_ralgapaks y cpfagcgakl`s j` alt`fad`lgac crtaffigacf Pl `lnkqu` pcrc fc `gklkbâc y ktrcs ga`lgacs skgacf`s `l X
Cfnr`jk Kfduâl
_ralgapaks y cpfagcgakl`s j` alt`fad`lgac crtaffigacf Pl `lnkqu` pcrc fc `gklkbâc y ktrcs ga`lgacs skgacf`s `l X
Cfnr`jk Kfduâl
_ralgapaks y cpfagcgakl`s j` alt`fad`lgac crtaffigacf. Cfnr`jk Kfduâl Gkpyradmt (g) 8?3> (g) 8?3> Cfnr`jk Kfdual. BAZ Fag`ls` _`rbassakl as m`r`hy drclt`j, nr`` kn gmcrd`, tk cly p`rskl khtcalald c gkpy kn tmas skntwcr` clj csskgact` csskgact`j j jkgub`ltc jkgub`ltctakl takl ffif`s (tm` "Wkntwcr`"), "Wkntwcr`"), tk j`cf j`cf al tm` Wkntwcr` Wkntwcr` watmkut watmkut r`stragt r`stragtakl, akl, algfujald algfujald watmkut fabatctakl fabatctakl tm` radmts tk us`, gkpy, bkjany, bkjany, b`rd`, b`rd`, puhfasm, jastrahut`, jastrahut`, suhfag`ls`, suhfag`ls`, clj/kr s`f f gkpa`s gkpa`s kn tm` Wkntwcr Wkntwcr`, clj tk p`rba p`rbatt p`rsk p`rskls ls tk wmkb tm` Wkntwcr Wkntwcr`` as nurlas nurlasm` m`j j tk jk sk, suhi`gt suhi`gt tk tm` nkffkwald gkljatakls9 Zm` chkv` gkpyradmt lktag` clj tmas p`rbassakl lktag` smcff h` algfuj`j al cff gkpa`s kr suhstcltacf pkrtakls kn tm` Wkntwcr`. Zm` skntwcr` as prkvaj`j cs as, watmkut wcrrclty kn cly ealj, `xpr`ss `xpr`ss kr abpfa`j, algfujald hut lkt fabat`j tk tm` wcrrclta`s wcrrclta`s kn b`rgmcltch b`rgmcltchafaty, afaty, ffitl`ss nkr c pcrtagufcr purpks` clj lklalnrald`b`lt. Al lk `v`lt smcff tm` cutmkrs kr gkpyradmt mkfj`rs h` fachf` nkr cly gfcab, jcbcd`s kr ktm`r fachafaty, wm`tm`r al cl cgtakl kn gkltrcgt, tkrt kr ktm`rwas`, crasald nrkb, kut kn kr al gkll`gtakl watm tm` skntwcr` kr tm` us` kr ktm`r j`cfalds al tm` skntwcr`.
Jas`ók j` pkrtcjc9 Bcraclc Xâks
3
_crc tkjk cqu`f qu` fc guraksajcj alsctasn`gmc f` gkrrk` j` alg`rtajubhr` y `sg`ptagasbk.
8
Âljag` d`l`rcf 3. Alt Altrkjugga rkjugga÷l ÷l
0
8. X`qu`r X`qu`raba`l aba`ltks tks y sud`r`lgacs sud`r`lgacs
37
8.?.3. Alstcf Alstcfcga÷l cga÷l j`f f`ldu f`lduci` ci` . . . . . . . . . . . . . . . . . . 3: 8.?.8. Alstcf Alstcfcga÷l cga÷l j` j` alt`rncz alt`rncz j` usucrak usucrak Xstujak Xstujak . . . . . . . 3> 8.?.7. Lkgakl` Lkgakl`ss Hãsagcs, Hãsagcs, cpr`lja cpr`lja`ljk `ljk X gkl swarf swarf . . . . . . . 3= 8.3. Bct` Bct`racf racf cjagaklcf cjagaklcf y g÷bk g÷bk trchcicr gkl gkl `f g÷jadk . . . . . . . . 31 8.8.. Gkl 8.8 Gkltcg tcgtk tk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8?
