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.., : 01.04.02 - 2011.. :

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. 1 - y aeppa pa. Oepaope opeee coca cooecyx pcoeex ooo pa p o ey po, a cooae ooex op ooo aeppa pa ooe aca pee co eo ocyo aaa ope.

Oepaope eo c ee oee o cpyeo pee epecex o ypae, oa coyc ece c oxo epa peopaoa. o o xo aa c aa yco, cao c ecoo eeo opo ypae, cpeaeoc acoo oe aCoya:

2, 0 (1) 2 paee (1) oe acao ceye e:

1 1,(2) oop ooe aca eo opaoe peee coeaoo a 1 2 1 (3) pe epaoe peopaoae 2 2 (4) coeaa apaoo oepaopa coy coooee,(5) eo oy epaoe peee aa c aa yco (1) ceye e:

1 1 1 2. (6) a ye oepaoc, coea oepaop eo peee oc ocaoo yepca xapaep, o ooe cooa eo o ox pax cyax. Ta, apep, p eo oo oy peee ypae aCoya paec eeeo. oee oo, exa c cooae coeaoo oepaopa oe paa aee eo peee pacpeo a ae epece oac aea, a oepaop pooo opa cee poox epao pooo opa, peee epeax ypae pooo opa. Coecoe peee oepaopx coooe epax peopaoa e cpe c ey, a ep , e oocc py pyy aeaec oea pax oace.

B ae 1 paccope ae ceeca ooo Ae, eepa, epa, yceee coeae oo, pe pcoeee epece e ooa ceeca.

Paccope oepaop Ae, opae oepaop ye x coca. Paccope coca ooo cx opo paccopex ceec c x ooo c ca Cpa.

oaa oooc paoe ceax y, a, apep, y ecce, o ooa x ceec oooc oepaopo ex p o, o oaaec oe p paoe co cea y aaec pae, oca oe poecc ye ac. oaao, a ee oepaopoo eoa oy pec peopaoa opy cypoa c yace ceax y ooo. peee papaoaoo eoa pee ypae ao poeocppoao a pepe ooeoo ypae eopoooc (7) c aa ycoe 0.(8) Cooecyee peee oe acao epax oepaopa o :

,(9) e (10) 2 Oepaop (9) coep cyy yx eoypyx e oe aca a yopoeoe poeee yx coeax oepaopo. ece a y aaoo yco (8) eeeo po ceyey pee ae aa:

2,,(11) e:

2,,(12),.(13) opy (11) o, o peee aa (7)(8) aaec oceoaeo pee oypyx oepaopo y (8) yoe a. o cyecy ec oepaopo pac ece oepaopa y a y po pee ooo ypae eopoooc e peopaoa ayccaBeeppacca. Toa e ax o ooex peooe o xapaepe y (peoaa oo cxooc epaa) oyae ceyee peee ypae (7):

.(14) Peya ec oepaopo xopoo e a pepe y, oopo peee ee oa :

1 0.(15) 1 o peya oo paccapa a ooee a aaeoo paa epa, poeo pee ooo ypae eopoooc ( 0 ) c ye aycca aece aaoo yco.

Oepaopa exa, cooaa a p pee ypae (7), oe yceo peea ypae peepa ac oe ocoo c :

0 (16) Eo peee oyaec oceoae ece oepaopa o cooo ac (y o pee) oepaopa pac ( 2 2 2 ) a y aaoo yco, e ca oeo aooo oe:

.(17) e ax-o ceax peooe ooceo oyae peyae peee aa (16) e:

.(18) o oe opeeeo cce paccapac a opypoa poaaopa oe ocoo c, oop coco y, pac eoo o oopae aea a.

Ha paccope epec cya aaoo yco e y p Ai, e apaep. B o cyae oyae:

2 Ai, Ai Ai.(19) Bpaa o peya epe y p oo epeeo, oyae a o aa aea p oopoo epocaeco oe coc poco pac aea, a eo: ae eeo op ec paoycopeo.

B ae 2 paccope aeaece oe ye oyopo c o cox cocax oypa. Texa oyopoo ye ocee o oepac aeoy yye e oo c o pe oyopx ao, o c o pe oe x oypa. peoe oe cxe oyopo co coo oypae aoo o, ayae a ycpoca, cocoe eeppoa yee c pa opa, oepa oca yee oex apo.

