%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: arXiv:astro-ph/0206431v2 12 Jul 2002 %%Pages: 13 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Math1Mono Courier %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R -P pk -K1 -z upper_gamma_3.dvi -o %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 2018.04.16:2244 %%BeginProcSet: texc.pro /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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y(time)h(dela)m(y)g(b)s(et)m(w)m(een)h(GW)g(bursts)e(and)h(GRB)h (within)d Fm(\006)p Fo(400)j(s,)g(and)e Fn(h)h Fm(\025)f Fo(6)p Fn(:)p Fo(5)12 b Fm(\002)g Fo(10)3132 4715 y Fl(\000)p Fq(19)3264 4748 y Fo(,)26 b(if)g(the)240 4861 y(time)34 b(dela)m(y)g(is)g(within)e Fm(\006)p Fo(5)i(s.)g(The)g(result)g(is)f (also)h(pro)m(vided)f(in)g(form)h(of)h(scaled)f(lik)m(eliho)s(o)s(d)240 4974 y(for)c(un)m(biased)f(in)m(terpretation)h(and)f(easier)i(use)f (for)g(further)f(analysis.)3721 5879 y Fr(1)p eop %%Page: 2 2 2 1 bop -9 -28 a Fs(1)193 b(In)m(tro)s(duction)-9 93 y Fr(One)39 b(of)f(the)h(most)g(imp)s(ortan)m(t)e(astroph)m(ysical)h (phenomena)h(still)e(lac)m(king)h(an)h(explanation)e(is)i(the)-9 214 y(origin)f(of)i(the)h(celestial)e(gamma-ra)m(y)f(bursts)k(\(GRB\).) e(These)i(are)f(p)s(o)m(w)m(erful)g(\015ashes)h(of)e(gamma-)-9 334 y(ra)m(ys)27 b(lasting)e(from)g(less)i(than)g(one)g(second)h(to)e (tens)h(of)f(seconds,)j(with)d(isotropic)f(distribution)g(in)h(the)-9 454 y(sky)-8 b(.)40 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b(Djorgo)m(vski)g([7)p (#cite.Djorgovski) [[147 605 153 617] [1 1 1 [3 3]] [0 0 1]] pdfm (])g (and)g(references)i(therein\).)e(Among)f(the)h(p)s(ossible)g (explanations)f(of)g(these)j(ev)m(en)m(ts,)-9 1056 y(whic)m(h)i(in)m(v) m(olv)m(e)f(h)m(uge)i(energy)f(releases)g(\(up)g(to)f(10)1853 1020 y Fq(54)1955 1056 y Fr(erg,)h(assuming)e(isotropic)g(emission\),)h (the)h(most)-9 1177 y(lik)m(ely)23 b(candidates)j(are)f(the)g(collapse) f(of)g(a)h(v)m(ery)i(massiv)m(e)e(star)g(\(h)m(yp)s(erno)m(v)-5 b(a\))26 b(and)f(the)g(coalescence)h(of)-9 1297 y(one)h(compact)f (binary)g(system)i(\(see,)g(e.g.,)f(reviews)h(b)m(y)g(Piran)e([8)p (#cite.Piran99) [[353 561 359 573] [1 1 1 [3 3]] [0 0 1]] pdfm (])g (and)h(M)m(\023)-46 b(esz\023)d(aros)28 b([9)p (#cite.Meszaros01) [[440 561 446 573] [1 1 1 [3 3]] [0 0 1]] pdfm (])f (and)g(references)-9 1417 y(therein\).)i(In)h(b)s(oth)f(cases)i (emission)d(of)h(gra)m(vitational)d(w)m(a)m(v)m(es)32 b(\(GW\))d(is)g(exp)s(ected)i(to)f(b)s(e)f(asso)s(ciated)-9 1538 y(with)38 b(them)g(\(e.g.)h(Ref.)g([10)p (#cite.ks) [[184 532 196 544] [1 1 1 [3 3]] [0 0 1]] pdfm (]\).)g (According)f(to)h(sev)m(eral)g(mo)s(dels,)f(the)h(duration)f(of)g(a)h (GW)f(burst)i(is)-9 1658 y(predicted)d(to)f(b)s(e)h(of)g(the)g(order)g (of)f(a)h(few)g(milliseconds)d(for)j(a)f(v)-5 b(ariet)m(y)37 b(of)f(sources,)j(including)c(the)-9 1779 y(coalescing)j(and)h(merging) f(blac)m(k)i(holes)f(and/or)g(neutron)h(star)f(binaries.)f(Therefore)j (GW)e(bursts)-9 1899 y(can)f(b)s(e)h(detected)h(b)m(y)f(the)g(presen)m (t)h(resonan)m(t)f(detectors,)h(designed)f(to)f(detect)h(GW)f(through)h (the)-9 2019 y(excitation)29 b(of)h(the)h(quadrup)s(ole)f(mo)s(des)g (of)g(massiv)m(e)h(cylinders,)g(resonating)f(at)g(frequencies)i(near)e (1)-9 2140 y(kHz.)240 2260 y(A)m(t)37 b(the)h(distances)g(of)e(the)i (GRB)e(sources)i(\()p Fj(\031)e Fr(1)h(Gp)s(c\),)g(the)g(GW)g(burst)h (asso)s(ciated)f(with)f(a)-9 2380 y(total)30 b(con)m(v)m(ersion)j(of)f (1-2)f(solar)f(masses)j(should)f(ha)m(v)m(e)h(amplitude)d(of)i(the)g (order)g(of)g Fk(h)c Fj(\031)g Fr(3)20 b Fj(\002)i Fr(10)3614 2344 y Fl(\000)p Fq(22)3743 2380 y Fr(.)-9 2501 y(The)47 b(presen)m(t)g(sensitivit)m(y)f(for)g(1)f(ms)h(GW)g(pulses)h(of)e(the)i (b)s(est)f(GW)g(an)m(tennas)h(with)f(signal)e(to)-9 2621 y(noise)39 b(ratio)e(\(SNR\))i(equal)g(to)g(unit)m(y)g(is)g Fk(h)g Fj(\031)g Fr(4)27 b Fj(\002)g Fr(10)2040 2585 y Fl(\000)p Fq(19)2208 2621 y Fr(\(see)40 b(e.g.)g(Ref.)f([11)p (#cite.piaamaldi) [[412 402 424 414] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(]\),)h(whic)m(h)f(requires)h(a)-9 2742 y(total)35 b(con)m(v)m(ersion)i(of)f(one)h(million)32 b(solar)k(masses)h(at)f(1)h (Gp)s(c.)f(Ho)m(w)m(ev)m(er,)j(although)d(detection)g(of)g(a)-9 2862 y(gra)m(vitational)30 b(signal)h(asso)s(ciated)i(with)g(a)g (single)f(GRB)h(app)s(ears)h(hop)s(eless,)g(detection)f(of)g(a)g (signal)-9 2982 y(asso)s(ciated)44 b(with)g(the)i(sum)e(of)g(man)m(y)h (ev)m(en)m(ts)i(could)d(b)s(e)h(more)f(realistic.)f(Th)m(us)j(w)m(e)g (launc)m(hed)f(a)-9 3103 y(program)34 b(dev)m(oted)j(to)e(studying)h (the)f(presence)j(of)d(correlations)f(b)s(et)m(w)m(een)k(GRB)d(ev)m(en) m(ts)i(detected)-9 3223 y(with)46 b(Bepp)s(oSAX)i(and)f(the)g(output)h (signals)e(from)f(gra)m(vitational)f(an)m(tennas)k(NA)m(UTILUS)h(and)-9 3344 y(EXPLORER.)240 3464 y(Searc)m(hing)43 b(for)g(correlation)f(b)s (et)m(w)m(een)j(GRB)e(and)g(GW)g(signals)f(means)i(dealing)e(with)h (the)-9 3584 y(di\013erence)49 b(b)s(et)m(w)m(een)h(the)f(emission)e (times)h(for)g(the)h(t)m(w)m(o)g(t)m(yp)s(es)h(of)e(phenomena.)h(F)-8 b(urthermore,)-9 3705 y(there)38 b(is)g(also)f(the)i(fact)f(to)g (consider)g(that)g(the)g(time)f(di\013erence)i(can)f(v)-5 b(ary)39 b(from)e(burst)h(to)g(burst.)-9 3825 y(In)30 b(the)h(presen)m(t)h(analysis)d(w)m(e)j(use)f(an)f(algorithm)d(based)32 b(on)e(cross-correlating)f(the)i(outputs)g(of)e(t)m(w)m(o)-9 3945 y(GW)j(detectors)i(\(see)g([12)p (#cite.finn) [[173 244 185 256] [1 1 1 [3 3]] [0 0 1]] pdfm (,)f(13)p (#cite.arturo) [[192 244 204 256] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(]\),)g(th)m(us)h(coping)e(with)h(the)g(problem)f(of)g(the)i(unkno) m(wn)g(p)s(ossible)e(time)-9 4066 y(di\013erence)h(b)s(et)m(w)m(een)h (GRB)e(and)h(GW)f(bursts,)i(and)f(also)f(of)g(the)h(unmo)s(delled)e (noise.)-9 4305 y Fs(2)193 b(Exp)s(erimen)m(tal)35 b(data)-9 4426 y Fr(The)25 b(Rome)f(group)g(op)s(erates)h(t)m(w)m(o)g(resonan)m (t)h(bar)e(detectors:)i(EXPLORER)f([14)p (#cite.as2) [[416 186 428 198] [1 1 1 [3 3]] [0 0 1]] pdfm (],)g (since)g(1990,)e(at)i(the)-9 4547 y(CERN)e(lab)s(oratories,)f(and)h(NA) m(UTILUS)i([15)p (#cite.nautilus) [[263 171 274 183] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(],)f(since)f(1995,)g(at)g(the)g(INFN)h(lab)s(oratories)d(in)h(F)-8 b(rascati.)-9 4667 y(The)30 b(t)m(w)m(o)f(detectors,)i(orien)m(ted)e (nearly)g(parallel,)d(are)k(v)m(ery)g(similar.)c(They)31 b(ha)m(v)m(e)f(op)s(erated)f(o)m(v)m(er)i(the)-9 4787 y(last)25 b(few)i(y)m(ears)g(with)f(v)-5 b(arious)26 b(lev)m(els)g(of)g(sensitivit)m(y)-8 b(,)26 b(and)g(since)h(Marc)m(h)g (1)2724 4751 y Fi(st)2812 4787 y Fr(2001)e(they)i(ha)m(v)m(e)h(b)s(een) f(in)-9 4908 y(op)s(eration)k(sim)m(ultaneously)h(with)g(the)h(b)s(est) h(ev)m(er)g(reac)m(hed)g(sensitivit)m(y)f(for)g(millisecond)c(bursts,) 34 b(of)-9 5028 y(the)27 b(order)g(of)g Fk(h)h Fj(\031)g Fr(\(4)11 b Fj(\000)g Fr(5\))g Fj(\002)g Fr(10)1167 4992 y Fl(\000)p Fq(19)1296 5028 y Fr(.)27 b(The)h(detectors)h(consist)e(of) g(massiv)m(e)g(cylindrical)e(bars)i(3)g(m)f(long)-9 5148 y(made)32 b(of)h(high)g(qualit)m(y)f(factor)h(Alumin)m(um)e(allo)m(y)h (5056.)g(The)i(GW)f(excites)h(the)g(\014rst)g(longitudinal)-9 5269 y(mo)s(de)24 b(of)h(the)h(bar,)f(whic)m(h)h(is)f(co)s(oled)g(to)g (liquid)f(helium)f(temp)s(erature)i(to)h(reduce)g(the)g(thermal)e (noise.)-9 5389 y(T)-8 b(o)33 b(measure)g(the)g(bar)g(strain)f(induced) i(b)m(y)f(a)g(GW,)g(a)f(secondary)j(mec)m(hanical)c(oscillator)g(tuned) i(to)-9 5510 y(the)c(cited)g(mo)s(de)f(is)g(moun)m(ted)i(on)e(one)i (bar)e(face)i(and)f(a)f(sensor)i(measures)g(the)g(displacemen)m(t)e(of) h(the)-9 5630 y(secondary)34 b(oscillator.)-9 5879 y(2)p eop %%Page: 3 3 3 2 bop -9 25 a Fr(T)-8 b(able)29 b(1:)58 b(Main)29 b(c)m (haracteristics)h(of)f(the)g(t)m(w)m(o)h(detectors.)h Fk(f)40 b Fr(indicates,)29 b(for)g(eac)m(h)h(detector,)h(the)e(t)m(w)m (o)-9 145 y(resonan)m(t)h(frequencies)h(and)f(\001)p Fk(f)40 b Fr(indicates)29 b(the)h(bandwidth.)g(The)g(relativ)m(ely)e (larger)h(bandwidth)g(of)-9 265 y(EXPLORER)k(is)f(due)h(to)f(an)h (impro)m(v)m(ed)f(readout)h(system.)p 160 356 3408 4 v 158 477 4 121 v 313 441 a(detector)p 811 477 V 221 w(latitude)p 1277 477 V 116 w(longitude)p 1772 477 V 99 w(orien)m(tation)p 2335 477 V 98 w(mass)p 2642 477 V 205 w Fk(f)p 3012 477 V 244 w(T)p 3237 477 V 185 w Fr(\001)p Fk(f)p 3566 477 V 158 597 V 811 597 V 1277 597 V 1772 597 V 2335 597 V 2440 561 a Fr(kg)p 2642 597 V 230 w(Hz)p 3012 597 V 202 w(K)p 3237 597 V 181 w(Hz)p 3566 597 V 160 600 3408 4 v 158 721 4 121 v 210 685 a(EXPLORER)p 811 721 V 101 w(46)p Fk(:)p Fr(45)1086 649 y Fi(o)1156 685 y Fr(N)p 1277 721 V 142 w(6)p Fk(:)p Fr(20)1545 649 y Fi(o)1615 685 y Fr(E)p 1772 721 V 257 w(39)2036 649 y Fi(o)2106 685 y Fr(E)p 2335 721 V 220 w(2270)p 2642 721 V 130 w(904.7)p 3012 721 V 123 w(2.6)p 3237 721 V 137 w Fj(\031)28 b Fr(9)p 3566 721 V 158 841 V 811 841 V 1277 841 V 1772 841 V 2335 841 V 2642 841 V 2718 805 a(921.3)p 3012 841 V 3237 841 V 3566 841 V 158 962 V 231 926 a(NA)m(UTILUS)p 811 962 V 123 w(41)p Fk(:)p Fr(82)1086 889 y Fi(o)1156 926 y Fr(N)p 1277 962 V 117 w(12)p Fk(:)p Fr(67)1569 889 y Fi(o)1639 926 y Fr(E)p 1772 962 V 233 w(44)2036 889 y Fi(o)2106 926 y Fr(E)p 2335 962 V 220 w(2270)p 2642 962 V 105 w(906.97)p 3012 962 V 99 w(1.5)p 3237 962 V 99 w Fj(\031)g Fr(0)p Fk(:)p Fr(4)p 3566 962 V 158 1082 V 811 1082 V 1277 1082 V 1772 1082 V 2335 1082 V 2642 1082 V 2693 1046 a(922.46)p 3012 1082 V 3237 1082 V 3566 1082 V 160 1085 3408 4 v 240 1352 a(The)j(data)f(ha)m(v)m (e)h(a)f(sampling)e(time)g(of)i(4.544)f(ms)h(and)g(are)g(pro)s(cessed)i (with)d(a)h(\014lter)g(matc)m(hed)-9 1472 y(to)45 b(delta-lik)m(e)f (signals)h(for)g(the)h(detection)g(of)g(short)g(bursts)h([16)p (#cite.fast) [[359 540 370 552] [1 1 1 [3 3]] [0 0 1]] pdfm (])f(.)f (The)i(\014lter)f(is)f(adaptiv)m(e)h(and)-9 1593 y(mak)m(es)c(use)h(of) f(p)s(o)m(w)m(er)h(sp)s(ectra)g(obtained)e(during)h(p)s(erio)s(ds)f(of) h(t)m(w)m(o)h(hours.)g(The)g(\014ltered)f(output)-9 1713 y(is)37 b(squared)i(and)f(normalized)d(using)j(the)g(detector)g (calibration,)d(suc)m(h)k(that)f(its)f(square)i(giv)m(es)f(the)-9 1834 y(energy)31 b(inno)m(v)-5 b(ation)29 b Fk(x)p Fr(\()p Fk(t)p Fr(\))j(for)e(eac)m(h)h(sample.)f(In)h(the)h(presence)g(only)f (of)f(w)m(ell)g(b)s(eha)m(v)m(ed)i(noise)f(due)g(to)-9 1954 y(the)f(thermal)e(motion)g(of)h(the)h(bar)g(and)g(to)f(the)i (electronic)e(noise)g(of)h(the)g(ampli\014er,)e(the)i(probabilit)m(y)-9 2074 y(densit)m(y)j(function)f(of)g Fk(x)p Fr(\()p Fk(t)p Fr(\))h(is)1160 2353 y Fk(f)11 b Fr(\()p Fk(x)p Fr(\))28 b(=)1703 2286 y(1)p 1491 2330 473 4 v 1491 2350 a Fh(p)p 1591 2350 373 4 v 81 x Fr(2)p Fk(\031)20 b(T)1772 2446 y Fi(ef)7 b(f)1908 2431 y Fk(x)1990 2353 y Fr(exp)2156 2213 y Fh(\024)2209 2353 y Fj(\000)2389 2286 y Fk(x)p 2296 2330 242 4 v 2296 2422 a Fr(2)17 b Fk(T)2419 2437 y Fi(ef)7 b(f)2548 2213 y Fh(\025)3645 2353 y Fr(\(1\))-9 2650 y(where)45 b Fk(x)p Fr(\()p Fk(t)p Fr(\))f(is)g(expressed)j(in)c (k)m(elvin)h(units,)g(and)g(the)g(a)m(v)m(erage)h(v)-5 b(alue)44 b(of)f Fk(x)p Fr(,)i Fk(T)3068 2665 y Fi(ef)7 b(f)3187 2650 y Fr(,)44 b(called)f Fp(e\013e)-5 b(c-)-9 2771 y(tive)48 b(temp)-5 b(er)g(atur)g(e)p Fr(,)48 b(giv)m(es)g(an)f (estimation)e(of)i(the)h(noise.)g(If)f(a)g(signal)f(of)h(energy)h Fk(E)54 b Fr(due)48 b(to)f(an)-9 2891 y(impulsiv)m(e)33 b(force)i(acting)e(on)i(the)g(bar)f(is)h(generated)g(at)f(time)g Fk(t)2370 2906 y Fi(o)2408 2891 y Fr(,)h(the)g(c)m(hange)g(of)g(the)g (\014ltered)f(data)-9 3011 y(energy)40 b(with)e(time,)g(neglecting)g (the)h(noise)g(con)m(tribution,)f(has)h(an)g(en)m(v)m(elop)s(e)h(whic)m (h)g(dep)s(ends)g(on)-9 3132 y(the)33 b(detector)g(bandwidth)g(as)f (follo)m(ws:)1181 3353 y Fk(E)1253 3368 y Fi(s)1290 3353 y Fr(\()p Fk(t)p Fr(\))c(=)f Fk(E)45 b Fj(\001)22 b Fr(exp)c([)p Fj(\000)p Fr(2)p Fk(\031)i Fj(j)p Fk(t)i Fj(\000)h Fk(t)2313 3368 y Fi(o)2352 3353 y Fj(j)17 b Fr(\001)p Fk(f)10 b Fr(])1082 b(\(2\))-9 3575 y(where)36 b(the)g(bandwidth)g(\001)p Fk(f)46 b Fr(is)35 b(giv)m(en)h(in)e(T)-8 b(able)35 b(1)p (#table.1) [[295 288 301 300] [1 1 1 [3 3]] [0 0 1]] pdfm (.)h(In)g (addition)d(to)i(the)h(w)m(ell)f(b)s(eha)m(v)m(ed)i(and)f(mo)s(d-)-9 3695 y(eled)e(noise)g(\(electronic)g(and)h(thermal)e(noise\),)h(other)h (sources)h(of)e(noise)h(are)f(activ)m(e,)h(sometimes)e(of)-9 3816 y(unkno)m(wn)c(origin.)d(This)i(requires)h(more)e(than)h(one)g (detector)h(to)f(b)s(e)g(sim)m(ultaneously)e(used,)k(in)d(order)-9 3936 y(to)32 b(discriminate)e(a)i(real)g(signal)f(from)g(noise.)240 4056 y(F)-8 b(or)31 b(our)g(detectors,)j(the)e(relationship)e(b)s(et)m (w)m(een)k(burst)e(energy)h Fk(E)38 b Fr(expressed)c(in)d(k)m(elvin)h (and)-9 4177 y(dimensionless)f(amplitude)g Fk(h)h Fr(is)h(giv)m(en)f(b) m(y)i([17)p (#cite.australia) [[272 216 283 228] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(])1042 4458 y Fk(E)f Fr(=)1532 4390 y Fk(h)1588 4354 y Fq(2)p 1261 4435 638 4 v 1261 4526 a Fr(\(7)p Fk(:)p Fr(97)21 b Fj(\002)i Fr(10)1692 4497 y Fl(\000)p Fq(18)1821 4526 y Fr(\))1859 4497 y Fq(2)1925 4347 y Fh(\020)2031 4390 y Fk(\034)2073 4405 y Fi(g)r(w)p 1995 4435 209 4 v 1995 4526 a Fr(1)32 b(m)o Fk(s)2213 4347 y Fh(\021)2273 4369 y Fq(2)2589 4458 y Fr([K])926 b(\(3\))-9 4730 y(where)33 b Fk(\034)314 4745 y Fi(g)r(w)440 4730 y Fr(is)f(the)h(duration)e(of)i(the)g(burst,)g(con)m(v)m(en)m(tionally) f(assumed)h(to)g(b)s(e)f Fk(\034)2990 4745 y Fi(g)r(w)3111 4730 y Fr(=)c(0)p Fk(:)p Fr(001)17 b(s.)240 4850 y(In)28 b(the)g(follo)m(wing,)e(for)h(a)h(giv)m(en)g(signal)e(of)h(energy)i Fk(E)6 b Fr(,)28 b(w)m(e)h(shall)e(use)h(the)h(signal-to-noise)c(ratio) 1602 5114 y Fk(S)6 b(N)k(R)29 b Fr(=)2022 5047 y Fk(E)p 1972 5091 177 4 v 1972 5183 a(T)2029 5198 y Fi(ef)7 b(f)3645 5114 y Fr(\(4\))240 5389 y(F)-8 b(or)45 b(the)i(GRB's)f(w)m(e)i (consider)e(the)h(observ)-5 b(ations)46 b(made)g(with)g(the)h(Gamma)d (Ra)m(y)i(Burst)-9 5510 y(Monitor)40 b(\(GRBM,)h([19)p (#cite.Frontera97) [[170 56 182 68] [1 1 1 [3 3]] [0 0 1]] pdfm (]\))g (ab)s(oard)f(the)i(Bepp)s(oSAX)g(satellite,)d(the)j(only)f(satellite)e (for)i(the)h(GRB)-9 5630 y(detection)35 b(in)g(op)s(eration)g(during)g (2001.)f(The)j(GRBM)e(is)h(an)f(all)f(sky)j(monitor)c(whic)m(h)k(op)s (erates)f(in)3721 5879 y(3)p eop %%Page: 4 4 4 3 bop -9 1998 a @beginspecial 60 @hscale 40 @vscale 0 @angle @setspecial %%BeginDocument: distri.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlendef} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode newpath gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1745 816 227 1156 bl 2040 2040 0 0 C 980 1020 m -26 Y 1 -4 d 3 -2 d 4 X s 975 1009 m 11 X s 995 1000 m 18 X 3 Y -1 3 d -2 2 d -3 1 d -4 X -3 -1 d -3 -3 d -2 -5 d -3 Y 2 -4 d 3 -3 d 3 -2 d 4 X 3 2 d 3 3 d s 1033 1020 m -3 X -3 -2 d -2 -4 d -26 Y s 1021 1009 m 10 X s 1051 1020 m -3 X -3 -2 d -2 -4 d -26 Y s 1039 1009 m 10 X s 1071 1026 m -3 -3 d -3 -5 d -3 -6 d -2 -7 d -6 Y 2 -8 d 3 -6 d 3 -4 d 3 -3 d s 1081 1020 m -32 Y s 1096 1009 m -15 -15 d s 1087 1000 m 11 -12 d s 1105 1000 m 19 X 3 Y -2 3 d -2 2 d -3 1 d -4 X -3 -1 d -3 -3 d -2 -5 d -3 Y 2 -4 d 3 -3 d 3 -2 d 4 X 3 2 d 4 3 d s 1134 1020 m -32 Y s 1143 1009 m 9 -21 d s 1161 1009 m -9 -21 d s 1169 1020 m 1 -2 d 2 2 d -2 2 d -1 -2 d cl s 1170 1009 m -21 Y s 1182 1009 m -21 Y s 1182 1003 m 5 5 d 3 1 d 5 X 3 -1 d 1 -5 d -15 Y s 1210 1026 m 3 -3 d 3 -5 d 3 -6 d 1 -7 d -6 Y -1 -8 d -3 -6 d -3 -4 d -3 -3 d s 1745 816 227 1156 C 227 1302 m -146 Y 52 X 146 Y 17 X 232 Y 18 X -86 Y 17 X 232 Y 18 X 146 Y 17 X -39 Y 18 X -193 Y 17 X -60 Y 18 X 107 Y 17 X -339 Y 18 X -146 Y 17 X 146 Y 35 X -146 Y 1466 X 146 Y s NC 227 1156 m 816 Y s 244 1156 m -17 X s 244 1194 m -17 X s 244 1227 m -17 X s 244 1255 m -17 X s 244 1280 m -17 X s 261 1302 m -34 X s 160 1312 m 3 1 d 5 5 d -32 Y s 244 1448 m -17 X s 244 1534 m -17 X s 244 1594 m -17 X s 244 1641 m -17 X s 244 1680 m -17 X s 244 1712 m -17 X s 244 1740 m -17 X s 244 1765 m -17 X s 261 1787 m -34 X s 130 1797 m 3 2 d 5 4 d -31 Y s 165 1803 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 244 1934 m -17 X s 227 1156 m 1745 X s 227 1190 m -34 Y s 262 1173 m -17 Y s 296 1173 m -17 Y s 331 1173 m -17 Y s 366 1173 m -17 Y s 401 1190 m -34 Y s 436 1173 m -17 Y s 471 1173 m -17 Y s 506 1173 m -17 Y s 541 1173 m -17 Y s 576 1190 m -34 Y s 611 1173 m -17 Y s 646 1173 m -17 Y s 680 1173 m -17 Y s 715 1173 m -17 Y s 750 1190 m -34 Y s 785 1173 m -17 Y s 820 1173 m -17 Y s 855 1173 m -17 Y s 890 1173 m -17 Y s 925 1190 m -34 Y s 960 1173 m -17 Y s 995 1173 m -17 Y s 1030 1173 m -17 Y s 1064 1173 m -17 Y s 1099 1190 m -34 Y s 1134 1173 m -17 Y s 1169 1173 m -17 Y s 1204 1173 m -17 Y s 1239 1173 m -17 Y s 1274 1190 m -34 Y s 1309 1173 m -17 Y s 1344 1173 m -17 Y s 1379 1173 m -17 Y s 1413 1173 m -17 Y s 1448 1190 m -34 Y s 1483 1173 m -17 Y s 1518 1173 m -17 Y s 1553 1173 m -17 Y s 1588 1173 m -17 Y s 1623 1190 m -34 Y s 1658 1173 m -17 Y s 1693 1173 m -17 Y s 1728 1173 m -17 Y s 1763 1173 m -17 Y s 1797 1190 m -34 Y s 1832 1173 m -17 Y s 1867 1173 m -17 Y s 1902 1173 m -17 Y s 1937 1173 m -17 Y s 1972 1190 m -34 Y s 225 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 362 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 386 1105 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 407 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 433 1127 m 3 2 d 4 4 d -31 Y s 536 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -5 1 d -3 X cl s 561 1105 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 582 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 604 1126 m 1 Y 2 3 d 1 2 d 3 1 d 7 X 3 -1 d 1 -2 d 2 -3 d -3 Y -2 -3 d -3 -4 d -15 -15 d 21 X s 711 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 735 1105 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 756 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 780 1133 m 17 X -9 -12 d 5 X 3 -1 d 1 -2 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -5 1 d -1 2 d -2 3 d s 886 1133 m -5 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 910 1105 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 931 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 967 1133 m -15 -21 d 23 X s 967 1133 m -31 Y s 1060 1133 m -4 -1 d -4 -5 d -1 -7 d -5 Y 1 -7 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1084 1105 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1105 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1145 1133 m -15 X -2 -13 d 2 1 d 4 2 d 5 X 4 -2 d 3 -3 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 1235 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1259 1105 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1280 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1321 1129 m -2 3 d -4 1 d -3 X -5 -1 d -3 -5 d -1 -7 d -8 Y 1 -6 d 3 -3 d 5 -1 d 1 X 5 1 d 3 3 d 1 5 d 1 Y -1 5 d -3 3 d -5 1 d -1 X -5 -1 d -3 -3 d -1 -5 d s 1409 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1433 1105 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1454 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -5 1 d -3 X cl s 1497 1133 m -15 -31 d s 1476 1133 m 21 X s 1584 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1608 1105 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1629 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1658 1133 m -5 -1 d -1 -3 d -3 Y 1 -3 d 3 -2 d 6 -1 d 5 -2 d 3 -3 d 1 -3 d -4 Y -1 -3 d -2 -2 d -4 -1 d -6 X -5 1 d -1 2 d -2 3 d 4 Y 2 3 d 3 3 d 4 2 d 6 1 d 3 2 d 2 3 d 3 Y -2 3 d -4 1 d -6 X cl s 1758 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1782 1105 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1804 1133 m -5 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1844 1123 m -1 -5 d -3 -3 d -5 -1 d -1 X -5 1 d -3 3 d -1 5 d 1 Y 1 5 d 3 3 d 5 1 d 1 X 5 -1 d 3 -3 d 1 -6 d -8 Y -1 -7 d -3 -5 d -5 -1 d -3 X -4 1 d -2 3 d s 1948 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1972 1105 m -2 -2 d 2 -1 d 2 1 d -2 2 d cl s 1989 1127 m 3 2 d 4 4 d -31 Y s 1745 816 227 1156 C 2040 2040 0 0 C 1745 816 227 1156 C 2040 2040 0 0 C 757 1821 m -34 Y s 757 1821 m 21 X s 757 1805 m 13 X s 757 1787 m 21 X s 786 1821 m 23 -34 d s 809 1821 m -23 -34 d s 820 1821 m -34 Y s 820 1821 m 14 X 5 -1 d 2 -2 d 2 -3 d -5 Y -2 -3 d -2 -2 d -5 -1 d -14 X s 854 1821 m -34 Y s 854 1787 m 19 X s 890 1821 m -4 -1 d -3 -3 d -2 -4 d -1 -4 d -9 Y 1 -4 d 2 -4 d 3 -3 d 4 -2 d 6 X 3 2 d 3 3 d 2 4 d 2 4 d 9 Y -2 4 d -2 4 d -3 3 d -3 1 d -6 X cl s 917 1821 m -34 Y s 917 1821 m 15 X 4 -1 d 2 -2 d 2 -3 d -3 Y -2 -3 d -2 -2 d -4 -2 d -15 X s 928 1805 m 12 -18 d s 951 1821 m -34 Y s 951 1821 m 21 X s 951 1805 m 13 X s 951 1787 m 21 X s 982 1821 m -34 Y s 982 1821 m 14 X 5 -1 d 2 -2 d 1 -3 d -3 Y -1 -3 d -2 -2 d -5 -2 d -14 X s 993 1805 m 11 -18 d s 1745 816 227 1156 C 2040 2040 0 0 C 1745 816 227 1156 C 2040 2040 0 0 C 117 1309 m 22 X s 123 1309 m -5 4 d -1 4 d 5 Y 1 3 d 5 1 d 16 X s 117 1339 m 16 X 5 2 d 1 3 d 5 Y -1 3 d -5 5 d s 117 1357 m 22 X s 117 1370 m 22 X s 123 1370 m -5 5 d -1 3 d 5 Y 1 3 d 5 2 d 16 X s 123 1388 m -5 5 d -1 3 d 5 Y 1 3 d 5 2 d 16 X s 105 1419 m 34 X s 122 1419 m -4 3 d -1 3 d 5 Y 1 3 d 4 3 d 4 2 d 4 X 5 -2 d 3 -3 d 1 -3 d -5 Y -1 -3 d -3 -3 d s 126 1448 m 19 Y -3 X -3 -1 d -2 -2 d -1 -3 d -5 Y 1 -3 d 4 -4 d 4 -1 d 4 X 5 1 d 3 4 d 1 3 d 5 Y -1 3 d -3 3 d s 117 1479 m 22 X s 126 1479 m -4 1 d -4 3 d -1 4 d 5 Y s 117 1522 m 1 -3 d 4 -3 d 4 -2 d 4 X 5 2 d 3 3 d 1 3 d 5 Y -1 3 d -3 4 d -5 1 d -4 X -4 -1 d -4 -4 d -1 -3 d -5 Y cl s 105 1556 m -3 Y 2 -3 d 5 -2 d 27 X s 117 1543 m 12 Y s 126 1581 m 19 Y -3 X -3 -2 d -2 -1 d -1 -3 d -5 Y 1 -4 d 4 -3 d 4 -1 d 4 X 5 1 d 3 3 d 1 4 d 5 Y -1 3 d -3 3 d s 117 1608 m 22 10 d s 117 1628 m 22 -10 d s 126 1636 m 19 Y -3 X -3 -2 d -2 -1 d -1 -3 d -5 Y 1 -4 d 4 -3 d 4 -1 d 4 X 5 1 d 3 3 d 1 4 d 5 Y -1 3 d -3 3 d s 117 1666 m 22 X s 123 1666 m -5 5 d -1 3 d 5 Y 1 4 d 5 1 d 16 X s 105 1699 m 28 X 5 1 d 1 4 d 3 Y s 117 1694 m 11 Y s 122 1733 m -4 -2 d -1 -5 d -5 Y 1 -4 d 4 -2 d 3 2 d 1 3 d 2 8 d 2 3 d 3 2 d 2 X 3 -2 d 1 -5 d -5 Y -1 -4 d -3 -2 d s 1745 816 227 1156 C NC 1745 816 227 113 bl 2040 2040 0 0 C 1066 -23 m -25 Y 2 -5 d 3 -1 d 3 X s 1062 -33 m 10 X s 1081 -42 m 18 X 3 Y -1 3 d -2 1 d -3 2 d -4 X -3 -2 d -3 -3 d -2 -4 d -3 Y 2 -5 d 3 -3 d 3 -1 d 4 X 3 1 d 3 3 d s 1119 -23 m -3 X -3 -1 d -2 -5 d -25 Y s 1107 -33 m 10 X s 1137 -23 m -3 X -3 -1 d -1 -5 d -25 Y s 1125 -33 m 11 X s 1745 816 227 113 C 227 267 m -154 Y 35 X 397 Y 17 X 266 Y 35 X -153 Y 17 X -50 Y 18 X -306 Y 35 X 153 Y 17 X -153 Y 18 X 153 Y 17 X -153 Y 18 X -154 Y 52 X 154 Y 17 X -154 Y 18 X 154 Y 17 X -154 Y 157 X 154 Y 35 X -154 Y 157 X 154 Y 18 X -154 Y 1047 X 154 Y s NC 227 113 m 816 Y s 244 113 m -17 X s 244 154 m -17 X s 244 188 m -17 X s 244 217 m -17 X s 244 243 m -17 X s 261 267 m -34 X s 160 276 m 3 2 d 5 5 d -32 Y s 244 420 m -17 X s 244 510 m -17 X s 244 573 m -17 X s 244 623 m -17 X s 244 663 m -17 X s 244 697 m -17 X s 244 727 m -17 X s 244 753 m -17 X s 261 776 m -34 X s 130 786 m 3 1 d 5 5 d -32 Y s 165 792 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 244 929 m -17 X s 227 113 m 1745 X s 227 147 m -34 Y s 262 130 m -17 Y s 296 130 m -17 Y s 331 130 m -17 Y s 366 130 m -17 Y s 401 147 m -34 Y s 436 130 m -17 Y s 471 130 m -17 Y s 506 130 m -17 Y s 541 130 m -17 Y s 576 147 m -34 Y s 611 130 m -17 Y s 646 130 m -17 Y s 680 130 m -17 Y s 715 130 m -17 Y s 750 147 m -34 Y s 785 130 m -17 Y s 820 130 m -17 Y s 855 130 m -17 Y s 890 130 m -17 Y s 925 147 m -34 Y s 960 130 m -17 Y s 995 130 m -17 Y s 1030 130 m -17 Y s 1064 130 m -17 Y s 1099 147 m -34 Y s 1134 130 m -17 Y s 1169 130 m -17 Y s 1204 130 m -17 Y s 1239 130 m -17 Y s 1274 147 m -34 Y s 1309 130 m -17 Y s 1344 130 m -17 Y s 1379 130 m -17 Y s 1413 130 m -17 Y s 1448 147 m -34 Y s 1483 130 m -17 Y s 1518 130 m -17 Y s 1553 130 m -17 Y s 1588 130 m -17 Y s 1623 147 m -34 Y s 1658 130 m -17 Y s 1693 130 m -17 Y s 1728 130 m -17 Y s 1763 130 m -17 Y s 1797 147 m -34 Y s 1832 130 m -17 Y s 1867 130 m -17 Y s 1902 130 m -17 Y s 1937 130 m -17 Y s 1972 147 m -34 Y s 225 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 362 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 386 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 407 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 433 85 m 3 1 d 4 5 d -32 Y s 536 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 561 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 582 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 604 83 m 2 Y 2 3 d 1 1 d 3 2 d 7 X 3 -2 d 1 -1 d 2 -3 d -3 Y -2 -3 d -3 -5 d -15 -15 d 21 X s 711 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 735 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 756 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 780 91 m 17 X -9 -12 d 5 X 3 -2 d 1 -1 d 2 -5 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -5 1 d -1 2 d -2 3 d s 886 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 910 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 931 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 967 91 m -15 -21 d 23 X s 967 91 m -32 Y s 1060 91 m -4 -2 d -4 -4 d -1 -8 d -4 Y 1 -8 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1084 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1105 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1145 91 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 1235 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1259 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1280 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1321 86 m -2 3 d -4 2 d -3 X -5 -2 d -3 -4 d -1 -8 d -7 Y 1 -7 d 3 -3 d 5 -1 d 1 X 5 1 d 3 3 d 1 5 d 2 Y -1 4 d -3 3 d -5 2 d -1 X -5 -2 d -3 -3 d -1 -4 d s 1409 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1433 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1454 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 1497 91 m -15 -32 d s 1476 91 m 21 X s 1584 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1608 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1629 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1658 91 m -5 -2 d -1 -3 d -3 Y 1 -3 d 3 -1 d 6 -2 d 5 -1 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -2 d -4 -1 d -6 X -5 1 d -1 2 d -2 3 d 5 Y 2 3 d 3 3 d 4 1 d 6 2 d 3 1 d 2 3 d 3 Y -2 3 d -4 2 d -6 X cl s 1758 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1782 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1804 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1844 80 m -1 -4 d -3 -3 d -5 -2 d -1 X -5 2 d -3 3 d -1 4 d 2 Y 1 4 d 3 3 d 5 2 d 1 X 5 -2 d 3 -3 d 1 -6 d -7 Y -1 -8 d -3 -5 d -5 -1 d -3 X -4 1 d -2 3 d s 1948 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1972 62 m -2 -2 d 2 -1 d 2 1 d -2 2 d cl s 1989 85 m 3 1 d 4 5 d -32 Y s 1745 816 227 113 C 2040 2040 0 0 C 1745 816 227 113 C 2040 2040 0 0 C 757 810 m -34 Y s 757 810 m 22 -34 d s 779 810 m -34 Y s 800 810 m -12 -34 d s 800 810 m 13 -34 d s 792 787 m 17 X s 822 810 m -24 Y 1 -5 d 3 -3 d 5 -2 d 3 X 5 2 d 4 3 d 1 5 d 24 Y s 864 810 m -34 Y s 852 810 m 23 X s 883 810 m -34 Y s 896 810 m -34 Y s 896 776 m 19 X s 924 810 m -24 Y 1 -5 d 3 -3 d 5 -2 d 3 X 5 2 d 4 3 d 1 5 d 24 Y s 980 805 m -3 3 d -5 2 d -6 X -5 -2 d -3 -3 d -3 Y 1 -3 d 2 -2 d 3 -2 d 10 -3 d 3 -1 d 2 -2 d 1 -3 d -5 Y -3 -3 d -5 -2 d -6 X -5 2 d -3 3 d s 1745 816 227 113 C 2040 2040 0 0 C 1745 816 227 113 C 2040 2040 0 0 C 117 273 m 22 X s 123 273 m -5 5 d -1 3 d 5 Y 1 3 d 5 2 d 16 X s 117 304 m 16 X 5 2 d 1 3 d 5 Y -1 3 d -5 5 d s 117 322 m 22 X s 117 335 m 22 X s 123 335 m -5 5 d -1 3 d 5 Y 1 3 d 5 1 d 16 X s 123 352 m -5 5 d -1 4 d 4 Y 1 4 d 5 1 d 16 X s 105 383 m 34 X s 122 383 m -4 3 d -1 4 d 5 Y 1 3 d 4 3 d 4 2 d 4 X 5 -2 d 3 -3 d 1 -3 d -5 Y -1 -4 d -3 -3 d s 126 412 m 20 Y -3 X -3 -2 d -2 -1 d -1 -4 d -5 Y 1 -3 d 4 -3 d 4 -2 d 4 X 5 2 d 3 3 d 1 3 d 5 Y -1 4 d -3 3 d s 117 443 m 22 X s 126 443 m -4 2 d -4 3 d -1 3 d 5 Y s 117 487 m 1 -3 d 4 -4 d 4 -1 d 4 X 5 1 d 3 4 d 1 3 d 5 Y -1 3 d -3 3 d -5 2 d -4 X -4 -2 d -4 -3 d -1 -3 d -5 Y cl s 105 521 m -3 Y 2 -4 d 5 -1 d 27 X s 117 508 m 11 Y s 126 545 m 20 Y -3 X -3 -2 d -2 -2 d -1 -3 d -5 Y 1 -3 d 4 -3 d 4 -2 d 4 X 5 2 d 3 3 d 1 3 d 5 Y -1 3 d -3 4 d s 117 573 m 22 9 d s 117 592 m 22 -10 d s 126 600 m 20 Y -3 X -3 -2 d -2 -2 d -1 -3 d -5 Y 1 -3 d 4 -3 d 4 -2 d 4 X 5 2 d 3 3 d 1 3 d 5 Y -1 3 d -3 4 d s 117 631 m 22 X s 123 631 m -5 5 d -1 3 d 5 Y 1 3 d 5 2 d 16 X s 105 663 m 28 X 5 2 d 1 3 d 3 Y s 117 658 m 12 Y s 122 697 m -4 -1 d -1 -5 d -5 Y 1 -5 d 4 -1 d 3 1 d 1 3 d 2 8 d 2 4 d 3 1 d 2 X 3 -1 d 1 -5 d -5 Y -1 -5 d -3 -1 d s 1745 816 227 113 C gr gr showpage end %%EndDocument @endspecial 172 2156 a Fr(Figure)32 b(1:)g(Distribution)e(of)i Fk(T)1308 2171 y Fi(ef)7 b(f)1460 2156 y Fr([K],)33 b(in)f(the)h(p)s (erio)s(d)e(1)h(Marc)m(h)i(through)e(17)g(July)h(2001.)-9 2456 y(the)38 b(range)f(from)g(40)g(to)g(700)g(k)m(eV,)i(with)e(a)g (GRB)g(detection)h(rate)g(of)f(ab)s(out)g(0.7)g(ev)m(en)m(ts/da)m(y)-8 b(.)41 b(F)-8 b(or)-9 2577 y(eac)m(h)34 b(GRB)e(whic)m(h)i(triggers)e (the)i(on-b)s(oard)e(trigger)g(logic,)f(high)h(time)g(resolution)g (\(up)h(to)g(0)p Fk(:)p Fr(5)49 b(ms\))-9 2697 y(time)31 b(pro\014les)i(are)g(transmitted.)g(In)g(addition,)f(1)17 b(s)32 b(coun)m(t)i(rates)g(from)e(the)h(GRBM)g(in)f(t)m(w)m(o)i (energy)-9 2817 y(bands)39 b(\(40)26 b Fj(\000)h Fr(700)17 b(k)m(eV)38 b(and)h Fk(>)55 b Fr(100)17 b(k)m(eV\))38 b(are)h(con)m(tin)m(uously)g(recorded)h(and)f(transmitted.)f(F)-8 b(rom)-9 2938 y(the)33 b(GRBM)f(data)g(rough)g(information)e(on)i(the)h (GRB)f(direction)g(can)h(also)e(b)s(e)i(deriv)m(ed)g([20)p (#cite.guidorzi) [[475 364 487 376] [1 1 1 [3 3]] [0 0 1]] pdfm (].) 240 3058 y(F)-8 b(or)25 b(the)h(presen)m(t)i(analysis)e(w)m(e)h(use)g (t)m(w)m(o)f(quan)m(tities)g(from)f(the)h(GRBM)g(data:)g(the)g(initial) c(time)-9 3178 y(of)28 b(eac)m(h)i(GRB)e(and)i(its)e(burst)i(duration.) e(In)h(the)h(p)s(erio)s(d)e(1)g(Marc)m(h)i(through)f(17)g(July)g(2001)f (w)m(e)i(ha)m(v)m(e)-9 3299 y(101)36 b(Bepp)s(oSAX)i(bursts,)g(but)f (only)g(51)f(o)s(ccur)i(at)e(times)h(when)h(b)s(oth)f(an)m(tennas)h(w)m (ere)g(op)s(erating.)-9 3419 y(The)33 b(GRB)f(fall)f(in)m(to)g(t)m(w)m (o)j(categories:)e(one)h(of)f(the)h(38)g(GRB)f(ev)m(en)m(ts)j(with)d (short)h(duration)e(\()p Fj(\024)45 b Fr(1)17 b(s\))-9 3540 y(and)35 b(another)h(one)g(of)f(63)h(GRB)f(with)g(longer)g (duration.)g(The)h(short)g(duration)f(ev)m(en)m(ts)j(include)d(all)-9 3660 y(the)46 b(GRB's)f(whic)m(h)i(did)e(not)g(trigger)g(the)h(on-b)s (oard)f(logic,)f(th)m(us)i(their)g(exact)g(duration)f(is)g(not)-9 3780 y(a)m(v)-5 b(ailable.)31 b(Indicating)i(with)g Fk(t)1143 3795 y Fi(\015)1222 3780 y Fr(\(trigger)f(time\))h(the)h(initial)c (time)j(for)g(the)h(GRB's,)g(for)g(eac)m(h)g(burst)-9 3901 y(w)m(e)41 b(considered)g(the)f(EXPLORER)h(and)f(NA)m(UTILUS)i (data)d(in)h Fk(t)2529 3916 y Fi(m)2636 3901 y Fr(=)g(800)f(s)i(in)m (terv)-5 b(als)39 b(cen)m(tered)-9 4021 y(at)33 b(the)g Fk(t)314 4036 y Fi(\015)392 4021 y Fr(\()p Fk(t)465 4036 y Fi(\015)549 4021 y Fj(\006)40 b Fr(400)33 b(s\).)h(Eac)m(h)g(in)m (terv)-5 b(al)32 b(is)h(co)m(v)m(ered)i(b)m(y)g(800)p Fk(=)p Fr(0)p Fk(:)p Fr(004544)26 b(=)j(176056)j(data)h(samples.)-9 4142 y(The)42 b(a)m(v)m(erage)g(v)-5 b(alue)40 b(of)h(the)g(data)g(giv) m(es,)g(in)g(absence)h(of)f(signal,)f(noise)g(temp)s(erature)h Fk(T)3414 4157 y Fi(ef)7 b(f)3534 4142 y Fr(.)41 b(The)-9 4262 y(distributions)e(of)i Fk(T)746 4277 y Fi(ef)7 b(f)906 4262 y Fr(obtained)41 b(for)f(these)i(stretc)m(hes)i(of)c(GW)h(data)g (are)g(sho)m(wn)h(in)e(Fig.)g(1)p (#figure.1) [[494 206 500 218] [1 1 1 [3 3]] [0 0 1]] pdfm (.)h(W)-8 b(e)-9 4382 y(note)35 b(the)g(go)s(o)s(d)f(b)s(eha)m(vior)h(of)f(b)s (oth)h(detectors.)h(In)g(view)f(of)g(this)f(go)s(o)s(d)g(b)s(eha)m (viour)h(w)m(e)h(though)m(t)f(to)-9 4503 y(limit)f(our)j(analysis)g(to) g(the)h(47)f(stretc)m(hes)j(with)d Fk(T)1905 4518 y Fi(ef)7 b(f)2060 4503 y Fk(<)36 b Fr(20)17 b(mK)36 b(on)i(b)s(oth)f(detectors,) i(losing)d(only)-9 4632 y(four)g(stretc)m(hes.)k(F)-8 b(or)36 b(these)i(stretc)m(hes)i(w)m(e)e(ha)m(v)m(e)g(the)g(follo)m (wing)c(a)m(v)m(erage)k(v)-5 b(alues:)3139 4607 y(\026)3120 4632 y Fk(T)3191 4585 y Fi(expl)3177 4660 y(ef)7 b(f)3360 4632 y Fr(=)36 b(8)p Fk(:)p Fr(8)17 b(mK)-9 4763 y(and)199 4737 y(\026)180 4763 y Fk(T)251 4726 y Fi(naut)237 4789 y(ef)7 b(f)429 4763 y Fr(=)28 b(6)p Fk(:)p Fr(1)17 b(mK.)-9 5027 y Fs(3)193 b(Cross-correlation)36 b(analysis)-9 5148 y Fr(Due)e(to)h(the)g(unkno)m(wn)i(time)c(gap)i(b)s(et)m(w)m(een)i (GW's)e(and)g(GRB's,)g(it)f(is)g(essen)m(tial)h(to)g(ha)m(v)m(e)h(at)e (least)-9 5269 y(t)m(w)m(o)46 b(indep)s(enden)m(t)h(GW)e(detectors)i (at)e(disp)s(osal.)f(In)i(suc)m(h)h(a)e(case)i(w)m(e)f(can)g (cross-correlate)g(the)-9 5389 y(t)m(w)m(o)33 b(outputs,)h(since)f(w)m (e)h(exp)s(ect)g(that,)e(if)g(an)m(y)h(GW)g(burst)g(arriv)m(es)g(on)g (the)g(Earth,)g(b)s(oth)g(detectors)-9 5510 y(resp)s(ond)28 b(at)f(the)i(same)e(time)g(within)f(the)i(tra)m(v)m(el)g(time)f (di\013erence)h(of)f(the)h(GW)g(burst.)g(EXPLORER)-9 5630 y(and)j(NA)m(UTILUS)j(b)s(eing)d(ab)s(out)g(700)17 b(km)30 b(apart,)h(the)h(maxim)m(um)e(tra)m(v)m(el)i(time)e (di\013erence)i(is)f(ab)s(out)-9 5879 y(4)p eop %%Page: 5 5 5 4 bop -9 1998 a @beginspecial 60 @hscale 40 @vscale 0 @angle @setspecial %%BeginDocument: correlazione.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y 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/basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlendef} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 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113 1959 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 1988 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 157 1980 m 2 Y 2 3 d 1 1 d 3 2 d 6 X 3 -2 d 2 -1 d 1 -3 d -3 Y -1 -3 d -3 -5 d -15 -15 d 21 X s 227 113 m 1745 X s 227 147 m -34 Y s 285 130 m -17 Y s 343 130 m -17 Y s 401 130 m -17 Y s 459 130 m -17 Y s 518 147 m -34 Y s 576 130 m -17 Y s 634 130 m -17 Y s 692 130 m -17 Y s 750 130 m -17 Y s 808 147 m -34 Y s 867 130 m -17 Y s 925 130 m -17 Y s 983 130 m -17 Y s 1041 130 m -17 Y s 1099 147 m -34 Y s 1158 130 m -17 Y s 1216 130 m -17 Y s 1274 130 m -17 Y s 1332 130 m -17 Y s 1390 147 m -34 Y s 1448 130 m -17 Y s 1507 130 m -17 Y s 1565 130 m -17 Y s 1623 130 m -17 Y s 1681 147 m -34 Y s 1739 130 m -17 Y s 1797 130 m -17 Y s 1856 130 m -17 Y s 1914 130 m -17 Y s 1972 147 m -34 Y s 183 73 m 27 X s 225 85 m 3 1 d 5 5 d -32 Y s 269 91 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 474 73 m 27 X s 516 85 m 3 1 d 5 5 d -32 Y s 551 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 780 73 m 27 X s 836 91 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 1098 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1398 91 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 1660 85 m 3 1 d 5 5 d -32 Y s 1695 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1951 85 m 3 1 d 4 5 d -32 Y s 1995 91 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -4 1 d -2 2 d -1 3 d s 1745 1859 227 113 C 254 1071 m 4 25 d 5 56 d 4 -14 d 4 -56 d 4 -16 d 4 -5 d 5 28 d 4 -51 d 4 -50 d 4 1 d 5 25 d 4 21 d 4 -64 d 4 -26 d 5 -5 d 4 24 d 4 67 d 4 62 d 4 35 d 5 27 d 4 12 d 4 -37 d 4 -20 d 5 -32 d 4 48 d 4 20 d 4 -11 d 4 3 d 5 -19 d 4 -42 d 4 11 d 4 -35 d 5 -55 d 4 13 d 4 20 d 4 81 d 4 24 d 5 -32 d 4 45 d 4 1 d 4 23 d 5 52 d 4 53 d 4 -34 d 4 -46 d 5 -56 d 4 34 d 4 28 d 4 16 d 4 18 d 5 -23 d 4 -28 d 4 -38 d 4 -46 d 5 -17 d 4 54 d 4 35 d 4 -15 d 4 -33 d 5 2 d 4 -6 d 4 -11 d 4 4 d 5 -4 d 4 -28 d 4 -51 d 4 -52 d 4 31 d 5 61 d 4 -3 d 4 3 d 4 -25 d 5 16 d 4 23 d 4 3 d 4 -25 d 5 -3 d 4 10 d 4 21 d 4 11 d 4 -7 d 5 -24 d 4 -14 d 4 -3 d 4 -3 d 5 30 d 4 11 d 4 -32 d 4 6 d 4 28 d 5 16 d 4 16 d 4 24 d 4 -12 d 5 13 d 4 -44 d 4 -39 d 4 -10 d 5 -40 d 4 12 d 4 39 d 4 18 d 4 2 d 5 12 d 4 -31 d 4 -57 d 4 -27 d 5 3 d 4 -6 d 4 -13 d 4 4 d 4 -25 d 5 -24 d 4 25 d 4 -11 d 4 7 d 5 -19 d 4 -24 d 4 48 d 4 22 d 4 48 d 5 6 d 4 -30 d 4 35 d 4 53 d 5 -25 d 4 -20 d 4 -14 d 4 23 d 5 -10 d 4 -35 d 4 -1 d 4 -5 d 4 23 d 5 45 d 4 -8 d 4 -19 d 4 70 d 5 27 d 4 -60 d 4 -59 d 4 -24 d 4 49 d 5 18 d 4 -62 d 4 -60 d 4 -16 d 5 8 d 4 51 d 4 -9 d 4 -12 d 4 -35 d 5 6 d 4 39 d 4 25 d 4 -31 d 5 -44 d 4 -16 d 4 5 d 4 -20 d 5 14 d 4 53 d 4 79 d 4 24 d 4 -45 d 5 -22 d 4 16 d 4 18 d 4 7 d 5 7 d 4 -5 d 4 -7 d 4 -24 d 4 -51 d 5 2 d 4 -1 d 4 22 d 4 45 d 5 28 d 4 X 4 -25 d 4 -26 d 4 52 d 5 9 d 4 -17 d 4 28 d 4 17 d 5 -2 d 4 -16 d 4 19 d 4 -24 d 5 -12 d 4 -43 d 4 -38 d 4 -25 d 4 -26 d 5 -17 d 4 30 d 4 31 d 4 -30 d 5 28 d 4 3 d s 1108 967 m 4 61 d 4 15 d 4 15 d 5 16 d 4 20 d 4 -41 d 4 -70 d 5 -75 d 4 -10 d 4 19 d 4 33 d 4 25 d 5 15 d 4 -13 d 4 -33 d 4 12 d 5 48 d 4 -11 d 4 -24 d 4 14 d 5 15 d 4 6 d 4 10 d 4 3 d 4 -11 d 5 -37 d 4 -42 d 4 -11 d 4 -38 d 5 4 d 4 14 d 4 28 d 4 -1 d 4 -10 d 5 -16 d 4 22 d 4 28 d 4 -7 d 5 19 d 4 43 d 4 24 d 4 -40 d 5 -62 d 4 22 d 4 -5 d 4 12 d 4 25 d 5 77 d 4 23 d 4 -17 d 4 27 d 5 33 d 4 8 d 4 19 d 4 -23 d 4 -1 d 5 13 d 4 9 d 4 -24 d 4 7 d 5 11 d 4 14 d 4 45 d 4 20 d 4 23 d 5 -14 d 4 -7 d 4 10 d 4 51 d 5 -3 d 4 -62 d 4 -48 d 4 -37 d 5 -22 d 4 -45 d 4 -29 d 4 42 d 4 86 d 5 37 d 4 -8 d 4 15 d 4 -50 d 5 -1 d 4 45 d 4 31 d 4 -25 d 4 -18 d 5 -44 d 4 20 d 4 29 d 4 -21 d 5 -13 d 4 34 d 4 -65 d 4 -67 d 4 11 d 5 -16 d 4 10 d 4 69 d 4 19 d 5 -3 d 4 9 d 4 11 d 4 12 d 5 -7 d 4 -72 d 4 -28 d 4 -5 d 4 -6 d 5 27 d 4 14 d 4 4 d 4 -23 d 5 1 d 4 44 d 4 15 d 4 -22 d 4 49 d 5 5 d 4 -49 d 4 -21 d 4 21 d 5 47 d 4 10 d 4 5 d 4 -20 d 4 30 d 5 1 d 4 -59 d 4 -59 d 4 -34 d 5 -61 d 4 -55 d 4 -17 d 4 -11 d 5 -16 d 4 -14 d 4 35 d 4 48 d 4 36 d 5 15 d 4 19 d 4 -29 d 4 -48 d 5 7 d 4 37 d 4 67 d 4 87 d 4 51 d 5 -1 d 4 -47 d 4 -42 d 4 6 d 5 9 d 4 35 d 4 3 d 4 -45 d 4 -30 d 5 -61 d 4 -49 d 4 -17 d 4 18 d 5 -38 d 4 51 d 4 47 d 4 42 d 5 12 d 4 5 d 4 39 d 4 17 d 4 -16 d 5 -55 d 4 -24 d 4 22 d 4 -73 d 5 -56 d 4 25 d 4 25 d 4 16 d 4 15 d 5 27 d 4 -34 d 4 -12 d 4 -16 d 5 66 d 4 101 d 4 12 d 4 -13 d 5 -6 d 4 -1 d 4 -11 d 4 -34 d 4 -5 d 5 -19 d 4 -46 d 4 -30 d 4 -10 d s /w 13 def /w2 {w 2 div} def /w3 {w 3 div} def 254 1071 258 1096 263 1152 267 1138 271 1082 275 1066 279 1061 284 1089 288 1038 292 988 296 989 301 1014 305 1035 309 971 313 945 318 940 322 964 326 1031 330 1093 334 1128 339 1155 343 1167 347 1130 351 1110 356 1078 360 1126 364 1146 368 1135 372 1138 377 1119 381 1077 385 1088 389 1053 394 998 398 1011 402 1031 406 1112 410 1136 415 1104 419 1149 423 1150 427 1173 432 1225 436 1278 440 1244 444 1198 449 1142 453 1176 457 1204 461 1220 465 1238 470 1215 474 1187 478 1149 482 1103 487 1086 491 1140 495 1175 499 1160 503 1127 508 1129 512 1123 516 1112 520 1116 525 1112 529 1084 533 1033 537 981 541 1012 546 1073 550 1070 554 1073 558 1048 563 1064 567 1087 571 1090 575 1065 580 1062 584 1072 588 1093 592 1104 596 1097 601 1073 605 1059 609 1056 613 1053 618 1083 622 1094 626 1062 630 1068 634 1096 639 1112 643 1128 647 1152 651 1140 656 1153 660 1109 664 1070 668 1060 673 1020 100 { m31} R 677 1032 681 1071 685 1089 689 1091 694 1103 698 1072 702 1015 706 988 711 991 715 985 719 972 723 976 727 951 732 927 736 952 740 941 744 948 749 929 753 905 757 953 761 975 765 1023 770 1029 774 999 778 1034 782 1087 787 1062 791 1042 795 1028 799 1051 804 1041 808 1006 812 1005 816 1000 820 1023 825 1068 829 1060 833 1041 837 1111 842 1138 846 1078 850 1019 854 995 858 1044 863 1062 867 1000 871 940 875 924 880 932 884 983 888 974 892 962 896 927 901 933 905 972 909 997 913 966 918 922 922 906 926 911 930 891 935 905 939 958 943 1037 947 1061 951 1016 956 994 960 1010 964 1028 968 1035 973 1042 977 1037 981 1030 985 1006 989 955 994 957 998 956 1002 978 1006 1023 1011 1051 1015 1051 1019 1026 1023 1000 1027 1052 1032 1061 1036 1044 1040 1072 1044 1089 1049 1087 1053 1071 1057 1090 1061 1066 1066 1054 1070 1011 1074 973 1078 948 1082 922 1087 905 1091 935 1095 966 100 { m31} R 1099 936 1104 964 1108 967 1112 1028 4 { m31} R 1116 1043 1120 1058 1125 1074 1129 1094 1133 1053 1137 983 1142 908 1146 898 1150 917 1154 950 1158 975 1163 990 1167 977 1171 944 1175 956 1180 1004 1184 993 1188 969 1192 983 1197 998 1201 1004 1205 1014 1209 1017 1213 1006 1218 969 1222 927 1226 916 1230 878 1235 882 1239 896 1243 924 1247 923 1251 913 1256 897 1260 919 1264 947 1268 940 1273 959 1277 1002 1281 1026 1285 986 1290 924 1294 946 1298 941 1302 953 1306 978 1311 1055 1315 1078 1319 1061 1323 1088 1328 1121 1332 1129 1336 1148 1340 1125 1344 1124 1349 1137 1353 1146 1357 1122 1361 1129 1366 1140 1370 1154 1374 1199 1378 1219 1382 1242 1387 1228 1391 1221 1395 1231 1399 1282 1404 1279 1408 1217 1412 1169 1416 1132 1421 1110 1425 1065 1429 1036 1433 1078 1437 1164 1442 1201 1446 1193 1450 1208 1454 1158 1459 1157 1463 1202 1467 1233 1471 1208 1475 1190 1480 1146 1484 1166 1488 1195 1492 1174 1497 1161 1501 1195 1505 1130 1509 1063 1513 1074 1518 1058 1522 1068 1526 1137 1530 1156 1535 1153 100 { m31} R 1539 1162 1543 1173 1547 1185 1552 1178 1556 1106 1560 1078 1564 1073 1568 1067 1573 1094 1577 1108 1581 1112 1585 1089 1590 1090 1594 1134 1598 1149 1602 1127 1606 1176 1611 1181 1615 1132 1619 1111 1623 1132 1628 1179 1632 1189 1636 1194 1640 1174 1644 1204 1649 1205 1653 1146 1657 1087 1661 1053 1666 992 1670 937 1674 920 1678 909 1683 893 1687 879 1691 914 1695 962 1699 998 1704 1013 1708 1032 1712 1003 1716 955 1721 962 1725 999 1729 1066 1733 1153 1737 1204 1742 1203 1746 1156 1750 1114 1754 1120 1759 1129 1763 1164 1767 1167 1771 1122 1775 1092 1780 1031 1784 982 1788 965 1792 983 1797 945 1801 996 1805 1043 1809 1085 1814 1097 1818 1102 1822 1141 1826 1158 1830 1142 1835 1087 1839 1063 1843 1085 1847 1012 1852 956 1856 981 1860 1006 1864 1022 1868 1037 1873 1064 1877 1030 1881 1018 1885 1002 1890 1068 1894 1169 1898 1181 1902 1168 1907 1162 1911 1161 1915 1150 1919 1116 1923 1111 1928 1092 1932 1046 1936 1016 1940 1006 96 { m31} R 2040 2040 0 0 C 1745 1859 227 113 C 2040 2040 0 0 C 889 52 m -1 3 d -5 2 d -5 X -5 -2 d -2 -3 d 2 -3 d 3 -2 d 8 -1 d 4 -2 d 1 -3 d -2 Y -1 -3 d -5 -2 d -5 X -5 2 d -2 3 d s 899 47 m 19 X 4 Y -1 3 d -2 1 d -3 2 d -5 X -3 -2 d -3 -3 d -2 -5 d -3 Y 2 -5 d 3 -3 d 3 -2 d 5 X 3 2 d 3 3 d s 948 52 m -4 3 d -3 2 d -5 X -3 -2 d -3 -3 d -2 -5 d -3 Y 2 -5 d 3 -3 d 3 -2 d 5 X 3 2 d 4 3 d s 965 57 m -3 -2 d -3 -3 d -2 -5 d -3 Y 2 -5 d 3 -3 d 3 -2 d 5 X 3 2 d 4 3 d 1 5 d 3 Y -1 5 d -4 3 d -3 2 d -5 X cl s 990 57 m -23 Y s 990 51 m 5 4 d 3 2 d 5 X 3 -2 d 1 -4 d -17 Y s 1038 68 m -34 Y s 1038 52 m -3 3 d -3 2 d -5 X -3 -2 d -4 -3 d -1 -5 d -3 Y 1 -5 d 4 -3 d 3 -2 d 5 X 3 2 d 3 3 d s 1067 52 m -1 3 d -5 2 d -5 X -5 -2 d -1 -3 d 1 -3 d 3 -2 d 9 -1 d 3 -2 d 1 -3 d -2 Y -1 -3 d -5 -2 d -5 X -5 2 d -1 3 d s 1745 1859 227 113 C 2040 2040 0 0 C 1745 1859 227 113 C 2040 2040 0 0 C 296 277 m -3 -3 d -2 -3 d -5 Y 2 -4 d 3 -3 d 5 -1 d 3 X 5 1 d 3 3 d 2 4 d 5 Y -2 3 d -3 3 d s 291 288 m 23 X s 301 288 m -5 2 d -3 3 d -2 3 d 5 Y s 291 316 m 2 -3 d 3 -4 d 5 -1 d 3 X 5 1 d 3 4 d 2 3 d 5 Y -2 3 d -3 3 d -5 2 d -3 X -5 -2 d -3 -3 d -2 -3 d -5 Y cl s 296 356 m -3 -1 d -2 -5 d -5 Y 2 -5 d 3 -1 d 3 1 d 2 3 d 2 8 d 1 4 d 3 1 d 2 X 3 -1 d 2 -5 d -5 Y -2 -5 d -3 -1 d s 296 384 m -3 -2 d -2 -5 d -4 Y 2 -5 d 3 -2 d 3 2 d 2 3 d 2 8 d 1 3 d 3 2 d 2 X 3 -2 d 2 -5 d -4 Y -2 -5 d -3 -2 d s 299 395 m 29 Y s 296 455 m -3 -3 d -2 -3 d -5 Y 2 -3 d 3 -4 d 5 -1 d 3 X 5 1 d 3 4 d 2 3 d 5 Y -2 3 d -3 3 d s 291 473 m 2 -3 d 3 -4 d 5 -1 d 3 X 5 1 d 3 4 d 2 3 d 5 Y -2 3 d -3 3 d -5 2 d -3 X -5 -2 d -3 -3 d -2 -3 d -5 Y cl s 291 497 m 23 X s 301 497 m -5 2 d -3 3 d -2 3 d 5 Y s 291 518 m 23 X s 301 518 m -5 2 d -3 3 d -2 3 d 5 Y s 301 538 m 19 Y -3 X -3 -2 d -2 -1 d -2 -3 d -5 Y 2 -3 d 3 -4 d 5 -1 d 3 X 5 1 d 3 4 d 2 3 d 5 Y -2 3 d -3 3 d s 280 568 m 34 X s 291 599 m 23 X s 296 599 m -3 -3 d -2 -3 d -5 Y 2 -3 d 3 -4 d 5 -1 d 3 X 5 1 d 3 4 d 2 3 d 5 Y -2 3 d -3 3 d s 280 614 m 27 X 5 1 d 2 4 d 3 Y s 291 609 m 11 Y s 280 630 m 2 2 d -2 1 d -2 -1 d 2 -2 d cl s 291 632 m 23 X s 291 651 m 2 -3 d 3 -3 d 5 -2 d 3 X 5 2 d 3 3 d 2 3 d 5 Y -2 3 d -3 3 d -5 2 d -3 X -5 -2 d -3 -3 d -2 -3 d -5 Y cl s 291 675 m 23 X s 298 675 m -5 5 d -2 3 d 5 Y 2 3 d 5 2 d 16 X s 1745 1859 227 113 C gr gr showpage end %%EndDocument @endspecial 158 x Fr(Figure)30 b(2:)i(The)g(cross-correlation)f Fk(R)q Fr(\()p 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4430 y(correlation)e Fk(R)q Fr(\()p Fk(\034)11 b Fr(\),)41 b(sho)m(wn)g(in)d(Fig.)h(2)p (#figure.2) [[238 185 244 197] [1 1 1 [3 3]] [0 0 1]] pdfm (.)g(No)h (signi\014can)m(t)f(correlation)f(is)h(visible.)f(In)i(particular,)e (at)-9 4550 y Fk(\034)51 b Fr(=)41 b(0)17 b(s)40 b(w)m(e)h(get)f(the)g (negativ)m(e)h(v)-5 b(alue)39 b(of)h Fj(\000)p Fr(0)p Fk(:)p Fr(0027.)f(W)-8 b(e)41 b(also)e(rep)s(eated)i(the)f(ab)s(o)m(v)m (e)h(calculations)-9 4671 y(separately)f(for)f(the)h(GRB's)g(with)f (short)h(\()p Fj(\024)g Fr(1)17 b(s\))40 b(and)g(long)e(\()p Fk(>)i Fr(1)17 b(s\))39 b(time)g(duration.)f(Again,)h(no)-9 4791 y(correlation)46 b(app)s(ears)i(b)s(et)m(w)m(een)i(EXPLORER)f(and) f(NA)m(UTILUS)i(using)d(a)h(windo)m(w)h(of)e Fj(\006)p Fr(400)17 b(s)-9 4911 y(cen)m(tered)34 b(at)e(the)h(GRB)f(arriv)-5 b(al)30 b(times.)-9 5148 y Fs(3.1)106 b(Mo)s(deling)37 b(the)g(a)m(v)m(erage)h(cross-correlation)-9 5269 y Fr(In)31 b(order)g(to)f(pro)m(vide)h(quan)m(titativ)m(e)g(information)d(out)i (of)h(this)f(n)m(ull)g(result,)h(w)m(e)h(need)f(to)g(mo)s(del)e(our)-9 5389 y(exp)s(ectations)g(for)g(the)g(a)m(v)m(erage)h(cross-correlation) e(at)g(zero)i(dela)m(y)f(time)f Fk(R)q Fr(\(0\),)g(hereafter)i (indicated)-9 5510 y(with)i Fk(R)287 5525 y Fq(0)326 5510 y Fr(,)h(under)g(the)g(h)m(yp)s(othesis)h(that)f(suc)m(h)h (signals)d(do)h(exist.)240 5630 y(This)h(mo)s(deling)d(means)i(going)f (through)i(the)g(follo)m(wing)d(considerations.)3721 5879 y(5)p eop %%Page: 6 6 6 5 bop -9 1998 a @beginspecial 60 @hscale 40 @vscale 0 @angle @setspecial %%BeginDocument: gaussian.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict 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w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlendef} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode newpath gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1745 1859 227 113 bl 1745 1859 227 113 C 2040 2040 0 0 C 1090 -23 m -31 Y s 1090 -23 m 13 X 5 -1 d 1 -2 d 2 -3 d -3 Y -2 -3 d -1 -1 d -5 -2 d -13 X s 1100 -38 m 11 -16 d s 1745 1859 227 113 C 227 113 m 458 X 73 Y 22 X -73 Y 21 X 37 Y 22 X -37 Y 22 X 146 Y 22 X 218 Y 22 X -36 Y 22 X 400 Y 21 X -146 Y 22 X 109 Y 22 X -109 Y 22 X 509 Y 22 X 37 Y 21 X -146 Y 22 X 182 Y 22 X 109 Y 22 X -36 Y 22 X 218 Y 22 X -327 Y 21 X 218 Y 22 X 327 Y 22 X -36 Y 22 X -328 Y 22 X -36 Y 21 X 182 Y 22 X -436 Y 22 X 145 Y 22 X -582 Y 22 X 327 Y 22 X -36 Y 21 X -254 Y 22 X -291 Y 22 X 181 Y 22 X -145 Y 22 X -73 Y 21 X 109 Y 22 X -291 Y 22 X 37 Y 22 X -109 Y 22 X 36 Y 21 X -36 Y 22 X -37 Y 393 X s 227 113 m 176 X 9 1 d 70 X 9 1 d 18 X 9 1 d 8 X 9 1 d 9 X 9 1 d 9 1 d 8 1 d 9 1 d 9 2 d 9 2 d 9 2 d 9 2 d 8 3 d 9 3 d 9 3 d 9 4 d 9 5 d 8 5 d 9 6 d 9 6 d 9 8 d 9 8 d 8 9 d 9 11 d 9 11 d 9 13 d 9 13 d 9 16 d 8 16 d 9 19 d 9 19 d 9 22 d 9 23 d 8 25 d 9 27 d 9 28 d 9 31 d 9 32 d 9 34 d 8 36 d 9 37 d 9 39 d 9 41 d 9 42 d 8 43 d 9 45 d 9 45 d 9 47 d 9 46 d 8 47 d 9 48 d 9 46 d 9 47 d 9 45 d 9 45 d 8 43 d 9 42 d 9 39 d 9 38 d 9 34 d 8 32 d 9 29 d 9 26 d 9 22 d 9 19 d 9 14 d 8 11 d 9 7 d 9 2 d 9 -1 d 9 -6 d 8 -9 d 9 -14 d 9 -17 d 9 -21 d 9 -25 d 8 -28 d 9 -31 d 9 -34 d 9 -36 d 9 -39 d 9 -41 d 8 -43 d 9 -44 d 9 -46 d 9 -46 d 9 -47 d 8 -47 d 9 -47 d 9 -47 d 9 -46 d 9 -46 d 9 -45 d 8 -43 d 9 -43 d 9 -41 d 9 -40 d 9 -38 d 8 -36 d 9 -34 d 9 -33 d 9 -31 d 9 -29 d 8 -27 d 9 -26 d 9 -23 d 9 -22 d 9 -21 d 9 -18 d 8 -17 d 9 -16 d 9 -14 d 9 -13 d 9 -12 d 8 -11 d 9 -9 d 9 -9 d 9 -8 d 9 -6 d 9 -6 d 8 -6 d 9 -5 d 9 -4 d 9 -3 d 9 -4 d 8 -2 d 9 -3 d 9 -2 d 9 -2 d 9 -1 d 8 -2 d 9 -1 d 9 -1 d 9 X 9 -1 d 9 -1 d 8 X 9 -1 d 18 X 9 -1 d 70 X 9 -1 d 141 X s NC 227 113 m 1859 Y s 261 113 m -34 X s 244 186 m -17 X s 244 259 m -17 X s 244 332 m -17 X s 244 404 m -17 X s 261 477 m -34 X s 244 550 m -17 X s 244 622 m -17 X s 244 695 m -17 X s 244 768 m -17 X s 261 841 m -34 X s 244 913 m -17 X s 244 986 m -17 X s 244 1059 m -17 X s 244 1132 m -17 X s 261 1204 m -34 X s 244 1277 m -17 X s 244 1350 m -17 X s 244 1422 m -17 X s 244 1495 m -17 X s 261 1568 m -34 X s 244 1641 m -17 X s 244 1713 m -17 X s 244 1786 m -17 X s 244 1859 m -17 X s 261 1932 m -34 X s 261 1932 m -34 X s 165 129 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -2 d 3 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 130 487 m 3 1 d 5 5 d -32 Y s 165 493 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 127 849 m 1 Y 1 3 d 2 2 d 3 2 d 6 X 3 -2 d 2 -2 d 1 -3 d -3 Y -1 -3 d -3 -4 d -16 -15 d 22 X s 165 857 m -5 -2 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 2 d -3 X cl s 128 1220 m 17 X -9 -12 d 5 X 3 -1 d 1 -2 d 2 -4 d -4 Y -2 -4 d -3 -3 d -4 -2 d -5 X -5 2 d -1 1 d -2 3 d s 165 1220 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 141 1584 m -16 -21 d 23 X s 141 1584 m -32 Y s 165 1584 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 144 1947 m -16 X -1 -13 d 1 1 d 5 2 d 5 X 4 -2 d 3 -3 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -1 d -5 X -5 1 d -1 2 d -2 3 d s 165 1947 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 227 113 m 1745 X s 227 147 m -34 Y s 270 130 m -17 Y s 314 130 m -17 Y s 358 130 m -17 Y s 401 147 m -34 Y s 445 130 m -17 Y s 488 130 m -17 Y s 532 130 m -17 Y s 576 147 m -34 Y s 619 130 m -17 Y s 663 130 m -17 Y s 707 130 m -17 Y s 750 147 m -34 Y s 794 130 m -17 Y s 838 130 m -17 Y s 881 130 m -17 Y s 925 147 m -34 Y s 968 130 m -17 Y s 1012 130 m -17 Y s 1056 130 m -17 Y s 1099 147 m -34 Y s 1143 130 m -17 Y s 1187 130 m -17 Y s 1230 130 m -17 Y s 1274 147 m -34 Y s 1317 130 m -17 Y s 1361 130 m -17 Y s 1405 130 m -17 Y s 1448 147 m -34 Y s 1492 130 m -17 Y s 1536 130 m -17 Y s 1579 130 m -17 Y s 1623 147 m -34 Y s 1667 130 m -17 Y s 1710 130 m -17 Y s 1754 130 m -17 Y s 1797 147 m -34 Y s 1841 130 m -17 Y s 1885 130 m -17 Y s 1928 130 m -17 Y s 1972 147 m -34 Y s 227 147 m -34 Y s 160 73 m 27 X s 207 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 231 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 252 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 278 85 m 3 1 d 5 5 d -32 Y s 320 73 m 27 X s 366 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 391 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 412 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 442 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 471 91 m -5 -2 d -1 -3 d -3 Y 1 -3 d 3 -1 d 6 -2 d 5 -1 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -2 d -4 -1 d -6 X -5 1 d -1 2 d -2 3 d 5 Y 2 3 d 3 3 d 4 1 d 6 2 d 3 1 d 2 3 d 3 Y -2 3 d -4 2 d -6 X cl s 494 73 m 27 X s 541 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 565 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 586 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 617 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 657 86 m -1 3 d -5 2 d -3 X -4 -2 d -3 -4 d -2 -8 d -7 Y 2 -7 d 3 -3 d 4 -1 d 2 X 4 1 d 3 3 d 2 5 d 2 Y -2 4 d -3 3 d -4 2 d -2 X -4 -2 d -3 -3 d -2 -4 d s 669 73 m 27 X s 716 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 740 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 761 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 791 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 827 91 m -15 -21 d 23 X s 827 91 m -32 Y s 843 73 m 27 X s 890 91 m -4 -2 d -4 -4 d -1 -8 d -4 Y 1 -8 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 914 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 935 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 966 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 988 83 m 2 Y 2 3 d 1 1 d 3 2 d 6 X 3 -2 d 2 -1 d 1 -3 d -3 Y -1 -3 d -3 -5 d -15 -15 d 21 X s 1098 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1219 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 1244 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1265 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1295 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1318 83 m 2 Y 1 3 d 2 1 d 3 2 d 6 X 3 -2 d 1 -1 d 2 -3 d -3 Y -2 -3 d -3 -5 d -15 -15 d 21 X s 1394 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1418 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1439 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1470 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1506 91 m -15 -21 d 22 X s 1506 91 m -32 Y s 1569 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1593 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1614 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1644 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1685 86 m -2 3 d -4 2 d -3 X -5 -2 d -3 -4 d -1 -8 d -7 Y 1 -7 d 3 -3 d 5 -1 d 1 X 5 1 d 3 3 d 1 5 d 2 Y -1 4 d -3 3 d -5 2 d -1 X -5 -2 d -3 -3 d -1 -4 d s 1743 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1767 62 m -1 -2 d 1 -1 d 2 1 d -2 2 d cl s 1788 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1819 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1847 91 m -4 -2 d -2 -3 d -3 Y 2 -3 d 3 -1 d 6 -2 d 4 -1 d 3 -3 d 2 -3 d -5 Y -2 -3 d -1 -2 d -5 -1 d -6 X -4 1 d -2 2 d -1 3 d 5 Y 1 3 d 3 3 d 5 1 d 6 2 d 3 1 d 1 3 d 3 Y -1 3 d -5 2 d -6 X cl s 1933 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1957 62 m -2 -2 d 2 -1 d 1 1 d -1 2 d cl s 1978 91 m -4 -2 d -4 -4 d -1 -8 d -4 Y 1 -8 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 2004 85 m 3 1 d 4 5 d -32 Y s 1745 1859 227 113 C gr gr showpage end %%EndDocument @endspecial 158 x Fr(Figure)27 b(3:)i(Distribution)d(of)j(the)g(a)m(v) m(erage)h(cross-correlation)e Fk(R)q Fr(\()p Fk(\034)11 b Fr(\))29 b(sho)m(wn)h(in)e(Fig.)g(2)p (#figure.2) [[446 458 452 470] [1 1 1 [3 3]] [0 0 1]] pdfm 29 w(and)h(Gaussian)-9 2277 y(\014t.)42 b(The)i(standard)f(deviation)f (calculated)g(directly)g(from)f(the)i(histogram)e(coincides)i(with)f (that)-9 2397 y(obtained)32 b(b)m(y)h(a)f(Gaussian)g(\014t)h(\(0.00189) e(and)i(0.00191,)e(resp)s(ectiv)m(ely\))240 2664 y(Let)40 b(us)g(supp)s(ose)h(that)f(GW)f(generate)i(signals)e(in)g(our)g(t)m(w)m (o)i(detectors)g(with)e(giv)m(en)h(signal-)-9 2784 y(to-noise)35 b(ratios,)f(sa)m(y)j Fp(SNR)1029 2799 y Fi(expl)1199 2784 y Fr(and)f Fp(SNR)1590 2799 y Fi(naut)1742 2784 y Fr(.)f(In)i(the)f(presen)m(t)i(case,)f(since)f(b)s(oth)g(detectors)h (ha)m(v)m(e)-9 2914 y(ab)s(out)25 b(the)i(same)f(sensitivit)m(y)h(\() 1179 2889 y(\026)1160 2914 y Fk(T)1231 2867 y Fi(expl)1217 2941 y(ef)7 b(f)1392 2914 y Fr(=)28 b(8)p Fk(:)p Fr(8)17 b(mK)24 b(and)2023 2889 y(\026)2004 2914 y Fk(T)2075 2878 y Fi(naut)2061 2940 y(ef)7 b(f)2253 2914 y Fr(=)27 b(6)p Fk(:)p Fr(1)17 b(mK\))25 b(and)i(are)f(parallel,)e(w)m(e)j(tak)m (e,)-9 3034 y(roughly)-8 b(,)31 b Fp(SNR)563 3049 y Fi(expl)724 3034 y Fj(\031)e Fr(SNR)1029 3049 y Fi(naut)1207 3034 y Fj(\031)f Fr(SNR.)33 b(W)-8 b(e)33 b(de\014ne)1619 3264 y(SNR)1819 3279 y Fi(R)1904 3264 y Fr(=)2017 3197 y Fk(R)2091 3212 y Fq(0)p 2017 3241 114 4 v 2017 3332 a Fk(\033)2072 3347 y Fi(R)3645 3264 y Fr(\(6\))-9 3483 y(where)45 b Fk(\033)339 3498 y Fi(R)442 3483 y Fr(is)f(the)g(standard) h(deviation)e(of)h(our)h(exp)s(ectations)g(of)f(the)g(dimensionless)g Fk(R)3469 3498 y Fq(0)3508 3483 y Fr(.)h(This)-9 3603 y(quan)m(tit)m(y)35 b(can)g(b)s(e)h(estimated)e(from)g(the)h(spread)h (of)e(the)i(man)m(y)f(a)m(v)-5 b(ailable)32 b(measuremen)m(ts)k(of)f Fk(R)q Fr(\()p Fk(\034)11 b Fr(\))-9 3724 y(for)33 b(di\013eren)m(t)h Fk(\034)46 b Fr(\(see)35 b(Fig.)e(2)p (#figure.2) [[194 270 199 282] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)h(The) h(distribution)d(of)i Fk(R)q Fr(\()p Fk(\034)11 b Fr(\))34 b(for)g(all)e(dela)m(y)i(times,)g(sho)m(wn)h(in)e(Fig.)g(3)p (#figure.3) [[515 270 521 282] [1 1 1 [3 3]] [0 0 1]] pdfm (,)-9 3844 y(can)j(b)s(e)h(mo)s(deled)f(b)m(y)h(a)g(Gaussian)f(\(see)i(solid) d(line)g(in)h(the)h(\014gure\),)g(and)g(the)g(standard)g(deviation)-9 3964 y(calculated)42 b(directly)i(from)e(the)i(histogram)e(coincides)i (with)g(that)f(obtained)g(b)m(y)i(a)f(Gaussian)f(\014t)-9 4085 y(\(0.00189)31 b(and)h(0.00191,)g(resp)s(ectiv)m(ely\).)240 4205 y(It)42 b(is)f(p)s(ossible)h(to)f(ev)-5 b(aluate)42 b Fk(\033)1414 4220 y Fi(R)1514 4205 y Fr(in)f(an)h(alternativ)m(e)f(w) m(a)m(y)i(\(see)g(App)s(endix)g(A\))f(,)g(using)g(the)-9 4326 y(n)m(um)m(b)s(er)31 b(of)f(GRB's)h Fk(N)845 4341 y Fi(\015)920 4326 y Fr(and)g(the)g(n)m(um)m(b)s(er)g(of)g(indep)s (enden)m(t)h(GW)e(data)h(samples)f Fk(N)3156 4341 y Fi(s)3193 4326 y Fr(,)h(in)f(eac)m(h)h(data)-9 4446 y(stretc)m(h)j(used)f(for)f (calculating)e(the)j(cross-correlation.)f(The)h(follo)m(wing)d(form)m (ula)h(is)h(obtained:)1549 4663 y Fk(\033)1604 4678 y Fi(R)1690 4663 y Fr(=)1956 4596 y(1)p 1804 4641 354 4 v 1804 4660 a Fh(p)p 1903 4660 255 4 v 1903 4741 a Fk(N)1981 4756 y Fi(s)2035 4741 y Fk(N)2113 4756 y Fi(\015)2184 4663 y Fk(:)1434 b Fr(\(7\))-9 4912 y(W)-8 b(e)33 b(estimate)f(the)i(n) m(um)m(b)s(er)f(of)g(indep)s(enden)m(t)h(data)f(p)s(oin)m(ts)g(b)m(y)h (the)f(n)m(um)m(b)s(er)h(of)e(indep)s(enden)m(t)i(data)-9 5032 y(of)d(EXPLORER)h(\(the)h(bandwidth)f(of)f(NA)m(UTILUS)i(is)f(m)m (uc)m(h)g(narro)m(w)m(er,)h(see)g(T)-8 b(able)32 b(1)p (#table.1) [[461 113 467 125] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(as)h (follo)m(ws)1372 5211 y Fk(N)1450 5226 y Fi(s)1515 5211 y Fr(=)27 b Fk(t)1653 5226 y Fi(m)1737 5211 y Fr(\001)p Fk(f)1866 5226 y Fi(expl)2028 5211 y Fj(\031)h Fr(7200)17 b Fk(;)1272 b Fr(\(8\))-9 5389 y(since)30 b(the)h(detector)g(data)f (are)g(correlated)g(within)f(a)h(time)f(1)p Fk(=)p Fr(\001)p Fk(f)11 b Fr(.)29 b(W)-8 b(e)31 b(\014nally)e(get)h Fk(\033)3171 5404 y Fi(R)3257 5389 y Fr(=)e(0)p Fk(:)p Fr(0017,)h(in)-9 5510 y(excellen)m(t)i(agreemen)m(t)g(with)g(the)g(v)-5 b(alue)31 b(0.0019)f(deduced)i(from)e(the)h(distribution)f(of)g Fk(R)q Fr(\()p Fk(\034)11 b Fr(\),)31 b(consid-)-9 5630 y(ering)g(the)i(roughness)h(of)e(our)h(estimation)d(of)i(the)h(n)m(um)m (b)s(er)g(of)f(indep)s(enden)m(t)i(data,)f Fk(N)3241 5645 y Fi(s)3277 5630 y Fr(.)