Modelos bayesianos hierárquicos no planeamento de recursos humanos

Texto

(1)UNIVERSIDADE DE LISBOA FACULDADE DE CIÊNCIAS DEPARTAMENTO DE ESTATÍSTICA E INVESTIGAÇÃO OPERACIONAL. Modelos bayesianos hierárquicos no planeamento de recurso humanos. Leonel Silva Vicente. Doutoramento em Estatística e Investigação Operacional (Especialidade em Probabilidade e Estatística). 2011.

(2)

(3) UNIVERSIDADE DE LISBOA FACULDADE DE CIÊNCIAS DEPARTAMENTO DE ESTATÍSTICA E INVESTIGAÇÃO OPERACIONAL. Modelos bayesianos hierárquicos no planeamento de recurso humanos. Leonel Silva Vicente. Doutoramento em Estatística e Investigação Operacional (Especialidade em Probabilidade e Estatística). Tese orientada pelo Professor Doutor Kamil Feridun Turkman. 2011.

(4)

(5) Dedico carinhosamente esta dissertação:. à memória da minha mãe e ao meu pai que através do seu sacrifício me deram a oportunidade de estudar; aos meus filhos André e Diogo, pois eles são a minha maior riqueza; à minha esposa Célia pela amizade incondicional em qualquer situação e pelo apoio e companheirismo ao longo de toda uma vida, suportando meus momentos de stress e de mau humor; e a todos aqueles que de alguma forma me incentivaram e apoiaram.. i.

(6)

(7) Resumo "O planeamento de recursos humanos (PRH) tem sido tradicionalmente utilizado pelas organizações para garantir que dispõem do número certo de pessoas, no lugar e no tempo certo" (Jackson e Schuler, 1990). Do ponto de vista da metodologia estatística, uma estrutura de recursos humanos (RH) pode ser descrita como um sistema dinâmico aleatório de stocks e fluxos. Em grande parte dos modelos estocásticos de RH, propostos na literatura, o erro nas previsões não é quantificado, sendo apenas estudada a dinâmica temporal dos valores médios dos stocks e fluxos. A primeira parte da tese tem como base o trabalho desenvolvido em Vicente e Turkman (2008), onde se considerou modelos markovianos e de renovamento para modelar o sistema de RH da Faculdade de Ciências da Universidade de Lisboa. Na segunda parte deste trabalho, pretende-se caracterizar os sistemas de RH de Instituições de Ensino Superior como processos de contagem multidimensionais. O objectivo é fazer inferências sobre a dinâmica temporal da estrutura de probabilidade desta cadeia de Markov multidimensional, ao contrário do habitual estudo dos valores esperados. A cadeia é tratada como não homogénea e os fluxos, bem como os stocks, como processos aleatórios, captando a dinâmica temporal através de um modelo bayesiano hierárquico. A flexibilidade destes modelos e a capacidade do WinBUGS em ajustar uma gama considerável de modelos, permite obter predições pontuais e intervalos de credibilidade, a médio e a longo prazo, para os stocks das categorias, as promoções, os recrutamentos e as saídas, considerando vários cenários. Adicionalmente, permite analisar as políticas a ser implementadas de forma que a evolução dos RH seja a pretendida. Palavras—chave: Planeamento de Recursos Humanos, modelos de Markov e modelos de Renovamento, modelos Bayesianos Hierárquicos, MCMC e WinBUGS. iii.

(8)

(9) Abstract "Manpower planning has traditionally been used by organizations to ensure that the right person is in the right job at the right time" (Jackson e Schuler, 1990). From a statistical methodological point of view, Manpower planning can be defined as a random dynamic system of stock and flows. In general, most manpower systems proposed in the literature do not try to model the probability structure of this random dynamic system, but merely try to model the how this system in average evolves in time. Vicente and Turkman (2008) applied at standard Markov and reneval processes to model the manpower system of the Faculty of Sciences of University of Lisbon and only studied the temporal dynamics of average values of stocks and flows. This work is reported in chapters 3 and 4. The second part of this theses treats the manpower system as a dynamic multidimensional counting process of stocks. The aim is to make inference on the whole probability structure of this dynamic multidimensional counting process, which is modeled as a multivariate non-homogeneous Markov chain. Inference on this process is made using Bayesian Hierarchical models and simulation based inference. Flexibility of these methods and the corresponding software WinBUGS permit the possibility of adjusting many different variants of the proposed model, as well as study the consequences of many different man power policies that may be adopted. Proposed model also allow us to make short and long time predictions together with their credible intervals on quantities such as future stocks, promotions, recruitments as well as wastages. Key words: Manpower Planning, Markov chains and Renewal processes, Bayesian Hierarchical models, MCMC and WinBUGS.. v.

(10)

(11) Agradecimentos É importante salientar que tudo que decorreu ao longo do meu doutoramento se deveu à colaboração e à amizade indispensáveis de todos que, de forma directa ou indirectamente, me apoiaram durante a realização deste trabalho. Nunca será demais destacá-los e agradecer a todos. Ao meu orientador, Professor Doutor Feridun Turkman, os meus sinceros agradecimentos pela orientação científica, o apoio, a amizade e seu incentivo, que foi crucial nos momentos menos bons. À Professora Doutora Maria Antónia Turkman, agradeço o seu apoio e os contributos que foram essenciais para a elaboração deste trabalho. Ao meu amigo, Professor Doutor Miguel Felgueiras, agradeço o seu empenho na leitura desta tese e as inúmeras sugestões que contribuíram para a melhoria da mesma. Aos amigos e colegas que me apoiaram e incentivaram a fazer o meu doutoramento e que me aconselharam nos momentos mais delicados. À direcção e aos funcionários dos serviços de RH da Faculdade de Ciências da Universidade de Lisboa, agradeço a sua preciosa contribuição na recolha dos dados que foram utilizados nesta tese. À Escola Superior de Tecnologia e Gestão de Leiria, por todo o apoio institucional. À Fundação para a Ciência e Tecnologia, agradeço o apoio financeiro concedido em parte através do Centro de Estatística e Aplicações da Universidade de Lisboa (bolsa de doutoramento SFRH /BD/45314 e os projectos FCT/PTDC/MAT/64353/2006 e FCT/POCI/2010).. vii.

(12)

(13) Notações e Lista de Siglas ⋄ Para a carreira docente, optou-se por designar as categorias de professor auxiliar, professor associado e professor catedrático simplesmente por auxiliar, associado e catedrático, respectivamente. ⋄ Em geral, variáveis aleatórias são representadas por letras maiúsculas e valores observados por letras minúsculas. ⋄ Letras gregas são usadas para denotar parâmetros. ⋄ Letras a bold representam vectores ou matrizes; para representar números usualmente considera-se a letra em itálico. ⋄ Designa-se por ys:t o conjunto de informação disponível no período s a t, ou seja, ys:t = (ys , ys+1 , . . . , yt−1 , yt ). ⋄ Será usada de forma indiferenciada o termo densidade para designar uma função de probabilidade ou uma função densidade de probabilidade. ⋄ p (·) é usada para representar uma função de probabilidade ou uma função densidade de probabilidade, consoante o contexto; p (x, y) representa a função de probabilidade (densidade de probabilidade) conjunta dos vectores aleatórios X e Y; p (y|x) representa função de probabilidade (densidade de probabilidade) condicionada de Y, dado o vector X. ⋄ π (θ): distribuição a priori de θ. ⋄ π (θ|x): distribuição a posteriori de θ dado x. ⋄ p (x|θ): modelo probabilístico. ⋄ L representa a função de verosimilhança, com parâmetros e dados observados de acordo com o contexto. ⋄ CODA: Convergence Diagnostic and Output Analysis software. ⋄ DIC: Deviance Information Criterion. ⋄ FCUL: Faculdade de Ciências da Universidade de Lisboa. ⋄ IC: Intervalo de credibilidade. ix.

(14) ⋄ MH: Metropolis Hastings. ⋄ MCMC: Markov Chain Monte Carlo. ⋄ PRH: Planeamento de Recursos Humanos. ⋄ RH: Recursos Humanos. ⋄ WinBUGS: Bayesian Inference using Gibbs Sampling for Windows.. x.

(15) Ðqglfh Fdsðwxor L1 Lqwurgxêær. 4. Fdsðwxor LL1 Frqfhlwrv ixqgdphqwdlv gh SUK h hvwdwðvwlfd ed|hvldqd. :. 41 Sodqhdphqwr gh uhfxuvrv kxpdqrv. :. 4141 Lqwurgxêær. :. 4151 Fdudfwhul}dêær grv x{rv. <. 4161 Fdghldv gh Pdunry. 48. 4171 Dsolfdêær gh fdghldv gh Pdunry qd prghodêær gh UK. 4:. 4181 Olplwdêøhv qr xvr gdv Fdghldv gh Pdunry. 53. 51 Lqihuíqfld ed|hvldqd. 54. 5141 Frqfhlwrv Ixqgdphqwdlv. 55. 5151 Pìwrgrv gh Prqwh Fduor yld Fdghldv gh Pdunry. 57. 5161 Gldjqövwlfrv gh frqyhujíqfld. 5;. 5171 Fulwìulr gh lqirupdêær gh ghvylr. 64. 5181 Dvshfwrv frpsxwdflrqdlv. 65. 61 Prghorv pdwulfldlv h prghorv gh hvsdêr gh hvwdgrv. 67. Fdsðwxor LLL1 Idfxogdgh gh Flíqfldv gd Xqlyhuvlgdgh gh Olverd. 78. 41 Vlvwhpd gh UK. 78. 51 Hyroxêær grv vwrfnv gd IFXO. 84. 61 Hyroxêær grv vwrfnv gd fduuhlud grfhqwh. 86. 6141 Hyroxêær grv vwrfnv sru ghsduwdphqwr. 86. 6151 Hyroxêær gd shufhqwdjhp gh grfhqwhv sru fdwhjruld. 89. 71 Hyroxêær grv vwrfnv gd fduuhlud qær grfhqwh. 8;. 81 Rv x{rv. 94 {l.

(16) {ll. ÐQGLFH. 8141 Uhfuxwdphqwrv h vdðgdv. 95. 8151 Surprêøhv gd fduuhlud grfhqwh. 97. 91 Hvwuxwxud gh lgdgh. 9;. 9141 Lqwurgxêær. 9;. 9151 Glvwulexlêær gh lgdghv grv grfhqwhv h qær grfhqwhv. 9<. Fdsðwxor LY1 Vlpxodêær xvdqgr prghorv pdunryldqrv h gh uhqrydphqwr. :6. 41 Prghorv gh Pdunry h gh uhqrydphqwr. :6. 51 Vlpxodêær xvdqgr plvwxud gh prghorv pdunryldqrv h gh uhqrydphqwr. :9. 61 Fdudfwhul}dêær gd shuvshfwlyd gh fduuhlud. ;3. 71 Hvwdflrqdulhgdgh/ frqwuroh h suhylvær. ;7. 7141 Lqwurgxêær. ;7. 7151 D hvwuxwxud grfhqwh gd IFXO. ;9. Fdsðwxor Y1 Prghorv ed|hvldqrv klhuäutxlfrv. <8. 41 Lqwurgxêær. <8. 51 Qrwdêøhv h frqyhqêøhv. <;. 61 Prghor. <<. 6141 Sduåphwurv gr prghor. 433. 6151 Yhurvlplokdqêd= suhvvxsrvwrv vreuh d ghshqgíqfld h dv glvwulexlêøhv. 434. 6161 Ixqêær yhurvlplokdqêd. 43<. 6171 Sulrulv. 444. 71 Lpsohphqwdêær gr prghor h dqäolvh grv sduåphwurv gr prghor. 446. 7141 Lpsohphqwdêær gr prghor. 446. 7151 Dqäolvh grv sduåphwurv gr prghor. 449. Fdsðwxor YL1 Frqwuror h hvwdflrqdulhgdgh xvdqgr prghorv ed|hvldqrv. 456. 41 Lqwurgxêær. 456. 51 Fhqäulr dfwxdo. 458. 5141 Hyroxêær grv vwrfnv. 459. 5151 Hyroxêær gdv surprêøhv. 45<.

(17) ÐQGLFH. {lll. 5161 Hyroxêær gdv vdðgdv h uhfuxwdphqwrv. 463. 5171 Glvwulexlêær gh lgdghv. 463. 61 Frqyhujíqfld sdud xp fhqäulr lghdo. 464. 6141 Lqwurgxêær. 464. 6151 Hvwudwìjldv d dgrswdu. 466. 71 Fhqäulr lghdo sdud d IFXO. 469. 7141 Ghvfulêær h fdudfwhul}dêær. 469. 7151 Hyroxêær grv vwrfnv. 473. 7161 Hyroxêær gdv surprêøhv. 477. 7171 Hyroxêær gdv vdðgdv h uhfuxwdphqwrv. 478. Fdsðwxor YLL1 Frqvlghudêøhv qdlv h wudedokr ixwxur. 47:. Dsíqglfh D1 Prghor 4. 486. Dsíqglfh E1 Prghor 5. 48<. Eleolrjudd. 49<. Ðqglfh Uhplvvlyr. 4:6.

