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Fp(3.12,)g(if)i(the) f(condition)f(\(2.1\))h(is)f(v)n(eri\014ed.)36 b(Note)27 b(that)g(these)g(functions)g(dep)r(end)g(on)0 5869 y Fh(14)p Fg(=apr)q(ile=)p Fh(2000;)h(18:23)1067 b Fp(3)p eop %%Page: 4 4 4 3 bop -5 83 a Fm(~)-37 b(a)44 95 y Ff(h)87 83 y Fm(;)14 b(\027)165 95 y Ff(h)208 83 y Fm(;)g(:)g(:)g(:)f(;)c(~)-37 b(a)436 95 y Fj(1)473 83 y Fm(;)14 b(\027)551 95 y Fj(1)589 83 y Fm(;)g(u)p Fp(,)27 b(directly)h(trough)g(the)g(endp)r(oin)n(ts)g (of)g(the)h(trees,)f(indirectly)g(trough)f Fm(z)2959 95 y Ff(h)3030 83 y Fp(and)h(the)0 232 y(quan)n(tities)f Fm(Z)440 244 y Ff(h)479 228 y Fd(0)505 232 y Fm(=)-5 b(Z)599 244 y Ff(h)638 228 y Fd(0)660 244 y Fq(\000)p Fj(1)777 232 y Fp(and)28 b Fm(\033)986 244 y Ff(h)1025 228 y Fd(0)1047 244 y Fq(\000)p Fj(1)1136 232 y Fp(\()p Fl(k)1218 202 y Fq(0)1242 232 y Fp(\),)g Fm(h)23 b(<)g(h)1532 202 y Fq(0)1578 232 y Fk(\024)g Fp(0,)k(app)r(earing)f(in)i(the)g(tree) g(expansions.)71 382 y(Let)g(us)f(de\014ne)880 531 y Fm(\026)930 543 y Ff(h)996 531 y Fp(=)d(sup)1084 602 y Ff(k)q Fq(\025)p Ff(h)1225 531 y Fp(max)p Fk(fj)p Fm(\025)1493 543 y Ff(k)1534 531 y Fk(j)p Fm(;)14 b Fk(j)p Fm(\016)1654 543 y Ff(k)1694 531 y Fk(jg)23 b Fm(;)1905 509 y Fp(\026)1902 531 y Fm(\025)1950 543 y Ff(h)2016 531 y Fp(=)h(sup)2104 602 y Ff(k)q Fq(\025)p Ff(h)2245 531 y Fk(j)p Fm(\025)2316 543 y Ff(k)2358 531 y Fk(j)f Fm(:)668 b Fp(\(2)p Fm(:)p Fp(12\))0 739 y(W)-7 b(e)28 b(w)n(an)n(t)f(to)g(pro)n(v)n(e)f(the)i (follo)n(wing)f(Lemma.)0 959 y Fl(2.2)88 b Fo(Lemma.)34 b Fn(Supp)l(ose)22 b(that)f Fm(u)g Fn(satis\014es)g(the)h(c)l(ondition) g(\()p Fl(I)p Fn(2.117\))i(and)e(let)f(us)g(c)l(onsider)h(the)g(e)l (quation)0 1109 y(\(2.11\))31 b(for)g(\014xe)l(d)e(values)h(of)c Fm(~)-37 b(a)964 1121 y Ff(h)1007 1109 y Fn(,)30 b Fm(Z)1119 1121 y Ff(h)p Fq(\000)p Fj(1)1277 1109 y Fn(and)g Fm(\033)1485 1121 y Ff(h)p Fq(\000)p Fj(1)1613 1109 y Fp(\()p Fl(k)1695 1079 y Fq(0)1719 1109 y Fp(\))p Fn(,)1807 1087 y Fp(~)1807 1109 y Fm(h)23 b Fk(\024)f Fm(h)h Fk(\024)g Fp(1)p 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Fm(Z)1602 1878 y Ff(h)p Fq(\000)p Fj(1)p 1545 1903 185 4 v 1587 1979 a Fm(Z)1644 1991 y Ff(h)1762 1922 y Fk(\024)23 b Fm(\015)1898 1888 y Fj(+)p Ff(c)1979 1896 y Fh(0)2011 1888 y Ff(\026)2051 1863 y Fh(2)2051 1905 y Fg(h)2117 1922 y Fm(;)955 b Fp(\(2)p Fm(:)p Fp(16\))0 2171 y Fn(for)31 b(some)f(c)l(onstant)f Fm(c)712 2183 y Fj(0)749 2171 y Fn(.)71 2321 y(Then,)41 b(if)j Fp(\026)-48 b Fm(")450 2333 y Fj(0)525 2321 y Fn(is)38 b(smal)t(l)h(enough,)h(ther) l(e)e(exist)g(some)g(c)l(onstants)k Fp(\026)-47 b Fm(")2217 2333 y Fj(1)2254 2321 y Fn(,)40 b Fm(\021)s Fn(,)g Fm(\015)2476 2290 y Fq(0)2499 2321 y Fn(,)g Fm(c)2600 2333 y Fj(1)2637 2321 y Fn(,)h Fm(B)t Fn(,)f(and)e(a)g(family)0 2470 y(of)f(intervals)g Fm(I)492 2440 y Fj(\()519 2424 y(\026)518 2440 y Ff(h)p Fj(\))587 2470 y Fn(,)651 2448 y Fp(~)650 2470 y Fm(h)d Fk(\024)833 2448 y Fp(\026)832 2470 y Fm(h)g Fk(\024)g Fp(0)p Fn(,)k(such)e(that)42 b Fp(\026)-47 b Fm(")1529 2482 y Fj(1)1600 2470 y Fk(\024)40 b Fp(\026)-48 b Fm(")1738 2482 y Fj(0)1775 2470 y Fn(,)39 b Fp(0)34 b Fm(<)g(\021)k(<)c Fp(1)p Fn(,)k Fp(1)c Fm(<)g(\015)2520 2440 y Fq(0)2578 2470 y Fm(<)g(\015)5 b Fn(,)38 b Fm(I)2831 2440 y Fj(\()2858 2424 y(\026)2857 2440 y Ff(h)p Fj(\))2960 2470 y Fk(\032)d Fm(I)3103 2440 y Fj(\()3130 2424 y(\026)3129 2440 y Ff(h)o Fj(+1\))3282 2470 y Fn(,)0 2619 y Fk(j)p Fm(I)66 2589 y Fj(\()93 2574 y(\026)92 2589 y Ff(h)p Fj(\))161 2619 y Fk(j)23 b(\024)g Fm(c)331 2631 y Fj(1)373 2619 y Fp(\026)-47 b Fm(")407 2631 y Fj(1)444 2619 y Fp(\()p Fm(\015)524 2589 y Fq(0)547 2619 y Fp(\))580 2574 y Fj(\026)579 2589 y Ff(h)652 2619 y Fn(and,)31 b(if)f Fm(\027)f Fp(=)22 b Fm(\027)1117 2631 y Fj(1)1178 2619 y Fk(2)h Fm(I)1299 2589 y Fj(\()1326 2574 y(\026)1325 2589 y Ff(h)p Fj(\))1394 2619 y Fn(,)767 2868 y Fk(j)p Fm(\027)831 2880 y Ff(h)874 2868 y Fk(j)g(\024)f Fm(B)10 b Fp(\026)-48 b Fm(")1113 2880 y Fj(1)1164 2776 y Fe(h)1203 2868 y Fm(\015)1251 2834 y Fq(\000)1313 2812 y Fh(1)p 1313 2821 29 4 v 1313 2854 a(2)1351 2834 y Fj(\()p Ff(h)p 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Fp(for)1055 3615 y(\026)1054 3637 y Fm(h)29 b Fk(\024)g Fm(h)g Fk(\024)f Fp(1)j(and)37 b(\026)-48 b Fm(")1672 3649 y Fj(0)1741 3637 y Fp(is)31 b(small)g(enough,)g(the)h(r.h.s.)47 b(of)32 b(\(2.11\))e(is)h(w)n(ell)0 3786 y(de\014ned)d(for)f Fm(h)c Fp(=)572 3764 y(\026)572 3786 y Fm(h)k Fp(and)h(w)n(e)f(can)g (write,)g(b)n(y)h(using)f(\(2.7\),)1244 4035 y Fm(\027)1286 4040 y Fj(\026)1285 4055 y Ff(h)p Fq(\000)p Fj(1)1436 4035 y Fp(=)22 b Fm(\015)5 b(\027)1613 4040 y Fj(\026)1612 4055 y Ff(h)1674 4035 y Fp(+)18 b Fm(b)1794 4040 y Fj(\026)1793 4055 y Ff(h)1854 4035 y Fp(+)g Fm(r)1975 4040 y Fj(\026)1974 4055 y Ff(h)2040 4035 y Fm(;)1032 b Fp(\(2)p Fm(:)p Fp(18\))0 4284 y(where)27 b Fm(b)277 4289 y Fj(\026)276 4304 y Ff(h)342 4284 y Fp(=)22 b Fm(c)465 4254 y Ff(\027)466 4301 y Fj(\026)465 4316 y Ff(h)p Fq(\000)p Fj(1)593 4284 y Fm(\015)642 4239 y Fj(\026)641 4254 y Ff(h)p Fq(\000)p Fj(1)769 4284 y Fm(\025)818 4289 y Fj(\026)817 4304 y Ff(h)888 4284 y Fp(and)28 b Fm(r)1088 4289 y Fj(\026)1087 4304 y Ff(h)1158 4284 y Fp(collects)f(all)g(terms)g(of)h(second)f(or)g (higher)f(order)h(in)33 b(\026)-47 b Fm(")2867 4296 y Fj(0)2904 4284 y Fp(.)71 4434 y(Note)40 b(also)f(that,)44 b(in)c(the)g(tree)g(expansion)f(of)h Fm(n)1680 4446 y Ff(h)1723 4434 y Fp(\()p Fm(\034)9 b Fp(\),)45 b(the)40 b(dep)r(endence)h(on)e Fm(\027)2681 4446 y Ff(h)2724 4434 y Fm(;)14 b(:)g(:)g(:)g(;)g(\027)2950 4446 y Fj(1)3027 4434 y Fp(app)r(ears)0 4583 y(only)32 b(in)h(the)g(endp)r(oin)n(ts)f (of)h(the)g(trees)f(and)g(there)g(is)h(no)f(con)n(tribution)g(from)g (the)h(trees)f(with)h Fm(n)e Fk(\025)g Fp(2)0 4733 y(endp)r(oin)n(ts,) 36 b(whic)n(h)f(are)f(only)g(of)g(t)n(yp)r(e)h Fm(\027)40 b Fp(or)34 b Fm(\016)s Fp(,)i(b)r(ecause)f(of)f(the)h(supp)r(ort)f (prop)r(erties)g(of)h(the)g(single)0 4882 y(scale)27 b(propagators.)34 b(It)28 b(follo)n(ws,)e(b)n(y)i(using)f(\()p Fl(I)p Fp(3.91\))g(and)g(\(2.14\)-\(2.16\),)f(that)1391 5131 y Fk(j)p Fm(r)1452 5136 y Fj(\026)1451 5151 y Ff(h)1494 5131 y Fk(j)d(\024)g Fm(c)1664 5143 y Fj(2)1701 5131 y Fm(\026)1752 5136 y Fj(\026)1751 5151 y Ff(h)1800 5131 y Fp(\026)-48 b Fm(")1833 5143 y Fj(0)1893 5131 y Fm(:)1179 b Fp(\(2)p Fm(:)p Fp(19\))71 5380 y(Let)28 b(us)f(no)n(w)g(\014x)h(a)f (p)r(ositiv)n(e)g(constan)n(t)g Fm(c)p Fp(,)h(consider)e(the)i(in)n (terv)-5 b(als)971 5629 y Fm(J)1025 5595 y Fj(\()p Ff(h)p Fj(\))1143 5629 y Fp(=)22 b([)p Fk(\000)1384 5573 y Fm(b)1420 5585 y Ff(h)p 1328 5610 191 4 v 1328 5686 a Fm(\015)h Fk(\000)18 b Fp(1)1547 5629 y Fk(\000)g Fm(c)6 b Fp(\026)-48 b Fm(")1705 5641 y Fj(1)1742 5629 y Fm(;)14 b Fk(\000)1909 5573 y Fm(b)1945 5585 y Ff(h)p 1853 5610 V 1853 5686 a Fm(\015)23 b Fk(\000)18 b Fp(1)2072 5629 y(+)g Fm(c)6 b Fp(\026)-48 b Fm(")2230 5641 y Fj(1)2267 5629 y Fp(])23 b Fm(:)759 b Fp(\(2)p Fm(:)p Fp(20\))0 5869 y Fh(14)p Fg(=apr)q(ile=)p Fh(2000;)28 b(18:23)1067 b Fp(4)p eop %%Page: 5 5 5 4 bop 0 83 a Fp(and)36 b(supp)r(ose)f(that)i(there)e(is)h(an)g(in)n (terv)-5 b(al)35 b Fm(I)1466 53 y Fj(\()1493 38 y(\026)1492 53 y Ff(h)p Fj(\))1597 83 y Fp(suc)n(h)h(that,)i(if)e Fm(\027)2131 95 y Fj(1)2205 83 y Fp(spans)f Fm(I)2483 53 y Fj(\()2510 38 y(\026)2509 53 y Ff(h)p Fj(\))2578 83 y Fp(,)j(then)e Fm(\027)2878 88 y Fj(\026)2877 103 y Ff(h)2957 83 y Fp(spans)f(the)0 232 y(in)n(terv)-5 b(al)29 b Fm(J)356 202 y Fj(\()383 187 y(\026)382 202 y Ff(h)p Fj(+1\))565 232 y Fp(and)h Fk(j)p Fm(\027)793 244 y Ff(h)836 232 y Fk(j)d(\024)32 b Fp(\026)-47 b Fm(")1017 244 y Fj(0)1084 232 y Fp(for)1214 211 y(\026)1213 232 y Fm(h)27 b Fk(\024)f Fm(h)h Fk(\024)f Fp(1.)44 b(Let)30 b(us)g(call)2088 211 y(~)2068 232 y Fm(J)2122 202 y Fj(\()2149 187 y(\026)2148 202 y Ff(h)p Fj(\))2247 232 y Fp(the)g(in)n(terv)-5 b(al)30 b(spanned)f(b)n(y)h Fm(\027)3180 237 y Fj(\026)3179 253 y Ff(h)p Fq(\000)p Fj(1)0 382 y Fp(when)e Fm(\027)258 394 y Fj(1)323 382 y Fp(spans)f Fm(I)593 352 y Fj(\()620 336 y(\026)619 352 y Ff(h)o Fj(\))688 382 y Fp(.)37 b(Equation)26 b(\(2.18\))h(can)g(b)r(e)h(written)g(in)g(the)g(form)972 616 y Fm(\027)1014 621 y Fj(\026)1013 636 y Ff(h)p Fq(\000)p Fj(1)1160 616 y Fp(+)1309 560 y Fm(b)1346 565 y Fj(\026)1345 580 y Ff(h)p 1253 597 191 4 v 1253 673 a Fm(\015)23 b Fk(\000)18 b Fp(1)1476 616 y(=)23 b Fm(\015)1612 524 y Fe(\020)1661 616 y Fm(\027)1703 621 y Fj(\026)1702 636 y Ff(h)1764 616 y Fp(+)1913 560 y Fm(b)1950 565 y Fj(\026)1949 580 y Ff(h)p 1857 597 V 1857 673 a Fm(\015)g Fk(\000)18 b Fp(1)2057 524 y Fe(\021)2125 616 y Fp(+)g Fm(r)2246 621 y Fj(\026)2245 636 y Ff(h)2312 616 y Fm(:)760 b Fp(\(2)p Fm(:)p Fp(21\))0 850 y(Hence,)28 b(b)n(y)f(using)g(also)g (the)h(de\014nition)g(of)f Fm(b)1411 862 y Ff(h)1482 850 y Fp(and)g(\(2.19\),)g(w)n(e)g(see)h(that)562 1084 y(min)517 1150 y Ff(\027)550 1158 y Fh(1)583 1150 y Fq(2)p Ff(I)662 1133 y Fh(\()686 1122 y(\026)684 1133 y Fg(h)p Fh(\))759 967 y Fe(\024)802 1084 y Fm(\027)844 1089 y Fj(\026)843 1104 y Ff(h)p Fq(\000)p Fj(1)990 1084 y Fp(+)1139 1028 y Fm(b)1176 1033 y Fj(\026)1175 1048 y Ff(h)p 1083 1065 V 1083 1141 a Fm(\015)23 b Fk(\000)18 b Fp(1)1283 967 y Fe(\025)1350 1084 y Fp(=)526 1320 y(=)23 b Fm(\015)106 b Fp(min)675 1385 y Ff(\027)710 1389 y Fh(\026)708 1400 y Fg(h)747 1385 y Fq(2)p Ff(J)834 1369 y Fh(\()858 1358 y(\026)856 1369 y Fg(h)q Fh(+1\))1002 1203 y Fe(\024)1046 1320 y Fm(\027)1088 1325 y Fj(\026)1087 1340 y Ff(h)1148 1320 y Fp(+)1255 1260 y Fm(b)1292 1265 y Fj(\026)1291 1281 y Ff(h)p Fj(+1)p 1241 1301 V 1241 1377 a Fm(\015)23 b Fk(\000)18 b Fp(1)1442 1203 y Fe(\025)1504 1320 y Fp(+)63 b(min)1587 1385 y Ff(\027)1620 1393 y Fh(1)1653 1385 y Fq(2)p Ff(I)1732 1369 y Fh(\()1756 1358 y(\026)1754 1369 y Fg(h)p Fh(\))1829 1203 y Fe(\024)1873 1320 y Fm(r)1911 1325 y Fj(\026)1910 1340 y Ff(h)1972 1320 y Fp(+)2136 1264 y Fm(\015)p 2065 1301 V 2065 1377 a(\015)23 b Fk(\000)18 b Fp(1)2265 1320 y(\()p Fm(b)2334 1325 y Fj(\026)2333 1340 y Ff(h)2395 1320 y Fk(\000)g Fm(b)2515 1325 y Fj(\026)2514 1340 y Ff(h)o Fj(+1)2640 1320 y Fp(\))2672 1203 y Fe(\025)2739 1320 y Fk(\024)526 1525 y(\024)23 b(\000)p Fm(\015)5 b(c)h Fp(\026)-48 b Fm(")802 1537 y Fj(1)856 1525 y Fp(+)18 b Fm(c)975 1537 y Fj(2)1018 1525 y Fp(\026)-48 b Fm(")1051 1537 y Fj(1)1094 1525 y Fp(\026)g Fm(")1127 1537 y Fj(0)1183 1525 y Fp(+)18 b Fm(c)1302 1537 y Fj(3)1339 1525 y Fm(\015)1388 1475 y Fj(\026)1387 1491 y Ff(h)1435 1525 y Fp(\026)-47 b