Content-Type: multipart/mixed; boundary="-------------0505311018166" This is a multi-part message in MIME format. ---------------0505311018166 Content-Type: text/plain; name="05-197.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-197.comments" AMS-Code: 47A10, 47A25, 47A35, 47A55, 81Q10 Previous versions (see mp_arc #03-296) of this manuscript contained several errors, but the final statement (Theorem 4.3) remained the same, except for a gap in the proof of u.d. of the Pr fer angles, which we discovered recently. ---------------0505311018166 Content-Type: text/plain; name="05-197.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-197.keywords" Off-diagonal Jacobi matrices, spectral transition, sparse perturbation, Transfer matrices, Prufer variables, uniformly distributed sequences ---------------0505311018166 Content-Type: application/postscript; name="stjacobi10-arch.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="stjacobi10-arch.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: stjacobi10-arch.dvi %%Pages: 31 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Courier Mathematica1Mono Times-Italic %%+ Times-Italic-Italic Times-Roman Mathematica2 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips stjacobi10-arch.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.05.31:1218 %%BeginProcSet: texc.pro %! 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Fr(0)111 3980 y Fv(is)37 b(a)f(compact)h(p)s(erturbation)g(of)e Ft(J)1445 3943 y Fr(0)1521 3980 y Fv(and)i(th)m(us,)h(b)m(y)g(W)-8 b(eyl's)37 b(in)m(v)-5 b(ariance)38 b(theorem,)g(the)f(essen)m(tial)111 4100 y(sp)s(ectrum)32 b(of)d Ft(J)40 b Fv(remains)31 b(the)f(same)h(as)f(that)g(of)g Ft(J)2003 4064 y Fr(0)2043 4100 y Fv(,)g Ft(\033)2155 4115 y Fr(ess)2247 4100 y Fv(\()p Ft(J)9 b Fv(\))28 b(=)f Ft(\033)t Fv(\()p Ft(J)2677 4064 y Fr(0)2717 4100 y Fv(\))g(=)h([)p Fq(\000)p Fv(2)p Ft(;)17 b Fv(2].)42 b(The)31 b(sp)s(ectrum)111 4220 y(of)h Ft(J)42 b Fv(in)33 b(this)g(sub)s(class)h(is)f(describ)s(ed)i(as)e (follo)m(ws.)111 4493 y Fl(Theorem)k(1.1)49 b Fk(L)-5 b(et)38 b Ft(J)k Fq(2)33 b Fm(H)1233 4508 y Fr(0)1309 4493 y Fk(with)k Fv(0)32 b Ft(<)h(\024)f(<)h Fv(1)p Fk(.)52 b(Then)37 b Ft(\033)t Fv(\()p Ft(J)9 b Fv(\))37 b Fk(is)g(pur)-5 b(ely)38 b(a.c.)52 b(if)3274 4368 y Fn(1)3237 4398 y Fs(X)3245 4610 y Fp(k)r Fr(=1)3398 4493 y Fq(j)p Ft(r)3470 4508 y Fp(k)3512 4493 y Fq(j)3540 4444 y Fr(2)3612 4493 y Ft(<)32 b Fq(1)111 4791 y Fk(and)i(pur)-5 b(ely)36 b(s.c.)44 b(if)911 4667 y Fn(1)875 4697 y Fs(X)882 4909 y Fp(k)r Fr(=1)1035 4791 y Fq(j)p Ft(r)1107 4806 y Fp(k)1149 4791 y Fq(j)1177 4743 y Fr(2)1244 4791 y Fv(=)28 b Fq(1)34 b Fk(and)h(the)f(\\sp)-5 b(arseness)34 b(p)-5 b(ar)g(ameter")34 b(is)g Ft(\014)g Fv(=)27 b Fq(1)p Fk(.)258 5097 y Fv(Theorem)39 b(1.1)f(ma)m(y)h(b)s(e)f(pro)m(v)m(en)h(along)f(the)h(lines)g(of)f (Theorem)h(1)p Ft(:)p Fv(7)f(of)f(Kiselev-Last-Simon)111 5218 y([KLS].)63 b(It)40 b(sho)m(ws)g(that)f(there)h(is)g(no)f(sp)s (ectral)h(transition)f(in)g(the)h(sub)s(class)h Fm(H)3159 5233 y Fr(0)3236 5218 y Fv(as)f Ft(\024)f Fv(v)-5 b(aries)40 b(in)111 5338 y(\(0)p Ft(;)17 b Fv(1\))o(,)41 b(at)d(least)i(under)f (the)g(sparseness)j(condition)d(\(1.5\).)62 b(In)39 b(order)g(to)f(o)s (ccur)h(a)g(transition)g(at)1941 5587 y(3)p eop %%Page: 4 4 4 3 bop 111 312 a Fv(a)36 b(non)m(trivial)h(v)-5 b(alue)36 b(of)g Ft(\024)p Fv(,)h Ft(J)45 b Fv(has)36 b(to)g(b)s(e)g(so)g(that)g (\(1.7\))f(do)s(es)i(not)f(hold)g(\(i.e.)54 b Ft(r)3124 327 y Fp(n)3204 312 y Fo(9)34 b Fv(0\))h(and)h(it)g(is)111 432 y(lik)m(ely)f(to)d(b)s(e)h(from)f(s.c.)44 b(to)33 b(\(dense\))h(p.p.,)f(with)g(a.c.)44 b(sp)s(ectrum)34 b(just)e(for)h Ft(\024)27 b Fv(=)h(0.)258 552 y(When)e Ft(r)579 567 y Fp(n)654 552 y Fo(9)h Fv(0,)g(i.e.)42 b(\(1.8\),)27 b(the)g(p)s(erturbation)f(is)g(not)g(compact,)i(whic)m(h) g(is)e(a)g(common)g(feature)111 673 y(with)41 b(the)g(theory)g(of)g (\(random\))f(disordered)i(systems.)70 b(This)42 b(is)f(the)g(case)g(w) m(e)h(consider)g(in)e(the)111 793 y(rest)33 b(of)f(the)g(pap)s(er.)44 b(W)-8 b(eyl's)34 b(in)m(v)-5 b(ariance)33 b(principle)h(is)e(th)m(us)i (not)e(applicable,)h(and)g(it)f(is)g(necessary)111 914 y(to)44 b(determine)j(the)e(sp)s(ectrum.)80 b(This)46 b(is)f(done)g(in)g(Section)g(2,)j(where)e(w)m(e)f(also)g(in)m(tro)s (duce)g(the)111 1034 y(necessary)36 b(notation.)46 b(In)34 b(Section)h(3)e(w)m(e)i(sho)m(w)g(that)e(a)g(sp)s(ecial)i(c)m(hoice)g (of)e(Pr)s(\177)-51 b(ufer)33 b(\(mo)s(dulus)i(and)111 1154 y(angle\))26 b(v)-5 b(ariables)27 b(is)f(particularly)g(con)m(v)m (enien)m(t)j(in)d(the)g(o\013{diagonal)f(case.)42 b(In)26 b(Section)h(4)e(w)m(e)i(recall)111 1275 y(the)39 b(basic)g(results)g (of)f(Last)g(and)h(Simon)f([LS)q(])g(that)g(w)m(e)h(need,)i(and)d (state)h(and)f(pro)m(v)m(e)h(our)f(main)111 1395 y(Lemma,)h(whic)m(h)f (roughly)f(states)h(that)f(the)g(sp)s(ectral)h(transition,)g(from)f (s.c.)57 b(at)37 b(small)g(coupling)111 1516 y(to)46 b(\(dense\))i(p.p.)84 b(at)46 b(large)g(coupling,)k(o)s(ccurs)d(whenev) m(er)i(the)d(corresp)s(onding)h(Pr)s(\177)-51 b(ufer)46 b(angles)111 1636 y(are)c(uniformly)h(distributed)g(\(u.d.\).)71 b(In)42 b(the)h(presen)m(t)g(case,)i(the)d(Pr)s(\177)-51 b(ufer)42 b(angles)g(are)g(exp)s(ected)111 1756 y(to)g(ha)m(v)m(e)h(a)e (con)m(tin)m(uous)i(asymptotic)g(distribution)g(function)f(\(a.d.f.\),) i(whic)m(h)f(is)g(near)f(uniform)111 1877 y(for)k(su\016cien)m(tly)i (small)f Ft(p)p Fv(.)84 b(Ho)m(w)m(ev)m(er,)52 b(ev)m(en)47 b(for)f(some)h(v)-5 b(alues)47 b(of)e Ft(p)h Fv(for)g(whic)m(h)h(the)g (a.d.f.)83 b(is)111 1997 y(not)43 b(uniform,)i(the)e(results)i(are)d (exp)s(ected)j(to)d(hold)h(b)s(ecause)h(the)f(strong)g(n)m(umerical)h (evidence)111 2117 y(presen)m(ted)35 b(in)e(Section)g(5.)43 b(Section)34 b(6)e(is)h(reserv)m(ed)i(to)d(a)h(conclusion)h(with)f(op)s (en)g(problems.)111 2444 y Fu(2)161 b(Some)53 b(Notation)g(and)h(a)g (Theorem)e(on)i(the)e(Sp)t(ectrum)111 2663 y Fv(A)43 b(b)s(ounded)h(Jacobi)f(matrix)g Ft(J)52 b Fv(is)43 b(a)g(matrix)g(of)f (a)h(self{adjoin)m(t)g(op)s(erator)f Ft(H)50 b Fv(on)43 b(a)g(separable)111 2784 y(Hilb)s(ert)38 b(space)g Fj(H)29 b Fv(:)52 b Ft(J)976 2799 y Fp(ij)1072 2784 y Fv(=)35 b(\()p Ft(')1285 2799 y Fp(i)1313 2784 y Ft(;)17 b(H)8 b(')1510 2799 y Fp(j)1546 2784 y Fv(\),)38 b(where)g Fq(f)p Ft(')2049 2799 y Fp(j)2086 2784 y Fq(g)2135 2816 y Fp(j)t Fn(\025)p Fr(0)2299 2784 y Fv(is)g(an)f(orthonormal)f(base)i (of)f Fj(H)29 b Fv(.)57 b(The)111 2904 y(sp)s(ectral)42 b(measure)h Ft(\026)e Fv(=)i Ft(d\032)e Fv(asso)s(ciated)h(to)e Ft(J)51 b Fv(is)41 b(giv)m(en)i(b)m(y)f(the)f(00{elemen)m(t)h(of)f(the) h(resolv)m(en)m(t)111 3025 y(matrix)33 b([A,)g(S])839 3256 y(\()p Ft(J)e Fq(\000)23 b Ft(\025I)8 b Fv(\))1208 3207 y Fn(\000)p Fr(1)1208 3285 y(00)1330 3256 y Fv(=)1433 3175 y Fs(\000)1479 3256 y Ft(')1543 3271 y Fr(0)1582 3256 y Ft(;)17 b Fv(\()p Ft(H)30 b Fq(\000)22 b Ft(\025)p Fv(\))1969 3207 y Fn(\000)p Fr(1)2080 3256 y Ft(')2144 3271 y Fr(0)2183 3175 y Fs(\001)2257 3256 y Fv(=)2360 3120 y Fs(Z)2460 3146 y Fn(1)2416 3345 y(\0001)2664 3188 y Fv(1)p 2572 3233 235 4 v 2572 3324 a Ft(x)g Fq(\000)h Ft(\025)2816 3256 y(d\032)p Fv(\()p Ft(x)p Fv(\))17 b Ft(:)527 b Fv(\(2.1\))258 3490 y(W)-8 b(e)32 b(in)m(tro)s(duce,)i(for)e Ft(\025)c Fq(2)g Fo(C)58 b Fv(and)33 b Ft(n)28 b Fq(2)g Fo(N)9 b Fv(,)39 b(a)32 b(2)22 b Fq(\002)g Fv(2)33 b(transfer)g(matrix) 1203 3782 y Ft(T)14 b Fv(\()p Ft(n;)j(n)22 b Fq(\000)g Fv(1;)17 b Ft(\025)p Fv(\))27 b(=)1912 3581 y Fs(0)1912 3761 y(@)2070 3654 y Ft(\025)p 2050 3698 96 4 v 2050 3789 a(p)2099 3804 y Fp(n)2249 3654 y Fq(\000)p Ft(p)2375 3669 y Fp(n)p Fn(\000)p Fr(1)p 2249 3698 264 4 v 2333 3789 a Ft(p)2382 3804 y Fp(n)2074 3893 y Fv(1)234 b(0)2564 3581 y Fs(1)2564 3761 y(A)2701 3782 y Ft(;)891 b Fv(\(2.2\))111 4079 y(asso)s(ciated)34 b(to)e(the)h Ft(l)892 4094 y Fr(2)948 4079 y Fv(\()p Fo(N)9 b Fv(\))d({solutions)33 b Ft(u)f Fv(of)g(\()p Ft(J)f Fq(\000)23 b Ft(\025I)8 b Fv(\))16 b Ft(u)28 b Fv(=)f(0,)33 b(and)f(set)733 4259 y Ft(T)14 b Fv(\()p Ft(n)p Fv(;)j Ft(\025)p Fv(\))27 b(:=)g Ft(T)14 b Fv(\()p Ft(n;)j(n)22 b Fq(\000)h Fv(1;)17 b Ft(\025)p Fv(\))g Ft(T)d Fv(\()p Ft(n)21 b Fq(\000)i Fv(1)p Ft(;)17 b(n)k Fq(\000)i Fv(2;)17 b Ft(\025)p Fv(\))g Fq(\001)g(\001)g(\001)d Ft(T)g Fv(\(0)p Ft(;)j Fq(\000)p Fv(1;)g Ft(\025)p Fv(\))g Ft(;)419 b Fv(\(2.3\))111 4439 y(with)42 b Ft(p)391 4454 y Fn(\000)p Fr(1)527 4439 y Fv(=)g(1.)68 b(If)41 b Ft(J)51 b Fq(2)42 b Fm(H)q Fv(,)g(in)g(view)g (of)e(\(1.2\))h(and)g(\(1.4\),)h(there)g(are)f(three)g(situations)h(to) f(b)s(e)111 4560 y(considered:)46 b(for)32 b Ft(n)39 b(=)-60 b Fq(2)28 b(f)o Ft(a)1056 4575 y Fp(j)1093 4560 y Ft(;)17 b(a)1188 4575 y Fp(j)1247 4560 y Fv(+)22 b(1)p Fq(g)1443 4592 y Fp(j)t Fn(\025)p Fr(1)1570 4560 y Fv(,)33 b Ft(T)14 b Fv(\()p Ft(n;)j(n)22 b Fq(\000)g Fv(1;)17 b Ft(\025)p Fv(\))32 b(is)h(equal)h(to)e(the)h(free)g(transfer)g (matrix)1507 4818 y Ft(T)1564 4833 y Fr(0)1604 4818 y Fv(\()p Ft(\025)p Fv(\))27 b(=)1868 4678 y Fs(\022)1983 4757 y Ft(\025)83 b Fq(\000)p Fv(1)1987 4878 y(1)125 b(0)2290 4678 y Fs(\023)2397 4818 y Fv(;)1195 b(\(2.4\))111 5051 y(for)32 b Ft(n)c Fv(=)g Ft(a)501 5066 y Fp(j)560 5051 y Fv(+)22 b(1)32 b(for)g(some)h Ft(j)h Fq(\025)28 b Fv(1,)955 5292 y Ft(T)14 b Fv(\()p Ft(n;)j(n)22 b Fq(\000)g Fv(1;)17 b Ft(\025)p Fv(\))27 b(=)h Ft(T)1721 5307 y Fr(+)1797 5292 y Fv(\()p Ft(a)1886 5307 y Fp(j)1922 5292 y Fv(;)17 b Ft(\025)p Fv(\))28 b(:=)2219 5152 y Fs(\022)2334 5231 y Ft(\025)83 b Fq(\000)p Fv(1)23 b(+)f Ft(r)2765 5246 y Fp(j)2338 5352 y Fv(1)226 b(0)2843 5152 y Fs(\023)2949 5292 y Fv(;)643 b(\(2.5\))1941 5587 y(4)p eop %%Page: 5 5 5 4 bop 111 312 a Fv(and)33 b(for)f Ft(n)c Fv(=)f Ft(a)690 327 y Fp(j)760 312 y Fv(for)32 b(some)h Ft(j)h Fq(\025)28 b Fv(1,)862 647 y Ft(T)14 b Fv(\()p Ft(n;)j(n)22 b Fq(\000)h Fv(1;)17 b Ft(\025)p Fv(\))27 b(=)g Ft(T)1628 662 y Fn(\000)1704 647 y Fv(\()p Ft(a)1793 662 y Fp(j)1830 647 y Fv(;)17 b Ft(\025)p Fv(\))27 b(:=)2126 447 y Fs(0)2126 626 y(@)2362 515 y Ft(\025)p 2265 560 252 4 v 2265 651 a Fv(1)22 b Fq(\000)h Ft(r)2480 666 y Fp(j)2677 515 y Fq(\000)p Ft(\025)p 2619 560 V 2619 651 a Fv(1)f Fq(\000)h Ft(r)2834 666 y Fp(j)2366 763 y Fv(1)305 b(0)2922 447 y Fs(1)2922 626 y(A)3042 647 y Ft(:)550 b Fv(\(2.6\))111 980 y(Let)28 b Ft(\025)f Fv(=)h(2)17 b(cos)f Ft(')28 b Fv(where)g Ft(')g Fq(2)g Fv(\(0)p Ft(;)17 b(\031)t Fv(\))26 b(\(see)j(Theorem)g (2.1)e(for)f(a)h(pro)s(of)g(that)g(this)h(parameterization)111 1100 y(is)33 b(exhaustiv)m(e\),)i(and)1528 1279 y Ft(U)k Fv(=)1736 1138 y Fs(\022)1851 1218 y Fv(0)135 b(sin)18 b Ft(')1851 1338 y Fv(1)83 b Fq(\000)17 b Fv(cos)g Ft(')2329 1138 y Fs(\023)3619 1279 y Fv(\(2.7\))111 1504 y(b)s(e)33 b(the)g(nonsingular)g(matrix)g(with)1498 1778 y Ft(U)1574 1737 y Fn(\000)p Fr(1)1697 1778 y Fv(=)1800 1637 y Fs(\022)1915 1717 y Fv(cot)17 b Ft(')83 b Fv(1)1918 1837 y(csc)18 b Ft(')85 b Fv(0)2299 1637 y Fs(\023)2406 1778 y Ft(:)111 2008 y Fv(The)34 b(matrix)f Ft(U)43 b Fv(has)33 b(a)f(remark)-5 b(able)33 b(prop)s(ert)m(y)h(of)e(transforming)h Ft(T)2639 2023 y Fr(0)2678 2008 y Fv(\()p Ft(\025)p Fv(\))g(in)m(to)f(a)h(pure)g (rotation)1049 2282 y Ft(R)18 b Fv(\()p Ft(')p Fv(\))27 b(=)1412 2142 y Fs(\022)1568 2221 y Fv(cos)17 b Ft(')130 b Fv(sin)18 b Ft(')1527 2342 y Fq(\000)f Fv(sin)g Ft(')83 b Fv(cos)17 b Ft(')2157 2142 y Fs(\023)2258 2282 y Fv(=)27 b Ft(U)10 b(T)2494 2297 y 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2987 y Fv(\))g Ft(U)1719 2951 y Fn(\000)p Fr(1)1814 2987 y Fv(.)88 b(F)-8 b(rom)47 b(\(2.3\))g(-)g(\(2.9\))g(and,)k(since)e(a)e(pro)s(duct)g(of)111 3107 y(rotations)33 b(is)g(a)f(rotation,)g(w)m(e)i(ha)m(v)m(e)228 3323 y Ft(U)10 b(T)k Fv(\()p Ft(n)p Fv(;)j Ft(\025)p Fv(\))p Ft(U)686 3282 y Fn(\000)p Fr(1)808 3323 y Fv(=)28 b Ft(R)18 b Fv(\(\()p Ft(n)k Fq(\000)h Ft(a)1311 3338 y Fp(k)1353 3323 y Fv(\))p Ft(')p Fv(\))17 b Ft(P)1573 3338 y Fr(+)p Fn(\000)1687 3323 y Fv(\()p Ft(a)1776 3338 y Fp(k)1818 3323 y Fv(\))p Ft(R)h Fv(\(\()p Ft(a)2075 3338 y Fp(k)2140 3323 y Fq(\000)23 b Ft(a)2291 3338 y Fp(k)r Fn(\000)p Fr(1)2424 3323 y Fv(\))p Ft(')p Fv(\))16 b Fq(\001)h(\001)g(\001)e Ft(P)2776 3338 y Fr(+)p Fn(\000)2890 3323 y Fv(\()p Ft(a)2979 3338 y Fr(1)3018 3323 y Fv(\))p Ft(R)j Fv(\(\()p Ft(a)3275 3338 y Fr(1)3314 3323 y Fv(\))p Ft(')p Fv(\))117 b(\(2.10\))111 3539 y(whic)m(h)34 b(will)g(b)s(e)e (useful)i(in)f(Section)g(3.)258 3659 y(According)g(to)f(\(1.2\))g(and)h 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Fv(\))28 b(=)f([)p Fq(\000)p Fv(2)p Ft(;)17 b Fv(2])52 b Ft(;)111 4874 y Fk(is)35 b(the)g(essential)f(sp)-5 b(e)g(ctrum)34 b(of)h Ft(J)9 b Fk(.)111 5097 y(Pr)-5 b(o)g(of.)40 b Fv(W)-8 b(e)25 b(restrict)h(ourselv)m(es)h(to)d(the)h(case)g Ft(J)37 b Fv(=)27 b Ft(J)2019 5112 y Fr(0)2083 5097 y Fv(giv)m(en)f(b)m(y)f(\(1.9\))f(with)h(0{b)s(oundary)f(condition)111 5218 y(at)32 b Fq(\000)p Fv(1.)44 b(W)-8 b(e)33 b(ha)m(v)m(e)1544 5338 y Ft(J)1598 5353 y Fp(\013)1675 5338 y Fv(=)28 b Ft(J)1833 5353 y Fr(0)1894 5338 y Fv(+)22 b(tan)17 b Ft(\013)33 b(\016)2288 5353 y Fr(0)2360 5338 y Ft(:)1184 b Fv(\(2.12\))1941 5587 y(5)p eop %%Page: 6 6 6 5 bop 111 312 a Fv(Clearly)-8 b(,)42 b(\()p Ft(\016)558 327 y Fr(0)598 312 y Ft(u)p Fv(\))691 341 y Fp(n)777 312 y Fv(=)d Ft(\016)935 327 y Fp(n)p Fr(0)1056 312 y Ft(u)1112 327 y Fr(0)1151 312 y Fv(,)i(is)f(a)f(rank)g(one)h(p)s (erturbation)f(of)g Ft(J)2579 327 y Fr(0)2657 312 y Fv(and)h Ft(\033)2909 327 y Fr(ess)3000 312 y Fv(\()p Ft(J)3092 327 y Fp(\013)3142 312 y Fv(\))e(=)h Ft(\033)3388 327 y Fr(ess)3480 312 y Fv(\()p Ft(J)3572 327 y Fr(0)3611 312 y Fv(\),)i(b)m(y)111 432 y(W)-8 b(eyl's)34 b(in)m(v)-5 b(ariance)34 b(principle.)45 b(Th)m(us)34 b(the)f(c)m(hoice)h Ft(J)j Fv(=)27 b Ft(J)2276 447 y Fr(0)2348 432 y Fv(en)m(tails)34 b(no)e(loss)i(of)e(generalit)m(y)-8 b(.)258 552 y(Let)43 b Ft(J)55 b Fq(2)46 b Fm(H)e Fv(with)g(\()p Ft(p)1117 567 y Fp(n)1164 552 y Fv(\))1202 582 y Fp(n)p Fn(\025)p Fr(0)1382 552 y Fv(so)f(that)g(0)j Fq(\024)h Ft(p)2002 567 y Fp(a)2039 577 y Fi(j)2121 552 y Fq(\024)g Fv(1,)f Fq(8)p Ft(j)6 b Fv(.)75 b(T)-8 b(o)44 b(pro)m(v)m(e)g Ft(\033)t Fv(\()p Ft(J)9 b Fv(\))46 b Fq(\022)h Fv([)p Fq(\000)p Fv(2)p Ft(;)17 b Fv(2])o(,)46 b(let)111 673 y Ft(u)27 b Fv(=)h(\()p Ft(u)392 688 y Fp(n)438 673 y Fv(\))476 702 y Fp(n)p Fn(\025)p Fr(0)641 673 y Fq(2)g Ft(l)764 688 y Fr(2)820 673 y Fv(\()p Fo(N)9 b Fv(\))d(.)44 b(W)-8 b(e)33 b(ha)m(v)m(e)1200 984 y(\()p Ft(u;)17 b(J)9 b(u)p Fv(\))26 b(=)1661 860 y Fn(1)1625 890 y Fs(X)1630 1099 y Fp(n)p Fr(=0)1785 984 y Fv(\()p Ft(u)1879 999 y Fp(n)1942 984 y Ft(u)1998 999 y Fp(n)p Fr(+1)2135 984 y Fv(\))16 b Ft(h)2245 999 y Fp(n)2309 844 y Fs(\022)2469 923 y Ft(u)2525 938 y Fp(n)2424 1044 y Ft(u)2480 1059 y Fp(n)p Fr(+1)2658 844 y Fs(\023)3571 984 y Fv(\(2.13\))111 1286 y(where)1558 1439 y Ft(h)1614 1454 y Fp(n)1688 1439 y Fv(=)1792 1299 y Fs(\022)1930 1378 y Fv(0)107 b Ft(p)2135 1393 y Fp(n)1907 1499 y Ft(p)1956 1514 y Fp(n)2109 1499 y Fv(0)2223 1299 y Fs(\023)2330 1439 y Ft(:)111 1665 y Fv(Inserting)1520 1786 y Ft(h)1576 1801 y Fp(n)1651 1786 y Fv(=)28 b Ft(\025)1812 1744 y Fr(+)1812 1810 y Fp(n)1887 1786 y Ft(P)1964 1744 y Fr(+)1950 1810 y Fp(n)2045 1786 y Fv(+)22 b Ft(\025)2200 1744 y Fn(\000)2200 1810 y Fp(n)2275 1786 y Ft(P)2352 1744 y Fn(\000)2338 1810 y Fp(n)111 1960 y Fv(in)m(to)45 b(\(2.13\),)h(where)f Ft(P)1014 1924 y Fn(\006)1000 1985 y Fp(n)1117 1960 y Fv(pro)5 b(jects)45 b(on)m(to)f(the)h(eigendirection)h(asso)s(ciated)f (to)f(the)g(eingen)m(v)-5 b(alue)111 2080 y Ft(\025)168 2044 y Fn(\006)168 2105 y Fp(n)255 2080 y Fv(=)27 b Fq(\006)p Ft(p)484 2095 y Fp(n)532 2080 y Fv(,)32 b(w)m(e)i(ha)m(v)m(e)1515 2255 y Fq(\000)p Fv(2)1662 2229 y(\026)1658 2255 y Ft(\025)27 b Fq(\024)1857 2188 y Fv(\()p Ft(u;)17 b(J)9 b(u)p Fv(\))p 1857 2232 294 4 v 1889 2324 a(\()p Ft(u;)17 b(u)p Fv(\))2189 2255 y Fq(\024)28 b Fv(2)2363 2229 y(\026)2360 2255 y Ft(\025)111 2493 y Fv(where)397 2467 y(\026)393 2493 y Ft(\025)g Fv(=)f(sup)728 2517 y Fp(n)792 2493 y Ft(\025)849 2457 y Fr(+)849 2518 y Fp(n)935 2493 y Fv(=)h(sup)1186 2517 y Fp(n)1249 2493 y Ft(p)1298 2508 y Fp(n)1373 2493 y Fv(=)f(1.)44 b(Hence)1335 2713 y Ft(\033)21 b Fv(\()p Ft(J)9 b Fv(\))27 b Fq(\022)1683 2633 y Fs(\002)1724 2713 y Fq(\000)p Fv(2)1871 2687 y(\026)1867 2713 y Ft(\025;)17 b Fv(2)2037 2687 y(\026)2034 2713 y Ft(\025)2090 2633 y Fs(\003)2159 2713 y Fv(=)28 b([)p Fq(\000)p Fv(2)p Ft(;)17 b Fv(2])33 b Ft(:)975 b Fv(\(2.14\))111 2933 y(Note)41 b(that,)h(b)s(ecause)g Ft(J)50 b Fv(is)41 b(a)g(symmetric)h (o\013{diagonal)e(matrix,)j(the)e(sp)s(ectrum)h(is)g(symmetric)111 3054 y(and)33 b(inf)419 3069 y Fp(n)482 3054 y Ft(\025)539 3018 y Fn(\000)539 3078 y Fp(n)626 3054 y Fv(=)28 b Fq(\000)17 b Fv(sup)971 3077 y Fp(n)1034 3054 y Ft(\025)1091 3018 y Fr(+)1091 3078 y Fp(n)1178 3054 y Fv(=)27 b Fq(\000)1362 3028 y Fv(\026)1358 3054 y Ft(\025)q Fv(.)43 b(In)33 b(order)g(to)f(pro)m(v)m(e)i(the)f(opp)s(osite)g(inclusion)1625 3274 y Ft(\033)21 b Fv(\()p Ft(J)9 b Fv(\))27 b Fq(\023)i Fv([)p Fq(\000)p Fv(2)p Ft(;)17 b Fv(2])33 b Ft(;)1265 b Fv(\(2.15\))111 3494 y(w)m(e)41 b(use)g(W)-8 b(eyl's)41 b(criterion)g(\(see)f(Theorem)i(VI)s(I)p Ft(:)p Fv(12)d(of)h([S1]\):)97 b(if)40 b Ft(A)g Fv(is)g(a)g(b)s(ounded)g(self{adjoin)m(t)111 3614 y(op)s(erator)35 b(in)i(separable)g(Hilb)s(ert)f(space)h Fj(H)29 b Fv(,)37 b Ft(\025)f Fv(is)g(a)g(p)s(oin)m(t)g(of)g(the)g(sp)s (ectrum)h Ft(\033)t Fv(\()p Ft(A)p Fv(\))f(of)g Ft(A)g Fv(if)g(and)111 3735 y(only)d(if)g(there)g(exist)h(a)e(sequence)j(\()p Ft( )1481 3750 y Fp(n)1529 3735 y Fv(\))1567 3764 y Fp(n)p Fn(\025)p Fr(0)1736 3735 y Fv(in)e Fj(H)c Fv(,)k(with)g Fq(k)p Ft( )2371 3750 y Fp(n)2418 3735 y Fq(k)28 b Fv(=)f(1,)33 b(suc)m(h)h(that)1500 3955 y(lim)1476 4014 y Fp(n)p Fn(!1)1677 3955 y Fq(k)p Fv(\()p Ft(A)22 b Fq(\000)g Ft(\025)p Fv(\))17 b Ft( )2134 3970 y Fp(n)2181 3955 y Fq(k)28 b Fv(=)f(0)17 b Ft(:)1116 b Fv(\(2.16\))258 4212 y(Let)25 b Ft(\025)j Fv(=)g(2)17 b(cos)f Ft(')p Fv(,)27 b Ft(')h Fq(2)g Fv([0)p Ft(;)17 b(\031)t Fv(],)27 b(and)f(de\014ne)h Ft( )1911 4227 y Fp(n)1986 4212 y Fv(=)g(\(1)p Ft(=)2225 4141 y Fq(p)p 2308 4141 59 4 v 71 x Ft(n)p Fv(\))16 b(\()p Ft(e)2503 4176 y Fp(i')2578 4212 y Ft(;)h(e)2667 4176 y Fp(i)p Fr(2)p Fp(')2776 4212 y Ft(;)g(:)g(:)g(:)f(;)h(e)3040 4176 y Fp(in')3157 4212 y Ft(;)g Fv(0)p Ft(;)g(:)g(:)g(:)o Fv(\))o(.)42 b(Clearly)111 4333 y Ft( )174 4348 y Fp(n)249 4333 y Fq(2)28 b Ft(l)372 4348 y Fr(2)428 4333 y Fv(\()p Fo(N)9 b Fv(\))39 b(and)32 b(w)m(e)i(claim)f(that)1518 4602 y Fq(k)p Fv(\()p Ft(J)e Fq(\000)23 b Ft(\025)p Fv(\))16 b Ft( )1965 4617 y Fp(n)2012 4602 y Fq(k)28 b(\024)g Ft(c)2247 4535 y Fv(ln)17 b Ft(n)p 2247 4579 157 4 v 2254 4599 a Fq(p)p 2337 4599 59 4 v 72 x Ft(n)3571 4602 y Fv(\(2.17\))111 4877 y(holds)37 b(with)h Ft(c)c Fv(=)g Ft(c)p Fv(\()p Ft(\014)6 b Fv(\))36 b(indep)s(enden)m(t)j(of)d Ft(n)h Fv(for)f(an)m(y)h Ft(J)44 b Fq(2)35 b Fm(H)q Fv(.)55 b(In)36 b(order)h(to)f(pro)m(v)m(e)i(\(2.17\),)f(notice)111 4998 y(that)30 b(\()p Ft(J)h Fq(\000)22 b Ft(\025)p Fv(\))17 b Ft( )717 5013 y Fp(n)794 4998 y Fv(consists)31 b(of)e(the)h(action)g (on)g Ft( )1909 5013 y Fp(n)1986 4998 y Fv(of)f(a)g(sum)i(of)e(lo)s (cal)g(matrices,)j(eac)m(h)e(b)s(ounded)h(in)111 5118 y(norm)25 b(b)m(y)h(one.)42 b(Tw)m(o)26 b(of)e(them)i(in)m(v)m(olv)m(e) i(the)d(extremes)i Ft(e)2186 5082 y Fp(i')2286 5118 y Fv(and)e Ft(e)2513 5082 y Fp(in')2630 5118 y Fv(,)i(and)e(there)h(are)f Ft(O)19 b Fv(\(ln)e Ft(n)p Fv(\))25 b(non{)111 5239 y(diagonal)37 b(matrices,)j(eac)m(h)e(acting)g(just)g(on)f(t)m(w)m(o)h(successiv)m(e) j(comp)s(onen)m(ts)e(of)e Ft( )3156 5254 y Fp(n)3204 5239 y Fv(.)58 b(The)38 b Ft(O)19 b Fv(\(ln)e Ft(n)p Fv(\))1941 5587 y(6)p eop %%Page: 7 7 7 6 bop 111 312 a Fv(comes)31 b(from)f(the)g(sequence)i(\()p Ft(a)1279 327 y Fp(j)1316 312 y Fv(\))1354 344 y Fp(j)t Fn(\025)p Fr(1)1510 312 y Fv(satisfying)f(the)f(sparseness)i(condition) e(\(1.5\),)g Ft(a)3306 327 y Fp(j)3371 312 y Fq(\030)e Ft(\014)3537 276 y Fp(j)3573 312 y Fv(,)i(with)111 432 y(at)i(most)h Ft(r)j Fv(p)s(oin)m(ts)d Ft(a)893 447 y Fp(j)962 432 y Fv(within)h([1)p Ft(;)17 b(n)p Fv(])o(,)33 b(where)h Ft(r)h Fv(is)e(suc)m(h)h(that)f Ft(\014)2482 396 y Fp(r)2547 432 y Fq(\024)28 b Ft(n)33 b Fv(or,)f(equiv)-5 b(alen)m(tly)d(,)1757 681 y Ft(r)30 b Fq(\024)1947 613 y Fv(ln)17 b Ft(n)p 1946 658 159 4 v 1946 749 a Fv(ln)g Ft(\014)2147 681 y(:)111 927 y Fv(This)34 b(pro)m(v)m(es)g(\(2.17\))e (and)h(therefore)g(\(2.15\).)258 1048 y(A)i(v)-5 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Ft(u)c Fv(=)f(\()p Ft(u)1940 2811 y Fr(0)1979 2796 y Ft(;)17 b(u)2079 2811 y Fr(1)2118 2796 y Ft(;)g(:)g(:)g(:)o Fv(\))32 b(of)g(\()p Ft(J)2549 2811 y Fp(\013)2621 2796 y Fq(\000)23 b Ft(\025)p Fv(\))16 b Ft(u)27 b Fv(=)h(0,)k(then)1448 2992 y Fl(u)1510 3007 y Fp(n)p Fr(+1)1675 2992 y Fv(=)c Ft(T)14 b Fv(\()p Ft(n;)j(n)22 b Fq(\000)h Fv(1;)17 b Ft(\025)p Fv(\))g Fl(u)2437 3007 y Fp(n)111 3246 y Fv(holds)45 b(for)f Ft(n)k Fv(=)g(0)p Ft(;)17 b Fv(1)p Ft(;)g(:)g(:)g(:)n Fv(,)47 b(with)e(initial)g(condition)g Fl(u)2172 3261 y Fr(0)2259 3246 y Fv(=)2383 3106 y Fs(\022)2525 3185 y Ft(u)2581 3200 y Fr(0)2498 3306 y Ft(u)2554 3321 y Fn(\000)p Fr(1)2689 3106 y Fs(\023)2810 3246 y Fv(=)2934 3106 y Fs(\022)3049 3185 y Fv(cos)17 b Ft(\013)3054 3306 y Fv(sin)g Ft(\013)3300 3106 y Fs(\023)3418 3246 y Fv(satisfying)111 3425 y(\(1.10\))32 b(for)g(some)h Ft(\013)c Fq(2)f Fv([0)p Ft(;)17 b(\031)t Fv(])o(.)258 3545 y(W)-8 b(riting)1615 3666 y Ft(T)1686 3624 y Fp(k)1672 3690 y