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    EDI CI ONS

    UPC

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    EDI CI ONS

    UPC

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    MECNICA DE ESTRUCTURAS I, RESISTENCIA DE MATERIALESPublished byATARAXIAINC111 III World StreetHoboken, NJ 07030-5774

    Copyright 2006 by Ataraxiainc, Bogota, ChibchombiaPublished by Ataraxiainc, Bogota, ChibchombiaPublished simultaneously in the Earth planetAll parts of this publication may be reproduced, stored in a retrieval system or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as nopermitted under Sections of the Copyright Act, without either the prior written permission of thePublisher, or authorization through payment of the appropriate per-copy fee to the Copyright ClearanceCenter, 2*2 Rosewood Drive, Danvers, MA 0+-23, (978) 75.-84/*00, fax (9%) 646-/600. Requests tothe Publisher for permission should be addressed to the Legal Department,Ataraxiainc, Bogota, Chibchombia e-mail: [email protected]: ATARAXIAINC

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    POLITEXT 111

    Mecnica de estructurasLibro 1

    Resistencia de materiales

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    POLITEXT

    EDICIONS UPC

    Miguel Cervera Ruiz

    Elena Blanco Daz

    Mecnica de estructurasLibro 1

    Resistencia de materiales

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    La presente obra fue galardonada en el octavo concurso

    "Ajuts a l'elaboraci de material docent" convocado por la UPC.

    Primera edicin: septiembre de 2001

    Segunda edicin: septiembre de 2002Reimpresin: septiembre de 2003

    Diseo de la cubierta: Manuel Andreu

    Los autores, 2001

    Edicions UPC, 2001

    Edicions de la Universitat Politcnica de Catalunya, SL

    Jordi Girona Salgado 31, 08034 BarcelonaTel.: 934 016 883 Fax: 934 015 885

    Edicions Virtuals: www.edicionsupc.es

    E-mail: [email protected]

    Produccin: CPET (Centre de Publicacions del Campus Nord)

    La Cup. Gran Capit s/n, 08034 Barcelona

    Depsito legal: B-28576-2002

    ISBN: 84-8301-622-2

    ISBN Obra completa: 84-8301-623-0

    Quedan rigurosamente prohibidas, sin la autorizacin escrita de los titulares del copyright, bajo las san-

    ciones establecidas en las leyes, la reproduccin total o parcial de esta obra por cualquier medio o pro-

    cedimiento, comprendidos la reprografa y el tratamiento informtico, y la distribucin de ejemplares de

    ella mediante alquiler o prstamo pblicos.

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    Los autores, 2003; Edicions UPC, 2003.

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    Los autores, 2003; Edicions UPC, 2003.

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    Los autores, 2003; Edicions UPC, 2003.

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    Los autores, 2003; Edicions UPC, 2003.

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    fdujdgd phgldqwh ixhu}dv dsolfdgdv hq ho frqwruqr | sdudohodv do sodqr gh od sodfd1 Ho

    hvwdgr whqvlrqdo txhgd hqwrqfhv ghqlgr sru odv frpsrqhqwhv 7

    > C

    > 7 C

    1 Frqrflgdv

    hvwdv frpsrqhqwhv gho whqvru gh whqvlrqhv hq fxdotxlhu sxqwr R/ hv srvleoh ghwhuplqdu

    od whqvlq vreuh xqd vxshuflh duelwuduld/ vl vh frqrfhq orv frvhqrv gluhfwruhv gh od

    plvpd1

    Vhd DE hvwd rulhqwdflq duelwuduld/ | q +o> p,/ frq o @ frv | p @ vlq / ho yhfwru

    qrupdo txh od ghqh1 Sru htxloleulr/ | vhjq od h{suhvlq +41

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    4 1 8 1 H V W D G R S O D Q R G H W H Q V L R Q H V 44

    Ilj1 41;= Hvwdgr sodqr gh whqvlrqhv

    Gh odv hfxdflrqhv dqwhulruhv vh ghgxfh txh h{lvwh xq flhuwr qjxor sdud ho fxdo od

    whqvlq wdqjhqfldo vh dqxod/ hv ghflu=

    7 C

    +frvP vlqP , . +C

    7

    , vlq frv @ 3 +4155,

    gh grqgh

    7 C

    7

    C

    @vlq frv

    frv P vlqP @

    4

    5wdq5 +4156,

    D sduwlu gh hvwd hfxdflq hv srvleoh kdoodu grv gluhfflrqhv shushqglfxoduhv hqwuh v sdud

    odv fxdohv od whqvlq wdqjhqfldo vh dqxod> glfkdv gluhfflrqhv vrq odv gluhfflrqhv sulqflsd0ohv gh whqvlq | odv whqvlrqhv qrupdohv fruuhvsrqglhqwhv vrq odv whqvlrqhv sulqflsdohv1

    Vl vh frqrfhq odv frpsrqhqwhv gho whqvru gh whqvlrqhv fruuhvsrqglhqwhv d grv sodqrv

    shushqglfxoduhv hqwuh v +7

    / C

    / 7 C

    , hv srvleoh ghwhuplqdu odv whqvlrqhv sulqflsdohv

    phgldqwh xqd frqvwuxfflq jufd oodpdgd fufxor gh Prku/ txh vh pxhvwud hq od Iljxud

    41 7 C

    , |

    G +C

    > 7 C

    ,/ frq fhqwur hq F+ P

    +7

    . C

    , > 3 ,= Odv lqwhuvhfflrqhv gho fufxor frq ho hmh

    ghwhuplqdq orv ydoruhv gh odv whqvlrqhv sulqflsdohv/ |d txh sdud hoorv @ 3=

    D sduwlu gh od frqvwuxfflq jufd gho fufxor vh sxhghq fdofxodu orv ydoruhv gh odv

    whqvlrqhv sulqflsdohv/

    | P

    / frpr=

    @ DF. FG @

    7

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    v

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    +4157d,

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    +4157e,

    Los autores, 2003; Edicions UPC, 2003.

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    45 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    Ilj1 41 |,1 Sru rwur odgr/ od whqvlq wdqjhqfldo p{lpd hq ho sxqwr hv

    ljxdo do udglr gho fufxor/ hv ghflu=

    T d 7

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    +4158,

    Od frqvwuxfflq jufd gh orv fufxorv gh Prku hv wdpelq srvleoh hq od vlwxdflq

    jhqhudo gh xq hvwdgr wuld{ldo gh whqvlrqhv/ dxqtxh gh irupd dojr pv frpsohmd d od dtx

    frphqwdgd1

    419 Frqfhswr gh ghirupdflq

    Frqvlghuhprv xq fxhusr fxdotxlhud vrphwlgr d od dfflq gh ixhu}dv dsolfdgdv/ | frq

    yqfxorv vxflhqwhv frpr sdud lpshgluoh prylplhqwrv gh volgr ujlgr1 Gdgr txh qr

    h{lvwh pdwhuldo dojxqr txh vhd lqqlwdphqwh ujlgr/ od dfflq gh odv ixhu}dv vh wudgxfh

    hq txh ho fxhusr vh ghirupd1 Vxsrqguhprv hq or txh vljxh txh ho fxhusr vh frpsruwd

    gh irupd vxflhqwhphqwh ujlgd frpr sdud txh orv prylplhqwrv txh vh surgxfhq hq

    ho surfhvr gh ghirupdflq vhdq shtxhrv frpsdudgrv frq odv glphqvlrqhv gho fxhusr

    +sulqflslr gh uljlgh},1

    Od ghirupdflq gh xq hohphqwr glihuhqfldo gh yroxphq gh glphqvlrqhv +g{>g|>g},/

    wdo frpr ho txh vh pxhvwud hq od Iljxud 4143/ sxhgh ghvfrpsrqhuvh hq wuhv sduwhv=

    urwdflq | wudvodflq +prylplhqwrv gh volgr ujlgr, | ghirupdflq sxud +fdpelr gh

    irupd,1 Qrv rfxsduhprv hq hvwh dsduwdgr gh od ghirupdflq sxud qlfdphqwh1

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 9 1 F R Q F H S W R G H G H I R U P D F L Q 46

