Mario Šavar - Zbirka rešenih ispitnih zadataka iz mehanike fluida.pdf

August 24, 2017 | Author: Danilo Mrdak | Category: N/A
Share Embed Donate


Short Description

Mehanika fluida...

Description



                    



                

  69(8ý,/,â7(8=$*5(%8 )$.8/7(76752-$5679$,%52'2*5$'1-(





0DULRâDYDU

=%,5.$5,-(â(1,+,63,71,+ =$'$7$.$,=0(+$1,.()/8,'$, 

                

=DJUHEWUDYDQM

,,  

,,,  

     3UHGJRYRU  

6DGUåDM RYH ]ELUNH þLQH ULMHãHQL ]DGDFL V QXPHULþNRJ GLMHOD LVSLWD L] NROHJLMD 0HKDQLND )OXLGD , RGUåDQLK X    L  JRGLQL 2YD ]ELUND QLMH ]DPLãOMHQD NDR HGXNDFLMVND ]ELUND ]DGDWDND X RYRM ]ELUFL QHPD ODNãLK LOXVWUDFLMVNLK SULPMHUD GHWDOMQLK REMDãQMHQMD WH RVQRYD WHRULMH  YHü NDR SRPRü VWXGHQWLPD SUL SULSUHPDQMX LVSLWD 1DGDP VH GD üH LP RYDM PDWHULMDO SRPRüL GD VH VWXGHQWL ãWR NYDOLWHWQLMH SULSUHPH ]D LVSLW L GD JD XVSMHãQR SRORåH 2YDMPDWHULMDOQLMHSUHJOHGDQOHNWRULUDQQLWLUHFHQ]LUDQSDNDRWDNDYYMHURMDWQRVDGUåLQHNHSRJUHãNHQDNRMLPD VH þLWDRFLPD XQDSULMHG LVSULþDYDP 2E]LURP GD SRVWRML SRWUHED ]D RYDNYLP PDWHULMDORP D SRVWXSDN LVSUDYOMDQMD L REMDYOMLYDQMDMHVSRULPXNRWUSDQ]ELUNDüHVHREMDYLWLQDZHEVWUDQLFDPDXRYDNYRPREOLNX=ELUNDMH]DSLVDQDX 3') IRUPDWX WH MH ]D QMHQR þLWDQMH SRWUHEDQ RGJRYDUDMXüL VRIWZDUH $FUREDW UHDGHU  6YH þLWDRFH NRML VX SURQDãOL SRJUHãNXLOLLPDMXQHNXVXJHVWLMXQDVDGUåDMRYH]ELUNHPROLPGDPLWRMDYHQDH±PDLODGUHVXPDULRVDYDU#IVEKU =ELUND WH QHNL GUXJL PDWHULMDOL ELW üH REMDYOMHQL QD ZHE VWUDQLFDPD .DWHGUH ]D 0HKDQLNX IOXLGD KWWSZZZIVEKUK\GUR 2YD]ELUNDQDVWDODMHNRPELQDFLMRPUD]OLþLWLKVRIWYHUVNLKDODWD :RUG0DWK7\SH0DWK&DG'3')FUHDWRU  NRMLVXQLVXXSRWSXQRVWLNRPSDWLELOQLDQHNHPDWHPDWLþNHVLPEROHUD]OLþLWRLQWHUSUHWLUDMX :RUGRYDJUþNDVORYDM LT0DWKFDG]DSLVXMHILTD0DWK7\SH I L- 0DWK7\SHRYXR]QDNX]DPDVHQLSURWRN P QHPRJXüHMH]DSLVDWLX 0DWK&DGXLWG =ERJWRJDVXQDVWDOHQHNHPDQMHJUHãNHNRMHVHQDGDPGDüXXVSMHWLRWNORQLWL      =DJUHEWUDYDQM







$XWRU

,9 

6DGUåDM 

6DGUåDM ,9 3RSLVR]QDND9,,, 'LPHQ]LMVNDDQDOL]D   ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  +LGURVWDWLND   ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  5HODWLYQRPLURYDQMH   ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN 

9 ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  %HUQRXOOLMHYDMHGQDGåED  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VWMHFDQMH   ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  &MHYRYRG  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  .ROLþLQDJLEDQMD  

9, ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,]HQWURSVNRVWUXMDQMH  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  5RWLUDMXüDVWUXMQDFLMHY  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  ,VSLW]DGDWDN  3ULORJ,VSLWQLURNRYL  ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ  

9,, ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   ,VSLWRGUåDQ   3ULORJ7DEOLFDL]HQWURSVNRJVWUXMDQMD  3ULORJ0RRG\HYGLMDJUDP   

  

9,,, 

3RSLVR]QDND 

)L]LNDOQDYHOLþLQD

2]QDND

SRYUãLQD

$6

/

P

EU]LQD]YXND

F

/7

PV

SURPMHU

'G

/

P

VLOD

)

0/7

JUDYLWDFLMD

J



/7 

PV

WHåLQVNLSURWRN

* 

0/7

1V

YROXPHQVNLPRGXOHODVWLþQRVWL

.

0/7

3D

  



-HGLQLFD X 6, VXVWDYX

1

PDVHQLSURWRN

TPDVHQL

07 

NJV

PRPHQWVLOH

0

0/7

1˜P

 

VQDJD

3

0/ 7 

:

WODN

S

0/7

3D

YROXPHQVNLSURWRN

4

/7 

PV

SOLQVNDNRQVWDQWD

5

/74

- NJ˜. 

SRWHQFLMDOPDVHQHVLOH

8

/7

PV

VSHFLILþQDXQXWUDãQMDHQHUJLMD

X

/7

-NJ

YROXPHQIOXLGD

9

/

P

EU]LQDVWUXMDQMDIOXLGD

Y

/7

 

 

PV

UDGVLOH

:

0/ 7 

-

JHRGHWVNDYLVLQD

]

/

P

JXVWRüDIOXLGD

U

0/ 

NJP

NRHILFLMHQWNLQHPDWLþNHYLVNR]QRVWL

Q

/7

PV

NRHILFLMHQWGLQDPLþNHYLVNR]QRVWL

P

0/7

3D˜V





EU]LQDYUWQMH

Z

7 

UDGV

NRHILFLMHQWWUHQMD

O





QDSUH]DQMH

W

0/7

1P

NXW

DEJGI



UDG

]UDþQRVW

H

/

NRHILFLMHQWSRYUãLQVNHQDSHWRVWL 

'LPHQ]LMD

V

P 

07 

1P

'LPHQ]LMVNDDQDOL]D 

             

'LPHQ]LMVNDDQDOL]D                   



    =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

,VSLW]DGDWDN

%U]LQDWRQMHQMDYQHNRJWLMHODXIOXLGXRYLVLRJUDYLWDFLMLJYROXPHQXWLMHOD9JXVWRüLWLMHODUJXVWRüLIOXLGDU WHRYLVNR]QRVWLIOXLGDP3ULPMHQRPSWHRUHPDRGUHGLWHRSüLREOLN]DYLVQRVWLEU]LQHYRGSUHRVWDOLKYHOLþLQD





9HOLþLQD

6LPERO

'LPHQ]LMD

9ROXPHQWLMHOD

9

/

*UDYLWDFLMD

J

/7

*XVWRüDWLMHOD

U

0/

%U]LQDWRQMHQMD

Y

/7

*XVWRüDIOXLGD

U

0/

9LVNR]QRVW

P

0/7

%URMYHOLþLQDQ GLPHQ]LMDN EURM3LSDUDPHWDUDQN  =DGLPHQ]LRQRQH]DYLVQHYHOLþLQHRGDELUHVHVNXS9JLU

9 J U [



\

]

/ /7 0/  [

\



 ]

0  /7 

0  ] ]   /   [  \  ] [  7   \

\ 

.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ

S

Y 9

J U

S

/7  / /7 

[

\

]

[

\

0/

 ]

0  /7 

0  ] ]  /    [  \  ] [    7    \ \   Y S J9 S

P 9

S

0/7  / /7 

[

J U \

[

0   ]

S

S

\

0/

 ]

0  /7 

] 

/     [  \  ] 7    \

]

[  

\  

P U J9

U U





)XQNFLRQDOQD]DYLVQRVWEU]LQHWRQMHQMDYRGSUHRVWDOLKYHOLþLQD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

§ P U · J9 I ¨  ¸ ¨ U J9 U ¸ © ¹

J  9 I S   S 

Y 

,VSLW]DGDWDN

6LOD RWSRUD 5 JLEDQMD WLMHOD X YLVNR]QRP VWODþLYRP IOXLGX ]DYLVLR RG GXOMLQH WLMHOD / JXVWRüH IOXLGD U GLQDPLþNR NRHILFLMHQWD YLVNR]QRVWL P YROXPHQVNRJ PRGXOD HODVWLþQRVWL . L EU]LQH JLEDQMD WLMHOD 8 3ULPMHQRP 3L WHRUHPDRGUHGLWHRSüLREOLN]DYLVQRVWLVLOHRWSRUD5RGSUHRVWDOLKYHOLþLQD=DGLPHQ]LRQRQH]DYLVDQVNXSX]PLWHU 8L/ 9HOLþLQD

6LPERO

'LPHQ]LMD

'XOMLQDWLMHOD

/

/

%U]LQD

8

/7

*XVWRüD

U

0/

6LODRWSRUD

5

0/7

9LVNR]QRVW

P

0/7

9ROPRGXOHODVWLþQRVWL

.

0/7

 %URMYHOLþLQDQ GLPHQ]LMDN EURM3LSDUDPHWDUDQN  =DGLPHQ]LRQRQH]DYLVQHYHOLþLQHRGDELUHVHVNXS/8LU



/ 8 U

/

[

[

\

]

/7 0/ \





]

0 /7 





0  ] ]   /  [  \  ] [  7 \

\ 

.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ

S

5 / 8

S

0/7  / /7 

[

\

U

]

[

0   ]

\

 ]

] 

/    [  \  ] 7   \

\ 



S

P / 8

S

0/7  / /7 

\

U [

0   ]



] \

0/

 ]

] 

/     [  \  ] 7    \

  

S

[

0  /7 

[ 

5 U8  /

S

0/

0  /7   

[ 

 

\ 

 

P U /8

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



'LPHQ]LMVNDDQDOL]D 

S

. / 8

S

0/7  / /7 

[

U

\

]

[

0   ]

0/

 ]

] 

/     [  \  ] 7   \ S

\

[ 

\ 

0  /7    





. U8 

)XQNFLRQDOQD]DYLVQRVWVLOHRWSRUD5RGSUHRVWDOLKYHOLþLQD

5

U8  / I S   S 

§ P . · U8  / I ¨  ¸ U 'Y U 8 ¹ © 



,VSLW]DGDWDN

8VOLMHG URWDFLMH FLOLQGUD RNR YODVWLWH RVL NXWQRP EU]LQRP Z GROD]L GR SUHWYRUEH GLMHOD PHKDQLþNH HQHUJLMH X

WRSOLQXNDRSRVOMHGLFDWUHQMD$NREU]LQDSUHWYRUEHPHKDQLþNHHQHUJLMHXWRSOLQX 4 ]DYLVLRGYLVNR]QRVWLIOXLGDP SURPMHUDFLOLQGUD'GXOMLQHFLOLQGUD/LNXWQHEU]LQHURWDFLMHZRGUHGLWHSULPMHQRPGLPHQ]LRQHDQDOL]HNROLNRüHVH SXWDSRYHüDWL LOLVPDQMLWL EU]LQDSUHWYRUEHPHKDQLþNHHQHUJLMHXWRSOLQXDNRVHNXWQDEU]LQDURWDFLMHSRYHüDGYD SXWDX]RVWDOHQHSURPLMHQMHQHSDUDPHWUH  9HOLþLQD

6LPERO

'LPHQ]LMD

3URPMHUFLOLQGUD

'

/

.XWQDEU]LQDURWDFLMH

Z

7

9LVNR]QRVW

P

0/7

'XOMLQDFLOLQGUD

/

/

4 

0/7

%U]LQD SUHWYRUEH PHKDQLþNH HQHUJLMHXWRSOLQVNX 

%URMYHOLþLQDQ GLPHQ]LMDN EURM3LSDUDPHWDUDQN  =DGLPHQ]LRQRQH]DYLVQHYHOLþLQHRGDELUHVHVNXS'ZLP



Z ' P [

\

]

7 / 0/ 7  [

\



 ]

0  /7 

0    ] ]    /  \  ] \   7  []

[ 



.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

S

[ \ ] 4 Z ' P

S

0/7  7  / [

\

0/ 7

 ]



0  /7 

0    ] ]  /    \  ] \ 

    

7   [  ] 4 S   Z 'P



[ 

/ '

S

%H]GLPHQ]LMVNL3LSDUDPHWDUPRUDRVWDWLNRQVWDQWDQSDDNRVHNXWQDEU]LQDURWDFLMHSRYHüDGYDSXWDX]RVWDOH QHSURPLMHQMHQHSDUDPHWUHEU]LQDSUHWYRUEHPHKDQLþNHHQHUJLMHXWRSOLQXSRYHüDWLüHVHþHWLULSXWD

S S



4  4

FRQVW § 4 · ¨   ¸ © Z ' P ¹ Z

§ 4 · ¨   ¸ © Z ' P ¹







Z





,VSLW]DGDWDN

8]SUHWSRVWDYNXGDNRGPDOHEU]LQHYWRQMHQMDWLMHODXPLUXMXüHPIOXLGDWDEU]LQDQH]DYLVLRGJXVWRüHIOXLGD YHü ]DYLVL RG WHåLQH * WLMHOD QMHJRYH NDUDNWHULVWLþQH OLQHDUQH GLPHQ]LMH / WH NRHILFLMHQWD GLQDPLþNH YLVNR]QRVWL P IOXLGD $NR MH L]PMHUHQR GD NXJOLFD SURPMHUD '   PP WRQH EU]LQRP Y   FPPLQ X YRGL NRHILFLMHQWD GLQDPLþNHYLVNR]QRVWLP 3DVRGUHGLWHNRMRPEU]LQRPYüHWRQXWLNXJOLFDSURPMHUD' PP QDþLQMHQDL] LVWRJPDWHULMDODNDRLNXJOLFDSURPMHUD' XXOMXNRHILFLMHQWDGLQDPLþNHYLVNR]QRVWLP 3DV  9HOLþLQD

6LPERO

'LPHQ]LMD

%U]LQDWRQMHQMD

Y

/7

7HåLQDWLMHOD

*

0/7

3URPMHUNXJOLFH

'

/

9LVNR]QRVWIOXLGD

P

0/7

 $NR ]D  GLPHQ]LRQR QH]DYLVDQ VNXS YHOLþLQD RGDEHUHPR * ' P PRUDPR SURYMHULWL GD OL VX RYH YHOLþLQH GLPHQ]LRQRQH]DYLVQH

0 / 7 ' P * / 0/ 7 0/7 0 / 7 0  \  ] ]   /  [  \  ] [  7   ]  \ \    [

[





 \

\

]

 ]

 



.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ %URMYHOLþLQDQ DEURMGLPHQ]LRQRQH]DYLVQLKYHOLþLQDN ]QDþLGDSRVWRMLQ±N 3LSDUDPHWDU

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

Y ' P * S /7 / 0/ 7 0/7 0 / 7 0  \  ] ]  /    [  \  ] [  7     \   ] \  Y'P S * [

S

\

[





]



 \

 ]

 







=DYULMHGQRVWL]DGDQHXWHNVWX]DGDWND S

Y˜ '˜ P

Y˜ '˜ P 

Y ˜'˜P

*

*

*



7HåLQDNXJOLFHUDþXQDVHSUHPDL]UD]X *

U 



˜' ˜S

U

*



 ˜ ' ˜ S



*

'

*

'





%U]LQDWRQMHQMDNXJOLFHL]QRVL Y

Y ˜'˜





P ˜ *

Y



'˜ P  ˜ *

Y ˜ '˜

P ˜ '



Y

'˜ P  ˜ '



 u  PV





 

,VSLW]DGDWDN



V

J

'RPHW WRSRYVNRJ ]UQD V RYLVL R SRþHWQRM EU]LQL ]UQD Y  NXWX WRSRYVNH FLMHYL D YLVLQD EUGD K L JUDYLWDFLML J 3ULPMHQR GLPHQ]LRQH DQDOL]H RGUHGLWH EH]GLPHQ]LMVNH S SDUDPHWUH WH QD LWH ]DYLVQRVW WLK EH]GLPHQ]LMVNLK SDUDPHWDUD ) S  S  «  SRPRüX MHGQDGåEHNRVRJKLFD

D K

   9HOLþLQD

6LPERO

'LPHQ]LMD

9LVLQDEUGD

+

/

*UDYLWDFLMD

*

/7

%U]LQD]UQD

Y

/7

'RPHW]UQD

V

/

.XWFLMHYL

D



 S D







S VK

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D  S

[

Y˜ J ˜ K

\

/˜ 7   ˜ /7  [˜ / \

  

0 / 7

/[\  7[ 

[  \ 

S

Y J˜ K 

,]MHGQDGåEHNRVRJKLFDVOLMHGL Y˜ FRV D ˜ W

[

]

V

W

K  V˜ WDQ D 

Y˜ FRV D

J

K  Y˜ VLQ D ˜ W 



˜W





J˜ V

˜ Y˜ FRV D







3DMHIXQNFLRQDOQD]DYLVQRVWSDUDPHWDUD 

V K



˜ WDQ D 



) S  S  S



J˜ K˜ V

˜ K ˜ Y˜ FRV D 



  S˜ WDQ S 









S 



˜ S ˜ FRV S







,VSLW]DGDWDN

7ODN S QD NUDMX KRUL]RQWDOQH FLMHYL NUR] NRMX IOXLG VWUXML X ODPLQDUQRP UHåLPX VWUXMDQMD RYLVL R WODNX QD SRþHWNXFLMHYLSWDQJHQFLMDOQRPQDSUH]DQMXQDVWMHQFLFLMHYLWZSURPMHUXFLMHYL'WHGXOMLQLFLMHYL/3ULPMHQRP GLPHQ]LRQHDQDOL]HRGUHGLWH]DYLVQRVWWODNDSRGSUHRVWDOLKYHOLþLQD  9HOLþLQD

6LPERO

'LPHQ]LMD

7ODN

S

0/7

7DQJHQFLMDOQRQDSUH]DQMH

WZ

0/7

'XOMLQLFLMHYL

/

/

7ODN

S

0/7

3URPMHUXFLMHYL

'

/

 $NR]DGLPHQ]LRQRQH]DYLVDQVNXSRGDEHUHPRWODNSLSURPMHUFLMHYL'RGQ YHOLþLQDPRJXüHMHQDþLQLWLQ N 3LSDUDPHWUD 

S

S S

S 

WZ S

S 

/ '



)L]LNDOQD]DYLVQRVWPRåHVHSULND]DWLSRPRüXVOMHGHüHJL]UD]D

) S   S   S 



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 



) S   S  

LOLS  

§WZ / ·  ¸ © S ' ¹

S

S) ¨

 

,VSLW]DGDWDN

%ULQNPDQRY EURM 1% þHVWR NRULãWHQ SUL DQDOL]L VWUXMDQMD RUJDQVNLK IOXLGD MH RGQRV GLVLSDFLMH L WRSOLQVNH SURYRGOMLYRVWLXIOXLGX%URMMH%H]GLPHQ]LMVNLSDUDPHWDUQDVWDRNRPELQDFLMRPGLQDPLþNRJNRHILFLMHQWDYLVNR]QRVWL P EU]LQH Y WRSOLQVNH YRGOMLYRVWL O L WHPSHUDWXUH IOXLGD 7 2GUHGLWH %ULQNPDQRY EURM SRG SUHWSRVWDYNRP GD MH XWMHFDMYLVNR]QRVWLOLQHDUDQ  9HOLþLQD

6LPERO

'LPHQ]LMD

'LQDPLþNLNRHILFLMHQWYLVNR]QRVWL

P

0/7

%U]LQD

Y

/7

7RSOLQVNDYRGOMLYRVW

O

0/7T

7HPSHUDWXUDIOXLGD

7

T



1%

P Y [ O \7 ]

0  /7  0 / 7 T



0/ 7  /7  0/7  T  





[

  \    [  \    [   \  \  ]





\

T ] 

 5MHãDYDQMHPVXVWDYDL]UDþXQDYDMXVHHNVSRQHQWLX%ULQNPDQRYXEURMX[ \ L] .RQDþQLL]JOHG EH]GLPHQ]LVNRJ%ULQNPDQRYRJEURMDMH 

1%

P Y  O7

    

,VSLW]DGDWDN

3ULPMHQRP GLPHQ]LMVNH DQDOL]H RGUHGLWH IXQNFLRQDOQX ]DYLVQRVWYHOLþLQHNDSOMLFH GQDL]OD]XL]VSUHMVDSQLFH DNR MH SR]QDWR GD YHOLþLQD NDSOMLFH RYLVL R SURPMHUX VDSQLFH ' EU]LQL Y X VDSQLFL WH VYRMVWYLPD IOXLGD JXVWRüL U YLVNR]QRVWLPLNRHILFLMHQWXSRYUãLQVNHQDSHWRVWLV =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

 9HOLþLQD

6LPERO

'LPHQ]LMD

3URPMHUVDSQLFH

'

/

%U]LQD

Y

/7

*XVWRüD

U

0/

3URPMHUNDSOMLFH

G

/

9LVNR]QRVW

P

0/7

3RYUãLQVNDQDSHWRVW

V

07

%URMYHOLþLQDQ GLPHQ]LMDN EURM3LSDUDPHWDUDQN  =DGLPHQ]LRQRQH]DYLVQHYHOLþLQHRGDELUHVHVNXS'YLU



' Y U

/

[

[

\

]

/7 0/ \





]

0 /7 





0  ] ]   /  [  \  ] [  7 \

\ 

.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ

S

G  '

S

P ' Y U

S

0/7  / /7  0/

[

\

] \

[

0   ]

0  /7 

] 

/     [  \  ] 7    \

\ 

P 'Y U

S

R ' Y U

S

07  / /7  0/

[

\

[

0   ]

] \

]

0  /7 

] 

/  [  \  ] 7   \



[ 

S

S

]

[ 



\ 

R 'Y  U

IXQNFLRQDOQD]DYLVQRVWSURPMHUDNDSOMLFHGRGSUHRVWDOLKYHOLþLQD

G

' I S   S 

§ P V · ' I¨   ¸ U 'Y 'Y U ¹ ©



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

,VSLW]DGDWDN

2GUHGLWHIXQNFLRQDOQX]DYLVQRVWSRWUHEQHSRJRQVNHVLOH)SRWSXQRSRWRSOMHQRJWRUSHGD6LOD]DYLVLRGGXOMLQH WRUSHGD/SURPMHUDWRUSHGD'EU]LQHWRUSHGDYGLQDPLþNRJNRHILFLMHQWDYLVNR]QRVWLIOXLGDPWHJXVWRüHIOXLGDU  9HOLþLQD

6LPERO

'LPHQ]LMD

'XOMLQDWRUSHGD

/

/

%U]LQD

Y

/7

*XVWRüD

U

0/

3URPMHUWRUSHGD

'

/

9LVNR]QRVW

P

0/7

3RJRQVNDVLOD

)

0/7

 %URMYHOLþLQDQ GLPHQ]LMDN EURM3LSDUDPHWDUDQN  =DGLPHQ]LRQRQH]DYLVQHYHOLþLQHRGDELUHVHVNXS/YLU



/ Y U

/

[

[

\

]

/7 0/ \





]

0 /7 





0  ] ]   /  [  \  ] [  7 \

\ 

.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ

S

'  /

S

P / Y U

S

0/7  / /7  0/

[

\

] \

[

0   ]

0  /7 

] 

/     [  \  ] 7    \

\ 

P /Y U

S

) / Y U

S

0/7  / /7  0/

[

\

[

0   ]

] \

]

0  /7 

] 

/    [  \  ] 7   \



[ 

S

S

]

[ 



\ 

) /Y U  

)XQNFLRQDOQD]DYLVQRVWSRJRQVNHVLOH)RGSUHRVWDOLKYHOLþLQD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'LPHQ]LMVNDDQDOL]D 

/ Y  U I S   S 

)

§' P · / Y  U I ¨  ¸ © / 'Y U ¹



,VSLW]DGDWDN

5DYQD SORþD MH SRWSXQR SRWRSOMHQD X IOXLG NRML MH X VWDFLRQDUQDUQRP UDYQLQVNRP YLVNR]QRP VWUXMDQMX SUHPD VOLFL 2GUHGLWH SULPMHQRP GLPHQ]LMVNH DQDOL]H IXQNFLRQDOQX ]DYLVQRVW VLOH RWSRUD ) UDYQH SORþH RG EU]LQH IOXLGD Y JXVWRüH IOXLGD U YLVNR]QRVWL P UD]OLNH WODNRYDLVSUHGLL]DSORþH'S SSWHãLULQHSORþHD

Y



S

   9HOLþLQD

6LPERO

'LPHQ]LMD

5D]OLNDWODND

'S

0/7

%U]LQD

Y

/7

*XVWRüD

U

0/

âLULQDSORþH

D

/

3RJRQVNDVLOD

)

0/7

9LVNR]QRVW

P

0/7

%URMYHOLþLQDQ GLPHQ]LMDN EURM3LSDUDPHWDUDQN  =DGLPHQ]LRQRQH]DYLVQHYHOLþLQHRGDELUHVHVNXSDYLU



D

D Y U

/

[

[

\

]

/7 0/ 

\



]

0 /7 





0  ] ]   /  [  \  ] [  7 \

\ 

.DNRMHUMHãHQMHRYRJVNXSDWULYLMDOQR]DNOMXþXMHVHGDMHVNXSGLPHQ]LRQRQH]DYLVDQ

S

'S D [ Y \ U ]

S

0/7  / /7  0/ [

\

]

0  /7 

0    ] ]  /     [  \   ] [  7   \ 'S S U Y

\ 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



S

'LPHQ]LMVNDDQDOL]D 

S

) D Y U

S

0/7  / /7  0/

[

\

] \

[

0   ]

]

0  /7 

] 

/    [  \  ] 7   \

[ 



\ 

S

) DY U

S

P D Y U

S

0/7  / /7  0/

 

[

\

] \

[

0   ]

]

0  /7 

] 

/     [  \  ] 7    \

[ 



\ 

P DY U

S

)XQNFLRQDOQD]DYLVQRVWVLOHRWSRUD)RGSUHRVWDOLKYHOLþLQD

D  Y  U I S   S 

)

§ 'S P · DY U I ¨   ¸ © Y U DY U ¹



,VSLW]DGDWDN

2GUHGLWHIXQNFLRQDOQX]DYLVQRVWLEU]LQHãLUHQMDWODþQRJSRUHPHüDMDF EU]LQDSXOVD NUR]DUWHULMHRGSURPMHUD DUWHULMH ' GHEOMLQH VWMHQNH NUYQH åLOH K JXVWRüH NUYL U +  [  K  [ @



¹

[

+K

[



˜ P



,]%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHLWHUDFLMVNLPSRVWXSNRPL]UDþXQDWLEU]LQXQDL]OD]XL]FLMHYL 

+[

§ O ˜ /  · ˜ Y ¨  ¸ © ' ¹ ˜ J

˜ J ˜ +  [

Y

§ O ˜ /  · ¨  ¸ © ' ¹

.RHILFLMHQWOLQLMVNRJWUHQMDOUDþXQDVHSUHPDL]UD]X O N  '  5H



§ OQ § N   · · ¨ ¨ ˜ '  ¸ ¸ 5H ¹ ¹ © ©



O

O N  '  

O



8]DVWRSQLPLWHUDFLMDPDSREROMãDYDPRWRþQRVWL]UDþXQDEU]LQHYQDL]OD]XL]FLMHYL

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



&MHYRYRG  Y

PV



Y˜ '

5Q



§ O ˜ /  · ˜ Y ¨  ¸ © ' ¹ ˜ J

+[

Y

PV

§ O ˜ /  · ¨  ¸ © ' ¹ Y˜ '

5Q 

Y

PV

O

Q

§ O ˜ /  · ˜ Y ¨  ¸ © ' ¹ ˜ J

+[

O N  '  5Q

˜ J ˜ +  [

Y



O

Q

Y

O N  '  5Q

˜ J ˜ +  [

§ O ˜ /  · ¨  ¸ © ' ¹





,]MHGQDGåEHKRUL]RQWDOQRJKLFDRGUH XMHVHGRPHWPOD]D 

J ˜ /

K[

˜ Y

/



 J

˜ Y˜ ˜ J˜ K  [

/

P





,VSLW]DGDWDN FLOLQGDU

LJOD

G

Y

'

UP

)

D

/

.ROLNDMHVLOD)SRWUHEQD]DSRWLVNLYDQMDVWDSDXQXWDULQMHNFLMH EU]LQRPY PPV+LSRGHUPDOQDLJODLPDXQXWDUQMLSURPMHUG  PPWHMHGXJD/ PP*XVWRüDMHIOXLGDXQXWDULQMHNFLMHU   NJP WH YLVNR]QRVW P    3DV 3UHWSRVWDYLWH GD QHPD FXUHQMD IOXLGD L]PH X VWDSD L FLOLQGUD LQMHNFLMH WH ]DQHPDULWH VYH ORNDOQH JXELWNH SUL VWUXMDQMX IOXLGD XQXWDU LQMHNFLMH 8 UD]PDWUDQMH MHSRWUHEQRX]HWLOLQLMVNHJXELWNHXQXWDUFLOLQGUDLLJOH=DGDQRMHD PP' PP

%U]LQXVWUXMDQMDIOXLGDNUR]KLSRGHUPDOQXLJOXPRJXüHMHL]UDþXQDWLL]MHGQDGåEHNRQWLQXLWHWD 





' ˜S

Y˜





G ˜S

Y





' G

Y



 PV





=D L]UDþXQDWH EU]LQH VWUXMDQMD SRWUHEQR MH XWYUGLWL UHåLPH VWUXMDQMD NDR L NRHILFLMHQWH OLQLMVNRJ WUHQMD XQXWDU FLOLQGUDWHXQXWDULJOH 5Q O

Y˜ '˜ U

5Q

P  5Q

O





5Q  O

 5Q 

Y˜ G ˜ U

5Q 

P O



 u 





.DNR VX RED 5H\QROGVRYD EURMD ]QDWQR LVSRG  RþLWR VH UDGL R ODPLQDUQRP VWUXMDQMX 'D EL L]UDþXQDOL SUHWODNS0QDþHOXNOLSDSRWUHEQRMHSRVWDYLWL%HUQRXOOLMHYXMHGQDGåEXRGþHODNOLSDGRNUDMDLJOH

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG  S0 U ˜J

S0

Y







Y

˜ J

˜ J

˜ §¨   O˜

©





 O˜

¸



D Y ˜ ' ˜ J

 ª §  · Y  Y  Y G  D Yº «¨ ¸ ˜  ˜  ˜ ˜ O˜  ˜ O˜ ˜ » ˜ U ˜ J  J /  ' J¼ ¬ © ¹ J  J

S0

EDU



6LOX)SRWUHEQX]DLVWLVNLYDQMHIOXLGDLLQMHNFLMHUDþXQDVHL]L]UD]D S0 ˜

)



' ˜S

)



1





,VSLW]DGDWDN J

+

G

SD

   2GUHGLWH UDGQX WRþNX SXPSH YLVLQX GREDYH L SURWRN GDELYLVLQDPOD]DYRGH U NJP P    3DV  YRGRVNRND ELOD +   P =DGDQR MH ..   .9   .V    ORNDOQL JXELWDN VDSQLFH L]UDåHQ X] YHüX EU]LQX  / P XNXSQDGXOMLQDVYLKFLMHYL ' P SURPMHUVYLK FLMHYL  3UHWSRVWDYLWH GD VX VYH FLMHYL L] WUJRYDþNRJ þHOLND=DGDQRMHG P

K  UP ' ..



.9

..

.9

 ,]YLVLQHPOD]DSRPRüX7RUULFHOOLMHYHIRUPXOHPRJXüHMHRGUHGLWLEU]LQXPOD]DQDL]OD]L]VDSQLFH Y

˜ J ˜ +



3RPRüXMHGQDGåEHNRQWLQXLWHWDPRJXüHMHRGUHGLWLEU]LQXXFMHYRYRGQRPVXVWDYX Y

Y˜

G

 

' 

3RPRüXEU]LQHYPRJXüHMHL]UDþXQDWL5H\QROGVRYEURMXFLMHYLDRQGDLNRHILFLMHQWOLQLMVNRJWUHQMDO ]DFLMHYL RGWUJRYDþNRJþHOLNDX]LPDVHGDMHYLVLQDKUDSDYRVWLN PP  5Q

Y˜ '˜ U P

O



§ OQ § N   · · ¨ ¨  ˜ '  ¸ ¸ 5Q ¹ ¹ © ©



O





8SRWUHERP%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLYLVLQXGREDYHSXPSHK 



§ O˜ /  ˜ .  ˜ . · ˜ Y  .   ˜ Y ¨ . 9¸ 6 ˜ J © ' ¹ ˜ J

K K

P

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



&MHYRYRG 

3URWRNNUR]SXPSXMHNRQVWDQWDQL]DGDQMHEU]LQRPY 

4

Y˜

G ˜S

 

4



P V



,VSLW]DGDWDN



D

2GUHGLWH UDGQX WRþNX SXPSH YLVLQX GREDYH L SURWRN GDELGRPHWSUHOMHYD VODSD POD]DYRGH U  NJPP 3DV ELRD PWHGD EL GHEOMLQD K POD]D MHGLQLþQH ãLULQH ELOD K   FP =DGDQR MH ..   .9   /   P XNXSQD GXOMLQD VYLK FLMHYL  '   P SURPMHU VYLK FLMHYL  3UHWSRVWDYLWH GD VX VYH FLMHYL L] WUJRYDþNRJ þHOLND 3UHWSRVWDYLWH XQLIRUPQL SURILO EU]LQH QD SUHOMHYX =DGDQRMH+ P

K J

+ SD

UP

 

' ..

.9



..

.9



%U]LQXYRGHQDSUHOMHYXPRJXüHMHRGUHGLWLL]MHGQDGåEHNRVRJKLFD +

Y[

J 

˜W



W

 ˜ +

D

J˜ D

+

Y[

˜ ˜ D ˜ + ˜ J

Y[

 

˜ Y[

PV





%U]LQXYRGHXQXWDUFMHYRYRGDPRJXüHMHRGUHGLWLL]MHGQDGåEHNRQWLQXLWHWD Y

Y[˜

K ˜ %˜  

' ˜S

Y

PV





=D SR]QDWX EU]LQX VWUXMDQMD XQXWDU FMHYRYRGD PRJXüH MH L]UDþXQDWL 5H\QROGVRY EURM WH NRHILFLMHQW WUHQMD OLQLMVNRJJXELWNDO 5Q

Y˜ '˜ U P

O

 N



§ OQ § ·· ¨ ¨  ˜ '   ¸ ¸ 5Q ¹ ¹ © ©

O







3RVWDYOMDQMHP%HUQRXOOLMHYHMHGQDGåEHL]PH XSUYRJLGUXJRJVSUHPQLND K

§ O˜ /  ˜ .  ˜ .  ¨ . 9 © '

 ·¸ ˜

Y



¹ ˜ J

+



L]UDþXQDYDVHYLVLQDGREDYHSXPSHWHSURWRNNUR]FMHYRYRG 

K

P

4



' ˜S 

4

  P V



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 



,VSLW]DGDWDN

2GUHGLWH SURWRN 4 NUR] VLVWHP SUHPD VOLFL DNR MH SDG WODND NUR] WXUELQL S7   EDU =DGDQR MH +   P +   P U   NJP Q   PV '   PP N  PP/ P/ P

SD J

QU '/N

+



SD

 

+

  '/N WXUELQ %HUQRXOOLMHYDMHGQDGåEDRGSRYUãLQHOLMHYRJGRSRYUãLQHGHVQRJVSUHPQLND + 

· Y § /  /  ¸ ˜ ' © ¹ ˜ J

S7

· ˜ 4 § /  /  ¸ ˜ ' © ¹ '˜ S˜ J 

+   ¨ O˜

U ˜J

+   ¨ O˜

,]RYHMHGQDGåEHSURWRN4MHGQDNMH

4

S7 § ·    +  ¸ ˜' ˜S ˜J ¨+   U ˜ J © ¹ /  / §   · ˜ ¨ O˜  ¸ ' © ¹ 

=DSUYXLWHUDFLMXSUHWSRVWDYOMDPR O

 

,WHUDWLYQLPSRVWXSNRPL]UDþXQDYDVHSURWRN4

4

4

S7 § ·    + ¸ ˜ ' ˜ S ˜ J ¨ +  U ˜J © ¹ · § /  / ˜ ¨ O˜  ¸ ' © ¹

4 O

S7 § ·    + ¸ ˜ ' ˜ S ˜ J ¨ +  U ˜J © ¹ · § /  / ˜ ¨ O˜  ¸ ' © ¹

4 O

 

P V

5Q

O N  '  5Q

 

P V

O N  '  5Q

˜ 4 '˜ S˜ Q O

5Q

˜ 4 '˜ S˜ Q O

5Q



 u 



5Q 



 u 



8VYDMDVHSURWRNRG4 OLWV

,VSLW]DGDWDN SD

J +

/ UQ

.

.

' =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3XPSDYLVLQHGREDYHKS PRVWYDUXMHSURWRNRG 4 OVNUR]VLVWHPSUHPDVOLFL2GUHGLWH]DNROLNRüH VH SRYHüDWL SURWRN NUR] VLVWHP DNR XJUDGLPR SXPSX YLVLQH GREDYH KS   P X] QHSURPLMHQMHQH RVWDOH YHOLþLQH =DGDQR MH '  P SURPMHU FMHYRYRGD  N  PP YLVLQDKUDSDYRVWLFMHYRYRGD / P+  PU NJPP 3DV

&MHYRYRG 

%HUQRXOOLMHYDMHGQDGåED]DVOXþDMSXPSHRGKS PHWUDYLVLQHGREDYHRGGHVQRJGROLMHYRJVSUHPQLND KS

§ / · ˜ 4 + ¨ O ˜  .  ¸ ˜ ' © ¹ '˜ S˜ J 

.RHILFLMHQWWUHQMDOUDþXQDVHL]L]UD]D O N  '  5H

 · · § § N ¨ OQ ¨ ˜ '   ¸ ¸ 5H ¹ ¹ © ©

˜ 4˜ U

5Q

4



5Q

'˜ S˜ P



 u 



O

O N  '  5Q

O





6XPDNRHILFLMHQDWDORNDOQLKJXELWDNDXFMHYRYRGXUDþXQDVHL]%HUQRXOOLMHYHMHGQDGåEH  º ª 4 K   ˜ ˜ O˜ /  +» «S ª¬'˜ S˜ J º¼  ¬ ¼ ˜ '˜ S˜ J ˜

.





.



4

 u 



%HUQRXOOLMHYDMHGQDGåED]DVOXþDMSXPSHYLVLQHGREDYHKS PHWUD K S

· ˜ 4 § / O ˜  . + ¨   ¸ ˜ ' © ¹ '˜ S˜ J 

3URWRN4VHL]UDþXQDYDLWHUDWLYQLPSRVWXSNRP

ª¬'˜ S˜ J˜ KS  + º¼ § / · ˜ ¨ O˜  . ¸ © ' ¹

4

˜ 4˜ U

5Q

5Q

'˜ S˜ P

4



 u 

ª¬'˜ S˜ J˜ KS  + º¼ § / · ˜ ¨ O˜  . ¸ © ' ¹

4

4

   

 u  P V

O

 

D

G



K



G U



,]PH X GYD YHOLND DNXPXODFLMVND MH]HUD XJUD HQD MH EUDQD V WXUELQRP =ERJ SRYHüDQMD VWXSQMD GMHORYDQMD WXUELQH LVSRG QMH MH PRQWLUDQ GLIX]RU 2GUHGLWH SRYHüDQMH VWXSQMD GMHORYDQMD DNR MH QHWR SDG WXUELQH K    P 3UHWSRVWDYLWH MHGQROLNH SURILOH EU]LQD SR VYLP SUHVMHFLPD WH GD MH ORNDOQL JXELWDN X GLIX]RUX MHGQDN  JXELWND QDJORJ SURãLUHQMD =DGDQRMHK  PK  PK  PK  PK   PG  PG  PU NJPQ PV W



K GLIX]RU



   

J K

O

 u  P V

,VSLW]DGDWDN S

O N  '  5Q

K







K















 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

%HUQRXOOLMHYDMHGQDGåEDXVOXþDMXEH]GLIX]RUD VDPRL]OD]QLJXELWDN  

KK7

˜ 4  



G  ˜S ˜J



,]RYRJL]UD]DPRJXüHMHL]UDþXQDWLSURWRNNUR]VLVWHP 4







˜ G  ˜ S˜ J ˜ ˜



J

˜ K   K7

 

4

P V



%HUQRXOOLMHYDMHGQDGåEDXVOXþDMXVGLIX]RURP JXELWDNXGLIX]RUXLL]OD]QLJXELWDN  

  § G  · ˜ 4  ¸˜  ˜ ¨       ¨ G  ¸¹ G ˜ S ˜ J G  ˜S ˜J ©  

KK7

˜ 4 

3URWRNXVOXþDMXVWUXMDQMDVGLIX]RURPL]UDþXQDYDVHSUHPDL]UD]X 4

K  K7 ª  § G · « ¸ ˜ ¨   « ¸ ¨ G ¹ © «   ˜   « G ˜ S˜ J G ˜ S ˜ J ¬ 

 

4



P V

» » » » ¼



3RYHüDQMHVWXSQMDGMHORYDQMDL]QRVL K

U ˜ J ˜ K 7 ˜ 4

K

U ˜ J ˜ K 7 ˜ 4







,VSLW]DGDWDN

2GUHGLWHYLVLQXK YRGHXVSUHPQLNXDNRXVSUHPQLN QHXWMHþHQLWLLVWMHþHYRGDU NJP Q  P V .RHILFLMHQW ORNDOQRJ JXELWND VYLK YHQWLOD QD VOLFL .9   =DQHPDULWH JXELWNH X UDþYL 3URPMHU VYLK FMHYRYRGD L]QRVL ' P=DGDQRMHK PK P/ P/  P /   P N   PP YLVLQD KUDSDYRVWL VYLK FMHYRYRGD 

SD









UQ

SD

J '

/

.9

.9

/

 0RGLILFLUDQD%HUQRXOOLMHYDMHGQDGåEDRGVSUHPQLND GR QDMYLãHJGRQDMQLåHJVSUHPQLND  

K

· ˜ 4 § /  /  ˜ . Y  ¸ ˜  K ¨ O˜ ' © ¹ S˜ J˜ ' 

$NRSUHWSRVWDYLPRNRHILFLMHQWWUHQMDO]DUHåLPSRWSXQHKUDSDYRVWL O



§ § N ·· ¨ OQ ¨  ˜ ' ¸ ¸ © © ¹¹



O



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



K

.9 /

K SD K

&MHYRYRG 

,]%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLSURWRN

4

ª¬ K  K ˜ S˜ J˜ 'º¼ § ©

˜ ¨ O˜

/  / '

4

· ¹

 

P V

 ˜ . Y  ¸



3RPRüXRYHYULMHGQRVWLSURWRNDL]UDþXQDYDPR5H\QROGVRYEURMWHQDYLNRHILFLMHQWWUHQMD 5Q

˜ 4



O

'˜ S˜ Q

§ OQ § N   · · ¨ ¨  ˜ '  ¸ ¸ 5Q ¹ ¹ © ©



O



5Q



 u 



1RYDYULMHGQRVWSURWRNDUDþXQDQDVDQRYLPNRHILFLMHQWRPWUHQMD

4

ª¬ K  K ˜ S˜ J˜ 'º¼ § ©

˜ ¨ O˜

/  / '

4

· ¹

 

P V

 ˜ . Y  ¸



'DOMQMLLWHUDWLYQLSRVWXSDNMHQHSRWUHEDQMHUELVHYULMHGQRVWSURWRNDVDPRQH]QDWQRSURPLMHQLOD%HUQRXOOLMHYD MHGQDGåEDRGVSUHPQLNDGRUDþYDQMDFLMHYL K

§ / ¨ O˜  . Y  © '

S0 · ˜ 4  ¹ S˜ J˜ ' U ˜ J 

¸ ˜

2GDWOHMHWRWDOQLSLH]RPHDUVNLSUHWODN S0  S0UDþYDQMD UJKUDþYDQMD XUDþYDQMXFLMHYL 

S0



   ª º 4 4 4 ˜ O˜ /  ˜ ˜ . Y  ˜ ˜U ˜J « K  ˜  » ª¬S ˜ J˜ ' º¼ ª¬S˜ J˜ ' º¼ ª¬S˜ J˜ ' º¼ ¼ ¬

S0

EDU



3RPRüXMHGQDGåEHPDQRPHWUDPRJXüHMHRGUHGLWLYLVLQXYRGHXVSUHPQLNX K

S0 U ˜J

K

P





,VSLW]DGDWDN

'YD VSUHPQLND SUHPD VOLFL VSRMHQD VX FMHYRYRGRP NYDGUDWQRJ SRSUHþQRJ SUHVMHND D   FP  XNXSQH GXOMLQH /   P &LMHY NYDGUDWQRJ SRSUHþQRJ SUHVMHND SRWUHEQR MH ]DPLMHQLWL RNUXJORP FLMHYLSURPMHUDGNRMDRVWYDUXMHLVWHUDGQHXYMHWH LVWL SURWRNX 4 L LVWX UD]OLNX YLVLQD +  3UHWSRVWDYLWH VWUXMDQMH X SRGUXþMX SRWSXQH WXUEXOHQFLMH WH YLVLQX KUDSDYRVWLN PP 

SD



J /

+

UQ D

0RGLILFLUDQD%HUQRXOOLMHYDMHGQDGåED]DVOXþDMVWUXMDQMDNUR]FLMHYNYDGUDWQRJSRSUHþQRJSUHVMHND

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG  ˜ D

'HN



'HN

D 

+

§ O ˜ /  · ˜ Y ¨ ' ¸ ˜ J HN © ¹

D 

4

Y

D

§ O ˜ /  · ˜ 4 ¨ D ¸ © ¹ ˜ J˜ D 

+



0RGLILFLUDQD%HUQRXOOLMHYDMHGQDGåED]DVOXþDMVWUXMDQMDNUR]FLMHYNUXåQRJSRSUHþQRJSUHVMHND 

+

§ O ˜ /  · ˜ Y ¨ ' ¸ ˜ J © ¹



˜4

Y

+



' ˜S

§ O ˜ /  · ˜ ˜ 4 ¨ ' ¸ © ¹ J˜ '˜ S 

,]MHGQDþDYDQMHPMHGQDGåELSRYLVLQL+LVUH LYDQMHPL]UDþXQDVHSURPMHUFLMHYL' 

§ O ˜ /  · ˜  ˜ 4 ¨  ¸ © ' ¹ J˜ '˜ S





§ O ˜ /  · ˜ 4 ¨  ¸ © D ¹ ˜ J˜ D

'



ª¬ O˜ /  ' ˜ º¼ ª¬ O˜ /  D Sº¼



=DSRþHWDNLWHUDWLYQRJSRVWXSNDSUHWSRVWDYOMDVH '

D

O

 N



·· § OQ § ¨ ¨  ˜ '   ¸ ¸ 5Q ¹ ¹ © ©

O



O

O

O



3URPMHU'XSUYRMLWHUDFLMLL]QRVL 

'



ª¬ O˜ /  ' ˜ º¼ ª¬ O˜ /  D Sº¼

'

P



DXGUXJRM 

'



ª¬ O˜ /  ' ˜ º¼ ª¬ O˜ /  D Sº¼

'

P



XVYDMDVHGDMHSURPMHUFMHYRYRGD' PP 

,VSLW]DGDWDN 

'

2GUHGLWH NROLNR SXWD VH VPDQML SURWRN NUR] FLMHY RNUXJORJ SUHVMHND X] LVWL SDGWODNDSRMHGLQLþQRMGXOMLQLFLMHYLDNRVHFLMHYSUHJUDGLYHUWLNDOQRPVWMHQNRP 3UHWSRVWDYLWH ODPLQDUQR VWUXMDQMH WH EHVNRQDþQR WDQNX SUHJUDGX 6WUXMDQMH VH RGYLMDXREDSUHJUD HQDGLMHODFLMHYL 

V|

3DGWODNDXFLMHYLEH]SUHJUDGHMHGQDNMHSDGXWODNDXFLMHYLVSUHJUDGRP 

/ Y O˜ ˜ ' ˜ J

O ˜

/



Y

˜ ' HN ˜ J



=DODPLQDUQRVWUXMDQMHNRHILFLMHQWWUHQMDOUDþXQDVHL]L]UD]D

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

O

O

5Q

˜ Q

˜ Q

O

Y˜ '

Y˜ 'HN



(NYLYDOHQWQLSURPMHUUDþXQDVHSUHPDL]UD]X 

' ˜S

˜ 'HN

' 



'HN



˜S  '

S

S   

$NRL]UD]H]DNRHILFLMHQWWUHQMDLHNYLYDOHQWQLSURPMHUXYUVWLPRXL]UD]]DSDGWODNDGRELYDVHL]UD] 

˜ Q / Y ˜ ˜ Y˜ ' ' ˜ J



Y

˜ ˜ Y˜ 'HN 'HN ˜ J

'

˜ Q

Y

/

Y



'HN





%U]LQH VWUXMDQMD X FLMHYL WH EU]LQD VWUXMDQMD X SUHJUD HQRM FLMHYL UDþXQDMX VH SUHPD IRUPXODPD X FLMHYL V SUHJUDGRPXMHGQRMSRORYLFLFLMHYLXVSRVWDYOMDVHSRORYLþQLSURWRN  ˜ 4

Y

Y



' ˜S

 ˜ 4 

˜ ' ˜ S



8YUãWDYDQMHWLKL]UD]DYRGLGRNRQDþQRJUMHãHQMD Y 

'

Y

2

 ˜4



S

 ˜' ˜S



'HN

'



'HN



˜

4

'˜S '˜S˜'HN

'˜S  ª  ª S º º « ' ˜ S˜ « '˜ »» ¬ ¬ S   ¼ ¼

S   

2



4

S   

4

S







S



,VSLW]DGDWDN QDVHOMH

J

+ MH]HUR SD

4



'

4 4

 ˜4

' SXPSD

/8.

 =D SRWUHEH RSVNUEH YRGRP QDVHOMD L]JUD HQ MH FMHYRYRGSURPMHUD' PPRGYXþHQLKFLMHYLXNXSQH GXOMLQH/8. NP3XPSDGREDYOMDOVYRGH JXVWRüH U   NJP NLQHPDWLþNRJ NRHILFLMHQWD YLVNR]QRVWL Q    PV  QDVHOMX NRMH VH QDOD]L QD YLVLQL +   P L]QDG UD]LQH MH]HUD WH RVWYDUXMH WRWDOQL SUHWODN YRGH X QDVHOMXS0 EDUD1DNRQGYDGHVHWRJRGLãQMHHNVSORDWDFLMH SRWUHEH ]D YRGRP VX VH SRYHüDOH SD MH SRWUHEQR GREDYLWL  YLãH YRGH X] LVWL WRWDOQL SUHWODN 2GUHGLWH SURPMHU G QRYRJFMHYRYRGDNRMLüHVHSRVWDYLWLXPMHVWRSRVWRMHüHJD ]DGRYROMDYD SRYHüDQH SRWUHEH ]D YRGRP V SRVWRMHüRP SXPSRP 3UL  SURUDþXQX ORNDOQH JXELWNH ]DQHPDULWH WH SUHWSRVWDYLWHGDMHYLVLQDKUDSDYRVWLNQRYRJFMHYRYRGDN  PP

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

%HUQRXOOLMHYDMHGQDGåED]DVWDULFMHYRYRG SULMHUHNRQVWUXNFLMH  KS

O ˜

 S0 / Y ˜ + ' ˜ J U ˜J 

=D]DGDQHXYMHWH]DGDWNDODNRVHL]UDþXQDNRHILFLMHQWWUHQMDDRQGDLYLVLQDGREDYHSXPSH ˜ 4

5Q

'˜ S˜ Q ˜ 4

Y



5Q

 u 

KS



' ˜S

O˜

O

O N  '  5Q

 S0 / Y ˜ + ' ˜ J U ˜J

KS

O



P



8 VOXþDMX UHNRQVWUXNFLMH FMHYRYRGD WUHED X]HWL SRVWRMHüX SXPSX LVWD YLVLQD GREDYH  D SRWUHEQR MH SURWRN SRYHüDWL]D 4

˜ 4

N

PP

˜ 4

5Q

'˜ S˜ Q

O N   '  5Q

O

O





%HUQRXOOLMHYDMHGQDGåED]DFMHYRYRGQDNRQUHNRQVWUXNFLMHJODVL 

S0 / ˜4  O ˜ ˜ + G G ˜ S˜ J U ˜J

KS



3RWUHEQLSURPMHUGFMHYRYRGDUDþXQDVHL]L]UD]D 

G



/

O˜

KS  + 

S0

˜

 ˜ 4

G



P

S ˜J

U ˜J



,WHUDWLYQLPSRVWXSNRPSREROMãDYDPRUMHãHQMH ˜ 4

5Q



KS  + 

O





/

O˜

G

O N   G  5Q

O

G ˜ S˜ Q

S0

˜

˜ 4

G



S ˜J

P

U ˜J





,VSLW]DGDWDN I

I



=D SRWUHEH QDYRGQMDYDQMD SRWUHEQR MH GREDYOMDWL4 PVRWYRUHQLPNDQDORPXREOLNX WUDSH]DSUHPDVOLFL2GUHGLWHQDJLENDQDODDDNRMH YLVLQD YRGH X NDQDOX K  P 3UHWSRVWDYLWH K VWUXMDQMH X UHåLPX SRWSXQH WXUEXOHQFLMH WH GD MH NDQDO L]JUD HQ RG EHWRQD YLVLQH KUDSDYRVWL N  3RSUHþQLSUHVMHNNDQDOD PP=DGDQRMHI D P

SD



4

D

J

D

 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG  %HUQRXOOLMHYDMHGQDGåED]DQDJQXWLNDQDO /˜ VLQ D 

Y





˜ J

/

Y

˜



'HN J



Y



VLQ D

˜ J

O˜





˜

4

'HN J ˜ $



(NYLYDOHQWQLSURPMHUUDþXQDPRSUHNRSRYUãLQHSRSUHþQRJSUHVMHNDLRSODNDQRJRSVHJD

D  K˜ WDQ I ˜ K

$

K

D  ˜ §¨

2

·

'HN

¸ © FRV I ¹

˜ $ 2 

=D]DGDQXYLVLQXKUDSDYRVWLLVWUXMDQMHXUHåLPXSRWSXQHWXUEXOHQFLMHSRPRüXL]UD]D6ZDPHHL-DQHUDþXQDVH NRHILFLMHQWWUHQMD O

 

1DJLENDQDOD]D]DGDQHSRGDWNHL]QRVL D

§



©

'HN

DVLQ ¨ O˜

· ¸ J ˜ $ ¹ 

˜

4

D



GHJ





,VSLW]DGDWDN J

SD '

VWDS

SRVXGD

2GUHGLWHPLQLPDOQLSRWUHEQLSUHWODNS0X NRPSHQ]DFLRQRMSRVXGLNRMLRVLJXUDYDGDNOLS VDYODGDYD VLOX )   1 SUL EU]LQL JLEDQMD NOLSD Y   PPPLQ 6YH ORNDOQH JXELWNH ]DQHPDULWH=DGDRMH' PPG PP /   P U   NJP P   3DV XOMH 

S0

Ka

G

Y



.RPSHQ]DFLRQD

/

 ,]SRWUHEQHVLOH)QDVWDSXL]UDþXQDYDVHSUHWODNXFLOLQGUXSURPMHUD' ˜ )

S 0

S0



' ˜S

EDU



,]MHGQDGåEHNRQWLQXLWHWDRGUH XMHVHEU]LQDVWUXMDQMDXFLMHYL 





' ˜S

Y˜





G ˜S

Y





' G

Y



PV





=DL]UDþXQDWXEU]LQXVWUXMDQMDXFLMHYLRGUH XMHVH5H\QROGVRYEURMWHNRHILFLMHQWWUHQMD 5Q

Y˜ G ˜ U

5Q

P



O

 5Q

O





.RHILFLMHQWJXELWNDQDJORJSURãLUHQMDSULXOD]XXFLOLQGDUUDþXQDVHSUHPDL]UD]X 

 § G · . 13  ¨   ¸  ' ¹  ©

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

L]%HUQRXOOLMHYHMHGQDGåEDPRJXüHMHL]UDþXQDWLWODNXNRPSH]DFLVNRMNRPRUL 

S0



U ˜J

Y

S 0

˜ J

U ˜J



Y



 §¨ O˜

/

© G

˜ J

 .13 ¸· ˜



Y

¹ ˜ J

S0

 ª  Y º S 0  Y  Y /  Y « ˜   ˜  ˜ ˜ O˜  ˜ ˜ .13» ˜ U ˜ J U ˜ J  J  J G  J ¬ J ¼

S0

EDU









$NR]DODPLQDUQRVWUXMDQMHX]PHPRXRE]LUNRHILFLMHQWLVSUDYNDNLQHWLþNHHQHUJLMH D



S0

   ª D Y º S0 D Y  Y /  Y «  ˜   ˜  ˜ ˜ O˜  ˜ ˜ .13» ˜ U ˜ J U ˜ J  J  J G  J ¬ J ¼

S0

EDU





,VSLW]DGDWDN SD



QU

J

+

'

W







K

'



/

2GUHGLWH UD]OLNX QLYRD + IOXLGD X DNXPXODFLMVNRP MH]HUX L NRPSHQ]DFLRQRM NRPRUL DNR MH QHWR SDG X WXUELQL K    P =DQHPDULWHORNDOQHJXELWNH=DGDQRMH'  P'  PU   NJP Q   PV /  P/  PN N   PPK P



/







 $NR SRVWDYLPR %HUQRXOOLMHYX MHGQDGåEX RG NRPSHQ]DFLRQH SRVXGHGRL]OD]DL]FMHYRYRGD KKW



/ · Y § ¨   O ˜ ' ¸ ˜ ˜ J © ¹  





0RJXüHMHL]UDþXQDWLEU]LQXXFMHYRYRGX 

O N  '  5H

Y





N

§ OQ § ·· ¨ ¨ ˜ '   ¸ ¸ 5H ¹ ¹ © © '

'  O˜ /



O





˜ ˜ '  O˜ / ˜



K  K J˜ ' W



,WHUDFLMVNLPSRVWXSNRPSREROMãDYDPRUMHãHQMH

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



Y





O N   '  

PV

O







&MHYRYRG '˜ Y

5Q

Q J˜

Y

5Q '

'  O˜ /





5Q

'

'



O N   '  5Q

O

O

K  K J˜ ' W

Y

PV







Q

Y



˜ ˜ '  O˜ / ˜

'˜ Y

5Q



 u 

 O˜ /





 u 





˜ ˜ '  O˜ / ˜

O N   '  5Q

O

O

K  K J˜ ' W

Y

PV









%U]LQXXSUYRPFMHYRYRGXL]UDþXQDYDPRL]MHGQDGåEHNRQWLQXLWHWD 

Y˜





' ˜ S





' ˜ S

Y





'

Y

 '

PV





3RVWDYOMHQMHP%HUQRXOOLMHYHMHGQDGåEHL]PH XDNXPXODFLMVNRJMH]HUDLNRPSHQ]DFLRQHNRPRUH 

/· Y § + ¨   O ˜ ¸˜ '  ¹ ˜ J © 

,]UDþXQDYDVHUD]OLNDQLYRDIOXLGD+ 5Q 

'˜ Y Q

5Q 



 u 

O

O N   '  5Q 

O





+

/ · Y § ¨   O˜ ' ¸ ˜ ˜ J ¹ ©

+

P





,VSLW]DGDWDN 

2GUHGLWHYULMHPHWSRWUHEQRGDVHSRSLMHGO&RFDFROHJXVWRüHU  NJP NRMDVHQDOD]LXRNUXJORMþDãLSURPMHUD' PP EH]OHGDL]SUHWKRGQRJ ]DGDWND  NUR] VODPNX SURPMHUD G    PP GXOMLQH /   FP 3UHWSRVWDYLWH NYD]LVWDFLRQDUQR VWUXMDQMH YLVNR]QRJ IOXLGD 5DGL MHGQRVWDYQLMHJ SURUDþXQD SUHWSRVWDYLWHGDMHNRHILFLMHQWWUHQMDONRQVWDQWDQLGDL]QRVLO =DGDQR MH S0   3D SRWODN QD YUKX VODPNH  XVLVQL NUDM VODPNH VH QDOD]L XYLMHN QHSRVUHGQRX]GQRþDãH

S

0



 þDãH

SD



J

U

/

G

9LVLQD + &RFD &ROH X þDãL UDþXQD VH L] ]DGDQRJ YROXPHQD IOXLGD L REOLND

+

˜ 9 

' ˜S

+

'

P



.ROLþLQD IOXLGDNRMLLVWHþHL]þDãHNUR]VODPNXXMHGLQLFLYUHPHQDMHGQDNDMHYROXPHQX]DNROLNRVHVPDQMLOD NROLþLQDIOXLGDXþDãL =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG  



G ˜S 

˜ GW

$ ] ˜ G]



3ULPMHQRP %HUQRXOOLMHYH MHGQDGåEH RG SRYUãLQH IOXLGD X þDãL SD GR XVLVQRJ NUDMD VODPNH RGUH XMH VH EU]LQD VWUXMDQMDIOXLGD S 0

]

U ˜J

Y

 /



˜ J

˜ §¨   O˜

©



˜ ª¬U ˜ J ˜ ]  /  S 0º¼

Y

¸ G¹

U ˜ §¨   O˜

©



¸





8YUãWHQMHPXJRUQMXMHGQDGåEXGRELYDVHL]UD] ˜ ª¬U ˜ J ˜ ]  /  S 0º¼ G ˜ S ˜ ˜ GW  / U ˜ §¨   O˜ ¸· G¹ ©



' ˜S 

˜ G]



6UH LYDQMHPL]UD]DLSRVWDYOMDQMDJUDQLFDLQWHJUDFLMH SXQDþDãD±SUD]QDþDãD  ' ˜ U ˜ §¨   O˜ 

©

GW

G





¸ G¹ ˜

' ˜ U ˜ §¨   O˜ 

G] ˜ ª¬U ˜ J ˜ ]  /  S0º¼

©

W

G





¸ G¹ ´ ˜µ µ ¶

+

 ˜ ª¬U ˜ J ˜ ]  /  S 0º¼

G]



5MHãHQMHPLQWHJUDODGRELYDVHYULMHPHSUDåQMHQMDþDãH

W





U ˜ §¨   O˜

©

G





¸ ª ˜ U ˜ J˜ +  ˜ U ˜ J˜ /  ˜ S0 ˜ U ˜ J ˜ /  ˜ S0 º ˜«  » U ˜ J U ˜ J ¬ ¼



W

V





,VSLW]DGDWDN 

J

DNXPXODWRU

+LGUDXOLþNL DNXPXODWRU  SUHPD VOLFL  SXQL VH NUR] FMHYRYRGXNXSQHGXOMLQH/ PSURPMHUDG PWH YLVLQHKUDSDYRVWLN PP2GUHGLWHSUHWODNS0NRMLMH SRWUHEDQGDELVHDNXPXODWRUSXQLRSURWRNRP4 OLWVWH SUHWODN S0 NRML VH SRVWLåH NDGD VH  DNXPXODWRU SUD]QL LVWLP SURWRNRP 2GUHGLWH VWXSDQM GMHORYDQMD DNXPXODWRUD =DGDQR MH '   PP *   W PDVD WHUHWD ]DMHGQR V FLOLQGURP DNXPXODWRUD  U   NJP P   3DV XOMH  8SR]RUHQMHSUHWODFLS0LS0YODGDMXQDLVWRPPMHVWX NDNR MHR]QDþHQRQDVOLFL VDPRMHVPMHUVWUXMDQMDIOXLGDUD]OLþLW

'

/ SS

G

 

7ODNXQXWDUDNXPXODWRUDVHUDþXQDL]XYMHWDGDMHWHåLQDXWHJDLFLOLQGUDDNXPXODWRUDMHGQDNDVLOLWODND *˜ J

S 0˜



' ˜S 

S 0

˜ J ˜ * 

' ˜S

S 0

EDU



5H\QROGVRYEURMLNRHILFLMHQWWUHQMDUDþXQDMXVHSUHPDL]UD]LPD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG U ˜ ˜ 4

5Q

5Q

G˜ S˜ P



O



O

5Q





%HUQRXOOLMHYDMHGQDGåEDNDGDVHDNXPXODWRUSXQL S 0

Y



U ˜J



S 0

˜ J

Y



U ˜J



˜ §¨ O˜

©

˜ J

/ G

 ¸·

¹

,]RYHMHGQDGåEHX]SULPMHQXL]UD]D]DSURWRNL]UDþXQDYDVHWODNQDXOD]XXFMHYRYRG 

S 0

˜ 4 ˜ U

S0 



G ˜S





˜ §¨ O˜



S0

¸ © G¹

EDU



%HUQRXOOLMHYDMHGQDGåEDXVOXþDMXSUDåQMHQMDDNXPXODWRUD S 0

S 0

U ˜J

U ˜J



Y



˜ J

˜ §¨ O˜

/

© G

 ¸·

¹

,]RYHMHGQDGåEHX]SULPMHQXL]UD]D]DSURWRNL]UDþXQDYDVHWODNQDL]OD]XL]FMHYRYRGD 

S 0

S0 

˜ 4 ˜ U 

G ˜S



˜ §¨ O˜

©

/ G

 ·¸

S 0

¹

EDU



6WXSDQMGMHORYDQMDDNXPXODWRUDUDþXQDVHL]RPMHUDGRELYHQHLXORåHQHVQDJH K

S 0˜ 4

K

S 0˜ 4







,VSLW]DGDWDN 

SD 2GUHGLWH NRHILFLMHQW ORNDOQRJ JXELWND YHQWLOD .Y ]D J VOXþDM VWDFLRQDUQRJ VWUXMDQMD IOXLGD SUHPD VOLFL =DGDQR UP ' MH+ PK P/ P' PN  .N K  . PPD P. .N Q PVU  ' NJP . Y  D  UP + %HUQRXOOLMHYDMHGQDGåED]DGHVQLVSUHPQLN 

+

Y



˜ J

˜ §¨   O˜

©



¸ '¹

Y

SD 'N

˜ J ˜ +   O˜

/

/ ' 

-HGLQD QHSR]QDQLFD MH NRHILFLMHQW WUHQMD O ]D SRþHWDN LWHUDFLMH SUHWSRVWDYOMDPR VWUXMDQMH X SRGUXþMX SRWSXQH WXUEXOHQFLMHSDNRHILFLMHQWRYLVLVDPRRUHODWLYQRMKUDSDYRVWL O

 

=DWDNRGRELYHQLNRHILFLMHQWWUHQMDOL]UDþXQDYDVHEU]LQD Y



PV 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

,WHUDWLYQLPSRVWXSNRPSREROMãDYDVHUMHãHQMH 

O



Y

PV



 u 

O



Y

PV





O



Y

PV



5Q

 u 

5Q 5Q

 u 



  

.DNR MH SUHPD XYMHWX ]DGDWND VWUXMDQMH VWDFLRQDUQR NROLþLQD IOXLGD NRML XOD]L X VSUHPQLN MHGQDND MH NROLþLQL IOXLGD NRML L]OD]L L] VSUHPQLND QHPD DNXPXODFLMH  ,] MHGQDNRVWL SURWRND ]DNOMXþXMHPR GD VX L EU]LQH X RED FMHYRYRGDLVWHMHUVXLSURPMHULFMHYRYRGDLVWL %HUQRXOOLMHYDMHGQDGåED]DJRUQMLFMHYRYRG K

Y



  .  .N  .Y J

Y ˜ J ˜ K

.Y

Y



   .  . N

.Y





  

,VSLW]DGDWDN J

G

 9RGD U NJPP 3DV SUHOMHYDVHVLIRQRP L] MHGQRJ MH]HUD ]D QDYRGQMDYDQMH X GUXJR SUHPD VOLFL NUR] FLMHYSURPMHUDG PP8NXSQDGXOMLQDFLMHYLMH/ P DYLVLQDKUDSDYRVWLMHN PP/RNDOQLJXELWDNXNROMHQX .N 2GUHGLWHSURWRNYRGHNUR]FLMHY=DGDQRMHK  P

K

SD



UP

 %HUQRXOOLMHYDMHGQDGåEDRGYLãHJSUHPDQLåHPDNXPXODFLMVNRPVSUHPQLNX 

K

§ ˜ .    O ˜ / · ˜ Y ¨ N  ¸ G ¹ ˜ J  ©

8 SUYRP LWHUDWLYQRP SRVWXSNX NRULVWLPR NRHILFLMHQW WUHQMD O UDþXQDQ ]D ]DGDQX UHODWLYQX KUDSDYRVW NG L SRGUXþMHSRWSXQHWXUEXOHQFLMH 

O

O N  G  5Q

O



4



§ ˜ .    O ˜ / · ˜  ¨ N  ¸ G¹ ©

,WHUDWLYQLPSRVWXSNRPSREROMãDYDPRUMHãHQMH

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



G ˜S ˜J

4 5Q



 

 u  P V ˜ 4˜ U G ˜ S˜ P

5Q



 u 



&MHYRYRG 



O

O N  G  5Q

O



4



G ˜S ˜J

§ ˜ .    O ˜ / · ˜  ¨ N  ¸ G¹ © 

O N  G  5Q

O

O



4





4

˜ 4˜ U

5Q

5Q

G ˜ S˜ P



G ˜S ˜J /·

§ ˜ .    O ˜ ˜  ¨ N  ¸ G¹ ©

 

 u  P V

4 5Q





 u 

 

 u  P V ˜ 4˜ U

5Q

G ˜ S˜ P



 u 





,VSLW]DGDWDN S

J

D

S

 2GUHGLWH NRHILFLMHQW RWSRUD YHQWLOD .  SUL NRPH üH SURWRNXJUDQLVYHQWLORPELWL4  OV=DGDQRMH/ P G   P N   PP VYH WUL FLMHYL VX LVWH GXOMLQH SURPMHUDLYLVLQHKUDSDYRVWL K PS  EDUU  NJPQ ÂPV Y

0



UQ

0

K



/GN



. Y

    =D RGUH LYDQMH VPMHUD VWUXMDQMD IOXLGD GD OL IOXLG XOD]L LOL L]OD]L L] OLMHYRJ VSUHPQLND  SUHWSRVWDYOMD VH GD L] GHVQRJ VSUHPQLND IOXLG L]OD]L SURWRNRP 4  D GD L] OLMHYRJ VSUHPQLND QDPD SURWRND 3RVWDYOMDQMHP %HUQRXOOLMHYH MHGQDGåEHL]PH XWDGYDVSUHPQLND 

5Q

O N  '  5H

KI

S0

˜ 4

5Q

G ˜ S˜ Q



 u 

 

N

§ § ·· ¨ OQ ¨ ˜ '   ¸ ¸ 5H ¹ ¹ © ©

O



O N  G  5Q

O





/ ˜ 4  O˜ ˜ G G˜ S˜ J U ˜J

KI

P



RþLWR MH GD VPR GRELOL QHJDWLYQX YLVLQX K  EL WUHEDR ELWL MHGQDN QXOL  SD üH SUHPDWRPHL]OLMHYRJVSUHPQLND IOXLGLVWMHFDWL3RVWDYOMDPR%HUQRXOOLMHYHMHGQDGåEHRGOLMHYRJLGHVQRJVSUHPQLNDGRGRQMHJVSUHPQLNDWHMHGQDGåEX NRQWLQXLWHWD I

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG  S0 U ˜J





˜ 4 / ˜ 4 / O˜ ˜  §¨ O˜    .Y ¸· ˜ G G˜ S˜ J © G ¹ G˜ S˜ J

K





˜ 4 / ˜ 4 /  §¨ O˜    .Y ¸· ˜ O˜ ˜ G G˜ S˜ J © G ¹ G˜ S˜ J

K

4  4

4



2GX]LPDQMHP%HUQRXOOLMHYLKMHGQDGåEL



S0



/ ˜ 4  / ˜ 4  O ˜ ˜  O ˜ ˜  G G ˜ S ˜ J G G ˜ S˜ J 

U ˜J

6UH LYDQMHPL]UD]DLXYUãWDYDQMHPMHGQDGåEHNRQWLQXLWHWD 



S0 ˜ G ˜ S ˜ J



U ˜ J ˜ ˜ / 



S0 ˜ G ˜ S ˜ J

O˜ 4  O˜ 4  4 

U ˜ J ˜ ˜ /  



˜ S0 ˜ G ˜



O˜ 4  O˜ 4

S



U ˜ /









O˜ 4  O˜ 4  ˜ O˜ 4˜ 4  O˜ 4



 3RWUHEQRMHULMHãLWLNYDGUDWQXMHGQDGåEXGDELGRELOLSURWRN D

O  O

 D ˜ 4

4

 E ˜ 4  F F E

E

O˜ 4

F



O˜ 4 

 



˜ S0 ˜ G ˜

S



U ˜ /

 

4

 P

 u 

V



=DRYXSRþHWQXLWHUDFLMXSUHWSRVWDYOMDVHGDVXVYLNRHILFLMHQWLWUHQMDOMHGQDNLSDVHNYDGUDWQDMHGQDGåEDVYRGL QDOLQHDUQX6RYDNRGRELYHQLPUMHãHQMHP]DSRþLQMHVHLWHUDWLYQLSRVWXSDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG ˜ 4

5Q 

O

D



5Q 

G ˜ S˜ Q O N  G  5Q 

O  O 

D ˜ 4  E ˜ 4  F

 u 

˜ 4  4

5Q 

O



O

E

O˜ 4

F

G ˜ S˜ Q O N  G  5Q 

O



˜ S0 ˜ G ˜

 S



U ˜ /



E  E  ˜ D ˜ F ˜ D

P

4



4

 u 

V



4



 u 





4





O˜ 4 



5Q 



E  E  ˜ D˜ F ˜ D

 P

V



3UYRUMHãHQMHQLMHIL]LNDOQRMHUMHSURWRNYHüLQDJRãWRMHL]OD]QLSURWRNSDXVYDMDPRGUXJRUMHãHQMH 8GUXJRPLWHUDFLMVNRPNRUDNXUMHãHQMHVHSREROMãDYD 5Q 

O D

˜ 4

5Q 

G ˜ S˜ Q O N  G  5Q  O  O

O E



 u 



O˜ 4



O˜ 4 



4

5Q 

G ˜ S˜ Q O N  G  5Q 

O F

˜ 4  4

5Q 

 



˜ S0 ˜ G ˜

O S



 u 







U ˜ /



E  E  ˜ D˜ F

4

˜ D

 P

 u 

V



.DNR VH RYD GYD UMHãHQMD YUOR PDOR UD]OLNXMX QHSRWUHEQR MH GDOMH LWHULUDWL 9Hü UDþXQDPR NRHILFLMHQW JXELWND YHQWLODL]%HUQRXOOLMHYHMHGQDGåEH S0 U ˜J 5Q 

.Y





˜ 4 / ˜ 4 / O˜ ˜  §¨ O˜    .Y ·¸ ˜ G G˜ S˜ J © G ¹ G˜ S˜ J

K

˜ 4

5Q 

G ˜ S˜ Q









 u  



O N  G  5Q 

O 



O

 

  S0 ˜ G ˜ S  K˜ U ˜ J˜ G ˜ S  ˜ O˜ /˜ 4 ˜ U  ˜ 4 ˜ U ˜ O˜ /  ˜ 4 ˜ U ˜ G ˜   4 ˜ U ˜ G







.Y





   =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

,VSLW]DGDWDN +

SD

J





UP

2GUHGLWHUDGQXWRþNXSXPSH YLVLQXGREDYHKS L SURWRN 4S  ]D VLWXDFLMX SUHPD VOLFL .DUDNWHULVWLND SXPSH ]DGDQD MH VOMHGHüLP L]UD]RP

D

^K `



/ '

S

S

.



