%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: arXiv:hep-ph/9906408v1 17 Jun 1999 %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R -P pk -K1 -z mc_radg.dvi -o %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 2017.12.15:1602 %%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 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729] 791] def (cite.FERRAD) [12 [57 588 57 600] 787] def (equation.10) [5 [175 648 423 591] 791] def (equation.11) [5 [114 448 481 460] 646] def (equation.12) [5 [115 356 480 368] 554] def (equation.13) [5 [177 258 418 270] 457] def (equation.14) [5 [171 150 424 162] 349] def (equation.15) [6 [103 573 492 585] 771] def (equation.16) [6 [110 487 437 416] 686] def (equation.1) [2 [220 520 375 532] 718] def (equation.17) [6 [84 147 511 112] 346] def (equation.2) [2 [198 390 398 402] 588] def (equation.18) [7 [144 561 372 535] 759] def (equation.3) [2 [164 53 431 65] 251] def (equation.19) [7 [170 365 426 377] 564] def (equation.4) [3 [127 419 468 431] 618] def (equation.5) [3 [159 267 436 279] 466] def (equation.6) [3 [187 194 408 206] 393] def (equation.7) [3 [210 153 386 165] 351] def (equation.8) [4 [152 390 443 402] 588] def (equation.9) [4 [152 31 444 43] 229] def (equation.20) [7 [123 287 473 299] 485] def (equation.21) [7 [116 190 479 202] 388] def (equation.22) [10 [264 365 331 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2728 531 a(k)2562 747 y Fn(\010)2604 726 y(\010)2562 756 y(\010)2604 735 y(\010)2691 936 y Fl(e\))-128 1145 y Fs(Figure)45 b(1:)139 b(F)-8 b(eynman)45 b(diagrams)f(con)m (tributing)g(to)h(the)h(Born)g(and)g(the)f(radiativ)m(e)g(correction)g (cross)-128 1265 y(sections)34 b(in)d(lepton-n)m(ucleus)i(scattering.) 1237 1645 y Fq(\033)1296 1604 y Ft(r)r(ad:cor)r(r)n(:)1603 1645 y Fs(=)27 b Fq(\033)1761 1660 y Ft(in)1855 1645 y Fs(+)22 b Fq(\033)2008 1660 y Ft(q)2068 1645 y Fs(+)g Fq(\033)2221 1660 y Ft(el)2303 1645 y Fs(+)g Fq(\033)2456 1660 y Ft(v)2497 1645 y Fq(:)1240 b Fs(\(1\))19 1829 y(In)39 b(this)f(rep)s(ort)g(w)m(e)i(presen)m(t)g(a)e(Mon)m(te-Carlo)g (generator)h(for)f(ev)m(en)m(ts)j(with)d(a)g(p)s(ossible)g(radiation)f (of)-128 1949 y(a)i(real)e(photon)i(in)f(deep)i(inelastic)c(lepton)j (scattering)f(\(DIS\))g(on)h(p)s(olarized)e(and)h(unp)s(olarized)g (targets.)-128 2069 y(It)47 b(should)g(b)s(e)h(noted)f(that)g(only)f (the)i(single)d(photon)i(exc)m(hange)i(\(no)e Fq(Z)2710 2033 y 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Fs(\(\001\))h(con)m(tains)g(not)g(only)f (the)i(con)m(tribution)e(from)f(the)j(Born)f(pro)s(cess)h(but)f(also) -128 3021 y(the)g(con)m(tributions)f(from)f(lo)s(op)g(corrections)i(\() p Fq(\033)1675 3036 y Ft(v)1716 3021 y Fs(\))f(and)h(from)e(m)m (ultiple)f(soft)i(photon)h(pro)s(duction)e(with)h(a)-128 3141 y(total)39 b(energy)h(not)g(exceeding)h(a)e(cut-o\013)h(parameter) f(\001.)65 b(In)40 b(handling)f(the)h(radiativ)m(e)f(corrections)g(t)m (w)m(o)-128 3262 y(approac)m(hes)31 b(ha)m(v)m(e)f(b)s(een)g(used,)h (the)f(one)f(dev)m(elop)s(ed)i(b)m(y)f(Mo)f(and)g(Tsai)g([1)p (#cite.MT) [[382 326 388 338] [1 1 1 [3 3]] [0 0 1]] pdfm (])g(and)g (the)h(one)g(giv)m(en)f(b)m(y)h(Bardin)-128 3382 y(and)e(Sh)m(umeik)m (o)g([2)p (#cite.BSh) [[135 311 140 323] [1 1 1 [3 3]] [0 0 1]] pdfm (].)42 b(These)29 b(t)m(w)m(o)g(formalisms)24 b(and)k(the)g (signi\014cance)g(of)f(the)h(cut-o\013)f(parameter)h(\001)g(will)d(b)s (e)-128 3502 y(discussed)39 b(b)s(elo)m(w)d(in)g(more)g(detail.)55 b(The)37 b(generator)g(con)m(tains)g(t)m(w)m(o)g(patc)m(hes)h(whic)m(h) f(can)g(b)s(e)g(considered)-128 3623 y(as)k(indep)s(enden)m(t)g (generators.)66 b(The)41 b(\014rst)f(one)g(is)g(based)h(on)f(the)g(F)m (OR)-8 b(TRAN)40 b(co)s(de)g(POLRAD)g(2.0)f([3)p (#cite.POLRAD20) [[529 282 535 294] [1 1 1 [3 3]] [0 0 1]] pdfm (]) -128 3743 y(handling)34 b(the)h(p)s(olarized)e(lepton-n)m(ucleon)i (scattering.)50 b(The)36 b(other)f(is)f(based)i(on)f(FERRAD)f([4)p (#cite.FERRAD) [[489 268 495 280] [1 1 1 [3 3]] [0 0 1]] pdfm (],)h(a) g(co)s(de)-128 3863 y(that)d(deals)g(with)g(the)h(unp)s(olarized)e (case.)44 b(They)34 b(will)c(b)s(e)i(referred)h(to)f(as)g(the)h(POLRAD) f(and)g(FERRAD)-128 3984 y(generator)j(throughout)g(the)h(text.)51 b(A)35 b(detailed)f(analytical)e(and)k(n)m(umerical)d(comparison)h(of)g (the)i(results)-128 4104 y(giv)m(en)d(b)m(y)h(the)f(t)m(w)m(o)g (generators)g(is)f(p)s(erformed.)-128 4459 y Fw(2)162 b(The)53 b(Kinematics)h(and)g(Main)h(Stages)d(of)i(Generation)-128 4707 y Fs(The)38 b(F)-8 b(eynman)36 b(diagram)e(for)i(the)h(Born)f (\(or)g(one)h(photon)f(exc)m(hange\))i(pro)s(cess)g(is)e(presen)m(ted)i (in)e(Fig.1)p (#figure.1) [[524 152 530 164] [1 1 1 [3 3]] [0 0 1]] pdfm (a.)-128 4827 y(Its)28 b(kinematics)d(is)h(completely)g(de\014ned)i(b)m(y)f(the) g(scattering)g(angle)f Fq(\022)j Fs(and)e(the)g(energy)h Fq(E)3186 4791 y Fk(0)3236 4827 y Fs(of)e(the)h(scattered)-128 4948 y(lepton,)j(t)m(w)m(o)h(v)-5 b(ariables)29 b(whic)m(h)h(are)g (usually)f(measured.)43 b(All)28 b(other)i(inclusiv)m(e)g(kinematical)d (v)-5 b(ariables)29 b(can)-128 5068 y(b)s(e)36 b(expressed)j(in)c (terms)g(of)g Fq(\022)k Fs(and)d Fq(E)1309 5032 y Fk(0)1332 5068 y Fs(.)53 b(Ha)m(ving)35 b(in)g(mind)g(the)h(lab)s(oratory)e (frame,)h(i.e.)53 b(the)36 b(frame)f(with)-128 5189 y(the)e(target)g(n) m(ucleus)g(at)g(rest)g(the)g(relev)-5 b(an)m(t)32 b(v)-5 b(ariables)32 b(are)809 5417 y Fq(Q)886 5376 y Fp(2)953 5417 y Fs(=)c(4)p Fq(E)6 b(E)1262 5376 y Fk(0)1301 5417 y Fs(sin)1421 5376 y Fp(2)1487 5349 y Fq(\022)p 1487 5394 49 4 v 1487 5485 a Fs(2)1546 5417 y Fq(;)212 b(\027)34 b Fs(=)27 b Fq(E)i Fo(\000)22 b Fq(E)2248 5376 y Fk(0)2271 5417 y Fq(;)212 b(x)28 b Fs(=)2753 5349 y Fq(Q)2830 5313 y Fp(2)p 2707 5394 209 4 v 2707 5485 a Fs(2)p Fq(M)10 b(\027)2925 5417 y(;)1079 5681 y(y)31 b Fs(=)1283 5614 y Fq(\027)p 1271 5658 79 4 v 1271 5750 a(E)1359 5681 y(;)212 b(W)1704 5640 y Fp(2)1771 5681 y Fs(=)27 b Fq(Q)1951 5640 y Fp(2)1991 5681 y Fs(\(1)p Fq(=x)22 b Fo(\000)h Fs(1\))e(+)h Fq(M)2614 5640 y Fp(2)2655 5681 y Fq(;)3764 5535 y Fs(\(3\))1856 5916 y(2)p eop %%Page: 3 3 3 2 bop -128 100 a Fs(where)34 b Fq(E)39 b Fs(is)31 b(the)i(b)s(eam)f (energy)-8 b(,)34 b Fq(Q)1201 63 y Fp(2)1273 100 y Fs(is)e(the)g (negativ)m(e)h(of)f(the)h(four-momen)m(tum)d(transfer)j(squared,)h Fq(\027)39 b Fs(the)-128 220 y(energy)d(transfer,)g Fq(x)f Fs(the)g(Bjork)m(en)g(scaling)e(v)-5 b(ariable,)34 b Fq(y)k Fs(the)d(normalized)d(energy)k(transfer,)f(and)g Fq(W)3679 184 y Fp(2)3753 220 y Fs(the)-128 340 y(mass)e(squared)i(of)d (the)i(hadronic)e(\014nal)h(state.)45 b(Radiativ)m(e)32 b(QED)h(corrections)g(\(R)m(C\))g(at)g(the)g(lo)m(w)m(est)h(order)-128 461 y(are)c(describ)s(ed)f(b)m(y)i(the)e(set)h(of)f(the)g(F)-8 b(eynman)29 b(graphs)g(sho)m(wn)i(in)d(\014g.)42 b(1)p (#figure.1) [[370 662 376 674] [1 1 1 [3 3]] [0 0 1]] pdfm (b-e.)h (Con)m(tributions)28 b(to)h(the)h(lo)m(w)m(est)-128 581 y(order)h(R)m(C)f(cross)h(section)f(come)g(from)e(the)j(diagrams)d(b\)) i(and)g(c\))g(and)h(from)d(the)j(in)m(terference)g(of)e(the)i(lo)s(op) -128 702 y(diagrams)g(d\))i(and)g(e\))f(with)h(the)g(Born)f(matrix)f (elemen)m(t)i(a\).)19 869 y(An)f(ev)m(en)m(t)i(registered)f(in)e(the)h (detector)h(with)f(certain)g(v)-5 b(alues)32 b(of)f Fq(E)2564 833 y Fk(0)2620 869 y Fs(and)h Fq(\022)j Fs(for)d(the)g(scattered)i (lepton)-128 990 y(can)d(either)g(b)s(e)g(a)g(non-radiativ)m(e)e(or)h (a)h(radiativ)m(e)f(ev)m(en)m(t,)j(i.e.)42 b(an)31 b(ev)m(en)m(t)h(con) m(taining)e(a)g(real)g(hard)h(radiated)-128 1110 y(photon.)42 b(F)-8 b(or)25 b(a)h(radiativ)m(e)f(ev)m(en)m(t)j(there)f(are)f(apart)f (from)g Fq(E)2087 1074 y Fk(0)2137 1110 y Fs(and)h Fq(\022)j Fs(three)e(additional)c(v)-5 b(ariables)25 b(necessary)-128 1230 y(to)38 b(\014x)g(the)h(kinematics)e(of)g(the)h(radiated)f(real)g (photon.)60 b(A)38 b(p)s(ossible)f(c)m(hoice)h(is)f(the)i(photon)f (energy)h Fq(E)3844 1245 y Ft(\015)-128 1351 y Fs(and)e(the)g(t)m(w)m (o)h(angles)e Fq(\022)769 1366 y Ft(\015)850 1351 y Fs(and)h Fq(\036)1102 1366 y Ft(\015)1146 1351 y Fs(,)h(where)g Fq(\022)1542 1366 y Ft(\015)1623 1351 y Fs(is)f(the)g(angle)f(b)s(et)m (w)m(een)i(the)f(real)f(and)h(the)g(virtual)e(photon)-128 1484 y(momen)m(ta)288 1458 y Fq(~)293 1484 y(k)30 b Fs(and)d Fq(~)-49 b(q)32 b Fs(=)731 1458 y Fq(~)736 1484 y(k)787 1499 y Fp(1)838 1484 y Fo(\000)921 1458 y Fq(~)926 1484 y(k)977 1499 y Fp(2)1044 1484 y Fs(\()p Fq(k)1133 1499 y Fp(1)p Ft(;)p Fp(2)1255 1484 y Fs(b)s(eing)26 b(the)i(momen)m(ta)e (of)h(the)h(initial)23 b(and)28 b(the)g(scattered)g(lepton\))f(and)-128 1618 y Fq(\036)-70 1633 y Ft(\015)4 1618 y Fs(is)i(the)h(angle)e(b)s (et)m(w)m(een)k(the)e(planes)f(de\014ned)i(b)m(y)f(the)g(momen)m(ta)f (\()2435 1591 y Fq(~)2440 1618 y(k)2491 1633 y Fp(1)2530 1618 y Fs(,)2582 1591 y Fq(~)2587 1618 y(k)2638 1633 y Fp(2)2677 1618 y Fs(\))g(and)h(\()2964 1591 y Fq(~)2969 1618 y(k)s Fs(,)f Fq(~)-48 b(q)t Fs(\).)42 b(F)-8 b(or)29 b(ev)m(en)m(ts)j(with)-128 1738 y(the)f(radiation)d(of)i(a)f(real)h (photon)g(the)g(kinematical)e(v)-5 b(ariables)29 b(describing)g(the)i (virtual)e(photon)h(and)g(used)-128 1858 y(to)35 b(generate)h(the)g (hadronic)f(\014nal)g(state)g(di\013er)g(from)f(eq.\(3)p (#equation.3) [[320 494 326 506] [1 1 1 [3 3]] [0 0 1]] pdfm (\))i(b)s (ecause)h(the)f(substitution)f Fq(q)h Fo(!)c Fq(q)c Fo(\000)c Fq(k)39 b Fs(has)-128 1979 y(to)e(b)s(e)g(made)g(in)f(their)h (de\014nition.)55 b(The)38 b(v)-5 b(ariables)36 b(obtained)h(after)f (this)h(substitution)f(will)f(b)s(e)i(referred)-128 2099 y(to)c(as)f('true')i(ones:)502 2320 y Fq(W)608 2279 y Fp(2)594 2345 y Ft(tr)r(ue)759 2320 y Fs(=)27 b Fq(W)968 2279 y Fp(2)1030 2320 y Fo(\000)22 b Fs(2)p Fq(E)1250 2335 y Ft(\015)1295 2320 y Fs(\()p Fq(\027)28 b Fs(+)22 b Fq(M)33 b Fo(\000)1734 2214 y Fj(q)p 1817 2214 331 4 v 106 x Fq(\027)1871 2291 y Fp(2)1933 2320 y Fs(+)22 b Fq(Q)2108 2291 y Fp(2)2164 2320 y Fs(cos)17 b Fq(\022)2356 2335 y Ft(\015)2401 2320 y Fs(\))p Fq(;)83 b(\027)2597 2335 y Ft(tr)r(ue)2762 2320 y Fs(=)28 b Fq(\027)g Fo(\000)23 b Fq(E)3114 2335 y Ft(\015)3159 2320 y Fq(;)502 2620 y(Q)579 2579 y Fp(2)579 2645 y Ft(tr)r(ue)744 2620 y Fs(=)k Fq(Q)924 2579 y Fp(2)986 2620 y Fs(+)22 b(2)p Fq(E)1205 2635 y Ft(\015)1250 2620 y Fs(\()p Fq(\027)28 b Fo(\000)1464 2514 y Fj(q)p 1547 2514 V 106 x Fq(\027)1601 2592 y Fp(2)1663 2620 y Fs(+)22 b Fq(Q)1838 2592 y Fp(2)1894 2620 y Fs(cos)17 b Fq(\022)2086 2635 y Ft(\015)2131 2620 y Fs(\))p Fq(;)353 b(x)2604 2635 y Ft(tr)r(ue)2769 2620 y Fs(=)2945 2553 y Fq(Q)3022 2517 y Fp(2)3022 2578 y Ft(tr)r(ue)p 2883 2597 339 4 v 2883 2689 a Fs(2)p Fq(M)10 b(\027)3084 2704 y Ft(tr)r(ue)3232 2620 y Fq(:)3764 2480 y Fs(\(4\))-128 2886 y(F)-8 b(or)32 b(non-radiativ)m(e)f(ev)m(en)m(ts)k (the)e(true)g(kinematics)f(exactly)h(coincide)f(with)g(\(3)p (#equation.3) [[404 371 410 383] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)19 3054 y(In)h(case)i(of)e(the)g(elastic)g(and)g(quasielastic)g(radiativ)m (e)f(pro)s(cesses)j(the)f(mass)f(squared)i(of)e(the)h(hadronic)-128 3174 y(\014nal)39 b(state)h(is)f(\014xed)h(imp)s(osing)d(additional)f (constrain)m(ts)k(on)f(the)h(true)g(kinematical)c(v)-5 b(ariables.)63 b(Indeed)-128 3295 y(the)33 b(follo)m(wing)d(ranges)j (are)g(allo)m(w)m(ed:)741 3422 y Fj(8)741 3497 y(>)741 3522 y(>)741 3547 y(>)741 3572 y(>)741 3596 y(>)741 3621 y(>)741 3646 y(<)741 3796 y(>)741 3821 y(>)741 3846 y(>)741 3870 y(>)741 3895 y(>)741 3920 y(>)741 3945 y(:)887 3507 y Fq(x)28 b Fo(\024)g Fq(x)1130 3522 y Ft(tr)r(ue)1295 3507 y Fo(\024)h Fs(1)113 b(for)55 b Fq(\033)1790 3522 y Ft(in)982 3745 y Fq(x)1037 3760 y Ft(tr)r(ue)1202 3745 y Fs(=)28 b(1)208 b(for)55 b Fq(\033)1790 3760 y Ft(q)857 3984 y Fq(x)912 3999 y Ft(tr)r(ue)1077 3984 y Fs(=)27 b Fq(M)1274 3999 y Ft(A)1332 3984 y Fq(=)-5 b(M)93 b Fs(for)55 b Fq(\033)1790 3999 y Ft(el)2098 3746 y Fq(Q)2175 3705 y Fp(2)2175 3771 y Ft(min)2336 3746 y Fo(\024)28 b Fq(Q)2518 3705 y Fp(2)2518 3771 y Ft(tr)r(ue)2683 3746 y Fo(\024)g Fq(Q)2865 3705 y Fp(2)2865 3771 y Ft(max)3764 3746 y Fs(\(5\))-128 4197 y(where)962 4357 y Fq(Q)1039 4316 y Fp(2)1039 4381 y Ft(max;min)1360 4357 y Fs(=)g Fq(Q)1541 4316 y Fp(2)1590 4289 y Fs(2\(1)22 b Fo(\000)g Fq(x)1902 4304 y Ft(r)1941 4289 y Fs(\)\(1)g Fo(\006)2187 4213 y(p)p 2270 4213 265 4 v 76 x Fs(1)g(+)g Fq(\015)2495 4260 y Fp(2)2535 4289 y Fs(\))g(+)g Fq(\015)2749 4253 y Fp(2)p 1590 4333 1198 4 v 1840 4425 a Fq(\015)1896 4396 y Fp(2)1958 4425 y Fs(+)g(4)p Fq(x)2160 4440 y Ft(r)2198 4425 y Fs(\(1)g Fo(\000)h Fq(x)2462 4440 y Ft(r)2500 4425 y Fs(\))3764 4357 y(\(6\))-128 4581 y(and)1147 4702 y Fq(\015)1203 4661 y Fp(2)1270 4702 y Fs(=)k(4)p Fq(M)1526 4661 y Fp(2)1566 4702 y Fq(x)1621 4661 y Fp(2)1661 4702 y Fq(=Q)1787 4661 y Fp(2)1827 4702 y Fq(;)212 b(x)2121 4717 y Ft(r)2187 4702 y Fs(=)27 b Fq(x=x)2449 4717 y Ft(tr)r(ue)2587 4702 y Fq(:)1150 b Fs(\(7\))19 4923 y(The)30 b(Mon)m(te-Carlo)g(pro)s(cedure)g(for)f(the)h(generation)f(of)h(ev)m (en)m(ts)i(with)d(a)g(p)s(ossible)g(photon)h(radiation)e(is)-128 5044 y(as)33 b(follo)m(ws:)-128 5211 y(It)d(starts)f(o\013)g(with)f (the)i(generation)e(of)h(the)g(kinematics)f(of)h(the)g(scattered)i (lepton)d(and)h(the)h(calculation)d(of)-128 5332 y(an)f(ev)m(en)m(t)h (w)m(eigh)m(t)f(from)f(these)i(kinematics.)40 b(Then)26 b(the)g(appropriate)f(scattering)h(c)m(hannel)g(\(non-radiativ)m(e;) -128 5452 y(elastic,)32 b(quasielastic)g(or)h(inelastic)e(radiativ)m(e) g(tail\))g(has)i(to)f(b)s(e)h(c)m(hosen)h(according)f(to)f(their)g(con) m(tribution)-128 5572 y(to)43 b(the)h(total)d(observ)m(ed)k(cross)f (section)f(\(see)h(\(2)p (#equation.2) [[272 48 278 60] [1 1 1 [3 3]] [0 0 1]] pdfm (\)\).)75 b(If)43 b(a)f(radiativ)m(e)g(c)m(hannel)i(is)e(selected)i(the)g (radiated)-128 5693 y(photon)30 b(has)g(to)f(b)s(e)g(generated)h(and)g (the)g(v)-5 b(alues)29 b(of)g(the)h(kinematical)d(v)-5 b(ariables)28 b(ha)m(v)m(e)i(to)f(b)s(e)h(re-computed)1856 5916 y(3)p eop %%Page: 4 4 4 3 bop -128 100 a Fs(in)33 b(order)h(to)f(obtain)f(the)i(true)g(v)-5 b(alues.)46 b(F)-8 b(or)33 b(eac)m(h)h(ev)m(en)m(t)i(the)e(w)m(eigh)m (t)f(has)h(to)f(b)s(e)h(recalculated.)46 b(The)34 b(new)-128 220 y(w)m(eigh)m(t)c(is)f(de\014ned)i(as)e(the)h(ratio)d(of)i(the)h (radiativ)m(ely)e(corrected)i(and)f(the)h(Born)f(cross)i(section.)42 b(After)29 b(this)-128 340 y(recalculation)h(the)j(w)m(eigh)m(ted)g (sum)e(of)h(all)e(ev)m(en)m(ts)k(\(generated)f(originally)28 b(in)j(accordance)i(with)f(the)g(Born)-128 461 y(cross)i(section\))f (giv)m(es)g(the)g(observ)m(ed)h(cross)g(section.)19 621 y(The)h(recalculation)c(of)j(the)g(w)m(eigh)m(t)g(requires)h(the)f(kno) m(wledge)h(of)e(the)i(cross)f(section)g(in)m(tegrated)g(o)m(v)m(er)-128 741 y(the)29 b(photon)e(momen)m(tum.)41 b(This)28 b(is)f(done)h (di\013eren)m(tly)g(in)f(the)h(t)m(w)m(o)h(theoretical)d(approac)m(hes) j(whic)m(h)f(will)e(b)s(e)-128 862 y(discussed)32 b(in)e(detail)f(in)g (the)i(subsections)h(b)s(elo)m(w.)42 b(In)31 b(the)g(Mo-Tsai)e(approac) m(h)i(an)f(additional)e(parameter)-128 982 y(\001)35 b(is)e(in)m(tro)s(duced)h(dividing)e(the)j(in)m(tegration)d(region)h (in)m(to)g(a)h(soft)g(and)g(a)g(hard)g(photonic)f(part.)48 b(No)34 b(suc)m(h)-128 1102 y(parameter)h(is)f(used)i(in)d(the)j (Bardin-Sh)m(umeik)m(o)d(approac)m(h.)50 b(Ho)m(w)m(ev)m(er,)38 b(in)c(b)s(oth)g(approac)m(hes)i(a)e(minimal)-128 1223 y(photon)h(energy)g Fq(E)596 1176 y Ft(\015)590 1246 y(min)758 1223 y Fs(is)f(adapted)h(in)f(generating)g(a)g(radiated)f (photon.)50 b(Only)34 b(if)f(the)i(photon)f(energy)i(is)-128 1343 y(ab)s(o)m(v)m(e)f(this)e(v)-5 b(alue)33 b(the)i(kinematics)d(of)h (the)i(photon)e(is)g(calculated)g(and)h(the)g(ev)m(en)m(t)i(b)s(ecomes) e(a)f(radiativ)m(e)-128 1464 y(one.)43 b(The)31 b(actual)e(v)-5 b(alue)29 b(of)g Fq(E)1011 1416 y Ft(\015)1005 1486 y(min)1169 1464 y Fs(dep)s(ends)i(on)f(the)g(aim)e(of)h(the)h(photon)g(generator.) 