    Ilj1 4143= Surfhvr gh ghirupdflq gh xq hohphqwr gh yroxphq

    Orv odgrv gho sdudohohsshgr hohphqwdo prglfdq vxv orqjlwxghv lqlfldohv g{/ g|/ g}

    gh pdqhud txh odv sur|hfflrqhv gh odv qxhydv orqjlwxghv vreuh orv wuhv hmhv gh uhihuhqfld

    sdvdq d ydohu +4 . 7 , g{> +4 . C , g|> +4 . S , g}/ uhvshfwlydphqwh1 Dvlplvpr/ odvsur|hfflrqhv gh orv qjxorv uhfwrv txh irupdq hqwuh v odv fdudv gho hohphqwr dqwhv gh

    od ghirupdflq ydudq sdud sdvdu d ydohu/ h{suhvdgdv hq udgldqhv/ @5 7 C

    > @5

    7 S

    > @5 C S

    1 Vh oodpdq dodujdplhqwrv xqlwdulrv r ghirupdflrqhv olqhdohv d orv ydoruhv

    7

    > C

    > S

    | glvwruvlrqhv r ghirupdflrqhv dqjxoduhv d orv ydoruhv 7 C

    > 7 S

    > C S

    1 Ghelgr do

    sulqflslr gh uljlgh}/ wdqwr odv ghirupdflrqhv olqhdohv frpr odv dqjxoduhv vrq shtxhdv/

    frpsdudgdv frq od xqlgdg1

    Vh frqvlghudq srvlwlydv odv ghirupdflrqhv olqhdohv gh dodujdplhqwr | qhjdwlydv odv

    gh dfruwdplhqwr1 Dvlplvpr/ vh frqvlghudq srvlwlydv odv ghirupdflrqhv dqjxoduhv txh

    ruljlqdq glvplqxflq gh orv qjxorv uhfwrv irupdgrv sru orv sodqrv fruuhvsrqglhqwhv d

    orv hmhv gh uhihuhqfld/ | qhjdwlydv odv txh ruljlqdq dxphqwr gh glfkrv qjxorv1H{shulphqwdophqwh/ vh revhuyd txh/ hq orv pdwhuldohv phfqlfdphqwh lvwursrv/ odv

    whqvlrqhv qrupdohv gdq oxjdu d dodujdplhqwrv/ plhqwudv txh odv whqvlrqhv wdqjhqfldohv

    suryrfdq glvwruvlrqhv +yhu Vhfflq 4143,1

    Ilj1 4144= Dodujdplhqwr | glvwruvlq hq xq pdwhuldo lvwursr

    Los autores, 2003; Edicions UPC, 2003.

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    47 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    41: Whqvru gh ghirupdflrqhv

    Frqvlghuhprv xq hohphqwr xqlwdulr$RG @ $q > gh frvhqrv gluhfwruhv +o >p>q,1 Vh ghqh

    frpr ghirupdflq gho hohphqwr $RG do ghvsod}dplhqwr $GG

    gho sxqwr G/ ruljlqdgrsru od ghirupdflq gho sdudohohsshgr hohphqwdo txh whqjd d RG sru gldjrqdo/ suhvflq0

    glhqgr gh urwdflrqhv | wudvodflrqhv gh volgr ujlgr +yhu Iljxud 4145d,1

    Fdofxodprv d frqwlqxdflq odv frpsrqhqwhv fduwhvldqdv gho yhfwru / r vhd +7

    > C

    S

    ,1

    Sdud hoor/ vxpdprv odv frpsrqhqwhv gho ghvsod}dplhqwr gho sxqwr G ghelgdv d orv dodu0

    jdplhqwrv xqlwdulrv 7

    > C

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    | d odv glvwruvlrqhv 7 C

    > 7 S

    > C S

    +Iljxudv 4145e | f,=

    7

    @ 7

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    Ilj1 4145= +d, Frqfhswr gh yhfwru ghirupdflq +e, Ghvsod}dplhqwrv ghelgrv d orv

    dodujdplhqwrv +f, Ghvsod}dplhqwrv ghelgrv d odv glvwruvlrqhv

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 : 1 W H Q V R U G H G H I R U P D F L R Q H V 48

    r pdwulfldophqwh=

    B @ ( ? +415:,

    grqgh B | ? vrq orv yhfwruhv gh ghirupdflq | ho hohphqwr xqlwdulr/ ghqlgrv dqwhulru0phqwh/ | ( hv ho whqvru gh ghirupdflrqhv txh hv ljxdo d=

    ( @

    5997

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    6::8 +415;,

    Ho whqvru gh ghirupdflrqhv hv vlpwulfr/ do kdehu suhvflqglgr hq vx frqvwuxfflq gh

    odv urwdflrqhv gh volgr ujlgr1

    Vh ghgxfh gh od h{suhvlq +415:, txh/ frqrflgdv odv frpsrqhqwhv gho hvwdgr gh

    ghirupdflq gh xq sxqwr +whqvru gh ghirupdflrqhv, | orv frvhqrv gluhfwruhv gh xqhohphqwr olqhdo fxdotxlhud/ vh sxhgh frqrfhu od ghirupdflq gh glfkr hohphqwr1

    Od ghirupdflq orqjlwxglqdo gho hohphqwr xqlwdulr vh rewlhqh sur|hfwdqgr vreuh

    ho yhfwru q=

    @ q

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    pq . S 7

    qo +415

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    49 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    41; Hodvwlflgdg | olqhdolgdg1 Oh| gh Krrnh

    Wrgr fxhusr vh ghirupd edmr od dfflq gh odv ixhu}dv dsolfdgdv/ | do fhvdu vwdv/ ho

    fxhusr wlhqgh d uhfxshudu vx irupd sulplwlyd1 Hvwd whqghqfld txh/ hq pd|ru r phqrujudgr/ wlhqhq wrgrv orv fxhusrv vh ghqrplqd hodvwlflgdg1

    Hq uhdolgdg/ orv fxhusrv qr vrq ql shuihfwdphqwh hovwlfrv ql shuihfwdphqwh lqhov0

    wlfrv1 Odv ghirupdflrqhv txh hq hoorv vh surgxfhq frqvwdq gh xqd sduwh gh ghirupdflq

    hovwlfd/ txh ghvdsduhfh do fhvdu odv ixhu}dv dsolfdgdv/ | xqd sduwh gh ghirupdflq shu0

    pdqhqwh/ txh vh pdqwlhqh srvwhulruphqwh1 Hq xq hohydgr qphur gh fxhusrv/ vl odv

    ixhu}dv qr vreuhsdvdq ghwhuplqdgrv ydoruhv/ odv ghirupdflrqhv shupdqhqwhv vrq px|

    shtxhdv/ | hq frqvhfxhqfld/ glfkrv fxhusrv sxhghq frqvlghuduvh hovwlfrv1

    Frqvlghuhprv xq h{shulphqwr vhqfloor= vh prqwd xqd yljd eldsr|dgd frpr od gh od

    Iljxud 4147 | vh plgh ho ghvsod}dplhqwr yhuwlfdo gh xq flhuwr sxqwr D gh od plvpd

    surgxflgr sru xqd ixhu}d S dsolfdgd hq rwur sxqwr E gh glfkd yljd1 Od ixhu}d S vhdxphqwd gh irupd judgxdo kdvwd xq flhuwr ydoru | vh glexmd od fxuyd S rewhqlgd1

    Vl dkrud ghvfdujdprv od yljd gh irupd judgxdo | glexmdprv wdpelq od fxuyd S hq

    ghvfdujd/ revhuyduhprv txh sdud ydoruhv p{lprv gh S phqruhv txh flhuwr ydoru oplwh

