rro^o)KHocTb 3ToMy B Te erpaQuu 14BbIr{ucAI4TeAbHOIi TexHI4Ke CnrHa bI HMeloT r.rM[y bcHyro $opuy u Ha3brBaroTcs McKpeT...
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rro^o)KHocTb 3ToMy B Te erpaQuu 14BbIr{ucAI4TeAbHOIi TexHI4Ke CnrHa bI HMeloT r.rM[y bcHyro $opuy u Ha3brBaroTcs McKpeTHbrMH curHaAaMII. nu$opMal{Hrl Henpepr,ranafl I4 ALICKperHan Qoprrlr,t upeAcraBleuur xpaCo3AaHIlfl, vrMeroT oCO6oe 3HarleHue rrpu pacCMOTpeHIlu BOnpocOB CpeACrB ITOMOITIbTO C HeHuq, [epeA,aq]r u o6pa6orKv uH$opuaLIHH BbIIIHCAUTE
bHOIi
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B uacroru.tree BpeMfl Bo BCex BbIrrI4cII'ITe,\l,HbIx MaluuHax uu{ropMarlr{s [peAcTaBA-r{eTCfl C II OMorrtrbro s^eKTpnqecKr4x cl{rna^oe. llpu rrucleHHoro 3HarreHHfl sTOM BO3MO)KHbIABe QOpuu [peAcTaBAeHnf KaKofr -/\I,I60 nepeMeHHori, naupr'ruep X: r B BnAe oAHOfO cHrHa/ra - HaIrpI4Mep' 3^eKTpHqecKoro Haflpf)KeHLtfl,Koropoe cpaBHIlMo c BelrlrruHoli X (anaaorrluHo eri), FIae4nnutlaM Ha BxoA Bblql4c^ure^lHoro ycrnpr.rMep, upu X:2003 policrBa Mo)KI{o [oAarb Harlpflx(eune 2,003 B (uaculra6 npeAcraB0,005 AeHHfl 0,001 B/e4.) Iaarl 10,015 B (uacurra6 rpeAcraBlesrlx
B/ea.); B BfiAe HeCKOALKHXClrfHaAOB - HeCKO bKHx LMnyAbCOB Haflpqlreuuit, Koropble cpaBHI4Mr,I c rrucrtoM eAIIHI4II n X, uncrr'olr 4ectrKoB g X, .IucaoM coreH e X H r. 4,. (c noMoulbro cxoAsoti flepeaa Qopua npeAcraBleHna ltrQopuaquu HellpeprreuOli. BeH71H aHaAOIoBOiI, Ha3hIBaeTCtI Be1r4qr1Hhr autraOra) rrpuHqlrnplluirMarb Morfr B raxorl eHHbIe npeACTaB ?rquHbr, {:opue, gHa.teHE 3HaKOAIa'IeCTBO B OupeAeAeHHoM Aro6bre rrr4atlbHo MaIIa3OHe. Be U6eCKOUeqHO BeAIlrIHna, npEHIrMaTbTaKaf MO)!(eT KOTOpbIe UeHuri, Ko, OrcroAa Ha3BaHI4fl _- HenpepblBHat BeAJ'IqlrHa 11HenpepblBHafl rrHrfOprnrarlux, CrrOeO nenpepblBl{OcTb oTqeT I.IBOBbIAeA.fleTOCHOBHOecgoi- OTCITCTBHepa3pbIBOB' npOMeX(yIKOB MeXAy 3HaCTBOTaKHx Be LITII1IH qeHnflMu, KoTopble Mox(eT npuHnMaTlr AaHHa' aHa^oroBaf BeII4ql{Ha.
B aHa oroBblx I{cnol53yercfl HeupepueHafl SopMa npeAcraBleHltfi B BbIIIHCAI4TEAbHbIXMAUII{HAX (ABM). 3TU UAUTUHbITTPCAHA3HAqEHbI ocHoBHoM AAr pelueHI4fl 3aAaq, onl{cblBaeMblx cllcreMaun 4u$$epeuqHalbHblx ypaBHeHI{I;r : H CCAeAOBaHLIfl nOBeAeHAf II OABHXHbTX O6'beK TOB, MOAe upoBaHl4q [pOqeCCOB Lt CIICTeM' perueHufl 3aAaq uapaMeT.a ptrqecKofi o[TI4MI,I3aIIuu u olrl4Ma bHoro ]mpaB^euua. YcrpoficrBaA HerIpepbIBHbIx clrtrraloB o6laAaror 6oaee BbIcoKI'IM 6rrcto6pa6ornx clrrrral, Bblrrolusrr, aro6oe ero oHLI Moryr 'InTerpapoBarb n. O4uaxo la3-3a clo)l(Hocrl4 r,r T' npeo6pa3oBaHl{e $ynxqnonaaruoe TexHr4qecKoft pea.lrusaql'rraycrpol)rcrB BbInoAHeHlrr ,rou{qecKHx ouepaqufi c HenpepbIBHbIMI4 cLIrHa aMu, Mr4Te^rHoro xpaueHnfl TaKr{x cnrperuarb 3aHa oB, r{x roqHoro LI3MepeHI,IqABM ne Morrr s$$er.rueHo IIHo6r,eMos 6oa-sruux rE o6pa6orxori xpaHeHI,IeM c cBfl3aHHble Aaqu, quSpoacli pellarorcfl nplrt r{c[ol-b3oBaHurr AerKo Koropble Qopuaqura, un$o pMaI{Lt u' peaauaye uoti (4ncnperuoli ) Qoprurr rpeAcraBleHux quQpoerrrrru 3AeKTpoHHbIMId BbIrrr'IcA-LITeAbHbIMr{MaIrrHHaMIl (3BM)' poAeficrBHeM,
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Bropar Qopua npeAcraBlenua undlopMaquu Ha3blBaercq AHcKpernori (c noMoI{bro ua6opa HarlpflrKeHrli, xax4oe n3 Koropblx coorBer'faxue BeAr4r{I4crByer oAHofi us quQp rrpeAcraRl-aeMori seauquuu). He onpeAe^eHHbr, rIpHHHMarouIne He Bce Bo3Mox(Hbre' a Arllub Bno Hr,re 3HaqeHuflr Ha3bIBaIOTCf AI,ICKpeTHbIMLT(upepuraUCrurlrra). B orrr'urrae O'r HeflpepblBgorl SeAu.II4HbI KOIHTIeCTBO3HaqeHlltl 4IaCXperUOft BeAr,rqEHbI BCerAa 6y4er KoHerrHbIM. HerrpepblBHylo r'I McKperl{yrc Cparunraa Qopuu [peAcraBAeHLIr IITO He[pephlBnpu uCno^53OBaHHI'I 3aMeTLITL', HeTpyAHo unQopuaqulr, norpe6yercs MaIIJI4HbI Bbrr4*rcuure^bHol; co3AaH:y.fl Hofi OopMbI A^.f (xa;x4an Be^aa{nHa upeAcTaB^teTcfl oAHI4Mr Merrbtuee quc^o ycrpolicrn a He lrecKo^-bKrrMrl CHrHa aMn), Ho sru ycrpotlcrea 6y4yr cao)KHee (oHH qn c^o cocTog H}rrl cHrH a^a ) . AOAXHbT pa3^UrraTb 3Har{HTe^}H o 6o^bru e e
52
KonrponuxbteBonpoebt 1. 2. 3. 4. 5. 6.