(18)

(19) FDSÐWXOR L. Lqwurgxêær. D lghld fhqwudo gd dqäolvh hvwdwðvwlfd gr SUK uhvlgh qd frqfhsêær gd rujdql}dêær h vhxv UK frpr xp vlvwhpd glqåplfr gh vwrfnv +qýphur gh shvvrdv h{lvwhqwhv hp ghwhuplqdgr juxsr qxp fhuwr whpsr, h x{rv +qýphur gh shvvrdv txh vh ghvorfdp hqwuh juxsrv qxp ghwhuplqdgr shuðrgr gh whpsr 0 surprêøhv/ vdðgdv h hqwudgdv,1 Dv shvvrdv txh wudedokdp qxpd rujdql}dêær srghp vhu fodvvlfdgdv hp fodvvhv/ juxsrv rx fdwhjruldv frp edvh hp fhuwrv dwulexwrv/ wdlv frpr survvær/ vh{r/ judx/ lgdgh/ whpsr gh vhuylêr rx txdotxhu rxwud irupd gh klhudutxld +Eduwkrorphz h rxwurv/ 4<<4> Xjzxrzr h PfFohdq/ 5333> Gh Ih|whu/ 5339,1 Dv fdwhjruldv ghyhp vhu pxwxd0 phqwh h{foxvlydv gh prgr txh xpd shvvrd/ hp fdgd lqvwdqwh/ vö srgh shuwhqfhu d xpd ýqlfd fdwhjruld1 Vxsøh0vh txh qær kä qhqkxpd glihuhqêd hqwuh rv phpeurv gd phvpd fdwhjruld/ r phvpr vxfhghqgr ãv wudqvlêøhv hqwuh fdwhjruldv/ lvwr ì/ wrgrv rv lqglyðgxrv gh xpd fdwhjruld wíp d phvpd suredelolgdgh gh wudqvlêær1 Yäulrv prghorv pdwhpäwlfrv gh SUK wíp vlgr ghvhqyroylgrv sdud ghvfuhyhu/ suhyhu h frqwurodu d hyroxêær ixwxud gh shvvrdo qdv glihuhqwhv fdwhjruldv gh xp vlvwhpd gh UK1 Rv prghorv pdlv xvxdlv qr SUK edvhldp0vh hp Fdghldv gh Pdunry h surfhvvrv gh uhqrydphqwr +Eduwkrorphz h rxwurv/ 4<<4> Zdqj/ 5338,1 Frqwxgr/ r hvwxgr gd glqåplfd whpsrudo gd hvwuxwxud gh suredelolgdgh gh Fdghldv gh Pdunry pxowlyduldgdv ì edvwdqwh frpsoh{r/ h frpr frqvhtxíqfld dvvxph0vh txh rv x{rv h{lvwhqwhv qrv vlvwhpdv gh UK/ h{fhswr dv vdðgdv/ vær sursruêøhv {dv txh uhsuhvhqwdp r x{r hvwdflrqäulr gh lqglyðgxrv hqwuh dv glihuhqwhv fdwhjruldv1 Phvpr sdud hvwhv vlvwhpdv/ ghpdvldgr vlpsolfdgrv/ qær ì srvvðyho id}hu xpd lqihuíqfld frpsohwd vreuh d hvwuxwxud hvwrfävwlfd gr surfhvvr1 Frqvhtxhqwhphqwh/ r huur qdv suhglêøhv qær ì jhudophqwh txdqwlfdgr/. 4.

(20) 5. L1 LQWURGXÊÆR. vhqgr dshqdv hvwxgdgd d glqåplfd whpsrudo grv ydoruhv hvshudgrv grv vwrfnv h x{rv frqvlghudqgr prghorv pdunryldqrv rx prghorv gh uhqrydphqwr1 Qdv ýowlpdv gxdv gìfdgdv krxyh judqghv pxgdqêdv qr vlvwhpd hgxfdwlyr gr Hqvlqr Vxshulru hp Sruwxjdo1 Dvvlvwlx0vh d xp judqgh dxphqwr gr qýphur gh Xqlyhuvlgdghv h gh Lqvwlwxwrv Srolwìfqlfrv/ ehp frpr d xp fuhvflphqwr gdv Lqvwlwxlêøhv h{lvwhqwhv1 Dfwxdophqwh/ r Hqvlqr Vxshulru ì uhvsrqväyho sru xp hohydgr qýphur gh hpsuhjd0 grv dr qðyho grfhqwh h qær grfhqwh1 Hqtxdqwr dqwhulruphqwh d íqidvh hud gdgd dr fuhvflphqwr/ dfwxdophqwh h{lvwh suhvvær vreuh dv Lqvwlwxlêøhv Vxshulruhv gh irupd txh d sulrulgdgh vhmd d txdolgdgh h qær d txdqwlgdgh1 Idfh d hvwd dowhudêær gh sulrulgdghv/ frqmxjdgd frp dvshfwrv hfrqöplfrv/ kdyhuä surydyhophqwh qhfhvvlgdghv gh pxgdqêdv txh hyhqwxdophqwh srghuær sdvvdu sru uhgxêøhv qr qýphur gh ixqflrqäulrv1 Pxlwdv Lqvwlwxlêøhv gh Hqvlqr Vxshulru uhgx}ludp gudvwlfdphqwh dv frqwudwdêøhv gh ixqflrqäulrv grfhqwhv h qær grfhqwhv/ kdyhqgr phvpr dojxpdv txh sudwlfdphqwh frqjhodudp dv frqwudwdêøhv1 Hvwd irupd gh djlu frqgx} d xpd uhgxêær öeyld gr qýphur wrwdo gh ixqflrqäulrv frp frqvhtxíqfldv gliðfhlv gh suhyhu1 D idowd gh xp hvwxgr vreuh rv fhqäulrv srvvðyhlv sdud r ixwxur frpsolfd r SUK gdv Lqvwlwxlêøhv gh Hqvlqr Vxshulru/ id}hqgr frp txh d fduuhlud grfhqwh h frqvhtxhqwhphqwh d fduuhlud qær grfhqwh whqkdp shuvshfwlydv srxfr ghqlgdv1 Gh irupd d whqwdu fropdwdu hvwd idowd gh hvwxgr/ hvwh wudedokr whp frpr sulqflsdo remhfwlyr r ghvhqyroylphqwr gh prghorv ed|hvldqrv txh shuplwdp ghvfuhyhu d glqåplfd whpsrudo grv vlvwhpdv gh UK gdv Lqvwlwxlêøhv gh Hqvlqr Vxshulru1 Rv prghorv ghvhq0 yroylgrv irudp dsolfdgrv ã hvwuxwxud gh UK gd Idfxogdgh gh Flíqfldv gd Xqlyhuvlgdgh gh Olverd +IFXO, sdud xpd dqäolvh0slorwr dqwhv gd vxd/ srvvðyho/ dsolfdêær d hvwux0 wxudv gh pdlruhv glphqvøhv1 Rv grlv vlvwhpdv gh UK +grfhqwh h qær grfhqwh, gd IFXO dsuhvhqwdp fdudfwhuðvwlfdv ehp glvwlqwdv1 D fduuhlud grfhqwh irl hvwxgdgd frp pdlru ghwdokh1 D dsolfdêær gh wìfqlfdv hvwdwðvwlfdv dr SUK hqyroyh txdwur idvhv txh vær h{srvwdv gh vhjxlgd1.

(21) L1 LQWURGXÊÆR. 6. D sulphlud idvh frqvlvwh qd ghvfulêær dghtxdgd gr vlvwhpd1 Sdud frqvhjxlu hvwh remhfwlyr d ghvfulêær ghyh vhu frpsohwd pdv wdpeìp vlpsohv h frqflvd1 Ì xvxdo rv hvwdwðvwlfrv vhuhp whqwdgrv d qhjoljhqfldu hvwd wduhid/ sdvvdqgr ã idvh gh prghodêær/ txh frqvwlwxl sdud r hvwdwðvwlfr xp ghvdr pdlv dolfldqwh1 Hvwh surfhglphqwr srgh prv0 wudu0vh ghvydqwdmrvr/ srlv srghp qhvwd idvh vhu frqkhflgrv dojxqv lqglfdgruhv txh hp pxlwr idflolwduær r dydqêr qdv idvhv vhjxlqwhv1 Hvwd idvh frvwxpd iruqhfhu rv uhvxowdgrv pdlv dsuhfldgrv shorv ghflvruhv/ rv txdlv jhudophqwh hvwær srxfr vhqvlelol}dgrv sdud d pdqlsxodêær gd lqfhuwh}d txh uhyhvwh rv uhvxowdgrv txh vh rewíp qrv sdvvrv srvwhulruhv1 D vhjxqgd idvh/ hp txh r hvwdwðvwlfr lqyhvwh pxlwr gr vhx whpsr/ ì d gd prgh0 odêær h vlpxodêær gh fhqäulrv1 Hvwd idvh frqvlvwh hp rewhu xp prghor pdwhpäwlfr txh wudgx}d/ wær ghgljqdphqwh txdqwr srvvðyho/ d rujåqlfd gr vlvwhpd uhodwlydphqwh drv UK1 Frp edvh qhvwh prghor luær vhu hihfwxdgdv dv vlpxodêøhv1 Xpd gdv sursulhgdghv grv prghorv gh SUK txh hphujh frpr dwudhqwh sdud rv ghflvruhv ì d srvvlelolgdgh gh vlpxodu r frpsruwdphqwr gr vlvwhpd qr ixwxur/ dgplwlqgr xp fhuwr qýphur gh klsöwhvhv1 Jhudophqwh dv vlpxodêøhv vær pdo lqwhusuhwdgdv shorv ghflvruhv txh dv hq0 fdudp frpr suhylvøhv1 Dv vlpxodêøhv ghyhp vhu hqwhqglgdv frpr dtxlor txh dfrqwhfhuä vh 1 1 1 h qær frpr dtxlor txh ydl dfrqwhfhu1 D whufhlud h d txduwd idvhv frqvlvwhp qr hvwxgr h frqfhsêær gh pìwrgrv h hvwudwìjldv txh shuplwdp dwlqjlu fhuwrv fhqäulrv1 D whufhlud idvh/ jhqhulfdphqwh ghvljqdgd sru frqwuror/ frqvlvwh hp hqfrqwudu hv0 wudwìjldv gh jhvwær gdv yduläyhlv frqwuroäyhlv shor ghflvru txh shuplwdp dwlqjlu ghwhu0 plqdgr fhqäulr/ h xpd yh} dwlqjlgr pdqwí0or rx/ vh iru fdvr glvvr/ id}hu frp txh hvwh whqkd d hyroxêær suhwhqglgd1 D txduwd h ýowlpd idvh ì xvxdophqwh ghvljqdgd sru ghvljq1 Hvwd idvh whp sduwl0 fxodu lpsruwåqfld txdqgr xpd qryd rujdql}dêær hvwä d vhu fuldgd h hp txh ì qhfhvväulr ghqlu hvwudwìjldv d dgrswdu gh prgr d dwlqjlu fhuwrv remhfwlyrv1 Hvwh sdvvr vhuä wdpeìp lpsruwdqwh qr fdvr gr ghflvru suhwhqghu surfhghu d xpd uhrujdql}dêær gh xpd ghwhuplqdgd rujdql}dêær1 Hp vðqwhvh/ r SUK iruqhfh dv ihuudphqwdv sdud dydoldu dv frqvhtxíqfldv gd dgrsêær gh fhuwdv sroðwlfdv rx hvwudwìjldv1.

(22) 7. L1 LQWURGXÊÆR. Qrv ýowlprv dqrv/ r qýphur wrwdo gh grfhqwhv h gh qær grfhqwhv gd IFXO vriuhx xpd uhgxêær frqvlghuäyho1 Hvwd uhgxêær ohydqwd dojxpdv txhvwøhv1 Vhuä txh dv gxdv fduuhludv hvwær d hyroxlu qr vhqwlgr ghvhmäyhoB Pdqwhqgr0vh d hyroxêær dfwxdo gdv fduuhludv txdo vhuä r vhx hvwdgr gdtxl d 43 rx 53 dqrvB R txh id}hu fdvr vh suhwhqgd dowhudu r uxpr gd dfwxdo hyroxêær grv grlv vlvwhpdv gd IFXOB Rv prghorv hvwdwðvwlfrv gh SUK shuplwhp/ d sduwlu gr frqkhflphqwr gd hyroxêær qrv ýowlprv dqrv grv grlv vlvwhpdv gh UK/ rewhu suhglêøhv shudqwh yäulrv fhqäulrv h sroðwlfdv dowhuqdwlydv/ rewhqgr dvvlp uhvsrvwdv sdud hvwdv txhvwøhv h sdud pxlwdv rxwudv1 Dwudyìv gh vlpxodêær vhuä srvvðyho whu xpd lghld fodud vreuh txdlv rv hihlwrv/ d pìglr h d orqjr sud}r/ gdv sroðwlfdv gh uhfuxwdphqwrv/ surprêøhv h vdðgdv vreuh d hvwuxwxud grv grlv vlvwhpdv1 Doìp ghvwd lqwurgxêær/ hvwd whvh ì frpsrvwd sru pdlv vhlv fdsðwxorv/ hvwuxwxudgrv gd irupd txh d vhjxlu vh ghvfuhyh1 Fdsðwxor LL Qhvwh fdsðwxor id}0vh xpd euhyh h{srvlêær vreuh rv frqfhlwrv ixqgdphqwdlv gh SUK/ gh hvwdwðvwlfd ed|hvldqd/ gh prghorv pdwulfldlv h gh prghorv gh hvsdêr gh hvwdgrv1 Ghvfuhyhp0vh dojxqv grv dvshfwrv txh fdudfwhul}dp r SUK qrphdgdphqwh dv fdudfwhuðvwlfdv grv x{rv txh rfruuhp qxpd rujdql}dêær/ gdv fdghldv gh Pdunry h grv prghorv pdunryldqrv1 Dglflrqdophqwh dsuhvhqwdp0vh dojxqv frqfhlwrv eävlfrv gh lqihuíqfld ed|hvldqd/ ghvfuhyhp0vh rv pìwrgrv gh Phwursrolv0Kdvwlqjv h gh dprvwudjhp Jleev h h{søh0vh dojxqv dvshfwrv uhodflrqdgrv frp d frqyhujíqfld gdv fdghldv rewlgdv shod dsolfdêær grv pìwrgrv PFPF1 Sru ýowlpr/ dsuhvhqwd0vh xpd euhyh h{srvlêær gh fdudfwhuðvwlfdv grv prghorv pdwul0 fldlv h gh prghorv gh hvsdêr gh hvwdgrv1 Irl frp edvh qhvwhv prghorv txh/ qrv fdsðwxorv Y h YL/ vh frqvwuxlx xp prghor ed|hvldqr sdud prghodu r vlvwhpd gh UK gd fduuhlud grfhqwh1.