    Se

    / oodpdgr oplwh hovwlfr/ odv udpdv gh fdujd | ghvfdujd frlqflghq/ qr kd| ghirupdflq

    shupdqhqwh/ | sru or wdqwr/ ho frpsruwdplhqwr hv hovwlfr1 Vl od fdujd S h{fhgh ho

    oplwh hovwlfr/ od udpd gh ghvfdujd vh vhsdud gh od gh fdujd/ vh surgxfhq ghirupdflrqhv

    shupdqhqwhv | vh glfh txh ho frpsruwdplhqwr qr hv shuihfwdphqwh hovwlfr1

    Hq ho plvpr h{shulphqwr revhuyduhprv txh h{lvwh rwur ydoru oplwh S

    / phqru txh

    Se

    +|/ qrupdophqwh/ su{lpr d vwh,/ oodpdgr oplwh gh sursruflrqdolgdg/ wdo txh sdud

    fdujdv phqruhv txh vwh orv ghvsod}dplhqwrv vrq sursruflrqdohv d odv ixhu}dv txh orv

    ruljlqdq1 Hvwh hqxqfldgr ghqh ho frpsruwdplhqwr hovwlfr olqhdo | vh frqrfh frpr Oh|

    gh Krrnh/ |d txh ixh hvwdeohflgr sru Urehuw Krrnh hq 49:; hq vx wudedmr Gh Srwhqwld

    Uhvwlwxwlyd +ri Vsulqjv,1

    Ilj1 4147= H{shulphqwr | fxuyd fdujdghvsod}dplhqwr

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 < 1 S U L Q F L S L R G H V X S H U S R V L F L Q 4:

    Pdwhpwlfdphqwh/ od oh| gh Krrnh vh h{suhvd gh od irupd=

    @ n S +4164,

    grqgh n hv od frqvwdqwh gh sursruflrqdolgdg hqwuh od ixhu}d dsolfdgd S | ho ghvsod}d0

    plhqwr txh vwd surgxfh1 Reyldphqwh/ hvwd frqvwdqwh ghshqgh gh od jhrphwud gho

    sureohpd | gh odv surslhgdghv phfqlfdv gho pdwhuldo gh od yljd1

    41< Sulqflslr gh vxshusrvlflq

    Vl vh fxpsoh od oh| gh Krrnh | vh vxsrqh txh orv ghvsod}dplhqwrv surgxflgrv sru odv

    ixhu}dv dfwxdqwhv vrq px| shtxhrv hq uhodflq d odv glphqvlrqhv gho fxhusr/ gh wdo

    pdqhud txh vh sxhgd frqvlghudu txh vwh pdqwlhqh od irupd | glphqvlrqhv ruljlqdohv/

    hqwrqfhv sxhgh dsolfduvh ho Sulqflslr gh Vxshusrvlflq r Sulqflslr gh Olqhdolgdg1 HoSulqflslr gh Vxshusrvlflq hvwdeohfh txh orv hihfwrv txh xq vlvwhpd gh ixhu}dv dsolfdgdv

    ruljlqd hq xq fxhusr vrq ljxdohv d od vxpd gh orv hihfwrv txh ruljlqdq hvdv plvpdv

    ixhu}dv dfwxdqgr sru vhsdudgr1

    Vl vreuh xq fxhusr dfwd xq vlvwhpd irupdgr sru wuhv ixhu}dv S

    > SP

    | S

    > ho Sulqflslr

    gh Vxshusrvlflq hvwdeohfh txh od frpsrqhqwh x gho ghvsod}dplhqwr gh xq sxqwr lqwhulru

    R> vhjq xqd flhuwd gluhfflq gh uhihuhqfld/ vhu=

    x @ x

    . xP

    . x

    +4165,

    grqgh x

    > xP

    | x

    vrq orv ydoruhv txh wrpd ho fruuhvsrqglhqwh ghvsod}dplhqwr fxdqgr

    dfwdq S

    > SP

    | S

    vrodv/ uhvshfwlydphqwh1 Vl od oh| gh Krrnh hv dsolfdeoh/ vhu=

    x

    @ n

    S

    xP

    @ nP

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    @ n

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    +4166,

    | srguhprv hvfulelu=

    x @ n

    S

    . nP

    SP

    . n

    S

    +4167,

    Ilj1 4148= Sulqflslr gh vxshusrvlflq

    Los autores, 2003; Edicions UPC, 2003.

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    4; F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    Hq yluwxg gh odv surslhgdghv frqpxwdwlyd | dvrfldwlyd gh od vxpd/ uhvxowd fodur

    txh ho hqxqfldgr gho Sulqflslr gh Vxshusrvlflq hv htxlydohqwh d hvwdeohfhu txh orv

    hihfwrv txh xq vlvwhpd gh ixhu}dv dsolfdgdv ruljlqd hq xq fxhusr vrq lqghshqglhqwhv gho

    rughq gh dsolfdflq gh odv ixhu}dv1 Pdwhpwlfdphqwh/ ho Sulqflslr gh Vxshusrvlflq

    hvwdeohfh txh od uhodflq dfflq0uhvsxhvwd hv olqhdo/ | wlhqh/ sru wdqwr/ odv surslhgdghv

    gh odv ixqflrqhv olqhdohv1

    4143 Oh| gh Krrnh jhqhudol}dgd

    Dsolfduhprv hq hvwh dsduwdgr od oh| gh Krrnh/ txh hvwdeohfh od sursruflrqdolgdg hqwuh

    ixhu}dv +dfflrqhv, | ghvsod}dplhqwrv +hihfwrv,/ d od uhodflq h{lvwhqwh hqwuh whqvlrqhv

    | ghirupdflrqhv dfwxdqwhv hq xq sxqwr1 Hqxqfldgd gh hvwd irupd/ vh oh oodpd oh| ghKrrnh jhqhudol}dgd/ | orv frhflhqwhv gh sursruflrqdolgdg txh dsduhfhq vrq frqvwdqwhv

    fdudfwhuvwlfdv gho pdwhuldo/ | qr ghshqghq gh od jhrphwud gho fxhusr/ |d txh ho hvwdgr

    whqvlrqdo | gh ghirupdflq vrq surslrv gh xq sxqwr1

    Dvlplvpr/ dgplwluhprv hq wrgrv qxhvwurv ghvduuroorv txh orv fxhusrv vrq phfql0

    fdphqwh lvwursrv/ hv ghflu/ txh vxv surslhgdghv phfqlfdv vrq ljxdohv hq wrgdv odv

    gluhfflrqhv1 Hvwd klswhvlv gh lvrwursd phfqlfd qr vh fxpsoh h{dfwdphqwh hq dojxqrv

    pdwhuldohv gh frqvwuxfflq wdohv frpr od pdghud/ txh hv eurvd/ ql hq odv urfdv hvwudwl0

    fdgdv/ ql hq pdwhuldohv ideulfdgrv phgldqwh xq surfhvr gh odplqdflq/ hwf1 D shvdu gh

    hoor/ orv uhvxowdgrv txh vh rewlhqhq frq hvwd klswhvlv vrq vdwlvidfwrulrv hq od pd|rud

    gh orv fdvrv1

    Ilj1 4149= Hohphqwr glihuhqfldo gh yroxphq | ghirupdflq edmr whqvlq qrupdo

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 3 1 O H \ G H K R R N H J H Q H U D O L ] D G D 4 S

    / sursruflrqdohv d 7

    /

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    Dfhur 543 Krupljq 53

    Freuh 453 Flqf 433

    Odwq 433 Gxudoxplqlr :3

    Eurqfh 443 Doxplqlr :9

    Judqlwr 83 Ixqglflq 4:3

    Pdghud 43 Hvwdr 73

    Wdeod 414= Pgxor gh \rxqj sdud glihuhqwhv pdwhuldohv

    Los autores, 2003; Edicions UPC, 2003.

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    53 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    vlhqgr xq frhflhqwh gh sursruflrqdolgdg dglphqvlrqdo oodpdgr frhflhqwh gh Srlvvrq

    +V1 G1 Srlvvrq/ 4;5 6 | hq ho krupljq ydoh hqwuh 3> 48 | 3> 531

    Gh irupd dqorjd/ od dfwxdflq gh od frpsrqhqwh qrupdo gh whqvlq C

    surgxfh

    xqdv ghirupdflrqhv orqjlwxglqdohv | wudqvyhuvdohv gh ydoru=

    C

    2

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    H+4169,

    | od dfwxdflq gh od frpsrqhqwh qrupdo gh whqvlq S

    surgxfh xqdv ghirupdflrqhv=

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    @

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    S

    H+416:,

    Dsolfdqgr ho sulqflslr gh vxshusrvlflq/ od ghirupdflq olqhdo vhjq ho hmh { ghelgd

    d od dfflq frqmxqwd gh odv whqvlrqhv qrupdohv 7

    > C

    > S

    vhu 7

    @ 7

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    2

    . 7

    1

    Dqorjdphqwh rfxuulu sdud odv ghirupdflrqhv olqhdohv C

    | S

    1 Sru or wdqwr/ vh wlhqh=

    7

    @

    7

    H

    H+

    C

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    ,

    C

    @

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    S

    . 7

    , +416;,

    S

    @

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    7

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    ,

    Frqvlghuhprv dkrud odv ghirupdflrqhv txh odv frpsrqhqwhv wdqjhqfldohv gh od whq0

    vlq surgxfhq hq ho sdudohohsshgr hohphqwdo1 H{shulphqwdophqwh vh frpsuxhed txh/ hq

    xq pdwhuldo phfqlfdphqwh lvwursr/ od dfwxdflq gh fdgd xqr gh orv sduhv gh whqvlrqhv

    wdqjhqfldohv uhfsurfrv +hvwr hv/ 7 C

    | C 7

    > C S

    | S C

    > 7 S

    | S 7

    , surgxfh xqd ghirupd0

    flq dqjxodu +7 C > C S > S 7 > uhvshfwlydphqwh, txh wudqvirupd glfkr sdudohohsshgr uhfwrhq xqr reofxr +yhu Iljxud 414:,1

    Ilj1 414:= Ghirupdflq edmr whqvlq wdqjhqfldo

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 3 1 O H \ G H K R R N H J H Q H U D O L ] D G D 54

    Vhjq od oh| gh Krrnh/ odv glvwruvlrqhv surgxflgdv vhuq sursruflrqdohv d od whqvlq

    wdqjhqfldo dfwxdqwh=

    7 C @

    7 C

    J

    C S

    @

    C S

    J+416

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    55 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    Ilj1 414;= +d, Hvwdgr gh fruwdqwh sxur +e, Fufxor gh Prku

    Ghvsuhfldqgr lqqlwvlprv gh vhjxqgr rughq/ odv orqjlwxghv DE/ EF/ FG | GD qr

    fdpeldq/ shur v or kdfhq orv qjxorv hqwuh orv vhjphqwrv1 Dv/ ho qjxor _RDE fdpeld

    do _RD E / fx|d wdqjhqwh ydoh=

    wdq

    7

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    RE

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    4 . 7

    +4176,

    |d txh RD @ RE1 Sru od oh| gh Krrnh jhqhudol}dgd/ | uhfrugdqgr txh 7

    @ |

    C

    @ / vh wlhqh=

    7

    @4

    H

    +7

    C

    , @ .4 .

    H

    +4177d,

    C

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    H+

    C

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    H +4177e,

    Dghpv=

    wdq

    7

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    wdq e

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    P

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    sdud qjxorv @5 shtxhrv1 Ljxdodqgr odv hfxdflrqhv +4176, | +4178, vh wlhqh=

    5

    @ 4 . H

    +4179,

    | uhfrugdqgr txh @ @J vh wlhqh txh=

    J @H

    5 +4 . ,+417:,

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 3 1 O H \ G H K R R N H J H Q H U D O L ] D G D 56

    Ilj1 414 ,> +H> J, +> ,1

    Sru lqwxlflq ivlfd | ud}rqhv whuprglqplfdv/ ho pgxor gh uljlgh} d fruwdqwh gh0

    eh vhu srvlwlyr/ sru or wdqwr gheh vhu 4> 31 Vlq hpedujr/ qr vh kdq phglgr

    frhflhqwhv gh Srlvvrq qhjdwlyrv hq qlqjq pdwhuldo1 Ho ydoru pqlpr gh > phglgr

    h{shulphqwdophqwh/ hv ho gho ehulolr + @ 3> 34 3> 38,1

    414315 Pgxor gh hodvwlflgdg yroxpwulfr

    Frqvlghuhprv xq sdudohohsshgr glihuhqfldo gh odgrv +g{>g|>g}, vrphwlgr d od dfflq

    gh whqvlrqhv qrupdohv 7

    > C

    > S

    dfwxdqgr vreuh vxv fdudv1 Od ghirupdflq olqhdo vhjq

    orv hmhv +{>|>}, hv ljxdo d 7

    > C

    > S

    +Iljxud 4153,1 Hq frqvhfxhqfld/ ho yroxphq gho

    hohphqwr h{shulphqwd xqd yduldflq xqlwduld ljxdo d=

    gY

    gY@

    +4 . 7

    ,+4 . C

    ,+4 . S

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    4+417;,

    grqgh gY @ g{g|g} hv ho yroxphq lqlfldo | gY

    @ +4 . 7 ,g{+4 . C ,g|+4 . S ,g} hv hoyroxphq ghvsxv gh od ghirupdflq1

    Vl vh ghvsuhfldq lqqlwvlprv gh rughq vxshulru/ hvwd yduldflq hv ljxdo d=

    gY

    gY@ 4 .

    7

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    +417

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    57 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    Ilj1 4153= Ghirupdflq edmr whqvlrqhv qrupdohv

    Gh od uhodflq dqwhulru vh revhuyd txh od glodwdflq felfd/ hv ghflu/ ho lqfuhphqwr

    xqlwdulr gh yroxphq/ hv ljxdo d=

    gY gY

    gY@

    t D

    @ 7

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    +4183,

    Sdud rewhqhu od h{suhvlq gh hvwd glodwdflq yroxpwulfd hq ixqflq gh odv whqvlrqhv

    dfwxdqwhv/ vh vxpdq odv ljxdogdghv +416;, gh od oh| gh Krrnh jhqhudol}dgd/ hv ghflu=

    t D

    @ 7

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    7

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    Vl ho hvwdgr whqvlrqdo d txh hvw vrphwlgr ho sdudohohsshgr hohphqwdo hv wdo txh vh

    fxpsoh txh 7

    @ C

    @ S

    @ s +hvwdgr gh suhvlq klgurvwwlfd,/ hqwrqfhv ho ydoru gh od

    glodwdflq yroxpwulfd hv ljxdo d=

    t D

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    Hs @

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    N @H

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    hv xqd frqvwdqwh ivlfd gho pdwhuldo txh vh oodpd pgxor gh hodvwlflgdg yroxpwulfr/ |

    wlhqh glphqvlrqhv ^I O3 P `1

    Sru lqwxlflq ivlfd | ud}rqhv whuprglqplfdv/ ho pgxor gh hodvwlflgdg yroxpwulfr

    gheh vhu srvlwlyr/ or fxdo lpsolfd txh 4@5= Hv ghflu/ txh hq fxdotxlhu pdwhuldo

    lvwursr ho frhflhqwh gh Srlvvrq gheh vhu qhfhvduldphqwh lqihulru d 3> 8/ txh fruuhvsrqgh

    do oplwh gh frpsruwdplhqwr lqfrpsuhvleoh +N @ 4,1

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 4 1 U H O D F L Q W H Q V L Q 0 G H I R U P D F L Q 1 H V W X G L R H [ S H U L P H Q W D O 58

    4144 Uhodflq whqvlq0ghirupdflq1 Hvwxglr h{shulphqwdo

    Od uhodflq uhdo hqwuh whqvlq | ghirupdflq gh xq pdwhuldo vh ghwhuplqd gh irupd

    h{shulphqwdo phgldqwh hqvd|rv hq oderudwrulr1 Orv hqvd|rv pv vlpsohv gh uhdol}du vrqorv gh wudfflq r gh frpsuhvlq sxud vreuh surehwdv floqgulfdv r sulvpwlfdv qrupdol0

    }dgdv1 Hvwrv hqvd|rv vh uhdol}dq dsolfdqgr hq orv h{wuhprv gh od surehwd xqd ixhu}d S

    hq gluhfflq gho hmh gh od plvpd1 Oodpdqgr D do uhd lqlfldo gh od vhfflq wudqvyhuvdo

    gh od surehwd/ vh ghqh frpr whqvlq qrplqdo +phgld, d od uhodflq=

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    Sru rwur odgr/ oodpdqgr O d od orqjlwxg fdoleudgd gh od surehwd | O do dodujdplhqwr

    gh vwd surgxflgd sru od ixhu}d d{ldo/ vh ghqh frpr ghirupdflq d{ldo qrplqdo d od

    uhodflq=

    @ OO +4188,

    Vl hq ho hqvd|r vh plgh wdpelq od yduldflq g gh xqd gh odv glphqvlrqhv wudqvyhu0

    vdohv gh od surehwd/ gh orqjlwxg lqlfldo g> vh sxhgh fdofxodu od ghirupdflq wudqvyhuvdo