42 b(In)30 b(general)g(photons)-128 1584 y(should)f(b)s(e)g(detected)h (in)e(the)h(calorimeter.)40 b(So)29 b(the)g(energy)g(threshold)g(of)f (the)h(calorimeter)e(sets)j(the)f(v)-5 b(alue)-128 1704 y(for)32 b Fq(E)99 1657 y Ft(\015)93 1727 y(min)227 1704 y Fs(.)19 1864 y(In)41 b(addition)d(one)j(needs)h(spin)e(a)m(v)m (eraged)i(and)e(spin)h(dep)s(enden)m(t)h(structure)g(functions,)g (quasielastic)-128 1985 y(suppression)c(factors)f(and)f(elastic)g (formfactors)f(to)h(calculate)g(the)h(Born)f(and)g(observ)m(ed)j(cross) e(sections.)-128 2105 y(This)44 b(is)f(tak)m(en)h(either)f(from)f (\014ts)i(to)f(exp)s(erimen)m(tal)f(data)h(or)g(from)f(mo)s(del)g (predictions.)75 b(A)43 b(recen)m(t)i(8-)-128 2226 y(parameter)28 b(\014t)h(from)e(ref.[5)p (#cite.nmc) [[174 450 179 462] [1 1 1 [3 3]] [0 0 1]] pdfm (])i(for)f (the)h(proton)f(and)h(deuterium)f(structure)i(function)e Fq(F)3087 2178 y Ft(p;d)3073 2247 y Fp(2)3182 2226 y Fs(\()p Fq(x;)17 b(Q)3396 2189 y Fp(2)3436 2226 y Fs(\))28 b(and)h(their)-128 2346 y(com)m(bination)c(for)564 2310 y Fp(3)604 2346 y Fs(He)h(\()p Fq(F)861 2286 y Fi(3)896 2310 y Fp(He)847 2371 y(2)1012 2346 y Fs(=)1125 2307 y Fp(1)p 1125 2323 36 4 v 1125 2380 a(3)1170 2346 y Fq(F)1247 2299 y Ft(p)1233 2368 y Fp(2)1296 2346 y Fs(+)1391 2307 y Fp(2)p 1391 2323 V 1391 2380 a(3)1436 2346 y Fq(F)1513 2310 y Ft(d)1499 2371 y Fp(2)1553 2346 y Fs(\))h(has)f(b)s(een)h(used.) 43 b(The)27 b(spin)f(dep)s(enden)m(t)i(structure)g(function)-128 2466 y Fq(g)-81 2481 y Fp(1)-41 2466 y Fs(\()p Fq(x;)17 b(Q)173 2430 y Fp(2)212 2466 y Fs(\))33 b(is)f(constructed)i(from)d(a)i (\014t)f(to)h(the)g(spin)f(asymmetry)h Fq(A)2415 2481 y Fp(1)2487 2466 y Fs([3)p (#cite.POLRAD20) [[374 421 380 433] [1 1 1 [3 3]] [0 0 1]] pdfm (])f (according)g(to)666 2727 y Fq(g)713 2742 y Fp(1)753 2727 y Fs(\()p Fq(x;)17 b(Q)967 2686 y Fp(2)1006 2727 y Fs(\))28 b(=)f Fq(A)1248 2742 y Fp(1)1288 2727 y Fs(\()p Fq(x)p Fs(\))p Fq(F)1482 2742 y Fp(1)1522 2727 y Fs(\()p Fq(x;)17 b(Q)1736 2686 y Fp(2)1776 2727 y Fs(\))27 b(=)2017 2660 y Fq(A)2090 2675 y Fp(1)2129 2660 y Fs(\()p Fq(x)p Fs(\))p Fq(F)2323 2675 y Fp(2)2363 2660 y Fs(\()p Fq(x;)17 b(Q)2577 2623 y Fp(2)2617 2660 y Fs(\))p 1955 2704 763 4 v 1955 2838 a(2)p Fq(x)2059 2717 y Fj(\022)2120 2838 y Fs(1)22 b(+)g Fq(R)q Fs(\()p Fq(x;)17 b(Q)2578 2809 y Fp(2)2618 2838 y Fs(\))2656 2717 y Fj(\023)2727 2727 y Fs(\(1)22 b(+)g Fq(\015)2990 2686 y Fp(2)3029 2727 y Fs(\))p Fq(:)670 b Fs(\(8\))19 3121 y(F)-8 b(or)44 b(the)h(structure)h(function)e Fq(R)q Fs(\()p Fq(x;)17 b(Q)1499 3085 y Fp(2)1539 3121 y Fs(\))44 b(b)s(eing)g(the)h(ratio)e(of)h(longitudinal)e(to)i(transv)m (erse)j(virtual)-128 3241 y(photon)32 b(absorption)e(cross)i(sections)g (Whitlo)m(w's)e(\014t)i([6)p (#cite.Whi) [[299 328 305 340] [1 1 1 [3 3]] [0 0 1]] pdfm (])f(w)m (as)h(used)g(and)f(assumed)h(to)f(b)s(e)g(A-indep)s(enden)m(t.)-128 3362 y(No)38 b(con)m(tributions)g(are)g(assumed)h(from)e(the)i(spin)f (dep)s(enden)m(t)i(structure)f(function)f Fq(g)3154 3377 y Fp(2)3193 3362 y Fs(\()p Fq(x;)17 b(Q)3407 3326 y Fp(2)3447 3362 y Fs(\).)60 b(F)-8 b(or)38 b(the)-128 3482 y(elastic)g (formfactors)f(a)g(\014t)i(to)e(exp)s(erimen)m(tal)h(data)f([7)p (#cite.ffhe) [[298 299 304 311] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(is)g (utilized.)58 b(The)39 b(quasielastic)f(radiativ)m(e)f(tail)f(is)-128 3603 y(calculated)25 b(in)f(accordance)i(with)f(ref.[8)p (#cite.ARST) [[228 285 234 297] [1 1 1 [3 3]] [0 0 1]] pdfm (].)41 b(In)25 b(con)m(trast)h(to)e(the)i(elastic)e(case)i(where)g(the)g (treatmen)m(t)f(is)f(exact)-128 3723 y(\(within)33 b(the)h(considered)g (order)g(of)f(p)s(erturbativ)m(e)g(theory\))h(here)h(the)e(Y-scaling)f (h)m(yp)s(othesis)j([9)p (#cite.Tho) [[486 270 492 282] [1 1 1 [3 3]] [0 0 1]] pdfm (])e(and)h (the)-128 3843 y(p)s(eaking)29 b(appro)m(ximation)e(\(quasielastic)h (structure)i(functions)f(are)g(ev)-5 b(aluated)29 b(at)f(the)i (quasielastic)e(p)s(eak\))-128 3964 y(are)33 b(applied.)19 4124 y(The)28 b(t)m(w)m(o)g(Mon)m(te)g(Carlo)f(generators)g(for)g (radiativ)m(e)f(ev)m(en)m(ts)k(a)m(v)-5 b(ailable)25 b(in)h(RADGEN)h(for)g(the)h(unp)s(olar-)-128 4244 y(ized)34 b(and)g(p)s(olarized)e(cases)j(are)f(describ)s(ed)h(b)s(elo)m(w.)47 b(The)35 b(theoretical)d(approac)m(hes,)k(the)e(appro)m(ximations)-128 4365 y(made,)29 b(and)g(the)g(dep)s(endence)i(of)d(the)h(radiativ)m(e)e (corrections)i(on)f(the)h(arti\014cial)d(parameter)i(\001)h(and)f(on)h (the)-128 4485 y(v)-5 b(alue)32 b(of)h(the)g(photon)f(detector)h (threshold)g Fq(E)1620 4438 y Ft(\015)1614 4508 y(min)1780 4485 y Fs(are)g(discussed.)-128 4811 y Fh(2.1)136 b(The)44 b(generator)j(for)e(the)g(unp)t(olarized)g(case)-128 5035 y Fs(The)24 b(unp)s(olarized)c(generator)j(is)e(based)i(on)f(the)h (F)m(OR)-8 b(TRAN)22 b(co)s(de)g(FERRAD35)f([4)p (#cite.FERRAD) [[423 113 429 125] [1 1 1 [3 3]] [0 0 1]] pdfm (].)40 b(The)23 b(co)s(de)g(calculates)-128 5156 y(the)31 b(radiativ)m(e)f (correction)g(to)h(deep)g(inelastic)e(scattering)i(of)f(unp)s(olarized) f(particles)h(in)g(accordance)i(with)-128 5276 y(the)h(analytical)e (form)m(ulae)g(giv)m(en)h(b)m(y)i(Mo)e(and)h(Tsai)f([1)p (#cite.MT) [[298 84 304 96] [1 1 1 [3 3]] [0 0 1]] pdfm (].)19 5436 y(The)h(result)g(for)f(the)h(lo)m(w)m(est)g(order)g(radiativ)m(e)e (correction)h(of)h(the)g(cross)g(section)g(is)663 5717 y Fq(\033)f Fs(=)27 b Fq(\016)896 5732 y Ft(R)954 5717 y Fs(\(\001\)\(1)22 b(+)g Fq(\016)1361 5732 y Ft(v)r(er)r(t)1516 5717 y Fs(+)g Fq(\016)1657 5732 y Ft(v)r(ac)1789 5717 y Fs(+)g Fq(\016)1930 5732 y Ft(sm)2029 5717 y Fs(\))p Fq(\033)2122 5732 y Fp(1)p Ft(\015)2224 5717 y Fs(+)g Fq(\033)2377 5732 y Ft(el)2459 5717 y Fs(+)g Fq(\033)2612 5732 y Ft(q)2672 5717 y Fs(+)g Fq(\033)2825 5732 y Ft(in)2897 5717 y Fs(\(\001\))p Fq(;)683 b Fs(\(9\))1856 5916 y(4)p eop %%Page: 5 5 5 4 bop -128 100 a Fs(where)30 b Fq(\033)205 115 y Fp(1)p Ft(\015)314 100 y Fs(is)e(the)i(one)f(photon)f(exc)m(hange)j(Born)e (cross)g(section)g(and)g Fq(\016)2513 115 y Ft(v)r(ac)2622 100 y Fs(,)h Fq(\016)2722 115 y Ft(v)r(er)r(t)2855 100 y Fs(,)f(and)g Fq(\016)3140 115 y Ft(sm)3268 100 y Fs(are)g (corrections)-128 220 y(due)g(to)f(v)-5 b(acuum)27 b(p)s(olarization)e (b)m(y)k(electron)f(and)g(m)m(uon)f(pairs,)i(v)m(ertex)h(corrections)e (and)g(residuum)f(of)h(the)-128 340 y(cancellation)j(of)h(infrared)g (div)m(ergen)m(t)h(terms)g(indep)s(enden)m(t)h(of)e(\001:)858 575 y Fq(\016)901 590 y Ft(v)r(ac)1094 575 y Fs(=)1262 508 y Fq(\013)p 1262 552 63 4 v 1264 644 a(\031)1352 429 y Fj(")1400 575 y Fo(\000)1487 508 y Fs(20)p 1487 552 98 4 v 1512 644 a(9)1617 575 y(+)1725 508 y(2)p 1725 552 49 4 v 1725 644 a(3)1801 575 y(ln)1912 508 y Fq(Q)1989 472 y Fp(2)p 1908 552 125 4 v 1908 644 a Fq(m)1993 615 y Fp(2)1993 668 y Ft(e)2065 575 y Fs(+)2173 508 y(2)p 2173 552 49 4 v 2173 644 a(3)2249 575 y(ln)2364 508 y Fq(Q)2441 472 y Fp(2)p 2356 552 132 4 v 2356 644 a Fq(m)2441 615 y Fp(2)2441 668 y Ft(\026)2498 429 y Fj(#)2563 575 y Fq(;)834 864 y(\016)877 879 y Ft(v)r(er)r(t)1094 864 y Fs(=)1262 796 y Fq(\013)p 1262 841 63 4 v 1264 932 a(\031)1352 718 y Fj(")1400 864 y Fo(\000)p Fs(2)23 b(+)1656 796 y(3)p 1656 841 49 4 v 1656 932 a(2)1732 864 y(ln)1844 796 y Fq(Q)1921 760 y Fp(2)p 1840 841 125 4 v 1840 932 a Fq(m)1925 903 y Fp(2)1974 718 y Fj(#)2039 864 y Fq(;)868 1146 y(\016)911 1161 y Ft(sm)1094 1146 y Fs(=)1262 1079 y Fq(\013)p 1262 1123 63 4 v 1264 1214 a(\031)1352 1000 y Fj(")1400 1146 y Fo(\000)1487 1079 y Fq(\031)1546 1043 y Fp(2)p 1487 1123 99 4 v 1512 1214 a Fs(6)1618 1146 y(+)f(Li)1804 1161 y Fp(2)1844 1025 y Fj(\022)1905 1146 y Fq(cos)2040 1105 y Fp(2)2089 1079 y Fq(\022)p 2089 1123 49 4 v 2089 1214 a Fs(2)2148 1025 y Fj(\023)2231 1146 y Fo(\000)2340 1079 y Fs(1)p 2340 1123 V 2340 1214 a(2)2416 1146 y(ln)2497 1103 y Fp(2)2537 1146 y Fs(\(1)f Fo(\000)i Fq(y)t Fs(\))2835 1000 y Fj(#)2899 1146 y Fq(;)789 b Fs(\(10\))-128 1386 y(where)45 b Fq(m)f Fs(is)g(the)g(lepton)f(mass)h (and)f(Li)1431 1401 y Fp(2)1471 1386 y Fs(\()p Fq(x)p Fs(\))k(=)f Fo(\000)1865 1315 y Fj(R)1921 1342 y Ft(x)1905 1412 y Fp(0)1981 1386 y Fq(dy)20 b Fs(ln)o(\(1)29 b Fo(\000)i Fq(y)t Fs(\))p Fq(=y)45 b Fs(is)f(the)g(dilogarithm)39 b(or)44 b(Sp)s(ence)-128 1507 y(function.)19 1657 y(The)39 b(cross)f(sections)h Fq(\033)894 1672 y Ft(el)953 1657 y Fs(,)g Fq(\033)1074 1672 y Ft(q)1113 1657 y Fs(,)g(and)f Fq(\033)1429 1672 y Ft(in)1538 1657 y Fs(are)g(the)g(con)m(tributions)f (from)g(radiativ)m(e)g(pro)s(cesses)j(\(i.e.)58 b(in-)-128 1778 y(cluding)33 b(real)h(photon)g(radiation\))d(for)j(elastic,)g (quasielastic)f(and)h(deep)h(inelastic)d(scattering.)48 b(They)36 b(can)-128 1898 y(b)s(e)d(calculated)f(in)g(terms)g(of)g(the) h(radiativ)m(e)f(tail)e(from)h(the)j(j)p Fq(th)e Fs(mass)h(lev)m(el)f Fq(\033)2779 1913 y Ft(j)351 2245 y Fq(\033)406 2260 y Ft(el)492 2245 y Fs(=)c Fq(\033)651 2260 y Ft(el)710 2245 y Fs(\()p Fq(M)842 2260 y Ft(A)900 2245 y Fq(;)17 b Fs(1\))p Fq(;)211 b(\033)1324 2260 y Ft(q)1390 2245 y Fs(=)27 b Fq(\033)1548 2260 y Ft(q)1587 2245 y Fs(\()p Fq(M)5 b(;)17 b Fs(1\))p Fq(;)211 b(\033)2148 2260 y Ft(in)2248 2245 y Fs(=)2448 2111 y Ft(W)2427 2127 y Fj(Z)2333 2371 y Ft(M)7 b Fp(+)p Ft(m)2525 2379 y Fg(\031)2602 2245 y Fq(dM)2747 2260 y Ft(h)2792 2245 y Fq(\033)2847 2260 y Ft(in)2918 2245 y Fs(\()p Fq(M)3050 2260 y Ft(h)3095 2245 y Fq(;)17 b(\022)3184 2260 y Ft(max)3328 2245 y Fs(\))p Fq(;)322 b Fs(\(11\))-128 2542 y(where)29 b Fq(M)243 2557 y Ft(h)316 2542 y Fs(=)419 2439 y Fj(q)p 502 2439 230 4 v 103 x Fq(W)608 2508 y Fp(2)594 2562 y Ft(tr)r(ue)758 2542 y Fs(and)e Fq(\033)997 2557 y Ft(j)1061 2542 y Fs(\()p Fq(j)34 b Fs(=)27 b Fq(el)r(;)17 b(q)t(;)g(in)p Fs(\))28 b(has)f(the)g(form)f(of)h(an)g(in)m(tegral)e(o)m(v)m(er)j Fq(\022)3032 2557 y Ft(\015)3077 2542 y Fs(,)g(the)g(angle)e(b)s(et)m (w)m(een)-128 2663 y(the)33 b(real)f(and)h(the)g(virtual)e(photons:)362 3011 y Fq(\033)417 3026 y Ft(j)454 3011 y Fs(\()p Fq(M)5 b(;)17 b(\022)680 3026 y Ft(max)824 3011 y Fs(\))28 b(=)1012 2876 y Ft(\022)1045 2884 y Fg(max)1032 2894 y Fj(Z)1037 3135 y Fp(0)1170 3011 y Fq(d\022)1266 3026 y Ft(\015)1366 3011 y Fq(T)1423 3026 y Fp(0)1462 3011 y Fs(\()p Fq(W)1606 2964 y Ft(j)1592 3033 y Fp(2)1643 3011 y Fs(\()p Fq(T)1738 3026 y Fp(1)1799 3011 y Fs(+)22 b Fq(T)1954 3026 y Fp(2)2016 3011 y Fs(+)g Fq(T)2171 3026 y Fp(3)2233 3011 y Fs(+)g Fq(T)2388 3026 y Fp(4)2449 3011 y Fs(+)g Fq(T)2604 3026 y Fp(5)2644 3011 y Fs(\))g(+)g Fq(W)2908 2964 y Ft(j)2894 3033 y Fp(1)2944 3011 y Fs(\()p Fq(T)3039 3026 y Fp(6)3101 3011 y Fs(+)g Fq(T)3256 3026 y Fp(7)3296 3011 y Fs(\)\))p Fq(:)316 b Fs(\(12\))19 3309 y(The)45 b(explicit)e(form)g(of)h(the)g (structure)i(functions)e Fq(W)2099 3262 y Ft(j)2085 3331 y Fp(1)p Ft(;)p Fp(2)2224 3309 y Fs(dep)s(ends)i(on)e(the)h(t)m(yp)s(e) g(of)f(the)h(tail.)76 b(The)-128 3429 y(terms)37 b Fq(T)205 3444 y Ft(i)270 3429 y Fs(are)g(kinematical)d(factors)j(\(see)h(ref.[1) p (#cite.MT) [[270 306 276 318] [1 1 1 [3 3]] [0 0 1]] pdfm (])e(for)h (details\).)55 b(The)37 b(in)m(tegration)e(limit)f Fq(\022)3302 3444 y Ft(max)3482 3429 y Fs(is)j(de\014ned)-128 3550 y(as)c Fq(\022)37 3565 y Ft(max)209 3550 y Fs(=)28 b Fq(min)p Fs(\()p Fq(\031)t(;)17 b(\022)675 3565 y Fp(\001)738 3550 y Fs(\))33 b(where)h Fq(\022)1136 3565 y Fp(\001)1232 3550 y Fs(can)f(b)s(e)f(found)h(from)e(the)i(relation)877 3821 y Fq(W)983 3779 y Fp(2)969 3845 y Ft(tr)r(ue)1134 3821 y Fs(=)27 b Fq(W)1343 3779 y Fp(2)1405 3821 y Fo(\000)22 b Fs(2\001\()p Fq(\027)29 b Fs(+)22 b Fq(M)33 b Fo(\000)2073 3714 y Fj(q)p 2156 3714 331 4 v 107 x Fq(\027)2210 3792 y Fp(2)2272 3821 y Fs(+)22 b Fq(Q)2447 3792 y Fp(2)2504 3821 y Fs(cos\()p Fq(\022)2717 3836 y Fp(\001)2781 3821 y Fs(\)\))p Fq(:)831 b Fs(\(13\))19 4007 y(An)40 b(arti\014cial)d (parameter)j(\001)g(had)h(to)e(b)s(e)i(in)m(tro)s(duced)f(to)g(divide)f (the)i(in)m(tegration)d(region)i(o)m(v)m(er)h(the)-128 4128 y(photon)d(energy)h(in)m(to)f(t)m(w)m(o)g(parts,)i(the)e(soft)g (and)g(the)h(hard)f(energy)h(regions.)59 b(The)39 b(hard)f(energy)h (region)-128 4248 y Fq(\033)-73 4263 y Ft(in)-1 4248 y Fs(\(\001\))47 b(can)g(b)s(e)f(calculated)g(without)g(an)m(y)i(appro) m(ximations.)84 b(The)47 b(soft)g(photon)f(part)h(is)f(calculated)-128 4368 y(for)g(photon)f(energies)h(approac)m(hing)g(zero.)83 b(After)45 b(cancellation)f(of)h(the)h(infrared)f(div)m(ergences)j(and) d(a)-128 4489 y(resummation)31 b(of)h(soft)h(m)m(ultiphoton)d (e\013ects)k(the)f(correction)g(factor)f(is)g(giv)m(en)g(b)m(y)829 4724 y Fq(\016)872 4739 y Ft(R)930 4724 y Fs(\(\001\))27 b(=)h(exp)1384 4577 y Fj(")1432 4724 y Fo(\000)1519 4656 y Fq(\013)p 1519 4700 63 4 v 1521 4792 a(\031)1609 4577 y Fj( )1674 4724 y Fs(ln)1784 4656 y Fq(E)p 1782 4700 82 4 v 1782 4792 a Fs(\001)1896 4724 y(+)22 b(ln)2102 4656 y Fq(E)2180 4620 y Fk(0)p 2102 4700 102 4 v 2112 4792 a Fs(\001)2213 4577 y Fj(!)16 b( )2361 4724 y Fs(ln)2473 4656 y Fq(Q)2550 4620 y Fp(2)p 2469 4700 125 4 v 2469 4792 a Fq(m)2554 4763 y Fp(2)2626 4724 y Fo(\000)22 b Fs(1)2774 4577 y Fj(!#)2905 4724 y Fq(:)783 b Fs(\(14\))19 4994 y(Note)40 b(that)g(w)m(e)g(follo)m(w)f(ref.