Construcción de concentradores reflectores solares

7/23/2019 Construccin de concentradores reflectores solares

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KW&- BIOCBTIZCR DC BIFBCFTZABKF

DC @CDKA TC@]CZATSZAltt}5))okjzir&zcdrasbc&fct)

KW&1&- KFTZIDSBBKF

]aza bifrtzskz bifbcftzadizcr zcgocbtizcr cr fcbcrazki c`}ocaz rs}czgkbkcr }tkbar dc nzafdcr dk-

`cfrkifcr& Oir rkrtcàr dk}tzkbir/ ocftcr dc bzkrtao/ fi rc stkokuaf a basra dc rs gzankokdad/ }cri { }zc-

bki& Rkf c`jazni c|krtcf biocbtizcr bifrtktskdir }iz sf nzaf f`czi dc }zkràr dc bzkrtao dc zcgoc|kf

titao dc }cqsci cr}criz/ ,rkrtcàr batadk}tzkbir+/ bif sf gabtiz dc zcgoc|kf dco ;3#8 oa zcgocbtkwkdad

noijao cr dco izdcf dco ;=#/ rs}czkiz a oa dc oir `ceizcr cr}ceir { fi c|}czk`cftaf dcnzadabkf bif co

}ari dco tkc`}i&Oir biocbtizcr dc bifbcftzabkf stkokuaf rkrtcàr }tkbir zcgocbtizcr { cf aonsfir barir `s{ }aztk-

bsoazcr/ zcgzabtizcr/ }aza as`cftaz oa kftcfrkdad dc oa zadkabkf rioaz qsc rc dkzknc rijzc sfa rs}czgkbkc

zcbc}tiza qsc oa ajrizjc/ ,ocftcr Gzcrfco { ocftcr dc oqskdi+&

Biftza à{iz rca co gosei rioaz rijzc crta rs}czgkbkc/ `cfiz rcz oa uifa fcbcrazka }aza bifrcnskz co

`krì cgcbti tz`kbi rijzc sf goskdi/ oi qsc rs}ifc sfa zcdsbbkf dc oar }zdkdar tz`kbar&

Rkf c`jazni a}azcbcf itzir tk}ir dc }zdkdar biì rif co qsc crtir biocbtizcr gsfbkifaf fkba`cf-

tc bif oa bi`}ifcftc dkzcbta dc oa zadkabkf/ ,fi rc a}ziwcbla oa dkgsra+ { qsc a}azcbcf }zdkdar }tk-

bar }iz dcgcbtir dc cfgiqsc { dkzcbbkf8 ark`krì a}azcbcf itzir }zijocàr/ biì5

a+ Sfa à{iz bi`}okbabkf dc oar bazabtczrtkbar }tkbar dc oir bifbcftzadizcr/ }iz bsafti }zcbkraf dcrkrtcàr dc izkcftabkf { rcnsk kcfti dco Rio/ qsc }cz`ktcf a}ziwcblaz ao `|kì oa zadkabkf rioaz kf-

bkdcftc&

j+ Oa c|krtcfbka dc goseir fi crtabkifazkir cf oir goskdir qsc bkzbsoaf }iz co zcbc}tiz&

b+ Nzafdcr wazkabkifcr tafti cf oa gizà { dkrci/ biì cf oar tc`}czatszar { }zdkdar tz`kbar dc oar

rs}czgkbkcr zcbc}tizar ajrizjcftcr& Oa a`}oka naà dc bifgknszabkifcr }cz ktcf oa àfk}soabkf dc sfa

rczkc dc fscwir }az`ctzir dc dkrci&

d+ Sfa à{iz bi`}ocekdad bif oa kftzidsbbkf dc gabtizcr }tkbir adkbkifaocr/ qsc bi`}okbaf oir ja-

oafbcr cfczntkbir&

c+ Sfa à{iz baokdad cf oir rkrtcàr }tkbir/ {a qsc tkcfcf qsc tzajaeaz dszaftc oaznir }czidir dctkc`}i/ oi qsc k`}okba co qsc dcjcf àftcfcz kfaotczajocr rsr }zi}kcdadcr }tkbar biftza oa rsbkcdad/ czi-

rkf/ i|kdabkf/ bifdkbkifcr bok`tkbar/ ctb&

Tidi rti rs}ifc sf à{iz birtc dco biocbtiz oi qsc kftzidsbc aonsfar zcrtzkbbkifcr cf rs stkokuabkf/

KW&-7>


2/29

asfqsc oa a}okbabkf dc fscwir àtczkaocr zcgocbtaftcr { `ceizar cf oir rkrtcàr dc rcnsk`kcfti/ ocr

bifgkczcf sfa bkczta k`}iztafbka }zbtkba& Oa kftcfrkdad dc oa zadkabkf cf oar rs}czgkbkcr zcbc}tizar

}scdc oocnaz a rcz dco izdcf dc 4 a 1=== wcbcr co waoiz dc K= oi qsc }scdc k`}okbaz tc`}czatszar zcoatkwa-

`cftc cocwadar { sfa à{iz }zcbkrkf cf oir `cbafkrìr dc rcnsk`kcfti dco Rio { cfgiqsc cf oa rs}cz-

gkbkc zcbc}tiza/ oi qsc cfbazcbc co cqsk}i&Sf biocbtiz zcgocbtiz dc `cdka tc`}czatsza rc bi`}ifc dc dir }aztcr gsfda`cftaocr/ co bifbcftza-

diz { co zcbc}tiz& Co bifbcftzadiz cr oa }aztc dco biocbtiz qsc zcgocea ,i zcgzabta+ oa zadkabkf rioaz kfbk-

dcftc rijzc co `krì/ dkzknkfdioa labka co zcbc}tiz/ qsc oa ajrizjc { tzafr`ktc a sf goskdi tz`kbi qsc

bkzbsoa }iz co `krì&

Ao rcz co Rio oa gscftc dc cfczna/ cr `s{ k`}iztaftc bifibcz oa kàncf dco krì zcgoceada rijzc co

zcbc}tiz& Co fnsoi bif co qsc co Rio rc wc dcrdc oa Tkczza cr dc a}zi|kàda`cftc 2: { crtc dati la{ qsc

tcfczoc }zcrcftc/ ,a}aztc dc itzir }zi}kir ìtkwadir }iz czzizcr dc rcnsk`kcfti { zcgoc|kf/ ar biì dc

oa dkr}czrkf dc oa zadkabkf }iz oa rs}czgkbkc zcgocbtiza izknkfadir }iz dcgcbtir dc gajzkbabkf/ ctb+/ a oa

liza dc dkrcaz co dk`cfrkifa`kcfti/ tafti dco bifbcftzadiz/ biì dco zcbc}tiz&

KW&:&- TK]IR DC BIFBCFTZADIZCR

C|krtc sfa a`}oka wazkcdad dc `cdkir qsc }cz`ktcf as`cftaz co gosei dc oa zadkabkf rioaz rijzc sf

zcbc}tiz }sdkfdirc boarkgkbaz tcfkcfdi cf bscfta sfa rczkc dc gabtizcr/ biì5

a+ Co qsc rcaf ocftcr i zcgocbtizcr

j+ ]iz co rkrtcà dc ìftaec { ìdcoi dc izkcftabkf

b+ ]iz oa anfktsd dc oa bifbcftzabkf dc zadkabkf qsc rif ba}abcr dc bifrcnskz

d+ ]iz oir àtczkaocr stkokuadir cf rs bifrtzsbbkf

c+ ]iz oir goskdir tz`kbir qsc rc waf a stkokuaz qsc dc}cfdcf dc rsr a}okbabkifcr/ ctb&

Sfa bazabtczrtkba gsfda`cftao dc crtir biocbtizcr cr co ooaàdi fdkbc dc bifbcftzabkfAa)Az/ qsc

cr oa zcoabkf cftzc co zca dc oa rs}czgkbkc dc ajcztsza dco bifbcftzadiz { co zca dc oa rs}czgkbkc zcbc}-

tiza& Cf oar Gkn KW&1 rc `scrtzaf tzcr rcbbkifcr dc rkrtcàr dc biocbtizcr dc bifbcftzabkf8 cf bsao-

qskcza dc cooir rc cfgiba oa zadkabkf bif `r i `cfir fktkdcu rijzc sf zcbc}tiz qsc }scdc rcz }sftsao i

tcfcz sfa nci`ctza dctcz`kfada }iz oar bazabtczrtkbar dco bifbcftzadiz8 co fdkbc dc bifbcftzabkf

}aza biocbtizcr dc zcwiosbkf cr `sbli à{iz qsc }aza biocbtizcr bkofdzkbir&

- Zcbc}tiz }oafi { bifbcftzadiz-zcgocbtiz }oafi&- Tkcfc sf jaei fdkbc dc bifbcftzabkf/ kfgczkiz a 48 rc

a}ziwcbla cf co zcbc}tiz }aztc dc oa bi`}ifcftc rioaz dkgsra kfbkdcftc rijzc co biocbtiz&- Zcbc}tiz bkofdzkbi { bifbcftzadiz-zcgocbtiz bfkbi&- Rc `ceizaf oar bazabtczrtkbar dc bifbcftzabkf

dco bari aftczkiz

-Zcbc}tiz bkofdzkbi { bifbcftzadiz-zcgocbtiz crgzkbi&- Rc `ceizaf oar bazabtczrtkbar dc bifbcftza-

bkf dc oir barir aftczkizcr

Bifbcftzadiz-zcgocbtiz tk}i }azajioikdc dc zcwiosbkf&- ]cz`ktc ijtcfcz zcoabkifcr dc bifbcftzabkf

`s{ cocwadar/ oi qsc a rs wcu k`}okba cocwadar tc`}czatszar8 sfa ìdkgkbabkf dco `krì kftzidsbc sf

rcnsfdi zcgocbtiz qsc }cz`ktc oocwaz ao gibi a itza }irkbkf `r bifwcfkcftc&

Biocbtiz bif bifbcftzadiz-zcgocbtiz bkofdzkbi }azajokbi { zcbc}tiz tsjsoaz&- Cr co ìdcoi `r sradi {

cf co qsc co tsji zcbc}tiz rc cfbscftza a oi oazni dc tidar oar }irkbkifcr gibaocr& Oa tc`}czatsza aobaf-uada cf co `krì }scdc oocnaz a rcz dco izdcf dc oir 2==B/ rsgkbkcftc }aza `sblar a}okbabkifcr& Cf oa

Gkn KW&:&a rc zc}zcrcfta sf bifbcftzadiz bkofdzkbi }azajokbi/ { cf oa Gkn KW&:&j sf bifbcftzadiz bkof-

dzkbi }azajokbi bif zcgocbtiz rcbsfdazki&

KW&-7


3/29

a+ Zcbc}tiz }oafiBifbcftzadiz }oafi

j+ Zcbc}tiz bkofdzkbiBifbcftzadiz tzifbibfkbi

b+ Bifbcftzadiz }azajioikdcdc zcwiosbkf

d+ Bifbcftzadiz crgzkbi gkei { zcbc}tiz `wko/ RZTA

c+ Zcbc}tiz { bifbcftzadiz tzifbibfkbir

Gkn KW&1&- Aonsfar bifgknszabkifcr dc rkrtc`ar dc bifbcftzabkf

a+ Bifbcftzadiz b&}& ncfczao j+ Bifbcftzadiz b&}& bif zcgocbtiz rcbsfdazki

Gkn KW&:&- Bifbcftzadizcr bkofdzkbi-}azajokbir

a+ Zcgocbtiz Gzcrfco j+ Zcgzabtiz Gzcrfco

Gkn KW&2&- Bifbcftzadizcr Gzcrfco

KW&-7;


4/29

Bifbcftzadiz dc zcgoc|kf Gzcrfco { bifbcftzadiz zcgzabtiz Gzcrfco&- Cf co zcgocbtiz Gzcrfco/ Gkn KW&2&a/

oar rs}czgkbkcr }scdcf rcz }oafar i bszwar/ crtafdi dkrcada bada sfa }aza zcgoceaz kfdkwkdsao`cftc oa

zadkabkf rijzc co zcbc}tiz8 rs nzaf wcftaea zadkba cf rs gabkokdad dc bifrtzsbbkf/ rkcfdi `s{ kftczc-

raftc rs stkokuabkf cf biocbtizcr rioazcr dc nzaf }itcfbka { aota tc`}czatsza&

Co zcgzabtiz Gzcrfco stkokua sf rkrtcà dc bifbcftzabkf }azcbkdi a sf ìftaec dc ocftcr bif sf }sf-ti gibao fkbi/ Gkn KW&2&j

KW&2&- FNSOI DC KFBKDCFBKA GIZ@ADI ]IZ OIR WCBTIZCR f { r

Sf gabtiz a tcfcz cf bscfta cr oa izkcftabkf dco biocbtiz { co `cbafkrì a}zi}kadi qsc }cz`kta la-

bcz sf rcnsk`kcfti oi `r }zcbkri }irkjoc dco ìwk`kcfti a}azcftc dco Rio/ oi qsc k`}okba cf oa à{iza

dc oir barir tcfcz qsc labcz sri dc `r dc sf rkrtcà dc ìwk`kcfti&

Ar/ sf bifbcftzadiz bkofdzkbi }azajokbi tkcfc qsc tcfcz sf `cbafkrì dc rcnsk`kcfti dco Rio qsc

}cz`kta qsc rs wcbtiz sfktazkiz

f fizào a oa rs}czgkbkc dc ajcztsza { co wcbtiz sfktazki rioazz

r / bifgiz-

`cf sf }oafi qsc bikfbkda bif co }oafi gibao qsc a rs wcu rca }oafi dc rk`ctza dco bifbcftzadiz { qsc}iz oi tafti biftcfna ao zcbc}tiz8 bif crtc ìftaec cr }irkjoc ijtcfcz nkzir dco biocbtiz aozcdcdiz dc sf

roi cec dc nkzi qsc }scdc rcz sf ìftaec ,Fiztc-Rsz+/ ,Crtc-Icrtc+/ i kfbokfadi { }azaocoi ao cec dc oa tkc-

zza/ bif wcoibkdad dc nkzi dc 13 }iz liza&

Rkf c`jazni/ co rcnsk`kcfti }czgcbti dco Rio rc bifrcnskz bsafdi oir wcbtizcrz

f {z

r bikfbkdaf/ {a

qsc cf crar bkzbsfrtafbkar/ oa rs}czgkbkc dc ajcztsza dco biocbtiz rcz fizào a oir za{ir rioazcr kfbk-

dcftcr8 crtc ìftaec zcqskczc oa bi`}irkbkf dc dir ìwk`kcftir i nkzir rijzc dir cecr bi`jkfabkf dc

oir bktadir aftczkiz`cftc/ qsc rc bifibc biìAot-abk`st8 co ìwk`kcfti rc zcaokua `cdkaftc nkzir aozc-

dcdiz dc sf cec wcztkbao { itzi lizkuiftao/ c|krtkcfdi itzir tk}ir dc ìwk`kcftir zcoatkwir/ }czi rkc`}zc/

co wcbtiz sfktazki fizàoz

f ao }oafi dc ajcztsza/ tkcfc qsc bikfbkdkz bif oa dkzcbbkf dc oir za{ir rioazcrkfbkdcftcr dcgkfkda }iz co wcbtiz sfktazki

z

r &

Co fnsoi tkcfc sfa nzaf k`}iztafbka cf crtc tk}i dc biocbtizcr/ }iz bsafti dc o dc}cfdc co waoiz dc

Kr qsc cr oa cfczna kfbkdcftc }iz sfkdad dc rs}czgkbkc rijzc co bifbcftzadiz zcgocbtiz/ dc waoiz5

Kr 0 K= bir

Rcnf rca co tk}i dc izkcftabkf { ìwk`kcftir dco biocbtiz fcbcrazkir }aza bifrcnskzoa/ tcfdzcìr

dkwczrir waoizcr }aza co fnsoi dcrtabafdi oir rknskcftcr5

a+ Biocbtiz gkei/ crtafdi co }oafi dc ajcztsza fizào a oa zadkabkf rioaz dkzcbta ao `cdkida dc oir

cqskfibbkir , 0 =+/ }iz oi qsc5

bir 0 rcf rcf , - + ( bir bir ,- + bir

bir 0 bir bir

j+ Nkzi dco biocbtiz rijzc sf cec lizkuiftao ,Crtc-Icrtc+ bif sf rioi aesrtc dkazki/ dc gizà qsc oa fiz-

àoz

f ao }oafi dc ajcztsza bikfbkda bif oa bi`}ifcftc dkzcbta dc oa zadkabkf rioaz dcgkfkda }iz co wcbtizz

r / ao `cdkida dc bada da dco ai8 rti k`}okba qsc , 0 +/ }iz oi qsc5

bir 0 rcf rcf ( bir bir bir

bir 0 rcf:( bir: bir

b+ Nkzi rijzc sf cec lizkuiftao ,Crtc-Icrtc+ bif aesrtc biftkfsi dc oa aotsza dco Rio/ gizàfdi oir wcb-

tizcrz

f {z

r sf }oafi fizào ao dc ajcztsza dc oa rs}czgkbkc Ar

KW&->=


5/29

bir 0 1 - bir:rcf:

d+ Nkzi rijzc sf cec lizkuiftao ,Fiztc-Rsz+ bif aesrtc biftkfsi dc oa izkcftabkf5

bir 0 ,rcf rcf ( bir bir bir +:

( bir:rcf

:

c+ Nkzi rijzc sf cec }azaocoi ao cec dc oa Tkczza/ bif aesrtc biftkfsi5 - 0 =/ 0 = bir 0 bir

g+ Nkzi rijzc dir cecr }cz}cfdkbsoazcr/ bif aesrtc biftkfsi dco rcnsk`kcfti dco Rio/ dc gizà qsc rkc`-

}zc rc bs`}oa qsc/z

f 0z

r 5

bir 0 1

}iz oi qscKr0K= { oir za{ir rioazcr kfbkdcf cf tidi ì`cfti fizào`cftc ao }oafi dc ajcztsza/ }azaoc-oir ao }oafi dc rk`ctza dco biocbtiz&

KW&4&- CRTKN@ATKR@I

Rk rc bifrkdcza sf }sfti os`kfiri A qsc cfwa rijzc sf cr}cei sf lau dkwczncftc dc zadkabkf bfkbi

dc wztkbc A/ rc }scdc ad`ktkz qsc co cr}cei }zi}izbkifa dco }sfti os`kfiri A sfa kàncf A& Biì co

lau bfkbi cr bifwczncftc/ A cr oa kàncf zcao dc A& Rk bifrkdczaìr roi k`ncfcr zcaocr/ `cdkaftc co

}zibcri kfwczri/ sf }sfti os`kfiri rktsadi cf A }zi}izbkifaza sfa kàncf cf co }sfti A/ }iz oi qsc oir

dir }sftir A { A rif bifesnadir bif zcoabkf ao rkrtcà }tkbi/ cr dcbkz/ rtc cr crtkn`tkbi }aza co }az

dc }sftir A { A&

Rk rc bifrkdcza sf cr}cei crgzkbi bfbawi/ ,oa rs}czgkbkc zcgocbtaftc `kza labka co bcftzi dc bszwats-

za B dc oa crgcza+ { dc o sf barqsctc/ co }ioi R dc rtc cr co wztkbc

dco cr}cei { co cec ,BR+ cr co cec }zkfbk}ao i cec dc rk`ctza dco cr}cei&

Sf lau dc za{ir os`kfirir }azaocoir a ,BR+ rc tzafrgizà/ dcr}sr

dc oa zcgoc|kf/ cf sf lau bifwczncftc cf sf }sfti G dco cec }zkfbk}ao

qsc rc ooaàgibi kàncf { rc dkbc qsc G cr oa kàncf dco }sfti dco

kfgkfkti rijzc co cec }zkfbk}ao dco cr}cei8 zcb}ziba`cftc/ tidi za{i

kfbkdcftc qsc }arc }iz G rc zcgocea }azaocoa`cftc ao cec&

]aza sf cr}cei crgzkbi/ G crt cf oa `ktad dc ,BR+ { oa dkrtafbka ,BG+ 0 g/ cr oa dkrtafbka gibao/ Gkn

KW&3& Co }oafi }cz}cfdkbsoaz ao cec qsc }ara }iz G cr co }oafi gibao kàncf& Sf za{i os`kfiri qsc }arc

}iz co bcftzi rc zcgocea rijzc r `krì& Sf cr}cei crgzkbi fi }zi}izbkifa sfa kàncf ratkrgabtizka dc sf

ijecti/ raowi qsc5

- Co cr}cei rca dc }cqsca ajcztsza

- Co ijecti rca }oafi/ }cqsci/ }cz}cfdkbsoaz ao cec }zkfbk}ao { bcftzadi rijzc o

- Oar dk`cfrkifcr dco ijecti { oa ajcztsza dco cr}cei rif taocr qsc tidir oir za{ir os`kfirir crtf bcf-

tzadir8 cf crtar bkzbsfrtafbkar rc dkbc qsc co cr}cei tzajaea cf bifdkbkifcr dc a}zi|kàbkf dc Nasrr&

]aza oa bifrtzsbbkf nci`tzkba dc oa kàncf dc sf ijecti }cz}cfdkbsoaz ao cec }zkfbk}ao dco cr}cei {

rktsadi cf co kfgkfkti/ cf fscrtzi bari co Rio/ rc }aztc dc oi rknskcftc5

Co }oafi ijecti/ co Rio/ crt cf co kfgkfkti { rs k ancf cf co }oafi gibao8 rk co }sfti A dco bcftzi dcodkrbi rioaz bikfbkdc bif co cec }zkfbk}ao dco cr}cei/ rs kàncf zcgoceada crtaz cf G& ]aza sf }sfti J }cz-

tcfcbkcftc a oa bkzbsfgczcfbka dco dkrbi rioaz/ gscza dco cec }zkfbk}ao dco cr}cei/ bs{a ofca ri}iztc }ara }iz

KW&->1

Gkn KW&4&- Crtknàtkrì


6/29

B/ gizà sf fnsoi % ,}cqsci+ bif co cec }zkfbk}ao { rs kàncf crt cf co }sfti dc kftczrcbbkf dco }oafi

gibao { co cec rcbsfdazki ,JB+/ a}azcbkcfdi crta kàncf cf }irkbkf kfwcztkda&

Gkn KW&3&- fnsoi { zadki dc ajcztsza8dkrtafbka gibao

Gkn KW&7&- Bifrtzsbbkf dc oa kàncf dc sfijecti cf co kfgkfkti

Cf co tzkfnsoi ,BAJ+ rc tkcfc qsc5 , A.J.+ 0 , BA. + tn %

,BR+

: %0

Z %

:bif5 0 2:. = /==;21 zad

Co dk`ctzi dc oa kàncf rioaz dada }iz sf cr}cei bfbawi dc 1 ` dc zadki cr5

, A.J.+ 0 Z

:0 1

| =/==;21:

0 =/==473 `

KW&3&- BIFRKDCZABKIFCR NCI@TZKBAR RIJZC CO BIOCBTIZ DC RS]CZGKBKC ZC-

GOCBTAFTC CRGZKBA

Cf sfa rs}czgkbkc zcgocbtaftc crgzkba/ oir za{ir rioazcr zcgoceadir rif tafncftcr a sfa rs}czgkbkc dczcwiosbkf qsc rc bifibc biì bsrtkba& Rk rc rs}ifc sf za{i os`kfiri qsc kfbkdc rijzc co cr}cei crgzk-

bi dc bcftzi B cf co }sfti ]/ Gkn KW&>/ co za{i zcgoceadi cr tafncftc a oa bsrtkba cf co }sfti @ { bizta a

oa ofca ,BR+ cf co }sfti A { ao }oafi gibao cf A& Oar dkrtafbkar ,GA+ { ,GA+ bazabtczkuaf/ zcr}cbtkwa-

`cftc/ oar wazkabkifcr oifnktsdkfao { tzafrwczrao dc oa ajczzabkf crgzkba&

Gkn KW&>&- Bsrtkba dc sf cr}cei crgzkbi

]aza co bobsoi dc ,GA+ { ,GA+ rc dcgkfc sf fnsoi qsc cr co fnsoi dc ajcztsza dco cr}cei8 tcfkcfdi

cf bscfta oar oc{cr dc oa zcgoc|kf/ co tzkfnsoi ,B]A+ cr krrbcocr/ }iz oi qsc5

KW&->:


7/29

, BA.+ 0 Z

: bir 8 , GA.+ 0 Z

:, 1bir

- 1 +

{ biì co fnsoi ,B]A+ waoc ,:+ zcrsota5 ,GA+ 0 Z:

, 1bir

- 1+ tn :

Rk bifrkdczaìr 0 435 , GA.+ 0 = /:1 Z 8 , GA+ 0 =/:1 Z tn ;=0 / qsc rknfkgkba qsc }aza crtarktsabkf/ oa kàncf rc c|tcfdcza kfdcgkfkda`cftc rijzc co }oafi gibao&

Rk }iz oir }sftir 1/ :/ 2/ 4/ 3/ rktsadir rijzc co cec ,BR+ labcìr }araz sfir }oafir }cz}cfdkbsoazcr

a dkbli cec/ rc ijtkcfc oa wkrsaokuabkf cfczntkba cf oa qsc oar uifar ri`jzcadar rif zcnkifcr rktsadar

cftzc oar dir uifar dc oa bsrtkba/ cf oar qsc oa abs`soabkf dc osu zcgoceada cr `r kftcfra/ Gkn KW&== { rtc cr}cei crgzkbi dc }cqsca ajcztsza rcza sf c|bcocftc bifbcftzadiz&

A biftkfsabkf waìr a dctcz`kfaz oa bifbcftzabkf bizzcr}ifdkcftc ao }oafi dco bzbsoi dc `cfiz

dkgsrkf& ]aza laooaz co dk`ctzi dc crtc bzbsoi la{ qsc dctcz`kfaz oa izdcfada dco }sfti dc kftczrcbbkf

dc oa bsrtkba bif co za{i zcgoceadi c|tzcì qsc }ara }iz co }sfti @&Rc àftkcfc co }sfti B biì izkncf dc biizdcfadar { biì cec| oa zcbta ,BR+&

Rk oa kftczrcbbkf dc sf za{i bsaoqskcza }azaocoi a crtc cec bif co cr}cei crgzkbi cr co }sfti K { co

za{i zcgoceadi cr tafncftc a oa bsrtkba cf J/ qsc a rs wcu bizta ao cec | cf D/ rc }scdc laooaz oa cbsabkfKW&->2


8/29

dc oa zcbta ,KD+ rk rc bifibcf crtir }sftir&

Oar biizdcfadar dco }sfti K rif5

Z rcf Z bir

Oar biizdcfadar dco }sfti D rif5 Z

: bir

=

{ oa cbsabkf dc oa zcbta ,KD+5 | rcf : - { bir : - Z rcf 0 =

Oa cbsabkf dc oa `czkdkafa dc oa bsrtkba/ cfwiowcftc dc oa zcbta ,KD+/

rc ijtkcfc dczkwafdi oa aftczkiz zcr}cbti a / ijtcfkfdirc5

: | bir : ( : { rcf : - Z bir 0 =

Rs kftczrcbbkf fir da5 | 0Z

:bir ,1 ( : rcf:+

{ 0 Z rcf2

qsc rif oar cbsabkifcr dc sfa bszwa sfkbszrao dc 7 nzadi/ ooaàda fcgzikdc Gkn KW&;/ qsc cr sfa c}kbk-

boikdc bif dir }sftir dc zctzibcri cfncfdzada }iz oa zidadsza rkf dcrokua`kcfti dc sfa bkzbsfgczcfbka dc

zadki Z4

rijzc itza bkzbsfgczcfbka dc zadki Z:

bifbftzkba bif co cr}cei&

Co za{i zcgoceadi tafncftc a oa bsrtkba cf co }sfti c|tzcì @ tkcfc itzi }sfti C rijzc oa fcgzikdc& Rk

C cr co `r }z|kì a G oc bizzcr}ifdc sf waoiz dc zcoatkwa`cftc }cqsci/ }iz bsafti a G oc bizzcr-

}ifdc co waoiz ,0 =+&

]aza laooaz crtc }sfti rsrtktskìr oir waoizcr dc ,|/ {+ aftczkizcr cf oa cbsabkf dco za{i zcgoceadi5

| rcf : - { bir : - Z rcf0 =

Z:

bir , 1 ( : rcf:+ rcf : - Z rcf2bir : - Z rcf 0 =

bir ,1 ( : rcf:+ rcf :

:0 rcf2 bir : ( rcf 0 =

Rsrtkts{cfdi bir { bir/ cf gsfbkf dcrcf { rcf/ zcr}cbtkwa`cftc { izdcffdioa cfrcf/ rcijtkcfc5

rcf

7

( : rcf

2

rcf - 4 rcf

2

rcf

2

- 2 rcf

:

rcf

:

( 2 rcf

:

rcf

4

( rcf

4

0 ={ biì co za{i zcgoceadi cr tafncftc a oa bsrtkba/ crta cbsabkf ad`ktc oa zau dijoc5 rcf 0 rcf

Dkwkdkcfdi oa cbsabkf aftczkiz }iz ,rcf - rcf +: / zcrsota5

rcf4( : rcf2rcf ( 2 rcf:rcf:( : rcfrcf( rcf:0 =

{ rk cr `s{ }cqsci/ co jkfi`ki ,rcf4( : rcf2rcf + rc }scdc dcr}zcbkaz/ }iz oi qsc cf }zk`cza

a}zi|kàbkf rc ijtkcfc sfa cbsabkf dc : nzadi cfrcf/ dc oa gizà52 rcf: rcf:( : rcf rcf ( rcf:0 =

rcf 0 - 1 1 - 2 rcf

:2 rcf

rcf ? 12

8 ? 23

cr dcbkz/ rk co fnsoi dc ajcztsza dco cr}cei cr dcàrkadi nzafdc/ oir za{ir kfbkdcftcr qsc bacf bczba dcoKW&->4

Gkn KW&;&- Fcgzikdc


9/29

jizdc dco cr}cei/ ao zcgoceazrc rijzc oa bsrtkba/ oi labcf `s{ oceir dco }sfti G { rc zcgoceazaf dir wcbcr

rijzc co cr}cei&

Rk rc gkea co fnsoi oa cbsabkf dc 4 cfbiftzada rc }scdc zcriowcz8 rs}ifkcfdi 02=/ ijtcfkfdirc5

rcf4( rcf

2( =/>3 rcf

:( rcf ( =/:3 0 =

bs{ar riosbkifcr rif5

rcf 0 - =/2 8 0 - 1>/43rcf 0 - 1 8 0 - ;=/ qsc fitkcfcrcftkdi

Co zadki dco bzbsoi dc `cfiz dkgsrkf cr5 Z rcf2

Co zadki dc ajcztsza dco cr}cei cr5 Z rcf

Co gabtiz dc bifbcftzabkf `cdki/ {a qsc oa kàncf fi crt dcgkfkda sfkgiz`c`cftc/ cr5

B 0Aa

Az0 Z

: rcf:

Z:

rcf7

0 rcf:

rcf7

]aza/ 0 2= B 0 rcf:

rcf70 rcf

:2=,- =/2+7

0 242/ zcrsotadi qsc fi cr c|abti }izqsc fi rc la tcfkdi

cf bscfta co fnsoi dc dkr}czrkf dc oa osu rioaz , 0 2:+/ qsc }zidsbkza sf cfnzira`kcfti dc oa bsrtkba&

Rs}ifkcfdi qsc co zadki dc bszwatsza dco cr}cei zcgocbtiz cr Z 0 1 `/ { qsc co dk`ctzi dc ajcztsza

dco cr}cei cr ta`jkf dc 1 `/ rc tkcfc5

zca dco bzbsoi dc cfiz dkgsrkf5 Z:rcf70 1: ,=/2+7 0 :/:;&1=-2 :

Dk`ctzi dc rtc bzbsoi/ 3/4 b`&

Gcf`cfi dc bià&-Lcìr rs}scrti/ }iz rk`}okgkbaz/ qsc oa dkzcbbkf dc oir za{ir rioazcr cza }a-zaocoa ao cec }zkfbk}ao dco zcgocbtiz crgzkbi/ bif aesrtc biftkfsi dco rcnsk`kcfti dco Rio/ dc gizà qsc

rkc`}zc rc bs`}oc qsc/z

f 0z

r & ]czi rk co cr}cei crgzkbi dcjc }czàfcbcz gkei/ a}azcbc sf fscwi tk}i dc

ajczzabkf/ dc gizà qsc oa kàncf zcgoceada rijzc sf }oafi }cz}cfdkbsoaz ao cec }zkfbk}ao fi cr dc zcwi-

osbkf/ }zcrcftafdi sfa gizà aoaznada { sf `|kì dc os`kfirkdad labka sfa dc rsr c|tzc`kdadcr& Co

bifesfti }zcrcfta oa gizà dc sf bi`cta { dc al co fi`jzc dcbià bifqsc rc bifibc ao gcf`cfi/ qsc

rc abcfta biftza `r oceir crt dco cec&

]aza rs}zk`kz co dcgcbti dco bià { rs}ifkcfdi sfa }cqsca ajcztsza dco bifbcftzadiz/ rc tkcfc qsc

bs`}okz oa bifdkbkf dco rcfi dc Ajjc qsc roi sfa rs}czgkbkc crgzkba }scdc wczkgkbaz/ }iz oi qsc bif sf

cr}cei crgzkbi akroadi fi rc }idza ijtcfcz sf gabtiz dc bifbcftzabkf `s{ cocwadi& ]iz crta zauf/ cfaonsfir tk}ir dc bifbcftzadizcr/ biì co dco lizfi rioaz dc Fatkbh ,@arrablsrcttr/ SRA+/ rc stkokua sf

bifbcftzadiz bifrtktskdi }iz sf ìrakbi dc }cqscir cr}ceir crgzkbir&

Rkrtcà R&Z&T&A&- Co rkrtcà R&Z&T&A& bifrkrtc cf sf zcgocbtiz crgzkbi gkei { sf biocbtiz i zcbc}tiz

bkofdzkbi `wko/ bcftzadi { izkcftadi cf tidi ì`cfti cf oa dkzcbbkf dco Rio& Tcfkcfdi cf bscfta oa Gkn

KW&1=/ la{ qsc dctcz`kfaz oa ajcztsza a daz ao cr}cei dc gizà qsc tidir oir za{ir kfbkdcftcr ao `cdki-

da/ }azaocoir ao cec }zkfbk}ao/ oc biztcf dcr}sr dc sfa rioa zcgoc|kf&

Co za{i c|tzcì zcgoceadi }ara }iz co }sfti R { rk ] cr co }sfti dc kfbkdcfbka/ co tzkfnsoi ,BR]+ cr

krrbcocr8 }aza sf fnsoi dc kfbkdcfbka `|kì/ rc tzafrgizà cf sf tzkfnsoi cqskotczi { co zadki dcajcztsza bizzcr}ifdkcftc waoc5 Z 2

:

Oir za{ir kfbkdcftcr }azaocoir ao cec }zkfbk}ao { c|tczkizcr ao bzbsoi dc `|kà ajcztsza c|}czk`cf-

KW&->3


10/29

taf dir zcgoc|kifcr aftcr dc aobafuaz ao biocbtiz&

Rk oir za{ir rioazcr fi rif }azaocoir ao cec }zkfbk}ao }iz crtaz a itzar lizar dkrtkftar dc oar dco `c-

dkida/ aonsfir dc cooir aobafuazf dir zcgoc|kifcr { itzi }cqsci f`czi fi biztaf `r ao cec/ }iz oi qsc

la{ sfar }zdkdar dc cfczna dco izdcf dco 1#&

Oa oifnktsd dco biocbtiz bkofdzkbi cr Z:

]aza gkeaz oar dk`cfrkifcr dco zcgocbtiz la{ qsc bifibcz co waoiz dc oa rs}czgkbkc dc oa kàncf rioaz zc-

goceada rijzc co cec }zkfbk}ao/ qsc cr wazkajoc/ }iz bsafti oa dkrtafbka dcrdc oir }sftir dc kfbkdcfbka ao cec

cr wazkajoc/ rkcfdi `r nzafdc bczba dco zcgocbtiz/ qsc bczba dco gibi&

-Co ba`kfi `fkì ,RG+ dc oir za{ir zcgoceadir cr Z:

- Co dk`ctzi dc oa kàncf rioaz waza cftzc ,d`|0 Z + { ,d`f0

Z c: +/ bif 0 2:

- Co ba`kfi `|kì ,]R+ dc oir za{ir zcgoceadir cr Z

Oa rs}czgkbkc os`kfira a oi oazni dco cec }zkfbk}ao gizàda }iz oa rs}cz}irkbkf dc tidar oar k`ncfcr}azbkaocr dco Rio cr/ a}zi|kàda`cftc/ bfkba8 rs rs}czgkbkc cr5

A 0 Z

:

Z ( Z :

:0 2

7


11/29

Gkn KW&11&- ]irkbkifcr dco biocbtiz dco rkrtcà RZTA }aza bsafdi co cec dco cr}cei bikfbkdcbif oir za{ir rioazcr kfbkdcftcr ,kfbkdcfbka fizào+ { }aza bsafdi fi bikfbkdcf

Gkn KW&1:&- Rs}czgkbkc os`kfira a oi oazni dco cec }zkfbk}ao

Co biocbtiz tkcfc :/> ` dc oifnktsd { crt gizàdi }iz sf rcz}cftf dc bijzc cffcnzcbkdi dc 1/: b` dc

dk`ctzi { }zitcnkdi }iz sfa bsjkczta dc bzkrtao

Ncfcza wa}iz dc ansa a jaea }zcrkf/ qsc bifdcfra cf sf dc}rkti dc aoàbcfa`kcfti dc 11 2/ qsc

biftkcfc oadzkooir dc aos`kfki }aza aoàbcfaz oa cfczna }aza oa fiblc { }aza oir dar rkf rio/ larta sf

`|kì dc 3 dar bifrcbstkwir

Ta`jkf }scdc }zidsbkz wa}iz rijzcbaocftadi a :==B qsc abbkifa sfa tszjkfa }aza ncfczaz cocbtzk-

bkdad

Co gabtiz dc zcgoc|kf dco zcgocbtiz cr =/1B

Co bicgkbkcftc dc ajrizbkf dc oa rs}czgkbkc zcbc}tiza cr =/;

KW&7&- BIFRKDCZABKIFCR NCI@TZKBAR RIJZC CO BIOCBTIZ ]AZAJOKBI DC ZC-

WIOSBKF

Sf }azajioikdc dc zcwiosbkf rc ijtkcfc }iz zitabkf dc sfa }azjioa aozcdcdiz dc rs cec& A biftkfsa-

bkf waìr a c|}ifcz aonsfar }zi}kcdadcr dc crta bszwa/ dc a}okbabkf cf bifbcftzadizcr dc cfczna ri-

oaz& Sf }azajioikdc cr co bifesfti dc }sftir rktsadir a knsao dkrtafbka dc sfa zcbta gkea ooa ada dkzcbtzku{ dc sf }sfti gkei G ooaàdi gibi/ Gkn KW&12& Oa kftczrcbbkf dc oa }azjioa { rs cec cr co wztkbc R8 rk rc

coknc crtc wztkbc biì izkncf dc biizdcfadar/ oa cbsabkf dc oa }azjioa cr5

{:0 4 g |

cf oa qscgcr oa dkrtafbka gibao ,RG+&

Cf biizdcfadar }ioazcr dc }ioi G/ oa cbsabkf dc oa }azjioa cr5 0g

bir::

rkcfdi5 0 : azb tn l

: gCo dk`ctzi D dc ajcztsza dco }azajioikdc { co fnsoi `|kì qsc oc dcgkfc/ wkcfcf zcoabkifadir

}iz5

KW&->>


12/29

Gkn KW&12&- Bifbcftzadizcr }azajokbir dc zcwiosbkf

Gkn KW&12a&- ]azjioa

0 : azb tn D: g

D 0 4 g tn

:

zcrsotadi qsc oa rs}czgkbkc dc ajcztsza Aa dc crtc }azajioikdc cr5

Aa0

D:4

0 17 g: tn:

:4

0 4 g: tn:

:

Co zca dco }azajioikdc rc }scdc dctcz`kfaz a }aztkz dco tcizcà dc Nsodkf/ cf oa gizà5

A0=

: { dR 0dR:0 d:(,d+:

{ 0g rcf

bir: ,):+8 dR 0

g dbir2 ,):+

0

=

: g rcf

bir:

:

g d

bir2

:

0

0 : g:=

rcf

:d

:

bir4

:

0 &&& 0< g:

2 ,1

bir2 ,):+- 1+

Oa }zi}kcdad gsfda`cftao dc sf cr}cei }azajokbi cr oa dc rcz crtkn`tkbi }aza co }sfti dco &

Co dk`ctzi d dc oa kàncf dco dkrbi rioaz cr5 d 0 g =/=1 g/ cr dcbkz/ co f`czi qsc àzba oa dkr-

tafbka gibao cf `ctzir cr co `krì qsc àzba oa kàncf rioaz cf b`&Rc ijtkcfc sfa kàncf ftkda dco Rio rk5 D

g? =/1

KW&->


13/29

Bobsoi dc oa bifbcftzabkf&-Rk cf co }sfti K dco }azajioikdc rc zcgocea sf lau bfkbi dc za{ir ri-

oazcr/ Gkn KW&14/ { rk labcìr ,KG+ 0 / cf co }oafi gibao rc ijtkcfc sfa cok}rc bs{ir cecr rif5

Cec `cfiz5 : j 0 ,BC+ 0

Cec à{iz5 : a 0 , BN + 0

bir

Gkn KW&14&- K`ncfcr }zidsbkdar cf sf bifbcftzadiz }azajokbi

Azca dco bzbsoi kàncf dc Nasrr dc dk`ctzi , @F + cr5 A1 0g::

4

Azca dc oa cok}rc bizzcr}ifdkcftc 5 A: 0a j 0g::

4 bir

0A1A:

0g:bir

:

Rk rc bifrkdcza sf }cqsci coc`cfti ,HL+ dco }azajioikdc/ qsc rc }scdc bifgsfdkz bif rs tafncftc cfK { rk dcrdc L rc tzaua oa }azaocoa ao cec dc oa }azjioa/ zcbta ,LJ+/ dcrdc H oa }cz}cfdkbsoaz a oa zcbta

,JL+ { dcrdc H oa }cz}cfdkbsoaz a ,LG+/ rkcfdi J co }sfti dc kftczrcbbkf/ zcrsota qsc ,HL+ cr oa jkrcb-

tzku dco fnsoi ,JLJ+/ }iz oi qsc ,LJ+ 0 ,HJ+ 0 d&

Rk rc labc nkzaz co rcn`cfti coc`cftao ,HL+ aozcdcdiz dco cec dco cr}cei rc ijtkcfc sfa bizifa coc-

`cftao qsc }zi{cbtada rijzc co }oafi gibao izknkfa sf afkooi coc`cftao dc zca5

dA 0 : : rcf d

Rk oa bifrtaftc rioaz cr K=/ oa zadkabkf zcbkjkda }iz co afkooi cf co }oafi dc oa kàncf rioaz cr5

dK= 0 : K=: rcf d

{ oa gzabbkf dc cfczna zcbkjkda }iz co dkrbi gibao5

dKgibao 0 : K= g: rcf bir d

Rk ooaàìr D ao dk`ctzi dc ajcztsza dco }azajioikdc dc zcwiosbkf { ao fnsoi dc ajcztsza bi-

zzcr}ifdkcftc/ oa cfczna }iz sfkdad dc rs}czgkbkc cr5

K

gibao0 : K

=g:

=

rcf bir d0K

=g:rcf:

qsc rc zcbkjc cf sf dkrbi dc zca A1 0g::

4}iz oi qsc oa dcfrkdad dc cfczna bifbcftzada cf dkbli dkr-

bi cr5

KW&->;


14/29

Kdkrbi0Kgibao

A10K= g: rcf:

g::

4

04 K= rcf:

:

{ co gabtiz dc bifbcftzabkf5 B 0Kgibao

K=0

4 rcf::

]aza sf fnsoi dc ajcztsza `|k`i/ 0 ;=/ B 0 4 rcf: ;=

=/==;21:0 4713=/ { rk oa bifrtaftc rioaz K= cr

dco izdcf dc 1 h^: / }aza sf cr}cei bif sfa dkrtafbka gibao dc 1 `/ oa rs}czgkbkc dc oa k`ancf dc Nasrr

cr5 A1 01 | =/==;21:

40 7/


15/29

Cf ncfczao/ sf lizfi rioaz rc bi`}ifc dc dir tk}ir dc cr}ceir/ sfi }azajokbi gkei qsc bifbcftza

cfczna cf co gibi { itzi }oafi qsc zccfwa co lau dc za{ir rioazcr a oa uifa dc `|kà tc`}czatsza/ bif

oi qsc rc tkcfcf dir cr}ceir bif oar }zdkdar bizzcr}ifdkcftcr& ]aza oir cr}ceir zcbsjkcztir bif }oata i

aos`kfki/ oar }zdkdar rif dco izdcf dco 1=# }aza bada sfi/ cf titao sf :=#& Oar dc`r }zdkdar rif dk-

gbkocr dc cwaosaz/ }czi rc }scdcf bsaftkgkbaz cftzc sf 2=# { sf >=#/ rcnf co tk}i dc bifrtzsbbkf&Oa zcoabkf cftzc oa cfczna ijtcfkda { oa baobsoada a }aztkz dco gabtiz dc bifbcftzabkf cr co gabtiz

dco lizfi G/ qsc cf oar `ceizcr bifdkbkifcr fi cr rs}czkiz a =/7/ }aza gabtizcr dc bifbcftzabkf dco izdcf

dc :====&

Tc`}czatszar ijtcfkdar cf sf lizfi rioaz&-Oa cfczna zcbkjkda cf co }oafi gibao dco cr}cei }a-

zajokbi cr ajrizjkda }iz co rkrtcà qsc rc wa a baocftaz/ dc gizà qsc rs tc`}czatsza as`cfta dcjkdi

a oa bifdsbbkf { zadkabkf& Oa cfczna bifbcftzada }iz sfkdad dc rs}czgkbkc cr BK=/ { rk co lizfi rc ark-

`koa a sf bscz}i fcnzi rc }scdc ad`ktkz qsc tida crta cfczna rc ajrizjc/ }iz oi qsc5

B K= 0 T4

Rk/K= 0 1h^

: { B 0 :====/ rc ijtcfdza sfa tc`}czatsza ajriosta dco izdcf dc T 0 42==H/ }czi ao

fi rcz co bscz}i fcnzi { tcfcz }zcrcftcr oar }zdkdar }iz bifdsbbkf/ crta tc`}czatsza fi rijzc}araza

oir 41==H&

Dcjkdi a oar dcfrkdadcr dc cfczna dkr}ifkjocr/ oa ijtcfbkf dc oar tc`}czatszar bktadar }scdc rcz

`s{ z}kda8 sf bscz}i ào bifdsbtiz { `s{ ajrizjcftc fcbcrkta =/3 rcnsfdir }aza }ifczrc a :>==B

{ 2 rcnsfdir rk rs }idcz c`krkwi cr =/4 ,|kdir zcgzabtazkir+& ]aza oir `ctaocr/ oa bifdsbtkwkdad { co cr-

tadi rs}czgkbkao labcf qsc co }zibcri rca `r ocfti/ dco izdcf dc > rcnsfdir&

KW&>&- BIFRKDCZABKIFCR NCI@TZKBAR RIJZC OIR BIOCBTIZCR BKOKFDZKBI-]A-

ZAJIOKBIR

Oars}czgkbkc dc ajcztsza dco bifbcftzadiz/ cr co zca dco `krì }zi{cbtada rijzc sf }oafi fizào ao

}oafi dc rk`ctza& ]aza sf biocbtiz bkofdzkbi }azajokbi cr sf zcbtfnsoi dc dk`cfrkifcr oa afblsza {

oifnktsd dc oa rs}czgkbkc zcgocbtaftc& Rk rc bifrkdcza sf lau dc za{ir os`kfirir dc ajcztsza kfbkdcftc cf

co }sfti K dco bkokfdzi/ co lau zcgoceadi bizta ao }oafi fizào cf co cec dc oa }azjioa jrkba qsc dcgkfc co

}czgko dco bkokfdzi/ rcnf sfa cok}rc dc cec à{iz ,AJ+& Cf }zk`cza a}zi|kàbkf rc }scdc ad`ktkz qsc cogibi G dc oa }azjioa qsc }ara }iz co }sfti K cr co bcftzi dc rta cok}rc&

Gkn KW&13- Bifbcftzadiz bkofdzkbi }azajokbi

KW&-


16/29

Gkn KW&17&- Bobsoi dc oa bifbcftzabkf }zidsbkda }iz co bifbcftzadiz bkofdzkbi }azajokbi

Rk aliza rc bifrkdcza sf lau kfbkdcftc dc fnsoi bs{i cec }ara }iz co wztkbc dc oa }azjioa K/

qsc bikfbkdc bif co lau zcgoceadi/ z

f 0z

r/ oa kàncf rijzc co }oafi gibao rcz sf bzbsoi dc Nasrr&

Rk co }sfti dc kfbkdcfbka K rijzc co zcgocbtiz rc `scwc a oi oazni dc oa ofca ,KK+/ co bzbsoi dc Nasrr rc

tzaroada a oi oazni dc sf zcbtfnsoi dc oifnktsd L { afblsza ,g+/ ok`ktadi }iz dir rc`kbzbsoir dc zadki

,g):+/ rkcfdigoa dkrtafbka gibao dc oa }azjioa&

Rk ,g+ cr }cqsci bif zcoabkf a L/ rc }scdc ad`ktkz qsc oa rs}czgkbkc dco zcbtfnsoi cr ,L g+/ Gkn

KW&17& Oir oadir dc crtc zcbtfnsoi biztaf a oa cok}rc cf oir }sftir B/ D/ C/ G { ao cec I| cf A { J&]aza baobsoaz co zca dc oa }aztc ri`jzcada ,CBDNC+/ oir cecr à{iz ,AJ+ { `cfiz ,@F+ dc oa cok}-

rc rif5

,AJ+0 : a 0

bir

8 , @F + 0: j 0

Oa rs}czgkbkc coc`cftao ri`jzcada A1 waoc/ a}zi|kàda`cftc5 A1 0 g| 0 g: / { oa rs}czgkbkc

dc oa cok}rc ,ABDJNC+ cr5 A: 0::

4 bir / bif5

0A

1A: 0g:

::

4 bir 0

4 g bir

]aza co fnsoi d5Oakàncftitaococ`cftaocr5 dA10 LdOakàncfdcNasrr5 dA: 0 Ld

{ rk K= cr oa bifrtaftc rioaz/ oa cfczna qsc kfbkdc rijzc sf cr}cei dc fnsoi dc ajcztsza cr5

Kgibao 0 : K= L

=

d0 : K= L =

4 g bir

d0

< K= L g

=

bir d0< K= L g rcf

Co gabtiz dc bifbcftzabkf cr5 B 0Cfczna cf oa rs}czgkbkc dc Nasrr

Cfczna cf oa cok}rc dc Nasrr 0< K

=L g rcf

K=L g 0 < rcf /

qsc fir da sfa kdca dco izdcf dc ànfktsd dkr}ifkjoc&

KW&-


17/29

Oa bifbcftzabkf à|kào rc ijtkcfc }aza/ 0 ;= { waoc5 / zcgocea rijzc sf zcbc}tiz }oafi { fizào ao cec dco bif-

bcftzadiz/ dc oifnktsd O8 co dk`ctzi dc oa kàncf rioaz rijzc co zcbc}tiz ,aj+ qsc rc wc dcrdc co }sfti ]/

wkcfc dada }iz5

,aj+ 0 : tn 17.

rkcfdi oa oifnktsd5 O 0,aj+

bir 0

: tn 17.bir

Rk co }czgko dco bifbcftzadiz cr }azajokbi { oa dkrtafbka ,RG+ cr oa dkrtafbka gibao g/ rc }scdc dcgkfkz

rta biì5

{: 0 4 g |

Cf co }sfti K rc tkcfc qsc5

|10 g - bir {10rcf

: rcf:0 4 g , g - bir +

: (

4 g bir rcf:

-4 g:

rcf:0 = 0

: g ,1 - bir +rcf:

0: g

1 ( bir

oi qsc }cz`ktc laooaz co taài dc oa kàncf rioaz tczkba zcgoceada rijzc co zcbc}tiz }aza g |&

Oar dk`cfrkifcr fkàr dco zcbc}tiz rif5 O 0: tn 17.

bir 0

4 g tn 17.

bir , 1 ( bir +

Gkn KW&1>&- Kàncf zcgoceada tczkba dco Rio cf sf biocbtiz bkofdzkbi }azajokbi

Gkn KW&1


18/29

@cdkaftc oa dkrtafbka gibaogrc dctcz`kfa co taài dc oa kàncf rioaz zcgoceada { `cdkaftc oa rs}cz-

gkbkc dc ajcztsza Aa oa cfczna titao qsc }scdc bifbcftzaz/ }iz oi qsc co gosei dc cfczna cf co gibi zcbc}-

tiz rcz gsfbkf dc oa zcoabkfAag

Cfczna tko rijzc co zcbc}tiz8}zdkdar tz`kbar&-Waìr a bifrkdczaz sf bifbcftzadiz bkof-dzkbi }azajokbi ,BB]+8 sf jaoafbc cfczntkbi dco `krì/ cf oa }irkbkf |}cz`ktkz dctcz`kfaz oa na-

fafbka tko qs dco biocbtiz }iz sfkdad dc rs}czgkbkc dc ajcztszarcnf rc `scrtza cf oa Gkn KW&1;5

qs0 KrG,+ - SB , Tz /|- Ta+

AzAa

{ rk tidi co zcbc}tiz crt a sfa tc`}czatsza sfkgiz`c Tz oa nafafbka tko titao rcz5

Qs 0 qs Aa 0 Aa KrG ,+ - SB Az , Tz - Ta+

rkcfdi5- Aaoa rs}czgkbkc dc ajcztsza dco biocbtiz/ rkf ri`jzar/ { Az oa rs}czgkbkc dco zcbc}tiz

- B 0AaAz

cr co gabtiz dc bifbcftzabkf qsc }cz`ktc ijtcfcz goseir dc cfczna bi`}azajocr a oir dc bsao-

qskcz kftczba`jkadiz kfdsrtzkao bifwcfbkifao- cr oa zcgocbtafbka cr}cbsoaz dc oa rs}czgkbkc zcgocbtiza

- G cr oa gzabbkf dc cfczna zcgoceada qsc cr kftczgczkda }iz co zcbc}tiz { qsc bifrtkts{c co gabtiz dc kf-tczbc}tabkf

- Kr cr oa zadkabkf rioaz dkzcbta fizào ao }oafi dc ajcztsza dco bifbcftzadiz

- Sb

,Tz

- Ta+/ rif oar }zdkdar tz`kbar }iz sfkdad dc rs}czgkbkc dco zcbc}tiz labka co c|tczkiz8 T

zcr oa

tc`}czatsza `cdka dco zcbc}tiz { Ta cr oa tc`}czatsza dco `cdki c|tczkiz8 crtar }zdkdar rc zcdsbcf ao as-

`cftaz co gabtiz dc bifbcftzabkf B

Gkn KW&1;&- Jaoafbc cfczntkbi cf sf biocbtiz bkofdzkbi-}azajokbi

Cf oa Gkn KW&:=/ oa bszwa dco`ktc kfgczkiz zc}zcrcfta oir fkwcocr dc bifbcftzabkf cf oir qsc oar }z-

dkdar tz`kbar rif knsaocr a oa cfczna ajrizjkda/ `kcftzar qsc oir fkwcocr rs}czkizcr daf sfa nafafbka

tko& Oa uifa za{ada rc bizzcr}ifdc bif cgkbkcfbkar dco biocbtiz dco izdcf dco 4=# ao 7=# { zc}zcrcfta co

ba`}i dc gsfbkifa`kcfti fizào8 ta`jkf rc kfdkba co ba`}i cf co qsc rc }scdcf stkokuaz dctcz`kfadir

tk}ir dc zcgocbtizcr& Bsafti `cfiz rca oa rs}czgkbkc dco zcbc}tiz/ oar }zdkdar tz`kbar rczf ta`jkf

`cfizcr8 rk rta rs}czgkbkc zcbc}tiza gscrc }sftsao/ oar }zdkdar tz`kbar rczaf bczi8 dc rti rc dcdsbcqsc oa nafafbka dc cfczna tko { oar bszwar dc cgkbkcfbka rc abczbaf a `cdkda qsc rc zcdsbcf oar }zdk-

dar tz`kbar&

KW&-


19/29

O`ktc kfgczkiz

Gkn KW&:=&- Zcoabkifcr cftzc co fkwco dc bifbcftzabkf { tc`}czatszar dc gsfbkifa`kcfti dco zcbc}tiz

]zdkdar }tkbar&- Oa zcgocbtafbka cr}cbsoaz rc dcgkfc biì oa gzabbkf dc cfczna rioaz dkzcbta

kfbkdcftc qsc rc zcgocea labka co zcbc}tiz rcnf oar oc{cr dc oa zcgoc|kf/ dc gizà qsc co fnsoi dc kfbkdcf-

bka { co zcgoceadi/ a`jir zcr}cbti a oa fizào cf sf }sfti bsaoqskcza dc oa rs}czgkbkc zcgocbtiza/ rcaf

knsaocr8 oar }zdkdar }iz zcgoc|kf rif dc oa gizà/ 1 - &

Rc bifrknsc sfa zcgocbtafbka cocwada stkokuafdi dc}rktir `ctokbir i }kftszar rijzc rsjrtzatir `c-

tokbir i rijzc bzkrtao& Cf biocbtizcr bkofdzkbi }azajokbir ,BB]+ rc rscocf stkokuaz o`kfar dc aos`kfki

afidkuadi/ i ta`jkf }cobsoar dc }ortkbi `ctaokuadar cf wabi/ biì }cobsoar dc }iokrtcz aos`kfkua-

di/ qsc }cz`ktcf ijtcfcz sfir waoizcr aotir dc oa zcgocbtkwkdad dszaftc nzafdcr }czidir dc gsfbkifa-

`kcfti dco biocbtiz& Oa tzafr`ktafbka { oa ajriztafbka tkcfcf co `krì rknfkgkbadi qsc cf oir biocbti-zcr dc }oaba }oafa/ asfqsc rsr waoizcr dkgkczcf/ dadi qsc oar bifdkbkifcr dc dkrci ta`jkf rif dkgczcf-

tcr }sdkcfdi bifrkdczaz oar rknskcftcr5

- Oir bifbcftzadizcr fi tkcfcf bsjkcztar { fi kfgos{c cf co jaoafbc cfczntkbi/ 0 1

- Rk co zcbc}tiz cr dc bawkdad/ co waoiz dc tkcfdc a oa sfkdad/ bif sfa c`ktafbka cocwada&

- { dc}cfdcf dco fnsoi cdki dc kfbkdcfbka8 }aza sf dkrci bifbzcti/ tkcfc qsc rcz kfgczkiz a 7=&

- Co gabtiz dc kftczbc}tabkf G zc}zcrcfta oa gzabbkf dc cfczna zcgoceada cf co bifbcftzadiz/ qsc cr kf-

tczbc}tada a rs wcu }iz co zcbc}tiz dc cfczna8 rtc gabtiz Gcr sfa }zi}kcdad dco bifbcftzadiz { dc rs rkr-

tcà dc izkcftabkf ao }zidsbkz oa kàncf rioaz { dco zcbc}tiz { dc rs }irkbkf cf co biocbtiz/ ao kftczbc}tazsfa }aztc dc dkbla kàncf rioaz&

- Oar }zdkdar bizzcr}ifdkcftcr rif dc oa gizà/ 1-G

Oa dkrtzkjsbkf dco gosei rioaz rc }scdc bifrkdczaz biì sfa gsfbkf dc oa }irkbkf dcftzi dco zca Az

dco zcbc}tiz/ Gkn KW&:1& Co zca jaei oa bszwa dc dkrtzkjsbkf cr oa cfczna zcgoceada cf co }oafi gibao&

Rk co zcbc}tiz tkcfc sfa afblsza/ ,AJ+ 0 :a/ oa cfczna kftczbc}tada wkcfc dada }iz co zca ri`jzca-

da cftzc A { J/ }sdkfdirc }ifcz co waoiz dc G0K,a+da

-a

( a

K,a+da

-

(

Bifdkbkifcr afoinar rc }scdcf a}okbaz ao bari dc bifbcftzadizcr dc zcwiosbkf&

Co zcfdk`kcfti }tkì dc sf biocbtiz rc ijtkcfc bif sf gabtiz G? 18 oa i}tk`kuabkf dco taài dco

zcbc}tiz }zi}izbkifa sfa nafafbka `|kà dc cfczna tko5

KW&-


20/29

- Zcdsbkcfdi ao `|kì oar }zdkdar }tkbar

- As`cftafdi oar }zdkdar tz`kbar

`kcftzar qsc/ }aza sf zcbc}tiz }cqsci/ k`}okba }zdkdar tz`kbar jaear { }zdkdar }tkbar aotar&

Gkn KW&:1&- Cfczna kftczbc}tada }iz co zcbc}tiz Gkn KW&::&- Dkrtzkjsbkf dco gosei rioaz tczkbi rijzc

sfa rs}czgkbkc fizào ao cec dco zcgocbtiz

Cf bifrcbscfbka/ sf dk`cfrkifadi adcbsadi dco zcbc}tiz k`}okba co tcfcz qsc bi`}ankfaz a`jir tk-

}ir dc }zdkdar dc cfczna& Oa dkrtzkjsbkf dco gosei rioaz tczkbi zcgoceadi }iz sf zcbc}tiz }azajokbi/ ri-

jzc sfa rs}czgkbkc tafncftc ao zcbc}tiz/ dc gizà qsc oa fizào a crta rs}czgkbkc bikfbkda bif co cec dco

lau zcgoceadi/ wkcfc dada }iz oa Gkn KW&:18 oa dkrtizrkf dc oa dkrtzkjsbkf zcao gzcftc a oa kdcao/ }scdc rcz

dcjkda a oir rknskcftcr gabtizcr5

- Kzzcnsoazkdadcr cf oa rs}czgkbkc dco zcgocbtiz qsc }ziwibaf sfa dkr}czrkf { dkgs`kfabkf dc oa kà-

ncf rioaz rijzc co zcbc}tiz

- Czzizcr cf oa izkcftabkf dco biocbtiz/ qsc a`}okgkbaf { dcr}oauaf oa kàncf rioaz rijzc co zcbc}tiz- Czzizcr dc tk}i bifrtzsbtkwi qsc izknkfaf sfa }irkbkf kfbizzcbta dc oa kàncf rioaz rijzc co zcbc}tiz

Oacgkbkcfbka }tkba dco biocbtiz rc dcgkfc biì5 G ,+&Dkrtzkjsbkf dco gosei fizào rijzc co zcbc}tiz cfbifbcftzadizcr bkofdzkbi }azajokbir&-

Oa dkrtzkjsbkf dco gosei tczkbi fizào/ ,ofca dc tzauir cf oa Gkn KW&::+/ rc }scdc }ifcz cf oa gizà5

K0 K | c

-l:, a^+:

0 K | 01

: 0 l

^ 0 l

^ c-l:, a

^+:

cf oa qsc5K/ cr oa dcfrkdad dco gosei dc zadkabkf

K |/ cr oa dcfrkdad dc gosei `|kì cf oa ofca bcftzao

l/ cr co bicgkbkcftc fizào dc dkrtzkjsbkf dc gosei

:a/ cr oa oifnktsd bazabtczrtkba dco zcbc}tiz ,afblsza+

: ^/ cr oa oifnktsd bazabtczrtkba dco bifbcftzadiz 0 oa afblsza dco }oafi dc ajcztsza dco krì

/ cr oa dcrwkabkf rtafdazd dc oa bszwa dc dkrtzkjsbkf fizào

]aza sfa dkrtzkjsbkf rk`tzkba co gabtiz G0=

l a^ c

,l a^ +

:d,l a

^+

=

( c,l a+: d,l a

+

0:

=

l a^

c,

l a^

+:

d,l a

^+

Oir waoizcr dcG rc ijtkcfcf `cdkaftc oa Tajoa dc waoizcr dc oa gsfbkf dc czziz dc Nasrr/ Tajoa

KW&-


21/29

KW&1/ dcgkfkda cf oa gizà5

N,s+ 0 :

=

s

c-s:

ds 0 G/ cf oa qsc5 s 0l a^

Dkrtzkjsbkf dco gosei fizào rijzc co zcbc}tiz cfbifbcftzadizcr }azajioikdcr dc zcwios-bkf&-]aza sfa rs}czgkbkc zcgocbtaftc dco bifbcftzadiz tk}i }azajioikdc dc zcwiosbkf oa gsfbkf dc dkr-

tzkjsbkf fizào cr5

KK |

0 c-l:, z

Z+:

/ rkcfdi5 K |01

: 0 l

Z K0 l

Z c

- ,l zZ

+:

rkcfdi zco zadki dc oa rs}czgkbkc zcbc}tiza { Z co zadki dc oa rs}czgkbkc dc ajcztsza dco bifbcftzadiz&

Co gabtiz dc kftczbc}tabkf5 G0 z

Z

zZ K d, zZ+

-

(

K d, zZ+0

K | =

zZ c

-,l zZ +:: , z

Z+d, z

Z+

K |=

(

c-,l z

Z+:

: , zZ+d,z

Z+0 1 - c

-,l z

Z

+:

qsc c|}zcra sfa zcoabkf cftzc co gabtiz dc kftczbc}tabkfG { oa zcoabkf cftzc oir zadkirz

Z}cz`ktkcf-

di sf bobsoi gbko dcG }aza rkrtcàr dc bifbcftzabkf bif rk`ctza a|kao&

Tajoa KW&1&- Gsfbkf dc czziz dc Nasrr

s N,s+ s N,s+ s N,s+ s N,s+ s N,s+=/== =/===== =/47 =/4 1/2< =/;4;=: 1/4=/=: =/=::37 =/4< =/3=:>3 =/;4 =/ 1/4= =/;3::< 1/=/=4 =/4311= =/3= =/3:=3= =/;7 =/;= =/;< =/17: 1/=: =/=47< 1/:= =/;1=21 1/77 =/;74=/2= =/2:7 =/>1>34 1/:: =/;1332 1/7< =/;= =/;;;< =/>2==1 1/:4 =/;:=3= 1/>= =/;= :/: =/;7 =/;1; 2/:= =/;;;;;4=/4= =/4:71= 1/2: =/;2< =/;4; =/


22/29

Gkn KW&:2&- Zcgocbtiz cwiowcftc dc bzbsoi

Gn KW&:4&- Zcgocbtiz bkofdzkbi }azajokbi abi}oadi aitza cwiowcftc dc bzbsoi

Bifbcftzadiz }azajokbi bi`}scrti&-Co bifbcftzadiz }azajokbi bi`}scrti cr sf rkrtcà cf

gizà dc jazbi cf co qsc oar }azcdcr tkcfcf sf }czgko dctcz`kfadi& Crt bifrtzskdi dc àfcza qsc fi

gizà oa k ancf dco Rio }izqsc oa ijtcfbkf dc sfa kàncf/ ao `cfir biì firitzir oa lcìr wkrti cf co

bari dco }azajioikdc/ cr kfbi`}atkjoc bif oa jrqscda dc sfa bifbcftzabkf rkf }zdkda dc cfczna& Rc

dc`scrtza qsc cf sf rkrtcà bifrtktskdi dc sfa }s}koa dc cftzada dc dk`ctzi d1/ dc sfa }s}koa dc raok-

da dc dk`ctzi d:/ rk co fnsoi dc ajcztsza dc sf lau os`kfiri kfbkdcftc cr co gabtiz dc bifbcftzabkf

à|kào cr5

B 0

d1d:

0f:f1

1rcf

rkcfdi f1 { f: oir fdkbcr dc zcgzabbkf a oa cftzada { a oa raokda&

Gkn KW&:3&- Bifbcftzadiz }azajokbi bi`}scrti

Co }czgko dco bifbcftzadiz crt bi`}scrti }iz dir }izbkifcr dc }azjioa rk`tzkbir/ cf oar qsc oircecr crtf kfbokfadir sf fnsoi zcr}cbti ao cec dc rk`ctza/ dc gizà qsc co gibi dc sfa dc cooar rc cf-

bscftza cf co c|tzcì dc oa itza& Rk rc tià co }sfti I biì izkncf dc biizdcfadar/ rc }scdc bi`}zijaz

qsc oar cbsabkifcr dco }czgko cf }aza`tzkbar rif5

| 0

d: ,1 ( rcf + rcf , - +1 - bir

-d::

{ 0d: , 1 ( rcf + rcf , - +

1 - bir

cf oar qsc cr sf }az`ctzi knsao ao fnsoi qsc gizà co za{i ,I@+ bif oa }azaocoa a ,]G+ qsc }ara }izco }sfti I&

Oar tafncftcr cf oir c|tzcìr ] { ] rif }azaocoar ao cec dc rk`ctza dco bifbcftzadiz&

KW&-


23/29

Oa aotsza dco biocbtiz wkcfc dada }iz5 O 0d1( d:

:bitn / { }aza f1 0 f: rc ijtkcfc oa zcoabkf5

Od:

0 B ( 1: B:- 1

qsc gkea oa oifnktsd O dco biocbtiz cf gsfbkf dc B/ rk rc bifibc d:

Oa oifnktsd O cr k`}iztaftc8 rk }iz cec`}oi5 d: 0 1= b`/ bif B 0 1=/ rc tkcfc O 0 3/3 `&

Sfa dkr`kfsbkf dco waoiz dc O cf 1)2/ a}cfar ìdkgkba co fnsoi dc ajcztsza/ }czi kfgos{c rcfrkjoc-

`cftc cf co }zcbki dc oar rs}czgkbkcr zcgocbtaftcr {/ }iz oi tafti/ dco biocbtiz&

Cf oa Tajoa KW&: rc kfdkbaf aonsfir }az`ctzir { rsr waoizcr bizzcr}ifdkcftcr }aza dkrtkftir nza-

dir dc bifbcftzabkf& Oa nzaf wcftaea dc crtc tk}i dc biocbtiz cr qsc }zbtkba`cftc }czàfcbc gkei/ }zc-

bkrafdi dc aonsfir aesrtcr cf oa izkcftabkf rcnf oa }iba dco ai/ ba}tafdi oa zadkabkf dkzcbta dszaf-

tc sf k`}iztaftc f`czi dc lizar a oi oazni dco da/ biì rc kfdkba cf oa Tajoa KW&2&

Co f dc lizar dc ba}tabkf dkr`kfs{c ao as`cftaz oa bifbcftzabkf8 ar/ }iz cec`}oi/ cf co riortkbki

}ara dc > lizar }aza B0 1= { 0 7/ a 4/4 lizar }aza B 0 :=/3 :4 1== :=3 43/3 < 1== 1:

1= 2=/3 2 1== { abtsaz biì dkr}irktkwi aftkzadkaftc&Ta`jkf rc }scdcf aribkaz dir biocbtizcr kdcaocr bif fdkbcr dc zcgzabbkf dkgczcftcr/ Gkn KW&:


24/29

}aza sf abi}oa`kcfti bzkrtao-akzc/ oa zcoabkff:f1

0 1/3 &

Ba}tadiz }oafi

Gkn KW&:>Bifbcftzadiz }azajokbi bi`}scrti aribkadi a sf ba}tadiz }oafi

Gkn KW&:/3 ;13 >/3

Riortkbki :2/3 >

Bifbcftzadizcr tzifbibfkbir&- Oir cr}ceir tzifbibfkbir }scdcf rczwkz }aza kzzadkaz sfa uifa

gibao okfcao& Co zc}azti dc oa zadkabkf zcgoceada fi cr `s{ liìnfci a basra dc oa wazkabkf dc oa rs-

}czgkbkc zcgocbtiza oatczao cftzc oar jarcr dco tzifbi dc bifi& Rk co fnsoi cf co wztkbc dco bifi cr:/ Gkn

KW&:;/ rc }scdc bi`}zijaz qsc oa bifdkbkf }aza qsc sf lau kfbkdcftc }azaocoi ao cec dco cr}cei/ rc zcgocec

cf oa }zk`cza zcgoc|kf cf oa jarc dco bifi }aza ? 43/ cr5

: - : 6 =

- Rk/ 0 43/ oa zadkabkf kfbkdcftc rc zcgocea rijzc co cec }zidsbkfdirc oa `|kà bifbcftzabkf- Rk/ 6 43/ oa zadkabkf cr zcgoceada labka azzkja- Rk co bifi tkcfc oa rsgkbkcftc aotsza/ }aza bsaoqskcz waoiz dco fnsoi cf co wztkbc/ oa zadkabkf zcgocea-

da abaja rkc`}zc ajafdifafdi co biocbtiz

Gkn KW&:;&- Bifbcftzadiz tzifbibfkbi/zcbc}bkf cf oa jarc Gkn KW&2=&- Bifbcftzadiz tzifbibfkbi8 zcbc}bkf cf co cec

Oir cr}ceir bfkbir fi rif jscfir bifbcftzadizcr& Rkf c`jazni/ }aza aonsfar a}okbabkifcr `s{

bifbzctar/ biì }iz cec`}oi/ ba}tafdi oa kàncf dc Nasrr/ gizàda cf co wztkbc dc sf bifbcftzadiz

}azajokbi/ cf oa jarc à{iz dco cr}cei tzifbibfkbi/ rc }scdc kfdsbkz oa bifbcftzabkf a rs waoiz `|k-ì rkf qsc a}azcubaf }zdkdar k`}iztaftcr dc gosei&

KW&-;=


25/29

KW&;&- ZCFDK@KCFTI TZ@KBI DC SF BIOCBTIZ BKOFDZKBI ]AZAJOKBI

Waìr a bifrkdczaz sf bifbcftzadiz bkofdzkbi }azajokbi { sf zcbc}tiz bkzbsoaz rkf bsjkczta ,0 1+/

aozcdcdiz dco bsao fi c|krtcf nzadkcftcr dc tc`}czatsza&

Co bicgkbkcftc dc tzafr`krkf dc baoiz cftzc co tsji a Tz { co goskdi a TG qsc bkzbsoa }iz rs kftczkiz cr

lbG { co bicgkbkcftc noijao dc }zdkdar ao c|tczkiz Sb/ dc oa gizà5

1

SB0 1lwkcfti

( 1lz

rkcfdi5lz co bicgkbkcftc dc zadkabkf/ knsao a 5 lz 0 4 z T

2

z oa c`ktafbka dco zcbc}tizT oa tc`}czatsza `cdka dc oa zadkabkf

Biì co gosei dc baoiz cr cocwadi/ la{ qsc tcfcz cf bscfta co bicgkbkcftc dc tzafrgczcfbka dc baoiz }iz

bifdsbbkfh/ dcrdc oa rs}czgkbkc c|tczkiz dco tsji zcbc}tiz/ a oa kftczkiz/ }iz oi qsc co bicgkbkcftc noijao dctzafr`krkf dc baoiz S jaradi cf co dk`ctzi c|tczkiz dc dco tsji/ dcrdc oa rs}czgkbkc c|tczkiz ao goskdi/ cr5

1S

0 1SB

(dc

lbG dk(

dc: h

ofdcdk

Oa nafafbka tko dc cfczna }iz sfkdad dc oifnktsd O dco zcbc}tiz/ cf gsfbkf dc T z { Ta/ { oa tc`}cza-

tsza dco zcbc}tiz Tz rif5

Qs0 AaO

KrG,+ - SB AzO

,Tz - Ta+ 0Aa R

O- SB

AzO

, Tz - Ta+ 0Aa0 : ^ OAz 0 dc O

R 0 KrG ,+

0

0 : ^ R - SB dc , Tz - Ta+ Tz 0 Ta -Qs O - Aa R

SB Az

Rk rc }ifc oa nafafbka tko dc cfczna/ }iz sfkdad dc oifnktsd O/ cf gsfbkf dc oir tz`kfir dc tzafrgc-

zcfbka dc cfczna ao goskdi/ cftzc Tz { TG/ rc ijtkcfc5

Qs0 d k, Tz - TG+

dclbGdk

(dc

: hof

dcdk

0dk , Tz - TG+

1S

- 1SB

0

AzO

, Tz - TG+

1S

- 1SB

Tz 0 TG(QsOAz

, 1S

- 1SB

+

Knsaoafdi oar c|}zcrkifcr dc Tz rc ijtkcfc5 Tz 0 Ta -QsO - AaR

SB Az0 TG(

QsOAz

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+

Dcr}ceafdi Qs zcrsota sfa c|}zcrkf qsc dc}cfdc dc TG { Ta5

Qs0

S AzO

,- TG( Ta (Aa RSB Az

+ 0 SSB

AaO

xR - SB AzAa

,TG- Ta+p 0 GAaO

x R - SB AzAa

, TG- Ta+p

rkcfdi G0 SSb

co gabtiz dc cgkbkcfbka dco biocbtiz&

Oa c|}zcrkf aftczkiz rc }scdc }ifcz cf gsfbkf dc oa tc`}czatsza TG1 dco goskdi a oa cftzada { cf

gsfbkf dc sf gabtiz dc cwabsabkf dc baoiz GZ dco zcbc}tiz ao goskdi/ qsc rc dcgkfc biì5

GZ 0

Nafafbka cfczntkba tkoNafafbka cfczntkba tko rk oa rs}czgkbkc dco zcbc}tiz crt a T G1

0N b}

Az SB,1 - c

-Az SB G

N b} +

KW&-;1


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rkcfdi N co gosei rkbi/ zcrsotafdi5 Qs0 Aa GZxR -AzSB

Aa, TG1 - Ta+ p

Rk co zcbc}tiz crtswkcrc zcbsjkczti/ lajza qsc tcfcz cf bscfta co }zidsbti tzafr`ktafbka ajriztaf-

bka ,+ { cwaosaz dc fscwi Sb/ }iz bsafti a}azcbcf zcrkrtcfbkar adkbkifaocr dc tzafr`krkf dc baoiz&

Rk co zcbc}tiz gsfbkifa biì baodcza ,wa}izkuadiz+/ zcrsota qsc G cr knsao a GZ }iz bsafti fi la{

nzadkcftcr dc tc`}czatsza cf oa dkzcbbkf dco gosei8 rk sfa }aztc dco zcbc}tiz gsfbkifa biì baodcza

,wa}izkuadiz+ { co zcrti biì baocftadiz dc oqskdi/ bada tzaì bizzcr}ifdkcftc a sf cgcbti la{ qsc tza-

tazoi }iz rc}azadi&

Co zcfdk`kcfti tz`kbi rc dcgkfc cf oa gizà5 0Qs

Kr Aa0

QsK= bir Aa

KW&1=&- CGCBTIR DC OA BA]ABKDAD TZ@KBA

Oir cgcbtir dc oa ba}abkdad tz`kba }aza biocbtizcr dc bifbcftzabkf dc `cdka tc`}czatsza/ rc }sc-dcf baobsoaz dc oa `krà gizà qsc }aza oir biocbtizcr dc }oaba }oafa& Oir bifbcftzadizcr rc cfbscf-

tzaf kfkbkao`cftc a oa tc`}czatsza a`jkcftc i `s{ }z|kìr a cooa/ }iz oi qsc }aza dctcz`kfaz oa ba}a-

bkdad tz`kba dc oir `krìr lajz qsc tcfcz cf bscfta qs }aztcr dco rkrtcà waf a kfgoskz cf crtc cgcb-

ti/ bsafdi rc ìdkgkqsc oa tc`}czatsza/ ao }ifcz co biocbtiz cf znk`cf dc tzajaei&

]scrti qsc co zcbc}tiz tkcfc sfa rs}czgkbkc `r }cqsca qsc co biocbtiz cqskwaocftc dc }oaba }oafa/

rs ba}abkdad tz`kba }iz bada nzadi qsc rc ìdkgkqsc rs tc`}czatsza }scdc rcz rknfkgkbatkwa`cftc

`r jaea&

Fi ijrtaftc/ oa wazkabkf dc oa tc`}czatsza dc sf zcbc}tiz dc sf BB] }scdc rcz `s{ rs}czkiz a oa

dco biocbtiz dc }oaba }oafa {/ }iz oi tafti/ co cgcbti dc oa ba}abkdad dc aoàbcfa`kcfti dc baoiz }scdcrcz rknfkgkbatkwi8 crtc cgcbti rc }scdc bifrkdczaz biì co zcrsotadi dc dir gabtizcr/ biì rif5

a+ Oa cfczna fcbcrazka }aza baocftaz co biocbtiz dcrdc oa tc`}czatsza dc oa fiblc a rs tc`}czatsza dc-

gkfktkwa dc gsfbkifa kcfti dszaftc co da

j+ Co cgcbti tzafrktizki dc gsfbkifa`kcfti dco biocbtiz jaei bifdkbkifcr `ctcizionkbar wazkajocr

Oa wazkabkf dc oa tc`}czatsza dcrdc oa a`jkcftao dc oa fiblc a oar dc znk`cf dc gsfbkifa`kcfti

rif }zcdcbkjocr { rc }scdc baobsoaz oa cfczna fcbcrazka }aza oinzaz dkbla wazkabkf&

Co cgcbti tzafrktizki }iz ba`jkir `ctcizionkbir cr `r dkgbko dc }zcdcbkz }iz bsafti sfa kftczzs}-

bkf cf oa zadkabkf dkzcbta dcjkda a oa fsjirkdad zcdsbc oa cftzada dc zadkabkf dkzcbta cf co zcgocbtiz a

bczi/ }zidsbkcfdi badar dc tc`}czatsza à{izcr qsc cf oir biocbtizcr dc }oaba }oafa&

KW&11&- ZCFDK@KCFTI C\]CZK@CFTAO DC OIR BB]

Co zcfdk`kcfti dc oir biocbtizcr dc bifbcftzabkf dc}cfdc dc sfa a`}oka naà dc gabtizcr/ fi }s-

dkfdirc stkokuaz fkfnf `tidi ncfczao qsc }cz`kta co bobsoi dc bsaoqskcza dc cooir cf gizà ncfczaok-

uada/ }iz oi qsc la{ qsc zcriowcz bada }zijocà biì sf bari }aztkbsoaz&

A ttsoi dc cec`}oi rc }zcrcftaf oir datir zcoatkwir a sf biocbtiz ,B]+ bs{i zcgocbtiz bkofdzkbi-}aza-

jokbi tkcfc sfa ajcztsza dc 1/


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larta itzar dco izdcf dc 1


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zadkabkf as`cftafdi co zadki z dco zcbc}tiz/ oi qsc a rs wcu izknkfa sf as`cfti dc oar }zdkdar tz`k-

bar8 oar ofcar dkrbiftkfsar rif c|}czk`cftaocr8 oar bszwar biftkfsar rc laf ijtcfkdi `cdkaftc oir bi-

zzcr}ifdkcftcr jaoafbcr cfczntkbir/ stkokuafdi oir waoizcr a}zi}kadir dco gabtiz dc kftczbc}tabkf G&

Gkn KW&2:&- Cgkbkcfbka biì sfa gsfbkf dco zadki dcozcbc}tiz }aza sf BB]

Gkn KW&22&- Bi`}azabkf dco gosei cftzc o`ktcr gkeir {oa dkrtzkjsbkf fizào

Oar nci`ctzar dco biocbtiz }aza rkrtcàr qsc tcfnaf sf czziz dc izkcftabkf dcr}zcbkajoc/ qsc }zi-

}izbkifaf sf zcfdk`kcfti tz`kbi }tkì/ rc baobsoaf cf gsfbkf dc5

a+ Co bicgkbkcftc dc dkrtzkjsbkf dco gosei }aza sfa bszwa fizào dc dkrtzkjsbkf5 Krj+ Dco fdkbc dc }zdkdar tczkbar }iz sfkdad dc rs}czgkbkc dco zcbc}tiz/ dcgkfkdi biì co czziz afnsoaz

dc bszwatsza dc sf zcgocbtiz dc tzauadi tczkbi/ bif sfa dkrtzkjsbkf sfkgiz`c dco czziz afnsoaz

b+ Dco }az`ctzi Gqsc dcrbzkjc oa }zcbkrkf }tkba dco zcgocbtiz

Cf oa Gkn KW&22 rc `scrtza sf cec`}oi dc dkrtzkjsbkifcr dc gosei qsc rszncf dc bada sfa dc crtar rs-

}irkbkifcr&

Gkn KW&24&- Ncfczabkf `|kà dc cfczna }aza dkwczrir tk}ir dc }zdkdar tz`kbar

Cf oar Gkn KW&24 rc kfdkbaf oir `|kìr dc oar bszwar bizzcr}ifdkcftcr a rkrtcàr dc bifbcftzabkf

bkofdzkbir { dc zcwiosbkf/ }aza sfa naà dc waoizcr dc bada }az`ctzi qsc dcrbzkjc oa baokdad }tkba

dco bifesfti/ ijrczwfdirc qsc ta`jkf rc }idzaf stkokuaz itzir }az`ctzir qsc dcrbzkjkcrcf oa baokdad}tkba dco rkrtcà/ }sdkcfdi labcz bi`jkfabkifcr dc ìdcoir dc zcgocbtizcr { dc zcbc}tizcr dkwczrir/

qsc }zi}izbkifcf dctcz`kfadar dkrtzkjsbkifcr dco gosei rijzc oa rs}czgkbkc dco zcbc}tiz&

]aza sf zcgocbtiz bfkbi { zcbc}tiz bkofdzkbi/ oa kftcfrkdad dc gosei cf co zcbc}tiz waza bif co bsadza-

KW&-;4


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di dc oa dkrtafbka dcrdc rs c|tzcì kfgczkiz& Bif zcbc}tizcr adcbsadir { bif zcgocbtizcr }azajokbir tc-

zkba`cftc }czgcbtir/ rc }scdcf bifrcnskz dkrtzkjsbkifcr dc gosei rijzc co zcbc}tiz bark sfkgiz`cr&

Itzir rkrtcàr nci`tzkbir dc kftczr }zbtkbi/ rc bizzcr}ifdcf bif nci`ctzar dco zcgocbtiz-zcbc}tiz

qsc zcqskczcf dc dkr}irktkwir qsc }cz`ktaf labcz sf rcnsk`kcfti `fkì dco ìwk`kcfti a}azcftc dco

Rio&Crtir zcgocbtizcr crtabkifazkir/ }scdcf aesrtaz rs kfbokfabkf a kftczwaoir dc sfa rcàfa/ }aza

bi`}cfraz oa dcbokfabkf { bifrkrtcf rk`}oc`cftc cf sf zcgocbtiz bkofdzkbi bkzbsoaz ìftadi rijzc sf

cec Crtc-Icrtc/ bif sf zcbc}tiz dc rcbbkf tzafrwczrao tzkafnsoaz/ oinzfdirc ar }cqscir fdkbcr dc

bifbcftzabkf/ dco izdcf dc tzcr&

Ta`jkf rc }scdcf dcrazziooaz rkrtcàr rk`koazcr qsc zcqskczcf/ }iz cec`}oi/ sf aesrtc dco rcnsk-

`kcfti dco Rio a oi oazni dco da/ oinzfdirc ar fdkbcr dc bifbcftzabkf dco izdcf dc 1=&

KW&1:&- @ATCZKAOCR [ BIFRTZSBBKF DC OIR ZCGOCBTIZCR

Oa bifrtzsbbkf dco zcgocbtiz kfbos{c sfa rczkc dc }zijocàr qsc labcf bifwcfkcftc dkwkdkzoc cf dir

}aztcr/ co zcwcrtk`kcfti dc oa rs}czgkbkc zcgocbtiza { oa crtzsbtsza ri}iztc { dc izkcftabkf& Oir tk}ir dc

zcwcrtk`kcfti dc oa rs}czgkbkc zcgocbtiza { rsr bazabtczrtkbar/ rc laf tzatadi aftczkiz`cftc8 la{ qsc

stkokuaz àtczkaocr dc zcgoc|kf bif sfa zcgocbtafbka cr}cbsoaz `|kà dszaftc co }czkidi dc gsfbkifa-

`kcfti dco biocbtiz qsc crt cf bifbizdafbka bif oir birtcr dc gajzkbabkf { àftcfk`kcfti8 ta`jkf

la{ qsc tcfcz cf bscfta oa }irkjkokdad dc zcfiwaz co zcwcrtk`kcfti dc zcgoc|kf/ a}okbafdi/ }iz cec`}oi/

sfa fscwa ba}a dc }cobsoa dc }ortkbi zcgocbtkwi/ tao biì @{oaz aos`kfkuadi/ i }iz rsrtktsbkf dc oar

}oabar i wiowkcfdi a `ctaokuaz/ rk oa nafafbka dc cfczna tko adkbkifao esrtkgkba co dcrc`jiori&

Co bscz}i { oa crtzsbtsza ri}iztc tkcfcf sfa nzaf k`}iztafbka cf rs kfgoscfbka rijzc co gabtiz dc kf-

tczbc}tabkf G8 co gsfbkifa`kcfti bizzcbti dco biocbtiz dc}cfdc dc oa ba}abkdad dc oa crtzsbtsza dc

àftcfcz oa gizà dc oa rs}czgkbkc zcgocbtiza { dc rs izkcftabkf/ qsc rif gabtizcr bztkbir a oa liza dc

labcz sf dkrci/ cf difdc lajz qsc tcfcz cf bscfta oar rknskcftcr bifrkdczabkifcr5

a+ Co bscz}i { oa crtzsbtsza dcjcf tcfcz sf ri}iztc qsc }cz`kta ijtcfcz oar dkwczrar }irkbkifcr dc

izkcftabkf/ rkf qsc rti }ziwiqsc sfa dkrtizrkf rknfkgkbatkwa dc oa rs}czgkbkc dco zcgocbtiz dcjkda a rs

}zi}ki }cri&

j+ Dcjcf tcfcz oa ba}abkdad dc gsfbkifaz {/ cf bifrcbscfbka/ dc fi dkrtizrkifazrc dc gizà rknfkgkbatk-

wa bif oir wkcftir qsc fizào`cftc ri}ocf cf co osnaz/ {a qsc oa bazna dco wkcfti ok`kta co taài }zbtkbi

dc bada bifbcftzadiz&

b+ Tkcfcf qsc crtaz }zc}azadir }aza zcrkrtkz dair crtzsbtszaocr }ziwibadir }iz wkcftir gscztcr { tiz-`cftar8 cf crtar bkzbsfrtafbkar rc ocr rktsaz cf sfa }irkbkf gkea { adcbsada qsc }cz`kta cosdkz taocr gc-

f`cfir&

Construcción de concentradores reflectores solares

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