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⎛,V ⎞ ⎜⎜ ⎟⎟ G ≤ G HI ⎝ ,D ⎠ HI



 &RPR λ S QmRKDYHUi IODPEDJHPORFDOQRHOHPHQWR EHI FP

⎛  ⎞ ⎜ ⎟ [  ≤ G  HI ⎝ ⎠

GV FP $HI $J $LQHI $J FP $LQHI >± [± [ ± @[ FP $HI ± FP

 9HULILFDomR GR HQULMHFHGRU GH ERUGD (OHPHQWR  G ±W ±>[± @  FP 

([HPSORVGHGLPHQVLRQDPHQWR  F 'HWHUPLQDomRGH1F5G EHI [ 1F5G

ρ

$HI I\ γ

×  [ 

 [ 

FP ≤ E

FP EHI FP

1F5G N1 'HWHUPLQDomRGH15G 15G pDIRUoDQRUPDOGHFRPSUHVVmRUH VLVWHQWHGHFiOFXORFDOFXODGDFRQIRUPHLWHP WRPDQGRVH ρ  D 'HWHUPLQDomRGD7HQVmR σ ρI\DVHU DSOLFDGDQDVHomRWUDQVYHUVDOGRSHUILO 

 9HULILFDomRGD0HVD(OHPHQWR  2FiOFXORGDODUJXUDHIHWLYDGHHOHPHQWRV XQLIRUPHPHQWHFRPSULPLGRVFRPHQULMHFHGRUGH ERUGD p IHLWR FRQVLGHUDQGRVH DV SUHVFULo}HV FRQVWDQWHVHPHDVGHILQLo}HVDSUHVHQWD GDVQDILJXUD E ±W ±>[± @  FP 2YDORUGHUHIHUrQFLDGRtQGLFHGHHVEHOWH]

σ = ρI \ [ N1FP

UHGX]LGRGRHOHPHQWRλ SR pFDOFXODGRFRQIRU PHHTXDomR



E 'HWHUPLQDomRGDiUHDHIHWLYD$HI  9HULILFDomRGD$OPD(OHPHQWR  E ±W ±>[± @  FP N FDVR³D´QDWDEHOD 

ψ &DVRD

σ  σ  N 

λ SR  λ SR 

 

λ SR ≥  ⇒ ,WHP&DVR,,, (OHPHQWR (QULMHFHGRU G ±W ± >[± @ FP



GW 

  [  FP 

,D >λ SR @W >[ @[   FP ' FPE FP

(TXDomR   EHI E λ S

 



,V   

 

≤ E

(TXDomR 

 '   E  &iOFXORGRFRHILFLHQWHGHIODPEDJHPORFDON

GHERUGD  ND ±

±[  ≤



⎛,V ⎞ ⎜⎜ ⎟⎟ G ≤ G HI ⎝ ,D ⎠ HI GV pDODUJXUDHIHWLYDUHGX]LGDGRHQULMHFHGRUGH ERUGD GV

 

⎛,V ⎞ N  ⎜⎜ ⎟⎟ ND ±   ⎝ ,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 (QULMHFHGRU G ±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



F 9HULILFDomRGD$OPD(OHPHQWR  1HVWDHWDSDDSRVLomRGD/LQKD1HXWUDGD 6HomR(IHWLYD/1H pGHWHUPLQDGDFRQVLGHUDQ GRVHXPSURFHVVRLWHUDWLYRFRQVHJXLQGRVHD FRQYHUJrQFLDTXDQGRDSRVLomRGD/1H GHXPD LWHUDomRQmRGLIHUHQFLDUPDLVGRTXHGDSR

VLomRGD/1H GDLWHUDomRDQWHULRU 2VFiOFXORVGDVSURSULHGDGHVGDVHomRHIH WLYDGRSHUILOVmRUHDOL]DGRVHPSUHJDQGRVHR ³PpWRGROLQHDU´LVWRpWRGRRPDWHULDOpDGPLWLGR FRPRFRQFHQWUDGRQDOLQKDPpGLDGDVHomROL QKDHVTXHOHWR HRVHOHPHQWRVVmRWUDWDGRVLVR ODGDPHQWHFRPROLQKDVUHWDVSDUWHSODQD RX FXUYDVGREUDV 2VYDORUHVDVVLPREWLGRVVmR PXOWLSOLFDGRVSHODHVSHVVXUDWGHPDQHLUDDRE WHUDVSURSULHGDGHVJHRPpWULFDVGHVHMDGDV