Kaxr,re ypoBIlI,I upo6,rerr.t[epeAaqu r'ilrt]opuaqraz Blt sHaere? Hasoeure uepu nHQopMaIIuI4 cI4HTaKcHrIecKoroypoBHq. Oxapaxrepnsyftre cyulHocrb lloHrlrl{t gHTponuu. Kax cBq3aHLIMexAy co6ofi IroHfiTlrr{Ko LIqecrBa uu@optrlaqun n eHrponuu? r{ro orrpeAelter repMnH ? flprane4u're [pLrMepLI coo6qenufr' coAep)Kau{r,rxoAHH (Ara, nocell},) 6ur taHSopuaqru' 3anuruure Sopuyau Xap'rara ra Lllennosa' flpn xaxolr ycrroalan tpopuyla LUeunoHa repexoAn'r r Qopuyrry Xap'r,'r,u? t{ro'raxoe a6crpartnr'rti al@anz'r? Aarlre onpe4err.eHr,reras6blToqltocTl4a Qaor{ra ucrovurra coo6uleHr'rrl. nxSopMaI{HI,I ceMaH'rl{qecKoro ypoBHt Blt gHae're? Karcue rr,repr,I 9ro'raxoe'reeaypyc? Kaxre uepu nH$opMaIIuH flparMarlrqecKoro ypoBHt BH sHaere?
7. B. 9. 10. 1L I 2. .A,ailreonpeAeleHHe 4esrHQopvaquu. 13. Hro raKoe Kaqecrno nHQoprvraquu? I4. Hasosnre ocHoBHbIecocraBlqroulne Kar{ec'rBaran{ropuaquu. 1.5. Kar BbI uoHl,IMaere3au{HII{eHI{ocrb H coAepx(are^},HocrI' r'ruoopntaquu ? 16. 9 eu A,ocrnraerca rpe6yertr,lri yponeHb 3aulsuleHnoctu rarrQopv'aquu? 17. Haeosnre ocHoBHFiexaaccrlQu xaq[IoHHble fi pl4suaru nn@opuaquu ? 18. Karr're BI,tAbII{ Qoputr upeAcraBleHran zHSoprraqru a uIr@opnaquoHHr,rx ct{creMax Bbt sHaere?
I"nga 3
e urHQo p l..ararJulvl II p e4c'raBneHuL
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3.1, CACTEMbI CTII C AE}{I fl \
crenecr{creMa. oua, xax LrABeHaAllarepl4rrHagcucreMa' e raxofr-ro I{3MepeHI{t B cI4CTeMe (Hanpl4M€pr HH CoxpaHr4^acbr{ Ao Haruux 4neri : I{3MepeBpeMeHr4:I .r : 60 MIrHr 1 Mr4H 60 C,anaaorl4qHo B CI'ICTeMe : : c)' 60 60 wtnu, I runn HHflyr^oB: 1"
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HaIaMeHoCucmeua c\uctenuf, - coBoKylrHocrb [pI4eMoB I{ npaBI4A OAHOBaHufl LI O6OgHa.IeHI4qqfice^, no3BO 'IOUII4X ycTaHoBI'tTb B3aI4MHO qucloM [peA'craBlenueM ero rr 3Haqnoe coorBercrBl'Ie MexAy aro6rtn B BI4Ae KoHer{Horo
r{I4C a CUMBO OB.