7. _ralg _ralgapak apakss hãsagks j` cpr`ljazci` cutkbctazcjk cutkbctazcjk 7.3. Lkgakl` Lkgakl`ss hãsagcs j` cpr`ljaz cpr`ljazci` ci` sup`rvascjk sup`rvascjk y lk sup`rvascjk sup`rvascjk
83 8:
7.3.3. Alt Altrkjugga rkjugga÷l ÷l c bkj`fazcga÷l bkj`fazcga÷l y gfcsaffigc gfcsaffigcga÷l ga÷l fal`cf fal`cf . . . . 80 7.3.8. Clãfas Clãfasas as j` j` r`dr`s r`dr`sa÷l a÷l fal`cf fal`cf . . . . . . . . . . . . . . . . 8> X`dr`sa÷l c fc b`jkgrajcj fc b`jkgrajcj , krad`l j` fc r`dr`sa÷l fal`cf
84
7.8. Gfcsaffi Gfcsaffigcga gcga÷l ÷l gkl bátkjks j` r`dr`sa r`dr`sa÷l ÷l fal`cf . . . . . . . . . . 78 7.8.3. @lt @ltr`lcb r`lcba`l a`ltk tk j` cfdkratbk cfdkratbk j` gfcsaffigcga gfcsaffigcga÷l ÷l fal`cf . . . 70 7.8.8. _ru`h _ru`hcc j`f cfdkratb cfdkratbkk j` gfcsaffigcg gfcsaffigcga÷l a÷l fal`cf fal`cf . . . . . . . 71 7.8.7. 7.8 .7. X`s X`sub` ub`l l . . . . . . . . . . . . . . . . . . . . . . . . . . :0
7
ÂLJAG@ D@L@XCF
:. Cfdk Cfdkratb ratbks ks j` gfcsaffi gfcsaffigcga÷ gcga÷l l fal`cf
:4
:.?.3. :.? .3. Gfc Gfcsaffi saffigcg gcga÷l a÷l j` bù bùfta ftapf` pf`ss gct gct`dk `dkrâc râcss gkl clãfasas clãfasas jas jas-grabalclt` fal`cf (FJC) . . . . . . . . . . . . . . . . . 03 :.?.8. Ncs` j` `l `ltr`lc tr`lcba`l ba`ltk tk . . . . . . . . . . . . . . . . . . 0> :.?.7. Pl bátkjk bátkjk j` b`jaga÷l b`jaga÷l j`f j`f j`s`bp`ók j`s`bp`ók sup`rvascjk sup`rvascjk . . >3 :.?.:. :.? .:. J`s J`s`bp` `bp`ók ók j` fc ncs` ncs` j` pru`hc pru`hcss . . . . . . . . . . . . >: :.?.0. Gfcsaffi Gfcsaffigcga gcga÷l ÷l j` gfa`lt`s, gfa`lt`s, gcsk gcsk j` r`tcaf bcre`t bcre`tald ald . . . >4 :.?.>. _r`pr _r`prkg`scba kg`scba`lt `ltkk j` jctks9 `sgcfcba` `sgcfcba`ltk ltk y lkrbcfazclkrbcfazcga÷l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 :.?.4. Ncs` j` `l `ltr`lc tr`lcba`l ba`ltk tk . . . . . . . . . . . . . . . . . . 4>
0. Cfdk Cfdkratb ratbks ks pr`jagtavks pr`jagtavks
=8
0.3. Gkl Gklt`xt t`xtkk mast÷r mast÷ragk agk . . . . . . . . . . . . . . . . . . . . . . . . =: 0.8. X`j` X`j`ss l`urklcf` l`urklcf`ss crtaffigacf` crtaffigacf`ss . . . . . . . . . . . . . . . . . . . => 0.8.3. _r`ja _r`jagga÷ gga÷l l j` pr`gak j` cggakl` cggakl`ss gkl r`j`s l`urklc l`urklcf`s f`s crtaffigacf`s . . . . . . . . . . . . . . . . . . . . . . . . . =1
>. Hahf Hahfakdrc akdrcnâc nâc
1>
:
Gcpâtufk 3 Altrkjugga÷l ‖At as lkt quat` c l`w aljustracf r`vkfutakl, hut as skb`tmald l`crfy tmct sgcf`. Kur r`fctaklsmaps watm gkbput`rs mcs gmcld`j. T` us`j tk prkdrcb tm`b, lkw w` gcl t`cgm tm`b‒ Maltkl (8?34) _ksahf`b`lt`, drcl pcrt` j` lksktrks m`bks `sgugmcjk qu` cfdkratbks ‖alt`fad`lt`s‒ r`cfazcl kp`rcgakl`s `l b`rgcjks hursãtaf`s gkl r`ljaba`ltks `ffiga`lt`s. Zcbhaál `s buy prkhchf` j`jugar qu` v`mâgufks j` gkljugga÷l cut÷lkbc ta`l`l sast`bcs j` alt`fad`lgac crtaffigacf qu` f`s p`rbat`l gkljugar j` nkrbc s`durc3 . Algfusav`, cfdulks mchrãl aj`ltaffigcjk qu` ul t`fánklk b÷vaf cf `sgugmcr gkbcljks j` vkz mcg` ul r`gklkgaba`ltk j` alt`fad`lgac crtaffigacf. W`durcb`lt` cfdulks j` lksktrks tcbhaál m`bks kht`lajk cfdulc lkga÷l j` alt`fad`lgac crtaffigacf pkr b`jak j` cfdùl tapk j` gklt`lajk fat`rcrak k gal`bctkdrãffigk. Asccg Csabkv, ncbksk `sgratkr j` ga`lgac ffigga÷l, skfâc algfuar `l sus 3
_kr `i`bpfk, fks cvclg`s `l gkljugga÷l cut÷lkbc k csastajc j` Ph`r Z`gmlkfkda`s.
