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1743 a(3)1266 1714 y Fh(;)1289 1686 y Fk(1)p 1289 1705
V 1289 1743 a(3)1315 1714 y Fh(;)1338 1686 y Fk(1)p 1338
1705 V 1338 1743 a(3)1364 1714 y()])p Fh(M)5 b Fd(jj)p
Fh(:)0 1803 y Fk(It)14 b(follo)o(ws)e(t)n(h)o(a)o(t)i
Fh(16)r Fk(()p Fh(x)9 b Fd(17)g Fh(y)q Fk())j Fd(24)g
Fh(16)r Fk(()p Fh(x)p Fk())i(b)q(eca)n(us)q(e)h(for)f(an)o(y)f(()p
Fh(f)r(;)7 b(g)q(;)g(h)p Fk(),)499 1894 y Fd(jj)p Fk(()p
Fh(f)r(;)g(g)q(;)g(h)p Fk())p Fh(M)e Fd(jj)k(24)j(jj)p
Fk(()p Fh(f)r(;)7 b(g)q(;)g(h)p Fk())p Fd(jj)e(jj)p
Fh(M)g Fd(jj)k(24)j(jj)p Fk(()p Fh(f)r(;)7 b(g)q(;)g(h)p
Fk())p Fd(jj)0 1985 y Fk(as)12 b(lon)o(g)e(as)i Fd(jj)p
Fh(M)5 b Fd(jj)10 b(24)h Fk(1.)17 b(Here)c Fd(jj)p
Fh(M)5 b Fd(jj)k Fk(i)q(s)i(t)n(h)o(e)i(m)o(a)o(tr)q(ix)c(norm)h(in)o
(d)o(u)o(ce)q(d)i(b)o(y)f(t)n(h)o(e)h(v)o(ect)o(or)h(p-norm)d
Fd(jj)p Fk(.)16 b(Thi)q(s)11 b(i)q(s)g(cert)o(ainly)0
2035 y(true)h(for)g(t)n(h)o(e)g(m)o(a)o(tr)q(ix)d Fh(M)17
b Fk(ar)q(i)q(s)q(in)o(g)10 b(f)q(rom)f(t)n(h)o(e)k(La)o(t)o(in)e
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Fd(17)p Fk(,)f(s)q(ince)h(t)n(h)o(e)g(ro)o(ws)g(an)o(d)f(colu)o(mns)0
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2333 y Fh(;)i(:)g(:)g(:)i Fk(sh)o(ould)j(b)q(e)g(b)q(et)n(t)o(er,)h(or)
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Fd(00)f Fk(for)g(re)q(s)q(id)o(ue)q(s)i(of)e(som)o(e)f(mo)q(d)o(ulus)
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(ely)f(pr)q(im)o(e)f(t)o(o)i(mo)q(d)o(ulus)e Fh(m)p Fk(,)i(su)o(c)o(h)g
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(ert)o(y)e(t)n(h)o(a)o(t)h(it)o(s)g(o)o(p)q(era)o(t)o(ion)f(t)o(a)o
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(tract)o(iv)o(e)g(fea)o(t)o(ure)g(of)f(com)n(bin)o(a)o(t)o(ion)d(RNG's)
j(i)q(s)f(t)n(h)o(a)o(t)h(t)n(h)o(ey)h(t)o(en)o(d)g(not)f(only)f(t)o(o)
h(m)o(ak)o(e)f(t)n(h)o(e)i(re)q(sul)o(t)o(s)0 2632 y(more)e(u)o
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o(d)o(en)o(t.)21 b(Giv)o(en)14 b Fh(x)1090 2638 y Fg(1)1108
2632 y Fh(;)7 b(x)1151 2638 y Fg(2)1169 2632 y Fh(;)g(x)1212
2638 y Fg(3)1230 2632 y Fh(;)g(:)g(:)g(:)12 b Fk(w)o(e)j(h)o(o)o(p)q(e)
g(t)n(h)o(a)o(t)g Fh(x)1583 2638 y Fg(1)1616 2632 y Fk(i)q(s)f(u)o
(niform)890 2757 y(4)p eop
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(t)o(o)k(crypt)o(ograph)o(y)m(.)j Fj(Computing)d(Surveys)f
Fc(11)p Fk(,)f(357-370,)f((1979).)0 1772 y([3])i(Bro)o(wn,M.)h(an)o
(d)h(Solomon,)c(H.)j(On)h(com)n(binin)o(g)e(ps)q(eudoran)o(dom)h(n)n(u)
o(m)n(b)q(er)g(gen)o(era)o(t)o(ors,)j(T)m(ec)o(hnical)d(Rep)q(ort)0
1821 y(No.)j(233,)13 b(Dept.)18 b(of)13 b(St)o(a)o(t)o(i)q(st)o(ics,)g
(St)o(anford)g(Univ)o(ers)q(it)o(y)m(.)18 b((1976).)0
1883 y([4])13 b(F)m(ushimi,)f(M.)h(an)o(d)h(T)m(ezuka,)g(5.)19
b(Th)o(e)14 b(k-di)q(str)q(ibu)o(t)o(ion)f(of)h(gen)o(eralize)q(d)h
(fee)q(dbac)o(k)g(shift)f(regi)q(st)o(er)h(ps)q(eudoran-)0
