12
4 Od Hvwdgvwlfd hv xqd udpd gh odv pdwhpwlfdv txh wudwd gh od uhfrsl0 odflq/ ho dqolvlv/ od lqwhusuhwdflq | od suhvhqwdflq gh xqd judq fdqwlgdg gh gdwrv qxpulfrv1 Hvwdgvwlfd Ghvfulswlyd = Frqmxqwr gh wfqlfdv hvwdgvwlfdv txh vh xwlol0 }dq sdud uhfrjhu/ fodvlfdu/ uhsuhvhqwdu | uhvxplu xq ghwhuplqdgr frqmxqwr gh gdwrv txh irupdq xqd pxhvwud rewhqlgd gh xqd sreodflq1 Hvwdgvwlfd Lqgxfwlyd r Lqihuhqfld Hvwdgvwlfd = Frqmxqwr gh pwrgrv txh vh ixqgdphqwdq hq od Whrud gh od Suredelolgdg | txh wlhqhq sru qdolgdg jhqhudol}du orv uhvxowdgrv/ rewhqlgrv phgldqwh xqd pxhvwud/ d wrgd xqd sreodflq1 Sreodflq = Fxdotxlhu frohfflq gh gdwrv txh wlhqhq flhuwdv fdudfwhuvwl0 fdv frpxqhv1 Xqlgdg Hvwdgvwlfd/ Lqglylgxr r Gdwr Hvwdgvwlfr = Fdgd xqr gh orv hoh0 phqwrv txh frpsrqhq od sreodflq1 Pxhvwud= Fxdotxlhu vxefrqmxqwr gh od sreodflq txh vhd uhsuhvhqwdwlyr gh hood1 Wdpdr gh od Sreodflq = Ho qphur gh hohphqwrv txh frpsrqhq od sr0 eodflq1 Fdudfwhuhv= Fdudfwhuvwlfdv ghvgh ho sxqwr gh ylvwd gh odv fxdohv vh hv0 wxgld xqd sreodflq1 Prgdolgdghv= Glihuhqwhv vlwxdflrqhv gh xq fdufwhu1 Fdudfwhuhv + Fxdolwdwlyr= Prgdolgdghv qr vrq phgleohv1 Fxdqwlwdwlyr= Prgdolgdghv vrq phgleohv1 +4, +4, Hq hvwh fdvr/ hq ho txh d odv prgdolgdghv gho fdufwhu vh ohv dvrfld xq qphur vh kdeod gh Yduldeoh Hvwdgvwlfd1 Y1 Hvwdgvwlfd ; A ? A = Glvfuhwd= Vxv srvleohv ydoruhv hvwq dlvodgrv Frqwlqxd= Vl sxhgh wrpdu wrgrv orv ydoruhv gh xq lqwhuydor Glvwulexflq gh Iuhfxhqfldv = Frqmxqwr gh orv ydoruhv txh suhvhqwd od yduldeoh mxqwr frq vxv iuhfxhqfldv1 Ghshqglhqgr gho wlsr gh iuhfxhqfldv txh vh frqvlghuhq kdeoduhprv gh Glvwulexflq gh Iuhfxhqfldv Devroxwdv/ Glvwulexflq gh Iuhfxhqfldv Uhodwlydv hwf1

Tema 01.pdf

Embed Size (px)

Citation preview

  • 4

    Od Hvwdgvwlfd hv xqd udpd gh odv pdwhpwlfdv txh wudwd gh od uhfrsl0odflq/ ho dqolvlv/ od lqwhusuhwdflq | od suhvhqwdflq gh xqd judq fdqwlgdggh gdwrv qxpulfrv1

    Hvwdgvwlfd Ghvfulswlyd= Frqmxqwr gh wfqlfdv hvwdgvwlfdv txh vh xwlol0}dq sdud uhfrjhu/ fodvlfdu/ uhsuhvhqwdu | uhvxplu xq ghwhuplqdgr frqmxqwrgh gdwrv txh irupdq xqd pxhvwud rewhqlgd gh xqd sreodflq1