Fr(0)1756 3666 y Fv(=)28 b Ft(T)1917 3681 y Fr(0)1973 3666 y Ft(T)2030 3681 y Fr(0)2086 3666 y Fq(\001)17 b(\001)g(\001)e Ft(T)2276 3681 y Fr(0)1860 3717 y Fs(|)p 1905 3717 139 12 v 139 w({z)p 2134 3717 V 139 w(})1959 3805 y Fp(k)r Fn(\000)p Fr(times)111 3943 y Fv(and)1317 4064 y Ft(T)1374 4079 y Fr(+)p Fp(;)p Fn(\000)1507 4064 y Fv(\()p Ft(a)p Fv(;)i Ft(\025)p Fv(\))28 b(=)f Ft(T)1923 4079 y Fr(+)1982 4064 y Fv(\()p Ft(a)p Fv(;)17 b Ft(\025)p Fv(\))g Ft(T)2284 4079 y Fn(\000)2343 4064 y Fv(\()p Ft(a)p Fv(;)g Ft(\025)p Fv(\))g Ft(;)111 4228 y Fv(where)34 b Ft(T)450 4243 y Fr(0)522 4228 y Fv(and)f Ft(T)769 4243 y Fn(\006)861 4228 y Fv(is)g(giv)m(en)g(b)m(y)h(\(2.4\)-\(2.6\),)d(equation)i (\(2.3\))f(can)h(b)s(e)g(written)g(as)396 4432 y Ft(T)d Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\))27 b(=)h Ft(T)920 4386 y Fp(n)p Fn(\000)p Fp(a)1055 4398 y Fi(k)1093 4386 y Fn(\000)p Fr(1)906 4457 y(0)1204 4432 y Ft(T)1261 4447 y Fr(+)p Fp(;)p Fn(\000)1395 4432 y Fv(\()p Ft(a)1484 4447 y Fp(k)1526 4432 y Fv(\))17 b Ft(T)1652 4380 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Fv(1)2812 4782 y Fs(\023)111 5139 y Fv(and)927 5292 y Ft(U)10 b(T)1060 5307 y Fn(\000)1120 5292 y Fv(\()p Ft(a)p Fv(\))p Ft(U)1323 5251 y Fn(\000)p Fr(1)1418 5292 y Ft(R)q Fv(\()p Fq(\000)p Ft(')p Fv(\))28 b(=)1841 5152 y Fs(\022)2263 5231 y Fv(1)459 b(0)1956 5352 y(\(1)p Ft(=p)2141 5367 y Fp(a)2205 5352 y Fq(\000)22 b Fv(1\))16 b(cot)h Ft(')83 b Fv(1)p Ft(=p)2848 5367 y Fp(a)2931 5152 y Fs(\023)1941 5587 y Fv(7)p eop %%Page: 8 8 8 7 bop 111 312 a Fv(in)m(to)33 b(\(2.9\))f(giv)m(es)1342 490 y Ft(P)1405 505 y Fr(+)p Fn(\000)1518 490 y Fv(\()p Ft(a)p Fv(\))c(=)1777 350 y Fs(\022)2002 429 y Ft(p)2051 444 y Fp(a)2356 429 y Fv(0)1891 550 y Ft(q)1934 565 y Fp(a)1993 550 y Fv(cot)17 b Ft(')83 b Fv(1)p Ft(=p)2434 565 y Fp(a)2516 350 y Fs(\023)3619 490 y Fv(\(3.2\))111 717 y(where)1682 857 y Ft(q)1725 872 y Fp(a)1795 857 y Fv(=)1929 790 y(1)p 1909 834 91 4 v 1909 925 a Ft(p)1958 940 y Fp(a)2031 857 y Fq(\000)23 b Ft(p)2180 872 y Fp(a)2221 857 y Ft(:)258 1082 y Fv(W)-8 b(e)31 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y Ft(\022)840 5203 y Fp(k)r Fr(+1)1001 5188 y Fv(=)28 b(tan)1246 5147 y Fn(\000)p Fr(1)1357 5048 y Fs(\022)1480 5121 y Fv(1)p 1440 5165 V 1440 5257 a Ft(p)1489 5228 y Fr(2)1489 5281 y Fp(a)1526 5293 y Fi(k)1595 5188 y Fv(tan)17 b Ft(\022)1798 5203 y Fp(k)1863 5188 y Fv(+)1974 5121 y Ft(q)2017 5136 y Fp(a)2054 5148 y Fi(k)p 1971 5165 V 1971 5257 a Ft(p)2020 5272 y Fp(a)2057 5284 y Fi(k)2126 5188 y Fv(cot)g Ft(')2337 5048 y Fs(\023)2432 5188 y Fv(+)22 b(\()p Ft(a)2619 5203 y Fp(k)r Fr(+1)2775 5188 y Fq(\000)g Ft(a)2925 5203 y Fp(k)2968 5188 y Fv(\))17 b Ft(')532 b Fv(\(3.9\))1941 5587 y(8)p eop %%Page: 9 9 9 8 bop 111 312 a Fv(for)32 b Ft(k)f Fq(\025)d Fv(1)k(and)1648 432 y Ft(\022)1693 447 y Fr(1)1760 432 y Fv(=)c Ft(\022)1909 447 y Fr(0)1971 432 y Fv(+)22 b Ft(a)2120 447 y Fr(1)2160 432 y Ft(')32 b(:)1288 b Fv(\(3.10\))111 618 y(W)-8 b(e)32 b(observ)m(e)g(that)f Ft(\022)878 633 y Fp(k)952 618 y Fv(and)1145 591 y Fs(e)1140 618 y Ft(\022)1185 633 y Fp(k)1259 618 y 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Fq(\000)g Fv(ln)17 b Ft(p)2619 1765 y Fr(2)2619 1831 y Fp(a)2656 1843 y Fi(k)2699 1725 y Fs(\001)2745 1636 y(\)!)2904 1652 y Fp(N)3004 1806 y Ft(;)540 b Fv(\(3.12\))111 2111 y(where)786 2231 y Ft(f)11 b Fv(\()p Ft(p;)17 b(\022)s Fv(\))28 b(=)f(ln)1291 2120 y Fs(\020)1350 2231 y Ft(p)1399 2190 y Fr(4)1455 2231 y Fv(cos)1586 2190 y Fr(2)1642 2231 y Ft(\022)e Fv(+)1810 2150 y Fs(\000)1856 2231 y Fv(sin)17 b Ft(\022)26 b Fv(+)2161 2150 y Fs(\000)2206 2231 y Fv(1)c Fq(\000)h Ft(p)2426 2190 y Fr(2)2465 2150 y Fs(\001)2528 2231 y Fv(cot)16 b Ft(')h Fv(cos)g Ft(\022)2967 2150 y Fs(\001)3012 2173 y Fr(2)3052 2120 y Fs(\021)3571 2231 y Fv(\(3.13\))111 2433 y(with)33 b(the)g(Pr)s(\177)-51 b(ufer)33 b(angles)g(\()p Ft(\022)1180 2448 y Fp(k)1223 2433 y Fv(\))1261 2462 y Fp(k)r Fn(\025)p Fr(0)1426 2433 y Fv(satisfying)h(the)f(recursion)h(relation)1263 2653 y Ft(\022)1308 2668 y Fp(k)r Fr(+1)1469 2653 y Fv(=)28 b Ft(g)t Fv(\()p Ft(p)1711 2668 y Fp(a)1748 2680 y Fi(k)1789 2653 y Ft(;)17 b(\022)1878 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y(b)s(elo)m(w)36 b(with)f(the)h(p)s(o)m(w)m(erful)g(theorems)g(of) e(Y.)h(Last)g(and)g(B.)g(Simon)h([LS])f(relating)g(the)g(nature)g(of) 111 4170 y(the)28 b(sp)s(ectrum)g(of)f Ft(J)36 b Fv(to)27 b(the)h(prop)s(erties)g(of)f(the)h(transfer)f(matrix)h Ft(T)i Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\):)41 b(the)27 b(essen)m(tial)i(supp)s(ort)111 4291 y(\006)181 4306 y Fp(ac)286 4291 y Fv(of)j(the)h(a.c.)44 b(part)32 b Ft(\026)1025 4306 y Fp(ac)1130 4291 y Fv(of)g(sp)s(ectral)h(measure)h Ft(\026)28 b Fv(=)f Ft(d\032)33 b Fv(\(2.1\))f(is)h(giv)m(en)h(b)m(y) 1043 4603 y(\006)1113 4618 y Fr(ac)1211 4603 y Fv(=)1315 4433 y Fs(\()1395 4603 y Ft(\025)28 b Fv(:)g(lim)17 b(inf)1568 4665 y Fp(N)7 b Fn(!1)1851 4536 y Fv(1)p 1831 4580 V 1831 4672 a Ft(N)1946 4479 y Fp(N)g Fn(\000)p Fr(1)1951 4509 y Fs(X)1957 4718 y Fp(n)p Fr(=0)2116 4603 y Fq(k)p Ft(T)30 b Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\))p Fq(k)2538 4555 y Fr(2)2605 4603 y Ft(<)28 b Fq(1)2809 4433 y Fs(\))3619 4603 y Fv(\(4.1\))258 4910 y(By)44 b(Theorems)i(1)p Ft(:)p Fv(6)e(and)g(1)p Ft(:)p Fv(7)g(of)g([LS])g(the) h(eigen)m(v)-5 b(alue)46 b(equation)f(\()p Ft(J)31 b Fq(\000)23 b Ft(\025I)8 b Fv(\))16 b Ft(u)47 b Fv(=)g(0)d(has)h(no)111 5031 y Ft(l)140 5046 y Fr(2)196 5031 y Fv(\()p Fo(N)9 b Fv(\))d({solutions)33 b(if)1549 5103 y Fn(1)1512 5133 y Fs(X)1517 5342 y Fp(n)p Fr(=0)1672 5227 y Fq(k)p Ft(T)d Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\))p Fq(k)2094 5179 y Fn(\000)p Fr(2)2216 5227 y Fv(=)28 b Fq(1)1199 b Fv(\(4.2\))1941 5587 y(9)p eop %%Page: 10 10 10 9 bop 111 312 a Fv(\(see)34 b(also)e(Theorem)i(2)p Ft(:)p Fv(1)f(in)f([SS)q(]\))g(and)h(an)g Ft(l)1773 327 y Fr(2)1829 312 y Fv(\()p Fo(N)9 b Fv(\))c({solution)33 b(if)928 588 y Ft(N)1006 603 y Fr(pp)1116 588 y Fq(\021)1258 464 y Fn(1)1221 494 y Fs(X)1227 703 y Fp(n)p Fr(=0)1382 588 y Fq(k)o Ft(T)e Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\))o Fq(k)1803 540 y Fr(2)1859 418 y Fs( )1975 464 y Fn(1)1938 494 y Fs(X)1942 706 y Fp(k)r Fr(=)p Fp(n)2099 588 y Fq(k)p Ft(T)30 b Fv(\()p Ft(k)s Fv(;)17 b Ft(\025)p Fv(\))o Fq(k)2516 540 y Fn(\000)p Fr(2)2611 418 y Fs(!)2689 440 y Fr(2)2757 588 y Ft(<)27 b Fq(1)17 b Ft(:)615 b Fv(\(4.3\))258 851 y(W)-8 b(e)32 b(sa)m(y)h(that)e(the)i(Pr)s(\177)-51 b(ufer)31 b(angles)i(\()p Ft(\022)1648 866 y Fp(k)1691 851 y Fv(\))1729 880 y Fp(k)r Fn(\025)p Fr(1)1893 851 y Fv(de\014ned)h(b)m(y)f(\(3.3\))e(ha)m(v)m(e)i(an)f(asymptotic)h (distribu-)111 972 y(tion)g(function)g(mo)s(dulo)f Ft(\031)37 b Fv(\(abbreviated)d(a.d.f.)43 b(mo)s(d)32 b Ft(\031)t Fv(\))h Ft(\027)6 b Fv(\()p Ft(x)p Fv(\))33 b(if,)g(for)f(an)m(y)h Ft(\022)e Fq(2)d Fv([0)p Ft(;)17 b(\031)t Fv(])993 1199 y(lim)959 1261 y Fp(N)7 b Fn(!1)1190 1132 y Fv(card)17 b(\()p Fq(f)o Ft(k)31 b Fv(:)d Ft(\022)1660 1147 y Fp(k)1731 1132 y Fq(2)g Fv([0)p Ft(;)17 b(\022)s Fv(\))p Ft(;)33 b Fv(1)27 b Fq(\024)h Ft(k)j Fq(\024)d Ft(N)10 b Fq(g)q Fv(\))p 1190 1176 1446 4 v 1868 1268 a Ft(N)2673 1199 y Fv(=)28 b Ft(\027)6 b Fv(\()p Ft(\022)s Fv(\))664 b(\(4.4\))111 1407 y(where)35 b(card)17 b(\()p Ft(S)6 b Fv(\))o(,)34 b(the)g(cardinalit)m(y)h(of)e(the)h(set)g Ft(S)6 b Fv(,)33 b(is)h(the)g(n)m(um)m(b)s(er)h(of)e(elemen)m(ts)j(in)d Ft(S)6 b Fv(.)46 b(Note)34 b(that)111 1527 y(the)44 b(function)h Ft(\027)53 b Fv(:)43 b([0)p Ft(;)17 b(\031)t Fv(])47 b Fq(!)f Fv([0)p Ft(;)17 b Fv(1])43 b(is)h(nondecreasing)h(righ)m(t)f (con)m(tin)m(uous)i(with)e Ft(\027)6 b Fv(\(0\))47 b(=)f(0)e(and)111 1647 y Ft(\027)6 b Fv(\()p Ft(\031)t Fv(\))28 b(=)g(1.)43 b(The)33 b(sequence)j(\()p Ft(\022)1239 1662 y Fp(k)1282 1647 y Fv(\))1320 1677 y Fp(k)r Fn(\025)p Fr(1)1485 1647 y Fv(need)e(not)e(ha)m(v)m(e)i(an)e(a.d.f)h(mo)s(d)f Ft(\031)37 b Fv(but)c(upp)s(er)874 1891 y(lim)17 b(sup)922 1972 y Fp(N)7 b Fn(!1)1200 1823 y Fv(card)17 b(\()p Fq(f)o Ft(k)31 b Fv(:)d Ft(\022)1670 1838 y Fp(k)1741 1823 y Fq(2)g Fv([0)p Ft(;)17 b(\022)s Fv(\))p Ft(;)33 b Fv(1)27 b Fq(\024)h Ft(k)j Fq(\024)d Ft(N)10 b Fq(g)q Fv(\))p 1200 1868 V 1878 1959 a Ft(N)2683 1891 y Fv(=)28 b(\010)2857 1906 y Fr(+)2916 1891 y Fv(\()p Ft(\022)s Fv(\))111 2112 y(and)33 b(lo)m(w)m(er)897 2262 y(lim)17 b(inf)930 2324 y Fp(N)7 b Fn(!1)1194 2195 y Fv(card)16 b(\()p Fq(f)p Ft(k)31 b Fv(:)d Ft(\022)1664 2210 y Fp(k)1735 2195 y Fq(2)g Fv([0)p Ft(;)17 b(\022)s Fv(\))p Ft(;)33 b Fv(1)27 b Fq(\024)h Ft(k)j Fq(\024)d Ft(N)10 b Fq(g)p Fv(\))p 1194 2239 V 1872 2331 a Ft(N)2677 2262 y Fv(=)28 b(\010)2851 2277 y Fn(\000)2910 2262 y Fv(\()p Ft(\022)s Fv(\))111 2451 y(distribution)44 b(functions,)i(with)d(0)i Fq(\024)g Fv(\010)1631 2466 y Fn(\000)1690 2451 y Fv(\()p Ft(\022)s Fv(\))g Fq(\024)g Fv(\010)2051 2466 y Fr(+)2111 2451 y Fv(\()p Ft(\022)s Fv(\))g Fq(\024)g Fv(1)d(for)g Ft(\022)48 b Fq(2)d Fv([0)p Ft(;)17 b(\031)t Fv(],)45 b(alw)m(a)m(ys)f(exist.)75 b(If)111 2571 y(\010)181 2586 y Fn(\000)293 2571 y Fq(\021)54 b Fv(\010)494 2586 y Fr(+)553 2571 y Fv(,)d(the)d(sequence)i(\()p Ft(\022)1316 2586 y Fp(k)1359 2571 y Fv(\))1397 2600 y Fp(k)r Fn(\025)p Fr(1)1577 2571 y Fv(has)e(an)f(a.d.f.)88 b(mo)s(d)47 b Ft(\031)t Fv(.)88 b(If)47 b(\010)2808 2586 y Fn(\000)2867 2571 y Fv(\()p Ft(\022)s Fv(\))53 b(=)g(\010)3243 2586 y Fr(+)3302 2571 y Fv(\()p Ft(\022)s Fv(\))g(=)g Ft(\022)d Fv(for)111 2692 y Ft(\022)g Fq(2)e Fv([0)p Ft(;)17 b(\031)t Fv(])o(,)47 b(the)d(sequence)j(\()p Ft(\022)1277 2707 y Fp(k)1320 2692 y Fv(\))1358 2721 y Fp(k)r Fn(\025)p Fr(1)1535 2692 y Fv(is)d(uniformly)h(distributed)g (mo)s(dulo)f Ft(\031)k Fv(\(abbreviated)d(u.d.)111 2812 y(mo)s(d)33 b Ft(\031)t Fv(\).)258 2932 y(F)-8 b(or)30 b(simplicit)m(y)-8 b(,)34 b(and)e(without)g(loss)g(of)f(generalit)m(y) -8 b(,)32 b(w)m(e)h(\014x)f(here)g(and)g(henceforth)g Ft(p)3412 2947 y Fp(a)3449 2959 y Fi(k)3519 2932 y Fv(=)c Ft(p)j Fv(for)111 3053 y(all)i Ft(k)s Fv(,)f(0)c Ft(<)f(p)h(<)g Fv(1,)k(and)h(tak)m(e)g Ft(A)28 b Fv(=)f(\()p Ft(a)1523 3068 y Fp(k)1566 3053 y Fv(\))1604 3082 y Fp(k)r Fn(\025)p Fr(1)1769 3053 y Fv(so)33 b(that)1648 3241 y Ft(a)1699 3256 y Fp(k)1764 3241 y Fq(\000)23 b Ft(a)1915 3256 y Fp(k)r Fn(\000)p Fr(1)2076 3241 y Fv(=)k Ft(\014)2240 3200 y Fp(k)3619 3241 y Fv(\(4.5\))111 3414 y(with)40 b Ft(a)391 3429 y Fr(0)470 3414 y Fv(=)f(0)g(i.)64 b(e.,)42 b Ft(a)981 3429 y Fp(k)1063 3414 y Fv(=)d Ft(a)1229 3429 y Fp(k)1272 3414 y Fv(\()p Ft(\014)6 b Fv(\))39 b(=)1563 3333 y Fs(\000)1609 3414 y Ft(\014)1670 3378 y Fp(k)r Fr(+1)1824 3414 y Fq(\000)23 b Ft(\014)1985 3333 y Fs(\001)2047 3414 y Ft(=)p Fv(\()p Ft(\014)32 b Fq(\000)27 b Fv(1\),)41 b Ft(\014)k(>)39 b Fv(1.)64 b(In)40 b(this)g(case)g(\(3.12\))f(and)111 3534 y(\(3.14\))32 b(read)1229 3766 y Ft(R)1304 3725 y Fr(2)1303 3791 y Fp(N)1398 3766 y Fv(=)1501 3596 y Fs( )1610 3699 y Fv(1)p 1590 3744 89 4 v 1590 3835 a Ft(p)1639 3806 y Fr(2)1705 3766 y Fv(exp)1871 3596 y Fs(\()1981 3699 y Fv(1)p 1961 3744 V 1961 3835 a Ft(N)2117 3642 y Fp(N)2076 3672 y Fs(X)2084 3884 y Fp(k)r Fr(=1)2237 3766 y Ft(f)27 b Fv(\()p Ft(\022)2395 3781 y Fp(k)2438 3766 y Fv(\))2476 3596 y Fs(\)!)2635 3613 y Fp(N)3619 3766 y Fv(\(4.6\))111 4005 y(with)1560 4126 y Ft(\022)1605 4141 y Fp(k)1676 4126 y Fv(=)g Ft(g)t Fv(\()p Ft(\022)1913 4141 y Fp(k)r Fn(\000)p Fr(1)2046 4126 y Fv(\))22 b(+)g Ft(\014)2265 4084 y Fp(k)2307 4126 y Ft(')1248 b Fv(\(4.7\))111 4280 y(where)34 b Ft(f)11 b Fv(\()p Ft(\022)s Fv(\))27 b(=)h Ft(f)11 b Fv(\()p Ft(p;)17 b(\022)s Fv(\))32 b(is)h(giv)m(en)h(b) m(y)f(\(3.13\),)f Ft(g)t Fv(\()p Ft(\022)s Fv(\))27 b(=)h Ft(g)t Fv(\()p Ft(p;)17 b(\022)s Fv(\))31 b(b)m(y)j(\(3.15\))d(and)i Ft(\022)3069 4295 y Fr(1)3142 4280 y Fv(b)m(y)g(\(3.10\).)258 4400 y(Let)26 b(us)h(assume)g(that)f(the)h(sequence)i(\()p Ft(\022)1723 4415 y Fp(k)1766 4400 y Fv(\))1804 4429 y Fp(k)r Fn(\025)p Fr(1)1963 4400 y Fv(giv)m(en)e(b)m(y)g(\(4.7\))f (has)g(the)h(con)m(tin)m(uous)h(a.d.f.)41 b(mo)s(d)111 4520 y Ft(\031)t Fv(,)33 b Ft(\027)6 b Fv(\()p Ft(\022)s Fv(\).)44 b(W)-8 b(e)33 b(ha)m(v)m(e)h(\(see)f(Theorem)h(7)p Ft(:)p Fv(2,)e(Chap.)44 b(1)33 b(of)f([KN]\):)111 4695 y Fl(Theorem)37 b(4.1)49 b Fk(A)39 b(se)-5 b(quenc)g(e)38 b Ft(!)g Fv(=)c(\()p Ft(\022)1581 4710 y Fp(k)1624 4695 y Fv(\))1662 4724 y Fp(k)r Fn(\025)p Fr(1)1834 4695 y Fk(of)k(r)-5 b(e)g(al)38 b(numb)-5 b(ers)38 b(has)g(the)h(c)-5 b(ontinuous)38 b(a.d.f.)56 b(mo)-5 b(d)111 4815 y Ft(\031)t Fk(,)35 b Ft(\027)6 b Fv(\()p Ft(\022)s Fv(\))p Fk(,)35 b(if)g(and)f(only)h(if)1196 5081 y Fv(lim)1162 5143 y Fp(N)7 b Fn(!1)1412 5013 y Fv(1)p 1392 5058 V 1392 5149 a Ft(N)1548 4956 y Fp(N)1507 4986 y Fs(X)1515 5198 y Fp(k)r Fr(=1)1668 5081 y Ft(f)27 b Fv(\()p Ft(\022)1826 5096 y Fp(k)1869 5081 y Fv(\))h(=)2054 5013 y(1)p 2048 5058 59 4 v 2048 5149 a Ft(\031)2134 4945 y Fs(Z)2234 4971 y Fp(\031)2189 5171 y Fr(0)2297 5081 y Ft(f)11 b Fv(\()p Ft(\022)s Fv(\))17 b Ft(d\027)6 b Fv(\()p Ft(\022)s Fv(\))17 b Ft(;)849 b Fv(\(4.8\))146 5338 y Fk(holds)34 b(for)h(every)g(c)-5 b(ontinuous)34 b(p)-5 b(erio)g(dic)34 b(function)h Ft(f)45 b Fk(of)35 b(p)-5 b(erio)g(d)34 b Ft(\031)t Fk(.)1917 5587 y Fv(10)p eop %%Page: 11 11 11 10 bop 258 312 a Fv(The)33 b(other)g(ingredien)m(t)h(is)f(the)g 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Fk(may)g(take)111 1344 y(any)e(value.)52 b(Then)37 b Ft(\033)t Fv(\()p Ft(J)1007 1359 y Fp(\013)1056 1344 y Fv(\))g Fk(has)g(only)g(dense)g (p.p.)51 b(sp)-5 b(e)g(ctrum)38 b(in)f Fv([)p Ft(a;)17 b(b)p Fv(])38 b Fk(for)f(a.e.)51 b(\(w.r.t.)h(L)-5 b(eb)g(esgue)111 1464 y(me)g(asur)g(e\))34 b Ft(\013)q Fk({b)-5 b(oundary)35 b(c)-5 b(ondition)33 b(\(1.10\).)111 1678 y(Pr)-5 b(o)g(of.)72 b Fv(T)-8 b(ak)m(e)44 b Ft(\025)g Fq(2)g Fv([)p Ft(a;)17 b(b)p Fv(])h Fq(n)p Ft(A)p Fv(.)72 b(By)43 b(\(4.10\),)h(\(1.9\))e (has,)j(for)d(this)g Ft(\025)p Fv(,)j(a)d Ft(l)2874 1693 y Fr(2)2914 1678 y Fv({solutions)h(on)f(\(0)p Ft(;)17 b Fq(1)p Fv(\))o(.)111 1798 y(Th)m(us,)33 b(b)m(y)e(Theorem)h Ft(I)8 b(I)g(:)p Fv(3)30 b(of)g([S2],)h(either)h Fl(1)p Ft(:)e(\025)h Fv(is)g(an)f(eigen)m(v)-5 b(alue)32 b(of)e Ft(J)40 b Fv(with)31 b(Neumann)h(b.)43 b(c.)g(\(i.)111 1967 y(e.,)33 b(corresp)s(onding)h(to)e Ft(u)1043 1982 y Fn(\000)p Fr(1)1164 1967 y Fv(=)c(0)k(in)h(\(1.10\),)f(or)g Ft(\013)d Fv(=)e(0\),)32 b(or)h Fl(2)p Ft(:)f(G)p Fv(\()p Ft(\025)p Fv(\))c(=)2807 1831 y Fs(Z)2923 1967 y Ft(d\032)p Fv(\()p Ft(y)t Fv(\))p Ft(=)17 b Fv(\()o Ft(\025)22 b Fq(\000)g Ft(y)t Fv(\))3522 1918 y Fr(2)3590 1967 y Ft(<)27 b Fq(1)p Fv(,)111 2136 y(where)45 b Ft(\032)f Fv(is)g(the)g(sp)s (ectral)g(measure)h(\(2.1\).)75 b(The)45 b(\014rst)f(alternativ)m(e)g Fl(1)p Ft(:)g Fv(can)g(hold)f(at)g(most)h(for)111 2256 y Ft(\025)g Fv(b)s(elonging)g(to)g(a)g(coun)m(table)h(set;)50 b(but,)d(b)m(y)e(h)m(yp)s(othesis,)k(\(4.10\))44 b(holds)g(in)g(a)g (set)h(of)e(p)s(ositiv)m(e)111 2376 y(Leb)s(esgue)32 b(measure,)g(i.)43 b(e.,)31 b(the)g(complemen)m(t)i(of)d(a)g(set)h(of)f (zero)h(Leb)s(esgue)h(measure.)44 b(Th)m(us,)32 b(ev)m(en)111 2497 y(excluding)k(the)f(coun)m(table)g(set)g(satisfying)g(the)f (\014rst)h(alternativ)m(e,)h(w)m(e)f(are)f(led)h(to)f(the)g(statemen)m (t)111 2617 y(that)j Ft(G)p Fv(\()p Ft(\025)p Fv(\))d Ft(<)g Fq(1)j Fv(for)f(a.)55 b(e.)h Ft(\025)36 b Fv(in)h([)p Ft(a;)17 b(b)p Fv(])q(,)38 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def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { 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.10317 .59833 L .10317 .01472 L .09524 .01472 L s 1 0 0 r .10317 .01472 m .10317 .59959 L .11111 .59959 L .11111 .01472 L F 0 g .10317 .01472 m .10317 .59959 L .11111 .59959 L .11111 .01472 L .10317 .01472 L s 1 0 0 r .11111 .01472 m .11111 .598 L .11905 .598 L .11905 .01472 L F 0 g .11111 .01472 m .11111 .598 L .11905 .598 L .11905 .01472 L .11111 .01472 L s 1 0 0 r .11905 .01472 m .11905 .59745 L .12698 .59745 L .12698 .01472 L F 0 g .11905 .01472 m .11905 .59745 L .12698 .59745 L .12698 .01472 L .11905 .01472 L s 1 0 0 r .12698 .01472 m .12698 .59614 L .13492 .59614 L .13492 .01472 L F 0 g .12698 .01472 m .12698 .59614 L .13492 .59614 L .13492 .01472 L .12698 .01472 L s 1 0 0 r .13492 .01472 m .13492 .599 L .14286 .599 L .14286 .01472 L F 0 g .13492 .01472 m .13492 .599 L .14286 .599 L .14286 .01472 L .13492 .01472 L s 1 0 0 r .14286 .01472 m .14286 .59502 L .15079 .59502 L .15079 .01472 L F 0 g .14286 .01472 m .14286 .59502 L .15079 .59502 L .15079 .01472 L .14286 .01472 L s 1 0 0 r .15079 .01472 m .15079 .59826 L .15873 .59826 L .15873 .01472 L F 0 g .15079 .01472 m .15079 .59826 L .15873 .59826 L .15873 .01472 L .15079 .01472 L s 1 0 0 r .15873 .01472 m .15873 .59737 L .16667 .59737 L .16667 .01472 L F 0 g .15873 .01472 m .15873 .59737 L .16667 .59737 L .16667 .01472 L .15873 .01472 L s 1 0 0 r .16667 .01472 m .16667 .59786 L .1746 .59786 L .1746 .01472 L F 0 g .16667 .01472 m .16667 .59786 L .1746 .59786 L .1746 .01472 L .16667 .01472 L s 1 0 0 r .1746 .01472 m .1746 .59424 L .18254 .59424 L .18254 .01472 L F 0 g .1746 .01472 m .1746 .59424 L .18254 .59424 L .18254 .01472 L .1746 .01472 L s 1 0 0 r .18254 .01472 m .18254 .60045 L .19048 .60045 L .19048 .01472 L F 0 g .18254 .01472 m .18254 .60045 L .19048 .60045 L .19048 .01472 L .18254 .01472 L s 1 0 0 r .19048 .01472 m .19048 .59931 L .19841 .59931 L .19841 .01472 L F 0 g .19048 .01472 m .19048 .59931 L .19841 .59931 L .19841 .01472 L .19048 .01472 L s 1 0 0 r .19841 .01472 m .19841 .60067 L .20635 .60067 L .20635 .01472 L F 0 g .19841 .01472 m .19841 .60067 L .20635 .60067 L .20635 .01472 L .19841 .01472 L s 1 0 0 r .20635 .01472 m .20635 .59848 L .21429 .59848 L .21429 .01472 L F 0 g .20635 .01472 m .20635 .59848 L .21429 .59848 L .21429 .01472 L .20635 .01472 L s 1 0 0 r .21429 .01472 m .21429 .59657 L .22222 .59657 L .22222 .01472 L F 0 g .21429 .01472 m .21429 .59657 L .22222 .59657 L .22222 .01472 L .21429 .01472 L s 1 0 0 r .22222 .01472 m .22222 .59646 L .23016 .59646 L .23016 .01472 L F 0 g .22222 .01472 m .22222 .59646 L .23016 .59646 L .23016 .01472 L .22222 .01472 L s 1 0 0 r .23016 .01472 m .23016 .59484 L .2381 .59484 L .2381 .01472 L F 0 g .23016 .01472 m .23016 .59484 L .2381 .59484 L .2381 .01472 L .23016 .01472 L s 1 0 0 r .2381 .01472 m .2381 .59833 L .24603 .59833 L .24603 .01472 L F 0 g .2381 .01472 m .2381 .59833 L .24603 .59833 L .24603 .01472 L .2381 .01472 L s 1 0 0 r .24603 .01472 m .24603 .59902 L .25397 .59902 L .25397 .01472 L F 0 g .24603 .01472 m .24603 .59902 L .25397 .59902 L .25397 .01472 L .24603 .01472 L s 1 0 0 r .25397 .01472 m .25397 .60176 L .2619 .60176 L .2619 .01472 L F 0 g .25397 .01472 m .25397 .60176 L .2619 .60176 L .2619 .01472 L .25397 .01472 L s 1 0 0 r .2619 .01472 m .2619 .59898 L .26984 .59898 L .26984 .01472 L F 0 g .2619 .01472 m .2619 .59898 L .26984 .59898 L .26984 .01472 L .2619 .01472 L s 1 0 0 r .26984 .01472 m .26984 .6 L .27778 .6 L .27778 .01472 L F 0 g .26984 .01472 m .26984 .6 L .27778 .6 L .27778 .01472 L .26984 .01472 L s 1 0 0 r .27778 .01472 m .27778 .60009 L .28571 .60009 L .28571 .01472 L F 0 g .27778 .01472 m .27778 .60009 L .28571 .60009 L .28571 .01472 L .27778 .01472 L s 1 0 0 r .28571 .01472 m .28571 .5958 L .29365 .5958 L .29365 .01472 L F 0 g .28571 .01472 m .28571 .5958 L .29365 .5958 L .29365 .01472 L .28571 .01472 L s 1 0 0 r .29365 .01472 m .29365 .59888 L .30159 .59888 L .30159 .01472 L F 0 g .29365 .01472 m .29365 .59888 L .30159 .59888 L .30159 .01472 L .29365 .01472 L s 1 0 0 r .30159 .01472 m .30159 .59834 L .30952 .59834 L .30952 .01472 L F 0 g .30159 .01472 m .30159 .59834 L .30952 .59834 L .30952 .01472 L .30159 .01472 L s 1 0 0 r .30952 .01472 m .30952 .59927 L .31746 .59927 L .31746 .01472 L F 0 g .30952 .01472 m .30952 .59927 L .31746 .59927 L .31746 .01472 L .30952 .01472 L s 1 0 0 r .31746 .01472 m .31746 .59461 L .3254 .59461 L .3254 .01472 L F 0 g .31746 .01472 m .31746 .59461 L .3254 .59461 L .3254 .01472 L .31746 .01472 L s 1 0 0 r .3254 .01472 m .3254 .59598 L .33333 .59598 L .33333 .01472 L F 0 g .3254 .01472 m .3254 .59598 L .33333 .59598 L .33333 .01472 L .3254 .01472 L s 1 0 0 r .33333 .01472 m .33333 .59767 L .34127 .59767 L .34127 .01472 L F 0 g .33333 .01472 m .33333 .59767 L .34127 .59767 L .34127 .01472 L .33333 .01472 L s 1 0 0 r .34127 .01472 m .34127 .59837 L .34921 .59837 L .34921 .01472 L F 0 g .34127 .01472 m .34127 .59837 L .34921 .59837 L .34921 .01472 L .34127 .01472 L s 1 0 0 r .34921 .01472 m .34921 .60288 L .35714 .60288 L .35714 .01472 L F 0 g .34921 .01472 m .34921 .60288 L .35714 .60288 L .35714 .01472 L .34921 .01472 L s 1 0 0 r .35714 .01472 m .35714 .59852 L .36508 .59852 L .36508 .01472 L F 0 g .35714 .01472 m .35714 .59852 L .36508 .59852 L .36508 .01472 L .35714 .01472 L s 1 0 0 r .36508 .01472 m .36508 .59719 L .37302 .59719 L .37302 .01472 L F 0 g .36508 .01472 m .36508 .59719 L .37302 .59719 L .37302 .01472 L .36508 .01472 L s 1 0 0 r .37302 .01472 m .37302 .59934 L .38095 .59934 L .38095 .01472 L F 0 g .37302 .01472 m .37302 .59934 L .38095 .59934 L .38095 .01472 L .37302 .01472 L s 1 0 0 r .38095 .01472 m .38095 .59951 L .38889 .59951 L .38889 .01472 L F 0 g .38095 .01472 m .38095 .59951 L .38889 .59951 L .38889 .01472 L .38095 .01472 L s 1 0 0 r .38889 .01472 m .38889 .59912 L .39683 .59912 L .39683 .01472 L F 0 g .38889 .01472 m .38889 .59912 L .39683 .59912 L .39683 .01472 L .38889 .01472 L s 1 0 0 r .39683 .01472 m .39683 .59803 L .40476 .59803 L .40476 .01472 L F 0 g .39683 .01472 m .39683 .59803 L .40476 .59803 L .40476 .01472 L .39683 .01472 L s 1 0 0 r .40476 .01472 m .40476 .59637 L .4127 .59637 L .4127 .01472 L F 0 g .40476 .01472 m .40476 .59637 L .4127 .59637 L .4127 .01472 L .40476 .01472 L s 1 0 0 r .4127 .01472 m .4127 .59481 L .42063 .59481 L .42063 .01472 L F 0 g .4127 .01472 m .4127 .59481 L .42063 .59481 L .42063 .01472 L .4127 .01472 L s 1 0 0 r .42063 .01472 m .42063 .59994 L .42857 .59994 L .42857 .01472 L F 0 g .42063 .01472 m .42063 .59994 L .42857 .59994 L .42857 .01472 L .42063 .01472 L s 1 0 0 r .42857 .01472 m .42857 .59729 L .43651 .59729 L .43651 .01472 L F 0 g .42857 .01472 m .42857 .59729 L .43651 .59729 L .43651 .01472 L .42857 .01472 L s 1 0 0 r .43651 .01472 m .43651 .5975 L .44444 .5975 L .44444 .01472 L F 0 g .43651 .01472 m .43651 .5975 L .44444 .5975 L .44444 .01472 L .43651 .01472 L s 1 0 0 r .44444 .01472 m .44444 .60031 L .45238 .60031 L .45238 .01472 L F 0 g .44444 .01472 m .44444 .60031 L .45238 .60031 L .45238 .01472 L .44444 .01472 L s 1 0 0 r .45238 .01472 m .45238 .59381 L .46032 .59381 L .46032 .01472 L F 0 g .45238 .01472 m .45238 .59381 L .46032 .59381 L .46032 .01472 L .45238 .01472 L s 1 0 0 r .46032 .01472 m .46032 .59902 L .46825 .59902 L .46825 .01472 L F 0 g .46032 .01472 m .46032 .59902 L .46825 .59902 L .46825 .01472 L .46032 .01472 L s 1 0 0 r .46825 .01472 m .46825 .59767 L .47619 .59767 L .47619 .01472 L F 0 g .46825 .01472 m .46825 .59767 L .47619 .59767 L .47619 .01472 L .46825 .01472 L s 1 0 0 r .47619 .01472 m .47619 .5956 L .48413 .5956 L .48413 .01472 L F 0 g .47619 .01472 m .47619 .5956 L .48413 .5956 L .48413 .01472 L .47619 .01472 L s 1 0 0 r .48413 .01472 m .48413 .5987 L .49206 .5987 L .49206 .01472 L F 0 g .48413 .01472 m .48413 .5987 L .49206 .5987 L .49206 .01472 L .48413 .01472 L s 1 0 0 r .49206 .01472 m .49206 .59607 L .5 .59607 L .5 .01472 L F 0 g .49206 .01472 m .49206 .59607 L .5 .59607 L .5 .01472 L .49206 .01472 L s 1 0 0 r .5 .01472 m .5 .59943 L .50794 .59943 L .50794 .01472 L F 0 g .5 .01472 m .5 .59943 L .50794 .59943 L .50794 .01472 L .5 .01472 L s 1 0 0 r .50794 .01472 m .50794 .60002 L .51587 .60002 L .51587 .01472 L F 0 g .50794 .01472 m .50794 .60002 L .51587 .60002 L .51587 .01472 L .50794 .01472 L s 1 0 0 r .51587 .01472 m .51587 .59867 L .52381 .59867 L .52381 .01472 L F 0 g .51587 .01472 m .51587 .59867 L .52381 .59867 L .52381 .01472 L .51587 .01472 L s 1 0 0 r .52381 .01472 m .52381 .60025 L .53175 .60025 L .53175 .01472 L F 0 g .52381 .01472 m .52381 .60025 L .53175 .60025 L .53175 .01472 L .52381 .01472 L s 1 0 0 r .53175 .01472 m .53175 .59935 L .53968 .59935 L .53968 .01472 L F 0 g .53175 .01472 m .53175 .59935 L .53968 .59935 L .53968 .01472 L .53175 .01472 L s 1 0 0 r .53968 .01472 m .53968 .5985 L .54762 .5985 L .54762 .01472 L F 0 g .53968 .01472 m .53968 .5985 L .54762 .5985 L .54762 .01472 L .53968 .01472 L s 1 0 0 r .54762 .01472 m .54762 .59932 L .55556 .59932 L .55556 .01472 L F 0 g .54762 .01472 m .54762 .59932 L .55556 .59932 L .55556 .01472 L .54762 .01472 L s 1 0 0 r .55556 .01472 m .55556 .60185 L .56349 .60185 L .56349 .01472 L F 0 g .55556 .01472 m .55556 .60185 L .56349 .60185 L .56349 .01472 L .55556 .01472 L s 1 0 0 r .56349 .01472 m .56349 .59797 L .57143 .59797 L .57143 .01472 L F 0 g .56349 .01472 m .56349 .59797 L .57143 .59797 L .57143 .01472 L .56349 .01472 L s 1 0 0 r .57143 .01472 m .57143 .59879 L .57937 .59879 L .57937 .01472 L F 0 g .57143 .01472 m .57143 .59879 L .57937 .59879 L .57937 .01472 L .57143 .01472 L s 1 0 0 r .57937 .01472 m .57937 .60138 L .5873 .60138 L .5873 .01472 L F 0 g .57937 .01472 m .57937 .60138 L .5873 .60138 L .5873 .01472 L .57937 .01472 L s 1 0 0 r .5873 .01472 m .5873 .5961 L .59524 .5961 L .59524 .01472 L F 0 g .5873 .01472 m .5873 .5961 L .59524 .5961 L .59524 .01472 L .5873 .01472 L s 1 0 0 r .59524 .01472 m .59524 .5989 L .60317 .5989 L .60317 .01472 L F 0 g .59524 .01472 m .59524 .5989 L .60317 .5989 L .60317 .01472 L .59524 .01472 L s 1 0 0 r .60317 .01472 m .60317 .60236 L .61111 .60236 L .61111 .01472 L F 0 g .60317 .01472 m .60317 .60236 L .61111 .60236 L .61111 .01472 L .60317 .01472 L s 1 0 0 r .61111 .01472 m .61111 .59843 L .61905 .59843 L .61905 .01472 L F 0 g .61111 .01472 m .61111 .59843 L .61905 .59843 L .61905 .01472 L .61111 .01472 L s 1 0 0 r .61905 .01472 m .61905 .60135 L .62698 .60135 L .62698 .01472 L F 0 g .61905 .01472 m .61905 .60135 L .62698 .60135 L .62698 .01472 L .61905 .01472 L s 1 0 0 r .62698 .01472 m .62698 .59673 L .63492 .59673 L .63492 .01472 L F 0 g .62698 .01472 m .62698 .59673 L .63492 .59673 L .63492 .01472 L .62698 .01472 L s 1 0 0 r .63492 .01472 m .63492 .59871 L .64286 .59871 L .64286 .01472 L F 0 g .63492 .01472 m .63492 .59871 L .64286 .59871 L .64286 .01472 L .63492 .01472 L s 1 0 0 r .64286 .01472 m .64286 .59713 L .65079 .59713 L .65079 .01472 L F 0 g .64286 .01472 m .64286 .59713 L .65079 .59713 L .65079 .01472 L .64286 .01472 L s 1 0 0 r .65079 .01472 m .65079 .59777 L .65873 .59777 L .65873 .01472 L F 0 g .65079 .01472 m .65079 .59777 L .65873 .59777 L .65873 .01472 L .65079 .01472 L s 1 0 0 r .65873 .01472 m .65873 .59763 L .66667 .59763 L .66667 .01472 L F 0 g .65873 .01472 m .65873 .59763 L .66667 .59763 L .66667 .01472 L .65873 .01472 L s 1 0 0 r .66667 .01472 m .66667 .60025 L .6746 .60025 L .6746 .01472 L F 0 g .66667 .01472 m .66667 .60025 L .6746 .60025 L .6746 .01472 L .66667 .01472 L s 1 0 0 r .6746 .01472 m .6746 .59567 L .68254 .59567 L .68254 .01472 L F 0 g .6746 .01472 m .6746 .59567 L .68254 .59567 L .68254 .01472 L .6746 .01472 L s 1 0 0 r .68254 .01472 m .68254 .59651 L .69048 .59651 L .69048 .01472 L F 0 g .68254 .01472 m .68254 .59651 L .69048 .59651 L .69048 .01472 L .68254 .01472 L s 1 0 0 r .69048 .01472 m .69048 .601 L .69841 .601 L .69841 .01472 L F 0 g .69048 .01472 m .69048 .601 L .69841 .601 L .69841 .01472 L .69048 .01472 L s 1 0 0 r .69841 .01472 m .69841 .5956 L .70635 .5956 L .70635 .01472 L F 0 g .69841 .01472 m .69841 .5956 L .70635 .5956 L .70635 .01472 L .69841 .01472 L s 1 0 0 r .70635 .01472 m .70635 .6007 L .71429 .6007 L .71429 .01472 L F 0 g .70635 .01472 m .70635 .6007 L .71429 .6007 L .71429 .01472 L .70635 .01472 L s 1 0 0 r .71429 .01472 m .71429 .60332 L .72222 .60332 L .72222 .01472 L F 0 g .71429 .01472 m .71429 .60332 L .72222 .60332 L .72222 .01472 L .71429 .01472 L s 1 0 0 r .72222 .01472 m .72222 .59901 L .73016 .59901 L .73016 .01472 L F 0 g .72222 .01472 m .72222 .59901 L .73016 .59901 L .73016 .01472 L .72222 .01472 L s 1 0 0 r .73016 .01472 m .73016 .59878 L .7381 .59878 L .7381 .01472 L F 0 g .73016 .01472 m .73016 .59878 L .7381 .59878 L .7381 .01472 L .73016 .01472 L s 1 0 0 r .7381 .01472 m .7381 .59547 L .74603 .59547 L .74603 .01472 L F 0 g .7381 .01472 m .7381 .59547 L .74603 .59547 L .74603 .01472 L .7381 .01472 L s 1 0 0 r .74603 .01472 m .74603 .59839 L .75397 .59839 L .75397 .01472 L F 0 g .74603 .01472 m .74603 .59839 L .75397 .59839 L .75397 .01472 L .74603 .01472 L s 1 0 0 r .75397 .01472 m .75397 .59762 L .7619 .59762 L .7619 .01472 L F 0 g .75397 .01472 m .75397 .59762 L .7619 .59762 L .7619 .01472 L .75397 .01472 L s 1 0 0 r .7619 .01472 m .7619 .59882 L .76984 .59882 L .76984 .01472 L F 0 g .7619 .01472 m .7619 .59882 L .76984 .59882 L .76984 .01472 L .7619 .01472 L s 1 0 0 r .76984 .01472 m .76984 .59972 L .77778 .59972 L .77778 .01472 L F 0 g .76984 .01472 m .76984 .59972 L .77778 .59972 L .77778 .01472 L .76984 .01472 L s 1 0 0 r .77778 .01472 m .77778 .59556 L .78571 .59556 L .78571 .01472 L F 0 g .77778 .01472 m .77778 .59556 L .78571 .59556 L .78571 .01472 L .77778 .01472 L s 1 0 0 r .78571 .01472 m .78571 .59802 L .79365 .59802 L .79365 .01472 L F 0 g .78571 .01472 m .78571 .59802 L .79365 .59802 L .79365 .01472 L .78571 .01472 L s 1 0 0 r .79365 .01472 m .79365 .59687 L .80159 .59687 L .80159 .01472 L F 0 g .79365 .01472 m .79365 .59687 L .80159 .59687 L .80159 .01472 L .79365 .01472 L s 1 0 0 r .80159 .01472 m .80159 .59803 L .80952 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sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll 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dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) 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.08147 L .10317 .01472 L .09524 .01472 L s 1 0 0 r .10317 .01472 m .10317 .08155 L .11111 .08155 L .11111 .01472 L F 0 g .10317 .01472 m .10317 .08155 L .11111 .08155 L .11111 .01472 L .10317 .01472 L s 1 0 0 r .11111 .01472 m .11111 .08138 L .11905 .08138 L .11905 .01472 L F 0 g .11111 .01472 m .11111 .08138 L .11905 .08138 L .11905 .01472 L .11111 .01472 L s 1 0 0 r .11905 .01472 m .11905 .08177 L .12698 .08177 L .12698 .01472 L F 0 g .11905 .01472 m .11905 .08177 L .12698 .08177 L .12698 .01472 L .11905 .01472 L s 1 0 0 r .12698 .01472 m .12698 .08205 L .13492 .08205 L .13492 .01472 L F 0 g .12698 .01472 m .12698 .08205 L .13492 .08205 L .13492 .01472 L .12698 .01472 L s 1 0 0 r .13492 .01472 m .13492 .08226 L .14286 .08226 L .14286 .01472 L F 0 g .13492 .01472 m .13492 .08226 L .14286 .08226 L .14286 .01472 L .13492 .01472 L s 1 0 0 r .14286 .01472 m .14286 .08172 L .15079 .08172 L .15079 .01472 L F 0 g .14286 .01472 m .14286 .08172 L .15079 .08172 L .15079 .01472 L .14286 .01472 L s 1 0 0 r .15079 .01472 m .15079 .08182 L .15873 .08182 L .15873 .01472 L F 0 g .15079 .01472 m .15079 .08182 L .15873 .08182 L .15873 .01472 L .15079 .01472 L s 1 0 0 r .15873 .01472 m .15873 .08282 L .16667 .08282 L .16667 .01472 L F 0 g .15873 .01472 m .15873 .08282 L .16667 .08282 L .16667 .01472 L .15873 .01472 L s 1 0 0 r .16667 .01472 m .16667 .08278 L .1746 .08278 L .1746 .01472 L F 0 g .16667 .01472 m .16667 .08278 L .1746 .08278 L .1746 .01472 L .16667 .01472 L s 1 0 0 r .1746 .01472 m .1746 .08305 L .18254 .08305 L .18254 .01472 L F 0 g .1746 .01472 m .1746 .08305 L .18254 .08305 L .18254 .01472 L .1746 .01472 L s 1 0 0 r .18254 .01472 m .18254 .08382 L .19048 .08382 L .19048 .01472 L F 0 g .18254 .01472 m .18254 .08382 L .19048 .08382 L .19048 .01472 L .18254 .01472 L s 1 0 0 r .19048 .01472 m .19048 .08407 L .19841 .08407 L .19841 .01472 L F 0 g .19048 .01472 m .19048 .08407 L .19841 .08407 L .19841 .01472 L .19048 .01472 L s 1 0 0 r .19841 .01472 m .19841 .08377 L .20635 .08377 L .20635 .01472 L F 0 g .19841 .01472 m .19841 .08377 L .20635 .08377 L .20635 .01472 L .19841 .01472 L s 1 0 0 r .20635 .01472 m .20635 .08402 L .21429 .08402 L .21429 .01472 L F 0 g .20635 .01472 m .20635 .08402 L .21429 .08402 L .21429 .01472 L .20635 .01472 L s 1 0 0 r .21429 .01472 m .21429 .08476 L .22222 .08476 L .22222 .01472 L F 0 g .21429 .01472 m .21429 .08476 L .22222 .08476 L .22222 .01472 L .21429 .01472 L s 1 0 0 r .22222 .01472 m .22222 .08451 L .23016 .08451 L .23016 .01472 L F 0 g .22222 .01472 m .22222 .08451 L .23016 .08451 L .23016 .01472 L .22222 .01472 L s 1 0 0 r .23016 .01472 m .23016 .08582 L .2381 .08582 L .2381 .01472 L F 0 g .23016 .01472 m .23016 .08582 L .2381 .08582 L .2381 .01472 L .23016 .01472 L s 1 0 0 r .2381 .01472 m .2381 .0866 L .24603 .0866 L .24603 .01472 L F 0 g .2381 .01472 m .2381 .0866 L .24603 .0866 L .24603 .01472 L .2381 .01472 L s 1 0 0 r .24603 .01472 m .24603 .08618 L .25397 .08618 L .25397 .01472 L F 0 g .24603 .01472 m .24603 .08618 L .25397 .08618 L .25397 .01472 L .24603 .01472 L s 1 0 0 r .25397 .01472 m .25397 .0863 L .2619 .0863 L .2619 .01472 L F 0 g .25397 .01472 m .25397 .0863 L .2619 .0863 L .2619 .01472 L .25397 .01472 L s 1 0 0 r .2619 .01472 m .2619 .08631 L .26984 .08631 L .26984 .01472 L F 0 g .2619 .01472 m .2619 .08631 L .26984 .08631 L .26984 .01472 L .2619 .01472 L s 1 0 0 r .26984 .01472 m .26984 .08693 L .27778 .08693 L .27778 .01472 L F 0 g .26984 .01472 m .26984 .08693 L .27778 .08693 L .27778 .01472 L .26984 .01472 L s 1 0 0 r .27778 .01472 m .27778 .0865 L .28571 .0865 L .28571 .01472 L F 0 g .27778 .01472 m .27778 .0865 L .28571 .0865 L .28571 .01472 L .27778 .01472 L s 1 0 0 r .28571 .01472 m .28571 .09038 L .29365 .09038 L .29365 .01472 L F 0 g .28571 .01472 m .28571 .09038 L .29365 .09038 L .29365 .01472 L .28571 .01472 L s 1 0 0 r .29365 .01472 m .29365 .09045 L .30159 .09045 L .30159 .01472 L F 0 g .29365 .01472 m .29365 .09045 L .30159 .09045 L .30159 .01472 L .29365 .01472 L s 1 0 0 r .30159 .01472 m .30159 .09005 L .30952 .09005 L .30952 .01472 L F 0 g .30159 .01472 m .30159 .09005 L .30952 .09005 L .30952 .01472 L .30159 .01472 L s 1 0 0 r .30952 .01472 m .30952 .08989 L .31746 .08989 L .31746 .01472 L F 0 g .30952 .01472 m .30952 .08989 L .31746 .08989 L .31746 .01472 L .30952 .01472 L s 1 0 0 r .31746 .01472 m .31746 .09008 L .3254 .09008 L .3254 .01472 L F 0 g .31746 .01472 m .31746 .09008 L .3254 .09008 L .3254 .01472 L .31746 .01472 L s 1 0 0 r .3254 .01472 m .3254 .09001 L .33333 .09001 L .33333 .01472 L F 0 g .3254 .01472 m .3254 .09001 L .33333 .09001 L .33333 .01472 L .3254 .01472 L s 1 0 0 r .33333 .01472 m .33333 .09078 L .34127 .09078 L .34127 .01472 L F 0 g .33333 .01472 m .33333 .09078 L .34127 .09078 L .34127 .01472 L .33333 .01472 L s 1 0 0 r .34127 .01472 m .34127 .09267 L .34921 .09267 L .34921 .01472 L F 0 g .34127 .01472 m .34127 .09267 L .34921 .09267 L .34921 .01472 L .34127 .01472 L s 1 0 0 r .34921 .01472 m .34921 .10017 L .35714 .10017 L .35714 .01472 L F 0 g .34921 .01472 m .34921 .10017 L .35714 .10017 L .35714 .01472 L .34921 .01472 L s 1 0 0 r .35714 .01472 m .35714 .09748 L .36508 .09748 L .36508 .01472 L F 0 g .35714 .01472 m .35714 .09748 L .36508 .09748 L .36508 .01472 L .35714 .01472 L s 1 0 0 r .36508 .01472 m .36508 .09702 L .37302 .09702 L .37302 .01472 L F 0 g .36508 .01472 m .36508 .09702 L .37302 .09702 L .37302 .01472 L .36508 .01472 L s 1 0 0 r .37302 .01472 m .37302 .09683 L .38095 .09683 L .38095 .01472 L F 0 g .37302 .01472 m .37302 .09683 L .38095 .09683 L .38095 .01472 L .37302 .01472 L s 1 0 0 r .38095 .01472 m .38095 .09784 L .38889 .09784 L .38889 .01472 L F 0 g .38095 .01472 m .38095 .09784 L .38889 .09784 L .38889 .01472 L .38095 .01472 L s 1 0 0 r .38889 .01472 m .38889 .09914 L .39683 .09914 L .39683 .01472 L F 0 g .38889 .01472 m .38889 .09914 L .39683 .09914 L .39683 .01472 L .38889 .01472 L s 1 0 0 r .39683 .01472 m .39683 .10037 L .40476 .10037 L .40476 .01472 L F 0 g .39683 .01472 m .39683 .10037 L .40476 .10037 L .40476 .01472 L .39683 .01472 L s 1 0 0 r .40476 .01472 m .40476 .10801 L .4127 .10801 L .4127 .01472 L F 0 g .40476 .01472 m .40476 .10801 L .4127 .10801 L .4127 .01472 L .40476 .01472 L s 1 0 0 r .4127 .01472 m .4127 .1158 L .42063 .1158 L .42063 .01472 L F 0 g .4127 .01472 m .4127 .1158 L .42063 .1158 L .42063 .01472 L .4127 .01472 L s 1 0 0 r .42063 .01472 m .42063 .11482 L .42857 .11482 L .42857 .01472 L F 0 g .42063 .01472 m .42063 .11482 L .42857 .11482 L .42857 .01472 L .42063 .01472 L s 1 0 0 r .42857 .01472 m .42857 .11376 L .43651 .11376 L .43651 .01472 L F 0 g .42857 .01472 m .42857 .11376 L .43651 .11376 L .43651 .01472 L .42857 .01472 L s 1 0 0 r .43651 .01472 m .43651 .11582 L .44444 .11582 L .44444 .01472 L F 0 g .43651 .01472 m .43651 .11582 L .44444 .11582 L .44444 .01472 L .43651 .01472 L s 1 0 0 r .44444 .01472 m .44444 .11855 L .45238 .11855 L .45238 .01472 L F 0 g .44444 .01472 m .44444 .11855 L .45238 .11855 L .45238 .01472 L .44444 .01472 L s 1 0 0 r .45238 .01472 m .45238 .12627 L .46032 .12627 L .46032 .01472 L F 0 g .45238 .01472 m .45238 .12627 L .46032 .12627 L .46032 .01472 L .45238 .01472 L s 1 0 0 r .46032 .01472 m .46032 .1442 L .46825 .1442 L .46825 .01472 L F 0 g .46032 .01472 m .46032 .1442 L .46825 .1442 L .46825 .01472 L .46032 .01472 L s 1 0 0 r .46825 .01472 m .46825 .16414 L .47619 .16414 L .47619 .01472 L F 0 g .46825 .01472 m .46825 .16414 L .47619 .16414 L .47619 .01472 L .46825 .01472 L s 1 0 0 r .47619 .01472 m .47619 .18213 L .48413 .18213 L .48413 .01472 L F 0 g .47619 .01472 m .47619 .18213 L .48413 .18213 L .48413 .01472 L .47619 .01472 L s 1 0 0 r .48413 .01472 m .48413 .21675 L .49206 .21675 L .49206 .01472 L F 0 g .48413 .01472 m .48413 .21675 L .49206 .21675 L .49206 .01472 L .48413 .01472 L s 1 0 0 r .49206 .01472 m .49206 .60332 L .5 .60332 L .5 .01472 L F 0 g .49206 .01472 m .49206 .60332 L .5 .60332 L .5 .01472 L .49206 .01472 L s 1 0 0 r .5 .01472 m .5 .31763 L .50794 .31763 L .50794 .01472 L F 0 g .5 .01472 m .5 .31763 L .50794 .31763 L .50794 .01472 L .5 .01472 L s 1 0 0 r .50794 .01472 m .50794 .19943 L .51587 .19943 L .51587 .01472 L F 0 g .50794 .01472 m .50794 .19943 L .51587 .19943 L .51587 .01472 L .50794 .01472 L s 1 0 0 r .51587 .01472 m .51587 .17425 L .52381 .17425 L .52381 .01472 L F 0 g .51587 .01472 m .51587 .17425 L .52381 .17425 L .52381 .01472 L .51587 .01472 L s 1 0 0 r .52381 .01472 m .52381 .15838 L .53175 .15838 L .53175 .01472 L F 0 g .52381 .01472 m .52381 .15838 L .53175 .15838 L .53175 .01472 L .52381 .01472 L s 1 0 0 r .53175 .01472 m .53175 .13617 L .53968 .13617 L .53968 .01472 L F 0 g .53175 .01472 m .53175 .13617 L .53968 .13617 L .53968 .01472 L .53175 .01472 L s 1 0 0 r .53968 .01472 m .53968 .12369 L .54762 .12369 L .54762 .01472 L F 0 g .53968 .01472 m .53968 .12369 L .54762 .12369 L .54762 .01472 L .53968 .01472 L s 1 0 0 r .54762 .01472 m .54762 .1169 L .55556 .1169 L .55556 .01472 L F 0 g .54762 .01472 m .54762 .1169 L .55556 .1169 L .55556 .01472 L .54762 .01472 L s 1 0 0 r .55556 .01472 m .55556 .11411 L .56349 .11411 L .56349 .01472 L F 0 g .55556 .01472 m .55556 .11411 L .56349 .11411 L .56349 .01472 L .55556 .01472 L s 1 0 0 r .56349 .01472 m .56349 .11372 L .57143 .11372 L .57143 .01472 L F 0 g .56349 .01472 m .56349 .11372 L .57143 .11372 L .57143 .01472 L .56349 .01472 L s 1 0 0 r .57143 .01472 m .57143 .11557 L .57937 .11557 L .57937 .01472 L F 0 g .57143 .01472 m .57143 .11557 L .57937 .11557 L .57937 .01472 L .57143 .01472 L s 1 0 0 r .57937 .01472 m .57937 .11442 L .5873 .11442 L .5873 .01472 L F 0 g .57937 .01472 m .57937 .11442 L .5873 .11442 L .5873 .01472 L .57937 .01472 L s 1 0 0 r .5873 .01472 m .5873 .10411 L .59524 .10411 L .59524 .01472 L F 0 g .5873 .01472 m .5873 .10411 L .59524 .10411 L .59524 .01472 L .5873 .01472 L s 1 0 0 r .59524 .01472 m .59524 .09946 L .60317 .09946 L .60317 .01472 L F 0 g .59524 .01472 m .59524 .09946 L .60317 .09946 L .60317 .01472 L .59524 .01472 L s 1 0 0 r .60317 .01472 m .60317 .09863 L .61111 .09863 L .61111 .01472 L F 0 g .60317 .01472 m .60317 .09863 L .61111 .09863 L .61111 .01472 L .60317 .01472 L s 1 0 0 r .61111 .01472 m .61111 .09709 L .61905 .09709 L .61905 .01472 L F 0 g .61111 .01472 m .61111 .09709 L .61905 .09709 L .61905 .01472 L .61111 .01472 L s 1 0 0 r .61905 .01472 m .61905 .09734 L .62698 .09734 L .62698 .01472 L F 0 g .61905 .01472 m .61905 .09734 L .62698 .09734 L .62698 .01472 L .61905 .01472 L s 1 0 0 r .62698 .01472 m .62698 .09735 L .63492 .09735 L .63492 .01472 L F 0 g .62698 .01472 m .62698 .09735 L .63492 .09735 L .63492 .01472 L .62698 .01472 L s 1 0 0 r .63492 .01472 m .63492 .09843 L .64286 .09843 L .64286 .01472 L F 0 g .63492 .01472 m .63492 .09843 L .64286 .09843 L .64286 .01472 L .63492 .01472 L s 1 0 0 r .64286 .01472 m .64286 .09864 L .65079 .09864 L .65079 .01472 L F 0 g .64286 .01472 m .64286 .09864 L .65079 .09864 L .65079 .01472 L .64286 .01472 L s 1 0 0 r .65079 .01472 m .65079 .09162 L .65873 .09162 L .65873 .01472 L F 0 g .65079 .01472 m .65079 .09162 L .65873 .09162 L .65873 .01472 L .65079 .01472 L s 1 0 0 r .65873 .01472 m .65873 .09123 L .66667 .09123 L .66667 .01472 L F 0 g .65873 .01472 m .65873 .09123 L .66667 .09123 L .66667 .01472 L .65873 .01472 L s 1 0 0 r .66667 .01472 m .66667 .09023 L .6746 .09023 L .6746 .01472 L F 0 g .66667 .01472 m .66667 .09023 L .6746 .09023 L .6746 .01472 L .66667 .01472 L s 1 0 0 r .6746 .01472 m .6746 .09006 L .68254 .09006 L .68254 .01472 L F 0 g .6746 .01472 m .6746 .09006 L .68254 .09006 L .68254 .01472 L .6746 .01472 L s 1 0 0 r .68254 .01472 m .68254 .08999 L .69048 .08999 L .69048 .01472 L F 0 g .68254 .01472 m .68254 .08999 L .69048 .08999 L .69048 .01472 L .68254 .01472 L s 1 0 0 r .69048 .01472 m .69048 .08943 L .69841 .08943 L .69841 .01472 L F 0 g .69048 .01472 m .69048 .08943 L .69841 .08943 L .69841 .01472 L .69048 .01472 L s 1 0 0 r .69841 .01472 m .69841 .09116 L .70635 .09116 L .70635 .01472 L F 0 g .69841 .01472 m .69841 .09116 L .70635 .09116 L .70635 .01472 L .69841 .01472 L s 1 0 0 r .70635 .01472 m .70635 .0888 L .71429 .0888 L .71429 .01472 L F 0 g .70635 .01472 m .70635 .0888 L .71429 .0888 L .71429 .01472 L .70635 .01472 L s 1 0 0 r .71429 .01472 m .71429 .08675 L .72222 .08675 L .72222 .01472 L F 0 g .71429 .01472 m .71429 .08675 L .72222 .08675 L .72222 .01472 L .71429 .01472 L s 1 0 0 r .72222 .01472 m .72222 .08634 L .73016 .08634 L .73016 .01472 L F 0 g .72222 .01472 m .72222 .08634 L .73016 .08634 L .73016 .01472 L .72222 .01472 L s 1 0 0 r .73016 .01472 m .73016 .08607 L .7381 .08607 L .7381 .01472 L F 0 g .73016 .01472 m .73016 .08607 L .7381 .08607 L .7381 .01472 L .73016 .01472 L s 1 0 0 r .7381 .01472 m .7381 .08613 L .74603 .08613 L .74603 .01472 L F 0 g .7381 .01472 m .7381 .08613 L .74603 .08613 L .74603 .01472 L .7381 .01472 L s 1 0 0 r .74603 .01472 m .74603 .08639 L .75397 .08639 L .75397 .01472 L F 0 g .74603 .01472 m .74603 .08639 L .75397 .08639 L .75397 .01472 L .74603 .01472 L s 1 0 0 r .75397 .01472 m .75397 .08723 L .7619 .08723 L .7619 .01472 L F 0 g .75397 .01472 m .75397 .08723 L .7619 .08723 L .7619 .01472 L .75397 .01472 L s 1 0 0 r .7619 .01472 m .7619 .08508 L .76984 .08508 L .76984 .01472 L F 0 g .7619 .01472 m .7619 .08508 L .76984 .08508 L .76984 .01472 L .7619 .01472 L s 1 0 0 r .76984 .01472 m .76984 .08478 L .77778 .08478 L .77778 .01472 L F 0 g .76984 .01472 m .76984 .08478 L .77778 .08478 L .77778 .01472 L .76984 .01472 L s 1 0 0 r .77778 .01472 m .77778 .08436 L .78571 .08436 L .78571 .01472 L F 0 g .77778 .01472 m .77778 .08436 L .78571 .08436 L .78571 .01472 L .77778 .01472 L s 1 0 0 r .78571 .01472 m .78571 .08322 L .79365 .08322 L .79365 .01472 L F 0 g .78571 .01472 m .78571 .08322 L .79365 .08322 L .79365 .01472 L .78571 .01472 L s 1 0 0 r .79365 .01472 m .79365 .08324 L .80159 .08324 L .80159 .01472 L F 0 g .79365 .01472 m .79365 .08324 L .80159 .08324 L .80159 .01472 L .79365 .01472 L s 1 0 0 r .80159 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Fv(=)32 b(\()p Ft(a)805 5167 y Fp(i)833 5152 y Ft(;)17 b(a)928 5167 y Fp(i)p Fr(+1)1046 5152 y Fv(\))35 b(suc)m(h)i(that)e Ft(\022)1604 5116 y Fn(0)1601 5178 y Fp(k)1644 5152 y Fv(\()p Ft(')p Fv(\))24 b Fq(\000)g Ft(\022)1957 5116 y Fn(0)1954 5177 y Fp(m)2021 5152 y Fv(\()p Ft(')p Fv(\))35 b(is)h(a)f(monotone)g(function)h(in)f (eac)m(h)h Ft(I)3599 5167 y Fp(i)3663 5152 y Fv(and)1917 5587 y(22)p eop %%Page: 23 23 23 22 bop 489 1984 a @beginspecial 91 @llx 3 @lly 459 @urx 230 @ury 3543 @rwi 2126 @rhi @setspecial %%BeginDocument: fig6h.