Y

SXPSD





FMHYRYRG]DQHPDULWH=DGDQRMH+ P/ P ' PN PP KUDSDYRVWFLMHYL .Y U NJPP Â3DV





   ˜ ^4`P  V  *XELWDN QD XOD]X X

P





3RVWDYOMDVH%HUQRXOOLMHYDMHGQDGåEDL]PH XOLMHYRJLGHVQRJUH]HUYRDUDWHXYUãWDYDPRL]UD]]DYLVLQXGREDYH SXPSH K3

+  §¨   .Y  O˜

©



˜ 4



+  §¨   .Y  O˜



¸˜ ' ¹ '˜ S˜ J

D  E˜ 4

©





˜ 4

¸˜ ' ¹ '˜ S˜ J



,]RYRJL]UD]DL]UDþXQDYDVHSURWRN4 4

D+

§   .  O˜ / · ˜   E ¨ Y ¸ ' ¹ '˜ S˜ J ©



=D SUHYL LWHUDFLMVNL NRUDN SUHWSRVWDYOMD VH VWUXMDQMH X UHåLPX SRWSXQH WXUEXOHQFLMH SD MH PRJXüH L]UDþXQDWL NRHILFLMHQWWUHQMD 

O N  '  5H



N

§ OQ § ·· ¨ ¨ ˜ '   ¸ ¸ 5H ¹ ¹ © ©



O

O N  '  5Q

O





SURWRNUDþXQDPRLWHUDFLMVNLPSRVWXSNRP 4

4

4



D+ /·



§  .  O ˜ ˜ E ¨ Y  ¸ ' ¹ '˜ S˜ J ©

§   .  O ˜ / ·˜   E ¨ Y  ¸ ' ¹ '˜ S˜ J ©

§   .  O ˜ / ·˜   E ¨ Y  ¸ ' ¹ '˜ S˜ J ©



KS

P

V

5Q O

O N  '  5Q

4 O

 P

 u 

V

O N  '  5Q

5Q O



D+

D  E˜ 4

O

 P

 u 



D+

DYLVLQDGREDYHMHGQDNDMH KS

4



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

4 O

 P

 u 

O N  '  5Q

V

5Q O

˜ 4˜ U '˜ S˜ P



5Q

 u 

5Q

 u 

5Q

 u 



˜ 4˜ U '˜ S˜ P



 ˜ 4˜ U '˜ S˜ P 





&MHYRYRG 

,VSLW]DGDWDN SD



,] UH]HUYRDUD V NRQVWDQWQLP QLYRRP YLVLQH +   P LVWMHþH YRGD JXVWRüH U   NJP YLVNR]QRVWL P   3DV NUR] KRUL]RQWDOQX FLMHY RG WUJRYDþNRJ þHOLND 2GUHGLWH L]OD]QL SURPMHU FLMHYL '  GD VH XVSRVWDYL SURWRN 4   PV=DGDQRMH/  P/  P'  PP.   

J +

UP



/

/







S









D

=DRGUH LYDQMHL]OD]QRJSURPMHUDFLMHYL' SRWUHEQRMH SRVWDYLWL %HUQRXOOLMHYX MHGQDGåEX RG SRYUãLQH YRGH X VSUHPQLNX SD GR L]OD]D L] FMHYRYRGD X]LPDMXüL X RE]LU VYH JXELWNHXNOMXþXMXüLLJXELWNHQDJORJSURãLUHQMD 

.

'



'









 § ' · ¸ .13 ¨   ¸ ¨ ' ¹ © 



/ / · Y § · Y § + ¨ .  O˜  .13 ¸  ¨   O˜ ¸ ' ' ¹ ˜ J © ¹ ˜ J ©

.RULVWHüLL]UD]GDMHEU]LQDIOXLGD Y

§

/

©

'

+  ¨ .   O ˜

4



·

4

 . 13 ¸

¹ ' ˜ S˜ J

' S MHGQDGåEDVHWUDQVIRUPLUDXREOLN 

'   O ˜ / 



˜ 4 



'  ˜S ˜J



7HMHL]OD]QLSURPMHUFLMHYL'



O ˜ /   ' 



'

ª« + ˜ S˜ J § / ·  »º  ¨ .   O ˜  . 13 ¸ ˜ ' « ˜ 4 © ¹ '  »¼  ¬

=DLWHUDWLYQRUMHãDYDQMHRYRJL]UD]SRWUHEQRMHXYHVWLSRþHWQHSUHWSRVWDYNH=DSRþHWQXLWHUDFLMXSUHWSRVWDYOMD VHGDMH' '=DFLMHYRGWUJRYDþNRJþHOLNDXVYDMDVHUHODWLYQDKUDSDYRVWN PP 13 ˜ 4˜ U

5Q 

'˜ S˜ P

5Q 

˜ 4˜ U '˜ S˜ P

O N  '  5Q 

O

O



O N  '  5Q 

O

O





,WHUDWLYQLPSRVWXSNRPL]UDþXQDYDVHL]OD]QLSURPMHUFLMHYL

O˜ /  '



'

ª« + ˜ S˜ J § / ·  º»  ¨ .  O˜  .13 ¸ ˜ ' « ˜ 4 © ¹ ' »¼ ¬ ˜ 4˜ U

5Q 

'˜ S˜ P 

'

O

O N  '  5Q 

O

'



.13

O˜ /  ' ª« + ˜ S˜ J § / ·  º»  ¨ .  O˜  .13 ¸ ˜ ' « ˜ 4 © ¹ ' »¼ ¬

P

'

· § ¨   ' ¸  ¨ ' ¸¹ ©



.13



P



 =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

,VSLW]DGDWDN 

1D UDGQRP VWROX WHåLQH *    N1 QDOD]L VH SUHGPHW WHåLQH *   1 NRML VH REUD XMH VNLGDQMHP VWUXJRWLQD VLORP 5   N1 6WRO V REUDWNRP NUHüH VH NRQVWDQWQRP EU]LQRP Y   PV SUHNR NOL]QH SRYUãLQH NRHILFLMHQWD WUHQMD P    SRNUHWDQL SRPRüX KLGUDXOLþNRJ VLVWHPD SUHPD VOLFL 2GUHGLWH KLGUDXOLþNH NDUDNWHULVWLNH SXPSH SURWRN 4 YLVLQX GREDYH + WH VQDJX 3  DNR VH SUHWSRVWDYOMDGDORNDOQLRWSRULþLQHOLQLMVNLKJXELWDND =DGDQRMH/ PG FP'  FP' FPU  NJPP 3DVK P

SD

V

UP

K

G

/

J

7



G

5

*

'

'



Y

*V

P7

 ,] ]DGDQH EU]LQH JLEDQMD REUDWND VWROD L VWDSD  L X] XSRWUHEX MHGQDGåEH NRQWLQXLWHWD PRJXüH MH L]UDþXQDWL EU]LQH LVSUHGLL]DVWDSDWHXSULYRGQLPNDQDOLPDSURPMHUDG Y

Y

4

Y˜



Y

' ˜ S  '

Y ˜

G

Y

Y

4

Y ˜



Y ˜

G ˜S 



'

 



Y

Y˜



Y ˜

 





 ' ˜ S

G ˜S 



'  ' G

Y





P

Y

V



P V



=D SR]QDWH EU]LQH VWUXMDQMD PRJXüH MH L]UDþXQDWL 5H\QROGVRYH EURMHYH WH NRHILFLMHQWH WUHQMD O ODPLQDUQL VOXþDM VWUXMDQMD  U ˜ Y˜ G

5Q  O

5Q 

P 

O

5Q 

U ˜ Y˜ G

5Q 

P 



O

5Q 

5Q 



O

 



$NRSRVWDYLPR%HUQRXOOLMHYXMHGQDGåEXRGVWDSDGRVORERGQHSRYUãLQHPRJXüHMHL]UDþXQDWLSUHWODNXGHVQRMNRPRUL S 0 U ˜J S 0

Y







/ Y /  K  §¨   ˜ O˜ ¸· ˜ G ¹ ˜ J ©

˜ J

ª

U ˜ J ˜ «/  K  §¨   ˜ O˜

¬

©

Y º / · Y ¸ ˜ ˜ J  ˜ J» G¹ ¼ 



S0



 u  3D



3RVWDYOMDQMHPUDYQRWHåHVLOD]DVWDSPRJXüHMHL]UDþXQDWLSUHWODNXOLMHYRMNRPRUL )V

S 0

*

V

 * ˜ P 7  5



S0˜

' ˜ S 

' ˜

 S 0

˜P 7 ˜*V  ˜P 7 ˜*  ˜5  S0˜S˜' ' ˜S









 ' ˜ S  

 S 0˜ S˜ '





S 0



 u  3D



$NR SRVWDYLPR %HUQRXOOLMHYX MHGQDGåEX NUR] FLMHOL VLVWHP RG OLMHYH GR GHVQH NRPRUH X]LPDMXüL X RE]LU L JXELWNH XODVNDXYHOLNLVSUHPQLN JRUQMLYHOLNLVSUHPQLNLGHVQDNRPRUD PRJXüHMHL]UDþXQDWLYLVLQXGREDYHSXPSH =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,





&MHYRYRG S 0 U ˜J





Y

˜ J

S 0

 KS

U ˜J





Y

 §¨   ˜ O˜

©

˜ J





/ · Y / · Y § ¸ ˜ ˜ J  ¨   ˜ O˜ ¸ ˜ ˜ J G¹ G¹ ©

  § S 0 Y · / · Y / · Y § § ¸   ¨   ˜ O˜ ¸ ˜  ¨   ˜ O˜ ¸ ˜ ¨  ˜ J © ˜ J ¹ G ¹ ˜ J © G ¹ ˜ J © U ˜ J U ˜J

S 0

KS KS

Y



SS

P

U ˜ J˜ K S

SS



 u  3D



3URWRNLVQDJDSXPSHUDþXQDVHL]L]UD]D 

4S

Y˜



G ˜S

 P

4S



 u 

3S

V

U ˜ J˜ K S˜ 4S

3S

:



 

,VSLW]DGDWDN

.OLPDWL]DFLMVNLYRGSUDYRNXWQRJSRSUHþQRJSUHVMHNDD[E [FP ]ERJ UHNRQVWUXNFLMH SURVWRULMH SRWUHEQR MH ]DPLMHQLWL NOLPDWL]DFLMVNLP YRGRPSUDYRNXWQRJSRSUHþQRJSUHVMHNDþLMDYLVLQDQLMHYHüDRGE  FP2GUHGLãLULQXNOLPDWL]DFLMVNRJYRGDNRMDRVLJXUDYDMHGQDNLSDGWODND SR MHGLQLFL GXOMLQL SUL LVWRP SURWRNX 3UHWSRVWDYLWH VWUXMDQMH X UHåLPX SRWSXQHWXUEXOHQFLMH=DGDQRMHN PP YLVLQDKUDSDYRVWL  

E

D

3RSUHþQL SUHVMHN NOLPDWL]DFLMVNRJ YRGD MH SUDYRNXWDQ SD MH SRWUHEQR XYHVWLHNYLYDOHQWDQSURPMHU ˜ D ˜ E

'H

'H

˜ D  ˜ E

P

'H

˜ D ˜ E  ˜ D   ˜ E 



3DGWODND]DREDVOXþDMDSRMHGLQLFLGXOMLQHPRUDELWLLVWL O˜

/



4

˜

O˜

'H D ˜ E ˜ ˜ J



DE

˜



˜ D ˜ E D ˜ E 

/

'H D ˜ E ˜ ˜ J  

O˜





4

˜

D  E

˜



˜ D ˜ E  D ˜ E    



2GQRVQRãLULQXNOLPDWL]DFLMVNRJYRGDUDþXQDPRL]L]UD]D 

D

D   E  D˜ E ˜

D  E

E



˜

O O



3RþHWQHSUHWSRVWDYNH]DSURUDþXQVX O







I N  'H  

O

O

D

D



,WHUDFLRQRSREROMãDYDPRUMHãHQMH

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG  

D

D  E 

D

D  E D˜ E ˜

 E

D  E D˜ E D  E 

D

˜

D

E

˜

D  E D˜ E D  E





˜

˜



E

D  E D˜ E D  E

˜



E

O O O O

˜

˜

O O O O

D

P

'H

D

P

'H

˜ D ˜ E  ˜ D  ˜ E  ˜ D ˜ E  ˜ D  ˜ E 

D

P

'H

D

P

'H









O

I N  'H  

O

I N  'H  

˜ D ˜ E  ˜ D  ˜ E  ˜ D ˜ E  ˜ D  ˜ E 











O

I N  'H  

O

I N  'H  



LGXüLPLWHUDFLRQLPNRUDNRPL]UDþXQDYDVHãLULQDNDQDODD PLGDOMQMLPLWHUDFLRQLPNRUDFLPDSREROMãDYDVH UMHãHQMHVDPRXþHWYUWRMGHFLPDOL



,VSLW]DGDWDN

2GUHGLWH YLVLQX + ]D VLVWHP SUHPD VOLFL DNR MHSURWRNNUR]FLMHY/GYDSXWDYHüLRGSURWRND NUR] FLMHY / 3UHWSRVWDYLWH NRQVWDQWDQ NRHILFLMHQWWUHQMDOXVYLPFLMHYLPDO  =DGDQRMH+ P' PP/  P' PP/ P' PP/ PU NJPQ PV

SD

J

+ +

 

/

/



'

'

=D RGUH LYDQMH YLVLQH + SRWUHEQR MH SRVWDYLWL GYLMH %HUQRXOOLMHYH MHGQDGåEH L WR RG OLMHYRJ VSUHPQLNDGRL]OD]DL]FLMHYLSURPMHUD'WHRG GHVQRJ VSUHPQLND GR L]OD]D L] FLMHYL SURPMHUD '

' / 

+





/ Y / · Y § O˜ ˜  ¨   O˜ ¸˜ ' ˜ J © ' ¹ ˜ J



/ Y / · Y § O˜ ˜  ¨   O˜ ¸˜ ' J ' ¹ J ©

+



-HGQDGåEDNRQWLQXLWHWD]DVLVWHPSUHPDVOLFL 4  4

˜ 4  4

4

4

˜ 4



8NROLNRMHGQDGåEXNRQWLQXLWHWDXYUVWLPRX%HUQRXOOLMHYHMHGQDGåEH 

+



/ ˜ ˜ 4 / · ˜ ˜ 4 § O˜ ˜  ¨   O˜ ¸ ˜ ' ' ˜ S˜ J © ' ¹ ' ˜ S˜ J  

+

/



˜ 4

,]SUYH%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLSURWRN4NUR]FLMHYSURPMHUD' =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



/ · ˜ ˜ 4 § O˜ ˜  ¨   O˜ ¸˜ ' ' ˜ S˜ J © ' ¹ ' ˜ S˜ J  



&MHYRYRG / · º ª § « ¨   O˜ ¸ » ' ¹ »  / © « ˜ O˜  ˜ ˜4   « »    ' ˜ S ˜ J ' ˜ S ˜ J   ¬ ¼

+









+

4 ˜ O˜

'

/

   ˜S ˜J





/ · § ¨   O˜ ¸ ' ¹ ©  ˜

'

   ˜S ˜J

 P

 u 

4



V



8YUãWHQMHPSURWRND4XGUXJX%HUQRXOOLMHYXMHGQDGåEXL]UDþXQDYDVHUD]LQDIOXLGDXGUXJRPVSUHPQLNX /





/ · ˜ ˜ 4 § O˜ ˜  ¨   O˜ ¸ ˜ ' ' ˜ S˜ J © ' ¹ ' ˜ S˜ J  

+

˜ 4

+

P



 

,VSLW]DGDWDN SD

9RGD JXVWRüH U   NJP VH SUHWDþH L] YLãHJ X QLåL VSUHPQLNNUR]SUDYRNXWQLEHWRQVNLNDQDOãLULQHE P GXOMLQH/ PSURWRNRP4 OV2GUHGLWHYLVLQXK YRGHXNDQDOX6YHORNDOQHJXELWNH]DQHPDULWH=DGDQRMH + PQ PV YLVNR]QRVWYRGH N PP YLVLQDKUDSDYRVWL]DEHWRQ 

J



.DQDO

UQ

K +

/



E

 S

3RWUHEQR MH XYHVWL HNYLYDOHQWQL SURPMHU MHU NDQDO LPD SUDYRNXWQL SRSUHþQL SUHVMHN =D SUYX LWHUDFLMX SUHWSRVWDYOMDPR GD MH YLVLQD YRGH X NDQDOX MHGQDND ãLULQL NDQDOD

D

'HN

$ 2

'HN

˜ E˜ K K  E



%HUQRXOOLMHYHMHGQDGåEDL]PH XYLãHJLQLåHJVSUHPQLND 

+

§   O˜ / · ˜ Y ¨ ' HN ¸ ˜ J © ¹



§   O˜ / · ˜ 4 ¨ ' HN ¸ ˜ J ˜ E ˜ K  © ¹



ª   O˜ /˜ K  E º ˜ 4 « » ˜ E˜ K ¼ ˜ J ˜ E ˜ K  ¬



=DWDNRL]UDþXQDWLHNYLYDOHQWQLSURPMHU SUHWSRVWDYNDK E UDþXQDPR5H\QROGVRYEURMLNRHILFLMHQWWUHQMD O N  '  5H

'HN



§ OQ § N   · · ¨ ¨ ˜ '  ¸ ¸ 5H ¹ ¹ © ©

P 5Q



 u 

5Q



O



˜ 4 'HN ˜ S˜ Q

O N  'HN  5Q



O





,]%HUQRXOOLMHYHMHGQDGåEHUDþXQDVHHNYLYDOHQWQLSURPMHUFMHYRYRGDSUHPDL]UD]X =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG 

ª¬ ˜ E˜ K  O˜ /˜ K  E º¼ ˜

+



4





˜ J ˜ E ˜ K 

,WHUDWLYQLPSRVWXSNRPGROD]LPRGRUMHãHQMD 

ª¬ ˜ E˜ K  O˜ /˜ ˜ K  E º¼ ˜

K 'HN

P

5Q



ª¬ ˜ E˜ K  O˜ /˜ ˜ K  E º¼ ˜

'HN

P

5Q



˜ J ˜ E ˜ + 

ª¬ ˜ E˜ K  O˜ /˜ ˜ K  E º¼ ˜

K

P

O



K

P

O



K

P



4

 u 



K



˜ J ˜ E ˜ +

 u 



K



4



4



˜ J ˜ E ˜ +





,VSLW]DGDWDN

2GUHGLWHSURPMHU'GLPQMDNDSUHPDVOLFLSRWUHEDQGDVHRVWYDULSURWRN4  PVYUXüLKGLPQLKSOLQRYDYLVNR]QRVWLP ˜ 3DV3UHWSRVWDYLWHGDMHWODN QD L]OD]X L] GLPQMDND MHGQDN RNROLãQRP WODNX L GD MH WODN X ORåLãWX MHGQDN RNROLãQRPWODNX XSR]RUHQMHSRWUHEQRMHX]HWLXRE]LUUD]OLNXDWPRVIHUVNRJWODND L]PH XYUKDGLPQMDNDLORåLãWD =DQHPDULWHVYHORNDOQHJXELWNH=DGDQRMH/  P N   PP YLVLQD KUDSDYRVWL XQXWDU GLPQMDND  SD   EDU DWPRVIHUVNL WODNQDYLVLQLORåLãWD UD NJPU' NJP  UDGLODNãHJSURUDþXQD SUHWSRVWDYLWHNRQVWDQWQXJXVWRüXRNROLãQRJ]UDNDLGLPQLKSOLQRYD 

J / '

 

K|



SD

  3UHPD XYMHWLPD ]DGDWND SRWUHEQR MH X]HWL X RE]LU UD]OLNX DWPRVIHUVNRJ WODND L]PH X YUKD GLPQMDND L ORåLãWD $WPRVIHUVNLWODNSD'QDYLVLQLYUKDGLPQMDNDUDþXQDVHL]MHGQDGåEHPDQRPHWUD S D'

SD  U D ˜ J ˜ /

S D'

EDU



3RVWDYOMDPR%HUQRXOOLMHYXMHGQDGåEXRGORåLãWDRGYUKDGLPQMDND SD U '˜ J

S D'



/ ˜ 4  §¨ O '˜  ¸· ˜ / ' U '˜ J © ¹ '˜ S˜ J 

=DUDþXQDQMHNRHILFLMHQWDWUHQMDOSUHPDL]UD]X O N  '  5H 

 

§ OQ § N   · · ¨ ¨ ˜ '  ¸ ¸ 5H ¹ ¹  © ©

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

&MHYRYRG SRWUHEQRMHSUHWSRVWDYLWLSURPMHUGLPQMDND']DSRþHWDNLWHUDWLYQRJSRVWXSND3UHWSRVWDYOMDPR' P ˜ 4˜ U '

5Q

5Q

'˜ S˜ P





 u 

O'

O N  '  5Q

O'





=DWDNRL]UDþXQDWLNRHILFLMHQWWUHQMDOLSUHWSRVWDYOMHQLSURPMHU'SURPMHUGLPQMDNDUDþXQDVHSUHPDL]UD]X P 

O'˜/  ' ˜

'



˜ 4 ˜ U '

SD  SD'  U '˜J˜/ ˜S

'

P



5MHãHQMHVHSREROMãDYDLWHUDWLYQLPSRVWXSNRPNDNRVOLMHGL ˜ 4˜ U '

5Q

5Q

'˜ S˜ P 

O'˜/  ' ˜

'

˜ 4˜ U '

5Q

'˜ S˜ P

˜ 4˜ U '

5Q

'˜ S˜ P

SD  SD'  U '˜J˜/ ˜S

'

O'˜/  ' ˜



 u 



O'

O'

'



 u 

P

O N  '  5Q



O'

 u 

O'

 u 



˜ 4 ˜ U '

SD  SD'  U '˜J˜/ ˜S

5Q



O N  '  5Q



5Q

O'˜/  ' ˜

O'

˜ 4 ˜ U '



'



 u 



 u 



O'

'

P

O N  '  5Q





˜ 4 ˜ U '

SD  SD'  U '˜J˜/ ˜S



'

P



.DRNRQDþQRUMHãHQMHXVYDMDVHSURPMHUGLPQMDND' P 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 



             

.ROLþLQDJLEDQMD 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD  

,VSLW]DGDWDN



.ROLNLPPRPHQWRP0WUHEDSULGUåDYDWLFLMHYSUHPDVOLFLGDVHQHSRþQH RNUHWDWL3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH+  PU NJP' PP5 PD E 

SD



J U



+



'

%U]LQD VWUXMDQMD QD L]OD]QLP SUHVMHFLPD ODNR VH UDþXQD SUHPD 7RUULFHOOLMHYRMMHGQDGåEL Y

˜ J ˜ +

Y



P V

5



,PSXOVQHIXQNFLMDQDL]OD]QLPSUHVMHFLPDMHGQDNHVX 

,

U ˜Y ˜

E

D 0



' ˜S

,



1



0RPHQWSRWUHEDQVSUHþDYDQMHRNUHWDQMDFLMHYLMHGQDNMHPRPHQWLPDLPSXOVQLKIXQNFLMD 0

5˜ , ˜ VLQ D  5˜ , ˜ VLQ E

0

1 ˜ P



 S

,VSLW]DGDWDN

.ROLND VLOD ) L PRPHQW 0 VYH WUL NRPSRQHQWH VLOH L PRPHQWD  RSWHUHüXMH VSRM FLMHYL L UH]HUYRDUD WRþND $  3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJIOXLGD=DGDQRMH+ PU NJP' PP5 PD E G K P

D

J U

+

$



'

K

G

,FRV G 



5



5 E



#

\

D 

E



\

[

 ,



[

D



%U]LQXVWUXMDQMDQDREDL]OD]DL]FLMHYLUDþXQDVHSUHPD7RUULFHOOLMHYRMIRUPXOL Y

˜ J ˜ +

Y



P V



,]MHGQDGåEHNRQWLQXLWHWDUDþXQDVHEU]LQDXWRþFL$ 

Y$˜

' ˜S 





' ˜S 



 Y˜

' ˜S 

Y$

˜ Y

Y$



P V



,]%HUQRXOOLMHYHMHGQDGåEHRGWRþNH$GRL]OD]DL]FLMHYLPRJXüHMHL]UDþXQDWLSUHWODNXWRþFL$

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD  S 0$ U ˜J







Y$

Y

˜ J

˜ J

S 0$

 









˜ Y  Y$ ˜ U

S 0$



 u  3D



,PSXOVQDIXQNFLMD,QDL]OD]XL]FLMHYLWHLPSXOVQDIXQNFLMDXWRþFL$UDþXQDMXVHSUHPDL]UD]LPD ,





U ˜Y ˜

' ˜S

,



1



S0$  U ˜Y$ ˜ '˜S 

,$

,$

1



2SWHUHüHQMHVSRMDFLMHYLLUH]HUYRDUD WRþND$ UDþXQDVHSUHPDL]UD]LPD )[ )\

, ˜ FRV D ˜ FRV G  , ˜ FRV E , ˜ VLQ D ˜ FRV G  , ˜ VLQ E

)[

1

)\

 1

)]

, ˜ VLQ G  ,$

)]

1

0[

)\˜ K

0[

1 ˜ P

0\

1 ˜ P

0]

1 ˜ P

0\ 0]

, ˜ VLQ G ˜ 5  )[˜ K

, ˜ FRV G ˜ VLQ D 5  , ˜ VLQ E ˜ 5





,VSLW]DGDWDN

)OXLGSUROD]LNUR]ILOWDUSURWRNRP4 PK SUL þHPX MH SDG WODND NUR] ILOWDU 'S   EDUD 2GUHGLWH UH]XOWDQWQX VLOX ) IOXLGD QD ILOWDU DNR MH SUHWODN QD XOD]X X ILOWDU S0   EDUD D XQXWUDãQML YROXPHQILOWUD9 O=DGDQRMH' PP' PPU NJP

S0

4

'



'

J



9



U

%U]LQXVWUXMDQMDQDXOD]QRPLL]OD]QRPSUHVMHNX L]ILOWUDUDþXQDPRL]MHGQDGåEHNRQWLQXLWHWD Y

4 

' ˜ S

Y



P V

4

Y



' ˜ S

Y



P

,

V



7ODNQDL]OD]QRPSUHVMHNXILOWUDUDþXQDVHL]L]UD]D S 0

S 0  'S

S 0



 u  3D



6LOXQDILOWDUUDþXQDPRL]MHGQDGåEHNROLþLQHJLEDQMD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,

.ROLþLQDJLEDQMD  

,

S0  U ˜Y ˜

' ˜ S

,

S0  U ˜Y ˜

' ˜ S

)[

,











 u  1

,

 u  1



 )]

)[  )]

)5



,



,  U ˜ J ˜ 9 

)5



 u  1

)]

 u  1

D

§ )] · ¸ © )[ ¹

DWDQ ¨

D

GHJ





,VSLW]DGDWDN

2GUHGLWH VLOX POD]D YRGH YDWURJDVQRJ ãPUND QD NURYLãWH NXüH SUHPD VOLFL 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJIOXLGD=DGDQRMHK PD PD  SURWRNNUR]POD]QLFXYDWURJDVQHFLMHYL4 OVU NJPE  Y

,

J E

D



K



[



Y

D

Y

J D

]



I

,





 

)



D



, 

,] MHGQDGåEH NRVRJ KLFD RGUH XMHPR EU]LQX QD L]OD] L] YDWURJDVQRJ ãPUND Y˜ FRV D ˜ W

W

D

D

Y˜ FRV D

D ˜ WDQ D  K

J

Y˜ VLQ D ˜ W 

J

Y˜ VLQ D ˜

D

D

˜



˜W



Y˜ FRV D

K





Y

 Y˜ FRV D 

J

D

˜ §¨

· ¸  © Y˜ FRV D ¹ J 

˜



K

D

D ˜ WDQ D 

J

˜

D



 Y˜ FRV D 



D˜ WDQ D  K ˜ FRV D 

Y



K

P V



9ULMHPHSRWUHEQRGDYRGDSUHYDOLSXWRGãPUNDGRNURYDUDþXQDVHL]L]UD]D W

D

W

Y˜ FRV D

V



8WUHQXWNXVXGDUDVNURYRPNRPSRQHQWHEU]LQHYRGHL]QRVH Y[

Y˜ FRV D

Y]

Y˜ VLQ D  J ˜ W

Y[



P V

Y]



P V



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

6PMHUEU]LQHYRGHXWUHQXWNXVXGDUDVNURYRPUDþXQDVHL]L]UD]D

§ Y] · ¸ © Y[ ¹

J

DWDQ ¨

J

GHJ



3UHPDXYMHWLPD]DGDWNDVWUXMDQMHMHQHYLVNR]QRSDPRåHSRVWRMDWLVDPVLODRNRPLWDQDSRYUãLQXNURYDSUHPD VOLFL.XWL]PH XEU]LQHLVLOHUDþXQDVHSUHPDL]UD]LPD S

I E  J )

S

I





E J

I

U ˜ 4˜ Y[  Y] ˜ FRV I 



GHJ )

1





,VSLW]DGDWDN

2GUHGLWH SUHWODN S0 SUL NRMHP VH RWYDUD VLJXUQRVQL YHQWLO SUHPDVOLFLPDVHP JWHSUHWODNS0SULNRMHPVHVLJXUQRVQL YHQWLO]DWYDUD=DGDQRMHG FP' FPG FPU  NJP G 

G



S

J 

D

 

'



G S



S

0





VSUHPQLN

0

8 VOXþDMX ]DWYRUHQRJ YHQWLOD WODN X VSUHPQLNX GMHOXMH QD NUXåQRM SRYUãLQL SURPMHUD G .RG RWYDUDQMD VLOD SUHWODND PRUD VDYODGDWLWHåLQX]DWYDUDþDYHQWLOD 

S 0 ˜

G ˜S

P ˜ J



˜ P ˜ J

S 0

S 0



G ˜S



 u  3D



8 VOXþDMX NDGD MH YHQWLO RWYRUHQ XVSRVWDYOMD VH VWUXMDQMH SD SRWUHEQH YHOLþLQH UDþXQDPR SRPRüX MHGQDGåEH NRQWLQXLWHWD%HUQRXOOLMHYHMHGQDGåEHLMHGQDGåEHNROLþLQHJLEDQMD S 0 U ˜J S 0 U ˜J

P ˜ J





Y



Y

˜ J Y

Y

˜ J





˜ Y ˜

˜ J



Y





˜

G





Y˜



˜ J ˜ G   

G ˜ S

S 0  U ˜ Y

§ G · G˜ S  ¸ ˜  ¨ ˜ G  ¸  ©  ¹



G ˜S

P ˜ J





Y



,



S0  U ˜Y ˜ G ˜S 

§ G ·  ¸  ¨ ˜ G  ¸ ©  ¹ ˜¨

˜¨

%U]LQXUDþXQDPRL]L]UD]D =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



.ROLþLQDJLEDQMD 

P˜J˜

Y

Y

·  º ª«§¨ G  ¸ ˜ G ˜ S˜ U» «¨ ˜ G  ¸ » ¬©  ¹ ¼



P

Y

V

Y˜

G



˜ G 



Y



P V



3UHWODNXVSUHPQLNXUDþXQDPRL]%HUQRXOOLMHYHMHGQDGåEH 

S0

Y

U ˜J

˜ J

U ˜ Y

S 0



S 0



3D





,VSLW]DGDWDN

2GUHGLWHUH]XOWDQWQXVLOX)IOXLGDQDOXN$%FMHYRYRGDGXOMLQH/  4 PSURPMHUD' PPSUHPDVOLFLSULSURWRNX4 OVLSUHWODNXS0%   EDU X SUHVMHNX % 3UHWSRVWDYLWH NYD]LVWDFLRQDUQR LVWMHFDQMH IOXLGD $ =DGDQRMHU NJP+ P 

S0%

'

,$



J

$

 

'D EL RGUHGLOL VLOX ) QD OXN $% SRWUHEQR MH SR]QDYDWL WODNRYH L EU]LQH QD SUHVMHFLPD $ L  % 3RWUHEQR MH SRVWDYLWL %HUQRXOOLMHYX MHGQDGåEXLMHGQDGåEXNRQWLQXLWHWD

,%

% 

%

+

S0%

'

+

UJ9

 S 0$ U ˜J Y



Y

S 0%



˜ J

+

U ˜J

˜ 4

Y



' ˜S





Y



S 0$

˜ J

S0%  U ˜ J ˜ +

S 0$

EDU

P V



,PSXOVQHIXQNFLMHQDSUHVMHFLPD$L%VHUDþXQDMXL]L]UD]D ,$





,$

1



S0$  U ˜ Y ˜



' ˜S 

,%





,%

 u  1



S0%  U ˜ Y ˜



' ˜S 





9ROXPHQIOXLGDXOXNX$%MHGQDNMH 

9

%$/˜

' ˜S 

9

%$

P



6LODQDOXN$%UDþXQDVHL]MHGQDGåEHNROLþLQHJLEDQMD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD  )[

,%

)

)[  )]



)[





)

 u  1

)]



 u  1

D

,$  U ˜ J ˜ 9

%$)]

§ )] · ¸ © )[ ¹

D

DWDQ ¨



 u  1

GHJ





,VSLW]DGDWDN

'YD POD]D YRGH GUåH X UDYQRWHåL NRFNX PDVH P ]JOREQR YH]DQDXWRþFL22GUHGLWHPDVXNRFNHDNRMHNRFNDQDJQXWD]D D   3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH D PDVH POD]RYD ]DQHPDULWH=DGDQRMHU NJPY PVG P 



D

D

J

D

,]JHRPHWULMHMHRþLWR 

2 I

N

S 

D

I

GHJ

Y

D

 D

N

˜ FRV I

D ˜   FRV I VLQ I

Y

G

D G

 

D

D

 J

D

 D

2

M ) Y G

D M

 

D

Y

 

2

 N

)



J

M

D



N

D



G

 

.DNRMHULMHþRQHYLVNR]QRPVWUXMDQMHQHPRJXüHMHSUHQLMHWLWDQJHQFLMDOQXNRPSRQHQWXVLOHQDSRYUãLQX3UHPDWRPH VLOD)L)PRUDMXELWLRNRPLWHQDSRYUãLQH SUHPDVOLNDPD ,PSXOVQHIXQNFLMHGLMHODPOD]DQDNRQVXGDUDVNRFNRP QLNDNR QH VXGMHOXMX X QRUPDOQRM NRPSRQHQWL VLOH QDOD]H VH X UDYQLQL RNRPLWRM QD VLOX  ,PSXOVQD IXQNFLMD POD]D MHGQDNDMH ,



U ˜Y ˜



G ˜S 

,

1



6LOH)L)MHGQDNHVX )

, ˜ FRV I

)

, ˜ VLQ I

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

)

1

)

1



.ROLþLQDJLEDQMD  0DVXNRFNHRGUH XMHPRL]XYMHWDGDMHVXPDPRPHQWDRNRWRþNH2MHGQDNDQXOL PN ˜ J ˜ PN ˜ J ˜

D˜   D˜   ,

PN



˜ FRV D  )˜ N   )˜ N  ˜ FRV D  , ˜ FRV I ˜

˜   ˜ FRV I ˜

D



˜ FRV I

 , ˜ VLQ I ˜



D˜   FRV I

PN

J˜ FRV D



VLQ I

NJ



 

,VSLW]DGDWDN

2GUHGLWH VLOX QD MHGQX ORSDWLFX X UHãHWFL MHGLQLþQH ãLULQH  NRMD VNUHüH VWUXMDQMH ]UDND ]D NXW D   3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMHY  PVS0 EDUDU NJPW PP  

Y

W

S

,

Y

W

S

D Y

)S

D  

,

,] MHGQDGåEH NRQWLQXLWHWD PRJXüH MH L]UDþXQDWL EU]LQXY Y ˜ W

D

Y

Y ˜ D Y

VLQ D

Y ˜ W Y

Y ˜ W ˜ VLQ D 

P V



,]%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLSUHWODNS0 S 0 U ˜J S 0



Y



˜ J S 0 

S 0 U ˜J



Y



˜ J

   ˜ Y ˜ U  ˜ Y ˜ U    

S 0

EDU



,PSXOVQHIXQNFLMHNDRLVLOD)SSUHWODNDS0UDþXQDMXVHL]L]UD]D , , )S

S0  U ˜Y ˜W˜% S0  U ˜Y ˜W˜VLQ D ˜% 

,

 u  1



,

 u  1

S 0 ˜ W ˜ FRV D ˜ %

)S





1



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

6LOHQDORSDWLFXUDþXQDPRL]L]UD]D )[

,  , ˜ VLQ D  )S ˜ FRV D

)[

1

)\

,˜ FRV D  )S ˜ VLQ D

)\

1



) I

)[  )\



§ )\ · ¸ © )[ ¹

DWDQ ¨

)