(23) L1 LQWURGXÊÆR. 8. Fdsðwxor LLL D ghvfulêær gr vlvwhpd gh UK gd IFXO ì hihfwxdgd qhvwh fdsðwxor1 Dqdolvd0vh d hyroxêær grv vwrfnv gd fduuhlud grfhqwh sru fdwhjruld h sru ghsduwdphqwr1 Ghylgr ã h{lvwíqfld gh glyhuvdv fduuhludv qær grfhqwhv h ghqwur gh fdgd xpd ghodv gh xp hohydgr qýphur gh fdwhjruldv/ rswrx0vh sru dsuhvhqwdu dshqdv dv hyroxêøhv grv vwrfnv gdv glyhuvdv fdwhjruldv1 Hvwdv dqäolvhv yíp dfrpsdqkdgdv shod hyroxêær gh wrgrv rv x{rv h{lvwhqwhv hp fdgd fduuhlud/ txhu grfhqwh txhu qær grfhqwh/ qrphdgdphqwh uhfuxwdphqwrv/ vdðgdv h surprêøhv1 Qhvwh fdsðwxor gä0vh d frqkhfhu rv grlv vlvwhpdv gh UK gd IFXO1 Dqdolvd0vh d hyroxêær gdv fduuhludv grfhqwh h qær grfhqwh/ qr shuðrgr gh 4<<; d 5339/ qrphdgdphqwh d hyroxêær grv vwrfnv/ grv x{rv h gdv glvwulexlêøhv gh lgdgh1 Fdsðwxor LY Qhvwh fdsðwxor/ dshvdu gh sru txhvwøhv gh uhdolvpr h jhqhudolgdgh vh frqvlghudu rv prghorv frpr hvwrfävwlfrv/ d lqfhuwh}d qær vhuä txdqwlfdgd/ fdqgr d dqäolvh frq0 qdgd ã ghwhuplqdêær grv ydoruhv pìglrv1 D txdqwlfdêær ghvwd lqfhuwh}d whp xpd lpsruwåqfld fuxfldo qxp wudedokr ghvwd qdwxuh}d shor txh vhuä remhfwr gh dqäolvh qrv Fdsðwxorv Y h YL1 Frpr d lgdgh grv lqglyðgxrv qxpd rujdql}dêær ì xp lqglfdgru pxlwr lpsruwdqwh/ sulqflsdophqwh hp vlvwhpdv hp frqwudfêær/ dqdolvd0vh d hyroxêær gd glvwulexlêær gh lgdghv sdud dv gxdv fduuhludv1 Xvdqgr prghorv pdunryldqrv/ hihfwxdudp0vh suhylvøhv/ dwudyìv gh vlpxodêær/ sdud d hyroxêær ixwxud grv vwrfnv h grv x{rv sdud rv grlv vlvwhpdv +grfhqwhv h qær grfhqwhv, gd IFXO shudqwh glyhuvrv fhqäulrv1 Sru ýowlpr/ dqdolvdudp0vh dv sroðwlfdv txh jdudqwhp d hvwdflrqdulhgdgh gd fduuhlud grfhqwh h dv sroðwlfdv pdlv dsursuldgdv sdud txh hvwd fduuhlud srvvd hyroxlu gh irupd frqwurodgd1.

(24) 9. L1 LQWURGXÊÆR. Fdsðwxor Y Sdud vhuhp xp lqvwuxphqwr hfd} qd jhvwær gh UK/ rv prghorv ghyhp iruqhfhu suhglêøhv frqäyhlv vreuh r lpsdfwr ixwxur gh txdotxhu hvwudwìjld gh jhvwær1 Dv suhglêøhv ghyhp vhu hihfwxdgdv frp xp judx txdqwlfäyho gh suhflvær gh irupd d phglu d lqfhuwh}d grv uhvxowdgrv suhylvwrv shorv prghorv1 Sdud whqwdu prghodu d glqåplfd whpsrudo sursøh0vh wudwdu d fdghld frpr qær kr0 prjìqhd h wudwdu rv x{rv h rv vwrfnv frpr surfhvvrv dohdwöulrv/ fdswxudqgr d glqåplfd gr whpsr dwudyìv gh xp prghor ed|hvldqr klhuäutxlfr1 Xpd frqvhtxíqfld ghvwd deru0 gdjhp ì d srvvlelolgdgh gh rewhu lqwhuydorv gh fuhglelolgdgh sdud dv suhglêøhv grv vwrfnv h grv x{rv1 Sursøh0vh dsolfdu hvwhv prghorv qr SUK gd IFXO/ frp d lqwhqêær gh ixwxudphqwh hvwhqghu d dqäolvh d rxwurv hvwdehohflphqwrv gh Hqvlqr Vxshulru1 Xvdqgr frpr h{hpsor d fduuhlud grfhqwh gd IFXO/ loxvwud0vh d srwhqfldolgdgh gd hvwdwðvwlfd ed|hvldqd qr SUK/ qrphdgdphqwh d irupd uhodwlydphqwh dfhvvðyho frpr ì srvvðyho hihfwxdu suhglêøhv sdud rv vwrfn h rv x{rv1 Dglflrqdophqwh/ ì srvvðyho dqdolvdu d yduldelolgdgh ghvvdv suhglêøhv dwudyìv gh vxpäulrv rx juäfrv gdv glvwulexlêøhv d srv0 whulrul1 Fdsðwxor YL Qhvwh fdsðwxor frqvlghurx0vh xpd ghwhuplqdgd hvwuxwxud sdud d fduuhlud grfhqwh h loxvwurx0vh frpr frqgx}lu r vlvwhpd d hvvd hvwuxwxud1 Sdud hihfwxdu dv vlpxodêøhv dgdswrx0vh r prghor sursrvwr qr fdsðwxor dqwhulru gh irupd txh hvwh shuplwlvvh id}hu suhglêøhv sdud d hyroxêær ixwxud grv vwrfnv h x{rv1 Ghvwd irupd/ vhuä srvvðyho yhulfdu txdo r qðyho gh surprêøhv h gh uhfuxwdphqwrv qhfhvväulrv sdud txh r vlvwhpd hyroxd gd irupd ghvhmäyho1 Fdsðwxor YLL Ilqdophqwh/ r ýowlpr fdsðwxor frqwhpsod dojxpdv frqvlghudêøhv qdlv h dojxpdv shuvshfwlydv vreuh wudedokrv ixwxurv1.

(25) FDSÐWXOR LL. Frqfhlwrv ixqgdphqwdlv gh SUK h hvwdwðvwlfd ed|hvldqd. 41 Sodqhdphqwr gh uhfxuvrv kxpdqrv. 4141 Lqwurgxêær1 D dqäolvh gh vlvwhpdv gh UK ì xpd frpsrqhqwh pxlwr lpsruwdqwh qr sodqhdphqwr gh xpd rujdql}dêær1 Qr hqwdqwr/ hvwd dqäolvh ghshqgh gr frpsruwdphqwr kxpdqr dowdphqwh lpsuhylvðyho h gr dpelhqwh vrfldo lqfhuwr hp txh d rujdql}dêær vh lqvhuh1 Lvwr frqgx} d txh r hvwxgr gh prghorv suredeloðvwlfrv rx hvwrfävwlfrv gh vlvwhpdv gh UK vhmd hvvhqfldo1 Glyhuvrv prghorv hvwrfävwlfrv irudp sursrvwrv h hvwxgdgrv qr sdv0 vdgr +Ydmgd/4<:;> Eduwkrorphz h rxwurv/ 4<<4> Zdqj/ 5338,1 Xpd judqgh ydulhgdgh grv prghorv hvwrfävwlfrv sursrvwrv srghp vhu fodvvlfdgrv hp grlv wlsrv= prghorv pdunryldqrv h prghorv gh uhqrydphqwr1 Hvwhv prghorv irudp xwlol}dgrv sdud dqdolvdu d hyroxêær gr vlvwhpd h txdlv dv sroðwlfdv dghtxdgdv gh irupd txh r vlvwhpd hyroxd gh irupd frqwurodgd +Eduwkrorphz/ 4<::> Gdylhv/ 4<:8/ 4<;5> Ydvvlolrx h Wvdqwdv/ 4<;7d/ e> Wvdqwdv/ 5334,1 Qhvwhv wudedokrv h qd judqgh pdlruld txh vh vhjxlx/ d txhvwær uh ohydqwh hud r frqwuror grv qýphurv suhylvwrv qrv yäulrv hvwdgrv gr vlvwhpd dwudyìv gr frqwuror grv uhfuxwdphqwrv h/ hp dojxpdv vlwxdêøhv/ gdv surprêøhv1 R frqwuror gd hyroxêær gr vlvwhpd gh uhfxuvrv ì ixqgdphqwdo sdud dv rujdql}dêøhv1 Sru rxwur odgr/ idfwruhv wdlv frpr d qhfhvvlgdgh gh rihuhfhu shuvshfwlydv dghtxdgdv gd fduuhlud rx d h{ljíqfld gr wudedokr glwduä iuhtxhqwhphqwh d lgdgh rx hvwuxwxud ghvhmäyhlv vhqgr d wduhid gr SUK yhulfdu vh wdo srgh vhu frqvhjxlgr h/ vh dvvlp iru/ gh txh irupd1 :.

(26) ;. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. R frpsruwdphqwr olplwh gh xp vlvwhpd gh Pdunry qær krprjìqhr txh hvwä hp h{sdqvær whp lpsruwåqfld suäwlfd frpr ì prvwudgr shod olwhudwxud hp vlvwhpdv gr UK +Ydvvlolrx 4<;4,1 Ydvvlolrx +4<;5, hvwxgrx r frpsruwdphqwr olplwh gh xp vlvwhpd frp uhfuxwdphqwr gh Srlvvrq h revhuyrx txh rv qýphurv gh lqglyðgxrv qdv glyhuvdv fdwhjruldv vær lqghshqghqwhv h wíp xpd glvwulexlêær dsur{lpdgd gh Srlvvrq1 Udjkdyhqgud +4<<4, xvrx xp prghor pdunryldqr sdud rewhu dv suredelolgdghv gh surprêær frqvlghudqgr xpd dydoldêær edvhdgd qd dqwljxlgdgh h qr ghvhpshqkr1 R frpsruwdphqwr ghshqghqwh gr whpsr gh prghorv hvwrfävwlfrv gh vlvwhpd gh UK frp r lpsdfwr gd suhvvær qdv surprêøhv irl hvwxgdgr sru \dgdydool h rxwurv +5335,1 Vhwokduh +533:, dqdolvrx dvshfwrv uhodflrqdgrv frp d rswlpl}dêær h hvwlpdêær gh prghorv hvwrfävwlfrv gh vlvwhpdv gh UK qrv txdlv lqfrusrud dojxqv idfwruhv wdlv frpr uhfuxwdphqwrv/ surprêøhv/ vdðgdv h irupdêær1 Dshvdu gh h{lvwlu xp ydvwr qýphur gh wudedokrv ghglfdgrv drv prghorv txh hq0 yroyhp x{rv gr wlsr sxvk/ srxfd dwhqêær whp vlgr ghglfdgd drv prghorv txh hqyroyhp x{rv gr wlsr sxoo1 Qr hqwdqwr/ h{lvwhp pxlwrv vlvwhpdv gh UK hp txh srghp rfruuhu x{rv sxvk h sxoo1 Sdud dqdolvdu hvwh wlsr gh vlvwhpdv/ Jhrujlrx h Wvdqwdv +5335, frqvlghurx xp prghor kðeulgr1 Qr hqwdqwr/ d vxd derugdjhp uhvwulqjlx0vh d vlvwhpdv hp txh r wrwdo gh ixqflrqäulrv ì frqkhflgr h fxmr qýphur gh ydjdv ì ghwhuplqdgr sdud wrgd d rujdql}dêær h qær hvshflfdphqwh sdud fdgd xpd gdv fdwhjruldv1 Hp fhuwdv rujdql}dêøhv qr hqwdqwr/ r qýphur gh ixqflrqäulrv h r qýphur gh ydjdv hvwær hvshflfdgdv dr qðyho gdv fdwhjruldv1 Gh Ih|whu +533:,/ dsuhvhqwd xp prghor kðeulgr txh shuplwh d prghodêær grv x{rv hqwuh wrgdv dv fdwhjruldv1 R prghor sur0 srvwr ì dghtxdgr sdud dv rujdql}dêøhv hp txh dv fdwhjruldv vær ghqlgdv sru fodvvhv gh klhudutxld1 Frqvhtxhqwhphqwh/ qhvwhv prghorv/ hp frpsdudêær frp rv prghorv wudglflrqdlv/ ì pdlv gliðflo d dqäolvh gd glqåplfd ixwxud gr vlvwhpd gh UK1. Xp prghor gh SUK ì xpd ghvfulêær pdwhpäwlfd txh ghvfuhyh d hyroxêær grv vwrfnv dr orqjr gr whpsr1 Ghyh lqfrusrudu d glqåplfd whpsrudo grv x{rv/ lvwr ì/ ghyh lqfrusrudu dv uhjudv gh frpr vh surfhvvdp dv surprêøhv/ dv vdðgdv h rv uhfuxwdphqwrv1.

