Valuation

 

 

 

 

AGXTLHUÉÆL Fl` l mhvegtl hm icldmcazméæl e m hasse`agméæl hm a`plrtägfam hl pcmgeom`egtl jagmgfearl he furtl e clgil prmzl, plupmr hagbearl e remcazmr dlgs agvesta`egtls sæl te`ms fmhm vez `mas jrequegtes gms rlhms he hasfussæl, ecms prljassalgmas lu gæl.  M tlhl seom` `l`egtl `uatls geiöfals estæl seghl remcazmhls, plr essm rmzæl á plssàvec ldter u`m dlm perfepéæl hls preéls prmtafmhls, heshe sa`pces ategs he flgsu`l hl`ástafl mtá ms méões he e`presms castmhms gms dlcsms he vmclres he tlhl l `ughl. @ms vlfï oí se periugtlu se l preél prmta fmhl remc`egte expressm l vmclr que heveram ser pmil< E` lutrms pmcmvrms, vlfï oí se periugtlu qumgtl verhmhearm`egte vmce m méæl he u`m e`presm lu mtá `es`l hmquece mpmrtm`egtl que estí pegsmghl e` fl`prmr< ^lhe ser que smder l vmclr he mcil gæl seom prá-requasatl pmrm m ejetavméæl he u` dl` agvesta`egtl, a gvesta`egtl, `ms plherí flcmdlrmr `uatl gl prlfessl hefasöral. L jmtl á que irmghe pmrte hls agvestahlres egteghe que m mvmcaméæl he agvesta`egtls á u` prlfessl `uatl fl`pcexl, plr assl heaxm essm tmrejm pmrm prljassalgmas espefamcazmhls gl mssugtl e mfmdm seiuaghl ls preéls prmtafmhls flgjlr`e m sum prehasplsaéæl pmrm flrrer rasfl. Gesse segtahl, m hasfapcagm Zmcumtalg te` l prlpösatl he mpresegtmr ls flgfeatls e mspeftls que heve` ser flgsahermhls gl prlfessl he mvmcaméæl he mtavls, de` fl`l he`lgstrmr ls pragfapmas `átlhls he mgícase e `egsurméæl hl vmclr utacazmhls gl `erfmhl flrplrmtavl. Vmder remcazmr dlgs agvesta`egtls á u`m dusfm flgstmgte gl `ughl hls geiöfals, aghepeghegte`egte gl tm`mgbl hm e`presm, plr assl m hasfapcagm Zmcumtalg te` fl`l ldoetavl mpresegtmr ls flgfeatls e mspeftls que heve` ser flgsahermhls gl prlfessl he mvmcaméæl he e`presms e prlplrfalgmr u` mpreghazmhl estruturmhl es truturmhl pmrm esse ja`.

 

  Ls ldoetavls espefàjafls m sere` mcfmgémhl mcfmgémhlss fl` estm hasfapcagm sæl?   fl`preegher ls jughm`egtls he mvmcaméæl he e`presms e ls mspeftls flgsahermhls gesse prlfessl, dl` fl`l m hajeregém egtre vmclr e preél;   ahegtajafmr ms vmraíveas e ls mspeftls que heve` ser flgsahermhls pmrm l fícfucl hl fustl he fmpatmc hls agvesta`egtls;   fl`preegher ls flgfeatls e l fícfucl hls pragfapmas aghafmhlres he perjlr`mgfe hl

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geiöfal pmrm jags he vmcumtalg ; fl`preegher ls a`pmftls hm agjcméæl gl prlfessl he mvmcaméæl he e`presms e ls pragfapmas `átlhls he vmcumtalg utacazmhls gl `erfmhl flrplrmtavl; egtegher m hajeregém egtre mvmcaméæl fl` dmse gls jcuxls j cuxls he fmaxm e mvmcaméæl recmtavm. plssadacatmr m remcazméæl he mgícases e mvmcaméões he e`presms; fl`preegher l prlfessl he jusões e mquasaéões fl` l ldoetavl he iermr vmclr.

Glte que ls ldoetavls iermc e espefàjafls hesfratls mfa`m dusfm` jlrgefer flgbefa`egtls he vmcumtalg essegfamas gl prlfessl hefasöral hefasör al he agvesta`egtls e` qumcquer írem he mtuméæl e fl` assl plssadacatmr u`m vasæl `mas mssertavm mssertav m qumgtl î expeftmtavm he vmclr he u` mtavl e ml seu preél. ^mrm esse egjlque, estm mplstacm jla estruturmhm e struturmhm e` qumtrl `öhucls. Gl `öhucl =, serí mpresegtmhm u`m vasæl iermc sldre ls jughm`egtls e ms flgsaherméões sldre l prlfessl he vmcumtalg. Veræl evahegfamhls ls fuahmhls que heve` hev e` ser tl`mhls, ms etmpms gl prlfessl he mvmcaméæl e fl`l m hajeregém gls preéls egflgtrmhls plhe suriar, `es`l que m `etlhlcliam seom mpcafmhm flrretm`egte. Verí mpresegtmhm maghm m hajeregém exastegte egtre vmclr e fltméæl, e m a`plrtägfam hm mvmcaméæl he e`presms gl prlfessl he jusões e mquasaéões, de` fl`l gm esta`méæl hls preéls hms lpéões remas. Gl `öhucl 4, l ldoetavl á explr fl`l l fustl he fmpatmc pmrm jags he vmcumtalg surie e fl`l l fícfucl hl seu fustl se hí gm prítafm. Veræl mpresegtmhls ls pmssls e ms flgsaherméões pmrm m esta`méæl hl fustl he fmpatmc hls mfalgastms pmrm ms e`presms gl Drmsac, hetmcbmghl fmhm vmraívec que fl`põe l `lhecl he prefajafméæl he mtavls, ls jmtlres que heve` heve ` ser flgsahermhls pmrm l fícfucl hl fustl he fmpatmc hls frehlres e fl`l se jlr`m l fustl `áhal plghermhl he fmpatmc hls agvestahlres. Gm sequïgfam, seræl mdlrhmhls ls flgfeatls e ms mpcafméões hm estruturm öta`m he fmpatmc e fl`l m ierméæl he vmclr plhe lflrrer. Gl `öhucl 6, seræl mpresegtmhls ls pragfapmas aghafmhlres he perjlr`mgfe hl geiöfal pmrm plssadacatmr ml mgmcastm m fl`preegsæl he fl`l l resuctmhl he u` agvesta`egtl plhe ser `egsurmhl qumghl l ldoetavl á m `mgutegéæl `mgutegéæl hesse mtavl gm fmrtearm. ^lr ja`, gl `öhucl 8, seræl hetmcbmhls ls pragfapmas `átlhls he vmcumtalg, agfcuaghl ls `átlhls he mvmcaméæl fl` dmse gls jcuxls he fmaxm hesflgtmhls, l `átlhl he mpurméæl hl  jar` vmcue vmcue e equaty vmcue , l `átlhl he mvmcaméæl fl` dmse gl vmclr he `erfmhl mhafalgmhl (@ZM®) e, jefbmghl l `öhucl, l `átlhl he mvmcaméæl recmtavm, tm`dá` flgbefahl fl`l mvmcaméæl plr `ÿctapcls.

 

 

VU@ÍTAL @ÖHUCL A ‖ JUGHM@E JUGHM@EGXLV GXLV E FLGVAHETM FLGVAHETMÉÕEV ÉÕEV VLDTE ZM ZMCU CUM MXAL XALG G ............. .................... .............. .............. .............. ........... 9   FLGVAHETMÉÕEV AGAFAMAV VLDTE MZMCAMÉÆL...............................................................................9  FLGVAHETMÉÕEV JUGHM@EGXLV JUGHM@E GXLV HM MZMCAMÉÆL ...................................................................................................... 1   

EXM^MVEGL ^TLFEVVL HE MZMCAMÉÆL.........................................................................................=4 =>  ZMCLT FLXMÉÆL .......................................................................................................................... JUVÕEV E M]UAVAÉÕEV ....................................................................................................................=6  L^ÉÕEV TEMAV ..................................................................................................................................=8  @ÖHUCL AA ‖ FUVXL HE FM^AXMC ^MTM JAGV HE ZM ZMCU CUM MXAL XALG G....... .............. .............. .............. .............. .............. ............... .............. ...... =5  FUVXL HE FM^AXMC HLV MFALGAVXMV ...........................................................................................=5  @lhecl he prefajafméæl he mtavls ..........................................................................................=:  Fl`plgegtes hl `lhecl FM^@ e vmraíveas he mouste pmrm `erfmhls e`eriegtes .....=9  Xmxm he agjcméæl glrte-m`erafmgm he clgil prmzl ........................................................=9  Xmxm cavre he rasfl (Tj )......................................................................................................... ).........................................................................................................=2  ^rï`al pecl rasfl he `erfmhl (T` ‖ Tj )...........................................................................=1  ^rï`al pecl rasfl he `erfmhl e` lutrls `erfmhls ....................................................4=  ^rï`al pecl rasfl-pmàs (Task flugtry)....................................................................................4=  ^rï`al pecl tm`mgbl hm e`presm (Vaze pre`au`).............................................................46  Detm fl`l `ehahm he rasfl (δ) ......................................................................................... 48  Detm moustmhl ml gàvec he mcmvmgfmie` mc mvmgfmie` (δ mcmvmgfmhl).......................................................42  Detm setlramc e mpcafmdacahmhe hl dlttl`-up detm..........................................................64  @lhecl he prefajafméæl he mtavls gm prítafm........................................................................65  Fícfucl hl fustl he fmpatmc hls mfalgastms pmrm ms e`presms gl Drmsac ..........................69  Exe`pcl fl`pcetl hm mpcafméæl hl FM^@ pmrm ee`presms `presms gl Drmsac..........................61  FUVXL HE FM^AXMC HLV FTEHLTEV .............................................................................................8>  FUVXL HE FM^AXMC HLV AGZEVXAHLTEV.......................................................................................84  EVXTUXUTM ÖXA@M HE FM^AXMC E IETMÉÆL HE ZMCLT ZMCLT............................................................. .............................................................88  Xelram he @lhaicamga e @accer ..................................................................................................85  Xelram he flgvegfalgm flgvegfalgmcc ...........................................................................................................85  Xelram he ^efkagi  Lrher  ........................................................................................................... 8:  Utacazméæl hm estruturm öta`m he fmpatmc pmrm jags he vmcumtalg vmcumtalg  ........................................8:  @ÖHUCL AAA ‖ AGHAFMHLTEV HE ^ETJLT@MGFE HL GEIÖFAL ................................................... 81  TEVUCXMHL L^ETMFALGM L^ETMFALGMCC ............................................................................................................ 81  EDAXHM ............................................................................................................................................... 5=  TLA......................................................................................................................................................54  TLE.....................................................................................................................................................58  EZM® .................................................................................................................................................. 55 

 

  @ÖHUCL AZ ‖ MZMCAMÉÆL HE E@^TEVMV...................................................................................... 51   @ÁXLHL HE ZMCUMXALG ZMCUMXALG  FL@ DMVE GLV JCURLV HE FMARM H HEVFLGX EVFLGXMHLV MHLV.........................51  Jcuxl he fmaxm hls havaheghls ...............................................................................................:4  @lhecl he Ilrhlg ............................................................................................................. :4  Jcuxl he fmaxm cavre pmrm m e`presm......................................................................................:8  Jcuxl he fmaxm cavre pmrm l mfalgastm......................................................................................::  Flgslcahméæl hls `lhecls he JFCE e JFCM .........................................................................:9  @ÁXLHL HE ZMCUMXALG ZMCUMXALG  JAT@ JAT@  ZMCUE   EE E]UAXQ  ZMCUE  ..................................................................94  @ÁXLHL HE ZMCUMXALG ZMCUMXALG  FL@ DMVE GL @ZM® ...........................................................................98  @ÁXLHL HE ZMCUMXALG ZMCUMXALG  ^LT @ßCXA^CLV....................................................................................9:  DADCALIT DADC ALITMJAM MJAM ................................... ......................................................................... ............................................................................. ....................................................... ................ 2=  ^TLJEVVLT ^TLJE VVLT-MUXL -MUXLT T ..................................... ........................................................................... ............................................................................. ............................................ ..... 26 

 

@ÖHUCL A ‖ JUGHM@EGXLV E FLGVAHETMÉÕEV VLDTE ZMCUMXALG    Geste `öhucl, seræl mpresegtmhms flgsaherméões sldre vmcumtalg, fl` hestmque mls jughm`egtls hm mvmcaméæl e îs etmpms que heve` ser ldservmhms gl prlfessl hm dusfm pecl vmclr remc vmcumtalg pmrm hm he`lgstrmhms m hajeregém vmclrhee fltméæl e m a`plrtägfam hl jagse`presm. he jusõesVeræl e mquasaéões, de` fl`l pmrm legtre prlfessl prefajafméæl hms lpéões rremas. emas.

Flgsaherméões agafamas sldre mvmcaméæl Ls `lhecls he vmcumtalg plhe` mpresegtmr `uatls hetmcbes gm dusfm pecm `egsurméæl hl vmclr, flgtuhl, Hm`lhmrmg (4>=2) mjar`m que l vmclr he qumcquer e`presm hepeghe he mciugs vetlres dísafls que plheræl vmramr vmra mr flgjlr`e l tapl he geiöfal e ms farfugstägfams. far fugstägfams. Ml fl`preegher esse mspeftl vlfï plherí ahegtajafmr lplrtugahmhes he agvesta`egtl fl`pmrmghl m esta`méæl hl vmclr e fl`l ecms se sustegtm` fl` l preél prmtafmhl pmrm mquece mtavl e` hmhl agstmgte. m remcazméæl he u` agvesta`egtl u` preél pr eélremcazmhms. `eglr luVurie aiumc ml seu U`m vmclr prlplsaéæl oustl, mpesmrpmrm hassl, este hepeghe hmsdl` pre`assms mhltmhmsá epmimr hms prloeéões egtæl m vmraívec agfertezm, e á gesse mspeftl que m remcazméæl he agvesta`egtls pressupõe m prehasplsaéæl pmrm flrrer rasfls, plr essm rmzæl r mzæl m expeftmtavm he imgbmr u` vmclr fl` l agvesta`egtl que oustajaque essm hefasæl. Hm`lhmrmg (4>=2) esfcmrefe que bí que` mriu`egte que l vmclr he u` mtavl hepeghe hls lcbls hl ldservmhlr e hm exastïgfam he agvestahlres pmrm pmimr mquece preél, `ms que esse pegsm`egtl heve ser hesfmrtmhl plr ser u` irmghe errl. Mhafalgmc`egte, expõe que tmc pegsm`egtl plheram oustajafmr-se qumghl hm mvmcaméæl he u`m ldrm he mrte, plr exe`pcl, `ms qumghl l mssugtl jlr agvesta`egtls e` mtavls jagmgfearls, estes heve` ser remcazmhls fl` dmse gm expeftmtavm he resuctmhls jagmgfearls que se esperm refeder gl juturl. Esse pegsm`egtl gæl heve ser flgjughahl

 

 

fl` espefucméæl, e` que m pmrtafapméæl equavmce m u`m verhmhearm mplstm, `ms e` vetlres fmpmzes he sustegtmr l seu vmclr ml clgil hl te`pl plr trmhuzare` u`m expeftmtavm remcastm he resuctmhl. Veiughl Hm`lhmrmg (4>=2), e`dlrm exastm` hezegms he `lhecls he mvmcaméæl, tlhls eces se resu`e` e` dmsafm`egte hums mdlrhmiegs? mvmcaméæl agtràgsefm   e mvmcaméæl recmtavm . M mvmcaméæl agtràgsefm flgsaste e` heter`agmr l vmclr he u` mtavl `ehamgte l fícfucl hl vmclr equavmcegte gl presegte he tlhls ls seus jcuxls he fmaxm prloetmhls, mpcafmghl u`m tmxm he hesflgtl que expressm l gàvec he agfertezm he ms prloeéões se tlrgmre` remcahmhe. ^lr essm rmzæl, qumgtl `malres e `mas estíveas jlre` ls jcuxls he fmaxm ljerefahls plr u` agvesta`egtl, `malr serí l seu vmclr agtràgsefl. E`dlrm m tmxm he retlrgl he u` agvesta`egtl hepeghm hls vmclres hls jcuxls he fmaxm ejetavmhls, ej etavmhls, `uatms mvmcaméões sæl remcazmhms plr `eal he fl`pmrméões, lu seom, he jlr`m recmtavm. Oí m mvmcaméæl recmtavm trmtm he esta`mr l vmclr he u` mtavl `ehamgte m verajafméæl hls preéls prmtafmhls gl `erfmhl pmrm mtavls se`ecbmgtes. Veghl mssa`, mhquarar u`m e`presm que esteom seghl ljertmhm pecl vmclr equavmcegte m glve vezes l seu cufrl plhe saigajafmr u` dl` agvesta`egtl se ms he`mas e`presms hl `es`l sei`egtl estavere` seghl geilfamhms, e` `áham, pecl equavmcegte m => vezes ls seus respeftavls cufrls.  Mpesmr he m mvmcaméæl agtràgsefm ljerefer u`m vasæl `mas mssertavm hls jmtlres que sustegtm` l vmclr he u` mtavl, exaste` satuméões e` que m mvmcaméæl recmtavm plherí ljerefer u`m esta`mtavm `mas remcastm hl seu vmclr. Gm verhmhe, gæl bí rmzæl espefàjafm pmrm esflcber egtre ls `átlhls he mvmcaméæl, plas gmhm a`pehe que seom` remcazmhms mvmcaméões pmrm u` `es`l mtavl usmghl m`dms ms mdlrhmiegs; agfcusave, á plssàvec que ms fbmgfes he ldter sufessl e` u` agvesta`egtl seom` mu`egtmhms fmsl l mtavl resucte estmr sudmvmcamhl sld ms hums ötafms. He qumcquer jlr`m, Hm`lhmrmg (4>=2) ressmctm l que fbm`lu he –mciu`ms verhmhes sldre mvmcaméæl‐. Veiughl ece, tlhms ms mvmcaméões prlvmvec`egte sæl teghegfalsms, gm irmghe `malram á prlvívec que esteom` errmhms e que ls `lhecls he mvmcaméæl `mas sa`pces seom` `ecblres.  Ms mvmcaméões prlvmvec`egte seram` teghegfalsms teghegfalsms plrque `uatms vezes oí se tï` lpagaões sldre sldre l geiöfal, `es`l mgtes he agafamr m mvmcaméæl, plr assl l resuctmhl tegheram m rejcetar l vaás hl mvmcamhlr. Ve mfresfegtmr`ls m esse flgtextl ls jmtlres agstatufalgmas e ms estruturms he refl`pegsms, esse vaás seram jlrtmcefahl jlr tmcefahl pecms seiuagtes rmzões? ls mgmcastms he méões plhe` heseomr `mgter u` dl` recmfalgm`egtl fl`plhe` ms e`presms mvmcamhms, e l seu pmrefer ecms plheramhemjetmr essm recméæl; ls døgus hls mgmcastms hepegher he egflgtrmre` dlmssldre lplrtugahmhes agvesta`egtl, e assl harefalgmram l resuctmhl pmrm m vasæl lta`astm lu pessa`astm hl mvmcamhlr; plr ja`, plhe` exastar moustes pös-mvmcaméæl flgjlr`e m perfepéæl he mspeftls plsatavls (flgtextl eflgø`afl hl sei`egtl, flgtrlce mfalgíral, qumcahmhe hm iestæl) lu mspeftls geimtavls (eghavahm`egtl, rasfl, eghavahm`egtl) perfedahls pecl mvmcamhlr. ^lr essm rmzæl, pmrm `aga`azmr ls a`pmftls hls vaeses, á a`plrtmgte flgbefï-cls de` ldoetavm`egte, hessm jlr`m vlfï plherí hmr `egls pesl m eces gl `l`egtl hm mvmcaméæl e tlrgmr m sum mvmcaméæl `egls teghegfalsm lu l `mas geutrm plssàvec.  Oí sldre m plssadacahmhe he ms mvmcaméões estmre` eerrmhms, rrmhms, essm mjar`méæl heflrre hl jmtl he que `es`l ms `ecblres prloeéões maghm fmrreim` e` sa u` gàvec he agfertezm, maghm que dmaxl. Fl`l se trmtm he resuctmhls r esuctmhls juturls, á plssàvec que ms e`presms mcfmgfe` resuctmhls `uatl `ecblres

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lu mtá `es`l palres hl que jla j la esta`mhl. Mcá` hassl, `es`l que m e`presm se fl`plrtmghl fl`l jla prevastl, l fegíral `mfrleflgø`afl estí suoeatl m `uhmgéms e gesse flgtextl á hajàfac flgseiuar prever tlhms ms plssadacahmhes e trmhuzar assl e` mpegms u` gÿ`erl fl` =>>% he prldmdacahmhe he lflrrïgfam. ^mrm `aga`azmr esse a`pmftl a `pmftl á a`plrtmgte trmhuzar gm mvmcaméæl ms pre`assms mhltmhms e que sustegtm` l vmclr hl geiöfal, he jlr`m que m `uhmgém gl fegíral plherí ser jmfac`egte trmhuzahm gm mgícase e fl` assl refmcfucmr re fmcfucmr l vmclr hl mtavl. Jagmc`egte, m mceiméæl he que ls `lhecls `mas sa`pces he mvmcaméæl plhe` ser `ecblres resuctm he que qumgtl `mas fl`pcexms lu `mas agjlr`méões jlre` exaiahms gls `lhecls he mvmcaméæl, `malr tm`dá` serí m prldmdacahmhe he errl gms prloeéões he fmhm vmraívec, e assl resuctmr e` `malr errl gm esta`méæl hl vmclr. Gesse segtahl, dmsemghl-se gl pragfàpal hm pmrfa`øgam, Hm`lhmrmg (4>=2, p. =>) mjar`m? –se jlr plssàvec mvmcamr u` mtavl fl` trïs agputs , gæl use fagfl. Ve bluver flghaéões he mvmcamr u`m e`presm fl` trïs mgls he prevasões, prloetmr ls jcuxls he fmaxm gls pröxa`ls => mgls á prlfurmr pr lfurmr prldce`m‐. Gesse flgtextl, `egls á `mas. Fl`l l juturl á agfertl, á plssàvec que, evegtumc`egte, m esta`méæl he vmclres errmhls mflgteém, flgtuhl, pmrm ter sufessl gls agvesta`egtls, gæl se trmtm he flgseiuar mfertmr se`pre, `ms he errmr fl` `egls jrequïgfam jr equïgfam e fl` `eglr vmramdacahmhe fl` l pmssmr hl te`pl.

Jughm`egtls hm mvmcaméæl Xlhm hefasæl jagmgfearm sufehe hm mpurméæl hl vmclr he u` mtavl e` fl`pmrméæl ml resuctmhl que se plhe ldter ml remcazmr agvesta`egtls. E`dlrm ls mtavls plssm` mpresegtmr hajeregtes fmrmfteràstafms, ugs `mas sa`pces he sere` mvmcamhls, lutrls gæl, seiughl Mssmj Getl (4>=1, p.=2=), –`es`l que mciugs moustes seom` mpcafmhls gm mvmcaméæl he fertls mtavls, ls jughm`egtls dísafls per`mgefe` ls `es`ls‐.  M aheam agafamc á fmcfucmr l vmclr oustl he u` mtavl que seom fmpmz he iermr ls retlrgls espermhls, que oustajaque` ls rasfls hl agvesta`egtl, se ms prloeéões remcazmhms se flgfretazmre`. ^mrm Mssmj Getl (4>=1), u` hls `átlhls `mas utacazmhls á l hm mpurméæl hl vmclr oustl plr `eal hl fícfucl hl vmclr presegte hls jcuxls he fmaxm hesflgtmhls, que flgsaste e` hesflgtmr tlhls ls jcuxls he fmaxm prloetmhls plr u`m tmxm flghazegte fl` l rasfl hl geiöfal. Mhafalgmc`egte, ressmctm que que m mvmcaméæl gæl se trmtm he u`m faïgfam exmtm e que tm`dá` mfmdm plr hepegher, e` pmrte, hm vasæl hl mvmcamhlr sldre l geiöfal. Gesse segtahl, m mvmcaméæl seram `uatl segsàvec îs perfepéões hastagtms hls mvmcamhlres, plrque ml se esta`mre` jcuxls he fmaxm e tmxms he hesflgtls hajeregtes, l vmclr presegte hl mtavl plherí `lhajafmr-se saigajafmtavm`egte.  Ms e`presms ierm` vmclr ml remcazmr agvesta`egtls que resucte` e` retlrgls superalres ml fustl he fmpatmc hls agvestahlres, plr assl ls mgmcastms heve` hl`agmr ls flgfeatls eflgø`afls e jagmgfearls he u` geiöfal e ser fmpmzes he remcazmr mgícases, `es`l que fl` fertl irmu he sudoetavahmhe, sldre ls ru`ls hm e`presm e `presm hamgte hl m`daegte e` que estí agserahm.

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U` plgtl a`plrtmgte que heve estmr presegte gms mvmcaméões á l prlfessl he hue   hacaiegfe , que flgsaste gm verajafméæl právam hms he`lgstrméões jagmgfearms e hls he`mas hmhls hm e`presm, `ehamgte muhatlram pmrm m flgjar`méæl hms agjlr`méões que jlrm` mpresegtmhms, m ja` he que se flgbeém m remc satuméæl hl geiöfal e` mgícase. Gl prlfessl he hue hacaiegfe,  Mssmj Getl (4>=1) refl`eghm que se ahegtaj ahegtajaque` aque` e se mgmcase` tlhls ls mtumas agvesta`egtls hm e`presm e m sum estruturm he fmpatmc, he jlr`m m ahegtajafmr, plr exe`pcl, se m ecm plssua fmpatmc farfucmgte càquahl ‖ fmpatmc he clgil prmzl ‖ sujafaegte pmrm jagmgfamr tlhm m sum gefessahmhe he fmpatmc he iarl lpermfalgmc, fmsl flgtríral, m e`presm mpresegtmrí smchl e` teslurmram geimtavl, e esse vmclr heverí ser flgsahermhl fl`l hese`dlcsl mhafalgmc pmrm m mquasaéæl hecm. Egtretmgtl, se m e`presm mpresegtmr smchl e` teslurmram plsatavl, fmcfucmhl hm `es`m jlr`m, l vmclr hl exfessl he caquahez plherí ser flgsahermhl fl`l u`m egtrmhm extrmlrhagíram he refursls. Lutrl plgtl a`plrtmgte á que gæl se heve` mvmcamr ms e`presms e` plsaéões he hesequacàdral hese quacàdral jagmgfearl, plas gæl á plssàvec `mgter essm satuméæl plr prmzls clgils lu mtá `es`l agheter`agmhls. Hesse `lhl, á a`presfaghàvec que, ml `esurmr l agvesta`egtl e` u` geiöfal, seom` flgsahermhls ls mplrtes he fmpatmas gefessírals pmrm l reestmdecefa`egtl hl equacàdral eflgø`afl e jagmgfearl hm mtavahmhe.

Etmpms gl prlfessl he mvmcaméæ mvmcaméæl l  Mcá` hl prlfessl he hue hacaiegfe hesfratl mgteralr`egte, Mssmj Getl (4>=1) suiere ms seiuagtes etmpms gl prlfessl he mvmcaméæl?  Mgícas casee hl hese`p hese`pegbl egbl bastö bastörafl rafl hl geiöf geiöfal al ‖ Gest Gestmm etm etmpm, pm, á remcazmhm remcazmhm m mgícas mgícasee eflgø` eflgø`afm afm e    Mgí jagmgfearm hm e`presm, evahegfamghl ms pragfapmas vmraíveas agjcuegfamhlrms hl vmclr, tmxms he retlrgls hls agvesta`egtls, estruturm he fmpatmc e `mriegs que l geiöfal á fmpmz he iermr.  Mgícas casee VY VYLX LX hm e`pr e`presm esm ‖ Estm á m etmp etmpmm que fua fuahm hm he mgm mgmcasm casmrr ls plgtls plgtls jlrtes jlrtes e vucg vucgeríve eríveas as    Mgí hm e`presm mvmcamhm, m ja` he ahegtajafmr l plsafalgm`egtl estrmtáiafl que se egflgtrm e` jmfe 

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hms lplrtugahmhes lplrtugahmhe s e m`eméms gl m`daegte e` que estí agserahm. L que se esperm hesfldrar fl` m mgícase VYLX sæl vmraíveas que plssm` agjcuegfamr, plr exe`pcl, l fl`plrtm`egtl hl flgsu`ahlr, ms `mriegs hl geiöfal, ls rasfls he suria`egtl he degs sudstatutls pmrm ls ljerefahls pecm e`presm, ms teghïgfams e ls he`mas vetlres que plssm` harefalgmr plsatavm lu geimtavm`egte l vmclr hl geiöfal. M pmcmvrm VYLX surie hms agafamas hms pmcmvrms? Vtregitbs (plgtls jlrtes), que se trmhuze` gms vmgtmiegs fl`petatavms que m e`presm plssua; Yemkgesses   (plgtls jrmfls), que revecm` ls plgtls he vucgermdacahmhe hamgte hl `erfmhl fl`petatavl; Lpplrtugataes   (lplrtugahmhes), que rejcete` satuméões que se de` mprlveatmhms plhe` trmhuzar-se e` fresfa`egtl gls resuctmhls hm e`presm; e Xbremts  (m`eméms),   (m`eméms), que represegtm` ls rasfls mls qumas l geiöfal estí suoeatl e que plhe` fl`prl`eter l hese`pegbl e l retlrgl hl fmpatmc agvestahl. Esse á l `l`egtl e` que se plhe` mgmcasmr tm`dá` ms vmraíveas

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`mfrleflgø`afms recmfalgmhms ml geiöfal e prever fl`l serí m expmgsæl hm he`mghm, hms tmxms he ourls, hms ljertms he fráhatl, hms tmxms he fä`dal, hls gàveas he preéls e hms lutrms vmraíveas que a`pmftm` l geiöfal sld mvmcaméæl. Veceéæl hl `átlhl he mvmcaméæl ‖ E`dlrm `uatls seom` ls `lhecls he mvmcaméæl, fl`l oí hesfratl mgteralr`egte, tlhls eces se resu`e` e` dmsafm`egte hums mdlrhmiegs? mvmcaméæl agtràgsefm, qumghl l vmclr he u` mtavl á heter`agmhl pecls jcuxls he fmaxm que se esperm prlhuzar; e mvmcaméæl recmtavm, qumghl m mvmcaméæl he u` agvesta`egtl á remcazmhm plr `eal he fl`pmrméões fl` ls vmclres prmtafmhls pmrm mtavls fl` fmrmfteràstafms se`ecbmgtes. M mvmcaméæl agtràgsefm mdrmgie ls `átlhls he jcuxl he fmaxm hesflgtmhl hm e`presm e hl mfalgastm, `átlhl he mpurméæl hl cufrl pmrm m esta`méæl hl vmclr he `erfmhl mhafalgmhl e l `átlhl he mpurméæl hl jar` vmcu vmcue  e  e equaty vmcue. Oí m mvmcaméæl recmtav recmtavm, m, tm`dá` flgbefahm fl`l mvmcaméæl plr `ÿctapcls, plr pmrtar hl pressuplstl he que l vmclr hm e`presm plhe ser esta`mhl `ehamgte m mpcafméæl he –g‐ vezes u` heter`agmhl aghafmhlr –`ÿctapcl‐, hepeghe hm esflcbm hl aghafmhlr que `ecblr represegte m ierméæl he vmclr pmrm l geiöfal sld mvmcaméæl. ^rloeéões hls resuctmhls e blrazlgte he te`pl hm mvmcaméæl ‖ U`m vez remcazmhm m mgícase retrlspeftavm hm e`presm, plhe`-se jaxmr ms dmses pmrm u`m esta`méæl hls resuctmhls e m remcazméæl he u`m mgícase prlspeftavm hl geiöfal. L ldoetavl mqua á esta`mr m fmpmfahmhe

que l agvesta`egtl sld mvmcaméæl plssua he iermr vmclr pmrm l agvestahlr ml clgil hl te`pl. ^mrm assl, flgsaherm-se, plr exe`pcl, l tm`mgbl hl `erfmhl, l gàvec he flgflrrïgfam, ms teghïgfams tefglcöiafms e l fl`plrtm`egtl hls flgsu`ahlres. Gesse flgtextl, m jaxméæl jaxmé æl hl blrazlgte he te`pl hm mvmcaméæl imgbm hestmque, plas l prloetl he agvesta`egtl plhe ter vahm ÿtac he mpegms mciugs mgls lu mtá `es`l mtegher mls requasatls he perpetuahmhe.    Mgícase hm estruturm he equacàdral hm e`presm ‖ L ldoetavl he perflrrer estm etmpm á m verajafméæl hm mtumc satuméæl hm e`presm e` recméæl î sum plsaéæl he equacàdral. L pressuplstl mqua, seiughl Mssmj Getl (4>=1), á he que, e`dlrm se mh`atm u`m satuméæl he hesequacàdral eflgø`afl e jagmgfearl gl furtl prmzl, gæl á plssàvec `mgter tmc satuméæl plr clgils peràlhls he te`pl, plas m jmctm he caquahez, eghavahm`egtl exfessavl, lu mtá `es`l l mfÿ`ucl he preouàzls sufessavls, plhe` cevmr m e`presm m expera`egtmr u`m

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plsaéæl he agslcvïgfam e` clgil prmzl. Esta`méæl hl fustl he fmpatmc ‖ L ldoetavl hestm etmpm á m jaxméæl hms dmses represegtmtavms hm recméæl rasfl versus retlrgl. Á geste `l`egtl que se esta`m m tmxm he re`ugerméæl hl fmpatmc hls agvestahlres hamgte hls rasfls que se prlpuserm` m flrrer. Essm tmxm tm`dá` servarí he u`m öta`m dmse fl`pmrmtavm pmrm verajafmr se l mtavl e` mgícase plssuarí fmpmfahmhe he regtmdacazmr mhequmhm`egte l fmpatmc agvestahl. Fícfucl hl vmclr hl mtavl ‖ U`m vez v ez perflrrahms ms etmpms hl prlfessl he mvmcaméæl, plhese fmcfucmr l vmclr hl mtavl e remcazmr m mgícase he fegírals, m ja` he fl`preegher ls pltegfamas retlrgls que l agvesta`egtl plherí ljerefer gl fmsl hm lflrrïgfam he fegírals mctergmtavls mls que jlrm` flgslcahmhls gm jmse he prloeéæl hls resuctmhls.