1

I

GHJ





,VSLW]DGDWDN

2GUHGLWH SUHWODN X VSUHPQLNX X NRML XWMHþH IOXLG SURWRNRP 4  PVGDELVLODQDQDJORSURãLUHQMHELODMHGQDNDQXOL6YHOLQLMVNH JXELWNH ]DQHPDULWH D RG ORNDOQLK JXELWDND X]PLWH X UD]PDWUDQMH JXELWDNXODVNDXYHOLNLVSUHPQLNLJXELWDNQDJORJSURãLUHQMD=DGDQR MHG P' PK PU NJP

S0

J

K

 

G

4

'

 U

%HUQRXOOLMHYDMHGQDGåEDRGXOD]QHFLMHYLGRSRYUãLQHVSUHPQLND SRGWODNRP S 0 U ˜J





Y

K

˜ J

S 0 U ˜J



 . 13˜

Y

˜ J





Y

˜ J 

%HUQRXOOLMHYDMHGQDGåEDRGXOD]QHFLMHYLGRWRþNHQHSRVUHGQRL]DQDJORJSURãLUHQMD S 0 U ˜J





Y

S 0

˜ J

U ˜J



 . 13˜

Y

˜ J



Y



˜ J 

,]RYHGYLMHMHGQDGåEHVOLMHGLUHODFLMD S 0

U ˜ J ˜ K  S 0



-HGQDGåEDNRQWLQXLWHWDLL]UD]]DNRHILFLMHQWJXELWNDQDJORJSURãLUHQMD Y

˜ 4

˜ 4

Y



' ˜S

 $ · §   ¨ ¸ $ ¹ ©

.13



G ˜S



,

8YUãWHQRX%HUQRXOOLMHYXMHGQDGåEX S 0 U ˜J

S 0





S 0



G ˜S ˜J



S 0 



   § G · ˜ 4 ˜ 4  ¨  ˜  ¸     U ˜J ' ¹ G ˜ S ˜ J ' ˜S ˜J  ©



˜ 4

˜ 4 ˜ U 



G ˜S

§ G

˜¨



©'



   · G · ˜ 4 ˜ U § G U ˜ J ˜ K  S  ˜  ¸ 0 ¨  ¸     ' ¹ ' ¹ G ˜S © '

G



-HGQDGåEDNROLþLQHJLEDQMD]DQDJORSURãLUHQMH XYMHW]DGDWNDMHGDVLOD)PRUDELWLMHGQDNDQXOL  =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,

.ROLþLQDJLEDQMD  )

,  ,

S

0





G ˜S  S

 U ˜Y  ˜

0



'˜S



 U ˜Y  ˜





       ª G · ˜ 4 ˜ U § G ˜ 4 º G ˜ S § ˜ 4 · ' ˜ S U ˜ J ˜ K  S  ˜   U ˜ ˜  U ˜ J ˜ K  S  U ˜ ˜ « 0 ¨  ¸ » ¨ 0 ¸        ' ¹ G ˜S © ' G ˜S ¼  ' ˜S ¹  ¬ © 

˜ U ˜

S 0

4

' ˜ S 



 U ˜ J˜ K  ˜

U

G ˜ S ˜ ' 







˜4

S0



EDU





,VSLW]DGDWDN

2GUHGLWHNXWJL]XYMHWDGDVLODIOXLGDJXVWRüHU NJP QDUDYQXSORþXEXGHPDNVLPDOQD3UHWSRVWDYLWHVWUXMDQMHLGHDOQRJ \ Y IOXLGD=DQHPDULWHXWMHFDMVXGDUDPOD]DXVUHGLQLSORþH=DGDQRMH Y PVG PY PVG PD E  D 

G

G



J



Y E

[

  ,PSXOVQHIXQNFLMHPOD]RYDYRGHUDþXQDMXVHL]L]UD]D

,





,

U ˜ Y ˜

G ˜ S 

,

1

,

1

D

\ G Y

G Y

)



,

U ˜ Y ˜



[

J

,



E ,



G ˜ S

,

3UHPD XYMHWX ]DGDWND SUHWSRVWDYOMD VH VWUXMDQMH QHYLVNR]QRJ IOXLGD SD VH QD SORþX QH PRåH SUHQLMHWL VLOD X VPMHUXNRRUGLQDWH[6LOD)PRUDELWLRNRPLWDQDSORþX-HGQDGåEDNROLþLQHJLEDQMDGDQDMHL]UD]RP )

,  ˜ VLQ D  J  ,  ˜ VLQ E  J 

0DNVLPXPVLOHWUDåLVHGDVHSUYDGHULYDFLMDVLOH)SRNXWXJL]MHGQDþLVQXORP G GJ

)

G GJ

,˜VLQ D  J  ,˜VLQ E  J

, ˜ FRV D  J  , ˜ FRV E  J



, ˜ FRV D ˜ FRV J  VLQ D ˜ VLQ J  , ˜ FRV E ˜ FRV J  VLQ E ˜ VLQ J

J

DWDQ «

ª ,˜ FRV D  ,˜ FRV E »º «¬ ,˜ VLQ D  ,˜ VLQ E »¼

J



GHJ



    =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

,VSLW]DGDWDN

1D YHOLNL VSUHPQLN SUHPD VOLFL SULNOMXþHQR MH NROMHQR V POD]QLFRP 1HSRVUHGQR SULMH NROMHQD XJUD HQ MH PDQRPHWDU NRML SUL ]DWYRUHQRM POD]QLFL SRND]XMH SUHWODN S0   EDU D NDGD VH POD]QLFD RWYRUL SUHWODN SDGQH QD S0   EDU 8] SUHWSRVWDYNX QHYLVNR]QRJ VWUXMDQMD RGUHGLWH NROLND MH WDGD VLOD QD NROMHQR L POD]QLFX =DGDQR MH ' PPU NJPD K  P9ROXPHQYRGHXNROMHQXLPOD]QLFL9 GP

S0

J



G

S0

'

D

K

  

,]XYMHWDGDPDQRPHWDUSRND]XMHSUHWODNS0 EDU]D]DWYRUHQXPOD]QLFXPRJXüHMHRGUHGLWLWRWDOQLSUHWODN X VSUHPQLNX WRWDOQL SUHWODN XNOMXþXMH L YLVLQX YRGH X VSUHPQLNX  NRML MH MHGQDN  S0   EDU 3RPRüX %HUQRXOOLMHYHMHGQDGåEHRGVSUHPQLNDGRXOD]DXPOD]QLFXPRJXüHMHRGUHGLWLEU]LQXQDXOD]XXPOD]QLFX S 0

S 0

U ˜J

U ˜J



Y



Y

˜ J



S0  S0

Y

U

 PV





 3RPRüX %HUQRXOOLMHYH MHGQDGåEH RG VSUHPQLND GR L]OD]D L] POD]QLFH PRJXüH MH RGUHGLWL EU]LQX QD L]OD]X L] POD]QLFH

S0  K˜ U ˜ J



S 0

K

U ˜J

Y

Y

˜ J



Y

U

PV





,]MHGQDGåEHNRQWLQXLWHWDPRJXüHMHRGUHGLWLL]OD]QLSURPMHUPOD]QLFH 

Y˜



' ˜S

Y˜



G ˜S

G





Y

G

Y



]

,PSXOVQHIXQNFLMHLVLOHUDþXQDPRL]L]UD]D ,



S0  U ˜Y ˜ '˜S 





G ˜S



 u  NJ PV

,

 u  NJ PV





U ˜ Y ˜

)[

,  ,˜ FRV D

)[

 u  NJ PV

)]

U ˜ J ˜ 9  ,˜ VLQ D

)]

NJ PV

)5

 u  NJ PV

)5



)[  )]





  =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



,

'

 D

,

[



,



G

K

,

P



 

E

§ § )] · ·  ¨ DWDQ ¨ ) ¸ ¸ ˜ © © [¹¹ S

E





.ROLþLQDJLEDQMD 

,VSLW]DGDWDN



EUDQD

SD

K U /

2GUHGLWH KRUL]RQWDOQX VLOX QD EUDQX MHGLQLþQH ãLULQH SUHPD VOLFL 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGDWHXQLIRUPQHSURILOHEU]LQDGRYROMQRGDOHNRRG EUDQHLQDSUHOMHYX=DGDQRMHK PK P K PK P/ PU NJP

J

K



K



K

 

  , ,

=DNRQWUROQLYROXPHQX]LPDVHYRGDNRMDRSODNXMHEUDQX 

.RQWUROQL YROXPHQ

'D EL L]UDþXQDOL LPSXOVQH IXQNFLMH SRWUHEQR MH RGUHGLWL EU]LQXLVSUHGEUDQHLEU]LQXQDSUHOMHYX,]NRVRJKLFDUDþXQDPR EU]LQXQDSUHOMHYXEUDQH 

Y˜ W

Y

/





W





˜ K  ˜ K  ˜ K



J˜ /

K  K  K

˜ Y



K  K  K

˜ ˜ /˜ K  K  K ˜ J

Y

PV





%U]LQDLVSUHGEUDQHUDþXQDVHL]MHGQDGåEHNRQWLQXLWHWD Y ˜ K   K 

Y˜ K 

Y



K

Y

K  K

PV





6LODQDEUDQXMHGLQLþQHãLULQH%L]QRVL ,

K  K ª º  U ˜ Y » ˜ K   K  ˜ % «U ˜ J ˜  ¬ ¼

,

 u  1

,

K · § ¨ U ˜ J˜  U ˜ Y ¸ ˜ K ˜ %  © ¹

,

1

)

,  ,

)

 u  1







      =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

,VSLW]DGDWDN J

S

 2GUHGLWHNRMRPVLORP)WUHEDRSWHUHWLWLNOLSSURPMHUDG FP GDELVHVSXãWDREU]LQRPY PVXFLOLQGUXSURPMHUD' FP LVSXQMHQRJ YRGRP JXVWRüH U   NJP 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD 8SXWD NRRUGLQDWQL VXVWDY SRVWDYLWH UHODWLYQR X RGQRVXQDNOLS

D

G

Y

)



Y



U

'

,





\



[

 

Y



-HGQDGåEDNRQWLQXLWHWDSRVWDYOMHQD]DNRRUGLQDWQLVXVWDYNRMLVHJLEDVDVWDSRP 

Y ˜

' ˜S

Y ˜



,

'  G ˜S 







,]MHGQDGåEHNRQWLQXLWHWDRGUH XMHVHL]OD]QDEU]LQD 

Y

Y˜

'

'



G

Y





PV





,]%HUQRXOOLMHYHMHGQDGåEHRGUH XMHVHSUHWODNQDSRYUãLQLFLOLQGUD 

S 0



U ˜J



Y

Y

˜ J

˜ J

S 0

Y

 

˜U



 Y 

S 0

EDU



6LODQDþHORVWDSDMHGQDNDMHUD]OLFLLPSXOVQLKIXQNFLMD )

'˜S  U ˜Y ˜ '

S0





  U ˜ Y ˜



 





 G ˜S

)



1



 

,VSLW]DGDWDN S



D

J K

G



K



,]PH X GYD YHOLND DNXPXODFLMVND MH]HUD XJUD HQD MH EUDQD V WXUELQRP =ERJ SRYHüDQMD VWXSQMD GMHORYDQMD WXUELQH LVSRG QMH MH PRQWLUDQ GLIX]RU 2GUHGLWH VLOX QD GLIX]RU DNR MH L]PMHUHQ QHWR SDG WXUELQH K    P 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJ IOXLGD L MHGQROLNH SURILOH EU]LQD SR VYLP SUHVMHFLPD=DGDQRMHK  PK  PK  PK   PK  PG  PG  PU NJP W





GLIX]RU

G



K



K





K

 

U

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

 











.ROLþLQDJLEDQMD 

$NRSRVWDYLPR%HUQRXOOLMHYXMHGQDGåEXL]PH XJRUQMHJLGRQMHJVSUHPQLNDPRJXüHMHL]UDþXQDWLSURWRNNUR] WXUELQX 

˜ 4

Y

K   K7

 G ˜ S



Y

˜ 4

J



4



G ˜ S ˜ J

 



˜ G  ˜ S˜ J ˜ ˜

 J

˜ K   K7

4

 

P V



%U]LQHQDXOD]XLL]OD]XL]GLIX]RUDUDþXQDMXVHL]MHGQDGåEHNRQWLQXLWHWD 

˜ 4

Y

Y

K   K7



G ˜ S

J



˜ 4 

4



G ˜ S ˜ J

 



˜ G  ˜ S˜ J ˜ ˜

 J

˜ K   K7

4

 

P V



3RVWDYOMDQMHP%HUQRXOOLMHYLKMHGQDGåELGRXOD]DLL]OD]DL]GLIX]RUDPRJXüHMHL]UDþXQDWLWODNRYHQDXOD]QRPL L]OD]QRPSUHVMHNXGLIX]RUD K  K 7  K

S 0 U ˜J





Y

˜ J

 § Y · ¨ K  K7  K   ˜  ¸ ˜ U ˜ J  J ¹ ©

S 0

K  K 7  K  K

S 0 U ˜J

S 0





Y

˜ J

 §  Y · ¨ K  K7  K  K  ˜ ¸ ˜ U ˜ J  J ¹ ©

S 0

EDU

S 0

EDU



3R]QDMXüLEU]LQHLWODNRYHQDXOD]QLPLL]OD]QLPSUHVMHFLPDGLIX]RUDPRJXüHMHL]UDþXQDWLLPSXOVQHIXQNFLMH ,  K   G ˜ S 9 , S 0  U ˜ Y ˜ ,  u  1 K  9  G ˜ S    , S 0  U ˜ Y ˜ ,  u  1 ,   











6LODKLGURVWDWVNRJWODNDVYDQMVNHVWUDQHGLIX]RUDMHGQDNDMHWHåLQLYRGHNRMD]DX]LPDSURVWRUL]PH XGLIX]RUDL VORERGQHSRYUãLQH6LOXXVOLMHGJLEDQMDIOXLGDPRåHVHL]UDþXQDWLSRPRüXLPSXOVQLKIXQNFLMD )YDQMVNL

U ˜ J˜ 9

)XQXWUDQML

,  ,  U ˜ J˜ 9



8NXSQDVLODQDGLIX]RUGRELMHVH]EUDMDQMHPRYLKGYDMXVLOD )

)YDQMVNL  )XQXWDUQML

)

  ª G ˜ S G ˜ Sº »J ,  ,  U ˜ « K   K  ˜  K ˜   ¼ ¬

)



 u  1



      =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

,VSLW]DGDWDN 

SD

2GUHGLWHYLVLQXRWYRUDKGDELVLODNRMDSULGUåDYDSUHJUDGQXVWMHQNX ]JOREQR YH]DQX X WRþFL $ ELOD PDNVLPDOQD WH RGUHGLWH L]QRV VLOH 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJ IOXLGD =DGDQR MH +   P G  PU NJPE P

J

U

) +

G

 SD

J

U

G Y[

K



E



+

$



,

\

K



)

,]QRVNRPSRQHQWHEU]LQHY VHL]UDþXQDYDL]7RUULFHOOLMHYHIRUPXOH [

Y[

E

˜ J ˜ +  K



3RPRüXMHGQDGåEL]DNRVLKLWDF

$

\

J 

˜W



W

6XPDPRPHQDWDRNRWRþNH$PRUDELWLMHGQDNDQXOL ) K ˜ +  , ˜ FRV D ˜ K  \

 

$NRXYUVWLPRYULMHGQRVWLPSXOVQHIXQNFLMH ) K ˜ +  , ˜ FRV D ˜ K  \



) K ˜ +

U ˜ Y˜ 4˜ FRV D ˜ K  \

) K ˜ +

U ˜ Y[˜ 4˜ K  \



,]YRGLVHMHGQDGåED]DVLOX) K XIXQNFLMLRGYLVLQHK 

) K ˜ +

U ˜ ˜ J ˜ +  K ˜ 

) K







G ˜S

ª

˜« K 

¬

 



º » ˜ J˜ +  K ¼ J˜ E



˜ ˜ K ˜ +  ˜ K  E ˜ S˜ G ˜ U ˜



J +



0DNVLPXPIXQNFLMH) K GRELYDVHL]L]UD]D

§  ˜ +  K · ˜ S˜ G˜ U ˜ J ¨ ¸ + © ¹

G ) K GK





2GQRVQRYLVLQDK]DNRMXMHVLOD) K PDNVLPDOQD K

) K

+

K



P

  











˜ ˜ K ˜ +  ˜ K  E ˜ S˜ G ˜ U ˜

J +

 =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

) K

1



E Y[

\

J˜ E



˜ J˜ +  K



.ROLþLQDJLEDQMD 

,VSLW]DGDWDN

J

=D ]DXVWDYOMDQMH NROLFD PDVH PN   NJ NRMD VH X SRþHWQRP WUHQXWNX NUHüX EU]LQRP Y   NPK NRULVWL VH ORSDWLFDMHGLQLþQHãLULQH2GUHGLWHGXOMLQXSXWDSRWUHEQRJGDEL NROLFDXVSRULODQDSRODSUYRELWQHEU]LQHDNRVHORSDWLFDSUHPD VOLFLXURQLGRGXELQHD FP3UHWSRVWDYLWHNYD]LVWDFLRQDUQR VWUXMDQMH QHYLVNR]QRJ IOXLGD 8SXWD 3UHWSRVWDYLWH GD VH NRRUGLQDWQLVXVWDYJLED]DMHGQRVNROLFLPD=DGDQRMHD  U NJP

D

Y

K  D

 3UHPDGUXJRP1HZWRQRYRP]DNRQX G P N˜ Y GW

)



J

$NRXYUVWLPR]DVLOXNRþHQMDLPSXOVQHIXQNFLMH G PN ˜ Y GW

)

G PN ˜ Y GW

U ˜ Y D ˜ E˜   FRV D



 ,  ,˜ FRV D



Y

D

YNROLFD 



K  

5DGLODNãHJ]DSLVDXYRGLPRNRQVWDQWX&,QWHJULUDQMHP VHL]YRGHL]UD]L &

,

D ˜ E ˜ U ˜

  FRV D

GY

PN

GW

&˜ Y

Y

GY



Y

D 

&˜ GW



,

&˜ W  &

Y



.RQVWDQWX&RGUH XMHPRL]XYMHWDGDMHXWUHQXWNXW EU]LQDELODY Y Y



Y

&˜ W  &





&

&˜   &

Y



%U]LQDNROLFDXIXQNFLMLYUHPHQDGDQDMHL]UD]RP 

Y

&˜ W 

Y

 Y

Y

  &˜ W˜ Y 

,]RYRJL]UD]DODNRVHGRELMHYULMHPHNRþHQMDNDGDEU]LQDY YSRVWLJQHSRORYLFXSUYRELWQHYULMHGQRVWL Y

Y



  &˜ Y˜ W

W



&˜ Y

W

V



,QWHJULUDQMHPL]UD]D]DEU]LQX EU]LQDMHGHULYDFLMDSXWDSRYUHPHQX GRELMHVHSXWNRþHQMD G [ GW

Y

Y   & ˜ Y˜ W

[

OQ   & ˜ W ˜ Y &

[

P



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

,VSLW]DGDWDN

2GUHGLWH VLOX IOXLGD QD UDYQX SORþX MHGLQLþQH ãLULQHSUHPDVOLFLDNRþDPDFYXþHSORþXEU]LQRPY   PV .ROLND MH SRWUHEQD VQDJD" 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD WH ]DQHPDULWH XWMHFDM JUDYLWDFLMH=DGDQRMHU NJPK PP D 



þDPDF

SD D

Y K



U 

þDPDF

5

,

SD

D K

,

.RQWUROQL YROXPHQ R]QDþHQ MH QD VOLFL FUYHQRP LVFUWNDQRP OLQLMRP ,PSXOVQD IXQNFMD UDþXQD VH SUHPD L]UD]X ,

Y

U



U ˜ Y ˜ K˜ %



6LODXKRUL]RQWDOQRPVPMHUXMHGQDNDMH ,  , ˜ FRV D

)[

)[

1



.DNRMHXYMHWRP]DGDWNDSUHWSRVWDYOMHQRVWUXMDQMHQHYLVNR]QRJIOXLGDVLOD5PRUDELWLRNRPLWDQDSORþX QHPD WUHQMDSDQDPDQLVLOHXVPMHUXSORþH  5

)[

5

VLQ D

1



6QDJDSRWUHEQD]DYXþXSORþHMHGQDNDMH 3

)[˜ Y

3

:





,VSLW]DGDWDN

D



2GUHGLWH VLOX QD VSRMQLFX UDþYX  NRMD VSDMD VYD WUL UH]HUYRDUD 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJ IOXLGD WH ]DQHPDULWH WHåLQX YRGH X VSRMQLFL 3UHWSRVWDYLWH GD VH YLVLQH QLYRD X UH]HUYRDULPD MHGLQLþQH ãLULQH QH PLMHQMD NDGD VH XVSRVWDYLVWDFLRQDUQRVWUXMDQMH=DGDQRMHK PK  PK PG PPS0 EDUDP NJD P U NJP



D

SD K

P

U G K

J

S0

G

K #

   

D





G

G

=DRGUH LYDQMHVPMHURYDVWUXMDQMDXVLVWHPXSRWUHEQRMHRGUHGLWLSLH]RPHWDUVNHYLVLQHXWULVSUHPQLND

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD  K S

K

K S

K 

K S

K 

P U ˜ D˜ % S0 U ˜J

KS

P

KS

P

KS

P



=ERJ QDMYHüH SLH]RPHWDUVNH YLVLQH RþLWR MH GD IOXLG VWUXML L] GHVQRJ VSUHPQLND X SUHRVWDOD GYD VSUHPQLND 3RPRüXSLH]RPHWDUVNLKYLVLQD7RUULFHOOLMHYHIRUPXOHLMHGQDGåEHNRQWLQXLWHWDPRJXüHMHL]UDþXQDWLEU]LQHXUDþYL Y

˜ J ˜ K S  KS

Y

PV

Y

˜ J ˜ K S  KS

Y

PV

Y

PV

Y

Y  Y









3RPRüX%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLWODNRYHQDSULNOMXþQLPSULUXEQLFDPDUDþYH 

S 0

U ˜ J˜ K S  U ˜

Y





S 0

S 0  U ˜

Y



S 0

S 0  U ˜



EDU

S 0

EDU

S 0

EDU



 U˜



Y

S 0 Y

 

 U˜

Y





6LODQDUDþYXMHGQDNDMH]EURMXVYHWULLPSXOVQHIXQNFLMHNRMHVXRULMHQWLUDQHSUHPDXQXWUDãQMRVWLUDþYH 





)]

S0  U ˜Y ˜ G ˜S  S0  U ˜Y ˜ G ˜S  S0  U ˜Y ˜ G ˜S

)]

1









 SD

,VSLW]DGDWDN

2GUHGLWH KRUL]RQWDOQX VLOX QD FMHYRYRG SUHPD VOLFL .UDM FLMHYL SRVWDYOMHQ KRUL]RQWDOQR QD YLVLQL [ RGUHGLWH L] XYMHWD GD MH GRPHW / POD]D YRGH U   NJPPDNVLPDODQ 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJIOXLGD=DGDQRMH' P/ P K P+ P

J

+ UQ

/ N

[ '



K

/

$NRSRVWDYLPRMHGQDGåEH]DNRVLKLWDF Y˜ W

/

K[

J 

˜W





K[

J ˜ / ˜ Y





L%HUQRXOOLMHYXMHGQDGåEX

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD  Y

+  [



˜ J 

L]YRGLVHXGDOMHQRVW/XIXQNFLMLYLVLQH[ ˜ K  [ ˜ Y



/R





/

J

˜ J ˜ +  [ ˜ K  [ J

˜ J˜ +  [ ˜ K  [

I [

J



7UDåHüLHNVWUHPIXQNFLMHI [ L]UDþXQDYDVHYLVLQD[]DNRMX/LPDHNVWUHP I [

˜ + ˜ K  ˜ + ˜ [  ˜ [˜ K  ˜ [

G I [ G[ 

[



˜ +  ˜ K  ˜ [

˜+ 

 

˜K

[



 P



=DWDNRL]UDþXQDWXYLVLQX[SRPRüX%HUQRXOOLMHYHMHGQDGåEHL]UDþXQDYDVHEU]LQDVWUXMDQMDXFLMHYL Y

+[



Y

˜ J



˜ J ˜ +  [

Y

PV





=ERJMHGQROLNRVWLSURILODFLMHYLEU]LQDMHXVYLPSUHVMHFLPDLVWD%HUQRXOOLMHYDMHGQDGåEDRGSRþHWNDGRNUDMD FLMHYLJODVL S 0 U ˜J



Y



˜ J

[

Y



S0

˜ J

U ˜ J˜ [

S0

EDU



3R]QDMXüLWODNQDXOD]XFLMHYODNRMHL]UDþXQDWLLVLOXQDFLMHYL]UD]OLNHLPSXOVQLKIXQNFLMDQDXOD]XLL]OD]XL] FLMHYL )

S

0





 U ˜Y ˜



' ˜S 



 U ˜Y ˜



' ˜S

)





,VSLW]DGDWDN $

JXPLFD

SD J 5 SD

2

SORYDN

1

/

G K

0OD] YRGH JXVWRüH U   NJP VWUXMX NUR] FMHYþLFX $ SURPMHUD G   PP L XGDUD X JXPLFX ]DWYDUDþDYRGHXYRGRNRWOLüX3RGL]DQMHPUD]LQHYRGHX YRGRNRWOLüX SRGLåH VH L SORYDN NRML SUHNR SROXåMD ]DQHPDULYH WHåLQH VDYODGDYD VLOX POD]D YRGH ) L SULEOLåDYD JXPLFX RWYRUX FMHYþLFH 3UHWSRVWDYLWH VWDFLRQDUQRVWUXMDQMHLGHDOQRJIOXLGDWHMHGQROLNHSURILOH EU]LQD 2GUHGLWH NROLNR SXWD MH VLOD SRWUHEQD ]D ]DWYDUDQMH RWYRUH FMHYþLFH YHüD RG VLOH SRWUHEQH ]D GUåDQMH JXPLFH X ]DWYRUHQRP VWDQMX DNR MH WRWDOQL SUHWODNYRGRYRGDS0 EDUD=DGDQRMHK FP/  FP5 FP 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

1HSRVUHGQR SULMH ]DWYDUDQMD FMHYþLFH VLOX )[$ UDþXQDPR SRPRüX MHGQDGåEH NROLþLQHJLEDQMDLLPSXOVQLKIXQNFLMD )[$

,



)[$

,



U ˜ Y ˜

G ˜S

)[$

 

,

,]%HUQRXOOLMHYHMHGQDGåEHRGWRþNHVWRWDOQLPSUHWODNRPGRWRþNHQHSRVUHGQR QDL]OD]XL]FMHYþLFHPRJXüHMHRGUHGLWLEU]LQX 

S 0

Y

U ˜J

˜ J

˜ S 0

Y

U

, 

8VOXþDMXSRWSXQRJ]DWYDUDQMDQDJXPLFXGMHOXMHVDPRVLODSUHWODND 

) [%

G ˜S

 S 0˜

 

2PMHUWLKGYDMXVLODMHGQDNMH

)[$ )[%

 § G ˜S · ¨ U ˜ Y˜ ¸  ¹ ©  § G ˜S · ¨  S0˜ ¸  ¹ ©

)[$ )[%

§  ˜ S0 G˜ S · ˜ ¨ U ˜ ¸  ¹ U ©  § G ˜S · ¨  S0˜ ¸  ¹ ©

)[$ )[%







,VSLW]DGDWDN

E

SD

'

)

'



J



E

E

 )



SD



D '



 

,

,

8 KRUL]RQWDOQRM UDYQLQL QDOD]L VH GYRNUDND UDþYD SUHPD VOLFL 2GUHGLWH VLOX IOXLGD QD UDþYX DNR MH VLOD POD]D QD UDYQX SORþX )   1 3UHWSRVWDYLWH QHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMH' PPU  NJPD E J 

, UY'S

 J



E

 

D

,

6LOD ) MHGQDND MH LPSXOVQRM IXQNFLML ,  ,] MHGQDGåEH NROLþLQH JLEDQMD]DUDYQXSORþXPRJXüHMHL]UDþXQDWLEU]LQXVWUXMDQMDY

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD    ' ˜S U ˜ Y ˜

)

Y





U ˜ '˜ S

˜ U ˜ S˜ )

Y

PV





3RPRüX GYLMH %HUQRXOOLMHYH MHGQDGåEH L MHGQDGåEH NRQWLQXLWHWD PRJXüH MH L]UDþXQDWL VYH EU]LQH L WODNRYH SRWUHEQH]DL]UDþXQDYDQMHVLOHQDUDþYX S 0 U ˜J





Y

Y



S0

˜ J

˜ J

U ˜J



Y˜



' ˜S

Y˜



' ˜S 





Y

˜ J

˜ J

Y

Y

Y

PV



 Y˜

' ˜S

Y



§  Y  Y · ¸ ˜U ˜J ¨ ˜  ˜  J ¹ © J

S 0



Y

Y  Y 

S 0



EDU



L]MHGQDGåEHNROLþLQHJLEDQMD]DUDþYXPRJXüHMHL]UDþXQDWLVLOX) 



,

S0  U ˜Y ˜ '˜S

)[

,˜ FRV J  ,˜ FRV E  ,˜ FRV D

)[

 u  1

)\

,˜ VLQ D  ,˜ VLQ J  ,˜ VLQ E

)\

1

)







)[  )\



,

)

U ˜ Y ˜

' ˜S

,





u  1



U ˜ Y ˜



' ˜S 



§ )\ · ¸ © )[ ¹

I

DWDQ ¨

I

GHJ





,VSLW]DGDWDN

2GUHGLWHIXQNFLRQDOQX]DYLVQRVWVLOH)POD]DYRGHQDSORþXRGNXWDD QDJLED SORþH 3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD WH VWUXMDQMH X KRUL]RQWDOQRMUDYQLQL=DGDQRMHG PPG PPY PVY  PVU NJP JXVWRüDIOXLGD  

Y

, D

 D 

G

\

)

\

I

 ,  

[

[

G

D

Y

 ,PSXOVQHIXQNFLMHRULMHQWLUDQHVXSUHPDXQXWUDDSRL]QRVXMHGQDNHVX 



G ˜ S

,

U ˜ Y ˜

,

1





,

U ˜ Y ˜

,



G ˜ S 

1



,]XYMHWDQHYLVNR]QRJVWUXMDQMDIOXLGDVOLMHGLGDMHVLOD)RNRPLWDQDSORþXWHSRL]QRVXMHGQDND =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

D

.ROLþLQDJLEDQMD  )

,˜ VLQ D  ,˜ FRV D

)[

) ˜ VLQ D

)\

) ˜ FRV D

S

I

D



˜ VLQ D  ˜ FRV D

)





,VSLW]DGDWDN

2GUHGLWHVLOXQDMHGQXORSDWLFXXUHãHWFL MHGLQLþQHãLULQH  NRMD VNUHüH VWUXMDQMH ]UDND ]D NXW D   3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJ IOXLGD =DGDQR MH Y   PV S0  EDUDU NJPW PP

Y

W

 

S

  ,

Y

W

 

S



D Y



D

)S

,

  

D

,]MHGQDGåEHNRQWLQXLWHWDPRJXüHMHL]UDþXQDWLEU]LQXY Y˜ W

Y˜ D

Y˜ W˜ VLQ D

Y˜ W

Y

Y

Y

VLQ D

PV





L]%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLSUHWODNS0 S 0 U ˜J



S 0

Y



˜ J S 0 

S 0 U ˜J  







Y

˜ J

˜ Y ˜ U 

 



˜ Y ˜ U

S0

EDU



,PSXOVQHIXQNFLMHNDRLVLOD)SSUHWODNDS0UDþXQDMXVHL]L]UD]D , , )S

S0  U ˜Y ˜W˜% S0  U ˜Y ˜W˜VLQ D ˜ % 

,

 u  1



,

1

S 0˜ W˜ FRV D ˜ %

)S



1



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

6LOHQDORSDWLFXUDþXQDPRL]L]UD]D )[

,  ,˜ VLQ D  )S˜ FRV D

)[

1

)\

,˜ FRV D  )S˜ VLQ D

)\

1

)[  )\

)

1

§ )\ · ¸ © )[ ¹

I

GHJ



) I



DWDQ ¨





,VSLW]DGDWDN J

2GUHGLWHNRMRPVLORP)WUHEDRSWHUHWLWLNOLSSURPMHUDG FP GDELVHVSXãWDREU]LQRPY PVXFLOLQGUXSURPMHUD' FP LVSXQMHQRJ YRGRP JXVWRüH U   NJP 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD 8SXWD NRRUGLQDWQL VXVWDY SRVWDYLWH UHODWLYQR X RGQRVXQDNOLS

SD



G

U

Y



Y

)



\



'

[

 



Y



-HGQDGåEDNRQWLQXLWHWDSRVWDYOMHQD]DNRRUGLQDWQLVXVWDYNRMLVHJLEDVDVWDSRP 

Y ˜

' ˜S

Y ˜



'  G ˜S 



,]MHGQDGåEHNRQWLQXLWHWDRGUH XMHVHL]OD]QDEU]LQD 

Y

Y˜

'

Y

'  G

PV





,]%HUQRXOOLMHYHMHGQDGåEHRGUH XMHVHSUHWODNQDSRYUãLQLFLOLQGUD S 0 U ˜J







Y

Y

˜ J

˜ J

S 0

Y

 

˜U



 Y 

S 0

EDU



6LODQDþHORVWDSDMHGQDNDMHUD]OLFLLPSXOVQLKIXQNFLMD )

S0



'˜S  U ˜Y ˜ '



 U ˜ Y ˜



 







 G ˜S 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,



)

1





,





.ROLþLQDJLEDQMD 

G

,VSLW]DGDWDN

2GUHGLWH VLOX ) QD NROMHQR X KRUL]RQWDOQRM UDYQLQL SUHPD VOLFL 3UL L]UDGL ]DGDWND SRWUHEQR MH ]DQHPDULWL VYH JXELWNH WUHQMD D X]HWL X RE]LU NRHILFLMHQWH LVSUDYND NROLþLQH JLEDQMDLNLQHWLþNHHQHUJLMH3URILOEU]LQHXFLMHYL]DGDQMHQD VOLFL=DGDQRMHS EDU4 OV' FPG  FPU NJPP 3DV

Y YPD[

0

Y YPD[

  =D SDUDEROLþQL SURILO QD XOD]X X NROMHQR UDþXQDPR VUHGQMX EU]LQX WH NRHILFLMHQWH LVSUDYND NROLþLQH JLEDQMD L NLQHWLþNHHQHUJLMHSUHPDL]UD]LPD

4

§U · ¸ ©5¹



§ U ·  ¨ ¸ © 5¹



 ¨

'

  5

5

4

´ µ Y˜ ˜ U˜ S GU ¶

4

´  µ § U · Y ˜   µ PD[ ¨ ¸ ˜ ˜ U˜ S GU  5 ¹ µ © ¶

4

 



˜ YPD[˜ 5 ˜ S







YVU˜ 5 ˜ S

D

§¨ ´  ·¸ ˜ µ Y G$ ¨ ¸  YVU ˜ $ © ¶ ¹

D

§´  · ˜ ¨ µ Y ˜ ˜ U˜ S GU ¸   YVU ˜ 5 ˜ S © ¶ ¹

D

ª´5 º   «µ ª » §  U ·º ˜ « µ «YPD[˜ ¨   ˜  ˜ U ˜ S G U » ¸»    YVU ˜ 5 ˜ S « µ ¬ 5 ¹¼ » © ¬ ¶ ¼

D D





˜ YPD[˜ 5 ˜ S



YVU

5



˜YVU 



˜ YPD[



˜ YPD[

E

§¨ ´  ·¸ ˜ µ Y G$ ¨ ¸  YVU ˜ $ © ¶ ¹

E

´  ˜ µ Y ˜ ˜ U˜ S GU   YVU ˜ 5 ˜ S ¶

E

´   µ ª §  U ·º ˜ µ «YPD[˜ ¨   ¸» ˜ ˜ U˜ S GU    5 ¹¼ YVU ˜ 5 ˜ S µ ¬ © ¶









5



5

E E



˜YVU 



˜ YPD[

 



=DHNVSRQHQFLMDOQLSURILOQDL]OD]XL]NROMHQDUDþXQDPRVUHGQMXEU]LQXWHNRHILFLMHQWHLVSUDYNDNROLþLQHJLEDQMD LNLQHWLþNHHQHUJLMHSUHPDL]UD]LPD 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

5

´ º ª µ » « U µ YPD[˜ «   §¨ ·¸ » ˜ ˜ U˜ S GU µ ¬ © 5¹ ¼ ¶

5

4

´ µ Y˜ ˜ U˜ S GU ¶ 



YVU˜ 5 ˜ S

D

D

D

D





˜ 5 ˜ YPD[˜ S

5

˜Y 



5

´ µ µ  ˜µ   YVU ˜ 5 ˜ S µ ¶



E

˜Y VU





ª §  º « ˜ ¨ ˜ YPD[·¸ » ¬ ©  ¹¼ 

˜ YPD[





˜ YPD[



˜ YPD[

ª §  º « ˜ ¨ ˜ YPD[¸· » ¬ ©  ¹¼ 



E







 ºº ª ª  »» « « U « YPD[˜ «   §¨ ·¸ » » ˜ ˜ U˜ S GU ¬ ¬ © 5 ¹ ¼¼



E





˜ 5 ˜ YPD[˜ S

´  ˜ µ Y ˜ ˜ U˜ S GU   YVU ˜ 5 ˜ S ¶

E





˜ YPD[

5

˜ YPD[



4



E

º ª´ 5  «µ ª »  ºº ª «µ « »  »» «  U ˜ « µ « YPD[˜ «   §¨ ·¸ » » ˜ ˜ U˜ S GU»   ¬ ¬ © 5 ¹ ¼¼ » YVU ˜ 5 ˜ S « µ ¬ ¶ ¼ 



