WWW.DISSERS.RU


...
    !

Pages:     | 1 |   ...   | 14 | 15 || 17 | 18 |   ...   | 25 |

Oac ycooc cpoc pocpace apaepo, o oop oaec pocpaco, oopaa oopoo c apaep cce. oeco apaepo oe , o paecoo opae aoee pacpocpae c a.

yc xapaepcecoe ypaee cce ee s3 + A s2 + B s + 1 = 0, (6.38) e A B apaep cce.

ycooc cce, cxo pep ypa, eoxoo ocaoo, o AB> 1, oya paa oac ycooc ye AB= 1.

Pc. 6.20 epoa Bepacoo B ococ apaepo A B paa oac ycooc pecae coo epoy, aaey epoo Bepacoo (pc. 6.20). Oac ycoo pao oeea pxoo.

pa oac ycooc oy ae, ec ppa y oe a0, an xapaepcecoo ypae peoce opeee ypa:

a0 = 0; an = 0; n-1 = 0. (6.39) Bopa x pa cooecye a yeoo op xapaepcecoo ypae, a pe - a co x ope. pae (6.39) paa pocpaco apaepo a p oace, oopx ycoo ye a oac, e opeee ypa 1,..., n-2 ooe.

6.8 ACTOTHE PTEP CTOBOCT acoe pep ycooc oo cy o ycooc cce aoaecoo ypae o y x acox xapaepc. pep oo cceoa ycooc cce cooo opa e pocy eoepecy eppea.

6.8.1 p apyea B ocoe acox pepe ycooc e cece ecoo eop y oecoo epeeoo pa apyea. yc a oo n- cee (6.27):

D(s) = a0 sn + an-1 sn-1 +... +an.

o oo cooec c eopeo ey oo peca e D(s) = a0 (s s1) (s s2)... (s sn), (6.40) e sj = j + ij op ypae D(s) = 0; j = 1, 2, , n.

a ope eoepec oe opae eopo, poee aaa oopa oe sj (pc. 6.21, a). a eo paa oy oecoo ca, a yo, opaoa eopo c ooe apaee eceo oc, apyey ae oecoo ca.

Be (s sj) eoepec opaac eopo, poee o sj pooo oe s (pc. 6.21, ).

p s = i, apep, oya:

D(i) = a0 (i s1) (i s2)... (i sn), (6.41) o cex eopo yy axoc a o oc (pc. 6.21, ).

Paccapa eop D(i), oya, o oy eo pae D(i ) = a0i s1i s2...i sn, (6.42) a apye. (6.43) Ec p a ooeoe apaee ocea yo pae po acoo cpe, o p ee aco o o + a eeap eop oopaaec a yo, ec ope pacooe cea o o oc, a - ec cpaa (pc. 6.21, ).

Pc. 6.21 p apyea Ec oo ee m pax ope (n m) ex, o p ee o - o + eee apyea eopa D(i ) pao cye yo oopoa eopa (i sj), .e.

(6.44) Oya eae ceyee pao: eee apyea D(i ) p ee aco o o + pao paoc ey co ex pax ope ypae D(s) = 0, yoeo a.

p ee aco o 0 o eee apyea eopa D(i ) ye oe ee. (6.45) o pao ooeo ocoy cex acox pepe.

6.8.2 pep Mxaoa o pep o cyecy ec eoepeco eppeae pa apyea copypoa 1938 . coec ye Mxao.

Paccapaec xapaepcec oo (6.27):

D(s) = a0 sn + a1 sn-1 +... + an.

aea s = i, po oecoy ooy, aaeoy ye Mxaoa.

D(i ) = a0 (i )n + a1 (i )n-1 +... + an = U() + i V() = D() ei(), (6.46) e ;

aa cooeceo eeceo o y Mxaoa; D() oy D(i); () aa D(i ).

p ee aco oe eopa D(i ) ye oca eoopy py oeco ococ, oopa aaec oopao Mxaoa.

p ee aco o 0 o yo oopoa eopa D opy aaa oopa pae (6.45):

oca co pax ope ooa (6.47) .e. m = 0, ec. (6.48) oceee ec eoxo ycoe ycooc, o eocao. oo, o oy eoxooe ocaooe ycoe ycooc, eoxoo c op, eae a o oc, .e. oo oc ycoe:

D(i ) 0. (6.49) opy (6.48 6.49) peca coo aeaecoe paee pep ycooc Mxaoa. oo, o ccea aoaecoo ypae a ycoa, eoxoo ocaoo, o oopa Mxaoa D(i ) p ee o o oepyc, e poxo epe y, opy aaa oopa po acoo cpe a yo, e n opo xapaepcecoo ypae.

ycox cce oopa Mxaoa aaec p = 0, a eeceo oyoc, .e. D(0) = an; poe oo c poco aco aa oa oooo opaca, .e.

eop oe oopaac oo po acoo cpe, a a opaca a eeapx eopo (i sj), ec caae a eopa D(i ).

Bc c pep ycooc oo copypoa cey opao:

nouoa aeamee nepeamoo yuu ACP (xapamepucmuecoo nouoa) opayemc yu Muxaoa. moo, mo cucmea amoamuecoo ynpaeu a ycmoua, eoxouo u ocmamoo, mo oopa Muxaoa npu ueeuu acmom om 0 o, auac npu = 0 a eecmeo nooumeo noyocu, oxou moo npomu acoo cmpeu noceoameo n apamo oopuamo nococmu, e n nopo xapamepucmuecoo ypaeu.

oopa Mxaoa ycox cce ee ay cpaey opy yxo ecoeoc o apae, oep oopoo pae cee xapaepcecoo ypae (pc. 6.22).

Pc. 6.22 oopa Mxaoa pao eycooc cce ec apyee ca oceoaeoc poxoe apao.

pep oopaa Mxaoa eycox cce pecae a pc. 6.23:

Pc. 6.23 oopa Mxaoa eycox cce:

a aaec a opaeo eceo oyoc;

e oxo n-apao oopao ococ;

e oxaae aao oopa Pc. 6.24 oopa Mxaoa epax cce:

a, ccea oe ycoa; ccea eycoa epax cce oopa Mxaoa opae a pc. 6.24. B epx yx cyax eoe eopa o ccey a ycooc, ocee e ccea eycoa.

ocpoee oopaa Mxaoa paec pooc o eoo opox oe, o eoo cooaex oopao. ep eo coc opeee pa oe oopaa Mxaoa, cooecyx cpoa ae aco. p opo eoe opeec oopa oex ee, pe paa coe yoe eopo, cpo co oopa.

Aapy oopa Mxaoa, oo ycao ceyee: oa oopa Mxaoa oceoaeo poxo apa, o eecea a oc epeceac ooepeo. B oax epecee c eeceo oc opaaec y a y V(), a oax epecee po c o oc ecea y U().

aco, p oopx pocxo epeceee oce, opeec op ypae (6.50) To epecee px U() V() c oc accc a aee ope ypae (pc. 6.25) U() = 0: 1, 3, 5, ; Pc. 6.25 ecea a cocae y Mxaoa:

a ycoa ccea; eycoa ccea V() = 0: 0, 2, 4, B o cyae ycoo cce oaeo coee epaeca 0 < 1 < 2 < 3 < 4 <...

Bc c oo pec ceyy opypoy pep ycooc:

Cucmea amoamuecoo ynpaeu yem ycmoua moa u moo moa, oa eecmea U() u ua V() yuu Muxaoa, npupaee y, uem ce ecmumee u nepeeauec opu, npue oee uco mux ope pao nopy xapamepucmuecoo ypaeu n, u npu = 0 yoemopemc ycoue U(0) > 0; V'(0) > 0.

6.8.3 pep Haca o aco pep papaoa 1932 . aepac ye Haco, o ooe cy o ycooc ayo cce o y AX paoyo cce.

yc epeaoa y paoyo cce ee ,.

epeaoa y ayo ACP o aay ypae:

.

Xapaepcecoe ypaee paoyo cce (n-o opa) opeeeo, a.

Xapaepcecoe ypaee ayo cce (n-o opa) paaec, a Paccop, o pecae ce paee 1 + W(s):

, (6.51) e xapaepcece oo, cooeceo, ayo paoyo ACP. oca s = i, oy AX paoyo cce (pc.6.26).

Beop, ceoaeo, ae ce coca ayo paoyo cce, o oy, a ee ce W(i ) oocPc. 6.26 AX paoyo cce eo (1, i0) oo cea o o ycooc ayo cce. B aee paccapaec AX, cooecya ooe acoa.

Be p cya coco paoec paoyo cce: ycoa, epaa eycoa.

1 c ya ccea paoyo coco ycoa. Toa eee apyea xapaepcecoo ooa paoyo cce coaco pep ycooc Mxaoa ye pao (6.48):

.

oo, o aya ccea a ycoa, oo oc paeco (6.48):

.

Oca ceye, o ppaee apyea eopa pao y:

(6.52) Coooee (6.52) oaae, o ycooc ayo cce eoxoo, o eop, aao oopoo axoc oe (1, i0), a oe, co o AX paoyo cce, e oxaa oy (1, i0) p ee o 0 o (pc. 6.27).

Pc. 6.27 AX:

a paoyo cce; y H(i ) Ta opao, pep Haca ac:

Ecu paoyma cucmea amoamuecoo ynpaeu ycmoua, mo ayma cucmea amoamuecoo ynpaeu yem ycmoua, ecu anumyo-aoa xapamepucmua paoymo cucme e oxamaem moy (-1, i0) npu ueeuu om o.

2 c ya ccea paoyo coco eycoa.

p paccope oooypx oooypx cce peypoa, coepax eycoe e, paoya ccea oe oaac eycoo.

yc paoyo coco ccea eycoa, p o xapaepcecoe ypaee paoyo cce ee m ope pao oyococ. Toa coaco py apyea (6.25):

Ec opeoa, o ccea ayo coco a ycoa, o oo oc paeco (6.48):

Bo cyae yo oopoa eopa H(i ) = ye pae (6.53) oceee oop o o, o AX y H(i ) p ee aco o 0 o oxaae aao oopa ooeo apae pa.

co oopoo eopa H(i ) opy aaa oopa pao cy oopoo eopa AX paoyo cce W(i ) opy o (1, i0). Ha ocoa oo eae ceya opypoa pep Haca.

Ecu paoyma cucmea amoamuecoo ynpaeu eycmoua, mo moo, mo ayma cucmea amoamuecoo ynpaeu a ycmoua, eoxouo u ocmamoo, mo AX paoymo cucme W(i) npu ueeuu acmom om 0 o oxamaa moy (-1, i0) nooumeo anpaeuu pa, e m - uco npax ope xapamepucmuecoo ypaeu paoymo cucme.

Pc. 6.28 AX:

a H(i ); W(i ) p m = Ha pc. 6.28 opae aece pepa AX H(i ) AX paoyo cce, cooecye ycoo ayo ccee, oopa paoyo coco eycoa m = 2.

p coo ope W(i ) oy oy apye p opeee ca ee oopoo opy o (1, i0). B o cyae yoo pe "pao epexoo", peoeoe . . Haoe epexo W(i ) epe eecey oc p opaca ooe, ec o pocxo cepxy , opae, ec o pocxo cy epx. Ec W(i ) aaec aaaec a oc, o oa coepae oepexoa. Toa pep Haca oo copypoa cey opao.

Ec paoya ccea aoaecoo ypae eycoa, o oo o aya ccea aoaecoo ypae a ycoa, eoxoo ocaoo, o paoc ey co ooex opaex epexoo AX paoyo cce W(i ) epe opeo eeceo oc (, 1) p ee aco o 0 o a paa, e m co pax ope xapaepcecoo ypae.

B aece pepa a pc. 6.29 opaea AX paoyo cce: co pax ope m = 2; co epexoo a ooPc. 6.29 AX paoyo cce p m = ex, o opae, x paoc paa 1 =, ceoaeo, aya ccea ycoa.

3 c ya ccea paoyo coco epaa.

B o cyae ccea oa coepa eppye e, oa xapaepcecoe ypaee paoyo cce ee op, pae y, acaec e (6.54) e opo acaa; A1(s) oo, e e ope, pax y.

Ayo-aoa xapaepca paoyo cce acaec e. (6.55) p = 0, W(i ) = AX peepeae pap, ooy pea opoc o ycooc ayo cce pyo, a a eco, oxaae AX oy (1, i0) e.

o coxpa opypoy pep ycox paoyo coco cce, p ocpoe oopaa Mxaoa p ee aco o o + oxo aao oopa o oyopyoc ecoeo aoo payca r. Toa yee op ay ao e yo oopoa, a ee op, .e. a eopo oepec a yo (pc. 6.30).

Pc. 6.30 Oxo aaa oopa o ye ecoeo aoo payca r Oxoy aaa oopa o ao ye rei cooecye epeaoa y paoyo cce (6.56) p r 0, payc R, a apye eec o o p ee o o.

Pc. 6.31 AX epao paoyo cce:

a c acao epoo opa, = 1; c acao opoo opa, = Ta opao, p e o oyopyoc ecoeo aoo payca ococ ope AX paoyo cce caa W(i ) oe pecaea e eopa ecoeo oo , oopaaeoc a oeco ococ o acoo cpee a yo, pa .

Pages:     | 1 |   ...   | 14 | 15 || 17 | 18 |   ...   | 25 |



2011 www.dissers.ru -

, .
, , , , 1-2 .