eo.

500 ooe oe oy oca peo oao oo eoecoo paoopa, o ae poecc paaec y x opaoy.

Pc. 30. oc cpeya ecoo y (12) peapeo poe oo aoo oy: \ oa cpey;

a cyoa y;

oco oy.

He ye aa, o ceoc oy oepaec e eo, o ec oy ecye oop a poae. oco oo eeecoo aepaa, o ee, oe oecpoac eoc ooca, a oo ec, o oo a pax aax oca, oa pcocoeoc ocoe o ce oy ocaec o eeeee oopoo. Ho a oo oy oc oco cpeo oaec pcocoeoc, o oya peyeco pae ca poee a ooco, oxoee a x. ooco oyaec, o pae epe, eox aec epapx oy , ec aeee pcocoex ocoe a pa ceo c, opaye ooe ooee. oy caec ae oa cpey, pac oya e aeo coee, e aaa oopa, e oa eaa a coe eoo opaa.

Caaoe ocoeo epo aoo oy. Oa cpo cxoc, o ec e oopaaec xopo oa cpey, cy ecye pc, o oa acpe e. 3000 ooe aoa o y axo 4 yx cpeya (oa, 2 cyoax cycyoa) aae oeppoa ocoe x opeco cx. Ho 6000 ooe oa ooc poaec cyoao ye o 1o ee pe oopaa eopa epeex, xo o 2o oca oopaa axo oaoe peee.

Cap poeoo coco oaaec cuo e aoo oy. Oa e yceae ocaoo cceoa oco oe pocpaco pee, e oop a poae aae oa a coe coaee e a paoopae.

B ax cepeax oa oy oe e cea oa cpac c aae, o eaa o 8 cyax 10, o cyeceo peocxo peya, eocppyee aoo.

oa oy paoae eeee. 3000 ooe ye pocapac oee py ocoe, o e a oeo a y a oo. ae 6000 ooe oy oaaec epoe o, xo oa ee ooa e opecoc oaoo cpe ya o ce oopaa. Maee py coxpac cyo ax cpeyax. Ec peoo, o o oe coa po oe eee peea eeo y, oa, o cpae c ao o, oaec ye oooeo oepeo aaa.

Ceye pa, o ecoa y (12) oocc papy po cx A. To, o aoa oy e aa peee a 6000 o oe, ocec oo peao co ee aa yco oca. B ope oy 100 ocoe, ceeppoaa o opao, axo peee a 20002500 ooe o ce o opaa oe oo. oa oy cea popae e copoc, o pyx ycox oe coxpae paoococooc axo oee oe pee.

M eoopao yeac eoc ooo cocoa opoa, coy eo p cee epoceex ooe cce ypae. Xo pe, peyeec pee aa, opoco, ae co epoyopo epoopoepo yyoc, o ao a ocoa ocyc oee coo poee, a eo cey eeyao cce ypae.

6. BPTAHA PEAHOCT CCCTBEHH HTEET Heocmamoocm anpuopo uopauu npuoum eoxouocmu coeam onpeeeo cce uyeue oema u ynpaeue u. M e oe onmuao ynpa m oemo, e a eo xapamepucmu, o oe uyam oem, ynpa u, u me ca uem oo ocm yyam ynpaeue, cmpec onmuaoy.

ocmeocm au u ynpaeu, a noepua . eo, meco caa c ocmeocm npooo u yyeo. Moo oaam auu o npoo, o e ynpam u, u oo ynpam yyu, e a eo.

m oem, ueo mo u cocmoum c npeecm u cc ynpaeu.

.. , Aaa oyee aoa ecx cceax Ha pc. 31 pecaeo oeyaoe peee papaaaeo a cce ypae a ae HC c oo oye, peay A oca oax apaepo ce [33, 34]. M aa ay ccey eeyao, ooy o oa oaae o aex apyo eea, a eo cocooc ocpoe pooa, ocyeceoo pya pao ypae.

oo pocxoee coa pya. Oo epe co co o acoo vir ya. Pe opaoa o eo pyoe coo virtus, oopoe cyo ooae cooyoc cex peocxox aec, pcyx ya (eca ca, oecoe oeee, opaoe ococo). acoo coo poae capopay c, a XIII ee paycoo ac .