(27) 41 SODQHDPHQWR GH UHFXUVRV KXPDQRV. <. R frqkhflphqwr gdv uhjudv ì fuxfldo h srghuä vhu rewlgr gluhfwdphqwh grv jhvwruhv gd rujdql}dêær rx lqihulgr d sduwlu gd hyroxêær sdvvdgd gd rujdql}dêær1 Xp prghor vdwlvidwöulr gh vlvwhpd gh UK ghyh gdu uhvsrvwdv d pýowlsodv txhvwøhv wdlv frpr dv txh vh vhjxhp1 Frpr iruqhfhu hvwlpdwlydv grv sduåphwurv gr vlvwhpdB Frpr suhgl}hu r frpsruwdphqwr ixwxur gr vlvwhpd vre yäuldv vxsrvlêøhvB Frpr hqfrqwudu dv phokruhv vroxêøhv idfh ãv uhvwulêøhv h drv remhfwlyrv sur0 srvwrv shorv jhvwruhvB Frpr hylwdu yäulrv sureohpdv gdqgr xp dylvr dqwhv gd vlwxdêær vh yhulfduB Ghyhuä pdqwhu0vh dv wd{dv gh surprêøhv rx dv wd{dv gh uhfuxwdphqwrB Vh/ hp yh} gd hyroxêær pdlv uäslgd/ vh suhwhqghu xpd hyroxêær gh irupd judgxdo/ txdlv dv wd{dv gh uhfuxwdphqwrv h gh surprêøhvB Pdqwhqgr dv wd{dv gh surprêøhv/ vhuä qhfhvväulr id}hu uhfuxwdphqwrvB Txdq0 wrvB H sdud txh fdwhjruldvB Vhuä txh d hvwdflrqdulhgdgh gr vlvwhpd ì jdudqwlgd txdotxhu txh vhmd r ydoru gd wd{d gh yduldêær gr wrwdo gh vwrfnvB Vh qxp ghwhuplqdgr lqvwdqwh d hvwuxwxud gh UK qær ì d pdlv dghtxdgd/ r txh id}hu sdud dwlqjlu xpd hvwuxwxud txh vhmd pdlv dghtxdgdB. 4151 Fdudfwhul}dêær grv x{rv1 D p gh gdu uhvsrvwdv d txhvwøhv frpr dv dqwhulruphqwh frorfdgdv/ r prghor frqvlghudgr ghyh lqfrusrudu rv sulqflsdlv idfwruhv txh ghwhuplqdp r frpsruwdphqwr gh xp vlvwhpd gh UK1 Ì qhfhvväulr frqkhfhu dv fdudfwhuðvwlfdv grv glyhuvrv wlsrv gh x{rv txh srghp rfruuhu qxpd rujdql}dêær/ qrphdgdphqwh dv vdðgdv/ surprêøhv h uhfuxwdphqwrv1.

(28) 43. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. Vdðgdv Rv ixqflrqäulrv gh xpd rujdql}dêær/ frqvrdqwh d fdwhjruld txh rfxsdp/ hvwær h{0 srvwrv d glihuhqwhv idfwruhv txh rv lq xhqfldp sdud ghl{du d rujdql}dêær1 Djudrwlv +4<;7, frqvlghurx txh rv prwlyrv gh dedqgrqr gh xpd rujdql}dêær vh srghp glylglu hp grlv wlsrv= fdxvdv qær qdwxudlv h fdxvdv qdwxudlv1 Dv fdxvdv qær qdwxudlv sdud vdlu ghshqghp gd hvwuxwxud lqwhuqd gd rujdql}dêær wdlv frpr idowd gh shuvshfwlyd gh surprêær/ vdwlvidêær qr wudedokr/ sureohpdv gh uhodflrqdphqwr frp rv frohjdv/ hwf1 Dv ud}øhv qdwxudlv sdud ghl{du d rujdql}dêær qær ghshqghp gd hvwuxwxud lqwhuqd gd rujdql}dêær/ h vær sru h{hpsor dsrvhqwdgruld h edl{d pìglfd1 Xp ixqflrqäulr txh vh dsrvhqwd gh irupd qdwxudo gd rujdql}dêær dsöv dwlqjlu d lgdgh sdud vh uhirupdu qær srgh vhu djuxsdgr frp dtxhohv txh ghl{dp d rujdql}dêær sru ud}øhv pìglfdv1 Dvvlp/ hp jhudo/ vær frqvlghudgdv wuív wd{dv glihuhqwhv gh vdðgdv uhodflrqdgdv/ uhvshfwlydphqwh/ frp d hvwuxwxud lqwhuqd gd rujdql}dêær/ d dsrvhqwdgruld h dv txhvwøhv pìglfdv1 Frq0 wuduldphqwh ãv vdðgdv sru ud}øhv qdwxudlv/ dv vdðgdv sru fdxvdv qær qdwxudlv srghp/ hp sduwh/ vhu frqwurodgdv shorv jhvwruhv/ phokrudqgr dv shuvshfwlydv gh surprêær/ dv frqglêøhv gh wudedokr h gh irupdêær1 H{lvwhp lqýphurv hvwxgrv gh SUK txh dqdolvdudp dv txhvwøhv uhodflrqdgdv frp dv vdðgdv +Ydvvlolrx/ 4<:9> Djudrwlv/ 4<;7> \dgdydool h rxwurv/ 5335,1 Sdud hvwxgdu d hyroxêær grv vlvwhpdv gh UK +grfhqwh h qær grfhqwh, gd IFXO ì fuxfldo r hvwxgr gdv vdðgdv/ srlv vær hvwdv txh/ qrv ýowlprv dqrv/ wíp frqwurodgr d vxd hyroxêær1 Fdvr qær h{lvwdp dowhudêøhv surixqgdv qrv vlvwhpdv gh UK/ d lq xíq0 fld gdv vdðgdv qd hyroxêær gd IFXO luä dxphqwdu dwhqghqgr dr uhgx}lgr qýphur gh uhfuxwdphqwrv h gh surprêøhv1 Frpr judqgh sduwh grv ixqflrqäulrv/ hvshfldophqwh qd fduuhlud grfhqwh/ vh dsur{lpd gd lgdgh gd uhirupd/ kdyhuä xp qdwxudo lqfuhphqwr qr qýphur gh vdðgdv1 D shufhqwdjhp gh vdðgdv sru dsrvhqwdêær whp ylqgr d dxphqwdu gh irupd uäslgd h/ qrv suö{lprv dqrv/ d dsrvhqwdêær vhuä r sulqflsdo prwlyr gd vdðgd grv ixqflrqäulrv gd IFXO1 Pdlv dlqgd/ d uhgxêær gh grfhqwhv luä frqgx}lu d txh r phvpr vxfhgd sdud rv ixqflrqäulrv qær grfhqwhv1 Frqvhtxhqwhphqwh/ r qýphur gh surprêøhv h gh uhfuxwdphqwrv ì dowdphqwh ghshqghqwh gr qýphur gh vdðgdv1.

(29) 41 SODQHDPHQWR GH UHFXUVRV KXPDQRV. 44. Surprêøhv Dv ydjdv txh vxujhp qd fdwhjruld pdlv edl{d vær xvxdophqwh suhhqfklgdv sru uh0 fuxwdphqwrv/ ylvwr txh dv ydjdv txh vxujhp qdv fdwhjruldv pdlv hohydgdv/ hp jhudo/ vær suhhqfklgdv dwudyìv gh surprêøhv1 Sru rxwur odgr/ dv surprêøhv txh rfruuhp ghylgr dr pìulwr grv ixqflrqäulrv uhgx}hp d srvvlelolgdgh gh xp hpsuhjdgr hflhqwh ghl{du d rujdql}dêær1 H{lvwhp lqýphurv fulwìulrv txh srghuær vhu dgrswdgrv sdud ghqlu dv surprêøhv qrphdgdphqwh= ixqflrqäulr frp pdlv whpsr qd fdwhjruld> surprêær ì dohdwöuld> surprêær gr ixqflrqäulr txh dwlqjlx fhuwrv fulwìulrv gh hflíqfld frqmxjdgr frp xp whpsr pðqlpr gh vhuylêr qd fdwhjruld1 R sulphlur fruuhvsrqgh d xvdu r whpsr gh vhuylêr dshqdv frpr fulwìulr gh surprêær r txh ohyd d txh d rujdql}dêær qær whqkd txdotxhu frqwuror1 R vhjxqgr ì xp fulwìulr txh shuplwh txh d jhuíqfld surpryd txdotxhu ixqflrqäulr ã vxd hvfrokd/ r txh wdpeìp qær ì ghvhmäyho1 Hp jhudo ì suhihuðyho frqvlghudu r whufhlur fulwìulr1 D jhuíqfld gh xpd rujdql}dêær ghyh rswdu sru xvdu sroðwlfdv gh surprêær txh pdqwhqkdp rv ixqflrqäulrv dowdphqwh prwlydgrv sdud txh hvwhv pdqwhqkdp dowrv ðqglfhv gh surgxwlylgdgh h txh rv ixqflrqäulrv hflhqwhv qær dedqgrqhp d rujdql}dêær1 Uhfuxwdphqwrv Sdud uhvsrqghu ãv surprêøhv h ãv vdðgdv gh xpd rujdql}dêær/ rv vwrfnv gdv yäuldv fdwhjruldv vær pdqwlgrv qrv qðyhlv ghvhmdgrv hp txdotxhu dowxud sru xp surfhvvr fkdpdgr uhfuxwdphqwr1 Vær dv sroðwlfdv gh uhfuxwdphqwr txh shuplwhp d xpd rujd0 ql}dêær pdqwhu/ dxphqwdu rx glplqxlu rv vhxv vwrfnv1 R x{r gr uhfuxwdphqwr srgh/ gh fhuwd irupd/ vhu frqwurodgr shorv jhvwruhv gd rujdql}dêær1 R uhfuxwdphqwr srgh vhu ihlwr gh glyhuvdv irupdv1 Dv ydjdv srghp vhu suhhqfklgdv frqvrdqwh hodv yær vxujlqgr rx srgh vhu shuplwlgd d vxd dfxpxodêær1 Qhvwh fdvr/ r vhx suhhqfklphqwr rfruuh hp shuðrgrv hvshfðfrv rx vhpsuh txh r qýphur wrwdo gdv ydjdv dofdqêd xp ghwhuplqdgr qðyho hvshfðfr/ gh irupd/ sru h{hpsor/ d plqlpl}du r fxvwr1 R uhfuxwdphqwr srgh.

(30) 45. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. vhu ihlwr shod suösuld rujdql}dêær rx sru dojxpdv djíqfldv h{whuqdv gh irupd d hylwdu dwudvrv h fxvwrv hohydgrv1 Dshvdu gh dv surprêøhv h gh rv uhfuxwdphqwrv srghuhp vhu gh fhuwd irupd frq0 wuroäyhlv shorv jhvwruhv wdo qær vxfhgh/ hp jhudo/ frp dv vdðgdv txh srghuær rfruuhu ghylgr d ghflvøhv shvvrdlv1 Rv x{rv txh rfruuhp qxpd rujdql}dêær lq xhqflduær gh irupd ghflvlyd d hvfrokd grv prghorv d dgrswdu1 Hvwhv srghp vhu fodvvlfdgrv gd vhjxlqwh irupd= x{rv hvwrfävwlfrv h ghwhuplqðvwlfrv> x{rv sxvk h sxoo> whpsr glvfuhwr h frqwðqxr1. Iox{rv hvwrfävwlfrv h ghwhuplqðvwlfrv Frqvlghud0vh frpr x{r ghwhuplqðvwlfr txdotxhu x{r hp txh qær h{lvwh txdotxhu lqfhuwh}d1 Dvvlp/ ghsdud0vh frp xp x{r ghvwh wlsr txdqgr/ sru h{hpsor/ xpd rujd0 ql}dêær {d r qýphur gh lqglyðgxrv rx d shufhqwdjhp gh lqglyðgxrv gh xpd fdwhjruld txh luä vhu surprylgd1 Qhvwhv fdvrv/ frpr qær kdyhuld txdotxhu lqfhuwh}d rv prghorv hvwdwðvwlfrv vhuldp uhohjdgrv sdud vhjxqgr sodqr1 Sru rxwur odgr/ qdv vdðgdv yroxqwäuldv h{lvwh xp qðyho gh lqfhuwh}d hohydgr shor txh hvwdv vær jhudophqwh frqvlghudgdv frpr hvwrfävwlfdv1 Hvwh qðyho gh lqfhuwh}d ì r uhvxowdgr gd frqmxjdêær gh lqýphurv idfwruhv1 Xpd yh} txh dv surprêøhv jhudophqwh ghshqghp gh ghflvøhv gdv dgplqlvwudêøhv h gd fdsdflgdgh grv lqglyðgxrv sdud dwlqjlu fhuwrv remhfwlyrv/ hvwhv vær frqvlghudgdv frpr x{rv hvwrfävwlfrv1 Dgplwlqgr d lqgh0 shqgíqfld grv lqglyðgxrv/ dv vdðgdv srghp vhu prghodgdv shod glvwulexlêær elqrpldo1 Dvvlp/ vh slm uhsuhvhqwdu d suredelolgdgh gh txdotxhu lqglyðgxr gd fdwhjruld l vhu sur0 prylgr ã fdwhjruld m/ hqwær r qýphur hvshudgr gh surprêøhv vhuä ljxdo d slm yh}hv r vwrfn gd fdwhjruld l1 Sru txhvwøhv gh uhdolvpr h jhqhudolgdgh luä frqvlghudu0vh/ frpr ì suäwlfd xvxdo/ rv prghorv frpr hvwrfävwlfrv/ dshvdu gh d dqäolvh fdu frqqdgd ã ghwhuplqdêær grv ydoruhv pìglrv1.

