4.27.huaidai.ps

是multiuser detection 这本书的习题解答, 很有用的书.

EB01E0A51303A41307A2130FA2131FA2133F137F13FF1203000F90B51280B7FCA4C601E0
C7FCB3A3ED01E0A9150302F013C0137F150790393FF80F8090391FFC1F006DB5FC6D13FC
01015B9038003FE023407EBE2C>116 D<D97FC049B4FCB50103B5FCA50003EC000F6C81
B3A85EA25EA25E7E6E491380017FD901F713FE9138F807E76DB512C7010F1407010313FE
9026007FF0EBFC00372E7CAC3E>I E /Fk 6 115 df<14075C5C147F5C1307133F000FB5
FCB6FC13F913C1EAF0011200B3B3B3A7497F010F13E0B712FEA4274F75CE3B>49
D<EC3FF849B57E010F14E090391FC01FF890397E0003FC01F86DB4FCD801E06D13804848
EC7FC0484815E048C8123F01C015F013F0486CEC1FF87FA56C5AA2EA03E0C9EA3FF0A317
E0167F17C016FF17804B13005E4B5A4B5A4B5AED3FC0DA07FFC7FC903803FFFC5DEDFF80
90C7EA1FE0ED07F8ED01FE6F7EEE7F8017C0EE3FE0EE1FF017F8A2EE0FFC17FEA2160717
FFA3120FEA3FC0487E487EA417FE160F5B6C4815FC90C8FC0078ED1FF87E003EED3FF06C
ED7FE06C7E6C6CECFFC0D803F0491380D801FC903807FE003A00FFC01FFC013FB512F001
0F14C0010391C7FC9038003FF830517BCE3B>51 D<EC1FF891B5FC010314C090390FF00F
E090391FC003F890397F8001FC01FEC77E0001157F4848EC3F805B0007ED1FC0484815E0
001F150F4915F0123F1607007F16F85BA217FC12FFA2160317FEA617FFA35E127FA37F00
3F5DA2121F6D5C000F151B0007153B7F6C6C1473000115E36C6C1301017FEB03C3903A3F
C00F83FE010FB51203010313FC010013F091C7FC160717FCA317F8A2160F17F0A2161FD8
03C015E0EA0FF0486CEC3FC01780167F170016FE150149495AD80FC0495A90C7485A6C6C
495A01E0495A2703FC01FFC7FC6CB55A6C6C13F8011F13E0010390C8FC30517BCE3B>57
D<B500FC95B512FCA36E5FD8007FF2F800D93DFF943803BFF0011D62A2011C6DEE073FA3
6E6C160EA36E6C161CA26E6C1638A36E6C1670A36E6C16E0A36E6CED01C0A26E6CED0380
A36E6DEC0700A36F6C140EA36F6C5CA26F6C5CA36F6C5CA36F6C5CA26F6C495AA36F6C49
5AA36F6D48C7FCA393387FC00EA2706C5AA3706C5AA3706C5AA3706C5AA270B45AA3705B
A3013E6E90C8FC137F496C4E7E000701F0027E4B7EB66C4BB612FC173CA35E527AD16B>
77 D<ECFFC0010F13F8013F13FE9039FF00FF80D801F0EB3FE0D803C0EB0FF0486C6D7E
01F86D7E000F816D13016F7EA3707E6C5AEA01E0C9FCA6ED3FFF020FB5FC9138FFFC7F01
071300EB1FF0EB7FC04848C7FCEA03FC485A485A485A123F5B485A187012FF90C8FCA216
FFA35D6D14BF007F14036DEB073F6C6C90390F1FC0E06C6C131E6C6C90393C0FE1C02707
FE01F013FF0001B5486C13806C6C90398003FE00D907FCC712F834367BB43B>97
D<01FFEB1F80B5EB7FF0913801FFF8913803E1FC91380783FE0003EB0F07C6131EEB7F1C
1438143091387003FC91386000F0160014E05CA45CB3AA8048487EB612F0A427347DB32E
>114 D E /Fl 6 122 df<020FB712FEF1FFE04A17F8869126000FFEC7EA1FFF6F480203
7F07007F030FEE3FE0747E4C150F747E031F707EA24C6F7EA2033F83865EA2037FEF7F80
A25EA215FF1CC05EA25CA293CAFCA24A18FFA25D1C801407A24B5EA2140F1C004B5EA214
1F634B1607A2023F601A0F5D63027F171F635D505A14FF505A5D505A4996C7FC6192C95B
4F5A491707624A4C5A4F5A01074D5A4F5A4A4CC8FC4E5A010F4C5AF00FF84A4B5AF07FC0
011F4B485ADD07FEC9FC017FED7FFCB912F018C04DCAFC17E0525278D158>68
D<020FB6D8C007B612E0A24A4B4815C0A2DA000F90C80007EB80006F486F90C7FC4C5E03
0F1607635EA2031F160F635EA2033F161F635EA2037F163F635EA203FF167F635EA24A17
FF6393C9FCA24A5E98C8FC5DA202075E6292B8FCA25C6203F8C81207A2021F160F625DA2
023F161F625DA2027F163F625DA202FF167F625DA24917FF6292C9FCA2495E97C9FC5CA2
01075E615CA2010F1607615CA2011F160FA2017F163FB600FC017FB512FEA45B5278D157
>72 D<EC01FCEC07FF021FEBC0E091397F03E3F8903901FC01F3903903F800FF4948137F
49485C4948133F495A137F49C76C5A5B1201485A5F120749143F120F495D121F167F123F
4992C7FCA25E127F495CA21501A248485CA21503EF03C016F890C7FC150717076CDA0FF0
1380A2031F130F033F14006C6CEB7FE003FF5B001FD901F7131E9026C003E7133E000F90
3907C3F03C2707E00F83137C3B03F03F01F8F83B01FFFC00FFF026007FF06D5AD91FC0EB
1F80323574B33C>97 D<EC01E0EC03F0EC07F8140FA315F015E0EC038091C7FCB2EB07C0
EB3FF0EB7FFCEBF87C3801E07E3803C03E3807803F120F495A5A121E123E003C5B5C127C
EA78015CEAF8035C120013075CA2130F5CA2131F5C133F5CA2137F91C7FCA24913785BA2
000114F84913F01203EBF80115E0A2EC03C013F0EC0780140F15000001131EEBF87C6CB4
5AEB7FE0EB1F801D5077CE24>105 D<EB0FC0D93FF0EC03C0D97FFCEC07E0D9F07C140F
3801E07E2603C03E141F2607803F15C0120F495A48163F001E1780123E003C5B4A147F00
7C1700EA78015CD8F8035D4A5C120013074A13015F130F5C1603011F5D5CA21607013F5D
5CA2160F017FEDE00F91C7FCA2161FEFC01F181EA2043F133E047F133C17806D02FF137C
4B14786E4814F8011F903907CFC0F09139C00F8FC1903B0FF03F07E3E0903B03FFFC03FF
C06DD9F0011380903B003FC0007E00383577B33F>117 D<EB0FC0D93FF0EC03C0D97FFC
EC07E0D9F07C140F3801E07E2603C03E141F2607803F15C0120F495A48163F001E178012
3E003C5B4A147F007C1700EA78015CD8F8035D4A5C120013074A13015F130F5C1603011F
5D5CA21607013F5D5CA2160F017F5D91C7FCA2161F5FA3163F4C5AA26D14FF5D6E4890C7
FC011F5B6E5A90380FF03F903903FFFCFE6D13F09038003FC0EC00015EA215035EA2D803
C0495AEA07F0000F4A5A121F4B5A4B5A4991C8FC5D018013FE391E0001FC001F495A6CEB
07E09038801FC03907E07F802603FFFEC9FCC613F8EB3F80334C77B339>121
D E /Fm 12 120 df<ED1FFE4AB512E0020F14FC023F14FF9126FFE00713C0D903FEC713
F0D907F0EC3FF8D91FC06E7E49C8EA07FE017E6F7E017883496F7F48486F7F1203498348
48167F01F88313FE6D6C153F486D82A4805CA37E6C5B6C48C95BD80078167F90CAFCA261
A218FF61A24D5B615F96C7FC4D5A60170F4D5AEF3FE04D5A4D5A4C48C8FCEE07FCEE1FF0
92381FFFC091260FFFFEC9FCA2EEFFE091C7EA07FCEE00FFEF3FC0EF1FF0717EEF07FE71
7E717F717F85727E727EA285727EA2727EA31A80A2841AC0A3EA07E0EA1FF8487E487EB5
FCA51A80605BA26C48180013F001C05E007CCA5B7E4E5A7E6D4C5A6C6C5F000717FF01F0
4B5B6C6C4B5B6C6C5F6CB4030F90C7FC6D6C4A5AD93FF04A5AD90FFCECFFF8902707FFE0
0713E0010190B612806D6C92C8FC020F14F8020314E09126001FFEC9FC42757AF14F>51
D<016017C001781603017E160FD97FC0ED7F8002F8913807FF00DAFFC0EBFFFE92B65A60
6018C0604DC7FC17F817E0017892C8FC020F13F891CBFCB3A8ED07FE92387FFFC00203B5
12F891390FF803FE91391F8000FF027CC7EA3FC04A6E7ED979E06E7ED97BC06E7ED97F80
6E7E91C87F017E6F7E017C6F13801378F07FC0017017E090CAFCF03FF0A219F8181FA219
FCA319FE180FA419FFA7EA1FE0487E487E487EA419FEA2181F5B4917FC5B0070CAFC183F
007818F8A26C18F0187F003E18E0001E17FF001F18C06C4C13806C7E6D4B13006C6C4B5A
6C6C4B5A6D4B5AD800FE4B5A017F4B5AD93FC049485AD91FF001075BD907FFD93FFEC7FC
6D90B55A010015F0023F14C0020749C8FC020013E0407579F14F>53
D<EE07FE93387FFFE00303B512F8030F14FE92393FF801FF923AFFC0001F804A90C7EA07
C0DA07FC6E7E4A486E7EDA1FE014004A4815784A4814014AC8EA0FF849484B7E4948153F
0107167F5C495A131F495AA249486F5A725A49486F5A95C8FC4890CCFCA25A5B1207A212
0F5BA2121FA25BA2123FA31620007F91380FFFC0033F13F84990B512FE913A03F000FF80
DA0780EB1FE04AC76C7E023E6E7E00FF013C6E7E4A6E7E4A6E7ED9F1E06F7E4A8201F370
7E5C01F7C96C7E8501FF160F4983A249707EA285A25B721380A51AC06C5AA57FA25B7F12
3FA5121F1A80A27F120F601A0012077F000360180F616C7E4E5A6C6D5E183F6D6C5E013F
4C5A6E15FF6D6C5E6D6C4A90C7FC6D6C4A5A6D6C4A5A6D6CEC1FF86D01C0EB7FF0913A7F
F803FFC0021FB65A6E4AC8FC020314F8DA007F13E0DB0FFEC9FC42757AF14F>I<BD12FE
A5D8003F01F0C96C7F01074916034BEE007F6D190F871B018788A2F43F801C1FA21C0FA2
1C07A31C03A21DC0A31C01A6F400E0191CA41D00A5193CA4197CA219FC18011803180F18
FF92B7FCA503C0C7FC180F180318011800197CA2193CA4191CA41D07A41D0E96C9FCA51D
1E1D1CA41D3CA31D381D78A31DF8A21C01A2F403F0A21C07A21C0F1C1F1C3FF4FFE0631B
0749191F6F4CB5FC013F6D163FBEFC1DC0A4607678F56C>69 D<B80203B712FCA5D8003F
01FCCAECF000010701E0051F1380A26D497190C7FCB3B3AA92BBFCA503C0CA120FB3B3AF
496D4D7FA2013F01FC94B512F0B80203B712FCA5667678F577>72
D<B812E0A5D8003F49CCFC010713F05D6D5BB3B3B3AC1C70A51CE0A81B01A31CC01B03A4
1B07A21B0FA21B1FA2F33F80A21B7F1BFF62621A0F621A7F494DB5FC6F150F013F6D4AB6
1200BDFCA5547678F563>76 D<ED1FFC4AB512C0020714F091391FF00FFC91397F8001FF
D901FEC7EA7FC049486E7E49486E7E49486E7E49486E7E49486E7E4948140101FF824890
C91380A24848EE7FC0A2485A000FEF3FE05BA2001F18F0181F485AA3007F18F8A349160F
A212FF90B9FCA301E0CBFCAB127F7FA3123FA36C7EA219386C7E1978000718707F000318
F06C6C17E018016C6DED03C06D6C1680013F16076D6CED0F006D6C151E6D6C5D6D6C5D6D
B44A5A6D6C6C495ADA3FE0EB1F80DA0FFE01FEC7FC0203B512F8DA007F13E0DB07FEC8FC
3D4D7BCB46>101 D<EB01F0EA07FFB5FCA51201EA007F133FA2131FB3B10507B512FEA5
050114C07149C7FC19F019C0614EC8FC60EF01F04D5A604D5A4DC9FC173E5F5F4C5A4C5A
4C5A4C5A4CCAFC163C5E16FC15014B7E4B7E5D033F7F037C7F5D9139F1F07FE09139F3E0
3FF0ECF7C09139FF801FF8ED000F02FC804A6D7E4A13034A80707F8284717E173F84717E
170F84717EA2717E717FA2717F727EA2727E85181F858585496C83D9FFFC037F13F0B600
FC0103B612C0A54A787AF753>107 D<D901F0902601FFC0ED0FFED807FF021F01FC92B5
12E0B5027F01FF020314F8922601FC0101C090390FE00FFE922803E0003FE090391F0001
FFDB0F80D91FF8017C6D13C04BC7000F4A147FC6023C912707FC01E06E7E013F496E6C48
486E7E011F0170DA01FF496E7E03F0160790260FF1E04CC8FCDAF3C06E019E6F7E4B169C
02F717BC92C913B802FFDC7FF86F7E4A5FA34A5FA44A5FB3B3A8496C4C6C4B7ED97FFF03
0301F8031F13C0B7D88007B600FC013FB612E0A57B4B7ACA86>109
D<ED07FE92387FFFE00203B512FC91390FFC03FF913A3FC0003FC04AC7EA0FE0D901FEEC
07F8D903F8EC01FC49486E7E4948157F49486F7E49486F7E017F8349C96C7E4916070001
844848707EA2000784491601000F84A24848701380A2003F19C0A349177F007F19E0A412
FF1AF0AD007F19E0A26D17FFA2003F19C0A46C6C4C1380A2000F1900A26C6C4C5AA26C6C
4C5A0001606D160F6C606D6C4B5A6D6C4B5AA26D6C4B5AD907F003FEC7FCD903FCEC03FC
6D6C4A5A6D6C6CEB1FF0DA3FE0EB7FC091270FFC03FFC8FC0203B512FCDA007F13E0DB07
FEC9FC444D7BCB4F>111 D<D903E0EB1FE0D80FFFECFFFCB501037F923907E01F809239
1F807FC092383E00FF4B4813E000011478D8007F13F090383FE1E015C0EB1FE39126E780
0013C0EF7F8092C7EA3F0002EF91C7FC14EE14FE5CA45CA55CB3B3A480133F90B5FCB712
C0A5334B7ACA3D>114 D<B600F0017FB500F849B512FCA5000149C849C8003F13E02600
7FF8DB3FF8030F13004A031F705A013F4DED03F8180F011F755A735E6D6C150766731503
6D6C63A24E7E6D6C50C7FC85606D6C031C160E866FEC387F6D63866FEC703F027F62866F
DAE01F1578023F1A70866F902601C00F15F0021F62866F90260380071401020F62866F90
260700031403020762866F010E01011407020397C8FC866F496D5C6E190E053C1580DC80
38027F131E6E191C057815C0DCC070023F133C037F183805F015E07048021F1378033F18
7004E116F092261FF1C0020F5BA204F316F892260FFB80913807F9C0A204FF16FD6F90C8
6CB45AA36F486F90C9FCA36F486F5AA36F48167CA24C163C047016386E4B7EC973>119
D E end
TeXDict begin

1 0 bop 1146 569 a Fm(ELE533)52 b(Homew)l(ork)f(6)1586
951 y Fl(Huaiyu)40 b(Dai)1561 1269 y Fk(31)e(Mar)g(1999)-186
1730 y Fj(PR)m(OBLEM)32 b(4.27.)43 b Fi(A)29 b(t)m(w)m(o-user)h(system)
g(emplo)m(ys)f(the)g(same)g(signature)g(w)m(a)m(v)m(eforms)h(and)f(b)s
(oth)f(users)j(are)-186 1850 y(receiv)m(ed)j(with)e(equal)h(p)s(o)m(w)m
(er:)1175 1970 y Fh(y)t Fi(\()p Fh(t)p Fi(\))27 b(=)h