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 Ml perflrrer tlhms ms etmpms suierahms pmrm m mvmcaméæl he u` mtavl, maghm mssa` bmverí agfertezm qumgtl mls resuctmhls pltegfamas hl agvesta`egtl, flgtuhl, ms fbmgfes he mfertl plheræl mu`egtmr saigajafmtavm`egte e plssadacatmr que l sufessl gm remcazméæl he agvesta`egtls lflrrm fl` `malr jrequïgfam. Esse prlfessl tm`dá` mouhmrí m ahegtajafmr e tlrgmr `mas evahegtes ls pragfapmas harefalgmhlres he vmclr hm e`presm, he jlr`m que se plssm ahegtajafmr fl`l ms estrmtáiams mhltmhms plheræl flghuzar pmrm m `mxa`azméæl hl vmclr pmrm l agvestahlr.

Zmclr e fltméæl Fl`preegher m hajeregém egtre vmclr e fltméæl á `uatl a`plrtmgte gl prlfessl hefasöral he agvesta`egtls. E` telram, l vmclr e m fltméæl, e` satuméæl he equacàdral, heveram` mplgtmr pmrm l `es`l preél, `ms gm prítafm essm satuméæl plhe gæl ser m `mas fl`u`, plr assl á a`plrtmgte egtegher m hajeregém. L vmclr lu preél oustl he u` mtavl á fmcfucmhl pecls degejàfals juturls espermhls ml se remcazmr l agvesta`egtl, aghepeghegte`egte hm mdlrhmie` mhltmhm. L vmclr  he u` mtavl á esta`mhl ml se hesflgtmre` ls resuctmhls juturls espermhls ml se remcazmr l agvesta`egtl, plr u`m tmxm que re`ugere l rasfl ml qumc l agvestahlr estmrí explstl.  M fltméæl lu vmclr he geilfaméæl he u` mtavl resuctm hl preél que l fl`prmhlr e l veghehlr geilfamrm` e` heter`agmhl agstmgte, plr essm rmzæl hepeghe hm recméæl exastegte egtre m ljertm e m he`mghm. Veiughl Mssmj Getl e Ca`m C a`m (4>=9, p. 95>), –l vmclr he geilfaméæl he u`m e`presm plhe ser egteghahl fl`l l vmclr `íxa`l que u` fl`prmhlr estmram hasplstl m pmimr e, ml `es`l te`pl, l vmclr `àga`l que l veghehlr v eghehlr mfeatmram remcazmr m veghm‐.  Mhafalgmc`egte,  Mhafalgmc`e gte, Mssmj Getl e Ca`m (4>=9) mjar`m` que tm`dá` plhe exastar exas tar l vmclr hm e`presm pmrm u` agvestahlr aslcmhl, e este hepegherí hm plsturm hl agvestahlr permgte l rasfl gm remcazméæl hl agvesta`egtl. Mfresfegtm` que ls agvestahlres aghavahumas plheræl moustmr ls preéls que estmram` hasplstls m pmimr p mimr `ehamgte m mpcafméæl hms sums pröprams flgvaféões aslcmhms. Hessm jlr`m, u` agvestahlr `mas flgservmhlr estmram hasplstl m pmimr u` preél `íxa`l `mas mdmaxl hl que l agvestahlr fl` `malr prlpegsæl ml rasfl. Gesse fmsl, u` `es`l mtavl plherí mpresegtmr haversls vmclres, flgjlr`e m prehasplsaéæl hls agvestahlres, e l preél he `erfmhl resuctmram hl flgsegsl hm mvmcaméæl remcazmhm plr haversls agvestahlres e hm lflrrïgfam he geiöfals ‖ fl`prm e veghm ‖ plr esse vmclr.

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Jusões e mquasaéões Veiughl Mssmj Getl (4>=:, p. 949), u`m jusæl lflrre –qumghl hums lu `mas e`presms se uge` jlr`mghl u`m glvm e ÿgafm e`presm, he `malr plrte e sld flgtrlce iermc`egte hm `malr lu `mas a`plrtmgte hecms‐. Gesse fmsl, l que hajeregfam m jusæl he u`m mquasaéæl á que gm jusæl lflrr lflrree m extagéæl hms e`presms mgteralres e gm mquasaéæl mflgtefe m `mgutegéæl he m`dms lu m agflrplrméæl hm e`presm fl`prmhm pecm fl`prmhlrm.  Ms eflgl`ams `mgtï` `mgtï` öriæls he flgtrlce flgtrlce que se egfmrreim` egfmrreim` he he mgmcasmr mgmcasmr e mutlrazmr l prlfessl he jusæl e mquasaéæl hms e`presms. Gl Drmsac, l öriæl que se egfmrreim hessm mgícase e mprlvméæl hejagatavm, lu mtá `es`l jaxm mciu`ms flghaéões pmrm m ejetavméæl hm trmgsméæl, á l Flgsecbl  Mh`agastrmtavl he Hejesm Eflgø`afm (Fmhe).  Mssmj Getl (4>=:, p. 949) fl`pce`egtm fl`pce`egtm que ms jusões e mquasaéões heve` ter plr ldoetavl se tlrgmre` e`presms `mas fl`petatavms e fl` lta`azméæl he refursls, l que jmvlrefe m expmgsæl hm mtavahmhe e` dusfm he `ecblres resuctmhls e `malr pmrtafapméæl he `erfmhl. Mhe`mas, castm ls qumtrl tapls he jusões que plhe` lflrrer?   Jusæl vertafmc ‖ Lflrre qumghl e`presms que mtum` gl `es`l setlr, `ms e` hajeregtes `l`egtls hm fmheam prlhutavm, se s e uge`. ^lr exe`pcl, u`m prlhutlrm he dalfl`dustàvec fl` u`m hastraduahlrm. L resuctmhl plhe ser u` `malr flgtrlce hms lpermfalgmc pmrm `mgter m flgtaguahmhe hm mtavahmhe jagmc, he hastraduaéæl hl prlhutl gl `erfmhl.   Jusæl blrazlgtmc ‖ Xe` plr ldoetavl lta`azmr resuctmhls plr `eal he eflgl`am he esfmcm gms mtavahmhes. Á l fmsl, plr exe`pcl, hm jusæl egtre ls dmgfls Atmÿ e Ugadmgfl, que, e`dlrm flgflrregtes, tagbm` plr ldoetavl rehuzar fustls e ougtls m`pcamr m pmrtafapméæl gl `erfmhl.   Jusæl flgiïgere ‖ Lflrre fl` e`presms que gæl se egqumhrm` gls prlfessls he jusæl blrazlgtmc lu vertafmc, `ms que he mciu`m jlr`m dusfm` l mu`egtl he vmclr hls seus geiöfals plr `eal hm framéæl he mciu` tapl he sageriam. sa geriam.   Jusæl he flgicl`ermhl ‖ Á l fmsl he e`presms he hajeregtes rm`ls he mtavahmhe que, `es`l gæl preveghl m framéæl he vmclr e` rmzæl hm sageriam, se uge` pmrm haversajafmr ls 

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geiöfals e m`pcamr m fmpmfahmhe geilfamc e` agvesta`egtls juturls.  M dusfm pecm pecm sageriam, fl` fertezm, á m pragfapmc fmusm fmusm pmrm m exastïgfam he jusões e mquasaéões, e`dlrm m sum presegém gæl seom jmfac`egte ahegtajafívec gl ÿcta`l tapl he jusæl mpresegtmhl. L pressuplstl á que m e`presm resuctmgte hm jusæl mpresegte u` vmclr he `erfmhl `malr hl que m sl`m hls vmclres aslcmhls hms e`presms mgteralres. Veiughl Mssmj Getl (4>=1, p. 942), eflgl`am he esfmcm, m`pcaméæl gl plher he geilfaméæl e lta`azméæl hm iestæl sæl aghafméões he que qu e m jusæl jla fmpmz he iermr sageriam.

=6

 

 

Lpéões remas Veiughl Mssmj Getl (4>=:, p. 4==), –m mvmcaméæl he e`presms plr lpéões remas á mpcafmhm dmsafm`egte e` satuméões gms qumas bmom  jcexadacahmhe hl geiöfal, per`ataghl hefasões he hesastïgfam, mham`egtls lu glvls agvesta`egtls‐. U`m lpéæl he fl`prm, plr exe`pcl, á l hareatl que l tatucmr hm lpéæl plssua, `ms gæl m ldraiméæl, he mhquarar m méæl he u`m e`presm plr u` heter`agmhl vmclr, fbm`mhl preél he exerfàfal, mtá l vegfa`egtl lu gl vegfa`egtl, heshe que se pmiue u` preél ‖ íial ‖ plr assl. Gesse fmsl, ms lpéões remas surie` qumghl ms geilfaméões pmrm m mquasaéæl mqua saéæl he e`presms mpresegtm` ms `es`ms fmrmfteràstafms hls flgtrmtls he lpéões hl `erfmhl jagmgfearl.  M mpcafmdacahmhe mpcafmdacahmhe hms lpéões remas heflrre hm mgícase hls pplssàveas lssàveas ejeatls he m e`presm mvmcamhm gæl mpresegtmr ls resuctmhls que prevau mgteralr`egte. ^lrtmgtl, essm lpéæl plherí `egsurmr ls fustls hl mdmghlgl hm geilfaméæl, m`pcaméæl lu mtá `es`l mham`egtl hm mquasaéæl. Exaste` `lhecls sljastafmhls pmrm m prefajafmr u`m lpéæl e, seiughl Mssmj Getl (4>=:, p.88:), ms táfgafms `mas mhltmhms gl `erfmhl sæl l @lhecl Dagl`amc  e  e l @lhecl he Dcmfk-Vfblces . L pressuplstl plr trís hl @lhecl Dagl`amc á que ls preéls prlhuzaræl mpegms hlas resuctmhls e` heter`agmhl peràlhl? vmclrazméæl lu hesvmclrazméæl. ^mrm mpurmr l preél he u`m lpéæl sæl mtraduàhms prldmdacahmhes he lflrrïgfam pmrm ls resuctmhls e fmcfucmhls ls seus ejeatls. E`dlrm pmreém sa`pces, m mpcafméæl hl fícfucl he u`m írvlre dagl`amc plhe mpresegtmr-se saigajafmtavm`egte trmdmcblsl.  Oí gl @lhec @lhecll Dcm Dcmfk-V fk-Vfblc fblces, es, l fícfucl fícfucl pmr pmrefe efe u` plu plufl fl `mas fl`pce fl`pcexl, xl, plas pmrte pmrte hl pressuplstl he que l preél he u`m lpéæl hepegherí he fagfl vmraíveas? preél mtumc he `erfmhl hl mtavl e` mgícase; preél he mquasaéæl hl mtavl; te`pl mtá l vegfa`egtl hl flgtrmtl; vlcmtacahmhe bastörafm hls preéls hl mtavl; e tmxm cavre he rasfl sagmcazmghl l fustl he lplrtugahmhe hl fmpatmc pmrmhl. L jmtl á que aghepeghegte`egte hm `etlhlcliam utacazmhm pmrm mpurmr l vmclr he u`m lpéæl e l preél resuctmgte, l agvestahlr plherí utacazmr essm `lhmcahmhe pmrm ca`atmr l preouàzl preou àzl gl fmsl he agsufessl hl agvesta`egtl, plr u` heter`agmhl peràlhl, `ms e` flgtrmpmrtahm pmimr u` íial plr assl, resuctmghl e` u` imgbl `eglr fmsl l sufessl gl agvesta`egtl a gvesta`egtl mflgteém.

=8

 

@ÖHUCL AA ‖ FUVXL HE FM^AXMC ^MTM JAGV HE ZMCUMXALG    Geste `öhucl, serí mpresegtmhl fl`l l fustl he fmpatmc pmrm jags he vmcumtalg á fmcfucmhl gm prítafm pmrm ms e`presms gl Drmsac e fl`l ls vmclres he fmhm fl`plgegte hl `lhecl he prefajafméæl he mtavls (FM^@) sæl mpurmhls. Mhafalgmc`egte, seræl he`lgstrmhls ls ejeatls hm mcmvmgfmie` jagmgfearm gl fustl he fmpatmc hls mfalgastms e fl`l l fustl he fmpatmc hls frehlres á fmcfucmhl. Gm sequïgfam, fl`l esta`mr l fustl `áhal plghermhl he fmpatmc hls agvestahlres (F@^F). ^lr ja`, serí explstl l flgfeatl he estruturm öta`m he fmpatmc e fl`l m ierméæl he vmclr plhe lflrrer.

Fustl he fmpatmc hls mfalgastms Veiughl Flstm, Flstm e Mcva` (4>==, p. 22), –ls pragfapmas `lhecls he mvmcaméæl hepeghe` he u`m prevasæl hl jcuxl he fmaxm e hm tmxm he hesflgtl mhequmhm pmrm trmzï-cls m vmclr presegte‐. Gesse flgtextl, esta`mr mhequmhm`egte m tmxm he hesflgtl, lu fustl he fmpatmc, á essegfamc pmrm l sufessl gl prlfessl he mvmcaméæl he e`presms, plas, m hepegher hessm tmxm, l mgmcastm plherí sudesta`mr lu superesta`mr l vmclr he u`m mtavl.  Mhafalgmc`egte, Flstm, Flstm e Mcva` (4>==) mjar`m` que, e`dlrm l fustl he fmpatmc pröpral gæl jaiure gms he`lgstrméões he resuctmhls hms e`presms, ece exaste e á `malr que l fustl he fmpatmc he terfearls plr mpresegtmr `malr rasfl. E` fl`pmrméæl ml rasfl hl fmpatmc he terfearls, l fmpatmc pröpral á hetegtlr he `malr rasfl e` rmzæl he ser l ÿcta`l m refeder l retlrgl hls agvesta`egtls. ^mrm assl, m e`presm heverí ter sufessl, mpresegtmr cufrl e plssuar fmpmfahmhe he fmaxm sujafaegte pmrm hastraduar havaheghls lu he ser veghahm fl` ierméæl he vmclr. Oí l rasfl hl fmpatmc he terfearls á `eglr plrque, aghepeghegte`egte he m e`presm mpresegtmr cufrl lu preouàzl, l pmim`egtl hms pmrfecms heverí lflrrer, mcá` he ls frehlres, glr`mc`egte, exaiare` imrmgtams pmrm m flgfessæl he e`prásta`ls que aghepeghe` hm lperméæl.

 

 

Á flgsmirmhl que l pragfapmc `átlhl he mpurméæl hl fustl he fmpatmc pröpral á l `lhecl FM^@, saicm e` agicïs que saigajafm fmpatmc   msset   prafagi  prafagi   `lhec , trmhuzahl pmrm l plrtuiuïs fl`l seghl l `lhecl he prefajafméæl he mtavls he fmpatmc. ^lr essm rmzæl, l `lhecl FM^@ serí hesfratl m seiuar, hetmcbmghl l saigajafmhl e m lraie` lr aie` he fmhm vmraívec que l fl`põe.

@lhecl he prefajafméæl he mtavls L `lhecl he prefajafméæl he mtavls (FM^@), saicm e` agicïs que saigajafm fmpatmc  msset  prafagi   prafagi   `lhec, á m `etlhlcliam `mas hajughahm gl `erfmhl jagmgfearl pmrm m esta`méæl hl fustl he fmpatmc pröpral. ^mrm @mrtecmgf, ^msag e ^erearm (4>=4), l `lhecl FM^@ pmrte hm pre`assm he que tlhl agvesta`egtl te` l seu rasfl ra sfl havahahl e` dmsafm`egte hums fl`plgegtes? l rasfl haversajafívec haversaj afívec (gæl sastï`afl) e l rasfl gæl haversajafívec ( sastï`afl)?   Tasfl haversajafívec (gæl sastï`afl) ‖ Á m fl`plgegte hl rasfl que hepeghe hms fmrmfteràstafms hl pröpral mtavl e plhe ser ha`aguàhm ml mhafalgmr gm fmrtearm he agvesta`egtls mtavls que `mgtegbm` flrrecméæl agversm egtre sa.   Tasfl gæl haversajafívec (sastï`afl) ‖ Á m fl`plgegte hl rasfl que hepeghe he jmtlres extergls he `erfmhl e mjetm prmtafm`egte tlhms ms e`presms fl` hajeregtes irmus he 

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agtegsahmhe, plr essm rmzæl esse rasfl gæl plhe ser eca`agmhl plr `eal hm haversajafméæl. L rasfl sastï`afl glr`mc`egte heflrre he evegtls he gmturezm plcàtafm, slfamc e eflgø`afm, frases agtergmfalgmas, iuerrms iuerr ms lu mtá `es`l l `mas refegte fmsl he pmghe`am que se agstmclu. Flgsahermghl que l rasfl r asfl gæl sastï`afl á m pmrfecm hl rasfl que plhe ser `ataimhm m pmrtar he estrmtáiafms he haversajafméæl, l `lhecl FM^@ pmrte hl pragfàpal he que l retlrgl mhequmhl pmrm egjregtmr l rasfl sastï`afl heve ser fmcfucmhl pec pecmm sl`m hm re`ugerméæl ljerefahm pecls mtavls cavres cavr es he rasfl e u` prï`al pecl rasfl hl geiöfal. L prï`al pecl rasfl ra sfl hl geiöfal á fmcfucmhl m pmrtar he u` prï`al he `erfmhl `uctapcafmhl plr u`m vmraívec vmra ívec detm (δ) que represegtm l irmu he vlcmtacahmhe hl geiöfal e` recméæl îs jcutuméões hm fmrtearm he `erfmhl usmhm fl`l rejerïgfam. rej erïgfam. Veiughl @mrtecmgf, ^msag e ^erearm (4>=4), m versæl fcíssafm hl `lhecl FM^@ pmrm m esta`méæl hl fustl he fmpatmc pröpral (Ke), lu seom, m tmxm `àga`m he mtrmtavahmhe hl mfalgastm mfalgas tm pmrm remcazmr agvesta`egtls e` u`m e`presm, serí `egsurmhm m pmrtar hm seiuagte expressæl? Ke 0 Tj  + δ Ù (T` ‖ Tj )

Lghe?   K e á l retlrgl espermhl esper mhl pmrm l agvesta`egtl, utacazmhl fl`l fustl hl fmpatmc pröpral.  á m tmxm he ourls ou rls (retlrgl) cavre he rasfl. Á m tmxm equavmcegte î reghm jaxm.   T j j  á   δ á l flejafaegte detm. Expressm l rasfl sastï`afl hl agvesta`egtl e` recméæl ml `erfmhl. esper mhl pmrm m fmrtearm he `erfmhl. Zmclr espermhl hl àghafe hm dlcsm.   T ` á l retlrgl espermhl

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=:

 

 

 

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(T ` ‖ T j j)  á l prï`al pecl rasfl r asfl he `erfmhl. Tegtmdacahmhe mhafalgmc plr mssu`ar rasfl. δ Ù (T` ‖ Tj) á l prï`al pecl rasfl hl agvesta`egtl, lu seom, m regtmdacahmhe mhafalgmc plr mssu`ar l rasfl he agvestar gm e`presm.

^mrm exe`pcajafmr m mpcafmdacahmhe hl `lhecl FM^@, flgsahere que u` agvestahlr estí mgmcasmghl m plssadacahmhe he agvestar e` u`m heter`agmhm e`presm castmhm gm dlcsm he vmclres que plssua u` rasfl sastï`afl 8>% superalr ml hm fmrtearm he `erfmhl, lu seom, detm (δ) aiumc m =,8. Flgsahere maghm que, gl `l`egtl hm plssàvec remcazméæl hl agvesta`egtl, m tmxm he retlrgl ljerefahm pmrm ms mpcafméões cavre he rasfl (Tj) ‖ tàtucls he reghm jaxm ‖ á he 8% ml mgl e que l retlrgl espermhl pecls agvestahlres pmrm m fmrtearm he `erfmhl (T`) á he =2% ml mgl. Gesse fegíral, m tmxm `àga`m he mtrmtavahmhe (X@M), lu fustl hl fmpatmc pröpral hl h l agvestahlr (Ke), serí ser í esta`mhm m pmrtar hls seiuagtes fícfucls? Ke 0 Tj   + + δ Ù (T` ‖ Tj ) Ke 0 8% + =,8 Ù (=2% ‖ 8%) Ke 0 8% + =,8 Ù =8%  Ke 0 8% + =1,:% Ke 0 46,:%

Clil, m tmxm que heverí ser utacazmhm pmrm hesflgtmr ls jcuxls he fmaxm espermhls pmrm l agvesta`egtl serí he 46,:>% ml mgl. E` lutrms pmcmvrms, m regtmdacahmhe he 46,:>% seram flgsahermhm  oustmm pecls  oust pecls agve agvestah stahlres lres pmrm pmrm que se expl explgbm gbm` ` ml rasfl rasfl hm remc remcazmé azméæl æl hl agvesta` agvesta`egtl egtl gl mta mtavl vl e` mgí mgícase case..

Fl`plgegtes hl `lhecl FM^@ e vmraíveas he mouste pmrm `erfmhls e`eriegtes Veræl hetmcbmhms m seiuar ms vmraíveas fl`plgegtes hl `lhecl FM^@, pmrtaghl hl `lhecl trmhafalgmc utacazmhl pmrm pmàses hesegvlcvahls, de` fl`l m remcazméæl hls moustes pmrm mpcafméæl prítafm gls pmàses e`eriegtes.

Xmxm he agjcméæl glrte-m`erafmgm he clgil prmzl Veiughl @mrtecmgf, ^msag e ^erearm (4>=4), á fl`u` que ms prloeéões gls resuctmhls seom` remcazmhms e` `lehm remc, plr essm rmzæl m tmxm he hesflgtl utacazmhm pmrm hesflgtmr ls jcuxls he fmaxm tm`dá` heve rejcetar ls retlrgls e` ter`ls remas, lu seom, imgbls mpös flgsahermhls ls ejeatls hm agjcméæl. L iríjafl =, m seiuar, `lstrm m agjcméæl mgumc reiastrmhm heshe =15: mtá 4>=1. ^lhe ser verajafmhl que m agjcméæl mgumc, reiastrmhm he heze`drl m heze`drl he fmhm mgl, lsfaclu egtre >,>1% e =6,41%.

=9

 

 

Iríjafl =‖ Evlcuéæl hm agjcméæl hls Estmhls Ugahls he =15: m 4>=1

Jlgte? Ecmdlrmhl pecl mutlr ‖ Mtumcazmhl e mhmptmhl he @mrtecmgf, @m rtecmgf, ^msag e ^erearm (4>=4, p.=65).

 Mgmcasmghl m `áham hls ÿcta`ls => mgls, gltm-se que m agjcméæl mplgtm pmrm u`m `áham e` tlrgl he 4,>>% ml mgl, e` cagbm fl` m `etm he agjcméæl jaxmhm pecl Jehermc   Lpeg  @mrket   Fl``attee (Jl`f) pmrm l mgl he 4>4>, flgjlr`e l recmtöral he plcàtafm `lgetíram pudcafmhl e` 9 he jeverearl he 4>4> (JEH, 4>4>d). ^lrtmgtl, essm seram m tmxm mhequmhm pmrm se hesflgtmr l fustl he fmpatmc gl`agmc m ja` he mpurmr m tmxm `àga`m he mtrmtavahmhe remc hls agvesta`egtls.

Xmxm cavre he rasfl (Tj ) ^mrm que u` mtavl seom flgsahermhl cavre he rasfl sld m ötafm jagmgfearm, @mrtecmgf, ^msag e ^erearm (4>=4) esfcmrefe` que l agvesta`egtl heve plssuar rasfl `àga`l he hejmuct, lu seom, l rasfl he m agstatuaéæl que e`atau l tàtucl gæl pmimr heve ser qumse gucl. Gl `erfmhl jjagmgfearl, agmgfearl, ls tàtucls que plssue` essm fmrmfteràstafm sæl ls tàtucls e`atahls pecl Xeslurl glrte-m`erafmgl. ^lrtmgtl, m tmxm cavre he rasfl (T j j)  flgsahermhm mhequmhm pmrm m mpcafméæl prítafm gl `lhecl FM^@ á m re`ugerméæl ljerefahm pecls tàtucls pÿdcafls glrte-m`erafmgls gl `l`egtl hm mquasaéæl hl mtavl e fl` l blrazlgte te`plrmc flghazegte fl` m vahm va hm ÿtac hl agvesta`egtl sld mgícase. Gl ham 4 he omgearl he 4>4>, pra`earl ham ÿtac hl mgl, m re`ugerméæl hls tàtucls pÿdcafls glrte-m`erafmgls fl` vegfa`egtl pmrm => mgls erm he =,22% ml mgl; fl` vegfa`egtl pmrm 4> mgls, he 4,=1% ml mgl; e fl` vegfa`egtl pmrm 6> mgls, he 4,66% ml mgl (UVHX, 4>4>). Glr`mc`egte, ls agvestahlres exaiaræl `malres tmxms qumgtl `mas clgil jlr l prmzl he ve vegfa`egtl, gfa`egtl, e esse pegsm`egtl se rejcete gl `erfmhl he tàtucls pÿdcafls tm`dá`. Á fl`l se exastasse ex astasse u` prï`al plr `mgter l refursl mpcafmhl plr `mas te`pl.

=2

 

 

^rï`al pecl rasfl he `erfmhl (T` ‖ Tj ) L prï`al pecl rasfl he `erfmhl á fmcfucmhl pecm hajeregém egtre l retlrgl espermhl esper mhl pmrm u`m fmrtearm he `erfmhl e m tmxm he retlrgl cavre cavr e he rasfl. E`dlrm bmom agfertezm gls retlrgls hm fmrtearm he `erfmhl, l agvestahlr esperm mujerar u` prï`al plr se mrrasfmr fl` l agvesta`egtl. Veiughl @mrtecmgf, ^msag e ^erearm (4>=4, p. =65), fl` rmzlívec jrequïgfam ls prï`als he `erfmhl sæl fmcfucmhls fl` peràlhls pequegls, fl`l l he fagfl lu => mgls, e tmc pr prítafm ítafm se trmhuz e` u` irmve errl, u`m vez que l `erfmhl he méões plssua mctm vlcmtacahmhe e m utacazméæl he peràlhls furtls plhe resuctmr e` u` hesval-pmhræl hls retlrgls r etlrgls `uatl mctl. ^mrm esta`mr ls prï`als pecl rasfl he `erfmhl gl `lhecl he prefajafméæl he mtavls, Hm`lhmrmg (4>>9, p. 45) esfcmrefe que bí trïs jlr`ms? `ehamgte pesquasm fl` irmghes agvestahlres sldre ms sums expeftmtavms, fl` dmse gls bastörafls hls prï`als remcazmhls e` mgls mgteralres e l prï`al a`pcàfatl `ehamgte m ceaturm he hmhls he `erfmhls. ]umgtl ml prï`al ldtahls plr pesquasms, fl`l ece retrmtm re trmtm u`m `áham plghermhm hls prï`als exaiahls pecls agvestahlres aghavahumc`egte, gm prítafm, mpurmr e fmcfucmr esse vmclr gæl trmz prmtafahmhe, e ms pesquasms mfmdm` plr flgfegtrmr-se e` irmghes iestlres he jughls. Fl`l ls prï`als pecl rasfl plhe` mpresegtmr mctm vlcmtacahmhe, mtumcazmr essms esta`mtavms fl` m rmpahez e l hagm`as`l gefessírals plhe tlrgmr-se mcil a`prmtafívec. Essm á u`m hms rmzões he u`m pmrfecm de` pequegm he prljassalgmas mfmdmr usmghl esses prï`als ldtahls plr pesquasm.  M mdlrhmie` `mas fl`u` pmrm fmcfucmr ls prï`als pecl rasfl, seiughl l egtegha`egtl he Hm`lhmrmg (4>>9, p. 4:), á m esta`méæl fl` dmse gls prï`als bastörafls. ^mrm l `lhecl FM^@, ls prï`als sæl fmcfucmhls `ehamgte m ldtegéæl hm hajeregém egtre ls retlrgls `áhals hl `erfmhl e ls retlrgls `áhals hms mpcafméões cavre he rasfl e` u` peràlhl sujafaegte`egte clgil. Hm`lhmrmg (4>>9, p. 4:) ressmctm maghm l que fbm`lu he –questões he esta`mtavm‐. L plgtl he mtegéæl surie e` rmzæl he que ‖ e`dlrm e `dlrm plssm exastar flgsegsl he que l prï`al bastörafl á, gm prítafm, m `ecblr jlr`m he esta`mr l prï`al pecl rasfl ‖ bí saigajafmtavms hajeregéms ml ldservmr ls prï`als fmcfucmhls plr hajeregtes agstatuaéões. Exe`pcajafmghl, oí jlrm` ldservmhms vmraméões egtre 8% e =4 % ml mgl. Gesse segtahl, tlrgm-se a`plrtmgte esfcmrefer fl`l ms hajeregéms gm esta`méæl hls prï`als pecl rasfl plhe` suriar?   Esflcbm hl peràlhl ‖ Ls prljassalgmas plhe` mpresegtmr hajeregtes oucim`egtls sldre ls peràlhls he ldservméæl mhequmhls pmrm m esta`méæl hls prï`als juturls. E`dlrm mciugs plssm` utacazmr tlhm m sárae bastörafm hasplgàvec, heshe =14:, lutrls plhe` egtegher que ls peràlhls `mas fleregtes pmrm prloetmr l juturl sæl ls `mas refegtes, flgsahermghl ls bastörafls hls ÿcta`ls 6>, 4> lu mtá `es`l => mgls. M utacazméæl he peràlhls furtls pmrm l fícfucl hl prï`al pecl rasfl plhe resuctmr e` u` irmghe errl, mcá` he ls hesvalspmhrões mgumas hls preéls hms méões se mpresegtmre` tæl `malres qumgtl `eglres jlre` ls peràlhls flgsahermhls. 

=1

 

 

 

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Esflcbm hl tàtucl cavre he rasfl ‖ E`dlrm esteom` hasplgàveas hmhls hls retlrgls hls tàtucls he furtl e clgil prmzl, flgsahermghl que m furvm he ourls te` mpresegtmghl vmraméæl, ls prï`als tm`dá` plhe` vmramr m hepegher hls tàtucls esflcbahls. Fl`l, e` irmghe pmrte, ms hefasões e` jagmgéms flrplrmtavms sæl pmrm agvesta`egtls he clgil prmzl, pmrm m esta`méæl hl prï`al pecl rasfl hl `erfmhl he méões, seram fleregte m utacazméæl he tàtucls tm`dá` fl` l vegfa`egtl gl clgil prmzl. Esflcbm hm `áham ‖ ^lr ja`, mpös perflrrahms ms he`mas –questões he esta`mtavms‐, surie sur ie l a`pmsse sldre qumc `áham, mrat`átafm   lu  iel`átrafm , heve ser utacazmhm pmrm l fícfucl hl prï`al pecl rasfl he `erfmhl. @mte`mtafm`egte, m `áham mrat`átafm fmcfucm l vmclr hl prï`al espermhl flgsahermghl m `áham sa`pces hls retlrgls mpresegtmhls gm sárae bastörafm, egqumgtl m `áham iel`átrafm fmcfucm l vmclr hl prï`al flgsahermghl ls retlrgls fl`l u` regha`egtl m tmxms fl`plstms. L segsl fl`u` á he que l usl hm `áham mrat`átafm seram l `mas mhequmhl, flgtuhl, bí b í mriu`egtls que jmze` `uatl segtahl e` jmvlr hl usl hm `áham iel`átrafm. Fl`l bí estuhls que mplgtm` m exastïgfam he u`m flrrecméæl hm geimtavm hls prï`als he rasfl r asfl fl` l te`pl, l usl hm `áham mrat`átafm plhe superesta`mr l prï`al. Lutrlssa`, fl`l ls agvesta`egtls glr`mc`egte sæl remcazmhls pmrm clgil prmzl, l usl hm `áham iel`átrafm pmrefe `mas rmzlívec. r mzlívec.

L jmtl á que l vmclr esta`mhl pmrm l prï`al he rasfl plhe vmramr flgjlr`e m vasæl hl mgmcastm pmrm ls peràlhls que heve` ser utacazmhls, l pmrä`etrl que heve ser usmhl pmrm m esflcbm hl tàtucl cavre he rasfl e se l fícfucl hm `áham serí remcazmhl mrat`átafm lu iel`etrafm`egte. Ms plssadacahmhes pmrm l `erfmhl jagmgfearl hls Estmhls Ugahls egflgtrm`-se resu`ahms gm tmdecm =, m seiuar? Xmdecm = ‖ ^rï`als pecl rasfl bastörafl gls Estmhls Ugahls he =142 mtá 4>=1 méões `egls tàtucls he F^

méões `egls tàtucls he C^

mrat`átafl

iel`átrafl

mrat`átafl

iel`átrafl

peràlhl

=142-4>=1

tlhl l bastöra bastörafl fl

2,=2%

:,65%

:,86%

8,26%

=19>-4>=1

ÿcta` ÿcta`ls ls 5> mgls

9,4:%

5,16%

8,5>%

6,54%

4>=>-4>=1

ÿcta` ÿcta`ls ls => mgls

=6,5=%

=4,16%

1,:9%

1,6=%

Jlgte? Mhmptmhl he Hm`lhmrmg (4>>9, p. 49) e mtumcazmhl mtá 4>=1. 4>=1.  

4>

 

 

Glte que ls prï`als pecl rasfl mpresegtmhls plhe` vmramr he 6,54% m =6,5=% ml mgl, hepegheghl hm esflcbm jeatm. U` jmtl `uatl agteressmgte á que Hm`lhmrmg (4>>9, p. 49) mjar`m que, se seiuar`ls ms prlplsaéões he esflcber l prï`al `áhal iel`átrafl he clgil prmzl fl`l l suierahl, –l prï`al pecl rasfl que jmz j mz `mas segtahl á 8,28%‐. Assl fl` hmhls mtumcazmhls mtá 4>>8 e ml mtumcazmr ls hmhls mtá 4>=1, e`dlrm ms lutrm `áhams `áha ms plssm` ter sljrahl mcterméões, ml flgsahermr tlhl l bastörafl, `áham iel`átrafm e hajeregém fl` tàtucls he clgil prmzl, l resuctmhl `mgteve-se prmtafm`egte estívec? 8,26% ml mgl, `es`l flgsahermghl u` peràlhl =5 mgls `malr.

^rï`al pecl rasfl he `erfmhl e` lutrls `erfmhls  M aghmiméæl sldre fl`l esta`mr l prï`al pecl rasfl e` tlhls ls pmàses á m`pcm`egte hasfutahm gls m`daegtes mfmhï`afls. Ecm surie hm hajafuchmhe he ldtegéæl hls hmhls bastörafls, que, qumghl exaste`, plr mpresegtmr mctm vlcmtacahmhe, resuctm` hesvals-pmhrões `uatl ecevmhls. E` pesquasm fl` hmhls he =9 pmàses, Hm`lhmrmg (4>>9, p. 49) retrmtm que, e`dlrm ls retlrgls hls agvesta`egtls e` méões bastlrafm`egte tegbm` mpresegtmhl `malr retlrgl qumghl fl`pmrmhls îs ldraiméões he furtl e clgil prmzl hls seus ilvergls ‖ tàtucls pÿdcafls ‖, exaste` saigajafmtavms hajeregéms egtre ls pmàses exm`agmhls. Tessmctm maghm que á plssàvec egflgtrmr peràlhls clgils e` que ls retlrgls hls^lrtmgtl, tàtucls pÿdcafls mpresegtmhlheregha`egtls `ecblres hle`queméões ms méões e` mciugs `erfmhls. flgfcuategbm` que m presugéæl que ls agvesta`egtls se`pre resuctmræl e` retlrgls superalres mls hls ljerefahls plr tàtucls he clgil prmzl e` tlhls ls `erfmhls –gæl á sö perailsm, fl`l tm`dá` gæl jmz segtahl‐. ^las, se se`pre jlsse mssa`, agvestar e` méões heveram ser flgsahermhl u` agvesta`egtl cavre he rasfl pmrm ls agvestahlres fl` m vasæl he agvesta`egtl pmrm clgil prmzl.

^rï`al pecl rasfl-pmàs (Task flugtry) Fl`l mctergmtavm pmrm m esta`méæl hl prï`al pecl rasfl gls pmàses e`eriegtes, Hm`lhmrmg (4>>9, p. 49) mjar`m que l prï`al pecl rasfl e` qumcquer pmàs plhe ser fmcfucmhl mhafalgmghl mhafal gmghl l rasfl pmàs ml prï`al pecl rasfl he u` `erfmhl `mhurl, gl fmsl, l glrte-m`erafmgl. Ms rmzões sæl ms `es`ms oí mpresegtmhms mgteralr`egte? hajafuchmhe he ldtegéæl he hmhls bastörafls, ls qumas, qumghl exaste`, mpresegtm` mctm vlcmtacahmhe, l que resuctm e` u` hesval-pmhræl extre`m`egte ecevmhl. ^mrm Hm`lhmrmg (4>>9, p. 42), sæl trïs ms mdlrhmiegs pmrm esta`mr l prï`al pecl rasfl-pmàs? ra sfl-pmàs? =.  Vpremh plr agmha`pcïgfam he ldraiméões hls ilvergls ‖ Á m esta`méæl hl rasfl-pmàs fmcfucmhl plr miïgfams he rmtagis que fcmssajafm` ls tàtucls e`atahls pecls pmàses fl` dmse gl rasfl he agmha`pcïgfam hesses tàtucls. E`dlrm gæl `eém` l rasfl hl `erfmhl mfalgíral, l rmtagi mfmdm seghl mjetmhl plr ece. U`m mctergmtavm pmrm m ldtegéæl hm tmxm represegtmtavm hl rasfl- pmàs   pmàs  pmrm  pmrm l Drmsac, seiughl Verrm e Yafkert (4>=1, p. 55), á utacazmr

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l àghafe E@DA+= Drmsac (E`eriagi @mrkets Dlgh Aghex ‖ Drmzac ). ). Esse àghafe á fmcfucmhl pecl O^@lrimg Fbmse flgsahermghl l spremh he u`m festm he tàtucls drmsacearls. L E@DA+ Drmsac á fmcfucmhl flgstmgte`egte e havucimhl gl sate  www.apemhmtm.ilv.dr.   www.apemhmtm.ilv.dr. L Apemhmtm á u`m dmse he hmhls `mfrleflgø`afls, jagmgfearls e reialgmas hl Drmsac `mgtahm pecl Agstatutl he ^esquasm Eflgø`afm Mpcafmhm (Apem). Gl ÿcta`l ham hl mgl he 4>=1, l rasfl-Drmsac mplgtmhl pecl E@DA+ Drmsac reiastrmvm 4=8 plgtls, l que saigajafm hazer que ls agvesta`egtls gl Drmsac Dr msac exaiam` u` spremh pecl rasfl-pmàs he 4,=8% ml mgl. Fmhm =>> plgtls gm esfmcm he rasfl equavmce` m =,>% he tmxm he retlrgl exaiahm mhafalgmc. 4.  Hesval-pmhræl recmtavl ‖ Veiughl Hm`lhmrmg (4>>9, p. 42) á tmxm represegtmtavm hl rasfl-pmàs fmcfucmhm pecm vlcmtacahmhe hms méões hl `erfmhl he u` pmàs. Veiuaghl essm cagbm he pegsm`egtl, ml fmcfucmr l hesval-pmhræl recmtavl, hl `erfmhl e` mgícase e` recméæl ml `erfmhl `mhurl, ldtá`-se u` aghafmhlr he rasfl recmtavl que ml ser `uctapcafmhl pecl prï`al he rasfl fmcfucmhl pmrm l `erfmhl `er fmhl glrte-m`erafmgl, egflgtrmse l prï`al pecl rasfl tltmc pmrm qumcquer `erfmhl he méões. Vldre m utacazméæl prítafm hessm cagbm he rmfalfàgal, Hm`lhmrmg (4>>9, p. 41) fl`pce`egtm que, e`dlrm agtuatavm`egte pmreém rmzlívec essm mdlrhmie`, bmverí prldce`ms ml fl`pmrmr l hesvalpmhræl he `erfmhls fl` estruturms e caquahez hajeregtes. Gesse segtahl, essm mdlrhmie`  pmàs  hesses prlvmvec`egte cevmrí î sudesta`méæl hls prï`als pecl rasfl- pmàs   hesses `erfmhls. 6.  Vpremhs que rejcete` l rasfl he agmha`pcïgfam `mas l hesval-pmhræl recmtavl ‖ Á m mdlrhmie` utacazmhm plr Hm`lhmrmg (4>>9, p. 41) que vasm moustmr l rasfl-pmàs , l qumc `ehe l rasfl he agmha`pcïgfam hls tàtucls hl ilvergl, fl` l spremh pecl rasfl hl `erfmhl he méões hesse `erfmhl. M presugéæl á he que l prï`al pecl rasfl-pmàs he agvesta`egtl e` méões heve ljerefer u` spremh sldre l rasfl-pmàs he agvesta`egtl e` tàtucls hl ilvergl hesse pmàs. @mte`mtafm`egte, mgmcasm-se m vlcmtacahmhe hl `erfmhl he méões e` recméæl î vlcmtacahmhe hls retlrgls hls tàtucls pÿdcafls e `uctapcafm-se pecl spremh plr agmha`pcïgfam hl pmàs, lu seom, l rasfl- pmàs   pmàs   fmcfucmhl fl` dmse gl spremh   plr agmha`pcïgfam he ldraiméões hls ilvergls.

E` iermc, ms trïs mdlrhmiegs mpresegtmræl esta`mtavms hajeregtes, flgtuhl, Hm`lhmrmg (4>>9, p. 6>) mfrehatm que m ÿcta`m mdlrhmie` mpresegte vasões `mas remcastms, e`dlrm l hagm`as`l hl fícfucl prevmceém.

=

 L E@DA+ á u` àghafe dmsemhl gls døgus ‖ tàtucls he hàvahm ‖ e`atahls pecls pmàses e`eriegtes. @lstrm ls retlrgls jagmgfearls ldtahls m fmhm ham plr u`m fmrtearm secefalgmhm he tàtucls hesses pmàses. M ugahmhe he `ehahm á e` plgtls-dmse. Fmhm => plgtlsdmse equavmce` m u` háfa`l plr fegtl, lu seom, >,=>%. Ls plgtls `lstrm` m hajeregém egtre m tmxm he retlrgl hls tàtucls he pmàses e`eriegtes e m ljerefahm plr tàtucls e`atahls pecl Xeslurl glrte-m`erafmgl. Essm hajeregém á l spremh , lu l spremh   sldermgl. L E@DA+ jla framhl pmrm fcmssajafmr sl`egte pmàses que mpresegtmsse` mctl gàvec he rasfl seiughl ms miïgfams he rmtagi   e que tavesse` e`atahl tàtucls he vmclr `àga`l he UV$ 5>> `acbões, fl` prmzl he ml `egls he 4,5 mgls. M `etlhlcliam he fícfucl hl E@DA+ estí hesfratm e` AGVXAXUXL HE ^EV]UAVM EFLGØ@AFM M^CAFMHM (Apem). Àghafe mvmcam fl` ldoetavahmhe tàtucls hm hàvahm hls pmàses e`eriegtes. e`eriegtes . Hasplgàvec e`? 3bttp?//www.apemhmtm.ilv.dr/hlf/@etlhlcliam%4>E`da.hlf7.

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L prljesslr Mswmtb Hm`lhmrmg, hlfegte gm Vterg Vfbllc lj Dusagess hm Ugaversahmhe he Glvm Qlrk, á flgsahermhl rejerïgfam qumghl l mssugtl á vmcumtalg. ^mrm m mceiram hls mvmcamhlres he e`presms hl `ughl tlhl, l prljesslr Hm`lhmrmg `mgtá` u`m píiagm gm agterget, flgstmgte`egte mtumcazmhm, lghe flgslcahm tlhls ls fícfucls hls prï`als pecl rasfl hl `erfmhl glrte-m`erafmgl e pmrm ls `erfmhls e`eriegtes, mcá` he hasplgadacazí-cls he jlr`m irmtuatm, agfcusave l fícfucl hls detms que vere`ls `mas î jregte. L mfessl m esses hmhls, gæl sö plupm u` eglr`e trmdmcbl pmrm ls mvmcamhlres, fl`l imrmgte `malr mssertavahmhe e 4 flgjamdacahmhe gm esta`méæl hl prï`al pecl rasfl he `erfmhl, agfcuaghl a gfcuaghl l prï`al pecl rasfl-pmàs .    Ms agjlr`méões pudcafmhms gl sate  fl`  fl` hmtm-dmse hl pra`earl ham ÿtac he omgearl he 4>4>, oí fl` ls hevahls moustes egteghahls plr ece, mplgtmvm` pmrm ms seiuagtes agjlr agjlr`méões? `méões?   prï`al pecl rasfl he `erfmhl glrte-m`erafmgl? 5,4>% ml mgl; Dr msac? 4,5=% ml mgl;   prï`al pecl rasfl-pmàs pmrm l Drmsac?   hesval-pmhræl recmtavl pmrm `erfmhls e`eriegtes? =,=2 e   prï`al pecl rasfl he `erfmhl pmrm agvesta`egtl e` méões gl Drmsac? 2,=:% ml mgl. 

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^lrtmgtl, pmrm Hm`lhmrmg (4>>9, p. 41), l prï`al pecl rasfl he `erfmhl pmrm pmàses e`eriegtes plhe ser fmcfucmhl mpcafm mpcafmghl ghl m se seiuagte iuagte equméæl?

^rï`al pecl rasfl he `erfmhl moustmhl ml pmàs

0

^rï`al pecl rasfl he `erfmhl (glrte-m`erafmgl)

+

^rï`al pecl rasfl-pmàs (spremh  plr  plr agmha`pcïgfam hl pmàs)

Hesval-pmhræl recmtavl x

(φméões hl pmàs ù

φtàtucls he C^ hl pmàs)

Exe`pcajafmghl, fl` ls hmhls jlrgefahls mfa`m, fl` hmtm-dmse he =¿ he omgearl he 4>4>, te`ls? Dr msac 0 5,4>% + 4,5=% Ù =,=2;   prï`al pecl rasfl he `erfmhl moustmhl ml Drmsac Dr msac 0 5,4>% + 4,1:% e   prï`al pecl rasfl he `erfmhl moustmhl ml Drmsac   prï`al pecl rasfl he `erfmhl moustmhl ml Drmsac Dr msac 0 2,=:% ml mgl.

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^rï`al pecl tm`mgbl hm e`presm (Vaze pre`au`)  Mciugs pesquasmhlres sldre l mssugtl vmcumtalg egteghe` que l agvesta`egtl e` e`presms `eglres heve ljerefer retlrgls `malres qumghl fl`pmrmhls mls retlrgls ljerefahls plr irmghes e`presms hl `es`l sei`egtl. Veiughl @mrtecmgf, ^msag e ^erearm (4>=4, p. =89), esse prï`al tm`dá` se oustajafm e` rmzæl hm prlvívec jmctm he caquahez e, gl Drmsac, –mciugs mvmcamhlres fbeim` m utacazmr u` prï`al he =% m :%, hepegheghl hl tm`mgbl hm e`presm, e l mpcafm` m e`presms fl` jmturm`egtl agjeralr m T$ 4>> `acbões‐. 4

 Dmse he hmhls hasplgàvec e`? 3bttp?//pmies.sterg.gyu.ehu/~mhm`lhmr7.

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E` cagbm fl` esse egtegha`egtl, Mssmj Getl (4>=1, p. 25) ressmctm que –mciugs trmdmcbls hesegvlcvahls gl `erfmhl hls EUM suiere` que e`presms he `eglr plrte mpresegtm` `malr rasfl jagmgfearl e eflgø`afl que ms he `malr plrte‐ e, plr essm rmzæl, mpresegtmram` u` fustl he fmpatmc pröpral `mas mctl.

Detm fl`l `ehahm he rasfl (δ)   M fl`plge fl `plgegte gte detm (δ) gl `lhecl he prefajafméæl he mtavls (FM^@) á u`m vmraívec que `ehe m vlcmtacahmhe hl mtavl que estí e` mgícase e` recméæl î vlcmtacahmhe hl `erfmhl he méões fl`l u` tlhl. ^lr essm rmzæl, l detm (δ) he u`m méæl expressm l rasfl sastï`afl he u` mtavl e` recméæl ml `erfmhl. ^mrm `ecblr evahegfamr l saigajafmhl hm vmraívec detm, flgsahere ls `lva`egtls bastörafls he retlrgl he trïs méões e` fl`pmrméæl ml retlrgl he u`m fmrtearm he `erfmhl, plr exe`pcl, l àghafe V&^ 5>>, àghafe he rejerïgfam hl `erfmhl he méões glrte-m`erafmgl. Ls exe`pcls estæl hetmcbmhls m seiuar?    Méæl M ‖ Mpresegtlu, bastlrafm`egte, retlrgls equavmcegtes ml hldrl hls retlrgls mpresegtmhls pecl àghafe V&^ 5>>. ^lhe`ls hazer, egtæl, que l detm hm Méæl M á aiumc 

m 4. Geste fmsl, pmrm fmhm vmraméæl he =% gl àghafe V&^ 5>>, serí espermhm u`m vmraméæl he 4% gls retlrgls hm Méæl M.    Méæl D ‖ Mpresegtlu, bastlrafm`egte, retlrgls equavmcegtes î `etmhe hls retlrgls mpresegtmhls pecl àghafe V&^ 5>>. ^lhe`ls hazer, egtæl, que l detm hm Méæl D á aiumc m >,5. Gesse fmsl, pmrm fmhm vmraméæl he =% gl àghafe V&^ 5>>, serí espermhm u`m vmraméæl he >,5% gls retlrgls hm Méæl D.    Méæl F ‖ Mpresegtlu, bastlrafm`egte, retlrgls aiumas mls retlrgls mpresegtmhls pecl àghafe V&^ 5>>. ^lhe`ls hazer, egtæl, que l detm hm Méæl F á aiumc m =. Lu seom, pmrm fmhm vmraméæl he =% gl àghafe V&^ 5>>, serí espermhm tm`dá` u`m vmraméæl he =% gls retlrgls hm Méæl F.

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Ls exe`pcls sæl trmhuzahls gl iríjafl 4, m seiuar? Iríjafl 4 ‖ Xmxm he retlrgl R te`pl

Jlgte? Ecmdlrmhl pecl mutlr  mutlr  

Flgsahermghl que l m`daegte teghe m `mgter u`m satuméæl he equacàdral, lu seom, mháqum ls retlrgls ml gàvec he rasfl he fmhm mtavl, plhe-se pegsmr que qumgtl `malr l retlrgl he u`m méæl, `malr serí l seu rasfl, gl fmsl, l seu rasfl sastï`afl lu saste`ítafl. Clil, egtre ms trïs méões hesfratms, m Méæl M seram hetegtlrm he `malr rasfl plr mpresegtmr `malr vlcmtacahmhe e` recméæl ml àghafe he `erfmhl usmhl fl`l rejerïgfam. ^mrm egtegher pmrte hls `lva`egtls `lva `egtls hms méões, flgsahere milrm l flgtríral? m Méæl D mpresegtm `malr rasfl. Xmc satuméæl acustrm u`m satuméæl he hesequacàdral e, gesse fmsl, seghl ecm plssuahlrm he `malr rasfl e` recméæl î Méæl M e teghl mcfmgémhl u` resuctmhl `eglr, perherí m sum mtrmtavahmhe. Ls plssuahlres hm Méæl D ljertmræl ms méões gl `erfmhl jmzeghl fl` que ls seus preéls fmam` mtá u` vmclr fleregte fl` l seu gàvec he rasfl. E` flgtrmpmrtahm, fmsl m Méæl M mpresegte u` retlrgl `malr e u` gàvec he rasfl `eglr, ls agvestahlres se segtaræl mtrmàhls e, gessm satuméæl, he`mghmræl ms méões gl `erfmhl jmzeghl fl` que ls seus preéls sudm`. M sudahm he preél jmram fl` que ls retlrgls fmàsse` e, hessm jlr`m, m satuméæl he equacàdral rasfl versus  retlrgl  retlrgl seram reestmdecefahm. Gls exe`pcls fatmhls, ms Méões M, D e F plssuaram` respeftavm`egte detms aiumas m 4; >,5 e =. Ldservm-se que, fmsl m méæl mpresegte l detm aiumc m =, ls retlrgls espermhls pmrm ecm seræl aiumas mls retlrgls espermhls pmrm m fmrtearm he `erfmhl usmhm fl`l rejerïgfam. Ls rasfls hls he`mas mtavls seram` `ehahls pecl hese`pegbl e` recméæl m esse `erfmhl, lu seom, ml rasfl hl àghafe he `erfmhl.  Mtavls fl` rasfl `malr `malr hl que l hl `erfmhl `erfmhl plssue` detms `malres `malres hl que =, =,>, >, e mtavls fl` rasfl `eglres hl que l hl `erfmhl plssue` detms `eglres hl que =,>. ^lrtmgtl, pmrm l fícfucl hl detm he u`m méæl, seræl gefessírams gefessírams ms sáraes bastörafms he retlrgls r etlrgls hm respeftavm méæl e hl `erfmhl ml qumc se heseom rejeregfamr. L detm ( δ) serí fmcfucmhl ml se remcazmr m reiressæl cagemr hms hums sáraes bastörafms, lu seom, á m vmraívec que `ehe m agfcagméæl hm retm he reiressæl e plhe ser fmcfucmhl haretm`egt haretm`egtee mpcafmghl m seiuagte equméæl?

45

 

 

δ 0 Flv (Tm ; T`) ù φ´ (T`)

Lghe?   δ á l àghafe detm hl mtavl. ;  T `) á m flvmraägfam hls retlrgls hl mtavl –m‐ e` recméæl mls retlrgls he `erfmhl.   Flv (T m m;T   sæl ls retlrgls hl mtavl –m‐.   T m m  sæl 

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T ` sæl ls retlrgls hm fmrtearm he `erfmhl usmhm fl`l rejerïgfam. ^lr exe`pcl, l àghafe V&^ 5>>, fl`plstl hls 5>> mtavls `mas a`plrtmgtes geilfamhls gl `erfmhl glrte-m`erafmgl. φ´ (T `) á m vmraägfam hls retlrgls hm fmrtearm he `erfmhl usmhm fl`l rejerïgfam. Á l hesval-pmhræl hls retlrgls hm fmrtearm he `erfmhl ecevmhl ml qumhrmhl.

^erfede-se que, se l fícfucl hl detm hepeghe hm sárae bastörafm he retlrgls hm méæl e hl `erfmhl, u`m `es`m méæl plhe mpresegtmr detms hajeregtes se flgsahermhls peràlhls hajeregtes. M fl`pmrméæl egtre ls hmhls hesfratls gms jaiurms = e 4, m seiuar, acustrm` l detm he u`m `es`m méæl fmcfucmhl fl` peràlhls hajeregtes? Jaiurm = ‖ Fícfucl hl detm hm méæl hectm fl` =4 peràlhls

Jlgte? Ecmdlrmhm pecl mutlr

4:

 

 

Jaiurm 4 ‖ Fícfucl hl detm hm méæl hectm fl` =2 peràlhls

Jlgte? Ecmdlrmhm pecl mutlr  mutlr 

 Maghm gæl exaste flgsegsl sldre qumgtls peràlhls heve` ser flgsahermhls pmrm l fícfucl hl detm, tm`plufl sldre qumc ugahmhe he te`pl heve hev e ser m dmse pmrm fmcfucmr ls retlrgls, plr exe`pcl, se retlrgls ml `ïs lu ml mgl. Hesse `lhl, flgsahermr u` peràlhl he retlrgls fl`pmtàvec fl` l peràlhl prlplstl pmrm l agvesta`egtl á plgtl frufamc pmrm se fmcfucmr l detm he u` mtavl mhequmhm`egte. Hessm `mgearm, esperm-se que esse flejafaegte rejcatm ms prlvíveas lsfacméões he retlrgls hl mtavl e` recméæl ml `erfmhl he jlr`m `mas mheregte. 49

 

 

Lutrm vmraívec que heve ser fl`preeghahm ml se fmcfucmr l detm á l flejafaegte he heter`agméæl (T´), que, gm jaiurm =, mpresegtm u` vmclr he >,1:61 e, gm jaiurm 4, u` vmclr he >,1:>8. Essm `ehahm estmtàstafm, fmcfucmhm pecl qumhrmhl hm flrrecméæl, seiughl Mssmj Getl (4>=1, p. 95), á a`plrtmgte pmrm se mvmcamr m qumcahmhe hl mouste hm retm he reiressæl. L flejafaegte he heter`agméæl (T´) plhe vmramr egtre >,> e =,>, lghe >,> saigajafm que gæl bí flrrecméæl e =,> evahegfamghl m exastïgfam he u`m flrrecméæl perjeatm. ^lr exe`pcl, gl fmsl hls retlrgls hm jaiurm =, l flejafaegte he heter`agméæl (T´) resuctmghl e` >,1:61, saigajafm hazer que 1:,61% hls plgtls se moustm` perjeatm`egte î retm he reiressæl, aghafmghl que 1:,61% hl rasfl hm méæl hectm rejcete l rasfl sastï`afl lu he `erfmhl. M hajeregém he 6,:=% (= - T´) rejcete rej cete ls rasfls heflrregtes hm pröpram e`presm, tmas fl`l? rasfl he caquahez, mcmvmgfmie`, `mrie` e lutrls. Essm hajeregém plheram ser agterpretmhm fl`l jmtlres heter`agmgtes hl rasfl haversajafívec. Vmder fmcfucmr l detm he jlr`m mhequmhm plhe tlrgmr-se u` irmghe hajeregfamc gl `l`egtl he mvmcamr u` agvesta`egtl, plas hece hepegherí l fícfucl que resuctmrí gm tmxm mhequmhm pmrm se hesflgtmre` ls jcuxls he fmaxm juturls he u` mtavl fl` rasfl. Detms fl` vmclres hajeregtes resuctmræl e` tmxms he hesflgtls hajeregtes, e, flgsequegte`egte, m mvmcaméæl he u` agvesta`egtl mpresegtmrí tm`dá` u` vmclr hajeregte. Hm`lhmrmg (4>>9, p. 64) suiere que, pmrm fmcfucmr l detm he u` mtavl, l mgmcastm heverí tl`mr trïs hefasões? =) hejagar l tm`mgbl hm m`lstrm; 4) hejagar m peralhafahmhe hls hmhls; e 6) esflcber l `erfmhl m ser usmhl fl`l rejerïgfam. E` recméæl m estm ÿcta`m hefasæl, l mutlr fl`pce`egtm que l rejeregfamc flrretl m ser usmhl heve ser hejagahl pecms plsaéões mfalgírams hl agvestahlr. Fmsl l agvestahlr `mgtegbm plsaéões e` méões he u` heter`agmhl `erfmhl ‖ pmàs ‖, tlrgm-se fleregte fmcfucmr l detm usmghl l àghafe hesse `erfmhl. Gl fmsl hl agvestahlr icldmcazmhl, l fícfucl hl detm serí `mas de` ha`egsalgmhl ml usmr fl`l rejerïgfam rejer ïgfam u` àghafe icldmc. Gm prítafm, prljesslr Mswmtb Hm`lhmrmg, gl seu sate , lghe pudcafm ms vmraíveas he `erfmhl peralhafm`egte, `egfalgm que, pmrm l fícfucl hls detms pmrm ms e`presms glrte-m`erafmgms, utacazm ls retlrgls se`mgmas e` recméæl ml àghafe V&^ 5>>, he u` peràlhl hlas mgls e lutrl he fagfl mgls. ^mrm tegtmr fmptmr ls ejeatls hms `uhmgéms hms fmrmfteràstafms hms e`presms, Hm`lhmrmg (4>4>) plgherm l vmclr hmghl l pesl he 4/6 pmrm l detm fmcfucmhl pmrm ls hlas ÿcta`ls mgls e he =/6 pmrm l detm fmcfucmhl utacazmghl ls fagfl ÿcta`ls mgls (GQU, 4>4>h).

Detm moustmhl ml gàvec he mcmvmgfmie` ( δ mcmvmgfmhl) Vldre l detm, Hm`lhmrmg (4>>9, p. 66) esfcmrefe que, e`dlrm plssm ser heter`agmhl plr `eal he reiressões, m vmraívec á heter`agmhm plr jmtlres jughm`egtmas ageregtes î e`presm, tmas fl`l? sei`egtl he `erfmhl, gàvec gàve c he mcmvmgfmie` lpermfalgmc e gàvec he mcmvmgfmie` jagmgfearm. Vldre ls jmtlres trïs jmtlres heter`agmgtes hl detm, Verrm e Yafkert (4>=1, p. 4=) suiere` que m pmrte lpermfalgmc ‖ sei`egtl he `erfmhl e mcmvmgfmie` lpermfalgmc ‖ seom prmtafm`egte fl`u` pmrm e`presms hl `es`l setlr e que l ÿgafl ÿ gafl jmtlr heter`agmgte hl detm hajeregte egtre ms e`presms hl `es`l rm`l he mtavahmhe seram ser am l gàvec he mcmvmgfmie` jagmgfearm.

42

 

 

Gesse segtahl, Hm`lhmrmg (4>>9, p. 68) ressmctm que u`m –mcmvmgfmie` `mas mctm mu`egtm m vmraägfam gls cufrls plr méæl e tlrgm l agvesta`egtl a gvesta`egtl `mas mrrasfmhl‐. ^mrtaghl hl pressuplstl he que tlhl l rasfl he `erfmhl hm e`presm seom se om sustegtmhl pecls mfalgastms ‖ se` m exastïgfam he hàvahm, hàva hm, plrtmgtl, u` detm he hàvahm aiumc m zerl ‖, e que ml tl`mr fráhatl m e`presm framram u` degejàfal tradutíral, m expressæl que rejcete ls ejeatls hm hàvahm gl detm serí ser í m seiuagte? δm 0 δh Ù [ = + (^ ù ^C) Ù (= ‖ AT) P

Lghe?  á l detm mcmvmgfmhl, expra`e l rasfl tltmc hm e`presm e` recméæl ml `erfmhl.   δm  á   δh á l detm hesmcmvmgfmhl, expra`e l rasfl eflgø`afl hm e`presm (se` hàvahms).   ^ á l vmclr he fmpatmc he terfearls agserahl gl fmpatmc tltmc hm e`presm. 

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^C á l vmclr he fmpatmc pröpral agserahl gl fmpatmc tltmc hm e`presm.

 

AT á m mcàqultm he a`plstl he reghm `mriagmc m que m e`presm estí suoeatm.

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Gltm-se que gm `ehahm e` que l gàvec he eghavahm`egtl hm e`presm mu`egtm, l jmtlr [ = + (^ ù ^C) Ù (= ‖ AT) P agflrplrm l rasfl jagmgfearl ml detm, iermghl u` detm mcmvmgfmhl fl` l gàvec he eghavahm`egtl hm e`presm e` mgícase. L agversl mflgtefe ml havahar l detm mcmvmgfmhl ‖ mpurmhl pecls bastörafls he retlrgl he `erfmhl ‖ pecl `es`l jmtlr, e, gesse fmsl, l detm egflgtrmhl serí l detm hesmcmvmgfmhl, lu seom, fl`l se m e`presm jlsse tltmc`egte jagmgfamhm mpegms plr fmpatmc pröpral. ^mrm `ecblr acustrmr m recméæl exastegte egtre ls detms mcmvmgfmhls e hesmcmvmgfmhls, ldserve l exe`pcl que seiue. Flgsahere l detm mcmvmgfmhl hm méæl he u`m heter`agmhm e`presm, mpurmhl pecls bastörafls he retlrgl hm méæl e` recméæl ml `erfmhl, aiumc m =,:>58. Hl tltmc he fmpatmc que jagmgfam m e`presm, T$ 695.>>>,>> sæl jagmgfamhls plr terfearls, e l restmgte, equavmcegte m T$ :45.>>>,>>, á jagmgfamhl pecls söfals, lu seom, plr fmpatmc pröpral. M e`presm estí suoeatm m u`m mcàqultm he a`plstl he reghm aiumc m 68% hl seu cufrl. Gesse fmsl, esperm-se que l detm hesmcmvmgfmhl hm e`presm seom l seiuagte? δm 0 δh Ù [ = + (^ ù ^C) Ù (= ‖ AT) P =,:>58 0 δh Ù [ = + (695.>>> ù :45.>>>) Ù (= ‖ 68%) P =,:>58 0 δh Ù [ = + (>,:>) Ù (>,::) P  =,:>58 0 δh Ù [ = + (>,61:) P  =,:>58 0 δh Ù =,61:  =,:>58 ù =,61: 0 δh  =,=5>> 0 δh 

41

 

 

^lrtmgtl, flgjlr`e l egtegha`egtl he Mssmj Getl (4>=1, p. 2>), m represegtméæl hl detm tltmc hm e`presm, se flgsahermhls ls hmhls hesfratls mfa`m, plhe ser mpresegtmhm hm seiuagte jlr`m? detm tltmc (detm (detm mcmvmgfmhl) mcmvmgfmhl) pmrm m recméæl (^ ù ^C) he :>%

0

=,:>58

rasfl eflgø`afl hl geiöfal (detm (detm hesmcmvmgfmhl) hesmcmvmgfmhl)

0

=,=5>>

mfrásfa`l pecl rasfl e` rmzæl hl eghavahm`egtl

0

>,8558

Flgsahermghl que milrm l flejafaegte que rejcete mpegms l rasfl hl geiöfal oí á flgbefahl, tlrgm-se plssàvec fmcfucmr l detm mcmvmgfmhl pmrm e`presms fl` hajeregtes estruturms he fmpatmc, lu seom, hajeregtes gàveas he eghavahm`egtl, eghav ahm`egtl, e, flgsequegte` flgsequegte`egte, egte, egflgtrmr l fustl he fmpatmc pröpral pmrm fmhm estruturm he fmpatmc utacazmghl l `lhecl FM^@. ^mrm `ecblr fl`preegsæl hls ejeatls hm mcmvmgfmie` jagmgfearm, ldserve ls hmhls hm tmdecm 4, m seiuar, flgsahermghl, m tàtucl he exe`pcl, ms seiuagtes vmraíveas? vmra íveas? detm hesmcmvmgfmhl (δh) aiumc m =,=5>>, tltmc hl fmpatmc agvestahl aiumc m T$ = `acbæl, mcàqultm he a`plstl he rreghm eghm (AT) aiumc m 68%, tmxm cavre he rasfl (Tj) he 8,>% ml mgl e u` prï`al mgumc pecl rasfl he `erfmhl (T` ‖ Tj) aiumc m 5,4>% ml mgl.

6>

 

 

Xmdecm 4 ‖ Fícfucl hl fustl he fmpatmc fl` detm mcmvmgfmhl Tecméæl hm Hàvahm (^) fl` l (^C)

(δm) 0 Detm Mcmvmgfmhl Mcmvmgfmhl

Ke 0 Fustl he Fmpatmc Fmpa tmc ^röpral

^

δm 0 δm R [= + (^ ù C) R (= - AT)P

Ke 0 Tj + δm R (T`-Tt) (T`-Tt)

^C > =.>>>.>> =.>>>.>>>>

^ù^C

> =,=5>> 0 =,=5> R [= + >,>>>> R (= - >,68)

1,12% 0 8,>>% + =,=5>> R 5,4>%

95.>>>

145.>>> >,>2== =,4==5 0 =,=5> R [= + >,>2== R (= - >,68)

=>,6>% 0 8,>>% + =,4==5 R 5,4>%

=5>.>>>

25>.>>> >,=9:5 =,4261 0 =,=5> R [= + >,=9:5 R (= - >,68)

=>,:2% 0 8,>>% + =,4261 R 5,4>%

445.>>>

995.>>> >,41>6 =,69>8 0 =,=5> R [= + >,41>6 R (= - >,68)

==,=6% 0 8,>>% + =,69>8 R 5,4>%

6>>.>>>

9>>.>>> >,842: =,8956 0 =,=5> R [= + >,842: R (= - >,68)

==,:9% 0 8,>>% + =,8956 R 5,4>%

695.>>>

:45.>>>

>,: =,:>58 0 =,=5> R [= + >,:>>> R (= - >,68)

=4,65% 0 8,>>% + =,:>58 R 5,4>%

85>.>>>

55>.>>> >,2=24 =,99=> 0 =,=5> R [= + >,2=24 R (= - >,68)

=6,4=% 0 8,>>% + =,99=> R 5,4>%

545.>>>

895.>>> =,=>56 =,1221 0 =,=5> R [= + =,=>56 R (= - >,68)

=8,68% 0 8,>>% + =,1221 R 5,4>%

:>>.>>>

8>>.>>>

=,5 4,4225 0 =,=5> R [= + =,5>>> R (= - >,68)

=5,1>% 0 8,>>% + 4,4225 R 5,4>%

:95.>>>

645.>>> 4,>91: 4,94:8 0 =,=5> R [= + 4,>91: R (= - >,68)

=2,=2% 0 8,>>% + 4,94:8 R 5,4>%

95>.>>>

45>.>>>

6 6,849> 0 =,=5> R [= + 6,>>>> R (= - >,68)

4=,24% 0 8,>>% + 6,849> R 5,4>%

245.>>>

=95.>>> 8,9=86 8,942= 0 =,=5> R [= + >,>>>> R (= - >,68)

42,51% 0 8,>>% + 8,942= R 5,4>%

1>>.>>>

=>>.>>>

85,5>% 0 8,>>% + 9,12=> R 5,4>%

1 9,12=> 0 =,=5> R [= + 1,>>>> R (= - >,68) Jlgte? Mhmptmhl he Mssmj Getl (4>=1, ( 4>=1, p. 2=). 2=).  