mttps9//www.uh`r.gkb/gata`s/pattshurdm/s`fn-jravald-uh`rs/
0
GC_ÂZPFK 3. ALZXKJPGGA×L lkv`fcs fc pksahafajcj j` ul sast`bc j` alt`fad`lgac crtaffigacf nulgaklcljk `l gklvav`lgac r`dufcr gkl mubclks ` algfusav` sud`râc qu` fks rkhkts pkjrâcl j`scrrkffcr `stcjks j` gklga`lgac sabafcr cf mubclk. Wkrpr`lj`lt`b`lt`, mky `l jâc `stks pfclt`cba`ltks r`suftcl cs`quahf`s pcrc cfdulks ga`ltâffigks y gkl barcs c s`r pcrt` j` lu`strc vajc gktajaclc `l ul nuturk lk buy f`iclk s`dùl sus prky`gtks. Cfdulks j` `stks pfclt`cba`ltks `xpfagcl fc ncgtahafajcj j` trclsn`rar fc gklga`lgac mubclc c ul krdclasbk rkh÷tagk pcrc b`jacjks j` `st` sadfk. Jabatry Asek`v, ul r`lkbhrcjk baffklcrak alt`r`scjk `l abpufscr j`scrrkffks j` alt`fad`lgac crtaffigacf ta`l` gkbk khi`tavk ffilclgacr y j`scrrkffcr ul prky`gtk j` cbhagakl`s g÷sbagcs. @f prky`gtk Cvctcr prkpkl` qu` pcrc `f cók 8?:0 fc t`glkfkdâc s`rã gcpcz j` trclsn`rar fc gklga`lgac mubclc c ulc gkbputcjkrc y csâ, fkdrcr fkld`vajcj p`rp`tuc j` fc `sp`ga` mubclc. Culqu` su`l` jaspcrctcjk t`l`r `l ulks cóks `st` tapk j` t`glkfkdâc, cfdulks cvclg`s yc skl tcldahf`s. @l `f 8?30 s` pr`s`lt÷ fc prab`rc ncs` j`f prky`gtk Cvctcr. Cpcr`lt`b`lt`, fks ga`ltâffigks ` ald`la`rks `lgcrdcjks j`f prky`gtk fkdrcl gkltrkfcr ul rkhkt cltrkpkb÷rffigk c trcvás j` ulc alt`rncz gkbputcgaklcf gkltrkfcjc gkl `f g`r`hrk mubclk, `s j`gar, gkltrkfcr c vkfultcj `f bkvaba`ltk j` ul cljrkaj` gkl s÷fk p`lscrfk. Fks cvclg`s j`f prky`gtk r`suftcl tcl ncsgalclt`s qu` cfdulks ga`ltâffigks gr``l qu` sa`ltc fcs hcs`s qu` suhycg`l fc albkrtcfajcj j` fc gklga`lgac mubclc. Gcjc jâc, fks cvclg`s `l t`glkfkdâc r`fcgaklcjc c alt`fad`lgac crtaffigacf skl abpr`saklclt`s. Wal `bhcrdk, `f krâd`l s` r`bkltc cf pcscjk5 bãs cffã j` fc `xast`lgac j` fcs gkbputcjkrcs gkbk s` gklkg`l mky `l jâc, algfusav`, `st` krad`l pu`j` s`r rcstr`cjk sadfks ctrãs. Drcl pcrt` j` fcs hcs`s j` alt`fad`lgac
>
GC_ÂZPFK 3. ALZXKJPGGA×L crtaffigacf qu` s` j`scrrkffc mky `l jâc, saqua`rc p`rt`l`g`l c `st` k `f clt`rakr baf`lak. _`lscjkr`s dra`dks gfãsagks, mcg` bãs j` jks baf cóks yc s`ltchcl fcs hcs`s j` fc alt`fad`lgac crtaffigacf y su jasgusa÷l bkj`rlc. _`rk, »G÷bk `s pksahf` qu` fks krâd`l`s j` cfdk t`glkf÷dagcb`lt` tcl `sp`gacfazcjk t`ldcl ul krad`l tcl r`bktk `l `f ta`bpk;. Cfdulks cutkr`s cs`durcl qu` fks nuljcb`ltks b`tkjkf÷dagks j` fc alt`fad`lgac crtaffigacf `stãl hcscjks `l t`krâcs j`f gklkgaba`ltk j`sj` mcg` ga`ltks j` cóks, y qu` cfdulks j` fks pr`g`ptks ta`l`l krâd`l`s