Fh(Ab)1583 1985 y Fg(1)1623 1970 y Fh(s)p Fi(\()p Fh(t)p
Fi(\))22 b(+)g Fh(Ab)2014 1985 y Fg(2)2054 1970 y Fh(s)p
Fi(\()p Fh(t)p Fi(\))g(+)g Fh(\033)t(n)p Fi(\()p Fh(t)p
Fi(\))p Fh(:)-186 2145 y Fi(\(a\))32 b(Sho)m(w)i(that)e(the)h(minim)m
(um)c(probabilit)m(y)i(of)h(error)g(is)g(equal)h(to)1419
2413 y Fh(P)1482 2428 y Ff(k)1524 2413 y Fi(\()p Fh(\033)t
Fi(\))28 b(=)1800 2346 y(1)p 1800 2390 49 4 v 1800 2481
a(4)1881 2413 y(+)1989 2346 y(1)p 1989 2390 V 1989 2481
a(2)2048 2413 y Fh(Q)p Fi(\()2173 2346 y(2)p Fh(A)p 2173
2390 122 4 v 2205 2481 a(\033)2305 2413 y Fi(\))-186
2658 y(and)33 b(is)f(ac)m(hiev)m(ed)i(b)m(y)1263 2796
y(^)1267 2822 y Fh(b)1308 2837 y Fg(1)1375 2822 y Fi(=)1475
2796 y(^)1479 2822 y Fh(b)1520 2837 y Fg(2)1587 2822
y Fi(=)28 b(sgn\()1870 2705 y Fe(Z)1953 2732 y Ff(T)1916
2894 y Fg(0)2025 2822 y Fh(y)t Fi(\()p Fh(t)p Fi(\))p
Fh(s)p Fi(\()p Fh(t)p Fi(\))p Fh(dt)p Fi(\))p Fh(:)-186
3031 y Fi(\(b\))33 b(Sho)m(w)g(that)f(the)h(bit-error-rate)e(of)h(the)h
(join)m(tly)e(optim)m(um\(maxim)m(um-lik)m(eli)o(ho)s(o)r(d\)detector)d
(is)k(equal)g(to)1169 3299 y Fh(P)1246 3258 y Ff(m)1232
3324 y(k)1312 3299 y Fi(\()p Fh(\033)t Fi(\))c(=)1588
3232 y(1)p 1588 3276 49 4 v 1588 3368 a(4)1669 3299 y(+)1777
3232 y(1)p 1777 3276 V 1777 3368 a(4)1836 3299 y Fh(Q)p
Fi(\()1961 3232 y Fh(A)p 1961 3276 74 4 v 1968 3368 a(\033)2044
3299 y Fi(\))22 b(+)2212 3232 y(1)p 2212 3276 49 4 v
2212 3368 a(4)2271 3299 y Fh(Q)p Fi(\()2396 3232 y(3)p
Fh(A)p 2396 3276 122 4 v 2427 3368 a(\033)2528 3299 y
Fi(\))p Fh(:)-186 3630 y Fj(Solution:)-186 3837 y Fi(\(a\))-186
4043 y(F)-8 b(or)40 b(the)i(t)m(w)m(o-user)g(case,)j(the)c(optim)m(um)f
(detector)i(whic)m(h)f(ac)m(hiev)m(es)i(the)f(mimim)m(um)37
b(probabilit)m(y)i(error)i(is)-186 4163 y(giv)m(en)33
b(b)m(y)g(\(4.9\):)1037 4329 y(^)1041 4355 y Fh(b)1082
4370 y Fg(1)1149 4355 y Fi(=)28 b(sgn\()p Fh(y)1480 4370
y Fg(1)1541 4355 y Fd(\000)1682 4288 y Fh(\033)1741 4252
y Fg(2)p 1651 4332 162 4 v 1651 4424 a Fi(2)p Fh(A)1773
4439 y Fg(1)1839 4355 y Fi(log)1991 4285 y(cosh)q([)2213
4242 y Ff(A)2266 4251 y Fc(2)2301 4242 y Ff(y)2336 4251
y Fc(2)2370 4242 y Fg(+)p Ff(A)2478 4251 y Fc(1)2513
4242 y Ff(A)2566 4251 y Fc(2)2600 4242 y Ff(\032)p 2213
4261 423 4 v 2386 4319 a(\033)2428 4300 y Fc(2)2646 4285
y Fi(])p 1991 4332 682 4 v 1991 4430 a(cosh)q([)2213
4388 y Ff(A)2266 4397 y Fc(2)2301 4388 y Ff(y)2336 4397
y Fc(2)2370 4388 y Fb(\000)p Ff(A)2478 4397 y Fc(1)2513
4388 y Ff(A)2566 4397 y Fc(2)2600 4388 y Ff(\032)p 2213