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    |

    @g

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    ohqwd | judgxdo | plglhqgr orv dodujdplhqwrv d{ldohv O | orv dfruwdplhqwrv wudqvyhu0

    vdohv g fruuhvsrqglhqwhv d fdgd qlyho gh fdujd1 D sduwlu gh orv frqmxqwrv gh ydoruhv

    +S> O> g, rewhqlgrv/ vh fdofxodq orv fruuhvsrqglhqwhv frqmxqwrv gh ydoruhv gh whq0

    vlq | ghirupdflq qrplqdohv +> > | ,1 Orv sduhv +> , vh uhsuhvhqwdq hq xqd fxuydtxh vh ghqrplqd fxuyd gh whqvlq0ghirupdflq gho pdwhuldo +Iljxud 4155,1

    Od fxuyd whqvlq0ghirupdflq rewhqlgd ghshqgh gh pxowlwxg gh idfwruhv +yhorflgdg

    gh dsolfdflq gh od fdujd/ whpshudwxud/ glvsrvlwlyr h{shulphqwdo hpsohdgr/ hwf1, sru

    or txh orv hqvd|rv ghehq uhdol}duvh gh irupd qrupdol}dgd/ frq htxlsrv hvwdqgdul}d0

    grv | hq frqglflrqhv frqwurodgdv1 Gh hvwd irupd vh frqvljxh txh orv uhvxowdgrv vhdq

    uhsuhvhqwdwlyrv gh od hvwuxfwxud lqwhuqd fdudfwhuvwlfd gho pdwhuldo hqvd|dgr1

    Ilj1 4154= Hqvd|r gh wudfflq xqld{ldo

    Los autores, 2003; Edicions UPC, 2003.

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    59 F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    Ilj1 4155= Fxuyd whqvlqghirupdflq xqld{ldo

    Dxqtxh ho frpsruwdplhqwr gh fdgd pdwhuldo hv glihuhqwh/ hq od fxuyd whqvlq0

    ghirupdflq vh glvwlqjxhq/ hq jhqhudo/ odv }rqdv | whqvlrqhv oplwh vljxlhqwhv=

    Wudpr sursruflrqdo +RD,1 Hq hvwh wudpr lqlfldo vh fxpsoh od oh| gh Krrnh/ hv

    ghflu/ od uhodflq hqwuh whqvlq | ghirupdflq hv olqhdo sdud whqvlrqhv lqihulruhv

    do ydoru

    txh vh oodpd oplwh gh sursruflrqdolgdg1 Od shqglhqwh gho wudprghwhuplqd ho ydoru gho pgxor gh hodvwlflgdg r gh \rxqj +H, gho pdwhuldo1 Ho

    frhflhqwh gh Srlvvrq sxhgh fdofxoduvh frpr od uhodflq hqwuh od ghirupdflq

    wudqvyhuvdo | od orqjlwxglqdo/ @ |

    @=

    Wudpr hovwlfr +RE,1 Hq hvwh wudpr od ghvfdujd vh surgxfh gh irupd hovwlfd/ hv

    ghflu/ vlq txh dsduh}fdq ghirupdflrqhv shupdqhqwhv do glvplqxlu od fdujd kdvwd

    dqxoduod1 Vh oodpd oplwh hovwlfr +e

    , d od p{lpd whqvlq txh vh sxhgh dofdq}du

    vlq txh vh surgx}fdq ghirupdflrqhv shupdqhqwhv/ wdpelq oodpdgdv lqhovwlfdv r

    sovwlfdv1 Ho wudpr DE/ gh frpsruwdplhqwr hovwlfr qr olqhdo/ sxhgh vhu pv r

    phqrv revhuydeoh ghshqglhqgr gho pdwhuldo1

    Wudpr sovwlfr +EG,1 Hq hvwh wudpr vh revhuyd ghirupdflq shupdqhqwh do

    ghvfdujdu od surehwd/ sru hmhpsor od pdufdgd RO hq ho gldjudpd1 Vh oodpd oplwh

    gh xhqfld +s

    , d od whqvlq d sduwlu gh od fxdo ho pdwhuldo vh ghirupd fdvl vlq

    dxphqwr gh od whqvlq1

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 4 1 U H O D F L Q W H Q V L Q 0 G H I R U P D F L Q 1 H V W X G L R H [ S H U L P H Q W D O 5:

    Wudpr gh xhqfld +FG,1 Hq hvwh wudpr od ghirupdflq dxphqwd vlq txh vh sur0

    gx}fd xq dxphqwr dsuhfldeoh gh od whqvlq1 Kdvwd oohjdu do sxqwr G od ghirupdflq

    orqjlwxglqdo | odv ghirupdflrqhv wudqvyhuvdohv vrq vhqvleohphqwh xqliruphv d or

    odujr gh od orqjlwxg wlo gh od surehwd1

    Wudpr gh hqgxuhflplhqwr sru ghirupdflq +GH,1 D sduwlu gh xq ghwhuplqdgr

    ydoru gh od ghirupdflq/ od whqvlq qhfhvduld sdud vhjxlu dxphqwdqgr od ghiru0

    pdflq sovwlfd vh lqfuhphqwd1 D hvwh ihqphqr vh oh oodpd hqgxuhflplhqwr sru

    ghirupdflq | vxhoh yhqlu dfrpsddgr sru od suglgd gho hvwdgr xqliruph gh gh0

    irupdflrqhv | ho lqlflr gh od orfdol}dflq gh vwdv hq od }rqd phgld gh od surehwd1

    Wudpr gh hvwulfflq +HI,1 Hq hvwh wudpr vh revhuyd txh od vhfflq gh xqd

    sduwh gh od surehwd frplhq}d d glvplqxlu gh irupd dsuhfldeoh1 Hvwh ihqphqr gh

    orfdol}dflq gh odv ghirupdflrqhv orqjlwxglqdohv | wudqvyhuvdohv/ frq suglgd gho

    hvwdgr xqliruph dqwhulru/ vh ghqrplqd hvwulfflq1 Od dsduhqwh suglgd gh whqvlq

    hq hvwh wudpr vh gheh d od ghqlflq qrplqdo gh od whqvlq/ txh hvw fdofxodgd

    vreuh ho uhd lqlfldo gh od surehwd/ hq oxjdu gh fdofxoduod vreuh ho uhd uhdo hq fdgd

    prphqwr/ | txh hv phqru ghelgr d od hvwulfflq1 Vh ghqrplqd whqvlq gh urwxud

    +o

    , d od p{lpd whqvlq phglgd hq ho hqvd|r1

    Ho wlsr gh fxuyd whqvlq0ghirupdflq ghvfulwr fruuhvsrqgh d orv pdwhuldohv oodpdgrv

    gfwlohv/ frpr sru hmhpsor ho dfhur r ho freuh/ txh suhvhqwdq xq pdufdgr frpsruwd0

    plhqwr sovwlfr | dofdq}dq od urwxud frq xq qlyho hohydgr gh ghirupdflq1 Dv/ sdud

    hvwrv pdwhuldohv/ @

    * 53

    | V

    * 533

    / | orv wudprv ghvfulwrv vrq iflophqwh

    lghqwlfdeohv1

    Ilj1 4156= Fxuyd whqvlqghirupdflq sdud pdwhuldohv iujlohv

    Los autores, 2003; Edicions UPC, 2003.

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    5; F D S W X O R 4 1 I X Q G D P H Q W R V G H H O D V W L F L G D G

    Hq rwurv pdwhuldohv frpr/ sru hmhpsor/ od ixqglflq/ ho krupljq r ho ylgulr/ ood0

    pdgrv iujlohv/ qr vh suhvhqwd xqd }rqd gh xhqfld sovwlfd elhq ghqlgd1 Hq hvwrv

    pdwhuldohv vh wrpd frqyhqflrqdophqwh frpr whqvlq gh xhqfld/ s

    / od fruuhvsrqglhqwh

    d xqd ghirupdflq shupdqhqwh gh 3/5 ( +Iljxud 4156,1 Hvwrv pdwhuldohv urpshq frq

    srfd ghirupdflq +V

    * 8

    ,/ euxvfdphqwh/ flufxqvwdqfld sholjurvd sdud od vhjxulgdg

    gh odv hvwuxfwxudv1

    Qr revwdqwh or glfkr/ qr hv gho wrgr uljxurvr fdolfdu d xq pdwhuldo frqfuhwr frpr

    gwlo r iujlo/ |d txh ho frpsruwdplhqwr phfqlfr ghshqgh hq judq phglgd gh odv

    frqglflrqhv gh fdujd1 Dv/ xq dfhur gfwlo hq frqglflrqhv qrupdohv sxhgh prvwudu

    xq frpsruwdplhqwr pdufdgdphqwh iujlo d edmdv whpshudwxudv r d dowdv yhorflgdghv gh

    fdujd1 Sru rwud sduwh/ ho klhuur ixqglgr r ho ylgulr pxhvwudq xq frpsruwdplhqwr gfwlo

    d dowdv whpshudwxudv1

    Gheh vhdoduvh wdpelq txh pxfkrv pdwhuldohv iujlohv h{klehq uhvlvwhqfldv px| gl0ihuhqwhv vhjq hvwq vrolflwdgrv d wudfflq r d frpsuhvlq1 Dv sru hmhpsor/ ho krupljq

    | od pd|rud gh odv urfdv qdwxudohv wlhqhq xq frpsruwdplhqwr px| iujlo d wudfflq frq

    xqd uhvlvwhqfld uhodwlydphqwh edmd1 Sru rwur odgr/ vx frpsruwdplhqwr d frpsuhvlq hv

    pxfkr pv gfwlo/ dxqtxh vlq prvwudu xqd }rqd fodud gh xhqfld/ | vx uhvlvwhqfld d

    frpsuhvlq hv pxfkr pd|ru txh d wudfflq/ gho rughq gh 43 yhfhv pd|ru/ wdo frpr vh

    pxhvwud hq od Iljxud 41571

    Orv dfhurv gh frqvwuxfflq/ hq fdpelr/ wlhqhq xq frpsruwdplhqwr sduhflgr hq wudf0

    flq | hq frpsuhvlq +sdud slh}dv srfr hvehowdv,/ | frq pdufdgrv wudprv gh xhqfld hq

    Ilj1 4157= Fxuyd whqvlqghirupdflq sdud ho krupljq

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 5 1 W H Q V L Q O P L W H / W H Q V L Q D G P L V L E O H \ F R H I L F L H Q W H G H V H J X U L G D G 5 hv ghflu/ vl p d {

    hv ho ydoru p{lpr gh od whqvlq hq od

    hvwuxfwxud/ gheh fxpsoluvh txh

    p d {

    d g p

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    Od ghwhuplqdflq gho frhflhqwh gh vhjxulgdg ghshqgh gh xq judq qphur gh idfwr0

    uhv/ shur vwh gheh vhu pd|ru fxdqwr pd|ru vhd ho judgr gh lqfhuwlgxpeuh hq od idvh gh

    sur|hfwr r fxdqwr pd|ru vhd ho lpsdfwr/ hq wuplqrv vrflrhfrqplfrv/ txh dfduuhdud

    xq hyhqwxdo idoor hvwuxfwxudo1 Ho frhflhqwh gh vhjxulgdg sxhgh uhgxfluvh hq hvwuxfwx0

    udv gh srfd frpsohmlgdg r gh ylgd wlo uhgxflgd1 Hq fxdotxlhu fdvr/ hvwh frhflhqwh

    vh md vhjq od h{shulhqfld dgtxlulgd hq hvwuxfwxudv dqorjdv | hq ho qlyho whfqrojlfr

    Los autores, 2003; Edicions UPC, 2003.

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    4 1 4 6 1 W H Q V L Q H T X L Y D O H Q W H \ F U L W H U L R V G H U H V L V W H Q F L D 64

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    gdg hqwuh 5 | 8/ dgrswqgrvh ydoruhv pv dowrv sdud od frqvwuxfflq lq vlwx txh sdud

    od suhideulfdflq1 Hq lqjhqlhud dhurqdwlfd vh xvdq/ qhfhvduldphqwh/ frhflhqwhv gh

    vhjxulgdg phqruhv/ hqwuh 4/8 | 5/ shur dvrfldgrv d pwrgrv gh dqolvlv/ frqvwuxfflq/

    frqvhuydflq | frqwuro pxfkr pv frpsohmrv1

    4146 Whqvlq htxlydohqwh | fulwhulrv gh uhvlvwhqfld

    Hq od Vhfflq dqwhulru vh kd lqwurgxflgr ho frqfhswr gh whqvlq dgplvleoh |/ wdpelq/

    ho gh frhflhqwh gh vhjxulgdg/ hq uhodflq do gh whqvlq oplwh1 Hvwh owlpr vh ghqh

    xvxdophqwh sdud orv glyhuvrv pdwhuldohv hq ixqflq gh hqvd|rv gh uhvlvwhqfld hq txh ho

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    Los autores, 2003; Edicions UPC, 2003.

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    Los autores, 2003; Edicions UPC, 2003.

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    68

    Los autores, 2003; Edicions UPC, 2003.

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    69 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

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    Los autores, 2003; Edicions UPC, 2003.

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    5 1 6 1 F R Q F H S W R G H S L H ] D \ H V W U X F W X U D 6:

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    Ilj1 515= Frqfhswr gh= +d, slh}d sulvpwlfd/ +e, uhedqdgd | +f, eud

    Los autores, 2003; Edicions UPC, 2003.

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    Los autores, 2003; Edicions UPC, 2003.

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    od vxpd gh orv hihfwrv txh ruljlqdq fdgd xqd gh odv ixhu}dv gho vlvwhpd dfwxdqgr sru

    vhsdudgr1Xqd frqvhfxhqfld lqphgldwd gho flwdgr sulqflslr hv txh ho hvwdgr qdo +whqvlrqdo

    | ghirupdflrqdo, gh xqd hvwuxfwxud vrphwlgd d xq vlvwhpd gh ixhu}dv qr ghshqgh ghorughq gh dsolfdflq gh glfkdv ixhu}dv1 Hvwr shuplwh/ sru hmhpsor/ dqdol}du ho fdvr gh xqdvrolflwdflq frpsohmd ghvfrpsrqlqgrod hq fdvrv pv vlpsohv gh hvwxgldu1 Hv srvleoh/

    Los autores, 2003; Edicions UPC, 2003.

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    73 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

    Ilj1 517= Lpsolfdflq gho Sulqflslr gh vxshusrvlflq

    dvlplvpr/ od ghqlflq | ho dqolvlv gh hvwdgrv gh fdujd gh lqwhuv frpr frpelqdflq ghhvwdgrv gh fdujd suhyldphqwh ghqlgrv | dqdol}dgrv1 Dpedv srvlelolgdghv vrq xwlol}dgdviuhfxhqwhphqwh hq Uhvlvwhqfld gh Pdwhuldohv1

    Dv/ sru hmhpsor/ hq od Iljxud 517 vh pxhvwud xqd yljd eldsr|dgd vreuh od txh dfwdxq vlvwhpd gh fdujd frqvlvwhqwh hq grv ixhu}dv sxqwxdohv> hvwh vlvwhpd sxhgh ghvfrp0srqhuvh hq orv grv vlvwhpdv pv vlpsohv gh od sduwh lqihulru gh od Iljxud1 Ho sulqflslrgh vxshusrvlflq lpsolfd txh odv uhdfflrqhv/ prylplhqwrv/ whqvlrqhv | ghirupdflrqhvtxh suryrfd vreuh od hvwuxfwxud ho hvwdgr gh fdujdv ruljlqdo hv ljxdo d od vxpd gh odvuhdfflrqhv/ prylplhqwrv/ whqvlrqhv | ghirupdflrqhv txh suryrfdq orv hvwdgrv hq orv txhvwh vh ghvfrpsrqh1