Fm(")1469 1537 y Fj(1)1529 1525 y Fm(;)3095 1280 y Fp(\(2)p Fm(:)p Fp(22\))0 1705 y(for)27 b(some)g(constan)n(t)g Fm(c)706 1717 y Fj(3)743 1705 y Fp(.)37 b(In)28 b(a)f(similar)g(w)n(a)n (y)f(w)n(e)h(can)h(sho)n(w)e(that)793 1939 y(max)756 2004 y Ff(\027)789 2012 y Fh(1)822 2004 y Fq(2)p Ff(I)901 1988 y Fh(\()925 1977 y(\026)923 1988 y Fg(h)q Fh(\))998 1822 y Fe(\024)1042 1939 y Fm(\027)1084 1944 y Fj(\026)1083 1959 y Ff(h)p Fq(\000)p Fj(1)1229 1939 y Fp(+)1378 1882 y Fm(b)1415 1887 y Fj(\026)1414 1903 y Ff(h)p 1322 1920 V 1322 1996 a Fm(\015)d Fk(\000)18 b Fp(1)1523 1822 y Fe(\025)1590 1939 y Fk(\025)k Fm(\015)5 b(c)h Fp(\026)-48 b Fm(")1800 1951 y Fj(1)1855 1939 y Fk(\000)18 b Fm(c)1974 1951 y Fj(2)2017 1939 y Fp(\026)-48 b Fm(")2050 1951 y Fj(1)2093 1939 y Fp(\026)g Fm(")2126 1951 y Fj(0)2182 1939 y Fk(\000)18 b Fm(c)2301 1951 y Fj(3)2338 1939 y Fm(\015)2387 1889 y Fj(\026)2386 1904 y Ff(h)2434 1939 y Fp(\026)-47 b Fm(")2468 1951 y Fj(1)2528 1939 y Fm(:)544 b Fp(\(2)p Fm(:)p Fp(23\))0 2193 y(It)26 b(follo)n(ws)f(that,)h(if)g Fm(c)g Fp(is)f(large)f(enough)h(and)31 b(\026)-47 b Fm(")1461 2205 y Fj(0)1524 2193 y Fp(is)25 b(small)g(enough,)h Fm(J)2182 2162 y Fj(\()2209 2147 y(\026)2208 2162 y Ff(h)p Fj(\))2302 2193 y Fp(is)g(strictly)f(con)n(tained)g(in)3155 2172 y(~)3135 2193 y Fm(J)3189 2162 y Fj(\()3216 2147 y(\026)3215 2162 y Ff(h)p Fj(\))3284 2193 y Fp(.)0 2342 y(On)k(the)g(other)f(hand,)h(it)g(is)g(ob)n(vious)e(that)i(there)g(is)g (a)f(one)g(to)h(one)g(corresp)r(ondence)d(b)r(et)n(w)n(een)j Fm(\027)3107 2354 y Fj(1)3173 2342 y Fp(and)0 2491 y(the)36 b(sequence)f Fm(\027)544 2503 y Ff(h)587 2491 y Fp(,)648 2469 y(\026)647 2491 y Fm(h)24 b Fk(\000)f Fp(1)36 b 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Fj(\()1101 3492 y(\026)1100 3507 y Ff(h)p Fj(\))1201 3537 y Fp(easily)g(follo)n(ws)f(\(2.18\))h(and)h(\(2.19\).)48 b(Let)31 b(us)h(denote)f(b)n(y)h Fm(\027)3099 3549 y Ff(h)3173 3537 y Fp(and)0 3687 y Fm(\027)46 3657 y Fq(0)41 3710 y Ff(h)84 3687 y Fp(,)136 3665 y(\026)135 3687 y Fm(h)23 b Fk(\024)f Fm(h)h Fk(\024)g Fp(1,)k(the)h(sequences)f(corresp) r(onding)f(to)h Fm(\027)1740 3699 y Fj(1)1777 3687 y Fm(;)14 b(\027)1860 3657 y Fq(0)1855 3708 y Fj(1)1915 3687 y Fk(2)24 b Fm(I)2037 3657 y Fj(\()2064 3641 y(\026)2063 3657 y Ff(h)p Fj(\))2132 3687 y Fp(.)37 b(W)-7 b(e)28 b(ha)n(v)n(e)983 3921 y Fm(\027)1024 3933 y Ff(h)p Fq(\000)p Fj(1)1170 3921 y Fk(\000)18 b Fm(\027)1299 3887 y Fq(0)1294 3942 y Ff(h)p Fq(\000)p Fj(1)1445 3921 y Fp(=)23 b Fm(\015)5 b Fp(\()p Fm(\027)1654 3933 y Ff(h)1715 3921 y Fk(\000)18 b Fm(\027)1844 3887 y Fq(0)1839 3942 y Ff(h)1882 3921 y Fp(\))h(+)f Fm(r)2053 3933 y Ff(h)2115 3921 y Fk(\000)g Fm(r)2237 3887 y Fq(0)2235 3942 y Ff(h)2301 3921 y Fm(;)771 b Fp(\(2)p 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Ff(h)2185 4987 y Fk(\000)19 b Fm(\027)2315 4953 y Fq(0)2310 5007 y Ff(h)2353 4987 y Fk(j)k Fm(:)673 b Fp(\(2)p Fm(:)p Fp(25\))0 5221 y(On)34 b(the)g(other)f(hand,)i(if)g Fm(h)e Fp(=)g(1,)i(this)f(b)r(ound)g(implies)g(that)g Fk(j)p Fm(\027)2085 5233 y Fj(1)2145 5221 y Fk(\000)22 b Fm(\027)2278 5191 y Fq(0)2273 5242 y Fj(1)2310 5221 y Fk(j)34 b(\024)f(j)p Fm(\027)2529 5233 y Fj(0)2589 5221 y Fk(\000)22 b Fm(\027)2722 5191 y Fq(0)2717 5242 y Fj(0)2754 5221 y Fk(j)p Fp(,)36 b(if)k(\026)-48 b Fm(")2957 5233 y Fj(1)3028 5221 y Fp(is)34 b(small)0 5370 y(enough;)d(hence)f(it) g(allo)n(ws)e(to)i(sho)n(w)f(inductiv)n(ely)h(that,)h(giv)n(en)e(an)n (y)h Fm(\015)2254 5340 y Fq(0)2276 5370 y Fp(,)h(suc)n(h)f(that)g(1)c Fm(<)h(\015)2910 5340 y Fq(0)2960 5370 y Fm(<)f(\015)5 b Fp(,)31 b(if)36 b(\026)-48 b Fm(")3270 5382 y Fj(1)0 5520 y Fp(is)27 b(small)h(enough,)f(then)1142 5669 y Fk(j)p Fm(\027)1206 5681 y Fj(1)1262 5669 y Fk(\000)18 b Fm(\027)1391 5635 y Fq(0)1386 5690 y Fj(1)1423 5669 y Fk(j)23 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Fm(\015)999 202 y Fq(0)p Fj(\()1045 187 y(\026)1044 202 y Ff(h)p Fq(\000)p Fj(1\))1198 232 y Fp(.)71 382 y(In)35 b(order)f(to)h(complete)g(the)g(pro)r(of)f(of)h(Lemma)g(2.2,)h(w)n(e)f (ha)n(v)n(e)f(still)h(to)g(pro)n(v)n(e)e(the)i(b)r(ound)h(\(2.17\).)0 531 y(Note)28 b(that,)g(if)g(w)n(e)f(iterate)g(\(2.11\),)g(w)n(e)g(can) g(write,)h(if)1715 509 y(\026)1714 531 y Fm(h)23 b Fk(\024)f Fm(h)h Fk(\024)g Fp(0)k(and)h Fm(\027)2303 543 y Fj(1)2363 531 y Fk(2)23 b Fm(I)2484 501 y Fj(\()2511 486 y(\026)2510 501 y Ff(h)p Fj(\))2579 531 y Fp(,)818 791 y Fm(\027)859 803 y Ff(h)925 791 y Fp(=)g Fm(\015)1061 756 y Fq(\000)p Ff(h)p Fj(+1)1253 649 y Fe(")1301 791 y Fm(\027)1342 803 y Fj(1)1398 791 y Fp(+)1570 687 y Fj(1)1526 712 y Fe(X)1481 891 y Ff(k)q Fj(=)p Ff(h)p Fj(+1)1706 791 y Fm(\015)1754 756 y Ff(k)q Fq(\000)p Fj(2)1879 791 y Fm(\014)1930 756 y Ff(\027)1926 811 y(k)1972 791 y Fp(\()p Fm(\027)2045 803 y Ff(k)2086 791 y Fm(;)14 b(:)g(:)g(:)f(;)h(\027)2311 803 y Fj(1)2349 791 y Fp(\))2381 649 y 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b Fp(\(2)p Fm(:)p Fp(28\))0 1749 y(\(2.27\))27 b(and)g(\(2.28\))g(are)g (equiv)-5 b(alen)n(t)27 b(to)445 2011 y Fm(\027)486 2023 y Ff(h)552 2011 y Fp(=)c Fk(\000)p Fm(\015)753 1977 y Fq(\000)p Ff(h)947 1908 y(h)906 1932 y Fe(X)861 2120 y Ff(k)q Fj(=)949 2104 y(\026)948 2120 y Ff(h)p Fj(+1)1085 2011 y Fm(\015)1133 1977 y