    Hvwdgvwlfd Lqgxfwlyd r Lqihuhqfld Hvwdgvwlfd= Frqmxqwr gh pwrgrv txhvh ixqgdphqwdq hq od Whrud gh od Suredelolgdg | txh wlhqhq sru qdolgdgjhqhudol}du orv uhvxowdgrv/ rewhqlgrv phgldqwh xqd pxhvwud/ d wrgd xqdsreodflq1

    Sreodflq= Fxdotxlhu frohfflq gh gdwrv txh wlhqhq flhuwdv fdudfwhuvwl0fdv frpxqhv1

    Xqlgdg Hvwdgvwlfd/ Lqglylgxr r Gdwr Hvwdgvwlfr= Fdgd xqr gh orv hoh0phqwrv txh frpsrqhq od sreodflq1

    Pxhvwud= Fxdotxlhu vxefrqmxqwr gh od sreodflq txh vhd uhsuhvhqwdwlyrgh hood1

    Wdpdr gh od Sreodflq= Ho qphur gh hohphqwrv txh frpsrqhq od sr0eodflq1

    Fdudfwhuhv= Fdudfwhuvwlfdv ghvgh ho sxqwr gh ylvwd gh odv fxdohv vh hv0wxgld xqd sreodflq1

    Prgdolgdghv= Glihuhqwhv vlwxdflrqhv gh xq fdufwhu1

    Fdudfwhuhv+

    Fxdolwdwlyr= Prgdolgdghv qr vrq phgleohv1 Fxdqwlwdwlyr= Prgdolgdghv vrq phgleohv1 +4,

    +4, Hq hvwh fdvr/ hq ho txh d odv prgdolgdghv gho fdufwhu vh ohv dvrfldxq qphur vh kdeod gh Yduldeoh Hvwdgvwlfd1

    Y1 Hvwdgvwlfd

    ;

    A

    ?

    A

    =

    Glvfuhwd= Vxv srvleohv ydoruhv hvwq dlvodgrv Frqwlqxd= Vl sxhgh wrpdu wrgrv orv ydoruhv

    gh xq lqwhuydor

    Glvwulexflq gh Iuhfxhqfldv= Frqmxqwr gh orv ydoruhv txh suhvhqwd odyduldeoh mxqwr frq vxv iuhfxhqfldv1 Ghshqglhqgr gho wlsr gh iuhfxhqfldvtxh vh frqvlghuhq kdeoduhprv gh Glvwulexflq gh Iuhfxhqfldv Devroxwdv/Glvwulexflq gh Iuhfxhqfldv Uhodwlydv hwf1

  • 5

    YDULDEOH HVWDGVWLFD XQLGLPHQVLRQDOFDUDFWHUVWLFDV

    Fdudfwhuvwlfdv r Phglgdv gh Srvlflq= Wudwdq gh uhvxplu | vlqwhwl}du hofrqmxqwr gh gdwrv phgldqwh xq ydoru qxpulfr/ vl hvwh ydoru qxpulfr vhvlwd kdfld ho fhqwur gh od glvwulexflq vh kdeod/ hqwrqfhv/ gh Phglgdv ghSrvlflq Fhqwudo r gh Whqghqfld Fhqwudo1

    Srvlflq =

    ;

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    =

    SrvlflqFhqwudo

    ;

    A

    A

    A

    ?

    A

    A

    A

    =

    Phgld Dulwpwlfd= % '[

    % s

    Phgldqd= Prgd=

    SrvlflqQr0Fhqwudo

    ;

    A

    A

    ?

    A

    A

    =

    Fxdqwlohv

    ;

    A

    A

    ?

