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STATNTICSAND DAIA ANIALYSN IN GEOLOGY Secondedition JohnC.Davis KansasGeologicalSurvey [xc. C.[anuc CTATI,ICTHTIECKWI'.I AHAJIH3 AAHHbIX B TEGJXOTMVT flepeeo4 c anr;rnrZcxoro Aor(Tcpa $usuxo-:r'':lT eivlaTHLjecKrIx Hav K B.-4. {'o.rrx_{.ieoou lI o g 1''-' laxtf uLri"l,qolt"oija f €OJIOf O-t':IHIlepaJ-IOfi{rleCKllX ItayK /1.A. Poduouoea B AByX K;rlrfAx KHP,II-A 1 JohnWiley and Sons New York ' Chichester' Brisbane Toronto ' Singapore re " 1990 MOCKBA "HE"II,PA NPENVCflOBI,lE EEK 26.3 Ag+ v"AK550.8.053:519 PexoMegroeaHo I{ li3raHlilo P, H. Koeanou. AenncAx. C. D,g4 A-'B Crailrcrttqecrttll xaHAr.rAaro)r f eoilofo-MlllleparoflicecKI{x HaIIi aHa;rll3 ;lal;F;Ijx B feoJ-IofllH:- fi_ep. c aHr.I.. 2-in./flep.n-.A. fony6eeofi;Ilo'r pel' A' A' PoArtoHoea' K H .1 .- I \ . : H e l P a ,1 9 9 0 ' 3 1 ' :c ' : L r ' : r ' ISBN 5-217-02122-3 a;rre 6' ar itcrnxu II VIsJloxeHbl MeroAbI MareMarl'Iqec(oi! cr YaT!-l:.Hori p b ] , n p u M e H n e M b ] e _ B c o B p e M e H H b l x r e o . ! o | l l q e c K l t x u c c f l e ! , o B aoH IHopMsJb,Iqx.Paccvor. npoBepKu xr3-iltcrltrlecKltx rllnore3: perlbl I't3BecrHora*p"ttpii" rt 'rp' Mauua-)'urnrr onuepa' Crrrol9l.a' HoM pacnpeA"n.u"'", xi"'epu" M e T O A a Mc T a T l l c T l l q e c K o H e n a p a l r l e T p h t i e e K l l M boaluioe u"r"unu"'yi"nerio roaHanH3aAaHHbIx'onucanrtflpoueJ.yDLra:f.allnganoc,'IeAoBaTe.]Iluocteil A a H H b r x : " " , . p n u n " u , n - , o p T o | o H a n b i ] a l . - n c . ] I i ' j o M l lBaaJpI bn H e rMpbeIc' c$Iu, nI frfr'p3ao'H H . o rapfapM ana"iirg' ;;;J.;O;;u;q"cneKrparbriuii ;;;;;;;;, I{Hfi H TpeHA' 3l i i l i M a r o q r . r x c n o 6 p a 6 o r x o i r x o ; i u .x,'llt reo'loros Bcex cneuuaJlbuocrell' qecrBeHIJbIX n * uuaarue""otx p e3y'qbraroB n a o'rrol.eultii' 4i3#iilFry35-s0 tsBN 0-47I-08079-9 ISBN 5-247-02t21-5 ISBN 5-247-02122-3 66K 26.8 bY John \\'ileY a n d S o n s , O ' A1986 ll : 1973, ' r i g h t s r e s e r v e d Published inc. in Canada sernulianeous-lY A. 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The expansionol statistics:Jour. Ro1'alSlaiistical Soc., 1953, seriesA, l16, p. l-6. 3. Grif fitis "/. C. Some aspectsof measurementin tire geosciences:Pennsl,ll a n i a S t a t e U n i v . M i n e r a l I n d u s t r i e s ,1 9 6 0 , 2 9 ,n o . 4 , p . 1 , 4 , 5 , 8 . 4 . G r i f f i t h s . I . C . S c i e n t i f i cm e t h o d i n a n a l l s i s - o l s e d i m e n l sM c G r a r v - H i l l , IIrt., New York, 1967,508 p. I4ueercr pyccxuii nepeBo,t:lput\$urc.{cr. Havvnue MeroabrlrccJ'reAoBagrlfl ocaAoqHbrxnopo,l. t\i\.,Mup, 1971. npon3Bonbno. JIOXHAq YBEPEHHOCTb pry rnaay l\4o)Kno 6u.no 6u 3aKonqr{rb cneAyroqr.rM npeAy_ npex<AeHr..rerra. flpnrrtensfl MaTeMaTL{qecKHeMeTOAbr, MO)KHo sany_ Tarbct B Tex n3 HHx' Koropble HMeIoT Hel{y]o [pereH3Hro Ha roql6 Ceeelcxr.r 2- 2 0 1 f.rasa 2 3JI EillE HTAP HAfl CTATI{ CTI,tKA Hecnrorpx Ha ro, qro He[oCpeACTBeHHbre gaS,rroAeuur feoJrofoB ofpaHrrqeHbi notsepxHocrnrc selrgori Kopbr, c r4x rloMourbro rrbrraIorct BbtrcHurb nprrpoLy tApa rr NlaHTuHa , Tat(xe r,ry6rtHHux c,roeB eeN{uoii xopu. Kpolre rofo, lisyqarorcfl npoqeccbl esorrordr.rur J e M J r r { rT a r i H e ,x a i i r o p o o 6 p a 3 o B a H H ei l p a 3 B H T H ef i O H T t r H e H T oH t se, AocrraeNrbreJ,JrRnpffN,rofouccJieAoBaHHs.Ec.na He cqlrrarb acrDo_ HoMoB, ro He ci'u{ecrByer Apyroii fpynrbr yqeHbrx, 6o.nee yaanbn_ HbIX or npeA\'lera IICC,leroBaHrtflIt rlluelourrrx N{eHbIxHeBo3r\Io)KHocrr gKCllepriN,relrtrpoBarb Ha.r{HlM, qel{ feoJlorll. feo,rorug B 3Haqtre.nluoir creileHrrocraercfl nayxoit, ocuosaHHor? ua ua6lrc4euu- 9X, B qACTHOCTII HA TAI(HX, IiOTOPbIE COACPX(AT 6O,TIUYIO AOJIIO HC. o n p e r e " r e H r { o c r r rB . c e r r s r r c 3 T H r { C T a r l c f i r r ( e r I p e A H a 3 H a q e HH Of p a r b o i p o l ' r r j \ ' i o l r c J b g n o A o 6 H H : i r r c c J l e A o B a u l r n .H t : .e c N r o r o q H a To' qro IIepBoHaqaxbHorepMI,rH <<crarlicrlrKa>> il\{er'r orHolueHHe K r r o A c q e T Vr l l t c r t o B b r xx a p a K l e p i l c T i r K , r i a K , H a I I p r i : r e p , I I p r r r r f p e B 6 e f i c 6 c n , c e i i q a c o H a n p t r M e H f l e r c qr A J r f l a H a , , n r 3 aA a H H_.rLau* b r x ,o c o Sesuo B yc,roBrrflx Heonpe-re,rreirHocrrr.crarucrrrqe&ira cKpbITo I{,111fiBHo Bcrperla}orcfi 'ra\{, fAe corepirilrrcfl 3.iieMeHT c,ryqarinocrri. leolorrr AoJrlKHbrriiderb npeACTaBreHrie o6 orgx 3all.aqe-\II o Tex crarllcrliqectilrr Irplier.rilx,rioropbre I]o3Bo,'rrrror I]x peuarb. qllcJarlll or 0 ao f Vqeuue o6uqso Bblpaxarcr BepoflrHocrb q x c , r o u n P o l r e H r o eo r 0 A O 1 0 0 v 0 ' E c n n M b T t l , i t r l3 K B H B a J e H T H b I M yoeAO)KAfl 3aBTpa 0, ltlt a6co',rrcruo ioBoprir'1. qro BepoETHOCTb MbI foecJIlI oAUaxo riro He 6yAer' 3aBTpa. AolKAs lcHbl B ToNr, yBepeHbl B ToMn r,rlrrlNI.r{To BepottrHocrb ,ll,oxAa 1, MH a6conrcrrio r a BepoarHocrb, Bbrpa)KeHHar KIrIl cnoco6ou' ?la.t. :,5' ;;*t; o npruaonoAb6nn co6ltrus' A6colrorsoft roJoSsa -"r".p*A."nd ...aepcHuOirrrcoOTBeTcTeyOrxpairHlle 3Haqe'Ilfl l',iia.rlbl' a pa3JIHq- n p o l { e } K y r o u u u e ' H a n p i l } 1 e p ' e c " t nr { b l soii crencull lBepeuHocill (a sHauur' q r o B e p o f l r H o c r bA o x A f l 3 a B r p . a p a a u a l i 2 loBoprr\{, 'ro>re 1/2), ltli cBOtO BblpaiKaelu He 6.vAer, ti roro, "iro JolKAfl MbI bc"III ToqKV 3peHIIfi c Hal'IMeHbuleficreneullo )Bepe.HIlocru' qro rofo, n'oiliAfi (a 3!4 paBHa rrro BepoflrHocrb .l,o>x!,tl foBoDrir.r, HeyBepeHHocrll' i l r 6 ' \ - . l c r , I ' 1 ) , I ' r u r B b l p a ; K a e Ml 4 e H b u y l o c r e n e H b TO|O' raii ]iali BepofTHOCTlAoxaq n 3 pa:a 6o"rr'ue BepotTHOCTl'I ri'io .lo;Ii,ltt ue 6-vAer, nOfiBiIelIIlf .loiKif llofvT 6ltrl ocHauil or{eHrirrBepoflTHOCTtr H o B a H L IH a l t H o f l l x r ] l a x r o p a x , a r a l i T l i e n a c v 6 r ' e t i r i l B g b l x o q y u e no3Bc'[faitn.x. .\1r,t, oJHario, 6yaen'l llcfioJb3oBarl' .u.p1'roi'lnoJXoA' TatBJIeHIIq' noBe!,eHilfl npe/(ulecTByIOIIIero ocHoBaHrru Ha rculrii 6 1 ' ,1,ya n o B e J , e H t i e e f o r , . o r o , r i a n l ) n \ { e l l , r i a K n o r o . r . a ,n p e A B r r J . e T b q e p e 3 < < o r H ocllB e p o t r H o c r l l I i o i l p c l A e J e l l u l o u r c , a t .T a , ' o i r l o ; t x o , r Te.']bHL]eqaCToTbI>>i{FITyi]TuBHonpIleN{,'IeNireo,Iora}IH'TaKKaK3Ta l i o } [ t e x u t r ' r e c H o c B r 3 a H a c [ o H f T I I e M O A H O p O A H O C TBn . H e K O T O pbr-\ c.rYqatx 6slsalor rIoJie3HbIApyrfie [oAXoAbI K o[peAereHl{Io e e p o n r H o c r H ,I I O N { b IU e 6 v A e l t H a H r r x o c T a H a B r ' l l l B a T b CTfal ,K K a K l KHIlrax Ouruepa [10] ii Qou Nlx:eca r - , u r rn o : p o 6 H o u 3 . r o i K e H b B [ 3 1.J BEPO'THOCTb Hecuorpt Ha ro, qro c}'x{ecrlt),er lrHoro pyKoBoAcrB rro reop r i r l n e p o R t H O C r e i rn, p e A c T a B J r e r c f l i r o r e 3 H b r r . l0 c r a H o B U , r . b c f l Ha ToM, t.aK oflpere,rflercrr Beporrr{oe co6urlre qepe3 Bo3Mo)xHoe. I' JIFJOOM'IBJ'ICi]IIII CYIIICCTBYCT HEI{OTOI]OE MHO}KECTBO (UUOrlA 6ecxoHeuuoe) rJ03Mox*rbrxIrcxoAoB, iioropbre Haxo!,rrcff B BepogruoctHoir 3aBficHMOCrLr, OIIrrcbrBaeuoiiqacrorori BCTpeqaeMocrH. AHaalt:apyg BeporrHocrr.r 3Tr.ix ricxoAoB, r{oiriHo ouen}rrb rroBeAe_ HHe H3)'qaemoro o6rexra v.ilH co6urr.rl B ilpolxd'ror{rr,ru 6yAyuelr. Kaxauft Hs Hac rr[.{eer rrHT}'rrrrrBr]oe npeAcraBJreHHeo BeporrH o c r t r . 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K n a c C l i q e c t i u i l4 l l c x p e r rir,rii npirvep, npHBoAIntltrieo BCex pylioBoICrBax r]o reopilr Bei ir,.li,t.o-ttic 6;Op g l r u o c r c i i , c n a ' : a u c 6 p o c a u r r c \ t n i ) a B r r i t b t i c . rt tf o y c x o A a : t i o r o p L , r cp a B H o B e p o f l T i l l , l . p e u ( a , r { r e p 6 a a H l r e r r \ { e e T, t B a I l o a r o l t y B e p o f l r H o c r bB b I [ a A e H I i ar e p 6 a p a B H a 1 2 . 3 t o , x o H e q H O , c s H a q a e r i t e r o , q r o B K a x < A o r {B T o p o N {6 p o c a H t t i r n l t n a 4 e ' r r e p 6 , i ctiopee ro, tITo npII Aocraroqgo 6ortltuoxl ql'lc're6pocaHrlft npua-r,,rrisure,rlHo no,'IoBuHa ltcxoAoB- rep6t,t. Epocanite MoHerbIoIieHb xoporuttit rpIiNIep Ar'Ifl I'l"l,IIrccrpaIIrltroilpeAer'leHHflBepotrllocTii. co6urue ul\{eer ABa IlcxoAa, Ii gAHH Ii3 HI1X oofl3are,'ibHo l\'.ler II\rerb Mecro; cc,'rlt He )IqllrblBarL' oqeHb rla.ryrc BepotlrHocrb ':CTO, I I T O ] \ { O H C T A M O } K C T B C T A T b P C 6 P O I T ' T ,T O B C C f J A BbINAAET ilIT" ,.c rep6, ,'rli6o peufiia. Ha ocHose cxeMbl 6pocaHul MoHerbI Mo)Kllo nocrpouTb HHTeilecHlro nocreAoBare,'Ibnocrb neporruocreft. Ec,ru BepoflTHocrb I r b r n a A e H u sr e p 6 a p a B H a l 1 2 , r o B e p o r r H o c r b B b I n a A e H I ' I f lA B y x rcp6on ilpr.rAByx 6pocaunrx paBHa l12.l12:114. !,anee Bepoarl t o c r b B b r r r a A e H I . I qr p e x r e p 6 o n n p n r p e x 6 p o c a H r n x p a B u a 2' 19, '112.112.1 2:l/8. O 6 o c H o B a H H ee r o r ? n p o r p e c c n r . rn p o c r o e . B n e p _ i B o M 6 p o c a H r r . rB e p o f l r H o c r bB b r i l a l e H r { r r e p 6 a l l 2 . T a x r ( a K ricxoA B T O p O f o6 p o c a n u a H e 3 a B r i c l r o r n e p B o f o , H a u r r B o 3 M o ) K H O C T I i n o J r y q r { r br e p 6 n o B r o p o M 6 p o c a H l l u c H o B a l 1 2 . l l o r c 6 H o 3 r o M y , T p e r b e 6 p o c a H r r eH e s a B H C r r ro r n p e l b r A \ . u l r . { xt,r B e p o a r H o c r b Bbr_ r r a A e u r i f lr e p 6 a B r p e r b e M 6 p o c a H l r u c n o s a p a B H a i 1 2 . 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TorAa noJryqaeM F L) I z\;;.\;;-n 51X t i lJ i:l 1 Ta6,rr.rua2.4 xpoMoM(Xt) n nnxenem(Xz) Y/ A2 n n sPi.r lcJreHhe olIeHKH KoBapnaqHfi MexAy fl - v ''tt *,,i1:ssj It tF.r?,-/F J \kt rn,n L r:l (2.21) 130 165 i00 26650 42 075 l9 500 29 700 34 075 42 025 65025 38025 48400 50225 IJO l6 900 27 225 10000 1 82 2 5 2t 025 ;=l XXr:675 Ecnu lru BblqucJrHMcJ-\r\rbr c\IerrraHHbrxnponsne.4euuti li c y M MbI KBaAparoB A,'rf BCex Bo3xroit{Hbtxtor,t6rruaqrrii narurrx rpex fiepeMeHgbrxr.is ra6,r. 2.3, ro [o.ryquM c"'reAyloil{yrcra6.rruuy nopa4xa 3X3: sPr,2:152 000- 2X22:93 375 (ilr0) (675) : 2150. 2150 covt2: ---- :537 '5. t Cr Ni SSc. SPnr-c, SPv c. AIIC[epcI{l[ ecrb rarixe Bce Heo6xoAlIMbIeAaHHbIeAJIfl BbIqI'lCJleHntl ,Y: (Hrrrierq) no $opuyne 2.12. 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Aorro,IHilTe,rIbHo rulHr,r.3ro oqeHxa KoeapHaqr.riirJrfi xpoMa H BaHaLHfl (covrs), H u K e . r r frl r B a H a A H f l ( c o v 2 3 ) t r A l t c l e p c r i r o B a H a A h r r ( s 3 2 ) . C . r r e a y r npoueAypaNl, rlcrror'rb3oBaHHbrM npH nocrpoeHl]r.rra6,'r. 2.4, euruuc,'ilire BerHrilruy (cov13). H a p u c . 2 . 1 4 r r p u s e A e n aA r . r a f p a M M ac o B M e c r H o r op a c f l p e A e n e HIIfl .{BYX ilEPEMCHHbIX, I{OTOPb]C TCCHO CBfl3AHbI }I HMCIOT AOBOJIb- T e n e p l , B o 3 B p a u a s c b r i f e o x r r M r r q e c r { r i MA a r I H b I M ,i l p u B e A e H HblM B ra6t. 2.3, MoxHo Bbtqirc.iurrt'oueHrci xonapuaqufr AJrrr BCex T p e x s n e M e H r o e . o 6 o s H a q a t r c o A e p ) K a H H rx p o M a L r H i l K e J r f c o o r uepee X1 H X2, Ir{o)KHoBbIrlHCd'I}tTb BeJIItqHHbI,[pHBeBeTCTBeHHO A e H H b r eB r a 6 J r . 2 . 4 . M w 3 H a e M r e n e p b A u c n e p c H n X 1 ( x p o u a ) H oIIeHKy KoBapHarInI{Me)KAy Xt vr Xz (xpolrtoru u uuxe.leu). 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Haoep,eHHas Koppelcurfl (2.24) Tax xax ,r r.r3Meprer.nuHefiuoe coorHoureHne Me)r{AyAByMenepeMeHHbrMH, MO)|(HO OnpeAenHTb xapaKTeprz3ylo_ ^rlprMyroJrr.rHHro, rrlyro 3aBHcHMocrb Mex{AyHr.rMu. 3ro saxHHfi aonpoc-crarucrHqeCKOrO KOppe,'IflIIAOHHOIOU perpeCCHOHHOfO aHaJIHgA, sBntIOUIefOCt ocHonort6o.luuruscrBaMeroAoB annpoKcl{MaUuu noBepxHocrefi. 52 Ta6"rIIua 25 Pasueprr paKoBIrH6Paxnono.q poaa ComPosita, r'ru Hexoropne Koppe.rflur4r.r MOKAy [epeMenH[,rMlr He orpaxaror cooTHollleHl,ill rraexAv HI]MH, Ho oHI-,I I,IHAyIIIIpoBaHbI onepaIlI-IflMI,I vnu npeo6paeonanuRur.r, KoropbrM 6u.tpr [oABeprrryrbr nepeMeHHste. ,[,ne He3aBr.rcnMbre cnyuafinue BeJrr{rrriHbr o6srqiro r.rMercTHyKopper'rqqaro. OAnaxo HeKoropbreonepaqr.rnHaA nepeMeH"'reByFo Hbrlvtrrr\{ofyr np}rBecrr.rI( KoppeJIflIlI,ILt, orJrHqHofior HyJIg, xorrr He cyulecrByeTHuKaKoro,rugefiuoro coorHorfieHr.rfl. XexAy Hr.rMH \-yilIecrByrotqile Koppeilfl\utr Moryr 6urt ueNrexeHbr r.rJlr.r 4axe o6P AXICHbI TAK'IMI{ O N C PA U H ' I M I - I . 53 Ta6nnua 2.6, Burqrc;eH.re cyMMxBaAparoB, cMeruanHux nponsne4enrii r xoarpSuqnenra xoppensqrnrroAaHHbrM ra6n.Z,d T a 6.rrlr ta 2.7 nJlfxte, -ll,,nusu (s crrr) ocefi o6PaaqoaraJlbKlt, co6panHofi Ha Ocu nePeuuc.leru n nopc,[,Ke nsmepeuufi xl \,2 338,56 285,6 I 184,96 I 2 9 ,9 6 6 0 ,8 4 3 9 ,6 9 rB , 4 16,9 13,6 1t,4 7rB 6,3 283,36 2 5 5 t, 9 148,24 l i 0 ,5 8 57,72 3 3 ,3 9 l( 2 3 7, 1 6 228,01 l i8,81 9 4 ,0 9 54,76 28,09 | r0 , I a7 C d e f X X , z : 1 6 3 96 o g h i \Y.-7,.1 sp;r:(888,48)- (74'4)(63'8) : g 7 , 3 7 .C o V 1 2y_{ : rn,nr. s s t : ( 1 0 3 e , 6 2 rr-' n ' : r " : 1 1 7 , 0 6s .s r : ( 7 6 0 , 9 2 f)T_ l 1 " t,': a b I17,06 rJ: :23,41. s,:Vr{T:4,84. s22:€jl: : 82,51. ro,so. s,:7T6So:+,00. 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N POBEPKA TTIIIOTE3b I O HOPMAJIb HOM PACN P EAEJI EH I,III llperx,r,e .{er\a t'poAo!'rxr.rrb usJroxeHHe, Bo3Bparr.rMcq Her\.{Hofo. Ha3a/l' Ii pacnpere,'ieH[flM gacTor H' B r]acrHocr]I, K HopManbHoMy pacfipeAeJresrrc' Ec.nu BMecro rofo qro6br paccr{arpr.rBarr osr60pIiy ro,rbr(o rrs luecrH 3rraqeHHr?,npeAcraBJreHHbrxB-ra6"u. 2.'c, is[repHTb AdrrHHbr paKoBHHOqeHb 6o"ultuofi KOrrJrexuHItComposita, ro MbI yBlrill4M, rlTo qacToTHag AaarpaMMa 6yaer BbIfJIflAeTb aHaJrO-2. rrrqHo rpaQury, uso6paxeHHoMy Ha puc. lg. CpeAHe:li, 3HaqeHHI' AJIHHbr,B if,aHH.M c"'ryqaepaBHoMy 14,2 vm, 6lae" coorsercr. BOBaTr,Haw6oilbutaq qacTora, a nocrenegso yMeHbrIIapilIHMCrIt4 yBer'Iur{HBarouruMCfl 3HaqeH}rrM 6yayr orBeqarb yMeHbIxarcrtli{ect rracrorbr' flpv6nnaureJrbHo. aee ipeiu paKoEHH.[OfiaAaror B rrpeAeJIbIHHrepna.na (p-s, p*s) c Uenrpo]v B roql,ie yt:14,2, rpnqeM orIeHKa craHAaprHofo orKJroHeuux npu6nu3HrerbHo DaBHa 4S ttv. Dd 3HaqeHsfig;tuttutoco6eirpoAa Compo' I'unorernqecxoepacflpeAeJIeHHe sLta Tenepr paccN{orpIIM u3N'lepeHlrtllxllpHHLI, Iioropble 6lt;rtr cAe.naHu npr] ucCJIeAoBaIIuII3Toii o,{eHb 6o.rrr,ruoli IioJiJIeKrt.llHCompositA. P a c i r p e " e , l e H l i es r o r o n o r { a 3 a r e . l f l n o $ o p t ' t e H a r l o \ l l ] H a e r p a c n p e ' AeXeHlle .l.,TIlHbI,IIo efo cpe.{Hee 3llaqeHlie }I cTaHIapTHoe OTK"IOI { e H r r eB 3 r O M C , r y q a e I i H b I e .o H o M O X e r B b I f J I f A e T b , I { a r i p H M e p ' f l o j r o 6 i i o r p a c p H x v ,I I 3 o 6 p a l l i e H H o M yH a p \ c . 2 . 2 0 , c o c p e I H I r M 3 H a ' qcHrietr,r 3,6 uu. i0,3 rravrrr craHAaprIJbIMorK.rloHeHHeM i\Lox{er\{dr}r Mbi crraBHr{BarbABa pacIIpeAe!'IeH]Itnpyr c ,[p]'.or\,{?H3\repeHHfl [poBeJIeHbrB OIHI]X I;l rex x{e eI[HHIIax, qro o6rerqaer npo6,lerrny cpaBHeHHflpacnpeAe,'IeHIIiiAJIIIHbI It unpHN{ox{Ho11306pa3arbB oAHoM H roM slr. 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Buecro srof o BbrqreM coorBercrBvrouee cpejr.Hec3Har{eHIJeI.{3 Kax(Aofo Ha6r}oA'eHHf B xa>r4orYtII3 AByx c o B c r i y i i r - r o c r e i f?l .o r y r { } r M H o B b r e3 H a q e H H q . 3 r o n p e o 6 p a 3 o B a H a e cnBttfaer KalKAoe H3 pactrpeAeJreHHftBAorb ropH3oHTa!'rbHoriocn AO "iex nop, noKa I{x rleHrpbr He coBilaAyT co sHaqeHueu 0, ln.nfIoulx\,tcfl cpe,qHHMA"ls o6oux npeo6pa3oBaHHbrx pacnpeAeJ'reur-rfi, I t s o 6 o a N e u H b r xH a p u c . 2 . 2 2 . 5 p a c c M o r p e u H o Mn p n M e p e M b r c B f l 3 a H b r p a 3 r r e p H o c r b o p e 3y"lbraroB u:uepeuHft, Bbrpa)KeHHofis r\arirruMerpax. flpir erou HIII(aKnx npo6,reu He BosHuKaer, ecJII{ usr 6yAerracpaBHnBarL,pac. npe.lereHlrq ,EJri{HbrH rxapHHbr, Ho ecJrrr Mbr 3axorr.tM cpaBHHBarb rrll DSCnPeAeJIeHH c sp a c n p e A e , r e H H f l M H X ,a p a K T e p H 3 y r o [ l l r M M rr ac. EA UY Ta6,ruua 2.10 tlc craH.qaprnoro 3HaqeHEs KyMyJtflrIrBHofi tpyuxqun pacnpeAeJl-eH lropManbHoro PacuPe4e;renun [15] -16 cTaH.[aPTH5le OTK,IOHlEHHg oT CpelHero 3taqeHHq I +ro 10 15 *L l^J fpi pnH rH^a , r z , f 2s -3, 0 3( qecrioe pacnp ercre-ioru 3,::. E r r e ?,r-9, s r r r v".f.lrorerl cHrrfi-rurrprrHsr contposita oiooef : . ,? _ari .2t,{aarpavna pacnpeAeneu&, sLHya're H -T:' ;.4;;;?; ;:,,T;:r',** -., I .-'9R -)7 -,) A _, I DQ to ol _9ll q -l -l R -r7 -1 ,6 t( -j .l 12 -1 ,2 -t 10 - iqr,n P_uc. 2.22. pacnpele.neuas HMero r Hy. n."oJ'".'pfi ,,.iu:f 3i:ffi:-#i.ral{;l4 prHoe orK,,IoHeHue,paBHoe cy paxo'r,H' ro HaM 3TO cn€r:r.Tb He yAacrca. clrulectByer xoe-nu6oAorrorHrre,,rb:":r,rrl Ka;t;6puJoiu"ru, Koropoe nosBo,rrer cAerarb HarIH paclpeAeaeHis oJlru"aorrlaMrr ot eAHHr.rq peulrt? Olno as raxax up.uu*u,i-# rr3Me- Ha3brBaerc'r., ona aq;efi: . o;;;, JiJr.".T:lff iu"fH?X' 1q1-1, Hl no'* r Joi"?"..39ru no HyneBoe cpe^r'ee "':""""fffi sesnrls;;;;;;;lhT#T.ffi :[r'i,:liT*ii;*llr."; 3HaseHrt pacnpeAerrellir as -dA;;; -n-rli"",ua1ltopewtrq ;;';".',i.il:H""*'rl:"n tr AeneHHs pu'"o.'" naup,noe o,nnon.n,e X;mX[#;:uJ::";1 pacioBafl nepeMeH'aq 60 I (l 4 0 ,0 0 1 0,0019 0 ,0 0 2 6 0, 0 0 3 5 0, 0047 0,0062 0 ,0082 0 ,0 1 0 7 0,0139 c,0179 0,0228 0,0287 0,0359 0,0446 0 ,0 5 4 8 0, 0668 0 ,0808 0,0968 0 ,I 1 5 1 0,1357 0,ll-87 Kyrr yJriqrHsHaq BeporTluocTb 0,1841 0 , 2 1l 9 0,2420 a,2743 0, 3085 0 ,3 4 4 6 0,3821 0,4207 0,4602 0, 5000 0,5000 0,5398 0, 5793 0 ,6 1 7 9 0 ,6ii54 0,6915 0,7257 0 ,7 5 8 0 0 , ;'B8l 0 ,8 15 9 C,8113 C T aH A a p r H b r e OTK,TOHEHHq Kyny.nsrHglidt BePOqTor cpe,lHero t{ocTb 3H aqe llilt -;-l I ;1,3 -j-i,4 :l7 -r1,6 -l-l {l A q -r9 0 :o 1 oo roD 'q I *2,6 _L9 7 --:..q oci -3.(i 0,8613 0,8849 0,9032 0,9192 0 ,9332 0,9452 0,9554 0 , 9 6 11 0,9713 0,9773 0 ,9 8 21 0 , 9 8 6r 0,9893 tr,99i8 t),9938 {J,9953 0,9965 0,9974 0 ,9 9 8 7 0 , 9 9 81 pu^ sgaqeHfiri Arlrr'hrlr *"p"*i"iloo.;fi.;;'b',;;:! srraqe'rri i[i:,.2:?9j_.--Pu.npuou4u""" posita ;;;"*1""t:luuu^_oco6eiipoti Ciii'ii'. MatbHylo eoprrry I Craxga0rnrte Kyl ya,qrHs. l l oT&'roil€Htr,i H A r B e p o t T - ll dr cpeAHero ll HOCTb 3HaqeHtrt ll relteer Zi : (X; - zL X)) t lr. o. atunarpr"vt Hop- (2.26) Tenepr, KaK 3To noKa3aHo puc. 2.23, HaurlrripuBbrer{acror p a 3 . ' u r L l r r b rcxo B o K y n H o c r e r p i o g a Composila HAeHrr.iqHbr. Xaparrep l i c T l l i i t l C T a H A a p ' I H O f OH O p I ' 1 3 r - I b L i O fpOa C f l p e . : ( e , r e H I I qO q e t t b X O p O mo lr3BecrHlt, a ta6lnr{bl [noi]iaAefi, orpaHuqeHHbrx yxa3ariHbil\{lt cerl{eHraMx M o } K H o H a f r r r . r n c q r r i B o B C e x - v . r e 6 H r r K a xn o lpuBoii, cTaTICTrlr\e. HalontHritvl, qTO nJlox-(aAil Bbipa)KarcTcfi npr\to qepe3 Bepoltrlrocrrr. tr4crio,rrayn cor(pauleHHyro ra6.tuuv (Hatpilrrep, ra6t. . 2 . 1 0 ) , u o > r < u os a - r t r n n r o 6 , v r c e e r r o R r H o c r t , c B f l s a H H y r oc o c . r i y u a f r H o tni u 6 o p x o f i u s H o p u a , r i H o r i c b e o x y r r H o c r r r s, H a q e H r r ri i o r o p o r l p a c n o , T o ) K e H bBr r r e K o r o p o M3 a A a H H o M u H T e p B a , , r eO. r s a i i c AJlfl 3rofo Hy)KHO3HaTb AtrcnepctrrocoBoriyrrHocTlr. ;laBafiTe cAe,rraeMHepea!'tbHoeIlpellno,'ro)tieHtle, qToMbt It(:cIeAoBa,lIl BCrocoBor(yrlHocTbpola Composita. 3ro 3HaqfiT, qTo i!{bl 3 H a c j t c p e A H e e3 H a r l e H r r e , aBHoe14,2 lttlt, u ux A J I H He e g r e M e H T o B p c r a H A a p r H o e o r r ( r ' r o H e H u ep,a B H o e 4 , 2 u r t . Ka,<osa BepoflTHocrb I l o t B . I i e H u r rn p n c l ! { a f i H o i v r nrr6ope o6pasua, lreuoueio 3 lru? Ar'Iff Ilo"IIl,geHliflorBera Ha 3ToT BOnpOCnpr,tBej,e\{3 r.lrvlx eAliHLII{alu craHAaprHofoorr(.iroHe}rrrfl I { 3 a r e M o d b a r n r , t c sx r a 6 , r . 2 . 1 0 : 2 : (3,0-14,2)14,7 : 6l Beporruocrb [oJ'ryqeHHrrnpeAcraBHreJrfl coBoKynHocrr,r p( Composita, AIruHa Koropofo MeHbrrre- 2,4 cran4apruux orKJro .HHfi, ecrt xyMyJrflrr.rBuaflBepoflrHocrb B eroii roqxe: no Haur ra6;t. 2.10 HafiAeu 3HaqeHHe0,0082, r(oropoe e geficrn[re,,rbHoc oqeHb va,ro. Tenepb BbiqtrcJrriMBepoqrHocrb rrosBJreHtrrrnpeAcra BHre":lt, .l,IIHHaKOTOpOfO npeBblrxaeT20 rUu. CHosa rpe6yeul'lo seru,riiHv npeo6pasyent B soDi{a.rbH.vro Qopuy: craux,aprHV _ 14,2) : 1,2. z : (2a,0 14,7 T a n r r a r : c v M M a p H a r ri l , , r o u t a j r bn o 4 x p r r a o r i H o p N { a r , r b u o rpoa c r r p e Ae,reHr.rspaBHa 1,00, ro BepoflrHocrb noJryqeHr.rfl BeJrHqHHbr ,x, paB_ sori rr"lil 6o.nlrueri 1,2 craH4aprHux crxncueHarl, r. e. 6o.urruel't, qehr cperHee, paBHa pasrrocru 1,00 n riyMv,rrfrlrBfloft Oeporrlroctli rrorrrvseHursHaqenur?,He npeBocxoAflrqux 1,2. L4laqe roBops, P ( x > - 1 , 2 ): 1 , 0- P ( x I 1 , 2 ) . T a 6 " l . 2 . 1 0 . l a e r H a ) , 1r i v M y J r f l T u B H b B r ee p o f l r H o c r r .B r l,{orb /.to 1,2, [ - r B b r q r l r a e \ , r a fBl e p o f i r H o c r b p a B H a 0 , 8 8 4 9 . f l o e r o t r v B e p o f l r H o c r b '1,0000 n o r B , l e H i l r o c o 6 e r l C o t r r p o s { . t a! ; ' r r l H H € €2 0 n a l r p a n H a _ 0 " 8 8 1 9 : - 0 , 1 1 5 1 , H . r r r H e r . { H o f r { r6,o{ . n t t u e o , I s o r ?4 e c a r o i r . T e n e D l t s l r r r r r r a J l i {B\ 1e p o f i ' H o c T u c , r y u a i ? l l c r o n l r 6 o p a c o m p o s i t a , l,,rrrita xoropofi :ionaAaern rrurepei,r or l5 ao 20 lru: "4"-Iff l) Xi:li z : ( 1 5 , 0- 1 4 , 21) 4 ,x7 0 , 2 , ,qas 20 r,i:i z : (20,0_ 14,2) f4,7x 1,2, P ( x < r , 2 ): 0 , 8 8 4 9 , P (x -< 0,2) : 0,5793, P(0,2-< x -< 1,2): 0,3056, T' e. ilprrrriepHoo.{,Harperb o6pasu,oo norraAaeTn sa4aaHuli rrHTe0EAT. I{eHrpallnaq rtpeAe,rbHaqreopeMa B aioi,l ''pr]repe npeAfioJrara,rrocb, qro nu6opxa 6u.na c4e.naua Ir3 HopMa,'rbHopacnpe4e,reuuoli coBoKyrrHocrn. K coxaJreHgro, MH o6H"ruo He 3HaeM, xaxoft Brrr rrNlee'r pacllpeAeJreHHe,u IrHofAa qro oHo 3HaqIITeJIbHoorr'Irlqaercfl n_oAo3peBaeN{' oT HopManbHofo. HE eroro He cJreAyer, qro HopMaJ'rbHoe paclpeAenesng 6ecno;regHO, TAK KAK HMCCT MCCTO 3AMCqATCJIbHAg IIEHTPAJIbHAE IPCAENb. Har r,eopeMa. osa yrBep)KAaeT, qro ec.rrlr au60pxlt Ii3B,rleqerrbl c,ryuarino lta ,rrc6oft coBoKynHocrtr,TO CpeAHrre,Bbrqr.rcJtreHHbIe !,Jtfl STHX AaHHbrx, a trMeHHontr6opouHbre cpeAHlie, flBJltroTcg c,lryqaii'62 Btr6oprta1 2 Bur6opna *+ oo o- "----"-------a Bur6oPra3o+-+ co Atr X l-^ooo z X3 83flrble Ha!'Aaqy u3 coBoxynlrocrn qePuc. 2.24. TPlr nlt6oPxu u3 nrrtl sa6,rrc.uessfi, 3Haqe'trr rn6opox o6osHaqeuut Cp;;il.c U-o6pa:ttltn PacflPere'reHueM' oes X K HOp' paCnpeAer'IeHI.IeKOTOpbIX CTpeMI'ITCfl HbIMU BeJIHql'IHaMI'I' O6beMa BbI6OpKH' ManbHOMynpu yne.ttr'rtleHI'rH Teopen{a raxercq Ha nepBblii B3r"itA [peAenbHafl [eurpallnafl rlonflrb' floqeMy cpeAHIIe BbI6opoK rpyAHo He Bnorne noHRruod; p a c n p e A e ' l e H H l oe' c n n o 6 p a 3 ' A o , r r x H b rn o A q l l H s r b c a n o p u a n s H o M y rllna' Irs conoxyn'ocrli -coBeplileHHoApyrolo;;;-'6;;" 3Ta ToM' llro B y6e4urbcfl ""6punot no3Bor'laer OAuaxo Mo!.eJII.lpoBaHI{e q r o n p o l { 3 Bo' M b I reopeMa Ha caMoM Aexe BepHa.flpe4nonoxHM' ornxqlloe coBepueHno HMenuleft .qilt,i eu6opKy Il3 coeoxynHocrll, B I ' { A a 'K a K 3 T o I I o ' o r H o p M a J- I b H o f op a c n p e A e J l e n u sU - o 6 p a s u o r o qa JIbHblx s a 6,n13.u.e' crb rrgAriBr.rAya Z'.i+. bo.,,'u a s ;;, ;;5' ;; iii. pacnpeAer'Ielliltl' KpaeB Hs AByx nuir s nu6oprie 6yaer ilonyrleHa ycpeA' 3naqeHufl eTII KorAa conoxyllHocrH. Koropbre coAep)Kar nltx Htriorcq c IIeJIbIo HaxoxAeHufl cpeAuefo apnQueriluecl{oro' 6oJIb' IIJI]C 3HAI]CHI]fl IIOIAIIIAIOTCfl HH3KHMI'I 3HAqCHUflMII' B PESYJIbTATC n o . r r v q a e r c rc p e A H e e ,6 . r u s x o e K q e n T p y p a c n p e J . e . [ e H H sT' o n l x o e o.reHl peAKrrx o6croflTe,'rbcrBax,KotAa Bce c.liyuaiiHo BbIOpaHHbIe sa6;rrc,tesufl OKa)KVrCs6.[r.rsxlrN.{,.nn6o K BbICOKHM3HaqeHl'ltlM! cpeAilero MbI nonytJHM .,'tu6o x caMbIM Hl.tstttl,t, npI{ BbIqHcJIeHI.Iu 3HaqeHHe,Koropoe CI{JIbHO OTIHqaeTcqoT qeHTpanbHofo' 3auetuu, uio ori6opoqHble cpeAHI'Ie3HaqeHI'Isl(nacrepu3ylorctl (co6uparcrcn n nyuxu)- n6,r[su IrenTpanbnoro 3HaqeHI{qrunorerll' r{ecKoro pacnpeae.rreHHeHa puc. 2.24. Ecnn sTor sKcnep}IMeHT noBTopurb rbrcflqy pa3 H 6o.rtture, To oKaxerctl, llro ou6opouHue .paln"e 6yAyr p"uanonu.atbcfl HanoAo6ue xopouro l.I3BecrHoli xo' nopr',raJlbnoiiKpHBoft. llo cyuecrBy' re xe caMble "roxoaoo6p-asLoft63,' F >,--,*M -,^^^r^.rrHnaDTHofiouu6roft'OuootlHcblBaer[3MeHrIItBocrb'Ko' ox'Aarb or cpeAHHx nu6opor< rpn noBropHoM :I:.:; ;;;; iutJyru .ri"rn""-; Crau4apruasorns6au6opet'tsroft xe conoxynnocrr'r' !-ia paBHa i/,^ uba*, FmL t^ s":J/71i, { i . ' lt l . / ;: 8 i i B a " l e H T H O t9 o7t se: o {ln. I-lei;rpa.,tlnaa xpex,eilLHaq reopeMa Il03Bo,'iler cQopn,lynupoL i , u . r .i tr r3 ' r I I C T l l q e c l . ; l l xep u T e p H I I ,o c H o B a H H b l eH a x a p a l { T e p I I c T I I K a x UX .!,ax(e B Tex cJr,vqaflx,KOf-14 rioplra.lr,uoli xpunoft, H npu.\,{eHflTb : o B o r i ) ' r r H o c r bI,I 3 t i o r o p o t i n : q r a e b t 6 o p K a , H e p a c 1 r p e A e J I e HHao p ,1rnoHo. flpe4no,lo>riiiM, qro IIar'leoHTo,'Iof, xoroprtfi 3a-HI'IMaJIctl COmpositA, nanten oqeHb 6O.nguVrc I{g,'t!'Iext11tn rrcc.neAoBaHLIeM IlJIllry'IloKpbITyIo6paxltono,lauu'I'lcronaeMbleBblf"rtIAtraHa!'lofrrr{Ho COmpOSitA,ItO tro pa3N{epaMOqeHb Be,rIHKIl,CpeJ.Hsfl.{,,rlllHa r e c r r H o 6 p a s u o n c o c r a B , ' I t l e rl l p I I : , { e p H o3 0 , 0 r ' r u . H a n o u u r i r ' 1 , u t o ilIL,I<<3HaeM>)'qTocpe!.HeeIIcTaHAapTHoeoTKJIoHeHIiflcoBoKytl. Hocru Compqsi\t coorBercrBeuuo paBHbI npaMepHo 142 tt 4,7 uuM o x n o J r r . Ic q u T a r b , q r o H o B a t a l t 6 o p x a 6 p a x u o n o 4 6 H n a H s s r e qeHa H3 eroft cosoriynuocru? Mu naoxeu onpe,{e"ry}irbpa3Hocrb Me}l(Ay cpeAHI.rM3HaqeHI'IeM narueri Hoeoft eu6opxtr II cpeAHuM 3Har{eH[eM coBoKy[Hocrn. 3ty KOTOpyIOMbI pa3Hocrb 3areM MO)KHOCpaBHIITbC n3MeHquBOCTbIO, 5lr xorerr r.rMerbA,'rfi cpeAHlix snaqeHltti nlt6opox, c.nyuaftHo nsB J ' r e q e r r H r ci x s a A a s H o f t c o B o K y [ H o c r v . 3 r a L I 3 M e H q H B o c r3ba A a e r ,cr craunaprHofi ourr6xoii u ffBJlflercq Qyurirlaefi KaK Aucnepclll'l - ' o B o K v n H o c r rT . ra, K u o 6 r e u a u s r 6 o p x r . Cpaeueune MexAy pa3Hocrbro cpeAHIIx H craHAaprnoft otttH6xotl ltorxuo ocyqecrBnrb no cJrer,yroulefi Qopitty.ne |h* rlm* W^- Pric 2 25. Pacnpe.re,resrre cpe.(rrero. l ; 1 . n r 6 o J r , i l t o f o q u c J r a n l r 6 o p o r o 6 r . e v a n , 33rrrLl.\Ha)"(aq1'li: coeoxl'nnocreii,c p a c I ] p e ; ] e J € H r r e i l ro, r , r r r r q a r c u { f i M C H Or HOpMa!'IbHofo. UeHTpaJhHat YBeIIJc eH! tr H3 KOlOp6lx trpe.(enb$afl TeopeMa n03BonreT yrBepxAarb, qro pacnpe,ae,re""" f no ,,"pe n cTpe\lliTcl K HOpMarbHovy. 4 - pacnpeAeteHffq rcxoaglrx sosoxl.neocre?, n e a r s r e ; r 6 o p r c a ; 6 - e - p a c n p e t r e l _ e H n c, [ a r s n u 6 o p o n o6rerra n:2 (6), tr:4 (8, u n-25 (el l22l pe3yJrbrarbr 6r'ly'r noJryqeHbr,ecJrH Haqarb rroqrt'l c .rrro6oro 4py_ roro l ,K , H a n p f i u e p , u s o - -6r o - -a' x e H o H a ^ I r c x o A H o f op a c f l p e A e , r r e H r . rKf a p u c . 