Ψ



σ σ 



2QGH Ψ pDUHODomR σσ HPSUHJDGDQR FiOFXORGRFRHILFLHQWHGHIODPEDJHPORFDON N > Ψ @> Ψ @ &DVR³G´QDWDEHOD  N > @> @ 

27HRUHPDGR(L[R3DUDOHORpXWLOL]DGRSDUD RVFiOFXORVGRPRPHQWRGHLQpUFLDGDVHomRHIH WLYD



&RPRλ S !  SRGHUi RFRUUHU IODPEDJHPORFDOQDDOPDGRSHUILO3RUWDQWRGHYH VHUFDOFXODGDDODUJXUDHIHWLYDGHVWHHOHPHQWR EHIFRQIRUPHVHJXH EHI FP ≤ E& FP

\FJ 

EHI 

FP

EHI FP −Ψ 

EHI FP EHIHEHIVmRDVODUJXUDVHIHWLYDVLQGLFDGDV QDILJXUD EHI EHI FPEF FP 6HJXQGDLWHUDomRFRQVLGHUDQGRDDOPDQmR WRWDOPHQWHHIHWLYD $SDUWHLQHIHWLYDGDDOPDp

)LJXUD  ± 7HQV}HV QD DOPD GR SHUILO HOHPHQWR 

σ  [

(− ) 

EQHJ EHI EHI ±EF FP

N1FP

&RPSUHVVmR  σ  [

(− ) 

N1FP

7UDomR 

([HPSORVGHGLPHQVLRQDPHQWR  2PyGXORGHUHVLVWrQFLDHOiVWLFRGDVHomR HIHWLYDHPUHODomRjILEUDFRPSULPLGDpFDOFXOD GRFRPEDVHQDVODUJXUDVHIHWLYDVGRVHOHPHQ WRVFRQIRUPHVHJXH

:HI = FP

(TXDomR ∴ 05G N1FP \FJ 

FP

2 HL[R QHXWUR PXGRX GH FP SDUD FPUHVXOWDQGRHPXPDGLIHUHQoDGH $FRQYHUJrQFLDGHVHMDGDIRLREWLGD &DOFXODQGRDVSURSULHGDGHVGDVHomRHIH WLYDWHPVH

0RPHQWRFDOFXODGRFRPEDVHQD IODPEDJHPODWHUDOFRPWRUomR)/7  2PRPHQWRIOHWRUUHVLVWHQWHGHFiOFXORUHIH UHQWHjIODPEDJHPODWHUDOFRPWRUomRWRPDQGR VHXPWUHFKRFRPSUHHQGLGRHQWUHVHo}HVFRQWL GDVODWHUDOPHQWHGHYHVHUFDOFXODGRSRU 05G >ρ)/7 :FHI I\@ γ

γ  

(TXDomR  :FHI pRPyGXORGHUHVLVWrQFLDHOiVWLFRGD VHomR HIHWLYD HP UHODomR j ILEUD FRPSULPLGD FDOFXODGRFRPEDVHQDVODUJXUDVHIHWLYDVGRVHOH PHQWRVFRQIRUPHLWHPDGRWDQGR σ ρ)/7I\ 2EWLGRRYDORUGH σSURFHGHVHRVFiOFXORV GHIRUPDDQiORJDjGRLWHPXWLOL]DQGRVHR SURFHVVRLWHUDWLYRSDUDDGHWHUPLQDomRGDSRVL omRGD/1H GDVHomRHIHWLYDHGDVSURSULHGDGHV JHRPpWULFDVFRUUHVSRQGHQWHV \FJ FP ,[¶ FP ,[ ,[¶ W FP ,[¶pRPRPHQWRGHLQpUFLDGDVHomRHIHWLYD FRQVLGHUDQGRVHR³PpWRGROLQHDU´ ,[pRPRPHQWRGHLQpUFLDGDVHomRHIHWLYD GRSHUILO 

D 9HULILFDomRGR)ODQJH&RPSULPLGR(OH PHQWR  3DUDEDUUDVFRPVHomRGXSODPHQWHVLPp WULFDRXPRQRVVLPpWULFDVXMHLWDVjIOH[mRHPWRU QRGRHL[RGHVLPHWULDHL[R[ HGHDFRUGRFRP DV SUHVFULo}HV DSUHVHQWDGDV QR LWHP  WHPVH 0H &EU1H\1HW 

(TXDomR

0H pRPRPHQWRIOHWRUGHIODPEDJHPODWHUDO FRPWRUomRHPUHJLPHHOiVWLFR &RQIRUPH LWHP  SDUD SHUILV PRQRVVLPpWULFRVWHPVH

λR pRtQGLFHGHHVEHOWH]UHGX]LGRGDEDUUD ρ)/7 = ρ )/7 p R IDWRU GH UHGXomR DVVRFLDGR j IODPEDJHPODWHUDOFRPWRUomRGDEDUUD

1H\ 



N1

1H\pDIRUoDQRUPDOGHIODPEDJHPHOiVWLFD SRUIOH[mRHPUHODomRDRHL[R\

$ WHQVmR GH FRPSUHVVmR DVVRFLDGD DR PRPHQWRFUtWLFRGHIODPEDJHPODWHUDOFRPWRUomR p

σ = ρ )/7 I\ = × = N1FP  1HW  U R



RQGH UR  U[ U\ [R

&RQVLGHUDQGRVHHVWDWHQVmRDSOLFDGDDR HOHPHQWRWHPVH E ±W ±>[± @  FP

1HW    [

λ SR  λ SR 



 