B ae 2 c oo ceax y a ecce, ooex a cya ox epeex, opoax y p oye oe aaece pee oyopoo ye (O) pax epoecx ox. Aaec yaec cep epoaoo ye peccoo epoa, yeoc ao oe, oopoe ocpye c pa acoa a oo, a yx ao opooax ococx pocpace.

cceyec e oypa aoo o oyopx apaepo a yee ocoo, cx x apo. B acoc, paccapaec oyop c a oe, aa cey paee:

2 =,,(20) 0, 1 o pecae coo ooee cpaoo oyopa c 1 2 .

Hao, o oo cpao oyope paaeec aoe oe ee pae py pyy ooe epo 1 2, epo e ec o cpa, pe oo oyopa yooe pacpeeee ye acao-cepo oa ocoa apoa yaec a eo oc. M coye, ooee y ecce, ;,, oope c pee pacpeoo ypae ecce oy aa, apep, ocpeco pooe y 1 1 1. (21) =,, ;, 2 2 2 2 = oe oaaec epaoe pecaee ooex y ecce:

,, ;, =, (22) x paoee p o ooe y ecce yx apyeo:

,, ;, =,,.(23) = ecoc O a oc opeeec pa o peoac acoa 2 2 1 ( /2) ( ) =, 2, =0 2. (24) 2 = 2 / = 1 1 2 /2 Booe oop, eop ee oe coy opy, o oa ypoaec a oc, e a apyea y ecce coc y, o ooe aca eo ao e =0 = 2,, (25) ( )/2 ( )/,, 1 ( 1)/2 ( 1)/ co cey apyea ooex y ecce:

1 2 2 =, =, 2 = 1.(26) 8 1 8 2 opa ye epeypa oc oyopa. apo cepe yxacooo oyopa opeec o eca y ecce ( ) 2 -ooe opa ( 1) 2 ooe opa ye, e oep yeo apo apoecoe co oyopa. ex ae eee apo e oo -ooey opa, a ee apo oo -ooey opa. eeoo = 3,5,7 ee apo ocycy, a ocaec eee apo e oe ooe opa.

opye ye ec apoa c oepo = acoo = 1. p aex 1 cep ye paao eec, ce apo opy. oa apoecoe co oyopa 2 1 ~, cep popeae coy opy, cocoy oceoaeoc oax acyo yo oceeo yeaec c poco ecoc. yee cx apo, ooe oop, ee co xapaep c eco oa acya, acoc o ae oyopx apaepo. oyopa c pa acoa 1 2, y ye cx apo e ceye ae oyopx apaepo 1 = 2 oe ae ceo.

aee ae 2 ocyac coca cep ocoo yxacooo oyopa (O). oaao, a O oe cooac peypoa ye oex apo , a opao, pec exe aepoo ye coa ycpoc coo eoc c y cepo. B ao oyope c eo opae epoecoe aoe oe ee e cocae, ocpye a pax acoax oo ococ c epoa / e eoe co, c pa aya:

1.(27) ecoc O a oc oyae, cey oo poeype:

2 2 2,, (28) 2, 2 4 2 e ecoc ye a oc opeeec, o cy, cey aopo:

,(29) 2 1 1 1 1 y ooee y ecce epao pecae:

2 1 1 2, (30) 2,, (31) 1 1 2 2 1 4 (32) 4 1 1 1 y oo aca epe p o o y ecce ( ). Ta, cooae aeaecoo aapaa c peee ooex y ecce x aee oa ooe ye ee ooex epeex eco ececeo oae xoe pee aa o O ao oe c ooeo epoeco ooeo. O oaae epec ocoeoc, ca c yee eo apo a oc. cex ex ae a eee, a ee apo oy yac a oc. B cyae eex ee apo e yac a oc. aee ae 2 oaao, a yxaco oyop oe eo cooa yce ocae opeeex apo cepa ye. Paccope pep O c = 2, 3, 5. oaao, o p = 2 opa apoa ae ca ca a oc p ax, o ec, oa aya opo aco oyopa aa (o oaeo). ox ae yee opo apo oee eco oa caoc cee, e epa apoa p 0. epa apoa e ycea ee, o pe a pe co ac o eo oe ae ooc oaea 0 cooecy opo ( paccopeo pepe p ). p eex aex, oa yee a oc coep oo eee apo, ae ec oooc peypoa ye apo a oc. Hapep, p = 0.5 pe apoa co oaea. oye ae pye epece peya, oope oaa, a cooecy opo apaepo oo oa yc yee pax apo acoc o ae oyopoo apaepa. poeocppoao, o p = 3 = 5 cyecye oac 1, e ocoa apoa opye p ax aex = 0.05 ceye apo pa po oo p 1. Bop = 0.pacpe oac, e opye ocoa apoa ye o o ~ 2. B o e pe op = 0.5 ep oee coe apo c 3 aeo oae, o pe a pe apoa ycea p cooecye ope oyopoo apaepa ~ 2. Oao p ao e ae oyopoo apaepa ~ 2, o pyo = 0.5, ce apo a cea oepy e cepeoo ocae ye a epo pee apoax. Taoe ceeoe ycee oex apo oe cooao p poepoa aepo a coox epoax (C) yee epaa epa eco ooeo O. ya o apo C c cooae caapx opy cpaoo o C, oy, o cyae = 0.5 ooc ace aeo caee, e p = 0.5 p = 0.