(31) 41 SODQHDPHQWR GH UHFXUVRV KXPDQRV. 46. Iox{rv sxvk h sxo +hpsxuudgr h sx{dgr, Qd hvfrokd grv prghorv ì ixqgdphqwdo yhulfdu txh wlsr gh x{rv srghuä rfruuhu qd rujdql}dêær1 Srghuær rfruuhu grlv wlsrv gh x{rv= sxvk h sxoo1 Xp lqglyðgxr srgh vhu surprylgr dxwrpdwlfdphqwh dr dwlqjlu fhuwrv uhtxlvlwrv1 Qhvwh fdvr/ gl}0vh txh hoh ì hpsxuudgr sdud rxwud fdwhjruld/ shor txh vh hvwä hp suhvhqêd gh xp x{r sxvk1 Qd fduuhlud grfhqwh/ d sdvvdjhp gh dvvlvwhqwh d dx{loldu ì xp x{r sxvk1 R dvvlvwhqwh ì %hpsxuudgr% sdud d fdwhjruld gh dx{loldu dsöv d frqfoxvær gr vhx grxwrudphqwr1 Qrv prghorv fxmdv fdwhjruldv vær ghqlgdv sru lgdgh rx whpsr gh vhuylêr rv x{rv vær gr wlsr sxvk/ srlv d sdvvdjhp gh xpd fdwhjruld sdud d vhjxlqwh ì dxwrpäwlfd dsöv whuhp vlgr fxpsulgrv rv uhtxlvlwrv gh whpsr1 Xp rxwur phfdqlvpr gh surprêær gh xp lqglyðgxr ì r vxujlphqwr gh xpd ydjd qxpd fdwhjruld vxshulru/ r txh rfruuh txdqgr vxujh xpd qryd ydjd qhvvd fdwhjruld1 D ydjd srgh vxujlu txdqgr xp lqglyðgxr ghvvd fdwhjruld vxshulru ì surprylgr d xpd rxwud fdwhjruld rx txdqgr dedqgrqd d rujdql}dêær1 Qhvwh fdvr/ gl}0vh txh r x{r ì gr wlsr sxoo/ srlv r lqglyðgxr irl %sx{dgr% sdud d fdwhjruld vxshulru1 Xpd yh} txh qær id} vhqwlgr shqvdu qd h{lvwíqfld gh ydjdv qr pxqgr h{whulru ã rujdql}dêær hqwær dv vdðgdv ghyhp vhu frqvlghudgdv frpr x{rv sxvk1 Rv uhfuxwdphq0 wrv h dv wudqvlêøhv ghqwur gd rujdql}dêær srghp vhu prghodgdv dwudyìv gh x{rv sxvk h2rx sxoo gh dfrugr frp r vlvwhpd d vhu prghodgr1 Ì lqwhuhvvdqwh yhulfdu d gxdolgdgh h{lvwhqwh hqwuh rv x{rv gh lqglyðgxrv h rv x{rv dvvrfldgrv gh ydjdv1 Gh idfwr/ txdqgr vxujh xpd ydjd qxpd fdwhjruld m h xp lqglyðgxr wudqvlwd gh xpd fdwhjruld l sdud hvvd fdwhjruld m/ d ydjd luä wudqvlwdu gd fdwhjruld m sdud d fdwhjruld l1 Sruwdqwr/ vh r x{r gh lqglyðgxrv iru gr wlsr sxoo hqwær r fruuhvsrqghqwh x{r gh ydjdv vhuä gr wlsr sxvk h uhflsurfdphqwh1 Hvwd gxdolgdgh shuplwh prghodu wrgrv rv vlvwhpdv sru x{rv sxvk 4 gh wudwdphqwr pdwhpäwlfr pdlv vlpsohv1 4Prghod0vh. rv x{rv gh lqglyðgxrv txdqgr hvwhv iruhp gr wlsr sxvk h txdqgr vær gr wlsr sxoo. prghod0vh r fruuhvsrqghqwh x{r gh ydjdv1.

(32) 47. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. Whpsr glvfuhwr h frqwðqxr Hp txdotxhu vlvwhpd h{lvwh/ dr orqjr gr whpsr/ d rfruuíqfld gh x{rv wdlv frpr uhfuxwdphqwrv/ vdðgdv h wudqvlêøhv hqwuh fdwhjruldv1 Qr wudwdphqwr ghvwhv x{rv/ r whpsr srgh vhu frqvlghudgr frpr glvfuhwr rx frqwðqxr1 Qxpd Lqvwlwxlêær gh Hqvlqr Vxshulru/ sru h{hpsor/ rv doxqrv fkhjdp txdvh vhpsuh qr lqðflr gr dqr ohfwlyr h d judqgh pdlruld whuplqd r vhx fxuvr qr qdo grv dqrv ohfwlyrv1 Qr hqwdqwr/ dv vdðgdv h dv hqwudgdv gh ixqflrqäulrv/ grfhqwhv h qær grfhqwhv/ srgh rfruuhu hp txdotxhu shuðrgr gr dqr1 Rv x{rv grv doxqrv vær frqvlghudgrv frpr x{rv gh whpsr glvfuhwr h rv grv ixqflrqäulrv frpr frqwðqxrv51 Gh xp prgr jhudo/ r wudwdphqwr glvfuhwr shuplwh rewhu prghorv pdlv vlpsohv pdv pdlv didvwdgrv gd uhdolgdgh1 Frqwxgr/ qd pdlruld gdv vlwxdêøhv/ rv prghorv glvfuhwrv rihuhfhp uhvxowdgrv vdwlvidwöulrv1 D rsêær shor frqwðqxr/ vhp gýylgd pdlv uhdo/ sru sduwlu gr sulqfðslr gh txh hp txdotxhu gld vh srgh gdu xpd hqwudgd/ xpd vdðgd rx xpd pxgdqêd gh fdwhjruld iruqhfh phokruhv uhvxowdgrv/ pdv ì pdlv vhqvðyho d lpshuihlêøhv grv gdgrv h qhfhvvlwd gh xpd pdlru txdqwlgdgh gh gdgrv h gh erd txdolgdgh1 R dfhvvr d phlrv lqirupäwlfrv fdgd yh} pdlv srwhqwhv ohyrx d xp dxphqwr gd whqgíqfld gh vh xvdu r frqwðqxr1 Qr hqwdqwr/ r wudwdphqwr glvfuhwr frqwlqxd d whu d vxd lpsruwåqfld hp vlwxdêøhv hp txh vh whp gh xvdu gdgrv srxfr äyhlv rx uhihuhqwhv d shuðrgrv klvwöulfrv pxlwr fxuwrv/ srlv rv prghorv glvfuhwrv uhyhodp pdlru urexvwh}1 Qr hvwxgr vreuh d IFXO/ whqgr hp frqwd txh d txdqwlgdgh gh gdgrv glvsrqðyhlv qær ì pxlwr hohydgd/ d rsêær pdlv ud}räyho/ sru xpd txhvwær gh urexvwh}/ vhuä d gh wudwdu r whpsr gh irupd glvfuhwd h qær gh irupd frqwðqxd1 Wrpdgd hvwd rsêær ì lpsruwdqwh txh txh dtxl sdwhqwh r txh vljqlfd hvwh wudwdphqwr glvfuhwr/ qr fdvr gh SUK1 D rsêær shor wudwdphqwr glvfuhwr ohyrx d frqvlghudu shuðrgrv gh xp dqr/ hp txh vh uhjlvwrx r qýphur gh rfruuíqfldv dr orqjr gh fdgd shuðrgr/ qrphdgdphqwh 5Qrwh0vh. txh/ hp whuprv whöulfrv/ txdotxhu x{r ì glvfuhwr srlv dshqdv srghp vhu uhjlvwdgrv qxp. frqmxqwr gh lqvwdqwhv txh irupdp xp frqmxqwr qxphuäyho1.

(33) 41 SODQHDPHQWR GH UHFXUVRV KXPDQRV. 48. uhfuxwdphqwrv/ vdðgdv h pxgdqêdv gh fdwhjruldv1 Gl}hu txh hp 5339 irudp uhfuxwdgrv 9 dx{lolduhv qær vljqlfd txh wrgrv hohv whqkdp vlgr uhfuxwdgrv qr phvpr gld rx hp gldv ghvfrqkhflgrv/ pdv vlp txh dr orqjr gr shuðrgr uhsuhvhqwdgr irudp uhfuxwdgrv 9 dx{lolduhv1 Gr phvpr prgr/ xpd suhylvær txh dsrqwh sdud d vdðgd gh 8 dx{lolduhv qr dqr gh 5345 qær vljqlfd txh vhmd suhylvðyho txh wrgrv dedqgrqdp d rujdql}dêær qr gld 64 gh Gh}hpeur gh 5345/ pdv vlp txh dr orqjr gr dqr gh 5345 ì suhylvðyho d vdðgd gh 8 dx{lolduhv1. 4161 Fdghldv gh Pdunry1 Dv fdghldv gh Pdunry vær xpd gdv ihuudphqwdv pdwhpäwlfdv xvdgdv sdud ghv0 fuhyhu h2rx lqyhvwljdu d glqåplfd gh xp vlvwhpd +sru h{hpsor/ hp UK gh rujdql0 }dêøhv/ qr vlvwhpd qdqfhlur/ qrv vhuylêrv gh vdýgh h gh hgxfdêær, hp txh d hyroxêær gr whpsr gr vlvwhpd ì ghvfulwd dwudyìv gh xp frqmxqwr gh yduläyhlv dohdwöuldv1 Qrwh0vh txh dv yduläyhlv vær frqvlghudgdv dohdwöuldv vh rv vhxv ydoruhv qær sxghuhp vhu suhglwrv frp fhuwh}d h whpsr glvfuhwr vljqlfd txh r hvwdgr gr vlvwhpd srgh vhu ylvwr vrphqwh hp dojxqv lqvwdqwhv hp yh} gh r vhu hp txdotxhu lqvwdqwh1 Xpd fdghld gh Pdunry ì xpd vhtxíqfld [ > [2 > = = = gh yduläyhlv dohdwöuldv1 R frqmxqwr gh ydoruhv txh hodv srghp dvvxplu ì fkdpdgr gh hvsdêr gh hvwdgrv/ rqgh [w ghqrwd r hvwdgr gr surfhvvr qr whpsr w1 Vh d glvwulexlêær gh suredelolgdgh gh [w / frqglflrqdo drv hvwdgrv sdvvdgrv/ ì xpd ixqêær dshqdv gh [w3 / hqwær= +414, S E[w ' {w m [f ' {f > [ ' { > = = = > [w3 ' {w3 ' S E[w ' {w m [w3 ' {w3 > rqgh i[l ' {l > l ' f> > = = = > wj vljqlfd txh d yduläyho dohdwöuld [l dvvxph r ydoru {l qr lqvwdqwh l/ h S ì d glvwulexlêær gh suredelolgdgh frqglflrqdgd gr vlvwhpd1 D h{suhvvær S E[w ' {w m [w3 ' {w3 ì ghvljqdgd sru suredelolgdgh gh wudqvlêær txh ghvfuhyh d srvvlelolgdgh gr vlvwhpd srghu wudqvlwdu sdud r hvwdgr {w qr suö{lpr lqvwdqwh w gdgr txh qr lqvwdqwh w vh hqfrqwud qr hvwdgr {w3 1 D htxdêær 414 loxvwud d suredelolgdgh gh Pdunry/ rx vhmd/ d suredelolgdgh gr vlvwhpd hvwdu qr hvwdgr {w > qr lqvwdqwh w/ ì lqghshqghqwh grv hvwdgrv rfxsdgrv dqwhv gr lqvwdqwh w 1 Lvwr vljqlfd txh d.