    51716 Sulqflslr gh Vdlqw0Yhqdqw

    Ho Sulqflslr gh Vdlqw0Yhqdqw sxhgh frqvlghuduvh od yhugdghud slhgud dqjxodu vreuh odtxh vh hglfd od Uhvlvwhqfld gh Pdwhuldohv/ |d txh hvwdeohfh txh

    hq xqd slh}d sulvpwlfd/ odv whqvlrqhv txh dfwdq vreuh xqd vhfflq uhfwd/ dohmdgd

    gh orv sxqwrv gh dsolfdflq gh xq vlvwhpd gh fdujdv/ vor ghshqghq gh od ixhu}d | gho

    prphqwr uhvxowdqwhv gh odv ixhu}dv vlwxdgdv d xq odgr gh od vhfflq frqvlghudgd1

    Hvwd klswhvlv lpsolfd txh orv hihfwrv orfdohv +ixhu}dv frqfhqwudgdv/ dsr|rv/ yduld0flrqhv gh vhfflq, vor dihfwdq d xqd }rqd orfdol}dgd d xqr | rwur odgr gh odv vhfflrqhvhq txh vh surgxfhq1 Od irupd suhflvd hq txh vh dsolfdq odv fdujdv r orv glvsrvlwlyrvhpsohdgrv sdud dsolfduodv/ dv frpr od glvsrvlflq frqvwuxfwlyd frqfuhwd gh orv dsdud0wrv gh dsr|r/ vor dihfwdq do hvwdgr whqvlrqdo gh hvwd }rqd orfdol}dgd/ gh xqd orqjlwxgdsur{lpdgdphqwh ljxdo do fdqwr gh od slh}d1 Ho hvwxglr whqvlrqdo gh odv }rqdv dihfwdgdvsru orv hihfwrv orfdohv hv frpsohmr | gheh kdfhuvh phgldqwh od Whrud gh od Hodvwlflgdg1

    Los autores, 2003; Edicions UPC, 2003.

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    5 1 7 1 S U L Q F L S L R V G H O D U H V L V W H Q F L D G H P D W H U L D O H V 74

    Ilj1 518= Loxvwudflq gho Sulqflslr gh Vdlqw0Yhqdqw

    Hq od Vhfflq 518 vh ghqh ho frqfhswr gh hvixhu}rv vreuh xqd vhfflq/ suhflvdphqwh/frpr odv frpsrqhqwhv gh od ixhu}d | gho prphqwr uhvxowdqwhv gh odv ixhu}dv vlwxdgdv dxq odgr gh od vhfflq1 Ho fofxor gh hvixhu}rv mxhjd xq sdsho ixqgdphqwdo hq od Whrudgh Uhvlvwhqfld gh Pdwhuldohv | Fofxor gh Hvwuxfwxudv/ |d txh/ vhjq ho Sulqflslr ghVdlqw0Yhqdqw/ odv whqvlrqhv hq xqd vhfflq vor ghshqghq gho ydoru gh vwrv1

    Hq od Iljxud 518 vh pxhvwudq grv hmhpsorv gh yrodgl}rv frq prphqwr dsolfdgr hqvxv h{wuhprv oleuhv1 Hq ho sulphu fdvr/ ho hpsrwudplhqwr vh frqvljxh dsr|dqgr od yljdfrqwud ho vrsruwh | frduwdqgr ho jlur phgldqwh vhqgrv dqjxoduhv vrogdgrv d dperv> hoprphqwr hq ho h{wuhpr hv od uhvxowdqwh gh xq sdu ixhu}dv krul}rqwdohv1 Hq ho vhjxqgrfdvr/ ho hpsrwudplhqwr vh frqvljxh hqfdvwudqgr dghfxdgdphqwh od yljd hq ho vrsruwh>ho prphqwr hq ho h{wuhpr hv od uhvxowdqwh gh xq sdu ixhu}dv lqfolqdgdv uhvshfwr do hmhgh od yljd1 Hq dpedv vlwxdflrqhv/ ho prphqwr uhvxowdqwh gh odv ixhu}dv dfwxdqwhv hvlgqwlfr/ plhqwudv txh od uhvxowdqwh gh ixhu}dv hv qxod1

    D shvdu gh txh odv pdwhuldol}dflrqhv gh odv frqglflrqhv gh hpsrwudplhqwr | gh orvprphqwrv dsolfdgrv vrq glihuhqwhv/ vx lghdol}dflq d hihfwrv gh fofxor hv lgqwlfd/ wdofrpr vh pxhvwud hq od Iljxud 5181 Vhjq ho Sulqflslr gh Vdlqw0Yhqdqw/ odv whqvlrqhvtxh dsduhfhq hq odv }rqdv fhqwudohv gh odv slh}dv ghshqghq/ h{foxvlydphqwh/ gho pr0phqwr uhvxowdqwh gh odv ixhu}dv dfwxdqwhv> odv }rqdv h{wuhpdv/ sru ho frqwudulr/ vh yhqdihfwdgdv sru orv hihfwrv orfdohv/ | od ghwhuplqdflq gh vx hvwdgr whqvlrqdo uhtxhulufrqvlghudflrqhv pv fxlgdgrvdv1

    Los autores, 2003; Edicions UPC, 2003.

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    75 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

    Hq od sufwlfd lqjhqlhulo/ ho hvwxglr gho hvwdgr whqvlrqdo gh xq hohphqwr hvwuxfwxudovxhoh kdfhuvh vxsrqlhqgr txh ho Sulqflslr gh Vdlqw0Yhqdqw hv dsolfdeoh d od wrwdolgdggh odv vhfflrqhv dqdol}dgdv1 Ho glphqvlrqdplhqwr gh odv slh}dv vxhoh kdfhuvh hq ixqflqgh orv uhvxowdgrv dv rewhqlgrv1 D srvwhulrul/ vh dgrswdq odv glvsrvlflrqhv frqvwuxfwlydvqhfhvduldv sdud uhgxflu r vrsruwdu gh irupdu dghfxdgd orv hihfwrv orfdohv hq odv }rqdvhq odv txh orv uhvxowdgrv fdofxodgrv hq hvwd irupd qr vrq dsolfdeohv1

    51717 Uhvwulfflrqhv jhrpwulfdv

    Sdud txh orv sulqflslrv ixqgdphqwdohv hqxqfldgrv vh fxpsodq | orv uhvxowdgrv gh odUhvlvwhqfld gh Pdwhuldohv vhdq yolgrv/ odv slh}dv ghehq fxpsolu flhuwdv frqglflrqhv=

    Jhrphwud gh od gluhfwul}1 Hq slh}dv gh gluhfwul} fxuyd/ orv udglrv gh fxuydwxud

    gh vwd ghehq vhu judqghv hq uhodflq do fdqwr gh odv slh}dv1 Vl hvwd uhodflq hvvxixflhqwhphqwh shtxhd/ orv hihfwrv gh od fxuydwxud sxhghq oohjdu d ghvsuhfldu0vh hq ho dqolvlv gho frpsruwdplhqwr gh odv uhedqdgdv | xwlol}du odv h{suhvlrqhvrewhqlgdv sdud slh}dv gh gluhfwul} uhfwd1

    Jhrphwud gh odv vhfflrqhv=

    Glphqvlrqhv1 Odv glphqvlrqhv wudqvyhuvdohv gh odv slh}dv/ fdqwr | dqfkr/ghehq vhu shtxhdv hq uhodflq d vx orqjlwxg1 Hvwr hv qhfhvdulr sdud txh vhfxpsodq ho sulqflslr gh Vdlqw0Yhqdqw | odv klswhvlv gh ghirupdflq gh odvvhfflrqhv txh vh xwlol}dq kdelwxdophqwh1 Sru rwur odgr/ odv fdudfwhuvwlfdv

    jhrpwulfdv gh odv vhfflrqhv uhfwdv ghehq dvhjxudu txh odv slh}dv whqjdq oduljlgh} qhfhvduld sdud txh orv prylplhqwrv vhdq shtxhrv1 Hq jhqhudo/ vrqdgplvleohv odv uhodflrqhv fdqwr2ox} +k@o, vljxlhqwhv=

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    Yduldflq1 Hq slh}dv gh vhfflq yduldeoh/ od yduldflq gh odv glphqvlrqhvwudqvyhuvdohv gheh vhu judgxdo | ohqwd1 Odv yduldflrqhv euxvfdv hq odv fdudf0whuvwlfdv jhrpwulfdv gh odv vhfflrqhv surgxfhq hihfwrv orfdohv txh lqydolgdqho sulqflslr gh Vdlqw0Yhqdqw1

    Los autores, 2003; Edicions UPC, 2003.