aee ae 2 pecae aaec eo pacea ye epoa, yeoc oyope, e ocoa ooea aoo o aoea a epoecoe oe oyopa:

= 0 0, 2, 0 1,(33) 2 1,(34) oe, ooce apeoc ocoo ooe aoo o aye epoeco ooe oyopoo o 0. B ae aae epo ec o opao oee coo paeop. o cpae co cepo ooo ocoo oyopa, coco apo, e pa cepax o opeeec apaepo paccpo :

2 =, 2 1,(35) 1 2 cep oyopa (33) a oc coco o c acoa:

2 0 2 0 = 0 1 2 3, 1, (36) 2 2 1 e oep apo. Teep paee peoacx aco a oc (36) ae yo ooe, oop ac oo o cy apao ooe ocoo ooe aoo o, opay eo apeoc. e ocooo o aaaec o oc oyopa c a epoo ac o x ca.

ecoc ye a oc p yco caoo ocooo aoo o opeeec po peoacx aco, acax epe oe y ecce ooee y p. p cpax apeocx ocooo epoecoo oe oo cooa ooee y ecce epex apyeo. ocoa ooea o po oe ex apo cepe opye eee apo.

aeaee o a, o ecoc ye ex apo opeeec oo oye apeoc ocooo o, a e ee apaee. Oca ceye, o c x oo, oo opepoa oc oyopa o apae ocooo o, a py paee ycpa o e e. eca pa ee cepa ye e ooe epoo ao-o opeeeo apae o oc, a paccpoe oepeoc oc epoo oyope p poxoe epoa ocooo aoo o. B ae 2 poeeo cceoae ype ocoo apo oyopa a a oc, a e ee, c cooae ooe y p, cppyee e ocooo aoo o. poeocppoa c peoaco aco yeee co acya. oaao, o e ypoaoo ya a a ecoc apo cee, e e ooe o oc a ao e yo. Bceo, o ooee o oc oyopa a yo 2 3 oaae ao e e a ecoc, a cooecyee ypoaoy yy oe.

C cooae ooo pae (36) cepa oyopa c ooe oco a oe oyeo ycoe peoc xopoo eco opy (35) ocoo aco ye ocoo oyopa p aoe caoo ocooo o:

1 3 1.(37) 2 2 Aa O ooe paccopee eo eoopooo ype cepax , eo oeaeo a paoo poa oep p pacpocpae yo oyopax ooe op epoecoo o o cycoao, o yoeopc ypae Macea. e ocooo aoo o epe cooecy apaep a opy cepao oyopa co 100 epoa oaae, o e ocoo ooe aoo o oyope peepeo a, oa aee 10-4. aeoe caee cepao pocxo oo oe apeoc > 1.510-4 0. Cya aeo eec c yeee ca epoo oyopa. Ta, oyopa c 2epoa pcyc ocooo aoo o = 110-4 cae cepao oc ye p ooe apeoce ocooo epeeoo oe 1 ~ 510-5. oee oo, acaa paya apeoc ocoo ooe aoo o aoo oyopa cocae 710-5 0. Toa oeo, o cae cepao oyopa c 200 epoa p = 110-4 0 oe ae. Ta a aoe oe e ee a pa ao opo ooceo epoecoo o oyope, o paccopeo cyae yo pa ce ep o aeoy papoa ocoo ooe o ee oeca e aya c oo.

a, ae 2 a poee aa ye ocoo oyopa ocooo aoo o a yee a a eo oc, a o poo yo e, c peee ex y ecce ox epeex. yea ocoo ooe aoo o paa exa ooex y p. cooae ooex op ceax y ox epeex ooo oy aaece pae cepa ecoc O, a ae peco e ocooo aoo o, p oopo aac aee cae cepa, op cepao pocpaceoo pacpeee ye oyopa, ace oo o e ocooo o.