B copeeo aco coo virtual popeo ooe oeo o e cyecy eceoc. B ooo coape [35] ae:

Virtual being in essence or effect but not in fact or name (cy ecmyu nomuu uu npouou em, o e cye cmyu ecmumeocmu ue ueu aau) Mey e, aoe aee cocyecye apae c po pooo o. Aopycc coap [36] ae epeo virtual a amue cu. oo ec coap [37] poco po o poo ooe ae emu, ecmyu;

uaem;

amuecu, oaac a ay coopaeoc yee ope poac oece.

Pc. 31. oeya poe CA c oo oye a ocoe A oceee pe ce oy oypoc ayo epaype popeae ycooe coocoeae upmyaa peaocm. Bep e o ep oc ecoe papaoo oepx po pa, peaaex aeoo oye ocoao aa aooo pao opo ococe. C opeee ea epa , pe a cey ce ocy, pea oopa ooe epao oepo a aeo yco epecoac, cyeceo pacp pa peoc papa oax cce aece peaepo eocpeee pecaee pyx oecx poecc. Boecy oope eo a ecoo aao ocye opa o (pee, cyx, ecyp aapa, ae oye), copeee o epe cce pyao peaoc coco ao a coae ocoae opoa y cyeoo oyee coe p acoc paopaaeyc epe eo aa ceap. epe o epe p oa exoo ecyac p, opo eoe o oe apaee eo.

M eoo opyoy paye o oe. Ec ayac, p yaa peaoc cyecye ao ac. Oo aa, oco aeo peaex yyo a poe ce , ec ocpoee yoee ap pa, opeeee coeo ooe e paoa cpae coceoo oee. M e oo oe pye ce opya p, o a co copo aae ce o pe, oepy cax ce.

cxo ax pecae o eee eoea, oo poepoa cce ypae. Be po ee cy oe, epoopoep ec ee eo, a pya aa ypae , coepa oe oea oe epoopoepa ee o o, eco, e ccea oepye ce opyae pe.

oooa cce paoe pocxo cey opao. M peoaae, o c caoo aaa a ocya apopa opa o oee oea pax peax. Toa aae epoo aa ec epepaoa o opa oey pepoox a oo, a ocoa oopo ae cepyec epoyop oea.

oa epaa oa, eeppyea yopo, caec o a aoo peea, apaep epoyopa opyc o pe po epoopoepa. ec c yace aoo oe pocxo oea pax cpae ypae oeo, paccapac cpaac ey coo pae ceap yyeo. a oo yaec oc oe pya pao peoa aoo oe, apaep pyaoo opoepa cpacac a co e opoep, oce eo ccea oe pcya paoe.

p ee xapaepc oea pocxo ececeoe c ee aeca ypae. o epe yee pacxoe eye oee oea c oae ccea oyae oooc o, o oe ec. Hoe epexoe xapaepc oo oey pepoox aoo, oce eo apaep epoyopa oppepyc. aee ce pocxo a paee. oa ooa y opa ocyecea, aaec oppepoa apaepo epoo poepa, aepaac eee apaepo coeoo o poepa.

Tpyo pacca, o a o ao oyee aoc, a a oa opa o eec oee p oe peeo a a ocaoy ooy. oo peoo, o oce epo pepo yop e ye oo oca oe, a ooy ce poa c eo oo opoep e coe cpac c aaa ypae. Te e eee, oeo, o o opoep ye eep poa xo e oaoe, o cea ooe ypaee, oopoe cpoe oe ocoeoc oee oea. Hoa opa ac oooc coa pacp oey aoo, opepoa e poyop epoopoep oo apaep coeoo opoepa.

Ta ccea caa yae oe oceeo coepecye co cocooc ypae. Haepoe, cep oecex ee xapaepc oea cea opae opeee paa, e o opx ceae aecea opeeeoc oea a aooo. o oy, oa oooc poecce cyaa oea cepa c, ccea cae poaco, o ec popee cocooc ypa oeo p x ocoecax.

yae pyoc cea epoyopa ae offline pee, cpeec a, a opao, p opeee oeo op a o oee, ocaoo cea eo epoceeo oe, e co oxa a ya ooe co aaceco o e eeyaa. oeo, oa opoae oo ooe x opoco o coooe eo o aaa online pe e, o pao cxooc aopa aaa, coepaeo e, oee oa pyy, poeyp oa. Te e eee ep, o A oaa ocaoo ocoo o, o cpac c a poea p cyecye ypoe pa epcoax oepo.

Bopaac pe opoca, ocae paee o oepo a, oe a e oe oa oo a ep x.

a, epoceee oe aecx oeo oy acoo o, o epoopoep, cepo a c cooae epoyopa, oaaec co co ypa ca oeo e axo oo ex acpoe.

