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E? 6 hohphqwrv glvwlqwrv txh sxhghq irupduvh gh prgr txh grv juxsrv vh glihuhqflhq hq txh wlhqhq dojýq hohphqwr glvwlqwr r sru od rughqdflöq gh vxv hohphqwrv1 Ho qýphur gh yduldflrqhv vlq uhshwlflöq hv= T6c? ' 6E? ' 6E6 E6 2E6 ? n Odv yduldflrqhv gh 6 wrpdgdv gh ? hq ? vrq odv glihuhqwhv pxhvwudv rugh0 qdgdv gh wdpdôr ? vhohfflrqdgdv hq xq pxhvwuhr vlq uhhpsod}dplhqwr gh xqd sreodflöq gh 6 lqglylgxrv1 Hmhpsor 4= Hq xqd fodvh gh 63 doxpqrv vh yd d hohjlu xqd whuqd sdud rfxsdu orv sxhvwrv gh Suhvlghqwh/ Vhfuhwdulr | Whvruhur Á fxäqwdv whuqdv glihuhqwhv sxhghq irupduvhB DQÄOLVLV FRPELQDWRULR " Hvwd fodur txh vh wudwd gh Tfc ' f 2b 2H ' 2eSf vhuäq odv glvwlqwdv srvlelolgdghv gh hohfflöq 451515 Yduldflrqhv frq uhshwlflöq Vl do irupdu orv juxsrv txh frqvwlwx|hq odv yduldflrqhv orv hohphqwrv sxhghq wrpduvh uhshwlgrv vh rewlhqhq odv yduldflrqhv frq uhshwlflöq gh 6 hohphqwrv wrpdgrv gh ? hq ?1 Ho qýphur gh yduldflrqhv frq uhshwlflöq hv= T -6c? ' 6? Odv yduldflrqhv frq uhshwlflöq gh 6 wrpdgdv gh ? hq ? vrq odv glihuhqwhv pxhvwudv rughqdgdv gh wdpdôr ? vhohfflrqdgdv hq xq pxhvwuhr frq uhhpsod}d0 plhqwr gh xqd sreodflöq gh 6 lqglylgxrv1 Hmhpsor 5= Fxäqwrv qýphurv gh grv fliudv vh sxhghq irupdu frq orv qýphurv 4/5/6/7 | 81 Hq hvwh fdvr vh sxhghq xwlol}du fxdotxlhud gh odv fliudv wdqwr sdud ho oxjdu gh odv ghfhqdv frpr sdud odv xqlgdghv/ vh wudwduðd sxhv gh yduldflrqhv gh 8 hohphqwrv wrpdgrv gh grv hq grv/ hv ghflu= T -Dc2 ' D2 ' 2D 4516 Shupxwdflrqhv 451614 Shupxwdflrqhv vlq uhshwlflöq Odv shupxwdflrqhv gh 6 hohphqwrv vrq odv glihuhqwhv rughqdflrqhv txh sxhghq kdfhuvh frq orv 6 hohphqwrv1 Sru wdqwr/ frlqflghq frq odv yduldflrqhv vlq uhshwlflöq gh 6 hohphqwrv wrpdgrv gh 6 hq 61 Ho qýphur gh shupxwdflrqhv hv= 6 ' 6- ' 6E6 E6 2 Hmhpsor 6= Xqd hqflforshgld gh 8 yroýphqhv/ gh fxäqwdv irupdv glvwlqwdv vh sxhgh frorfdu hq xqd hvwdqwhuðd D ' D- ' D e 2 ' 2f # DQÄOLVLV FRPELQDWRULR 451615 Shupxwdflrqhv frq uhshwlflöq Frqvlgìuhvh xq frqmxqwr gh 6 hohphqwrv gh orv fxdohv o vrq glvwlqwrv/ dsduh0 flhqgr ho sulphur ? yhfhv/ ho vhjxqgr ?2 yhfhv/ 111/ ho u0ìvlpr ?o yhfhv/ frq ? n ?2 n n ?o ' 61 D odv glihuhqwhv rughqdflrqhv gh hvwh frqmxqwr gh 6 hohphqwrv vh ohv ghqrplqd shupxwdflrqhv frq uhshwlflöq1 Ho qýphur gh shupxwdflrqhv frq uhshwlflöq hv= ?Q c? -6 cc?o ' 6 ? - ?2 -?o - Odv shupxwdflrqhv frq uhshwlflöq uhsuhvhqwdq odv glihuhqwhv sduwlflrqhv gh o juxsrv txh sxhghq kdfhuvh hq xq frohfwlyr gh 6 lqglylgxrv gh irupd txh hq ho sulphu juxsr kd| ? lqglylgxrv/ hq ho vhjxqgr ?2 /111 | hq ho u0ìvlpr kd| ?o 1 Hmhpsor 7= Vl hq xq dxod gh 48 doxpqrv | vh ghvhd irupdu wuhv htxlsrv gh edorqfhvwr +fdgd htxlsr gh 8 mxjdgruhv,1 ÁFxäqwdv srvlelolgdghv kd| sdud fdgd xqrB1 DcDcD ' -D D' .DS.DS D- D- D- 4517 Frpelqdflrqhv Odv frpelqdflrqhv vh ghqhq frpr ho qýphur gh glvwlqwrv juxsrv txh vh sxhghq kdfhu frq xq frqmxqwr gh hohphqwrv gh irupd txh qr lpsruwd ho rughq hq ho txh vh hqfxhqwuhq hvwrv hohphqwrv1 Ghshqglhqgr gh vl hq fdgd juxsr sxhgh dsduhfhu uhshwlgr ho plvpr hohphqwr r qr vh glvwlqjxluäq hqwuh frpelqdflrqhv frq uhshwlflöq | vlq uhshwlflöq1 Sdud ho fäofxor gho qýphur gh frpelqdflrqhv hv ýwlo od vljxlhqwh ghqlflöq vl ?? | & vrq grv qýphurv qdwxudohv wdohv txh & ?/ ho qýphur frpelqdwrulr & hvwä gdgr sru od h{suhvlöq/ ?E? E? 2E? & n ? ?E& G' ' &&E& E& 2 & Surslhgdghv= 41 ? ' ? ' 51 ? f ? '? 61 ? 71 ? & ' ? ?!& ?& ' &- E?!&- FRPELQDFLRQHV $ 81 91 ? ? ?n & ! n & ' & ? ? ? ? ? ? n n n n f 2 ? ' E n ' 2 Xq uhvxowdgr lpsruwdqwh/ txh shuplwh phgldqwh h{suhvlrqhv frq qýphurv frpelqdulrv h{suhvdu od srwhqfld gh xq elqrplr hv ho ghqrplqdgr Elqrplr gh Qhzwrq txh glfh txh gdgrv grv qýphurv fxdohvtxlhud @ | K | xq hqwhur srvlwlyr ? vh yhulfd txh= ? ? [ ? E@ n K ' @ K?! 'f 451714 Frpelqdflrqhv vlq uhshwlflöq Gdgr xq frqmxqwr gh 6 hohphqwrv glvwlqjxleohv/ vh ghqrplqdq frpelqdflrqhv gh 6 wrpdgdv gh ? hq ? d orv glihuhqwhv juxsrv gh ? hohphqwrv txh sxhghq irupduvh gh prgr txh grv juxsrv vh glihuhqflhq hq txh wlhqhq dojýq hohphqwr glvwlqwr +qr lpsruwd ho rughq,1 Ho qýphur gh frpelqdflrqhv vlq uhshwlflöq hv= 6E6 E6 2E6 ? n 6 ' 6c? 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T -6c? Qr Lpsruwd ho rughq 6c? -6c? &