Papaoa a oxo ooe oy aaecoe peee aa c epoec o eox cox cocax oypa. Hecop a ayyc cooc cooa eoa ooex y ecce, o ooe poea o pace ye o pecco pe oy oe aaece pee O pax epoecx ox. Caoc eo ocy ec cc oyex pee x aa. Ha eo ocoe aae, o yxaco oyop oe eo cooa yce ocae opeeex apo cepe O.

oaa aaeca opa pee ooe poec aa aa ao ooe o. Oe, o ccepa aeo aaecoe peee, yaee caee cepa ypee cepax , eee eco peax ycpocax c aa co epoo py xapaepca. eae aaece pee, yae e oyopx apaepo, oypa o oyope , a opao, eo ocpy, a ae yae e ooex oe, a, apep, aoo o e ocaooo aoo o oyope, aeo c oo opoax ceax y. Ha ocoe oyex pee oo a paece peoea o yye ocpy, oeca cae cepa ee apaepo ycpoc c e oae eeaex apo yceo eepa yx aco. oee oo, papaoa oxo a ocoe opoax ceax y ooe aaec pe opoc o ye paec oo oyopa co co yoo coo oypae epoecoo o eo pa cae.

Tpe aa cppye pee aeaecoo aapaa pcecoo aaa p oepoa ecx e, eax ocoe pax poecco exe opyae cpee. Hapep, paccopea aeaeca oe pacpocpae o epo ee, oe aox ooo yox poecco ooooex cecx ao. Paccope exooece pee ocpoex oee. p o cooa aoee o ec oxo poea. poeocppoao, a ea ecx poecco, oecex a e e e opyae cpee exe, x ye c oo aeax aeaecx eoo po popa aaa aeaec pee, oo ec ce opee peoea o yye exoo oa opyae ac cpe.

poeeo cceoae pacpocpae ypyx o eo ope c yeo aax ape. p o oye ypae ax oea aopoo cpe poooo eoopooo aaoo ape. Paccapaec cxoo oopoa opoa cpea o oece ax, o cpae c oy ypyoc, ape ca. yeo pacpocpaee ocx o ao ay opoo cpee c eoopo aa apee.

oyeo peee aa o pacpocpae o cpee c aaoeoopo apee. Ca, o yox acx e ocycy oe coe ape, oaa eaop eopa aax ape a o cpae c oy ypyoc, ocae cpey ep cap y ae. Tpey oopooc aaoo ae eoopooc ape ca (p yco eo aoc), oyae, o epe capa, ocae ypy o cpe, e ac o oopa. o ooe pea ypae oea cpe, coy eop oye. Haaoe apee peoaaec ac o oopa oa, e eop pa pa 0 0, 0 axoc cepcooo coooe eoyeoo ypae. Ta opao, peoaaec, o aaoe apee ca eoopoo peyeceo o apae 0.

Tao oxo oo ypoc ce pe ypaee, acee o oo capo epeeo. Hoaao, o opaa pee o eop oye ye axoc a o e acoe, o eoyeoe peee. Paccope opee pep aax 1 ape, acx o oopa a .

Cya aaoo ape a 1/ch xapaepe e, o eoyeoe peee 0 eec oo cpee, e aaoe apee. Haaoe apee eo ooceo = 0. Hp o, ec eoyeoe peee 0 oe eo ooceo y, apep, o opaa coep a ocpy o e, a ayxa c poco e. B o cyae oa epepa. Ec eeo, apep, o opaa pee ee pap oe = 0. B ao oace > 0 < 0 oa ee aaoe yoy e ocpy ayxa o e.

2) Haaoe apee a xapaepo e, o peee apee ec peoac opao o. B o cyae opaa epepa a p eo, a p eeo. Oa coep ocpyee c acoo 2 caaeoe.

Moo peoo, o ec paccope eeec cao e y Xecaa ( ) aaoe apee a pee cya ape a th o, epoo, oye p o pap pee ye oca pey. p o oe oaac, o cyecy ae o, oope yy po yaaoy xapaepy oooo c ape a ce papa cpe.

aee ae 3 ye opoc epeoca cpe pax ycox c yeo oeypx eo, oax a poacae eee epa. Hecop a o, o opoc peca pee ceo eep epec, o ae epec c o pe yea ecx aopo, oecex a e e e p ocpoe aeaecx oee cox ecx poecco, oope e oy poco coepoa ocae cex e a poypoe, o, o e pe, o ac o x pey yea ecx eo, ex eco a poacae. Bop cooecyeo aeaecoo aapaa, ea ecx apoapaepo, eo ocax pocxoee a poacae x a apoxapaepc poecco ax a epeoc acc, oea pyx e, pecae e oo exec eep epec, o ao c ayo o pe. Ta, apep, a ye pexep oo caeo cpe c yeo oeypx eo eo xapaepc p ee x poaaax. Ceye oe, o o acoeo pee e ycaoeo aeoo cooec ey cepea a eopeec pecaa ye caex ooo poaaax, e cceoa caex ooo ooo ao ooc pooc paeo. C cooae eop oye a pooc paoee ypae HaeCoca o aoy apaepy (ooee co aaa eo e) cyae yx- pexepoo caoapoo oepecoo ooa. eocppyec aa po caeoc eo pape ae ooa cpe.

oye pee pooo ooe copoc ooa, pacpeee ae ooa acc aae. poaapoao e ea coe ooa ooceo ceo aaa, oopoe ee eco a poacaax, a xapaepc ooa. oyex pee ceye ee xapaep pacpeee ae ooa acc cece caeoc oeypx eo. Caeoc yeae oo acc, o e poec cee p oe ooe ae a xoe xoe. Coee ooa o ceo aaa po ee oey yee copoc ooa acc cpe, oee cyeceoy p x epeaax ae. Ta, p oo epeae ae caeoc cpe oc ocoo a yeee epeoca acc, a p ao epeae ae aeee a coe ooa o ceo aao yeee ooa acc.

Paccapa opay oc oa ooey copoc, oo cea o o pee copoc acc o epao cea cece aoa coxpae acc. pe paaec c poee cpe o aay e xoy, e yeaec pocaae ooa ooceo ceo, o copooaec ae poco paea ae. oyee pae aecx epeex oy cooa pacea copoc, pacpeee ae ooa acc aaax pax oypa c yeo xapaepx x acao ecx eo, x a epeoc cpe ay ooa.

aee ae 3 yac pacpocpaee epeoc cpe ceax ao opcx aepaax a ce poecco oeypo y yeo y o e aee. ocpoea yepa oe epeoca aa opco cpee o ece paeo oepa ae. cceyec pacpeeee pocpace oepa copoa apo cec ao poecce epeoca acc ao oo aoo cec opco aepae yopa. pooc aa eoepecx ecx coc aepaa yopa a epeoc ooeo cec. pooc ooee ocpoeo yepo oe epeoca cec ao a pexep cya. B aece pee ocpoeo cxe oepyec epeoc copoa yope oopooo eea a c oep epoo. yaec epeoc copoa cocae aoo cec oyxa aceoo ooo apa epe opc yop aaeco oepxoc. Paccapaec ooe ooee copoa a aaaope, copooaeoe eee ooo apa, oecpyeoc yope. Ta opao, oepyec epeoc ooe aoo cec opax pcyc e o o. Paccapaec exa yae oc op a ce yeo oe o ece paea ae. pooc oepoae eoopooo pacpeee opcoc aepaa, aceo o oaoo ae paea ae. oce opeeec a ec apaepa aa, a eoepec ocoeoc oypa aao oa cec ao ooo apa. B o oece papaaac oe oypa oox oyy cec aao c e acaoo cooa y yeo oe oca aox peaeo aaeco ococ oy oc opcoo aepaa. pooc cpaee pecaa ocpoeo eopeeco oe epeoca ooe aoo cec c cepea a. Oe ee pa, o c o pe aeaecoo oepoa ecoo poecca ee epay aay, ooe ocae oopo c yeo a pa cex cocax poecco pecaec pae pyo o. Ta opao, pea aay o oepoa oeca ecx poecco, o cooa oxo oca cooecy e cceoa aeaec aapa epoa cooecy aop apoapaepo, ya ocoe ocoeoc eco cya eo oca ce poecc, eae ocoe aaex e. p o eaeo oy pocoe peee, eee o ec cc c co po ax apaepo cox ecx poecco oy e aeeoe a oa opeeex execx pee. Peee o aa ocao ao paee. Boeo oepoae eo opcoc coc op eeo acoc o oaoo paea ae yea acoo aoe oo op yopa e poae. poeocppoao e x eo a xapaepc ycpoc, paaax epec o a ce epoxeco pea oopoa copoa, oopx pec opce epa epeoca ao.

Peya, oyee c peee pao a oe epeoca aoo cec ycox epeaa ae oepa opco yope cyae epeoca copoa aaecoy co, oaa aoc aaecoo oxoa p pee oox aa.

poeocppoa e oaoo ace yopa ao p cox aex ae eo epeaa, oa ae poc ae e po pocy ooa acc peaea yope.