-9 5879 y(6)p eop %%Page: 7 7 7 6 bop -9 1998 a @beginspecial 60 @hscale 40 @vscale 0 @angle @setspecial %%BeginDocument: fig5.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlendef} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode newpath gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 759 816 227 1156 bl 759 816 227 1156 C NC 227 1156 m 816 Y s 261 1156 m -34 X s 244 1183 m -17 X s 244 1210 m -17 X s 244 1238 m -17 X s 244 1265 m -17 X s 261 1292 m -34 X s 244 1319 m -17 X s 244 1346 m -17 X s 244 1374 m -17 X s 244 1401 m -17 X s 261 1428 m -34 X s 244 1455 m -17 X s 244 1482 m -17 X s 244 1510 m -17 X s 244 1537 m -17 X s 261 1564 m -34 X s 244 1591 m -17 X s 244 1618 m -17 X s 244 1646 m -17 X s 244 1673 m -17 X s 261 1700 m -34 X s 244 1727 m -17 X s 244 1754 m -17 X s 244 1782 m -17 X s 244 1809 m -17 X s 261 1836 m -34 X s 244 1863 m -17 X s 244 1890 m -17 X s 244 1918 m -17 X s 244 1945 m -17 X s 261 1972 m -34 X s 42 1154 m 28 X s 89 1172 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 113 1143 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 1172 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 160 1166 m 3 1 d 5 5 d -32 Y s 12 1290 m 27 X s 59 1308 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 4 4 d 1 8 d 4 Y -1 8 d -4 4 d -4 2 d -3 X cl s 83 1279 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 104 1308 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 134 1308 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 174 1308 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 3 d s 165 1444 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 59 1580 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 4 4 d 1 8 d 4 Y -1 8 d -4 4 d -4 2 d -3 X cl s 83 1551 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 104 1580 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 134 1580 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 174 1580 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 3 d s 89 1716 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 113 1687 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 1716 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 160 1710 m 3 1 d 5 5 d -32 Y s 59 1852 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 4 4 d 1 8 d 4 Y -1 8 d -4 4 d -4 2 d -3 X cl s 83 1823 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 104 1852 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 130 1846 m 3 1 d 5 5 d -32 Y s 174 1852 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 3 d s 89 1988 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 113 1959 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 1988 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 157 1980 m 2 Y 2 3 d 1 1 d 3 2 d 6 X 3 -2 d 2 -1 d 1 -3 d -3 Y -1 -3 d -3 -5 d -15 -15 d 21 X s 227 1156 m 759 X s 353 1190 m -34 Y s 404 1173 m -17 Y s 454 1173 m -17 Y s 505 1173 m -17 Y s 556 1173 m -17 Y s 606 1190 m -34 Y s 657 1173 m -17 Y s 708 1173 m -17 Y s 758 1173 m -17 Y s 809 1173 m -17 Y s 859 1190 m -34 Y s 353 1190 m -34 Y s 303 1173 m -17 Y s 252 1173 m -17 Y s 859 1190 m -34 Y s 910 1173 m -17 Y s 961 1173 m -17 Y s 309 1115 m 28 X s 352 1127 m 3 2 d 4 4 d -31 Y s 386 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -5 1 d -3 X cl s 605 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 838 1127 m 3 2 d 5 4 d -31 Y s 873 1133 m -4 -1 d -4 -5 d -1 -7 d -5 Y 1 -7 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 759 816 227 1156 C -129 1440 m 2 1 d 2 X 1 28 d 2 10 d 2 6 d 2 -31 d 2 5 d 2 8 d 1 -17 d 2 -15 d 2 18 d 2 -1 d 2 -7 d 2 -41 d 1 -28 d 2 -28 d 2 23 d 2 11 d 2 -20 d 2 -19 d 2 3 d 1 X 2 17 d 2 10 d 2 X 2 -7 d 2 12 d 1 2 d 2 3 d 2 8 d 2 12 d 2 16 d 2 -17 d 1 -11 d 2 14 d 2 29 d 2 -4 d 2 -37 d 2 -11 d 1 -4 d 2 34 d 2 18 d 2 3 d 2 -10 d 2 21 d 1 17 d 2 -23 d 2 -7 d 2 -2 d 2 10 d 2 X 2 9 d 1 13 d 2 6 d 2 -36 d 2 -11 d 2 -1 d 2 -22 d 1 16 d 2 10 d 2 -17 d 2 -12 d 2 -5 d 2 -5 d 1 14 d 2 17 d 2 60 d 2 51 d 2 16 d 2 -82 d 1 -51 d 2 9 d 2 -11 d 2 6 d 2 -17 d 2 -4 d 1 23 d 2 34 d 2 18 d 2 3 d 2 -18 d 2 -1 d 1 -18 d 2 33 d 2 32 d 2 33 d 2 26 d 2 -22 d 2 -69 d 1 -20 d 2 -7 d 2 -6 d 2 18 d 2 -1 d 2 -20 d 1 2 d 2 -25 d 2 -11 d 2 9 d 2 10 d 2 -29 d 1 -14 d 2 9 d 2 7 d 2 13 d 2 20 d 2 15 d 1 -9 d 2 -33 d 2 -30 d 2 13 d 2 3 d 2 38 d 1 25 d 2 14 d 2 1 d 2 15 d 2 38 d 2 -2 d 2 -7 d 1 -8 d 2 13 d 2 -16 d 2 11 d 2 -19 d 2 -16 d 1 -19 d 2 -11 d 2 15 d 2 -7 d 2 -20 d 2 9 d 1 25 d 2 27 d 2 37 d 2 31 d 2 -18 d 2 -47 d 1 -19 d 2 30 d 2 21 d 2 -21 d 2 -36 d 2 1 d 1 14 d 2 -26 d 2 -34 d 2 11 d 2 -1 d 2 -7 d 2 -4 d 1 5 d 2 X 2 8 d 2 30 d 2 24 d 2 19 d 1 -32 d 2 -26 d 2 4 d 2 X 2 -1 d 2 22 d 1 24 d 2 29 d 2 19 d 2 4 d 2 -27 d 2 -9 d 1 15 d 2 -33 d 2 -34 d 2 8 d 2 -12 d 2 -35 d 1 24 d 2 2 d 2 -17 d 2 4 d 2 16 d 2 2 d 2 27 d 1 -15 d 2 -17 d 2 10 d 2 19 d 2 -19 d 2 -2 d 1 14 d 2 5 d 2 13 d 2 -13 d 2 -10 d 2 -14 d 1 5 d 2 -10 d 2 7 d 2 8 d 2 -8 d 2 -23 d 1 18 d 2 35 d s 242 1481 m 2 -2 d 2 -21 d 2 X 2 6 d 1 25 d 2 -28 d 2 -31 d 2 -1 d 2 20 d 2 16 d 2 -32 d 1 -7 d 2 -4 d 2 10 d 2 42 d 2 34 d 2 16 d 1 4 d 2 -9 d 2 -33 d 2 -27 d 2 -26 d 2 26 d 1 8 d 2 -11 d 2 -2 d 2 -7 d 2 -15 d 2 11 d 1 -20 d 2 -31 d 2 3 d 2 1 d 2 40 d 2 9 d 1 -20 d 2 22 d 2 -1 d 2 12 d 2 32 d 2 35 d 2 -13 d 1 -22 d 2 -24 d 2 25 d 2 21 d 2 16 d 2 5 d 1 -12 d 2 -15 d 2 -19 d 2 -24 d 2 -10 d 2 26 d 1 17 d 2 -7 d 2 -11 d 2 11 d 2 -1 d 2 -3 d 1 6 d 2 X 2 -12 d 2 -26 d 2 -30 d 2 16 d 1 30 d 2 -11 d 2 1 d 2 -12 d 2 8 d 2 20 d 2 11 d 1 -2 d 2 1 d 2 5 d 2 12 d 2 4 d 2 -10 d 1 -17 d 2 -11 d 2 -6 d 2 -2 d 2 12 d 2 7 d 1 -17 d 2 5 d 2 13 d 2 4 d 2 6 d 2 17 d 1 -4 d 2 3 d 2 -32 d 2 -30 d 2 -3 d 2 -18 d 1 10 d 2 16 d 2 -1 d 2 -8 d 2 -2 d 2 -22 d 2 -37 d 1 -18 d 2 1 d 2 -3 d 2 -10 d 2 11 d 2 -8 d 1 -15 d 2 13 d 2 -2 d 2 6 d 2 -5 d 2 -8 d 1 27 d 2 10 d 2 31 d 2 5 d 2 -13 d 2 24 d 1 35 d 2 -16 d 2 -12 d 2 -9 d 2 18 d 2 -5 d 1 -17 d 2 3 d 2 1 d 2 18 d 2 26 d 2 -6 d 2 -12 d 1 36 d 2 12 d 2 -29 d 2 -36 d 2 -17 d 2 25 d 1 16 d 2 -34 d 2 -35 d 2 -13 d 2 8 d 2 31 d 1 -7 d 2 -6 d 2 -20 d 2 -3 d 2 14 d 2 13 d 1 -25 d 2 -27 d 2 -6 d 2 11 d 2 -2 d 2 15 d 1 29 d 2 41 d 2 18 d 2 -24 d 2 -10 d 2 11 d 1 11 d 2 6 d 2 3 d 2 -7 d 2 -3 d 2 -13 d 2 -26 d 1 X 2 1 d 2 13 d 2 27 d 2 20 d 2 -2 d 1 -13 d 2 -11 d 2 28 d 2 -2 d 2 -17 d 2 15 d 1 16 d 2 5 d 2 -4 d 2 9 d 2 -11 d 2 -7 d 1 -24 d 2 -14 d 2 -10 d 2 -10 d 2 X 2 28 d 1 31 d 2 -1 d 2 4 d 2 -18 d 2 16 d 2 -6 d 2 1 d s 616 1470 m 1 4 d 2 10 d 2 -28 d 2 -48 d 2 -46 d 2 -5 d 1 14 d 2 22 d 2 18 d 2 5 d 2 -12 d 2 -24 d 1 3 d 2 29 d 2 -4 d 2 -16 d 2 9 d 2 4 d 1 -8 d 2 3 d 2 X 2 -5 d 2 -18 d 2 -21 d 1 -4 d 2 -20 d 2 6 d 2 9 d 2 14 d 2 -1 d 2 -1 d 1 -5 d 2 6 d 2 10 d 2 -3 d 2 13 d 2 27 d 1 13 d 2 -24 d 2 -39 d 2 13 d 2 4 d 2 10 d 1 14 d 2 47 d 2 12 d 2 -12 d 2 16 d 2 13 d 1 3 d 2 6 d 2 -15 d 2 -6 d 2 2 d 2 7 d 1 -8 d 2 13 d 2 12 d 2 11 d 2 23 d 2 12 d 2 15 d 1 -10 d 2 -5 d 2 6 d 2 24 d 2 -5 d 2 -37 d 1 -29 d 2 -21 d 2 -10 d 2 -19 d 2 -19 d 2 26 d 1 52 d 2 24 d 2 -5 d 2 7 d 2 -34 d 2 -11 d 1 20 d 2 16 d 2 -18 d 2 -9 d 2 -31 d 2 6 d 1 18 d 2 -6 d 2 1 d 2 25 d 2 -36 d 2 -34 d 2 11 d 1 -6 d 2 4 d 2 40 d 2 8 d 2 -5 d 2 1 d 1 6 d 2 2 d 2 -4 d 2 -42 d 2 -8 d 2 7 d 1 -1 d 2 21 d 2 15 d 2 2 d 2 -12 d 2 -6 d 1 19 d 2 1 d 2 -17 d 2 27 d 2 6 d 2 -20 d 1 -11 d 2 8 d 2 27 d 2 11 d 2 5 d 2 -6 d 2 20 d 1 X 2 -33 d 2 -34 d 2 -15 d 2 -27 d 2 -29 d 1 -16 d 2 -16 d 2 -12 d 2 -7 d 2 17 d 2 24 d 1 17 d 2 3 d 2 6 d 2 -15 d 2 -34 d 2 4 d 1 25 d 2 41 d 2 48 d 2 34 d 2 7 d 2 -28 d 1 -21 d 2 8 d 2 6 d 2 22 d 2 X 2 -26 d 2 -10 d 1 -30 d 2 -28 d 2 -5 d 2 11 d 2 -24 d 2 24 d 1 31 d 2 20 d 2 2 d 2 -3 d 2 16 d 2 8 d 1 -10 d 2 -30 d 2 -7 d 2 24 d 2 -36 d 2 -23 d 1 18 d 2 14 d 2 9 d 2 5 d 2 7 d 2 -26 d 1 -19 d 2 -23 d 2 36 d 2 55 d 2 4 d 2 -12 d 2 -9 d 1 4 d 2 X 2 -16 d 2 3 d 2 -13 d 2 -32 d 1 -17 d 2 -9 d 2 -29 d 2 -5 d 2 -15 d 2 22 d 1 37 d 2 18 d 2 -4 d 2 7 d 2 8 d s 989 1435 m 2 5 d 1 20 d 2 4 d 2 -17 d 2 -8 d 2 -16 d 2 -2 d 1 -15 d 2 -29 d 2 2 d 2 1 d 2 -14 d 2 -12 d 2 25 d 1 24 d 2 12 d 4 X 2 -5 d 2 19 d 1 -13 d 2 -10 d 2 24 d 2 13 d 2 20 d 2 10 d 1 17 d 2 -12 d 2 -12 d 2 16 d 2 9 d 2 -12 d 1 -39 d 2 -13 d 2 -6 d 2 -10 d 2 X 2 8 d 1 -1 d 2 14 d 2 -15 d 2 -20 d 2 -11 d 2 10 d 1 -17 d 2 -39 d 2 -9 d 2 16 d 2 21 d 2 X 2 -24 d 1 1 d 2 5 d 2 -7 d 2 9 d 2 20 d 2 22 d 1 3 d 2 1 d 2 15 d 2 21 d 2 12 d 2 -25 d 1 -27 d 2 -38 d 2 -5 d 2 -16 d 2 -22 d 2 3 d 1 19 d 2 46 d 2 21 d 2 -12 d 2 3 d 2 6 d 1 12 d 2 25 d 2 9 d 2 -5 d 2 18 d 2 8 d 2 -4 d 1 -7 d 2 -6 d 2 -18 d 2 -9 d 2 5 d 2 11 d 1 22 d 2 25 d 2 8 d 2 -2 d 2 2 d 2 -15 d 1 -39 d 2 -5 d 2 -12 d 2 -26 d 2 -40 d 2 -10 d 1 29 d 2 8 d 2 6 d 2 24 d 2 -5 d 2 16 d 1 20 d 2 15 d 2 -14 d 2 -33 d 2 -6 d 2 19 d 2 25 d 1 -12 d 2 -5 d 2 -9 d 2 -47 d 2 -29 d 2 -9 d 1 -1 d 2 -8 d 2 -1 d 2 17 d 2 28 d 2 31 d 1 -4 d 2 8 d 2 -10 d 2 -4 d 2 5 d 2 13 d 1 7 d 2 -34 d 2 -32 d 2 -17 d 2 13 d 2 34 d 1 12 d 2 -9 d 2 15 d 2 28 d 2 -27 d 2 -25 d 2 -17 d 1 3 d 2 2 d 2 28 d 2 44 d 2 -3 d 2 -14 d 1 -5 d 2 -14 d 2 9 d 2 6 d 2 36 d 2 15 d 1 -1 d 2 -16 d 2 -36 d 2 -19 d 2 -15 d 2 -13 d 1 -15 d 2 -4 d 2 14 d 2 19 d 2 -5 d 2 2 d 1 34 d 2 24 d 2 53 d 2 32 d 2 -4 d 2 2 d 2 -12 d 1 X 2 27 d 2 13 d 2 -23 d 2 5 d 2 32 d 1 11 d 2 -14 d 2 -10 d 2 12 d 2 -2 d 2 7 d 1 -6 d 2 5 d 2 X 2 -13 d 2 -20 d s /w 13 def /w2 {w 2 div} def /w3 {w 3 div} def 0 1460 1 1409 3 1418 5 1407 7 1413 9 1396 11 1392 12 1415 14 1449 16 1467 18 1470 20 1452 22 1451 23 1433 25 1466 27 1498 29 1531 31 1557 33 1535 35 1466 36 1446 38 1439 40 1433 42 1451 44 1450 46 1430 47 1432 49 1407 51 1396 53 1405 55 1415 57 1386 58 1372 60 1381 62 1388 64 1401 66 1421 68 1436 69 1427 71 1394 73 1364 75 1377 77 1380 79 1418 80 1443 82 1457 84 1458 86 1473 88 1511 90 1509 92 1502 93 1494 95 1507 97 1491 99 1502 101 1483 103 1467 104 1448 106 1437 108 1452 110 1445 112 1425 114 1434 115 1459 117 1486 119 1523 121 1554 123 1536 125 1489 126 1470 128 1500 130 1521 132 1500 134 1464 136 1465 137 1479 139 1453 141 1419 143 1430 145 1429 147 1422 149 1418 150 1423 152 1423 154 1431 156 1461 158 1485 160 1504 161 1472 163 1446 165 1450 167 1450 169 1449 171 1471 172 1495 174 1524 176 1543 178 1547 180 1520 182 1511 100 { m31} R 183 1526 185 1493 187 1459 189 1467 191 1455 193 1420 194 1444 196 1446 198 1429 200 1433 202 1449 204 1451 206 1478 207 1463 209 1446 211 1456 213 1475 215 1456 217 1454 218 1468 220 1473 222 1486 224 1473 226 1463 228 1449 229 1454 231 1444 233 1451 235 1459 237 1451 239 1428 240 1446 242 1481 244 1479 34 { m31} R 246 1458 248 1458 250 1464 251 1489 253 1461 255 1430 257 1429 259 1449 261 1465 263 1433 264 1426 266 1422 268 1432 270 1474 272 1508 274 1524 275 1528 277 1519 279 1486 281 1459 283 1433 285 1459 286 1467 288 1456 290 1454 292 1447 294 1432 296 1443 297 1423 299 1392 301 1395 303 1396 305 1436 307 1445 308 1425 310 1447 312 1446 314 1458 316 1490 318 1525 320 1512 321 1490 323 1466 325 1491 327 1512 329 1528 331 1533 332 1521 334 1506 336 1487 338 1463 340 1453 342 1479 343 1496 345 1489 347 1478 349 1489 351 1488 353 1485 354 1491 356 1491 358 1479 360 1453 362 1423 364 1439 365 1469 367 1458 369 1459 371 1447 373 1455 375 1475 377 1486 378 1484 380 1485 382 1490 384 1502 386 1506 388 1496 389 1479 391 1468 393 1462 395 1460 397 1472 399 1479 400 1462 402 1467 404 1480 406 1484 408 1490 410 1507 411 1503 413 1506 415 1474 417 1444 419 1441 421 1423 422 1433 424 1449 426 1448 428 1440 100 { m31} R 430 1438 432 1416 434 1379 435 1361 437 1362 439 1359 441 1349 443 1360 445 1352 446 1337 448 1350 450 1348 452 1354 454 1349 456 1341 457 1368 459 1378 461 1409 463 1414 465 1401 467 1425 468 1460 470 1444 472 1432 474 1423 476 1441 478 1436 479 1419 481 1422 483 1423 485 1441 487 1467 489 1461 491 1449 492 1485 494 1497 496 1468 498 1432 500 1415 502 1440 503 1456 505 1422 507 1387 509 1374 511 1382 513 1413 514 1406 516 1400 518 1380 520 1377 522 1391 524 1404 525 1379 527 1352 529 1346 531 1357 533 1355 535 1370 536 1399 538 1440 540 1458 542 1434 544 1424 546 1435 547 1446 549 1452 551 1455 553 1448 555 1445 557 1432 559 1406 560 1406 562 1407 564 1420 566 1447 568 1467 570 1465 571 1452 573 1441 575 1469 577 1467 579 1450 581 1465 582 1481 584 1486 586 1482 588 1491 590 1480 592 1473 593 1449 595 1435 597 1425 599 1415 601 1415 603 1443 604 1474 606 1473 608 1477 610 1459 612 1475 100 { m31} R 614 1469 616 1470 617 1474 619 1484 4 { m31} R 621 1456 623 1408 625 1362 627 1357 628 1371 630 1393 632 1411 634 1416 636 1404 638 1380 639 1383 641 1412 643 1408 645 1392 647 1401 649 1405 650 1397 652 1400 654 1400 656 1395 658 1377 660 1356 661 1352 663 1332 665 1338 667 1347 669 1361 671 1360 673 1359 674 1354 676 1360 678 1370 680 1367 682 1380 684 1407 685 1420 687 1396 689 1357 691 1370 693 1374 695 1384 696 1398 698 1445 700 1457 702 1445 704 1461 706 1474 707 1477 709 1483 711 1468 713 1462 715 1464 717 1471 718 1463 720 1476 722 1488 724 1499 726 1522 728 1534 730 1549 731 1539 733 1534 735 1540 737 1564 739 1559 741 1522 742 1493 744 1472 746 1462 748 1443 750 1424 752 1450 753 1502 755 1526 757 1521 759 1528 761 1494 763 1483 764 1503 766 1519 768 1501 770 1492 772 1461 774 1467 775 1485 777 1479 779 1480 781 1505 783 1469 785 1435 787 1446 788 1440 790 1444 792 1484 794 1492 796 1487 798 1488 799 1494 801 1496 803 1492 100 { m31} R 805 1450 807 1442 809 1449 810 1448 812 1469 814 1484 816 1486 818 1474 820 1468 821 1487 823 1488 825 1471 827 1498 829 1504 831 1484 832 1473 834 1481 836 1508 838 1519 840 1524 842 1518 844 1538 845 1538 847 1505 849 1471 851 1456 853 1429 855 1400 856 1384 858 1368 860 1356 862 1349 864 1366 866 1390 867 1407 869 1410 871 1416 873 1401 875 1367 877 1371 878 1396 880 1437 882 1485 884 1519 886 1526 888 1498 889 1477 891 1485 893 1491 895 1513 897 1513 899 1487 901 1477 902 1447 904 1419 906 1414 908 1425 910 1401 912 1425 913 1456 915 1476 917 1478 919 1475 921 1491 923 1499 924 1489 926 1459 928 1452 930 1476 932 1440 934 1417 935 1435 937 1449 939 1458 941 1463 943 1470 945 1444 946 1425 948 1402 950 1438 952 1493 954 1497 956 1485 958 1476 959 1480 961 1480 963 1464 965 1467 967 1454 969 1422 970 1405 972 1396 974 1367 976 1362 978 1347 980 1369 981 1406 983 1424 985 1420 987 1427 100 { m31} R 989 1435 991 1440 992 1460 994 1464 4 { m31} R 996 1447 998 1439 1000 1423 1002 1421 1003 1406 1005 1377 1007 1379 1009 1380 1011 1366 1013 1354 1015 1379 1016 1403 1018 1415 1020 1415 1022 1415 1024 1410 1026 1429 1027 1416 1029 1406 1031 1430 1033 1443 1035 1463 1037 1473 1038 1490 1040 1478 1042 1466 1044 1482 1046 1491 1048 1479 1049 1440 1051 1427 1053 1421 1055 1411 1057 1411 1059 1419 1060 1418 1062 1432 1064 1417 1066 1397 1068 1386 1070 1396 1071 1379 1073 1340 1075 1331 1077 1347 1079 1368 1081 1368 1083 1344 1084 1345 1086 1350 1088 1343 1090 1352 1092 1372 1094 1394 1095 1397 1097 1398 1099 1413 1101 1434 1103 1446 1105 1421 1106 1394 1108 1356 1110 1351 1112 1335 1114 1313 1116 1316 1117 1335 1119 1381 1121 1402 1123 1390 1125 1393 1127 1399 1128 1411 1130 1436 1132 1445 1134 1440 1136 1458 1138 1466 1140 1462 1141 1455 1143 1449 1145 1431 1147 1422 1149 1427 1151 1438 1152 1460 1154 1485 1156 1493 1158 1491 1160 1493 1162 1478 1163 1439 1165 1434 1167 1422 1169 1396 1171 1356 1173 1346 1174 1375 1176 1383 1178 1389 100 { m31} R 1180 1413 1182 1408 1184 1424 1185 1444 1187 1459 1189 1445 1191 1412 1193 1406 1195 1425 1197 1450 1198 1438 1200 1433 1202 1424 1204 1377 1206 1348 1208 1339 1209 1338 1211 1330 1213 1329 1215 1346 1217 1374 1219 1405 1220 1401 1222 1409 1224 1399 1226 1395 1228 1400 1230 1413 1231 1420 1233 1386 1235 1354 1237 1337 1239 1350 1241 1384 1242 1396 1244 1387 1246 1402 1248 1430 1250 1403 1252 1378 1254 1361 1255 1364 1257 1366 1259 1394 1261 1438 1263 1435 1265 1421 1266 1416 1268 1402 1270 1411 1272 1417 1274 1453 1276 1468 1277 1467 1279 1451 1281 1415 1283 1396 1285 1381 1287 1368 1288 1353 1290 1349 1292 1363 1294 1382 1296 1377 1298 1379 1299 1413 1301 1437 1303 1490 1305 1522 1307 1518 1309 1520 1311 1508 1312 1508 1314 1535 1316 1548 1318 1525 1320 1530 1322 1562 1323 1573 1325 1559 1327 1549 1329 1561 1331 1559 1333 1566 1334 1560 1336 1565 1338 1565 1340 1552 1342 1532 89 { m31} R 2040 2040 0 0 C 759 816 227 1156 C 2040 2040 0 0 C 378 1870 m -17 X -1 -15 d 1 2 d 5 2 d 5 X 5 -2 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -5 -2 d -5 X -5 2 d -1 1 d -2 3 d s 400 1870 m -5 -2 d -3 -4 d -2 -9 d -4 Y 2 -9 d 3 -4 d 5 -2 d 3 X 5 2 d 4 4 d 1 9 d 4 Y -1 9 d -4 4 d -5 2 d -3 X cl s 441 1859 m -23 Y s 441 1852 m 5 5 d 3 2 d 5 X 3 -2 d 1 -5 d -16 Y s 458 1852 m 5 5 d 4 2 d 4 X 4 -2 d 1 -5 d -16 Y s 489 1870 m -34 Y s 512 1870 m -23 -23 d s 497 1855 m 15 -19 d s 759 816 227 1156 C 2040 2040 0 0 C 759 816 227 1156 C 2040 2040 0 0 C 371 1795 m -3 -3 d -3 -5 d -4 -7 d -1 -8 d -6 Y 1 -8 d 4 -7 d 3 -5 d 3 -3 d s 389 1788 m -5 -1 d -2 -3 d -4 Y 2 -3 d 3 -2 d 7 -1 d 5 -2 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -2 d -5 -2 d -6 X -5 2 d -2 2 d -1 3 d 5 Y 1 3 d 4 3 d 4 2 d 7 1 d 3 2 d 2 3 d 4 Y -2 3 d -5 1 d -6 X cl s 423 1788 m -5 -1 d -3 -5 d -2 -8 d -5 Y 2 -8 d 3 -5 d 5 -2 d 3 X 5 2 d 3 5 d 2 8 d 5 Y -2 8 d -3 5 d -5 1 d -3 X cl s 455 1788 m -5 -1 d -3 -5 d -1 -8 d -5 Y 1 -8 d 3 -5 d 5 -2 d 3 X 5 2 d 4 5 d 1 8 d 5 Y -1 8 d -4 5 d -5 1 d -3 X cl s 512 1772 m -2 3 d -5 2 d -4 X -5 -2 d -2 -3 d 2 -3 d 3 -2 d 8 -1 d 3 -2 d 2 -3 d -2 Y -2 -3 d -5 -2 d -4 X -5 2 d -2 3 d s 522 1795 m 3 -3 d 3 -5 d 3 -7 d 2 -8 d -6 Y -2 -8 d -3 -7 d -3 -5 d -3 -3 d s 759 816 227 1156 C NC 759 816 1213 1156 bl 759 816 1213 1156 C NC 1213 1156 m 816 Y s 1247 1156 m -34 X s 1230 1183 m -17 X s 1230 1210 m -17 X s 1230 1238 m -17 X s 1230 1265 m -17 X s 1247 1292 m -34 X s 1230 1319 m -17 X s 1230 1346 m -17 X s 1230 1374 m -17 X s 1230 1401 m -17 X s 1247 1428 m -34 X s 1230 1455 m -17 X s 1230 1482 m -17 X s 1230 1510 m -17 X s 1230 1537 m -17 X s 1247 1564 m -34 X s 1230 1591 m -17 X s 1230 1618 m -17 X s 1230 1646 m -17 X s 1230 1673 m -17 X s 1247 1700 m -34 X s 1230 1727 m -17 X s 1230 1754 m -17 X s 1230 1782 m -17 X s 1230 1809 m -17 X s 1247 1836 m -34 X s 1230 