j`sj` fks p`lscjkr`s gfãsagks dra`dks, `stk mcg` bãs j` ul pcr j` baf`laks. _crc `lt`lj`r fks pralgapaks hãsagks j` alt`fad`lgac crtaffigacf (k gucfqua`rc j` sus v`rta`lt`s), `s l`g`scrak gklkg`r fc nkrbc `l qu` fks mubclks cjquarabks gklkgaba`ltk y fcs rczkl`s pkr fcs gucf`s `st` gklkgaba`ltk `s abpkrtclt`. @s nuljcb`ltcf, p`lscr `l tárbalks j` cjquasaga÷l j` gklkgaba`ltk cf bkb`ltk j` trctcr j` `ls`ócr c p`lscr k `bufcr fc nkrbc `l qu` rczklcl fks s`r`s mubclks. Fc ga`lgac qu` `stujac fc nkrbc `l qu` p`lscbks `s gklkgajc gkbk `past`bkfkdâc. @f `stujak j`f gklkgaba`ltk mc sajk t`bc g`ltrcf `l fc ffifksknâc pkr sadfks y jak krad`l c fc `past`bkfkdâc. @f tárbalk `past`bkfkdâc ta`l` krad`l dra`dk y s` gkbpkl` j` `past`b` (s`baffc) y fkdks (`stujak). Plc vcra`jcj alb`lsc j` cutkr`s y gkrra`lt`s j`f p`lscba`ltk gkbpkl`l `stc jav`rsc pcrt` j` fc ffifksknâc, `l `st` fahrk s÷fk s` b`lgaklc ulc balùsgufc p`rk nuljcb`ltcf pcrt` j` fc `past`bkfkdâc qu` jc krâd`l c fks pralgapaks j` alt`fad`lgac crtaffigacf. @lt`lj`r fc nkrbc `l qu` s` kradalc `f gklkgaba`ltk j`sj` fc `past`bkfkdâc p`rbat` gkbpr`lj`r fc nkrbc `l qu` s` pr`s`ltcl cfdulks j` fks pcrcjadbcs j` alt`fad`lgac crtaffigacf y `f pkrquá cfdulks cutkr`s gklsaj`rcl qu` tcf
4
GC_ÂZPFK 3. ALZXKJPGGA×L ‖alt`fad`lgac‒ crtaffigacf lk `xast`. Pl gklg`ptk hãsagk qu` ta`l` sadfks j` jasgusa÷l `s skhr` `f krad`l j`f gklkgaba`ltk. Cfdulks ffif÷sknks `stchf`g`l qu` c trcvás j` fks s`ltajks (vastc, kfnctk, tcgtk `tg) s` khta`l` alnkrbcga÷l skhr` fk qu` lks rkj`c. Cjagaklcfb`lt` c fks s`ltajks, tcbhaál pfclt`cl qu` j` nkrbc b`ltcf-alt`rlc fks mubclks kht`l`bks gklkgaba`ltk y `stk iustaffigc fc `xast`lgac j` fc abcdalcga÷l y fks su`óks, pkr `i`bpfk. NfcsaŊsea (8?3>) `stchf`g` qu` fks prab`rks ffif÷sknks `l jastalduar `ltr` p`rg`pga÷l s`lskracf y p`rg`pga÷l b`ltcf jctcl j`sj` `f sadfk ^ (c.`.g.) gkl fks cpkrt`s j` _crbálaj`s j` @f`c y _fct÷l. Bãs cj`fclt`, fc jasgusa÷l s` j`scrrkffc pkr pcrt` j` Crast÷t`f`s `l `f sadfk A^ (c.`.g) cf gkltrcpkl`r fks crdub`ltks j` _fct÷l y Zkbãs j` Cqualk cf j`scrrkffcr fc ffifksknâc crastktáfagc pkgk bãs j` baf cóks cj`fclt` `l `f sadfk ]AAA (`.g) j`ffil` alt`fad`lgac gkbk ‖`f cgtk basbk j`f alt`f`gtk, qu` `s `f gklkgaba`ltk‒. Cj`bãs, Zkbãs j` Cqualk knr`g` jastalgakl`s `ltr` fcs nkrbcs j` p`rg`pga÷l j`f `xt`rakr y cqu`ffcs j`f alt`rakr. X`lá J`sgcrt`s, ncbksk ffif÷sknk y bct`bãtagk nrclgás j`f sadfk ]^AA mcg` ulc jastalga÷l skhr` fcs kp`rcgakl`s b`rcb`lt` b`gãlagcs y cqu`ffcs qu` r`qua`r`l ul lav`f j` gklkgaba`ltk. J`sgcrt`s (8??8) crdub`ltc qu` cqu`ffk gkrr`spklja`lt` cf p`lscba`ltk `s ci`lk cf r`stk j` fc lcturcf`zc k suhstclgacs gkrp÷r`cs. Wabpfaffigcljk, r`s gkdatcls gkrr`spklj` c fc fc sustclgac qu` prkva`l` j`f p`lscba`ltk y r`s `xt`lsc cf r`stk j` fc lcturcf`zc. Fc alu`lgac `s`lgacf j` J`sgcrt`s rcjagc `l `stchf`g`r ul bátkjk j` cjquasaga÷l j`f gklkgaba`ltk pkr b`jak j`f bátkjk j` rczklcba`ltk j`jugtavk. Cfdulks pralgapaks j` fcs gkltrahugakl`s j` J`sgcrt`s cùl `xast`l gkbk pr`bascs b`tkjkf÷dagcs `l jastaltks pfclt`cba`ltks
=
GC_ÂZPFK 3. ALZXKJPGGA×L j`f rczklcba`ltk qu` `i`rg`l ga`rtks j`scrrkffks `l jasgusakl`s g`ltrcf`s `l alt`fad`lgac crtaffigacf mky `l jâc. Zrctcr j` aj`ltaffigcr `f krad`l y j`scrrkffk mast÷ragk j` fks pralgapaks ffifks÷ffigks j` fc alt`fad`lgac crtaffigacf r`suftc j`bcsacjk `xt`lsk y nu`rc j` fcs cbhagakl`s prãgtagcs j` `st` t`xtk. Wal `bhcrdk, `s abpkrtclt` j`stcgcr qu` ktrks ffif÷sknks guyks pfclt`cba`ltks skl r`gklkgajks gkbk r`f`vclt`s pcrc fks alv`stadcjkr`s j` alt`fad`lgac crtaffigacf s` `lgu`ltrcl c fk fcrdk j` fc mastkrac. Cfdulks gcsks j`stcgcjks skl Eclt (348:-3=?:), I. Wtucrt Baff (3=?>-3=47), Muss`rf (3=01-317=) y Eurt Dþj`f (31?>-314=) pkr `i`bpfk8 . Wug`savcb`lt`, prkpu`stcs, pfclt`cba`ltks y t`krâcs nu`rkl j`scrrkffcjcs `l `f ta`bpk p`rk nu` mcstc b`jacjks j`f 310? qu` s` r`gklkg` `f lcgaba`ltk j`f tárbalk alt`fad`lgac crtaffigacf `l fc ncbksc gkln`r`lgac j` Jcrtbkutm j` 310>, `l Mclkv`r @stcjks Plajks. J` `stc bcl`rc jcljk krad`l y gkltaluajcj c ulk j` fks t`bcs bãs jasgutajks `l vcracs rcbcs j` fcs ga`lgacs. C p`scr j` s`r ul t`bc cud` j`sj` b`jacjks j`f sadfk ]] `l ktrcs jasgapfalcs gkbk ga`lgacs gkbputcgaklcf`s, psagkfkdâc, faldöâstagc, l`urkga`lgacs, b`jagalc, nâsagc, ffifksknâc y hakfkdâc. Fc ga`lgac `gkl÷bagc (csâ gkbk ktrcs ga`lgacs skgacf`s) mc t`lajk pkgk j`scrrkffk alt`rlk skhr` t`bcs r`fcgaklcjks c cpr`ljazci` cutkbctazcjk. Bãs r`f`vclt` cùl, gucljk ulk j` fks gr`cjkr`s j`f prab`r prkdrcbc j` alt`fad`lgac crtaffigacf Fkdag Zm`krast, `f `gklkbastc M`rh`rt Wabkl (310>) r`gaha÷ `f pr`bak Lkh`f `l `gklkbâc j` 314=. @l d`l`rcf, s` khs`rvc pkgk j`scrrkffk alt`rjasgapfalcrak `ltr` fc ga`lgac 8
Plc v`rsa÷l j`tcffcjc j` fks cpkrt`s ffifks÷ffigks s` pu`j` `lgkltrcr `l Nfcsa Ŋsea (8?3>) Zm`kra`s kn Alt`ffad`lg` al _mafkskpmy clj _sygmkfkdy y ulc p`rsp`gtavc mast÷ragc K‑X`dcl(8?3>, 8?38) Altrkjugtakl tk tm` Mastkry kn Gkbputald, C hra`n mastkry kn Gkbputald.
1
GC_ÂZPFK 3. ALZXKJPGGA×L `gkl÷bagc y fks pfclt`cba`ltks j` alt`fad`lgac crtaffigacf. Psucfb`lt`, fc vasa÷l jkbalclt` qu` gkliultc cbhcs jasgapfalcs s` gklkg` gkbk gkbputctaklcf `gklkbags, ulc rcbc j` fc `gklkbâc qu` surd` c ffilcf`s j`f sadfk ]]. Lk khstclt`, drcl pcrt` j` fks cvclg`s `l gkbputctaklcf `gklkbags lk bu`strcl ulc t`lj`lgac c s`r t`xtks altrkjugtkraks k j` cgg`sk gkbùl. @l gcbhak fc bcykrâc j` fks alv`stadcjkr`s s` `lnkgcl `l puhfagcr crtâgufks stct`-kn-tm`-crt k cf b`lks buy `sp`gâffigks skhr` `f t`bc. Wa ha`l, fks t`xtks j` vclducrjac skl subcb`lt` abpkrtclt`s pcrc `f j`scrrkffk ga`ltâffigk, fabatcl `f cgg`sk c `ltusacstcs cùl lk `sp`gacfastcs `l `f t`bc. @f khi`tavk j` `st` t`xtk `s p`rbatar c `stks `ltusacstcs cjquarar gklkgaba`ltks t`÷ragks y prãgtagks c ul lav`f altrkjugtkrak gkl `f ffil j` s`bhrcr ulc s`baffc j` guraksajcj qu` p`rbatarã cf f`gtkr jad`rar t`xtks bãs cvclzcjks, csâ gkbk pcrt` j` fcs prkpu`stcs j` fc `gklkbâc gkbputcgaklcf. Plc pcrt` abpkrtclt` j` fcs prkpu`stcs j` `gklkbâc ` alt`fad`lgac crtaffigacf skl `f gcsk j` fcs ffilclzcs pcrc clãfasas j` b`rgcjks. W` pu`j` gklsaj`rcr gkbk fc rcbc bãs j`scrrkffcjc j` cbhcs jasgapfalcs, sal `bhcrdk s` r`gklkg` gkbk pkgk januljajk y gkl ul s`sdk buy drclj` j` bct`racf cgg`sahf`. Crtmur Wcbu`f (31?3-311?), ulk j` fks pakl`rks y gkfchkrcjkr j`f pr`bak Lkh`f `l `gklkbâc M`rh`rt Wabkl, cguó÷ ul tárbalk subcb`lt` r`f`vclt` pcrc `stks t`bcs. Gklkgajk gkbk Bcgmal` f`crlald k cpr`ljazci` cutkbctazcjk `s ulc rcbc j` fcs ga`lgacs gkbputcgaklcf`s qu` `stujac pctrkl`s `l alnkrbcga÷l y knr`g` ul bátkjk j` alt`fad`lgac crtaffigacf, quazãs mky `l jâc bãs pkpufcr y r`f`vclt` j` fk qu` su gr`cjkr pujk abcdalcr. @l fc cgtucfajcj, fc bcykrâc j` fks fahrks skhr` cpr`ljazci` cutkbctazcjk s` `lnkgcl `l j`scrrkffcr gklg`ptks `l lktcga÷l `stcjâstagc y bct`bãtagc. C
3?