[1)p (#cite.MT) [[202 118 208 130] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(in)f (\014xing)g(that)h(part)g(of)f(the)h(soft)g(photon)g(correction)g(whic) m(h)g(should)-128 5115 y(b)s(e)46 b(exp)s(onen)m(tiated.)81 b(Another)45 b(p)s(ossible)f(v)-5 b(arian)m(t)44 b(is)h(the)g(w)m (ell-kno)m(wn)g(prescription)f(of)h(ref.[10)p (#cite.Suura) [[491 103 502 115] [1 1 1 [3 3]] [0 0 1]] pdfm (].)80 b(The)-128 5235 y(dep)s(endence)30 b(on)e(\001)g(is)f(the)h (de\014ciency)h(of)e(the)h(metho)s(d.)41 b(On)27 b(the)h(one)g(hand)g (this)f(arti\014cial)e(parameter)i(has)-128 5355 y(to)d(b)s(e)g(c)m (hosen)h(su\016cien)m(tly)g(large)d(to)h(a)m(v)m(oid)h(n)m(umerical)e (instabilities)f(b)s(ecause)k(for)e(\001)28 b(=)g(0)23 b(the)h(con)m(tribution)-128 5476 y Fq(\033)-73 5491 y Ft(in)-1 5476 y Fs(\(\001\))31 b(gets)g(in\014nite.)42 b(On)31 b(the)g(other)g(hand)g(it)f(has)h(to)f(b)s(e)h(c)m(hosen)i (su\016cien)m(tly)e(small)d(to)j(reduce)h(the)f(soft)-128 5596 y(photon)h(region)f(whic)m(h)h(is)f(calculated)g(only)g(appro)m (ximately)-8 b(.)41 b(If)32 b(the)g(threshold)g(o)m(v)m(er)g(the)g (photon)g(energy)-128 5717 y(is)h(lo)m(w)f(enough,)h(it)e(is)h (customary)h(to)f(use)i(the)f(same)f(v)-5 b(alue)32 b(for)g(the)h (parameters)g(\001)g(and)f Fq(E)3335 5669 y Ft(\015)3329 5739 y(min)3463 5717 y Fs(.)1856 5916 y(5)p eop %%Page: 6 6 6 5 bop -128 100 a Fh(2.2)136 b(The)44 b(generator)j(for)e(the)g(p)t (olarized)g(case)-128 322 y Fs(The)h(p)s(olarized)d(generator)i(is)f (constructed)i(utilizing)41 b(the)k(F)m(OR)-8 b(TRAN)45 b(co)s(de)g(POLRAD)f(2.0)g([3)p (#cite.POLRAD20) [[506 678 512 690] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g (11)p (#cite.ASh) [[520 678 532 690] [1 1 1 [3 3]] [0 0 1]] pdfm (].) -128 442 y(This)38 b(co)s(de)f(is)g(based)h(on)f(the)h(metho)s(d)f(of)f (co)m(v)-5 b(arian)m(t)37 b(cancellation)e(of)i(infrared)f(div)m (ergences)j(dev)m(elop)s(ed)-128 563 y(b)m(y)30 b(Bardin)e(and)h(Sh)m (umeik)m(o)g([2)p (#cite.BSh) [[189 649 195 661] [1 1 1 [3 3]] [0 0 1]] pdfm (].)43 b(The)30 b(\014nal)e(form)m(ula)f(for)h(the)h(cross)h(section)f(free)h (of)e(infrared)g(div)m(ergences)-128 683 y(do)s(es)41 b(not)e(include)g(an)m(y)i(arti\014cial)c(parameter)i(lik)m(e)g(\001.) 65 b(Ho)m(w)m(ev)m(er,)44 b Fq(E)2546 636 y Ft(\015)2540 706 y(min)2714 683 y Fs(has)c(to)f(b)s(e)h(in)m(tro)s(duced)g(if)f(the) -128 803 y(co)s(de)c(is)e(used)i(considering)e(the)i(generation)e(of)g (real)g(radiated)g(photons.)48 b(The)35 b(cross)g(section)f(form)m(ula) e(of)-128 924 y(ref.[11)p (#cite.ASh) [[76 606 88 618] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(can)g(b) s(e)g(rewritten)f(in)m(to)g(a)g(form)g(similar)d(to)j(eq.\(9)p (#equation.9) [[316 606 322 618] [1 1 1 [3 3]] [0 0 1]] pdfm (\):)261 1202 y Fq(\033)g Fs(=)c Fq(\016)495 1217 y Ft(R)552 1202 y Fs(\()p Fq(E)668 1155 y Ft(\015)662 1225 y(min)796 1202 y Fs(\)\(1)22 b(+)g Fq(\016)1084 1217 y Ft(v)r(er)r(t)1239 1202 y Fs(+)g Fq(\016)1380 1217 y Ft(v)r(ac)1511 1202 y Fs(+)g Fq(\016)1652 1217 y Ft(sm)1752 1202 y Fs(\))p Fq(\033)1845 1217 y Fp(1)p Ft(\015)1947 1202 y Fs(+)g Fq(\033)2100 1217 y Ft(add)2215 1202 y Fs(\()p Fq(E)2331 1155 y Ft(\015)2325 1225 y(min)2458 1202 y Fs(\))g(+)g Fq(\033)2671 1217 y Ft(el)2753 1202 y Fs(+)g Fq(\033)2906 1217 y Ft(q)2966 1202 y Fs(+)g Fq(\033)3119 1217 y Ft(in)3191 1202 y Fs(\()p Fq(E)3307 1155 y Ft(\015)3301 1225 y(min)3434 1202 y Fs(\))p Fq(:)216 b Fs(\(15\))19 1403 y(In)38 b(the)h (ultrarelativistic)c(appro)m(ximation)h(\()p Fq(Q)1783 1367 y Fp(2)1860 1403 y Fo(\035)h Fq(m)2082 1367 y Fp(2)2122 1403 y Fs(\))h(the)h(corrections)f Fq(\016)2914 1418 y Ft(v)r(er)r(t)3048 1403 y Fs(,)h Fq(\016)3157 1418 y Ft(v)r(ac)3266 1403 y Fs(,)h(and)f Fq(\016)3572 1418 y Ft(sm)3709 1403 y Fs(tak)m(e)-128 1524 y(the)h(same)g(form)e(as)h(in) g(eq.\(10)p (#equation.10) [[185 534 197 546] [1 1 1 [3 3]] [0 0 1]] pdfm (\))1118 1488 y Fp(1)p (#Hfootnote.1) [[206 534 211 546] [1 1 1 [3 3]] [0 0 1]] pdfm 1157 1524 a Fs(.)64 b(The)40 b(co)m(v)-5 b(arian)m(t)39 b(form)f(of)h(the)h(radiativ)m(e)e(tails)g(for)h(a)g(n)m(uclear)g (target)-128 1644 y(with)33 b(atomic)d(n)m(um)m(b)s(er)j Fq(A)g Fs(is)f(as)h(follo)m(ws:)317 1916 y Fq(\033)372 1931 y Ft(in)526 1916 y Fs(=)83 b Fo(\000)p Fq(\013)825 1875 y Fp(3)864 1916 y Fq(y)951 1782 y Ft(\034)982 1790 y Fg(max)970 1799 y Fj(Z)918 2033 y Ft(\034)949 2043 y Fg(min)1107 1916 y Fq(d\034)1270 1808 y Fp(4)1228 1833 y Fj(X)1231 2015 y Ft(i)p Fp(=1)1394 1806 y Ft(k)1431 1816 y Fg(i)1366 1833 y Fj(X)1364 2015 y Ft(j)t Fp(=1)1504 1916 y Fq(\022)1549 1931 y Ft(ij)1610 1916 y Fs(\()p Fq(\034)11 b Fs(\))1774 1782 y Ft(R)1827 1790 y Fg(max)1804 1799 y Fj(Z)1741 2043 y Ft(R)1794 2053 y Fg(min)1952 1916 y Fq(dR)2228 1849 y(R)2303 1813 y Ft(j)t Fk(\000)p Fp(2)p 2088 1893 481 4 v 2088 1985 a Fs(\()p Fq(Q)2203 1956 y Fp(2)2265 1985 y Fs(+)22 b Fq(R)q(\034)11 b Fs(\))2529 1956 y Fp(2)2579 1916 y Fo(=)2651 1931 y Ft(i)2679 1916 y Fs(\()p Fq(R)q(;)17 b(\034)11 b Fs(\))p Fq(;)329 2269 y(\033)384 2284 y Ft(el)526 2269 y Fs(=)83 b Fo(\000)772 2201 y Fq(\013)835 2165 y Fp(3)874 2201 y Fq(y)p 772 2246 154 4 v 793 2337 a(A)866 2308 y Fp(2)971 2131 y Ft(\034)1002 2142 y Fg(Amax)1013 2152 y Fj(Z)938 2386 y Ft(\034)969 2397 y Fg(Amin)1173 2269 y Fq(d\034)1266 2284 y Ft(A)1382 2161 y Fp(4)1340 2186 y Fj(X)1343 2368 y Ft(i)p Fp(=1)1506 2158 y Ft(k)1543 2168 y Fg(i)1478 2186 y Fj(X)1476 2368 y Ft(j)t Fp(=1)1615 2269 y Fq(\022)1660 2284 y Ft(ij)1721 2269 y Fs(\()p Fq(\034)1801 2284 y Ft(A)1859 2269 y Fs(\))2204 2201 y(2)p Fq(M)2357 2165 y Fp(2)2347 2226 y Ft(A)2405 2201 y Fq(R)2480 2154 y Ft(j)t Fk(\000)p Fp(2)2479 2227 y Ft(el)20 b(A)p 1907 2246 1002 4 v 1907 2337 a Fs(\(1)i(+)g Fq(\034)2156 2352 y Ft(A)2213 2337 y Fs(\)\()p Fq(Q)2366 2308 y Fp(2)2428 2337 y Fs(+)g Fq(R)2600 2352 y Ft(el)e(A)2731 2337 y Fq(\034)2773 2352 y Ft(A)2830 2337 y Fs(\))2868 2308 y Fp(2)2918 2269 y Fo(=)2990 2228 y Ft(el)2990 2293 y(i)3048 2269 y Fs(\()p Fq(R)3160 2284 y Ft(el)3219 2269 y Fq(;)d(\034)3305 2284 y Ft(A)3362 2269 y Fs(\))p Fq(;)349 2610 y(\033)404 2625 y Ft(q)526 2610 y Fs(=)83 b Fo(\000)772 2543 y Fq(\013)835 2507 y Fp(3)874 2543 y Fq(y)p 772 2587 154 4 v 812 2679 a(A)971 2476 y Ft(\034)1002 2484 y Fg(max)990 2493 y Fj(Z)938 2727 y Ft(\034)969 2737 y Fg(min)1127 2610 y Fq(d\034)1290 2502 y Fp(4)1248 2527 y Fj(X)1251 2710 y Ft(i)p Fp(=1)1414 2500 y Ft(k)1451 2510 y Fg(i)1386 2527 y Fj(X)1384 2710 y Ft(j)t Fp(=1)1524 2610 y Fq(\022)1569 2625 y Ft(ij)1630 2610 y Fs(\()p Fq(\034)11 b Fs(\))1990 2543 y(2)p Fq(M)2143 2507 y Fp(2)2183 2543 y Fq(R)2258 2496 y Ft(j)t Fk(\000)p Fp(2)2257 2568 y Ft(el)p 1769 2587 837 4 v 1769 2679 a Fs(\(1)22 b(+)g Fq(\034)11 b Fs(\)\()p Fq(Q)2182 2650 y Fp(2)2244 2679 y Fs(+)22 b Fq(R)2416 2694 y Ft(el)2475 2679 y Fq(\034)11 b Fs(\))2566 2650 y Fp(2)2616 2610 y Fo(=)2688 2563 y Ft(q)2688 2633 y(i)2726 2610 y Fs(\()p Fq(R)2838 2625 y Ft(q)2876 2610 y Fq(;)17 b(\034)11 b Fs(\))p Fq(:)677 b Fs(\(16\))-128 2936 y(The)37 b(in)m(tegration)c(limits)g(are)i(determined)g(b)m(y)h Fq(\034)1706 2951 y Ft(max;min)2032 2936 y Fs(=)c Fq(Q)2217 2900 y Fp(2)2257 2936 y Fq(=)p Fs(2)p Fq(M)2459 2900 y Fp(2)2498 2936 y Fq(x)p Fs(\(1)25 b Fo(\006)2766 2836 y Fj(q)p 2849 2836 623 4 v 100 x Fs(1)d(+)g(4)p Fq(M)3171 2908 y Fp(2)3211 2936 y Fq(x)3266 2908 y Fp(2)3306 2936 y Fq(=Q)3432 2908 y Fp(2)3471 2936 y Fs(\),)36 b Fq(R)3646 2951 y Ft(min)3812 2936 y Fs(=)-128 3070 y(2)p Fq(M)10 b(E)103 3022 y Ft(\015)97 3093 y(min)232 3070 y Fs(,)35 b(and)g Fq(R)560 3085 y Ft(max)735 3070 y Fs(=)c(\()p Fq(W)986 3033 y Fp(2)1049 3070 y Fo(\000)24 b Fs(\()p Fq(M)34 b Fs(+)24 b Fq(m)1501 3085 y Ft(\031)1548 3070 y Fs(\))1586 3033 y Fp(2)1626 3070 y Fs(\))p Fq(=)p Fs(\(1)f(+)g Fq(\034)11 b Fs(\).)50 b(The)36 b(quan)m(tities)f Fq(\022)2791 3085 y Ft(ij)2886 3070 y Fs(are)g(kinematical)d(factors,)-128 3190 y(and)c Fo(=)129 3205 y Ft(i)184 3190 y Fs(are)f(some)h(com)m (binations)d(of)i(the)h(DIS)f(structure)h(functions,)h(elastic)d (formfactors)g(or)h(quasielastic)-128 3310 y(resp)s(onse)36 b(functions)e(\(see)h(ref.[11)p (#cite.ASh) [[198 320 210 332] [1 1 1 [3 3]] [0 0 1]] pdfm (])f(for)f (details\).)47 b(The)35 b(sum)f(o)m(v)m(er)h Fq(i)f Fs(corresp)s(onds)h (to)f(con)m(tributions)f(from)-128 3431 y(spin)k(a)m(v)m(eraged)h(\()p Fq(i)d Fs(=)f(1)p Fq(;)17 b Fs(2\))36 b(and)h(spin)g(dep)s(enden)m(t)h (\()p Fq(i)d Fs(=)g(3)p Fq(;)17 b Fs(4\))36 b(structure)i(functions.)56 b(In)37 b(the)g(case)g(of)g(the)-128 3551 y(elastic)43 b(and)h(quasielastic)f(radiativ)m(e)f(tail)g(there)i(is)f(no)h(in)m (tegration)e(o)m(v)m(er)j Fq(R)f Fs(b)s(ecause)h(the)f Fq(R)h Fs(range)f(is)-128 3672 y(reduced)e(to)d(the)h(constan)m(t)h(v) -5 b(alues)39 b Fq(R)i Fs(=)f Fq(R)1547 3687 y Ft(el)20 b(A)1718 3672 y Fs(and)39 b Fq(R)i Fs(=)f Fq(R)2219 3687 y Ft(el)2318 3672 y Fs(\()p Fq(R)2430 3687 y Ft(el)2528 3672 y Fs(=)g(\(2)p Fq(M)10 b(\027)34 b Fo(\000)27 b Fq(Q)3098 3635 y Fp(2)3138 3672 y Fs(\))p Fq(=)p Fs(\(1)f(+)h Fq(\034)11 b Fs(\)\))40 b(due)g(to)-128 3792 y(the)33 b(\014xed)h(\014nal)e(hadron)h(mass.)43 b(In)m(v)-5 b(arian)m(ts)33 b(with)f(the)h(index)g("A")f(con)m(tain)g(the)h(n)m(ucleus)h(momen)m (tum)d Fq(p)3831 3807 y Ft(A)-128 3912 y Fs(instead)i(of)f Fq(p)h Fs(\()p Fq(p)489 3876 y Fp(2)489 3937 y Ft(A)573 3912 y Fs(=)28 b Fq(M)781 3876 y Fp(2)771 3937 y Ft(A)828 3912 y Fs(\).)19 4070 y(Apart)35 b(from)e(the)i(usual)g (ultrarelativistic)c(appro)m(ximation)i(another)i(one)g(w)m(as)h(made)e (when)i(the)g(eqs.)-128 4190 y(\(9)p (#equation.9) [[61 214 67 226] [1 1 1 [3 3]] [0 0 1]] pdfm (\))c(and)g (\(14)p (#equation.14) [[103 214 114 226] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(w)m(ere)i(obtained,)e(namely)g(the)h(photon)g(energy)h(w)m(as)f (considered)h(to)e(b)s(e)h(small)e Fq(E)3466 4154 y Ft(\015)3538 4190 y Fo(\034)d Fq(E)6 b(;)17 b(E)3865 4154 y Fk(0)-128 4311 y Fs(in)33 b(the)i(region)d Fq(E)528 4275 y Ft(\015)603 4311 y Fq(<)d(E)786 4264 y Ft(\015)780 4334 y(min)914 4311 y Fs(.)47 b(In)34 b(POLRAD,)f(the)h(term)g Fq(\033)2053 4326 y Ft(add)2167 4311 y Fs(\()p Fq(E)2283 4264 y Ft(\015)2277 4334 y(min)2411 4311 y Fs(\))f(is)h(added)g(to)f(tak)m(e)i(the)f (di\013erence)h(of)-128 4431 y(this)e(appro)m(ximation)d(to)i(the)h (exact)h(form)m(ula)c(in)m(to)i(accoun)m(t:)104 4747 y Fq(\033)159 4762 y Ft(add)274 4747 y Fs(\()p Fq(E)390 4699 y Ft(\015)384 4769 y(min)518 4747 y Fs(\))83 b(=)f Fo(\000)p Fq(\013)937 4705 y Fp(3)977 4747 y Fq(y)1063 4612 y Ft(\034)1094 4620 y Fg(max)1082 4629 y Fj(Z)1030 4864 y Ft(\034)1061 4874 y Fg(min)1220 4747 y Fq(d\034)1383 4639 y Fp(4)1341 4663 y Fj(X)1343 4846 y Ft(i)p Fp(=1)1477 4547 y Fj(8)1477 4622 y(>)1477 4647 y(<)1477 4796 y(>)1477 4821 y(:)1551 4747 y Fq(\022)1596 4762 y Ft(i)p Fp(1)1660 4747 y Fs(\()p Fq(\034)11 b Fs(\))1824 4597 y Fp(2)p Ft(M)c(E)1990 4564 y Fg(\015)1986 4620 y(min)1905 4629 y Fj(Z)1910 4870 y Fp(0)2113 4679 y Fq(dR)p 2113 4723 126 4 v 2139 4815 a(R)2276 4600 y Fj(")2400 4679 y Fo(=)2472 4694 y Ft(i)2500 4679 y Fs(\()p Fq(R)q(;)17 b(\034)11 b Fs(\))p 2334 4723 481 4 v 2334 4815 a(\()p Fq(Q)2449 4786 y Fp(2)2511 4815 y Fs(+)22 b Fq(R)q(\034)11 b Fs(\))2775 4786 y Fp(2)2847 4747 y Fo(\000)2956 4679 y(=)3028 4694 y Ft(i)3057 4679 y Fs(\(0)p Fq(;)17 b Fs(0\))p 2956 4723 318 4 v 3057 4815 a Fq(Q)3134 4786 y Fp(4)3284 4600 y Fj(#)1783 5141 y Fs(+)1905 5031 y Ft(k)1942 5041 y Fg(i)1877 5058 y Fj(X)1875 5241 y Ft(j)t Fp(=2)2015 5141 y Fq(\022)2060 5156 y Ft(ij)2121 5141 y Fs(\()p Fq(\034)11 b Fs(\))2285 4991 y Fp(2)p Ft(M)c(E)2451 4959 y Fg(\015)2447 5015 y(min)2366 5024 y Fj(Z)2371 5265 y Fp(0)2564 5141 y Fq(dR)2839 5074 y(R)2914 5038 y Ft(j)t Fk(\000)p Fp(2)p 2700 5118 481 4 v 2700 5210 a Fs(\()p Fq(Q)2815 5181 y Fp(2)2877 5210 y Fs(+)22 b Fq(R)q(\034)11 b Fs(\))3141 5181 y Fp(2)3191 5141 y Fo(=)3263 5156 y Ft(i)3291 5141 y Fs(\()p Fq(R)q(;)17 b(\034)11 b Fs(\))3539 4942 y Fj(9)3539 5017 y(>)3539 5042 y(=)3539 5191 y(>)3539 5216 y(;)3629 5141 y Fq(:)59 b Fs(\(17\))-128 5444 y(Therefore,)45 b(the)c(results)g(obtained)f (with)h(the)g(help)g(of)f(POLRAD)g(are)h(indep)s(enden)m(t)h(of)f(the)g (threshold)-128 5564 y(parameter)33 b Fq(E)417 5517 y Ft(\015)411 5587 y(min)577 5564 y Fs(b)m(y)g(construction.)p -128 5625 1607 4 v -15 5686 a Ff(1)22 5717 y Fe(It)28 b(should)f(b)r(e)h(noted)g(that)g(con)n(tributions)e(from)i Fu(\034)9 b Fe(-leptons)27 b(and)h(quark)e(lo)r(ops)h(w)n(ere)g (included)h(in)n(to)f Fu(\016)3301 5729 y Fd(v)r(ac)3434 5717 y Fe([11)p (#cite.ASh) [[487 31 497 43] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(].)1856 5916 y Fs(6)p eop %%Page: 7 7 7 6 bop -128 100 a Fw(3)162 b(Comparison)52 b(and)i(Numerical)g (Results)-128 395 y Fh(3.1)136 b(Analytical)46 b(comparison)-128 627 y Fs(The)h(expressions)f(for)f(the)h(spin)f(indep)s(enden)m(t)h (part)f(of)g(the)g(radiativ)m(e)f(tails)g(in)g(eq.)82 b(\(16)p (#equation.16) [[465 642 476 654] [1 1 1 [3 3]] [0 0 1]] pdfm (\))45 b(ha)m(v)m(e)h(b)s(een)-128 747 y(compared)38 b(analytically)e(with)h(the)i(radiativ)m(e)e(tails)f(giv)m(en)j(b)m(y)g (eqs.