1863 m -17 X s 1230 1890 m -17 X s 1230 1918 m -17 X s 1230 1945 m -17 X s 1247 1972 m -34 X s 1059 1154 m 27 X s 1105 1172 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1130 1143 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1146 1166 m 3 1 d 5 5 d -32 Y s 1028 1290 m 28 X s 1075 1308 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1099 1279 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 1120 1308 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 1160 1308 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 3 d s 1151 1444 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1075 1580 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1099 1551 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 1120 1580 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 4 X 4 2 d 3 4 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -4 X cl s 1160 1580 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 3 d s 1105 1716 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1130 1687 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1146 1710 m 3 1 d 5 5 d -32 Y s 1075 1852 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1099 1823 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 1116 1846 m 3 1 d 5 5 d -32 Y s 1160 1852 m -15 X -2 -14 d 2 2 d 4 1 d 5 X 4 -1 d 3 -3 d 2 -5 d -3 Y -2 -4 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 3 d s 1105 1988 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1130 1959 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1143 1980 m 2 Y 2 3 d 1 1 d 3 2 d 6 X 3 -2 d 2 -1 d 1 -3 d -3 Y -1 -3 d -3 -5 d -15 -15 d 21 X s 1213 1156 m 759 X s 1339 1190 m -34 Y s 1390 1173 m -17 Y s 1440 1173 m -17 Y s 1491 1173 m -17 Y s 1542 1173 m -17 Y s 1592 1190 m -34 Y s 1643 1173 m -17 Y s 1694 1173 m -17 Y s 1744 1173 m -17 Y s 1795 1173 m -17 Y s 1845 1190 m -34 Y s 1339 1190 m -34 Y s 1289 1173 m -17 Y s 1238 1173 m -17 Y s 1845 1190 m -34 Y s 1896 1173 m -17 Y s 1947 1173 m -17 Y s 1295 1115 m 28 X s 1338 1127 m 3 2 d 4 4 d -31 Y s 1372 1133 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -5 1 d -3 X cl s 1591 1133 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1824 1127 m 3 2 d 5 4 d -31 Y s 1859 1133 m -4 -1 d -4 -5 d -1 -7 d -5 Y 1 -7 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 759 816 1213 1156 C 857 1528 m 2 -24 d 2 -16 d 1 -10 d 2 -12 d 2 X 2 -3 d 2 -18 d 2 -17 d 1 16 d 2 38 d 2 23 d 2 13 d 2 -16 d 2 -28 d 1 -18 d 2 3 d 2 -25 d 2 -12 d 2 -8 d 2 -15 d 2 33 d 1 -1 d 2 -12 d 2 -23 d 2 -32 d 2 -33 d 2 -4 d 1 16 d 2 19 d 2 -25 d 2 -12 d 2 5 d 2 9 d 1 16 d 2 11 d 2 35 d 2 13 d 2 -10 d 2 19 d 1 12 d 2 -17 d 2 -11 d 2 -20 d 2 -2 d 2 -4 d 1 -6 d 2 -16 d 2 -17 d 2 -16 d 2 -3 d 2 15 d 2 16 d 1 -12 d 2 -11 d 2 1 d 2 17 d 2 5 d 2 10 d 1 6 d 2 14 d 2 9 d 2 6 d 2 3 d 2 -47 d 1 -7 d 2 -2 d 2 19 d 2 -9 d 2 25 d 2 11 d 1 -17 d 2 8 d 2 11 d 2 X 2 24 d 2 9 d 1 -2 d 2 -2 d 2 -5 d 2 -28 d 2 -15 d 2 13 d 1 16 d 2 13 d 2 6 d 2 31 d 2 27 d 2 -10 d 2 -34 d 1 -29 d 2 3 d 2 8 d 2 22 d 2 16 d 2 7 d 1 9 d 2 X 2 -1 d 2 7 d 2 12 d 2 -7 d 1 -17 d 2 24 d 2 -11 d 2 -6 d 2 -4 d 2 -4 d 1 15 d 2 14 d 2 -6 d 2 7 d 2 -10 d 2 -29 d 1 -18 d 2 -1 d 2 21 d 2 24 d 2 7 d 2 17 d 2 -6 d 1 -11 d 2 -8 d 2 -7 d 2 -9 d 2 4 d 2 11 d 1 -2 d 2 -13 d 2 -9 d 2 -12 d 2 -17 d 2 9 d 1 20 d 2 16 d 2 2 d 2 4 d 2 -8 d 2 7 d 1 -16 d 2 -23 d 2 8 d 2 5 d 2 8 d 2 18 d 1 14 d 2 2 d 2 7 d 2 4 d 2 14 d 2 10 d 2 -15 d 1 -29 d 2 -27 d 2 -26 d 2 4 d 2 6 d 2 -30 d 1 -27 d 2 -9 d 2 19 d 2 18 d 2 33 d 2 -12 d 1 -30 d 2 -15 d 2 -11 d 2 16 d 2 6 d 2 52 d 1 35 d 2 -21 d 2 -16 d 2 -8 d 2 1 d 2 32 d 1 22 d 2 -10 d 2 -11 d 2 -30 d 2 -10 d 2 15 d 2 7 d 1 -10 d 2 -16 d 2 16 d 2 2 d 2 9 d 2 26 d 1 -6 d 2 1 d 2 7 d 2 -9 d 2 34 d 2 5 d 1 23 d 2 -7 d 2 -23 d 2 -11 d 2 -6 d 2 15 d 1 3 d 2 -2 d s 1228 1509 m 2 -24 d 2 -10 d 2 -8 d 2 2 d 1 21 d 2 1 d 2 6 d 2 14 d 2 4 d 2 17 d 2 -4 d 1 -6 d 2 -13 d 2 -3 d 2 10 d 2 36 d 2 4 d 1 -5 d 2 -4 d 2 -19 d 2 -33 d 2 -25 d 2 -7 d 1 -40 d 2 -25 d 2 -32 d 2 -7 d 2 9 d 2 19 d 1 -21 d 2 8 d 2 20 d 2 6 d 2 30 d 2 31 d 1 4 d 2 -4 d 2 -2 d 2 -18 d 2 -17 d 2 -10 d 2 -2 d 1 -19 d 2 -26 d 2 X 2 4 d 2 -13 d 2 -16 d 1 -7 d 2 -3 d 2 4 d 2 36 d 2 40 d 2 26 d 1 -2 d 2 -10 d 2 -3 d 2 21 d 2 -15 d 2 -14 d 1 X 2 -11 d 2 -1 d 2 18 d 2 33 d 2 19 d 1 31 d 2 -20 d 2 -3 d 2 -2 d 2 -11 d 2 -10 d 2 -21 d 1 8 d 2 10 d 2 -8 d 2 16 d 2 3 d 2 -15 d 1 25 d 2 33 d 2 12 d 2 -14 d 2 X 2 -1 d 1 2 d 2 -6 d 2 -36 d 2 15 d 2 -11 d 2 -43 d 1 -38 d 2 -21 d 2 4 d 2 18 d 2 34 d 2 4 d 1 14 d 2 20 d 2 -3 d 2 20 d 2 8 d 2 -4 d 2 -3 d 1 16 d 2 6 d 2 X 2 -9 d 2 X 2 -16 d 1 -20 d 2 -15 d 2 9 d 2 -32 d 2 -33 d 2 18 d 1 33 d 2 -7 d 2 -1 d 2 29 d 2 4 d 2 -11 d 1 -9 d 2 -11 d 2 -1 d 2 -4 d 2 -30 d 2 -3 d 1 -1 d 2 -4 d 2 17 d 2 12 d 2 16 d 2 31 d 2 11 d 1 -3 d 2 -17 d 2 2 d 2 8 d 2 -13 d 2 -15 d 1 -28 d 2 4 d 2 22 d 2 28 d 2 54 d 2 35 d 1 -17 d 2 -35 d 2 -46 d 2 -20 d 2 -14 d 2 -11 d 1 -5 d 2 -28 d 2 25 d 2 11 d 2 13 d 2 40 d 1 14 d 2 6 d 2 -4 d 2 -20 d 2 -21 d 2 8 d 1 6 d 2 10 d 2 6 d 2 6 d 2 6 d 2 33 d 2 15 d 1 -4 d 2 5 d 2 -21 d 2 -22 d 2 10 d 2 11 d 1 2 d 2 10 d 2 -8 d 2 8 d 2 -22 d 2 -24 d 1 -3 d 2 -14 d 2 -24 d 2 -31 d 2 -2 d 2 32 d 1 38 d 2 2 d 2 -2 d 2 22 d 2 36 d 2 8 d 1 32 d 2 13 d 2 -47 d 2 -71 d 2 -44 d 2 -23 d 2 -25 d s 1602 1372 m 1 -7 d 2 3 d 2 -6 d 2 16 d 2 13 d 2 13 d 1 27 d 2 11 d 2 -19 d 2 -5 d 2 -7 d 2 -30 d 1 -32 d 2 -19 d 2 -10 d 2 -4 d 2 11 d 2 -10 d 1 -15 d 2 -18 d 2 24 d 2 15 d 2 -4 d 2 12 d 1 17 d 2 27 d 2 30 d 2 51 d 2 31 d 2 7 d 2 -34 d 1 -11 d 2 9 d 2 -5 d 2 -8 d 2 -6 d 2 -4 d 1 -17 d 2 -1 d 2 13 d 2 43 d 2 -2 d 2 -17 d 1 -8 d 2 17 d 2 39 d 2 -8 d 2 -3 d 2 8 d 1 -8 d 2 -16 d 2 -28 d 2 -23 d 2 -34 d 2 -23 d 1 X 2 23 d 2 19 d 2 14 d 2 -8 d 2 3 d 2 25 d 1 X 2 -4 d 2 7 d 2 14 d 2 7 d 2 8 d 1 -23 d 2 -23 d 2 10 d 2 -15 d 2 -22 d 2 -23 d 1 -4 d 2 -7 d 2 1 d 2 20 d 2 15 d 2 -26 d 1 -5 d 2 21 d 2 -12 d 2 -15 d 2 -5 d 2 24 d 1 -1 d 2 X 2 1 d 2 -3 d 2 -18 d 2 -8 d 2 9 d 1 9 d 2 -14 d 2 -2 d 2 -9 d 2 8 d 2 29 d 1 19 d 2 4 d 2 19 d 2 3 d 2 26 d 2 7 d 1 5 d 2 -18 d 2 -9 d 2 -21 d 2 -28 d 2 -13 d 1 -39 d 2 -14 d 2 -7 d 2 3 d 2 18 d 2 -7 d 1 28 d 2 35 d 2 24 d 2 10 d 2 21 d 2 3 d 2 -13 d 1 -13 d 2 -24 d 2 -25 d 2 X 2 5 d 2 -4 d 1 -9 d 2 12 d 2 38 d 2 10 d 2 -5 d 2 -7 d 1 12 d 2 -7 d 2 -17 d 2 11 d 2 30 d 2 -21 d 1 -21 d 2 -5 d 2 -4 d 2 12 d 2 16 d 2 7 d 1 -11 d 2 -11 d 2 3 d 2 -8 d 2 -3 d 2 -4 d 2 9 d 1 -4 d 2 -14 d 2 25 d 2 8 d 2 6 d 2 -1 d 1 20 d 2 22 d 2 4 d 2 -24 d 2 14 d 2 20 d 1 -10 d 2 -28 d 2 -4 d 2 -26 d 2 -27 d 2 -11 d 1 18 d 2 7 d 2 3 d 2 12 d 2 1 d 2 -2 d 1 4 d 2 12 d 2 12 d 2 -6 d 2 -8 d 2 -18 d 2 18 d 1 X 2 -33 d 2 5 d 2 23 d 2 31 d 2 -10 d 1 -3 d 2 -16 d 2 -20 d 2 -9 d 2 42 d 2 30 d 1 25 d 2 4 d 2 8 d 2 -15 d 2 17 d s 1975 1511 m 2 -1 d 1 13 d 2 -16 d 2 -5 d 2 2 d 2 -5 d 2 -1 d 1 -6 d 2 -11 d 2 23 d 2 -26 d 2 -30 d 2 -24 d 2 -7 d 1 3 d 2 -23 d 2 -4 d 2 2 d 2 -13 d 2 4 d 1 6 d 2 7 d 2 30 d 2 -7 d 2 18 d 2 12 d 1 -11 d 2 -11 d 2 -25 d 2 16 d 2 2 d 2 2 d 1 17 d 2 -18 d 2 -12 d 2 -8 d 2 -11 d 2 18 d 1 -2 d 2 -2 d 2 3 d 2 -5 d 2 14 d 2 17 d 1 11 d 2 4 d 2 -35 d 2 12 d 2 17 d 2 -19 d 2 -16 d 1 15 d 2 -2 d 2 -5 d 2 -25 d 2 7 d 2 19 d 1 16 d 2 -1 d 2 -4 d 2 -4 d 2 16 d 2 9 d 1 -17 d 2 -2 d 2 -25 d 2 -30 d 2 -18 d 2 -22 d 1 4 d 2 16 d 2 4 d 2 -15 d 2 -2 d 2 8 d 1 9 d 2 28 d 2 46 d 2 24 d 2 -3 d 2 -15 d 2 5 d 1 -36 d 2 -14 d 2 -13 d 2 -20 d 2 -4 d 2 23 d 1 33 d 2 X 2 -19 d 2 19 d 2 22 d 2 24 d 1 10 d 2 22 d 2 23 d 2 -4 d 2 -5 d 2 -23 d 1 -38 d 2 -42 d 2 -4 d 2 1 d 2 -18 d 2 3 d 1 27 d 2 20 d 2 -7 d 2 -5 d 2 -15 d 2 -13 d 2 2 d 1 15 d 2 49 d 2 13 d 2 -22 d 2 -13 d 2 13 d 1 9 d 2 -46 d 2 13 d 2 24 d 2 3 d 2 -9 d 1 7 d 2 29 d 2 29 d 2 29 d 2 11 d 2 18 d 1 14 d 2 -22 d 2 -19 d 2 -15 d 2 -24 d 2 -32 d 1 5 d 2 -6 d 2 -11 d 2 -7 d 2 22 d 2 53 d 2 41 d 1 18 d 2 10 d 2 -15 d 2 -22 d 2 2 d 2 -68 d 1 -13 d 2 35 d 2 18 d 2 23 d 2 3 d 2 -24 d 1 -12 d 2 11 d 2 19 d 2 5 d 2 9 d 2 20 d 1 4 d 2 -5 d 2 11 d 2 22 d 2 -26 d 2 -48 d 1 -33 d 2 -20 d 2 4 d 2 30 d 2 17 d 2 -16 d 2 -31 d 1 1 d 2 19 d 2 -7 d 2 5 d 2 3 d 2 -4 d 1 9 d 2 -18 d 2 -13 d 2 18 d 2 -10 d 2 -4 d 1 2 d 2 -26 d 2 -27 d 2 -8 d 2 -29 d s 857 1528 859 1504 861 1488 862 1478 864 1466 866 1466 868 1463 870 1445 872 1428 873 1444 875 1482 877 1505 879 1518 881 1502 883 1474 884 1456 886 1459 888 1434 890 1422 892 1414 894 1399 896 1432 897 1431 899 1419 901 1396 903 1364 905 1331 907 1327 908 1343 910 1362 912 1337 914 1325 916 1330 918 1339 919 1355 921 1366 923 1401 925 1414 927 1404 929 1423 930 1435 932 1418 934 1407 936 1387 938 1385 940 1381 941 1375 943 1359 945 1342 947 1326 949 1323 951 1338 953 1354 954 1342 956 1331 958 1332 960 1349 962 1354 964 1364 965 1370 967 1384 969 1393 971 1399 973 1402 975 1355 976 1348 978 1346 980 1365 982 1356 984 1381 986 1392 987 1375 989 1383 991 1394 993 1394 995 1418 997 1427 998 1425 1000 1423 1002 1418 1004 1390 1006 1375 1008 1388 1009 1404 1011 1417 1013 1423 1015 1454 1017 1481 1019 1471 1021 1437 1022 1408 1024 1411 1026 1419 1028 1441 1030 1457 1032 1464 1033 1473 1035 1473 1037 1472 1039 1479 100 { m31} R 1041 1491 1043 1484 1044 1467 1046 1491 1048 1480 1050 1474 1052 1470 1054 1466 1055 1481 1057 1495 1059 1489 1061 1496 1063 1486 1065 1457 1066 1439 1068 1438 1070 1459 1072 1483 1074 1490 1076 1507 1078 1501 1079 1490 1081 1482 1083 1475 1085 1466 1087 1470 1089 1481 1090 1479 1092 1466 1094 1457 1096 1445 1098 1428 1100 1437 1101 1457 1103 1473 1105 1475 1107 1479 1109 1471 1111 1478 1112 1462 1114 1439 1116 1447 1118 1452 1120 1460 1122 1478 1123 1492 1125 1494 1127 1501 1129 1505 1131 1519 1133 1529 1135 1514 1136 1485 1138 1458 1140 1432 1142 1436 1144 1442 1146 1412 1147 1385 1149 1376 1151 1395 1153 1413 1155 1446 1157 1434 1158 1404 1160 1389 1162 1378 1164 1394 1166 1400 1168 1452 1169 1487 1171 1466 1173 1450 1175 1442 1177 1443 1179 1475 1180 1497 1182 1487 1184 1476 1186 1446 1188 1436 1190 1451 1192 1458 1193 1448 1195 1432 1197 1448 1199 1450 1201 1459 1203 1485 1204 1479 1206 1480 1208 1487 1210 1478 1212 1512 1214 1517 1215 1540 1217 1533 1219 1510 1221 1499 1223 1493 100 { m31} R 1225 1508 1226 1511 1228 1509 1230 1485 4 { m31} R 1232 1475 1234 1467 1236 1469 1237 1490 1239 1491 1241 1497 1243 1511 1245 1515 1247 1532 1249 1528 1250 1522 1252 1509 1254 1506 1256 1516 1258 1552 1260 1556 1261 1551 1263 1547 1265 1528 1267 1495 1269 1470 1271 1463 1272 1423 1274 1398 1276 1366 1278 1359 1280 1368 1282 1387 1283 1366 1285 1374 1287 1394 1289 1400 1291 1430 1293 1461 1294 1465 1296 1461 1298 1459 1300 1441 1302 1424 1304 1414 1306 1412 1307 1393 1309 1367 1311 1367 1313 1371 1315 1358 1317 1342 1318 1335 1320 1332 1322 1336 1324 1372 1326 1412 1328 1438 1329 1436 1331 1426 1333 1423 1335 1444 1337 1429 1339 1415 1340 1415 1342 1404 1344 1403 1346 1421 1348 1454 1350 1473 1351 1504 1353 1484 1355 1481 1357 1479 1359 1468 1361 1458 1363 1437 1364 1445 1366 1455 1368 1447 1370 1463 1372 1466 1374 1451 1375 1476 1377 1509 1379 1521 1381 1507 1383 1507 1385 1506 1386 1508 1388 1502 1390 1466 1392 1481 1394 1470 1396 1427 1397 1389 1399 1368 1401 1372 1403 1390 1405 1424 1407 1428 1408 1442 1410 1462 1412 1459 1414 1479 100 { m31 } R 1416 1487 1418 1483 1420 1480 1421 1496 1423 1502 1425 1502 1427 1493 1429 1493 1431 1477 1432 1457 1434 1442 1436 1451 1438 1419 1440 1386 1442 1404 1443 1437 1445 1430 1447 1429 1449 1458 1451 1462 1453 1451 1454 1442 1456 1431 1458 1430 1460 1426 1462 1396 1464 1393 1465 1392 1467 1388 1469 1405 1471 1417 1473 1433 1475 1464 1477 1475 1478 1472 1480 1455 1482 1457 1484 1465 1486 1452 1488 1437 1489 1409 1491 1413 1493 1435 1495 1463 1497 1517 1499 1552 1500 1535 1502 1500 1504 1454 1506 1434 1508 1420 1510 1409 1511 1404 1513 1376 1515 1401 1517 1412 1519 1425 1521 1465 1522 1479 1524 1485 1526 1481 1528 1461 1530 1440 1532 1448 1533 1454 1535 1464 1537 1470 1539 1476 1541 1482 1543 1515 1545 1530 1546 1526 1548 1531 1550 1510 1552 1488 1554 1498 1556 1509 1557 1511 1559 1521 1561 1513 1563 1521 1565 1499 1567 1475 1568 1472 1570 1458 1572 1434 1574 1403 1576 1401 1578 1433 1579 1471 1581 1473 1583 1471 1585 1493 1587 1529 1589 1537 1590 1569 1592 1582 1594 1535 1596 1464 1598 1420 100 { m31} R 1600 1397 1602 1372 1603 1365 1605 1368 4 { m31} R 1607 1362 1609 1378 1611 1391 1613 1404 1614 1431 1616 1442 1618 1423 1620 1418 1622 1411 1624 1381 1625 1349 1627 1330 1629 1320 1631 1316 1633 1327 1635 1317 1636 1302 1638 1284 1640 1308 1642 1323 1644 1319 1646 1331 1647 1348 1649 1375 1651 1405 1653 1456 1655 1487 1657 1494 1659 1460 1660 1449 1662 1458 1664 1453 1666 1445 1668 1439 1670 1435 1671 1418 1673 1417 1675 1430 1677 1473 1679 1471 1681 1454 1682 1446 1684 1463 1686 1502 1688 1494 1690 1491 1692 1499 1693 1491 1695 1475 1697 1447 1699 1424 1701 1390 1703 1367 1704 1367 1706 1390 1708 1409 1710 1423 1712 1415 1714 1418 1716 1443 1717 1443 1719 1439 1721 1446 1723 1460 1725 1467 1727 1475 1728 1452 1730 1429 1732 1439 1734 1424 1736 1402 1738 1379 1739 1375 1741 1368 1743 1369 1745 1389 1747 1404 1749 1378 1750 1373 1752 1394 1754 1382 1756 1367 1758 1362 1760 1386 1761 1385 1763 1385 1765 1386 1767 1383 1769 1365 1771 1357 1773 1366 1774 1375 1776 1361 1778 1359 1780 1350 1782 1358 1784 1387 1785 1406 1787 1410 1789 1429 100 { m31} R 1791 1432 1793 1458 1795 1465 1796 1470 1798 1452 1800 1443 1802 1422 1804 1394 1806 1381 1807 1342 1809 1328 1811 1321 1813 1324 1815 1342 1817 1335 1818 1363 1820 1398 1822 1422 1824 1432 1826 1453 1828 1456 1830 1443 1831 1430 1833 1406 1835 1381 1837 1381 1839 1386 1841 1382 1842 1373 1844 1385 1846 1423 1848 1433 1850 1428 1852 1421 1853 1433 1855 1426 1857 1409 1859 1420 1861 1450 1863 1429 1864 1408 1866 1403 1868 1399 1870 1411 1872 1427 1874 1434 1875 1423 1877 1412 1879 1415 1881 1407 1883 1404 1885 1400 1887 1409 1888 1405 1890 1391 1892 1416 1894 1424 1896 1430 1898 1429 1899 1449 1901 1471 1903 1475 1905 1451 1907 1465 1909 1485 1910 1475 1912 1447 1914 1443 1916 1417 1918 1390 1920 1379 1921 1397 1923 1404 1925 1407 1927 1419 1929 1420 1931 1418 1932 1422 1934 1434 1936 1446 1938 1440 1940 1432 1942 1414 1944 1432 1945 1432 1947 1399 1949 1404 1951 1427 1953 1458 1955 1448 1956 1445 1958 1429 1960 1409 1962 1400 1964 1442 1966 1472 1967 1497 1969 1501 1971 1509 1973 1494 100 { m31} R 1975 1511 1977 1510 1978 1523 1980 1507 4 { m31} R 1982 1502 1984 1504 1986 1499 1988 1498 1989 1492 1991 1481 1993 1504 1995 1478 1997 1448 1999 1424 2001 1417 2002 1420 2004 1397 2006 1393 2008 1395 2010 1382 2012 1386 2013 1392 2015 1399 2017 1429 2019 1422 2021 1440 2023 1452 2024 1441 2026 1430 2028 1405 2030 1421 2032 1423 2034 1425 2035 1442 2037 1424 2039 1412 2041 1404 2043 1393 2045 1411 2046 1409 2048 1407 2050 1410 2052 1405 2054 1419 2056 1436 2057 1447 2059 1451 2061 1416 2063 1428 2065 1445 2067 1426 2069 1410 2070 1425 2072 1423 2074 1418 2076 1393 2078 1400 2080 1419 2081 1435 2083 1434 2085 1430 2087 1426 2089 1442 2091 1451 2092 1434 2094 1432 2096 1407 2098 1377 2100 1359 2102 1337 2103 1341 2105 1357 2107 1361 2109 1346 2111 1344 2113 1352 2114 1361 2116 1389 2118 1435 2120 1459 2122 1456 2124 1441 2126 1446 2127 1410 2129 1396 2131 1383 2133 1363 2135 1359 2137 1382 2138 1415 2140 1415 2142 1396 2144 1415 2146 1437 2148 1461 2149 1471 2151 1493 2153 1516 2155 1512 2157 1507 2159 1484 2160 1446 2162 1404 2164 1400 100 { m31} R 2166 1401 2168 1383 2170 1386 2171 1413 2173 1433 2175 1426 2177 1421 2179 1406 2181 1393 2183 1395 2184 1410 2186 1459 2188 1472 2190 1450 2192 1437 2194 1450 2195 1459 2197 1413 2199 1426 2201 1450 2203 1453 2205 1444 2206 1451 2208 1480 2210 1509 2212 1538 2214 1549 2216 1567 2217 1581 2219 1559 2221 1540 2223 1525 2225 1501 2227 1469 2228 1474 2230 1468 2232 1457 2234 1450 2236 1472 2238 1525 2240 1566 2241 1584 2243 1594 2245 1579 2247 1557 2249 1559 2251 1491 2252 1478 2254 1513 2256 1531 2258 1554 2260 1557 2262 1533 2263 1521 2265 1532 2267 1551 2269 1556 2271 1565 2273 1585 2274 1589 2276 1584 2278 1595 2280 1617 2282 1591 2284 1543 2285 1510 2287 1490 2289 1494 2291 1524 2293 1541 2295 1525 2297 1494 2298 1495 2300 1514 2302 1507 2304 1512 2306 1515 2308 1511 2309 1520 2311 1502 2313 1489 2315 1507 2317 1497 2319 1493 2320 1495 2322 1469 2324 1442 2326 1434 2328 1405 89 { m31} R 2040 2040 0 0 C 759 816 1213 1156 C 2040 2040 0 0 C 1346 1862 m 2 Y 1 3 d 2 1 d 3 2 d 7 X 3 -2 d 2 -1 d 1 -3 d -4 Y -1 -3 d -4 -5 d -16 -16 d 23 X s 1386 1870 m -5 -2 d -3 -4 d -2 -9 d -4 Y 2 -9 d 3 -4 d 5 -2 d 3 X 5 2 d 4 4 d 1 9 d 4 Y -1 9 d -4 4 d -5 2 d -3 X cl s 1427 1859 m -23 Y s 1427 1852 m 5 5 d 3 2 d 5 X 3 -2 d 1 -5 d -16 Y s 1444 1852 m 5 5 d 4 2 d 4 X 4 -2 d 1 -5 d -16 Y s 1475 1870 m -34 Y s 1498 1870 m -23 -23 d s 1483 1855 m 15 -19 d s 759 816 1213 1156 C 2040 2040 0 0 C 759 816 1213 1156 C 2040 2040 0 0 C 1357 1795 m -3 -3 d -3 -5 d -4 -7 d -1 -8 d -6 Y 1 -8 d 4 -7 d 3 -5 d 3 -3 d s 1375 1788 m -5 -1 d -2 -3 d -4 Y 2 -3 d 3 -2 d 7 -1 d 5 -2 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -2 d -5 -2 d -6 X -5 2 d -2 2 d -1 3 d 5 Y 1 3 d 4 3 d 4 2 d 7 1 d 3 2 d 2 3 d 4 Y -2 3 d -5 1 d -6 X cl s 1433 1772 m -1 3 d -5 2 d -5 X -5 -2 d -2 -3 d 2 -3 d 3 -2 d 8 -1 d 4 -2 d 1 -3 d -2 Y -1 -3 d -5 -2 d -5 X -5 2 d -2 3 d s 1443 1795 m 3 -3 d 3 -5 d 4 -7 d 1 -8 d -6 Y -1 -8 d -4 -7 d -3 -5 d -3 -3 d s 759 816 1213 1156 C NC 759 816 227 113 bl 759 816 227 113 C NC 227 113 m 816 Y s 261 113 m -34 X s 244 141 m -17 X s 244 168 m -17 X s 244 195 m -17 X s 244 222 m -17 X s 261 249 m -34 X s 244 277 m -17 X s 244 304 m -17 X s 244 331 m -17 X s 244 358 m -17 X s 261 385 m -34 X s 244 413 m -17 X s 244 440 m -17 X s 244 467 m -17 X s 244 494 m -17 X s 261 521 m -34 X s 244 549 m -17 X s 244 576 m -17 X s 244 603 m -17 X s 244 630 m -17 X s 261 657 m -34 X s 244 685 m -17 X s 244 712 m -17 X s 244 739 m -17 X s 244 766 m -17 X s 261 793 m -34 X s 244 821 m -17 X s 244 848 m -17 X s 244 875 m -17 X s 244 902 m -17 X s 261 929 m -34 X s 261 113 m -34 X s 42 111 m 28 X s 89 129 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 113 100 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 129 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 4 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -4 X cl s 160 123 m 3 2 d 5 4 d -32 Y s 12 247 m 27 X s 59 265 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -2 d 3 X 4 2 d 4 5 d 1 7 d 5 Y -1 7 d -4 5 d -4 1 d -3 X cl s 83 236 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 104 265 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 134 265 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 4 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -4 X cl s 174 265 m -15 X -2 -13 d 2 1 d 4 2 d 5 X 4 -2 d 3 -3 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 4 d s 165 401 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -2 d 3 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 59 537 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -2 d 3 X 4 2 d 4 5 d 1 7 d 5 Y -1 7 d -4 5 d -4 1 d -3 X cl s 83 508 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 104 537 