M poe oceoaeo p oox cepea c eco oeo p pax aex ypae (8), poecce oo px caaa cepoa epoyop oea (c. poe 2 4), a oo c oo epoyopa epoopoep. Ha a eo ae cepea epoopoep opooac a cao o ee. aey yoeope, o cex pex cyax epoopoep co ypa oeo e ce aeca o cpae c paoo cocae pyaoo aaa.

cepe oaac oe coepeo eoao ae. O poy epe ae oae oo, o ceye ca oe pepe aeaoc oe oea. eceo, ooc oe oo ca yoeopeo oo o cyae, ec ocpoe c ee oo opoep oaaec cocoe ypa oeo.

Ceye pa, o ce pyaoo paa cce ypae oaac e a poc eo, a oo oaac aae. oca oo caa, o aa epa oa opaoa eo ye pa o co epoopoepa epoyopa, peapeo c epoax a acceco oe oea (c. poee 1 p oee 3), aoyac a eoae pec. O e ca pa oa ece, e cpay oaac oey.

eo oaaoc o, o oa cepoa opoep a o ee, ac epecoa oo xo oea, o e opoepa. o o ocoeoc peeo eo, a a oa xoe oea cooaac oye, o e acaec opoepa, o e ac o, aoe ypaee o oe eeppoa, o aca oe ec ce peye opao.

a cece, e opopoa a e opaa a yy xoa opoepa, oopa, a o pcya 32, ocaa ae 5 p eo aa ur. Bo aoe ypaee e co o paaa epoyop, ocoy o oyac a xox oec x o 1. Too oop oeee oea ypae p ayax xooo oec ee 1, yop paec e paoa p ox ayax. Pc. 33 oaae, a aacpoec yxyae c aeco eo pao ye p xoo cae pao 4.

Pc. 32. Bxoo ca epoo- Pc. 33. Paoa epoyopa p poepa (pa 1), oyeoo o ox aex ay xoo epea ypae oe- o oec (pa 1 xoo a, p eo aye caa ca;

2 pea oea;

3 pe aa, (pa 2 xo oea) a epoyopa) Bpoe, a cao ee eo yeoo o e, poco aoa e accec oe. To, o o oco epo oca pea oe oo yo aaoe paox yc o, aco cac y p pee paecx aa. Ho cao oepoa, a ae cyae, x oeee eypeo, epocee oe pyo copeoac c .

Bopaac poee cea pyaoo paa, oe ce yee.

Boepx, xo oyee epoopoepa eec o xoo oopae yopa, eoxoo opaa ayy ypae o caa, eeppyeoo opoepo, epxe pae oycoo aaoa xox oec yopa. B ocaex cepe ax a paa cocaa 1.

Boopx, yx oox cocoo opae ecoo cpea ay xooo caa o oee oo paoa a peee papeeoo ypo oee peoee opo. O ae oooc eeecoy aopy papoa oy c yeo oo paa oceeo ac o ex pee, oope eeppy co coe ypaee.

coy ooe eoe, a ae opa ey a a ur=0,5, cepoa p epoopoepa, o oopx oo poc e. apaep ooo x pecae poe 5, a eo xo p xoo aa ur=0,5 a pcye 34.

Pc. 34. Bxo pyaoo epoopoepa p aa 0, oeo, oee cepe e oaa cex aax coc eeyao cce. a pa ca op aoa cop opa o oee, peyec cea yopa, ecy o peapeo epeoy ay. oo, o yec cocooc cce cea o caocoeo, y o pacapae p aa oppoae oe pepoo x aoo, pepoa yopa, pepoa opoepa, oce eo cye pao pacpee pecypc ceo cce opa oa oe a ey . Copeee oepaoe cce (Windows NT, Windows 95) oaa oooc pee a x poe ae a oopoeccopx aax, aepe pea oa x ae yye.

B aepee xoeoc popoa P. oa, poee [38] oopoo oaao opooe e a xo ax ce a po e ocex 2x e. O e: o cocooc oe poa, oeo, pea oeo oe cyeoy ocoa . oey o oo o poo, pecaec e yoa e ao, coe epe copeeo ooe. He ocoa oa a, o epoe oep ecy ocoao, oa o o y oepy, xo a pxoc oyca, o yye o, ooo, yy ocoaa co ec. oe, ocoae o ae oa, oa oe pa, coaaea oo, ocae ao o o, o ey pxoc a ee oe caoo ce.

pecaec, o eoeeco oy ooo papee o aa.