Ff(k)q Fq(\000)p Fj(1)1259 2011 y Fm(\014)1310 1977 y Ff(\027)1306 2032 y(k)1351 2011 y Fp(\()p Fm(\027)1424 2023 y Ff(k)1465 2011 y Fm(;)14 b(:)g(:)g(:)g(;)g(\027)1691 2023 y Fj(1)1728 2011 y Fp(\))19 b(+)f Fm(\015)1910 1977 y Fq(\000)p Fj(\()p Ff(h)p Fq(\000)2080 1962 y Fj(\026)2079 1977 y Ff(h)o Fj(\))2147 2011 y Fm(\027)2189 2016 y Fj(\026)2188 2031 y Ff(h)2254 2011 y Fm(;)2458 1989 y Fp(\026)2457 2011 y Fm(h)23 b(<)g(h)g Fk(\024)f Fp(1)h Fm(:)233 b Fp(\(2)p Fm(:)p Fp(29\))71 2286 y(The)28 b(discussion)e(follo)n(wing)h(\(2.18\))g(implies)h(that)1223 2516 y Fk(j)p Fm(\014)1297 2482 y Ff(\027)1293 2537 y(k)1339 2516 y Fp(\()p Fm(\027)1412 2528 y Ff(k)1453 2516 y 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y Fg(h;n)1079 4019 y(;)p Fb(P)p Fd(2P)1220 4027 y Fg(\034)1259 4019 y(;)p Fb(r)p Fh(:)p Fg(P)1357 4027 y(v)1387 4039 y Fh(0)1423 4019 y(=\()p Fg(f)1516 4031 y Fh(1)1549 4019 y Fg(;f)1596 4031 y Fh(2)1629 4019 y(\))p Fg(;)840 4106 y(\033)874 4118 y Fh(1)906 4106 y(=)p Fg(!)986 4118 y Fh(1)1018 4106 y(=\()p Fd(\000)p Fh(1\))1178 4094 y Fg(l)p Fd(\000)p Fh(1)1276 4106 y Fg(\033)1310 4118 y Fh(2)1342 4106 y(=\()p Fd(\000)p Fh(1\))1502 4094 y Fg(l)1527 4106 y(!)1564 4118 y Fh(2)1596 4106 y(=+1)1746 3840 y Fe(X)1734 4018 y Ff(T)k Fq(2)p Fc(T)1987 3840 y Fe(X)1963 4006 y Fg(\013)p Fd(2)p Fg(A)2083 4020 y(T)1902 4062 y(q)1929 4070 y(\013)1972 4062 y Fh(\()p Fg(P)2030 4070 y(v)2060 4082 y Fh(0)2097 4062 y(\)=0)2214 3918 y Fm(z)2257 3875 y Fj(\()p Ff(l)p Fj(\))2253 3944 y Ff(h)2334 3918 y Fp(\()p Fm(\034)c(;)14 b Fl(P)p Fm(;)g Fl(r)p Fm(;)g(T)7 b(;)14 b(\013)p Fp(\))24 b Fm(;)248 b Fp(\(3)p Fm(:)p Fp(22\))0 4283 y(where,)27 b(if)h Fl(x)g Fp(is)g(the)g(space)f 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4780 y Fg(i)1307 4763 y Fj(\))1140 4837 y Ff(j)1167 4845 y Fg(\013)1210 4837 y Fj(\()p Ff(v)1271 4817 y Fd(\003)1269 4858 y Fg(i)1306 4837 y Fj(\))1338 4808 y Fp(\()p Fl(x)1420 4820 y Ff(i)1448 4808 y Fm(;)14 b Fl(y)1535 4820 y Ff(i)1563 4808 y Fp(\))p Fm(K)1672 4772 y Ff(h)1711 4780 y Fg(i)1666 4832 y Ff(v)1701 4812 y Fd(\003)1699 4853 y Fg(i)1741 4808 y Fp(\()p Fl(x)1823 4820 y Ff(v)1858 4801 y Fd(\003)1856 4842 y Fg(i)1898 4808 y Fp(\))1930 4716 y Fe(in)2126 4730 y(Y)2038 4909 y Ff(v)g Fi(not)24 b(e.p.)2374 4752 y Fp(1)p 2344 4789 102 4 v 2344 4865 a Fm(s)2383 4877 y Ff(v)2422 4865 y Fp(!)2469 4695 y Fe(Z)2566 4808 y Fm(dP)2662 4820 y Ff(T)2701 4828 y Fg(v)2742 4808 y Fp(\()p Fl(t)2811 4820 y Ff(v)2850 4808 y Fp(\))g Fk(\001)185 5068 y(\001)41 b Fp(det)14 b Fm(G)443 5034 y Ff(h)482 5042 y Fg(v)518 5034 y Ff(;T)577 5042 y Fg(v)443 5089 y Ff(\013)617 5068 y Fp(\()p Fl(t)686 5080 y Ff(v)726 5068 y Fp(\))758 4976 y Fe(h)828 4990 y(Y)811 5168 y Ff(l)p Fq(2)p Ff(T)916 5176 y Fg(v)976 5047 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Fg(l)2230 5108 y Ff(;!)2294 5081 y Fh(+)2292 5130 y Fg(l)2345 5068 y Fp(\()p Fl(x)2427 5080 y Ff(l)2472 5068 y Fk(\000)k Fl(y)2605 5080 y Ff(l)2630 5068 y Fp(\)])2685 4976 y Fe(i)q(o)2803 5068 y Fm(:)3095 4812 y Fp(\(3)p Fm(:)p Fp(23\))71 5370 y(The)31 b(notations)e(are)h(the)h(same)f(as)g(in)h Fk(x)p Fl(I)p Fp(3.10)e(and)h(w)n(e)h(can)f(deriv)n(e)g(for)g Fm(z)2433 5327 y Fj(\()p Ff(l)p Fj(\))2429 5395 y Ff(h)2509 5370 y Fp(\()p Fm(\034)5 b(;)14 b Fl(P)p Fm(;)g Fl(r)p Fm(;)g(T)7 b(;)14 b(\013)p Fp(\))32 b(a)e(b)r(ound)0 5520 y(similar)d(to)h(\()p Fl(I)p Fp(3.110\),)f(without)i(the)f(v)n (olume)g(factor)f Fm(L\014)32 b Fp(\(the)d(in)n(tegration)e(o)n(v)n(er) f Fm(x)2654 5532 y Ff(v)2687 5540 y Fh(0)2752 5520 y Fp(is)i(done)g(k)n(eeping)0 5669 y Fl(x)34 b Fp(\014xed\).)54 b(The)34 b(only)e(relev)-5 b(an)n(t)33 b(di\013erence)g(is)g(that)h (the)g(b)r(ounds)f(\()p Fl(I)p Fp(3.83\))g(and)g(\()p Fl(I)p Fp(3.107\))f(ha)n(v)n(e)h(to)g(b)r(e)0 5869 y Fh(14)p Fg(=apr)q(ile=)p Fh(2000;)28 b(18:23)1046 b Fp(17)p eop %%Page: 18 18 18 17 bop 0 83 a Fp(mo)r(di\014ed,)25 b(in)e(order)f(to)h(tak)n(e)f(in) n(to)h(accoun)n(t)f(the)i(prop)r(erties)e(of)h(the)h(extended)f(lo)r (calization)f(op)r(eration,)0 232 y(b)n(y)27 b(substituting)h Fm(z)t Fp(\()p Fm(P)705 244 y Ff(v)745 232 y Fp(\))g(and)k(~)-47 b Fm(z)s Fp(\()p Fm(P)1093 244 y Ff(v)1133 232 y Fp(\))28 b(with)h Fm(z)t Fp(\()p Fm(P)1511 244 y Ff(v)1550 232 y Fm(;)14 b(l)1612 244 y Ff(v)1651 232 y Fp(\))28 b(and)k(~)-47 b Fm(z)t Fp(\()p Fm(P)2000 244 y Ff(v)2040 232 y Fm(;)14 b(l)2102 244 y Ff(v)2141 232 y Fp(\),)28 b(resp)r(ectiv)n(ely)-7 b(,)27 b(with)526 600 y Fm(z)t Fp(\()p Fm(P)654 612 y Ff(v)693 600 y Fm(;)14 b(l)755 612 y Ff(v)794 600 y Fp(\))23 b(=)937 355 y Fe(8)937 429 y(>)937 454 y(>)937 479 y(>)937 504 y(<)937 654 y(>)937 678 y(>)937 703 y(>)937 728 y(:)1025 411 y Fp(1)82 b(if)28 b Fk(j)p Fm(P)1301 423 y Ff(v)1341 411 y Fk(j)23 b Fp(=)g(4,)k Fm(l)1592 423 y Ff(v)1654 411 y Fp(=)c(0)1025 510 y(1)82 b(if)28 b Fk(j)p Fm(P)1301 522 y Ff(v)1341 510 y Fk(j)23 b Fp(=)g(2,)k Fm(l)1592 522 y Ff(v)1654 510 y Fp(=)c(0)k(and)1973 448 y Fe(P)2060 535 y Ff(f)7 b Fq(2)p Ff(P)2186 543 y Fg(v)2240 510 y Fm(!)s Fp(\()p Fm(f)i Fp(\))23 b Fk(6)p Fp(=)f(0)h Fm(;)1025 610 y Fp(2)82 b(if)28 b Fk(j)p Fm(P)1301 622 y Ff(v)1341 610 y Fk(j)23 b Fp(=)g(2,)k Fm(l)1592 622 y Ff(v)1654 610 y Fp(=)c(0)k(and)1973 548 y Fe(P)2060 635 y Ff(f)7 b Fq(2)p Ff(P)2186 643 y Fg(v)2240 610 y Fm(!)s Fp(\()p Fm(f)i Fp(\))23 b(=)f(0)h Fm(;)1025 710 y Fp(1)82 b(if)28 b Fk(j)p Fm(P)1301 722 y Ff(v)1341 710 y Fk(j)23 b Fp(=)g(2,)k Fm(l)1592 722 y Ff(v)1654 710 y Fp(=)c(1)k(and)1973 647 y Fe(P)2060 735 y Ff(f)7 b Fq(2)p Ff(P)2186 743 y Fg(v)2240 710 y Fm(\033)s Fp(\()p Fm(f)i Fp(\))p Fm(!)s Fp(\()p Fm(f)g Fp(\))23 b(=)g(0)f Fm(;)1025 809 y Fp(0)82 b(otherwise.)3095 600 y(\(3)p Fm(:)p Fp(24\))534 1056 y(~)-47 b Fm(z)s Fp(\()p Fm(P)656 1068 y Ff(v)696 1056 y Fm(;)14 b(l)758 1068 y Ff(v)798 1056 y Fp(\))23 b(=)940 914 y Fe(\()1021 967 y Fp(1)83 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Fh(0)1483 1442 y Fj(\()p Ff(P)1551 1450 y Fg(v)1581 1462 y Fh(0)1618 1442 y Fj(\)+)p Ff(l)1716 1450 y Fg(v)1746 1462 y Fh(0)1782 1442 y Fj(])1907 1397 y Fe(Y)1819 1576 y Ff(v)14 b Fi(not)24 b(e.p.)2115 1384 y Fe(n)2170 1476 y Fm(C)2235 1380 y Fe(P)2323 1400 y Fg(s)2351 1408 y(v)2323 1467 y(i)p Fh(=1)2432 1436 y Fq(j)p Ff(P)2494 1444 y Fg(v)2524 1457 y(i)2554 1436 y Fq(j\000j)p Ff(P)2688 1444 y Fg(v)2723 1436 y Fq(j)2770 1476 y Fk(\001)320 1749 y(\001)425 1693 y Fp(1)p 395 1730 102 4 v 395 1806 a Fm(s)434 1818 y Ff(v)473 1806 y Fp(!)506 1657 y Fe(\020)556 1749 y Fm(Z)613 1761 y Ff(h)652 1769 y Fg(v)691 1749 y Fm(=)-5 b(Z)785 1761 y Ff(h)824 1769 y Fg(v)859 1761 y Fq(\000)p Fj(1)948 1657 y Fe(\021)998 1674 y Fq(j)p Ff(P)1060 1682 y Fg(v)1095 1674 y Fq(j)p Ff(=)p Fj(2)1186 1749 y Fm(\015)1234 1715 y Fq(\000)p Fj([)p Fq(\000)p Fj(2+)1451 1685 y Fd(j)p Fg(P)1506 1693 y(v)1542 1685 y Fd(j)p 1451 1702 111 4 v 1491 1735 a Fh(2)1571 1715 y Fj(+)p Ff(l)1643 1723 y Fg(v)1678 1715 y Fj(+)p Ff(z)r Fj(\()p Ff(P)1831 1723 y Fg(v)1867 1715 y Ff(;l)1908 1723 y Fg(v)1943 1715 y Fj(\)+)2034 1685 y Fh(~)-32 b Fg(z)q Fh(\()p Fg(P)2118 1693 y(v)2155 1685 y(;l)2194 1693 y(v)2229 1685 y Fh(\))p 2030 1702 222 4 v 2127 1735 a(2)2262 1715 y Fj(])2285 1657 y Fe(o)2363 1749 y Fm(;)3095 1620 y Fp(\(3)p Fm(:)p Fp(26\))0 1971 y(with)626 2121 y Fk(\000)p Fp(2)17 b(+)843 2065 y Fk(j)p Fm(P)919 2077 y Ff(v)959 2065 y Fk(j)p 843 2102 139 4 v 892 2178 a Fp(2)1010 2121 y(+)h Fm(l)1118 2133 y Ff(v)1176 2121 y Fp(+)g Fm(z)t Fp(\()p Fm(P)1387 2133 y Ff(v)1426 2121 y Fm(;)c(l)1488 2133 y Ff(v)1527 2121 y Fp(\))19 b(+)1676 2065 y(~)-47 b Fm(z)s Fp(\()p Fm(P)1798 2077 y Ff(v)1839 2065 y Fm(;)14 b(l)1901 2077 y Ff(v)1940 2065 y Fp(\))p 1671 2102 301 4 v 1801 2178 a(2)2005 2121 y Fk(\025)2103 2065 y Fp(1)p 2103 2102 42 4 v 2103 2178 a(2)2177 2121 y Fm(;)97 b Fk(8)p Fm(v)16 b Fi(not)25 b(e.p.)d Fm(:)414 b Fp(\(3)p Fm(:)p Fp(27\))71 2323 y(Hence,)29 b(w)n(e)f(can)g(pro)r(ceed)f(as)h(in)h Fk(x)p Fl(I)p 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Fe(8)481 5465 y(<)481 5614 y(:)554 5560 y Fk(\000)662 5504 y Fp(1)p 629 5541 108 4 v 629 5617 a Fm(L\014)791 5481 y Fe(X)761 5657 y Ff(!)r Fj(=)p Fq(\006)p Fj(1)1099 5481 y Fe(X)954 5674 y Fc(k)994 5658 y Fd(0)1016 5674 y Fj(:)p Ff(C)1087 5647 y Fd(\000)p Fh(1)1083 5694 y(0)1164 5674 y Fj(\()p Fc(k)1230 5658 y Fd(0)1252 5674 y Fj(\))p Ff(>)p Fj(0)1377 5560 y Fm(C)1436 5572 y Fj(0)1474 5560 y Fp(\()p Fl(k)1556 5526 y Fq(0)1580 5560 y Fp(\))1612 5493 y Fe(\000)1668 5560 y Fk(\000)18 b Fm(ik)1823 5572 y Fj(0)1879 5560 y Fp(+)g Fm(!)s(v)2060 5526 y Fq(\003)2057 5581 y Fj(0)2098 5560 y Fm(k)2144 5526 y Fq(0)2167 5493 y Fe(\001)2222 5538 y Fp(^)2205 5560 y Fm( )2262 5517 y Fj(\()p Fq(\024)p Fj(0\)+)2259 5585 y Fc(k)2299 5569 y Fd(0)2321 5585 y Ff(;!)2471 5538 y Fp(^)2454 5560 y Fm( )2511 5517 y Fj(\()p Fq(\024)p Fj(0\))p Fq(\000)2508 5585 y Fc(k)2548 5569 y Fd(0)2570 5585 y Ff(;!)2704 5390 y Fe(9)2704 5465 y(=)2704 5614 y(;)2815 5560 y Fm(;)3095 5401 y Fp(\(3)p Fm(:)p Fp(30\))0 5869 y Fh(14)p Fg(=apr)q(ile=)p Fh(2000;)28 b(18:23)1046 b Fp(18)p eop %%Page: 19 19 19 18 bop 602 113 a Fm(V)669 79 y Fj(\()p Ff(L)p Fj(\))771 113 y Fp(\()p Fm( )860 79 y Fj(\()p Fq(\024)p Fj(0\))1001 113 y Fp(\))24 b(=)e Fm(\025)1192 70 y Fj(\()p Ff(L)p Fj(\))1192 135 y(0)1308 0 y Fe(Z)1354 189 y Fa(T)1410 197 y Fg(L;\014)1525 113 y Fm(d)p Fl(x)i Fm( )1699 70 y Fj(\()p Fq(\024)p Fj(0\)+)1696 135 y Fc(x)p Ff(;)p Fj(+1)1891 113 y Fm( )1948 70 y Fj(\()p Fq(\024)p Fj(0\))p Fq(\000)1945 135 y Fc(x)p Ff(;)p Fq(\000)p Fj(1)2141 113 y Fm( )2198 70 y Fj(\()p Fq(\024)p Fj(0\)+)2195 135 y Fc(x)p Ff(;)p Fq(\000)p Fj(1)2390 113 y Fm( )2447 70 y Fj(\()p Fq(\024)p Fj(0\))p Fq(\000)2444 135 y Fc(x)p Ff(;)p Fj(+1)2640 113 y Fp(+)1052 352 y(+)18 b Fm(\016)1175 309 y Fj(\()p Ff(L)p Fj(\))1172 374 y(0)1320 273 y Fe(X)1291 449 y Ff(!)r Fj(=)p Fq(\006)p Fj(1)1484 352 y Fm(i!)1581 239 y Fe(Z)1627 427 y Fa(T)1683 436 y Fg(L;\014)1799 352 y Fm(d)p Fl(x)23 b Fm( )1972 317 y Fj(\()p Fq(\024)p Ff(h)p Fj(\)+)1969 372 y Fc(x)p Ff(;!)2170 352 y Fm(@)2214 364 y Ff(x)2256 352 y Fm( )2313 317 y Fj(\()p Fq(\024)p Ff(h)p Fj(\))p Fq(\000)2310 372 y Fc(x)p Ff(;!)2535 352 y Fm(;)3095 253 y Fp(\(3)p Fm(:)p Fp(31\))0 619 y(where)30 b Fk(N)311 631 y Ff(L)361 619 y Fp(\()p Fl(k)443 589 y Fq(0)467 619 y Fp(\))e(=)f Fm(C)678 631 y Fj(0)716 619 y Fp(\()p Fl(k)798 589 y Fq(0)822 619 y Fp(\)\()p Fm(L\014)t Fp(\))1026 589 y Fq(\000)p Fj(1)1115 619 y Fp([)p Fm(k)1184 589 y Fj(2)1181 639 y(0)1242 619 y Fp(+)20 b(\()p Fm(v)1402 589 y Fq(\003)1399 639 y Fj(0)1441 619 y Fm(k)1487 589 y Fq(0)1510 619 y Fp(\))1542 589 y Fj(2)1579 619 y Fp(])1602 589 y Fj(1)p Ff(=)p Fj(2)1707 619 y Fp(,)31 b Fm(\025)1809 576 y Fj(\()p Ff(L)p Fj(\))1809 641 y(0)1941 619 y Fp(and)g Fm(\016)2146 576 y Fj(\()p Ff(L)p Fj(\))2143 641 y(0)2278 619 y Fp(ha)n(v)n(e)e(the)i(role)e(of)i(the)g(running)0 768 y(couplings)24 b(on)g(scale)g(0)g(of)h(the)g(original)e(mo)r(del,)j (but)f(are)f(not)g(necessarily)f(equal)i(to)f(them,)i Fa(T)2976 780 y Ff(L;\014)3111 768 y Fp(is)f(the)0 918 y(\(con)n(tin)n(uous,)d(as)g(in)g Fk(x)p Fl(I)p Fp(3.15\))f(torus)g([0) p Fm(;)14 b(L)p Fp(])7 b Fk(\002)g Fp([0)p Fm(;)14 b(\014)t Fp(])22 b(and)g Fm( )1808 887 y Fj(\()p Fq(\024)p Fj(0\))1971 918 y Fp(is)g(the)g(\(con)n(tin)n(uous\))g(Grassmanian)e(\014eld)0 1067 y(on)25 b Fa(T)168 1079 y Ff(L;\014)303 1067 y Fp(with)h(an)n(tip) r(erio)r(dic)e(b)r(oundary)g(conditions.)36 b(Moreo)n(v)n(er,)23 b(the)i(in)n(teraction)f(with)i(the)f(external)0 1216 y(\014eld)k Fk(B)239 1186 y Fj(\(1\))327 1216 y Fp(\()p Fm( )416 1186 y Fj(\()p Fq(\024)p Fj(1\))557 1216 y Fm(;)14 b(\036)p Fp(\))29 b(is)g(substituted)g(with)g(the)g(corresp)r(onding)d (expression)h(on)h(scale)g(0,)g(depriv)n(ed)g(of)0 1366 y(the)g(irrelev)-5 b(an)n(t)26 b(terms,)i(that)g(is)186 1617 y Fk(B)244 1582 y Fj(\(0\))332 1617 y Fp(\()p Fm( )421 1582 y Fj(\()p Fq(\024)p Fj(0\))562 1617 y Fm(;)14 b(\036)p Fp(\))24 b(=)820 1538 y Fe(X)791 1714 y Ff(\033)r Fj(=)p Fq(\006)p Fj(1)982 1504 y Fe(Z)1079 1617 y Fm(d)p Fl(x)p Fm(\036)p Fp(\()p Fl(x)p Fp(\))1349 1524 y Fe(\020)1400 1617 y Fm(e)1439 1582 y Fj(2)p Ff(i\033)r Fc(p)1577 1590 y Fg(F)1625 1582 y Fc(x)1669 1617 y Fm( )1726 1582 y Fj(\()p Fq(\024)p Ff(h)p Fj(\))p Ff(\033)1723 1637 y Fc(x)p Ff(;\033)1913 1617 y Fm( )1970 1573 y Fj(\()p Fq(\024)p Ff(h)p Fj(\))p Ff(\033)1967 1637 y Fc(x)p Ff(;)p Fq(\000)p Ff(\033)2176 1617 y Fp(+)18 b Fm( )2316 1582 y Fj(\()p Fq(\024)p Ff(h)p Fj(\))p Ff(\033)2313 1637 y Fc(x)p Ff(;\033)2504 1617 y Fm( )2561 1582 y Fj(\()p Fq(\024)p Ff(h)p Fj(\))p Fq(\000)p Ff(\033)2558 1637 y Fc(x)p Ff(;\033)2800 1524 y Fe(\021)2886 1617 y Fm(:)186 b Fp(\(3)p Fm(:)p Fp(32\))0 1925 y(W)-7 b(e)34 b(shall)g(call)f Fm(Z)571 1882 y Fj(\(2)p Ff(;L)p Fj(\))565 1950 y Ff(h)725 1925 y Fp(,)j Fm(z)827 1882 y Fj(\(2)p Ff(;L)p Fj(\))823 1950 y Ff(h)980 1925 y Fp(,)g Fm(Z)1102 1882 y Fj(\()p Ff(L)p Fj(\))1096 1950 y Ff(h)1237 1925 y Fp(and)e Fm(z)1448 1882 y Fj(\()p Ff(L)p Fj(\))1444 1950 y Ff(h)1583 1925 y 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Fm(;)14 b(\016)2354 2815 y Fq(\003)2392 2849 y Fp(\))2424 2757 y Fe(i)2487 2849 y Fm(;)585 b Fp(\(3)p Fm(:)p Fp(34\))0 3113 y(where)31 b Fm(a)288 3070 y Fj(\()p Ff(L)p Fj(\))288 3138 y Ff(h)421 3113 y Fp(are)g(the)h(running)f(couplings)f(in)i(the)g(appro)n(ximated)e (Luttinger)h(mo)r(del)h(\(b)n(y)g(symmetry)0 3263 y Fm(\027)46 3219 y Fj(\()p Ff(L)p Fj(\))41 3288 y Ff(h)171 3263 y Fp(=)23 b(0,)f(since)f Fm(\027)29 b Fp(=)22 b(0,)h(see)e Fk(x)p Fp(2.4\),)h(1)6 b(+)g Fm(\014)1307 3232 y Fj(\(2\))1419 3263 y Fp(=)23 b(\(1)6 b(+)g Fm(z)1701 3219 y Fj(\(2\))1697 3288 y Ff(h)1790 3263 y Fp(\))p Fm(=)p Fp(\(1)g(+)g Fm(z)2054 3275 y Ff(h)2096 3263 y Fp(\))22 b(and)g(1)6 b(+)g Fm(\014)2476 3232 y Fj(\(2)p Ff(;L)p Fj(\))2653 3263 y Fp(=)23 b(\(1)6 b(+)g Fm(z)2935 3219 y Fj(\(2)p Ff(;L)p Fj(\))2931 3288 y Ff(h)3089 3263 y Fp(\))p Fm(=)p Fp(\(1)g(+)0 3412 y Fm(z)43 3369 y Fj(\()p Ff(L)p Fj(\))39 3437 y Ff(h)144 3412 y Fp(\).)71 3562 y(The)28 b(Luttinger)h(mo)r(del)f(has)g(a)g(sp)r 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Fj(\()p Ff(h)p Fj(\))1377 920 y Ff(!)r(;!)1485 904 y Fd(0)1538 896 y Fp(with)k(the)f(propagators)g(\026)-45 b Fm(g)2369 853 y Fj(\()p Ff(h)p Fj(\))2366 920 y Ff(!)r(;!)2474 904 y Fd(0)2500 896 y Fp(,)28 b(de\014ned)f(in)g(\(3.61\).)36 b(By)0 1045 y(using)27 b(the)h(symmetry)f(relations)814 1264 y(\026)-45 b Fm(g)854 1230 y Fj(\()p Ff(h)p Fj(\))851 1285 y Ff(!)r(;!)962 1264 y Fp(\()p Fm(x;)14 b(x)1125 1276 y Fj(0)1164 1264 y Fp(\))23 b(=)g Fk(\000)s Fp(\026)-45 b Fm(g)1415 1230 y Fj(\()p Ff(h)p Fj(\))1412 1285 y Ff(!)r(;!)1523 1264 y Fp(\()p Fk(\000)p Fm(x;)14 b Fk(\000)p Fm(x)1816 1276 y Fj(0)1853 1264 y Fp(\))23 b(=)j(\026)-45 b Fm(g)2039 1221 y Fj(\()p Ff(h)p Fj(\))2036 1285 y(+)p Ff(;)p Fj(+)2162 1264 y Fp(\()p Fm(!)s(x;)14 b(x)2380 1276 y Fj(0)2417 1264 y Fp(\))24 b Fm(;)881 1439 y Fp(\026)-45 b Fm(g)921 1395 y Fj(\()p Ff(h)p Fj(\))918 1459 y Ff(!)r(;)p Fq(\000)p Ff(!)1081 1439 y Fp(\()p Fl(x)p Fp(\))24 b(=)i(\026)-45 b Fm(g)1350 1395 y Fj(\()p Ff(h)p Fj(\))1347 1459 y Ff(!)r(;)p Fq(\000)p Ff(!)1510 1439 y Fp(\()p Fk(\000)p Fl(x)p Fp(\))24 b(=)e Fm(!)6 b Fp(\026)-45 b Fm(g)1898 1395 y Fj(\()p Ff(h)p Fj(\))1895 1459 y(+)p Ff(;)p Fq(\000)2021 1439 y Fp(\()p Fl(x)p Fp(\))24 b Fm(;)3095 1345 y Fp(\(4)p Fm(:)p Fp(12\))0 1644 y(it)k(is)g(easy)e(to)i(sho)n(w)e(that)i(w)n(e)f (can)h(write)873 1880 y(\026)863 1901 y(\012)923 1861 y Fj(3)p Ff(;)p Fj(0)923 1926 y Ff(L;\014)1033 1901 y Fp(\()p Fl(x)p Fp(\))c(=)f(cos)o(\(2)p Fm(p)1486 1913 y Ff(F)1541 1901 y Fm(x)p Fp(\))1629 1880 y(\026)1620 1901 y(\012)1680 1913 y Fj(1)p Ff(;L;\014)1843 1901 y Fp(\()p Fl(x)p Fp(\))d(+)2069 1880 y(\026)2060 1901 y(\012)2120 1913 y Fj(2)p Ff(;L;\014)2283 1901 y Fp(\()p Fl(x)p Fp(\))k Fm(;)651 b Fp(\(4)p Fm(:)p Fp(13\))520 2185 