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 134 537 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 4 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -4 X cl s 174 537 m -15 X -2 -13 d 2 1 d 4 2 d 5 X 4 -2 d 3 -3 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 4 d s 89 673 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 113 644 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 673 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 4 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -4 X cl s 160 667 m 3 2 d 5 4 d -32 Y s 59 809 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -2 d 3 X 4 2 d 4 5 d 1 7 d 5 Y -1 7 d -4 5 d -4 1 d -3 X cl s 83 780 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 104 809 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 130 803 m 3 2 d 5 4 d -32 Y s 174 809 m -15 X -2 -13 d 2 1 d 4 2 d 5 X 4 -2 d 3 -3 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 4 d s 89 945 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 113 916 m -1 -1 d 1 -2 d 2 2 d -2 1 d cl s 134 945 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 4 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -4 X cl s 157 938 m 1 Y 2 3 d 1 2 d 3 1 d 6 X 3 -1 d 2 -2 d 1 -3 d -3 Y -1 -3 d -3 -4 d -15 -16 d 21 X s 227 113 m 759 X s 353 147 m -34 Y s 404 130 m -17 Y s 454 130 m -17 Y s 505 130 m -17 Y s 556 130 m -17 Y s 606 147 m -34 Y s 657 130 m -17 Y s 708 130 m -17 Y s 758 130 m -17 Y s 809 130 m -17 Y s 859 147 m -34 Y s 353 147 m -34 Y s 303 130 m -17 Y s 252 130 m -17 Y s 859 147 m -34 Y s 910 130 m -17 Y s 961 130 m -17 Y s 309 73 m 28 X s 352 85 m 3 1 d 4 5 d -32 Y s 386 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 605 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 838 85 m 3 1 d 5 5 d -32 Y s 873 91 m -4 -2 d -4 -4 d -1 -8 d -4 Y 1 -8 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 759 816 227 113 C -129 397 m 2 2 d 2 X 1 25 d 2 10 d 2 5 d 2 -29 d 2 3 d 2 7 d 1 -15 d 2 -15 d 2 16 d 2 -1 d 2 -8 d 2 -38 d 1 -24 d 2 -22 d 2 22 d 2 10 d 2 -16 d 2 -19 d 2 3 d 1 X 2 13 d 2 8 d 2 X 2 -8 d 2 10 d 1 4 d 2 6 d 2 11 d 2 17 d 2 19 d 2 -12 d 1 -8 d 2 15 d 2 26 d 2 -6 d 2 -34 d 2 -13 d 1 -6 d 2 28 d 2 17 d 2 4 d 2 -7 d 2 21 d 1 18 d 2 -20 d 2 -5 d 2 -3 d 2 7 d 2 -1 d 2 4 d 1 8 d 2 5 d 2 -35 d 2 -13 d 2 -2 d 2 -25 d 1 11 d 2 7 d 2 -14 d 2 -9 d 2 -2 d 2 -1 d 1 18 d 2 18 d 2 60 d 2 53 d 2 16 d 2 -79 d 1 -51 d 2 4 d 2 -13 d 2 4 d 2 -18 d 2 -4 d 1 21 d 2 29 d 2 19 d 2 7 d 2 -12 d 2 1 d 1 -14 d 2 36 d 2 32 d 2 32 d 2 20 d 2 -26 d 2 -67 d 1 -20 d 2 -10 d 2 -13 d 2 13 d 2 -5 d 2 -20 d 1 1 d 2 -25 d 2 -8 d 2 7 d 2 12 d 2 -25 d 1 -13 d 2 10 d 2 5 d 2 10 d 2 20 d 2 13 d 1 -12 d 2 -31 d 2 -28 d 2 14 d 2 5 d 2 37 d 1 26 d 2 15 d 2 5 d 2 18 d 2 36 d 2 -3 d 2 -7 d 1 -9 d 2 9 d 2 -16 d 2 5 d 2 -17 d 2 -13 d 1 -16 d 2 -12 d 2 13 d 2 -5 d 2 -18 d 2 11 d 1 26 d 2 28 d 2 35 d 2 29 d 2 -16 d 2 -45 d 1 -22 d 2 24 d 2 18 d 2 -19 d 2 -31 d 2 2 d 1 15 d 2 -22 d 2 -28 d 2 10 d 2 X 2 -4 d 2 -3 d 1 5 d 2 3 d 2 8 d 2 27 d 2 21 d 2 15 d 1 -31 d 2 -27 d 2 3 d 2 X 2 -3 d 2 21 d 1 23 d 2 29 d 2 19 d 2 6 d 2 -27 d 2 -8 d 1 12 d 2 -32 d 2 -36 d 2 1 d 2 -16 d 2 -33 d 1 21 d 2 1 d 2 -17 d 2 6 d 2 14 d 2 X 2 23 d 1 -13 d 2 -14 d 2 11 d 2 16 d 2 -20 d 2 -6 d 1 9 d 2 3 d 2 12 d 2 -12 d 2 -9 d 2 -8 d 1 8 d 2 -4 d 2 9 d 2 12 d 2 -3 d 2 -17 d 1 20 d 2 37 d s 242 449 m 2 1 d 2 -17 d 2 3 d 2 8 d 1 22 d 2 -27 d 2 -28 d 2 X 2 24 d 2 21 d 2 -26 d 1 -5 d 2 -2 d 2 10 d 2 36 d 2 28 d 2 10 d 1 -2 d 2 -16 d 2 -36 d 2 -31 d 2 -28 d 2 21 d 1 6 d 2 -10 d 2 1 d 2 -5 d 2 -14 d 2 10 d 1 -20 d 2 -29 d 4 X 2 35 d 2 7 d 1 -22 d 2 15 d 2 -3 d 2 11 d 2 34 d 2 35 d 2 -10 d 1 -17 d 2 -19 d 2 27 d 2 21 d 2 16 d 2 6 d 1 -9 d 2 -14 d 2 -18 d 2 -24 d 2 -10 d 2 21 d 1 15 d 2 -6 d 2 -8 d 2 16 d 2 6 d 2 2 d 1 7 d 2 X 2 -12 d 2 -24 d 2 -27 d 2 13 d 1 27 d 2 -10 d 2 2 d 2 -10 d 2 8 d 2 20 d 2 12 d 1 -2 d 2 1 d 2 5 d 2 12 d 2 X 2 -12 d 1 -15 d 2 -11 d 2 -7 d 2 -3 d 2 7 d 2 5 d 1 -18 d 2 5 d 2 12 d 2 X 2 4 d 2 16 d 1 -4 d 2 1 d 2 -31 d 2 -28 d 2 -3 d 2 -16 d 1 8 d 2 11 d 2 -3 d 2 -12 d 2 -7 d 2 -24 d 2 -39 d 1 -22 d 2 -1 d 2 -5 d 2 -10 d 2 11 d 2 -5 d 1 -14 d 2 15 d 2 X 2 7 d 2 -2 d 2 -5 d 1 26 d 2 10 d 2 32 d 2 9 d 2 -12 d 2 24 d 1 35 d 2 -13 d 2 -11 d 2 -4 d 2 20 d 2 -1 d 1 -14 d 2 4 d 2 2 d 2 17 d 2 22 d 2 -7 d 2 -14 d 1 31 d 2 10 d 2 -26 d 2 -33 d 2 -15 d 2 23 d 1 17 d 2 -31 d 2 -31 d 2 -12 d 2 12 d 2 30 d 1 -4 d 2 -5 d 2 -23 d 2 -5 d 2 10 d 2 7 d 1 -28 d 2 -28 d 2 -5 d 2 11 d 2 X 2 18 d 1 31 d 2 39 d 2 19 d 2 -19 d 2 -7 d 2 12 d 1 9 d 2 9 d 2 4 d 2 -7 d 2 -3 d 2 -13 d 2 -23 d 1 3 d 2 5 d 2 12 d 2 24 d 2 20 d 2 -1 d 1 -10 d 2 -9 d 2 26 d 2 -3 d 2 -16 d 2 15 d 1 19 d 2 10 d 2 -1 d 2 13 d 2 -3 d 2 7 d 1 -7 d 2 5 d 2 12 d 2 16 d 2 30 d 2 58 d 1 67 d 2 30 d 2 -26 d 2 -63 d 2 -25 d 2 -38 d 2 -26 d s 616 531 m 1 -17 d 2 -6 d 2 -39 d 2 -54 d 2 -47 d 2 -6 d 1 11 d 2 19 d 2 12 d 2 X 2 -18 d 2 -30 d 1 -2 d 2 25 d 2 -5 d 2 -18 d 2 4 d 2 -2 d 1 -11 d 2 2 d 2 -1 d 2 -4 d 2 -13 d 2 -17 d 1 -1 d 2 -16 d 2 5 d 2 10 d 2 15 d 2 2 d 2 2 d 1 -4 d 2 3 d 2 8 d 2 -3 d 2 13 d 2 28 d 1 15 d 2 -20 d 2 -36 d 2 13 d 2 5 d 2 6 d 1 11 d 2 42 d 2 10 d 2 -13 d 2 13 d 2 9 d 1 X 2 4 d 2 -14 d 2 -6 d 2 1 d 2 4 d 1 -7 d 2 17 d 2 14 d 2 11 d 2 20 d 2 10 d 2 13 d 1 -10 d 2 -7 d 2 3 d 2 20 d 2 -4 d 2 -34 d 1 -29 d 2 -19 d 2 -8 d 2 -15 d 2 -13 d 2 26 d 1 50 d 2 24 d 2 -6 d 2 6 d 2 -32 d 2 -13 d 1 16 d 2 11 d 2 -19 d 2 -9 d 2 -29 d 2 5 d 1 17 d 2 -5 d 2 3 d 2 25 d 2 -31 d 2 -30 d 2 12 d 1 -5 d 2 3 d 2 34 d 2 6 d 2 -5 d 2 1 d 1 5 d 2 1 d 2 -3 d 2 -35 d 2 -4 d 2 11 d 1 6 d 2 22 d 2 17 d 2 1 d 2 -12 d 2 -9 d 1 14 d 2 -2 d 2 -20 d 2 21 d 2 1 d 2 -20 d 1 -12 d 2 9 d 2 26 d 2 13 d 2 7 d 2 -1 d 2 23 d 1 2 d 2 -30 d 2 -29 d 2 -11 d 2 -22 d 2 -26 d 1 -15 d 2 -18 d 2 -13 d 2 -9 d 2 14 d 2 16 d 1 15 d 2 1 d 2 5 d 2 -13 d 2 -31 d 2 5 d 1 21 d 2 38 d 2 46 d 2 33 d 2 10 d 2 -22 d 1 -19 d 2 7 d 2 5 d 2 21 d 2 X 2 -26 d 2 -7 d 1 -25 d 2 -23 d 2 -6 d 2 10 d 2 -21 d 2 22 d 1 27 d 2 16 d 2 1 d 2 -4 d 2 11 d 2 6 d 1 -8 d 2 -25 d 2 -2 d 2 25 d 2 -30 d 2 -18 d 1 19 d 2 11 d 2 8 d 2 X 2 1 d 2 -29 d 1 -26 d 2 -24 d 2 31 d 2 45 d 2 -1 d 2 -13 d 2 -12 d 1 6 d 2 X 2 -13 d 2 5 d 2 -11 d 2 -29 d 1 -16 d 2 -10 d 2 -28 d 2 -5 d 2 -16 d 2 17 d 1 37 d 2 18 d 2 -1 d 2 8 d 2 10 d s 989 382 m 2 8 d 1 22 d 2 7 d 2 -12 d 2 -5 d 2 -16 d 2 -4 d 1 -13 d 2 -30 d 2 -1 d 2 -6 d 2 -14 d 2 -13 d 2 21 d 1 21 d 2 11 d 2 X 2 3 d 2 -2 d 2 19 d 1 -12 d 2 -9 d 2 25 d 2 13 d 2 18 d 2 10 d 1 15 d 2 -11 d 2 -11 d 2 16 d 2 10 d 2 -10 d 1 -33 d 2 -10 d 2 -2 d 2 -5 d 2 4 d 2 9 d 1 -3 d 2 12 d 2 -18 d 2 -22 d 2 -14 d 2 5 d 1 -17 d 2 -38 d 2 -11 d 2 13 d 2 18 d 2 1 d 2 -22 d 1 5 d 2 8 d 2 -5 d 2 6 d 2 19 d 2 23 d 1 2 d 2 -4 d 2 12 d 2 18 d 2 10 d 2 -22 d 1 -27 d 2 -34 d 2 -1 d 2 -9 d 2 -16 d 2 6 d 1 19 d 2 47 d 2 25 d 2 -9 d 2 6 d 2 7 d 1 10 d 2 26 d 2 8 d 2 -6 d 2 14 d 2 6 d 2 -4 d 1 -8 d 2 -4 d 2 -15 d 2 -5 d 2 8 d 2 11 d 1 22 d 2 26 d 2 6 d 2 -3 d 2 2 d 2 -18 d 1 -43 d 2 -10 d 2 -14 d 2 -28 d 2 -39 d 2 -11 d 1 23 d 2 9 d 2 4 d 2 20 d 2 -8 d 2 14 d 1 19 d 2 13 d 2 -16 d 2 -32 d 2 -9 d 2 14 d 2 21 d 1 -9 d 2 -4 d 2 -6 d 2 -40 d 2 -23 d 2 -5 d 1 2 d 2 -7 d 2 -2 d 2 14 d 2 26 d 2 29 d 1 -5 d 2 5 d 2 -9 d 2 -3 d 2 5 d 2 10 d 1 7 d 2 -30 d 2 -32 d 2 -18 d 2 10 d 2 29 d 1 8 d 2 -12 d 2 11 d 2 23 d 2 -29 d 2 -26 d 2 -16 d 1 1 d 2 4 d 2 25 d 2 39 d 2 -2 d 2 -11 d 1 1 d 2 -11 d 2 12 d 2 10 d 2 34 d 2 15 d 1 -1 d 2 -15 d 2 -34 d 2 -17 d 2 -12 d 2 -12 d 1 -12 d 2 -3 d 2 15 d 2 18 d 2 -2 d 2 3 d 1 33 d 2 25 d 2 50 d 2 29 d 2 -2 d 2 3 d 2 -12 d 1 1 d 2 26 d 2 11 d 2 -22 d 2 6 d 2 31 d 1 13 d 2 -8 d 2 -5 d 2 13 d 2 X 2 7 d 1 -7 d 2 X 2 -3 d 2 -15 d 2 -20 d s 0 434 1 383 3 387 5 374 7 378 9 360 11 356 12 377 14 406 16 425 18 432 20 420 22 421 23 407 25 443 27 475 29 507 31 527 33 501 35 434 36 414 38 404 40 391 42 404 44 399 46 379 47 380 49 355 51 347 53 354 55 366 57 341 58 328 60 338 62 343 64 353 66 373 68 386 69 374 71 343 73 315 75 329 77 334 79 371 80 397 82 412 84 417 86 435 88 471 90 468 92 461 93 452 95 461 97 445 99 450 101 433 103 420 104 404 106 392 108 405 110 400 112 382 114 393 115 419 117 447 119 482 121 511 123 495 125 450 126 428 128 452 130 470 132 451 134 420 136 422 137 437 139 415 141 387 143 397 145 397 147 393 149 390 150 395 152 398 154 406 156 433 158 454 160 469 161 438 163 411 165 414 167 414 169 411 171 432 172 455 174 484 176 503 178 509 180 482 182 474 100 { m31} R 183 486 185 454 187 418 189 419 191 403 193 370 194 391 196 392 198 375 200 381 202 395 204 395 206 418 207 405 209 391 211 402 213 418 215 398 217 392 218 401 220 404 222 416 224 404 226 395 228 387 229 395 231 391 233 400 235 412 237 409 239 392 240 412 242 449 244 450 34 { m31} R 246 433 248 436 250 444 251 466 253 439 255 411 257 411 259 435 261 456 263 430 264 425 266 423 268 433 270 469 272 497 274 507 275 505 277 489 279 453 281 422 283 394 285 415 286 421 288 411 290 412 292 407 294 393 296 403 297 383 299 354 301 354 303 354 305 389 307 396 308 374 310 389 312 386 314 397 316 431 318 466 320 456 321 439 323 420 325 447 327 468 329 484 331 490 332 481 334 467 336 449 338 425 340 415 342 436 343 451 345 445 347 437 349 453 351 459 353 461 354 468 356 468 358 456 360 432 362 405 364 418 365 445 367 435 369 437 371 427 373 435 375 455 377 467 378 465 380 466 382 471 384 483 386 483 388 471 389 456 391 445 393 438 395 435 397 442 399 447 400 429 402 434 404 446 406 446 408 450 410 466 411 462 413 463 415 432 417 404 419 401 421 385 422 393 424 404 426 401 428 389 100 { m31} R 430 382 432 358 434 319 435 297 437 296 439 291 441 281 443 292 445 287 446 273 448 288 450 288 452 295 454 293 456 288 457 314 459 324 461 356 463 365 465 353 467 377 468 412 470 399 472 388 474 384 476 404 478 403 479 389 481 393 483 395 485 412 487 434 489 427 491 413 492 444 494 454 496 428 498 395 500 380 502 403 503 420 505 389 507 358 509 346 511 358 513 388 514 384 516 379 518 356 520 351 522 361 524 368 525 340 527 312 529 307 531 318 533 318 535 336 536 367 538 406 540 425 542 406 544 399 546 411 547 420 549 429 551 433 553 426 555 423 557 410 559 387 560 390 562 395 564 407 566 431 568 451 570 450 571 440 573 431 575 457 577 454 579 438 581 453 582 472 584 482 586 481 588 494 590 491 592 498 593 491 595 496 597 508 599 524 601 554 603 612 604 679 606 709 608 683 610 620 612 595 100 { m31 } R 614 557 616 531 617 514 619 508 4 { m31} R 621 469 623 415 625 368 627 362 628 373 630 392 632 404 634 404 636 386 638 356 639 354 641 379 643 374 645 356 647 360 649 358 650 347 652 349 654 348 656 344 658 331 660 314 661 313 663 297 665 302 667 312 669 327 671 329 673 331 674 327 676 330 678 338 680 335 682 348 684 376 685 391 687 371 689 335 691 348 693 353 695 359 696 370 698 412 700 422 702 409 704 422 706 431 707 431 709 435 711 421 713 415 715 416 717 420 718 413 720 430 722 444 724 455 726 475 728 485 730 498 731 488 733 481 735 484 737 504 739 500 741 466 742 437 744 418 746 410 748 395 750 382 752 408 753 458 755 482 757 476 759 482 761 450 763 437 764 453 766 464 768 445 770 436 772 407 774 412 775 429 777 424 779 427 781 452 783 421 785 391 787 403 788 398 790 401 792 435 794 441 796 436 798 437 799 442 801 443 803 440 100 { m31} R 805 405 807 401 809 412 810 418 812 440 814 457 816 458 818 446 820 437 821 451 823 449 825 429 827 450 829 451 831 431 832 419 834 428 836 454 838 467 840 474 842 473 844 496 845 498 847 468 849 439 851 428 853 406 855 380 856 365 858 347 860 334 862 325 864 339 866 355 867 370 869 371 871 376 873 363 875 332 877 337 878 358 880 396 882 442 884 475 886 485 888 463 889 444 891 451 893 456 895 477 897 477 899 451 901 444 902 419 904 396 906 390 908 400 910 379 912 401 913 428 915 444 917 445 919 441 921 452 923 458 924 450 926 425 928 423 930 448 932 418 934 400 935 419 937 430 939 438 941 438 943 439 945 410 946 384 948 360 950 391 952 436 954 435 956 422 958 410 959 416 961 416 963 403 965 408 967 397 969 368 970 352 972 342 974 314 976 309 978 293 980 310 981 347 983 365 985 364 987 372 100 { m31} R 989 382 991 390 992 412 994 419 4 { m31} R 996 407 998 402 1000 386 1002 382 1003 369 1005 339 1007 338 1009 332 1011 318 1013 305 1015 326 1016 347 1018 358 1020 358 1022 361 1024 359 1026 378 1027 366 1029 357 1031 382 1033 395 1035 413 1037 423 1038 438 1040 427 1042 416 1044 432 1046 442 1048 432 1049 399 1051 389 1053 387 1055 382 1057 386 1059 395 1060 392 1062 404 1064 386 1066 364 1068 350 1070 355 1071 338 1073 300 1075 289 1077 302 1079 320 1081 321 1083 299 1084 304 1086 312 1088 307 1090 313 1092 332 1094 355 1095 357 1097 353 1099 365 1101 383 1103 393 1105 371 1106 344 1108 310 1110 309 1112 300 1114 284 1116 290 1117 309 1119 356 1121 381 1123 372 1125 378 1127 385 1128 395 1130 421 1132 429 1134 423 1136 437 1138 443 1140 439 1141 431 1143 427 1145 412 1147 407 1149 415 1151 426 1152 448 1154 474 1156 480 1158 477 1160 479 1162 461 1163 418 1165 408 1167 394 1169 366 1171 327 1173 316 1174 339 1176 348 1178 352 100 { m31} R 1180 372 1182 364 1184 378 1185 397 1187 410 1189 394 1191 362 1193 353 1195 367 1197 388 1198 379 1200 375 1202 369 1204 329 1206 306 1208 301 1209 303 1211 296 1213 294 1215 308 1217 334 1219 363 1220 358 1222 363 1224 354 1226 351 1228 356 1230 366 1231 373 1233 343 1235 311 1237 293 1239 303 1241 332 1242 340 1244 328 1246 339 1248 362 1250 333 1252 307 1254 291 1255 292 1257 296 1259 321 1261 360 1263 358 1265 347 1266 348 1268 337 1270 349 1272 359 1274 393 1276 408 1277 407 1279 392 1281 358 1283 341 1285 329 1287 317 1288 305 1290 302 1292 317 1294 335 1296 333 1298 336 1299 369 1301 394 1303 444 1305 473 1307 471 1309 474 1311 462 1312 463 1314 489 1316 500 1318 478 1320 484 1322 515 1323 528 1325 520 1327 515 1329 528 1331 528 1333 535 1334 528 1336 528 1338 525 1340 510 1342 490 89 { m31} R 2040 2040 0 0 C 759 816 227 113 C 2040 2040 0 0 C 363 821 m 3 1 d 5 5 d -34 Y s 400 827 m -5 -1 d -3 -5 d -2 -8 d -5 Y 2 -8 d 3 -5 d 5 -2 d 3 X 5 2 d 4 5 d 1 8 d 5 Y -1 8 d -4 5 d -5 1 d -3 X cl s 433 827 m -5 -1 d -4 -5 d -1 -8 d -5 Y 1 -8 d 4 -5 d 5 -2 d 3 X 5 2 d 3 5 d 2 8 d 5 Y -2 8 d -3 5 d -5 1 d -3 X cl s 473 816 m -23 Y s 473 810 m 5 4 d 3 2 d 5 X 3 -2 d 2 -4 d -17 Y s 491 810 m 5 4 d 3 2 d 5 X 3 -2 d 2 -4 d -17 Y s 522 827 m -34 Y s 544 827 m -22 -22 d s 530 813 m 14 -20 d s 759 816 227 113 C 2040 2040 0 0 C 759 816 227 113 C 2040 2040 0 0 C 371 725 m -3 -3 d -3 -5 d -4 -7 d -1 -8 d -6 Y 1 -8 d 4 -7 d 3 -5 d 3 -3 d s 389 719 m -5 -2 d -2 -3 d -4 Y 2 -3 d 3 -1 d 7 -2 d 5 -2 d 3 -3 d 1 -3 d -5 Y -1 -3 d -2 -2 d -5 -1 d -6 X -5 1 d -2 2 d -1 3 d 5 Y 1 3 d 4 3 d 4 2 d 7 2 d 3 1 d 2 3 d 4 Y -2 3 d -5 2 d -6 X cl s 423 719 m -5 -2 d -3 -5 d -2 -8 d -5 Y 2 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 2 8 d 5 Y -2 8 d -3 5 d -5 2 d -3 X cl s 455 719 m -5 -2 d -3 -5 d -1 -8 d -5 Y 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 4 5 d 1 8 d 5 Y -1 8 d -4 5 d -5 2 d -3 X cl s 478 725 m 3 -3 d 3 -5 d 4 -7 d 1 -8 d -6 Y -1 -8 d -4 -7 d -3 -5 d -3 -3 d s 535 702 m -2 4 d -5 1 d -5 X -5 -1 d -1 -4 d 1 -3 d 4 -2 d 8 -1 d 3 -2 d 2 -3 d -2 Y -2 -3 d -5 -1 d -5 X -5 1 d -1 3 d s 759 816 227 113 C NC 759 816 1213 113 bl 759 816 1213 113 C NC 1213 113 m 816 Y s 1247 113 m -34 X s 1230 141 m -17 X s 1230 168 m -17 X s 1230 195 m -17 X s 1230 222 m -17 X s 1247 249 m -34 X s 1230 277 m -17 X s 1230 304 m -17 X s 1230 331 m -17 X s 1230 358 m -17 X s 1247 385 m -34 X s 1230 413 m -17 X s 1230 440 m -17 X s 1230 467 m -17 X s 1230 494 m -17 X s 1247 521 m -34 X s 1230 549 m -17 X s 1230 576 m -17 X s 1230 603 m -17 X s 1230 630 m -17 X s 1247 657 m -34 X s 1230 685 m -17 X s 1230 712 m -17 X s 1230 739 m -17 X s 1230 766 m -17 X s 1247 793 m -34 X s 1230 821 m -17 X s 1230 848 m -17 X s 1230 875 m -17 X s 1230 902 m -17 X s 1247 929 m -34 X s 1059 111 m 27 X s 1105 129 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1130 100 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1146 123 m 3 2 d 5 4 d -32 Y s 1151 265 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -2 d 3 X 4 2 d 3 5 d 2 7 d 5 Y -2 7 d -3 5 d -4 1 d -3 X cl s 1105 401 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1130 372 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1146 395 m 3 2 d 5 4 d -32 Y s 1105 537 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1130 508 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1143 530 m 1 Y 2 3 d 1 2 d 3 1 d 6 X 3 -1 d 2 -2 d 1 -3 d -3 Y -1 -3 d -3 -4 d -15 -16 d 21 X s 1105 673 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1130 644 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1145 673 m 16 X -9 -12 d 5 X 3 -1 d 1 -2 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 4 d s 1105 809 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1130 780 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1157 809 m -15 -21 d 22 X s 1157 809 m -32 Y s 1105 945 m -4 -1 d -3 -5 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -2 d 3 X 5 2 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 1130 916 m -2 -1 d 2 -2 d 1 2 d -1 1 d cl s 1160 945 m -15 X -2 -13 d 2 1 d 4 2 d 5 X 4 -2 d 3 -3 d 2 -4 d -3 Y -2 -5 d -3 -3 d -4 -2 d -5 X -4 2 d -2 1 d -1 4 d s 1213 113 m 759 X s 1339 147 m -34 Y s 1390 130 m -17 Y s 1440 130 m -17 Y s 1491 130 m -17 Y s 1542 130 m -17 Y s 1592 147 m -34 Y s 1643 130 m -17 Y s 1694 130 m -17 Y s 1744 130 m -17 Y s 1795 130 m -17 Y s 1845 147 m -34 Y s 1339 147 m -34 Y s 1289 130 m -17 Y s 1238 130 m -17 Y s 1845 147 m -34 Y s 1896 130 m -17 Y s 1947 130 m -17 Y s 1295 73 m 28 X s 1338 85 m 3 1 d 4 5 d -32 Y s 1372 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -5 2 d -3 X cl s 1591 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1824 85 m 3 1 d 5 5 d -32 Y s 1859 91 m -4 -2 d -4 -4 d -1 -8 d -4 Y 1 -8 d 4 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 759 816 1213 113 C 857 298 m 2 -12 d 2 -9 d 1 -6 d 2 -8 d 2 X 2 -2 d 2 -9 d 2 -8 d 1 6 d 2 20 d 2 15 d 2 6 d 2 -8 d 2 -12 d 1 -9 d 2 1 d 2 -11 d 2 -5 d 2 -3 d 2 -10 d 2 17 d 1 1 d 2 -7 d 2 -14 d 2 -15 d 2 -16 d 2 -3 d 1 7 d 2 9 d 2 -13 d 2 -8 d 2 2 d 2 6 d 1 11 d 2 7 d 2 18 d 2 6 d 2 -6 d 2 10 d 1 6 d 2 -8 d 2 -6 d 2 -10 d 2 -1 d 2 -3 d 1 -4 d 2 -7 d 2 -8 d 2 -7 d 2 -1 d 2 9 d 2 7 d 1 -4 d 2 -1 d 2 -1 d 2 8 d 2 3 d 2 1 d 1 2 d 2 7 d 2 4 d 2 3 d 2 1 d 2 -22 d 1 -3 d 2 -3 d 2 11 d 2 -4 d 2 10 d 2 5 d 1 -10 d 2 2 d 2 6 d 2 2 d 2 11 d 2 3 d 1 1 d 2 -2 d 2 -3 d 2 -13 d 2 -7 d 2 5 d 1 9 d 2 7 d 2 2 d 2 17 d 2 16 d 2 -5 d 2 -18 d 1 -14 d 2 3 d 2 2 d 2 11 d 2 6 d 2 3 d 1 7 d 2 3 d 2 -1 d 2 4 d 2 6 d 2 -4 d 1 -7 d 2 12 d 2 -6 d 2 -2 d 2 -2 d 2 -2 d 1 5 d 2 7 d 2 -7 d 2 1 d 2 -5 d 2 -15 d 1 -8 d 2 X 2 9 d 2 13 d 2 3 d 2 7 d 2 -2 d 1 -5 d 2 -4 d 2 -3 d 2 -4 d 2 3 d 2 6 d 1 1 d 2 -8 d 2 -4 d 2 -3 d 2 -8 d 2 7 d 1 10 d 2 10 d 2 -1 d 2 1 d 2 -1 d 2 4 d 1 -11 d 2 -14 d 2 2 d 2 3 d 2 3 d 2 8 d 1 7 d 2 1 d 2 5 d 2 2 d 2 5 d 2 3 d 2 -8 d 1 -15 d 2 -11 d 2 -10 d 2 1 d 2 3 d 2 -14 d 1 -12 d 2 -5 d 2 9 d 2 9 d 2 14 d 2 -6 d 1 -14 d 2 -7 d 2 -4 d 2 9 d 2 1 d 2 27 d 1 18 d 2 -8 d 2 -8 d 2 -1 d 2 1 d 2 15 d 1 11 d 2 -6 d 2 -7 d 2 -14 d 2 -5 d 2 7 d 2 3 d 1 -5 d 2 -7 d 2 10 d 2 3 d 2 4 d 2 10 d 1 -7 d 2 X 2 4 d 2 -3 d 2 16 d 2 1 d 1 12 d 2 -3 d 2 -13 d 2 -2 d 2 -1 d 2 7 d 1 -1 d 2 -2 d s 1228 291 m 2 -13 d 2 -7 d 2 -2 d 2 2 d 1 8 d 2 1 d 2 1 d 2 3 d 2 2 d 2 8 d 2 -2 d 1 -4 d 2 -4 d 2 3 d 2 4 d 2 17 d 2 5 d 1 -1 d 2 -3 d 2 -9 d 2 -17 d 2 -10 d 2 -2 d 1 -22 d 2 -16 d 2 -18 d 2 -5 d 2 5 d 2 9 d 1 -12 d 2 5 d 2 10 d 2 3 d 2 15 d 2 19 d 1 3 d 2 -1 d 2 X 2 -9 d 2 -5 d 2 -5 d 2 1 d 1 -7 d 2 -14 d 2 X 2 3 d 2 -5 d 2 -11 d 1 -5 d 2 -3 d 2 5 d 2 18 d 2 24 d 2 11 d 1 -3 d 2 -8 d 2 -1 d 2 11 d 2 -6 d 2 -10 d 1 -4 d 2 -9 d 2 X 2 10 d 2 16 d 2 9 d 1 18 d 2 -12 d 2 X 2 1 d 2 -6 d 2 -8 d 2 -9 d 1 4 d 2 4 d 2 -7 d 2 6 d 2 2 d 2 -7 d 1 13 d 2 16 d 2 6 d 2 -8 d 2 X 2 -1 d 1 -1 d 2 -2 d 2 -16 d 2 6 d 2 -5 d 2 -18 d 1 -20 d 2 -10 d 2 2 d 2 11 d 2 19 d 2 5 d 1 5 d 2 8 d 2 -2 d 2 10 d 2 8 d 2 2 d 2 -2 d 1 5 d 2 X 2 2 d 2 -4 d 2 1 d 2 -6 d 1 -14 d 2 -8 d 2 3 d 2 -14 d 2 -16 d 2 7 d 1 17 d 2 -4 d 2 5 d 2 19 d 2 1 d 2 -6 d 1 -5 d 2 -7 d 2 -3 d 2 -4 d 2 -11 d 2 2 d 1 X 2 -3 d 2 10 d 2 9 d 2 8 d 2 13 d 2 3 d 1 -1 d 2 -7 d 2 4 d 2 5 d 2 -3 d 2 -1 d 1 -9 d 2 7 d 2 17 d 2 18 d 2 36 d 2 28 d 1 -7 d 2 -21 d 2 -35 d 2 -23 d 2 -21 d 2 -18 d 1 -14 d 2 -23 d 2 10 d 2 8 d 2 16 d 2 33 d 1 21 d 2 14 d 2 5 d 2 -6 d 2 -7 d 2 7 d 1 1 d 2 2 d 2 3 d 2 -1 d 2 2 d 2 14 d 2 16 d 1 9 d 2 16 d 2 -9 d 2 -15 d 2 3 d 2 5 d 1 2 d 2 7 d 2 -5 d 2 -1 d 2 -17 d 2 -15 d 1 X 2 -4 d 2 -8 d 2 -12 d 2 12 d 2 38 d 1 45 d 2 33 d 2 37 d 2 50 d 2 61 d 2 52 d 1 71 d 2 49 d 2 -77 d 2 -113 d 2 -92 d 2 -66 d 2 -57 d s 1602 350 m 1 -34 d 2 -20 d 2 -22 d 2 -1 d 2 11 d 2 10 d 1 16 d 2 5 d 2 -13 d 2 -12 d 2 -21 d 2 -32 d 1 -29 d 2 -15 d 2 -7 d 2 -8 d 2 -5 d 2 -18 d 1 -18 d 2 -11 d 2 12 d 2 12 d 2 6 d 2 16 d 1 19 d 2 21 d 2 18 d 2 28 d 2 24 d 2 15 d 2 -7 d 1 -1 d 2 1 d 2 -6 d 2 -3 d 2 X 2 5 d 1 -2 d 2 6 d 2 10 d 2 24 d 2 -2 d 2 -16 d 1 -10 d 2 5 d 2 18 d 2 -7 d 2 -7 d 2 -1 d 1 -10 d 2 -12 d 2 -13 d 2 -16 d 2 -19 d 2 -14 d 1 X 2 10 d 2 10 d 2 7 d 2 -6 d 2 1 d 2 15 d 1 3 d 2 -4 d 2 1 d 2 5 d 2 4 d 2 4 d 1 -11 d 2 -11 d 2 5 d 2 -9 d 2 -9 d 2 -11 d 1 -3 d 2 -5 d 2 X 2 10 d 2 10 d 2 -12 d 1 1 d 2 10 d 2 -5 d 2 -7 d 2 -6 d 2 12 d 1 X 2 1 d 2 2 d 2 -3 d 2 -12 d 2 -4 d 2 3 d 1 5 d 2 -8 d 2 -1 d 2 -4 d 2 6 d 2 13 d 1 9 d 2 5 d 2 11 d 2 1 d 2 13 d 2 1 d 1 3 d 2 -10 d 2 -4 d 2 -7 d 2 -13 d 2 -4 d 1 -19 d 2 -11 d 2 -6 d 2 -1 d 2 7 d 2 -3 d 1 13 d 2 18 d 2 14 d 2 7 d 2 10 d 2 2 d 2 -8 d 1 -9 d 2 -12 d 2 -12 d 2 X 2 -1 d 2 -2 d 1 -5 d 2 8 d 2 19 d 2 7 d 2 -1 d 2 -5 d 1 3 d 2 -2 d 2 -7 d 2 8 d 2 13 d 2 -9 d 1 -12 d 2 -1 d 2 -3 d 2 4 d 2 8 d 2 6 d 1 -2 d 2 -4 d 2 1 d 2 -4 d 2 -3 d 2 -2 d 2 5 d 1 -3 d 2 -5 d 2 13 d 2 3 d 2 5 d 2 X 1 10 d 2 10 d 2 2 d 2 -11 d 2 4 d 2 7 d 1 -8 d 2 -14 d 2 1 d 2 -10 d 2 -13 d 2 -5 d 1 11 d 2 5 d 2 2 d 2 7 d 2 -1 d 2 X 1 -4 d 2 3 d 2 5 d 2 -5 d 2 -6 d 2 -8 d 2 10 d 1 2 d 2 -15 d 2 4 d 2 13 d 2 16 d 2 -5 d 1 X 2 -9 d 2 -12 d 2 -3 d 2 19 d 2 16 d 1 13 d 2 X 2 6 d 2 -9 d 2 10 d s 1975 292 m 2 2 d 1 6 d 2 -7 d 2 -5 d 2 1 d 2 -3 d 2 -2 d 1 -4 d 2 -6 d 2 13 d 2 -11 d 2 -12 d 2 -12 d 2 -4 d 1 -1 d 2 -15 d 2 -3 d 2 1 d 2 -5 d 2 3 d 1 4 d 2 3 d 2 16 d 2 -4 d 2 6 d 2 8 d 1 -4 d 2 -5 d 2 -12 d 2 7 d 2 1 d 2 X 1 6 d 2 -8 d 2 -3 d 2 -1 d 2 -2 d 2 11 d 1 -2 d 2 -4 d 2 -1 d 2 -3 d 2 7 d 2 9 d 1 7 d 2 3 d 2 -21 d 2 3 d 2 9 d 2 -7 d 2 -8 d 1 7 d 2 X 2 -2 d 2 -15 d 2 7 d 2 12 d 1 4 d 2 -1 d 2 -4 d 2 1 d 2 8 d 2 5 d 1 -11 d 2 -1 d 2 -10 d 2 -14 d 2 -11 d 2 -11 d 1 X 2 6 d 2 2 d 2 -6 d 2 5 d 2 5 d 1 4 d 2 19 d 2 21 d 2 10 d 2 -4 d 2 -9 d 2 2 d 1 -21 d 2 -8 d 2 -5 d 2 -9 d 2 -1 d 2 11 d 1 18 d 2 3 d 2 -8 d 2 11 d 2 9 d 2 15 d 1 3 d 2 10 d 2 12 d 2 -4 d 2 -4 d 2 -13 d 1 -19 d 2 -19 d 2 -3 d 2 -2 d 2 -8 d 2 X 1 12 d 2 10 d 2 -4 d 2 -4 d 2 -7 d 2 -8 d 2 1 d 1 10 d 2 23 d 2 3 d 2 -11 d 2 -7 d 2 6 d 1 7 d 2 -21 d 2 9 d 2 14 d 2 6 d 2 -2 d 1 4 d 2 12 d 2 12 d 2 15 d 2 5 d 2 8 d 1 7 d 2 -10 d 2 -13 d 2 -7 d 2 -11 d 2 -13 d 1 1 d 2 -3 d 2 -4 d 2 -2 d 2 9 d 2 24 d 2 22 d 1 12 d 2 4 d 2 -14 d 2 -13 d 2 1 d 2 -30 d 1 -6 d 2 17 d 2 9 d 2 11 d 2 2 d 2 -11 d 1 -5 d 2 4 d 2 7 d 2 2 d 2 5 d 2 8 d 1 1 d 2 -3 d 2 7 d 2 12 d 2 -10 d 2 -25 d 1 -17 d 2 -7 d 2 2 d 2 16 d 2 10 d 2 -8 d 2 -18 d 1 1 d 2 9 d 2 -6 d 4 X 2 -3 d 1 5 d 2 -8 d 2 -5 d 2 8 d 2 -5 d 2 3 d 1 5 d 2 -14 d 2 -13 d 2 -3 d 2 -14 d s 857 298 859 286 861 277 862 271 864 263 866 263 868 261 870 252 872 244 873 250 875 270 877 285 879 291 881 283 883 271 884 262 886 263 888 252 890 247 892 244 894 234 896 251 897 252 899 245 901 231 903 216 905 200 907 197 908 204 910 213 912 200 914 192 916 194 918 200 919 211 921 218 923 236 925 242 927 236 929 246 930 252 932 244 934 238 936 228 938 227 940 224 941 220 943 213 945 205 947 198 949 197 951 206 953 213 954 209 956 208 958 207 960 215 962 218 964 219 965 221 967 228 969 232 971 235 973 236 975 214 976 211 978 208 980 219 982 215 984 225 986 230 987 220 989 222 991 228 993 230 995 241 997 244 998 245 1000 243 1002 240 1004 227 1006 220 1008 225 1009 234 1011 241 1013 243 1015 260 1017 276 1019 271 1021 253 1022 239 1024 242 1026 244 1028 255 1030 261 1032 264 1033 271 1035 274 1037 273 1039 277 100 { m31} R 1041 283 1043 279 1044 272 1046 284 1048 278 1050 276 1052 274 1054 272 1055 277 1057 284 1059 277 1061 278 1063 273 1065 258 1066 250 1068 250 1070 259 1072 272 1074 275 1076 282 1078 280 1079 275 1081 271 1083 268 1085 264 1087 267 1089 273 1090 274 1092 266 1094 262 1096 259 1098 251 1100 258 1101 268 1103 278 1105 277 1107 278 1109 277 1111 281 1112 270 1114 256 1116 258 1118 261 1120 264 1122 272 1123 279 1125 280 1127 285 1129 287 1131 292 1133 295 1135 287 1136 272 1138 261 1140 251 1142 252 1144 255 1146 241 1147 229 1149 224 1151 233 1153 242 1155 256 1157 250 1158 236 1160 229 1162 225 1164 234 1166 235 1168 262 1169 280 1171 272 1173 264 1175 263 1177 264 1179 279 1180 290 1182 284 1184 277 1186 263 1188 258 1190 265 1192 268 1193 263 1195 256 1197 266 1199 269 1201 273 1203 283 1204 276 1206 276 1208 280 1210 277 1212 293 1214 294 1215 306 1217 303 1219 290 1221 288 1223 287 100 { m31} R 1225 294 1226 293 1228 291 1230 278 4 { m31} R 1232 271 1234 269 1236 271 1237 279 1239 280 1241 281 1243 284 1245 286 1247 294 1249 292 1250 288 1252 284 1254 287 1256 291 1258 308 1260 313 1261 312 1263 309 1265 300 1267 283 1269 273 1271 271 1272 249 1274 233 1276 215 1278 210 1280 215 1282 224 1283 212 1285 217 1287 227 1289 230 1291 245 1293 264 1294 267 1296 266 1298 266 1300 257 1302 252 1304 247 1306 248 1307 241 1309 227 1311 227 1313 230 1315 225 1317 214 1318 209 1320 206 1322 211 1324 229 1326 253 1328 264 1329 261 1331 253 1333 252 1335 263 1337 257 1339 247 1340 243 1342 234 1344 234 1346 244 1348 260 1350 269 1351 287 1353 275 1355 275 1357 276 1359 270 1361 262 1363 253 1364 257 1366 261 1368 254 1370 260 1372 262 1374 255 1375 268 1377 284 1379 290 1381 282 1383 282 1385 281 1386 280 1388 278 1390 262 1392 268 1394 263 1396 245 1397 225 1399 215 1401 217 1403 228 1405 247 1407 252 1408 257 1410 265 1412 263 1414 273 100 { m31} R 1416 281 1418 283 1420 281 1421 286 1423 286 1425 288 1427 284 1429 285 1431 279 1432 265 1434 257 1436 260 1438 246 1440 230 1442 237 1443 254 1445 250 1447 255 1449 274 1451 275 1453 269 1454 264 1456 257 1458 254 1460 250 1462 239 1464 241 1465 241 1467 238 1469 248 1471 257 1473 265 1475 278 1477 281 1478 280 1480 273 1482 277 1484 282 1486 279 1488 278 1489 269 1491 276 1493 293 1495 311 1497 347 1499 375 1500 368 1502 347 1504 312 1506 289 1508 268 1510 250 1511 236 1513 213 1515 223 1517 231 1519 247 1521 280 1522 301 1524 315 1526 320 1528 314 1530 307 1532 314 1533 315 1535 317 1537 320 1539 319 1541 321 1543 335 1545 351 1546 360 1548 376 1550 367 1552 352 1554 355 1556 360 1557 362 1559 369 1561 364 1563 363 1565 346 1567 331 1568 331 1570 327 1572 319 1574 307 1576 319 1578 357 1579 402 1581 435 1583 472 1585 522 1587 583 1589 635 1590 706 1592 755 1594 678 1596 565 1598 473 100 { m31} R 1600 407 1602 350 1603 316 1605 296 4 { m31} R 1607 274 1609 273 1611 284 1613 294 1614 310 1616 315 1618 302 1620 290 1622 269 1624 237 1625 208 1627 193 1629 186 1631 178 1633 173 1635 155 1636 137 1638 126 1640 138 1642 150 1644 156 1646 172 1647 191 1649 212 1651 230 1653 258 1655 282 1657 297 1659 290 1660 289 1662 290 1664 284 1666 281 1668 281 1670 286 1671 284 1673 290 1675 300 1677 324 1679 322 1681 306 1682 296 1684 301 1686 319 1688 312 1690 305 1692 304 1693 294 1695 282 1697 269 1699 253 1701 234 1703 220 1704 220 1706 230 1708 240 1710 247 1712 241 1714 242 1716 257 1717 260 1719 256 1721 257 1723 262 1725 266 1727 270 1728 259 1730 248 1732 253 1734 244 1736 235 1738 224 1739 221 1741 216 1743 216 1745 226 1747 236 1749 224 1750 225 1752 235 1754 230 1756 223 1758 217 1760 229 1761 229 1763 230 1765 232 1767 229 1769 217 1771 213 1773 216 1774 221 1776 213 1778 212 1780 208 1782 214 1784 227 1785 236 1787 241 1789 252 100 { m31} R 1791 253 1793 266 1795 267 1796 270 1798 260 1800 256 1802 249 1804 236 1806 232 1807 213 1809 202 1811 196 1813 195 1815 202 1817 199 1818 212 1820 230 1822 244 1824 251 1826 261 1828 263 1830 255 1831 246 1833 234 1835 222 1837 222 1839 221 1841 219 1842 214 1844 222 1846 241 1848 248 1850 247 1852 242 1853 245 1855 243 1857 236 1859 244 1861 257 1863 248 1864 236 1866 235 1868 232 1870 236 1872 244 1874 250 1875 248 1877 244 1879 245 1881 241 1883 238 1885 236 1887 241 1888 238 1890 233 1892 246 1894 249 1896 254 1898 254 1899 264 1901 274 1903 276 1905 265 1907 269 1909 276 1910 268 1912 254 1914 255 1916 245 1918 232 1920 227 1921 238 1923 243 1925 245 1927 252 1929 251 1931 251 1932 247 1934 250 1936 255 1938 250 1940 244 1942 236 1944 246 1945 248 1947 233 1949 237 1951 250 1953 266 1955 261 1956 261 1958 252 1960 240 1962 237 1964 256 1966 272 1967 285 1969 285 1971 291 1973 282 100 { m31} R 1975 292 1977 294 1978 300 1980 293 4 { m31 } R 1982 288 1984 289 1986 286 1988 284 1989 280 1991 274 1993 287 1995 276 1997 264 1999 252 2001 248 2002 247 2004 232 2006 229 2008 230 2010 225 2012 228 2013 232 2015 235 2017 251 2019 247 2021 253 2023 261 2024 257 2026 252 2028 240 2030 247 2032 248 2034 248 2035 254 2037 246 2039 243 2041 242 2043 240 2045 251 2046 249 2048 245 2050 244 2052 241 2054 248 2056 257 2057 264 2059 267 2061 246 2063 249 2065 258 2067 251 2069 243 2070 250 2072 250 2074 248 2076 233 2078 240 2080 252 2081 256 2083 255 2085 251 2087 252 2089 260 2091 265 2092 254 2094 253 2096 243 2098 229 2100 218 2102 207 2103 207 2105 213 2107 215 2109 209 2111 214 2113 219 2114 223 2116 242 2118 263 2120 273 2122 269 2124 260 2126 262 2127 241 2129 233 2131 228 2133 219 2135 218 2137 229 2138 247 2140 250 2142 242 2144 253 2146 262 2148 277 2149 280 2151 290 2153 302 2155 298 2157 294 2159 281 2160 262 2162 243 2164 240 100 { m31} R 2166 238 2168 230 2170 230 2171 242 2173 252 2175 248 2177 244 2179 237 2181 229 2183 230 2184 240 2186 263 2188 266 2190 255 2192 248 2194 254 2195 261 2197 240 2199 249 2201 263 2203 269 2205 267 2206 271 2208 283 2210 295 2212 310 2214 315 2216 323 2217 330 2219 320 2221 307 2223 300 2225 289 2227 276 2228 277 2230 274 2232 270 2234 268 2236 277 2238 301 2240 323 2241 335 2243 339 2245 325 2247 312 2249 313 2251 283 2252 277 2254 294 2256 303 2258 314 2260 316 2262 305 2263 300 2265 304 2267 311 2269 313 2271 318 2273 326 2274 327 2276 324 2278 331 2280 343 2282 333 2284 308 2285 291 2287 284 2289 286 2291 302 2293 312 2295 304 2297 286 2298 287 2300 296 2302 290 2304 290 2306 290 2308 287 2309 292 2311 284 2313 279 2315 287 2317 282 2319 285 2320 290 2322 276 2324 263 2326 260 2328 246 89 { m31} R 2040 2040 0 0 C 759 816 1213 113 C 2040 2040 0 0 C 1364 827 m -17 X -1 -14 d 1 1 d 5 2 d 5 X 5 -2 d 3 -3 d 2 -5 d -3 Y -2 -5 d -3 -3 d -5 -2 d -5 X -5 2 d -1 2 d -2 3 d s 1386 827 m -5 -1 d -3 -5 d -2 -8 d -5 Y 2 -8 d 3 -5 d 5 -2 d 3 X 5 2 d 4 5 d 1 8 d 5 Y -1 8 d -4 5 d -5 1 d -3 X cl s 1427 816 m -23 Y s 1427 810 m 5 4 d 3 2 d 5 X 3 -2 d 1 -4 d -17 Y s 1444 810 m 5 4 d 4 2 d 4 X 4 -2 d 1 -4 d -17 Y s 1475 827 m -34 Y s 1498 827 m -23 -22 d s 1483 813 m 15 -20 d s 759 816 1213 113 C 2040 2040 0 0 C 759 816 1213 113 C 2040 2040 0 0 C 1357 739 m -3 -4 d -3 -4 d -4 -7 d -1 -8 d -7 Y 1 -8 d 4 -6 d 3 -5 d 3 -3 d s 1375 732 m -5 -1 d -2 -4 d -3 Y 2 -3 d 3 -2 d 7 -1 d 5 -2 d 3 -3 d 1 -4 d -4 Y -1 -4 d -2 -1 d -5 -2 d -6 X -5 2 d -2 1 d -1 4 d 4 Y 1 4 d 4 3 d 4 2 d 7 1 d 3 2 d 2 3 d 3 Y -2 4 d -5 1 d -6 X cl s 1433 716 m -1 3 d -5 2 d -5 X -5 -2 d -2 -3 d 2 -3 d 3 -2 d 8 -2 d 4 -1 d 1 -3 d -2 Y -1 -3 d -5 -2 d -5 X -5 2 d -2 3 d s 1443 739 m 3 -4 d 3 -4 d 4 -7 d 1 -8 d -7 Y -1 -8 d -4 -6 d -3 -5 d -3 -3 d s 759 816 1213 113 C gr gr showpage end %%EndDocument @endspecial 158 x Fr(Figure)36 b(4:)i(The)h(dimensionless)e (cross-correlation)f Fk(R)q Fr(\()p Fk(\034)11 b Fr(\))39 b(a)m(v)m(eraged)g(o)m(v)m(er)g(the)f(47)f(data)h(stretc)m(hes,)-9 2277 y(for)i(v)-5 b(arious)41 b(applied)f(signals.)g(In)i(the)g (\014gures)g(on)f(the)h(left)e(t)m(w)m(o)i(signals,)f(100)f(mK)h(and)g (50)g(mK,)-9 2397 y(w)m(ere)e(applied,)e(under)i(the)f(assumption)f (that)h(the)h(GW)e(arriv)-5 b(al)36 b(times)h(b)s(e)h(within)f Fj(\006)p Fr(400)17 b(s)38 b(of)g(the)-9 2517 y(corresp)s(onding)j(GRB) h(arriv)-5 b(al)39 b(times.)i(The)i(\014gures)g(on)e(the)i(righ)m(t)e (sho)m(w)i(the)f(result)g(for)f(applied)-9 2638 y(signals)g(of)i(50)f (mK)g(and)h(20)f(mK,)g(within)g(a)h(time)e(windo)m(w)j(of)e Fj(\006)p Fr(4)17 b(s)43 b(\(that)g(is,)f(GW)h(bursts)h(and)-9 2758 y(GRB's)32 b(nearly)g(sim)m(ultaneous\).)240 3065 y(In)25 b(App)s(endix)g(A,)g(the)g(follo)m(wing)c(imp)s(ortan)m(t)i (relationship)g(b)s(et)m(w)m(een)j(the)f(measured)g(quan)m(tit)m(y)-9 3186 y(S)p Fk(N)10 b(R)207 3201 y Fi(R)294 3186 y Fr(\(at)29 b Fk(\034)39 b Fr(=)28 b(0)17 b(s\))29 b(and)g(the)h(p)s(ossible)e (signals)g(expressed)k(in)c(term)h(of)g(signal)e(to)i(noise)g(ratio)f Fp(SNR)-9 3306 y Fr(is)k(obtained:)1438 3499 y Fp(SNR)1637 3514 y Fi(R)1722 3499 y Fr(=)c Fp(SNR)2024 3457 y Fq(2)2080 3347 y Fh(r)p 2180 3347 143 4 v 2190 3431 a Fk(N)2268 3446 y Fi(\015)p 2190 3476 123 4 v 2194 3567 a Fk(N)2272 3582 y Fi(s)3645 3499 y Fr(\(9\))-9 3743 y(In)i(order)h(to)f(c)m(hec)m (k)j(the)e(mo)s(del)d(for)i(the)h(a)m(v)m(erage)h(cross-correlation)d (at)h(zero)h(dela)m(y)f(time,)f(and)i(th)m(us)-9 3864 y(Eq.)25 b(9)p (#equation.9) [[91 253 97 265] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g(w)m(e) g(p)s(erformed)g(a)f(test)h(b)m(y)h(adding)e(to)g(the)h(data,)g(for)f (eac)m(h)h(GRB,)f(signals)g(of)g(giv)m(en)h(amplitude)-9 3984 y(at)k(the)i(same)f(time)f(for)h(the)g(t)m(w)m(o)h(detectors.)h (The)f(results)g(are)f(giv)m(en)g(in)g(Fig.4)p (#figure.4) [[416 239 422 251] [1 1 1 [3 3]] [0 0 1]] pdfm (,)e(where) k(w)m(e)f(sho)m(w)h(the)-9 4104 y(cross-correlation)k(for)h(some)g (applied)g(signals)f(for)h(the)h(t)m(w)m(o)g(time)e(windo)m(ws)j(of)e Fj(\006)p Fr(400)17 b(s)37 b(and)h Fj(\006)p Fr(4)17 b(s.)-9 4225 y(The)43 b(results)g(here)g(are)f(giv)m(en)g(in)g(terms)g (of)g(the)h(dimensionless)e(a)m(v)m(erage)j(cross-correlation,)d(but)-9 4345 y(in)34 b(the)h(\014gure)h(w)m(e)g(ha)m(v)m(e)g(also)f(indicated)f (the)h(energies)h(of)e(the)i(input)f(signals.)f(W)-8 b(e)35 b(notice)g(that,)g(as)-9 4466 y(predicted)29 b(b)m(y)h(Eq.)h(9)p (#equation.9) [[159 181 165 193] [1 1 1 [3 3]] [0 0 1]] pdfm (,)e(the) g(S)p Fk(N)10 b(R)1207 4481 y Fi(R)1295 4466 y Fr(increases)30 b(b)m(y)g(reducing)g(the)f(in)m(terv)-5 b(als)29 b(of)g(the)g (cross-correlation,)-9 4586 y(for)j(a)g(giv)m(en)h(S)p Fk(N)10 b(R)q Fr(.)-9 4887 y Fs(3.2)106 b(Relations)36 b(b)s(et)m(w)m(een)i(SNR)1405 4902 y Fi(R)1463 4887 y Fs(,)f(burst)h(energy)g(and)g(dimensionless)e(amplitude)-9 5009 y Fr(Since)52 b(w)m(e)h(require)f(the)h(result)f(in)f(terms)h(of)g (GW)f(amplitudes)g Fk(h)p Fr(,)h(w)m(e)h(need)g(to)f(relate)g(cross-)-9 5130 y(correlation)30 b(quan)m(tities)j(to)f(energies.)240 5250 y(F)-8 b(rom)31 b(Eqs.)j(\(4)p (#equation.4) [[162 87 168 99] [1 1 1 [3 3]] [0 0 1]] pdfm (\))e(and)h (\(9)p (#equation.9) [[204 87 210 99] [1 1 1 [3 3]] [0 0 1]] pdfm (\)) f(w)m(e)h(obtain)1211 5584 y Fk(E)h Fr(=)27 b Fk(T)1477 5599 y Fi(ef)7 b(f)1614 5443 y Fh(\022)1697 5516 y Fp(SNR)1895 5474 y Fq(2)1895 5541 y Fi(R)1953 5516 y Fk(N)2031 5531 y Fi(s)p 1697 5561 371 4 v 1821 5652 a Fk(N)1899 5667 y Fi(\015)2078 5443 y Fh(\023)2151 5458 y Fq(1)p Fi(=)p Fq(4)2419 5584 y Fr([K])1048 b(\(10\))3721 5879 y(7)p eop %%Page: 8 8 8 7 bop -9 30 a Fr(T)-8 b(able)33 b(2:)68 b(Comparison)33 b(of)g(energies)i(calculated,)e(using)h(Eq.)h(\(10)p (#equation.10) [[359 713 371 725] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)e (and)h(sim)m(ulated)f(\(v)-5 b(alues)34 b(of)f(an)-9 151 y(input)f(signal)f(that)h(pro)s(duces)i Fk(S)6 b(N)k(R)1377 166 y Fi(R)1435 151 y Fr(=2\).)p 604 247 2522 4 v 602 367 4 121 v 653 331 a(windo)m(w)p 1024 367 V 359 w Fk(E)38 b Fr([mK])p 1962 367 V 727 w Fk(E)h Fr([mK])p 3123 367 V 602 488 V 795 452 a(s)p 1024 488 V 242 w(calculated,)32 b(Eq.)i(\(10)p (#equation.10) [[285 663 297 675] [1 1 1 [3 3]] [0 0 1]] pdfm (\))p 1962 488 V 99 w(sim)m(ulated)d(\(input)h(signals\))p 3123 488 V 604 491 2522 4 v 602 612 4 121 v 703 575 a Fj(\006)p Fr(400)p 1024 612 V 481 w(43.8)p 1962 612 V 913 w(45)p 3123 612 V 602 732 V 727 696 a Fj(\006)p Fr(40)p 1024 732 V 506 w(24.6)p 1962 732 V 913 w(27)p 3123 732 V 602 852 V 727 816 a Fj(\006)p Fr(16)p 1024 852 V 506 w(19.6)p 1962 852 V 913 w(19)p 3123 852 V 602 973 V 751 937 a Fj(\006)p Fr(4)p 1024 973 V 531 w(13.8)p 1962 973 V 913 w(14)p 3123 973 V 604 976 2522 4 v -9 1233 a(It)25 b(w)m(ould)h(app)s(ear)f(that)g Fk(E)32 b Fr(decreases)c(with)d (increasing)g Fk(N)2149 1248 y Fi(s)2185 1233 y Fr(,)h(i.e.)f (bandwidth,)h(but)g(it)e(can)i(b)s(e)g(demon-)-9 1354 y(strated)33 b(that)f Fk(T)590 1369 y Fi(ef)7 b(f)742 1354 y Fr(decreases)35 b(linearly)30 b(with)j(increasing)e(bandwidth.) 240 1474 y(In)i(terms)f(of)g(the)h(dimensionless)f(amplitude,)f(using)h (Eq.)h(\(3)p (#equation.3) [[369 540 375 552] [1 1 1 [3 3]] [0 0 1]] pdfm (\))g (with)f Fk(\034)2863 1489 y Fi(g)r(w)2983 1474 y Fr(=)17 b(1)32 b(ms)g(w)m(e)i(get,)1445 1693 y Fk(h)28 b Fr(=)f(7)p Fk(:)p Fr(97)22 b Fj(\002)g Fr(10)2025 1652 y Fl(\000)p Fq(18)2155 1603 y Fj(p)p 2238 1603 79 4 v 90 x Fk(E)1287 b Fr(\(11\))-9 1898 y(with)32 b(E)h(expressed)i(in)d(k)m(elvin.)g(W)-8 b(e)33 b(\014nally)f(get,)g(using)h(Eqs.)h(\(6)p (#equation.6) [[352 489 358 501] [1 1 1 [3 3]] [0 0 1]] pdfm (\))e (and)g(\(10)p (#equation.10) [[394 489 406 501] [1 1 1 [3 3]] [0 0 1]] pdfm (\))1338 2177 y(SNR)1537 2192 y Fi(R)1623 2177 y Fr(=)1726 2037 y Fh(\022)1859 2110 y Fk(E)p 1809 2155 177 4 v 1809 2246 a(T)1866 2261 y Fi(ef)7 b(f)1996 2037 y Fh(\023)2069 2059 y Fq(2)2131 2177 y Fj(\001)2181 2026 y Fh(r)p 2280 2026 143 4 v 2290 2110 a Fk(N)2368 2125 y Fi(\015)p 2290 2155 123 4 v 2294 2246 a Fk(N)2372 2261 y Fi(s)3597 2177 y Fr(\(12\))-9 2446 y(W)-8 b(e)39 b(observ)m(e)j(that)d(a)g(negativ)m (e)g(v)-5 b(alue)39 b(of)g(SNR)1793 2461 y Fi(R)1890 2446 y Fr(giv)m(es)h(a)f(negativ)m(e)h(v)-5 b(alue)39 b(for)g Fk(E)3109 2410 y Fq(2)3148 2446 y Fr(.)g(T)-8 b(o)40 b(c)m(hec)m(k)i(the)-9 2566 y(v)-5 b(alidit)m(y)40 b(of)h(Eq.)i(\(10)p (#equation.10) [[155 409 167 421] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)e (w)m(e)j(applied)c(sev)m(eral)j(signals)e(for)g(v)-5 b(arious)42 b(time)e(windo)m(ws)j(of)f(correlation)-9 2687 y(and)36 b(compared)g(the)h(energies)g(of)f(the)h(input)f(sim)m (ulated)f(signals)g(to)i(the)f(v)-5 b(alues)37 b(calculated)e(using)-9 2807 y(Eq.)j(\(10)p (#equation.10) [[97 380 109 392] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)g (This)g(is)f(done)i(in)e(the)h(follo)m(wing)e(w)m(a)m(y:)j(w)m(e)g (note)f(that)g Fk(R)2584 2822 y Fq(0)2624 2807 y Fr(,)g(in)f(the)h (absence)i(of)d(applied)-9 2928 y(signals,)27 b(is)i(not)g(n)m(ull)f (for)g(eac)m(h)i(time)e(windo)m(w.)h(W)-8 b(e)29 b(determine)g(the)g (signal)f(w)m(e)i(m)m(ust)f(apply)g(in)f(order)-9 3048 y(to)d(increase)i(the)g(v)-5 b(alue)26 b(of)f Fk(R)1052 3063 y Fq(0)1092 3048 y Fr(,)h(obtained)g(b)s(efore)g(the)h (application)d(of)i(the)g(signals,)f(b)m(y)j(t)m(w)m(o)f(standard)-9 3168 y(deviations.)d(W)-8 b(e)25 b(then)h(use)g(Eq.