%%Creator: %!PS-Adobe-2.0 dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: sol_prac_rel.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -f sol_prac_rel %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.12.01:1747 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (sol_prac_rel.dvi) @start %DVIPSBitmapFont: Fa cmsy6 6 2 /Fa 2 49 df<B712C0A322037A8D30>0 D<EA01E0EA03F0A4EA07E0A213C0120FA21380 A2EA1F00A2121EA2123E123CA25AA3127012F05A12600C1A7E9B12>48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmti12 12 17 /Fb 17 122 df<EC1F80EC7FE0903901F07070903907C039F890380F801D90381F001F01 3E6D5A137E5B484813075E485A120749130F000F5DA2485A151F003F5D5BA2153F007F92 C7FC90C7FCA25D157E12FEA29238FE0380EDFC071700A2007E13015E913803F80E140700 3E010F131E161C6C131C02385B3A0F80F078783A07C3E07C703A01FF801FE03A007E0007 80292D76AB32>97 D<EC0FE0EC7FF8903801F81E903807E00F90390F80078090381F0003 017E14C049131F0001143F5B4848EB7F801207485AED3E00484890C7FCA2485AA2127F90 C9FCA35A5AA45AA5ED0180ED03C0ED0780A2007CEC0F00007E141E003E147C15F06CEB03 E0390F800F802607C07EC7FC3801FFF838007FC0222D75AB2D>99 D<EE07F0ED03FFA39238000FE01607160FA217C0A2161FA21780A2163FA21700A25EA216 7EA216FEA25EEC1F80EC7FE1903801F071903907C039F890380F801D90381F001F013E13 0F017E5C5B48481307A248485C120749130F120F5E485A151F123F495CA2153F127F90C7 90C7FCA25DA200FE147EA29238FE0380160703FC1300A2007E13015E913803F80E140700 3E010F131E161C6C131C02385B3A0F80F078783A07C3E07C703A01FF801FE03A007E0007 802C4676C432>I<EC0FE0EC7FF8903801F83E903807C00F90391F800780EB3F00017E14 C0491303485A48481307000715805B000F140F484814005D4848133E15FCEC07F0007FEB FFC0D9FFFEC7FC14C090C9FC5A5AA55AA4ED0180ED03C0007CEC0780A2007EEC0F00003E 141E157C6C14F06CEB03E03907800F802603C07EC7FC3801FFF838003FC0222D75AB2D> I<EE0F80EE3FE0EEF870923801F038923803E0F8923807E1FC16C3ED0FC7A2EE87F89238 1F83F0EE81E0EE8000153F93C7FCA45D157EA415FE5DA349B512FEA390260001F8C7FCA3 14035DA414075DA4140F5DA4141F5DA4143F92C8FCA55C147EA314FE5CA413015CA4495A A35C1307121C007F5B12FF495AA291C9FC485AEAF81E485AEA7878EA1FF0EA07C02E5A83 C51E>I<15FCEC03FF91390F83838091393E01CFC091387C00EF4A13FF4948137F010315 804948133F495A131F4A1400133F91C75A5B167E13FE16FE1201495CA215011203495CA2 1503A2495CA21507A25EA2150F151F5E0001143F157F6C6C13FF913801DF8090387C039F 90383E0F3FEB0FFCD903F090C7FC90C7FC5DA2157EA215FEA25DA2001C495A127F48495A 14074A5A485C023FC8FC00F8137E387C01F8381FFFE0000390C9FC2A407BAB2D>I<14FE 137FA3EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C157F9039 3F83FFC091388F81F091381E00F802387F4948137C5C4A137EA2495A91C7FCA25B484814 FE5E5BA2000314015E5BA2000714035E5B1507000F5DA249130F5E001F1678031F137049 1480A2003F023F13F0EE00E090C7FC160148023E13C01603007E1680EE070000FEEC1E0F ED1F1E48EC0FF80038EC03E02D467AC432>I<143C147E14FE1301A3EB00FC14701400AE 137C48B4FC3803C780380703C0000F13E0120E121C13071238A21278EA700F14C0131F00 F0138012E0EA003F1400A25B137EA213FE5B12015BA212035B141E0007131C13E0A2000F 133CEBC038A21478EB807014F014E0EB81C0EA0783EBC7803803FE00EA00F8174378C11E >I<D801F0D90FE0EB07F0D803FCD97FF8EB3FFC28071E01F03EEBF81F3E0E1F03C01F01 E00F80271E0F8700D983807F001C018E90390F870007003C019C148E003801B802DC8002 F814FC26781FF05C0070495CA24A5C00F0494948130FD8E03F6091C75B1200043F141F49 60017E92C7FCA24C143F01FE95C7FC49147E6104FE147E1201494A14FE610301EE078000 0305011400494A14F8A2030302035B0007F0F00E495C1A1E0307EDE01C000F193C494A15 3862030F020113F0001FF0F1E0494A903800FF800007C7D80380023EC7FC492D78AB50> 109 D<D801F0EB0FE0D803FCEB7FF83A071E01F03E3A0E0F03C01F001ED987001380001C
018E130F003C139C003801B814C014F838781FF000705BA25C00F049131FD8E03F158091 C7FC1200163F491500137EA25E01FE147E5B16FE5E12014913015E170F00030203130E49 14F0A20307131E0007EDE01C5B173CEEC038000F167849157017E0ED03C1001FEDE3C049 903801FF000007C8127C302D78AB37>I<EC0FE0EC7FFC903801F83E903907E00F809039 0F8007C0EB1F00017EEB03E04914F0A248481301484814F81207485AA2485AA2485A1503 127F90C7FCA215074815F05AA2150F16E05AED1FC0A21680153F16005D157E5D007C495A 007E495A003E5C4A5A6CEB1F80260F803EC7FC3807C0FC3801FFF038003F80252D75AB32 >I<D903E0137E903A07F801FF80903A0E3C0783E0903A1C1E0F01F0903A3C1F1C00F801 385B017849137C01705BA24A48137E01E05BA292C7FC00015B13C0147EC7FC02FE14FEA2 5CA20101140117FC5CA20103140317F85CA20107EC07F0A24AEB0FE0A2010F15C0EE1F80 163F1700496C137E5E4B5A9138B803F090393F9C07E091389E0F80DA07FEC7FCEC01F849 C9FCA2137EA213FEA25BA21201A25BA21203A21207B512F0A25C2F3F7FAB32>I<D801F0 EB3F803A03FC01FFF03A071E03C0F83A0E0F0F007C001E90389E01FC001C139CECB80300 3813F0A2D91FE013F80078EC00E00070491300A200F05BEAE03F91C8FC1200A25B137EA3 13FE5BA312015BA312035BA312075BA3120F5BA3121F5B0007C9FC262D78AB29>114 D<EC0FE0EC7FF8903801F01E903803C00F90390780078090380F0003011E14C015074913 1FA2017CEB3F801378137CED0E0092C7FC137E137F14F014FF6D13C06D13F06D7F6D7F13 00EC0FFE14011400157F81120E003F141E487EA2153E48C7123CA200FC5C12705D007849 5A6C495A6CEB0F80260F803EC7FC3803FFF838007FC0222D7AAB28>I<1470EB01F8A313 035CA313075CA3130F5CA3131F5CA2007FB512E0B6FC15C0D8003FC7FCA25B137EA313FE 5BA312015BA312035BA312075BA3120F5BA2EC0780001F140013805C140E003F131EEB00 1C143C14385C6C13F0495A6C485AEB8780D807FEC7FCEA01F81B3F78BD20>I<137C48B4 14072603C780EB1F80380703C0000F7F000E153F121C0107150012385E1278D8700F147E 5C011F14FE00F05B00E05DEA003FEC0001A2495C137E150313FE495CA215071201495CA2 030F13380003167849ECC070A3031F13F0EE80E0153F00011581037F13C06DEBEF830000 0101148090397C03C787903A3E0F07C70090391FFE01FE903903F000782D2D78AB34>I< 137C48B414072603C780EB1F80380703C0000F7F000E153F001C1600130712385E007815 7EEA700F5C011F14FE00F0495B12E0EA003FEC00015E5B137E150301FE5C5BA215070001 5D5BA2150F00035D5BA2151F5EA2153F12014BC7FC6D5B00005BEB7C0390383E0F7EEB1F FEEB03F090C712FE5DA214015D121F397F8003F0A24A5A4848485A5D48131F00F049C8FC 0070137E007813F8383801F0381E07C06CB4C9FCEA01FC294078AB2F>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmbx12 12 27 /Fc 27 122 df<EC01E01403EC0FC0EC1F80EC3F00147E5C1301495A495A5C130F495A13 3F5C137F49C7FCA2485AA2485AA212075BA2120F5BA2121FA25B123FA4485AA612FFA25B AE7FA2127FA66C7EA4121F7FA2120FA27F1207A27F1203A26C7EA26C7EA26D7E133F8013 1F6D7E1307806D7E6D7E1300147E80EC1F80EC0FC0EC03E014011B6476CA2C>40 D<12F07E127E7E6C7E6C7E6C7E7F6C7E6C7E12007F137F80133F806D7EA26D7EA26D7EA2 801303A2801301A280A27F1580A4EC7FC0A615E0A2143FAE147FA215C0A6ECFF80A41500 5BA25CA213035CA213075CA2495AA2495AA2495A5C137F91C7FC13FE5B1201485A485A5B 485A485A48C8FC127E12F85A1B647ACA2C>I<EA07C0EA1FF0EA3FF8EA7FFC12FF13FEA2 13FFA47E7E7EEA07CFEA000FA2131F131EA2133EA2133C137C13F8A2EA01F0120313E0EA 07C0EA1F801300121E120C1022788E1F>44 D<EA07C0EA1FF0EA3FF8EA7FFCEAFFFEA7EA 7FFCEA3FF8EA1FF0EA07C0C7FCAEEA07C0EA1FF0EA3FF8EA7FFCEAFFFEA7EA7FFCEA3FF8 EA1FF0EA07C00F2C78AB1F>58 D<B712E0A5D8001F90C7FCB3B3B3A4B712E0A523447DC3 2A>73 D<B64BB512FE8181A281D8003F6D91C7EA780081013D7F81133C6E7E6E7F6E7F6E 7F6E7F82806E7F6E7F6F7E6F7F83816F7F6F7F6F7F6F7F6F7F8382707F707F707F707F84 82707F707F717E7113807113C019E0837113F07113F87113FC7113FE19FF847213F88484 8484A28484197F193F191FA2190F1907B61603190119001A78A24F447CC358>78 D<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB1FFC6D6D7E486C6D7E A26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC1307013F13F19038FFFC0100 0313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C5B4B13F0D83FFE013E EBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9FC322F7DAD36>97 D<EB7FC0B5FCA512037EB1ED0FF892B57E02C314E002CF14F89139DFC03FFC9139FF000F FE02FCEB03FF4A6D13804A15C04A6D13E05CEF7FF0A218F8173FA318FCAC18F8A2177F18 F0A3EFFFE06E15C06E5B6E491380027C491300496C495A903AFC1FC07FFC496CB512F0D9 F00314C049C691C7FCC8EA1FF036467DC43E>I<EC3FFC49B512C0010F14F0013F14FC90 397FF003FE9039FFC001FF0003495A48494813805B120F485AA2485A6F1300007F6E5AED
00784991C7FCA212FFAC6C7EA3123F6DEC03C0A26C6C1407000F16806D140F6C6DEB1F00 6C6D133E6C01F05B3A007FFC03F86DB55A010F14C0010391C7FC9038003FF82A2F7CAD32 >I<EE03FEED07FFA5ED001F160FB1EC3FE0903803FFFC010FEBFF8F013F14CF9039FFF8 07FF48EBC00148903880007F4890C7123F4848141F49140F121F485AA3127F5BA212FFAC 127FA37F123FA26C6C141FA26C6C143F0007157F6C6C91B5FC6CD9C00314FC6C9038F01F EF6DB5128F011FEBFE0F010713F89026007FC0EBF80036467CC43E>I<EC3FF80103B57E 010F14E0013F8090397FF83FF89039FFC007FC48496C7E48496C7E48486D1380485A001F ED7FC05B003FED3FE0A2127F5B17F0161F12FFA290B7FCA401F0C9FCA5127FA27FA2123F 17F06C7E16016C6C15E06C6C14036C6DEB07C06C6DEB0F806C01F0EB3F0090397FFE01FE 011FB55A010714F0010114C09026001FFEC7FC2C2F7DAD33>I<EDFF80020F13E0027F13 F049B512F849EB8FFC90390FFE0FFE90381FFC1F14F8133FEB7FF0A2ED0FFCEBFFE0ED03 F0ED00C01600ABB612F8A5C601E0C7FCB3B0007FEBFFE0A527467DC522>I<EB7FC0B5FC A512037EB1ED07FE92383FFF8092B512E002C114F89139C7F03FFC9138CF801F9139DF00 0FFE14DE14FC4A6D7E5CA25CA35CB3A7B60083B512FEA537457CC43E>104 D<137C48B4FC4813804813C0A24813E0A56C13C0A26C13806C1300EA007C90C7FCAAEB7F C0EA7FFFA512037EB3AFB6FCA518467CC520>I<EB7FC0B5FCA512037EB3B3B3A3B61280 A519457CC420>108 D<90277F8007FEEC0FFCB590263FFFC090387FFF8092B5D8F001B5 12E002816E4880913D87F01FFC0FE03FF8913D8FC00FFE1F801FFC0003D99F009026FF3E 007F6C019E6D013C130F02BC5D02F86D496D7EA24A5D4A5DA34A5DB3A7B60081B60003B5 12FEA5572D7CAC5E>I<90397F8007FEB590383FFF8092B512E0028114F8913987F03FFC 91388F801F000390399F000FFE6C139E14BC02F86D7E5CA25CA35CB3A7B60083B512FEA5 372D7CAC3E>I<EC1FFC49B512C0010714F0011F14FC90397FF80FFF9026FFC0017F4849 6C7F4848C7EA3FE000078248486E7E49140F001F82A2003F82491407007F82A400FF1780 AA007F1700A46C6C4A5AA2001F5E6D141F000F5E6C6C4A5AA26C6C6CEBFFE06C6D485B27 007FF80F90C7FC6DB55A010F14F8010114C09026001FFCC8FC312F7DAD38>I<90397FC0 0FF8B590B57E02C314E002CF14F89139DFC03FFC9139FF001FFE000301FCEB07FF6C496D 13804A15C04A6D13E05C7013F0A2EF7FF8A4EF3FFCACEF7FF8A318F017FFA24C13E06E15 C06E5B6E4913806E4913006E495A9139DFC07FFC02CFB512F002C314C002C091C7FCED1F F092C9FCADB67EA536407DAC3E>I<DA3FE0131E902603FFFC133E010F01FF137E013F14 80903AFFF80FE0FE489038E003F148EBC0014890388000FB4890C7127F49143F001F151F 485A160F5B127FA3485AAC6C7EA46C7EA26C6C141F163F6C6C147F6C15FF6C6D5A6C9038 E003EF6C9038F01FCF6DB5128F011FEBFE0F010313F89038007FC091C7FCAD0307B512FC A536407CAC3B>I<90387F807FB53881FFE0028313F0028F13F8ED8FFC91389F1FFE0003 13BE6C13BC14F8A214F0ED0FFC9138E007F8ED01E092C7FCA35CB3A5B612E0A5272D7DAC 2E>I<90391FFC038090B51287000314FF120F381FF003383FC00049133F48C7121F127E 00FE140FA215077EA27F01E090C7FC13FE387FFFF014FF6C14C015F06C14FC6C80000380 6C15806C7E010F14C0EB003F020313E0140000F0143FA26C141F150FA27EA26C15C06C14 1FA26DEB3F8001E0EB7F009038F803FE90B55A00FC5CD8F03F13E026E007FEC7FC232F7C AD2C>I<EB01E0A51303A41307A2130FA2131FA2133F137F13FF1203000F90B51280B7FC A4C601E0C7FCB3A3ED01E0A9150302F013C0137F150790393FF80F8090391FFC1F006DB5 FC6D13FC01015B9038003FE023407EBE2C>I<D97FC049B4FCB50103B5FCA50003EC000F 6C81B3A85EA25EA25E7E6E491380017FD901F713FE9138F807E76DB512C7010F14070103 13FE9026007FF0EBFC00372E7CAC3E>I<B6903803FFFCA5000101E09038003E006C163C 80017F5D8017F8013F5D6E1301011F5D6E1303010F5D6E13076D5DED800F6D92C7FC15C0 5E6DEBE01E163E6D143CEDF07C027F1378EDF8F8023F5B15FD021F5B15FF6E5BA36E5BA2 6E90C8FCA26E5AA26E5AA21578362C7EAB3B>I<B5D8FE1FB539801FFFF0A500019027C0 003FE0C7EA7C007114786E17F86C6F6C5C6E1601017F6E6C5CA26E011F1403013F6F5C6E 013F1407011F6F5CA26E0179140F010F048090C7FC6E01F95C6D02F0EBC01E15806D9026 81E07F5B18E003C3157C6D9139C03FF07815E76DDA801F5B18F803FF14F96E9039000FFD E018FF6E486D5BA36E486D5BA26E486D90C8FCA24B7F02075DA26E48147C4B143C4C2C7E AB51>I<B6903803FFFCA5000101E09038003E006C163C80017F5D8017F8013F5D6E1301 011F5D6E1303010F5D6E13076D5DED800F6D92C7FC15C05E6DEBE01E163E6D143CEDF07C 027F1378EDF8F8023F5B15FD021F5B15FF6E5BA36E5BA26E90C8FCA26E5AA26E5AA21578 A215F85D14015D001F1303D83F805B387FC007D8FFE05B140F92C9FC5C143E495A387FC1 F8EB07F06CB45A6C5B000790CAFCEA01FC36407EAB3B>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmr10 10 4 /Fd 4 54 df<EB01C013031307131F13FFB5FCA2131F1200B3B3A8497E007FB512F0A31C 3879B72A>49 D<EB0FF0EB7FFE48B57E3903E03FE0390F000FF0000E6D7E486D7E486D7E
123000706D7E126012FCB4EC7F807FA56CC7FC121CC8FCEDFF00A34A5A5D14035D4A5A5D 140F4A5A4A5A92C7FC147C5C495A495A495A495A91C8FC011EEB01805B5B491303484814 00485A485A000EC75A000FB6FC5A5A485CB6FCA321387CB72A>I<1538A2157815F8A214 0114031407A2140F141F141B14331473146314C313011483EB030313071306130C131C13 1813301370136013C01201EA038013005A120E120C5A123812305A12E0B712F8A3C73803 F800AB4A7E0103B512F8A325397EB82A>52 D<0006140CD80780133C9038F003F890B5FC 5D5D158092C7FC14FC38067FE090C9FCABEB07F8EB3FFE9038780F803907E007E0903880 03F0496C7E12066E7EC87EA28181A21680A4123E127F487EA490C71300485C12E000605C 12700030495A00385C6C1303001E495A6C6C485A3907E03F800001B5C7FC38007FFCEB1F E0213A7CB72A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmr7 7 1 /Fe 1 51 df<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F80A4 127CC7FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0EA01 80390300030012065A001FB5FC5A485BB5FCA219267DA521>50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmmi7 7 1 /Ff 1 121 df<90387C03C03901FF0FF03907079C30390E03B078000CEBF0F8001813E1 123015F0396007C0E015001200A2495AA449C7FC15301238007C1460EAFC3E15C0EAF87E 39F06F03803970C70700383F83FE381F01F81D1B7D9926>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmsy10 14.4 1 /Fg 1 1 df<007FBA12FEBCFCA36C19FE4805769F5D>0 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmr12 14.4 5 /Fh 5 62 df<15E01401EC03C0EC0780EC0F00141E5C147C5C495A13035C495A130F5C13 1F91C7FC133E137EA25BA2485AA25B1203A2485AA3120F5BA2121FA25BA2123FA290C8FC A35AA5127EA312FEB3A3127EA3127FA57EA37FA2121FA27FA2120FA27F1207A36C7EA212 017FA26C7EA2137EA2133E7F80130F8013076D7E8013016D7E147C143C8080EC0780EC03 C0EC01E014001B7974D92E>40 D<12E07E12787E7E7E6C7E7F6C7E6C7E7F1200137C137E 133E133F7F6D7E80A26D7EA26D7EA2130180A26D7EA380147EA2147FA280A21580A2141F A315C0A5140FA315E0B3A315C0A3141FA51580A3143FA21500A25CA2147EA214FE5CA349 5AA25C1303A2495AA2495AA25C49C7FC5B133E137E137C5B12015B485A485A5B48C8FC12 1E5A5A5A5A1B797AD92E>I<14075C5C147F5C1307133F000FB5FCB6FC13F913C1EAF001 1200B3B3B3A7497F010F13E0B712FEA4274F75CE3B>49 D<EC7FE0903803FFFE010F6D7E 013F14E0D9FF0013F8D801F8EB1FFCD803E06D7E4848EB03FF48486D138090C813C0001E 16E0001C157F003CED3FF012380078ED1FF81270A2B4ED0FFC13C07FA66C5A6C5A000EC8 FCC9EA1FF8A317F0163FA2EE7FE017C016FF17804B1300A24B5A4B5A5E4B5A4B5A4B5A5E 4BC7FC15FE4A5A4A5A4A5A4A5A5D4A5A4AC8FC147E5C4948141CEB03E0495A4948143891 C8FC131E5B5B491578485A48481570484815F048B7FCA25A5A5AB812E0A42E4F7ACE3B> I<007FBB12F8BC12FCA36C1AF8CFFCB3007FBB12F8BC12FCA36C1AF84E1D7AAB5B>61 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmmi10 10 4 /Fi 4 121 df<EC3FC0903801FFF0903807E03C90380F800E90383F0007017E131F4913 7F484813FF485A485A120F4913FE001F143848481300A2127F90C8FCA35A5AA45AA31503 1507007E1406150E003E143C003F14706C14E0390F8007C03907C03F003801FFF838003F C020267DA424>99 D<13F8D803FE1438D8070F147C000E6D13FC121C1218003814011230 D8701F5C12601503EAE03F00C001005B5BD8007E1307A201FE5C5B150F1201495CA2151F 120349EC80C0A2153F1681EE0180A2ED7F0303FF130012014A5B3A00F8079F0E90397C0E 0F1C90393FFC07F8903907F001F02A267EA430>117 D<01F8EB03C0D803FEEB07E0D807 0F130F000E018013F0121C12180038140700301403D8701F130112601500D8E03F14E000 C090C7FC5BEA007E16C013FE5B1501000115805B150316001203495B1506150E150C151C 151815385D00015C6D485A6C6C485AD97E0FC7FCEB1FFEEB07F024267EA428>I<903907 E001F090391FF807FC9039783E0E0F9039E01F1C1FD801C09038383F803A03800FF07F01 00EBE0FF5A000E4A1300000C157E021F133C001C4AC7FC1218A2C7123FA292C8FCA25CA2 147EA214FEA24A130CA20101141C001E1518003F5BD87F81143801835C00FF1560010714
