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3. EJPTG@VHHEØJ C OC FXPC@ÍXPEHC FR^FTEMFJPCO ·SVÅ FX FXPC@ÍXPEHC7 Oc fstc`ístehc fs ujc rcmc `f ocs mctfmãtehcs quf trctc `f rfujer, gracjezcr, cjcoezcr ejtfrprftcr `ctgsuj hgj fo prgpøsetg sgouhegjcrc ocs ogs `fhesegjfs. prgdofmcs hgte`ecjgs, fj tg`gs ogsfhcmpgs, y `cj`g sgpgrtf `f rchegjcoe`c` Fo ofjauckf `f oc fstc`ístehc fs oc mctfmãtehc, fj hgjsfhufjhec, sf rfquefrf `fo hgjghemefjtg `f ogs iuj`cmfjtgs mctfmãtehgs y `f ogs mg`fogs `f rfprfsfjtcheøj pcrc hgmprfj`fr ogs cohcjhfs `f sus cpoehchegjfs. ·FJ SVÅ ÃTFCX @FO HGJGHEMEFJPG XF C^OEHC OC FXPC@ÍXPEHC7 Ocs `fhesegjfs fj fo muj`g chtuco sf tgmcj fj dcsf `f `ctgs. Oc fstc`ístehc sf cpoehc fj tg`cs ocs ãrfcs `fo hgjghemefjtg hgmg sgj; ogs jfaghegs, oc c`mejestrcheøj, ocs hefjhecs cargpfhucrecs, oc mf`ehejc, fo `fpgrtf, oc psehgogaíc, ocs hefjhecs sghecofs, afjåtehc y mfkgrcmefjtg afjåtehg `f pocjtcs y cjemcofs, ocs hefjhecs degoøaehcs y cmdefjtcofs, oc ej`ustrec y oc ejafjefríc fj afjfrco. ·HØMG XF @EYE@F OC FXPC@ÍXPEHC7 Oc fstc`ístehc sf `eve`f fj `fshreptevc f ejifrfjheco. Fstc`ístehc `fshreptevc.- rcmc `f oc fstc`ístehc rfochegjc`c hgj ocs mf`ehegjfs, oc gracjezcheøj `f ogs `ctgs y prfsfjtcheøj fj tcdocs g ieaurcs pcrc `fshreder ogs ctredutgs, hcrchtfrístehcs g prgpef`c`fs `f ujc mufstrc fstc`ístehc g `f ujc pgdocheøj. Fstc`ístehc ejifrfjheco.- Oc ejifrfjhec fstc`ístehc sf ejtfrfsc fj `gs tepgs `f prgdofmcs; oc fstemcheøj `f ogs pcrãmftrgs `f oc pgdocheøj y ocs prufdcs `f bepøtfses. Oc ejifrfjhec sf `ftfrmejc fj tårmejgs `f prgdcdeoe`c` y servf pcrc oc tgmc `f `fhesegjfs, csumefj`g uj jevfo `f refsag y frrgr. frrgr. ·HVÃOFX XGJ OC PÅHJEHCX FXPC@ÍXPEHCX ^CTC FO CJÃOEXEX @F @CPGX7 @CPGX7 Fj fo `fscrrgoog `f ogs måtg`gs fstc`ístehgs, ocs tåhjehcs sf dcscdcj fj supgsehegjfs chfrhc `f oc jcturcofzc `f oc pgdocheøj `gj`f sf tgmcj ocs mufstrcs. ^ufstg quf fstgs vcogrfs `f oc pgdocheøj sgj pcrãmftrgs, åstcs tåhjehcs fstc`ístehcs sf hgjghfj hgmg pcrcmåtrehcs. Ocs tåhjehcs fstc`ístehcs quf jg sf dcscj fj supgsehegjfs jumfrgscs je sfvfrcs chfrhc `f ogs pcrãmftrgs sf oocmcj jg pcrcmåtrehcs hgj cmpoec cpoehcheøj fj tg`cs ocs hefjhecs. Påhjehcs pcrcmåtrehcs.- ^crc fmpofcr ocs tåhjehcs fstc`ístehcs ‟pcrcmåtrehcs”, ogs `ctgs `fdfj prgvfjer `f gdsfrvchegjfs oedrfs y sfr gdtfje`gs mf`ecjtf mf`ehegjfs fj fshcocs `f ejtfrvcog hgjstcjtf (sej hfrg rfco y hgj hfrg rfco), hgj vcrecjzc bgmgaåjfc y fifhtgs `f jcturcofzc c`etevc. Fj fstf hcsg, fo cjãoeses fstc`ístehg, uscj`g tåhjehcs pcrcmåtrehcs, fs mãs hgjiecdof y ûteo quf ocs jg pcrcmåtrehcs.
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Hucj`g ogs `ctgs hgrrfspgj`fj c vcrecdofs hucjtetctevcs `f jcturcofzc hgjtejuc (`ctgs måtrehgs) sf fspfrc tfjfr ujc `estreduheøj jgrmco. Påhjehcs jg pcrcmåtrehcs.- Ocs tåhjehcs ‟jg pcrcmåtrehcs” sf `fdfj fmpofcr pcrc cjcoezcr `ctgs prgvfjefjtfs `f pgdochegjfs g mufstrcs `f `estreduhegjfs oedrfs, `f vcrecdofs hucoetctevcs g hucjtetctevcs y mf`e`cs hgj hucoquefr fshcoc. ^crc ogs cjãoeses `f hgjtfgs y hucj`g sf trctc mufstrcs `f tcmcóg pfqufóg (hgmg j = 9), ocs tåhjehcs jg pcrcmåtrehcs rfsuotcj ocs ûjehcs cprgpec`cs. cprgpec`cs. @CPGX ·HØMG XF HOCXEIEHCJ OGX @CPGX7 @CPGX7 Fj oc fstc`ístehc sf trcdckc hgj `ctgs. Ogs `ctgs sgj fo rfsuotc`g `f ocs gdsfrvchegjfs quf rfcoezc fo ejvfsteac`gr. Ogs `ctgs hgjstetuyfj ujc ujc hgofhheøj `f uj jûmfrg `f gdsfrvchegjfs rfochegjc`cs sgdrf ujc g mãs vcrecdofs tgmc`cs sgdrf ej`eve`ugs `f ujc mufstrc g pgdocheøj. Vjc hcrchtfrístehc hcrchtfrístehc hgmûj `f ogs `ctgs fs oc vcrecheøj fxestfjtf fjtrf foogs. ^gr fkfmpog, sesf tgmc oc prg`uhheøj ej`eve`uco `f 3> pocjtcs `f mcíz fs prgdcdof quf je sequefrc `gs `f fsgs `ctgs sfcj eaucofs. Ogs `ctgs puf`fj hocseiehcrsf fj hucoetctevgs g hucjtetctevgs. @ctgs hucjtetctevgs.- sgj cqufoogs quf rfsuotcj `f mf`ehegjfs g `f hgjtfgs. Ogs `ctgs hucjtetctevgs pcscj `f uj vcogr c gtrg sej ejtfrrupheøj y sf fxprfscj mf`ecjtf jûmfrgs fjtfrgs g irchhegjcregs. Ogs `ctgs hucjtetctevgs sf sud`eve`fj fj hgjtejugs y `eshrftgs. @ctgs hgjtejugs.- sgj cqufoogs quf gdtefjfj mf`ecjtf mf`ehegjfs uscj`g ejstrumfjtgs g fquepgs y puf`fj tfjfr hucoquefr vcogr `f oc rfhtc rfco. ^gr fkfmpog; uscj`g ujc hejtc måtrehc sf gdtefjf `ctgs `f tcmcóg, hgj uj tfrmømftrg sf gdtefjf `ctgs `f tfmpfrcturc, hgj uj vfoghímftrg sf gdtefjfj `ctgs `f vfoghe`c`, hgj ujc dcocjzc sf gdtefjf `ctgs `f pfsg, hgj uj pouveømftrg sf me`f oc hcjte`c` `f oouvec hcí`c fj ujc uje`c` `f tefmpg, fjtrf gtrgs. @ctgs `eshrftgs.- sgj ogs quf rfsuotcj `f bchfr hgjtfgs y hgrrfspgj`fj c jûmfrgs fjtfrgs. ^gr fkfmpog; fo jûmfrg `f irutgs pgr ãrdgo. Ogs `ctgs `eshrftgs pcscj `f uj vcogr c gtrg hgj ujc ejtfrrupheøj< ocs hctfagrícs rfprfsfjtcj vcogrfs `estejtgs quf sf rfprfsfjtcr mf`ecjtf jûmfrgs jûm frgs fjtfrgs. @ctgs hucoetctevgs.- sgj cqufoogs rfochegjc`gs hgj oc hocseiehcheøj g hctfagrezcheøj. Ogs `ctgs hucoetctevgs sf sud`eve`fj fj jgmejcofs y gr`ejcofs. @ctgs jgmejcofs ..- sgj `ctgs hctfaørehgs quf puf`fj sfr hg`eiehc`gs jumårehcmfjtf pfrg`fjg tefjfj ujc rfocheøj crdetrcrec fjtrf ogs jûmfrgs cseajc`gs y fo vcogr oc vcrecdof.
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@ctgs gr`ejcofs .- sgj .- sgj `ctgs quf co sfr hg`eiehc`gs jumårehcmfjtf aucr`cj ujc hgrrfspgj`fjhec kfrãrquehc `f ogs jûmfrgs cseajc`gs y fo vfr`c`frg vcogr `f oc vcrecdof. ·SVÅ HCTCHPFTÍXPEHCX @FDF PFJFT VJ EJXPTVMFJPG @F MF@EHEØJ ^CTC PGMCT @CPGX7 @CPGX7 Ocs hcrchtfrístehcs `f uj ejstrumfjtg `f mf`eheøj sgj; vcoe`fz y hgjiecdeoe`c`. Ycoe`fz.- Xf rfiefrf c oc prfheseøj hgj quf uj ejstrumfjtg me`f og quf sf `fsfc mf`er. Hgjiecdeoe`c`.- Xf rfiefrf co arc`g fj quf su cpoehcheøj rfpfte`c, co mesmg sukftg u gdkftg, prg`uhf fo mesmg rfsuotc`g. Ogs ichtgrfs quf cifhtcj oc hgjiecdeoe`c` y oc vcoe`fz `f ogs `ctgs tgmc`gs hgj ejstrumfjtgs sgj; oc emprgvescheøj, ogs ejstrumfjtgs jg hcoedrc`gs, ocs uje`c`fs `f mf`e`c jg cprgpec`cs y ocs hgj`ehegjfs `f trcdckg. ·SVÅ XEAJEIEHC FRCHPEPV@ U ^TFHEXEØJ FJ OC PGMC @F @CPGX7 Oc hcoe`c` `f oc tgmc `f `fhesegjfs fstc`ístehcs `fpfj`f `f oc hcoe`c` `f ogs `ctgs y åstgs `fpfj`fj `f oc hcoe`c` `f ogs fquepgs f ejstrumfjtgs `f mf`eheøj, `f oc rfspgjscdeoe`c` y prgifsegjcoesmg `f ogs ejvfsteac`grfs y fquepgs `f cpgyg csí hgmg `f ocs fshcocs `f mf`eheøj y uje`c`fs `f mf`e`c. Oc hcoe`c` `f ogs `ctgs sf vcogrc mf`ecjtf oc fxchtetu` y oc prfheseøj `f ogs `ctgs. Oc fxchtetu` fxchtetu` `f `f ogs `ctgs sf rfiefrf c quf tcj hfrhc sf fjhufjtrc fo vcogr mf`e`g `fo vcogr rfco. Fj tårmejgs fstc`ístehgs, oc fxchtetu` fstã rfochegjc`c hgj fo sfsag `f ujc fstemcheøj. Hucjtg mfjgr fs fo sfsag fs mãs fxchtc oc fstemcheøj. Fstg `fpfj`f `fo ejvfsteac`gr, `fo fvcoucr, `fo csestfjtf g tgmc`gr `f `ctgs, quefjfs `fdfj sfr pfrsgjcs rfspgjscdofs y defj igrmc`cs fj ogs ogs prghf`emefjtgs. Vj fvcouc`gr `f hcmpg `fdf ‟scdfr og quf bchf y pcrc og quf bchf”. Oc fxchtetu` `f uj rfsuotc`g sf fxprfsc mf`ecjtf fo frrgr cdsgoutg quf fs oc `eifrfjhec fjtrf fo vcogr fxpfremfjtco y fo vcogr vfr`c`frg. Oc prfheseøj sf rfiefrf c oc `espfrseøj `f uj hgjkujtg `f vcogrfs gdtfje`gs `f mf`ehegjfs rfpfte`cs. C mfjgr `espfrseøj mcygr fs oc prfheseøj. Vjc mf`e`c hgmûj `f oc vcrecdeoe`c` fs oc `fsvecheøj fstãj`cr `f ocs mf`ehegjfs y oc prfheseøj sf puf`f fstemcr hgmg ujc iujheøj `f fooc. ^TGDOFMC TFXVFOPG Focdgrcr uj mcpc hgjhfptuco quf eoustrf oc rfocheøj fjtrf fxchtetu` y prfheseøj `f ogs `ctgs pcrc cjãoeses fstc`ístehg.
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^TFHEXEØJ
FRCHPEPV@
@fpfj`f `f oc hcoedrcheøj `f ogs ejstrumfjtgs y `f oc pocjeiehcheøj `f ocs mf`ehegjfs
@fpfj`f `f oc rfspgjscdeoe`c` y igrmcheøj
• Ejvfsteac`gr • Gpfrcregs • Csestfjtfs
• Fquepgs `f mf`eheøj • Fshcocs `f mf`eheøj • Mgmfjtg `f oc mf`eheøj
Hgjiecjzc fj ogs `ctgs
Ycoe`fz `f ogs `ctgs
^rghfsg `f cjãoeses
·HÛCJPGX @FHEMCOFX VXCT ^CTC FO CJÃOEXEX @F @CPGX7 Fo ejvfsteac`gr `fiejf ocs uje`c`fs `f mf`e`c y ogs `íaetgs c uscr fj fo prghfsg `f cjãoeses, fj iujheøj `fo jevfo `f prfheseøj rfqufre`g. Xe oc prfaujtc iufrc; ·Suå rfj`emefjtg fj leogs `f hchcg sfhg/bfhtãrfc prg`ukg fj fo 4>>27. Oc rfspufstc pg`ríc sfr 84> leogs/bfhtãrfc y jg 836,22 leogs/ leogs/bfhtãrfc. bfhtãrfc. Xe oc prfaujtc iufrc; ·Suå rfj`emefjtg fj tgjfoc`cs `f hchcg sfhg/bfhtãrfc prg`ukg fj fo 4>>27. Oc rfspufstc pg`ríc sfr >,84> tgjfoc`cs måtrehcs/bfhtãrfc y jg >,83622 tgjfoc`cs måtrehcs/bfhtãrfc. måtrehcs/bfhtãrfc. ·HØMG XF GTACJE[C VJC DCXF @F @CPGX7 Ogs `ctgs puf`fj sfr `f `eifrfjtf jcturcofzc. ^crc sfr cjcoezc`gs rfquefrfj fstcr gracjezc`gs fj ujc dcsf `f `ctgs y åstc sf hcrchtfrezc pgr tfjfr trfs fofmfjtgs; fo jûmfrg `f rfaestrg, oc vcrecdof y fo vcogr. Hcsg.- uj hcsg g rfaestrg fs ujc uje`c` `f gdsfrvcheøj y fstã `ftfrmejc`g pgr oc Hcsg.mufstrc. Ycrecdof. Ycrecdof.- fs oc prgpef`c`, hcrchtfrístehc g rcsag `f ogs ej`eve`ugs u gdkftgs quf puf`f sfr mf`e`g fj ujc mufstrc g pgdocheøj fstc`ístehc.
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@ctg.- fs fo vcogr `f oc rfprfsfjtcheøj hucoetctevc g hucjtetctevc `f uj ctredutg, @ctg.- hcrchtfrístehc g prgpef`c`, quf rfsuotc `f oc mf`eheøj. ·HVÃOFX XGJ OGX XÍMDGOGX MÃX VXC@GX FJ FXPC@ÍXPEHC7 FXPC@ÍXPEHC7 copbc
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^TGDOFMC TFXVFOPG; @ctgs `f seftf hcrchtfrístehcs cargjømehcs `fo hogj J^-4>40 `f hciå rgdustc, `fspuås `f 32 mfsfs `fo fstcdofhemefjtg fj fo hcmpg3. ^ocjtc
Coturc `f pocjtc (hm)
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@eãmftrg `f hgpc (hm)
Jûmfrg `f rcmcs/tcoog prejhepco
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4.
YCTECHEØJ DEGOØAEHC
Oc vcrecheøj degoøaehc fs oc tfj`fjhec `f tg`gs ogs sfrfs vevgs c `eifrfjhecrsf ujgs `f gtrgs. Fj oc jcturcofzc jg fxestfj ej`eve`ugs fxchtcmfjtf eaucofs, hucj`g muhbg sgj pcrfhe`gs. Ogs afmfogs e`åjtehgs, ogs hogjfs y ogs bídre`gs tefj`fj c sfr semeocrfs fj su afjgtepg< sej fmdcrag, pgr ocs hgj`ehegjfs `fo cmdefjtf ifjgtípehcmfjtf tefj`fj c `eifrfjhecrsf. 4.3. CPTEDVPGX @F VJC ^GDOCHEØJ ·HVÃOFX XGJ OGX CPTEDVPGX DEGOØAEHGX MÃX EM^GTPCJPFX @F VJC 3
. Dcjhg `f afrmgpocsmc `f hciå rgdustc. Hfjtrg Fx Fxpfremfjtco pfremfjtco HGI HGIFJCH-@VDOEJXC. FJCH-@VDOEJXC. 4>>2.
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^GDOCHEØJ7 Ogs ctredutgs degoøaehgs mãs empgrtcjtfs `f ujc pgdocheøj vfaftco g cjemco sgj ogs seauefjtfs; oc jctcoe`c`, mgrtcoe`c`, `estreduheøj fj f`c`fs, mearcheøj, hrfhemefjtg pgdochegjco, `fjse`c`, pfreg`ehe`c` y ãrfc `f `estreduheøj. ·HØMG XF @FIEJF C OC JCPCOE@C@7 Jctcoe`c`.- fs oc hcpche`c` Jctcoe`c`.- hcpche`c` ejtríjsfhc quf tefjf tg`c pgdocheøj `f cumfjtcr fo jûmfrg `f ej`eve`ugs fj dcsf `f su hcpche`c` rfprg`uhtevc. Oc jctcoe`c` sf puf`f mf`er y hucjteiehcr cjcoezcj`g fo ejhrfmfjtg `f oc pgdocheøj fj uj `ftfrmejc`g tefmpg, c trcvås `f oc tcsc tcsc `f jctcoe`c`. Oc tcsc `f jctcoe`c` fs rfsuotc`g rfsuotc`g `f oc rfocheøj fjtrf ogs ej`eve`ugs jche`gs vevgs y ujc uje`c` `f tefmpg `ftfrmejc`g. ·HØMG @F @FIEJF OC MGTPCOE@C@7 Mgrtcoe`c`.- fs oc hcjte`c` `f ej`eve`ugs `f ujc pgdocheøj quf mufrf fj uj tefmpg Mgrtcoe`c`.- fs `ftfrmejc`g, yc sfc pgr chhe`fjtf g pgr quf bcj hgmpoftc`g su hehog `f ve`c. Oc mgrtcoe`c` puf`f sfr mf`e`c y hucjteiehc`c mf`ecjtf oc tcsc `f mgrtcoe`c`. Fj ocs pgdochegjfs vfaftcofs `rãstehcs y cjemcofs ujc tcsc mgrtcoe`c`bumcjcs, jcturco, pfrgtg`cs tcmdeåj ghurrfj setuchegjfs qufbcy cifhtcj ocs `f pgdochegjfs vfaftcofs y cjemcofs hgmg sgj ocs aufrrcs, ocs pfstfs y gtrgs ichtgrfs quf cifhtcj ocs pgdochegjfs. ·SVÅ XF FJPEFJ@F ^GT MEATCHEØJ7 Mearcheøj.- sf rfiefrf co jûmfrg `f ej`eve`ugs quf fjtrcj g scofj `f ujc pgdocheøj g `f uj fspcheg iísehg `fieje`g, fj uj tefmpg `c`g. Hucj`g scofj `f ujc pgdocheøj y vcj bchec gtrc sf `fjgmejc fmearcheøj y hucj`g oofacj `fs`f gtrc pgdocheøj sf oocmc ejmearcheøj. Xf puf`f mf`er y hucjteiehcr c trcvås `f ujc tczc `f mearcheøj. ·C SVÅ XF TFIEFTF OC @EXPTEDVHEØJ @F F@C@FX FJ VJC ^GDOCHEØJ7 @estreduheøj `f f`c`fs.- fs f`c`fs.- fs fo jûmfrg `f ej`eve`ugs prfsfjtfs fj ujc pgdocheøj pgr hctfagrícs `f f`c`. Fstc `estreduheøj puf`f sfr cjcoezc`c fj tårmejgs cdsgoutgs g rfoctevgs. ·HØMG XF @FIEJF FO HTFHEMEFJPG ^GDOCHEGJCO7 Hrfhemefjtg.- fs oc ejtfrchheøj `f oc jctcoe`c`, mgrtcoe`c`, mearcheøj y `estreduheøj `f f`c`fs fj uj `ftfrmejc`g tefmpg< setucheøj quf pfrmetf c oc pgdocheøj cumfjtcr g `esmejuer su jûmfrg `f ej`eve`ugs. Fstc puf`f mf`ersf mf`ecjtf oc tcsc `f hrfhemefjtg pgdochegjco. ^gr fkfmpog; 8,0%/cóg. ·HØMG XF @FIEJF @FJXE@C@ ^GDOCHEGJCO7 ^GDOCHEGJCO7 @fjse`c` pgdochegjco .- fs oc rfocheøj fjtrf fo jûmfrg ej`eve`ugs `f ujc pgdocheøj fjpgdochegjco.uj ãrfc `ftfrmejc`c. Xf me`f c trcvås `f uj`fíj`ehf. ^gr fkfmpog; pocjtcs/bfhtãrfc, ogmdrehfs/mftrg huc`rc`g.
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·HØMG XF @FIEJF OC ^FTEG@EHE@C@7 ^FTEG@EHE@C@7 ^freg`ehe`c`.- fs fo hcmdeg quf suirf ujc pgdocheøj fj fo rfstg `f sus ^freg`ehe`c`.- hcrchtfrístehcs `urcjtf `urcjtf uj `ftfrmejc`g `ftfrmejc`g tefmpg. ^gr fkfmpog; ogs hehogs `f `fscrrgoog `f vcrecs fspfhefs `f ofpe`øptfrgs, quf sgog fj su fstc`g ocrvco sf hgjstetuyfj fj pocacs y cpcrfhfj fj åpghcs fspfhíiehcs. 4.4. ICHPGTFX @FPFTMEJCJPFX @F OC YCTECDEOE@C@ DEGOØAEHC DEGOØAEHC ·HVÃOFX XGJ OGX ICHPGTFX SVF @FPFTMEJCJ OC YCTECHEØJ DEGOØAEHC7 Oc vcrecheøj degoøaehc sf `fdf c ogs ichtgrfs; afjgtepg (A), cmdefjtf (C), ejtfrchheøj afjgtepg x cmdefjtf (AC) y fifhtgs mutchegjcofs. Pg`g hcrãhtfr g rcsag ifjgtípehg `f uj ej`eve`ug quf prfsfjtc vcrecheøj sf hgjghf hgmg vcrecdof.
}
CMDEFJPF • Xufog • Hoemc • Mcjfkg
IFJGPE^G
AFJGPE^G • Afjfs • Bfrfjhec
·HVÃOFX XGJ OGX PE^GX @F YCTECDEOE@C@ DEGOGAEHC7 DEGOGAEHC7 Oc vcrecheøj degoøaehc puf`f sfr hgjtejuc g `eshgjtejuc. Ycrecheøj hgjtejuc.- Oc vcrecheøj hgjtejuc fs cqufooc `gj`f sf gdsfrvc ujc hgjtejue`c` `f ogs fifhtgs quf `ftfrmejcj uj hcrãhtfr ifjgtípehg `f uj ej`eve`ug g `f ogs ej`eve`ugs `f ujc pgdocheøj. Oc vcrecheøj hgjteju hgjtejucc sf csghec uj hcrãhtfr `f bfrfjhec hucjtetctevc (ejtfrvefjf ujc arcj hcjte`c` `f afjfs) y sf rfprfsfjtc arãiehcmfjtf fj oc `fjgmejc`c `estreduheøj jgrmco. C oc vcrecheøj hgjtejuc sf csghecj ogs hcrchtfrfs hucjtetctevgs g måtrehgs hgmg; coturc `f pocjtc, pfsg `f ogs irutgs, pfsg `f oc degmcsc, hgjtfje`g `f hogrgieoc, fjtrf gtrgs. Ycrecheøj `eshgjtejuc.- Oc vcrecheøj `eshgjtejuc fs oc tfj`fjhec, quf sf gdsfrvc fj ogs ej`eve`ugs y ocs pgdochegjfs vfaftcofs y cjemcofs, c prfsfjtcr `eshgjtejue`c` fj sus rcsags g hcrchtfrfs< fs `fher, quf ogs ifjgtepgs sgj iãheomfjtf `eifrfjhecdofs fj igrmc vesuco. Fj fstf hcsg ocs `eifrfjhecs fjtrf ogs ej`eve`ugs sgj `f jcturcofzc hucoetctevc. Ogs fifhtgsg mutchegjcofs `f ogs sfrfs sf fxprfscj vfaftcofs fj oc vcrecheøj hucoetctevc `f uj rcsag hcrãhtfr ifjgtípehg. Pg`csvevgs ocs pgdochegjfs y cjemcofs tefjfj ujc tcsc jcturco `f mutcdeoe`c`. Xe fj ujc pgdocheøj `f pocjtcs `f pgrtf cotg, `f
1
mcjfrc hcsuco sf fjhufjtrc ujc pocjtc fjcjc quf fj ocs afjfrchegjfs pgstfregrfs rfprg`uhf fstc hcrchtfrístehc, sf trctcríc `f uj hcsg `f mutcheøj. Ogs fifhtgs mutchegjcofs sf fxprfscj fj ujc vcrecheøj `f jcturcofzc `eshgjtejuc `f ogs hcrchtfrfs ifjgtípehgs. 4.8. MF@EHEØJ @F OC YCTECDEOE@C@ ·HØMG XF ^VF@F MF@ET OC YCTECDEOE@C@7 Oc mf`eheøj `f oc vcrecheøj hgjstetuyf fo chtg `f rfaestrcr oc ejigrmcheøj (tgmc `f `ctgs) `f hc`c vcrecdof, fj ogs ej`eve`ugs quf hgjigrmcj ujc mufstrc g pgdocheøj. ^crc rfcoezcr ocs mf`ehegjfs sf uscj fshcocs. C hc`c fshcoc `f mf`eheøj of hgrrfspgj`f uj hefrtg hgjkujtg `f gpfrchegjfs c`mesedofs. Ocs fshcocs `f mf`eheøj sgj; jgmejco, gr`ejco, `f ejtfrvcog hgjstcjtf sej hfrg rfco (irfhufjtfmfjtf e`fjteiehc`c hgmg fshcoc `f ejtfrvcog) y `f ejtfrvcog hgjstcjtf hgj hfrg rfco (e`fjteiehc`c tcmdeåj hgmg fshcoc `f rczøj g `f prgpgrheøj). ·SVÅ FX VJC FXHCOC JGMEJCO7 Oc fshcoc pgr jgmejco pfrmetf sgog ogsujc ej`eve`ugs gdkftgs `f ujc mufstrc pgdocheøj sus hucoe`c`fs qufhocseiehc jg tefjfj rfocheøjufjtrf sí. Ogs jûmfrgs fj ocg fshcoc jgmejco sempofmfjtf ftequftcj ogs `ctgs< fj rfcoe`c` jg sgj vfr`c`frgs jûmfrgs. Hucj`g ogs `ctgs bcj se`g gdtfje`gs uscj`g uscj`g fshcoc jgmejco sgog hcdfj ogs cjãoeses jg pcrcmåtrehgs. ^gr fkfmpog; ·Huãofs sgj ogs huotevgs mãs empgrtcjtfs `f oc hgstc7 3. 4. 8. 0.
Hchcg Dcjcjg Hciå rgdustc ^comc cirehcjc
·SVÅ FX VJC FXHCOC GT@EJCO7 Oc mf`eheøj fj fshcoc gr`ejco `f ej`eve`ugs u gdkftgs hgjse`frc oc rfocheøj fjtrf hctfagrícs, fstcdofhefj`g uj gr`fj g rcjag `f mcygr c mfjgr, g vehfvfrsc. Ogs `ctgs gdtfje`gs hgj fshcoc gr`ejco puf`fj sfr cjcoezc`gs uscj`g ocs tåhjehcs jg pcrcmåtrehcs y fj coaujgs hcsgs, cpgyc`g fj trcjsigrmchegjfs fspfhecofs, sf puf`fj uscr ocs tåhjehcs pcrcmåtrehcs. ^gr fkfmpog; Fshcoc gr`ejco pcrc oc fvcoucheøj `f oc ejhe`fjhec `f rgyc `fo hciå Fshcoc Hø`eag @fshrepheøj Cusfjhec `f síjtgmcs. síjtgmcs. Tfsestfjtf > T 3 4 8
MT MX X
Dckc ejhe`fjhec `f oc`ffjifrmf`c`. Mg`frc`cmfjtf rfsestfjtf Mf`ecjc ejhe`fjhec oc fjifrmf`c`. Mg`frc`cmfjtf sushfptedof Cotc ejhe`fjhec `f oc fjifrmf`c`. fjifrmf`c`. Xush Xushfptedof fptedof 2
·SVÅ FX VJC FXHCOC @F EJPFTYCOG HGJXPCJPF XEJ HFTG TFCO7 Oc fshcoc `f ejtfrvcog hgjstcjtf sej hfrg rfco, irfhufjtfmfjtf e`fjteiehc`c sgog hgmg fshcoc `f ejtfrvcog, tefjf ogs fofmfjtgs `f oc fshcoc gr`ejco y, c`fmãs, pfrmetf hgjghfr oc `estcjhec fjtrf `gs jûmfrgs hgjsfhutevgs `f oc mf`eheøj, c pcrter `f uj hfrg crdetrcreg. Ogs `ctgs gdtfje`gs hgj fshcocs `f ejtfrvcog puf`fj sfr cjcoezc`gs uscj`g ocs tåhjehcs jg pcrcmåtrehcs y pcrcmåtrehcs, p crcmåtrehcs, hgj coaujcs rfstrehhegjfs. ^gr fkfmpog; oc mf`eheøj `f oc tfmpfrcturc (arc`gs hfjtíarc`gs g arc`gs Icbrfjbfet (I> = 5/6 H> + 84) g oc mf`eheøj `fo tefmpg fj bgrcs (>BB = 40BGG). ^crc fstcs mf`ehegjfs sf uscj ejstrumfjtgs `f mf`eheøj hgmg sgj ogs tfrmømftrgs y ogs rfogkfs. ·SVÅ FX VJC FXHCOC @F EJPFTYCOG HGJXPCJPF HGJ HFTG TFCO G @F ^TG^GTHEØJ7 Oc fshcoc `f ejtfrvcog hgjstcjtf hgj hfrg rfco, tcmdeåj fs e`fjteiehc`c hgmg fshcoc `f prgpgrheøj ø rczøj, tefjf su greafj uj pujtg hfrg vfr`c`frg. `ctgs gdtfje`gs hgj fshcocs `f rczøj puf`fj sfr cjcoezc`gs uscj`g ocs tåhjehcs jg pcrcmåtrehcs y pcrcmåtrehcs. Ogs `ctgs sgj gdtfje`gs mf`ecjtf mf`ehegjfs uscj`g ejstrumfjtgs (hejtc måtrehc, dcocjzc, fjtrf gtrgs), `f fstc mcjfrc sf hgjghf oc `estcjhec fxchtc fjtrf `gs jûmfrgs hgjsfhutevgs `f oc mf`eheøj. Fstgs sgj vfr`c`frgs jûmfrgs hgj ogs hucofs sf puf`fj bchfr tg`gs ogs hãohuogs y prufdcs pcrcmåtrehcs y jg pcrcmåtrehcs. ^gr fkfmpog; coturc `f pocjtc, `eãmftrg `f tcoog, pfsg `fo irutg, oetrgs `f ofhbf/vchc, leoømftrgs/bgrc. 8.
FXPC@ÍXPEHC @FXHTE^PEYC
·HØMG XF @FIEJF FXPC@ÍXPEHC @FXHTE^PEYC7 Oc fstc`ístehc `fshreptevc tefjf fo prgpøsetg `f `fshreder ogs rcsags, ctredutgs g hcrchtfrfs ifjgtípehgs `f ocs pgdochegjfs vfaftcofs g cjemcofs< csí hgmg, `f ocs hcrchtfrístehcs `f ogs gdkftgs quf sgj mf`edofs mf`ecjtf `eifrfjtfs fshcocs, fj `ftfrmejc`cs hgj`ehegjfs `f tefmpg y fspcheg. Hgmg pcrtf `f oc fstc`ístehc `fshreptevc sf mfjhegjcj; fo cjãoeses `f irfhufjhecs, oc arciehcheøj `f ocs irfhufjhecs, ocs mf`e`cs `f tfj`fjhec hfjtrco y ocs mf`e`cs `f `espfrseøj. 8.3. CJÃOEXEX @F ITFHVFJHECX ·@F SVÅ PTCPC FO CJÃOEXEX @F ITFHVFJHECX7 ITFHVFJHECX7 Vjc irfhufjhec sf rfiefrf c oc hcjte`c` `f vfhfs quf sf rfpetf uj `ftfrmejc`g vcogr `f oc vcrecdof fj ujc sfref `f `ctgs. Oc `estreduheøj `f irfhufjhecs fs uj hgjkujtg `f `ctgs carupc`gs hctfagrícs `gj`f sf ej`ehc `f gdsfrvchegjfs hc`c ujc `f foocs.fj Fo cjãoeses `f irfhufjhecs ejhouyffoocjûmfrg `estreduheøj `f irfhufjhecspcrc y oc arciehcheøj `f ogs rfsuotc`gs. Oc `estreduheøj `f irfhufjhecs fs uj rfsumfj tcduoc`g
5
`f uj hgjkujtg `f `ctgs quf mufstrc oc irfhufjhec `f `ctgs `f hc`c ujc `f ocs hocsfs quf jg sf trcsocpcj, hgj fo gdkftevg `f prgpgrhegjcr ujc pfrspfhtevc `f ogs `ctgs. Fo cjãoeses `f irfhufjhecs irfhufjhecs fs ujc tåhjehc jg pcrcmåtrehc. pcrcmåtrehc. Fo cjãoeses `f irfhufjhecs puf`f sfr `f `gs tepgs; `f ujc vcrecdof (ujevcrec`c) g `f `gs vcrecdofs (devcrec`c). Cjãoeses `f irfhufjhecs `f ujc sgoc vcrecdof.- fstf cjãoeses trctc ujc sgoc vcrecdof, pgr og quf sf hgjghf tcmdeåj hgmg cjãoeses ujevcrec`g, fj uj sfjte`g g fj ujc sgoc `erfhheøj. Cjãoeses `f irfhufjhecs `f `gs vcrecdofs.- fstf cjãoeses trctc semuotãjfcmfjtf `gs vcrecdofs, pgr og quf sf hgjghf tcmdeåj hgmg cjãoeses fj `gs `erfhhegjfs, devcrec`g g fj `gs sfjte`gs. ·SVÅ TFXVOPC@GX XF GDPEFJF HGJ VJ CJÃOEXEX @F ITFHVFJHECX7 ITFHVFJHECX7 Vj cjãoeses `f irfhufjhecs pfrmetf hocseiehcr ujc sfref `f `ctgs y rfprfsfjtcrogs irfhufjhecs cdsgoutcs, irfhufjhec cdsgoutc chumuoc`c, irfhufjhecs rfoctevcs, irfhufjhec rfoctevc chumuoc`c. Irfhufjhec cdsgoutc.- Fs fo jûmfrg `f `ctgs quf hgrrfspgj`fj c hc`c hctfagríc g hocsf. Oc irfhufjhec cdsgoutc sf rfprfsfjtc arãiehcmfjtf fj uj bestgarcmc g fj uj pgoíagjg `f irfhufjhecs. Hgj ocs irfhufjhecs gr`fjc`cs `f mcygr c mfjgr sf hgjstruyf uj `ecarcmc `f ^crftg. Irfhufjhec cdsgoutc chumuoc`c.- Xf hcohuoc sumcj`g ocs irfhufjhecs `f hocsf `fs`f fo premfr ejtfrvcog bcstc oc irfhufjhec `f hocsf `fo ejtfrvcog `f ejtfrås. Fo vcogr ûotemg `f ocs irfhufjhecs chumuoc`cs hgrrfspgj`frã co vcogr `f oc sumctgrec tgtco `f ogs `ctgs. Irfhufjhec rfoctevc.- Xf gdtefjf `eve`efj`g hc`c ujc `f ocs irfhufjhecs `f hocsf fjtrf fo jûmfrg tgtco `f gdsfrvchegjfs. ^uf`f sfr rfprfsfjtc`c fj pgrhfjtckf. Oc irfhufjhec`frfoctevc puf`fC`fmãs, rfprfsfjtcrsf arãiehcmfjtf uj iehcs bestgarcmc pgoíagjg irfhufjhecs. sf puf`f rfprfsfjtcr fj arã arãiehcs `f pcstfog fj uj Irfhufjhec rfoctevc chumuoc`c.- Xf hcohuoc sumcj`g ocs irfhufjhecs `f hocsf rfoctevcs `fs`f fo premfr ejtfrvcog bcstc oc irfhufjhec `f hocsf `fo ejtfrvcog `f ejtfrås. Fo vcogr ûotemg `f ocs irfhufjhecs rfoctevcs chumuoc`cs hgrrfspgj`frã co vcogr `f 3>> pgr hefjtg. Oc arciehcheøj `f ogs vcogrfs `f oc irfhufjhec rfoctevc sf hgjghf hgmg gkevc. ·SVÅ FX VJC HOCXF F EJPFTYCOG @F HOCXF7 HOCXF7 Vjc hocsf, fj fo cjãoeses `f irfhufjhecs, sf rfiefrf c ujc hctfagríc `f `ctgs sej trcsocpfs. Vjc mcrhc `f hocsf fs fo pujtg mf`eg `f hc`c ejtfrvcog `f hocsf. Vj ejtfrvcog `f hocsf sf rfiefrf c su tcmcóg sej trcsocpfs. Fo jûmfrg `f hocsfs puf`f sfr pcr g empcr. Hucj`g fo jûmfrg `f hocsfs fs empcr sf puf`f vesucoezcr vesucoezcr `f mfkgr mcjfrc fo hgmpgrtcmefjtg `f oc `estreduheøj bchec oc `frfhbc y bchec oc ezquefr`c `f
3>
uj vcogr hfjtrco. Fo jûmfrg `f hocsfs `fpfj`f `fo jûmfrg `f `ctgs, pfrg fs hgjvfjefjtf fjtrf hejhg y trfhf. Fo ejtfrvcog `f hocsf sf puf`f gdtfjfr mf`ecjtf oc `eifrfjhec fjtrf fo oímetf supfregr (`ctg mãs cotg `f oc sfref gr`fjc`c) y fo oímetf ejifregr (`ctg mcs dckg `f oc sfref gr`fjc`c), `eve`e`g pcrc fo jûmfrg `f hocsfs pocjfc`g pgr fo ejvfsteac`gr. Ejtfrvcog `f hocsf = Oímetf mcygr - Oímetf mfjgr Jûmfrg `f hocsfs Fo ejtfrvcog `f hocsf tcmdeåj og puf`f `fiejer fo ejvfsteac`gr, sfaûj ocs jfhfse`c`fs `fo fstu`eg. 8.3.3. CJÃOEXEX @F ITFHVFJHECX @F VJC YCTECDOF ·HØMG XF @FIEJF VJ CJÃOEXEX @F ITFHVFJHECX VJEYCTEC@G7 VJEYCTEC@G7 Fo cjãoeses `f irfhufjhecs `f ujc sgoc vcrecdof tcmdeåj sf hgjghf hgmg ujevcrec`c, fj uj sfjte`g g fj ujc sgoc `erfhheøj. Jgrmcomfjtf, fstf cjãoeses cjãoeses sf cpoehc cpoehc c oc vcrecdof `fo mcygr ejtfrås `fo ejvfsteac`gr. ·SVÅ PE^GX @F @EXPTEDVHEGJFX VJEYCTEC@CX XF ^VF@FJ GDXFTYCT7 Ocs `estreduhegjfs `f ujc vcrecdof puf`fj sfr `f ogs seauefjtfs tepgs; jgrmco, jg jgrmco, hgj csemftríc c oc `frfhbc y hgj csemftríc c oc ezquefr`c.
@estreduheøj jgrmco
@estreduheøj jg jgrmco
Csemftríc c oc `frfhbc
Csemftríc c oc ezquefr`c
^TGDOFMC TFXVFOPG Fj ujc sfref gr`fjc`c `f `ctgs4 `f coturc (fj hfjtímftrgs) `f 8> pocjtcs `f hciå rgdustc8 tgmc`cs co czcr, rfcoezcr fo cjãoeses `f irfhufjhecs fj uj sfjte`g. 383 366 392
386 39> 314
382 39> 310
303 39> 316
306 393 315
301 394 328
363 390 326
363 396 322
360 396 351
366 391 355
Fo oímetf mcygr fs 355 hfjtímftrgs y fo oímetf mfjgr fs 383 hfjtímftrgs. ^crc fo cjãoeses `f irfhufjhecs sf `fiejf seftf hctfagrícs. Fo ejtfrvcog `f hocsf hocsf fs `f 3> 4
. Fo cjãoeses `f irfhufjhecs sf puf`f bchfr uscj`g fo prgarcmc Fxhfo. . @ctgs `f hciå hgjeogj `f 32 mfsfs `f fstcdofhemefjtg fstcdofhemefjtg fj fo hcmpg. HGIFJCH, 4>>2.
8
33
uje`c`fs. Ocs hocsfs sf carupcj carupcj `fs`f 383‘30>, 303‘36>, 303‘36>, ….. bc bcstc stc 323-35> hfjtímftrgs. Cjãoeses `f irfhufjhecs Hocsfs 383 - 30> 303 - 36> 363 - 39> 393 - 31> 313 - 32> 323 - 35> 353 - 4>>
Hgjtrgo
Irfhufjhec
Irfhufjhec cdsgoutc Irfhufjhec
Cdsgoutc 8 8 2 1 0 8 4
EEE EEE EEEEEEEE EEEEEEE EEEE EEE EE
Xumc
chumuoc`c 8 9 30 43 46 42 8>
Irfhufjhec rfoctevc
rfoctevc 3> 3> 41 48 38 3> 1
8>
chumuoc`c 3> 4> 01 1> 28 58 3>>
3>>
·HØMG TF^TFXFJPCT ATÃIEHCMFJPF OGX @CPGX @F VJ CJÃOEXEX @F ITFHVFJHECX7 ITFHVFJHECX7 Ogs `ctgs `fo cjãoeses `f irfhufjhecs puf`fj sfr rfprfsfjtc`gs fj `estejtgs arãiehgs hgmg; bestgarcmc, pgoíagjg `f irfhufjhecs, gkevc y `ecarcmc `f ^crftg. Bestgarcmc.- @fshredf ujc `estreduheøj `f irfhufjhec uteoezcj`g ujc sfref `f rfhtãjauogs c`ychfjtfs `gj`f oc coturc `f hc`c rfhtãjauog fs prgpgrhegjco c oc irfhufjhec `f hocsf quf rfprfsfjtc. 5 2 s c t j c 1 o p f ` g r 9 f m û j 6 ; c t u 0 o g s d c 8 c e h j f 4 u h f r I 3
2 1
0 8
8
8 4
> 383- 30>
303- 36>
363- 39>
393- 31>
313- 32>
323- 35>
353- 4>>
Coturc `f pocjtc (hm)
34
Fo `fjgmejc`g måtg`g tcoog y bgkcs (XPFM (XPFM & OFCI) fs ujc rfprfsfjtcheøj `f uj bestgarcmc `edukcj`g ogs `ctgs. Vscj`g ogs `ctgs `fo cjãoeses `f irfhufjhecs ujevcrec`g, sf `ftfrmejc quf fo tcoog 38 tefjf ocs bgkcs; 3,6 y 2< fo tcoog 30 tefjf ocs bgkcs; 3, 6 y 1< fo tcoog 36 tefjf ocs bgkcs; 3, 3, 0, 6 y 6< y csí suhfsevcmfjtf. Pcoog 38 30 36 39 31 32 35
Bgkcs 3 3 3 > 4 8 1
6 6 3 > 0 6 5
2 1 0 > 6 2
6 3 5
6 4
0
6
6
1
2
^goíagjg `f irfhufjhecs.- Hgjsestf `f sfamfjtgs `f oíjfc hgjfhtcj`g ogs pujtgs igrmc`gs pgr oc ejtfrsfhheøj `f ocs mcrhcs `f hocsf y ocs irfhufjhecs `f hocsf. 8>
41 46
) % ( 4> c v e t c o f r 36 c e h j f u h 3>
48
38 3>
3>
3>
r f I
1 6
> 383- 30>
303- 36>
363- 39>
393- 31>
313- 32>
323- 35>
353- 4>>
Coturc `f pocjtc (hm)
38
Gkevc.- tcmdeåj sf hgjghf hgmg `ecarcmc chumuoctevg y fs oc arciehcheøj oejfco `f Gkevc.oc irfhufjhec rfoctevc chumuoc`c. 3>>
3>>
58
5>
28
2>
) % ( c v e t c o f r c e h j f u h f r I
1>
1> 9> 6>
01
0> 8>
4>
4> 3>
3>
> 383- 30>
303- 36>
363- 39>
393- 31>
313- 32>
323- 35>
353- 4>>
Coturc `f pocjtc (hm)
@ecarcmc `f ^crftg.- Fo `ecarcmc `f ^crftg fs ujc rfprfsfjtcheøj `f ocs irfhufjhecs cdsgoutcs g rfoctevcs fj uj gr`fj fspfhíiehg, sfaûj fo ejtfrås `fo ejvfsteac`gr, `f mcygr c mfjgr g vehfvfrsc. Fstf tepg `f arãiehg fs hgjvfjefjtf uscr pcrc `fiejer pregre`c`fs, fspfhecomfjtf hucj`g ocs hocsfs fstãj fj ujc fshcoc jgmejco. ^gr fkfmpog; pregrezcheøj `f prgdofmcs quf oemetcj oc prg`uhheøj `f uj huotevg
uscj`g fo `ecarcmc `f ^crftg.
30
Fj fstf hcsg, fo ejvfsteac`gr `fhe`erã fstu`ecr pgr sfpcrc`g g fj uj fxpfremfjtg ichtgreco fo premfrg, ogs `gs premfrgs g ogs trfs premfrgs ichtgrfs. 8.3.4. GPTCX PÅHJEHCX @F CJÃOEXEX VJEYCTEC@G ·FREXPFJ GPTCX PÅHJEHCX @F CJÃOEXEX U TF^TFXFJPCHEØJ ATÃIEHC FJ FXPC@ÍXPEHC @FXHTE^PEYC @F VJC XGOC YCTECDOF7 Xf bcj `fscrrgooc`g gtrcs tåhjehcs jg pcrcmåtrehcs pcrc fo cjãoeses `f ujc vcrecdof quf ejhouyf cjãoeses y arciehcheøj hgmg; hucrteofs, quejteofs, pfrhfjteofs y `ecarcmc `f hckc. Hucrteofs.- fs ujc tåhjehc `f cjãoeses `f `ctgs quf me`fj oc ‟tfj`fjhec jg hfjtrco” `f ujc `estreduheøj. Ogs vcogrfs S3, S4 y S8 `eve`fj co hgjkujtg `f `ctgs gr`fjc`gs fj huctrg pcrtfs eaucofs. Fo prghf`emefjtg pcrc fo cjãoeses `f hucrteofs fs fo seauefjtf; • • • • •
Gr`fjcr ocs gdsfrvchegjfs fj gr`fj hrfhefjtf y oghcoezcr oc mf`ecjc g vcogr hfjtrco `f oc sfref gr`fjc`c `f `ctgs. Fo premfr hucrteo (S3) fs oc mf`ecjc `fo premfr arupg `f gdsfrvchegjfs setuc`cs cdckg (g c oc ezquefr`c) ezquef r`c) `f oc mf`ecjc afjfrco. Fo sfauj`g hucrteo (S4) `f ujc sfref gr`fjc`c `f `ctgs fs su mf`ecjc afjfrco. Fo tfrhfr hucrteo S8 fs oc mf`ecjc `f ocs gdsfrvchegjfs setuc`cs crredc (g c oc `frfhbc) `f oc mf`ecjc afjfrco `f oc sfref gr`fjc`c `f `ctgs. Fo rcjag ejtfrhucrteo fs oc `eifrfjhec fjtrf fo f o tfrhfr y fo prem premfr fr hucrteo (S8-S3).
Suejteofs.- Ogs quejteofs sgj mf`e`cs `f ‟tfj`fjhec jg hfjtrco” `f ujc sfref gr`fjc`c `f `ctgs. Ogs pujtgs `f oc `eveseøj `f uj hgjkujtg gr`fjc`g `f ujc sfref `f `ctgs `eve`e`g fj 6 pcrtfs, rfhedfj fo jgmdrf `f quejteofs. ^crc fo cjãoeses cjãoeses `f ogs quejteofs sf `eve`f oc sfref gr`fjc`c `f `ctgs fj hejhg pcrtfs eaucofs, cpoehcj`g ogs mesmgs hgjhfptgs `fo cjãoeses `f hucrteofs. ^frhfjteofs.- Ogs pfrhfjteofs sgj tcmdeåj mf`e`cs `f ‟tfj`fjhec jg hfjtrco” `f ujc sfref gr`fjc`c `f `ctgs. Ogs pujtgs `f `eveseøj `f uj hgjkujtg gr`fjc`g `f ujc sfref `f `ctgs `eve`e`g fj 3>> pcrtfs, rfhedfj fo jgmdrf `f pfrhfjteofs. Ogs hucrteofs hgrrfspgj`fj c ogs pfrhfjteofs 46, 6> y 16. •
Xe Op fs oc pgseheøj `fo pfrhfjteo `fsfc`g. O p
= (j)
p
3>>
@øj`f j fs fs fo jûmfrg `f `ctgs y p fo fo pfrhfjteo (pgr fkfmpog; fo pfrhfjteo 88 fs ^ 88, fo pfrhfjteo 6> fs ^6> quf tcmdeåj fs oc mf`ecjc g S4< fo pfrhfjteo 46 fs ^46=S3 y fo pfrhfjteo 16 fs ^16=S8. Fo prghf`emefjtg `f hãohuog `fo p -åsemg -åsemg pfrhfjteo fs fo seauefjtf;
36
• • • •
Gr`fjcr ogs `ctgs `f mcjfrc cshfj`fjtf. Xf hcohuoc O p Xe Op jg fs fjtfrg, sf rf`gj`fc. Fo vcogr fjtfrg ejmf`ectg mcygr quf O p ej`ehc oc pgseheøj `fo p- åsemg åsemg pfrhfjteo. Xe Op fs fjtfrg, fo p- åsemg åsemg pfrhfjteo fs fo prgmf`eg `f ogs vcogrfs `f ogs `ctgs udehc`gs fj (e) f (e+3).
@ecarcmc `f hckc.- Ogs hejhg jûmfrgs quf rfsumfj ujc `estreduheøj `f `ctgs sgj rfprfsfjtc`gs arãiehcmfjtf pgr uj `ecarcmc `f hckc. O = Gdsfrvcheøj mãxemc S8 = Pfrhfr hucrteo S4 = Mf`ecjc S3 = ^remfr hucrteo X = Gdsfrvcheøj míjemc Ogs oc`gs ejifregr y supfregr `f oc hckc vcj `fo premfr co tfrhfr hucrteo. ^gr og tcjtg, oc coturc `f oc hckc fs oc cmpoetu` `fo 6>% `f ogs `ctgs hfjtrcofs. Fo sfamfjtg `fo ejtfregr `f oc hckc ej`ehc oc mf`ecjc. Ogs fxtrfmgs `f ogs sfamfjtgs pfrpfj`ehuocrfs c ogs oc`gs supfregr f ejifregr ej`ehcj, rfspfhtevcmfjtf, ogs vcogrfs mãxemg y míjemg `f oc `estreduheøj `f `ctgs. `ctgs. ^TGDOFMC TFXVFOPG Cjãoeses `f hucrteofs; Pgmcj`g hgmg dcsf `f trcdckg oc sfref gr`fjc`c `f `ctgs `f coturc (hm), fj ujc mufstrc `f 8> pocjtcs `f hciå rgdustc0, rfcoezcr fo cjãoeses `f hucrteofs. 383 386 366 39> 392 314
• • • •
• •
382 303 306 39> 39> 393 310 316 315
301 363 363 360 366 394 390 396 396 391 328 326 322 351 355
Hgmg oc sfref tefjf 8> `ctgs, oc mf`ecjc (vcogr hfjtrco) fs fo hgrrfspgj`efjtf co prgmf`eg `f ogs `gs vcogrfs hfjtrcofs fj oc sfref gr`fjc`cs `f `ctgs (`ctg 36premfr = 393 hucrteo hm y `ctg hm), quf `c uj vcogr hfjtímftrgs. Fo (S3)39 fs =oc394 mf`ecjc `fo premfr arupg`f`f393,6 gdsfrvchegjfs, `fdckg `f oc mf`ecjc afjfrco< fj fstf hcsg hgrrfspgj`f co vcogr 363 hfjtímftrgs. Oc mf`ecjc `f oc sfref gr`fjc`c `f `ctgs tgtco, quf fj fstf hcsg hgrrfspgj`f co vcogr 393,6 hfjtímftrgs, fs fo sfauj`g hucrteo (S4). Fo tfrhfr hucrteo S8 fs oc mf`ecjc `fo sfauj`g arupg `f gdsfrvchegjfs (crredc `f oc mf`ecjc afjfrco), fj oc sfref gr`fjc`c `f `ctgs y hgrrfspgj`f co vcogr 310 hfjtímftrgs. Fo rcjag ejtfrhucrteo fs oc `eifrfjhec fjtrf ogs vcogrfs `fo tfrhfr y premfr hucrteofs (S8-S3). ^gr og tcjtg, fo rcjag ejtfrhucrteo = 310 ‘ 363 = 48 hfjtímftrgs. Ogs hucrteofs sf puf`fj rfprfsfjtcr arãiehcmfjtf.
0
. Coturc `f pocjtc `f hciå Tgdustc `fspuås `f 32 mfsfs `f fstcdo fstcdofhemefjtg. fhemefjtg. HGIFJCH, 4>>2.
39
46%
46% S 33 =363
46% S 44 = 393,6
46% S 8 8 =310,>
^TGDOFMC TFXVFOPG Cjãoeses `f pfrhfjteofs; pfrhfjteo fs; hcohuocr fo pfrhfjteo 46, 46, tgmcj`g hgmg dcsf `f trcdckg oc sfref gr`fjc`c `f `ctgs `f coturc (hm), fj ujc mufstrc `f 8> pocjtcs `f hciå rgdustc, rfcoezcr fo cjãoeses `f pfrhfjteofs. 383 386 366 39> 392 314
O p
= (j)
382 303 306 39> 39> 393 310 316 315
301 363 363 360 366 394 390 396 396 391 328 326 322 351 355
p
3>>
O p = = (8>) (46/3>>) = 1,6 ≂ O p = = 2 ^gr og tcjtg, fj oc pgseheøj 2 `f oc sfref gr`fjc`c `f 8> `ctgs (j) sf udehc fo `ctg 363, quf hgrrfspgj`f hgrrfspgj`f co hucrteo S3co . pfrhfjteo 46. Fo `ctg 363, fj fo cjãoeses `f hucrteofs, ^TGDOFMC TFXVFOPG @ecarcmc `f hckc; Tfcoezcr hckc; Tfcoezcr fo `ecarcmc `f hckc, cjcoezcj`g oc sfref gr`fjc`c `f `ctgs `f coturc (hm), fj ujc mufstrc `f 8> pocjtcs `f hciå rgdustc (usc`cs fj fo cjãoeses `f irfhufjhecs fj uj sfjte`g).
O
X S3
S4
310
363 383
S8 355
393,6
Hgmg sf puf`f gdsfrvcr bcy uj oeafrg sfsag bchec oc ezquefr`c. Oc `estcjhec fjtrf fo hucrteo S8 y hucrteo S4 (= 34,6 hm) fs mcygr quf oc `estcjhec fjtrf fo hucrteo S 4 y hucrteo S3 (=3>,6 hm). 8.3.4. CJÃOEXEX @F ITFHVFJHECX ITFHVFJHECX @F @GX YCTECDOFX ·HØMG XF @FIEJF VJ CJÃOEXEX @F ITFHVFJHECX DEYCTEC@G7 Fo cjãoeses `f irfhufjhecs devcrec`g hgjse`frc `gs vcrecdofs semuotãjfcmfjtf fj fo cjãoeses< pgr fstg sf hgjghf tcmdeåj hgmg cjãoeses fj `gs sfjte`gs g fj `gs `erfhhegjfs. Fj fstf cjãoeses sf hgjse`frc tg`gs ogs fofmfjtgs hgjhfptucofs ej`ehc`gs pcrc fo cjãoeses `f irfhufjhecs. i rfhufjhecs. Jgrmcomfjtf, fj åstf cjãoeses sf rfochegjc vcrecdofs `f `gs fj `gs. Oc vcrecdof `f mcygr ejtfrås (pgr fkfmpog; prg`uhheøj) vfrsus ocs gtrcs vcrecdofs `f fstu`eg.
31
^TGDOFMC TFXVFOPG Fj ujc sfref `f `ctgs `f `gs vcrecdofs6; coturc (fj hfjtímftrgs) y ogjaetu` `f rcmc `f 8> pocjtcs `f hciå rgdustc tgmc`cs co czcr 9, rfcoezcr fo cjãoeses `f irfhufjhecs fj `gs sfjte`gs. Ogjaetu` `f rcmc (hm) Ycrecdofs
?16
38> - 30> 303 - 36> 363 - 39> 393 - 31> 313 - 32> 323 - 35> 353 - 4>> Irfhufjhec cdsgoutc Irfhufjhec cdsgoutc chumuoc`c Irfhufjhec rfoctevc Irfhufjhec rfoctevc chumuoc`c ) m h ( c t j c o p f ` c r u t o C
• • •
EEE EE E
19?2>
23?26
E EEEEE E
EE EEEE
29?5>
E
EE EEE E
53?
E E EE
9
1
1
9
0
9
38
4>
49
8>
4>
48
48
4>
38
4>
08
91
21
3>>
Irfhufjhe Irfhufjhe c cdsgoutc Irfhufjhe c chumuoc` c rfoctevc Cdsgoutc c 8 8 3> 8 9 3> 2 30 41 43 48 1 0 46 38 8 42 3> 4 8> 1 8>
Irfhufjhec rfoctevc chumuoc`c 3> 4> 01 1> 28 58 3>>
Fj fstf fkfrheheg, ogs vcogrfs `f ocs hfo`cs sf rffmpoczcrgj hgj oíjfcs `f hgjtrgo, cujquf tcmdeåj sf pu`g rfprfsfjtcr jumårehcmfjtf. Fo cjãoeses ej`ehc ujc tfj`fjhec `f ‟c mcygr coturc `f pocjtc mcygr ogjaetu` `f rcmc”. Hcdfj tg`cs ocs rfprfsfjtchegjfs arãiehcs ej`ehc`cs pcrc fo cjãoeses `f irfhufjhecs ujevcrec`g.
8.4. MF@E@CX @F PFJ@FJHEC HFJPTCO ·HVÃOFX XGJ OCX ^TEJHE^COFX MF@E@CX @F PFJ@FJHEC HFJPTCO7 Ocs mf`e`cs `f tfj`fjhec hfjtrco sgj; oc mf`ec, oc mf`ecjc y oc mg`c. Oc mf`ec sf 1
hocseiehc fj sempof, cretmåtehc, afgmåtrehc y pgj`frc`c , fjtrf ocs mãs empgrtcjtfs. ·HØMG XF HCOHVOC VJC MF@EC XEM^OF7 Mf`ec sempof.sempof.- sf hcohuoc sumcj`g fo vcogr mãxemg y fo vcogr míjemg `f ujc sfref `f `ctgs (gr`fjc`c ø jg) `eve`e`g pcrc `gs. Oc mf`ec sempof sgog fs ujc rfifrfjhec `f pgr `gj`f fstã fo prgmf`eg `f oc sfref `f `ctgs. (Re Mãxemc + Re Míjemc) R =
4
6 . 9 1
Fo gr`fjcmefjtg `f ogs `ctgs sf puf`f bchfr uscj`g fo prgarcmc Fxhfo . ^ocjtcs `f oc vcref`c` Hgjeogj `fspuås `f 32 mfsfs `f fstcdofhemefjtg. HGIFJCH, 4>>2.
. Fo hãohuog `f ocs mf`e`cs `f tfj`fjhec hfjtrco hfjtrco sf puf`f rfcoezcr uscj`g fo prgarcmc Fxhfo.
32
^TGDOFMC TFXVFOPG Fj oc seauefjtf sfref gr`fjc`c `f `ctgs, hcohuocr oc mf`ec sempof. 60, 66, 66, 66, 69, 69, 61, 61, 62, 62, 62, 65, 9>, 9>, 9>, 9>, 9>, 94, 98, 90, 96, 96, 99, 91, 95, 1>, 1>, 13, 16, 11, 2> (Re Mãxemc + R e Míjemc)
R =
4
R = (2> ‘ 60)/4 = 91 ·HØMG XF HCOHVOC VJC MF@EC CTEPMÅPEHC7 Mf`ec cretmåtehc.- sf hcohuoc sumcj`g tg`gs ogs vcogrfs `f oc sfref `f `ctgs `eve`e`g pcrc fo jûmfrg `f gdsfrvchegjfs. j
R =
x 3 + x 4
+ ... + x j j
∓ x e = e =3
j
^TGDOFMC TFXVFOPG Fj oc seauefjtf sfref gr`fjc`c `f `ctgs, hcohuocr oc mf`ec cretmåtehc. 60, 66, 66, 66, 69, 69, 61, 61, 62, 62, 62, 65, 9>, 9>, 9>, 9>, 9>, 94, 98, 90, 96, 96, 99, 91, 95, 1>, 1>, 13, 16, 11, 2> j
∓ xe x
=
e =3
j
R = (60+66+66………..+2>)/83 = 3.504/83 = 94,9 Xf puf`f gdsfrvcr ujc `eifrfjhec fjtrf ocs mf`ecs cretmåtehc y sempof. ·HØMG XF HCOHVOC VJC MF@EC AFGMÅPTEHC7 Mf`ec afgmåtrehc.- fs oc rcíz j-åsemc `fo prg`uhtg `f tg`gs ogs vcogrfs jumårehgs. Fj ujc mf`ec ûteo pcrc fstemcr prgmf`egs `f pghgs `ctgs hgj vcogrfs muy `eifrfjtfs. Pefjf cpoehcheøj fj fo fstu`eg `f bídre`gs. j
R A
= j x3. x4 .... xj = j ∇( xe ) e =3
^TGDOFMC TFXVFOPG Hgjse`frcj`g ogs prgmf`egs `f prg`uhheøj `f `gs oíjfcs purcs `f mcíz, hcohuocr fo prgmf`eg `f oc prgafjef. Fj fstf hcsg, hcdf oc mf`ec afgmåtrehc `f ocs prg`uhhegjfs `f ogs `gs prgafjetgrfs. ^3 = 36> uje`c`fs
35
^4 = 9> uje`c`fs (36>)(9>) >,6 = 50,21 uje`c`fs
^3^4 =
Xe sf hcohuocrc oc mf`ec cretmåtehc sf gdtefjf fo vcogr `f 3>6 quf fs muy `eifrfjtf `f oc mf`ec afgmåtrehc, quf fj fstcs herhujstcjhecs fj mãs hgjiecdof. ·HØMG XF HCOHVOC VJC MF@EC ^GJ@FTC@C7 ^GJ@FTC@C7 Mf`ec pgj`frc`c.- fs muy cpoehcdof fs fo cjãoeses `f oc ejigrmcheøj bestørehc. Fstc mf`e`c suraf hgmg ujc igrmc `f `eshremejcr oc empgrtcjhec `f hc`c `ctg fj fo hãohuog `fo prgmf`eg c trcvås `f uj ichtgr `f pgj`frcheøj quf cseajc fo pfsg `f hc`c `ctg `fjtrg `f oc mufstrc g pgdocheøj. @f cpoehcheøj fj c`mejestrcheøj. j
∓ R p
=
w e xe
e=3 j
∓ e
w
e
=3
^TGDOFMC TFXVFOPG Vj carehuotgr bc hgmfrhecoezc`g hchcg sfhg, fj quejtcofs, c `eifrfjtfs prfhegs, hcohuocr oc mf`ec pgj`frc`c `fo prfheg/quejtco. Cóg
Suejtcofs `f hchcg sfhg
4>>9 4>>1 4>>2
36> 491 40> 961
^rfheg ujetcreg Ejarfsgs (`øocrfs/quejtco) (`øocrfs) 91 56 3>4
3>.>6> 46.896 40.02> 65.256
j
∓ R p
=
w e xe
e =3 j
∓
= 65.256/961 = 53,4 `øocrfs/quejtco we
e =3
Xe frrøjfcmfjtf sf hcohuocrc fo prgmf`eg `fo prfheg fj dcsf `f ogs prfhegs ujetcregs, sf tfj`ríc ujc mf`ec cretmåtehc `f 22 `øocrfs/quejtco, vcogr quf jg fs hgrrfhtg. ·SVÅX FX OC MF@ECJC7 Oc mf`ecjc fs ujc mf`e`c `f tfj`fjhec hfjtrco quf hgrrfspgj`f co vcogr hfjtrco fj ujc sfref gr`fjc`c `f `ctgs. `ctgs. Xe oc sfref `f `ctgs fs empcr, oc mf`ecjc fs fo `ctg hfjtrco. Xe oc sfref `f `ctgs fs pcr, fjtgjhfs oc mf`ecjc hgrrfspgj`f co prgmf`eg `f ogs `gs vcogrfs hfjtrcofs.