(34) 49. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. suredelolgdgh gr hvwdgr gr surfhvvr gh Pdunry qr suö{lpr lqvwdqwh vhuä ghwhuplqdgd dshqdv shor hvwdgr dfwxdo h ì lqghshqghqwh gd hyroxêær klvwöulfd grv hvwdgrv dqwhulruhv gr vlvwhpd1 Ghqrwdqgr sru slmw d suredelolgdgh gd wudqvlêær gh xp vlvwhpd gr hvwdgr l sdud r hvwdgr m/ d pdwul} gh wudqvlêær ì ghqlgd sru= 5 s = = = sNw 9 w 9 1 111 111 +415, w ' 9 11 7 sNw = = = sNNw. 6. : : :> 8. rqgh N ì r qýphur gh hvwdgrv srvvðyhlv sdud r vlvwhpd1 Hvwd pdwul} w whp dv vhjxlqwhv sursulhgdghv= f slmw h. N [. slmw ' > l> m ' > = = = > N=. m'. Qrwh0vh txh dojxqv dxwruhv xvdp d ghvljqdêær gh fdghld gh Pdunry txdqgr dv sur0 edelolgdghv gh wudqvlêær vær lqghshqghqwhv gr whpsr1 Vh dv suredelolgdghv gh wudqvlêær yduldp frp r whpsr/ d fdghld ghvljqd0vh sru fdghld gh Pdunry qær krprjìqhd1 Ghqrwh0vh hvwdv suredelolgdghv sru tw ' Evw > = = = > vNw / rqgh d frpsrqhqwh vlw > l ' > = = = > N> uhsuhvhqwd d suredelolgdgh gr vlvwhpd hvwdu qr hvwdgr l qr lqvwdqwh w S frp N l' vlw ' Ew ' f> > = = =1 Lvwr shuplwh frqfoxlu txh= tw ' tw3 w3 > w ' > 2> = = = =. Sdud xp surfhvvr hp txh d pdwul} ì hvwdflrqäuld +w ' ,/ d uhodêær hqwuh d suredelolgdgh gr hvwdgr lqlfldo tf h tw srgh vhu rewlgd gh irupd uhfxuvlyd d sduwlu gd htxdêær dqwhulru r txh frqgx} d= tw ' tf w > w ' f> > = = = > rqgh ì d pdwul} gh wudqvlêær sdud xp sdvvr h w ì d pdwul} gh wudqvlêær sdud w sdvvrv1.

(35) 41 SODQHDPHQWR GH UHFXUVRV KXPDQRV. 4:. Ghsrlv gh dsuhvhqwdu dojxqv frqfhlwrv hvvhqfldlv gd whruld gdv Fdghldv gh Pdunry/ qd suö{lpd vhfêær ghvwdfd0vh d vxd dsolfdêær qd prghodêær grv UK1. 4171 Dsolfdêær gh fdghldv gh Pdunry qd prghodêær gh UK1 Xpd hvwuxwxud gh UK srgh vhu frqyhqlhqwhphqwh ghvfulwd frpr xp vlvwhpd glqåplfr dohdwöulr gh vwrfnv h x{rv1 R qýphur gh lqglyðgxrv hp fdgd fdwhjruld vhuä ghvljqdgr sru vwrfn gd fdwhjruld rx wrwdo gh hihfwlyrv gd fdwhjruld1 Vh krxyhu N fdwhjruldv/ r vwrfn Qlw uhsuhvhqwduä r qýphur hvshudgr gh lqglyðgxrv qd fdwhjruld l qr lqvwdqwh w h w ' EQw > = = = => QNw uhsuhvhqwduä r frqmxqwr gh vwrfnv gd rujdql}dêær qr lqvwdqwh w1 Frpr fdgd lqglyðgxr gd rujdql}dêær vö srghuä shuwhqfhu d xpd ýqlfd fdwhjruld hqwær S r qýphur wrwdo gh hihfwlyrv/ Qw > ì ghqlgr sru Qw ' N l' Qlw = R yhfwru grv vwrfnv. w iruqhfh xpd %irwrjudd% gd rujdql}dêær qr lqvwdqwh w pdv qdgd qrv gl} vreuh d. hyroxêær ixwxud ghvwd1 Gh prgr d ghvfuhyhu d glqåplfd whpsrudo grv vwrfnv/ ì suhflvr frpsohphqwä0orv frp x{rv/ qrphdgdphqwh frpr ì txh rv lqglyðgxrv vh pryhp gh xpd fdwhjruld sdud rxwud1 Rv x{rv vær frqvwlwxðgrv sru wuív frpsrqhqwhv/ wudqvlêøhv/ vdðgdv h uhfuxwdphqwrv1 Dv wudqvlêøhv srghp vhu ylvwdv frpr vhqgr rv lqglyðgxrv txh vh pryhp hqwuh glihuhqwhv fdwhjruldv ghqwur gd rujdql}dêær1 Frqvlghudp0vh frpr vdðgdv rv lqglyðgxrv txh dedqgrqdp d rujdql}dêær sru glyhuvdv ud}øhv wdlv frpr pruwh/ lq0 ydolgh}/ ghvshglphqwr2ghplvvær/ dsrvhqwdêær/ hqtxdqwr r uhfuxwdphqwr srgh vhu ylvwr frpr xpd surprêær gh xp lqglyðgxr irud gd rujdql}dêær sdud xpd gdgd fdwhjruld gd rujdql}dêær1 Dvvlp/ frqvlghudqgr r lqwhuydor xqlwäulr Ew > w/ r. x{r Plmw ' slm Ql>w3 /. l> m ' > = = = > N> uhsuhvhqwd r qýphur hvshudgr gh lqglyðgxrv txh vh pryhp gd fdwh0 jruld l sdud d fdwhjruld m qhvwh lqwhuydor/ rqgh slm 6 ì d suredelolgdgh gh wudqvlêær gh xp lqglyðgxr txh qr lqvwdqwh w hvwä qd fdwhjruld l h txh qr lqvwdqwh w shuwhqfh ã fdwhjruld m +Eduwkrorphz h rxwurv/ 4<<4,1 Dshvdu gh whrulfdphqwh qær h{lvwluhp 6Frqvlghud0vh. vær frqvwdqwhv1. txh dv suredelolgdghv gh wudqvlêær/ ehp frpr dv wd{dv gh vdðgd h gh uhfuxwdphqwrv/.

(36) 4;. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. uhvwulêøhv ã hvfrokd grv lqwhuydorv gh whpsr xqlwäulrv/ hvwhv ghyhuær vhu hvshflfdgrv gh dfrugr frp dv qhfhvvlgdghv gh sodqhdphqwr gd rujdql}dêær1 D pdwul} irupdgd sru wrgrv rv x{rv Plmw > l ' > = = = > N/ ghvljqd0vh sru pdwul} gh wudqvlêøhv h ghqrwd0vh sru w 1 Hvwd pdwul} ì xvxdophqwh hvsduvd srlv/ sru h{hpsor/ vh iru lpsrvvðyho uhjuhglu qd fduuhlud klhuäutxlfd whp0vh txh Plmw ' f txdqgr l A m1 D pdwul} w srghuä whu wrgrv rv hohphqwrv Plmw > frp m 9' l n > qxorv/ vlwxdêær txh rfruuh txdqgr dv fdwhjruldv vær ghqlgdv shod lgdgh grv lqglyðgxrv rx shor vhx whpsr gh vhuylêr/ h hp txh vh frqvlghud xp dqr frpr shuðrgr gh whpsr1 D pdwul} w dsuhvhqwd dshqdv rv x{rv lqwhuqrv ã rujdql}dêær/ shor txh ì qhfhvväulr frqvlghudu rv x{rv hqwuh d rujdql}dêær h r pxqgr h{whulru/ rx vhmd/ rv uhfuxwdphqwrv h dv vdðgdv1 Qrwh0vh txh dv vdðgdv srghp vhu frqvlghudgdv frpr d EN n 0ìvlpd fdwhjruld1 Dglflrqdophqwh/ dgplwlqgr txh d pdwul} w ghqlgd hp 415/ ì lqyduldqwh qr whpsr/ whp0vh txh=. +416,. 5. 9 s 9 9 s2 '9 9 11 9 1 7 sN. = = = sN = = = s2N 11 === 1 = = = sNN. 6 s>Nn : : s2>Nn : :1 11 : : 1 8 sN>Nn. Ghqrwdqgr djrud dv N sulphludv froxqdv sru h d ýowlpd froxqd sru ' Ez > = = = > zN / txh uhsuhvhqwd r yhfwru gdv wd{dv gh vdðgd hp txh zl l ' > = = = > N/ srgh vhu ylvwr frpr d suredelolgdgh gh xp lqglyðgxr txh hvwä qd fdwhjruld l dedqgrqdu d rujdql}dêær gxudqwh xp lqwhuydor xqlwäulr1 Frqvhtxhqwhphqwh yhulfd0vh txh= N [. slm n zl ' > l ' > = = = > N=. m'. Vhjxqgr Eduwkrorphz h rxwurv +4<<4,/ xp vlvwhpd gh UK srgh vhu ghvfulwr dwudyìv gd htxdêær= +417,. w ' w3 E n h n {Qw h>.

(37) 41 SODQHDPHQWR GH UHFXUVRV KXPDQRV. 4<. rqgh {Qw ' Qw Qw3 ì r qýphur gh oxjduhv fuldgrv qxpd rujdql}dêær txh hvwhmd hp h{sdqvær h h ' Eu > = = = > uN ì ghvljqdgr sru yhfwru gdv wd{dv gh uhfuxwdphqwr/ rqgh ul ì d suredelolgdgh gh xp lqglyðgxr vhu uhfuxwdgr sdud d fdwhjruld l1 Dvvlp/ whp0vh txh SN l' ul ' = Frpr ì xp yhfwru froxqd hqwær h ì xpd pdwul} fxmr hohphqwr E hlm ' zl um 1 Whqgr hp frqwd txh r qýphur wrwdo gh uhfuxwdphqwrv ì ghqlgr sru Uw ' {Qw nQ w3 / hqwær d htxdêær 417 ì htxlydohqwh d= +418,. w ' w3 n Uw h>. rqgh +w ' Uw h ì r yhfwru grv uhfuxwdphqwrv sdud fdgd fdwhjruld gd rujdql}dêær1 Grlv fdvrv sduwlfxoduhv gd htxdêær 418 vær rv vhjxlqwhv= txdqgr qær kä oxjdu ã ghvsurprêær/ rx vhmd/ slm ' f sdud l A m/ shor txh ì xpd pdwul} wuldqjxodu vxshulru> txdqgr/ doìp gd uhvwulêær dqwhulru/ dv surprêøhv vö srghp rfruuhu sdud d fodvvh lphgldwdphqwh vxshulru/ rx vhmd= slm ' f frp m A l n h m ? l/ rqgh l> m ' > = = = > N= Qhvwh fdvr/ vær qxorv wrgrv hohphqwrv gh txh qær shuwhqêdp ã gldjrqdo sulqflsdo rx ã vxe0gldjrqdo vxshulru1 Hvwdv pdwul}hv vær ghyhudv revhuydgdv hp dqäolvhv gh vlvwhpdv gh UK gh lqýphudv rujdql}dêøhv1 Dv suredelolgdghv gh wudqvlêær slm srghp vhu hvwlpdgdv d sduwlu grv gdgrv klvwöulfrv grv vwrfnv h x{rv xvdqgr r pìwrgr gd pä{lpd yhurvlplokdqêd S plmw s lm ' Sw > w qlw. rqgh plmw ì r qýphur revhuydgr gh lqglyðgxrv txh pxgd gd fdwhjruld l sdud d fdwhjruld. m gxudqwh r shuðrgr Ew > w/ qlw ì r qýphur revhuydgr gh lqglyðgxrv qd fdwhjruld l qr lqvwdqwh w/ h d vrpd ì hihfwxdgd vreuh r shuðrgr gh whpsr gh gdgrv klvwöulfrv glvsrqðyhlv1 Dv suredelolgdghv gh vdðgdv h gh uhfuxwdphqwrv srghp vhu hvwlpdgdv gd phvpd irupd txh dv suredelolgdghv gh wudqvlêær1.