B aro6ofi cucTeMe cqHc^eHr4fl aU6upaercs
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B 3aBHcIlMocrI4 or Mecronolo)Keuug aAsaBI'IT, npeAcTaB^t-
rculuftco6oticoBoKy[HocTbHeKoTopblxCI4MBo^oB(caoazalrsrraxoa), uoxno c noMolqbro Koroporo B pe3y^braTe KaKl4x-/ru6o ouepaqufr IIpeAcTaBIlTrano6oeKoAI{qecTBo.I4:o6paxeHl{e^106010KoAI.IaIecTBa - quQpaura (oraar' cifro)' Ha3blBaercfl qHcAoM' a cI4MBoAbI aaQaanra Ka'KAoro I43 Cur'reoabl aaQaaura AoA)KHII 6rrru paaHrrMrl H 3Harreul{e HUX AONKHO 6Hrl ragsecrHo. BcoapeueHHoMMllpeHaI,I6oAeepacflpocTpaHeHHoIlflB^'eTcqAeCSggaHO C CflTUrIHafl CITCTeMaCqI{CAeHLtf' [pOI4CXOX(AeHIIe KOTOpOt]r nepe6blla BeKe XIII s ra Ila^bueBbrM CrreTOM.oHa soglruK a n Irln4ura crrnc^ecllcreMy HeceHa r Eapouy apa6artln. flostottly A\ectrHqHylo tlnce^ qlrsHHs cTa H Ha3brBaTb apa6crofi , a ucno^s3yeMble A^-fl 3anI4CU 7' B' 9 6' 5' 4' 3' 0, 1,2, pbr, KoropbIMI4 MbI Tenepb Irolb3yeMcx, apa6cranu. C4aruHxapeMeHA^.'InoAcqeToBI4BbIql4c^eHraftnpzuerrr^llcbpa3. BOCTOKeAoBoAtAtrrrHbre CuCTeMbIcqlaclenua. HaupnMep, Ha Apeggeln{ cracreua. MnoHo rxr4poKo 6rraa pacupocrpal{eHa ABeHaAIIaTepr.IqHaff (uolxra, BI{AKrr' Tape KI4 I'I T' A') u ceftrrac crILTaIor Aro""" ,rpLp,t"tsr - ABeHaAIIarb. 3Ta cucreMa cql,rclre)KrrHaMr4.Hrac,rloMecgI{eB B roAy I Qy' : tZ Hrrfl coxpaul{Aacb e aHralllicxori cucreue rnrep (HanpuMep' : B ltpen12 neucon)' (1 uuaa-l'raHr 4rorirron) I4 B AeHe)KHoIi cucreMe rreMBasu^oHecyutrecTBoBa^aBecbMac^o)KHagIuecTl{Aec,{TepuqHag
54
Henosuquonilaf,'cucmey.actlucilenun-cucreMa'srotopoicl'tMBoalI, o6ogHa.rarculr4e
(uosr'rqrau)a uso6paxenull
rrl{cla'
3anracuquc^aAeHeuogzquourrolicHcTeMectll4c^eHH'Dlvroxter : 6urr upe4craB^eHa BbIPa)KeHrreM A o = D t + D 2 + . . . + D N = , . I - D r, rAe A, -
3a[?Icb qI'IcAaA B cucreMe cqI4cIeHI'It Di Dr-
ctrMBo bI cl{c-
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i f raqcHHc(o6oaHa'iacltocxo.nuvccrno)
uo cleocyqecrBltercs 3anncr qplcel s srofi cucretlre cquc.lr'eHl4.fl Ayrouu4M npaBI{AaM: 1) ecrrr.rqflOpa cleBa MeHbure,vervrqrlQpa cnpaBa' To AeBaflql{Qpa BrtrrqaTaercfH3 npaBoli (IV: I < 5, cae4onarenruo, 5 - 1 :4, XL: 10 < 50' cleAoBarelbHo,50 - 10 :40); 2l eclvt rlr4Qpa cnpaBa MeHbIue I{ALI paBHa lluQpe cleBar To 3rH 5 + 1+ 1+ 1: B,XX: q r a s p u c K ^ a A b l B a r o r c r ( 5V*I 1: : 6 , V I I I :
1 0 +1 0: 2 0 ) . Tare, .rHc,l,o 1964 s puucxoi ctlcreMe crrl4cleHrlF uMeel' BrrA MCMLXIV (N4- 1000,CM - 900, LX - 60, IV - 4), a4ecr (AeBflrbCOT))nOAf{aeTCA nOCpeACTBOMBbITIHTaHLIflI43 (TbICfrII4D qI4CAa (CTO))' ( uecTbAecfT )) - ilocpeAc'rBoM c^ox(eHHff ( [flTHAeCfl Tu )) rr (AiecfTr{ })' (qeTblpe) - nocpeACTBoM BbITIHTaHVIfrU3 (rIflTH)) (eAHHI'IIIbID. B o6u1eu c frae Heno3[rI-lHoHHr,Ie cucreMbl crrnc eHllfl xapaKTepl43yrorcfl c O)KHsIMI,Icnoco6anu 3anucu rrl4cel u upaBI{AaMIa Br'IuoIHeHuq olepaqair. B Hacroflutree BpeMf Bce Hav6olee pacnpoapuQueruvecKrrx cTpaHer{Hbre cucTeMbl cqnc eHl4fl oTHocflTcfl K pa3pflAy no3rlI{IIOHHIJx.
BbrxAectrTr,lnoc^eAoBa're^bHr,Ix qlrce^, a Bce nocleAyrcIqne quc^a, HartHHagc 10 r,rr, A., o6o3Ha.rarorcfly)Ke 6es ucnolbsoBaHlrfl HoBrrx quQp. .A,ecaruvHaacucreMa cqucAeHuf ocnoBaHa Ha roMr tITo AecflTbeArrHHIl KaxAofo pa3pflAa o6re4raHarorcfl B oAHy eAIlHlrI{y coceAHero crapluero pa 3pffAar uo SToMyKar(Asrrl paspxp, zMeer Bec, pannuil creneHrr I 0. cae AOBareAlHo,3HarreHneo4noir u roli x(e qu$pu onpeAelsercl ee MecTo[olox(eHrreM B u:o6pa:reurru qrrcla, xapaKTepla3yeMblMcreneHbro rrl,tcla 222.22IIH+pa 2 nonropaqncla 10. Haupnrr.rep,B I43o6paJKeHIal4 groM qll$pa 2 ogna.raer Kolr'IqecrBo pa3, npu rlepBafl cleBa uflTr, ercq (ee paBeH eropas KoltlqecrBo Bec 102); coreH AecflTKou (ee aec pa(ee paBeH rec 100),'rereepraa KolfiqecrBo eALIHI{II l0), Tperts aeu (ee paBeH l0t) rannran quQsec eA,I{HrrIIbI Ko/tfiqecrBo Aecrrrbrx 4o,lefi pa - Kolr4rrecrBo corblx 4oaerl eAnHuIIbI (ee aec paBeH l0-2).To ecrr rfnc/\o 222.22 Mor(er 6uTr, paaaox(eHo rlo crelreHrM'racaa 10: 222.22:
2 x 1 0 2* 2 x l } t + 2 x 1 0 0 +2 x l 0 - t * 2 x 1 0 2.