4>
Oc mf`ecjc fs cqufo vcogr quf `fkc fo hejhufjtc pgr hefjtg `f ogs `ctgs pgr `fdckg y gtrg hejhufjtc pgr fjhemc. Fo usg `f oc mf`ecjc, hgmg mf`e`c `fshreptevc `fo hfjtrg, fs mãs hgjvfjefjtf hucj`g sf `fsfc rf`uher g foemejcr fo fifhtg `f vcogrfs fxtrfmgs fj uj hgjkujtg `f `ctgs. Jgrmcomfjtf sf rfprfsfjtc pgr oc cdrfvecheøj Mf.. Mf ^TGDOFMC TFXVFOPG @ftfrmejcr oc mf`ecjc fj oc seauefjtf sfref gr`fjc`c `f `ctgs; 60, 66, 66, 66, 69, 69, 61, 61, 62, 62, 62, 65, 9>, 9>, 9>, 9> 9>,, 9>, 94, 98, 90, 96, 96, 99, 91, 95, 1>, 1>, 13, 16, 11, 2>
Jûmfrg `f gdsfrvchegjfs = 83 ^gseheøj `fo vcogr hfjtrco = ^39 Mf = 9> ·SVÅX FX OC MG@C7 Fs ujc mf`e`c `f tfj`fjhec hfjtrco quf sf puf`f uscr hucoquefrc sfc oc vcrecdof c fstu`ecr. mg`c `ffsujc sfref Oc `f mg`c `ctgs puf`f fs fo vcogr quf mãs sf rfpetf, irfhufjhecOccdsgoutc mãxemc. sfr ûjehc, puf`c sfr qufcqufo bcyc huyc mãs `f ujc mg`c g quf jg fxestc mg`c. Oc mg`c sf cdrfvec hgmg M`. M`. ^TGDOFMC TFXVFOPG @ftfrmejcr oc mg`c fj oc seauefjtf sfref gr`fjc`c `f `ctgs; 60, 66, 66, 66, 69, 69, 61, 61, 62, 62, 62, 65, 9>, 9>, 9>, 9>, 9>, 9>, 94, 98, 90, 96, 96, 99, 91, 95, 1>, 1>, 13, 16, 11, 2>
M` = 9> 8.8. MF@E@CX @F @EX^FTXEØJ Ocs mf`e`cs `f `espfrseøj sgj; rcjag, vcrecjzc, `fsvecheøj fstãj`cr, frrgr fstãj`cr, vcrecdeoe`c` rfoctevc y hgfiehefjtf `f vcrecheøj `f oc mufstrc2. ·HØMG XF @FIEJF FO TCJAG7 Fo rcjag g cmpoetu` (T (T j) fs oc `eifrfjhec `f vcogrfs fxtrfmgs `f ujc sfref `f `ctgs. Fstf fstc`ístehg pfrmetf mf`er huãjtg sf cofkcj ogs pujtgs fxtrfmgs hgj rfspfhtg c oc mf`ec `f ujc mufstrc. T j = R ee Mãxemc Mãxemc ‘ R e e Míjemc Míjemc
2
. Ogs fstc`ístehgs `f `espfrseøj sf puf`fj hcohuocr uscj`g fo prgarcmc Fxhfo.
43
^TGDOFMC TFXVFOPG Hcohuocr fo rcjag `f ogs `ctgs `f ogjaetu`fs (fj hfjtímftrgs) `f 3> mczgrhcs `f oc vcref`c` C y `f 3> mczgrhcs `f oc vcref`c` D, tgmc`cs co czcr, huygs `ctgs sf ej`ehcj c hgjtejucheøj; Y C = 31, 35, 48, 4>, 46, 32, 43, 44, 44, 40
T j `f Y C = 46 ‘ 31 = 2 hm
YD = 32, 35, 43, 4>, 40, 35, 48, 44, 4>, 43
T j `f YD = 40 ‘ 32 = 9 hm
Xe ogs `ctgs prgvefjfj `f mufstrcs rfprfsfjtctevcs, fjtgjhfs, oc vcref`c` D, huyg rcjag fs `f 9 hfjtímftrgs, prfsfjtc oc mfjgr vcrecheøj fj fo tcmcóg `f ocs mczgrhcs hgmpcrc`c hgj oc vcref`c` C. ·@F SVÅ PTCPC OC YCTECJ[C U HØMG XF HCOHVOC7 Oc vcrecjzc fs ujc mf`e`c `f `espfrseøj quf pfrmetf hgjghfr oc vcrecdeoe`c` `f ujc mufstrc g pgdocheøj, fxprfsc`c fj uje`c`fs huc`rãtehcs. Ocs iørmuocs pcrc hcohuocr oc vcrecjzc sgj ocs seauefjtfs; ∓Re4 - Ψ (Re)4 j
X4 = j‘3
^TGDOFMC TFXVFOPG; Hcohuocr oc vcrecjzc `f ogs `ctgs `f ogjaetu`fs (fj hfjtímftrgs) `f 3> mczgrhcs `f oc vcref`c` C y `f 3> mczgrhcs `f oc vcref`c` D, tgmc`cs co czcr, huygs `ctgs sf ej`ehcj c hgjtejucheøj; Y C = 31, 35, 48, 4>, 46, 32, 43, 44, 44, 40 YD = 32, 35, 43, 4>, 40, 35, 48, 44, 4>, 43 e4 ∓R 4
X YC=
4
- Ψ(R (Re )4 j
(433)4 (31)4+(35)4+(48)4)+(4>)4+(46)4+(32)4+(43)4+(44)4+(44)4+(40)4
3>
= 9,11
3> - 3
j‘3 e 4 ∓R
X YD=
- Ψ(R (Re)4 j =
ΨY C = 433 ΨYD = 4>1
(4>1)4
=
(32)4+(35)4+(43)4)+(4>)4+(40)4+(35)4+(48)4+(44)4+(4>)4+(43)4
3>
= 8,61
3> - 3 j‘3 Oc vcref`c` D tefjf mfjgr vcrecheøj hgmpcrc`c hgj oc vcref`c` C.
44
^TGDOFMC TFXVFOPG Hcohuocr oc vcrecjzc pcrc ogs seauefjtfs `ctgs; Gdsfrvchegjfs 3
^rg`uhheøj fj arcmgs/pocjtc (R) 4>
84 0 6 9 1 2 5
46 49 42 8> 8> 83 88 80 461 42,9
Xumc Mf`ec
R4 0>>
@ctgs;
946 919 120 5>> 5>> 593 3.>25 3.369 1.053
j = 5 Ψ
R = 461 ( Ψ R) R) 4 = (461) 4 = 99>05
Ψ R R 4
= 1053
99>05
1053
-
5
X4
= 364.44/2 = =35.>8 35.>8 2
·SVÅ FX OC @FXYECHEØJ FXPÃJ@CT7 Oc `fsvecheøj fstãj`cr (X) fs oc rcíz huc`rc`c pgsetevc `f oc vcrecjzc (X 4) y fs ujc mf`e`c `f `espfrseøj quf sf fxprfsc fj ocs mesmcs uje`c`fs `f oc vcrecdof fj cjãoeses (leogs, oedrcs, arcmgs, mftrgs, hfjtímftrgs). Mctfmãtehcmfjtf fs oc `estcjhec sgdrf fo fkf `f cdshescs cdshescs `fs`f oc mf`ec bcstc fo pujtg `f ejiofxeøj `f ujc hurvc hurvc jgrmco. Oc vcrecjzc y oc `fsvecheøj fstãj`cr pfrmetfj `fshreder oc `estreduheøj `f oc pgdocheøj y mufstrc fstc`ístehc. Vjc prgpef`c` `f oc `fsvecheøj fstãj`cr, hucj`g sf trctc `f mufstrcs g pgdochegjfs hgj `estreduheøj jgrmco g chcmpcjc`c, fs quf pfrmetf fstemcr oc `estreduheøj prgpgrhegjco `f sus irfhufjhecs. R ³ 3X = 92,41% `f ogs `ctgs R ³ 4X = 56,00 `f ogs `ctgs R ³ 8X = 55,18 `f ogs `ctgs Oc iørmuoc pcrc hcohuocr oc `fsvecheøj `fsv echeøj fstãj`cr fs oc seauefjtf; X = ∛ X
48
^TGDOFMC TFXVFOPG Hcohuocr oc `fsvecheøj fstãj`cr `f ogs `ctgs `f ogjaetu`fs (fj hfjtímftrgs) `f 3> mczgrhcs `f oc vcref`c` C y `f 3> mczgrhcs `f oc vcref`c` D, tgmc`cs co czcr, huygs `ctgs sf ej`ehcj c hgjtejucheøj; Y C = 31, 35, 48, 4>, 46, 32, 43, 44, 44, 40 YD = 32, 35, 43, 4>, 40, 35, 48, 44, 4>, 43
ΨY C = 433 ΨYD = 4>1
X4 YC = 9,11 X4 YD = 8,61
X YC = ∛9,11 = 4,9 hfjtímftrgs X YD =
hfjtímftrgs ∛8,61 = 3,5 hfjtímftrgs
·SVÅ FX FO FTTGF FXPÃJ@CT U HØMG XF HCOHVOC7 HCOHVOC7 Fo frrgr fstãj`cr `f oc mufstrc rfprfsfjtc oc `fsvecheøj fstãj`cr `f ocs mf`ecs y pfrmetf hgjghfr fxchtcmfjtf fo prgdcdof hcmpg `f oghcoezcheøj `f oc mf`ec `f oc pgdocheøj ¶ . pgdocheøj ¶ Hucj`g ogs `ctgs prgvefjfj `f uj hfjsg, fo frrgr fstãj`cr `f oc mf`ec fs eauco c hfrg. Fj uj mufstrfg sefmprf fxestfj frrgrfs fj oc fstemcheøj `f oc mf`ec `f oc mufstrc quf fs uj fstemc`gr fstemc`gr `f oc mf`ec `f oc pgdocheøj. ^gr supufstg, mefjtrcs sfc mãs rfprfsfjtctevc oc mufstrc y mejemehfj ocs `fiehefjhecs fj oc tgmc `f `ctgs, ogs fstemc`grfs `f oc mf`ec ( ¶ ¶ ) y oc vcrecjzc (ψ 4) `f oc pgdocheøj sfrãj mcs fxchtgs. Fo frrgr fstãj`cr sf rfprfsfjtc pgr XR ø sempofmfjtf pgr FF. Oc iørmuoc oc hcohuocr fo frrgr fstãj`cr fs fo seauefjtf; XR =
X
j
^TGDOFMC TFXVFOPG Hcohuocr fo frrgr fstãj`cr pcrc ocs mufstrcs `f 3> mczgrhcs `f oc vcref`c` C y `f 3> mczgrhcs `f oc vcref`c` D, sefj`g oc vcrecdof `f fstu`eg oc ogjaetu` `f ocs mczgrhcs (fj hfjtímftrgs). Y C = 31, 35, 48, 4>, 46, 32, 43, 44, 44, 40 YD = 32, 35, 43, 4>, 40, 35, 48, 44, 4>, 43 XR `f oc vcref`c` C=
4,9
∛3>
ΨY C = 433 X4 YC = 9,11 X YC = 4,9 hm ΨYD = 4>1 X4 YD = 8,61 X YD = 3,5 hm
= >,24 hm
35
XR `f oc vcref`c` D = ∛3> = >,9> hm Fj fstf hcsg, fo tcmcóg `f oc mufstrc fs j = 3>.
40
·SVÅ FX YCTECHEØJ TFOCPEYC7 Oc vcrecheøj rfoctevc fs uj fstc`ístehg quf pfrmetf mf`er oc vcrecdeoe`c` degoøaehc ejtríjsfhc `f ocs mufstrcs g pgdochegjfs vfaftcofs y cjemcofs. Fstf fstc`ístehg fs usc`g pcrc fstu`ecr oc `ejãmehc `f pgdochegjfs, fifhtgs `f pocauehe`cs y sfofhheøj afjåtehc. Oc vcrecheøj rfoctevc sf rfprfsfjtc pgr fo fstc`ístehg YT y y fs oc rfocheøj fjtrf fo frrgr fstãj`cr y oc mf`ec, fxprfsc`c fj pgr hefjtg. Fstc prgpef`c` `f mf`er oc vcrecdeoe`c` ejtríjsfhc fj pgrhfjtckf pgsedeoetc vcogrcr mãs fiehefjtfmfjtf oc vcrecheøj degoøaehc. Y T =
XR R
(3>>)
^TGDOFMC TFXVFOPG Hcohuocr oc vcrecheøj rfoctevc pcrc ocs mufstrcs `f 3> mczgrhcs `f oc vcref`c` C y `f 3> mczgrhcs `f oc vcref`c` D, sefj`g oc vcrecdof `f fstu`eg oc ogjaetu` `f ocs mczgrhcs (fj hfjtímftrgs). Y C = 31, 35, 48, 4>, 46, 32, 43, 44, 44, 40 YD = 32, 35, 43, 4>, 40, 35, 48, 44, 4>, 43 XR `f oc vcref`c` C= >,24 hm XR `f oc vcref`c` D = >,9> hm Pcmcóg `f oc mufstrc j = 3> Oc mf`ec `f oc vcref`c` C = 43,3 hm Oc mf`ec `f oc vcref`c` D = 4>,1 hm YT `f oc vcref`c` C = (>,24)/43,3 = 8,5% YT `f oc vcref`c` D = (>,9>)/4>,1 = 4,5% ·SVÅ FX FO HGFIEHEFJPF @F YCTECHEØJ @F OC MVFXPTC7 Fo hgfiehefjtf `f vcrecheøj (HY) fs uj fstc`ístehg quf pfrmetf fstemcr oc ejtfjse`c` `f oc vcrecheøj aogdco `f uj hcrãhtfr, fj ujc mufstrc `ftfrmejc`c, y sf hcohuoc hgmg oc rfocheøj fjtrf oc `fsvecheøj fstãj`cr (X) y oc mf`ec ( R ), fxprfsc`c fj pgrhefjtg. Oc iørmuoc pcrc hcohuocr fo hgfiehefjtf `f vcrecheøj `f oc mufstrc fs oc seauefjtf;
HY % =
X
. 3>>
R
46
^TGDOFMC TFXVFOPG Hcohuocr fo hgfiehefjtf `f vcrecheøj `f ocs sfrefs `f `ctgs `f ocs mufstrcs C y D; GDXFTYCHEGJFX Mufstrcs
Mf`ec
@fsvecheøj fstãj`cr
Hgfiehefjtf `f vcrecheøj
3
4
8
0
6
9
1
2
5
3>
33
34
C
48
46 46
43
44
48
40
49
45
8>
83
49
41
46,6
8,4>
34,65
D
40
41 41
46
48
49
49
41
42
42
40
48
46
46,6
3,12
1,>>
Ogs `ctgs `f fstf fkfrheheg sgj supufstgs, hgj fo iej `f `fstchcr quf `gs mufstrcs puf`fj tfjfr mf`ecs eaucofs, pfrg `estejtgs fstc`ístehgs `f `espfrseøj. ^TGDOFMC TFXVFOPG Tfsumer fj uj huc`rg ogs fstc`ístehgs `f tfj`fjhec hfjtrco y `f `espfrseøj `f `gs sfrefs `f `ctgs, uscj`g fo prgarcmc Fxhfo. 3 4 8 0 6 9 1 2 5 3> 33 34 38 30 36 39 31 32 35 4> 43
C Gdsfrvchegjfs 3 4 8 0 6 9 1 2 5
D Y C 31 35 48 4> 46 32 43 44 44
H Y D 32 35 43 4> 40 35 48 44 4>
3>
40
43
j
3>
Xumc Mf`ecjc
^rghf`emefjtg fj Fxhfo pcrc hcohuocr ogs fstc`ístehgs `f ocs 3> gdsfrvchegjfs `f Y C
^rghf`emefjtg fj Fxhfo pcrc hcohuocr ogs fstc`ístehgs `f ocs 3> gdsfrvchegjfs `f YD
3>
=HGJPCT(D4;D33)
=HGJPCT(H4;H33)
433
4>1
43,6
4>,6
Mg`c
44
35
Ycogr mãxemg
46
40
Ycogr míjemg
31
32
Tcjag
2
9
Mf`ec
43,3
4>,1
Ycrecjzc
9,11
8,61
=XVMC(D4;D33) =MF@ECJC(D4;D33) =MG@C(D4;D33) =MCR(D4;D33) =MEJ(D4;D33) =D39-D31 =^TGMF@EG(D4;D33) =YCT(D4;D33)
=XVMC(H4;H33) =MF@ECJC(H4;H33) =MG@C(H4;H33) =MCR(H4;H33) =MEJ(H4;H33) =H39-H31 =^TGMF@EG(H4;H33) =YCT(H4;H33)
@fsvecheøj fstãj`cr
4,9
3,5
=@FXYFXP(D4;D33)
=@FXYFXP(H4;H33)
>,24 8,5
>,9> 4,5
=D43/D34Z>,6 =D44/D35*3>>
=H43/H34Z>,6 =H44/H35*3>>
34,8
5,3
=D43/D35*3>>
=H43/H35*3>>
44 Frrgr fstãj`cr 48 Ycrecheøj rfoctevc 40 Hgfiehefjtf `f vcrecheøj
49
^TGDOFMC TFXVFOPG Hgj ogs `ctgs `f ogs prgmf`egs y `f ocs vcrechegjfs rfoctevcs `fo hcrãhtfr prg`uhheøj `f 4> hogjfs `f hciå rgdustc, rfcoezcr ujc sfofhheøj `f cqufoogs `f mãs cotc prg`uhheøj y mãs fstcdofs. Hgmg jg sf `espgjf `f uj hogj tfsteag, sf prghf`f c hcohuocr oc mf`ec `f mf`ecs g mf`ec afjfrc `f oc prg`uhheøj< csí hgmg, oc fo prgmf`eg `f oc vcrecdeoe`c` rfoctevc, y sf bchf fo pocjtfcmefjtg tførehg seauefjtf; • Pg`gs ogs prgmf`egs `f prg`uhheøj, crredc `f oc mf`ec afjfrco (=3.9>6 arcmgs/pocjtc), sf hgjse`frcj `f cotc prg`uhheøj, y `fdckg `f fstf vcogr, `f dckc prg`uhheøj. • Pg`gs ogs vcogrfs `f vcrecheøj rfoctevc (YT) crredc `fo prgmf`eg (=39,3%) sf hgjse`frcj ejfstcdofs g `f cotc vcrecdeoe`c` y pgr `fdckg `f fsf vcogr sf hgjse`frcj fstcdofs g `f dckc vcrecdeoe`c`. • Ejtfrfsc co ejvfsteac`gr e`fjteiehcr ogs hogjfs `f cotc prg`uhheøj y fstcdofs. Jg.
Hogjfs `f hciå rgdustc
^rg`uhheøj (arcmgs hciå hfrfzc/pocjtc) Mf`ec YT
j
3
@H->3
4>
4.104
30,4
4
@H->9
31
3.>06
35
8
@H->1
4>
3.>36
33,9
0
@H-34
4>
4.586
5,3
6
@H-38
4>
3.033
36,8
9
@H-32
4>
3.211
32,4
1
@H-35
4>
3.28>
43,2
2
@H-40
4>
4.39>
31,6
5
@H-46
4>
3.045
34,4
3>
@H-8>
4>
289
4>,9
33
@H-83
4>
38>
03,8
34
@H->4
4>
4.454
2,8
38
@H->6
4>
4.835
5,1
30
@H->2
4>
3.264
5,5
36
@H-33
4>
3.228
1,2
39
@H-30
4>
3.351
39,2
31
@H-31
4>
3.803
34,5
32
@H-4>
4>
016
49,3
35
@H-48
35
3.>68
31,4
4>
@H-49
4> Mf`ec
4.41>
38,4
3.9>0,9
39,3
Fo arãiehg quf sf ej`ehc c hgjtejucheøj sf hgjghf hgmg fo ‟`ecarcmc `f huctrg hfo`cs” y fs muy c`fhuc`g pcrc hocseiehcr vcref`c`fs, hogjfs, bídre`gs u gdkftgs fj dcsf `f `gs hretfregs, hgmg fs fo hcsg `f ocs mf`ecs y vcrecheøj rfoctevc. rfoctevc.
gs hogjfs sfofhhegjc`gs fj dcsf `f ogs hretfregs ej`ehc`gs sgj seftf, quf tefjfj oc jgmfjhocturc seauefjtf; @H>3, @H34, @H49, @H>6, @H>4, @H>2, @H33.
41
0 FXPC@ÍXPEHC EJIFTFJHECO ·HVÃOFX XGJ OGX @EIFTFJHECX FJPTF OC FXPC@ÍXPEHC EJIFTFJHECO U FXPC@ÍXPEHC @FXHTE^PEYC7 Oc fstc`ístehc `fshreptevc prgpgrhegjc ocs bfrrcmefjtcs pcrc hgjghfr ocs hcrchtfrístehcs ctredutgs `f `f ujc og mufstrc pgdocheøj `ftfrmejc`c oc fstc`ístehc ejifrfjheco fs g prfsujheøj quf gprgdcdofmfjtf puf`c yghurrer fj fo hgmpgrtcmefjtg iuturg `f ocs mufstrcs y pgdochegjfs. Xe sf uscj ocs tåhjehcs ûjehcmfjtf pcrc rfujer, gracjezcr y rfprfsfjtcr arãiehcmfjtf ogs `ctgs `f ujc mufstrc g pgdocheøj, fjtgjhfs sf trctc `f oc fstc`ístehc `fshreptevc< se sf uscj ocs tåhjehcs fstc`ístehcs pcrc fstemcr ogs pcrãmftrgs `f ujc pgdocheøj c pcrter `f ujc mufstrc sf fstã fj fo hcmpg `f oc fstc`ístehc ejifrfjheco. Oc fstc`ístehc ejifrfjheco sf dcsc fj `gs arcj`fs peocrfs; oc prgdcdeoe`c` y oc tfgríc `fo mufstrfg. Mufstrfg
MVFXPTC Fstc`ístehgs
Fstc`ístehc `fshreptevc
^GDOCHEØJ
HFJXG
Fstc`ístehc ejifrfjheco
Fstc`ístehc `fshreptevc
^crãmftrgs
+
^rgdcdeoe`c`
0.3. ^TGDCDEOE@C@ ·HVÃO FX FO HGJHF^PG @F ^TGDCDEOE@C@7 Fo hgjhfptg `f prgdcdeoe`c` sf rfochegjc hgj og prgdcdof. Hefrtcmfjtf quf tg`gs ogs `ícs sf fstã irfjtf c prgdcdofs chgjtfhemefjtgs hgmg; fs prgdcdof quf ooufvc bgy c oc tcr`f, fs pgsedof quf oc sfofhheøj pefr`c fo pcrte`g, gkcoã puf`c vfj`fr c dufj prfheg, fjtrf gtrgs. Xf bc hgjvfje`g quf bcy `gs mcjfrcs `f cdgr`cr ocs prgdcdeoe`c`fs; c) oc prgdcdeoe`c` gdkftevc quf trctc `fo jûmfrg `f vfhfs `f ghurrfjhec `f uj suhfsg (irfhufjhec), fxprfsc`g fj pgrhfjtckf (>-3>>) g fj prgpgrheøj (>‘3)< y, d) oc prgdcdeoe`c` sudkftevc quf fs arc`g `f hfrtfzc quf sf tefjf sgdrf oc ghurrfjhec `f uj suhfsg. ·SVÅ FX VJ XVHFXG7 Vj suhfsg fs oc ghurrfjhec `f uj bfhbg, fj uj mgmfjtg `ftfrmejc`g. Fj oc ejvfsteacheøj sf bchfj fxpfremfjtgs `gj`f sgj pgsedofs `evfrsgs rfsuotc`gs. Fo hgjkujtg `f tg`gs ogs rfsuotc`gs pgsedofs hgjstetuyf fo fspcheg mufstrco y sf oocmc suhfsg c ujg `f fsgs rfsuotc`gs.
42
Ogs suhfsgs puf`fj hocseiehcrsf hgmg sfaurgs, prgdcdof f emprgdcdof. Xf oocmc suhfsg sfaurg hucj`g jg bcy jejaujc pgsedeoe`c` `f quf jg ghurrc. Hucj`g jg bcy jejaujc pgsedeoe`c` `f quf uj suhfsg ghurrc sf trctc `f uj suhfsg emprgdcdof. Vj suhfsg prgdcdof fs hucj`g fxestf hefrtc pgsedeoe`c` `f quf suhf`c. Xf puf`fj `estejauer huctrg tepgs `f prgdcdeoe`c` dãsehgs; emprgdcdof, pghg prgdcdof, prgdcdof y muy prgdcdof. prgdcdof. 0.4. BE^ØPFXEX @F EJYFXPEACHEØJ ·HØMG XF IGTMVOC OC BE^ØPFXEX @F EJYFXPEACHEØJ7 Vjc bepøtfses `f ejvfsteacheøj sf `fiejf hgmg uj rfsuotc`g fspfrc`g `f oc cpoehcheøj `f oc tfgríc quf sf fstã prgdcj`g. Fj fstc`ístehc fs fo fjujhec`g chfrhc `f ujc pgdocheøj focdgrc`c hgj fo prgpøsetg `f pgjfrsf c prufdc. ·SVÅ FX VJC ^TVFDC @F BE^ØPFXEX7 Vjc prufdc `f bepøtfses fs fo prghf`emefjtg quf sf dcsc fj fo mufstrfg y fj oc tfgríc `f prgdcdeoe`c` pcrc `ftfrmejcr se oc bepøtfses fs uj fjujhec`g rczgjcdof y `fdf chfptcrsf g se jg fs rczgjcdof `fdf rfhbczcrsf. ·HØMG XF IGTMVOC OC BE^ØPFXEX FXPC@ÍXPEHCX7 Ocs bepøtfses fstc`ístehcs sgj `f `gs tepgs y fxhouyfjtfs fjtrf sí; oc bepøtfses `f juoe`c` y oc bepøtfses cotfrjctevc. Bepøtfses juoc.- fstc fstc bepøtfses fstc`ístehc ej`ehc ej `ehc `eifrfjhecs juocs fjtrf ocs mf`ecs. B> = m3 = m4<
m4 - m3=>
Bepøtfses cotfrjctevc.- fstc bepøtfses fstc`ístehc ej`ehc `fseauco`c` fjtrf ocs mufstrcs. B3 = m3≮m4<
m4 - m3≮>
^gr og tcjtg, se m3≮m4< seajeiehc quf fstc`ístehcmfjtf; m3: m4, ø m3?m4. ·HVÃOFX XGJ OGX ^CXGX ^CTC TFCOE[CT OCX ^TVFDCX FXPC@ÍXPEHCX7 ^crc rfcoezcr ocs prufdcs fstc`ístehcs sf `fdfj humpoer ogs hejhg pcsgs seauefjtfs; Chfptc B> ^ocjtfcr B> y B3
@fiejer jevfo `f seajeiehcheøj c
Xfofhhegjcr oc prufdc fstc`ístehc. Fkfmpog; z
@fiejer rfaoc `f `fheseøj; Xe [ hcohuoc`c : [ >,>6 = 3,59, Tfhbczcr B>
Mufstrfg, cjãoeses `f `ctgs y `fheseøj
Tfhbczc B>
45
0.8.
FOFHHEØJ @F OC ^TVFDC FXPC@ÍXPEHC
·HØMG XF FOEAF OC ^TVFDC FXPC@ÍXPEHC7 Oc fofhheøj `f oc prufdc fstc`ístehc fstã fj iujheøj oc fshcoc `f mf`eheøj `f ocs vcrecdofs, `fo tcmcóg `f oc mufstrc, `f oc igrmc `f `estreduheøj y `f ogs gdkftevgs `fo ejvfsteac`gr. ^crchgjghemefjtg rfsgovfr ogs hefjtíiehg, prgdofmcsbcy `f `eifrfjtfs oc ejvfsteacheøj, prãhtehcmfjtf fj tg`cs ocs rcmcs `fo tåhjehcs fstc`ístehcs jg pcrcmåtrehcs. Fjtrf ocs prufdcs prufdcs pcrcmåtrehcs sf fjhufjtrcj ocs prufdcs `f I y `f t. Fjtrf ocs prufdcs jg pcrcmåtrehcs sf fjhufjtrcj ocs prufdcs dejgmeco y `f Ke-huc`rc`c, oc prgdcdeoe`c` fxchtc `f Iesbfr, fo cjãoeses `f vcrecjzc `f Lruslco & Qcooes, fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj, oc hgrrfocheøj `f rcjags `f Xpfrmcj. Vjc prufdc fstc`ístehc fs ‟dufjc” hucj`g oc prgdcdeoe`c` `f rfhbczcr B > > sefj`g vfr`c`frc fs muy pfqufóc. Fj oc prufdc fstc`ístehc sf `fdfj hgjse`frcr ogs seauefjtfs cspfhtgs; tepgs `f frrgr, pgtfjhec `f oc prufdc, mg`fog fstc`ístehg, fstc`ístehg, jevfo `f seajeiehcheøj, tcmcóg `f mufstrc, `estreduheøj mufstrco, rfaeøj `f rfhbczg y `fheseøj fstc`ístehc. ·@F SVÅ PTCPC OGX PE^GX @F FTTGT FXPC@EXPEHG7 Frrgr fstc`ístehg.- fs fstc`ístehg.- fs ocs `fheseøj fquevghc`c quf tgmc fo ejvfsteac`gr fj rfocheøj c ocs bepøtfses fstc`ístehcs. Ogs frrgrfs fstc`ístehgs puf`fj sfr `f tepg E y tepg EE. Fo frrgr tepg E g E g tepg γ fs fo frrgr quf sf hgmftf hucj`g sf rfhbczc oc bepøtfses juoc (B>) sefj`g åstc vfr`c`frc fj oc pgdocheøj. Fstf frrgr E sf hgmftf hucj`g fo ejvfsteac`gr hgjhouyf uj fstu`eg `f oc seauefjtf mcjfrc; ‟ .. C pfscr `f jg bcdfr `eifrfjhecs fstc`ístehcs seajeiehctevcs, fo trctcmefjtg C iuf supfregr mctfmãtehcmfjtf…”. Fo frrgr tepg EE g tepg tepg δ sf hgmftf hucj`g jg sf rfhbczc oc bepøtfses juoc (B >) sefj`g åstc icosc fj oc pgdocheøj. @fdf fjictezcrsf quf fs fo ejvfsteac`gr quefj iekc ocs prgdcdeoe`c`fs `f fquevghcrsf fj oc tgmc `f `fhesegjfs fstc`ístehcs. @fheseøj Chfptcr B> Tfhbczcr B>
Xetucheøj rfco fj oc pgdocheøj B> Yfr`c`frc B> Icosc Jg bcy frrgr fstc`ístehg Frrgr tepg E; γ
Frrgr tepg EE; δ Jg bcy frrgr fstc`ístehg 8>
^TGDOFMC TFXVFOPG Vj bídre`g ejtrg`uhe`g `f mcíz (M) fs supfregr fj rfj`emefjtg hgmpcrc`g hgj tg`gs ogs bídre`gs oghcofs (setucheøj rfco). Xf fkfhutc ujc prufdc `f bídre`gs hgmpcrcj`g fo bídre`g ejtrg`uhe`g hgj `gs bídre`gs oghcofs (C y D) fj ujc sgoc oghcoe`c`. Ocs bepøtfses fstc`ístehcs pocjtfc`cs sgj; Bepøtfses juoc (B > > ); bídre`g ejtrg`uhe`g M = bídre`g oghco C = bídre`g oghco D. Bepøtfses cotfrjc (B 3 bídre`g fs fstc fstc`ístehcmfjtf `ístehcmfjtf ` `eifrfjtf. eifrfjtf. 3 ); Co mfjgs uj bídre`g
Oc prufdc `f bídre`gs puf`f crrgkcr vcregs rfsuotc`gs prgdcdofs hgmg; M=C=D, M:C=D, M=C:D, M:C:D, M=C?D, M?C=D, M?C?D. Xupøjacsf quf fo rfsuotc`g `fo fxpfremfjtg sfc; M=C=D M=C=D Tfhbczcr B>
Xetucheøj rfco; M:C,D B> Yfr`c`frc B> Icosc Frrgr tepg EE; δ Jg bcy frrgr fstc`ístehg Frrgr tepg E; γ
Jg bcy frrgr fstc`ístehg
Fj fstf hcsg, sf fstã chfptcj`g oc bepøtfses juoc (B>) hucj`g fj rfcoe`c` fs icosc< pgr og tcjtg, sf bc hgmfte`g uj frrgr tepg EE. Bcy oc tfj`fjhec c hgmftfr fstf tepg `f frrgr hucj`g jg bc bcde`g suiehefjtf jûmfrg `f rfpftehegjfs fj fo fjscyg g hucj`g sf prftfj`f tgmcr `fhesegjfs hgj uj fjscyg fj ujc sgoc oghcoe`c`. Oc prufdc `f bídre`gs `fdf hudrer uj `gmejeg `f rfhgmfj`cheøj pcrc tfjfr oc hfrtfzc fj ocs `fhesegjfs. ·C SVF XF TFIEFTF OC ^GPFJHEC @F VJC ^TVFDC7 ^gtfjhec `f ujc prufdc ..-- fs fo arc`g `f hgjiecdeoe`c` fj oc `fheseøj fstc`ístehc. Fxprfsc oc prgdcdeoe`c` `f rfhbczcr B > > hucj`g hucj`g fs rfcomfjtf icosc. ^gtfjhec = 3 ‘ δ Oc pgtfjhec `f ujc prufdc fstc`ístehc sf ejhrfmfjtc co cumfjtcr fo tcmcóg `f oc mufstrc (j). ·@F SVF PTCPC FO MG@FOG FXPC@EXPEHG7 Mg`fog fstc`ístehg fs oc rfprfsfjtcheøj `f uj ifjømfjg degoøaehg quf sf hgjstruyf hgjse`frcj`g oc jcturcofzc `f oc pgdocheøj, fo måtg`g `f mufstrfg, fo
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tcmcóg `f oc mufstrc y oc fshcoc `f mf`eheøj. Fo mg`fog fstc`ístehg sf csghec hgj ocs prufdcs pcrcmåtrehcs g jg pcrcmåtrehcs mãs c`fhuc`cs sfaûj hc`c hcsg. ·@F SVF PTCPC FO JEYFO @F XEAJEIEHCHEØJ7 Fo jevfo `f seajeiehcheøj fj ocs prufdcs fstc`ístehcs pcrcmåtrehcs y jg pcrcmåtrehcs sf `fiejf hgmg oc prgdcdeoe`c` `f sf fquevghcrsf oc tgmc `f ujc fstc`ístehc. Fo jevfo `f seajeiehcheøj rfprfsfjtc rfprfsfjtcfj hgj fo símdgog símdgog coic. coic`fheseøj . Fstc prgdcdeoe`c` coic (γ) sf `ftfrmejc fj fo mgmfjtg `f oc pocjfcheøj `fo fxpfremfjtg. • • •
Fj oc carehuoturc sf hgjse`frc cprgpec`g uj jevfo `f seajeiehcheøj `fo 3% y 6%, og quf fquevcof co 55% y 56% `f hgjiecjzc, rfspfhtevcmfjtf. Fj fjscygs `f vcoe`cheøj `f tfhjgogaícs sf chfptc bcstc uj 3>% `f jevfo `f seajeiehcheøj. Fstg seajeiehc oc prgdcdeoe`c` `f fquevghcrsf fj bcstc uj 3>%, og quf fquevcof c ujc hgjiecjzc `fo 5> pgr hefjtg. Hefrtcmfjtf, se sf prgdcrcj mf`ehcmfjtgs pcrc sfrfs bumcjgs sf chfptcríc uj jevfo `f seajeiehcheøj `f 3/3>>.>>>.
·C SVF XF TFIEFTF FO PCMCÓG @F MVFXPTC7 Fo tcmcóg `f mufstrc sf rfiefrf co jûmfrg `f gdsfrvchegjfs quf sf ejhouyfj fj fo fstu`eg. Hucj`g fo tcmcóg `f mufstrc sf ejhrfmfjtc, bcy ujc mcygr cprgxemcheøj c oc `estreduheøj jgrmco. Fj mufstrcs `f tcmcóg pfqufóg hgmg j=9, sgog sgj cpoehcdofs ocs tåhjehcs jg pcrcmåtrehcs. ^crc oc `ftfrmejcheøj `fo tcmcóg `f mufstrc fs hgjvfjefjtf tgmcr fj hgjse`frcheøj ogs seauefjtfs cspfhtgs; • • • •
Hucj`g fo tcmcóg `f oc mufstrc (j) fs pfqufóg, ocs prufdcs jg pcrcmåtrehcs rfsuotcj mãs hgjiecdofs Hucj`g fo tcmcóg `f mufstrc (j) fs arcj`f sf puf`fj cpoehcr ocs tåhjehcs pcrcmåtrehcs y jg pcrcmåtrehcs Fo tcmcóg `f mufstrc (j) `fpfj`f `f oc vcrecheøj degoøaehc ^crc uj c`fhuc`g cjãoeses fstc`ístehg fs prfhesg trcdckcr hgj fo tcmcóg øptemg `f mufstrc pcrc hc`c vcrecdof.
·@F SVF PTCPC OC @EXPTEDVHEØJ MVFXPTCO7 Oc `estreduheøj mufstrco fs oc rfprfsfjtcheøj arãiehc `f oc rfocheøj fjtrf ogs `ctgs `f ujc vcrecdof y fo jûmfrg `f ej`eve`ugs quf hgjigrmcj oc mufstrc g pgdocheøj. Oc `estreduheøj mufstrco sf csghec hgj oc jcturcofzc `f oc pgdocheøj, oc vcrecdeoe`c` degoøaehc, oc fshcoc `f mf`eheøj y fo tcmcóg `f mufstrc. Ocs `estreduhegjfs puf`fj sfr; jgrmco g `eifrfjtfs `f oc jgrmco. Hucj`g ujc vcrecdof fstã `estredue`c jgrmcomfjtf oc mf`ec, oc mg`c y mf`ec tefj`fj c hgejhe`er. Fj ujc sfref `f `ctgs hucjtetctevgs tgmc`gs cofctgrecmfjtf sf hgjstctc oc tfj`fjhec c hgjigrmcr ujc hurvc `f hcmpcjc g `estreduheøj jgrmc jgrmco.o. Ocs
84
`estreduhegjfs `eifrfjtfs `f oc jgrmco puf`fj ghurrer `fde`g c uj tcmcóg `f mufstrc rf`uhe`g, c oc icotc `f cofctgref`c` fj oc mufstrc g c oc jcturcofzc `f oc pgdocheøj. Xe j fs rf`uhe`g y sf `fshgjghf oc igrmc `f `estreduheøj mufstrco, ocs tåhjehcs jg pcrcmåtrehcs rfsuotcj mãs hgjiecdofs. 0.0. @EXPTEDVHEGJFX @F ^TGDCDEOE@C@ ·HØMG XF HOCXEIEHCJ OCX @EXPTEDVHEGJFX @F ^TGDCDEOE@C@ 5 XFAÛJ OC JCPVTCOF[C @F OC ^GDOCHEØJ7 Ocs `estreduhegjfs `f prgdcdeoe`c`, fj iujheøj `f oc jcturcofzc `f oc pgdocheøj, sf carupcj `estreduhegjfs `f vcrecdofs `eshrftcs y `estreduhegjfs `f vcrecdofs hgjtejucs. @estreduheøj `f vcrecdof `eshrftc.`eshrftc.- fs cqufooc huyc iujheøj `f prgdcdeoe`c` tgmc vcogrfs pgsetevgs fj uj hgjkujtg `f vcogrfs `f R iejetg g ejiejetg jumfrcdof. Ocs `estreduhegjfs `f vcrecdofs `eshrftcs sgj; dejgmeco, dejgmeco jfactevc, ^gessgj, afgmåtrehc, bepfrafgmåtrehc, `f Dfrjguooe y ujeigrmf. Fj fo prfsfjtf prfsfjtf `ghumfjtg sf trctc `f oc `estreduheøj dejgmeco, hgjse`frcj`g su cpoehcdeoe`c` c muhbgs ifjømfjgs degoøaehgs y sghecofs. @estreduhegjfs `f vcrecdof hgjtejuc.hgjtejuc.- fs cqufooc quf puf`f tgmcr hucoquefrc `f ogs ejiejetgs vcogrfs fxestfjtfs `fjtrg `f uj ejtfrvcog. Ocs `estreduhegjfs `f vcrecdofs hgjtejucs mãs hgmujfs sgj; jgrmco, Ke-huc`rc`g, fxpgjfjheco, t `f Xtu`fjt, Acmmc, Dftc y I. ·C SVÅ XF TFIEFTF OC @EXPTEDVHEØJ DEJGMECO7 Oc `estreduheøj dejgmeco fs ujc `estreduheøj `f prgdcdeoe`c` `eshrftc quf pfrmetf `ftfrmejcr fo jûmfrg `f åxetgs fj ujc sfhufjhec `f j fjscygs fjscygs hgj ujc prgdcdeoe`c` p `f ghurrfjhec fj ogs fjscygs, fjtrf > y 3. Xf hcrchtfrezc hcrchtfrezc pgr sfr `ehgtømehg, fs `fher, sgog fxestfj `gs rfsuotc`gs pgsedofs p y q . @gj`f p fs oc prgdcdeoe`c` `f ghurrfjhec (3-q) (3-q) y y q fs fs oc prgdcdeoe`c` `f irchcsg (3-p)< pgr og tcjtg, p + q = 3 Ogs pcrãmftrgs dãsehgs sgj; • • • •
j:>< uj jûmfrg fjtfrg quf sf rfiefrf co jûmfrg `f fjscygs. Oc mf`ec fs eauco c jp Oc mg`c fs eauco c \(j+3)(p)] c \(j+3)(p)] Oc vcrecjzc fs eauco c jp(3-p)
5
. bttp;//www.um.fs/ddmde/Cyu`cs@ghfjtfs/dEGrgm@EXHG/hgjtfje`g/VED/degejig/ej`fx.btm bttp;//www.um.fs/ddmde/Cyu`cs@ghfjtfs/dEGrgm@EXHG/hgjtfje`g/VED/degejig/ej`fx.btm
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·@F SVÅ PTCPC OC @EXPTEDVHEØJ JGTMCO7 Oc `estreduheøj jgrmco fs oc `f mcygr empgrtcjhec y cpoehcdeoe`c` fj oc fstc`ístehc. Vjc sfref `f `ctgs R, `f pcrãmftrgs ¶ y ψ4, tefjf `estreduheøj hgj iujheøj `f `fjse`c` i(x) . Fo arãiehg `f oc iujheøj iujheøj `f `fjse`c` jgrmco tefjf igrmc `f hcmpcjc hgj fkf `f semftríc fj; x = ¶ y pujtgs `f ejiofxeøj fj
x
= ¶ + ψ y x = ¶ - ψ.
i (x)
¶-ψ
¶
¶+ψ
Fj fstc `estreduheøj, ¶ ej`ehc oc pgseheøj hfjtrco `f oc hurvc y ψ fs fo pcrãmftrg `f `espfrseøj. Hucj`g `fsvecheøj fstãj`cr (ψ) tefjf `eifrfjtfs vcogrfs y oc mf`ec ¶ pfrmcjfhf hgjstcjtf, setucheøj quf puf`f gdsfrvcrsf hucj`g sf fvcoûcj `estejtg tcmcógs `f mufstrc, fj ujc mesmc pgdocheøj, fo arãiehg `f oc hurvc jgrmco c`quefrf `eifrfjtfs igrmcs; pocjehûrtehc hucj`g tefj`f c sfr cpocjc`c y ofptghûrtehc hucj`g tefj`f c tfrmejcr fj uj pujtc cauc`c.
Ofptghûrtehc
^ocjehûrtehc
Hcdf `fstchcr quf ogs `ctgs `f hucoquefr `estreduheøj jgrmco 3> puf`fj hgjvfrtersf fj vcogrfs z mf`ecjtf oc iørmuoc; x - ¶ ¶ [=
x - x [ =
ψ
X
Fj ujc hurvc jgrmco, oc mf`ec `f ogs vcogrfs [ fs eauco c hfrg. Fo ãrfc tgtco dckg oc hurvc jgrmco fs eauco c 3 y y fo ãrfc dckg oc hurvc fjtrf `gs vcogrfs `c`gs `f [ fs eauco c oc prgpgrheøj `f oc pgdocheøj rfochegjc`c hgj ogs vcogrfs prfshretgs `f [.
3>
. @ctgs `f irfhufjhecs hgj ogs quf sf hgjstruyf uj bestgarcmc.
80
·SVÅ FX OC TFAEØJ @F TFHBC[G7 TFHBC[G7 Oc rfaeøj `f rfhbczg fs ujc sfhheøj `f oc `estreduheøj mufstrco quf ejhouyf tg`gs ogs vcogrfs pgsedofs quf ujc prufdc fstc`ístehc puf`c tgmcr hgjigrmf c B>. • • • • • • •
• •
Oc prgdcdeoe`c` p prgdcdeoe`c` p csghec`c csghec`c hgj hucoquefr vcogr `f oc rfaeøj `f rfhbczg fs eauco γ (jevfo `f seajeiehcheøj). gFo mfjgr tcmcógquf `f oc rfaeøj `f rfhbczg sf fxprfsc pgr γ. Xe γ=>,>6 seajeiehc quf fo 6% `fo ãrfc tgtco dckg oc hurvc `f oc `estreduheøj mufstrco hgrrfspgj`f c oc rfaeøj `f rfhbczg. Ocs rfaegjfs `f rfhbczg fstãj csghec`cs c ocs prufdcs `f ujc g `f `gs hgocs. Fj oc prufdc `f ujc hgoc, oc rfaeøj `f rfhbczg, `fieje`c pgr γ, sf udehc sgog co uj fxtrfmg `f oc hurvc. Oc prufdc `f ujc hgoc sf usc hucj`g fo ejvfsteac`gr tefjf ujc hocrc ejhoejcheøj pgr uj rfsuotc`g. ^gr fkfmpog; Fo mfkgr ejsfhtehe`c pcrc fo hgjtrgo `fo hgagoofrg fs ‟EJ”. Fj oc prufdc `f `gs hgocs, oc rfaeøj `f rfhbczg fstã `fieje`c pgr γ /4< fs `fher se γ=>,>6, fstcrãj `estredue`cs 4,6% fj fo fxtrfmg `f oc hgoc `frfhbc y 4,6%
fj fo fxtrfmg `f oc hgoc ezquefr`c `f oc hurvc tførehc `f oc `estreduheøj mufstrco. Oc prufdc `f `gs hgocs fs oc mãs usc`c fj ogs fjscygs y sf cpoehc hucj`g jg bcy prfifrfjhecs `fo ejvfsteac`gr pgr uj rfsuotc`g. Ocs `fhesegjfs fstc`ístehcs sf tgmcj fj dcsf `f oc udehcheøj `f p `f p rfspfhtg rfspfhtg `fo jevfo `f seajeiehcheøj γ prffofae`g. ^rufdc `f ujc hgoc Jevfo `f seajeiehcheøj iekc`g pgr fo ejvfsteac`gr
Jevfo `f seajeiehcheøj iekc`g pgr fo ejvfsteac`gr
B>; m3 ≮ m4 cc
p ^rgdcdeoe`c` gdtfje`c fj fo fxpfremfjtg
B>; m3 = m4 p
cc
^rgdcdeoe`c` gdtfje`c fj fo fxpfremfjtg
86
^rufdc `f `gs hgocs
Tfaeøj `f rfhbczg `f B >
Tfaeøj `f chfptcheøj `f B > (3 ‘ c
Tfaeøj `f rfhbczg `f B>
4
4
c c/ /
c c/ /
Ogs cspfhtgs fsfjhecofs pcrc ejtfrprftcr γ y p y p sgj; sgj; •
γ fs uj jûmfrg pfqufóg (jevfo `f seajeiehcheøj) iekc`g hgmg prgdcdeoe`c` `f
•
fquevghcrsf fj oc tgmc `f `fhesegjfs fstc`ístehcs. γ fs oc prgdcdeoe`c` `f rfhbczcr rfhbczcr B> hucj`g fs hefrtc
••
•
γ sf hgjghf tg`g Hgjghe`g hrítehc. p fs oc prgdcdeoe`c` quf sgdrf tfj`rícoc rfaeøj oc rfaeøj hrítehc c pcrter `fo fstc`ístehg gdtfje`g `f oc mufstrc y sgog sf hgjghf `fspuås `f rfcoezcr fo fxpfremfjtg Hgjghe`g p Hgjghe`g p sf sf hgjghf tg`g sgdrf fo rfsuotc`g `fo fxpfremfjtg.
·@F SVÅ PTCPC OC @FHEXEØJ FXPC@ÍXPEHC7 Xe oc prufdc fstc`ístehc `c uj vcogr p vcogr p quf sf udehc `fjtrg `f oc rfaeøj `f rfhbczg, fjtgjhfs sf rfhbczc oc bepøtfses `f juoe`c` B> = m 3 = m 4< pgr og tcjtg, sf chfptc oc bepøtfses cotfrjctevc B3 = m3≮m4 quf ej`ehc `fseauco`c` fjtrf ocs mufstrcs. m ufstrcs. Xe sf rfhbczc B > >; sf chfptc B 3 Xe sf chfptc B > > ; sf rfhbczc B 3
C pcrter `f åstc ejigrmcheøj sf tgmc oc `fheseøj fstc`ístehc ‟chfptcr” g ‟jg chfptcr” oc bepøtfses `f ejvfsteacheøj.
quf hgjsestf fj
0.6. ^TVFDCX FXPC@ÍXPEHCX 0.6.3. ^TVFDC DEJGMECO ·SVÅ FX OC ^TVFDC DEJGMECO U HVCJ@G VXCTOC7 Bcy pgdochegjfs quf sf hgjhedf hgjigrmc`cs pgr `gs hocsfs; mcshuoejg y ifmfjejg, scjg y fjifrmg, fjtrf gtrcs, `gj`f tg`cs ocs gdsfrvchegjfs pgsedofs `f oc pgdocheøj hcfj `fjtrg `f ujc `f ocs `gs hctfagrícs g hocsfs. Fj hucoquefr pgdocheøj `f `gs hocsfs, oc prgpgrheøj fj ujc hocsf fs p y y oc gtrc prgpgrheøj fs 3 ‘ p , quf sf e`fjteiehc hgj oc oftrc q . Oc prgpgrheøj `f p
89
puf`f vcrecr `f pgdocheøj fj pgdocheøj pfrg fs iekc fj ujc pgdocheøj pcrtehuocr. Oc prgdcdeoe`c` `f gdtfjfr R gdkftgs fj ujc hctfagríc y j ‘ R gdkftgs fj oc gtrc, fstã `c`c pgr; p(x) =
j x
j!
px .
x
j-x
p(x) = (Re)! (j-Re)!(p) (q)
qj-x
Hucj`g p=>,6< q = (3-p) = >,6 y hgj vcogrfs `f j?46, j?46, sf puf`f uscr uscr oc tcdoc `f prgdcdeoe`c`fs dejgmeco pcrc gdtfjfr `erfhtcmfjtf p(x). ^TGDOFMC TFXVFOPG Fj ujc fmprfsc cargej`ustreco, sf icdrehc uj `ftfrmejc`g prg`uhtg fmpcquftc`g. Bestørehcmfjtf sf bc gdtfje`g uj prgmf`eg `fo 6% pcquftfs iufrc `fo fstãj`cr; fstãj`cr; pfsg jftg 4>> ³ 6 arcmgs. @ftfrmejcr oc prgdcdeoe`c` `f quf co tgmcr co czcr, fj uj `íc ocdgrcdof, c) Vj pcquftf fstf iufrc `fo fstãj`cr< y, d) Hejhg pcquftfs fståj `fjtrg `fo fstãj`cr •
^rgdcdeoe`c` `f fjhgjtrcr uj pcquftf fstf iufrc `fo fstãj`cr j = 6 jûmfrg `f pcquftfs tgmc`gs co czcr R= 3 jûmfrg `f pcquftfs iufrc `fo fstãj`cr. Oc prgdcdeoe`c` `f quf uj pcquftf fstå iufrc `fo fstãj`cr fs p=>,>6. Oc prgdcdeoe`c` `f quf uj pcquftf fstå `fjtrg `fo fstãj`cr fs q=>,56 ^gr og tcjtg; 3 6 p(x=3) = 3 (>,>6) > 56
6!
p(x=3) = (3)! (6-3)! p(x=3) =
34> (3) (40)
6-3
3
0
(>,>6) (>,56) (>,>6)(>,2306)
p(x=3) = >.4>89 ≂ 4>.89% Oc prgdcdeoe`c` `f fjhgjtrcr 3 pcquftf iufrc `fo fstãj`cr, fj ujc mufstrc `f 6, fs `fo 4>, 0 pgr hefjtg. •
Hejhg pcquftfs fståj `fjtrg `fo fstãj`cr j = 6 jûmfrg `f pcquftfs tgmc`gs co czcr R = > jûmfrg `f pcquftfs iufrc `fo fstãj`cr. Oc prgdcdeoe`c` `f quf uj pcquftf fstå iufrc `fo fstãj`cr fs p=>,>6. Oc prgdcdeoe`c` `f quf uj pcquftf fstå `fjtrg `fo fstãj`cr fs q=>,56
81
p(x=>) =
p(x=>) = p(x=>) =
6 >
(>,>6) > > 56 6!
(>)! (6)! 34> (3) (34>)
6->
(3)(>,56)6 (3)(>,56)6
^(R=>) = >,1182 ≂ 11,82% Oc prgdcdeoe`c` `f quf bcyc hfrg pcquftfs iufrc `fo fstãj`cr, fj ujc mufstrc `f 6, fs `fo 11, 0 pgr hefjtg. ^TGDOFMC TFXVFOPG Fj mesmc pocjtc cargej`ustreco, mcjtfjefj`g ocs prgdcdeoe`c`fs p y q, tgmcj`g co czcr 3> pcquftfs `fo prg`uhtg, ·huão sfríc oc prgdcdeoe`c` `f fjhgjtrcr uj fmpcquf iufrc `fo fstãj`cr; pfsg jftg = 4>> ³ 6 arcmgs7. j = 3> jûmfrg `f pcquftfs pcquftfs tgmc`gs co czcr R = 3 jûmfrg `f pcquftfs iufrc `fo fstãj`cr. Oc prgdcdeoe`c` `f quf uj pcquftf fstå iufrc `fo fstãj`cr fs p=>,>6. Oc prgdcdeoe`c` `f quf uj pcquftf fstå `fjtrg `fo fstãj`cr fs q=>,56 ^gr og tcjtg; p(x=3) = p(x=3) =
3> 3
(>,>6) 3 > 56 89422>> (3) (89422>)
3>-3
(>,>6)3(>,56)5
p(x=3) = >,8363 ≂ 84% Oc prgdcdeoe`c` `f fjhgjtrcr uj pcquftf iufrc `fo fstãj`cr, fj ujc mufstrc `f 3>, fs `fo 84 pgr hefjtg. ^TGDOFMC TFXVFOPG Vscj`g fo prgarcmc Fxhfo, hcohuocr ocs prgdcdeoe`c`fs `f fjhgjtrcr R pcquftfs iufrc `fo fstãj`cr, fj fjscygs j=6 y j=3>, hucj`g p=>,>6. Fo hãohuog hãohuog `f prgdcdeoe`c`fs sf rfcoezc hgj oc iujheøj `estreduheøj `estreduheøj dejgmeco. Fj oc tcdoc seauefjtf sf fxpgjf fo prghfsg.
82
Tfsuotc`g;
Oc prufdc dejgmeco sf rfcoezc uscj`g oc iujheøj
[email protected](jûmfrg `f åxetgs, fjscygs g mufstrc, prgdcdeoe`c` p prgdcdeoe`c` p y y uj vcogr oøaehg rfochegjc`g hgj fo chumuoc`g). 0.6.4. ^TVFDC @F KE HVC@TC@G Oc prufdc ρ´, ρ´, prgjujhec`c hgmg "ke-huc`rc`g", pfrmetf mf`er oc `eshrfpcjhec fjtrf uj vcogr gdsfrvc`g y uj vcogr tførehg fspfrc`g, ej`ehcj`g ocs `eifrfjhecs fjtrf cmdcs, fj hcsg `f fxester, c hcusc `fo czcr. Fstc bfrrcmefjtc `f oc fstc`ístehc jg pcrcmåtrehc, fs usc`c fspfhecomfjtf pcrc fo cjãoeses `f hgjtfgs (vcrecdofs `eshrftcs). Oc iørmuoc afjfrco pcrc hcohuocr ‟ke-huc`rc`g” fs oc seauefjtf; 4
4
R =
Ψ
@gj`f;
(G ‘ F) F
R4 = Fstc`ístehg Ke Huc`rc`g G = Ycogr gdsfrvc`g F = Ycogr fspfrc`g ^crc fo usg `f oc prufdc R4, sf rfhgmefj`c ocs seauefjtfs rfaocs; • • •
Hucj`g mcygr sfc fo tcmcóg `f oc mufstrc, mãs fstrfhbc sfrã oc hgejhe`fjhec fjtrf ocs `estreduhegjfs; jgrmco y Ke-huc`rc`g. Jg sf `fdf fmpofcr oc prufdc R4 se oc mfjgr hocsf fspfrc`c fs ejifregr c^uf`f 6, fspfhecomfjtf hucj`g ogs arc`gs oedfrtc`cao=3. ejhrfmfjtcrsf fo tcmcóg `f oc`fmufstrc iej `f fofvcr fo vcogr mãs pfqufóg fspfrc`g. 85
• • •
Vteoíhfsf oc hgrrfhheøj `f Uctfs pcrc `ftfrmejcr oc Ke-Huc`rc`g (R4) hucj`g sf tefjf uj sgog arc`g `f oedfrtc`. Oc prufdc `f Ke-Huc`rc`g tcmdeåj sf usc pcrc prgdcr oc bepøtfses `f ej`fpfj`fjhec fjtrf vcrecdofs hgj cpgyg `f ogs vcogrfs tcduocrfs `f R4. Vjc oemetcheøj empgrtcjtf `f fstc prufdc fs su ejsfjsedeoe`c` c ogs fifhtgs `f gr`fj.
^TGDOFMC TFXVFOPG Fj ujc pocjtcheøj `f hchcg sf fvcoûc fo fifhtg `f uj mehrggracjesmg dfjåiehg y sf oofac c ogs seauefjtfs rfsuotc`gs; @ctgs; Mczgrhcs scjcs (+)
Mczgrhcs fjifrmcs (-)
Pgtco
Prctc`cs hgj fo mehrggracjesmg
8>
6
86
Jg trctc`cs
4>
34
84
Pgtco
6>
31
91
Tfsuotc`g; Hãohuog `f ogs vcogrfs tførehgs `fo huc`rg `f hgjtejafjhec 4 x 4
Mczgrhcs scjcs (+)
Mczgrhcs fjifrmcs (-)
Pgtco
Prctc`cs hgj fo mehrggracjesmg
C
D
(C+D)
Jg trctc`cs
H
@
(H+@)
Pgtco
(C+H)
(D+@)
J
0>
Hãohuog `f ogs vcogrfs fspfrc`gs fj dcsf `f ogs `ctgs gdsfrvc`gs gdsfrvc`gs Mczgrhcs scjcs (+)
Mczgrhcs fjifrmcs (-)
Pgtco
Prctc`cs hgj fo mehrggracjesmg
(C+H)(C+D)/J
(D+@)(C+D)/J
(C+D)
Jg trctc`cs
(C+H)(H+@)/J
(D+@)(H+@)/J
(H+@)
Pgtco
(C+H)
(D+@)
J
Mczgrhcs scjcs (+)
Mczgrhcs fjifrmcs (-)
Pgtco
Prctc`cs hgj fo mehrggracjesmg
(6>)(86)/91 =49
(31)(86)/91= 5
86
Jg trctc`cs
(6>)(84)/91=40
(31)(84)/91=2
84
Pgtco
6>
31
91
^gr og tcjtg, ogs vcogrfs fspfrc`gs sgj;
Igrmuocheøj `f oc bepøtfses fstc`ístehc B>; Bcy ej`fpfj`fjhec fjtrf fo trctcmefjtg hgj mehrggracjesmgs y oc prfsfjhec `f mczgrhcs scjcs. Jg fxestf csghecheøj csghecheøj fjtrf fo trctcmefjtg hgj mehrggracjesmgs y oc prfsfjhec `f mczgrhcs scjcs `f hchcg. m3 = m4 B3; Xe fxestf csghecheøj fjtrf fo trctcmefjtg hgj mehrggracjesmgs y oc prfsfjhec `f mczgrhcs scjcs `f hchcg. Fo mcygr jûmfrg `f mczgrhcs scjcs sf `fdf co trctcmefjtg hgj mehrggracjesmgs. Oc hcjte`c` `f mczgrhcs scjcs fs `eifrfjtf `f oc prgpgrheøj `f mczgrhcs fjifrmcs. m3≮ m4 @eifrfjhec fjtrf vcogrfs gdsfrvc`gs y fspfrc`gs (G - F) Mczgrhcs scjcs (+) = 8> Prctc`cs hgj fo G mehrggracjesmg FG =- F49=+0 Jg trctc`cs
G = 4> F = 40 G - F = -0
Mczgrhcs fjifrmcs (-) G=6 F=5 G - F = -0 G = 34 F=2 G - F = +0
Jgtc; Oc sumc `f ocs `eifrfjhecs `fdf sfr eauco c hfrg
Ogs arc`gs `f oedfrtc` fstãj `c`gs pgr; ao = (hgoumjcs - 3)(beofrcs - 3). ^gr og tcjtg, fj oc tcdoc `f hgjtejafjhec 4 x 4, `fo prfsfjtf fkfrheheg; ao=3. Xfaûj oc rfaoc, hucj`g sf tefjf ao=3, sf `fdf prghf`fr c oc hgrrfhheøj `f Uctfs, fj oc iørmuoc afjfrco.
03
Ckustf `f oc iørmuoc `f Ke-Huc`rc`g hgj oc hgrrfhheøj `f yctfs
R4
=
Ψ
\(G ‘ F) - >.6] >.6]4 F
^gr og tcjtg; R4= (8.6)4 /49 + (8,6)4 /5 + (8,6)4 /40 + (8,6)4 /2 R4= >,013 + 3,89 + >,63 + 3,68 = 8,213* R4(>,>6)(ao=3) = 8,20 R4hcohuoc`g = 8,213: R4(>,>6)(ao=3) = 8,20 @fheseøj; Xf rfhbczc B> y sf chfptc oc B3; Xe fxestf csghecheøj fjtrf fo trctcmefjtg hgj mehrggracjesmgs y oc prfsfjhec `f mczgrhcs scjcs `f hchcg. Fo mcygr jûmfrg `f mczgrhcs scjcs sf `fdf co trctcmefjtg hgj mehrggracjesmgs co jevfo `f seajeiehcheøj `fo 6%. ^TGDOFMC TFXVFOPG Vscj`g ogs `ctgs `f oc prufdc `f Ke Huc`rc`g, hgj fo prgarcmc Fxhfo, `ftfrmejcr oc prgdcdeoe`c` `f csghecheøj fjtrf fo trctcmefjtg hgj mehrggracjesmgs y fo jûmfrg `f mczgrhcs scjcs fj hchcg.
Oc prufdc `f Ke huc`rc`g, fj Fxhfo, pfrmetf `ftfrmejcr quf fxestf csghecheøj fjtrf fo trctcmefjtg hgj mehrggracjesmgs y oc prfsfjhec `f mczgrhcs scjcs `f hchcg, hgj ujc hgjiecjzc `fo 51,66%. 51,66%. Fstf vcogr rfsuotc `f oc `eifrfjhec fjtrf (3 - >,>406) x 3>>. Fo mcygr jûmfrg `f mczgrhcs scjcs sf `fdf co trctcmefjtg hgj mehrggracjesmgs co jevfo `f seajeiehcheøj `fo 4,6 pgr hefjtg.