N1 1HW pDIRUoDQRUPDOGHIODPEDJHPHOiVWLFD SRUWRUomR

λ SR ≥  ⇒ &DVR,,,

&E pRFRHILFLHQWHGHHTXLYDOrQFLDGHPR PHQWRQDIOH[mRTXHDIDYRUGDVHJXUDQoDpWR PDGRLJXDODQHVWHH[HPSOR

(OHPHQWR (QULMHFHGRU G ±W ± >[± @ FP

0H &EU1H\1HW  0H [[[   N1FP :F :[ FP

,V 

GW 

FP



,D >λ SR @W >[ @[   FP ' FPE FP

3DUD λ  ρ )/7 ±λ 

'  E





([HPSORVGHGLPHQVLRQDPHQWR  GHI FP

⎛'⎞ ND ± ⎜ ⎟ ±[  ≤ ⎝ E ⎠ 

GV

⎛,V ⎞ ⎜⎜ ⎟⎟ G ≤ G HI ⎝ ,D ⎠ HI

 

⎛,V ⎞ N  ⎜⎜ ⎟⎟ ND ±   ⎝ ,D ⎠ ±   ≤ ND 

[

GV 

[  ≤ GHI 

GV FP

N 

F 9HULILFDomRGD$OPD(OHPHQWR   

3ULPHLUD LWHUDomR FRQVLGHUDQGR D DOPD WRWDOPHQWHHIHWLYD



  EHI E λ S EHI [

≤ E  ⎞  ⎛ ⎟ FP ≤ E [ ⎜−  ⎝ ⎠

FP EHI FP E  9HUL I LF DomR  G R  (QULM HF HG R U G H %R UG D (OHPHQWR 

\FJ FP

G ±W ±>[± @  FP N 





 &RPR λ S     QmR KDYHUi IODPEDJHPORFDOQRHQULMHFHGRU



)LJXUD   7HQV}HV QD DOPD GR SHUILO HOHPHQWR 

&RQVLGHUDQGRVHDVHPHOKDQoDHQWUHWULkQ JXORVUHWkQJXORVWHPVH

σ  N1FP 7UDomR 

σ  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  GRWLSR8HQULMHFLGRYLGHILJXUD VXEPHWLGDV 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 GHYLGRjDomRGRYHQWR

3DUDRVFiOFXORVWHPVH &RPSUHVVmR 1F6G N1 0[6G N1FP 0\6G  1F5G N1 15G N1 0[5G N1FP 1H[ N1 &P[ DIDYRUGDVHJXUDQoD

'HWHUPLQDomRGH1F5G $IRUoDQRUPDOGHFRPSUHVVmRUHVLVWHQWHGH FiOFXOR 1F5G GHYHVHUFDOFXODGDSRU 1F5G

γ  

(TXDomR 

5HVXOWDQGR

D  'HWHUPLQDomR  G D 7HQV mR σ ρI\ D VHU DSOLFDGDQDVHomRWUDQVYHUVDOGRSHUILO 2.

2.

$IRUoDQRUPDOGHIODPEDJHPHOiVWLFD1HGH XPSHUILOFRPVHomRPRQRVVLPpWULFDFXMRHL[R [ pRHL[RGHVLPHWULDpRPHQRUYDORUGHQWUHRV REWLGRVSRUIOH[mRRXSRUIOH[RWRUomR •

  0RQWDQWH GH [[[ FRP DE HU W X U D Q D DO P D V X E P HW L G R  j FRPSUHVVmRFHQWUDGD 'DGRVJHUDLV

ρ $HI I\  γ

1H[ 

)RUoDQRUPDOGHIODPEDJHPHOiVWLFDSRU IOH[mRHPUHODomRDRHL[R[



N1



([HPSORVGHGLPHQVLRQDPHQWR •

)RUoDQRUPDOGHIODPEDJHPHOiVWLFDSRU IOH[mRHPUHODomRDRHL[R\

π (, \

(. / )

1H\



\ \

π  ×  × 

(× )



N1

λR 

$I\

×   



1H

(TXDomR 

•

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1HW

&RPR1H[W N11H\ N1 ⇒ 1H N1

UR  U[ U\ [R (TXDomR 

2QGH λR pRtQGLFHGHHVEHOWH]UHGX]LGRGD EDUUD 1DWDEHODYrVHTXHDFXUYDGHUHVLV WrQFLDjFRPSUHVVmRDVVRFLDGDjIODPEDJHPSRU IOH[mRSDUDRSHUILO8HpDFXUYD³E´RXVHMD