2 . 2 5 , B 3 q r o M l r 3 K H r 4 f r il I . J l . f l a n u s a iZZl.'' T a x x a r p a c n p e A e J r e u u en l r 6 o p o q H b r x c p e A H r z x c r p e M r . r r c r K HopManbHoMy' To efo Mo)KHo onllcarb ro,ilbr{o crarrcruxaAByMfl M H- C p . A H A Mr r ; l , H c r r e p c l l e f K i.ax reopernvecxoe, TaK H 3M[rrptq e c K o e u c c J l e x o B a H H rr r o K a s b r B a r o rq, r o cpeAHee3'aqeHue sH6op o q H b r xc p e A H t r xp a B H o c p e ] H e M y c o B o K y r r H o c r Hr ,. e. f;^:St. cn e p c u s n u 6 o p o u u o i r c p e 4 H e l i p a n H a A l c n e p c u u c o B o K y r r H o c r[ u uA , eleuuofi sa o6relr aur6opxu,un" ,1* :a2 ln. CraHlaprHoe orK,,roHeH u e n u 6 o p o q H b r xc p e A H u x e c r b l < s a A p a r g b l r lK o p e H b r . r 3 3roro qflcila v Ha3brBaercr craHAaprHoit ourn6xon o[euNn cpeAHeto, I,TJII{ 64 o .\'-p c/t :_ X-Pt 01/ ', (2.28) ln 3ail,reruu, qro npoBepfleMafl crarucrur{a BbMIIcJIgercfl TaKIIM . 1 6 p a s o n aq,r o o H a s r o q H o c r t t o K B a B a , ' t e H T H ar i p H T e p u r c ,I i c n o , ' t b :rl/eMoNrvAJrfl cralr.q,aprr.r3arrur.r nepeneHHofi (cu. ypanueuue 2.26). I ll)oBepfleMascrarrrcruxa Z Hoprr.raJrbHo pacnpeAeJreHaco cpeAHilM l l { a q e H H e Mp, a B H b I MH y J l F OI,I C T a H A a p r H b I M O T K J I O H e H H epMa,B H b l M ir.I'ttHirlle,ec,ru nu6opoqgoe cpeAHee Aericrenrertgo 6tr.rro noJlyqeIio ,{Jittrrrnorerri,{ecKcii coBoKyrrHocrlt. Ecnu Z xpaftHe BeJIITKo'ro illtl BIlpaBe 3aKJltoqilTb,rITo HaIIla nst6opxa ne 6ltna r3f'Ta rr3 3TOH conoxfttuocru. (Doplra,rnuoe peuleHae, oAHaKo, rpe6yer, qro6lt lrlt npoBe!'cTaHoBrr.rincoorBercrByloqylo npolreAypy AJ'InBbIqIlcJIeHI'Ifl l)fieMoir crarr.rcrlrKII. 5-201 Bep{q,T_O oHa BO3HIII(aeT fleosbrfi uaf B crarlrcrnqecxofinpoaepKerrrnores- $oprray.nu- r , r . p ; . , o T I l c D ! - i t i ' ] t . 1 , 3 H a t r l v i c \ / l . n e J l e poAa' Hao6opor' ecrll l l , I n l . , " ' ; 1 , . , i , ,, e, i : i e o t u i l 6 l . o i i r r c p B o f o poBr(airollxoAruleriranoresu o6 ucc.ne4yeuor? nepeuesnor?. O6uqO fl t l " ' ) i : 1 B - l O - , , , t , ' , " i l l r l o i c 3 ; 1 I l l ) l l H l l \ 1 a ( ' ' l CT C O tsCptl]aeTC O t l ' i,:. Ho raKaf rnrrore3aHa3brBaercrr Hy,reooft,o6osHaqaercflHo v, B ilalt:eMy llPllNiePy' rlpOIi"IJliO'rT'ililp):eNl i i l i o : l l l i l i { a n C b cyxlHocrrr,r-iBJlfiercs runore:or?o6 orcyrcrBHripa3rnqnt. Hanpri,',, ,;.,.1a. rITo AaHHafl ett6opxa B3flTa H3 coBc)Mep, Moli(Ho irpeAfio/'ro)KnTl!, Kyrrllocrrr, nvenuqeir 3aAaHHoe cpeAHee 3HarreHr.le. Hy.tesal rfirrore3a Bbrpaxaercq B Sopue He : !.1,r: !-ro, (2.30) I-It : pLr*Lro, T. e.. r{To cpeAHee3}raqeHHecoBoriyrrHocTrr, }r3 Noropofi 6H,[a ssgra B b r 6 o p K a ,H e p a B H o 3 a A a H H o M y3 H a q e t r r r r cp r o .T e n e p u p a c c M o r p r . i N i J r p o u e A " V p br irp o B e p r i r if i l r o r e 3 i r p r r 3 a A a i r H o My p o B H e s H a q n r { o c r H . 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B HaruenanpriMepe Mr,t Aol)r(HEr 6yaeu npeAnoloxrlTb, 1116 c p e A H e e3 H a q e H u ec c B o x y n H o c r r , u B r i o r o p o f i d H , r r r s s s r l r 6 p a x l i o noAbI' rlaroAt{Iu}iecfl Ha nJIllre, coBnaAaer co cpeAI{HIu3HaqeHHeNI c o B o K y r r H o c r tpr o A a C o t r p o s i l a . C$oprrry,rripoBaBHyr,ieByioriirroresy, Mbr Aod,rlKHbryi{asarb n a,'rbrepriarr.rnyli I{ei.i. llolxoAsu{as aJrbrepHarr.rBaB erori crlrl,itlalr Moxcr 6utl cnervnuefi: HAITCTO CTATTICTIIqECKOIO : !,uC.ielJHI)'le nOHflTIIF fz note:a Ir nJIIITbI:lro .r n'iiirbl+po B..ci;:rDlritJlbllofru I oaoou a rJrirlr nptrtll,lre; r i a r c o D o r <nt )r i o c r t . l | ll llpann.rsuoeperxettue Oruu6na I;epBcroPoAa | I ocoSl c nJllirLl tl'i npl'luannr>I<ar ccaonlnHot'rll Ouru6xa Bropofo PoAa Iipanirir'uoe peu;eltlle CO- ' . , C C i , < < i - [I l r l I ] T b l ) ) O T H O C I I T C t t ' K O ] l e r l ] l O ' K C p e A H C ] ' { y 3 H a r i i - ' l i l l i O c Ir'iil{TbI' JOii\. jittocTrr, 1( rio.l opoit I]pilHzt,]l,ijetrii.,T oc06rl, co5p.l]llibie L-rci}:''f}locrb crir'i ttcrlillect{llx npoueiiypax i3 pacnpo,:rpatteHHIix r- rl liil3blp o A a o 5 o : J I . I a r i l l e T C t i . { e p € 3 rrore.,rel{H'l orull6Kir lrcpBoto Rael'cflypoBHe\{3Haq}l}.locTII;3Tvl]epofll.IiCClb'lroil{Ho:..:i:i].bAo qro6bl Mirllul\,lllilllpoBiiTb BepoFTgpHl{cHeHurr ripgTepur. A,rg roro pO;li.l' 3ailillilelll HJi.'ieByiC fllItOO 1 ) O f O 8 1 O L t I l i 6 l ( 1 1 itOC'fr, ItO:IRJlCIIttfl ,re:i). ijl)rr ycJroBrrri, rrTO OHa 61.'.ier o'i'ri"roHefl . Ei,'!il f flllo'i'l3a oT' l ' 0 B c l l o t t T I I o c l ' b n c t i i J . i : : H l l : i c u l l a . i l i l l ; ' r c r i l c f o 1 ; ( l ' r 1 3l l i l t 3 I . : , ' t o H r i c -cff i . t'o"' t i i i i r ) , ' r - i J , T 0 f . { a I i i i K B e p o E l l l o c T b 1 i o : ' i B ; 1 e H I ' I foi 1 g r l 6 . i i i I i l ? l l o t o I t : t B L t C i' 1 l l, T[1i ](aK oHil 3ajiaeTCu sapaHee. EC;rtt, OAHaI(O. lipllTglllli ( r . e . U 5 , ' , ' : : , 3 ' - qI l i l l O r ! C n l ) i r B O . 1 r r 1 r { O T I ( . I I O H e } t r t I O} l y . r I C : l O i i r U n O r e : u t C.ieBepOuTliOClb T O n O f l B , ' l - q e lC f l H e l i C T O p a t le3i riprrlutvaercli), J r s l b o r r r i r 6 r i yB r O p o r o p o A a . 3 r r B e p o t l l l o c r l p , o o o 6 t t : e f c g c p t ' a pllBeHCifi cpe.lliux i r e u . i i l a ' c r H a . ' I : i r i l tol t6 p a 3 o N I e, c i l l t r I 4 I I O T e 3O : j l I l / , ' i ) l i l e l C t l , l , l b I A e " r I a C XB 4 b I B O AO ' i ' O \ { , L I T O A B e I i 3 y t I a e i ' t i j e i ' C ? 0 l i Y I l l l O C li { i l N { e l O T p a 3 J ' i I l r { H b l e C i l e j l . H : ' i C3 H n q e H I I t i l I _ B 3 l ) O t r l l C l ' l b 'loro, rtro ripriHgro ogn6orlHoe peueHle, paBHa a. C ;1p1'roii tlloriln Cl-tq.1i11it' 1.)OHl,lrC'llttt 116 Ue OTBepraeTCu' yTBep)li,iellHe O TOI'1, jlllr. ., uoBrlli) ,.lIoc'i eii coBllil.l.aloT, Moxie'f oI(a3aTbctl "[o)i(ll;ri\{ c Hoi i : r r , . r . ' r i r c i iB e l ) o z T H o c T b i o B . ilce c'ia'rgct'lqe1rKue i{ptiTep}rlt CCHoBaHbI Ha ilpeAllo.iiol{ieiiIIH, ' , f ( ) I l \ ' , ' t c u a f l f u ; i o ' fc 3 a t t a , r b r e p i l i l i t i B : t t ( I I e r l B 3 : i l lu l i o l l c K . T i c q a l o r -rJ)-\,' .ilp)'fil li BNlecre o6pa:yrc;t' 1io'rlHoe x'Il{o}KecrBo co6lirritl. Tar :'ilt'; ll)',rIcBUrl fIl.tio'ie3:l 3aIII.lCblBl:i.ii-]t1B flBHCx,IB!1Ae, TO il"tlbTcpl{3illi-r:l -lo"rilr{lta 6r,lrb AoBoJibHo o6lleii. Ec,rli Ho orBepfaerc:1, To MbI 'lilin a C l r i , r tr O 3 a A i l F r F r O eC O O ' r ' l t O t H e y . r l c B O i il i l u eL I e e , O I I U C b l B a e X l O H ll() i c3oir, llc IlbIito,TIt;!ercfl. Do.rlee rofo, I'lcrllHlloe coorrio[IeHHe B -, ioM c,rI)'q;lc co!,eplKrircfl B o6rIIHpH0l,l MHo)KecrBe a,lr,TepHarl'IB' 3:itirtoqer{Hbrx B o6uef{ a.rrb'lcpHarrrBe. /vlbl He Mo)KeM oillr€,u,€Jll{Tb' iilil(oe Ii3 coorltoueHrrri ucrr.{HHo; Mlrl I\{o)KeM ToJIbKo ycrzlHoBllrb' KaKoe H3 coorHotuegufi ge BIrtIIoJIHrercq. HHorAa ts MareMarl'lqecl(oii cralrrc'rnKe npaMeHeHue crarucruqecKlix KpI{TepI{eB no3BoJlfl- 5* o/ X1?ti"'i"'%T".i#'i'#; Hgrepecve-r-31'JJ#1""X;*1{,"1:v,'':r*":"'ff 0/o 3AH, or p aHHqen- eT IOBOpHTb o6 <<onpoBeplKeHr.iu Hy/'reBoi',{ r}rrroTe3br>> npoTrrBaJIbrepHartrBbro Heycnexe onpoBepx{eHHe. Heycnex onpoBep)Kenr.Ifi, Kp rrr uuecxa."_::':::;;;;;";, I{OTOPOMY COOTBCTCTBYCT HCII38ECTHAfl BEPOflTHOCTb IIPHHfTHfl ouru6oquoro pe[reHris, He cJry)Kr]T3r{BrrBa,leHror,r npuHflTlrfl rulloTCSST. CTATIiCTHIiCCKHC IiPITTCPIIH B HCKOTOPOI,I CMbIC,ICHC ]lTO|YT c K a 3 a T b H a M , q T O U \ { e H H Ol t t e e T M € C T Oa, T O J t b t ( ot l o r Y T c K a 3 a T b , qefo HeT. . . B o : n p a q a f l c b K ^ H ) - , ' r e s oriiil n o r c 3 c t r u . i t b r e p H a r r j B eo, n p e I e J , l e H H o i i Q o p u y " r a u a ( 2 . 2 9 ) n ( 2 . 3 0 ) , n p e - l n o . r j o x l r N rq, r o r , r b r c o q , r H y p O P e H _3bH a q L t M O C T(l rt . c . B e p o r r H o c r r , o r L r i t 6 x u t r e p B o f o p o A a ) a:0,05 noAxoAflu,\uNr .lJlfl Ha[Jrrx ue.rreii.i.iirrnrr crloBa]tH, ]rbi Aon y c K a e M B o 3 M o ) K H o c r tl p r . i 6 n n : H r e , / r r , H 5o p a z u a 1 0 0 n c n u r a , H l i r ? o r u H 6 o q n oo r B e p r H y r b n p o B e p E e M y i of l i n o r e 3 y B c , 1 )q a e , K o f A a o H a BepHa. llpe,r.no"roixilNl,qro Auclrepcuf coBoKvnHocrli, 'to otHorIeHlrlo K t t o r o p o f r B e A e r c r r r p o B e p K a ,H a M H 3 8 e c r H a . I l a n e o H r o " r r o ro n p e . l e qro Ar]cilepcHfl suaqeuilfi A,tilHbr .1";tfl coBoKyIIHocrH oco6efi vrlr.IJi, p o y a C o n t p o s i t a p s . F . u a2 2 , 1 ( H a n o u H n n , q r o c r a H A a l l r r { o eo r K , r r o H e H I 4 e6 u n o 4 , 7 ) . T e n e p r M o ) K H or p o p u a , l o H os a r r u c a r b c r a r i l u r i r r i e cxaii rparepuii c,re;yrouulr o6pasora: 1 ) n y c r l r r p o B e p r e M a qr u n o r e 3 a r { a J b r e p r i i t r t . t B ar { } r e } o r B l { A Ho: Pt: &0, Ht: Wt+poi 2 ) n p u H r l u a e My p o B e u b s n a r ; r l M o c r u :a : 0 , 0 5 ; 3) onuHc,rneM crarlrcrriqecxuli xpHreprrt:i: 7 -_ L x-Fo -_=:. ol/ l t tn (2.31) Ec,ru asr6opKa B3flTa HayAaqy ns Hopr'rarrrbuofi coeorylrHocrn c ttssecruoii 4zcnepcaeli, ro crarr.rcrnqecxHri xpurepuil Z 6yler pacn p e A e n e Hu o p M a ! ' r b H oc o c p e A H H r ,3, rH a q e H t r e Mp, a B H b r MH y d ' i r oH, A I C nepcueii, panuoli eAriHrue. Mu npzunrur corJrarreHrre o roi{, rrro n p n 6 , r n s u r e d r b H oo A u H p a 3 l r a 2 0 u c n l r r a H u i l l A o n y c K a e r c r r o u u 6oqgoe orKJroHenr.le rnlrore3br o paBeucrBe c-peAnr.rx, B To BpeMffKaK o u a B e p H a . V l u a w n c , ' r o B a M r i ,M b r n p i t l r u t r a e M 5 f l e - u u r Z y p o B e H b pr.rcKarrJrlrBepoflrHocrl ouriz6KrrnepBofo poAa paBH)'ro0,05. OnpeHOpMa,lbHoropacnlle.r.e.reHuqo6AeJrI{MA,'rfl CraHAapTLr3OBaHHOfO ,'IacTb,3aKrloqaloulyio 5% nJIolr1aAlIno4 xpunorl HopMa,'lbHoropacf l p e A e n e n l r f l .3 r a o 6 l a c r b H a 3 b t B a e r c rr i p n r u ' J e c x o i i .E c , r l r e t r q u c ,{eHuoesHaqenue crarucrarrecKoro Kpurepilr nonaraer B ery o6JracTb, Mbr BbrllyNiAeHbroTKJIoHfirbHyJIeBylo runoTe3y. T a r < r a r a J l b r e p H a r r . i B a - l p o c r o o a H o i r 3 H e p r B e H c r B ,T o r a , r i o resa 6yAer orKJIoHeHa,ecJIr{ sHaqeHue KpnrepHfl cJrurxKo}I Be,'rr4Ko r{Jrn cJr}[rrKoMMaJIO.3rO SHaqI.Ir,qTo cyuecTByloT rpr.i Bo3MoxHble c n r y a r l H l r : l - r :1l - t o ; P r l p o H n a p r < p 0 . B A a H H o N {c n y q a e H a c H e 68 rr.Tror{ *, vraLr 2,b pacnpeAerleHut' HopMa'rrb'oro lllli-'^r'rt"q o6pasorl: MbI ^'' pe"o*nLpol^arb.-caeAyloul'I'lM MoIKH;CiasaHuoe l",,orr (illKJafl lluA ":"f"tff J.t.""?"# ,",I*",pu1Tr:::ll*'""J#T"?i,13i,Tt;f reoper11:::'L,:;;#";;;ilr;;;.-"e."'1 Arlcrepcur HopManbHo l:i;;:il;$";ii";;;;-vn1oc-rr rax}rienporo Mbr3HaeM u3Becrl{a' Bpa3' 3ZlKr'lIoe€HbI J c o 6 e i l ' p a 3 M e p b lK o r o p b l x i1"nr"o" .ol"p,tun'* o C o 6 e r l npi{xoAnrcn Ha ( n . l n'tpta"i'* p"ttp' paBt":.:l:1" r r r r q n b r xn p e A e n a x AJIHH-Y' Hr"'terculuii u 'rt"'po"I'13 ::,i:,tr""'' rrlrepBrr li3B!'leqeHbl " b'n"non"Hunu) ' Ec"itt oco6u Hyro ,tB).\{ cTaHAap'IHb'*' no!'I\IqenHn BeponrHol'rrb e'ioii coeoK,vnHocrr'rt""r';;;ttt 96!1::*' p a c f l p e J ' e " l c ] I l l t l1 ) : l B H a x p r l a o i i i l H r e p B a r e KpIinu6opNrz ,rArnno* nol coorBercrBylonlcl'1"t:]-":--::':l:i rrJloluaAIl," 3aKJIIoqeHHofi oqeHb iu 06flacru,- coorBercrB)'toueti eori. Ecru noi6opr:.^n"s'riuHe flBJltl3Haq[T' -qro gaura er't6opra rtaroti BepoflTltocrnt, npoaepleilor:l rflIloTe"o yKa3aHHOii "o ercr nu6oproil Hs iouo*yn"o.r_r,r, HeKoropan RIrorl'e oli:^:.,r{Meerctr .,or?,xoropylo MbI J;fi;;&' o6II3 l{p^Irrn-q'ecroii uoi6op'*y H3Bileoo oltpeAeJIeHHu"u"po"'"ocrb o6r'13crH' r<putuuecxoii nn95?I:"oit ,rracrlr coBoKynHocrn, paBHaq poAa Composita' HanllIUeM: Boenpauran.o,.'ilf'*tpy l) Ho : !i n,lllrbl : 14,2 t'ttvt; H t : Ft nrl'trbl t' 14,2 xtttt', 2) a : 0,05; 30'0'14,2 : 8 , 2 ' 3l t: *n oTBepraeTcpeAHI,IX Msr yNe 3HaeM'qTo |IlnoTesa-opaBeHcTBe 'rlu6o cluluBeJII{Ko' innufioM cfl, ecrll{ nl,6opouuoe";ffi;;;6o Kpllrep'lo' rpeAcraBi"* *uno. 3rb npraeoi'r K ABycropouneMy Koropan no corrlao6nacrb' u- pi"'.''z.ia.'Kp""udtxaq ;;;;;;; pacnpeAe50/snnouaAH HopMaJIbHoro Ilennlo AoJIx{Ha "o,l.p*rio Prrc. 2.26. 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Pacnpe,lenesueCrlnaexra c reBttrbro crenegflMHcso6oAbl 7: (Tr-x)/s,, (2.33) 77 T a x x a r r a 6 r l i q H b l e 3 H a q e H i i qA B y c r o p o H n e f o K p l ' r r e p [ s c 1 B c r e IIeHt{N{llcBo6oAbI, cooTBercrByloul[e l0 0/s-IlotuyypoBHIO 3HaqIIMOc r u ( 5 % H a K a l K A o M K o H I I e p a c i l p e A e J l e H u s ) ,p a B H b I - 2 , 7 0 v 3HaqeHue He lrorraAaer B KpurllqecKylo 062, 10, ro Bbrrlr.rc,'reHFroe ,rracrb i.r Hyd'reByrofiltrore3y He,lrb3rrorKJIoHHTb. (HanouHuu, qro r(pr4rliqecKrlfl06racrb oxBarbrBaer 10% nr'IoqaALI noA Kpl'{Bofi l-pacnpeAe,reHua). OrcrcAa cJleAyer, IIro Her ocHoBaHI'IiiltpeArloJrafarb, IIT0 ABe Iz3yqaeMble Bbl60pKI4 B3urbl U3 COBOKynHOCTeU' H M e l o u { r r xp a 3 H b r ec p e A H H e3 H a q e H I i f l . A,rs roro qro6bl npLIMeHtIrb3Tor Kpllrepafi, ueo6xoAllx'loBbInoJi6bITb iilrrb cdrreAylouueycJioBrrrr.Bo-repnltx, o6e nu6opr<14AO,'IX{HbI Iror'i){el{br Ha oc}loBaH,Hullpou,eAypbl cni,tlsfiHofo BbI6opzl. Bo-ero- Ta6nuua 2.13 nopltcrocrnAecrrr{ _ Pesy,ntrarrrfi3MepeHHq o6parqon [ecqaH[KoB Tenc,lnn neHcurbBaHcxoro Bo3pacra, dacceriu pexu Vuu.q, Bafiouusr Florrep o6Dasua flopacrocrs, o[ pbl;r,, 3HeqeHHtl C,Iyqai1HblX Be,'IIltiHH B COBOKyIHOCTflX'H3 I{OTOpblx HoprleJIbHblN{ Slt.rtu ugn,terictii-.r t;t ti.topxLt, .i.cJitt(Hbt otiucbtBarbct pac]lj]ele,leH]ieh{. B-TpeTbllx, Ai.icilepcuu 3rl'lx coBoKynHoc-LeiLAOJI)KnepDofo ycd'IoBLIq B bo,'IbulllHcrtse Hbr 6birb paBHLr. BunolHcslte oAuaxo efo HeBblllo,rHefeo,'rorr{qecKHx 3aAaq [paBepl]]b'rpyAHo. HIle B Cr"ryqae, ecJII{ Bbl6opKLt I{Meror cl.lJ'lbHoe H c14cTeN,l:!.1I]qecl(oe c i r r € r J - l € H i 4(€r a r r n T o M c J r y q a e , K o f A a L I s M e p e H U t ln o p n c r o c r l r I p o BOAflTCfl TC"ribt{OB 06pa3r,ax, 83flrbIX H3 npoAyl(TIlBHbl}l :'}oH rlJlu ireqlrrHrrrx noJreii), Moltter ttsHTbct{ cepbe3IIbIM HcroqHIlKoM ollII{o l{ol)x.{a,rIbHocrr pa...:ipe[eJ€5ox. KoHc,Jlro, itlloBeili(\, ar,rot"rbr rrriri 3Haqerririi rilrU:rr:lKa IlJyqaeltoii eonoxyllHocr]{ Mo]Klio npoBe.3itr, o,lUeKO OAIIO ',i'O,'rbKO OlIi.4OHeHHe01' HOpl{a,'IbHOCTI,I lleAKO rlpLiij0;in'r' K Ir3MeHeHHiO pe3yr'IbTaTOB, B OCO0eHHOCTUec'l!l r:Ul6OpO.tr a r i c o B o K y l i H o c r b i l o c T a T o r i F l o B e r l l K a . T p e r r ' e y c J I o B H e- p a B e H C T Bax{Ho, TaK KaK Iioqrll tso Irlcitepcuir ,l.eyx col]oKyIIHocreli -oqeHb KplrTeptll{ ocHoBaHbI Ha npcAno,'Io]Kelll{iI o paBCe CTa',irrcTfiqecKlie s e H C i B e g r r c n e p c a i i c p a B F i r r B a e r r l l , l xc o B o l ( y r l H o c r e i i . 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Cynaua 189 Cpe4Hee18,9 s,:28,21,-s:4,82 r'r1e Sc - {lueHKa Cl,aHAap'rHofo crK,'roHeHrrs pa3riocTri MCX{A} _T1 II X2, Ito,IIlrreHHas no llByx,r o5.be:lHHeHsbrr,r B;r60pKii[,r. 3TV c)ut]H.. tiy se lric))iiiio BbirllicJIriTb Iro qiojrlry,le "e _ Jp -r,' | -i---, -1- *nr_ _r n, 3 4 e c r , . 9 ,-. o 6 b e A r r H e n [ r a foi r l e n x , i c r a H A a p r l l o r o o r K . q o H e r r r i ,i]r,a i r AeHIIa fl r{o}16nHa r{Iler:lAByx tsbr5 op oriHbrx Luc jiepcfi r:r: .:-(nr--l)sr2-i-(rr-l)srz nrtr72-2 ,o.r, \z'')'ri ' fAe HHAeKCbT COOTBeTCTByIOT Bbr6opKaM r.i3 6acccfiHoB Erifxoplr fi V H H A F u e e p . l l p o q e c c o S b e . l t i H e H l r r. I B V x B b r 6 o p o Ki i p i i B o l r r r t { , t o [o,'t]tflTe.rrbHbnvl cTeneH-rrM cBoSoAL,I, TaK Kat{ Tpe6yeTct olleHliTb .j.iB;l napal'rerpa or2 11oz2. 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BHaqeHrrr12-pacnpeAeleHun Kpnrnuecxne c v creneHffMtl csoSoAr,t n p l l 3 a A a H H o My p o B H e 3 H a q H M O C T IIIl 7 ] Vpoeess gnaqsllocrH 0, o/o n 222:F/-\'t-t'\' TJ\ i-t a (2.44\ P' Y-,6 I I 2 To oHa Tax rar 3Ta crarlrcrirKa crporlrcfl no BbI6opotIHbIM.qaHI{bIM, H 3 M e H s e r c go r a u 6 o p x u x n u 6 o p x e . E c , r a B 3 f i T b B c e B o 3 t l o i K H b l e n u 6 o p x u o 6 ' b e M a n H 3 H o p M a n r s o l i c o B o K ) r I I H o c r IIII H a H e c r t i c o ' orBercrBylourfie ur{ 3uarreHufl222 s,a rpa$ux, ro oHII Syayr noAquueHu 12-pacfipeAerer{[to. Pacnpe.le,'ieHrley2 sanucut or riuc,'Ia creneseri cBoooAbr,Koropoe cBfl3aHo c o6reuou coorBercrBYlouiux BbI6 o p o r < . T ' r { n u . r H a s K p H B a f l 1 2 - p a c n p e g e , ' r e H r . 1r rf sl o 6 p a x r e H a H a plic. 2.33, a 3HarleHrrg12-pacnpe,le,'reHtrfl creAd'Igpa3,'Ifir{HbIxq14ce,r] n e s e i i c e o S o r r , sur y p o e H e i t 3 H a r { u M o c r r rn p a B e J , e H ssr r a 5 , ' I . 2 . 1 8 . Orlrerlnr, qro KprrBafl 12-pacnpe4e,.'IeHIrfl,TaK )Ke KaK I{ KpIIBaf F-pacnpe:e.rreHrrfl,BbrxoArrr u3 Haqa,rraKoopAHHar II, rrpoxoAfl qepe3 [o,{oxri]Telrbubre 3HaqeHilq, crpeMiircl r 6ecrogeqsocru. fIoApaccMorpeHo B KHI'Ire,rlu [23] . po6Ho 12-pacnpeg,eJleHue Pacrpelenevue y2 IrMeer 6o.nruroe sHaqeHlle B rlpatirl{I(e, TaK KaK ero Mox(Ho IIc[o,Tb3oBarb A,'Ifl llpoBepKII fHrlore3, coAep;Ka' TaK LI nopfl.IKoBble AaHHbIe.!,o cnx nop uIHx KaK HON{HHaJrbHbre, MbI paccMarptiBa,'tu ro,ilbKo MeroAbl I.IccJleAotsaHIlfl l.aHHbIx, npe.I,craBrsroullx co6oii pe3yr'IbrarbI H3MepeHHr gHaqeHttii nepeMeHuux. Tenepb )Ke MbI o6parl.IilIcfl I( HeKoropblM NIeroAaM HsyqeHfifi AaHHbrx rroAclrera, HaIIpHMep raKI]u, KaK r{l.icdroMopcKlIx exeii ga eAI.IHAqyn,'IOXIaAIIMOpCKOIO AHa, Il"llI qrcro Kpl{cTa,'LtoBIL'Iarfio' pacnoilo)KeliHbrx Ha llepeceqeHlruur,ru$a, Hi-lll 9IIC,{o 3epeH KJIa3a, saAausori rpaHyJloMerpuuecxor? Q p a x q u u n p a s . r p o 6 , r e H i I o MI I e c qaHLiKe. 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A,rlrepHaruBofi IO,'lOlI{eHIle, rITO 3TO pacnpeAer'IeHue He Cord'laCyeTcflC HOpMaJIbHLI\I 3 a K O I { O M .3 g a q e g u e c r a r H C T L I q e c K o f o K p I l r e p l , l f l M o x { H o B b l q l l c , l l i r L , , rryTeM noIpa3Ae"'IellHs 06JIacrH OnpeIeJIeHHfl CTaIIAapTHOfO HOpf l a. H e K o T o p o e q u c , r o o r p e 3 K o B . B e p o l r M a r ' r b H o f o p a c n p e A e d ' I e H i 1 -H HOCTb rOrO, rITO OAHO C,'IyqaiiHOe Ha6,'IioAeHue, I'l3Bd'leqeHHCeIJ3 c T a H . q a p T H o f o H o p M a , ' l b H o r o p a c n p e A e " I l e H r l f l ,I I O I ] a A a e r B 0 A I I H I l 3 oTpe3KoB, paBHa ILIIOqaAi.I nO.I, KpHBol'I B npe!,e,'lax orpe3lia- I'lcIioJrb3yfi 3TI,I BepOflTHOCTI{,MO}KHO Bblrincr'luTb o}ltulaeNloe qilcilo Ha6rroAeHHir e Kax(AoM orpe3Ke. ONI'rAaevue qacrorbl B Kalli.lo\t oTpesKe 3areM cpaBHIlBalorcf c coorBercTBylollIiMu Bbl6opoql'lbll'lll qacToTaMi-i. Ec.[H eru qHcr'Ia 3HaqllTe"lbHo orK,r]oHflIoTcfl oT oi'liHqTo6bl Bbl6opKa 6bLrIz'lH3BreqeHa Tl3 AaeMblX, TO Ma,'loBepofTrlo, 14cnoJb3yfl 12-pacnpelelreHlle. Mo1I{Ho HopMa,'rbHoii conoxyluocru. u <<Ma'rloBeponpltgarr BepoflTHocTHbIfi cMblc,rl c,qoBaM <<3Haql4Mblii>> 'THbIfi>>. Vra:ausrtii ilryJIe crarIIcrLIqecKHfi o lsl \ui-Ei)' X - : l dr , - r.le o; 100 BbIql'lcr'lffercfl rlo KptrrepHil - L:i ' qHciro Ha6.IllcAellrlirn i -r,r l(,lacce, Fi - {lop- (2.45) oil{fi!,aeMoe rIIlc'rIG t ,l g eroM K,'iacce.llpe:no,raraercfl, riro ltlleercn k pazHa6"'IloJ,eHI.tri K J r a c c o B( u , r u u H r e p B a J ' r o B ) . JrrqHblx B e r o r i 3 a . 1 a q e3 H a q e H r . rcer a r l r c r l r q e c K o r o r { p I I T e p u t B b I q I i c J g ercfl c IOMOIIIbIOnOApa3Ae,reHua06"'IacTLI onpeIeJIeHI.Ifl Ha6JIIO.lacMbrx 3Har{eHririHa rreKoTopoeqr]c,''iooTpe3KoB,HanpHMeil qeTblpe, Ho TaK, qTo6br IrM cooTBeTcTBoBaJH paBHbren,'roxlaAi.InoJ, Hop\,ra,'tbHot? 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KATCTOPI,IN BO3BOAI,ITC'I B 102 Kareropns s1 -o o1 cTarHcrrrr{ecKofoKpl4Tepr.rg He Mofyr 6urr orpuu,areJlbHblMli.c,reAoBare,lbHo, 12-t<prrrepuftBcefAa qBrflercfl oAHocropoHHLIM,II 06- H o f o o r K J o H e H i i , qs : 9 , 2 7 . l l o a r o n y ocyuecrB.lfercf Ilo Qopvy.ne T a 6 ; rn a a 2 . 2 1 C r a H g , a p r u s o n a H H b l e3 H a q e H f i t lc o J e H o c r t l r c r p y n n l t p o B a H H H e p a c n p e A e n e H H t lr a K i l M o 0 p a 3 o M ' .[Jtg Fp ' oBepKu rltnore3bl o HopMarbHoM qro KaxAofi rpynne coorBercTByeT neponrnocrr 0,25 l ra6.{. 2.20. B ta6n' C r a u 4 a p r u 3 o B a H H b l e 3 H a I I e H I ' { f l n p u B e , u , e H bB qerblpe 2.21 npHneleHbr pe3yr'rbrarbr pa36r4eHrifl Bceii Bbl6opKri ..Ha riaTef6-pgri. EC.lu-BbI6opKy MOIKHO Cq1lrarb Ia3B.IeqeHHOit ltS uOp' varrtHOii COBOKyIIHOCTH,TO Cr'IeAyeT OlKI4LaTb 1tp66,riH31Te"']bHO l2 Ua6.rrrcAeuuit sa KarefOpIIFO. Blt.It{Cntlq 3HaqeHIIs l{pllrepilfl X2' nO"IyrI HN'IC"rIeAylon 14en po M Cx{yTOriHbIe pe3ydlbTarbl : ( 1 4 - 1 2 ) 2 \ ( 8- i 2 ) ' : r ( 1 3 - 1 2 )2 ' , 7,": t2 a ( 1 3- 1 2 ) : _ |' 1 2 t 2 -- o 22-: ,, - 1,E3. 2,71 1016-uoro Buquc.ressoe3HaqeHue X2MenbneKpurllqecKoro IpoBIifl sHaquMocrt4 ri oAHoticrereHll cBo6oAbI.Iloarouy Her ocHoeanllli cql'ITarb, tITo paclpeAe,'IeHl'Ie 3HaqeHnii cor'I€Hocru B fioBepxHOpI{a"IIbHOro HOCTHbTx Bo.u,ax cyulecrBeHHo OTKJOHfleTCg oT 3aKOHa. He npoBepurb rlllrore3y y 2 Ilo3Bortter crarnctura Koueuuo, To,lbKo o HopMa"'tL,HoMp acnpeAed'leHllIl. Mu t'roxelr npHMeHurb STor x p t r r e p u i r . [ , J 1 f lr r p o B e p i i l t r 1 4 n c r e 3 L l o J I I o 6 o \ { . x p y r o \ { 3 a l < o i l e p a c - 103 [ t p € J e , { € H I I f lH ' a n p l {N l e p ' T aK o M , K a K J I o l H o p M a r ' I b H b, l 3f iK C I I o H e H I I I I arrblrbtri H r. A. flpu erou npoqe;lypa [poBepKH He lr3MeHqercfl, r0 XOTg ti]IC,TO CTCNCHCIi CBO6O.1bI B KA>KAOM CTYqAC 3ABHC]iT OT III4CJIA : oueHitBaeMr,rx napaMerpoB.KoxpaH [7] noipo6r{o paccMarpxBaer 3TH BOnpocbr. o r0 J I O f H O P M A Jt I H O E p A C n P E A E JETHU E H APyr[E nPEO6PA3OBAHIIq rllCTOfpaMNIa, IlOKa3brBaIOUlafl KoHUeHTpaqltlO MeAH B OCalloq- H O \ ' {D \ : C , r eH a I O X O H e .H a u e l i n p e A c r a B , r r e Haoc r r M M e r p H q H opea c |rpe.le,teHile,THIILITIHOe A,rtfl MHOfax Apyfax feor'rofllqecKl.{xnepeEc.nu sa6.rrloAeHl.{fl, rrpeAcraBr'reHHbre Ha pr4c. 2.34 u 2.35, npeo6pasonarr n .norapzQMltqecKyr,oQoprury (r-. e. nlrecro rrepeMeHu u x X l r c r l o J r b 3 y r o r cn q e p e M e H n u eY ; : l o g X ; , r o M b r y 6 e 4 a l r c a , u r o t4x pac-npeAeJreHLifl craHyr npu6,,ilrszre.ltHo HopMa!'rbHL,rMr.t ( p u c . 2 . 3 6 v 2 . 3 7 ) . T a x n e n e p e M e H H b r er r a 3 b r B a r o r c rJ r o r H o p M a , ' r b Kat( OHI1I r{aCTo BcTper]aroTCfl B reoJjofHH, L a l'lrlrlllrltlllrlrlll o >10r'rc 100 200 300 400 500 6c0 70q 800 900 1000 t ' lp o g g n r i ' r e x o c r b noJlu , rsrc 6apperei Prrc 2 . 3 , 1 . f r r c r o r p a M M a p a c n p e a e , ' l e H u qn p o l y l i r l l B H o c r n - H e $ r e H o c i t b l x n o ' ' j i i i ' o r ' Kpblrblx n ,Il,eueepcrou 6accetlHes 1969 r' 35 s 30 ^ t( {d'" 6on fil T :ZYtln r.r I(t'i-F)z t "z: . 10 120 't40 160 180 200 220 24 Cu,r/r TO J'tofHop- Mar'rbHoepacnpeAeJreHfieB BbtctrrerlcrcneHI,I Balt(Ho. O4uaxo ec,rrt o f p a H Hq r i T b c r rp a c c M o T p e H r . r enNp{e o 6 p a e o n a H H b r xn e p e M e H Hxb r Yi , a H e c a t r r i x X 1 , T o c s o r i c r e a r ' r o r H o p M a a b H o rpoa c n p e A e J r e H r iM g olKt { o n p o c r o o x a p a K T e p u s o B a r cbc t r n x o f t H a H o p M a r r b H o pe a c n p e A e ,reHIre. C p e r H e e r r A r { c n e p c r n , l o r a p u s r a u q e c K un p e o 6 p a s o e a H H o ini e p e u e H H o r i Y i H a x o A r r r C fol 6 b r q H b r M cnoco6oM: (9 n_l O , l u : r r i o B r e p N r r r H a xr i c x o A H o ! ' H r e n p e o 6 p a : o e a u H o rnepeueuHoft .i X; 104 o on J1s MCHFIb].X. I aK rF J00 )I o q o t: ,\'lHorre feo,'Iofr.tqecxt4enepeMeHltr,teoqeBHrHo He IrorqilHrrorcff H O p r , r a J b H o Mp) ra c n p e / i e J r e H H FEoc. n H , u a n p r . r M e p H , a H e c r r .H r a rpatpux o6'leubr Heqlrflr{brxrroJierl (puc. 2.34), ro no.tryueHHoepacnpeAeJIeHre 6yaer s ntrcrlefi creneHr.racHNlMerpuqsur,r.Eo,rturrrHcrBo r t o r e i i l r a J r b rr r o p a 3 M e p y , H o u M e e r c q y 6 u s a r c u q a q f l o c d t e A o B a r e , r b u o . c r l 6 o l e e K p l , n H b r xn o , t e r t , H e M H o f o p e A K H x r H t a H T o B ,K o r o p b r e 3 r J a q H T e , l b Hnop e B o c x o A f l TA p y r H e n o o 6 r e u y . f e o x u n r u q e c K r . r e n e pe\reHHbre,rroABepfHyrue onpo60naHrrroB Ilpollecce feoxlrMr.rqecKoI ' o I I C C ' : I e A o B a H HHf a i ' I I p i l M e p 'T a K I I e ' K a K K o H I I e H T p a I { 1 4 f l J I e H aB ce r,raTepr.ra,le rrr'ril KoHrleHrpauHfl r4oJ.a, o6Hapy>xeu_ PacTriTe.rrbHo\r l r a r B n p o 6 a x r p y H r o B b r x B o A , T a K X { e r t o , l q r H f l r o r c f la c a M M e r p u q HbrIr llaclrpere,'reHHstB r . p a c n p e , l e ! ' i e H H f lpxa 3 M e p o B3 e p e H B o c a A r i a x r ; l r i o B b t p a l K e H aa c I . I M M e T p X fUl , r \ e J l a f lc, l r c T e M ax . n a c c l t s u x a _ c fal 3 r o M $ a x r e [ 2 1 ] . r r a p H c . 2 . 3 5 n p e j r , c r a B r ' r e L r , r r i.r- r . ' H o B b r B a e rH HbrNlil. F i 6 r lia F F 200 !c 2.35. fncrorp:rr{rr C o ; 1 € D } t { a t t u rM e ; l l t B o c a r l o t l H b l x n o p o . l a x H a n " ' I o u { a . l i l Hauceu n lOxoue [291 cpel.liec Y cooreercrByer I{opH:lc_ n-fi creIleHLIII3 npot43BeAesvilXi l:ct't: n/ t' TIX,, (2.48) x o r o p r r i r r r e 3 b r B a e r c f rl e o M e r p l r q e c K u Mc p e A H v M , G M . C l t M e o n f I a H a . l o r H q e H) , t o l s K o o H o 3 H a q a e r ' r l r o S J I e M e H T byl K a 3 a H H o f o Bcr'le.(3a HuM psAa nepeMHoxalorcr, a He cKJlaAblBalorcfl.fI rax)l(e HMeer npeAe,lbl, aHad'IotriqHbte reM, Koropble Hcrlo,{b3ylorcflnp}l 3 H a K e c y M M l r p o B a H n s> . t r 4 s o r A a g r a n p e A e J I b I e, c J I I t o H l I o q e B I I A - t05 l- ,ru f o ,oo o 2s0 r Y ^^l o rf L *. urf (t o.o^r r0 ): ';I o t q O aaqn o.,"" ,! \o s J ' noolofnrru"o'.oro"l r"," J3ffju,e;r00000 I q Pac 2.36. fxcrorpaMr{a pacflf Macura6 QreHocHnx no'reit, O r . KpLIrbIx ff.ff;i'.X Jf "#J:i,itT' f nHe . l c r a p u 0 u "' u.recrufi. B3qro x: xap6yxf AaBroKa, .U.eBllca i- s20 .i = l,30to s = 0,4123 n=158 d_ F a10 5 t- I o ra"o aa aa ,t, c oj aa a a f :.%.20 30 40 50 60 [ 1. n o u 1 a g r , r b r c . a K P o B xyno;r3ule 'rlync co'rflHblMu Puc. 2.38.O6teuut He$rnuux garexefi, cBt3aHHblx ure,ll$e (Mex''rxancruii sa,run). flo ceirc' 3uaHe Ha BHeuHeM*ont"na"tirouou Mltr{ecKI.tM AaHHbIM 1,6 1,9 2,0 .1,4 (coAepHaH e Cu, Pnc' 2'37' fumorparttratooto*ft111n*15-"""3:'ooq''x flpe:crasaeHa a .roraplsMlrvecxov uacura6e nopoaaxHa n'roulara [29] I{bI, onvcr(arorcfl.Tax,,t r:e .y,:2, Xr:3, Xe:4, paBHo i : r ",. fIXr-2X3X 1:21. noraplis-\'-rrr,ecKrr ripeo.6pa:onasHor:i neperreuHori Hag----4]orrprrrn brBaer crr reoMer it uqecrrcii :I rrcnepcireri irc nu,, na.terrr ira si.:s?:T'"r(#) (2.491 Ha nparruKe, rioHeqHo, npou{enpeo6pa:oearbHaurr sa6nn,l,eHas, 83rB r.tx.norapl.rrfivtul, H 3are\r Bbrqrlcrtrrbr.i_\cpelgee II AncnepcHto. 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[ a c T e i r , T a K r r r o 3 T o r K p i r r ep H i i H e n o s B o J l t l e r v T B e p l , K A a r bq, r o o 6 b e M b r n p o f H o 3 o B B A B l x p e f H o H a x p a 3 J I I I q a IOTC'], Bocto'tut:ti I' .\ 2 l'- peeuoH 802 t7+ 158 140 166 328 o10 99 l6 B 6 4 7 l0 J 3anaduoui pezuoH rl 312 b5 i'^ 't' . I'v^ )'g 220 276 i54 473 666 t .:2 9 ll 5r I t+ l5 K p r i r r r u e c x u e 3 n a r r e u u r 7 o , n p l r n e . { e H H b rB e Ta6n. 2.22, npuuuvaIOTCrr. 3a HrlKriiie !pe.{,enbr,T. e. oHir I]pHfoAHbr.].,'rf npoBepKH HV! ' I e B o i i f r r f r o r e 3 b r :H s : E ( X ) > - E ( r ' j e t: E(X)1 trpH aj'rbrepHarr{BH ( C H n e o , ' r E o 6 o s u a q a e r < < I r a r e M a r r r l r e c K o ex ( H A a H r { e >r r> <E(y). xaparirepn3yer I{eHrp pacnpeleireHlrr, 3a KoTopbili MolKeT 6btrb n p H H f i T OK a K C p e 4 H e e3 H a q e H i i e ,T a K t r M e , [ f i a H a . ) c o o r s e r c t s r - r c I q H e [ p e A e J r b rA i r f i B e p x H e f o K p H r r r q e c K o r o3 H 3 q e H r r f\l{ o x ( H o H a i l r r r rro QopMyne t l t t t- T q . 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Bapxaur 3ure"tq ._ Trtoxlt Haa6o,lee I{Hrepeil,nfl lpoBepKI] peDei{crc e H , T a K K a K o H M O i I ( e r6 u r l u c n o , ' t b 3 o B a H , a K H N Io 6 p a 3 o M , I I e B a A H c n e p c u f tn 4 n y x n t t 6 o p x a x I I t { B " { t l e r c f l T aHa JIOTOM npocrof O l -Iipl'lrepl'Ifl. IIapa\,reTp}rqecKIIM I4HorAa cflyqaercfl, qro ABa u,ru 6o.lee Ha6JIIoAeHufinpll paHilill' p o B a H H Hn O J I y q e I O TO A U H a K O B b Ipea H r n . 3 r o s s n e H l l e H o i r l l r i l i l 3 B a H r i ec B f l 3 a H f l b l xp a H f o B . 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H y , r e e a a r n i r o r e 3 a , K o r o p y r c r p e 6 y e r c a t t p o B e p r . t r b ,r a K o B a : BCe coBoKynHocrlr, lr3 Koropbrx 83trbr BH6op'rgs,rrMer.oro.[r.rHaKotsble paclpeAe,rretrur. A.ritrepuaruBa cocrolrr B ToM, r{To ro MeHbuefi r,tepe oAHa u3 coBoKylrHocrerl rrlreer ueHTpaJlblroe3HArIeHIIe, orrurrHoe or ,rtpyfux. llpe4no.laraercf, qro Bce Ha6,roAesus 6ltnH 8* llD cc6pilllbtc,'ryqatiHbl\r rr rrro Bbr6oprill o6pa30Nr He3aBricHMbr ;1pyror .epyfa. ,II,.nacyunaurpaHroBNIoxHoBbrr{ucrurbcrarncrriri}. Kpacx,'ra.Ita,t,tu rca H _ j,IItt bo,'iee,'left(afl r.tMeer Lln-I Soplra k 12 r t r l [ R r - , r ( \ ' - + -l ) ' 2 l i .Y(\ +l) lJ flp i-1 Bbtqxcr'reHlt:i aJlre6palqcctitt k tr 12 N(/i+l) E i-t 2 'p\. R -3(N+ nk l). (2.53) 3KBlBarenrHag (2.54) rl(pitrlrvecrue3HaqeHfitH ra6ymrpoBaHbr roJrbrioA,riflTpex esrdo.poK,Ka)KAaffH3 Koropbrxcocrorrr 6o,{eeqeM u3 nqrtr ua6.,rrcAeHuri (cu., uanpirtrep,[30, ra6,r. 0]). 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H e x o r o p oe ycoBepIUeHcrBoBaHHeKpL{replrfl, n p HHaA,'Ie}Kax.(ee,II u,r,rueQopc1' [24] , oAHaKo, Ito3Bo!'rflerricnod'rb3oBarbMeroA I(o,ruoroponaCnupHoea A,'rr npoBepxn 6,tn:ocrH au6opouHoro pacnpeAeJleul4fl ,I{ HopMsJIbHON,ly H AI.rCnepCpeAHI'rM C 3apaHee He OnpeAe"IeHHblNIH t2l Ta6rarra 2.26 3sar{eHufl Kpxrepuql(o,rruoroponaKpuruuecrne Cruupnona I n:l 2 3 ,1 5 6 7 B I 10 it t2 1? tq 15 16 T7 l8 l9 20 ll .e00l.s50l . 6 8 4 .17 7 6 .18 4 2 . 5 6 5 1 . 6 3. 6 7 018 . 4 e 3 1 . 5 6.624 51 . 4 4 7 .15 0 e .15 6 3 . 4 r 0 1 . 4 6 .8511 9 . 3 8 r 1 . 4 3 .6418 3 .3581.4r01 .33e1.3871 .430 .3231.3691 .4C9 .3081 .3521. 3 9 1 .2961 .3381. o / D .2851.3251 .361 .2751 .3141 .349 .2661 .3041 .338 . 2 5 8 1 . 2 e.327 51 . 2 5 0 1 . 2 8.328 61 .2+41 .2791 .309 .2371 .2711 .3 0 1 .2321.2651. 2 9 4 ! .990 .900 .78s .689 .627 .995 ---91 q?q .829 .731 .669 .ot I .617 .538 .576 . 5 0 7 q,{ o .480 . 5 1 3 .qot .419 .404 .390 .377 .366 .346 .337 .329 .489 .468 .419 43' .418 .404 .392 .3Bl . 3 7| .361 .352 A n n p o r t c r t i var{ l r l l,;tn n)40 .226 . 2 5 9 2 2 .221 t < 2 23 . 2 1 6 a l 1 ot ,1' .242 2E . 2 0 8 . 2 3 8 2e . 2 0 1 t a ? 2 i . 2 0 0 99A 28 . 1 9 7 t9( 29 . 193 ,91 30 . 1 9 0 . 2 t B . 187 .214 JZ .184 ol r 33 . l B 2 . 2 0 8 . t7s .205 JA AR . t 7 7 tn9 36 , 1 74 t q q itt .t72 .196 38 . 1 7 0 l q 4 3g . 1 6 8 . l 9 t 40 . 1 6 5 . 1 8 9 I .07 .287 .28l .275 .269 9At- .259 .254 .250 'LA ,.4 0 .238 .234 .23r ,11 oq, . 3 2t .3!4 .307 .3 0 1 .295 . ?90 .284 .279 .27it ,270 . t66 .262 .2sB ,^4 . 2 5i .3{+ .337 .330 ln : .3t7 . 3 1I .305 .300 .295 .290 .285 .281 .)77 .273 9AO l 52 r. 6 3 ln. 7tL cueri. 3ro )coBepiueHcrBoBaHrre n03BoJrser ficnoJib3oBarb u3.ito)IieHHbILiMeTo.l aHa,'IofI.IqHO TOMy, Kar{ r{br HcrIoJIb3OBa,l[npouejly. x T e 6 , 1 .2 . ! 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KpijrH,iecKrre 3Har{eH}rr Kprrreplrn I(o"rl,ioropoB[]Cuupuora npHBeAelrbrB ra6r. 2.26, xotx ra6flr.rl{a Aoge:eqa ,[uu]l ! , o 3 H a q e H L I fnl : 4 0 . f l p u 6 , r u x e H H b r e 3 H a q e H u f L I I A 6 o , r t u r n x r t \ { o x H o H a i i T r . r t o S o p M y a a M , y K a 3 a H H b r MB r a 6 " r u q e . E m n : 1 8 H y p o B H f l 3 H a q r r M o c r r .ar: 0 , 1 0 K p r r r n q e c K o e3 H a q e H n eK - C panH o 0 ,1 7 . B t t q l r c , r e H u a f l c r a r u c r u r ( a K - C p a B r J a ( 0 , 7 0 - 0 , 6 , 1) = = , i!2 i . JZJ .221 9L7 . 2 1 8 ,i + 4 .262 c)l ( . 2 + l .258 912 .238 , 2t 0 .2ir5 .2D2 I .36 i i; t "'i = = 0 , 0 6 . 3 r o s H a q e H u eH e f i o n a l a e r B K p r . r r r i q e c K y roo6 J . i a c r b .f l o 3rorly orK.IIoHHTbHyJreByrorI,Inoresy o ToNr, qTo Bbr60pKa rioJryqeHa Ir3 coBoKynHocTLtc HopMaJrbrrr,rM pacnpe,qeJleHrieM, HeJrb3F. gJreNleHTapHbtx Ha erolt If br 3aKaHqlrBaeMII3/'ro)KeHae c'rarl.rcrriqeci{rzxlporleAyp, Ho He rroToMy rrro paccMoTpe,'rrr lrx Bo Bceii no.'tHore, a [onpocry A,'rfi TOro, r{To6br nepeiiTu K ,4pyr]rM Bolrpoca\r. Pnccuarpunaeuufi MareplraJl sBrffercn oqeHb KparI{HM H3,'roxeHIIelvIIIo,IyroAOBOrOBBOAHO|OKypca B NIareMarltqecKyloCTaTHCTHK\', I{ Koropouy 4o6auleHu as6paHHbref,'raBbrH3 6o,'reecneur.ra'rrbH b l x K y p c o B .A n r o p H e p a c c q u r b r B a ' {H a r o , r r r o c y M e e TB c T o , I b r \ I a , ' I o M o 6 b e r v i eA a r b c r p o r o e o 6 o c H o B a H r eo 6 c 1 r 6 g 2 e l { b r xB o n p o c o B . C,xHaxo npe!,craB,'rflercfl,rrro rr3Jrolr{eHHoro 6yeer [ocrSTouHo,(r'rfl I ] e p B o r o 3 H a K o N l c r B ac o c H o B H b r M rI.iIo H f f T I l f l M HT e o p I l H n p o B e p K I { C T i I T H C T T i q E C I i I I XI I I N O T E 3 . H p c : ; n r r u a r i H oK p a r x c e H 3 J I o x e H l r en p o u e . l y p n p o B e p K H c r a r l r cru..recIifix fri[ore3 lvro)Kerc,ryx(HTb BBe!,eHr.reM e 6o,']ee cnoxHblli x n o c r ' r e A y r o x r u xr , r a g a x . 3 r o r K p \ . r B o r - r p o c o Bp, a c c M a r p r { B a e M b r B \ r a r e p I r a . r I H e H c q e p n b r B a e rc o A e p ; { a H H f I u a r e } t a r L l q e c t { o fci r a r H cruKn. Vgnrrac u Po6eprc Bo BBeAeHr.ur K cBoerl KHrlre [33] yr<a- )Kr.rBoiirr yBr'reKareJibHbrrl 3btBaIoT: <<cTaTrrcTr.rKa IpeAMeT, Ho ee n3vqeHr.ieoqeHb qacTo IrpoTeKaeTcJIHluKoM BflJIo>>. I4snoxus ery HayKy B KOHTeKCTe reOJrOfHqeCKrrX 3aAaq, MOIKHOHaAeflTbcfl,qTo 3ra KHr.rranpe!,cTaBHTaHTepec Ad'It feo,rotoB, HMeroult{x AeJIo co crarrrcrrrqecrrort o6pa6orxoii IaHHbrx. CNhCOK JII,ITEPATYPbI l. Aicltiso:t "I., A ne'"vapproach to null correlations of proportions: Jour. oi i r r t ' J A s s o c . , 4 l a t l r e m a i iC c aelo l o s v ,1 9 8 1 1 , 3 ,o . 1 7 5 - 1 8 9 . 2. Aichisott./., and Brown Al.-C.,1g69,Tlie lognormal distribution: with special referenceto its uses in economics:cambridge univ. Press, cambridge, lg'6g, p. 176. .^_ S.-4:h R. 8., Basic probability theory; John \\riley and Sons, Inc., Nerv york, l97tl, 337 n. ColepNrrr'..no,tHoer3Jrorieurre$u,roco$cxux ocuoB Teoplltr eepoaruocrefi r.r Marel,rarrr.tecxoiicrarrcrttKu. | , F 3 A l g y / . I / . , - D i s t r i b u t i o n - l r eset a t i s t i c a lt e s t s :P r e n t i c e - H a l lI,n c . , E n g i e n-oorC l l i f i s , N . J . , 1 9 6 8 ,3 3 8 p . JTir iljrnrl ioAepxHr Harr6orrce no,rsnil ncpeqeHbra6auq A,rs HenapaMerpt{qecKu.\ riprrTCprreB. p r e s s , C h i c a g o ,l g 7 l , g 9 p ,(H.Ir:l . - 5 . C i t o l l e sF . , R a t i o c o r r e l a i i o n :U n i r , . C h i c a g o col€p;Nnr no4po6uoeu3,roxeHnepe3y.rbraroBcrarucrnr{ecKr{x }rcc,reAoBai'lllit i 1s6sap1tflu rpyrlx cnoco6oeonpeAer,terrut 3aMriuyrbtxAaHIlbIx.flpunoAxrcx n p t t r l i p b r ; i l r e o \ r r { t r r r .f l o c r p o e H H a al a o i H o B et J ' o c a n e x q n i r ,o H a J e r r o . q o cTl nil a. , ,t e d . C h . t t t t e UR . F . s t a t i s t i c a l m e t h o d s i n g e o l o g y : G e o r g e A l l e n a n d U n i o n L : o l r d ( ' i - r1, 9 8 3 ,1 e , 9p . h r r e e r c ap v e c x H fni c p e s o . l : - V a Hpu" .O . C r a r u c r H q e c x u e rrero:br B reoJ'lorillr. I{.,-Mup, 1987,'i87 c. Heiurpe r"lanu sroir KHHirinocBsrqerrl,r llenspailte'rpnqecKHM crarHcrrlqecr{HM r{pnTepnsM,KoTopbre aBTop peKoMeHAyeT, Tali IieK oHtt o6,terqanr BbrqltcJ'IeHufl. Annals of r\{athematicalSia_ ,. ..7_ Cc,cltranW. G., The test of goodness_of_fit: t r s t i c s ,1 9 5 2 ,. 3 ,o . 3 1 5 3 4 5 . t23 nonp trics t a t i s t i c s2. n d e d . : J o h n W i l e y a n d g""f ,f::'nl.i Y;,i; ?d68l';a! arame Do,t turrHcreo rr3 )'nonflHyrr,rx s' srori r"rl^4tse,en ap aMeTp uqecriu.\ lip }rTepueB p acg stor'i rrHure.B qactHocrus Helr -fi cMoTpeHo co.lep)KuTcfl orteHb no,.rHoe ri:l,,ro;rieHlre, IipuTepneB cKaqKoB. 9 D u c h a o r t h I Z . E . S t a t i s l i c a r t e c h n i q L r e si n t e c h n o r o g i c a l r c s e a r c h .M e t h u e n a n d C o . , L o n d o n , 1 9 6 8 ,3 0 3 r r . o . q H a r s d T y q u r ' X f i c a M b r xp ' a c n p o c r p a H e H H b r x KHH. no crar'c'rrie, flperHa3HaqeHa . a ! ' r f lf i c c d ' r e . q o B a r e n e xr le, , t a r o t r - l u i n p i r l r e H a r u c r a r u c r i l q e c x r i c nporle.l\pbr. Eo,rluoe B H H r l r a H I ' IyeA e r e H o ' ' r z r ] r p o B a H H r o s r i c l e p t M e H r a . H e c M o T p g H a c . r o ] l i H D C T b3 T r X BonpocoB, oHu craHoBtrcr ,\ocTlrnHbrr,{u 6 . , r a r o t a'.fr.ni,il."i,lii,i'.,r.".J] pq 6.lecrguier,ry rr3.rtol.KeHr{ro. r0. FisherR. 1.. Statisticaj methods,na Bo.vd, Edinburgh, 1978,175p. ori'er and rJ xHIlre u3,'rafaercq 38oJttoqu,crarlrcrrrqccrioii ltr,rc,ru.f,r. 3 H 5 nocssruenur ri:.roiNeHrrrc ocHoBTeopIrHnepoRrllocreir, ee nourrlrii ,, a,oa,larr,,ii,^"orrai^"ru,u" il3 Hlrx. ll. Folh R. L. Siagis t e x t L r i a i ; ; i ; ; i i y i n s e d i n r c n r a r lr,o c l i s .J o u r . S e d i nrentr-rp y c l r o l o g y , l 9 S l . 2 1. o, pf . 1 2 7 - _ : l J 0 . r 2 . f r e u n d J . E . , w r L i a r n s F . J . D i 'c t'i'o r r a r y T o u i l i ' e of basis stalistics, . \ c C r a r v I { i l J , I r r c . ,N e r v Y o r k . 1 9 6 6 .i S S i.. l eologl' oi l n t ' i . A s s o c . f o r , \ l a t h e m a t i c a C relatiousbett'eenproportions'Jour' 1977 , 9, P. 5a3-562-.. ^ " 'rO'.'Krumbein F' , 4 -A n i n t r o d u c t i oino s t a t i s t i c aml o d e l s \V. C'.and'Gtallbil,L, 1 9 6 54, 7 5p . nil{':,t:q#;[l]fi "*];;Tl) ii:'H"rif nont'no ;,;;;;'itv.q." " 5'.';'"'il;.i;i;.il;' "9-69Yv-':P::'-T."-)),,:'':'J'1oi1l"' lpail5un,t @. Crarucrltqe'liIIe Mo'le'lll B 6- 10 clreAyer.o6parurr H? r'rt o;t:-:.. oco6oe BHHMaHIIe teocrarucrltliu. Oco-6oe ,;;;;;;;;;mrrriu. o6,qacru LtlHJ"lau:le,ti?{I:l petrographv' oi sedimentary lGirual .,t, f 2t. Kruntbei, IV. C. anabitiiiii',t . r.n. o I i " t ' C . " r r i ' - a t -t ' t , l n c , N e w \ o r l i ' 1 9 3 85' { 9 n ' d e c i s i o n s3,r d e d . I l . r c u u I t , Iirii".i. 2 2 . L a p t t rt . r . s L . i i . t i ' . ; ' i ; . ' ; ; i . ; " ' 8 7p ' e . " . ; J o i u l ' o r i c h ,I n c . ,N e r vY o r l t ,l 9 B 2 8 Brll.7[peIcTaBneHbISl(cnepHMeIITbInoI'Io;leIIIpoBaHlrrc.lolia3aTeJ'Ibc,tBueHTnPeacJbHoflreoPeMbI' n r.tuuoit '""";5'.' v. 1' EdwardsBros' Inc ' Ann Arbor' t{-i"c-. n. staiitillar inference, , r i i c h ,1 9 6 16, 5 8P . ''o 3!'leMellraplloll cr3'III'rrl''c' rolr npe,lcrao,naer co6oit oHUIiI(,'lonelu'o if.p"i,ii H a r . { t , ( H o e o c o 6 o e B H r l M a H H ec ' 1 e ' i ) e r o 6 p a t r r r ; ll:.roxerure B BbIclreu;;;;a;; .r. 7, o xoropoii paccr{arpuBaerct.Xr-pacnpenereHl'Ie' r"" r a r"t4.'[tltitorl norrnaliiv -gi1h H.' W.^"O;'tG-Hrfiitoloto\'-srnitnou test for iil,,"lXii}'..iJ;i.Tf;L:;:Xf;..ui.i',?;"j;:i;:1'J: ih-eAmericanStatisticalAssociaironl96T, i:,e"r""i:1n*",,*Xll:l{]l,i,ilJ; nJ*;,'i;";.;i r,r.un'i,rla"iliirn..'rtii (r.rHexoropnx rleuseecrHu) Sopr,ry,ru crarucr'ueixri.\ iipr,reprreB ;"r1;i;"":.t"n_r 1 3 . G r i f f i t h s " / . c . S c i e n t i f i ci n e t h o d i n i h e a n a r y s i s o f s e d i r n e n t sM : cGi:rrvHill. tnc., New )'orlt, p. rri;;;;.;'pi:..,ru,i n.p.ro 7: rputBrpttrc S_Oq 19_6"1r oca!,oqHHx frc. Ha_ 'qHbre Mero,qbrHcc!,re,[o-BaHilfl nopo-1,_L1.,lirrp,'1gi,t,"'[ii", f taw't 13-22 rB,'rflrorcq-BBeAeHr,eNr n nprunial"yrg cra'rcrur{y. oco6'ri uHrepeg n erori xurre npaA.tuu.l.::T_H3.ro,*erJ'e nbnpocrrn,cBr3aHHbr\c xoppeiirHbrM,ere_ NaMIt cTaTlrcTilqecKl.tx SKCneDHMeHTOB. 1 4 . G u e n t h e rl Z . C ^ C r i n c e p t so f s t r i i s t i c a l i n f e r e n c e . 2 n d e c l . ,i \ i c ( j r a r y - I I i l l , I n c . . N e w ) ' o r k , 1 9 7 3 ,b l 2 p . u,*iaroe BBeAeHHc .tTylII ;1.1qTex, xro xoqeT " u e .B n r r u r e3 a r p o H ) T ' l r p o r i l ' ' noJysrrrrrltariclnr],\,ruHeop\rau u r r B M a J ' I OO M6 r e K p y f B o n p o c o no, ' r , r u r r oH e c o _ ' ,D.epxauluxctB KHuraxraxol.o o6telra. Statistical lables anC tormulas,John Wilel,and S<.rrrs, y*rrl,1nflfttrA., Inc., Ncrv 16' Hichs c. R. Fundamental-concepisin the design of experime'ts, 2'd cd' andWinston, Nii" v-i,'igzi,"zs" p. Llolt,Rinehart P,r'x_o-s-o,qcrso no excnepLr,reura il rac[epcroH]totrvaHaJri3y.B i.r. 6 ,u,'raHflpoBaHurc npI'rBoItrct rpaQrruecxaa uHTepnpeTauri,83aut,rod,elcrnriu:;rx.1n1.x(.rrr.iropriblx nr'raHoB u nprrN{epbr. 17. Kellauaa F. til., ed., pen-g^uin_Honr:yrvell book oi tables, penguin Boolis, L l d . , H a r m o n d s r i o r i h ,E n g l a n c l ,f d b e , - Z -pS. ' " " -s tllaretlraruqecKHe ra6rxrlbr, npr.rBeIeHHbrei)rofi Ku[re,.BL-rrltrc,rleHbl Ha OBM $rrprrofi Eiectronic Data process'ingDrvision-oi'iion.y,u.it--cii"i'^ilta."li.y,,rbrarbr ganucaubl 6u'ryu Ha MafHr'rrrrori,r..-.ure, u autaonrrnaoara'lt. IroaroMy o Hri.KMor.riHo cKa3aTb,qTo Hx He Kaca,lacbpyr{a qe,{oBeKafi OHII He coLepNar ol]jfiaroK, o 6 u q u o B K p a A b r B a r c q f i xsc r r a K u e u . a r e p u a . n o_rITO Ti .a 6 n . 2 . 1 1 , 2 . 1 4 u 2 . l B 2 - i r r ; t : ruurn [x' flenuca B3rrrj r13xuurn [17]-l-nrnauutu"o, c pa3perueHlr,au.r.opa. 18.Koch G. S., Jr. R . F . S t a t i s t i c a la n a l i r s i s , o fg e o i o g , . u t d , , t r . ^ a n d _ L i n l i Dover, Inc., Neri'york, 1981,8b0 p. d.;;;;;;;;Hoe r.r3AaHrre npe4*an.raer codori fiepeneqarr(y oparfiHa,,rbHoro AByxroMHuKa. CoAepNur nolpo6uoe.n*oia"ra .rr_ TlrcrurlecKofo aHann3areo,l-orlrqecKnx AaHHbIx,B qacrHocTnAaHHbIxonp0608aHjtr. Brrrn'iaer uoApo6uoeu3Jro)KeHr.re nu6opouuux'&enr,noeroAos arrcnepcnouuofo aHa"qrr3au MHoxecrBeHHorlperpeccur.t.llo,upo6uo oa r;? ? " - ' n' 2 i1.Q" iQt-a. 1i0i a . rettticee v a l t t r i i o n as n d e c o n o m i cd e c i s i o n sP .4. lV. Petroleum ' l 1 B p 1 9 7 5 , J ' , N . C I i f l s , I l a l l , I n c . ,E n g l " e u ' o o d pl(npCAe lt'HJtii, B r;r. 3 npercraB.IIeHo nolpo6Hoe lI3"lollicHIIe B e p o t ' l l l o e r H b l \ HeC$:rl 'n1 . h . . . , , , i l p .a133BBeeAAKxeeu n " r p eeuqaatroouI It It It \x(cffll n p u John WrleY 26. Par;ctt E., -\lodern probablllty tileory and its applicaLion. 464 p Y o r k . 1960, 1 9 6 0 , 464 S o n s Inc., I t . t c . . Nerv N e r v York, P'. ancl Sons, """ Publ' ; ; " ] i ; , ; ; ; ; ; i C . ; . - i ; t t " d u c t i o n ' t o q u a n i i t a t i ' e p a l e o n t o l o g i 'E l s e ' i e r C o . ,A m s l e r c l a n t1, 9 7 1 , 2 2 6P . cra3.rleMeHT_:ipHoil no_npfir'IoxeHtIIo p} KOBO-1CTBO Hacroqre"lsHoper{otreHl}'eMOe . f J I . b C O A e p X { a T C t T a r ' l J ' I I l U b ln p O T I T C T H X HK 3 a A a r I a M 9 K O ! ' I O r u U i l n a ! ' I e O 3 K O J ' l O r l l H B B erOii xUure. Onttcasli itO,,lXuTenbHOCTlt XU3HII, T. e. TeMbI, He 3aTpaf[BaeMble r'-" aK)Ke MHOflle HenapaMerpHqecKHe l\leTO'lLI.. ig. i-oltiirsoni. E., iomputer applicationsin peiroleum geologl'. Hutchinson RossPubl.Co.,NervYork, 1982,164p. o6paueHo Ha nocrpoeHueIiapr. BHuMaHlte He6o,rliliaqKHllra,B xoropofi ocHoBHoe 29. Saaper R. and Sinclair A. L' F a c t o r a n a l y s i s o f s t r e a m s e d i m e t t tg e o c h e m i c a ld a l a i r o m t h e M o u n t N a n s e n a r e a ,Y u l < o nT e r r i t o r y , C a n a d a ,N l i n e r l r l o g i c a D e p o s i t a ,1 9 7 4 I, , p . 2 4 3 - 2 5 2 . 3 0 . S i e g e l S . , N o n p a r a m e t r i cs t a t i s t i c sfor the behavioral scicnces.I'LcCrrrv' L l i l l . I n c . , N e r vY o r k , 1 9 5 6 ,3 1 2 p . (J,lrra quTaeMhtx uraeMhlx K {eloAaM KHirf HiIr n no o H HenapaIIeTpHqecKI-Iil e n a p a M e r p u r i e c K u r l xxlel(JAaM. O 4 t t a In3 ts n nepBbrx epBbIX u uaa6o,ree aa6o,ree q 3 1 . a o n ' . l l i s e s R . , P r o b a b i l i t y ,s t a t i s t i c sa n d t r u t h ' D o Y e r ,N e N Y o r k , l 9 8 l ' nt,l n -" tP " 3 r o r c r a p n i r n e p e B o f ( 1 9 3 9 r . ) K H r . t r f i H e M e t l K o r o K J l a c c I . I K at B . l r e r c f l x o p o u r l ] I BBe.qeHr.reM n $u,rocoQcxr.re Borrpocbr crarucTtiKn. flepeue TpH rJxEbI ilocBtluLeHbl I . I a B H brl l o 5 Da 3 0 \ , t o n D e t r e J r e H l . lBr cc'freedorn. p o f lT H o c r t l . Jour.oi Educational Ps"vhology,1940; 32. lY'aiher H. .1i.Desreesof , 3 / ,p . 2 5 3 - 2 6 9 . Or.rilqrroe ceo6oasL rr3J'roxeHue noHrruqcreneseii 33. Wallis W. A. and RobertsH. V. Statistics,a new approach.The Free p r e s so f G l e t r c o eN, e w Y o r k , 1 9 5 6 .6 4 6 p . 3aHHirtare,rruoe c MnoxecrBoM[pIIMepoB,tlcropntl, anerBBeAeHne B crarr.rcrr-rKy IoTOB O npolrcxox<.qeHlllr npoueAypA l4x IrpU,'IO)KeHlltx. Arff Tex" craTHcTfiqecriltx K]O NPEANOqUTAET NOBCCTBOBAHI{M E ATCMATI-IKE. Hbre Bonpocbr YB.IICKATCTbHOC " np"*.poi.-d:jlg;f_,1;dfi;;5;.Tl'"'ff.'i'j":',T":0,:1.."J;H";i""; tt4er o6 nHr€p-[peratttJu .q,aHHhrx c -nocro"Hlroiicylrnaot. l 9 K o r h . 1 . o . E r a m i n a t r o no f t h e c h a l : e i r i r u s l i a i p r o c e r l r r r iec r t2l iestingcor- - frasa 3 M A T P 1 4 I I H A qA T T E 6 P A B BHAecJIeAYIoqeii MarPlrlrbl: f..;:"-., ]:ffi:;, x':fii:l COV6.-,v1 s2sr lcovu_., 3ra r"'rasa [ocBffilreHanarpuuuori a.ure6pe.EonruiugcrBo Me. ror{oB' rloropbre6yayr paccMorpeHbr B cJieAyroquxrr'raBax,ocHo- BaHbI Ha onepallaflx c MarpHl{aMIr, qacro BL,]IOJIHfleMblxBbrqHc,'rgT e J r b H b r M I M a I i l u H a M I t . o c o 6 o e B H I i N { a r { H e6 y e e r y A e r e H o M a r e M a TflqecKIIll oilepaqutM, Koropble ,re)Kar B ocHoBe aHar'tli3a [oBepxgOCTCIi ]'PCHAA, ]n{CTOAA IdIIABHbIX KO[,IIIOHCHT,AHCKPI,IMIJHAHTHOIO aHar'r3a rr 4p. 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Taxoe H3JroxeHrieHerrp[foAHo A.[s sror? xoporxori fJraBbr, Ir Mid orpaHtlqxMct roJrbKo_TeopeMaMtr,Koropbre norpe6ynrcn e rocreAyloqeM r.r3JiolreHnn.fipa sroM npeArroqreHue6yaei orAaHo H e A O K a 3 a T e J r b C T B a Mr r, p u M e p a M . MATPI,IIIA Ilarp;rqa-3ro H a 6 o p q ? r c e J rp, a c n o J r o ) K e H H s rsf r B H A e n p q M o Ta6.nnqtr, ToqHo raroii >Ke, KaK ra6nut\a AaHHbrx.B rrlarl,ronuuort p l i u H o f i a . r r e 6 p e r a 6 n u g a p a c c M a r p r . r B a e r cH s e xax ua6op orAenbHbrx S.rrelieHToB, a KaK eA[Hoe IIeJIOe,qTo IIpHBoAHTK sHaq[TeIb_ HbrMynpoueHrreM peAa npoqeAyp ?r 3aBr.rcrjrlrocrefi. Bo oropofi r,raBe orMerJaJrocb,rrro orAe.ntguri sJieMeHTMarpxubl o6u,ruo o6osHaqaercfl 6l,rxsor?c np[nucaHHbrl\rri BHrI3y HHAeKcaMa.Sneuegraur i\'raTpr.rubr IIoryT 6Hrl !,ricnepcHr.rIr KoBapr{aurj}I,pe3y,'IbTaTuga6,rn4eHnii, xog$QllqueHrbr cr.rcreMu ypanHeHlrii H npocro .lrro6ue qI]c,'Ia. Tar, HanpaMep, B r;r. 2 rpe6oBaJrocb BbrqtrcJrarboqeHKH Ar.rcnepcHrt n KoBapr{r](ufi gnn coAepx{aHriri lraxpoa,,reMeHroB,nprlBeA e H H b r xs r a 6 r . 2 . 3 . f l o . r r y u e H H b rpee 3 y J r b r a r b rM o x H o n p e A c r a B n r b t26 CoVy-v1 COVgr-V CoV1,s1-V s$ H a 6 o p q t I c e J I ( A o n y c r u t n l , s H a ' { e H l . l l i n e o e u eX,H n(X) o t i ' it"'tn v)'npeAcrae* ,reuHsrriB BHAe*orti"'uii,"o6oi"* o6o:Ha'raercx[X] , ltxll. K B a A p a r H s t ec x o 6 x n s o r ' B arofi KHllre 6yayr npllMeHnrbctl l e J I b H b I e g J I e M e H T b l " N { a T p l I u b l 6 y a l ' r . o 6 o 3B Ha r pBeH- b I M I t r r ' II Il 'al rTebpcagr 3 y pa erBJcI a 8 1 , n " u n , , c u H A e K c a M uu, a n p u l t e p t l l : l o o 6 u r e 3KBHqanrcs u raKHe -v.noun"a 66ot"auent1fl'l(aK lnll' fxl'i' Hru 3"Ie{li cHriaeoJl KaK 6yxnlt, -O-3Harlaer rpeqecKl{e -xii', BaJreHTHbIe M a r p I lqa e c i I I I iX] \reHr i-ii crpoKr* iio-'.ron6Ua. 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I.4l : I Cj, ro no.'ryuurtr il2 |:irl il ti l'iil |'lil 3X2 He'lb3r yM' Heo6xoAlltrloorMerltrb, qro Marprl(y [opflAKa quclo cro'n6uonnep' rai< xat< Sxg, Hoxarb Ha Marpl4t(y-nop"anu (iuui He paBHo rruc"Iy crpoK nropofi l{arpl4rrbr ;;;';;d;ut (nrtr). mxn Ha MarPItuY B peay,rlrare yMHoxeHI4s MarpIIubI noprrAKa noptAoK l r o p s A K a n X m r o n y q a e r c g K B a A p a r H a t Marpr{qa,ilpfiqeM pesy.llrHPYr'ourefi nopnlox o n p e A e ' r f l e T n e p e M H o x a e M b l xM a T p } l q MATDHUbI: F2 L+ b il$:l:t't;:l OAnaro, noMeHgB[epeMno)KaeMb]eMarpHIrbI MecraMIi, no'lyql{M ttilus:t:[ii 48 L:: ;J[::z:, ,l:] 63-| 4t tnl 34 45.1 npor.r3O6uran $oprvry,raeJreMeHra MarprI(bI IC], ne.nrrortr.eficR BeAeHHeM AByx Marplrq,I,IMeerc,re4yroqulieu4: 3t rt4 32 50r yMHoxeHrieMMarpr.rr{br Onepaurant/].tBl :[C] uaauraaror [B] ua AHa.norn,Iso,o Marpilr{e[.4] rooopart qro oHa Marpuuy [A] c"rrena. yMuox(eHaHa MarpI{qV[f] crpaBa. 3ro npocrefturzftcnoco6 onpeAeneHHfl yMHoxeHHflMarpl{q. 132 Ma'I'puqH'19 I'Ix^npoII3ABe KBaAparHble Ec,ltt nepeuHolKalorcfl roro xe [optAKa' ,.rJnu. rar<xe 6yaer xeaAparuoit'uarpuuet't ro B MarprlublnopsAKoB*x'y^:.:r' ec.runepeMHolKl'rrb A;;;;; npoll3BeAeHl.ie e' r' Marpnuy nopflAKa ntrXf , ]iunorut. noJyqHM u*..t qnc.'iocrpoK' paBuoequc-JlycrpoK fi;o;; ":p191^)l:lprrrlbr' Ha' pu"io"'u'ucny croJr6q'osiropoii^uarpttUlr' ' qtrc"tocTo",lotloB, roptAKa MarpHuy ua 5X3 nofrrrxl l\larpllqy non*ap, yMHolKafl 5x2: 5 " x i , i t o . t y " r l MM a r p H u yn o p r n N a cii: n \al Z o*0p1. 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[ B ] : t c l : l a , r b oa o b r* a r b o a f t t f 3auerun, qro xorn xax [,4], raK v [B] coaepxar ro"lbKo no ;lBe r(oMnoHeHrbl,cBeprra [C] cortepxHr rpI'I KoMnoHeHrbI.B o6ueM c,'lyqae, ec,ru nepnliii BeKTop, yqacTBylouuti n cneprl{e, coTO CBepTKaCOJ,ep' a BTOpOt- /?13,'leMeHTOB Jep)Kl{T /? 3r'leMeHTOB' >xur n* m-l a,reNleHros. P o 6 u H s o HN T p e i i r e n l [ 7 ] a a r o r i 4 H r e p e c H o er p a $ u u e c x o e o 6 l t t c H e H H eo l r e p a r r u H c B e p r b r B a H x s .1 4 c n o . [ l s y f l H x M e r o A , c B e p H e M I R a B e K T o p a ,x a x , l n f t r . r 3K o r o p b t x c o . ( e p N { H Tr p l l 3 , r e M e H T aL. H a t{aJa crpouu ra6.rr.rqy HJrr.rMarpuuy, B Koropoti o4uu BeKTop onPere"tqer crpoKI.I, a 4pyrofi BeKrop - cro"l6qlt. S,leueHrlt s aroii ]\rarprrqe_ npoH3BeAeHHfl crpoK ua cro;r6qu bo br b, 1,, :',ii,:',/,] :',1:', f l o " ' r y u e u H yM l oa r p r r u yT e n e p b n o . I p a 3 A e " ' I s e M Ha noJlocxu, Ha,' r.r.l H_a f l rlTo or Hil;.11Hefo J'IeBofo xl ili.ltrlt"r 3"rte\{eHT no,rIocKH yf,'ra .qo BepxHefo npaBoro, TaK e c r l c r o " t r 6 e u ,e c d r u I J A T Hc n p a B l B l t t t 3 , 135 I.I eCTb CTpOKa, eCilil tl(Tll CreBa BBepX, T. e. W'?x,1A S,reueHrur BeKTopa [C] cocronr Ir3 cyMM sJIeMeHToBnoJrocrcr, HasLr:f.afr, c BepxHero ,'reBoroyr,ra. HanpLIMep, : lCl l a o b o a r b o* a o b r a z b o * * a f t r f a o b z a z b t * a f t z a z b z f. 3ro s rotlHocrr.rror qJreH,roropufi HaxoAHTcflc fioMolrlbro [pHBeAeHHofo BbIIrIe ypaBHeHHr, 3altetuM, rrro, KaK I.t oxHAarocb, tIIIcJ r oq " r e H o B n [C] ecrr 3+3-l:5. t r l H c n o e a p a c c M o r p r . r M , r u c n e H H H fni p H M e p , f l p o A e M o H c r p a p o BaB oJ.HoBpeMeHHo, KaK oAHH BeKTop rlroxer 6lrrl ceepHyr c Apyr u u n H o i r p a 3 M e p H o c r n .I l y c r l 3 a A a H b rA B a B e K r o p a : [,4]:[l 3 5 7 2], tBl:t6 2 41. Cneprxa IC] 6yaer HMerb ceMb q,reHos.I,lcno,'rtsvsrpa0rrqecKr.rfi Mero,[,,Hx Mo)KHo:g^afiru rro cxeMe 624 lffi Taxuu o6paBoM, co: 5, :20, cr:18* 2 c,:30* 6+ 4-40, ct:42+10+12:64, c n : 1 2+ 1 4+ 2 0 : 4 6 , -?9 C 5 : =4 + 2 8 Cs: B, O E P A I U E H 1 4MEA T P I T qH C I , I C T E M bYIP A B H E H I , I H B A a s s o u p a 3 A e n e M b r o n p e A e r ' r n Mo n e p a q u r , oH a A M a r p i r u a M H , o 6 p a r H y l o o n e p a q u n y M H o ) K e H r z r3, H a f l n p H 3 r o M , q r o D p s ] l o e A e O4uaro, ficnoJrbr€HH€ oAnoft MaTpHrrbrHa Apyrylo HeBbrrro,'rnr.{uo. 3yq npaBlura MaTpHqHOfOyMHOXeHAfl, MOIKHOBBeCTI{COOTBeTCTBylouee lloHsrue, AJrs qero Heo6xo4arraopeul.trb MarpurrHoe ypaBorHocr{re,rrbHo HeuseecrHoft rtiarpnusi [X]. n"enuet/l . [X] : [B] Heo6xoAr.rrlronoArIepKHyTb,r{To 9To oAHa Hs uaH6oIee Ba}KHbrx onepauuft uarpauuofi alre6pu, Koropafl 6y4er HeoAHoKparHoHcloJIb3oBarbct B AaJlbHefiueu, B r{acrHocrH AJIfl,peuenHff ct{creM y p a e u e H u f tB A H c K p r . r M H H a H r HrorM rpeHA-aHarrv3ax. fIpnaeAeHHoe Bbriile ypaBHcHHe peixaercfl c rroMourbroHaxox(r , e H u f l M a r p l r q b r [ A ] - t , o 6 p a r r r o i i n r a r p u : g e[ A ] , K o r o p a f l ) ' j l o B , r e r B o p r e r c o o r H o u r e H r 4 r[o, 4 ] . [ A ] - t : I l ] . Tar KaK yMHoxeHHertrarpr.r. IIbI Ha eAIzHaI{HyIoIlIaTpHIIy,[I] ee He Ir3MeHfleT,MbI MoxeTT yMHo. Nr.rrr o6e ,r{a'crr.r ypaBHeHr.{nsa lAl r, a peary"rr,Tareqero N{arprrqa q a c r r . ry p a B H e H H f H l c q e 3 r r e r .B r o x e B p e M r rM b r H a x o [,4] a,rrenori He.r,r3BecrHori Marpuubr [X] 'lepea Marpgrlbr [B] n Ar.llt.Bblpax{eHne 6hrs isa-apainofi. hcxoto Aorr)KHa Lts [.4]-'._-MarpHqa LAI o6e qacru ua rtrarpriqy, o6paruyrox [,4], t,4].lXl:[Bl,-yr'rgoxrErr,r I,fiii: : xr,roryrrHM "'i !1r ; f fl;:;tfIiLrfl,l ffiI r lxl : [4]-'. [B]. (3.3) Taxuu o6pasou, sa1\aqa,o6p-a,tuan yMHoxeHuroMarpHtL cBoMarpnuu [X], onpeAeJiennolicoouiouear.iel{ 4lircs K HaxolKAegi.rrc (3.3). B HeKoropbrxc.tryvairxo6faiuyro^Marp[rly safirn He,,rb3fl, TaK KaK B npordecceo6pauleuHaHHofAa npuxoArlrct BblnoJrHrrb Ae,'reHHe Ha HyJrb.Heo6paruruaflMarpHrraHa3brBaercq BbrpolKAeHHoLr,Ho raKue Marpnrlbrs sroft rJraBeMbrpaccMarplrBarbn6 6yaeu. I I P O I I C A Y P Y O O P A U I C H H gM A T P H U M O ) K H O N P O I I J I J I I O C T P H P O B A T b , peuas clrcreMy ypaanennft B MarpurrHoft Qopnie. 