4 LQWHJUDOHV gh OÐQHD | gh VXSHUILFLH +Vhulh 5, 4 d, Kdoodu/ frpr lqwhuvhfflöq gh grv vxshuflhv/ od fxuyd gh hfxdflrqhv sdudpìwulfdv { @ d frv5 w> | @ d frv w vhq w> } @ d vhq w> w 5 ^3> 5,= e, Kdoodu xqdv hfxdflrqhv sdudpìwulfdv gh od fxuyd lqwhuvhfflöq gho flolqgur {5 . |5 @ d5 > | ho sodqr } @ 3= Vroxflöq= d, {5 . | 5 . } 5 d5 @ 3> {} 5 d| 5 @ 3= e, { @ d frv w> | @ d vhq w> } @ 3/ 3 w ? 5= 5 Vhd od fxuyd { @ w5 4> | @ w6 w> } @ vhq w frq 5 w 5 1 ÁHv pýowlsoh ho sxqwr +3> 3> 3, gh glfkd fxuydB1 Vroxflöq= Vð1 6 d, Kdoodu od uhfwd wdqjhqwh d od kìolfh flufxodu { @ frv w> | @ vhq w> } @ w . 6 hq ho sxqwr fruuhvsrqglhqwh d } @ 71 e, Kdoodu odv uhfwdv wdqjhqwhv d od fxuyd { @ w5 4> | @ w6 w> } @ vhq w hq orv sxqwrv fruuhvsrqglhqwhv d w4 @ 4 | w5 @ 41 Vroxflöq= d, { 5 |vhq 4 {frv 4 vhq 4 @ frv 4 | } @ 5 @ = @ }7 4 1 e, Sdud w4 @ 4 od uhfwd wdqjhqwh hv 7 d, Vhd od fxuyd { @ frv w> | @ vhq w> } @ wj w sdud 3 ? w ? vl vh hihfwýd xqd uhsdudphwul}dflöq kdflhqgr wj w @ 1 51 { 5 @ | 5 @ } 1 Sdud w5 @ 4 od uhfwd wdqjhqwh hv Kdoodu odv qxhydv hfxdflrqhv sdudpìwulfdv gh od fxuyd e, Vhd od fxuyd vlwxdgd hq ho sodqr R[\ / gh hfxdflrqhv sdudpìwulfdv { @ w5 4> | @ vhq w sdud 4 w 41 Dqdol}du vl od uhsdudphwul}dflöq gdgd sru w @ 4 frq 5 ^3> 5` | w @ 4 5 frq 5 ^3> 4`/ fdpeldq r qr od rulhqwdflöq gh od fxuyd1 Vroxflöq= d, { @ s 4 >| 4.# @ s 4.# > } @ > 5 +3> 4,1 e, Ho fdpelr gh sduäphwur gdgr sru w @ 4/ qr fdpeld od rulhqwdflöq gh od fxuyd1 Ho fdpelr gh sduäphwur gdgr sru w @ 4 5 vð fdpeld od rulhqwdflöq gh od fxuyd1 8 Gdgd od fxuyd { @ w> | @ w5 > } @ w6 / frq w 5 ^3> 4`/ vh slgh= d, Kdoodu xqd qxhyd sdudphwul}dflöq hq ixqflöq gh / vlhqgr w @ 5 = e, Hvwxgldu vl ho sxqwr +3> 3> 3, hv xq sxqwr qr vlqjxodu sdud dpedv sdudphwul}dflrqhv/ mxvwlfdqgr ho uhvxowdgr1 Vroxflöq= d, { @ 5 > | @ 7 > } @ 9 / frq 5 ^3> 4`1 e, Ho sxqwr +3> 3> 3, hv xq sxqwr qr vlqjxodu sdud od sdudphwul}dflöq { @ w> | @ w5 > } @ w6 1 Ho sxqwr +3> 3> 3, hv xq sxqwr vlqjxodu sdud od sdudphwul}dflöq { @ 5 > | @ 7 > } @ 9 1 9 Fdofxodu od orqjlwxg gh xqd hvslud gh od kìolfh flufxodu { @ d frv w> | @ d vhq w> } @ ew> sdud w 5 ^3> 5` = s Vroxflöq= 5 d5 . e5 = : d, Kdoodu od hfxdflöq lpsoðflwd gh od vxshuflh gh hfxdflrqhv sdudpìwulfdv { @ dx frv y> | @ dx vhq y> } @ ex/ sdud 4 ? x ? 4> 3 y ? 5> d A 3> e A 31 e, H{suhvdu od vxshuflh gh hfxdflöq lpsoðflwd Vroxflöq= d, {# .| # d# }# e# {# d# . |# e# }# f# @ 4 frq d> e> f 5 7. > hq irupd sdudpìwulfd1 @ 3= e, { @ d frvk x frv > | @ e frvk x vhq > } @ f vhqk x/ frq 4 ? x ? 4/ 3 ? 5= ; d, Kdoodu ho sodqr wdqjhqwh d od vxshuflh { @ x . y> | @ x y> } @ x5 y5 hq ho sxqwr +5> 3> 3,1 e, Kdoodu ho sodqr wdqjhqwh do sduderorlgh } @ {5 . | 5 hq ho ruljhq gh frrughqdgdv1 Vroxflöq= d, 5| } @ 31 e, } @ 31 < Vhd od vxshuflh { @ x . y> | @ x y> } @ xy/ sdud 4 ? x ? 4> 4 ? y ? 41 Vh slgh= d, Kdoodu hq ho sxqwr +5> 3> 4, od uhfwd wdqjhqwh d od fxuyd vreuh od vxshuflh gdgd sru x @ y1 e, Kdoodu ho äqjxor txh irupdq odv fxuydv txh sdvdq sru ho sxqwr +5> 3> 4, | fx|dv wdqjhqwhv vrq W x | W y 1 5 Vroxflöq= d, { @ } . 4> | @ 31 e, @ duf frv 4 6= 43 Vxsrqjdprv txh i hv xq fdpsr hvfdodu | I hv xq fdpsr yhfwruldo1 Ghprvwudu txh gly+iI , @ ui I . i gly I 1 44 Ghprvwudu txh vl xq yhfwru wlhqh gluhfflöq frqvwdqwh/ hqwrqfhv vx urwdflrqdo hv shushqglfxodu d hvd gluhfflöq1 45 Vhd d xq yhfwru frqvwdqwh | U ho yhfwru gh srvlflöq1 Vh frqvlghud ho yhfwru y @ d U1 Ghprvwudu txh gly y @ 31 46 Vxsrqjdprv txh I hv xq fdpsr yhfwruldo gh fodvh F 5 1 Ghprvwudu txh gly+urw I , @ 3= 47 Vxsrqjdprv txh i hv xq fdpsr hvfdodu1 Ghprvwudu txh gly ui @ 7i1 48 Fdofxodu od lqwhjudo gh oðqhd gho fdpsr yhfwruldo I d or odujr gh od fxuyd F hq orv vljxlhqwhv fdvrv= d, I +{> |> }, @ +{> |> },1 F = +w, @ +frv w> vhq w> w,> 3 w 5= e, I +{> |, @ +|> {,1 F = iurqwhud gho fxdgudgr m{m . m|m 4 hq vhqwlgr qhjdwlyr1 f, I +{> |> }, @ +|> {> } 5 ,1 F = od sduäerod | @ {5 > } @ 6 ghvgh { @ 4 kdvwd { @ 51 Vroxflöq= d, 55 1 e, 71 f, :6 = 49 U Vhd j+{> |> }, @ 4 | F ho dufr gh kìolfh gh hfxdflrqhv +w, @ +frv w> vhq w> w,> w 5 ^3> 5`1 Fdofxodu od lqwhjudo gh oðqhd jgv= F s Vroxflöq= 5 5= # 4: Vhd I +{> |, @ +{5 > | 5 , | F od plwdg vxshulru gh od holsvh {d# . U Fdofxodu F I gv/ hq grqgh F vh uhfruuh ghvgh +d> 3, d +d> 3,1 Vroxflöq= |# e# @ 4= 5 6 6d = 4; Kdoodu od lqwhjudo gh oðqhd gho fdpsr I +{> |> }, @ {5 . {> }| 5 > {} 5 / d or odujr gh od fxuyd lqwhuvhfflöq gh odv vxshuflhv {5 . 5|5 . 6} 5 @ 9> 6} @ {5 . 5|5 = Vroxflöq= 3= U 4< Fdofxodu od lqwhjudo gh oðqhd F 5|} 5 g{ . {} 5 g| . 6{|}g} vlhqgr F od fxuyd irupdgd sru orv vljxlhqwhv dufrv gh fxuyd= F4 @ +{> |> }, 5 76 @{5 . | 5 . } 5 @ d5 > | @ 3> { 3> } 3 > F5 @ +{> |> }, 5 76 @{5 . | 5 . } 5 @ d5 > {5 . | 5 d{ @ 3> | 3> { 3> } 3 rulhqwdgd srvlwlydphqwh1 Vroxflöq= d% 65 = U 53 Fdofxodu od lqwhjudo gh oðqhd {g{.|g| .}g} d or odujr gho dufr gh kìolfh gh hfxdflrqhv sdudpìwulfdv { @ 7 frv w> | @ 7 vhq w> } @ 6w/ sdud 3 w 51 Vroxflöq= 4;5 = 54 Fdofxodu od lqwhjudo gh oðqhd Vroxflöq= U ugu . u5 g d or odujr gh od fxuyd gh hfxdflöq u @ vhq > 3 1 5= 55 Gdgd od irupd glihuhqfldo 5{|}g{ . {5 } . 5|h} g| . {5 | . | 5 h} g}= d, ÁDgplwh ixqflöq srwhqfldoB1 e, Hq fdvr dupdwlyr/ fdofxodu xqd ixqflöq srwhqfldo1 Vroxflöq= d, Vð dgplwh ixqflöq srwhqfldo1 e, i+{> |> }, @ {5 |} . |5 h} = 56 Gdgr ho fdpsr gh ixhu}dv I +{> |, @ |l . {m/ kdoodu ho wudedmr gh I d or odujr gh odv fxuydv= 6 d, 4 gdgd sru | @ { hqwuh orv sxqwrv +3> 3, | +4> 4,1 e, 5 gdgd sru | @ {5 hqwuh orv sxqwrv +3> 3, | +4> 4,1 f, 6 gdgd sru | @ {6 hqwuh orv sxqwrv +3> 3, | +4> 4,1 g, 7 gdgd sru | @ {6 +{ 4, oq+{ . 5, . { hqwuh orv sxqwrv +3> 3, | +4> 4,1 Vroxflöq= Odv fxdwur ydohq 4= | 57 Vhdq odv ixqflrqhv S +{> |, @ {# .| # | T+{> |, @ { @ frv w> | @ vhq w sdud w 5/ vh slgh= { {# .| # | odv fxuydv 4 = { @ frv w> | @ vhq w sdud 3 w | 5 = d, Frpsuredu txh hq wrgr 75 h{fhswr hq ho ruljhq gh frrughqdgdv vh yhulfd U U e, Glvfxwlu ud}rqdgdphqwh vl vh yhulfd " S g{ . Tg| @ # S g{ . Tg|1 f, Fdofxodu dpedv lqwhjudohv sru vhsdudgr1 Vroxflöq= e, Qr vh sxhgh dupdu txh dpedv lqwhjudohv vhdq ljxdohv1 f, U " CT C{ @ CS C| 1 S g{ . Tg| @ > U # S g{ . Tg| @ = 58 Vhd G xq grplqlr vlpsohphqwh gh 75 | i+{> |, xqd ixqflöq gh fodvh F 5 hq G1 Suredu txh xqd frqglflöq K Ci frqh{r Ci vxflhqwh sdud txh od lqwhjudo C{ g| C| g{ vhd qxod d or odujr gh wrgd fxuyd vlpsoh | fhuudgd frqwhqlgd hq G/ hv # # txh i vhd xqd ixqflöq dupöqlfd/ hv ghflu txh vh fxpsod CC{i# . CC|i# @ 31 K | { 59 Kdoodu {# .| # g{ {# .| # g| vlhqgr od holsvh gh hfxdflrqhv sdudpìwulfdv= { @ 7 frv w> | @ 6 vhq w/ sdud 3 w 51 Vroxflöq= 5= 5: Vhd xqd fxuyd sodqd/ vlpsoh/ fhuudgd/ fx|d h{suhvlöq hq frrughqdgdv sroduhv hv u @ u+,> 3 4 5 51 U Ghprvwudu txh ho äuhd gho uhflqwr G/ hqfhuudgr sru / ylhqh gdgd sru 45 "# u5 +,g1 Fdofxodu ho äuhd gho uhflqwr G lqwhulru d od fduglrlgh gh hfxdflöq u @ 4 . frv / sdud 3 51 Vroxflöq= 6 5 = 5; Fdofxodu ho wudedmr uhdol}dgr sru xqd sduwðfxod vrphwlgd do fdpsr gh ixhu}dv I +{> |, @ h{ | 6 l . +frv | . {6 ,m txh uhfruuh od flufxqihuhqfld xqlwduld F hq vhqwlgr frqwudulr d odv djxmdv gho uhorm1 Vroxflöq= 6 5 = | { 5 6 5 5< Gdgrv ho fdpsr gh ixhu}dv I @ {# .| # l {# .| # m .6} n | od fxuyd gh hfxdflrqhv sdudpìwulfdv { @ w> | @ w .w 4> } @ w . 6/ fdofxodu ho wudedmr qhfhvdulr sdud oohydu xqd sduwðfxod gh pdvd xqlgdg/ d or odujr gh > ghvgh ho sxqwr S4 @ +4> 4> 5, kdvwd ho sxqwr S5 @ +4> 4> 7,1 Vroxflöq= . 89= 63 Frpsuredu ho whruhpd gh Juhhq sdud od ixqflöq I +{> |, @ +5{6 | 6 > {6 . | 6 , vreuh od uhjlöq irupdgd sru ho dqloor flufxodu P @ i+{> |,@d5 {5 . | 5 e5 j1 Vroxflöq= Dpedv lqwhjudohv ydohq 65 e7 d7 = 64 Fdofxodu phgldqwh xqd lqwhjudo gh oðqhd ho äuhd gh od uhjlöq hqfhuudgd sru od fxuyd { @ w+w 4,> | @ w+w6 4,> w 5 ^3> 4` = Vroxflöq= 4 63 = 65 Kdoodu ho wudedmr uhdol}dgr sru ho fdpsr I +{> |, @ +6{5 |7 > 6| 5 {6 , sdud pryhu xqd sduwðfxod gh pdvd p ghvgh ho sxqwr +4> 3, do sxqwr +3> 4, d or odujr gh od fxuyd {6 . | 6 @ 41 Vroxflöq= 46 47 = 5 66 Fdofxodu ho wudedmr uhdol}dgr sru ho fdpsr I +{> |> }, @ 7{| 6{5 } . 4> 5+{5 . 4,> 5{6 } 6} 5 sdud pryhu xqd sduwðfxod gh pdvd p ghvgh ho sxqwr +4> 4> 4, do sxqwr } . { . 5| @ 3= I56 > 3> I56 d or odujr gh od fxuyd {5 . | 5 . 5} 5 @ 7> 7 Vroxflöq= I <43 6 . 8= 67 d, Kdoodu ho äuhd gh od vxshuflh V gho sduderorlgh } @ {5 . | 5 ghwhuplqdgd sru 3 } 71 e, Kdoodu ho äuhd gh od vxshuflh gho wurqfr gh sduderorlgh V> | @ {5 . } 5 4/ frq 3 | 61 f, Kdoodu ho äuhd gh xqd vhplhvihud gh udglr d1 $ $ $ Vroxflöq= d, 9 4: # 4 1 e, 9 4: # 8 # 1 f, 5d5 = 68 Kdoodu ho äuhd gh od vxshuflh V gh hfxdflrqhv sdudpìwulfdv { @ frv x frv y> | @ frv x vhq y> } @ vhq x sdud 3 x 7 > 3 y x1 Vroxflöq= I .77 5 I = 7 5 69 Kdoodu od lqwhjudo UU 5 { . | 5 gV/ hq grqgh V hv od vxshuflh gho frqr } 5 @ 6 {5 . |5 / frq 3 } 61 V Vroxflöq= <= 6: Vhd V od vhplhvihud {5 . | 5 . } 5 d5 @ 3> } 31 Kdoodu Vroxflöq= UU 5 { . | 5 gV= V 7 7 6 d = 6; Vhd ho fdpsr yhfwruldo I @ {}l . 6{|m 5}n1 UU d, Kdoodu V I gV sru phglr gho whruhpd gh Jdxvv/ grqgh V hv od vxshuflh iurqwhud gho vöolgr Y @ i+{> |> }, 5 76 @{5 . | 5 4> 3 } 6j= e, Kdoodu ho xmr gluhfwdphqwh1 Vroxflöq= 6 5 = 6< Vxsrqjdprv txh Y hv xq vöolgr gh yroxphq 46 xqlgdghv olplwdgr sru od vxshuflh UU fhuudgd V/ | txh U hv ho fdpsr yhfwruldo ghqlgr sru ho yhfwru gh srvlflöq/ r vhd/ U+{> |> }, @ {l . |m . }n1 Kdoodu V U gV= Vroxflöq= 6<= U 73 Dsolfdu ho whruhpd gh Vwrnhv sdud ghprvwudu txh | 6 g{ . {6 g| } 6 g} @ 6 5 hq grqgh hv od lqwhuvhfflöq gho 5 5 flolqgur { . | @ 4 frq ho sodqr { . | . } @ 4 | vh vxsrqh vx rulhqwdflöq srvlwlyd1 74 Yhulfdu ho whruhpd gh Vwrnhv sdud ho fdpsr yhfwruldo I +{> |> }, @ +6|> {}> |} 5 , | od vxshuflh V gho sduderorlgh 5} @ {5 . | 5 olplwdgd sru ho sodqr } @ 5/ frqvlghudqgr hq V od qrupdo h{whulru | hq vx frqwruqr F od rulhqwdflöq ghwhuplqdgd sru V1 Vroxflöq= Dpedv lqwhjudohv ydohq 53= U 75 Dsolfdu ho whruhpd gh Vwrnhv sdud kdoodu od lqwhjudo gh oðqhd F |5 } 5 g{ . +} 5 {5 ,g| . +{5 |5 ,g} hq grqgh F hv od lqwhuvhfflöq gh od vhplhvihud {5 . |5 . } 5 @ 7{> } A 3 | ho flolqgur {5 . | 5 @ 5{= Vroxflöq= 3= 76 Dsolfdu ho whruhpd gh od glyhujhqfld sdud fdofxodu od lqwhjudo gh vxshuflh gho fdpsr yhfwruldo I @ +{6 > | 6 > } 5 , vreuh od iurqwhud gho vöolgr olplwdgr sru orv sduderorlghv } @ {5 . | 5 > } @ 4 {5 | 5 frq od rulhqwdflöq gh od qrupdo h{whulru1 Vroxflöq= 6 ; = 77 Yhulfdu ho whruhpd gh Jdxvv sdud ho fdpsr yhfwruldo I @ gh udglr 41 6 7 6 6 7 { > {| > {} uhvshfwr d od hvihud gh fhqwur +3> 3> 3, | Vroxflöq= Dpedv lqwhjudohv ydohq 3= 78 Vxsrqjdprv txh V hv od vxshuflh gh hfxdflrqhv sdudpìwulfdv { @ x frv y> | @ x vhq y> } @ x5 / sdud 3 x 6> 3 y 5 / | vhd ho fdpsr yhfwruldo U @ {l . |m . }n1 Fdofxodu ho xmr gh U d wudyìv gh V hq ho vhqwlgr gh od qrupdo 8 h{whulru1 Vroxflöq= ;4 ; = 79 Xqd kholfrlgh vh ghqh phgldqwh od sdudphwul}dflöq W = G $ 76 / gdgd sru { @ u frv > | @ u vhq > } @ vlhqgr G od uhjlöq 3 5/ 3 u 41 Kdoodu vx äuhd | vx fhqwur gh judyhgdg/ vxsrqlhqgr ghqvlgdg frqvwdqwh1 s s Vroxflöq= Duhd @ 5 . oq 4 . 5 = {J @ |J @ 3> }J @ =