\(10)p (#equation.10) [[215 337 227 349] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f (with)g(the)h(v)-5 b(alue)24 b Fk(S)6 b(N)k(R)2201 3183 y Fi(R)2287 3168 y Fr(=)28 b(2.)c(The)i(result)f(is)g(sho)m(wn)h(in)e (T)-8 b(able)25 b(2)p (#table.2) [[515 337 521 349] [1 1 1 [3 3]] [0 0 1]] pdfm (.)-9 3289 y(The)h(agreemen)m(t)f(b)s(et)m(w)m(een)i(the)e(v)-5 b(alues)25 b(of)g(the)g(sim)m(ulated)f(input)h(signals)e(and)j(the)f(v) -5 b(alues)25 b(calculated)-9 3409 y(using)32 b(Eq.)h(\(10)p (#equation.10) [[127 308 139 320] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f (sho)m(ws)i(that)f(our)f(mo)s(del)f(is)h(correct.)-9 3642 y Fs(4)193 b(Inference)38 b(of)f(the)h(GW)f(burst)g(amplitude)-9 3763 y Fr(Ha)m(ving)i(presen)m(ted)j(the)f(exp)s(erimen)m(tal)d(metho)s (d)i(and)g(the)g(mo)s(del)e(for)i(the)g(a)m(v)m(eraged)h(correlation)-9 3884 y(at)e(zero)h(dela)m(y)g(time)f Fk(R)896 3899 y Fq(0)936 3884 y Fr(,)h(w)m(e)h(can)f(infer)f(the)h(v)-5 b(alues)40 b(of)g(GW)f(amplitude)f Fk(h)i Fr(consisten)m(t)h(with)f (the)-9 4004 y(observ)-5 b(ation.)41 b(W)-8 b(e)43 b(note)f(that,)g (using)g(Eqs.)i(10)p (#equation.10) [[275 237 286 249] [1 1 1 [3 3]] [0 0 1]] pdfm 41 w(and)f(6)p (#equation.6) [[315 237 321 249] [1 1 1 [3 3]] [0 0 1]] pdfm (,)f (energy)h Fk(E)2538 4019 y Fq(0)2620 4004 y Fr(is)e(related)h(to)g(the) g(measured)-9 4124 y(cross-correlation)31 b Fk(R)792 4139 y Fq(0)864 4124 y Fr(b)m(y)1087 4405 y Fk(E)1159 4420 y Fq(0)1227 4405 y Fr(=)c Fk(T)1387 4420 y Fi(ef)7 b(f)1523 4265 y Fh(\022)1611 4338 y Fk(N)1689 4353 y Fi(s)p 1607 4382 V 1607 4474 a Fk(N)1685 4489 y Fi(\015)1739 4265 y Fh(\023)1813 4287 y Fq(1)p Fi(=)p Fq(4)1945 4405 y Fj(\001)1995 4265 y Fh(\022)2078 4338 y Fk(R)2152 4353 y Fq(0)p 2078 4382 114 4 v 2078 4474 a Fk(\033)2133 4489 y Fi(R)2201 4265 y Fh(\023)2275 4287 y Fq(1)p Fi(=)p Fq(2)2543 4405 y Fr([K])924 b(\(13\))-9 4674 y(Hence,)38 b(the)g(data)f(are)h(summarized)e(b)m(y)i(an)g(observ)m(ed)h(a)m(v)m (erage)g(squared)f(energy)h Fk(E)3229 4638 y Fq(2)3223 4698 y(0)3304 4674 y Fr(=)d Fj(\000)p Fr(1)p Fk(:)p Fr(11)26 b Fj(\002)-9 4794 y Fr(10)89 4758 y Fl(\000)p Fq(3)199 4794 y Fr(K)275 4752 y Fq(2)314 4794 y Fr(,)j(at)f Fj(\000)p Fr(1)p Fk(:)p Fr(4)h(standard)g(deviation)e(from)h(the)h(exp)s(ected)h (v)-5 b(alue)28 b(in)g(the)h(case)g(of)g(noise)f(alone,)g(as)-9 4915 y(calculated)i(with)i(the)g(aid)f(of)g(Eq.)i(\(12)p (#equation.12) [[231 127 243 139] [1 1 1 [3 3]] [0 0 1]] pdfm (\))e (where)i(w)m(e)g(put)f(SNR)2294 4930 y Fi(R)2380 4915 y Fr(=)27 b Fj(\000)p Fr(1)p Fk(:)p Fr(4.)32 b(The)h(standard)f (deviation,)-9 5035 y(expressed)38 b(in)e(terms)g(of)g(squared)h (energy)-8 b(,)37 b(is)f(obtained)g(from)e(Eq.)j(\(12)p (#equation.12) [[384 113 395 125] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)f (in)f(the)i(case)g(SNR)3493 5050 y Fi(R)3585 5035 y Fr(=)c(1,)-9 5155 y(whic)m(h)g(giv)m(es)g Fk(\033)564 5172 y Fi(E)620 5153 y Fg(2)686 5155 y Fr(=)27 b(0)p Fk(:)p Fr(79)22 b Fj(\002)h Fr(10)1183 5119 y Fl(\000)p Fq(3)1293 5155 y Fr(K)1369 5114 y Fq(2)1408 5155 y Fr(.)-9 5389 y Fs(4.1)106 b(Probabilistic)34 b(result)i(and)j(upp)s(er)f(limits)-9 5510 y Fr(According)26 b(to)g(the)i(mo)s(del)d(discussed)j(ab)s(o)m(v)m (e,)g(in)e(the)h(case)h(of)e(GW)g(signals)g(of)g(energy)i Fk(E)6 b Fr(,)27 b(w)m(e)h(exp)s(ect)-9 5630 y Fk(E)69 5594 y Fq(2)63 5655 y(0)135 5630 y Fr(to)f(b)s(e)h(a)f(random)f(n)m(um) m(b)s(er,)i(mo)s(deled)e(with)h(a)g(Gaussian)g(probabilit)m(y)e(densit) m(y)j(function)f(around)-9 5879 y(8)p eop %%Page: 9 9 9 8 bop 746 1274 a @beginspecial 88 @llx 4 @lly 376 @urx 182 @ury 2721 @rwi @clip @setspecial %%BeginDocument: finaleh.eps 0 185.938 translate 1 -1 scale gsave 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 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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 pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale 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Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 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 { 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 } 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b(time.)h(Here,)i(instead,)g(w)m(e)g(only)f(require)h(that)f (the)g(time)f(gap)h(b)s(et)m(w)m(een)j(the)e(GRB)-9 5630 y(and)g(the)h(GW)f(burst)h(b)s(e)g(within)e(a)h(giv)m(en)h(time)e (windo)m(w.)i(Similar)c(comparison)i(can)i(b)s(e)f(made)g(with)3673 5879 y(11)p eop %%Page: 12 12 12 11 bop -9 -28 a Fr(the)40 b(A)m(URIGA/BA)-8 b(TSE)42 b(result)e([29)p (#cite.cerdonio) [[226 720 238 732] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(],)h(where)g(an)f(upp)s(er)h(limit)c(\\)j Fk(h)2584 -13 y Fi(RM)7 b(S)2804 -28 y Fj(\024)41 b Fr(1)p Fk(:)p Fr(5)f(10)3185 -64 y Fl(\000)p Fq(18)3355 -28 y Fr(with)f(C.L.)-9 92 y(95\045)g(")h(is)f(estimated)g(under)i(the)f(assumption)g(that)f (GW's)h(arriv)m(e)g(at)g(the)g(GRB)f(time)g(within)f(a)-9 213 y(time)31 b(windo)m(w)i(of)f Fj(\006)p Fr(5)h(s.)240 333 y(Finally)-8 b(,)26 b(w)m(e)k(remark)f(that)g(this)g(metho)s(d)f (can)h(b)s(e)h(applied)e(for)g(an)m(y)i(exp)s(ected)h(dela)m(y)e(b)s (et)m(w)m(een)-9 454 y(GRB)j(and)i(GW,)f(with)g(appropriate)g(time)f (shifting)f(of)i(the)h(in)m(tegration)e(windo)m(w)i(with)f(resp)s(ect)h (to)-9 574 y(the)f(GBR)e(arriv)-5 b(al)31 b(time,)g(according)h(to)g (the)h(prediction)f(of)g(the)h(c)m(hosen)h(mo)s(del.)-9 790 y Fs(6)193 b(Ac)m(kno)m(wledgmen)m(ts)-9 910 y Fr(W)-8 b(e)24 b(thank)h(F.)f(Camp)s(olungo,)e(R.)i(Lenci,)g(G.)g(Martinelli,)d (E.)k(Serrani)f(,)g(R.)g(Simonetti)e(and)i(F.)g(T)-8 b(abac-)-9 1030 y(c)m(hioni)31 b(for)h(precious)h(tec)m(hnical)f (assistance.)i(W)-8 b(e)33 b(also)e(thank)i(Dr.)f(R.)h(Elia)e(for)h (her)h(con)m(tribution.)-9 1246 y Fs(App)s(endix)k(A)240 1367 y Fr(Giv)m(en)23 b(t)m(w)m(o)g(indep)s(enden)m(t)h(detectors,)g (let)e Fk(x)p Fr(\()p Fk(t)p Fr(\))h(and)g Fk(y)t Fr(\()p Fk(t)p Fr(\))f(b)s(e)h(the)h(measured)f(quan)m(tities,)f(whic)m(h)-9 1487 y(are)32 b(the)h(\(\014ltered\))g(data)f(in)g(our)g(case.)240 1607 y(W)-8 b(e)25 b(in)m(tro)s(duce)g(the)g(v)-5 b(ariables)24 b Fk(\030)5 b Fr(\()p Fk(t)p Fr(\))27 b(=)h Fk(x)p Fr(\()p Fk(t)p Fr(\))6 b Fj(\000)12 b Fr(\026)-55 b Fk(x)27 b Fr(and)d Fk(\021)t Fr(\()p Fk(t)p Fr(\))k(=)g Fk(y)t Fr(\()p Fk(t)p Fr(\))6 b Fj(\000)13 b Fr(\026)-56 b Fk(y)28 b Fr(where)k(\026)-55 b Fk(x)28 b Fr(=)g Fk(E)6 b Fr([)p Fk(x)p Fr(])28 b(=)g Fk(T)3651 1622 y Fi(ef)7 b(f)-9 1728 y Fr(and)39 b(\026)-56 b Fk(y)31 b Fr(=)d Fk(E)6 b Fr([)p Fk(y)t Fr(])27 b(=)g Fk(T)734 1743 y Fi(ef)7 b(f)854 1728 y Fr(.)32 b(W)-8 b(e)33 b(recall)e(that)i(the)g (cross-correlation)e(function)h(is)1300 1957 y Fk(r)s Fr(\()p Fk(\034)11 b Fr(\))28 b(=)1618 1815 y Fh(P)1723 1919 y Fi(i)1751 1890 y Fr(\()p Fk(\030)5 b Fr(\()p Fk(t)1910 1905 y Fi(i)1938 1890 y Fr(\))22 b Fj(\001)g Fk(\021)t Fr(\()p Fk(t)2173 1905 y Fi(i)2223 1890 y Fr(+)g Fk(\034)11 b Fr(\)\))p 1618 1935 833 4 v 1751 1954 a Fh(p)p 1851 1954 467 4 v 9 x(P)1956 2067 y Fi(i)2001 2038 y Fk(\030)2049 2009 y Fq(2)2104 1963 y Fh(P)2226 2038 y Fk(\021)2278 2009 y Fq(2)3597 1957 y Fr(\(21\))-9 2198 y(with)41 b(summation)f (extended)k(up)e(to)f(the)h(n)m(um)m(b)s(er)h(of)e(indep)s(enden)m(t)i (samples)e Fk(N)3113 2213 y Fi(s)3150 2198 y Fr(.)h(W)-8 b(e)42 b(calculate)-9 2244 y Fh(P)112 2319 y Fk(\030)160 2283 y Fq(2)227 2319 y Fr(=)330 2244 y Fh(P)452 2319 y Fk(\021)504 2283 y Fq(2)571 2319 y Fr(=)28 b Fk(N)753 2334 y Fi(s)789 2319 y Fk(T)860 2283 y Fq(2)846 2345 y Fi(ef)7 b(f)966 2319 y Fr(.)31 b(Th)m(us)1269 2234 y Fh(p)p 1369 2234 494 4 v 10 x(P)1491 2319 y Fk(\030)1539 2290 y Fq(2)1600 2319 y Fj(\001)1649 2244 y Fh(P)1771 2319 y Fk(\021)1823 2290 y Fq(2)1890 2319 y Fr(=)c Fk(N)2071 2334 y Fi(s)2108 2319 y Fk(T)2179 2283 y Fq(2)2165 2345 y Fi(ef)7 b(f)2285 2319 y Fr(.)31 b(W)-8 b(e)31 b(easily)f(v)m(erify)h (that)g Fk(E)6 b Fr([)p Fk(r)s Fr(\()p Fk(\034)11 b Fr(\)])28 b(=)f(0.)-9 2439 y(In)32 b(the)h(absence)i(of)d(an)m(y)h(correlated)f (signal)f(w)m(e)j(also)d(ha)m(v)m(e)j Fk(E)6 b Fr([)p Fk(r)s Fr(\(0\)])28 b(=)f(0.)240 2560 y(Let)33 b(us)g(calculate)f(the)h (v)-5 b(ariance)32 b(of)h Fk(r)s Fr(\()p Fk(\034)11 b Fr(\).)32 b(W)-8 b(e)34 b(notice)e(that)h(when)h(squaring)e(the)h(n)m (umerator)-9 2680 y(of)k(Eq.21)p (#equation.21) [[102 395 114 407] [1 1 1 [3 3]] [0 0 1]] pdfm 37 w(and)h(taking)f(the)g(a)m(v)m(erage,)i(the)f(cross-terms)g(v)-5 b(anish)37 b(if)f(the)i Fk(N)2781 2695 y Fi(s)2855 2680 y Fr(data)f(are)h(indep)s(enden)m(t)-9 2800 y(from)31 b(eac)m(h)i(other.)g(Then,)h(since)f(also)f Fk(\030)37 b Fr(and)32 b Fk(\021)k Fr(are)d(indep)s(enden)m(t)h(v)-5 b(ariables,)31 b(w)m(e)j(obtain)832 3076 y Fk(\033)891 3035 y Fq(2)887 3101 y Fi(r)958 3076 y Fr(=)1072 2933 y Fh(P)1177 3037 y Fi(i)1205 3008 y Fr(\()p Fk(\030)5 b Fr(\()p Fk(t)1364 3023 y Fi(i)1392 3008 y Fr(\))p Fk(\021)t Fr(\()p Fk(t)1555 3023 y Fi(i)1605 3008 y Fr(+)22 b Fk(\034)11 b Fr(\)\))1832 2972 y Fq(2)p 1072 3053 800 4 v 1269 3144 a Fr(\()p Fk(N)1385 3159 y Fi(s)1421 3144 y Fk(T)1492 3110 y Fq(2)1478 3172 y Fi(ef)c(f)1598 3144 y Fr(\))1636 3115 y Fq(2)1910 3076 y Fr(=)2023 3009 y Fk(N)2101 3024 y Fi(s)2160 3009 y Fj(\001)22 b Fk(E)6 b Fr([)p Fk(\030)2363 2972 y Fq(2)2402 3009 y Fr(])p Fk(E)g Fr([)p Fk(\021)2586 2972 y Fq(2)2625 3009 y Fr(])p 2023 3053 630 4 v 2134 3144 a(\()p Fk(N)2250 3159 y Fi(s)2287 3144 y Fk(T)2358 3110 y Fq(2)2344 3172 y Fi(ef)h(f)2464 3144 y Fr(\))2502 3115 y Fq(2)2690 3076 y Fr(=)2837 3009 y(1)p 2803 3053 115 4 v 2803 3144 a Fk(N)2881 3159 y Fi(s)3597 3076 y Fr(\(22\))240 3301 y(The)45 b(previous)g(considerations)f(still)e (apply)i(to)g(the)h(cum)m(ulativ)m(e)e(cross-correlation)h Fk(R)q Fr(\()p Fk(\034)11 b Fr(\),)-9 3421 y(obtained)36 b(b)m(y)j(a)m(v)m(eraging)e Fk(N)1056 3436 y Fi(\015)1137 3421 y Fr(indep)s(enden)m(t)i Fk(r)s Fr(\()p Fk(\034)11 b Fr(\).)37 b(The)h(\014nal)f(v)-5 b(ariance)37 b(for)g(the)g (cross-correlation)-9 3542 y Fk(R)q Fr(\()p Fk(\034)11 b Fr(\))33 b(is)1629 3707 y Fk(\033)1688 3665 y Fq(2)1684 3731 y Fi(R)1770 3707 y Fr(=)1978 3639 y(1)p 1884 3684 238 4 v 1884 3775 a Fk(N)1962 3790 y Fi(s)1999 3775 y Fk(N)2077 3790 y Fi(\015)3597 3707 y Fr(\(23\))240 3913 y(Let)39 b(us)g(no)m(w)g(consider)h(an)e(energy)i(signal)d Fk(S)44 b Fr(on)39 b(b)s(oth)g(detectors)h(at)e(the)h(same)g(time.)e (The)-9 4034 y(exp)s(ected)i(v)-5 b(alue)37 b(of)g(the)h (cross-correlation)f Fk(r)s Fr(\()p Fk(\034)11 b Fr(\))37 b(at)h Fk(\034)48 b Fr(=)36 b(0)h(will)e(b)s(e)j(p)s(ositiv)m(e.)f(In)h (the)g(case)h(of)e Fk(N)3733 4049 y Fi(s)-9 4154 y Fr(indep)s(enden)m (t)c(data)g(the)g(signal)d Fk(S)39 b Fr(will)30 b(app)s(ear)i(in)g(one) h(datum)f(only)g(and)h(w)m(e)g(ha)m(v)m(e:)938 4379 y Fk(E)6 b Fr([)p Fk(R)q Fr(\()p Fk(\034)39 b Fr(=)27 b(0\))22 b Fj(\000)h Fk(R)q Fr(\()p Fk(\034)39 b Fj(6)p Fr(=)28 b(0\)])f(=)2195 4312 y Fk(S)2261 4276 y Fq(2)p 2102 4356 292 4 v 2102 4447 a Fk(N)2180 4462 y Fi(s)2217 4447 y Fk(T)2288 4413 y Fq(2)2274 4475 y Fi(ef)7 b(f)2431 4379 y Fr(=)2544 4312 y Fk(S)f(N)k(R)2773 4276 y Fq(2)p 2544 4356 269 4 v 2621 4447 a Fk(N)2699 4462 y Fi(s)3597 4379 y Fr(\(24\))-9 4632 y(where)35 b(w)m(e)h(put)f Fk(S)6 b(N)k(R)32 b Fr(=)1027 4593 y Fi(S)p 978 4609 146 4 v 978 4666 a(T)1019 4678 y Fb(ef)6 b(f)1134 4632 y Fr(.)34 b(W)-8 b(e)35 b(note)g(that,)f(in)g(Eq.24)p (#equation.24) [[322 161 334 173] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h Fk(E)6 b Fr([)p Fk(R)q Fr(\()p Fk(\034)43 b Fj(6)p Fr(=)30 b(0\)])h(=)g(0)j(also)g(when)h(a)g(signal)-9 4762 y(is)d(presen)m(t.) 240 4883 y(Putting)g(also)1418 5052 y(SNR)1617 5067 y Fi(R)1702 5052 y Fr(=)1816 4985 y Fk(E)6 b Fr([)p Fk(R)q Fr(\()p Fk(\034)39 b Fr(=)28 b(0\)])p 1816 5029 517 4 v 2018 5121 a Fk(\033)2073 5136 y Fi(R)3597 5052 y Fr(\(25\))-9 5252 y(\(as)k(already)g(b)s(een)i(de\014ned)g(in)e(the)h(text)g(in)f (Eq.)h(6)p (#equation.6) [[292 87 298 99] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(w)m(e)i(obtain)1432 5495 y(SNR)1632 5510 y Fi(R)1717 5495 y Fr(=)27 b(SNR)2020 5453 y Fq(2)2059 5344 y Fh(r)p 2159 5344 143 4 v 2169 5428 a Fk(N)2247 5443 y Fi(\015)p 2169 5472 123 4 v 2173 5563 a Fk(N)2251 5578 y Fi(s)2301 5495 y Fk(:)1269 b Fr(\(26\))-9 5879 y(12)p eop %%Page: 13 13 13 12 bop -9 -28 a Fs(References)39 93 y Fr([1])49 b(G.)32 b(J.)h(Fishman)e(and)i(C.)g(A.)g(Meegan,)g(Ann)m(ual)f(Rev)i(Astr.)f (Astroph)m(ys.)h(33)e(\(1995\))g(415)39 214 y([2])49 b(G.)32 b(J.)h(Fishman)e(and)i(D.)f(H.)h(Hartmann,)f(Scien)m(ti\014c)g (American,)g(July)g(\(1997\).)39 334 y([3])49 b(G.)32 b(Bo)s(ella)f(et)h(al.,)g(Astron.)h(Astroph)m(ys.)i(Suppl.)d(122)g (\(1997\),)g(299)39 454 y([4])49 b(E.)33 b(Costa)g(et)g(al.)e(Nature,)i (387)f(\(1997\))g(783)39 575 y([5])49 b(J.)33 b(V)-8 b(an)32 b(P)m(aradijs)h(et)f(al.,)g(Nature,)h(386)f(\(1997\),)f(686)39 695 y([6])49 b(D.)32 b(A.)h(F)-8 b(rail)30 b(et)j(al.,)e(Nature,)i(389) f(\(1997\))g(261)39 816 y([7])49 b(S.)30 b(G.)g(Djorgo)m(vski)f(et)h (al.,)f(in:)g(Pro)s(c.)i(IX)f(Marcel)g(Grossmann)f(Meeting,)h(eds.)h (V.)f(Gurzady)m(an,)191 936 y(R.)i(Jan)m(tzen,)i(and)f(R.)f(Ru\016ni,)h (Singap)s(ore:)e(W)-8 b(orld)32 b(Scien)m(ti\014c,)g(in)g(press)i (\(2001\))39 1056 y([8])49 b(T.)33 b(Piran,)f(Ph)m(ys.)j(Rep.,)e(314)e (\(1999\),)h(575)39 1177 y([9])49 b(P)-8 b(.)33 b(M)m(\023)-46 b(esz\023)d(aros,)34 b(Science)g(291)d(\(2001\),)h(79)-9 1297 y([10])48 b(K.)37 b(S.)g(Thorne,)h(in)e(Recen)m(t)i(Adv)-5 b(ances)38 b(in)e(General)h(Relativit)m(y)-8 b(,)35 b(edited)i(b)m(y)g (A.)g(Janis)g(and)g(J.)191 1417 y(P)m(orter,)c(Birkhauser,)g(Boston,)g (\(1992\),)f(196)-9 1538 y([11])48 b(P)-8 b(.)33 b(Astone,)g(CQG)g (19,7)f(\(2002\),)f(1443-1448)-9 1658 y([12])48 b(S.)33 b(Finn)f(et)g(al.,)g(Ph)m(ys.Rev.)j(D)d(60,)g(121101)f(\(1999\))-9 1779 y([13])48 b(G.)32 b(Mo)s(destino)h(and)f(A.)h(Moleti)e(Ph)m(ys.)k (Rev.)e(D65,)f(022005)f(\(2002\))-9 1899 y([14])48 b(P)-8 b(.)33 b(Astone)g(et)g(al.)f(Ph)m(ys.)i(Rev.)f(D47,)f(362)g(\(1993\))-9 2019 y([15])48 b(P)-8 b(.)33 b(Astone)g(et)g(al.,)f(Astroparticle)f(Ph) m(ys.)k(7)d(\(1997\),)g(231-243)-9 2140 y([16])48 b(P)-8 b(.)38 b(Astone,)g(C.)g(Buttiglione,)d(S.)j(F)-8 b(rasca,)37 b(G.V.)h(P)m(allottino)c(and)k(G.)f(Pizzella,)f(Il)h(Nuo)m(v)m(o)h(Ci-) 191 2260 y(men)m(to)32 b(20,9)g(\(1997\))-9 2381 y([17])48 b(P)-8 b(.Astone)34 b(et)f(al.)e(Pro)s(c.)i("Gra)m(vitational)c (Astronom)m(y")j(pag)h(189)191 2501 y(Ed.)g(D.E.McClelland)f(and)h (H.A.Bac)m(hor,)g(W)-8 b(orld)32 b(Scien)m(ti\014c)g(1991)-9 2621 y([18])48 b(G.)43 b(Pizzella)e("Status)j(of)e(resonan)m(t)i(bar)f (detectors")h(ICTP)h(Conference)f(on)f(Gra)m(vitational)191 2742 y(W)-8 b(a)m(v)m(es)39 b(2000,)d(T)-8 b(rieste,)38 b(Italy)-8 b(,)37 b(5-9)f(Jun)i(2000.)e(Published)h(in)g(\\T)-8 b(rieste)37 b(2000,)f(Gra)m(vitational)191 2862 y(w)m(a)m(v)m(es",)f (243-255)-9 2982 y([19])48 b(F.)32 b(F)-8 b(ron)m(tera)33 b(et)f(al.,)g(Astron.)h(&)f(Astroph)m(ys.)j(Suppl.)d(122)g(\(1997\),)g (357)-9 3103 y([20])48 b(C.)40 b(Guidorzi)e(et)h(al.,)g(in:)g Fp(Gamma{R)-5 b(ay)41 b(Bursts)g(in)g(the)g(After)-5 b(glow)41 b(Er)-5 b(a)p Fr(,)40 b(eds.)g(E.)g(Costa,)g(F.)191 3223 y(F)-8 b(ron)m(tera)32 b(&)h(J.)f(Hjorth)h(\(Springer-V)-8 b(erlag,)30 b(Berlin\),)i(p.)h(43)f(\(2001\).)-9 3344 y([21])48 b(G.)23 b(Mo)s(destino)g(el)f(al.)g(Pro)s(c.)h(V)-8 b(ulcano)23 b(W)-8 b(orkshop)24 b(1998)e("F)-8 b(ron)m(tier)22 b(Ob)5 b(jects)24 b(in)e(Astroph)m(ysics",)191 3464 y(pag.)32 b(295)191 3584 y(Ed.)h(F.Gio)m(v)-5 b(annelli)29 b(and)k(G.Manno)s(cc)m (hi)f(Editrice)g(Comp)s(ositori,)e(Bologna,)h(Italy)h(1999)-9 3705 y([22])48 b(G.)28 b(D')g(Agostini)f Fp(Bayesian)j(r)-5 b(e)g(asoning)29 b(in)i(high-ener)-5 b(gy)30 b(physics:principles)f (and)h(applic)-5 b(ations)191 3825 y Fr(CERN)42 b(99-03)e(\(1999\))g (This)i(rep)s(ort)f(and)h(related)f(references)i(can)f(b)s(e)g(found)f (at)g(the)h(URL:)191 3946 y(h)m(ttp://www-zeus.roma1.infn.it/)p Fj(\030)p Fr(agostini/prob+stat.h)m(tml)p [[95 243 392 255] [1 1 1 [3 3]] [0 0 1]] (http://www-zeus.roma1.infn.it/~agostini/prob+stat.html) pdfm -9 4066 a([23])48 b(J.)73 b(Breit)m(w)m(eg)g(et)g(al.)e(\(ZEUS)i (collab)s(oration\),)c(Eur.)74 b(Ph)m(ys.)g(J)f(C14)f(\(2000\))g (239-254)191 4186 y Fa(hep-ex/9905039)p [[95 215 181 227] [1 1 1 [3 3]] [0 0 1]] (http://arxiv.org/abs/hep-ex/9905039) pdfm -9 4307 a Fr([24])48 b(G.)32 b(D'Agostini)f(and)h(G.)h(Degrassi,)f (Eur.)h(Ph)m(ys.)h(J.)f(C)g(10)f(\(1999\))f(663-675)g Fa(hep-ph/9902226)p [[438 200 524 212] [1 1 1 [3 3]] [0 0 1]] (http://arxiv.org/abs/hep-ph/9902226) pdfm -9 4427 a Fr([25])48 b(P)-8 b(.)33 b(Astone)g(and)g(G.)f(D'Agostini,)f (CERN-EP/99-126)h(and)g Fa(hep-ex/9909047)p [[369 186 455 198] [1 1 1 [3 3]] [0 0 1]] (http://arxiv.org/abs/hep-ex/9909047) pdfm -9 4547 a Fr([26])48 b(G.)35 b(D'Agostini,)f Fp(Over)-5 b(c)g(oming)36 b(priors)h(anxiety)p Fr(,)f(in)m(vited)f(con)m (tribution)f(to)i(the)g(monographic)191 4668 y(issue)k(of)e(the)i (Revista)e(de)i(la)e(Real)g(Academia)g(de)h(Ciencias)g(on)g(Ba)m(y)m (esian)g(Metho)s(ds)h(in)f(the)191 4788 y(Sciences,)34 b(ed.)f(J.M.)g(Bernardo)g(\(1999\))f Fa(physics/9906048)p [[277 142 369 154] [1 1 1 [3 3]] [0 0 1]] (http://arxiv.org/abs/physics/9906048) pdfm Fr(.)-9 4909 y([27])48 b(P)-8 b(.)33 b(Astone,)g(G.)g(Pizzella,)e (Astroparticle)g(Ph)m(ysics)j(16)f(\(2002\))e(441-450)-9 5029 y([28])48 b(G.)54 b(D'Agostini,)f(Pro)s(c.)i(XVI)s(I)s(I)g(In)m (ternational)f(W)-8 b(orkshop)55 b(on)g(Maxim)m(um)f(En)m(trop)m(y)i (and)191 5149 y(Ba)m(y)m(esian)f(Metho)s(ds,)h(Garc)m(hing)d(\(German)m (y\),)i(July)f(1998,)f(V.)i(Dose,)g(W.)f(v)m(on)h(der)g(Lin-)191 5270 y(den,)36 b(R.)e(Fisc)m(her,)h(and)g(R.)g(Preuss,)h(eds,)g(Klu)m (w)m(er)f(Academic)f(Publishers,)h(Dordrec)m(h)m(t,)h(1999,)191 5390 y Fa(physics/9811046)p [[95 70 187 82] [1 1 1 [3 3]] [0 0 1]] (http://arxiv.org/abs/physics/9811046) pdfm Fr(.)-9 5510 y([29])48 b(P)-8 b(.)33 b(T)-8 b(ricarico)31 b(et)i(al.,)e(Ph)m(ys.)k(Rev.)e(D,)f(63,)g(082002)g(\(2001\))3673 5879 y(13)p eop %%Trailer end end userdict /end-hook known{end-hook}if %%EOF