y(\026)511 2206 y(\012)571 2218 y Fj(1)p Ff(;L;\014)734 2206 y Fp(\()p Fl(x)p Fp(\))24 b(=)e(2)1120 2127 y Fe(X)1015 2305 y Ff(h)1054 2289 y Fd(\003)1088 2305 y Fq(\024)p Ff(h;h)1238 2289 y Fd(0)1260 2305 y Fq(\024)p Fj(0)1411 2148 y Fp(\()p Fm(Z)1506 2105 y Fj(\(1\))1500 2173 y Ff(h)p Fq(_)p Ff(h)1623 2157 y Fd(0)1649 2148 y Fp(\))1681 2118 y Fj(2)p 1369 2187 392 4 v 1369 2263 a Fm(Z)1426 2275 y Ff(h)p Fq(\000)p Fj(1)1553 2263 y Fm(Z)1610 2275 y Ff(h)1649 2258 y Fd(0)1671 2275 y Fq(\000)p Fj(1)1770 2113 y Fe(h)1813 2206 y Fp(\026)-45 b Fm(g)1853 2163 y Fj(\()p Ff(h)p Fj(\))1850 2226 y(+)p Ff(;)p Fj(+)1975 2206 y Fp(\()p Fm(x;)14 b(x)2138 2218 y Fj(0)2176 2206 y Fp(\))s(\026)-45 b Fm(g)2251 2163 y Fj(\()p Ff(h)2316 2137 y Fd(0)2339 2163 y Fj(\))2248 2226 y(+)p Ff(;)p Fj(+)2374 2206 y Fp(\()p Fk(\000)p Fm(x;)14 b(x)2602 2218 y Fj(0)2640 2206 y Fp(\)+)1828 2454 y(+)21 b(\026)-45 b Fm(g)1954 2411 y Fj(\()p Ff(h)p Fj(\))1951 2474 y(+)p Ff(;)p Fq(\000)2077 2454 y Fp(\()p Fm(x;)14 b(x)2240 2466 y Fj(0)2279 2454 y Fp(\))s(\026)-45 b Fm(g)2354 2411 y Fj(\()p Ff(h)2419 2386 y Fd(0)2441 2411 y Fj(\))2351 2474 y(+)p Ff(;)p Fq(\000)2477 2454 y Fp(\()p Fm(x;)14 b(x)2640 2466 y Fj(0)2679 2454 y Fp(\))2711 2362 y Fe(i)2773 2454 y Fm(;)3095 2305 y Fp(\(4)p Fm(:)p Fp(14\))544 2713 y(\026)535 2734 y(\012)595 2746 y Fj(2)p Ff(;L;\014)758 2734 y Fp(\()p Fl(x)p Fp(\))24 b(=)1026 2655 y Fe(X)983 2834 y Ff(h;h)1081 2818 y Fd(0)1103 2834 y Fq(\024)p Fj(0)1254 2677 y Fp(\()p Fm(Z)1349 2634 y Fj(\(2\))1343 2702 y Ff(h)p Fq(_)p Ff(h)1466 2685 y Fd(0)1492 2677 y Fp(\))1524 2647 y Fj(2)p 1212 2715 V 1212 2791 a Fm(Z)1269 2803 y Ff(h)p Fq(\000)p Fj(1)1397 2791 y Fm(Z)1454 2803 y Ff(h)1493 2787 y Fd(0)1515 2803 y Fq(\000)p Fj(1)1614 2642 y Fe(h)1667 2655 y(X)1705 2830 y Ff(!)1803 2734 y Fp(\026)-45 b Fm(g)1843 2691 y Fj(\()p Ff(h)p Fj(\))1840 2755 y(+)p Ff(;)p Fj(+)1966 2734 y Fp(\()p Fm(!)s(x;)14 b(x)2184 2746 y Fj(0)2222 2734 y Fp(\))s(\026)-45 b Fm(g)2297 2691 y Fj(\()p Ff(h)2362 2666 y Fd(0)2384 2691 y Fj(\))2294 2755 y(+)p Ff(;)p Fj(+)2420 2734 y Fp(\()p Fm(!)s(x;)14 b(x)2638 2746 y Fj(0)2676 2734 y Fp(\))p Fk(\000)1671 2982 y(\000)k Fp(2)s(\026)-45 b Fm(g)1839 2939 y Fj(\()p Ff(h)p Fj(\))1836 3003 y(+)p Ff(;)p Fq(\000)1962 2982 y Fp(\()p 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Fe(X)1611 3762 y Ff(h)p Fj(=)p Ff(h)1740 3746 y Fd(\003)1788 3521 y Fe( )1864 3605 y Fm(Z)1927 3562 y Fj(\(1\))1921 3630 y Ff(h)p 1864 3643 152 4 v 1890 3720 a Fm(Z)1947 3732 y Ff(h)2025 3521 y Fe(!)2091 3538 y Fj(2)2161 3642 y Fp(\026)2142 3663 y Fm(G)2207 3619 y Fj(\()p Ff(h)p Fj(\))2207 3688 y(1)p Ff(;L;\014)2370 3663 y Fp(\()p Fl(x)p Fp(\))k Fm(;)564 b Fp(\(4)p Fm(:)p Fp(16\))776 4057 y(\012)836 4017 y Fj(3)p Ff(;b)836 4082 y(L;\014)946 4057 y Fp(\()p Fl(x)p Fp(\))24 b(=)1181 4036 y(\026)1171 4057 y(\012)1231 4069 y Fj(2)p Ff(;L;\014)1394 4057 y Fp(\()p Fl(x)p Fp(\))c(+)1676 3953 y Fj(0)1632 3978 y Fe(X)1611 4157 y Ff(h)p Fj(=)p Ff(h)1740 4140 y Fd(\003)1788 3915 y Fe( )1864 3999 y Fm(Z)1927 3956 y Fj(\(2\))1921 4025 y Ff(h)p 1864 4038 V 1890 4114 a Fm(Z)1947 4126 y Ff(h)2025 3915 y Fe(!)2091 3932 y Fj(2)2161 4036 y Fp(\026)2142 4057 y Fm(G)2207 4014 y Fj(\()p Ff(h)p Fj(\))2207 4082 y(2)p Ff(;L;\014)2370 4057 y Fp(\()p Fl(x)p Fp(\))k Fm(;)564 b Fp(\(4)p Fm(:)p Fp(17\))246 4418 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Fm(;)312 b Fp(\(4)p Fm(:)p Fp(42\))1166 5669 y Fm(\016)s Fp(\012)1266 5635 y Fj(3)p Ff(;c)1353 5669 y Fp(\()p Fl(x)p Fp(\))24 b(=)e(\012)1638 5635 y Fj(3)p Ff(;c)1725 5669 y Fp(\()p Fl(x)p Fp(\))d Fk(\000)f Fm(s)p Fp(\()p Fl(x)p Fp(\))24 b Fm(:)954 b Fp(\(4)p Fm(:)p Fp(43\))0 5869 y Fh(14)p Fg(=apr)q(ile=)p Fh(2000;)28 b(18:23)1046 b Fp(33)p eop %%Page: 34 34 34 33 bop 71 83 a Fp(Since)32 b(an)n(y)g(graph)f(con)n(tributing)h(to)g (the)h(expansion)f(of)g(\012)1976 53 y Fj(3)p Ff(;a)2069 83 y Fp(\()p Fl(x)22 b Fk(\000)f Fl(y)q Fp(\))34 b(has)e(only)g(t)n(w)n (o)f(propagators)0 232 y(of)37 b(scale)f Fk(\024)j Fp(0)e(connected)g (to)g Fl(x)g Fp(or)g Fl(y)q Fp(,)1325 211 y(^)1316 232 y(\012)1376 202 y Fj(3)p Ff(;a)1469 232 y Fp(\()p Fl(k)p Fp(\))h(has)f(supp)r(ort)g(on)f(a)h(set)g(of)g(v)-5 b(alue)37 b(of)g Fl(k)h Fp(suc)n(h)f(that)0 382 y Fk(j)p Fm(k)s Fk(j)23 b(\024)g Fp(2)p Fm(\015)5 b(t)323 394 y Fj(0)382 382 y Fm(<)23 b(\031)s Fp(;)j(hence)e(w)n(e)g(can)g(calculate)1416 361 y(^)1407 382 y(\012)1467 352 y Fj(3)p Ff(;a)1560 382 y Fp(\()p Fl(k)p Fp(\))i(b)n(y)e(thinking)g(\012)2198 352 y Fj(3)p Ff(;a)2291 382 y Fp(\()p Fl(x)p Fp(\))i(as)e(a)g(function) h(on)f Fa(R)3090 345 y Fj(2)3127 382 y Fp(.)36 b(Let)0 531 y(us)28 b(supp)r(ose)f(that)h Fk(j)p Fl(k)p Fk(j)23 b Fm(>)g Fp(0)k(and)h Fk(j)p Fm(k)s Fk(j)23 b(\025)f(j)p Fl(k)p Fk(j)p Fm(=)p Fp(2;)27 b(then)588 716 y(^)579 737 y(\012)639 703 y Fj(3)p Ff(;a)732 737 y Fp(\()p Fl(k)p Fp(\))d(=)958 624 y Fe(Z)1055 737 y Fm(d)p Fl(x)p Fm(e)1187 703 y Ff(i)p Fc(kx)1294 737 y Fp(\012)1354 703 y Fj(3)p Ff(;a)1447 737 y Fp(\()p Fl(x)p Fp(\))g(=)1691 681 y Fm(i)p 1682 718 46 4 v 1682 794 a(k)1752 624 y Fe(Z)1849 737 y Fm(d)p Fl(x)1956 670 y Fe(\002)1991 737 y Fm(e)2030 703 y Ff(i)p Fc(kx)2155 737 y Fk(\000)18 b Fp(1)2280 670 y Fe(\003)2328 737 y Fm(@)2372 749 y Ff(x)2414 737 y Fp(\012)2474 703 y Fj(3)p