YVU

· §´  ˜ ¨ µ Y ˜ ˜ U˜ S GU ¸   ¹ YVU ˜ 5 ˜ S © ¶ 

VU

D

4





8SRWUHERP %HUQRXOOLMHYH MHGQDGåEH UDþXQDPR WODN QD NUDMX NROMHQD D SULPMHQRP MHGQDGåEH NROLþLQH JLEDQMD VLOHQDNROMHQR D S0 U ˜J

S 0



 D ˜

D



˜ 4



S 0



U ˜J



' ˜S ˜J

E



E







 D ˜

˜ 4 



G ˜S ˜J

  º ª S0 4 4   ˜ D ˜   ˜ D ˜ «   » ˜U ˜J  º  º   U ˜J ª ª ' ˜ S ˜ J G ˜ S ˜ J ¬ ¬ ¼ ¬ ¼¼

S0

EDU

)[

  ª § ˜ 4 · º ˜ ' ˜ S S  U ˜ E ˜ « 0 ¨ »  ¸ ¬ © ' ˜S ¹ ¼ 

)\

  ª § ˜ 4 · º ˜ G ˜ S S  U ˜ E ˜ « 0 ¨ »  ¸ ¬ © G ˜S ¹ ¼ 

)[

1

)\

1



 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



.ROLþLQDJLEDQMD 

,VSLW]DGDWDN

2GUHGLWH KRUL]RQWDOQX VLOX ) QD EUDQX SUHPD VOLFL âLULQD EUDQH RNRPLWR QD UDYQLQX VOLNH /   P 3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD WH XQLIRUPQH SURILOHEU]LQHGRYROMQRGDOHNRLVSUHGLL]DEUDQH=DGDQR MHU NJP+ PK PK FPG  P' P

SD

J



U G

+

'



K



K







3RVWDYOMDQMHP%HUQRXOOLMHYHMHGQDGåEHL]PH XWRþDNDLVSUHGLL]DEUDQH 

+



Y

Y

K

˜ J

˜ J 

WHX]XSRWUHEXMHGQDGåEHNRQWLQXLWHWD Y˜ /˜ +

Y˜ /˜ K

4

4

Y

/˜ +

Y

4 /˜ K 

PRJXüHMHL]UDþXQDWLSURWRN4NUR]EUDQXWHEU]LQHVWUXMDQMD 



4

+



˜ J ˜ / ˜ +



K

4



˜ J ˜ / ˜ K

4





˜ J ˜ +  K  K

4

Y

Y

/˜ +

4

Y

/˜ K





4

 +



P V





PV



Y

PV





3RVWDYOMDQMHPLPSXOVQLKIXQNFLMDL]UDþXQDYDVHVLODQDEUDQX   

,





,



   ,

§ U ˜ J ˜ +  U ˜ Y  · /˜ + ¨  ¸  © ¹

,

u  1

)[



,  ,

,

§ U ˜ J ˜ K  U ˜ Y  · /˜ K ¨  ¸  © ¹

,

u  1

)[





 u  1



 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

,VSLW]DGDWDN '

SD

 2GUHGLWH DNVLMDOQX VLOX QD YHQWLODWRU NRML XEDFXMH VYMHåL ]UDN JXVWRüH U   NJP SURWRNRP 4   PV  X SURVWRULMX 3UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMH' PPS0 3D SUHWODNXSURVWRULML  

S0

J

 %U]LQDVWUXMDQMDNUR]YHQWLODWRUL]UDþXQDYDVHL]L]UD]D ˜ 4

Y

Y



' ˜S

PV





3RVWDYOMDQMHP %HUQRXOOLMHYH MHGQDGåEH RG WRþNH L]YDQ SURVWRULMH NUR] FMHYRYRG GR WRþNH XQXWDU SURVWRULMH L]UDþXQDYDVHYLVLQDGREDYHYHQWLODWRUD KY

S 0



U ˜J

Y



S 0

KY

˜ J

U ˜J

Y





KY

˜ J

P



3RVWDYOMDQMHP %HUQRXOOLMHYH MHGQDGåEH RG WRþNH QHSRVUHGQR SULMH YHQWLODWRUD GR WRþNH XQXWDU SURVWRULMH L]UDþXQDYDVHWODNLVSUHGYHQWLODWRUD S 0 U ˜J



Y



˜ J

S 0

 KY

U ˜J



Y



S 0

˜ J

S 0  U ˜ J ˜ K Y

S 0



u  EDU



3RVWDYOMDQMHP %HUQRXOOLMHYH MHGQDGåEH RG WRþNH QHSRVUHGQR SULMH YHQWLODWRUD GR WRþNH QHSRVUHGQR L]D YHQWLODWRUDL]UDþXQDYDVHWODNL]DYHQWLODWRUD S0 U ˜J



Y



˜ J

S 0

 KY

U ˜J



Y



˜ J

S 0

S 0  U ˜ J ˜ K Y



S 0

 u  EDU



3RVWDYOMDQMHPMHGQDGåEHNROLþLQHJLEDQMDL]UDþXQDYDVHDNVLMDOQDVLODQDYHQWLODWRU )

S0





'˜S  S



 U ˜Y ˜

0



'˜S



 U ˜Y ˜

)

1





,VSLW]DGDWDN 

2GUHGLWH VLOX ) QD UDþYX SUHPD VOLFL 3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD =DGDQR MH K   P K   P K   P K   P K   P '   PP SURPMHU VYLK FMHYRYRGD  U   NJP 9   OLW YROXPHQYRGHXUDþYL   8 VOXþDMX QHYLVNR]QRJ VWUXMDQMD IOXLG VWUXML RG PMHVWD V QDMYHüRP SLH]RPHWDUVNRP YLVLQRP SUHPD PMHVWLPD V QLåRP SLH]RPHWDUVNRP YLVLQRP ,] 7RUULFHOOLMHYHMHGQDGåEHUDþXQDPREU]LQHVWUXMDQMD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

J U

U

U

SD U

K

K G

K

K K

.ROLþLQDJLEDQMD  ˜ J ˜ K   K 

Y

Y

˜ J ˜ K   K 

˜ J ˜ K   K 

Y



,]MHGQDGåEHNRQWLQXLWHWDUDþXQDPREU]LQXVWUXMDQMDXNUDMQMHOLMHYRMFLMHYL 

Y˜



' ˜S

 Y

Y˜



PV



' ˜S

 Y˜





' ˜S 

Y



 Y˜

PV

' ˜S

Y



Y   Y  Y





Y

PV



Y

PV





,]%HUQRXOOLMHYHMHGQDGåEHUDþXQDPRWODNQDSULUXEQLFLNUDMQMHOLMHYHFLMHYL 

K

K 

Y

˜ J

S 0



S 0

U ˜J

 §  Y · ¨ K  K   ˜ ¸ ˜ U ˜ J  J ¹ ©



$QDORJQRUDþXQDPRLRVWDOHWODNRYH QHVPLMHVH]DERUDYLWLL]OD]QLJXELWDN  

K S 0

Y

˜ J





S 0

K

U ˜J

Y

˜ J 

K  K ˜ U ˜ J

K  K ˜ U ˜ J

S 0

S 0

K  K ˜ U ˜ J



,PSXOVQHIXQNFLMHUDþXQDMXVHL]L]UD]D ,

,



S0  U ˜Y ˜ '˜S 



S0  U ˜Y ˜ '˜S 



,

S0  U ˜Y ˜ '˜S

,

S0  U ˜Y ˜ '˜S









6LODQDUDþYXMHGQDNDMH )

U ˜ J ˜ 9  ,  ,  ,  ,

)

1



 

,VSLW]DGDWDN 

'



SD   

5

2GUHGLWH VLOX ) QD OLMHYDN SUHPD VOLFL 3UHWSRVWDYLWH VWDFLRQDUQR QHYLVNR]QR VWUXMDQMH IOXLGD WH ]DQHPDULWH WHåLQX OLMHYND =DGDQR MH 4  OLWV' PG P+ FP5 FPK#U  NJP

K

U J

+ G



,]L]UD]D]DSURWRNRGUH XMHVHEU]LQDQDYUKXOLMHYND 

4

Y˜

'S 

Y

˜ 4 

'S

Y

PV





=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

8 VWDFLRQDUQRP VWUXMDQMX NROLþLQD IOXLGD NRMD XOD]L X OLMHYDN PRUD ELWL MHGQDND NROLþLQL IOXLGD NRMD L]OD]L L] OLMHYND ˜ 4

Y

Y



G S

PV





%HUQRXOOLMHYDMHGQDGåEDRGSRYUãLQHQDYUKXOLMHYNDGRGQDOLMHYND 

Y

K

K

˜ J

P



,]JHRPHWULMVNHVOLþQRVWLWURNXWDVOLMHGL K

+

U

5

U

K +

˜5

U

P



,PSXOVQHIXQNFLMHLWHåLQDIOXLGDXOLMHYNXUDþXQDMXVHSUHPDL]UD]LPD   ' ˜S U ˜ Y ˜

,

 G U ˜ Y ˜

,







˜S

*



U ˜ J˜

K ˜ U ˜ S 



6LODQDOLMHYDNMHGQDNDMH )

*  ,  ,

)

1



 

,VSLW]DGDWDN 

2GUHGLWH SRPDN VWRãFD [ DNR MH EU]LQD VWUXMDQMD Y   PV  NUR] FLMHY SURPMHUD '   P SUHPD VOLFL 3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD  XQLIRUPQHSURILOHEU]LQHQDVYLPSUHVMHFLPDWHNRQVWDQWDQWODNXSUHVMHNX 8WMHFDMJUDYLWDFLMH]DQHPDULWH=DGDQRMHG PF 1P NUXWRVW RSUXJH U NJPJXVWRüDIOXLGD

[

F G

 ,]MHGQDGåEHNRQWLQXLWHWDUDþXQDVHEU]LQDQDSUHVMHNX 



' ˜S

Y˜



'  G ˜S 



Y



' 

' G



Y

PV



Y 

,]%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLUD]OLNXWODNRYDQDSUHVMHNXL S U ˜J 'S





S

˜ J

U ˜J

Y

S  S





Y

˜ J 'S

U 





˜ Y  Y





6LODQDNRQXVMHGQDNDMHUD]OLFLLPSXOVQLKIXQNFLMD

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'S

EDU



'



.ROLþLQDJLEDQMD  

)

U ˜Y ˜

)

S

)

U ˜Y ˜



' ˜S  

 § '  G · ' ˜S ¸ ˜ S  'S˜  ©  ¹



 U ˜ Y ˜ ¨





'S 

'



'S  S

 U ˜Y ˜





 U ˜ Y ˜











 G ˜S

 U ˜ Y ˜

'  G ˜S





G S

 S ˜





'S

 'S ˜



)



1



3RPDNVHUDþXQDL]L]UD]D )

[

[

F

P





,VSLW]DGDWDN 

2GUHGLWH )\ NRPSRQHQWX VLOH QD UDþYX NRMD VH QDOD]L X KRUL]RQWDOQRMUDYQLQLSUHPDVOLFLDNRMH)[NRPSRQHQWDVLOHMHGQDND ' QXOL=DGDQRMH4 OVU NJPD E G  PP' PP

' E

D \



[

 3RWUHEQR MH SRVWDYLWL %HUQRXOOLMHYH MHGQDGåEH MHGQDGåEX NRQWLQXLWHWD L MHGQDGåEX NROLþLQH JLEDQMD [ NRPSRQHQWX  GD EL L]UDþXQDOLWODNRYHLEU]LQHQDVYLPSUHVMHFLPD

G SD



4

S 0/



U ˜J

Y/



Y

˜ J

,/ ˜ VLQ D





S 0'

˜ J

U ˜J







Y'

Y

˜ J

˜ J





G ˜S 



Y/ ˜



' ˜S 



 Y/ ˜

' ˜S 



S0/  U ˜Y/ ˜ '˜S ˜VLQ D S0'  U ˜Y' ˜ '˜S ˜VLQ E

,'˜ VLQ E







'RELYHQMHVXVWDYRþHWLULMHGQDGåEHVþHWLULQHSR]QDQLFHNRMLMHSRWUHEQRULMHãLWL Y

˜ 4

Y'



G ˜S



G

 

'

 Y/

S 0/



U



˜ Y  Y/





S 0'

ª«  « ¬

U



§ G

˜ Y  ¨ Y˜

 © '

 · »º » ¹¼

 Y/ ¸

º º  ª ª    ª U ˜ Y  Y   U ˜ Y º ˜ ' ˜ S ˜ VLQ D « U ˜ « Y  § Y˜ G  Y · »  U ˜ § Y˜ G  Y · » ˜ ' ˜ S ˜ VLQ E « / /» ¨  /¸ » ¨  /¸ »  « « ¬ ¼  ¬ ¬ © ' ¹¼ © ' ¹¼ 





MHGQDGåEXNROLþLQHJLEDQMD [NRPSRQHQWD SRWUHEQRMHVUHGLWLLULMHãLWL

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

ª«  ˜ Y   « ¬

ª U ˜ Y  Y   U ˜ Y º ˜ VLQ D « / /» ¬ ¼ VLQ E



Y





VLQ D

§ G · Y  ¨ Y˜  Y/ ¸  © ' ¹

VLQ E



 Y/ ˜

§ G · ¨ Y˜   Y / ¸ © ' ¹

U



» » ¼







2þLWRMHSRWUHEQRULMHãLWLNYDGUDWQXMHGQDGåEX

Y



D

D VLQ ˜ '  Y ˜ ' VLQ E





 Y/ ˜

VLQ D

VLQ E







E



Y/

˜'  '

















˜ Y˜ G ˜ '

F

VLQ D VLQ E





 Y ˜ G  ˜ Y˜ G ˜ Y/ ˜ '  Y/ ˜ '













˜' ˜Y  Y ˜'  Y ˜G





D ˜ Y/  E ˜ Y /  F

E  E  ˜ D ˜ F

Y/

˜ D







P V



'UXJR UMHãHQMH NYDGUDWQH MHGQDGåEH QH GDMH IL]LNDOQR UMHãHQMH 3RWUHEQL WODNRYL L EU]LQH L]UDþXQDYDMX VH L] L]UD]D G



Y'



Y'





'

 Y/ P V



S 0'

 u  3D

S 0'

U

S 0/ S 0/







˜ Y  Y/





 ª  · º» «  § G ˜ Y  ¨ Y˜  Y/ ¸ »   « ' ¬ © ¹¼

U



u  3D



9HUWLNDOQXNRPSRQHQWXVLOHUDþXQDPRL]L]UD]D NDRMHKRUL]RQWDOQDNRPSRQHQWDSUHPDXYMHWX]DGDWNDMHGQDND QXOLWRMHXMHGQRLXNXSQDVLOD 







G ˜S

,

U ˜Y ˜

,

1

)\



,/ ,/



S0/  U ˜Y/ ˜ '˜S 

1

,  ,/ ˜ FRV D  ,'˜ FRV E

)\



,'

S0'  U ˜ Y' ˜ '˜S

,'

1



1





,VSLW]DGDWDN

2GUHGLWH VLOX ) POD]D YRGH QD SORþX SUHPD VOLFL 3UHWSRVWDYLWH E QHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMH[ P] PG P D E U NJP    ,]MHGQDGåEHNRVRJKLFDPRJXüHMHRGUHGLWLEU]LQXQDL]OD]XL]POD]QLFH

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

[

Y G J

]

SD



D

.ROLþLQDJLEDQMD  [

Y˜ FRV E

]

Y



J 

W

W

˜ W  Y˜ VLQ E W 

J 

˜

[

[

[

Y˜ FRV E J

]



[

˜ §¨

·  [˜ WDQ E ¸

]  [˜ WDQ E ˜ FRV E

J

© Y˜ FRV E ¹



Y



Y

]





P

D [

W

V

W

Y˜ FRV E

D V



 ,]MHGQDGåEHNRVRJKLFDPRJXüHMHL]UDþXQDWLEU]LQXQHSRVUHGQRLVSUHGSORþHNDRLNXWPOD]DYRGHQHSRVUHGQR LVSUHGSORþH Y[

J

Y˜ FRV E

Y]

§ Y] · ¸ © Y[ ¹

J

DWDQ ¨

Y˜ VLQ E  J˜ W

Y[

GHJ

Y



P

Y]

V





Y[  Y ]

Y



P V



P V



=ERJQHSRVWRMDQMDWUHQMD VWUXMDQMHLGHDOQRJIOXLGD QHPDQLNRPSRQHQWHVWUXMDQMDXVPMHUXSORþHYHüSRVWRML VDPRNRPSRQHQWDVLOHRNRPLWDQDSORþX 

4





G ˜S 

)

U ˜ Y˜ 4˜ VLQ D  J

)

1





,VSLW]DGDWDN

)OXLGSUROD]LNUR]ILOWDUSURWRNRP4 PKSULþHPX MHSDGWODNDNUR]ILOWDU'S EDUD2GUHGLWHUH]XOWDQWQX VLOX)IOXLGDQDILOWDUDNRMHSUHWODNQDXOD]XXILOWDUS0  EDUDDXQXWUDãQMLYROXPHQILOWUD9 O=DGDQRMH ' PP' PPU NJP  

 ,

S0 '

 

'

J



4 9 U

  ,

'

' UJ9

 'D EL VH L]UDþXQDOD VLOD QD ILOWDU SRWUHEQR MH L]UDþXQDWL WODNRYH L EU]LQHQDSUHVMHFLPDL

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD  ˜ 4

Y



Y S 0

˜ 4

Y

 ' ˜ S

P



' ˜ S

Y

V

S 0  'S



S 0

P V



 u  3D



=DNRQWUROQLYROXPHQSUHPDVOLFLUDþXQDMXVHLPSXOVQHIXQNFLMHWHNRPSRQHQWHVLOHSUHPDVOMHGHüLPL]UD]LPD

S0  U ˜Y ˜ '˜S

,

S0  U ˜Y ˜







)5





,



)[

,

)[

u  1

)]

,  U ˜ J ˜ 9

)]

 u  1



' ˜ S 



)[  )]



)5

 u  1

D



§ )] · ¸ © )[ ¹

DWDQ ¨

D

GHJ





,VSLW]DGDWDN

'YD POD]D YRGH GUåH X UDYQRWHåL NRFNX PDVH P ]JOREQR YH]DQD X WRþFL 2 2GUHGLWH PDVX NRFNHDNRMHNRFNDQDJQXWD ]DD 3UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHDPDVHPOD]RYD ]DQHPDULWH=DGDQRMHU NJPY PVG P 



D

D

D

 ,]JHRPHWULMHMHRþLWR I

N

S 

J

D

2 I

GHJ

Y

D

 D

D ˜   FRV I

N

˜ FRV I

VLQ I

Y

G

D G

 

D

D

 J

D

 D

N

 2 )



G

M

D



M

Y

D



D M

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

     

)

N

2 



D

Y G

J

.ROLþLQDJLEDQMD   .DNRMHULMHþRQHYLVNR]QRPVWUXMDQMHQHPRJXüHMHSUHQLMHWLWDQJHQFLMDOQXNRPSRQHQWXVLOHQDSRYUãLQX3UHPDWRPH VLOD) L) PRUDMXELWLRNRPLWHQDSRYUãLQH SUHPDVOLNDPD ,PSXOVQHIXQNFLMHGLMHODPOD]DQDNRQVXGDUDVNRFNRP QLNDNR QH VXGMHOXMX X QRUPDOQRM NRPSRQHQWL VLOH QDOD]H VH X UDYQLQL RNRPLWRM QD VLOX  ,PSXOVQD IXQNFLMD POD]D MHGQDNDMH 

,







U ˜Y ˜

G ˜S 

,

1



6LOH) L) MHGQDNHVX 



, ˜ FRV I

)

)

, ˜ VLQ I

)

1

)

1



0DVXNRFNHRGUH XMHPRL]XYMHWDGDMHVXPDPRPHQWDRNRWRþNH2MHGQDNDQXOL PN ˜ J ˜ PN ˜ J ˜

D˜   D˜   ,

PN



˜ FRV D  )˜ N   )˜ N  ˜ FRV D  , ˜ FRV I ˜

˜   ˜ FRV I ˜

D



˜ FRV I

 , ˜ VLQ I ˜



D˜   FRV I

PN

J˜ FRV D

VLQ I

NJ





 

,VSLW]DGDWDN

6LOD RWSRUD SURILOD DYLRQVNRJ NULOD MHGLQLþQH ãLULQH PMHUL VH X ]UDþQRPWXQHOXãLULQHE P2GUHGLWHVLOXQDSURILODNRVXQD SUHVMHFLPDLVQLPOMHQLSURILOLEU]LQHSUHPDVOLFL3UHWSRVWDYLWH NRQVWDQWDQ WODN QD VYDNRP YHUWLNDOQRP SUHVMHNX =DGDR MH  U  NJPS0 EDUY PV

E Y





E

S0

 

3URILOEU]LQHQDL]OD]QRPEULGXSURILODDYLRQVNRJNULOD]DGDQMHL]UD]RP Y  \

Y ˜

˜ \ E 

,] MHGQDGåEH NRQWLQXLWHWD PRJXüH MH L]UDþXQDWL EU]LQX Y ]ERJ VLPHWULþQRVWL X UD]PDWUDQMH MH X]HWD VDPR JRUQMD SRORYLFDVOLNH  E

E Y˜ ˜ % 

´ µ Y ˜ ˜ \ ˜ % G \  µ E ¶

 

˜ Y˜ E ˜ %

 

˜ E ˜ Y˜ %

Y

˜ Y



.DNR VX SURILOL EU]LQD QD L]OD]QRP EULGX NULOD UD]OLþLWL RG SUDYRNXWQLK SRWUHEQR MH X UD]PDWUDQMH X]HWL X RE]LU L NRHILFLMHQWHLVSUDYNDNROLþLQHJLEDQMDLNLQHWLþNHHQHUJLMH VUHGQMDEU]LQDQDL]OD]QRPSUHVMHNXMHGQDNDMHYVUHG Y 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD 

§¨ ´  ·¸ ˜ µ Y G$ ¨ ¸  YVU ˜ $ © ¶ ¹ 

D

E

´  µ ˜ E µ  Y ˜ %˜ ¶ 

D

§¨ ´  ·¸ ˜ µ Y G$ ¨ ¸  YVU ˜ $ © ¶ ¹ 

E

E



§ ˜ Y ˜ ˜ \ · ˜ % G \ ¨  ¸ E ¹ ©

E

´  µ ˜ E µ  Y ˜ %˜ ¶ 



D

E



§ ˜ Y ˜ ˜ \ · ˜ % G \ ¨  ¸ E ¹ ©





3RPRüX%HUQRXOOLMHYHMHGQDGåEHPRJXüHMHL]UDþXQDWLSUHWODNQDL]OD]QRPEULGXNULOD NRGSRVWDYOMDQMDMHGQDGåEH SRWUHEQRMHX]HWLXRE]LUYVUHG Y  S 0 U ˜J





Y

S 0

J

U ˜J





D ˜ Y

S 0

J



U

S 0 







˜ Y  D ˜ Y

S0

EDU



,]MHGQDGåEHNROLþLQHJLEDQMDSRPRüXLPSXOVQLKIXQNFLMDPRJXüHMHL]UDþXQDWLVLOXQDNULOR 

)[

,  ,

)[

S

0











 U ˜ Y E ˜ %  S0  E ˜ U ˜ Y E ˜ %

)[

 1





,VSLW]DGDWDN

2GUHGLWHEU]LQXYNROLFDSRJRQMHQLKPOD]RPYRGHSURPMHUDG  PP3UHWSRVWDYLWHGDVHRWSRU]UDNDUDþXQDSUHPDL]UD]X)'  &'U]Y$ WH SUHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD =DGDQR MH Y PVD &' $ PU NJPU]  NJP

J



Y

D

Y

G

    3ULUMHãHQMXRYRJ]DGDWNDSRWUHEQRMHXYHVWLSRPLþQLNRRUGLQDWQLVXVWDYNRMLVHJLEDVDNROLFLPDEU]LQRPY5HODWLYQD EU]LQDZQDVWUXMDYDQMDIOXLGDQDORSDWLFXMHGQDNDMHZ Y±Y,]MHGQDGåEHUDYQRWHåHVLOD VLODRWSRUDMHGQDNDMHVLOL GRELYHQRML]MHGQDGåEHNROLþLQHJLEDQMDXUHODWLYQRPVXVWDYX  )'

&'˜

&'˜ U] 



U] 

˜Y ˜ $



˜Y ˜ $

)

,  , ˜ FRV D

U ˜ Y R  Y ˜ 



G ˜S 



U ˜Z ˜



G ˜S

˜   FRV D



˜   FRV D



5MHãHQMHPRYHNYDGUDWQHMHGQDGåEHGRELYDVHWUDåHQDEU]LQDNROLFDY

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD    U] º  ª G ˜ S G ˜S G ˜S  « ˜   FRV D ˜ U  &'˜ ˜ $» ˜ Y  ˜ Y˜ U ˜ ˜   FRV D ˜ Y  ˜   FRV D ˜ U ˜ Y   ¼   ¬ 



G ˜S

D



˜   FRV D ˜ U  &'˜



D˜Y  E˜Y  F

U] 



˜$



E

˜ Y˜ U ˜

Y

ªE « « «E « ¬



G ˜S 



˜   FRV D

G ˜S

F



º » ˜ D » »  E  ˜ D ˜ F » ˜ D ¼

˜   FRV D ˜ U ˜ Y





E  ˜ D˜ F

§ · P ¨ ¸ ©  ¹ V

Y



8VYDMDVHIL]LNDOQRUHDOQRUMHãHQMHY PV  

,VSLW]DGDWDN

 2GUHGLWH VLOX QD UDþYX SUHPD VOLFL 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJIOXLGDJXVWRüHU NJP=DGDQRMH' FP G FPD + PK P9 P YROXPHQ YRGHXQXWDUUDþYH 

SD



+

J

 '

 ,] 7RULFHOO\HYH MHGQDGåEH L]UDþXQDYDMX VH EU]LQH QD L]OD]QLP SRYUãLQDPD Y

˜ J˜ +

Y

Y

˜ J˜ +  K

Y

 

K

P V

D G

P V

G



,]MHGQDGåEHNRQWLQXLWHWDL]UDþXQDYDVHEU]LQDQDXOD]XXUDþYX 

Y ˜

' ˜S







G ˜S Y   Y ˜ 





Y



Y  Y ˜

G



Y



'



P V



3RPRüX%HUQRXOOLMHYHMHGQDGåEHUDþXQDVHSUHWODNQDXOD]QRMSRYUãLQLXUDþYX +

S 0



U ˜J

Y



S 0

˜ J

U ˜J˜+ 

U 

˜ Y



S 0

EDU



,PSXOVQHIXQNFLMHUDþXQDPRL]L]UD]D 



G ˜S

,

U ˜ Y ˜

,

1







G ˜S

,

U ˜ Y ˜

,

1



,



,

1





 ' ˜S S 0  U ˜ Y ˜ 



 =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

.ROLþLQDJLEDQMD   6LODQDUDþYXUDþXQDVHL]MHGQDGåEHNROLþLQHJLEDQMD )[

,  ,  ,˜ FRV D

)[

1

)]

, ˜ VLQ D  U ˜ J ˜ 9

)]

1

)5

1

)5 E









)[  )]

§ )] · ¸ © )[ ¹

E

DWDQ ¨

,

'

G



,

K



D ,

G



GHJ



 

,VSLW]DGDWDN 

S

2GUHGLWH VLOX ) NRMD SULGUåDYD SORþX PDVH P    NJ ]JOREQR SULþYUãüHQX X WRþNL $ 3UHWSRVWDYLW QHYLVNR]QR VWUXMDQMHIOXLGDWH]DQHPDULWHWHåLQXPOD]DYRGH=DGDQRMH/ P+ PK PD P' PG  FPD U NJP SORFH

J

D

) U

K

G

+



S

J

D

 

/

D

K



'

$

)



D

,



PJ

G

+



Y

˜ J˜ K

Y



P

Y

/

V

' ,



˜ J ˜ +

Y







$

1DSORþXVOMHGHüHVLOHVLODWHåLQHSORþHPJVLOD)WHVLOHPOD]D YRGH SUHGVWDYOMHQH LPSXOVQLP IXQNFLMDPD ,  GR ,   %U]LQH POD]DYRGHUDþXQDVHL]7RULFHOO\HYHMHGQDGåEH



,

D



,

,

D





P V



,PSXOVQHIXQNFLMHVHUDþXQDMXSUHPDL]UD]LPD ,



U ˜ Y ˜



G ˜S 

,



U ˜ Y ˜



' ˜S 

,

1

,



u  1



'DELSORþDELODXUDYQRWHåLVXPDPRPHQDWDRNRWRþNH$PRUDELWLMHGQDNDQXOL ,PSXOVQHIXQNFLMH, GR, QHþLQH PRPHQWRNRWRþNH$  

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



.ROLþLQDJLEDQMD  / ) ˜ /  PSORFH ˜ J˜ ˜ FRV D  ,˜ +  K  ,˜ D 

)



/ PSORFH ˜ J ˜ ˜ FRV D  , ˜ +  K  , ˜ D  /



)

1



 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,]HQWURSVNRVWUXMDQMH 

              

,]HQWURSVNRVWUXMDQMH

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,]HQWURSVNRVWUXMDQMH  

,VSLW]DGDWDN

3UL L]HQWURSVNRP LVWMHFDQMX ]UDND     5   -NJ.  L] VSUHPQLNDNUR]NRQYHUJHQWQXVDSQLFXSURPMHUD' PPL]PMHUHQMH PDVHQLSURWRNTPDVHQL NJV2GUHGLWHWODNLWHPSHUDWXUXXVSUHPQLNX DNRMHWHPSHUDWXUDL]OD]QRJPOD]D- &DWODNS  EDU

S-





S-









'

*XVWRüDIOXLGDXL]OD]QRPPOD]XUDþXQDVHL]MHGQDGåEHVWDQMDSOLQD S

5˜ 7

U

U

S

U

5˜ 7



NJ 

P



%U]LQDIOXLGDXL]OD]QRPPOD]XUDþXQDVHL]MHGQDGåEH]DPDVHQLSURWRN ˜ T PDVHQL



T PDVHQL

U  ˜ Y ˜

' ˜S

Y



Y



U ˜ ' ˜ S



P V



7HPSHUDWXUDIOXLGDXVSUHPQLNX XVWDQMXPLURYDQMD UDþXQDVHL]%HUQRXOOLMHYHMHGQDGåEH N

N  

˜

S U



Y 



N

N  

˜ 5˜ 7

§ S N   Y  · ¨ ¸ ˜  ˜ ¸ 5 ¨ U  N © ¹ 

7

7

.



*XVWRüDIOXLGDXVSUHPQLNXUDþXQDVHSRPRüXMHGQDGåEHL]HQWURSH

U U

§ 7 · ¨ ¸ © 7 ¹





N 

N 

U

§ 7 · ¸ © 7 ¹

U ˜ ¨

U



NJ 

P



7ODNIOXLGDXVSUHPQLNXUDþXQDVHL]MHGQDGåEHVWDQMDSOLQD S

U  ˜ 5˜ 7

S

EDU



 

,VSLW]DGDWDN

,]UDþXQDM SURPMHU ' SUDYLOQR SURãLUHQH VDSQLFH WODN X POD]X MHGQDN MH WODNX RNROLQH  NRMD RVLJXUDYD SRWLVQX VLOX S7 SURWXJUDGQHUDNHWHRG) 1DNRMH]DGDQWODNXNRPRUL G L]JDUDQMDS EDUDDWHPSHUDWXUDL]JDUDQMD7 . 3OLQRYH L]JDUDQMD VPDWUDMWH VDYUãHQLP SOLQRP X L]HQWURSVNRPVWUXMDQMX 5 -NJ.   =DGDQRMHSD EDUD

G

SD

 ,]MHGQDGåEHVWDQMDSOLQDPRJXüHMHL]UDþXQDWLJXVWRüXIOXLGDXNRPRULVDJRULMHYDQMD S U

5˜ 7

U

S 5˜ 7

U



NJ 

P



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,]HQWURSVNRVWUXMDQMH 

3RPRüXMHGQDGåEHL]HQWURSHL]UDþXQDYDVHJXVWRüDIOXLGDXL]OD]QRPPOD]X 

S

SD

N

N

U

§ SD · ¸ © S ¹

U

U

N

U ˜ ¨

U



NJ 

P



,]%HUQRXOOLMHYHMHGQDGåEH]DL]HQWURSVNRVWUXMDQMHL]UDþXQDYDVHEU]LQDXL]OD]QRPPOD]X N

˜

S

N   U

N

˜

SD

N   U





Y



§ S

˜ N

Y

N

˜¨

© U

SD ·



Y

¸ U ¹



P V



3RPRüXMHGQDGåEHNROLþLQHJLEDQMDUDþXQDPRL]OD]QLSURPMHUVDSQLFH )

  ' ˜ S U ˜ Y ˜

˜ )

'



'



U ˜ Y ˜ S

PP





,VSLW]DGDWDN



.UR]NRQYHUJHQWQR±GLYHUJHQWQXVDSQLFX]UDN 5 -NJ.     L]HQWURSVNL LVWMHþH X DWPRVIHUX PDVHQLP SURWRNRP TPDVHQL   NJP $NR X VSUHPQLNX YODGD WODN S   EDUD RGUHGLWH SURPMHU ' L]OD]QRJSUHVMHNDSUDYLOQRSURãLUHQHVDSQLFH=DGDQRMHSD PEDU ' PP 

'

S

'



SD

   .RG SUDYLOQR SURãLUHQH VDSQLFH WODN RNROLQH MHGQDN MH WODNX X POD]X ,] RGQRVD WODNRYD L] WDEOLFD ]D L]HQWURSVNR VWUXMDQMHPRJXüHMHRGUHGLWL0DFKRYEURMXL]OD]QRPSUHVMHNX \

SD

\

S



0





.DNRMH0DFKRYEURMYHüLRGMHGDQVWUXMDQMHMHQDG]YXþQRSDMHQDMXåLSUHVMHNNULWLþDQSUHVMHN,]WDEOLFD]D  L]HQWURSVNRVWUXMDQMH]D0 RGQRVSRYUãLQHMH$$NULW  

$

˜

' ˜ S 

$



$

' ˜ S 

'





 u  P  S

˜ S˜ $

     =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'

P



,]HQWURSVNRVWUXMDQMH 

,VSLW]DGDWDN 

7 S

.UR]NRQYHUJHQWQRGLYHUJHQWQXVDSQLFX]UDN 5 -NJ.    LVWMHþHXDWPRVIHUX2GUHGLWHPDVHQLSURWRNNUR]SUDYLOQRSURãLUHQXVDSQLFX SUHPDVOLFL=DGDQRMH' PPS EDUDSD EDUD7 .

'



'



SD

 

 ,] RGQRVD WODNRYD SDS    RþLWR MH GD MH VWUXMDQMH QDG]YXþQR SD X QDMXåHP SUHVMHNX YODGDMX NULWLþQLXYMHWL,]WDEOLFD]DL]HQWURSVNRVWUXMDQMH]D0 ODNRMHL]UDþXQDWLNULWLþQLWODNLWHPSHUDWXUX S NU

˜ S 

7NU

7 ˜ 

S NU

EDU

7NU

.



