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⎝ ,D ⎠ ± ≤ ND [ GV ⎛⎞ ⎜ ⎟ [ ≤ G HI ⎝ ⎠ GV FP $HI $J $LQHI N $J FP $HI ± FP EHI E λ S EHI $LQHI >±[±[ ±@[ FP F'HWHUPLQDomRGH15G ≤ E [ [ 125G FP ≤ E 15G N1 FP )OH[mR EHI FP 9HULILFDomR GR (QULMHFHGRU GH ERUGD (OHPHQWR G ±W ±>[±@ FP 2PRPHQWRIOHWRUUHVLVWHQWHGHFiOFXOR 05G GHYHVHUWRPDGRFRPRRPHQRUYDORUFDOFXODGR HP 0R PHQWR F DOF XODGR FR P EDVH QR LQtFLRGRHVFRDPHQWR D 9HU L I L F Do mR G R )O DQ J H &R P S U L P L G R (OHPHQWR &RPR λ S QmR KDYHUi IODPEDJHPORFDO GHI FPODUJXUDHIHWLYDGRHQULMHFHGRU 2 FiOFXOR GD ODUJXUD HIHWLYD GH HOHPHQWRV XQLIRUPHPHQWHFRPSULPLGRVFRPHQULMHFHGRUGH ERUGD p IHLWR FRQVLGHUDQGRVH DV SUHVFULo}HV FRQVWDQWHVHPHDVGHILQLo}HVDSUHVHQWDGDV QDILJXUD E ±W ±>[±@ FP ([HPSORVGHGLPHQVLRQDPHQWR 2YDORUGHUHIHUrQFLDGRtQGLFHGHHVEHOWH] UHGX]LGRGRHOHPHQWRλ SR pFDOFXODGR FRQIRUPHHTXDomR λ SR λ SR EHI [ FP ≤ E FP EHI FP E 9HUL I L F Do mR G R HQU LM HF HG R U G H E R UG D (OHPHQWR G ±W ±>[±@ FP λ SR ≥ ⇒ ⇒ ,WHP&DVR,,, GpDODUJXUDGRHQULMHFHGRUGHERUGD (OHPHQWR (QULMHFHGRUG ±W ± >[±@ FP ,V [ GW FP N FRQIRUPHWDEHOD ,D >λ SR @W >[@[ FP ' FPE FP ' E ⎛'⎞ ⎜ ⎟ ND ±⎝ E ⎠ ±[ ≤ ⎛,V ⎞ N ⎜⎜ ⎟⎟ ND ± ⎝ ,D ⎠ ± ≤ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ &RPR λ S QmRKDYHUi IODPEDJHPORFDO GHI FPODUJXUDHIHWLYDGRHQULMHFHGRUGH ERUGD GV [ GHI ≤ GHI 2QGHGV pDODUJXUDHIHWLYDUHGX]LGDGR HQULMHFHGRUGHERUGD ND N GV [ ≤ GHI GV FP EHI E λ S ≤ E F9HULILFDomRGD$OPD(OHPHQWR 1HVWDHWDSDDSRVLomRGD/LQKD1HXWUDGD 6HomR(IHWLYD/1HpGHWHUPLQDGDFRQVLGHUDQ GRVHXPSURFHVVRLWHUDWLYRFRQVHJXLQGRVHD FRQYHUJrQFLDTXDQGRDSRVLomRGD/1H GHXPD LWHUDomRQmRGLIHUHQFLDUPDLVGRTXHGDSR VLomRGD/1H GDLWHUDomRDQWHULRU 2VFiOFXORVGDVSURSULHGDGHVGDVHomRHIH WLYDGRSHUILOVmRUHDOL]DGRVHPSUHJDQGRVHR ³PpWRGROLQHDU´LVWRpWRGRRPDWHULDOpDGPLWLGR FRPRFRQFHQWUDGRQDOLQKDPpGLDGDVHomROL QKDHVTXHOHWRHRVHOHPHQWRVVmRWUDWDGRVLVR ODGDPHQWHFRPROLQKDVUHWDVSDUWHSODQDRX FXUYDVGREUDV2VYDORUHVDVVLPREWLGRVVmR PXOWLSOLFDGRVSHODHVSHVVXUDWGHPDQHLUDDRE WHUDVSURSULHGDGHVJHRPpWULFDVGHVHMDGDV Ψ σ σ 2QGH Ψ pDUHODomR σσ HPSUHJDGDQR FiOFXORGRFRHILFLHQWHGHIODPEDJHPORFDON N > Ψ @> Ψ @ &DVR³G´QDWDEHOD N >@>@ 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N1FP &RPSUHVVmR Ψ σ σ \FJ FP &DOFXODQGRDVSURSULHGDGHVGDVHomRHIHWLYD WHPVH N > Ψ @> Ψ @ EHI E λ S ≤ E EHI FP ≤ EF FP EHI FP EHI FP EHI EHI FPEF FP 6HJXQGDLWHUDomRFRQVLGHUDQGRDDOPD QmRWRWDOPHQWHHIHWLYD \FJ FP ,[¶ FP ,[ FP $SDUWHLQHIHWLYDGDDOPDp EQHJ FP 2PRPHQWRIOHWRUUHVLVWHQWHGHFiOFXORFRPEDVH QDIODPEDJHPODWHUDOFRPWRUomRp ∴ 05G N1FP 9HULILFDomRGDIODPEDJHPSRU GLVWRUomR \FJ FP &RP R REMHWLYR GH VLPSOLILFDU R GLPHQVLRQDPHQWRQR$QH[R'GD$%171%5 