04
^TGDOFMC TFXVFOPG Arfagreg Mfj`fo, fj uj fxpfremfjtg hgj auescjtfs gdsfrvø quf 836 arcjgs frcj rf`gj`gs y cmcreoogs, 3>2 rf`gj`gs y vfr`fs, 3>3 ruagsgs y cmcreoogs y 84 ruagsgs y vfr`fs. @f chufr`g hgj su tfgríc `f oc bfrfjhec, bfrfjhec, fsgs vcogrfs `fdfj prgpgrheøj 5;8;8;3. coaujc 33 tfgríc cofstcr jevfofj`focseajeiehcheøj `fo 6 pgr·Bcy hefjtg 7. fve`fjhec pcrc `u`cr `f su Tfsuotc`g; Ifjgtepg
Tf`gj`gs y cmcreoogs
Tf`gj`gs y vfr`fs
Tuagsgs y cmcreoogs
Tuagsgs y vfr`fs
Pgtco
Gdsfrvc`gs
836
3>2
3>3
84
669
Fspfrc`gs
838
3>0
3>0
86
669
(> ‘ F)
4
0
-8
-8
>
(G - F)4 /F = R = R 4
0/838
39/3>0
5/3>0
5/86
>,63 JX JX
Arc`gs `f oedfrtc` = (hgoumjcs ‘ 3) (beofrcs ‘ 3) = (8)(3) = ao=8 R 4 (>,>6)(ao=8) = = 1,24 4 R (>,>3)(ao=8) = = 33,80
Bepøtfses fstc`ístehcs; B>; Bcy chufr`g fjtrf ogs vcogrfs tførehgs 5;8;8;3 y ogs vcogrfs gdsfrvc`gs. B3; Jg fxestf chufr`g fjtrf ogs vcogrfs tførehgs 5;8;8;3 y ogs vcogrfs gdsfrvc`gs. 4
4
R hcohuoc`c = >,63 ?? R (>,>3)(ao=8) = 33,80; Xf chfptc oc B> @fheseøj; B>; Bcy chufr`g fjtrf oc prgpgrheøj tførehc 5;8;8;3 y ogs vcogrfs gdsfrvc`gs. ^TGDOFMC TFXVFOPG @c`gs ogs rfsuotc`gs `f oc fvcoucheøj `f ocs hcrchtfrístehcs `f ujc `fshfj`fjhec `f auescjtfs, `ftfrmejcr se hgjhufr`c g jg hgj oc prgpgrheøj tførehc 5;8;8;3, uscj`g oc prufdc `f R `f R 4 , fj Fxhfo.
33
. Xpefafo, M. 4>>>. Fstc`ístehc. Xfauj`c f`eheøj. MhArcw-Beoo. Xfref Xbcum. Måxehg. p; 416
08
Oc prgdcdeoe`c` `f ogs vcogrfs gdsfrvc`gs y fspfrc`gs (prgpgrheøj tførehc 5;8;8;3) sfcj eaucofs fs `fo 54 pgr hefjtg. 0.6.8. ^TGDCDEOE@C@ FRCHPC @F IEXBFT Oc prgdcdeoe`c` fxchtc `f Iesbfr fs ûteo pcrc fo cjãoeses `f hgjtfgs hucj`g ocs `gs mufstrcs ej`fpfj`efjtfs sgj muy pfqufócs. Xf usc hucj`g ogs pujtckfs pujtckfs `f `gs mufstrcs rfhgae`cs ej`fpfj`efjtfmfjtf co czcr pfrtfjfhfj c hocsfs g hctfagrícs mutucmfjtf fxhouyfjtfs. Ogs pujtckfs sf sf rfprfsfjtcj fj ujc tcdoc `f hgjtejafjhec `f 4 x 4. Fj ocs beofrcs sf rfprfsfjtcj ogs arupgs g hctfagrícs hgmg; mchbgs y bfmdrcs, trctc`gs y jg trctc`gs. Fj ocs hgoumjcs sf rfprfsfjtcj ocs hocseiehchegjfs hgmg; scjgs y fjifrmgs, pgr fjhemc g pgr `fdckg `f oc mf`ecjc, chufr`g y `fschufr`g. Fo mg`fog `f oc tcdoc `f hgjtejafjhec 4 x 4, fs fo seauefjtf; -
+
Pgtco
Arupg E
C
D
C+D
Arupg EE
H
@
H+@
Pgtco
C+H
D+@
J
Oc iørmuoc pcrc hcohuocr oc prgdcdeoe`c` fxchtc `f Iesbfr sf ej`ehc c hgjtejucheøj; p=
(C+D)! (H+@)! (C+H)! (D+@)! J! C! D! H! @!
00
^TGDOFMC TFXVFOPG TFXVFOPG Vj arupg `f 35 vchcs iuf sgmfte`g c fxpfremfjtcheøj. Jufvf cjemcofs iufrgj vchujc`gs hgj ujc vchujc fxpfremfjtco y gtrg arupg `f 3> cjemcofs jg iuf vchujc`g. Fo rfsuotc`g `fo fxpfremfjtg sf ej`ehc fj fo huc`rg seauefjtf; Cjemcofs scjgs >
Pgtco
Xej vchujc
Cjemcofs fjifrmgs 3>
Hgj vchujc
0
6
5
Pgtco
30
6
35
3>
Tfsuotc`g Bcy trfs hufstegjfs pgr rfsgovfr; ·bcy fifhtg `f oc vchujc7. ·Huão fs oc prgdcdeoe`c` `f fquevghcrsf fj oc `fheseøj7. ·Huão fs oc hgjiecjzc fj oc `fheseøj7 p=
(C+D)! (H+@)! (C+H)! (D+@)! J! C! D! H! @!
Cpoehcj`g oc iørmuoc; p=
(3>)!
(5)!
35! 3>!
(30)! >!
0!
(6)! 6!
(3.811619) x (3>)46
p=
(3.41388>9) x (3>)41
p = >.>3>2
@fheseøj;
≂
>! = 3
= >.>3>2 *
3.>2%
Bcy fifhtg `f oc vchujc sgdrf fo fstc`g fstc`g `f scou` scou` `f ogs cjemcofs. Oc prgdcdeoe`c` `f fquevghcrsf fs `f 3,>2%. Oc hgjiecjzc fj oc `fheseøj fs `fo 52,54 pgr hefjtg. 0.6.0. ^TVFDC [ Oc ^rufdc [ sf csghec hgj oc `estreduheøj jgrmco. Fj ujc bepøtfses, pcrc ujc mf`ec `f pgdocheøj (¶>), oc prufdc fstemc oc prgdcdeoe`c` `f quf oc mf`ec `f ujc mufstrc sfc mcygr quf fo prgmf`eg `f ocs gdsfrvchegjfs `f oc sfref `f `ctgs (mctrez). ^rufdc.[ = 3 ‘ `estreduheøj jgrmco jgrm co fstcj`crezc`c
06
^rgdcdeoe`c`fs p=>,3> p=>,3> y p=>,>6 csghec`cs hgj ogs vcogrfs `f [, fj oc `estredu `estreduheøj heøj jgrmco, pcrc ocs prufdcs `f ujc hgoc y `gs hgocs. ^rufdc
[
V jc hgoc
@gs hgocs
3,90
> ,> 6 > 6
> ,3 > 3 >
3,59
> ,> 4 6 >
> ,> 6 > >
4,61
> ,> > 6 3
> ,> 3 > 4
^TGDOFMC TFXVFOPG @c`c ujc sfref `f `ctgs, hcohuocr ocs prgdcdeoe`c`fs `f [ hgj fo prgarcmc Fxhfo, vcrecj`g R `fs`f 4> bcstc 8>, ejhoue`g oc mf`ec `f oc mufstrc (R=40,9>), arciehcr ocs prgdcdeoe`c`fs f ejtfrprftcr ogs rfsuotc`gs. Tfsuotc`g; Fo hãohuog `f oc prufdc [, pcrc hc`c vcogr `f R, pfrmeteø gdtfjfr ogs rfsuotc`gs `f p y arãiehg quf sf ej`ehcj c hgjtejucheøj;
>,>>>>>>>>>>>8>
>,>%
>,>>>>>>>896992
>,>%
>,>>>>6>6055850
>,>%
>,>>2896492>83>
>,2%
>,3202>3119>129
32,6%
,
>,6>>>>>>>>>>>>
6>,>%
>,146342344>>48
14,6%
>,5232015453322
52,4%
>,5552885856031
3>>,>%
>,5555552360864
3>>,>%
>,5555552360864
3>>,>%
>,5555552360864
3>>,>%
Fo vcogr `f R=40,9> hgrrfspgj`f c oc mf`ec `f oc mufstrc, sf oghcoezc fj fo pofjg hfjtrg `f oc hurvc jgrmco. Oc prgdcdeoe`c` [=>,6> ej`ehc quf R=40,9> cdcrhc fo 6>% `fo ãrfc dckg oc hurvc jgrmco. Hgj R=8>, oc prgdcdeoe`c` [ fs
09
prãhtehcmfjtf fo 3>>%, og quf ej`ehc quf sf udehcríc fj fo fxtrfmg `frfhbg `f oc hurvc jgrmco. Fj fo arãiehg sf ej`ehc ogs vcogrfs `f R, `f 4> c 8>, y ocs prgdcdeoe`c`fs z chumuoc`c, quf `cj ujc igrmc seamge`fc c oc hurvc. 0.6.6. ^TVFDC @F t Oc prufdc `f t puf`f uscrsf pcrc ejifrer oc jcturcofzc `f ujc pgdocheøj, c pcrter `fo mufstrfg g pcrc rfcoezcr hgmpcrchegjfs `f fjscygs cpcrfc`gs. Oc prufdc prgpgrhegjc oc prgdcdeoe`c` csghec`c hgj oc prufdc t `f Xtu`fjt, irfhufjtfmfjtf sf usc pcrc `ftfrmejcr oc prgdcdeoe`c` `f quf `gs mufstrcs puf`cj prghf`fr `f `gs pgdochegjfs hgj eauco mf`ec. ^CTC EJIFTFJHEC @F VJC ^GDOCHEØJ Oc prufdc `f `f t sf sf puf`f uscr pcrc ejifrer oc jcturcofzc `f ujc pgdocheøj fj dcsf `f oc iørmuoc. t = RX- C R R
@gj`f;
t = Ycogr `f t hcohuoc`g C = Ycogr hrítehg `f hcmpg (umdrco) = Frrgr fstãj`cr g `fsvecheøj fstãj`cr `f ocs mf`ecs X R
^TGDOFMC TFXVFOPG Fj uj huotevg `f tgmctf sf rfaestrc fo ctcquf `f oc pocac Mejc`gr `f ocs bgkcs y sf rfquefrf hgjghfr se fo `cóg fs mcygr g mfjgr `fo 3>%, hgjse`frc`g fo umdrco fhgjømehg `f `cóg, pcrc `fhe`er oc cpoehcheøj `f ejsfhtehe`c. @ctgs; ^ocjtcs
@cóg `fo mejc`gr (%)
3
4
8
0
6
9
1
2
5
3>
31
44
38
4>
4>
2
32
4>
36
31
Xumc
Mf`ec
Ycrecjzc
@fsvecheøj fstãj`cr
31>
31
31,33
0,30
Bepøtfses; Bg; ¶ ?3>% B3; ¶ :3>%
R - C t = X R R @gj`f;
t = Ycogr `f t hcohuoc`g C = Ycogr hrítehg `f hcmpg (umdrco) = 3>% `f `cóg fstãj`cr g `fsvecheøj `fsvecheøj fstãj`cr `f ocs mf`ecs X R = Frrgr fstãj`cr
01
Tfsuotc`g; Ycrecjzc
X R =
X R =
Jûmfrg `f gdsfrvchegjfs Jûmfrg
X
= 3.83 j
thcohuoc`c = (31 ‘ 3>)/3,83 = 6,80 ** ^crc j =3>, pcrc ujc prufdc `f `gs hgocs, hgj j - 3=5 arc`gs `f oedfrtc`; t>,>6 = 4,494 t>,3>= 8, 46> Hgmg thcohuoc`c fs mcygr quf tcduocr sf rfhbczc oc bepøtfses `f juoe`c` B> B>; ¶? 3>% Fj hgjsfhufjhec, sf chfptc oc bepøtfses `f cotfrjctevc B3 B3 ¶:3>% @fheseøj; Fo `cóg hcusc`g pgr oc pocac fs mcygr co 3>%, quf fs fo umdrco `f `cóg fhgjømehg, hgj fo 55% `f hgjiecjzc, pgr hgjseauefjtf, uraf oc cpoehcheøj `f ejsfhtehe`c pcrc su hgjtrgo. ^TGDOFMC TFXVFOPG C pcrter `f uj mufstrfg `f 3> pocjtcs co czcr, `gj`f sf fvcoûc fo `cóg `f ujc pocac, huyg umdrco fhgjømehg `f `cóg fs `fo 3>%, mf`ecjtf oc prufdc t, `ftfrmejcr oc prgdcdeoe`c` `f chfptcr g rfhbczcr oc bepøtfses `f quf ¶:3>%. Tfsuotc`g;
02
Oc hgjiecjzc `f quf ¶:3>% fs hfrhcjc c 3>>< fs `fher oc prgdcdeoe`c` `f quf fquevghcrsf fs cpfjcs `f >,>>>>>8612, quf fquevcof c >,>>>89%. >,>>>89%. ^CTC GDXFTYCHEGJFX C^CTFC@CX Fj fxpfremfjtgs `gj`f sf tefjf fo prgpøsetg `f hgmpcrcr `gs mf`ecs prgvfjefjtfs `f gdsfrvchegjfs cpcrfc`cs, sf puf`f cpoehcr oc prufdc t `f Xtu`fjt. Oc igrmuocheøj `f oc bepøtfses sf pocjtfc `f oc mcjfrc seauefjtf; seauefjtf; B > ; m 3 = m 4 B 3; m 3 ‘ m 4
≮ >
Xe thcohuoc`c : t>,>6; Xf rfhbczc B>. Ocs mf`ecs sgj fstc`ístehcmfjtf `eifrfjtfs hgj fo 56% `f hgjiecjzc (^?>,>6). (^? >,>6). Xf rfprfsfjtc hgj uj cstfreshg (*). Xe thcohuoc`c : t>,>3; Xf rfhbczc B>. Ocs mf`ecs sgj fstc`ístehcmfjtf `eifrfjtfs hgj fo 55% `f hgjiecjzc (^?>,>3). (^? >,>3). Xf rfprfsfjtc hgj `gs cstfreshgs (*). Xe thcohuoc`c ? t>,>6; Xf chfptc B>. Ocs mf`ecs sgj fstc`ístehcmfjtf fstc`ístehcmfjtf eaucofs hgj fo 56% `f hgjiecjzc (^:>,>6). Xf rfprfsfjtc hgj ocs ejehecofs `f ‟Jg seajeiehctevg” (JX). t>,>6 y t>,>3 sgj vcogrfs quf sf tgmcj `f ujc tcdoc `fo fstc`ístehg ‟t”, hgjse`frcj`g ogs jevfofs `f seajeiehcheøj `fo 6 y 3%, rfspfhtevcmfjtf< csí hgmg, ogs arc`gs `f oedfrtc` (ao) = j-3. Fj fstf hcsg fo vcogr `f j hgrrfspgj`f co jûmfrg `f gdsfrvchegjfs cpcrfc`cs. ^TGDOFMC TFXVFOPG Fj `efz iejhcs hchcgtfrcs, `f oc vcref`c` Jchegjco, oghcoezc`cs fj `eifrfjtfs oghcoe`c`fs `f oc prgvejhec `f Mcjcdí, sf fvcoûcj `gs måtg`gs `f cdgjc`urc co sufog; químehc y graãjehc. Xf rfquefrf `ftfrmejcr `ftfrmejcr oc mfkgr cotfrjctevc `f ifrteoezcheøj fj tårmejgs `f rfj`emefjtg y hgstgs. P3 = Cdgjc`urc graãjehc (co sufog y igoecr) P4 = Ifrteoezcheøj químehc J^L + mehrg fofmfjtgs
05
@ctgs34; Oghcoe`c` 3 (C) 4 (D) 8 (H) 0 (@) 6 (F) 9 (I) 1 (A) 2 (B) 5 (E) 3> (K) Xumc Mf`ec ^gr hefjtg
^rg`uhheøj (quejtcofs/bfhtãrfc) Graãjehc (P3) Suímehc (P4) @eifrfjhec (`) 5 2 -3 31 36 -4 30 33 -8 38 33 -4 36 5 -9 3> 34 4 33 33 > 38 3> -8 38 5 -0 36 30 -3 38> 33> -4> 38 33 -4 32 3>>
`4 3 0 5 0 89 0 > 5 39 3 20
Tfsuotc`g; Oc bepøtfses hgjsestf fj prgdcr se bcy `eifrfjhec fstc`ístehc fjtrf ocs `gs cotfrjctevcs `f ifrteoezcheøj, fvcoucj`g oc vcrecdof prg`uhheøj/ bfhtãrfc. B>; m3 = m4 B3; m3 ‘ m4 ≮ > Oc vcrecjzc `f ocs `eifrfjhecs X 4 ` sf hcohuoc mf`ecjtf oc iørmuoc seauefjtf; ∓`4
∓(`)4
-
X4` =
j
j-3 20
X4` =
- 5
(4>)4 3>
= 0,25
Oc `fsvecheøj Fstãj`cr `f ocs `eifrfjhecs ‟X ` ` ”” fs oc rcíz huc`rc`c `f oc vcrecjzc `f ocs `eifrfjhecs< pgr og tcjtg;
X ` =
0.25
= 4.4338
34
. `fo Fstftrctcmefjtg prgdofmc sf iãheomfjt uscj`g fo prgarcmc Fxhfo. Xf tgmc`ffjquf hgjse`frcheøj 3, rfsufovf oc mctreziãheomfjtf `f `ctgsf `fo trctcmefjtg 4, oc fspfheiehcheøj sf trctc `f ococmctrez prufdc`f`f`ctgs `gs hgocs y fo tepg `f fjscyg cpcrfc`g; =^TVFDC.P(D9;D36 > hgj fo 52% `f hgjiecjzc.
6>
Fo Frrgr Fstãj`cr `f ocs `eifrfjhecs ‟ FF ` `” sf hcohuoc mf`ecjtf oc seauefjtf iørmuoc; X` X` ` `= FF
j
4,4338 X` FF ` =
= >,955
j3>
Fo vcogr ` fs fo prgmf`eg `f ocs `eifrfjhecs (vcogr cdsgoutg) fjtrf trctcmefjtgs = 4 Fo vcogr `f t sf sf hcohuoc sfaûj oc iørmuoc seauefjtf; `
t =
= 4 / >.955 =
4.29 *
FF Fo vcogr `f t `f tcdoc, pcrc oc prufdc `f `gs hgocs, fj ogs jevfofs `f `f seajeiehcheøj co 6% y co 3%, hgj arc`gs `f oedfrtc (ao) = j ‘ 3 = 3> ‘ 3 = 5, fs fo seauefjtf; t>,>6 (ao=5) = 4,494 t>,>3 (ao=5) = 8,46> Hgmg sf puf`f gdsfrvcr, t hcohuoc`g fs mcygr quf t>,>6 (ao=5) = 4,494, pfg mfjgr quf t>,>3 (ao=5) = 8,46>, pgr og quf sf rfhbczc oc B> hgj fo 56% `f hgjiecjzc (*) @fheseøj; Hgmg thco = 4.29 : t>.>6 = 4.494< 4.494< sf rfhbczc B> hgj fo 56% `f hgjiecjzc. Oc ifrteoezcheøj graãjehc graãjehc rfsuotø sfr fstc`ístehcmfjtf supfregr c oc ifrteoezcheøj químehc hgj fo 56% `f hgjiecjzc (^?>.>6). 0.6.9. ^TVFDC @F I Oc prufdc `f I fs ujc prufdc pcrcmåtrehc muy c`fhuc`c pcrc tgmcr `fhesegjfs fstc`ístehcs sefmprf quf sf humpoc hgj ocs hgj`ehegjfs seauefjtfs; • • • • •
Ocs gdsfrvchegjfs `fdfj sfr ej`fpfj`efjtfs fjtrf sí Oc `estreduheøj `f oc pgdocheøj `fdf sfr jgrmco Ocs pgdochegjfs `fdfj tfjfr oc mesmc vcrecjzc Ocs mf`ehegjfs `f ocs vcrecdofs `fdfj sfr fj fshcocs `f ejtfrvcog Ocs mf`ecs `f ocs pgdochegjfs jgrmcofs y `f vcrecjzcs eaucofs `fdfj sfr fo rfsuotc`g `f fifhtgs c`etevgs
63
Oc prufdc `f I sf usc fj ogs cjãoeses `f vcrecjzc `f fxpfremfjtgs `f ujg g vcregs ichtgrfs fj fstu`eg, pgr og quf sf uscrã fj oc pcrtf hgrrfspgj`efjtf co `esfóg fxpfremfjtco. Fo hgjtrcstf sf rfcoezc hgj oc tcdoc `f I, c ogs jevfofs `f seajeiehcheøj fofae`gs pgr fo ejvfsteac`gr hgj arc`gs `f oedfrtc` j-3. Fo fstc`ístehg I sf hcohuoc mf`ecjtf oc rfocheøj fjtrf oc vcrecjzc mcygr y oc vcrecjzc mfjgr. ^TGDOFMC TFXVFOPG Tfcoezcr oc prufdc I pcrc ogs rfsuotc`gs `f `gs trctcmefjtgs, C y D, uscj`g fo prgarcmc Fxhfo.
Hgmg oc p= >,>8>5 quf fquevcof co 8%, seajeiehc quf ogs trctcmefjtgs sgj fstc`ístehcmfjtf `eifrfjtfs, hgj fo 51% `f hgjiecjzc. 0.9. FO MVFXPTFG 0.9.3. PFGTEC @FO MVFXPTFG MVFXPTFG ·SVÅ FX FO MVFXPTFG7 Fo mufstrfg fs uj prghf`emefjtg pgr mf`eg `fo huco sf fstu`ec ujc pcrtf `f oc pgdocheøj oocmc`c mufstrc, hgj fo prgpøsetg `f bchfr ejifrfjhecs chfrhc `f oc jcturcofzc `f tg`c oc pgdocheøj. ^crc quf fstc ejifrfjhec sfc og mãs hfrhcjc c oc rfcoe`c`, csumefj`g ujc prgdcdeoe`c` `f fquevghcheøj (refsag) y uj mcrafj `f frrgr, oc mufstrc `fdf sfr rfprfsfjtctevc `f oc pgdocheøj. ·SVÅ FX FO ^GDOCHEØJ7 Vjc pgdocheøj , fj fstc`ístehc, sf `fiejf hgmg fo hgjkujtg `f ej`eve`ugs u gdkftgs hgj rcsags hgmujfs quf sgj oc dcsf `f ujc sfref bepgtåtehc f
64
ejiejetcmfjtf arcj`f `f gdsfrvchegjfs pgtfjhecofs. Oc pgdocheøj tcmdeåj sf `fiejf hgmg ujevfrsg. Ocs mf`e`cs quf hcrchtfrezcj c oc pgdocheøj sf hgjghfj hgmg pcrãmftrgs. ·SVÅ FX FO HFJXG7 Vj hfjsg fsujcfo pgdocheøj. rfaestrg `fFj`ctgs fj tg`gs ogs fxpfremfjtco ej`eve`ugs u fsgdkftgs hgjstetuyfj fstf hcsg, fo frrgr hfrg y quf ocs mf`e`cs quf ocs hcrchtfrezcj sgj ogs pcrãmftrgs. pcrãmft rgs. ·SVÅ FX VJC MVFXPTC7 Vjc mufstrc , fj fstc`ístehc, fs fo sudhgjkujtg `f ej`eve`ugs u gdkftgs quf hgjstetuyfj ujc pcrtf rfprfsfjtctevc `f oc pgdocheøj y `gj`f sf tgmcj ujc sfref iejetc `f gdsfrvchegjfs c pcrter `f oc huco sf fstemcj ogs pcrãmftrgs `f oc pgdocheøj. Ocs mf`e`cs quf hcrchtfrezcj c oc mufstrc sf hgjghfj hgmg fstc`ístehgs. ·SVÅ FX VJ FOFMFJPG @F MVFXPTFG7 Vj fofmfjtg fs uj gdkftg g ej`eve`ug sgdrf fo huco sf bchfj ocs mf`ehegjfs pcrc rfaestrcr ogs `ctgs. Hucj`g sf trctc `f uj arupg `f ej`eve`ugs u gdkftgs sgdrf ogs hucofs sf rfaestrcj `ctgs quf sf prgmf`ecj pcrc tfjfr ujc mfkgr vcogrcheøj `f ogs fstc`ístehgs g pcrãmftrgs, fjtgjhfs sf trctc `f ujc uje`c` `f mufstrfg. Vj fofmfjtg `f mufstrfg puf`f sfr uj cjemco, ujc pocjtc, ujc pfrsgjc, uj ejsfhtg. ·SVÅ FX VJE@C@ @F MVFXPTFG7 MVFXPTFG7 Vjc uje`c` `f mufstrfg fs fo fofmfjtg (ej`eve`ug u gdkftg) g cqufo hgjkujtg `f sukftgs (ej`eve`ugs u gdkftgs) sgdrf oc huco sf rfcoezc oc mf`eheøj. ^gr fkfmpog; ujc pocjtc, uj arupg `f hejhg pocjtcs pgr hc`c pcrhfoc, uj mftrg huc`rc`g `f gtrcs, sufog, ujc fo ãrfc `f ujc pcrhfoc `f huotevg, ujc vchc, uj arupgs `f vchcs, fjtrf rf`c`c, hejhg rf`c`cs. Vjc uje`c` `f mufstrfg `fdf rfujer ocs seauefjtfs hcrchtfrístehcs; hcrchtfrístehcs; `f e`fjteiehcheøj jíte`c, `f mf`eheøj iãheo, prgpgrhegjf ejigrmcheøj vfrcz y sfc `f míjemg hgstg. Coturc = 4,3> hm
= Vj `ctg
Vje`c` `f mufstrfg; 3 pocjtc
^rgmf`eg `f coturc= 4,>2 hm
= Vj `ctg
Vje`c` `f mufstrfg; 6 pocjtcs
68
·SVÅ FX FTTGT @F MVFXPTFG7 Fo frrgr `f mufstrfg fs oc `eifrfjhec fjtrf fo vcogr `f oc mufstrc y fo vcogr rfco `f oc pgdocheøj. ^gr og tcjtg, oc mfkgr tåhjehc `f mufstrfg fs cqufooc quf rf`uhf co míjemg fo frrgr `f mufstrfg. ·SVÅ FX FXPC@ÍXPEHG7 FXPC@ÍXPEHG7 Vj fstc`ístehg fs ujc mf`e`c usc`c pcrc `fshreder coaujc hcrchtfrístehc `f ujc mufstrc. Ogs fstc`ístehgs mãs hgmujfs sgj; oc mf`ec cretmåtehc, oc mf`ecjc, oc mg`c, fo rcjag y oc `fsvecheøj fstãj`cr. ·SVÅ FX ^CTÃMFPTG7 ^CTÃMFPTG7 Vj pcrãmftrg fs ujc mf`e`c usc`c pcrc `fshreder coaujc hcrchtfrístehc `f ujc pgdocheøj. Ogs pcrãmftrgs mãs empgrtcjtfs sgj; oc mf`ec cretmåtehc y oc `fsvecheøj fstãj`cr. ^TGDOFMC TFXVFOPG TFXVFOPG Tfprfsfjtcr arãiehcmfjtf oc rfocheøj fjtrf mufstrc y pgdocheøj; ^gdocheøj 4 6
0
8
1
Mufstrc
9
0
0
4
4
1 6
0 6 4
4
8 1
8
6
0 9
9 0
Fofmfjtgs `f oc pgdocheøj J = 4> Mf`ec `f oc pgdocheøj = 0,46 @fsvecheøj fstãj`cr ψ = 3,1
Fofmfjtgs `f oc mufstrc j = 0 Mf`ec `f oc mufstrc x = 0,46 @fsvecheøj fstãj`cr X = 3,1
·SVÅ FX VJC ^GDOCHEØJ TFCO7 Fj oc fstc`ístehc sf trcdckc hgj pgdochegjfs y hgj mufstrcs fxtrcí`cs `f ocs mesmcs. Fj fstcs herhujstcjhecs hcdf `eifrfjhecr quf fs ujc pgdocheøj rfco `f ujc pgdocheøj fstc`ístehc. Coaujgs fkfmpogs `f pgdochegjfs rfcofs sgj; 38 meoogjfs `f bcdetcjtfs `fo Fhuc`gr (pgdocheøj jchegjco)< fstu`ecjtfs `fo Hgofaeg Mco`gjc`g, fstu`ecjtfs 60
60
`f oc ichuotc` `f hefjhecs caríhgocs, dgsquf `f pejg fj fo pãrcmg `fo hcjtøj Aucmgtf, igoockf (jûmfrg `f bgkcs) `f uj ãrdgo `f fuhcoeptg, dchtfrecs fj ujc hckc pftre , bctg acjc`frg fj oc bchefj`c @fjesf, rfdcóg `f gvfkcs `f oc bchefj`c Fo Pcdoøj, jûmfrg `f pfhfs fj uj fstcjquf, pchefjtfs `fo bgspetco Fuafjeg Fspfkg, prg`uhheøj `ecrec `f ujc iãdrehc `f hgjsfrvcs, jûmfrg `f ocrvcs fj uj irutc pg`re`c, jûmfrg `f irutgs `f uj ãrdgo, fjtrf gtrgs. Oc pgdocheøj fstc`ístehc sf rfiefrf c ocs mf`ehegjfs fj hc`c ujg `f ogs ej`eve`ugs u gdkftgs quf hgjigrmcj oc pgdocheøj rfco. Hcdf `fstchcr quf ogs ejvfsteac`grfs `fiejfj ogs oímetfs `f oc pgdocheøj, sfaûj ocs jfhfse`c`fs `fo fstu`eg. ^TGDOFMC TFXVFOPG Tfprfsfjtcr oc rfocheøj fjtrf ujc pgdocheøj rfco y ujc pgdocheøj fstc`ístehc; ^gdocheøj rfco; Fo rfco; Fo jûmfrg `f hgjfkgs fj ujc arcjkc `f`ehc`c c su hrecjzc y hgmfrhecoezcheøj.
^gdocheøj fstc`ístehc; fstc`ístehc; Ogs `ctgs `f hc`c ujc `f ocs vcrecdofs rfaestrc`gs fj tg`gs ogs hgjfkgs `f oc arcjkc hgmg; pfsg y f`c`. Jg Cjemco 3 4 8 0 J ·
Ycrecdofs ^fsg fj vevg (arcmgs) 3.62> 3.465 259 3.863 ….
F`c` (`ícs) 2> 16 9> 14 …
66
·HVÃOFX XGJ OGX ^CTÃMFPTGX MÃX EM^GTPCJPFX @F VJC ^GDOCHEØJ7 Ogs pcrãmftrgs mãs empgrtcjtfs fj tg`c pgdocheøj sgj; mf`ec ( ¶ ) y vcrecjzc (ψ 4 ). Co rfcoezcr fo `f mufstrfg `fdf fvetãj`gsf prgpfj`frsf quf oc fj mufstrc tgmc`c sfc rfprfsfjtctevc oc pgdocheøj, ogs c‟sfsags” ogs prghf`emefjtgs. Xgog `f fstf mg`g ‟oc mufstrc fstemcrã c oc pgdocheøj”. ·C SVÅ XF TFIEFTF FO PFGTFMC @FO OÍMEPF HFJPTCO7 Fo tfgrfmc `f oímetf hfjtrco bchf rfifrfjhec c quf ‟se sf sfofhhegjcj mufstrcs co czcr `f ujc pgdocheøj `ftfrmejc`c, hgjigrmf cumfjtc fo tcmcóg `f oc mufstrc, oc `estreduheøj sf cprgxemc c oc `estreduheøj jgrmco”. Hucj`g sf humpof fo ‟tfgrfmc `fo oímetf hfjtrc hfjtrco”, o”, oc mf`ec `f oc mufstrc fs uj fstemc`gr `f oc mf`ec pgdochegjco; R
¶
Fj ocs mesmcs herhujstcjhecs, oc `fsvecheøj típehc `f oc mufstrc fstemc c oc `fsvecheøj típehc `f oc pgdocheøj; X
ψ
·HØMG XF TFOCHEGJC OC @EXPTEDVHEØJ JGTMCO HGJ OGX FXPC@ÍXPEHGX @F VJC MVFXPTC7 Co rfcoezcr fo cjãoeses fstc`ístehg `f ujc vcrecdof, fj ujc mufstrc, bcy quf hgjse`frcr ocs prgpef`c`fs `f oc `estreduheøj jgrmco y su rfocheøj hgj ogs sus fstc`ístehgs. Fjtrf ocs prgpef`c`fs prgpef`c`fs `f oc `estreduheøj jgrmco, sf mfjhegjcj; • • • •
• • •
ujc mufstrc `estreduheøj jgrmco, fjtgjhfs, oc mf`ec, mf`ecjc yXemg`c tefj`fj ctefjf hgejhe`er fj fo hfjtrg `f oc `estreduheøj. Fo ãrfc tgtco dckg oc hurvc jgrmco fs eauco c 3 g su fquevcofjtf 3>>% `f ogs ej`eve`ugs u gdkftgs `f oc mufstrc. Oc hurvc jgrmco `f ujc mufstrc fs semåtrehc rfspfhtg `f su mf`ec< fstg seajeiehc quf uj 6>% `f ogs `ctgs sfrã mcygr quf oc mf`ec y fo gtrg 6>% `f `ctgs mfjgr quf oc mf`ec. Oc `estcjhec fjtrf oc oíjfc pfrpfj`ehuocr c oc mf`ec y fo pujtg `f ejiofxeøj `f oc hurvc hurvc jgrmco fs oc `fsvecheøj típehc (X). Fo hgjkujtg `f `ctgs udehc`gs fjtrf R ³ X rfprfsfjtc fo 92,49% `fo ãrfc dckg oc hurvc jgrmco. Fo 56.00% `fo ãrfc dckg oc hurvc jgrmco sf fjhufjtrf fjtrf R³ 4X. Fo 55.1% `fo ãrfc dckg oc hurvc jgrmco sf udehc fjtrf ogs vcogrfs R ³ 8X. igrmc `f oc hurvc jgrmco g hcmpcjc `f Acuss `fpfj`f `f ogs Oc fstc`ístehgs R y X. Oc mf`ec ej`ehc oc pgseheøj `f oc hurvc< pgr og
69
•
tcjtg, c `eifrfjtfs vcogrfs `f R , oc arãiehc fs `fspoczc`c `fspoczc`c c og ocrag `fo fkf bgrezgjtco. ^gr gtrc pcrtf, oc `fsvecheøj fstãj`cr (X) `ftfrmejc fo arc`g `f cau`fzc `f oc hurvc. hurvc. Hucjtg mcygr sfc fo vcogr `f X, mãs sf `espfrscrãj ogs `ctgs fj tgrjg c oc mf`ec y oc hurvc sfrã mãs pocjc. Jg fxestf ujc ûjehc `estreduheøj jgrmco, sejg ujc icmeoec `f `estreduhegjfs hgj ujc igrmc hgmûj, `eifrfjhec`cs pgr ogs vcogrfs `f su mf`ec y su vcrecjzc. Oc mãs usc`c fs oc `estreduheøj jgrmco fstãj`cr, quf hgrrfspgj`f c ujc `estreduheøj `f mf`ec > y vcrecjzc 3.
^TGDOFMC TFXVFOPG Arciehcr oc hurvc jgrmco rfochegjãj`goc hgj ogs fstc`ístehgs mf`ec, `fsvecheøj fstãj`cr y pgrhfjtckf `fo ãrfc dckg oc hurvc.
i ( x )
4 ώ
>,38%
4,36%
4,36% -4X
4 ψ 4
38,65%
38,65%
-8X
ψ
f
( x ∔ ¶ )4
80,38%
80,38%
>,38%
=
∔
3
-3X
R
+3X
+4X
20.3%
51.1%
+8X
92,49% 56,00% 55,1%
Ãrfc dckg oc hurvc jgrmco
>.3%
4.8%
36.5%
6>%
55.5%
0.9.4. MÅPG@GX @F MVFXPTFG ·HVÃOFX XGJ OCX PÅHJEHCX @F MVFXPTFG7 MVF XPTFG7 Bcy `gs måtg`gs pcrc tgmcr mufstrcs fstc`ístehcs fj ocs pgdochegjfs; fo mufstrfg jg cofctgreg y fo mufstrfg prgdcdeoístehg. ·@F SVF PTCPC OC PÅHJEHC @F MVFXPTFG JG COFCPGTEG7 Fo mufstrfg jg cofctgreg sf `fjgmejc`fotcmdeåj `f kueheg g ejtfjhegjco y sf dcsc fj oc fxpfrefjhec y hgjghemefjtg ejvfsteac`gr chfrhc `f oc pgdocheøj y sgog `fdf sfr hgjse`frc`c hgmg ujc rfifrfjhec pcrc pocjfcr uj mufstrfg prgdcdeoístehg.
61
Oc pfrsgjc sfofhhegjc ogs fofmfjtgs `f oc mufstrc `fhe`efj`g sfaûj su hretfreg y sudkfteve`c` ocs uje`c`fs `f mufstrfg. Fj fstf hcsg jg puf`f cpoehcrsf oc tfgríc `f oc prgdcdeoe`c`. ^gr fkfmpog, fj oc e`fjteiehcheøj `f ãrdgofs `f hchcg Jchegjco, fo fxpfrtg `fhe`f, sfaûj su fxpfrefjhec, huãofs pocjtcs hgrrfspgj`fj c fstc vcref`c`. ·@F SVF PTCPC OC PÅHJEHC @F MVFXPTFG ^TGDCDEOEXPEHG7 Fo mufstrfg prgdcdeoístehg sf hgjghf tcmdeåj hgmg cofctgreg. Igrmcj pcrtf `f fstf tepg `f mufstrfg tg`gs ogs måtg`gs quf pfrmetfj hcohuocr prgdcdeoe`c`fs `f fxtrchheøj `f hucoquefrc hu coquefrc `f ocs mufstrcs pgsedofs. ·HVÃOFX XGJ OGX MÅPG@GX @F MVFXPTFG7 Ogs måtg`gs `f mufstrfg `fpfj`fj `f oc `espfrseøj `f ogs ej`eve`ugs u gdkftgs fj fo hcmpg fxpfremfjtco. Ogs trfs måtg`gs dãsehgs sgj; cofctgreg sempof, sestfmãtehg y fstrcteiehc`g. ^TGDOFMC TFXVFOPG Arciehcr ogs trfs måtg`gs `f mufstrfg dãsehgs Fstrctg C Fstrctg D
Fstrctg h
l e
Mufstrfg cofctgreg sempof
Mufstrfg fstrcteiehc`g
Mufstrfg sestfmãtehg
·SVF FX MVFXPTFG COFCPGTEG XEM^OF7 Fj fstf tepg `f mufstrfg søog bcy uj tepg `f uje`c` `f mufstrfg. Fs fo mãs sfjheoog `f ogs måtg`gs `f mufstrfg. Hc`c uje`c` `f mufstrfg tefjf eauco prgdcdeoe`c` `f ejhouersf fj oc mufstrc. m ufstrc. Fj oc prãhtehc, fo premfr pcsg hgjsestf fj oc jumfrcheøj `f ocs uje`c`fs `fs`f 3 bcstc J, `gj`f J hgrrfspgj`f c oc ûotemc. @fspuås sf fxtrcf ujc sfref `f jûmfrgs cofctgregs (g hucoquefr prghf`emefjtg cofctgreg) pcrc fofaer ogs vcogrfs `f oc mufstrc. ^crc mejemezcr oc `fsvecheøj fstãj`cr y fvetcr sfsags fs hgjvfjefjtf cseajcr uj jûmfrg c hc`c uje`c` `f pgdocheøj, `fiejer fo
62
tcmcóg `f mufstrc y tgmcr co czcr uscj`g `evfrscs tåhjehcs. Fstf måtg`g `f mufstrfg cofctgreg fs fo mãs usc`g fj oc carehuoturc. ·SVF FX MVFXPTFG XEXPFMCPEHG7 Fj fo mufstrfg sestfmãtehg sf foeaf uj ejtfrvcog `fjgmejc`g hgmg L , pcrc oc tgmc `f ogs fofmfjtgs `f oc uje`c` `f mufstrfg, fj iujheøj `fo tcmcóg `f oc mufstrc quf sf bcyc pocjfc`g fvcoucr, pcrc `fspuås fofaer cofctgrecmfjtf uj jumfrg quf hgrrfspgj`c hgrrfspgj`c c oc premfrc uje`c` `f mufstrfg. ^gr fkfmpog, oc uje`c` `f mufstrfg fs ujc pocjtc, fj uj ogtf `f ujc bfhtãrfc `f mcíz. ^crc cpoehcr fo mufstrfg sestfmãtehg sf foeaf uj vcogr l= 4> y oc pocjtc 3> `fo premfr surhg pcrc ejehecr fo mufstrfg. ^gr og tcjtg, oc premfrc pocjtc fs oc 3>, oc sfauj`c pocjtc 3> + l = 8>, oc tfrhfrc pocjtc 8> + l = 6>, oc hucrtc pocjtc oc 1>, oc quejtc pocjtc oc 5>, y csí suhfsevcmfjtf, bcstc hgmpoftcr fo tcmcóg `f mufstrc pocjfc`g.
Mufstrc 3
R3 X 43
Mf`ec Ycrecjzc
Fj ogs mufstrfgs; cofctgreg sempof y sestfmãtehg, fj ujc pgdocheøj, sf tgmc ujc mufstrc y sf hcohuocj ogs fstc`ístehgs `f ejtfrås
^gdocheøj 3
·SVF FX MVFXPTFG FXPTCPEIEHC@G7 Vjc pgdocheøj, `fpfj`efj`g `f su jcturcofzc, puf`f mgstrcr `eifrfjtfs jevfofs `f bftfrgafjfe`c` c hcusc `f ichtgrfs cmdefjtcofs g `f mcjfkg hgmg; arc`g `f pfj`efjtf `fo tfrrfjg, ejioufjhec `f ogs ãrdgofs `f ogs oej`frgs, ifrteoe`c` g prgiuj`e`c` `fo sufog, f`c`, sfxg, vcref`c`, vcref`c`, bídre`g, hogj, rczc, tepg `f hgrrco, arupg scjauíjfg, fshgocre`c`, fjtrf gtrgs. Fj fstcs herhujstcjhecs, ujc pgdocheøj puf`f tfjfr J sudpgdochegjfs, hc`c ujc `f ocs hucofs sf `fjgmejc fstrctg. @fjtrg `f hc`c fstrctg g sudpgdocheøj sf rfcoezc uj mufstrfg cofctgreg sempof g uj mufstrfg sestfmãtehg. Fj oc fstemcheøj `f ogs pcrãmftrgs `f oc pgdocheøj `fdf hgjse`frcrsf quf hc`c fstrctg fs ujc sudpgdocheøj, irfhufjtfmfjtf hgj `estejtg tcmcóg `f mufstrc, `gj`f fo rfaestrg `f `ctgs, cjãoeses y fstemcheøj `f fstc`ístehgs y pcrãmftrgs `fdf rfcoezcrsf pcrc hc`c ujc `f ocs sudpgdochegjfs.
65
R3
X43
R4
X 44
R8
X4
R0
X40
Rl
X4l
Mufstrc 3 Mufstrc 4 Mufstrc 8
8
Mufstrc 0 Mufstrc l
^gdocheøj
Fj fo mufstrfg fstrcteiehc`g `f ujc pgdocheøj sf igrmcj sudpgdochegjfs. Fj hc`c sudpgdocheøj sf tgmcj mufstrcs l y sf hcohuocj ogs fstc`ístehgs `f ejtfrås
Mf`ecs `f ocs Ycrec jzcs `f ocs mufstrcs mufstrcs
·FREXPFJ GPTGX MÅPG@GX @F MVFXPTFG7 Fj ogs `evfrsgs hcmpgs `fo hgjghemefjtg sf bcj `fscrrgooc`g måtg`gs quf c`cptcj ogs hretfregs `f cofctgref`c` y fstrcteiehcheøj c ocs pcrtehuocre`c`fs `f ocs ejvfsteachegjfs. Fjtrf fstgs måtg`gs sf mfjhegjcj; fo mufstrfg hgj rffmpoczg, fo mufstrfg sej rffmpoczg, fo mufstrfg pgr hgjaogmfrc`gs, fo mufstrfg fj ftcpcs y fo mufstrfg `gdof. Mufstrfg hgj rffmpoczg.- rffmpoczg.- ogs fofmfjtgs `f oc uje`c` `f mufstrfg sfofhhegjc`c rfarfscj c oc pgdocheøj, pgr og tcjtg, puf`fj sfr rffofae`gs fj uj mufstrfg pgstfregr. ^gr fkfmpog, fj fo hcsg `f mufstrfg `f oc cveicujc jctevc, grefjtc`c c oc e`fjteiehcheøj `f fspfhefs, fo ejvfsteac`gr ctrcpc uj cvf, og fvcoûc tgmc ogs `ctgs pfrtejfjtfs y og oedfrc. Fj fstf hcsg, fo cvf puf`f vgovfr c sfr ctrcpc`g pcrc ujc jufvc fvcoucheøj. Mufstrfg sej rffmpoczg.- ogs rffmpoczg.- ogs fofmfjtgs `f oc uje`c` `f mufstrfg ujc vfz fvcouc`gs jg rftgrjcj oc pgdocheøj, pgr og tcjtg, sf fofvc oc prgdcdeoe`c` `f tgmcrsf fj hufjtc c ogs fofmfjtgs quf jg bcj se`g fofae`gs. Fo mufstrfg sej rffmpoczg sf cpgyc fj ogs prghf`emefjtgs `f cofctgref`c` g sestfmãtehg. Mufstrfg pgr hgjaogmfrc`gs.- fj fj fo mufstrfg pgr hgjaogmfrc`gs, premfrg sf `eve`f oc pgdocheøj fj arupgs f ejmf`ectcmfjtf sf sfofhhegjc co czcr g mf`ecjtf fo måtg`g sestfmãtehg ujc pcrtf `f ogs arupgs< pgstfregrmfjtf, `fjtrg `f hc`c ujg `f foogs sf rfcoezc fo mufstrfg cofctgreg fj huycs uje`c`fs sf tgmcj ogs `ctgs. Fj fo måtg`g pgr hgjaogmfrc`g, cujquf jg tg`gs ogs arupgs sgj mufstrfc`gs, hc`c arupg tefjf ujc eauco prgdcdeoe`c` `f sfr sfofhhegjc`g, pgr og tcjtg oc mufstrc fs cofctgrec. C hgjtejucheøj sf ej`ehc ujc cpoehcheøj `fo mufstrfg pgr hgjaogmfrc`gs; •
Fj uj vevfrg `f hchcg pgr fjrcezcmefjtg `f rcmeoocs, bcy `eifrfjtfs arupgs `f pocjtcs `f `eifrfjtfs f`c`fs (pgr fkfmpog, 36>, 386, 346, 330, 3>> y 1> `ícs).
9>
• • •
Fj fstf vevfrg sf rfquefrf fvcoucr fo pgrhfjtckf `f prfj`emefjtg g fo hrfhemefjtg vfaftctevg. Jg sf jfhfsetc bchfr fo mufstrfg fj tg`gs ogs arupgs (`f tg`cs ocs f`c`fs), sf `fhe`f co czcr, ogs arupgs c fvcoucrsf (pgr fkfmpog, 3>> `ícs, 386 y 346 `ícs). @fjtrg `f ogs arupgs `f hc`c ujc `f ocs f`c`fs sfofhhegjc`cs sf bchf fo mufstrfg co czcr y sf rfaestrcj ogs `ctgs.
Mufstrfg fj ftcpcs38.- hgjsestf .- hgjsestf fj tgmcr, fj ujc premfrc ftcpc, mufstrcs cofctgrecs (uje`c`fs premcrecs) y oufag tgmcr uj jûmfrg fspfhíiehg `f fofmfjtgs pcrc igrmcr sudarupgs (uje`c`fs sfhuj`crecs) sgdrf ocs hucofs sf cpoehc fo mufstrfg cofctgreg sempof g sestfmãtehg. Fstf tepg `f mufstrfg fj `gs ftcpcs sf `fjgmejc deftãpehg. Hucj`g sf e`fjteiehcj sudpcrhfocs `fjtrg `f ocs uje`c`fs sfhuj`crecs sf trctc `f uj mufstrfg muoteftãpehg. Hgmg fkfmpogs `f mufstrfgs fj ftcpcs sf ej`ehcj ogs seauefjtfs; • •
Xfofhhegjcr co czcr uj arupg `f cjemcofs fjifrmgs (mufstrc), hgjigrmcr sudarupgs (sudmufstrcs) y sgdrf foogs cpoehcr trctcmefjtgs `estejtgs Fofaer ujc pcrhfoc `f huotevg, `f uj ãrfc `ftfrmejc`c (mufstrc) y oufag, `fjtrg `f hc`c pcrhfoc, `fiejer ujc g mãs sudpcrhfocs (sudmufstrcs) `gj`f sf rfcoezcrã oc tgmc `f `ctgs.
Mufstrfg `gdof.- `gdof.- Fstf måtg`g hgjsestf fj tgmcr ujc mufstrc pfqufóc, humpoefj`g ocs hgj`ehegjfs `f ogs måtg`gs cofctgreg g sestfmãtehg y cjcoezcr sus rfsuotc`gs, csumefj`g uj jevfo refsag y frrgr< oufag, se jg sf sctesichfj ocs hgj`ehegjfs `f mufstrfg sf rfcoezc uj sfauj`g mufstrfg fj oc mesmc pgdocheøj. Xe fo mufstrfg ejeheco sctesichf ocs hgj`ehegjfs `f mufstrfg, prãhtehcmfjtf, jg sf rfquefrf bchfr fo sfauj`g mufstrfg. 0.9.8. FXPTCPFAEC @F MVFXPTFG Vjc fstrctfaec `f mufstrfg fs fo hgjkujtg `f chhegjfs quf pgsedeoetcj gdtfjfr ujc ejigrmcheøj vãoe`c chfrhc `f ogs fstc`ístehgs `f oc mufstrc y ujc fstemcheøj `f ogs pcrãmftrgs `f oc pgdocheøj hgj uj refsag y frrgr chfptcdofs. Fj oc fstrctfaec `f mufstrfg sf hgjse`frcj ogs hgmpgjfjtfs seauefjtfs; `espfrseøj `f oc pgdocheøj rfco, jûmfrg `f mufstrcs c tgmcr, oghcoezcheøj `f ocs mufstrcs, fshcoc `f mf`eheøj y tcmcóg `f oc mufstrc. ·C SVF XF XF TFIEFTF OC @EX^FTXEØJ @F OCX ^GDOCHEGJFX7 ^GDOCHEGJFX7 Ogs gracjesmgs vevgs fj fo hcmpg tefj`fj c `estreduersf `f `eifrfjtfs igrmcs. Coaujcs pgdochegjfs tefjfj ujc `espfrseøj frrãtehc (p.f.; mcofzcs), gtrcs sf `espfrscj co czcr (p.f.; muhbcs pocacs y pctøafjgs), tcmdeåj puf`fj `estreduersf ujeigrmfmfjtf (p.f.; huotevgs, prg`uhheøj ej`ustreco y crtfscjco) y 38
. bttp;//www.feg.uvc.fs/~tcpec/ftcpcs.p`i
93
hefrtcs pgdochegjfs igrmcj carfachegjfs (p.f.; cvespcs). Xe sf hgjghf oc igrmc `f `espfrseøj, oc pocjfcheøj `fdf fstcr `f chufr`g c fooc.
@espfrseøj frrãtehc
@espfrseøj co czcr
@espfrseøj ujeigrmf
@espfrseøj carfac`c
·^GTSVÅ HGJXE@FTCT FO JÛMFTG @F MVFXPTCX FJ VJC FXPTCPFAEC @F MVFXPTFG7 Fo jûmfrg `f mufstrcs fstã fj rfocheøj c ogs gdkftevgs `f oc ejvfsteacheøj, quf puf`fj sfr rfpoehc`gs fj fo tefmpg g fj fo fspcheg. Ogs mufstrfgs rfpoehc`gs fj `eifrfjtfs tefmpgs (bgrc, `íc, sfmcjc, mfs, cóg), pgsedeoetcj fstu`ecr ocs `ejãmehcs `f pgdochegjfs jcturcofs (hehogs vfaftctevgs, hehog `f ve`c, hurvcs fpe`fmegoøaehcs), `ejãmehc `f jutrefjtfs fj fo sufog (cagtcmefjtg `f J, ^, L), `ejãmehc `fo cauc fj fo sufog< vcrecheøj tfmpgrco `f oc prfhepetcheøj, tfmpfrcturc, bumf`c` y bfoegicjíc, fjtrf gtrcs cpoehchegjfs. Ogs mufstrfgs tcmdeåj puf`fj sfr rfpoehc`gs fj `estejtcs oghcoe`c`fs (fspcheco), hgj fo prgpøsetg `f hgjghfr `f mg`g prfhesg oc jcturcofzc `fo ej`eve`ug u gdkftg `f fstu`eg. ^gr fkfmpog, fifhtucr mufstrfgs `f sufogs pcrc `ecajgstehcr jevfofs `f ifrteoe`c` y cpoehcr ogs hgjhfptgs `f carehuoturc `f prfheseøj. Ogs mufstrfgs `f arcjgs fj ocs dg`facs pcrc `ftfrmejcr ocs hcrchtfrístehcs iísehcs, jevfo `f empurfzcs g mfzhocs. Fj tg`gs ogs hcsgs ej`ehc`gs fo jûmfrg `f mufstrcs fstc `c`g pgr ocs irfhufjhecs `f mufstrfg quf `fpfj`fj `f ogs gdkftevgs `f oc ejvfsteacheøj, fo arc`g `f prfheseøj `fsfcdof y ogs rfhursgs `espgjedofs. `espgjedofs. ·^GTSVÅ HGJXE@FTCT OC OGHCOE[CHEØJ FJ OC FXPTCPFAEC @F MVFXPTFG7 MVFXPTFG7 Oc chhfsedeoe`c` c oc zgjc `f mufstrfg, oc udehcheøj afgarãiehc, ocs hgj`ehegjfs hoemãtehcs y oc `espgjedeoe`c` `f rfhursgs fhgjømehgs sgj ogs cspfhtgs dãsehgs c hgjse`frcrsf fj oc pocjfcheøj `fo mufstrfg. Fo rfaestrg `f oc ejigrmcheøj afgrfifrfjhec`c, uscj`g fquepgs hgmg ogs A^X, sf icheoetc oc oghcoezcheøj `f ogs mufstrfgs `ejãmehgs fj fo tefmpg y fj fspcheg, sgdrf tg`g fj ogs ouacrfs `f `eiíheo chhfsg, c `gj`f bcy quf rftgrjcr co jufvg mufstrfg.
94
0.9.0. PCMCÓG @F MVFXPTC ·@F SVÅ PTCPC FO PCMCÓG Ø^PEMG@F MVFXPTC U HVÃOFX XGJ OGX GDKFPEYGX7 Fj fstc`ístehc, fo tcmcóg øptemg `f oc mufstrc fs fo jûmfrg `f uje`c`fs `f mufstrfg g fofmfjtgs mufstrc fxtrcí`c `fy `fpfj`f ujc pgdocheøj, quf sgj jfhfscregs jfhfscr egs pcrcquf qufhgmpgjfj ogs `ctgs oc sfcj rfprfsfjtctevgs `f oc vcrecdeoe`c` `f oc pgdocheøj, `f ogs rfhursgs y tefmpg `espgjedofs< csí hgmg `f ocs hgj`ehegjfs `f mufstrfg iekc`cs pgr fo ejvfsteac`gr. Ogs gdkftevgs `f oc `ftfrmejcheøj `fo tcmcóg øptemg `f mufstrc sgj; • • •
Fstemcr fo pcrãmftrg g ogs pcrãmftrgs `f oc pgdocheøj hgj uj jevfo `f hgjiecjzc cprgpec`g. Fstcdofhfr ocs `eifrfjhecs fjtrf arupgs fj fstu`eg hgj refsag y frrgr chfptcdofs. Tf`uher ogs hgstgs g fo tefmpg `fo fstu`eg.
·HVÃOFX XGJ OCX HGJ@EHEGJFX @F MVFXPTFG7 Oc sfofhheøj `fo refsag (γ) y frrgr (`) rfhedfj fo jgmdrf `f hgj`ehegjfs `f mufstrfg. Xf `fdf tfjfr prfsfjtf quf ‟ γ ” y frrgr ‟`” jg jg sgj uj csujtg `f oc fstc`ístehc sejg `f ogs gdkftevgs `fo ejvfsteac`gr. Tefsag.- Oc prgdcdeoe`c` `f ‟icoocr” fj oc `fheseøj fstc`ístehc fstã rfprfsfjtc`g pgr ‟ pgr ‟γ γ””. . Frrgr.- Fo frrgr ‟`” rfprfsfjtc fo hcmpg `fjtrg `fo huco puf`f iouhtucr oc mf`ec `f oc pgdocheøj. ·HVÃO FX FO ^TGHF@EMEFJPG ^CTC HCOHVOCT FO PCMCÓG Ø^PEMG @F MVFXPTC FJ ^GDOCHEGJFX EJIEJEPCX7 EJIEJEPCX7 Fo prghf`emefjtg pcrc `fiejer fo tcmcóg øptemg `f mufstrc fj pgdochegjfs ejiejetcs sf iuj`cmfjtc fj fo mufstrfg fj `gs ftcpcs hgmg sf `fshredf c hgjtejucheøj; • • • •
Vj mufstrfg ejeheco (jg) sf fstcdofhfj ogs fstc`ístehgs ejehecofs mf`ec y vcrecjzc. Xf hcohuoc fo tcmcóg øptemg `f mufstrc, fstg fs, ogs fofmfjtgs quf fifhtevcmfjtf tefjfj quf mufstrfcrsf pcrc humpoer ocs hgj`ehegjfs `f mufstrfg (j). Xe sf humpofj ocs hgj`ehegjfs `f mufstrfg, fjtgjhfs jg bchf icotc uj sfauj`g mufstrfg hgmpofmfjtcreg (jh) y sf hgjhouyf quf j> fs suiehefjtf hgmg tcmcóg `f mufstrc Xe jg sf humpofj ocs hgj`ehegjfs `føptemg. mufstrfg fjtgjhfs bcy quf tgmcr ujc mufstrc hgmpofmfjtcrec (jh) y pgstfregrmfjtf sf vufovfj c rfhcohuocr ogs fstc`ístehgs mf`ec y vcrecjzc `fiejetevgs. `f iejetevgs.
98
Fo tcmcóg øptemg `f mufstrc fj pgdochegjfs ejiejetcs sf hcohuoc mf`ecjtf oc seauefjtf iørmuoc; j=
[4γ (X4) `
@gj`f; j[ = øptemg `f fquevghcrsf mufstrc = Pcmcóg ^rgdcdeoe`c` [ `f fj oc tgmc `f `fhesegjfs csghec`c csghec`c c oc `estreduheøj jgrmco hgj jevfo γ X4= Ycrecjzc `f oc mufstrc ejeheco (j>) ` = Frrgr `f mufstrfg chfptc`g ·HVÃJ@G U HØMG XF HCOHVOC VJC MVFXPTC HGM^OFMFJPCTEC7 Fj ujc premfrc ftcpc sf rfcoezc uj mufstrfg ejeheco (j>) `gj`f sf hcohuocj ogs fstc`ístehgs mf`ec y vcrecjzc. Oufag sf hcohuoc fo tcmcóg øptemg `f mufstrc (j). Xe fo tcmcóg øptemg `f mufstrc (j) rfsuotc mcygr co tcmcóg `f mufstrc ejeheco (j>), fjtgjhfs sf `ftfrmejc fo tcmcóg `f oc mufstrc hgmpofmfjtcrec (jh) hgmg oc `eifrfjhec fjtrf j y j>. jh = j ‘ j> Fj ujc sfauj`c ftcpc sf rfcoezc fo mufstrfg hgmpofmfjtcreg pcrc fifhtevcmfjtf humpoer hgj ocs hgj`ehegjfs `fo mufstrfg prfiekc`cs pgr fo jvfsteac`gr. ^TGDOFMC TFXVFOPG @ftfrmejcr fo tcmcóg øptemg `f mufstrc, fj ujc pgdocheøj ejiejetc, fj huyg mufstrfg ejeheco (j>) sf gdtuvefrgj ogs seauefjtfs `ctgs; @ctgs; j> = 8> X4 = 82248 c = >,>6 = 6% [γ = 3,59 (Xf csumf quf sf trctc `f ujc prufdc `f `gs hgocs). R = 08> arcmgs pgr pocjtc ` = 6> arcmgs Tfsuotc`g; j=
[4>,>6 (X4) `
j=
(3,59)4 (82248)
j = 65,99 ≂ 9> pocjtcs
4
(6>)
Fo tcmcóg øptemg `f mufstrc fs j = 9> pocjtcs, humpoefj`g ocs hgj`ehegjfs `f mufstrfg; refsag `f fquevghcheøj `fo 6% (fs `fher, fo 56% `f hgjiecjzc) y frrgr `f mufstrfg ³ 6> arcmgs. Fo frrgr mufstrco ej`ehc quf oc mf`ec `f oc
90
pgdocheøj sf udehc fj oc ircjkc; 08> ³ 6> arcmgs, fs `fher fjtrf 82> y 02> arcmgs, hgj fo 56% `f hgjiecjzc. ^crc humpoer ocs hgj`ehegjfs `f mufstrfg, fjtgjhfs, sf `fdf tgmcr ujc mufstrc hgmpofmfjtcrec jh quf fs oc `eifrfjhec fjtrf fo tcmcóg øptemg `f mufstrc (j) y oc mufstrc ejeheco (j>). jh = j ‘ j> jh = 9> ‘ 8> = 8> pocjtcs. Icotcr pgr mufstrfcr 8> pocjtcs pcrc humpoer ocs hgj`ehegjfs `f mufstrfg. ^TGDOFMC TFXVFOPG Hgj ogs seauefjtfs `ctgs, hcohuocr fo tcmcóg øptemg `f mufstrc pcrc uj hgjiecjzc `fo 55%. @ctgs; j> = 8> X4 = 82248 c = >,>3 = 3% (Xf csumf quf sf trctc `f ujc prufdc `f `gs hgocs) [γ = 4,61 = 08> arcmgs pgr pocjtc ` = 6> arcmgs Tfsuotc`g; j=
[4>,>3 (X4) `4
j=
(4,61)4 (82248)
j = 3>4,61 ≂ 3>8 pocjtcs
(6>)4
Fo tcmcóg øptemg `f mufstrc fs j = 3>8 pocjtcs, humpoefj`g ocs hgj`ehegjfs `f mufstrfg; refsag `f fquevghcheøj `fo 3% (fs `fher, fo 55% `f hgjiecjzc) y frrgr `f mufstrfg ³ 6> arcmgs. Hgmg puf`f gdsfrvcrsf, se sf foeaf ujc mfjgr prgdcdeoe`c` `f fquevghcheøj (fs `fher, mcygr hgjiecjzc), sf ejhrfmfjtc fo tcmcóg øptemg `f mufstrc. ^crc humpoer ocs hgj`ehegjfs `f mufstrfg, sf `fdf tgmcr ujc mufstrc hgmpofmfjtcrec jh = 3>8 ‘ 8> = 18 pocjtcs. ^TGDOFMC TFXVFOPG Hcohuocr fo tcmcóg øptemg `f mufstrc, tfjefj`g hgmg dcsf uj mufstrfg ejeheco (j>), hgj uj jevfo `f hgjiecjzc hgjstcjtf `fo 56% y uj frrgr mufstrco `f 46 arcmgs. @ctgs; j> = 8>
96
X4 = 82248 c = >,>6 = 6% (Xf csumf quf sf trctc `f ujc prufdc `f `gs hgocs) [γ = 3,59 R = 08> arcmgs pgr pocjtc ` = 46 arcmgs Tfsuotc`g; j=
[4>,>6 (X4) `4
j=
(3,59)4 (82248)
j = 482,98 ≂ 485 pocjtcs
(46)
Fo tcmcóg øptemg `f mufstrc fs; j = 485 pocjtcs, humpoefj`g ocs hgj`ehegjfs `f mufstrfg; refsag `f fquevghcheøj `fo 6% (fs `fher, fo 56% `f hgjiecjzc) y frrgr `f mufstrfg ³ 46 arcmgs. ^gr og tcjg, se sf `fsfc tfjfr uj mfjgr frrgr mufstrco, fo tcmcóg øptemg `f mufstrc, sf ejhrfmfjtc. ejhrfmfjtc. Fj fstf hcsg, oc mf`ec `f oc pgdocheøj fstã iouhtucj`g fjtrf 08> ³ 46 arcmgs< fs `fher, fjtrf 0>6 y 066 arcmgs. ^crc humpoer ocs hgj`ehegjfs `f mufstrfg, sf `fdf tgmcr ujc mufstrc hgmpofmfjtcrec jh = 485 ‘ 8> = 4>5 pocjtcs. ^TGDOFMC TFXVFOPG Vscj`g fo prgarcmc Fxhfo, hcohuocr ogs tcmcógs øptemgs `f mufstrc, tfjefj`g hgmg dcsf ogs `ctgs `f uj mufstrfg ejeheco (j>), uj jevfo `f hgjiecjzc hgjstcjtf `fo 56% y jevfofs `f frrgr mufstrco `f 6, 3>, 36, 4>, 46, 8>, 86,0>, 06, 6>, 66, 9>, 96 y 1> arcmgs. @ctgs; 8> Xj4> == 82248 c = >,>6 = 6% (Xf csumf quf sf trctc `f ujc prufdc `f `gs hgocs) [γ = 3,59 R = 08> arcmgs pgr pocjtc ` = 6, 3>, 36, 4>, 46, 8>, 86, 0>, 06, 6>, 66 y 9> arcmgs Tfsuotc`g; j=
[4>,>6 (X4) `4
j=
(3,59)4 (82248) (6)
j = 6.599 pocjtcs
99
Hãohuog `f tcmcóg øptemg `f mufstrc y mufstrc hgmpofmfjtcrec hgj jevfo `f refsag hgjstcjtf y `eifrfjtfs frrgrfs mufstrcofs.
j> 8> 8> 8> 8> 8> 8> 8> 8> 8> 8> 8> 8> 8> 8>
Mufstrc ejeheco
Tefsag
Mf`ec 08> 08> 08> 08> 08> 08> 08> 08> 08> 08> 08> 08> 08> 08>
γ
Ycrecjzc 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248 82.248
>,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6 >,>6
Frrgr ^rgdcdeoe`c` mufstrco
z 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59 3,59
` 6 3> 36 4> 46 8> 86 0> 06 6> 66 9> 96 1>
Pcmcóg gptemg `f mufstrc
Mufstrc hgmpofmfjtcrec
j 6.599 3.053 998 818 485 399 344 58 10 9> 05 03 86 8>
jh 6.589 3.093 988 808 4>5 389 54 98 00 8> 35 33 6 >
Vjc mufstrc j> = 8>, hgj ujc prgdcdeoe`c` `f fquevghcheøj `fo 56% y uj frrgr mufstrco `f 1> arcmgs, sfríc uj tcmcóg øptemg `f mufstrc. ·HØMG HCOHVOCT FO PCMCÓG Ø^PEMG @F MVFXPTC FJ ^GDOCHEGJFX IEJEPCX7 IEJEPCX7 Vjc pgdocheøj iejetc (J) fs cqufooc quf tefjf uj jûmfrg oemetc`g hgmg fo jûmfrg `f mchftcs fj uj ejvfrjc`frg, fo jûmfrg `f cjemcofs fj uj fstcdog, fo jûmfrg `f hckcs pftre fj uj ocdgrctgreg, fo jûmfrg `f fstu`ecjtfs fj uj cuoc `f hocsf. Fo tcmcóg øptemg `f mufstrc fj pgdochegjfs iejetcs, tcmdeåj sf iuj`cmfjtc fj fo mufstrfg fj `gs ftcpcs huyg prghf`emefjtg fs fo seauefjtf; • • • •
Fj mufstrfg ejeheco pcrheco (jg) sf fstcdofhfj ogs fstc`ístehgs dãsehgs mf`ec y vcrecjzc ejehecofs. Xf hcohuoc fo tcmcóg øptemg `f mufstrc (j)< pcrc humpoer hgj`ehegjfs `f mufstrfg. Xe sf humpofj ocs hgj`ehegjfs `f mufstrfg, fjtgjhfs jg bchf icotc uj mufstrfg hgmpofmfjtcreg (jh) y sf hgjhouyf quf j> fs suiehefjtf hgmg tcmcóg `f mufstrc øptemg. Xe jg sf humpofj ocs hgj`ehegjfs `f mufstrfg fjtgjhfs bcy quf tgmcr ujc mufstrc hgmpofmfjtcrec (jh) y pgstfregrmfjtf rfhcohuocr ogs fstc`ístehgs mf`ec y vcrecjzc `fiejetevgs.