3HaqenHn HeasBecTHbIX B s r o M c r y r { a e X r : 2 y t x z : S . f l o n u i a e n c s H a i r c u I , I x .H c noJb3yq yMHo)KeHHe u o6paqesue MarpHrl: 4n * l0x, :36, lOxr*30,12:110. 3ry cucreuy ypaBHeiriifinro>xso3arrucarbB MarpurruoftSopue: LlJIH lcl : [6 20 40 64 46 32 8]. 136 e 6o"rluliucrBe CTaTHcrItCoeprxa He OqeHb[uHpOKOLlcnoJ'tbSyeTcg JIl1lxb aHa,'lH3Bp_eIIeHqeCKHXOnepaU,Hfr,I.ICKJIIOIIeHIIe COCTaBJISeT ufix pn4on.^Mu eule BcrpernMcq c eroti npoueaypoii, KorAa 6yaevr paccMarprBarl QH.utrpaqurc (cru. r"rl.4). t , 4 l . t x l: [ B ] , 137 rAe [.4] - Marpi{qa Ko3QQnqueuroB, HeH3[X] - BeKrop-cror'I6er{ Becrubrx,[B] - BeKrop-cro,'r6eq npanux qacreii ypanueuafi. B uaureuqacrHoMc,'ryqae f.i l:l t".l:f .?:l LlO 301 Lr, l Lll0 l 9 r o 6 s r p e u u r b 3 T o y p a B H e n u e ,H e o 6 x o g r . r u oo 6 p a r a r b M a r p n u y [ . 4 ] , r o r . l a n p o r r 3 B e A e H H eM a r p u q [ , 4 ] - ' u [ B ] l a c r H a M B e K r o p .peureHrar[X]. Bosr\aoxHo, quTare,'rrcHe [oHflTHo, nor{eMy cr.rcreMyypaegeHufr M o ) K H or r p e A c r a B l l r bB y K a 3 a H u o i l u a r p r u H o r l Q o p m e . L l r o 6 u y 6 e At4rbcflB oror'i, noperioMeHAyelrnepeMHolKHfbMarpr.ruy [,4] N nexrop-cro,l6eq [X]. B pesy,rlrare AoJr)KeHno,lyqnTbcrr BeKrop-cro.[6 e u " ' r e e n xq a c r e i i y p a o u e u n r : r : [+ [;fi:J:[4x1*1Qxs [;-*14:):[ ,0.,*,0., ] Tenepl peurr\r cucreMy l,paeueuuri c rioNlourblo o6paureHnq i ta r p t t M a r p u u b r [ A ] . f l o l l e c r r N r N { a r p u ( y [ , 4 ] c , r e a a o r e A H H H I I H on Ha u s r [ / ] H B r , r f i o . i r H I rB] rc e u e o 6 x o g , t r r t o roe[ e p a q u t r o A H o B p e u e H H o o 6 e u x M a r p r r q a \ . L I e . , r oa r u . r o n e p e u r t i i- c B e c r l l A I I a f o H a . : r b H b r e Marpullbr [A] x eauHl{rraNI,a Bce ocra"IbHlle - K Hy,'rflN{. a.rreMeHTbr 3ro ebrno,ruflercn c rroMorrlbroAe"reHIIacrpoK MarpHrrbr[,4] ua xoncraHTbI, a rari;{ie IIX cr'ro)r{eHIIflIIJII tsbrrnrraHlif. fIoc,re.,logate,rrHocrb orlepaquitc.nelyrcqaa: J) D. 4. r38 ,( I 1 0 30 I 0 Orr 1 0 otr 5 I lf JL tl l0 0l 0,25 0 01 0,25 0 -2,5 I Ilarpuuy [,4] norreutaeupfiIo]r c e,l!ru r r q H o ilir a r p u q e r l[ 1 1 flepryro crpoKy Ae.rrnrHa 4, no,lyvaen r t p H3 T o l t I H a M e c r ec 1 1 Bstqrrraenus nroporl crpoK!r yAecrrreIrerrH)'rclcpByro, no,ryqaerr0 ua lreCT€ O21 0 , 2 5 0 I Le;rru nropyro crpoKy Ha 5, no,'ry-0,5 0 , 2 qaelt I Ha N{ocred22 I I | I I ,5 -0,5 I I'uHoxaeu Bropyrc crpoKy y.a 2,5 f 0,2 lnsL,rrrraeM e e u 3 n e p a o i i ,n o J v q a e M0 | -0,5 L J rravecreay2 ll - f - 1 r 0 l: f r 0l Jl [_i,3 3,;]L r o s o j l o rorcfl c"'reAyIouHe paBeH" T a x x a x [ , 4 ] - ' . [ A ] : [ 1 ] , r o Bbrno,'tHff CTBA: lA)-'.tAl. txl : IAJ-'. [B], t / 1. [ x ] : t l l - ' . [ B ] , txl : [/]-'.[B]. Vr4HoxHe Marpllqy lAl-t Hylo Marpuuy [X]: nu Marpuuy [B], uafi,1eM Hell3Becr- -3:l] [-J:i [,fi]-L3l IAI-' ] 3 a r e l t , y M H o l K a nH H ) K H r o rcor p o r i y , n o r ' r y q a e M ? Mu no,ryul'l,rH o6paraylo Marpiluy. A"'rt{ ilpoBepKII npaD{1.'TtrHo' yMHo;,llrrb HcxoAHyIo Marpnu)- [A] ua cru o6paur,eHur Aocrar_o_rr_Ho no.rryrreHHyro Marptruy [A]-1, rr B pe3y.lbrare Ao,'riKHaro.rvqilrbcfl e l u H H q H a rM r aTpirqa llOx,f30x,l Blrno,rHtts gro yMHolKeHile,BbI y6e;1nrecl, qro clrcreMa 3anrlIIo IIpaBH,laM yMHo]lielrHfl MaTcaHa npaBli,rrHo. .[,etlcTBI{Te,'rbHo, pu[ noJ]q4€M + l0 1 0 30 [i 1 0 .. |i ' , l : [ 4 x , + l o x , l LlO 30J Lr,J |. ; IBI : [X] Berrop-croJr6eq X coAepN(Lrr IrcKoMbIe Heu3BecrHbre Jq:2, cx z : 3 . B c n o n a u s a s ,q r o u M e H H o3 T r r 3 H a q e H H t y A o B , ' r e T B o p f . Jur H xoAHbIMypaBHeHuflM,l,tst y6ex4aeMcq B ToM, rITo HaUJII{ )cy H x2 IIDABIiJIbHO. PaccuorpuM exre or,uH npuMep ypanneHuiic ^peueHlrr cu.creMbr rroMoulbro o6pauleuur MarpHqbt. SarH[reM npuBeAeHHbre HlI)Ke )'paBueHHfB l M a r p H r r H o i iQ o p m e u uafiAev x1 H x2, o6paulaq.\,rarpuuy cHcTeMbI: 2xr * xz -- 4, 3 x r+ 4 x 2 : 1 . rrpH o6pauleHnu tratKparxo 3aIItIrrleM oI]epauHIl, BbIIlo,rrHseMbre puubr: I lil;;l:fil i3 2' | l - ' l : l 4 t 5- l l 5 . l 4) L3 L- els 2t5J -;,1 3 t-;j; til:l_;l t39 l ' Cne4oeareJrbHo, snaqeHttq Hea3BecrHbrx6y4yr ---2. x1:S 1q trg2a 3auersM, rITo olrricaHHaffnpor{eAypaorrenbHa[oMHHaerKJraccnqecxrifia.nre6pauvecxafiuero;1 perueHlrsclrcreMbrAByx ypaBHesnfi. B caMoMAeJre,perxeHlre cucreMbr ypanHeuufi- nall6o;ree BaxHoe npr.rMeHeHr.re npoqeAypbro6pau,enur Marpnq. B 4aHHolr c,'IyqaenpeHMyqecTBoMaTpHqHbrx MeTonoBno cpaBHeHllro c MeToAalrHo6uquofi anre6ptt 3aK,trrcqaeTcg B ToM, rrTo oHIr 6olee cHcreMarH3rrpoBaHbr r.r Jryque noAAaroTcfl apofpaN{MrIpoBaHrno. bo.rluruHcrBo npoueAyp, orucaHubrx B cr'reAyroq[x fJraBax,nprr. BoAHrK peueur{roctrcreMypaeueHuft.3rH cucrervrHo6srqHosanu. CbIBaIOTCfl B MaTpI-II{HOM Bl{Ae II peUaIOTCfiOIICaHHbIM BbrrII€ r\t€T o A o M . O n e p a q H r b o 6 p a u l e u n n M a r p u u M o l K H or r p r r M e g r r r bK K B a A . paTHbIM M^arp^HrIaM ,rrc6oro noptAKa, a He roJrbKo K MarpHrIaM rropr,AKa 2X2, paccMorpeHHbrr,rB npr.rMepax. V6e4lrrecb B 3rolr, ooparuB rrpI,lBe.IegHylo Hr.rxe Marpnuy noprAra 3X3: [;::] Ec.nn uu saxorrlM o6parurt AriafoHaJrbHyro Marpt{uy,To gaAarra oKaxercfl 3naqr.rreJrbHo npoille. O6parnar Marpnrla- 9To npocro AnaroHailbrafl. M_arpl{qa,HenyneBbregJreMeHTbI xoropofi - 06parubre BeJn{qr.IHbI coorBercrByroulnxsJleMeHToB o6paulaeuoftuarpflrlbr.PaccuorpuMMarpr{qy[A] nopaaxa3X3: ':l :6'"1,1 [l' tl I^ €c' c.ryqatx He o6ssare,rlHoo6pauarb N{arpHuY, B Henoroprr-\ nn rpe6yercq ro,rrbriopeut{rb cucreMyypanuenufi.B paccltotpeu' sreN.{eHros rnrarprrqh[X], yaon' r{oMrlpnMepeMbrucKa!'II{3HaqeHHff ypaeHeuHrc "qerBopEloueii f + [r,, 3oJ I U f 3 8I l:Irrol C sroii ueJrbro rror o6paru.rrrr Marpuuy [A] u HaITIJIIIMarpiluy {X], yuuoixun LAI-I Hq [B]. Buecro 3roro MoxHo 6si"ro_n_ptMoI'Icl r o , ' r b 3 o B a r bM a r p i r q y [ B ] n o M e p e r o r o , K a K M a r p u u a [ A ] n p e o 6 ' MarpHuy. c srofi qe,'Iblo yAo6Ho pa3oBbrBa,'racbB ell,HHriqHyrro r.icrroJrb3oBarbTari Ha3brBaellyIo paclIIHpeHHyIOMaTpHIIy, COCTOg' cro,r6uos. Berrop-cro.l6eq [B] sanurr,raer ul!'ro H3 /2 crpoK v n{l cro.n6eq pacufipeHuoft uarpnqbl, ocraJlbnaq qacrb een*l-it o6paqaercn. tr4cnona3ys oror cnoco6, r{arpr{qa flopsAr(a nXnpeur,rM Ty x(e 3a.u,aqy: t. 4,0 10,0 10,0 30,0 38,0 110,0 2, 1,0 I,0 2,5 3,0 9,5 I1,O 1,0 0,0 2,5 0,5 v ,ll llepnyro crpory BblqnraeMrre rropol A 1,0 0,0 0,0 0,5 2,0 1,5 Vrtroxennyrc ua 5 eropyto crpoKy BbtqrrraeM rie nepnori .). 1,0 0,0 0,0 1,0 tn 3,0 Bropyto crpoKy Ae.'run Ha 0,5 U att l 0 l '1"., Ir, l Vt uarpuu lAl tt [B] cocraBrlneDt Marpr{uynopflAxa nX (n+l) flepsyro crpoKy AenrIM sa pyrc- ua l0 4, Bro. 1,5 a22 Hexoropste xolvr6Huaunl.IAoBoJbHo c,tox(Hblx onepailufi craHoeCJ'lIIBxOrIfiU{HeB HIIX N{aTpflIlbIAIIaroBflTCt OqeHb IIpOCTbIMLi, ga rrbHbjg; H a np rruep, p accMorprrM -y N{Ho)KeHr.re [A1-t : [A]'h :lAl-'t' . E c . t r u [ A l - N r a r p n r r a [ o p s A K a 3 X 3 , r o r p o n 3 B e A e g u ep a n n o : :{ Ii' "1,]-' l^ tl V rru 0 I It w 00 [40 - r f - V ozz 0 I V ass cron6eq nonyuenuofi Taxxn o6pasort, B pe3yJlbrare n*l-tt xrarpurrbr coAeplr(fiT perueHl4ecllcreMbI ypasHeuaft, a HcxoAHaE . IlIarDgua sa NreHeHae.u,nsuquofi .II,.riao6paqeHI,ts i\{arp}rq r.i3BecreHpnl MareN{arHirecKIIXnpoMeroAoB cogAaHbl ueAyp, 3ac,'rylKrrBarcuaXBHriManfiq. Aecsrxu ypanneunfi pe[reHus cncreM lr cyqecrBy]or corHn nporpaMMAJrrr ntrx aepcufi. Hexotoptte LI3 HHx npeAHasuaqeubl c[equaJlbHo AJrn Marplrq qacrHoro BHAa, raKrrx, KaK pa3pex(eHHbreMaTpHrIu (r. e. MarpHIIbI, coAepx{aqfie Muofo HyJieBbIxeneueuron) uJrH Marpnrlbl, o6.naAarculue HeKoropbrMn TllnaMrl cuMMerpull. So.nruruHcrBo BbrqHcJruTeJrbHbrx rIeHTpoB HMeeT cTaHAapTHbrenporpaMMbl B cBol{x 6u6luorexax, npeAna3naqeHHbreAJrfl BbrnoJrHeHuff Marpr.ItrHblxonepauufi. I-Ieo6xoan,rto3apaHee c HHMrr o3HaKoMrlrbcfl, npelKAe geM n o r p e 6 y e r c q B b l n o , ' I H r r np a 6 o r y , o i l e p u p y r c 6 o r l r u u l t n M a c c H B a a{}r AaHHbIX. t41 i7 I T P A H C I I OH P O B A H N E ,I{eKoroporiIIoc,{eAoBaTerbHocTrr onepauHir.O n p e 4 e , r n r e J r bc a M B o detA, lAl unu o6o3Haqaercs JllrqecKu O l e p a q n a 3 a M e H b rc r o , r 6 q o e M a r p n u b r c r p o r i a M r r H a 3 b r ) l a e r c f i T p aH c n o H f l p o B a H L I e M . l-Ianptu r ep, rrarpHrra att orr l azzl tl3:l Iloc"te TpaHcnoHIlpoBaHlIfllrMeeT BHA 3il O t l t e t r l M , q r o I r o c , . t er p a H c n o H r r p o B a H l nf i e p B a f l c r p o K a c r a . T t r j nepBbrM cro,r6qona, a BTopafl crpoKa - BropbrM cro,r6uopr. Ec.llr o6o:saqrrro Marpuqy uepes [l], ro MarpH(y, no,'ryqeHHyrrp l aHcnoHHpoBaHHeM M a r p u r r r , r[ , 4 ] , o 6 o s s a q u n [ A ] r . l l p u r p a H c n o H r . r p o A;; nepexo,t,HT B a H H T3I . n e M e H T B 3 r ' r e M e HoTj i . B o u g o r H x 3 a A a q a x , p a c c M a r p u B a e M b r xn r , r . 6 , q a c r o 6 y 4 e l r r r o , ' r b 3 o B a r b c r r e M , r l r o B e K r o p - c r p o K a M a r p r r q u [ A ] n p n r p a H c n o H n p o B a H H rni p e B p a u a e r ct B BeKrop-cro,r6eq Marpr.rubr[,4]r. Bexrop-crpor(a rr Ber{ro.pcro,r6eu, lo,'ryqarorcq oAHH u3 Apyforo rpancno:HapoBarxueM.HanptrMep, Il 234lLl Lil lloexe 6yae:u HMerb MHofo cJryqaeB,KorAa Marplaqa yMHoxiaercs Ha Marprruy, rpaHcnoHl{poBaHuy}o x r sefi. Ec"ru uarpuua [Xf IrMeer n crpoK u m cron6uoB, ro rpancrroHupoBaHHaflx nefi [X]' 6yaer lrMerb /r? crpoK u n cron6\oe. Vl\aHoxatr Marpurly [X] c,reea H a r p a H c n o H u p o B a H H y rxo u e f t n a r p n u y , M b r n o r y r { a e M K B a A p a r H y } o , cuMMerpHriecKyroMarprlqy [opflAxa ntXl?, Ha3brBaeuyrolrenuureil - [por.I3BeLeHL{eM MarpHUbr[X]. Vrunoxax rr.rarpaUy[X] rr,rarpuu,efi c n p a B a H a r p a H c n o H u p o B a H H y l ox u e i i N { a r p n u y , n o , r r y q a e MK B a A parHylo cl'IMMerpnqecKyloMaTpHIIy llopflr].Ka nXn', Ha3bIBaeMVIO 6o"rlurori Marpilqeii - npon3Be5eHueMrraarpilqlr[X]. oII PEAEJI I,tTEJlt4 Harrreft noc"re,qner? flpex4e ueu nepet?rH K H3,'ro)KeHi.rro rer,ru" xacarouteficq co6crseHHltx sHaqeHHfru co6creegHHx BeKroDoB. ocraHoBuMcfl KoporKo Ha onpeAeJI[TeJIeMarpHIIbr.Onpe4e,rrareJrb 3TO quc,'lo,npunr{cblBaeMoe KBalparHol.j Marpilue B pe3y,[brare I to taa Qzr OH ertqucnflercff KaK cyMMa z! u,renoe elr4a (- l)u ari, a:i,... ani,r, ( 3.4) T A e n - q l r c r ' r oc r p o K ( l t , r a c r o , r 6 u o e ) u a r p u q t t ; i 1 , i z , . . . , i n . H e K o r o p a g[ e p e c r a n o B K aq n c e " l 1 , 2 , . . . , n ; k - q u c , r t o r p a H c r t o sHIur? nap a,reMeHToB,Heo6xotrtINIbtxAr'rR Toro, ttro6bt pacnoJlo,>KI.IT HbH r e K c bB r flopfAxe 1,2, ..., n. KaNAnfi q,res eroii cyiln{br coAep}KHTno orHoivr}r3,qeMeHTyrI3 r<a>x;toficrpoKH u Kax(Aofo cro,r5qa. fipoqeac BbrqncJreHufloirpeAe.rrre"'rfl Haq[Haercfi c ou6opa no i T p O K rgr , r l O 6 p a S O B a H I Ipf a l 3,'InqHbl\ o A H O M y3 , r e M e H T yU : X a X < 4 O iC r o u 6 u s a u u r ? . S , r e l t e r i r b r K a > K A o r oq . [ e H a c y r l r M b Ie r t 6 u p a n r c R l t s , c r p o KB e c r e c r B e H H o M n o p f l A x e l , 2 , . . . , n , o A H a K oK a > K A a fKf o M 6lrHarrilq Moxier corepxiarr, Torblio tlo o.{,HoMy3I€M€HT} Hs Kax(aoro cro,r6qa. HanpnMep, B Nrarpnue riopsAKa 3X3 tuoNuo BbIe r, o a , ' r e N { e H T b I 6parr xou6uuaqltlo attaztazz. O6parure BHHivtaHttq p a c r l o , ; r aaf r o T c f i B n o p f l A K e B o 3 p a c T a H H qH X r l e p B b r x l l H A e K c o B n o M e p o B c r p o r i . K a ; r r a s n o r , r 6 n H a u n rc o A e p x n r p o B H o n o o A H o M y a,rreMenryus xaxiroii crpoKII r.r Kaxi.qoro cro,r6qa. Tpe6yercn er'rS o a r r B C e B o 3 M o N i H l r er o v 6 u H a [ r n l . c o c r a B J r e H H b rrea K H M c l t o c o 6 o e r . E c . , r u \ { a r p r r ( a r . i } , { e e nr o p g . q o r (n X n , T o r a K u x x o r r 6 l r u a q u i i 6y.aer n! Tax xax nopfl.r.oriyMHo)KeHHnqttcerrrHe B,'tufler Ha pe3y,'lbrar, T. €. Cl ,azzazt:a22Q1ia3i:4s3A22411 it T. A.' 'IO MoX{Ho npolI3BO,'lbHO i l 3 N r e H i l r br r o p f l . l o i i 3 J e ! r e H T o Ba o r o 6 p a H H u . r x o u 6 n s a u r r n x . l l o [ b r r a e ] r c n e r r 6 p a r r 3 , , r e N l e H rrbarn , q r o 6 r t u x B T o p b r el l n r e K c b r , r , ' r t r H o N r e p ac r o , r 6 u o s , p a c f i o " r r o x i u , ' r u cBb n o p t A K e B o 3 p a c r a H H a .f l e p e craHoBKy NIo)r(HoBbinoirHllrb, IreHRfl ,'r106bre .{Ba coce.IH}rxa,teMeHT a M e c r a M r r . B l , r n o " l n f i f l o n e p a q r r r o ,H y i K H o c o c q H T a r b , c K o , ' r b K o cAe,rraHonepecraHoBoK, Heo6xojlltN,rbrxr,,'rr roro, qro6u HHxeKCbr B Hyx{Ho}r nopflAKe. Ec,qrr .q.rs 3Toro norpe6oBapaclro.roiKr.LryHCb . r r o c bq e r H o e r r u c , r or e p e c r a H o B o l i( r . e . 0 , 2 , 4 , 6 , B , . . . ) , r o n p o u3BeAeHHe3THX 3.leMeHroe 6epercfl c tto"rro;^t<rrexbnbrM3HaKo]r. E c . r y n6 u , r o H c n o " ' r b 3 o B a HHoe q e r H o eq H C , ' r on e p e c r a H o B o x ( r . e . l , ro nporr3Be.leH6 u e p e r c r c o r p l r r l a r e , r r b H b3rHMa K o M . 3,5,7,...), B uarpuue noprlxa 2X2 f oazt, t I ut1 ozz) coAepxaulHx JlIolKHo gaftru ro"rIbKo Aee xoM6lrHar{Hu a"reMeHTots, r43 no oAHoMy 9,'leMeHry r.r3 KaxAoft cTpoKH rr3 KalKAofo cToJr6qa,Q r r d z z H A 1 2 A 2 1B. r O p U e I I H A e K C bBI l { " q e H eA 1 1 A 2 2p A C f I O J I O X ( e H Bb I ecTecTBeHHoM rropsAKe rr [epecraHoBoK He Tpe6yIoT. Lhc,ro nepecTaHoBoK paBHo Hy,'Fo, rioSToMy 3HaK npor.ISBeAeHr.rg noJroiKHTe,lbHbIr?.oAHaKO SJreMeHTbI B qJIeHaXArz Lt Qzr HyXTHOnOMeHflTbMeCTaMU, qro6br HX BTOpbreHHAeKCbT pacnoJroxuJrr4cbB HyxiHoM rropsAKe. 3ro rpe6yer oAHofi nepecraHoBKll, rroeroMy pe3yJrbrar 6yaer c orpuuareJrbubrM 3HaKoM. I4Tarc, olpeAeJruTeJrbMarpi{qbr nopfAKa2x2 panen Att d r' q- lI : t Otdzz-Qtzdzr. n e p e c r a H o B oHKe r p e 6 y e r c a . f l e p e c r a H o e x uAJA O . 1 1 A y A 3 2 :d 1 1 A 3 2 d 2 9 A pA 23A31: A,pd, BsAzs: A t t dt zQzg O,pA21A4: d,21&12A3s A 1g A 2 1 Q 3 2 :A 2 1 ds d 4 2 : A 27 A3 2 A1s A 9 Q 2 2 Q . 3: 1 A 13A s t A z z : d s t A n A 2 2 : A 3 1 4 2 2 d1 3 ft:1, k:2, k:1, h:2, ft:3. s H a Ksuat * s H a xguax * s H a x- Vrax, B orIpeAerHTeJIe rpH IIoJIo)KIIT€r'tL'Hbtx tI rpll orpi{Irare,ilbHblx q,'IeHa. Cx,raAnrnaq q,'IeHbI (c cooreercTByloxlllMH 3i{eKal\ll'i),' rIoJ'tyqr]M ! 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' r a u 3 l e p B o l i , 3 a r e M H 3 B T o p o f t ,T p e r b e r l ,. . . , n - f t , H c n o n b 3 y f [pLI 3ToM He 6oJlee onHofo s.rrel{eHTaI.r3 Ka}KAoro cTOJ6qa, }1KaKOM6nHaIIHH,!.{OBr'IeTBOpgIOqI{e x{eM Bce BO3MO>KHbIe STHM VCJ'IOBIigM: flepnufi, Tperr.rfilr ntrblfi LI3 3rl{x q,rrenoB rpe6ylor verHoro LLLTCTA OIICPAIIHfi,AJIfl TOfO IITO6bI IIX BTOPbIEI.IHAEKCbI PACNOJIO}I{[.:rr{cbB noprAKe Bo3pacTaHI{n.fina Tofo rrTo6br uHAeKcbrocT?r'rbHbrx gJreMeHToBpacfioJrox(I.lJrllcbB nOptAKe BO3paCTaHHs,Tpe6yercq HerrerHoequcJro o[epaquf{, I.t no3ToMy oHH orpl{rlaTeJrbHb], Crn a At'tea fl,, [oryqae M: lAl:48-0 + 3 - 1 8+ 0 - 8 : 2 5 . 3HaKa KaxAoro rLIIeHaHaM Hy)KHo BbrflcHr.rrb, ,[.nr onpe,qed'IeHufl qro6br Bropbre cKoJrbKo nepecTalloBoK HeooxoALIMOBbInO,rrHr.rTb, ,ueHa ay(r22a3g B IIoptAKe l, 2, pacnoJloxuJlHcb 3..II,ng I.lHAeKcbI Sror ueroA Bbrqncrenlis onpeAeJrl.ireJrronucaH flemoQpeqilo s uoHofpaQun l5l. Eo.uee o6qerpuusrblft noAXoA, LIsJro)KeHHsrrl f u p n u V u n e p a [ 2 ] , o c n o u a n H a r a K H a 3 b I B a e M o M e r o A ea J r r e 6 p a u qecKI,Ix AoTIoJIHeHI{ft,HO rlo cyqecTBy Ma,'IO oTJll.tqaeTcflOT ll3r'rox{eHHofo. Teueps MbI yxe yMeeM Bblqr.IcJrflrbonpeAenureJlb KBaAparHot? Marpltllbl, Ho eule HescHo, qro gro raKoe. Onpe4e.nureJluBo3HLIKasaAarrax, HO qaqe BCerOOHr.rHetBHO yqacTBylor IOT B paSJrLIqHbIX ypaBHeHIlfi. ql,Irare.nu Mof He saMeTI'ITbI'lX IIpIt B perueHH?tCPICTeM t44 l0-201 d,11d.22Asg, A11d.2slg2, Apd2gAs1, Q.12d.21lgg, AgA21Ag2, 49d22O,31. 145 paccMoTpeHIIII 3rofo Bofrpoca, Ho cKpbITo oIIpeAe.ry['lTeJII{IICilO.IIb' .soBa.rrrrcbB npoqecce o6paqenfifl Marpuubl. Peurult cllcreMy AByx ypanHeHilli: atfit * rpe4crae,rnr,.u .".::f;' &pa2: 0.1, p a H e en p u M e p e : o a npuBeAeHHoM f t r p o n e p H ua r o n p a B H J ' I H 'nl f"'l:f.?il In Llo 3ol L',J LrroJ (3.5a) ure"Tl I.f, 3 s a nes aterrrt e o 6errx,npo6nx p a BHbI oIIpeAe.rl |: *oo'., "1':;;;# ";l l;;|: ti;] loo',', (3.56) Hrrcnrtrerl Bbrpax{eHr.rfl [Jtfl x1 paBeH onpeAe,txre.{}o ro):40. I l ?l l?l:138.30)-(rro l0 3ol A l u y ; x e B b l f l c n u r ' r r rq,r o B e K T o p - c r o n 6 e ( H e r l 3 B e c r H b l x t r r x z ,Mo>Ker6urr nailAeH c rroMourbrco6paueuuq Nlarputrbt.OAsaxo nul MolKeN4uafitu HeH3BecrHbtec noilIournlo 06stqultx a,rre6panqecKIIX npeo6p a sonanuii. flo"'tyuHu . - -- - , , j , - L b r o r . , - f t r z b " "t orrorr- oLzQzl V .. "' : ertb"-brdz, orr,r.u- orrou' H e r p y , l n o 3 a M e r l l r b , q r o 3 H a M e H a r e J I yH 3 T H x a u p a x < e n u i i oAIiHaxoeur.3ro onpe4eflIlre,'rbMarplrtrbl [A], r. e. 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VpaeueHHe 3arrcart e $opn,te (tAl-rul).[x] : [0], ( 3.13) rge ft[1]- eAaHri_quas Marpurta[/], yrranoxeHnaa Ha qricJrol, (no-n plAor Marpnubr[1] raroii xe, xax noprAoK Marpnrrbr t/l). Marpnqal,[/] nopnar<a 3X3 HlreerBrrA LIII: [s;:] (3.r4) Hcno.nssyn trpHnrrylo 3altHcb, fioryrrrlM c,'reAyroulyK)CI,ICTEMY 5',paeHeunft: (art - I ) x t + a t z x z* Q 6 x s : 0 , (ar, - lu)x, + d2sxs:0, a e f i r * a e z x z* ( a t t - l , ) x 3 : g . Qtzxr * (3.r5) peAe"'IilTeJIIr KoropbIX flBr'tflIorcfl qticJIHTer'tgMHgrHX oruoueHufi, €c_TbHla'r€Bofr cro,.r6eq, oTr.{ onpeAe,'ruTeJrltpaBHbr H-v.[rc. Taxullt o6pasolt, rvr- to1 rAr' 143 i-I att dn &b 0r, - I CIys | : 2, -'esz 0. 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Tenepl >Ke paccMorpuu 6o.lee c,roxHsrii B KoropoM ucI r o J b 3 y e r c f l c n c r e M a . y p a a H e u u i i , r { o r o p y r c M b r H e o I H o K p r , f H op a c _ c M a r p u B a , ' rB u b r [ i e .I l y c r s A a H a M a r p u u a n o p a g r < a2 X 2 : 4 rr ,r ,rr-_ | [10 flonropreu l0l. 301 4- )" 10 t0 30--r l0 30-e I ^' J-,rl "l:(:-11(3-1)+24:0 1,2-5i*30:0. rorcn no Qopuy,re Bbrrir{c,'rrr KopHuaroro YPaBHeHrs ( I 1 , 9 ( - 'lut o u | z ^ tuL- 5+V'=es : 2 , 5 * 4 , 9 i , 2 b-V -v, :2,5 - 4,9i, ^ ---nnz: 20:0. *t-3a)!v=1a"=a:T 2a 2'l 33,4, _ 34+VW6 -_-_--'-' lz : 0,6. Mu uoxeu npoBepnrb3 T X 3 H a r I e H H t , n o A c T a B U B I i X !rHTeJ'tb. vqurlteag ouru6xuoKpyfJreHufl , noJrylraeM B OrrpeAe_ 10 : ( - 2 9 , 4()- 3 , 4 ) - ( 1 0 ) !(0 ) : _ 0 , 0 4 30 33,4 l0 4 -- 0,6 (3,4.) (29,4)- (10)(10,y : - 0,04. l0 30- 0,6t- t_ Taxnu o6pa3oM,co6crBeHHbre 3 H a q e H r i fH l aii4eHu BepHoc roq3HaKOB. HOCTbTO AO AByX AeCfTI,Ir{Hblx 150 -t) ^ rpe6yer Mur nu4tlu, r{ro Haxo}KAeHIreropHeii 3Toro ypaBHeHufl ql'lcer'I'TOtAa OTpI{UaTer'lbHblx I{3 r<opirefi KBaApaTHbIx H3B.rleLreHug trIcno,rlsyr$oprray,ry Ar'rs onpeAe,rreHHrxopHefi KBajfparHoro 4-33,4 10 I l2-L ^1 L- , 2 - yp aBHeHi{fl, rro!'ryqaeM lr: BL,IqHC,ltlqroropltit, no,[yquM -o : (4- t)(30-1)- 100:0 1\2- 3 4 ? \ + - b+l/br-4,0c l--u B'-li:o' I I'TJIYI 1: t241 | I n r - L _ 6 3 1| b ^io onpeAe'll{re"i Io .l;:T.t"tf M Hy.rI llprzpanHae r zrl- 'g"rIH !,alee 4-7 l0 "."p;;";;;";^-'ty2, K a 3 a T b , K a K H e N l O f y T e O a U U X U y f l A O I I O " I H I ' I T e " l b H b l e O C ' I I O >: K H e H I ' l q ' Marpulrbl ;;; s uairci co6crBeHnbre sHar{eHI'Iqcr'IeAyloqeii n;t;; r Bce [poAe,']aHHbreB npeAbrAyilreM nprrMepe Aeii- CTBHg: no- qucJIa, coAep)Kaul]e KaK',neiigraure'rrIAe fr, lz - KO!1II.r'IelicHble q a c r H , B K . r l F o q a r c u r uq ea c " l o i : ' l - l ' K ctlaHyIo, TaK Ir MHIIMVIO HMeIor Aelictsurenr'Hlte crblo, cuMMerpllt{Hble }larpHIrbl BcerAa , ' e 6 o , ' I l l u H H C T B eH a u H x B t I t { H C " l e H l I i i ' c o 6 c T B e H H b r 3e H a r I e H I t f i H 3HaqeHIIf BeliTopaNIIi iI CO6cTBeHHbINII{ CBfl3aHHbIx C CO6CTBeHHbII,Iil MII,}ICIIoJb3yI.oTcfllioBapuaqrloHHble'KoppeJIqIIHoHHbleI{JIIIaHaJIor n q H b l e M a T p H I I b [ ,I i o T o p b l e B c e f A a C I I M N l e T p H q H b I ' 3HaTenepn pacclrorpriri iipoqeAyp_y BbIr{IIc,'IeH}IfiCO6CTBeHHbIX qesuii l,ra inrarpriqblnopflAKa 3X3: Bl rl l : 0 - 4 -.20 -+o B | | t2 -26 J L -oo IlpupanHue aeM Hy,{Fo coorBercrB}'Ioulllli orpe!'€'tlIir0rb 2 r-). 0-). -4 -4 B I -20 l:0, -40 B-r, - Grt t2 -26 - )"1 -l'3 +2]'"2+8]":0. nocJie qero rlo,'Iyqltlt lDt 3ro - ry6nuecxoeypaBneHue,r.rMeroulee rpr.r KopHs.Fagno>xHs ero Ha Mnoxr.rreJrx, MoxeM sanr{carb (f-4) (f-0) (t+2):0 E KopHafu:4, ?uz:Q,}us:-2. noJIyqI{M Xorq usroxenHbre[pueMbr npr.rMeHr.rMbr K Marprrqe.nrc6orono. ptAKa, HaxoxAeHr.re xopHeft [oJIHHoMoB BbrcoKr.tx creneuefi flBr'rgercq HerefKolisa4auer?. O6uqno co6crseuHsre sHaqeHrirHtxonrrrcfi! He c IloMolqblopeueHr.rflrroJrr{HoMl,IarrbHbrx ypaeneHuil,a c IIoMorqbroMeroAoBMarpur{Hbrx npeo6pasonauuii,cyuuocrb Koropbrx cocrol{TB rroc/'reAoBareJlbHbrx npn6,rnxeHi.rtxK co6crseui{trM3HaqeHHflM.3ra lreroAbroKa3aJrucb rrpHMeHr.rMbIMH ToJrbKo6,raro4apx. 14cnoJrb3oBaHrn 6ucrpo4eiicreyrouiHx 3BM, nosBoJrflloi{iix 3a BecbMaxoporrcaftnpoMelr{yror(BpeMenr.r nafira npu6nnx<enuoepeuIeHIte,a 3aTeMyToqHHTbefo B TelteHLIeHecKoJrbKr.IX MHHyT. lerrepb, K9rla Mbr noryrlnJrH npeAcTaBJreHHe o npoue.u,ypeBbrrIHc'IIeHLIg co6ctgeHHutx sHa.IeHLIft,Mo)KHorro[blTarbcfl noHflTb H Hx cyuluocrb. Marpizl(y Mo>KHopaccMaTpgBaTb KaK Ha6op sHa.reHr.rft KoopALIHarroqeK B n-MepHoM npocrpaHcrBe. Marpuqa nopsAr(a. 2X2 coorsercrByer n,nocnofi nonepxiocrn, TaKofi >Ke, KaK Jrlrcr 6yn,Iaru.Taxnu o6pasou, Marpr.rqHbre oltepaqun MoxHo rpaKroBarb. reoMerpllqecr<n.Tar, Marprrqa F n c . 3 . 1 . J o a s e x r o p a ,o n p e a e l r e H H b l e aMlr nopflJ.xaMarpHUblzXZ 3,leMeHl Prrc. 3.2. 3.rnllnc, onpe'le'reHHut-t 9 . t c \ r e ial l1 l1l r l r r n H u b ln o p R l l i r z X z ' Co6crgeHnlte Beliropbl Marptlu,bl coorBgl' CTByTT InaBH!'IM nOJIyOCflMSIJItrnca t4 Br | rr r. f, r-_ | 18 4l ottpeAeJrrerABe roqKr.r["'rocnocrr.t c KoopAr.rHaraura (4,8) a (8,a)Srlr roqKll coorBercrByroTAByM nexroparr,rHa KoopAr.tHarnofi i,rrocKOCTH,BbIXOASUIUM H3 HaqaJIa KOOpAIiHaT,KaK 3TO nOKaSaHOHa pHc. 3.1. Oruerrnr, qro B KaltecrBe KoopAlruar roqeK MolKHo r4cnoJrb3oBarb u cronbqu Marpurlbr, qro He Buecer cyrqecrBeuHbrx HsrueHeHnftB Haurn paccylxAeHlrg. Ens, ofipeAe.rreHuocrrr 6yaera Aeficreoearb co crpoKaMr.r. flpe4ctannu ce6e, qto ABe rorrKl.L're>KarHa s!'i.{trncec qeHTpoM B Haqale KoopAliHar. TorAa gJrr'ralc 6y4er npeAcraB.rrrrb Kpr.{Byl.o, IlpoxoAflulyrc qepe3 3TI{ ToqKH. B pesy.irilare co6crneHHbreBHaqeHwfr Marprtlbr oKa)Kyrcfl paBHbrMv AnnHaM 6onturoii u uanoft nolyocefi sroro g,rrJrnnca.B HaureM npr.rMepeco6ctaeHHne 3naqenrrfi pannu hr:12,}uz:-4. Heo6xoAutrlo orMeruTb, uro orHoIIIeHHt no.nyoceri Mo>KHoHcIIo,'rb3oBarbKaK Mepy BbrrrHyrocrrr g/'Inr{trca,uro rpa$ruecr{r.{ noK a 3 a H o H a p a c . 3 . 2 . f l e p n o e c o 6 c r s e H H o e3 H a q e H H ex a p a x r e p t i 3 y e r 6o.ururyn floJlyocb, AJrrlHaroropoft or ueHrpa .qo calrori yla,lreHioft o r H e r o r o q K r . rx p l i n o i i p a B u a l 2 e 4 H u t q a l r . B r o p o e c o 6 c r e e n H o e s H a q e H i ] eX a p a K T e p H 3 y e TM a , r y r c n o . r y O c b ,H a x o i l q l q-pasHa ylocq Bo BTOporl uernepra KoopAHHarsoii flJrocKocrr{.Ee 4,lllHa 4 e.quH r I r l a M u 6 e p e r c n c o 3 H a K o MM L r H y c .E c , r u 6 u r 4 e e 4 a u H u e r o r r K a 6ltlu 6.nuxe Apyr K Apyry, To orHorreHlre [oJryoceli llsN{eHr..trocr t52 coorBerPrrc. 3.3. VA"'linessulir 3JlJll.l[c' KOTOpOIt CreyrOUtll'r MaTpllqe, 9'leMeHTbl gaAalot TOqKn c pacc oflHl'IflMI.IMexiAy --ltttr, M e H b l r l l t M l l 'q e M H a p l ' r c ' 3 ' 2 ' Co6ctget:Hste BeKToobl noJlyocnvfl qBntorca Puc. 3.4. Marpuqa, cogePxaxr.aq paBHbIe cTpoKH' npITBOAATK BblpolKAeHHOMy snnlrllcy - [ptMot{ TJIaBHbI\1fi 3'[nHnca ecr'rlr 6u. HanPunaeP' Iu,lrMtlMarpnqy BbI6paHbI TOqKI'I c : [3 :] rAr M arpllllbl oo co6cTBeHHbIM I'I 3HaqeHI'lsMI'I o6paayrc' KOOpAlrHaraua, 6yayt uI{cJIa}q:14, Lz: - -2. 153 3ro noxasauorpa$uuecKr.r Ha pric. 33. Eo.rlruas noJr).ocb AaH_ HOI-O 3,rr"rHI,ca HalrHoro60"rrrueMa,'rori.Ec,rll .rsc olr6pauur,re rouKri coBfiararor,T. e: ABe crpoxrr Marpur{broJriuariond, To tsropoe co6crneusoe3HaqeHHe craubezrcs pinurrn Hy.Tio,]r paccMarpH_ gaer4lrrio,rr"ru''cBbrpo)KAaercl n nprryrc. 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Bexropr,rB TpexMepHoM,npocrpaHcrB^e, onpeae.qreMbre S.IelreHT{1[{lt MaTp u r r b rn o p r a K o3 X 3 . 1i)li Ec,ru sH TIIrareJrbHoH3yqn!'rusry r!'raBy u AerairrbHonpopa6oTa,rH npr{Mepbl (a rarxe o64yrrla,ru Bo3Mo}Kuocrb KoMnJreKcHoro, Mero.loe e 6o,ree cJrolKHblx sa4auax), npuMeHeHHt H3,rro)KeHHbrx K TOMy, qrO6u nepeiiru K H3y[OArOToBr'reHbI TO y)Ke AOCTaTOqHO qeHItIO COBpeMeHHblx N{eTOAOB, npH}IeHfieMblXB BbIrIllC,'IliTe,'IbHblX reoJrorhr{ecKuxHccJleAoBaHfirx.Mlr nonsrtaJH,cbH3,rrorrrrrbB ylpoulesHor? Qopue ocnoBbr uarprunoli a,rre6pur. KaK orNte.IaJlocbB rperleft r,'IaBe, crarHcruKa c,'tfiIIIKoM c,'ioxiHat HayKa, qro6u ee tvio>xlto6lt.[o us,roxllTb B onHoii r,taee HrH aa]Ke s oAHoft IiHHre. Matpavuaa a,rre6pa rox{e Aocraror{Ho c,'Iox{Ha, u ee HeJIb3t xoporuo H3,rloxr.rrbHa Hecr{o,'rbKnxcrpaHII4ax. O"q,uaxo. HaM I(axerct,. !;;!'r {iTo qHTaTejrb no.lvtl1n {_e^Ko-Topoe np€AcraareHr.re O MeToAax MaT_ alre6pu, sro .*i-?e3 rpyAa ycBonrbocuoBbr l-TT,9i _nosBon,i" Bt'IqrcdlItreJIbHbIX MeroAoB, Koropbre'6ynyr li3JroxteHbl AaJIee. laana 4 AHAJI I,I3 TIOCJIEAO BAT EJIbHOCTEI'I AAH H bIX CNI4COK .III4TEPATYP bI l. Dalis p. t., Th of matrices,2nd ed' John wiley york, Ig73,5en;na.thematics and Sons, ll-..:-Nu* ro reopurMarpnr{. c MrrrrManbHbrM *:X;3ilT.5;;Xtfipfl::.11-"ftvue6uar< Ko.,ru- 2 o;!;" i "';;;'"i^ffi:,"l,l"1#,lii , c:j: .ii;, J,!?t?f flfil;;,: ;;; ed: Bro. F?:.lf Monterev, ci.,'r-rjdz', *: ::ll. c-o., ;. " K'ura tB'lsercs oinrru s3 Har.tnyqulix pyr(oBoAerBro ;r''ipr'##;;..?t#t"u" 3' could P' on the.^g"eographic,interpretation^or eigenvalies: ration:Trans.Insr. Britis-hdrcolraptersj;;.';;; an initiar expro. 1967,58_86 o. t'lHrvHrusHbrir B3rrra Ha reopr.lio..ioo.rs.n;or;,.rra,reHrrfi u nexropor c HcnoJrb3oBaHHeM reorrerp'qecK"-..::i.4gi_"Jt--M;;.p;; orJraq'ofixni.rru,npe4uasuaqacrllrlHo "roii ":'ii fiIi #t):"tN "no'o'bsan l ^l{.- P'u.rog,u.r-o.-r lr iiror. ": york, Igdfl?tii'|.'"alvsis-a practicalapproach:Ma.tffi'rl'oo'prtr. Lo., .lnc.,New (-olepxrrTnpor{eA\.Dhr k jXT" ;ol;&?"" T.il;,fi 3;ifi :Hiil?Ti lffli"",1i",gll5$.;1"ff :fJ.XT 1"*1 )'fJl#: $ttlifrezzo tslal groM B A. "f' Matricesand iransformations: Dover,Inc., New york, cxpouuou neDeu3qagr.ltH3Becrgofoyve6Hrra c,oAepxarc, TpaAuquogHbtir o'qsoceu-ecrpo"o"v ffiltj#rtlr*: *vp.i' "l"pit,il'i a.,rreop'l ni-"i"nfr&""p'Mephr theorv andrinear argebra : Hor t, Rinehart, ft,f3;;f:^rnc" 1;Jl liS#?l?il',%il N.