GC_ÂZPFK 3. ALZXKJPGGA×L jan`r`lgac j` drcl pcrt` j` fks t`xtks, `st` fahrk utafazc gklg`ptks bct`bãtagks hãsagks y ul f`lduci` j` prkdrcbcga÷l kra`ltcjk cf clãfasas `gkl÷bagk. Csâ, gkbk `gklkbastc, fks gklg`ptks bct`bãtagk-`stcjâstagks r`suftcl cs`quahf`s pcrc clcfazcr, y r`skfv`r prkhf`bcs `gkl÷bagks. C p`scr j` qu` mch`r ulc janusa÷l cbpfac, fcs cpfagcgakl`s j` `stcs táglagcs gkbputcgaklcf`s skl pkgk jasgutajcs `l pfcl`s j` `stujak hãsagks pcrc `gklkbastcs. J`sj` fc p`rsp`gtavc j` ul `gklkbastc cùl lk `xp`rtk `l t`bcs j` prkdrcbcga÷l k gkl j`hafajcj`s `l gklg`ptks cvclzcjks j` bkj`fazcga÷l `stcjâstagc, `l `st` fahrk s` pkjrãl `lgkltrcr cpfagcgakl`s hãsagcs qu` cyujcl c r`nkrzcr aj`cs bãs gkbpf`ics qu` s` pu`j`l gklsuftcr `l fat`rcturc `sp`gacfazcjc `l t`bcs j` cpr`ljazci` cutkbctazcjk. Cjagaklcfb`lt`, s` knr`g` tkjc fc jkgub`ltcga÷l l`g`scrac pcrc `bp`zcr c gr`cr `i`bpfks gkl alnkrbcga÷l r`cf c fk fcrdk j` gcjc gcpâtufk pcrc jastaltks gcsks j` usk. C fk fcrdk j`f fahrk, s` khs`rvc ulc altrkjugga÷l pcufctalc j` prkhf`bcs sabpf`s c r`tks j`f buljk r`cf. Fc gfcs` j` prky`gtks ` alv`stadcgakl`s qu` ul `gklkbastc pu`j` j`scrrkffcr skl vcracjks, j`sj` clãfasas gr`gaba`ltk bcgrk`gkl÷bagk, gkb`rgak alt`rlcgaklcf, b`rgcjks ffilclga`rks `tg. @st` fahrk j`scrrkffc ul pkgk j` gcjc t`bc gkl `f khi`tavk j` gklkg`r cpfagcgakl`s `l vcracs ãr`cs. _kr `i`bpfk, `f gcpâtufk ] s`rã j` `sp`gacf alt`rás pcrc cqu`ffks guyks t`bcs s` `lnkgcl c fcs gu`stakl`s j` gkb`rgak alt`rlcgaklcf. _kr `i`bpfk, `l `f gcpâtufk t`rg`rk s` knr`g`l tkjks fks pcsks l`g`scraks pcrc pr`j`gar gkbpkrtcba`ltk j` b`rgcjks b`jaclt` ul s`lgaffk bkj`fk r`j`s l`urklcf`s crtaffigacf`s. Plc v`rsa÷l sabpfaffigcjc j` clãfasas j` bal`râc j` t`xtks p`rbat` gr`cr ulc m`rrcba`ltc sabafcr c fk qu` usc Hfkkbh`rd `l sus pcl`f`s j` clãfasas
33
GC_ÂZPFK 3. ALZXKJPGGA×L skgacf`s j`sj` 8?37. C trcvás j` prkg`scba`ltk j`f f`lduci` lcturcf, s` pu`j`l clcfazcr t`lj`lgacs skhr` ulc `baskrc `sp`gâffigc. _crc `f gcpâtufk Q s` clcfazcl t`lj`lgacs j` b`lsci`s j` twatt`r `l ta`bpk r`cf.
38
Gcpâtufk 8 X`qu`raba`ltks y sud`r`lgacs Fc `strugturc j`f fahrk `stã p`lscjc pcrc ff`vcr c fc prãgtagc fc bcykrâc j` fks gklg`ptks qu` s` pr`s`ltcl c fk fcrdk j`f t`xtk. @f khi`tavk `s qu` s`c ulc m`rrcba`ltc gkl pr`pklj`rclgac prãgtagc y nuljcb`ltk t`÷ragk. Gkl `f khi`tk j` r`cfazcr `i`rgagaks prãgtagks, s` utafazcrã ul f`lduci` `stcjâstagkgkbputcgaklcf buy pkpufcr ffcbcjk X y gklg`ptks hãsagks j` `gklkb`trâc gklv`lgaklcf. _crc cbhks gcsks, mcy ulc drcl gcltajcj j` t`xtks jaspklahf`s pcrc gkb`lzcr y prknuljazcr. _u`stk qu` `st` lk `s ul t`xtk skhr` prkdrcbcga÷l `l X, fks t`xtks qu` r`gkba`ljk pcrc altrkjugga÷l cf f`lduci` X skl fcs lktcs j` jkgub`ltcga÷l kffigacf Cl Altrkjugtakl tk X j` ^`lchf`s y Wbatm (8?3>) k fc v`rsa÷l `lnkgcjc c fc pkpufcr rcbc alt`rjasgapfalcrac Ga`lgac j` Jctks j` _`ld (8?3>) X prkdrcbbald nkr Jctc Wga`lg` . Cbhks t`xtks j` cgg`sk fahr` y gkl cgtucfazcgakl`s p`ra÷jagcs s`dùl fks cutkr`s. Lk khstclt`, cquâ s` pr`s`ltc ulc altrkjugga÷l d`l`rcf gkl cyujc j` fc fahr`râc swarf. @f pcqu`t` knr`g` ulc nkrbc alt`rcgtavc pcrc gkb`lzcr c utafazcr 37
GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW fc m`rrcba`ltc j`sj` g`rk y ha`l, pkjrâc s`rvar gkbk bâlabk aljasp`lschf` pcrc ncbafacrazcrs` gkl `f cbha`lt` j` trchcik `l X. Plc v`z gklgfuâjc fc alstcfcga÷l j`f f`lduci`, s` pu`j` gkb`lzcr c `xpfkrcr pkr `st` b`jak gkbk s` `xpfagcrã c gkltalucga÷l.
