%!PS-Adobe-2.0 %%Creator: dvips 5.519 Copyright 1986, 1993 Radical Eye Software %%Title: ver2.dvi %%CreationDate: Tue May 5 15:34:48 1998 %%Pages: 15 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips -o testSU.ps ver2 %DVIPSSource: TeX output 1998.05.05:1532 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{ statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N 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Fj(if)g(b)n(oth)h(is)f(end-p)n(oints)f(ar)n(e)h(in)g(the) h(same)f Fo(\000\(U)864 2677 y Fg(i)878 2670 y Fo(\))p Fj(,)g(for)g(some)h Fl(i)12 b Fi(2)h(f)p Fo(1)p Fl(;)8 b Fo(2)p Fi(g)p Fj(.)964 2795 y Fo(7)p eop %%Page: 8 9 8 8 bop 0 42 a Fk(Claim)18 b(2.4)23 b Fj(F)m(or)16 b(any)g(go)n(o)n(d)g (set)g Fo(U)g Fj(and)g(any)h(p)n(artition)f(of)g Fo(U)p Fj(,)h(at)f(le)n(ast)1282 24 y Fg(\017)p 1281 31 17 2 v 1281 57 a Ft(3)1302 42 y Fl(N)1344 25 y Ft(2)1379 42 y Fj(e)n(dges)f(disturb)i(the)f(p)n(artition.)0 148 y Fk(Pro)q(of:)37 b Fo(Eac)o(h)16 b(partition)g(of)g(V)h(has)f(at)f (least)h Fl(\017N)892 131 y Ft(2)927 148 y Fo(violating)h(edges)g (\(i.e.,)e(edges)i(with)f(b)q(oth)h(end-p)q(oin)o(ts)g(on)0 204 y(the)d(same)g(side\).)20 b(W)l(e)14 b(upp)q(er)h(b)q(ound)g(the)f (n)o(um)o(b)q(er)g(of)g(these)g(edges)g(whic)o(h)h(are)f(not)f (disturbing.)21 b(Actually)l(,)15 b(w)o(e)0 261 y(upp)q(er)h(b)q(ound)g (the)g(n)o(um)o(b)q(er)f(of)g(edges)g(whic)o(h)h(ha)o(v)o(e)f(an)g 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2407 y Ft(1)1096 2400 y Fi(j)g Fl(>)h Fo(0.)18 b(This)11 b(is)g(indeed)i(the)d(case,)h (but)g(pro)o(ving)g(it)0 2456 y(is)i(less)g(straigh)o(tforw)o(ard)d (than)j(it)f(seems,)h(the)f(problem)i(b)q(eing)f(that)f(the)h Fl(\020)1288 2463 y Fg(i;j)1326 2456 y Fo('s)f(are)h(not)f(pairwise)h (indep)q(enden)o(t.)0 2513 y(Y)l(et,)i(since)h(the)f(sum)f(of)h(the)g (co)o(v)m(ariances)g(of)g(the)g(dep)q(enden)o(t)h Fl(\020)1116 2520 y Fg(i;j)1155 2513 y Fo('s)e(is)i(quite)f(small,)h(Cheb)o(yshev's) f(Inequalit)o(y)0 2579 y(is)20 b(still)g(v)o(ery)f(useful)i(\(cf.,)d ([1)o(,)i(Sec.)f(4.3]\).)31 b(Sp)q(eci\014cally)l(,)23 b(letting)d Fl(\026)1222 2554 y Ft(def)1227 2579 y Fo(=)1287 2547 y Fs(P)1330 2590 y Fg(v)q Fh(2)p Ft(V)1405 2579 y Fl(p)1428 2562 y Ft(0)1447 2579 y Fo(\()p Fl(v)r Fo(\))p Fl(p)1530 2562 y Ft(1)1547 2579 y Fo(\()p Fl(v)r Fo(\))e(\(=)i Fk(E)p Fo(\()p Fl(\020)1770 2586 y Fg(i;j)1809 2579 y Fo(\)\),)f(and)952 2795 y(10)p eop %%Page: 11 12 11 11 bop 0 13 24 2 v 0 49 a Fl(\020)23 60 y 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