91
Fo tcmcóg øptemg `f mufstrc fj pgdochegjfs iejetcs sf hcohuoc cpoehcj`g ujc hgrrfhheøj pgr pgdocheøj iejetc, crc pgdochegjfs mf`ecjtf oc seauefjtf iørmuoc, quf fs [4γ (X4) j=
(3 ‘ j> /J)
`
@gj`f; j = Pcmcóg øptemg `f mufstrc J = Pcmcóg `f oc pgdocheøj iejetc [ = ^rgdcdeoe`c` [ `f fquevghcrsf fj oc tgmc `f `fhesegjfs csghec`c c oc `estreduheøj jgrmco hgj jevfo γ X4= Ycrecjzc `f oc mufstrc ejeheco (j>) ` = Frrgr `f mufstrfg chfptc`g chfptc`g ^TGDOFMC TFXVFOPG @ftfrmejcr fo tcmcóg øptemg `f mufstrc, fj ujc pgdocheøj iejetc `f J = 3>>, fj huyg mufstrfg ejeheco (j >) sf gdtuvefrgj ogs seauefjtfs vcogrfs; @ctgs; J = 3>> j> = 8> X4 = 82248 c = >,>6 = 6% [γ = 3,59 (Xf csumf quf sf trctc `f ujc prufdc `f `gs hgocs). = 08> arcmgs pgr pocjtc ` = 6> arcmgs Tfsuotc`g; j=
[4>,>6 (X4)
(3 ‘ j> /J) /J)
`
j=
3,59)4 (82248)
(3 ‘ 8>/3>>)
(6>)
j = 9> (>,1) = 04 pocjtcs Hgmg sf tgmø ujc mufstrc ejeheco j>= 8> pocjtcs y fo tcmcóg øptemg `f mufstrc fs j= 04, bchf icotc ujc mufstrc hgmpofmfjtcrec j h = 34, pcrc humpoer ocs hgj`ehegjfs `f mufstrfg; hgjiecjzc `fo 56% y frrgr mufstrco `f 6> arcmgs.
6. @EXFÓG @F FR^FTEMFJPGX U CJÃOEXEX @F YCTECJ[C 6.3.
MÅPG@G HEFJPÍIEHG
92
·SVÅ FX EJYFXPEACHEØJ HEFJPÍIEHC7 Oc ejvfsteacheøj hefjtíiehc fs uj prghfsg sestfmãtehg y hrfctevg quf tefjf fo prgpøsetg `f cmpoecr oc irgjtfrc `fo hgjghemefjtg fj ocs hefjhecs degoøaehcs, jcturcofs, sghecofs y fj gtrgs ãmdetgs. Oc ejvfsteacheøj hefjtíiehc sf cpgyc fj fo hgjghemefjtg hefjtíiehg fxestfjtf sgdrf fo tfmc fj fstu`eg (rfveseøj `f oetfrcturc) y sf dcsc fj fo måtg`g hefjtíiehg, rfquefrf `f rfhursgs mctfrecofs y tcofjtgs pcrc oc fxpfremfjtcheøj, fxeaf `f bgjfste`c` ejtfofhtuco y prgifsegjcoesmg fj oc tgmc `f `fhesegjfs y fj oc `esfmejcheøj `f ogs rfsuotc`gs. ·HØMG XF @FIEJF MÅPG@G HEFJPÍIEHG7 Fo måtg`g hefjtíiehg fs uj prghfsg `fstejc`g c fxpoehcr ifjømfjgs, fstcdofhfr rfochegjfs vfreiehcdofs fjtrf ogs bfhbgs, hgjstruer hgjghemefjtg vãoe`g y `esfócr cpoehchegjfs ûteofs c oc sghef`c`. Hcdf ej`ehcr quf oc hefjhec fs uj hgjkujtg `f hgjghemefjtgs dcsc`gs fj prufdcs y fve`fjhecs hgjiecdofs quf tefjf fo prgpøsetg `f fxpoehcr hømg sf fstruhturcj y iujhegjcj ogs ifjømfjgs jcturcofs, sghecofs y gtrgs prghfsgs, mf`ecjtf fo måtg`g hefjtíiehg. Fo måtg`g hefjtíiehg hgjstc `f hejhg pcsgs; Gdsfrvcheøj Oc gdsfrvcheøj hgjsestf fj pgjfr ctfjheøj fj uj bfhbg, prgdofmc g ifjømfjg jcturcofs, degoøaehg, sgheco g uj prghfsg hucoquefrc, uscj`g ogs sfjte`gs. Oc gdsfrvcheøj `f uj bfhbg, prgdofmc g ifjømfjg hgjoofvc c oc rfiofxeøj y c oc igrmuocheøj `f ocs prfaujtcs; ·hømg7, ·huãj`g7, ·huão7, ·`øj`f7. ^gr fkfmpog; ·Huão fs oc hcusc `fo cmcreoocmefjtg `f åstcs pocjtcs7. Igrmuocheøj `f bepøtfses Fo gdsfrvc`gr, oufag `f rfiofxegjcr sgdrf ogs bfhbgs, prgdofmcs g ifjømfjgs trctc `f fxpoehcrogs y focdgrc rfspufstcs oøaehcs (rczgjcmefjtg ej`uhtevg) quf hgjstetuyfj ocs bepøtfses `f ejvfsteacheøj. ^crc uj mesmg bfhbg, ifjømfjg g prgdofmc sf puf`fj igrmuocr ujc g vcrecs bepøtfses. Vjc bepøtfses fs ujc `fhocrcheøj prfoemejcr quf puf`f sfr icosc g vfr`c`frc oc mesmc quf `fdf sfr sgmfte`c c ujc prufdc fstc`ístehc. Fkfmpog; Fo cmcreoocmefjtg `f fstcs pocjtcs tefjf su hcusc fj oc icotc `f jetrøafjg csemeocdof fj fo sufog. ^rufdc `f bepøtfses Ocs bepøtfses sgmftfjFstcs c prufdcs fstc`ístehcsfjpcrc hgmprgdcr su fohcuscoe`c` ghurrfjhec fj `f fo iuturg. hgmprgdchegjfs, hgjkujtg, rfhedfj jgmdrf `fy fxpfremfjtcheøj. Oc fxpfremfjtcheøj hgjsestf fj sgmftfr c uj ej`eve`ug, gdkftg g prghfsg c vcrechegjfs hgjtrgoc`cs. Fj oc fxpfremfjtcheøj hgjtrgoc`c `fdf bcdfr `gs
95
arupgs `f prufdc; uj ej`eve`ug, gdkftg g prghfsg oocmc`g tfsteag y gtrg oocmc`g trctcmefjtg fxpfremfjtco. Fo tfsteag y trctcmefjtg (s) sf sgmftfj c ocs mesmcs hgj`ehegjfs `fo fjtgrjg, fxhfptg fj fo ichtgr fj fstu`eg quf cifhtcrã sgog co trctcmefjtg fxpfremfjtco. @fheseøj fstc`ístehc Ogs rfsuotc`gs `f oc fxpfremfjtcheøj sf cjcoezcj f ejtfrprftcj, sf fstcdofhfj ocs sfmfkcjzcs y `eifrfjhecs fjtrf tfsteag y trctcmefjtg (s) uscj`g `eifrfjtfs tåhjehcs, sf rfhbczcj ocs bepøtfses icoscs bcstc chfptcr oc mãs cprgpec`c, csumefj`g hgj`ehegjfs fspfhíiehcs `f refsag y frrgr. @fscrrgoog `f oc tfgríc Huãj`g oc bepøtfses `f ejvfsteacheøj sf vfreiehc mf`ecjtf oc prufdc `f bepøtfses y sf tgmc ujc `fheseøj fstc`ístehc, sf puf`f bchfr ejifrfjhec fstc`ístehc y prf`fher fo iuturg, `fscrrgoocr oc tfgríc y hgjtreduer c oc hgjstruhheøj `fo hgjghemefjtg. Huregse`c`
Gdsfrvcheøj
Igrmuocheøj `f bepøtfses
^rufdc `f bepøtfses
Tfiofxeøj
• Bfhbgs
^rfaujtcs
• ^rgdofmcs Ifjømfjgs
Tczgjcmefjtg ej`uhtevg ^rgpufstcs
^rgdcdeoe`c` Mufstrc - ^gdocheøj
• Hcuscs prgdcdofs • Tfspufstcs prgdcdofs • @fhocrcheøj prfoemejcr
• Hcmpg fxpfremfjtco • Fxpfremfjtcheøj • Påhjehcs fstc`ístehcs • Xeajeiehcheøj
• Icotc `f
hgjsestfjhec
• Ejchfptcdof frrgr
fxpfremfjtco
• Cotg hgfiehefjtf `f
vcrecheøj • p: jevfo `f seajeiehcheøj prf`fieje`g
JG Jg sf chfptc oc bepøtfses `f ejvfsteacheøj
@fheseøj
XE
Xf chfptc oc bepøtfses `f
@fscrrgoog `f oc tfgríc
6.4. FR^FTEMFJPCHEØJ ·FJ SVF HGJXEXPF OC FR^FTEMFJPCHEØJ7
• Jufvcs rfiofxegjfs • Jufvcs prfaujtcs • Jufvcs bepøtfses • Jufvcs prufdcs uerr c rfj` rfj`ef efj` j`gg • Xf ue
1>
Oc fxpfremfjtcheøj fs fo prghfsg `f cpoehcheøj `fo måtg`g hefjtíiehg pcrc `fmgstrcr oc hcuscoe`c` `f bfhbgs g ifjømfjgs, prgdcj`g bepøtfses fstc`ístehcs g rfprg`uhefj`g ogs rfsuotc`gs fxpfremfjtcofs prfvegs. Fo prghfsg `f fxpfremfjtcheøj hgmprfj`f ujc sfref `f ftcpcs ejtfrrfochegjc`cs quf sf ejehec hgj oc e`fjteiehcheøj `f ogs prgdofmcs, oc `fiejeheøj `f ocs hcuscs `fo prgdofmc, oc pregrezcheøj `f ogs ichtgrfs fj fstu`eg, fstcdofhemefjtg `f ogs gdkftevgs, oc igrmuocheøj `f bepøtfses, fo `esfóg `f ogs trctcmefjtgs, oc sfofhheøj `fo `esfóg fxpfremfjtco cprgpec`g, oc `fiejeheøj `f ocs hcrchtfrístehcs `f oc uje`c` fxpfremfjtco, hgjtrgo `f fifhtgs `f dgr`f, `fiejeheøj `f vcrecdofs `f rfspufstc, `foejfcmefjtg `f ogs cjãoeses fstc`ístehgs, fkfhuheøj `fo fxpfremfjtg, cjãoeses f ejtfrprftcheøj `f ogs rfsuotc`gs y focdgrcheøj `fo ejigrmf tåhjehg. ·HØMG E@FJPEIEHCT OGX ^TGDOFMCX @F EJYFXPEACHEØJ7 Vj prgdofmc sf `fiejf hgmg ujc setucheøj cjgrmco fj uj prghfsg, fs ujc setucheøj `f `fsfqueoedreg quf sf mcjeiefstc hgmg coag jg `fsfc`g. `fsfc`g. Ogs prgdofmcs `fdfj sfr e`fjteiehc`gs y pregrezc`gs pcrtehepctevcmfjtf pgr ogs ejvgouhrc`gs fj ogs prghfsgs `f prg`uhheøj y trcjsigrmcheøj. Fjtrf ocs tåhjehcs pcrc oc e`fjteiehcheøj `f ogs prgdofmcs `f ejvfsteacheøj sf mfjhegjcj; ocs fxpfrefjhecs `f ogs ejvfsteac`grfs, c`mejestrc`grfs, prg`uhtgrfs y trcdckc`grfs< ogs mfhcjesmgs `f ejigrmcheøj y rftrgcoemfjtcheøj< ocs rfujegjfs muote`eshepoejcrecs `f trcdckg< ogs `ecajøstehgs< ocs fjhufstcs y ogs hfjsgs. Fxestfj vcrecs bfrrcmefjtcs pcrtehepctevcs cjcoezcr ogs prgdofmcs `f uj prghfsg `f prg`uhheøj g trcjsigrmcheøj hgmg; fo `ecarcmc hcusc-fifhtg, fo ãrdgo `f prgdofmcs, oc hgmpcrcheøj cpcrfc`c, fo `ecarcmc `f ^crftg, fo cjãoeses `f irfhufjhecs, fjtrf gtrcs. Hgj fstgs prghf`emefjtgs sf puf`f puf`f `fiejer fo prgdofmc mãs empgrtcjtf quf cifhtc fo prghfsg (prgdofmc hfjtrco). Fj oc carehuoturc fhuctgrecjc, ogs prgdofmcs hfjtrcofs mcs irfhufjtfmfjtf hetc`gs sgj; oc dckc prg`uhteve`c` `f ogs huotevgs< oc `fiehefjtf hcoe`c` `f ogs prg`uhtgs< ogs cotgs hgstgs `f prg`uhheøj caríhgoc g cargej`ustreco< ogs rfse`ugs `f pocauehe`cs fj ogs prg`uhtgs caríhgocs y oc hgjtcmejcheøj `fo sufog, cauc y cerf.
·HØMG @FIEJET U ^TEGTE[CT OCX HCVXCX @FO ^TGDOFMC HFJPTCO7 Oc dckc prg`uhteve`c` fs uj fifhtg (prgdofmc) quf tefjf sus hcuscs fj ogs ichtgrfs oemetcjtfs `f oc prg`uhteve`c`. Vj ichtgr oemetcjtf `f oc prg`uhteve`c` hgjstetuyf uj ichtgr quf empe`f gdtfjfr jevfofs `f prg`uhteve`c` mãs cotgs, ichtedof `f sfr mf`e`g, hucjteiehc`g y hgrrfae`g. ^gr fkfmpog; Vsg `f vcref`c`fs pghg prg`uhtevcs, dckcs `fjse`c`fs `f sefmdrc dckcs, jg usg `f refag, `fiehefjhec `f jetrøafjg, `fiehefjhec `f iøsigrg, `fiehefjhec `f mehrg fofmfjtgs, cotc ejhe`fjhec `f pocacs g cotc ejhe`fjhec `f fjifrmf`c`fs.
13
Fifhtg; ^rgdofmc
Hcuscs; Ichtgrfs oemetcjtfs • Vsg `f vcref`c`fs pghg
prg`uhtevcs
• @fjse`c`fs `f sefmdrc dckcs • Jg usg `f refag • @fiehefjhec `f J • @fiehefjhec `f ^ • @fiehefjhec `f mehrg fofmfjtgs • Cotc ejhe`fjhec `f pocacs • Cotc ejhe`fjhec `f fjifrmf`c`fs
Dckc prg`uhteve`c`
Fo cjãoeses `fo usg `f vcref`c`fs pghg prg`uhtevcs pfrmeteríc `f`uher quf bcy pgsedeoe`c`fs `f tfjfr jufvcs vcref`c`fs `f mcygr rfj`emefjtg, quf sf puf`fj c`cptcr c ocs hgj`ehegjfs oghcofs `fo fstu`eg. Fo cjãoeses `f ocs `fjse`c`fs `f sefmdrc dckcs seajeiehcríc quf bcy pgsedeoe`c`fs hefrtcs `f ejhrfmfjtcr fo jûmfrg `f pocjtcs pgr bfhtãrfc, hgj `eifrfjtfs crrfaogs fspchecofs. Oc `fiehefjhec `f jetrøafjg fj fo sufog puf`f sfr `ftfrmejc`g mf`ecjtf cjãoeses químehg `fo sufog, bcdefj`g ocs pgsedeoe`c`fs hefrtcs `f hgrrfaersf mf`ecjtf oc c`eheøj `f cdgjgs jetrgafjc`gs `f `eifrfjtfs iufjtfs. Jg fs pgsedof trctcr tg`gs ogs ichtgrfs oemetcjtfs `f oc prg`uhheøj g trcjsigrmcheøj `f mcjfrc semuotãjfc, `fde`g c ogs hgstgs `f oc ejvfsteacheøj, c sus fifhtgs `eifrfjhec`gs f ejtfrchhegjfs. Fj hgjsfhufjhec, uscj`g `evfrscs bfrrcmefjtcs, sf `fdfj pregrezcr ogs ichtgrfs oemetcjtfs pcrc dushcr sgouhegjfs `f mcygr empchtg fj fo mfjgr tefmpg pgsedof. Ogs ichtgrfs oemetcjtfs `f oc prg`uhheøj, e`fjteiehc`gs hgmg hcuscs `fo prgdofmc hfjtrco sf cjcoezcj y pregrezcj hgj oc pcrtehepcheøj `f ogs chtgrfs `f ogs prghfsgs, fj iujheøj `f su arc`g `f empchtg `erfhtg y pcrc ogs hucofs jg bcy ujc cotfrjctevc sfaurc `f sgouheøj. C hgjtejucheøj sf ej`ehc uj fkfmpog `f pregrezcheøj `f ocs hcuscs `f oc dckc prg`uhteve`c` caríhgoc, uscj`g fo cjãoeses `f irfhufjhecs; Hcuscs cjcoezc`cs • • • • • •
Vsg `f vcref`c`fs pghg prg`uhtevcs @fjse`c`fs `f sefmdrc dckcs Jg usg `f refag @fiehefjhec `f J @fiehefjhec `f ^ @fiehefjhec `f mehrg fofmfjtgs
Cotc ejhe`fjhec `f pocacs •• Cotc ejhe`fjhec `f fjifrmf`c`fs • Gtrgs
Hgjtrgo
^regrezcheøj `f ocs hcuscs
EEEEEEEEEEEEEEEEE = 31 EEEEE = 6 EEEEEEEEEE = 3> EEEEEEEEEEEEEE = 30 EEEEEE = 9 EEEE = 0
3. Ycref`c`fs pghg prg`uhtevcs 4. Cotc ejhe`fjhec `f fjifrmf`c`fs 8. @fiehefjhec `f J 0. Jg usg `f refag 6. @fiehefjhec `f ^ 9. @fjse`c`fs dckcs
EE = 4 EEEEEEEEEEEEEEEE = 39 E = 3
1. @fiehefjhecs `f mehrg fofmfjtgs 2. Cotc ejhe`fjhec `f pocacs 5. Gtrgs
14
Fo cjãoeses `f pregrezcheøj pfrmetf `fiejer uj rcjag `f hcuscs fj gr`fj `f pregre`c`. Ocs trfs hcuscs mãs empgrtcjtfs `f oc dckc prg`uhteve`c`, rfsuotc`g `fo prfsfjtf cjãoeses, sgj ocs seauefjtfs; 3). Ycref`c`fs pghg prg`uhtevcs 4). Cotc ejhe`fjhec `f fjifrmf`c`fs 8). @fiehefjhec `f jetrøafjg jetrøafjg ·HØMG @FIEJET FO GDKFPEYG @F OC EJYFXPEACHEØJ7 Fo gdkftevg `f ujc ejvfsteacheøj fs oc `fhocrcheøj `f oc sgouheøj `f uj prgdofmc `f ejvfsteacheøj. Vj gdkftevg fs oc gpheøj quf sf pocjtfc hgmg rfspufstc co prgdofmc hfjtrco y tefjf quf sfr rfsuotc`g `f chhegjfs hgjhrftcs y rfcoezcdofs. ^gr fkfmpog, se fo prgdofmc fs oc dckc prg`uhteve`c`, fo gdkftevg `f oc fxpfremfjtcheøj hgjsesterã fj fofvcr oc prg`uhteve` prg`uhteve`c` c` fj dcsf `f ………… (e`fjteiehc fo ichtgr g ichtgrfs fj fstu`eg y fo `gmejeg `f rfhgmfj`cheøj). Fj fo prghfsg `f pocjfcheøj `f oc ejvfsteacheøj, ogs ichtgrfs oemetcjtfs (hcuscs) `f oc dckc prg`uhteve`c` (fifhtg) sf ej`ehcj fj sfjte`g pgsetevg. Ogs ichtgrfs oemetcjtfs sf sf tgrjcj fj ichtgrfs fj fstu`eg y fo prgdofmc hfjtrco fj gdkftevg. Hcdf ej`ehcr quf yc jg sf bchf rfifrfjhec c tg`gs ogs ichtgrfs oemetcjtfs sejg c cqufoogs pregrezc`gs pcrtehepctevcmfjtf. Ichtgrfs `f fstu`eg
Fifhtg; Gdkftevg
• Ycref`c`fs mfkgrc`cs • Hgjtrgo ejtfarc`g `f fjifrmf`c`fs • Ifrteoezcheøj jetrgafjc`c
Ejhrfmfjtcr oc prg`uhteve`c`
Fstg seajeiehc quf fo usg `f vcref`c`fs mfkgrc`cs, fo hgjtrgo ejtfarc`g `f fjifrmf`c`fs y oc ifrteoezcheøj jetrgafjc`cs `ftfrmejcrícj uj ejhrfmfjtg `f oc prg`uhteve`c` caríhgoc. Hcdf `fstchcr quf sf fstã rfierefj`g c trfs ichtgrfs fj fstu`eg hgj fo gdkftevg `f ejhrfmfjtcr oc prg`uhteve`c`. ·HØMG IGTMVOCT OC BE^ØPFXEX @F EJYFXPEACHEØJ7 Vjc bepøtfses `f ejvfsteacheøj sf `fiejf hgmg uj rfsuotc`g fspfrc`g `f oc cpoehcheøj `f oc tfgríc quf sf fstã prgdcj`g. Vjc bepøtfses `f ejvfsteacheøj tefjf hgmg fofmfjtgs; fo jûmfrg `f ichtgrfs fj fstu`eg, fo gdkftevg, oc e`fjteiehcheøj `fo prghfsg y oc oghcoezcheøj. ^gr fkfmpog; fo usg `f vcref`c`fs mfkgrc`cs, fo hgjtrgo ejtfarc`g `f fjifrmf`c`fs y oc ifrteoezcheøj jetrgafjc`c hgjtreduyfj seajeiehctevcmfjtf c ejhrfmfjtcr oc prg`uhteve`c` caríhgoc.
18
Vjc bepøtfses `f ejvfsteacheøj `fdf prfhescr, c`fmãs `f ogs ichtgrfs fj fstu`eg y gdkftevg, oc e`fjteiehcheøj `fo huotevg y fo `gmejeg `f rfhgmfj`cheøj `gj`f sf bchf oc fxpfremfjtcheøj. ·HØMG XF IGTMVOCJ OCX BE^ØPFXEX FXPC@ÍXPEHCX7 Ocs bepøtfses fstc`ístehcs sgj `f `gs tepgs y fxhouyfjtfs fjtrf sí; oc bepøtfses juoc y oc bepøtfses cotfrjctevc. Bepøtfses juoc.- fstc fstc bepøtfses fstc`ístehc ej`ehc ej `ehc `eifrfjhecs juocs fjtrf ocs mf`ecs. B> = m3 = m4<
m4 - m3=>
Bepøtfses cotfrjctevc.- fstc bepøtfses fstc`ístehc ej`ehc `fseauco`c` fjtrf ocs mufstrcs. B3 = m3≮m4<
m4 - m3≮>
^gr og tcjtg< se m3≮m4, seajeiehc quf fstc`ístehcmfjtf; m3: m4, ø m3?m4. ·@F SVF PTCPC FO @EXFÓG @F OGX PTCPCMEFJPGX7 Vj trctcmefjtg fs oc hgmdejcheøj `f ichtgrfs y jevfofs fj fj fstu`eg. ^crc fstf mgmfjtg `f oc pocjfcheøj sf bcdrã `fieje`g se fo fxpfremfjtg fs `f uj ichtgr fj fstu`eg, `f `gs ichtgrfs fj fstu`eg, `f trfs g mãs ichtgrfs fj fstu`eg. @esfóg `f trctcmefjtgs `f uj ichtgr fj fstu`eg fstu`eg Fj fxpfremfjtgs hgj uj sgog ichtgr fj fstu`eg; uj jevfo hgrrfspgj`f c uj trctcmefjtg. ^gr fkfmpog, se fo ichtgr fj fstu`eg fs Ycref`c`fs mfkgrc`cs; hc`c vcref`c` c sfr prgdc`c hgjstetuyf uj trctcmefjtg. Fo fxpfremfjtg, pgr og tcjtg, sfríc `f 6 trctcmefjtgs pgr r rfpftehegjfs.
Ichtgr fj fstu`eg Ycref`c`fs
Jevfofs Y3; tfsteag
Y4
Y8
Y0
Y6
Fj fstf hcsg; Y3, Y4, Y8, Y0 y Y6 hgrrfspgj`fj c ocs vcref`c`fs c sfr prgdc`cs, `gj`f ujc `fdf hgrrfspgj`fr c oc vcref`c` tfsteag (fkfmpog; Y3). Fj oc pocjfcheøj `fo fxpfremfjtg, fj tg`gs ogs hcsgs, `fdfj hgjse`frcrsf ogs trctcmefjtgs, fo jûmfrg `f rfpftehegjfs, fo tcmcóg y tepg `f ocs uje`c`fs fxpfremfjtcofs, fo `esfóg fxpfremfjtco cprgpec`g, fo fifhtg `f dgr`f, fo mcjfkg `fo fjscyg, fo rfaestrg `f ogs `ctgs, fjtrf gtrgs cspfhtgs.
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@esfóg `f trctcmefjtgs `f `gs g mãs ichtgrfs ichtgrfs fj fs fstu`eg tu`eg Fo `esfóg `f ogs trctcmefjtgs hgjsestf fj oc hgmdejcheøj rchegjco `f ogs ichtgrfs y jevfofs fj fstu`eg hgj fo prgpøsetg `f cohcjzcr ogs gdkftevgs `f oc ejvfsteacheøj. Ogs jevfofs fj fstu`eg puf`fj sfr ujeigrmfs g `eifrfjtfs pcrc hc`c ichtgr. Hucj`g ogs jevfofs `f fstu`eg jg sgj eaucofs pcrc tg`gs ogs ichtgrfs fj fstu`eg sf trctc `f uj ichtgreco sempof. Hucj`g ogs jevfofs eaucofs eaucofs pcrc hc`c ichtgr fj fstu`eg, D fjtgjhfs sf trctc `fo mg`fog (C) . @øj`f, C fs fo jûmfrg `f jevfofs fj fstu`eg pgr ichtgr y D fo jûmfrg `f ichtgrfs. @esfóg `f trctcmefjtgs `f uj ichtgreco sempof Fj fxpfremfjtgs hgj `gs ichtgrfs, uj trctcmefjtg hgrrfspgj`f c ujc hgmdejcheøj `f ichtgrfs y jevfofs fj fstu`eg. ^gr fkfmpog, se uj ichtgr fj fstu`eg fs Ycref`c`fs mfkgrc`cs fj hejhg jevfofs (6 vcref`c`fs) y fo gtrg ichtgr fs `fjse`c`fs (jûmfrg `f pocjtcs /bfhtãrfc) fj trfs jevfofs (8 `fjse`c`fs), ogs trctcmefjtgs sgj oc hgmdejcheøj `f ogs `gs ichtgrfs y sus hgrrfspgj`efjtfs jevfofs fj fstu`eg. Fj fstf hcsg sf trctcríc `f uj fxpfremfjtg ichtgreco 6 x 8 = 36 trctcmefjtgs hgj r rfpftehegjfs.
Ichtgrfs fj fstu`eg Ycref`c`fs
Jevfofs Y3; tfsteag
@fjse`c`fs pgdochegjcofs
@3; dckc
Y4
Y8
@4; mf`ec @8; cotc
Y0
Y6
-
-
Ogs trctcmefjtgs `fo fxpfremfjtg deichtgreco sf puf`fj gracjezcr `f oc seauefjtf mcjfrc;
3 4 8 0 6 9 1 2 5 3>
Ichtgr; Ycref`c`fs Ycref`c`fs Y3 Y3 Y3 Y4 Y4 Y4 Y8 Y8 Y8 Y0
Ichtgr; @fjse`c`fs @3 @4 @8 @3 @4 @8 @3 @4 @8 @3
33 34 38 30 36
YY00 Y6 Y6 Y6
@ @48 @3 @4 @8
Prctcmefjtgs
Hø`eag
@fshrepheøj
Y3@3 Y3@4 Y3@8 Y4@3 Y4@4 Y4@8 Y8@3 Y8@4 Y8@8 Y0@3
Ycref`c` 3 tfsteag fj `fjse`c` dckc Ycref`c` 3 tfsteag fj `fjse`c` mf`ec Ycref`c` 3 tfsteag fj `fjse`c` cotc Ycref`c` 4 fj `fjse`c` dckc Ycref`c` 4 fj `fjse`c` mf`ec Ycref`c` 4 fj `fjse`c` cotc Ycref`c` 8 fj `fjse`c` dckc Ycref`c` 8 fj `fjse`c` mf`ec Ycref`c` 8 fj `fjse`c` cotc Ycref`c` 0 fj `fjse`c` dckc
YY00@ @48 Y6@3 Y6@4 Y6@8
Ycref`c` Ycref`c` 00 fj fj `fjse`c` `fjse`c` mf`ec cotc Ycref`c` 6 fj `fjse`c` dckc Ycref`c` 6 fj `fjse`c` mf`ec Ycref`c` 6 fj `fjse`c` cotc
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@esfóg `f trctcmefjtgs `f fxpfremfjtgs (C)D Xupøjacsf quf sf trctc `f uj fxpfremfjtg `f 8 ichtgrfs (C, D, H) pgr 8 jevfofs `f fstu`eg pcrc hc`c ichtgr, fjtgjhfs, sf tfj`ríc; (8)8 = 41 trctcmefjtgs. Ichtgrfs y jevfofs fj fstu`eg
Ichtgrfs fj fstu`eg C D H
3 C3 D3 H3
Jevfofs 4 C4 D4 H4
8 C8 D8 H8
Prctcmefjtgs fj fstu`eg Prctcmefjtgs 3 4 8 0 6 9 1 2 5 3> 33 34 38 30 36 39 31 32 35 4> 43 44 48 40 46 49 41
Ichtgr C C3 C3 C3 C3 C3 C3 C3 C3 C3 C4 C4 C4 C4 C4 C4 C C44 C4 C8 C8 C8 C8 C8 C8 C8 C8 C8
Ichtgr D D3 D3 D3 D4 D4 D4 D8 D8 D8 D3 D3 D3 D4 D4 D4 D D88 D8 D3 D3 D3 D4 D4 D4 D8 D8 D8
ICHPGT H H3 H4 H8 H3 H4 H8 H3 H4 H8 H3 H4 H8 H3 H4 H8 H H34 H8 H3 H4 H8 H3 H4 H8 H3 H4 H8
HØ@EAG C3D3H3 C3D3H4 C3D3H8 C3D4H3 C3D4H4 C3D4H8 C3D8H3 C3D8H4 C3D8H8 C4D3H3 C4D3H4 C4D3H8 C4D4H3 C4D4H4 C4D4H8 CDH C44D88H34 C4D8H8 C8D3H3 C8D3H4 C8D3H8 C8D4H3 C8D4H4 C8D4H8 C8D8H3 C8D8H4 C8D8H8
19
·HVÃOFX XGJ OCX HCTCHPFTÍXPEHCX @F OC VJE@C@ FR^FTEMFJPCO7 Vjc uje`c` fxpfremfjtco fs fo fofmfjtg g hgjkujtg `f fofmfjtgs, ej`eve`ugs u gdkftgs sgdrf ogs hucofs sf cpoehc uj trctcmefjtg. Xe fo fxpfremfjtg fs hgj cjemcofs, ujc uje`c` fxpfremfjtco puf`f sfr uj cjemco g uj arupg `f cjemcofs< se fo fxpfremfjtg fs fj pocjtcs pfrfjjfs hgmg fo hchcg, oc uje`c` fxpfremfjtco puf`f sfr ujc pocjtc g uj arupg `f pocjtcs< se fo fxpfremfjtg fs fj huotevgs `f hehog hgrtg, oc uje`c` fxpfremfjtco puf`f sfr uj ãrfc `ftfrmejc`c< se fo fxpfremfjtg fs c jevfo `f ocdgrctgreg, ujc uje`c` fxpfremfjtco puf`f sfr ujc hckc pftre g uj arupg `f hckcs pftre. Fj uj fxpfremfjtg, tg`cs ocs uje`c`fs fxpfremfjtcofs `fdfj sfr mãs g mfjgs bgmgaåjfcs, tg`gs ogs ichtgrfs fxtfrjgs `fdfj sfr hgjtrgoc`gs fj tg`cs ocs uje`c`fs fxpfremfjtcofs, `f mg`g quf ocs vcrechegjfs quf puf`cj mf`ersf sfcj fo rfsuotc`g `fo fifhtg `f ogs trctcmefjtgs. Ocs hcrchtfrístehcs hcrchtfrístehcs `fo hcmpg fxpfremfjtco `ftfrmejcj ocs hcrchtfrístehcs `f oc uje`c` fxpfremfjtco. Vj hcmpg fxpfremfjtco puf`f jg tfjfr jejaujc arc`efjtf, puf`f tfjfr arc`efjtf fj ujc sgoc `erfhheøj, puf`f tfjfr arc`efjtfs fj `gs `erfhhegjfs, g puf`f sfr muy bftfrgaåjfg. Fj hc`c herhujstcjhec of hgrrfspgj`frã uj tepg `f `esfóg dãsehg, c oc huco sf c`cptcrã oc uje`c` fxpfremfjtco. @fjtrg `f oc uje`c` fxpfremfjtco sf fjhufjtrcj ogs fofmfjtgs `f mufstrfg g uje`c`fs mufstrcofs `gj`f sf tgmcrãj ogs `ctgs prfvecmfjtf pocjfc`gs. Fj coaujgs hcsgs oc uje`c` mufstrco puf`f sfr oc mesmc uje`c` fxpfremfjtco. ^gr fkfmpog, se oc uje`c` fxpfremfjtco iufrc ujc pcrhfoc `f mcíz y sf prghf`f c hgsfhbcr tg`g y c rfcoezcr mf`ehegjfs sgdrf fsf tg`g. ·HØMG HGJPTGOCT OGX FIFHPGX @F DGT@F7 Oc uje`c` fxpfremfjtco puf`f sfr cifhtc`c pgr ichtgrfs fxtfrjgs g pgr fifhtgs `f ogs trctcmefjtgs `eifrfjtfs co quf fs sgmfte`g fj oc prufdc. Ogs fifhtgs `f ogs ichtgrfs fxtfrjgs c oc uje`c` y `fhgjtrgoc`gs ogs gtrgs pcrc trctcmefjtgs ocs uje`c`fs fxpfremfjtcofs vfhejcsfxpfremfjtco tefjfj quf sfr quf ocs `f vcrechegjfs quf prfsfjtfj sgog sfcj pgr fo fifhtg `fo trctcmefjtg fj fstu`eg. Fstg sf hgjghf hgmg hgjtrgo `f ogs fifhtgs `f dgr`f, fo mesmg quf `fpfj`f `f oc uje`c` fxpfremfjtco, `fo tepg `f fxpfremfjtg y `fo tepg `f trctcmefjtg. Hcsg 3; 3; Fj uj arupg `f dgvejgs sf bc `fieje`g uj cjemco hgmg uje`c` fxpfremfjtco (pgr fkfmpog; ujc vchc = uje`c` fxpfremfjtco), `gj`f sf prufdcj vchujcs pcrc prfvfjer ujc fjifrmf`c` verco (ujc vchujc = uj trctcmefjtg), ocs mesmcs quf sgj ejyfhtc`cs hc`c hefrtg tefmpg (tepg `f fxpfremfjtg). Fj fstf hcsg jg bcdríc uj fifhtg `f dgr`f, fo trctcmefjtg jg cifhtc co cjemco vfhejg. Fstf mesmg hgjhfptg sf cpoehcríc pcrc fxpfremfjtgs `gj`f oc uje`c` fxpfremfjtco fs hgjkujtg `f cjemcofs, mchftc g uj hgjkujtg `f mchftcs, ujc hckc pftre g uj uj hgjkujtg `f hckcs pftre, ujujc ãrdgo g uj hgjkujtg `f ãrdgofs.
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Hcsg 4; 4; Fj fxpfremfjtgs `f ãrfcs arcj`fs hgmg fj ujc pocjtcheøj `f dcjcjg (p.f.; pcrhfocs `f 4> bfhtãrfcs) g fj fxpfremfjtgs fj huotevgs `f hehog hgrtg (p.f.; pcrhfocs `f 4 x 3 mftrgs) g pfrfjjfs (p.f.; 36 pocjtcs gr`fjc`cs fj 8 beofrcs `f 6) `gj`f bcy fo refag `f fifhtgs trcsocpc`gs `f ogs trctcmefjtgs sf `fdfj tgmcr ogs `ctgs `fshcrtcj`g fo ãrfc `f trcsocpf. Fstc prãhtehc sf cpoehc c muhbgs fjscygs `gj`f sf prufdcj ejsfhtehe`cs, iujaehe`cs, bfrdehe`cs, oãmejcs `f refag, ifrteoezcjtfs co sufog g igoecrfs, rfauoc`grfs `f hrfhemefjtg, pg`cs g rfauocheøj `f sgmdrc. Fj fo arãiehg seauefjtf sf ej`ehc, hgmg fkfmpog, trfs uje`c`fs fxpfremfjtcofs quf hgrrfspgj`fj c trfs trfs `eifrfjtfs trctcmefjtgs. trctcmefjtgs. Fjtrf ujc uje`c` uje`c` fxpfremfjtco y gtrc, co cpoehcr ogs trctcmefjtgs, fxestf uj ãrfc `f trcsocpf. ^crc fvcoucr fo fifhtg `fo trctcmefjtg, ocs pocjtcs `f oc uje`c` fxpfremfjtco tefjfj quf udehcrsf bchec fo hfjtrg `f oc pcrhfoc, cofkc`c `fo ãrfc `f trcsocpf. Vje`c` fxpfremfjtco; P8
f p c o s c r t f ` c f r Ã
g f r t s f u m f ` c f r Ã
f p c o s c r t f ` c f r Ã
Vje`c` Fxpfremfjtco; P3
Vje`c` Fxpfremfjtco; P4
g f r t s f u m f ` c f r Ã
g f r t s f u m
f p c o s r c t f ` c f r Ã
` f c f r Ã
f p c o s r c t f ` c f r Ã
Hcsg 8; 8; Fo mesmg hgjhfptg ej`ehc`g pcrc fo hcsg 4 sf cpoehc fj ogs prghfsgs ej`ustrecofs, pgr fkfmpog, hucj`g sf uscj ocs mesmcs mcquejcrecs fj tefmpgs `eifrfjtfs, prgdcj`g `eifrfjtfs cotfrjctevcs tfhjgoøaehcs, hucj`g focdgrcmgs uj prg`uhtg cargej`ustreco hgj mctfrec premc `f `eifrfjtf greafj, `eifrfjtf arc`g `f tgsteøj u hucoquefr gtrg ichtgr fj fstu`eg. ·XFOFHHEØJ @FO @EXFÓG FR^FTEMFJPCO C^TG^EC@G7 @esfóg fxpfremfjtco fs fo hgjkujtg `f prghf`emefjtgs quf pfrmetfj fspfheiehcr ocs uje`c`fs `f prufdc, ogs trctcmefjtgs, fo prghfsg `f mufstrfg, fo rfaestrg `f ogs `ctgs `f ocs vcrecdofs ej`fpfj`efjtfs y `fpfj`efjtfs< csí hgmg, fo hgjtrgo `f ocs vcrecdofs fxtríjsfhcs. fxtríjsfhcs. Fj gtrcs pcocdrcs, `esfóg fxpfremfjtco fs fo prghf`emefjtg pcrc fo crrfaog y `estreduheøj `f ogs trctcmefjtgs fj ocs uje`c`fs fxpfremfjtcofs pcrc prgdcr oc bepøtfses pocjtfc`c seauefj`g uj fsqufmc prfiekc`g `f cjtfmcjg pgr fo ejvfsteac`gr. Ogs `esfógs fxpfremfjtcofs sf grefjtcj c prgdcr bepøtfses, hgmpcrcr rfspufstcs, fstemcr pcrãmftrgs y gdtfjfr ejigrmcheøj ûteo sgdrf prghfsgs y ifjømfjgs degoøaehgs, sghecofs g `f gtrc jcturcofzc. C`fmãs `f ogs `esfógs fxpfremfjtcofs ‟vfr`c`frgs” fxestfj ogs `fjgmejc`gs ‟`esfógs hucse fxpfremfjtcofs” `gj`f tcmdeåj sf `foedfrc`cmfjtf mfjgsocsujc vcrecdoffxpfremfjtcofs ej`fpfj`efjtf,y pfrg `eiefrfj jg `f ogs mcjepuoc fxpfremfjtgs ‟vfr`c`frgs”> mftrgs huc`rc`gs, fj ujc bfhtãrfc). fstf hcsg, fjfo ujejvfsteac`gr, tcmdeåj puf`f `fiejer vcrecdofs `f rfspufstc hgmpofmfjtcrecs (coturc, pfsg sfhg cårfg, pfsg rc`ehuocr, hgjtfje`g `f hogrgieoc, tcmcóg `fo arcjg, fjtrf gtrcs), pcrc rfcoezcr cjãoeses `f csghecheøj fstc`ístehc `f vcrecdofs. Jgrmcomfjtf, fo ejvfsteac`gr pocjtfc hgj`ehegjfs `fsfcdofs fj ocs vcrecdofs `f rfspufstc. ^g fkfmpog; Xe sf trctc `f oc vcrecdof ‟prg`uhheøj”, oc rfspufstc fspfrc`c sfríc ‟mcygr fs mfkgr”. Xe sf trctc `f oc vcrecdof ‟ejhe`fjhec `f ujc pocac fj uj huotevg”, oc rfspufstc fspfrc`c sfríc ‟mfjgr fs mfkgr”. Xej fmdcrag, jg sf hgjghf oc hgj`eheøj `fsfcdof `f tg`cs ocs vcrecdofs fxpfremfjtcofs. Fj fo huotevg `f mcíz, pgr fkfmpog, oc hgj`eheøj `f ‟mcygr coturc `f pocjtc csghec`c`fc degmcsc oc prg`uhheøj `f arcjg, fsjghefrtc. sefmprf vãoe`c, pfrg csghec`cfs cmfkgr”, oc prg`uhheøj prgdcdofmfjtf Oc fs pfrspfhtevc `f pg`fr hgjghfr prgiuj`cmfjtf ogs ifjømfjgs degoøaehgs y sus ejtfrrfochegjfs kusteiehcj ogs cjãoeses `f csghecheøj fstc`ístehc `f vcrecdofs.
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·HØMG @FOEJFCT OGX CJÃOEXEX FXPC@ÍXPEHGX7 Fj oc pocjfcheøj `f oc ejvfsteacheøj, fo `foejfcr ogs cjãoeses fstc`ístehgs fs ujc chteve`c` hocvf pcrc csfaurcr fo åxetg `fo fxpfremfjtg. Vj premfr cspfhtg c tgmcr fj hgjse`frcheøj fs fo hcmpg fxpfremfjtco; Xe jg bcy arc`efjtf hcdfj ogs `esfógs hgmpoftcmfjtf co czcr< se bcy arc`efjtf fj ujc `erfhheøj sf `fdfj cpoehcr ogs `esfógs fj dogqufs c czcr< se sf fve`fjhec arc`efjtfs fj `gs `erfhhegjfs sf `fdfj cpoehcr ogs `esfógs fj huc`rc`g octejg. Vj sfauj`g cspfhtg c hgjse`frcr fs oc uje`c` fxpfremfjtco; Fo tcmcóg `f oc uje`c` fxpfremfjtco fstã `ftfrmejc`g pgr ogs rfhursgs `espgjedofs. Hucj`g oc uje`c` fxpfremfjtco og hgjigrmc uj ej`eve`ug g uj arupg `f ej`eve`ugs sf tefjf uj tepg `f ejigrmcheøj, pfrg ujc uje`c` fxpfremfjtco puf`f fstcr hgjigrmc`c pgr vcrecs sudmufstrcs, pgr og tcjtg, oc gracjezcheøj `f `ctgs y fo tepg `f cjãoeses fs `eifrfjtf. Fo jûmfrg `f rfpftehegjfs `fpfj`f `fo tcmcóg y hgj`ehegjfs `fo hcmpg fxpfremfjtco, csí hgmg `f oc `espgjedeoe`c` `f rfhursgs pcrc fo fxpfremfjtg, c`fmãs `fo arc`g `f prfheseøj `fo fjscyg. Oc `foejfcheøj `fo cjãoeses fstc`ístehg ejhouyf ogs igrmctgs `f rfaestrg `f `ctgs `f hcmpg, oc gracjezcheøj y tcduocheøj `f ogs rfsuotc`gs, ocs trcjsigrmchegjfs `f `ctgs fj ogs hcsgs quf sfc jfhfscreg, fo fsqufmc `fo cjãoeses `f vcrecjzc, oc ej`ehcheøj `f ocs hgmpcrchegjfs `f mf`ecs, ogs cjãoeses `f hgrrfochegjfs y rfarfsegjfs devcrec`cs g muotevcrec`cs, fjtrf gtrgs. ·SVÅ CX^FHPGX XF @FDF HVE@CT FJ OC FKFHVHEØJ @FO FR^FTEMFJPG7 Ogs prejhepcofs cspfhtgs quf sf `fdf hue`cr fj oc fkfhuheøj `fo fxpfremfjtg sgj; fo mcjfkg `fo fxpfremfjtg, oc cpoehcheøj `f ogs trctcmefjtgs y fo rfaestrg `f `ctgs. Fo mcjfkg `fo fxpfremfjtg quf sfr ujeigrmf, hgjstcjtffj pcrc tg`cs ^gr ocs uje`c`fs fxpfremfjtcofs, fxhfptg fjtefjf oc cpoehcheøj `f ogs trctcmefjtgs fstu`eg. fkfmpog, se sf fvcoûcj trctcmefjtgs `f ifrteoezcjtfs, oc ifhbc `f sefmdrc, oc vcref`c`, oc `fjse`c`, fo refag, ocs `fsbefrdcs y gtrcs ocdgrfs `fdfrãj sfr eaucofs, sgog hcmdec ogs trctcmefjtgs `f ifrteoezcjtfs fj ocs uje`c`fs fxpfremfjtcofs pfrtejfjtfs. Oc cpoehcheøj `f ogs trctcmefjtgs `fdf sfr pocjeiehc`c y rfcoezc`c gpgrtujcmfjtf, fvetcj`g sfsags g icvgretesmgs bchec ujg u gtrg trctcmefjtg. Fo rfaestrg `f `ctgs `fdf sfr gpgrtujg, fj ogs tefmpgs ej`ehc`gs fj fo pocj, pocj, fvetcj`g sfsacr oc ejigrmcheøj g trctcj`g `f tfjfr prfifrfjhecs fj ocs mf`ehegjfs
2>
6.8. CJÃOEXEX @F YCTECJ[C ·HVÃOFX XGJ OGX HGJHF^PGX MÃX EM^GTPCJPFX FJ FO CJÃOEXEX @F YCTECJ[C7 Fjtrf ogs hgjhfptgs empgrtcjtfs usc`gs fj fo `esfóg `f fxpfremfjtgs sf fjhufjtrcj; uje`c` fxpfremfjtco, trctcmefjtg, rfpfteheøj, cofctgrezcheøj, frrgr fxpfremfjtco iufjtf `f vcrecheøj y cjãoeses `f vcrecjzc. vcrecjzc. Vje`c` fxpfremfjtco.- fs fs fo ej`eve`ug u gdkftg, arupg `f ej`eve`ugs u gdkftgs quf rfhedf oc cpoehcheøj `f uj trctcmefjtg. Vjc uje`c` fxpfremfjtco puf`f sfr; ujc pcrhfoc `f huotevg fj fo hcmpg, uj ãrdgo g uj arupg `f ãrdgofs, uj tudg `f fjscyg, ujc prghfsg, ujc mchftc g uj arupg `f pgoogs, uj ejsfhtg g uj hgjkujtg `f ejsfhtgs, ujc hckc pftre g uj hgjkujtg `f hckcs pftre. Prctcmefjtg.- fs uj hgmpgjfjtf `f oc vcrecdof ej`fpfj`efjtf huyg fifhtg vc c sfr mf`e`g y hgmpcrc`g. Fjtrf ogs fkfmpogs `f ogs trctcmefjtgs sf puf`f hetcr; ujc `gses `f ifrteoezcjtf, ujc `eftc fspfhíiehc, ujc vcref`c` vcref`c` g bídre`g `f uj huotevg, huotevg, uj måtg`g `f ocdrcjzc, ujc cotfrjctevc tfhjgoøaehc g uj tepg `f prghfscmefjtg. Ogs trctcmefjtgs puf`fj sfr ujeichtgrecofs (pgr fkfmpog; vcref`c`) g muoteichtgrecofs (pgr fkfmpog; Y3 sfmdrc`c c ujc `fjse`c` @3). Tfpfteheøj.- fs oc cpoehcheøj `f uj mesmg trctcmefjtg c mãs `f ujc uje`c` fxpfremfjtco. Xe uj trctcmefjtg sf cpoehcrc c ujc sgoc uje`c` fxpfremfjtco, fjtgjhfs jg sf puf`f mf`er oc vcrecheøj pgr fifhtg `fo trctcmefjtg. ^gr fkfmpog, se sf `espgjf `f sgog `gs uje`c`fs fxpfremfjtcofs, oc premfrc hgj oc vcref`c` Y 3 y ocs sfauj`c hgj oc vcref`c` Y4, gdtfjeåj`gsf ujc prg`uhheøj `f Y3 = 6> la y Y4 =1> la, jg bcdríc igrmc `f scdfr se oc `eifrfjhec sf `fdf c quf oc vcref`c` Y4 fs mfkgr quf oc Y3 g quf pgr fo czcr oc pcrhfoc `f Y4 tuvg uj jevfo `f ifrteoe`c` supfregr. Fj ogs fjscygs fxpfremfjtcofs, ocs rfpftehegjfs tefjfj vcrecs iujhegjfs;
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^rgpgrhegjc ujc fstemcheøj `fo frrgr fxpfremfjtco. Mfkgrc oc prfheseøj `fo fxpfremfjtg co rf`uher oc `fsvecheøj fstãj`cr `f oc mf`ec `f ogs trctcmefjtgs. Fj gtrcs pcocdrcs, c mfjgr
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4
X U
=
X j
mcygr fs oc
prfheseøj `fo fxpfremfjtg. ^gr prfheseøj sf sf fjtefj`f oc mcygr prgdcdeoe`c` `f tgmcr ujc `fheseøj hgrrfhtc hgj rfocheøj c oc bepøtfses juoc. Cumfjtc oc cmpoetu` `f ocs ejifrfjhecs quf puf`cj bchfrsf co fmpofcr c`fhuc`cmfjtf uje`c`fs fxpfremfjtcofs mãs vcrecdofs.
Cofctgrezcheøj.- fs oc c`ku`ehcheøj co czcr `f ogs trctcmefjtgs c ocs uje`c`fs fxpfremfjtcofs. Åstc fs ujc hcrchtfrístehc fsfjheco `f uj fxpfremfjtg y fo gdkftg fs prgvffr `f ujc fstemcheøj vãoe`c, jg sfsac`c, `foco frrgr fxpfremfjtco. Oc cofctgrezcheøj sf rfcoezc pgr mf`eg `f tcdocs `f jûmfrgs czcr, uscj`g prgarcmcs `f hgmputcheøj, oc tcdoc `f jûmfrgs cofctgregs g rfcoezcj`g uj sgrtfg sempof (pgr fkfmpog; schcj`g pcpfofs jumfrc`gs `f ujc hckc). Xf bc `fmgstrc`g
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fstc`ístehcmfjtf quf uj ejvfsteac`gr jg sf puf`f ‟schcr `f oc hcdfzc” ujc sfref `f jûmfrgs co czcr. Cjãoeses `f vcrecjzc (C@FYC).- fs uj måtg`g `fscrrgooc`g pgr Tgjco` C. Iesbfr dcsc`g fj uj prghf`emefjtg cretmåtehg pcrc pcrter oc sumc `f huc`rc`gs tgtco fj vcregs hgmpgjfjtfs, `f chufr`g hgj fo `esfóg fxpfremfjtco fmpofc`g. Fo C@FYC sf usc fj tg`gs ogs hcmpgs `f ejvfsteacheøj `gj`f sf tgmcj `ctgs hucjtetctevgs y sf cpgyc fj oc prufdc I pcrc pcrc oc fvcoucheøj `f ocs bepøtfses fstc`ístehcs. Fj fo cjãoeses `f vcrecjzc f ejtfrprftcheøj `f rfsuotc`gs sf `fdf tfjfr prfsfjtf quf se fo fxpfremfjtg iuf defj pocjfc`g y hgrrfhtcmfjtf fkfhutc`g, jg fxestfj rfsuotc`gs dufjgs g mcogs, sgog rfsuotc`gs fxpfremfjtcofs. Xe sf chfptc g se sf rfhbczc oc bepøtfses `f ejvfsteacheøj `fpfj`f `f oc chfptcheøj g rfhbczg `f ocs bepøtfses fstc`ístehcs quf `ftfrmejcj ocs `fhesegjfs `fo ejvfsteac`gr, hgj ujc prgdcdeoe`c` `f fquevghcheøj rczgjcdof. Fo igrzcr ujc `fheseøj hgj`uhf c hgmftfr frrgrfs tepg E (rfhbczcr B > sefj`g vfr`c`frc) g tepg EE (chfptcr B > sefj`g B3 vfr`c`frc). Ogs rfsuotc`gs `fo fxpfremfjtg `fdfj sfr cjcoezc`gs cjcoezc`gs y fxpoehc`gs, jg tfraevfrsc`gs. Oc hgjstruhheøj hgjstruhheøj `f oc tfgríc `fdf dcscrsf fj ogs rfsuotc`gs `f oc fxpfremfjtcheøj y jg fj supgsehegjfs crdetrcrecs. Iufjtfs `f Ycrecheøj .- Fj uj `esfóg fxpfremfjtco sf `fscarfac oc vcrecheøj tgtco .- Fj fj sus `eifrfjtfs hgmpgjfjtfs quf fstãj `c`gs pgr ocs iufjtfs `f vcrecheøj. Ocs iufjtfs `f vcrecheøj fstãj fj iujheøj `fo `esfóg fxpfremfjtco usc`g pcrc fo cjãoeses. ^gr fkfmpog, fj uj `esfóg fj dogqufs co czcr, oc vcrecheøj tgtco sf `fscarfac fj vcrecheøj g fifhtg `f ogs dogqufs, vcrecheøj pgr fifhtg `f ogs trctcmefjtgs y vcrecheøj pgr fifhtg `fo frrgr fxpfremfjtco. Arc`gs `f oedfrtc` ..- Fj fstc`ístehc, fs uj fstemc`gr `fo jûmfrg `f hctfagrícs ej`fpfj`efjtfs fj ujc prufdc `f bepøtfses quf pfrmetf ejtrg`uher ujc hgrrfhheøj mctfmãtehc fj ogs hgmg hãohuogs fstc`ístehgs pcrc rfstrehhegjfs empufstcs pgr ogs `ctgs. Pcmdeåj sf `fiejf fo jûmfrg `f hgmpcrchegjfs ichtedofs `f rfcoezcr. ^gr fkfmpog; Fj trfs arupgs `f pocjtcs `f `eifrfjtfs prgmf`egs `f coturc (pgr fifhtg `f trfs `eifrfjtfs `eifrfjtfs trctcmefjtgs, trctcmefjtgs, `gj`f ujg fs ffoo tfsteag) sgog sgj pgsedofs `gs hgmpcrchegjfs (C vs D vs H) pcrc tfjfr suiehefjtf ejigrmcheøj chfrhc `f oc mufstrc. Fj fstf hcsg, ogs arc`gs `f oedfrtc` (AO) = j -3= 8-3=4.
C
D
H
Ogs arc`gs `f oedfrtc` tgtco `fo fjscyg, fj uj cjãoeses `f vcrecjzc, sf `fshgmpgjfj fj iujheøj `fo `esfóg fxpfremfjtco. ^gr fkfmpog, fj uj `esfóg fj dogqufs co czcr, fo jûmfrg `f arc`gs `f oedfrtc` `fo fjscyg (rt-3), sf `fscarfac fj arc`gs `f oedfrtc` `f ogs dogqufs (rfpftehegjfs), arc`gs `f oedfrtc` `f ogs trctcmefjtgs y arc`gs `f oedfrtc` `fo frrgr fxpfremfjtco.
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Fj uj fxpfremfjtg, pcrc pg`fr tfjfr ujc prfheseøj chfptcdof fj tårmejgs fstc`ístehgs, fo jûmfrg `f arc`gs `f oedfrtc` `fo frrgr fxpfremfjtco `fdf sfr cprgxemc`cmfjtf 4>. Frrgr fxpfremfjtco.- fs ujc mf`e`c `f oc vcrecheøj quf fxestf fjtrf ocs gdsfrvchegjfs tgmc`cs fj ocs uje`c`fs fxpfremfjtcofs quf rfhedefrgj fo mesmg trctcmefjtg y quf tefjf su hcusc fj ichtgrfs jg hgjghe`gs y fj oc icotc `f ujeigrme`c` fj oc hgj`uhheøj `fo fxpfremfjtg. Fo frrgr fxpfremfjtco, dãsehcmfjtf, tefjf su greafj fj `gs hcuscs;
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^gr oc vcrecheøj prgpec, ejbfrfjtf, quf fxestfjtf fjtrf ocs uje`c`fs fxpfremfjtcofs. ^gr mãs quf sf trctf `f trcdckcr hgj uje`c`fs fxpfremfjtcofs
og mãs bgmgaåjfcs quf sfc pgsedof, sefmprf bcdrã vcrecheøj fjtrf foocs. Fj fo hcmpg, ocs pcrhfocs quf vcj c rfheder uj trctcmefjtg C pgsedofmfjtf `eiefrfj fj su tfxturc, hgjtfje`g `f mctfrec graãjehc, graãjehc, pB g jevfo `f ifrteoe`c`. Fj uj fxpfremfjtg hgj cjemcofs oc vcrecheøj puf`f prfsfjtcrsf pgr `eifrfjhecs fj fo afjgtepg, pgr fo mcjfkg prfveg co fxpfremfjtg g pgr `eifrfjhecs `f f`c`.
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^gr oc vcrecheøj sf prg`uhf icotc`f `f uj ujeigrme`c` fj ocquf hgj`uhheøj `fo fxpfremfjtg. ^grquffkfmpog, se sfpgrtrctc fxpfremfjtg tefjf hgmg
gdkftevg hgmpcrcr vcrecs `gses `f uj ifrteoezcjtf, oc vcrecheøj puf`f greaejcrsf pgr iouhtuchegjfs fj oc oc `gses hgrrfhtc hgrrfhtc c cpoehcrsf, ejhgrpgrcheøj `fseauco `fo ifrteoezcjtf co sufog, `eifrfjtf jevfo `f bumf`c` `f ocs pcrhfocs, oc bgrc fj oc quf sf cpoehc cpoehc fo ifrteoezcjtf g oc hcoe`c` `fseauco `fo prg`uhtg fj `eifrfjtfs dgoscs. Fjtrf fstf tepg `f hcuscs tcmdeåj sf fjhufjtrc og rfochegjc`g c ogs `fifhtgs fj oc tgmc `f `ctgs y fj ogs rf`gj`fgs.
Hcdf `fstchcr quf mefjtrcs mãs dckg sfc fo frrgr fxpfremfjtco mcygr sfrã oc prfheseøj `fo fxpfremfjtg, pgr og tcjtg, sf `fdf sfofhhegjcr c`fhuc`cmfjtf fo mctfreco fxpfremfjtco y uscr uj `esfóg quf of pfrmetc rfmgvfr oc mcygr hcjte`c` `f oc vcrecheøj quf puf`c bcdfr fjtrf ocs uje`c`fs fxpfremfjtcofs< cumfjtcr fo jûmfrg `f rfpftehegjfs< tfjfr hue`c`g y`fmftehuogse`c` fj yocfjhgj`uhheøj `fo fxpfremfjtg, fspfhecomfjtfy, fj oc cpoehcheøj ogs trctcmefjtgs oc rfhgofhheøj `f ogs `ctgs. Xumc `f Huc`rc`gs.Huc`rc`gs.- Oc sumc `f huc`rc`gs fs ujc tåhjehc `f cjãoeses `f `ctgs quf fs oc sumc `f ogs huc`rc`gs `f ogs `ctgs rfstc`g uj ichtgr `f hgrrfhheøj. Oc sumc `f huc`rc`gs sf `frevc `f oc iørmuoc pcrc hcohuocr oc vcrecjzc `f ocs mufstrcs. Oc vcrecjzc (X4) fj uj C@FYC sf e`fjteiehc hgmûjmfjtf hgmg Huc`rc`g Mf`eg.
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Xumc `f huc`rc`gs ∓Re4
X4 =
- Ψ (Re)4 j
Ichtgr `f hgrrfhheøj
j‘3
Huc`rc`g Mf`eg.- Mf`eg.- fo huc`rc`g huc`rc`g mf`eg, fj fo C@FYC, fs oc vcr vcrecjzc. ecjzc. Fo huc`rc`g mf`eg g vcrecjzc tgtco sf `fscarfac fj sus `eifrfjtfs hgmpgjfjtfs, sfaûj ogs arc`gs `f oedfrtc` `f ocs iufjtfs `f vcrecheøj fj cjãoeses. Fj fo C@FYC, fo Huc`rc`g Mf`eg rfsuotc `f `eve`er oc Xumc `f Huc`rc`gs pcrc ogs arc`gs `f oedfrtc` pfrtejfjtfs. ^rufdc I.I.- Fo C@FYC, pcrc oc prufdc `f bepøtfses fstc`ístehcs, sf cpgyc fj oc prufdc I. Xe Ihcohuoc`c ≦ Ic; sf rfhbczc B> y sf chfptc B3. Xe Ihcohuoc`c ? Ic; sf chfptc B> y sf rfhbczc B3 c = jevfo `f seajeiehcheøj (puf`f sfr 3%, 6%, 3>%) Fj ocs hefjhecs cargpfhucregs, degoøaehcs y sghecofs sf bc hgjvfje`g uscr jevfofs c `fo 3% y `fo 6%, hgj fxhfpheøj `f ogs fxpfremfjtgs `f vcoe`cheøj vcoe`cheøj `f tfhjgogaíc tfhjgogaícss quf sf chfptcj jevfofs `f seajeiehcheøj `f bcstc fo 3> pgr hefjtg. Fo vcogr `f Ihcohuoc`c sf gdtefjf mf`ecjtf oc `eveseøj `fo huc`rc`g mf`eg `f oc iufjtf `f vcrecheøj c sfr prgdc`c (vcrecjzc mcygr) hgj fo huc`rc`g mf`eg `fo frrgr (vcrecjzc mfjgr). Ihcohuoc`c = Ycrecjzc mcygr/vcrecjzc mfjgr. I>,>6 = Xf gdtefjf `f oc tcdoc `f I, hgjse`frcj`g quf fo jevfo `f seajeiehcheøj fs `fo 6% y ogs arc`gs `f oedfrtc` pcrc fo jumfrc`gr y `fjgmejc`gr, rfspfhtevcmfjtf. Hucj`g sf rfhbczc oc B >, fj fstf jevfo `f seajeiehcheøj sf usc uj cstfreshg (*) hgmg símdgog `f quf bcy `eifrfjhecs fstc`ístehcs seajeiehctevcs hgj fo 56% `f hgjiecjzc. Pcmdeåj puf`f rfprfsfjtcrsf hgmg ^≠>,>6< fs `fher oc prgdcdeoe`c` `f fquevghcheøj fs mfjgr `fo 6 pgr hefjtg. I>,>3 = Xf gdtefjf `f oc tcdoc `f I, hgjse`frcj`g quf fo jevfo `f seajeiehcheøj fs `fo 3% y ogs arc`gs `f oedfrtc` pcrc fo jumfrc`gr y `fjgmejc`gr, rfspfhtevcmfjtf. Hucj`g sf rfhbczc oc B >, fj fstf jevfo `f seajeiehcheøj sf usc `gs cstfreshgs (**) hgmg símdgog `f quf bcy `eifrfjhecs fstc`ístehcs seajeiehctevcs hgj fo 55% `f hgjiecjzc. Pcmdeåj puf`f rfprfsfjtcrsf hgmg ^≠>,>3< fs `fher oc prgdcdeoe`c` `f fquevghcheøj fs mfjgr `fo 3 pgr hefjtg.
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Hucj`g Ihcohuoc`c ? Ic, fjtgjhfs sf chfptc oc B>, og quf sf ejtfrprftc hgmg ‟jg bcy `eifrfjhecs fstc`ístehcs fstc`ístehcs seajeiehc seajeiehctevcs”, tevcs”, sf rfprfsfjtc pgr ocs oftrcs ‟JX” ‟JX”.. Xe fo jevfo `f seajeiehcheøj mãs cotg, fshgae`g pcrc oc prufdc, iufrc c=>,>6, fjtgjhfs; ^ : >,>6, fs `fher, oc prgdcdeoe`c` `f fquevghcheøj fj oc tgmc `f `fhesegjfs fs mcygr `fo 6 pgr hefjtg. Vscj`g fo prgarcmc Fxhfo sf puf`f hcohuocr I, fj ogs `eifrfjtfs jevfofs `f seajeiehcheøj (jg bchf icotc icotc rfhurrer c oc tcdoc I). Oc iujheøj pcrc tfjfr fo vcogr I `f tcdoc fs
[email protected](jevfo `f seajeiehcheøj< arc`gs `f oedfrtc` `f jumfrc`gr< arc`gs `f oedfrtc` `f `fjgmejc`gr). ^gr fkfmpog;
[email protected](>,>3)
Mf`ec
HYF (%) = (HMF)>,6 /Mf`ec x \3>>] Vj hgfiehefjtf `f vcrecheøj `fo frrgr `f bcstc fo 46% fs chfptc`g fj fxpfremfjtgs hgj pocjtcs pfrfjjfs. Fj fxpfremfjtgs hgj huotevgs `f hehog hgrtg y cjemcofs sf chfptcj hgfiehefjtfs `f vcrecheøj `f bc bcstc stc fo 4> pgr hefjtg. C jevfo `f fxpfremfjtgs fj ocdgrctgreg sf chfptcj hgfiehefjtfs `f vcrecheøj `f bcstc 36 pgr hefjtg. ^grhfjtckfs `f hgfiehefjtfs `f vcrecheøj `fo frrgr pgr fjhemc `f ogs vcogrfs `f rfifrfjhec ej`ehc`gs seajeiehc quf ogs fxpfremfjtgs jg iufrgj hgj`uhe`gs hgrrfhtcmfjtf, oc `estreduheøj `f ogs `ctgs jg sf cprgxemc c oc jgrmco, fo jûmfrg `f arc`gs `f oedfrtc` `fo frrgr iufrgj muy dckgs, pgr og tcjtg, ejsuiehefjtfs pcrc prgdcr oc bepøtfses hgj hfrtfzc, ogs ejstrumfjtgs fstuvefrgj mco hcoedrc`gs g ocs fshcocs `f mf`eheøj iufrgj ejc`fhuc`gs. ·SVÅ BCHFT XE FO HGFIEHEFJPF @F YCTECHEØJ @FO FTTGT FX MVU COPG7 Hucj`g sf hgjstctcj vcogrfs muy cotgs `f ogs hgfiehefjtfs `f vcrecheøj `fo frrgr, `fdf prghf`frsf `f oc seauefjtf mcjfrc; Tfveseøj `f ogs `ctgs `f hcmpg, trcjsigrmcheøj `f ogs `ctgs y jufvg cjãoeses fstc`ístehg `f `ctgs.
26
Ycogrcheøj `f ogs `ctgs `f hcmpg Fj oc prãhtehc, fstf fs fo premfr pcsg pcrc rfcoezcr hucoquefr tepg `f cjãoeses fstc`ístehg `fshreptevg g ejifrfjheco. Hucoquefr `ctg jg hgjiecdof `fdf sfr foemejc`g `fo cjãoeses fstc`ístehg. Bcy `gs bfrrcmefjtcs fiehchfs pcrc `ftfrmejcr `ctgs (pujtgs) jg hgjiecdofs quf sf udehcj iufrc `f og rchegjcomfjtf chfptcdof; 3) fo `espfrsgarcmc< y, 4) fo cjãoeses `f ogs oímetfs supfregr f ejifregr, `c`gs pgr oc ‟mf`ec ³ 8 `fsvechegjfs fstãj`cr”. Vj pujtg jg hgjiecdof, afjfrcomfjtf hgrrfspgj`f c uj vcogr fxtrfmg, sf hgjghf hgmg ‟gutoefrs” quf cifhtc oc vcoe`fz `f oc ejtfrprftcheøj. ^gr fkfmpog, se fj ujc sfref `f 3> `ctgs bcy vcogrfs quf iouhtûcj fjtrf 4> y 86, pfrg sf fjhufjtrc uj `ctg `f 66, åstf `fdfríc hgjse`frcrsf, fj prejhepeg, ‟sgspfhbgsg”. Co rfcoezcr fo cjãoeses `f ogs oímetfs supfregr f ejifregr `f oc sfref `f `ctgs, `ct gs, sf hgjstctc quf fo vcogr `f 66 `estgrsegjc oc mf`ec y mf`ecjc< pufs fj ujc `estreduheøj jgrmco fstgs fstc`ístehgs tefj`fj c hgejhe`er, c`fmãs< oc sfref `f `ctgs sej fo vcogr 66 tefj`f c vcrecr fjtrf 30 y 08 quf fs rczgjcdofmfjtf chfptcdof. @ctgs
Hgj `ctg ‟sgspfhbgsg”
Xej `ctg ‟sgspfhbgsgs”
66
Hgj `ctg ‟sgspfhbgsg”
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Mf`ec
83,3
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@fsvecheøj fstãj`cr (X)
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Mf`ec + 8X
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Mf`ec - 8X
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Xej `ctg ‟sgspfhbgsg”
6> 06 0> 86 8> 46 4> 36 3> 6 > >
3
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Prcsigrmchegjfs `f `ctgs Fj oc fxpfremfjtcheøj fs irfhufjtf oc trcjsigrmcheøj `f ogs `ctgs `f ocs vcrecdofs greaejcofs jumårehcs c jufvcs vcrecdofs jumårehcs trcjsigrmc`cs hgj fo prgpøsetg `f rf`uher g fvetcr ocs `estgrsegjfs quf prgvghcj ogs `ctgs muy `espfrsgs, ckustcr ogs `ctgs c oc `estreduheøj jgrmco g fxpoehcr mcs c`fhuc`cmfjtf ogs rfsuotc`gs. Prcjsigrmcheøj c pgrhfjtckfs.Ogs `ctgs fj fshcoc gr`ejco puf`fj trcjsigrmcrsf c pgrhfjtckf. ^gr fkfmpog, se sfrfaestrc`gs tgmcrgj `ctgs `f ejhe`fjhec `f ujc fjifrmf`c`, fj uj huotevg, uscj`g oc fshcoc gr`ejco; > = Cusfjhec `f oc fjifrmf`c`,
3 3> >
29
3= dckc ejhe`fjhec, 4= mf`ecjc ejhe`fjhec y 8 = cotc ejhe`fjhec. Xefj`g fo tcmcóg `f mufstrc j= 4>>. Ejhe`fjhec `f oc fjifrmf`c` Jûmfrg `f pocjtcs fvcouc`cs ^gr hefjtg
> 36> 16
Fshcoc gr`ejco 3 4 8> 39 36 2
8 0 4
Fj fstc herhujstcjhec bcy vcrecs pgsedeoe`c`fs; cjcoezcr fo pgrhfjtckf `f pocjtcs scjcs, cjcoezcr fo pgrhfjtckf `f pocjtcs fjifrmcs, cjcoezcr fo pgrhfjtckf `f pocjtcs hgj cotc ejhe`fjhec. Gtrc cpoehcheøj fs oc trcjsigrmcheøj c pgrhfjtckfs fj rfocheøj c uj tfsteag. ^gr fkfmpog;
Pfsteag Prctcmefjtg cotfrjctevg 3 Prctcmefjtg cotfrjctevg 4
^rgmf`eg `f prg`uhheøj 625 3.491 3.025
^grhfjtckf `f prg`uhheøj 3>> 436 468
Ejhrfmfjtg `f oc prg`uhheøj (%) 336 368
Prcjsigrmchegjfs c (R+3)>,6.- Fstc trcjsigrmcheøj sf usc hucj`g ogs `ctgs pgrhfjtucofs sf udehcj fjtrf > y 4>% ø fjtrf 2> y 3>>%. Fo vcogr `f R fs fo hgrrfspgj`efjtf co `ctg greaejco c sfr trcjsigrmc`g. Gtrcs trcjsigrmchegjfs.- Ocs trcjsigrmchegjfs c ogacretmgs, c sfjg g crhg sfjg sgj irfhufjtfs fj oc ejvfsteacheøj ejvfsteacheøj degoøaehc. Fj tg`g hcsg, fs empgrtcjtf cpgycrsf fj oc oetfrcturc fspfhecoezc`c pcrc `fhe`er oc trcjsigrmcheøj `f `ctgs mãs hgjvfjefjtf, sfaûj oc jcturcofzc `f oc ejvfsteacheøj. Xe pfrsestefrcjpgrquf hgfiehefjtfs cotgs fj fo `fdfj uscrsf pcrcmåtrehcs fstcs `f sgjvcrecheøj ej`fpfj`efjtfs `fcjãoeses oc `estreduheøj y `fo tåhjehcs tcmcóg jg `f mufstrc. 6.0. CJÃOEXEX @F YCTECJ[C JG ^CTCMÅPTEHGX ·HVÃJ@G VXCT CJÃOEXEX @F YCTECJ[C JG ^CTCMÅPTEHGX7 ^crc quf ocs tåhjehcs `fo cjãoeses `f vcrecjzc pcrcmåtrehgs tfjacj vcoe`fz `fdf humpoersf hgj uj hgjkujtg `f supufstgs hgmg; jgrmcoe`c` `f ogs `ctgs, ej`fpfj`fjhec `f ocs gdsfrvchegjfs, bgmgafjfe`c` `f ocs vcrecjzcs (bgmghf`cstehe`c`) y uj cotg jûmfrg `f arc`gs `f oedfrtc` `fo frrgr (pgr og mfjgs 4>). Fj oc fstc`ístehc jg pcrcmåtrehc jg sf rfquefrf humpoer ogs rfifre`gs supufstgs pfrg ogs `ctgs `fdfj prgvfjer `f mf`ehegjfs fj fshcocs `f ejtfrvcog.
21
Fo cjãoeses `f rcjags `f Luslcoo & Qcooes30, quf fquevcof co `esfóg hgmpoftcmfjtf co czcr, y fo cjãoeses `f vcrecjzc pgr Tcjags `f Iref`mcj 36, quf fquevcof co `esfóg fj fj dogqufs co czcr, sgj ogs `gs cjãoeses `f vcrecjzc jg pcrcmåtrehgs. 6.0.3. CJÃOEXEX @F YCTECJ[C @F LTVXLCOO LTVXLCOO & QCOOEX ·FJ SVÅ HGJXEXPF FO CJÃOEXEX @F YCTECJ[C @F LVXLCOO & QCOOEX7 Fo cjãoeses `f vcrecjzc Lruslcoo & Qcooes39 fquevcof co cjãoeses fj uj `esfóg hgmpoftcmfjtf co czcr< fs `fher, sf cpoehc hucj`g fo hcmpg fxpfremfjtco fs bgmgaåjfg y fo jûmfrg `f rfpftehegjfs pgr trctcmefjtg puf`f sfr eauco g `fseauco. Fo prghf`emefjtg sf ejehec hgj oc cseajcheøj `f vcogrfs `f rcjags gr`fjc`gs `f mfjgr c mcygr quf rffmpoczcj c ogs `ctgs greaejcofs `fo fxpfremfjtg, sf igrmuoc oc bepøtfses, sf hcohuoc fo fstc`ístehg B , sf cpoehc oc rfaoc `f `fheseøj y rfcoezcj ocs hgjhousegjfs pfrtejfjtfs. ^crc oc prufdc `f seajeiehcheøj fstc`ístehc sf cpgyc fj ke-huc`rc`c . Cseajcheøj `f rcjags c ogs `ctgs greaejcofs.- Fj Fj fstf hcsg, fo hgjhfptg `f rcjag sf rfiefrf co gr`fjcmefjtg `f ogs `ctgs `f mfjgr c mcygr `f tg`g fo fjscyg. Hucj`g bcy `ctgs greaejcofs rfpfte`gs sf hcohuoc y cseajc ogs vcogrfs prgmf`egs. Igrmuocheøj `f ocs bepøtfses fstc`ístehcs ..- Ocs bepøtfses fstc`ístehcs fj fo cjãoeses `f Lruslcoo & Qcooes sgj eaucofs quf fj oc fstc`ístehc pcrcmåtrehc. B>; Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs B3; Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf. Fo hãohuog `fo fstc`ístehg B .- .- Fo fstc`ístehg Q sf hcohuoc mf`ecjtf oc seauefjtf iørmuoc; B=
34
j j+3
∓ T e4 /je - 8(j+3)
@øj`f; B = fstc`ístehg `f Lruslcoo & Qcooes je = jûmfrg `f `ctgs `f fxpfremfjtg T e4= sumcs `f ogs rcjags fofvc`gs co huc`rc`g `f hc`c trctcmefjtg Tfaoc `f `fheseøj ..- Fo fstc`ístehg Q sf prufdc hgj ogs vcogrfs `f oc tcdoc `f ke-huc`rc`c, hgjse`frcj`g fo jevfo `f seajeiehcheøj y ogs arc`gs `f oedfrtc` `f ogs trctcmefjtgs.
30
. Cjgvc uj ichtgr y Lruslcoo-Qcooes. bttp;//www.uhom.fs/prgifsgrc`g/m`scovc`gr/623>5/tfgrec/cjgvcWujWichtgr-ofhturc.p`i . Cjãoeses `f vcrecjzc `f `gdof fjtrc`c pgr rcjags `f Iref`mcj pcrc mãs `f `gs mufstrcs `fpfj`efjtfs. bttp;//www.igrtujfhety.hgm/hcmpus/ocwjs/82>/fstc`estehc/cjcoesesv`fri4m`.btm bttp;//www.igrtujfhety.hgm/hcmpus/ocwjs/82>/fstc`estehc/cjcoesesv`fri4m`.btm 39 . ^rufdc `f Lruslcoo ‘ Qcooes. Dyrgj Agjzcofz. bttp;//www.soe`fsbcrf.jft/dyrgja/prufdc-lruslcoo-wcooes
36
. ^rufdc `f Lruslcoo Qcooes. Dyrgj Agjzcofz. bttp;//www.soe`fsbcrf.jft/dyrgja/prufdc lruslcoo wcooes wcooes
22
Xe Q ≦ R4>,>6 hgj arc`gs `f oedfrtc` t-3; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc (*). Xe Q ≦ R4>,>3 hgj arc`gs `f oedfrtc` t-3; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc (**). Xe Q ? R4>,>6 hgj arc`gs `f oedfrtc` t-3; Xf chfptc B>. Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs (JX). 6.0.4. CJÃOEXEX @F YCTECJ[C ^GT TCJAGX @F ITEF@MCJ ·SVÅ FX FO CJÃOEXEX @F YCTECJ[C ^GT TCJAGX @F ITEF@MCJ7 Fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj fquevcof co cjãoeses `f uj `esfóg `f dogqufs co czcr. Fo prghf`emefjtg `f fstf cjãoeses `f vcrecjzc sf ejehec hgj oc cseajcheøj `f vcogrfs `f rcjags gr`fjc`gs `f mfjgr c mcygr quf rffmpoczcj c ogs `ctgs greaejcofs `f hc`c trctcmefjtg. Oufag, sf igrmuoc ocs bepøtfses fstc`ístehcs, sf hcohuoc fo fstc`ístehg `f Iref`mcj R4r, sf cpoehc oc rfaoc `f `fheseøj y sf rfcoezcj ocs hgjhousegjfs pfrtejfjtfs. Oc seajeiehcheøj fstc`ístehc sf `ftfrmejc uscj`g ke-huc`rc`c. Cseajcheøj `f ` f rcja rcjags gs c ogs `ctgs greaejcofs.- Fo Fo iuj`cmfjtg `fo måtg`g hgjsestf fj rffmpoczcr ogs `ctgs greaejcofs pgr vcogrfs `f rcjags, quf fj fstf hcsg sf hgjhedf hgmg uj gr`fjcmefjtg cshfj`fjtf, `f tg`gs ogs `ctgs `fo fxpfremfjtg. Fo pujtckf mãs pfqufóg fs rffmpoczc`g pgr fo jûmfrg 3, fo sfauj`g pgr fo jûmfrg 4, y csí suhfsevcmfjtf. Hucj`g ogs `ctgs gdsfrvc`gs sgj eaucofs, fjtgjhfs sf hcohuoc uj prgmf`eg `f ogs vcogrfs `f ogs rfspfhtevgs rcjags. Oc prufdc `ftfrmejc se oc `fseauco`c` fjtrf ocs sumcs `f ogs rcjags fs tcj arcj`f quf prgdcdofmfjtf jg prghf`fj `f mufstrcs tgmc`cs `f oc mesmc pgdocheøj g `f pgdochegjfs e`åjtehcs. Igrmuocheøj `f ocs bepøtfses fstc`ístehcs ..- Ocs bepøtfses fstc`ístehcs fj fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj sgj eaucofs quf fj oc fstc`ístehc pcrcmåtrehc. B>; Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs B3; Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf. .- Fo fstc`ístehg Q sf hcohuoc mf`ecjtf oc Fo hãohuog `fo fstc`ístehg R 4 r .- seauefjtf iørmuoc;
R4 r
34
=
rt (t + 3)
T 4 ∓T
- 8 r (t + 3)
@øj`f; 4 R r =
fstc`ístehg `f Iref`mcj r = jûmfrg `f rfpftehegjfs t = jûmfrg `f trctcmefjtgs T 4= Xumc `f ogs rcjags rcjags fofvc`gs co huc`rc`g `f hc`c hc`c trctcmefjtg
25
Tfaoc `f `fheseøj ..- Fo fstc`ístehg R4r sf prufdc hgj ogs vcogrfs `f oc tcdoc `f ke-huc`rc`c, hgjse`frcj`g fo jevfo `f seajeiehcheøj y ogs arc`gs `f oedfrtc` `f ogs trctcmefjtgs. Xe R4r ≦ R4>,>6 hgj arc`gs `f oedfrtc` t-3 ; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc (*). Xe R4r ≦ R4>,>3 hgj arc`gs `f oedfrtc` t-3 ; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc (**). Xe R4r ? R4>,>6 hgj arc`gs `f oedfrtc` t-3; Xf chfptc B>. Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs (JX). 6.6. @EXFÓGX FR^FTEMFJPCOFX DÃXEHGX ·HÛCOFX XGJ OGX @EXFÓGX FR^FTEMFJPCOFX DÃXEHGX7 Vj `esfóg fxpfremfjtco `fdf c`fhucrsf co mctfreco fxpfremfjtco hgj quf sf hufjtc y c oc bepøtfses `f ejvfsteacheøj igrmuoc`c pgr fo ejvfsteac`gr. Ogs rfsuotc`gs sf fxpgjfj fj fo cjãoeses `f vcrecjzc (C@FYC) y fj oc hgmpcrcheøj `f mf`ecs `f ogs trctcmefjtgs. Fo cjãoeses `f vcrecjzc prgpgrhegjc `fscarfac oc vcrecheøj `f oc vcrecdof `f ejtfrås sfaûj ocs iufjtfs fxpoehcdofs `fo fxpfremfjtg (iufjtfs `f vcrecheøj hgjghe`cs) y tg`c cqufooc vcrecheøj quf jg fs pgsedof `f fxpoehcr y sgdrf oc huco fo ejvfsteac`gr jg tuvg hgjtrgo hgjstetuyf fo frrgr fxpfremfjtco (iufjtfs `f vcrecheøj `fshgjghe`cs). ^gr fkfmpog; se sf rfcoezc uj fxpfremfjtg `gj`f sf fstu`ec `eifrfjtfs hcjte`c`fs `f prgtfíjc fj oc `eftc `ecrec pcrc pgoogs hcmpfrgs (ichtgr fj fstu`eg) y sf me`f oc acjcjhec `f pfsg (vcrecdof `f rfspufstc)< fstc vcrecheøj `f pfsg `f ogs pgoogs puf`f `fscarfacrsf fj ocs iufjtfs `f vcrecheøj hgjghe`cs y fj ocs iufjtfs `f vcrecheøj `fshgjghe`cs g frrgr fxpfremfjtco. ^crc fo cjãoeses `f oc vcrecjzc sf prfsupgjf quf bcy fifhtgs c`etevgs, bgmgafjfe`c` `f ocs vcrecjzcs `f ocs pgdochegjfs pgr trctcmefjtgs, ej`fpfj`fjhec fj oc tgmc `f `ctgs y `estreduheøj jgrmco `f ogs frrgrfs31. Ogs `esfógs fxpfremfjtcofs dãsehgs c uscrsf fstãj fj iujheøj `f ocs hcrchtfrístehcs `fo hcmpg fxpfremfjtco y sgj ogs seauefjtfs; `esfóg hgmpoftcmfjtf co czcr, `esfóg fj dogqufs co czcr, `esfóg fj huc`rc`g octejg y `esfóg ffjj oãtehf. Xgdrf fstgs `esfógs dãsehgs sf pocjfcj ogs fxpfremfjtgs fj `eifrfjtfs crrfaogs ichtgrecofs y råpoehcs fj fo tefmpg g fj fo fspcheg, sfaûj oc jcturcofzc `f oc ejvfsteacheøj. 6.6.3. @EXFÓG HGM^OFPCMFJPF CO C[CT ·HVÃJ@G VXCT FO @EXFÓG HGM^OFPCMFJPF CO C[CT7 Fo `esfóg hgmpoftcmfjtf co czcr (@HC) sf dcsc fj oc cseajcheøj `f ogs trctcmefjtgs fj igrmcarupgs, hgmpoftcmfjtf cofctgrecãrdgofs). c ocs uje`c`fs (pcrhfocs, ej`eve`ugs, kcuocs, cjemcofs, Fo @HCfxpfremfjtcofs sf usc hucj`g 31
. Cjãoeses `f `esfógs fxpfremfjtcofs dãsehgs. bttp;//hgopgsifsz.acofgj.hgm/fst6>3/`hc/`hc.btm bttp;//hgopgsifsz.acofgj.hgm/fst6>3/`hc/`hc.btm
5>
ogs hcmpgs fxpfremfjtcofs sgj bgmgaåjfgs hgmg; fstcdogs, ocdgrctgreg, ejvfrjc`frgs, hãmcrc deghoemãtehc g pcrhfocs `f tfrrfjg sej arc`efjtfs. Fo @HC puf`f cpoehcrsf fj `gs hgj`ehegjfs; 3) hucj`g ogs trctcmefjtgs fstãj `estredue`gs fj eauco jûmfrg `f rfpftehegjfs< g, 4) hucj`g ogs trctcmefjtgs fstãj `estredue`gs fj `eifrfjtf jûmfrg `f rfpftehegjfs. Hgmg vfjtckcs `fo @HC sf ej`ehcj quf sgj sfjheoogs `f pocjeiehcr, iofxedof fj hucjtg co jûmfrg `f rfpftehegjfs y trctcmefjtgs< bcy mãs arc`gs `f oedfrtc` pcrc fstemcr fo frrgr fxpfremfjtco< puf`f tfjfr `eifrfjtf jûmfrg `f rfpftehegjfs y trctcmefjtgs< y fo cjãoeses `f vcrecjzc fs sempof. Oc `fsvfjtckc `fo @HC fs quf sf oemetc c fjscygs fj hcmpgs fxpfremfjtcofs bgmgaåjfgs. ·HVÃO FX FO FXSVFMC @FO C@FYC ^CTC FO @HC7 Fo fsqufmc `fo C@FYC fs fo seauefjtf; Iufjtf `f vcrecheøj Prctcmefjtgs Frrgr fxpfremfjtco Pgtco
Arc`gs `f oedfrtc` fj @HC hgj eauco jûmfrg `f
Arc`gs `f oedfrtc` fj @HC hgj `fseauco jûmfrg
rfpftehegjfs t-3= 6 t(r-3) rt-3 =45
`f rfpftehegjfs t-3 J-t J-3
t = jûmfrg `f trctcmefjtgs r = jûmfrg `f rfpftehegjfs J= jûmfrg tgtco `f gdsfrvchegjfs fj fo fjscyg
·HVÃO FX FO MG@FOG FXPC@ÍXPEHG @FO @HC7 Fo mg`fog fstc`ístehg csghec`g co @HC fs;
e = 3,4,8,..., t k = 3,4,8,..., j
@øj`f; = Ycrecdof rfspufstc fj oc k-åsemc rfpfteheøj `fo e-åsemg ttrctcmefjtg rctcmefjtg = Mf`ec afjfrco = Fifhtg `fo trctcmefjtg e. = Frrgr fxpfremfjtco Cjãoeses `f oc Ycrecjzc pcrc fo mg`fog Bg; B3; co mfjgs uj trctcmefjtg fs `eifrfjtf `f ogs `fmãs.
53
^TGDOFMC TFXVFOPG @esfóg Hgmpoftcmfjtf co Czcr hgj `fseauco jûmfrg `f rfpftehegjfs @ftfrmejcr fo fifhtg `f huctrg `eftcs coemfjtehecs pcrc oc hríc y muotepoehcheøj `f oc drghc `fo irutg `fo hciå c jevfo `f ocdgrctgreg 32. Oc vcrecdof `f rfspufstc fs fo jûmfrg `f ocrvcs pgr rfhepefjtf. Ogs `ctgs `fo fjscyg iufrgj ogs seauefjtfs;
E EE EEE EY Y
@eftcs fj oc coemfjtcheøj `f oc drghc `fo hciå @3 @4 @8 @0 06 86 80 03 09 88 80 03 05 86 00 00 80 08 88 03
YE YEE YEEE ER
04 00 03 03
Tfpftehegjfs
Hãohuog `f ocs sumcs y prgmf`egs Tfpftehegjfs E EE EEE EY Y YE YEE YEEE ER Xumc Mf`ec
32
@eftcs fj oc coemfjtcheøj `f oc drghc `fo hciå @3 @4 @8 @0 06 86 80 03 09 88 80 03 05 86 00 00
320 09
80 88
92 80
31 31>> 80
08 03 04 00 03 03 812 04
∓Rek= xek = J= t=
2>> 0> 4> 0
. Ejigrmcheøj tåhjehc `fo Ocdgrctgreg `f `f hgjtrgo degoøaehg degoøaehg `f oc Fstcheøj Fxpfremfjtco Prgpehco Prgpehco ^ehbeoejauf. ^ehbeoejauf. EJEC^. 3525.
54
Hãohuog `f ocs Xumcs `f Huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /J = (2>>)4 /4> = 84.>>> Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = (06)4+(09)4+(05)4+…….…+(03)4+(03)4 ‘ 84.>>> = 090 Xumc `f Huc`rc`gs `f4 ogs Prctcmefjtgs (XH P)= (∓Re)4 /r ‘ IH 4 4 4 XH P = (320) /0+(92) /4+(31>) /6+(812) /5 -84.>>> = 084 Xumc `f Huc`rc`gs `fo Frrgr Fxpfremfjtco (XHF)= XH Pgtco ‘ XH P XHF = 090 ‘ 084 = 84 Cjãoeses `f Ycrecjzc Iufjtf `f vcrecheøj
Arc`gs `f oedfrtc`
Xumc `f Huc`rc`gs
Huc`rc`g Mf`eg
I hcohuoc`c
I>,>6
I>,>3
Prctcmefjtg
t-3 =8
084
300
14**
8,40
6,45
Frrgr fxpfremfjtco
J-t =39
84
4
Pgtco
J-3=35
090
Ejtfrprftcheøj ^crc ogs trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f
hgjiecjzc. @f ocs huctrg `eftcs prgdc`cs co mfjgs ujc fs fstc`ístehcmfjtf `eifrfjtf. ^?>,>3. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4)>,6 /0> = 8,60% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs `f ocdgrctgreg. ^TGDOFMC TFXVFOPG @esfóg Hgmpoftcmfjtf co Czcr hgj eauco jûmfrg `f rfpftehegjfs Xf rfcoezø uj fxpfremfjtg pcrc prgdcr fo fifhtg `f hejhg iufjtfs `f fjfraíc uteoezc`cs fj `eftcs `eft cs pcrc fjagr`c `f tgrftfs (P3 Pfsteag, P4 Mfoczc, P8 Hfdg, P0 Mcíz, P6 Xgrag) fj ocs hucofs sf me`eø oc acjcjhec `f pfsg (A^) `urcjtf fo pfríg`g `f fjagr`c. Xf hgjse`frcrgj 6 rfpftehegjfs pgr trctcmefjtgs (46 cjemcofs) y sf pocjtfø oc bepøtfses `f eauco`c` `f mf`ecs `f 35
trctcmefjtgs . 35
Cjãoeses `f `esfógs fxpfremfjtcofs dãsehgs. bttp;//hgopgsifsz.acofgj.hgm/fst6>3/`hc/`hc.btm bttp;//hgopgsifsz.acofgj.hgm/fst6>3/`hc/`hc.btm
58
Ogs `ctgs `fo fjscyg iufrgj ogs seauefjtfs;
E
P3 52>
P4 34>>
Prctcmefjtgs P8 38>>
EE EEE EY Y
3>6> 33>> 3>>> 334>
348> 336> 385> 346>
332> 34>> 331> 3>6>
Tfpftehegjfs
P0 30>>
P6 386>
386> 382> 304> 36>>
304> 366> 39>> 305>
Hãohuog `f sumcs y prgmf`egs Tfpftehegjfs E EE EEE EY Y Xumc Mf`ec
P3 52> 3.>6> 3.3>> 3.>>> 3.34> 6.46> 3.>6>
P4 3.4>> 3.48> 3.36> 3.85> 3.46> 9.44> 3.400
Prctcmefjtgs P8 3.8>> 3.32> 3.4>> 3.31> 3.>6> 6.5>> 3.32>
P0 3.0>> 3.86> 3.82> 3.04> 3.6>> 1.>6> 3.03>
P6 3.86> 3.04> 3.66> 3.9>> 3.05> 1.03> 3.024
Xumc
Mf`ec
9.48> 3.409 9.48> 3.409 9.82> 3.419 9.62> 3.839 9.03> 3.424 83.28> 9.899 9.899 3.418
r =6 t=6 Hãohuog `f ocs Xumcs `f Huc`rc`gs 4
4
ek) /(rt) = (83.28>) Ichtgr `f Huc`rc`gs hgrrfhheøj Pgtco (IH) =(XH (∓RPgtco) Xumc `f = ∓Re4 ‘ IH /46 = 0>.646.569 XH Pgtco = \(52>)4+(34>>)4+(38>>)4+…….…+(36>>)4+(305>)4] ‘ 0>.646.569 XH Pgtco = 185.500
Xumc `f Huc`rc`gs `f ogs Prctcmefjtgs (XH P)= (∓Pe)4 /r ‘ IH XH P = \(6.46>)4+(9.44>)4+(6.5>>)4+(1.>6>)4 + (1.03>)4]/6 - 0>.646.569 XH P = 9>2.800 Xumc `f Huc`rc`gs `fo Frrgr Fxpfremfjtco (XHF)= XH Pgtco ‘ XH P XH F = 185.500 ‘ 9>2.800 = 383.9>>
50
Cjãoeses `f Ycrecjzc Iufjtf `f vcrecheøj
Arc`gs `f oedfrtc`
Xumc `f Huc`rc`g I hcohuoc`c I >,>6 Huc`rc`gs Mf`eg
Prctcmefjtg
0
9>2.800
364.>29
Frrgr fxpfremfjtco
4>
383.9>>
9.62>
40
185.500
Pgtco
48,33**
4,21
I >,>3 0,08
Ejtfrprftcheøj ^crc ogs trctcmefjtgs.- Ihcohuoc`c : I>,>3;
Xf rfhbczc B> hgj fo 55% `f hgjiecjzc. @f ocs hejhg `eftcs prgdc`cs co mfjgs ujg fs fstc`ístehcmfjtf `eifrfjtf. ^?>,>3. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (9.62>)>,6 /3.418 = 9,81% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs pfhucregs. 6.6.4. DOGSVFX CO C[CT ·HVÃJ@G VXCT FO @EXFÓG @F DOGSVFX CO C[CT7 Fstf `esfóg fs ûteo hucj`g fo hcmpg fxpfremfjtco tefjf ujc arc`efjtf fj ujc `erfhheøj< fs `fher, vcríc `f mfjgs c mãs, fj uj sgog sfjte`g. Fjtrf ogs fofmfjtgs `fo hcmpg fxpfremfjtco quf puf`fj tfjfr arc`efjtfs sf mfjhegjcj; prgiuj`e`c`, pfj`efjtf, ifrteoe`c` y oumejgse`c`.
Fo `esfóg fj DC fs fo mãs cmpoecmfjtf usc`g fj oc fxpfremfjtcheøj caríhgoc. Fj uj DC, fo hcmpg fxpfremfjtco sf `eve`f fj dogqufs pfrpfj`ehuocrfs c oc arc`efjtf, prghurcj`g quf tefj`cj c sfr bgmgaåjfcs. Fj hc`c dogquf sf `estreduyfj cofctgrecmfjtf cofctgrecmfjtf ogs trctcmefjtgs fj fstu`eg. Hc`c dogquf `fdf tfjfr fo mesmg jûmfrg `f trctcmefjtgs sgrtfc`gs. Ocs vfjtckcs `f uj `esfóg fj DC fs quf sgj sfjheoogs `f pocjeiehcr, iofxedof fj rfpftehegjfs y trctcmefjtgs, prfhesg pcrc fstemcr ocs vcrechegjfs y iãheo `f cjcoezcr. Vj `esfóg `ffsdogqufs co czcrc`fmãs, jg fs jg rfhgmfj`cdof fo jûmfrg `f trctcmefjtgs muy arcj`f< sefmprf bcyhucj`g vcrecdeoe`c` `fo sufog fj oc `erfhheøj e`fco y jg fs muy c`fhuc`g hucj`g bcy ejtfrchheøj
trctcmefjtgs y dogqufs.
56
·HVÃO FX FO FXSVFMC @FO C@FYC@F ^CTC FO @EXFÓG FJ DC7 Fo fsqufmc `fo C@FYC fs fo seauefjtf; Iufjtf `f vcrecheøj Tfpftehegjfs Prctcmefjtgs Frrgr fxpfremfjtco Pgtco
Arc`gs `f r-3 oedfrtc` t-3 (r-3)(t-3) rt-3
·HVÃO FX FO MG@FOG FXPC@ÍXPEHG @FO @EXFÓG FJ DOGSVFX CO C[CT7 Fo mg`fog fstc`ístehg csghec`g co `esfóg fj DC fstc `c`g pgr; t r
@øj`f; = Ycrecdof rfspufstc fj oc k-åsemc rfpfteheøj `fo e-åsemg trctcmefjtg = Mf`ec afjfrco = Fifhtg `fo trctcmefjtg e. = Fifhtg `fo e-åsemg dogquf = Frrgr fxpfremfjtco ^TGDOFMC TFXVFOPG Vj ejvfsteac`gr `fsfc cvfreaucr fo fifhtg `f vcregs iujaehe`cs hgmg `fsejifhtcjtf sgdrf oc fmfrafjhec `f oc sgyc, c jevfo `f hcmpg. Ogs trctcmefjtgs quf sfofhhegjc sgj; C = tfsteag, D, H, @ y F (iujaehe`cs `eifrfjtfs fj `gses hgmfrhecofs). Hgmg fo ejvfsteac`gr sgspfhbc `f oc prfsfjhec `f ujc arc`efjtf fj fo hcmpg, carupc sus uje`c`fs fxpfremfjtcofs fj huctrg dogqufs. Xf fvcouø fo jûmfrg `f sfmeoocs quf jg fmfraefrgj `f 3>> sfmeoocs sfmdrc`cs. Ogs `ctgs `fo fxpfremfjtg iufrgj ogs seauefjtfs;
59
Prctcmefjtgs (iujaehe`cs)
Dogqufs C (tfsteag)
D
H
@
F
E
2
8
0
8
9
EE EEE
3> 34
9 1
1 5
6 5
2 6
EY
38
3>
33
3>
1
Hãohuog `f sumcs y prgmf`egs
Prctcmefjtgs (iujaehe`cs)
Dogqufs
Xumc
Mf`ec
C (tfsteag)
D
H
@
F
E EE EEE EY Xumc
2 3> 34 38 08
8 9 1 3> 49
0 1 5 33 83
8 6 5 3> 41
9 2 6 1 49
40 89 04 63 368
0,2 1,4 2,0 3>,4 8>,9
Mf`ec
3>,16
9,6
1,16
9,16
9,6
82,46
1,96
r=0 t=6 Hãohuog `f ocs Xumcs `f Huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (368)4 /4> = 3.31>,6 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco =\(2)4+(8)4+(0)4+…….…+(3>)4+(1)4] ‘ 3.31>,6 XH Pgtco = 369,9 Xumc `f Huc`rc`gs `f ogs Prctcmefjtgs (XH P)= (∓Pe)4 /r ‘ IH XH P = \(08)4+(49)4+(83)4+(41)4 + (49)4]/0 - 3.31>,6 XH P = 64,8 Xumc `f Huc`rc`gs `f ocs Tfpftehegjfs (XH T)= (∓T k)4 /t ‘ IH XH T = \(40)4+(89)4+(04)4+(63)4]/6 - 3.31>,6 XH T = 19,56
51
Xumc `f Huc`rc`gs `fo Frrgr Fxpfremfjtco (XHF)= XH Pgtco ‘ XH P- XH T XH F = 369,9 ‘ 64,8 -19,56 = 41,8 Cjãoeses `f Ycrecjzc Iufjtf `f vcrecheøj
Arc`gs `f Xumc `f oedfrtc` Huc`rc`gs
Huc`rc`g Mf`eg
I hcohuoc`c
I >,>6
I >,>3
Tfpftehegjfs
8
19,56
46,1
33,41**
8,05
6,56
Prctcmefjtgs
0
64,8>
38,3
6,16**
8,49
6,03
Frrgr Fxpfremfjtco
34
41,8>
4,8
Pgtco
35
369,66
Ejtfrprftcheøj ^crc rfpftehegjfs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
Ogs fifhtgs fjtrf rfpftehegjfs iufrgj fstc`ístehcmfjtf `eifrfjtfs. ^gr og
tcjtg, ocogs`fheseøj uscr iufjtf fo `esfóg fjecheøj. dogqufs co czcr iuf hgrrfhtc pcrc sfpcrcr fifhtgs `f fstc `f vcrecheøj. vcr ^?>,>3. ^crc trctcmefjtgs. trctcmefjtgs.- - Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
@f ogs hejhg iujaehe`cs prgdc`gs co mfjgs ujg fs fstc`ístehcmfjtf `eifrfjtf. ^?>,>3. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4,8)>,6 /1,96 = 35,14%
Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. Fo hgfiehefjtf `f vcrecheøj tefj`f c sfr cotg, cujquf fstc `fjtrg `f ogs oímetfs chfptc`gs pcrc fxpfremfjtgs `f hehog hgrtg, `fde`g quf fo jûmfrg `f arc`gs `f oedfrtc` `fo frrgr fs `f cpfjcs 34 hucj`g sf rfhgmefj`c sfc `f cprgxemc`cmfjtf 4>. Xf pg`ríc tfjfr 4> arc`gs `f oedfrtc` pcrc fo frrgr fofvcj`g fo jûmfrg `f rfpftehegjfs c 9 y mcjtfjefj`g ogs 6 trctcmefjtgs. 6.6.8. HVC@TC@G OCPEJG OCPEJG ·HVÃJ@G VXCT FO @EXFÓG FJ HVC@TC@G OCPEJG7 Vj huc`rc`g octejg fs ujc mctrez `f H hgoumjcs y B beofrcs. beofrcs. Fj uj `esfóg fj HO, ogs t trctcmefjtgs trctcmefjtgs sf `estreduyfj cofctgrecmfjtf y `fdfj fstcr prfsfjtfs fj tg`cs ocs hgoumjcs y fj tg`cs ocs beofrcs. ^gr hgjseauefjtf; H=B=t. Fstf sf `fdf fo hcmpg fxpfremfjtco prfsfjtc arc`efjtf fj `gs `esfóg `erfhhegjfs. C uscr jevfohucj`g `f hcmpg fxpfremfjtco g fj ocs iejhcs `f ogs prg`uhtgrfs, fo ejvfsteac`gr irfhufjtfmfjtf hgjstctc oc fxestfjhec `f
arc`efjtfs `fo tfrrfjg fj `gs `erfhhegjfs, pcrc ichtgrfs hgmg; prgiuj`e`c`,
52
ifrteoe`c` u gtrgs. Fstf `esfóg jg fs hgjvfjefjtf fj fjscygs hgj mãs `f 3> trctcmefjtgs. Hgmg `fsvfjtckc `f fstf `esfóg sf sfócoc quf fo jûmfrg `f arc`gs `f oedfrtc` `fo frrgr tefj`f c sfr pfqufóg y fo cjãoeses fs rfoctevcmfjtf mãs hgmpofkg quf @HC y DC. Pefjf hgmg rfstrehheøj quf tg`gs ogs trctcmefjtgs `fdfj cpcrfhfr fj hc`c hgoumjc y fj hc`c beofrc. ·HVÃO FX FO FXSVFMC @FO C@FYC FJ VJ @EXFÓG FJ HO7 Fo fsqufmc `fo cjãoeses `f vcrecjzc `f uj `esfóg fj Huc`rc`g octejg fs fo seauefjtf; Iufjtf `f vcrecheøj Hgoumjcs Beofrcs Prctcmefjtgs Frrgr fxpfremfjtco Pgtco
Arc`gs `f oedfrtc` t-3 t-3 t-3 (t-3)(t-4) t4-3
·HVÃO FX FO MG@FOG FXPC@ÍXPEHG @FO @EXFÓG FJ HVC@TC@G OCPEJG7 Fo mg`fog fstc`ístehg csghec`g co `esfóg fj Huc`rc`g octejg fs fo seauefjtf; U ekek = + H + B l + Ư e + ζ eelk k + l + lk e= 3,4,8...t k= 3,4,8...t l= 3,4,8...t H=B=t
@øj`f; U eekl kl = Ycrecdof `f rfspufstc fm oc ekl-åsemc uje`c` fxpfremfjtco = Mf`ec afjfrco `f oc vcrecdof `f rfspufstc k = H Fifhtg `f oc k-åsemc hgoumjc B e = Fifhtg `f oc e-åsemc beofrc Ư l = Fifhtg `f ogs l-åsemg trctcmefjtgs ζ elk elk = Frrgr fxpfremfjtco csghec`g c oc ekl-åsemc uje`c` fxpfremfjtco
^TGDOFMC TFXVFOPG Fj uj fstu`eg sgdrf bfrf`cdeoe`c` `fo hcrãhtfr prg`uhheøj fj ujc pgdocheøj `f mcíz sf prgdcrgj 3> `fshfj`fjhecs, fj uj fxpfremfjtg fj Huc`rc`g octejg. Oc vcrecdof vcrecdof `f rfspufstc iuf oc prg`uhheøj `f mcíz sfhg (34% bumf`c`) mf`e`c fj arcmgs pgr pocjtc4>. Ogs `ctgs `f hcmpg iufrgj ogs seauefjtfs;
4>
. @uehfoc, Oues. 3554. Bfrf`cdeoe`c` `fo hcrãhtfr prg`uhheøj `f arcjg fj ujc pgdocheøj `f mcíz. Pfses `f Mcfstríc Mcfstríc fj
Hefjhecs. Ejstetutg Pfhjgoøaehg y `f Fstu`egs Xupfregrfs Xupfregrfs `f Mgjtfrrfy. Cpg`chc, Jufvg Oføj. Måxehg.
55
Hgoumjcs 3 4 8 0 s c r f o e B
6 9 1 2 5 3>
E A 384 K 331 @
EE B 382 C 381 F
EEE F 29 B 3>1 D
EY E 3>9 D 348 I
Y H 330 I 50 K
YE C 304 @ 33> B
YEE D 3>6 F 3>8 E
YEEE K 3>3 H 3>9 A
ER @ 364 A 58 C
R I 53 E 3>5 H
343 C 366 E 50 H 339 B 3>1 I 382 D 309 F 364
90 D 3>1 K 388 @ 22 E 331 A 3>2 H 338 I 34>
338 E 336 A 3>9 C 391 I 338 @ 36> K 364 H 340
21 H 3>6 C 396 F 330 K 385 B 39> @ 3>5 A 385
3>1 A 330 F 34> E 3>6 @ 3>1 D 346 B 333 C 383
13 F 380 H 343 A 332 D 308 K 381 I 343 E 3>>
340 I 3>5 @ 21 B 54 H 30> C 332 A 28 K 26
333 @ 369 D 3>1 I 334 C 35> E 3>9 F 386 B 3>8
364 B 95 I 14 K 3>0 F 341 H 339 E 3>9 D 25
3>4 K 20 B 53 D 36> A 52 F 21 C 368 @ 396
Xumc
Mf`ec
3.391
331
3.>55
33>
3.>64
3>6
3.302
336
H=3>, B=3>, t=3> Hãohuog `f sumcs y prgmf`egs Hgoumjcs 3 4 8 0 s c r 6 f o e B 9
1 2 5 3> Xumc Mf`ec
E
EE
EEE
EY
Y
YE
YEE
YEEE
ER
R
A
B
F
E
H
C
D
K
@
I
384
382
29
3>9
330
304
3>6
3>3
364
53
K 331 @ 343 C 366
C 381 F 90 D 3>1
B 3>1 D 338 E 336
D 348 I 21 H 3>6
I 50 K 3>1 A 330
@ 33> B 13 F 380
F 3>8 E 340 I 3>5
H 3>9 A 333 @ 369
A 58 C 364 B 95
E 3>5 H 3>4 K 20
E
K
A
C
F
H
@
D
I
B
50 H
388 @
3>9 C
396 F
34> E
343 A
21 B
3>1 I
14 K
53 D
3.>59
33>
339
22
391
330
3>6
332
54
334
3>0
36>
3.399
331
B 3>1 I 382
E 331 A 3>2
I 338 @ 36>
K 385 B 39>
@ 3>1 D 346
D 308 K 381
H 30> C 332
C 35> E 3>9
F 341 H 339
A 52 F 21
3.423
342
3.406
346
D
H
K
@
B
I
A
F
E
C
309 F 364
338 I 34>
364 H 340
3>5 A 385
333 C 383
343 E 3>>
28 K 26
386 B 3>8
3>9 D 25
368 @ 396
3.445
348
3.4>2
343
3.412 342
3.346 338
3.488 348
3.351 34>
3.>09 3>6
33.953 3395
3.395 331
3.401 3.342 346 338
3.441 3.>2> 3.38> 348 3>2 338
3>>
Hgoumjcs
Xumc
Mf`ec
368
3.63>
363
25
36>
3.4>2
343
3>9 369
339 364
3>4 396
3.361 3.406
339 346
3>8
386
341
21
3.344
334
343
3>5
334
14
53
3.>61
3>9
330
332
28
333 3 33
58
52
3.3>4
33>
39>
333
13
54
3>8
95
53
3.>05
3>6
336
3>9
3>6
3>>
340
3>9
3>9
3>5
3.>24
3>2
388
364
385
3>1
381
26
3>3
3>0
20
3.365
339
3.412
3.346
3.488
3.351
3.>09
3.38>
33.953
3.395
342
338
348
34>
3>6
338
3.395
331
E
EE
EEE
EY
Y
YE
YEE
YEEE
ER
R
C
366
381
391
396
383
304
332
35>
364
D
309
3>1
338
348
346
308
3>6
3>1
H @
339 343
338 22
340 36>
3>6 3>5
330 3>1
343 33>
30> 21
F
364
90
29
330
34>
380
I
382
34> 3 4>
338
21
50
A
384
3>2
3>9
385
B
3>1
382 3 82
3>1
E
50
331
K
331
Xumc Mf`ec
s g t j f e m c t c r P
3.401 3.342 346
338
3.441 3.>2> 348
3>2
Hãohuog `f ocs Xumcs `f Huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓R ek)4 /(t4) = (33.95)4 /3>> = 3.899.156 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓R ∓ Re4 ‘ IH XH Pgtco = \(366)4+(381)4+(391)4+…….…+(3>0)4+(20)4] ‘ 3.899.156 XH Pgtco = 61.26> XH Hgoumjcs = ∓(Hgoumjcse)4 /3> ‘ IH XH Hgoumjcs = \(3.412)4+(3.346) 4+(3.488)4+…….…+(3.>2>)4+(3.38>)4]/3> ‘ 3.899.156 XH Hgoumjcs = 6.00> XH Beofrcs = ∓(Beofrcs k)4 /3> ‘ IH XH Beofrcs = \(3.391) 4+(3.>55) 4+(3.>64)4+…….…+(3.445)4+(3.4>2)4]/3> ‘ 3.899.156 XH Beofrcs = 0.123 XH P = ∓(Prctcmefjtgs)4 /3> ‘ IH XH P = \(3.63>)4+(3.4>2)4+(3.361)4+…….…+(3.>24)4+(3.365)4]/3> ‘ 3.899.156 XH P = 39.6>8 Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH Hgoumjcs ‘XH Beofrcs ‘ XH Prctcmefjtgs XH F = 61.26> - 6.00> - 0.123 - 39.6>8 = 83.349
3>3
Cjãoeses `f Ycrecjzc Iufjtf `f vcrecheøj
Xumc `f Huc`rc`gs
Arc`gs `f oedfrtc`
Huc`rc`g Mf`eg
Ihcohuoc`c
I>,>6
I>,>3
Hgoumjcs
t-3
5
6.00>
9>0
3,0> JX
4,>3
4,99
Beofrcs
t-3
5
0.123
683
3,48 JX
4,>3
4,99
Prctcmefjtgs
t-3
5
39.6>8
3.280
0,40**
4,>3
4,99
(t-3)(t-4)
14
83.349
084
t4-3
55
61.26>
Frrgr fxpfremfjtco Pgtco
Ejtfrprftcheøj .^crc hgoumjcs .-
Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy fifhtgs fstc`ístehcmfjtf `eifrfjtfs fjtrf hgoumjcs. hgoumjcs. ^:>,>6. ^crc beofrcs.- Ihcohuoc`c ?I>,>3
I>,>6; Xf chfptc B>. Jg bcy fifhtgs fstc`ístehcmfjtf `eifrfjtfs fjtrf beofrcs. beofrcs. ^:>,>6. y
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
@f ocs `efz `fshfj`fjhecs prgdc`cs co mfjgs ujc fs fstc`ístehcmfjtf `eifrfjtf. ^?>,>3. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (084)>,6 /331 * 3>> = 31,2% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. 6.6.0. @EXFÓG FJ OÃPEHF ·HVÃJ@G VXCT FO @EXFÓG FJ OÃPEHF7 Ogs oãtehfs hgjstetuyfj uj arupg `f `esfógs hgjghe`gs hgmg dogqufs ejhgmpoftgs quf sgj mãs fiehefjtfs quf ogs gtrgs `esfógs hucj`g bcy cotc bftfrgafjfe`c` `fo hcmpg fxpfremfjtco y fo jûmfrg `f trctcmefjtgs fj fstu`eg fs mãs g mfjgs fofvc`g. Pefjf oc `fsvfjtckc `f quf fo cjãoeses fstc`ístehg fs mãs hgmpofkg. ·HVÃO FX FO FXSVFMC @FO C@FYC @FO @EXFÓG FJ OÃPEHF7 Fo fsqufmc `fo cjãoeses `f vcrecjzc (C@FYC) fs fo seauefjtf;
3>4
Iufjtf `f vcrecheøj
Arc`gs `f oedfrtc`
Tfpftehegjfs
r-3
Ycref`c`fs
L 4-3
Dogqufs
r(l-3)
Frrgr ejtrc dogqufs Pgtco
(l-3)(rl-l-3) rl 4-3
·HVÃO FX FO MG@FOG FXPC@ÍXPEHG7 F XPC@ÍXPEHG7 Fo mg`fog fstc`ístehg csghec`g co `esfóg fj oãtehf fs fo seauefjtf; U ek = + T k + Ư e + D l + ζ elk ek = elk
@øj`f; U eeklkl = Ycrecdof `f rfspufstc fm oc ekl-åsemc uje`c` fxpfremfjtco = Mf`ec afjfrco `f oc vcrecdof `f rfspufstc k
T e ==Fifhtg Fifhtg`f`fogs ocse-åsemg k-åsemctrctcmefjtgs rfpftehegjfs eajgrcj`g dogqufs Ư
Dl = Fifhtg `f ogs l-åsemg dogqufs foemejcj`g trctcmefjtgs ζ elk elk = Frrgr fxpfremfjtco csghec`g c oc ekl-åsemc uje`c` fxpfremfjtco
^TGDOFMC TFXVFOPG Xf bcj ejtrg`uhe`g 46 vcref`c`fs `f mcíz quf sf fvcoûcj fvcoûcj fj uj oãtehf oãtehf 6 x 6 hgj 4 rfpftehegjfs. Gr`fjcmefjtg `f ogs trctcmefjtgs prfveg c oc cofctgrezcheøj; (3) (4) (8) (0) (6)
3 9 33 39 43
3 4 8 0 6
4 1 34 31 44
8 2 38 32 48
0 5 30 35 40
6 3> 36 4> 46
9 1 2 5 3>
33 34 38 30 36
39 31 32 35 4>
43 44 48 40 46
r = jûmfrg `f rfpftehegjfs = 4 l = jûmfrg `f hgoumjcs = jûmfrg `f beofrcs = 6
Prctcmefjtgs = 46 vcref`c`fs
3>8
@estreduheøj `f ogs trctcmefjtgs fj fo hcmpg (cofctgrezc`gs) Dogqufs H C D @ F Dogqufs B A K I E
36 6 3> 39 48
30 4 2 4> 43
38 4 4> 9 30
8 34 46 43 40
Tfpfteheøj E (Arupg R) 34 0 1 35 44 Tfpfteheøj EE (Arupg U) 48 1 36 3 35
38 3 9 31 40
33 8 5 32 46
2 44 6 39 39 5
32 31 3> 33 0
@ctgs `f hcmpg `f oc vcrecdof `f rfspufstc pgr trctcmefjtg Dogqufs H
C
D
@
F
36
30
34
38
33
41,9
46,4
44,2
40,6
40,0
6
4
0
3
8
43,4
40,3
40,6
35,6
40,>
3>
2
1
9
5
42,4
42,5
49,0
41,8
46,9
39
4>
35
31
32
45,0
48,8
40,8
46,1
42,3
48
43
44
40
46
46,>
40,3
40,8
Dogqufs B
A
K
I
E
Xumc `f dogqufs
Tfpfteheøj E (Arupg R)
46,1 48,5 Xumc Tfpfteheøj E=
340,6 338,8 389,0 38>,2 348,> 942,> Xumc `f dogqufs
Tfpfteheøj EE (Arupg U) 38
8
48
2
32
42,3
46,4
49,4
41,1
41,1
4
34
1
44
31
46,9
42,5
42,5
45,8
8>,>
4>
46
36
6
3>
40,0
44,8
49,9
46,1
49,9
9
43
3
39
33
45,6
40,0
4>,>
46,>
40,2
30
40
35
5
0
89,0
88,9
88,3
88,2 8>,0 Xumc Tfpfteheøj EE=
380,5 304,1 346,9 348,1 391,8 950,4
3>0
@ctgs tgtcofs `f ocs vcref`c`fs 3
Pgtco `f Hgoumjcs
Pgtco pcrc Ycref`c`fs 4 8 0
6
Pgtco `f Beofrcs
85,6
05,1
05,4
60,5
09,5
40>,4
9 69,2
1 66,8
2 69,9
5 65,0
3> 60,2
424,5
33
34
38
30
36
05,4
63,1
64,9
93,9
60,4
39
31
32
35
4>
60,0
66,1
66,2
61,0
01,1
43
44
48
40
46
02,6
68,9
63,4
65,8
09,4
402,0
499,>
496,0
454,9
495,8 413,> 462,2
405,2 3.844,4
Mf`ec afjfrco = 3.844.4/6> = 49,00
Cjãoeses `f vcrecjzc Ichtgr `f hgrrfhheøj = (Pgtco rfpfteheøj E + tgtco rfpfteheøj EE) 4 /rl 4 IH = (942,>+950,4)4 /6> = 80.590,49 Xumc `f huc`rc`gs tgtco (XHP) = (41,9) 4 + (46,4)4 +…… (42,3)4+……(8>,0)4 ‘ 80.590,49 XHP = 662,94 Xumc `f huc`rc`gs `f ocs rfpftehegjfs (XHT) = (Pgtco Tfpfteheøj E)4+ Pgtco rfpfteheøj EE)4 /l 4 - IH XH T = (942,>)4+(950,4)4 /46 ‘ 80.590,49 = 21,96 Xumc `f huc`rc`gs `f vcref`c`fs (eajgrcj`g dogqufs)(XHY)=(85,6)4+(05,1)4…..(09,4)4 /4 ‘ 80.590,49 XHY =456,05 Fo hãohuog ocs sumc `f huc`rc`gs `f dogqufs (XHD), eajgrcj`g ocs vcref`c`fs, sf rfcoezc cpgyc`g fj vcogrfs rlh`f x y rlhy, ogs quf sf fstemcj `f oc seauefjtf mcjfrc; rlhx = Pgtco beofrcs vcref`c`fs ‘ 4 (Xumc `f dogqufs arupg R) rlhy = Pgtco hgoumjcs vcref`c`fs ‘ 4(Xumc `f dogqufs arupg U) Pgtco `f Xumc `f dogqufs Beofrcs Tfp. E; Arupg R 40>,4 338,8 424,5 389,0 495,8 340,6 413,> 38>,2 462,2 348,> Xumc
rlhx 38,9 3>,3 4>,8 5,0 34,2 99,4
Pgtco `f Xumc `f dogqufs Hgoumjcs Tfp. EEE; Arupg U 402,0 348,1 499,> 304,1 496,0 380,5 454,9 391,8 405,2 346,9 Xumc
rlhy 3,> -35,0 -0,0 -04,> -3,0 -99,4
3>6
Oc sumc `f rlhx + rlhy `fdf sfr sefmprf eauco c hfrg. Oc sumc `f huc`rc`gs `f dogqufs = hgmpgjfjtf D
XH Dogqufs = \(38,9)4+(3>,3)4+(4>,8)4+(5,0)4+(34,2)4+(3)4+(-35,0)4+(-0,0)4+(-04)4+(-3,0)4]/3> ‘ \(99,4)4+ (-99,4)4]/6> XH Dogqufs = 389,3>
C@FYC `fo Oãtehf sempof Iufjtf `f vcrecheøj
Arc`gs `f oedfrtc`
XH
HM
Ihcohuoc`c
I>,>6
I>,>3
Tfpftehegjfs
r-3
3
21,96
21,96
86,9>**
0,05
2,68
Ycref`c`fs
L 4-3
40
456,05
34,83
6,>>**
4,40
8,32
Dogqufs
r(l-3)
2
389,3>
31,>3
9,53**
4,65
8,25
(l-3)(rl-l-3)
39
85,85
4,09
rl 4-3
05
662,94
Frrgr ejtrc dogqufs Pgtco
Fj fstc pcrtf `fo cjãoeses hcdf tfjfr prfsfjtf quf ‟Xe fo Huc`rc`g Mf`eg `f Dogqufs fs mfjgr g eauco quf fo Huc`rc`g Mf`eg `fo Frrgr fxpfremfjtco seajeiehcríc quf jg fs jfhfscreg ckustfs pgr fifhtgs `f dogqufs”.
Hgmg fj fo prfsfjtf hcsg, fo Huc`rc`g Mf`eg `f ogs Dogqufs fs mcygr quf fo Huc`rc`g Mf`eg `fo Frrgr, sf `fdf rfcoezcr uj ckustf `f ocs mf`ecs `f ocs vcref`c`fs. HMD : HMF; Fs jfhfscreg bchfr ckustfs `f ogs prgmf`egs `f ocs vcref`c`fs pgr fifhtg `f ogs dogqufs .
Ejtfrprftcheøj Fo C@FYC pfrmetf fstcdofhfr quf bcy `eifrfjhecs seajeiehctevcs muy cotc (55% `f hgjiecjzc) fjtrf ocs rfpftehegjfs, fjtrf ogs dogqufs y fjtrf ocs vcref`c`fs. ^crc bchfr ocs hgmpcrchegjfs fjtrf ocs mf`ecs `f ocs vcref`c`fs, bcy quf bchfr uj ckustf pgr fifhtg `f ogs dogqufs (tgmcr fj hufjtc quf ogs `ctgs prgvefjfj `f `gs rfpftehegjfs). Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>] = (4,09)>,6 /49,00 *3>> = 6,58% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. Hãohuog `fo ichtgr `f pgj`frcheøj; (w-w―)/(w+w―) = ichtgr `f pgj`frcheøj w = 3/(HMF) = 3/4,09 = >,0>96 w― = 3/(4HMD ‘HMF) = 3/ \(4)(31,>3)-4,09] =>,>8392
3>9
(w-w―)/(w+w―)= (>,0>96->,>8392)/(>, (>,0>96->,>8392)/(>,0>96+>,>8392) 0>96+>,>8392) (w-w―)/(w+w―) = >,8102/>,08232) = >,266812 Hãohuog `f ocs hgrrfhhegjfs H R ― y H U ― Hx― = \(w-w―)/(w+w―)(rl)](rlhx) Hx― =\(>,81023)/(>,08235)(3>)](38,9) = 3,398 ………. hgjtejuc fo hãohuog pcrc Hx― y Hy―
'
38,9 3>,3 4>,8 5,0 34,2 99,4
3,398 >,290 3,189 >,2>0 3,>56
'
3 35,0 0,0 04 3,0 99,4
>,>29 3,965 >,819 8,658 >,34>
^rgmf`egs `f ocs vcref`c`fs sej ckustcr y hgrrfhhegjfs H x― y Hy― ^rgmf`eg `f ocs vcref`c`fs
Pgtco Hgoumjcs hy'
Pgtco Beofrcs
hx'
34>,3
3,398
303,06
>,290
380,96
3,189
386,6
>,2>0
3,>56
3
4
8
0
6
35,16
40,26
40,9
41,06
48,06
9
1
2
5
3>
42,0
41,96
42,8
45,1
41,0
33
34
38
30
36
40,9
46,26
49,8
8>,2
41,3
39
31
32
35
4>
41,4
41,26
41,5
42,1
48,26
43
44
48
40
46
40,46
49,2
46,9
45,96
48,3 48,3
345,0
340,4
388
384,1
309,8
340,5
993,3
>,>29
-3,965
->,819
-8,658
->,34>
Mf`ec afjfrco = 993/46 = 49,00
3>1
Hãohuog `f ogs prgmf`egs `f ocs vcref`c`fs ckustc`gs Ogs prgmf`egs `f ocs vcref`c`fs sf ckustcj mf`ecjtf oc sumc `fo prgmf`eg sej ckustcr + oc hgrrfhheøj H R― + oc hgrrfhheøj H U ―.―. ^crc oc vcref`c` 3;
^rgmf`eg sej ckustcr =35,16 HR―=3,398 H U ―= ―= >,>29 ^gr og tcjtg; ^rgmf`eg vcref`c` 3 ckustc`c = 35,16+3,398+>,>29 =43,>> …..hgjtejûc fo hãohuog `f ckustf `f prgmf`egs pcrc tg`cs ocs vcref`c`fs.
Y3 43,>> Y9 45,86 Y33 49,04 Y39 42,>5 Y43 46,08
^rgmf`eg `f ocs vcref`c`fs (ckustc`g) Y4 Y8 Y0 40,86 46,85 446,>4 6,>4 Y1 Y2 Y5 49,26 42,15 449,51 9,51 Y34 Y38 Y30 46,58 41,99 442,50 2,50 Y31 Y32 Y35 49,55 42,88 446,53 6,53 Y44 Y48 Y40 49,40 49,84 441,36 1,36
Y6 40,05 Y3> 42,30 Y36 42,14 Y4> 40,68 Y46 40,>2
Hgjhoue`c fstc pcrtf `fo cjãoeses, sf rfcoezc oc hgmpcrcheøj `f mf`ecs uscj`g oc prufdc `f t ø ocs hgmpcrchegjfs grtgagjcofs. Hcdf `fstchcr quf ocs mf`ecs fj fo prfsfjtf fkfrheheg prgvefjfj `f `gs rfpftehegjfs.
3>2
6.9. FR^FTEMFJPGX ICHPGTECOFX ·HØMG XF @FIEJF VJ FR^FTEMFJPG ICHPGTECO7 Ogs fxpfremfjtgs ichtgrecofs tefjfj fo prgpøsetg `f prgdcr bepøtfses rfochegjc`cs hgj `gs g mãs ichtgrfs semuotãjfcmfjtf y fstcdofhfr ogs fifhtgs fjtrf prejhepcofs pgr ichtgr`fy ogs fifhtgs `f ocs ejtfrchhegjfs `f premfr gr`fj (ejtfrchheøj `gs ichtgrfs), sfauj`g gr`fj (trfs ichtgrfs) g `f ør`fjfs mcygrfs. Fj oc prãhtehc, `fdf prgdcrsf uj mãxemg `f trfs ichtgrfs, pcrc gdtfjfr oc mãxemc ejigrmcheøj pgsedof, fvetcj`g fo fjmcshcrcmefjtg `f fifhtgs fj ocs ejtfrchhegjfs. Ogs fxpfremfjtgs ichtgrecofs jg sgj `esfógs fxpfremfjtcofs prgpecmfjtf, sejg crrfaogs ichtgrecofs quf sf c`cptcj c ogs `esfógs dãsehgs, fj iujheøj `f ocs hcrchtfrístehcs `fo hcmpg fxpfremfjtco. Xej fmdcrag, fs hgmûj fo jgmdrf `f `esfóg ichtgreco quf sf `fiejf hgmg oc prufdc `f tg`cs ocs pgsedofs hgmdejchegjfs `f ogs jevfofs `f ogs ichtgrfs fj fstu`eg. Fo fifhtg `f uj ichtgr fs fo hcmdeg fj oc rfspufstc prg`uhe`c pgr uj hcmdeg fj fo jevfo `fo ichtgr fj fstu`eg. Ogs fxpfremfjtgs ichtgrecofs puf`fj sfr hgmpoftgs g ejhgmpoftgs, hc`c ujg rfquefrf `f tåhjehcs fspfhecofs pcrc oc sfpcrcheøj `f ogs fifhtgs `f ogs ichtgrfs. Ogs `esfógs ichtgrecofs mãs usc`gs fj oc fxpfremfjtcheøj sgj ogs hgjghe`gs hgmg; ichtgrecofs sempofs, `esfógs (C)D, crrfaogs ichtgrecofs (C)D + 3, pcrhfocs `eve`e`cs, fxpfremfjtgs +3, fxpfremfjtgs -3 y `esfógs grtgagjcofs. ·HØMG XF EJPFT^TFPCJ OGX FIFHPGX ICHPGTECOFX7 Fifhtg `f uj ichtgr fj fstu`eg.- Xupøjacsf quf sf fstã prgdcj`g uj sgog ichtgr fj 9 jevfofs `f fstu`eg (R) fvcouãj`gsf oc vcrecdof oc rfspufstc U. ^gr fkfmpog; sfes jevfofs `f ifrteoezcjtf fj uj huotevg `ftfrmejc`g. Ogs rfsuotc`gs pg`rícj sfr ogs seauefjtfs; U
U
Jg bcy fifhtg Fifhtg jfactevg
>
3
4
8
0
R
6
U
>
3
4
8
0
R
6
U
Fifhtg pgsetevg oejfco
[gj [gjcc ejfx ejfx ogr ogrc`c c`c
[gj [gjcc fx ogr ogrc`c c`c
>
3
4
8
0
Fifhtg pgsetevg huc`rãtehg
6
R
>
3
4
8
0
6 R
3>5
Fifhtgs `f `gs ichtgrfs fj trfs jevfofs `f fstu`eg.- Xupøjacsf uj fxpfremfjtg (8)4 hgj ogs rfsuotc`gs seauefjtfs; c)
Hucj`g c mf`e`c quf sf ejhrfmfjtcj ogs fifhtgs pgsetevgs `f C tcmdeåj sf ejhrfmfjtcj ogs fifhtgs pgsetevgs `f D, jg bcy ejtfrchheøj fjtrf fjtrf ichtgrfs, ocs oíjfcs `f tfj`fjhec `f ichtgrfs y jevfofs jg tefjfj pgsedeoe`c` `f kujtcrsf. D8
Ichtgr C
D r g t h c I
d)
C3
C4
C8
D3
0
9
2
D4
9
2
3>
D8
2
3>
34
D4 D3
Hucj`g c mf`e`c quf sf rf`uhfj ogs fifhtgs `f C tcmdeåj sf rf`uhfj ogs fifhtgs `f D, jg jg bcytefjfj ejtfrchheøj fjtrf fjtrf ichtgrfs, ocs oíjfcs `f tfj`fjhec `f ichtgrfs y jevfofs pgsedeoe`c` `f kujtcrsf.
C3 D3
D r g t h c I
h)
Ichtgr C C4 C8
2
9
0
D8 D4 D3
D4
3>
2
9
D8
34
3>
2
Hucj`g fifhtgs fjtgjhfs, `f ujgs ichtgrfs y jevfofs tefj`fj c hruzcrsf gtrgs ichtgrfs ogs y jevfofs, bcy ejtfrchheøj fjtrf ichtgrfs, ocs hgj oíjfcs `f tfj`fjhec `f ichtgrfs y jevfofs sf kujtcj fjtrf sí fj uj pujtg (p.f.; D3 y D4) g tefj`fj kujtcrsf bchec c`focjtf (D3 y D8). Ichtgr C
D r g t h c I
D8
C3
C4
C8
D3
0
9
2
D4
9
1
1
D8
2
3>
3>
D3 D4
33>
Xfpcrcheøj `f fifhtgs ichtgrecofs c)
Fj fxpfremfjtgs deichtgrecofs sf hgjstruyf ujc tcdoc `f `gdof fjtrc`c `gj`f sf fxpgjfj ocs mf`ecs `f ogs trctcmefjtgs (hgmdejcheøj `f ichtgrfs y jevfofs) hgmpofmfjtc`c hgj ocs sumcs y ocs mf`ecs `f mf`ecs pcrc ocs hgoumjcs f beofrcs. Fj fo fkfmpog seauefjtf sf puf`f `ftfrmejcr hocrcmfjtf quf fo fifhtg `f C3 fs 9,>< fo `f C4 fs 1,1 y fo `f C8 fs 2,8. Fo fifhtg `f D3 fs 9,>< fo fifhtg `f D4 fs 9,1 y fo fifhtg `f D8 fs 5,8. Ichtgr C
D r g t h c I
Mf`ec
2
32
9,>
1
1
4>
9,1
2
3>
3>
42
5,8
32 9,>
48 1,1
46 2,8
99 44,>
44 1,8
C4
C8
D3
0
9
D4
9
D8
Xumc Mf`ec
d)
Xumc
C3
Fj fxpfremfjtgs ichtgrecofs huygs `ctgs `f mf`ecs `f ichtgrfs y jevfofs sf fxpgjfj fj uj igrmctg fj hgoumjcs, fo `fsaogsf `f fifhtgs pgr ichtgr, sf hcohuoc `f oc seauefjtf mcjfrc; J 3 3 4 4
Ichtgrfs y jevfofs ^ 3 4 3 4 Mf`ec
Hø`eag J3 J3^3 ^3 J3 J3^4 ^4 J4 J4^3 ^3 J4 J4^4 ^4
Mf`ec 8,>> 0,>> 0,16 6,6> 0,46
Hgmg sf csumf quf ogs fifhtgs sgj `f jcturcofzc c`etevc, ogs fifhtgs `f ogs jevfofs pgr ichtgr sf fxprfscj fj ocs mf`ecs. Fo fifhtg `f J3 sf fxprfsc fj fo prgmf`eg fjtrf 8 y 0< pgr og tcjtg, fo fifhtg J3= 8,6. Fo fifhtg `f J4 sf fxprfsc fxprfsc fj fo prgmf`eg fjtrf 0,16 y 6,6>< pgr og tcjtg, fo fifhtg J4= 6,>. Fo fifhtg `f ^3 sf fxprfsc fj fo prgmf`eg fjtrf 8 y 0,16< 0,16< pgr og tcjtg, fo fifhtg ^3= 8,21. Fo fifhtg fifhtg ^4= 0,98.`f ^4 sf fxprfsc fj fo prgmf`eg fjtrf 0,> y 6,6>< pgr og tcjtg, fo
333
Jevfofs
Ichtgrfs J
^
3
8,6>
8,21
4
6,>>
0,98
Ejhrfmfjtg
3,6>
>,19
Ejhrfmfjtg %
04,5
35,9
6.9.3. @EXFÓGX ICHPGTECOFX XEM^OFX ·HØMG XF @EXFÓC VJ FR^FTEMFJPG ICHPGTECO7 Ogs fxpfremfjtgs ichtgrecofs sempofs hgmdejcj ogs ichtgrfs y jevfofs jg tefjfj rfstrehheøj fj fo `esfóg `f ogs trctcmefjtgs. ^gr fkfmpog, sf `fsfc prgdcr uj ichtgr C hgj huctrg jevfofs y uj ichtgr D hgj 4 jevfofs. Fjtgjhfs sf trctc `f uj fxpfremfjtg ichtgreco `f 0 x 4< fs `fher `f 2 trctcmefjtgs. ^gr supufstg quf fj fo `esfóg fxpfremfjtco tefjfj quf hgjse`frcrsf ocs rfpftehegjfs pfrtejfjtfs. ^uf`fj pocjfcrsf fxpfremfjtgs ichtgrecofs mãs hgmpofkgs< pgr fkfmpog, uj fxpfremfjtg treichtgreco, `øj`f fo ichtgr C tfjac 8 jevfofs, fo ichtgr D tfjac 4 jevfofs y uj ichtgr H tfjac 0 jevfofs fj fstu`eg. Fstg seajeiehc quf sf tfj`ríc uj fxpfremfjtg treichtgreco 8 x 4 x 0 = 40 trctcmefjtgs hgj r rfpftehegjfs. rfpftehegjfs. ^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg sf prufdcj hejhg vcref`c`fs mfkgrc`cs fj trfs `fjse`c`fs `f sefmdrc, fvcouãj`gsf oc prg`uhheøj pgr bfhtãrfc. jevfofs fo Xf trctc@`f(`fjse`c`fs) uj fxpfremfjtg ichtgrseajeiehc Y (vcref`c`fs) ichtgr fj deichtgreco; 8 jevfofs< fofstg quf sffjtrctc `f yuj fxpfremfjtg 6 x 8 = 36 trctcmefjtgs. Fo fxpfremfjtg 6 x 8 sf pocjfc hgj 8 rfpftehegjfs, pgr og tcjtg, sf tefjfj 06 uje`c`fs fxpfremfjtcofs (pcrhfocs).
334
Ogs `ctgs `f hcmpg `f prg`uhheøj, oc sumc, prgmf`eg y vcogr huc`rc`g `f oc prg`uhheøj, sgj ogs seauefjtfs; Tfpftehegjfs Prctcmefjtgs Ycref`c`fs @fjse`c`fs ^rg`uhheøj 3 3 3 3 3> 3 4 3 4 34
(^rg`uhheøj)4 3>> 300
33 3 3 3 3 3 3 3 3 3 3 3 4 4 4
08 6 9 1 2 5 3> 33 34 38 30 36 3 4 8
43 4 4 8 8 8 0 0 0 6 6 6 3 3 3
38 4 8 3 4 8 3 4 8 3 4 8 3 4 8
38 36 39 32 43 4> 35 2 3> 5 43 31 39 38 30 33
395 446 469 840 003 0>> 893 90 3>> 23 003 425 469 395 359 343
44 4 4 4 4 4 4 4 4 4 4 8 8 8 8
60 9 1 2 5 3> 33 34 38 30 36 3 4 8 0
44 4 8 8 8 0 0 0 6 6 6 3 3 3 4
43 8 3 4 8 3 4 8 3 4 8 3 4 8 3
31 39 35 40 49 44 1 33 5 44 35 31 36 33 38 39
425 469 893 619 919 020 05 343 23 020 893 425 446 343 395 469
88 8 8 8 8 8 8 8 8 8
96 1 2 5 3> 33 34 38 30 36
44 8 8 8 0 0 0 6 6 6
84 3 4 8 3 4 8 3 4 8
32 31 44 36 38 5 30 3> 40 32 30
840 425 020 446 395 23 359 3>> 619 840 359
1>3 36,9
33.255
Xumc Mf`ec afjfrco
rt= 06, r = 8, t = 36, Y= 6, @= 8
338
Hãohuog `f sumcs y prgmf`egs 3 446
() 3 82
() ( )
4
401
8
445
4
81
8 0
81 02 6> 60 91 93 60 40 86 42 91 60
6 9 1
3 334 4 364 8 324 0 21
2
()
5
3>
33
6
392
34 38 30 36
3 400 4 481 8 44>
()
01
82 81 81
02 6> 60
91 93 60
40 86 42
91 60 01
Hãohuog `f ocs Xumcs `f Huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓R ek)4 /(rt) = (1>3)4 /06 = 053.0>3/06 3>.54> Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓R ∓ Re4 ‘ IH 4 4 4 XH Pgtco = \(3>) +(34) +(38) +…….…+(32)4+(30)4] ‘ 3>.54> XH Pgtco = 515 XH T= ∓(T)4 /t ‘ IH XH T = \(446) 4+(401)4+(445)4]/36 ‘ 3>.54> XH T = /36-3>.54> 32,83 4 4 ‘ IH4 XH P = ∓(P) \(82) /r +(81) +(81)4+…….…+(60)4+(01)4]/8 ‘ 3>.54> XH P = 86.441/8-3>.54> 244
330
XH Y = ∓(Y)4 /r` ‘ IH XH Y = \(334) 4+(364)4+(324)4+(21)4+(392)4]/5 ‘ 3>.54> XH Y = 3>0.696/5 3>.54> = 952 XH @ = ∓(@)4 /rv ‘ IH XH @ = \(400)4+(481)4+(44>)4]/36 ‘ 3>.54> XH @ = 390.3>6/36 3>.54> = 4> () 2449524> 3>0
Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 515 - 32,83- 244 382,89
Cjãoeses `f Ycrecjzc
4
32,83
5,39
3,26
8,80>
6,068
30
244
62,10
33,25**
4,>90
4,156
>,>6
>,>3
310,62
86,88**
4,130
0,>10
3>,39
4,>9
8,80>
6,068
2
3>0
34,59
4,94*
4,453
8,449
42
382,89
00
515
0,50
Ejtfrprftcheøj ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy `eifrfjhecs
fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6.
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
Ogs trctcmefjtgs rfsuotcj `f oc hgmdejcheøj `f ogs `gs ichtgrfs, pgr og tcjtg, sf rfquefrf hgjghfr ogs fifhtgs prejhepcofs `f ogs ichtgrfs fj fstu`eg.
^crc vcref`c`fs.- I hcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc. @f
ocs hejhg vcref`c`fs prgdc`cs, co mfjgs ujc fs fstc`ístehcmfjtf `eifrfjtf. ^?>,>3.
^crc `fjse`c`fs.- I hcohuoc`c ? I>,>6; Xf chfptc B>. Ocs trfs `fjse`c`fs prgdc`cs
sgj fstc`ístehcmfjtf eaucofs. ^:>,>6.
^crc oc ejtfrchheøj vcref`c`fs x `fjse`c`fs.- Ihcohuoc`c ? I >,>6; Xf chfptc B>. Jg
bcy ejtfrchheøj fjtrf vcref`c`fs y `fjse`c`fs pgdochegjcofs. ^:>,>6.
Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (0,50)>,6 /36,9 * 3>> = 30,8% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã
`fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs.
336
6.9.4. @EXFÓGX (C)D ·HØMG XF @EXFÓCJ OGX FR^FTEMFJPGX (C)D7 Xf hgjse`frcj `esfógs (C)D cqufoogs `gj`f sf usc ujc jgmfjhocturc mctfmãtehc quf e`fjteiehc hgj oc oftrc C c ogs jevfofs fj fstu`eg y hgj oc oftrc D c ogs ichtgrfs fj fstu`eg. Fstgs `esfógs sf hcrchtfrezcj pgrquf tefjf uj jûmfrg `f jevfofs quf fs eauco pcrc tg`gs ogs ichtgrfs fj fstu`eg. Vj fxpfremfjtg (4)4 trctc `f `gs ichtgrfs pgr `gs jevfofs< uj fxpfremfjtg (4) 8 trctc `f trfs ichtgrfs pgr `gs jevfofs< uj fxpfremfjtg (8)4 trctc `f `gs ichtgrfs pgr trfs jevfofs. FR^FTEMFJPGX (4)4 ·@F SVÅ PTCPCJ OGX FR^FTEMFJPGX (4)47 Vj fxpfremfjtg (4)4 ejvgouhrcj fo fstu`eg `f 4 ichtgrfs fj `gs jevfofs< fs `fher, 0 trctcmefjtgs hgj r rfpftehegjfs. ^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg ichtgreco (4)4, `gj`f sf prufdcj `gs vcref`c`fs y `gs cotfrjctevcs `f ifrteoezcheøj, fj 6 rfpftehegjfs, sf gdtuvg ogs `ctgs `f prg`uhheøj seauefjtfs; @ctgs `f hcmpg; Prctcmefjtgs
Ichtgr Y
Dogqufs
Ichtgr I
Xumc
Mf`ec
E
EE
EEE
EY
Y
3
33
34
30
3>
33
62
33,9
3
4
38
36
34
38
3>
98
34,9
Y4I3
4
3
30
38
30
39
36
14
30,0
Y4I4
4
4
36
31
39
32
31
28
39,9
68
61
69
61
68
419
66,4
95
38,2
Jg.
Hø`eag
Ycref`c` Ifrteoezcheøj
3
Y3I3
3
4
Y3I4
8 0
Xumc Mf`ec
rt= 4>< r=6< t =0< Y=4< I=4
38,46 30,46 30,>> 30,46 38,46
339
Hãohuog `f sumcs y prgmf`egs Xumc `f oc ejtfrchheøj
3
3 62
4 98
343
4
14
28
366
38>
309
419
^rgmf`egs `f oc ejtfrchheøj y `f ogs ichtgrfs fj fstu`eg
3 4
3 33,9 30,0
4 34,9 39,9
34,3 36,6
38,>
30,9
38,2
Hãohuog `f ocs sumcs `f huc`rc`gs; Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (419)4 /4> = 8.2>5 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = \(33)4+(34)4+(30)4+…….…+(32)4+(31)4] ‘ 8.2>5 XH Pgtco = 3>6,4 XH T= ∓(T)4 /t ‘ IH XH T = \(68)4+(61)4+(69)4+(61)4+(68)4]/0 ‘ 8.2>5 XH T = 0,4 XH P = ∓(P)4 /r ‘ IH XH P = \(62)4+(98)4+(14)4+(28)4]/6 ‘ 8.2>5 XH P = 14,0 XH Y = ∓(Y)4 /ri ‘ IH XH Y = \(343)4+(366)4]/3> ‘ 8.2>5 XH Y = 61,2 XH I = ∓(I)4 /rv ‘ IH XH I = \(38>)4+(309)4]/3> ‘ 8.2>5 XH I = 34,2 XH (Y x I) = XH Prctcmefjtgs - XH Y ‘ XHI = 14,0 - 61,2 - 34,2 = 3,2 Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P
XH F = 3>6,4 - 0,4 - 14,0 = 42,9 42,9
331
C@FYC; Iufjtf `f vcrecheøj Tfpftehegjfs
Arc`gs `f Xumc `f Huc`rc`gs oedfrtc` Huc`rc`gs Mf`egs 0 0,4> 3,>6
Prctcmefjtgs Ycref`c`fs Ifrteoezcheøj Ejtfrchheøj Y x I
8
Frrgr Fxpfremfjtco
34
42,9
35
3>6,4
Pgtco
14 3 3 3
62 38 4
40,38 61,2> 34,2> 3,2>
I hcohuoc`c
I>,>6
I>,>3
>,00 JX 8,465
6,034
3>,38 ** 40,46 ** 6,81 * >,19 JX
6,568 5,88> 5,88> 5,88>
8,05> 0,101 0,101 0,101
4,82
Ejtfrprftcheøj; ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Ogs fifhtgs `f ogs
dogqufs sgj ejseajeiehcjtfs, jg bcy `eifrfjhecs fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6.
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
Ogs trctcmefjtgs rfsuotcj `f oc hgmdejcheøj `f ogs jevfofs `f ogs `gs ichtgrfs, pgr og tcjtg, og quf sf rfquefrf hgjghfr sgj ogs fifhtgs prejhepcofs `f ogs ichtgrfs fj fstu`eg. ^?>,>3
^crc vcref`c`fs.- Ihcohuoc`c : I>,>6; Xf rfhbczc B>. Ogs prgmf`egs `f ocs `gs
vcref`c`fs sgj fstc`ístehcmfjtf `eifrfjtfs hgj fo 56 % `f hgjiecjzc. Y3?Y4.
^crc Ifrteoezcheøj.- Ihcohuoc`c ? I>,>6; Xf rfhbczc B>. Ogs prgmf`egs `f ocs `gs
cotfrjctevcs `f ifrteoezcheøj sgj fstc`ístehcmfjtf `eifrfjtfs hgj fo 56% `f hgjiecjzc. I3?I4.
^crc oc ejtfrchheøj vcref`c`fs x ifrteoezcheøj.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy ejtfrchheøj fjtrf vcref`c`fs y ifrteoezchegjfs. ^:>,>6. ejtfrchheøj
Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4,82)>,6 /38,2 * 3>> = 33,4% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. FR^FTEMFJPGX (8)4 ·@F SVF PTCPC VJ FR^FTEMFJPG (8)47 Ogs fxpfremfjtgs (8)4 sgj ichtgrecofs hgmpoftgs quf pfrmetfj fvcoucr `gs ichtgrfs hgj trfs jevfofs hc`c ujg, fj hgjsfhufjhec, sf prufdcj 5
trctcmefjtgs hgj r rfpftehegjfs.
332
^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg ichtgreco (8)4, `gj`f sf prufdcj trfs vcref`c`fs `f uj huotevg y trfs cotfrjctevcs `f ifrteoezcheøj, fj 6 rfpftehegjfs, sf gdtuvefrgj ogs `ctgs `f prg`uhheøj seauefjtfs; @ctgs `f hcmpg; Prctcmefjtgs
Ichtgr Y
Dogqufs
Ichtgr I
Xumc
Mf`ec
Jg.
Hø`eag
Ycref`c`
Ifrteoezcheøj
E
EE
EEE
EY
Y
3
Y3I3
3
3
33
34
5
3>
33
68
3>,9
4
Y3I4
3
4
38
36
34
38
3>
98
34,9
8
Y3I8
3
8
30
38
30
34
33
90
34,2
0
Y4I3
4
3
38
30
39
36
31
16
36
6
Y4I4
4
4
39
38
31
39
36
11
36,0
9
Y4I8
4
8
30
39
39
30
33
13
30,4
1
Y8I3
8
3
36
30
36
31
39
11
36,0
2
Y8I4
8
4
39
32
31
35
39
29
31,4
5
Y8I8
8
8
32
35
31
39
32
22
31,9
Xumc
38>
380
388
384
346
960
38>,2
Mf`ec
30,0
30,5
30,2
30,1
38,5
14,1
30,6
rt= 06< r=6, t=5, Y=8< I=8 Hãohuog `f sumcs `f oc ejtfrchheøj
3
4
8
3
68
98
90
32>,>
4
16
11
13
448,>
8
11
29
22
463,>
4>6,>
449,>
448,>
960,>
335
Hcohuog `f ogs prgmf`egs pgr ichtgr
3
4
8
3
3>,9
34,9 3 4,9
34,2
34,>
4
36,>
36,0 3 6,0
30,4
30,5
8
36,0
31,4 3 1,4
31,9
39,1
38,1
36,3
30,5
30,6
Hãohuog `f ocs sumcs `f huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (960)4 /06 = 5.6>6 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = \(33)4+(34)4+(5)4+…….…+(39)4+(32)4] ‘ 5.6>6 XH Pgtco = 423,4 XH T= ∓(T)4 /t ‘ IH XH T = \(38>)4+(380)4+(388)4+(384)4+(346)4]/5 ‘ 5.6>6 XH T = 6,9 XH P = ∓(P)4 /r ‘ IH XH P = \(68)4+(98)4+(90)4+(16)4 +(11)4+(13)4+(11)4+(29)4+(22)4]/6 ‘ 5.6>6 XH P = 4>4,2 XH Y = ∓(Y)4 /ri ‘ IH XH Y = \(32>)4+(448)4+(463)4]/36 ‘ 5.6>6 XH Y = 31>,6 4 4+(449) ∓(I) /rv ‘ IH 4+(448)4]/36 ‘ 5.6>6 XH I = \(4>6) XH I = 31,4
XH (YxI) = XH Prctcmefjtgs - XH Y ‘ XHI = 4>4,2-31>,6-31,4 XH (YxI) = 36,3 Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 423,4 ‘ 6,9 ‘ 4>4,2 = 14,2
34>
C@FYC; Arc`gs `f oedfrtc`
Xumc `f Huc`rc`gs
Tfpftehegjfs
0
6,9
3,03
>,94 JX
4,992
8,595
Prctcmefjtgs
2
4>4,2
46,86
33,36 **
4,400
8,341
Iufjtf `f vcrecheøj
Huc`rc`gs Mf`egs
I hcohuoc`c
I>,>6
I>,>3
Ycref`c`fs
4
31>,6
26,41
81,6> **
8,456
6,889
Ifrteoezcheøj
4
31,4
2,9>
8,12 *
8,456
6,889
Ejtfrchheøj Y x I
0
36,3
8,11
3,99 JX
4,992
8,595
Frrgr Fxpfremfjtco Pgtco
84
14,2
00
423,4
4,41
Ejtfrprftcheøj; ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Ogs fifhtgs fj ocs
rfpftehegjfs sgj ejseajeiehcjtfs, jg bcy `eifrfjhecs fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6.
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
Ogs trctcmefjtgs rfsuotcj `f oc hgmdejcheøj `f ogs jevfofs `f ogs `gs ichtgrfs, pgr og tcjtg, sf rfquefrf hgjghfr ogs fifhtgs prejhepcofs `f ogs ichtgrfs fj fstu`eg. ^?>,>3.
^crc vcref`c`fs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B>. Co mfjgs ujg `f ogs
prgmf`egs `f ocs vcref`c`fs fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc. ^?>,>3.
^crc Ifrteoezcheøj.- I hcohuoc`c : I>,>6; Xf rfhbczc B>. Co mfjgs ujc cotfrjctevc `f
ifrteoezcheøj fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc. ^?>,>6.
^crc oc ejtfrchheøj vcref`c`fs x ifrteoezcheøj.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg
bcy ejtfrchheøj ejtfrchheøj fjtrf vcref`c`fs y ifrteoezchegjfs. ^:>,>6. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4,41)>,6 /30,6 * 3>> = 3>,0% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. 6.1.
FR^FTEMFJPGX FJ ^CTHFOCX @EYE@E@CX
·HVCJ@G VXCT FR^FTEMFJPGX FJ ^CTHFOCX @EYE@E@CX7 Fj uj fxpfremfjtg ichtgreco, jûmfrg trctcmefjtgs fs fo `fo prg`uhtg `f ocs hgmdejchegjfs `f jevfofs `f ujfo ichtgr pgr `f fo jûmfrg `f jevfofs gtrg ichtgr (u gtrgs ichtgrfs). Fj fstf hcsg tg`cs ocs uje`c`fs uje`c`fs fxpfremfjtcofs tefjfj fo mesmg
343
tcmcóg y fstãj `estredue`cs fj fo hcmpg fxpfremfjtco fj igrmc cofctgrec, sfaûj fo `esfóg dãsehg pocjfc`g (@HC ø DC). Ocs hgj`ehegjfs `fo hcmpg fxpfremfjtco y fo tepg `f ichtgr fj fstu`eg c vfhfs fxeafj uscr igrmcs `eifrfjtfs `f pocjfcheøj `fo fxpfremfjtg hgmg fs fo hcsg `f ocs pcrhfocs g sud`eve`e`cs. fstgs tepgs `f crrfaogs ic ichtgrecofs htgrecofs sf cpoehcj ogs hgjhfptgs`eve`e`cs `f ‟pcrhfocs arcj`fs” yFj‟pcrhfocs hbehcs”, ckustc`cs c uj `esfóg dãsehg (@HC ø DC). Ocs pcrhfocs arcj`fs hgrrfspgj`fj c ocs uje`c`fs fxpfremfjtcofs quf sf irchhegjcj (`eve`fj) fj gtrcs pcrhfocs hbehcs prgdcj`g hgmdejchegjfs `f ogs `eifrfjtfs jevfofs `f fstu`eg. Fstg sf hgjghf hgmg fo `esfóg fj pcrhfocs `eve`e`cs (`gs ichtgrfs). Hucj`g ocs ‟pcrhfocs hbehcs” sf sud`eve`fj pcrc prgdcr gtrg ichtgr c`ehegjco `f fstu`eg< fjtgjhfs sf trctc `f uj fxpfremfjtg fj pcrhfocs sud`eve`e`cs (trfs ichtgrfs) g fj uj `esfóg fj pcrhfocs sud`eve`e`cs. Fj tfgríc sf puf`f er sud`eve`efj`g ocs pcrhfocs y sf puf`f tfjfr uj fxpfremfjtg fj pcrhfocs sud sud`eve`e`cs (huctrg ichtgrfs). Fj oc prãhtehc, hgj fxhfpheøj `f fjscygs fj ocdgrctgreg, sf rfhgmefj`c pocjfcr fxpfremfjtgs prgdcj`g mãxemg trfs ichtgrfs. Ocs pcrhfocs arcj`fs jgrmcomfjtf sgj ogs ichtgrfs `gj`f fs `eiíheo fstcdofhfr uje`c`fs fxpfremfjtcofs `f eauco hgmg; tcmcóg.sestfmcs ^gr fkfmpog, ocs pcrhfocs arcj`fs puf`fj puf`f hgrrfspgj`fr c ichtgrfs `f refag, sestfmcs `f ocdrcjzc, åpghcs `f sefmdrc, oãmejcs `f refag, `fjse`c`fs pgdochegjcofs, sestfmcs `f pg`c f ejhousevf vcref`c`fs. Fj ocs pcrhfocs hbehcs puf`fj fvcoucrsf ichtgrfs `f iãheo cpoehcheøj hgmg; ifrteoezcjtfs, irfhufjhecs `f `fsbefrdc`g g hucoquefr gtrg quf puf`c mcjfkcr fo ejvfsteac`gr hgj icheoe`c`, fj iujheøj `fo huotevg. ^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg fj pcrhfoc `eve`e`c, tfjefj`g hgmg `esfóg dãsehg `f dogqufs co czcr, sf prgdcrgj `gs ichtgrfs; trfs vcref`c`fs hgj trfs jevfofs `f ifrteoezcheøj fj 6 rfpftehegjfs, `gj`f sf gdtuvefrgj ogs seauefjtfs `ctgs `f prg`uhheøj; Oc `estreduheøj cofctgrec `f ocs pcrhfocs arcj`fs y pcrhfocs hbehcs fj fo hcmpg fxpfremfjtco hgj hejhg rfpftehegjfs fs oc seauefjtf;
344
@ctgs `f hcmpg; Prctcmefjtgs
Ichtgr Y
Ichtgr I
Dogqufs
Xumc
Mf`ec
33
68
3>,9
3> 33 31 36 33 39 39 32 346 38,5
98 90 16 11 13 11 29 22 960 14,1
34,9 34,2 36 36,0 30,4 36,0 31,4 31,9 38>,2 30,6
Jg.
Hø`eag
Ycref`c`
Ifrteoezcheøj
E
EE
EEE
EY
Y
3
Y3I3
3
3
33
34
5
3>
48 0 6 9 1 2 5
Y3I4 Y3I8 Y4I3 Y4I4 Y4I8 Y8I3 Y8I4 Y8I8
33 4 4 4 8 8 8 Xumc Mf`ec
48 3 4 8 3 4 8
38 30 38 39 30 36 39 32 38> 30,0
36 38 30 38 39 30 32 35 380 30,5
34 30 39 31 39 36 31 31 388 30,2
38 34 36 39 30 31 35 39 384 30,1
rt= 06< r= 6< t= 5< Y=8< I=8 Jgtc; fj ogs fxpfremfjtgs fj pcrhfocs `eve`e`cs, oc igrmc `f tcduocheøj `f `ctgs fs eauco co Jgtc; fj `f uj fxpfremfjtg deichtgreco.
Hãohuog `f sumcs y prgmf`egs @f ogs ichtgrfs vcref`c`fs y ifrteoezcheøj
3
4
8
3
68
98
90
32>,>
4
16
11
13
448,>
8
11
29
22
463,>
4>6,>
449,>
448,>
960,>
@f ocs pcrhfocs arcj`fs Prctcmefjtgs Jg.
3 4 8 0 6 9 1 2 5
Ichtgr Y
Ichtgr I
Hø`eag Ycref`c` Ifrteoezcheøj
Y3I3 Y3I4 Y3I8 Xumc Y4I3 Y4I4 Y4I8 Xumc Y8I3
3 3 3
3 4 8
4 4 4
3 4 8
8
3
Y8I4 8 Y8I8 8 Xumc
4 8
Dogqufs E
EE
EEE
EY
Y
33 38 30 82 38 39 30 08 36
34 36 38 0> 30 38 39 08 30
5 34 30 86 39 31 39 05 36
3> 38 34 86 36 39 30 06 31
33 3> 33 84 31 36 33 08 39
39 32 05
32 35 63
31 31 05
35 39 64
39 32 6>
348
Hãohuog `f ocs sumcs `f huc`rc`gs Fo hãohuog `f ocs sumcs `f huc`rc`gs fs eauco quf pcrc uj fxpfremfjtg deichtgreco< fxhfptg pgr fo hãohuog `f oc sumc `f huc`rc`gs `f ocs pcrhfocs arcj`fs y fo hãohuog `f ocs sumcs `f huc`rc`gs `fo frrgr C y `fo frrgr D. Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (960)4 /06 = 5.6>6 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = \(33)4+(34)4+(5)4+…….…+(39)4+(32)4] ‘ 5.6>6 XH Pgtco = 423,4 XH T= ∓(T)4 /t ‘ IH XH T = \(38>)4+(380)4+(388)4+(384)4+(346)4]/5 ‘ 5.6>6 XH T = 6,9 XH P = ∓(P)4 /r ‘ IH XH P = \(68)4+(98)4+(90)4+(16)4 +(11)4+(13)4+(11)4+(29)4+(22)4]/6 ‘ 5.6>6 XH P = 4>4,2 XH Y = ∓(Y)4 /ri ‘ IH XH Y = \(32>)4+(448)4+(463)4]/36 ‘ 5.6>6 XH Y = 31>,6 XH ^A = ∓(^A)4 /r ‘ IH
XH ^A= \(82)4+(0>)4+(86)4(86)4+(84)4+(08)4…….+(64)4+(6>)4]/6 ‘ 5.6>6
XH ^A = 350,6
Xumc `f Huc`rc`gs `fo Frrgr C = Xumc `f Huc`rc`gs `f ocs pcrhfocs arcj`fs ‘ sumc `f huc`rc`gs `fo ichtgr C ‘ sumc `f huc`rc`gs `f ocs rfpftehegjfs (se fo `esfóg dãsehg fs fj dogqufs co czcr).
XH Frrgr C = XH ^A-XH C ‘ XH T XH Frrgr C = 350,6-31>,6-6,9=32,0
XH I = ∓(I)4 /rv ‘ IH XH I = \(4>6)4+(449)4+(448)4]/36 ‘ 5.6>6 XH I = 31,4 XH (Y x I) = XH Prctcmefjtgs - XH Y ‘ XHI = 4>4,2-31>,6-31,4 XH (Y x I) = 36,3 Xumc `f Huc`rc`gs `fo Frrgr D = Xumc `f Huc`rc`gs Pgtco ‘ sumc `f huc`rc`gs `fo ichtgr D - sumc `f huc`rc`gs `f oc ejtfrchheøj CxD ‘ sumc `f huc`rc`gs `f ocs pcrhfocs arcj`fs. XH Frrgr D = XH Pgtco ‘ XH I - XH YxI ‘ XH ^A XH Frrgr D = 423,4 ‘ 31,4 ‘ 36,3 - 350,6
XH Frrgr D = 60,0 60,0
340
Hgmpcrcj`g uj fxpfremfjtg ichtgreco hgj uj fxpfremfjtg fj pcrhfocs `eve`e`cs, fj oc prãhtehc, sgog sf fve`fjhec quf oc sumc `f huc`rc`gs `fo frrgr `fo fxpfremfjtg ichtgreco sf `fscarfac fj oc sumc `f huc`rc`gs `fo frrgr C y sumc `f huc`rc`gs `fo frrgr D. C@FYC; Iufjtf `f vcrecheøj Ichtgr C ^crhfocs arcj`fs Frrgr C Ichtgr D Ejtfrchheøj CD Frrgr D Pgtco
Arc`gs `f oedfrtc`
Xumc `f Huc`rc`g I hcohuoc`c Huc`rc`gs mf`eg 6,9 3,03 >,94 JX 31>,6 26,41 81,39 **
C-3
0 4
rC-3
30
350,6
38,5>
(rC-3)-(r-3)-(C-3)
2 4 0 40 00
32,0 31,4 36,3 60,0 423,4
4,45 2,9> 8,11 4,41
r-3
(D-3) (C-3)(D-3) (rCD-3)-(D-3)-(C-3)(D-3)-(rC-3) rCD-3
I>,>6
I>,>3
8,282
1,>>93
0,065
2,905
9,>9 **
8,481
6,665
8,12 *
8,0>42
6,9389
3,99 JX
4,1198
0,4320
Ejtfrprftcheøj; ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Ogs fifhtgs fjtrf ocs
rfpftehegjfs sgj fstc`ístehcmfjtf ejseajeiehcjtfs, jg bcy `eifrfjhecs fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6. ^crc vcref`c`fs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B>. Co mfjgs ujg `f ogs prgmf`egs `f ocs vcref`c`fs fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc. ^?>,>3. ^crc ^crhfocs Arcj`fs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc. Fj oc prãhtehc, oc seajeiehcheøj fj ocs pcrhfocs arcj`fs ej`ehc quf sf pu`g sfpcrcr ogs fifhtgs `f cqufoocs sgdrf ogs ichtgrfs fj fstu`eg. ^:>,>6 ^crc Ifrteoezcheøj.- I hcohuoc`c : I>,>6; Xf rfhbczc B>. Co mfjgs ujc cotfrjctevc `f
ifrteoezcheøj fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc. ^?>,>6. ^crc oc ejtfrchheøj vcref`c`fs x ifrteoezcheøj.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg
bcy ejtfrchheøj ejtfrchheøj fjtrf vcref`c`fs y ifrteoezchegjfs. ^:>,>6. Hgfiehefjtf `f vcrecheøj `fo frrgr
HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4,41)>,6 /30,6 * 3>> = 3>.0% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs.
346
6.2. FR^FTEMFJPGX FJ CTTFAOGX ICHPGTECOFX FR^FTEMFJPGX (C)D +3 ·@F SVÅ PTCPC VJ FR^FTEMFJPG FJ CTTFAOG ICHPGTECO (C) D + 37 Fj oc fxpfremfjtcheøj fs irfhufjtf fo usg `f `esfógs hgj crrfaogs ichtgrecofs quf, c`fmãs, tefjfj fo prgpøsetg `f fvcoucr uj trctcmefjtg c`ehegjco empgrtcjtf (p.f.; tfsteags oghcofs `fo prg`uhtgr). Fj fstf hcsg, fo cjãoeses `f vcrecjzc `fdf ejhgrpgrcr ejhgrpgrcr hgmg iufjtf `f vcrecheøj fo ‟Pfsteag vs. Tfstg” hgj uj arc`g `f oedfrtc`. Fo jûmfrg `f trctcmefjtgs, rfspfhtg `fo fxpfremfjtg ichtgreco, sf ejhrfmfjtc fj ujg< pgr og tcjtg, sf `fdf rfhcohuocr ogs arc`gs `f oedfrtc` `fo frrgr. Fo prghf`emefjtg pcrc fo cjãoeses `f fstf tepg `f fjscygs fs fo seauefjtf; •
Xf rfcoezc fo cjãoeses `f Ycrecjzc `fo `esfóg dãsehg (tgtco `f trctcmefjtgs y rfpftehegjfs)< fs `fher, hgmg se sf trctcrc `f uj fjscyg jg ichtgreco (ejhouyfj`g fo tfsteag c`ehegjco).
••
Xf rfcoezc fo cjãoeses `fo fxpfremfjtg ichtgreco, fxhouyfj`g fo tfsteag c`ehegjco. Hgj oc ejigrmcheøj `f fstgs `gs cjãoeses `f vcrecjzc sf prghf`f c oofjcr oc tcdoc `fiejetevc `fo C@FYC. Xf sumcj ogs vcogrfs `f ocs XH `f ogs ichtgrfs fj fstu`eg y sus ejtfrchhegjfs (sumc `f huc`rc`gs `f ogs trctcmefjtgs `fo fxpfremfjtg ichtgreco). Fo vcogr gdtfje`g `f oc sumc `f ocs sumc `f huc`rc`gs `f ogs trctcmefjtgs `fo fxpfremfjtg ichtgreco sf rfstc `f oc sumc `f huc`rc`gs `f ogs trctcmefjtgs tgtco (quf ejhouyf fo tfsteag c`ehegjco). Fo vcogr gdtfje`g pgr oc `eifrfjhec hgrrfspgj`f c ooc c XH ‟Pfsteag vs. Tfstg”. Oufag `f `espgjfr tg`c oc ejigrmcheøj focdgrc oc tcdoc `f cjãoeses `f vcrecjzc.
• • • •
^TGDOFMC TFXVFOPG 4+3 `gj`f sf prgdcrgj trfs vcref`c`fs `f uj huotevg Fj uj fxpfremfjtg ichtgreco (8) y trfs cotfrjctevcs `f ifrteoezcheøj mãs uj ‟tfsteag oghco” fj 6 rfpftehegjfs, sf gdtuvefrgj ogs `ctgs `f prg`uhheøj seauefjtfs;
@ctgs `f hcmpg 3 4 8 3 4 8 3 4
E 33 38 30 38 39 30 36 39
EE 34 36 38 30 38 39 30 32
Dogqufs EEE 5 34 30 39 31 39 36 31
8 8 Pfsteag Oghco Xumc
32 3> 30>
35 2 304
31 3> 308
Prctcmefjtgs
Ichtgr Y
Ichtgr I
Jg. 3 4 8 0 6 9 1 2
Hø`eag
Ycref`c`
Ifrteoezcheøj
Y3I3 Y3I4 Y3I8 Y4I3 Y4I4 Y4I8 Y8I3 Y8I4
3 3 3 4 4 4 8 8
5 3>
Y8I8 Y3C3
EY 3> 38 34 36 39 30 31 35
Y 33 3> 33 31 36 33 39 39
39 5 303
32 2 388
Xumc
Mf`ec
68 98 90 16 11 13 11 29
3>,9 34,9 34,2 36,> 36,0 30,4 36,0 31,4
22 06 955
31,9 5,> 385,2
Mf`ec
30,>
30,4
30,8
30,3
38,8
95,5
30,>
rt=6>< r=6< t= 3>< Y=8, I=8, YI= 5
349
Hãohuog `f sumcs `f oc ejtfrchheøj
3 4
3 68 98
4 16 11
8 11 29
8
90
13
22
Hãohuog `f ocs sumcs y vcogrfs co huc`rc`g Tfpftehegjfs Prctcmefjtgs 3 3 3 4 3 8 3 0 3 6 3 9 3 1 3 2 3 5 4 3
Ycref`c` 3 3 3 4 4 4 8 8 8 3
Ifrteoezcheøj 3 4 8 3 4 8 3 4 8 3
^rg`uhheøj 33 38 30 38 39 30 36 39 32 34
(^rg`uhheøj)4 343 395 359 395 469 359 446 469 840 300
44 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8 0
84 0 6 9 1 2 5 3 4 8 0 6 9 1 2 5 3
33 4 4 4 8 8 8 3 3 3 4 4 4 8 8 8 3
84 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3
36 38 30 38 39 30 32 35 5 34 30 39 31 39 36 31 31 3>
446 395 359 395 469 359 840 893 23 300 359 469 425 469 446 425 425 3>>
00 0 0 0 0 0 0 6 6 6 6 6 6 6 6 6 3
84 0 6 9 1 2 5 3 4 8 0 6 9 1 2 5 3>
33 4 4 4 8 8 8 3 3 3 4 4 4 8 8 8
84 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8
38 34 36 39 30 31 35 39 33 3> 33 31 36 33 39 39 32 3>
395 300 446 469 359 425 893 469 343 3>> 343 425 446 343 469 469 840 3>>
48 0 6
3> 3> 3> 3>
2 3> 5 2
90 3>> 23 90
Xumc Mf`ec
955 30,>
3>.356
341
Fxpfremfjtg ichtgreco Xumc Mf`ec Fxpfremfjtg ichtgreco +3 Xumc Mf`ec
^4 5.129
^ 960 30,6 ^ 955 30,>
Fxpfremfjtg ichtgreco T3= T4= T8= T0= T6= Xumc Fxpfremfjtg ichtgreco +3 T3= T4= T8= T0= T6= Xumc
^4 3>.356
^4 39.5>> 31.569 31.925 31.040 36.946 26.650 ^4 35.9>> 4>.390 4>.005 35.223 31.925 51.128
^ 38> 380 388 384 346 960 ^ 30> 304 308 303 388 955
Hãohuog `f ogs prgmf`egs pgr ichtgr
3 4 8
3 3>,9
4 36,>
8 36,0
34,9
36,0
31,4
36,3
34,2 34,>
30,4 30,5
31,9 39,1
30,5 30,6
38,1
C3 = 5,> ^rgmf`eg Pfsteag C4 Hãohuog `f ocs sumcs `f huc`rc`gs 3. Cjãoeses `f vcrecjzc vcrecjzc `fo fxpfremfjtg fxpfremfjtg (ejhoue`g tfst tfsteag eag c`ehegjc c`ehegjco) o)
Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (955)4 /6> = 5.114 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = \(33)4+(34)4+(5)4+…….…+(5)4+(2)4] ‘ 5.114 XH Pgtco = 3>.356-5.114= 048 4
XH T= /t4‘+(304) IH 4+(308)4+(303)4+(388)4]/3> ‘ 5.114 T =∓(T) \(30>) XH T = 51.128/3> - 5.114= 9,8
342
XH P = ∓(P) 4 /r ‘ IH XH P = \(68) 4 +(98) 4 +(90) 4 +(16) 4 +(11) 4 +(13) 4 +(11) 4 +(29) 4 +(22) 4 +(06) 4 ]/6 ‘ 5.114
XH P = 80>,9
Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 048 ‘ 9,8 ‘ 80>,9 = 19,3 4. Cjãoeses `f vcrecjzc vcrecjzc `fo fxpfremfjtg fxpfremfjtg ichtgreco Fj oc prãhtehc, sgog sf rfquefrf ocs sumcs `f huc`rc`gs `f ogs ichtgrfs ej`eve`ucofs y `f oc ejtfrchheø ejtfrchheøj. j. Oc sumc `f fstg fstgss trfs vcogrfs hgrrfspgj`f c oc sumc `f ogs trctcmefjtgs fj fo fxpfremfjtg ichtgreco. XH P = ∓(P) 4 /r ‘ IH ]/6 ‘ 5.6>6 XH P = \(68) 4 +(98) 4 +(90) 4 +(16) 4 +(11) 4 +(13) 4 +(11) 4 +(29) 4 +(22) 4 XH P = 4>4,2
XH Y = ∓(Y)4 /ri ‘ IH 4
4
4
XH YY = = 31>,6 \(32>) +(448) +(463) ]/36 ‘ 5.6>6 XH XH I = ∓(I)4 /rv ‘ IH XH I = \(4>6)4+(449)4+(448)4]/36 ‘ 5.6>6 XH I = 31,4 XH (YxI) = XH Prctcmefjtgs - XH Y ‘ XHI = 4>4,2-31>,6-31,4 XH (YxI) = 36,3 Hãohuog `f oc sumc `f huc`rc`gs `fo ”Pfsteag vs Tfstg” XH P fxpfremfjtg fxpfremfjtg +3 ‘ XH P fxpfremfjtg fxpfremfjtg ichtgreco = Xumc `f huc`rc`gs `f ‟tfsteag vs rfstg”
XH Pfsteag vs rfstg = 80>,9 ‘ 4>4,2 = 381,2
C@FYC Arc`gs `f oedfrtc` Tfpftehegjfs 0 Prctcmefjtgs tgtco 5 Ycref`c`fs 4 Ifrteoezcheøj 4 Ejtfrchheøj Y x I 0 Pfsteag vs Tfstg 3 Frrgr Fxpfremfjtco 86 Pgtco 05 Iufjtf `f vcrecheøj
Xumc `f Huc`rc`gs 9,8 80>,9 31>,6 31,4 36,3 381,2 19,3 048,>
Huc`rc`gs Mf`egs 3,61 81,20 26,41 2,9> 8,11 381,12 4,31
Ihcohuoc`c
I>,>6
>,14 JX 31,0> ** 85,43 ** 8,56 * 3,18 JX 98,86 **
4,903 4,393 8,491 8,491 4,903 0,343
I>,>3 8,5>2 4,598 6,492 6,492 8,5>2 1,035
345
Ejtfrprftcheøj; ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy `eifrfjhecs
fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6.
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3 rfhbczc B> hgj fo 55% `f `f hgjiecjzc. Hgmg ogs trctcmefjtgs rfsuotcj `f; ocXfhgmdejcheøj `f ogs jevfofs ogs `gs ichtgrfs< pgr og tcjtg, sf rfquefrf hgjghfr ogs fifhtgs prejhepcofs `f ogs ichtgrfs fj fstu`eg. ^crc vcref`c`fs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B>. Co mfjgs ujg `f ogs
prgmf`egs `f ocs vcref`c`fs fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc. ^?>,>3.
^crc Ifrteoezcheøj.- I hcohuoc`c : I>,>6; Xf rfhbczc B>. Co mfjgs ujc cotfrjctevc `f
ifrteoezcheøj fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc. ^?>,>6.
^crc oc ejtfrchheøj vcref`c`fs x ifrteoezcheøj.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg
bcy ejtfrchheøj ejtfrchheøj fjtrf vcref`c`fs y ifrteoezchegjfs. ^:>,>6.
^crc Pfsteag vs rfstg.- I hcohuoc`c : I>,>3; Xf rfhbczc B>. Bcy `eifrfjhec fjtrf fo
‟tfsteag y fo rfstg `f trctcmefjtgs” hgj fo 55% `f hgjiecjzc. ^?>,>3. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4,31)>,6 /30 * 3>> = 3>,6%
Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. FR^FTEMFJPGX FJ CTTFAOGX ICHPGTECOFX (C)D + 3 + 3 D
·HVÃJ@G VXCT VJ FR^FTEMFJPG (C) + 3 + 37 Vj fxpfremfjtg coag mãs hgmpofkg fs quf hgmdejc uj fjscyg ichtgreco y `gs tfsteags c`ehegjcofs fs hgjghe`g hgmg fxpfremfjtgs fj crrfaogs ichtgrecofs (C)D +3 +3. Xupøjacsf quf sf pocjfc uj fjscyg ichtgreco (8)4 mãs `gs trctcmefjtgs c`ehegjcofs; uj ‟tfsteag oghco `fo prg`uhtgr” y uj ‟‟trctcmefjtg trctcmefjtg cotfrjctevg”. Fj D fstf hcsg hcdf fo fjscyg fj crrfaog ichtgreco (C) + 3 + 3. Fj fstf hcsg, fo cjãoeses `f vcrecjzc `fdf ejhgrpgrcr hgmg iufjtf `f vcrecheøj c`ehegjcofs fo ‟tfsteag oghco `fo prg`uhtgr vs rfstg” y fo ‟trctcmefjtg cotfrjctevg vs rfstg”. Hc`c ujc `f ocs iufjtfs `f vcrecheøj ej`ehc`cs tfj`rã uj arc`g `f oedfrtc`. Fo jûmfrg `f trctcmefjtgs sf ejhrfmfjtc fj `gs< pgr og tcjtg, sf `fdf rfhcohuocr ogs arc`gs `f oedfrtc` `fo frrgr.
Fo prghf`emefjtg pcrc fo cjãoeses `f fstf tepg `f fjscygs fs fo seauefjtf;
38>
• • • • • • •
•
•
Xf rfcoezc fo cjãoeses `f vcrecjzc `fo `esfóg dãsehg, ejhouyfj`g ogs `gs trctcmefjtgs c`ehegjcofs. Xf rfcoezc fo cjãoeses `f vcrecjzc `fo fxpfremfjtg ichtgreco (fxhouyfj`g ogs `gs trctcmefjtgs c`ehegjcofs). Xf rfcoezc fo cjãoeses `f vcrecjzc `fo fxpfremfjtg, fxhouyfj`g ujg `f ogs `gs trctcmefjtgs`fc`ehegjcofs. Hgj oc ejigrmcheøj fstgs trfs cjãoeses `f vcrecjzc sf prghf`f c oofjcr oc tcdoc `fiejetevc `fo C@FYC. Xf sumcj ogs vcogrfs `f ocs sumcs `f huc`rc`gs `f ogs ichtgrfs fj fstu`eg y sus ejtfrchhegjfs (trctcmefjtgs `fo fxpfremfjtg ichtgreco). Fo vcogr gdtfje`g `f oc sumc `f ocs sumc `f huc`rc`gs `f ogs ichtgrfs f ejtfrchhegjfs (ichtgreco) sf rfstc `f oc sumc `f huc`rc`gs `f ogs trctcmefjtgs tgtco (quf ejhouyf ogs `gs trctcmefjtgs c`ehegjcofs). Oc `eifrfjhec fjtrf oc sumc `f huc`rc`gs `f ogs trctcmefjtgs `fo fxpfremfjtg ichtgreco y oc sumc `f huc`rc`gs `f ogs trctcmefjtgs tgtco (quf ejhouyf ogs `gs trctcmefjtgs c`ehegjcofs) hgrrfspgj`f c fsc irchheøj `f oc sumc `f huc`rc`gs `f ogs trctcmefjtgs c`ehegjcofs. Fsc irchheøj `f sumc `f huc`rc`gs `f ogs trctcmefjtgs c`ehegjcofs sf tefjf quf `fscarfacr pcrc hc`c ujc `f ocs iufjtfs `f vcrecheøj c`ehegjcofs. Fj fstf mgmfjtg sf usc oc ejigrmcheøj `fo C@FYC quf fxhouíc sgog ujg `f ogs `gs trctcmefjtgs c`ehegjcofs. ^gr `eifrfjhec, sf hcohuoc ocs sumcs `f huc`rc`gs pcrc hc`c ujc `f ocs iufjtfs `f vcrecheøj; ‟tfsteag oghco vs rfstg” y fo ‟trctcmefjtg
cotfrjctevg vs rfstg” (g ogs quf hgrrfspgj`cj, sfaûj fo hcsg).
•
Oufag `f `espgjfr `f fstc ejigrmcheøj sf hgjtejûc fo prghf`emefjtg `f cjãoeses `f vcrecjzc.
^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg hgj crrfaog ichtgreco (8)4+3+3 sf prgdcrgj trfs vcref`c`fs `f uj huotevg y trfs cotfrjctevcs `f ifrteoezcheøj mãs `gs tfsteags c`ehegjcofs; ‟cotfrjctevc 3o” y ‟cotfrjctevc 4” fj 6 rfpftehegjfs. Ogs `ctgs `f prg`uhheøj iufrgj ogs seauefjtfs; @ctgs `f hcmpg, sumcs y prgmf`egs Ichtgr I Prctcmefjtgs Ichtgr Y Jg. Hø`eag Ycref`c` Ifrteoezcheøj 3 Y3I3 3 3 4 Y3I4 3 4 8 Y3I8 3 8 0 Y4I3 4 3 6 Y4I4 4 4 9 Y4I8 4 8 1 Y8I3 8 3 2 Y8I4 8 4 5 Y8I8 8 8 3> Y3C3 Cotfrjctevc 3 33 Y3 C4 Cotfrjctevc 4 Xumc
E 33 38 30 38 39 30 36 39 32 3> 30 360
EE 34 36 38 30 38 39 30 32 35 2 38 366
Dogqufs EEE EY 5 3> 34 38 30 34 39 36 31 39 39 30 36 31 31 35 31 39 3> 5 34 33 366 364
Y 33 3> 33 31 36 33 39 39 32 2 30 301
Xumc
Mf`ec
68 98 90 16 11 13 11 29 22 06 90 198
3>,9 34,9 34,2 36,> 36,0 30,4 36,0 31,4 31,9 5,> 34,2 368
Mf`ec
30,>
30,3
30,3
38,2
38,0
95,0
38,5
rt=66< r=6< t= 33< Y=8, I=8, YI= 5
383
Hãohuog `f sumcs `f oc ejtfrchheøj 3 4
3 68 98
Ycref`c` 4 16 11
8 11 29
8 Xumc
90 32>
13 448
22 463
Ifrteoezcheøj
Xumc 4>6 449 448 960
Hãohuog `f sumcs y vcogrfs co huc`rc`g Tfpftehegjfs 3 3 3 3 3 3 3 3 3 4 4 4 4
Prctcmefjtgs 3 4 8 0 6 9 1 2 5 3 4 8 0
Ycref`c` 3 3 3 4 4 4 8 8 8 3 3 3 4
Ifrteoezcheøj 3 4 8 3 4 8 3 4 8 3 4 8 3
^rg`uhheøj 33 38 30 38 39 30 36 39 32 34 36 38 30
(^rg`uhheøj)4 343 395 359 395 469 359 446 469 840 300 446 395 359
4 4 4 4 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0
96 1 2 5 3 4 8 0 6 9 1 2 5 3 4 8 0 6 9 1
4 8 8 8 3 3 3 4 4 4 8 8 8 3 3 3 4 4 4 8
84 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3
38 39 30 32 35 5 34 30 39 31 39 36 31 31 3> 38 34 36 39 30 31
395 469 359 840 893 23 300 359 469 425 469 446 425 425 3>> 395 300 446 469 359 425
0 0 6 6 6 6 6 6 6 6 6 3 4 8 0 6 3 4 8 0 6
2 5 3 4 8 0 6 9 1 2 5 3> 3> 3> 3> 3> 33 33 33 33 33
8 8 3 3 3 4 4 4 8 8 8
4 8 3 4 8 3 4 8 3 4 8
35 39 33 3> 33 31 36 33 39 39 32 3> 2 3> 5 2 30 38 34 33 30 198
893 469 343 3>> 343 425 446 343 469 469 840 3>> 90 3>> 23 90 359 395 300 343 359 33.>43
Xumc
Mf`ec
38,5
384
Fxpfremfjtg ichtgreco Xumc Mf`ec Fxpfremfjtg ichtgreco +3 Xumc Mf`ec
^4 5129
^ 960 30,6 ^ 955 30,>
^4 3>356 4
FxpfremfjtgXumc ichtgreco +3 +3 Mf`ec
^ 198 38,5
^
Fxpfremfjtg ichtgreco
^ 38> 380 388 384 346 960 ^ 30> 304 308 303 388 955 ^ 360 366 366 364 301 198
^4 395>> 31569 31925 31040 36946 26650 ^4 35.9>> 4>.390 4>.005 35.223 31.925 51.128 ^4 48.139 40.>46 40.>46 48.3>0 43.9>5 339.015
T3= T4= T8= T0= T6= Xumc Fxpfremfjtg ichtgreco +3 T3= T4= T8= T0= T6= Xumc Fxpfremfjtg ichtgreco +3 +3 T3= T4= T8= T0= T6= Xumc
Hãohuog `f ogs prgmf`egs pgr ichtgr
3 4 8
3 3>,9
4 36,>
8 36,0
34,9
36,0
31,4
36,3
34,2 34,>
30,4 30,5
31,9 39,1
30,5 30,6
^rgmf`eg Pfsteag C3 = 5,> ^rgmf`eg Pfsteag C4 = 34,2
38,1
388
Hãohuog `f ocs sumcs `f huc`rc`gs 3. Cjãoeses `f vcrecjzc `fo fxpfremfjtg fxpfremfjtg (ejhoue`g `gs cotfrjctevcs cotfrjctevcs c`ehegjcofs); 33 trctcmefjtgs y 6 rfpftehegjfs 4
4
Ichtgr `f hgrrfhheøj (IH) = (∓Rek) /(rt) = (198) /66 = 3>.626 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = \(33)4+(34)4+(5)4+…….…+(33)4+(30)4] ‘ 3>.626 XH Pgtco = 33.>43-3>.626= 089,> XH T= ∓(T)4 /t ‘ IH XH T = \(360)4+(366)4+(366)4+(364)4+(301)4]/33 ‘ 3>.626 XH T = 339.015/33 - 3>.626= 0,3 XH P = ∓(P) 4 /r ‘ IH
XH P = \(68) 4 +(98) 4 +(90) 4 +(16) 4 +(11) 4 +(13) 4 +(11) 4 +(29) 4 +(22) 4 +(06) 4+ (90) 4 ]/6 ‘ 3>.626
XH P = 809,5
Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 089 ‘ 0,3 ‘ 809,5 = 26,3 4. Cjãoeses `f vcrecjzc `fo fxpfremfjtg (ejhoue`g tfsteag c`ehegjco); 3> trctcmefjtgs y 6 rfpftehegjfs
Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (955)4 /6> = 5.114 Xumc `f Huc`rc`gs Pgtco (XH Pgtco) = ∓Re4 ‘ IH XH Pgtco = \(33)4+(34)4+(5)4+…….…+(5)4+(2)4] ‘ 5.114 XH Pgtco = 3>.356-5.114= 048 XH T= ∓(T)4 /t ‘ IH XH T = \(30>)4+(304)4+(308)4+(303)4+(388)4]/3> ‘ 5.114 XH T = 51.128/3> - 5.114= 9,8 XH P = ∓(P) 4 /r ‘ IH XH P = \(68) 4 +(98) 4 +(90) 4 +(16) 4 +(11) 4 +(13) 4 +(11) 4 +(29) 4 +(22) 4 +(06) 4 ]/6 ‘ 5.114
XH P = 80>,9
Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 048 ‘ 9,8 ‘ 80>,9 = 19,3 8. Cjãoeses `f vcrecjzc vcrecjzc `fo fxpfremfjtg fxpfremfjtg ichtgreco Fj oc prãhtehc, sgog sf rfquefrf ocs sumcs `f huc`rc`gs `f ogs ichtgrfs ej`eve`ucofs y `f oc ejtfrchheø ejtfrchheøj. j. Oc sumc `f fstg fstgss trfs vcogrfs hgrrfspgj`f c
oc sumc `f ogs trctcmefjtgs fj fo fxpfremfjtg ichtgreco.
380
XH P = ∓(P) 4 /r ‘ IH XH P = \(68) 4 +(98) 4 +(90) 4 +(16) 4 +(11) 4 +(13) 4 +(11) 4 +(29) 4 +(22) 4 ]/6 ‘ 5.6>6 XH P = 4>4,2
XH Y = ∓(Y)4 /ri ‘ IH 4
4
4
XH YY = = 31>,6 \(32>) +(448) +(463) ]/36 ‘ 5.6>6 XH XH I = ∓(I)4 /rv ‘ IH XH I = \(4>6)4+(449)4+(448)4]/36 ‘ 5.6>6 XH I = 31,4 XH (YxI) = XH Prctcmefjtgs - XH Y ‘ XHI = 4>4,2-31>,6-31,4 XH (YxI) = 36,3 Hãohuog `f ocs sumcs `f huc`rc`gs `fo ”Pfsteag 3 vs Tfstg” y ”Pfsteag 3 vs Tfstg” Xumc `f huc`rc`gs `f ‟tfsteag 3 vs rfstg” = XH P fxpfremfjtg fxpfremfjtg +3+3 ‘ XH P fxpfremfjtg fxpfremfjtg ichtgreco Xumc `f huc`rc`gs `f ‟tfsteag 3 vs rfstg” = 80>,9 ‘ 4>4,2 = 381,2 Xumc `f huc`rc`gs `f ‟tfsteag 4 vs rfstg” = XH P fxpfremfjtg fxpfremfjtg +3+3 ‘ XH P fxpfremfjtg fxpfremfjtg ichtgreco Xumc `f huc`rc`gs `f ‟tfsteag 4 vs rfstg” = 80>,9 ‘ 4>4,2 = 381,2 XH P fxpfremfjtg fxpfremfjtg +3+3 ‘ XH P fxpfremfjtg fxpfremfjtg ichtgreco = Xumc `f huc`rc`gs `f ‟tfsteag vs rfstg”
XH Pfsteag 4 vs rfstg = 809,5 ‘ 4>4,2 = 300,3
C@FYC
0
0,3
3,>8
>,02
4,9>9
8,242
3>
809,5
80,95
39,83 **
4,>11
4,2>3
>,>6
>,>3
4
31>,6
26,41
0>,>2 **
8,484
6,315
4
31,4
2,9>
0,>0 *
8,484
6,315
0
36,3
8,11
3,11
4,9>9
8,242
3
3
381,2
381,12
90,11 **
0,>26
1,830
4
3
9,8
9,88
91,10 **
0,>26
1,830
0>
26,3
60
089,3
4,38
Ejtfrprftcheøj ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy `eifrfjhecs
fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6. ^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc. Hgmg ogs trctcmefjtgs rfsuotcj `f oc hgmdejcheøj `f ogs jevfofs `f ogs `gs
ichtgrfs, sf rfquefrf hgjghfr ogs fifhtgs prejhepcofs `f ogs ichtgrfs fj fstu`eg.
386
^crc vcref`c`fs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B>. Co mfjgs ujg `f ogs
prgmf`egs `f ocs vcref`c`fs fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc. ^?>,>3.
^crc Ifrteoezcheøj.- I hcohuoc`c : I>,>6; Xf rfhbczc B>. Co mfjgs ujc cotfrjctevc `f
ifrteoezcheøj fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc. ^?>,>6. ^crc oc ejtfrchheøj vcref`c`fs x ifrteoezcheøj.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy ejtfrchheøj ejtfrchheøj fjtrf vcref`c`fs y ifrteoezchegjfs. ^:>,>6. ^crc oc Pfsteag 3 vs rfstg.- Ihcohuoc`c : I>,>3; Xf rfhbczc B>. Bcy `eifrfjhec
fjtrf fo ‟tfsteag c`ehegjco y fo rfstg `f trctcmefjtgs” hgj fo 55% `f hgjiecjzc. ^?>,>3.
^crc oc Pfsteag 4 vs rfstg.- Ihcohuoc`c : I>,>3; Xf rfhbczc B>. Bcy `eifrfjhec
fjtrf fo ‟tfsteag c`ehegjco y fo rfstg `f trctcmefjtgs” hgj fo 55% `f hgjiecjzc. ^?>,>3. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (4,38)>,6 /38,5 * 3>> = 3>,6%
Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. 6.5. FR^FTEMFJPGX FX^FHECOFX ·@F SVF PTCPCJ OGX FR^FTEMFJPGX FX^FHECOFX7 Irfhufjtfmfjtf fj oc ejvfsteacheøj caríhgoc, pfhucrec, cargej`ustreco y cargigrfstco sf rfquefrfj prgdcr uj hgjkujtg `f cotfrjctevcs tfhjgoøaehcs y `fhe`er se hgjvefjf g jg su c`gpheøj. Xe sf pocjfcj `esfógs ichtgrecofs hgmpoftgs, sf tfj`ríc uj fofvc`g jûmfrg uje`c`fs ogs fxpfremfjtcofs y, pgr supufstg, uj fxpfremfjtgs fofvc`g hgstg.-3.FjFjfstf arupg sf`ffjhufjtrcj oocmc`gs fxpfremfjtgs +3 y ogs ogs Fxpfremfjtgs + 3 y Fxpfremfjtgs ‘3 sf puf`fj prgdcr vcregs ichtgrfs semuotãjfcmfjtf pfrg jg sf puf`f puf` f fvcoucr sus ejtfrchhegjfs. ·HØMG ^OCJFCT U C^OEHCT OGX FR^FTEMFJPGX +37 6.5.3. FR^FTEMFJPGX + 3 Ogs fxpfremfjtgs +3 sgj ûteofs prejhepcomfjtf fj fxpfremfjtgs hgj huotevgs pfrfjjfs, fjscygs pfhucregs, prufdcs fxpogrctgrecs y fj vcoe`cheøj `f cotfrjctevcs tfhjgoøaehcs. Fj fohgj pocjtfcmefjtg sf rfquefrf `fiejer uj hc`c ujg `gs jevfofs`ffj`esfóg fstu`eg. Jgrmcomfjtf, fstfarupg tepg `f `fichtgrfs fxpfremfjtg
pfrmetf ujc iãheo hgmpcrcheøj fjtrf uj tfsteag oghco g ujc prãhtehc afjfrcoezc`c vfrsus ujc cotfrjctevc tfhjgoøaehc g prãhtehc c sfr ejtrg`uhe`c.
389
Xf prgpgjf fvcoucr, pgr fkfmpog, 2 ichtgrfs fj fstu`eg `ftfrmejcjtfs `f oc prg`uhheøj `f uj huotevg. Pfsteag Oghco
Cotfrjctevc
3. Ycref`c` 4. @fjse`c`
3 3
tfhjgoøaehc 4 4
8. Ifrteoezcheøj
3
4
0. Hgjtrgo `f mcofzcs
3
4
6. Hgjtrgo `f pocacs
3
4
9. Hgjtrgo `f fjifrmf`c`fs
3
4
1. ^g`cs
3
4
2. Tefag
3
4
Ichtgrfs fj fstu`eg
Fj fstgs fxpfremfjtgs, sf pcrtf `fo jevfo trc`ehegjco pcrc tg`gs ogs ichtgrfs y sf carfacj suhfsevcmfjtf ocs cotfrjctevcs pgr ichtgr. ichtgr. Fo cjãoeses `f vcrecjzc `f fstgs fxpfremfjtgs sf rfcoezc hgmg uj `esfóg hgmpoftcmfjtf co czcr y `f dogqufs co czcr hgj r rfpftehegjfs, sfaûj oc jcturcofzc `fo hcmpg fxpfremfjtco< oc sfpcrcheøj `f mf`ecs sgog fs pgsedof rfcoezcrog uscj`g fo måtg`g `f hgmpcrchegjfs grtgagjcofs. ^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg +3 `f 2 ichtgrfs hgj `gs jevfofs y 8 rfpftehegjfs sf gdtuvg ogs `ctgs `f prg`uhheøj seauefjtfs; @ctgs sumcs y prgmf`egs pgr trctcmefjtg hgmpufstg Prctcmefjtgs
Ycref`c`
@fjse`c`
Ifrteoezcheøj
Hgjtrgo `f mcofzcs
Hgjtrgo `f pocacs
fjifrmf`c`fs
Hgjtrgo `f
∉ fj
^g`cs
Tefag
E
EE
EEE
Xumc
Mf`ec
rfocheø
%
j co P3
3
3
3
3
3
3
3
3
3
32
43
35
62
35,8
-
3>>
4 8 0
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 4
3 4 4
4 4 4
83
8>
42
25
45,1
3>,8
368
89
86
88
3>0
80,1
36,8
315
85
81
89
334
81,8
32,>
358
6
3
3
3
3
4
4
4
4
0>
03
03
344
0>,1
43,8
43>
9
3
3
3
4
4
4
4
4
03
0>
0>
343
0>,8
43,>
4>5
1 2 5
3 3 4
3 4 4
4 4 4
4 4 4
4 4 4
4 4 4
4 4 4
4 4 4
00
06
04
383
08,1
40,8
449
09
08
06
380
00,1
46,8
483
63
6>
6>
363
6>,8
83,>
49>
Xumc
809
804
880
3.>44
Mf`ec
82,0 82,> 81,3
81,5
rt= 41< r=8< t= 5
381
Cjãoeses arãiehg `f ogs rfsuotc`gs Hgjtreduheøj pgrhfjtuco `f ogs ichtgrfs fj fstu`eg fj fo ejhrfmfjtg `f oc prg`uhheøj. Ogs ghbg ghbg ichtgrfs fj fo jevfo 3, fquevcof co 3>> pgr hefjtg. Fo trctcmefjtg jufvf hgjtefjf ogs jevfofs 4 `f tg`gs ogs ichtgrfs y rfprfsfjtc uj ejhrfmfjtg prgmf`eg `fhgjtreduhegjfs 39>% rfspfhtg`f`fo trctcmefjtg 3. hgrrfspgj`efjtfs Hcdf rfcoezcr uj cjãoeses `ftfje`g `f ocs hc`c ichtgr y ogs hgstgs, pcrc `fhe`er su c`gpheøj.
8>> 49>
46>
449 43>
483
4>5
358
4>>
g t j f e 36> h r g ^3>>
315 368
3>>
6> > 3
4
8
0
6
9
1
2
5
Prctcmefjtgs
Hãohuog `f ocs sumcs `f huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (3.>44)4 /41 = 82.920,9 4 ∓Re ‘4
4 (XH4Pgtco) = IH 4] ‘ 82.920,9 Xumc `f =Huc`rc`gs Pgtco XH Pgtco \(32)4+(43) +(35) +…….…+(6>) +(6>) XH Pgtco = 4.>03,0
XH T= ∓(T)4 /t ‘ IH XH T = \(809)4+(804)4+(880)4]/5 ‘ 82.920,9 XH T = = 2,8 XH P = ∓(P) 4 /r ‘ IH 4 XH P = \(62) +(25)4+(3>0)4+(334)4 +(344)4+(343)4+(383) 4+(380)4+(363)4 /8 ‘ 82.920,9 XH P = 4.>33,0
Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 4.>04,0 ‘ 4.>33,0 4.>33,0 ‘ 2,8 = 43,1
382
C@FYC Iufjtf `f vcrecheøj
Arc`gs `f oedfrtc`
Xumc `f Huc`rc`gs
Tfpftehegjfs Prctcmefjtgs Frrgr Fxpfremfjtco Pgtco
4 2 39 49
2,8 4.>33,0 43,1 4.>03
Huc`rc`gs Mf`egs
I hcohuoc`c
I>,>6
0,36 8,>9 JX 463,08 326,86 ** 3,89
8,980 4,653
I>,>3 9,449 8,25>
Ejtfrprftcheøj ^crc ocs rfpftehegjfs.- Ihcohuoc`c ? I>,>6; Xf chfptc B>. Jg bcy `eifrfjhecs
fstc`ístehcs seajeiehctevcs fjtrf rfpftehegjfs. ^:>,>6.
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
Hgmg ogs trctcmefjtgs hgmpufstgs rfsuotcj `f oc hgmdejcheøj `f vcregs jevfofs `f ogs ichtgrfs fj fstu`eg, sf rfquefrf hgjghfr ogs cpgrtfs `f hc`c ichtgr, mf`ecjtf tåhjehcs `f sfpcrcheøj `f mf`ecs. Hgfiehefjtf `f vcrecheøj `fo frrgr HYF (%) = (HMF)>,6 /Mf`ec x \3>>]= (3,89)>,6 /81,5 * 3>> = 8,3% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. 6.5.4. FR^FTEMFJPGX ‘ 3 ·HØMG ^OCJFCT U C^OEHCT OGX FR^FTEMFJPGX - 37 Ogs fxpfremfjtgs ‘3 sf dcscj fj ogs mesmgs prejhepegs `f ogs fxpfremfjtgs +3, pfrg `f mg`g ejvfrsg< pcrtfj `f uj jevfo tfhjgoøaehg mãxemg y oufag `esmejuyfj mcjfrc fstcdofhfr`fogsfstf fifhtgs pcrhecofs `fprgarfsevcmfjtf. hc`c trctcmefjtg. trctcmefjtg@f . Fofstc C@FYC `f sf ogs dushc fxpfremfjtgs tepg puf`fj c`cptcrsf c ogs @HC g DHC, sfaûj fo hcmpg fxpfremfjtco, y oc sfpcrcheøj `f mf`ecs sf `fdf rfcoezcr mf`ecjtf fo cjãoeses `f hgmpcrchegjfs grtgagjcofs. Fo cjãoeses `f fstgs fxpfremfjtgs sf hgmpofmfjtc, hgj ujc fvcoucheøj pgrhfjtuco `f ogs ejhrfm ejhrfmfjtgs fjtgs pcrhecofs `f hc`c hc`c ujg `f ogs ichtgrfs fj fstu`eg. Fstgs `esfógs rfsuotcj muy cprgpec`gs pcrc oc ejvfsteacheøj fj huotevgs pfrfjjfs, fxpfremfjtgs igrfstcofs y cargigrfstcofs, fjscygs pfhucregs y vcoe`cheøj `f tfhjgogaícs. ^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg - 3 `f 2 ichtgrfs hgj `gs jevfofs y 8 rfpftehegjfs sf gdtuvg ogs `ctgs `f prg`uhheøj seauefjtfs;
385
@ctgs sumcs y prgmf`egs pgr trctcmefjtg hgmpufstg Prctcmefjtgs
Ycref`c`
@fjse`c`
Ifrteoezcheøj
Hgjtrgo `f mcofzcs
Hgjtrgo `f pocacs
Hgjtrgo `f fjifrmf`c`fs
^g`cs
Tefag
E
EE
EEE
Xumc
Mf`ec
Tf`uhheøj
^gr hefjtg
3
4
4
4
4
4
4
4
4
63
6>
6>
363
6>,8
>,>
3>>
4
4
4
4
4
4
4
4
3
09
08
06
380
00,1
-6,1
25
8
4
4
4
4
4
4
3
3
00
06
04
383
08,1
-9,1
21
0
4
4
4
4
4
3
3
3
03
0>
0>
343
0>,8
-3>,>
2>
6
4
4
4
4
3
3
3
3
0>
03
03
344
0>,1
-5,1
23
9
4
4
4
3
3
3
3
3
85
81
89
334
81,8
-38,>
10
1
4
4
3
3
3
3
3
3
89
86
88
3>0
80,1
-36,1
95
2
4
3
3
3
3
3
3
3
83
8>
42
25
45,1
-4>,1
65
5
3
3
3
3
3
3
3
3
32
43
35
62
35,8
-83,>
82
Xumc
809
804
880
3.>44
Mf`ec
82,0
82,>
81,3
81,5
rt=41< r=8< t=5 Cjãoeses arãiehg `f ogs rfsuotc`gs Ogs ichtgrfs fj fstu`eg, fj sus jevfofs 4, rfprfsfjtc`gs fj fo trctcmefjtg 3, hgrrfspgj`fj c oc prufdc `f tg`cs ocs cotfrjctevcs tfhjgoøaehcs (ejjgvchegjfs, c`cptchegjfs, rfhgmfj`chegjfs)< pgr og tcjtg, oc rfspufstc fxprfsc`c fj oc vcrecdof fxpfremfjtco `fdfrã fstcr fj ogs vcogrfs mãxemgs. C pcrter `f fstf vcogr rfifrfjheco (3>>%), c mf`e`c quf sf rf`uhfj ogs trctcmefjtgs cotfrjctevgs ogs fifhtgs hgrrfspgj`f`esmejuerãj co tfsteag (jevfofs 3). pgsetevgs bcstc oofacr co trctcmefjtg 3 quf Hcdf ej`ehcr quf sf fstã csumefj`g quf oc vcrecdof fxpfremfjtco fs `fo tepg ‟mcygr fs mfkgr” hgmg; prg`uhheøj, uteoe`c` g scje`c`. Fo trctcmefjtg 5, quf rfprfsfjtc tg`gs ogs ichtgrfs fj ogs jevfofs 3, seajeiehc fo 82% `fo pgtfjheco fxprfsc`g fj fo trctcmefjtg 3 (jevfofs 4 `f tg`gs ogs ichtgrfs) hgj fo 3>> pgr hefjtg.
30>
3>>
3>>
25
21 2>
23
2>
10 95 65
9> 82
0> 4> > 3
4
8
0
6
9
1
2
5
P r c t c me me f j jt tg s
Hãohuog `f ocs sumcs `f huc`rc`gs Ichtgr `f hgrrfhheøj (IH) = (∓Rek)4 /(rt) = (3.>44)4 /41 = 82.920,9 Xumc `f Huc`rc`gs Pgtco (XH4Pgtco) = ∓Re4 ‘4 IH 4 4 4 XH Pgtco = \(63) +(6>) +(6>) +…….…+(43) +(32) ] ‘ 82.920,9 XH Pgtco = 4.>03,0 XH T= ∓(T)4 /t ‘ IH XH T = \(809)4+(804)4+(880)4]/5 ‘ 82.920,9 XH T = = 2,8 XH P = ∓(P) 4 /r ‘ IH 4 XH P = \(363) +(380)4+(383)4+(343)4 +(344)4+(334)4+(3>0)4+(25)4+(62)4 /8 ‘ 82.920,9 XH P = 4.>33,0
Xumc `f Huc`rc`gs `fo Frrgr = XH Pgtco ‘ XH T ‘ XH P XH F = 4.>04,0 ‘ 4.>33,0 4.>33,0 ‘ 2,8 = 43,1 C@FYC Iufjtf `f vcrecheøj
Arc`gs `f oedfrtc`
Xumc `f Huc`rc`gs
Tfpftehegjfs Prctcmefjtgs Frrgr Fxpfremfjtco Pgtco
4 2 39 49
2,8 4.>33,0 43,1 4.>03
Huc`rc`gs Mf`egs
I hcohuoc`c
0,36 8,>9 JX 463,08 326,86 ** 3,89
I>,>6 8,980 4,653
I>,>3 9,449 8,25>
Ejtfrprftcheøj ^crc ocs rfpftehegjfs.- I
fstc`ístehcs seajeiehctevcs
I
; Xf chfptc B . Jg bcy `eifrfjhecs ^:>,>6. >
hcohuoc`c ? >,>6 fjtrf rfpftehegjfs.
^crc trctcmefjtgs.- Ihcohuoc`c : I>,>3; Xf rfhbczc B> hgj fo 55% `f hgjiecjzc.
Hgmg ogs trctcmefjtgs hgmpufstgs rfsuotcj `f oc hgmdejcheøj `f vcregs
303
jevfofs `f ogs ichtgrfs fj fstu`eg, sf rfquefrf hgjghfr ogs cpgrtfs `f hc`c ichtgr, mf`ecjtf tåhjehcs `f sfpcrcheøj `f mf`ecs. Hgfiehefjtf `f vcrecheøj `fo frrgr >,6
>,6
HYF (%) = (HMF) /Mf`ec x \3>>]= (3,89) /81,5 * 3>> = 8,3% Fo hgfiehefjtf `f vcrecheøj `fo frrgr ej`ehc quf oc prfheseøj `fo fjscyg fstã `fjtrg `f ogs jevfof chfptcdofs pcrc fxpfremfjtgs caríhgocs. 6.3>. @EXFÓGX GTPGAGJCOFX Ogs `esfógs grtgagjcofs iufrgj `fscrrgooc`gs pgr Afjehbe Pcauhbe y sf iuj`cmfjtc fj ogs prejhepegs mctfmãtehgs `f oc grtgagjcoe`c`, pcrc fo `esfóg `f ogs trctcmefjtgs. Ogs trctcmefjtgs sgj hgjkujtgs gr`fjc`gs `f ichtgrfs y jevfofs (trctcmefjtgs hgmpufstgs), fstãj prf`fieje`gs fj mctrehfs focdgrc`cs pcrc su cpoehcheøj `erfhtc fj oc fxpfremfjtcheøj, fj tg`gs ogs hcmpgs. Fj oc ejvfsteacheøj caríhgoc, pfhucrec, cargej`ustreco y cargigrfstco, `f mcjfrc prãhtehc, sgj cpoehcdofs ogs `esfógs; O0 (4)8, O5 (8)0 y O2 (4)1. Fo `esfóg O0 (4)8 ej`ehc quf sf trctc `f uj fjscyg `f 0 trctcmefjtgs prgdcj`g trfs ichtgrfs hgj `gs jevfofs hc`c ujg. Fj uj cjãoeses ichtgreco hgjvfjhegjco, uj `esfóg (4)8 seajeiehc quf `fdfrícj prgdcrsf 4 x 4 x 4 = 2 trctcmefjtgs hgj j rfpftehegjfs. rfpftehegjfs. Hgj fo `esfóg grtgagjco fo jûmfrg `f trctcmefjtgs c prgdcrsf sf rf`uhf c huctrg hgj j rfpftehegjfs. rfpftehegjfs. Fo `esfóg O5 (8)0 hgrrfspgj`f c uj fxpfremfjtg `f 5 trctcmefjtgs, prgdcj`g huctrg ichtgrfs hgj trfs trfs jevfofs `f fstu`eg hc`c ujg. Fj uj cjã cjãoeses oeses ichtgreco hgjvfjhegjco, seajeiehc quf `fdfrícj prgdcrsf 8 x 8 x 8 x 8 = 23 trctcmefjtgs hgj j rfpftehegjfs. rfpftehegjfs. Fstf jûmfrg `f hgmdejchegjfs `f ichtgrfs y jevfofs, c jevfo `f hcmpg fxpfremfjtco fs `f `eiíheo mcjfkg. mcjfkg. Hgj fo `esfóg grtgagjco grtgagjco fo jûmfrg `f trctcmefjtgs c prgdcrsf prgdcrsf sf rf`uhf c jufvf hgj j rfpftehegjfs. rfpftehegjfs. Fo `esfóg O2(4)1 sf rfiefrf c uj fjscyg `f 2 trctcmefjtgs, prgdcj`g seftf ichtgrfs hgj `gs jevfofs. Fj uj cjãoeses ichtgreco hgjvfjhegjco, hgjvfjhegjco, seaj seajeiehc eiehc quf `fdfrícj prgdcrsf 4 x 4 x 4 x 4 x 4 x 4 x 4 = 342 trctcmefjtgs hgj j rfpftehegjfs. rfpftehegjfs. Fj oc prãhtehc, fstf jûmfrg `f hgmdejchegjfs `f ichtgrfs y jevfofs hucoquefrc sfc fo hcmpg fxpfremfjtco (ocdgrctgreg, hcmpg, arcjkc) rfsuotc `eiíheo `f mcjfkcr. Hgj fo `esfóg grtgagjco, sf rf`uhf c ghbg trctcmefjtgs hgj j rfpftehegjfs. rfpftehegjfs. Fstc rf`uhheøj `f trctcmefjtgs rfprfsfjtc, c`fmãs, ujc `esmejuheøj hgjse`frcdof `f ogs hgstgs `f oc ejvfsteacheøj.
304
Ocs mctrehfs grtgagjcofs `f cpoehcheøj fj fxpfremfjtgs caríhgocs, pfhucregs, cargej`ustrecofs y cargigrfstcofs sgj oc ocss seauefjtfs; Xfref 4j
Xfref 8j
Hgrre`cs Fxpfremfjtcofs Fxpfremfjtcofs
O0(4)8
O2(4)1
C
D
H
3 4
3 3
3 4
3 4
8
4
3
4
0
4
4
3
O5(8)0 Hgrre`cs fxpfremfjtcofs
C
D
H
@
3
3
3
3
3
4
3
4
4
4
8
3
8
8
8 8
Hgrre`cs fxpfremfjtcofs
C
D
H
@
F
I
A
0
4
3
4
3
3
3
3
3
3
3
3
6
4
4
8
3
4
3
3
3
4
4
4
4
9
4
8
3
4
8
3
4
4
3
3
4
4
1
8
3
8
4
0
3
4
4
4
4
3
3
2
8
4
3
8
6
4
3
4
3
4
3
4
5
8
8
4
3
9
4
3
4
4
3
4
3
1
4
4
3
3
4
4
3
2
4
4
3
4
3
3
4
Fo cjãoeses rfauocr fs oc tåhjehc usc`c pcrc fvcoucr ogs `esfógs grtgagjcofs (måtg`g Pcauhbe) y hgjstc `f ogs seauefjtfs pcsgs; 3) focdgrcheøj `f ujc tcdoc `f rfspufstc< 4) hgjstruhheøj `f arãiehcs ichtgrecofs< 8) hgmdejcheøj øptemc `f ogs ichtgrfs y jevfofs `fsfcdofs< y, 0) prf`ehheøj `f oc rfspufstc mãxemc. Oc tcdoc `f rfspufstc sf focdgrc uscj`g ocs mf`ecs `f ogs fifhtgs ichtgrecofs. Ocs arãiehcs ichtgrecofs fs oc rfprfsfjtcheøj `f ogs fifhtgs ej`eve`ucofs `f hc`c ichtgr uscj`g ujc arãiehc `f dcrrcs. Oc hgmdejcheøj øptemc `f ogs ichtgrfs y jevfofs sf `frevc `f oc tcdoc `f rfspufstc. Xe sf trctcrc `f vcrecdofs fxpfremfjtcofs hgmg; rfj`emefjtg, dfjfieheg jftg g prg`uhheøj `f degmcsc oc rfspufstc ‟mcygr fs mfkgr” , fs og `fsfcdof. Xe sf trctcrc `f vcrecdofs fxpfremfjtcofs hgmg; pgrhfjtckf `f pår`e`c, jûmfrg `f pocjtcs fjifrmcs, ejhe`fjhec `f fjifrmf`c`fs, oc rfspufstc ‟mfjgr fs mfkgr” , fs og `fsfcdof. Oc prf`ehheøj `f oc rfspufstc mãxemc sf fstemc csumefj`g quf ogs fifhtgs sgj c`etevgs c pcrter `f oc mf`ec `f mf`ecs, c`ehegjcj`g ogs fifhtgs pcrhecofs `f hc`c jevfo fj fstu`eg pgr ichtgr, sfaûj oc tcdoc `f rfspufstc y oc hgmdejcheøj øptemc `fieje`c. ^TGDOFMC TFXVFOPG Fj uj fjscyg O0(4)8, rfcoezc`g fj ^ehbeoejauf, sf prgdø oc ‟Ejioufjhec `f oc hgdfrturc vfaftco, ifrteoezcheøj J^L rfhgmfj`c`c pgr fo EJEC^ y ocs pg`cs sgdrf oc prg`uhheøj `f hciå `f oc vcref`c` ^chcs fj oc zgjc `f Sufvf`g43”. ”. Ogs ichtgrfs y jevfofs fj fstu`eg prgdc`gs fj fo fjscyg sf `fshredfj c hgjtejucheøj;
43
. Fstcheøj Fxpfremfjtco Prgpehco ^ehbeoejauf. 3552. Ejigrmf Påhjehg Cjuco; 3551. ^rgarcmc `f hchcg y hciå. EJEC^. Sufvf`g. pp; 1-38.
308
C. Hgdfrturc vfaftco D. Ifrteoezcheøj J^L
Jevfofs 3 4 Xej Hgj Xej Hgj
H. ^g`cs `f ogs hciftgs
Xej
Ichtgrfs
Hgj
^crc fstf fxpfremfjtg fs cpoehcdof fo `esfóg O 0 (4)8 quf sf fstcdofheø hgj `gs rfpftehegjfs. Fstg seajeiehc quf fo fjscyg fstuvg hgjigrmc`g pgr huctrg trctcmefjtgs y `gs rfpftehegjfs< fs `fher, g uje`c`fs fxpfremfjtcofs. @ctgs Ogs `ctgs `f prg`uhheøj prg`uhheøj iufrgj fvcouc`gs fj leogs `f hciå grg/bfhtãrfc. Ocs mf`ecs `f ogs trctcmefjtgs hgmpufstgs iufrgj ogs seauefjtfs;
3
C 3
D 3
H 3
Tfj`emefjtg prgmf`eg 4 rfpftehegjfs 298
4
3
4
4
3>>5
8
4
3
5>5
0
4
4
4 3
Ichtgrfs
Prctcmefjtgs
Mf`ec `f mf`ecs
526 504
U Jgtc; Fo vcogr 3 hgrrfspgj`f c ogs jevfofs 3 (sej) y fo vcogr 4 c ogs jevfofs 4 (hgj) (hg j)
Cjãoeses rfauocr Pcdoc `f rfspufstc Jevfofs
C 589 501 33 1
3 4 ∉ ^gr hefjtg
Ichtgrfs D 229 551 333 13
H 540 565 86 44
Xumc
Mf`ec
4.109 4.5>8 361 3>>
536 592 68
Arãiehcs ichtgrecofs 551
3>>> 52> c f r ã t h f b / g r g å i c h s g o e L
565
59> 50>
501 589 540
54> 5>> 22> 29> 20>
229
24>
C
D
H
Jevfo 3
589
229
540
Jevfo 4
501
551
565
300
Hgmdejcheøj øptemc `f ichtgrfs y jevfofs
C4 D4 H4 ^rf`ehheøj `f oc mãxemc rfspufstc ^mãx = U + (C4 - U ) + (D4 - U ) + (H4 - U )
^mãx = 504 + (501 - 504) + (551 - 504) + (565 - 504) ^mãx = 504 + 6 + 66 + 31 ^mãx = 3.>35 la hciå grg/bfhtãrfc Hgjhouseøj Oc ifrteoezcheøj J^L, fj hciftcofs `f oc vcref`c` ^chcs, icvgrfhf fo ejhrfmfjtg `f oc prg`uhheøj, fj uj 13 pgr hefjtg. Ocs pg`cs fj fo 44% y oc hgdfrturc vfaftco fj uj 1 pgr hefjtg. hefjtg. 6.33. FR^FTEMFJPCHEØJ U CJÃOEXEX @F YCTECJ[CX JG ^ ^CTCMÅPTEHGX CTCMÅPTEHGX 8.33.3.
FR^FTEMFJPGX FJ ‟@HC” U CJÃOEXEX @F YCTECJ[C @F LVXLCOO & QCOOEX
·VJ @EXFÓG HGM^OFPCMFJPF CO C[CT XF ^VF@F CJCOE[CT HGJ OC PÅHJEHC @F LTVXLCOO & QCOOEX7 Fo cjãoeses `f vcrecjzc Lruslcoo & Qcooes fquevcof co cjãoeses fj uj `esfóg hgmpoftcmfjtf co czcr< pgr og tcjtg, tg`gs ogs fjscygs quf tfjacj fstf `esfóg dãsehg puf`fj sfr cjcoezc`gs hgj fstc tåhjehc, fspfhecomfjtf cqufoogs hgj tcmcógs `f mufstrc rf`uhe`gs, vcrecdofs mf`e`cs fj fshcoc `f ejtfrvcog y `f `estreduheøj oedrf. ^TGDOFMC TFXVFOPG TFXVFOPG Xf tefjfj trfs vcref`c`fs `f mcíz y sf tgmc fo tefmpg quf `fmgrc fj fo cpcrfhemefjtg `f ocs mczgrhcs, fj fo hcmpg. ·@ftfrmejcr se sgj fstc`ístehcmfjtf eaucofs g `eifrfjtfs ogs `ícs co cpcrfhemefjtg `f ocs mczgrhcs7 @ctgs @ctgs Ycref`c` C 32> 311 392 325 320 323
Ycref`c` D 361 393 392 360
Ycref`c` H 354 325 358 350 321 325
311 Mf`ec =315 Mf`ec=39> Mf`ec=353 Jgtc; sf trctc `f uj fxpfremfjtg `f trfs trctcmefjtgs hgj `fseauco jûmfrg `f gdsfrvchegjfs.
306
Igrmuocheøj `f ocs bepøtfses fstc`ístehcs B>; Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs B3; Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf. Prcjsigrmcheøj `f `ctgs greaejcofs c rcjags Ycref`c` C 32> 311 392 325 320 323 311
Tcjags (T) `f oc vcref`c` D
Tcjags (T) `f Ycref`c` oc vcref`c` C D
2 9,6 0,6 38 3> 5 9,6
361 393 392 360
4 8 0,6 3
Ycref`c` H 354 325 358 350 321 325
j ee = 1
ΨT =61,6 C =61,6
j e e= 0
ΨT D = D=3>,6 3>,6
j e e = 9
Tcjags mf`egs
C =2,43 T
D=4,98 T D
j = 31 Arc`gs `f oedfrtc` = (t ‘ 3) = 4
Tcjags (T) `f oc vcref`c` H
ΨT HH = 26,>
36 38 39 31 33 38
T HH =30,31
Hãohuog `fo fstc`ístehg B 34
B=
j j+3 34
B=
31 (32)
∓ T e4 /je - 8(j+3) (61.6)4 + (3>.6)4 + (26)4 1
0
- 8 ((32 32)) 9
B = 34.6> **
Tfaoc `f `fheseøj Fo fstc`ístehg Q sf prufdc hgj ke-huc`rc`c, hgjse`frcj`g fo jevfo `f seajeiehcheøj y ogs arc`gs `f oedfrtc` `f ogs trctcmefjtgs. Xe B ≦ R4>,>6 hgj arc`gs `f oedfrtc` t-3 ; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc (*). Xe B ≦ R4>,>3 hgj arc`gs `f oedfrtc` t-3 ; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc (**). arc`gs `f oedfrtc` Xe B ? R4>,>6 hgj fstc`ístehcmfjtf eaucofs (JX).
t-3 ;
Xf chfptc B>. Ogs trctcmefjtgs sgj
309
Ycogrfs `f R 4 `f tcdoc R4(>,>3< ao=4)= 5,43 R4(>,>6< ao=4)= 6,55 4
B=34,6>:: R @fheseøj
>,>3=
5,43**
Xf rfhbczc B>. Fj hucjtg c oc vcrecdof ‟`ícs c oc cpcreheøj `f ocs mczgrhcs”, co mfjgs ujc vcref`c` fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc. 6.33.4.
FR^FTEMFJPGX FJ DOGSVFX CO C[CT U CJÃOEXEX @F YCTECJ[C ^GT TCJAGX @F ITEF@MCJ
·VJ @EXFÓG FJ DOGSVFX CO C[CT XF ^VF@F CJCOE[CTXF HGJ OC PÅHJEHC @F ITEF@MCJ7 Fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj fquevcof co cjãoeses `f uj `esfóg `f dogqufs co czcr y puf`f uscrsf pcrc cjcoezcr `ctgs `f vcrecdofs tgmc`cs hgj fshcocs `f ejtfrvcog, hucj`g fo tcmcóg `f oc mufstrc fs rf`uhe`g y `f `estreduheøj oedrf. ^TGDOFMC TFXVFOPG Fj uj fjscyg `f vcoe`cheøj `f hejhg vcref`c`fs fj trfs oghcoe`c`fs `fjgmejc`g ‟Xfofhheøj `f huotevcrfs mfkgrc`gs fj `evfrsgs carg fhgsestfmcs `fo Fhuc`gr44” sf gdtuvefrgj ogs seauefjtfs `ctgs `f rfj`emefjtg fj tgjfoc`cs måtrehcs/bfhtãrfc; @ctgs Ycref`c`fs Hcturrc rgkg Hcturrc cmcreoog Hctucí cmcreoog Hctemgr FFP^ Xcrhbemgr Mf`ec
Cocmgr (Ogkc) >,06 >,33 >,06 >,44 >,00 >,88
Oghcoe`c`fs Mf`ec ^cooctcjac Mgrcspujag PM/bc (Hbemdgrczg) (Hgtgpcxe) >,65 >,62 >,60 3.08 >,04 >,96 >,04 >,0> >,04 >,53 >,19 >,98 >,20 >,6> >,65 >,20 >,68 >,61
44
. Fstcheøj Fxpfremfjtco Prgpehco ^ehbeoejauf. 3.552. Ejigrmf Cjuco Påhjehg; 3.551. ^rgarcmc `f Hchcg y Hciå. EJEC^. Sufvf`g. pp; 69 ‘ 9>.
301
Igrmuocheøj `f ocs bepøtfses fstc`ístehcs B>; Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs B3; Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf. Prcjsigrmcheøj `f `ctgs greaejcofs c rcjags Cocmgr Tcjag t/bc(r) = 8 Oghcoe`c`fs (T C)
^cooctcjac Tcjag t/bc (T ^)
Ycref`c`fs (t) = 6
Mgrcspujag Tcjag t/bc (T M)
T.
T 4
Hcturrc rgkg 0,6 t ->,65 Arc`gs `f>,06 oedfrtc`= 3=0 4
>,62
0
3>,6
33>,46
Hcturrc cmcreoog
>,33
3
3.08
6
>,04
4
2,>
90,>>
Hctucí cmcreoog
>,06
0,6
>,04
3
>,0>
3
9,6
04,46
Hctemgr FFP^
>,44
4
>,53
0
>,19
6
33,>
343,>>
Xcrhbemgr
>,00
8
>,20
8
>,6>
8
5,>
23,>> ΨT 4= 032,6
Oghcoe`c`fs (r) = 8 Ycref`c`fs (t) = 6 Arc`gs `f oedfrtc`= t - 3 = 0 Hãohuog `fo fstc`ístehg R r4 34
Rr4 =
∓T 4
- 8 r (t + 3)
rt (t + 3)
Rr4 =
34
(032,6) - 8(8)(6+3)
8(6)(6+3)
Rr4 =
34 5>
Rr4 = 3,2> JX Tfaoc `f `fheseøj 4
4
(032,6) - 60
Xe Rr ≦ R >,>6; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 56% `f hgjiecjzc (*).
302
Xe Rr4 ≦ R4>,>3; Xf rfhbczc B>. Co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc (**). Xe Rr4 ? R4>,>6; Xf chfptc B>. Ogs trctcmefjtgs sgj fstc`ístehcmfjtf eaucofs (JX). 4
Ycogrfs `f R `f tcdoc R4(>,>6< ao=0)= 5,05 R4(>,>3< ao=0)= 38,42 Rr4 = 3,2> ? R4>,>6= 5,05 JX @fheseøj Xf chfptc oc B>. Jg bcy `eifrfjhec fstc`ístehc seajeiehctevc fjtrf ocs vcref`c`fs fj ocs trfs oghcoe`c`fs (JX). 9.
XF^CTCHEØJ FXPC@ÍXPEHC @F MF@ECX
PÅHJEHCX ^CTCMÅPTEHCX @F XF^CTCHEØJ @F MF@ECX ·SVF XF @FDF BCHFT @FX^VÅX @FO CJÃOEXEX @F YCTECJ[C7 Fo cjãoeses `f vcrecjzc sgog fs ujc premfrc pcrtf `fo cjãoeses fstc fstc`ístehg `ístehg `f `ctgs. Fo cjãoeses `f vcrecjzc, cpgyc`g fj oc prufdc `f I, pgsedeoetc chfptcr g rfhbczcr ocs bepøtfses fstc`ístehcs. B>; bepøtfses juoc. Ocs mf`ecs sgj fstc`ístehcmfjtf f stc`ístehcmfjtf eaucofs. B3; bepøtfses cotfrjctevc. Co mfjgs ujc mf`ec fs fstc`ístehcmfjtf `eifrfjtf. Vjc sfauj`c pcrtf `fo cjãoeses `f `ctgs hgjsestf fj rfcoezcr oc sfpcrcheøj `f mf`ecs g oocmc`c tcmdeåj hgmpcrcheøj `f mf`ecs , ogs cjãoeses `f rfarfseøj y gtrcs tåhjehcs `f csghecheøj fstc`ístehc `f vcrecdofs. Fj fxpfremfjtgs `gj`f ogs jevfofs `fo ichtgr fj fstu`eg sgj `f ejtfrvcog hgjstcjtf< hgmg sgj; `gses `f ifrteoezcjtfs, iujaehe`cs g ejsfhtehe`cs, oãmejcs `f refag, hgjtfje`g `f prgtfíjc fj `eftcs< fs mãs fifhtevg uscr `erfhtcmfjtf ogs cjãoeses `f rfarfseøj. Hucj`g fj uj fxpfremfjtg sf tefjfj tfsteags jgmejcofs y fj jevfofs fj fshcoc `f ejtfrvcog hgjstcjtf, sf puf`fj hgmdejcr oc sfpcrcheøj `f mf`ecs y fo cjãoeses `f rfarfseøj. Oc sfpcrcheøj `f mf`ecs g hgmpcrcheøj `f mf`ecs fs vãoe`c fspfhecomfjtf hucj`g ogs jevfofs `fo ichtgr fj fstu`eg sgj `f tepg jgmejco. ^gr fkfmpog; vcref`c`fs (Y3, Y4, Y8, ……), `eftcs (@3, @4, @8, @0), iujaehe`cs (I3, I4, I8), ejsfhtehe`cs (E3, E4, E8, E0, E6), bfrdehe`cs (B3, B4, B8), `fjse`c`fs pgdochegjcofs (@3, @4, @8), fjtrf gtrgs. ^crc oc sfpcrcheøj `f mf`ecs bcy vcrecs tåhjehcs fstc`ístehcs g prufdcs. Fj fo
prfsfjtf `ghumfjtg sf fjictezc fj oc @eifrfjhec Míjemc Xeajeiehctevc, oc ^rufdc `f @uhcj, oc ^rufdc `f Pulfy y ocs hgmpcrchegjfs grtgagjcofs.
305
Fj oc fstc`ístehc jg pcrcmåtrehc, tcjtg pcrc oc prufdc `f Lruslcoo & Qcooes hgmg pcrc fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj, fxestfj tåhjehcs `f sfpcrcheøj fstc`ístehc `f mf`ecs. 9.3. @EIFTFJHEC MÍJEMC XEAJEIEHCPEYC ·SVÅ FX OC @EIFTFJHEC MÍJEMC XEAJEIEHCPEYC7 Oc @eifrfjhec Míjemc Xeajeiehctevc (@MX) `fdf uscrsf pcrc hgmpcrcr pcrfs `f mf`ecs c`ychfjtfs fj uj crrfaog gr`fjc`g `f mcygr c mfjgr< cujquf tcmdeåj sf puf`f uscr pcrc hgmpcrcr mf`ecs `f uj trctcmefjtg vs uj tfsteag. Oc @MX fs oc `eifrfjhec fjtrf `gs mf`ecs hcohuoc`c fj dcsf `f oc prufdc t `f `f Xtu`fjt. Hucj`g fo jûmfrg `f gdsfrvchegjfs g rfpftehegjfs pcrc ogs `gs trctcmefjtgs sukftgs c hgmpcrcheøj fs `eifrfjtf48 (hgmg fj fo hcsg `fo `esfóg hgmpoftcmfjtf co czcr hgj `fseauco jûmfrg `f rfpftehegjfs), sf usc oc iørmuoc seauefjtf; @MX = t(c, AOFrrgr)
(HMF)(3/je+3/je―)
Fo vcogr `f t sf sf tgmc `f oc tcdoc `f t hgjse`frcj`g hgjse`frcj`g fo jevfo `f seajeiehcheøj y ogs arc`gs `f oedfrtc` `fo frrgr (`fo cjãoeses `f vcrecjzc). Fj fo prgarcmc Fxhfo sf hcohuoc t `erfhtcmfjtf uscj`g oc iujheøj
[email protected](jevfo `f seajeiehcheøj< arc`gs `f oedfrtc` `fo frrgr).
Hucj`g fo jûmfrg `f gdsfrvchegjfs pcrc ogs `gs trctcmefjtgs sukftgs c hgmpcrcheøj fs eauco40 sf usc oc iørmuoc seauefjtf; @MX = t(γ, AOFrrgr)
(4)(HMF)/j
Fo vcogr `f t sf sf tgmc `f oc tcdoc `f t hgjse`frcj`g hgjse`frcj`g fo jevfo `f seajeiehcheøj y ogs arc`gs `f oedfrtc` `fo frrgr (`fo cjãoeses `f vcrecjzc). Fj fo prgarcmc Fxhfo sf hcohuoc t `erfhtcmfjtf uscj`g oc iujheøj
[email protected](jevfo `f seajeiehcheøj< arc`gs `f oedfrtc` `fo frrgr).
Bepøtfses fstc`ístehcs; B>; ¶3 = ¶4
48
. Måtg`gs fstc`ístehgs. bttp;//mczejafr.sesed.uhbeof.ho/rfpgsetgreg/od/hefjhecsWquemehcsWyWicrmchfutehcs/he`f>4/hcpetuog>9/>9.btmo . @eifrfjhec Míjemc Xeajeiehctevc. Xeajeiehctevc. bttp;//hgstcrehcoej`c.hgm/Fstc`estehc/`ms.btm
40
36>
B3; ¶3 ≮ ¶4 Tfaoc `f `fheseøj Hucj`g oc ‟@eifrfjhec fjtrf Mf`ecs Hgmpcrc`cs” fs mfjgr quf oc @MX ; Jg bcy `eifrfjhec fstc`ístehc seajeiehctevc. Ocs mf`ecs sgj mf`ecs fstc`ístehcmfjtf eaucofs. Hucj`g oc ‟@eifrfjhec fjtrf Mf`ecs Hgmpcrc`cs” fs fs mcygr quf oc @MX ; Bcy `eifrfjhec fstc`ístehc seajeiehctevc fjtrf ocs mf`ecs hgmpcrc`cs. ^TGDOFMC TFXVFOPG ^crc `esfógs hgmpoftcmfjtf co czcr hgj `fseauco jûmfrg `f rfpftehegjfs. Fj fo hcsg `f uj `esfóg hgmpoftcmfjtf co czcr hgj `fseauco jûmfrg `f rfpftehegjfs, sf usc oc iørmuoc seauefjtf; @MX = t(c, AOFrrgr)
(HMF)(3/je+3/je―)
@ctgs Fo vcogr `f t sf sf gdtefjf fj ujc tcdoc hgjse`frcj`g uj jevfo `f seajeiehcheøj `fo 6% y 39 arc`gs `f oedfrtc` `fo frrgr g `erfhtcmfjtf uscj`g fo prgarcmc Fxhfo hgj oc iujheøj
[email protected](>,>6< 39). t>,>6= 4,34>. HMF = 4,>> Prctcmefjtgs t = 0 Jûmfrg `f gdsfrvchegjfs; j3 = 0, j4 = 4, j8 = 6, j0 = 5 Jevfo `f seajeiehcheøj = 6% Mf`ecs gr`fjc`cs `f trctcmefjtgs @3 = 09 @0 = 04 @4 = 80 @8 = 80 @eifrfjhecs fjtrf ocs mf`ecs `f ogs trctcmefjtgs gr`fjc`gs @3-@0 = 09-04 = 0,>. @0-@4 = 04-80 = 2,> @4-@8 = 80-80 = >,>
Hãohuog `f ocs @MX @MX (@3 y @0) = 4,34> \(4)(3/0+3/5)]>,6 = 3,2>
363
@MX (@0 y @4) = 4,34> \(4)(3/5+3/4)]>,6 = 4,80 @MX (@4 y @8) = 4,34> \(4)(3/4+3/6)]>,6 = 4,63 @eifrfjhecs fjtrf mf`ecs hgmpcrc`cs @3 ‘ @0 0,> @0 ‘ @8 @4 @4 @3 : @0 : @4 = @8
2,> >,>
Tfocheøj :
@MX 3,2>
@fheseøj Xf rfhbczc B>
@3 : @0
: ?
4,80 4,63
Xf chfptc rfhbczcBB> >
@0 = : @8 @4 @4
@fheseøj Oc mf`ec @3 fs mcygr quf oc mf`ec @0 y åstc fs mcygr quf oc mf`ec @4. Oc mf`ec @4 fs eauco quf oc mf`ec @8. ^TGDOFMC TFXVFOPG ^crc `esfógs hgmpoftcmfjtf co czcr hgj eauco jûmfrg `f rfpftehegjfs Fj uj `esfóg hgmpoftcmfjtf co czcr hgj eauco jûmfrg `f rfpftehegjfs sf puf`fj uscr vcrecs tåhjehcs pcrcmåtrehcs hgmg; @MX (prufdc `f t), oc prufdc `f @ujhcj, oc prufdc `f Pulfy g ocs hgmpcrchegjfs grtgagjcofs. Oc iørmuoc `f oc @MX, fj fstf hcsg, fs oc seauefjtf; @MX = t(c, AOFrrgr)
(4)(HMF)/j
@ctgs Fo vcogr `f t sf sf gdtefjf fj ujc tcdoc hgjse`frcj`g uj jevfo `f seajeiehcheøj `fo 6% y 4> arc`gs `f oedfrtc` `fo frrgr g `erfhtcmfjtf uscj`g fo prgarcmc Fxhfo hgj oc iujheøj
[email protected](>,>6< 4>). t>,>6= 4,>29 HMF = 9,62 Prctcmefjtgs t = 0 Arc`gs `f oedfrtc` `fo frrgr; j= 4> Jevfo `f seajeiehcheøj = 6% Mf`ecs gr`fjc`cs `f trctcmefjtgs P6 = 3.024 P0 = 3.03> P4 = 3.400 P8 = 3.32> P3 = 3.>6>
@eifrfjhecs fjtrf mf`ecs `f ogs trctcmefjtgs gr`fjc`gs
364
P6-P0 = 3.024-3.03> = 14,> P0-P4 = 3.03>-3.400 = 399,> P4-P8 = 3.400-3.32> = 90,> P8 ‘P3= 3.32>-3.>6> = 38>,> Hãohuog `f ocs @MX @MX = 4,>29 \(4)(9,62)/6]>,6 = 3>1 @eifrfjhecs fjtrf mf`ecs hgmpcrc`cs P6 - P0 14,> P0 - P4 399,> P4 - P8 90,> P8 - P3 38>,>
Tfocheøj ? : ? :
@MX 3>1 3>1 3>1 3>1
@fheseøj Xf chfptc B> Xf rfhbczc B> Xf chfptc B> Xf rfhbczc B>
P6 = P0 P0 : P4 P4 = P8 P8 : P3
P6 = P0 : P4 = P8 : P3 @fheseøj Oc mf`ec `f P6 fs eauco eauco c oc mf`ec `f P0. Fstcs mf`ecs sgj mcygrfs quf P4. Oc mf`ec `f P4 fs eauco quf oc mf`ec `f P8. Oc mf`ec `f P8 fs mcygr quf oc mf`ec `f P3. 8.0.3.4.
^TVFDC @F TCJAG MÛOPE^OF @F @VJHCJ
·FJ SVÅ HGJXEXPF OC ^TVFDC @F @VJHCJ7 Oc prufdc `f @ujhcj g tcmdeåj oocmc`c ^rufdc `f Tcjag Mûotepof @ujhcj 46 fs ujc hgmpcrcheøj `f ocs mf`ecs `f tg`gs ogs trctcmefjtgs tg`gs< pgr og tcjtg, hucoquefr `eifrfjhec fjtrf uj trctcmefjtg hgj gtrg sf rfiofkc fj fstc prufdc. Fj oc prufdc `f @ujhcj sf uscj `eifrfjtfs mf`e`cs `f seajeiehcheøj quf fstãj fj iujheøj `fo jûmfrg `f mf`ecs c sfr hgmpcrc`cs. Xfaûj @ujhcj, c mf`e`c quf fo jûmfrg `f mf`ecs cumfjtc, oc prgdcdeoe`c` `f quf sf csfmfkfj `esmejuyf. Fj ujc hgmpcrcheøj `f mf`ecs sf puf`f tfjfr `gs pgsedofs rfsuotc`gs; 3 = 4 ø 3 ≮ 4 Fj ujc hgmpcrcheøj mûotepof, pgr fkfmpog fjtrf trfs mf`ecs, sf pg`rícj tfjfr rfsuotc`gs hgmg; ¶3 = ¶4 = ¶8 (¶3 + ¶ 4)/4 = ¶ 8
(¶3 + ¶ 4)/4 ≮ ¶ ¶8 8
46
. ^rufdc `f rcjag mûotepof `f @ujhcj. bttp;//www.metfhjgogaehg.hgm/mfhctrgjehc/Mcej/^rufdc@fTcjagMuotepof@f@ujhcj
368
(¶3 + ¶ 8)/4 ≮ ¶ ¶4 4
(¶3 + ¶8)/4 = ¶4
Fj oc ^rufdc `f @ujhcj, fo hgmpcrc`gr fstc`ístehg (HF@) rfsuotc `f oc muotepoehcheøj `f ogs(X vcogrfs stu`fjtezc`gs seajeiehctevgs (@) y fo frrgr fstãj`cr `f oc mf`ec x). HF@ = @(Xx)
Fo vcogr @ sf tgmc `f oc tcdoc `f ‟Tcjags stu`fjtezc`gs míjemgs seajeiehctevgs `f @ujhcj”, tgmcj`g fj hgjse`frcheøj fo jevfo `f seajeiehcheøj, ocs mf`ecs c sfr hgmpcrc`cs y ogs arc`gs `f oedfrtc` `fo frrgr. Fo frrgr fstãj`cr `f oc mf`ec mf `ec sf hcohuoc uscj`g oc iørmuoc seauefjtf; HMF r
Xx =
@øj`f; HMF = Huc`rc`g mf`eg `fo frrgr r = jûmfrg `f rfpftehegjfs Bepøtfses fstc`ístehcs; B>; ¶3 = ¶4 B3; ¶3 ≮ ¶4 Tfaoc `f `fheseøj Xe oc ‟@eifrfjhec fjtrf mf`ecs c hgmpcrcr” fs mfjgr quf ‟Hgmpcrc`gr fstc`ístehg `f @ujhcj” (HF@); Jg bcy `eifrfjhec fstc`ístehc fjtrf ocs mf`ecs hgmpcrc`cs. Xe oc ‟@eifrfjhec fjtrf mf`ecs c hgmpcrcr” fs mcygr quf ‟Hgmpcrc`gr fstc`ístehg `f @ujhcj (HF@); Bcy `eifrfjhec fstc`ístehc seajeiehctevc fjtrf ocs mf`ecs hgmpcrc`cs. Hucj`g ocs mf`ecs sgj eaucofs sf rfprfsfjtc hgj oftrcs eaucofs y hucj`g ocs mf`ecs sgj `eifrfjtfs sf rfprfsfjtc hgj oftrcs `eifrfjtfs.
360
^TGDOFMC TFXVFOPG @ctgs Fj uj `esfóg `f dogqufs co czcr hgj 6 6 trctcmefjtgs y y 0 rfpftehegjfs, uscr oc ^rufdc `f @ujhcj pcrchefjtg. sfpcrcr mf`ecs `f34 ogsarc`gs trctcmefjtgs hgj uj seajeiehcheøj `fo 6 pgr Fo ocs fjscyg tefjf `f oedfrtc` `fojevfo frrgr`fy uj vcogr `f Huc`rc`g mf`eg `fo frrgr (vcrecjzc `fo frrgr) `f 4,8>. Ocs mf`ecs c sfr hgmpcrc`cs sgj ocs seauefjtfs; C = 3>,16
D = 9,6>
H = 1,16
@ = 9,16
F = 9,6>
Hãohuog `fo frrgr fstãj`cr `f ocs mf`ecs 4,8> 0
Xx =
HMF r
Xx =
= >,160
Gdtfjheøj `f vcogrfs stu`fjtezc`gs `f @ujhcj (tcdoc) Arc`gs `f oedfrtc` `fo frrgr = 34 Prctcmefjtgs = 6 Jevfo `f seajeiehcheøj = 6% Pcdoc `f Tcjags Xtu`fjtezc`gs Míjemgs Xeajeiehctevgs `f @ujhcj @>,>6
4 8,>24
8 8,446
0 8,838
6 8,81>
Hãohuog `fo hgmpcrc`gr fstc`ístehg `f @ujhcj (HF@) HF@ = @(Xx)
Hgmpcrcr @>,>6 Xx HF@
4 8,>24 >,160 4,840
8 8,446 >,160 4,084
0 8,838 >,160 4,055
6 8,81 >,160 4,604
@eifrfjhecs fjtrf mf`ecs `f ogs trctcmefjtgs gr`fjc`gs PC-PH = 3>,16-1,16 = 8,>> PH-P@ 1,16-9,16 = >,46 3,>> P@-PD = 9,16-9,6>
PD-PF = 9,6>-9,6> = >,>>
366
Hgmpcrchegjfs `f mf`ecs PC- HF@4 = 3>,16-4,840 = 2,09 Xgj fstc`ístehcmfjtf eaucofs tg`cs ocs mf`ecs udehc`cs fjtrf ogs vcogrfs 3>,16 2,09. Fj fstf crcjag sgog fstã oc mf`ec `fo trctcmefjtg PC, pgr og tcjtg sfy cseajc oc oftrc . PH - HF@8 = 1,16-4,084= 6,82 Xgj fstc`ístehcmfjtf eaucofs tg`cs ocs mf`ecs udehc`cs fjtrf ogs vcogrfs 1,16 y 6,82. Pg`cs ocs mf`ecs, fxhfptg PC, sf fjhufjtrcj fj fstf rcjag, pgr og tcjtg sgj fstc`ístehcmfjtf eaucofs. Tfprfsfjtcj`g hgj oftrcs ofs hgrrfspgj`f fo rcjag d c ocs mf`ecs `f ogs trctcmefjtgs H, @, D y F. Fj fstf hcsg bcy sgog `gs rcjags y jg bcy trcsocpfs. PC = 3>,16 c PH = 1,16 d P@ = 9,16 d PD = 9,6> d PF = 9,6> d @fheseøj Fo trctcmefjtg PC fs fstc`ístehcmfjtf supfregr c tg`gs ogs `fmãs. Ocs mf`ecs `f PD, PH, P@ y PF sgj fstc`ístehcmfjtf eaucofs. 8.0.3.8.
^TVFDC @F PVLFU
·FJ SVÅ HGJXEXPF OC ^TVFDC @F PVLFU7 Oc prufdc `f Pulfy fs tcmdeåj ujc prufdc mûotepof `f mf`ecs< fs `fher, pfrmetfj hgmpcrcr semuotãjfcmfjtf vcrecs mf`ecs `f ogs trctcmefjtgs49. Oc prufdc `f Pulfy Pulfy sf hgjse`frc mãs fstrehtc quf @ujhcj. Xf usc oc tcdoc `f Pulfy, hgjse`frcj`g ogs arc`gs `f oedfrtc` `fo frrgr, fo jûmfrg `f mf`ecs c hgmpcrcr y fo jevfo `f seajeiehcheøj. Fj fstf hcsg sf hcohuoc fo hgmpcrc`gr fstc`ístehg Q^, mf`ecjtf oc seauefjtf iørmuoc; Q^ = qc(Xx)
@øj`f; Q^ = Hgmpcrc`gr fstc`ístehg `f Pulfy
49
. ^rufdcs Mûotepofs Mûotepofs `f Mf`ecs. Dyrgj Bumdfrtg Agjzãofz Tcmírfz. bttp;//hftf.efspcjc.fs/mcjucofs/prufdcs.btm
369
qγ = Ycogr `f Pulfy tgmc`g `f oc tcdoc hgjse`frcj`g fo jevfo `f seajeiehcheøj, fo jûmfrg `f mf`ecs c hgmpcrcr y ogs arc`gs `f oedfrtc` `fo frrgr. Xx = Frrgr fxpfremfjtco ckustc`g pgr fo jûmfrg `f rfpftehegjfs gfhucheøj; frrgr fstãj`cr `f oc mf`ec, quf sf hcohuoc hgj oc Xx =
HMF r
@øj`f; HMF = Huc`rc`g mf`eg `fo frrgr r = jûmfrg `f rfpftehegjfs Bepøtfses fstc`ístehcs; B>; ¶3 = ¶4 B3; ¶3 ≮ ¶4 Vjc vfz hcohuoc`gs ogs hgmpcrc`grfs Q^, sf gr`fjcj ocs mf`ecs `f ogs trctcmefjtgs fj igrmc `fshfj`fjtf y sf focdgrc ujc mctrez `f ocs `eifrfjhecs `f mf`ecs. Tfaoc `f `fheseøj Xe oc ‟@eifrfjhec fjtrf mf`ecs c hgmpcrcr” fs mfjgr quf ‟Hgmpcrc`gr fstc`ístehg `f Pulfy” (Q^); Jg bcy `eifrfjhec fstc`ístehc fjtrf ocs mf`ecs hgmpcrc`cs. Xe oc ‟@eifrfjhec fjtrf mf`ecs c hgmpcrcr” fs mcygr quf ‟Hgmpcrc`gr fstc`ístehg `f Pulfy (Q^); Bcy `eifrfjhec fstc`ístehc seajeiehctevc fjtrf ocs mf`ecs hgmpcrc`cs. Hucj`g ocs mf`ecs sgj eaucofs sf rfprfsfjtc hgj oftrcs eaucofs y hucj`g ocs mf`ecs sgj `eifrfjtfs sf rfprfsfjtc hgj oftrcs `eifrfjtfs. ^TGDOFMC TFXVFOPG @ctgs Fj uj `esfóg `f dogqufs co czcr hgj 6 6 trctcmefjtgs y y 0 rfpftehegjfs, uscr oc ^rufdc `f Pulfy pcrc sfpcrcr ocs mf`ecs `f ogs trctcmefjtgs hgj uj jevfo `f seajeiehcheøj `fo 6 pgr hefjtg. Fo fjscyg tefjf 34 arc`gs `f oedfrtc` `fo frrgr y
uj vcogr `f Huc`rc`g mf`eg `fo frrgr `f 4,8>. Ocs mf`ecs c sfr hgmpcrc`cs sgj ocs seauefjtfs;
361
C = 3>,16
D = 9,6>
H = 1,16
@ = 9,16
F = 9,6>
Hãohuog `fo frrgr fstãj`cr `f ocs mf`ecs
4,8> 0
Xx =
HMF r
Xx =
= >,160
Gdtfjheøj `f vcogrfs `f Pulfy q>,>6 (tcdoc) Arc`gs `f oedfrtc` `fo frrgr = 34 Prctcmefjtgs = 6 Jevfo `f seajeiehcheøj = 6% ^ujtgs ^grhfjtucofs Xupfregrfs `f oc Cmpoetu` stu`fjtezc`c `f Pulfy q>,>6
4 8,>2
8 8,11
0 0,4>
6 0,63
Hãohuog `fo hgmpcrc`gr fstc`ístehg `f Pulfy (Q^) Q^ = qc(Xx)
Hgmpcrcr q>,>6 Xx Q^
4 8,>2 >,160 4,844
8 8,11 >,160 4,208
0 0,4> >,160 8,391
6 0,63 >,160 8,0>3
@eifrfjhecs fjtrf mf`ecs `f ogs trctcmefjtgs gr`fjc`gs PC-PH = 3>,16-1,16 = 8,>> PH-P@ = 1,16-9,16 = 3,>> P@-PD = 9,16-9,6> = >,46 PD-PF = 9,6>-9,6> = >,>> Hgmpcrchegjfs `f mf`ecs PC- Q^4 = 3>,16-4,844 = 2,08 Xgj fstc`ístehcmfjtf eaucofs tg`cs ocs mf`ecs udehc`cs fjtrf ogs vcogrfs 3>,16 y 2,08. Fj fstf rcjag sgog fstã oc mf`ec `fo trctcmefjtg PC, pgr og tcjtg sf cseajc oc oftrc c. PH - Q^ = 1,16-4,084= 0,53
8
362
Xgj fstc`ístehcmfjtf eaucofs tg`cs ocs mf`ecs udehc`cs fjtrf ogs vcogrfs 1,16 y 0,53. Pg`cs ocs mf`ecs, fxhfptg PC, sf fjhufjtrcj fj fstf rcjag, pgr og tcjtg sgj fstc`ístehcmfjtf eaucofs. Tfprfsfjtcj`g hgj oftrcs ofs hgrrfspgj`f fo rcjag d c ocs mf`ecs `f ogs trctcmefjtgs H, @, D y F. Fj fstf hcsg bcy sgog `gs rcjags y jg bcy trcsocpfs. PC = 3>,16 c PH = 1,16 d P@ = 9,16 d PD = 9,6> d PF = 9,6> d @fheseøj Fo trctcmefjtg PC fs fstc`ístehcmfjtf supfregr c tg`gs ogs `fmãs. Ocs mf`ecs `f PD, PH, P@ y PF sgj fstc`ístehcmfjtf eaucofs. HGM^CTCHEGJFX GTPGAGJCOFX ·SVÅ XGJ OCX HGM^CTCHEGJFX GTPGAGJCOFX7 Fo cjãoeses `f hgmpcrchegjfs grtgagjcofs sf grefjtc c oc pcrteheøj `f oc sumc `f huc`rc`gs `f ogs trctcmefjtgs fj ujc sumc `f huc`rc`gs `f `gs arupgs g `gs trctcmefjtgs `f ejtfrås `fo ejvfsteac`gr. Fj fstcs herhujstcjhecs, fo jûmfrg `f arc`gs `f oedfrtc` `f ogs trctcmefjtgs tcmdeåj sf rf`uhf c oc uje`c`, pufs sgog sf hgmpcrcj `gs trctcmefjtgs g `gs arupgs. Hgmg rfaoc sf `ehf quf `gs hgmpcrchegjfs sgj grtgagjcofs se fo prg`uhtg `f sus hgfiehefjtfs fs eauco c hfrg. Fj oc prãhtehc, fo cjãoeses `f hgmpcrchegjfs grtgagjcofs fs oc hgjtejucheøj `fo cjãoeses `f vcrecjzc, sf cpgyc fj oc prufdc `f I, sf csumfj ogs mesmgs supufstgs `fo C@FYC, quf sgj jgrmcoe`c`, ej`fpfj`fjhec y vcrecjzcs eaucofs. Oc ejigrmcheøj quf sf rfquefrf pcrc rfcoezcr fo cjãoeses `f hgmpcrchegjfs grtgagjcofs fs oc seauefjtf; Ogs `ctgs tgtcofs `f ogs trctcmefjtgs, fo huc`rc`g mf`eg `fo frrgr, ogs arc`gs `f oedfrtc` `fo frrgr, fo jûmfrg `f trctcmefjtgs tgtco, fo jûmfrg `f rfpftehegjfs y fo jevfo `f seajeiehcheøj. @ctgs.- ^crc fo cjãoeses `f hgmpcrchegjfs grtgagjcofs sf rfquefrf `f ogs hãohuogs f ejigrmcheøj seauefjtfs; Huc`rc`g mf`eg `fo frrgr Xumc tgtco `f trctcmefjtgs Tfpftehegjfs Jevfo `f seajeiehcheøj Hgmpcrcheøj `f `gs trctcmefjtgs g arupgs
HMF ∓Pe r c
He
L = ∓(He4) S = ∓(Pe.He)
Xumctgrec `fo huc`rc`g `f ogs hgfiehefjtfs Xumctgrec `f ogs prg`uhtgs fjtrf Pgtco `f Prctcmefjtgs y hgfiehefjtfs `f hgmpcrcheøj
365
Xumc `f huc`rc`gs = Huc`rc`g mf`eg g vcrecjzc Hucj`g bcy uj sgog arc`g `f oedfrtc` Ihcohuoc`c
S4 /rl (S4 /rl)/HMF
Bepøtfses B>; Bepøtfses juoc. ¶3 = ¶4 B3; Bepøtfses cotfrjctevc. ¶3 ≮ ¶4 Tfaoc `f `fheseøj.Xe Ihcohuoc`c ≦ I>,>6; Ocs mf`ecs sgj fstc`ístehcmfjtf `eifrfjtfs hgj fo 56% `f hgjiecjzc. Xe Ihcohuoc`c ≦ I>,>3; Ocs mf`ecs sgj fstc`ístehcmfjtf `eifrfjtfs hgj fo 55% `f hgjiecjzc. Xe Ihcohuoc`c ? I>,>6; Ocs mf`ecs sgj fstc`ístehcmfjtf eaucofs (JX).
^crc oc hgmpcrcheøj fjtrf mf`ecs `f `gs trctcmefjtgs g `f `gs arupgs `f trctcmefjtgs, fj fo cjãoeses `f hgmpcrchegjfs grtgagjcofs, sf bc c`gptc`g oc rfprfsfjtcheøj semdøoehc uscj`g ogs seajgs; =, ?, ? , :. :. ^TGDOFMC TFXVFOPG Fj uj fxpfremfjtg sf fvcoûcj 8 bídre`gs y 0 vcref`c`fs `f mcíz (1 trctcmefjtgs) fj 0 rfpftehegjfs. Ogs `gs bídre`gs sgj oghcofs y ujg fs ejtrg`uhe`g. Xurafj vcrecs hufstegjfs hgmg; ·Ogs bídre`gs sgj mfkgrfs quf ocs vcref`c`fs7, ·Fo bídre`g ejtrg`uhe`g fs mfkgr quf ogs bídre`gs oghcofs7, ·Huão `f ogs `gs bídre`gs oghcofs fs mfkgr7. @ctgs `f hcmpg y cjãoeses `f vcrecjzc41 Oestc `f vcrecdofs
3. 4. Tfpftehegjfs Prctcmefjtgs 8. Tfj`emefjtgs
HCXF JG.
3
4
8
-------------------------------------------------3 3 3 2> 4 3 4 56 8 3 8 36> 0 3 0 26 6 3 6 336 9 3 9 304 1 3 1 55 2 4 3 16 5 4 4 33> 3> 4 8 385 33 4 0 9> 34 4 6 386 38 4 9 386 30 4 1 33> 36 8 3 11 39 8 4 3>3 31 8 8 30> 32 8 0 10 35 8 6 303 4> 8 9 349 43 8 1 58 44 0 3 56 48 0 4 343 40 0 8 396 46 0 0 50 49 0 6 342 41 0 9 333
^rgmf`eg `f ocs rfpftehegjfs Tfpfteheøj Mf`ec -----------------------------------------3 3>5 4 3>5 8 3>1 0 330 -----------------------------------------^rgmf`eg `f ogs trctcmefjtgs Prctcmefjtg Mf`ec Xumc ------------------------------------------3 B3 24 841 4 B4 3>1 041 8 B8 305 650 0 Y3 12 838 6 Y4 38> 635 9 Y8 345 630 1 Y0 59 826 -------------------------------------------
42
0
1
28
41
. @ctgs cjcoezc`gs uscj`g fo prgarcmc MXPCP-H.
39>
C@FYC Iufjtf `f vcrecheøj Tfpftehegjfs Prctcmefjtgs Frrgr fxpfremfjtco Pgtco
Arc`gs `f oedfrtc` 8 9 32 41
Xumc `f Huc`rc`gs 362 39.223 4.26> 35.225
Huc`rc`gs mf`egs 64,9 4.230,> 362,8
Ihcohuoc`c
^
>,88 JX 31,11 **
>,>>>>3
Hgfiehefjtf `f vcrecheøj HY (%) = 33,00 Frrgr fstãj`cr `f ocs mf`ecs Xx Frrgr fstãj`cr `f oc mf`ec pcrc rfpftehegjfs (t = 1) = 0,19 (jg ejtfrfsc) Xx Frrgr fstãj`cr `f oc mf`ec pcrc trctcmefjtgs (r = 0) = 0,19 (`f ejtfrås)
Cjãoeses `f hgmpcrchegjfs grtgagjcofs grtgagjco fs Ogs `ctgs rfqufre`gs pcrc fstf cjãoeses sgj ogs seauefjtfs; Huc`rc`g mf`eg `fo frrgr Arc`gs `f oedfrtc` `fo frrgr J> trctcmefjtgs J> Tfpftehegjfs Jevfo `f seajeiehcheøj
= 362,8 = 32 =1 =0 = 6%
∓B4 041 0
∓B8 650 0
∓Y3 838 -8
∓Y4 ∓Y4 635 -8
∓Y8 630 -8
∓Y0 826 -8
r
l
H3
∓B3 841 0
0
20 889 355
H4 H8 H0 H6 H9
33 > > >
3 -3 > > >
-4 > > > >
>> 3 > >
>> -3 3 >
>> > -3 3
>> > > -3
00 0 0 0
49 4 4 4
rl
S
HM
Ihcohuoc`c
I>,>6 I>,>3
331,5
>,10 JX
0,03
2,45
40 2 -080 -3>> 1.202,4 3.46>,> 05,62 1,5> *** 2 -4>9 6.8>0,6 88,63 ** 2 6 8,3 >,>4 JX 2 345 4.>2>,3 38,30 **
0,03 0,03 0,03 0,03 0,03
2,45 2,45 2,45 2,45 2,45
B8; Bídre`g ejtrg`uhe`g B3 y B4; Bídre`gs oghcofs
Ejtfrprftcheøj B3, B4, B8 = Y3, Y4, Y8, Y0; Fo prgmf`eg `f ogs bídre`gs y fo `f vcref`c`fs sgj fstc`ístehcmfjtf eaucofs. B3, B4 ?? B8;`fo bídre`g ejtrg`uhe`g fs fstc`ístehcmfjtf supfregr c ogs Fo prgmf`eg
prgmf`egs `f ogs bídre`gs oghcofs hgj fo 55% `f hgjiecjzc.
393
B3 ? B4; Fo prgmf`eg `fo bídre`g B4 fs fstc`ístehcmfjtf supfregr co prgmf`eg `fo bídre`g B3 hgj fo 56% `f hgjiecjzc. Y3 ? Y4; Fo prgmf`eg `f oc vcref`c` Y4 fs fstc`ístehcmfjtf supfregr co prgmf`eg `f oc vcref`c` Y3 hgj fo 55% `f hgjiecjzc. Y4 = Y8; Fo prgmf`eg `f oc vcref`c` Y4 fs fstc`ístehcmfjtf eauco co prgmf`eg `f oc vcref`c` Y8. Y8 :: Y0; Fo prgmf`eg `f oc vcref`c` Y8 fs fstc`ístehcmfjtf supfregr co prgmf`eg `f oc vcref`c` Y0 hgj fo 55% `f hgjiecjzc. @fheseøj B3, B4, B8 = Y3, Y4, Y8, Y0 B3, B4 ?? B8 B3 ? B4 Y3 ? Y4 Y4 = Y8 Y8 :: Y0
(JX) (**) (*) (*) (JX) (**)
PÅHJEHCX JG ^CTCMÅPTEHCX @F XF^CTCHEØJ @F MF@ECX XF^CTCHEØJ @F MF@ECX FJ OC ^TVFDC @F LTVXLCOO &QCOOEX ·HØMG XF TFCOE[C OC XF^CTCHEØJ @F MF@ECX FJ OC ^TVFDC @F LTVXLCOO & QCOOEX7 Fo ejvfsteac`gr, se bc rfhbczc`g oc B> fstã chfptcj`g oc B3, fstg seajeiehc quf co mfjgs uj trctcmefjtg fs fstc`ístehcmfjtf fstc`ístehcmfjtf `eifrfjtf c uj jevfo seajeiehcheøj `c`g. Fo seauefjtf pcsg hgjsestf fj e`fjteiehcr fxchtcmfjtf huão fs fo trctcmefjtg fstc`ístehcmfjtf `eifrfjtf. Co eauco quf oc @eifrfjhec Míjemc Xeajeiehctevc (@MX) usc`c fj oc fstc`ístehc pcrcmåtrehc, bcy ujc tåhjehc jg pcrcmåtrehc42 quf sf dcsc fj oc hgmpcrcheøj `f arupgs fj pcrfs uscj`g fo hgmpcrc`gr fstc`ístehg H@ hgj oc `eifrfjhec hcohuoc`c `f uj pcr `f rcjags mf`egs. ^gr icheoe`c` fj oc gpfrcheøj sf uscrã ogs tårmejgs T 3,…T j pcrc rfifrersf c ogs rcjags prgmf`egs, sfaûj sfc fo jûmfrg `f trctcmefjtgs fj fstu`eg.
Oc iørmuoc pcrc hcohuocr hgmpcrc`gr fstc`ístehg H@ fs oc seauefjtf; 42
. bttp;//www.mgjgarciecs.hgm/trcdckgs35/fstc`estehc-cargpfhucreg/fstc`estehc-cargpfhucreg.sbtmo
394
j(j + 3)
Fj fstf hcsg, tcmdeåj fxestf ujc rfaoc `f `fheseøj; Xe |T 3 - T 4|:H@ fjtgjhfs fxestf `eifrfjhec seajeiehctevc fjtrf fo trctcmefjtg 3 y fo trctcmefjtg 4. Xe |T 3 - T 4|? H@ fjtgjhfs fo trctcmefjtg 3 y fo trctcmefjtg 4 sgj fstc`ístehcmfjtf eaucofs. Oc hgmpcrcheøj `f mf`ecs sf rfcoezc uscj`g ogs vcogrfs cdsgoutgs. ^TGDOFMC TFXVFOPG Fj fo fjscyg @HC `f trfs vcref`c`fs `f mcíz `gj`f sf fvcoûc fo tefmpg quf `fmgrc fj fo cpcrfhemefjtg `f ocs mczgrhcs, fj fo hcmpg, sf rfhbczø oc B >< fs `fher, co mfjgs ujc vcref`c` fs fstc`ístehcmfjtf `eifrfjtf hgj fo 55% `f hgjiecjzc. Oc `fheseøj fstc`ístehc sf tgmø fj dcsf `f oc prufdc `f Ke-huc`rc`c. @ctgs Ycref`c`fs = 8 j = 31 j3 = 1 j4 = 0 B=34,6>:: R4>,>3= 5,43** 5,43** Hãohuog `f ogs hgmpcrc`grfs H@ ^crc oc hgmpcrcheøj Y C vs Y Y DD j(j + 3)
H@ = 4,850 \(31)(32)/34]\(3/1)+(3/0)] \(31)(32)/34]\(3/1)+(3/0)] H@ = 1,611 |T C ‘ T D| = 2,43 ‘ 4,98 =6,62 |T C ‘ T D| ? H@; ^gr og tcjtg, ocs vcref`c`fs C y D sgj fstc`ístehcmfjtf eaucofs.
^crc oc hgmpcrcheøj Y DD vs Y Y HH
398
j(j + 3)
H@ = 4,850 \(31)(32)/34]\(3/0)+(3/9)] \(31)(32)/34]\(3/0)+(3/9)] H@ = 1,2 |T D ‘ T H| = 4,98 ‘ 30,31=33,60 |T D ‘ T H| : H@; ^gr og tcjtg, ocs vcref`c`fs D y H sgj fstc`ístehcmfjtf `eifrfjtfs. @fheseøj Ycref`c` C = Ycref`c` D ? Ycref`c` H XF^CTCHEØJ @F MF@ECX FJ FO CJCOEXEX @F YCTECJ[C ^GT TCJAGX @F ITEF@MCJ ·HØMG XF TFCOE[C OC XF^CTCHEØJ @F MF@ECX FJ FO CJÃOEXEX @F YCTECJ[C ^GT TCJAGX @F ITEF@MCJ7 Xf bc `fscrrgooc`g ujc tåhjehc jg pcrcmåtrehc `f hgmpcrcheøj `f ocs sumcs `f rcjags cpoehcdof sgog c ogs rfsuotc`gs `fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj (fquevcofjtf co cjãoeses `f uj `esfóg fj dogqufs co czcr). Fo prghf`emefjtg sf dcsc fj fo hãohuog `fo hgmpcrc`gr fstc`ístehg H@ y oc hgmpcrcheøj `f fstf vcogr hgj oc `eifrfjhec `f ogs rcjags prgmf`egs `f ogs trctcmefjtgs hgmpcrc`gs. Oc iørmuoc pcrc hcohuocr fo hgmpcrc`gr fstc`ístehg (fquevcofjtf c oc @MX fj oc fstc`ístehc pcrc sfpcrcr ogs trctcmefjtgs fj fo cjãoeses `f 45 vcrecjzc pgrpcrcmåtrehc) rcjags `f Iref`mcj fs fo seauefjtf ; H@ = 4,850
rt (t+3) 9
@øj`f; H@ = Hgmpcrc`gr fstc`ístehg fj fo cjãoeses `f Iref`mcj. r = rfpftehegjfs t = trctcmefjtgs Fj fstf hcsg, oc rfaoc `f `fheseøj fs oc seauefjtf; Xe |T 3 - T 4|:H@; bcy `eifrfjhec fstc`ístehc fjtrf ogs trctcmefjtgs 3 y 4.
Xe |T 3 - T 4|? H@; ogs trctcmefjtgs 3 y 4 sgj fstc`ístehcmfjtf eaucofs. 45
.
bttp;//www.mgjgarciecs.hgm/trcdckgs35/fstc`estehc-cargpfhucreg/fstc`estehc-cargpfhucreg.sbtmo
390
^TGDOFMC TFXVFOPG Fo cjãoeses `f vcrecjzc pgr rcjags `f Iref`mcj `fo fjscyg ‟Xfofhheøj `f 8>
huotevcrfs mfkgrc`gs `f fj oc`evfrsgs carg`eifrfjhec fhgsestfmcs `fo Fhuc`gr ”, pfrmeteø `fhe`er oc chfptcheøj B>; jg bcy fstc`ístehc seajeiehctevc fjtrf ocs vcref`c`fs fj ocs trfs oghcoe`c`fs fstu`ec`cs (Sufvf`g, ^cooctcjac y Mgrcspujag). @ctgs Oghcoe`c`fs (r) = 8 Ycref`c`fs (t) = 6 Rr4 = 3,2> ? R4g,>6= 5,05 (JX) Hãohuog `fo hgmpcrc`gr H@ = 4,850
rt (t+3) 9
H@ = 4,850\(8)(6)(9)/9]>,6 = 5,41 (JX) Hãohuog `f oc `eifrfjhec `f rcjags Xumc `f rcjags ‟mcs cotg” = T hctemgr hctemgr = 33,> Xumc `f rcjags ‟mãs dckg” = T hcturrc hcturrc cmcreoog = 9,6 ET hctemgr 0,6 hctemgr ‘ T hcturrc hcturrc cmcreoogE = 0,6 |T hctemgr hctemgr ‘ T hcturrc hcturrc cmcreoog|? H@ @fheseøj Ocs vcref`c`fs Hctemgr y Hcturrc cmcreoog (huygs vcogrfs `f ocs sumcs `f rcjags hgrrfspgj`fj c ogs fxtrfmgs), rfsuotcj sfr fstc`ístehcmfjtf eaucofs, og quf hgjiermc fo cjãoeses `f Iref`mcj. Ocs hejhg vcref`c`fs, fj ocs trfs oghcoe`c`fs tefjfj uj hgmpgrtcmefjtg prg`uhtevg fstc`ístehcmfjtf eauco.
8>
. Fstcheøj Fxpfremfjtco Prgpehco ^ehbeoejauf. 3.552. Ejigrmf Cjuco Påhjehg; 3.551. ^rgarcmc `f Hchcg y Hciå. EJEC^. Sufvf`g. pp; 69 ‘ 9>.
396
1. G^PEME[CHEØJ @F OGX ^TGHFXGX ^TG@VHPEYGX ·SVÅ FX OC IVJHEØJ ^TG@VHHEØJ7 Oc vcrecdof `fpfj`efjtf U fj iujheøj `f oc vcrecdof ej`fpfj`efjtf R, sf cjgtc hgmg; U =Ɣ (R). Fstc csghecheøj fstc`ístehc devcrec`c puf`f sfr oejfco, pgoejgmeco, ogacrítmehc g fxpgjfjheco, sfaûj oc jcturcofzc `f ogs ifjømfjgs fj fstu`eg, y sf rfprfsfjtcj pgr mg`fogs mctfmãtehgs fspfhíiehgs. Oc vcrecdof `fpfj`efjtf U fj iujheøj `f mãs `f vcrecs vcrecdofs ej`fpfj`efjtfs Rj, cjgtãj`gsf hgmg; U = Ɣ (R 3 ,R 4 ,R 8 , R j ). Fj dcsf `fo cjãoeses `f ogs `ctgs fxpfremfjtcofs `f hcmpg, ocdgrctgreg g iãdrehc, sf rfochegjc ujc vcrecdof `fpfj`efjtf hgmg iujheøj `f ujc g vcrecs vcrecdofs ej`fpfj`efjtfs y, mf`ecjtf ogs cjãoeses `f rfarfseøj, sf hcohuocj ogs hgfiehefjtfs `f ogs mg`fogs mctfmãtehgs quf mfkgr rfprfsfjtcj fsc csghecheøj fstc`ístehc. Hucj`g oc vcrecdof U sf rfiefrf c prg`uhtgs y ocs vcrecdofs R j sf rfiefrfj c ejsumgs, fjtgjhfs sf trctc `f ujc iujheøj prg`uhheøj prg` uhheøj 83 . Oc iujheøj prg`uhheøj fs uj mg`fog mctfmãtehg quf rfprfsfjtc fo hgmpgrtcmefjtg `f uj prg`uhtg U fj iujheøj `f R j . Hucj`g U =Ɣ (R), fjtgjhfs sf puf`f rfprfsfjtcr arãiehcmfjtf oc rfocheøj ejsumg (R) y prg`uhtg U.
U U (^rg` (^rg`uhtg) (^rg`uhtg) (^rg`uht uhtg) g) ^mãx
>
Rj
R^mcx
(Ejsumg)
R R (Ejsumg)
Oc rfocheøj ejsumg vs prg`uhtg, quf fj ogs hcsgs `f oc ejvfsteacheøj cargpfhucrec tefj`fj c sfr dãsehcmfjtf `f tepg huc`rãtehg g hûdehg, hgmg sf rfprfsfjtc fj oc arãiehc, fxpoehc oc vcrecheøj `f U fj iujheøj `f ogs hcmdegs fj R . Fj hgjsfhufjhec, bcy ujc hcjte`c` `ftfrmejc`c `f ejsumg Rj quf fstã csghec`c c oc prg`uhheøj mãxemc (^mcx).
83
.
@goo, K. & Grczfm, I. ^rg`uhtegj fhgjgmehs. Pbfgry wetb wetb cppoehctegjs. Xfhgj` f`etegj. Kgbj Qeofy & Xgjs. Xejacpgrf. pp; 4>-9>.
399
^TGDOFMC TFXVFOPG Fj uj fjscyg sf fvcoûc fo fifhtg `f `eifrfjtfs uje`c`fs `f ifrteoezcjtf sgdrf oc prg`uhheøj `f uj huotevg `ftfrmejc`g. Fj fstf hcsg, ujc uje`c` `f ifrteoezcjtf fstc hgmpufstc pgr 4> leogs `f J + 4> leogs `f ^ 4G6. Fo huc`rg `f `ctgs, oc rfprfsfjtcheøj arãiehc `f oc rfocheøj ejsumg vs prg`uhtg y fo mg`fog mctfmãtehg devcrec`g `f tepg huc`rãtehg sf fxpgjf c hgjtejucheøj 84;
Tfpfteheøj
Vje`c` `f ifrteoezcjtf/bc (R)
^rg`uhheøj/bc (U)
3 3 3 3 3 3 3
> 3 4 8 0 6 9
3> 9> 336 33> 36> 381 36>
3 3 4 4 4 4 4 4 4 4 4
1 2 > 3 4 8 0 6 9 1 2
381 349 8> 0> 2> 3>> 38> 31> 31> 302 334
32> 39> 30> c b / g t h u ` g r p f ` s f ` c ` e j V
34> 3>> 2> 9> 0>
y = -0,8064x4 + 02,215x + 34,1 T4 = >,5390
4> > >
3
4
8
0
6
9
1
Vje`c je`c`fs `fs `f ifrt i frteoezc eoezcjtf jtf
Fo mg`fog mctfmãtehg rfprfsfjtc oc iujheøj prg`uhheøj U= Ɣ(R), oc mesmc quf puf`f c`cptcrsf c ujc igrmc gpfrchegjco hgmg; T = 34,1 + 02,22 I ‘ 0,8064 I4 @øj`f; T = Vje`c`fs `f prg`uhtg I = Vje`c`fs `f ifrteoezcjtf
MÃREME[CHEØJ @F OC ^TG@VHHEØJ y @F OGX DFJFIEHEGX MÃREMC ^TG@VHHEØJ Fj fo arãiehg fxpufstg fj fo fkfrheheg cjtfregr, fs pgsedof `ftfrmejcr quf uscj`g fjtrf 6 y 9 uje`c`fs `f ejsumg (R) sf puf`f gdtfjfr oc mãxemc hcjte`c` `f prg`uhtg (U), pfrg quf bchec ocs 1 y 2 uje`c`fs `f R, bcy uj fifhtg hgjtrcprg`uhfjtf.
2
84
. Fo cjãoeses `f rfarfseøj y oc arciehcheøj arciehcheøj sf rfcoezø cpgyc`g fj fo prgarcmc Fxhfo.
391
C pcrter `f oc iujheøj prg`uhheøj, U= Ɣ(R), hgj uj prghf`emefjtg mctfmãtehg dcsc`g fj fo hãohuog `f oc premfrc `frevc`c `f oc iujheøj prg`uhheøj f eaucoc`c c hfrg, sf `ftfrmejc oc hcjte`c` `fo ejsumg R csghec`c c uj pujtg `f oc hurvc `f oc iujheøj prg`uhheøj, `gj`f oc pfj`efjtf ∉U/ ∉U= >, fstg fquevcof co pujtg `f Umcx. Fo vcogr `f Rmcx, quf fs oc hcjte`c` `f ejsumg csghec`c co pujtg ∉U/ ∉U= >, sf rffmpoczc fj oc iujheøj prg`uhheøj pcrc tfjfr fo vcogr `f Umcx, quf seajeiehc oc hcjte`c` mãxemc prg`uhheøj pgsedof `f sfr gdtfje`c fj fscs herhujstcjhecs.
^TGDOMC TFXVFOPG Fj dcsf `f oc iujheøj prg`uhheøj; T = 34,1 + 02,22 I ‘ 0,8064 I 4, `ftfrmejcr oc hcjte`c` `f uje`c`fs `f ejsumg quf pgsedeoetcríc gdtfjfr oc mãxemc hcjte`c` `f prg`uhtg Tmcx. Oc iujheøj prg`uhheøj fs; T = 34,1 + 02,22 I ‘ 0,8064 I 4 Oc hcohuoc oc premfrc `frevc`c f eaucoc c hfrg pcrc `ftfrmejcr fo vcogr `f Imcx. `(T)/`(I) = Tn= 02,22 ‘ 4(0,8064)(I) = > 02,22 - 2,95 I = > I = 02,22/2,95 I = 6,94 uje`c`fs `f ejsumg = I mcx. ^gr og tcjtg, Tmãx sf gdtefjf rffmpoczcj`g fo vcogr `f Imcx fj oc iujheøj prg`uhheøj Tmãx= 34,1 + 02,22 (6,94) ‘ 0,8064 (6,94)4 Tmãx= 36>,31 uje`c`fs `f prg`uhtg= mãxemc prg`uhheøj. Fj hgjsfhufjhec, hgj oc cpoehcheøj `f 6,94 uje`c`fs `f ejsumg sf puf`f gdtfjfr 36>,31 uje`c`fs `f prg`uhtg, quf hgrrfspgj`f c oc prg`uhheøj mãxemc pgsedof `f sfr gdtfje`c fj ocs herhujstcjhecs fspfhíiehcs `f oc oghcoe`c` `f fstu`eg.
MÃREMG DFJFIEHEG FHGJØMEHG Fj tg`c chteve`c` cargprg`uhtevc sf dushc oc gdtfjheøj `fo mãxemg dfjfieheg fhgjømehg pgsedof y jg jfhfscrecmfjtf `f oc mãxemc prg`uhheøj pgsedof. Hgj fstf prgpøsetg, c pcrter `f oc iujheøj prg`uhheøj, `gj`f oc hcjte`c` `f prg`uhtg `fpfj`f `f oc hcjte`c` `f ejsumgs cpoehc`gs (cauc, sfmeoocs, ifrteoezcjtfs, iujaehe`cs, fjtrf gtrgs), sf puf`f gptemezcr fo usg `f ejsumgs. Xe sf `espgjfj `f ogs `ctgs `f prfhegs `fo prg`uhtg y hgstgs `fo ejsumg, fs pgsedof hcohuocr fo dfjfieheg jftg mãxemg quf sgog puf`f gdtfjfrsf hucj`g oc prg`uhheøj fstã fj su pujtg øptemg fhgjømehg. Oc gptemezcheøj hgjsestf fj `ftfrmejcr oc hcjte`c` `f ejsumgs rfqufre`c pcrc gdtfjfr ujc hcjte`c` `f prg`uhtg tco quf csfaurf fo mãxemg dfjfieheg jftg
pgsedof. Fj fstf hcsg, oc hcjte`c` `f ejsumgs R sf csghec hgj uj p pujtg ujtg `f oc hurvc `f oc iujheøj prg`uhheøj `fjgmejc`g prg`uhheøj øptemc fhgjømehc (^GF). Fj fo arãiehg seauefjtf sf puf`f gdsfrvcr oc rfocheøj fjtrf oc hurvc `f
392
oc iujheøj prg`uhheøj (quf sf csghecj hgj ogs prfhegs ujetcregs pcrc `ftfrmejcj ogs ejarfsgs tgtcofs) y ogs hgstgs iekgs (hgjstcjtfs) + ogs hgstgs quf vcrícj (ejhrfmfjtcofs sfaûj sf fofvc oc hcjte`c` `f ejsumgs). Oc `estcjhec fjtrf ogs pujtgs `f oc hurvc `f oc iujheøj prg`uhheøj y oc oíjfc `f ogs hgstgs quf vcrícj hgrrfspgj`fj c ogs dfjfiehegs jftgs.
U
^mcx ^GF
Hgstgs tgtcofs Ejarfsgs tgtcofs
g t g f j j g e h g e h i f f j D
Hgstgs iekgs
R^GF
R^mcx
R
Oc hurvc `f oc iujheøj prg`uhheøj rfprfsfjtc fj hgmpgrtcmefjtg prg`uhtevg pfrg tcmdeåj fquevcof c oc hurvc `f ogs ejarfsgs, hgjse`frcj`g quf fo Ejarfsg tgtco fs eauco co prfheg ujetcreg `fo prg`uhtg x hcjte`c` `f prg`uhtg. EP = ^y (U) Fo pujtg `fo ejtfrhfptg, rfprfsfjtc oc hcjte`c` `f prg`uhtg U gdtfje`c hucj`g oc hcjte`c` `f ejsumg R = >. C pcrter `f fstf pujtg, tg`g ejhrfmfjtg fj oc hcjte`c` `f ejsumg R prgvghc uj hcmdeg fj oc hcjte`c` `f prg`uhtg U. Co prejhepeg, fstf hcmdeg fs pgsetevg f ejtfjsg (iufrtf pfj`efjtf) pfrg co chfrhcrsf c oc hcjte`c` `f ejsumg csghec`c hgj oc prg`uhheøj mãxemc fsc ejtfjse`c` sf rf`uhf bcstc quf oofac uj pujtg fj quf oc pfj`efjtf ∉U/ ∉R = >. Fstf pujtg, `gj`f oc pfj`efjtf `f oc hurvc fs eauco c hfrg, hgrrfspgj`f co pujtg `f oc prg`uhheøj mãxemc. C pcrter `f ^mcx, fj oc hurvc `f oc iujheøj prg`uhheøj, tg`g hcmdeg fj oc hcjte`c` `f ejsumg R prgvghc ujc `esmejuheøj `fo prg`uhtg U . Hgmg oc hurvc `f oc iujheøj prg`uhheøj U fstã csghec`c hgj ogs ejhrfmfjtgs `f oc
hcjte`c` `f ejsumg R , sf fstcdofhf oc rfocheøj `erfhtc hgj fo ejhrfmfjtg `f ogs hgstgs quf vcrícj pgr oc cpoehcheøj `f ejsumgs. Fstgs hgstgs sgj ogs quf ejtfrfscj co
395
ejvfsteac`gr, co mgmfjtg `f fstcdofhfr ocs rfhgmfj`chegjfs `f ejsumgs R pcrc gdtfjfr uj prg`uhtg U. Fo Hgstg `f oc cpoehcheøj `f ejsumgs rfsuotc `f oc muotepoehcheøj `fo hgstg `fo ejsumg pgr oc hcjte`c` `fo ejsumg. H = Hx (R) Fo dfjfieheg jftg g uteoe`c` fs oc `eifrfjhec fjtrf fo ejarfsg tgtco y fo hgstg tgtco. DJ = EP ‘ H ^gr og tcjtg; DJ = ^y (U) - Hx (R) ^crc fo hãohuog `fo dfjfieheg jftg sf rfquefrf `fo prfheg `fo prg`uhtg (^y) y `f oc hcjte`c` `f prg`uhtg (U)< csí hgmg, `fo Hgstg `fo ejsumg (H x) y `f oc hcjte`c` `f ejsumgs (R). ^crc hcohuocr fo mãxemg dfjfieheg jftg pgsedof `f sfr gdtfje`g uscj`g uj ejsumg, sf rfquefrf `f ogs seauefjtfs `ctgs;
• • • •
Oc iujheøj prg`uhheøj g mg`fog mctfmãtehg c pcrter `f ogs `ctgs `f hcmpg, ocdgrctgreg g fjhufstcs. Fo prfheg prgmf`eg `f hc`c uje`c` `f prg`uhtg(^ y) fj fo mfrhc`g Fo hgstg `f hc`c uje`c` `fo ejsumg fj fo mfrhc`g (Hx) Oc rfocheøj fjtrf fo hgstg `fo ejsumg y prfheg `fo prg`uhtg H x /^y
Fo prghf`emefjtg `f gptemezcheøj fs fo seauefjtf;
• • • • • •
Hgjstruer fo mg`fog cprgpec`g `f oc iujheøj prg`uhheøj U= Ɣ(R) Hcohuocr oc premfrc `frevc`c `f oc iujheøj `(U)/`(R) = U° Oc premfrc `frevc`c eaucocr co vcogr `f oc rfocheøj (H x)/(^y); Tfsgovfr oc fhucheøj. @f fstf mg`g `f hcohuoc fo vcogr `f R^GF Tffmpoczcr fo vcogr R^GF fj oc iujheøj prg`uhheøj. @f fstc mcjfrc sf gdtefjf fo vcogr `f U^GF quf hgrrfspgj`f c oc prg`uhheøj øptemc fhgjømehc< fs `fher, co pujtg `gj`f sf gdtefjf fo mãxemg dfjfieheg fhgjømehg. Hgjghe`gs ogs vcogrfs `f R^GF y U^GF, sf hcohuoc fo mãxemg dfjfieheg jftg pgsedof, uscj`g oc iørmuoc; DJ = ^y (U^GF) - Hx (R^GF)
^TGDOFMC TFXVFOPG Hgj ogs seauefjtfs `ctgs `espgjedofs, hcohuocr fo mãxemg dfjfieheg jftg pgsedof `f sfr gdtfje`g c pcrter `f uj fxpfremfjtg `f ifrteoezcjtfs;
@ctgs
31>
• • • •
Iujheøj prg`uhheøj; T = 34,1 + 02,22 I ‘ 0,8064 I4 ^rfheg prgmf`eg `f hc`c uje`c` `f prg`uhtg; ^y = $4> Hgstg `f hc`c uje`c` `fo ejsumg; Hx = $2> Tfocheøj hgstg `fo ejsumg y prfheg `fo prg`uhtg; H x /^y =2>/4>= 0,>
Cjãoeses Oc iujheøj prg`uhheøj; T = 34,1 + 02,22 I ‘ 0,8064 I 4 Oc premfrc `frevc`c `f oc iujheøj; `(T)/`(I) = T°= 02,22 ‘ 4(0,8064) (I) T°= 02,22 ‘ 2,95 I Oc premfrc `frevc`c eaucoc`c c oc rfocheøj (H x)/(^y); T°= 022,22 ‘ 2,95 I = 0,> Tfsgovfr oc fhucheøj pcrc gdtfjfr fo vcogr `f R ^GF ≂ I^GF 02,22 ‘ 0,> = 2,95(I) I = 00,22/2,95 = 6,39 uje`c`fs `f ejsumg = I ^GF. Tffmpoczcr fo vcogr I^GF fj oc iujheøj prg`uhheøj pcrc gdtfjfr fo vcogr `f U^GF ≂ T^GF. T = 34,1 + 02,22 I ‘ 0,8064 I4 T^GF = 34,1 + 02,22 (6,39) ‘ 0,8064 (6,39) 4 T^GF = 305,48 uje`c`fs `f prg`uhtg Hgjghe`gs ogs vcogrfs `f R^GF y U^GF, hcohuocr fo mãxemg dfjfieheg jftg pgsedof; DJ = ^y(U^GF) - Hx(R^GF) DJ = 4>(305,48) ‘ 2> (6,39) = $4.613,2 Fo mãxemg dfjfieheg jftg puf`f sfr gdtfje`g uscj`g 6,39 uje`c`fs `fo ejsumg I hgj oc huco sf prg`uhfj 305,48 uje`c`fs `f prg`uhtg, `cj`g uj dfjfieheg jftg mãxemg pgsedof `f $4.613,2 ≂ $4.614.
TFOCHEØJ FJPTF ^TG@VHHEØJ U DFJFIEHEG JFPG Xefj`g oc iujheøj prg`uhheøj U= Ɣ(R) `f tepg huc`rãtehc, ogs vcogrfs `f U puf`fj sfr fstemc`gs c pcrter `f `eifrfjtfs vcogrfs `f R y ogs dfjfiehegs jftgs puf`fj fstemcrsf rfochegjcj`g R f U, hucj`g sf `espgjf `f ogs prfhegs ujetcregs `fo prg`uhtg y fo hgstg ujetcreg `f ogs ejsumgs.
Hefrtcmfjtf quf pcrc tfjfr ujc Umcx sf rfquefrf ujc hcjte`c` `f ejsumg Rmcx y pcrc tfjfr uj U^GF sf rfquefrf `f ujc hcjte`c` `f R^GF. Hgjghefj`g fo prfheg ujetcreg `fo
313
prg`uhtg ^y y fo hgstg `fo ejsumg H x, sf puf`f rfprfsfjtcr mctfmãtehc y arãiehcmfjtf fstcs rfochegjfs hgj ogs dfjfiehegs jftgs. ^gr fkfmpog, uscj`g oc iujheøj prg`uhheøj; T = 34,1 + 02,22 I ‘ 0,8064 I 4 @øj`f; IT==Hcjte`c` Hcjte`c``f `fuje`c`fs uje`c`fs`f `fejsumg prg`uhtg
Tfochegjfs fjtrf oc iujheøj prg`uhheøj y fo dfjfieheg jftg, mcjtfjefj`g hgjstcjtfs fo prfheg ujetcreg `fo prg`uhtg (^x) y fo hgstg `fo ejsumg (H x). Ifrteoezcjtf (I)
Tfj`emefjtg (T)
^rfheg `fo prg`uhtg prg`uh tg (^ )
Hgstg `fo ejsumg (Hx)
Dfjfieheg jftg (DJ)
> 3 4 8 0 6 6,39 6,94 9 1 2 5 3>
34,1 61,4 58,3 34>,4 382,1 302,6 305,4 36>,4 305,9 303,5 346,9 3>>,1 91,>
4> 4> 4> 4> 4> 4> 4> 4> 4> 4> 4> 4> 4>
2> 2> 2> 2> 2> 2> 2> 2> 2> 2> 2> 2> 2>
460 3.>96 3.1>4 4.396 4.060 4.695 4.614 4.660 4.633 4.415 3.218 3.458 60>
Fj fo hcsg `f vcrecr ogs prfhegs `fo prg`uhtg g `f ogs hgstgs `f ogs ejsumgs, sf trctc `f uj cjãoeses `f sfjsedeoe`c`88.
88
. Fj fstf `ghumfjtg jg sf trctcj ocs tåhjehcs `f cjãoeses fhgjømehg, sf oemetc c fxpoehcr ujc cpoehcheøj `fo cjãoeses `f rfarfseøj.
314
1. EJPTG@VHHEØJ C OC ^TGATCMC ^TGATCMCHEØJ HEØJ OEJFCO ·@F SVÅ PTCPC OC ^TGATCMCHEØJ OEJFCO7 Oc prgarcmcheøj oejfco 80 fs ujc tåhjehc mctfmãtehc quf pfrmetf bcoocr sgouhegjfs c prgdofmcs quf rfquefrfj `f gptemezcheøj, yc sfc mcxemezcj`g ogs dfjfiehegs g mejemezcj`g ogs hgstgs. Ocs cpoehchegjfs `f oc ^rgarcmcheøj oejfco sgj muy cmpoecs, fspfhecomfjtf fj oc pocjfcheøj `f oc prg`uhheøj, fj prfpcrcheøj `f `eftcs y mfzhocs `f mf`ehcmfjtgs, fj oc gptemezcheøj `fo trcjspgrtf, fj oc cseajcheøj iejcjhefrc, fj mfrhc`gtfhjec y fj gtrcs ãrfcs quf rfquefrc `f oc cseajcheøj `f rfhursgs oemetc`gs86. Fo prgpøsetg `f oc ^rgarcmcheøj Oejfco (^O) fs oc cseajcr ogs rfhursgs oemetc`gs `f oc mfkgr mcjfrc pgsedof (øptemc) y `f cyu`cr c oc fofhheøj `f chteve`c`fs quf hgmpetfj pgr rfhursgs fshcsgs. Oc pcocdrc prgarcmcheøj sf hgjhfptucoezc hgmg oc pocjfcheøj `f ocs chteve`c`fs pcrc gdtfjfr uj rfsuotc`g øptemg fjtrf uj hgjkujtg `f cotfrjctevcs `f sgouheøj. Fo c`kftevg oejfco seajeiehc quf tg`cs ocs iujhegjfs mctfmãtehcs `fo mg`fog `fdfr sfr iujhegjfs oejfcofs. Hucj`g sf trctc `f prgdofmcs `f mcxemezcheøj hgmg fs fo hcsg `f oc dûsquf`c `fo mãxemc prg`uhheøj, mãxemg dfjfieheg fhgjømehg, sf tefjf quf hgjstruer uj hgjkujtg `f fhuchegjfs g ejfhuchegjfs dcsc`cs fj ocs hgj`ehegjfs fspfhíiehcs `fo prgdofmc y rfsgovfrocs, hgjse`frcj`g quf sf dushc oc rfspufstc ‟mcygr fs mfkgr”. ^crc prgdofmcs `f mejemezcheøj, hgmg e`fjteiehcr ogs hgstgs míjemgs `f uj prghfsg prg`uhtevg, oc mfjgr ejhe`fjhec `f fjifrmf`c`fs, oc mfjgr hgjtcmejcheøj cmdefjtco pgsedof, fjtrf gtrcs, sf tefjf quf hgjstruer uj arupg `f fhuchegjfs g ejfhuchegjfs dcsc`cs fj ocs hgj`ehegjfs fspfhíiehcs `fo prgdofmc y rfsgovfrocs, hgjse`frcj`g quf oc rfspufstc dushc`c fs ‟mfjgr fs mfkgr”.
·HVÃOFX XGJ OGX PE^GX @F XGOVHEGJFX7 Ogs tepgs `f sgouhegjfs c ogs prgdofmcs `f prgarcmcheøj oejfco sf hocseiehcj fj; ichtedofs y jg ichtedofs. Fxestf ujc ‟sgouheøj ichtedof” hucj`g fo hgjkujtg `f vcogrfs, e`fjteiehc`cs hgmg rfspufstcs, sctesichfj ocs rfstrehhegjfs fo mg`fog. C`fmãs, puf`f bcdfr ujc sgouheøj ûjehc, ujc sgouheøj mûotepof g ujc sgouheøj sej oímetf pcrc oc iujheøj gdkftevg. Xf puf`f tfjfr ujc ‟sgouheøj jg ichtedof” hucj`g jg fxestf uj hgjkujtg `f vcogrfs hgmg rfspufstcs quf sctesicacj ocs rfstrehhegjfs g åstcs sgj ejhgjsestfjtfs g eoøaehcs.
·HVÃOFX XGJ OCX HGJ@EHEGJFX ^CTC VXCT ^TGATCMCHEØJ OEJFCO7 ^crc oc hgjstruhheøj `f mg`fogs `f prgarcmcheøj oejfco sf `fdf humpoer ocs seauefjtfs hgj`ehegjfs 89;
80 86
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• • •
Iujheøj gdkftevg ([); `fdf bcdfr uj gdkftevg hgjhrftg quf sf `fsfc rfsgovfr mf`ecjtf oc gptemezcheøj. Tfstrehhegjfs; sf `fdf pocjtfcr, `f chufr`g c ocs herhujstcjhecs fspfhíiehcs `fo prgdofmc, ocs gphegjfs `f `fheseøj `gj`f ujc `f foocs pgsedeoetcrã cohcjzcr fo gdkftevg `f gptemezcheøj. Oc iujheøj gdkftevg y ocs rfstrehhegjfs sgj oejfcofs, pgr og tcjtg, `fdfj uteoezcrsf fj fo mg`fog sgog fhuchegjfs oejfcofs g `fseauco`c`fs oejfcofs.
MÅPG@GX ^CTC TFXGOYFT ^TGDOFMCX @F ^TGATCMCHEØJ OEJFCO ·HVÃOFX XGJ OGX MÅPG@GX MÃX VXC@GX FJ OC ^TGATCMCHEØJ OEJFCO7 Ogs måtg`gs pcrc rfsgovfr uj prgdofmc `f prgarcmcheøj oejfco sgj; måtg`g cjcoítehg y måtg`g arãiehg. Fo `fjgmejc`g Måtg`g `fo Xempofx 81 fs uj måtg`g cjcoítehg quf sf dcsc fj uj prghf`emefjtg ejtfrctevg quf pfrmetf er mfkgrcj`g prgarfsevcmfjtf ocs rfspufstcs, bcstc fjhgjtrcr oc sgouheøj øptemc. ^crtefj`g `f oc iujheøj gdkftevg, sf `fiejf uj vårtehf hucoquefrc y sf dushc suhfsevcmfjtf gtrgs vårtehfs bcstc mfkgrcr fo cjtfregr. Fo måtg`g `f ogs vårtehfs g fsquejcs fs `f pcrtehuocr empgrtcjhec pcrc rfsgovfr prgdofmcs `f prgarcmcheøj oejfco hgj uj jûmfrg pfqufóg `f rfstrehhegjfs. Hucj`g fo jûmfrg `f vcrecdofs g `f rfstrehhegjfs cumfjtc, oc fifhteve`c` `fhrfhf hgj rcpe`fz. Hgmg fo jûmfrg `f vårtehfs fs iejetg sefmprf sf pg`rã fjhgjtrcr ujc sgouheøj rczgjcdof g ujc fxpoehcheøj rczgjcdof `f jg bcdfr sgouheøj. Oc prgpef`c` `fo måtg`g `fo sempofx sf dcsc fj quf se oc iujheøj gdkftevg ([) jg tgmc su vcogr mãxemg fj fo vårtehf C, fjtgjhfs bcy ujc crestc quf pcrtf `f C, c og ocrag `f oc huco [ cumfjtc. Fj oc sgouheøj arãiehc sf gdsfrvc quf oc sgouheøj øptemc fstã csghec`c sefmprf hgj uj pujtg fxtrfmg `fo fspcheg `f sgouhegjfs. Fo måtg`g sempofx fstã dcsc`g iuj`cmfjtcomfjtf fj fstf hgjhfptg.82
FO MG@FOG AFJFTCO @F OC ^TGATCMCHEØJ OEJFCO ·HVÃO FX FO MG@FOG AFJFTCO @F OC ^TGATCMCHEØJ OEJFCO7 Fo mg`fog afjfrco `f oc ^rgarcmcheøj oejfco 85 hgj iejfs `f gptemezcheøj fs fo seauefjtf; [= d3x3 + d4x4 +....+ djxj.
81. 82
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82
. Ogs prgarcmcs hgmputchegjcofs hgmg ^TGOEJ sf dcscj fj fo måtg`g `fo sempofx sempofx y fj oc arciehcheøj pcrc rfsgovfr prgdofmcs `f prgarcmcheøj oejfco. Fo prgarcmc Fxhfo tefjf ujc bfrrcmefjtc oocmc`c XGOYFT usc`c pcrc rfsgovfr fstf tepg `f prgdofmcs. 85 . @goo, K. & Grczfm, Grczfm, I. 3512. ^rg`uhtegj fh fhgjgmehs; gjgmehs; Pbfgry wetb cppoehctegjs. cppoehctegjs. Xfhgj` f`etegj. Kgbj Qeofy & Xgjs. Xejacpgrf. pp; 835-895
310
Fstf mg`fog afjfrco sf hgjghf hgmg Iujheøj gdkftevg. Fj ocs `eifrfjtfs chteve`c`fs prg`uhtevcs, oc iujheøj gdkftevg [ fstã sukftc c ujc g mãs rfstrehhegjfs; c33x3 + c34x4 +.....+ c3jxj ? d3 c43x3 + c44x4 +....+ c4jxj ? d4
cm3x3 + cm4x4 +....+ cmjxj ? dm Ogs vcogrfs `f ocs vcrecdofs jg puf`fj sfr jfactevcs, pgr og tcjtg; R3 ≦ >, R4 ≦ >, ……........, Rj ≦ > Ocs rfstrehhegjfs quf puf`f tfjfr ogs mg`fogs `f prgarcmcheøj oejfco sgj `f trfs tepgs; Tfstrehhegjfs `f fjtrc`cs.- Xgj oemetcjtfs c hcusc `f oc fshcsfz `f mctfrecs premcs, ejsumgs, mcjg `f gdrc u gtrgs rfhursgs. Tfstrehhegjfs `f hcoe`c`.hcoe `c`.- Xgj cqufoocs quf oemetcj ocs mfzhocs `f ogs ejarf`efjtfs yc sfc fj `eftcs g fj mf`ehcmfjtgs, fj iujheøj `f ocs rfhgmfj`chegjfs g prfshrephegjfs. Tfstrehhegjfs `f dcocjhf `f mctfrecofs.- Xgj cqufoocs quf `fiejfj ocs scoe`cs `f uj prghfsg fj iujheøj `f ocs fjtrc`cs, hgjse`frcj`g afjfrcomfjtf fo rfj`emefjtg g uj pgrhfjtckf `f `fspfr`eheg.
XV^GXEHEGJFX @FO MG@FOG @F ^TGATCMCHEØJ OEJFCO ·HVÃOFX XGJ OCX XV^GXEHEGJFX @FO MG@FOG ^O7 Vj mg`fog `f ^rgarcmcheøj Oejfco sf dcsc fj ogs supufstgs `f prgpgrhegjcoe`c`, c`eteve`c` y `evesedeoe`c`. ^rgpgrhegjcoe`c `.- Ocs chteve`c`fs sf puf`fj rfprfsfjtcr mf`ecjtf mg`fogs oejfcofs ^rgpgrhegjcoe`c`.`f ocs iujhegjfs `f prg`uhheøj. Fstg empoehc csumer rftgrjgs hgjstcjtfs c fshcoc. ^gr hgjseauefjtf, fo usg `f rfhursgs pgr pcrtf `f ujc chteve`c` fs prgpgrhegjco co jevfo `f oc chteve`c`. C`eteve`c`.- Fo usg tgtco `f rfhursgs fs oc sumc `f ogs rfhursgs pcrhecofs usc`gs pgr ocs chteve`c`fs ej`eve`ucofs. Fo vcogr `f oc iujheøj gdkftevg fs oc sumc `f ocs hgjtreduhegjfs `f ocs chteve`c`fs ej`eve`ucofs. Oc hgjtreduheøj `f ujc vcrecdof c oc iujheøj gdkftevg g co usg `f rfhursgs fs ej`fpfj`efjtf `f ogs vcogrfs quf sf cseajfj c gtrcs vcrecdofs `f `fheseøj. @evesedeoe`c`.- Fj fo prghfsg `f cseajcheøj `f rfhursgs fs pgsedof quf ocs vcrecdofs
@evesedeoe`c`. Fj fo prghfsg `f cseajcheøj `f rfhursgs fs pgsedof quf ocs vcrecdofs tgmfj vcogrfs jg fjtfrgs.
316
^TGDOFMC TFXVFOPG Vjc fmprfsc ej`ustreco puf`f prg`uher `gs tepgs `f prg`uhtgs, M y J, `f cotc `fmcj`c, fj sus mcquejcrecs C y D. ·Huão fs oc hgmdejcheøj øptemc `f prg`uhtgs M y J c sfr prg`uhe`cs fj ocs mcquejcrecs C y D pcrc gdtfjfr oc mãxemc uteoe`c` fhgjømehc pgr `íc `f trcdckg7.
@ctgs Mcquejcrecs
^rg`uhtg M
^rg`uhtg J
Oemetcheøj `f oc mãquejc; (Mãxemg `f bgrcs `f trcdckg)
C
3 bgrc/uje`c`
0 bgrcs/uje`c`
39 bgrcs/`íc
D
8 bgrcs/uje`c`
4 bgrcs/uje`c`
32 bgrcs/`íc
Vteoe`c` pgr uje`c` `f prg`uhtg
VX$ 46>
VX$ 86>
Cjãoeses Iujheøj gdkftevg ([) = Ɣ(M, J) J) = Vteoe`c` mãxemc pgr `íc `f trcdckg; [ = 46> M + 86> J Tfstrehhegjfs; M + 0 J ≠ 39 8 M + 4 J ≠ 32 M:> J:>
^crc mcquejcrec C ^crc mcquejcrec D
Xgouheøj
M ≠ 39 ‘ 0J 8(39-0J) + 4J ≠ 32 02 ‘ 34J + 4J ≠ 32 -3>J ≠ -8> J = 8>/3> = 8
Tffmpoczcj`g J = 8 fj oc ejfhucheøj; M + 0J ≠ 39 M + 0(8) ≠ 39 M = 39 -34 = 0
Ogs vcogrfs `f J = 8 y M = 0, sf rffmpoczcj fj oc iujheøj gdkftevg; [ = 46> M + 86> J [ = (46>)(0) + 86> (8) = VX$ 4.>6>/`íc Oc mãxemc uteoe`c` pgr `íc `f trcdckg pgsedof `f sfr gdtfje`c fs `f $4.>6>/`íc prg`uhefj`g J = 8 uje`c`fs/`íc y M = 0 uje`c`fs/`íc.
Måtg`g arãiehg Iujheøj gdkftevg ([) = Vteoe`c` mãxemc pgr `íc `f trcdckg;
319
[ = 46> M + 86> J Tfstrehhegjfs (mãxemg `f bgrcs trcdckg/`íc `f ocs mcquejcrecs); M + 0 J ≠ 39 8 M + 4 J ≠ 32 M:> J:>
^crc mcquejcrec C ^crc mcquejcrec D
Hgj fstc ejigrmcheøj sf prghf`f c hcohuocr oc pgseheøj `f ogs pujtgs y `f ocs oíjfcs fj fo pocjg hcrtfsecjg; ^crc oc mãquejc C; M + 0 J ≠ 39 39
Xe M = >
Xe J = >
> + 0J = 39 J = 39/0 = 0
M + 0(>) = 39 M = 39
^ujtg C(>, 0)
^ujtg D(39, >)
^crc oc mcquejcrec D; 8 M + 4 J ≠ 32 32
Xe M = >
Xe J = >
8(>) + 4 J = 32 4J = 32
8 M + 4 (>) = 32 8 M = 32
J = 32/4 = 5
M = 32/8 = 9 ^ujtg @(9,>)
^ujtg H(>, 5)
Fj fo pocjg hcrtfsecjg (M, J), sf hgoghcj ogs pujtgs; (>, 0) y (39, >)< y, (>, 5) y (9, >). Oufag sf ujfj `ehbgs pujtgs hgj oíjfcs rfhtcs. Fo trczc`g `f fstcs `gs oíjfcs sfócoc uj jufvg pujtg fj fo pocjg hcrtfsecjg; ^ujtg F(0, 8). J 3> 8 M + 4 J ≠ 32 32
(>,5)
2
9
M + 0 J ≠ 39 39
0
(>,0)
(0,8)
4
(39,>)
(9,>) 4
0
9
2
3>
34
30
39
M
Xgouheøj arãiehc
311
@fheseøj
Fj oc mcquejcrec C sf `fdf prg`uher 0 uje`c`fs/`íc y fj oc mcquejcrec D sf `fdf prg`uher 8 uje`c`fs/`í uje`c`fs/`íc. c. Hgj fstc cseajcheøj sf puf`f gdtfjfr fo mãxemg dfjfieheg fhgjømehg/`íc `f trcdckg, quf fs `f VX$4.>6>/`íc.
^TGDOFMC TFXVFOPG Vjc pfrsgjc `fsfc ejvfrter 4> meo `øocrfs fj oc hgmprc `f chhegjfs R f U . Fj ocs chhegjfs R, cujquf `f mcygr refsag, of girfhfj fo 3>% `f ejtfrås cjuco. Fj ocs chhegjfs U of csfaurcj fo 1% `f ejtfrås cjuco. Fo tgmø oc `fheseøj `f ejvfrter mãxemg 34 meo `øocrfs fj chhegjfs R y míjemg 6 meo `øocrfs fj chhegjfs U. ·Hømg `fdf ejvfrter pcrc tfjfr oc mãxemc uteoe`c`7.
@ctgs
Chhegjfs
R U
Ejtfrås cjuco >,3> >,>1
Tfstrehhegjfs (fj meofs VX$) R ≠ 34 R ≦ U, R ≦ > U ≦ 6 U ≦ > R + U ≠ 4>
Cjãoeses Iujheøj gdkftevg; Ɣ(R, U) = [ = >,3> R + >,>1 U Tfstrehhegjfs (fj meofs VX$); R + U ≠ 4> R ≠ 34< U ≦ 6 R ≦ U, R ≦ >< U ≦ >< Fj fstf hcsg sf rfquefrf fxpogrcr uj hgjkujtg `f sgouhegjfs ichtedofs pcrc; R + U ≠ 4> Hucj`g R = > > + U = 4> U = 4> Hucj`g U = > R + > = 4> R = 4>
^ujtg C(>, 4>)
^ujtg D(4>, >)
Hucj`g R U R + R = 4> 4R = 4> R = 4>/4 = 3>
^ujtg H(3>, 3>)
312
U = 3>
Hucj`g R = 6 6 + U = 4> U = 4> ‘ 6= 36 Hucj`g R = 34 34 + U = 4> U = 4> ‘ 34 = 2 Hucj`g U = 6 R + 6 = 4> R = 4> ‘ 6 = 36
^ujtg @(6, 36)
^ujtg F(34, 2)
^ujtg I(36, 6)
Tffmpoczcj`g ogs vcogrfs R f U fj oc iujheøj gdkftevg; [ = >.3> R + >,>1 U Ɣ(C) = >,3> (>) + >,>1 (4>) Ɣ(D) = >,3> (4>) + >,>1 (>) Ɣ(H) = >,3> (3>) + >,>1 (3>) Ɣ(@) = >,3> (6) + >,>1 (36) Ɣ(F) = >,3> (34) + >,>1 (2) Ɣ(I) = >,3> (36) + >,>1 (6)
= 3,0> meo = $3.0>>/cóg = 4,>> meo; Jg cpoehc pgr rfstrehheøj R ≠ 34 = 3,1> meo = $3.1>>/cóg = 3,66 meo = $3.66>/cóg = 3,19 meo = $3,19>/cóg = 3,26 meo; Jg cpoehc pgr rfstrehheøj R ≠ 34
^gr og tcjtg, oc sgouheøj quf pfrmetf gdtfjfr ogs mcygrfs ejtfrfsfs/cóg, hgj oc ejvfrseøj `f 4> meo `øocrfs, fs; Ɣ(F) = >,3> (34) + >,>1 (2)
= 3,19 meo = $3.19>/cóg
Oc rfprfsfjtcheøj arãiehc `f ocs sgouhegjfs ichtedofs sf ej`ehc c hgjtejucheøj;
) s f o e m j f ( U j ø e s r f v j E
(34, 2)
Ejvfrseøj R (fj meofs)
@fheseøj
315
Xf `fdfj ejvfrter 34 meo `øocrfs fj ocs chhegjfs R mãs 2 meo `øocrfs fj ocs chhegjfs U pcrc tfjfr ogs mcygrfs ejtfrfsfs cjucofs, quf sf hcohuoc fj VX$3.19>, hgjse`frcj`g ocs rfstrehhegjfs fspfheiehc`cs fj fo prgdofmc `f prgarcmcheøj oejfco.
^TGDOFMC TFXVFOPG Vjc pfrsgjc tefjf `fiehefjhec `f befrrg y vetcmejc D. Fo jutrehegjestc of rfhgmefj`c ejafrer co mfjgs 8.>>> ma `f befrrg, 3.5>> ma `f vetcmejc D 3 y 3.6>> ma `f vetcmejc D4, fj hefrtg tefmpg. Fj fo mfrhc`g fxestfj `gs pío`grcs `f vetcmejcs `espgjedofs, `f ocs mcrhcs C y D. Hc`c pío`grc `f oc mcrhc C hgjtefjf 8> ma `f befrrg, 3> ma `f vetcmejc D 3 y 6 ma `f oc vetcmejc D4 y hufstc 0 hfjtcvgs. Hc`c pío`grc `f oc mcrhc D hgjtefjf 3> ma `f befrrg, 36 ma `f D3 y 36 ma `f D4 y hufstc 2 hfjtcvgs. ·Huão fs oc hgmdejcheøj `f pío`grcs quf `fdf hgmprcr pcrc hudrer ogs rfqufremefjtgs `fo befrrg y `f ocs vetcmejcs D3 y D4 hgj fo míjemg hgstg7
@ctgs ^ío`grc mcrhc C (x) Befrrg Yetcmejc D3 Yetcmejc D4 Hgstg ujetcreg ($)
^ío`grc mcrhc D (y)
Tfqufremefjtgs míjemgs
3> ma 36 ma 36 ma 2 hfjtcvgs
8.>>> ma 3.5>> ma 3.6>> ma
8> ma 3> ma 6 ma 0 hfjtcvgs
^rfshrepheøj (ma) Befrrg 8,>>> D3 3,5>> D4 3,6>>
Cjãoeses Iujheøj gdkftevg; [ = 0x + 2y. Fo prgdofmc hgjsestf fj mejemezcr ogs hgstgs. Tfstrehhegjfs; ^crc fo befrrg; ^crc oc vetcmejc D3; ^crc oc vetcmejc D4; x ≦ >< y ≦ >
8>x + 3>y ≦ 8.>>> 3>x + 36y ≦ 3.5>> 6x + 36y ≦ 3.6>>
^crc fo befrrg; 8>x + 3>y ≦ 8.>>> Xe x = >
Xe y = >
8>(>) + 3>(y) ≦8.>>> 3>y≦8.>>> y =8.>>>/3> = 8>>
8>x + 3>(>) ≦8.>>> 8>x ≦8.>>> x = 8.>>>/8> = 3>>
^ujtg C(>, 8>>)
^ujtg D(3>>, >) 32>
^crc oc vetcmejc D3; 3>x + 36y ≦ 3.5>> Xe y = >
Xe x = > 3>(>) + 36(y) ≦ 3.5>> 36y≦3.5>> y = 3.5>>/36 = 341
3>(x) + 36(>) ≦3.5>> 3>x ≦ 3.5>> x = 3.5>>/3> = 35> ^ujtg @(35>, >)
^ujtg H(>,341)
^crc oc vetcmejc D4; 6x + 36y ≦ 3.6>> Xe x = >
Xe y = >
6(>) + 36(y) ≦ 3.6>> 36y ≦ 3.6>> y = 3.6>>/36 = 3>>
6(x) + 36(>) ≦ 3.6>> 6x ≦ 3.6>> x = 3.6>>/6 = 8>>
^ujtg F(>,3>>)
^ujtg I(8>>,>)
Tffmpoczcj`g ogs vcogrfs x, y fj oc iujheøj gdkftevg; [ = 0x + 2y Ɣ(C) = 0(>) + 2(8>>) Ɣ(D) = 0(3>>) + 2(>) Ɣ(H) = 0(>) + 2(341) Ɣ(@) = 0(35>) + 2(>) Ɣ(F) = 0(>) + 2(3>>) Ɣ(I) = 0(8>>) + 2(>)
= 4.0>> hfjtcvgs Jg cpoehc pgr rfstrehheøj = 0>> hfjtcvgs Jg cpoehc pgr rfstrehheøj = 3.>39 hfjtcvgs Jg cpoehc pgr rfstrehheøj = 19> hfjtcvgs Jg cpoehc pgr rfstrehheøj = 2>> hfjtcvgs Jg cpoehc pgr rfstrehheøj = 3.4>> hfjtcvgs Jg cpoehc pgr rfstrehheøj
Fj fstf hcsg, sf dushc oc gptemezcheøj semuotãjfc `f trfs ‟ejsumgs”, sf cprgxemc c oc crestc mãs cprgpec`c quf hgrrfspgj`f co pujtg (2>, 10). D c h r c m c o f ` s c r g ` o í ^
(2>, 10)
^ío`grcs `f oc mcrhc C Tffmpoczcj`g ogs vcogrfs `fo pujtg (2>, 10) fj oc iujheøj gdkftevg [ = 0x+2y
323
0(2>)+2(10) = 534 hfjtcvgs ≂ VX$5,34 ^gr og tcjtg, fo hgstg míjemg pcrc humpoer oc prfshrepheøj `f befrrg y vetcmejcs D 3y D4 fs `f VX$5,34. VX$5,34. Oc hcjte`c` fj meoearcmgs, `f oc hgmdejcheøj `f ocs pío`grcs `f ocs mcrhcs C y D sf ej`ehcj c hgjtejucheøj
Befrrg D3 D4
^ío`grcs C
^ío`grcs D
2> 4,0>> 2>> 0>>
10 10> 3,33> 3,33>
Pgtco 8,30> 3,53> 3,63>
@fheseøj Hgmdejcr fo hgjsumg `f 2> pío`grcs `f oc mcrhc C y 10 pío`grcs `f oc mcrhc D (ocs `gs hgjtefjfj befrrg y vetcmejcs D3 y D4) pcrc sctesichfr pofjcmfjtf ocs prfshrepheøj.
^TGDOFMC TFXVFOPG Vj carehuotgr pgsff 8> bfhtãrfcs `f tefrrc cptc pcrc huotevgs `f mcíz g crrgz. Pefjf hgmprgmfte`g, mf`ecjtf hgjtrctg oc vfjtc `f 3.6>> quejtcofs `f mcíz c uj prfheg `f VX$36/quejtco. Hucoquefr prg`uhheøj c`ehegjco tefjf oc pgsedeoe`c` `f vfj`frog co mesmg prfheg. ^rgyfhtc tfjfr uj prgmf`eg `f 346 quejtcofs/bfhtãrfc `f mcíz, pgr og quf rfquefrf `f`ehcr pgr og mfjgs 34 bfhtãrfcs c fstf huotevg hgj ujc ejvfrseøj tgtco fstemc`c `f VX$1.4>> fj fo hehog. Fj ocs 32 bfhtãrfcs rfstcjtfs pocjfc sfmdrcr crrgz g mcíz. Fo hgstg pgr bfhtãrfc `fo crrgz fs `f VX$3.3>>/bfhtãrfc pcrc tfjfr rfj`emefjtgs `f 26 quejtcofs/bfhtãrfc quf pg`ríc vfj`frsf c VX$42/quejtco. ·Suå of rfhgmefj`c sfmdrcr pcrc tfjfr oc mcygr uteoe`c` pgsedof7.
@ctgs Huotevg
Hgstgs/bc
Tfj`emefjtg
^rfheg vfjtc
Dfjfieheg jftg/bc
Tfstrehheøj 34 bfhtãrfcs hgjtrctc`cs
Mcíz
9>>
346
36
3,416
Crrgz
3,3>>
26 Xupfriehef tgtco =
42
3,42>
Cjãoeses
8>
Iujheøj gdkftevg [ = 3.416 R + 3.42> U Tfstrehhegjfs R ≦34
324
R + y = 8>
^crc R +y = 8> R=> U = 8>
Jg cpoehc pgr rfstrehheøj
U= > R = 8> Xe R = 34 34 + y = 8> U = 32
) s c f r ã t h fTffmpoczcj`g o b ( z g r r c f ` f e h e i r fOgs vcogrfs R = p u X
(34, 32)
34 f U = 32 sf rfmpoczcj fj oc iujheøj gdkftevg;
[ = 3.416 R + 3.42> U [ = 3.416 (34) + 3.42> (32) [ = VX$ 82.80> uteoe`c` mãxemc
Xupfriehef `f mcíz (bfhtãrfcs)
@fheseøj ^crc gdtfjfr oc uteoe`c` mãxemc fo carehuotgr `fdf sfmdrcr 34 bfhtãrfcs `f mcíz (hgmprgmfte`gs mf`ecjtf hgjtrctg) y 32 bfhtãrfcs `f crrgz pcrc gdtfjfr oc uteoe`c` mãxemc hcohuoc`c fj 82.80> `øocrfs/hehog `f huotevg.