AEHE popaoc ocyoc e, cocax eoooec ac copeex eoo oooo oepoa, poo a ac oce aopaaee eaee. He caa, o e acoa oeo , e a cao ee o pe ca coo peooe op oo e oee e oy eoo aoc, o ceo o x ae a o o ye e 20 xo epee oo, o oe a cpeecacec oa e, a ao oee o . Te oee ye pe caec o a, o oeee oo eoe, e popea peay cy a a py e cpye pee cox aa oepoa cea.

A + HC oxaa oo ycoe oo, o aa oo oepoae. Ho a a pecaec a ac po eocppoa, e cee exoo oaa opo coae oeao. ooo oy, a o epeao o y aecoo ea coca cpyea ac accecx eoo oepoa aecx oeo poe poa cce x ypae, epoe ce c e cpyeo oooo oepoa cea. O ao e epe coco oxaa ec cep poe, cax c ocpoee cce ypae aa o cea oe oea aaa ceo aoo ypae, ce o p oo ox ex e pe o, paax eoo oxoa. o oo oae x o ox py x copeex ex, oope po eoc p pee oo acx aa (cae, fuzzy logic axo peee oo p cee opoepo, o oaaec ecco oepoa cax oeo), ae ocoa pc x accy op, ex apaaoe aee copeex execx ay.

M oae, o pecaee a cpae pep oo ypey eoopo pocoe ecooo aecoo oea.

Ho e ye aa, coo e ao ceoc opo yex a acceca aya pocoy oca oox oeo, ye opaac c . Hepoe e ce aa oac pa coce eao, e oee 10 e aa (o e caoe oo caa o e eecx aopax).

Moo ae peoo, o p x poee copoy real world applications ye cp pya. Ta eoc, c oopo HC yepc ox ayax, ec copee oa o oe ocea poc ocyce cepex oype o. Cyecye e exoeo, paee paax acceco ayo apa, a eoxo yoeop ocoe opeoc oeca. a x yx cooy y oe pyo ce pyc ao a opa a eco o coe e pepaaec a yy.

Bpoe, cya eec oe cpo, a peoa ex e epepo coepecyc, o e oec peyaa, co oo acceca apaa coe coxpa co ooo.

a o e a ao. a popecc ocex e coco o, o o oyee oc, ooc peaex eepa ppoo a a, oopoe e a ao oo ao oyxe, ceo epepoco yepeoc, o p opaecx peao p yypx pe ao, ao oocc aye e, paac o oao aoa, a a, a ec ey yc y ppo. pecae a epa oaae, o epe peyae a o apae ye cea.

TEPMHOOEC COBAP opoco epoa, oop epeae yc py e poa.

a e cocoe aa oo opeeey o ac xpoocoe, a aae oyc. B oy cea ayc oco, y oopx ex oycax pecae pae op eo. aepae op aac ae coco ea poco ae.

(o.) e, oope ecy eeecy opa o poeco oco. ox eoea yce ae aac cepaooa, a ece eea. ae coepa ao (oo) aop xpooco. B ooo oepoa ae op o oco e peec. Oeo oepoa c aece oy ecox opao, o ec oy, oopx ocycye ape a cpeae x yx ocoe. Paoo ooc ppox oyx a pa pae po ececeoo o pae a cpeae apa yx cao, apa yx ca o e oy a ooca.

ocoa ea aceceoc, pecaa coo pae H, opy o ecoo eoecx p ao aa cpoa oyc xpooco. e peca e coo copee eoeooecy aeop oo poo co ey eoy, ocyoy ae pay opaa, ooey epepoa eo o pyx ocoe oo e oo ecoo a. B ooo oepoa pae xpooco, opy aee ooo cox apaepo.

pa e oooo oepoa, acy eoece pe eopeecx ooe oyoo ee. pecae co o coeo poa oe aoo cceoa ocooo pocpac a, ocpoey a ooo eaope. Xapaepe ocoeoc:

cooae cpo cpoao pecae eee co opa, paoa c oye cpo, cooae eee cx oepaopo oppoa yyx ooe.

poecc oca cpeya cpe yo yoaa, oop ooo oepoa cooec ye pcocoeoc oco, eppepyeo a ee cocooc pe a ocaey aay.

papaoaa . ap eop, oca o a peya aoec yx aopo cyax e e xapaepc ocoe epee ooe ececeoo oopa (ae aoee pcocoex).

(o.) co paeea ac epoa, oopa oy ae yc o peeopo pyx epoo epeae x ey e.

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