*-voii', i"e;i:'i ;? "ill ;: flil J:::gl Bsoaubr-ri *ypc . nb,l j analysis:prentice_Halt, T"ft ,, ,o,:lt,;S:opr'yliiri-rienal "^", "tri::";t:"ff f f,, f N.l" ieb;, ,tf".,"u1gt:ggg ;66"; _cl, ;',iJ"? l,'iiJ;e'ne -;;;;'.;; Bonpoco', cBrsas'hrx "x?y,:,9:l.t.xl*t,y.:::f €BepTrrI. .l"bld:;**"; c oneparrrerr NOCJIEAOBATEJIb HOCTH T EOJIOT Hq ECKI{XAA H HbIX B srofi r!'raBe MbI paccMorpnM MeroAbI HccJIeAoBaHsfl. AaHHbIx, rioropbre xapaKTepn3yrorcq cBol,rMnoJIolKeHHeMHa rprMofi. Anq TAKilX AAHHbIX CYUIECTBCHHYIO POJIb HIPAET MCCTO, 3AHHMAEMOE HC- 3HatteuueM B 4aHuoti noc,leAoBareJlbHoKoropblM onpeAer'IeHHbIM crg. MgoxecrBo AaHHbix raKofo runa r{acro Bcrpeqaercg B reo'lorlru. HanpuMep, oHLI Moryr npeAcraB,'Irru co6oil noc,'reAoBare,'ibn I'vIllnpt43HaKoB,reoxIzMLIqecKI.{x Hocrb sHaqeg[ft ,]rLtroJIort{qecKI.IX HeparornrrecKl{x xapaKTepncruK npo6, nsnrbrx IIo pa3pe3y I.IJ'IIIB 6ypouoii cKBaxLIHe, gHaqeir[fi gJleKTpt]qecKoroKaporaxa ueQrrHbrx cKBax(LIH,3apen{crpnpoBaHHbtx nplr6opal,rH. K atori o6uteit K a r e r o p l t r l M o x H o o r H e c r H T a K x e A a H H b l e ,H 3 M e H f l o l q H e c fcl T e q e Hr.reMBpeMeHI,I,HaIIpl.iMepH3MepeHHtlcToKa BoAbI B peKe, xapaltTepricrrlKu Ao6nqtt ra3a Il3 criBaxiLIHbI.Me'roru lr3yrleHrq nocJleAoBareJrbHocreiioAttoittepHblxAaHHbIX MoxHo orHecru K aHaJIlI3J/ Mofyr BpeMeHHbrxpg,rl,oB,HecMoTpflHa ro qTo [oc"tIeAoBaTe,rIbHocTI{ ea , K H n p O C T p a H C T B e H HSbaI eB H x a p a K T e p r r 3 o B a TKba K B p e N I e H H b IT cl.,tMocTi.l. llpexi4e qeM [epexoAnTb K fi3'to]tieHulo MeroAoB Hcc,'IeAoBaHHfl TaKnx lrocr'reAoBare"rssocrefiH paccMorpeHl'llortptlMepoB I'{3 reoJlo['uH, ocTaHoBulvlc.rrHa pa3JIHqHblx TLitrax [oc,'IeAoBaTensnocreii npfixo.4ljTcgBcTpeIJaTbctlteOJIOfy'3rO UOXer ;f,?HHtiX,C l{OTOpbIMI{ 6rttr, nocrreAoBare,tbHocrl a6co"rrcTHorotiHblx llsuepeHnft KaK 3Haqenuii usyuaettoft nepenreHuofi,TaK I'I sHaqeHilft iIIKa,'ibI,BAorb Koropoli p acfloJl.ox(elrblpe3y,'Ibrarbl l{3Mepenuil. 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Bo-eropltx, ltuTepBa,'1bl'BAO,'1bKOTOpbIXpaCIIOJ'IafarcTCfl AaHHble' TOXie nMeIOT onpe4e.,reuHyn Be,'IilrlHlly.f.ny6nna CKBaIKLIHHs 900 M B .4,ecqTb pa-a npennuraer rny6nHy B 90 lt, a AecflrI.IJIerI{eMei(Ay 1940 u rITo H Aectrl{J'Ierl{e Me)K' 1950 r. ltMeer ry x{e npoAo"lxiur€ilrrHOCTb, lAl Y Ay 1950 u 1960 r. Ha errtx 3aMeqaHl{rxBBlrAylrx rpnBrra,lbuocrr, He cToIt,'Io 6rI ocraHae,'nlBaTbcfl,Ho, KaK MbI yBHAI.IMn Aa"lrUeirIreM, AaiIeKo He Bce reo,rotuqecKae fioc,rleAoBarerrbHocrH o6na.qarcr TaKr.rMrI cBoircrBaMLL B Kaqecree rrpuMepa paccMorpr.rMrrocJreAoBare,'ibHocrb crparrlrp a SH.lecxux AaHHbrx,o6p asooa uHyro Jrr.troJrof uqecKr{MH p a3HoBrlAHocrflMrl fopHbrx rtopo!- cJrara]oulnx ocaAoqH.y]oro,rqy. Taxori noc,rreAoBareJrbHocrbro Mo)KHo cr{r.rrarbcepHIo (cHlr3y BBepx) H3Becr' HgK- r"rlruirctlrri c,'raHeu- H3BecrHgK- fJruHr4 crnfi c.nageq- ttecqaHHK- yfo,'rb - r.rrnHllcrbrfi c.uaueq- HgBecrHgK. Mu xoruNt KaK-TO OCMbICTTTeHHO OII[CaTb 3Ty nOCr'IeAOBaTe,]IbHOCTb, O.qHaKOHe r.{ox{eMeu6parr A,'Ig Hee lxKa,'iy. OqeeuAuo, uro oro u3MeHeHHe "IliToJrornqecKHxnpr.i3HaKoBnpoucxoAr.tTB TeqeHHeonpeAe"'reHHoro B p e M e H I 4H, o y H a c H e r H r { K a K o r oc n o c o 6 a e u 6 o p a c o o r B e r c r B y r o xleii BpeMeHHoitrura,ru. Mu MofJIH 6u Hcno"rr3oBarb l,{otrlHocrb, HO OHa MOXeT Or{eHbCHr'tbHO II3MeHffTbCfl OT MeCTaK MeCTy,AaX{e. rropoA ocraercfl Heusil,{eHHotl. ecrru rrocJreAoBareJrbno,crb Tarau o6pa3oM, Hcno,lb3oBaHHeMorrlHocTunopoA BpgA JtI.rIIoMoxieT HaM B Ha[rHX HccJreAoBaHHsx. Tor Qarr, uro r.i3BecrHflKB pa3pe3e cronT Ha TpeTbeMMecTe,a yfor'Ib - Ha [IecToM, He I]MeeTToto 3HaqeHl{fl, Koropoe Mo)KHo6uno 6n Bbrpa3nrb qlrcJroM (ro, uro HoMep 6 s4eoe 6 o n n u e H o M e p a3 , A , r g H a c H e H M e e r c u u c l a ) . A g a , t o r r i q n o J r u r o ,totnqecKritl cocraB cJIoeB He Mo)Ker 6utl nupaxeH Ha .Ilacu'Iogott rrlKaJIe.Mo>Nuo ro,rbKo gaKoAI.rpoBarb tlpr.rBeAeHHyr,o noc,rreAoBare/'rbHocrb, Hanpr.rMep,TaKr{M o6paaou: l-2-l-2-3-4-2-1, rAe u3Becrnsx o6osuaqaercfl rrnQpoft l, rnusucruft c.naHeq- 2, recrraHuK- 3, yro.nr - 4. Ho raKafl, ycJroBHocrbcoBepueHHo ltpo* rr3BoJIbHaH He BbrpalKaeTHuKaKrix cooTHo[Ienufi IrleN4y pa3HoBIrAHocrgMH nopoA. Oqesr4AHo,qro oTa flocd'reAoBare!'rbHocrb craBl]T. IrepeA uccJreAoBare,trMr.I 6o.rluree qficJro pagflHqHbrx npo6,'reM,r{eM] sro 6nino B paHee paccMorpeHHbrxrrpnMepax. I4naercrcs, oAHaKo, Apyfue Bo3MoxHocru. flycm, Harrpr4Mep, Hac HHTepecyer HeKoropafl a3MepseMafl xapaKTepHcTr.rKa, BxoAflulafl B nocJreAoBareJrbHocrb. llpegno.noxaM, rrro Mbr ycraHoBH,'IB, 3naqeHus coAep)KaHrrft6opa n xax4ofi ,'rnro,'roruqecxofipasnonHg,H o c r l { p a c c M a r p u B a e u o i i c e p } I q . 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Xe.irarentrio 6bt,'Io 6u norry'Irttb c I{x noMolqblo o6uy}o B COCTaBefpaHaTa, oAHaKo 3TI'l AaHHbIe KaIraprr.IHy r.I3MeHeHUft u He noAAalorcs rpqMoii ItH' )Kyrcfl AoBoJIbHoHe3aKoHoMepHbIMIl [poBeAeH]rq_ aHailu3a Tepllperarll1lH.B Ka.IecrBe nepBoro [Iafa CerH. xeilareJlbHo r\{ox{Honocrpoirrb Hx oqeHK}I AnR paBHOMepHOft MexAy roqKa}ll,l eu6parl paccrosHl{e 0,5 lt. B Kar{ecrBer.rHTepBaJra 3,qecl MbI craJIKLIBaeMctc noJIo)KeHlleM,orJIlir{arcurul{cg or pac- 48 Pttc. 1.2. I l o c , ' r e J o B a T e , ' r b H o c TAba H H b I x , p a c c M a T p r r B a e M a qK a K cryneHuaran Synx. uufl liJrrr <ripuBaq npqMoyIoJ'IbHHKoB> JU 40 P i r c . 4 . 3 . 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Iioc.'relb-eareJlbHocrb, e xoropoii cocrosHl{e s oAgofi TolIKe B BepotrHocTHoM cMblcJle JIHIITb qacrHqllo 3aBl',lcltT__ornpeAblAyuefo cocrofHllfl, Ha3bIBaeTCR tr,tapxoncroft uenblg. HaSeaHHaq TaI( B qecTb pyccKofo MaTeMATVKa A. A' Mapxor:a, oua flB,'IteTct npor,leiKyroqHbrM SBeHoM Me>KAy no"'IHocTbro onpeAeJIeHHblMI{ (Aerep\{IrHripOBaHuttruu) U COBep11IeHHOCJIyqaftHbIMIi nOC.;leAOBaTeJIbl{O- [;glfa=[,ij"frf"lii *i] Kpr.rrepurt, onrrcautnfie rr. 2 #:.."-lly 191enufiMarpr.irlbr .1r_-111ouuHaer Ka)KAbrrl3,'reMeHr qacror riep"*o4u pHlo, B KoropytoBxoAj.rrxar na6.nro4e"uoe, cocraBJrseri(arer.o_ TaK rI oN(r.iAaeMoe qlic_ d'Iolepe_\oAoe. 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(ur..opr" eKrloqa'Ior nepexo4u-A-A, A-*C, C*A u C'-+C' H3 Bcex sJIeKortrduuupyeMbleKarefopl.lll Mofyr 6urs o6pasoBaHbl nepe-tr KoM6uHaIIuft D crpoKu 3.rieMe'roB Bcex B, ;;;; "i6oru A-jD, C*B u C'->D.' flo,'ryuaeuaq crargcrl'IKa y't ""^"""ajr', Ha qenl Maopaeiea yKa3blBaer cton,{u.Haur crparurpa$rnuecr<rrft 3 fal B U C H M O C T b KOtsa [epBOfO nOpgAKa' T. e. CTaTIICTUTIeCKa cyulecrByer MexAy AByMfl coceAHlIMI{ToqKaMLI.CyutecrnyrcT TaKNe cgor:rirsa MapKoBocrl{ Bblclxllx nopflAKoB' HanpHuep, noc,'IeAoBareJ'rbHocrlMaprooa BToporo [oprAKa yKa3blBaer Ha 3HalIIiM]'Io MI'I AAH' VC,TIOBHYIO MC}KAYTOIIKAI\{U, II PCAIUCCTBY}OUIH 3ABI'ICHMOCTb soil na AByx npeArlecrByloulfixrlarax. C norr,rbnrrrcMarpI.IIrbInepexoAHblxeepoarHocreft MbI M O X e l l oueHllrb,T. e, [peAcKa3arbJIHroJIorunsa O,0 u (Ha gea g a 6 , r n Aeurzn) Bbrue sexoropoii 4auuoft roqKll. flpe4no"'toxuu' I-ITO MbI HaqaJrl{c n3BecrHsKa(cocroruue B). 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TaK KaK ceiiqac y Hac B pacnopnlKeHullItMelorcfl HoBbIe HA6TIOACHHfl, MbI N{O}KCM IIO.].CqItTATb CYMMY KBAAPATOB, BO3H[I- K a r o u y m r r 3 - 3 a H e A o c r a r o q H o f ir o q H o c r H a n n p o K c l l M a [ u u ( s s r n ) , cJlyqal?HoliKoMn cyMM)' KBaAparoB, coorBercrByloulyp <<ql'Icroii>> l o H e H r e ( S S e r ) , K o r o p b l e p a 3 6 l { B a } o r c y M M y K B a A p a r o Bo r K J i o H e MbI N{OHA6,IrcAEHHI'I IIAP TIOBTOPHbIX HUii HA ABC qACTI.{.B C.NYUAC no QopMyJle xeM HaiirH Beflr.iqr.rHy n S S p 6: l l 2 > \ Y r - Y * ) " . 14 D7 l KOMNOHCgTA O6uraq Alcnepcgs a 6 ({lrc.lo cteneHefi cso6oarr tr3]leHqHBocrH SSn SSp SSrr SSpe SSr 4pur"pHr KarlecrBa npu6,ruxenlrq. Kp,,r"p"n coorBercrB's MoreJIIr, I n-2 (n-2\-k h F-r$HreDnfi MSn MSo MSl,' MSpa TAHHfl, TAK )KE KAK I,I CC I]ACJIO CTEIICHCIi CBO6OAbI SSrF:SSo-SSpe. (4.28) C o e c e M H e o 6 f l 3 a r e J l b H o , q r o 6 b t M b l n p o B o A I ' I J I HA y 6 r l l p \ ' ! o u { n e I.r3MepeHHf B KaxAoIi Tor{Ke, Ho ecJIH 3To cJ,e,rlarb' To aHa.rlH3 TaKlKe HcIloJIb3OBaTb y,x,acTcr ocyxlecTBuTb 6o,'Iee roqHo. Moxuo 6o.nee aByx noBropeHlat:t Yt EJls I(a)KAOfO 3HaqeHtlfi X;, IIpH 3TOM 6O,lee CJIO]KBbIr{[CdIeHHe BeIHrruHbr SSpr. CTaHOBiITCfl HeCKO!'IL,KO HbrM. 3rH r.r Apyflre ycoBepileHcTBoBaHHff ol]ucaHbl B KHI4faX flO p e r p e c c f i o H H o MayH a , l i r s yJ I u [ 3 5 ] , f i p e i i r e p a r r C u n r a [ 1 7 ] , u n a u r H e 6 y A e r { o c r a H a B J l u B a r b c fHl a H H x 6 o J l e e[ o A p o 6 H o . aHailH3a nptiBe' C x e n a u o 4 u Q a q t l p o B a H H o r oA L I c n e p c H o H H o r o A e H a B r a 6 n . 4 . 1 5 . I 4 c n o . n t s y a o 6 t e 4 u H e u H b l e A a H H b I e[ o A B y M ss pr cHoHHbIfi a Ha"Ipl3 H BbIql'lcJIIITe AHCnep cKBaxL{Ha M, BbI,TIOJIHI.{Te u s s r r . c p e a n e e 3 H a q e H l l ec y M ] 4 b l K B a A p a r o B s s " u f B ! ' I t l e r c f perpeccl{t'f. OTHOCHTeIbHO IIII'HPIL7 O[eHKOri gilf| 62y.x,T. e. AHCnepCHH n o OHo naxoAllrct QoPuY,re MSou: SSpu/ft, 212 (4.2e) MSe'.lMSpe6 n-l fAc R - qrrcd'roToqeK, B KoTopblx npoBeAeHbl lroBTopHbrer.r3MepeHHr{. B HarrreMcJryqae Mbr cAeJraJrH3To AJrg Bcex ToqeK, H [o3Tou1- ft paeHo nf2, rax KaK rroJroBriHaHa6JlroAeHr.rii Yt Ay6nupoBaHa. BoA'1urorNre,iaJrlr,qro BeJrr{qr.rHa SS2 annxerct Mepoii Ar.rcnepcur.r KPi/f pefpecclta [Jrloc HeKoropoe cMerrleHae,Koropoe Mo)Ker Bo3HrrKlryrb H3-3a Bbr6opa HerroAxoAqrqer?MoAe'rrH,n rrosToMy cpeAHee 3HaqeHHeKBaApaToBssrF fBJrfleTcs orleHKofi ToJrbKo 3Toro cMeuteHflfl. MbI nox<eu npoBecTrr rrpoBepr(y [prrroAHocTK MoAe,'rH, BbIrrHcJInq 3HaqeHHe F : MSul(I4Srr). 3ra senlt.{ilHa nMeer oAHy creneHb cBo6oAbI Arfl Kax(Aoi'tro'iIIyTeM Bblql{CyMMa KBaAparOBSSrr HaxO.U,llTCfl KI{, a OCTaTOqHafl MSa/MSo' (4.30) Ec.[a ssrq[c,'renHoe 3HaqeHr.IeKpHTepaq flortaAaer B Kpnrr.rqecKylo o6Jracrb, To Mbr AodrrxHbrcAeJraTbBbrBoA,qTo flocTpoeHHafl MOAeJrbHe OrBerraeTAeftcTBuTeJrbHocTlr. Ecnn nponepKa He npHBoMOACJIPI, TO O6E OUCHKI{AH,CNCDC}Ift AAT K OTKJIOHCHI,Irc MO)KHOCJIO. )KHrb (I4Sz rl MS ou:7y1So) re orreHr.rrbKaqecrBo arfipoKcr.{Mauur{, KaK Mbr lelaJrri 3TO paHbule. Bltqfic,rure .F-oTHoUeHHew Aono,rrHltr e i a 6 J r . 4 . 1 5 , a 3 a r e M o n p e A e n r i r e ,t B J i t e r c f l J r I { s r a n p o c r a s J r n Heiir{ar MoAe,rrbAocraroqHo xopouer?. Ha pr-rc.4.lZ wio6pa)r(eHbr qerblpe Bo3MoxHbIe curyalrl4l'I Arq AByx xapaKreplzcrl{K, oAHa LI3 K o r o p b r x - c o o T B e T c T B H eM o A e J r [ , a B r o p a f l - K a q e c T B o a n f l p o K c l i Mauar. He;ltHeftnafl perpeccfis lloc,ue Bbrr{HcreHarr^F-rprzrepua 4.nn npoBepKr,r coorBercrBufl MoAera Bbr6oporrHbrM AaHHbrMBbI Moxere npalirn K BbrBoAy, qTo nptMafl Ju.rHr.rfl HeaAeKBarHonpeAcraBnrer ;br6opry. rlro AeJrarb nOCl1e 3TOnO, 3aBI,lCIiT OT IIpeAMeTa HCCJIeAOBAHVfl t4 OT BaIIIlrx 3Ha- HHii H,'tHAofaroK o coorHoueHalr MexAy [epeMeHHbrMH X H y. 213 a c' -;---:- " L KOpOcrb P1c. 1.18. Teopern_uecxatrpaeKropHtl oroan,,t 6ortl6u, c6poueHIIoftc caMo- t a J JIETA b o f o p o \f, ? . ocl c) ao r o ll aat- j g -!---:-t .Vpanllerrue,B KoropoM Bce nepeMeHHblecyMMupylorcg, IIa3bIBa' T a, K K a K C o o r H o [ I e H I ] sM e x A y B c e M Hr I a p a M HH M e ' ercr JtrrHerir{blM rpaqlIzKaMH IIpqMbIe iltrHLtH. Pacuupeuue nepBoHaro1 .'BorlMrr qaJ'rbrJo|oypaBHeHI{t]c IloMolqbl,o Ao6aBJIeHHflcJIeAyrcqHX Crene' P u c . 1 . 1 7 .B o s N { o r x H scrrey r r a l r, ' r H H e f i Hpoei ir p e c c H n[ 1 7 ] : perpecctlt lI TOrlllocTb atrnPoKa;tlraqxH yAoBneTBopilrrnbHilB: .t-cylqgcTBeHilat JdHcillrar y;loBncrBopHTeJbHofi orc)''r013He ,ruHciiHolt T0r:ttocrH atrnpoKCItiirl{HH: DerpeccHtr nplr TocllocrB antrpoKfts\r-:llHIl; cy!qecrBegitafl ll 3Lattn;lhl11 fleAocraroK llrHel'iHag pcrpeccll' p e f p e c c u H H : ; . o c r a r o K T o , i l t o c r I t S n n poilcnM:l:'ii' crcryrcrBlle H 3 H o ' i l i : j t r l i i l!leiiuoij dI z- tr'Iuoi',ta ilonilro nI,Ierb Bno.rIHe ojll)ere,rieiilloe l'lIieFille g q'r;r-tli ilepeirclilrrnx. Il:lrrpiruep, ec,xr{ ciil\tore'r c6iiiict,rGaer 6oM5)" ,' . IIpeIic6pcf eri cotii,rilTijiJJleHliel,lBe'Iijtll \1bl l,fr).,iri:rt{ ltire.icl'ia3e : i-, 'r: jeCp e l l i t i S C l t l r i O T p a e i i l O i r u l O , I i O l C p e t I O f i p C . r . e J l t i e T CCt li i o p O ' J ' i L ' i . ' . f i r i ' l ,teia rJ HZirpilB,'r€iiitoii{ ilHIt3 ycKopeHireM cDoSoAtlcfo f,rrr cHii. ( p l c . 4 . 1 8 ) ; - r e, . c r e h r e , T i t i o , I l a p a 6 o , ' I a o q e H b x o p o r u o o r t t l ' . , i B : l e ' i TpaeKropHio naAeHr.{fl 6oLt6st. c apyrori crop0}Ibl, \IbI }I(}xieil ilrlqei'O He 3li[l'i'I) O i]:lBilCIlMOCTit l!{eiKAy ;lUyIIti IIepeMeHHbl}'Itt -i' il y (ee l,tc;rxe'r lr {ie c}'[iec'r I]oBa ib) tt ltpoc'ro .)io'rI1]{ Iiorriyql{'lb, IJrJlpa) r i e r i l l e o J . i i o i i r i 3 H u \ q e p e 3 A p y l - y ' 1 , 3c. c ' b i t l H o I I l u r l i 3 a A t q ' i H a r o A t T C > 1M e ; j i . l ) ' 3 ' i i l M I l " l ' q v l I f l l i p l r l H l l l ' i u C J l t l n n ' t , , : M I d I l i l e J I l o J a l a erlt IIa,:llrriire uDr.irtlrilHoir cBff3H, HO IIe 3lineX,I ee QollNlbI. B tloc.leAe J)'I!rt,!1X \.{i,] \{oxieM rlo;io6iJil'ib 3llilp(rl(cl'lrTlrD)10u{ce llrrr IByx rliO OHO il0-,1O)KeT )''pilBl{ellIle K rll'lCiCii{lillCti IallIlLINl B ii:i;(e}l{/le' tl:rr'I npCflCHrI'Ib Cyl]{eCTByIOUIIe COOTITOlxeHI{lluJIi{}Ke TO'IFtO OtI]lca'ib Oopr\4y:ji:stict.tliocrir IreperlcHHbIX,{ I1 }". TaKIle yireBHeI{iIti B i i 6 : t l t a r o l ' c ' l I l 1 1 ' I C M y ,q T o c l l - \ i . i o i r l c l ] i i , t { -.r\ ' - i i l e T c r ia i l f l p o l ! a l t M I I p o Bii',rL \iHCi'ire l(":iilaei,l rf y tniilttii, il IICllc.[b3)']OTCtl B Tex e ,jl\''].itix, liorAzl I4cjilFtiIblli BlrA tf ;'rititililr Heil3BCc'ieH. BosvorxHr'r p a3,rri lrllbre r rin bI aufi p oKCuMIipyKru-(ux SyH KIlfl ii, fi o qaule Bcefo H(rllo,lb3yefcH iio.rllilloMllnflbHi]fl annpoKcHMeullfi, 3aKJiloqarcularrcfl B TOM, qlC fJ liaqeclBe IlpH6"'lll)Kalouleii r!yurultll B.br6HIlaercfl cyNlN{a Ue!'Iblx crenetleli He3aoilcl.{Moii nepeltcn'xot'i: Y i : b o ) r b J i a b 2 X i 2* b s X i s+ . . . ' + b * X i ^ . 214 (4.31) H C i i r ] P I I B O A I i TK T O M Y , I . I T OI P A O I ] K H A q H H A E TI ' C K P I ' I B N f l T b C AO. A I ' I H jloiro.iir{lrrerbHblft gJIeH 3acraBJIfleT npflMyI.o l'I3MeHIiTbHzKJIOH,BTO' poii jiono,[Hured'tbHbtit t]fle]l npl.lBoALIT K Bo3HHI(HoBeHI'IIoAByx roqreK nepeili6a u r. A. vse.uHqaBaloulatlcf HCKpI.IBJIeHHOCTb IO3BOIjoAxoAHTb K I{CXOAHbIM roqHo 6o,ree AaHHbIM. .ll]rrilil Aefi/'rrrtr CTBHT€I'II,IIO, CC,{E ITi,]CTO AOIIOJIHHTCJIbHbIXTITCHOB AOCTIIIHET (n-i), ro JrHHIis fipoilAer rotrHo qepe3 Kax(Ay]o AaHHyIo rorlKy. O A r r a x o B n o c r p o e H l . t r { T a K o i i J I l . i H u HM a J I o c M b t c i l a , T a K K a K o H a H e flBrrrercrr 6o,ree eoQexrnauofi, I{eM caMLl }tc)loilHble AaHHbIe. I(poue 'foro, Hafi6oJlee BalKHyr.o HHQopMaqHIo o AaIIHoM MaccLIBe MoxHo qJIeHOB B nOJILIcoxp aHHTb c IIcilo,lb3oBaIII{eM JILiIIIb HeCKO,.'lbKI,lX HoMHaJTbHOMypaBHeHr.rH. Ha p14c. 4j l9 r.r3o6paxeHbr pa3rr.lrrHbre pa3JIIlqTLIIIbI fIOJII{HOlt{IiaJIbHbIXSaBHCI4MOCTeII, COOTBeTCTByIOUIHX HHM CrerreHffM 2pfyMeHTa. MaI{cHMa,'ibHaq cTe[eHb, Hc[oJIb3oBaHHar B noJlHHOMfiaJrbr{oM y p a B H e r { u [ , H a 3 b r B a e T c f lc T e r r e H b l o y p a B H e Ht{f, T. e. Yi: bo * bdr -l bzXi2 * bsXis -- IroJilrHor,rua,'rbHoeypaBHeHHe TpeTbeii cTeneHlr. Tarosa )Ke cTeneHb ypaBrreHliff Y;:bXi3, rax KaK oHo flBrqercff qacrHbrr{ cJlyqaeNi npexblAyqefo [pr{ be, b1 u b2, paBHbIx Hynlo. florusouHa"rbHoe ypilBHeHire crpot.rrcf Ilo Ha6Jr]oAeHHfM c noMotrlbro MeToAa HaliMelrbIUux KBaApaToB, a npo(ecc STofo [ocTpoeHHq Ha3brBaeTcg r0a6opoM Kpr.rBofi. llprr eurno,rHeHur.r HeKoroDbrx crarucrr.IqecKllx vcJroBufr KacecrB O a l l l p o r i c r r M a r l i r H H e e 3 H a r r H M o c T bM o f y T 6 u T b n p o e e p e H b r c I I o MOUlbrc pefpeccHoHHbrx MeToAoB, aHaJrorHirHbrx y)Ke paccMoTpeH- HbrM.3rrr crarHcrr.rqecKnenpoqeAypbr gBnqrorcfl cocTaBHoriqacrblo T a K H a 3 b r B a e M o f oH e n a H e f i H o r op e r p e c c n o H H o t o allails3a. tlro6sr alnpoKcnMupoBarb AaHHbre r{pHBori Bropofo rropflAKa , (HnH r.(BaAparr.rqHori ypaBKpHBofi), Hy)KHo cocraBr.rrbHOpMaJrbHbre 2t5 Y=-1,0+1,0x 9 = 2 , 8 + 5 , 3x - 0 . 4X ' - 0 . 0 1 3 r o u a r p u q H o e ) : p a B H e H I I eM o } l { H o p e u H T b , I . { c r o ! ' l b 3 - Ynqp o B r J ' l .3 . , 3 a u e r u v , u r o u e A ) ' p y . r , r a r p u u H o iai , r r e 6 p u , n p H B e A e H H y l o C r e I l e H I l H e s a B H S H M Oniei p e v e H g o l i . B b l c o x u e B X o A t l r a siu"grcreMy B M a T p I { q e ,p a B H a y , l B o e H H c n o r . ' l b 3 ) I e M a f l c T e I I e H b , B b t c o x a r r cartan u o i i c r e r r e H I In o r l l H o M a , x o r o p u t i l l ! { b l x o r r l } ' l n o l o 6 p a r l K H . l y q a e \IbtM JlirHHIJIv.3ro o6croqre,'llcrBo f B,'lteTcq lJIaBHblMHcToqHlzKoM lpOfpaMMaX llO.l.iHllOylta,rlUOia i n11pOo r u r . r ( ; O xB B b t q H C , l I l T e d ' l b H b Il X ' r ' a K K a l ( 3 J I e M e H T F ,nl p a B O f o H H ) K H e | O )r"Ia MaTptlllbl KoKCilt\,riiitiltr, Bc'llltlllH-l/ ;rll{rrruric'HroB Mof}'T Ha MHofo nopflAKoB IlpeBbluarb .r.i,.-ti,reu'ic,e nl}llBeCT}l y r J I a M O ) K e T M a T p H r { U . 3 r O B e p x H e f O "{eBOfO I1 C]U{eCT, rr u t l 6 X a U O K p Y f , r e H x f I l [ O T e p e 3 H a T I H M O C TB x i , l r i . r i - . i 1 t r rO r l e f O 6 1 r ; 1 1 ' rU e y C r O f i U A n b l eU J t l { H e L l e i t i i L n - \l r r r { t p a x , l ) C 3 \ ' " r l b T a T O M i 1 l . ' l c ; t i i l l ) l Lp . etrreHUflcrlcreMbl ypanueuHii. floAo_6noe paCCMOlpClille J l r i x i i , . ' 1 u qc o j l e p l K l l r c t l B K H I { f e v e c r , ' r e l i r < a [ 5 9 ] . Y = 2 4 , 1- 7 . 7x + 1 , 2x - 0 , 0 7X " + 0 , 0 0 x1" ( . i p . .x r r ' 1 t a M a r p t l u b t x o a Q Q u u u e H r o Bc r a H e r O I ] C B I I A H O I I , C C . I I H \ 1 1 , irl c l o , - r b 3 ) ' c \ {I i e p e M e H H y I oX 0 , x o r o p a R p a B H a I .4,rq BCex lia6, , ' t K ) . itr(r r i i - \ i . M u l l , t o x e l t : J a H ) ' M e p o i a r b B C e c r r p o K H u c ' r o r 6 t l t t l t a t p i l r i l { | i r , \ ' p a B H e H I , l f lC r ' I e A Y I O U I I ' IOMO p a 3 O M : b i:I i:I *,"1_ Prtc. 4.19' Kpi,norsfio,'rrrr{oMrrarbHoii perpeccln rJrfl Bo3pacrarcunxcreneueiinepeuerinori X: 4-npt\ra! n I H H f l , c o o T B e T c T B y r o u a qM H o f O q J I e H yn e p B O l i cTetret]n;6_ KBa.[DarHqecK:it KpBRafl u;lt (prBafl Bropofi creneir; a _ if,iri'n, nnn ng^"u, TpeTbefi cTeseHe: ?o xq veer iBr iei ,p r o f i c r e n c s x K p i l B"ay q HerlIrfl c BK!'IrOr{eH}{eM qJIeHoB.,II,ea nopnaaJlbHbrx AOno,'iHrireJrbHbrx ypaBHeHHs (4.13) H (4.14) rpeBparqarcrcfl B coBoKyruocrb rpex ypaBHeHr.rfi: 2Y:bon*bDXtbz2X2, lXY : boZX + bt2X2 * bz1Xa, 2X2r' : bo2X2* bDXs *.bz2Xa. (4.32) qro cyMM14 poBaHHeBL,riroJ,rHsercn tro BceM -flo4pasyrvreBaercs, Ha6rroreHuffrvr or I no n. llepenuiae ux B rvrarpuqHoft tto_ SopMe, nyrlaeM r . f#::':,lfr:l-t;hl (4.33) L>X22X'2X'J L A 916 Y ll Il (4.34) 3 . r c ' , r e u r u rM a r l l x u b r l < o s r p S i r u u e H r o Ba, r a K i r i e c r o , ' I 6 u o B t i o l t p r f u u r r e H i o n b u t r l r a e n x q a c r e i r Y r g , ' l R r o r c qc y M l I a M r I c M e t t r a H H b t x n p o r r : r n e i t e H l l ie " r e r a e H r o Bc r p o K I r c r o " r 6 r l o s c 3 a A a H H b t l I I .Hi o M C p a v r r . I l u e r r B B r r A Vc H a q e H u e. X 0 , M b r o i l p e r e , r f l e M 3 , r I e N I c H A T t, | .l: r t , A p y f r r e s d r e r , l e H r bele p x u e r i c r p o K x n o , I ) / q a l o r c f l) * N I - t t o ; i i e l r r €r r I u a c o o r B e r c r B y l o u r u i r c r o " r 6 e q . H a n p n u e p , s " r e I t c r n . . l. - ,I r a ' f p H u b p t aBeH:f3'X2,::X5. HanouHrlu, qro Irpn yMHoi r ( c r r u l r i r o K a 3 a r e , r l uc r e n e l l f i c K , l a A b I B a r c T c f'l1, . e . . X o . X b : X " + 0 . - i . . r r i r . ' r , ' r r o c r p a q u rerb r u H c , r e H r n ir,r c n o r b 3 y e M b r xn p l r n o c r p o e H l . u ri . J ) ;B H e H u f lH e , r [ H e i i H o l ip e f p e c c u l , n p o a ] t a l r u 3 H p y e Mc o B N { e c r I I ( ) - l r r l i r i , r c' r a 6 a u u 4 . 1 1 u 4 . 1 4 . f l o c r p o u M K B a A p a r u , r r r ) ' racn n p o ticu\Iaur4lo, qro no3Bo!'ruITHaM y6e.qurtca ts ToM, riro IroBbrureHIIe cTellelrlr ilpHBo;IIrTK 3HalIi4Te,lbHOMy yr'tyq[ieHHlo KaqeCTBaallnpoKclrr'lii u Hu. Ilo;ulHol,rna ilbras. KpriBafl nlopoir crefl eHrr, nog,o6paHuan K 3 r u M J . a H H b r Ml ,r : o 6 p a x e u a u a p u c . 4 . 2 0 . B A a H l t o M c " l y t { l t e y p a B H L - l r Jpr ee f p e c c r r l rH r r e e r c , r e l y r c u r u r i n u g , : Yi : Po* prX; * 9zXi2: 122,9-7,9Xi * 0,1X,2. 2t7 Puc. 4.20. Kpunan no.nuuollnanlHoir perpeccriu nropofi creneHu,nor'ryrreHHaH no 3aMepaMBJ'laxuocrn,B3flTbIM n3 Ta6nHq 4.ll u 4.14 Ta6nsua 4.16 onpeAexenlllt 3HarlHMocrtl flHcr;epcnoHultfi auanfis Anc perpeccg[ rloflo,'IHt4TelLHblx rt,leHoB s nerHHefiHoii :n.-...,,,,-Fl, lr"^, I | c 2 I rr u4oS Ro z, lllsn'"1lSp'"') i:r oe^o r o,,- i SS,- , I t I us,-, | /vts,-,i,\I.s,,toi - ^e f-p.c' c^-' I , , : r-a-f l p I rll cS( n^ r^ S | I itl _____t_l ittl ! " '- ' l 'r ts '- 'i 'tts ' 'll ltl _----i- B sroxa rrpIi Mepe HeoSxoAIIx'rIie A,rff BbrnourHeHlr fl .ar,raclreD cli o HHorO aIIaJI[3a CTa'r.IrCTI]I{Lr tipHHLIivIarOT C,{elyrcil{He 3HaqeHHr: ssr : 21363,0; 5S' : 689,8; R2 := 0,97; SSR: 20673,2; S S P E: 1 2 6 , 0 ; R : 0,9B. .rlerxo y6eAHrbcrr,r{ro 3rraqerrusssz fi sSpr raKire l,Ke,Liilri!i B cryqae rliueiruofi arrl]pOKCANrar-\riH, TaK K:1ricrr]{ He coAepiKarorleHOr(Be"rr4r{}tu }'. ](ax x,{ox<Ho 5sr,toorr<rz1arb, 60"reerlt6rar KBaI\l)a- TUqHafl Iipi{Bafl 6.tri;r<e noAxojlfi.r r Ha6,rrc,laeMbrN{ Ar.lH}rbtM, rlgy ilprr}ieri Jrt|Htlfl. cymlrit Ktsar,p:iroB ott<,togesirii orHocI|r.t,'ibHo .lrrHirrr pefpeocufi ylreHbuH,L:.rcb c blT7,8 Ao 699,8. Oio t-trtli,ruoe yh{eHbueH]le, IiO 3ra pa3Hitr,a ire tscefAa 6bt}laer. cro.li; :Jr;lrrfi_ ' fe i i b H a , 1 ' a 6 n r r q y t l H C i t e p c i i o l I l I o fo a H a , ' i t I 3 a ] r i o ) t i H o c H o t s ; r i ) a i _r , t r { p r . i r b , A r r an p o t e p r ( r r : i o i i . r a p l x r e p r r c r t i K u ( r a 6 " , i . 4 . 1 6 ) . I(ax i',to;xtrc; ),,BriAeTb lr:: liofi Ta6,,ti.iIlbr, cy,\{1,{a riBrr,-{p.,tIofl lio"tyqaeTcn B pe3yJIbTaT€ Br:irtxT3HIifi cylitIL,i KIlztilpliToB ;l,ri)r Jrrii{eii_ uoii tityHxilriu s5a1 i13 ai{r.rcfr.{'lrroir cyrrtulr r(Baip.lro3 _.i.i!fi KBaJ.paTuuuoir tfyrrrrrirIi ss,"z. 3rl Hor]afl cyillMa r{Ba!,paroil ;m,1fl€.fcJ{ l'repoti yr'ryrruetrirn KaqecrBa 2rrpoI{ctrivaqlnt ts pe3y!,Ib't.lle Bile_leH I { f l A O i l O J H A T e J r F r r r o fror r . i e t i aB ) ' p a B H e H L I ep e i p e c c r l { . g i . , ; t r i r - c p l l l r (cra. ra6,rr. -1.16) rr,u B€r.rrieHH:rK , o i o p a a o 6 o s H a q e u ) r q e D-e el 16? ssz-r, rrcrro!'r-b3yercn itlrtr oqeHKr. Aono,'rHrrre,rbHoriaucnepclrii p e f p e c c f i I i . E e g H a t l l r N ' rrobe n p o B e p fe r c f l r o q H o r a K H M X e _ o 6 p a 3 0 M , r { a K U A J l ' . C a M O f Oy p a B H e H r z rpr e r p e c c H r i .E c n u o x o u , r a r , e . n u H O e 3 I I a q e H a e. F - x p l r r e p f l r l r o n a A a e r B K p I l T U r { e c K y I o 6 , r a , , : f , -T .o 2lB lina,rp lr i ]icHIte ,lroc or'n"no i fi n-J h4Snz I i.rirrt:lr ,'r'r'':rcpct,rtl ' ssr: , r 1 r r r r ,1 , , , i i f , i i l l l t , i l J ' r 1 l L! n t SSr l"-ri LIli,ilfaf]iillloio npoBel)ittr rr'.r;,jrnii 3Harr{riocrll xrt .,.. ,, i r. l . t , t c l , i l l Oc l n t , t i i r t u i i . liplli irrriert6tj' ytscrliccil}ltl KaqectBa KBaApartrqHoit annDoKcH- II ef o B pefpeccHio . t r Jj l i r : r ; , , i r i , i i i q , r e n A : i e r c y r i i c c ' l ' B c l i l l b l i l B K r a ' A I l e c ) / i 1 i e C TBSH. , . O X l l z l H r 1 r ' r ) . 3 H a t l C H X e EC.ttt,t X<e IIOJl\iilelll{Oe t,[e-i\.{] t't B 1 ) e fp C C q . X e H B K , l a A a 3 F I a q l i \ l O i O I i e A e i e T i.tO, ti .ri.()itOJI'itttTC.rII'lli,li'i c\'tI'to I{pIlrepIlii <(ii)) Mo)l(er 6uru or\'lcrllTL,, ilcr,(,'xorrttuio 1,,,,, qB!'IfleTCf' H e < 6 > T a l i l ' l M trictlili'llllbll\1, R 10 Birer"{u I(alx Kpl'iTepur} A'IIfl <(a>) IlpeLHa:JIlaqell jT6 rip{)1CXO.t\it'i'llOl'OMy, u'lO XpltrepHii I'I t ' l l ( r r r , : . i r , . r i l - l t t t O ' fC ' i t t , t O p i i B e H a T B e I I y . r i l O I i O l l 6 l ' l H a l . ( ! I 1 l r ' l l i H e i i H b I l i r l a c r b o } : : l ' N I o N i e r j t i , i l e l l o B . r i l l l i x n u H e j i l { r f : ' r o l t 1,llr.r i,,! i i llpil 'fO BpeMtl I{al{ BX.IlaA I{Ba'IlpaTtlqllOf O i r ' lL r ' , 1 ! l i l C O l i O 3 I i a r l l i N l O i i ' B 'iorta l l t { a r t e H I i e K p t l T e i i n t l < < a > >6 ) r ; l 3 T ;,,ielit f,\.'ic.r (rrletlb lrir3ritlM. a r O ; 1 a p l 3 f l a q i i T e r 'ibHLrNIJ' Br'1}ltlIliliO OX.}iOrO 'n}lL'\'tilrc; rrCitiibtX{ 6,f , : . 1 e Hj : " I i t l o u l r{o)l(eT oliil32'li:'lE. qio 3Haql1tr'ibI\ill tlB'rItlr:l:li:Ii1r : ) ' i( ' r i l r i ' r r o i l t i H l l : l A B y x , n u 6 o a 6 a r i , q e l I a , . r l l r 6 o I l l l o A I I F I I i : l ; i B Y x , r , ' r ( ' l i I r i l i i t i 1 l B a ' l f ] € ' t c l l3 I I i l t I I N { b l M . 3aBIICIl1l:ilr:c.qb y){c Mor, 33irle'fllTb, qTo lioppe.[rlur]oH]Iaf rl'lIeFIoil roH o E l ' l x 1,1(ri,'tl :1{.LiAa }'ijer'ilirluBaeTctl npli Ao6SB,rlcHI'1ll To xo(tt-1)' . r r r r l i ( ) \ i1i E c n l r r r H c J r o q . t e H o B n o J I I 4 H o M a A o c r l l r a e r or paBIlbIM 1,00 tlesaellcltMo 3qlqrltii.ileHr KoppcJ'tflUl.lli cralloBl{Tcfl i i : c i t c u u p a : 6 p o c a . u . a i { H b r xr o q e K . O A n a x o [ p I i B e A e H H b I e B b l l l r e K p l l reptiit itor(zl3btBalor, rITo yBe.rtuqeH[e Kogqb0uulleHra Koppe'[flul{l{ IJe H N { e e TC r a T r . i c T u q e c K } t Xo C H o B a H H f i .f l p H 3 T O M e C J I HC p e . ( I I H e 3 H a q e HHfl iirr?,np3ToB o1 K,'loHeHHii yBeJii'iqH;alorcff, ro 'F-orsotuenue, xa- 219 paKTepI'r3yloulee3Har{uMocrb aIInpoKcliMar{LrH, yMeHb[raercrr.oteHKa ALrctlepcIiIrqacrHqHo saBHcIIT or qlc,,ta ira6.trcneHrrii, ucrrt.r,,tl_ 3oBaHHblx,(,1q ee Bblqucd'IeHIIf , vrJrrlor qr.rcJlacrenetreri ceo6o!.1t. lloc"re4uee nocroqHHo yMeHbIUaercfl ro Mepe yBeirHrrertfirrq!rcr,ra x o a Q Q a q u e H r o BB y p a B H e H r r r p r e r p e c c r . r HH . inoi.lnl,u (cu r.rr.2), q T O M b I T e p s e M B T o q H O , c TH r ra K a ) K A O Mo U e H H B a e M o lrvi ra p a M e T p e oAHy creneur cno60gH Ir qro xoeQ$uqaeHru b rroJruHoNifta.rrbHoro ypaBHeHr.rEqB,'rflrorcffoueHKar,rHxoeQSrqueHroB pefpeccau p. rlpu nlrno,'IHeHr.i'uonpeAer'reHHbrxcrarHcraqecxux' ipe6oeaHari IlpolleAypy npoBepKli rHrrore3bro He3Haqr.rMocru 406an,rsenauxq,reIroB MOX{r'ropacnpocrpal{j.rrb Ha r{.rreHbl60,ree BbICOKLIX CreneHet?s ) ' i p a B H e H H rf r o d ' r H H O M u a , r l u opiei f p e c c I I l I . E c , r z n o , r y q e H r l ei i o r r o J r IIIITeJIbt{brxna6,rrc,qeaufi pea"ruuo, ro or? KptrrepHH Nrui.