,]MHGQDGåEHVWDQMDSOLQDL]UDþXQDYDVHJXVWRüDIOXLGD U NU

SNU 5˜ 7NU



U NU

NJ P



0DVHQLSURWRNNUR]NRQYHUJHQWQRGLYHUJHQWQXVDSQLFXUDþXQDVHL]L]UD]D 

T PDVHQL

U NU˜ F ˜ 5˜ 7NU˜

' ˜ S 

TPDVHQL

NJ V

 



,VSLW]DGDWDN 

=UDN 5  -NJ.      L]HQWURSVNL VWUXML L] YHOLNRJ VSUHPQLND X NRMHP YODGD WODN S   EDU NUR] NRQYHUJHQWQR GLYHUJHQWQX VDSQLFX SURPMHUD '  YDNXXP S  PP X ]UDþQL WXQHO SURPMHUD '   PP SXPSD ' ' SD 2GUHGLWHWODNSL0DFKRYEURMNDGDIOXLGX]UDþQRP S WXQHOX VWUXML SRG]YXþQR .ROLNL WODN S PRUDPR ' SRVWLüL YDNXXP SXPSRP GD EL X ]UDþQRP WXQHOX VWUXMDQMH SUHãOR X QDG]YXþQR L NROLNL MH 0DFKRY ' EURM=DGDQRMHSD EDU' PP 

 2GQRVWODNDXVSUHPQLNXLWODNDXL]OD]QRPPOD]X DNRMHVDSQLFDSUDYLOQRSURãLUHQD   SDS    ,]WDEOLFD]DL]HQWURSVNRVWUXMDQMH0 L$ $NU  SDMHRGDWOHNULWLþDQSUHVMHN$NU $  'S    'S P 

2GQRVNULWLþQRJSUHVMHNDLSUHVMHNDPMHUQHVHNFLMHXWXQHOX =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,]HQWURSVNRVWUXMDQMH 

 $$NU 'S$NU   ,]WDEOLFD]DL]HQWURSVNRVWUXMDQMHRGQRVSRYUãLQD$$NU PRåHVHQDüLQDGYDPMHVWDLWR  =DSRG]YXþQRVWUXMDQMH 0 SS S EDU  =DQDG]YXþQRVWUXMDQMH 0 SS S EDU 

,VSLW]DGDWDN 

G

2GUHGLWH L]OD]QL SURPMHU ' SUDYLOQR SURãLUHQH NRQYHUJHQWQR ± GLYHUJHQWQHVDSQLFHNUR]NRMXL]HQWURSVNLVWUXML]UDN 5 -NJ.    =DGDQRMHS EDUSD EDU7 .G  PP

'

S7

  

SD

,]RGQRVDWODNRYDXVSUHPQLNXLDWPRVIHUVNRJWODND SD



S



0RJXüHMHL]WDEOLFD]DL]HQWURSVNRVWUXMDQMHRGUHGLWL0DFKRYEURMQDL]OD]QRPSUHVMHNXNRGSUDYLOQRSURãLUHQH VDSQLFH0 =DWDM0DFKRYEURMRGQRVSRYUãLQHL]OD]QRJSUHVMHNDLNULWLþQRJSUHVMHNDL]QRVL $NU



G ˜

S 

$

˜ $NU

$





u  P



,]OD]QLSURPMHUSUDYLOQRSURãLUHQHVDSQLFH'L]QRVL 

$

' ˜S 

'

˜ $ S

'

P



 

,VSLW]DGDWDN

=UDN 5   -NJ.      LVWLþH L] UH]HUYRDUD X DWPRVIHUX NUR] NRQYHUJHQWQR GLYHUJHQWQX VDSQLFX 8 QDMXåHP SUHVMHNX VDSQLFH G   PP ]UDN VWUXML EU]LQRP ]YXND 3UHWODN X UH]HUYRDUX L]QRVL S0   EDUD D WHPSHUDWXUDW &3RWUHEQRMHL]UDþXQDWLPDVHQLSURWRNTPDVHQLNUR]VDSQLFXNDRLL]OD]QLSURPMHU'SRGXYMHWRP GDWODNQDL]OD]XL]VDSQLFHL]QRVLSD EDU DWPRVIHUVNLWODN  ,]RGQRVDWODNRYDXUH]HUYRDUXLL]OD]QRJWODNDSUHPDWDEOLFDPD]DL]HQWURSVNRVWUXMDQMHPRJXüHMH]DNOMXþLWL GDMHVWUXMDQMHQDG]YXþQR =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,]HQWURSVNRVWUXMDQMH  SD



S

0





8WRPVOXþDMXXQDMXåHPSUHVMHNXVWUXMDQMHMHNULWLþQRRGQRVQRIOXLGVWUXMLEU]LQRP]YXND 0

S



7



S

7

U



$



U

$NU





,]RGQRVD]DNULWLþQLSUHVMHNUDþXQDVHVWDQMHQDNULWLþQRPSUHVMHNX 7

7 ˜ 

S

5˜ 7

U

U ˜ 

U

U U

7

. S 5˜ 7

Y

N ˜ 5˜ 7

Y

U

NJ P

PV







NJ P



0DVHQLSURWRNUDþXQDVHL]L]UD]D 

T PDVHQL

U ˜ Y˜

G ˜S

TPDVHQL



NJ V

 

,]WDEOLFD]DL]HQWURSVNRVWUXMDQMH]D0 NRMLYODGDXL]OD]QRPSUHVMHNXUDþXQDVHL]OD]QDSRYUãLQD 

$



$NU

˜ $

G

S

G ˜S

$

˜

G

P

$







 u  P





,VSLW]DGDWDN G



=UDN 5 -NJ.   L]HQWURSVNLVWUXMLSUDYLOQRSURãLUHQX NRQYHUJHQWQR ± GLYHUJHQWQX VDSQLFX WODN X L]OD]QRP POD]X MHGQDN MH DWPRVIHUVNRPWODNX 2GUHGLWHPDVHQLSURWRNLL]OD]QLSURPMHU'DNRMH SURPMHUJUODG PPDEU]LQDXL]OD]QRPPOD]X0 0DFK=DGDQR MHSD EDU7 .

'

S7

 SD

  ,]WDEOLFD]DL]HQWURSVNRVWUXMDQMH]D0 RþLWDYDMXVHRGQRVLYHOLþLQD

0

S



S

7



7

U



U



$ $NU





.ULWLþQLSUHVMHN QDMXåL ]DGDQMHSURPMHURPGSDMHPRJXüHL]UDþXQDWLLL]OD]QLSURPMHU' 

$L]

'L] S 



˜ $NU

˜

G S 

'L]

G ˜ 

'L]

P



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

,]HQWURSVNRVWUXMDQMH  )L]LNDOQHYHOLþLQHQDL]OD]QRPSUHVMHNXUDþXQDMXVHSUHPDL]UD]LPD SD

S

7L]



SD

7 ˜ 

5˜ 7L]

U L]

SD

U L]

U L]

5˜ 7L]



0DVHQLSURWRNUDþXQDVHL]L]UD]D 

T PDVHQL

U L] ˜ YL]˜ $L]

U L] ˜ 0 ˜ N ˜ 5˜ 7L]˜

'L] ˜ S

TPDVHQL





NJ V





,VSLW]DGDWDN

,]UDþXQDM SURPMHU ' SUDYLOQR SURãLUHQH VDSQLFH WODN X POD]X MHGQDN MH WODNX RNROLQH  NRMD RVLJXUDYD SRWLVQX VLOX S SURWXJUDGQHUDNHWHRG) 1DNRMH]DGDQWODNXNRPRUL L]JDUDQMDS EDUDDWHPSHUDWXUDL]JDUDQMD7 . G  3OLQRYH L]JDUDQMD VPDWUDMWH VDYUãHQLP SOLQRP X L]HQWURSVNRPVWUXMDQMX 5 -NJ.   =DGDQR MHSD EDUD

G

D

S7





  ,]MHGQDGåEHVWDQMDSOLQDPRJXüHMHL]UDþXQDWLJXVWRüXIOXLGDXNRPRULVDJRULMHYDQMD S U

5˜ 7

U

S

U

5˜ 7



NJ 

P



3RPRüXMHGQDGåEHL]HQWURSHL]UDþXQDYDVHJXVWRüDIOXLGDXL]OD]QRPPOD]X 

S

SD

N

N

U

§ SD · ¸ © S ¹

U

U

N

U ˜ ¨

U



NJ 

P



,]%HUQRXOOLMHYHMHGQDGåEH]DL]HQWURSVNRVWUXMDQMHL]UDþXQDYDVHEU]LQDXL]OD]QRPPOD]X N

˜

S

N   U

N

˜

SD

N   U





Y



§ S

˜ N

Y

N

˜¨

© U



SD ·

Y

¸ U ¹



3RPRüXMHGQDGåEHNROLþLQHJLEDQMDUDþXQDPRL]OD]QLSURPMHUVDSQLFH )



U ˜ Y ˜



' ˜ S 

'

˜ ) 

U ˜ Y ˜ S

  

,VSLW]DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

'

PP



P V



NJ 

P



,]HQWURSVNRVWUXMDQMH 

=UDN 5 -NJ.  L]HQWURSVNLVWUXMLNUR]NRQYHUJHQWQXVDSQLFXX DWPRVIHUX2GUHGLWHPDVHQLSURWRNTPDVHQLDNRMHL]OD]QLSURPMHUVDSQLFHG  PP=DGDQRMHS  EDU7  .S  EDU 

D



G

S7



3URYMHURP RGQRVD WODNRYD XQXWDU L L]YDQ VSUHPQLND ]DNOMXþXMHPR GD MH VWUXMDQMHXJUOXNRQYHUJHQWQHVDSQLFHNULWLþQR SD

SD

S

 

S S





,]WDEOLFD]DL]HQWURSVNRVWUXMDQMHRþLWDYDVHUHGDN]D0  0

S



U



S

U

7



7





*XVWRüDIOXLGDXVSUHPQLNXUDþXQDVHL]MHGQDGåEHVWDQMDSOLQD S

U

U

5˜ 7



NJ 

P



6WDQMHIOXLGDQDL]OD]QRPSUHVMHNXUDþXQDVHL]L]UD]D U

U  ˜ 

U



NJ 

P

7

7 ˜ 

7

.



0DVHQLSURWRNUDþXQDVHSUHPD 

T PDVHQL

U  ˜ Y ˜

G ˜S 



T PDVHQL

U ˜ N ˜ 5˜ 7 ˜

G ˜S 

T PDVHQL



NJ V



               =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY 

         

5RWLUDMXüDVWUXMQDFLMHY

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY 

,VSLW]DGDWDN

8] SUHWSRVWDYNX QHYLVNR]QRJ VWUXMDQMD RGUHGLWH NXWQX EU]LQX Z VORERGQR URWLUDMXüH FLMHYL SUHPD VOLFL 7UHQMH X OHåDMX VH ]DQHPDUXMH =DGDQRMHS0 EDUD+ FP/ FP5 FPG PPU NJP

302 J



U

 

5



+

/ Z



D



G

Y X 5



/

,]JHRPHWULMVNRJRGQRVDFLMHYLSUHPDVOLFL DVLQ §¨

D



D

¸ © 5¹

GHJ



=ERJXYMHWDVORERGQRURWLUDMXüHFLMHYLWURNXWEU]LQHMHSUDYRNXWQLWURNXWSDVOLMHGLUHODFLMD Z˜5

Z ˜ VLQ D 

X

%HUQRXOOLMHYDMHGQDGåED]DVORERGQRURWLUDMXüXFLMHYSUHPDVOLFL S 0 U ˜J



Z X

+





Z ˜

˜ J

  VLQ D J

§ S0 ·  +¸ © U ˜J ¹

˜ J ˜ ¨



Z

Z

FRV D



P V



.XWQDEU]LQDVORERGQRURWLUDMXüHFLMHYLL]QRVL Z

Z

5

˜ VLQ D

Z

V







,VSLW]DGDWDN

2GUHGLWH NXW E GYDMX L]OD]QLK NUDNRYD URWLUDMXüH þHWYHURNUDNH FLMHYL SUHPD VOLFLGDELRQDVORERGQRURWLUDODNXWQRPEU]LQRPZ UDGV=DGDQRMH5 FP5 FPG PP' PP+ P  Y



X 



Y Z Z X G SD Z E

SD J U

+ '





E

G



5

Z G SD

5





3RVWDYOMDQMHP %HUQRXOOLMHYH MHGQDGåEH ]D URWLUDMXüX VWUXMQX FLMHY RG VORERGQH SRYUãLQH GR VYDNRJ RG L]OD]D L] þHWYHURNUDNH URWLUDMXüH FLMHYL PRJXüHMHL]UDþXQDWLUHODWLYQHEU]LQHQDL]OD]LPDL]FLMHYL

E

G



E

5

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY  X

Z ˜ 5

X



Z  X

+

Z ˜ 5



˜ J 

Z  X

+

Z

˜ J˜ +  X 



Z

˜ J˜ +  X 



Z



Z





˜ J

P V

P V



3UHPD XYMHWX ]DGDWND þHWYHURNUDND UDþYD URWLUD NDR VORERGQR URWLUDMXüD FLMHY 7R SRGUD]XPLMHYD GD VH VQDJD QLWL QH GRGDMH QLWL QH RGX]LPD WM GD MHGDQ NUDN FLMHYL UDGL X SXPSQRP D GUXJL X WXUELQVNRP UHåLPX UDGD 6QDJD GRELYHQDQDWXUELQVNRPNUDMXFLMHYLSRWURãLVHQDSXPSQRP 3S

 U ˜ J ˜ ª« ˜ X ˜ YT »º ˜ 4 ¬J ¼



3W 

U ˜ X ˜ YT˜ Z ˜

 U ˜ J ˜ ª« ˜ X ˜ YT »º ˜ 4 ¬J ¼









G ˜S

U ˜ X  ˜ YT˜ Z ˜



G ˜S

X ˜ YT˜ Z



X  ˜ YT˜ Z



QDVOLFLVXQDFUWDQLSXPSQLLWXUELQVNLNUDMFLMHYLVSULSDGDMXüLPWURNXWLPDEU]LQD,]MHGQRVWDYQHJHRPHWULMVNH DQDOL]HWURNXWDEU]LQDVOLMHGL YT

X

YT

Z ˜ VLQ E  X 



8YUãWHQMHPRYLKL]UD]DXMHGQDGåEXMHGQDNRVWLVQDJDSXPSHLWXUELQHL]UDþXQDYDVHWUDåHQLNXWE 





X ˜ Z˜ VLQ E  X ˜ Z 

E





X  ˜ Z

ª X ˜ Z   X˜ Z DVLQ «  « X  ˜ Z ¬





º» » ¼

E

GHJ



 

,VSLW]DGDWDN U

E G

 2GUHGLWHGRPHW5POD]DSROMHYDþDWUDYHNRMLVHRNUHüHNXWQRP EU]LQRP Z   UDGV EH] WUHQMD X OHåDMHYLPD =DGDQR MH U   FPE + P 

Z

3ROMHYDþWUDYHUDGLNDRVORERGQRURWLUDMXüDFLMHY XYMHWGDQHPD WUHQMDXOHåDMLPD SDMHL]OD]QLWURNXWEU]LQDSUDYRNXWDQ

E



Y

 5

+

 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

X

E

Z

5RWLUDMXüDVWUXMQDFLMHY 

 2ERGQXEU]LQXXLDSVROXWQXEULQXYUDþXQDPRL]L]UD]D X Y

Z ˜U X ˜ WDQ E

X

PV

Y

PV







'RPHWPOD]DUDþXQDPRL]KRUL]RQWDOQRJKLFD 5U 5

Y˜ W

J

+

 Y˜ §¨ ˜ ˜ J ˜ + ·¸  U ©J ¹



5

˜W



P





,VSLW]DGDWDN

E



2GUHGLWHNRQVWDQWQXNXWQXEU]LQLYUWQMHZURWLUDMXüHFLMHYLSUHPD VOLFLQDNRMXGMHOXMHYDQMVNLPRPHQW0 1PDNRMHSURWRNNUR] FLMHY 4   OPLQ 2GUHGLWH NXWQX EU]LQX YUWQMH FLMHYL DNR VH FLMHY VORERGQR RNUHüH X] LVWH RVWDOH XYMHWH =DGDQR MH 5   P '   PPU NJPE 

Z



0

5HODWLYQDEU]LQDVWUXMDQMDZ EU]LQDVWUXMDQMDNUR]FLMHY UDþXQDVH SUHPDL]UD]X Z

Z

˜ 4

E



' ˜S



 J

˜ X˜ Y T

Y X

9LVLQDGREDYHSXPSHMHGQDNDMH KS

5

'

5

'

Z



0

2ERGQD NRPSRQHQWD DSVROXWQH EU]LQH YT  UDþXQD VH L] L]UD]D ]D YDQMVNL PRPHQW0

0

3

U ˜ J ˜ K S˜ 4

 U ˜ J ˜ §¨ ˜ Z ˜ 5˜ YT ¸· ˜ 4 ©J ¹

Z

Z

Z

0

YT

YT

U ˜ 4˜ 5

PV





2ERGQDEU]LQDXUDþXQDVHL]WURNXWDEU]LQD YT

X  Z˜ FRV E

X

YT  Z˜ FRV E

X

PV





.XWQDEU]LQDYUWQMHFLMHYLL]QRVL Z

X 5

Z

V



1

Z ˜  S

1

V





8VOXþDMXVORERGQRURWLUDMXüHFLMHYL

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY  Z˜ FRV E

X

X

Z

Z

5

V



1

Z ˜  S

1

V





,VSLW]DGDWDN

2GUHGLWHNXWQXEU]LQXURWDFLMHZVORERGQRURWLUDMXüHFLMHYLSUHPDVOLFL =DGDQRMH+ P' PG P5 PS0 EDUU  NJP

302



J

 Z

U

Y



 X

Z

6QDJD UD]YLMDQD QD SXPSQRM VWUDQL MHGQDND MH VQD]L UD]YLMHQRM QD WXUELQVNRMVWUDQL U ˜ J ˜ KS˜ 4

G

X



5

G

'

U ˜ J ˜ K S˜ 4



X˜ YT˜ Z˜

+

Y



G ˜S

X˜ YT˜ Z˜



' ˜S 



2ERGQHEU]LQHX LXVXMHGQDNHRE]LURPGDVHQDOD]HQDLVWRPUDGLMXVX 

%HUQRXOOLMHYDMHGQDGåED]DURWLUDMXüXVWUXMQXFLMHYSRVWDYOMHQDGRSUHVMHNDL S 0 U ˜J



Z X

+



˜ J



.DNRVXRERGQHEU]LQHX LXMHGQDNHL]%HUQRXOOLMHYHMHGQDGåEH]DURWLUDMXüXVWUXMQXFLMHY]DNOMXþXMHPRGDVX LUHODWLYQHEU]LQHZMHGQDNH 

X

X

Z

Z



1DNRQVUH LYDQMDMHGQDGåEDMHGQDNRVWLVQDJDL]JOHGD Y T˜ G





Y T˜ '



$NRXYUVWLPRL]WURNXWDEU]LQDRGQRVH Y T

XZ

Y T

ZX



,]YRGLVHL]UD] X  Z ˜ G

X







Z  X ˜ '

G  ' G  '



8YUãWHQMHPJRUQMHJL]UD]DX%HUQRXOOLMHYXMHGQDGåEX]DURWLUDMXüXFLMHY

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY 

ª G  ' º Z  « Z˜ »   ¬ G  ' ¼







S 0

Z X

+

U ˜J



S 0

˜ J

U ˜J

+

˜ J



1DNRQVUH LYDQMDL]UDþXQDYDVHUMHãHQMH



X





S0  + ˜ U ˜ J U

G  ' G  '

X

Z







 G ' ˜ ˜ ˜  G ˜ '

Z

5

Z

PV

X

PV

Z

V











,VSLW]DGDWDN 

D

2GUHGLWHSURWRN4NUR]SROMHYDþWUDYHSUHPDVOLFLDNRVH]D SRJRQSROMHYDþDNRULVWLXWHJPDVHPX NJ ]DQHPDULWHWUHQMHX OHåDMHYLPD 2GUHGLWHWRWDOQLSUHWODNXFMHYRYRGQRMPUHåLQDNRMX S0WRW MH SROMHYDþ SULNOMXþHQ DNR MH NXWQD EU]LQD YUWQMH SROMHYDþD NRQVWDQWQD L L]QRVL Z   UDGV 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJIOXLGD=DGDQRMHG PP+a5 FP5  FPU NJPD   Z

PX

G

,] WURNXWD EU]LQD RþLWR MH GD MH RERGQD NRPSRQHQWD DSVROXWQH EU]LQH MHGQDNDRERGQRMEU]LQL

X

Y

SD

+



Y T

X

J

5 5



0RPHQWSRWUHEDQ]DRNUHWDQMHSROMHYDþDWUDYHMHGQDNMHPRPHQWXWHåLQHXWHJD U ˜ J˜ + ˜ 4

P X ˜ J˜ 5 

Z



9LVLQDGREDYHSROMHYDþDWUDYHMHGQDNDMH +

 J

X

˜ Y T˜ X



J 

3URWRNNUR]REDNUDNDSROMHYDþDMHGQDNMH 

4

˜ Z ˜

G ˜S  

-HGQDGåEDMHGQDNRVWLPRPHQDWDJODVL P X ˜ J˜ 5 







U ˜ J˜ + ˜ 4

U ˜X ˜4

U ˜ Z˜5  ˜4

Z

Z

Z



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY 

,]RYHMHGQDGåEHODNRMHL]UD]LWLSURWRN 4

PX ˜ J ˜

Z ˜ 5





U ˜ Z ˜ 5

   

4



 u  P V



5HODWLYQDLRERGQDEU]LQDUDþXQDMXVHL]L]UD]D Z

˜ 4

X



G ˜S

Z ˜ 5

Z

PV



X

PV





7RWDOQLSUHWODNXFMHYRYRGQRPVLVWHPXUDþXQDVHL]%HUQRXOOLMHYHMHGQDGåEH]DURWLUDMXüXVWUXMQXFLMHY 

S 0WRW

Z X

U ˜J

˜ J





S 0WRW











˜ Z  X ˜U

S 0WRW

EDU





,VSLW]DGDWDN

2GUHGLWH NXWQX EU]LQX YUWQMH Z VORERGQR URWLUDMXüH FLMHYL SUHPD VOLFL 3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH+ PU  NJP' PP5 PD E J  

SD



J U



+

 J

 

U ˜ J˜ K S˜ 4

X

X ˜ YT˜ Z˜



X

Z YT

' ˜S 

Y



Z

Z

YT

X

Z 

X Y

X  Z˜ VLQ D ˜ FRV J

˜ VLQ D ˜ FRV J  VLQ E

E







=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

T

 



X

'

5

Z

,]WURNXWDEU]LQDVOLMHGLUHODFLMD Z˜ VLQ E  X





' ˜S

.DNRVHLMHGDQLGUXJLNUDMFLMHYLQDOD]HQDLVWRPUDGLMXVXRERGQH EU]LQHVXMHGQDNH8]MHGQDNHRERGQHEU]LQHL]%HUQRXOOLMHYHMHGQDGåEH ]D URWLUDMXüX VWUXMQX FLMHY VOLMHGL GD VX L UHODWLYQH EU]LQH MHGQDNH 3D VH JRUQMDMHGQDGåEDVYRGLQDREOLN X

D

U ˜ J ˜ K S˜ 4



X˜ YT˜ Z ˜

'

5

'D EL VLVWHP SUHPD VOLFL URWLUDR NDR VORERGQR URWLUDMXüD FLMHY VQDJD UD]YLMDQH QD MHGQRP NUDMX NUDM FLMHYL X SXPSQRP UHåLPX UDGD  WURãL VH ]D URWDFLMXGUXJRJNUDMDFLMHYL NUDMFLMHYLXWXUELQVNRPUHåLPXUDGD  E

 

Y

T

 

Y



D

ZFRV J 

5RWLUDMXüDVWUXMQDFLMHY 

%HUQRXOOLMHYDMHGQDGåED]DURWLUDMXüXVWUXMQXFLMHY 

Z X

+



Z 



+

˜ J

ª Z ˜ VLQ D ˜ FRV J  VLQ E º « » ¬ ¼ ˜ J





,]RYHMHGQDGåEHODNRVHGRELMHUHODWLYQDEU]LQDWHRERGQDEU]LQD ˜ J ˜ +

Z 

VLQ D ˜ FRV J  VLQ E

Z

X





˜ VLQ D ˜ FRV J  VLQ E



Z

PV

X

PV







.XWQDEU]LQDVORERGQRURWLUDMXüHFLMHYL X

Z

Z

5

V





 

,VSLW]DGDWDN

2GUHGLWHGRPHWPOD]D5SROMHYDþDWUDYHNRMLMHSULNOMXþHQ QD YRGRYRGQX PUHåX WRWDOQRJ SUHWODND S0   EDUD =DQHPDULWHWUHQMHXOHåDMHYLPD=DGDQRMH+ PU  FPG PPD E  U NJP  

E

U

G





Z

 ,] XYMHWD VORERGQR URWLUDMXüH FLMHYL QHPD WUHQMD X OHåDMHYLPD L]OD]QLWURNXWEU]LQDMHSUDYRNXWDQ X

Z˜ FRV E 

%HUQRXOOLMHYDMHGQDGåED]DURWLUDMXüXVWUXMQXFLMHY 

S0

Z X

U ˜J

˜ J

E D 5



+



Z

8YUãWHQMHP SUHWKRGQRJ L]UD]D X %HUQRXOOLMHYX MHGQDGåEXL]UDþXQDYDVHUHODWLYQD EU]LQD ˜ S 0 Z

U

+

  FRV E

X

Y

 ˜ J ˜ + 

E

Z

PV





,]WURNXWDEU]LQDVOLMHGL Y

Z˜ VLQ E

Y

PV





'RPHWPOD]DUDþXQDVHL]MHGQDGåEH]DNRVLKLWDF+RUL]RQWDOQDNRPSRQHQWDEU]LQH]DGDQDMHL]UD]RP W ˜ Y˜ FRV D

/

W

/

Y˜ FRV D 

9HUWLNDOQDNRPSRQHQWDEU]LQH]DGDQDMHL]UD]RP =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5RWLUDMXüDVWUXMQDFLMHY  W ˜ Y˜ VLQ D  J˜

+

W



 

6XSVWLWXFLMRPYUHPHQDWGRELYDVHL]UD] 

/

Y˜ FRV D /

§ / · ¨ ¸ Y˜ FRV D ¹ © ˜ Y˜ VLQ D  J˜ +  

˜ VLQ D 

FRV D

 



˜ J˜

/

Y˜FRV D 

+





.YDGUDWQDMHGQDGåEDGDMHGYDUMHãHQMD]D/ /

/

 J

   º ª VLQ D  ˜ VLQ D ˜ Y  ˜ J ˜ + » ¬ FRV D Y˜ FRV D ¼

˜ Y ˜ FRV D ˜ «

 J





   º ª VLQ D  ˜ VLQ D ˜ Y  ˜ J˜ + » ˜ FRV D Y FRV D ¬ ¼

˜ Y ˜ FRV D ˜ « 



/

P

/

P



8VYDMDVHSR]LWLYQRUMHãHQMH 5

/  U

5

P





,VSLW]DGDWDN

 2GUHGLWH NXW E GYDMX L]OD]QLK NUDNRYD URWLUDMXüH þHWYHURNUDNH FLMHYL SUHPD VOLFLGDELRQDVORERGQRURWLUDODNXWQRPEU]LQRPZ UDGV=DGDQRMH5 FP5 FPG PP' PP+ P

SD J

 X 



U

Y Z Z X G SD Z E

Y



+ '



E





G

5

Z G SD

5



E



3RVWDYOMDQMHP %HUQRXOOLMHYH MHGQDGåEH ]D URWLUDMXüX VWUXMQX FLMHY RG VORERGQH SRYUãLQH GR VYDNRJ RG L]OD]D L] þHWYHURNUDNH URWLUDMXüH FLMHYL PRJXüHMHL]UDþXQDWLUHODWLYQHEU]LQHQDL]OD]LPDL]FLMHYL 

+

Z



Z  X 









Z   Z ˜ 5

˜ J

+

˜ J 



˜ J ˜ +  Z ˜ 5

Z



P V

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

Z



Z  X 



G







E

5

Z   Z ˜ 5

˜ J

˜ J 



˜ J ˜ +  Z ˜ 5

Z



P V



5RWLUDMXüDVWUXMQDFLMHY 

3UHPD XYMHWX ]DGDWND þHWYHURNUDND UDþYD URWLUD NDR VORERGQR URWLUDMXüD FLMHY 7R SRGUD]XPLMHYD GD VH VQDJD QLWL QH GRGDMH QLWL QH RGX]LPD WM GD MHGDQ NUDN FLMHYL UDGL X SXPSQRP D GUXJL X WXUELQVNRP UHåLPX UDGD 6QDJD GRELYHQDQDWXUELQVNRPNUDMXFLMHYLSRWURãLVHQDSXPSQRP U ˜ 4 ˜ J ˜ + 

U ˜ 4 ˜ J ˜ + 



QDVOLFLVXQDFUWDQLSXPSQLLWXUELQVNLNUDMFLMHYLVSULSDGDMXüLPWURNXWLPDEU]LQD,]MHGQRVWDYQHJHRPHWULMVNH DQDOL]HWURNXWDEU]LQDVOLMHGL X

Z ˜ 5

X



X

Z ˜ 5

X



P

YT

V P

X Z˜ VLQ E  X

ZT

V



8YUãWHQMHPRYLKL]UD]DXMHGQDGåEXMHGQDNRVWLVQDJDSXPSHLWXUELQHL]UDþXQDYDVHWUDåHQLNXWE 

Z˜

G ˜S 



˜ YT˜ X 



Z˜

G ˜S 

˜ YT˜ X 

ȼ

ª Z˜ X  Z˜ X  « Z ˜ X ¬

DVLQ «

E







E

» ¼



Z˜ Z˜ VLQ E  X  ˜ X

Z˜ X ˜ X 

GHJ





,VSLW]DGDWDN

SD

 2GUHGLWH VQDJX SUHGDQX JHQHUDWRUX 3 DNR MH NXWQD EU]LQX YUWQMH SULPLWLYQHWXUELQHSUHPDVOLFLZ V=DGDQRMH+ PG  P5 PE U NJP

J

U +



'

%HUQRXOOLMHYD MHGQDGåED ]D URWLUDMXüX FLMHY RG VORERGQH SRYUãLQH VSUHPQLNDGRL]OD]DL]SULPLWLYQHWXUELQH 

Z X

+



Z

˜ J ˜ J˜ +  5˜ Z

Z



Z

˜ J ˜ +  X 

JHQHUDWRU



E 5

P V

Z˜ FRV E  X

YT





E

Y



 G ˜S U ˜ J ˜ ª« ˜ YT ˜ X »º ˜ Z˜ ˜ J  ¬ ¼





3

U ˜ Z˜ FRV E  Z ˜ 5 ˜ Z ˜ 5˜ Z ˜ G ˜ S 

E

G

Z E

8YUãWHQMHPXMHGQDGåEX]DVQDJXWXUELQH U ˜ J ˜ KS ˜ 4

G



 X

3

SD



,]WURNXWDEU]LQDQDL]OD]XL]WXUELQHRþLWRMH YT

Z

U ˜ Z˜ FRV E  X ˜ X ˜ Z˜

3

N:



G ˜S 

˜





=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL                

3ULORJ,VSLWQLURNRYL

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 8 FLOLQGULþQRM SRVXGL SURPMHUD '   P LVSXQMHQRJ YRGRP JXVWRüH U   NJP GR YLVLQH +   P SOLYD GUYHQL YDOMDN SURPMHUD G   FP YLVLQH/ FPJXVWRüHGUYHWDU NJP2GUHGLWHXGDOMHQRVW FLOLQGULþQHSRVXGHQDNRQãWRSRVXGX]DURWLUDPRNXWQRPEU]LQRPZ UDGV  2GUHGLWHPDVXXWHJDNRMDMHSRWUHEQDGDELEUDQDMHGLQLþQHãLULQHPDVHP NJXOHåLãWHQDXWRþFL$RVWDODX UDYQRWHåQRPSRORåDMX=DGDQRMH/ PO PD PK PD   =D GREDYX YRGH JXVWRüH  NJP L] MH]HUD GR DNXPXODFLMVNRJ UH]HUYRDUD VPMHãWHQRJ QD YLVLQL K   P NRULVWLVHSXPSDVOMHGHüHNDUDNWHULVWLNH^KS`P ^4`PV^4`PV6YLORNDOQLJXELFLXNOMXþXMXüL L JXELWDN XODVND X YHOLNL VSUHPQLN L]QRVH .8.   D OLQLMVNH JXELWNH ]DQHPDULWH 2GUHGLWH ]D NROLNR üH VH SRYHüDWLSURWRNDNRVHX]SRVWRMHüLSXPSXSULNOMXþLSXPSDLVWLKNDUDNWHULVWLNDD VHULMVNLE SDUDOHOQR&MHYRYRG MHXQXWUDãQMHJSURPMHUD' P

 .ROLNLP PRPHQWRP 0 WUHED SULGUåDYDWL FLMHY SUHPD VOLFL GD VH QH SRþQH RNUHWDWL 3UHWSRVWDYLWH VWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH+ PU NJP' PP5 PD E    %U]LQDWRQMHQMDYQHNRJWLMHODXIOXLGXRYLVLRJUDYLWDFLMLJYROXPHQXWLMHOD9JXVWRüLWLMHODUJXVWRüLIOXLGDU WHRYLVNR]QRVWLIOXLGDP3ULPMHQRPSWHRUHPDRGUHGLWHRSüLREOLN]DYLVQRVWLEU]LQHYRGSUHRVWDOLKYHOLþLQD  

J

SD



U



G

EUDQD

J /

/



PJ

O



+

D



K

D

U $

'



XWHJ SD



D

Z



=DGDWDN=DGDWDN  

DNXPXODFLMVNL VSUHPQLN

J

 

SD

SD

J

 

K

SXPSD

'

U +

     

' SD 5

MH]HUR E

D 0

=DGDWDN=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 8FLOLQGULþQRMSRVXGLSURPMHUD' PLYLVLQH+ PQDOD]HVHGYDIOXLGDUD]OLþLWHJXVWRüH3RVXGDMH LVSXQMHQDYRGRPJXVWRüHU NJPGRYLVLQHK PWHXOMHPJXVWRüHU NJPGRYLVLQHK  P2GUHGLWHSUHWODNXWRþFL$QDNRQãWRSRVXGX]DURWLUDPRNXWQRPEU]LQRPZ UDGV  2GUHGLWHWODNSNRMLüHYODGDWLXQXWDUFLOLQGULþQHSRVXGHL]UD HQHRGDOXPLQLMDJXVWRüHU$ NJPDNRMH XWUHQXWNXSULMHXUDQMDQMDXYRGXJXVWRüHU NJPSRVXGDELODLVSXQMHQD]UDNRPQDDWPRVIHUVNRPWODNXSD EDUD3UHWSRVWDYLWHL]RWHUPQXNRPSUHVLMX]UDNDXQXWDUSRVXGHWH]DQHPDULWHWHåLQX]UDND=DGDQRMH+ PK FP' FPG FP  2GUHGLWHNROLNLMHPLQLPDOQLSUHWODNXVLVWHPXSUHPDVOLFLXNROLNRMHL]PMHUHQPDNVLPDOQLSUHWODNXVLVWHPXS  EDUD=DGDQRMHU NJPQ PV+ PK PK P/ P' PP/XN  PN PP KUDSDYRVWFLMHYL .8/ .9   .ROLND VLOD ) L PRPHQW 0 VYH WUL NRPSRQHQWH VLOH L PRPHQWD  RSWHUHüXMH VSRM FLMHYL L UH]HUYRDUD WRþND $  3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH+ PU NJP' PP5 PD  E G K P  8]SUHWSRVWDYNXQHYLVNR]QRJVWUXMDQMDRGUHGLWHNXWQXEU]LQXZVORERGQRURWLUDMXüHFLMHYLSUHPDVOLFL7UHQMDX OHåDMXVH]DQHPDUXMH=DGDQRMHS0 EDUD+ FP/ FP5 FPG PPU NJP  

J

Z

 SD

+

'



J ' K

G

   

K

S

+

U

K

U

U

$ =DGDWDN=DGDWDN $  SD K  SD +  

K





/# =DGDWDN SD  

J U + G

+

$



'

 K

G

 

302

J

 U



/$ N '

#

5 /

5

D

\

E  =DGDWDN=DGDWDN [

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWHVLOXQDSRNORSDFFLOLQGULþQHSRVXGHSUHPDVOLFLNRMDMHSULMHURWDFLMDELODLVSXQMHQDYRGRPJXVWRüHU  NJPGRYLVLQHK FP1DNRQURWDFLMHXSRVXGLRVWDQHSRORYLFDSUYRELWQRJYROXPHQDYRGH=DGDQRMH ' FPG FP+ FP  2GUHGLWHVLOXNRMRPMHSRWUHEQRSULGUåDYDWLYDOMNDVWL]DWYDUDþMHGLQLþQHãLULQH]JOREQRXþYUãüHQXWRþFL$SUHPD VOLFL=DGDQRMH+ P5 PK PU NJP  5HYHU]LELOQL DJUHJDW X SXPSQRP SRJRQX SUHSXPSDYD YRGX L] MH]HUD X DNXPXODFLMVNL VSUHPQLN WH MH X WXUELQVNRP UDGX SUL VSXãWDQMX YRGH L] DNXPXODFLMVNRJ VSUHPQLND X MH]HUR $JUHJDW LPD NDUDNWHULVWLNX ]DGDQX MHGQDGåERP ^K$`P   ± >^4`PV@ 2GUHGLWH VQDJH UHYHU]LELOQRJ DJUHJDWD NDGD UDGL X WXUELQVNRP L SXPSQRP SRJRQX .ROLNL MH VWXSDQM GMHORYDQMD SRVWURMHQMD" =DQHPDULWH VYH ORNDOQH JXELWNH L]X]HY JXELWND XODVNDXYHOLNLVSUHPQLN=DGDQRMH+ P' P/ NP XNXSQDGXOMLQDFMHYRYRGD N PP YLVLQDKUDSDYRVWLFMHYRYRGD U NJPQ PV  )OXLG SUROD]L NUR] ILOWDU SURWRNRP 4   PK SUL þHPX MH SDG WODND NUR] ILOWDU 'S   EDUD 2GUHGLWH UH]XOWDQWQXVLOX)IOXLGDQDILOWDUDNRMHSUHWODNQDXOD]XXILOWDUS0 EDUDDXQXWUDãQMLYROXPHQILOWUD9  O=DGDQRMH' PP' PPU NJP  ,]UDþXQDMWHSURWRN4NUR]FLMHYSUHPDVOLFLX]SUHWSRVWDYNXGDMHNRHILFLMHQWSURWRND&G =DGDQRMH'  PPG PPK FPK FPK FPU NJPU NJP  

SD

 J

 

U

=DGDWDN J 



  DNXPXODFLMVNL VSUHPQLN

 SD

+



UHYHU]LELOQL DJUHJDW

'

S0 9

SD





U

MH]HUR





4

'





'

J





)

=DGDWDN





5

Z





K

'





+

$

+

K

U





J

SD

G

 SD



=DGDWDN





K

 ' U

K 

=DGDWDN

J

U 



K 

 G

=DGDWDN 4

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWH YULMHPH SRWUHEQR GD VH FLOLQGULþQD NDSD PDVH P   NJ VSXVWL QD VWXS SURPMHUD '   FP =DQHPDULWHWUHQMHL]PH XNDSHLVWXSDWHSUHWSRVWDYLWHVDYUãHQREUWYOMHQMH=DGDQRMHG PPFG +  FPU NJP  2GUHGLWH WODN X QHSRNUHWQRM SULNOMXþQRM FLMHYL DNR MH PDVD SRNUHWQRJ FLOLQGUD P   NJ =DQHPDULWH XWMHFDMH WUHQMDLEU]LQHJLEDQMDSRNUHWQRJFLOLQGUDWHSUHWSRVWDYLWHVDYUãHQREUWYOMHQMH=DGDQRMHS EDUDG PP G PPG FPG FPG FPG FP  .OLPDWL]DFLMRQLYRGSUDYRNXWQRJSRSUHþQRJSUHVMHNDD[E [FP]ERJUHNRQVWUXNFLMHSURVWRULMHSRWUHEQR MH ]DPLMHQLWL NOLPDWL]DFLRQLP YRGRP SUDYRNXWQRJ SRSUHþQRJ SUHVMHND þLMD YLVLQD QLMH YHüD RG E   FP 2GUHGL ãLULQX NOLPDWL]DFLRQRJ YRGD NRMD RVLJXUDYD MHGQDNL SDG WODND SR MHGLQLFL GXOMLQL SUL LVWRP SURWRNX 3UHWSRVWDYLWHVWUXMDQMHXUHåLPXSRWSXQHWXUEXOHQFLMH=DGDQRMHN PP YLVLQDKUDSDYRVWL   2GUHGLWH VLOX POD]D YRGH YDWURJDVQRJ ãPUND QD NURYLãWH NXüH SUHPDVOLFL3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJ IOXLGD=DGDQRMHK PD PD SURWRNNUR]POD]QLFXYDWURJDVQHFLMHYL4 OVU  NJPE   3ULL]HQWURSVNRPLVWMHFDQMX]UDND   5 -NJ. L]VSUHPQLNDNUR]NRQYHUJHQWQXVDSQLFXSURPMHUD'  NJV2GUHGLWHWODNLWHPSHUDWXUXXVSUHPQLNXDNRMHWHPSHUDWXUD PPL]PMHUHQMHPDVHQLSURWRN P L]OD]QRJPOD]D- &DWODNS EDU SULNOMXþQD  FLMHY G J SD SRPLþQL  FLOLQGDU  G G  + G '  QHSRPLþQL G  FLOLQGDU G   

G

 

=DGDWDN



















=DGDWDN



GRYRGXOMD SRGWODNRPS   





 

E



D

J

 E

 D

 



=DGDWDN





D

   

S-





 S-

  



' 







=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

=DGDWDN

K

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWHSUHWODNS0SRWUHEDQ]DRWYDUDQMHVLJXUQRVQRJYHQWLODSUHPDVOLFLDNRMHVLODXRSUX]L) 10DVD NXJOLFHP J=DGDQRMHG FP5 FPD   2GUHGLWHKRUL]RQWDOQXVLOX)SRWUHEQX]DGUåDQMHSUHJUDGH2$MHGLQLþQHãLULQHSUHPDVOLFL3UHJUDGDMH]JOREQR YH]DQDXWRþNL2=DGDQRMH+ P5 P/ PU NJP  =DSRWUHEHRSVNUEHYRGRPQDVHOMDL]JUD HQMHFMHYRYRGRGYXþHQLKFLMHYLXNXSQHGXOMLQH/8. NP3XPSD GREDYOMDOVYRGH JXVWRüHU NJPNLQHPDWLþNRJNRHILFLMHQWDYLVNR]QRVWLQ PV QDVHOMX NRMH VH QDOD]L QD YLVLQL K   P L]QDG UD]LQH MH]HUD WH RVWYDUXMH WRWDOQL SUHWODN YRGH X QDVHOMX S0   EDUD 1DNRQGHVHWRJRGLãQMHHNVSORDWDFLMHSRWUHEH]DYRGRPVXVHSRYHüDOHSDMHSRWUHEQRGREDYLWLYLãHYRGHX] LVWL WRWDOQL SUHWODN 8VOLMHG NRUR]LMH YLVLQD KUDSDYRVWL VH SRYHüDOD QD N   PP 2GUHGLWH NROLNR SXWD VH SRYHüDODSRWUHEQDVQDJD]DWUDQVSRUWYRGH3ULSURUDþXQXORNDOQHJXELWNH]DQHPDULWH=DGDQRMH' PP  2GUHGLWHSUHWODNS0SULNRMHPVHRWYDUDVLJXUQRVQLYHQWLOSUHPDVOLFLPDVHP JWHSUHWODNS0SULNRMHPVH VLJXUQRVQLYHQWLO]DWYDUD=DGDQRMHG FP' FPG FPU NJP  2GUHGLWH NXW E GYDMX L]OD]QLK NUDNRYD URWLUDMXüH þHWYHURNUDNH FLMHYL SUHPD VOLFL GD EL RQD VORERGQR URWLUDOD NXWQRPEU]LQRPZ UDGV=DGDQRMH5 FP5 FPG PP' PP+ P   

' J

SD

 

D

2







WODNXVSUHPQLNXS0 =DGDWDN 

 

+

5

 

)

SD

/



G



J

SD

















5

U

=DGDWDN

 G

  

QDVHOMH

J

 





S0S0VSUHPQLN

'

 MH]HUR S D

J

' G



+



SD G

/8.