Maca aoo aopa apaepo oa oo peapye ooe cec ao oepxoc pea paaec paceeo ye, cae ece eoepece xapaepc opcoo yopa ce oox ey a aao. oaao, o cooae exaa yeo oe a ce cyeceoo paea ae, oaeo peoeo a oo oypa epeyxc aao, oopa coeae peyeca eea peeao oypa, ae oooc o a 2040% opaee a aca o, paaae a ee oa ooo eea o cpae c eco eeo oypae aao, oox aoe peae. C yeo poeeoo oepoa eoopooo aoe op o oo ee yae a ce cooo ooa yope peaaec cooa oee coe ae eo epea a xoe ce oax aoe peae aao.

B ae 4 ae cocpeooeo a ecx ex, ocaex Caapo oe aoec eeapx ac, acoc, ee epocao ceope. poaapoa op ap cea yapx 3 3-ap, oope ecy a ece aaee accoe coco apo epo, pacoppy x cocee coco aoaa caoo aoec ee cyepo accox coco. Oo ceae apo ocaec ape aooaMacaa, oopa opeeea a, o oa ecye a ece accoe coco x apo c epec apo 3 pacoppye x oe cocee coco caoo aoec :

' '.(38) ' Ha pae ee ap cea oy opeee a ae cepeax ax. oo coyc ae o cax pacaax cooecyx apo aa yoo eypyoo pacce epo a apoax. Hapye CP-cep cax poeccax cooecye oeca aa y eeo ap cea caec, o aaeoe apyee CP-cep pocxo ceo a ce ooo o y ae o a.

Ha peoe oe coeae apaepa ap cea apo epo, ocoae a cooa oepaopo coe:

,(39) e ec ape 3 3 c ooe apaepa , oopa oe acaa ceye apoo ope, o oece yapoc ap :

0 3 0 2,(40) 3 2 pe apaep oeae a apyee CP-cep, a apaep a ceae apo. oaao, o oa apaepa ec aoee oe opo ap cea, oopo oyac ce ece apaepa, ocyac ee coca. poeeo cpaee oo apaepa c eepaopo pocpacex pae ope oepaopo coe. peepea eo CPapye peoaa, o ee ap e ecee ae, oy apy cea ope, cooecye pocpaceoy pae a yo opy cpoao oc, apaee oopo aao e eopo :

0, 0. (41) Ec oo yo pae 0, o ceae ey apa ceae, apa cea caoc eo ape.

Hae CP-apyae a papyae y cep, poaae ocaa poca eoepeca apa cea. Ocyaec ye CP-apyae a oo apaepa ap cea oece pecae ap pexepx pae a opeee yo opy eoopo pocpaceo oc. Hapyee CP ee co eoepecy eppea coeao apaepa ap cea apo. B acoc, -ooea eopa apae pae pecae yooc pae pocpace caoc oeco.

poeocppoaa oooc eepa ox apaepa ap cea c ee apya CP-eoc eo.

Ta, apa oe pecaea e cy eceo oeco ace:

1 2.(42) p ope aece ap pae:

0 2 Rot 0 2,(43) 3 2 yaec e apyee CP-eoc oeo caaeo :

2 0 1 CP 2 0 1,(44) 2 0 2 e 3,. (45) oyea oa apa cea Rot CP ee ae e ee, a apa o pae epe, c ooc o.

Heocpecea poepa ooe yec yapoc ap. Hacaa e CP-apyaa apa aoae apy cea ao, ecyy a ap c eco eeo (1,3) (3,1):

,(46).(47) Taoe peopaoae coxpae opy:

1,(48) opooaoc:

0.(49) apaepa c oepaopo coeo ooe e cooecy apye CP a paoe o y ecce oe CP-apyay ac, coepay ay o ocax apaepo ape cea cey opao:

2 0 2 2 CP 0 1 0,(50) 2 0 2 2 e 3.(51) Cyecye poo copea apa, oa e opaa apa CP, aa, o oeo ceyee oeco:

CP CP (52) Aaoe ocpoe ap oo poec epo.

Oe o cya apo coco oo pcyc aopaocx a. a, coeaa apa epoo cea, yapa o ocpoe, aaa cey opao:

,(53) e apye coe:

0 1 3 1 0 2.(54) 3 2 Ta a y 12 23 opa 1, e oe ycao ay e epapx, a cyae c apa, e eec ece a apaep, o ooo aa . Apoa opa ap oeceae yapoc ap epoo cea.

apaep oeae a apyee CP, a apaep peypy ceae apoao.

C oo apaepa (53)(54) oo eeppoa oy apaepa a ocoe coeaoo pecae c apo coeo, oopa yapa pecae epoe ceae e poee ap:

Rot CP Mjr,(55) oopo ee ape oe, oeae cooeceo coy pae 0 Rot 0,(56) apye CP:

CP CP (57) c 0 0 1 CP 0 0 0 (58) 1 0 aopaoc aa 1 2 :

Mjr,(59) e apye coe aa ape 1 2 0 Mjr 0 2 0.(60) 0 0 apaep paaeo ac (56) apaepa (55) opee yo pae e eop oc pae cey opao:

,,,,(61) 2 2.(62) Cpaa (41) c yeo (61), (62) c cepea a o cea epo, oyae ceye ae apaepo coeao ap (56):

0 5831 0 2415 0 7599.(63) Hoa apaepa ao eocppye ooeoc cea apo epo. cpae cepeax ax pacao op ap cea oyae aee ya oopoa 56. oee oo, c aaoo (61) ooe eoo eopa oc pae coeao op ap apooo cea cepeax ax, oyae, o oc pae cea epo apo coca yo, 45 payca. o a ec aepao opypoo oe ooeoc yo cea apo epo.

Heocpecea poepa oepae yapoc ap MCP CP Mjr, MCP MCP,(64) ce coeao apaepa (55) ap cea epo:

.(65) ece ap cea a eop epo c opeee acca ae eop epo c opeee apoaa, e a apyax CP eo aoo a epo:

MCP 2 1 2 3,(66) e apa pae pecae yooc pae 1 1 2 3 2, 1, 3, (67) 1 2 2 2, 1 2,,, 2 (68) 2 1 2 3 2.(69) opy (67)(69) oy paccapac a coeo poa paee a yo 2, opeee CP-apyae ao c eca , x poee.

a, eooe apooe ceae e oo oeo oo poec apae ey apa cea apo epo Caapo oe. coeaa apaepa ap cea ooe eeppoa ee oe yape apaepa c ee apya CP eo. ooa apaepa oe oea p ye opoco apye cep o Bceeo, o oopo, o-oy, poxoa o oece apye CP-eoc a apoo, a eoo ceope.. Hapyee CP, yeoe p oo paoco a, oe coeac c eo aopaocx a ape epoo cea. x aoe ece yoo ya coeao pecae ap cea, e ee cooecy ap oe, oopo poeeo aeee paeee pax a oeax paoe p o y ecce (cp. (50)). To aa aa o cea epo c yeo cex CP-apyax eo oe pooc caapo apaepa, o o ocaoo coe, e ee oy eo eppepyeoy peyay. B o e pe, c cooae peoeo ccepa coeao apaepa ap cea eo pacoppoa eop coco epo, e a apyax CP eo aoo a epo, a poeocppoao a opyax (66)(69). ecaaoo aae, o coeaoe pecaee ap cea oyee a ee ocoe peya eppea oy oe p aae opaoe ax o oc epo eyxc acoee pe apyex cepeax.

B ae 5 pecae eoope peya cceoa eoo pa paaox eo (2+1)-epo aoo epoae () o ee oe p oeo eepaype ooc.

poeocppoaa oooc eepa ea epaCaoca (C) a a ce e eeo o, a a ce oeo eepayp ooc, a ae poaapoaa acoc paaooo ca oooeco acc ooa o apeoc o ep ooa.

pecae pace a aa epooc ooopaoa epoopox ap o ee ao oe. Pacca paao c acc epoa a y ep epoa apeoc aoo o, a ae ye a ea epaCaoca. Bcea aa poaeoc yepoo epooo aa oaao, o e C ycpae ee pacxooc cax ex ox.

poeocppoao ooee e cepe epoo a ce oeo ooc epooo aa. p o ee oeoo ea C ycpae e oeceae cxooc paaooo ca acc epoa p oeo eepaype. C e oye yaax oo poee ea pace opaooo oepaopa ooa o ee ao oe. B acoc, o poeeo cceoae cya ooceo caoo o cox ep ooa: 0 2/,. Cpaee peyao, oyex ypyoo pacce ooo (2+1)-epoo cya, c peyaa (3+1)-epo epoa, oaae, o poc ay poecca c yeee apaepa = p 1 (2+1)-ep pocxo o aoy 1/3, 2/ o pe a (3+1)-ep aya pace a. B o e pe cyae 1 a ac ay pacce, opeea ceee oopoe e e -ap, ee ce (2+1)-ep a 1/2 8 3, a (3+1)ep cooecya pecoea paa. Oao peaa ac ay pacce ooa, oopa ae paao c acc 2 ooa = 2, p 1 poopoaa, o coaae c peyao (3+1)-epo .