AHalorn.rHo: 725:7 x 102*2x l0'*5x
3. 1. 1. floru
gltorrHbre
cr4sreMbr
cr{ncaeHrr.x
\ Crzcrelry cqLrcAeHHF,a xoropoti 3HarreHl4eqa@psr oflpeAeltercs ee Mecrorrolo)KeHl4eM (nosuqneit) a uso6pax<envrr 'lucua, lta3bIBalor no3urluor{Hodl.
Yuopxp,ovennuri na6op cI{MBoAoB(qzQp) { a o,a,,...,a}, ncrolb3ye rruri 4rla upeAcraBleHl,tfl AIo6bIx qucel B 3aAaHHoi Iro3IIIIHoHHoilrcucreMe cqr4cleHng, Ha3blBaroree aAQoBumoM,quclo cI4MBoAoB(IreISp) n + 1aaQanurap: Ha3hrBaror p-utnoti,
e e o c H o B a H u e M , ac a M y c l ' I c r e M y c q n c ^ e H H s
1 3 0 4 . 5:
1x 103*3x 102*0x 101+4x100+5x 10-1;
5 0 3 2 8 . 1:5 5 x 1 0 a+ 0 x 1 0 3 + 3 x 1 0 2 * 2 x 1 0 1 + B x1 0 0 * l x 1 0 ' ' * 5 x 1 0 - 2 . Tarculr o6pa3oM, ato6oe quclo A Mo)KHonpeAcraBl4TbB BI{Ae[o^HHOMaUyreM pa3^orKeHlrfl efo no crerleHfll{.ruc/\a l0: A , o = a n x 1 0 n+ o n - rx l 0 n ' r + . . . + o rx 1 0 1* c o x 1 0 0 * a - rx 1 0 - t + . . . +
-l-c_.x 10''+ ...,
CaruroftupuerruHoft 4a.r Hac flBlserctr AecflTuqHafl cl'IcreMa cr{Hc^ e * v r f l .E e a a Q a r u r - 1 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , a9 )o, c H o B a H L Ipe : 1 0 ,T . e . B 3Torl cr4creMeA^t 3anucu.uo6rrx quce^ rcrlo^b3yercr ro^bKo Aecarb pa3HbrxcHMBo oB (IINQp). 3ru qn$pu BBeAeHbI 4irfl o6o3Harreul'Iflnep56
( 31 .)
[oc^eAoBare^r,Hocrb us xos$Quqr{eHToB Koroporo upeAcraB^ser co6oli AecxruqHyro 3anHcb rrl,rcla Ar0: A ,o :
Ocnoaanue nosIaqI4oHHoIicHcreMtI cqrrc eHIlq - KoALIqecrBopa3ll4qHsrx quQp, r4cnolb3yeMblx 4u raso6pax(eHl,tfiril4cel B 4artnofi cncreMe cqr{c^eHus.
100;
anan-,...e tao.a_f..a_m...
(3.2)
cly)r(Lr Aag IIe yIo qacrb rrscla or 4po6Hoi, To.{xa, orAelsrou{afl groll [ocleAo[o3t4lluu a xax4oli 3HaseHItIi KoHKperHbrx Qurcarlrar IILtQp I,I flBlflercq Hatla"rroM orcqera. BarelbHocrl4 B o6qertr c ) rae 4a-a 3aAaHI4fl p-vt-ull'oit crrcreMbl cqlacleHufi Heo6ocHoBaHI4e p u arr$arurr cocroflu{ufi us p pa3xoAr{Mo olpeAelxrb Ar4rrHbrxcr{MBo oB (qzQp) Qi, i:1,...,p. 3a ocuosaHlre cHcreMbI Mo)KHo npI4HflTb ato6oe HarypalbHoe rrl4cAO ABa, Tpu, rrerblpe I4 T. A. o6aFrHo B KaqecrBe aa$aruTa 6epyrca
57
[ocleAoBarelbHbre IleAbIe rrLIc a ot 0 4o (p- l) BK rotrLITe rHo. A.lr-s 3a[r4cH rrpol{3BolbHoro qnc/\a B ABoItqHoi cLcTeMe cql4c/\eHlrt I4crrol!3yrorcfl rILrSpbI0, 1,rponvHofi - 0, l,2,tnrepwrHoi - 0, 1,2,3, 4 rar. 4, B rex clf{aflx, KorAa o6uleupnuarsrx (apa6crux) qu Qp He xBaTaer M.a o6ogHa.renar Bcex cuMBo oB alQanuta c?ICTeMbIcqucleHr.rrc ocHoBaHHeMp> 10,lrcIIo^b3yror 6yxaeHnoe 0603Haqeuue qu$p a,b,c,d,e,f, .Arrr,rupurvrepaB Ta6rr. 3.2 uprane4eHu aaQaenrbl HeKoropblx cl4cTEM
U
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5
Tadtuua 3.2
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Cucreua cqucreHm
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5
8 10 l2 to
A : o
1* a I : oxPo* a -,xp' 1..'* a -^xp'^ n
= \ q*p*, k=-m
(3.3)
CIIHCACHI4q.