VmRDSUHVHQWDGDVDOJXPDVLQIRUPD o}HV~WHLVSDUDTXHVHMDPGLVSHQVDGDVDVYHUL ILFDo}HVGDIODPEDJHPSRUGLVWRUomR $R ILQDO GH QRYH LWHUDo}HV DOFDQoDVH D FRQYHUJrQFLDGHVHMDGDREWHQGR $WDEHOD'GDQRUPDEUDVLOHLUDDSUHVHQWD RVYDORUHVPtQLPRVGDUHODomR'EZ GHVHo}HV ([HPSORVGHGLPHQVLRQDPHQWR GRWLSR8HQULMHFLGRYLGHILJXUDVXEPHWLGDV jFRPSUHVVmRFHQWUDGDSDUDGLVSHQVDUDYHULIL FDomRGDIODPEDJHPSRUGLVWRUomRHDWDEHOD' DSUHVHQWDRVYDORUHVPtQLPRVGDUHODomR'EZGH VHo}HVGRWLSR8HQULMHFLGRH=HQULMHFLGRVXE PHWLGDVjIOH[mRFRPRPHVPRREMHWLYR 3DUDRSHUILO8H[[[WHPVH EI PP EZ PP ' PP W PP EIEZ EZW 'EZ $QDOLVDQGRDVUHODo}HVREWLGDVSRGHVH FRQFOXLUTXHILFDPGLVSHQVDGDVDVYHULILFDo}HV GD IODPEDJHP SRU GLVWRUomR SRU QmR FRUUHVSRQGHU DR PRGR FUtWLFR GR SHUILO 8H [[ TXDQGR VXEPHWLGR j FRPSUHVVmR FHQWUDGDHjIOH[mR &RQFOXVmR 2PRPHQWRUHVLVWHQWHGHFiOFXORpRPHQRU GRVPRPHQWRVGHWHUPLQDGRVFRPEDVHQRLQtFLR GHHVFRDPHQWRRXSDUDDIODPEDJHPODWHUDOFRP WRUomRRXVHMD 05G N1FP05G N1FP (QWmR 05G N1FP %DUUDVXEPHWLGDjIOH[mRFRPSRVWD $ IRUoDQRUPDO VROLFLWDQWHGH FiOFXORH R PRPHQWRIOHWRUVROLFLWDQWHGHFiOFXORGHYHPVD WLVID]HUDVVHJXLQWHVHTXDo}HVGHLQWHUDomR (TXDomR H (TXDomR 2QGH 1F6G p D IRUoD QRUPDO GH FRPSUHVVmR VROLFLWDQWHGHFiOFXORFRQVLGHUDGDFRQVWDQWHQD EDUUD 0[6G 0\6G VmR RV PRPHQWRV IOHWRUHV VROLFLWDQWHVGHFiOFXORQDVHomRFRQVLGHUDGDHP UHODomRDRVHL[RV[H\UHVSHFWLYDPHQWH 1F5G pDIRUoDQRUPDOGHFRPSUHVVmRUH VLVWHQWHGHFiOFXORFRQIRUPHLWHP 15G pDIRUoDQRUPDOGHFRPSUHVVmRUH VLVWHQWHGHFiOFXORFDOFXODGDFRQIRUPHLWHP WRPDQGRVH ρ 0[5G 0\5G VmRRVPRPHQWRVIOHWRUHVUH VLVWHQWHVGHFiOFXORHPUHODomRDRVHL[RV[H\ UHVSHFWLYDPHQWHFDOFXODGRVFRQIRUPHLWHP FRP&E 1H[ 1H\ VmR DV IRUoDV QRUPDLV GH IODPEDJHPHOiVWLFDHPUHODomRDRVHL[RV[H\ UHVSHFWLYDPHQWHFDOFXODGDVSRU 1H[ π (, [ (.[/[ ) H1H\ π (, \ (. / ) \ \ &P[&P\ VmRRVFRHILFLHQWHVGHHTXLYDOrQ FLDGHPRPHQWRQDIOH[mRFRPSRVWDHPUHODomR DRVHL[RV[H\UHVSHFWLYDPHQWH 3HUILO8H[[HW PP (VIRUoRVGHFiOFXORFRQVLGHUDGRV 1RUPDO1F6G N1 0RPHQWRIOHWRUHPUHODomRD[0[6G 0RPHQWRIOHWRUHPUHODomRD\0\6G &RPSULPHQWRVHIHWLYRVGHIODPEDJHPGDEDUUD .[ /[ PP.\ /\ PPH.W /W PP ÈUHD%UXWDGD6HomR7UDQVYHUVDOGR3HUILO$J FP 'LkPHWURGDDEHUWXUD PP 3DUDRPRQWDQWHFRQVLGHUDGRDDomRGR YHQWRJHUDPRPHQWRDSHQDVHPUHODomRDRHL[R [VLPSOLILFDQGRDVYHULILFDo}HV 4XDQWR DRV FRPSULPHQWRV HIHWLYRV GH IODPEDJHPGDEDUUDVmRFRQVLGHUDGDVDVPHV PDVREVHUYDo}HVIHLWDVQRH[HPSOR ,[,\VmRRVPRPHQWRVGHLQpUFLDGDVHomR EUXWDHPUHODomRDRVHL[RV[H\UHVSHFWLYDPHQ WH .[/[.\/\VmRRVFRPSULPHQWRVHIHWL YRVGHIODPEDJHPHPUHODomRDRVHL[RV[H\ UHVSHFWLYDPHQWH 1H[ π (, [ (.[/[) π × × (× ) N1 &RQVLGHURXVHSDUDHVWHH[HPSORRPHV PRPRQWDQWHGRH[HPSORDSUHVHQWDGRHP PDVVHPRPRPHQWRIOHWRUVROLFLWDQWHGHFiOFXOR 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