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Ì ¼ Ì . +. Ì= DWDQÌ . Ì ¼ . ¼ . - ¼ . ¼ . + . - . ¼ . Ì ¼ Ì . +. Í [ j ( Ë . ¼ ¼ . ¼ . + ¼ . ¼ . + . - . ¼ . Ì ¼ Ì . +. Ì= DWDQÌ . Ì ¼ . ¼ . + ¼ . ¼ . + . - . ¼ . Ì ¼ Ì . +. Í [ [ ( . [ = [' - [% . \ = \ ' - \ % .O = [ \ \ \ [ \ O \ [ \ \ \ [ \ O ) ) )- . O ) )- . ) O Û Ü Ü Ü Ü Ü Ü Ü Ý Û Ü Ü Ü Ü Ü Ü Ü Ý O - ([' - [% ) - ( \ ' - \ % ) - O O 1yWHVH TXH HQ ODV (F \ D SDUWLU GH OD FXDOHV VH SXHGH GHWHUPLQDU OD SRVLFLyQ GH FXDOTXLHU SXQWRGHOJUXSRVyORVHUHTXLHUHQ DGHPiVGHODVPHGLGDVGH ORVHVODERQHV ODVSRVLFLRQHVGHORV SXQWRV%\'GHORVHOHPHQWRVGHDUUDVWUH 3DUD OD GHWHUPLQDFLyQ GH ODV YHORFLGDGHV OLQHDOHV \ DQJXODUHV GH ORV HVODERQHV GLIHUHQFLDPRV FRQ UHVSHFWRDOWLHPSRODVHFXDFLRQHV\2EWHQHPRV ÑY%[ - O ¼ w ¼ VHQj = Y'[ - O ¼ w ¼ VHQj Ò ÓY%\ + O ¼ w ¼ FRV j = Y'\ + O ¼ w ¼ FRV j (OLPLQDQGRw GHDPEDVHFXDFLRQHV\GHVSHMDQGRw VHREWLHQH w = WDQj ¼ (- Y%\ + Y'\ ) - Y%[ + Y'[ O ¼ (WDQj ¼ FRVj - VHQ j ) $SDUWLUGHOD(FSXHGHQREWHQHUVHODVH[SUHVLRQHVSDUDODYHORFLGDGDQJXODUGHORWURHVODEyQ\ODV YHORFLGDGHVOLQHDOHVGHFXDOTXLHUSXQWRGHOJUXSRORVSDUiPHWURVUHTXHULGRVDTXt\DVRQFRQRFLGRV 'HULYDQGROD(FREWHQHPRV ÑÔ D%[ - O ¼ VHQ j ¼ e - O ¼ FRV j ¼ w = D'[ - O ¼ VHQ j ¼ e - O ¼ FRV j ¼ w Ò ÔÓD%\ + O ¼ FRV j ¼ e - O ¼ VHQ j ¼ w = D'\ + O ¼ FRV j ¼ e - O ¼ VHQ j ¼ w 'HFX\DVROXFLyQHVSRVLEOHGHWHUPLQDUe e = ( D%[ - D'[ - O FRV j w + O FRV j w - WDQj - D%\ + D'\ + O VHQ j w - O VHQ j w O FRV j WDQj - O VHQ j ) 'H GRQGH VH REWLHQHQ HO UHVWR GH SDUiPHWURV QHFHVDULRV SDUD OD VROXFLyQ WRWDO GHO SUREOHPD FLQHPiWLFR GHO JUXSR 3DUD HO UHVWR GH WLSRV GH JUXSRV GH VHJXQGD FODVH YHU )LJ VH SXHGHQ SODQWHDU FRQVLGHUDFLRQHV VHPHMDQWHV \ REWHQHU ODV H[SUHVLRQHV HTXLYDOHQWHV ODV TXH VH PXHVWUDQ HQVHJXLGD 'LFKR WUDEDMR SHUPLWH OD VROXFLyQ GH FXDOTXLHU PHFDQLVPR FRPSXHVWR GH JUXSRV GH VHJXQGDFODVH *UXSRGHVHJXQGDFODVHGHOVHJXQGRWLSR )LJ*UXSRGHVHJXQGDFODVHGHOVHJXQGRWLSR (FXDFLyQGHSRVLFLyQ/DVHFXDFLRQHVGHSRVLFLyQSRVHHQLJXDOIRUPDTXHODV(F\SHURHQ GRQGH . O = WDQ q ([ % + D VHQ q ) + D FRVq . [ = -O . \ = O D = \( FRV q - [( VHQ q (FXDFLyQGHYHORFLGDGHV w = 9%\ + D VHQ qw - D FRV q - VHF qw ([ % + O FRV j + D VHQ q ) - WDQ q (9%[ + D FRV qw + D VHQ q ) - O (WDQ q VHQ j + FRV j ) GRQGH D = 9(\ FRVq - \ ( VHQ qw - 9([ VHQq - [( FRVqw (FXDFLyQGHDFHOHUDFLRQHV [ + WDQq (D%[ - O FRV j w ( ) ] VHF q ¼ ( [ % + O FRV j + D VHQ q ) WDQqw + e + w (9%[ - O VHQ j w + D VHQ q + D FRVqw ) + e = - D%\ + O VHQ j w - D VHQ qw - D FRVqw - D VHQ q ¼ e + D FRVq ) + D FRVqw - D VHQ qw + D FRVq ¼ e + D VHQ q O (FRV j + VHQ j ) GRQGH D = D(\ FRVq - 9(\ VHQ qw - \ ( FRVqw - \ ( VHQ qe - D([ VHQ q - 9([ FRVqw - [( VHQ qw + [( FRVqe *UXSRGHVHJXQGDFODVHGHOWHUFHUWLSR )LJ*UXSRGHVHJXQGDFODVHGHOWHUFHUWLSR (FXDFLyQGHSRVLFLyQ/DVHFXDFLRQHVGHSRVLFLyQWDPELpQSRVHHQLJXDOIRUPDTXHODV(F\ HQGRQGH . [ = [ ' - [ % . \ = \ % - \ ' . 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