Ff(;a)2567 737 y Fp(\()p Fl(x)p Fp(\))24 b Fm(;)367 b Fp(\(4)p Fm(:)p Fp(44\))0 943 y(since)30 b(\012)266 913 y Fj(3)p Ff(;a)359 943 y Fp(\()p Fl(x)p Fp(\),)i(b)n(y)e(\()p Fl(I)p Fp(1.16\),)g(is)g(a)f (smo)r(oth)h(function)h(of)f(fast)g(decrease)f(as)g Fk(j)p Fl(x)p Fk(j)f(!)f(1)p Fp(.)45 b(If)30 b Fk(j)p Fm(k)s Fk(j)e Fm(<)e Fk(j)p Fl(k)p Fk(j)p Fm(=)p Fp(2,)0 1093 y(it)i(has)e(to)h(b)r(e)h(true)f(that)h Fk(j)p Fm(k)865 1105 y Fj(0)902 1093 y Fk(j)23 b(\025)g(j)p Fl(k)p Fk(j)p Fm(=)p Fp(2)k(and)g(w)n(e)g(write)g(a)f(similar)h(iden)n(tit)n(y)-7 b(,)27 b(with)h Fm(k)2633 1105 y Fj(0)2698 1093 y Fp(in)f(place)g(of)g Fm(k)j Fp(and)0 1242 y Fm(@)44 1254 y Ff(x)82 1262 y Fh(0)146 1242 y Fp(in)e(place)f(of)h Fm(@)594 1254 y Ff(x)635 1242 y Fp(.)37 b(In)28 b(b)r(oth)g(case)f(w)n(e)g(can)g (write,)h(b)n(y)f(using)g(\()p Fl(I)p Fp(1.16\),)311 1448 y Fk(j)343 1427 y Fp(^)334 1448 y(\012)394 1414 y Fj(3)p Ff(;a)487 1448 y Fp(\()p Fl(k)p Fp(\))p Fk(j)d(\024)761 1392 y Fm(C)p 746 1429 97 4 v 746 1505 a Fk(j)p Fl(k)p Fk(j)866 1335 y Fe(Z)912 1524 y Fq(j)p Fc(x)p Fq(j\025j)p Fc(k)p Fq(j)1124 1507 y Fd(\000)p Fh(1)1394 1392 y Fm(d)p Fl(x)p 1227 1429 428 4 v 1227 1505 a Fp(1)18 b(+)g Fk(j)p Fl(x)p Fk(j)1466 1481 y Fj(3+2)p Ff(\021)1617 1489 y Fh(1)1683 1448 y Fp(+)g Fm(C)1845 1335 y Fe(Z)1892 1524 y Fq(j)p Fc(x)p Fq(j\024j)p Fc(k)p Fq(j)2104 1507 y Fd(\000)p Fh(1)2197 1448 y Fm(d)p Fl(x)2466 1392 y Fk(j)p Fl(x)p Fk(j)p 2300 1429 V 2300 1505 a Fp(1)h(+)f Fk(j)p Fl(x)p Fk(j)2540 1481 y Fj(3+2)p Ff(\021)2691 1489 y Fh(1)2761 1448 y Fm(:)311 b Fp(\(4)p Fm(:)p Fp(45\))0 1665 y(A)26 b(ev)n(en)f(b)r(etter)g(b)r(ound)h(can)f(b)r(e)h(pro)n(v)n(ed)d(for)i Fk(j)s Fp(^)-45 b Fm(s)1488 1677 y Fj(1)p Ff(;\033)1586 1665 y Fp(\()p Fl(k)p Fp(\))p Fk(j)p Fp(,)27 b Fm(\033)f Fp(=)d Fk(\006)p Fp(1,)i(b)n(y)g(using)g(\(3.48\).)35 b(Hence,)26 b(uniformly)0 1815 y(for)h Fm(u)c Fk(!)g Fp(0,)k Fk(j)428 1794 y Fp(^)419 1815 y(\012)479 1785 y Fj(3)p Ff(;a)572 1815 y Fp(\()p Fl(k)p Fp(\))p Fk(j)19 b Fp(+)f Fk(j)s Fp(^)-45 b Fm(s)873 1827 y Fj(1)p Ff(;\033)971 1815 y Fp(\()p Fl(k)p Fp(\))p Fk(j)24 b(\024)f Fm(C)6 b Fk(j)p Fl(k)p Fk(j)1381 1785 y Fq(\000)p Fj(1)1498 1815 y Fp(for)27 b Fk(j)p Fl(k)p Fk(j)d(\025)f Fp(1)k(and)582 1965 y(1)p 582 2002 42 4 v 582 2078 a(2)634 2021 y Fk(j)666 2000 y Fp(^)657 2021 y(\012)717 1986 y Fj(3)p Ff(;a)810 2021 y Fp(\()p Fl(k)p Fp(\))p Fk(j)19 b Fp(+)f Fk(j)s Fp(^)-45 b Fm(s)1111 2033 y Fj(1)p Ff(;\033)1209 2021 y Fp(\()p Fl(k)p Fp(\))p Fk(j)24 b(\024)f Fm(C)1537 1904 y Fe(\024)1581 2021 y Fp(1)18 b(+)1734 1965 y(1)g Fk(\000)g(j)p Fl(k)p Fk(j)1973 1934 y Fj(2)p Ff(\021)2040 1942 y Fh(1)p 1734 2002 344 4 v 1845 2078 a Fp(2)p Fm(\021)1928 2090 y Fj(1)2087 1904 y Fe(\025)2168 2021 y Fm(;)97 b Fp(0)22 b Fm(<)h Fk(j)p Fl(k)p Fk(j)g(\024)g Fp(1)f Fm(:)361 b Fp(\(4)p Fm(:)p Fp(46\))71 2227 y(This)32 b(b)r(ound)h(is)f(div)n (ergen)n(t)f(for)h Fk(j)p Fl(k)p Fk(j)f(!)g Fp(0,)i(if)g Fm(\021)1574 2239 y Fj(1)1642 2227 y Fm(<)d Fp(0,)j(that)g(is)f(if)h Fm(J)2235 2239 y Fj(3)2303 2227 y Fm(<)d Fp(0;)35 b(ho)n(w)n(ev)n(er,)c (if)i Fm(u)d Fk(6)p Fp(=)g(0)i(and)0 2376 y Fk(j)p Fl(k)p Fk(j)24 b(\024)e Fp(\001,)28 b(w)n(e)f(easily)g(get)g(from)h(\()p Fl(I)p Fp(1.16\))f(\(with)h Fm(n)23 b Fp(=)g(0\))k(the)h(b)r(etter)g(b) r(ound)868 2526 y(1)p 868 2563 42 4 v 868 2639 a(2)920 2582 y Fk(j)952 2561 y Fp(^)943 2582 y(\012)1003 2548 y Fj(3)p Ff(;a)1096 2582 y Fp(\()p Fl(k)p Fp(\))p Fk(j)19 b Fp(+)f Fk(j)s Fp(^)-45 b Fm(s)1397 2594 y Fj(1)p Ff(;\033)1495 2582 y Fp(\()p Fl(k)p Fp(\))p Fk(j)24 b(\024)e Fm(C)1822 2465 y Fe(\024)1866 2582 y Fp(1)c(+)2019 2526 y(1)g Fk(\000)g Fp(\001)2231 2496 y Fj(2)p Ff(\021)2298 2504 y Fh(1)p 2019 2563 317 4 v 2117 2639 a Fp(2)p Fm(\021)2200 2651 y Fj(1)2345 2465 y Fe(\025)2426 2582 y Fm(:)646 b Fp(\(4)p Fm(:)p Fp(47\))71 2788 y(In)28 b(a)f(similar)g(w)n(a)n(y)-7 b(,)26 b(b)n(y)h(using)h(\()p Fl(I)p Fp(1.17\),)f(one)g(can)g(pro)n(v)n (e)f(that)674 2994 y Fk(j)706 2973 y Fp(^)697 2994 y(\012)757 2960 y Fj(3)p Ff(;b)843 2994 y Fp(\()p Fl(k)p Fp(\))p Fk(j)20 b Fp(+)e Fk(j)s Fp(^)-45 b Fm(s)1145 3006 y Fj(2)1182 2994 y Fp(\()p Fl(k)p Fp(\))p Fk(j)24 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Fp(=)23 b Fm(e)1056 1690 y Fq(\000)p Ff(i\033)r(\013)1214 1698 y Fb(x)1256 1720 y Fm(\036)1305 1690 y Ff(\033)1305 1741 y Fc(x)p Ff(;!)1413 1720 y Fp(,)28 b(w)n(e)f(get)543 1971 y Fm(U)9 b Fp(\()p Fm(\036)p Fp(\))23 b(=)g Fk(\000)14 b Fp(log)1033 1858 y Fe(Z)1129 1971 y Fm(P)1194 1937 y Fj(\()p Ff(L;h)p Fj(\))1354 1971 y Fp(\()p Fm(d )1486 1937 y Fj([)p Ff(h;)p Fj(0])1620 1971 y Fp(\))g(exp)1807 1879 y Fe(n)1881 1971 y Fk(\000)k Fm(V)2031 1937 y Fj(\()p Ff(L)p Fj(\))2133 1971 y Fp(\()p Fm( )2222 1937 y Fj([)p Ff(h;)p Fj(0])2374 1971 y Fp(+)g Fm(e)2496 1937 y Fq(\000)p Ff(i\013)2618 1971 y Fm(\036)p Fp(\))p Fk(\000)741 2189 y(\000)824 2110 y Fe(X)862 2284 y Ff(!)958 2076 y Fe(Z)1055 2189 y Fm(d)p Fl(x)23 b Fm( )1228 2155 y Fj([)p Ff(h;)p Fj(0]+)1225 2209 y Fc(x)p Ff(;!)1413 2097 y Fe(\020)1462 2189 y Fm(e)1501 2155 y Ff(i\013)1567 2163 y Fb(x)1609 2189 y Fm(D)1680 2155 y Fj([)p Ff(h;)p Fj(0])1678 2209 y Ff(!)1813 2189 y Fm(e)1852 2155 y Fq(\000)p Ff(i\013)1970 2163 y Fb(x)2031 2189 y 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