\(11)p (#equation.11) [[370 627 382 639] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f (and)h(\(12)p (#equation.12) [[419 627 431 639] [1 1 1 [3 3]] [0 0 1]] pdfm (\))e (for)h(the)g(unp)s(olarized)-128 868 y(case)c(using)e(the)h(algebraic)e (programming)f(system)j(REDUCE)g(3.5.)43 b(It)33 b(turned)g(out)g(that) 620 1302 y Fo(\000)23 b Fs(2)p Fq(M)873 1196 y Fj(q)p 956 1196 331 4 v 106 x Fq(\027)1010 1274 y Fp(2)1072 1302 y Fs(+)f Fq(Q)1247 1274 y Fp(2)1347 1194 y(3)1305 1219 y Fj(X)1304 1402 y Ft(j)t Fp(=1)1443 1302 y Fs(\002)1519 1317 y Fp(2)p Ft(i)1582 1302 y Fs(\()p Fq(\034)11 b Fs(\))p Fq(R)1786 1261 y Ft(j)t Fk(\000)p Fp(3)1996 1302 y Fs(=)83 b Fq(T)2212 1317 y Fp(1)2274 1302 y Fs(+)22 b Fq(T)2429 1317 y Fp(2)2491 1302 y Fs(+)g Fq(T)2646 1317 y Fp(3)2708 1302 y Fs(+)g Fq(T)2863 1317 y Fp(4)2924 1302 y Fs(+)g Fq(T)3079 1317 y Fp(5)3119 1302 y Fq(;)642 1615 y Fo(\000)p Fs(2)p Fq(M)872 1509 y Fj(q)p 956 1509 V 956 1615 a Fq(\027)1010 1586 y Fp(2)1072 1615 y Fs(+)g Fq(Q)1247 1586 y Fp(2)1347 1507 y(3)1305 1532 y Fj(X)1304 1714 y Ft(j)t Fp(=1)1443 1615 y Fs(\002)1519 1630 y Fp(1)p Ft(i)1582 1615 y Fs(\()p Fq(\034)11 b Fs(\))p Fq(R)1786 1574 y Ft(j)t Fk(\000)p Fp(3)1996 1615 y Fs(=)83 b Fq(T)2212 1630 y Fp(6)2274 1615 y Fs(+)22 b Fq(T)2429 1630 y Fp(7)2469 1615 y Fq(:)1219 b Fs(\(18\))19 1960 y(F)-8 b(rom)25 b(these)k(relations)c(one)j(can)f (easily)f(sho)m(w)i(that)f(the)h(form)m(ulae)d(for)i(the)g(radiativ)m (e)f(tails)g(are)h(exactly)-128 2080 y(the)33 b(same)g(when)h(no)e (spin)h(is)f(considered.)19 2248 y(All)k(corresp)s(onding)i(terms)g(in) f(\(9)p (#equation.9) [[222 447 228 459] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h(and)g(\(15)p (#equation.15) [[265 447 277 459] [1 1 1 [3 3]] [0 0 1]] pdfm (\))g (coincide)f(exactly)i(and)f(there)h(is)e(only)h(one)g(additional)-128 2368 y(term)h Fq(\033)167 2383 y Ft(add)321 2368 y Fs(in)g(eq.)65 b(\(15)p (#equation.15) [[152 433 164 445] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)e(This)40 b(term)f(can)g(b)s(e)h(considered)g(as)g(c)m (haracterizing)f(the)h(qualit)m(y)e(of)h(the)h(soft)-128 2489 y(photon)k(appro)m(ximation)d(and)j(can)f(b)s(e)h(calculated)e (analytically)f(b)m(y)j(expanding)g(it)e(in)h(the)h(parameter)-128 2609 y Fq(\017)29 b Fs(=)e(2)p Fq(M)10 b(E)274 2562 y Ft(\015)268 2632 y(min)402 2609 y Fq(=Q)528 2573 y Fp(2)568 2609 y Fs(:)813 2931 y Fq(\033)868 2946 y Ft(add)983 2931 y Fs(\()p Fq(E)1099 2884 y Ft(\015)1093 2954 y(min)1226 2931 y Fs(\))28 b(=)f Fq(\017)1444 2864 y(\013)p 1444 2908 63 4 v 1446 3000 a(\031)1522 2931 y Fs(\026)-54 b Fq(\033)1572 2946 y Fp(0)1634 2931 y Fo(\000)23 b Fq(\017)1783 2864 y(\013)1846 2828 y Fp(3)1885 2864 y Fq(y)p 1783 2908 154 4 v 1802 3000 a(Q)1879 2971 y Fp(2)1946 2931 y Fs(\()p Fq(\016)2027 2946 y Ft(\034)2071 2931 y Fq(F)2134 2946 y Fp(1)2195 2931 y Fs(+)g Fq(\016)2337 2946 y Fp(22)2411 2931 y Fq(F)2474 2946 y Fp(2)2514 2931 y Fs(\))f(+)g Fq(O)s Fs(\()p Fq(\017)2827 2890 y Fp(2)2866 2931 y Fs(\))p Fq(;)784 b Fs(\(19\))-128 3150 y(where)39 b(\026)-54 b Fq(\033)209 3165 y Fp(0)282 3150 y Fs(is)32 b(obtained)g(in)g(terms)g (of)g(the)h(Born)g(cross)g(section)g Fq(\033)2308 3165 y Fp(0)2348 3150 y Fs(:)426 3585 y(\026)-54 b Fq(\033)476 3600 y Fp(0)544 3585 y Fs(=)27 b Fq(\033)702 3600 y Fp(0)759 3336 y Fj(8)759 3411 y(>)759 3436 y(>)759 3461 y(>)759 3486 y(<)759 3635 y(>)759 3660 y(>)759 3685 y(>)759 3710 y(:)874 3463 y Fq(F)937 3478 y Fp(1)1004 3463 y Fo(!)h Fq(J)1186 3478 y Fp(0)1225 3463 y Fq(x)1280 3422 y Fp(2)1330 3396 y Fq(@)5 b(F)1449 3411 y Fp(1)p 1330 3440 160 4 v 1353 3531 a Fq(@)g(x)1521 3463 y Fo(\000)23 b Fq(\016)1664 3478 y Ft(\034)1707 3342 y Fj(\022)1769 3463 y Fo(\000)p Fs(2)p Fq(F)1958 3478 y Fp(1)2020 3463 y Fs(+)f Fq(x)2183 3396 y(@)5 b(F)2302 3411 y Fp(1)p 2183 3440 V 2206 3531 a Fq(@)g(x)2375 3463 y Fs(+)22 b Fq(Q)2550 3422 y Fp(2)2606 3396 y Fq(@)5 b(F)2725 3411 y Fp(1)p 2599 3440 174 4 v 2599 3531 a Fq(@)g(Q)2732 3502 y Fp(2)2783 3342 y Fj(\023)874 3707 y Fq(F)937 3722 y Fp(2)1004 3707 y Fo(!)28 b Fq(J)1186 3722 y Fp(0)1225 3585 y Fj(\022)1286 3707 y Fq(x)1341 3665 y Fp(2)1391 3639 y Fq(@)5 b(F)1510 3654 y Fp(1)p 1391 3683 160 4 v 1415 3775 a Fq(@)g(x)1583 3707 y Fs(+)22 b Fq(xF)1799 3722 y Fp(2)1839 3585 y Fj(\023)1922 3707 y Fo(\000)g Fq(\016)2064 3722 y Ft(\034)2108 3585 y Fj(\022)2169 3707 y Fo(\000)p Fs(2)p Fq(F)2358 3722 y Fp(2)2420 3707 y Fs(+)g Fq(x)2583 3639 y(@)5 b(F)2702 3654 y Fp(2)p 2583 3683 V 2607 3775 a Fq(@)g(x)2775 3707 y Fs(+)22 b Fq(Q)2950 3665 y Fp(2)3007 3639 y Fq(@)5 b(F)3126 3654 y Fp(2)p 3000 3683 174 4 v 3000 3775 a Fq(@)g(Q)3133 3746 y Fp(2)3183 3585 y Fj(\023)3244 3707 y Fq(:)3715 3585 y Fs(\(20\))-128 3926 y(The)34 b(quan)m(tities)e Fq(J)577 3941 y Fp(0)617 3926 y Fs(,)g Fq(\016)719 3941 y Ft(\034)763 3926 y Fs(,)g(and)h Fq(\016)1055 3941 y Fp(22)1162 3926 y Fs(dep)s(end)h(only)e(on)h(kinematical)d(v)-5 b(ariables:)408 4248 y Fq(\016)451 4263 y Ft(\034)522 4248 y Fs(=)693 4181 y Fq(xy)p 636 4225 222 4 v 636 4316 a Fs(1)21 b Fo(\000)i Fq(y)867 4127 y Fj(\022)928 4248 y Fs(1)f Fo(\000)h Fs(2)17 b(ln)1272 4181 y(2)p Fq(E)1399 4144 y Fk(0)p 1272 4225 151 4 v 1304 4316 a Fq(m)1432 4127 y Fj(\023)1515 4248 y Fo(\000)23 b Fq(xy)1722 4127 y Fj(\022)1783 4248 y Fs(1)f Fo(\000)g Fs(2)17 b(ln)2126 4181 y(2)p Fq(E)p 2126 4225 127 4 v 2147 4316 a(m)2263 4127 y Fj(\023)2324 4248 y Fq(;)212 b(J)2617 4263 y Fp(0)2684 4248 y Fs(=)28 b(2\(ln)2986 4181 y Fq(Q)3063 4144 y Fp(2)p 2982 4225 125 4 v 2982 4316 a Fq(m)3067 4288 y Fp(2)3139 4248 y Fo(\000)23 b Fs(1\))p Fq(;)990 4549 y(\016)1033 4564 y Fp(22)1136 4549 y Fs(=)28 b Fo(\000)p Fs(4)1376 4481 y(2)22 b Fo(\000)g Fq(y)p 1376 4525 222 4 v 1461 4617 a(y)1624 4549 y Fs(ln)o(\(1)g Fo(\000)h Fq(y)t Fs(\))e Fo(\000)i Fs(2)p Fq(J)2228 4564 y Fp(0)2289 4549 y Fo(\000)2398 4481 y Fs(4)p Fq(M)2551 4445 y Fp(2)2591 4481 y Fq(x)p 2398 4525 249 4 v 2464 4617 a(Q)2541 4588 y Fp(2)2657 4549 y Fq(\016)2700 4564 y Ft(\034)2743 4549 y Fq(:)3715 4394 y Fs(\(21\))-128 4773 y(The)37 b(\014rst)f(term)g(in)f(eq.\(19)p (#equation.19) [[167 144 179 156] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (corresp)s(onds)h(to)e(the)i(appro)m(ximation)c Fq(E)2522 4788 y Ft(\015)2600 4773 y Fs(=)g(0)j(in)f(argumen)m(ts)h(of)f (structure)-128 4894 y(functions)25 b(\(terms)g(with)f(deriv)-5 b(ativ)m(es\))25 b(and)g(the)g(photonic)f(propagator)g(\(terms)h (without)f(deriv)-5 b(ativ)m(e\).)40 b(The)-128 5014 y(second)h(term)f(in)f(eq.\(19)p (#equation.19) [[158 115 170 127] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (app)s(ears)g(when)g(the)h(appro)m(ximation)c(is)i(applied)g(to)g (kinematical)e(terms)j(lik)m(e)-128 5134 y Fq(T)-71 5149 y Fp(1)p Ft(::)p Fp(7)76 5134 y Fs(as)33 b(in)f(eq.\(12)p (#equation.12) [[128 101 140 113] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)19 5302 y(The)40 b(n)m(umerical)d(analysis)i(p)s(erformed)f(for)h(HERMES)h (kinematics)e(sho)m(ws)j(that)e(the)h(di\013erence)f(b)s(e-)-128 5422 y(t)m(w)m(een)34 b(b)s(oth)d(generators)h(in)e(the)i(unp)s (olarized)e(case)i(due)g(to)f(this)g(additional)e(con)m(tribution)h(is) h(negligible.)1856 5916 y(7)p eop %%Page: 8 8 8 7 bop 141 3307 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 4252 @rwi 4252 @rhi @setspecial %%BeginDocument: q2x.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 /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr newpath } 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 tlen def} 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 gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 3 lw 794 681 227 1247 bl 2268 2268 0 0 C 794 681 227 1247 C NC 1 lw 227 1247 m 681 Y s 249 1347 m -22 X s 238 1367 m -11 X s 238 1387 m -11 X s 238 1407 m -11 X s 238 1427 m -11 X s 249 1447 m -22 X s 238 1467 m -11 X s 238 1487 m -11 X s 238 1507 m -11 X s 238 1527 m -11 X s 249 1547 m -22 X s 238 1567 m -11 X s 238 1587 m -11 X s 238 1608 m -11 X s 238 1628 m -11 X s 249 1648 m -22 X s 238 1668 m -11 X s 238 1688 m -11 X s 238 1708 m -11 X s 238 1728 m -11 X s 249 1748 m -22 X s 238 1768 m -11 X s 238 1788 m -11 X s 238 1808 m -11 X s 238 1828 m -11 X s 249 1848 m -22 X s 249 1347 m -22 X s 238 1327 m -11 X s 238 1307 m -11 X s 238 1287 m -11 X s 238 1267 m -11 X s 249 1848 m -22 X s 238 1868 m -11 X s 238 1888 m -11 X s 238 1908 m -11 X s /xs 0 def (50) /Helvetica-Bold 43 stwn gsave 181 1331 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (50) show gr /xs 0 def (100) /Helvetica-Bold 43 stwn gsave 181 1432 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (100) show gr /xs 0 def (150) /Helvetica-Bold 43 stwn gsave 181 1532 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (150) show gr /xs 0 def (200) /Helvetica-Bold 43 stwn gsave 181 1632 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (200) show gr /xs 0 def (250) /Helvetica-Bold 43 stwn gsave 181 1732 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (250) show gr /xs 0 def (300) /Helvetica-Bold 43 stwn gsave 181 1832 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (300) show gr 227 1247 m 794 X s 227 1264 m -17 Y s 288 1264 m -17 Y s 331 1264 m -17 Y s 364 1264 m -17 Y s 391 1264 m -17 Y s 414 1264 m -17 Y s 434 1264 m -17 Y s 452 1264 m -17 Y s 468 1281 m -34 Y s /xs 0 def (10) /Helvetica-Bold 43 stwn gsave 452 1172 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (10) show gr /xs 0 def (-1) /Helvetica-Bold 35 stwn gsave 504 1204 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 35 sf 0 0 m (-1) show gr 572 1264 m -17 Y s 633 1264 m -17 Y s 676 1264 m -17 Y s 709 1264 m -17 Y s 736 1264 m -17 Y s 759 1264 m -17 Y s 779 1264 m -17 Y s 797 1264 m -17 Y s 813 1281 m -34 Y s /xs 0 def (1) /Helvetica-Bold 43 stwn gsave 813 1172 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1) show gr 917 1264 m -17 Y s 977 1264 m -17 Y s 1021 1264 m -17 Y s 794 681 227 1247 C 3 lw 123 1247 m 515 Y 295 X 93 Y 93 X -169 Y 57 X -134 Y 41 X -111 Y 33 X -57 Y 26 X -56 Y 23 X -36 Y 19 X -17 Y 18 X -11 Y 15 X -11 Y 14 X 1 Y 13 X -6 Y 12 X 2 Y 11 X -3 Y 20 X 53 Y 9 X -53 Y 154 X 18 Y 3 X -18 Y 3 X s 334 1727 m 24 Y s 334 1768 m 23 Y s /w 17 def /w2 {w 2 div} def /w3 {w 3 div} def 334 1759 m20 472 1814 m 26 Y s 472 1857 m 27 Y s 472 1849 m20 542 1646 m 20 Y s 542 1683 m 21 Y s 542 1675 m20 590 1517 m 15 Y s 590 1549 m 16 Y s 590 1541 m20 626 1430 m 12 Y s 626 1459 m 12 Y s 626 1451 m20 656 1370 m 9 Y s 656 1396 m 8 Y s 656 1387 m20 680 1313 m 4 Y s 680 1334 m 4 Y s 680 1325 m20 701 1290 m 1 Y s 701 1308 m 2 Y s 701 1300 m20 719 1272 m20 736 1264 m20 750 1257 m20 764 1249 m 3 Y s 764 1252 m 3 Y s 776 1247 m 1 Y s 776 1248 m 2 Y s 788 1247 m 1 Y s 788 1248 m 1 Y s 798 1247 m 1 Y s 808 1247 m 1 Y s 817 1287 m 1 Y s 817 1305 m 2 Y s 817 1297 m20 978 1263 m20 NC 794 681 1247 1247 bl 794 681 1247 1247 C NC 1 lw 1247 1247 m 681 Y s 1270 1315 m -23 X s 1259 1329 m -12 X s 1259 1343 m -12 X s 1259 1356 m -12 X s 1259 1370 m -12 X s 1270 1383 m -23 X s 1259 1397 m -12 X s 1259 1411 m -12 X s 1259 1424 m -12 X s 1259 1438 m -12 X s 1270 1452 m -23 X s 1259 1465 m -12 X s 1259 1479 m -12 X s 1259 1492 m -12 X s 1259 1506 m -12 X s 1270 1520 m -23 X s 1259 1533 m -12 X s 1259 1547 m -12 X s 1259 1560 m -12 X s 1259 1574 m -12 X s 1270 1588 m -23 X s 1259 1601 m -12 X s 1259 1615 m -12 X s 1259 1628 m -12 X s 1259 1642 m -12 X s 1270 1656 m -23 X s 1259 1669 m -12 X s 1259 1683 m -12 X s 1259 1696 m -12 X s 1259 1710 m -12 X s 1270 1724 m -23 X s 1259 1737 m -12 X s 1259 1751 m -12 X s 1259 1764 m -12 X s 1259 1778 m -12 X s 1270 1792 m -23 X s 1259 1805 m -12 X s 1259 1819 m -12 X s 1259 1833 m -12 X s 1259 1846 m -12 X s 1270 1860 m -23 X s 1259 1873 m -12 X s 1259 1887 m -12 X s 1259 1901 m -12 X s 1259 1914 m -12 X s 1270 1928 m -23 X s 1270 1315 m -23 X s 1259 1302 m -12 X s 1259 1288 m -12 X s 1259 1275 m -12 X s 1259 1261 m -12 X s /xs 0 def (25) /Helvetica-Bold 43 stwn gsave 1202 1300 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (25) show gr /xs 0 def (50) /Helvetica-Bold 43 stwn gsave 1202 1368 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (50) show gr /xs 0 def (75) /Helvetica-Bold 43 stwn gsave 1202 1436 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (75) show gr /xs 0 def (100) /Helvetica-Bold 43 stwn gsave 1202 1504 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (100) show gr /xs 0 def (125) /Helvetica-Bold 43 stwn gsave 1202 1572 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (125) show gr /xs 0 def (150) /Helvetica-Bold 43 stwn gsave 1202 1640 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (150) show gr /xs 0 def (175) /Helvetica-Bold 43 stwn gsave 1202 1708 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (175) show gr /xs 0 def (200) /Helvetica-Bold 43 stwn gsave 1202 1776 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (200) show gr /xs 0 def (225) /Helvetica-Bold 43 stwn gsave 1202 1844 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (225) show gr /xs 0 def (250) /Helvetica-Bold 43 stwn gsave 1202 1912 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (250) show gr 1247 1247 m 794 X s 1247 1281 m -34 Y s 1314 1264 m -17 Y s 1380 1264 m -17 Y s 1446 1264 m -17 Y s 1512 1281 m -34 Y s 1578 1264 m -17 Y s 1644 1264 m -17 Y s 1710 1264 m -17 Y s 1777 1281 m -34 Y s 1843 1264 m -17 Y s 1909 1264 m -17 Y s 1975 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 1247 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (2) /Helvetica-Bold 43 stwn gsave 1512 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (2) show gr /xs 0 def (4) /Helvetica-Bold 43 stwn gsave 1777 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (4) show gr /xs 0 def (6) /Helvetica-Bold 43 stwn gsave 2041 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (6) show gr 794 681 1247 1247 C 3 lw 1247 1247 m 71 Y 40 X -12 Y 79 X 386 Y 40 X 119 Y 40 X -98 Y 40 X -152 Y 39 X -57 Y 40 X -52 Y 40 X -48 Y 39 X -44 Y 40 X -10 Y 40 X -14 Y 39 X -23 Y 40 X -10 Y 40 X -9 Y 39 X -3 Y 40 X -12 Y 40 X -2 Y 40 X -6 Y 39 X -24 Y s 1267 1318 m 4 Y s 1267 1345 m 4 Y s /w 23 def /w2 {w 2 div} def /w3 {w 3 div} def 1267 1334 m20 1307 1288 m 1 Y s 1307 1311 m 1 Y s 1307 1300 m20 1347 1288 m 1 Y s 1347 1311 m 1 Y s 1347 1300 m20 1386 1667 m 24 Y s 1386 1714 m 24 Y s 1386 1702 m20 1426 1762 m 28 Y s 1426 1812 m 28 Y s 1426 1801 m20 1466 1608 m 21 Y s 1466 1652 m 21 Y s 1466 1640 m20 1505 1562 m 19 Y s 1505 1604 m 19 Y s 1505 1593 m20 1545 1489 m 15 Y s 1545 1527 m 16 Y s 1545 1516 m20 1585 1439 m 13 Y s 1585 1475 m 13 Y s 1585 1463 m20 1624 1390 m 10 Y s 1624 1422 m 10 Y s 1624 1411 m20 1664 1342 m 7 Y s 1664 1371 m 6 Y s 1664 1360 m20 1704 1323 m 5 Y s 1704 1350 m 5 Y s 1704 1339 m20 1744 1319 m 4 Y s 1744 1346 m 4 Y s 1744 1334 m20 1783 1297 m 2 Y s 1783 1322 m 1 Y s 1783 1310 m20 1823 1289 m 1 Y s 1823 1312 m 1 Y s 1823 1301 m20 1863 1286 m 1 Y s 1863 1309 m 1 Y s 1863 1298 m20 1902 1286 m20 1942 1280 m20 1982 1277 m20 2021 1272 m20 NC 794 681 227 340 bl 2268 2268 0 0 C 794 681 227 340 C NC 1 lw 227 340 m 681 Y s 249 440 m -22 X s 238 460 m -11 X s 238 480 m -11 X s 238 500 m -11 X s 238 520 m -11 X s 249 540 m -22 X s 238 560 m -11 X s 238 580 m -11 X s 238 600 m -11 X s 238 620 m -11 X s 249 640 m -22 X s 238 660 m -11 X s 238 680 m -11 X s 238 700 m -11 X s 238 720 m -11 X s 249 740 m -22 X s 238 760 m -11 X s 238 780 m -11 X s 238 800 m -11 X s 238 820 m -11 X s 249 840 m -22 X s 238 860 m -11 X s 238 880 m -11 X s 238 900 m -11 X s 238 921 m -11 X s 249 941 m -22 X s 249 440 m -22 X s 238 420 m -11 X s 238 400 m -11 X s 238 380 m -11 X s 238 360 m -11 X s 249 941 m -22 X s 238 961 m -11 X s 238 981 m -11 X s 238 1001 m -11 X s /xs 0 def (50) /Helvetica-Bold 43 stwn gsave 181 424 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (50) show gr /xs 0 def (100) /Helvetica-Bold 43 stwn gsave 181 