qlrcla A a p-uuuoit cncreMe cvplcleHurt tBltercf qu$p ar. locleAoBarelbHocrb Hanpuuep, AecflTHqHoe quclo 35 e cuctelulax cqficAeHI,Iq c ocHoBanuer"r P 6y4er uMeTb Br{A: l4so6paxeu?reM
P paspnght 12 quc,\o
5B
1
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2x4t + 0x4t i 3x4o 1 x 3 t + 0 x 3 2* 2 x 3 t + 2 x 3 o lx2t + 0x2{ + 0x23 + 0x22+lx2t+lx2o
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4ericrar,ra HaA qnclaMra s No6oil noar'rquouuolZ CI{CTCMECTII4CACHT{'NPOII3BOMTCfl IIO TEM )KE TIPABI{ AMI I{TO II B AEHa npaBIa aX BbICgrrn.IHOi CtICTeMe, TaK KaK BCe OHI4OCHOBbIBaIOTCS [oAHeHr4r A ehctnnfi,HaA cooTBeTcTByroilItrMr,r no71HHoMaMz. FIpu eror'r Hyx(Ho ToAbKo rro^s3oBaTbct TeMH raorruqauu clox(eHr4s H yruHorKeHrrgr KoTopble I{MeloT MecTo ilpl{ A,aHHOMOCHOBaHLIHp CIACTeMbIcquc-
rAe or - r{uspbr cHcreMbl cquc^eHu.f,;n u m - quc^o qe^blx tt 4po6Hbrx pa3pgAoBrcoorBercrBeHHor Ao- sanncb rruc^a A e p-n'ruofi cucTEME
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4
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AaolrqHaq TponuHaa 9ernepuvnaa Ilarepuunar Bocut'repuvxaa ,IIecgru.{Hat .Ilrcuaartarepuvnaa LllecrnaarlareprqHas
4
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t0
+ Bxl2o
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28
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61
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(3.4)
C: gx N.
He oAHIIM Ecau npuuarb, rrro xax4ptla pa3psA trucla npeAcraBleH 3 eMeHToM c g ycrotluuBblMrr co cro flrrr4fl.lav\ a g 3leMe HTaun, xa;x4u li (3.4) n3 KOTOpbrx r4rMeer o4no ycrorisHBoe cocroflHl{e, To [oKa3arear Koropoe Heo6xoAI4orrpeAe xr yc^oBHoe Ko I,IqecrBo o6opy4oaanEs, MO 3arparr.lTb Ha rrpeAcraB^eHHe quce^ B 3ToIi cncreMe. B cBff3u c 3TI4M uoKa3are^b (3.4) Hasuaalor rloKa3are^eM SKoHoMHrrHocru cl4creMbl' ql4clo, Koropoe Mo)KHo H3o6pa3nrb B cl{creMe c Maxcuua;rrHoe ocHoBaHneM g,'
Ao^-:{
(3.s)
- I'
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(3.6)
logo(Ao^*+ 1).
1). Tor4a 4aa rrro6ori cracreMbr cqncleHl{lr C : q logr(Ao^*+ rITo Be IdrrI4Ha g tB7151erct HeupepbIBHoI'I BeAH'ILlHovI. ,A,onycruu, or Be r4BeAItquHy C xar Qyuxquro IIpu erou 6y4err.r paccMarpl{Barb quHbr g. Tenepr eclr4 3a eAHHHqy I43MepeHnfl o6opy4oraru,tfl rIpI,IHffTb ycrlonHrui 3AeMeHT c oAHI{M ycroftuuaarM cocroqHueM, To 4lrfl cpaBHeHUq AByX CI4CTeMCrrUC eHl{fl MO)KHO BBeCTI.IOTHOCUTeAbHTUIUOXa3aTe^b 3KOHOMUqHOCTU:
F : qlogo(Aq^- + 1)/ [2log r(A, ^**
I )],
(3,7)
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62
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z
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Pnc. 3,4. 3asucltMocrs orrlocl{TelbHoro IIoKa3are^t 3KOHOM]lrlHocTI'l or ocHoBaHl,t.t cncTeMhl cquc^eHI'lg
TbI Bbrno^HeHl4fl B Hrrx apu$uerzqecKldx u AoruqecKrax 4eficrarari, npeA[oqTeHPre B HacTotrqee BpeMf oTAaeTcgABoHqHoIi cHcTeMe cqncorl4qe cKr4e gAeMeHTbI, CooTBeTcTByIOUIHe AeHHfi . .A,etic.runre^bHo, 3TOI1CgCTeMe, Aolrr(Hbr HMeTb Bcero ABa ycToftqI,IBbIX COCTOSHI4n.3aB 3TOM CArIae K 3aAarle o6napyAaqa pa3^r4rreHlrfl cr{rHaAOB CBOAT4TCS 3HaqI{TeAbHo npoqe' ApsQvto uer), ero I4AI4 (ecrr nlrnyarc xeul{fl B Aerqe ocyqecTBAflIOTCl TaK)Ke r.r Aofr4secKne MeTr,rsecKr4e AeficTBufl ABor4rrHofi cllcreMe.
3,l.2,tlepeBoA qr4cel I43o,4Hofi cr4creMbr c'lvc;l.euusr B APyryrc 3AAarry [epeBoAa qnc^a us o4Holi clIcTeMbI cqHc^eA Hr{t B Apyryro r o6u1en clfrae [20]. llycrr u3BecrHa 3auucb'rltc^a p.' OCHOBaHLIeM C eHIIfl CTIIIIC B CI4CTeMe PaccuorpuM
Ao=Qnxf + an-r\t-' + '..+ atx pt + aoxf * a"x pt +"'+ n
(3.8)
* a--x p-^: .L o*P*, 1.
rAe a, -
k=_m
qHOpbI p-uuuoir cucreMbl (0 < o, < p-1).