(38) 53. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. R prghor ghqlgr dwudyìv gd htxdêær 418/ srgh vhu xvdgr sdud suhyhu shuv grv UK gdv rujdql}dêøhv wdlv frpr/ sru h{hpsor/ glvwulexlêøhv grv lqglyðgxrv shodv glih0 uhqwhv fdwhjruldv/ dwudyìv gr yhfwru w / idfh d glyhuvdv frqglêøhv lqlfldlv f / sroðwlfdv gh wudqvlêøhv lqwhuqdv h gh uhfuxwdphqwrv1 Sru rxwur odgr/ r prghor srgh wdpeìp vhu xvdgr sdud dqdolvdu txh sroðwlfdv gh surprêær h gh uhfuxwdphqwr vær qhfhvväuldv sdud pdqwhu xpd ghwhuplqdgd hvwuxwxud gh sursruêær gh lqglyðgxrv qdv glyhuvdv fdwhjruldv iQlw @Qw > l ' > = = = > Nj sdud xpd rujdql}dêær hp txh r vwrfn wrwdo hvwä {r E{Qw ' f/ sdud xpd rujdql}dêær hp h{sdqvær E{Qw A f rx hp frqwudfêær E{Qw ? f1 Frqiruph ghvfulwr dqwhulruphqwh/ rv x{rv gh wudedokdgruhv vær fodvvlfdgrv hp x{rv sxvk h sxoo 1 Rv prghorv gh Pdunry vær dghtxdgrv sdud suhyhu r frpsruwdphqwr ixwxur grv vlvwhpdv gh UK gh rujdql}dêøhv hp txh rv x{rv vær gr wlsr sxvk/ rqgh qær kä uhvwulêær gh glvsrqlelolgdgh gh ydjdv/ gh surprêøhv h gh uhfuxwdphqwrv/ sru h{hpsor/ rv ixqflrqäulrv vær dxwrpdwlfdphqwh frorfdgrv +surprylgrv, sdud fdwhjr0 uldv vxshulruhv dsöv xp shuðrgr hvshfðfr gh whpsr gh vhuylêr rx ghsrlv gh frqfoxlu ghwhuplqdgd irupdêær +Eduwkrorphz h rxwurv/ 4<<4,1 Qdv rujdql}dêøhv hp txh dv surprêøhv h rv uhfuxwdphqwrv vö rfruuhp sdud suhhqfkhu ydjdv/ rx vhmd/ txdqgr vh suhwhqgh txh rv vwrfnv iQlw > l ' > = = = > Nj vh pdqwhqkdp {rv/ hp jhudo/ vær xvdgrv prghorv gh uhqrydphqwr1 Qd pdlru sduwh gdv rujdql}dêøhv/ hvwhv grlv wlsrv gh x{rv frh{lvwhp/ r txh vh wudgx} qxp dxphqwr vljqlfdwlyr gd frpsoh{lgdgh qd prghodêær gd glqåplfd grv UK1. 4181 Olplwdêøhv qr xvr gdv Fdghldv gh Pdunry1 Dsuhvhqwdp0vh gh vhjxlgd dojxpdv gdv olplwdêøhv qr xvr gdv Fdghldv gh Pdunry qd prghodêær gh vlvwhpdv gh UK1 Rv prghorv gh Pdunry vær fodvvlfdgrv frpr %ghvfulwlyrv% rx %h{sorudwöulrv%/ srlv qær shuplwhp rswlpl}du rv uhvxowdgrv1 Qær shu0 plwhp/ sru h{hpsor/ surpryhu d plqlpl}dêær grv fxvwrv rshudflrqdlv rx d pd{lpl}d0 êær gd surgxwlylgdgh1 Sxunlvv +4<9<,/ Exgqlfn +4<;;, h Vhwokduh +533:, vær dojxqv grv wudedokrv txh uhfruuhp d prghorv gh rswlpl}dêær sdud prghodu vlvwhpdv gh UK1 Hp.

(39) 51 LQIHUÍQFLD ED\HVLDQD. 54. vhjxqgr oxjdu/ rv prghorv gh Pdunry vær olqhduhv qr vhqwlgr gh txh qær lqfrusrudp r phfdqlvpr gh ihhgedfn +Eduwkrorphz h rxwurv/ 4<<4,/ txh srgh vhu lpsruwdqwh qd suäwlfd1 Vær uhodwdgrv hvwxgrv txh ghprqvwudp txh rv prghorv qær olqhduhv wíp phokru ghvhpshqkr txh rv prghorv olqhduhv vlpsohv +\rxqj h Ydvvlolrx/ 4<:7,1 Ilqdophqwh/ kä xpd h{ljíqfld gr wdpdqkr gd dprvwud sdud qv hvwdwðvwlfrv1 R qýphur gh shvvrdv hp fdgd fdwhjruld qær srgh vhu pxlwr shtxhqr/ fdvr frqwuäulr r fäofxor gdv suredelolgdghv gh wudqvlêær whqgh d vhu lqvwäyho1 Sdud vlvwhpdv gh UK gh shtxhqdv glphqvøhv ì pdlv dghtxdgr r uhfxuvr d wìfqlfdv gh vlpxodêær/ wdlv frpr Prqwh Fduor/ rqgh dv wudqvlêøhv lqglylgxdlv srghp vhu vlpxodgdv h{solflwdphqwh hp yh} gh vh wudedokdu dshqdv frp rv lqglyðgxrv djuhjdgrv hp fdwhjruldv1 Zdqj +5338, dsuhvhqwd xpd uhylvær grv prghorv h{lvwhqwhv sdud r SUK h h{sorud r srwhqfldo gd prghodêær sdud dv fduuhludv plolwduhv1 Frqvlghud txh rv prghorv xvdgrv qr SUK vh srghp glylglu hp txdwur juxsrv= prghorv gh fdghld gh Pdunry/ prghorv gh vlpxodêær/ prghorv gh rswlpl}dêær h prghorv gh jhvwær gd fdghld gh iruqhflphqwr +vxsso| fkdlq pdqdjhphqw, dwudyìv gh vlvwhpdv glqåplfrv1 Sdud fdgd xp ghvwhv wlsrv gh prghorv/ ghvwdfd r irupdolvpr pdwhpäwlfr vxemdfhqwh h rv frqfhlwrv/ h glvfxwh dv srvvðyhlv olplwdêøhv1 Xvdqgr vlvwhpdv glqåplfrv/ dsuhvhqwd xpd shuvshfwlyd gh prghodêær gd fduuhlud plolwdu sdud dv iruêdv dupdgdv dxvwudoldqdv/ h hp sduwlfxodu sdud r H{ìuflwr1. 51 Lqihuíqfld ed|hvldqd. Qhvwd vhfêær dsuhvhqwd0vh xpd euhyh uhylvær vreuh rv sulqflsdlv frqfhlwrv hqyroylgrv qr surfhglphqwr gh lqihuíqfld ed|hvldqd/ ghvfuhyhp0vh rv pìwrgrv gh dprvwudjhp Jleev h gh Phwursrolv0Kdvwlqjv/ dsuhvhqwdp0vh fulwìulrv txh shuplwhp dydoldu rx qær d frqyhujíqfld gh fdghldv vlpxodgdv h sru ýowlpr vær hihfwxdgdv dojxpdv frqvlghudêøhv vreuh dvshfwrv frpsxwdflrqdlv1.

(40) 55. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. 5141 Frqfhlwrv Ixqgdphqwdlv1 Xp sureohpd lpsruwdqwh qd lqihuíqfld hvwdwðvwlfd ì d hvwlpdêær grv sduåphwurv gh xp prghor/ ghgx}lgrv d sduwlu gh xp frqmxqwr gh gdgrv1 Jhudophqwh/ dv lqihuíqfldv vreuh rv sduåphwurv txh vh edvhldp hp pìwrgrv hvwdwðvwlfrv foävvlfrv frqvlvwhp qd rewhqêær gh hvwlpdgruhv gh pðqlprv txdgudgrv rx hvwlpdgruhv gh pä{lpd yhurvlpl0 okdqêd h gd vxsrvlêær gh sursulhgdghv dvvlpswöwlfdv sdud hvvhv hvwlpdgruhv1 Qd derugdjhp ed|hvldqd/ holplqd0vh r xvr gh sursulhgdghv dvvlpswöwlfdv h drv sduåphwurv vær dwulexðgdv glvwulexlêøhv gh suredelolgdgh/ qær h{lvwlqgr glvwlqêær ixq0 gdphqwdo hqwuh txdqwlgdghv revhuyäyhlv h sduåphwurv gh xp prghor hvwdwðvwlfr/ srlv wrgrv vær frqvlghudgrv txdqwlgdghv dohdwöuldv +Jlonv h rxwurv/ 4<<9,1 D xwlol}dêær gh lqirupdêær d sulrul hp lqihuíqfld ed|hvldqd uhtxhu d hvshflfdêær gdv glvwulexlêøhv d sulrul sdud rv glihuhqwhv sduåphwurv gr prghor1 Hvwdv glvwulexlêøhv uh hfwhp r frqkhflphqwr txh vh whp vreuh rv sduåphwurv ghvfrqkhflgrv dqwhv gh dydoldu rv gdgrv +Er{ h Wldr/ 4<<5,1 R frqkhflphqwr d sulrul vreuh rv sduåphwurv ì prglfdgr sru phlr gd ixqêær gh yhurvlplokdqêd/ txh srgh vhu ylvwd frpr d uhsuhvhqwdêær gd lqirupdêær frqwlgd qrv gdgrv vreuh rv sduåphwurv1 Vre r srqwr gh ylvwd ed|hvldqr/ d lqirupdêær glvsrqðyho vreuh xp sduåphwur rx xp yhfwru sdudpìwulfr srgh vhu uhvxplgd suredelolvwlfdphqwh dwudyìv gh xpd glv0 wulexlêær7/ ghqrwdgd sru glvwulexlêær d sulrul E1 D lqirupdêær vreuh srgh vhu dfwxdol}dgd revhuydqgr0vh xpd txdqwlgdgh dohdwöuld ) uhodflrqdgd frp 1 Hvwd dfwxdol}dêær ì frqvhjxlgd frpelqdqgr d sulrul E frp d ixqêær yhurvlplokdqêd O Em) ' s E)m1 Hvwh surfhvvr ì frqkhflgr qr xqlyhuvr hvwdwðvwlfr frpr r whruhpd gh Ed|hv/ h srgh vhu irupdol}dgr gr vhjxlqwh prgr= +514,. s Em) '. frp +515,. s E) '. ]. s E)> g '. X. 7Hvwh. s E)m E s E> ) ' > s E) s E) ]. s E)m E g>. X. whupr vhuä xvdgr gh irupd lqglihuhqfldgd sdud ghvljqdu xpd ixqêær gh suredelolgdgh rx. xpd ixqêær ghqvlgdgh gh suredelolgdgh1.

(41) 51 LQIHUÍQFLD ED\HVLDQD. 56. rqgh X uhsuhvhqwd r hvsdêr sdudpìwulfr1 R ghqrplqdgru gd h{suhvvær 514 qær ghshqgh gh / wruqdqgr0vh dvvlp s E) xpd frqvwdqwh qrupdol}dgrud sdud d glvwulexlêær d srvwhulrul1 Vhqgr dvvlp/ d h{suhvvær 514 srgh vhu uhhvfulwd qd irupd xvxdo= +516,. s Em) 2 s E)m E =. D h{suhvvær 516 ghl{d ehp fodud d lghld gh txh d glvwulexlêær gd srvwhulrul ì iuxwr gd frpelqdêær gdv lqirupdêøhv suryhqlhqwhv grv gdgrv h gdv lqirupdêøhv vxemhfwlydv/ rx vhmd/ d srvwhulrul ì sursruflrqdo ã yhurvlplokdqêd yh}hv d sulrul1 Wrgd d lqihuíqfld uhodwlyd d xp ghwhuplqdgr sduåphwur ì uhdol}dgd xwlol}dqgr0vh d glvwulexlêær d srvwhulrul/ srghqgr hvwd vhu uhvxplgd sru phlr gd pìgld/ gd prgd/ gd phgldqd/ gr ghvylr sdguær/ grv lqwhuydorv gh fuhglelolgdgh h grv lqwhuydorv gh pä{lpd glvwulexlêær d srvwhulrul +Sdxolqr h rxwurv/ 5336,1. Suhylvær Dwudyìv gd glvwulexlêær suhglwlyd ì srvvðyho d rewhqêær gh suhylvøhv gh ixwxudv revhuydêøhv1 Dsöv revhuydu )/ srgh vhu ghvhmäyho suhyhu xpd ixwxud revhuydêær ) sdud r suö{lpr lqvwdqwh/ d txdo wdpeìp hvwä uhodflrqdgd frp dwudyìv gh s E) m 1 Sdud lvvr/ vxsøh0vh txh/ frqglflrqdgr d / ) h ) vær lqghshqghqwhv1 Dvvlp srgh0vh rewhu d glvwulexlêær s E) m) gd vhjxlqwh irupd= . s E) m) '. ]. s E) > m) g. ]. s E) m> ) s Em) g. ]. s E) m s Em) g1. X. '. X. '. X.

(42) 57. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. Ghvwh prgr/ shufheh0vh d fdudfwhuðvwlfd gh dfwxdol}dêær gr prghor1 D glvwulexlêær d srvwhulrul gh / dsöv revhuydu )/ djh frpr d sulrul qr fäofxor gd srvwhulrul qr lqvwdqwh vhjxlqwh/ hp txh ) dlqgd qær irl revhuydgr1. 5151 Pìwrgrv gh Prqwh Fduor yld Fdghldv gh Pdunry1 D glvwulexlêær d srvwhulrul s Em)/ hp jhudo/ qær srgh vhu rewlgd gh irupd h{dfwd srlv qær ì srvvðyho rewhu h{suhvvøhv dqdoðwlfdv sdud rv lqwhjudlv hqyroylgrv1 Sdud xowudsdvvdu hvvhv sureohpdv/ yäuldv hvwudwìjldv srghp vhu frqvlghudgdv/ qrphdgd0 phqwh/ dsur{lpdêøhv ixqgdphqwdgdv hp uhvxowdgrv dvvlpswöwlfrv/ pìwrgrv gh lqwh0 judêær qxpìulfd/ pìwrgrv gh Prqwh Fduor vlpsohv h pìwrgrv gh Prqwh Fduor yld Fdghldv gh Pdunry +PFPF,1 Ghvwh prgr/ hp jhudo/ d lqihuíqfld ì edvhdgd hp dprvwudv rewlgdv shodv glvwulexlêøhv frqglflrqdlv frpsohwdv d srvwhulrul/ xvdqgr surfhvvrv gh vlpxodêær phgldqwh lwhudêøhv txh xwlol}dp rv pìwrgrv PFPF/ frpr r gh dprvwudjhp Jleev +Fdvhod h Jhrujh/ 4<<6,1 Dv glvwulexlêøhv frqglflrqdlv frpsohwdv fruuhvsrqghp ã glvwulexlêær gh xp sduåphwur hvshfðfr/ vhqgr rv rxwurv ydoruhv grv sduåphwurv qr prghor frqvlghudgrv frqkhflgrv rx {dgrv/ h vær qhfhvväuldv sdud fdgd sduåphwur d vhu hvwlpdgr1 Rv pìwrgrv PFPF vær surfhvvrv lwhudwlyrv txh qær id}hp vxsrvlêær vreuh d irupd gd glvwulexlêær d srvwhulrul1 D lghld ghvwhv pìwrgrv ì frqvwuxlu xpd fdghld gh Pdunry/ fxmd glvwulexlêær gh htxloðeulr vh dsur{lph r pä{lpr srvvðyho gd glvwulexlêær d srvwh0 ulrul/ dsöv xp qýphur qlwr gh vlpxodêøhv ghvvd fdghld1 Dsöv xp orqjr h vxflhqwh shuðrgr gh lwhudêøhv/ vhuä dofdqêdgd d fkdpdgd glvwulexlêær d srvwhulrul hvwdflrqäuld1 Txdotxhu dprvwud txh vh wrph ghvwd glvwulexlêær vhuä frqvlghudgd frpr xpd dprvwud gd yhugdghlud glvwulexlêær d srvwhulrul grv sduåphwurv1 Hqwuh rv pìwrgrv gh frqvwuxêær gd fdghld gh Pdunry pdlv xwlol}dgrv/ hvwær rv pìwrgrv gh Phwursrolv0Kdvwlqjv h gh dprvwudjhp Jleev1 Dv ghvfulêøhv gh dperv srghp vhu hqfrqwudgdv/ pdlv ghwdokdgdphqwh/ hp Jdphupdq +4<<:,1.