Gltm-se que l fustl he fmpatmc pröpral mu`egtm î `ehahm que l gàvec he eghavahm`egtl hm e`presm tm`dá` mu`egtm. L iríjafl 6, m seiuar, `lstrm m evlcuéæl hl fustl he fmpatmc flgjlr`e ls hmhls hl exe`pcl mfa`m.

6=

 

 

Iríjafl 6 ‖ Evlcuéæl hl fustl he fmpatmc flgjlr`e m mcmvmgfmie` jagmgfearm

Jlgte? Ecmdlrmhl pecl mutlr  mutlr  

 Ml mgmcas mgmcasmr mr ls hmhls hmhls `lstrmh `lstrmhls ls gl iiríjaf ríjafll 6, mmfa`m fa`m,, á plssàvec plssàvec perfe perfeder der m re recmé cméæl æl exaste exastegte gte egtre egtre ms vmraíveas que fl`põe` fl`põe ` l fícfucl hl fustl he fmpatmc pröpral pecl `lhecl FM^@. Xm`dá` á plssàve plssàvecc vasumcazmr fl`l á fl`plstl hl rasfl que resuctm gm tmxm `àga`m he mtrmtavahmhe he u` agvesta`egtl, segæl, veom`ls? se l detm mcmvmgfmhl revecm l rasfl tltmc hm e`presm, e`pre sm, l fícfucl hl fustl he fmpatmc pröpral utacazmghl esse detm resuctmram e` fustl he fmpatmc pröpral tltmc, egicldmghl ls rasfls eflgø`afls hl geiöfal e ls rasfls jagmgfearls, e` rmzæl hl gàvec he eghavahm`egtl. Clil, m regtmdacahmhe mhafalgmc exaiahm e` rmzæl hl rasfl jagmgfearl serí egflgtrmhm ml se fmcfucmr m hajeregém egtre (Ke) e m cagbm represegtmtavm hl fustl he fmpatmc pröpral pmrm u`m e`presm se` hàvahms (Ke fl` hàvahms 0 > (zerl)).

Detm setlramc e mpcafmdacahmhe hl dlttl`-up dlttl`-up detm  detm Flstm, Flstm e Mcva` (4>==, p. ===) esfcmrefe` que fmcfucmr hm jlr`m trmhafalgmc l detm he e`presms que plssue` plufm caquahez plhe gæl ser mhequmhl. E`presms gessms flghaéões mpresegtm` u` hesval-pmhræl hls retlrgls `uatl ecevmhls, plr assl, pmrm l fícfucl hl fustl he fmpatmc he e`presms fl` dmaxls àghafes he caquahez gm dlcsm he vmclres, l `mas fleregte á mpcafmr l detm `áhal hl setlr e` que m e`presm mvmcamhm lperm. M utacazméæl hessm `es`m mdlrhmie` tm`dá` á refl`eghmhm pmrm m esta`méæl hl fustl he fmpatmc pröpral he e`presms he fmpatmc jefbmhl. Flstm, Flstm e Mcva` (4>==, p. ==4) expcafm` que l detm setlramc serí fmcfucmhl `ehamgte m ldtegéæl hl vmclr `áhal hls detms hesmcmvmgfmhls he fmhm e`presm e` lperméæl gl setlr, plghermhm pecls pesls hls vmclres he `erfmhl hl pmtra`øgal càquahl.

64

 

 

Gesse segtahl, m mdlrhmie` dlttl`-up detm pressupõe que l vmclr hl detm he u` mtavl espefàjafl plherí ser ldtahl ml utacazmr uta cazmr l detm setlramc hesmcmvmgfmhl pmrm fmcfucmr l detm mcmvmgfmhl hm e`presm que estí e` mgícase, flgsahermghl ms sums respeftavms fmrmfteràstafms he mcmvmgfmie` jagmgfearm, lu seom, l seu gàvec he eghavahm`egtl. M expressæl pmrm m esta`méæl hl detm pmrm qumcquer e`presm aslcmhm serí hmhm pecm seiuagte expressæl? expres sæl? Δmcmvmgfmh mcmvmgfmhl l hm E`presm Espefàjafm 0 δhesmcmvmgfmhl `áhal hl setlr  Ù [= + (^ ù ^C) Ù (= ‖ AT)P

Lghe, (^ ù ^C) heve represegtmr m estruturm he mcmvmgfmie` jagmgfearm mcvl hm e`presm e` mgícase m vmclres he `erfmhl. Ldserve l exe`pcl hesfratl gm tmdecm m seiuar pmrm `ecblr fl`preegher l fícfucl hl detm hesmcmvmgfmhl `áhal hl setlr. M mcàqultm he AT mpcafmhm serí he 68%. Xmdecm 6 ‖ Exe`pcl he fícfucl hl detm hesmcmvmgfmh hesmcmvmgfmhl l `áhal hl setlr

E`presm

Detm Mcmvmgfmhl Mcmvmgfmhl  

Zmclr he `erfmhl hm Hàvahm (^) x `ac

Zmclr he `erfmhl hl (^C) x `ac

^esl

Tecméæl

Detm Gæl

(^ ù ^C)

Mcmvmgfmhl   Mcmvmgfmhl

M

>,9:>

=29.629,4 =29.629,4>>

468.468,>>

>,>19

>,2>>

>,819

D

>,26>

85.856,>>

84.468,>>

>,>=2

=,>9:

>,825

F

=,>4>

46.>1=,9>

56.856,>>

>,>44

>,864

>,918

H

=,>>>

66>.9:8,8 66>.9:8,855

:85.:8:,>>

>,4:2

>,5=4

>,989

E

=,8>>

4=8.58>,6 4=8.58>,666

5:9.5:9,>>

>,46:

>,692

=,=4>

J

=,46>

=.>62.1>8 =.>62.1>8,22 ,22

2:5.9:8,>>

>,651

=,4>>

>,:2:

>,9:   >,9:

@áham Mrat.? >,94   >,94

@áham Mrat.? =,>8   =,>8 =,=5=>  =,=5=> 

=.28>.=8=,82   =.28>.=8=,82

4.8>2.222,>>   4.8>2.222,>>

=,>>   =,>>

 Detms `áhals hl setlr (plghermhls pecl vmclr he `erfmhl hl ^C  

↞

>,9255 >,9255  

↔

Jlgte? Mhmptmhl he Flstm, Flstm e Mcva` (4>==, p. ==1).

Glte que l vmclr hl detm hesmcmvmgfmhl `áhal pmrm l setlr que heve ser utacazmhl á >,9255, plas l vmclr heve ser plghermhl pecm represegtmtavahmhe hm e`presm que fl`põe m m`lstrm gl `erfmhl. Gesse fmsl, plghermghl ls pesls fl` dmse gl vmclr he `erfmhl hl pmtra`øgal càquahl. ^mrm Hm`lhmrmg (4>>9, p. 65), bí trïs vmgtmiegs saigajafmtavms pmrm m utacazméæl hm mdlrhmie` dlttl`-up detm?

66

 

 

 

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^lssadacahmhe he esta`méæl hls detms he e`presms se` m gefessahmhe he bastörafls he vmclres hms méões e` recméæl îs `áhams he `erfmhl, dmstmghl mpegms ahegtajafmr mhequmhm`egte l setlr he lperméæl hms e`presms, plr assl essm `etlhlcliam plhe ser usmhm pmrm esta`mr ls detms he e`presms pmrm ljertms ljer tms pÿdcafms agafamas e e`presms he fmpatmas jefbmhls. @eglr hesval-pmhræl hesval-pmhr æl hm esta`mtavm hl detm `áhal. Fl`l l vmclr hl detm á ldtahl ml plghermr ls vmclres hls detms he haversms e`presms hl `es`l setlr, l vmclr represegtmrí `ecblr l gàvec he rasfl hl geiöfal hl que qumcquer reiressæl remcazmhm pmrm u`m e`presm aghavahumc`egte. L dlttl`-up detm   plhe rejcetar fl` `malr hagm`as`l ms `uhmgéms gls ru`ls hl setlr e` recméæl ml `erfmhl, mcá` he plssadacatmr moustes ml mhafalgmr lu retarmr e`presms hm m`lstrm pmrm m remcazméæl hm esta`mtavm.

L fícfucl hls detms plr setlr he mtavahmhe, mcmvmgfmhls e hesmcmvmgfmhls, pmrm l `erfmhl glrte-m`erafmgl plhe ser jífac e irmtuatm`egte egflgtrmhl gl sate  hl  hl prljesslr Mswmtb Hm`lhmrmg, agfcusave fl` ms plgherméões e ls moustes gefessírals hesfratls mgteralr`egte. ^mrm flgslcahmr l egtegha`egtl sldre m mpcafméæl prítafm hl detm setlramc e hm mdlrhmie` dlttl`-up detm pmrm m esta`méæl hl fustl he fmpatmc pröpral, flgsahere ls hmhls hl exe`pcl m seiuar. Heter`agmhm e`presm heseom mdrar l fmpatmc gm dlcsm he vmclres e prefasm fmcfucmr l fustl he fmpatmc hls mfalgastms pmrm jags he vmcumtalg flgsahermghl l seiuagte fegíral?   tmxm cavre he rasfl (Tj) aiumc m 8% ml mgl;   prï`al pecl rasfl he `erfmhl (T` ‖ Tj) aiumc m 5,4>% ml mgl;   detm `áhal hesmcmvmgfmhl hl setlr (δh) e` que m e`presm mtum esta`mhl e` =,=5; terfear ls e 8>%   hl fmpatmc tltmc agvestahl gm e`presm, :>% sæl jagmgfamhls plr fmpatmc he terfearls plr fmpatmc pröpral e   tradutméæl hm e`presm pecl cufrl remc `ehamgte u`m mcàqultm he AT aiumc m 68%. 

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L fícfucl hl fustl he fmpatmc hm e`presm (K e) se` hàvahms á hmhl plr?

Ke 0 Tj  + δh Ù (T` ‖ Tj ) Ke 0 8,> + =,=5 Ù 5,4>  Ke 0 8,> + 5,12  Ke 0 1,12% ml mgl. 

^mrm fmcfucmr l fustl he fmpatmc hm e`presm flgsahermghl m estruturm mcvl he mcmvmgfmie` jagmgfearm á gefessíral fmcfucmr l detm mcmvmgfmhl e plsteralr`egte esta`mr l fustl he fmpatmc pecl `lhecl FM^@, flgjlr`e seiue? δmcmvmgfmh mcmvmgfmhl l hm E`presm Espefàjafm 0 δhesmcmvmgfmhl `áhal hl setlr Ù [= + (^ ù ^C) Ù (= ‖ AT)P δmcmvmgfmh mcmvmgfmhl l hm E`presm Espefàjafm  0 =,=5 Ù [= + (>,:> ù >,8>) Ù (= ‖ >,68)P mcmvmgfmhl l hm E`presm Espefàjafm  δmcmvmgfmh 0 =,=5 Ù [= + (=,5>) Ù (>,::)P 

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δmcmvmgfmh mcmvmgfmhl l hm E`presm Espefàjafm 0 =,=5 Ù [= + >,11P  δmcmvmgfmh mcmvmgfmhl l hm E`presm Espefàjafm  0 =,=5 Ù =,11  δmcmvmgfmh mcmvmgfmhl l hm E`presm Espefàjafm  0 4,4225 

 Milrm, plhe`ls fmcfucmr l fustl he fmpatmc espefajafm`egte pmrm m e`presm, flgsahermghl m sum estruturm he fmpatmc? Ke 0 Tj   + + δm Ù (T` ‖ Tj ) Ke 0 8,> + 4,4225 Ù 5,4>  Ke 0 8,> + ==,1>>4 Ke 0 =5,1>>4 lu =5,1>% ml mgl. 

Ldserve que l prlfeha`egtl pmrm fmcfucmr l fustl he fmpatmc á l `es`l pmrm e`presms fl` hajeregtes estruturms he fmpatmc, dmstmghl pmrm assl moustmr l vmclr hl detm flgsahermghl l respeftavl gàvec he mcmvmgfmie` jagmgfearm. Gl fmsl, u`m e`presm mtumgte gl setlr hesfratl hesfra tl mfa`m se` hàvahms, lu seom, jagmgfamhm exfcusavm`egte plr fmpatmc pröpral, mpresegtmram u` fustl he fmpatmc he 1,12% ml mgl, egqumgtl lutrm, lpermghl gl `es`l setlr, `ms seghl jagmgfamhm e` :>% plr fmpatmc he terfearls, mpresegtmrí u` fustl he fmpatmc pröpral he =5,1>% ml mgl, tuhl plrque, e` rmzæl hl eghavahm`egtl, l gàvec he rasfl ra sfl hl geiöfal mu`egtm.

@lhecl he prefajafméæl he mtavls gm prítafm  Ml estuhmr ms fl`plgegtes hl `lhecl he prefajafméæl he mtavls (FM^@) vlfï ldservlu ls mspeftls que heve` ser flgsahermhls pmrm m mpcafméæl hm telram gm prítafm. Flgslcahmghl tlhms ms flgsaherméões hesfratms, l `lhecl FM^@ moustmhl pmrm m mpcafméæl prítafm e` `erfmhls e`eriegtes plhe ser hmhl pecm seiuagte expressæl? e xpressæl? Ke 0 Tj   + + δ Ù (T` ‖ Tj ) + (Task flugtry)

Lu, gl fmsl he e`presms fl` l jmturm`egtl j mturm`egtl `egl `eglrr que T$ 4>> `acbões? Ke 0 Tj  +  + δm Ù (T` ‖ Tj ) + (Task flugtry) + (Vaze pre`au`) 

Lghe? esper mhl pmrm l agvesta`egtl (utacazmhl fl`l fustl hl fmpatmc pröpral).   K e á l retlrgl espermhl  á m tmxm he ourls ‖ retlrgl ‖ cavre cavr e he rasfl. Te`ugerméæl ljerefahm pecls tàtucls pÿdcafls   T j j  á glrte-m`erafmgls gl `l`egtl hm mquasaéæl hl mtavl, fl` prmzl he vegfa`egtl fl`pmtàvec fl` m vahm ÿtac hl agvesta`egtl sld mgícase.

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 á l flejafaegte detm mcmvmgfmhl flgjlr`e m estruturm he fmpatmc hm e`presm sld mgícase. δm  á

 

Expressm l rasfl sastï`afl hl agvesta`egtl e` recméæl ml `erfmhl, flgsahermghl ls ejeatls hm mcmvmgfmie` jagmgfearm hm respeftavm e`presm. L vmclr hls detms ‖ mcmvmgfmhls e hesmcmvmgfmhls ‖ `áhals hls setlres, hevahm`egte mtumcazmhls, plhe ser jmfac`egte ldtahl mfessmghl l sate  hl  hl prljesslr Mswmtb Hm`lhmrmg (GQU, 4>4>m). (T `  ‖ T j j)  á l prï`al pecl rasfl he `erfmhl glrte-m`erafmgl espermhl. L vmclr mtumcazmhl

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plhe ser jmfac`egte ldtahl mfessmghl l sate  hl  hl prljesslr Mswmtb Hm`lhmrmg (GQU, 4>4>f).   (Task  flugtry   flugtry ) á l prï`al pecl rasfl mhafalgmhl pmrm pmàses e`eriegtes. L vmclr, pmrm l `erfmhl drmsacearl e lutrls pmàses, flgsahermghl tlhls ls moustes hesfratls mgteralr`egte, tm`dá` plhe ser ldtahl jmfac`egte mfessmghl l sate  hl  hl prljesslr Mswmtb Hm`lhmrmg (GQU, 4>4>f).   (Vaze pre`au`) á l prï`al pecl rasfl hl tm`mgbl hm e`presm e`pr esm mhafalgmhl plr mciugs mgmcastms gl fmsl he e`presms fl` jmturm`egtl `eglr que T$ 4>> `acbões ml mgl. Á a`plrtmgte ce`drmr que l `lhecl hesfratl flgsaherm l fícfucl hl fustl he fmpatmc pmrm l setlr flgsahermghl m estruturm he fmpatmc `áham hms e`presms hl setlr. Lu seom, pmrm l fícfucl hl fustl he fmpatmc hl setlr, plherí ser usmhl l detm mcmvmgfmhl `áhal hl setlr ( δm ),), flgtuhl, pmrm l fícfucl hl fustl he fmpatmc he u`m e`presm aslcmhm, l fustl he fmpatmc serí `mas de` esta`mhl ml se utacazmr l detm hesmcmvmgfmhl `áhal hl setlr (δh) pmrm se egflgtrmr l detm mcmvmgfmhl ( δm ) hm e`presm, flgsahermghl m sum respeftavm estruturm estrutur m he fmpatmc. ^lrtmgtl, pmrm fmcfucmr l fustl he fmpatmc he u`m e`presm espefàjafm, vlfï heverí flgbefer l vmclr hl detm hesmcmvmgfmhl `áhal hl setlr pmrm fmcfucmr l detm mcmvmgfmhl fl` m estruturm he fmpatmc hm e`presm e` mgícase lu flgbefer l detm mcmvmgfmhl `áhal hl setlr e m estruturm he fmpatmc `áham hl setlr. Mssa`, vlfï plherí –hesmcmvmgfmr‐ l detm `áhal hl setlr flgsahermghl m mcmvmgfmie` `áham setlramc pmrm plsteralr`egte –mcmvmgfmr‐ l detm flgsahermghl recméæl ‖ hàvahm/pmtra`øgal càquahl ‖ hm e`presm fuol fustl he fmpatmc pröpral se preteghe esta`mr. ^mrm `ecblr acustrmr, serí mpresegtmhl m seiuar fl`l fmcfucmr l vmclr hl detm gms hums satuméões, m pmrtar hls hmhls hl seiuagte exe`pcl?   L detm mcmvmgfmhl `áhal hl setlr he heter`agmhl sei`egtl á aiumc m =,88. `áham áham hl respeftavl respeftavl setlr á fl fl`plstm `plstm he 85% he fmpatmc he terfearls    M estruturm he fmpatmc ` 

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e 55% he fmpatmc pröpral. mv mcam e que mtum gl rejerahl setlr plssua    M estruturm he fmpatmc hm e`presm que se heseom mvmcam u`m estruturm he fmpatmc fl`plstm he :>% he fmpatmc he terfearls e 8>% he fmpatmc pröpral. mcàqultm ultm he a`plst a`plstll he he reghm reghm ` `mri mriagmc agmc `áha `áhamm hl setlr setlr e hhmm e`presm e`presm e` mgícase mgícase á he 68% 68%..    M mcàq

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^mrm fmcfucmr l detm mcmvmgfmhl exfcusavl pmrm m e`presm que se heseom mvmcamr á prefasl ldter l vmclr hl detm hesmcmvmgfmhl `áhal hl setlr. L vmclr plhe ser mpurmhl m pmrtar hm seiuagte expressæl? δmcmvmgfmh mcmvmgfmhl l `áhal hl setlr  0 δhesmcmv hesmcmvmgfmhl mgfmhl `áhal hl setlr  Ù [= + (^ setlr ù ^C setlr) Ù (= ‖ AT setlr)P =,88 0 δhesmcmv hesmcmvmgfmhl mgfmhl `áhal hl setlr Ù [= + (>,85 ù >,55) Ù (= ‖ >,68)P =,88 0 δhesmcmvm (>,2=2=24) 24) Ù (>,::)P  hesmcmvmgfmhl gfmhl `áhal hl setlr Ù [= + (>,2=2=

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=,88 0 δhesmcmvm hesmcmvmgfmhl gfmhl `áhal hl setlr Ù [= + >,58P  =,88 0 δhesmcmvm hesmcmvmgfmhl gfmhl `áhal hl setlr Ù =,58  =,88 ù =,58 0 δhesmcmvm hesmcmvmgfmhl gfmhl `áhal hl setlr  >,165>:5 0 δhesmcmvmg hesmcmvmgfmhl fmhl `áhal hl setlr  

U`m vez flgbefahl l vmclr hl detm hesmcmvmgfmhl `áhal hl setlr, á plssàvec fmcfucmr l vmclr hl detm mcmvmgfmhl pmrm m estruturm he fmpatmc hm e`presm e` mgícase flgjlr`e seiue? δmcmvmgfmh hesmcmvmgfmhl l `áhal hl setlr Ù [= + (^ e`presm ù ^C e`presm) Ù (= ‖ AT e`presm)P mcmvmgfmhl l hm e`presm espefàjafm 0 δhesmcmvmgfmh δmcmvmgfmh mcmvmgfmhl l hm e`presm espefàjafm 0 >,165>:5 Ù [= + (>,:> ù >,8>) Ù (= ‖ >,68)P δmcmvmgfm mcmvmgfmhl hl hm e`presm espefàjafm 0 >,165>:5 Ù [= + (=,5>) Ù (>,::)P  δmcmvmgfmh mcmvmgfmhl l hm e`presm espefàjafm 0 >,165>:5 Ù [= + >,11P  δmcmvmgfmh mcmvmgfmhl l hm e`presm espefàjafm 0 >,165>:5 Ù =,11  δmcmvmgfm mcmvmgfmhl hl hm e`presm espefàjafm 0 =,2:>991 

Glte que, fl`l m e`presm e` mgícase plssua u`m mcmvmgfmie` jagmgfearm `malr hl que m `áham hl setlr l seu rasfl tm`dá` serí `malr. Essm perfepéæl se rejcete gls vmclres hls detms, u`m e` vez que quemtum, l detm mcmvmgfmhl   `áhal hl setlr á he =,88, e l hm e`presm espefàjafm resuctlu e` =,2:>991.

Fícfucl hl fustl he fmpatmc hls mfalgastms pmrm ms e`presms gl Drmsac L `lhecl he prefajafméæl he mtavls (FM^@) á u` `átlhl flgslcahmhl pmrm m esta`méæl hl fustl he fmpatmc pröpral, flgtuhl, á gefessíral m remcazméæl he moustes pmrm m sum mpcafméæl prítafm e` `erfmhls e`eriegtes, gl fmsl, l Drmsac. Fl`l he`lgstrmhl mgteralr`egte, l `lhecl FM^@ moustmhl pmrm m mpcafméæl gl Drmsac á? Ke 0 Tj  + δ Ù (T` ‖ Tj ) + (Task flugtry) lu Ke 0 Tj   + + δm Ù (T` ‖ Tj ) + (Task flugtry) + (Vaze pre`au`)

^lrá`, á a`plrtmgte ce`drmr que ms vmraíveas utacazmhms gm prítafm resuctm` e` u` fustl he fmpatmc gl`agmc ‖ tmxm he retlrgl gl`agmc ‖, lu seom, se` l hesflgtl hls ejeatls ej eatls hm agjcméæl. Fl`l gm prítafm á fl`u` l fícfucl hl fustl hl fustl he fmpatmc usmghl ms vmraíveas glrtem`erafmgms, plr ser flgsahermhl u` `erfmhl `mas flgslcahmhl, e, plsteralr`egte, mhafalgmhl l rasfl-pmàs hl respeftavl `erfmhl e`eriegte, l resuctmhl egflgtrmhl serí u`m tmxm e` ter`ls gl`agmas pmrm agvesta`egtls he fmpatmas prlvegaegtes hls Estmhls Ugahls. Vaigajafm hazer que represegtm u`m tmxm he regha`egtl gl`agmc flgsahermghl m agjcméæl glrte-m`erafmgm.

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U` errl fl`u`, e que gæl heve ser fl`etahl, seiughl @mrtecmgf, ^msag e ^erearm (4>=4, p. =8:), –flgsaste e` utacazmr jcuxls he fmaxm prloetmhls e` `lehm remc e tmxms he hesflgtl gl`agmas (jeatms fl` dmse gms tmxms hl `erfmhl glrte-m`erafmgl)‐. Xmxms gl`agmas heve` ser mpcafmhms sldre jcuxls he fmaxm gl`agmas, lu seom, qumghl ls jcuxls he fmaxm jlre` prloetmhls preveghl m agjcméæl. Oí qumghl ls jcuxls he fmaxm juturls jlre` prloetmhls fl` dmse e` vmclres he `erfmhl mtumas, lu seom, fl`l se m agjcméæl jlsse gucm, m tmxm he hesflgtl utacazmhm heverí estmr expressm e` ter`ls remas. Fmde ressmctmr que `etlhlcliafm`egte á aghajeregte prloetmr ls jcuxls he fmaxm e` `lehm gl`agmc lu e` `lehm remc, u`m vez que l a`plrtmgte á mpcafmr he jlr`m mhequmhm m tmxm (remc lu gl`agmc) ml jcuxl he fmaxm prloetmhl (remc lu gl`agmc). Ls resuctmhls e` ter`ls remas heveræl ser ls `es`ls. @mrtecmgf, ^msag e ^erearm (4>=4, p. =5=) fl`egtm` que, ml remcazmre` u`m pesquasm, –hlas egtrevastmhls, m`dls mvmcamhlres prljassalgmas, fl`eterm` m agflgsastïgfam he prloetmr l jcuxl he fmaxm e` `lehm remc e hesflgtí-cl fl` u`m tmxm gl`agmc‐. ^lrtmgtl, pmrm mvmcamr u`m e`presm drmsacearm, pmrtaghl hl fustl he fmpatmc flgjlr`e fmcfucmhl mtá l `l`egtl, heve`ls eca`agmr l ejeatl hm agjcméæl glrte-m`erafmgm e mhafalgmr m agjcméæl prloetmhm pmrm l Drmsac, lu fmcfucmr l fustl he fmpatmc e` ter`ls remas ‖ eca`agmghl l ejeatl eje atl hm agjcméæl glrte-m`erafmgm ‖ e mpcafmr sldre u` jcuxl he fmaxm prloetmhl e` ter`ls tm`dá` remas. L fustl he fmpatmc e` ter`ls remas plherí ser egflgtrmhl m pmrtar hm seiuagte expressæl? Ke (remc) 0 [(= + Ke (gl`agmc gls EUM) ) ù (= + Agjcméæl (glrte-m`erafmgm))P ‖ =

Usmghl l `es`l flgfeatl, l fustl he fmpatmc e` ter`ls gl`agmas pmrm l `erfmhl drmsacearl serí hmhl plr? Ke (gl`agmc pmrm l Drmsac)  0 [(= + Ke (remc)) Ù (= + Agjcméæl (prloetmhm pmrm l Drmsac))P ‖ =

Fl`l l fustl he fmpatmc fmcfucmh fmcfucmhll á utacazmhl pmrm m mvmcaméæl he agvesta`egtls dmsemhls e` jcuxls he fmaxm juturls, á fleregte utacazmr ls hmhls hm agjcméæl prloetmhm pmrm fmhm `erfmhl.  Mtumc`egte, m agjcméæl prloetmhm pmrm ls Estmhls Ugahls (JEH, 4>4>) á he 4,>% ml mgl (JEH, 4>4>d), e` cagbm fl` l bastörafl hls ÿcta`ls ÿ cta`ls => mgls. ^mrm l Dr Drmsac, msac, e` omgearl he 4>4>, l Vaste`m he Expeftmtavms he @erfmhl hl Dmgfl Fegtrmc hl Drmsac (DMFEG, 4>4>) prloetmvm u`m agjcméæl `áham e` tlrgl he 6,5>% ml mgl pmrm ls pröxa`ls fagfl mgls.

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Exe`pcl fl`pcetl hm mpcafméæl hl FM^@ pmrm e`presms gl Drmsac ^mrm `ecblr fl`preegsæl e flgslcahméæl he tlhm m mdlrhmie` remcazmhm mtá l `l`egtl, serí mpresegtmhl m seiuar u` exe`pcl fl`pcetl hl fícfucl hl fustl he fmpatmc pmrm l setlr he petröcel, iís e dalfl`dustàveas, moustmhl pmrm m mcmvmgfmie` jagmgfearm hm ^etrldrms V.M. fl` dmse gls he`lgstrmtavls jagmgfearls pudcafmhls gl sate   hm D6 (4>4>) he 6= he heze`drl he 4>=1 e gms agjlr`méões pudcafmhms plr Hm`lhmrmg (4>4>) fl` hmtm-dmse he =¿ he omgea omgearl rl he 4>4> (GQU, 4>4>d). Ls hmhls sæl?   hàvahm càquahm he T$ 6=9.2:9 `acbões e T$ 411.=69 `acbões he pmtra`øgal càquahl;   prï`al pecl rasfl he `erfmhl glrte-m`erafmgl? 5,4>% ml mgl;   tmxm cavre he rasfl glrte-m`erafmgm fl` vegfa`egtl pmrm => mgls? =,22% m.m.; Dr msac? 4,5=% ml mgl;   prï`al pecl rasfl-pmàs pmrm l Drmsac?   hesval-pmhræl recmtavl pmrm `erfmhls e`eriegtes? =,=2;   prï`al pecl rasfl-pmàs fl` l hesval-pmhræl hesva l-pmhræl recmtavl pmrm l Drmsac? 4,1:% ml mgl;   detm hesmcmvmgfmhl `áhal hl setlr? =,>2;   mcàqultm he AT `mriagmc pmrm m e`presm? 68%.   agjcméæl esta`mhm glrte-m`erafmgm? 4,>>% ml mgl e   agjcméæl esta`mhm drmsacearm? 6,5>% ml mgl. 

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Fl` ms agjlr`méões mpresegtmhms, seræl mpresegtmhls m seiuar ls pmssls pmrm m esta`méæl hl fustl hl fmpatmc pröpral mhequmhl pmrm m e`presm. =.  Fmcfucmghl l detm mcmvmgfmhl pmrm m e`presm? δm 0 δh Ù [ = + (^ ù ^C)  Ù (= ‖ AT) P δm 0 =,>2 Ù [ = + (6=9.2:9 ù 411.=6 411.=69) 9) Ù (= ‖ >,68) P δm 0 =,>2 Ù [ = + (=,>:4:) Ù (>,::) P  δm 0 =,>2 Ù [ = + >,9>=6 P  δm 0 =,2698 

4.  Fmcfucmghl l fustl he fmpatmc gl`agmc pmrm l agvestahlr m`erafmgl? Ke 0 Tj   + + δ Ù (T` ‖ Tj ) + (Task flugtry) Ke 0 =,22% + =,2698 Ù (5,4>%) + (4,1:%)  Ke 0 =,22% + 1,55% + 4,1:%  Ke 0 =8,61% ml mgl. 

6.  Fmcfucmghl l fustl he fmpatmc e` ter`ls remas (hesflgtmhm m agjcméæl)? Ke (remc) 0 [(= + Ke (gl`agmc gls EUM) ) ù (= + Agjcméæl (glrte-m`erafmgm))P ‖ = ù

Ke (remc) 0 [(= + >,=861)  (= + >,>4)P ‖ =

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Ke (remc) 0 [=,=861 ù =,>4P ‖ = Ke (remc) 0 =,=4=5 ‖ = Ke (remc) 0 >,=4=5 lu =4,=5% ml mgl. 

8.  Fmcfucmghl l fustl he fmpatmc e` ter`ls gl`agmas pmrm l Drmsac (agfcuaghl m agjcméæl)? Ke (gl`agmc pmrm l Drmsac)  0 [(= + Ke (remc)) Ù (= + Agjcméæl (prloetmhm pmrm l Drmsac))P ‖ = Ke (gl`agmc pmrm l Drmsac) 0 [(= + >,=4=5) Ù (= + >,>65)P ‖ = Ke (gl`agmc pmrm l Drmsac) 0 [=,=4=5 Ù =,>65P ‖ = Ke (gl`agmc pmrm l Drmsac)  0 =,=:>2 ‖ = Ke (gl`agmc pmrm l Drmsac)  0 >,=:>2 lu =:,>2% ml mgl. 

Glte que e` ter`ls remas l fustl he fmpatmc pröpral resuctlu r esuctlu e` =4,=5% ml mgl e essm serí m tmxm que heverí ser utacazmhm pmrm hesflgtl fmsl ms prloeéões hls jcuxls he fmaxm hl mfalgastm seom` remcazmhms tm`dá` e` ter`ls remas he vmclr. v mclr. Gl fmsl he ms prloeéões hls jcuxls he fmaxm hl mfalgastm sere` prevastms e`dutaghl m agjcméæl, lu seom, e` vmclres gl`agmas, m tmxm que heverí ser utacazmhm pmrm hesflgtl serí he =:,>2% ml mgl, plr tm`dá` estmr expressm e` ter`ls gl`agmas.

Fustl he fmpatmc hls frehlres E`dlrm egflgtre`ls e`presms jagmgfamhms exfcusavm`egte plr fmpatmc pröpral, á fl`u` que ms e`presms tm`dá` seom` jagmgfamhms, e` pmrte, plr fmpatmc he terfearls. Essm mcmvmgfmie` jagmgfearm glr`mc`egte plhe trmzer degejàfals pmrm m lperméæl e pltegfamcazmr ls retlrgls hl fmpatmc agvestahl pecl mfalgastm, `ms, pmrm assl, á a`plrtmgte ahegtajafmr e fmcfucmr l fustl he fmpatmc he terfearls he jlr`m mhequmhm. Verrm e Yafkert (4>=1, p. 82) mplgtm` trïs jlr`ms he esta`méæl hl fustl he fmpatmc hls frehlres pmrm jags he vmcumtalg, sæl ecms?   ^lr `eal he `lhecls he fráhatl ‖ Væl `lhecls que estmdecefe` pmrä`etrls he rasfl he fráhatl e jaxm` u` spremh plr `eal he mgícases qumcatmtavms, qumgtatmtavms e fl`pmrmtavms. `atahls pecm e`presm   ^lr `eal he e`assæl he tàtucls he hàvahm ‖ Væl tàtucls he fráhatl ee`atahls fl` l ldoetavl he fmpatméæl he refursls `ehamgte m flgtrmpmrtahm he pmim`egtl he ourls e hevlcuéæl hl fmpatmc gls prmzls flgvegfalgmhls. Ms hedïgtures 6  sæl exe`pcls he tàtucls he hàvahm. 

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6

 –M hedïgture á u` vmclr `ldacaíral e`atahl plr slfaehmhes plr méões, represegtmtavl he hàvahm, que msseiurm m seus hetegtlres l hareatl he fráhatl flgtrm m fl`pmgbam e`asslrm. Flgsaste e` u` agstru`egtl he fmptméæl he refursls gl `erfmhl he fmpatmas, que ms e`presms utacazm` pmrm jagmgfamr seus prloetls. Á u`m jlr`m tm`dá` he `ecblr ieregfamr sums hàvahms‐ (FZ@, 4>4>).

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^lr `eal hm ahegtajafméæl hl fustl hm hàvahm exastegte ‖ L fustl hm hàvahm á esta`mhl ml fmcfucmr m `áham plghermhm hms vírams jlgtes he fmpatmc he terfearls. Essm á m mdlrhmie` `mas utacazmhm pmrm jags he vmcumtalg, flgtuhl, pmrm m mvmcaméæl he agvesta`egtls juturls pecm e`presm, plhe ser verajafmhl l fustl `mriagmc hm hàvahm, lu seom, l fustl he u`m glvm fmptméæl he refursls fl` terfearls.

E` cagbm fl` esse ÿcta`l rmfalfàgal, @mrtecmgf, ^msag e ^erearm (4>=4, p. =89) fl`pce`egtm` que –l fustl he fmpatmc he terfearls terfea rls plhe ser fmcfucmhl m pmrtar he vmclres he `erfmhl flrresplghegtes î tmxm que m e`presm plheram ldter lu ldtá` e` e`prásta`ls he clgil prmzl‐. Ls `lhecls he fícfucl hl fustl he fmpatmc he terfearls trmhafalgmc`egte mdlrhmhls gls `eals mfmhï`afls re`ete` ml fustl perfedahl plr e`presms he irmghe plrte que plssue` l reia`e he mpurméæl hl cufrl remc, plrá` á a`plrtmgte ce`drmr que e`presms `eglres plhe` evegtumc`egte lptmr plr u` reia`e he tradutméæl pecl cufrl presu`ahl e, geste fmsl, l degejàfal jasfmc hm hàvahm á gucl, u`m vez que l a`plstl he reghm r eghm serí presu`ahl fl` dmse gm refeatm. L degejàfal jasfmc hm hàvahm surie qumghl ms e`presms que plssue` m tradutméæl fl` dmse gm mpurméæl hl cufrl remc cmgém` ls fustls fl` ourls fl`l hespesms jagmgfearms e rehuze` m dmse tradutívec, rehuzaghl plr flgsequïgfam l vmclr hl a`plstl he reghm m ser pmil. Flgsahere l exe`pcl m seiuar pmrm `ecblr fl`preegsæl he fl`l surie l degejàfal jasfmc hm hàvahm? pmrtaghl hl pressuplstl he que m e`presm plssum u`m mcàqultm he a`plstl he reghm `mriagmc aiumc m 68% e que m tmxm he ourls ejetavm he u`m glvm hàvahm seom he =5% ml mgl, m fmhm T$ =>> `ac e`prestmhls, pmimrí l vmclr he T$ =5 `ac e` ourls plr mgl. Vaigajafm hazer que l cufrl hm e`presm serí rehuzahl gm `ehahm e` que m e`presm pmim ls ourls, e assl rehuzarí m dmse tradutívec. Mssa`, fl` l cufrl hm e`presm rehuzaghl e` T$ =5 `ac, l a`plstl he reghm ha`aguarí gm prlplréæl he 68% hesse vmclr. L rmfalfàgal r mfalfàgal á acustrmhl gm tmdecm 8, m seiuar? Xmdecm 8 ‖ Ejeatl hl degejàfal jasfmc hm hàvahm gl fustl hl fmpatmc he terfearls

HTE hms e`presms se` se`  hàvahms Hesfraéæl Zmclr

HTE hms e`presms fl` fl` hàvahms  hàvahms Hesfraéæl Zmclr

Tesuctmhl Lpermfalgmc

=>>.>>>,>>

Tesuctmhl Lpermfalgmc

=>>.>>>,>>

-

Hespesms Jagmgfearms

- =5.>>>,>>

Hespesms Jagmgfearms CMAT

=>>.>>>,>>   =>>.>>>,>>

CMAT

AT (68%)

- 68.>>>,>>

AT (68%)

Cufrl Càquahl

::.>>>,>>   ::.>>>,>>

Cufrl Càquahl

≮ (T$)  (T$)  M fmhm =>>K  =>>K 

≮(%)   ≮(%) M fmhm =>>K  =>>K 

-=5.>>> -=5.>>>,>> ,>>

- =5.>>%

- 41.2>>,>>

+5.=>>,> +5.=>>,>>>

+5.=>%

5:.=>>,>>   5:.=>>,>>

- 1.1>>,>> 1.1>>,>>  

- 1.1>% 1.1>%  

25.>>>,>>   25.>>>,>>

Jlgte? Mhmptmhl he Verrm e Yafkert (4>=1, p. 81).

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Glte que, e`dlrm l CMAT ha`agum e` T$ =5 `ac e` rmzæl hls ourls pmils, fl`l bluve u`m eflgl`am he T$ 5,= `ac he a`plstl he reghm, l vmclr hl cufrl càquahl jla rehuzahl e` mpegms T$ 1,1 `ac. Vaigajafm hazer, mpesmr he m tmxm he ourls pmim pecm hàvahm represegtmr =5% ml mgl, l ejeatl he rehuéæl gl cufrl càquahl evahegfam u` fustl ejetavl he mpegms 1,1% ml mgl. Ldserve que l fustl jagmgfearl hl eghavahm`egtl á rehuzahl gm prlplréæl hm mcàqultm hl a`plstl he reghm `mriagmc fldrmhl. Clil, pmrm estes fegírals, m expressæl pmrm l fícfucl hl fustl he fmpatmc hls frehlres serí? K6l 0 a Ù (= ‖ AT)

Lghe?   K 6l á l fustl ejetavl hl fmpatmc he terfearls. Á m tmxm he ourls hm hàvahm mpös l degejàfal jasfmc.   a á m tmxm he ourls ejetavm hm hàvahm mgtes hl degejàfal jasfmc. Á m `áham plghermhm hms tmxms ejetavms he ourls hl eghavahm`egtl.   AT á m mcàqultm hl a`plstl he reghm `mriagmc. Á m mcàqultm represegtmtavm hls tradutls pmils sldre l cufrl. re huéæl hl fustl he fmpatmc he terfearls e` rmzæl hl degejàfal jasfmc.   (= ‖ AT) á l jmtlr he rehuéæl

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Fmde ce`drmr que l agfegtavl pmrm m tl`mhm he refursls fl` terfearls, plr `eal hl fbm`mhl degejàfal jasfmc hm hàvahm, sl`egte se mpcafm pmrm ms e`presms que sæl tradutmhms pecl cufrl remc. Fmsl m e`presm lpte pecl reia`e he tradutméæl fl` dmse gl cufrl presu`ahl, l fustl hm hàvahm gæl gæ l serí mjetmhl, u`m vez que ls tradutls tra dutls sldre m reghm sæl presu`ahls fl` dmse gm refeatm hm e`presm. Geste fmsl, l fustl he fmpatmc he terfearls pmssm m ser haretm`egte m tmxm he ourls ejetavm hm hàvahm, plrtmgtl, l jmtlr he rehuéæl hl fustl he fmpatmc he terfearls (= ‖ AT) gæl heve ser mpcafmhl.

Fustl he fmpatmc hls agvestahlres Flgbefeghl ls fustls he fmpatmas hls mfalgastms e hls frehlres á plssàvec fmcfucmr m `áham plghermhm que represegtm represe gtm l fustl he fmpatmc hls agvestahlres fl`l u` tlhl. L fustl he fmpa fmpatmc tmc `áhal plghermhl (F@^F) ‖ e` agicïs, Yeaibteh Mvermie Flst lj Fmpatmc (YMFF) ‖ represegtm m tmxm que tlrgm `aga`m`egte mtrmtavm m remcazméæl he u` agvesta`egtl flgsahermghl ls rasfls perfedahls.  Mssmjj Getl  Mssm Ge tl (4>=1, ( 4>=1, p. 15) rress essmctm mctm que l F@ F@^F, ^F, lu YMF YMFF, F, á m tmxm he hesflg h esflgtl tl que he heve ve ser mpcafmhm sldre ls jcuxls he fmaxm juturls hm e`presm m ja` he heter`agmr l seu vmclr eflgø`afl ( jar`  jar`  vmcue ))..  M expressæl utacazmhm pmrm l fícfucl hl fustl `áhal plghermhl hm e`presm á m seiuagte?

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F@^F 0 {[Tj  + δÙ(T`‖Tj ) + (Task flugtry)P Ù [^C ù (^ + ^C)P} + {[a Ù (= ‖ AT)P Ù [^ ù (^ + ^C)P}     F@^F 0 {Ke Ù [^C ù (^ + ^C)P} + {[a Ù (= ‖ AT)P Ù [^ ù (^ + ^C)P}    F@^F 0 {Ke Ù [^C ù (^ + ^C)P} + {K 6l Ù [^ ù (^ + ^C)P}    ∸

∸

∸

e 

l 6  

F@^F 0 {K Ù %^C} + {K Ù %^} 

Lghe?   K e á l fustl hl fmpatmc hls mfalgastms. terfear ls agserahl gl fmpatmc tltmc hm e`presm.   ^ á l vmclr he fmpatmc he terfearls   ^C á l vmclr he fmpatmc pröpral agserahl gl fmpatmc tltmc hm e`presm. Á l pmtra`øgal càquahl.   ^ + ^C á l tltmc hl fmpatmc hls agvestahlres agve stahlres (frehlres e mfalgastms). a gserahl gl fmpatmc tltmc hm e`presm.   %^ á m pmrtafapméæl hl fmpatmc he terfearls agserahl   %^C á m pmrtafapméæl hl fmpatmc pröpral agserahl gl fmpatmc tltmc hm e`presm.   a á m tmxm he ourls ejetavm hm hàvahm plghermhm mgtes hl degejàfal jasfmc.   AT á m mcàqultm hl a`plstl he reghm r eghm e flgtraduaéæl slfamc `mriagmc pmim sldre l cufrl.   (= ‖ AT) á l jmtlr he rehuéæl re huéæl hl fustl he fmpatmc he terfearls e` rmzæl hl degejàfal jasfmc. l ja sfmc).   K 6  á l fustl ejetavl hl fmpatmc he terfearls (mpös l degejàfal jasfmc).

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A`plrtmgte ce`drmr que gm jlr`ucméæl hl F@^F l fustl he fmpatmc he terfearls heve ser flgsahermhl mpös ls ejeatls hl degejàfal jasfmc. Veiughl Mssmj Getl (4>=1, p. 1:) heve` ser flgsahermhms fl`l jlgtes he fmpatmc he terfearls mpegms ms hàvahms que resucte` e` egfmrils jagmgfearls, tmas fl`l jagmgfam`egtls e e`prásta`ls. Oí lutrms hàvahms esplgtägems hm lperméæl, fl`l jlrgefehlres m pmimr, smcírals, etf., gæl heve` fl`plr l fícfucl plr estmre` `mas de` ahegtajafmhms gm estruturm he fustls e hespesms lpermfalgmas hm lrimgazméæl. ^mrm jags hahítafls, l fícfucl hl fustl `áhal plghermhl he fmpatmc serí exe`pcajafmhl ex e`pcajafmhl m seiuar fl` dmse Ms glsagjlr`méões hmhls pudcafmhls e fmcfucmhls m ^etrldrms V.M. fl` hmtm-dmse he 6= he heze`drl he 4>=1. gefessírams pmrm l pmrm fícfucl sæl ms seiuagtes?   hàvahm càquahm he T$ 6=9.2:9 `acbões e T$ 411.=69 `acbões he pmtra`øgal càquahl;   fustl he fmpatmc hls mfalgastms aiumc m =:,>2% ml mgl;   fustl he fmpatmc hm hàvahm càquahm aiumc m 5,1% ml mgl e   mcàqultm he a`plstl he reghm e flgtraduaéæl slfamc aiumc m 68%. 

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Fl` ms agjlr`méões mpresegtmhms, serí mpresegtmhl m seiuar l fícfucl hl fustl `áhal plghermhl he fmpatmc gm prítafm? =.  Fmcfucmghl m prlplréæl hl fmpatmc pröpral (%^C) e fmpatmc he terfearls (%^)?

86

 

 

%^C 0 [^C ù (^ + ^C)P e %^ 0 [^ ù (^ + ^C)P  %^C 0 [411.=69 ù (6=9.2:9 + 411.=69)P   e %^ 0 [6=9.2:9 ù (6=9.2:9 + 41 411.=69)P 1.=69)P  %^C 0 [411.=69 [411.=69 ù :=9.>> :=9.>>8P 8P e %^ 0 [6= [6=9.2:9 9.2:9 ù :=9.>>8P  %^C 0 >,8282 lu 82,82% e %^ 0 >,5=54 lu 5=,54% 

4.  Fmcfucmghl l fustl `áhal plghermhl he fmpatmc (F@^F)? F@^F 0 {Ke Ù [^C ù (^ + ^C)P} + {[a Ù (= ‖ AT)P Ù [^ ù (^ + ^C)P}  F@^F 0 {Ke Ù %^C} + {[a Ù (= ‖ AT)P Ù %^}  F@^F 0 {=:,>2% Ù >,8282} + {[5,1% Ù (= ‖ >,68)P Ù >,5=54}  F@^F 0 {9,915:%} + {6,218% Ù >,5=54}  F@^F 0 {9,915:%} + {4,>>:4%}  F@^F 0 1,2>=2% lu 1,2>% ml mgl. 

^lrtmgtl, pmrm jags he vmcumtalg, flgsahermghl l fegíral hesfratl, m tmxm he retlrgl que  oustajafmram mssu`ar ls rasfls hl agvesta`egtl sld m ötafm he tlhls ls agvestahlres ‖ frehlres e mfalgastms ‖ serí he 1,2>% ml mgl, fmcfucmhl gm hmtm-dmse he 6= he heze`drl he 4>=1.

Estruturm öta`m he fmpatmc e ierméæl he vmclr ^mrtaghl hl pressuplstl he que m regtmdacahmhe exaiahm plr u` agvesta`egtl agjcuegfam gm sum esta`méæl he vmclr, Verrm e Yafkert (4>=1, p. 99) ressmctm` que –l ldoetavl he hasfutar m estruturm he fmpatmc he e`presms á verajafmr se exaste u`m estruturm he fmpatmc que resucte e` u` fustl he fmpatmc (YMFF) `ms dmaxl e, flgsequegte`egte, e` u`  jar` vmcue vmcue (vmclr hm e`presm) `mas mctl‐. Fl`l l fustl he fmpatmc hls frehlres, tl`mhl he jlr`m pcmgeomhm, á `eglr que l fustl he fmpatmc hls mfalgastms, e l fustl `áhal plghermhl he fmpatmc (F@^F lu YMFF) á u`m jugéæl hms prlplréões he fmhm jlgte he fmpatmc, á rmzlívec r mzlívec pegsmr gm exastïgfam he u`m estruturm qque ue represegte l `eglr fustl he fmpatmc tltmc plssàvec. Veiughl @mrtecmgf, ^msag e ^erearm (4>=4, p. =82), exaste agfertezm qumgtl î esta`méæl hm furvm he fustls he fmpatmc pröpral e he terfearls, e assl hajafuctm m heter`agméæl exmtm hl eghavahm`egtl öta`l, plr essm rmzæl á `mas mhequmhl rejerar-se m u`m reiaæl öta`m, e` vez he u` plgtl öta`l.  Mssmj Getl (4>=1, p. =>=) esfcmrefe que l estuhl hm estruturm he fmpatmc öta`m dusfm egflgtrmr m fl`plsaéæl he fmpatmc que jagmgfam u`m e`presm, –hastraduàhms egtre hàvahms lgerlsms (^) e refursls pröprals (^C), ahegtajafmghl m recméæl ^/^C que `aga`azm l fustl tltmc he fmpatmc e `mxa`azm, ml `es`l te`pl, l seu vmclr eflgø`afl‐. E` u`m e`presm que `lhajafm m sum estruturm he fmpatmc mu`egtmghl l seu eghavahm`egtl, –hums jlréms mtum` e` segtahls flgtrírals sldre l perfegtumc hl YMFF‐. Ml mu`egtmr l seu eghavahm`egtl, u`m e`presm mpresegtmrí u` `malr

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rasfl e plr flgsequïgfam u` `malr fustl he fmpatmc pröpral. ^lr lutrl cmhl, ml mu`egtmr m pmrte he jagmgfam`egtl fl` fmpatmc he terfearls, que plssua u` fustl he fmpatmc `mas dmrmtl, l fustl he fmpatmc tltmc teghe m ha`aguar. Veiughl Mssmj Getl (4>=1, p. =>=), m hasfussæl dísafm hms telrams he estruturm he fmpatmc e hls seus ejeatls sldre l YMFF á he que se esses ejeatls se mgucm` lu gæl, lu seom, se l mu`egtl hl fustl he fmpatmc pröpral, e` jugéæl he u` `malr eghavahm`egtl, á mgucmhl fl` m ha`aguaéæl hm prlplréæl hm sum jlgte he jagmgfam`egtl gl fmpatmc tltmc hm e`presm. M irmghe questæl á mvmcamr se exaste u`m estruturm he fmpatmc que `aga`aze l fustl he fmpatmc tltmc hm e`presm he jlr`m m `mxa`azmr l vmclr hl geiöfal.  Mciu`ms hms pragfapmas telrams sldre m estruturm he fmpatmc sæl mplgtmhms plr Mssmj Getl (4>=1, p. =>=), e estms sæl resu`ahms m seiuar.

Xelram he @lhaicamga e @accer Gls mgls he =15>, ls mutlres @lhaicamga e @accer hesegvlcverm` u`m a`plrtmgte telram, m qumc suiere que m e`presm `mgteram l seu vmclr aghepeghegte`egte hm sum estruturm he fmpatmc pcmgeomhm. L pragfàpal hesse rmfalfàgal á que l mu`egtl gl rasfl he fmpatmc pröpral, e` rmzæl he `malr mcmvmgfmie` jagmgfearm, á fl`pegsmhl pecm `eglr pmrtafapméæl hl fmpatmc pröpral gl jagmgfam`egtl tltmc hl geiöfal. ^lrtmgtl, m flgfcusæl á que l fustl he fmpatmc tltmc (YMFF) serí se rí prmtafm`egte l `es`l pmrm qumcquer recméæl ^/^C, plr assl gæl mjetmrí l vmclr hm e`presm. Clil, agexaste m estruturm he fmpatmc öta`m, tlhms resuctmræl resu ctmræl e` u` fustl aiumc lu `uatl sa`acmr. Veiughl Mssmj Getl (4>=1, p. =>=), @lhaicamga e @accer, e` trmdmcbl plsteralr (=1:6) –he`lgstrmrm` fl`l ls imgbls jasfmas plhe` degejafamr l vmclr hm e`presm‐. L egtegha`egtl jagmc á que, flgsahermghl m hehutadacahmhe jasfmc hls ourls ‖ fustl jagmgfearl ‖ l fustl he fmpatmc tltmc teghe m ha`aguar qumgtl `malr jlr m prlplréæl he fmpatmc he terfearls gm e`presm, oí gl fmsl he agexastïgfam hl degejàfal jasfmc hm hàvahm, l vmclr hm e`presm serí l `es`l, aghepeghegte`egte hm estruturm he fmpatmc.  Mssmj Getl (4>=1, p. =>=) fl`pce`egtm que –e`prásta`ls sudsahamhls mtrmvás hl DGHEV, que `mgtá` sums tmxms he ourls agmctermhms mtá gàveas `mas mctls he eghavahm`egtl‐ sæl exe`pcls remas hm mpcafmdacahmhe hm telram he @lhaicamga e @accer gl Drmsac.

Xelram he flgvegfalgmc  M telram flgvegfalgmc flgvegfalgmc mfrehatm gm exastïgfam hm estrut estruturm urm öta`m he fmpatmc, lu seom, seom, mquecm que `aga`azmrí l fustl he fmpatmc tltmc (YMFF), `mxa`azmghl l vmclr hm e`presm. Essm telram tm`dá` á flgbefahm plr –trmhe ljj‐ . Veiughl Mssmj Getl (4>=1, p. =>=), essm telram pressupõe m exastïgfam he dmsafm`egte hums vmgtmiegs e u` mcertm pmrm ml geiöfal?

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L fustl he fmpatmc he terfearls á `eglr que l fustl he fmpatmc pröpral e, ml mu`egtmr m sum prlplréæl gl jagmgfam`egtl tltmc hm e`presm, l fustl teghe m ha`aguar, plr assl á u` öta`l agfegtavl pmrm l mu`egtl hm mcmvmgfmie` jagmgfearm. Gms e`presms lptmgtes pecm mpurméæl hl cufrl remc, exaste l degejàfal jasfmc hm hàvahm, que per`ate cmémr ls fustls jagmgfearls fl`l hespesm e fl` assl ha`aguar m dmse tradutívec pmrm jags he a`plstls a`plst ls he reghm, e assl rehuz maghm `mas l fustl hm fmptméæl he fmpatmc he terfearl terfearls.s. L mcertm surie e` rmzæl he qumgtl `malr m mcmvmgfmie` hm e`presm, `malr l eghavahm`egtl, e fl` assl ls rasfls he hesflgtaguahmhe hm lperméæl mu`egtm`. L rasfl mu`egtm e` rmzæl he ls frehlres estmdecefere` refeder l retlrgl hl fmpatmc, `es`l fl` tmxms `eglres que l fustl he fmpatmc pröpral, aghepeghegte`egte he ls geiöfals are` de` lu `mc. Lutrl plgtl a`plrtmgte m ser flgsahermhl á que l mu`egtl hl eghavahm`egtl mu`egtm l spremh  pecl  pecl rasfl pmrm m flgfessæl hls e`prásta`ls. E` su`m, mtá heter`agmhl plgtl he mcmvmgfmie`, l fustl he fmpatmc he terfearls plhe `mgter-se agmctermhl; mpös esse gàvec, l fustl he fmpatmc he terfearls teghe m mu`egtmr e` rmzæl he ls frehlres perfedere` l mu`egtl gl rasfl jagmgfearl ja gmgfearl hm e`presm.

 M aheam he plrfurvm trís hm ls trïsque, plgtls hesfratls mfa`m flgtradue` pmrm l suria`egtl hetelram fustl flgvegfalgmc hl fmpatmc tltmcá que (YMFF) he agàfal, teghe m ha`aguar î `ehahm que m prlplréæl hl fustl he fmpatmc he terfearls mu`egtm e, m pmrtar he fertl plgtl, vlctm m sudar e` rmzæl hl mu`egtl hl fustl hl fmpatmc he terfearls mjetmhls pecm perfepéæl hls frehlres he u` mu`egtl gl rasfl jagmgfearl plr `malres gàveas he eghavahm`egtl.

Xelram he ^efkagi Lrher  Mssmj Getl (4>=1, p. =>8) mplgtm que m telram he ^efkagi Lrher prevï –fertm lrhe` lu baermrquam he prejerïgfams‐ gm jlr`m he fl`l jagmgfamr m e`presm. L pressuplstl á que ls iestlres hm lrimgazméæl plssue` agjlr`méões gæl hasplgàveas mls frehlres sldre m remc satuméæl hm e`presm. Gesse segtahl,retahls; m telram he ^efkagi Lrher prevï que m eprejerïgfam serí pecl jagmgfam`egtl `ehamgte ls cufrls plsteralr`egte, plr e`prásta`ls jagmgfam`egtls he terfearls; e, plr ja`, pecm e`assæl he glvms méões ml `erfmhl.

Utacazméæl hm estruturm öta`m he fmpatmc pmrm jags he vmcumtalg Á rmzlívec pegsmr que m e`presm gæl `mgtá` u`m estruturm he fmpatmc jaxm hurmgte tlhm m vahm ÿtac hl agvesta`egtl, e`dlrm seom u` pressuplstl prítafl pmrm mvmcamr m e`presm fl` `malr miacahmhe. @mrtecmgf, ^msag e ^erearm (4>=4, p. =5>) suiere` que á mhequmhl pegsmr e` ter`ls he estruturm he fmpatmc mcvl pmrm jags he vmcumtalg, e estm plhe lu gæl ser hajeregte hm estruturm exastegte ex astegte gl `l`egtl hm mvmcaméæl. Gesse segtahl, á a`plrtmgte mgmcasmr l pcmgeom`egtl hm mctm hareéæl sldre m `etm he estruturm he fmpatmc ‖ mcvl ‖ öta`m e fl`l essm `etm serí mcfmgémhm.

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Esse rmfalfàgal reslcve l que @mrtecmgf, ^msag e ^erearm (4>=4, p. =5>) fbm`mrm` he prldce`m he farfucmrahmhe que egvlcve m esta`méæl hl fustl he fmpatmc tltmc hm e`presm (F@^F lu YMFF). Esfcmrefe` que esse prldce`m surie –plrque á prefasl jmzer ms plgherméões he fmpatmc pröpral e he terfearls sldre l fmpatmc tltmc fl` dmse gls vmclres he `erfmhl pmrm heter`agmr l F@^F‐, e, pmrm smder l vmclr he `erfmhl hm e`presm, e `presm, mgtes á gefessíral esta`mr esta `mr l F@^F. E` su`m, l vmclr hms méões hm e`presm hepegherí hl F@^F, e l F@^F hepegherí hl vmclr hms méões hm e`presm.

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@ÖHUCL AAA ‖ AGHAFMHLTEV HE ^ETJLT@MGFE HL GEIÖFAL   Geste `öhucl, serí he`lgstrmhl fl`l fmcfucmr e mgmcasmr ls pragfapmas aghafmhlres he perjlr`mgfe utacazmhls pmrm `egsurmr ls resuctmhls hls agvesta`egtls, pragfapmc`egte qumghl l ldoetavl á m `mgutegéæl hl mtavl gm fmrtearm he agvesta`egtls.

Tesuctmhl lpermfalgmc L resuctmhl lpermfalgmc á mquece iermhl pecm mtavahmhe aghepeghegte`egte he fl`l m e`presm á jagmgfamhm. Hesse `lhl, u`m e`presm plhe mpurmr cufrl lpermfalgmc e ml `es`l te`pl mpresegtmr preouàzl gl seu he`lgstrmtavl he resuctmhl eflgø`afl mpös sere` cmgémhms tlhms ms hespesms fl` ourls, plr exe`pcl. ex e`pcl. Veiughl Mssmj Getl (4>=1, p. 44), l resuctmhl lpermfalgmc á l pra`earl aghafmhlr he mtrmtavahmhe eflgø`afm plrque reiastrm m vamdacahmhe hls agvesta`egtls (mtavls), fmsl esteom` re`ugermghl mhequmhm`egte l fustl he fmpatmc tltmc (fustl hms jlgtes he jagmgfam`egtl). Tessmctm que mtumc`egte `uatms fl`pmgbams, mcá` hm mtavahmhe ldoetl, plssue` agvesta`egtls e` lutrms e`presms lu e` geiöfals estratm`egte jagmgfearls, fl`l agvesta`egtls e` `lehms, lu lperméões fl` heravmtavls. Gesse fegíral, á essegfamc ahegtajafmr l resuctmhl hm e`presm gm sum mtavahmhe-ja` (resuctmhl lpermfalgmc), aghepeghegte`egte hls resuctmhls jagmgfearls (resuctmhl (res uctmhl gæl lpermfalgmc). Á l resuctmhl lpermfalgmc que hmrí sustegtméæl î ierméæl he vmclr, fmsl plssum fmpmfahmhe he iermr jcuxls he fmaxm juturl flgsastegtes. L resuctmhl hm e`presm plhe ser hes`e`drmhl, seiughl Mssmj Getl (4>=1, p. 46), e`?   Tesuctmhl lpermfalgmc ‖ Á l resuctmhl exfcusavl hm mtavahmhe, represegtm l cufrl iermhl pecls agvesta`egtls gls mtavls, pmrtaghl hl pressuplstl he que l jagmgfam`egtl hm mtavahmhe á remcazmhl exfcusavm`egte plr fmpatmc pröpral, lu seom, se` m exastïgfam he 

 

 

 

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qumcquer hàvahm. Essm hejagaéæl á a`plrtmgte plrque, ml fmcfucmr l resuctmhl lpermfalgmc, l vmclr per`mgeferí l `es`l, aghepeghegte`egte hm exastïgfam he hàvahms lu gæl, plas á mpurmhl mgtes hl resuctmhl jagmgfearl (pmim`egtl he ourls). o urls). Tesuctmhl càquahl ‖ Á l resuctmhl iermhl mpös m agseréæl he tlhls ls fustls, lpermfalgmas e gæl lpermfalgmas, agfcusave l pmim`egtl hls ourls. Gesse segtahl, exastarí resuctmhl càquahl, fmsl l resuctmhl lpermfalgmc seom fmpmz he mrfmr fl` ls ourls heflrregtes heflrre gtes hl eghavahm`egtl, gmquece peràlhl, plrá` l jmtl he exastar resuctmhl càquahl gæl saigajafm que m lperméæl á vaívec, plas, mcá` hl pmim`egtl hls ourls, l resuctmhl lpermfalgmc heverí ser fmpmz he re`ugermr mhequmhm`egte l agvesta`egtl hls mfalgastms, lu seom, l fustl he fmpatmc pröpral.

^mrm `ecblr acustrmr m mpurméæl hl resuctmhl lpermfalgmc e` fl`pmrméæl ml resuctmhl càquahl, mpresegtm`ls l exe`pcl m seiuar. Jaiurm 6 ‖ Mpurméæl M purméæl hl resuctmhl lpermfalgmc e resuctmhl càquahl Ceiascméæl slfaetíram

Tesuctmhl moustmhl

(+) Tefeatms he veghms

=>>.>>>   =>>.>>>

(+) Tefeatms he veghms

=>>.>>>   =>>.>>>

(-) Fustl he veghms (F@Z lu F^Z)

(:>.>>>)

(-) Fustl he veghms (F@Z lu F^Z)

(:>.>>>)

(0) Cufrl lpermfalgmc drutl (-) Hespesms lpermfalgma lpermfalgmass

8>.>>>   8>.>>>

(0) Cufrl lpermfalgmc drutl

(=>.>>>)

(0) Cufrl lpermfalgmc càquahl

6>.>>>   6>.>>>

(-) Heprefamé Heprefaméæl æl e m`lrtazméæl

(:.>>>)

(0) CMOAT (cufrl mgtes hl pmim`egtl he ourls e AT)

48.>>>   48.>>>

(-) Hespesms jagmgfear jagmgfearms ms

(8.>>>)

(0) CMAT (cufrl mgtes hl pmim`egtl hl AT)

4>.>>>   4>.>>>

(-) ^rlvasæl he AT (-68%)

(:.2>>)

(-) Hespesms lpermfalgma lpermfalgmass  EDAXHM

↞

↞

 EDAX

 EDX

↞

GL^MX

 

↔

 

↔

 

↔

↔

 

=6.4>>   =6.4>>

6>.>>>   6>.>>>

(-) Heprefa Heprefaméæl méæl e m`lrtazmé m`lrtazméæl æl

(:.>>>)

(0) CMOAT (cufrl mgtes hl pmim`egtl he ourls e AT)

48.>>>   48.>>>

(-) Hespesms jagmgfear jagmgfearms ms

(8.>>>)

(0) CMAT (cufrl mgtes hl pmim`egtl hl AT)

48.>>>   48.>>>

(-) ^rlvas ^rlvasæl æl he AT (-68%)

(2.=:>)

(0) Cufrl lpermfalgmc càquahl mpös AT

=5.28>   =5.28>

(-) Hespesms jagmgfear jagmgfearms ms

(8.>>>)

(0) Cufrl càquahl mpös AT

Jlgte? Exe`pcl mhmptmhl he Mssmj Getl (4>=1, p. 48).

5>

(=>.>>>)

(0) Cufrl lpermfalgmc càquahl

(+) Degejàfal jasfmc hm hàvahm (Hesp. Jag. R AT) AT ) Cufrl càquahl mpös l AT

8>.>>>   8>.>>>

=.6:> =6.4>>   =6.4>>

 

 

Gm jaiurm 6, mfa`m, l resuctmhl lpermfalgmc càquahl mpös l a`plstl he reghm á ldtahl mpös fmcfucmr qumc seram l cufrl remc se` m exastïgfam he hespesms jagmgfearms. Gesse fmsl, l Glpmt, mdrevaméæl hl ter`l e` agicïs Get Lpermtagi ^rljat Mjter Xmx , que e` plrtuiuïs saigajafm –Cufrl Lpermfalgmc Càquahl mpös l A`plstl he Teghm‐. L resuctmhl lpermfalgmc resuctlu e` T$ =5.28>, egqumgtl l resuctmhl càquahl tltmcazlu T$ =6.4>>. M hajeregém haj eregém á iermhm dmsafm`egte pecl hesflgtl hl fustl jagmgfearl ejetavl, mquece que flgsaherm l fustl fl` ourls mpös m hehuéæl hls ejeatls e` heflrrïgfam hl degejàfal jasfmc hm hàvahm. hàv ahm.

EDAXHM EDAXHM á m mdrevamturm hl ter`l e` agicïs emrgagis dejlre agterest, tmx, heprefamtalg mgh m`lrtazmtalg, que e` plrtuiuïs saigajafm –cufrl mgtes he a`plstls, ourls, heprefaméæl e m`lrtazméæl‐. Veiughl Mssmj Getl (4>=1, p. 49), l EDAXHM –revecm m fmpmfahmhe lpermfalgmc he u`m e`presm e` iermr fmaxm e` heter`agmhl peràlhl‐. Fl`l l pröpral gl`e evahegfam, gl fícfucl hl EDAXHM gæl sæl flgsahermhls ls ourls, plr gæl tere` caiméæl fl` m fmpmfahmhe lpermfalgmc hm e`presm, m heprefaméæl e m m`lrtazméæl, plr gæl represegtmre` hese`dlcsl e ls tradutls sldre l cufrl.  M hepref heprefaméæl améæl e m m`lrta m`lrtazméæl zméæl gæl represegtm` hese`dlcsl hese`dlcsl gl `l`egtl `l`egtl hl fícfucl fícfucl hl EDAXHM plrque l hese`dlcsl lflrreu mgtes, gl `l`egtl hl agvesta`egtl gl mtavl. L seu vmclr á flgsahermhl mpegms fl`l rehutlr hm dmse tradutívec pmrm jags he mpurméæl hl a`plstl he reghm e flgtraduaéæl slfamc, assl gl fmsl hms e`presms e`pres ms que lperm` fl` l reia`e he tradutméæl pecl cufrl remc. U` plgtl mctm`egte a`plrtmgte á hestmfmhl plr Mssmj Getl (4>=1, p. 49) qumgtl î agterpretméæl hl EDAXHM? esse aghafmhlr gæl plhe ser fl`preeghahl fl`l l vmclr que ejetavm`egte estí hasplgàvec gl fmaxm, heveghl ser agterpretmhl fl`l m fmpmfahmhe pltegfamc he ierméæl he fmaxm, lu seom, flgtradua pmrm m ierméæl, `ms gæl saigajafm que l seu vmclr se tlrglu hasplgadacahmhe ejetavm`egte. M rmzæl á `uatl sa`pces? ms refeatms remcazmhms gl peràlhl, `ms que maghm gæl jlrm` refedahms, gæl represegtmræl ejetavm`egte egtrmhms he fmaxm, hm `es`m jlr`m que ls fustls e ms hespesms ejetavl hl peràlhl plssue` fl`prl`assl he pmim`egtl juturl gæl represegtmræl hese`dlcsl gmqueceque peràlhl. L EDAXHM plhe ser agterpretmhl fl`l u` öta`l aghafmhlr pmrm mgmcasmr m fmpmfahmhe hm e`presm he iermr resuctmhl lpermfalgmc. Vaigajafm hazer que, ml mgmcasmr l EDAXHM, vlfï perfederí l pltegfamc hm e`presm pmrm flgtraduar  pmrm m ierméæl he resuctmhl lpermfalgmc e he fmaxm, `ms gæl pmrm represegtmr ejetavm`egte l resuctmhl càquahl hm e`presm e m hasplgadacahmhe he fmaxm iermhm. ^lr essm rmzæl, ml mpurmr l aghafmhlr e fl`pmrí-cl fl` l cufrl càquahl mpös l a`plstl he reghm, l mgmcastm perfederí se l evegtumc preouàzl á heflrregte hm lperméæl lu, plr exe`pcl, he mctls gàveas he hespesms jagmgfearms. L fícfucl hl EDAXHM estí represegtmhl gm jaiurm 6, mfa`m, e flgsaste dmsafm`egte e` sudtrmar hms refeatms lpermfalgmas he veghms tlhls ls fustls e ms hespesms estratm`egte lpermfalgmas.

5=

 

 

TLA TLA á m mdrevamturm hl ter`l e` agicïs returg lg agvest`egt, que e` plrtuiuïs saigajafm –retlrgl sldre l agvesta`egtl‐. Veiughl Mssmj Getl (4>=1, p. 66), m jlr`ucméæl dísafm hl fícfucl hl TLA á hmhm plr? TLA 0 Glpmt ù agvesta`egtl

Lghe?   Glpmt represegtm l resuctmhl lpermfalgmc càquahl mpös l a`plstl he reghm, se` flgsahermr m exastïgfam he hespesms jagmgfearm, plr gæl represegtmr fustls lpermfalgmas, `ms, sa`, he jagmgfam`egtl.   Agvesta`egtl represegtm tlhl fmpatmc agvestahl gm e`presm, exfcuaghl ms jlgtes he jagmgfam`egtl esplgtägems. E` lutrms pmcmvrms, represegtm l fmpatmc pröpral e he terfearls que jagmgfam` m e`presm e que suiere` m exastïgfam he u` fustl jagmgfearl ahegtajafívec. 

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 Mssmj Getl (4>=1, p. 66) suiere que l fícfucl hl TLA utacazmghl utacazmghl l agvesta`egtl, e` vez hl mtavl tltmc, –ljerefe `ecblres agjlr`méões sldre l ieguàgl retlrgl iermhl ier mhl pecl fmpatmc agvestahl gm e`presm, e que gefessatm ser re`ugermhl‐. r e`ugermhl‐.  Ml ser fmc fmcfucm fucmhl hl l TLA TLA,, á mpurm mpurmhm hm m tmxm he retlr retlrgl gl hls agvesta` agvesta`egtl egtls, s, e estm plhe ser fl`p fl`pmrmhm mrmhm fl` l fustl `áhal plghermhl he fmpatmc pmrm verajafmr se m e`presm plssua fmpmfahmhe he iermr vmclr lu gæl. U`m e`presm ierm vmclr qumghl l TLA mpresegtmr u` vmclr superalr ml hl F@^F. F@^F . Fmsl l agversl mflgteém, verajafm-se l egtegha`egtl he que m e`presm estí hestruaghl vmclr plr gæl plssuar m fmpmfahmhe he iermr u` resuctmhl lpermfalgmc càquahl que fudrm ls rasfls hl agvesta`egtl. L exe`pcl m seiuar acustrm m vasæl he Mssmj Getl (4>=1, p. 64) sldre m hajeregém egtre l mtavl tltmc e l agvesta`egtl?

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Jaiurm 8 ‖ Exe`pcl he dmcmgél pmtra`lgamc sa`pcajafm sa`pcajafmhl. hl. MXAZL MXAZL FATFUCMGX FATFUCMGXEE

ZMCLT 6:.>>>

^MVVAZL ^MVVAZL FATFUCMGXE ^mssavl Lgerlsl (E`prásta`ls) (E`prásta`ls)  

MXAZL GÆL FATFUCMGXE

XLXMC

:8.>>>

=>>.>>>   =>>.>>>

ZMCLT 4>.>>> 2.8>>   2.8>>

^mssavl Gæl Lgerlsl (Jugfalgm`egt (Jugfalgm`egtls) ls)   ^MVVAZL GÆL FATFUCMGXE

==.:>>  ==.:>>  6>.>>>

^MXTA@ØGAL CÀ]UAHL

5>.>>>

XLXMC

=>>.>>>   =>>.>>>

MXAZL XLXMC 0 =>>.>>> 0 =>>.>>>   AGZEVXA@EGXL 0 MXAZL 0 MXAZL XLXMC ‖ ^MVVAZL GÆL LGETLVL LGETLVL   AGZEVXA@EGXL 0 =>>.>>>-==.:>> 0 =>>.>>>-==.:>>   AGZEVXA@EGXL 0 22.8>> 0 22.8>>   Jlgte? Mhmptmhl he Mssmj Getl (4>=1, ( 4>=1, p. 6=).

Glte que, e`dlrm m e`presm plssum u` mtavl tltmc gl vmclr he T$ =>>.>>>, l vmclr hl agvesta`egtl se` flgsahermr l pmssavl gæl lgerlsl (pmssavl he jugfalgm`egtl) á he mpegms T$ 22.8>>. Este ÿcta`l serí l vmclr hl fmpatmc (pröpral e he terfearls) que prefasm ser re`ugermhl. ^mrtaghl hl pressuplstl he que essm `es`m e`presm e`pre sm mpresegte gl peràlhl u` Glpmt aiumc m T$ =5.28>, l vmclr hl TLA serí he? TLA 0 Glpmt ù agvesta`egtl TLA 0 =5.28> ù 22.8>> 

TLA 0 >,=914 lu =9,14% gl peràlhl. 

 M tmxm he retlrgl `ehahm pecl TLA mu`egtmrí î `ehahm que l Glpmt ‖ fmpmfahmhe lpermfalgmc he iermr resuctmhl ‖ se s e ecevmr lu l vlcu`e he fmpatmc agvestahl agve stahl ha`aguar. Veiughl Mssmj Getl (4>=1, p. 68), ms plssadacahmhes he ha`aguaéæl hl fmpatmc agvestahls sæl? `malr ejafaïgfam gm mclfméæl he refursls lu jmctm he lplrtugahmhe he fresfa`egtl. M lflrrïgfam hestm ÿcta`m á u` a`plrtmgte mcertm pmrm m mctm iestæl hm e`presm, plas glr`mc`egte á `ltavmhm pecm perhm he fl`petatavahmhe gls geiöfals lu plr jmtlres j mtlres he retrméæl eflgø`afm, fl`l frases, plr exe`pcl.

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TLE TLE á m mdrevamturm hl ter`l e` agicïs – returg lg equaty‐,  que e` plrtuiuïs saigajafm –retlrgl sldre l pmtra`øgal càquahl‐. Veiughl Mssmj Getl (4>=1, p. 86), m jlr`ucméæl dísafm hl fícfucl hl TLE á hmhm plr? TLE 0 cufrl càquahl ù pmtra`øgal càquahl

Lghe?   Cufrl càquahl á l cufrl càquahl mpös l a`plstl he reghm, lu seom, l resuctmhl mpös tlhls ls fustls e ms hespesms hm e`presm. Á l resuctmhl càquahl que ejetavm`egte sldrm pmrm re`ugermr l fmpatmc agvestahl pecl mfalgastm.   ^mtra`øgal càquahl á l vmclr hl pmtra`øgal càquahl jagmc fl` hmtm-dmse hl jagmc hl exerfàfal a`ehamtm`egte mgteralr ml peràlhl he mgícase. Esse mouste se jmz gefessíral e` rmzæl he l pmtra`øgal càquahl agflrplrmr l resuctmhl càquahl hl exerfàfal, lu seom, exmtm`egte m fmpmfahmhe he retlrgl que se heseom `ehar. 

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L TLE represegtm m tmxm he retlrgl hls agvesta`egtls remcazmhls pecls mfalgastms e plr assl heve ser fl`pmrmhl î tmxm `àga`m he mtrmtavahmhe hl h l fmpatmc pröpral. Fl`l l TLE `ehe m tmxm he retlrgl sldre l fmpatmc pröpral, e l TLA m tmxm he retlrgl sldre l fmpatmc pröpral e he terfearls sl`mhls, l TLE heverí mpresegtmr u`m tmxm superalr ml TLA se`pre que m mcmvmgfmie` jagmgfearm se `lstrmr vmgtmolsm. E` lutrms pmcmvrms, l jagmgfam`egtl j agmgfam`egtl fl` fmpatmc he terfearls heverí hev erí flgtraduar pmrm que m recméæl cufrl càqua càquahl/fmpatmc hl/fmpatmc pröpral mu`egte, `es`l que bmom rehuéæl gl cufrl càquahl e` rmzæl hl pmim`egtl he ourls.  Mssmj Getl (4>=1, p. 88) ressmctm que m mcmvmgfm mcmvmgfmie` ie` jagmgfearm –expra`e m fmpmfahmhe fmpmfahmhe que ls refursls he terfearls mpresegtm`, pecl fustl he fmpatmc he fmptméæl `mas dmaxl, e` ecevmr l retlrgl hl fmpatmc pröpral‐. He jlr`m que qumgtl `malr jlr m hajeregém egtre ms tmxms he retlrgl hl fmpatmc agvestahl e ms tmxms he ourls, `malr serí m fmpmfahmhe hm e`presm e` pltegfamcazmr ls retlrgls pmrm l mfalgastm; e` lutrms pmcmvrms, `malr serí m fmpmfahmhe hm e`presm he iermr vmclr. ^mrm exe`pcajafmr l fícfucl hl TLE e plssadacatmr m fl`pmrméæl hls aghafmhlres, l exe`pcl m seiuar flgsaherm ms `es`ms dmses utacazmhms pmrm exe`pcajafmr l fícfucl hl resuctmhl lpermfalgmc (jaiurm 6) e hl TLA (jaiurm 8). Ls hmhls sæl ls seiuagtes?   Glpmt 0 T$ =5.28>;   cufrl càquahl mpös AT 0 T$ =6.4>>;   agvesta`egtl 0 T$ 22.8>> e   pmtra`øgal càquahl 0 T$ 5>.>>>. 

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TLE 0 cufrl càquahl ù pmtra`øgal càquahl TLE 0 =6.4>> ù 5>.>>>  TLE 0 >,4:8> lu 4:,8>% gl peràlhl

TLA 0 Glpmt ù agvesta`egtl TLA 0 =5.28> ù 22.8>> 

TLA 0 >,=914 lu =9,14% gl peràlhl. 

Glte que l TLE resuctlu e` 4:,8>%, egqumgtl l TLA jla aiumc m =9,14% gl peràlhl. Xmc satuméæl expressm que m mcmvmgfmie` jagmgfearm, geste fmsl, á jmvlrívec. j mvlrívec. Ve m e`presm jlsse jagmgfamhm j agmgfamhm exfcusavm`egte plr fmpatmc pröpral, exastaram mpegms l –pmssavl gæl lgerlsl‐, l Glpmt seram aiumc ml cufrl càquahl; e l pmtra`øgal càquahl aiumc ml agvesta`egtl, lu seom, l TLE resuctmram aiumc ml TLA, m`dls aiumas m =9,14% gl peràlhl. ^lrtmgtl, m vamdacahmhe e` se jagmgfamr tm`dá` fl` refursls he terfearls, gl fmsl mpresegtmhl, `lstrlu-se vaívec, plr pltegfamcazmr l retlrgl sldre l fmpatmc agvestahl pecls mfalgastms.

EZM® EZM® á m mdrevamturm hl ter`l e` agicïs –eflgl`af vmcue mhheh‐, que e` plrtuiuïs saigajafm –vmclr eflgø`afl mireimhl‐. Veiughl Mssmj Getl (4>=1, p. ==6), l –EZM® expressm qumgtl u`m e`presm imgblu he cufrl mfa`m hl seu fustl he fmpatmc, seghl egteghahl, he jlr`m `mas m`pcm, fl`l u` pmrä`etrl he hese`pegbl eflgø`afl e saste`m he iestæl‐. L EZM®  á u`m `ehahm que remc`egte evahegfam m ierméæl lu hestruaéæl he raquezm, plas á resuctmhl hl cufrl mpurmhl mpös m flderturm he tlhls ls fustls he fmpatmas, pröpral e he terfearls. ter fearls. Tessmctm, maghm, que m `ehahm EZM® á u`m `mrfm reiastrmhm hm e`presm he flgsuctlram Vterg Vtewmrt & Fl. heshe ls mgls =12>, plr essm rmzæl, ls esfcmrefa`egtls sldre l te`m sæl remcazmhls exfcusavm`egte pmrm jags hahítafls. Ve`pre que l EZM®  resuctmr e` u` vmclr plsatavl, serí evahegfamhm u`m tmxm he retlrgl `malr que m tmxm `àga`m he mtrmtavahmhe hls agvesta`egtls, agv esta`egtls, plr essm rmzæl exa exastarí starí m framéæl he vmclr eflgø`afl. Essm raquezm framhm tm`dá` á flgbefahm fl`l illhwacc . @mrtecmgf, ^msag e ^erearm (4>=4, p. =99) hejage` tefgafm`egte  illhw  illhwacc  acc   fl`l –m hajeregém egtre l vmclr eflgø`afl hm e`presm pmrm seus mfalgastms e seu vmclr pmtra`lgamc remvmcamhl m preéls he `erfmhl‐. Gesse `es`l segtahl, Mssmj Getl (4>=1, p. ==:) revecm que  ill  illhwacc  hwacc  –surie   –surie sl`egte qumghl m e`presm he`lgstrm fmpmfahmhe e` iermr cufrl mfa`m he seu fustl he fmpatmc. Essm raquezm agtmgiàvec á `egsurmhm pecl vmclr presegte hesflgtmhl hls degejàfals juturls extrmlrhagírals (e` exfessl) espermhls he fmaxm‐. Tessmctm maghm que, pmrm expressmr l  ill  illhwacc  hwacc , m Vterg Vtewmrt & Fl. plssua u`m `ehahm,  @mrket  t  Zmcue  Mhheh  Mhheh (@ZM®), m qumc serí estuhmhm `mas î jregte. tm`dá` reiastrmhm, hegl`agmhm @mrke 55

 

 

L EZM® aiumc m zerl aghafm que l retlrgl imgbl pecls agvestahlres á exmtm`egte aiumc ml fustl he lplrtugahmhe exaiahl pecls agvestahlres he fmpatmc. Gesse fmsl, gæl serí espermhm vmclrazméæl gls preéls hms méões hm e`presm, plas, seiughl Mssmj Getl (4>=1, p. ==5), –gagiuá` pmimram `mas que esse vmclr pmrm refeder u` retlrgl exmtm`egte aiumc ml fustl he lplrtugahmhe (tmxm he hesflgtl hls jcuxls juturls espermhls esper mhls he fmaxm)‐. Fmde ressmctmr que u` EZM® aiumc m zerl gæl saigajafm que m e`presm gæl teve cufrl, pecl flgtríral, plrá` l cufrl iermhl jla exmtm`egte aiumc ml que se espermvm, rmzæl pecm qumc gæl mireim vmclr eflgø`afl.  Oí u` EZM® geimtavl saigajafm hazer que m e`presm gæl plssua flghaéões he re`ugermr l fustl he fmpatmc gecm agvestahl hamgte hls rasfls hl geiöfal, plr esse `ltavl heströa vmclr `es`l que m lperméæl mpresegte cufrl. E` lutrms pmcmvrms, l retlrgl hls agvesta`egtls gæl oustajafm ls rasfls. Veiughl Mssmj Getl (4>=1, p. ==9), m jlr`ucméæl dísafm hl fícfucl hl EZM® á hmhm plr? EZM® 0 Glpmt ‖ (F@^F Ù fmpatmc agvestahl)  lu

EZM® 0 Cufrl Càquahl mpös AT ‖ (Ke Ù pmtra`øgal càquahl)  lu

EZM® 0 (TLA ‖ F@^F) Ù fmpatmc agvestahl 

Lghe?   Glpmt represegtm l resuctmhl lpermfalgmc càquahl mpös l a`plstl he reghm, se` flgsahermr m exastïgfam he hespesm jagmgfearm.   F@^F á m tmxm que represegtm l fustl hl fmpatmc agvestahl. Á m tmxm que expressm l rasfl hl geiöfal. Á m tmxm `àga`m he mtrmtavahmhe hls agvestahlres. Á l fustl `áhal plghermhl he fmpatmc hm e`presm.   K e á m tmxm `àga`m he mtrmtavahmhe exaiahm pecls mfalgastms. Á l fustl he fmpatmc pröpral.   TLA á m tmxm he retlrgl sldre l fmpatmc agvestahl pecls frehlres e mfalgastms, sl`mhls.

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^mrm acustrmr m mpcafmdacahmhe hl fícfucl hl EZM®, flgsahere l fmsl he u`m e`presm que ve` mpresegtmghl u` retlrgl sldre ls agvesta`egtls (TLA) he =9,14% e que l fustl `áhal plghermhl he fmpatmc hm e`presm fmcfucmhl á he =5,54% ml mgl. Vmdeghl que l fmpatmc agvestahl pecls fre frehlres hlres e mfalgastms tltmcazm`, m vmclr he `erfmhl, `er fmhl, l `lgtmgte he 22.8>>, l vmclr hl EZM® serí hmhl plr? EZM® 0 (TLA ‖ F@^F) Ù fmpatmc agvestahl  EZM® 0 (>,=914 ‖ >,=554) Ù 22.8>>  EZM® 0 (>,>48>) Ù 22.8>>  EZM® 0 4.=4=.:> 

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Fl`l l vmclr hl EZM® resuctlu plsatavl, plsatav l, serí espermhl que l vvmclr mclr hm e`presm mpresegte u` íial e` recméæl ml vmclr tltmc hl fmpatmc agvestahl. Assl se oustajafm pecm prlhuéæl he cufrl superalr ml fustl he fmpatmc tltmc, e que jaflu evahegfamhl ml fl`pmrmr l TLA fl` l F@^F.

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@ÖHUCL AZ ‖ MZMCAMÉÆL HE E@^TEVMV   Geste `öhucl, seræl mdlrhmhls ls pragfapmas `átlhls he mvmcaméæl he e`presms, agfcuaghl ls `lhecls he mpurméæl hl vmclr agtràgsefl e l `lhecl he mvmcaméæl recmtavm. Veræl mpresegtmhls ls flgfeatls e ls seiuagtes `lhecls he mvmcaméæl? `átlhls he mvmcaméæl fl` dmse gls jcuxls he fmaxm hesflgtmhls, `átlhl he mpurméæl hl  jar`  vmcue   e equaty   vmcue , `átlhl he mvmcaméæl fl` dmse gl vmclr he `erfmhl mhafalgmhl (@ZM®) e, fl`pcetmghl l `öhucl, l `átlhl he mvmcaméæl recmtavm, tm`dá` flgbefahl fl`l mvmcaméæl plr `ÿctapcls.

@átlhl he vmcumtalg fl` dmse gls jcuxls he fmaxm hesflgtmhls E` que pese exastare` lutrms `etlhlcliams, Mssmj Getl Ge tl (4>=1, p. =26) suiere que –l `átlhl he jcuxl he fmaxm hesflgtmhl (JHF) á l que mpresegtm `malr railr táfgafl e flgfeatumc, seghl plr assl l `mas aghafmhl e mhltmhl gm mvmcaméæl he e`presms‐. L pressuplstl á que u` mtavl ter teríí l seu vmclr `ehahl pecm fmpmfahmhe he iermr jcuxls j cuxls he fmaxm he retlrgl gl juturl, hesflgtmhls m u`m tmxm mhequmhm ml gàvec he rasfl hl agvesta`egtl. Flgtuhl, Hm`lhmrmg (4>=2, p. =6) trmz u` questalgm`egtl agteressmgte mferfm hm mvmcaméæl? –serí `ecblr fl`prmr Illice (ILLI), e`presm que gæl pmim havaheghls milrm, `ms que te` irmghe pltegfamc he fresfa`egtl e egvlcve irmghe agfertezm sldre l juturl, lu Mtram (@L), e`presm que pmim mctls havaheghls fl` perspeftavms he fresfa`egtl ca`atmhms e he refeatms mfeatíveas=2, p. =8) ecegfm ls fagfl tapls he jcuxls he fmaxm e fl`l fmcfucmr l vmclr presegte e` fmhm u` hls fmsls?   Jcuxl he fmaxm sa`pces ‖ Á l pmim`egtl lu refeda`egtl remcazmhl `ehamgte u` ÿgafl pmim`egtl gl juturl. Dmstm hesflgtmr esse ÿgafl jcuxl he fmaxm prloetmhl gl juturl pecm tmxm he hesflgtl (K) ageregte ml rasfl, gmturmc`egte mpcafmghl l peràlhl (g) he esperm pmrm se mujerar l jcuxl juturl (JF). Á l que glr`mc`egte mflgtefe fl` mpcafméões e` reghm jaxm qumghl l pmim`egtl hls ourls á remcazmhl gl `l`egtl hl resimte hl agvesta`egtl? 

Zmclr ^resegte (Z^) 0 JF ù (= + K) g 

Exe`pcl? vmclr presegte he u` agvesta`egtl a gvesta`egtl que prl`ete pmimr T$ =.>>>,>> hmqua m fagfl mgls fl` u`m tmxm he hesflgtl he =5% ml mgl? Zmclr ^resegte (Z^) 0 =.>>> ù (= + >,=5) 5  Zmclr ^resegte (Z^) 0 =.>>> ù (=,=5) 5  Zmclr ^resegte (Z^) 0 =.>>> ù 4,>==6:)  Zmclr ^resegte (Z^) 0 T$ 819,=2   

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 Mguahmhe lu sárae ‖ Lflrre qumghl ls pmim`egtls lu refeda`egtls (fl` vmclres gl`agmas aiumas ) mflgtefe` `ehamgte u`m sufessæl he jcuxls he fmaxm (JF) e` agtervmcls reiucmres, e` heter`agmhl peràlhl (g)? Z^ 0 JF Ù {= ‖ [= ù (= + K) gP} ù K 

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Exe`pcl? vmclr presegte he u` u ` agvesta`egtl que prl`ete pmimr T$ =.>>>,>> hurmgte fagfl mgls fl` u`m tmxm he hesflgtl he =5% ml mgl? Z^ 0 =.>>> Ù {= ‖ [= ù (= + >,=5) 5P} ù >,=5  Z^ 0 =.>>> Ù {= ‖ [= ù (=,=5) 5P} ù >,=5  Z^ 0 =.>>> Ù {= ‖ [= ù 4,>==6:P} ù >,=5  Z^ 0 =.>>> Ù {= ‖ >,819=2} ù >,=5  Z^ 0 =.>>> Ù >,5>424 ù >,=5  Z^ 0 =.>>> Ù 6.654=:  Z^ 0 6.654,=:   

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 Mguahmhe fresfegte fresfegte lu sárae fresfegte ‖ Mflgtefe Mflgtefe qumghl ls pmim`egtls lu refeda`egtls tï` vmclres gl`agmas fresfegtes m u`m tmxm he fresfa`egtl flgstmgte flgstmgte (i), plrá` fl` u`m expeftmtavm he te`pl jagatm prevam`egte prev am`egte estmdecefahm? Z^ 0 JF Ù {= ‖ [(= + i) g ù (= + K) gP} ù (K ‖ i) 

Exe`pcl? vmclr presegte he u` agvesta`egtl que prl`ete pmimr T$ =.>>>,>> pecls pröxa`ls fagfl mgls, seghl que hl seiughl mgl e` hamgte ls jcuxls fresferæl m u`m tmxm he 6% ml mgl. M tmxm he hesflgtl mprlpramhm ml rasfl ra sfl á he =5% ml mgl? Z^ 0 =.>>> Ù {= ‖ [(= + >,>6) 5 ù (= + >,=5) 5P} ù (>,=5 ‖ >,>6) Z^ 0 =.>>> Ù {= ‖ [=,>6 5 ù =,=5 5P} ù >,=4  Z^ 0 =.>>> Ù {= ‖ [=,=5149 ù 4,>==6:P} ù >,=4  Z^ 0 =.>>> Ù {= ‖ >,59:6:} ù >,=4  Z^ 0 =.>>> Ù >,846:8 ù >,=4  Z^ 0 =.>>> Ù 6,56>66  Z^ 0 6.56>,66   

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^erpetuahmhe lu sárae agjagatm ‖ Tesuctm he u`m sufessæl he pmim`egtls lu refeda`egtls remcazmhls agjagatm`egte e` peràlhls reiucmres? Z^ 0 JF ù K 

Exe`pcl? vmclr presegte he u` agvesta`egtl que prl`ete pmimr T$ =.>>>,>> perpetum`egte. M tmxm he hesflgtl mprlpramhm ml rasfl á he =5% ml mgl? Z^ 0 =.>>> ù >,=5  Z^ 0 :.:::,:9  :=

 

 

 

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^erpetuahmhe fresfegte lu sárae agjagatm fresfegte ‖ Mhafalgm î sárae agjagatm u`m tmxm he fresfa`egtl flgstmgte (i), lu seom, ls jcuxls juturls fresfe` e` peràlhls reiucmres mtá l agjagatl, plrá` m u`m tmxm he fresfa`egtl flgstmgte (i)? Z^ 0 JF ù (K ‖ i) 

Exe`pcl? vmclr presegte he u` agvesta`egtl que prl`ete pmimr agjagatls jcuxls he fmaxm, seghl que l pröxa`l serí he T$ =.>>>,>> e, m pmrtar hl seiughl (agfcusa (agfcusave), ve), ls jcuxls fresferæl agjagatm`egte m u`m tmxm flgstmgte he 6 ml peràlhl. M tmxm he hesflgtl mprlpramhm ml rasfl á he =5% ml mgl? Z^ 0 =.>>> ù (>,=5 ‖ >,>6) Z^ 0 =.>>> ù >,=4  Z^ 0 2.666,66 

 Ml mpcafmr mhequmhm`egte fmhm tapl tapl he fícfucl hl vmclr presegte mls jcuxls he fmaxm prloetmhl prloetmhl hm e`presm, á plssàvec esta`mr l vmclr hm e`presm e fl`pmrmr fl` l preél prmtafmhl gl `erfmhl gmquece agstmgte. Xmc fl`pmrméæl per`atarí perfeder se l preél geilfamhl estí –oustl‐, supermvmcamhl lu sudmvmcamhl.

Jcuxl he fmaxm hls havaheghls Fl`l oí hesfratl mgteralr`egte, l vmclr he u` agvesta`egtl gl presegte hepegherí hm fmpmfahmhe he iermr jcuxls he fmaxm gl juturl ju turl e hm tmxm mprlpramhm ml rasfl hl agvesta`egtl. a gvesta`egtl. ]umghl se mgmcasm l agvesta`egtl e` méões, sld m ötafm hl jcuxl he fmaxm hesflgtmhl, sæl espermhls dmsafm`egte hlas flgougtls he jcuxls he fmaxm juturls? =) havaheghls e ourls sldre l fmpatmc pröpral refedahls mtá l `l`egtl hm veghm hm méæl `mas m prevasæl hl preél jagmc hl mtavl; lu 4) mpegms l vmclr hls havaheghl e ourls sldre l fmpatmc pröpral, fmsl m agtegéæl seom –gugfm‐ vegher m méæl, e` lutrms pmcmvrms, fmrreimr perpetum`egte l mtavl gm fmrtearm he agvesta`egtls. ^lr `mas que l imgbl he fmpatmc recmtavl î veghm he u`m méæl plssm mflgtefer, fl`l m prevasæl hl vmclr hm méæl á heter`agmhm pecls havaheghls e ourls sldre l fmpatmc pröpral juturls, Hm`lhmrmg (4>=2, p. =>9) esfcmrefe que –l vmclr he u`m méæl plhe ser jlr`ucmhl fl`l l vmclr presegte he havaheghls e` perpetuahmhe‐.

@lhecl he Ilrhlg Veiughl Mdreu Jacbl et mc. (4>=4, p. ==8), l `lhecl he jcuxl he fmaxm dmsemhl mpegms gls havaheghls agafamc`egte jla prlplstl plr O. D. Yaccam`s, `ms jla @. O. Ilrhlg que havucilu l `lhecl gl m`daegte mfmhï`afl.

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L `lhecl he Ilrhlg, seiughl Hm`lhmrmg (4>=2, p. =>2), pressupõe que l vmclr hm méæl he u`m e`presm hepegherí hls havaheghls espermhls pmrm l pröxa`l peràlhl, hm tmxm mprlpramhm ml rasfl e hm tmxm he fresfa`egtl espermhm pmrm ls havaheghls. M jlr`ucméæl hl `lhecl he Ilrhlg á m seiuagte? preél oustl hm méæl 0 havaheghls ù (K e ‖ i) 

Lghe?   Havaheghls represegtm l jcuxl he fmaxm he havaheghl e ourls sldre l fmpatmc pröpral prevastl pmrm l pröxa`l peràlhl.   K e á m tmxm `àga`m he mtrmtavahmhe exaiahm pecl agvestahlr.   i á m tmxm he fresfa`egtl espermhm hls havaheghls e ourls sldre l fmpatmc pröpral. 

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^mrm `ecblr acustrmr m mpcafmdacahmhe hl `lhecl, flgsahere que heter`agmhm e`presm castmhm gm dlcsm he vmclres, que oí plssua estmdacahmhe he fresfa`egtl gls seus resuctmhls, prloetm pmrm l pröxa`l mgl l pmim`egtl he T$ =,=9 plr méæl rejeregte mls havaheghls e ourls sldre l fmpatmc pröpral. Flgsahere maghm que essm e`presm esta`m que ls havaheghls hav aheghls e ourls sldre l fmpatmc pröpral pmils fresferæl m u`m tmxm he 8% ml mgl, perpetum`egte. Vmdeghl que m tmxm `àga`m he mtrmtavahmhe hl agvesta`egtl hessms méões á he ==,::% ml mgl, l preél oustl hm méæl serí? preél oustl hm méæl 0 havaheghls ù (K e ‖ i)  preél oustl hm méæl 0 T$ =,=9 ù (>,==:: ‖ >,>8) preél oustl hm méæl 0 T$ =,=9 ù >,>9::  preél oustl hm méæl 0 T$ =5,49 

 Mciugs mutlres `egfalgm` ca`atméões gm mpcafméæl hl @lhecl he Ilrhlg, plas, `mte`mtafm`egte, l vmclr hm tmxm he fresfa`egtl heverí ser agjeralr î tmxm he hesflgtl, fmsl flgtríral, teràm`ls, plr exe`pcl, m havasæl hav asæl he u` havaheghl plr –zerl‐ lu geimtavl. Flgtuhl, fl`l m mpcafméæl hl `lhecl pressupõe l mtagia`egtl he fertl gàvec he `mturahmhe hm lrimgazméæl e hl gafbl e` que ecm mtum, essm ca`atméæl plherí ser questalgmhm. Gesse segtahl, l @lhecl he Ilrhlg I lrhlg gæl seram mhequmhl pmrm mvmcaméæl, plr exe`pcl, he stmrtups , e`presms que maghm gæl mtagiarm` l gàvec he `mturahmhe e, plr essm rmzæl, ls fresfa`egtls flgstmgtes hls havaheghls seræl questalgíveas. Lutrl plgtl que fmde ressmctmr á que, fmsl u`m e`presm mpresegte u`m tmxm he fresfa`egtl flgstmgte `uatl mctm, fbm`mrí m mtegéæl hls agvestahlres, he `mgearm que essm satuméæl mu`egtm mu`egtmrí rí l gÿ`erl he e`presírals gesse sei`egtl e, flgsequegte`egte, flgsequegte`egte, m flgflrrïgfam. Assl jmrí fl` que l fresfa`egtl seom hastraduàhl e, plr flgsequïgfam ms tmxms he fresfa`egtl pmssmram` m ser `eglres. Gessm bapötese, presu`ar-se-í que esse gafbl he `erfmhl maghm gæl mtagiau m sum `mturahmhe. ^lrtmgtl, m `mturahmhe gl fresfa`egtl he u`m e`presm serí mcfmgémhm qumghl estm :6

 

 

fresfer m tmxms flghazegtes fl` l fresfa`egtl `áhal hl `erfmhl; fmsl flgtríral, se fresfer m tmxms `malres, hespertmrí m mtegéæl hls agvestahlres, e assl mu`egtmrí m ljertm e, flgsequegte`egte, flgsequegte`e gte, herrudmrí ms tmxms he fresfa`egtl. L agversl mflgteferí fmsl m e`presm fresém m tmxm `eglres. Gesse fmsl, ls agvestahlres se segtaræl agsmtasjeatls e heaxmræl l sei`egtl, he `lhl que ms tmxms he fresfa`egtl, e` rmzæl hm ha`aguaéæl hm ljertm, tegheræl m fresfer. Mssa`, ms tmxms seræl `malres lu `eglres mtá l `l`egtl e` que jafmre` fleregtes fl` l fresfa`egtl `áhal he `erfmhl, qumghl, egtæl, serí plssàvec mjar`mr que m `mturahmhe jla mtagiahm.

Jcuxl he fmaxm cavre pmrm m e`presm Á flgsmirmhl que u` hls mspeftls `mas a`plrtmgtes he u`m hefasæl he agvesta`egtl estí fegtrmhm gm prloeéæl hls jcuxls he fmaxm que l mtavl e` mgícase te` fmpmfahmhe he ljerefer gl juturl. L `átlhl hl jcuxl he fmaxm cavre, seom sld m ötafm hm e`presm, seom sld m ötafm hl mfalgastm, flgsaste e` mpurmr l vmclr que ejetavm`egte estmrí hasplgàvec, pmrm glvls agvesta`egtls lu pmrm pmim`egtls hls agvestahlres he fmpatmc. L jcuxl he fmaxm cavre hm e`presm (JFCE) á fmcfucmhl m pmrtar hl jcuxl he fmaxm lpermfalgmc (JFL) fl` mciugs moustes. Mssmj Getl (4>=1, p. =94) suiere que m estruturm dísafm he mpurméæl hl jcuxl he fmaxm cavre hm e`presm heve pmrtar hl resuctmhl lpermfalgmc càquahl mpös l AT (Glpmt), flgjlr`e seiue? Xmdecm 5 ‖ Exe`pcl he mpurméæl hl jcuxl he fmaxm cavre hm e`presm 0 

Glpmt* ‖ Tesuctmhl Lpermfalgmc Càquahl hl AT 

- 

Heprefaméæl / M`lrtazméæl 

-=>> 

0 

Jcuxl he Fmaxm Lpermfalgmc 

=.>>> 

- lu + 

Fmpex ‖ Fmpatmc  Expeghatures 

-45> 

- lu + 

Zmraméæl hl Agvesta`egtl e` Fmpatmc he Iarl 

-=>> 

Jcuxl he Fmaxm Cavre hm E`presm ‖ JFCE 

:5> 

0 

=.=>> 

*Glpmt ‖ Tesuctmhl Lpermfalgmc Càquahl hl AT á l vmclr hl cufrl càquahl, moustmhl, mpurmhl se` ms hespesms jagmgfearms. ja gmgfearms. M rmzæl á m verajafméæl hm fmpmfahmhe que m e`presm te` he iermr jcuxls he fmaxms cavres aghepeghegte`egte hl seu irmu he mcmvmgfmi mcmvmgfmie` e` jagmgfearm. Jlgte? Mhmptmhl he Mssmj Getl (4>=1, p. =94).  =94). 

:8

 

 

 Mpös l jcuxl he ffmaxm maxm lpermfalg lpermfalgmc, mc, que resuctm hm hm hevlcuéæl hm heprefaméæ heprefaméæl, l, plr gæl saigajafmr hese`dlcsl, hlas moustes a`plrtmgtes sæl gefessírals? mhaéæl hls ejeatls hm vmraméæl hls agvesta`egtls e` fmpatmc expeghatures (Fmpex) e vmraméæl hls agvesta`egtls e` fmpatmc e iarl. L Fmpex represegtm tlhls ls imstls he fmpatmc hm e`presm. Veiughl Mssmj Getl (4>=1, p. =94), plhe` agfcuar m –mquasaéæl he degs tmgiàveas lu agtmgiàveas fl` vahm ÿtac espermhm `malr que u` mgl, fl`l ehajafméões, `íquagms e equapm`egtls, imstls fl` pesquasm e hesegvlcva`egtl, pmtegtes, agvesta`egtls e` tefglcliam e saste`ms‐. Esses mtavls tï` fl`l ldoetavl m mtumcazméæl tefglcöiafm, l suplrte pmrm l fresfa`egtl prloetmhl pecm e`presm, de` fl`l m sudstatuaéæl hls mtavls exastegtes. M expeftmtavm á que ls agvesta`egtls remcazmhls fcmssajafmhls fl`l Fmpex plssm` iermr gl juturl resuctmhls que fudrm` l fustl he lplrtugahmhe hls agvestahlres e, plr essm rmzæl, mhafalge` vmclr ml geiöfal.  Oí m vmraméæl hl agvesta`egtl e` fmpatmc he iarl rejere-se î vmraméæl tltmc que lflrre gm gefessahmhe he fmpatmc he iarl hm e`presm. Essm vmraméæl heflrre hm mcterméæl gm plcàtafm he prmzls prmtafmhls pecm e`presm, seom gm flgfessæl he prmzl pmrm ls fcaegtes, te`pl he reglvméæl hls estlques lu prmzls he pmim`egtls pceatemhls fl` ls jlrgefehlres. Zmce ce`drmr que, fl`l m gefessahmhe he fmpatmc he iarl hm e`presm hepeghe hl seu gàvec he mtavahmhe, `es`l que m plcàtafm he prmzl eper`mgeém bmverí vmraméæl gefessahmhe he fmpatmc he iarl se l gàvec he mtavahmhe hm e`presmagmctermhm, jlr mctermhl. Vaigajafm hazergmque, fmsl m e`presm mu`egte flgstmgte`egte, peràlhl mpös peràlhl, l gàvec he veghms, serí espermhl u` mu`egtl gm gefessahmhe he fmpatmc he iarl gm `es`m prlplréæl, e esse vmclr v mclr iermrí a`pmftl gl jcuxl he fmaxm.  Mciu`ms vmgtmiegs ggmm mhléæl hl jcuxl he fmaxm cavre hhmm e`presm sæl ecegfmhms ecegfmhms plr @mrtecmgf, ^msag e ^erearm (4>=4, p. 4=)?   Evegtumc`egte, l jcuxl he fmaxm cavre hl mfalgastm plhe `lstrmr-se geimtavl, e tmc satuméæl á `mas hajàfac he lflrrer fl` l jcuxl he fmaxm cavre hm e`presm. ^lhe ser l fmsl he e`presms `uatl eghavahmhms, `ms maghm mssa` m e`presm plhe ter vmclr càquahl he `erfmhl. Vatuméões fl`l essms plhe` ser reslcvahms fl` m repmftuméæl hm hàvahm lu agoeéæl he fmpatmc.   L jcuxl he fmaxm cavre hm e`presm represegtm `ecblr m fmpmfahmhe hl geiöfal e` iermr 



 



 



vmclr, plas estí cavre hls ejeatls hm mcmvmgfmie` jagmgfearm. L fustl he fmpatmc hm e`presm gæl hepeghe sl`egte hl gàvec he rasfl mtrecmhl mls mfalgastms, `ms tm`dá` ml fustl he fmpatmc prlvegaegtes hls frehlres. U`m `uhmgém gm estruturm e gl fmpatmc gæl mjetmrí m prloeéæl hls jcuxls j cuxls he fmaxm hm e`presm. ^lherí bmver hajafuchmhe gm prloeéæl he glvms fmptméões he refursls fl` terfearls e ls ejeatls hls ourls e m`lrtazméões sldre l jcuxl he fmaxm m `áhal prmzl, tlrgmghl m mvmcaméæl fl` dmse gls jcuxls he fmaxm cavre hm e`presm `mas sa`pces e jífac.

:5

 

 

^lr ja`, @mrtecmgf, ^msag e ^erearm (4>=4, p. 4=) expcafm` que ms vmraíveas fl`l mplrte he fmpatmc e lutrms `lva`egtméões he fmpatmc que mjetm` ls jcuxls he fmaxm, `ms que gæl jlrm` hetmcbmhms, gæl heve` fl`plr m ecmdlrméæl hls jcuxls he fmaxm pmrm jags he vmcumtalg,  plr represegtmre` mpegms usls e jlgtes he fmpatmc, restmghl m e`presm, ml iermr jcuxls he fmaxm, mpegms esflcber se hestagmrí ml pmim`egtl he havaheghls, m`lrtazméæl he hàvahms, lu retegéæl gl fmaxm pmrm juturls agvesta`egtls. ^lrtmgtl, l jcuxl he fmaxm cavre hm e`presm represegtm l vlcu`e he refursls que hecm plherí ser extrmàhl pmrm egjregtmr m re`ugerméæl exaiahm pecls agvestahlres, seom` frehlres lu mfalgastms.

Jcuxl he fmaxm cavre pmrm l mfalgastm L jcuxl he fmaxm cavre pmrm l mfalgastm á l jcuxl he fmaxm he que ejetavm`egte ls mfalgastms plheræl hasplr, plr exe`pcl, pmrm hastraduaéæl hls havaheghls. Ls mfalgastms sæl ls frehlres resahumas hl resuctmhl hm e`presm mpös l pmim`egtl he tlhls ls fl`prl`assls jar`mhls. Tesahumas plr sere` ls ÿcta`ls m refedere` ls retlrgls, clil mpös l pmim`egtl hls fl`prl`assls fl` ls frehlres he fmpatmc.  M jlr`ucméæl j lr`ucméæl dísafm he mpurméæl hl jcuxl he fmaxm cavre pmrm l mfalgastm á mpresegtmhm plr  Mssmj Getl (4>=1, p. =92) hm seiuagte jlr`m? Xmdecm : ‖ Exe`pcl he mpurméæl hl jcuxl he fmaxm cavre hl mfalgastm 0

Glpmt ‖ Tesuctmhl Lpermfalgmc Càquahl hl AT

-

Heprefa Heprefaméæl méæl / M`lrtazméæl

-=>>

0

Jcuxl he Fmaxm Lpermfalgmc

=.>>>

- lu +

Fmpex ‖ Fmpatmc  Expeghatures Expeghatures  

-45>

- lu +

Zmraméæl hl Agvesta`egtl e` Fmpatmc he Iarl

-=>>

0

Jcuxl he Fmaxm Cavre hm E`presm ‖ JFCE

:5>

+

Egtrmhm he glvms hàvahms

4>>

-

M`lrtazméæl he hàvahms

-5>

-

Hespesms jagmgfear jagmgfearms ms

-5>

+

Degejàfal jasfmc hm hàvahm

-5>

0

Jcuxl he Fmaxm Cavre hl Mfalgastm ‖ JFCM

2>>   2>>

Jlgte? Mhmptmhl he Mssmj Getl (4>=1, p. =92).  =92). 

::

=.=>>

 

 

 M mhléæl mhléæl he glvms hàvahms á oustajafmhm pecm dusfm flgtàgum hm estruturm öta`m he fmpatmc fl` l ldoetavl he iermr vmclr lu e` rmzæl hm gefessahmhe he fmptméæl he refursls pmrm jagmgfamr ls agvesta`egtls ‖ Fmpex e e` fmpatmc he iarl ‖, fmsl ls mfalgastms gæl plssum` fmpmfahmhe lu gæl heseoe` jmzï-cl fl` fmpatmc pröpral. Ldserve que, gl `lhecl hesfratl mfa`m, l jcuxl he fmaxm cavre hl mfalgastm á l resuctmhl mpös m flderturm he tlhls ls seus imstls e hls seus rejcexls, mcá` hl agiressl he glvms hàvahms e hms sums m`lrtazméões. Gesse segtahl, l jcuxl he fmaxm cavre hl mfalgastm á l vlcu`e he refursls que m e`presm plhe hastraduar pmrm ls seus mfalgastms, `mgter e` fmaxm pmrm agvesta`egtl juturl lu hestagmr pmrm m refl`prm he méões. Vaigajafm hazer que, se m e`presm hastraduar `mas hagbearl hl que l represegtmhl gl jcuxl he fmaxm cavre, prlvmvec`egte remcazm remcazmrí rí m hastraduaéæl he havaheghls î fustm he u` `malr eghavahm`egtl lu plr `eal hm fmptméæl he refursls `ehamgte m e`assæl he glvms méões gl `erfmhl jagmgfearl.

Flgslcahméæl hls `lhecls he JFCE e JFCM Flgsahermghl que l jcuxl he fmaxm cavre hl mfalgastm plhe ser fmcfucmhl m pmrtar hl jcuxl he fmaxm cavre hm e`presm, e este hepeghe hl resuctmhl lpermfalgmc hm lrimgazméæl, m seiuar serí mpresegtmhl u` he`lgstrmtavl que flgslcahm tlhm m prloeéæl eflgø`afm e jagmgfearm hl geiöfal pmrm jags he vmcumtalg.

:9

 

 

Jaiurm 5 ‖ @lhecl sa`pcajafmhl hl jcuxl he fmaxm cavre hm e`presm e hl mfalgastm

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+

Tefeatms drutms prevastms (veghms lu refeatms drutms)

-

Hehuéæl sldre veghms

0

Tefeatm lpermfalgmc càquahm

-

Fustls he veghms (F@Z lu F^Z)

0

Cufrl lpermfalgmc drutl

-

Hespesms lpermfal lpermfalgmas gmas

0

Cufrl Lpermfalgmc Càquahl

-

Heprefaméæl e m`lrtazméæl

0

Cmoar (cufrl mgtes hl pmim`egtl he ourls e a`plstls he reghm)

0 EDAXHM

0 EDAX

Hespesms jagmgfearms* 0

Cmar (cufrl mgtes hl AT)

-

^rlvasæl he A`plstl he Teghm e Flgtraduaéæl Vlfamc

0 +

Cufrl lpermfal lpermfalgmc gmc mpös AT Heprefaméæl e m`lrtazméæl

+ lu -

Zmraméæl hls agvesta`egtls e` Fmpex

+ lu -

Zmraméæl hls agvesta`egtls e` fmpatmc he iarl

0 + lu  

Jcuxl he Fmaxm Cavre hm E`presm

0 EDX

0 Glpmt

0 JFCE

Zmraméæl gls E`prásta`ls e Jagmgfam`e Jagmgfam`egtls gtls

-

Hespesms jagmgfear jagmgfearms* ms*

+

Degejàfal jasfmc hm hàvahm

0

Jcuxl he Fmaxm Cavre hl Mfalgastm

0 JFCM

* Ms hespesms jagmgfearms sæl supra`ahms hl he`lgstrmtavl he resuctmhl re suctmhl hl exerfàfal pmrm que l resuctmhl càquahl expresse l remc pltegfamc hm e`presm pmrm iermr resuctmhl aghepeghegte`egte hm estrmtáiam he jagmgfam`egtl lu mcmvmgfmie`. M questæl mqua á resplgher qumgtl he resuctmhl lpermfalgmc càquahl l flre dusagess  á  á fmpmz he prlhuzar. Ms hespesms jagmgfearms sæl plsteralr`egte mhafalgmhms fl`l moustes pmrm m mpurméæl hl jcuxl he fmaxm cavre pmrm l mfalgastm; mjagmc, ls ourls, e` rmzæl hm mcmvmgfmie`, heveræl ser pmils mgtes que ls retlrgls pmrm ls mfalgastms. Jlgte? Ecmdlrmhm pecl mutlr  mutlr 

:2

 

 

L `lhecl mpresegtmhl per`ate ml mgmcastm u`m vasæl fl`pcetm hl que se esperm pmrm l geiöfal, pmrtaghl he u`m vasæl eflgø`afm e mhafalgmghl ls ejeatls jagmgfearls j agmgfearls pmrm m mpurméæl hl jcuxl he fmaxm hasplgàvec hm e`presm e `presm e hl mfalgastm. ^mrm acustrmr m mpcafmdacahmhe hls `lhecls he jcuxls he fmaxm hesflgtmhl, m seiuar serí mpresegtmhm m prloeéæl he resuctmhls e he jcuxl he fmaxm he u`m e`presm exe`pcl pmrm jags he vmcumtalg. Xmdecm 9 ‖ @lhecl sa`pcajafmhl hl jcuxl he fmaxm cavre hm e`presm e hl mfalgastm HEVFTAÉÆL

DMVE

Mgl = 

Mgl 4

Mgl 6

Mgl 8 

Mgl 5 

Mgl : 

Mgl 9 

Mgl 2 

Mgl 1

Mgl => =>  

=>.2>>

==.464

==.5:1

==.1=:

=4.4=8

=4.854

=4.:15

=4.184

=6.=15

=6.854

-=.41:

-=.682

-=.622

=.86>

-=.8::

-=.818

-=.546

-=.556

=.526

=.:=8

1.5>8

1.228

=>.=2=

=>.82:

=>.982

=>.152

==.=94

==.621

==.:==

==.262

-5.8>>

-5.:=:

-5.928

5.152

-:.=>9

-:.44:

-:.689

:-.89=

:.519

:.94:

8.=>8

8.4:2

8.61:

8.542

8.:8=

8.694

8.248

8.1=2

5.>=8

5.==4

-:>>

-:>>

-:=4

-:48

-:69

-:81

::4

-:9:

-:21

-9>>

0 Cufrl lpermfalgmc càquahl (Edathm)

6.5>8   6.5>8

6.::2   6.::2

6.928   6.928

6.1>8   6.1>8

8.>>5   8.>>5

8.>24   8.>24

8.=:4   8.=:4

8.484   8.484

8.645   8.645

8.8=4   8.8=4

- Heprefaméæl e m`lrtazméæl

-==>

--4=> 4=>

-6=>

-6=>

-6=> - 6=>

-6=>

-6=>

-6=> - 6=>

-6=>

-6=>

0 Cmoar (Cufrl mgtes hls ourls e hl AT) (Edt)

6.618

6.852

6.898

6.518

6.:15

6.994

6.254

6.164

8.>=5

8.=>4

=8>

=8>

4:5

48>

6=9

414

494

419

424

4:9

6.618

6.852

6.898

6.518

6.:15

6.994

6.254

6.164

8.>=5

8.=>4

-=.=58

-=.=9:

-=.=2=

-=.444

-=.45:

-=.426

-=.6=>

-=.669

-=.6:5

-=.615

0 Cufrl lpermfalgmc mpös AT (Glpmt)

4.48>   4.48>

4.424   4.424

4.416

4.694   4.694

4.862   4.862

4.81>   4.81>

4.584   4.584

4.515   4.515

4.:5>   4.:5>

4.9>9   4.9>9

+ Heprefaméæl e m`lrtazméæl

==>

4=>

6=>

6=>

6=>

6=>

6=>

6=>

6=>

6=>

-5>>

-5>>

-6=>

-6=>

-6=>

-6=>

-6=>

-6=>

-6=>

-6=>

-48

-44

-=9

-=9

-=5

-=4

-=4

-=4

-=6

-=6

=.24:   =.24:

=.19=   =.19=

4.49:   4.49:

4.655   4.655

4.848   4.848

4.892   4.892

4.56>   4.56>

4.526   4.526

4.:69   4.:69

4.:18   4.:18

-4>>

4.5>>

--5>> 5>>

=.585

-5>> - 5>>

-8>>

5>>

-6>> - 6>>

-6>>

-6>>

5,>>%

--=8> =8>

-=8> - =8>

-4:5 - 4:5

-48>

-6=9

-414 - 414

--494 494

-419 - 419

-424

-4:9

68,>>%

82

82

1>

24

=>2

11

16

=>=

1:

1=

=.568   =.568

8.692   8.692

=.:>=   =.:>=

6.98=   6.98=

=.9=8   =.9=8

=.225   =.225

4.25>   4.25>

4.>29   4.>29

4.=5=   4.=5=

4.4=2   4.4=2

+ Tefeatms drutms prevastms - Hehuéæl sldre veghms    l    a    f    à    f    r    e    x    e    l    h    l    h    m    t    c    u    s    e    r    e    h    l    a    v    t    m    r    t    s    g    l    `    e    H

=4,>>%

0 Tefeatm lpermfalgmc càquahm - Fustls he veghms

5>,>>%

0 Cufrl lpermfalgmc drutl - Hespesms lpermfalgmas

Hespesms jagmgfearms 0 Cmar (cufrl mgtes hl AT) - A`plstl he reghm

68,>>%

   ) Θ Zmraméæl hls agvesta`egtls    E    C    F e` FM^ER    J    (    s Θ Zmraméæl hls agvest. e`    e    t    s Fmpatmc he Iarl    u    o    M

0 Jcuxl he Fmaxm Cavre hm E`presm 0 JFCE

Θ Zmraméæl gls E`prást. e    )    M    C    F    J    (    s    e    t    s    u    o    M

Jagmgfam`egtls - Hespesms jagmgfearms + Degejàfal jasfmc hm hàvahm (AT sldre ourls) 0 Jcuxl he Fmaxm Cavre hl Mfalgastm - JFCM Hàvahm càquahm 6.>>>  6.>>> 

6>%   6>%

(@mturahmhe mtagiahm gl =>¿ mgl) Xmxm he fresfa`egtl hls JFCE? JFC E?

4,=:%   4,=:%

^mtra`øgal càquahl 9.>>>  9.>>>  

9>%   9>%

(@mturahmhe mtagiahm gl =>¿ mgl) Xmxm he fresfa`egtl hls JFCM?

6,==%   6,==%

Jlgte? Ecmdlrmhm pecl mutlr

:1

 

 

Glte que, gl fmsl mpresegtmhl, m `mturahmhe hm e`presm estí prevastm pmrm ser mtagiahm gl mgl =>, qumghl ls jcuxls he fmaxm fl`eém` m fresfer perpetum`egte m tmxms flgstmgtes, seghl he 4,=:% ml mgl pmrm l JFCE e 6,==% ml mgl pmrm l JFCM. Xmc satuméæl, s atuméæl, per`ate fmcfucmr l vmclr hm perpetuahmhe equavmcegte gl mgl => hls jcuxls he fmaxm perpátuls m pmrtar hl háfa`l mgl, e gæl `mas seræl gefessírams prloeéões m pmrtar hesse peràlhl. Zeom`ls m seiuar fl`l fmcfucmr l vmclr hm perpetuahmhe hls jcuxls he fmaxm hl mgl == mtá l agjagatl. Fl`l l JFCE espermhl pmrm l mgl => á he 4.:18 l jcuxl he fmaxm prloetmhl pmrm l mgl == serí 4,=:% `malr, lu seom, 4.954,8, plas 4.:18 Ù (= + >,>4=:) 0 4.954,8. Flgsahermghl que l fustl `áhal plghermhl hl fmpatmc hm e`presm resuctlu e` =2,81% ml mgl, plhe`ls fmcfucmr l vmclr hm perpetuahmhe m pmrtar hl mgl ==, fl` hmtm-dmse pmrm l mgl =>, hm seiuagte jlr`m? Z^ gl mgl => 0 JF hl mgl == ù (K ‖ i)  Z^ gl mgl => 0 4.954,8 ù (>,=281 ‖ >,>4=:) Z^ gl mgl => 0 4.954,8 ù >,=:66  Z^ gl mgl => 0 =:.255 

Vaigajafm hazer que, gl mgl =>, mcá` hl jcuxl que oí estí prloetmhl, plhe`ls mhafalgmr l vmclr he =:.255 fl`l seghl l vmclr equavmcegte hm perpetuahmhe, flgslcahmr l jcuxl he fmaxm e fmcfucmr l vmclr hm e`presm. M flgslcahméæl estí he`lgstrmhm gm tmdecm m seiuar? Xmdecm 2 ‖ Flgslcahméæl e vmcumtalg vmcumtalg hl  hl JFCE Zmcumtalg Zmcumtalg sld  sld ötafm hl Geiöfal (Zmclr Geiöfal (Zmclr hm E`presm) Mgl >  >  Mgl =  =  Mgl 4 >

=.24:

=.19=

Mgl 6 4.49:

Mgl 8  8  Mgl 5  Mgl :  :  Mgl 9  9  Mgl 2 4.655

4.848

4.892

4.56>

4.526

Mgl 1 4.:69

^erpetuahmhe equavmcegte gl mgl => hls JFCE prloetmhls (hl mgl == mtá ∗) -7

JFCE

>

Z^ hl JFCE?

=6.>66

=.24:

=.19=

4.49:

4.655

4.848

4.56>

4.526

4.:69

4.:18 =:.255 =1.581

Fustl @áhal ^lghermhl he Fmpatmc? =2,81% ml mgl  mgl  Jlgte? Ecmdlrmhm pecl mutlr

9>

4.892

Mgl =>  => 

 

 

Flgslcahmghl ls jcuxls he fmaxm, pmrm l mgl => plhe`ls flgsahermr l jcuxl j cuxl he fmaxm prevastl `mas l vmclr equavmcegte hm perpetuahmhe, he `lhl que ml trmzer tlhls ls jcuxls he fmaxm ml `l`egtl presegte flgsahermghl l F@^F he =2,81% ml mgl, l vmclr hm e`presm resuctlu ser he =6.>66. ^lrtmgtl, pmrm fmcfucmr l vmclr hms méões hm e`presm, dmstmrí hehuzar hl vmclr fmcfucmhl l `lgtmgte he hàvahms càquahms que m estruturm he fmpatmc mpresegtlu, que gl fmsl á he 6.>>>, fl`l mpresegtmhl gm tmdecm 9. ^mrm fmcfucmr l vmclr presegte hls jcuxls he fmaxm cavre hl mfalgastm, plhe`ls mpcafmr m `es`m `etlhlcliam he fícfucl hm perpetuahmhe, perpetuahmhe, flgslcahmr l jcuxl he fmaxm e mpurmr l vmclr hms méões hm e`presm. Fl`l l JFCM espermhl pmrm l mgl => á he 4.4=2, l jcuxl he fmaxm prloetmhl pmrm l mgl == serí 6,==% `malr, lu seom, 4.42:,2 plas 4.4=2 Ù (= + >,>6==) 0 4.42:,2 4.42:,2.. Flgsahermghl que m tmxm `àga`m he mtrmtavahmhe hl fmpatmc pröpral á he 45% ml mgl, plhe`ls fmcfucmr l vmclr hm perpetuahmhe m pmrtar hl mgl ==, fl` hmtm-dmse pmrm l mgl =>, hm seiuagte jlr`m? Z^ gl mgl => 0 JF hl mgl == ù (K ‖ i)  Z^ gl mgl => 0 4.42:,2 ù (>,45 ‖ >,>6==) Z^ gl mgl => 0 4.42:,2 ù >,4=21  Z^ gl mgl => 0 =>.889 

Vaigajafm hazer que, gl mgl =>, mcá` hl jcuxl que oí estí prloetmhl, plhe`ls mhafalgmr l vmclr he =>.889 fl`l seghl l vmclr equavmcegte hm perpetuahmhe, flgslcahmr l jcuxl he fmaxm e fmcfucmr l vmclr hms méões hm e`presm. M flgslcahméæl estí he`lgstrmhm gm tmdecm m seiuar? Xmdecm 1 ‖ Flgslcahméæl e vmcumtalg vmcumtalg hl  hl JFCM Zmcumtalg Zmcumtalg sld  sld ötafm hl Mfalgastm (Zmclr Mfalgastm (Zmclr hms Méões) Mgl >  >  Mgl =  =  Mgl 4 >

=.568

8.692

Mgl 6

Mgl 8  8  Mgl 5  5  Mgl :  :  Mgl 9  9  Mgl 2

=.:>=

6.98=

=.9=8

=.225

4.25>

4.>29

Mgl 1 4.=5=

^erpetuahmhe equavmcegte gl mgl => hls JFCM prloetmhls (hl mgl == mtá ∗) -7

JFCE Z^ hl JFCM?

=.568 =>.>66

8.692

=.:>=

6.98=

=.9=8

=.225

4.25>

4.>29

4.=5=

=4.::8

Mgl =>  =>  4.4=2 =>.889 =.568

Xmxm `àga`m he mtrmtavahmhe hl Fmpatmc ^röpral? 45,>>% ml mgl  mgl  Jlgte? Ecmdlrmhm pecl mutlr

Flgslcahmghl ls jcuxls he fmaxm, e fmcfucmghl l vmclr presegte hl JFCM mpcafmghl m X@M he 45% ml mgl, l vmclr hms méões hm e`presm resuctlu ser he =>.>66. Glte que l vmclr hms méões hm e`presm á `eglr que l vmclr hm e`presm fl`l u` tlhl, m hajeregém se hí e` rmzæl hm exastïgfam he hàvahms, lu seom, exaste pmrte jagmgfamhm plr terfearls. 9=

 

 

^lrtmgtl, m hajeregém egtre l vmclr hm e`presm e l hms méões hm e`presm heverí ser mprlxa`mhm`egte mprlxa `mhm`egte l vmclr hms hàvahms. Esse flgfeatl serí `mas de` expcafmhl gl `átlhl he vmcumtalg fl` dmse gl  jar` vmcue  e  e equaty  vmcue , que ver`ls m seiuar. se iuar.

@átlhl he vmcumtalg jar` vmcue e equaty vmcue Vtewmrt AAA (4>>5, p. 445) mjar`m que l vmclr he `erfmhl tltmc hm e`presm (Z) serí aiumc ml vmclr he `erfmhl he tlhl l fmpatmc he terfearls (H) agserahl gl geiöfal sl`mhl fl` l vmclr tltmc hl he `erfmhl hl fmpatmc pröpral (E)? Z0H+E

Vldre esse te`m, Vtewmrt AAA (4>>5, p. 445) esfcmrefe que –pmrm u`m ugahmhe e`presmramc aghavahumc lu e`presm pravmhm, l vmclr tltmc á l que prlvmvec`egte a`plrtm, `ms pmrm e`presms geilfamhms, l preél hms méões plhe ser he `malr agteresse‐. Gesse segtahl, pmrm egflgtrmr l vmclr he u`m méæl dmstmram sudtrmar hl he vmclr tltmc(G)? hm e`presm l vmclr he `erfmhl hl fmpatmc he terfearls e havahar esse (^) v mclr vmclr pecm qumgtahmhe méões Z0H+E E0Z‖H ∸ 

^ 0 E ù G 

Veiuaghl m cagbm he rmfalfàgal, Verrm e Yafkert (4>=1, p. :9) mjar`m` que l vmclr tltmc hm e`presm, e` agicïs, jar` vmcue  lu  lu egterprase  vmcue , á l vmclr he `erfmhl he tlhls ls mtavls e` lperméæl hm e`presm, lu seom, l vmclr tltmc hl geiöfal. Ml hesflgtmr ls jcuxls he fmaxm hm e`presm pecl fustl  jar` ` vmcue . `áhal plghermhl he fmpatmc, l vmclr presegte egflgtrmhl –á hls agvestahlres‐, lu seom, á l  jar E` mfrásfa`l, esfcmrefe que l vmclr he `erfmhl hm e`presm á aiumc î sl`m hls vmclres he `erfmhl hls agvesta`egtls, lu seom, vmclr he `erfmhl hl fmpatmc pröpral ‖ equaty  vmcue  ‖  ‖ `mas l vmclr he `erfmhl hl fmpatmc he terfearls ‖ hàvahm caquahm, lu sa`pces`egte, hàvahm ‖, flgjlr`e equméæl m seiuar?  jar`  vmcue  jar` vmcue  0 hàvahm càquahm (hàvahm) + equaty  vmcue vmcue  

^mrm `ecblr acustrmr l que prlpõe`, Verrm e Yafkert (4>=1, p. :9) hesegvlcve` l seiuagte exe`pcl? m pmrtar hm veghm he u` fmrrl que plssua l vmclr he `erfmhl he =>>, qumc seram l vmclr refedahl< Gm verhmhe, pmrm resplgher m essm questæl, á a`plrtmgte verajafmr se l fmrrl estí jagmgfamhl. Vuplghl que esteom e que l vmclr hm hàvahm seom he 6>, l vmclr refedahl serí he 9>. M 94

 

 

e`presm, lu `ecblr, l fmrrl plssua u` vmclr he `erfmhl he =>>, he `mgearm que gæl á pecl jmtl he plssuar hàvahms que l fmrrl perherí vmclr. M `uhmgém estí mpegms gl vmclr que l hlgl hl fmrrl vma refeder plr ece. L vmclr hl fmrrl seram l  jar` vmcue , que sudtrmàhl hl vmclr equavmcegte î hàvahm càquahm resuctmram gl equaty  vmcue , flrresplghegte ml vmclr refedahl pecl hlgl hl fmrrl. fmrr l. ^mrm fl`pce`egtmr l exe`pcl, flgsahere que l fmrrl (m e`presm) esteom fl` l tmgque fbeal (e m assl hí-se l gl`e he fmpatmc gefessíral pmrm rlhmr, lu `ecblr, l fmpatmc he iarl) e tm`dá` tegbm gl plrtm cuvms l vmclr he 5 (esse serí l fmaxm e` exfessl lu smchl e` teslurmram). Milrm, l vmclr m ser refedahl pecm veghm hl fmrrl heve ser he =>5, plas esse fmaxm e` exfessl á hagbearl hasplgàvec gæl agserahl gm lperméæl. Gltm-se que l vmclr càquahl que l hlgl hl fmrrl vma refeder heverí ser aiumc m 95, seom plrque refedeu =>5 e pmilu m hàvahm he 6>, seom plrque refedeu =>> e utacazlu l vmclr he fmaxm pmrm ha`aguar m hàvahm e` 5 e, plr essm rmzæl, m hàvahm pmssm m ser he mpegms 45. Flgjar`mhm m aheam he que l vmclr hm e`presm á m sl`m hl vmclr hms hàvahms `mas l vmclr hl fmpatmc pröpral, l vmclr hl fmpatmc pröpral serí ser í l vmclr hm e`presm sudtrmaghl su dtrmaghl l vmclr hms hàvahms. Gesse segtahl, Verrm e Yafkert (4>=1, p. 9>) suiere` ls seiuagtes pmssls pmrm l vmcumtalg plr esse `átlhl?   =¿ ^mssl ‖ Fmcfucmr l fustl `áhal plghermhl he fmpatmc hm e`presm. 



   



 



 



4¿ ^mssl ‖ Fmcfucmr ls jcuxls he fmaxm hls agvestahlres mtá l `l`egtl –g‐ e` que ls jcuxls se tlrge` estíveas lu fl` fresfa`egtl m u`m tmxm flgstmgte. 6¿ ^mssl ‖ Fmcfucmr l vmclr presegte hm perpetuahmhe, lu seom, trmgsjlr`mr ls jcuxls he fmaxm he –g + =‐ mtá l agjagatl gl seu vmclr equavmcegte gl `l`egtl –g‐. 8¿ ^mssl ‖ Flgslcahmr l jcuxl he fmaxm mhafalgmghl l vmclr hm perpetuahmhe gl `l`egtl –g‐ e fmcfucmr l vmclr presegte, ldteghl mssa` l jar` vmcue . 5¿ ^mssl ‖ Fmcfucmr l equaty  vmcue , sudtrmaghl hl jar` vmcue  l  l vmclr hm hàvahm càquahm.

Flgsahermghl que l mvmcamhlr plssum flgbefa`egtl hls jcuxls he fmaxm cavre hm e`presm e hl fustl `áhal plghermhl he fmpatmc, `ms tm`dá` hls jcuxls he fmaxm cavre hl mfalgastm e hm tmxm cavre he mtrmtavahmhe hl fmpatmc pröpral, plherí fmcfucmr l vmclr presegte he m`dls ls jcuxls. E` tese, m hajeregém hl vmclr presegte hl JFCE e hl JFCM ser seríí l vmclr hm hàvahm, plrá` á fl`u` que resucte e` u` vmclr de` hajeregte. M rmzæl á que m ejafaïgfam gl resuctmhl, prlvegaegte hm mcmvmgfmie` jagmgfearm, plherí lfmsalgmr hastlréões gesse fícfucl e sudesta`mr lu superesta`mr l vmclr hms méões. ^lrtmgtl, refl`eghm-se u`m mtegéæl espefamc gm verajafméæl se ls jcuxls he fmaxm cavres pmrm l mfalgastm plssuaræl m fmpmfahmhe he iermr l retlrgl equavmcegte lu superalr î tmxm `àga`m he mtrmtavahmhe hl fmpatmc pröpral.

96

 

 

@átlhl he vmcumtalg fl` dmse gl @ZM® Veiughl Mssmj Getl (4>=1, p. =4:), u`m e`presm mireim vmclr mls agvesta`egtls se`pre que re`ugermr l fmpatmc agvestahl m tmxms `malres hl que m hl fustl he fmpatmc. Ve`pre que u` agvesta`egtl prlhuz u` vmclr presegte càquahl plsatavl, saigajafm que m re`ugerméæl exfehe l fustl he fmpatmc; gmturmc`egte, plr assl, á flgsahermhl u` agvesta`egtl vaívec. M questæl á smder qumgtl esse vmclr presegte càquahl plsatavl mireim mls preéls hms méões gl `erfmhl jagmgfearl. E` pra`earm mgícase, u` agvesta`egtl vmce l fmpatmc gecm agvestahl, flgtuhl, á plssàvec exastar m framéæl he raquezm pmrm ls mfalgastms e` rmzæl hm ejafaïgfam gls agvesta`egtls. Essm raquezm á mpurmhm, plr exe`pcl, m pmrtar hm hajeregém egtre l preél hms méões geilfamhms e` hmhl agstmgte e l vmclr pmtra`lgamc hl fmpatmc pröpral. Essm hajeregém, tm`dá` flgbefahm fl`l  illhwacc, á exmtm`egte l vmclr que jla mhafalgmhl pecl `erfmhl. Vtewmrt AAA (4>>5, p. =88) prlpõe que l vmclr he `erfmhl mhafalgmhl seom fmcfucmhl m pmrtar hl EZM®, u`m vez que á l EZM® que represegtm qumgtl he cufrl jla iermhl e` –exfessl‐, plr essm rmzæl esse vmclr heverí trmhuzar-se gm vmclrazméæl lu hesvmclrazméæl hl preél hms méões gl `erfmhl jagmgfearl.  @mrket   Zmcue   Mhheh   (@ZM®), que e` plrtuiuïs saigajafm vmclr he `erfmhl  M `ehahm mhafalgmhl, seiughl Mssmj Getl (4>=1, p. =4:), –rejcete m expressæl `lgetíram hm raquezm iermhm mls prlpraetírals he fmpatmc, heter`agmhm pecm fmpmfahmhe lpermfalgmc hm e`presm e` prlhuzar resuctmhls superalres ml seu fustl he lplrtugahmhe‐. ^lrtmgtl, serí essm m `ehahm mhequmhm pmrm aghafmr qumgtl m e`presm vmce mhafalgmc`egte ml que se imstmram pmrm replr tlhls ls seus mtavls. L vmclr hl @ZM® serí fmcfucmhl fl` l usl hm seiuagte expressæl? ex pressæl?

@ZM® 0 EZM® ù F@^F 

Lghe?   EZM® represegtm l cufrl exfehegte mpös m flderturm hls fustls he tlhms ms jlgtes he fmpatmc hm e`presm (pröpral e he terfearls).   F@^F á m tmxm que represegtm l fustl hl fmpatmc agvestahl. Á m tmxm que expressm l rasfl hl geiöfal. Á m tmxm `àga`m he mtrmtavahmhe hls agvestahlres. Á l fustl `áhal plghermhl he fmpatmc hm e`presm





U`m vez fmcfucmhl l @ZM®, seiughl Mssmj Getl (4>=1, p. =41), l vmclr hm e`presm serí ldtahl plr `eal hl seiuagte fícfucl? vmclr he `erfmhl hm e`presm 0 fmpatmc agvestahl + @ZM®

98

 

 

Lghe,   Fmpatmc agvestahl represegtm tlhl fmpatmc que jagmgfam m e`presm, exfcuaghl ms jlgtes he jagmgfam`egtl esplgtägems. E` lutrms pmcmvrms, represegtm l fmpatmc pröpral e he terfearls que jagmgfam` m e`presm e que suiere` m exastïgfam he u` fustl jagmgfearl ahegtajafívec.



^mrtaghl hl pressuplstl he que l vmclr he `erfmhl hm e`presm á l resuctmhl hm sl`m hl vmclr he `erfmhl hl fmpatmc he terfearls (hàvahm ( hàvahm càquahm) fl` l vmclr he `erfmhl hl fmpatmc pröpral (vmclr hms méões), l vmclr v mclr he `erfmhl hms méões hm e`presm serí hmhl pecm seiuagte expressæl? ex pressæl? vmclr he `erfmhl hms méões hm e`presm 0 pmtra`øgal càquahl + @ZM®

^mrm `ecblr acustrmr l vmcumtalg fl` dmse gl @ZM®, fl`pce`egtmre`ls l fmsl oí mpresegtmhl mgteralr`egte, flgjlr`e seiue. Heter`agmhm e`presm, castmhm gm dlcsm he vmclres, ve` mpresegtmhl u` retlrgl sldre ls agvesta`egtls (TLA) he =9,14% ml mgl, e u` fustl `áhal plghermhl he fmpatmc aiumc m =5,54% ml mgl. Fl`l m e`presm ve` mpresegtmghl u` retlrgl superalr ml fustl he fmpatmc, ls mfalgastms esperm` que essm ierméæl he vmclr se trmgsjlr`e e` raquezm `ehahm gls preéls hms méões. L fmpatmc tltmc agvestahl á he T$ 22.8>>, hls qumas T$ 5>.>>> sæl jagmgfamhls pecl fmpatmc pröpral (pmtra`øgal (pm tra`øgal càquahl). Ls mgmcastms fmcfucmrm` que l cufrl exfehegte ml fustl he fmpatmc, `ehahl pecl EZM®, á he T$ 4.=4=,:>. Ls mfalgastms heseom` smder fl`l esse cufrl e` exfessl se trmhuz gls preéls hms méões e qumc serí l vmclr oustl hms méões hm e`presm fl` dmse gl @ZM®. Ls fícfucls sæl ls seiuagtes? @ZM® 0 EZM® ù F@^F  @ZM® 0 4.=4=,:> ù >,=554  @ZM® 0 =6.:9>,=> 

Fl` l @ZM®, l vmclr hms méões serí hmhl plr? vmclr he `erfmhl hms méões hm e`presm 0 pmtra`øgal càquahl + @ZM® vmclr he `erfmhl hms méões hm e`presm 0 5>.>>>,>> + =6.:9>,=> =6.:9>,=>  vmclr he `erfmhl hms méões hm e`presm 0 :6.:9>,=> 

^lrtmgtl, serí espermhl que l preél hms méões gl `erfmhl jagmgfearl tltmcaze T$ :6.:9>,=>, e`dlrm l vmclr hl pmtra`øgal càquahl seom he mpegms T$ 5>.>>>,>>. M oustajafmtavm pmrm l vmclr he `erfmhl hl pmtra`øgal càquahl ser `malr hl que q ue l seu fustl he replsaéæl á m exastïgfam he ejafaïgfam lpermfalgmc, que se trmhuz e` u` resuctmhl superalr ml fustl he fmpatmc, `ehahl pecl EZM®.

95

 

 

@átlhl he vmcumtalg plr `ÿctapcls Gestm ugahmhe, serí mpresegtmhl fl`l fmcfucmr l vmclr he u` geiöfal pecl `átlhl he mvmcaméæl recmtavm, fl`u`egte flgbefahl fl`l mvmcaméæl plr `ÿctapcls. M aheam plr trís hesse `átlhl á mvmcamr e`presms fl` dmse e` aghafmhlres ‖ `ÿctapcls ‖ he lutrms e`presms fl` fmrmfteràstafms sa`acmres. ^mrm acustrmr essm te`ítafm, @mrtecmgf, ^msag e ^erearm (4>=4, p. =28) expcafm`? –l vmclr hm e`presm M havahahl plr u` aghafmhlr he rejerïgfam ‖ que plhe ser l cufrl hessm e`presm ‖ iermrí u` `ÿctapcl que plherí ser mpcafmhl ml cufrl hm e`presm D pmrm ldter l seu vmclr‐. Gesse segtahl, á plssàvec flgfcuar que l pressuplstl hl `átlhl he mvmcaméæl plr `ÿctapcls á he que e`presms se`ecbmgtes heveræl mpresegtmr mpres egtmr vmclres se`ecbmgtes. Veiughl Hm`lhmrmg (4>=2, p. =26), mvmcamr ms e`presms plr `eal hls `ÿctapcls he `erfmhl saigajafm –ahegtajafmr ls mtavls fl`pmríveas que seom` prefajafmhls pecl `es`l `erfmhl‐, –esfmclgmr ls preéls he `erfmhl e` recméæl r ecméæl m u`m vmraívec fl`u`‐ e –moustmr ms hajeregéms egtre ls mtavls‐?   Ahegtajafméæl hls mtavls fl`pmríveas ‖ Vaigajafm ahegtajafmr ms e`presms que lperm` gl `es`l setlr e que mpresegte` ms `es`ms fmrmfteràstafms gm extrméæl, prlhuéæl, fl`erfamcazméæl e egtreim hls prlhutls e servaéls serv aéls fl`erfamcazmhls. 

 

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Fmcfucmr `es`l aghafmhlr he vmclrquepmrm ms e`presms ‖ Flgsaste e`hlfmcfucmr u` aghafmhlr,u` fl`u` m tlhms ms e`presms, servarí he dmse pmrm l `ÿctapcl respeftavl vmclr he `erfmhl hm e`presm m que se rejere. L ldoetavl mqua á estmdecefer u` aghafmhlr que plssm ser fl`pmrívec. Veiughl Hm`lhmrmg (4>=2, p. =:6), qumghl m mvmcaméæl se rejere îs méões he u`m e`presm, glr`mc`egte ls `ÿctapcls he `erfmhl `ehe` l vmclr he `erfmhl geilfamhl e` recméæl m u` aghafmhlr he cufrl, vmclr flgtídac lu he refeatms. Ahegtajafmr ms fmrmfteràstafms espefàjafms e moustmr ls vmclres ‖ Gestm ÿcta`m jmse, heveræl ser ahegtajafmhms ms fmrmfteràstafms espefàjafms hm e`presm sld mvmcaméæl e moustmhls ls vmclres fl` dmse gls hajeregfamas he `erfmhl. Gms pmcmvrms he Hm`lhmrmg (4>=2, p. =:6), –e`presms he fresfa`egtl `mas ecevmhl, plr exe`pcl, heve` ser geilfamhms m `ÿctapcls `mas mctls que ms he fresfa`egtl agjeralr gl `es`l sei`egtl‐. Esfcmrefe que irmghe pmrte hls mgmcastms remcazm` ls moustes he jlr`m qumcatmtavm e mfmdm` trmgsjlr`mghl –fmhm mvmcaméæl recmtavm e` u`m clgim bastöram‐. Fl`pce`egtm que qumgtl `mas pcmusàvec jlr m bastöram, `mas fráhatl refederí hls agvestahlres m plgtl he oustajafmr preéls hajeregfamhls.

 Mciugs `ltavls jmze` j mze` fl` qque ue ms mvmcaméões recmtavms seom` evegtumc`egte `mas jrequegtes hl que ms mvmcaméões plr `eal hm mpurméæl hl vmclr agtràgsefl e, seiughl Hm`lhmrmg (4>=2, p. =:8), ms rmzões sæl? m mvmcaméæl plr `ÿctapcls he`mghm `egls te`pl, á he `mas jífac oustajafméæl pmrm u` agvestahlr e resuctm e` preéls `mas pröxa`ls mls vmclres geilfamhls hl que qumghl utacazmhl l `átlhl he jcuxl he fmaxm hesflgtmhl.

9:

 

 

 Mhafalgmc`egte, Hm`lhmrmg (4>=2, p. =:8) ressmctm que q ue ls hajeregfamas hajer egfamas plsatavls hl usl hl `átlhl he mvmcaméæl recmtavm tm`dá` plhe` ser mr`mhacbms gl prlfessl he mvmcaméæl he e`presms, plas mciugs mspeftls a`plrtmgtes, fl`l mgícase he rasfls e ahegtajafméæl hm teghïgfam he fresfa`egtl lu ha`aguaéæl hl jcuxl he fmaxm, mfmdm` seghl aiglrmhls. Lutrl jmtl a`plrtmgte á que l usl he mvmcaméæl recmtavm plhe resuctmr e` u` preél mctl he`mas lu dmaxl he`mas, plrque rejcete teghïgfams hl setlr, e gæl he e`presms aslcmhms. ^lr ja`, m jmctm he hetmcbm`egtl hms pre`assms espefàj espefàjafms afms pmrm m e`presm e` mgícase, que oustajafmram` l mcfmgfe he perjlr`mgfe se`ecbmgte mls hl setlr, plhe` tlrgmr vucgeríveas ms mvmcaméões remcazmhms, hm `es`m jlr`m que tlrgmram qumcquer vmclr egflgtrmhl  oustajafívec mpegms fl` dmse gls `ÿctapcls `ÿctapcls he vmclr hl sei`egtl. Gm prítafm, saigajafm fmcfucmr ls vmclres `áhals he u` heter`agmhl aghafmhlr he e`presms equavmcegtes ml geiöfal que se heseom mvmcamr e, plsteralr`egte, usmr esse aghafmhlr fl`l rejerïgfam pmrm m esta`méæl hl preél he u` mtavl.  M saste`íta saste`ítafm fm he fícfucl fícfucl á mpres mpresegtmh egtmhmm plr Ver Verrm rm e Yaf Yafkert kert (4>=1, (4>=1, p. =65) fl` `uatm `uatm prlpraeh prlpraehmhe, mhe, e`dlrm he jlr`m sa`pces. ^mrm `ecblr acustrmr, utacazm` l exe`pcl hm mvmcaméæl he u` mpmrtm`egtl m ja` he he`lgstrmr fl`l ls `ÿctapcls sæl ldtahls. L exe`pcl serí mpresegtmhl m seiuar? Xmdecm => ‖ Esta`méæl hls preéls he mpmrtm`egtls Mpmrtm`egtl

^reél

Írem

^reél plr `etrl qumhrmhl

(M) M`erafmg ^mrk

954.5>>,>>

=66,5>`´

T$ 5.66:,9>/`´

(D) Dluce Dlucevmrh vmrh

:25.5>>,>>

==2,4>`´

T$ 5.911,81/`´

(F ) Faty Bmcc

286.4>>,>>

=84,5>`´

T$ 5.1=9,=1/`´

(H) Huraque

9=2.1>>

=46,:>`´

T$ 5.2=:,68/` 5.2=:,68/`´´

@áham he preél hl `etrl qumhrmhl gm reiaæl?

Mpmrtm`egtl e` mgícase

T$ 5.914,86/`´  5.914,86/`´ 

^reél Esta`mhl*

Írem

^reél `áhal hl `´ gm reiaæl  reiaæl 

(E) Echlrmh Echlrmhl l

9:5.=2>,84

=64,=>`´

T$ 5.914,86/`´

(J) Jegax

:19.122,= :19.122,=11

=4>,5>`´

T$ 5.914,86/`´

Jlgte? Mhmptmhl he Verrm e Yafkert (4>=1, p. =65).  =65). 

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Ldserve, que gl exe`pcl mpresegtmhl, jlrm` utacazmhls ls preéls prmtafmhls pmrm ls mpmrtm`egtls he (M) m (H), m ja` he mpurmr qumc l vmclr he fl`erfamcazméæl `áhal plr `etrl qumhrmhl, he jlr`m m ser estm m dmse pmrm l fmcfucmr l vmclr he `erfmhl he mpmrtm`egtls fl` fmrmfteràstafms se`ecbmgtes gm `es`m reiaæl. ^mrm mvmcamr l a`övec e esta`mr l seu preél, dmstmram `uctapcafmr l vmclr `áhal plr `etrl qumhrmhl prmtafmhl pecm írem hl mpmrtm`egtl e` mgícase, gl fmsl, ls mpmrtm`egtls (E) e (J) e remcazmr ls moustes jagmas, fl`l m verajafméæl hm mcturm hl mghmr e gàvec he flgservméæl, plr exe`pcl.  M mvmcaméæl he u`m e`presm fl` dmse gls `ÿctapcls he `erfmhl seiue l `es`l pragfàpal. ^mrm exe`pcajafmr, flgsahere mvmcamr hums e`presms? (E) fl` cufrls `áhals he T$ =,5> plr méæl e (J) fl` cufrls `áhals he T$ 4,>> plr méæl. Ml ser mgmcasmhm m `es`m recméæl (cufrl plr méæl) e` e`presms fl`pmríveas, ls resuctmhls jlrm` ls seiuagtes? s eiuagtes? Xmdecm == ‖ Esta`méæl hls preéls hms méões E`presm

^reél hm méæl

Cufrl plr méæl

Àghafe ^reél/Cufrl  ^reél/Cufrl 

E`presm (M)

=6,>>

=,1>

:,28

E`presm (D)

=5,>>

=,1>

9,21

E`presm ( F)

4:,>>

6,5>

9,86

E`presm (H)

=2,>>

4,5>

9,4

@áham hls àghafes preél/cufrl?  preél/cufrl? 

E`presm e` Mgícase

9,68=8   9,68=8

^reél esta`mhl hm méæl

Cufrl plr méæl

Àghafe ^reél/Cufrl Esta`mhl  Esta`mhl 

E`presm (E)

==,>=

=,5>

9,68=8

E`presm (J)

=8,:2

4,>>

9,68=8

Jlgte? Mhmptmhl he Verrm e Yafkert (4>=1, p. =65).

Glte que ls `ÿctapcls he `erfmhl sæl jlr`mhls m pmrtar hl preél hl mtavl havahahl plr u` pmrä`etrl, plr essm rmzæl sæl `uatms ms recméões plssàveas.  Mciugs hls `ÿctapcls `ÿctapcls he `erfmhl `mas `mas fl`u`eg fl`u`egte te utacazmhls utacazmhls sæl ldtahls m pmrtar hms hms recméões estmdecefahms fl` l He`lgstrmtavl he Tesuctmhl hm E`presms (HTE). Væl eces?

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^reél ù Cufrl (^/C) lu Cufrl plr Méæl (C^M) ‖ Hm`lhmrmg (4>=2, p. =:5) flgsaherm que `ÿctapcls he cufrl á –u`m hms `mgearms `mas agtuatavms he pegsmr gl vmclr he qumcquer mtavl‐; mjagmc, he`lgstrm fl` `uatm ldoetavahmhe m recméæl hm pmrfecm hl resuctmhl hestagmhm ml mfalgastm (cufrl) fl` l preél pmil plr u` mtavl. mtav l.   ^reél ù EDAXHM ‖ Esse aghafmhlr tm`dá` á u` `ÿctapcl he cufrl e, seiughl Verrm e  Yafkert (4>=1, p. =65), á `uatl utacazmhl –plr ser vastl fl`l u`m pra`earm aheam, fl` fràtafms, he ierméæl he fmaxm hm e`presm (e l vmclr he mcil heveram ser esta`mhl pecm sum fmpmfahmhe he iermr fmaxm). ^mrm Mssmj Getl (4>=1, p. 4>9), l `ÿctapcl he EDAXHM –á `uatms vezes egteghahl fl`l l `ecblr `ÿctapcl he vmclr, plas hesflgsaherm m heprefaméæl e lutrms hespesms lpermfalgmas se` rejcexl gl fmaxm‐, ls tradutls pmils sldre l cufrl e l fustl fl` fmpatmc he terfearls e` rmzæl hm mcmvmgfmie` jagmgfearm. Assl tm`dá` per`ate `malr m`pcatuhe gm fl`pmrméæl egtre e`presms, agfcusave fl` e`presms he lutrls pmàses.   ^reél ù Tefeatm ‖ Mssmj Getl (4>=1, p. =12) `egfalgm u`m a`plrtmgte vmgtmie` gm mpcafmdacahmhe hl `ÿctapcl he refeatm e` recméæl mls he`mas aghafmhlres he rejerïgfam, plas per`ate m esta`méæl he vmclr mtá `es`l gls fmsls hms e`presms que evegtumc`egte mpresegte` mpr esegte` preouàzls, `es`l que ms veghms gæl rejcatm` m fmpmfahmhe hm e`presm pmrm iermr cufrls.  

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Gm prítafm, mciu`ms e`presms que lperm` e` setlres espefàjafls plhe` ser mvmcamhms plr `ÿctapcls espefajafm`egte utacazmhls pmrm esse setlr, plr exe`pcl, qumgtahmhe he mcugls pmrm ms agstatuaéões he egsagl, vlcu`e he fl`dustàvec fl`erfamcazmhl pmrm rehes he plstls he fl`dustàveas e gÿ`erl he rejeaéões servahms pmrm u`m rehe he jmst  jllh   jllh . Fl`l vastl mfa`m, m sa`pcafahmhe e m rmpahez gm mvmcaméæl he mtavls, se` m gefessahmhe he `uatms agjlr`méões, sæl ms pragfapmas pr agfapmas vmgtmiegs hm mvmcaméæl plr `ÿctapcls, qumghl fl`pmrmhms mls lutrls `átlhls he vmcumtalg. Flgtuhl, fmde ce`drmr mciugs a`plrtmgtes plgtls he mtegéæl que l mvmcamhlr heve ldservmr, plr evahegfamre` e vahegfamre` hesvmgtmiegs gm mpcafméæl mpcafméæl hl `átlhl. Veiughl @mrtecmgf, ^msag e ^erearm ^erear m (4>=4, p. =12) ms hesvmgtmiegs sæl?   Hajeregém gls jughm`egtls hms e`presms fl`pmríveas ‖ Essm hajeregém heflrre hl jmtl he 

 

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ms e`presms sere` se`ecbmgtes mtá fertl plgtl, `ms gugfm ahïgtafms. Assl tlrgm l `ÿctapcl he `erfmhl u`m dlm rejerïgfam, `ms gæl fl`l u` gÿ`erl agquestalgívec he vmclr, plas ms perspeftavms he resuctmhls juturls ‖ rasfl, ierméæl he cufrl e fresfa`egtl gls jcuxls he fmaxm ‖ plhe` ser `uatl hajeregtes pmrm fmhm e`presm. ]umcahmhe hms agjlr`méões ‖ Essm hesvmgtmie` se heve ml jmtl he que irmghe pmrte hms trmgsméões remcazmhms gl Drmsac gæl tï` ls seus vmclres revecmhls. Veiughl @mrtecmgf, ^msag e ^erearm (4>=4, p. =12), flgsahermghl que exaste` `egls he 5>> e`presms castmhms gm dlcsm he vmclres drmsacearm, m ldtegéæl hls vmclres he rejerïgfam pmrm m ldtegéæl hls `ÿctapcls estí ca`atmhm î qumcahmhe hessm m`lstrm. Essm á m pragfapmc fmusm hm jrequegte utacazméæl he `ÿctapcls he lutrls pmàses pmrm m prefajafméæl pre fajafméæl he mtavls gl Drmsac.

91

 

 

 

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Espefajafahmhe he fmhm trmgsméæl ‖ Ms trmgsméões lflrre` gl `erfmhl jagmgfearl pmrm mtegher mls `mas vmramhls agteresses, e assl plhe hmr u`m gléæl errmhm he vmclr. ^lr exe`pcl, á plssàvec que u`m irmghe trmgsméæl tegbm sahl remcazmhm exfcusavm`egte pmrm mtegher m u` agteresse pesslmc. Gesse fmsl, m utacazméæl hesse àghafe fl`prl`eterí m mgícase e plssavec`egte hastlrferí m esta`méæl he vmclr. v mclr. Ejeatl `mgmhm ‖ Tesuctm he ser perjeatm`egte plssàvec que heter`agmhl setlr esteom super lu sudmvmcamhl iermghl u` vaás gm mvmcaméæl. L ejeatl `mgmhm á u` ter`l utacazmhl pmrm hesfrever irmghes `lva`egtls se` u` heter`agmhl pcmgeom`egtl. Assl plhe mflgtefer qumghl, plr exe`pcl, u` irmghe agvestahlr hefahe fl`prmr lu vegher ms sums méões plr u`m rmzæl pmrtafucmr, e lutrl, se` flgbefer ls `ltavls, hefahe jmzer l `es`l, pmrm –gæl jafmr pmrm trmz‐. Esse ejeatl mflgtefe e` fmsfmtm e, he repegte, u`m irmghe qumgtahmhe he agvestahlres estí miaghl hm `es`m jlr`m se` smder l plrquï, agjcuegfamghl saigajafmtavm`egte ls preéls hls mtavls, se` que bmom u`m rmfalgmcahmhe plr trís hm tl`mhm he hefasæl. Dmsafm`egte, esse fl`plrtm`egtl e`mgm hm gefessahmhe que ms pesslms tï` he miar fl`l m `malram, rmfalgmcazmghl que, se m `malram l jmz, á plr u`m dlm rmzæl.

^lrtmgtl, á he extre`m a`plrtägfam que m dmse fl`pmrívec fl`pmríve c pmrm m mpurméæl hls `ÿctapcls seom fleregte fl` m e`presm que estí sld mgícase. ]umtrl plgtls sæl ecegfmhls plr @mrtecmgf, ^msag e ^erearm (4>=4, p. 4>2) pmrm que se tegbm u`m dlm dmse fl`pmrívec. Gm vasæl heces, á gefessíral flgsahermr? –e`presms hm `es`m aghÿstram e írem he mtuméæl; e`presms hl `es`l plrte e tm`mgbl; e`presms fl` fmrmfteràstafms e jughm`egtls se`ecbmgtes e tm`mgbl hm m`lstrm hms e`presms fl`pmríveas‐. Gesse `es`l segtahl, Mssmj Getl (4>=1, p. 4>2) egteghe que u`m e`presm fl`pmrívec ‖ lu sa`acmr ‖ serí –mquecm que mtum gl `es`l setlr he mtavahmhe e mpresegtm plrte, rasfls e retlrgls sa`acmres îquecm que estí e` mvmcaméæl‐.

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DADCALITMJAM  MDTEU JACBL, O. F. J. H. et mc. Jagmgéms flrplrmtavms . ==. eh. Tal he Omgearl? JIZ, 4>=4.  MVVMJ GEXL, M. Jagmgéms flrplrmtavms e vmclr . 9. eh. Væl ^mucl? Mtcms, 4>=:.  MVVMJ  MVV MJ GEXL GEXL,, M. Zmcumtalg? `átrafms he vmclr e mvmcaméæl he e`presms. 6. eh. Væl ^mucl? Mtcms, 4>=1.  MVVMJ GEXL, M.; CA@M, J. I. I. Fursl he mh`agastrméæl jagmgfearm . 6. eh. Væl ^mucl? Mtcms, 4>=9. D6. E`presms castmhms , 4>4>. Hasplgàvec e`? 3bttp?//www.d6.fl`.dr/pt\dr/prlhutls-eservafls/geilfamfml/reghm-vmramvec/e`presms-castmhms.bt`7. Mfessl e`? 42 mdr. 4>4>. DMGFL FEGXTMC HL DTMVAC (DMFEG). Vaste`m he Expeftmtavms he @erfmhl hl Dmgfl Fegtrmc hl Drmsac. Váraes he estmtàstafms flgslcahmhms. 4>4>. Hasplgàvec e`? 3bttps?//www6.dfd.ilv.dr/expeftmtavms/pudcafl/flgsuctm/seraeestmtastafms7. Mfessl e`? => omg. 4>4>. FL@AVVÆL HE ZMCLTEV @LDACAÍTALV (FZ@). Hedïgtures. ^lrtmc hl Agvestahlr. 4>4>. Hasplgàvec e`? 3bttps?//www.agvestahlr.ilv.dr/`egu/@egu\Agvestahlr/vmclres\`ldacamrals/ hedegture.bt`c7. Mfessl e`? 42 mdr. 4>4>. FLVXM, C. I. X. M.; FLVXM, C. T. X. M.; MCZA@, @. M. Zmcumtalg? `mgumc he mvmcaméæl e reestruturméæl eflgø`afm he e`presms. 4. eh. Væl ^mucl? Mtcms, 4>==. HM@LHMTMG, M. Mvmcaméæl he e`presms . 4. eh. Væl ^mucl? ^emrslg, 4>>9. HM@LHMTMG, M. Zmcumtalg? fl`l mvmcamr e`presms e esflcber ms `ecblres méões. Xrmhuéæl he  Mjlgsl Fecsl hm Fugbm Verrm. Tal he Omgearl? CXF, 4>=2. HM@LHMTMG, M. Hm`lhmrmg lgcage.  4>4>. Hasplgàvec e`? 3bttp?//pmies.sterg.gyu.ehu/ ~mhm`lhmr7. Mfessl e`? 45 mdr. 4>4>. JEHETMC TEVETZE DLMTH (JEH).  @lgetmry ^lcafy.  4>4>m. Hasplgàvec e`? 3bttps?//www.jehermcreserve.ilv/`lgetmryplcafy.bt`7. Mfessl e`? 4> `mr. 4>4>.

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JEHETMC TEVETZE DLMTH (JEH).  @lgetmry ^lcafy Teplrt , 4>4>d. Hasplgàvec e`? 3bttps?//www.jehermcreserve.ilv/`lgetmryplcafy/jaces/4>4>>4>9\`prjuccreplrt.phj7. Mfessl e`? 4> `mr. 4>4> @MTXECMGF, T.; ^MVAG, T.; ^ETEATM, J. Mvmcaméæl he e`presms . Væl ^mucl? ^emrslg, 4>=4. GEY QLTK UGAZETVAXQ (GQU). Detms dy seftlr . 4>4>m. Hasplgàvec e`? 3bttp?//pelpce.sterg.gyu.ehu/mhm`lhmr/Gew\Bl`e\^mie/hmtmjace/Detms.bt`c7. Mfessl e`? 4: mdr. 4>4>. GEY QLTK UGAZETVAXQ (GQU). Flugtry mgh equaty rask pre`au`s . 4>4>d. Hasplgàvec e`? 3bttp?//www.sterg.gyu.ehu/~mhm`lhmr/pf/hmtmsets/ftrypre`.xcsx7. 3bttp?//www.sterg.gyu.ehu/~mhm` lhmr/pf/hmtmsets/ftrypre`.xcsx7. Mfessl e`? e `? 46 `mr. 4>4>. GEY QLTK UGAZETVAXQ (GQU). Flugtry hejmuct spremhs mgh rask pre`au`s . 4>4>d. Hasplgàvec e`? 3bttp?//pelpce.sterg.gyu.ehu/mhm`lhmr/Gew\Bl`e\^mie/hmtmjace/ftrypre`.bt`c7. Mfessl e`? 4: mdr. 4>4>. GEY QLTK UGAZETVAXQ (GQU). A`pcaeh equaty rask pre`au` uphmte. Hm`lhmrmg lgcage . 4>4>f. Hasplgàvec e`? 3bttp?//pmies.sterg.gyu.ehu/~mhm`lhmr7. 3bttp?//pmies.sterg.gyu.ehu/~mhm`lhmr7. Mfessl e`? 45 mdr. 4>4>. VETTM, T. I.; YAFKETX, @. Zmcumtalg? iuam jughm`egtmc e `lhecmie` e` Exfec. Væl ^mucl?  Mtcms, 4>=1. VXEYMTX AAA, I. D. E` dusfm hl vmclr ? l iuam he EZM pmrm estrmteiastms. Xrmhuéæl he Ltíval Tadearl he @ehearls. Væl ^mucl? Dllk`mg, 4>>5. U.V. HE^MTX@EGX LJ XBE XTEMVUTQ (UVHX). Hmacy tremsury yaech furve rmtes . 4>4>. Hasplgàvec e`? 3bttps?//www.tremsury.ilv/reslurfe-fegter/hmtm-fbmrt-fegter/agterest-rmtes/^mies/ XextZaew.mspx4>7. Mfessl e`? 4 omg. 4>4>

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^TLJEVVLT-MUXLT FMTCLV EHUMTHL ^TMHL JEUVET JLT@MÉÆL MFMHÏ@AFM @estre e` Mirlgeiöfal e Hesegvlcva`egtl Teialgmc pecm Jmfuchmhe he Eflgl`am hm Ugaversahmhe Jehermc he @mtl Irlssl (UJ@X).   Espefamcastm e` Iestæl E`presmramc pecm Jughméæl Ietucal Zmrims (JIZ).   Espefamcastm e` Iestæl Jagmgfearm, Flgtrlcmhlram e  Muhatlram pecm JIZ.   Dmfbmrec e` Hareatl pecm Ugaversahmhe he Fuamdí (Ugaf).  

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ER^ETAÏGFAMV ER^ETAÏGFAMV ^TLJAVVALGMAV  

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Á haretlr exefutavl hm VJR ^mrtafapméões e Geiöfals, e`presm he mssesslram espefamcazmhm e` iestæl e`presmramc, flgtrlcmhlram e jagmgéms. Á flgsuctlr e pmcestrmgte gms írems he Iestæl E`presmramc, Iestæl hl Fmpatmc he Iarl e Jagmgéms Flrplrmtavms e Fl`plrtm`egtmas. Á ahemcazmhlr e söfal hm slcuéæl e` iestæl jagmgfearm gm`da.fl`. Á `e`drl he Flgsecbls Flgsuctavls he Mh`agastrméæl he Irupls Eflgø`afls. Mtulu fl`l FEL, Haretlr mh`agastrmtavl e jagmgfearl e he XA he Irupls Eflgø`afls fl` mtuméæl gmfalgmc. Lfuplu l fmril he flgtrlccer  e`  e` irupls eflgø`afls e slfaehmhes mgøga`ms. Á flgsuctlr e pmcestrmgte gms írems he iestæl e`presmramc, iestæl hl fmpatmc he iarl e jagmgéms flrplrmtavms e fl`plrtm`egtmas. Hesegvlcveu trmdmcbls he mgícase he geiöfals, saste`ms he ieregfam`egtl e prlfessls, fl` kglw blw   e` ieregfam`egtl he pcmgacbms ecetrøgafms pmrm mpcafméæl e` dusagess agteccaiegfe  (DA).  (DA).

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