{(ltc) Hc_ X I O J I b 3 O B A T b A X O N T 6 H H A U U HC K P I I T C P i l E M N P O B E P K I i O T C V T C T B I - ' fIii P i i - 6nnx<euun, unu KpHreprreM rrlrcro c,rryuaiiuoii xo.urnorreursr. . I ' T a O J ' ]4 . l / n p I l B e A e H al o n o , r H f i T e r , t b H acqx e M a AItCireDCr.{oHHoto a H a J u r 3 aA. ., ' r f K B a A p a r H , + i o r p i erpeccau H O6reruueuHoii nu60pxi.r sgaqeul.rir B,'ralKHocrlr ocaAKa. B u e x o r o p u x c J r y q a r x H a c M o x ( e r a H T e p e c o B a r bH e r o J r b K o r r o - TYqEHI]E OIICHOK B 3AAAHHbIX TOqKAX HTI,I OTKJIOHCHI,Ifl OT JII|HHH pefpeccHll' Ho 14 ee HaKr'loH I.I 3HaqeHae, npH KoropoM 3Tor HaKJIOH H3MeHflercf. B xaqecrBe npHMepa 3aAaqH raKoro rrifla Mbr pac- Ta6nsua 4.17 Pery,tlraru AHcnepcnoHHoro aHaJlx3aArc onpeAereHrs3HaqrMocrfi KBaAparli,rHofiperpeccr,r,coAepxaHnn BoAbrB ocaAKer r,ry6ntrrr Hcroquux Ir3\teHquBocra Cyrrlra xta4 PATOB CpeluHc KBallpaTbI I-rDqrenall ,rlunefisas perpeccfiq :277 .83a :98.96 O6uraq AHC11epcfiq alra,qpararH,aa perpeccHr Bbrcoxo 3HaquMa. pefpeccHr n-pHBoArir x 3HaqHreJrbHoMy yryqneHHro c^,,^.-.1.{":ao":lrqHae gMalulr no cpaBHcHHpc .nuseilsofi perpeccuerl. 220 xaqecri};r aflrDoK- n oT b C K B a X { u H e ' CMOrpriM crparurpa$tlqecKyIO 11OCJIeAOBaTe,'lbHOC 'tacttl noo6vpeHuori n nopo,qax HI'I)KHefo naJleo3ofl B BocroqHofi gB;1fl,locb BoCHccd'teAoBaHI.{g feo,'IofHqe.cKoro I_le"rrurc Oxnaionu. c T a H o B ! ' r e H H ey c l O e u f t , c y x I e C T B O B a B U H X B O B p e M f l $ O p n , 1 H p o e a u l t r H or,lo;r<eirnir. LI:y,leHHat roJllua cocroltr ll:J c,'IocB aJ'leEi"o"lurIl t I T o I I N I e I oT o l l l l K o T o p b l x AonycKanocb, riecqaHLrKa,oTHOCI-ITeJ'lbHo IIp€AIlortO}KeCAe"raHO feOJIOfaMH 6u,rO IlpOHCxox{AeHHe. ),.loDCKOe Mepe H11a,qro ocaAoqgrtii 6accelig 11ocrerleHHo IIano,'IHflJIcg, 11, no KMecrro HarrpaBJreHLrIO ilLr]ginfl, npoABlrfa,'racb TOfo KaK 6eperonat TOIroatO)r(et{t{toCKBaXUHbI, MOUIHOCTb1OCJIeAOBaTeIbHOO6pa:OeanTbItUItXCrl Ci-'IOeBIIeCllaHHKa yBe!'IUqUBaJIaCl. TO,rUa HaCql'ITbIBa,'Ia H3Mepflrb Ka>KAbIfI ariue o6peueHttreJlbHo Nf 6r,I .51un anoau u 6st,rO C"IOR i r : : i H H X . B r t e C r O 3 T O I O 6 b l , l a X 3 M e p e H a M O U I H O C T bK a i K A O T O n3MepeHHfi (3 Nr). 3ru irecrr:rritjKaqepe3 HHrepBa!'I B 10 Qyron I.lHrepecHo 3Harb, c-VulecrByer feonory rf)riBeJCHbi n ra6.l.4.18. OTAe,YIbHOTOCJIOfl I'I O6qeft 3aBtiCtiMOCTb MelKAy MO,XIHOCTbIO "lir t{TO CyMMapHag rroulnoCTbtO HaKol,rteHHOrO OCaAKa. OrlterHV, a MOilIHOCTb roql{ax' rfgrcuponauHblx B l",lollHocrb X usueptergg rrHAirBrJAya,'tbtlblXCr'tOeBpaCCMaTpl4BaeTcq I(aK CJyr{afiHatl BeJIIIqHTa6.nnrra 4.18 M o u l u o c r s c r ' l o e n n e c q a H [ K a B K J I a c r H q e c K i l xo r l o x e H l t t x HqlxHero nareo3oc n Ox,naxotue HHreDBa,r.\, $Yrut l0 20 30 40 50 60 70 80 90 100 ll0 120 130 140 150 160 170 180 190 200 210 220 230 240 250 I l o u r H o c r b Y . . u r o r ' l u nl l t t u r " o o u n . { , $ v r n ll qt 7,1 5,9 6,2 4,1 3.9 5,0 44 6R 50 6,I 7,7 7,0 5,t, 9,8 6q 5,2 6,8 8,5 7,1 10,4 6,7 8,6 A4 260 270 280 290 300 310 320 33(-) 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 M o u r H o c r b} ' . g o i l r m t 8,5 8,9 10,7 144 tE o 1 2, l 15,3 9,0 ll ,2 8,9 9,0 65 11,0 t? o ol lt ,2 t 7, 3 15,8 ll,l ilI l8,9 9,6 t 7, 9 12,8 15,0 221 rI tr4ttutr'tl'l Ha, qro rro3BO,rrrieTHCIrOJrb3OBaTbperpecclloHHyIO MOAeJIb. B 3aKJlnqarculyrcctl fHrIOTe3y' rlpoBepl'ITb c,rroBar{I4,feoror loJIX{eH oTHyJItl. o T , ' l l { q a e T c f 3 H a e l z M o i r l q r o p e f p e c c H r { x o a t } s H u r r c r { r TOil{, r o n i l c a H H b r M B b r u e N { e T o A o Mn o f l } ' q e r l o y p a B H e f l o c . n e r o f o r ( aH l v l o l K r l o o U e H l l T b A H c l l e p c ] 4 l ' oo T H o c l i Hue perpeccvu Y;:bc-lbrXi' BeJIHTIHI{)IflfSo. flOc.leA}Iioio IlCIIoJlb3yf Te,,rbHo JrlrFrrru llerfecCuu, t-cTa'IllB CBOIo oqelleAb I\{O)KHOUCIIOT'lb3oBaTbA'[tl BblIIllcJIe]l]',Iff C'III KH: (4.35) (MSn), c n e a u e e 3 r i a q e H l i t r i B a A p a r o B c, B r 3 a H H o ec o r K I C I I e H u e u 3 r o yKa' I i a K c B o 6 o t b l , c r e i i e H e i ? n 2 H a pie'o SSl, .lcnelr'oN{y H a xorurS S x r { B a I l : l r o B c v i l r M a I 4 c i p a B r ' i e r r r r a r 4 . 1 2 . r a 6 t . ;;;;-" cfl n0 $opvy.ne tl 5:y : tE-t,." #,' 3r'a tsertrqill{r I 91,\i----{2Xrf n . 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(lilloiliTe,{Llio fipocTo lonyqaTb cTojlbKo Tor]eK rta xpilll;;, (,r{rJi]l,. r<ororpeOyerca. 241 CETMEHTHPOtsAH Hb!E [IOCJIENOBATEJI bHOCTII 3ounponaHue 3onapooanue-gro pagAeJre'He nocteAoBareJlbHocrrrB orHocrrC,'IbHOOAHOPOAHbIC CCIMCHTbI,rAX<AUfi I.I3 KOTOPbIXOTJI[I!IE}IOT , r p f i , ' r e r a n r r u x c e r M e H T o B .l I a . r I e o H r o n o r u , H a n p u M e p , n p u 6 e r a : c r ;{ 30HUl,\OBar{uro crparHrpaQuvecnofi noc,reAoBrrerbHCCTri Ha ocI{OBe.COOTBercTByroqefi us6brroqHocrH }rcKorraer{bTxMtrKp03,'reMeHi ' c r . { a n n u e o n p o 6 o n a H H f lM o r y r 6 n r s p a s , q e J r e H iBr r o r g o c r { T e , , i b Ho o_T.r{opolrrrrie I.rHTepBaJrbr tr 6lrlyr jt0G;-lcr?B,rIflTb 3oHbr Itocro-riir_ HOii coorBe'lcTn1,rcuieii crparHrpa$fiqecriirN{ errlrir.iu:I\.r. "rriro,!oirrri, 'r iiorvqennLre no;;lrrnrioii pirrror{ery}rrrccri(.;ri "(,1;tttlte laBepcoB, pa:se;lnoil, Iloil,paeAer'irroTCf Ha 3oHLI, rioropi,re :"roryr 6r,iir, riHrcl,_ Ilpcl lipcBarlbl IiaI( Iloqca oA]{opoAIir\ix ci(aJrbilbrx crpyxryp ri.irir u ; i n e pz r ; u ra: q l l i i . H u e e r c s A B a o c n o B r { b r xr r o A x o A a K 3 o r { i r p o B a u l r r of .l p o c r e i i r u r i i l 143 lul;( I{a3bIBaercrI <(uroIiaJIbI{brM ltoucI{or{ tpaHIIu>>.Oll ocHoor,u H a I l o l l c l i e B H e 3 a I ] H o r ou 3 M e H e H r i t Ic p e A H I i x s H a q e H u t i , r i J t H , r ] T o 3r{BHBadrcl'trFro, Ha IrollcKe naH50.ueec}i.ribljoro Ir3i'leHeHeqfpeAire:i Tir TIocJic.iaR:lrc;iirHocru.finn oirpc.{e",jeHIIfl t-paHHu l\{ctr(jlv frogBeirH b r D i H3 0 H a M } rB A O J Trbp a B e p c a v l 6 c r c p [ 5 6 ] - p a s a u , r u e T b 4 c K o J r b , Stlu{efo cPeAgero. PsA sHaqelrrrii rr3),qaercs ricc.qeJ.oBlireJrbHrrrr,{ .4BIl)KeHIleM K.o. p o r K o r o H H T e p B a J i a B A o / I b r l o c J I e A o B a r e , ' I b H o c T ' i r . L K o J r b 3 n u l l r i i.liH T e p B a " H T a 3 b r B a e r c foi K F r o MC . u pacnaAaercfiHaALe sacru: cefN'reHT o r r o g K a i * / z n o c l e A o B a r e J r b H o c r rrro r o q x H i u Apyroii cerMeHr or rorrKr.ri Eo ro\xu i-11.. Mepa, HasbrBaeMarro6o6ueHHsir,{ paccror{Hr.ieM,Bbr!rrIcJrflercg J.r;t pa3Hocreli ltex4y cerMeHTaMriBHyrplI AByx no,'roBHHoKoKHa. o6o6utessoe paccrosHHeecrb orsouesxe, o6iasoeauHoe AeJreurrex{ KBanpaTa,pa3HocTa Mex{Ay cpeAHr.rMH3HaqeHr.IsMHAByX c{ti_ MerrroB sa o6teAuueHHyio Alrcllepcurc [ocJreAoBare.nr,rrocrer? B cciM e H T a x .O 6 o s H a q H t r3 r o c p e A H e ec e f l , { e H T ao r . r i A o J i - p r e e p e 3 X 1 s efo, Ar.rcilepcHroqepe3 sl2; cpeAHee cefMeHTa oT Ji AO xr_r, .re0e: ,\2 ri Atrclepcurc qepe3 s22. TorTia o6o6u{eugafl pa3riocTr, Ccri) p. - (T, -7r)t (4.53) s , 2* . , r r 3luerirna, qro o6teArueHHafl Aucnepcnfl ecrb npocro cyliMa Arrcr e p c l r r ? I B y x c e r M e H T o BT, a K r a n o 6 a c e r M e H T ac o A e p x { i r o ! . } i r ) l i T O ) K e q I i : J I OH a 6 n n A e g H f i .T a x N < e3 a M c l i r M , v r o t i . i ; c l , r e ] J i i o i , r i l r ; I nlre 1r 'torrcK tIoc,'ieAoBareJ'IbHocrli He Moryr rlortacrb B pa3.nHqi{l-le 3tlHI:i. , flpe,r.cran,leHuena rpa$zre h xax QJrnxrluu D2 npuno1ur K r]peo5p:i:tonanuro rrcxoAHoto rpaBepca B HoByio irocJieir,oBare,'rbHocrb, i r . ; r c p o i i r i r a l r n i i b r 3 o H H r , r e r o rB H A o c l p L r x i r i i x o B . I - { a p i t c . 4 . 2 . 5 , a IipCrIC'l i.l3.4eHO iIepBOHaqaJIbHOe Ifi€CTTII(iLTOI{eTpODOe CeqeHlleB.ItC,r1b 242 OJ l- In a aa ,4 'ig :!,)0 tl ,l oi 4 .) ,,] r:tlleu;te )il: ti.l C':'let:li:. i.26. 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V j 6 c r e p o i ; , v 6 n H n o B a "IiI p o f p a M I \ { Yt i a s : b r x e S O P T P A [ ] ' 'tolirr:r peeij;l3J1e'io'i'or MeroA [Iaxox{Aeullt{ fpi]Hllt\ son [1"'7I rio .:A2 Ibr oluo r'{3 Bo3paxeHr.rrl nporHn MeroAoB JroKaJrbHororroHcKa upaHllll cocroHT B ToM' tITo oHH Mofyr npl{BecrH K noJ'ryqeHrrro Heo6uquoro q+cila rpaHarr, s qacruocra, i uau6o,ree lis^{eiiqasorr qacrH IIocneAoBareJrbHocrI].fro6a,rsHoe S0HHpoBaHHeocHoBaHo na 4pyrori HAee, a HMeHHoHa pas6aeHun [ocJreAoBareJrbHocri.tB 3 a p a H e e 3 a A a H H o eq t c J l o c e f M e H T o B 'K o r o p b l e B H y T p e H H eH a c r o J l b Ko oAHopoAHbI'HacKoJIbKo3To Bo3Mo)KlIo,lI orJIilqHbIor IrDHJIerarcilILrX CeTMeHTOB HaCTOJIbKO, HacKoJrbKo3TO BO3MOXHO. OAHa us nepBbrx H san6o.nee rtpaKri.rqHbrx npor{eAyp raKofo po;1a 6u"ua peKoMeHAoBaHa !,xul.nol,r f2l], xoropr,rfr uino,rrgosa,,r H r e p a q H o H H y r oB e p c l r l o A l l c n e p c H o H H 0 r oa H a d l u s a .c u a q a J r a I l o c d r r e A o B a r e r b H o c r b A e J i I I T c f lH ' a IBa cerMeIITa,oqeHb KoporKyro HaIIAJIbHYIO qACTb H OCTATOK IIOCJICAOBATCIIbHOCTA. CYUNAA KBAAPATOB BIryrpLr cerMeHToBssw Bbrr{acJrrreTcrr no Qopuyne " mni SSr: lm ) l Z)_lJt, . r, ,r , - A ' . ri ) . ,I 4\. '_ .l r r , - , n . Z_J i:l i:l I (4.54) i=t rAe ,rrr- l-a roqra BHyrpHi-ro cerueHra,-r,.- cpeAHee i_ro cer_ M e H T a ' n 1 - g H C l r O T o q e K a i - U C e r U e H T e ,r n - q l r c J l o c e r M e H T O B . C ) ' n r n r a K B a A p a r o B M e ) K A y c e r M e H T a M aS S a s B , r y q e r c nv e p o f t z s _ NreHEr.rB_ocrtr cpeAHHx cerMeHToB orHocprre,,rbHo-l .., o6qero cpe4nero o6teAaueHgofi nocJreAoBaTeJrbuocru HJrri srs,, " ' n-t m TI (k.,-X "-' U :' (4.55) i -1 P a a 6 u e u n e r r a A B a c e f M e H T aA B u x e r c r B A o J r bn o c J r e n o B a r e J { b _ r{ocru, ri B Ka)KAoM noJIo)KeHlIi BbrqllcJlrrlorcflABe ee,,IaqrrHtlSSuz rr SSo. A.tq KaxAofo Bo3Mo>KHoroIroJro)KeHr.is rpanr.rubrBbrrrr.tcJrflETCfl OTHOII]EHI,IE ssa-- ss, ^ { .: -....---. D,); (1.56) flo.rioxesue, coorBercrByror.r(eeMaKcIrMaJIbHoMy 3riaLieHirroR, Bi,r6 u p a e r c R B K a q e c r B en e p n o l i s o n a r s u o r l f p a r r r u i b r " ,[,a,riee, noBTcpeHHe]{npoqccca BcraBKU AonoJrr{iire,'rbHofirpirriuqrJ, Kor'opat cnoBa AoJril{na aaBarb r,rar{crlMyMR, erlr ABe sogbl CHOBarrc.tpa3,{errrrotcs. 30snpoBaHrie rioBTopf;ercrr Ac rex I1o;-.. 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Ec,r[ s pa3pe3e uaxrbr 6y4er co4epxartctr MHoro rroBroprrculuxcfi 3JreMeHToB, To 3To npnBeAer x ueo6uxuoBeHno BbIcoKnMgHaqeHr{RM orgoueuuji, xaparreptl3yloul'Ix coBnaAeHlIt, H K 3HaqlITe"IbHbIM orK!'roHeHuflMor ox<rrAaeMof0CpeAHeroqHcJra cosnaneHr.rfi. I4grepf l p e r a r r H n r p a r f r H r o n ,x a p a K T e p r r 3 y ] o u r u X8 3 a r r M o c B f l 3 un,p o n o 4 r r r i a a H a , ' r o r r r ( r Hror H r e p n p e r a u r r rK r o p p e r , r o r p a M MO . 4Haro r<oeQ$ilqueur B3aHMocBs3H Bblqllc,{flercqHa ocHoBaHIIIrHoMHHaJIbHbIX AaHHbrx,I.t B cHJiy sToro uuSopuaqHt, coAepxauaflcfl B rrocJreAoBaTeJrbHocTH, sHar{HTer'rbHo 6e.u,uee,rreM B oKB[BaJreHTHoM BpeMenH6u pngy. Tar MbI llcrloJlb3yeMKaqecTBeHHbre IlK AaHHbre,To He Mo>KeMoxr{AaTb Toro r(e pe3y"Ibrara, xoropufi MoxHo 6st.no 6lr no,,ryqHTbnpr.r aHanll3e Hacroexrrrx Bper,leuudrxpflAoB. Oror Qarrop neo6xoaui,lo yuanptl llHrepnperau[u pesy,rtraroB ro B3aHMocBssrMH aBrol:t^u^1lo accoquauHtM. r8-201 273 NOJIYBAPI{OTPAMMbI Tepir,tlu reocrarucrr.ira ceiiqac rxupoKo npr{Meuflercfl K clreqlr.ar'rbHbrM BerBflM nprrK,'IaAHoficrarHcruKlr, HarIaJIo pa3Brrrufl Koroporl 6n.no [o,'ro)KeHo f. Marepouor,r n lJ,eurpe lrareuarrrqecrofi rrroptlo,rornlr s @oHteH6,ro,tDpaHqHq. Uerr reocrarncrr{Krr cocroflJIa B trccJIeAoBaHuitnpo6,renr, noropbie Bo3HIlKarcT TorAa, KorAa o 6 u i q s a g c r a r r r c r u r { e c K a r r e o p f i t l r c r r o J r b 3 y e r c gB o q e H K e H 3 M e H e Hrrfi cc4epNaHufi pyAbr B pyAHoNrrene. 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Ec.nu paccroflHue Me;*'Ay A, to no'n5''paBHo uexoropofi Be,'Illq_HHe npo6arraano nprrvofi JtrtHLtLt 4ircnepcux rnrox<er6Hrr sr{q1rcilera Anr paccroaHuft, xpatultx A: ^( n: pefr{oB criBax{uHervrero:loM Kaporax{a.B orurnqueor c.uyuaiiubrx, Ilar'Irr3oBaHHbIe nepelleHHble He[pepbrBHbl oT Tor{KLI K-TorlKe, Ho I{3ilteHeHl4fl UX HaCTO,lbI{OCr'tOXiHbr,qTO OHII He I\{OfyT ObrTb OnilCaHbI I I i I Sl rx, - x,rh:,2. / M l \ (4.76\ T o r r o J o i i i e H u i is p y 4 u u x e . O A H a x o t o r $ a x r , q r o o 6 b e M r , rn p o 6 n orHoI'r \'rHolr{ecrBer3MepflnTcfl e x5'6rruecxlrx caHTHI\rerpax,a B Ha Ap)'ic:'1- n x5'6liuecrirrx \,reTpax, aeil:6ex<go AoJix(eHB,'tr:rflTb CXelly tl3lJel{qllBOcrll coprHocrll pyAbl, KOTopy}o lvtbI KapTItpyeI{ B p)'.{,rrn(e. f,raeuaJi gaAaI{a reocrarllcrr{Kn - cBr3arb pe3}r,'IbrarbI, [ o r ) / q e H H b r en o o A s o i i 6 a : e ( u a n p u r t e p , o 6 p a s q u r i e p n a ) , c p € i s L p l , r o f i 6 a s l r ( n a n p r r M e p ,3 r ( c [ , { y a 3 ) ' . q b T a T a N rrrri o , J ] q e H H b r M rA. n TarlrroHr{Iie6noiitt ) . feocrarlrcrrrKa no3Bo,rrterAarb or{eHKHQopuu pefuolra,'rIr3IIpo- [€peMeHB srilx o6o3HaqeHu.gxxi - 3HaqeHHeperHoHa,'IIl3OnaHnot? 3HarIeHIte, B3qroe uepe: & HOfi, nSRrOft s roqxe i; xi+n-Apyroe n H r e p B a J r o BM . m noeroMy HaIIJII{ cyMMy KBaAparoB pasuocrei? Mex<Ay3HaqeHtrqMHpefvoHar'r.r3oeaHuoiinepenteuriofiB rtape roqeK, qro qncpaccroflHueu Ah. t{rrc.noroqeK pa3Ae,reHHbrx.. _paBHon, TaK Jro cpaBHeHuliruex4y rrapaN{r{ToqeK ecrn n-h. Ec,rr uu Bbrqucd'raM rroJryAricnepcwuAJrtlpa3d'rr.rqHblx sHaqeHnlilr, To Mbr MolKeM HaHecrn pe3yJ'rbrarbrria rpaQun B Br.rAenorrlBapitorpaMMbr, se,'rsFourericraHaJroroM r{opper'rorpaMMbI. Ha plrc. 4.41 npeACTaB,rreHa rror'lyBapr.iorpaMMa, coorBercrByrcuafl r,ry6lrue ceiicM I I T I e C KO HT p a ) K a l o u l . e ffoo p t i 3 o H T aH [ o c T p o e H H a t n o H 3 i l l e p e H f i f M B A o J I bc e i r c , u r q e c x o r on p o q b r r . n rn, p r r B e A e H n o r os a p u c . 4 . 4 2 . 3 a u e T H M , r r r o K o f A a p a c c r o f l H r i eN , r e x { Aryo q K a M r r o n p o 6 o n a u u f l p a B H c { } t . r i o , T o 3 r r a q e r { L iee x a N A o r ' rT o r { K ec p a B H r i B a e T c cg c a M H Mc o 6 o i i . Cure4onareabHo,BCe pa3HOCTilpaBHbr HyJrrO,H noJryAHcIIepCHR Aj1fi Je ecrb Iry"lr. Ec,'rr.rAft - ualo6 paccroiruue, TorrKr.rrrpH cpaBHeHril.i oKa3brBarorcfloqeHb rIoxoiKrrMt4,ri ilonyAr.rcnepcI4fl6y4er MaJra. llo Mepe yBe!'rr{qeHfifl paccroffHufl Aft CpanuunaeNrbre ror{KH craHoBrrcfi cr'r?o€ecBrr3aHHbtrvrH Apyr c ApyfoM H paccroflHr.rflMe)KAyHHMr.r yBe_ JIIIrIHBalorctr,rtTo rptrBoAUT K 6Onlrurlrr.r 3HaqeHHnM1r,. flpeAnono) l { H M ' q T O H a H e l ( O T O p OpMa C C T O 9 H I I I I cpaBHI{BaeMbT l eO i t K I t H a X O ral{ Aa,'Ie,Ko, r{ro oHtr He cBfl3aHbr {11." Apyf c ApyroM, H ux KBa.q6yayr paBHbr ro BeJrHqHHe Aricrepcurr orHocnre.4r,l:l:t ^p_1t_""crefi Hofo cpeAHero 3Har{eHHi.no,ry4Hclepcuq 6o.ree H^epacrer }r [od'iyBapuofpaMMa nepexoArir n n,rocryrc^ o6,uacrr, uasoioaeuyrc ttopo- q1A lg* n a r i o i i - . n u 6 op e r l , r x p u o r i A e r e p M H H H p o e a H H oQi ry u x r l H e r l . nepeNreHHafl l,aixe Hecllorpfl Ha ro rrro periroHaru3ripoBaHHaq H e r r p e p b r B uB a n p o c r p a H c r B e ,o 6 b r q H oH e B o 3 M o x H o3 H a r b e e 3 u a q e Hrie B ,qro6oii Toqrie. Biuecro ororo ee 3HarreHuqlr3BecrHbrroJrl'rio 6,naro4apr npodalr, Koropbre 6epyrcr B oripe.qeJeHHblx r\{ecrax. P a s v e p , B l r A , o p r r e H T a r l u fH l l p o c r p a i r c r B e H H o e p a 3 M e q e H r r eg ' l r r x n p o 6 c o c r a B , r r f i l o r6 a s y p e n r o H a . r u g o s a n H o r l n e p e l r e n u o f i . 3 r a n e p e M e H H a fnl p i r n 3 \ r e H e r { } r xuo r f l 6 u o g u o r o l r 3 a r r { x n a p a v e r p o n 6 y A e r i r M e r b p a 3 J n q u b r ex a p a K T e p r i c r u x r r .H a n p u N r e p ,n p e A n o J r o ) K r i N { , q]'o t\4btxoTrrrt onpele,r[rTb il3\reHqiiBocTbcopTa BIipan,leHHblxp]rA e Hro";rLr6AeHoBo\r ilrecropolKAeHlur.BepoRrno, pe3yJrbrar aHa!'Irr3a 5 - c aH r l r , . , r e r p o B o rKoe pu a , [ o . q , v q e H H o f n o p H a / ' r \ { a 3 H o N6{y p e uu r r , 6 y [poo H3 pyAr{brx oTBe[€T OTr'tr{aTbcgOr pe3yJrbTaTarr3Nle.r]brreHr.rfl cn)'qaflx Mof,'ilr 6rtssqrl Bo6oux Mbr BTor{HocrH To }Ke ca\,roe "rr.,e. TIIICJ]C ilPO6, II OHII MOIJIII 6IT 6ITTI ilO,'IYqCHbI Ii3 I,IACHTIIIiHbIX I\IEC. 2I? Pnc. 4.41. floaynapnorpaulta a6coarcrHbIXorMeroK KpoBnHMe,rogoir$opuaBAonbuopcxonoceiicrIHH,rr3MepeHHoir Inrqecr(ofo pa3pe3a s MarerraHoson nporHBe.9n,rn [38] . 1i : ,rlfiHHq, u3o6paxeHHaq roqKalrn, IpeAcraBnfler ropor. HnK trtrcnepcHm, Bo3BhrueHHil H prBsa yKa3aHHhrfr crDenPaur, 8380 lre. HHxe Koroporo Koil, - paccroqHHe, Da3flocrb trexay,uHcneDcHr)lH H noporon cqHTaeTcfl llanofi (3,5 KM) nDeue6pexulro ou T. e. noJIyAIrcah Apyr or Apyra, Ho Il Allcnepcul{srnx pa3HocTefi' no onpegeneHa 6strs QopMyn nepgra MolKer .tl, 'n : - 2n E{r Xr- X*o)- I n >(x, - X r * r ) )' . (4.77) pefnoHaJrri3oBaHHofiIIepeMeHHoft 3anaeruM, tITo cpe.!.Hee3HalreHire perIiOHaJlIl3oBaHHol? IIepeMeHHoftXi+n, TAK cPe.]Hee TaKXie Xi ecrb KaK 3TO-Te ptAKe, T. e. 2 x i e c a \ l b l e Ha6,'IrorteHlrfi,ToJIbKo 83flTbIe B ApyfoM lXi tlo- Xfi tn nn 0 J o 1600 s 6 I ; 18oo Q s o 2 a L l1 t I I 2000 Puc. 4.12. floAnoqeenHHe crp)'KTypHbte a6co,rroruure orMerKtt KpoB,'ru Nre,rosori Soplraquu,oueH e H H b tneo o r D a x e H H pc e i r c v r r qecKxx BoJrHBnonb 2l-KHnoMerpoBofo MopcKororpanepcan Marer'IltaHoBorrnpo":IlrBe.Ceirc,l.tuqecKue H3MepeHHrr B3qrbl s 300MerpoBollrrHrepea;re[38] [oM. PaccrogHlre, Ha KoropoM non-vAltcflepcllflIIpll6"1[xaercq K AIlcne{repcHr.r, Ha3brBaercf paHfoM, HJriIpa3MaxoM peflioHaJili3oBaHHoft peMeHHofi,oHo onpeAerrFeToKpecTHocrb, B rlpeAe,'Ia.\Koropoli Bce cBf3aHbr Apyf c ApyfoM. no,'rolKeHHrr A"'ls Heroropoii npou3BoJlbHoft Toqt{H B rlpocrpaHcrBe I\{bI I{o' x{eM npeAcTaBlrrb ce6e oKpecTHocTbKaK cHMMeTpI{qHbiilIiHrepBa"'I (u"rn n.nouta.r,b,rl'III o6aeM, B 3aBlIctIMocrH or pa3MepHocrI'I) BoK p y r r o q K H . E c . n [ p e r u o H a , ' I I I 3 o B a H H a frlI e p e M e H H a gc r a l { H o H a p H a rr.rrr.iBcioAy IIMeer o.],HoH To )Ke cpeAHee 3HaqeHIIe,To JIIO60enO' OT UeHT' BHe 3TOfo IIHTepBaJIacoBep[IeHHo He3aBHC]lMO JIO)KeHr.{e pa"{bHoriToqKn H He lvlox{er ,[aBarl lIHq]opMauIIIOBOl{pyr 3HaqeHIIfi [epei\4eHHoitB 3roll roqr{e. B npe.{e.naxsroti pefHoHa,'rr{sHpoBanHoir o K p e c T H o c r u ,o A H a K o ,p e f l r o H a , , ' I I I 3 I I p O B a H Hnaeqp e M e H H a fB o B c e x H a 6 r r o A a e N { b rrxo q K a x c B r 3 a H a c p e r H o H a J I H 3 o B a H H oIilie p e M e H H o f { Mo)KeT6lttl ncno.ttb3oBaTOqlie I.I, CJIeAOBaTeJIbHo, B IIeHTpadlbHOit H& ,[Jf oueHKrr ee 3HaqeHr.is.Ecrrlt ML'IHcnoJIb3yeMMHoiKecTBoII3MepeHHfi,cAe,laHHbtxB TorrKax BHyrpi{ 3Toft oKpecrHocTllAJIfl oqeHTOI{B UEHTPAJIbHOft NEPCMCHHOft KII 3HAI{CHI,IS PEI}1OHA,'IH3OBAHHOI"I a 6 e c f l e q I I T c o 6 c T B e H H b l eB e c a , I ( o T o p b l e Ke, TO nOJryBapHofpaMIlo 6url n p unticaHbI Ka)KAO)Iy LI3MepeHLIrc. AO,'riKHbr OcraHoelirrcfi Koporlio Ha QaKTe, Koropblft 6y4er HaDI IIoJIe3eH KBaAno3x(e. ilo,ryAUcnepcllfl paBHa He To,tbKo cpeAHeMy3HaqeHLIIo paToB pa3HocTeli A,'Ig nap TorIeK, pacnoJloxeHHblx Ha paccTogHllli 276 6Urs paeua uynrc p bO , ' l x { H a ' a 3 H O C TA XXi,-rr - g. 2Xi nn K o u 6 u u l t p y t c Y M r ! b I ,n o J l y q a e N I floarouy 14 0 0 o I 4nv (2Xt-ZX*n) ln : lZ(X, - Xi+n)lln: 0. tIfleHa p_afloAcraersn a (4.77), MbI BIIAI{M,qro r{IlcJIIlreJIbBToporo qro (4,76). ypaBHeHHeM c ypaBHeHl'le coBnaAaer 3ro BeH HyJrio,TaK 3aueruu, rITo 3To coorHo[IeHIIe crporo cnpaBeAJIIrBoroJIbKo rofAa' . cnH AaHHbIe K O r A a p e r H o H a . q l I 3 o B a H H[aefpl e M e H H a qc T a u l { o H a p H aE I',I3MeflOCJIeAOBaTeJIbHOCTI'I To cpeAHee 3Har{eHI'{e He cTarluoHapHbI, Hflercfl Blrecre c h, w (4.77) Ao.IIxHo 6rtrl uoAllQnqupoaauo. o]K[Aarb, Itllenrcfl MareMarllqecKne coorHoKar u cJle,u.oBa,lo TaKHMII, rueHug Melr(Iy no.'ryAucnepcneitn ApyrIrMH CTaTI'ICTI{KaMH, II,Hff rrfl H aBTOKoppeJIff . EC,rn pernoHa,'IHsoBaHHafl Kari aBToKoBapr{ail LIL [epeMeHHaq cTaqlloHapHa, TO [O,IlyAHCnepCUtA"Ig paCCTOgHrIg. paBHa pasHocTrr \rexAy 4ucnepcueii rr [pocTpaHcTBeHHofiaBroKoBapuaqfiefi A,rrRroro )Ke paccroflunx (puc. 4.43). Ec.nu perao[alrr4s O B a H H a f[ e p e N r e H H a sH e T o J r b K oc T a ( [ o H a p H a , H o 1 4c T a H A a p T H 3 o BaHa raK, qro6or cpeAHeepaBHsJ'rocbHy,'no, a Ancflepcnt eAHHHqe, ro loryBapnorpa]rrra 6yler 3epKaJ'rbHbrM orpa)KeHrreMaBToKoppe- rsuaouuofiSyHxurur {puc.4.44). I( coxaneHriro, qacro pefnoHav'in3oBauHbre nepeMeHHl,reHe craq H o H a p H b rc, K o p e eo H H o T p a x a r o T H 3 M e H e H I i H f x c p e A H H Xs H a q e H r . r f t or roqKu K ToqKe. EcnH uu [olibrraeMcfl rrocrporirb [oJryBapHorpaMMy 4"ra raxoir nepeivreuHofi, ro o6HapyxaM, qro oua Molr{er He uMerb onucaHnbix strrtre csoficre. 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CoorsoureHlreuexiAy nory.qucnep$reri1,rru aBToKOBaplrauraerl rja crarlHoHapHofiperrroHa.rrr:bnaHHofi nepeMeHHoi. yAo "6Hbrft, Ho Bce*:. il: 1-:"""':u t ^: :*f :*f ":"J:1?; i ; ; ; t ; ; peHHo-MoxeY".T:i::"i '":#? {::.'.pTff ^lll- Li'^oroft ::":T11 ::1'.11? qro T,npoll3Bor'IbHofi B npeAerlax o r 2- A u c n e p c n q s a 6 a n A e g H i l H r H l B T o K o B a pvat\trg Atrfl lara 0. Ils 3HaqcHnii BHa 9To. ro lrHoxecTBa ?rr:Oo2 6ii..",io"iu AYJ' - i;;i;i;. ^rt Httelt, uanpliltep (.luHetiurtii Ph 7500 t p s0 0 0 2500 Prc. 4.44.CoorHOUeHlle MelriAy no"'ryArrcuepc,.refr "[h n aBroKoppe- 0 .'rrrUueii 0/, A,,qq cTa qn oHa pH.Il perrloHSJl.t3o - itrrrlrlrl,'rrl 1n r. B:rHrrofi rapeyesnorl q f i c r e H r r i r ,B 3 B e u l e H H o cep e A H e eB c e X T O q e KB H y r p n o r i p e c r H o c r H BOKpyr roqKH i. flpuQr 6yler riMerFJsnl_xpr.rnofi, annpoxcnMi.rpy_ loqer? perHoHa,'rn3oBaHHyro nepeMeHHyr,o. Ec,urr Aprror slr.recru rr: p e r r 4 o H f l r r r 3 o B a H H onfer p e r v { e H H oT f iO , O C T a T K UR i : x i - X ; caNiu aa. ' l y r p e f u o H a " l l { 3 o B a H H y Inoe p e M e l { H y I o , H M e t o u l - v r cop e A H H e3 r r a q e Htrfl, paBHbreHyJrro.Apyrulrrr cJ'roBaMIr, ocraTKr.i65rgyr cTar{uoHap_ HbrN{uu N,ro}Krro locTpor.rTbHx no,'iyBapHofpaMMy. 3ACCI ilfT,I HCO)KIIAAHHO TIPIIXOAHM K IIPO6J'ICMC I{IiKJTHIIHOCTI.T. 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BUeCTOgroro oKpecTHocTb orrpeAe.riseTct KaK 278 h;L4noro*"tr, " -,i,.^.',"^ rnnDGhL nnn^Tllf,r R { p> - Ke' BLbr nl ept a .lplrQr MolKHoanrpoKcllMgpoBarbnpocrblM Xo:Zb$i xpll qlr ) ll"rll{JKe x o : I ( b 1 X r+ b 2 X i 2 ) I cex ( x u a . a . p a r u u H r , ;i p i i i l Q r ) . B : r i r Q o p v y , r _ r tB x o A f r K o o p A I { H a r b B q r o r a K c y il{eO K p e c T H o c T I l ' n p o l l 3 B o . l b H o l l , r l a H i r o r _ "r o q e t i B H . V r p H II oKpecrHocr}I, pa3\{epoM Ap}IQroN{ Ntex.qv B3alt\rocBfi3u .ii'yg . c n t t o x p e c T H o c T bB e , l l I K a 'B b l r { l l c J l e i l o . r l v B a l ) l i o r p a \ t l l o foi c T a T K o B E I a 6or'iblxoM qllc,te roqeK' H ApI'ISr i i u o ' a p i ' 4 , t i o i r S ' t o c H o B a H bH rlaAxoit xpHnoit. B erolt c.ryqae oqeHb np-egcranlrrb 6j':er *or,i,u a nO' ocraTKtr Oyli,'r iaparirepHsoBaTbcfl -6O,rlruoliH3)1SHr{HBOCTbIO, C , r e A o e a r e "'Isuo, n o $ o p r u e ' c . ' t o x i u o i i ,rynapuorpariua oliaxeics 6oiibill]'to Ha 6yAer B.rluflrb olipecrHocru NIa,loIi pa3]tepa cneUircfruiia O C T a T I { OuB I l a n p O r r 3 \ { e H r u t B o c TobU e H K l IA p I I S T a , H a } ' N { e H b u e H l i e c T o T y B a p I I O i pa l l l t b I . O n p e , r e , , i e i r uK e o 3 Q Q l l q l l e n r o Bb l p u . Q r a r p e 6 y e r - p e u e H l z s H e x o T O p O f Oq u L t J a c o B M e c T H b l x. v p a B H e H l l H[ o B b I u e H H o I i c J I o ) K H o c T I I ' f lO p a 3 A e . [ a , n o c B g l l l e H H o t o o n l r c a H r r eK o r o p b l l o T K . - I a J b l B a e T CA x p a f i r H u r y . E x t t H c r s e H H b l en e p e \ I e H H b I e B 3 T I ' { xy p a B H e H H g x - 9 T o paccTof Hl{fiN{_Me)KI,}' pa3,'IHqHr'IM no.rlyAltcne!rcllli,cooTBeTcTByFou{ile r o . r K o i i c H o \ i e p o \ 1I l i l p y r l r u t I T o q K a M uB p a c c M a r p ] I B a e M o foi K p e . c r H o c r u . O A r r a l i o o u I I e u l e H e n a t o r n o , ' I y B a p t { o f p a M M buI s, x o r o p o t " t c,rre,r.yer[o,I\rqilTb ]reo6xoArlNlbleno,'IyAI{c[epcHH. MoxHo AonycII\{eer raxoii-.nlt60 ecrecTBeHHbIit Lng' Trrrb, rrro no.-rvBaprrorpaMMa r{ee BtrA, il uc[o.lt,3oBaTb efo B KarIecTBe rlepBoro npu6.na\rreHltr. K cqacrrto, ,refKo rrpeABurerb BIIA npocroii no,rynapaofpaMMbl, I I 3 T O[ O 3 B O . - I R C I IT C I I O J I b 3 O B aOTKbp € C T H O CH TabC T O / ' I b KMOa J I O | Op a 3 N{epa,Hacr(o.'lbtio3To B03Mo;.t{Ho. 3ricnepttrreHraJbHbreorreHKrrApri$Ta Bblrll,rratorcflH3 cooTBercr' Bvlollllrx tra6,rn:.esrrii, a pe:y.lurare r{efo no,'Iyqaercf MHo)KecrBo 3 r i c n e p r r M e H T a . r b H ro, cr xr a r K o B . l l o e r u , v o c r a r K a M M o l K H oB b i q l i c ' " r l l l T bI I O , l y B a p r r o f p a N { \ 1r r} 3 3 T € r \ r c p a B H H T b e e c T o f i n o . r l y B a p I . r o r p a r t r t o r i , r i o r o j ) a r 6 u n a a u 6 p a H a B K a l r e c r B en e p B o f o n p u 6 J I H > K e ttttl. Ec"'1t c:.e.i"utttte npeg,no"'totxeHltq To o6e 6br,'IiInpaBn.qbHbIr\4II, OIIII COBIAAVT.II N,IO}KHO CqIITATb,qTO OOPMA APfiQTA Ii IIOJIYBAp t t o f i ) a l r M b ro n p c l e , { e H b ry c 1 r e u H o . 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B raxux o6crosre.nlcrBax rpyAHo cKagarb, KofAa Mbr Aocrr.tfrier,taQQexra or Nou6uHaqnri ouenoK. l l o . r y n a p a o r p a M M a o r p a x a e r - n p o c r p a H c r B e H H o en o B e A e H r c e DerHoHarH3OBaHHbn i Xe p e M e H H b r xl r J r Hu x o c r a r K o n . H e N o r o p u e u ! e 3r'rrr3r.rp oB?Hu.u.eQ op nau noJ'ryBap rzorpa MM Aa Hbr tta puc. 4',48. H a p r . r c .4 . 4 5 ,a n p H B e A e H an o , r y e a p a o r p a M M an a p a 6 o . n r z u e c K o r o Tura, Kacaroqarcfl ocu x B Haqarre KoopAHHar. Oua u.l.rrrocrpnpyer oqeHb rr'raAKoeH3MeHeHr.ie peflroHaJrH3OeauHoft nepel,leuuoli. Ha puc.. 4.45,6 npegcrawreHa noJryBapr.rofpaMMa, uMeroqafl BrrA [ps_ M O r ?r H H r ' r a ;o H a y K a 3 b r B a e rH a y u e p e u i o e H H e n p e p b r B H oIer 3 M e H e HHe peraoHa,'iH30BaHHoft nepeu.euHoft. Llcruuuai c.nyuafiuax nepeMeHHar ue 6yAer HelpepbrBHofi,u ee ttoJryBapaorparr,rir,ra 6y4er ropnloHrad'ilHoli .nHunefi, opAriHara xoropofi panna 4Hcnepcriu (puc. 4.45, a). B Hexoropbrx cflyr{aqx uo"rryaapnorpanruaue npbxo4ur ve_ pe3 HaqaJroKoopAnHar, a uMe_ernpa a6cqwcce, panuofi HyJrr,o, HeHy_ JreBoe3HaqeHHe.3ror c,ryuafi c_oorsercrnyer <i64eKry caMopoAxos>).OH uso6paxen .10 I{? puc. 4.45, e. B reopuz se,,ru.{Hnbi Ao,rxHa 6lrrl panua HyJrro.SQSexr caMopoAKoBBosHr.rKaer rofAa, KofAa pe_ raoHaJIH30BaHHaflrrepeMeHHaflHacro,rIbKo orua60qHo onDere.'leHa q rT,o [ o J r y B a p H o f p a M M aB b r x o A H TH 3 H ] ' _ Ha KOpOTKOM paCCTOflHHL i l f l H a y p o B e H be Q Q e x r a c a M o p o A K o B H a p a c c r o r H l r x , M e H b r r e N { , q e M n H T e p B a ,o r upo6onauuR. Mo4elnponaHr.te noJryBapHorpaMM B n p u H q u n e o K c n e p r r M e H T a J r b H anf lo , r y B a p H o r p a M M a N , r o x e r obrTb npflMo [crroJ'rb3cBa[a Alrfl.troJryqeHr.rfloqeHoK, KOTODbTe Mbr p a c c M o r p u M B c , r e A y r o q e i i r , r a s e . O A s a x o n o . T y B a p u o r p a M M ra. r 3 B e _ c r H a r o , ' r b K oB. A r i c K p e r u o u H a 6 o p e r o q e K , p a c n o , q o x e H H b r H x a pac_ c r o f f H n E x A / r ; u a r p a K T t r r \ e ,o A H a t i o ,n o ; t l B a p H o f p a M M b rM o f y r r r o - "l'-l lr 16"-l npO6 n OIUUMeTOAOM D r 4 o r p a N r Mfel p o B o A u T c f lO 6 u q n O H a r J I a 3 O K , ;;;.'K;;o^ igl onr"otuaer rr ,naer rpl'rMepbl pyqHbIX Buulacreuuir, B ro BpeMfl riax o"'rea [38] npueoAr{T npofpaMMy BllrIHjJIeHI{flJIHnefinOfi no,,tlrBapllorpaMMbl,Iauercirlefi TOT >l<eyr,lOnOfi XOoQQUutreHT B Haqa,'le KoopAI.IHaT, KaK Il SKCnepI'IMeHTaIbHaqnoJIyBap ' ilorpaMMa' B uaeane r{oAer'tb,osl6pauual A,'Ig ttpeAcraBJleHvflnoJlyBapl'rorpaMMbr, HaqrrHaeTcf B HaIIa,'IeKoopAI{HaT,fJIaAKo Bo3pacTaeTAo lieroroporo BepxHero npeAer'la, 3areM ocraercfl Ha oAHoM rlos a pnc' . c r o q H n o My p o B H e . C Q e p u u e c x a g M o A e r ' l bn' p e A c r a B , ' I e H H aH 4.46, o6nai,aer eruul't csoiicleaMr' Oua onpeAe,rena no Qopuy,le "{n:oo" (+-#) _h i -\ a - napa6oalvecxag Ooptra, uoKa3brBaouIf,9 OrnHqHy0 HenpepbrBHocTb perHoHa.rH3oBaHHoii ncpcueHHoii; 6 tusefiuas noKaSbtBabtrIas yMepeHHyro He_ QOpna, npepbrBnocrb; o-ropu3oHTaJrrual dtoD_ \rr.. ypoBHs (t02, cooraercreynuaa iny,iaiiHori nepclreluor'r, rre trlrcrotrteli trDoJBTOKOppc.ltuillr: aes_ rprKr cllroll0fKoB. IJtH tBHOe OI:(.toHcl(IIe "nrop. .! ]i rl cBIaapcHHoi fl poaf i) { l l b t oT ]laca,!a KoopaHHaT, IroKa3LIBanrqee, qTo pertroHaJIff3OBaHrrag trepelreHHtq cHJbHo ff3tleHqfiBa npn pacqeu ]tHTeDBat onDocTotHttx, IIeHb[Hx 608a HHq (4.79\ ). Tr,:ootl.l-et Ha puc. 4.47 cpaanuBarorcfl c$epuuecxafl Ir 3KcnouenufiaJlbnaq MoAed'rx.SrcnoHesqvailbrafl KpiiBar HuKorAa He ,ttocrllfaer cBoefo npeAe,'rbHoro3HaqeHut, a npu6lulKaercfl K HeMy acnMIITorl.IqecKIL .3rra.IHr,no,'iyArrclepcuf 3KcnoHegqua,ruuoiiMoAe,IIlIHI,t)Ke,ueru cQeD I I q e c K a s ,A " I I qB c e X g H a . I e u H i i/ 1 , u e u g u u x , r { e M p a 3 M e p O 6 , r a C r l t .B.xuflHr,ls. ,rllrHetiHaq MoAe,'rbnpoure, ueu cQepnuecKafl I,IJIIIaKcrloHeHllllar'lbHafl, TaK KaK OHa HMeeT TOr'lbKO OAHH [apaMeTp' HaKJIOH. M o A e a r i r M e e rB r 4 A 1n:ah Pnc. 4.45. I4lea.luslrponaHHbre no!'ryBapuof paM\.rbr: (4.78) .q.'IflBcex paccronulfi Brlr'lorbAo o6,lacru BltllflHrlfl'[oJIyBapnofpaMMbr a. 3a npere.'iaua arofi rpaHHIrbI 7n:602. CQepnuecras MoAeJIb o6uquo xapatirepll3yercfl KaK I'iAea,'IrJHasQopua noJlyBaplrorparInar,r.I4uorAa rrclo.nb3yercfl Apyf ag MoAeJIb- gKcrIoHeHt4HaIIbHag' 6 i,l---',1./280 ' B,'IqeTH S 3 a B I i C H MOOT T O 1 O g rpe6oearnCflA1fl.lp6ux paCCrOnHuii 3KcnpuutlHe arOfi Ai'lCKpeTHag cfl, JrgOHo KpaTHbIUA u"ru Her. flo n p e 4 c T a B JIeHa 6 u r l A 6 J I ) K H a n e D g M S H T a J , r b Hnagr ,r' t y B a p H o f p a M M . a Mo)Ker6strl eutqucK o r o p a f l H e n p e p l r n u o r i Q y H n u n e f i ' rt.lotop"n -neHa f i o a 64,'ttt o p N,lrc6oro l o A e , ' l )Ke,'laeMolo b H o f o y p a BpaccroqHnq' HeHHsKoKcnepl'IMeHra'nluoft[oJIyBa- (4.80) ii npeACraB",rser co6oii npsNrylo, npoxoAflulyrc qepe3 Haqa,'ro KoopAIIIiar. OqeeuAHo,3Ta More,rib He NIo)Ker fiN{erb ntrKa, TaK KaK oHa p a c r e r l r e o r p a r r l q e s s o . t r 4 H o r A a . { H H e i i u a q M o A e J r bn p o H 3 B o J I b H oM o , i l t t r p u u u p y e r c f l c n o ] , r o u l b l o B c r a B I i t I B H e 3 a n H o r o u 3 r ' t o M aB T o q K e n I { iiil, r(ali, Hanprr\rep, 1n: ah _ riln h < a, Apucrpourrr !,;xe#,:Jfi'noli]"rr:i: (4.81) rar{ueMoAerrr, Tat( Kari rrcrro,:rb3oBaurre "purrKeoIIeHoK npeAnoxpafirHHra A,,rflnod,tyrleHHfl r'laraer HenpepbrBHocrbH r!'IaAKOeI.l3MeHeHLIe paMMbI. [Or'IyBapt{Of :{J-fHaKo A,rtf paccrolHufi, suaunre,rrbHo MeHFrtuttxrpaHHIIbI,.rIllHeft281 2 6o i ) 6s Puc. 4.46. CQepuuecxanMoAe,'rb ro,'IyBapI{orpaMMbI. i 6-vxeofi a o6o:saqeua a6cqucca rouru, B K o r o p o r i n o J y B a p f l o r p a M N r ac r a E o B i l T c t paBHoil AHctrepcHr oo2 Plc. 4.47,3xcnosesuualruat u crfepuqecKaflMoAe,rHnolrr)-Baprrof p ar\,IMbr. O6e vole.na uyenr ortrru t4 Tor )r!e Haqa,rr,ulrriHan.rou [9] : J-3KcnoHegrlnanbHat yoJenb: 2-cde, pHqecxaq MoleJb Hafl MOAeJrbrBr'rqeTcfl rrAeaJlbHoxopouefi anlpoKcfiMarlueii. 3re xopotxo Br.rAHoHa puc. 4.47, rle o6e nro4enu, csepuqecKaq H 3Kc* noHeHrlua,'rbHar,loqTr.r coBnaAaroTc nprrMofi JrnHr.reiis6nueu Heqa. c , r I , Ip e r H o H a r ' r H 3 o B a H Hnaef lp e M e H H a r6 u . n a o n p o . r a K o o p A r i H a TE 6oeaHa c AocraroqHofi nJrorHocrblo, orHocr{Te,rrbHo o6,'racr[ BJirrflHrrfl, To 3Haqr.rMbixpa3,'rrrqHiiMe)KAy orIeHKaMu,[o,tyqeHHbrMri B yc"rroBHsx"rruHetlHoil, c+ep[qecKoit u;tu Apyroft MoAe,rruHeT. CNEKTPAJIbHbIH AHAJIIN3 q H3MeHrri.tBocr}t Crexrp a,rrH brr?a I{a JrH3- 3To MeroA p a3!'roxeHrr BpeNreHHoropflAa Ha oTAe,rbHble KoM[oHeHTbr, cooTBeTcTByror{He HJru LJrIrHeHHTepBaJroB, B npeAed'raxKoTopbtx IrpoAo,rr)KrlTeJrbHocTr.i 3Ta rr3MeHqIrBOCTb npoflB,'rfleTcX.!,nn ero ocyuecTBr'teHuffBpeltteHHofi psA paccMarpuBaercfl KaK cyMMa 6o.rrnroro qr{c,'ra6o;ree npocTbrx BpeMeHHbrxprrAoB, rrMerouIHX Br.iApefy,'rspHbrx cuHycorrJ,c pa3,'IHqHbrMu aivrn,'II.rTyA,aNlI.I, TOqKa\tH. AJIIIHaMUBO,'IHH HaqaJIbHbIMH B e u t q u c , ' I e H n f lM x o l I { H on p e A n o r a f a r b , q r o c u H y c o u A b lH e 3 a B n c u M b I Apyf or Apyfa. Tar< rar< cyMMa Bcex srux cuHycoHAAaeT rrcxoAHbrft' r O B C e XC x H y C O r r A aAXO . ] i K B p e M e H H Op i i f l A , r O C y M M a u 3 M e H e H H iB pflAa. Ha 6brrb paBHa o6qeii r.r3MeHr{uBocru i i a , ' i H 3H M e e r i l a 3 B p a s l H u l r l r x p y K o B o A c r B a xc n e K T p a d r r b H barH J ' J I ] T i H b I CI I A 3 B A H I I f l , HANPHMCP IAPMOH]iqCCKI'TIi AHAJIH3, AHA.IIIIS, @ypoe urrrr qacrorurrri auaurrag.HassaHr.ieororo r\{eroAaBoc:icAur K Teoprtl{ My3bn{n, H3yqarcil{erl 3aKot{oMepHocrtr,cBfl3aHHbIec Ko,{€* 6auusl,ru. B XVII BeKe KenJrep, irprilreHrfl coorHoueHufl rapN{oHHqecr(ofo aHaJrrl3a,HariAeHHbre Hvr n apHsueTrrKe,reoMeTpHHr{ M.v3bIKe, oTKpbLII3aKOHbrrrJraHeTapHofo ABr.rxeHr.rfl. oAgaNo xau Ear r r c r O y p r , e ( 1 7 6 8 - 1 8 3 0 r r . ) 4 o r < a 3 a ! 'or 6 r l y r , o r e o p e M y o r o M , q r o : ilro6afl,oAHo3HarrHasHenpepblBHaffSyHKrrr.rflMolKer 6urr npe4cranJreHa B BuAe pflAa H3 CUHyCOI4A.Jra TeOpeMaTerrepb Hocr4r ero. r]Mfl. npex{Ae qeM noApo6Ho u3J'rararbreopHro prAoB @yple, ltlt. l l o . l ) . l i l r r Jo n p e A e , l u T bp f l I T e p M r r H o BB. o J b r [ u H c T B o3 T r ! x T e p \ l l t ] l o B : 282 U HCIIO,'Ib3yeTCfltIpU aHa,'ll{3e 3,'IeKTp[qeB3fiTO Ii3 3.qeKTpOlfeXHVKll Ii,,* ."rnr,'IoB. Xorfl 3,'ieKTpuqecKufi clirHa,r npeAcraB,rfler co6oii i , r , , r a n a , , u a 3 H e p f l i l i B o J I H b Ic r e q e H t t e M B p e M e H i l , I I H l K e H e p h I J l o 6 q r B ocllli,llrotpaQe. flpu usflpeActr:!J rb ce6e efo <<3aMopox{eHrlblM>> ,rb;rieur;i reopilu pflAots @ypre IIHX{eHepbI BcefAa npeAno,'taralor, qTo criiHa.[ Il3MeHfieTcf co BpeMeHeM, oAHaKo TOT QaI{T, qTo OI]II g C C , [ e A Y I O TC H f H a , ' I K a I i n p O C T p a H C T B e H H Ofel B . r ] e H I I eH a 3 K p a H e O C qTO BpeMfl H npocTpaHcTBo cqllTaIoTcfl uIl.']to|paQa, yKa3bIBaIoT, HecoMHeHHo, NlaTeMaTIlqecI{H 3TO I(OppeKTHO, 14 Ta ?BIibI"!iil. !) irBHotll) ItuN<euepbl [oJIb3y]orcfl TaKHN{ c Koropofi .[efKocrb, ireoco::;-iauualt tITo 3TI] ABa noHflTIiff, KaK noIIyxleHIIe]I, [{o)i{er y6eLuTb Hac B ToNI, Ha[Ie ]I3Jio)KeHI.IeTepI{HHO' llOerOmy B3aIlN{O3aMeHteMbI. npaBlrro, B 6or']blxHHcTBe pa0T"III{qaeTcfl oT TaKoBoro HecKo"rlbKo loiltqeciiu 6or rr.r aHaJILI3Ycl{fHaJIoB. Ha puc. 4.48 ueo6paxeH roBropsrcuiliics cHrHaJI, Koropbni Bo!'IHofi.PaccroqHlreor \1O:xHoorrHcarbqlrcror?cHHycoHAaJIbHoft O.IIHOIi TOTIKI{ BOJIHbI AO 3KBI1BAJ'ICHTHOftTOqKIt HA CJIEAYIOUC'i BO"'I- 1,. Hacrora f -xapanreplIcTHKa, lle lrzl3I,rBaercflA,quHofiBoJrHL,r o6- .t - qIICdIIOBO,IH' yI(JIa.U,bIBaIOUIIIXCfi l" B eAUririily A,'rrrHbrlr"qH BpeMeHa. B 6O"riluHHCTBe LiH)KeHepHbIXpaC:reroB ciirHaJr xapaKTepll3yercs Ilacroroii. B reolorHqecKHx 3aAaqax 1)aTllAt A"'lIiHe BOr'jHbI't. e. I: Tpe6yeMoe AJIfl rlHrepecHee rrMeTb AeJro c AJir.rHofiBo,lHbI. Bpevl, TOIO TJTO6bITIPABIIJIbHbIfiCHIHA,4 NOBTOPHJICS,HA3bIBACTCSCfO TIC. puOAoM. lepNIHH IIepHOA fl8,'IfleTCf 3KBI']BaJIeHTOM AJIHHbI BOJIHbI'HO IIepTIOAll3N{epfeTcfl B eAIIHIIIIaX BpeMeHIl, HatIpHMep B MH,rl,lll4ceKyHIax, ii rie B eArrHr.ruax paccTorHr.rq, T. e. B caHTuMeTpax. fIpH onucaH r r r l T a x r r x E B , l e H l t f i , K a K M o p c K H e B o J I H b t ,y A o 6 H o n o , ] b 3 o B a r b c f l K a K l.iilrrort tso.lrrbt, raK rr nepnoAoM. [.nHHa BoJlHbr B ST0M cJryqae I]3illeDrreTcfl r(ar{ paccTofHxe Me}KAy rpe6Hfl\,rIr coceAHlix BO,'IH, IIeplll).1-.h3ii BpeMfl, Tpe6yeMoe AJ]q Toro rITo6bI ABe [ocr'IeAoBaTe,'Ibl l l r r e B C . r H b rn p o u . [ r r r p u x c l r p o n a u H y r o T o q K y o T c q e T a , H a I I p H M e p K o iieu B0"ltircpe3a. 3ro BpeMeHHoii [poMe)KyroK Me)KAy il,roMeHroM notir].reurr,eo,tHoir Bo,rrrrbrn MoMeHToN{rroflB,reHufl Apyroii. (BoaHltxHoIlet{ire repl{riHa flepnoAuqecKr]ii c,'roBy [epuoA, Koropoe o6fl3aHo o_:l:lerlaeTcrrfHaJ't, IIoB'IopffIourlilcfl c IrpaBIl.rrbHbtMHuHTepBailaMIr.) I t ( r . l o B l . r H ap a c c r o s H r r q o r B [ a A r r H b r B o . r H b r A o r p e 6 H r H a 3 b l B a e r c f l :r.)i n"rlT\rIor:i (ll . ) tla lrrc. 4.49 uso6pax(eHbr ABe oAxHaKoBbre cnHycor.rAaJibnbre i i i r l i 1 3 l , i € c, \ r e u l e H t r b r e O T H O C H T e " r r b H ; t op l r A p y f a . C O O r s e r c r s y l o r q n e i : r . 1i l l r r " r n r ) ' A r , t r r A"rurlbI BoJH oAuIIaKoBbI. PasHocrr Me)KAy 3Hai'i ilill \.il ) r rr )': nptl AaHHoM 3HaqeHilIt Jf; ofip€!€rflercfl pa3r'rl{qr1eil s tltrt:e r,rex(Ay Sro pas,raune Mox{Ho oltrcarb c AByNrfl Bo.rrHaMr.r. Il-o\i'llllbio c!a:onbro yr"lra O, a ero onpeAerreHue yflcHurb ce6e c no!lollltrlo prrc. 4.50. lloocroe MexaHuqeaKoe rptrcroco6reH[e Ar'rfl no' - r \ : e H r r : :c l i r i ' c o 1 . 1 a . - r b H o i i B o . t H b r c o C T o r r Tr 4 s n v c l a p a A H y c a r , B p a 'uiir iotr.eioctl c nocroflHlrorl cKopocrblo. Kapau4,aru,' saxpen,reHuuii 283 Vro.n d,i 6yAer KoopAuHaraY roropofi paBua Asin(2nxilx*q). X ecrt o6uar AJrwHa sarucu; t2rr'nlX*q). B arux BblpaxeHr.rffx rITo yro.n HaqaJlbultti orMeTHTb, B I.IcxOAHoM [o,'lo]Keor:e Baxgo I )^ -t- l: Puc. 4.48.Peryaapuoe noBropeHue crrl,- HvLt flBilfleTcfl nOCToqHHbIM AJIfl BCeX IIOCJIeAyIOUIHX gHarleHzti HycolrAa,lbHoir BoJtHbr : g l H u a r o n n u ; r 4- a M n t u T y A a a&t- KoopAIrHarbl Y u yrna a. KoucraHra g Ha3brBaercflSan,rrrrryAbr yfr'IoM, LIJII.I aofi, $asoruM SasoBofixoucraHroii.Tpu napaMerpa- Puc. 4.49. .[,ae criHl.coilla,rbHbre Bo.,lHbr. KoropbreH:eHrrrqHbt no Qopue. P . a l ; l u q u qv e x A y _ ) r n y t \ J t s c t r c U u 4 g q e c x o r o 3 H a q e u r r g. y - r a p a x r i p a : y r o rp i e i o c r e e a g A B y x a s , r e o n u t xS o p u Fl_r__J_l__J 2i1n0 Puc. 4.50. flpocroe MexaHlqecKoe ilplrcnoco6,,reHre A , I f B H q e p q H B a H H t C l l H y c o u f a , t b H o i B O J r r H br r y T e M Dpeo6p,a3o-BaHtB i f lp a u { a T e J r b H o r o , l B H x ( e H HB f l, , r u H e f r HOe (4r. Pa3.rrlrque Me)KAy yrJtoM g paAuycoM AHCKA u aMn,rrr.rryAori a_ Qasoaurlr ).rJov cr_ruyiolrAaJlbHofi BoflHbr (6). lI:o6paxeHa qacrb BoJHbi coorBercrH3MeHeHHroyf!'ra (D or HyJ,rqAo 3HarreHur, :ry51" HeMHorliM 6o,lbuero 2n paguau, r. e. noqrr{ oAHoMy_ nojrHoMy noBopoTy .lucKa rruHrrro, :: :l:l^Ti.,_IIpHcoeArlIeHHoMK Kparo ahcKa,Bbrqepr{HBaer Ha oyMafe' ABlrrarcueficfl c IIOCTOflHHOT{cKOpOCTbIO rroA I{OH{OM, crepxHr. era auuns, rBd'rrercfl cnHycor.rAaJibHoii xpa-fr1i, rrMea: r u ArrrIHvBo'rHbI, npeAcraBrrrrouyrcco6ofi: f.T.:i..i.Y":y:!!!QYHxtturocKopocrr'rBparqe'r'rflAricKa ri cKopocrri.ABrrxeHrrf ..'^ 6yuarH. 3HaqeHHe Y s rrogoMroroxeHuil paBHo'y:A;i";. Ec,ra uu xorrzMBblr{eprl.rrb nor'iHyi BoJrHy,To roqKa 3aKpenJleHIrq crepxHs Ha lrrcKe Ao"[xHa c4e"rram nbaHru? o6opor BoKpyr UeHrpaAricKa,r. e. noBepHyrbcflHa g60oHiln Ha 2n paa:nin. nplAqTO NO,'IO)KHM' MbI HAqI.IHAEM BbIqCPqI,IBAHI.IE NPU [POiI3BOTbHOM HAqaJrbHoMnoJrox{eH'r.r__Kapa'Aarxa Ha 6yMare, KoTOpOeMbr Ha3oBeM HyrreBbrM.vron cr *.T{I r{eHrpoM Ar.rcKau fopr.r3oH^l1paHAaruoM, raJrbnofi JrllHrlefi Ha 6yuare r{Meer HeKoropoe snarreHr.re g ap;;. 4'51).Ec.nuuu o npoleccepa6o*r c-np"6opolo-.a""".it." un"r, Ha paccroqH*e xi H ocraHoB,Mcfl' To KapaHAar[ oKa]Kercfl B Torr*e.. 284 O[HcbrBaaMrrJlttryAa, IJtr4Ha BOJIHbIU QaeOOrtfi yf OJr- nOJTHOCTbIO nr Qopuy BoJIHbI.@asoeHfi yroJl cnHycolrAarluoti Bo,'rHbIr{3Mepflercfl or ropH3oHra,/Ilsoli nHHnn, I]poxoAtulefi uepes IIeHTp. Ec"rrul.rlr xoruM rrocrporirb ptA Bo,'rHpae,ruunoft $opurr, To A"'rR sroro HyxHo I,t3MeHurb aMnJII{TyAy, AJIr.{HyBo,rrnbr u.nn Qasoanft KpHByro,no rpop],ro,'r. Mo)KHo raKx{e on}rcarb Ko,cnHycouAaJrbHyro \{e r.rAeHraqHyrocr.IHycoIr4a;rrttoil, Ho xapaKrep}I3ylorJrylocx QasooT BepTLiKaJIbHofi npruor?, npoxo4nulefi BbrMyriloM B, NslrepaenabrM qepe3 ueHTp ycrpoftcrea. IZHIrtvmcfloBaMLI,KoclrHycouAaJrbuasBoJIno Sase ua 90o, u.nu ua nl2 paHa or"'l[qaercfl or cllHycor.rAaJrrHofi ,lnas. Ecnll K HaueMy ycrpoficrny [pncoeAuHr.nl 4pyrofi Kapar{Aail} riaK aro yra3aHo Ha puc. 4.52, "to Mbr cMoxeM BbrqepruTboAHoBpegonHu. OqeTaK H KocrlHyconAa,'IbHyto MeHHor{aK clrHycor.rAaJlbHyro, BnAHo, rrro oHIt oTJrl{qalorcfloAHa or gpyrofi To,'rbKoQasoeuv yr:ro:,r. Mu MolKeM cyMMapoBarb ocHoBH[,rerpr,rroHoMerpnqecKuecoorHo[IeHlis c rroMourb]opuc. 4.53, npeAcraB"rqrcuero cllHycouAaltbluyro Kpr.rByo.3ro pasJroxeH[e AaHo B repMrrHax Qynxqnn Kooruypa3"roxeHr.Ie,BeAyulee K ToMy )Ke cooTHoueca, Ho sKBr'rBa,'reHTHoe HtiIo, ocHoBaHoHa cunyce. ,[,onycruu, rrro Bo,'IHaHa paccroffunn X Ir.rri 3a BpeMfl X yr,ra4unaercfl qeJruxorrr..IIp6a.E TosKa X n npe,reilax orofo uuTepBad'raMo>Ker 6url oupaxeua B paAr.raHaxc norroulbro $op vy,rru o6pau{euun (4.82) 0 : 2nxlX. Tenepu xoopAuHarbrX uoxpunarcr r.rHrepBa!'r or 0 p.o 2n papltan" 4na y4o6crBa Mbr npeAnor'roxtrM,irro aMnJruryAaxpunof.ipaBHa eALIHHTIe. Tor4a ypaBHeHrre i<punoftrrMeerBltA (4.83) Y: cos0. 3ta al,rr"rrrryAa MoNier 6srrr saN{eueua .1rc6ofi,lpyrori ann,rrry1oli nlrocTo y\,rHo)tieHrreM Ha xoa$QHrlueur A: (4.84) Y : .4 cos0. tItrc,tIo qrrK,toB, I(oropoe B C T p e q a e T c f lB H y T p H o c H c B H o f o r r H T e p B a . q a l u a c r o r a ) , l r o N e r 6 l r r l yBelrHqeHo rrr'ru yMeHb[IeHo yMHo)Ke.Hueu 0 ua riorQQlqueur ft: I: cosk0. (4.85) o, K a r g 3 p 1 1 a o B a HNIar{crlMyM BO,rrHbr HaxoArrrc9 B HarraJIeKOOpAHtlaT, uo oH N,ro)Ker 6r,rrl c4nuHyr e ,trro6oerto,qoiiieHrleBbiqt{TaHtleNt Q a 3 o B o f oy r r , r aq : Y : c o s ( 0- O ) . (4.86) K o v 6 r a u u p y a n c e erlt nrotru(lr.rKarrlrrr, ur,r nafiAeu, qro !t106afl KpH2r.i 1L z n 37c 2 2m ztt 1rr 0 Pnc. 4.52.Crnycou4alruaqu KocHHy- Pnc. 4.53. Cuuycou,la,rluasso,'rHa.06* COrijl,a,'IbHafl BOr'IHbI, COOTBeTCTByIOUIIe BPAUIEHHIO AI-iCKA. u r B - coorBerc?BeHno <fasoeue yrnbr ,qns c ri HycoH,qaJrbHoi Lr KocrJHycoI,Aa.IIbHorlBo,rlH. l l 3 o 6 p a x e H u e c o q j : B e r c r B v e r H 3 M e H e H g l oy r ra (D or syrq ,4o 3HaqeHrg, neusortu 6olr,uero 2r paAuaH, r, e, oAHoMy noBopory .!.ucKa ulaq A"'lrrHaxpnnor"rpanwa2n pa.illraH : r r c u l r r i r r H T e p B a JTr .a r r a x B c [ e K T p a , ' r b H o M a H a J I u 3 eM o x H o c i i o M 6lrHupoearl MHofo pagJlnqHbrxtapMoHIrK AJIfl [oJr_yqenirflHcxoAuofo n p e v e u u 6 r o p f l A a , T o r { H A e K cf t u e o 6 x o A l r MA r q o 6 o g n a q e u l r f lB o , r H o eori Qopuur qacrHoro BrrAa. !,a,ree Mbr MoxeM r{cnoJlb3oBarbrprlronoMerpfirrecKoe paBeHCrBOArfl pasHocTrrAByx yrJroB: cos(R-S) : cosScosR + sinSsinR. llepenrrcao paBeHcrBo (4.87),no,ryqriM Yn : ABcos(DncosftO* .4nsin Or sin &9. (4.88) 3rc nulpax<eHue Mox(er6urr ynpoqeHo, ecr'r[ onpeAe,'r]trb r<o:$,,.pH'flpt Ulleilrbl ctn:AncosqA u pn:Aa sin cpp. erolr noryoua*t Yn : aocosftO* pesin &0. (4 89) .rlroSofr rpelreuHofipng, xaxoil 6n cnoxsocrtr oH Hrr 6ol.n(rrcri"rotlaq Tor c.rty,lair,I{orAa oH HenpepbtBeHIJd'IlI 6es usr'IoN4oB II .f,'IgI.:e;KAoro 3uaqeHLrflx Mo)Ker 6ltrt onpeAedrreHoroJIbKo onuo 3Haqeutte Y), \,ioxier 6url npe4craBd'reH B Br{AecyMMbrprAoB r(oclluycorrAa"rrbllbB t xo r T H o, [ p e A e , T e H H b trxa K f i M o 6 p a : o u , r a x t t : c 6 p a ; n e _ l l o H a p l c . 4 . 5 4 . 3 r o - B b r p a x { e H r r ce o o r H o [ r e H r r g( D v D l e : 'P;rc4.5!. nocreneHtroe Qasonoroyrra or Haqa,'IbHoro srlatlerruJi C). ,4,rnror,re1onar"n.11:Itnt"" b H b l x 3 H a q e H H i ix i , Y i : A sin(:nrri,t+(D) Ir or:2;r.[rl.y+(D Bar peryflflpHori cfir{ycorAa"lbrJori Qopnrr,rMOX{er 6nrr BIINE euc,roft Has rreaer." I:;J:d; " 986 sanucarra B (4.87) lix ;,,-, ] lr'cr,roM urrx.rroB ua 6a- y : s 0 1 p us i n4 0 . I a,,coh (4.!r0) t'-n JalleruM, vro (4.90)-3ro ypaBHentre,rrrueiruoe, ?. e. BCetr"[enl,r cli.la.\brBa rorcfl BMecre.Ono u anouuuaer no Sop lre iror,iilitoM na.tb'pii,Hee pefpeccuro,Koropyrc ML,rpaccMorpeJrrr s sroft f,'raBe. Sylo u.-\'paBHeHrlu q"o'euot @ypuerprrrolroNrerprrrecKue cosftO a sin F0 3l(BItBa,reHTHtt clr-eneHubrll qvleHaM TaKI.rx Mgofoq/IeHoe, tiaK Xz u ,r !\oe{yrh1ir.,:errr,r c { ' r ,r I g r , S T r r x q , r e H o B M o f v r 6 u r r H a j i l e H b r M e i87 rhnDll\'.rl2Ml n-l o v,l 'o i - -2! : ]rr; S t.,f l l hlJ"\,ttj i=o / 2ril; \ l, (4.e1) n-l 2 Tt )',cosI z"ift-\. ^-./,A--' 6 \- v ', \r^/ (4.e2) k4J\n/ i=o Kali N{oilieT[oKa3aTbcfl Ha nep' cJIO)KHbI, H e c r o J l b 3rr 1'ltaeHetltlq B ur,tii e:;l.ln,'l; BI-,1 PalKeHufl B CKO6Kaxecrb npocro rIpeAcraBJIe[IHOe npeueHHoro ec"rlt o6ulyto TorrKrr, l l O . l O > t t e t t t l e l f i A"rt{Hy r)r liJAHaX nfl.tir oIpei(e.iTrlrb xax 2r p a A H a H .B c r r . r r yr p I I r o H o N { e r p I I q e c I ( I ICXO ' r)'trr0 UieHIlil Iio3QipllqrlellT B0 ncerla paBeH HyJIIo,& ao 1'np61,u"t." \nJ I - _ - n-l o^: -J-I r,, ,TH ,tt \nnr\n/\nn \^"^" Prc. 4.54. Pesyrorar c.roxeHrrfl \^l^/ J rapMoHuKKocrHycor.rAaJrb. a - $ y ' t r a v e u r a n b ' a f l ' J r f f n c p B a s r a p"X"r.t#??ilr.rrr,Hbrx ' o H r x a - l : 0 , 5 . , A ^ : 1 . _( D 1 ^ 0 . : _ o p a nr a p M o H H K a A : 0 . 3 , k = 2 . O : 0 , : a - 3 p e r j a _ r a o u t t s n x a A : 0 , 3 , t - C , O : l S " : ' r _ "6. ' o #Bi T i rapMoHrKa 4-0,25, k-7, O:180": a rperbq (')+i,;^"ffyi:i,Jfi,'"#1.'i"iiill"ixfuJ'i'],l,1ul;ria,l"t" rapu6uuxa, +"ix'f; , n r r o c B r o p a q H r p e r b n r a p y o H H K H(,a r + ( 6 r + ( s l ; u _ Bropat' rperbg H M a q r a p N t o H r x fA l l*tulifll\iantloc ceab' ToroM HaaMeHburrx KBaAparoe. OAuaxo ecJrHMbI nonblTaeMcs oqe. HIITb 3TI4XOEQSUqUCHTbI MATPHI{HbIMI,I MCTOAAMI.I II CCJII{rPC6YCrCr cnpeAe/'IIITbi\IHofo rapMoHI'tK,To MbI oqeHb cKopo croJlrueMcq c freII p eoAo,'rrr[,ibrN{ri Bbrq Hc druTeJrbHb]Mr.rTpyA HOCT' MI.I. fapuoHlluecrufi aHarns li ll E,c.lr epelreusor? pflA npeAcraB!,lffer4eficrnure,rbHo nepuonuqe_ c K o e q B . n e H H eN, r b rM o x < e Mi l c r o , ' r b 3 o B a r br e x H H K y r a x H a s t i e a e M o f o rapMollilqecKoro aHafllt3a Ailfl,pas,'roxeHr.rg. ptr!.a Ha ero cocraBHble qacri.r. BpeueuHtre pflAbr, _o6naAarcuIHeceoficrsoM neploAr.rlrHocrrr, B c r p e , r a r o r c f lB n p r r p o n e . 3 r o , H a [ p ] r M e p , $ n y x r y a q r i u p u n v . n o aw or'lliBoB' ce3oHl{bieu3MeHeHIiflTeMrleparypbI, noc,IIeAoBareJlblrocrl,I c . r l o e Bo' u u t a x > x e B K J r l o q a r o3r a n r i c u , n o p o ) . r { A e H H br laeK r 4 M r rn p r r 5 o p a r , r u ,x a x 4 n Q p a K r o M e r p X - " r y u e i i ( n p e o 6 p a s o B a H t r e@ y p l e raK U XA a H H b r Xg B . r r q e r c qc r e [ [ a , r b H o r l r e r r o r i ) . B ' p e l r e u n o f ip " a M o x e r 6urr coeor(ynHocrbro ua6.nrcgeHlrii n 4ncr<perHoM NrHoirecrBerot l e K ' p a c r o , r o x ( e H I { b r cx p a B H b r NH{ H T e p B a r ' r o M A n npocrpaucrse. Ec_ 'rr1 HMeercq n 3Trrx roqeK, oAHa rr3 KOTOpbrxecrb t ro xoarpsfirur€HTbraA rI pA pflAa @ypre r\ror]T 6brrl sbr,rrrc,'reHHro cJrenvrcurr{M 28s (4.e3) -v q r o e c r b K a K p a 3 c p e A H e en p e n a e u i l 6 r op n 4 a . l 4 H 4 e x c l t I l 3 M C H f l I O T C ' I s e r o K o H t l e ,a s e o r l A o o r 0 l H a t r a " r rnep e v e H H 6 r o p n r a I o n - l n Jt.r toro, uto6r,r npaBll.nbHonepeBecrt'I Ilor'lox{eHl4en e p B o r oH a 6 , r r c . 1 e u l i tB p a A l i a H b l . CnlreAe.rnn rioaQSnrlneHrli cxhH pr, lz-ofi rapN{oHrllill,MbI Mo}KeM B BUAC OII i) C]C.I IiTb A N,IN''II{TYAY BOJIHOBOii QOP IT,IST Ar:1,7f t6. (4.e4) O a : o e b r i i v r o . n f t - o i i f a p N , I o H I { KpHa B e H (4.e5) @r : tg-I(pnlan). 3 a AaH>>. y f o J l , < < s a i t t r l T a H f e H c K o r o p o r o B l r p a r x e H r r et g - l o s H a u a e t : E r - . 1 r rB A r r c K p e T H O M H a 6 O p er 0 q e K C o 6 p a H b IA a H H b l eA J I ' p e f \ ' . l n p n o i i c r r H \ r c o r r A rT, ro, 4 u c f i e p c i l l s r o i i n u 6 o p x l t c B t 3 a H a c a M n " r l l l r1,1oii erofi so.rruoeofiQopvru. B npege,ne Allcnepcilfl ecrb npocro Il O.'lO B II H a I(B a.[,p aT a a MII'll'lTyALI, sn2: Ar,2l2: ]{,'ll{ (ar2 * Ff)12. (4.e6) Tali riax reopeNla @yple yrBeplKAaer, rlro BpeMeHHofipflA Mo)KHo MHornx cuHycouAar'tlurtx tityttt<uHfiu'nu l) a cc),rarpnBarb IiaK c-vNrNry r z li ) r . t o H r r Kr ,o A r r c n e p c i l r rB p e M e H H 6 r op n 4 a g B J l f l e r c r f l p o c r o c y M t n r o r.it r r c n e p c r r ier r n x c a N { b l xr a p M o H u t { .M t t u o x < e u r l o s r o M y B b I p a 3 t l r b r r r c n e p c r r r cf t - o l i r a p M o r r i a x rr { a K r r p o [ o p l l u o H a J l b H y ] q oa c r b o r o 6 t u e i ' tA l r c f i e p c r r [ n p e v e n H 6 r o p s A a , H 3 K o r o p o r o o H a 6 u " r a n o n y 'tetta. Ec,rrr N{brBbrqnc"rrr.rM A;IrrHHbrfi p"A fapMoHr.rK,To Ar.rcfiepcl{n T I O C J C : I O B A T C I ' I b I I b IT XA P M O H I I K M O X { H O HAHCCTII HA NCPI4OAOIPAMMY, Il.rrl, Iiari HHorAa foBopflT. lr:o6pasuru 4ucxperHuft u.rl.l .rluseiiurtfi e H e p i e r l t q e c x n f ic n e x t o . 3 r o e c r o r i o f l D o c r v n p e A c r a B d ' I e H Isl ea B I { crrllocrn rracrorbr H.rrrr Alrcnepcurr or qi.rc.rla"fapMoHHK k, tt tpaawI l l i o l l H on p e n c r a B n q e r c rB n r r 4 e ,y x a s a H H o MH a p n c . 4 . 5 5 . -( T e p u u IIln 3Heprrrr r'r A r l c n e p c r J r frl B r r r o r c r r c r r H o H u M a r u rnr ;e p n u t f i H 3 I { H X 289 Mecsqnstfi croK BoAbt B Orirn 6pr Hox6pa Aexa6pl T a 6 n : n u a4 . 2 9 (eutyrxu (n corunxamfiMos) KefinKpr.rx, f,uBapb @eeparb N{apr pert 240 54 73 59 308 200 270 219 204 346 150 87 276 48 97 135 278 130 86 22 463 637 325 221 195 313 295 401 146 173 230 281 161 98 216 389 416 40 579 469 103 tt7 t12 291 532 508 518 788 449 79 466 425 73 29t An- Muri IlnHs l.lu.rr, iv.t I o 19.-r3 l 954 I'r950 lii5 CD I 957 r958 i 959 l 9c0 Puc. 4.55. Ilepnogorpalrruar{ecsqHorororoKa Keiie-KpHr<, I(enryxnu Cneqaalsurre 3HaqeHHs yKa3hlBaIor, qro noroR Hneer e.nIlrcrBcHHbrrl treproAfl,lecKHil t.oJflqlrLIIl uilKit. Stteprrtu nplIBe;let{bt a KBatrparax €,4!IHHtI u3NlepeHlIt, xoroptne paBrrbl cotLrM qactgv rrofiua i0 lqill tfi62 l 963 I 9e4 19 6 5 I !r66 I 967 1ti68 1969 1970 l9 4 30 13 6 t72 t0 1 0 6 432 t7 I 36 2 6 9 79 52 i6 6 1 4 1 124 3 347 7 2 2 357 ll9 3B 27t 22 tt2 9l 5 0 2 4 7 3 6 3 t2 2 I 4 7 I t4 7 z 147 139 59 192 392 235 102 68 476 330 52 45 146 202 50 238 237 568 354 J I 8 35 t97 28 a o 68 q A 236 l 9 24 l 9 364 414 1 5 9 79 96 25 l 4 21 l l 8 3l 332 2 5 476 33 199 9 l 74 4 0 206 38 7 l8 7614 24283 64388 6l-r2 369 170 542 133 14 48 18 3887 29 ll 8216 512 4l t4 t4 15 29 75 27 66 14 6 CeH- ""Ono | t2 30 4 3 ll 7 16 17 27 c oca,4KaMff roAa, [aqffHat co6paHlt ts-TeqeHHe ooraroro flprrreqaHtre. !,aHHue ri3'noMa nocJleu:deNarb ceHTg6perl, ans Toro qto6u ro,qa I ronqeq nperLlAyilrero .rri;r6pr loiri,IeJIbtsoCTll B Cepe!I{He :slru [24]. 7 I 9( n b n CO 1957 1959 .|961 1963 1965 1967 1969l-o4or 1956 t958 '960 1967 1964 1966 1g5E 19',t0 P u c . 4 . 5 6 . M e c s , n r u i i noroK KefiB-KpHK,KeHryKKli3a nepHoAc oxrr6pfl 1952 r. ao ceHrn6pq1970 r. 19 5 4 6 u r a n e g e HB 3 J r e K T p o r e x H H K er r r e n e p b u n p o K o r i c n o , ' r b 3 y e r c rB o BCeX06,laCTgXTeXHltKIt,a:Hail:/.Se r{3oct{tHaJIoBu pacII03HaBaHr.{u 6 p a x e H n f i . ) I 4 c x o A u u r f ic r e n e H H o r lp s A n p e A c r - a s , ' r e H u a pHC.4.56. BpeueHuori prA npeAcraBJrfler MecqqHbrficroK BoAbr n Kefin Kpur s K e H r y x r u ; A a H H b r en p u B e A e H bB r ra6Jr.4.29, nsnrofi us [24]. IIepHoAofpaMMa rroKa3brBaeT,qTo r.r3MeHeHHr Mecflr{HbrxcToKoB r.rMeI o T f o A u q n b r i i ( 1 2 - u e c n r I H b l i i )n e p H o A , n , ' r i o c c J r y q a i i H a t r i c M r r o - 3rJiL.,aeTcfHeO6pa6OTaHHbII\tCneKTpONI Ll tlB,lfeTctl OUeHKOfI IICTHH' H O i 0 c n e K T p a , n " l l t c n e K T p a c o B o K y n H o c T H . 3 T I { O U e H K H C B t r 3 a H b rc KOTOpble He Mooqellb 60,'irutiil.ru craHAaprHbIMIl [ofpeuHocrtMI{, f\-T 6l'rrb yNIeHbueHbI npI yBe.[Ht]eHrrr n no IIplrqHHaNI, Koropble 6yA-r'r oryr,qiueHbt B C,'IeA-VIO[ieMpa3Aele. HenOrOpue I'133THx 0ltr116cll( N , l O f V TO K a 3 a T b C E. l O l K H b l N r l lB c u , q y c N r e [ I I l B a H U g r l e A o l y c T l l M o B b l C O K I i - \r t a C T O TC H u 3 K H M I t q a C T O T a M u .3 r U e H C O r u e q a C T O T b l ,A J I I ' l H b I I J O . T HK O r o p b r x M e H b u e , q e M A B O i i H O e p a c c T o f l H l . I e M e x A y T o q K a M I { onpo6cBaHllfl, He Nloryr 6ltrn o6HapyxeHbl. HaliBllcmax qacrora, HafiKeHcra' ee tioiopzlr NlolKer 6urt o6napyx{eHa, ecrb qacrora MexAy nocJ'leAoBa' A , 4 r r j a B o , ' r H b rp a B l l a 2 A , r l e A - p a c c r o n u t t e re.tLlii)lliili Ha6.[IOAeHI4flNIu.flpfir{l'iHy, IIo KoTopol? AHcrlepcull qacrot' lne npeAe,'ra HaiixauCra CoBnaAaIOT c AIJcnepcusMI4 6ou'Iee HIls- r r a c r o r , M o x { H oJ e f K o y B I I A e r bH a p r c . 4 . 5 7 . T e i n tH e M e H e eM o x H o c r a r t t c r l l q e c K l l M l ' { M e r o A a M I In p o B e p f i T b ' c ) l u e c ' l ' B y e r. [ l l A o M i l H a H r ] t a txl o M I I o I l e H T aB n e p ] l o A o r p a M M eK. p u r e plit?, per{oMeHAoBaHHbIii <Duuepou, ocHoBaHHa BbIqI'lcJIeHI'lH cneKT- HEHTA. yxasauuuMBbrrleo6pasou,r.rHorAa Cnexrp, BbrqucJrer{Hbrrl Ha290 ^-l.bb boooqHbrq rH'Te083n a P nc. 4.57. BucoxoaueprerurlecKafl cHHyc o H A a " l b H a f B o , l t l a ( I I p e p b l B H c T a t lJ M l A l - t c K p e r H o MM H O Hun), tta6,rrc4eHHatB X ( e C r B e T o q e l ( , A a e r O T t l e T ' t l I B oB U A H y I O nonrrt' tilgxoit qacrorbl (cil,1oulIlaff ,'lu' Hnn) 291 p a , ' I b H O r O3 H a q e H l l f l S A 2 , K O T O p O gn p e B b t g a e T 3 H a q e H U e O i i 2 e D e l t e H _ Irofo pfl,rra, cocraBJreHlrofo rr3 He3aBLrCUMr,rx c,'ryqariHbrx roqeK. KpH_ Tepltri ocHoBaH Ha BblrltlcJeHl.nr orHolrleHu, g:.s2-.,r/2s', ( 4 . 