SD SXPSD 



=DGDWDN







=DGDWDN J

U



+



'

 

5

  











Z G SD

E

E  G 5 =DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 ,]D NUPHQRJ ]UFDOD þDPFD SULþYUãüHQ MH YHQWXULPDWDU GD EL FUSLR YRGX JXVWRüH U   NJP  L] þDPFD 2GUHGLWHPLQLPDOQXEU]LQXþDPFDNRGNRMH]DSRþLQMHFUSHQMHYRGH SUD]QDSULNOMXþQDFLMHY WHPLQLPDOQXEU]LQX NRGNRMHMHFUSHQMHMRãXYLMHNPRJXüH SXQDSULNOMXþQDFLMHY =DGDQRMHK  PK  PK  P ' FPG FP  2GUHGLWH PDNVLPDOQX PDVX SRQWRQD NRML VH PRåH SRGLJQXWL QD REDOX YLVLQH F   P D GD QH GR H GR SUHOLMHYDQMDYRGH JXVWRüHU NJP SUHNR]DGQMHJUXEDSRQWRQD=DGDQRMH% P ãLULQDSRQWRQD  / PK P  =D SRWUHEH RSVNUEH YRGRP QDVHOMD L]JUD HQ MH FMHYRYRG RG YXþHQLK FLMHYL XNXSQH GXOMLQH /    NP L XQXWUDãQMHJ SURPMHUD '   PP 3XPSD GREDYOMD  OV YRGH JXVWRüH U   NJP  NLQHPDWLþNRJ NRHILFLMHQWD YLVNR]QRVWL Q     P V  QDVHOMX NRMH VH QDOD]L QD YLVLQL +   P L]QDG UD]LQH MH]HUD WH RVWYDUXMHWRWDOQLSUHWODNYRGHXQDVHOMXS EDUD1DNRQGYDGHVHWRJRGLãQMHHNVSORDWDFLMHSRWUHEH]DYRGRPVX VH SRYHüDOH SD MH SRWUHEQR GREDYLWL  YLãH YRGH X] LVWL WRWDOQL SUHWODN =ERJ JXELWDND YRGH FLMHYL VX V XQXWUDãQMH VWUDQH SODVWLILFLUDQH VORMHP GHEOMLQH  PP SRYUãLQVNH KUDSDYRVWL  PP  2GUHGLWH NROLNR SXWDVH SRYHüDODSRWUHEQDVQDJD]DWUDQVSRUWYRGH3ULSURUDþXQXORNDOQHJXELWNH]DQHPDULWH  2GUHGLWHUH]XOWDQWQXVLOX)IOXLGDQDOXN$%FMHYRYRGDGXOMLQH/ PSURPMHUDG PPSUHPDVOLFLSUL SURWRNX 4   OV L SUHWODNX S    EDU X SUHVMHNX % 3UHWSRVWDYLWH NYD]LVWDFLRQDUQR LVWMHFDQMH IOXLGD =DGDQRMHU NJP + P  &LOLQGULþQD SRVXGD SUHPD VOLFL LPD QD GQX L SODãWX GYD MHGQDND RWYRUD VYDNL SRYUãLQH $    PP  NRHILFLMHQWDSURWRND&  ,]UDþXQDMWHYULMHPHSRWUHEQRGDVHVORERGQDSRYUãLQDVSXVWL]DYLVLQXKLWRD  DNRVHSRVXGDSUD]QLVDPRNUR]RWYRUQDSODãWXE DNRVHSRVXGDSUD]QLVDPRNUR]RWYRUQDGQX3UHWSRVWDYLWH NYD]LVWDFLRQDUQRLVWMHFDQMHIOXLGD=DGDQRMH+ FP' FPK FP J  K J / SD  K SD K  F SRQWRQ  K

 U

 





U

' 



G









 

J =DGDWDN



 QDVHOMH





=DGDWDN

4

J

$ 



S0%

'

 

+

'



+

%

/8.

    MH]HUR SXPSD SD =DGDWDN SD J   





=DGDWDN



  











+





&G

K

$ $ &G  =DGDWDN '

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWHYLVLQHK K LK XQXWDUVSUHPQLNDSUHPDVOLFLNRMHVHXVSRVWDYHSULVWDFLRQDUQRPVWUXMDQMXSURWRNRP 4 OV3UHWSRVWDYLWHL]RWHUPQXNRPSUHVLMX]UDNDXVUHGQMHPVSUHPQLNX=DGDQRMHS  EDU+  PU NJP K  PK  PG  PG  PPG  PPG  PP  2GUHGLWH PDVX YDOMND MHGLQLþQH ãLULQH SUHPD VOLFL ]JOREQR YH]DQRJ X WRþFL $ GD EL YDOMDN ELR X UDYQRWHåL =DGDQRMHU NJP 5 P  ,]PMHUHQMHSURWRNNUR]FMHYRYRGQLVLVWHPSUHPDVOLFLRG4 P V2GUHGLWHYLVLQXSMHãþDQHKUDSDYRVWL =DGDQRMH+ P/ P' PU NJP .  .  Q  P V  'YDPOD]DYRGHGUåHXUDYQRWHåLNRFNXPDVHP]JOREQRYH]DQDXWRþFL22GUHGLWHPDVXNRFNHDNRMHNRFND QDJQXWD]DD  3UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHDPDVHPOD]RYD]DQHPDULWH=DGDQRMHU NJP  Y PVG P  ,]UDþXQDM SURPMHU '  SUDYLOQR SURãLUHQH VDSQLFH WODN X POD]XMHGQDNMHWODNXRNROLQH NRMDRVLJXUDYDSRWLVQX VLOX SURWXJUDGQH UDNHWH RG )   1 DNR MH ]DGDQ WODN X NRPRUL L]JDUDQMD S    EDUD D WHPSHUDWXUD L]JDUDQMD7  .3OLQRYHL]JDUDQMDVPDWUDMWHVDYUãHQLPSOLQRPXL]HQWURSVNRPVWUXMDQMX 5 -NJ.    =DGDQRMHS  EDUD 

G



J

S

 

+

K

 

K U



G

5

G K

K

$ SD

U

K G

 

J

S0



=DGDWDN









=DGDWDN

 

D

D

  SD

J

   

.



D

+

/ UQ

2 .

Y

'

 



=DGDWDN



J













=DGDWDN

D G =DGDWDN

Y

D G

 SD

  

G S7

G 









=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHVPMHUVWUXMDQMDLSURWRNNRMLüHVHXVSRVWDYLWLL]PH XWULUH]HUYRDUD MHGLQLþQHãLULQH ]DVLWXDFLMHSUHPD VOLFL D L E 3UHWSRVWDYLWH GD VH YLVLQH QLYRD X UH]HUYRDULPD QH PLMHQMD NDGD VH XVSRVWDYL VWDFLRQDUQR VWUXMDQMH =DGDQRMHK  PK  PK  PG PPS  EDUDP NJD PU NJP   2GUHGLWHPDVXYDOMNDP MHGLQLþQHãLULQH DNRMHYLVLQDKYDOMNDNRMDVHQDOD]LL]QDGSRYUãLQHYRGHK P 9DOMDNSURPMHUDG FPLVSXQMHQMHGRMHGQHWUHüLQHYROXPHQDYRGRPJXVWRüHU NJP   2GUHGLWH YLVLQX K  YRGH X VSUHPQLNX DNR X VSUHPQLN XWMHþH  XNXSQRJ SURWRND NUR] VLVWHP  .RHILFLMHQW ORNDOQRJJXELWNDVYLKYHQWLODQDVOLFL.  VYHOLQLMVNHJXELWNH]DQHPDULWHNDRLJXELWNHXUDþYL3URPMHUVYLK FMHYRYRGDL]QRVL' P=DGDQRMHK  PK  PU NJP   2GUHGLWH VLOX QD MHGQX ORSDWLFX X UHãHWFL MHGLQLþQH ãLULQH  NRMD VNUHüH VWUXMDQMH ]UDND ]D NXW D    3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMHY  PVS  EDUDU NJP W PP  6LODRWSRUD5JLEDQMDWLMHODXYLVNR]QRPVWODþLYRPIOXLGX]DYLVLRRGGXOMLQHWLMHOD/JXVWRüHIOXLGDUGLQDPLþNR NRHILFLMHQWDYLVNR]QRVWLPYROXPHQVNRJPRGXODHODVWLþQRVWL.LEU]LQHJLEDQMDWLMHOD83ULPMHQRP3LWHRUHPD RGUHGLWHRSüLREOLN]DYLVQRVWLVLOHRWSRUD5RGSUHRVWDOLKYHOLþLQD=DGLPHQ]LRQDOQRQH]DYLVDQVNXSX]PLWHU8 L/ 

D



D

D

D

SD

G

G K

U

K

J

S0

P

K

U



J

S0

P

K



D

SD

 

D

K

G

G K

 



=DGDWDND

G







 SD

 SD



K



.9

 

.9 





 W

  

.9

=DGDWDN

 

U

'

 

SD

J

J

'

U



G =DGDWDNE





















=DGDWDN

Y

S



D

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

=DGDWDN

K K

SD K

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 8SROXNXJODVWRMSRVXGLLVSXQMHQRMYRGRPJXVWRüHU NJP SOLYDYDOMDNPDVHP NJ.ROLNRL]QRVL XGDOMHQRVW D L]PH X GQD SRVXGH L YDOMND NDGD VH SRVXGD ]DURWLUD NRQVWDQWQRP NXWQRP EU]LQRP Z   V  =DGDQRMH5 PU PK P  .XJODSURPMHUD5 PLPDVHP NJ]DWYDUDSUROD]L]PH XGYDUH]HUYRDUDSUHPDVOLFL.ROLNLPRUDELWL SURPMHUGRWYRUDGDELNXJOLFD]DSOLYDODNDGDXGUXJRPUH]HUYRDUXYLVLQDKGRVHJQHUD]LQXK P=DGDQRMH + PU NJP   2GUHGLWHRGQRVSURPMHUD'GGDELORNDOQLJXELFL]DRWYRUL]PH XGYDVSUHPQLNDSUHPDVOLFLELOLPLQLPDOQL 6YHOLQLMVNHJXELWNH]DQHPDULWHDRGORNDOQLKJXELWDNDX]PLWHXUD]PDWUDQMHJXELWDNXODVNDXYHOLNLVSUHPQLNL JXELWDNQDJORJSURãLUHQMD  2GUHGLWH SUHWODN X VSUHPQLNX X NRML XWMHþH IOXLG SURWRNRP 4   P V GD EL VLOD QD QDJOR SURãLUHQMH ELOD MHGQDND QXOL 6YH OLQLMVNH JXELWNH ]DQHPDULWH D RG ORNDOQLK JXELWDND X]PLWH X UD]PDWUDQMH JXELWDN XODVND X YHOLNLVSUHPQLNLJXELWDNQDJORJSURãLUHQMD=DGDQRMHG P' PK PU NJP   2GUHGLWHSURPMHUEDORQD'PDVHP  NJLVSXQMHQRJWRSOLP]UDNRP 5 -NJ. WHPSHUDWXUHW  &GDELPRJDRQRVLWLWHUHWPDVHP NJ JXVWRüDWHUHWDU NJP  =DGDQRMHS  EDUDW   & J SD



SD

 

J +

U K

 

5



G

U

D



U

5

K

U

 

=DGDWDN  SD







J



=DGDWDN S0

K

J

 

K



'

G

G



'

4



U

 



=DGDWDN









 W

 







=DGDWDN WD

'

 



SD

=DGDWDN

SD

J

SODPHQLN

WHUHW

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWH UD]OLNX [ QLYRD YRGH JXVWRüH U   NJP  X UH]HUYRDULPD QDNRQ ãWR VH XVSRVWDYL VWDFLRQDUQR VWUXMDQMH 8 SRþHWQRP WUHQXWNX RED UH]HUYRDUD VX ELOD SUD]QD 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD WH L]RWHUPQXNRPSUHVLMX]UDNDXGHVQRPUH]HUYRDUX=DGDQRMH' FPG FP4 OV+ PK P S  EDUD  2GUHGLWHPDVXPSRNORSFDREOLNDSODãWDVWRãFDDNRUD]OLNDQLYRDYRGHJXVWRüHU NJP L]QRVL[  FP 3UHWSRVWDYLWH GD MH SRNORSDF X WUHQXWNX SRODJDQMD QD UD]LQX YRGH ELR SRWSXQR LVSXQMHQ ]UDNRP SUL DWPRVIHUVNRPWODNXS  EDUDWHGDMHQDNRQWRJD]UDNL]RWHUPQRVWODþHQ=DGDQRMH' P+ P  8QXWDU]DãWLWQHFLMHYLYDQMVNRJSURPMHUD' PSRWUHEQRMHSRVWDYLWLWULRGQRVQRþHWLULFLMHYLSUHPDVOLFL GLPHQ]LRQLUDQH WDNR GD VH GRWLþX 2GUHGLWH RGQRV SURWRND ]D LVWL SDG WODND SR MHGLQLFL GXOMLQH X RED VOXþDMD 3UHWSRVWDYLWHGDVXVYHVWMHQNHFLMHYLGHEOMLQHV FPWHSUHWSRVWDYLWHVWUXMDQMHXODPLQDUQRPUHåLPX  2GUHGLWHNXWJL]XYMHWDGDVLODIOXLGDJXVWRüHU NJP QDUDYQXSORþXEXGHPDNVLPDOQD3UHWSRVWDYLWH VWUXMDQMHLGHDOQRJIOXLGD=DQHPDULWHXWMHFDMVXGDUDPOD]DXVUHGLQLSORþH=DGDQRMHY  PVG  PY  PVG  PD  E    8VOLMHG URWDFLMH FLOLQGUD RNR YODVWLWH RVL NXWQRP EU]LQRP Z GROD]L GR SUHWYRUEH GLMHOD PHKDQLþNH HQHUJLMH X

]DYLVLRGYLVNR]QRVWLIOXLGD WRSOLQXNDRSRVOMHGLFDWUHQMD$NREU]LQDSUHWYRUEHPHKDQLþNHHQHUJLMHXWRSOLQX 4 P SURPMHUD FLOLQGUD ' GXOMLQH FLOLQGUD / LNXWQHEU]LQHURWDFLMH ZRGUHGLWHSULPMHQRPGLPHQ]LRQDOQHDQDOL]H NROLNR üH VH SXWD SRYHüDWL LOL VPDQMLWL  EU]LQD SUHWYRUEH PHKDQLþNH HQHUJLMH X WRSOLQX  DNR VH NXWQD EU]LQD URWDFLMHSRYHüDGYDSXWDX]RVWDOHQHSURPLMHQMHQHSDUDPHWUH

  

SD

J

4

SD

U







U

G

K

 

+ [





+

[



J

'

S0

' =DGDWDN

' 





=DGDWDN

 

\

 

V

 

'

 

=DGDWDN

G



V 

G

J



  

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

Y E

D

'

V

 

V

Y



=DGDWDN

[

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWHWODNXWRþFL$QDYDQMVNRPSODãWXFLOLQGULþQHSRVXGHSUHPDVOLFLNDGDVH]DURWLUDNRQVWDQWQRPNXWQRP EU]LQRPZ UDGV=DGDQRMH' FPG FP+ FPK FPU NJP   2GUHGLWHPDVXPLSRORåDMDWHUHWDDNRVHSRQWRQPDVHP  NJQDJQH]DNXWD  =DGDQRMH+  PK FP/ P% P ãLULQDSRQWRQDRNRPLWRQDVOLNX U NJP   2GUHGLWH SURPMHU '  FLMHYL L] XYMHWD GD VH UD]LQD +  YRGH U   NJP  Q    P V  XQXWDU VSUHPQLNDQDPLMHQMD=DGDQRMH+  P+  P+  P'  P'  PN PP KUDSDYRVWVYLKFLMHYL /  P/  P/  P  1D YHOLNL VSUHPQLN SUHPD VOLFL SULNOMXþHQR MH NROMHQR V POD]QLFRP 1HSRVUHGQR SULMH NROMHQD XJUD HQ MH PDQRPHWDUNRMLSUL]DWYRUHQRMPOD]QLFLSRND]XMHSUHWODNS  EDUDNDGDVHPOD]QLFDRWYRULSUHWODNSDGQH QD S    EDU 8] SUHWSRVWDYNX QHYLVNR]QRJ VWUXMDQMD RGUHGLWH NROLND MH WDGD VLOD QD NROMHQR L POD]QLFX =DGDQRMH' PPU NJP D  K P9ROXPHQYRGHXNROMHQXLPOD]QLFL9 GP   8]SUHWSRVWDYNXGDNRGPDOHEU]LQHYWRQMHQMDWLMHODXPLUXMXüHPIOXLGDWDEU]LQDQH]DYLVLRGJXVWRüHIOXLGD YHü]DYLVLRGWHåLQH*WLMHODQMHJRYHNDUDNWHULVWLþQHOLQHDUQHGLPHQ]LMH/WHNRHILFLMHQWDGLQDPLþNHYLVNR]QRVWL PIOXLGD$NRMHL]PMHUHQRGDNXJOLFDSURPMHUD' PPWRQHEU]LQRPY FPPLQXYRGLNRHILFLMHQWD GLQDPLþNH YLVNR]QRVWL P   3DV RGUHGLWH NRMRP EU]LQRP Y  üH WRQXWL NXJOLFD SURPMHUD '    PP QDþLQMHQDL]LVWRJPDWHULMDODNDRLNXJOLFDSURPMHUD' XXOMXNRHILFLMHQWDGLQDPLþNHYLVNR]QRVWLP 3DV 

SD

G



J

  



K SD

K

'



WHUHW

D

+





J

/

D

+





U

U

$

=DGDWDN

Z









=DGDWDN

SD

J





 

+



S0

  /N 

+

+

/N

'

S0 K

G

D

/N

 =DGDWDN

'

'

 

J

'









=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHVLOX)QDSUHJUDGXNROLFD $% MHGLQLþQHãLULQHNRMDVHXEU]DYDMXXGHVQRNRQVWDQWQRPDNFHOHUDFLMRPD PV=DGDQRMH+ PK P/ PU NJP   2GUHGLWH VLOX ) SRWUHEQX ]D RWYDUDQMH SRNORSFD SUHPD VOLFL ]JOREQR YH]DQRJ X $ 3RNORSDF MH REOLND MHGQDNRNUDþQRJWURNXWDYLVLQHK PLED]HD P=DGDQRMH+ PD  U NJP   8 QRUPDOQRP UHåLPX UDGD FMHYRYRGRP /  WUDQVSRUWLUD VH QDVHOMX SUHPD VOLFL 4   P V YRGH U    EDUD 3UHWSRVWDYLWH GD MH SRWURãQMD YRGH NJP  Q   P V SUL WRWDOQRP SUHWODNX X QDVHOMX S NRQVWDQWQD VYLK  VDWD L GD VH  VDWL ]D SRJRQ SXPSH NRULVWL HOHNWULþQD HQHUJLMD VWDQGDUGQH FLMHQH D  VDWL HOHNWULþQD HQHUJLMD NRMD MH  MHIWLQLMD 2GUHGLWH XãWHGX X   XNROLNR EL VH QDVHOMH  VDWL RSVNUEOMLYDOR FMHYRYRGRP /  L] DNXPXODFLMVNRJ UH]HUYRDUD LVNOMXþHQD SXPSD  D  VDWL MHIWLQLMD WDULID HO HQHUJLMH  SXPSD LVWRYUHPHQRFMHYRYRGRP/ RSVNUEOMXMHQDVHOMHLFMHYRYRGRP/ SXQLDNXPXODFLMX=DGDQRMH+ P/   NP/  NP/  NP' P SURPMHUVYLKFMHYRYRGD N PP KUDSDYRVWVYLKFLMHYL S EDUD WRWDOQLSUHWODNXQDVHOMX =DQHPDULWHVYHORNDOQHJXELWNHNDRLJXELWNHLVSUHGSXPSH.ROLNLüHELWL WRWDOQLSUHWODNXQDVHOMXNDGDVHQDVHOMHRSVNUEOMXMHVDPRL]DNXPXODFLMVNRJUH]HUYRDUD  2GUHGLWH KRUL]RQWDOQX VLOX QD EUDQX MHGLQLþQH ãLULQH SUHPD VOLFL 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD WH XQLIRUPQHSURILOHEU]LQDGRYROMQRGDOHNRRGEUDQHLQDSUHOMHYX=DGDQRMHK  PK  PK  P K  P/ PU NJP   2GUHGLWHGRPHW5POD]DSROMHYDþDWUDYHNRMLVHRNUHüHNXWQRPEU]LQRPZ UDGVEH]WUHQMDXOHåDMHYLPD =DGDQRMHU FPE  + P J D SD  J SD $  $ +  D U D  K + U  ) K 

%

/

=DGDWDN



/

 









=DGDWDN

J

+





/'N



/'N

SXPSD

 SD

QDVHOMH

/'N

 











U

=DGDWDN

EUDQD

SD



K

J

U



/



E G

Z E

K

 

K



K

5

 





=DGDWDN





=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,





=DGDWDN

+

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 7ULFMHYþLFHSURPMHUDG  PPG  PPLG  PPLVSXQMHQHVXWHNXüLQRPJXVWRüHU NJP GR YLVLQHK FP2GUHGLWHYLVLQHK K LK QDNRQãWRFMHYþLFH]DURWLUDPRNRQVWDQWQRPNXWQRPEU]LQRP Z  UDGV=DGDQRMH5  FP5  FP  8 KRUL]RQWDOQR SRVWDYOMHQRP NUXåQRP FLOLQGUX MHGLQLþQH ãLULQH LVSXQMHQRJ YRGRP U   NJP  SRVWDYOMHQD MH SUDYRNXWQD SORþD MHGLQLþQH ãLULQH 3UL NRMHP NXWX D VH KYDWLãWH KLGURVWDWVNH VLOH QD JRUQMX SRYUãLQX SORþH QDOD]L QD QDMYHüRM GXELQL L SUL NRMHP NXWX D  VLOD KLGURVWDWNRJ WODND QD JRUQMX SRYUãLQX SORþH SRSULPDPDNVLPDOQXYULMHGQRVW=DGDQRMH5 P  2GUHGLWH PDNVLPDOQL GRPHW /  POD]D YRGH U   NJP  Q     P V  .UDM FLMHYL SRVWDYOMHQ MH KRUL]RQWDOQRQDYLVLQL[6YHORNDOQHJXELWNH]DQHPDULWH5DGLMHGQRVWDYQLMHJSURUDþXQDSUHWSRVWDYLWHVWUXMDQMHX UHåLPXSRWSXQHWXUEXOHQFLMH=DGDQRMH' P/ PN PP YLVLQDKUDSDYRVWLFLMHYL K  P+ P  2GUHGLWHNRMRPVLORP)WUHEDRSWHUHWLWLNOLSSURPMHUDG FPGDELVHVSXãWDREU]LQRPY PVXFLOLQGUX SURPMHUD' FPLVSXQMHQRJYRGRPJXVWRüHU NJP 3UHWSRVWDYLWHVWUXMDQMHLGHDOQRJIOXLGD8SXWD NRRUGLQDWQLVXVWDYSRVWDYLWHUHODWLYQRXRGQRVXQDNOLS  .UR] NRQYHUJHQWQR ± GLYHUJHQWQX VDSQLFX ]UDN 5   -NJ.      L]HQWURSVNL LVWMHþH X DWPRVIHUX   NJP  $NR X VSUHPQLNX YODGD WODN S    EDUD RGUHGLWH SURPMHU '  L]OD]QRJ PDVHQLP SURWRNRP P SUHVMHNDSUDYLOQRSURãLUHQHVDSQLFH=DGDQRMHS  PEDU'  PP  

G

G



SD

5

  

SD J

5

U

J SORþD

D

5

K

K



G

K

K



Z 

=DGDWDN  SD 







 J

=DGDWDN

J



SD

G

+

 UQ

 

[ '



Y

)

/ N

U /

K

'

 









S

'

=DGDWDN



'



SD







=DGDWDN

 









=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHYULMHPHSRWUHEQRGDVHUD]LQDXREDNXJODVWDVSUHPQLNDL]MHGQDþL8SRþHWQRPWUHQXWNXOLMHYLVSUHPQLN MHELRSRWSXQRSXQDGHVQLSRWSXQRSUD]DQ3UHWSRVWDYLWHNYD]LVWDFLRQDUQRVWUXMDQMHLGHDOQRJIOXLGDWHSRWSXQR LVSXQMHQXSUHOMHYQXFLMHYXSRþHWQRPWUHQXWNX=DGDQRMH5 PG P  7URNXWDVWLSRNORSDF$2%XOHåLãWHQMHLRNUHWOMLYRNREULGD2%SUHPDVOLFL6LOD)GMHOXMHVKYDWLãWHPXWRþFL$X VPMHUXRNRPLWRPQDSRNORSDF.ROLNDMHYHOLþLQDVLOH)SRWUHEQD]DGUåDQMHSRNORSFDXUDYQRWHåQRPSRORåDMX =DGDQRMHU NJP + PD P/ P  .ROLND MH VLOD ) SRWUHEQD ]D SRWLVNLYDQMD VWDSD XQXWDU LQMHNFLMH EU]LQRP Y   PPV +LSRGHUPDOQDLJODLPD XQXWDUQML SURPMHU G   PP WH MH GXJD /   PP *XVWRüD MH IOXLGD XQXWDU LQMHNFLMH U   NJP  WH YLVNR]QRVWP  3DV3UHWSRVWDYLWHGDQHPDFXUHQMDIOXLGDL]PH XVWDSDLFLOLQGUDLQMHNFLMHWH]DQHPDULWH VYHORNDOQHJXELWNHSULVWUXMDQMXIOXLGDXQXWDULQMHNFLMH8UD]PDWUDQMHMHSRWUHEQRX]HWLOLQLMVNHJXELWNHXQXWDU FLOLQGUDLLJOH=DGDQRMHD PP' PP  ,]PH X GYD YHOLND DNXPXODFLMVND MH]HUD XJUD HQD MH EUDQD V WXUELQRP =ERJ SRYHüDQMD VWXSQMD GMHORYDQMD WXUELQH LVSRG QMH MH PRQWLUDQ GLIX]RU 2GUHGLWH VLOX QD GLIX]RU DNR MH L]PMHUHQ QHWR SDG WXUELQH K   P 3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGDLMHGQROLNHSURILOHEU]LQDSRVYLPSUHVMHFLPD=DGDQRMHK  P K  PK  PK  PK  PG  PG  PU NJP   .UR] NRQYHUJHQWQR GLYHUJHQWQX VDSQLFX ]UDN 5   -NJ.      LVWMHþH X DWPRVIHUX 2GUHGLWH PDVHQL SURWRNNUR]SUDYLOQRSURãLUHQXVDSQLFXSUHPDVOLFL=DGDQRMH'  PPS  EDUDS  EDUD7   . J J  SD SD  D SD 5 5 + 2 )  U $ /  %



G

  





=DGDWDN

 











SD

=DGDWDN

FLOLQGDU

LJOD

G



J Y

'

UP

)

K

G

 











K

D

/

GLIX]RU

=DGDWDN

U

  

 7 S

 ' 







'



SD







K

=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



=DGDWDN

G

K

K

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWH YLVLQX K QLYRD X VSUHPQLNX NRML üH VH XVSRVWDYLWL X VWDFLRQDUQRP UHåLPX VWUXMDQMD 3UHWSRVWDYLWH VWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH4 P V+ P' PG P  2GUHGLWHVLOX YHOLþLQXVPMHULKYDWLãWH QDSROXNXJODVWL]DWYDUDþSUHPDVOLFL=DGDQRMH5 P+ PU NJP D    2GUHGLWHUDGQXWRþNXSXPSH YLVLQXGREDYHLSURWRN GDELYLVLQDPOD]DYRGH U NJP P   3DV YRGRVNRNDELOD+ P=DGDQRMH.  .  .  ORNDOQLJXELWDNVDSQLFHL]UDåHQX]YHüX EU]LQX / P XNXSQDGXOMLQDVYLKFLMHYL ' P SURPMHUVYLKFLMHYL 3UHWSRVWDYLWHGDVXVYHFLMHYLL] WUJRYDþNRJþHOLND=DGDQRMHG P  2GUHGLWHYLVLQXRWYRUDKGDELVLODNRMDSULGUåDYDSUHJUDGQXVWMHQNX]JOREQRYH]DQXXWRþFL$ELODPDNVLPDOQD WHRGUHGLWHL]QRVVLOH3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH+ PG PU  NJP E P  'RPHW WRSRYVNRJ ]UQD V RYLVL R SRþHWQRM EU]LQL ]UQD Y  NXWX WRSRYVNH FLMHYL D YLVLQD EUGD K L JUDYLWDFLML J 3ULPMHQRP GLPHQ]LVNH DQDOL]H RGUHGLWH EH]GLPHQ]LVNH S SDUDPHWUH WH QD LWH ]DYLVQRVW WLK EH]GLPHQ]LVNH SDUDPHWDUD) S S « SRPRüXMHGQDGåEHNRVRJKLFD  

4

SD

SD

K



J

 











'



D

U

=DGDWDN

+

+

G

G





J

5

 

=DGDWDN











  

G

SD



J

+



+

G

K

'



E



..

 



.9

=DGDWDN

..

.9 



J



V

$





=DGDWDN



=DGDWDN

D

  

)

UP





J

U

K 



SD











K



 

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHPDNVLPDOQXGR]YROMHQXDNFHOHUDFLMXNRMRPNROLFDPRJXXEU]DYDWLDGDQHGR HGRSUHOLMHYDQMDSUHNR UXEDNROLFD  2GUHGLWH JXVWRüX PDWHULMDOD U  RG NRMHJD MH QDSUDYOMHQD SROXFLOLQGULþQD JUHGD MHGLQLþQH GXåLQH DNR MH JUHGD QDJQXWDXRGQRVXQDSRYUãLQXYRGHJXVWRüHU NJP ]DNXWD  WH]JOREQRYH]DQDXWRþFL$  2GUHGLWHUDGQXWRþNXSXPSH YLVLQXGREDYHLSURWRN GDELGRPHWSUHOMHYD VODSD POD]DYRGH U NJP  P  3DV ELRD PWHGDELGHEOMLQDKPOD]DMHGLQLþQHãLULQHELODK FP=DGDQRMH.  .  / P XNXSQDGXOMLQDVYLKFLMHYL ' P SURPMHUVYLKFLMHYL 3UHWSRVWDYLWHGDVXVYHFLMHYLL] WUJRYDþNRJþHOLND3UHWSRVWDYLWHXQLIRUPQLSURILOEU]LQHQDSUHOMHYX=DGDQRMH+ P  =D]DXVWDYOMDQMHNROLFDPDVHP NJNRMDVHXSRþHWQRPWUHQXWNXNUHüXEU]LQRPY NPKNRULVWLVH ORSDWLFDMHGLQLþQHãLULQH2GUHGLWHGXOMLQXSXWDSRWUHEQRJGDELNROLFDXVSRULODQDSRODSUYRELWQHEU]LQHDNRVH ORSDWLFD SUHPD VOLFL XURQL GR GXELQH D   FP 3UHWSRVWDYLWH NYD]LVWDFLRQDUQR VWUXMDQMH QHYLVNR]QRJ IOXLGD 8SXWD3UHWSRVWDYLWHGDVHNRRUGLQDWQLVXVWDYJLED]DMHGQRVNROLFLPD=DGDQRMHD  U NJP   =UDN 5  -NJ.      L]HQWURSVNL VWUXML L] YHOLNRJ VSUHPQLND X NRMHP YODGD WODN S    EDU NUR] NRQYHUJHQWQRGLYHUJHQWQXVDSQLFXSURPMHUD'  PPX]UDþQLWXQHOSURPMHUD'  PP2GUHGLWHWODNS  L0DFKRYEURMNDGDIOXLGX]UDþQRPWXQHOXVWUXMLSRG]YXþQR.ROLNLWODNS PRUDPRSRVWLüLYDNXPSXPSRPGD ELX]UDþQRPWXQHOXVWUXMDQMHSUHãORXQDG]YXþQRLNROLNLMH0DFKRYEURM=DGDQRMHS  EDU'  PP 

F



F

F

J J



SD D

 F



5

U

F



$

U



D

  

=DGDWDN

 D













=DGDWDN

K

 



J

+

J

SD

D

Y

 UP



K 

 '

 











D .. .9 =DGDWDN

 

YDNXP SXPSD

'

S



 

..

.9 

 S

 '

=DGDWDN SD '









'

=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 3RNORSDFQDFLOLQGULþQRMSRVXGLXPLURYDQMXSUHPDVOLFLSULGUåDYDVHSRGWODNRPS  EDUXSRVXGL3UL NRMRM NXWQRM EU]LQL URWDFLMH Z üH VH  SRNORSDF RWYRULWL =DGDQR MH +   P +  P5 PU  NJP   'YDFLOLQGULþQDVSUHPQLNDSUHPDVOLFLSRYH]DQDVXFMHYRYRGRPVXJUD HQLPYHQWLORP8VLWXDFLMLSUHPDVOLFL YHQWLOMH]DWYRUHQDGHVQLMHVSUHPQLNSRWSXQRLVSXQMHQ]UDNRPSRGDSVROXWQLPWODNRPS  EDU2GUHGLWH YLVLQXK GRNRMHüHVHGHVQLVSUHPQLNLVSXQLWLYRGRPDNRVHYHQWLORWYRUL3UHWSRVWDYLWHL]RWHUPQRVWODþLYDQMH ]UDNDXGHVQRPVSUHPQLNX=DGDQRMHS  PEDU'  P'  P+  P+  PU  NJP   2GUHGLWHSURWRN4NUR]VLVWHPSUHPDVOLFLDNRMHSDGWODNDNUR]WXUELQLS EDU=DGDQRMH+  P+  PU NJP Q  P V' PPN PP/  P/  P  2GUHGLWH VLOX IOXLGD QD UDYQX SORþX MHGLQLþQH ãLULQH SUHPD VOLFL DNR þDPDF YXþH SORþX EU]LQRP Y   PV .ROLNDMHSRWUHEQDVQDJD"3UHWSRVWDYLWHVWUXMDQMHLGHDOQRJIOXLGDWH]DQHPDULWHXWMHFDMJUDYLWDFLMH=DGDQRMHU  NJP K PPD    2GUHGLWHNRQVWDQWQXNXWQXEU]LQLYUWQMHZURWLUDMXüHFLMHYLSUHPDVOLFLQDNRMXGMHOXMHYDQMVNLPRPHQW0  1PDNRMHSURWRNNUR]FLMHY4 OPLQ2GUHGLWHNXWQXEU]LQXYUWQMHFLMHYLDNRVHFLMHYVORERGQRRNUHüHX] LVWHRVWDOHXYMHWH=DGDQRMH5 P' PPU NJP E   

SD

 

S0

J

5

'



+

+



+ K

U

U



J

+

'

  





 

SD

Z =DGDWDN







J

QU



=DGDWDN

'/N



+ SD

 +

  







 þDPDF  





WXUELQ 



=DGDWDN

E

SD D

Y

Z

U

  

5

'

K

 

 '/N 

0  







=DGDWDN





=DGDWDN



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHYULMHPHSRWUHEQR]DSUDåQMHQMHOLMHYND WUDNWXUD SUHPDVOLFL3UHWSRVWDYLWHNYD]LVWDFLRQDUQRVWUXMDQMH QHYLVNR]QRJIOXLGD=DQHPDULWHYULMHPHSRWUHEQRGDVHLVSUD]QLFMHYþLFDSURPMHUDG=DGDQRMH' FPG  FP+ FPK FP  .RFND VWUDQLFH D   P L JXVWRüH U    NJP   GMHORPLþQR MH XURQMHQD X YRGX JXVWRüH U   NJP SUHPDVOLFL2GUHGLWHUHDNFLMXXWRþFL$ VLOXLPRPHQW =DGDQRMHD  K FP  3XPSDYLVLQHGREDYHK  PRVWYDUXMHSURWRNRG4 OVNUR]VLVWHPSUHPDVOLFL2GUHGLWH]DNROLNRüHVH SRYHüDWLSURWRNNUR]VLVWHPDNRXJUDGLPRSXPSXYLVLQHGREDYHK  PX]QHSURPLMHQMHQHRVWDOHYHOLþLQH =DGDQRMH' P SURPMHUFMHYRYRGD N PP YLVLQDKUDSDYRVWLFMHYRYRGD / P+ P U NJP P  3DV  2GUHGLWH VLOX QD VSRMQLFX UDþYX  NRMD VSDMD VYD WUL UH]HUYRDUD 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJ IOXLGD WH ]DQHPDULWH WHåLQX YRGH X VSRMQLFL 3UHWSRVWDYLWH GD VH YLVLQH QLYRD X UH]HUYRDULPD MHGLQLþQH ãLULQH QH PLMHQMD NDGDVHXVSRVWDYLVWDFLRQDUQRVWUXMDQMH=DGDQRMHK  PK  PK  PG PPS  EDUD P NJD PU NJP   2GUHGLWHNXWQXEU]LQXURWDFLMHZVORERGQRURWLUDMXüHFLMHYLSUHPDVOLFL=DGDQRMH+ P' PG  P5 PS  EDUU NJP  J '  $  

J



K

+



U

 =DGDWDN

G





K







=DGDWDN



D



J



+

/

 UQ



.

=DGDWDN 



'



    



K







302

P

U

.





D

D

SD

SD





D

G K 







G =DGDWDN

U + G

=DGDWDN        G    5

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

G

K #

J

'

J

S0

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWHVLOXQDVWUDåQMXVWUDQX$%NROLFDREOLNDMHGQDNRVWUDQLþQHSUL]PHVWUDQLFHE PSUHPDVOLFLDNR NROLFD MHGLQLþQH ãLULQH XEU]DYDMX X] NRVLQX NRQVWDQWQRP DNFHOHUDFLMRP D   PV   =DGDQR MH K   P YLVLQDIOXLGDXNROLFLPDXVWDQMXPLURYDQMDQDUDYQRMSRGOR]L D  U NJP   2GUHGLWHYLVLQX+NRGNRMHüHVHRWYRULWLNXJODVWL]DWYDUDþ]JOREQRXþYUãüHQXWRþFL$=DQHPDULWHPDVHSROXJD =DGDQRMH5 PG FPD PE PF PP NJU NJP  ,]PH X GYD YHOLND DNXPXODFLMVND MH]HUD XJUD HQD MH EUDQD V WXUELQRP =ERJ SRYHüDQMD VWXSQMD GMHORYDQMD WXUELQHLVSRGQMHMHPRQWLUDQGLIX]RU2GUHGLWHSRYHüDQMHVWXSQMDGMHORYDQMDDNRMHQHWRSDGWXUELQHK P 3UHWSRVWDYLWHMHGQROLNHSURILOHEU]LQDSRVYLPSUHVMHFLPDWHGDMHORNDOQLJXELWDNXGLIX]RUXMHGQDNJXELWND QDJORJSURãLUHQMD=DGDQRMHK  PK  PK  PK  PK  PG  PG  PU  NJP Q  P V  2GUHGLWH KRUL]RQWDOQX VLOX QD FMHYRYRG SUHPD VOLFL .UDM FLMHYL SRVWDYOMHQ KRUL]RQWDOQR QD YLVLQL [ RGUHGLWH L] XYMHWD GD MH GRPHW /  POD]D YRGH U   NJP PDNVLPDODQ 3UHWSRVWDYLWH VWUXMDQMH QHYLVNR]QRJ IOXLGD =DGDQRMH' P/ PK P+ P  9RGHQLVDW NOHSVLGUD SUHPDVOLFLVOXåL]DPMHUHQMHYUHPHQD2GUHGLWHSURPMHUGJUODNOHSVLGUHGDELVHJRUQMD SRYUãLQDNDSOMHYLQHVSXãWDODNRQVWDQWQRPEU]LQRPY PPV3UHWSRVWDYLWHVWUXMDQMHLGHDOQRJIOXLGDWHGDMH JRUQMLVSUHPQLNQDSRþHWNXLVWMHFDQMDELRLVSXQMHQGRYLVLQH+=DGDQRMH' FP+ FP    

J

$

SD

SD

=DGDWDN



F U

K



D

+



U J K

K

G

=DGDWDN



K

 

PJ

=DGDWDN

SD

 

5

G

D





D

%



E

$

J

GLIX]RU

K

G

'

K

U J

SD

J

+ UQ

=DGDWDN

N

#

/ '

+ G

[ K

/

=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 7ODNS QDNUDMXKRUL]RQWDOQHFLMHYLNUR]NRMXIOXLGVWUXMLXODPLQDUQRPUHåLPXVWUXMDQMDRYLVLRWODNXQDSRþHWNX FLMHYL S   WDQJHQFLMDOQRP QDSUH]DQMX QD VWMHQFL FLMHYL W  SURPMHUX FLMHYL ' WH GXOMLQL FLMHYL / 3ULPMHQRP GLPHQ]LRQHDQDOL]HRGUHGLWH]DYLVQRVWWODNDS RGSUHRVWDOLKYHOLþLQD  2GUHGLWHPDVXP SROXNXJODVWHSRVXGHNRMDMHXURQMHQDGRGXELQHK P8QXWDUSROXNXJODVWHSRVXGHSOLYD NXJODSURPMHUDU PSUHPDVOLFL=DQHPDULWHGHEOMLQXVWMHQNHSROXNXJODVWHSRVXGH=DGDQRMH5 FP U NJP   2GUHGLWHYLVLQXK YRGHXVSUHPQLNXDNRXVSUHPQLNQHXWMHþHQLWLLVWMHþHYRGDU NJP Q   P V .RHILFLMHQW ORNDOQRJ JXELWND VYLK YHQWLOD QD VOLFL .    =DQHPDULWH JXELWNH X UDþYL 3URPMHU VYLK FMHYRYRGDL]QRVL' P=DGDQRMHK  PK  P/  P/  P/  PN PP YLVLQDKUDSDYRVWLVYLKFMHYRYRGD   0OD]YRGHJXVWRüHU NJP VWUXMXNUR]FMHYþLFX$SURPMHUDG PPLXGDUDXJXPLFX]DWYDUDþDYRGHX YRGRNRWOLüX 3RGL]DQMHP UD]LQH YRGH X YRGRNRWOLüX SRGLåH VH L SORYDN NRML SUHNR SROXåMD ]DQHPDULYH WHåLQH VDYODGDYD VLOX POD]D YRGH ) L SULEOLåDYD JXPLFX RWYRUX FMHYþLFH 3UHWSRVWDYLWH VWDFLRQDUQR VWUXMDQMH LGHDOQRJ IOXLGDWHMHGQROLNHSURILOHEU]LQD2GUHGLWHNROLNRSXWDMHVLODSRWUHEQD]D]DWYDUDQMHRWYRUHFMHYþLFHYHüDRGVLOH SRWUHEQH]DGUåDQMHJXPLFHX]DWYRUHQRPVWDQMXDNRMHWRWDOQLSUHWODNYRGRYRGDS  EDUD=DGDQRMHK  FP/ FP5 FP  2GUHGLWH SURWRN 4 NUR] SROMHYDþ WUDYH SUHPD VOLFL DNR VH ]D SRJRQ SROMHYDþD NRULVWL XWHJ PDVH P    NJ ]DQHPDULWHWUHQMHXODåDMHYLPD 2GUHGLWHWRWDOQLSUHWODNXFMHYRYRGQRMPUHåLQDNRMXMHSROMHYDþSULNOMXþHQDNR MH NXWQD EU]LQD YUWQMH SROMHYDþD NRQVWDQWQD L L]QRVL Z   UDGV 3UHWSRVWDYLWH VWUXMDQMH LGHDOQRJ IOXLGD =DGDQRMHG PP+a5  FP5  FPU NJP D   

J



SD

SD



UQ

5

 

K

U

U

.9



=DGDWDN

=DGDWDN

   

SD



J



5 SD



SD K

/ D

G K

S0WRW

SD

+

PX

2

SORYDN

/

=DGDWDN

 

K

.9

$

JXPLFD

K .9

/





/

'





SD

J

G =DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

5 5

J

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWH SURPMHU G FMHYRYRGD SUHPD VOLFL GD EL QLYR X VSUHPQLNX  RVWDR QD LVWRM YLVLQL 3UHWSRVWDYLWH QHYLVNR]QRVWUXMDQMHIOXLGD3UHWSRVWDYLWHNRQVWDQWQXYLVLQXXVSUHPQLNX=DGDQRMH+  P+  P +  P'  PP'  PP  2GUHGLWH VLOX ) SRWUHEQX GD EL VH NYDGUDWQD JUHGD MHGLQLþQH GXOMLQH ]JOREQR XþYUãüHQD X WRþNL 2 GUåDOD X UDYQRWHåL=DGDQRMHD PU NJP   'YDVSUHPQLNDSUHPDVOLFLVSRMHQDVXFMHYRYRGRPNYDGUDWQRJSRSUHþQRJSUHVMHND D FP XNXSQHGXOMLQH /   P &LMHY NYDGUDWQRJ SRSUHþQRJ SUHVMHND SRWUHEQR MH ]DPLMHQLWL RNUXJORP FLMHYL SURPMHUD G NRMD RVWYDUXMH LVWH UDGQH XYMHWH LVWL SURWRNX 4 L LVWX UD]OLNX YLVLQD +  3UHWSRVWDYLWH VWUXMDQMH X SRGUXþMX SRWSXQH WXUEXOHQFLMHWHYLVLQXKUDSDYRVWLN PP  8KRUL]RQWDOQRMUDYQLQLQDOD]LVHGYRNUDNDUDþYDSUHPDVOLFL2GUHGLWHVLOXIOXLGDQDUDþYXDNRMHVLODPOD]DQD UDYQXSORþX) 13UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMH' PPU NJP D   E  J    2GUHGLWH YULMHPH PMHUHQR RG RWYDUDQMD YHQWLOD SRWUHEQR GD VH QDSXQL SRVXGD SUHPD VOLFL 3UHWSRVWDYLWH NYD]LVWDFLRQDUQRVWUXMDQMHQHYLVNR]QRJIOXLGD8SURUDþXQXMHSRWUHEQRX]HWLXRE]LUGHEOMLQXFLMHYLG=DGDQR MHK  P FRQVWG PPK  FPK  FP' FP 

SD

    +  



6SUHPQLN

D

SD

)

6SUHPQLN

 

2

SD

 

J

G

+

+

S0

J

U

D

'

'

=DGDWDN

SD

=DGDWDN

J +

/

=DGDWDN

UQ E

D SD

'

SD

)

' J

K

J

E

G

SRVXGD

SD K

YHQWLO

SD '

K

D =DGDWDN

' =DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHDNFHOHUDFLMXD SRVPMHUXLYHOLþLQL NRFNDVWRJVSUHPQLNDSUHPDVOLFLLVSXQMHQRJIOXLGRPJXVWRüHU  NJP DNRVX]DGDQHUD]OLNHWODNRYDQDSURVWRUQLPGLMDJRQDODPD=DGDQRMH'S  EDU'S  EDU'S EDUE P  2GUHGLWH YLVLQX + VWXSFD YRGH NRG NRMHJ üH GRüLGRRWYDUDQMDSROXNXJODVWRJSRNORSFDSROXPMHUD5 FP 3UHWSRVWDYLWHGDVXVYHSROXJH]DQHPDULYHWHåLQHDGDMHXWHJSURPMHUDG FPL]UD HQRGPDWHULMDODJXVWRüH U   NJP =DGDQRMHU NJP D PE PF PH P  2GUHGLWHNROLNRSXWDVHVPDQMLSURWRNNUR]FLMHYRNUXJORJSUHVMHNDX]LVWLSDGWODNDSRMHGLQLþQRMGXOMLQLFLMHYL DNR VH FLMHY SUHJUDGL YHUWLNDOQRP VWMHQNRP 3UHWSRVWDYLWH ODPLQDUQR VWUXMDQMH WH EHVNRQDþQR WDQNX SUHJUDGX 6WUXMDQMHVHRGYLMDXREDSUHJUD HQDGLMHODFLMHYL  2GUHGLWH IXQNFLRQDOQX ]DYLVQRVW VLOH )POD]DYRGHQDSORþXRGNXWDDQDJLEDSORþH3UHWSRVWDYLWHQHYLVNR]QR VWUXMDQMHIOXLGDWHVWUXMDQMHXKRUL]RQWDOQRMUDYQLQL=DGDQRMHG  PPG  PPY  PVY   PVU NJP  JXVWRüDIOXLGD   2GUHGLWHL]OD]QLSURPMHU'SUDYLOQRSURãLUHQHNRQYHUJHQWQR±GLYHUJHQWQHVDSQLFHNUR]NRMXL]HQWURSVNLVWUXML ]UDN 5 -NJ.   =DGDQRMHS  EDUS  EDU7  .G PP F E +  *  $ H G )  ( D SD J J ]  

\

[



'



&

E



5

 $

%

U

V|

=DGDWDN



+

 

=DGDWDN



'



G

 V|

=DGDWDN

Y \

G

[

' G

S7

Y

=DGDWDN SD =DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

D

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWH SRORåDM YHUWLNDOQH RVL X RGQRVX QD LVKRGLãWH $ RNR NRMH NRFNDVWL VSUHPQLN SUHPD VOLFL URWLUD NRQVWDQWQRPNXWQRPEU]LQRPZ UDGV6SUHPQLNMHLVSXQMHQIOXLGRPJXVWRüHU NJP =DGDQRMH 'S  3D'S 3DE P  2GUHGLWHXGDOMHQRVWFXWHJDSURPMHUDG FPL]UD HQRJRGPDWHULMDODJXVWRüHU   NJP RG]JORED $ NRG NRMHJ üH GRüLGRRWYDUDQMDSROXNXJODVWRJSRNORSFDSROXPMHUD5 FPSUHPDVOLFL3UHWSRVWDYLWHGD YLVLQD+VWXSFDYRGH+ FPWHGDVXVYHSROXJH]DQHPDULYHWHåLQH=DGDQRMHU NJPD P E PF PH P  =DSRWUHEHRSVNUEHYRGRPQDVHOMDL]JUD HQMHFMHYRYRGSURPMHUD' PPRGYXþHQLKFLMHYLXNXSQHGXOMLQH /  NP3XPSDGREDYOMDOVYRGH JXVWRüHU NJP NLQHPDWLþNRJNRHILFLMHQWDYLVNR]QRVWLQ   P V QDVHOMXNRMHVHQDOD]LQDYLVLQL+ PL]QDGUD]LQHMH]HUDWHRVWYDUXMHWRWDOQLSUHWODNYRGHX QDVHOMX S   EDUD 1DNRQ GYDGHVHWRJRGLãQMH HNVSORDWDFLMH SRWUHEH ]D YRGRP VX VH SRYHüDOH SD MH SRWUHEQR GREDYLWLYLãHYRGHX]LVWLWRWDOQLSUHWODN2GUHGLWHSURPMHUGQRYRJFMHYRYRGDNRMLüHVHSRVWDYLWLXPMHVWR SRVWRMHüHJ D ]DGRYROMDYD SRYHüDQH SRWUHEH ]D YRGRPVSRVWRMHüRPSXPSRP3ULSURUDþXQXORNDOQHJXELWNH ]DQHPDULWHWHSUHWSRVWDYLWHGDMHYLVLQDKUDSDYRVWLNQRYRJFMHYRYRGDN PP  2GUHGLWH VLOX QD MHGQX ORSDWLFX X UHãHWFL MHGLQLþQH ãLULQH  NRMD VNUHüH VWUXMDQMH ]UDND ]D NXW D    3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMHY  PVS  EDUDU NJP W PP  %ULQNPDQRY EURM 1 þHVWR NRULãWHQ SUL DQDOL]L VWUXMDQMD RUJDQVNLK IOXLGD MH RGQRV GLVLSDFLMH L WRSOLQVNH SURYRGOMLYRVWL X IOXLGX %URM MH EH]GLPHQ]LVNL SDUDPHWDU QDVWDR NRPELQDFLMRP GLQDPLþNRJ NRHILFLMHQWD YLVNR]QRVWL P EU]LQH Y WRSOLQVNH YRGOMLYRVWL O L WHPSHUDWXUH IOXLGD 7 2GUHGLWH %ULQNPDQRY EURM SRG SUHWSRVWDYNRPGDMHXWMHFDMYLVNR]QRVWLOLQHDUDQ + F E  * Z  $ H S ) G D  ( D J J     ]

' [

\

 [



=DGDWDN

%

V|

QDVHOMH

J



U

\

 $ 

+

5

&

=DGDWDN

 + MH]HUR SD

'

/8. W

Y

SXPSD S =DGDWDN

D =DGDWDN =ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWH NROLþLQX IOXLGD X VSUHPQLFLPD   L QDNRQSUDåQMHQMDNRFNDVWRJVSUHPQLNDVWUDQLFHD PNUR] RWYRU SURPMHUD G   FP QD GQX VSUHPQLND SUHPD VOLFL 3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD WH GD MH VSUHPQLNQDSRþHWNXELRSRWSXQRLVSXQMHQIOXLGRP=DGDQRMHE PF P  2GUHGLWHVLOX)SRWUHEQX]DSULGUåDYDQMHSRNORSFDMHGLQLþQHãLULQHSUHPDVOLFL]JOREQRXþYUãüHQLPXWRþFL$ =DGDQRMHD PE P5 PU NJP D  K P  =DSRWUHEHQDYRGQMDYDQMDSRWUHEQRMHGREDYOMDWL4 PVRWYRUHQLPNDQDORPXREOLNXWUDSH]DSUHPDVOLFL 2GUHGLWH QDJLE NDQDOD D DNR MH YLVLQD YRGH X NDQDOX K  P 3UHWSRVWDYLWH VWUXMDQMH X UHåLPX SRWSXQH WXUEXOHQFLMHWHGDMHNDQDOL]JUD HQRGEHWRQDYLVLQHKUDSDYRVWLN PP=DGDQRMHM  D P  2GUHGLWHNRMRPVLORP)WUHEDRSWHUHWLWLNOLSSURPMHUDG FPGDELVHVSXãWDREU]LQRPY PVXFLOLQGUX SURPMHUD' FPLVSXQMHQRJYRGRPJXVWRüHU NJP 3UHWSRVWDYLWHVWUXMDQMHLGHDOQRJIOXLGD8SXWD NRRUGLQDWQLVXVWDYSRVWDYLWHUHODWLYQRXRGQRVXQDNOLS  2GUHGLWH VLOX ) QD SUHJUDGX NROLFD $%  NRMD VH XEU]DYDMX XGHVQR NRQVWDQWQRP DNFHOHUDFLMRP D   PV =DGDQRMH+ PK P/ PU NJP % P ãLULQDNROLFD  

SD

 

E

D







F

=DGDWDN



SD

G

 

)

J

SD   F F

E

5

D

U

M



D =DGDWDN

D

M

J

SD G

 

SD 4

K

J

 

3RSUHþQLSUHVMHNNDQDOD

D =DGDWDN /

/

U

U

' =DGDWDN

% +

Y

)

 

K

$





J

K =DGDWDN

$ D

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWHYULMHPHSRWUHEQRGDVHSRWSXQRLVSUD]QLFLOLQGULþQDSRVXGDSURPMHUD' FPXNRMRMSOLYDYDOMDN SURPMHUDG FPSUHPDVOLFL3UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMHG  PP+ PK  FP  2GUHGLWHJXVWRüXU NRFNDVWRJXWHJDGDELSRNORSDFMHGLQLþQHãLULQHSUHPDVOLFL]JOREQRXþYUãüHQXWRþFL$ELR XUDYQRWHåL=DGDQRMHU NJP D FPE FPF FP+ FPK FPD    2GUHGLWHPLQLPDOQLSRWUHEQLSUHWODNS XNRPSHQ]DFLRQRMSRVXGLNRMLRVLJXUDYDGDNOLSVDYODGDYDVLOX) 1 SULEU]LQLJLEDQMDNOLSDY PPPLQ6YHORNDOQHJXELWNH]DQHPDULWH=DGDRMH' PPG PP/  PU NJP P 3DV XOMH   2GUHGLWHVLOX)IOXLGDQDNROMHQRXKRUL]RQWDOQRMUDYQLQLSUHPDVOLFL3ULL]UDGL]DGDWNDSRWUHEQRMH]DQHPDULWL VYHJXELWNHWUHQMDDX]HWLXRE]LUNRHILFLMHQWHLVSUDYNDNROLþLQHJLEDQMDLNLQHWLþNHHQHUJLMH3URILOEU]LQHXFLMHYL ]DGDQMHQDVOLFL=DGDQRMHS EDU4 OV' FPG FPU NJP P 3DV  3ULPMHQRP GLPHQ]LMVNH DQDOL]H RGUHGLWH IXQNFLRQDOQX ]DYLVQRVW YHOLþLQH NDSOMLFH G QD L]OD]X L] VSUHM VDSQLFH DNRMHSR]QDWRGDYHOLþLQDNDSOMLFHRYLVLRSURPMHUXVDSQLFH'EU]LQLYXVDSQLFLWHVYRMVWYLPDIOXLGDJXVWRüLU YLVNR]QRVWLPLNRHILFLMHQWXSRYUãLQVNHQDSHWRVWLV   

G

J

J

 

D

K

 

+

SUHJUDGD $

G

=DGDWDN

E

   Y

VWDS

.RPSHQ]DFLRQD SRVXGD

J

 SD '



+ U

=DGDWDN G

S0

Ka

G

Y YPD[

 

K D

F

'

 

SD

U

SD

/

Y

=DGDWDN

YPD[

§U · ¸ ©5¹

 ¨



§ U · ¸ © 5¹

 ¨



=DGDWDN

 

4

'

      

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHYULMHPHWSUDåQMHQMDFLOLQGULþQRJVSUHPQLNDSURPMHUD' FPDNRMHRþLWDQMHQDPDQRPHWUXL]QRVL K  ] ] MH YLVLQD YRGH X VSUHPQLNX  L QD PLMHQMD VH WLMHNRP SUDåQMHQMD VSUHPQLND 3UHWSRVWDYLWH NYD]LVWDFLRQDUQRVWUXMDQMHIOXLGD=DGDQRMH+ PG PPU NJPU NJP/|FF   NRHILFLMHQWNRQWUDNFLMHPOD]D   2GUHGLWHPDVXYDOMNDMHGLQLþQHGXOMLQHGDELRWYRUVSUHPQLNDSUHPDVOLFLRVWDR]DWYRUHQ=DGDQRMH' P + PK PD U NJP  2GUHGLWHUD]OLNXQLYRD+IOXLGDXDNXPXODFLMVNRPMH]HUXLNRPSHQ]DFLRQRMNRPRULDNRMHQHWRSDGXWXUELQLKW  P=DQHPDULWHORNDOQHJXELWNH=DGDQRMH' P' PU NJPQ PV/  P/ PN N PPK P  2GUHGLWHKRUL]RQWDOQXVLOX)QDEUDQXSUHPDVOLFLâLULQDEUDQHRNRPLWRQDUDYQLQXVOLNH/ P3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD WH XQLIRUPQH SURILOH EU]LQH GRYROMQR GDOHNR LVSUHG L L]D EUDQH =DGDQR MH U   NJP+ PK PK FPG P' P

 2GUHGLWHNXWQXEU]LQXYUWQMHZVORERGQRURWLUDMXüHFLMHYLSUHPDVOLFL3UHWSRVWDYLWHVWUXMDQMHQHYLVNR]QRJIOXLGD =DGDQRMH+ PU NJP' PP5 PD E J  

SD

SD

 

'

 U



+

 /



G

K =DGDWDN

SD



K

U

  

D

=DGDWDN





SD QU

'

SD

+

J

U

J

G

+

' K

  

'

+

U

J

J

K

' /



SD

=DGDWDN

 /

 

=DGDWDN

J U

+

 J

 =DGDWDN '

5 E

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,



K

D

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 2GUHGLWH IXQNFLRQDOQX ]DYLVQRVW SRWUHEQH SRJRQVNH VLOH ) SRWSXQR SRWRSOMHQRJ WRUSHGD R GXOMLQL WRUSHGD / SURPMHUXWRUSHGD'EU]LQLWRUSHGDYGLQDPLþNRJNRHILFLMHQWXYLVNR]QRVWLIOXLGDPWHJXVWRüLIOXLGDU  2GUHGLWHXGDOMHQRVW+JRUQMHJUXEDNRFNHOHGD D PPU/ NJP RGGQDRNUXJOHþDãHSURPMHUD'  PP8þDãLVHQDOD]LGO&RFD&ROHJXVWRüHU NJP  2GUHGLWHYULMHPHWSRWUHEQRGDVHSRSLMHGO&RFD&ROHJXVWRüHU NJP NRMDVHQDOD]LXRNUXJORMþDãL SURPMHUD '   PP EH] OHGD L] SUHWKRGQRJ ]DGDWND  NUR] VODPNX SURPMHUD G    PP GXOMLQH /   FP 3UHWSRVWDYLWH NYD]LVWDFLRQDUQR VWUXMDQMH YLVNR]QRJ IOXLGD 5DGL MHGQRVWDYQLMHJ SURUDþXQD SUHWSRVWDYLWH GD MH NRHILFLMHQWWUHQMDONRQVWDQWDQLGDL]QRVLO =DGDQRMHS0 3D SRWODNQDYUKXVODPNH XVLVQL NUDMVODPNHVHQDOD]LXYLMHNQHSRVUHGQRX]GQRþDãH  2GUHGLWH DNVLMDOQX VLOX QD YHQWLODWRU NRML XEDFXMH VYMHåL]UDNJXVWRüHU NJPSURWRNRP4 PVX SURVWRULMX3UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMH' PPS0 3D SUHWODNXSURVWRULML   2GUHGLWHGRPHWPOD]D5SROMHYDþDWUDYHNRMLMHSULNOMXþHQQDYRGRYRGQXPUHåXWRWDOQRJSUHWODNDS0 EDUD =DQHPDULWHWUHQMHXOHåDMHYLPD=DGDQRMH+ PU FPG PPD E U NJP 

S0

 

SD

J



D



U/

U

 

G

'



'

=DGDWDN

=DGDWDN

 

/

U

+





SD

J

'

U



E G

  SD 

J

E





D



5

 

Z

S0

=DGDWDN

D +

=DGDWDN

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 5DYQD SORþD MH SRWSXQR SRWRSOMHQD X IOXLG NRML MH X VWDFLRQDUQDUQRP UDYQLQVNRP YLVNR]QRP VWUXMDQMX SUHPD VOLFL2GUHGLWHSULPMHQRPGLPHQ]LMVNHDQDOL]HIXQNFLRQDOQX]DYLVQRVWVLOHRWSRUD)UDYQHSORþHRGEU]LQHIOXLGD YJXVWRüHIOXLGDUYLVNR]QRVWLPUD]OLNHWODNRYDLVSUHGLL]DSORþH'S SSWHãLULQHSORþHD  2GUHGLWH PLQLPDOQX XGDOMHQRVW [ NRG NRMH QHüH GRüL GR RWYDUDQMD SUHJUDGH MHGLQLþQH ãLULQH ]JOREQR YH]DQH X WRþFL$=DQHPDULWHWHåLQXSUHJUDGH=DGDQRMHU NJP/ P+ PK PD   +LGUDXOLþNLDNXPXODWRUSUHPDVOLFLSXQLVHNUR]FMHYRYRGXNXSQHGXOMLQH/ PSURPMHUDG PWH YLVLQHKUDSDYRVWLN PP2GUHGLWHSUHWODNS0NRMLMHSRWUHEDQGDELVHDNXPXODWRUSXQLRSURWRNRP4  OLWVWHSUHWODNS0NRMLVHSRVWLåHNDGDVHDNXPXODWRUSUD]QLLVWLPSURWRNRP2GUHGLWHVWXSDQMGMHORYDQMD DNXPXODWRUD=DGDQRMH' PP* W PDVDWHUHWD]DMHGQRVFLOLQGURPDNXPXODWRUD U NJPP   3DV XOMH  8SR]RUHQMH SUHWODFL S0 L S0 YODGDMX QD LVWRP PMHVWX NDNR MH R]QDþHQR QD VOLFL  VDPR MH VPMHUVWUXMDQMDIOXLGDUD]OLþLW  2GUHGLWHVLOX)QDUDþYXSUHPDVOLFL3UHWSRVWDYLWHQHYLVNR]QRVWUXMDQMHIOXLGD=DGDQRMHK PK P K PK PK P' PP SURPMHUVYLKFMHYRYRGD U NJP9 OLW YROXPHQ YRGHXUDþYL   =UDN 5   -NJ.      LVWMHþH L] UH]HUYRDUD X DWPRVIHUX NUR] NRQYHUJHQWQR GLYHUJHQWQX VDSQLFX 8 QDMXåHP SUHVMHNX VDSQLFH G   PP]UDNVWUXMLEU]LQRP]YXND3UHWODNXUH]HUYRDUXL]QRVLS0 EDUDD NUR] VDSQLFX NDR L L]OD]QL SURPMHU ' SRG WHPSHUDWXUD W   & 3RWUHEQR MH L]UDþXQDWL PDVHQL SURWRN P XYMHWRPGDWODNQDL]OD]XL]VDSQLFHL]QRVLSD EDU DWPRVIHUVNLWODN  

SD



J

 Y



D



S

+

S

/

U

$

 =DGDWDN



=DGDWDN

 J

DNXPXODWRU



J '

U

U

  /

  S0  S0



U

K

=DGDWDN



=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

U K K

G

=DGDWDN

SD

K

K G

 

K

[





D

3ULORJ,VSLWQLURNRYL

,VSLWRGUåDQ

 9HUWLNDOQLVWRåDFYLVLQH+ FPLSROXPMHUDED]H5 FPLVSXQMHQYRGRPJXVWRüHU NJPURWLUD NXWQRPEU]LQRPZ2GUHGLWHGRNRMHYLVLQHKMHVWRåDFELRLVSXQMHQYRGRPSULMHURWDFLMHDNRWLMHNRPURWDFLMH VORERGQDSRYUãLQDWDQJLUDSODãWVWRãFDQDYLVLQL+SUHPDVOLFL  2GUHGLWH JXVWRüX U NYDGUDWQH JUHGH MHGLQLþQH ãLULQH GD EL JUHGD ]JOREQR YH]DQD X WRþFL $ ELOD X UDYQRWHåL =DGDQRMH+ PK D PD U NJP  2GUHGLWHNRHILFLMHQWORNDOQRJJXELWNDYHQWLOD.Y]DVOXþDMVWDFLRQDUQRJVWUXMDQMDIOXLGDSUHPDVOLFL=DGDQRMH+ PK P/ P' PN PPD P. .N Q PVU  NJP  2GUHGLWHVLOX)QDOLMHYDNSUHPDVOLFL3UHWSRVWDYLWHVWDFLRQDUQRQHYLVNR]QRVWUXMDQMHIOXLGDWH]DQHPDULWHWHåLQX OLMHYND=DGDQRMH4 OV' PG P+ FP5 FPK#U NJP  2GUHGLWH YULMHPH W SUDåQMHQMD SUDYRNXWQRJ VSUHPQLND SRWSXQR ]DWYRUHQRJ SUHPD DWPRVIHUL MHGLQLþQH ãLULQH SUHPDVOLFL3RWUHEQRMHL]UDþXQDWLLYULMHPHSUDåQMHQMDRGXãQHFLMHYL=DGDQRMH' PG FPD  PE P+ P&G K P J SD  SD 5  

Z



U

+

+

 

J

U

D

+

K

U

D

  

K

U

 =DGDWDN

K .

 

' SD

      

'

.N

.Y

5

K



UP



=DGDWDN

' D

/ SD

+ 'N

U J

=DGDWDN J

UP

 

$

SD

+

SD

J

+

G

D

=DGDWDN

' G

K

=DGDWDN

&G

E

=ELUNDULMHãHQLK]DGDWDNDL]0HKDQLNHIOXLGD,

3ULORJ,VSLWQLURNRYL 

,VSLWRGUåDQ

 2GUHGLWHSURWRN4]DVLVWHPSUHPDVOLFL3UHWSRVWDYLWHVWDFLRQDUQRVWUXMDQMHQHYLVNR]QRJIOXLGD=DGDQRMH'  PG P+ PK PK PU NJP  2GUHGLWHUHDNFLMXXWRþFL$ VLOXLPRPHQW ]DVLWXDFLMXSUHPDVOLFL=DQHPDULWHWHåLQXSUHJUDGHMHGLQLþQHãLULQH =DGDQRMHD PE PU NJP  9RGD U   NJP P   3DV  SUHOMHYD VH VLIRQRP L] MHGQRJ MH]HUD ]D QDYRGQMDYDQMH X GUXJR SUHPD VOLFLNUR]FLMHYSURPMHUDG PP8NXSQDGXOMLQDFLMHYLMH/ PDYLVLQDKUDSDYRVWLMHN PP /RNDOQLJXELWDNXNROMHQX.N 2GUHGLWHSURWRNYRGHNUR]FLMHY=DGDQRMHK P  2GUHGLWH SRPDN VWRãFD [ DNR MH EU]LQD VWUXMDQMD Y   PV  NUR] FLMHY SURPMHUD '   P SUHPD VOLFL 3UHWSRVWDYLWH QHYLVNR]QR VWUXMDQMH IOXLGD XQLIRUPQH SURILOH EU]LQH QD VYLP SUHVMHFLPD WH NRQVWDQWDQ WODN X SUHVMHNX8WMHFDMJUDYLWDFLMH]DQHPDULWH=DGDQRMHG PF 1P NUXWRVWRSUXJH U  NJPJXVWRüDIOXLGD  2GUHGLWH]DYLVQRVWLEU]LQHãLUHQMDWODþQRJSRUHPHüDMDF EU]LQDSXOVD NUR]DUWHULMHXIXQNFLMLSURPMHUDDUWHULMH ' GHEOMLQH VWMHQNH NUYQH åLOH V JXVWRüH NUYL U
View more...

Comments

Copyright ©2017 KUPDF Inc.
SUPPORT KUPDF