Paccao ooeeoe paee paaooo ca ep epoa ocoo coco 0 ao oe c yeo aa oooecoo ea C a oyea acoeca opya eo ao ocpoc 2 1 = / yepoo epooo aa, e = / 0. Cpaee oyex peyao ceaoo oooec paoo cya = 0 c cooecy peyaa (3+1)-ep ceye o oee ao ocpoc 2 1 a y oeoo apaepa. B ooceo cao oe 2 1 pacxoc oapec p 0, o pe a 3 1 cpec oeo ocae. B co oe 2 1 c poco apeoc o yae cpee, e 3 1. C yeo oeo oooeco acc ycpaec oapeca pacxooc ao ocpoc 2 1 cao oe ( 0), p o 2 1. p oeo eepaype ooc ye ea C po oeoc epooo accooo oepaopa ye ooeeo pe, o pe a o pacxoc papaco oac a accoo oooe cyae ocyc oooeco acc ooeeo pe (2+1)-epo .

pecae ae peya cceoa oeo eepayp ooc a paao c ep epoa oooec acco ( 0 ) (2+1)-epo :

2 2 / / / = Li1, 1, 2 4 (70) / / / Li1, 3, 4 e apaep ( = 1,2,3,4) opeee coaco 2 2 2 1 1 1 1 =, 2 = 2, 3 =, 4 = (71) 2 2 2 , = Li, 0 1,(72) 2 e Li =,,1 =. (73) = eao cceoa cya ooc poeoo epooo aa. B apoo-cepo cyae epoa ea acca a poaapoaa peee x ( / 2 ) cox ( 2 ) eepayp. Oaaoc, o eepayp c acc p x eepaypax opaee. Oao o a o cpae c ao eeepaypoo caaeoo, opeeeoo oooeco acco ooa, ooy oa paaoa opaa acce epoa oaaec ooeo. C poco eepayp caaeoe ( ) ee a pace, a o oac cox eepayp eepayp a c ep epoa caoc opy. oee oo, 2 2 p 0 ao cepc pae = / 8, . e. e oeo ooc ( xoea) coa e cepe epoa. Oao p o oeo ae apa ep, 0 0 , o pae epe, ooeeo pe e ye e oae.

oo yaax e peyao, cceoa ae ao pao a opoc, a oooc apye apooo apaoc a ce ooeex opao apoooy ec (2+1)-epx eaeex apoox eopx p oeo eepaype, a ae oooc ee occaoe c yeo ooeex ao. Ha oyeo ooe paee o ac oeoeepaypoo eoo ec pocpace paepoc (2+1), oopa ypyec acc epoa, axoc a oe oopeeo a aeex, a eaeex apoox oe ceao oypa, oopa po apye P-eoc. o ceao oaec aa oypa, oopo oeceaec paeco y epecx eacoc o pee ax oe.

Ta opao, oo cea ceye oe o o cceoa eo oe paepoc . Mae coca ooo p copae paepoc pocpaca-pee c (3+1) o (2+1) cyeceo ec. Paao c acc epoa ao oe ea aa ocpoc, .

e. ae coca epoo, ae pao ec p epexoe o (3+1)-epo (2+1)-epo . e oeoc 0 , , , , . (2+1)- - .

, 5 Z. , , .

. + +Z + .

, , , >1000 , + + Z+.

, .

, :

1. ( , , .) , , , , , .

2. .

, . . , , .

3. , .

4. , , , . , .

5. . , , , , .

, -.

6. - . .

, - .

.

7. - (2+1)- . , - .

8. Z-.

(2+1) . , P-, SU(2)U(1)- .

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[28].G. Dattoli, H. M. Srivastava, K. V. Zhukovsky, rthogonality properties of the hermite and related polynomials, J. Comp. Appl. Math. 182, Issue (2005) 165-172.

[29].G. Dattoli, H. M. Srivastava, K. V. Zhukovsky, A new family of integral transforms and their applications, Integral Transform Spec. Funct., 17, N(2006) 31-37.

[30].G. Dattoli, H. M. Srivastava, K. V. Zhukovsky, Operational methods and Differential Equations with Applications to Initial-Value problems, Appl.

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[32].P. Blasiak, G. Dattoli, A. Horzela, K. A. Penson, K. Zhukovsky, Motzkin numbers, central trinomial coefficients and hybrid polynomials, J. Integer Seq. 11 (2008) Article 08.1.1, 1-11.

[33].G. Dattoli, M. Migliorati, K. V. Zhukovsky, Summation Formulae and Stirling Numbers, Int. Math. Forum, 4, N41 (2009) 2017-2040.

[34].G. Dattoli, K. V. Zhukovsky, Evolution of time dependent linear potentials and non-spreading Airy wave packets, Appl. Math. Comput. 217 (2011) 79667974.

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