9 7) r A e s 2 m a x- u a r t 6 o , r t r u l t r ? - g,uclepctrn n e p l l o A o t p a M M b I H s 2 .,nuN o1l._Yeuu6roptAa. KpllrttqecKoe 3HaqeHneg Ans cneKrpa,rrb"_t^-t"t9 HoH BepoflrHocrn p p\aercs.@op;uy"rofi lnp-1nnt g=l--e ^-t , (-tr.gg) r!,e ilt:nf2, ec;ttt npe-ueHHoir pfl.q coAepx{ilrqer}roeqxcJrosa6.rrogeHur?,__rr n7: (n-l)12, ecnu lt ueqeruo.Ec,rHnpoaepreMaflcrara_ crlll(a g [peRbllxaer Iipllrllr]eclio€ 3112t19sile g, To N{o)KHonpeA[o.no)rirrrb' rrro [epuoAHqecKag r(oMroHeHTa CyurecrByer. Ec.nir IIpoBep t e M a f l c r a r l l c r l l K a H e n p e B o c x o A I I TK p l l r t i q e c K o e3 H a r { e H l . tT eo , Ha6,rrc,'ta-elruiicnerirpa,rluini nrrn s2-u* MolKer tso3HiJKHyrbc,ryuafi_ u u n , to 6 p a s o l r . HenpepunHuri cnexrp l a p u o r r r . i e c r i r f i a H a , ; l r 3I r n o c r p o e H r i en e p f i o r o r p r i M n , r bl lr. i i r r. - u r .. Hel'iroro cIIerirpa rleleco,o6pasHurs rex c.[yqaflx, KofAa rrcc.re.!,yetrrurrinper,relruolipa4 4ericrnrireurtHo nepogHqen. B [pupo,ne Bcrpe_ qaercfl HeMHofo ecrecrBeHHblxtn,teuuti, o6,raAatouttx rtcruHnoft |IepllOAIIqIIOCTblO, He CTIIITafl tB.qeHtjfl, CBfl3aIJHLIe C aCTDOHO]IIIqe_ I{l'lKJrla\'ln, TaI{llMlI, KaK MecqqHbte npil,'t}tBbt H oT,,iltBbt lr"'U.I ce3OHHbre Ir:lMeIleHlrq. bo.lluuHcreo reo.rrorliqecKllX SpeX4eUHdrX OgcltllMu r ec, . r y u a l i l r s t e .f l o c , r e 4 0 e a r e J r b H o c rH JOB ile nepilor'rrrrrecKia b a3bIBaercfl c,ryqaritrofi,ec,r[r otla Mo)r{eT6lrrl oxapar{Tepil30BaHaTo.rrbtioc nor{olublo cTaTllcrl]qecl(ll.xxapaKTepHCTIIK, B npoTaBolor'Io>KHocTb .lerel)MHHrrponaHuor? nocle.loBare.rrbHocrir,n xoropori cocrosHrre ivroN{er 6blrb roqHo [percr{a3aHo r]o ee r<oaip$uqueriraru. !,ax<e B rex c r - r y q a r x ,r ( O f A aa p e u e n u o i i p f l ! 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H e l p e p l r o i l r - , r r i c n e r < i p r r M e e r B r r A I l e n p e p r r r B H o xf rp u n o i i , n u r p a x a l o u l e i r 3 a B r . r c l i M o c T b/ I i l c n e D c r r r o rT qacrorbr, rr aHa.rrorxqeH H c r r p e p b r n H o $i ry H X r l H Hp a c I p e A e J r e r j r { B f ep O n T t r O C r eC u .; ' 1 l l C i l e p C U f l N ,nt lpt ,O n O p q u o r r s . r l b H b t \ 4n 1J 1 O t U a I f lU r r O A c n e t { T p a " r r b H on rpi l r n o i t M e x < ; l yr p a t { l q H L , l M rr.rra c r o r a M r r .O 6 u t a s n " l o x { a A r , n o , l c f i e K T p o Mp a B r r a o S u r e i i A u c n e p c r r u n p e u e H H 6 r o p n l a , . o 6 0 p o r , , r u H e i i H U f iC n e x t D n e A . ' r f l l i o r o p o f o o r r a B b r q l r c . 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Exrrrc il Vorrc [29] r e i r ; l i a u { a f l c f fB x t i r i f o i i o u e u r i e c r r e K T p as . i 2 , Iacnpocrl)aHgercg Ha no.:l'Jcyrracror, rrurpuua xoropofi BoKpyf f panna -l-l/n. llo iuepe Y B e , r l r q e H r r tf tl o 6 u \ a s r r H r p o p n r r u r z rc, o 4 e p ) K a u a f f c f l B A p r c n e p c r t r l clexTpa, pacnpeAe,rrreTcfl Ha yBe,lnqflBatoUleecr rjuc,Io noJlocoK v]reiib[rarcurerlcl runprrrilr. B pesl'"rrnrare yBeJxr{eHue /, Ae.rraer so3r,'roTriHori oueHr(y AHcnepcr.rr.r e 6o"'reey3Ktix noJrocKaxqacror, AaB a f l c M e u l e H H y r oo u e H r { yr r c r r . i H H o f oc n e r ( T p a .o A n a x o o u e H K a c r a H g a p r u o i i o u r u 6 x l r s r l l x 6 o . i r e ev 3 K r { x r o . [ o c F I e v j l v q u a e r c s . E a p r " u e r r [ 5 ] r r e p n r , r e 1 ' a i p l 6 o r a . r r t e r o f y n a e H o r l ' r e u ucrr a H l a p r r r o f i o r u i l 6 x u B c n e K T p a r - r b H bor xr l e H K a xH a o c I { o B e a . [ f o p L I T M a , H a 3 b r B a e M o r o , l r r 6M o e r o A o Mc K o J r b 3 f l u l e roor \ H a , , r l r 6 od l l , r t r D a u u e i i , . r n 6 o c r , ' t a x H B a H u e u , , r n 6 on p o c r p a H C T B e H H b ryMc p e A H e H u e M . AnroxoppenffurroHHyroQ1'uxquro Mo)KHo oirpeAeJrrirbB3BerrreHr{brM rreror,ol{ ,raroBoro oKHa H,rH Qu,llrpa, [1 B3BerueHHataBToKopped,ror p a M M a N { o x { e r6 l t r l n p e o 6 p a 3 o B a H aB c l e K T D a ! ' I t , H v roo6 . l a c r u . B e c a n p r r g a r c r o c o 6 o e 3 H a q e H l l e6 o . r e e N o l r o r n u r , I, t a f a M , x o r o prrte ocr{oBaHbrHa 6o,'lrllev qrJC.rre ua6nrcAeHuft, qeu 6onee AJIHHH b r e, r r a f n .C l p y r o i i c r c p o i r b r u e o 6 p a 6 o r a s s s r f i c n e r r p r r o i l i e r 6 n r r Bbiqllc,lleHII 3are\{ cf"rla)l(eHB3BeIIltlBaHLteM H ycpeAHeHxeMBMecre c nIir,'reraloitlil\,rH c n e r { T p a " r r b i l b r M3[ H a q e H u q M 1M 1 .H o x e c r s o B e c o B Ha3blBaercq cneKTpa"rrbHblltt oriHoM tr;li Qlr.ltrpoM n qB,'Itercfl npeo 6 p a s o n a H r r e r ,(rD v p u e . n a f o B o r o o K H a . O 6 a I , r e r o 4 a I a r o r a K B H B a pe3\'"rrbTaTbI, ,'reHTHbre KoTopr,tet{o}KHo xapar{Teplr3oBaTb KaK CMag L.rB :lHrre rrr'r rr cf Jaxiu BaHte ArrcnepcrrrlnDtiMbrKalouLlrx qacroT. , \ { H o x i e c r e oo r { o H H . rH S r r , rr r p o n p a c i u a r p r i e a , , r o c rp, a 3 . l r r q H bMr H a B T o p a r ' r l rc; r e M a o K o H , r r M e r o u r a rH i a r { . [ y q u ] r r ec e o f i c r B a , n p e A c r a B ,rser co6ori HauBbrcrxee x o c r r r ) K e H r r eB a r { a J r r . i sBep e M e H H b IpXs A o B . O . r H o r r : u a r r 6 o . r c eu l r r p o r ( o r r c n o , r F , 3 y e l b r \o K o H- 9 T o $ r r n r , r p T r , r o x r r - X a H n r u r a , x o r o p u r i B c n e K T p a . [ r H o i io 6 . t a c r u r r N r e e rB H I '.t: . - I t .2 ":_l '.. I I -. ,. 2 l _ r o I I l p e o 6 p a s o B a r r r r e@ y p n e { l r i " r r r p a Jafl ecTb l i "' , ' - I 1 l 2 \ '. /2 tl. Tlroxrr-Xauuuura (4.104) B o6ilacrrl (4.1051 .o.-ll \ t. l 3 r a Q o 1 t r r 1 , , rot an l l e r f e J l r e rB e c a a B T o K o p p e . r t x u i r o u n or lfyi u r i u n l r , x o tX/o:1,0 npu Hy"rreBoM . r r a r eA o lQpar- !{.];IKo y6i'tnaer or 3Haqennn l i T r : 0 , 0 n p r r N r a K c r r N { a . l b r { loaM r e l . K a x i A s r i i ' x o e r p $ i i u r r e H ra B r o , riolti)e.rlflqnrryMrrox{aeTCffHa coorBercrByroululi eN4yBec Ao BbrnoJrH e n n f l n p e o 6 p a : o n a u r r a@ 1 ' p r , e V . p a e H e H i r e( a . 1 0 2 ) "r r p H H H M a eB r r.{A / s,'-3(l r- I 1_l 29e \ slil',r,cos2.ttl. (4.1(rG) ,riaroB' oNua, o6rtqHo .nlt6o s o6,'Iacru I.IAPYTHe Moxso nPeAJIoxI4Tb qacror' TaK K a K H X n p l l M e H e H I . r6el t e a e r J e f q e r u ,'In60B o6nacru a ro 4PYrorl'IIIupor<o licno.tttsyeuoe fIap3eHoBcl{oe n oAnotiQoPve, OKHO HMCCTBI'IA 1 V, Jittl '|,, "L2 HyJIe\{,, I lq r., iraroB Nre)KAy Wr:2(1- I ,1- I I UL ) ' \ ) ( + 1. 0 7 1 ( 4.l 08) , r r a r o Bo r L l 2 l o L . xapaK' Ilpaxriluecxafl cTpaTefxs uccJreIOBaHlIfl cneKrpar'lbHblx .l.e;,,icrrrK C,rVqaiiHL,rx epeveuHltr pflAoB BI{.lloqaeT cJeAyloutle uafll. ypaBrlrrb AaIIl. Ecnn Heo6xo4lruo, u36aBilrL' or rpeHAa li'lil p e r p e c c t i l l Y . 1u a i I I 3 a r e M u a i t r H ,'uta, *,u,,".uHe xoa$$llqrleHrbl ocrarlill: Yi':Yi*Yi. cra' 2. Buquc,rtlru anrot<opperflqxrc llcxoAHoro pr4a (ec'nu oH I'' J l a r a M a K c l l M y M a Y ' e n , l o t l A o p s A a n . i u i n o " ,rrrouapeH) u.rlt BbIpeI{oMeHAyIor aBropbl Hetioropue nl3. He flpeBocxogut xoropni't lrirc,irflTb 6o,'lee y3t{ile nl)eAe'rbl A"rlfl Malicl'IN{yMa 'qara' HailpllMel; n170. nl\, nl6 unpr Aa>Ne S;-' 3. Buqnc"nrrrt Heo6pa6oraHHyiO C[eXTpa!'lbHyio [,r]oTHOCTb y p a Bp e A e , l l e n H o e o f l O y p l e , r r c n o , r r b 3 y fA l I r c K p e T H o en p e o 6 p a e o e a a r i e ( 4 . 1 0 2 ) . ireHHeM 4. Cr,ra,l.rrrt ueo6pa6oraHHnii cneKrp, llclloJlb3yt OKHOTbIOi(liXausrrgra (ypanueHr1e 4.104) B Kal{ecrBe cKoJIb3tlIeIo cpeAHefo rl,irfl rro.rryqeHlltl cf,'IalKeHHOii OIIeHKII AHcrlepcua c[eKTpa' o q e s l r A H o , B c n e K T p z t . n b H o Ma H a J i l I 3 e I I M e e T c t l M H O f o C I I O C O O O B Ha ol(oHqaTenluuli peKOTOpoe o6_a>NeTB.rr11flHue npuHflTr, ^peuteHrie, oHrr a l l a , l s 3 H p y e n , 1 o f in o c ' [ e / ? , s b l 6 o p A , 1 1 H b r n n " , p o q a r c r .,vnorur. n'Ooutano"OCrtt (eC,rU 3TO HaXOAIITCtI BO B"laCTil tlCC'le4OAafe.lr) ; NIilricrrN{ztJI)ttofOd'Iara L; U Ot<tta,IIClO.lb3yeMorO A.'Ifl Crr'laXHBaHHg. ci:t:rr Me;^riAy 3TlrMri nepeMeHHbtNgl ri trx BJ1,19HHe KaK Ha pa3pe[ r e H i l e . T a r { r r H a 3 H a q r { N r o c T bo f J a x { e H H o f o c n e i i T p a o 6 c y ) K A e H b I I 1 O r l ') o 6 i r o B l i H I I r e E H t u t u c a u V o m c a [ 2 9 ] . Bbtno,rnqfl aHaJIil3 Oyple, MLI IIpeodpa3oBa,lil HaIlIx AaHHble H3 olnoft o6'{acrlt s 1p1ttyro. Mlr uaqaeu c Ha6'rllof.eHtiii sa Qopuofi r;aBncr.rMocrrl 3HaqeHltrl Yl or I{oopAIiH&T Toqel{ npocrpaHcrBa il'rltl TOqeK O6pa3yeT ClifHar'I I'lr'IHBOJ'IIlper,ieHII ;r;. |IOC,{eAOBaTe,IIbttOCTb KoopAllnar X s Y' rroByro $oDlly, onpeAe.IleHrtyrc B nJocKocrll B r i o u b r y u i e . o t o p " t , q r o A a H H b t eH a x o A s r c q B o B p e M e . H H 6uf rn u i t i ) c l c r p a H c i B e H u o iol 6 n a " t n t t 3 a B t l c r r o r n e p e M e H n o f iX , o 6 o 3 H a .taloul'efi KoopAHHaTbrToqeK Bo BpeMeHa HJILIpaccToqHl're.OnpeAe. l l l B K o r r { I I o H e H Tqbat c r o T B c l { l H a ! ' I e , N ' l b n l p e o 6 p a 3 o B a J I uA a H H b I eB r l a c r o r H y r co 6 " r a c r b . @ u g l ' r q e c x a ga H a , r l oHf f l M o x { e r 6 l t t u u : o 6 p a x e co.rlHeqHblx Ila Ha pflcyHKe, tAe [peAcraBr'leH e$Q-exr_ OTpa]KeHI'Ifl N{o}KcBera 6e-noro (puc. 4.58). Cson npr.r3M "ryuefi or s"ep^a,noHbrx Ho paccMarpunarl KaK KoMnJIeKcI{yrcBo,'IHoByIoQoptnty'I{3MeHflIo' 297 II It, I $ I & t$ t lllIiocfi Lr TerreHileMBpeMeHUlr CocTctrulvlo Il3 cBeTa pa3JIHqHbIX n o . ; r l r ) .f l p r r : l r a . { e r i c r a y e r 5 a x q a c r o r s n l i a u a _ U L . ' ' ; o r l( i i . , i i t ; 1 . ' l u H "Iili-li:TOl) Ii pa3Je,ritleT O l,lJtfrTPb! T I t I 1r B De3Vd,Ib- l)VlO FIe.r;b,rflIIoJIyqIITb HuKaKrrM Ap)'flrM CIIOCO6Olt. I t It, I1\'(IOIi Ha efO COCTaB.rtflIOIqUe qaCtlI, T : l r e r r e f o H a r r r c r r . r e e r r o i r y q a e r c r rp a A y r a . K a x A a q o N p a i u e H H a s Iro.luCa or.ileirrrercHor coceAHeri nponexrl'rouuori soHoii, lllupHr-ra xoropol:i nl)onol)rliloH2r'Ibtrzr pa3HocTri ilx A.rtrrHBo.,tH]r,rili qacToT, a ! n r r e H C r i u t r o c r bx a x . l ( o i i r o , t o c t r t n p o t t o l ) i l t j o H a , t b H aB r { J r a A y AaH_ uoil x,runlr iio.,rHr,ttr o6qyrc ugregcrionocrr, I.IcxoAHoronyuxa. I4cc . l c . ' i o B a H t r cen e K T p a r r c r o r i H H K ac B ef a \ { o ) t i e r c K a 3 a r b H a M r , i H o f o e o cTpoeHr.rillicToqHilKa cBe.t.a,efo rer\1IlepaT\,pe, IIprrl)o.l,eBeu],ecTBa, ci\|03b lioropoe ltpoxo.r,t{TcBer rr rari ra.[ee. Aila.lorttquo ficc"rte_{o_ B a r rI i e q a c l ' o r H o f o c n e K T pa r a u s o t i n o c , r t e r o B a r e . r t b H o cM r HO X { e rp a c c K a ; l a r b r r a l r o e f o r r p x i l o A er . rr r c r o r t H r r r i eA, a r b r r H ( r o p l l a r l t r r or,i o r o - @rtlurpotr I ra 3 b t B a e r c q M a r e t r a r l r r e c r l l i . r o n e p a l o p , x o r o D b t t l z s - MeHrersarauubril. npeneusoilpflA s .qpy|oiiepe-veuuoir pnA, uiraenr4uii rpe6l,er,rr,,ro-r!opuy'. Taxrreonc'parolbrriasLrgarorcl-<QH.nlrpaIlll>, TaK Iiali fiepBoHaqa.rlbHo oHII n]leJcraB.Itflr'ILIcb 3.rreKTpoHHLIMH ]13 cerr{ cortDorr.iBr,regtrfitr Qit"rorpvrcu:,lMtt qe.r]fl]itr, cocrofllrlutlii evriocreii, rrc[oJlb3ye]rbr.x Ar'tfl ni,t6opouuoro [oAaB,[eHHfl Hr'tH yc]tr e r r l r r c n e q l r r f r r u e c K u - \ .r r a c r o r B 3 , r e r i r p o H H L I . \ C r . t f H a , l a x . T e n e p l r e x < e Q y u x u r r r r n o n p e o 6 p a 3 o B a H r r r o u r r ( r o o a u x c r i r H a . r l o BB b r l r o d , r r { r r r o r ' cfl Ha Ko:rrrrbtioTepax a,{aTeMaTl{qecKit\1[ QH,llrpaull. ocHoelrl leo- puri Qu.nlrpaqun6tr,ru sa,'rox{eHbr Flop6eprou Buuepolr n pa6orax Iro crarrrcl'r{qecxoii TeoprrH cBg3u,rr 3TareopuflHaxoArrrcnoerrpaxTrrrrecKoe npHi{eHeirue lpn o6pa6oTrie ceiiclrrrqecxrrx cilfHaroB r{ jlaHrrbrx a3pOQOrOCbeMOK. B cn"ry erOro 6O,llnttltcrBo TepMIIHOB Teoprlu tplrllrpaUrzl{ rpo}l3olIJ,'lo He H3 KJlacchqecKoii crarHcrllKll' a t r a r t g > x e H e p H o i i3 " I I e K T p o H I l K uu S t t s l i x l t . fior'tyittulHHau6onee uIIlpoKoe npuMeroAtt reopx[ Qu,rlrpaqu[ i l C C r t € ! , O B a H I I I { o T p a ) K e H H b I X C e i l c N t i l q e C l i } l xJ . a H H b l x . i l p t t MeHeH;e I l c c . t e A o e a H I J e C e t ? C M u q e c t i t t xc B o l i C T B O T p a i K e H r l b l x c l l f l l a " r l O B O C I I o C H r l l a . l a ( c e i t C t r . t t t u e c K r3f lH e l ) r H f f n l ) O t l a r r o r r a C o 3 4 a H f i HB x O . 1 H O t O 3aTeM rotopufi il3BollHrcf B3pblBoM AHHaMHTa HJIII Bu6paropov), B pe3yJlbrare nof.noueH14q SHepfIIu cHrHa.ra no NIef'e {rrrlrrpyercfl qacrorbl IIof.]oefo nl,TelllecrBIifl cKB03b 3eMHyIO TO'rlilly. Bltcoxtte q T O c e i i C x l l l . l e CKIl\ Iig,le6arlllii n p l l p O ; 1 a T a K C I I J t b H O , 6 O . [ e e Ula1OTCfl qro Bo"lHbI HII3tr3MeHfeTcl tro Mepe ux nepe,lBll)lieHlltl. !,o6aettv, titrx qacroT [epeMeUarcTCff qepe3 ropHble nopOi],bI6o.,Iee 6ntcrpO, Bcn"IIeCK CTaHOBIITCfi CMa3aHHbI}I ll rar{ KaK Haqa,'IbHbtii OCrpuii , l c . ' r a 6 . r e l r H b t l . {B. b t . \ o ; i H o l i c t t r u a l , x o r o p u r : t o 6 l l a p v x i } l B a e r c g H a 6 0 cttrI13 Orpa)KeH_llt? i ) o I { r r C B e p x H o c T H b t xy i I a B . x t i B a T e . l e i l , . C o c T O l l T ira.roe, Bo3BparuBlUuicn u: 6olee r.r,v6ot<ux rop[3oIIToB. K co;ria.teHil]o, noc,rle ilx nyreuiecTBllfl oTpa;IieHHble Bo"rIHblclL'IbHo Ae$op)rupoBaHbI tl HX TpyAHO lilrTeplpeTHpoBarb. 3 a A a q a r e o ( p r . r s H K -a y c r p a H l t r b H a c r o . : I b l t o , H a c l i o i l b l i o 3 T o B o 3 Koropblrl ],roxiHo, BpeAHbre a{r{rerrur $H.rorpautttt, Quslluecxoit cer?cvuqeirHricurna"'r6u,r no4nepxes. 3ro Ae,'Iaercfl[yreM o6pauti$ponurau $ttrlrpaull, Koropble 6orxu ceiicMH.recKrrx3anucefi qacToTut,o6ocrpanT oTpalKeH[ItlIl rovcTpaHfl}or He)Ke,rraTe,rlbHble B 3 a i l u c l l . t a B . r r f l n ru y N { AO rex nop, IIoI{a rpe6yeurrii, uo oc.ra6.'reuHr,rii crrrHa,rrtre 6yr1er BbIAe.rIeH. B cH.ny roro qro MHorHe ts03MylleHIIf ceiic\,{rlrlecxllxcurHaJoB L l a c r o r H oc o f . q a c o B a u l t ,r e o o u s u x o e o c o 6 e l l H o l l l l r e p e c y l o r S u " l s r creulleHepllpy]or IIJiI YCTpaHtlloT p b r , r i o r o p b r e n p e J . I ] o q T l l r e . l b HrO r p r r . r e c x r rqea c r o r b r . C e f i c u l t q e c x a a Q H n l r p a u t t x q a c r o [ p o B o A I I T c f l e a r o i i o 6 " n a c r l 4q a c r o r c r l o M o x l b l on p e o 6 p a s o n a u t i n@ y p l e c e i l c \ I l l qACTCfi CNCKTPA H IICCIi}I,\ CHfIIAJIOB Ii YCTPAIIEH}Ifl HEX{€r'ISTC,TIbIIbIX roc"ireitYroulefo n p e o 6 l ) a 3 o B a H I { f lo r Q t t l i ' r p o n a H H o f o c n e x r p a o 6 i ) a r H o u ! . e i i c r s r r r e J b H y l oo 6 " l a c r r . O A I r a x o B T o t l H o c r l lT o r x e n p o I l e c c ) i o T i i e r 6 r ' t r r p e a . l t t 3 o B a Hn p e o 5 p a s o n a H u e M$ l i , r l r p a o 6 . ' I a c r n Oypue B pea.rbHbleAaltubte u iloc"reA,vloiueiicBeprKofi ero npeo6pa' : l ( ) B a l r r r cf f c e i i c r r r r q e c x l l M l3r a t l t t c r M I tc H f H S , r ' t oT Ba. t i x a x a r l t Q H . l r r qacToT H IIOonpeAed'IeHHbix npetrHa3rraqeHbr ilpo)ioxiAeHtlfl I.ltl 1)l,r ti 1l ti ll li i Puc 1.58. flpu::'la crlxHr r{acrcrubr\{iiHarH3aroposr,npeo6pa:_vroulrru 6e,ruir Hi,i r na p e v e H r r 6or i6 . r a c r r r )B e r u c o c r r B r i r r ev r : r u D a g caei (u npocrpancrBerruo HIJx qBeroB (o6racrr uacro,r) 298 jla B"rleHtrrrApyf Hx qacToT, TO OHII H 33 biBaIOTCtl BIjCOKOqaCTOTH blMi{, ]I II3KOqACTOTHbIMIIII.T] HbIMII QH.] bTPA MU, H IIO.r'IOC T e o p e r r r u e c l i l r M o I K I { o n o c r p o l l r b c o B e p I I J e H H b i eQ t t . l l r p u l , I i o r o p r r e 6 y , r . y r r r p O n 1 r g 1 1 2 1C 6 I i f H a r ' t b tC n e U l t Q l t U e C K ] l xr l a c T O T I I I l e n p O ' Ilvcriarb .npyrrre qacrorbt, Ho ratitle Qultrpu o6blqHo rpy-lllo pea' .lrt3oBarb. 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Marplrqa B Toru{ocru raiiaq irie, KaK rvu ltorru- 6n no,rvrilrrb' ecJlri 6u nprrra"lir rioHeq Aairuofi loc,lreAoBare.lbHocrH 3a Haq a ' 1 o ' B b l r l H c " r I I { J IB He p o f i T H o c r l r n e p e x o A o B c B e p x y B H H 3 H s a r e N I ruarplruy repexoAHbr x Bepoff rHocreii.Marplrua neperolu brx BeporrrHocreiicBepxyBHr3yria3aHaHu)Ke. { ,1 dl t M,-r rLrrrur AlBl cl Dt_ Cyuurr no crol6uau trepexortHbt-\ AB 0 ll 40 l,+ 6 Aa ,Uarpuua nepexoAgbrx neponrnocrefi {lJr nepexoroB cBepxy BHH3) ":'"; ABCD 2 l0-l 13 3 | 0 el rs o_l 22 20 30 22 A lB I c | D l_ C y n r r ul o cro"r6uau 0,00 0.18 0,64 0,18 1,00 0,55 0,00 0,30 0.15 I,00 0,07 (r,43 0,00 0.50 1,00 ( ) . 4 5_ r 0 .t 4 | o . qI I o,oo_l 1,00 B n r o 6 o l t c r ' r y q a e ,r r M e e MJ ' I r r\ , r b rA e J o c o c r p o K a M l r u n r t cro,n6uaMII, BCe a.rreMeHTbr crl)oKlr l.r,qlrcro,ri6ua J.e,1flTcflHa cyMMy 9..rle_ MeHToBeroii crpoxu r.ul cro,ti6qa, npr{qeM sTH cyMML,r coKpau{aIorcfl rrpi{.Bbtqric.leHtrriorHorrleHrrflnpou3BeAeirnftlrex<r1y crpoxa Mr il.'ru cron6uarnIlr.llosroMy ror xe pesyrmar noJryqaercr, ecJrHnpol r 3 B e c r ns r r i o f l e p a r l r H n p r M o c u a r p n u e f r n e p e x o 4 u u r xq a c r o o . Ir[ep a n p a n o f i 8 3 a r r M o 3 a M e H r e M o c r l rc o c r o n H r i i i A u B uo,u"ar""r.o i(ari ornoueHtie irpoi.r3BeAeHtri Anyx cro"r6uoe: AB Is:?3I-:f:;;] | 0,64l** | o,so I o,18l--._lo,rs Mepa npaaofi esaul4osaMeHreN{ocru paBHaRa.e:0,4g. flpyrrre 3JreMeHrbr Haxo,{rrcfl aHa!'rofrrr{Ho. lIo.THaqMarpr{qanpanoii uiair314 I I 4 u r e p n p e r a q r r aa r o r i M a r p l r u b rr a K a f l x { e , K a K I I L i H r e p n p e r a l l l { x oTr'rutqilecocToHTJII{lUb xrarpirubl uep rrenoii B3alrNt03alvreHrreI,rocTt'l; { a o c t t o B a H l i HT e H A e H n T o \ { , ( i r o c x o A c r B o n H e f ry c r a H a B x t t B a e r c t H LIr'II{lloullrr oj(HIIX Ir rex iKe coclosHufi 6utru npe.l.ruecrByloul.HMH c.'reAyIoxIHMH. H a x o u e u , M r , r l { o r i e r , r o f l p e A e " r t H T bM a r p l t q y M e p 8 3 a H M H o i ig a \ . r e H f l e M o c r rKl a K M a r p r l u y n p o u s e e . l . e u t r t tB c e x n a p s u a q e u u l ?u e p l t n p a a o f i 8 3 a H N { o 3 a N I e H t t e M o cTr.IeI ,. "resoii Cii: Li1Ri1 (4.1l5l 3 r a n , t e p ax a p a x r e p r r 3 y e r 6 " r t t s o c r bo A I I o f o c o c r o r H l l f l c A p y f l r N { OTHOCHTeJIbHLIe qaCTOTbl' C l(OTOpbIlIlI sTIl COCTOflHI'1flIIoflB.IlfflOTCff B nocr'lelotsaTe,'lL'HOCTII, T. e. BXOAflT N{eX{Ay CXOAHbIMII COgneN{eHToB AByx I\IarxrHo}KecrBeHHLIx crofllruiRN{rr. flporrsaerleHlre I , I N I C C T B I { N , B 3 A I , t M 0 3 A M C H f E M O C T I t NIIII qepes l-t ,oo o,l3 I o,l 3 l ,Oc | 0,22 o,og l_0,16 0,90 0,22 o,I 6-l 0,09 0,90| l,o0 0,06| (1,06 1,00_l > p a p x r l q e c K o r op a 3 l l e u i e H l r f l . Mlr lroxte,v nocrpourb <(AepeBo> ue i J i { o r c l ) o N ,}Ir r { a 3 a H bcr B f l 3 r i o A r r o f o c o c T o f l H u t c A p y f H M I { a o c H o B e I r - \ 8 3 a u M H o i ie a r 4 e H s e N , t o c r u r B r i o r o p o N { } t 3 y q a e N { b tceo c r o q H i l f l)aciloJox(eHbr B rroDfl.l,Kerrx ualt6o,rrtulefi egattlto3aNleHtteN{ocrtl. &lero;r.r.rnocrpoeHufl raKHX <<AepeBbeB>> c rroMourbro3BM 6yayr p a c c l { o l p e H r ) rB f . r r . 6 . T e n e p r i K e \ r b r o f p a H u q f r M c f lr 3 y r { e H u e Mp e 3 y " 1 b ' r ' , , l T fopBy n l i l p o B a l l r r r < < I e p e B a >N>r a T p [ u 8 3 a l , r M o 3 a M e H t e N , r o c T l , l , I l o c T l r o e H l r o f oA r ' t f l c r I a r u r p a ( r r r r r e c K o f o p a 3 p e 3 a , I I p e A C T a B " r e r ] H o f o H a p r i c . ' 1 . 6 , 1T. a x u e r p r r < < A e p e B ar>r s>o 6 p a x < e H rl ,rra p H c . 4 . 6 5 . f l c n o , q r o B r r D r e u r o c B f l 3 a H bK f l6 u r e r o l p e A u e c r B y r a r {c r o q K U 3 p e H r . r o I0lqef(1,Tari r{ c TortKrt3peIIufl rrocJleAyloqeto cocToflHufl. f l c R e r . r a u t r e c t {H e J a B H o n y 6 , n n x a q l n r , n o c B f u { e H H b r e a H a J I I I 3 y B 3 a t l . \ l O 3 i l , \ , { e H f l e X { O C T I IB f e O , r I O f l t t t e C I ( i l X 3 a A a q a X , H e M O f y T C , ' l y > K H T b eule'l)riHN{ ;r(oKa33Te,,tbcTBOMnO.te3HOCTX, IIpilMeHeHilfl 3T14X MeTO- A o B I J r e t ) . r r o r r r r3r x. c n e p r r M e H T b ri l,c r r o J l b 3 y l o u r r e A a H H b r en o c r p a r l t r p a Q r r u e c r o M yp a 3 p e 3 ) ' B K a r . r 3 a c eo, r ( a 3 a r ' u r c rbr o . r r e 3 H b r M Br r. r{ t r r e p I I p e r a u r t L It l r { K . [ o r e M .B c e o r l o x e u H s , B o t r r e A t r t l rB e gror 6olnurot? p a 3 p e 3 , 6 t l n r r p a c x , r a c c r r $ n q l p o a a H o r H a l 8 / ' r H T o . r r o r n q e c K l {cxo 315 pe3y"IlbraroMHatrIHXucc!'IeAoBaulifiAo.ltNtto 6urt roAl,l. KogeqHbINI c n e u v Q t t u e c K l l x3 a A a q , a p a c u l l p e H r l e H a r l l l x g u a u n f t o p " t a u n a nu lpolicxoAfr BHyTp]l 3eu.nu. npoU"aau", KOTOpble ,t L n eB C B aa Cnpaaa B3aruso P u c . 4 . 6 5 .lpynnri crparurparpu,tecKt_\ cocrornuli, nocrpoeuHbre no rperr r'na\4 CNLiCOKTII,ITEPATYPbI IIep 83atr.It03aMeHfi eMOCTIt. C o c r o r n t g B U D agaAOrllqsbl IrO tx nolo)KeHHr\1 n crparrrpa$avccKoii Iofje:lcBAreILll.)aIfi arch Soc. Jottr., 2. Anderson R. Y. and,Koopnnns L. H. Harntot.ticanalysis of varve time ser i e s .J o u r . G e o p h y s i c aRl e s e a r c h1, 9 6 3 ,6 B ,p . 8 7 7 - 8 9 3 . 3. Annstrbng,ll. and R. !abin (. Vario-grantmodels nrust be-positivedeiinite. 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J, o u r . ,1 g 6 8 ,6 J , p . l 0 9 l - 1 1 3 1 . crofl rrr{r1.Aua,rns B3aHMO3a Mer{ffeMocrrr 6r,r,r uclo,,rl3cBaH c qe"irbro llaxox{AeHIIfl trtHHIIM&rbrlororII.rc,'rad-'ir.{ToJorHqecKIIX pa3HoBr4AHocTeir, Heo6xoAurvrbrx r"r1fl onpeAe,rrerlrflnoc.rJefoBare",rbHocrrr. 6.ryaro_ NAPfl 3TOMY YAA,'IOCb rI36C}IiATb I{JIACCII(bI4KAIIHH II3BECTHflKOB IIO TIX p s c n o J o x i e H r r l oB p a 3 p _ e 3 e r r_o 6 b e r ( T r l B H OC O 3 r a T b o n p e r e . D e H H v r O r{uK"rrrrecKyroMoJ,eJb . Ir4] Beporr'o, sTOT MeroA rvroxH. y"n"tutio I I C n o J b 3 o B a T [bp ] r p e u e H r i ] r . C p y f u x c r p a r r r r p a c p f i r r e c r ( ] r x 3a!,a.t, a TaK;'r{enpH ncc,rreAoBaHrjflx MfiHeparbHbrxIIapafeHe3lrcoB. gro)'r Ha Mbr 3alia.rrrtlBaelrpaccN{orpeHrieMeroAoBrlccJeAoBarrrfl roc"rleAoBare,'IbHOCTeii AaHHbtx.Ha ult o[ircaHbl Hali60,rieeqacro IIcnoJbS]'eMIrleB Hacrofltqee BpeN'rfl' teo,'roflrt npor{eAypbr r MeroJL,r, ]ioTopbre rro3Bo,'rlJrrrnoaryt11j16 rrHTepecHbre pe3yilbraibr Ir B ApyfHX o 6 . l a c r s x . o ^ r r a r < oH a ' ' r e r . { 3 r ' ] o x i e H rHeH K a K r i u, i o p r r o * t naian .ur,T a T b r c q e p n b r B a r o u l i r MI,i ^ M O ) K e 'cr , l y q l l T b c r , q T o B KOHerrHoM r.rofe rroJre3HbrMrr n,'rfi riayri o 3eM,1eoKa)Ky.r'cfl coBceM Apyfxe }rero_ibr. oruaxo paccMorpeHHbre B o n p o c b ro x ; a r b r B a r o r 3 H a q l i r e J b H b r rK' rr ) y r 3atraq I{ cocTaB"rrfroTocl{oBy A"rrflrloc,,relyrorllero rr3yqeHlt'I tr til)oA O , r l K e H r rr9r c c , ' l e n o B a H H I i . o r v e r l l i u t , q r o r e o " l o f u t e H 3 y q a . r l rn p o 6 r e v y a H a J r 3 a rocJ.reAoBare,'rbtocrer?!aHHbrx B Tofi xg Mepe, r{arx3ar,aqt tccr,IeroBaHrfi p a c n p e A e J l e r { r r bA r xa H H b r xB n p o c r p a H c r B e . B u o , r u e B e p o f l T H O',r O aHa"rr,3r{apr [or'ryqrrr ctsoe pa3tsurrre 6narogapn roMy, qro oH rrHr r o x o H C I I O , ' I r b 3 0 B a ,r' ,r{cga n p e r c r { a 3 a H I r t { r u H a u c o n u x ' : a r p a r n p r r PA3BCAKE }IECTO-POX(ACHIIii IiAr HCOTflHE,IX,IAK H TBCPAbIX NOJIC3HbIX I r c i { o f l a e \ , t r r l x .F I e c o r r a H e H H oM , eroAbr aHarl3a AByMepHbtx .qaHHbrx o q e H b B a x ( r { b r 'r . {M r ' r p a c c M o T p r r MH X B r d r . 5 . o a H a x o npeAcKa3aHrre Quuaucoer'r-x npn6u,refi He Mo;^r{er cJry)Krrrb AoKa3are,rbcr.BoNr B n o.r'rb3yrrp rnvreHeHaq p acc M^oTpeHH brx MeTOAOBAJrg usyrreHHfl rrocJle- A o B a r e . r b r - r o c r eAf ia H H b r x .C x o p e e c , r e A y e T o 6 p a r u r l ' u n i i * u n , r . uu noreHl{ua r'rr,Hbre BO3MO)KHOCTn MeroAa a nro Maru,IecKofi Kopper,Irqrr Lr x a l ) o r a x r b r x A r r a f p a M M C K B a I K u HH J t r rH a M e r o A r r 3 y q e H l r fnl p o A o . r i il{llTeJIbHOCTrr BpeMenlr Mex{Ay Byr,rKaHHqecxu,r.ta rrsnepx(eHuflMrrHJrH selt"r]eTpflCeHHffMLL SfH saAaqrr erue He peueHrJr,II Hlt ojlHH tls rr3_ r'lo)I{eHrIbIX 3Aecb MeroAoB He Mo)KeT-npereHAoBarbHa ro, qro oH peueHre.oaHaxorro Meperoro riaKxrbr 1.1:1"y1^"j.erBopr.rre"rbHoe y3HaBarb o feoJrofrJqecKr.rxnocJieAoBare,rrbHocrflx, :L{:_y *u-Tor. oyAyr no-aBrtrbcfl Bce 60"qeeMou{Hbrelr ycoBeprueHcrBoBaHHbre Me- olu i oll 23. 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A n i n t r o d u c t i o ni o i h e i h e o r . ;o f s t a t i s t i c s . 1 . 1t l r e d . ,H l I r r e r P u b l .C o . ,N e u , \ ' o r k ,I 9 6 9 , 7 0 1n . 6 4 . Y e tj'e i : i t l t V . S t a c l u ; s 1 i pc r o i e s s e si n h 5d r o l o g y . W a t e r R e s o r i r c e P s ubli. c i rt i o u s .F o r t C c l l i n s ,C o l o . ,1 9 7 2 ,2 7 6 p . 4 1 . P a n n f s h rHt . A . a n r l B r i e r G . . WS , .o r r r ea p p l i c a t i o nosf s i a t i s l i c sl o n r e i e o rologv Pennsrlr:rrrrS i i rl a i e t ' r r i r : . _ 1 , v .o;,1,1)l:i:''"r,slft.^ll,li-,::,Unii-rriiu p r ; ' k : "p",'isdslbi,i"i p ' r . 1 9 6 5 . 2 c an U n i i e r r i i , Firrl 42. Qur'nbui!e,41 ff. Associa iatedrneasdrernents, Butter;"rthr', London,1952, 2 7 9p . 43. Rar.,rr,r J A r . A n i n t r o d u c t i o nt o s p e i - i r a la n a l l . s i s .p i o n l _ t d . .I _ o n d o n . 1 9 7 1 , 1 7p4. l :i : 1''' nl T,Xl,:t,S";Geo phr.sicat signal anarysis. prentice.Hatr, !,?0":::3r.f;,3^i"r; 9 ,'. .o?:n;:),-r.,'I'; " oi );o^*{i'#.i.1: t aticaI etem enrs rorcom putergra. ":?gg,,rdq g 7 6**m .2 - i ' 9 ' ; n n ' .1t^rfdf;{:,?i, ;^,t;9:l: In "Tc . , , N c uY u r t i .*"f rb ^ H i t t .. , a n d H t g n g . i i .' '' nAq;_" _ 6i 8p'p' t i c a l i o no f c l r r s t e d ,1t ee_\,xl4tia6' nr .dd. Rp oi cst uerne f e rA ld r e t e c t i o nt o p r oocceessssi ni ng g . . , T e . cr fyi .. - rriclrrre Tec-h R Roenp . 6 g - 6 l i l ^ ^ _ ^ , , , o r e ^ i ^ _ ^ ^ - ^ _ r ^ _ t r . - . , o i , \ l a r v l a n d . . . C o l l e g- upea r i < 'I.l d . , j g O g fO + p . " " c o m p r r e r S c i t , n c ec e n t e r , U n i * 4'/."s aski n M. i . ^;a'' th; ; I;i;,,;" tuur u b:' , l;- ..'.r{ir l \ u l1ooanssssoc o ci, i ass ssion,a neti, geological too l . J o u r . 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