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 459 230 %%HiResBoundingBox: 91.5625 3.1875 458.75 229.938 %%Creator: (Mathematica 5.0 for Microsoft Windows) %%CreationDate: (Friday, April 15, 2005) (15:09:55) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: font Mathematica1Mono %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: Mathematica1Mono %%DocumentFonts: Courier %%+ Mathematica1Mono %%EndComments 0 233.125 translate 1 -1 scale 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch 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.1553 Mdot .74676 .15522 Mdot .7469 .15513 Mdot .74704 .15505 Mdot .74717 .15496 Mdot .74731 .15488 Mdot .74744 .15479 Mdot .74758 .15471 Mdot .74771 .15463 Mdot .74785 .15454 Mdot .74798 .15446 Mdot .74812 .15437 Mdot .74825 .15429 Mdot .74839 .15421 Mdot .74852 .15413 Mdot .74866 .15405 Mdot .74879 .15396 Mdot .74893 .15388 Mdot .74906 .15379 Mdot .74919 .15371 Mdot .74933 .15363 Mdot .74946 .15355 Mdot .74959 .15346 Mdot .74973 .15338 Mdot .74986 .1533 Mdot .74999 .15322 Mdot .75013 .15314 Mdot .75026 .15306 Mdot .75039 .15297 Mdot .75052 .15289 Mdot .75065 .15281 Mdot .75079 .15273 Mdot .75092 .15265 Mdot .75105 .15256 Mdot .75118 .15248 Mdot .75131 .1524 Mdot .75144 .15232 Mdot .75158 .15224 Mdot .75171 .15216 Mdot .75184 .15208 Mdot .75197 .152 Mdot .7521 .15192 Mdot .75223 .15184 Mdot .75236 .15176 Mdot .75249 .15168 Mdot .75262 .15159 Mdot .75275 .15151 Mdot .75288 .15143 Mdot .75301 .15135 Mdot .75314 .15127 Mdot .75327 .15119 Mdot .7534 .15111 Mdot .75352 .15103 Mdot .75365 .15095 Mdot .75378 .15087 Mdot .75391 .15079 Mdot .75404 .15071 Mdot .75417 .15063 Mdot .75429 .15056 Mdot .75442 .15048 Mdot .75455 .1504 Mdot .75468 .15032 Mdot .75481 .15024 Mdot .75493 .15016 Mdot .75506 .15008 Mdot .75519 .15 Mdot .75531 .14993 Mdot .75544 .14985 Mdot .75557 .14977 Mdot .7557 .14969 Mdot .75582 .14961 Mdot .75595 .14954 Mdot .75607 .14946 Mdot .7562 .14938 Mdot .75633 .14931 Mdot .75645 .14923 Mdot .75658 .14915 Mdot .7567 .14907 Mdot .75683 .14899 Mdot .75695 .14892 Mdot .75708 .14884 Mdot .7572 .14876 Mdot .75733 .14869 Mdot .75745 .14861 Mdot .75758 .14853 Mdot .7577 .14845 Mdot .75783 .14838 Mdot .75795 .1483 Mdot .75808 .14823 Mdot .7582 .14815 Mdot .75832 .14807 Mdot .75845 .148 Mdot .75857 .14792 Mdot .75869 .14784 Mdot .75882 .14777 Mdot .75894 .14769 Mdot .75906 .14762 Mdot .75919 .14754 Mdot .75931 .14746 Mdot .75943 .14739 Mdot .75955 .14731 Mdot .75968 .14724 Mdot .7598 .14716 Mdot .75992 .14709 Mdot .76004 .14701 Mdot .76017 .14693 Mdot .76029 .14686 Mdot .76041 .14678 Mdot .76053 .14671 Mdot .76065 .14663 Mdot .76077 .14656 Mdot .76089 .14648 Mdot .76102 .14641 Mdot .76114 .14633 Mdot .76126 .14626 Mdot .76138 .14618 Mdot .7615 .14611 Mdot .76162 .14603 Mdot .76174 .14596 Mdot .76186 .14589 Mdot .76198 .14581 Mdot .7621 .14574 Mdot .76222 .14567 Mdot .76234 .14559 Mdot .76246 .14552 Mdot .76258 .14544 Mdot .7627 .14537 Mdot .76282 .1453 Mdot .76294 .14522 Mdot .76306 .14515 Mdot .76317 .14508 Mdot .76329 .145 Mdot .76341 .14493 Mdot .76353 .14486 Mdot .76365 .14478 Mdot .76377 .14471 Mdot .76389 .14464 Mdot .764 .14457 Mdot .76412 .14449 Mdot .76424 .14442 Mdot .76436 .14435 Mdot .76447 .14427 Mdot .76459 .1442 Mdot .76471 .14413 Mdot .76483 .14406 Mdot .76494 .14398 Mdot .76506 .14391 Mdot .76518 .14384 Mdot .76529 .14377 Mdot .76541 .1437 Mdot .76553 .14362 Mdot .76564 .14355 Mdot .76576 .14348 Mdot .76588 .14341 Mdot .76599 .14333 Mdot .76611 .14326 Mdot .76622 .14319 Mdot .76634 .14312 Mdot .76646 .14305 Mdot .76657 .14297 Mdot .76669 .1429 Mdot .7668 .14283 Mdot .76692 .14276 Mdot .76703 .14269 Mdot .76715 .14262 Mdot .76726 .14255 Mdot .76738 .14248 Mdot .76749 .14241 Mdot .76761 .14234 Mdot .76772 .14227 Mdot .76784 .14219 Mdot .76795 .14212 Mdot .76806 .14205 Mdot .76818 .14198 Mdot .76829 .14191 Mdot .76841 .14184 Mdot .76852 .14177 Mdot .76863 .1417 Mdot .76875 .14163 Mdot .76886 .14156 Mdot .76897 .14149 Mdot .76909 .14142 Mdot .7692 .14135 Mdot .76931 .14128 Mdot .76942 .14121 Mdot .76954 .14114 Mdot .76965 .14107 Mdot .76976 .141 Mdot .76987 .14094 Mdot .76999 .14087 Mdot .7701 .1408 Mdot .77021 .14073 Mdot .77032 .14066 Mdot .77043 .14059 Mdot .77055 .14052 Mdot .77066 .14045 Mdot .77077 .14038 Mdot .77088 .14032 Mdot .77099 .14025 Mdot .7711 .14018 Mdot .77121 .14011 Mdot .77133 .14005 Mdot .77144 .13998 Mdot .77155 .13991 Mdot .77166 .13984 Mdot .77177 .13977 Mdot .77188 .1397 Mdot .77199 .13963 Mdot .7721 .13957 Mdot .77221 .1395 Mdot .77232 .13943 Mdot .77243 .13936 Mdot .77254 .1393 Mdot .77265 .13923 Mdot .77276 .13916 Mdot .77287 .13909 Mdot .77298 .13903 Mdot .77309 .13896 Mdot .7732 .13889 Mdot .77331 .13882 Mdot .77342 .13876 Mdot .77352 .13869 Mdot .77363 .13862 Mdot .77374 .13855 Mdot .77385 .13849 Mdot .77396 .13842 Mdot .77407 .13835 Mdot .77418 .13829 Mdot .77428 .13822 Mdot .77439 .13815 Mdot .7745 .13809 Mdot .77461 .13802 Mdot .77472 .13795 Mdot .77482 .13789 Mdot .77493 .13782 Mdot .77504 .13776 Mdot .77515 .13769 Mdot .77525 .13762 Mdot .77536 .13756 Mdot .77547 .13749 Mdot .77558 .13743 Mdot .77568 .13736 Mdot .77579 .13729 Mdot .7759 .13723 Mdot .776 .13716 Mdot .77611 .1371 Mdot .77622 .13703 Mdot .77632 .13696 Mdot .77643 .1369 Mdot .77654 .13683 Mdot .77664 .13677 Mdot .77675 .13671 Mdot .77685 .13664 Mdot .77696 .13657 Mdot .77707 .13651 Mdot .77717 .13644 Mdot .77728 .13638 Mdot .77738 .13632 Mdot .77749 .13625 Mdot .77759 .13618 Mdot .7777 .13612 Mdot .7778 .13605 Mdot .77791 .13599 Mdot .77801 .13592 Mdot .77812 .13586 Mdot .77822 .1358 Mdot .77833 .13573 Mdot .77843 .13567 Mdot .77854 .1356 Mdot .77864 .13554 Mdot .77875 .13547 Mdot .77885 .13541 Mdot .77895 .13534 Mdot .77906 .13528 Mdot .77916 .13521 Mdot .77927 .13515 Mdot .77937 .13509 Mdot .77947 .13502 Mdot .77958 .13496 Mdot .77968 .1349 Mdot .77978 .13483 Mdot .77989 .13477 Mdot .77999 .13471 Mdot .78009 .13465 Mdot .7802 .13458 Mdot .7803 .13452 Mdot .7804 .13445 Mdot .78051 .13439 Mdot .78061 .13433 Mdot .78071 .13426 Mdot .78081 .1342 Mdot .78092 .13414 Mdot .78102 .13407 Mdot .78112 .13401 Mdot .78122 .13395 Mdot .78132 .13389 Mdot .78143 .13382 Mdot .78153 .13376 Mdot .78163 .1337 Mdot .78173 .13363 Mdot .78183 .13357 Mdot .78193 .13351 Mdot .78204 .13345 Mdot .78214 .13338 Mdot .78224 .13332 Mdot .78234 .13326 Mdot .78244 .1332 Mdot .78254 .13313 Mdot .78264 .13307 Mdot .78274 .13301 Mdot .78284 .13295 Mdot .78295 .13289 Mdot .78305 .13282 Mdot .78315 .13276 Mdot .78325 .1327 Mdot .78335 .13264 Mdot .78345 .13258 Mdot .78355 .13251 Mdot .78365 .13245 Mdot .78375 .13239 Mdot .78385 .13233 Mdot .78395 .13227 Mdot .78405 .1322 Mdot .78415 .13214 Mdot .78425 .13208 Mdot .78435 .13202 Mdot .78445 .13196 Mdot .78454 .1319 Mdot .78464 .13184 Mdot .78474 .13178 Mdot .78484 .13172 Mdot .78494 .13166 Mdot .78504 .1316 Mdot .78514 .13154 Mdot .78524 .13147 Mdot .78534 .13141 Mdot .78543 .13136 Mdot .78553 .13129 Mdot .78563 .13123 Mdot .78573 .13117 Mdot .78583 .13111 Mdot .78593 .13105 Mdot .78602 .13099 Mdot .78612 .13093 Mdot .78622 .13087 Mdot .78632 .13081 Mdot .78642 .13075 Mdot .78651 .13069 Mdot .78661 .13063 Mdot .78671 .13057 Mdot .78681 .13051 Mdot .7869 .13045 Mdot .787 .13039 Mdot .7871 .13033 Mdot .7872 .13027 Mdot .78729 .13021 Mdot .78739 .13015 Mdot .78749 .13009 Mdot .78758 .13003 Mdot .78768 .12997 Mdot .78778 .12991 Mdot .78787 .12985 Mdot .78797 .12979 Mdot .78807 .12973 Mdot .78816 .12967 Mdot .78826 .12961 Mdot .78836 .12955 Mdot .78845 .12949 Mdot .78855 .12943 Mdot .78864 .12938 Mdot .78874 .12932 Mdot .78884 .12926 Mdot .78893 .1292 Mdot .78903 .12914 Mdot .78912 .12908 Mdot .78922 .12902 Mdot .78931 .12896 Mdot .78941 .1289 Mdot .7895 .12884 Mdot .7896 .12879 Mdot .78969 .12873 Mdot .78979 .12867 Mdot .78988 .12861 Mdot .78998 .12855 Mdot .79007 .12849 Mdot .79017 .12843 Mdot .79026 .12837 Mdot .79036 .12832 Mdot .79045 .12826 Mdot .79055 .1282 Mdot .79064 .12814 Mdot .79074 .12809 Mdot .79083 .12803 Mdot .79092 .12797 Mdot .79102 .12791 Mdot .79111 .12785 Mdot .79121 .1278 Mdot .7913 .12774 Mdot .79139 .12768 Mdot .79149 .12762 Mdot .79158 .12756 Mdot .79167 .1275 Mdot .79177 .12745 Mdot .79186 .12739 Mdot .79195 .12733 Mdot .79205 .12727 Mdot .79214 .12722 Mdot .79223 .12716 Mdot .79233 .1271 Mdot .79242 .12704 Mdot .79251 .12699 Mdot .79261 .12693 Mdot .7927 .12687 Mdot .79279 .12681 Mdot .79288 .12676 Mdot .79298 .1267 Mdot .79307 .12664 Mdot .79316 .12658 Mdot .79325 .12653 Mdot .79335 .12647 Mdot .79344 .12641 Mdot .79353 .12636 Mdot .79362 .1263 Mdot .79371 .12624 Mdot .79381 .12618 Mdot .7939 .12613 Mdot .79399 .12607 Mdot .79408 .12602 Mdot .79417 .12596 Mdot .79426 .12591 Mdot .79436 .12585 Mdot .79445 .12579 Mdot .79454 .12574 Mdot .79463 .12568 Mdot .79472 .12563 Mdot .79481 .12557 Mdot .7949 .12551 Mdot .79499 .12546 Mdot .79509 .1254 Mdot .79518 .12535 Mdot .79527 .12529 Mdot .79536 .12523 Mdot .79545 .12518 Mdot .79554 .12512 Mdot .79563 .12507 Mdot .79572 .12501 Mdot .79581 .12496 Mdot .7959 .1249 Mdot .79599 .12485 Mdot .79608 .12479 Mdot .79617 .12473 Mdot .79626 .12468 Mdot .79635 .12462 Mdot .79644 .12457 Mdot .79653 .12451 Mdot .79662 .12446 Mdot .79671 .1244 Mdot .7968 .12435 Mdot .79689 .12429 Mdot .79698 .12424 Mdot .79707 .12418 Mdot .79716 .12412 Mdot .79725 .12407 Mdot .79734 .12401 Mdot .79742 .12396 Mdot .79751 .1239 Mdot .7976 .12385 Mdot .79769 .12379 Mdot .79778 .12374 Mdot .79787 .12368 Mdot .79796 .12363 Mdot .79805 .12358 Mdot .79814 .12352 Mdot .79822 .12347 Mdot .79831 .12341 Mdot .7984 .12336 Mdot .79849 .12331 Mdot .79858 .12325 Mdot .79867 .1232 Mdot .79875 .12314 Mdot .79884 .12309 Mdot .79893 .12304 Mdot .79902 .12298 Mdot .79911 .12293 Mdot .79919 .12287 Mdot .79928 .12282 Mdot .79937 .12276 Mdot .79946 .12271 Mdot .79954 .12266 Mdot .79963 .1226 Mdot .79972 .12255 Mdot .79981 .1225 Mdot .79989 .12244 Mdot .79998 .12239 Mdot .80007 .12234 Mdot .80016 .12228 Mdot .80024 .12223 Mdot .80033 .12217 Mdot .80042 .12212 Mdot .8005 .12207 Mdot .80059 .12201 Mdot .80068 .12196 Mdot .80076 .12191 Mdot .80085 .12185 Mdot .80094 .1218 Mdot .80102 .12175 Mdot .80111 .12169 Mdot .8012 .12164 Mdot .80128 .12158 Mdot .80137 .12153 Mdot .80145 .12148 Mdot .80154 .12142 Mdot .80163 .12137 Mdot .80171 .12132 Mdot .8018 .12127 Mdot .80188 .12122 Mdot .80197 .12116 Mdot .80206 .12111 Mdot .80214 .12106 Mdot .80223 .12101 Mdot .80231 .12096 Mdot .8024 .1209 Mdot .80248 .12085 Mdot .80257 .1208 Mdot .80265 .12074 Mdot .80274 .12069 Mdot .80282 .12064 Mdot .80291 .12059 Mdot .80299 .12054 Mdot .80308 .12048 Mdot .80316 .12043 Mdot .80325 .12038 Mdot .80333 .12033 Mdot .80342 .12028 Mdot .8035 .12022 Mdot .80359 .12017 Mdot .80367 .12012 Mdot .80376 .12007 Mdot .80384 .12001 Mdot .80393 .11996 Mdot .80401 .11991 Mdot .8041 .11986 Mdot .80418 .11981 Mdot .80426 .11975 Mdot .80435 .1197 Mdot .80443 .11965 Mdot .80452 .1196 Mdot .8046 .11955 Mdot .80468 .11949 Mdot .80477 .11944 Mdot .80485 .11939 Mdot .80493 .11934 Mdot .80502 .11929 Mdot .8051 .11924 Mdot .80519 .11919 Mdot .80527 .11914 Mdot .80535 .11909 Mdot .80544 .11903 Mdot .80552 .11898 Mdot .8056 .11893 Mdot .80569 .11888 Mdot .80577 .11883 Mdot .80585 .11878 Mdot .80593 .11873 Mdot .80602 .11868 Mdot .8061 .11862 Mdot .80618 .11857 Mdot .80627 .11852 Mdot .80635 .11847 Mdot .80643 .11842 Mdot .80651 .11837 Mdot .8066 .11832 Mdot .80668 .11827 Mdot .80676 .11822 Mdot .80684 .11817 Mdot .80693 .11812 Mdot .80701 .11807 Mdot .80709 .11801 Mdot .80717 .11796 Mdot .80725 .11791 Mdot .80734 .11786 Mdot .80742 .11781 Mdot .8075 .11776 Mdot .80758 .11771 Mdot .80766 .11766 Mdot .80775 .11761 Mdot .80783 .11756 Mdot .80791 .11751 Mdot .80799 .11746 Mdot .80807 .11741 Mdot .80815 .11736 Mdot .80823 .11731 Mdot .80832 .11726 Mdot .8084 .11721 Mdot .80848 .11716 Mdot .80856 .11711 Mdot .80864 .11706 Mdot .80872 .11701 Mdot .8088 .11696 Mdot .80888 .11691 Mdot .80896 .11686 Mdot .80905 .11681 Mdot .80913 .11676 Mdot .80921 .11671 Mdot .80929 .11666 Mdot .80937 .11661 Mdot .80945 .11656 Mdot .80953 .11651 Mdot .80961 .11646 Mdot .80969 .11641 Mdot .80977 .11636 Mdot .80985 .11632 Mdot .80993 .11627 Mdot .81001 .11622 Mdot .81009 .11617 Mdot .81017 .11612 Mdot .81025 .11607 Mdot .81033 .11602 Mdot .81041 .11598 Mdot .81049 .11593 Mdot .81057 .11588 Mdot .81065 .11583 Mdot .81073 .11578 Mdot .81081 .11573 Mdot .81089 .11568 Mdot .81097 .11563 Mdot .81105 .11558 Mdot .81113 .11553 Mdot .81121 .11549 Mdot .81129 .11544 Mdot .81137 .11539 Mdot .81145 .11534 Mdot .81152 .11529 Mdot .8116 .11524 Mdot .81168 .11519 Mdot .81176 .11515 Mdot .81184 .1151 Mdot .81192 .11505 Mdot .812 .115 Mdot .81208 .11495 Mdot .81216 .1149 Mdot .81223 .11486 Mdot .81231 .11481 Mdot .81239 .11476 Mdot .81247 .11471 Mdot .81255 .11466 Mdot .81263 .11461 Mdot .81271 .11456 Mdot .81278 .11452 Mdot .81286 .11447 Mdot .81294 .11442 Mdot .81302 .11437 Mdot .8131 .11433 Mdot .81317 .11428 Mdot .81325 .11423 Mdot .81333 .11418 Mdot .81341 .11414 Mdot .81349 .11409 Mdot .81356 .11404 Mdot .81364 .114 Mdot .81372 .11395 Mdot .8138 .1139 Mdot .81388 .11385 Mdot .81395 .1138 Mdot .81403 .11376 Mdot .81411 .11371 Mdot .81419 .11366 Mdot .81426 .11361 Mdot .81434 .11357 Mdot .81442 .11352 Mdot .81449 .11347 Mdot .81457 .11342 Mdot .81465 .11338 Mdot .81473 .11333 Mdot .8148 .11328 Mdot .81488 .11323 Mdot .81496 .11319 Mdot .81503 .11314 Mdot .81511 .11309 Mdot .81519 .11305 Mdot .81526 .113 Mdot .81534 .11295 Mdot .81542 .1129 Mdot .81549 .11286 Mdot .81557 .11281 Mdot .81565 .11276 Mdot .81572 .11272 Mdot .8158 .11267 Mdot .81588 .11262 Mdot .81595 .11257 Mdot .81603 .11253 Mdot .8161 .11248 Mdot .81618 .11243 Mdot .81626 .11239 Mdot .81633 .11234 Mdot .81641 .11229 Mdot .81648 .11225 Mdot .81656 .1122 Mdot .81664 .11215 Mdot .81671 .11211 Mdot .81679 .11206 Mdot .81686 .11201 Mdot .81694 .11197 Mdot .81701 .11192 Mdot .81709 .11187 Mdot .81717 .11183 Mdot .81724 .11178 Mdot .81732 .11173 Mdot .81739 .11169 Mdot .81747 .11164 Mdot .81754 .1116 Mdot .81762 .11155 Mdot .81769 .1115 Mdot .81777 .11146 Mdot .81784 .11141 Mdot .81792 .11137 Mdot .81799 .11132 Mdot .81807 .11128 Mdot .81814 .11123 Mdot .81822 .11118 Mdot .81829 .11114 Mdot .81837 .11109 Mdot .81844 .11105 Mdot .81852 .111 Mdot .81859 .11095 Mdot .81867 .11091 Mdot .81874 .11086 Mdot .81881 .11082 Mdot .81889 .11077 Mdot .81896 .11072 Mdot .81904 .11068 Mdot .81911 .11063 Mdot .81919 .11059 Mdot .81926 .11054 Mdot .81933 .11049 Mdot .81941 .11045 Mdot .81948 .1104 Mdot .81956 .11036 Mdot .81963 .11032 Mdot .8197 .11027 Mdot .81978 .11023 Mdot .81985 .11018 Mdot .81993 .11014 Mdot .82 .11009 Mdot .82007 .11004 Mdot .82015 .11 Mdot .82022 .10995 Mdot .82029 .10991 Mdot .82037 .10986 Mdot .82044 .10982 Mdot .82051 .10977 Mdot .82059 .10973 Mdot .82066 .10968 Mdot .82073 .10964 Mdot .82081 .10959 Mdot .82088 .10955 Mdot .82095 .10951 Mdot .82103 .10946 Mdot .8211 .10942 Mdot .82117 .10937 Mdot .82125 .10933 Mdot .82132 .10928 Mdot .82139 .10924 Mdot .82147 .1092 Mdot .82154 .10915 Mdot .82161 .10911 Mdot .82168 .10906 Mdot .82176 .10902 Mdot .82183 .10897 Mdot .8219 .10893 Mdot .82197 .10888 Mdot .82205 .10884 Mdot .82212 .10879 Mdot .82219 .10875 Mdot .82226 .10871 Mdot .82234 .10866 Mdot .82241 .10862 Mdot .82248 .10857 Mdot .82255 .10853 Mdot .82262 .10849 Mdot .8227 .10844 Mdot .82277 .1084 Mdot .82284 .10835 Mdot .82291 .10831 Mdot .82298 .10826 Mdot .82306 .10822 Mdot .82313 .10817 Mdot .8232 .10813 Mdot .82327 .10809 Mdot .82334 .10804 Mdot .82341 .108 Mdot .82349 .10795 Mdot .82356 .10791 Mdot .82363 .10787 Mdot .8237 .10782 Mdot .82377 .10778 Mdot .82384 .10773 Mdot .82391 .10769 Mdot .82399 .10765 Mdot .82406 .1076 Mdot .82413 .10756 Mdot .8242 .10751 Mdot .82427 .10747 Mdot .82434 .10743 Mdot .82441 .10738 Mdot .82448 .10734 Mdot .82455 .1073 Mdot .82463 .10725 Mdot .8247 .10721 Mdot .82477 .10716 Mdot .82484 .10712 Mdot .82491 .10708 Mdot .82498 .10703 Mdot .82505 .10699 Mdot .82512 .10695 Mdot .82519 .1069 Mdot .82526 .10686 Mdot .82533 .10681 Mdot .8254 .10677 Mdot .82547 .10673 Mdot .82554 .10669 Mdot .82561 .10664 Mdot .82568 .1066 Mdot .82575 .10656 Mdot .82582 .10651 Mdot .82589 .10647 Mdot .82597 .10643 Mdot .82604 .10639 Mdot .82611 .10634 Mdot .82618 .1063 Mdot .82625 .10626 Mdot .82632 .10621 Mdot .82638 .10617 Mdot .82645 .10613 Mdot .82652 .10609 Mdot .82659 .10604 Mdot .82666 .106 Mdot .82673 .10596 Mdot .8268 .10591 Mdot .82687 .10587 Mdot .82694 .10583 Mdot .82701 .10578 Mdot .82708 .10574 Mdot .82715 .1057 Mdot .82722 .10565 Mdot .82729 .10561 Mdot .82736 .10557 Mdot .82743 .10553 Mdot .8275 .10549 Mdot .82757 .10544 Mdot .82764 .1054 Mdot .8277 .10536 Mdot .82777 .10532 Mdot .82784 .10527 Mdot .82791 .10523 Mdot .82798 .10519 Mdot .82805 .10515 Mdot .82812 .1051 Mdot .82819 .10506 Mdot .82826 .10502 Mdot .82832 .10498 Mdot .82839 .10493 Mdot .82846 .10489 Mdot .82853 .10485 Mdot .8286 .10481 Mdot .82867 .10476 Mdot .82874 .10472 Mdot .8288 .10468 Mdot .82887 .10464 Mdot .82894 .10459 Mdot .82901 .10455 Mdot .82908 .10451 Mdot .82915 .10447 Mdot .82921 .10443 Mdot .82928 .10439 Mdot .82935 .10435 Mdot .82942 .10431 Mdot .82949 .10426 Mdot .82956 .10422 Mdot .82962 .10418 Mdot .82969 .10414 Mdot .82976 .1041 Mdot .82983 .10406 Mdot .82989 .10401 Mdot .82996 .10397 Mdot .83003 .10393 Mdot .8301 .10389 Mdot .83017 .10385 Mdot .83023 .10381 Mdot .8303 .10377 Mdot .83037 .10372 Mdot .83044 .10368 Mdot .8305 .10364 Mdot .83057 .1036 Mdot .83064 .10356 Mdot .83071 .10352 Mdot .83077 .10347 Mdot .83084 .10343 Mdot .83091 .10339 Mdot .83098 .10335 Mdot .83104 .10331 Mdot .83111 .10327 Mdot .83118 .10323 Mdot .83124 .10319 Mdot .83131 .10315 Mdot .83138 .1031 Mdot .83144 .10307 Mdot .83151 .10303 Mdot .83158 .10298 Mdot .83165 .10294 Mdot .83171 .1029 Mdot .83178 .10286 Mdot .83185 .10282 Mdot .83191 .10278 Mdot .83198 .10274 Mdot .83205 .1027 Mdot .83211 .10266 Mdot .83218 .10262 Mdot .83225 .10258 Mdot .83231 .10254 Mdot .83238 .1025 Mdot .83244 .10246 Mdot .83251 .10242 Mdot .83258 .10237 Mdot .83264 .10233 Mdot .83271 .10229 Mdot .83278 .10225 Mdot .83284 .10221 Mdot .83291 .10217 Mdot .83297 .10213 Mdot .83304 .10209 Mdot .83311 .10205 Mdot .83317 .10201 Mdot .83324 .10197 Mdot .8333 .10193 Mdot .83337 .10189 Mdot .83344 .10185 Mdot .8335 .10181 Mdot .83357 .10177 Mdot .83363 .10173 Mdot .8337 .10169 Mdot .83376 .10165 Mdot .83383 .10161 Mdot .8339 .10157 Mdot .83396 .10153 Mdot .83403 .10149 Mdot .83409 .10145 Mdot .83416 .10141 Mdot .83422 .10137 Mdot .83429 .10133 Mdot .83435 .10129 Mdot .83442 .10125 Mdot .83448 .10121 Mdot .83455 .10116 Mdot .83462 .10112 Mdot .83468 .10109 Mdot .83475 .10105 Mdot .83481 .10101 Mdot .83488 .10096 Mdot .83494 .10093 Mdot .83501 .10089 Mdot .83507 .10085 Mdot .83514 .10081 Mdot .8352 .10077 Mdot .83527 .10073 Mdot .83533 .10069 Mdot .83539 .10065 Mdot .83546 .10061 Mdot .83552 .10057 Mdot .83559 .10053 Mdot .83565 .10049 Mdot .83572 .10045 Mdot .83578 .10041 Mdot .83585 .10037 Mdot .83591 .10033 Mdot .83598 .10029 Mdot .83604 .10025 Mdot .8361 .10021 Mdot .83617 .10017 Mdot .83623 .10013 Mdot .8363 .10009 Mdot .83636 .10006 Mdot .83643 .10002 Mdot .83649 .09998 Mdot .83655 .09994 Mdot .83662 .0999 Mdot .83668 .09986 Mdot .83675 .09982 Mdot .83681 .09978 Mdot .83687 .09974 Mdot .83694 .0997 Mdot .837 .09966 Mdot .83707 .09962 Mdot .83713 .09958 Mdot .83719 .09955 Mdot .83726 .09951 Mdot .83732 .09947 Mdot .83739 .09943 Mdot .83745 .09939 Mdot .83751 .09936 Mdot .83758 .09932 Mdot .83764 .09928 Mdot .8377 .09924 Mdot .83777 .0992 Mdot .83783 .09916 Mdot .83789 .09912 Mdot .83796 .09908 Mdot .83802 .09904 Mdot .83808 .099 Mdot .83815 .09896 Mdot .83821 .09893 Mdot .83827 .09889 Mdot .83834 .09885 Mdot .8384 .09881 Mdot .83846 .09877 Mdot .83853 .09873 Mdot .83859 .0987 Mdot .83865 .09866 Mdot .83872 .09862 Mdot .83878 .09858 Mdot .83884 .09854 Mdot .8389 .0985 Mdot .83897 .09847 Mdot .83903 .09843 Mdot .83909 .09839 Mdot .83916 .09835 Mdot .83922 .09831 Mdot .83928 .09828 Mdot .83934 .09824 Mdot .83941 .0982 Mdot .83947 .09816 Mdot .83953 .09812 Mdot .83959 .09808 Mdot .83966 .09805 Mdot .83972 .09801 Mdot .83978 .09797 Mdot .83984 .09793 Mdot .83991 .09789 Mdot .83997 .09785 Mdot .84003 .09781 Mdot .84009 .09778 Mdot .84015 .09774 Mdot .84022 .0977 Mdot .84028 .09766 Mdot .84034 .09762 Mdot .8404 .09758 Mdot .84047 .09755 Mdot .84053 .09751 Mdot .84059 .09747 Mdot .84065 .09743 Mdot .84071 .09739 Mdot .84078 .09735 Mdot .84084 .09732 Mdot .8409 .09728 Mdot .84096 .09724 Mdot .84102 .09721 Mdot .84108 .09717 Mdot .84115 .09713 Mdot .84121 .0971 Mdot .84127 .09706 Mdot .84133 .09702 Mdot .84139 .09698 Mdot .84145 .09695 Mdot .84152 .09691 Mdot .84158 .09687 Mdot .84164 .09683 Mdot .8417 .09679 Mdot .84176 .09676 Mdot .84182 .09672 Mdot .84188 .09668 Mdot .84195 .09665 Mdot .84201 .09661 Mdot .84207 .09657 Mdot .84213 .09653 Mdot .84219 .09649 Mdot .84225 .09646 Mdot .84231 .09642 Mdot .84237 .09638 Mdot .84243 .09634 Mdot .8425 .09631 Mdot .84256 .09627 Mdot .84262 .09623 Mdot .84268 .0962 Mdot .84274 .09616 Mdot .8428 .09612 Mdot .84286 .09608 Mdot .84292 .09605 Mdot .84298 .09601 Mdot .84304 .09597 Mdot .8431 .09593 Mdot .84316 .0959 Mdot .84323 .09586 Mdot .84329 .09582 Mdot .84335 .09579 Mdot .84341 .09575 Mdot .84347 .09571 Mdot .84353 .09568 Mdot .84359 .09564 Mdot .84365 .0956 Mdot .84371 .09557 Mdot .84377 .09553 Mdot .84383 .09549 Mdot .84389 .09545 Mdot .84395 .09542 Mdot .84401 .09538 Mdot .84407 .09534 Mdot .84413 .09531 Mdot .84419 .09527 Mdot .84425 .09523 Mdot .84431 .0952 Mdot .84437 .09516 Mdot .84443 .09512 Mdot .84449 .09509 Mdot .84455 .09505 Mdot .84461 .09501 Mdot .84467 .09498 Mdot .84473 .09494 Mdot .84479 .0949 Mdot .84485 .09487 Mdot .84491 .09483 Mdot .84497 .09479 Mdot .84503 .09476 Mdot .84509 .09472 Mdot .84515 .09468 Mdot .84521 .09465 Mdot .84527 .09461 Mdot .84533 .09457 Mdot .84539 .09454 Mdot .84545 .0945 Mdot .84551 .09446 Mdot .84557 .09443 Mdot .84563 .09439 Mdot .84569 .09435 Mdot .84574 .09432 Mdot .8458 .09428 Mdot .84586 .09424 Mdot .84592 .09421 Mdot .84598 .09417 Mdot .84604 .09413 Mdot .8461 .0941 Mdot .84616 .09406 Mdot .84622 .09403 Mdot .84628 .09399 Mdot .84634 .09395 Mdot .8464 .09392 Mdot .84646 .09388 Mdot .84651 .09385 Mdot .84657 .09381 Mdot .84663 .09377 Mdot .84669 .09374 Mdot .84675 .0937 Mdot .84681 .09367 Mdot .84687 .09363 Mdot .84693 .09359 Mdot .84699 .09356 Mdot .84704 .09352 Mdot .8471 .09349 Mdot .84716 .09345 Mdot .84722 .09341 Mdot .84728 .09338 Mdot .84734 .09334 Mdot .8474 .09331 Mdot .84745 .09327 Mdot .84751 .09323 Mdot .84757 .0932 Mdot .84763 .09316 Mdot .84769 .09313 Mdot .84775 .09309 Mdot .8478 .09305 Mdot .84786 .09302 Mdot .84792 .09298 Mdot .84798 .09295 Mdot .84804 .09291 Mdot .8481 .09288 Mdot .84815 .09284 Mdot .84821 .09281 Mdot .84827 .09277 Mdot .84833 .09274 Mdot .84839 .0927 Mdot .84844 .09266 Mdot .8485 .09263 Mdot .84856 .09259 Mdot .84862 .09256 Mdot .84868 .09252 Mdot .84873 .09249 Mdot .84879 .09245 Mdot .84885 .09242 Mdot .84891 .09238 Mdot .84897 .09235 Mdot .84902 .09231 Mdot .84908 .09228 Mdot .84914 .09224 Mdot .8492 .0922 Mdot .84925 .09217 Mdot .84931 .09213 Mdot .84937 .0921 Mdot .84943 .09206 Mdot .84948 .09203 Mdot .84954 .09199 Mdot .8496 .09196 Mdot .84966 .09192 Mdot .84971 .09189 Mdot .84977 .09186 Mdot .84983 .09182 Mdot .84989 .09178 Mdot .84994 .09175 Mdot .85 .09171 Mdot .85006 .09168 Mdot .85012 .09164 Mdot .85017 .09161 Mdot .85023 .09157 Mdot .85029 .09154 Mdot .85034 .0915 Mdot .8504 .09147 Mdot .85046 .09143 Mdot .85052 .0914 Mdot .85057 .09136 Mdot .85063 .09133 Mdot .85069 .09129 Mdot .85074 .09126 Mdot .8508 .09122 Mdot .85086 .09119 Mdot .85091 .09115 Mdot .85097 .09112 Mdot .85103 .09108 Mdot .85108 .09105 Mdot .85114 .09101 Mdot .8512 .09098 Mdot .85125 .09095 Mdot .85131 .09091 Mdot .85137 .09088 Mdot .85142 .09084 Mdot .85148 .09081 Mdot .85154 .09077 Mdot .85159 .09074 Mdot .85165 .0907 Mdot .85171 .09067 Mdot .85176 .09063 Mdot .85182 .0906 Mdot .85188 .09056 Mdot .85193 .09053 Mdot .85199 .0905 Mdot .85205 .09046 Mdot .8521 .09043 Mdot .85216 .09039 Mdot .85221 .09036 Mdot .85227 .09032 Mdot .85233 .09029 Mdot .85238 .09026 Mdot .85244 .09022 Mdot .85249 .09019 Mdot .85255 .09015 Mdot .85261 .09012 Mdot .85266 .09009 Mdot .85272 .09005 Mdot .85277 .09002 Mdot .85283 .08998 Mdot .85289 .08995 Mdot .85294 .08992 Mdot .853 .08988 Mdot .85305 .08985 Mdot .85311 .08981 Mdot .85317 .08978 Mdot .85322 .08974 Mdot .85328 .08971 Mdot .85333 .08968 Mdot .85339 .08964 Mdot .85344 .08961 Mdot .8535 .08958 Mdot .85356 .08954 Mdot .85361 .08951 Mdot .85367 .08947 Mdot .85372 .08944 Mdot .85378 .08941 Mdot .85383 .08937 Mdot .85389 .08934 Mdot .85394 .0893 Mdot .854 .08927 Mdot .85405 .08923 Mdot .85411 .0892 Mdot .85417 .08917 Mdot .85422 .08913 Mdot .85428 .0891 Mdot .85433 .08907 Mdot .85439 .08903 Mdot .85444 .089 Mdot .8545 .08896 Mdot .85455 .08893 Mdot .85461 .0889 Mdot .85466 .08886 Mdot .85472 .08883 Mdot .85477 .0888 Mdot .85483 .08876 Mdot .85488 .08873 Mdot .85494 .0887 Mdot .85499 .08866 Mdot .85505 .08863 Mdot .8551 .0886 Mdot .85516 .08857 Mdot .85521 .08853 Mdot .85527 .0885 Mdot .85532 .08847 Mdot .85538 .08843 Mdot .85543 .0884 Mdot .85549 .08836 Mdot .85554 .08833 Mdot .85559 .0883 Mdot .85565 .08826 Mdot .8557 .08823 Mdot .85576 .0882 Mdot .85581 .08816 Mdot .85587 .08813 Mdot .85592 .0881 Mdot .85598 .08806 Mdot .85603 .08803 Mdot .85609 .08799 Mdot .85614 .08796 Mdot .85619 .08793 Mdot .85625 .08789 Mdot .8563 .08786 Mdot .85636 .08783 Mdot .85641 .0878 Mdot .85647 .08776 Mdot .85652 .08773 Mdot .85657 .0877 Mdot .85663 .08767 Mdot .85668 .08763 Mdot .85674 .0876 Mdot .85679 .08757 Mdot .85684 .08753 Mdot .8569 .0875 Mdot .85695 .08747 Mdot .85701 .08743 Mdot .85706 .0874 Mdot .85711 .08737 Mdot .85717 .08734 Mdot .85722 .08731 Mdot .85728 .08727 Mdot .85733 .08724 Mdot .85738 .08721 Mdot .85744 .08717 Mdot .85749 .08714 Mdot .85755 .08711 Mdot .8576 .08708 Mdot .85765 .08704 Mdot .85771 .08701 Mdot .85776 .08698 Mdot .85781 .08694 Mdot .85787 .08691 Mdot .85792 .08688 Mdot .85797 .08684 Mdot .85803 .08681 Mdot .85808 .08678 Mdot .85814 .08675 Mdot .85819 .08671 Mdot .85824 .08668 Mdot .8583 .08665 Mdot .85835 .08661 Mdot .8584 .08658 Mdot .85846 .08655 Mdot .85851 .08652 Mdot .85856 .08648 Mdot .85862 .08645 Mdot .85867 .08642 Mdot .85872 .08639 Mdot .85878 .08635 Mdot .85883 .08632 Mdot .85888 .08629 Mdot .85893 .08626 Mdot .85899 .08622 Mdot .85904 .08619 Mdot .85909 .08616 Mdot .85915 .08613 Mdot .8592 .0861 Mdot .85925 .08606 Mdot .85931 .08603 Mdot .85936 .086 Mdot .85941 .08597 Mdot .85947 .08593 Mdot .85952 .0859 Mdot .85957 .08587 Mdot .85962 .08584 Mdot .85968 .08581 Mdot .85973 .08577 Mdot .85978 .08574 Mdot .85983 .08571 Mdot .85989 .08568 Mdot .85994 .08565 Mdot .85999 .08561 Mdot .86005 .08558 Mdot .8601 .08555 Mdot .86015 .08552 Mdot .8602 .08549 Mdot .86026 .08545 Mdot .86031 .08542 Mdot .86036 .08539 Mdot .86041 .08536 Mdot .86047 .08532 Mdot .86052 .08529 Mdot .86057 .08526 Mdot .86062 .08523 Mdot .86068 .0852 Mdot .86073 .08516 Mdot .86078 .08513 Mdot .86083 .0851 Mdot .86088 .08507 Mdot .86094 .08504 Mdot .86099 .085 Mdot .86104 .08497 Mdot .86109 .08494 Mdot .86115 .08491 Mdot .8612 .08488 Mdot .86125 .08485 Mdot .8613 .08481 Mdot .86135 .08478 Mdot .86141 .08475 Mdot .86146 .08472 Mdot .86151 .08469 Mdot .86156 .08466 Mdot .86161 .08462 Mdot .86167 .08459 Mdot .86172 .08456 Mdot .86177 .08453 Mdot .86182 .0845 Mdot .86187 .08447 Mdot .86193 .08443 Mdot .86198 .0844 Mdot .86203 .08437 Mdot .86208 .08434 Mdot .86213 .08431 Mdot .86218 .08428 Mdot .86224 .08425 Mdot .86229 .08422 Mdot .86234 .08419 Mdot .86239 .08415 Mdot .86244 .08412 Mdot .86249 .08409 Mdot .86255 .08406 Mdot .8626 .08403 Mdot .86265 .084 Mdot .8627 .08396 Mdot .86275 .08393 Mdot .8628 .0839 Mdot .86285 .08387 Mdot .86291 .08384 Mdot .86296 .08381 Mdot .86301 .08377 Mdot .86306 .08374 Mdot .86311 .08371 Mdot .86316 .08368 Mdot .86321 .08365 Mdot .86326 .08362 Mdot .86332 .08358 Mdot .86337 .08355 Mdot .86342 .08352 Mdot .86347 .08349 Mdot .86352 .08346 Mdot .86357 .08343 Mdot .86362 .0834 Mdot .86367 .08337 Mdot .86372 .08333 Mdot .86378 .0833 Mdot .86383 .08327 Mdot .86388 .08324 Mdot .86393 .08321 Mdot .86398 .08318 Mdot .86403 .08315 Mdot .86408 .08311 Mdot .86413 .08309 Mdot .86418 .08305 Mdot .86423 .08302 Mdot .86428 .08299 Mdot .86434 .08296 Mdot .86439 .08293 Mdot .86444 .0829 Mdot .86449 .08287 Mdot .86454 .08284 Mdot .86459 .08281 Mdot .86464 .08277 Mdot .86469 .08274 Mdot .86474 .08271 Mdot .86479 .08268 Mdot .86484 .08265 Mdot .86489 .08262 Mdot .86494 .08259 Mdot .86499 .08256 Mdot .86504 .08253 Mdot .86509 .0825 Mdot .86515 .08247 Mdot .8652 .08243 Mdot .86525 .0824 Mdot .8653 .08237 Mdot .86535 .08234 Mdot .8654 .08231 Mdot .86545 .08228 Mdot .8655 .08225 Mdot .86555 .08222 Mdot .8656 .08219 Mdot .86565 .08215 Mdot .8657 .08212 Mdot .86575 .08209 Mdot .8658 .08206 Mdot .86585 .08203 Mdot .8659 .082 Mdot .86595 .08197 Mdot .866 .08194 Mdot .86605 .08191 Mdot .8661 .08188 Mdot .86615 .08185 Mdot .8662 .08182 Mdot .86625 .08179 Mdot .8663 .08176 Mdot .86635 .08173 Mdot .8664 .0817 Mdot .86645 .08167 Mdot .8665 .08164 Mdot .86655 .0816 Mdot .8666 .08157 Mdot .86665 .08154 Mdot .8667 .08151 Mdot .86675 .08148 Mdot .8668 .08145 Mdot .86685 .08142 Mdot .8669 .08139 Mdot .86695 .08136 Mdot .867 .08133 Mdot .86705 .0813 Mdot .8671 .08127 Mdot .86715 .08124 Mdot .8672 .08121 Mdot .86724 .08118 Mdot .86729 .08115 Mdot .86734 .08112 Mdot .86739 .08109 Mdot .86744 .08106 Mdot .86749 .08103 Mdot .86754 .081 Mdot .86759 .08097 Mdot .86764 .08094 Mdot .86769 .08091 Mdot .86774 .08088 Mdot .86779 .08085 Mdot .86784 .08082 Mdot .86789 .08079 Mdot .86794 .08076 Mdot .86799 .08073 Mdot .86803 .0807 Mdot .86808 .08067 Mdot .86813 .08064 Mdot .86818 .08061 Mdot .86823 .08058 Mdot .86828 .08055 Mdot .86833 .08052 Mdot .86838 .08049 Mdot .86843 .08046 Mdot .86848 .08043 Mdot .86853 .0804 Mdot .86857 .08037 Mdot .86862 .08034 Mdot .86867 .08031 Mdot .86872 .08028 Mdot .86877 .08025 Mdot .86882 .08022 Mdot .86887 .08019 Mdot .86892 .08016 Mdot .86897 .08013 Mdot .86901 .0801 Mdot .86906 .08007 Mdot .86911 .08004 Mdot .86916 .08001 Mdot .86921 .07998 Mdot .86926 .07995 Mdot .86931 .07992 Mdot .86936 .07989 Mdot .8694 .07987 Mdot .86945 .07984 Mdot .8695 .07981 Mdot .86955 .07978 Mdot .8696 .07975 Mdot .86965 .07972 Mdot .8697 .07969 Mdot .86974 .07966 Mdot .86979 .07963 Mdot .86984 .0796 Mdot .86989 .07957 Mdot .86994 .07954 Mdot .86999 .07951 Mdot .87004 .07948 Mdot .87008 .07945 Mdot .87013 .07942 Mdot .87018 .07939 Mdot .87023 .07936 Mdot .87028 .07934 Mdot .87033 .07931 Mdot .87037 .07928 Mdot .87042 .07925 Mdot .87047 .07922 Mdot .87052 .07919 Mdot .87057 .07916 Mdot .87061 .07913 Mdot .87066 .0791 Mdot .87071 .07907 Mdot .87076 .07904 Mdot .87081 .07901 Mdot .87086 .07898 Mdot .8709 .07895 Mdot .87095 .07892 Mdot .871 .07889 Mdot .87105 .07887 Mdot .8711 .07884 Mdot .87114 .07881 Mdot .87119 .07878 Mdot .87124 .07875 Mdot .87129 .07872 Mdot .87134 .07869 Mdot .87138 .07866 Mdot .87143 .07863 Mdot .87148 .0786 Mdot .87153 .07857 Mdot .87157 .07854 Mdot .87162 .07851 Mdot .87167 .07849 Mdot .87172 .07846 Mdot .87177 .07843 Mdot .87181 .0784 Mdot .87186 .07837 Mdot .87191 .07834 Mdot .87196 .07831 Mdot .872 .07828 Mdot .87205 .07826 Mdot .8721 .07823 Mdot .87215 .0782 Mdot .87219 .07817 Mdot .87224 .07814 Mdot .87229 .07812 Mdot .87234 .07809 Mdot .87238 .07806 Mdot .87243 .07803 Mdot .87248 .078 Mdot .87253 .07797 Mdot .87257 .07794 Mdot .87262 .07791 Mdot .87267 .07788 Mdot .87272 .07786 Mdot .87276 .07783 Mdot .87281 .0778 Mdot .87286 .07777 Mdot .8729 .07774 Mdot .87295 .07772 Mdot .873 .07769 Mdot .87305 .07766 Mdot .87309 .07763 Mdot .87314 .0776 Mdot .87319 .07757 Mdot .87323 .07754 Mdot .87328 .07751 Mdot .87333 .07748 Mdot .87338 .07746 Mdot .87342 .07743 Mdot .87347 .0774 Mdot .87352 .07737 Mdot .87356 .07734 Mdot .87361 .07731 Mdot .87366 .07729 Mdot .8737 .07726 Mdot .87375 .07723 Mdot .8738 .0772 Mdot .87385 .07717 Mdot .87389 .07714 Mdot .87394 .07711 Mdot .87399 .07708 Mdot .87403 .07706 Mdot .87408 .07703 Mdot .87413 .077 Mdot .87417 .07697 Mdot .87422 .07694 Mdot .87427 .07691 Mdot .87431 .07689 Mdot .87436 .07686 Mdot .87441 .07683 Mdot .87445 .0768 Mdot .8745 .07677 Mdot .87455 .07675 Mdot .87459 .07672 Mdot .87464 .07669 Mdot .87469 .07666 Mdot .87473 .07663 Mdot .87478 .0766 Mdot .87483 .07657 Mdot .87487 .07655 Mdot .87492 .07652 Mdot .87496 .07649 Mdot .87501 .07646 Mdot .87506 .07643 Mdot .8751 .0764 Mdot .87515 .07637 Mdot .8752 .07634 Mdot .87524 .07632 Mdot .87529 .07629 Mdot .87534 .07626 Mdot .87538 .07623 Mdot .87543 .0762 Mdot .87547 .07617 Mdot .87552 .07615 Mdot .87557 .07612 Mdot .87561 .07609 Mdot .87566 .07606 Mdot .87571 .07603 Mdot .87575 .07601 Mdot .8758 .07598 Mdot .87584 .07595 Mdot .87589 .07592 Mdot .87594 .0759 Mdot .87598 .07587 Mdot .87603 .07584 Mdot .87607 .07581 Mdot .87612 .07579 Mdot .87617 .07576 Mdot .87621 .07573 Mdot .87626 .0757 Mdot .8763 .07567 Mdot .87635 .07565 Mdot .8764 .07562 Mdot .87644 .07559 Mdot .87649 .07556 Mdot .87653 .07553 Mdot .87658 .0755 Mdot .87662 .07548 Mdot .87667 .07545 Mdot .87672 .07542 Mdot .87676 .07539 Mdot .87681 .07536 Mdot .87685 .07534 Mdot .8769 .07531 Mdot .87694 .07528 Mdot .87699 .07525 Mdot .87704 .07522 Mdot .87708 .0752 Mdot .87713 .07517 Mdot .87717 .07514 Mdot .87722 .07511 Mdot .87726 .07509 Mdot .87731 .07506 Mdot .87736 .07503 Mdot .8774 .075 Mdot .87745 .07498 Mdot .87749 .07495 Mdot .87754 .07492 Mdot .87758 .07489 Mdot .87763 .07486 Mdot .87767 .07484 Mdot .87772 .07481 Mdot .87776 .07478 Mdot .87781 .07475 Mdot .87785 .07472 Mdot .8779 .0747 Mdot .87795 .07467 Mdot .87799 .07464 Mdot .87804 .07461 Mdot .87808 .07459 Mdot .87813 .07456 Mdot .87817 .07453 Mdot .87822 .0745 Mdot .87826 .07448 Mdot .87831 .07445 Mdot .87835 .07442 Mdot .8784 .07439 Mdot .87844 .07437 Mdot .87849 .07434 Mdot .87853 .07431 Mdot .87858 .07428 Mdot .87862 .07426 Mdot .87867 .07423 Mdot .87871 .0742 Mdot .87876 .07417 Mdot .8788 .07415 Mdot .87885 .07412 Mdot .87889 .07409 Mdot .87894 .07407 Mdot .87898 .07404 Mdot .87903 .07401 Mdot .87907 .07398 Mdot .87912 .07396 Mdot .87916 .07393 Mdot .87921 .0739 Mdot .87925 .07388 Mdot .8793 .07385 Mdot .87934 .07382 Mdot .87939 .07379 Mdot .87943 .07377 Mdot .87947 .07374 Mdot .87952 .07371 Mdot .87956 .07368 Mdot .87961 .07366 Mdot .87965 .07363 Mdot .8797 .0736 Mdot .87974 .07358 Mdot .87979 .07355 Mdot .87983 .07352 Mdot .87988 .07349 Mdot .87992 .07347 Mdot .87997 .07344 Mdot .88001 .07341 Mdot .88005 .07338 Mdot .8801 .07336 Mdot .88014 .07333 Mdot .88019 .0733 Mdot .88023 .07327 Mdot .88028 .07325 Mdot .88032 .07322 Mdot .88037 .07319 Mdot .88041 .07317 Mdot .88045 .07314 Mdot .8805 .07311 Mdot .88054 .07309 Mdot .88059 .07306 Mdot .88063 .07303 Mdot .88068 .07301 Mdot .88072 .07298 Mdot .88076 .07295 Mdot .88081 .07292 Mdot .88085 .0729 Mdot .8809 .07287 Mdot .88094 .07284 Mdot .88099 .07282 Mdot .88103 .07279 Mdot .88107 .07276 Mdot .88112 .07274 Mdot .88116 .07271 Mdot .88121 .07268 Mdot .88125 .07266 Mdot .88129 .07263 Mdot .88134 .0726 Mdot .88138 .07258 Mdot .88143 .07255 Mdot .88147 .07252 Mdot .88151 .07249 Mdot .88156 .07247 Mdot .8816 .07244 Mdot .88165 .07241 Mdot .88169 .07239 Mdot .88173 .07236 Mdot .88178 .07233 Mdot .88182 .0723 Mdot .88186 .07228 Mdot .88191 .07225 Mdot .88195 .07223 Mdot .882 .0722 Mdot .88204 .07217 Mdot .88208 .07214 Mdot .88213 .07212 Mdot .88217 .07209 Mdot .88221 .07206 Mdot .88226 .07204 Mdot .8823 .07201 Mdot .88235 .07199 Mdot .88239 .07196 Mdot .88243 .07193 Mdot .88248 .07191 Mdot .88252 .07188 Mdot .88256 .07185 Mdot .88261 .07183 Mdot .88265 .0718 Mdot .88269 .07177 Mdot .88274 .07175 Mdot .88278 .07172 Mdot .88282 .07169 Mdot .88287 .07167 Mdot .88291 .07164 Mdot .88295 .07161 Mdot .883 .07159 Mdot .88304 .07156 Mdot .88309 .07153 Mdot .88313 .07151 Mdot .88317 .07148 Mdot .88322 .07145 Mdot .88326 .07143 Mdot .8833 .0714 Mdot .88335 .07138 Mdot .88339 .07135 Mdot .88343 .07132 Mdot .88347 .0713 Mdot .88352 .07127 Mdot .88356 .07125 Mdot .8836 .07122 Mdot .88365 .07119 Mdot .88369 .07117 Mdot .88373 .07114 Mdot .88378 .07111 Mdot .88382 .07109 Mdot .88386 .07106 Mdot .88391 .07103 Mdot .88395 .07101 Mdot .88399 .07098 Mdot .88404 .07096 Mdot .88408 .07093 Mdot .88412 .0709 Mdot .88416 .07088 Mdot .88421 .07085 Mdot .88425 .07083 Mdot .88429 .0708 Mdot .88434 .07077 Mdot .88438 .07075 Mdot .88442 .07072 Mdot .88446 .07069 Mdot .88451 .07067 Mdot .88455 .07064 Mdot .88459 .07062 Mdot .88464 .07059 Mdot .88468 .07056 Mdot .88472 .07054 Mdot .88476 .07051 Mdot .88481 .07048 Mdot .88485 .07046 Mdot .88489 .07043 Mdot .88494 .0704 Mdot .88498 .07038 Mdot .88502 .07035 Mdot .88506 .07033 Mdot .88511 .0703 Mdot .88515 .07028 Mdot .88519 .07025 Mdot .88523 .07023 Mdot .88528 .0702 Mdot .88532 .07018 Mdot .88536 .07015 Mdot .8854 .07012 Mdot .88545 .0701 Mdot .88549 .07007 Mdot .88553 .07005 Mdot .88557 .07002 Mdot .88562 .06999 Mdot .88566 .06997 Mdot .8857 .06994 Mdot .88574 .06992 Mdot .88579 .06989 Mdot .88583 .06987 Mdot .88587 .06984 Mdot .88591 .06981 Mdot .88596 .06979 Mdot .886 .06976 Mdot .88604 .06974 Mdot .88608 .06971 Mdot .88612 .06969 Mdot .88617 .06966 Mdot .88621 .06964 Mdot .88625 .06961 Mdot .88629 .06959 Mdot .88634 .06956 Mdot .88638 .06953 Mdot .88642 .06951 Mdot .88646 .06948 Mdot .8865 .06946 Mdot .88655 .06943 Mdot .88659 .0694 Mdot .88663 .06938 Mdot .88667 .06935 Mdot .88672 .06933 Mdot .88676 .0693 Mdot .8868 .06928 Mdot .88684 .06925 Mdot .88688 .06923 Mdot .88693 .0692 Mdot .88697 .06918 Mdot .88701 .06915 Mdot .88705 .06912 Mdot .88709 .0691 Mdot .88714 .06907 Mdot .88718 .06905 Mdot .88722 .06902 Mdot .88726 .069 Mdot .8873 .06897 Mdot .88734 .06895 Mdot .88739 .06892 Mdot .88743 .0689 Mdot .88747 .06887 Mdot .88751 .06885 Mdot .88755 .06882 Mdot .8876 .06879 Mdot .88764 .06877 Mdot .88768 .06874 Mdot .88772 .06872 Mdot .88776 .06869 Mdot .8878 .06867 Mdot .88785 .06864 Mdot .88789 .06862 Mdot .88793 .06859 Mdot .88797 .06857 Mdot .88801 .06854 Mdot .88805 .06851 Mdot .8881 .06849 Mdot .88814 .06847 Mdot .88818 .06844 Mdot .88822 .06842 Mdot .88826 .0684 Mdot .8883 .06837 Mdot .88834 .06835 Mdot .88839 .06832 Mdot .88843 .0683 Mdot .88847 .06827 Mdot .88851 .06824 Mdot .88855 .06822 Mdot .88859 .06819 Mdot .88863 .06817 Mdot .88868 .06814 Mdot .88872 .06812 Mdot .88876 .06809 Mdot .8888 .06807 Mdot .88884 .06804 Mdot .88888 .06801 Mdot .88892 .06799 Mdot .88897 .06796 Mdot .88901 .06794 Mdot .88905 .06791 Mdot .88909 .06789 Mdot .88913 .06786 Mdot .88917 .06784 Mdot .88921 .06781 Mdot .88925 .06779 Mdot .8893 .06776 Mdot .88934 .06774 Mdot .88938 .06771 Mdot .88942 .06769 Mdot .88946 .06766 Mdot .8895 .06764 Mdot .88954 .06761 Mdot .88958 .06759 Mdot .88962 .06756 Mdot .88966 .06754 Mdot .88971 .06751 Mdot .88975 .06749 Mdot .88979 .06746 Mdot .88983 .06744 Mdot .88987 .06741 Mdot .88991 .06739 Mdot .88995 .06736 Mdot .88999 .06734 Mdot .89003 .06731 Mdot .89007 .06729 Mdot .89012 .06726 Mdot .89016 .06724 Mdot .8902 .06721 Mdot .89024 .06719 Mdot .89028 .06716 Mdot .89032 .06714 Mdot .89036 .06711 Mdot .8904 .06709 Mdot .89044 .06706 Mdot .89048 .06704 Mdot .89052 .06701 Mdot .89056 .06699 Mdot .8906 .06696 Mdot .89065 .06694 Mdot .89069 .06692 Mdot .89073 .06689 Mdot .89077 .06687 Mdot .89081 .06684 Mdot .89085 .06682 Mdot .89089 .06679 Mdot .89093 .06677 Mdot .89097 .06675 Mdot .89101 .06672 Mdot .89105 .0667 Mdot .89109 .06667 Mdot .89113 .06665 Mdot .89117 .06662 Mdot .89121 .0666 Mdot .89125 .06657 Mdot .89129 .06655 Mdot .89134 .06653 Mdot .89138 .0665 Mdot .89142 .06648 Mdot .89146 .06645 Mdot .8915 .06643 Mdot .89154 .0664 Mdot .89158 .06638 Mdot .89162 .06636 Mdot .89166 .06633 Mdot .8917 .06631 Mdot .89174 .06628 Mdot .89178 .06626 Mdot .89182 .06623 Mdot .89186 .06621 Mdot .8919 .06618 Mdot .89194 .06616 Mdot .89198 .06613 Mdot .89202 .06611 Mdot .89206 .06608 Mdot .8921 .06606 Mdot .89214 .06603 Mdot .89218 .06601 Mdot .89222 .06599 Mdot .89226 .06596 Mdot .8923 .06594 Mdot .89234 .06591 Mdot .89238 .06589 Mdot .89242 .06586 Mdot .89246 .06584 Mdot .8925 .06582 Mdot .89254 .06579 Mdot .89258 .06577 Mdot .89262 .06574 Mdot .89266 .06572 Mdot .8927 .0657 Mdot .89274 .06567 Mdot .89278 .06565 Mdot .89282 .06562 Mdot .89286 .0656 Mdot .8929 .06557 Mdot .89294 .06555 Mdot .89298 .06552 Mdot .89302 .0655 Mdot .89306 .06547 Mdot .8931 .06545 Mdot .89314 .06542 Mdot .89318 .0654 Mdot .89322 .06538 Mdot .89326 .06535 Mdot .8933 .06533 Mdot .89334 .0653 Mdot .89338 .06528 Mdot .89342 .06525 Mdot .89346 .06523 Mdot .8935 .06521 Mdot .89354 .06519 Mdot .89358 .06516 Mdot .89362 .06514 Mdot .89366 .06511 Mdot .8937 .06509 Mdot .89374 .06506 Mdot .89378 .06504 Mdot .89382 .06502 Mdot .89386 .06499 Mdot .8939 .06497 Mdot .89394 .06494 Mdot .89398 .06492 Mdot .89402 .0649 Mdot .89406 .06487 Mdot .89409 .06485 Mdot .89413 .06482 Mdot .89417 .0648 Mdot .89421 .06477 Mdot .89425 .06475 Mdot .89429 .06473 Mdot .89433 .0647 Mdot .89437 .06468 Mdot .89441 .06465 Mdot .89445 .06463 Mdot .89449 .06461 Mdot .89453 .06458 Mdot .89457 .06456 Mdot .89461 .06453 Mdot .89465 .06451 Mdot .89469 .06449 Mdot .89473 .06446 Mdot .89477 .06444 Mdot .8948 .06442 Mdot .89484 .06439 Mdot .89488 .06437 Mdot .89492 .06434 Mdot .89496 .06432 Mdot .895 .0643 Mdot .89504 .06427 Mdot .89508 .06425 Mdot .89512 .06423 Mdot .89516 .0642 Mdot .8952 .06418 Mdot .89524 .06416 Mdot .89528 .06413 Mdot .89531 .06411 Mdot .89535 .06409 Mdot .89539 .06406 Mdot .89543 .06404 Mdot .89547 .06401 Mdot .89551 .06399 Mdot .89555 .06397 Mdot .89559 .06394 Mdot .89563 .06392 Mdot .89567 .0639 Mdot .8957 .06387 Mdot .89574 .06385 Mdot .89578 .06383 Mdot .89582 .0638 Mdot .89586 .06378 Mdot .8959 .06375 Mdot .89594 .06373 Mdot .89598 .06371 Mdot .89602 .06368 Mdot .89606 .06366 Mdot .89609 .06363 Mdot .89613 .06361 Mdot .89617 .06359 Mdot .89621 .06357 Mdot .89625 .06354 Mdot .89629 .06352 Mdot .89633 .0635 Mdot .89637 .06347 Mdot .8964 .06345 Mdot .89644 .06342 Mdot .89648 .0634 Mdot .89652 .06338 Mdot .89656 .06336 Mdot .8966 .06333 Mdot .89664 .06331 Mdot .89668 .06328 Mdot .89671 .06326 Mdot .89675 .06324 Mdot .89679 .06322 Mdot .89683 .06319 Mdot .89687 .06317 Mdot .89691 .06315 Mdot .89695 .06312 Mdot .89698 .0631 Mdot .89702 .06308 Mdot .89706 .06305 Mdot .8971 .06303 Mdot .89714 .06301 Mdot .89718 .06298 Mdot .89722 .06296 Mdot .89725 .06294 Mdot .89729 .06291 Mdot .89733 .06289 Mdot .89737 .06287 Mdot .89741 .06285 Mdot .89745 .06282 Mdot .89749 .0628 Mdot .89752 .06278 Mdot .89756 .06275 Mdot .8976 .06273 Mdot .89764 .06271 Mdot .89768 .06268 Mdot .89772 .06266 Mdot .89775 .06264 Mdot .89779 .06261 Mdot .89783 .06259 Mdot .89787 .06257 Mdot .89791 .06254 Mdot .89795 .06252 Mdot .89798 .0625 Mdot .89802 .06247 Mdot .89806 .06245 Mdot .8981 .06243 Mdot .89814 .0624 Mdot .89818 .06238 Mdot .89821 .06236 Mdot .89825 .06233 Mdot .89829 .06231 Mdot .89833 .06229 Mdot .89837 .06227 Mdot .8984 .06224 Mdot .89844 .06222 Mdot .89848 .0622 Mdot .89852 .06217 Mdot .89856 .06215 Mdot .89859 .06213 Mdot .89863 .0621 Mdot .89867 .06208 Mdot .89871 .06206 Mdot .89875 .06203 Mdot .89878 .06201 Mdot .89882 .06199 Mdot .89886 .06196 Mdot .8989 .06194 Mdot .89894 .06192 Mdot .89897 .0619 Mdot .89901 .06187 Mdot .89905 .06185 Mdot .89909 .06183 Mdot .89913 .0618 Mdot .89916 .06179 Mdot .8992 .06176 Mdot .89924 .06174 Mdot .89928 .06172 Mdot .89932 .06169 Mdot .89935 .06167 Mdot .89939 .06165 Mdot .89943 .06163 Mdot .89947 .0616 Mdot .8995 .06158 Mdot .89954 .06156 Mdot .89958 .06153 Mdot .89962 .06151 Mdot .89966 .06149 Mdot .89969 .06147 Mdot .89973 .06144 Mdot .89977 .06142 Mdot .89981 .0614 Mdot .89984 .06137 Mdot .89988 .06135 Mdot .89992 .06133 Mdot .89996 .06131 Mdot .89999 .06128 Mdot .90003 .06126 Mdot .90007 .06124 Mdot .90011 .06121 Mdot .90014 .06119 Mdot .90018 .06117 Mdot .90022 .06115 Mdot .90026 .06112 Mdot .9003 .0611 Mdot .90033 .06108 Mdot .90037 .06105 Mdot .90041 .06103 Mdot .90045 .06101 Mdot .90048 .06099 Mdot .90052 .06096 Mdot .90056 .06094 Mdot .9006 .06092 Mdot .90063 .0609 Mdot .90067 .06087 Mdot .90071 .06085 Mdot .90074 .06083 Mdot .90078 .06081 Mdot .90082 .06079 Mdot .90086 .06076 Mdot .90089 .06074 Mdot .90093 .06072 Mdot .90097 .0607 Mdot .90101 .06067 Mdot .90104 .06065 Mdot .90108 .06063 Mdot .90112 .06061 Mdot .90116 .06058 Mdot .90119 .06056 Mdot .90123 .06054 Mdot .90127 .06051 Mdot .9013 .06049 Mdot .90134 .06047 Mdot .90138 .06045 Mdot .90142 .06042 Mdot .90145 .0604 Mdot .90149 .06038 Mdot .90153 .06035 Mdot .90156 .06033 Mdot .9016 .06031 Mdot .90164 .06028 Mdot .90168 .06026 Mdot .90171 .06024 Mdot .90175 .06022 Mdot .90179 .06019 Mdot .90182 .06017 Mdot .90186 .06015 Mdot .9019 .06013 Mdot .90193 .0601 Mdot .90197 .06008 Mdot .90201 .06006 Mdot .90205 .06004 Mdot .90208 .06002 Mdot .90212 .05999 Mdot .90216 .05997 Mdot .90219 .05995 Mdot .90223 .05992 Mdot .90227 .0599 Mdot .9023 .05988 Mdot .90234 .05986 Mdot .90238 .05983 Mdot .90242 .05981 Mdot .90245 .05979 Mdot .90249 .05977 Mdot .90253 .05974 Mdot .90256 .05972 Mdot .9026 .0597 Mdot .90264 .05968 Mdot .90267 .05965 Mdot .90271 .05963 Mdot .90275 .05961 Mdot .90278 .05959 Mdot .90282 .05956 Mdot .90286 .05954 Mdot .90289 .05952 Mdot .90293 .0595 Mdot .90297 .05948 Mdot .903 .05945 Mdot .90304 .05943 Mdot .90308 .05941 Mdot .90311 .05939 Mdot .90315 .05936 Mdot .90319 .05934 Mdot .90322 .05932 Mdot .90326 .0593 Mdot .9033 .05928 Mdot .90333 .05925 Mdot .90337 .05923 Mdot .90341 .05921 Mdot .90344 .05919 Mdot .90348 .05916 Mdot .90352 .05914 Mdot .90355 .05912 Mdot .90359 .0591 Mdot .90363 .05908 Mdot .90366 .05906 Mdot .9037 .05903 Mdot .90373 .05901 Mdot .90377 .05899 Mdot .90381 .05897 Mdot .90384 .05895 Mdot .90388 .05893 Mdot .90392 .0589 Mdot .90395 .05888 Mdot .90399 .05886 Mdot .90403 .05884 Mdot .90406 .05881 Mdot .9041 .05879 Mdot .90414 .05877 Mdot .90417 .05875 Mdot .90421 .05873 Mdot .90424 .0587 Mdot .90428 .05868 Mdot .90432 .05866 Mdot .90435 .05864 Mdot .90439 .05862 Mdot .90443 .05859 Mdot .90446 .05857 Mdot .9045 .05856 Mdot .90453 .05853 Mdot .90457 .05851 Mdot .90461 .05849 Mdot .90464 .05847 Mdot .90468 .05845 Mdot .90471 .05843 Mdot .90475 .0584 Mdot .90479 .05838 Mdot .90482 .05836 Mdot .90486 .05834 Mdot .9049 .05832 Mdot .90493 .0583 Mdot .90497 .05828 Mdot .905 .05825 Mdot .90504 .05823 Mdot .90508 .05821 Mdot .90511 .05819 Mdot .90515 .05817 Mdot .90518 .05814 Mdot .90522 .05812 Mdot .90526 .0581 Mdot .90529 .05808 Mdot .90533 .05806 Mdot .90536 .05803 Mdot .9054 .05801 Mdot .90544 .05799 Mdot .90547 .05797 Mdot .90551 .05795 Mdot .90554 .05793 Mdot .90558 .0579 Mdot .90562 .05788 Mdot .90565 .05786 Mdot .90569 .05784 Mdot .90572 .05782 Mdot .90576 .0578 Mdot .90579 .05777 Mdot .90583 .05775 Mdot .90587 .05773 Mdot .9059 .05771 Mdot .90594 .05769 Mdot .90597 .05766 Mdot .90601 .05764 Mdot .90605 .05762 Mdot .90608 .0576 Mdot .90612 .05758 Mdot .90615 .05755 Mdot .90619 .05753 Mdot .90622 .05751 Mdot .90626 .05749 Mdot .9063 .05747 Mdot .90633 .05744 Mdot .90637 .05742 Mdot .9064 .0574 Mdot .90644 .05738 Mdot .90647 .05736 Mdot .90651 .05734 Mdot .90654 .05731 Mdot .90658 .05729 Mdot .90662 .05727 Mdot .90665 .05725 Mdot .90669 .05723 Mdot .90672 .05721 Mdot .90676 .05719 Mdot .90679 .05717 Mdot .90683 .05714 Mdot .90686 .05712 Mdot .9069 .0571 Mdot .90694 .05708 Mdot .90697 .05706 Mdot .90701 .05704 Mdot .90704 .05702 Mdot .90708 .05699 Mdot .90711 .05697 Mdot .90715 .05695 Mdot .90718 .05693 Mdot .90722 .05691 Mdot .90725 .05689 Mdot .90729 .05687 Mdot .90733 .05685 Mdot .90736 .05682 Mdot .9074 .0568 Mdot .90743 .05678 Mdot .90747 .05676 Mdot .9075 .05674 Mdot .90754 .05672 Mdot .90757 .0567 Mdot .90761 .05668 Mdot .90764 .05665 Mdot .90768 .05663 Mdot .90771 .05661 Mdot .90775 .05659 Mdot .90778 .05657 Mdot .90782 .05655 Mdot .90785 .05653 Mdot .90789 .05651 Mdot .90793 .05648 Mdot .90796 .05646 Mdot .908 .05644 Mdot .90803 .05642 Mdot .90807 .0564 Mdot .9081 .05638 Mdot .90814 .05636 Mdot .90817 .05634 Mdot .90821 .05632 Mdot .90824 .0563 Mdot .90828 .05628 Mdot .90831 .05626 Mdot .90835 .05623 Mdot .90838 .05621 Mdot .90842 .05619 Mdot .90845 .05617 Mdot .90849 .05615 Mdot .90852 .05613 Mdot .90856 .05611 Mdot .90859 .05609 Mdot .90863 .05606 Mdot .90866 .05604 Mdot .9087 .05602 Mdot .90873 .056 Mdot .90877 .05598 Mdot .9088 .05596 Mdot .90884 .05594 Mdot .90887 .05591 Mdot .90891 .05589 Mdot .90894 .05587 Mdot .90898 .05585 Mdot .90901 .05583 Mdot .90905 .05581 Mdot .90908 .05579 Mdot .90912 .05577 Mdot .90915 .05574 Mdot .90919 .05572 Mdot .90922 .0557 Mdot .90926 .05568 Mdot .90929 .05566 Mdot .90932 .05564 Mdot .90936 .05562 Mdot .90939 .0556 Mdot .90943 .05558 Mdot .90946 .05556 Mdot .9095 .05553 Mdot .90953 .05551 Mdot .90957 .05549 Mdot .9096 .05547 Mdot .90964 .05545 Mdot .90967 .05543 Mdot .90971 .05541 Mdot .90974 .05539 Mdot .90978 .05537 Mdot .90981 .05535 Mdot .90985 .05533 Mdot .90988 .05531 Mdot .90991 .05529 Mdot .90995 .05527 Mdot .90998 .05525 Mdot .91002 .05522 Mdot .91005 .0552 Mdot .91009 .05518 Mdot .91012 .05516 Mdot .91016 .05514 Mdot .91019 .05512 Mdot .91023 .0551 Mdot .91026 .05508 Mdot .91029 .05506 Mdot .91033 .05504 Mdot .91036 .05502 Mdot .9104 .05499 Mdot .91043 .05497 Mdot .91047 .05496 Mdot .9105 .05494 Mdot .91054 .05491 Mdot .91057 .05489 Mdot .9106 .05487 Mdot .91064 .05485 Mdot .91067 .05483 Mdot .91071 .05481 Mdot .91074 .05479 Mdot .91078 .05477 Mdot .91081 .05475 Mdot .91085 .05473 Mdot .91088 .0547 Mdot .91091 .05468 Mdot .91095 .05466 Mdot .91098 .05464 Mdot .91102 .05462 Mdot .91105 .0546 Mdot .91109 .05458 Mdot .91112 .05456 Mdot .91115 .05454 Mdot .91119 .05452 Mdot .91122 .0545 Mdot .91126 .05447 Mdot .91129 .05445 Mdot .91133 .05443 Mdot .91136 .05441 Mdot .91139 .05439 Mdot .91143 .05437 Mdot .91146 .05435 Mdot .9115 .05433 Mdot .91153 .05431 Mdot .91156 .05429 Mdot .9116 .05427 Mdot .91163 .05425 Mdot .91167 .05423 Mdot .9117 .05421 Mdot .91173 .05419 Mdot .91177 .05417 Mdot .9118 .05415 Mdot .91184 .05413 Mdot .91187 .05411 Mdot .91191 .05408 Mdot .91194 .05407 Mdot .91197 .05405 Mdot .91201 .05403 Mdot .91204 .05401 Mdot .91208 .05398 Mdot .91211 .05396 Mdot .91214 .05394 Mdot .91218 .05392 Mdot .91221 .0539 Mdot .91225 .05388 Mdot .91228 .05386 Mdot .91231 .05384 Mdot .91235 .05382 Mdot .91238 .0538 Mdot .91241 .05378 Mdot .91245 .05376 Mdot .91248 .05374 Mdot .91252 .05372 Mdot .91255 .0537 Mdot .91258 .05368 Mdot .91262 .05366 Mdot .91265 .05364 Mdot .91269 .05361 Mdot .91272 .05359 Mdot .91275 .05358 Mdot .91279 .05355 Mdot .91282 .05353 Mdot .91285 .05351 Mdot .91289 .05349 Mdot .91292 .05347 Mdot .91296 .05345 Mdot .91299 .05343 Mdot .91302 .05341 Mdot .91306 .05339 Mdot .91309 .05337 Mdot .91312 .05335 Mdot .91316 .05333 Mdot .91319 .05331 Mdot .91323 .05329 Mdot .91326 .05327 Mdot .91329 .05325 Mdot .91333 .05323 Mdot .91336 .05321 Mdot .91339 .05319 Mdot .91343 .05316 Mdot .91346 .05315 Mdot .91349 .05313 Mdot .91353 .05311 Mdot .91356 .05308 Mdot .91359 .05306 Mdot .91363 .05304 Mdot .91366 .05302 Mdot .9137 .053 Mdot .91373 .05298 Mdot .91376 .05296 Mdot .9138 .05294 Mdot .91383 .05292 Mdot .91386 .0529 Mdot .9139 .05288 Mdot .91393 .05286 Mdot .91396 .05284 Mdot .914 .05282 Mdot .91403 .0528 Mdot .91406 .05278 Mdot .9141 .05276 Mdot .91413 .05274 Mdot .91416 .05272 Mdot .9142 .0527 Mdot .91423 .05268 Mdot .91426 .05266 Mdot .9143 .05264 Mdot .91433 .05262 Mdot .91436 .0526 Mdot .9144 .05258 Mdot .91443 .05256 Mdot .91446 .05254 Mdot .9145 .05252 Mdot .91453 .0525 Mdot .91456 .05248 Mdot .9146 .05246 Mdot .91463 .05244 Mdot .91466 .05242 Mdot .9147 .0524 Mdot .91473 .05238 Mdot .91476 .05236 Mdot .9148 .05234 Mdot .91483 .05232 Mdot .91486 .0523 Mdot .9149 .05228 Mdot .91493 .05226 Mdot .91496 .05224 Mdot .915 .05222 Mdot .91503 .0522 Mdot .91506 .05218 Mdot .9151 .05216 Mdot .91513 .05214 Mdot .91516 .05212 Mdot .91519 .0521 Mdot .91523 .05208 Mdot .91526 .05206 Mdot .91529 .05204 Mdot .91533 .05202 Mdot .91536 .052 Mdot .91539 .05198 Mdot .91543 .05196 Mdot .91546 .05194 Mdot .91549 .05192 Mdot .91553 .0519 Mdot .91556 .05188 Mdot .91559 .05186 Mdot .91562 .05183 Mdot .91566 .05181 Mdot .91569 .0518 Mdot .91572 .05178 Mdot .91576 .05176 Mdot .91579 .05174 Mdot .91582 .05172 Mdot .91586 .0517 Mdot .91589 .05168 Mdot .91592 .05166 Mdot .91595 .05163 Mdot .91599 .05161 Mdot .91602 .05159 Mdot .91605 .05157 Mdot .91609 .05155 Mdot .91612 .05153 Mdot .91615 .05151 Mdot .91618 .05149 Mdot .91622 .05147 Mdot .91625 .05145 Mdot .91628 .05143 Mdot .91632 .05141 Mdot .91635 .05139 Mdot .91638 .05137 Mdot .91641 .05135 Mdot .91645 .05133 Mdot .91648 .05131 Mdot .91651 .0513 Mdot .91654 .05128 Mdot .91658 .05126 Mdot .91661 .05124 Mdot .91664 .05122 Mdot .91668 .0512 Mdot .91671 .05118 Mdot .91674 .05116 Mdot .91677 .05114 Mdot .91681 .05112 Mdot .91684 .0511 Mdot .91687 .05108 Mdot .9169 .05106 Mdot .91694 .05104 Mdot .91697 .05102 Mdot .917 .051 Mdot .91703 .05098 Mdot .91707 .05096 Mdot .9171 .05094 Mdot .91713 .05092 Mdot .91716 .0509 Mdot .9172 .05088 Mdot .91723 .05086 Mdot .91726 .05084 Mdot .91729 .05082 Mdot .91733 .05081 Mdot .91736 .05079 Mdot .91739 .05077 Mdot .91742 .05075 Mdot .91746 .05073 Mdot .91749 .05071 Mdot .91752 .05069 Mdot .91755 .05067 Mdot .91759 .05065 Mdot .91762 .05063 Mdot .91765 .05061 Mdot .91768 .05059 Mdot .91772 .05057 Mdot .91775 .05055 Mdot .91778 .05053 Mdot .91781 .05051 Mdot .91785 .05049 Mdot .91788 .05047 Mdot .91791 .05045 Mdot .91794 .05043 Mdot .91798 .05042 Mdot .91801 .0504 Mdot .91804 .05038 Mdot .91807 .05036 Mdot .91811 .05034 Mdot .91814 .05032 Mdot .91817 .0503 Mdot .9182 .05028 Mdot .91823 .05026 Mdot .91827 .05025 Mdot .9183 .05022 Mdot .91833 .0502 Mdot .91836 .05019 Mdot .9184 .05017 Mdot .91843 .05015 Mdot .91846 .05013 Mdot .91849 .05011 Mdot .91852 .05009 Mdot .91856 .05007 Mdot .91859 .05005 Mdot .91862 .05003 Mdot .91865 .05001 Mdot .91869 .04999 Mdot .91872 .04998 Mdot .91875 .04996 Mdot .91878 .04994 Mdot .91881 .04992 Mdot .91885 .0499 Mdot .91888 .04988 Mdot .91891 .04986 Mdot .91894 .04984 Mdot .91897 .04982 Mdot .91901 .04981 Mdot .91904 .04979 Mdot .91907 .04977 Mdot .9191 .04975 Mdot .91913 .04973 Mdot .91917 .04971 Mdot .9192 .04969 Mdot .91923 .04967 Mdot .91926 .04965 Mdot .91929 .04963 Mdot .91933 .04961 Mdot .91936 .04959 Mdot .91939 .04957 Mdot .91942 .04955 Mdot .91945 .04953 Mdot .91949 .04951 Mdot .91952 .04949 Mdot .91955 .04947 Mdot .91958 .04945 Mdot .91961 .04943 Mdot .91965 .04941 Mdot .91968 .04939 Mdot .91971 .04938 Mdot .91974 .04936 Mdot .91977 .04934 Mdot .91981 .04932 Mdot .91984 .0493 Mdot .91987 .04928 Mdot .9199 .04926 Mdot .91993 .04924 Mdot .91996 .04922 Mdot .92 .0492 Mdot .92003 .04919 Mdot .92006 .04917 Mdot .92009 .04915 Mdot .92012 .04913 Mdot .92016 .04911 Mdot .92019 .04909 Mdot .92022 .04907 Mdot .92025 .04905 Mdot .92028 .04903 Mdot .92031 .04901 Mdot .92035 .04899 Mdot .92038 .04898 Mdot .92041 .04896 Mdot .92044 .04894 Mdot .92047 .04892 Mdot .9205 .0489 Mdot .92054 .04888 Mdot .92057 .04886 Mdot .9206 .04884 Mdot .92063 .04882 Mdot .92066 .04881 Mdot .92069 .04879 Mdot .92073 .04877 Mdot .92076 .04875 Mdot .92079 .04873 Mdot .92082 .04872 Mdot .92085 .0487 Mdot .92088 .04868 Mdot .92091 .04866 Mdot .92095 .04864 Mdot .92098 .04862 Mdot .92101 .0486 Mdot .92104 .04858 Mdot .92107 .04856 Mdot .9211 .04854 Mdot .92114 .04852 Mdot .92117 .04851 Mdot .9212 .04849 Mdot .92123 .04847 Mdot .92126 .04845 Mdot .92129 .04843 Mdot .92132 .04841 Mdot .92136 .04839 Mdot .92139 .04837 Mdot .92142 .04835 Mdot .92145 .04834 Mdot .92148 .04832 Mdot .92151 .0483 Mdot .92154 .04828 Mdot .92158 .04826 Mdot .92161 .04824 Mdot .92164 .04822 Mdot .92167 .0482 Mdot .9217 .04818 Mdot .92173 .04817 Mdot .92176 .04815 Mdot .9218 .04813 Mdot .92183 .04811 Mdot .92186 .04809 Mdot .92189 .04807 Mdot .92192 .04805 Mdot .92195 .04804 Mdot .92198 .04802 Mdot .92201 .048 Mdot .92205 .04798 Mdot .92208 .04796 Mdot .92211 .04794 Mdot .92214 .04792 Mdot .92217 .0479 Mdot .9222 .04789 Mdot .92223 .04787 Mdot .92226 .04785 Mdot .9223 .04783 Mdot .92233 .04781 Mdot .92236 .04779 Mdot .92239 .04777 Mdot .92242 .04775 Mdot .92245 .04774 Mdot .92248 .04772 Mdot .92251 .0477 Mdot .92254 .04768 Mdot .92258 .04766 Mdot .92261 .04764 Mdot .92264 .04762 Mdot .92267 .04761 Mdot .9227 .04759 Mdot .92273 .04757 Mdot .92276 .04755 Mdot .92279 .04753 Mdot .92282 .04751 Mdot .92286 .04749 Mdot .92289 .04747 Mdot .92292 .04746 Mdot .92295 .04744 Mdot .92298 .04742 Mdot .92301 .0474 Mdot .92304 .04738 Mdot .92307 .04737 Mdot .9231 .04735 Mdot .92313 .04733 Mdot .92317 .04731 Mdot .9232 .04729 Mdot .92323 .04727 Mdot .92326 .04725 Mdot .92329 .04723 Mdot .92332 .04722 Mdot .92335 .0472 Mdot .92338 .04718 Mdot .92341 .04716 Mdot .92344 .04714 Mdot .92347 .04712 Mdot .92351 .0471 Mdot .92354 .04709 Mdot .92357 .04707 Mdot .9236 .04705 Mdot .92363 .04703 Mdot .92366 .04701 Mdot .92369 .04699 Mdot .92372 .04697 Mdot .92375 .04695 Mdot .92378 .04693 Mdot .92381 .04692 Mdot .92384 .0469 Mdot .92388 .04688 Mdot .92391 .04686 Mdot .92394 .04684 Mdot .92397 .04682 Mdot .924 .0468 Mdot .92403 .04679 Mdot .92406 .04677 Mdot .92409 .04675 Mdot .92412 .04673 Mdot .92415 .04671 Mdot .92418 .04669 Mdot .92421 .04668 Mdot .92424 .04666 Mdot .92427 .04664 Mdot .92431 .04662 Mdot .92434 .0466 Mdot .92437 .04658 Mdot .9244 .04656 Mdot .92443 .04655 Mdot .92446 .04653 Mdot .92449 .04651 Mdot .92452 .04649 Mdot .92455 .04647 Mdot .92458 .04645 Mdot .92461 .04643 Mdot .92464 .04641 Mdot .92467 .0464 Mdot .9247 .04638 Mdot .92473 .04636 Mdot .92476 .04634 Mdot .92479 .04632 Mdot .92483 .04631 Mdot .92486 .04629 Mdot .92489 .04627 Mdot .92492 .04625 Mdot .92495 .04623 Mdot .92498 .04621 Mdot .92501 .04619 Mdot .92504 .04618 Mdot .92507 .04616 Mdot .9251 .04614 Mdot .92513 .04613 Mdot .92516 .04611 Mdot .92519 .0461 Mdot .92522 .04608 Mdot .92525 .04606 Mdot .92528 .04604 Mdot .92531 .04602 Mdot .92534 .046 Mdot .92537 .04598 Mdot .9254 .04596 Mdot .92543 .04595 Mdot .92546 .04593 Mdot .9255 .04591 Mdot .92553 .04589 Mdot .92556 .04588 Mdot .92559 .04586 Mdot .92562 .04584 Mdot .92565 .04582 Mdot .92568 .0458 Mdot .92571 .04578 Mdot .92574 .04577 Mdot .92577 .04575 Mdot .9258 .04573 Mdot .92583 .04571 Mdot .92586 .04569 Mdot .92589 .04567 Mdot .92592 .04566 Mdot .92595 .04564 Mdot .92598 .04562 Mdot .92601 .0456 Mdot .92604 .04558 Mdot .92607 .04557 Mdot .9261 .04555 Mdot .92613 .04553 Mdot .92616 .04551 Mdot .92619 .04549 Mdot .92622 .04548 Mdot .92625 .04546 Mdot .92628 .04544 Mdot .92631 .04542 Mdot .92634 .0454 Mdot .92637 .04539 Mdot .9264 .04537 Mdot .92643 .04535 Mdot .92646 .04533 Mdot .92649 .04531 Mdot .92652 .04529 Mdot .92655 .04528 Mdot .92658 .04526 Mdot .92661 .04524 Mdot .92664 .04522 Mdot .92667 .0452 Mdot .9267 .04518 Mdot .92673 .04517 Mdot .92676 .04515 Mdot .92679 .04513 Mdot .92682 .04511 Mdot .92685 .04509 Mdot .92688 .04507 Mdot .92691 .04506 Mdot .92694 .04504 Mdot .92697 .04502 Mdot .927 .045 Mdot .92703 .04498 Mdot .92706 .04496 Mdot .92709 .04495 Mdot .92712 .04493 Mdot .92715 .04491 Mdot .92718 .04489 Mdot .92721 .04488 Mdot .92724 .04486 Mdot .92727 .04484 Mdot .9273 .04482 Mdot .92733 .0448 Mdot .92736 .04479 Mdot .92739 .04477 Mdot .92742 .04475 Mdot .92745 .04473 Mdot .92748 .04471 Mdot .92751 .04469 Mdot .92754 .04468 Mdot .92757 .04466 Mdot .9276 .04464 Mdot .92763 .04462 Mdot .92766 .04461 Mdot .92769 .04459 Mdot .92772 .04457 Mdot .92775 .04455 Mdot .92778 .04454 Mdot .92781 .04452 Mdot .92784 .0445 Mdot .92787 .04448 Mdot .9279 .04446 Mdot .92793 .04445 Mdot .92796 .04443 Mdot .92799 .04441 Mdot .92802 .04439 Mdot .92805 .04437 Mdot .92808 .04436 Mdot .92811 .04434 Mdot .92814 .04432 Mdot .92817 .0443 Mdot .9282 .04428 Mdot .92823 .04427 Mdot .92826 .04425 Mdot .92829 .04423 Mdot .92832 .04421 Mdot .92835 .0442 Mdot .92837 .04418 Mdot .9284 .04416 Mdot .92843 .04414 Mdot .92846 .04412 Mdot .92849 .0441 Mdot .92852 .04409 Mdot .92855 .04407 Mdot .92858 .04405 Mdot .92861 .04403 Mdot .92864 .04401 Mdot .92867 .044 Mdot .9287 .04398 Mdot .92873 .04396 Mdot .92876 .04394 Mdot .92879 .04393 Mdot .92882 .04391 Mdot .92885 .04389 Mdot .92888 .04387 Mdot .92891 .04386 Mdot .92894 .04384 Mdot .92897 .04382 Mdot .929 .0438 Mdot .92902 .04378 Mdot .92905 .04377 Mdot .92908 .04375 Mdot .92911 .04373 Mdot .92914 .04371 Mdot .92917 .0437 Mdot .9292 .04368 Mdot .92923 .04366 Mdot .92926 .04364 Mdot .92929 .04362 Mdot .92932 .04361 Mdot .92935 .04359 Mdot .92938 .04357 Mdot .92941 .04355 Mdot .92944 .04354 Mdot .92947 .04352 Mdot .9295 .0435 Mdot .92952 .04348 Mdot .92955 .04347 Mdot .92958 .04345 Mdot .92961 .04343 Mdot .92964 .04341 Mdot .92967 .0434 Mdot .9297 .04338 Mdot .92973 .04336 Mdot .92976 .04334 Mdot .92979 .04333 Mdot .92982 .04331 Mdot .92985 .04329 Mdot .92988 .04327 Mdot .92991 .04326 Mdot .92994 .04324 Mdot .92996 .04322 Mdot .92999 .0432 Mdot .93002 .04319 Mdot .93005 .04317 Mdot .93008 .04315 Mdot .93011 .04313 Mdot .93014 .04312 Mdot .93017 .0431 Mdot .9302 .04308 Mdot .93023 .04307 Mdot .93026 .04305 Mdot .93029 .04303 Mdot .93031 .04301 Mdot .93034 .043 Mdot .93037 .04298 Mdot .9304 .04296 Mdot .93043 .04294 Mdot .93046 .04292 Mdot .93049 .04291 Mdot .93052 .04289 Mdot .93055 .04287 Mdot .93058 .04285 Mdot .93061 .04284 Mdot .93064 .04282 Mdot .93066 .0428 Mdot .93069 .04279 Mdot .93072 .04277 Mdot .93075 .04275 Mdot .93078 .04273 Mdot .93081 .04272 Mdot .93084 .0427 Mdot .93087 .04268 Mdot .9309 .04266 Mdot .93093 .04264 Mdot .93095 .04263 Mdot .93098 .04261 Mdot .93101 .04259 Mdot .93104 .04257 Mdot .93107 .04256 Mdot .9311 .04254 Mdot .93113 .04252 Mdot .93116 .04251 Mdot .93119 .04249 Mdot .93122 .04247 Mdot .93124 .04245 Mdot .93127 .04244 Mdot .9313 .04242 Mdot .93133 .0424 Mdot .93136 .04239 Mdot .93139 .04237 Mdot .93142 .04235 Mdot .93145 .04233 Mdot .93148 .04232 Mdot .9315 .0423 Mdot .93153 .04228 Mdot .93156 .04227 Mdot .93159 .04225 Mdot .93162 .04223 Mdot .93165 .04221 Mdot .93168 .04219 Mdot .93171 .04218 Mdot .93173 .04216 Mdot .93176 .04214 Mdot .93179 .04213 Mdot .93182 .04211 Mdot .93185 .04209 Mdot .93188 .04207 Mdot .93191 .04206 Mdot .93194 .04204 Mdot .93197 .04202 Mdot .93199 .042 Mdot .93202 .04199 Mdot .93205 .04197 Mdot .93208 .04195 Mdot .93211 .04193 Mdot .93214 .04192 Mdot .93217 .0419 Mdot .93219 .04189 Mdot .93222 .04187 Mdot .93225 .04185 Mdot .93228 .04183 Mdot .93231 .04182 Mdot .93234 .0418 Mdot .93237 .04178 Mdot .9324 .04176 Mdot .93242 .04175 Mdot .93245 .04173 Mdot .93248 .04171 Mdot .93251 .0417 Mdot .93254 .04168 Mdot .93257 .04166 Mdot .9326 .04164 Mdot .93262 .04163 Mdot .93265 .04161 Mdot .93268 .04159 Mdot .93271 .04158 Mdot .93274 .04156 Mdot .93277 .04154 Mdot .9328 .04153 Mdot .93282 .04151 Mdot .93285 .04149 Mdot .93288 .04147 Mdot .93291 .04146 Mdot .93294 .04144 Mdot .93297 .04142 Mdot .933 .0414 Mdot .93302 .04139 Mdot .93305 .04137 Mdot .93308 .04135 Mdot .93311 .04134 Mdot .93314 .04132 Mdot .93317 .0413 Mdot .9332 .04128 Mdot .93322 .04127 Mdot .93325 .04125 Mdot .93328 .04124 Mdot .93331 .04122 Mdot .93334 .0412 Mdot .93337 .04118 Mdot .93339 .04117 Mdot .93342 .04115 Mdot .93345 .04113 Mdot .93348 .04112 Mdot .93351 .0411 Mdot .93354 .04108 Mdot .93356 .04106 Mdot .93359 .04105 Mdot .93362 .04103 Mdot .93365 .04101 Mdot .93368 .041 Mdot .93371 .04098 Mdot .93373 .04097 Mdot .93376 .04095 Mdot .93379 .04093 Mdot .93382 .04091 Mdot .93385 .0409 Mdot .93388 .04088 Mdot .9339 .04086 Mdot .93393 .04085 Mdot .93396 .04083 Mdot .93399 .04081 Mdot .93402 .0408 Mdot .93405 .04078 Mdot .93407 .04076 Mdot .9341 .04075 Mdot .93413 .04073 Mdot .93416 .04071 Mdot .93419 .0407 Mdot .93422 .04068 Mdot .93424 .04066 Mdot .93427 .04064 Mdot .9343 .04063 Mdot .93433 .04061 Mdot .93436 .04059 Mdot .93438 .04058 Mdot .93441 .04056 Mdot .93444 .04055 Mdot .93447 .04053 Mdot .9345 .04051 Mdot .93453 .04049 Mdot .93455 .04048 Mdot .93458 .04046 Mdot .93461 .04044 Mdot .93464 .04043 Mdot .93467 .04041 Mdot .93469 .04039 Mdot .93472 .04038 Mdot .93475 .04036 Mdot .93478 .04034 Mdot .93481 .04033 Mdot .93483 .04031 Mdot .93486 .04029 Mdot .93489 .04028 Mdot .93492 .04026 Mdot .93495 .04024 Mdot .93497 .04023 Mdot .935 .04021 Mdot .93503 .04019 Mdot .93506 .04017 Mdot .93509 .04016 Mdot .93511 .04014 Mdot .93514 .04012 Mdot .93517 .04011 Mdot .9352 .04009 Mdot .93523 .04007 Mdot .93525 .04005 Mdot .93528 .04004 Mdot .93531 .04002 Mdot .93534 .04001 Mdot .93537 .03999 Mdot .93539 .03997 Mdot .93542 .03996 Mdot .93545 .03994 Mdot .93548 .03992 Mdot .93551 .0399 Mdot .93553 .03989 Mdot .93556 .03987 Mdot .93559 .03985 Mdot .93562 .03984 Mdot .93565 .03982 Mdot .93567 .0398 Mdot .9357 .03979 Mdot .93573 .03977 Mdot .93576 .03975 Mdot .93578 .03973 Mdot .93581 .03972 Mdot .93584 .0397 Mdot .93587 .03968 Mdot .9359 .03967 Mdot .93592 .03965 Mdot .93595 .03963 Mdot .93598 .03962 Mdot .93601 .0396 Mdot .93604 .03958 Mdot .93606 .03957 Mdot .93609 .03955 Mdot .93612 .03953 Mdot .93615 .03952 Mdot .93617 .0395 Mdot .9362 .03948 Mdot .93623 .03947 Mdot .93626 .03945 Mdot .93629 .03943 Mdot .93631 .03942 Mdot .93634 .0394 Mdot .93637 .03939 Mdot .9364 .03937 Mdot .93642 .03935 Mdot .93645 .03934 Mdot .93648 .03932 Mdot .93651 .0393 Mdot .93653 .03929 Mdot .93656 .03927 Mdot .93659 .03925 Mdot .93662 .03923 Mdot .93664 .03922 Mdot .93667 .0392 Mdot .9367 .03919 Mdot .93673 .03917 Mdot .93676 .03915 Mdot .93678 .03914 Mdot .93681 .03912 Mdot .93684 .0391 Mdot .93687 .03909 Mdot .93689 .03907 Mdot .93692 .03906 Mdot .93695 .03904 Mdot .93698 .03902 Mdot .937 .03901 Mdot .93703 .03899 Mdot .93706 .03897 Mdot .93709 .03896 Mdot .93711 .03894 Mdot .93714 .03892 Mdot .93717 .03891 Mdot .9372 .03889 Mdot .93722 .03888 Mdot .93725 .03886 Mdot .93728 .03884 Mdot .93731 .03883 Mdot .93733 .03881 Mdot .93736 .03879 Mdot .93739 .03878 Mdot .93742 .03876 Mdot .93744 .03874 Mdot .93747 .03872 Mdot .9375 .03871 Mdot .93753 .03869 Mdot .93755 .03867 Mdot .93758 .03866 Mdot .93761 .03864 Mdot .93764 .03862 Mdot .93766 .03861 Mdot .93769 .03859 Mdot .93772 .03857 Mdot .93775 .03856 Mdot .93777 .03854 Mdot .9378 .03852 Mdot .93783 .03851 Mdot .93786 .03849 Mdot .93788 .03847 Mdot .93791 .03846 Mdot .93794 .03844 Mdot .93796 .03842 Mdot .93799 .03841 Mdot .93802 .03839 Mdot .93805 .03837 Mdot .93807 .03836 Mdot .9381 .03834 Mdot .93813 .03832 Mdot .93816 .03831 Mdot .93818 .03829 Mdot .93821 .03828 Mdot .93824 .03826 Mdot .93826 .03824 Mdot .93829 .03823 Mdot .93832 .03821 Mdot .93835 .03819 Mdot .93837 .03818 Mdot .9384 .03816 Mdot .93843 .03814 Mdot .93846 .03813 Mdot .93848 .03811 Mdot .93851 .0381 Mdot .93854 .03808 Mdot .93856 .03806 Mdot .93859 .03805 Mdot .93862 .03803 Mdot .93865 .03802 Mdot .93867 .038 Mdot .9387 .03798 Mdot .93873 .03797 Mdot .93875 .03795 Mdot .93878 .03793 Mdot .93881 .03792 Mdot .93884 .0379 Mdot .93886 .03789 Mdot .93889 .03787 Mdot .93892 .03785 Mdot .93894 .03784 Mdot .93897 .03782 Mdot .939 .03781 Mdot .93903 .03779 Mdot .93905 .03777 Mdot .93908 .03776 Mdot .93911 .03774 Mdot .93913 .03773 Mdot .93916 .03771 Mdot .93919 .0377 Mdot .93922 .03768 Mdot .93924 .03767 Mdot .93927 .03766 Mdot .9393 .03764 Mdot .93932 .03762 Mdot .93935 .03761 Mdot .93938 .03759 Mdot .9394 .03757 Mdot .93943 .03756 Mdot .93946 .03754 Mdot .93949 .03752 Mdot .93951 .03751 Mdot .93954 .03749 Mdot .93957 .03748 Mdot .93959 .03746 Mdot .93962 .03744 Mdot .93965 .03743 Mdot .93967 .03741 Mdot .9397 .0374 Mdot .93973 .03738 Mdot .93976 .03736 Mdot .93978 .03735 Mdot .93981 .03733 Mdot .93984 .03731 Mdot .93986 .0373 Mdot .93989 .03728 Mdot .93992 .03727 Mdot .93994 .03725 Mdot .93997 .03723 Mdot .94 .03722 Mdot .94002 .0372 Mdot .94005 .03718 Mdot .94008 .03717 Mdot .9401 .03715 Mdot .94013 .03713 Mdot .94016 .03712 Mdot .94019 .0371 Mdot .94021 .03709 Mdot .94024 .03707 Mdot .94027 .03705 Mdot .94029 .03704 Mdot .94032 .03702 Mdot .94035 .03701 Mdot .94037 .03699 Mdot .9404 .03698 Mdot .94043 .03696 Mdot .94045 .03694 Mdot .94048 .03693 Mdot .94051 .03691 Mdot .94053 .03689 Mdot .94056 .03688 Mdot .94059 .03686 Mdot .94061 .03685 Mdot .94064 .03683 Mdot .94067 .03681 Mdot .94069 .0368 Mdot .94072 .03678 Mdot .94075 .03677 Mdot .94077 .03675 Mdot .9408 .03674 Mdot .94083 .03672 Mdot .94085 .03671 Mdot .94088 .03669 Mdot .94091 .03668 Mdot .94093 .03666 Mdot .94096 .03664 Mdot .94099 .03663 Mdot .94101 .03661 Mdot .94104 .0366 Mdot .94107 .03658 Mdot .94109 .03656 Mdot .94112 .03655 Mdot .94115 .03653 Mdot .94117 .03652 Mdot .9412 .0365 Mdot .94123 .03648 Mdot .94125 .03647 Mdot .94128 .03645 Mdot .94131 .03643 Mdot .94133 .03642 Mdot .94136 .0364 Mdot .94139 .03639 Mdot .94141 .03637 Mdot .94144 .03636 Mdot .94147 .03634 Mdot .94149 .03633 Mdot .94152 .03631 Mdot .94155 .03629 Mdot .94157 .03628 Mdot .9416 .03626 Mdot .94163 .03625 Mdot .94165 .03623 Mdot .94168 .03621 Mdot .94171 .0362 Mdot .94173 .03618 Mdot .94176 .03617 Mdot .94178 .03615 Mdot .94181 .03614 Mdot .94184 .03612 Mdot .94186 .03611 Mdot .94189 .03609 Mdot .94192 .03608 Mdot .94194 .03606 Mdot .94197 .03605 Mdot .942 .03603 Mdot .94202 .03602 Mdot .94205 .036 Mdot .94208 .03598 Mdot .9421 .03597 Mdot .94213 .03595 Mdot .94215 .03594 Mdot .94218 .03592 Mdot .94221 .0359 Mdot .94223 .03589 Mdot .94226 .03587 Mdot .94229 .03586 Mdot .94231 .03584 Mdot .94234 .03582 Mdot .94237 .03581 Mdot .94239 .03579 Mdot .94242 .03578 Mdot .94244 .03576 Mdot .94247 .03574 Mdot .9425 .03573 Mdot .94252 .03571 Mdot .94255 .0357 Mdot .94258 .03568 Mdot .9426 .03566 Mdot .94263 .03565 Mdot .94266 .03563 Mdot .94268 .03562 Mdot .94271 .0356 Mdot .94273 .03559 Mdot .94276 .03557 Mdot .94279 .03556 Mdot .94281 .03554 Mdot .94284 .03552 Mdot .94287 .03551 Mdot .94289 .03549 Mdot .94292 .03548 Mdot .94294 .03546 Mdot .94297 .03544 Mdot .943 .03543 Mdot .94302 .03541 Mdot .94305 .0354 Mdot .94307 .03538 Mdot .9431 .03537 Mdot .94313 .03535 Mdot .94315 .03533 Mdot .94318 .03532 Mdot .94321 .0353 Mdot .94323 .03529 Mdot .94326 .03527 Mdot .94328 .03526 Mdot .94331 .03524 Mdot .94334 .03522 Mdot .94336 .03521 Mdot .94339 .03519 Mdot .94341 .03518 Mdot .94344 .03516 Mdot .94347 .03515 Mdot .94349 .03513 Mdot .94352 .03511 Mdot .94355 .0351 Mdot .94357 .03508 Mdot .9436 .03507 Mdot .94362 .03505 Mdot .94365 .03504 Mdot .94368 .03502 Mdot .9437 .03501 Mdot .94373 .03499 Mdot .94375 .03497 Mdot .94378 .03496 Mdot .94381 .03494 Mdot .94383 .03493 Mdot .94386 .03491 Mdot .94388 .0349 Mdot .94391 .03488 Mdot .94394 .03487 Mdot .94396 .03485 Mdot .94399 .03483 Mdot .94401 .03482 Mdot .94404 .0348 Mdot .94407 .03479 Mdot .94409 .03477 Mdot .94412 .03476 Mdot .94414 .03474 Mdot .94417 .03473 Mdot .9442 .03471 Mdot .94422 .0347 Mdot .94425 .03468 Mdot .94427 .03467 Mdot .9443 .03465 Mdot .94433 .03464 Mdot .94435 .03462 Mdot .94438 .0346 Mdot .9444 .03459 Mdot .94443 .03457 Mdot .94445 .03456 Mdot .94448 .03454 Mdot .94451 .03453 Mdot .94453 .03451 Mdot .94456 .03449 Mdot .94458 .03448 Mdot .94461 .03446 Mdot .94464 .03445 Mdot .94466 .03443 Mdot .94469 .03442 Mdot .94471 .0344 Mdot .94474 .03439 Mdot .94477 .03437 Mdot .94479 .03436 Mdot .94482 .03434 Mdot .94484 .03432 Mdot .94487 .03431 Mdot .94489 .03429 Mdot .94492 .03428 Mdot .94495 .03426 Mdot .94497 .03425 Mdot .945 .03423 Mdot .94502 .03422 Mdot .94505 .0342 Mdot .94507 .03419 Mdot .9451 .03417 Mdot .94513 .03415 Mdot .94515 .03414 Mdot .94518 .03412 Mdot .9452 .03411 Mdot .94523 .03409 Mdot .94525 .03408 Mdot .94528 .03406 Mdot .94531 .03405 Mdot .94533 .03403 Mdot .94536 .03401 Mdot .94538 .034 Mdot .94541 .03398 Mdot .94543 .03397 Mdot .94546 .03395 Mdot .94549 .03394 Mdot .94551 .03392 Mdot .94554 .0339 Mdot .94556 .03389 Mdot .94559 .03388 Mdot .94561 .03386 Mdot .94564 .03384 Mdot .94567 .03383 Mdot .94569 .03381 Mdot .94572 .0338 Mdot .94574 .03378 Mdot .94577 .03377 Mdot .94579 .03375 Mdot .94582 .03374 Mdot .94584 .03372 Mdot .94587 .0337 Mdot .9459 .03369 Mdot .94592 .03367 Mdot .94595 .03366 Mdot .94597 .03364 Mdot .946 .03363 Mdot .94602 .03361 Mdot .94605 .0336 Mdot .94607 .03358 Mdot .9461 .03357 Mdot .94613 .03355 Mdot .94615 .03353 Mdot .94618 .03352 Mdot .9462 .0335 Mdot .94623 .03349 Mdot .94625 .03347 Mdot .94628 .03346 Mdot .9463 .03344 Mdot .94633 .03343 Mdot .94636 .03341 Mdot .94638 .0334 Mdot .94641 .03338 Mdot .94643 .03337 Mdot .94646 .03335 Mdot .94648 .03334 Mdot .94651 .03332 Mdot .94653 .03331 Mdot .94656 .03329 Mdot .94658 .03328 Mdot .94661 .03326 Mdot .94664 .03325 Mdot .94666 .03323 Mdot .94669 .03321 Mdot .94671 .0332 Mdot .94674 .03318 Mdot .94676 .03317 Mdot .94679 .03315 Mdot .94681 .03314 Mdot .94684 .03312 Mdot .94686 .03311 Mdot .94689 .03309 Mdot .94691 .03308 Mdot .94694 .03306 Mdot .94697 .03304 Mdot .94699 .03303 Mdot .94702 .03301 Mdot .94704 .033 Mdot .94707 .03298 Mdot .94709 .03297 Mdot .94712 .03295 Mdot .94714 .03294 Mdot .94717 .03292 Mdot .94719 .03291 Mdot .94722 .03289 Mdot .94724 .03288 Mdot .94727 .03286 Mdot .94729 .03285 Mdot .94732 .03283 Mdot .94734 .03281 Mdot .94737 .0328 Mdot .9474 .03278 Mdot .94742 .03277 Mdot .94745 .03275 Mdot .94747 .03274 Mdot .9475 .03272 Mdot .94752 .03271 Mdot .94755 .03269 Mdot .94757 .03268 Mdot .9476 .03266 Mdot .94762 .03265 Mdot .94765 .03263 Mdot .94767 .03262 Mdot .9477 .0326 Mdot .94772 .03259 Mdot .94775 .03257 Mdot .94777 .03255 Mdot .9478 .03254 Mdot .94782 .03253 Mdot .94785 .03251 Mdot .94787 .0325 Mdot .9479 .03248 Mdot .94792 .03247 Mdot .94795 .03245 Mdot .94797 .03243 Mdot .948 .03242 Mdot .94803 .0324 Mdot .94805 .03239 Mdot .94808 .03237 Mdot .9481 .03236 Mdot .94813 .03235 Mdot .94815 .03233 Mdot .94818 .03231 Mdot .9482 .0323 Mdot .94823 .03228 Mdot .94825 .03227 Mdot .94828 .03226 Mdot .9483 .03224 Mdot .94833 .03223 Mdot .94835 .03221 Mdot .94838 .0322 Mdot .9484 .03218 Mdot .94843 .03217 Mdot .94845 .03215 Mdot .94848 .03214 Mdot .9485 .03212 Mdot .94853 .03211 Mdot .94855 .03209 Mdot .94858 .03208 Mdot .9486 .03206 Mdot .94863 .03205 Mdot .94865 .03203 Mdot .94868 .03202 Mdot .9487 .032 Mdot .94873 .03199 Mdot .94875 .03197 Mdot .94878 .03196 Mdot .9488 .03194 Mdot .94883 .03193 Mdot .94885 .03191 Mdot .94888 .0319 Mdot .9489 .03188 Mdot .94893 .03187 Mdot .94895 .03185 Mdot .94898 .03184 Mdot .949 .03182 Mdot .94903 .03181 Mdot .94905 .03179 Mdot .94908 .03177 Mdot .9491 .03176 Mdot .94913 .03174 Mdot .94915 .03173 Mdot .94918 .03172 Mdot .9492 .0317 Mdot .94922 .03169 Mdot .94925 .03167 Mdot .94927 .03166 Mdot .9493 .03164 Mdot .94932 .03163 Mdot .94935 .03162 Mdot .94937 .0316 Mdot .9494 .03159 Mdot .94942 .03157 Mdot .94945 .03156 Mdot .94947 .03154 Mdot .9495 .03153 Mdot .94952 .03151 Mdot .94955 .0315 Mdot .94957 .03148 Mdot .9496 .03147 Mdot .94962 .03145 Mdot .94965 .03144 Mdot .94967 .03142 Mdot .9497 .03141 Mdot .94972 .03139 Mdot .94975 .03138 Mdot .94977 .03136 Mdot .9498 .03135 Mdot .94982 .03133 Mdot .94984 .03132 Mdot .94987 .0313 Mdot .94989 .03129 Mdot .94992 .03127 Mdot .94994 .03126 Mdot .94997 .03124 Mdot .94999 .03123 Mdot .95002 .03121 Mdot .95004 .0312 Mdot .95007 .03118 Mdot .95009 .03117 Mdot .95012 .03115 Mdot .95014 .03114 Mdot .95017 .03112 Mdot .95019 .03111 Mdot .95022 .03109 Mdot .95024 .03108 Mdot .95026 .03106 Mdot .95029 .03105 Mdot .95031 .03103 Mdot .95034 .03102 Mdot .95036 .031 Mdot .95039 .03099 Mdot .95041 .03097 Mdot .95044 .03096 Mdot .95046 .03094 Mdot .95049 .03093 Mdot .95051 .03091 Mdot .95054 .0309 Mdot .95056 .03088 Mdot .95058 .03087 Mdot .95061 .03086 Mdot .95063 .03084 Mdot .95066 .03083 Mdot .95068 .03081 Mdot .95071 .0308 Mdot .95073 .03079 Mdot .95076 .03077 Mdot .95078 .03076 Mdot .95081 .03074 Mdot .95083 .03073 Mdot .95086 .03071 Mdot .95088 .0307 Mdot .9509 .03068 Mdot .95093 .03067 Mdot .95095 .03065 Mdot .95098 .03064 Mdot .951 .03063 Mdot .95103 .03061 Mdot .95105 .0306 Mdot .95108 .03058 Mdot .9511 .03057 Mdot .95112 .03055 Mdot .95115 .03054 Mdot .95117 .03052 Mdot .9512 .03051 Mdot .95122 .03049 Mdot .95125 .03048 Mdot .95127 .03046 Mdot .9513 .03045 Mdot .95132 .03043 Mdot .95134 .03042 Mdot .95137 .03041 Mdot .95139 .03039 Mdot .95142 .03038 Mdot .95144 .03036 Mdot .95147 .03035 Mdot .95149 .03033 Mdot .95152 .03032 Mdot .95154 .0303 Mdot .95156 .03029 Mdot .95159 .03027 Mdot .95161 .03026 Mdot .95164 .03024 Mdot .95166 .03023 Mdot .95169 .03021 Mdot .95171 .0302 Mdot .95173 .03019 Mdot .95176 .03017 Mdot .95178 .03016 Mdot .95181 .03014 Mdot .95183 .03013 Mdot .95186 .03011 Mdot .95188 .0301 Mdot .95191 .03008 Mdot .95193 .03007 Mdot .95195 .03005 Mdot .95198 .03004 Mdot .952 .03003 Mdot .95203 .03001 Mdot .95205 .03 Mdot .95208 .02998 Mdot .9521 .02997 Mdot .95212 .02995 Mdot .95215 .02994 Mdot .95217 .02992 Mdot .9522 .02991 Mdot .95222 .02989 Mdot .95225 .02988 Mdot .95227 .02986 Mdot .95229 .02985 Mdot .95232 .02983 Mdot .95234 .02982 Mdot .95237 .0298 Mdot .95239 .02979 Mdot .95241 .02977 Mdot .95244 .02976 Mdot .95246 .02974 Mdot .95249 .02973 Mdot .95251 .02972 Mdot .95254 .0297 Mdot .95256 .02969 Mdot .95258 .02967 Mdot .95261 .02966 Mdot .95263 .02964 Mdot .95266 .02963 Mdot .95268 .02961 Mdot .9527 .0296 Mdot .95273 .02959 Mdot .95275 .02957 Mdot .95278 .02956 Mdot .9528 .02954 Mdot .95283 .02953 Mdot .95285 .02951 Mdot .95287 .0295 Mdot .9529 .02948 Mdot .95292 .02947 Mdot .95295 .02945 Mdot .95297 .02944 Mdot .95299 .02942 Mdot .95302 .02941 Mdot .95304 .0294 Mdot .95307 .02938 Mdot .95309 .02937 Mdot .95311 .02935 Mdot .95314 .02934 Mdot .95316 .02932 Mdot .95319 .02931 Mdot .95321 .0293 Mdot .95324 .02928 Mdot .95326 .02927 Mdot .95328 .02925 Mdot .95331 .02924 Mdot .95333 .02922 Mdot .95336 .02921 Mdot .95338 .0292 Mdot .9534 .02918 Mdot .95343 .02917 Mdot .95345 .02915 Mdot .95348 .02914 Mdot .9535 .02912 Mdot .95352 .02911 Mdot .95355 .0291 Mdot .95357 .02908 Mdot .9536 .02907 Mdot .95362 .02905 Mdot .95364 .02904 Mdot .95367 .02903 Mdot .95369 .02901 Mdot .95372 .029 Mdot .95374 .02898 Mdot .95376 .02897 Mdot .95379 .02895 Mdot .95381 .02894 Mdot .95383 .02892 Mdot .95386 .02891 Mdot .95388 .02889 Mdot .95391 .02888 Mdot .95393 .02887 Mdot .95395 .02885 Mdot .95398 .02884 Mdot .954 .02882 Mdot .95403 .02881 Mdot .95405 .02879 Mdot .95407 .02878 Mdot .9541 .02877 Mdot .95412 .02875 Mdot .95415 .02874 Mdot .95417 .02872 Mdot .95419 .02871 Mdot .95422 .0287 Mdot .95424 .02868 Mdot .95426 .02867 Mdot .95429 .02865 Mdot .95431 .02864 Mdot .95434 .02863 Mdot .95436 .02861 Mdot .95438 .0286 Mdot .95441 .02859 Mdot .95443 .02857 Mdot .95446 .02856 Mdot .95448 .02854 Mdot .9545 .02853 Mdot .95453 .02851 Mdot .95455 .0285 Mdot .95457 .02849 Mdot .9546 .02847 Mdot .95462 .02846 Mdot .95465 .02845 Mdot .95467 .02843 Mdot .95469 .02842 Mdot .95472 .0284 Mdot .95474 .02839 Mdot .95476 .02837 Mdot .95479 .02836 Mdot .95481 .02835 Mdot .95484 .02833 Mdot .95486 .02832 Mdot .95488 .0283 Mdot .95491 .02829 Mdot .95493 .02828 Mdot .95495 .02826 Mdot .95498 .02825 Mdot .955 .02823 Mdot .95503 .02822 Mdot .95505 .02821 Mdot .95507 .02819 Mdot .9551 .02818 Mdot .95512 .02816 Mdot .95514 .02815 Mdot .95517 .02813 Mdot .95519 .02812 Mdot .95521 .02811 Mdot .95524 .02809 Mdot .95526 .02808 Mdot .95529 .02806 Mdot .95531 .02805 Mdot .95533 .02804 Mdot .95536 .02802 Mdot .95538 .02801 Mdot .9554 .02799 Mdot .95543 .02798 Mdot .95545 .02796 Mdot .95547 .02795 Mdot .9555 .02793 Mdot .95552 .02792 Mdot .95554 .02791 Mdot .95557 .02789 Mdot .95559 .02788 Mdot .95562 .02786 Mdot .95564 .02785 Mdot .95566 .02784 Mdot .95569 .02782 Mdot .95571 .02781 Mdot .95573 .02779 Mdot .95576 .02778 Mdot .95578 .02776 Mdot .9558 .02775 Mdot .95583 .02774 Mdot .95585 .02772 Mdot .95587 .02771 Mdot .9559 .02769 Mdot .95592 .02768 Mdot .95595 .02767 Mdot .95597 .02765 Mdot .95599 .02764 Mdot .95602 .02762 Mdot .95604 .02761 Mdot .95606 .02759 Mdot .95609 .02758 Mdot .95611 .02757 Mdot .95613 .02756 Mdot .95616 .02754 Mdot .95618 .02753 Mdot .9562 .02751 Mdot .95623 .0275 Mdot .95625 .02748 Mdot .95627 .02747 Mdot .9563 .02745 Mdot .95632 .02744 Mdot .95634 .02743 Mdot .95637 .02742 Mdot .95639 .0274 Mdot .95641 .02739 Mdot .95644 .02737 Mdot .95646 .02736 Mdot .95648 .02734 Mdot .95651 .02733 Mdot .95653 .02732 Mdot .95655 .0273 Mdot .95658 .02729 Mdot .9566 .02728 Mdot .95662 .02726 Mdot .95665 .02725 Mdot .95667 .02723 Mdot .95669 .02722 Mdot .95672 .02721 Mdot .95674 .02719 Mdot .95677 .02718 Mdot .95679 .02717 Mdot .95681 .02715 Mdot .95684 .02714 Mdot .95686 .02713 Mdot .95688 .02711 Mdot .95691 .0271 Mdot .95693 .02708 Mdot .95695 .02707 Mdot .95697 .02706 Mdot .957 .02704 Mdot .95702 .02703 Mdot .95704 .02701 Mdot .95707 .027 Mdot .95709 .02699 Mdot .95711 .02697 Mdot .95714 .02696 Mdot .95716 .02695 Mdot .95718 .02693 Mdot .95721 .02692 Mdot .95723 .0269 Mdot .95725 .02689 Mdot .95728 .02688 Mdot .9573 .02686 Mdot .95732 .02685 Mdot .95735 .02683 Mdot .95737 .02682 Mdot .95739 .02681 Mdot .95742 .02679 Mdot .95744 .02678 Mdot .95746 .02676 Mdot .95749 .02675 Mdot .95751 .02673 Mdot .95753 .02672 Mdot .95756 .02671 Mdot .95758 .02669 Mdot .9576 .02668 Mdot .95763 .02666 Mdot .95765 .02665 Mdot .95767 .02664 Mdot .9577 .02662 Mdot .95772 .02661 Mdot .95774 .0266 Mdot .95776 .02659 Mdot .95779 .02657 Mdot .95781 .02656 Mdot .95783 .02655 Mdot .95786 .02653 Mdot .95788 .02652 Mdot .9579 .02651 Mdot .95793 .02649 Mdot .95795 .02648 Mdot .95797 .02646 Mdot .958 .02645 Mdot .95802 .02644 Mdot .95804 .02642 Mdot .95807 .02641 Mdot .95809 .02639 Mdot .95811 .02638 Mdot .95813 .02637 Mdot .95816 .02635 Mdot .95818 .02634 Mdot .9582 .02633 Mdot .95823 .02631 Mdot .95825 .0263 Mdot .95827 .02629 Mdot .9583 .02627 Mdot .95832 .02626 Mdot .95834 .02624 Mdot .95836 .02623 Mdot .95839 .02622 Mdot .95841 .0262 Mdot .95843 .02619 Mdot .95846 .02618 Mdot .95848 .02616 Mdot .9585 .02615 Mdot .95853 .02614 Mdot .95855 .02612 Mdot .95857 .02611 Mdot .95859 .02609 Mdot .95862 .02608 Mdot .95864 .02607 Mdot .95866 .02605 Mdot .95869 .02604 Mdot .95871 .02603 Mdot .95873 .02601 Mdot .95876 .026 Mdot .95878 .02598 Mdot .9588 .02597 Mdot .95882 .02596 Mdot .95885 .02594 Mdot .95887 .02593 Mdot .95889 .02592 Mdot .95892 .0259 Mdot .95894 .02589 Mdot .95896 .02587 Mdot .95899 .02586 Mdot .95901 .02585 Mdot .95903 .02583 Mdot .95905 .02582 Mdot .95908 .02581 Mdot .9591 .02579 Mdot .95912 .02578 Mdot .95915 .02577 Mdot .95917 .02575 Mdot .95919 .02574 Mdot .95921 .02572 Mdot .95924 .02571 Mdot .95926 .0257 Mdot .95928 .02569 Mdot .95931 .02567 Mdot .95933 .02566 Mdot .95935 .02565 Mdot .95937 .02563 Mdot .9594 .02562 Mdot .95942 .02561 Mdot .95944 .02559 Mdot .95947 .02558 Mdot .95949 .02557 Mdot .95951 .02555 Mdot .95953 .02554 Mdot .95956 .02553 Mdot .95958 .02551 Mdot .9596 .0255 Mdot .95962 .02548 Mdot .95965 .02547 Mdot .95967 .02546 Mdot .95969 .02545 Mdot .95972 .02543 Mdot .95974 .02542 Mdot .95976 .0254 Mdot .95978 .02539 Mdot .95981 .02538 Mdot .95983 .02536 Mdot .95985 .02535 Mdot .95988 .02533 Mdot .9599 .02532 Mdot .95992 .02531 Mdot .95994 .0253 Mdot .95997 .02528 Mdot .95999 .02527 Mdot .96001 .02525 Mdot .96003 .02524 Mdot .96006 .02523 Mdot .96008 .02521 Mdot .9601 .0252 Mdot .96013 .02519 Mdot .96015 .02518 Mdot .96017 .02516 Mdot .96019 .02515 Mdot .96022 .02514 Mdot .96024 .02512 Mdot .96026 .02511 Mdot .96028 .0251 Mdot .96031 .02508 Mdot .96033 .02507 Mdot .96035 .02506 Mdot .96037 .02504 Mdot .9604 .02503 Mdot .96042 .02502 Mdot .96044 .025 Mdot .96047 .02499 Mdot .96049 .02497 Mdot .96051 .02496 Mdot .96053 .02495 Mdot .96056 .02493 Mdot .96058 .02492 Mdot .9606 .02491 Mdot .96062 .02489 Mdot .96065 .02488 Mdot .96067 .02486 Mdot .96069 .02485 Mdot .96071 .02484 Mdot .96074 .02482 Mdot .96076 .02481 Mdot .96078 .0248 Mdot .9608 .02479 Mdot .96083 .02477 Mdot .96085 .02476 Mdot .96087 .02474 Mdot .96089 .02473 Mdot .96092 .02472 Mdot .96094 .02471 Mdot .96096 .02469 Mdot .96098 .02468 Mdot .96101 .02466 Mdot .96103 .02465 Mdot .96105 .02464 Mdot .96107 .02462 Mdot .9611 .02461 Mdot .96112 .0246 Mdot .96114 .02458 Mdot .96116 .02457 Mdot .96119 .02456 Mdot .96121 .02454 Mdot .96123 .02453 Mdot .96125 .02452 Mdot .96128 .02451 Mdot .9613 .02449 Mdot .96132 .02448 Mdot .96134 .02447 Mdot .96137 .02446 Mdot .96139 .02444 Mdot .96141 .02443 Mdot .96143 .02441 Mdot .96146 .0244 Mdot .96148 .02439 Mdot .9615 .02437 Mdot .96152 .02436 Mdot .96155 .02435 Mdot .96157 .02433 Mdot .96159 .02432 Mdot .96161 .02431 Mdot .96164 .02429 Mdot .96166 .02428 Mdot .96168 .02427 Mdot .9617 .02425 Mdot .96173 .02424 Mdot .96175 .02423 Mdot .96177 .02421 Mdot .96179 .0242 Mdot .96181 .02419 Mdot .96184 .02417 Mdot .96186 .02416 Mdot .96188 .02414 Mdot .9619 .02413 Mdot .96193 .02412 Mdot .96195 .0241 Mdot .96197 .02409 Mdot .96199 .02408 Mdot .96202 .02406 Mdot .96204 .02405 Mdot .96206 .02404 Mdot .96208 .02402 Mdot .96211 .02401 Mdot .96213 .024 Mdot .96215 .02398 Mdot .96217 .02397 Mdot .96219 .02396 Mdot .96222 .02394 Mdot .96224 .02393 Mdot .96226 .02392 Mdot .96228 .0239 Mdot .96231 .02389 Mdot .96233 .02388 Mdot .96235 .02386 Mdot .96237 .02385 Mdot .9624 .02384 Mdot .96242 .02382 Mdot .96244 .02381 Mdot .96246 .0238 Mdot .96248 .02379 Mdot .96251 .02377 Mdot .96253 .02376 Mdot .96255 .02375 Mdot .96257 .02373 Mdot .9626 .02372 Mdot .96262 .02371 Mdot .96264 .02369 Mdot .96266 .02368 Mdot .96268 .02367 Mdot .96271 .02365 Mdot .96273 .02364 Mdot .96275 .02362 Mdot .96277 .02361 Mdot .9628 .0236 Mdot .96282 .02359 Mdot .96284 .02357 Mdot .96286 .02356 Mdot .96288 .02355 Mdot .96291 .02353 Mdot .96293 .02352 Mdot .96295 .0235 Mdot .96297 .02349 Mdot .96299 .02348 Mdot .96302 .02347 Mdot .96304 .02345 Mdot .96306 .02344 Mdot .96308 .02343 Mdot .96311 .02341 Mdot .96313 .0234 Mdot .96315 .02339 Mdot .96317 .02338 Mdot .96319 .02336 Mdot .96322 .02335 Mdot .96324 .02334 Mdot .96326 .02332 Mdot .96328 .02331 Mdot .9633 .0233 Mdot .96333 .02328 Mdot .96335 .02327 Mdot .96337 .02326 Mdot .96339 .02324 Mdot .96341 .02323 Mdot .96344 .02322 Mdot .96346 .0232 Mdot .96348 .02319 Mdot .9635 .02318 Mdot .96353 .02317 Mdot .96355 .02315 Mdot .96357 .02314 Mdot .96359 .02313 Mdot .96361 .02311 Mdot .96364 .0231 Mdot .96366 .02309 Mdot .96368 .02307 Mdot .9637 .02306 Mdot .96372 .02305 Mdot .96375 .02304 Mdot .96377 .02303 Mdot .96379 .02301 Mdot .96381 .023 Mdot .96383 .02299 Mdot .96386 .02297 Mdot .96388 .02296 Mdot .9639 .02295 Mdot .96392 .02293 Mdot .96394 .02292 Mdot .96397 .02291 Mdot .96399 .02289 Mdot .96401 .02288 Mdot .96403 .02287 Mdot .96405 .02286 Mdot .96408 .02285 Mdot .9641 .02283 Mdot .96412 .02282 Mdot .96414 .02281 Mdot .96416 .0228 Mdot .96419 .02278 Mdot .96421 .02277 Mdot .96423 .02276 Mdot .96425 .02274 Mdot .96427 .02273 Mdot .96429 .02272 Mdot .96432 .0227 Mdot .96434 .02269 Mdot .96436 .02268 Mdot .96438 .02266 Mdot .9644 .02265 Mdot .96443 .02264 Mdot .96445 .02262 Mdot .96447 .02261 Mdot .96449 .0226 Mdot .96451 .02258 Mdot .96454 .02257 Mdot .96456 .02256 Mdot .96458 .02255 Mdot .9646 .02253 Mdot .96462 .02252 Mdot .96464 .02251 Mdot .96467 .02249 Mdot .96469 .02248 Mdot .96471 .02247 Mdot .96473 .02245 Mdot .96475 .02244 Mdot .96478 .02243 Mdot .9648 .02242 Mdot .96482 .0224 Mdot .96484 .02239 Mdot .96486 .02238 Mdot .96488 .02236 Mdot .96491 .02235 Mdot .96493 .02234 Mdot .96495 .02233 Mdot .96497 .02231 Mdot .96499 .0223 Mdot .96502 .02229 Mdot .96504 .02227 Mdot .96506 .02226 Mdot .96508 .02225 Mdot .9651 .02223 Mdot .96512 .02222 Mdot .96515 .02221 Mdot .96517 .02219 Mdot .96519 .02218 Mdot .96521 .02217 Mdot .96523 .02215 Mdot .96525 .02214 Mdot .96528 .02213 Mdot .9653 .02211 Mdot .96532 .0221 Mdot .96534 .02209 Mdot .96536 .02208 Mdot .96539 .02206 Mdot .96541 .02205 Mdot .96543 .02204 Mdot .96545 .02203 Mdot .96547 .02201 Mdot .96549 .022 Mdot .96552 .02199 Mdot .96554 .02198 Mdot .96556 .02196 Mdot .96558 .02195 Mdot .9656 .02194 Mdot .96562 .02192 Mdot .96565 .02191 Mdot .96567 .0219 Mdot .96569 .02189 Mdot .96571 .02187 Mdot .96573 .02186 Mdot .96575 .02185 Mdot .96578 .02184 Mdot .9658 .02183 Mdot .96582 .02181 Mdot .96584 .0218 Mdot .96586 .02179 Mdot .96588 .02178 Mdot .96591 .02176 Mdot .96593 .02175 Mdot .96595 .02174 Mdot .96597 .02172 Mdot .96599 .02171 Mdot .96601 .0217 Mdot .96603 .02169 Mdot .96606 .02167 Mdot .96608 .02166 Mdot .9661 .02165 Mdot .96612 .02163 Mdot .96614 .02162 Mdot .96616 .02161 Mdot .96619 .02159 Mdot .96621 .02158 Mdot .96623 .02157 Mdot .96625 .02156 Mdot .96627 .02154 Mdot .96629 .02153 Mdot .96632 .02152 Mdot .96634 .0215 Mdot .96636 .02149 Mdot .96638 .02148 Mdot .9664 .02147 Mdot .96642 .02146 Mdot .96644 .02144 Mdot .96647 .02143 Mdot .96649 .02142 Mdot .96651 .02141 Mdot .96653 .02139 Mdot .96655 .02138 Mdot .96657 .02137 Mdot .96659 .02136 Mdot .96662 .02135 Mdot .96664 .02133 Mdot .96666 .02132 Mdot .96668 .02131 Mdot .9667 .0213 Mdot .96672 .02128 Mdot .96675 .02127 Mdot .96677 .02126 Mdot .96679 .02125 Mdot .96681 .02123 Mdot .96683 .02122 Mdot .96685 .02121 Mdot .96687 .02119 Mdot .9669 .02118 Mdot .96692 .02117 Mdot .96694 .02115 Mdot .96696 .02114 Mdot .96698 .02113 Mdot .967 .02112 Mdot .96702 .02111 Mdot .96705 .02109 Mdot .96707 .02108 Mdot .96709 .02107 Mdot .96711 .02106 Mdot .96713 .02104 Mdot .96715 .02103 Mdot .96717 .02102 Mdot .9672 .02101 Mdot .96722 .02099 Mdot .96724 .02098 Mdot .96726 .02097 Mdot .96728 .02096 Mdot .9673 .02094 Mdot .96732 .02093 Mdot .96734 .02092 Mdot .96737 .0209 Mdot .96739 .02089 Mdot .96741 .02088 Mdot .96743 .02087 Mdot .96745 .02085 Mdot .96747 .02084 Mdot .96749 .02083 Mdot .96752 .02082 Mdot .96754 .0208 Mdot .96756 .02079 Mdot .96758 .02078 Mdot .9676 .02077 Mdot .96762 .02075 Mdot .96764 .02074 Mdot .96766 .02073 Mdot .96769 .02072 Mdot .96771 .02071 Mdot .96773 .02069 Mdot .96775 .02068 Mdot .96777 .02067 Mdot .96779 .02066 Mdot .96781 .02065 Mdot .96783 .02063 Mdot .96786 .02062 Mdot .96788 .02061 Mdot .9679 .02059 Mdot .96792 .02058 Mdot .96794 .02057 Mdot .96796 .02056 Mdot .96798 .02054 Mdot .968 .02053 Mdot .96803 .02052 Mdot .96805 .02051 Mdot .96807 .0205 Mdot .96809 .02048 Mdot .96811 .02047 Mdot .96813 .02046 Mdot .96815 .02044 Mdot .96817 .02043 Mdot .9682 .02042 Mdot .96822 .02041 Mdot .96824 .0204 Mdot .96826 .02039 Mdot .96828 .02037 Mdot .9683 .02036 Mdot .96832 .02035 Mdot .96834 .02033 Mdot .96837 .02032 Mdot .96839 .02031 Mdot .96841 .0203 Mdot .96843 .02028 Mdot .96845 .02027 Mdot .96847 .02026 Mdot .96849 .02025 Mdot .96851 .02024 Mdot .96853 .02023 Mdot .96856 .02021 Mdot .96858 .0202 Mdot .9686 .02019 Mdot .96862 .02018 Mdot .96864 .02017 Mdot .96866 .02015 Mdot .96868 .02015 Mdot .9687 .02013 Mdot .96872 .02012 Mdot .96875 .02011 Mdot .96877 .02009 Mdot .96879 .02008 Mdot .96881 .02007 Mdot .96883 .02006 Mdot .96885 .02004 Mdot .96887 .02003 Mdot .96889 .02002 Mdot .96891 .02001 Mdot .96894 .01999 Mdot .96896 .01998 Mdot .96898 .01997 Mdot .969 .01996 Mdot .96902 .01994 Mdot .96904 .01993 Mdot .96906 .01992 Mdot .96908 .01991 Mdot .9691 .01989 Mdot .96913 .01988 Mdot .96915 .01987 Mdot .96917 .01986 Mdot .96919 .01984 Mdot .96921 .01983 Mdot .96923 .01982 Mdot .96925 .01981 Mdot .96927 .01979 Mdot .96929 .01978 Mdot .96931 .01977 Mdot .96934 .01976 Mdot .96936 .01974 Mdot .96938 .01973 Mdot .9694 .01972 Mdot .96942 .01971 Mdot .96944 .01969 Mdot .96946 .01968 Mdot .96948 .01967 Mdot .9695 .01965 Mdot .96952 .01964 Mdot .96955 .01963 Mdot .96957 .01962 Mdot .96959 .01961 Mdot .96961 .01959 Mdot .96963 .01958 Mdot .96965 .01957 Mdot .96967 .01956 Mdot .96969 .01955 Mdot .96971 .01954 Mdot .96973 .01952 Mdot .96975 .01951 Mdot .96978 .0195 Mdot .9698 .01948 Mdot .96982 .01947 Mdot .96984 .01946 Mdot .96986 .01945 Mdot .96988 .01943 Mdot .9699 .01942 Mdot .96992 .01941 Mdot .96994 .0194 Mdot .96996 .01938 Mdot .96998 .01937 Mdot .97001 .01936 Mdot .97003 .01935 Mdot .97005 .01933 Mdot .97007 .01932 Mdot .97009 .01931 Mdot .97011 .0193 Mdot .97013 .01928 Mdot .97015 .01927 Mdot .97017 .01926 Mdot .97019 .01925 Mdot .97021 .01924 Mdot .97023 .01923 Mdot .97026 .01921 Mdot .97028 .0192 Mdot .9703 .01919 Mdot .97032 .01918 Mdot .97034 .01916 Mdot .97036 .01915 Mdot .97038 .01914 Mdot .9704 .01912 Mdot .97042 .01911 Mdot .97044 .0191 Mdot .97046 .01909 Mdot .97048 .01907 Mdot .97051 .01906 Mdot .97053 .01905 Mdot .97055 .01904 Mdot .97057 .01902 Mdot .97059 .01901 Mdot .97061 .019 Mdot .97063 .01899 Mdot .97065 .01897 Mdot .97067 .01896 Mdot .97069 .01895 Mdot .97071 .01894 Mdot .97073 .01892 Mdot .97075 .01891 Mdot .97078 .0189 Mdot .9708 .01889 Mdot .97082 .01888 Mdot .97084 .01886 Mdot .97086 .01885 Mdot .97088 .01884 Mdot .9709 .01883 Mdot .97092 .01881 Mdot .97094 .0188 Mdot .97096 .01879 Mdot .97098 .01878 Mdot .971 .01876 Mdot .97102 .01875 Mdot .97105 .01874 Mdot .97107 .01873 Mdot .97109 .01872 Mdot .97111 .0187 Mdot .97113 .01869 Mdot .97115 .01868 Mdot .97117 .01867 Mdot .97119 .01866 Mdot .97121 .01865 Mdot .97123 .01863 Mdot .97125 .01862 Mdot .97127 .01861 Mdot .97129 .0186 Mdot .97131 .01858 Mdot .97133 .01857 Mdot .97136 .01856 Mdot .97138 .01855 Mdot .9714 .01854 Mdot .97142 .01852 Mdot .97144 .01851 Mdot .97146 .0185 Mdot .97148 .01848 Mdot .9715 .01847 Mdot .97152 .01846 Mdot .97154 .01845 Mdot .97156 .01843 Mdot .97158 .01842 Mdot .9716 .01841 Mdot .97162 .0184 Mdot .97164 .01838 Mdot .97166 .01837 Mdot .97169 .01836 Mdot .97171 .01835 Mdot .97173 .01834 Mdot .97175 .01832 Mdot .97177 .01831 Mdot .97179 .0183 Mdot .97181 .01829 Mdot .97183 .01828 Mdot .97185 .01826 Mdot .97187 .01825 Mdot .97189 .01824 Mdot .97191 .01823 Mdot .97193 .01821 Mdot .97195 .0182 Mdot .97197 .01819 Mdot .97199 .01818 Mdot .97201 .01816 Mdot .97203 .01815 Mdot .97206 .01814 Mdot .97208 .01813 Mdot .9721 .01811 Mdot .97212 .0181 Mdot .97214 .01809 Mdot .97216 .01808 Mdot .97218 .01806 Mdot .9722 .01805 Mdot .97222 .01804 Mdot .97224 .01803 Mdot .97226 .01801 Mdot .97228 .018 Mdot .9723 .01799 Mdot .97232 .01798 Mdot .97234 .01797 Mdot .97236 .01795 Mdot .97238 .01794 Mdot .9724 .01793 Mdot .97242 .01792 Mdot .97244 .01791 Mdot .97247 .01789 Mdot .97249 .01788 Mdot .97251 .01787 Mdot .97253 .01786 Mdot .97255 .01785 Mdot .97257 .01783 Mdot .97259 .01782 Mdot .97261 .01781 Mdot .97263 .0178 Mdot .97265 .01779 Mdot .97267 .01777 Mdot .97269 .01776 Mdot .97271 .01775 Mdot .97273 .01774 Mdot .97275 .01772 Mdot .97277 .01771 Mdot .97279 .0177 Mdot .97281 .01769 Mdot .97283 .01768 Mdot .97285 .01766 Mdot .97287 .01765 Mdot .97289 .01764 Mdot .97291 .01763 Mdot .97293 .01761 Mdot .97295 .0176 Mdot .97298 .01759 Mdot .973 .01758 Mdot .97302 .01757 Mdot .97304 .01755 Mdot .97306 .01754 Mdot .97308 .01753 Mdot .9731 .01752 Mdot .97312 .01751 Mdot .97314 .01749 Mdot .97316 .01748 Mdot .97318 .01747 Mdot .9732 .01746 Mdot .97322 .01745 Mdot .97324 .01743 Mdot .97326 .01742 Mdot .97328 .01741 Mdot .9733 .0174 Mdot .97332 .01738 Mdot .97334 .01737 Mdot .97336 .01736 Mdot .97338 .01735 Mdot .9734 .01734 Mdot .97342 .01732 Mdot .97344 .01731 Mdot .97346 .0173 Mdot .97348 .01729 Mdot .9735 .01728 Mdot .97352 .01726 Mdot .97354 .01725 Mdot .97356 .01724 Mdot .97358 .01723 Mdot .97361 .01722 Mdot .97363 .01721 Mdot .97365 .0172 Mdot .97367 .01718 Mdot .97369 .01717 Mdot .97371 .01716 Mdot .97373 .01715 Mdot .97375 .01714 Mdot .97377 .01713 Mdot .97379 .01711 Mdot .97381 .0171 Mdot .97383 .01709 Mdot .97385 .01708 Mdot .97387 .01707 Mdot .97389 .01706 Mdot .97391 .01705 Mdot .97393 .01703 Mdot .97395 .01702 Mdot .97397 .01701 Mdot .97399 .017 Mdot .97401 .01698 Mdot .97403 .01697 Mdot .97405 .01696 Mdot .97407 .01695 Mdot .97409 .01694 Mdot .97411 .01693 Mdot .97413 .01691 Mdot .97415 .0169 Mdot .97417 .01689 Mdot .97419 .01688 Mdot .97421 .01687 Mdot .97423 .01685 Mdot .97425 .01684 Mdot .97427 .01683 Mdot .97429 .01682 Mdot .97431 .01681 Mdot .97433 .01679 Mdot .97435 .01678 Mdot .97437 .01677 Mdot .97439 .01676 Mdot .97441 .01675 Mdot .97443 .01674 Mdot .97445 .01672 Mdot .97447 .01671 Mdot .97449 .0167 Mdot .97451 .01669 Mdot .97453 .01667 Mdot .97455 .01666 Mdot .97457 .01665 Mdot .97459 .01664 Mdot .97461 .01663 Mdot .97463 .01662 Mdot .97465 .01661 Mdot .97467 .01659 Mdot .97469 .01658 Mdot .97471 .01657 Mdot .97473 .01656 Mdot .97475 .01655 Mdot .97477 .01653 Mdot .97479 .01652 Mdot .97481 .01651 Mdot .97483 .0165 Mdot .97485 .01649 Mdot .97487 .01648 Mdot .97489 .01647 Mdot .97491 .01645 Mdot .97493 .01644 Mdot .97495 .01643 Mdot .97497 .01642 Mdot .97499 .01641 Mdot .97501 .0164 Mdot .97504 .01638 Mdot .97506 .01637 Mdot .97508 .01636 Mdot .9751 .01635 Mdot .97512 .01633 Mdot .97514 .01632 Mdot .97516 .01631 Mdot .97518 .0163 Mdot .9752 .01629 Mdot .97522 .01628 Mdot .97524 .01626 Mdot .97526 .01625 Mdot .97527 .01624 Mdot .97529 .01623 Mdot .97531 .01621 Mdot .97533 .0162 Mdot .97535 .01619 Mdot .97537 .01618 Mdot .97539 .01617 Mdot .97541 .01616 Mdot .97543 .01614 Mdot .97545 .01613 Mdot .97547 .01612 Mdot .97549 .01611 Mdot .97551 .0161 Mdot .97553 .01608 Mdot .97555 .01607 Mdot .97557 .01606 Mdot .97559 .01605 Mdot .97561 .01604 Mdot .97563 .01603 Mdot .97565 .01601 Mdot .97567 .016 Mdot 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1346 y(Kiselev,)34 b(Last)e(and)g(Simon)h([KLS])f(\(see)h(also)f(Lemma) g(2)p Ft(:)p Fv(2\))g(w)m(e)h(can)f(get)g(rid)g(of)g(the)g(sup)h(in)f (\(A.2\))111 1466 y(using)h(the)g(fact)g(that)f Ft(T)14 b Fv(,)33 b(and)f(consequen)m(tly)k Ft(T)1893 1481 y Fp(U)1980 1466 y Fv(=)27 b Ft(U)10 b(T)k(U)2306 1430 y Fn(\000)p Fr(1)2402 1466 y Fv(,)32 b(is)h(a)g(unimo)s(dal)f(matrix.) 44 b(W)-8 b(e)33 b(ha)m(v)m(e)818 1686 y Fq(k)p Ft(T)925 1701 y Fp(U)984 1686 y Fl(v)1043 1701 y Fr(0)1082 1686 y Fq(k)1132 1638 y Fr(2)1199 1686 y Fv(=)28 b(sin)1423 1645 y Fr(2)1479 1686 y Fv(\()p Ft(\022)1562 1701 y Fr(0)1624 1686 y Fq(\000)22 b Ft(\022)1771 1645 y Fn(\003)1811 1686 y Fv(\))16 b Fq(k)p Ft(T)e Fq(k)2036 1638 y Fr(2)2036 1715 y Fp(U)2117 1686 y Fv(+)22 b(cos)2345 1645 y Fr(2)2401 1686 y Fv(\()p Ft(\022)2484 1701 y Fr(0)2546 1686 y Fq(\000)h Ft(\022)2694 1645 y Fn(\003)2734 1686 y Fv(\))16 b Fq(k)p Ft(T)e Fq(k)2959 1638 y Fn(\000)p Fr(2)2959 1715 y Fp(U)3086 1686 y Ft(;)111 1906 y Fv(where)34 b Ft(\022)441 1870 y Fn(\003)513 1906 y Fv(is)f(the)g(angle)g(in)g(whic)m(h)h(the)f (in\014m)m(um)h(is)f(attained,)g(and)1290 2165 y Fq(k)p Ft(T)14 b Fq(k)1460 2194 y Fp(U)1547 2165 y Fq(\024)1919 2098 y Fv(1)p 1662 2142 562 4 v 1662 2233 a Fq(j)p Fv(sin)j(\()p Ft(\022)1909 2248 y Fr(0)1971 2233 y Fq(\000)23 b Ft(\022)2119 2204 y Fn(\003)2158 2233 y Fv(\))p Fq(j)2251 2165 y(k)o Ft(T)2357 2180 y Fp(U)2416 2165 y Fl(v)2475 2180 y Fr(0)2515 2165 y Fq(k)49 b Ft(:)111 2445 y Fv(No)m(w,)33 b(for)f(an)m(y)i(pair)e Ft(\022)942 2409 y Fr(1)939 2470 y(0)982 2445 y Ft(;)49 b(\022)1106 2409 y Fr(2)1103 2470 y(0)1173 2445 y Fq(2)28 b Fv([)q(0)p Ft(;)17 b(\031)t Fv(])32 b(with)h(0)27 b Ft(<)h Fq(j)o Ft(\022)1983 2409 y Fr(1)1980 2470 y(0)2045 2445 y Fq(\000)23 b Ft(\022)2193 2409 y Fr(2)2190 2470 y(0)2232 2445 y Fq(j)28 b Ft(<)f(\031)t(=)p Fv(2,)1158 2595 y Fs(\014)1158 2655 y(\014)1191 2679 y Fv(sin)1328 2599 y Fs(\000)1373 2679 y Ft(\022)1421 2638 y Fp(i)1418 2704 y Fr(0)1480 2679 y Fq(\000)c Ft(\022)1628 2638 y Fn(\003)1667 2599 y Fs(\001)1713 2595 y(\014)1713 2655 y(\014)1746 2621 y Fn(\000)p Fr(1)1868 2679 y Fq(\024)1974 2595 y Fs(\014)1974 2655 y(\014)2007 2679 y Fv(sin)2143 2599 y Fs(\000)2189 2679 y Ft(\022)2237 2638 y Fr(1)2234 2704 y(0)2298 2679 y Fq(\000)g Ft(\022)2446 2638 y Fr(2)2443 2704 y(0)2486 2599 y Fs(\001)2548 2679 y Ft(=)p Fv(2)2646 2595 y Fs(\014)2646 2655 y(\014)2679 2621 y Fn(\000)p Fr(1)111 2899 y Fv(holds)33 b(for)f(at)h(least)g(one)g(of)f Ft(i)c Fq(2)g(f)p Fv(1)p Ft(;)17 b Fv(2)p Fq(g)o Fv(.)43 b(Hence)34 b(\(A.2\))e(can)h(b)s(e)g(replaced)h(b)m(y)637 3168 y Fq(k)p Ft(T)c Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\))p Fq(k)27 b(\024)1502 3100 y Ft(C)p 1201 3145 679 4 v 1201 3236 a Fq(j)p Fv(sin)17 b(\()p Ft(\022)1451 3202 y Fr(1)1448 3261 y(0)1513 3236 y Fq(\000)23 b Ft(\022)1661 3202 y Fr(2)1658 3261 y(0)1700 3236 y Fv(\))17 b Ft(=)p Fv(2)p Fq(j)1932 3168 y Fv(max)1907 3234 y Fp(i)p Fn(2f)p Fr(1)p Fp(;)p Fr(2)p Fn(g)2155 3168 y Ft(R)2229 3183 y Fp(N)2297 3168 y Fv(\()p Ft(\022)2383 3127 y Fp(i)2380 3192 y Fr(0)2419 3168 y Fv(\))28 b Fq(\021)2609 3143 y Fs(e)2590 3168 y Ft(C)49 b Fv(max)2684 3234 y Fp(i)p Fn(2f)p Fr(1)p Fp(;)p Fr(2)p Fn(g)2932 3168 y Ft(R)3006 3183 y Fp(N)3074 3168 y Fv(\()p Ft(\022)3160 3127 y Fp(i)3157 3192 y Fr(0)3197 3168 y Fv(\))32 b Ft(:)301 b Fv(\(A.4\))111 3444 y(Since)34 b Ft(\022)411 3459 y Fr(0)483 3444 y Fv(in)f(\(A.3\))g(is)g(arbitrary)-8 b(,)32 b(w)m(e)i(write)1273 3664 y Fq(k)p Ft(T)c Fv(\()p Ft(n)p Fv(;)17 b Ft(\025)p Fv(\))p Fq(k)27 b(\025)h Ft(C)1904 3623 y Fn(\000)p Fr(1)2073 3664 y Fv(max)2048 3730 y Fp(i)p Fn(2f)p Fr(1)p Fp(;)p Fr(2)p Fn(g)2296 3664 y Ft(R)2370 3679 y Fp(N)2438 3664 y Fv(\()p Ft(\022)2524 3623 y Fp(i)2521 3688 y Fr(0)2561 3664 y Fv(\))k Ft(:)937 b Fv(\(A.5\))111 3934 y(These)35 b(estimates)f(pla)m(y)f(an)g(imp)s(ortan)m(t)f(role)h(in)g(the)g(pro)s (of)e(of)i(Lemma)g(4.3.)1531 4162 y FD(Ac)m(kno)m(wledgmen)m(t)258 4415 y Fv(W)-8 b(e)29 b(thank)h(Profs.)43 b(B.)29 b(Simon,)h(A.)g (Klein)f(and)h(A.)f(Lop)s(es)h(for)e(instructiv)m(e)k(commen)m(ts.)44 b(W.)30 b(W.)111 4536 y(should)39 b(lik)m(e)g(to)f(thank)g(Prof.)59 b(J.)38 b(S.)g(Ho)m(wland)h(and)f(Prof.)59 b(A.)38 b(Jo)m(y)m(e)h(for)f (fruitful)f(con)m(v)m(ersations)111 4656 y(and)c(remarks.)111 4989 y Fu(References)111 5208 y Fv([A])240 b(N.)36 b(I.)g(Akhiezer.)h (\\The)g(classical)g(momen)m(t)f(problem)h(and)e(some)i(related)f (questions)i(in)478 5328 y(analysis",)c(Oliv)m(er)g(&)e(Bo)m(yd)h(1965) 1917 5587 y(29)p eop %%Page: 30 30 30 29 bop 111 312 a Fv([AA])167 b(V.)41 b(I.)h(Arnold)f(and)g(A.)g(Av)m (ez.)i(\\Ergo)s(dic)e(Problems)h(of)f(Classical)h(Mec)m(hanics",)k (Ben-)478 432 y(jamin,)33 b(New)h(Y)-8 b(ork)32 b(1968)111 636 y([C])243 b(Kai)27 b(Lai)g(Ch)m(ung.)i(\\A)e(course)h(in)g (Probabilit)m(y)g(theory",)h(Academic)g(Press)g(-)e(2nd)g(edition)478 756 y(\(1974\))111 959 y([CFKS])49 b(H.L.)41 b(Cycon,)j(R.G.)39 b(F)-8 b(ro)s(ese,)43 b(W.)e(Kirsc)m(h)g(and)g(B.)f(Simon.)h(\\Sc)m (hr\177)-49 b(odinger)42 b(Op)s(erators:)478 1080 y(with)50 b(Application)h(to)e(Quan)m(tum)h(Mec)m(hanics)i(and)e(Global)e (Geometry",)55 b(Springer-)478 1200 y(V)-8 b(erlag)33 b(\(1987\))111 1403 y([H])240 b(J.)36 b(S.)g(Ho)m(wland.)g(\\Quan)m (tum)g(stabilit)m(y")h(in)e Fk(Schr\177)-50 b(odinger)37 b(op)-5 b(er)g(ators)p Fv(,)35 b(Ed.)h(E.)g(Balslev.)478 1524 y(Lecture)e(Notes)f(in)g(Ph)m(ysics)i Fl(403)p Fv(,)e(Springer)g (V)-8 b(erlag)33 b(\(1992\))111 1727 y([K])237 b(Ab)s(el)39 b(Klein.)g(\\Extended)i(States)e(in)g(the)g(Anderson)h(Mo)s(del)f(on)f (the)h(Bethe)h(Lattice",)478 1848 y(Adv.)34 b(Math.)f Fl(133)p Fv(,)f(163-184)f(\(1998\))111 2051 y([KLS])122 b(Alexander)31 b(Kiselev,)g(Y)-8 b(oram)29 b(Last)h(and)f(Barry)g (Simon.)h(\\Mo)s(di\014ed)g(Pr)s(\177)-51 b(ufer)28 b(and)i(EF)m(GP)478 2171 y(transforms)48 b(and)g(the)g(sp)s(ectral)g(analysis)h(of)e (one{dimensional)i(Sc)m(hr\177)-49 b(odinger)49 b(op)s(era-)478 2292 y(tors",)33 b(Comm)m(un.)h(Math.)f(Ph)m(ys.)h Fl(194)p Fv(,)f(1-45)e(\(1997\))111 2495 y([KN])164 b(L.)28 b(Kuip)s(ers)h(and)f (H.)g(Niederrreiter.)h(\\Uniform)f(Distribution)g(of)f(Sequences"John)k (Wi-)478 2616 y(ley)j(&)e(Sons)h(\(1974\))111 2819 y([LS])198 b(Y)-8 b(oram)42 b(Last)g(and)g(Barry)g(Simon.)g(\\Eigenfunctions,)k (transfer)d(matrices,)i(and)d(abso-)478 2939 y(lutely)30 b(con)m(tin)m(uous)h(sp)s(ectrum)f(of)e(one{dimensional)i(Sc)m(hr\177) -49 b(odinger)30 b(op)s(erators",)g(In)m(v)m(en)m(t.)478 3060 y(Math.)j Fl(135)p Fv(,)g(329-367)e(\(1999\))111 3263 y([LS1])149 b(Y)-8 b(oram)45 b(Last)g(and)g(Barry)g(Simon.)g(\\Mo) s(di\014ed)h(Pr)s(\177)-51 b(ufer)44 b(and)h(EF)m(GP)g(transforms)h (and)478 3384 y(deterministic)30 b(mo)s(dels)f(with)f(dense)h(p)s(oin)m (t)f(sp)s(ectrum",)i(J.)d(F)-8 b(unct.)28 b(Anal.)g Fl(154)p Fv(,)h(513-530)478 3504 y(\(1998\))111 3707 y([PBM])89 b(A.)38 b(P)-8 b(.)38 b(Prudnik)m(o)m(v,)k(Y)-8 b(u.)38 b(A.)g(Bryc)m(hk)m(o)m(v)i(and)e(O.)f(I.)h(Maric)m(hev.)i(\\In)m (tegrals)e(and)g(Series.)478 3828 y(V)-8 b(ol.)33 b(1.)f(Elemen)m(tary) j(functions",)e(Gordon)f(&)h(Breac)m(h)g(\(1986\))111 4031 y([R])241 b(Christian)33 b(Remling)f(\\A)g(Probabilistic)h (Approac)m(h)f(to)f(One-dimensional)j(Sc)m(hr\177)-49 b(odinger)478 4151 y(Op)s(erators)28 b(with)g(Sparse)h(P)m(oten)m (tials",)h(Comm)m(un.)f(Math.)f(Ph)m(ys.)h Fl(185)p Fv(,)g(313-323)d (\(1997\))111 4355 y([S])259 b(Barry)33 b(Simon.)h(\\The)f(classical)h (momen)m(t)g(problem)g(as)f(a)f(self-adjoin)m(t)i(\014nite)f (di\013erence)478 4475 y(op)s(erator",)f(Adv.)i(Math.)e Fl(137)p Fv(,)h(82-203)e(\(1998\))111 4679 y([S1])210 b(Mic)m(hael)33 b(Reed)e(and)h(Barry)f(Simon.)g(\\Metho)s(ds)h(of)e(Mo) s(dern)i(Mathematical)g(Ph)m(ysics)i(I:)478 4799 y(F)-8 b(unctional)33 b(Analysis",)h(revised)h(and)d(enlarged)h(edition,)h (Academic)g(Press)g(\(1980\))111 5002 y([S2])210 b(Barry)38 b(Simon.)f(\\Sp)s(ectral)g(analysis)i(of)d(rank)i(one)f(p)s (erturbations)h(and)f(applications",)478 5123 y(CRM)26 b(Pro)s(ceedings)h(and)e(Lecture)h(Notes)g Fl(8)p Fv(,)g(109-149,)f (Amer.)h(Math.)g(So)s(c.,)g(Pro)m(vidence)478 5243 y(\(1995\))1917 5587 y(30)p eop %%Page: 31 31 31 30 bop 111 312 a Fv([SS])205 b(B.)50 b(Simon)h(and)f(G.)f(Stolz.)i (\\Op)s(erators)e(with)i(singular)f(con)m(tin)m(uous)i(sp)s(ectrum,)k (V.)478 432 y(Sparse)34 b(p)s(oten)m(tials",)f(Pro)s(c.)g(Amer.)g (Math.)g(So)s(c.)g Fl(124)p Fv(,)f(2141-2143)f(\(1988\))111 636 y([SW])159 b(B.)43 b(Simon)g(and)g(T.)g(W)-8 b(ol\013.)43 b(\\Singular)g(con)m(tin)m(uous)h(sp)s(ectrum)g(under)g(rank)f(one)g(p) s(er-)478 756 y(turbations)e(and)f(lo)s(calization)h(for)e(random)i (Hamiltonians",)h(Comm)m(un.)g(Pure)f(Appl.)478 876 y(Math)33 b Fl(39)p Fv(,)g(75-90)e(\(1986\))1917 5587 y(31)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0505311018166--