α



1HW 

α pRIDWRUGHLPSHUIHLomRLQLFLDO

⎡ π  × × ⎤ ⎫⎪  ⎧⎪     ×     + ⎨ ⎢ ⎥⎬   [⎪⎩ ⎣ (× ) ⎦ ⎪⎭

β

N1 •

)RUoDQRUPDOGHIODPEDJHPHOiVWLFDSRU IOH[RWRUomR

 ⎡ ⎛ [R ⎞ ⎤⎥ ⎢ 1H[1HW>− ⎜⎜ ⎟⎟ @ 1H[ + 1HW ⎢ ⎝ UR ⎠ ⎥ − − 1H[W =   ⎢ ⎥  1H[ + 1HW  ⎛ [R ⎞ ⎢ ⎥ >− ⎜⎜ ⎟⎟ @⎢ ⎥ ⎝ UR ⎠ ⎢⎣ ⎥⎦

(TXDomR ⎡ ⎡ ⎛ − ⎞ ⎤ ⎤ ⎢ × × × ⎢− ⎜ ⎟ ⎥⎥ ⎢ ⎝  ⎠ ⎦⎥ ⎥ +  ⎢ ⎣ ⎢− − ⎥ 1H[W = +   ⎡ ⎛ − ⎞ ⎤ ⎢ ⎥ × ⎢− ⎜ ⎟ ⎥⎢ ⎥ ⎥⎦ ⎣⎢ ⎝  ⎠ ⎦⎥ ⎢⎣

1H[W N1



[

(

)

× + α λR −  + λR (TXDomR

]



β pRSDUkPHWURHPSUHJDGRQRFiOFXORGRIDWRU GHUHGXomRDVVRFLDGRjIODPEDJHP ρ  ρ

[β +



(β



− λ R

)]

   (TXDomR

ρ pRIDWRUGHUHGXomRDVVRFLDGRjIODPEDJHP GDEDUUD σ = ρI \ [ N1FP E 'HWHUPLQDomRGDiUHDHIHWLYD$HI  9HULILFDomRGD$OPD(OHPHQWR  E ±W ±>[± @  FP N FDVR³D´QDWDEHOD

ψ

&DVRD

σ  σ 

2YDORUGHUHIHUrQFLDGRtQGLFHGHHVEHOWH]

N 

λS =

E W ⎡ ⎛ N(⎞ ⎤ ⎢ ⎜ ⎟ ⎥ ⎝ σ ⎠ ⎦⎥ ⎣⎢



  ⎡ ⎛[⎞ ⎤ ⎟⎥ ⎢ ⎜ ⎝  ⎠ ⎥⎦ ⎢⎣

E ±W ±>[± @  FP

UHGX]LGRGRHOHPHQWRλ SR pFDOFXODGRFRQIRUPH HTXDomR

 

E W

λ SR  λ SR ⎡ ⎛ (⎞ ⎤ ⎢ ⎜ ⎟ ⎥ ⎝ σ ⎠ ⎥⎦ ⎣⎢



  ⎡ ⎛⎞ ⎤ ⎟⎥ ⎢ ⎜ ⎝  ⎠ ⎥⎦ ⎢⎣

  

(TXDomR   λ SR  ⇒ ,WHP&DVR,, 3DUDRFiOFXORGDODUJXUDHIHWLYDGRHOHPHQ WRFRPDEHUWXUDUHFRUUHVHDRLWHP%GDV SUHVFULo}HVGR$,6, TXHWUDWDGRVHOHPHQ WRV HQULMHFLGRV XQLIRUPHPHQWH FRPSULPLGRV H FRP DEHUWXUDV FLUFXODUHV (TXDo}HV % H %  ⎡

E⎢ −

⎢ EHI = ⎣

  'K ⎤ − ⎥ λ S E ⎥⎦ ≤ E±'K

λ S

'K pRGLkPHWURGDDEHUWXUD PP ⎡   ×  ⎤ × ⎢− −   ⎥⎦ ⎣ EHI = 

FP ≤

± FP EHI FP  9HULILFDomRGD0HVD(OHPHQWR  2 FiOFXOR GD ODUJXUD HIHWLYD GH HOHPHQWRV XQLIRUPHPHQWHFRPSULPLGRVFRPHQULMHFHGRUGH ERUGD p IHLWR FRQVLGHUDQGRVH DV SUHVFULo}HV FRQVWDQWHVHPHDVGHILQLo}HVDSUHVHQWDGDV QDILJXUD

(OHPHQWR (QULMHFHGRU G ±W ± >[± @ FP

,V 

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