E03AFE0E7C01C0D87C1C495A2778383E0FC7FC391FF00FFC3907C003F029267EA42F> 120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmsy10 10 1 /Fj 1 49 df<EB0F80EB1FC0EB3FE0A3137FA214C0A2EBFF80A314005A5BA3485AA25B12 075BA3485AA25BA2121F5BA248C7FCA2123EA2127E127CA2127812F8A25A132A7EAD17> 48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmmi12 14.4 3 /Fk 3 119 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmr6 6 2 /Fl 2 51 df<1438B2B712FEA3C70038C7FCB227277C9F2F>43 D<EA01FC3807FF80381C 0FC0383003E0386001F0EB00F812F86C13FCA2147C1278003013FCC7FC14F8A2EB01F0EB 03E014C0EB0780EB0F00131E13385B5B3801C00CEA0380380600185A5A383FFFF85AB512 F0A216217CA01E>50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmmi6 6 1 /Fm 1 121 df<3801F01E3907FC7F80390E1CE1C038180F8100301383007013071260EC 0380D8001EC7FCA45BA21580003014C0397878018012F8EC030038F0FC0638E19C1C387F 0FF8381E03E01A177D9523>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmex10 10 18 /Fn 18 119 df<151E153E157C15F8EC01F0EC03E01407EC0FC0EC1F8015005C147E5CA2 495A495AA2495AA2495AA2495AA249C7FCA2137EA213FE5B12015BA212035BA21207A25B 120FA35B121FA45B123FA548C8FCA912FEB3A8127FA96C7EA5121F7FA4120F7FA312077F A21203A27F1201A27F12007F137EA27FA26D7EA26D7EA26D7EA26D7EA26D7E6D7EA2147E 80801580EC0FC0EC07E01403EC01F0EC00F8157C153E151E1F94718232>16 D<12F07E127C7E7E6C7E7F6C7E6C7E12017F6C7E137EA27F6D7EA26D7EA26D7EA26D7EA2 6D7EA26D7EA280147E147F80A21580141FA215C0A2140F15E0A3140715F0A4140315F8A5 EC01FCA9EC00FEB3A8EC01FCA9EC03F8A515F01407A415E0140FA315C0141FA21580A214 3F1500A25C147E14FE5CA2495AA2495AA2495AA2495AA2495AA249C7FC137EA25B485A5B 1203485A485A5B48C8FC123E5A5A5A1F947D8232>I<160F161F163E167C16F8ED01F0ED 03E0ED07C0150FED1F801600153E157E5D4A5A5D14034A5A5D140F4A5AA24AC7FC143E14 7E5CA2495AA2495AA2495AA2130F5CA2495AA2133F91C8FCA25B137E13FEA25B1201A25B 1203A35B1207A35B120FA35BA2121FA45B123FA690C9FC5AAA12FEB3AC127FAA7E7FA612 1F7FA4120FA27FA312077FA312037FA312017FA212007FA2137E137F7FA280131FA26D7E A2801307A26D7EA26D7EA26D7EA2147E143E143F6E7EA26E7E1407816E7E1401816E7E15 7E153E811680ED0FC01507ED03E0ED01F0ED00F8167C163E161F160F28C66E823D>I<12 F07E127C7E7E6C7E6C7E6C7E7F6C7E1200137C137E7F6D7E130F806D7E1303806D7EA26D 7E147C147E80A26E7EA26E7EA26E7EA2811403A26E7EA2811400A281157E157FA2811680 A2151F16C0A3150F16E0A3150716F0A31503A216F8A4150116FCA6150016FEAA167FB3AC 16FEAA16FC1501A616F81503A416F0A21507A316E0150FA316C0151FA31680153FA21600 5DA2157E15FE5DA214015DA24A5AA214075DA24A5AA24A5AA24AC7FCA2147E147C14FC49 5AA2495A5C1307495A5C131F49C8FC137E137C5B1201485A5B485A485A48C9FC123E5A5A
5A28C67E823D>I<B512F8A500F8C7FCB3B3B3B3B3B3B3B3B3B3A8B512F8A515C66B822C> I<B512F8A5C7FCB3B3B3B3B3B3B3B3B3B3A8B5FCA515C67F822C>I<EE01E01603EE07C0 EE0F80161F1700163E5E5E15015E4B5A15074B5A5E151F4BC7FC153E157E5DA24A5A1403 5D14075D140F5D141F5D143F92C8FC5C147E14FE5C1301A25C13035C1307A25C130FA249 5AA3495AA3137F91C9FCA25B5BA312015BA31203A25BA21207A35BA2120FA35BA3121FA4 5BA2123FA75B127FAC90CAFC5AB3B3A27E7FAC123F7FA7121FA27FA4120FA37FA31207A2 7FA31203A27FA21201A37F1200A37F7FA280133FA36D7EA36D7EA2130780A21303801301 80A2130080147E147F8081141F81140F8114078114038114016E7EA2157E153E153F6F7E 150F826F7E15036F7E821500167C82821780160FEE07C0EE03E016012BF86C8242>32 D<12F07E127C7E123F7E6C7E6C7E6C7E7F12016C7E7F137E133E133F6D7E130F806D7EA2 6D7E80130180130080147E147F8081141F81140F81140781A2140381140181A2140081A2 157FA36F7EA382151FA282150FA3821507A382A21503A282A31501A282A31500A382A482 A21780A7163F17C0AC161F17E0B3B3A217C0163FAC1780167FA71700A25EA45EA31501A3 5EA21503A35EA21507A25EA3150F5EA3151F5EA2153F5EA34BC7FCA315FEA25D1401A25D 14035D1407A25D140F5D141F5D143F92C8FC5C147E14FE5C13015C13035C495AA2495A5C 131F49C9FC133E137E5B5B485A12035B485A485A48CAFC5A123E5A5A5A2BF87E8242>I< B61280A600FCC8FCB3B3B3B3B3B3B3B3B3B3B3B3B3A2B61280A619F86A8230>I<B61280 A6C7121FB3B3B3B3B3B3B3B3B3B3B3B3B3A2B6FCA619F8808230>I<B512E0A500F8C7FC B3B3B3B3B3B3B3ACB512E0A513946E8227>104 D<B512E0A5EA0003B3B3B3B3B3B3B3AC B5FCA513947F8227>I<1B301B78A21BF8A21BF01A01A21BE01A03A21BC01A07A21B801A 0FA21B0062A21A1E1A3EA21A3C1A7CA21A781AF8A262A21901A2621903A2621907A26219 0FA297C7FC61A2191E193EA2193C197CA2197819F8A2611801A2611803A261A21807A261 180FA296C8FC60A2181E183EA2183C187C131001301678017016F813F860000116011203 486C5E000F1603121DD838FE5E00701607126000C05FEA407F0000160FA26D6C92C9FC5F A2171E6D6C143EA2173C6D6C147CA2177817F86D7E5F16016D7E5F1603A26D6C5C1607A2 6D6C5C160FA294CAFC027F5BA2161EEC3F80163EA2163C91381FC07CA2167891380FE0F8 A25E15E1EC07F15E15F3EC03FB5E15FFA26E5BA36E90CBFCA35D157EA2157C153C15384D 96788353>113 D<1B301B78A21BF8A21BF0A21A01A21BE0A21A03A21BC0A31A07A21B80 A21A0FA21B00A262A21A1EA21A3EA21A3CA21A7CA21A78A21AF8A262A31901A262A21903 A262A21907A262A2190FA297C7FCA261A2191EA2193EA2193CA3197CA21978A219F8A261 A21801A261A21803A261A21807A261A2180FA296C8FCA360A2181EA2183EA2183CA2187C 131018781330017016F8A201F85E120117011203486C5EA2120D001D16031219D830FE5E 12700060160712C000405FEA007F170FA295C9FC6D7E5FA2171EA26D6C143EA2173CA217 7C6D7E1778A36D6C14F8A25FA216016D7E5FA21603A26D6C5CA21607A26D6C5CA2160FA2 94CAFC147F5EA2161EEC3F80A2163EA2163CEC1FC0167CA21678A291380FE0F8A25EA2EC 07F1A25EA215F3EC03FB5EA215FFA26E5BA48093CBFCA4157EA4157C153C15384DC87883 53>I<1B301B78A31BF8A21BF0A31A01A21BE0A31A03A21BC0A31A07A21B80A41A0FA21B 00A362A21A1EA31A3EA21A3CA31A7CA21A78A31AF8A262A41901A262A31903A262A31907 A262A3190FA297C7FCA461A2191EA3193EA2193CA3197CA21978A319F8A261A41801A261 A31803A261A31807A261A3180FA296C8FCA460A2181EA3183EA2183CA3187C1310187813 30A2017016F8A201F85EA212011701120360487EA2120D001D16031219D838FE5E123012 700060160712E000C05FEA407F1200170FA295C9FCA26D7E5FA2171EA36D7E173EA2173C A36D6C147CA21778A317F86D7E5FA316016D7E5FA416036D7E5FA31607A26D6C5CA3160F A294CAFC147FA25EA2161EA2EC3F80A2163EA2163CEC1FC0A2167CA21678A2EC0FE016F8 A25EA3EC07F1A25EA315F3EC03FB5EA415FF805EA48093CBFCA5157EA5157C153CA21538 4DFA788353>I<18301878B11318A21338133C137C13FC7F1201A2487E7F120738063F80 120E120C381C1FC01218123838300FE01260A212C06D7E1200A26D7EA36D7EA36D7EA314 7FA36E7EA36E7EA36E7EA36E7EA36E7EA36E7EA36E7EA3157FA36F7EA36F7EA36F7EA36F 7EA36F7EA36F7EA46F7EA3167FA3EE3F80A3EE1FC0A3EE0FE0A3EE07F0A3EE03F8A3EE01 FCA3EE00FEA3177FA3EF3FF8A3171FA3170FA31707A31703A31701A31700A31870186035 97778158>I<126012F0B3B3B012600436468158>I<007FB512FEB7FCA215FE00F0C8FCB3 B3AB12602034468358>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmmi8 8 16 /Fo 16 123 df<013FB512FEEEFFC0903A00FE0007F0EE01F84AEB007E8301018118804A 140F18C00103150718E05CA21307A25CA2130FA24A140FA2131F18C04A141FA2013F1680 173F91C81300A249157EA2017E5D5F01FE14014C5A494A5A4C5A00014BC7FC163E4914FC ED03F00003EC1FC0B7C8FC15F8332D7CAC3A>68 D<90263FFFFC90381FFF80A2D900FEC7 3803F80018E04AEC07804DC7FC0101151C5F4A14E04C5A01034A5A040EC8FC4A5B5E0107
14E04B5A9138E00780030EC9FC010F131F157F4A487E14C190391FC71FC014CEEC9C0F02 F07F90383FE00702C07FEC0003825B6F7E137E6F7E13FE167F5B707E1201161F49818312 03B539E001FFFEA2392D7CAC3C>75 D<EB01F8EB0FFE90383E0780EB7C01D801F813C038 03F0073807E00FEA0FC001801380121F48C8FCA25A127EA312FE5AA51560007C14E0EC01 C0EC03806CEB0F00001E131C380F81F83807FFE0C648C7FC1B1F7D9D1F>99 D<157C4AB4FC913807C380EC0F87150FEC1F1FA391383E0E0092C7FCA3147E147CA414FC 90383FFFF8A2D900F8C7FCA313015CA413035CA413075CA5130F5CA4131F91C8FCA4133E A3EA383C12FC5BA25B12F0EAE1E0EA7FC0001FC9FC213D7CAE22>102 D<14FCEB03FF90380F839C90381F01BC013E13FCEB7C005B1201485A15F8485A1401120F 01C013F0A21403121F018013E0A21407A215C0A2000F130F141F0007EB3F80EBC07F3803 E1FF3800FF9F90383E1F0013005CA2143EA2147E0038137C00FC13FC5C495A38F807E038 F00F80D87FFEC7FCEA1FF81E2C7E9D22>I<1307EB0F80EB1FC0A2EB0F80EB070090C7FC A9EA01E0EA07F8EA0E3CEA1C3E123812301270EA607EEAE07C12C013FC485A120012015B 12035BA21207EBC04014C0120F13801381381F01801303EB0700EA0F06131EEA07F8EA01 F0122E7EAC18>105 D<27078007F0137E3C1FE01FFC03FF803C18F0781F0783E03B3878 E00F1E01263079C001B87F26707F8013B00060010013F001FE14E000E015C0485A491480 0081021F130300015F491400A200034A13076049133E170F0007027EEC8080188149017C 131F1801000F02FCEB3F03053E130049495C180E001F0101EC1E0C183C010049EB0FF000 0E6D48EB03E0391F7E9D3E>109 D<EB01F8EB0FFF90383F078090387C03C0D801F813E0 3903F001F0EA07E0D80FC013F8EB8000121F48C7FC14015A127EA2140300FE14F05AA2EC 07E0A2EC0FC0A2007CEB1F801500143E6C5B6C485A380F83E03803FF80D800FCC7FC1D1F 7D9D22>111 D<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C0000713 F000069038E003E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C0133EA2 017EEB1F80A2017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FFC7FC EBF0FC000390C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>I<3807C01F390F F07FC0391CF8E0E0383879C138307B8738707F07EA607E13FC00E0EB03804848C7FCA212 8112015BA21203A25BA21207A25BA2120FA25BA2121FA290C8FC120E1B1F7E9D20>114 D<EB07E0EB3FF8EB781EEBF0063801E0073803C00F141FA20007131E140CEBE00013F8EB FF806C13E06C13F06C13F8EB3FFC13011300147C0078133C12FCA2147C48137800E013F8 14F0386001E0387807C0381FFF00EA07F8181F7C9D21>I<EA01E0D807F8130ED80E3C13 1FD81C3E5B0038143E12301270D8607E137ED8E07C137C12C013FC484813FC00005C1201 5B140100035C13E0A2020313200007ECE06013C0A216E0020713C00003EB0FC09038E01F C191383BE1803901F071E33A007FE0FF0090381F803C231F7E9D29>117 D<D801E01370D807F813F8380E3C01D81C3E13FC1238003013000070147CEA607ED8E07C 133812C013FC485A0000143012015B1570000314605B15E015C01207EBC00115801403EC 070000031306EBE00E00015BEBF07838007FE0EB1F801E1F7E9D22>I<013F137C9038FF C1FF3A01C1E383803A0380F703C0390700F60F000E13FE4813FC12180038EC0700003049 C7FCA2EA200100005BA313035CA301075B5D14C000385CD87C0F130600FC140E011F130C 011B131C39F03BE038D8707113F0393FE0FFC0260F803FC7FC221F7E9D28>120 D<EA01E0D807F8130ED80E3C131FD81C3E133F0038143E12301270D8607E137ED8E07C13 7C12C013FC484813FC000014F812015B1401000314F013E0A21403000714E013C0A21407 15C00003130FEBE01F143F3901F07F8038007FEFEB1F8FEB001F1500A2003E133EA2007E 5B5C387C01F0387003E0383007C0383C0F80D80FFEC7FCEA03F0202C7E9D23>I<011E13 30EB3F809038FFC07048EBE0E0ECF1C03803C0FF9038803F80903800070048130EC75A5C 5C5C495A495A49C7FC131E13385B491340484813C0485A38070001000EEB0380380FE007 391FF81F0038387FFF486C5A38601FFC38E00FF038C003C01C1F7D9D21>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr8 8 14 /Fp 14 58 df<B6FCA318037BA623>22 D<13031307130E131C1338137013F0EA01E013 C01203EA0780A2EA0F00A2121EA35AA45AA512F8A25AAB7EA21278A57EA47EA37EA2EA07 80A2EA03C0120113E0EA00F013701338131C130E1307130310437AB11B>40 D<12C07E12707E7E7E120FEA0780120313C0EA01E0A2EA00F0A21378A3133CA4131EA513 1FA2130FAB131FA2131EA5133CA41378A313F0A2EA01E0A2EA03C013801207EA0F00120E 5A5A5A5A5A10437CB11B>I<EC0380B3A4B812FCA3C7D80380C7FCB3A42E2F7CA737>43 D<EB3FC0EBFFF03803E07C48487E48487E497E001EEB0780A2003E14C0A248EB03E0A500 FC14F0B0007C14E0A3007E1307003E14C0A36CEB0F806C14006D5A3807C03E3803F0FC38 00FFF0EB3FC01C2D7DAB23>48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387F FFFEA2172C7AAB23>I<EB7F803801FFF0380780FC380E003F48EB1F8048EB0FC05A0060
EB07E012F000FC14F07E1403A3007C1307C7FCA215E0140F15C0141F1580EC3F00147E14 7C5C495A495A495A495A011EC7FC5B5B4913305B485A4848136048C7FC000E14E0001FB5 FC5A4814C0B6FCA21C2C7DAB23>I<EB3FC03801FFF03807C0FC380E007E487FEC1F8000 3F14C0A2EB800F1300A2000C131FC7FC1580A2EC3F00143E5C5CEB03F0EBFFC014F0EB00 FC143FEC1F8015C0140F15E0A2EC07F0A21238127C12FEA3EC0FE012F8006014C0007013 1F6C1480001EEB3F00380780FC3801FFF038007FC01C2D7DAB23>I<140EA2141E143EA2 147E14FEA2EB01BE1303143E1306130E130C131813381330136013E013C0EA0180120313 001206120E120C5A123812305A12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E2D7EAC 23>I<000CEB0180380FC01F90B512005C5C14F014C0D80C7EC7FC90C8FCA8EB1FC0EB7F F8380DE07C380F801F01001380000E130F000CEB07C0C713E0A2140315F0A4127812FCA4 48EB07E012E0006014C00070130F6C14806CEB1F006C133E380780F83801FFE038007F80 1C2D7DAB23>I<EB03F8EB0FFE90383E0780EBF8013901F007C03803E00FEA07C0EA0F80 A2391F00078091C7FC123EA2127EA2127CEB0FC038FC3FF0EBF07C38FDC01EB4487E0100 1380EC07C04814E0A214034814F0A4127CA3127EA2003E14E01407121E001F14C06CEB0F 803907801F003803C03E6C6C5A38007FF0EB1FC01C2D7DAB23>I<1230123C003FB512F8 A215F05A15E039700001C000601480140348EB0700140E140CC7121C5C143014705C495A A2495AA249C7FCA25B130E131EA2133EA3133C137CA413FCA913781D2E7CAC23>I<EB1F C0EBFFF03803E07C3807801E48487E001EEB0780A248EB03C0A4123E1407003F1480381F C00F01E01300EBF81E6C6C5A3807FFF86C13E0C6FCEB3FF8EBFFFC3803C7FFD807831380 D81F0013C0001E133F48EB1FE0007C13070078EB03F012F84813011400A46C14E0007813 01007C14C0003C13036CEB0780390F800F003807E03C3801FFF038003FC01C2D7DAB23> I<EB3F80EBFFF03803E0783807C03E48487E48487E003E14801407007E14C0127C00FC14 E01403A315F0A5007C1307127EA2003E130F7E6C131F3807803B3803E0F33800FFC39038 3F03E013001407A215C0A2140F001E1480003F14005C143E143C003E5B001C5B380E03E0 3807FF80D801FEC7FC1C2D7DAB23>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmsy10 12 8 /Fq 8 113 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<0060160600F8160F6C16 1F007E163F6C167E6C6C15FC6C6CEC01F86C6CEC03F06C6CEC07E06C6CEC0FC06C6CEC1F 80017EEC3F006D147E6D6C5B6D6C485A6D6C485A6D6C485A6D6C485A6D6C485ADA7E3FC7 FCEC3F7E6E5A6E5A6E5AA24A7E4A7EEC3F7EEC7E3F4A6C7E49486C7E49486C7E49486C7E 49486C7E49486C7E49C7127E017E8049EC1F804848EC0FC04848EC07E04848EC03F04848 EC01F84848EC00FC48C9127E007E163F48161F48160F00601606303072B04D>2 D<16C04B7EB3AC007FBA1280BB12C0A26C1980C8D801E0C9FCB3A9007FBA1280BB12C0A2 6C198042427BC14D>6 D<49B4FC010F13E0013F13F8497F48B6FC4815804815C04815E0 4815F0A24815F8A24815FCA3B712FEA96C15FCA36C15F8A26C15F0A26C15E06C15C06C15 806C15006C6C13FC6D5B010F13E0010190C7FC27277BAB32>15 D<007FBA1280BB12C0A2 6C1980CEFCB0007FBA1280BB12C0A26C1980CEFCB0007FBA1280BB12C0A26C1980422C7B AE4D>17 D<18034E7E85180385180185727E1978197C8585737E86737E737E007FBA7EBB 7E866C85CDEA0FC0747EF203F8F200FEF37F80F31FE0F307FC983801FF80A2983807FC00 F31FE0F37F8009FEC7FCF203F8F207E0505A007FBBC8FCBB5A626C61CCEA03F04F5A4F5A 624FC9FC193E61197819F84E5A6118036118076172CAFC59387BB464>41 D<126012F0B3B3B3B3B3A81260046474CA1C>106 D<1B0C1B1E1B3EA21B7CA21BF8A2F2 01F0A2F203E0A2F207C0A2F20F80A2F21F00A21A3EA262A262A24F5AA2621903A24F5AA2 4F5AA24FC7FCA2193EA261A261A24E5AA24E5AA24E5AA24E5AA2010C4CC8FC133C017C16 3EEA01FE00035F487E001E5F00387FD8707F4B5A00E07FD8003F4B5A80011F4B5AA26E4A 5A130F6E4AC9FC13076E143E13036E5C13016E5C7F6F5B027F1301A26F485A143F6F485A 141F6F485A140F6F48CAFC1407EDFC3E14035E15FE02015B15FF6E5BA26F5AA26F5AA26F 5AA26FCBFC150E4F647A8353>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmsy8 8 3 /Fr 3 113 df<B812C0A32A037A9137>0 D<137813FE1201A3120313FCA3EA07F8A313F0 A2EA0FE0A313C0121F1380A3EA3F00A3123E127E127CA35AA35A0F227EA413>48 D<18031807180F180E181E181C183C18381878187018F018E01701EF03C0188017071800 5F170E171E171C173C17381778177017F05F16015F16035F160701C092C7FC486C5C0007 151E486C141C003F153CD873F8143800E31578D801FC147016F06C6C5C1501017F5C1503 D93F805B1507D91FC090C8FC5D90380FE00E151E903807F01C153C903803F83815786D6C 5A5DEB00FF5D147F5D143F92C9FC80141E140E38427C823B>112 D E
%EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmmi12 12 28 /Fs 28 127 df<EE1FE0EE7FFC923801E03F923907800F8092390E0007C04BEB03E04B13 014B14F04B13004A4814F85D14034AC8FC1406140E020C1401141C021815F00238140302 3015E01707027015C00260140F188002E0EC1F004A143E5F010190383FF1F84AB512E092 38C01F8092B57E010390383FF1F091C87E1778177C49811306A283130E130CA3011C1680 1318A30138ED3F001330A301705D177E136017FE01E05DA24C5AA200014B5A6D4A5A01B0 4A5A5FD803B84AC7FC0118147E011C5C6DEB01F0486CEB07C0270603C03FC8FC903800FF FCEC3FC0000E90CAFC120CA3121C1218A312381230A312701260A312E0A235597DC537> 12 D<EB01FCD907FF15E0011F13C0017F6DEB01C090B56C1480486E13032603FE071500 2707F000FC5B01C0017C130648C76C130E001E021E130C001C80003C6E131C0038161848 6E1338EE8030006002011370176000E016E0C86D5A150016C15F16C394C7FC16E316E716 66166E166CA2167C1678A3167016F05EA35EA31501A25E1503A44BC8FCA35D150EA45DA4 5DA333417EAB33>I<147002F8140E0101153FA301035DA24A147EA2010715FEA24A5CA2 010F1401A24A5CA2011F1403A24A5CA2013F1407A291C75BA249140FA2017E5DA201FE02 1F1318183849ED8030A20001033F13701860EE7F005E486C16E0DB01DF13C09238039F01 6DD9071F1380489039801E0F83903BF7C078078700903AE1FFE003FE903AE07F8000F800 0F90CAFCA25BA2121FA25BA2123FA290CBFCA25AA2127EA212FEA25A123835417DAB3B> 22 D<010FB612FC013F15FE5B48B712FC4816F82707E001C0C7FC01805B380F0003121E 121C5A4849C8FC126012E000405BC7FC140E141EA45CA3147CA2147814F8A4495AA31303 A25C1307A3130FA25C6D5A2F2C7EAA2A>28 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00 0A0A78891B>58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A31201 1380120313005A1206120E5A5A5A12600B1D78891B>I<F001C0F007E0181FF07FC09438 01FF00EF07FCEF1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0030390C8FCED0FF8ED3FE0 EDFF80DA03FEC9FCEC1FF8EC7FE0903801FF80D907FECAFCEB1FF0EB7FC04848CBFCEA07 FCEA1FF0EA7FC048CCFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FE903801 FF809038007FE0EC1FF8EC03FE913800FF80ED3FE0ED0FF8ED03FF030013C0EE3FF0EE0F FCEE01FF9338007FC0EF1FF0EF07FCEF01FF9438007FC0F01FE01807F001C03B3878B44C >I<1618163C167CA2167816F8A216F01501A216E01503A216C01507A21680150FA2ED1F 00A2151E153EA2153C157CA2157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5C A2141E143EA2143C147CA25CA25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133E A2133C137CA2137813F8A25B1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2 123C127CA2127812F8A25A126026647BCA31>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA 01FF38007FC0EB1FF0EB07FE903801FF809038007FE0EC1FF8EC03FE913800FF80ED3FE0 ED0FF8ED03FF030013C0EE3FF0EE0FFCEE01FF9338007FC0EF1FF0EF07FCEF01FF943800 7FC0F01FE0A2F07FC0943801FF00EF07FCEF1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0 030390C8FCED0FF8ED3FE0EDFF80DA03FEC9FCEC1FF8EC7FE0903801FF80D907FECAFCEB 1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC048CCFC12FC12703B3878B44C>I<91B87E19 F019FC02009039C00007FF6F489038007FC003FFED1FE0737E93C86C7E737E19014A707E 5D1A7FA20203EF3F805DA21BC014075DA3140F4B17E0A3141F4B17C0A3143F4B167FA302 7F18804B16FFA302FF180092C95A62A24917034A5F19076201034D5A5C4F5A620107173F 4A5F4FC7FC19FE010F4C5A4A15034E5AF00FE0011F4C5A4A4B5A06FFC8FC013FED01FCEF 0FF84AEC3FE001FF913803FF80B848C9FC17F094CAFC4B447CC351>68 D<91B912FCA3020001C0C7123F6F48EC03F803FF1501190093C91278A21A385C5DA30203 17305DA314074B1460A218E0020F4B13005DA21701021F5D4B13031707170F023F027FC8 FC92B6FCA391397FC0007E4B131EA2170E02FF140C92C7FCA2171C49031813035C611906 010392C7FC4A160E190C191C010717184A163819301970130F4A5E180161011F16034A15 074E5A013F163F4EC7FC4AEC03FF01FFED3FFEB9FCA26046447CC348>I<91B600E049B5 12C0A3020001E0C8383FF800DB7F80ED1FE003FF94C7FC1A3E93C9127862F101C04A4C5A 4B4BC8FC191C6102035E4B5DF003804EC9FC0207150E4B14386060020F4A5A4B0107CAFC 170E5F021F14784B13F84C7E1603023F130F4B487E163BEEE1FF91387FC1C1DB83807FED 8700159CDAFFB86D7E5D03C06D7E5D4990C7FC4A6E7EA2717E13034A811707A201076F7E 5C717EA2130F4A6E7FA2727E131F5C727E133F854A82D9FFE04B7EB600E0010FB512E05F A252447CC353>75 D<91B500C0933803FFFE63630200F1FE00DB6FE0EE1BF803EF171F1B 3703CFEF67F0A21BCF0201EF018F038F60DB87F0ED030F1B1F020317060307040C5BA2F2 183F020717300206616F6C15601B7F020E17C0020CDC018090C7FCA24F485A021C160602 18606F6C5C1A0102381618023004305BA2F16003027016C00260606F6CEB01801A0702E0 ED03004A03065CA24E130F01015E4A60047F5B1A1F01035E91C74A5CA24D48133F494BC7 FC010661EE3F861A7F010E158C010C039892C8FCA205B05C011C15E001186001386E5A19
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
C00018495A001C49C8FC6C137C380781F83803FFE0C66CC9FC2C407DAB30>I<027CEB01 8049B413034901801300010F6D5A49EBE00E6F5A90393F03F838903978007EF80170EB1F F00160EB01E001E05C49495A90C748C7FC150E5D5D5D5D4A5A4A5A4AC8FC140E5C5C5C5C EB03C049C9FC130E49141C4914185B49143848481430491470D8039014F048B4495A3A0F EFC007C0391E03F01FD81C01B55A486C91C7FC485C00606D5A00E0EB3FF048EB0FC0292D 7CAB2D>I<16301678167CA2163C163E163F82007FB712C0B8FCA27EC9EA7F0016FC4B5A 4B5A5E4B5AA26FC7FC2A146EC631>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmr12 12 79 /Ft 79 124 df<1618163CA2167EA216FFA24B7FA24B6C7EA29238063FE0A24B6C7EA24B 6C7EA292383807FC153092387003FE15609238E001FF15C002016D7F5D02036E7E92C7FC 4A6E7E1406020E6E7E140C021C6E7E141802386E7E143002706E7E146002E06E7E5C0101 6F7F5C0103707E91C9FC183F010683181F4983180F49831807498318034983A249707EA2 4848701380A248CBEA7FC0A20006F03FE0A248F01FF0A2001FBA12F8A24819FCA24819FE A2BCFC48477CC651>1 D<9239FFC001FC020F9038F80FFF913B3F803E3F03C0913BFC00 077E07E0D903F890390FFC0FF0494890383FF81F4948EB7FF0495A494814E049C7FCF00F E04991393FC0038049021F90C7FCAFB912F0A3C648C7D81FC0C7FCB3B2486CEC3FF0007F D9FC0FB512E0A33C467EC539>11 D<4AB4FC020F13E091387F80F8903901FC001C49487F D907E0130F4948137F011FECFF80495A49C7FCA25B49EC7F00163E93C7FCACEE3F80B8FC A3C648C7FC167F163FB3B0486CEC7FC0007FD9FC1FB5FCA330467EC536>I<913801FFC0 020FEBFB8091387F803F903801FC00494813FFEB07E0EB1FC0A2495A49C7FC167F49143F 5BAFB8FCA3C648C7123FB3B2486CEC7FC0007FD9FC1FB5FCA330467EC536>I<121EEA7F 80EAFFC0A9EA7F80ACEA3F00AB121EAC120CA5C7FCAA121EEA7F80A2EAFFC0A4EA7F80A2 EA1E000A4778C61B>33 D<001EEB03C0397F800FF000FF131F01C013F8A201E013FCA300 7F130F391E6003CC0000EB000CA401E0131C491318A3000114384913300003147090C712 604814E0000614C0000E130148EB038048EB070048130E0060130C1E1D7DC431>I<0430 14C00478497EA204F81303A24C5CA203011407A24C5CA20303140FA24C91C7FCA203075C A24C131EA2030F143EA293C7123CA24B147CA2031E1478A2033E14F8A2033C5CA2037C13 01007FBA12F8BB12FCA26C19F8C72801F00007C0C7FC4B5CA30203140FA24B91C8FCA402 075CA24B131EA3020F143E007FBA12F8BB12FCA26C19F8C7003EC700F8C8FC023C5CA202 7C1301A202785CA202F81303A24A5CA201011407A24A5CA20103140FA24A91C9FCA20107 5CA24A131EA2010F143EA291C7123CA249147CA2011E1478A2010C143046587BC451>I< 121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A12 06120E5A5A5A12600B1D78C41B>39 D<140C141C1438147014E0EB01C01303EB0780EB0F 00A2131E5BA25B13F85B12015B1203A2485AA3485AA348C7FCA35AA2123EA2127EA4127C A312FCB3A2127CA3127EA4123EA2123FA27EA36C7EA36C7EA36C7EA212017F12007F1378 7FA27F7FA2EB0780EB03C01301EB00E014701438141C140C166476CA26>I<12C07E1270 7E7E7E120F6C7E6C7EA26C7E6C7EA21378137C133C133E131E131FA2EB0F80A3EB07C0A3 EB03E0A314F0A21301A214F8A41300A314FCB3A214F8A31301A414F0A21303A214E0A3EB 07C0A3EB0F80A3EB1F00A2131E133E133C137C13785BA2485A485AA2485A48C7FC120E5A 5A5A5A5A16647BCA26>I<16C04B7EB3AB007FBAFCBB1280A26C1900C8D801E0C9FCB3AB 6F5A41407BB84C>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A3 12011380120313005A1206120E5A5A5A12600B1D78891B>I<B612C0A61A067F9721>I<12 1EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>I<1618163C167CA2167816F8A216 F01501A216E01503A216C01507A21680150FA2ED1F00A2151E153EA2153C157CA2157815 F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143EA2143C147CA25CA25C13 01A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C137CA2137813F8A25B1201A2 5B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA2127812F8A25A12602664 7BCA31>I<14FF010713E090381F81F890383E007C01FC133F4848EB1F8049130F4848EB 07C04848EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8FC4815FEA54815FFB3 A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0000315C06D130F 6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE0010090C7FC28447CC131>I< 143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E007FB6FCA3204278C1 31>I<EB03FE90381FFFC0017F13F03901F80FFC3903C001FE48486C7E000EC7EA7F8048 EC3FC0ED1FE04815F00030140F007015F800601407126CB415FC7F7F1503A46C4813076C C7FCC8FC16F8A2150F16F0151F16E0A2ED3FC0ED7F8016005D5D4A5A4A5A4A5A5D4A5A4A 5A4AC7FC147C5C5C495A495A495A49C7120C131E5B013814185B5B485A4848143848C812 30000E1570001FB612F0A25A5AB712E0A326427BC131>I<49B4FC010F13E0013F13FC90 38FE01FE3A01F0007F80D803C0EB3FC048C7EA1FE0120EED0FF0EA0FE0486C14F8A21507
7F5BA26C48130FEA03C0C813F0A3ED1FE0A2ED3FC01680ED7F0015FE4A5AEC03F0EC1FC0 D90FFFC7FC15F090380001FCEC007FED3F80ED1FC0ED0FE016F0ED07F816FC150316FEA2 150116FFA3121EEA7F80487EA416FE491303A2007EC713FC00701407003015F80038140F 6C15F06CEC1FE06C6CEB3FC0D803E0EB7F803A01FE01FE0039007FFFF8010F13E0010190 C7FC28447CC131>I<ED0380A21507150FA2151F153FA2157F15FFA25CEC03BF153F1407 1406140C141C141814301470146014C013011480EB03005B13065B131C13185B13701360 13E0485A5B120390C7FC1206120E120C5A123812305A12E0B812C0A3C8383F8000ADEDFF E0027FEBFFC0A32A437DC231>I<000615C0D807C0130701FCEB7F8090B612005D5D5D15 E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F090383800FC01F0137ED807C0 7F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216FCA5123E127F487EA416 F890C712075A006015F0A20070140F003015E00038EC1FC07E001EEC3F806CEC7F006C6C 13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F826447BC131>I<EC07FCEC3F FF91B512C0903903FC03E0903907E000F0D91FC0133849C71258017EEB01FC01FE130349 1307485A485AA24848EB03F8000FEC01F092C7FC485AA3485AA3127FA29038007F809038 01FFF090380780FC39FF0E003E49EB1F8049EB0FC049EB07E0136001E0EB03F04914F815 0116FC5BED00FEA390C812FFA47EA57F123FA216FE121F15016D14FC120FED03F86C7EED 07F06C6C14E06C6CEB0FC06C6CEB1F80017EEB3F0090383F80FE90380FFFF8010313E001 00138028447CC131>I<121CA2EA1F8090B712C0A3481680A217005E0038C8120C003015 1C00705D0060153016705E5E4814014B5A4BC7FCC81206150E5D151815385D156015E04A 5AA24A5A140792C8FC5CA25C141E143EA2147E147CA214FCA21301A3495AA41307A6130F AA6D5AEB01C02A457BC231>I<14FF010713E0011F13F890387F00FE01FC133FD801F0EB 1F804848EB0FC049EB07E00007EC03F048481301A290C713F8481400A47FA26D130116F0 7F6C6CEB03E013FC6C6CEB07C09039FF800F806C9038C01F006CEBF03EECF87839007FFE F090383FFFC07F01077F6D13F8497F90381E7FFFD97C1F1380496C13C02601E00313E048 486C13F000079038007FF84848EB3FFC48C7120F003EEC07FE150148140016FF167F4815 3FA2161FA56C151E007C153EA2007E153C003E157C6C15F86DEB01F06C6CEB03E06C6CEB 07C0D803F8EB1F80C6B4EBFF0090383FFFFC010F13F00101138028447CC131>I<14FF01 0713E0011F13F890387F80FC9038FC007E48487F4848EB1F804848EB0FC0000FEC07E048 5AED03F0485A16F8007F140190C713FCA25AA216FE1500A516FFA46C5CA36C7E5D121F7F 000F5C6C6C130E150C6C6C131C6C6C5BD8007C5B90383F01E090390FFF80FE903801FE00 90C8FC150116FCA4ED03F8A216F0D80F801307486C14E0486C130F16C0ED1F80A249EB3F 0049137E001EC75A001C495A000F495A3907E01FE06CB51280C649C7FCEB1FF028447CC1 31>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121EEA7F80A2EAFFC0A4EA7F 80A2EA1E000A2B78AA1B>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121E12 7FEAFF80A213C0A4127F121E1200A512011380A3120313005A1206120E120C121C5A5A12 600A3E78AA1B>I<007FBAFCBB1280A26C1900CEFCB0007FBAFCBB1280A26C190041187B A44C>61 D<EB0FFC90387FFFC03901F007F039078001FC000EC77E48147F48EC3F804815 C00060141F00FE15E07E7FA56CC7FC001CEC3FC0C8FCED7F80A2EDFF004A5AEC03F84A5A 5D4A5A4A5A92C7FC143E143C5CA2147014F05CA25C1301A35CA990C9FCAAEB03C0EB0FF0 A2497EA46D5AA2EB03C023467BC52E>63 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3 ED30FFA203707FED607FA203E07FEDC03FA2020180ED801FA2DA03007F160FA202068016 07A24A6D7EA34A6D7EA34A6D7EA20270810260147FA202E08191B7FCA249820280C7121F A249C87F170FA20106821707A2496F7EA3496F7EA3496F7EA201788313F8486C83D80FFF 03037FB500E0027FEBFFC0A342477DC649>65 D<B8FC17E017FC00019039C00003FF6C6C 4801007FEF3FC0717E717E717E84170384170184A760A21703601707604D5A4D5AEF7FC0 4DC7FCEE03FEEE3FF091B65A17FC0280C7B47EEF1FC0EF0FF0717E717E717E717E198018 7F19C0A2183F19E0A8F07FC0A2198018FF4D1300A24D5AEF0FFC4D5AEF7FE048486C9038 03FFC0B9C7FC17FC17C03B447CC345>I<DB0FFE146092B500C013E0020314F0913A0FFC 01FC0191393FC0003E02FFC7EA0F83D903FCEC03C74948EC01E74948EC00FF4948157F49 48153F4948151F49C9120F485A491607120348481603A248481601A248481600A2123FA2 491760127FA31900485AAE6C7EA21960A2123F7FA2001F18E07F000F18C0A26C6C160119 806C6C160312016DEE07006C6C16066D6C150E6D6C5D6D6C5D6D6C15786D6C5D6D6C4A5A D900FFEC0780DA3FC0011FC7FCDA0FFC13FC0203B512F0020014C0DB0FFEC8FC3B487BC5 46>I<B8FC17F017FC00019039C00007FF6C499038007FC0017FED1FE0EF07F0EF03FC71 7E717E84727E727E727EA2727E85180385A2180185A38584A31A80AD1A00A36061A36118 0361180761180F614E5A183F614EC7FC18FEEF03FC4D5AEF1FE001FFED7FC0486DD907FF C8FCB812FC17F094C9FC41447CC34B>I<B912F0A3000101C0C7127F6C6C48EC0FF81703 1701170018781838A2181CA3180CA4180E1806160CA21800A5161CA2163C167CED01FC91 B5FCA3EC8001ED007C163C161CA2160CA793C8FCB08048487EB612F8A337447CC340>70
D<DB0FFE146092B500C013E0020314F0913A0FFC01FC0191393FC0003E02FFC7EA0F83D9 03FCEC03C74948EC01E74948EC00FF4948157F4948153F4948151F49C9120F485A491607 120348481603A248481601A248481600A2123FA2491760127FA396C7FC485AAD4CB612C0 6C7EA293C7387FF000725A003F171F7FA2121F7F120FA26C7EA26C7E6C7EA26C7E6D7E6D 6C153F6D7E6D6C157F6D6C15E7D903FEEC01C7D900FFEC0383DA3FE0EB0F01DA0FFCEBFE 000203B500F81360020002E090C7FCDB0FFEC9FC42487BC54D>I<B6D8C003B6FCA30001 01E0C70007138026007F80913801FE00B3A991B7FCA30280C71201B3AC2601FFE0913807 FF80B6D8C003B6FCA340447CC349>I<B612F0A3C6EBF0006D5A6D5AB3B3B3A4497E497E B612F0A31C447DC323>I<B612F8A3000101E0C9FC6C6C5A5CB3B31830A418701860A518 E0A3EF01C0A217031707A2170F173F177FEE01FF48486C011F1380B9FCA334447CC33D> 76 D<B56C933807FFFC6E5EA20001F1FE0026006FE0EE1BF8A3D967F01633A2D963F816 63A3D961FC16C3A3D960FEED0183A2027FED0303A36E6C1406A36E6C140CA26E6C1418A3 6E6C1430A36E6C1460A26E6C14C0A36E6CEB0180A3037FEB0300A292383F8006A36F6C5A A36F6C5AA26F6C5AA36F6C5AA36F6C5AA26FB45AA370C7FC13F0A2486C143ED80FFFEF0F FEB500F0011C0107B512FCA34E447BC359>I<B56C020FB5FC8080C6040013F06D6CED1F 80D96FF8ED0F00A2D967FC1506EB63FEA2EB61FF01607FA26E7E6E7EA26E7E6E7EA26E7E 6E7EA26E7E6E7FA26F7E6F7EA26F7E6F7EA26F7E6F7EA26F7E6F1380A2EE7FC0EE3FE0A2 EE1FF0EE0FF8A2EE07FCEE03FEA2EE01FF701386A2EF7FC6EF3FE6A2EF1FF6EF0FFEA217 071703A217011700A201F0167E183E487ED80FFF161EB500F0150EA2180640447CC349> I<ED1FFC4AB512C0913907F007F091391F8000FC027EC7123FD901F8EC0FC049486E7E49 486E7E49486E7E49486E7E49C9127E017E8201FE834848707E4848707EA24848707EA200 0F84491603001F84A24848707EA3007F84A24982A300FF1980AD6C6C4C1300A4003F606D 1603A2001F60A26C6C4C5AA26C6C4C5AA20003606D161F6C6C4C5A000060017F4CC7FC6E 5D013F5E6D6C4A5AD907E0EC03F06D6C4A5AD901FCEC1FC0D9007E4AC8FCDA1F8013FC91 3907F007F00201B512C09126001FFCC9FC41487BC54C>I<B712FCEEFFC017F800019039 C0000FFC6C6C48EB01FF9338007F80EF1FE0170FEF07F018F8EF03FCA218FE1701A218FF A718FEA2170318FCA2EF07F818F0EF0FE0EF1FC0EF7F80933801FE00EE0FFC91B612F017 800280C9FCB3AA3801FFE0B612C0A338447CC342>I<B712E016FF17C000019039C0003F F86C6C48EB03FCEE00FF717E717E717E717E717EA284170384A760A21707604D5AA24D5A 4D5A4DC8FCEE01FEEE07F8EE3FE091B6C9FC16FC913980007F80EE0FE0707EEE03FC707E 160083717EA2717EA784A71A6084171FA21AE0716C13C02601FFE002071301B600C01680 943801FC03943900FE0700CBEA3FFEF007F843467CC348>82 D<49B41303010FEBE00701 3F13F89039FE00FE0FD801F8131FD807E0EB079F49EB03DF48486DB4FC48C8FC4881003E 81127E82127C00FC81A282A37E82A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE 6CEBFFE06C14FC6C14FF6C15C0013F14F0010F80010180D9001F7F14019138001FFF0303 1380816F13C0167F163F161F17E000C0150FA31607A37EA36C16C0160F7E17806C151F6C 16006C5D6D147ED8FBC05CD8F9F0495AD8F07C495A90393FC00FE0D8E00FB51280010149 C7FC39C0003FF02B487BC536>I<003FB912F8A3903BF0001FF8001F01806D481303003E C7150048187C0078183CA20070181CA30060180CA5481806A5C81600B3B3A54B7EED7FFE 49B77EA33F447DC346>I<B600C0010FB5FCA3000101E0C813F026007F80ED1F80F00F00 A21806B3B3A7180E6D6C150CA2181C131F6E1518010F163818306D6C1570606D6C14016D 6C5D6D6CEC0780027F4AC7FC6E6C131EDA1FE0137C913907FC03F00201B55A6E6C1380DB 07FCC8FC40467CC349>I<B692383FFFF0A3000301E003071300C649ED01FC4A5E017F70 5A6E5E133F616E1501011F5FA26D6C4BC7FCA28001071606A26E150E0103160CA26D6C5D A2806D5EA26F1470027F156081023F5DA281021F4A5AA26F1303020F92C8FC8102071406 A26F130E0203140CA26E6C5BA2816E5CA2EE8070037F1360A26F6C5AA216E092381FE180 A216F3030F90C9FC16FBED07FEA36F5AA36F5AA26F5AA3166044467EC349>I<B60107B5 00F890380FFFFEA3000301E0D9001F90C813F06C0180DA0FFCED3FC091C86C48ED1F006C 871C0E6D6C6E7E1C0CA26D6C6F5DA36EDA06FF1538011F1A30A26E020E6D1470010FDB0C 7F1560A26E021C7F0107DB183F5DA2856D6CDA301F4A5AA36D6C4A6C6C49C7FCA36D6C4A 6C6C1306A3DB80016E130E027FDA8003140CA2DBC00380023FDA00015CA203E081021F01 066D5CA36E6C486E6C5AA36E6C486E6C5AA36F48EC1FE1020360A2DBFE7015F302010160 020F90C8FCA2DBFFE015FB6E49EC07FEA36F486E5AA36FC86C5AA3031E6F5AA4030C1660 5F467EC364>I<B66C91380FFFFCA3000101F8C8000313C026007FE0923800FE0061013F 17F06D6C5E80010F5F6D6C4B5A18036D6C93C7FC6E15066D160E6D6D140C181C6E6C1418 6E6C5C18706E6C146018E06E6C5C6E6C495A17036E6C91C8FC5F6E6C13066E6D5A171C92 387FC0185FED3FE06F6C5A17E06F6C5AEEF980ED07FF6F90C9FCA26F5AB3A6923807FF80 0203B6FCA346447FC349>89 D<EAFFFCA4EAF000B3B3B3B3B3A2EAFFFCA40E6476CA1B> 91 D<01C01318000114384848137048C712E0000EEB01C0000C1480001C130300181400
00385B003013060070130E0060130CA300E0131C481318A400CFEB19E039FFC01FF801E0 13FCA3007F130FA2003F130701C013F8390F0001E01E1D71C431>I<EAFFFCA4EA003CB3 B3B3B3B3A2EAFFFCA40E647ECA1B>I<EB07FC90383FFF809038F80FE03903C003F048C6 6C7E000E6D7ED80FC0137E486C137F6D6D7EA36F7EA26C5AEA0380C8FCA4EC0FFF49B5FC 90380FFE1FEB3FC0EBFF00EA03FC485A485A485A485A127F5B176048C7FCA3153FA36D13 7F007F14EF6D9038C7E0C0003F13013A1FE00783F13B07F81E03FF802701FFFC0113003A 001FE0007C2B2E7CAC31>97 D<EA01FC12FFA3120712031201B3EC03FC91380FFF809138 3C07E091387001F89039FDE0007E02807F01FFEC1F8091C713C049EC0FE049140717F0A2 EE03F8A217FCA2160117FEAB17FC1603A217F8A2EE07F0A26DEC0FE017C06D141F01FBEC 3F80D9F380EB7E00D9E1C05B9039E0F001F89039C03C07E09039801FFF80C7D803FCC7FC 2F467DC436>I<EC7F80903803FFF090380FC07C90383F000F01FCEB03804848EB01C000 03140F4848EB1FE049133F120F485AA2485AED1FC0007FEC070092C7FCA290C9FC5AAB7E 7FA2123F16307F001F15706C6C146016E06C6C14C06C6C13010001EC03806C6CEB070001 3F131E90381FC078903807FFF001001380242E7DAC2B>I<167FED3FFFA315018182B3EC 7F80903803FFF090380FC07C90383F000E017E1307496D5AD803F87F48487F5B000F8148 5AA2485AA2127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038 077F806C6C010E13C0013F011C13FE90380FC0F8903803FFE09026007F0013002F467DC4 36>I<EB01FE903807FFC090381F03F090387E00FC49137E48487F485A4848EB1F80000F 15C049130F121F484814E01507A2007F15F090C7FCA25AA390B6FCA290C9FCA67EA27FA2 123F16306C7E1670000F15606D14E06C6C14C0000314016C6CEB03806C6CEB0700013E13 1E90381F80F8903803FFE0010090C7FC242E7DAC2B>I<EC0FE0EC7FF8903801F81E9038 03F03F90390FE07F8090381FC0FF5C133F495AA2ED7F0001FE131C92C7FCAFB67EA3C648 C8FCB3B2486C7E007F13FFA321467EC51E>I<EE0F80D901FCEB7FE0903A0FFF81F0F090 393F07E3819039FC01FF033A01F800FE014848017E13E00007027FC7FC497F000F814913 1F001F81A9000F5D6D133F000792C7FC6D5B0003147E6C6C5B6D485A3903BF07E090380F FF80260701FCC8FC90CAFCA25AA37F6C7E7F90B512F86C14FF16E06C15F86C6C8048B67E 3A07C0000FFF48481300003FC8EA3F80003E151F48ED0FC0A2481507A56C150F007C1680 007E151F003E16006C153E6C6C5CD807E0495AD801F8EB07E0D8007FEB3F8090261FFFFE C7FC010113E02C427DAC31>I<EA01FC12FFA3120712031201B3EC01FE913807FFC09138 1E07F091383801F802707FECE000D9FDC07F5C01FF147F91C7FCA25BA35BB3A8486CECFF 80B5D8F83F13FEA32F457DC436>I<EA01E0EA07F8A2487EA46C5AA2EA01E0C8FCADEA01 FC12FFA3120712031201B3B0487EB512F8A315437DC21C>I<143C14FFA2491380A46D13 00A2143C91C7FCADEC7F80EB3FFFA31300147F143FB3B3AA123E127F39FF807F00A2147E A25C6C485A383C01F06C485A3807FF80D801FEC7FC195785C21E>I<EA01FC12FFA31207 12031201B3A292381FFFE0A36F1300ED07F816E05E5E030EC7FC5D5D5D5D4A5A4A5A4AC8 FC5CEC3F804A7E14FF9038FDCFE09038FF8FF01407496C7E01FC7F14016E7E81816F7E82 151F6F7E821507826F7E8282486C491380B5D8F81F13F8A32D457DC433>I<EA01FC12FF A3120712031201B3B3B3A5487EB512F8A315457DC41C>I<D801FC01FFEC1FE000FF0107 01E0EBFFFC913B0F03F801E07F913C3C01FC07803F800007903C7000FE0E001FC0000349 D97E1C130F2601FDC0D97F38804A143001FFDA3FF06D7E91C75BA2495DA3495DB3A8486C 4A6C497EB5D8F81FB50003B512E0A34B2C7DAB52>I<3901FC01FE00FF903807FFC09138 1E07F091383801F8000701707F0003EBE0002601FDC07F5C01FF147F91C7FCA25BA35BB3 A8486CECFF80B5D8F83F13FEA32F2C7DAB36>I<EC7F80903803FFF090380FC0FC90383E 001F496D7E496D7E48486D7E48486D7E48486D7E000F81A24848147E003F157FA290C87E 481680A44816C0AA6C1680A26D147F003F1600A2001F157E6D14FE000F5D6D130100075D 6C6C495A6C6C495A6C6C495A013E49C7FC90381FC0FE903807FFF89038007F802A2E7DAC 31>I<3901FC03FC00FF90380FFF8091383C07E091387001F83A07FDE000FE0003018013 7FD801FFEC3F8091C7EA1FC04915E049140F17F0160717F8160317FCA3EE01FEABEE03FC A3EE07F8A217F0160F6D15E0EE1FC06D143F17806EEB7E00D9FDC05B9039FCF003F89138 3C0FE091381FFF80DA03FCC7FC91C9FCAE487EB512F8A32F3F7DAB36>I<91387F800390 3903FFE00790380FE07890393F801C0F90387E000E496D5AD803F8EB039F0007EC01BF49 14FF48487F121F5B003F81A2485AA348C8FCAB6C7EA3123F7F121F6D5C120F6D5B12076C 6C5B6C6C497E6C6C130E013F131C90380FC0F8903803FFE09038007F0091C7FCAEEEFF80 033F13FEA32F3F7DAB33>I<3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9 C000015B13FBEC007E153C01FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>I<9038 3FE0183901FFFC383907E01F78390F0003F8001E1301481300007C1478127800F81438A2 1518A27EA27E6C6C13006C7E13FC383FFFE06C13FC6C13FF6C14C06C14E0C614F0011F13 F81300EC0FFC140300C0EB01FE1400157E7E153EA27EA36C143C6C147C15786C14F86CEB 01F039F38003E039F1F00F8039E07FFE0038C00FF01F2E7DAC26>I<1306A5130EA4131E
A3133E137EA213FE12011207001FB512F0B6FCA2C648C7FCB3A4150CAA017E131C017F13 18A26D133890381F8030ECC070903807E0E0903801FFC09038007F001E3E7EBC26>I<D8 01FC147F00FFEC3FFFA300071401000380000181B3A85EA35DA212006D5B017E9038077F 80017F010E13C06D011C13FE90380FC078903803FFF09026007F8013002F2D7DAB36>I< B539F001FFFCA3000790C7EA7FE06C48EC1F8000011600160E1200160C017F5CA280013F 5CA26E1370011F146080010F5CA2ECF00101075CA26D6C48C7FCA26E5A01011306A26D6C 5AA214FF6E5AA215B8EC3FB015F06E5AA36E5AA26E5AA36EC8FC2E2C7EAA33>I<B500E0 B539E03FFF80A30007903C000FFE000FFC00D803FCD903F8EB03F8F001E0120103015D6D 80000060A26D6E13036DD9037E91C7FCA20280017F5B013FD9063F1306A2D91FC06E5AED 0C1FA2D90FE06E5AED180FA2D907F06E5AED3007A2D903F86E5AED6003A2902601FCE06D 5AEDC00117FCD900FFECFD80ED800017FF027F92C8FC92C77EA26E147E023E143EA2021E 143C021C141CA2412C7EAA46>I<B539F007FFFCA30003D9C00113C0C6496C1300017F14 FC013F5C6E13E06D7E010F495A6D6C485A02F890C7FC903803FC060101130E6E5A903800 FF186E5AEC3FF05D141F140F6E7E81140FEC0DFCEC19FEEC38FF4A7E9138603F8002C07F 0101131F49486C7E02007F01066D7E010E1303496D7E013C80017C80D801FC1580D80FFE 4913C0B5D8800F13FFA3302B7FAA33>I<B539F001FFFCA3000790C7EA7FE06C48EC1F80 00011600160E0000150C6D141C6D1418A26E1338013F1430A26D6C5BA26E13E0010F5CA2 6D6C485AA2ECF803010391C7FCA2903801FC06A2ECFE0E0100130CA2EC7F18A215B8EC3F B0A2EC1FE0A36E5AA26E5AA36EC8FCA21406A35CA25CA2123C007E5BB4FC5CA25CEAFE01 387C0380D87007C9FCEA3C1EEA0FFCEA03F02E3F7EAA33>I<003FB612E0A29038C0003F 90C713C0003CEC7F800038ECFF00A20030495A0070495AA24A5A0060495AA24A5A4A5AA2 C7485A4AC7FC5B5C495A13075C495A131F4A1360495A495AA249C712C0485AA2485A485A 1501485A48481303A24848EB07804848131F00FF14FF90B6FCA2232B7DAA2B>I<B9FCA2 3002809B31>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmbx12 17.28 24 /Fu 24 122 df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
C0DE007F7F071F13F8737F737F737F73808885888688A2747FA688A688A676140FF71F80 A374801F3F86771400745E746E5BB96E6E5B746E485A75EBFE07091F90B55A090715E009 015DCF003F91C7FC0A0013FC71647AE178>82 D<DBFFFCEC01E0020FD9FFE01303027F02 FC130749B7130F0107EEC01F011F16F049D9C007EBF83F4948C7383FFE7FD9FFF8020FB5 FC4801E014014849804849153F91C97E484882001F834982003F83845B007F187FA2193F A200FF181FA27F190FA27FA26D17078080806C01F893C7FC80ECFF8015F86CECFFC016FC 6CEDFFE017FE6CEEFFE018F86C17FE6C717E6C846C846D17F86D836D836D8313036D1880 6D6C17C0020F17E01401DA000F16F01500040715F8EE007F1703050014FC183F84060713 FE84A2007C8300FC83A2197FA3193F7EA31AFC7EA27F1AF86D177F7F1AF06D17FF6D18E0 6D5E01FF18C06E4B138002E04B130002F84B5A02FFED3FFC01CF01E0ECFFF8018301FF01 0F5B010191B65A6D6C5E48011F93C7FC48010315FC48D9003F14E048020149C8FC476677 E35A>I<B9041FB612F8A6D8000302F0CB003FEBC0006D6EDE07FEC7FC1EF86D6E180F6E 6D61535A6E6D183F6E6E60535A6E6E17FF6E6E95C8FC525A6E6E16036E6E5F525A6E6E16 0F6F6D5F525A6F6D163F6F6E5E525A6F6E15FF6F6E4A90C9FC646F6E14036F6E4A5A646F 6E140F706D4A5A64706D4A5A706E137F64706E49CAFC706E5A63706E485A70ECF8076370 6E485A71EBFE1F07FF5B714A5A7114FF637192CBFC8362715C8362715C8462B3AF043FB8 12C0A675627EE17A>89 D<913803FFFE027FEBFFF00103B612FE010F6F7E4916E090273F FE001F7FD97FE001077FD9FFF801017F486D6D7F717E486D6E7F85717FA2717FA36C496E 7FA26C5B6D5AEB1FC090C9FCA74BB6FC157F0207B7FC147F49B61207010F14C0013FEBFE 004913F048B512C04891C7FC485B4813F85A5C485B5A5CA2B55AA45FA25F806C5E806C04 7D7F6EEB01F96C6DD903F1EBFF806C01FED90FE114FF6C9027FFC07FC01580000191B548 7E6C6C4B7E011F02FC130F010302F001011400D9001F90CBFC49437CC14E>97 D<903807FF80B6FCA6C6FC7F7FB3A8EFFFF8040FEBFF80047F14F00381B612FC038715FF 038F010014C0DBBFF0011F7FDBFFC001077F93C76C7F4B02007F03F8824B6F7E4B6F1380 4B17C0851BE0A27313F0A21BF8A37313FCA41BFEAE1BFCA44F13F8A31BF0A24F13E0A24F 13C06F17804F1300816F4B5A6F4A5B4AB402075B4A6C6C495B9126F83FE0013F13C09127 F00FFC03B55A4A6CB648C7FCDAC00115F84A6C15E091C7001F91C8FC90C8000313E04F65 7BE35A>I<92380FFFC04AB512FC020FECFF80023F15E091B712F80103D9FE037F499039 F0007FFF011F01C0011F7F49496D7F4990C76C7F49486E7F48498048844A804884485B72 7E5A5C48717EA35A5C721380A2B5FCA391B9FCA41A0002C0CBFCA67EA380A27EA27E6E16 0FF11F806C183F6C7FF17F006C7F6C6D16FE6C17016D6C4B5A6D6D4A5A6D01E04A5A6D6D EC3FE0010301FC49B45A6D9026FFC01F90C7FC6D6C90B55A021F15F8020715E0020092C8 FC030713F041437CC14A>101 D<EB0FE0EB3FF8497E48B5FCA24880A24880A76C5CA26C 91C7FCA238007FFC6D5AEB0FE090C9FCAF903807FF80007FB5FCA6C6FC7F7FB3B3AEB712 C0A622657BE42C>105 D<903807FF80B6FCA6C6FC7F7FB3B3B3B3ADB712E0A623647BE3 2C>108 D<902607FF80D91FFFEEFFF8B691B500F00207EBFF80040702FC023F14E0041F 02FF91B612F84C6F488193267FE07F6D4801037F922781FE001F9027E00FF0007FC6DA83 F86D9026F01FC06D7F6DD987F06D4A487F6DD98FC0DBF87EC7804C6D027C80039FC76E48 8203BEEEFDF003BC6E4A8003FC04FF834B5FA24B5FA24B94C8FCA44B5EB3B2B7D8F007B7 D8803FB612FCA67E417BC087>I<902607FF80EB1FFFB691B512F0040714FC041F14FF4C 8193267FE07F7F922781FE001F7FC6DA83F86D7F6DD987F07F6DD98FC0814C7F039FC780 15BE03BC8003FC825DA25DA25DA45DB3B2B7D8F007B71280A651417BC05A>I<923807FF E092B6FC020715E0021F15F8027F15FE494848C66C6C7E010701F0010F13E04901C00103 7F49496D7F4990C87F49486F7E49486F7E48496F13804819C04A814819E048496F13F0A2 4819F8A348496F13FCA34819FEA4B518FFAD6C19FEA46C6D4B13FCA36C19F8A26C6D4B13 F0A26C19E06C6D4B13C0A26C6D4B13806C6D4B13006D6C4B5A6D6D495B6D6D495B010701 F0010F13E06D01FE017F5B010090B7C7FC023F15FC020715E0020092C8FC030713E04843 7CC151>I<D90FFFEB0FFCB690383FFF8093B512E04B14F04B14F8923907FC7FFC92390F E0FFFEC6EC1F806DD93F0113FF6D133E157E157C15F8A215F07013FEA24BEB7FFCEF3FF8 EF0FE04B90C7FCA55DB3B0B712F8A638417BC042>114 D<913A3FFF8007800107B5EAF8 1F011FECFE7F017F91B5FC48B8FC48EBE0014890C7121FD80FFC1407D81FF0801600485A 007F167F49153FA212FF171FA27F7F7F6D92C7FC13FF14E014FF6C14F8EDFFC06C15FC16 FF6C16C06C16F06C826C826C826C82013F1680010F16C01303D9007F15E0020315F0EC00 1F1500041F13F81607007C150100FC81177F6C163FA2171F7EA26D16F0A27F173F6D16E0 6D157F6D16C001FEEDFF806D0203130002C0EB0FFE02FCEB7FFC01DFB65A010F5DD8FE03 15C026F8007F49C7FC48010F13E035437BC140>I<EC07E0A6140FA5141FA3143FA2147F A214FF5BA25B5B5B5B137F48B5FC000F91B512FEB8FCA5D8001F01E0C8FCB3AFEF0FC0AC 171F6D6D1480A2173F6D16006F5B6D6D137E6D6D5B6DEBFF836EEBFFF86E5C020F14C002 035C9126003FFCC7FC325C7DDA3F>I<902607FFC0ED3FFEB60207B5FCA6C6EE00076D82
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ndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop -47 331 3750 4 v -47 530 a Fu(PHYSICS)53 b(2040)345 b(Solutions)53 b(to)h(Relativit)l(y)i(Problems)p -47 661 V 72 943 a Ft(1.)49 b(\(v)-5 b(ariation)30 b(on)i(T)-8 b(ext)34 b(Problem)e(7,)g(page)h(82\))197 1064 y(Observ)m(er)k Fs(S)k Ft(assigns)35 b(the)g(follo)m(wing)e(spacetime)i(co)s(ordinates) f(to)h(an)g(ev)m(en)m(t:)50 b Fs(x)36 b Ft(=)f(200)f(km,)197 1184 y Fs(y)f Ft(=)d(20)g(km,)g Fs(z)35 b Ft(=)30 b(500)g(km,)g(and)g Fs(t)h Ft(=)f(100)f Fs(\026)p Ft(s.)43 b(What)30 b(are)h(the)f(co)s (ordinates)g(of)g(this)g(ev)m(en)m(t)i(in)197 1304 y(the)i Fs(S)432 1268 y Fr(0)489 1304 y Ft(frame)f(whic)m(h)i(mo)m(v)m(es)g(in) e(the)i(direction)d(of)i(increasing)f Fs(x)i Ft(with)e(sp)s(eed)i(0.9)p Fs(c)p Ft(?)48 b(Chec)m(k)197 1425 y(y)m(our)35 b(answ)m(ers)i(b)m(y)f (using)e(the)i(in)m(v)m(erse)g(Loren)m(tz)f(transformation)e(equations) i(to)g(obtain)e(the)197 1545 y(original)c(data.)313 1749 y Fq(\017)48 b Ft(It)39 b(is)g(often)g(con)m(v)m(enien)m(t)i(to)d (express)j Fs(c)e Ft(in)g(km/)p Fs(\026)p Ft(s)f(and)h(3)26 b Fq(\002)h Ft(10)2833 1712 y Fp(8)2911 1749 y Ft(m/s)39 b(=)g(0.3)f(km/)p Fs(\026)p Ft(s.)411 1869 y(The)c(Loren)m(tz)f (transformation)e(equations)h(giv)m(e:)881 2128 y Fs(x)936 2087 y Fr(0)1042 2128 y Ft(=)83 b Fs(\015)5 b Ft(\()p Fs(x)23 b Fq(\000)f Fs(v)t(t)p Ft(\))60 b(=)1955 2061 y(1)p 1802 2105 354 4 v 1802 2123 a Fq(p)p 1885 2123 271 4 v 76 x Ft(1)22 b Fq(\000)h Fs(\014)2117 2170 y Fp(2)2166 2128 y Ft(\()p Fs(x)f Fq(\000)h Fs(\014)6 b(ct)p Ft(\))1042 2383 y(=)1396 2316 y(1)p 1211 2360 418 4 v 1211 2378 a Fq(p)p 1294 2378 335 4 v 81 x Ft(1)22 b Fq(\000)h Ft(0)p Fs(:)p Ft(9)1590 2431 y Fp(2)1639 2383 y Ft([\(200)32 b(km)o(\))22 b Fq(\000)h Ft(\(0)p Fs(:)p Ft(9\)\(0)p Fs(:)p Ft(3)32 b(km)o Fs(=\026)p Ft(s\)\(100)p Fs(\026)p Ft(s\)])1042 2576 y(=)83 b(397)32 b(km)885 2721 y Fs(y)937 2680 y Fr(0)1042 2721 y Ft(=)83 b Fs(y)63 b Ft(=)e(20)32 b(km)886 2866 y Fs(z)935 2825 y Fr(0)1042 2866 y Ft(=)83 b Fs(z)65 b Ft(=)60 b(500)32 b(km)901 3036 y Fs(t)936 2995 y Fr(0)1042 3036 y Ft(=)83 b Fs(\015)5 b Ft(\()p Fs(t)22 b Fq(\000)1477 2969 y Fs(v)p 1462 3013 82 4 v 1462 3104 a(c)1504 3076 y Fp(2)1553 3036 y Fs(x)p Ft(\))61
b(=)2005 2969 y(1)p 1853 3013 354 4 v 1853 3031 a Fq(p)p 1936 3031 271 4 v 76 x Ft(1)22 b Fq(\000)h Fs(\014)2168 3078 y Fp(2)2217 3036 y Ft(\()p Fs(t)f Fq(\000)2421 2969 y Fs(\014)p 2421 3013 61 4 v 2430 3104 a(c)2492 3036 y(x)p Ft(\))1042 3302 y(=)1396 3234 y(1)p 1211 3279 418 4 v 1211 3297 a Fq(p)p 1294 3297 335 4 v 81 x Ft(1)g Fq(\000)h Ft(0)p Fs(:)p Ft(9)1590 3349 y Fp(2)1639 3302 y Ft([\(100)p Fs(\026)p Ft(s\))e Fq(\000)2273 3234 y Ft(\(0)p Fs(:)p Ft(9\))p 2117 3279 512 4 v 2117 3370 a(\(0)p Fs(:)p Ft(3)32 b(km)p Fs(=\026)p Ft(s\))2639 3302 y(\(200)f(km\)])1042 3492 y(=)83 b Fq(\000)p Ft(1147)32 b Fs(\026)p Ft(s)61 b(=)82 b Fq(\000)22 b Ft(1)p Fs(:)p Ft(15)32 b(ms)411 3712 y(No)m(w,)i(plugging)c(these)k(in)m(to)e(the)h (in)m(v)m(erse)h(Loren)m(tz)f(transformations;)830 3971 y Fs(x)83 b Ft(=)g Fs(\015)5 b Ft(\()p Fs(x)1276 3930 y Fr(0)1322 3971 y Ft(+)22 b Fs(v)t(t)1506 3930 y Fr(0)1529 3971 y Ft(\))60 b(=)1926 3904 y(1)p 1773 3948 354 4 v 1773 3966 a Fq(p)p 1856 3966 271 4 v 76 x Ft(1)22 b Fq(\000)h Fs(\014)2088 4013 y Fp(2)2137 3971 y Ft(\()p Fs(x)2230 3930 y Fr(0)2276 3971 y Ft(+)f Fs(\014)6 b(ct)2512 3930 y Fr(0)2535 3971 y Ft(\))968 4227 y(=)1322 4159 y(1)p 1137 4203 418 4 v 1137 4221 a Fq(p)p 1220 4221 335 4 v 82 x Ft(1)22 b Fq(\000)h Ft(0)p Fs(:)p Ft(9)1516 4274 y Fp(2)1565 4227 y Ft([\(397)32 b(km)o(\))22 b(+)h(\(0)p Fs(:)p Ft(9\)\(0)p Fs(:)p Ft(3)31 b(km)p Fs(=\026)p Ft(s\)\()p Fq(\000)p Ft(1147)p Fs(\026)p Ft(s\)])968 4419 y(=)83 b(200)32 b(km)834 4565 y Fs(y)86 b Ft(=)d Fs(y)1179 4523 y Fr(0)1262 4565 y Ft(=)60 b(20)32 b(km)836 4710 y Fs(z)87 b Ft(=)c Fs(z)1176 4669 y Fr(0)1260 4710 y Ft(=)60 b(500)32 b(km)850 4880 y Fs(t)83 b Ft(=)g Fs(\015)5 b Ft(\()p Fs(t)1256 4838 y Fr(0)1302 4880 y Ft(+)1425 4812 y Fs(v)p 1410 4856 82 4 v 1410 4948 a(c)1452 4919 y Fp(2)1501 4880 y Fs(x)1556 4838 y Fr(0)1580 4880 y Ft(\))60 b(=)1976 4812 y(1)p 1824 4856 354 4 v 1824 4874 a Fq(p)p 1907 4874 271 4 v 76 x Ft(1)22 b Fq(\000)h Fs(\014)2139 4922 y Fp(2)2188 4880 y Ft(\()p Fs(t)2261 4838 y Fr(0)2306 4880 y Ft(+)2414 4812 y Fs(\014)p 2414 4856 61 4 v 2423 4948 a(c)2485 4880 y(x)2540 4838 y Fr(0)2563 4880 y Ft(\))968 5145 y(=)1322 5078 y(1)p 1137 5122 418 4 v 1137 5140 a Fq(p)p 1220 5140 335 4 v 81 x Ft(1)f Fq(\000)h Ft(0)p Fs(:)p Ft(9)1516 5193 y Fp(2)1565 5145 y Ft([\()p Fq(\000)p Ft(1147)p Fs(\026)p Ft(s\))f(+)2323 5078 y(\(0)p Fs(:)p Ft(9\))p 2168 5122 512 4 v 2168 5214 a(\(0)p Fs(:)p Ft(3)32 b(km)o Fs(=\026)p Ft(s\))2689 5145 y(\(397)g(km\)])968 5336 y(=)83 b(100)32 b Fs(\026)p Ft(s)p eop %%Page: 2 2 2 1 bop 72 331 a Ft(2.)49 b(\(v)-5 b(ariation)30 b(on)i(T)-8 b(ext)34 b(Problem)e(28,)g(page)g(84\))197 451 y(An)g(exp)s(erimen)m (ter)g(in)g(the)g Fs(S)38 b Ft(frame)31 b(arranges)h(to)g(trigger)f(t)m (w)m(o)h(\015ash)m(bulbs)h(sim)m(ultaneously)-8 b(,)197 572 y(a)31 b(red)i(\015ash)f(lo)s(cated)f(at)h(the)g(origin)e(and)i(a)f (green)i(\015ash)f(at)g Fs(x)p Ft(=10)g(km.)43 b(An)32 b(observ)m(er)h(in)e(the)197 692 y Fs(S)263 656 y Fr(0)326 692 y Ft(frame,)41 b(mo)m(ving)e(at)h(a)g(sp)s(eed)h(of)f(0.75)p Fs(c)f Ft(in)h(the)g(direction)f(of)h(increasing)f Fs(x)p Ft(,)k(also)c(views)197 812 y(these)34 b(\015ashes.)238 1016 y(\(a\))48 b(What)33 b(time)e(in)m(terv)-5 b(al)32 b(b)s(et)m(w)m(een)i(them)e(do)s(es)i(she)f(\014nd?)313 1178 y Fq(\017)48 b Ft(Lab)s(el)21 b(the)i(co)s(ordinates)e(b)m(y)i
(the)f(colour)f(of)g(the)h(ligh)m(t.)39 b(So)21 b(w)m(e)i(are)f(giv)m (en)g(that)g Fs(t)3305 1193 y Fo(g)3345 1178 y Fq(\000)p Fs(t)3457 1193 y Fo(r)3524 1178 y Ft(=)27 b(0,)411 1298 y Fs(x)466 1313 y Fo(r)540 1298 y Ft(=)34 b(0,)k Fs(x)819 1313 y Fo(g)894 1298 y Ft(=)d(10)h(km,)h(and)g Fs(\014)k Ft(=)34 b(0)p Fs(:)p Ft(75.)56 b(F)-8 b(rom)35 b(the)i(Loren)m(tz)g (equation)g(for)f(the)h(time)411 1419 y(co)s(ordinate:)936 1639 y Fs(t)971 1597 y Fr(0)971 1663 y Fo(g)1033 1639 y Fq(\000)23 b Fs(t)1168 1597 y Fr(0)1168 1663 y Fo(r)1289 1639 y Ft(=)83 b Fs(\015)5 b Ft([\()p Fs(t)1604 1654 y Fo(g)1667 1639 y Fq(\000)22 b Fs(t)1801 1654 y Fo(r)1839 1639 y Ft(\))h Fq(\000)2024 1571 y Fs(v)p 2009 1615 82 4 v 2009 1707 a(c)2051 1678 y Fp(2)2101 1639 y Ft(\()p Fs(x)2194 1654 y Fo(g)2256 1639 y Fq(\000)g Fs(x)2411 1654 y Fo(r)2449 1639 y Ft(\)])1289 1882 y(=)1680 1815 y(1)p 1458 1859 494 4 v 1458 1876 a Fn(q)p 1541 1876 411 4 v 100 x Ft(1)f Fq(\000)h Ft(\()p Fs(:)p Ft(75\))1913 1947 y Fp(2)1962 1882 y Ft([0)f Fq(\000)2300 1815 y Ft(\()p Fs(:)p Ft(75\))p 2169 1859 463 4 v 2169 1951 a(\()p Fs(:)p Ft(3)32 b(km)p Fs(=\026)p Ft(s\))2642 1882 y(\(10)g(km)22 b Fq(\000)h Ft(0\)])1289 2119 y(=)83 b Fq(\000)p Ft(37)p Fs(:)p Ft(8)33 b Fs(\026)p Ft(s)233 2360 y(\(b\))48 b(Whic)m(h)33 b(\015ash)g(do)s(es)g(she)h(sa)m(y)g(o)s(ccurs)f(\014rst?)313 2522 y Fq(\017)48 b Ft(The)34 b(fact)e(she)i(measured)f Fs(t)1442 2486 y Fr(0)1442 2546 y Fo(g)1504 2522 y Fq(\000)23 b Fs(t)1639 2486 y Fr(0)1639 2546 y Fo(r)1705 2522 y Fs(<)k Ft(0)33 b(means)f(she)i(sa)m(w)f(the)g(green)h(\015ash)f (\014rst.)72 2725 y(3.)49 b(\(v)-5 b(ariation)30 b(on)i(T)-8 b(ext)34 b(Problem)e(24,)g(page)g(84\))197 2846 y(The)e(mean)e (lifetime)e(of)i(particles)g(called)f(m)m(uons)i(stopp)s(ed)h(in)e(a)g (lead)g(blo)s(c)m(k)h(in)f(a)h(lab)s(oratory)197 2966 y(is)38 b(measured)g(to)g(b)s(e)g(2.2)g Fs(\026)p Ft(s.)61 b(The)39 b(mean)f(lifetime)d(of)i(high-sp)s(eed)i(m)m(uons)f(observ)m (ed)i(from)197 3086 y(cosmic)29 b(ra)m(ys)i(observ)m(ed)h(from)d(the)h (earth)h(is)e(measured)i(to)e(b)s(e)i(22)e Fs(\026)p Ft(s.)43 b(What)30 b(is)g(the)g(sp)s(eed)h(of)197 3207 y(these)j(cosmic)e(ra)m(y)h(m)m(uons?)313 3410 y Fq(\017)48 b Ft(The)36 b(prop)s(er)e(lifetime)d(of)j(the)h(m)m(uon)f(is)f(that)h (found)h(for)f(those)g(whic)m(h)h(are)g(\\stopp)s(ed")411 3530 y(\(i.e.,)c(brough)m(t)h(to)e(rest\))i(in)e(the)i(lead)e(blo)s(c)m (k.)43 b(This)31 b(is)g(giv)m(en)g(as)g(2.2)g Fs(\026)p Ft(s)g(so)g Fs(\034)3252 3545 y Fp(0)3320 3530 y Ft(=)c(2)p Fs(:)p Ft(2)k Fs(\026)p Ft(s.)411 3651 y(The)k(cosmic)d(ra)m(y)i(m)m (uons)g(ha)m(v)m(e)h(a)e(longer)f(observ)m(ed)k(lifetime)30 b(b)s(ecause)35 b(of)e(their)g(sp)s(eed)411 3785 y(in)f(the)h(observ)m (er's)i(frame.)43 b(That)33 b(is,)f Fs(\034)1867 3800 y Fo(cosmic)2113 3785 y Ft(=)c Fs(\015)5 b(\034)2315 3800 y Fp(0)2387 3785 y Ft(where)34 b Fs(\015)f Ft(=)27 b(1)p Fs(=)2954 3685 y Fn(q)p 3037 3685 391 4 v 100 x Ft(1)22 b Fq(\000)g Fs(v)3258 3756 y Fp(2)3298 3785 y Fs(=c)3389 3756 y Fp(2)3460 3785 y Ft(so)1571 4071 y Fs(\015)33 b Ft(=)1768 4003 y Fs(\034)1810 4018 y Fo(cosmic)p 1768 4048 261 4 v 1858 4139 a Fs(\034)1900 4154 y Fp(0)2067 4071 y Ft(=)2194 4003 y(22)p 2180 4048 125 4 v 2180 4139 a(2)p Fs(:)p Ft(2)2342 4071 y(=)28 b(10)411 4330 y(No)m(w,)1899 4589 y Fs(\015)88 b Ft(=)2359 4522 y(1)p 2207 4566 354 4 v 2207 4584 a Fq(p)p 2290 4584 271 4 v 76 x Ft(1)21 b Fq(\000)i Fs(\014)2521 4631 y Fp(2)1544 4844 y Ft(so)228 b Fs(\015)1915 4803 y Fp(2)2038 4844 y Ft(=)2317 4777
y(1)p 2207 4821 V 2207 4913 a(1)21 b Fq(\000)i Fs(\014)2438 4884 y Fp(2)1855 5097 y Fs(\014)1916 5056 y Fp(2)2038 5097 y Ft(=)83 b(1)21 b Fq(\000)2400 5029 y Ft(1)p 2377 5073 96 4 v 2377 5165 a Fs(\015)2433 5136 y Fp(2)1894 5376 y Fs(\014)89 b Ft(=)2197 5224 y Fn(s)p 2280 5224 286 4 v 152 x Ft(1)21 b Fq(\000)2483 5309 y Ft(1)p 2460 5353 96 4 v 2460 5444 a Fs(\015)2516 5416 y Fp(2)411 5657 y Ft(And)33 b(with)e Fs(\015)i Ft(=)27 b(10)k(w)m(e)i(get)f Fs(\014)h Ft(=)28 b(0)p Fs(:)p Ft(99499)i(or)i Fs(v)j Ft(=)d(0)p Fs(:)p Ft(99499)p Fs(c)e Ft(=)i(\(0)p Fs(:)p Ft(99499\)\(3)18 b Fq(\002)j Ft(10)3518 5621 y Fp(8)3557 5657 y Ft(\))32 b(=)411 5777 y(2)p Fs(:)p Ft(98)22 b Fq(\002)h Ft(10)805 5741 y Fp(8)876 5777 y Ft(m/s.)p eop %%Page: 3 3 3 2 bop 72 331 a Ft(4.)49 b(\(v)-5 b(ariation)30 b(on)i(T)-8 b(ext)34 b(Problem)e(39,)g(page)g(85\))197 451 y(Observ)m(er)44 b Fs(S)j Ft(notes)c(that)f(t)m(w)m(o)g(coloured)g(\015ashes)h(of)f (ligh)m(t,)g(separated)h(b)m(y)g(1.5)f(km,)i(o)s(ccur)197 572 y(along)e(the)j(p)s(ositiv)m(e)e(branc)m(h)i(of)f(the)g Fs(x)g Ft(axis.)78 b(A)44 b(red)g(\015ash)h(o)s(ccurs)g(\014rst,)i (follo)m(w)m(ed)c(after)197 692 y(2.5)d Fs(\026)p Ft(s)h(b)m(y)g(a)f (green)h(\015ash,)i(the)e(latter)f(b)s(eing)g(the)h(more)e(distan)m(t)i (from)e(the)i(origin)d(of)i(her)197 812 y(reference)35 b(frame.)44 b(A)33 b(second)i(observ)m(er,)g Fs(S)1821 776 y Fr(0)1844 812 y Ft(,)e(obtains)g(exactly)h(the)f(same)g(n)m (umerical)f(v)-5 b(alues)197 933 y(for)33 b(the)g(time)f(di\013erence)i (and)f(the)h(absolute)f(spatial)f(separation)h(b)s(et)m(w)m(een)i(the)f (t)m(w)m(o)g(ev)m(en)m(ts)197 1053 y(but)f(declares)g(that)f(the)h (green)g(\015ash)g(o)s(ccurs)h(\014rst.)238 1257 y(\(a\))48 b(What)33 b(is)f(the)h(relativ)m(e)f(sp)s(eed)i(of)e Fs(S)1744 1221 y Fr(0)1800 1257 y Ft(with)g(resp)s(ect)i(to)e Fs(S)6 b Ft(?)313 1419 y Fq(\017)48 b Ft(De\014ning)36 b(\001)p Fs(t)f Fq(\021)g Fs(t)1102 1434 y Fo(g)1167 1419 y Fq(\000)25 b Fs(t)1304 1434 y Fo(r)1379 1419 y Ft(\(where)37 b(the)g(subscripts)h(refer)f(to)f(the)h(colour)e(of)h (the)h(\015ash\),)411 1539 y(w)m(e)d(ha)m(v)m(e)g(from)d(the)i(Loren)m (tz)h(transformation)c(equations:)1268 1777 y Fs(t)1303 1735 y Fr(0)1303 1801 y Fo(g)1366 1777 y Fq(\000)22 b Fs(t)1500 1735 y Fr(0)1500 1801 y Fo(r)1621 1777 y Ft(=)83 b Fs(\015)5 b Ft([\()p Fs(t)1936 1792 y Fo(g)1999 1777 y Fq(\000)22 b Fs(t)2133 1792 y Fo(r)2172 1777 y Ft(\))g Fq(\000)2357 1709 y Fs(v)p 2341 1753 82 4 v 2341 1845 a(c)2383 1816 y Fp(2)2433 1777 y Ft(\()p Fs(x)2526 1792 y Fo(g)2588 1777 y Fq(\000)h Fs(x)2743 1792 y Fo(r)2781 1777 y Ft(\)])732 b(\(1\))1357 1956 y Fs(c)p Ft(\001)p Fs(t)1515 1915 y Fr(0)1621 1956 y Ft(=)83 b Fs(\015)5 b Ft([)p Fs(c)p Ft(\001)p Fs(t)23 b Fq(\000)g Fs(\014)6 b Ft(\001)p Fs(x)p Ft(])1210 b(\(2\))411 2176 y(But)27 b(w)m(e)h(are)f(giv)m(en)g(that)g(\001)p Fs(t)1465 2140 y Fr(0)1516 2176 y Ft(=)h Fq(\000)p Ft(\001)p Fs(t)p Ft(.)42 b(Plugging)25 b(this)i(in)m(to)f(\(2\))g(and)h(dividing)e (through)411 2297 y(b)m(y)34 b Fs(c)p Ft(\001)p Fs(t)f Ft(giv)m(es:)1626 2460 y Fq(\000)p Ft(1)28 b(=)g Fs(\015)1956 2338 y Fn(\022)2017 2460 y Ft(1)22 b Fq(\000)h Fs(\014)2269 2392 y Ft(\001)p Fs(x)p 2258 2436 159 4 v 2258 2528 a(c)p Ft(\001)p Fs(t)2427 2338 y Fn(\023)3578 2460 y Ft(\(3\))411 2671 y(W)-8 b(e)34 b(ha)m(v)m(e)h(that)e(\001)p Fs(x)d Ft(=)e(1)p Fs(:)p Ft(5)33 b(km)g(and)h(\001)p Fs(t)29
b Ft(=)g(2)p Fs(:)p Ft(5)p Fs(\026)p Ft(s)k(so)h(\001)p Fs(x=c)p Ft(\001)p Fs(t)c Ft(=)f(2)k(and)g(equation)g(\(3\))411 2792 y(b)s(ecomes:)1721 3012 y Fq(\000)p Ft(1)83 b(=)g Fs(\015)27 b Fq(\000)c Ft(2)p Fs(\014)6 b(\015)1150 b Ft(\(4\))1682 3157 y(2)p Fs(\014)6 b(\015)87 b Ft(=)c Fs(\015)27 b Ft(+)22 b(1)1264 b(\(5\))411 3377 y(No)m(w,)42 b(b)m(y)f(de\014nition)e Fs(\015)44 b Ft(=)c(1)p Fs(=)1562 3301 y Fq(p)p 1644 3301 271 4 v 1644 3377 a Ft(1)22 b Fq(\000)h Fs(\014)1876 3348 y Fp(2)1954 3377 y Ft(whic)m(h)40 b(squaring)g(and)g(rearranging)e(leads)h(to)411 3497 y(the)33 b(relation)e Fs(\014)998 3461 y Fp(2)1037 3497 y Fs(\015)1093 3461 y Fp(2)1160 3497 y Ft(=)d Fs(\015)1320 3461 y Fp(2)1381 3497 y Fq(\000)23 b Ft(1.)43 b(So)33 b(squaring)f(b)s(oth)h(sides)g(of)f(\(5\))g(giv)m(es:)1718 3717 y(4)p Fs(\014)1828 3676 y Fp(2)1867 3717 y Fs(\015)1923 3676 y Fp(2)2045 3717 y Ft(=)83 b Fs(\015)2260 3676 y Fp(2)2322 3717 y Ft(+)22 b(2)p Fs(\015)27 b Ft(+)22 b(1)1572 3863 y(4\()p Fs(\015)1715 3822 y Fp(2)1776 3863 y Fq(\000)h Ft(1\))82 b(=)h Fs(\015)2260 3822 y Fp(2)2322 3863 y Ft(+)22 b(2)p Fs(\015)27 b Ft(+)22 b(1)1421 4008 y(3)p Fs(\015)1526 3967 y Fp(2)1587 4008 y Fq(\000)h Ft(2)p Fs(\015)k Fq(\000)22 b Ft(5)83 b(=)g(0)411 4373 y(The)34 b(solution)d(of)h(this)g(is)g(of)h(the)g(form;)1619 4658 y Fs(\015)g Ft(=)1817 4590 y Fq(\000)p Fs(b)23 b Fq(\006)2057 4509 y(p)p 2140 4509 345 4 v 81 x Fs(b)2181 4561 y Fp(2)2243 4590 y Fq(\000)g Ft(4)p Fs(ac)p 1817 4634 669 4 v 2101 4726 a Ft(2)p Fs(a)411 4903 y Ft(whic)m(h,)34 b(with)e Fs(a)c Ft(=)f(3,)33 b Fs(b)28 b Ft(=)f Fq(\000)p Ft(2,)33 b(and)g Fs(c)28 b Ft(=)f Fq(\000)p Ft(5)33 b(giv)m(es)1117 5220 y Fs(\015)g Ft(=)1315 5137 y(2)22 b Fq(\006)1485 5037 y Fn(q)p 1568 5037 547 4 v 100 x Ft(4)g Fq(\000)h Ft(4\(3\)\()p Fq(\000)p Ft(5\))p 1315 5196 800 4 v 1628 5288 a(2\(3\))2152 5220 y(=)2265 5152 y(1)f Fq(\006)2436 5070 y(p)p 2519 5070 98 4 v 82 x Ft(16)p 2265 5196 352 4 v 2417 5288 a(3)2654 5220 y(=)2768 5152 y(1)g Fq(\006)g Ft(4)p 2768 5196 220 4 v 2853 5288 a(3)411 5495 y(No)m(w,)49 b Fs(\015)h Ft(m)m(ust)45 b(b)s(e)g Fs(>)k Ft(0)44 b(so)h(the)h(only)e (allo)m(w)m(ed)g(solution)f(is)i Fs(\015)53 b Ft(=)c(5)p Fs(=)p Ft(3.)80 b(Therefore,)411 5616 y Fs(\014)34 b Ft(=)27 b(4)p Fs(=)p Ft(5)h(and)h(the)g(relativ)m(e)f(sp)s(eed)h(of)g (the)g(t)m(w)m(o)g(frames)f(is)g(0)p Fs(:)p Ft(8)p Fs(c)g Ft(with)h Fs(S)3069 5580 y Fr(0)3120 5616 y Ft(mo)m(ving)f(in)f(the)411 5736 y(+)p Fs(x)i Ft(direction)f(in)g Fs(S)6 b Ft(.)42 b([Y)-8 b(ou)29 b(can)g(v)m(erify)g(this)g(b)m(y)g(stic)m(king)g(this)f (v)-5 b(alue)29 b(for)f Fs(v)k Ft(bac)m(k)e(in)e(\(2\)])p eop %%Page: 4 4 4 3 bop 233 331 a Ft(\(b\))48 b(Whic)m(h)33 b(\015ash)g(will)e Fs(S)1199 295 y Fr(0)1254 331 y Ft(sa)m(y)j(w)m(as)f(most)f(distan)m(t) h(from)e(the)i(origin)e(of)h(her)h(frame?)313 488 y Fq(\017)48 b Ft(Using)33 b(the)g(Loren)m(tz)g(transformation)d(equation)j(for)f Fs(x)h Ft(w)m(e)g(ha)m(v)m(e)1328 692 y Fs(x)1383 651 y Fr(0)1383 717 y Fo(g)1446 692 y Fq(\000)23 b Fs(x)1601 651 y Fr(0)1601 717 y Fo(r)1667 692 y Ft(=)k Fs(\015)5 b Ft([\()p Fs(x)1946 707 y Fo(g)2009 692 y Fq(\000)23 b Fs(x)2164 707 y Fo(r)2202 692 y Ft(\))f Fq(\000)h Fs(v)t Ft(\()p Fs(t)2486 707 y Fo(g)2548 692 y Fq(\000)g Fs(t)2683 707 y Fo(r)2721 692 y Ft(\)])411 896 y(whic)m(h,)32 b(with)e Fs(\015)j Ft(=)27 b(5)p Fs(=)p Ft(3,)j Fs(v)i Ft(=)27
b(\(4)p Fs(=)p Ft(5\))p Fs(c)p Ft(,)j Fs(x)1886 911 y Fo(g)1944 896 y Fq(\000)19 b Fs(x)2095 911 y Fo(r)2161 896 y Ft(=)27 b(1)p Fs(:)p Ft(5)j(km,)h(and)f Fs(t)2832 911 y Fo(g)2890 896 y Fq(\000)18 b Fs(t)3020 911 y Fo(r)3086 896 y Ft(=)28 b(2)p Fs(:)p Ft(5)p Fs(\026)p Ft(s,)i(giv)m(es:)895 1148 y Fs(x)950 1107 y Fr(0)950 1172 y Fo(g)1013 1148 y Fq(\000)22 b Fs(x)1167 1107 y Fr(0)1167 1172 y Fo(r)1233 1148 y Ft(=)1347 1080 y(5)p 1347 1125 49 4 v 1347 1216 a(3)1406 1148 y([\(1)p Fs(:)p Ft(5)32 b(km)o(\))23 b Fq(\000)1930 1080 y Ft(4)p 1930 1125 V 1930 1216 a(5)1989 1148 y(\(0)p Fs(:)p Ft(3)32 b(km)p Fs(=\026)p Ft(s\)\(2)p Fs(:)p Ft(5)p Fs(\026)p Ft(s\))27 b(=)h(1)p Fs(:)p Ft(5)k(km)411 1381 y(So,)h(as)g(in)f Fs(S)6 b Ft(,)32 b(the)h(green)g(\015ash)g(is)f (the)h(most)f(distan)m(t)h(in)f(the)h Fs(S)2771 1345 y Fr(0)2826 1381 y Ft(frame.)72 1580 y(5.)49 b(A)33 b(particle)e(w)m (as)j(observ)m(ed)h(to)e(b)s(e)g(created)g(at)g(t)g(=)f(10)h(ns,)g(tra) m(v)m(el)g(with)g(sp)s(eed)h Fs(u)3243 1595 y Fo(x)3319 1580 y Ft(=)f(-\()p Fs(c)p Ft(/2\),)197 1700 y(and)j(then)g(to)f(deca)m (y)i(at)f(t)f(=)h(30)f(ns.)54 b(T)-8 b(o)35 b(an)h(observ)m(er)h(who)f (w)m(as)h(mo)m(ving)e(with)g(a)g(sp)s(eed)i(of)197 1821 y(-\(4/5\))p Fs(c)31 b Ft(along)g(the)i(common)e Fs(x)23 b Fq(\000)g Fs(x)1577 1785 y Fr(0)1633 1821 y Ft(axis:)238 2020 y(\(a\))48 b(What)33 b(w)m(as)h(the)f(v)m(elo)s(cit)m(y)f(of)g (the)h(particle)e(during)h(its)g(trip?)313 2177 y Fq(\017)48 b Ft(The)34 b(v)m(elo)s(cit)m(y)e(transformation)f(equation)h(is:)1778 2414 y Fs(u)1834 2373 y Fr(0)1834 2438 y Fo(x)1905 2414 y Ft(=)2037 2346 y Fs(u)2093 2361 y Fo(x)2158 2346 y Fq(\000)23 b Fs(v)p 2019 2391 307 4 v 2019 2482 a Ft(1)f Fq(\000)2199 2443 y Fo(u)2240 2451 y Fm(x)2279 2443 y Fo(v)p 2199 2459 117 4 v 2225 2517 a(c)2256 2498 y Fl(2)411 2683 y Ft(Here)34 b Fs(u)698 2698 y Fo(x)769 2683 y Ft(=)27 b Fq(\000)p Ft(\()p Fs(c=)p Ft(2\))33 b(and)f Fs(v)g Ft(=)27 b Fq(\000)p Ft(\(4)p Fs(=)p Ft(5\))p Fs(c)33 b Ft(so)1454 2951 y Fk(u)1521 2901 y Fj(0)1521 2980 y Fi(x)1656 2951 y Fh(=)1856 2870 y Fk(u)1923 2888 y Fi(x)2000 2870 y Fg(\000)27 b Fk(v)p 1840 2923 358 4 v 1840 3033 a Fh(1)f Fg(\000)2054 2985 y Fi(u)2102 2997 y Ff(x)2144 2985 y Fi(v)p 2054 3005 133 4 v 2084 3074 a(c)2120 3050 y Fe(2)1656 3290 y Fh(=)1901 3208 y Fg(\000)p Fh(\()2053 3161 y Fi(c)p 2050 3180 42 4 v 2050 3249 a Fd(2)2101 3208 y Fh(\))g Fg(\000)h Fh(\()p Fg(\000)2442 3161 y Fd(4)p 2442 3180 V 2442 3249 a(5)2493 3208 y Fk(c)p Fh(\))p 1840 3262 811 4 v 1840 3377 a(1)f Fg(\000)2044 3276 y Fn(h)q(\020)2133 3377 y Fg(\000)2236 3330 y Fd(1)p 2236 3349 42 4 v 2236 3418 a(2)2288 3276 y Fn(\021)19 b(\020)2407 3377 y Fg(\000)2510 3330 y Fd(4)p 2510 3349 V 2510 3418 a(5)2561 3276 y Fn(\021i)1656 3587 y Fh(=)1844 3506 y Fk(c)p 1840 3559 59 4 v 1840 3669 a Fh(2)233 3854 y Ft(\(b\))48 b(What)39 b(w)m(as)h(the)f(distance)g(b)s(et)m(w)m(een)i(the)e(p)s (osition)e(where)j(the)f(particle)e(w)m(as)j(created)411 3975 y(and)33 b(the)g(p)s(osition)e(at)h(whic)m(h)h(it)f(deca)m(y)m (ed?)313 4132 y Fq(\017)48 b Ft(In)33 b(the)g Fs(S)39 b Ft(frame)31 b(this)i(distance)f(\001)p Fs(x)d Fq(\021)f Fs(x)1968 4147 y Fp(2)2030 4132 y Fq(\000)23 b Fs(x)2185 4147 y Fp(1)2257 4132 y Ft(is)32 b(just)514 4386 y(\001)p Fs(x)d Ft(=)e Fs(u)838 4401 y Fo(x)882 4386 y Ft(\001)p Fs(t)h Ft(=)f Fs(u)1185 4401 y Fo(x)1229 4386 y Ft(\()p Fs(t)1302 4401 y Fp(2)1363 4386 y Fq(\000)c Fs(t)1498 4401 y Fp(1)1538 4386 y Ft(\))k(=)h Fq(\000)1797 4318
y Fs(c)p 1794 4362 49 4 v 1794 4454 a Ft(2)1853 4386 y(\(30)22 b Fq(\000)g Ft(10\))27 b(=)2387 4318 y Fq(\000)p Ft(\(0)p Fs(:)p Ft(3)33 b(m)p Fs(=)p Ft(ns)o(\)\(20)f(ns)q(\))p 2387 4362 832 4 v 2779 4454 a(2)3257 4386 y(=)27 b Fq(\000)p Ft(3)33 b(m)411 4621 y(where)38 b(the)f(con)m(v)m(enien)m(t)i(units)d (for)g Fs(c)h Ft(of)f(m/ns)g(w)m(ere)i(used.)57 b(So)36 b(the)h(distance)g(is)f(3)h(m.)411 4741 y(In)c Fs(S)599 4705 y Fr(0)655 4741 y Ft(this)f(distance)h(is)f(giv)m(en)h(b)m(y)g (the)g(Loren)m(tz)h(transformation)c(equation)596 4984 y(\001)p Fs(x)732 4943 y Fr(0)784 4984 y Ft(=)d Fs(\015)5 b Ft([\001)p Fs(x)23 b Fq(\000)g Fs(v)t Ft(\001)p Fs(x)p Ft(])28 b(=)1585 4917 y(5)p 1585 4961 49 4 v 1585 5052 a(3)1660 4863 y Fn(\024)1704 4984 y Ft(\()p Fq(\000)p Ft(3)k(m\))22 b Fq(\000)2141 4863 y Fn(\022)2203 4984 y Fq(\000)2290 4917 y Ft(4)p 2290 4961 V 2290 5052 a(5)2349 4863 y Fn(\023)2426 4984 y Ft(\(0)p Fs(:)p Ft(3)33 b(m)p Fs(=)p Ft(ns)o(\)\(20)f(ns)q(\))3181 4863 y Fn(\025)3252 4984 y Ft(=)c(3)k(m)243 5244 y(\(c\))49 b(Ho)m(w)33 b(m)m(uc)m(h)g (time)e(elapsed)h(b)s(et)m(w)m(een)i(the)f(instan)m(t)f(it)f(w)m(as)i (created)g(and)f(the)h(instan)m(t)f(it)411 5364 y(deca)m(y)m(ed?)313 5522 y Fq(\017)48 b Ft(There)25 b(are)e(t)m(w)m(o)i(w)m(a)m(ys)g(to)e (calculate)f(this.)40 b(The)24 b(sp)s(eed)h(of)e(the)h(particle)e(in)g Fs(S)3197 5485 y Fr(0)3244 5522 y Ft(is)h Fs(u)3389 5485 y Fr(0)3389 5546 y Fo(x)3460 5522 y Ft(=)k Fs(c=)p Ft(2)411 5642 y(and)49 b(it)f(tra)m(v)m(elled)h(a)f(distance)i(\001)p Fs(x)1776 5606 y Fr(0)1849 5642 y Ft(=)e(3)h(m)f(so,)53 b(using)c Fs(u)2696 5606 y Fr(0)2696 5667 y Fo(x)2795 5642 y Fq(\021)55 b Ft(\001)p Fs(x)3063 5606 y Fr(0)3087 5642 y Fs(=)p Ft(\001)p Fs(t)3252 5606 y Fr(0)3325 5642 y Ft(\(i.e.,)d(the)411 5762 y(de\014nition)32 b(of)g Fs(u)1012 5726 y Fr(0)1012 5787 y Fo(x)1055 5762 y Ft(\),)h(w)m(e)h(ha) m(v)m(e)1206 6021 y(\001)p Fs(t)1322 5980 y Fr(0)1373 6021 y Ft(=)1487 5954 y(\001)p Fs(x)1623 5918 y Fr(0)p 1487 5998 161 4 v 1517 6090 a Fs(u)1573 6105 y Fo(x)1685 6021 y Ft(=)1826 5954 y(\001)p Fs(x)1962 5918 y Fr(0)p 1798 5998 216 4 v 1798 6090 a Ft(\()p Fs(c=)p Ft(2\))2051 6021 y(=)2211 5954 y(2\(3)e(m\))p 2165 5998 380 4 v 2165 6090 a(0)p Fs(:)p Ft(3)g(m)p Fs(=)p Ft(ns)2582 6021 y(=)c(20)k(ns)p eop %%Page: 5 5 5 4 bop 411 331 a Ft(Y)-8 b(ou)39 b(arriv)m(e)f(at)g(the)h(same)f (result)h(\(of)f(course!\))62 b(using)38 b(the)h(Loren)m(tz)g (transformation)411 451 y(equation:)524 685 y(\001)p Fs(t)640 644 y Fr(0)691 685 y Ft(=)28 b Fs(\015)867 563 y Fn(\024)911 685 y Ft(\001)p Fs(t)23 b Fq(\000)1175 617 y Fs(v)p 1160 661 82 4 v 1160 753 a(c)1202 724 y Fp(2)1251 685 y Ft(\001)p Fs(x)1387 563 y Fn(\025)1459 685 y Ft(=)1573 617 y(5)p 1573 661 49 4 v 1573 753 a(3)1648 539 y Fn(")1696 685 y Ft(\(20)32 b(ns)q(\))22 b Fq(\000)2117 563 y Fn(\022)2178 685 y Fq(\000)2265 617 y Ft(4)p 2265 661 V 2265 753 a(5)2324 563 y Fn(\023)2402 539 y( )2643 617 y Ft(1)p 2477 661 380 4 v 2477 753 a(0)p Fs(:)p Ft(3)33 b(m)p Fs(=)p Ft(ns)2867 539 y Fn(!)2950 685 y Ft(\(3)f(m\))3189 539 y Fn(#)3264 685 y Ft(=)c(20)k(ns)233 938 y(\(d\))48 b(Ho)m(w)35 b(can)g(observ)m(ers)i(in)c(t)m(w)m(o)i(frames)f(mo)m(ving) f(with)h(a)g(relativ)m(e)g(v)m(elo)s(cit)m(y)g(observ)m(e)i(the)411 1058 y(same)k(v)-5 b(alues)40 b(for)f(the)i(distance)f(co)m(v)m(ered)i (and)e(lifetime)d(for)i(this)h(particle?)64 b(Do)s(esn't)411 1179 y(this)33 b(con)m(tradict)f(relativit)m(y)f(\(i.e.,)i(what)g(happ)
s(ened)h(to)e(length)g(con)m(traction)g(and)h(time)411 1299 y(dilation\)?)313 1449 y Fq(\017)48 b Ft(The)36 b(particle)d(has)i(the)g Fc(same)40 b(sp)s(eed)c Ft(in)e(b)s(oth)g (frames,)h(only)f(it)f(is)h(going)g(to)g(the)h(left)411 1569 y(in)44 b Fs(S)50 b Ft(and)45 b(to)f(the)h(righ)m(t)f(in)g Fs(S)1600 1533 y Fr(0)1623 1569 y Ft(.)79 b(So)45 b(the)g Fs(\015)k Ft(factor)44 b(is)g(the)h(same)g(in)e(b)s(oth)i(of)f(these) 411 1689 y(frames)33 b(and)g(time)f(dilation)e(and)k(length)e(con)m (traction)h(e\013ects)h(are)g(therefore)f(of)g(equal)411 1810 y(magnitude)h(\(since)h(it)e(is)i(the)g(sp)s(eed)h(of)e(the)h(ob)5 b(ject)35 b(relativ)m(e)f(to)g(the)i(observ)m(er)g(that)e(is)411 1930 y(b)s(eing)e(measeured)i(here\).)72 2121 y(6.)49 b(A)43 b(particle)f(is)g(observ)m(ed)j(to)e(ha)m(v)m(e)h(a)f(v)m(elo)s (cit)m(y)e Fs(~)-47 b(u)45 b Ft(=)g(\()p Fs(c=)p Ft(4)p Fs(;)17 b(c=)p Ft(2)p Fs(;)g Ft(0\))41 b(in)i(the)g Fs(S)49 b Ft(frame.)74 b(The)197 2242 y Fs(S)263 2205 y Fr(0)321 2242 y Ft(frame)35 b(is)g(mo)m(ving)g(at)g(a)h(sp)s(eed)g(of)g(\(4/5\)) p Fs(c)e Ft(in)h(the)h(direction)f(of)g Fb(de)-5 b(cr)g(e)g(asing)34 b Fs(x)i Ft(along)e(the)197 2362 y(common)d Fs(x)23 b Fq(\000)f Fs(x)819 2326 y Fr(0)875 2362 y Ft(axis.)313 2553 y Fq(\017)48 b Ft(W)-8 b(e)33 b(ha)m(v)m(e)h Fs(v)e Ft(=-\(4/5\))p Fs(c)f Ft(and)h(so)h Fs(\015)38 b Ft(=)32 b(\(5/3\).)238 2702 y(\(a\))48 b(What)33 b(is)f Fs(u)839 2666 y Fr(0)839 2727 y Fo(x)883 2702 y Ft(?)43 b(\(Y)-8 b(ou)32 b(can)h(giv)m(e)g(it)e(in)h(terms)h(of)f(a)g(fraction)f(of)i Fs(c)p Ft(\))313 2852 y Fq(\017)48 b Ft(The)34 b(v)m(elo)s(cit)m(y)e (transformation)f(equation)h(for)g Fs(x)h Ft(giv)m(es:)1161 3122 y Fs(u)1217 3081 y Fr(0)1217 3146 y Fo(x)1288 3122 y Ft(=)1419 3054 y Fs(u)1475 3069 y Fo(x)1541 3054 y Fq(\000)22 b Fs(v)p 1402 3098 307 4 v 1402 3190 a Ft(1)g Fq(\000)1582 3151 y Fo(u)1623 3159 y Fm(x)1662 3151 y Fo(v)p 1582 3167 117 4 v 1608 3224 a(c)1639 3206 y Fl(2)1746 3122 y Ft(=)1913 2939 y Fn(\020)1975 2996 y Fo(c)p 1972 3012 36 4 v 1972 3070 a Fp(4)2040 3035 y Fq(\000)g(\000)2226 2996 y Fp(4)p 2226 3012 V 2226 3070 a(5)2272 2939 y Fn(\021)2338 3035 y Fs(c)p 1860 3098 574 4 v 1860 3208 a Ft(1)g Fq(\000)2030 3112 y Fn(\020)2090 3169 y Fp(1)p 2090 3185 36 4 v 2090 3242 a(4)2135 3112 y Fn(\021)16 b(\020)2251 3208 y Fq(\000)2338 3169 y Fp(4)p 2338 3185 V 2338 3242 a(5)2384 3112 y Fn(\021)2453 2939 y(\020)2513 2996 y Fp(21)p 2513 3012 71 4 v 2513 3070 a(20)2593 2939 y Fn(\021)2659 3035 y Fs(c)p 2453 3098 249 4 v 2560 3151 a Fp(6)p 2560 3167 36 4 v 2560 3225 a(5)2739 3122 y Ft(=)2853 3054 y(7)p 2853 3098 49 4 v 2853 3190 a(8)2911 3122 y Fs(c)233 3412 y Ft(\(b\))48 b(What)33 b(is)f Fs(u)839 3375 y Fr(0)839 3436 y Fo(y)880 3412 y Ft(?)44 b(\(Y)-8 b(ou)32 b(can)h(giv)m(e)f(it)g(in)g(terms)g(of) g(a)h(fraction)e(of)h Fs(c)p Ft(\))313 3561 y Fq(\017)48 b Ft(Similarly)-8 b(,)29 b(for)j Fs(u)1050 3576 y Fo(y)1091 3561 y Ft(:)1375 3736 y Fs(u)1431 3695 y Fr(0)1431 3761 y Fo(y)1500 3736 y Ft(=)1785 3669 y Fs(u)1841 3684 y Fo(y)p 1614 3713 439 4 v 1614 3804 a Fs(\015)5 b Ft(\(1)21 b Fq(\000)1888 3765 y Fo(u)1929 3773 y Fm(x)1968 3765 y Fo(v)p 1888 3781 117 4 v 1914 3839 a(c)1945 3820 y Fl(2)2015 3804 y Ft(\))2090 3736 y(=)2351 3626 y Fo(c)p 2349 3642 36 4 v 2349 3699 a Fp(2)p 2204 3713 326 4 v 2204 3726 a Fn(\020)2263 3783 y Fp(5)p 2263 3799 36 4 v 2263 3857 a(3)2308 3726 y Fn(\021)c(\020)2434 3783 y Fp(6)p 2434 3799 V 2434 3857 a(5)2479 3726 y Fn(\021)2567 3736 y Ft(=)2684 3669 y Fs(c)p 2680 3713 49 4 v 2680