524 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (100) show gr /xs 0 def (150) /Helvetica-Bold 43 stwn gsave 181 624 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (150) show gr /xs 0 def (200) /Helvetica-Bold 43 stwn gsave 181 724 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (200) show gr /xs 0 def (250) /Helvetica-Bold 43 stwn gsave 181 825 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (250) show gr /xs 0 def (300) /Helvetica-Bold 43 stwn gsave 181 925 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (300) show gr 227 340 m 794 X s 227 357 m -17 Y s 288 357 m -17 Y s 331 357 m -17 Y s 364 357 m -17 Y s 391 357 m -17 Y s 414 357 m -17 Y s 434 357 m -17 Y s 452 357 m -17 Y s 468 374 m -34 Y s /xs 0 def (10) /Helvetica-Bold 43 stwn gsave 452 265 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (10) show gr /xs 0 def (-1) /Helvetica-Bold 35 stwn gsave 504 297 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 35 sf 0 0 m (-1) show gr 572 357 m -17 Y s 633 357 m -17 Y s 676 357 m -17 Y s 709 357 m -17 Y s 736 357 m -17 Y s 759 357 m -17 Y s 779 357 m -17 Y s 797 357 m -17 Y s 813 374 m -34 Y s /xs 0 def (1) /Helvetica-Bold 43 stwn gsave 813 265 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1) show gr 917 357 m -17 Y s 977 357 m -17 Y s 1021 357 m -17 Y s 794 681 227 340 C 3 lw 123 340 m 528 Y 295 X 58 Y 93 X -200 Y 57 X -92 Y 41 X -90 Y 33 X -61 Y 26 X -64 Y 23 X -31 Y 19 X -20 Y 18 X -12 Y 15 X -7 Y 14 X -5 Y 13 X -1 Y 12 X -2 Y 11 X -1 Y 20 X 53 Y 9 X -53 Y 154 X 16 Y 3 X -16 Y 3 X s 334 868 m 25 Y s 334 910 m 25 Y s /w 17 def /w2 {w 2 div} def /w3 {w 3 div} def 334 902 m20 472 921 m 27 Y s 472 965 m 27 Y s 472 956 m20 542 762 m 21 Y s 542 800 m 22 Y s 542 792 m20 590 618 m 16 Y s 590 651 m 16 Y s 590 643 m20 626 528 m 12 Y s 626 557 m 12 Y s 626 549 m20 656 449 m 8 Y s 656 474 m 7 Y s 656 465 m20 680 410 m 4 Y s 680 431 m 4 Y s 680 422 m20 701 383 m 2 Y s 701 402 m 2 Y s 701 394 m20 719 372 m20 736 358 m20 750 351 m20 764 341 m 3 Y s 764 344 m 2 Y s 776 340 m 1 Y s 776 341 m 2 Y s 788 340 m s 788 340 m 1 Y s 798 340 m 1 Y s 817 384 m 2 Y s 817 403 m 1 Y s 817 394 m20 978 353 m20 NC 794 681 1247 340 bl 794 681 1247 340 C NC 1 lw 1247 340 m 681 Y s 1270 408 m -23 X s 1259 422 m -12 X s 1259 435 m -12 X s 1259 449 m -12 X s 1259 463 m -12 X s 1270 476 m -23 X s 1259 490 m -12 X s 1259 503 m -12 X s 1259 517 m -12 X s 1259 531 m -12 X s 1270 544 m -23 X s 1259 558 m -12 X s 1259 572 m -12 X s 1259 585 m -12 X s 1259 599 m -12 X s 1270 612 m -23 X s 1259 626 m -12 X s 1259 640 m -12 X s 1259 653 m -12 X s 1259 667 m -12 X s 1270 680 m -23 X s 1259 694 m -12 X s 1259 708 m -12 X s 1259 721 m -12 X s 1259 735 m -12 X s 1270 748 m -23 X s 1259 762 m -12 X s 1259 776 m -12 X s 1259 789 m -12 X s 1259 803 m -12 X s 1270 816 m -23 X s 1259 830 m -12 X s 1259 844 m -12 X s 1259 857 m -12 X s 1259 871 m -12 X s 1270 885 m -23 X s 1259 898 m -12 X s 1259 912 m -12 X s 1259 925 m -12 X s 1259 939 m -12 X s 1270 953 m -23 X s 1259 966 m -12 X s 1259 980 m -12 X s 1259 993 m -12 X s 1259 1007 m -12 X s 1270 1021 m -23 X s 1270 408 m -23 X s 1259 395 m -12 X s 1259 381 m -12 X s 1259 367 m -12 X s 1259 354 m -12 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image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr newpath } 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 tlen def} 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 gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 3 lw 794 681 227 1247 bl 794 681 227 1247 C 227 1247 m 8 X 1 Y 16 X 1 Y 8 X 1 Y 15 X 3 Y 16 X -1 Y 8 X 6 Y 8 X 5 Y 8 X 2 Y 8 X 1 Y 8 X 11 Y 8 X 19 Y 8 X 80 Y 8 X 484 Y 8 X -466 Y 8 X -75 Y 8 X -27 Y 8 X -4 Y 7 X -10 Y 8 X -7 Y 8 X -4 Y 8 X -1 Y 8 X -2 Y 16 X 3 Y 8 X -5 Y 8 X -4 Y 8 X -1 Y 8 X 5 Y 8 X -5 Y 8 X 4 Y 8 X -4 Y 8 X 3 Y 8 X -2 Y 15 X -2 Y 8 X -1 Y 16 X -1 Y 8 X 2 Y 8 X -1 Y 8 X 3 Y 8 X -3 Y 8 X 1 Y 8 X 1 Y 16 X 1 Y 8 X -4 Y 8 X 2 Y 8 X -1 Y 15 X 3 Y 8 X -3 Y 8 X -4 Y 8 X 6 Y 8 X -1 Y 8 X -4 Y 8 X 3 Y 8 X 2 Y 8 X -3 Y 8 X 1 Y 8 X 2 Y 8 X 2 Y 8 X -4 Y 8 X 3 Y 8 X -4 Y 8 X 2 Y 7 X -1 Y 8 X 4 Y 8 X -3 Y 8 X 2 Y 8 X 4 Y 8 X -3 Y 8 X 4 Y 8 X 5 Y 8 X 4 Y 8 X 9 Y 8 X 16 Y 8 X 36 Y 8 X 50 Y 8 X -50 Y 8 X -44 Y 8 X -18 Y 7 X -3 Y 8 X -8 Y 8 X -3 Y 16 X -5 Y 8 X 2 Y 8 X -4 Y 24 X -1 Y 8 X 1 Y 8 X 1 Y 8 X 1 Y 16 X -5 Y s NC 1 lw 227 1247 m 681 Y s 261 1247 m -34 X s 244 1267 m -17 X s 244 1286 m -17 X s 244 1305 m -17 X s 261 1324 m -34 X s 244 1343 m -17 X s 244 1362 m -17 X s 244 1381 m -17 X s 261 1400 m -34 X s 244 1420 m -17 X s 244 1439 m -17 X s 244 1458 m -17 X s 261 1477 m -34 X s 244 1496 m -17 X s 244 1515 m -17 X s 244 1534 m -17 X s 261 1554 m -34 X s 244 1573 m -17 X s 244 1592 m -17 X s 244 1611 m -17 X s 261 1630 m -34 X s 244 1649 m -17 X s 244 1668 m -17 X s 244 1688 m -17 X s 261 1707 m -34 X s 244 1726 m -17 X s 244 1745 m -17 X s 244 1764 m -17 X s 261 1783 m -34 X s 244 1802 m -17 X s 244 1821 m -17 X s 244 1841 m -17 X s 261 1860 m -34 X s 261 1860 m -34 X s 244 1879 m -17 X s 244 1898 m -17 X s 244 1917 m -17 X s /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 181 1232 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (200) /Helvetica-Bold 43 stwn gsave 181 1308 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (200) show gr /xs 0 def (400) /Helvetica-Bold 43 stwn gsave 181 1385 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (400) show gr /xs 0 def (600) /Helvetica-Bold 43 stwn gsave 181 1461 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (600) show gr /xs 0 def (800) /Helvetica-Bold 43 stwn gsave 181 1538 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (800) show gr /xs 0 def (1000) /Helvetica-Bold 43 stwn gsave 181 1614 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1000) show gr /xs 0 def (1200) /Helvetica-Bold 43 stwn gsave 181 1691 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1200) show gr /xs 0 def (1400) /Helvetica-Bold 43 stwn gsave 181 1767 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1400) show gr /xs 0 def (1600) /Helvetica-Bold 43 stwn gsave 181 1844 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1600) show gr 227 1247 m 794 X s 227 1281 m -34 Y s 259 1264 m -17 Y s 290 1264 m -17 Y s 322 1264 m -17 Y s 354 1264 m -17 Y s 386 1281 m -34 Y s 417 1264 m -17 Y s 449 1264 m -17 Y s 481 1264 m -17 Y s 513 1264 m -17 Y s 544 1281 m -34 Y s 576 1264 m -17 Y s 608 1264 m -17 Y s 640 1264 m -17 Y s 671 1264 m -17 Y s 703 1281 m -34 Y s 735 1264 m -17 Y s 767 1264 m -17 Y s 798 1264 m -17 Y s 830 1264 m -17 Y s 862 1281 m -34 Y s 894 1264 m -17 Y s 925 1264 m -17 Y s 957 1264 m -17 Y s 989 1264 m -17 Y s 1021 1281 m -34 Y s /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 227 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (0.005) /Helvetica-Bold 43 stwn gsave 386 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.005) show gr /xs 0 def (0.01) /Helvetica-Bold 43 stwn gsave 544 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.01) show gr /xs 0 def (0.015) /Helvetica-Bold 43 stwn gsave 703 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.015) show gr /xs 0 def (0.02) /Helvetica-Bold 43 stwn gsave 862 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.02) show gr /xs 0 def (0.025) /Helvetica-Bold 43 stwn gsave 1021 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.025) show gr 794 681 227 1247 C NC 3 lw 794 681 1247 1247 bl 794 681 1247 1247 C 1247 1247 m 1 Y 8 X 4 Y 16 X -2 Y 16 X 2 Y 8 X -1 Y 8 X -1 Y 8 X 1 Y 16 X 3 Y 8 X 2 Y 16 X -6 Y 8 X 4 Y 7 X -1 Y 8 X 2 Y 8 X -2 Y 16 X 1 Y 8 X -5 Y 8 X 2 Y 8 X 5 Y 8 X -1 Y 8 X -2 Y 8 X 7 Y 8 X -1 Y 8 X -2 Y 8 X -1 Y 8 X 3 Y 8 X 5 Y 7 X 1 Y 8 X -2 Y 8 X -3 Y 8 X -5 Y 8 X 11 Y 8 X 8 Y 8 X 1 Y 16 X 2 Y 8 X -8 Y 8 X 20 Y 8 X 2 Y 8 X 13 Y 8 X 4 Y 8 X 5 Y 8 X 24 Y 7 X 48 Y 8 X 114 Y 8 X 361 Y 8 X -18 Y 8 X -367 Y 8 X -95 Y 8 X -40 Y 8 X -27 Y 8 X -3 Y 8 X -19 Y 8 X -4 Y 8 X -3 Y 8 X 5 Y 8 X -14 Y 8 X 1 Y 8 X -11 Y 7 X 3 Y 8 X 7 Y 8 X -17 Y 8 X 4 Y 8 X 4 Y 16 X 3 Y 8 X -9 Y 16 X -5 Y 8 X 5 Y 8 X -2 Y 8 X 3 Y 8 X -6 Y 24 X 2 Y 7 X 1 Y 8 X -5 Y 24 X 1 Y 8 X 1 Y 8 X -4 Y 8 X 2 Y 8 X 1 Y 16 X -1 Y 8 X -2 Y 8 X -3 Y 8 X 6 Y 8 X -2 Y 8 X -2 Y 7 X 2 Y 8 X 1 Y 8 X -1 Y 8 X -3 Y 8 X -2 Y s NC 1 lw 1247 1247 m 681 Y s 1281 1247 m -34 X s 1264 1276 m -17 X s 1264 1305 m -17 X s 1264 1334 m -17 X s 1281 1363 m -34 X s 1264 1392 m -17 X s 1264 1420 m -17 X s 1264 1449 m -17 X s 1281 1478 m -34 X s 1264 1507 m -17 X s 1264 1536 m -17 X s 1264 1565 m -17 X s 1281 1593 m -34 X s 1264 1622 m -17 X s 1264 1651 m -17 X s 1264 1680 m -17 X s 1281 1709 m -34 X s 1264 1738 m -17 X s 1264 1766 m -17 X s 1264 1795 m -17 X s 1281 1824 m -34 X s 1281 1824 m -34 X s 1264 1853 m -17 X s 1264 1882 m -17 X s 1264 1911 m -17 X s /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 1202 1232 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (200) /Helvetica-Bold 43 stwn gsave 1202 1347 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (200) show gr /xs 0 def (400) /Helvetica-Bold 43 stwn gsave 1202 1462 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (400) show gr /xs 0 def (600) /Helvetica-Bold 43 stwn gsave 1202 1577 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (600) show gr /xs 0 def (800) /Helvetica-Bold 43 stwn gsave 1202 1693 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (800) show gr /xs 0 def (1000) /Helvetica-Bold 43 stwn gsave 1202 1808 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1000) show gr 1247 1247 m 794 X s 1247 1281 m -34 Y s 1287 1264 m -17 Y s 1327 1264 m -17 Y s 1366 1264 m -17 Y s 1406 1264 m -17 Y s 1446 1281 m -34 Y s 1486 1264 m -17 Y s 1525 1264 m -17 Y s 1565 1264 m -17 Y s 1605 1264 m -17 Y s 1644 1281 m -34 Y s 1684 1264 m -17 Y s 1724 1264 m -17 Y s 1763 1264 m -17 Y s 1803 1264 m -17 Y s 1843 1281 m -34 Y s 1882 1264 m -17 Y s 1922 1264 m -17 Y s 1962 1264 m -17 Y s 2002 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (-1) /Helvetica-Bold 43 stwn gsave 1247 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (-1) show gr /xs 0 def (-0.5) /Helvetica-Bold 43 stwn gsave 1446 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (-0.5) show gr /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 1644 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (0.5) /Helvetica-Bold 43 stwn gsave 1843 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.5) show gr /xs 0 def (1) /Helvetica-Bold 43 stwn gsave 2041 1193 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1) show gr 794 681 1247 1247 C NC 3 lw 794 681 227 340 bl 794 681 227 340 C 227 340 m 402 Y 8 X -228 Y 8 X -72 Y 8 X -17 Y 8 X -25 Y 7 X -19 Y 8 X 4 Y 8 X 2 Y 8 X -6 Y 8 X -17 Y 8 X 10 Y 8 X -10 Y 8 X 2 Y 8 X 9 Y 8 X -11 Y 8 X 2 Y 8 X -2 Y 8 X -8 Y 8 X 4 Y 8 X -3 Y 8 X 4 Y 7 X -4 Y 8 X -4 Y 8 X 1 Y 8 X 7 Y 8 X -9 Y 8 X 2 Y 8 X 1 Y 8 X -1 Y 8 X -3 Y 8 X 2 Y 8 X -1 Y 8 X 3 Y 8 X -2 Y 8 X 2 Y 16 X 3 Y 8 X -2 Y 7 X -3 Y 8 X -5 Y 8 X 7 Y 8 X -2 Y 8 X -4 Y 8 X 6 Y 24 X 3 Y 16 X -2 Y 8 X 3 Y 8 X -1 Y 8 X -5 Y 8 X 6 Y 15 X -2 Y 8 X 9 Y 8 X -5 Y 8 X -4 Y 8 X 4 Y 8 X -6 Y 8 X 7 Y 8 X 4 Y 8 X 7 Y 8 X -13 Y 8 X 4 Y 8 X 14 Y 8 X -8 Y 16 X 13 Y 15 X 4 Y 8 X 11 Y 16 X 25 Y 8 X -9 Y 8 X 32 Y 8 X 6 Y 8 X 41 Y 8 X 87 Y 8 X 220 Y 8 X 153 Y 8 X -613 Y 151 X s NC 1 lw 227 340 m 681 Y s 261 340 m -34 X s 244 373 m -17 X s 244 406 m -17 X s 244 438 m -17 X s 261 471 m -34 X s 244 504 m -17 X s 244 537 m -17 X s 244 569 m -17 X s 261 602 m -34 X s 244 635 m -17 X s 244 668 m -17 X s 244 700 m -17 X s 261 733 m -34 X s 244 766 m -17 X s 244 799 m -17 X s 244 831 m -17 X s 261 864 m -34 X s 244 897 m -17 X s 244 930 m -17 X s 244 962 m -17 X s 261 995 m -34 X s 261 995 m -34 X s /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 181 324 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (200) /Helvetica-Bold 43 stwn gsave 181 455 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (200) show gr /xs 0 def (400) /Helvetica-Bold 43 stwn gsave 181 586 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (400) show gr /xs 0 def (600) /Helvetica-Bold 43 stwn gsave 181 717 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (600) show gr /xs 0 def (800) /Helvetica-Bold 43 stwn gsave 181 848 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (800) show gr /xs 0 def (1000) /Helvetica-Bold 43 stwn gsave 181 979 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (1000) show gr 227 340 m 794 X s 519 374 m -34 Y s 578 357 m -17 Y s 637 357 m -17 Y s 696 357 m -17 Y s 755 357 m -17 Y s 814 374 m -34 Y s 519 374 m -34 Y s 460 357 m -17 Y s 401 357 m -17 Y s 342 357 m -17 Y s 283 357 m -17 Y s 814 374 m -34 Y s 873 357 m -17 Y s 932 357 m -17 Y s 991 357 m -17 Y s /xs 0 def (10) /Helvetica-Bold 43 stwn gsave 519 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (10) show gr /xs 0 def (20) /Helvetica-Bold 43 stwn gsave 814 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (20) show gr 794 681 227 340 C NC 3 lw 794 681 1247 340 bl 794 681 1247 340 C /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 1372 353 1272 365 1260 373 1740 373 1803 374 2021 371 1467 388 1487 387 1511 386 1632 388 1678 381 1803 385 1856 386 1943 382 1338 394 1407 394 1591 391 1702 388 1710 390 1724 394 1788 392 1995 391 1273 397 1335 397 1475 397 1666 401 1708 396 1882 397 1288 401 1327 402 1414 403 1491 402 1531 406 1544 406 1550 405 1571 407 1627 406 1682 404 1719 403 1740 406 1823 404 1836 405 1849 406 1881 408 1887 403 1954 406 1974 404 2037 405 1280 412 1319 414 1349 413 1374 411 1384 412 1406 413 1449 413 1455 409 1483 410 1505 414 1568 413 1579 414 1667 408 1688 413 1725 412 1738 414 1746 411 1753 411 1800 414 1826 411 1843 409 1865 412 1990 410 1351 416 1359 419 1398 420 1408 416 1432 415 1438 415 1454 420 1458 416 1510 420 1538 416 1587 415 1611 422 1617 416 1634 419 1642 418 1657 416 1663 420 1732 416 1780 417 1810 416 1827 421 1912 415 1914 418 1959 419 1970 419 1980 416 1998 419 2012 417 2018 418 100 { m20} R 1324 424 1351 427 1403 428 1411 428 1424 427 1437 426 1464 428 1481 427 1521 426 1540 424 1561 424 1578 425 1584 427 1596 427 1604 422 1606 426 1628 425 1637 422 1660 429 1707 427 1722 423 1732 428 1751 428 1791 423 1879 428 1903 427 1913 429 1918 428 1982 422 1991 427 1995 426 1322 433 1355 433 1403 435 1409 435 1424 430 1444 430 1451 430 1454 430 1465 431 1470 433 1486 435 1521 429 1526 429 1545 434 1552 431 1562 430 1567 429 1576 435 1586 435 1595 431 1602 433 1620 435 1627 435 1635 431 1651 429 1659 433 1662 430 1672 430 1688 432 1698 430 1704 434 1712 431 1722 435 1731 430 1754 434 1761 429 1769 434 1773 431 1812 431 1819 433 1830 433 1858 430 1869 431 1878 430 1963 432 1975 434 2012 435 2032 432 1289 440 1355 440 1369 438 1387 440 1429 439 1444 438 1451 436 1454 441 1467 437 1474 437 1484 439 1502 441 1513 442 1520 438 1532 438 1536 436 1543 441 1560 436 1571 438 1575 436 1584 440 100 { m20} R 1598 438 1607 437 1618 438 1626 442 1632 441 1643 440 1648 441 1657 437 1666 439 1676 441 1684 442 1688 441 1698 437 1707 440 1718 436 1727 442 1733 437 1746 439 1755 441 1761 435 1766 439 1775 438 1780 436 1793 436 1800 436 1821 436 1834 440 1854 437 1860 440 1872 438 1898 440 1921 440 1923 439 1937 439 1972 442 2036 436 1276 444 1290 444 1323 448 1329 443 1339 446 1361 444 1388 448 1394 448 1434 445 1445 444 1449 447 1457 445 1464 445 1476 443 1481 447 1498 443 1507 445 1510 443 1525 448 1528 444 1540 449 1544 448 1551 446 1561 449 1565 443 1580 447 1585 446 1586 447 1594 444 1596 446 1600 446 1602 442 1610 446 1614 449 1617 444 1620 445 1628 444 1625 444 1635 445 1633 448 1631 448 1638 446 1637 443 1644 444 1647 446 1652 442 1648 447 1652 443 1657 449 1658 445 1654 444 1666 445 1665 444 1666 444 1673 445 1671 448 1669 446 1682 444 1681 446 1687 446 1688 448 1692 443 1694 448 1705 449 100 { m20} R 1707 444 1714 448 1722 444 1727 444 1738 444 1753 444 1762 446 1766 444 1776 444 1783 447 1792 444 1803 448 1812 446 1824 448 1841 444 1848 444 1855 443 1869 443 1879 443 1885 443 1914 444 2001 443 1289 454 1302 453 1305 450 1313 454 1320 453 1339 452 1423 453 1432 449 1440 455 1451 456 1466 456 1484 451 1486 453 1498 455 1508 451 1516 452 1520 452 1526 451 1540 452 1545 451 1551 453 1562 453 1573 451 1567 449 1576 455 1582 452 1583 454 1596 452 1591 455 1599 449 1599 453 1602 450 1604 452 1612 456 1608 450 1611 450 1611 449 1610 450 1614 454 1617 453 1620 452 1618 455 1618 449 1618 450 1616 452 1614 452 1628 454 1623 455 1622 450 1623 451 1624 455 1621 452 1623 451 1628 449 1627 453 1621 449 1622 455 1623 449 1626 454 1624 451 1629 455 1635 454 1629 454 1633 456 1630 455 1633 455 1633 454 1633 450 1632 456 1632 452 1630 455 1633 452 1633 452 1629 456 1633 455 1636 452 1629 455 1636 450 100 { m20} R 1635 450 1636 449 1635 449 1631 452 1636 452 1643 453 1637 453 1644 452 1644 451 1640 452 1637 453 1642 453 1638 451 1643 449 1640 455 1641 450 1641 452 1637 452 1644 455 1642 456 1642 450 1642 454 1642 449 1638 451 1643 456 1638 455 1641 454 1643 450 1641 455 1644 453 1642 453 1642 456 1641 450 1637 456 1644 450 1642 450 1642 453 1641 450 1643 455 1642 451 1638 449 1643 452 1643 451 1637 453 1643 456 1639 452 1642 450 1640 453 1636 456 1637 450 1640 449 1637 450 1642 452 1642 455 1639 456 55 { m20} R 1650 454 1648 453 1647 453 1648 450 1647 451 1650 453 1646 452 1649 455 1647 451 1651 452 1650 456 1647 452 1650 453 1646 451 1645 452 1650 451 1647 456 1650 454 1649 455 1648 453 1652 453 1645 449 1649 449 1649 450 1652 455 1651 451 1652 456 1651 455 1651 449 1650 455 1649 450 1647 453 1648 452 1652 455 1652 454 1648 453 1649 454 1646 452 1647 450 1649 454 1649 449 1649 452 1645 451 1648 450 1651 451 1652 450 1660 454 1653 456 1658 455 1657 451 1660 455 1659 454 1653 450 1657 451 1659 452 1657 453 1656 454 1655 453 1655 452 1653 449 1659 453 1656 454 1657 453 1654 453 1659 453 1657 451 1659 450 1660 449 1660 452 1662 455 1665 455 1668 456 1663 453 1664 454 1661 456 1660 452 1665 450 1664 454 1660 452 1662 451 1661 452 1660 452 1672 451 1676 450 1670 455 1670 453 1676 451 1670 456 1669 454 1675 454 1676 452 1681 451 1676 453 1684 450 1677 455 1691 453 1689 449 1686 449 1698 455 1696 451 100 { m20} R 1695 451 1701 450 1706 454 1711 454 1710 455 1719 455 1731 452 1737 452 1735 454 1740 455 1755 455 1759 453 1767 450 1779 455 1782 450 1791 451 1804 450 1825 450 1874 456 1890 454 1892 453 1936 456 1950 454 1957 450 1972 453 1988 451 2012 449 2034 454 1250 460 1266 460 1301 462 1329 457 1368 458 1383 456 1400 460 1408 456 1416 458 1425 459 1437 461 1439 458 1458 458 1464 458 1483 459 1492 456 1499 458 1506 460 1510 458 1521 458 1526 460 1539 460 1548 458 1543 458 1550 462 1559 458 1567 461 1577 457 1576 460 1583 458 1592 461 1594 458 1599 457 1608 456 1609 457 1620 460 1616 461 1615 461 1623 461 1623 461 1628 463 1636 462 1635 458 1635 456 1641 456 1641 460 1642 459 1643 462 1645 458 1651 459 1652 456 1659 460 1654 461 1659 456 1657 462 1666 457 1662 458 1667 461 1670 460 1671 457 1673 459 1683 459 1680 456 1686 459 1686 460 1693 462 1692 461 1705 460 1703 460 1714 461 1721 458 1721 456 100 { m20} R 1727 462 1732 457 1740 458 1753 462 1762 458 1766 458 1778 457 1785 459 1792 460 1803 457 1805 462 1822 462 1834 457 1858 459 1876 458 1898 456 1919 460 1928 459 1936 461 1953 460 1967 461 1971 462 1979 461 2007 460 2039 457 1264 465 1327 466 1342 469 1345 467 1351 466 1388 465 1393 468 1416 466 1427 465 1450 468 1455 469 1484 465 1502 466 1532 463 1547 468 1551 467 1564 466 1569 464 1581 464 1588 464 1593 468 1602 469 1607 464 1611 465 1615 466 1624 469 1622 465 1632 465 1644 468 1647 466 1658 468 1663 465 1675 468 1681 465 1685 465 1693 464 1701 466 1708 469 1710 463 1718 467 1726 465 1735 464 1747 465 1755 466 1757 466 1768 466 1771 466 1780 468 1794 465 1795 467 1816 463 1827 468 1839 468 1850 467 1862 465 1882 464 1930 468 1947 469 1958 467 1969 463 1250 473 1266 472 1272 474 1299 471 1319 473 1322 473 1332 476 1361 471 1368 470 1382 470 1419 476 1433 473 1447 474 1469 473 1475 470 100 { m20} R 1482 476 1496 471 1506 474 1517 473 1527 473 1540 473 1542 474 1550 475 1563 470 1577 473 1588 476 1595 475 1600 475 1612 474 1622 473 1629 473 1637 474 1646 476 1656 470 1666 476 1675 475 1677 476 1687 474 1716 472 1730 474 1736 474 1741 470 1750 471 1766 473 1778 474 1779 471 1787 473 1804 470 1816 472 1824 470 1834 470 1840 470 1921 476 1931 473 1942 475 1953 474 1980 470 2024 472 1255 478 1276 482 1291 482 1338 479 1350 478 1372 482 1378 480 1414 480 1439 479 1453 482 1459 477 1464 482 1480 482 1501 481 1504 483 1517 483 1521 477 1532 481 1535 478 1548 479 1562 481 1566 477 1579 480 1585 477 1604 481 1609 477 1614 477 1633 482 1648 479 1660 478 1664 477 1672 480 1678 476 1688 477 1701 481 1710 477 1725 482 1739 480 1741 479 1748 480 1758 481 1765 478 1775 480 1781 478 1797 482 1809 478 1818 477 1827 481 1843 479 1849 477 1852 481 1864 478 1875 481 1906 479 1972 479 2001 482 2020 480 100 { m20} R 2039 482 1253 484 1260 484 1272 484 1421 485 1468 488 1493 484 1505 488 1523 483 1542 484 1561 487 1565 487 1593 487 1606 488 1619 490 1628 488 1631 484 1643 487 1651 487 1653 487 1664 486 1678 488 1689 486 1715 485 1740 490 1767 487 1775 483 1780 488 1788 484 1822 487 1833 489 1863 489 1870 488 1880 488 1904 489 1932 485 1939 485 1946 489 1987 488 2033 489 2037 486 1254 492 1292 494 1324 492 1346 493 1363 494 1444 494 1453 492 1485 491 1506 493 1510 497 1542 495 1552 491 1562 491 1568 493 1583 495 1607 493 1613 495 1624 497 1631 495 1675 495 1729 490 1752 494 1770 495 1776 491 1780 495 1790 493 1800 491 1814 495 1849 493 1875 495 1908 495 1954 496 1957 492 1972 494 1248 500 1300 498 1360 499 1398 500 1452 503 1456 500 1463 501 1516 499 1525 498 1545 500 1600 503 1627 501 1630 502 1640 503 1649 500 1680 499 1694 497 1721 499 1753 498 1789 497 1813 501 1846 501 1867 497 1888 499 99 { m20} R 1894 499 1925 499 1937 500 1944 497 1953 498 1347 505 1378 510 1407 507 1450 510 1493 507 1502 505 1530 506 1536 507 1543 508 1559 505 1572 508 1587 504 1614 508 1657 506 1670 504 1697 505 1733 505 1780 507 1803 506 1809 508 1812 506 1856 510 1901 509 1940 508 1952 506 1959 505 1987 504 2012 510 1262 514 1381 515 1424 511 1434 514 1499 516 1502 514 1515 511 1519 511 1529 512 1534 512 1542 517 1553 517 1558 517 1591 514 1613 517 1622 516 1679 514 1720 517 1735 511 1799 512 1806 514 1829 512 1866 511 1267 523 1283 524 1344 523 1483 519 1533 519 1556 518 1580 519 1598 518 1614 521 1647 522 1672 519 1679 521 1696 520 1727 521 1737 518 1745 524 1765 522 1787 518 1797 521 1815 519 1827 522 1839 518 1859 517 1957 518 1981 522 1290 524 1299 525 1331 528 1342 530 1357 526 1413 526 1449 530 1484 528 1487 528 1531 528 1565 528 1572 527 1586 531 1604 525 1613 530 1653 527 1666 528 1705 524 1726 530 100 { m20} R 1734 524 1749 530 1761 529 1801 530 1808 527 1855 530 1926 529 1932 524 1958 529 2011 525 1294 537 1300 532 1350 534 1409 534 1425 534 1473 535 1500 531 1527 533 1541 534 1569 531 1633 532 1650 533 1666 537 1732 533 1740 535 1757 534 1793 533 1875 537 1937 531 1941 536 1976 531 2016 536 2030 532 2035 536 1250 541 1273 541 1348 543 1366 541 1389 541 1425 539 1477 542 1481 543 1514 542 1523 538 1598 538 1625 542 1722 539 1733 541 1758 543 1775 538 1877 538 1894 542 1957 542 1274 548 1324 548 1356 549 1365 545 1418 545 1498 550 1532 549 1544 549 1551 548 1571 545 1684 550 1707 546 1716 549 1906 547 2010 549 2028 548 1272 555 1313 553 1345 555 1445 554 1469 552 1506 555 1537 556 1552 552 1589 556 1609 551 1681 552 1687 552 1696 555 1800 556 1861 558 1881 551 1929 555 1945 552 2005 551 2013 558 1262 558 1441 561 1513 562 1799 563 1811 563 1829 559 1858 562 1919 563 1935 559 1953 561 1992 564 100 { m20} R 1264 566 1335 571 1418 567 1423 571 1472 568 1535 571 1561 569 1602 566 1621 570 1645 570 1669 566 1708 570 1733 571 1762 571 1778 571 1796 566 1816 569 1845 570 1867 567 1939 570 1948 569 1477 578 1489 572 1537 572 1581 576 1589 575 1620 572 1657 577 1662 573 1672 573 1688 577 1723 573 1952 575 2039 574 1293 583 1367 580 1381 584 1412 579 1422 582 1464 581 1586 584 1594 583 1610 579 1613 581 1640 581 1704 581 1713 581 1733 583 1751 581 1774 580 1783 584 1815 579 1823 580 1915 579 1950 581 2019 584 1376 590 1504 590 1586 586 1659 591 1696 586 1730 586 1764 588 1819 586 1863 591 1913 589 1969 589 1974 587 1988 587 1337 597 1347 596 1352 595 1489 593 1519 595 1536 594 1581 592 1616 594 1629 592 1637 596 1647 595 1660 596 1662 594 1696 595 1702 596 1735 599 1742 598 1803 594 1810 593 1839 595 1870 598 1985 598 1380 602 1388 605 1414 604 1438 603 1461 602 1635 600 1729 603 1842 600 1848 605 100 { m20} R 1894 601 1328 610 1413 611 1463 607 1492 609 1500 608 1536 607 1569 606 1621 612 1665 606 1699 607 1731 612 1919 608 1259 614 1302 617 1353 615 1559 614 1569 618 1587 616 1645 616 1661 613 1676 615 1878 616 1900 614 1919 614 1980 618 1467 621 1485 625 1568 625 1603 626 1618 625 1705 620 1827 625 1835 624 1870 624 1939 623 1948 620 1959 622 1311 628 1541 628 1577 626 1603 631 1738 630 1795 627 1877 631 1887 630 1968 629 2027 633 1250 635 1453 634 1588 639 1589 635 1619 634 1738 638 1820 639 1829 638 1862 636 1882 639 1900 636 1922 640 1412 645 1425 644 1447 644 1476 643 1524 645 1560 645 1635 644 1683 644 1686 643 1769 642 1798 646 1938 646 1958 645 1981 640 1357 650 1443 650 1489 653 1516 648 1524 648 1554 651 1651 649 1696 650 1713 649 1717 648 1744 652 1814 651 1903 652 1343 657 1390 655 1481 657 1502 655 1569 658 1578 655 1638 655 1719 658 1743 653 1753 657 1778 660 1792 659 1869 655 100 { m20} R 1930 657 1259 663 1373 664 1501 660 1527 661 1702 662 1713 663 1748 661 1818 667 1849 665 1910 666 1927 665 1352 671 1384 668 1422 672 1515 672 1566 672 1585 670 1672 671 1678 669 1751 673 1786 671 1856 672 1876 672 1927 668 2012 671 1313 675 1434 677 1456 674 1541 680 1577 678 1592 677 1604 676 1612 679 1631 678 1663 679 1770 674 1772 677 1821 674 1844 675 1851 674 1388 683 1439 687 1482 685 1545 683 1551 684 1589 685 1622 681 1640 680 1715 687 1807 686 2027 685 1253 688 1356 691 1360 694 1411 692 1435 688 1506 692 1611 691 1673 693 1767 688 1773 693 1818 690 1897 690 1973 693 1250 696 1258 699 1467 696 1502 698 1604 701 1615 699 1726 694 1849 697 1868 696 1925 696 1957 699 1368 707 1483 701 1555 701 1739 707 1752 702 1931 704 1957 704 1284 708 1319 709 1351 710 1367 714 1433 711 1499 711 1532 708 1565 712 1586 714 1652 711 1686 710 1696 710 1721 713 1859 712 1873 714 1905 709 99 { m20} R 1347 718 1423 719 1448 720 1500 716 1600 720 1658 721 1696 720 1751 717 1762 716 1806 718 1878 715 1909 719 1939 719 2035 718 1516 725 1524 726 1602 723 1915 727 1949 723 1363 734 1400 732 1543 730 1590 732 1649 735 1653 732 1664 734 1688 732 1739 735 1783 733 2041 733 1315 741 1471 737 1479 740 1517 738 1542 736 1568 741 1610 740 1623 735 1654 737 1699 736 1705 738 1751 737 1824 736 1866 738 1902 740 1925 739 1460 747 1539 743 1551 746 1583 744 1644 743 1652 747 1855 748 1955 748 1401 749 1476 752 1542 752 1572 755 1634 750 1665 751 1680 749 1737 755 1745 749 1784 754 1790 755 1856 753 1956 749 1295 759 1423 756 1457 759 1484 761 1503 756 1553 756 1609 760 1615 759 1720 756 1763 760 1786 759 1793 760 1855 756 1908 756 1995 758 1462 768 1476 767 1525 762 1579 769 1616 764 1647 766 1716 766 1778 766 1844 765 1853 769 1869 768 1935 764 1465 773 1511 775 1552 770 1558 774 1584 775 1696 772 100 { m20} R 1740 769 1831 775 1838 769 1857 775 1883 770 1915 774 1942 774 1979 772 1305 782 1435 782 1510 782 1533 778 1564 782 1567 779 1588 780 1638 781 1647 781 1796 777 1814 782 1822 777 1858 782 1868 778 1983 776 2005 776 1357 784 1463 786 1533 786 1535 783 1555 787 1561 784 1576 788 1618 786 1656 788 1679 789 1753 782 1757 786 1766 783 1782 788 1790 784 1835 785 1847 783 1894 783 1905 788 1913 787 1962 789 1995 783 1430 793 1474 796 1502 795 1529 790 1564 796 1571 795 1581 790 1611 791 1617 795 1634 790 1660 796 1674 793 1680 795 1723 795 1733 792 1825 792 1970 795 1378 797 1426 800 1435 802 1462 803 1580 799 1603 797 1616 798 1627 797 1629 801 1639 799 1648 798 1680 796 1699 798 1729 801 1750 801 1823 803 1869 798 1889 796 2031 799 1327 810 1426 806 1444 810 1480 803 1608 808 1618 804 1665 803 1681 806 1686 807 1712 807 1770 806 1843 804 1868 803 1299 815 1320 815 1492 816 1532 812 1574 811 100 { m20} R 1606 815 1618 811 1628 811 1640 811 1659 813 1663 810 1682 810 1737 816 1777 815 1940 815 1340 821 1419 823 1472 823 1591 822 1611 823 1624 818 1646 820 1687 818 1708 823 1762 821 1927 820 1948 821 1257 828 1335 829 1353 824 1423 828 1434 829 1507 825 1539 826 1578 825 1585 825 1593 829 1601 826 1608 829 1650 827 1663 828 1672 828 1685 828 1694 826 1701 827 1718 828 1744 829 1310 832 1430 837 1446 832 1558 835 1573 833 1595 834 1650 834 1661 835 1674 830 1699 830 1745 832 1748 834 1832 833 1842 830 1868 832 1891 835 1413 839 1509 843 1519 842 1556 843 1593 838 1602 843 1606 839 1620 841 1624 