1933 y(dom)d(n)n(u)o(m)n(b)q(ers.)19 b Fj(Communic)n(ations)c(A)o(CM)e
Fc(26)p Fk(,)g(516-523,)f((1983).)0 1994 y([5])i(K)o(en)o(d)o(all,)i
(D.)f(G.)g(an)o(d)g(Ba)o(bin)o(gt)o(on-Smit)n(h,)f(B.)i(Ran)o(domn)o(e)
q(ss)f(an)o(d)g(ran)o(dom)f(samplin)o(g)g(n)n(u)o(m)n(b)q(ers,)i
Fj(J.)g(R)n(oyal)0 2044 y(Statist.)i(So)n(c.)h Fc(101)14
b Fk(146-)f(166,(1938).)j(See)e(also)g Fj(J.)g(R)n(oyal)h(Statist.)k
(So)n(c.)g(Supplement)c Fc(6)f Fk(51-36,)e((1939).)0
2106 y([6])g(Kn)n(u)o(t)n(h,)j(D.)d(E.)h Fj(The)i(A)o(rt)e(of)h
(Computer)g(Pr)n(o)n(gr)n(amming,)g(V2:)19 b(Semi-numeric)n(al)13
b(A)o(lgorithms)p Fk(,)f(2n)o(d)h(Edit)o(ion,)0 2156
y(Addi)q(son-W)m(e)q(sley)m(,)f(Readin)o(g,)i(Mass.,)g((1981).)0
2217 y([7])k(Lewi)q(s,T.)f(G.)h(an)o(d)g(P)o(ayn)o(e,)i(W.)e(H.)g(Gen)o
(eralize)q(d)i(fee)q(dbac)o(k)f(shift)g(regi)q(st)o(er)g(ps)q(eudoran)o
(dom)f(n)n(u)o(m)n(b)q(er)h(al-)0 2267 y(gor)q(it)n(hms.)d
Fj(Journal)f(A)o(CM)f Fc(20)p Fk(,)f(456-468,)f((1973).)879
2757 y(10)p eop
%%Page: 11 11
11 10 bop 62 -41 a Fk([8])14 b(MacLaren,)g(M.)g(D.)g(an)o(d)g
(Marsaglia,)f(G.)h(Uniform)e(ran)o(dom)h(n)n(u)o(m)n(b)q(er)h(gen)o
(era)o(t)o(ors,)i Fj(J.)f(A)o(CM)f Fc(12)p Fk(,)g(83-89)0
9 y((1965).)0 70 y([9])d(Marsaglia,)g(G.)h(Ran)o(dom)e(n)n(u)o(m)n(b)
q(ers)j(f)q(all)d(m)o(ainly)g(in)i(t)n(h)o(e)h(plan)o(e)q(s.)k
Fj(Pr)n(o)n(c)n(e)n(e)n(dings)d(National)f(A)n(c)n(ademy)h(Scienc)n(e)0
120 y Fc(61)p Fk(,)f(25-28)g((1968).)0 182 y([10])e(Marsaglia,)g(G.)h
(Th)o(e)h(stru)o(ct)o(ure)h(of)e(lin)o(ear)h(con)o(gruen)o(t)o(ial)f(s)
q(equence)q(s,)j Fj(Applic)n(ations)f(of)f(Numb)n(er)h(The)n(ory)f(to)0
232 y(Numeric)n(al)h(A)o(nalysis)p Fk(.)k(Z.)c(K.)f(Zarem)n(ba,)g(Ed.,)
g(Acad)o(emic)g(Pre)q(ss,)j(New)e(Y)m(or)o(k,)g((1972).)0
293 y([11])e(Marsaglia.)17 b(G.)12 b(an)o(d)h(L.)g(H.)g(Tsay)m(,)f(Ma)o
(tr)q(ice)q(s)i(an)o(d)f(t)n(h)o(e)h(stru)o(ct)o(ure)h(of)e(ran)o(dom)f
(n)n(u)o(m)n(b)q(er)h(s)q(equence)q(s.)20 b Fj(Line)n(ar)0
343 y(A)o(lgebr)n(a)14 b(and)i(Its)e(Applic)n(ations)g
Fc(67)g Fk(147-156,)d((1985))0 405 y([12])f(Marsaglia,)h(G.)g(an)o(d)
g(Bray)m(,)h(T.)f(A.)h(On)o(e-lin)o(e)f(ran)o(dom)f(n)n(u)o(m)n(b)q(er)
i(gen)o(era)o(t)o(ors)h(an)o(d)f(t)n(h)o(e)q(ir)g(us)q(e)h(in)e(com)n
(bin)o(a)o(t)o(ion,)0 454 y Fj(Communic)n(ations)k(A)o(CM)f
Fc(11)p Fk(,)f(757-759,)f((1968).)0 516 y([13])i(Marsh)o(all,)h(A.)g
(W.)f(an)o(d)h(Olkin,)g(I.)g Fj(Ine)n(qualities:)21 b(The)n(ory)16
b(of)h(Majorization)f(and)h(its)f(Applic)n(ations)p Fk(,)f(Aca-)0
566 y(d)o(emic)e(Pre)q(ss,)j(New)e(Y)m(or)o(k,)g((1979).)0
628 y([14])g(Whit)n(t)n(le)q(s)q(ey)m(,)h(J.)g(R.)f(B.)i(On)f(t)n(h)o
(e)h(m)n(ul)o(t)o(idim)n(ens)q(ion)o(al)c(u)o(niformit)o(y)h(of)h(ps)q
(eudoran)o(dom)h(n)n(u)o(m)n(b)q(er)g(gen)o(era)o(t)o(ors.)0
677 y Fj(Comm.)k(A)o(CM)13 b Fc(12)h Fk(247,)e((1969).)879
2757 y(11)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF