FDOFXOR 440P Krmd gh Sureohpdv Ghulydgdv Sdufldohv 572362<< 4 Grplqlrv/ Fxuydv | Vxshuflhv gh Qlyho 41 Lqglfdu ho wlsr gh vxshuflh | uhsuhvhqwduod hvtxhpäwlfdphqwh +d, b%2 n +2 n S5 2 ' b +e, e%2 n e+2 5 2 ' e +f, +2 n 5 2 %2 ' +g, 5 2 %2 +2 ' +h, +2 %2 ' 5 +i, +2 n 5 2 ' %2 +j, %2 n e5 2 ' S +k, +5 ' +l, 5 ' E%2 n +2 +m, %2 5 2 +2 ' +n, 5 2 %2 + 2 ' b +o, S+2 n b5 2 e%2 ' f 51 Ghwhuplqdu xqd hfxdflöq gh od vxshuflh rewhqlgd do jludu od fxuyd douhghgru gho hmh f 4 +d, od uhfwd 5 ' 2+c + fc 5 f +e, od sduäerod 5 ' n +2 +f, phgld holsvh 5 2 n 2+2 ' +g, ho fðufxor + 2 n E5 2 ' +Glylgluor hq grv sduwhv | rewhqhu grv hfxdflrqhv/ uhvxowd xq wrur, 61 Ghwhuplqdu ho grplqlr gh odv vljxlhqwhv ixqflrqhv s e %2 +2 +e, s E%c + ' s 2%2 +2 +d, s E%c + ' v %2 +2 +g, s E%c +c 5 ' *?E%+5 +f, s E%c + ' +h, s E%c +c 5 ' @hUt?E %n+n5 71 Rewhqhu odv fxuydv gh qlyho gh odv vljxlhqwhv ixqflrqhv +d, s E%c + ' % n + +e, s E%c + ' e %2 +2 +f, s E%c + ' %2 +2 +g, s E%c + ' m%m n m+m +h, s E%c + ' *?E%+ 81 Rewhqhu odv vxshuflhv gh qlyho gh odv vljxlhqwhv ixqflrqhv +d, s E%c +c 5 ' *?E%2 n +2 n 5 2 %2 + 2 5 2 n n S e b +f, s E%c +c 5 ' 5 %2 +2 +e, s E%c +c 5 ' +g, s E%c +c 5 ' 2%2 n 5 2 +h, s E%c +c 5 ' %2 n +2 5 2 5 5 Oðplwhv | Frqwlqxlgdg 41 Rewhqhu orv oðplwhv vljxlhqwhv= +d, %2 n 2%+ +2 n D E%c+ <Efcf n %2 n + 2 *4 +e, s *4 < E%c+ Efcf % ULt + n %2 n +2 +f, *4 < E%c+ Efcf +g, *4 < E%c+ Ec ULt e%+ t m%+m +h, @hUt?E%*+ E%c+ <Efc n %+ *4 51 Rewhqhu orv oðplwhv vljxlhqwhv= +d, %2 +2 E%c+ <Efcf % + *4 +e, %+ + 2% n 2 E%c+ <Ec % *4 +f, t? %+ E%c+ <Efcf %+ *4 6 +g, e+ t? % E%c+ <Efcf % *4 +h, *4 < E%c+ Ecf %+ 61 Xvdu frrughqdgdv sroduhv sdud rewhqhu orv vljxlhqwhv oðplwhv= +d, *4 < E%c+ Efcf %+ %2 +2 %2 n +2 +e, % E%c+<Efcf %2 n + 2 *4 +f, %2+2 E%c+<Efcf %2 n + 2 *4 +g, *4 < E%2 n + 2 t? E%c+ Efcf %2 n +2 +h, t?E%2 n +2 *4 E%c+ <Efcf %2 n +2 71 Phgldqwh oðplwhv gluhfflrqdohv ghprvwudu txh qr h{lvwhq orv vljxlhqwhv oðplwhv= +d, *4 < 2%+ n +2 E%c+ Efcf %2 7 +e, *4 < E%c+ Efcf s % % n +2 2 +f, %+ E%c+ <Efcf m%+m *4 +g, %2 +2 E%c+ <Efcf %2 n + 2 *4 +h, %e +2 E%c+ <Efcf %e n + 2 *4 81 Phgldqwh oðplwhv sru fdplqrv ghprvwudu txh qr h{lvwhq orv vljxlhqwhv oðplwhv= +d, 2%2+ E%c+ <Efcf %e n + 2 *4 +e, + e E% n +2 E%c+ <Efcf % *4 91 Fdofxodu ho oðplwh phgldqwh ghvduuroor gh wd|oru= t? %2 t? +2 *4 E%c+ <Efcf %2 +2 :1 Rewhqhu orv oðplwhv vljxlhqwhv= +d, %+5 E%c+c5 <Efcfcf n % n + 2 n 5 2 *4 2 8 +e, s *4 < E%c+c5 Efcfcf %2 n +2 n 5 2 ULt %+5 +f, t? % t? + t? 5 E%c+c5 <Efcfcf %+5 *4 +g, # *4 < E%c+c5 Ec2c n n % + 5 $ +h, *4 < Et?2 % n ULt2 + n tiU2 5 E%c+c5 Efcfcf 6 Ghulydgdv Sdufldohv | Glihuhqfldelolgdg 41 Vhd 2 sE%c + ' e%+ Frpsuredu odv ljxdogdghv | s%+ ' s+% s%%+ ' s%+% ' s+%% 51 Vhd sE%c + ' %+ %2 +2 %2 n +2 sdud E%c + 9' Efc f | s Efc f ' f1 +d, Prvwudu txh s%Efc f ' s+ Efc f ' f1 +e, Fdofxodu s% | s+ hq xq sxqwr E%c + 9' Efc f1 +f, Prvwudu txh s%+ Efc f 9' s+% Efc f1 9 61 Hfxdflöq gh Odsodfh Od hfxdflöq Y 2s Y 2s Y2s n n 'f Y%2 Y+2 Y5 2 vh frqrfh frpr hfxdflöq gh Odsodfh1 Suredu txh odv vljxlhqwhv ixq0 flrqhv vrq vroxflöq gh glfkd hfxdflöq= +d, s E%c +c 5 ' E% @2 n E+ K2 2E5 S2 +e, s E%c +c 5 ' t E% @2 n E+ K2 n E5 S2 t +f, s E%c +c 5 ' *? E% @2 n E+ K2 71 Ghwhuplqdu ydoruhv gh @/ K | S wdohv txh sE%c +c 5 ' t? @% t? K+ ULt S5 vhd vroxflöq gh od hfxdflöq gh Odsodfh1 81 Hfxdflöq gh Rqgdv Od hfxdflöq 2 Y2s 2Y s ' S Y|2 Y%2 vh frqrfh frpr hfxdflöq gh rqgdv1 Suredu txh odv vljxlhqwhv ixqflrqhv vrq vroxflöq gh glfkd hfxdflöq= +d, s E%c | ' @ t?E% S| n K t?E% n S| +e, s E%c | ' t? S| t? % +f, s E%c | ' *?E@% n @S|EK% KS| 91 Fdofxodu od olqhdol}dflöq uE%c + gh s E%c + hq ho sxqwr txh vh lqglfd +d, s E%c + ' ff 2f%2 f+2 ( +e, s E%c + ' %2 %+ n +2( +f, s E%c + ' e3 E%2 n+2 +h, s E%c + ' % +( ' Ec 2 | ' E*2c * +g, s E%c + ' E% n +*22* ( 2 ' Ec ' Ec ' Ec : :1 Rewhqhu od olqhdol}dflöq gh s E%c +c 5 hq orv sxqwrv lqglfdgrv= +d, s E%c +c 5 ' %+ n %5 n +5( ' Ec c 1 s +e, s E%c +c 5 ' %2 n +2 n 5 2 ( ' Efc c f1 +f, s E%c +c 5 ' e3% t?E+ n 5( +g, s E%c +c 5 ' @hU|@? %+5( ;1 Vhd s E%c + ' %+ %2 n +2 ' Efc fc Z1 ' Ec fc 21 vl E%c + 9' Efc f( s Efc f ' f +d, Fdofxodu s% Efc f | s+ Efc f1 +e, Suredu txh s qr hv frqwlqxd ql glihuhqfldeoh hq Efc f1 <1 Vhd s E%c + ' s %+ n +2 %2 vl E%c + 9' Efc f( s Efc f ' f +d, Fdofxodu s% Efc f | s+ Efc f1 +e, Suredu txh s hv frqwlqxd shur qr glihuhqfldeoh hq Efc f1 Vhd s E%c + ' s e %+ n +2 %2 vl E%c + 9' Efc f( s Efc f ' f +d, Fdofxodu s% Efc f | s+ Efc f1 +e, Suredu txh s hv frqwlqxd | glihuhqfldeoh hq Efc f1 431 Xqd ixqflöq frq ghulydgdv sdufldohv frqwlqxdv hv glihuhqfldeoh shur xqd ixqflöq sxhgh vhu glihuhqfldeoh | vxv ghulydgdv sdufldohv qr vhu frqwlqxdv1 Vhd s E%c + ' E%2 n +2 t? s 2 % n +2 vl E%c + 9' Efc f( s Efc f ' f1 +d, Ghprvwudu txh s% Efc f ' s+ Efc f ' f1 +e, Frpsuredu od glihuhqfldelolgdg gh s hq Efc f1 ; +f, Fdofxodu od ghulydgd sdufldo s% hq fxdotxlhu rwur sxqwr E%c + 9' f | frpsuredu txh glfkd ghulydgd qr hv frqwlqxd hq Efc f1 441 Vh ghvhd frqvwuxlu xq ghsövlwr gh irupd floðqgulfd gh udglr o ' 2 p | dowxud ' p 1 +d, Hvwlpdu ho lqfuhphqwr gh yroxphq {T phgldqwh _T vl o vh lqfuh0 phqwd hq ffp | hq ffp1 ÁFxdo hv lqfuhphqwr hvwlpdgr gh yroxphq hq wdqwr sru flhqwrB +e, Vl o vh plgh frq xq huuru qr pd|ru txh ho 2I | frq xq huuru qr pd|ru txh ho fDI/ hvwlpdu ho huuru hq wdqwr sru flhqwr txh vh frphwh hq ho fäofxor gho yroxphq1 +f, Ghwhuplqdu xq fxdgudgr douhghgru gho sxqwr Eo ' 2c ' sdud txh ho yroxphq yduðh hq phqrv gh f61 451 Wuhv uhvlvwruhv frq - ' ff/ -2 ' 2ff | - ' 2eD rkplrv vh frorfdq hq xq flufxlwr frqhfwdgrv hq sdudohor1 Od uhvlvwhqfld htxlydohqwh gho frqmxqwr ylhqh h{suhvdgd sru od iöupxod ' n n - -2 - +d, Ghprvwudu txh _- ' - 2 - _- n - 2 -2 _-2 n - 2 - _- +e, Hvwlpdu xq pdujhq gh huuru hq orv uhvlvwruhv/ frq ho plvpr wdqwr sru flhqwr hq orv wuhv/ sdud txh - qr fdpelh hq päv gh xq D sru flhqwr1 7 Uhjod gh fdghqd1 Ghulydflöq Lpsoðflwd 41 Vhdq sE%c + ' E%2 n + 23*2 E n % n %2+ +2 *e %E| ' |2 +E| ' | < +d, Rewhqhu od ghulydgd gh 8 E| ' s E%E|c +E| uhvshfwr d | phgldqwh vxvwlwxflöq | ghulydflöq +e, Rewhqhu od plvpd ghulydgd phgldqwh od uhjod gh od fdghqd1 51 Uhshwlu ho hmhuflflr dqwhulru frq s E%c + ' ULtE%2+ %E| ' e2| +E| ' tiU | 61 Vhdq s E%c +c 5 %E| +E| 5E| %2 +5 t?E% n + n 5 t?E|2e| t?E| ULt | |e3| ' ' ' ' +d, Rewhqhu od ghulydgd gh 8 E| ' s E%E|c +E|c 5E| uhvshfwr d | ph0 gldqwh vxvwlwxflöq | ghulydflöq +e, Rewhqhu od plvpd ghulydgd phgldqwh od uhjod gh od fdghqd1 71 Vhd 5 ' sE%c + frq % ' o ULt w/ + ' o t? w1 Frpsuredu od vljxlhqwh iöupxod txh dsduhfh hq whruðd gh fdpsrv hohfwurpdjqìwlfrv/ # Y Y5 o o Yo Yo $ n Y 25 Y 25 Y 2 5 ' n o2 Yw 2 Y%2 Y+2 81 Ghwhuplqdu orv ydoruhv gh 6 sdud orv fxdohv 5 ' s E+ n 6% hv vroxflöq gh od hfxdflöq hq ghulydgdv sdufldohv @ Y 25 Y25 Y25 n S n K ' f Y%2 Y+Y% Y+2 91 Xqd ixqflöq s E%c + vh glfh krprjìqhd gh judgr ? vl s E|%c |+ ' |? s E%c + 43 +d, Ghprvwudu txh xqd ixqflöq krprjìqhd gh judgr ? vdwlvidfh od vljxlhqwh hfxdflöq % Ys Ys n+ ' ?sE%c + Y% Y+ +e, Frpsuredu txh od ixqflöq s E%c + ' %D % +2 n 2%+e .+D hv xqd ixqflöq krprjìqhd | txh vdwlvidfh od hfxdflöq dqwhulru1 :1 Hqfrqwudu phgldqwh ghulydflöq lpsoðflwd gh od hfxdflöq s s s s %n +n 5 ' odv ghulydgdv sulphudv | vhjxqgdv gh 5 uhvshfwr gh % h + hq ho sxqwr Ec c 1 ;1 Uhshwlu ho hmhuflflr dqwhulru frq od hfxdflöq e5 t?E% n + n e+ t?E% n 5 n e% t?E+ n 5 ' f | ho sxqwr EZc Zc Z1 <1 Lqglfdu orv sxqwrv hq orv txh od hfxdflöq %e n +e n 5 2 n 2%5 2+5 n D ' f ghqh lpsoðflwdphqwh xqd ixqflöq 5 ' }E%c + | fdofxodu vxv ghulydgdv sulphudv1 431 Fdofxodu phgldqwh ghulydflöq lpsoðflwd gh odv hfxdflrqhv 2 n 2 n %2 n +2 n 5 2 ' f 2 n 2 2%+5 ' f odv ghulydgdv sulphudv | vhjxqgdv gh | uhvshfwr gh %/ + | 51 44