63
Tpe6yercx nali:ru 3a[rrcb groro x(e.rracrra A B cl4creMe cqllcleHufl ocHoBaHr4eM d.' Ao:
bnx d" *bn-rx dn'l+ ...* b,x dt *
box d0 *
c
b-,x d-' + '.. +
* b -- ' - x d - ^: . L b * d * , k=-m
(3.e)
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Ilprn uepeaoAe cleAyer [pllAepxuBarbcfl rrpaBl4,racoxpaHeul,Ifl To!IB pa3Hblx cllcreMax, rlpuqeM IIoA ToqHocrbro trSO6pa.)XeUl'lfr,t{I'zc/ra HOCTH M aAIuerO (npaaoro) pa3pflAa, noHHMaercff 3HaqeHr.reeMHI,IIIbI CaMOTO ncnolb3yeMoro B 3a[I4cI{ tII4c a B ToIl u.lrt{uHorl cracreMe cqucleHnfl, cpeAIlycm reflepb nepeBoA Ao -+ Ao A,ol)KeH ocyu{ecrBlsrbcs B gToM clyqae AAfl uepeBoAiaAlo6oro cTBaMU p-u.firofr apnQuerurn. qncla rdc[rro,lrr3yro'r npaBuuo geueHun - 44tt nepeBoAa qeaorl qacru qr4c^a,u npaBu o yMHoKeHufr- A t nepeBoAa ero 4po6uoti'IacrH. Ilepenog qelrt.x v-ucel. Brtpaxtenua (3.8) u (3.9) 4,,r.aqelblx qncel 6yayr nMerb cae4ytoult tti BI,IAcoorB ercrBeHHo :
(Ao+
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a p-nvHoii uucaa A, 3a[I4cauHoro B Aecs'ruqHyro crcreMy (o,,an,, ... eo , e.t a.2 ,,, a..le cBoAt4Tcfl cllcreMe cqHcAeHHq B BHAeA,,: Aru : au p' * au-rpn't + .. * oopt'* KBbIr{I4cIeHuto3HaqeHutMHoroar^eHa p ' ^ p ' t c p e A c rBaMuAecq'1'u'JHoli aprlQrreraxra. * + . . " + a . , + a.l e.rp2 llepeeo4
A o = b n x d n * b n _ , x d " - +1 . , . + b r x d r + b 0 ,
(3,11)
Ao:
ucxouue rlHQ-
b n x d n * b r - , x d n - t+ . . . + b r x d r + b o ,
IAe/ dl: lAr/ dl\+ IAe/ dl^, rryelAo/ d]u - qerrarqacrb alacrrroro- HenolHoealacrHoe; 1 A " /d l " : l ,
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2
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j
1 , , :r * r ,* r x 2 , * l x ? * r x 2 ' : 1 1 , 5 , 0 .
( 3 .l 3 )
- a p o 6 H a r r l a c r b q a c r r l o r o 'o c m a m o K
U J TOK OT AeAeHus Ao ua d. qacrb [epeuurxeM
B BHAe:
l A e / d l = b , x d " - 1* b , - , x d " 2 + . . . + b i b o / d . 3
(3.12)
r4e b. - ucKoMble quSpEI g d-u.IHoIl cl4creMe cqI{c eHLIt' quclo .{4x oupe4eaeHraa bo pa3AeAr,IMo6e'racrl,I paBeHcrBa (3.12) ua d, upnvelr a AeBofi qacrll upot43BeAeMAeAeHLe,tto l3yffcb npaBI4 aMH ptrt{Hofi apu$ueruxr,r (rax KaK 3arl}rcb xracaaAo a p-uuuoft cl4creMe cru4cAeHr.rrrr{3BecrHa). BsneruarvlB rlacrHoM lA,/ dl qe^ylo u 4po6uyto qacrr{:
flpuuep 3.
64
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Ilpaayro
Paspr4rr tlucrro
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Y.rurErgafl, qro b- { d, npupaagffeM MexAy co6oti nolfreHHble Abre r4 4po6uue qacrl{ paBeucrBa (3.14):
I A e / d l u : b n X d n ' t+ b n t x d " ' 2 1 ' ' . . + b r ,
(3'14) IIe-
(3.15)
f o"*o^o*1
L 5 a-zro
d
l:
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Taxuu o6pasor"r,uaa4uruftxoeS$uqueur D0B pa3lox(eHun (3.I l) oupe.l,e^teTcfl
cooTHoIrreHI{eM :
f or*o*o*f bo : d " L , l:
o cmamox,
(3.16)
r. e. boflBl.aercn ocrarKoM orAeAeHHfl Aouad. floao:xuu: Atr:
IAo/dlu:
b . x d " - 1 + b n _ rx d n ' 2 + . . . * b , .
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Ao: d-rx p'' + a-rXp'' 1..'* a--x p'+'..,
( 3.1e) (3.20)
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KacKaA,a- 3To HarrpDKeHI,te BblcoKoro y-poBnfl. llpu uo4a.re Ha BxoA Ha[pff)KeHr{fl BbrcoKoro ypoBHfl TpaH3l,rcrop I4l"/ saxpur, a rpaH3r4crop W2 orKpbrr. Ha orrxo4e ycrauaBluBaercn Hanpfl)Kenue HH3Koro ypoBHr. Taxnu o6pasou, 4auHruft xano.resoli KacKaApeallr3yer rrornqecKyro QyHxrluro HE. Crre4yer orMerr4'rb oAHy BUKHyIo oco6eHHocrr KMTA,II-KArorra H HHTerpa^bHbrx Mr{KpocxeM Ha ero ocHoBe: B cTaTuqecKoM pex(rrMe norpe6menar or r{croqHr{Kanr,ITaaur MorrlHocrb MeubrueHa HecKoAbKO UOP.CIAKOBIIO CPABHCHI{IO C MOIIIHOCTbIO CAMbIX MAAOMOIIIHbIX
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Cxeua AoruqecKoro 3AeMeHTaHa ocHoBe KM!,,Il-xrrtoqa npI,IBeAeHa Ha puc. 4.35. Ecrru Ha o6a BxoAa rroAarb curHallbr HH3Koro )rpoBHt, To rpaH3lrcropn I/I3 vt W4 6ylyr orKpbrrLl, TaK KaK I{MeIor KaHa c npoBopMocrbro p-Tv[ar a rpan3]rcrophr WI n W2 - gaKpbrrbr, TaK KaK r.rMeror KaHaAc npoBoAlrMocrbro n-Tr.rua, Taxnr'r o6pasou, Ha BbrxoAe ycrauoBurcff Hanpsr(eHne BhrcoKoro ypoBHfl (rr,oruvecrar e4rlHuqa). IIpn no4ave HarrpruKeHr{rBblcoKoro ypoBHfl xors 6tr Ha oAr{H H3 BxoAoB coorBercrByrouquti Tpan3llcrop W3 uttu VI4 :axpoercflr a TpaH3r{crop WI uttu W2 coorsercrBenno orKpoercr. Ha nuxo4e ycTaHoBlrrcr Hanpfix(eHrdeHr,r3KoroypoBHu (aoruvecxratl uoar). Bra4no, qro AaHHafl cxeMa pealr{3yer Aorr,rqecKyro $ynrqrrc VILIA-}{E. Ycrpoficrno 6agosoro eleMeHra I4-HE rar 6u o6parHo ycrpoficrBy 3leMeura IdJ\IrI-HE: uapaaaelruo coeA,HHeHbITpaH3l,rcropbl c KaHar aMu p-Tr{rra,a [ocleAotsare ]Ho - c KaHaAaMI4n-Tldua (puc. 4.36).
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H-HE HaocrroBeKMp'fl-xruoua Pnc"4.36.Aorrrecxgll 3^eMeHT 9ro6sr nocTpolrTb aoru.recrnft 3 eMeHTC TpeMfi cocToflHnffMl4,c nocrre4oaale.n-rnrrri BbrxoAoMAOrHqeCKOro3 eMeHTaHyrKHo BICnrOvUTr ( pnc. 4. 3 7 )' KoMMyraql'lr K Iorr n orr.eaofi uIfi AByxn o^-spu CI'IrHaAaM}Ic IIpoyupaBlrroTcE w2 I u w rpaH3r{cTOpOB 3araopsr ypoBHe curnarra s, ra aucoroM IIpn u @r. o, TUBOIOAO)KHIrMI{ $asauu H K IOq paW2 SaKpoloTcfl, I4l u rpansHcropur ypoBHe s, Hlr3KOM orKpbIT' 6y4et x,rrrov " S, S, clrrH.IAoB o6parHofi IIpu BoMKHercu. @aae altcoxoouHofi, qerrb cTaHeT cxeMbl BbrxoAHar rorr 3aKpoeTcg, K Kor4a c oqeHb 6o.,trurrEu coflpoTr{B1esuett z, Crrgatu oT BhIxoAa ou{secKOrO 3AeMeHTa He CMOryr npofirr.r n arrxo4norl npoBoA. Taruv o6panoc^e Kj\loqa KoMMyraquH MO)KHOHerIOCpe.d'crBeHHo 3OM, BbIXOA,bI
165
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QparuentaMI'lKpocxeMLr Pnc.4.38.flonepevnoecetleHl4e Ha ocrasluuxcg ylacTKax SnlrTaKCI{aAbHoro c^og n-Tllfla co3AaroT 3Ieneo6xo4nubre cTpyKTypbr lv\-fi IIO yrIeHtIt aKTLIBHbIxI{ flacc]tBHblx rlacos4aHa 6utr Mo)Ker uyreu 4aoftnofi all$$ysrlu MeHroB. Tar, c BbIBoAaME or Bcex 3IeKTpoAoB s oAuoi Hapuas n-p-n-crpyKTypa nolyflpoBoAHuxosoll crpyrrypu 6o'rro6pasoBaHltll IIpu *oa*o"t". II eHKa MoKc]rAa KpeMHutt' KoTopag [peAoxpaHfltuyro po.'\b nrpaer aos4eicraufi' B npoue'KyrotlHblx orleBHeIITHIIX or eT noBepxHocrll crpyKrypbl ora rr,reuflolyflpoBo4Huroaoi paqusx no u3roroBAeHI{Io npl{Mecefr Te ot 4uQQysuta upeAoxpaHqrcull4M Ka clyxr<eHnfl
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5. CpaaHuraeM oi c x. Ec,rrnQ,7 x, To uepexoAr'Iu ryraeanuro ecAH oi < x, nepexoAnM K yxaaanurc 2, 180
AaropuruaMr,r B coBpeMennofr MareMarr,rKenplrHrrro Ha3LrBarbKoHcrpyKTr,rBHo 3aAaBaeMhrecoorBercrBr"rrr MexAy cAoBaMI4a a6crparrHux aa$aanrax [2]. Kax 6rno orMeqeHo Bbrure, uo4 a6crpaKTHbrMaaQaaurou uoHlruaror aro6yro KoHeqnyro coBoKy[Hocrr o6rexroB, Ha3brBaeMux6yrBaMH u^u Cr{MBOAaMr.r AaHHOTOarr,$annra. llpu erou npupop\a 3Tr4x a6crpaxrHrrx aaQannroa o6beKtoB He lrMeer 3HaqeHr4s,Cratvrgo.troM Mo)r(Ho crrrrrarb, HarrpnMepr 6yxru arrQauura xaxoro-rrrl6o fl 3brKa, qu$pbr, ruo6ue 3HaKr4,pIdcyHKI.ILI T. n. A.t$aarr, rax rrro6oe r"rHo)r(ecrBo,3aAaercfl rrepeqlrcrrenneM ero g e-
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Tax, a aaQanure A cIoBaMr{ 6y4yr ruo6ue nocle.l,oBarelbHocru cr, e p! e re je., a4a4vrr. rr.r B aa$arnre C - x, f, xf, fx, xxt W vIT, n, B ero cocraB Hollpu pacruupeur.rn aaQaazra, T. e. rrpLt BKAroqeHr.rH rroHtTr{e cloBa Mo)KeTnpeTepueTb cyrqecTBeHHoer,r3MeBbrxcuMBo./r'oB, HeHHe.Tax, a aa$aaureA : 10,1,2,3, 4, 5, 6, 7, B,9) Bbrpa)Keur{e( 15+ 68> 3HaKoMcyruMhr,a a aaSanpe.AcraB .aer co6ofi4aa clloBa, coeArdHeHHbre sHTeA': {+, 0, 1,2,3,4,5,6, 7, 8, 9} sro6y4ero4no c oBo.