    A

    A

    =

    Fxduwlohv= ' E Ghflohv= ( Eb Shufhqwlohv= Ebb

    Fpr gh uhsuhvhqwdwlydv vrq hvwdv phglgdvBGlvshuvlq= Od pd|ru r phqru vhsdudflq gh orv ydoruhv uhvshfwr gh rwur

    txh suhwhqgh txh vhd vx vqwhvlv1Phglgdv gh Glvshuvlq= Wudwdq gh fxdqwlfdu od yduldelolgdg r hvsdufl0

    plhqwr gh xq frqmxqwr gh revhuydflrqhv lqirupdqgr dfhufd gh od pd|ru rphqru uhsuhvhqwdwlylgdg gh odv phglgdv gh whqghqfld fhqwudo1

    Glvshuvlq=

    ;

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    =

    Devroxwdv=

    ;

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    =

    Uhfruulgr r Udqjr= - ' % % U1 Lqwhufxduwolfr= - ' ' ' Ghvyldflq devroxwd phgld uhvshfwr

    gh od phgldqd== ( '

    [

    s m % m =

    Ghvyldflq devroxwd phgld uhvshfwrgh od phgld= ( '

    [ s m % % m

    Yduldq}d= j

    '[

    ! s E% %

    Ghvyldflq Wslfd= j ' ns

    j"

    Uhodwlydv= Frhflhqwh gh Yduldflq gh Shduvrq= T ' j%

  • 6

    Prphqwrv

    ;

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    =

    Fhqwudohvr uhvshfwr % = > '

    [

    s E% %

    ;

    A

    A

    ?

    A

    A

    =

    > '

    > ' f

    > ' j

    Qr0Fhqwudohvr uhvshfwr ruljhq = 6 '

    [

    s %

    +

    6 '

    6 ' %

    Fdudfwhuvwlfdv gh Irupd= Wudwdq gh fdudfwhul}du od irupd gh xqd glv0wulexflq phgldqwh xq qglfh uhvxplgr1

    Irupd =

    ;

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    A

    =

    Dvlphwud=

    ;

    A

    A

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    A

    A

    =

    Frhflhqwh gh dvlphwud gh Ilvkhu

    '>

    j

    ;

    A

    A

    A

    ?

    A

    A

    A

    =

    ' f( G1 Vlpwulfd

    : f( G1 Dvlpwulfd Srvlwlyd

    f > G1 Dvlpwulfd Qhjdwlyd

    Fxuwrvlv=

    ;

    A

    A

    A

    A

    A

    A

    ?

    A

    A

    A

    A

    A

    A

    =

    Frhf1 gh Dsxqwdplhqwr r Fxuwrvlv gh Ilvkhu

    '>

    j

    ;

    A

    A

    A

    ?

    A

    A

    A

    =

    ' f , Phvrfuwlfd

    : f , Ohswrfuwlfd f , Sodwlfuwlfd

    Phglgdv gh Dsxqwdplhqwr r Fxuwrvlv= Wudwdq gh hvwxgldu od glvwulex0flq gh iuhfxhqfldv hq od }rqd fhqwudo gh od glvwulexflq1 Vh dsolfdq d glv0wulexflrqhv fdpsdqliruphv/ hv ghflu/ xqlprgdohv | vlpwulfdv r oljhudphqwhdvlpwulfdv1

  • 7

    YDULDEOHV HVWDGVWLFDV ELGLPHQVLRQDOHVGLVWULEXFLQ ELGLPHQVLRQDO GH IUHFXHQFLDV

    Wdeod gh Fruuhodflq

    f 2 t e e

    + e

    e +

    e e

    + ?

    e e % ? ? ? ? 111

    111 111 111 111e e

    % ? ? ? ? 111

    111 111 111 111e e

    % ? ? ? ?

    ? ? ? ? ?

    ? ' ? '

    [

    [

    ? '

    [

    [

    ? ( s '

    ? ?

    (

    [

    [

    s '

    ? n n ? '

    [

    ? ' ? E mr ( ? n n ? '

    [

    ? ' ? E sJ

    ? '

    [

    !? " '

    #[

    $ !? " $ ( s " '

    #[

    $ !s $ '?

    "?

    ( s " $ '

    [

    !s $ '?

    " $?

    c

    [

    % & 's ( ' '

    )[

    ( * +s ( , '

    -[

    ' * +s , ' '

    ? ( , G Ghqhq od glvwulexflq pdujlqdo vhjq ho fdufwhu f

    %'%'[

    . s . / % . ( j0

    1 '[

    . s . / E% . %0

    ? / 2 G Ghqhq od glvwulexflq pdujlqdo vhjq ho fdufwhu t

    +'+'[

    2 s / 2 + 2 ( j0

    3 '[

    4 s 5 4 E+ 4 +6

  • 8

    Glvwulexflrqhv Frqglflrqdgdv= Vrq glvwulexflrqhv xqlglphqvlrqdohv re0whqlgdv d sduwlu gh odv glvwulexflrqhv elglphqvlrqdohv/ txh h{suhvdq od glv0wulexflq gh xqd gh odv grv yduldeohv sdud xq ydoru r frqmxqwr gh ydoruhvgh od rwud yduldeoh1 Vrq glvwulexflrqhv xqlglphqvlrqdohv hq odv fxdohv suh0yldphqwh vh ghqh xqd frqglflq1

    Prphqwrv qr0fhqwudohv r uhvshfwr gho ruljhq=

    6 '

    [

    [

    % + s

    Prphqwrv Fhqwudohv r uhvshfwr gh od Phgld=

    >

    '

    [

    [

    E% % E+ + s

    Fryduldq}d= Hv xqd phglgd gh od yduldelolgdg frqmxqwd gh odv yduldeohvf h t 1 Ho vljqr gh od fryduldq}d lqglfd ho vhqwlgr hq ho txh ydudq frqmxq0wdphqwh odv grv yduldeohv1 +>

    L E%c + ' j '

    [

    [

    E% % E+ + s

    Vl od j : f , Odv yduldeohv f h t ydudq hq ho plvpr vhqwlgr

    Vl od j f , Odv yduldeohv f h t ydudq hq vhqwlgr rsxhvwr1

    Whrud gh Uhjuhvlq= Frqvlvwh hq od evtxhgd gh xqd ixqflq txhh{suhvh or phmru srvleoh ho wlsr gh uhodflq hqwuh grv r pv yduldeohv1Xqd gh odv dsolfdflrqhv pv lqwhuhvdqwh txh wlhqh od Uhjuhvlq hv od ghSuhghflu/ hv ghflu/ frqrflgr ho ydoru gh xqd gh odv yduldeohv/ hvwlpdu hoydoru txh suhvhqwdu od rwud yduldeoh uhodflrqdgd frq hood1

    Whrud gh Fruuhodflq= Hvwxgld ho judgr gh ghshqghqfld hqwuh odv yd0uldeohv hv ghflu/ vx remhwlyr hv phglu ho judgr gh dmxvwh h{lvwhqwh hqwuhod ixqflq whulfd +ixqflq dmxvwdgd, | od qxeh gh sxqwrv1

    t G Yduldeoh ghshqglhqwh/ h{solfdgd r hqgjhqdf G Yduldeoh lqghshqglhqwh/ h{solfdwlyd r h{jhqd1

  • 9

    SUREDELOLGDG

    H{shulphqwr Ghwhuplqvwlfr r Fdxvdo= Fxdqgr do uhshwluor hq lgqwlfdvfrqglflrqhv vlhpsuh suhvhqwd ho plvpr uhvxowdgr1 +Orv ihqphqrv txh vhhvwxgldq hq Txplfdv/ Ivlfdv hwf1,

    H{shulphqwr Dohdwrulr= Fxdqgr do uhshwluor hq lgqwlfdv frqglflrqhvsxhgh suhvhqwdu uhvxowdgrv glvwlqwrv hq fdgd uhdol}dflq1 Hq hvwrv ihqph0qrv qr vh sxhgh suhghflu ho uhvxowdgr1

    Vxfhvr hohphqwdo= Fdgd xqr gh orv uhvxowdgrv gh xq h{shulphqwr dohd0wrulr lqghvfrpsrqleohv hq rwurv pv vlpsohv1 Hm= Hq ho h{shulphqwrdohdwrulr gho odq}dplhqwr gh xq gdgr1 Orv vxfhvrv hohphqwdohv vrq=ij c i2j c ij c iej c iDj | iSj

    Hvsdflr pxhvwudo= Ho frqmxqwr gh wrgrv orv vxfhvrv hohphqwdohv gh xqh{shulphqwr dohdwrulr1 , ' ic 2c c ec Dc Sj

    Vxfhvr= Wrgr vxefrqmxqwr gho hvsdflr pxhvwudo . r frqmxqwr gh vxfhvrvhohphqwdohv1 Hm= vdfdu xq qphur sdu/ r vdfdu lpsdu 1Vh glfh txh kd rfxuulgr xq vxfhvr vl orv uhvxowdgrv gho h{shulphqwrdohdwrulr lqfox|hq d dojxqrv gh orv uhvxowdgrv txh ghqhq do vxfhvr1

    Ho Vxfhvr vhjxur txh hv ho surslr hvsdflr pxhvwudo . Ho Vxfhvr lpsrvleoh txh hv ho frqmxqwr >

    Ghflflq fovlfd gh Suredelolgdg= Uhjod gh Odsodfh= Vxsrqlhqgr wrgrvorv fdvrv htxlsuredeohv

    E 'q gh fdvrv idyrudeohv gho vxfhvr

    q gh fdvrv srvleohv gho h{shulphqwr

    Ghqlflq D{lrpwlfd gh suredelolgdg= Vhd . xq hvsdflr pxhvwudo | xqd fodvh gh vxefrqmxqwrv gho hvsdflr pxhvwudo .1

    =

    .c

    $ - 5 $ E

    D[L= E f1 Sdud wrgr vxfhvr 5 D[LL= E. ' D[LLL= Vl c c c c vrq vxfhvrv lqfrpsdwleohv grv d grv/ hv ghflu _ ' fc

    ; 9' / hqwrqfhv

    EV

    ' E ^ ^ ^ ^ ' E n n E n '

    [

    E

  • :

    YDULDEOH DOHDWRULDGdgd xqd ixqflq gh suredelolgdg ghqlgd hq ho hvsdflr pxhvwudo .

    Vh oodpd Yduldeoh Dohdwruld +y1d1, d xqd ixqflq gh ydoru uhdo/ f/ ghqlgdhq . gh irupd txh wudqvirupd orv uhvxowdgrv gh . hq q

    uhdohv1

    Yduldeoh Dohdwruld Glvfuhwd= Vl ho frqmxqwr gh ydoruhv txh sxhgh wrpduhv frqwdeoh r elhq vl od yduldeoh wrpd xq qphur qlwr gh ydoruhv ghwhupl0qdgrv1

    Yduldeoh Dohdwruld Frqwlqxd= Vl ho frqmxqwr qxpulfr hv ho frqmxqwr ghorv qphurv uhdohv r elhq vl od yduldeoh wrpd xq qphur lqqlwr gh ydoruhv1

    Ixqflq gh Glvwulexflq gh od y1 d1 f= 8 E% ' df %o ;%

    8 G - $ dfc o gh irupd txh;% 5 -c 8 E% ' df %o

    y1 d1 glvfuhwd y1 d1 frqwlqxdIxqflq gh Suredelolgdg= R Ixqflq gh Ghqvlgdg= sE%

    R ' df ' % o

    4,

    [

    R ' | 5, R f ;

    4, sE% f ;% 5,

    ]

    sE% _ '

    6, d@ f Ko '

    ]

    sE% _

    Hvshudq}d Pdwhpwlfd Hvshudq}d Pdwhpwlfd

    ,dfo '[

    % T ,dfo '

    ]

    %sE% _

    V@hEf ' ,

    Ef ,Ef

    ' V@hEf '

    ]

    E% , dfo

    sE% _

    '[

    T E% ,Ef

    YDULDEOHV DOHDWRULDV ELGLPHQVLRQDOHV

    Vl f h t vrq y1d1 lqghshqglhqwhv,

    ;

    A

    A

    ?

    A

    A

    =

    , dft o ' , dfo , dt o

    J Efc t ' f

    V@h Ef t ' V@h Ef n V@h Et

  • ;

    GLVWULEXFLRQHV FRQWLQXDVGLVWULEXFLQ QRUPDO

    GLVWULEXFLQ QRUPDO E>> j= f # E>> jc fxdqgr vx ixqflq ghghqvlgdg ylhqh gdgd sru od vljxlhqwh h{suhvlq=4 %c > 4c + j : f

    sE% '

    js2Z

    e E% >

    2j

    c

    Ixqflq gh glvwulexflq= 8 E% ' df %o '

    ]

    sE| _| '

    ]

    js2Z

    e

    _|

    Jufdphqwh uhsuhvhqwd ho uhdhqfhuudgd hqwuh od fxuyd + ' sE|/ixqflq gh ghqvlgdg/ ho hmh f| od uhfwd f ' %

    GLVWULEXFLQ QRUPDO Ef> = sE5 ' s2Z

    e 5

    2 frq 4 5 n4c

    Glvwulexflq gh Shduvrq1f c f c c f c ? y1 d1 l1 l1 vhjq xqd Ef( , f

    nf

    n nf

    #

    Ho fdpsr gh yduldelolgdg hv Efc n4 Od fxuyd hv dvlpwulfd srvlwlyd Ghshqgh gho sduphwur ?c sru or txh

    qr kd| xqd fxuyd qlfd/ frpr vxfhghfrq od glvwulexflq Qrupdo wlslfdgd1

  • > jc vhohfflrqdprv xqd p1d1v1 gh wdpdr ?c % c % c c % cd sduwlu gh hood txhuhprv hvwlpdu/ phgldqwh xq lqwhuydor gh frqdq}d/xq sduphwur ghvfrqrflgr w Hohjlgr xq k Ef k srvlwlyr/ whqhprvtxh ghqlu grv ixqflrqhv w

    E%

    c % c c % | w E%

    c % c c % gh orv ydoruhv

    pxhvwudohv Ew w wdohv txh

    dw w w o ' k sdud dojq k : fc

    hqwrqfhv vh sxhgh ghflu txh w

    | w

    ghwhuplqd xq lqwhuydor txh wlhqh odsuredelolgdg k gh frqwhqhu do sduphwursreodflrqdo w

  • 44

    k = Frhflhqwh gh Frqdq}d r Qlyho gh Frqdq}d

    k = Hv ulhvjr gh txh ho lqwhuydor qr frqwhqjd ho ydoru gho sduphwurd hvwlpdu wc sru or txh k uhfleh ho qrpeuh gh Ulhvjr gho Huuru ghoLqwhuydor/ Qlyho gho Huuru gho Lqwhuydor r Qlyho gh Vljqlfdflq 1

    w | w = Oplwh lqihulru | vxshulru gh frqdq}d/ uhvshfwlydphqwh1

    +Ydvh Odud +5335/ Fdswxor c j | R

    Frqwudvwh gh Klswhvlv

    Od klswhvlv vreuh od txh vh ghvhd ghflglu uhfleh ho qrpeuh gh KlswhvlvQxod | vh ghqrwd sru M

    Od klswhvlv txh vh dfhswd/ vl vh uhfkd}d od klswhvlv qxod uhfleh ho qrp0euh gh Klswhvlv Dowhuqdwlyd | vh ghqrwd sru M Jhqhudophqwh od klswhvlvdowhuqdwlyd hv od qhjdflq gh od klswhvlv qxod 1

    Xq Frqwudvwh r Whvw gh Klswhvlv hv xq surfhglplhqwr phgldqwh ho fxdoqrv ghflglprv sru M r sru M

    Huuru gh Wlsr L r huuru k = Uhfkd}du od klswhvlv M fxdqgr hv flhuwd

    uhfkd}du M * M hv flhuwd

    ' k( f k

    Huuru gh Wlsr LL r huuru q= Dfhswdu od klswhvlv M fxdqgr hv idovd

    ghflglu M * M hv idovd

    ' q( f q

    Orv ydoruhv gho hvwdgvwlfr gh frqwudvwh txh qrv frqgxfhq d uhfkd}du odklswhvlv M irupdq od Uhjlq Fuwlfd r Uhjlq gh Uhfkd}r gho frqwudvwh |orv ydoruhv txh qrv frqgxfhq d ghflglu M irupdq od Uhjlq gh Dfhswdflq1

    Qlyho gh vljqlfdflq= Hv ho huuru kc hv ghflu od suredelolgdg gh txh hohvwdgvwlfr gh frqwudvwh fdljd hq od uhjlq gh uhfkd}r1

    Ho uhvxowdgr gh xq whvw r frqwudvwh gh klswhvlv vh glfh=

    Hvwdgvwlfdphqwh Vljqlfdwlyr= fxdqgr vh uhfkd}d M Hvwdgvwlfdphqwh Qr0Vljqlfdwlyr= fxdqgr vh dfhswd M

  • 45

    Frqwudvwhv Sdudpwulfrv= Vh frqrfh od irupd gh od glvwulexflq | orvsduphwurv vrq ghvfrqrflgrv1

    Frqwudvwhv Qr0Sdudpwulfrv= Qr vh frqrfh od irupd gh od glvwulexflqgh od sreodflq1 Hm= Whvw gh od erqgdg gh dmxvwh/ whvw gh lqghshqghqfld 111

    Wlsrv gh uhjlrqhv fuwlfdv= Gdgd xqd y1 d1 f frq i1 gh ghqvlgdg sEwc whv ghvfrqrflgr | w hv ho ydoru sursxhvwr sdud w M w ' w

    M w : w M w w =Klswhvlv Dowhuqdwlyd hv Xqlodwhudo1 +UhjlqFuwlfd Xqlodwhudo,

    M w 9' w Klswhvlv Dowhuqdwlyd hv Elodwhudo +U1 F1 Elodwhudo1,

    Srwhqfld gh xq frqwudvwh= Ew ' qEw Ew ' qEw '

    uhfkd}du M * M hv idovd

    '

    ghflglu M * M hv flhuwd

    Fulwhulrv Jhqhudohv sdud orv Frqwudvwhv

    Fdofxodu xqd fdqwlgdg h{shulphqwdo + d sduwlu gh orv gdwrv | xqdfdqwlgdg whulfd + d sduwlu gh odv wdeodv/ frpsduqgrodv gh od vljxlhqwhirupd=

    Vl , Dfhswdu M ( Vl , Uhfkd}du M

    Ho ydoru r ydoxh r qlyho fuwlfr r qlyho pqlpr gh vljqlfdflq= Hvho huuru gh od sulphud uhjlq fuwlfd gh uhfkd}r1 Hv ho uhd txh ghmd d odghuhfkd od

    Vl k , Dfhswdu M ( Vl k , Uhfkd}du M

    Odud Sruudv/ D1P1+5335,1 Hvwdgvwlfd sdud Flhqfldv Elrojlfdv | Flhqfld Dpelhq0wdohv1 Sureohpdv | H{phqhv uhvxhowrv Hg1 Sur|hfwr Vxu