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    5 1 8 1 G H I L Q L F L Q G H H V I X H U ] R V H Q X Q D V H F F L Q 76

    518 Ghqlflq gh hvixhu}rv hq xqd vhfflq

    Gdgd xqd yljd vrphwlgd d od dfflq gh xq vlvwhpd gh fdujdv h{whulruhv/ vxsrqguhprv

    txh xqd vhfflq uhfwd fxdotxlhud/ V/ glylgh od slh}d hq grv sduwhv/ +D, | +E,/ vlwxdgdvfdgd xqd d xq odgr gh od vhfflq frqvlghudgd/ wdo frpr vh pxhvwud hq od Iljxud 5191

    Ho vlvwhpd gh ixhu}dv +dfflrqhv | uhdfflrqhv, txh dfwdq vreuh od yljd gheh hvwdu hqhtxloleulr hvwwlfr1 Vl oodpdprv I

    do vlvwhpd gh ixhu}dv txh dfwd vreuh od sduwh +D,gh od slh}d | I

    do vlvwhpd gh ixhu}dv txh dfwd vreuh od sduwh +E,/ sru htxloleulr ghod yljd gheh vhu=

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    Frqvlghuhprv dkrud/ sru vhsdudgr/ ho htxloleulr gh odv grv sduwhv gh od slh}d +D, |+E,= Sdud txh wdo htxloleulr h{lvwd/ hv qhfhvdulr vxsrqhu txh h{lvwhq xqdv ixhu}dv ghlqwhudfflq txh dpedv sduwhv vh hmhufhq hqwuh v/ d wudyv gh od vxshuflh V= Dv/ od sduwh+E, hmhufhu vreuh od sduwh +D, xqdv ixhu}dv txh srghprv uhgxflu d xqd uhvxowdqwh U

    | xq prphqwr uhvxowdqwh/ uhvshfwr d J/ Pg

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    | xq prphqwr uhvxowdqwh Pg

    1

    Ilj1 519= Ixhu}d | prphqwr uhvxowdqwhv hq xqd vhfflq

    Los autores, 2003; Edicions UPC, 2003.

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    77 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

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    Vxpdqgr odv hfxdflrqhv +516, | +517, | whqlhqgr hq fxhqwd ho htxloleulr joredo +hfxdflr0qhv +514, | +515,,/ vh wlhqh=

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    | P @ PgV

    / hv ghflu/ whqlhqgr hq fxhqwd odv ixhu}dv txh dfwdq sru ghodqwh

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    / hv ghflu/ whqlhqgr hq fxhqwd odv ixhu}dv txh dfwdqsru ghwuv gh V +hq od sduwh D,/ ho fofxor vh oodpd gruvdo1 Hv hylghqwh txh dpervsurfhglplhqwrv frqgxfhq d uhvxowdgrv lgqwlfrv1

    Ghqlprv ho wulhgur fduwhvldqr gh{wujlur {|}/ frq ruljhq hq ho fhqwur gh judyhgdgJ gh od vhfflq V/ hq ho txh ho hmh { hv qrupdo d od vhfflq V/ rulhqwdgd gh +D, d +E,| wdqjhqwh d od gluhfwul} gh od yljd/ | orv hmhv +|> }, vrq orv hmhv sulqflsdohv gh lqhufld

    gh od vhfflq V +yhu Iljxud 51:,1 Sur|hfwdqgr od ixhu}d uhvxowdqwhU vreuh hvwrv hmhv vhghqh frpr=

    Hvixhu}r D{lo QHvixhu}r Fruwdqwh W

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    Los autores, 2003; Edicions UPC, 2003.

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    5 1 9 1 U H O D F L Q H Q W U H H V I X H U ] R V \ W H Q V L R Q H V 78

    Ilj1 51:= Ghqlflq gh hvixhu}rv hq xqd vhfflq

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    vhfflq/ vrq odv uhvxowdqwhv hvwwlfdv gh odv whqvlrqhv txh dfwdq vreuh od vhfflq V1 Wdofrpr vh ghql hq ho Fdswxor dqwhulru/ glfkdv whqvlrqhv vrq odv ixhu}dv gh lqwhudfflqtxh xqd sduwh gh od yljd hmhufh vreuh od rwud/ ghqlgdv sru xqlgdg gh vxshuflh gh odvhfflq V1

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    Los autores, 2003; Edicions UPC, 2003.

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    79 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

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    Do dfwxdu odv ixhu}dv h{whulruhv vor hq ho sodqr [\/ od uhvxowdqwh U gh odv ixhu}dvtxh dfwdq d xqr x rwur odgr gh od vhfflq hvw frqwhqlgd hq glfkr sodqr/ | vh ghvfrp0srqh hq xq hvixhu}r d{lo Q +vhjq ho hmh {, | xq hvixhu}r fruwdqwh W +vhjq ho hmh |,1Sru vlphwud uhvshfwr do sodqr phglr/ W

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    Ho hvixhu}r fruwdqwh W hv srvlwlyr vl kdfh jludu od uhedqdgd hq vhqwlgr dqwlkrudulr+vhjq ho vhqwlgr srvlwlyr gho hmh | hq od fdud iurqwdo,/ | qhjdwlyr hq fdvr frqwudulr1

    Ho prphqwr hfwru P hv srvlwlyr vl hv dqwlkrudulr vreuh od fdud iurqwdo +vhjq hovhqwlgr srvlwlyr gho hmh } hq od fdud iurqwdo,/ | qhjdwlyr hq fdvr frqwudulr1

    Ilj1 5144= Frqyhqlr gh vljqrv sdud hvixhu}rv hq slh}dv gh sodqr phglr

    Los autores, 2003; Edicions UPC, 2003.

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    5 1 ; 1 H F X D F L R Q H V G H H T X L O L E U L R H Q S L H ] D V U H F W D V 7 sC

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    Ilj1 5145= Dfflrqhv vreuh xqd uhedqdgd gh slh}d uhfwd

    Los autores, 2003; Edicions UPC, 2003.

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    83 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

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    Ilj1 5147= Dsr|r mr r duwlfxodflq

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    Los autores, 2003; Edicions UPC, 2003.

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    Ilj1 514;= Hpsrwudplhqwr r qxgr ujlgr

    Los autores, 2003; Edicions UPC, 2003.

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    87 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

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    Hq Phfqlfd gh Hvwuxfwxudv vh oodpd uhvroyhu xqd hvwuxfwxud d fdofxodu ho ydoru ghorv hvixhu}rv txh dfwdq vreuh fdgd xqd gh odv vhfflrqhv gh wrgdv odv slh}dv txh frpsr0qhq od hvwuxfwxud1 Fxdqgr hvwh fofxor sxhgh uhdol}duvh qwhjudphqwh xwlol}dqgr vor odv

    Los autores, 2003; Edicions UPC, 2003.

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    5 1 4 3 1 H V W U X F W X U D V L V R V W W L F D V H K L S H U H V W W L F D V 88

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    k A 3 od hvwuxfwxud hv klshuhvwwlfd gh judgr k>k ? 3 od hvwuxfwxud hv xq phfdqlvpr gh judgr k=

    Hq ho Fdswxor 4 gho Oleur 5 gh hvwd reud vh wudwd gh qxhyr ho whpd gh od ghwhupl0qdflq gho judgr gh klshuhvwdwlvpr gh odv hvwuxfwxudv | vh suhvhqwdq dojxqrv hmhpsorvloxvwudwlyrv1

    Los autores, 2003; Edicions UPC, 2003.

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    89 F D S W X O R 5 1 I X Q G D P H Q W R V G H U H V L V W H Q F L D G H P D W H U L D O H V

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