AtaQaaumnur onepsmopolr, Lr u atQasumnuu onodpax,exuerr Ha3bIBaIOT BCqKOe COOTBeTCTBI{e, COIOCTaBA-srOil{ee C OBaM HeKOTOpOTO a aa@aeure. Qanzta cloBa B ToM x(e uln Bp,pyroM Qllrcupoaaunorr
flpu erou nepauf, alSannr Ha3brBaercffBxoAHbrM,aropofi - BbrxoAiHbrMa,rQaaurou AaHHoro olepaTopa. B cayrae coBuaAeHufl BxoAHoro H BblxoAuoro arrQarnroB roBopflT, uro aaSaaurnrrri oneparop 3aAaH B coorBercrBylouleM aaQaanre. Ecrru cr - cloBo a aaQaaure A, a F - cloBo a anQaaute B, ro a-lSaanrHhu;ro[eparop fu: F . Ilpe4[olaraercsr qro ycrpoficrao ynpaBleHuff MaITII{HbIMo)Ker HaxoA}ITbct B HeKoTopoM KoHeqHoMql{cle cocroflsuti. CocrotHr4e ycrporlcrra ynpaarreHug qacro Ha3bIBaIorBrryTpeHHuMcocrolHueM MaIIrLtHbI. O4Ho us srnx cocro gnnri Ha3blBaercff 3aK rorrr{TeAbHbIMH ynpaBlfl er oKoHqaHI{eM pa6oru MarrrlrHbr.
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203
B fl BSrreueHrapHble aKTbr, aHiIAotI,IqHbIe AorIrIecKI{M ouepaqutM' HOM rr^r{ He'BHOM BnAe BBOMTCfl I{ UpI{ OIIpeAeAeH]r}I rloHflT]It BbIrro^HeHLrff AA|OpI,ITMa B a6CTpaKTHOfi TeopI4I4 iI TOpHTMOB. Haupr'rIrlep, Ilpla BbIIIoAHeHIitII HopMaAbHorO a ropI4TMa nOCAe paCCMOTpeHI'Ifl oqepeAHori Qopuyrru noAcraHoBKI4 ocyu{ecrB -flercfl A1460 rrepexod, K c^eAFouler:r $oprtryae noAcraHoBKHt |vr6o ocTaHoBKa, rrra6o uepexo4 x [epBori soprvryrre rroAcraHoBKI4 CXeMbI a^rop]rrMa. B rvraurr'rne TbropHHra AofuqecKorl onepallHeli Mo)I(Ho cqlITarb ABLTTKeHHeIeHTbI BnpaBo HAIII BAeBO B 3aBI4CHMOCTIIOT COCTOflHLIflMaIUlIHbl U UpOquTaHHOrO CI,IMBO./rA. O4naxo,
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5.5.1. OneparopHbre aanoPr4TMbrBan Xao
npr{Ka3a c HoMepoM d,. Ecrrn x<e @(x) He onpeAeleHo, To ueperiru x BbrrrolHeHr{rc HaA qr.IcAoMx [pI,IKasa C nOUepOU B. 3ax,uo.r[relbHoMy cocroff Hr.rroMarItI{HbrTbropr,rura B oleparopHbrx aAropHTMaX cOOTBeTCTByeT npr{Ka3 Br{Aa:
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205
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no HecKoAtKI{M 2) o4norperrreHHiul [epeAasa KoAosoli xorr6znaqul{ pa6orarou4uM KaHirAaM; [ap€r ,relbHo KoAoB' T. e. KoAoB' I4c[paB3) llcuorrrsoBanl{e KoppeKTupynu{I{x ,tr:rroull{x orun6rcu. rBl-aercs carIoBTopeHHe KoAoBoti xou6nsaql{H MHoroxparHoe peaII414 AerKo rloBbltueHHtr MbrM rrpocrrtlr cnoco6oM AocroBepHocrll uu$opnepeAaqu crcreMax Hlr3KocKopocrl{blx B 3yercrr, oco6enno 3a l4crtrHHblrl cltrurarr fiplaHlaMaror ror' KoroMarlpu4. B erou clfrae B MHOTOKpaTHO [OBTOpeHpsrri 6orruuee KoAr.ItrecTBo pa3 noflBl-fllcfl rlorIpI4 ngrl4KpargoM Tax, ecJrfi cl,IrHa^oa. Hollr uocle.a,oBarelbHocrl{ To npu11010' < uocleAoBarelbuocrb 1> uorr.yreHa crrMBola BTopeHlrfi Hr{Maercf pellreHLre B rrolb3y cu MBoAa < I >, Cyu{ecrBeHHbIM HeAocrarKoM TaKoro cuoco6a gBlnercfl 6oaruroe yBeAI{qeHI'Ie BpeMeHI'I [epertaKoe )Ke ylueHbrueHue cKopocrra. Ecarl xo4oAaqu u, cleAoBarelbHor gas xoM6LrHaIII4r noBTopnercfl n pa3, To cKopocrb cHl{)Kaercfl B n pa3.
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ouru6xu [9]. B cscteuax c POC nepe.d,aBaeMoecoo6ulerue KoAr4pyercq o6Hapy)Kr{Barou{uu orura6xu KoAoM, Ha npueMuoi cropone fipoBepflercfi Ha,rlrqne racxa:reHrari r xo4,oaofi rou6unaqrau. Ecar,t ourra6xn o6uapyx(eHbr,ro no o6parHoMy KaHa y nocbr/\aeTcf cr.rrHa^nepecnpoca. IIoyqag gToTcr,rfHa r [epeAaTrruK [oBTOpfleT [epeAaHHyro xorr.r6nuallHro. B clyrae orcyrcrBufl curHala ([epecnpoc> uo o6parHoMy KaHa y rrepeAaBarb uo^e3HyIo un$opr"raql4ro B cropony uepep,arouleli MO)KHO
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