4407 423 4 v 2386 4465 a(\033)2428 4446 y Fc(2)2646 4430
y Fi(])2683 4355 y(\))1102 b(\(1\))-186 4617 y(With)32
b Fh(A)139 4632 y Fg(1)206 4617 y Fi(=)c Fh(A)383 4632
y Fg(2)450 4617 y Fi(=)g Fh(A)p Fi(,)k Fh(\032)c Fi(=)g(1)k(and)h
Fh(y)e Fi(=)1321 4546 y Fe(R)1376 4572 y Ff(T)1360 4642
y Fg(0)1448 4617 y Fh(y)t Fi(\()p Fh(t)p Fi(\))p Fh(s)p
Fi(\()p Fh(t)p Fi(\))p Fh(dt)p Fi(,)h(it)f(can)i(b)s(e)g(simpli\014ed)e
(as:)1483 4820 y(^)1487 4846 y Fh(b)1528 4861 y Fg(1)1595
4846 y Fi(=)d(sgn\()p Fh(y)e Fd(\000)c Fh(f)11 b Fi(\()p
Fh(y)t Fi(\)\))1547 b(\(2\))-186 5066 y(where)1297 5243
y Fh(f)11 b Fi(\()p Fh(y)t Fi(\))27 b(=)1636 5176 y Fh(\033)1695
5140 y Fg(2)p 1624 5220 122 4 v 1624 5312 a Fi(2)p Fh(A)1773
5243 y Fi(log)1925 5173 y(cosh)q([)2147 5130 y Ff(Ay)r
Fg(+)p Ff(A)2345 5106 y Fc(2)p 2147 5149 233 4 v 2225
5207 a Ff(\033)2267 5188 y Fc(2)2390 5173 y Fi(])p 1925
5220 492 4 v 1925 5324 a(cosh)q([)2147 5281 y Ff(Ay)r
Fb(\000)p Ff(A)2345 5262 y Fc(2)p 2147 5301 233 4 v 2225
5358 a Ff(\033)2267 5339 y Fc(2)2390 5324 y Fi(])2427
5243 y(\))1358 b(\(3\))1857 5655 y(1)p eop
2 1 bop -186 167 a Fi(It)33 b(can)f(easily)g(b)s(e)h(seen)h(that)e
Fh(f)11 b Fi(\()p Fh(y)t Fi(\))32 b(is)g(an)g(o)s(dd)h(symmetric)e
(function)h(with)1207 460 y Fh(f)1266 395 y Fa(0)1293
460 y Fi(\()p Fh(y)t Fi(\))26 b(=)1856 389 y(sinh\()2078
350 y Fg(2)p Ff(A)2166 326 y Fc(2)p 2078 365 123 4 v
2101 423 a Ff(\033)2143 404 y Fc(2)2211 389 y Fi(\))p
1561 436 984 4 v 1561 537 a([cosh)q(\()1821 494 y Fg(2)p
Ff(Ay)p 1821 513 126 4 v 1845 571 a(\033)1887 552 y Fc(2)1956
537 y Fi(\))c(+)g(cosh)q(\()2347 497 y Fg(2)p Ff(A)2435
478 y Fc(2)p 2347 513 123 4 v 2369 571 a Ff(\033)2411
552 y Fc(2)2479 537 y Fi(\)])3823 460 y(\(4\))-186 742
y(F)-8 b(urther)33 b(insp)s(ection)f(rev)m(eals)h(that)1005
1030 y Fh(f)1064 965 y Fa(0)1090 1030 y Fi(\(0\))27 b(=)1473
959 y(sinh\()1695 920 y Fg(2)p Ff(A)1783 896 y Fc(2)p
1695 936 V 1717 993 a Ff(\033)1759 974 y Fc(2)1827 959
y Fi(\))p 1356 1006 627 4 v 1356 1107 a([1)22 b(+)g(cosh)q(\()1785
1067 y Fg(2)p Ff(A)1873 1048 y Fc(2)p 1784 1083 123 4
v 1807 1141 a Ff(\033)1849 1122 y Fc(2)1917 1107 y Fi(\)])2020
1030 y Fh(<)27 b Fi(tanh\()2366 962 y(2)p Fh(A)2488 926
y Fg(2)p 2366 1006 162 4 v 2398 1098 a Fh(\033)2457 1069
y Fg(2)2538 1030 y Fi(\))g Fd(\024)h Fi(1)1066 b(\(5\))-186
1312 y(and)1603 1433 y Fh(f)1662 1368 y Fa(0)1689 1433
y Fi(\()p Fh(y)t Fi(\))26 b Fd(\024)j Fh(f)2008 1368
y Fa(0)2034 1433 y Fi(\(0\))1664 b(\(6\))-186 1605 y(So)45