842 1633 843 1649 842 1657 841 1666 842 1674 839 1679 838 1712 839 1751 841 1768 840 1919 843 1950 837 1309 847 1360 846 1449 850 1485 846 1510 844 1535 847 1557 846 1560 848 1580 848 1582 847 1596 845 1597 847 1622 847 1637 846 1651 844 1676 850 1686 845 1697 850 1701 849 1727 848 1746 846 1752 849 100 { m20} R 1760 850 1824 845 1834 846 1853 849 1373 856 1398 857 1427 851 1524 853 1538 854 1569 852 1602 855 1611 851 1617 853 1627 855 1658 856 1666 852 1669 855 1682 851 1691 854 1701 855 1715 856 1724 856 1772 855 1786 852 1791 854 1824 854 1829 856 1988 856 2019 852 1510 859 1567 860 1582 858 1603 862 1615 863 1623 858 1632 859 1650 857 1662 858 1674 860 1677 863 1690 862 1694 863 1723 864 1727 863 1799 863 1958 861 1431 867 1483 870 1494 866 1513 867 1548 870 1550 865 1587 867 1596 869 1609 871 1613 864 1625 866 1633 870 1650 865 1659 865 1667 864 1671 869 1680 869 1688 869 1705 868 1719 869 1730 866 1732 868 1740 868 1755 865 1764 867 1847 870 1864 866 1930 869 1544 877 1551 876 1560 872 1570 876 1579 875 1588 873 1594 872 1603 877 1605 877 1613 872 1627 877 1636 874 1638 874 1650 873 1660 876 1663 872 1670 875 1682 875 1691 874 1695 872 1706 873 1713 873 1719 871 1730 875 1738 874 1753 874 100 { m20} R 1770 871 1783 876 1795 875 1896 875 1373 884 1468 880 1564 881 1565 878 1600 880 1606 878 1616 880 1627 880 1626 879 1632 878 1642 882 1646 880 1650 881 1660 883 1667 881 1672 883 1683 879 1689 880 1702 880 1713 885 1718 883 1736 884 1757 884 1769 884 1792 882 1806 881 1400 886 1423 886 1494 891 1521 888 1539 889 1548 885 1557 888 1571 887 1576 888 1587 890 1596 890 1603 885 1608 889 1613 891 1622 887 1624 885 1635 885 1629 891 1636 886 1637 889 1640 885 1638 891 1647 888 1645 889 1653 889 1659 891 1664 889 1669 886 1673 890 1682 886 1687 889 1692 891 1705 885 1708 888 1728 885 1734 889 1744 887 1750 888 1769 888 1780 887 1803 888 1942 888 1263 897 1384 896 1522 893 1535 895 1548 895 1553 895 1563 893 1577 896 1596 893 1598 893 1610 895 1612 893 1617 893 1623 892 1623 897 1635 892 1631 892 1630 893 1630 894 1644 898 1638 896 1642 894 1643 895 1637 894 1641 897 1642 898 1643 893 99 { m20} R 1647 896 1649 897 1652 892 1647 895 1645 892 1645 892 1654 896 1653 892 1659 894 1666 891 1667 896 1672 893 1675 896 1677 895 1687 895 1695 896 1709 894 1730 894 1732 898 1749 894 1756 892 1808 895 1812 895 1834 891 1876 892 1354 900 1496 898 1512 899 1526 903 1548 903 1565 903 1580 905 1583 904 1590 899 1600 899 1609 900 1617 904 1615 901 1626 903 1627 899 1625 905 1632 902 1635 899 1631 905 1631 903 1629 901 1642 901 1639 899 1644 904 1643 900 1643 900 1638 900 1644 904 1637 901 1638 898 1644 900 1642 900 1640 903 1641 901 1643 902 1649 902 1649 903 1651 902 1652 900 1649 898 1646 900 1650 899 1649 902 1651 905 1651 903 1647 902 1646 901 1652 901 1645 899 1652 903 1656 902 1654 904 1654 903 1654 899 1655 903 1661 900 1668 899 1671 900 1683 905 1692 904 1703 898 1730 899 1734 901 1745 902 1800 902 1316 911 1518 906 1545 911 1553 905 1571 911 1592 909 1601 907 1607 910 1612 909 1614 905 100 { m20} R 1627 909 1621 910 1627 912 1634 909 1633 906 1631 909 1634 909 1644 906 1641 911 1637 910 1643 907 1638 910 1640 906 1647 906 1647 905 1648 910 1650 911 1647 910 1645 906 1651 911 1651 909 1646 907 1655 910 1657 909 1656 908 1659 909 1662 908 1664 912 1671 910 1684 907 1686 907 1695 909 1705 911 1765 908 1772 910 1882 910 1946 908 1328 913 1336 914 1407 915 1443 912 1486 916 1539 914 1555 913 1562 912 1573 916 1575 916 1585 918 1593 916 1601 918 1606 913 1620 912 1626 913 1627 915 1631 914 1631 914 1637 914 1641 916 1650 914 1648 917 1657 914 1659 918 1658 918 1662 912 1661 913 1671 916 1683 916 1688 916 1699 916 1704 917 1716 918 1732 918 1444 924 1508 920 1523 925 1539 922 1555 923 1581 923 1596 920 1608 922 1620 924 1628 924 1634 922 1632 922 1644 920 1648 921 1659 920 1666 925 1669 921 1680 919 1690 921 1697 924 1703 920 1713 919 1728 924 1798 920 1899 923 1453 926 1516 927 1541 928 100 { m20} R 1547 932 1557 927 1570 928 1580 927 1588 930 1595 931 1612 927 1620 930 1625 928 1633 929 1643 932 1649 927 1654 932 1662 931 1673 929 1679 929 1699 929 1715 930 1728 930 1808 931 2004 929 1397 935 1413 932 1433 937 1470 935 1532 936 1557 938 1580 937 1595 934 1604 938 1610 936 1619 937 1629 938 1650 937 1654 935 1667 937 1672 939 1680 935 1687 934 1695 938 1723 938 1731 936 1738 939 1982 932 1271 945 1430 942 1504 941 1533 942 1562 945 1590 944 1600 939 1609 944 1615 945 1624 940 1641 944 1644 946 1653 940 1661 939 1677 943 1738 941 1779 942 1373 950 1521 947 1530 950 1554 950 1560 952 1567 953 1575 947 1594 948 1638 948 1645 946 1656 947 1664 951 1675 951 1686 948 1696 948 1721 948 1780 951 1922 947 1550 958 1590 953 1618 953 1702 958 1789 953 1803 954 1900 953 2006 959 1261 963 1460 961 1494 962 1564 964 1619 960 1627 961 1635 961 1698 966 1762 960 1770 963 1779 960 1789 966 1795 964 100 { m20} R 1935 966 2014 961 1279 969 1433 966 1511 969 1602 970 1644 968 1654 969 1681 973 1836 968 1518 976 1588 980 1625 973 1644 973 1677 974 1703 975 1746 977 1520 983 1550 982 1565 985 1576 986 1679 981 1722 985 1589 990 1676 987 1867 990 2012 991 1368 999 1537 999 1591 994 1608 995 1696 996 1816 997 1884 998 1266 1004 1301 1002 1557 1004 1633 1001 1650 1006 1976 1003 1545 1010 1629 1010 1641 1009 1647 1009 1708 1010 1718 1009 1738 1012 1793 1008 1959 1013 1967 1009 1341 1015 1501 1018 1551 1016 1649 1015 1665 1016 1679 1018 1705 1020 1818 1016 2018 1019 59 { m20} R NC 1 lw 1247 340 m 681 Y s 1281 340 m -34 X s 1264 354 m -17 X s 1264 367 m -17 X s 1264 381 m -17 X s 1264 395 m -17 X s 1281 408 m -34 X s 1264 422 m -17 X s 1264 435 m -17 X s 1264 449 m -17 X s 1264 463 m -17 X s 1281 476 m -34 X s 1264 490 m -17 X s 1264 503 m -17 X s 1264 517 m -17 X s 1264 531 m -17 X s 1281 544 m -34 X s 1264 558 m -17 X s 1264 572 m -17 X s 1264 585 m -17 X s 1264 599 m -17 X s 1281 612 m -34 X s 1264 626 m -17 X s 1264 640 m -17 X s 1264 653 m -17 X s 1264 667 m -17 X s 1281 680 m -34 X s 1264 694 m -17 X s 1264 708 m -17 X s 1264 721 m -17 X s 1264 735 m -17 X s 1281 748 m -34 X s 1264 762 m -17 X s 1264 776 m -17 X s 1264 789 m -17 X s 1264 803 m -17 X s 1281 816 m -34 X s 1264 830 m -17 X s 1264 844 m -17 X s 1264 857 m -17 X s 1264 871 m -17 X s 1281 885 m -34 X s 1264 898 m -17 X s 1264 912 m -17 X s 1264 925 m -17 X s 1264 939 m -17 X s 1281 953 m -34 X s 1264 966 m -17 X s 1264 980 m -17 X s 1264 993 m -17 X s 1264 1007 m -17 X s 1281 1021 m -34 X s /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 1202 324 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (0.0025) /Helvetica-Bold 43 stwn gsave 1202 392 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.0025) show gr /xs 0 def (0.005) /Helvetica-Bold 43 stwn gsave 1202 460 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.005) show gr /xs 0 def (0.0075) /Helvetica-Bold 43 stwn gsave 1202 528 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.0075) show gr /xs 0 def (0.01) /Helvetica-Bold 43 stwn gsave 1202 596 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.01) show gr /xs 0 def (0.0125) /Helvetica-Bold 43 stwn gsave 1202 665 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.0125) show gr /xs 0 def (0.015) /Helvetica-Bold 43 stwn gsave 1202 733 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.015) show gr /xs 0 def (0.0175) /Helvetica-Bold 43 stwn gsave 1202 801 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.0175) show gr /xs 0 def (0.02) /Helvetica-Bold 43 stwn gsave 1202 869 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.02) show gr /xs 0 def (0.0225) /Helvetica-Bold 43 stwn gsave 1202 937 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.0225) show gr /xs 0 def (0.025) /Helvetica-Bold 43 stwn gsave 1202 1005 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.025) show gr 1247 340 m 794 X s 1327 374 m -34 Y s 1366 357 m -17 Y s 1406 357 m -17 Y s 1446 357 m -17 Y s 1486 374 m -34 Y s 1525 357 m -17 Y s 1565 357 m -17 Y s 1605 357 m -17 Y s 1644 374 m -34 Y s 1684 357 m -17 Y s 1724 357 m -17 Y s 1763 357 m -17 Y s 1803 374 m -34 Y s 1843 357 m -17 Y s 1882 357 m -17 Y s 1922 357 m -17 Y s 1962 374 m -34 Y s 1327 374 m -34 Y s 1287 357 m -17 Y s 1962 374 m -34 Y s 2002 357 m -17 Y s 2041 357 m -17 Y s /xs 0 def (-0.4) /Helvetica-Bold 43 stwn gsave 1327 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (-0.4) show gr /xs 0 def (-0.2) /Helvetica-Bold 43 stwn gsave 1486 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (-0.2) show gr /xs 0 def (0) /Helvetica-Bold 43 stwn gsave 1644 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0) show gr /xs 0 def (0.2) /Helvetica-Bold 43 stwn gsave 1803 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.2) show gr /xs 0 def (0.4) /Helvetica-Bold 43 stwn gsave 1962 286 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 43 sf 0 0 m (0.4) show gr 794 681 1247 340 C 2268 2268 0 0 C gsave 295 1962 t 0 r 0 0 m /Times-BoldItalic findfont 68 sf 0 0 m (N) show currentpoint pop 0 t /Times-BoldItalic findfont 48 sf 0 -23 m (w) show gr gsave 295 1055 t 0 r 0 0 m /Times-BoldItalic findfont 68 sf 0 0 m (N) show currentpoint pop 0 t /Times-BoldItalic findfont 48 sf 0 -23 m (w) show gr gsave 1315 1962 t 0 r 0 0 m /Times-BoldItalic findfont 68 sf 0 0 m (N) show currentpoint pop 0 t /Times-BoldItalic findfont 48 sf 0 -23 m (w) show gr gsave 1315 1055 t 0 r 0 0 m /Symbol findfont 68 sf 0 0 m (q) show currentpoint pop 0 t /Symbol findfont 48 sf 0 -23 m (g) show gr gsave 930 1123 t 0 r 0 0 m /Symbol findfont 68 sf 0 0 m (q) show currentpoint pop 0 t /Symbol findfont 48 sf 0 -23 m (g) show gr gsave 1916 1123 t 0 r 0 0 m /Symbol findfont 68 sf 0 0 m (f) show currentpoint pop 0 t /Symbol findfont 48 sf 0 -23 m (g) show gr gsave 1860 204 t 0 r 0 0 m /Symbol findfont 68 sf 0 0 m (f) show currentpoint pop 0 t /Symbol findfont 48 sf 0 -23 m (g) show gr gsave 851 204 t 0 r 0 0 m /Times-BoldItalic findfont 68 sf 0 0 m (E) show currentpoint pop 0 t /Symbol findfont 48 sf 0 -23 m (g) show gr gr gr showpage end %%EndDocument @endspecial 1054 1535 a Fl(a\))1573 b(b\))1054 3000 y(c\))1578 b(d\))-128 3274 y Fs(Figure)32 b(3:)89 b Fa(The)35 b(distribution)g(of)g(the)g(r)-5 b(adiation)34 b(angles)h Fq(\022)2101 3289 y Ft(\015)2181 3274 y Fa(a\))f(and)h Fq(\036)2553 3289 y Ft(\015)2632 3274 y Fa(b\))g(and)g(of)f(the)i(ener) -5 b(gy)35 b(c\))f(of)h(the)-128 3395 y(r)-5 b(adiate)g(d)35 b(photon)f(for)h Fq(x)28 b Fs(=)f(0)p Fq(:)p Fs(1)35 b Fa(and)f Fq(y)d Fs(=)d(0)p Fq(:)p Fs(8)p Fa(.)44 b(The)34 b(two-dimensional)f(distribution)i(d\))f(shows)g Fq(\022)3533 3410 y Ft(\015)3613 3395 y Fa(vs)h Fq(\036)3791 3410 y Ft(\015)3835 3395 y Fa(.)-128 3688 y Fs(=)40 b(0.1)f(and)h Fq(y)j Fs(=)c(0.8.)64 b(The)41 b(t)m(w)m(o)f(p)s(eaks)h(seen)g(in)e (the)h Fq(\022)2009 3703 y Ft(\015)2093 3688 y Fs(distribution)e(of)h (Fig.3)p (#figure.3) [[422 274 428 286] [1 1 1 [3 3]] [0 0 1]] pdfm 38 w(corresp)s(ond)h(to)g(the)g Fq(s)p Fs(-)-128 3809 y(and)31 b Fq(p)p Fs(-p)s(eak)f(emerging)e(from)h(collinear)f (radiation)g(along)g(the)j(direction)e(of)g(the)i(incoming)d(and)i (outgoing)-128 3929 y(lepton,)j(resp)s(ectiv)m(ely)-8 b(.)19 4097 y(F)g(urther)38 b(results)g(on)f(the)h(n)m(umerical)f (comparison)f(of)h(the)i(p)s(olarized)d(and)i(unp)s(olarized)e(case)j (in)e(the)-128 4217 y(co)m(v)-5 b(arian)m(t)26 b(and)h(Mo-Tsai)f (approac)m(h,)i(resp)s(ectiv)m(ely)-8 b(,)29 b(can)e(b)s(e)g(found)f (in)g(the)h(refs.[12)p (#cite.KSh) [[418 211 429 223] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g(13)p (#cite.BarBad) [[436 211 448 223] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(].)42 b(Fig.4)25 b(of)h(ref.)g([13)p (#cite.BarBad) [[524 211 535 223] [1 1 1 [3 3]] [0 0 1]] pdfm (])-128 4337 y(presen)m(ts)38 b(the)e(\001-dep)s(endence)i(of)d(the)h(radiativ) 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b(of)f(the)h(R)m(C)h(factor)e(as)h(a)f(function)g(of)h(kinematical)d(v) -5 b(ariables.)90 b(Both)49 b(the)g(observ)m(ed)i(and)-128 5227 y(Born)d(cross)h(sections)g(can)f(b)s(e)g(split)f(in)m(to)g(spin)h (a)m(v)m(eraged)h(and)f(spin)g(dep)s(enden)m(t)i(parts)f(\()p Fq(\033)3471 5191 y Ft(obs;B)s(or)r(n)3812 5227 y Fs(=)-128 5348 y Fq(\033)-69 5311 y Ft(obs;B)s(or)r(n)-73 5372 y(u)228 5348 y Fs(+)8 b Fq(p)361 5363 y Ft(b)395 5348 y Fq(p)444 5363 y Ft(t)474 5348 y Fq(\033)533 5311 y Ft(obs;B)s(or)r(n)529 5372 y(p)821 5348 y Fs(,)27 b Fq(p)924 5363 y Ft(b;t)1029 5348 y Fs(are)f(b)s(eam)f(and)h(target)g(p)s (olarizations\))d(allo)m(wing)g(to)i(de\014ne)j(the)e(R)m(C)g(factors) 1856 5916 y(9)p eop %%Page: 10 10 10 9 bop -213 2010 a @beginspecial 0 @llx 0 @lly 227 @urx 227 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: sigcor.