3804 a Ft(4)243 4005 y(\(c\))49 b(What)29 b(is)g Fq(j)n Fs(~)-47 b(u)860 3969 y Fr(0)882 4005 y Fq(j)28 b Ft(\(i.e.,)i(the)f (magnitude)e(of)g Fs(~)-47 b(u)1964 3969 y Fr(0)1986 4005 y Ft(\)?)42 b(\(Y)-8 b(ou)29 b(can)g(giv)m(e)g(it)f(in)g(terms)g (of)h(a)f(fraction)411 4125 y(of)33 b Fs(c)p Ft(\))313 4275 y Fq(\017)899 4456 y Fs(u)955 4415 y Fr(0)1005 4456 y Ft(=)28 b Fq(j)n Fs(~)-47 b(u)1193 4415 y Fr(0)1216 4456 y Fq(j)27 b Ft(=)1374 4358 y Fn(q)p 1457 4358 548 4 v 98 x Ft(\()p Fs(u)1551 4428 y Fr(0)1551 4481 y Fo(x)1595 4456 y Ft(\))1633 4428 y Fp(2)1694 4456 y Ft(+)22 b(\()p Fs(u)1886 4428 y Fr(0)1886 4481 y Fo(y)1927 4456 y Ft(\))1965 4428 y Fp(2)2032 4456 y Ft(=)28 b Fs(c)2178 4290 y Fn(s)p 2261 4290 581 4 v 45 x(\022)2332 4389 y Ft(7)p 2332 4433 49 4 v 2332 4525 a(8)2391 4335 y Fn(\023)2452 4351 y Fp(2)2513 4456 y Ft(+)2611 4335 y Fn(\022)2682 4389 y Ft(1)p 2682 4433 V 2682 4525 a(4)2741 4335 y Fn(\023)2802 4351 y Fp(2)2869 4456 y Ft(=)2983 4307 y Fq(p)p 3066 4307 98 4 v 82 x Ft(53)p 2983 4433 181 4 v 3049 4525 a(8)3173 4456 y Fs(c)233 4669 y Ft(\(d\))48 b(An)26 b(observ)m(er)h(in) d(the)h Fs(S)1274 4632 y Fr(0)1323 4669 y Ft(frame)f(measures)i(the)f Fs(y)2212 4632 y Fr(0)2260 4669 y Ft(comp)s(onen)m(t)g(of)f(the)i Fb(momentum)e Ft(\(i.e.,)411 4789 y Fs(p)460 4753 y Fr(0)460 4814 y Fo(y)502 4789 y Ft(\))32 b(of)g(the)h(particle)f(to)g(b)s(e)h (0.6)f(MeV/)p Fs(c)p Ft(.)44 b(What)33 b(is)f(the)h(rest)g(mass)f(of)g (the)h(particle?)313 4938 y Fq(\017)48 b Ft(The)34 b Fs(y)664 4902 y Fr(0)719 4938 y Ft(comp)s(onen)m(t)e(of)h(the)g(momen)m (tum)e(is)h(de\014ned)i(as:)1651 5115 y Fs(p)1700 5074 y Fr(0)1700 5140 y Fo(y)1769 5115 y Ft(=)27 b Fs(mu)2013 5074 y Fr(0)2013 5140 y Fo(y)2082 5115 y Ft(=)h Fs(\015)5 b(m)2327 5130 y Fp(0)2367 5115 y Fs(u)2423 5074 y Fr(0)2423 5140 y Fo(y)411 5292 y Ft(where)1228 5431 y Fs(\015)33 b Ft(=)1614 5364 y(1)p 1426 5408 427 4 v 1426 5425 a Fn(q)p 1509 5425 344 4 v 107 x Ft(1)21 b Fq(\000)1689 5485 y Fp(\()p Fo(u)1757 5466 y Fa(0)1780 5485 y Fp(\))1807 5466 y Fl(2)p 1689 5508 153 4 v 1733 5566 a Fo(c)1764 5547 y Fl(2)1889 5431 y Ft(=)2249 5364 y(1)p 2003 5408 542 4 v 2003 5425 a Fn(r)p 2086 5425 459 4 v 133 x Ft(1)h Fq(\000)2256 5462 y Fn(\020)2316 5464 y Fr(p)p 2375 5464 71 3 v 55 x Fp(53)p 2316 5535 130 4 v 2363 5593 a(8)2455 5462 y Fn(\021)2505 5484 y Fp(2)2582 5431 y Ft(=)2761 5364 y(8)p 2695 5408 181 4 v 2695 5426 a Fq(p)p 2779 5426 98 4 v 2779 5508 a Ft(11)411 5734 y(Therefore)543 5945 y Fs(m)628 5960 y Fp(0)696 5945 y Ft(=)841 5871 y Fs(p)890 5835 y Fr(0)890 5896 y Fo(y)p 809 5922 153 4 v 809 6014 a Fs(\015)5 b(u)921 5985 y Fr(0)921 6038 y Fo(y)1000 5945 y Ft(=)1145 5871 y Fs(p)1194 5835 y Fr(0)1194 5896 y Fo(y)1235 5871 y Fs(c)p 1113 5922 195 4 v 1113 6014 a(\015)g(u)1225 5985 y Fr(0)1225 6038 y Fo(y)1266 6014 y Fs(c)1346 5945 y Ft(=)1498 5878 y(\(0)p Fs(:)p Ft(6)32 b(MeV)r(\))p 1460 5922 518 4 v 1460 5935 a Fn(\020)1566 5992 y Fp(8)p 1519 6008 130 4 v 1519 6018 a Fr(p)p 1578 6018 71 3 v 55 x Fp(11)1658 5935 y Fn(\021)17 b(\020)1784 5992 y Fp(1)p 1784 6008 36 4 v 1784 6066 a(4)1829 5935 y Fn(\021)1896 6032 y Fs(c)1938 6003 y Fp(2)2015 5945 y Ft(=)27 b(\()p Fs(:)p Ft(3\)\()2308 5858 y Fq(p)p 2391 5858 98 4 v 87 x Ft(11)o(\))33 b(MeV)q Fs(=)q(c)2857 5904 y Fp(2)2924 5945 y Ft(=)28 b(1)p Fs(:)p Ft(00)j(MeV)q Fs(=)q(c)3531 5904 y Fp(2)p eop %%Page: 6 6
6 5 bop 72 331 a Ft(7.)49 b(An)30 b(an)m(tiproton)f(is)h(a)g(particle)e (iden)m(tical)h(to)h(the)g(proton)g(in)f(all)f(resp)s(ects)k(except)g (that)d(it)g(has)197 451 y(the)39 b(opp)s(osite)f(c)m(harge)h(\(i.e.,)h (it)e(has)h(the)g(same)f(c)m(harge)h(as)g(the)g(electron\).)62 b(An)39 b(an)m(tiproton)197 572 y(ha)m(ving)32 b(a)g(kinetic)g(energy)h (equal)f(to)g(\(2/3\)M)1908 587 y Fo(p)1947 572 y Fs(c)1989 536 y Fp(2)2061 572 y Ft(strik)m(es)h(a)f(proton)g(whic)m(h)h(is)e(at)h (rest.)44 b(They)197 692 y(annihilate)35 b(yielding)i(t)m(w)m(o)h (photons.)60 b(That)38 b(is,)h(the)g(initial)34 b(state)k(con)m(tains)g (only)f(a)h(proton)197 812 y(and)31 b(an)g(an)m(tiproton)e(and)i(the)h (\014nal)e(state)h(con)m(tains)g(only)f(t)m(w)m(o)i(photons.)43 b(The)32 b(t)m(w)m(o)f(photons)197 933 y(emerge)38 b(from)f(the)h (reaction)f(tra)m(v)m(elling)g(forw)m(ard)h(or)f(bac)m(kw)m(ard)j(on)e (the)g(line)f(along)f(whic)m(h)197 1053 y(the)d(an)m(tiproton)e(tra)m (v)m(elled.)238 1257 y(\(a\))48 b(What)d(energies)h(do)e(the)i(photons) f(ha)m(v)m(e)h(and)f(in)f(whic)m(h)h(direction)f(is)g(eac)m(h)i(photon) 411 1377 y(heading)33 b(\(i.e.,)f(either)g(along)f(or)h(against)g(the)h (original)c(an)m(tiproton)j(direction\)?)313 1539 y Fq(\017)48 b Ft(The)43 b(initial)37 b(state)42 b(con)m(tains)g(t)m(w)m(o)g(ob)5 b(jects)42 b({)g(an)f(an)m(tiproton)f(and)i(a)f(proton)g(ha)m(ving)411 1659 y(energy)33 b(and)f(momen)m(ta)f(of)h Fs(E)1525 1674 y Fp(\026)-41 b Fo(p)1590 1659 y Ft(=)32 b Fs(K)1787 1674 y Fp(\026)-41 b Fo(p)1853 1659 y Ft(+)32 b Fs(M)2055 1674 y Fo(p)2095 1659 y Fs(c)2137 1623 y Fp(2)2208 1659 y Ft(and)g Fs(~)-49 b(p)2452 1674 y Fp(\026)-41 b Fo(p)2517 1659 y Ft(=)32 b Fs(p)2680 1674 y Fp(\026)-41 b Fo(p)2746 1659 y Ft(\(all)29 b(the)k(motions)d(in)h(the)411 1780 y(problem)d(are)h(along)f(the)i(one)f(axis,)h(call)d(it)h(the)h Fs(x)h Ft(axis\),)g(and)f Fs(E)2803 1795 y Fo(p)2872 1780 y Ft(=)g Fs(M)3071 1795 y Fo(p)3111 1780 y Fs(c)3153 1744 y Fp(2)3221 1780 y Ft(and)h Fs(~)-50 b(p)3456 1795 y Fo(p)3524 1780 y Ft(=)27 b(0,)411 1900 y(resp)s(ectiv)m(ely)-8 b(.)64 b(Therefore,)42 b(the)e(total)d(energy)j(and)f(momen)m(tum)f(of) h(the)g(initial)c(state)411 2020 y(are:)455 2260 y Fs(E)527 2275 y Fo(i)638 2260 y Ft(=)83 b Fs(E)875 2275 y Fp(\026)-41 b Fo(p)931 2260 y Ft(+)22 b Fs(E)1101 2275 y Fo(p)1169 2260 y Ft(=)27 b Fs(K)1361 2275 y Fp(\026)-41 b Fo(p)1417 2260 y Ft(+)22 b(2)p Fs(M)1658 2275 y Fo(p)1698 2260 y Fs(c)1740 2219 y Fp(2)1807 2260 y Ft(=)1921 2193 y(2)p 1921 2237 49 4 v 1921 2328 a(3)1979 2260 y Fs(M)2073 2275 y Fo(p)2113 2260 y Fs(c)2155 2219 y Fp(2)2217 2260 y Ft(+)g(2)p Fs(M)2458 2275 y Fo(p)2498 2260 y Fs(c)2540 2219 y Fp(2)2607 2260 y Ft(=)2720 2193 y(8)p 2720 2237 V 2720 2328 a(3)2779 2260 y Fs(M)2873 2275 y Fo(p)2913 2260 y Fs(c)2955 2219 y Fp(2)436 2535 y Fs(p)485 2550 y Fo(i)513 2535 y Fs(c)83 b Ft(=)g Fs(p)852 2550 y Fp(\026)-41 b Fo(p)886 2535 y Fs(c)28 b Ft(=)1059 2438 y Fn(q)p 1142 2438 637 4 v 97 x Fs(K)1232 2506 y Fp(2)1231 2559 y(\026)-41 b Fo(p)1294 2535 y Ft(+)22 b(2)p Fs(K)1530 2550 y Fp(\026)-41 b Fo(p)1563 2535 y Fs(M)1657 2550 y Fo(p)1697 2535 y Fs(c)1739 2506 y Fp(2)1806 2535 y Ft(=)1910 2368 y Fn(s)p 1993 2368 1270 4 v 46 x(\022)2064 2467 y Ft(2)p 2064 2512 49 4 v 2064 2603 a(3)2123 2535 y Fs(M)2217 2550 y Fo(p)2257 2535 y Fs(c)2299 2506 y Fp(2)2338 2414 y Fn(\023)2399 2429 y Fp(2)2461 2535 y Ft(+)22 b(2)2625 2414 y Fn(\022)2695 2467 y Ft(2)p 2695 2512 V 2695 2603 a(3)2754 2535 y Fs(M)2848 2550 y Fo(p)2888 2535 y Fs(c)2930 2506 y Fp(2)2970 2414 y Fn(\023)3047 2535 y Fs(M)3141 2550 y Fo(p)3181 2535 y Fs(c)3223 2506 y Fp(2)3290 2535
y Ft(=)3404 2467 y(4)p 3404 2512 V 3404 2603 a(3)3463 2535 y Fs(M)3557 2550 y Fo(p)3597 2535 y Fs(c)3639 2494 y Fp(2)411 2791 y Ft(The)39 b(\014nal)e(state)h(consists)h(of)e(t)m(w)m (o)i(photons.)59 b(T)-8 b(ak)m(e)39 b(photon)f(#1)g(to)f(b)s(e)h(going) e(in)h(the)411 2911 y(p)s(ositiv)m(e)26 b Fs(x)h Ft(direction)f(so)h (it)e(has)i(energy)h(and)e(momen)m(tum)g(of)g Fs(E)2795 2926 y Fp(1)2861 2911 y Ft(and)g Fs(p)3093 2926 y Fp(1)3161 2911 y Ft(=)h Fs(E)3336 2926 y Fp(1)3376 2911 y Fs(=c)p Ft(.)41 b(The)411 3032 y(second)30 b(photon)e(could,)h(in)e(principle,) h(b)s(e)h(going)d(in)i(either)g(the)h(p)s(ositiv)m(e)e(or)h(negativ)m (e)h Fs(x)411 3152 y Ft(direction)34 b(so)g(it)g(has)g(energy)i(and)e (momen)m(tum)f(of)h Fs(E)2420 3167 y Fp(2)2494 3152 y Ft(and)g Fs(p)2734 3167 y Fp(2)2804 3152 y Ft(=)d Fq(\006)p Fs(E)3060 3167 y Fp(2)3100 3152 y Fs(=c)p Ft(.)49 b(Therefore,)411 3273 y(the)33 b(total)e(energy)j(and)f(momen)m(tum)e(of)h(the)h (\014nal)f(state)h(are:)1714 3493 y Fs(E)1786 3508 y Fo(f)1915 3493 y Ft(=)83 b Fs(E)2146 3508 y Fp(1)2208 3493 y Ft(+)22 b Fs(E)2378 3508 y Fp(2)1696 3638 y Fs(p)1745 3653 y Fo(f)1790 3638 y Fs(c)83 b Ft(=)g Fs(E)2146 3653 y Fp(1)2208 3638 y Fq(\006)22 b Fs(E)2379 3653 y Fp(2)411 3858 y Ft(W)-8 b(e)36 b(can)f(see)h(from)d(this)i(that)g(photon)f(#2)h (m)m(ust)g(b)s(e)g(going)f(in)g(the)h(negativ)m(e)g Fs(x)g Ft(direc-)411 3978 y(tion)41 b(\(i.e.,)j Fs(p)904 3993 y Fp(2)986 3978 y Ft(=)f Fq(\000)p Fs(E)1254 3993 y Fp(2)1294 3978 y Fs(=c)p Ft(\))e(since)h(otherwise)h Fs(E)2234 3942 y Fp(2)2228 4003 y Fo(f)2302 3978 y Fq(\000)28 b Fs(p)2456 3942 y Fp(2)2456 4003 y Fo(f)2502 3978 y Fs(c)2544 3942 y Fp(2)2626 3978 y Ft(=)43 b(0,)h(whic)m(h)e(is)f(imp)s(ossible) 411 4099 y(\(since)32 b(it)e(implies)f(that)i(this)g(frame)g(is)g (going)f(the)h(sp)s(eed)i(of)e(ligh)m(t!\).)41 b(Therefore,)33 b(using)411 4219 y(conserv)-5 b(ation)33 b(of)f(energy)i(and)e(linear)f (momen)m(tum:)1098 4478 y Fs(E)1170 4493 y Fo(f)1276 4478 y Ft(=)60 b Fs(E)1484 4493 y Fo(i)1823 4478 y Ft(=)-16 b Fq(\))310 b Fs(E)2365 4493 y Fp(1)2427 4478 y Ft(+)22 b Fs(E)2597 4493 y Fp(2)2664 4478 y Ft(=)2778 4411 y(8)p 2778 4455 V 2778 4546 a(3)2836 4478 y Fs(M)2930 4493 y Fo(p)2970 4478 y Fs(c)3012 4437 y Fp(2)1061 4711 y Fs(p)1110 4726 y Fo(f)1155 4711 y Fs(c)61 b Ft(=)f Fs(p)1443 4726 y Fo(i)1471 4711 y Fs(c)310 b Ft(=)-16 b Fq(\))310 b Fs(E)2365 4726 y Fp(1)2427 4711 y Fq(\000)22 b Fs(E)2598 4726 y Fp(2)2666 4711 y Ft(=)2779 4644 y(4)p 2779 4688 V 2779 4779 a(3)2838 4711 y Fs(M)2932 4726 y Fo(p)2972 4711 y Fs(c)3014 4670 y Fp(2)411 4966 y Ft(Solving)34 b(giv)m(es)h Fs(E)1071 4981 y Fp(1)1143 4966 y Ft(=)d(2)p Fs(M)1394 4981 y Fo(p)1434 4966 y Fs(c)1476 4930 y Fp(2)1550 4966 y Ft(and)j Fs(E)1814 4981 y Fp(2)1886 4966 y Ft(=)c(\(2)p Fs(=)p Ft(3\))p Fs(M)2310 4981 y Fo(p)2349 4966 y Fs(c)2391 4930 y Fp(2)2466 4966 y Ft(with)k(photon)g(#1)g(going)e(in)h(the)411 5087 y(same)27 b(direction)f(as)g(the)i(original)23 b(an)m(tiproton)j (and)g(photon)h(#2)g(tra)m(v)m(elling)e(against)g(the)411 5207 y(direction)32 b(of)g(the)h(original)c(an)m(tiproton.)233 5369 y(\(b\))48 b(As)35 b(measured)g(in)f(a)g(rest)h(frame)f(of)g(the)h (an)m(tiproton,)f(what)h(energy)g(do)s(es)g(eac)m(h)g(of)f(the)411 5489 y(photons)f(ha)m(v)m(e?)313 5651 y Fq(\017)48 b Ft(The)38 b(an)m(tiproton)e(is)h(mo)m(ving)f(in)g(the)h(lab)f(in)g(the) i(+)p Fs(x)f Ft(direction)f(with)g(kinetic)h(energy)411 5772 y Fs(K)500 5787 y Fp(\026)-41 b Fo(p)562 5772 y Ft(=)27 b(\(2)p Fs(=)p Ft(3\))p Fs(M)982 5787 y Fo(p)1022 5772 y Fs(c)1064 5735 y Fp(2)1135 5772 y Ft(so)1661 5943
y Fs(\015)33 b Ft(=)28 b(1)22 b(+)2074 5876 y Fs(K)2163 5891 y Fp(\026)-41 b Fo(p)p 2028 5920 216 4 v 2028 6012 a Fs(M)2122 6027 y Fo(p)2162 6012 y Fs(c)2204 5983 y Fp(2)2281 5943 y Ft(=)2394 5876 y(5)p 2394 5920 49 4 v 2394 6012 a(3)p eop %%Page: 7 7 7 6 bop 411 331 a Ft(and)36 b(hence)g Fs(u)939 346 y Fp(\026)-41 b Fo(p)1004 331 y Ft(=)32 b(\(4)p Fs(=)p Ft(5\))p Fs(c)p Ft(.)50 b(So)34 b(if)g(w)m(e)i(call)e(the)h(lab)f(the)h Fs(S)41 b Ft(frame)34 b(and)h(the)h(an)m(tiproton)411 451 y(rest)i(frame)f(the)g Fs(S)1123 415 y Fr(0)1183 451 y Ft(frame,)h(then)g Fs(v)h Ft(=)c Fs(u)1976 466 y Fp(\026)-41 b Fo(p)2045 451 y Ft(=)35 b(\(4)p Fs(=)p Ft(5\))p Fs(c)i Ft(and)g Fs(\015)j Ft(=)c(\(5)p Fs(=)p Ft(3\).)56 b(The)38 b(photons)411 572 y(tra)m(v)m(el)29 b(along)f(the)h(common)e Fs(x)14 b Fq(\000)g Fs(x)1703 536 y Fr(0)1758 572 y Ft(axis)28 b(so)h Fs(p)2117 587 y Fo(x)2189 572 y Ft(=)f Fs(p)f Ft(=)h Fs(E)6 b(=c)p Ft(.)42 b(F)-8 b(or)28 b(the)h(t)m(w)m(o)h(photons)f(w)m(e)411 692 y(ha)m(v)m(e)i(that)e Fs(E)913 707 y Fp(1)982 692 y Ft(=)g(2)g Fs(M)1259 707 y Fo(p)1299 692 y Fs(c)1341 656 y Fp(2)1380 692 y Ft(,)h Fs(p)1486 707 y Fp(1)1555 692 y Ft(=)f Fs(E)1732 707 y Fp(1)1772 692 y Fs(=c)p Ft(,)g Fs(E)1991 707 y Fp(2)2060 692 y Ft(=)g(\(2/3\))p Fs(M)2482 707 y Fo(p)2521 692 y Fs(c)2563 656 y Fp(2)2603 692 y Ft(,)h(and)f Fs(p)2895 707 y Fp(2)2964 692 y Ft(=)g(-)p Fs(E)3174 707 y Fp(2)3213 692 y Fs(=c)p Ft(.)42 b(No)m(w)30 b(w)m(e)411 812 y(can)h(use)h(the)f(Loren)m(tz)h(transformation)c (equation)j(to)f(get)h(the)g(photon)g(energies)g(in)f Fs(S)3653 776 y Fr(0)3676 812 y Ft(.)801 1015 y Fs(E)879 973 y Fr(0)986 1015 y Ft(=)83 b Fs(\015)5 b Ft(\()p Fs(E)28 b Fq(\000)22 b Fs(v)t(p)1538 1030 y Fo(x)1582 1015 y Ft(\))791 1208 y Fs(E)869 1167 y Fr(0)863 1233 y Fp(1)986 1208 y Ft(=)83 b Fs(\015)5 b Ft(\()p Fs(E)1311 1223 y Fp(1)1372 1208 y Fq(\000)23 b Fs(v)t(p)1572 1223 y Fp(1)1611 1208 y Ft(\))60 b(=)g Fs(\015)1918 1087 y Fn(\024)1962 1208 y Fs(E)2034 1223 y Fp(1)2095 1208 y Fq(\000)23 b Fs(v)2262 1087 y Fn(\022)2333 1141 y Fs(E)2405 1156 y Fp(1)p 2333 1185 112 4 v 2368 1277 a Fs(c)2455 1087 y Fn(\023\025)2637 1208 y Ft(=)60 b Fs(\015)5 b(E)2901 1223 y Fp(1)2941 1208 y Ft(\(1)21 b Fq(\000)i Fs(\014)6 b Ft(\))986 1448 y(=)1154 1380 y(5)p 1154 1424 49 4 v 1154 1516 a(3)1213 1448 y(\(2)p Fs(M)1394 1463 y Fo(p)1434 1448 y Fs(c)1476 1407 y Fp(2)1515 1448 y Ft(\))1570 1327 y Fn(\022)1631 1448 y Ft(1)22 b Fq(\000)1812 1380 y Ft(4)p 1812 1424 V 1812 1516 a(5)1870 1327 y Fn(\023)986 1687 y Ft(=)1154 1620 y(2)p 1154 1664 V 1154 1756 a(3)1213 1687 y Fs(M)1307 1702 y Fo(p)1347 1687 y Fs(c)1389 1646 y Fp(2)791 1924 y Fs(E)869 1883 y Fr(0)863 1949 y Fp(2)986 1924 y Ft(=)83 b Fs(\015)5 b Ft(\()p Fs(E)1311 1939 y Fp(2)1372 1924 y Fq(\000)23 b Fs(v)t(p)1572 1939 y Fp(2)1611 1924 y Ft(\))60 b(=)g Fs(\015)1918 1803 y Fn(\024)1962 1924 y Fs(E)2034 1939 y Fp(2)2095 1924 y Fq(\000)23 b Fs(v)2262 1803 y Fn(\022)2324 1924 y Fq(\000)2411 1857 y Fs(E)2483 1872 y Fp(2)p 2411 1901 112 4 v 2446 1993 a Fs(c)2533 1803 y Fn(\023\025)2714 1924 y Ft(=)60 b Fs(\015)5 b(E)2978 1939 y Fp(2)3018 1924 y Ft(\(1)22 b(+)g Fs(\014)6 b Ft(\))986 2164 y(=)1154 2096 y(2)p 1154 2141 49 4 v 1154 2232 a(3)1213 2164 y(\(2)p Fs(M)1394
2179 y Fo(p)1434 2164 y Fs(c)1476 2123 y Fp(2)1515 2164 y Ft(\))1570 2043 y Fn(\022)1631 2164 y Ft(1)22 b(+)1810 2096 y(4)p 1810 2141 V 1810 2232 a(5)1869 2043 y Fn(\023)986 2356 y Ft(=)83 b(2)p Fs(M)1288 2371 y Fo(p)1327 2356 y Fs(c)1369 2315 y Fp(2)72 2576 y Ft(8.)49 b(A)29 b(particle)f(whic)m (h)i(is)f(a)h(b)s(ound)f(state)h(of)f(a)g(quark)h(and)g(an)f(an)m (tiquark)h(is)f(called)f(a)h(meson.)43 b(A)197 2696 y(meson)37 b(has)g(a)f(particular)f(mass)i(v)-5 b(alue)36 b(whic)m(h)h(is)f (ultimately)e(dep)s(enden)m(t)39 b(on)d(the)h(t)m(yp)s(es)h(of)197 2817 y(constituen)m(t)31 b(quarks)h(and)e(the)h(strength)g(of)f(the)h (in)m(teraction)e(b)s(et)m(w)m(een)j(them)f(\(the)f(so-called)197 2937 y(colour)g(force\).)43 b(An)31 b(analogous)e(system)j(is)e(the)h (h)m(ydrogen)h(atom)e(whic)m(h)h(is)f(the)h(b)s(ound)g(state)197 3058 y(of)c(a)h(proton)f(and)h(an)g(electron.)42 b(The)29 b(h)m(ydrogen)g(atom)d(has)j(a)e(particular)f(mass)i(whic)m(h)h(is)e (not)197 3178 y(just)35 b(the)f(sum)h(of)f(the)h(proton)f(and)g (electron)h(masses.)50 b(A)34 b Fs(D)2487 3142 y Fp(0)2561 3178 y Ft(meson)g(\(whic)m(h)h(consists)g(of)f(a)197 3298 y Fb(charm)c Ft(quark)j(and)e(an)h Fb(up)f Ft(an)m(tiquark\))h(is) e(tra)m(v)m(elling)g(through)i(the)f(lab)s(oratory)f(and)i(breaks)197 3419 y(up)40 b(in)m(to)f(\(i.e.,)i(deca)m(ys)h(in)m(to\))d(a)g Fs(K)1519 3382 y Fr(\000)1618 3419 y Ft(meson)h(and)g(a)g Fs(K)2300 3382 y Fp(+)2399 3419 y Ft(meson.)65 b(The)41 b Fs(K)3055 3382 y Fp(+)3154 3419 y Ft(meson)e(is)h(left)197 3539 y(at)e(rest)h(in)f(the)h(lab)s(oratory)e(frame.)60 b(The)40 b(rest)f(mass)f(of)g(the)h Fs(D)2647 3503 y Fp(0)2725 3539 y Ft(meson)f(is)g(1864)g(MeV/)p Fs(c)3663 3503 y Fp(2)197 3659 y Ft(while)29 b(the)h Fs(K)704 3623 y Fr(\000)793 3659 y Ft(and)g Fs(K)1070 3623 y Fp(+)1159 3659 y Ft(mesons)g(ha)m(v)m(e)h(the)f(same)g(rest)g(mass)g(v)-5 b(alue)29 b(of)g(493.7)g(MeV/)p Fs(c)3451 3623 y Fp(2)3491 3659 y Ft(.)43 b(F)-8 b(or)197 3780 y(comparison,)31 b(the)i(proton)g(rest)g(mass)f(is)g(938.272)g(MeV/)p Fs(c)2398 3744 y Fp(2)2438 3780 y Ft(.)238 3978 y(\(a\))48 b(What)33 b(are)g(the)g(rest)g(masses)g(of)f(the)h Fs(D)1890 3942 y Fp(0)1962 3978 y Ft(and)g Fs(K)2242 3942 y Fr(\000)2333 3978 y Ft(mesons)g(in)f(kilograms?)313 4135 y Fq(\017)48 b Ft(\(2)31 b(marks\))g(The)i(con)m(v)m(ersion)f(factor)f(\(giv)m(en)g (in)g(the)h(App)s(endix)f(in)g(the)h(text)f({)g(pg)h(334\))411 4255 y(is)d(1)g(kg)h(=)f(5)p Fs(:)p Ft(6)15 b Fq(\002)g Ft(10)1149 4219 y Fp(29)1253 4255 y Ft(MeV/)p Fs(c)1549 4219 y Fp(2)1589 4255 y Ft(.)42 b(So,)30 b Fs(m)1903 4270 y Fo(D)1995 4255 y Ft(=)e(1864)p Fs(=)p Ft(5)p Fs(:)p Ft(6)15 b Fq(\002)g Ft(10)2674 4219 y Fp(29)2775 4255 y Ft(=)28 b(3)p Fs(:)p Ft(33)15 b Fq(\002)g Ft(10)3258 4219 y Fr(\000)p Fp(27)3416 4255 y Ft(kg)30 b(and)411 4376 y Fs(m)496 4391 y Fo(K)593 4376 y Ft(=)d(493)p Fs(:)p Ft(7)p Fs(=)p Ft(5)p Fs(:)p Ft(6)21 b Fq(\002)i Ft(10)1312 4339 y Fp(29)1414 4376 y Ft(=)k(8)p Fs(:)p Ft(82)22 b Fq(\002)g Ft(10)1910 4339 y Fr(\000)p Fp(28)2072 4376 y Ft(kg.)233 4532 y(\(b\))48 b(What)33 b(is)f(the)h(kinetic)f(energy)i (of)e(the)h Fs(K)1949 4496 y Fr(\000)2041 4532 y Ft(meson?)313 4689 y Fq(\017)48 b Ft(\(6)23 b(marks\))h(The)g(initial)19 b(state)24 b(consists)g(of)f(a)g Fs(D)2142 4653 y Fp(0)2205 4689 y Ft(with)g(momen)m(tum)f Fs(~)-49 b(p)2970 4704 y Fo(D)3057 4689 y Ft(and)23 b(energy)i Fs(E)3612 4704 y Fo(D)3676 4689 y Ft(.)411 4810 y(The)f(\014nal)d(state)i(consists)g (of)f(t)m(w)m(o)h Fs(K)29 b Ft(mesons.)41 b(The)23 b Fs(K)2425 4773 y Fp(+)2507 4810 y Ft(is)f(at)g(rest)h(\(i.e.,)h(its)d
(momen)m(tum)411 4930 y(is)36 b(0\).)55 b(If)36 b(w)m(e)i(denote)f(the) g Fs(K)43 b Ft(rest)37 b(mass)g(b)m(y)g Fs(m)2209 4945 y Fo(K)2314 4930 y Ft(then)g(the)g Fs(K)2802 4894 y Fp(+)2897 4930 y Ft(total)e(energy)j(in)d(the)411 5050 y(lab)i(frame)f(is)h(just) h(its)f(rest)h(energy)g(giv)m(en)g(b)m(y)g Fs(m)2295 5065 y Fo(K)2364 5050 y Fs(c)2406 5014 y Fp(2)2445 5050 y Ft(.)58 b(Denote)38 b(the)g Fs(K)3133 5014 y Fr(\000)3229 5050 y Ft(energy)h(and)411 5171 y(momen)m(tum)c(b)m(y)j Fs(E)1139 5186 y Fo(K)1244 5171 y Ft(and)f Fs(~)-50 b(p)1486 5186 y Fo(K)1591 5171 y Ft(and)36 b(recall)f(that)h(the)h(t)m(w)m(o)g Fs(K)44 b Ft(mesons)37 b(ha)m(v)m(e)g(the)g(same)411 5291 y(mass,)h(they)g(are)e(just)i(opp)s(ositely)d(c)m(harged.)57 b(In)37 b(other)g(w)m(ords,)i Fs(m)2934 5308 y Fo(K)2999 5289 y Fa(\000)3089 5291 y Ft(=)c Fs(m)3285 5308 y Fo(K)3350 5289 y Fl(+)3439 5291 y Ft(=)f Fs(m)3634 5306 y Fo(K)411 5411 y Ft(and)f(w)m(e)h(ha)m(v)m(e)g(for)e(the)h Fs(D)1371 5375 y Fp(0)1442 5411 y Ft(and)g Fs(K)1722 5375 y Fr(\000)1814 5411 y Ft(mesons:)1592 5614 y Fs(m)1677 5572 y Fp(2)1677 5638 y Fo(D)1742 5614 y Fs(c)1784 5572 y Fp(4)1906 5614 y Ft(=)83 b Fs(E)2143 5572 y Fp(2)2137 5638 y Fo(D)2224 5614 y Fq(\000)22 b Fs(p)2372 5572 y Fp(2)2372 5638 y Fo(D)2436 5614 y Fs(c)2478 5572 y Fp(2)3578 5614 y Ft(\(6\))1588 5759 y Fs(m)1673 5718 y Fp(2)1673 5783 y Fo(K)1742 5759 y Fs(c)1784 5718 y Fp(4)1906 5759 y Ft(=)83 b Fs(E)2143 5718 y Fp(2)2137 5783 y Fo(K)2228 5759 y Fq(\000)22 b Fs(p)2376 5718 y Fp(2)2376 5783 y Fo(K)2445 5759 y Fs(c)2487 5718 y Fp(2)3578 5759 y Ft(\(7\))411 5961 y(\(These)j(expressions)g (are,)g(of)e(course,)j(v)-5 b(alid)21 b(for)h(an)m(y)i(particle\).)39 b(No)m(w,)26 b(the)d(quan)m(titativ)m(e)411 6081 y(expression)32 b(for)d(the)h(conserv)-5 b(ation)30 b(of)f(energy)i(and)f(momen)m(tum)f (is)g(that)h Fs(E)3239 6096 y Fo(i)3295 6081 y Ft(=)d Fs(E)3470 6096 y Fo(f)3546 6081 y Ft(and)p eop %%Page: 8 8 8 7 bop 412 331 a Fs(~)-50 b(p)460 346 y Fo(i)523 331 y Ft(=)34 b Fs(~)-49 b(p)682 346 y Fo(f)763 331 y Ft(where)38 b Fs(i)f Ft(and)f Fs(f)47 b Ft(refer)37 b(to)f(the)h(initial)32 b(and)37 b(\014nal)e(states)i Fb(of)i(the)f(system)p Ft(.)55 b(F)-8 b(or)411 451 y(this)33 b(particular)d(question)j(this)g (b)s(ecomes:)1380 671 y Fs(E)1452 686 y Fo(i)1508 671 y Ft(=)28 b Fs(E)1684 686 y Fo(D)1831 671 y Ft(=)83 b Fs(E)2062 686 y Fo(f)2135 671 y Ft(=)28 b Fs(m)2324 686 y Fo(K)2392 671 y Fs(c)2434 630 y Fp(2)2496 671 y Ft(+)22 b Fs(E)2666 686 y Fo(K)1427 817 y Fs(~)-49 b(p)1476 832 y Fo(i)1531 817 y Ft(=)28 b Fs(~)-49 b(p)1684 832 y Fo(D)1831 817 y Ft(=)83 b Fs(~)-49 b(p)2039 832 y Fo(f)2112 817 y Ft(=)28 b Fs(~)-50 b(p)2264 832 y Fo(K)411 1037 y Ft(Substituting)32 b(these)i(expressions)g(in)m(to)e(equation)g(\(6\))h(giv)m(es:)1140 1257 y Fs(m)1225 1216 y Fp(2)1225 1281 y Fo(D)1290 1257 y Fs(c)1332 1216 y Fp(4)1454 1257 y Ft(=)83 b Fs(E)1691 1216 y Fp(2)1685 1281 y Fo(D)1771 1257 y Fq(\000)23 b Fs(p)1920 1216 y Fp(2)1920 1281 y Fo(D)1984 1257 y Fs(c)2026 1216 y Fp(2)1454 1402 y Ft(=)83 b(\()p Fs(m)1736 1417 y Fo(K)1805 1402 y Fs(c)1847 1361 y Fp(2)1908 1402 y Ft(+)22 b Fs(E)2078 1417 y Fo(K)2147 1402 y Ft(\))2185 1361 y Fp(2)2246 1402 y Fq(\000)h Fs(p)2395 1361 y Fp(2)2395 1427 y Fo(K)2463 1402 y Fs(c)2505 1361 y Fp(2)1454 1547 y Ft(=)83 b Fs(m)1698 1506 y Fp(2)1698 1572 y Fo(K)1767 1547 y Fs(c)1809 1506 y Fp(4)1870 1547 y Ft(+)22 b(2)p Fs(m)2102 1562 y Fo(K)2171 1547 y Fs(c)2213 1506 y Fp(2)2252
1547 y Fs(E)2324 1562 y Fo(K)2415 1547 y Ft(+)g Fs(E)2591 1506 y Fp(2)2585 1572 y Fo(K)2676 1547 y Fq(\000)g Fs(p)2824 1506 y Fp(2)2824 1572 y Fo(K)2893 1547 y Fs(c)2935 1506 y Fp(2)411 1767 y Ft(and)33 b(using)f(\(7\))h(w)m(e)g(ha)m(v)m(e)1462 1987 y Fs(m)1547 1946 y Fp(2)1547 2012 y Fo(D)1611 1987 y Fs(c)1653 1946 y Fp(4)1720 1987 y Ft(=)28 b(2)p Fs(m)1958 1946 y Fp(2)1958 2012 y Fo(K)2026 1987 y Fs(c)2068 1946 y Fp(4)2130 1987 y Ft(+)22 b(2)p Fs(m)2362 2002 y Fo(K)2430 1987 y Fs(c)2472 1946 y Fp(2)2512 1987 y Fs(E)2584 2002 y Fo(K)411 2207 y Ft(Th)m(us)35 b(w)m(e)e(ha)m(v)m(e)1541 2462 y Fs(E)1613 2477 y Fo(K)1764 2462 y Ft(=)1933 2394 y(\()p Fs(m)2056 2358 y Fp(2)2056 2419 y Fo(D)2142 2394 y Fq(\000)23 b Ft(2)p Fs(m)2376 2358 y Fp(2)2376 2419 y Fo(K)2444 2394 y Ft(\))p Fs(c)2524 2358 y Fp(2)p 1933 2438 631 4 v 2147 2530 a Ft(2)p Fs(m)2281 2545 y Fo(K)411 2722 y Ft(Recall)42 b(that)i(the)g(kinetic)f(energy)h Fs(K)51 b Ft(is)43 b(related)g(to)g(the)h(total)e(energy)j Fs(E)k Ft(b)m(y)c Fs(K)53 b Ft(=)411 2842 y Fs(E)19 b Fq(\000)13 b Fs(m)677 2857 y Fp(0)717 2842 y Fs(c)759 2806 y Fp(2)799 2842 y Ft(.)42 b(So,)29 b Fs(K)1110 2857 y Fo(K)1206 2842 y Ft(=)e Fs(E)1381 2857 y Fo(K)1463 2842 y Fq(\000)13 b Fs(m)1638 2857 y Fo(K)1707 2842 y Fs(c)1749 2806 y Fp(2)1816 2842 y Ft(and)28 b(plugging)e(in)h(the)i(v) -5 b(arious)27 b(rest)i(masses)f(giv)m(es)411 2963 y Fs(K)494 2978 y Fo(K)590 2963 y Ft(=)g(2)p Fs(:)p Ft(531)k(GeV.)243 3125 y(\(c\))49 b(What)33 b(w)m(as)h(the)f(total)e(energy)i(of)f(the)h Fs(D)1948 3088 y Fp(0)2020 3125 y Ft(meson?)313 3286 y Fq(\017)48 b Ft(\(6)39 b(marks\))g(Conserv)-5 b(ation)39 b(of)f(energy)i(ga)m(v)m(e)g(us)f(the)g(expression)i Fs(E)2982 3301 y Fo(D)3084 3286 y Ft(=)e Fs(m)3284 3301 y Fo(K)3352 3286 y Fs(c)3394 3250 y Fp(2)3460 3286 y Ft(+)26 b Fs(E)3634 3301 y Fo(K)411 3407 y Ft(and)33 b(w)m(e)h(just)f(solv)m(ed)g(for)f Fs(E)1452 3422 y Fo(K)1520 3407 y Ft(.)44 b(So,)1365 3627 y Fs(E)1437 3642 y Fo(D)1584 3627 y Ft(=)83 b Fs(m)1828 3642 y Fo(K)1897 3627 y Fs(c)1939 3586 y Fp(2)2000 3627 y Ft(+)22 b Fs(E)2170 3642 y Fo(K)1584 3821 y Ft(=)83 b Fs(m)1828 3836 y Fo(K)1897 3821 y Fs(c)1939 3780 y Fp(2)2000 3821 y Ft(+)2108 3754 y(\()p Fs(m)2231 3718 y Fp(2)2231 3779 y Fo(D)2318 3754 y Fq(\000)22 b Ft(2)p Fs(m)2551 3718 y Fp(2)2551 3779 y Fo(K)2620 3754 y Ft(\))p Fs(c)2700 3718 y Fp(2)p 2108 3798 V 2323 3890 a Ft(2)p Fs(m)2457 3905 y Fo(K)1584 4084 y Ft(=)83 b Fs(m)1828 4099 y Fo(K)1897 4084 y Fs(c)1939 4043 y Fp(2)2000 4084 y Ft(+)2108 4017 y Fs(m)2193 3981 y Fp(2)2193 4041 y Fo(D)2258 4017 y Fs(c)2300 3981 y Fp(2)p 2108 4061 231 4 v 2123 4153 a Ft(2)p Fs(m)2257 4168 y Fo(K)2371 4084 y Fq(\000)23 b Fs(m)2556 4099 y Fo(K)2625 4084 y Fs(c)2667 4043 y Fp(2)1584 4347 y Ft(=)1753 4280 y Fs(m)1838 4244 y Fp(2)1838 4304 y Fo(D)1903 4280 y Fs(c)1945 4244 y Fp(2)p 1753 4324 V 1767 4415 a Ft(2)p Fs(m)1901 4430 y Fo(K)411 4607 y Ft(Plugging)31 b(in)h(the)h(rest)g(masses)h(giv)m(es) f Fs(E)1924 4622 y Fo(D)2016 4607 y Ft(=)27 b(3)p Fs(:)p Ft(519)32 b(GeV.)233 4769 y(\(d\))48 b(What)d(w)m(ould)f(b)s(e)g(the)h (magnitude)e(of)g(the)i(momen)m(tum)d(of)i(the)h Fs(K)3029 4733 y Fp(+)3132 4769 y Ft(meson)f(in)f(the)411 4890 y(frame)h(where)h(the)f Fs(D)1253 4854 y Fp(0)1336 4890 y Ft(meson)g(w)m(ould)g(ha)m(v)m(e)i(b)s(een)e(at)g(rest?)78 b(\(Hin)m(t:)66 b(T)-8 b(ak)m(e)45 b(the)g Fs(D)3664 4854 y Fp(0)411 5010 y Ft(meson)33 b(\015igh)m(t)f(direction)f(to)i(b)s
(e)f(along)g(the)h Fs(x)g Ft(axis.\))313 5172 y Fq(\017)48 b Ft(\(6)24 b(marks\))h Fc(\(Note:)44 b(In)28 b(this)f(part)h(of)h(the) f(question,)h(only)f(the)g Fs(K)3062 5136 y Fp(+)3149 5172 y Fc(and)h(not)f(the)411 5292 y Fs(K)501 5256 y Fr(\000)590 5292 y Fc(is)i(referred)g(to)f(so,)j(as)f(opp)s(osed)g(to)e (the)h(previous)g(part)g(of)g(the)g(question,)411 5413 y(the)43 b(subscript)f Fs(K)50 b Fc(will)41 b(no)m(w)h(refer)h(to)g (the)f Fs(K)2391 5377 y Fp(+)2451 5413 y Fc(\))p Ft(.)57 b(In)37 b(the)h(lab)e(frame)h(\(call)e(this)411 5533 y(the)29 b Fs(S)k Ft(frame\),)28 b(the)h Fs(K)1257 5497 y Fp(+)1344 5533 y Ft(is)e(at)h(rest)h(\(so)f Fs(~)-49 b(p)1940 5550 y Fo(K)2005 5531 y Fl(+)2086 5533 y Fq(\021)29 b Fs(~)-50 b(p)2240 5548 y Fo(K)2336 5533 y Ft(=)28 b(0\))g(and)g(the)g Fs(D)2987 5497 y Fp(0)3054 5533 y Ft(has)g(momen)m(tum)412 5654 y Fs(~)-50 b(p)460 5669 y Fo(D)558 5654 y Ft(whic)m(h)34 b(w)m(e)g(will)d(tak)m(e)k(to)e(b)s(e)h(along)e(the)i Fs(x)f Ft(axis.)46 b(That)34 b(is,)f(the)h(co)s(ordinate)f(system)411 5774 y(is)e(de\014ned)h(suc)m(h)h(that)e Fs(~)-49 b(p)1320 5789 y Fo(D)1411 5774 y Ft(=)28 b(\()p Fs(p)1602 5789 y Fo(D)1666 5774 y Fs(;)17 b Ft(0)p Fs(;)g Ft(0\).)41 b(Call)30 b(the)h(frame)f(where)j(the)e Fs(D)3132 5738 y Fp(0)3202 5774 y Ft(w)m(ould)g(b)s(e)g(at)411 5894 y(rest)e(the)f Fs(S)826 5858 y Fr(0)876 5894 y Ft(frame.)41 b(W)-8 b(e)28 b(get)g(the)g(energy)h(and)e(momen)m(tum)g(comp)s(onen)m (ts)h(of)f(a)g(particle)p eop %%Page: 9 9 9 8 bop 411 331 a Ft(or)40 b(system)i(in)d(di\013eren)m(t)i(frames)f(b) m(y)h(using)f(the)h(Loren)m(tz)g(transformations.)65 b(Recall,)411 451 y(the)33 b(Loren)m(tz)h(transformations)d(are:)1631 671 y Fs(p)1680 630 y Fr(0)1680 696 y Fo(x)1807 671 y Ft(=)83 b Fs(\015)5 b Ft(\()p Fs(p)2109 686 y Fo(x)2175 671 y Fq(\000)2300 604 y Fs(v)p 2284 648 82 4 v 2284 740 a(c)2326 711 y Fp(2)2376 671 y Fs(E)h Ft(\))1634 851 y Fs(p)1683 810 y Fr(0)1683 876 y Fo(y)1807 851 y Ft(=)83 b Fs(p)2015 866 y Fo(y)1635 996 y Fs(p)1684 955 y Fr(0)1684 1021 y Fo(z)1807 996 y Ft(=)g Fs(p)2015 1011 y Fo(z)1623 1142 y Fs(E)1701 1100 y Fr(0)1807 1142 y Ft(=)g Fs(\015)5 b Ft(\()p Fs(E)28 b Fq(\000)23 b Fs(v)t(p)2360 1157 y Fo(x)2403 1142 y Ft(\))411 1362 y(Since)33 b(in)e(the)i Fs(S)38 b Ft(frame)32 b Fs(~)-50 b(p)1367 1377 y Fo(K)1463 1362 y Ft(=)28 b(0,)k(then)h(\()p Fs(p)1984 1325 y Fr(0)1984 1386 y Fo(K)2052 1362 y Ft(\))2090 1377 y Fo(y)2159 1362 y Ft(=)28 b(\()p Fs(p)2350 1377 y Fo(K)2418 1362 y Ft(\))2456 1377 y Fo(y)2525 1362 y Ft(=)f(0,)32 b(\()p Fs(p)2823 1325 y Fr(0)2823 1386 y Fo(K)2892 1362 y Ft(\))2930 1377 y Fo(z)2997 1362 y Ft(=)c(\()p Fs(p)3188 1377 y Fo(K)3256 1362 y Ft(\))3294 1377 y Fo(z)3361 1362 y Ft(=)g(0)k(and)1516 1608 y Fq(j)p Ft(\()p Fs(p)1631 1566 y Fr(0)1631 1632 y Fo(K)1699 1608 y Ft(\))1737 1623 y Fo(x)1781 1608 y Fq(j)27 b(\021)h Fs(p)1990 1566 y Fr(0)1990 1632 y Fo(K)2142 1608 y Ft(=)82 b Fs(\015)2382 1540 y(v)p 2366 1584 V 2366 1676 a(c)2408 1647 y Fp(2)2458 1608 y Fs(E)2530 1623 y Fo(K)2142 1753 y Ft(=)g Fs(\015)5 b(v)t(m)2492 1768 y Fo(K)411 1973 y Ft(\(since)41 b Fs(p)745 1988 y Fo(K)853 1973 y Ft(=)f(0)f(and)h(so)g Fs(E)1453 1988 y Fo(K)1562 1973 y Ft(=)g Fs(m)1763 1988 y Fo(K)1832 1973 y Fs(c)1874 1937 y Fp(2)1913 1973 y Ft(\).)65 b(The)41 b(relativ)m(e)e(sp)s(eed)i(b)s(et)m(w)m(een)h(the)e Fs(S)46 b Ft(and)411 2093 y Fs(S)477 2057 y Fr(0)545 2093 y Ft(frames)e(is,)k
(b)m(y)d(de\014nition,)i(the)e(sp)s(eed)h(of)e(the)i Fs(D)2482 2057 y Fp(0)2565 2093 y Ft(in)e(the)h Fs(S)51 b Ft(frame)44 b(and)g(since,)411 2214 y(again)36 b(b)m(y)i (de\014nition,)g Fs(p)1332 2229 y Fo(D)1431 2214 y Ft(=)e Fs(\015)5 b(m)1684 2229 y Fo(D)1748 2214 y Fs(v)t Ft(,)38 b(therefore)g Fs(\015)5 b(v)39 b Ft(=)c Fs(p)2580 2229 y Fo(D)2644 2214 y Fs(=m)2778 2229 y Fo(D)2843 2214 y Ft(.)57 b(So)37 b Fs(p)3116 2178 y Fr(0)3116 2238 y Fo(K)3220 2214 y Ft(=)e Fs(\015)5 b(v)t(m)3523 2229 y Fo(K)3627 2214 y Ft(=)411 2334 y Fs(p)460 2349 y Fo(D)524 2334 y Ft(\()p Fs(m)647 2349 y Fo(K)716 2334 y Fs(=m)850 2349 y Fo(D)914 2334 y Ft(\).)72 b(Substituting)41 b(in)g(the)i(result)f (from)f(the)h(part)g(\(c\))g(of)g(this)f(question,)411 2454 y(namely)32 b Fs(E)822 2469 y Fo(D)914 2454 y Ft(=)c Fs(m)1103 2418 y Fp(2)1103 2479 y Fo(D)1167 2454 y Fs(c)1209 2418 y Fp(2)1248 2454 y Fs(=)p Ft(2)p Fs(m)1431 2469 y Fo(K)1532 2454 y Ft(yields:)1419 2698 y Fs(p)1468 2656 y Fr(0)1468 2722 y Fo(K)1619 2698 y Ft(=)83 b Fs(p)1827 2713 y Fo(D)1901 2630 y Fs(m)1986 2645 y Fo(K)p 1901 2674 154 4 v 1903 2766 a Fs(m)1988 2781 y Fo(D)1619 2989 y Ft(=)1788 2921 y Fs(m)1873 2936 y Fo(K)p 1788 2965 V 1790 3057 a Fs(m)1875 3072 y Fo(D)1952 2821 y Fn(s)p 2035 2821 509 4 v 2045 2921 a Fs(E)2123 2887 y Fp(2)2117 2946 y Fo(D)p 2045 2965 137 4 v 2072 3057 a Fs(c)2114 3028 y Fp(2)2213 2989 y Fq(\000)23 b Fs(m)2398 2954 y Fp(2)2398 3013 y Fo(D)2462 2989 y Fs(c)2504 2960 y Fp(2)1619 3293 y Ft(=)1788 3225 y Fs(m)1873 3240 y Fo(K)p 1788 3269 154 4 v 1790 3361 a Fs(m)1875 3376 y Fo(D)1952 3112 y Fn(v)1952 3158 y(u)1952 3208 y(u)1952 3258 y(t)p 2039 3112 657 4 v 2076 3225 a Fs(m)2161 3191 y Fp(4)2161 3249 y Fo(D)2225 3225 y Fs(c)2267 3196 y Fp(4)p 2049 3269 284 4 v 2049 3361 a Ft(4)p Fs(m)2183 3327 y Fp(2)2183 3385 y Fo(K)2252 3361 y Fs(c)2294 3332 y Fp(2)2365 3293 y Fq(\000)g Fs(m)2550 3258 y Fp(2)2550 3317 y Fo(D)2614 3293 y Fs(c)2656 3264 y Fp(2)1619 3572 y Ft(=)1788 3505 y(1)p 1788 3549 49 4 v 1788 3641 a(2)1847 3572 y Fs(c)1889 3466 y Fn(q)p 1972 3466 474 4 v 106 x Fs(m)2057 3538 y Fp(2)2057 3597 y Fo(D)2143 3572 y Fq(\000)g Ft(4)p Fs(m)2377 3538 y Fp(2)2377 3597 y Fo(K)411 3825 y Ft(So,)29 b(again,)f(plugging)e(in)h(the)h(rest)h(masses)g(w)m(e)g(\014nd)f(that) g(the)g(the)h(momen)m(tum)d(the)j Fs(K)3644 3789 y Fp(+)411 3945 y Ft(w)m(ould)k(ha)m(v)m(e)h(in)e(the)h(rest)g(frame)f(of)g(the)h Fs(D)2030 3909 y Fp(0)2101 3945 y Ft(as)g Fs(p)2270 3909 y Fr(0)2270 3970 y Fo(K)2366 3945 y Ft(=)28 b(1)p Fs(:)p Ft(58)k(GeV/)p Fs(c)p Ft(.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF