WWW.DISSERS.RU

    !


Pages:     || 2 | 3 | 4 | 5 |   ...   | 8 |
. A. poye CPETHA MATEMATA Oco eop pao aopa aa eoe ocoe 2000 519.2 22.174 80 poye . A 80 cpea aeaa (oco eop pao aopa aa): e. ocoe / CA. C., 2000. 82 c.: .

Paccope ocoe opeee o eop pao, eoxoe pee eoopx pax aa cpeo aea (opeeee oax pacco ey oeco oeo, oc pecoo y aae ceeoo apoa ypae, op peoex apao cce o oecy pepe). Ocyac oxo papaoe oepx aopo aa a ocoe oee eop pao.

eoe ocoe peaaeo cyeo ceaoc Cce aoapoaoo poepoa, a ae cyeo pyx ceaoce, coyx eop pao pee aa.

Peee:

aepa poeoo eeea Ca-eepypcoo acoo ocyapceoo execoo yepcea;

aa execx ay oe B.. ono - Ca-eepypc ocyapce yepce apoocecoo popocpoe, 2000 . A. poye, 2000 2 BBEEHE Teop pao, c paeo cpeo aea, coyec oca ye ooe ey cpe oea. eoepec oe oo peca e oeca oe, aaex epa paa, a ooe ey , ca ep. Ec e opepoa, o x aa pepa, a ca pa eopepoa, a ec opepoa, o x aa ya, a ca pa opepoa, oppao.

e coe ocoe pocee e ee (o, coeee ), eop pao cpo x opooe ooopae op, aee op pa coca peyae caoc oe cpyeo p cceoa cax paoopax cce.

B cao o paa coeac eopeo-oecee, oaope oooece ace, o eae eop pao yo, poc o opypo ocpoe oee, a ae e o cpyeo pee aa, oocxc pooy pyy ayx eepx poe. Moo yoy o c opoc ocpypoa cce aoapoaoo poepoa, cce popapoa BM coa oepaox cce, cceoa oepa ypae, aeaeco c papao pacopo, aeapoe apoae poeoo pooca, aa ceeoo apoa ypae (C), aece oece aa opa yx oeo, oo py ooecx aa, poe aa.

Beco o paa aco coyec oe ce, oa poe ocox, co cpyypx, ooe pae aac eoope oecee xapaepc oe . p o oo pea poe ocpoe epecx cee, cce c cceoa poecco epea opa, opa oax appyo ooo cex, apep ocpoe ce oe pao p poepoa e. p o pepa () ya ce cac cooece opeeee oecee xapaepc ep, apa ooa.

e aoo ypca coco o, o oao cyeo c oco o eop pao ep pecae o oex eop pao, x poex pee eoopx pax aa c cooae aopecoo oxoa c oooc pee BM.

1. OCHOBHE OPEEEH OHT 1.1. ee eop oec opeee ocox o eop pao yy cooa eoope cee eop oec. Moeco opayec cooyoc cpex oeo, xc eea oeca, ooaac A = {a, b, c }, e a, b, c ee oeca A.

peoaaec, o opex eea a oeca A cea oo opee, pae ee a oecy A (ooaaec aA) e pae (aA ).

Moeco A aaec oe, ec e coepc oeoe co eeo, apep, A={a1, a2, , a }. co n an aec oeco eeo A ooaaec epe |A|. Moeco, cocoee ooo eea, ooaaec epe {a}. Moeco, e coepaee eeo, aaec yc ooaaec, apep A= oaae, o A ycoe oeco.

1.1.1. Onepauu a oecmau Boeoc oec (ooeco) oepa.

Ec xA (e x o ee) ceye xB, o A aa ooeco B (AB) oop, o A oeo B (A coepc B, B coep A). Hapep, ec A={a,b} B={a, b, c}, o AB.

ooee oec oepa (cya).

Moeco AB ae ce ee oec A B e oope eeo, apep yc A={a, b}, B={b, c}, oa AB= ={a, b, c}.

epeceee oec oepa.

Moeco AB ae ee oe oec A B, apep:

1. yc A={a, b}, B={b, c}, oa AB={b}.

2. yc A={a, b}, B={c, d}, oa AB=.

ooee oec oepa \ (ae).

Moeco A\B ae ce ee oeca A, e paeae B, . e. A ac ee oe c B. Hapep, yc A={a, b}, B={b, c}, oa A\B={a}.

Teopeo-oeceoe poeee oepa.

yc A B a oeca. epe AB ooa oeco, cocoee yopoex ap (a,b), ax, o aA, bB. ae oop, cAB oa oo oa, oa c ec apa (a, b), pe aA, bB.



Hapep, yc A={a, b}, B={c, d}, oa AB={(a, c), (a, d), (b, c), (b, d)}.

oee oeo opeee ee oe npoueeu oecma caoo a ce.

opoe, eapo (p), poeee oeca V caoo a ce (oopoe ooaaec VV) aaec oeco cex yopoex ap (s, t), e sV tV. ec (s, t) (t, s) paccapac a pae ee, ca cya s=t.

Ec co eeo |V|=n, o VV coco n2 yopoex ap. Hapep, yc V={v1, v2, v3}, oa VV={(v1, v1), (v1, v2), (v1, v3), (v2, v1), (v2, v2), (v2, v3), (v3, v1), (v3, v2), (v3, v3)}.

Heyopoe poeee oeca V caoo a ce (ooa a V&V) aaec oeco cex pax eyopoex ap [s, t], p o ap [s, t] [t, s] ae a e, a p eapoo poee, oycaec coaee eeo ap, . e. s=t. p |V|=n oeco V&V coco n(n+1)/2 pax eyopoex ap. Hapep, yc V={v1, v2, v3}, oa V&V={[v1, v1], [v1, v2], [v1, v3], [v2, v2], [v2, v3], [v3, v3]}.

Cpae ooe: ABA, ABB, AAB, BAB.

Hapep, ec AB, BC, o AC, ooy peex e coooe ceye, o ABAB.

Cpae ae opy cpyoc:

(AB)C=(AB)(BC), (AB)C=(AC)(BC).

Paeco oec oepa =.

A=B cpaeo oa oo oa, oa AB AB.

1.1.2. Omoeue Bee oe omoeu. oop, o a A aao ooee R, ec aao ooeco R eapoa poee AA (RAA).

ee aA axoc ooe R eey bA (acaec a aRb) oa oo oa, oa (a,b)R. p o cyece opo eeo: oe , o a axoc ooe R eey b, o b e axoc ooe R a.

Ooee aaec: a) cuempu, ec aRb oa oo oa, oa bRa; ) peecu, ec oo aA aRa; ) mpaumu, ec aRb bRc ceye aRc; ) amucuempu, ec aRb bRa ceye a=b.

oeca cex ooe eec acc ooe, oopeeo cepx, pax peecx. Tae ooe aac ooe aeoc.

1.1.3. Omopaeue Tep omopaeue (a oe ooaoo cooec) yu yy paccapac a co. Cae, o aao oopaee f : XY, ec aoy eey xX coocae ee f(x)Y.

yc f: XY eoopoe oopaee. Ec AX, o opao A p oopae f aaec oeco eeo BY aoe, o yB oa oo oa, oa cyecye xA ao, o y=f(x). poopao CY p oopae f aaec oeco DX aoe, o xD oa oo oa, oa f(x)C. Opa poopa ooa cooeceo f(A) f (C). Oepa opaa poopaa oeca yoeop coooe:

f 1 (AB) = f 1(A) f 1(B), f (AB) = f (A) f (B);

f 1 (AB) = f 1(A) f 1(B), f (AB) f(A) f(B);

f 1 (Y \ A) = X \ f 1(A), f (X \ A) f (X) \ f (A).

Oao e yepa, o f(AB)=f(A)f(B) f(X\A)=f(X)\f(A).

ocaoo paccope ocooe oopaee f : XY (aoe, o f(x)=y0X oo xX).

Oopaee aaec auo-ooa, ec f(x)=Y oo yY oeco f1({y}) coco ooo eea. Hepyo e, o opeeeo oopaee f 1: YX. eo, f 1(y)=a oa oo oa, oa f 1({y})={a}.

1.2. Ocoe o pao 1.2.1. eoempuecoe npecmaeue pao pee e opee oe paa aoee oe ope, oeo paccope eoepecy opy pao. o oo c caoo aaa oy yooe, aoe pecaee pax o cpyyp, oope yy paccapac aee. o pa acpao cce aee (o ooe coca, yae eop pao) eoopoy eoepecoy pay. p eoopo ueauauu oe ece cpyyp oo paccapa a eoepece pa ya c oo eoo eop pao. Hapep, e paa oo peca ccey ce y opoe, ec peepe po ocex, a epecee ca oa.

eoepec pa ec eoepeca oypa cpyypa pocpace, cocoa oeca oe, aocax oeco epepx, caoeepeceaxc px.

Ha pc. 1.1 oaao ooe pecaee eoepecoo paa, c oo oopoo oo pocppoa eoope ep eop pao.

C o eop pao ee v aac epa paa, a coee x eopepoae (u) pepa ya, ec cae cpea, oa paa eopuemupoa pa (pc.1.1,a) opuemupoa pa (copaeo oppa) (pc.1.1,). Ec oeco ep (V) peep (y) (U) oeo, o pa aaec oe. M ye paccapa oo oee pa.

a) v3 v6 v2 u6 vvuuuvuu3 u4 v1 vu3 uuuu2 uv2 vPc. 1.1. eoepecoe pecaee pao:

a eopepoa pa; opepoa pa Bep, cae pepo yo, aac ceu. Ec cee ep ca oee e o pepo yo, o ae pepa (y) aac pa, apae (u3, u4 a pc. 1.1,a; u2, u3 a pc. 1.1,), a ca pa aaec ypao, .

e. pa a pc. 1.1 c ypaa. Bep, ecae c py, aac uoupoau, apep, v4 a pc. 1.1,a. Pepo (ya), aaeec aaaeec oo oe, aaec ee (e u6 a pc. 1.1,a u7 a pc. 1.1,). oop, o pepo (ya) eo pae o e py pyy, ae oop, ep, ee pepy (ye), c eo oe oa, apep, a pc. 1.1,a pepy u1 e ep v1 v3, a epe v3 e pepa u1, u3, u4.





Booe oop, oeco y U (o e ep V) oe yc, oa oop, o pa poe.

1.2.2. Acmpame pa eoepecoe pecaee pao, c a, pyo oaec aeaeco opaoe, ooy eoxoo eo opaoa peca opeeee paa oee oe acpao e. Xo oe pa, pecae peae oe (oce x eaa), c eoepec paa, c o pe eop pao, x ecea cpyypa ocoeoc coco o, o c a pepo ca e (ooo coaae) ep.

Tae pepa (y) ep opeee e a ao ee. oe uuemocmu peep (y) u ux oex epu ec yaea eop pao, oopa ocpoea c yeo eo o ocoeoc e yae peao ppo ep peep (y).

Beee o acmpamoo paa ooe, o-epx, ac o cyax eoepecx xapaepc, coxpa aoee cyecee oaope coca paa, o-opx, pacp oooc poe eop, a a oe peae cpyyp e oaope coca, oope oeo cceoa c oo aeaecoo aapaa eop pao. Hapep, p poepoa cooo e (execoo popaoo) e paa oo aa coooee ey oe paoa, oope coca coe poe. B o cyae ep peca oee pao, a ooe eoc paa opaa oceoaeoc oe opeeex pao.

opaa paa oe pa pae op, oope paccop aee. Hapep, eceya aa coep c opa, eoxoy oca eoepecoo paa (pc. 1.1,a):

Bep, cooecye, Pepa . e. ee, pepa u1 v1, vu2 v1, vu3 v1, vu4 v2, vu5 v5, vu6 vvocoy opaa oepa eopepoax opepoax pao e o, pee x acpae oca oeo.

1.3. Ocoe o eopepoax pao 1.3.1. Acmpame onucau eopuemupoax pao yc V eycoe oeco ep paa vV. Pepo, coe e ep vi vj, aaec eyopoea apa [vi, vj] u = vi,v u =,vi [vj, vi]. Pepo ooaaec , a oeco ( ) j v j peep paa ooaaec U.

Moeco peep ec oe ooeco eyopoU eoo poee V&V c eea a [v, w], e v, wV oyco coaee eeo ap v = w.

Toa pa G oo opee a cooyoc eycoo oeoo oeca ep V oeca peep U (ooo ycoo) ooaa G=(V, U ). p ao opeee paa ooee eoc ep peep aaec e o. Hapep, eoepecoo paa (pc.1.2) cooecy acpa pa oo oca a oeca:

ep V={v1, v2, v3, v4} peep U ={[v1, v2], [v2, v3], [v3, v4], [v4, v2], [v4, v1]}.

Moo ec oopaee eoc ( e) paa G. Ec ep v, wV c pa (oe) ou u a pepa U, o o oo ooa ~[v, w] (aec u u coee ep v w) ec oopaee ( )=[v, w] o u oaae, o pepo eo ao ep v w aoopo ep e pepy.

L1 LL1 Luuu4 uL4 LL4 u3 LPc. 1.2. eoepec pa Pc. 1.3. eoepec pa e ooae peep c ooaee peep Toa pa G oo oca a aeaecy ccey G=(V, U, ), cocoy yx oec V (ep) U (peep) oopae eoc oeca U V&V (oeco eyopoex ap eeo a [v, w]V).

Hapep, eoepecoo paa (pc.1.3) cooecy acpa pa oo oca a oeca:

u u u u u V={v1, v2, v3, v4}, U ={,,,, } oopae eoc 1 2 3 4 u u u u u ={ ~[v1, v2], ~[v2, v3], ~[v3, v4], ~[v4, v1], ~[v4, v2]}.

1 2 3 4 ocoy oopaee eoc paa ae oeco peep paa U, ocoy ocae paa a cooyoc oeca ep V oopae oeca U V&V a G=(V, ) ooc opeee pa.

1.3.2. oae cocma eopuemupoax pao oca pax cpyypx coc pao oeo ec p ooex o, oope ocoeo ao cppyc a pepe eoepecx pao, oaax e, a ae a pc. 1.4.

u u Ec =[v, w], o v w aac pauu moau eaco o oo, ec pa eoepec e.

u u ee =[v, v] aaec pepo c eceo pao ou u o, . e. e ea oo epe, apep e a 4 pc. 1. 4.

apaeu (pa) aauc pepa, ec o coe o u L1 L2 e e ep, apep ~[v1, v2] uu ~[v1, v2]. B acoc, e e, uee oo o e epe, L3 c apae, apep Lu u .

4 uupa G, e apaee pepa, aaec ypao, aPc. 1.4. pep pep ypa a pc. 1.1 1.4.

Pages:     || 2 | 3 | 4 | 5 |   ...   | 8 |










2011 www.dissers.ru -

, .
, , , , 1-2 .