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 /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr newpath } 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 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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 gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 3 lw 681 681 114 114 bl 681 681 114 114 C NC 1 lw 114 114 m 681 Y s 131 114 m -17 X s 122 131 m -8 X s 122 148 m -8 X s 122 165 m -8 X s 122 182 m -8 X s 131 199 m -17 X s 122 216 m -8 X s 122 233 m -8 X s 122 250 m -8 X s 122 267 m -8 X s 131 284 m -17 X s 122 301 m -8 X s 122 318 m -8 X s 122 335 m -8 X s 122 352 m -8 X s 131 369 m -17 X s 122 386 m -8 X s 122 403 m -8 X s 122 420 m -8 X s 122 437 m -8 X s 131 454 m -17 X s 122 471 m -8 X s 122 488 m -8 X s 122 505 m -8 X s 122 522 m -8 X s 131 539 m -17 X s 122 556 m -8 X s 122 573 m -8 X s 122 590 m -8 X s 122 607 m -8 X s 131 624 m -17 X s 122 641 m -8 X s 122 658 m -8 X s 122 675 m -8 X s 122 692 m -8 X s 131 709 m -17 X s 122 726 m -8 X s 122 743 m -8 X s 122 760 m -8 X s 122 777 m -8 X s 131 795 m -17 X s /xs 0 def (0) /Helvetica-Bold 31 stwn gsave 79 102 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0) show gr /xs 0 def (10) /Helvetica-Bold 31 stwn gsave 79 187 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (10) show gr /xs 0 def (20) /Helvetica-Bold 31 stwn gsave 79 272 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (20) show gr /xs 0 def (30) /Helvetica-Bold 31 stwn gsave 79 358 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (30) show gr /xs 0 def (40) /Helvetica-Bold 31 stwn gsave 79 443 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (40) show gr /xs 0 def (50) /Helvetica-Bold 31 stwn gsave 79 528 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (50) show gr /xs 0 def (60) /Helvetica-Bold 31 stwn gsave 79 613 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (60) show gr /xs 0 def (70) /Helvetica-Bold 31 stwn gsave 79 698 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (70) show gr /xs 0 def (80) /Helvetica-Bold 31 stwn gsave 79 783 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (80) show gr 114 114 m 681 X s 151 131 m -17 Y s 170 122 m -8 Y s 189 122 m -8 Y s 208 122 m -8 Y s 227 131 m -17 Y s 246 122 m -8 Y s 265 122 m -8 Y s 284 122 m -8 Y s 303 131 m -17 Y s 322 122 m -8 Y s 341 122 m -8 Y s 359 122 m -8 Y s 378 131 m -17 Y s 397 122 m -8 Y s 416 122 m -8 Y s 435 122 m -8 Y s 454 131 m -17 Y s 473 122 m -8 Y s 492 122 m -8 Y s 511 122 m -8 Y s 530 131 m -17 Y s 549 122 m -8 Y s 568 122 m -8 Y s 586 122 m -8 Y s 605 131 m -17 Y s 624 122 m -8 Y s 643 122 m -8 Y s 662 122 m -8 Y s 681 131 m -17 Y s 700 122 m -8 Y s 719 122 m -8 Y s 738 122 m -8 Y s 757 131 m -17 Y s 151 131 m -17 Y s 132 122 m -8 Y s 114 122 m -8 Y s 757 131 m -17 Y s 776 122 m -8 Y s /xs 0 def (0.6) /Helvetica-Bold 31 stwn gsave 151 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.6) show gr /xs 0 def (0.8) /Helvetica-Bold 31 stwn gsave 227 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.8) show gr /xs 0 def (1) /Helvetica-Bold 31 stwn gsave 303 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1) show gr /xs 0 def (1.2) /Helvetica-Bold 31 stwn gsave 378 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.2) show gr /xs 0 def (1.4) /Helvetica-Bold 31 stwn gsave 454 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.4) show gr /xs 0 def (1.6) /Helvetica-Bold 31 stwn gsave 530 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.6) show gr /xs 0 def (1.8) /Helvetica-Bold 31 stwn gsave 605 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.8) show gr /xs 0 def (2) /Helvetica-Bold 31 stwn gsave 681 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (2) show gr /xs 0 def (2.2) /Helvetica-Bold 31 stwn gsave 757 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (2.2) show gr 681 681 114 114 C 1 1 0 c 114 114 m 128 X 3 Y 8 X 15 Y 7 X 46 Y 8 X 76 Y 7 X 119 Y 8 X 44 Y 8 X 100 Y 7 X -50 Y 8 X 204 Y 7 X -37 Y 8 X 21 Y 7 X 9 Y 8 X -49 Y 7 X -52 Y 8 X 95 Y 8 X -59 Y 7 X -55 Y 8 X -22 Y 7 X -81 Y 8 X 14 Y 7 X -15 Y 8 X -28 Y 8 X -43 Y 7 X -48 Y 8 X 4 Y 7 X -26 Y 8 X -37 Y 7 X -5 Y 8 X -19 Y 8 X -15 Y 7 X -6 Y 8 X -7 Y 7 X -96 Y f [] 0 sd 3 lw black 114 114 m 128 X 3 Y 8 X 15 Y 7 X 46 Y 8 X 76 Y 7 X 119 Y 8 X 44 Y 8 X 100 Y 7 X -50 Y 8 X 204 Y 7 X -37 Y 8 X 21 Y 7 X 9 Y 8 X -49 Y 7 X -52 Y 8 X 95 Y 8 X -59 Y 7 X -55 Y 8 X -22 Y 7 X -81 Y 8 X 14 Y 7 X -15 Y 8 X -28 Y 8 X -43 Y 7 X -48 Y 8 X 4 Y 7 X -26 Y 8 X -37 Y 7 X -5 Y 8 X -19 Y 8 X -15 Y 7 X -6 Y 8 X -7 Y 7 X s 1 lw [] 0 sd 1 1 0 c 484 114 m 93 Y 8 X -15 Y 7 X -17 Y 8 X 4 Y 8 X -6 Y 7 X -2 Y 8 X -5 Y 7 X -1 Y 8 X -15 Y 7 X 6 Y 8 X -13 Y 8 X 10 Y 15 X -13 Y 7 X -5 Y 15 X -2 Y 8 X -4 Y 7 X 7 Y 8 X -10 Y 8 X -1 Y 7 X -1 Y 8 X 3 Y 7 X -3 Y 8 X 1 Y 7 X -7 Y 8 X 3 Y 8 X -6 Y 7 X 2 Y 8 X -3 Y 7 X 3 Y 8 X -3 Y 136 X f [] 0 sd 3 lw black 484 210 m -3 Y 8 X -15 Y 7 X -17 Y 8 X 4 Y 8 X -6 Y 7 X -2 Y 8 X -5 Y 7 X -1 Y 8 X -15 Y 7 X 6 Y 8 X -13 Y 8 X 10 Y 15 X -13 Y 7 X -5 Y 15 X -2 Y 8 X -4 Y 7 X 7 Y 8 X -10 Y 8 X -1 Y 7 X -1 Y 8 X 3 Y 7 X -3 Y 8 X 1 Y 7 X -7 Y 8 X 3 Y 8 X -6 Y 7 X 2 Y 8 X -3 Y 7 X 3 Y 8 X -3 Y 136 X s 1 lw [] 0 sd 1 1 0 c 855 114 m 15 X f [] 0 sd 3 lw black 855 114 m 15 X s 908 908 0 0 C gsave 148 817 t 0 r 0 0 m /Times-BoldItalic findfont 51 sf 0 0 m (N) show currentpoint pop 0 t /Times-BoldItalic findfont 36 sf 0 -17 m (w) show gr gsave 602 34 t 0 r 0 0 m /Times-BoldItalic findfont 51 sf 0 0 m (RC factor) show gr gr gr showpage end %%EndDocument @endspecial -128 2214 a Fs(Figure)33 b(4:)89 b(The)34 b(t)m(ypical)f(distribution)e(of)-128 2334 y(the)i(radiativ)m(e)f (correction)g(factor.)2125 1890 y @beginspecial 0 @llx 0 @lly 227 @urx 227 @ury 2267 @rwi 2267 @rhi @setspecial %%BeginDocument: allu.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 /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr newpath } 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 tlen def} 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 gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 3 lw 681 681 114 114 bl 681 681 114 114 C NC 1 lw 114 114 m 681 Y s 131 114 m -17 X s 122 131 m -8 X s 122 148 m -8 X s 122 165 m -8 X s 131 182 m -17 X s 122 199 m -8 X s 122 216 m -8 X s 122 233 m -8 X s 131 250 m -17 X s 122 267 m -8 X s 122 284 m -8 X s 122 301 m -8 X s 131 318 m -17 X s 122 335 m -8 X s 122 352 m -8 X s 122 369 m -8 X s 131 386 m -17 X s 122 403 m -8 X s 122 420 m -8 X s 122 437 m -8 X s 131 454 m -17 X s 122 471 m -8 X s 122 488 m -8 X s 122 505 m -8 X s 131 522 m -17 X s 122 539 m -8 X s 122 556 m -8 X s 122 573 m -8 X s 131 590 m -17 X s 122 607 m -8 X s 122 624 m -8 X s 122 641 m -8 X s 131 658 m -17 X s 122 675 m -8 X s 122 692 m -8 X s 122 709 m -8 X s 131 726 m -17 X s 122 743 m -8 X s 122 760 m -8 X s 122 777 m -8 X s 131 795 m -17 X s /xs 0 def (0.8) /Helvetica-Bold 31 stwn gsave 79 102 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.8) show gr /xs 0 def (0.9) /Helvetica-Bold 31 stwn gsave 79 170 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.9) show gr /xs 0 def (1) /Helvetica-Bold 31 stwn gsave 79 238 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1) show gr /xs 0 def (1.1) /Helvetica-Bold 31 stwn gsave 79 306 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.1) show gr /xs 0 def (1.2) /Helvetica-Bold 31 stwn gsave 79 375 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.2) show gr /xs 0 def (1.3) /Helvetica-Bold 31 stwn gsave 79 443 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.3) show gr /xs 0 def (1.4) /Helvetica-Bold 31 stwn gsave 79 511 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.4) show gr /xs 0 def (1.5) /Helvetica-Bold 31 stwn gsave 79 579 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.5) show gr /xs 0 def (1.6) /Helvetica-Bold 31 stwn gsave 79 647 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.6) show gr /xs 0 def (1.7) /Helvetica-Bold 31 stwn gsave 79 715 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.7) show gr /xs 0 def (1.8) /Helvetica-Bold 31 stwn gsave 79 783 t 0 r xs neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1.8) show gr 114 114 m 681 X s 114 131 m -17 Y s 129 122 m -8 Y s 144 122 m -8 Y s 159 122 m -8 Y s 174 122 m -8 Y s 189 131 m -17 Y s 204 122 m -8 Y s 219 122 m -8 Y s 235 122 m -8 Y s 250 122 m -8 Y s 265 131 m -17 Y s 280 122 m -8 Y s 295 122 m -8 Y s 310 122 m -8 Y s 325 122 m -8 Y s 341 131 m -17 Y s 356 122 m -8 Y s 371 122 m -8 Y s 386 122 m -8 Y s 401 122 m -8 Y s 416 131 m -17 Y s 431 122 m -8 Y s 446 122 m -8 Y s 462 122 m -8 Y s 477 122 m -8 Y s 492 131 m -17 Y s 507 122 m -8 Y s 522 122 m -8 Y s 537 122 m -8 Y s 552 122 m -8 Y s 568 131 m -17 Y s 583 122 m -8 Y s 598 122 m -8 Y s 613 122 m -8 Y s 628 122 m -8 Y s 643 131 m -17 Y s 658 122 m -8 Y s 673 122 m -8 Y s 689 122 m -8 Y s 704 122 m -8 Y s 719 131 m -17 Y s 734 122 m -8 Y s 749 122 m -8 Y s 764 122 m -8 Y s 779 122 m -8 Y s 795 131 m -17 Y s /xs 0 def (0.1) /Helvetica-Bold 31 stwn gsave 114 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.1) show gr /xs 0 def (0.2) /Helvetica-Bold 31 stwn gsave 189 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.2) show gr /xs 0 def (0.3) /Helvetica-Bold 31 stwn gsave 265 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.3) show gr /xs 0 def (0.4) /Helvetica-Bold 31 stwn gsave 341 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.4) show gr /xs 0 def (0.5) /Helvetica-Bold 31 stwn gsave 416 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.5) show gr /xs 0 def (0.6) /Helvetica-Bold 31 stwn gsave 492 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.6) show gr /xs 0 def (0.7) /Helvetica-Bold 31 stwn gsave 568 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.7) show gr /xs 0 def (0.8) /Helvetica-Bold 31 stwn gsave 643 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.8) show gr /xs 0 def (0.9) /Helvetica-Bold 31 stwn gsave 719 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (0.9) show gr /xs 0 def (1) /Helvetica-Bold 31 stwn gsave 795 79 t 0 r xs 2 div neg 0 t 0 0 m /Helvetica-Bold findfont 31 sf 0 0 m (1) show gr 681 681 114 114 C 3 lw 189 480 m 26 X 22 1 d 24 2 d 4 1 d 25 3 d 21 4 d 22 5 d 8 2 d 24 7 d 18 6 d 15 6 d 16 7 d 2 1 d 24 12 d 16 10 d 13 8 d 11 8 d 12 10 d 19 18 d 12 12 d 11 11 d 9 11 d 8 11 d 8 11 d 9 13 d 11 20 d 9 15 d 6 12 d 5 12 d 6 14 d 6 14 d 7 18 d 6 18 d 7 20 d 6 19 d 6 21 d s [12 12] 0 sd 189 337 m 42 6 d 34 6 d 48 10 d 28 7 d 31 10 d 33 11 d 11 4 d 40 16 d 21 9 d 15 8 d 31 18 d 16 10 d 14 11 d 15 12 d 19 18 d 11 11 d 7 9 d 17 21 d 7 11 d 7 11 d 7 13 d 17 32 d 5 13 d 5 13 d 4 12 d 4 13 d 3 10 d 5 18 d 5 22 d 4 20 d 5 24 d 5 24 d 5 28 d 4 26 d 5 31 d s [] 0 sd 189 306 m 76 19 d 76 19 d 60 17 d 15 5 d 44 14 d 22 9 d 10 4 d 33 16 d 15 8 d 14 9 d 14 9 d 19 15 d 11 9 d 7 8 d 17 18 d 7 9 d 7 9 d 6 10 d 1 2 d 14 24 d 6 12 d 6 12 d 4 11 d 4 11 d 4 12 d 5 16 d 5 19 d 4 17 d 6 23 d 5 22 d 5 24 d 4 23 d 4 20 d s [12 12] 0 sd 189 225 m 32 10 d 34 9 d 10 3 d 35 8 d 41 10 d 75 18 d 62 14 d 14 4 d 43 12 d 20 5 d 13 4 d 25 9 d 12 4 d 20 8 d 11 5 d 7 3 d 18 9 d 7 5 d 6 4 d 6 4 d 1 1 d 7 6 d 8 7 d 7 7 d 7 8 d 7 8 d 2 2 d s [] 0 sd 189 134 m 30 7 d 30 6 d 16 3 d 25 5 d 51 9 d 75 14 d 60 11 d 16 3 d 43 9 d 21 5 d 12 2 d 24 7 d 13 3 d 21 6 d 11 4 d 6 2 d 19 7 d 7 3 d 6 3 d 6 3 d 8 5 d 7 5 d 8 5 d 8 6 d 7 5 d s [12 12] 0 sd 189 140 m 34 7 d 35 7 d 7 1 d 76 14 d 75 14 d 53 10 d 23 5 d 39 8 d 21 5 d 16 4 d 24 7 d 13 4 d 20 6 d 11 4 d 7 3 d 18 7 d 7 3 d 7 3 d 6 4 d 8 5 d 7 5 d 8 6 d 7 6 d 8 6 d s 908 908 0 0 C 681 681 114 114 C 908 908 0 0 C gsave 757 45 t 0 r 0 0 m /Times-BoldItalic findfont 51 sf 0 0 m (y) show gr 681 681 114 114 C 908 908 0 0 C 681 681 114 114 C 908 908 0 0 C gsave 151 829 t 0 r 0 0 m /Symbol findfont 51 sf 0 0 m (d) show currentpoint pop 0 t /Times-BoldItalic findfont 36 sf 0 -17 m (u,p) show gr 681 681 114 114 C 908 908 0 0 C 681 681 114 114 C 908 908 0 0 C gsave 166 658 t 0 r 0 0 m /Times-BoldItalic findfont 51 sf 0 0 m (x=0.02) show gr 681 681 114 114 C 908 908 0 0 C 681 681 114 114 C 908 908 0 0 C gsave 681 488 t 0 r 0 0 m /Times-BoldItalic findfont 51 sf 0 0 m (x=0.1) show gr 681 681 114 114 C 908 908 0 0 C 681 681 114 114 C 908 908 0 0 C gsave 643 182 t 0 r 0 0 m /Times-BoldItalic findfont 51 sf 0 0 m (x=0.65) show gr 681 681 114 114 C [] 0 sd 1 lw 166 651 m 106 X s 341 498 m -69 153 d s 341 364 m -69 287 d s 673 481 m 99 X s 568 434 m 105 47 d s 568 325 m 105 156 d s 114 250 m 681 X s gr gr showpage end %%EndDocument @endspecial 2282 2093 a(Figure)50 b(5:)161 b(The)53 b(spin)e(a)m(v)m(eraged)h(\(full)2282 2214 y(lines\))68 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b(Mon)m(te-Carlo)f(generator)f(RADGEN)h(1.0)f (including)f(radiativ)m(e)h(ev)m(en)m(ts)j(in)d(DIS)h(on)g(p)s (olarized)e(and)-128 5235 y(unp)s(olarized)26 b(targets)h(ha)m(v)m(e)h (b)s(een)g(presen)m(ted.)44 b(Tw)m(o)27 b(patc)m(hes)i(of)d(the)i (generator,)g(one)f(for)f(the)h(unp)s(olarized)-128 5355 y(case)34 b(based)g(on)f(the)h(F)m(OR)-8 b(TRAN)32 b(co)s(de)i (FERRAD35)e(and)h(the)g(other)g(for)g(the)g(p)s(olarized)e(case)j (based)g(on)-128 5476 y(the)g(F)m(OR)-8 b(TRAN)33 b(co)s(de)g(POLRAD)f (2.0)h(w)m(ere)h(compared)f(and)g(tested.)46 b(This)33 b(generator)g(is)g(implemen)m(ted)-128 5596 y(in)m(to)47 b(the)i(HERMES)f(Mon)m(te-Carlo)g(program)e(HMC.)j(The)f(F)m(OR)-8 b(TRAN)48 b(co)s(de)g(of)f(the)i(Mon)m(te)f(Carlo)-128 5717 y(generator)33 b(RADGEN)f(1.0)g(is)g(a)m(v)-5 b(ailable)30 b(on)j(request.)1832 5916 y(10)p eop %%Page: 11 11 11 10 bop -128 100 a Fw(Ac)l(kno)l(wledgemen)l(ts)-128 363 y Fs(W)-8 b(e)30 b(are)f(grateful)e(to)i(N.Sh)m(umeik)m(o)g(for)f 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Fq(\022)s Fs(.)1832 5916 y(11)p eop %%Page: 12 12 12 11 bop -128 100 a Fw(References)-79 360 y Fs([1])49 b(L.W.Mo)33 b(and)g(Y.S.Tsai,)g Fa(R)-5 b(ev.)34 b(Mo)-5 b(d.)35 b(Phys.)d Fr(41)p Fs(,)h(205)f(\(1969\);)73 481 y(Y.S.Tsai,)h(SLA)m(C-PUB-848,)f(1971.)-79 684 y([2])49 b(D.Bardin)31 b(and)i(N.Sh)m(umeik)m(o,)g Fa(Nucl.)i(Phys.)e Fs(B)f Fr(127)p Fs(,)h(242)f(\(1977\))-79 887 y([3])49 b(I.Akushevic)m(h,)35 b(A.Ilyic)m(hev,)e(N.Sh)m(umeik)m(o,)g(A.Sorok)m (o,)g(A.T)-8 b(olk)j(ac)m(hev,)33 b Fa(Comp.)g(Phys.)i(Comm.)c Fr(104)p Fs(,)73 1008 y(201)h(\(1997\))-79 1211 y([4])49 b(FERRAD)30 b(3.5)g(.)h(This)g(co)s(de)g(w)m(as)h(\014rst)f(created)h (b)m(y)f(J.)g(Drees)g(for)g(EMC)h(and)e(further)i(dev)m(elop)s(ed)f(b)m (y)73 1332 y(M.)i(Dueren.)-79 1535 y([5])49 b(NMC)33 b(collab)s(oration,)d Fa(Nucl.)35 b(Phys.)d Fs(B)h Fr(371)p Fs(,)g(3)f(\(1992\))-79 1738 y([6])49 b(K.)32 b(Ab)s(e)h Fa(et)i(al.)e Fs([E143)f(Collab)s(oration],)d(hep-ex/9808028)p [[265 508 345 520] [1 1 1 [3 3]] [0 0 1]] (http://arxiv.org/abs/hep-ex/9808028) pdfm (;)73 1859 y(L.W.)k(Whitlo)m(w,)f(SLA)m(C-rep)s(ort-357\(1990\))-79 2062 y([7])49 b(J.S.McCarth)m(y)-8 b(,)35 b(I.Sic)m(k)e(and)g (R.R.Whitney)-8 b(,)32 b Fa(Phys.R)-5 b(ev.)33 b Fs(C)g Fr(15)p Fs(,)f(1396)g(\(1977\))-79 2266 y([8])49 b(I.Akushevic)m(h,)f (D.Ryc)m(kb)s(osc)m(h,)f(N.Sh)m(umeik)m(o)c(and)f(A.T)-8 b(olk)j(ac)m(hev,)46 b(HERMES)e(In)m(ternal)e(Note)h(96-)73 2386 y(025,)32 b(1996.)-79 2589 y([9])49 b(A.K.Thompson)33 b(et)g(al.,)e Fa(Phys.)k(R)-5 b(ev.)35 b(L)-5 b(ett.)33 b Fr(68)p Fs(,)g(2901)e(\(1992\))-128 2793 y([10])49 b(D.R.Y)-8 b(ennie,)32 b(S.F)-8 b(rautc)m(hi,)32 b(H.Suura,)i Fa(A)n(nn.)g(Phys.)h(\(N.Y.\))e Fr(13)p Fs(,)f(379)g(\(1961\))-128 2996 y([11])49 b(I.V.Akushevic)m(h)35 b(and)e(N.M.Sh)m(umeik)m(o,)g Fa(J.)i(Phys.)e Fs(G)f Fr(20)p Fs(,)h(513)e(\(1994\))-128 3200 y([12])49 b(P)-8 b(.P)g(.Kuzhir,)33 b(N.M.Sh)m(umeik)m(o,)g Fa(Sov.J.Nucl.Phys.)g Fr(55)p Fs(,)f(1086)g(\(1992\))-128 3403 y([13])49 b(B.Badelek,)33 b(D.Bardin,)f(K.Kurek)h(and)g(C.Sc)m (holz,)g Fa(Z.)h(Phys.)f Fs(C)g Fr(66)p Fs(,)g(591)e(\(1995\))-128 3606 y([14])49 b(K.)32 b(Ac)m(k)m(ersta\013)j Fa(et)g(al.)d Fs([HERMES)i(Collab)s(oration],)29 b Fa(Phys.)35 b(L)-5 b(ett.)33 b Fs(B)g Fr(404)p Fs(,)g(383)e(\(1997\))1832 5916 y(12)p eop %%Trailer end end userdict /end-hook known{end-hook}if %%EOF