(43) 51 LQIHUÍQFLD ED\HVLDQD. 58. Pìwrgr gh dprvwudjhp Jleev R pìwrgr gh dprvwudjhp Jleev irl sursrvwr lqlfldophqwh ghqwur gr frqwh{wr gh uhfrqvwuxêær gh lpdjhqv sru Jhpdq h Jhpdq +4<;7,1 Srvwhulruphqwh/ rxwurv wuded0 okrv frpr r gh Jhoidqg h Vplwk +4<<3, frqwulexðudp sdud r ghvhqyroylphqwr ghvwd phwrgrorjld/ uhyhodqgr r vhx srwhqfldo qxpd dpsod jdpd gh dsolfdêøhv hvwdwðvwlfdv1 D lghld ghvvh pìwrgr ì d gh/ vxfhvvlydphqwh/ vh uhwludu dprvwudv gd glvwulexlêær gh fdgd l0ìvlpd frpsrqhqwh gr yhfwru gh sduåphwurv/ vhqgr rv rxwurv ydoruhv grv sduåphwurv qr prghor frqvlghudgrv frqkhflgrv rx {dgrv1 Dvvlp/ r pìwrgr gh dprvwudjhp Jleev ì hvvhqfldophqwh xp hvtxhpd lwhudwlyr gh dprvwudjhp gh xpd fdghld gh Pdunry fxmr qýfohr gh wudqvlêær ì irupdgr shodv glvwulexlêøhv frqglflrqdlv frpsohwdv1 Ì xpd wìfqlfd sdud jhudu yduläyhlv dohdwöuldv gh xpd glvwulexlêær +pdujlqdo, vhp txh vh frqkhêd d vxd ghqvlgdgh1 R pìwrgr suhwhqgh vlpxodu xp sdvvhlr dohdwöulr qr hvsdêr sdudpìwulfr X/ txh frqylumd sdud xpd glvwulexlêær hvwdflrqäuld txh/ hp hvwdwðvwlfd ed|hvldqd/ ì d glvwulexlêær d srvwhulrul1 R pìwrgr gh dprvwudjhp Jleev whp vlgr ýwlo qd uhvroxêær gh sureohpdv pxowlgl0 phqvlrqdlv h ì ghqlgr hp whuprv gh vxeyhfwruhv gh 1 Vhmd r yhfwru gh sduåphwurv glylglgr hp n vxeyhfwruhv/ ' E > = = = > n > h vxsrqkd0vh txh dv glvwulexlêøhv frqgl0 flrqdlv gh fdgd vxeyhfwru +txh srgh vhu xp sduåphwur rx xp yhfwru gh sduåphwurv, l / gdgr wrgrv rv rxwurv/ vhmdp frqkhflgdv1 Hvwdv glvwulexlêøhv vær ghqrplqdgdv glv0 wulexlêøhv frqglflrqdlv frpsohwdv h vær ghqrwdgdv sru= s E m 2 > = = = > n > ) > s2 E2 m >

(44) > = = = > n > ) > = = = > sn En m > = = = > n3 > ) 1 rx gh irupd deuhyldgd= sl El m 3l > ) > l ' > = = = > n/ rqgh 3l ' E > = = = > l3 > ln>===> n uhsuhvhqwd r yhfwru txh vh rewìp gh sru holpl0 qdêær gd l0ìvlpd frpsrqhqwh h ) ì r yhfwru gdv revhuydêøhv1 R pìwrgr gh dprvwudjhp Jleev ì dsuhvhqwdgr qr dojrulwpr 41.

(45) 59. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. Ef Ef 41 Frqvlghudu xp yhfwru lqlfldo txdotxhu Ef ' > = = = > n shuwhqfhqwh dr vxsruwh gd glvwulexlêær1. 51 Hp fdgd lwhudêær l E> = = = > Q El El3 jhudu gh s m 3 > ) > El El El3 El3 El3 > jhudu 2 gh s2 2 m )> > 2 >

(46) > = = = > n El El El3 El3 jhudu El > = = = > n > ) >

(47) gh s

(48)

(49) m > 2 >

(50) 11 1. El El jhudu n gh sn n m 3n > ) > El El El h id}hu ' > = = = > n 1 Dojrulwpr 4= Dprvwudjhp Jleev1. Vhjxqgr Jdphupdq +4<<:,/ ã phglgd txh r qýphur gh lwhudêøhv dxphqwd/ d vh0 txíqfld dsur{lpd0vh gd vxd frqglêær gh htxloðeulr1 Ghvwh prgr/ dvvxph0vh txh d frq0 yhujíqfld ì dwlqjlgd qxpd lwhudêær fxmd glvwulexlêær hvwhmd duelwuduldphqwh suö{lpd gd glvwulexlêær gh htxloðeulr1 Dshvdu gh rv uhvxowdgrv whöulfrv jdudqwluhp d frqyhujíq0 fld gr pìwrgr gh dprvwudjhp Jleev/ d vxd xwlol}dêær qd suäwlfd srgh vhu edvwdqwh frpsolfdgd txdqgr vh whp prghorv pxlwr frpsoh{rv1 Sru rxwur odgr/ qhp vhpsuh ì srvvðyho d dprvwudjhp gluhfwd d sduwlu gdv glv0 wulexlêøhv frqglflrqdlv frpsohwdv ghylgr ãv vxdv irupdv qær frqkhflgdv/ frpsoh{lgdgh rx fxvwr frpsxwdflrqdo hohydgr1 Qhvwh frqwh{wr/ r pìwrgr gh Phwursrolv0Kdvwlqjv ì xpd erd rsêær ghylgr ã vxd h{lelolgdgh h jhqhudolgdgh1 Hvwh pìwrgr irl lqlfldo0 phqwh sursrvwr sru Phwursrolv h/ srvwhulruphqwh/ jhqhudol}dgr sru Kdvwlqjv +4<:3,1 D frpelqdêær hqwuh rv pìwrgrv gh Jleev h Phwursrolv0Kdvwlqjv whp vlgr dpsodphqwh dgrswdgd1.

(51) 51 LQIHUÍQFLD ED\HVLDQD. 5:. Phwursrolv0Kdvwlqjv Qhvwh pìwrgr/ xp ydoru ì jhudgr d sduwlu gh xpd glvwulexlêær dx{loldu h ì dfhlwh frp xpd gdgd suredelolgdgh1 Hvwh phfdqlvpr gh fruuhfêær jdudqwh d frqyhujíqfld gd fdghld sdud d glvwulexlêær gh htxloðeulr txh/ qhvwh fdvr/ ì d glvwulexlêær d srvwhulrul1 Hvwh pìwrgr xwlol}d xpd ixqêær ghqvlgdgh dx{loldu t E=m8/ gh wdo irupd txh/ txdqgr r surfhvvr hvwä qr hvwdgr l > r fdqglgdwr d hvwdgr vhjxlqwh/ W > ì jhudgr d sduwlu ghvvd ixqêær1 R qryr ydoru W ì dfhlwh/ frp suredelolgdgh ghqlgd sru= ; E W t El W A ? vh l t W ml A f 4? > l t W l l W E E > > ' A = fdvr frqwuäulr. frpr r qryr hvwdgr gd fdghld qd lwhudêær l n / rx ì uhmhlwdgr frp suredelolgdgh l > W h shupdqhfh qr hvwdgr l 1 R pìwrgr gh Phwursrolv0Kdvwlqjv srgh vhu hvshflfdgr dwudyìv gr dojrulwpr 51 41. Ef Ef Hvshflfdu xp yhfwru lqlfldo Ef ' > = = = > n > r qýphur gh lwhudêøhv Q> d ixqêær sursrqhqwh t =ml 1 Lqlfldol}du r frqwdgru. gh lwhudêøhv hp l ' f1. 51 Hp fdgd lwhudêær l Ef> = = = > Q l, jhudu xp fdqglgdwr W d sduwlu gh t ml > ll, fdofxodu d suredelolgdgh gh dfhlwdêær l > W h jhudu. x X Ef> > lll, vh x l > W hqwær frqvlghudu ln ' W / fdvr frqwuäulr/ frqvlghudu ln ' l >. ly, lqfuhphqwdu r frqwdgru gh l sdud l n 1 Dojrulwpr 5= Phwursrolv0Kdvwlqjv1. 8Hvwd. ixqêær ì xvxdophqwh/ ghvljqdgd sru ixqêær sursrqhqwh1.

(52) 5;. LL1 FRQFHLWRV IXQGDPHQWDLV GH SUK H HVWDWðVWLFD ED\HVLDQD. Qrv pìwrgrv PFPF/ dv dprvwudv vær rewlgdv vhtxhqfldophqwh/ frp d glvwulexlêær grv ydoruhv ghshqghqgr dshqdv gr ýowlpr ydoru dprvwudgr h/ sruwdqwr/ irupdqgr xpd fdghld gh Pdunry1 Ghvwd irupd dv dprvwudv vxfhvvlydv vær ghshqghqwhv hqwuh vl/ ghylgr ã fruuhodêær hqwuh rv ydoruhv dprvwudlv jhudgrv1 Yäulrv surfhglphqwrv vær sursrvwrv qd olwhudwxud sdud hvwd dydoldêær +sru h{hpsor/ Frzohv h Fduolq/ 4<<9> Urehuw h Fdvhood/ 5337,1 Sdud d dydoldêær gd frqyhujíqfld ì qhfhvväulr frqvlghudu glihuhqwhv fdghldv lql0 fldgdv frp ydoruhv glvwlqwrv1 Doìp glvwr/ d p gh vh rewhu dprvwudv lqghshqghqwhv gd glvwulexlêær doyr/ jhudophqwh/ vær qhfhvväuldv pxlwdv lwhudêøhv gr pìwrgr sdud txh vh srvvd ghvfduwdu xpd txdqwlgdgh vxflhqwh gh lwhudêøhv jhudgdv qr shuðrgr gh dtxhfl0 phqwr1. 5161 Gldjqövwlfrv gh frqyhujíqfld1 Xp grv pdlruhv sureohpdv gd dsolfdêær grv pìwrgrv PFPF ì gldjqrvwlfdu vh xpd fdghld frqyhujlx rx qær sdud d glvwulexlêær doyr1 Xpd vroxêær sdufldo sdud hvwh sureohpd ì frqvhjxlgd frqvlghudqgr yäuldv fdghldv frp glyhuvrv ydoruhv lqlfldlv h hqwær frpsdudu r frpsruwdphqwr ghqwur h hqwuh dv fdghldv1 R wudedokr gh Jlonv h rxwurv +4<<9, ì xpd h{fhohqwh frohfwåqhd gh glyhuvrv wh{wrv vreuh rv pìwrgrv PFPF h rv pìwrgrv sdud ghwhfwdu frqyhujíqfld h dxwrfruuhodêær1 Xpd txhvwær fkdyh qr gldjqövwlfr gh frqyhujíqfld ì r shuðrgr gh dtxhflphqwr +exuq lq,/ shuðrgr rqgh rv ydoruhv gd fdghld dlqgd qær dwlqjludp d vxd glvwulexlêær hvwdflrqäuld1 Qhvwh shuðrgr lqlfldo/ dv revhuydêøhv jhudgdv srghp yduldu qxpd dpsod jdpd gh ydoruhv h dsuhvhqwdu iruwh ghshqgíqfld hp uhodêær drv ydoruhv frp txh d fdghld vh lqlflrx1 Vhjxqgr Dpdudo Wxunpdq +5333,/ d hvfrokd gr qýphur gh lwhudêøhv ghshqgh/ gd udslgh} gh frqyhujíqfld gd fdghld sdud r hvwdgr gh htxloðeulr h gd hvwuxwxud gh fruuh0 odêær gdv frpsrqhqwhv1 Dvvlp= vö vh ghyh frqvlghudu sdud d dprvwud/ hvwdgrv gd fdghld rewlgrv dsöv r shuðrgr gh dtxhflphqwr/ d sduwlu gr txdo kdmd jdudqwld gh txh r htxloðeulr irl dwlqjlgr>.