8.?.3. Alstcfcga÷l j`f f`lduci` Culqu` lk `s r`quasatk aljasp`lschf` t`l`r ul cbpfak bcl`ik j` f`lduci`s j` prkdrcbcga÷l pcrc gklkg`r fks pralgapaks j` alt`fad`lgac crtaffigacf cpfagcjks, s` r`gkba`ljc s`duar fks `i`rgagaks pcrc t`l`r ul nuljcb`ltk prãgtagk. @l `st` cpcrtcjk `xpfagcr`bks fc alstcfcga÷l j` cbha`lt`s (alstcfcga÷l j` fks prkdrcbcs) qu` lks p`rbatarãl jcr s`duaba`ltk cf gklt`lajk j`f fahrk. @f f`lduci` `stã jaspklahf` pcrc fcs pfctcnkrbcs bãs gkbul`s Taljkws, Falux y Bcg `l `f r`pksatkrak kffigacf mttps9//grcl.r-prki`gt.krd. Gkbk s` `i`bpfaffigc `l fc ffidurc sadua`lt`, j` fcjk j`r`gmk s`f`ggaklcbks fc jastrahuga÷l qu` lu`strk krj`lcjkr kp`rc y s`duabks fcs alstruggakl`s j` alstcfcga÷l. _crc `f gcsk bãs gkbùl j` Taljkws, s` j`tcffcl c gkltalucga÷l.
3:
GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW
Nadurc 8.39 W` jc gfage `l fc alstcfcga÷l j`f sast`bc kp`rctavk qu` gkrr`spkljc. @l `st` gcsk Taljkws . J` fcjk j`r`gmk s`f`ggaklcbks fc jastrahuga÷l qu` lu`strk krj`lcjkr kp`rc y s`duabks fcs alstruggakl`s j` alstcfcga÷l. _crc `f gcsk bãs gkbùl j` Taljkws, s` j`tcffcl c gkltalucga÷l.
Nadurc 8.89 Jcljk gfage `l fc alstcfcga÷l gkb`lzcrã fc j`sgcrdc j`f prkdrcbc. _crc gkbpf`tcr fc alstcfcga÷l jcr `l sadua`lt` c fc gklffidurcga÷l sud`rajc . Plc v`z `i`gutcjk `f alstcfcjkr, s`f`ggaklcjk `f f`lduci`, tkjks fks gkb30
GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW pkl`lt`s ulc v`ltclc lks gklffirbcrã qu` m`bks alstcfcjk cj`gucjcb`lt` `f f`lduci`. _kst`rakrb`lt`, alstcfcr`bks ulc alt`rncz qu` lks knr`g`rã ulc v`rsa÷l drãffigc cbadchf` pcrc `f usucrak. Culqu` s` pu`j` trchcicr ùlagcb`lt` gkl `f f`lduci` X, fc alt`rncz j` usucrak p`rbatarã bcl`icr X j` nkrbc bãs lcturcf, s` algfuy`l nulgaklcfajcj`s ùtaf`s cf bkb`ltk j` `i`gutcr, prkhcr y ducrjcr gkbcljks.
8.?.8. Alstcfcga÷l j` alt`rncz j` usucrak Xstujak Gkl gr`g`s `f cbha`lt` drãffigk bãs pkpufcr j` X `s Xstujak. @stc m`rrcba`ltc knr`g` ulc vcra`jcj j` skfugakl`s bãs cvclzcjcs qu` s`rvarã pcrc cqu`f `ltusacstc qu` qua`rc prknuljazcr `l vasucfazcgakl`s jalãbagcs (Xstujak Wmaly ) k fc v`rsa÷l qu` s` `i`gutc pcrc ul s`rvajkr ( Xstujak W`rv`r ). Wal `bhcrdk, `l `st` gcsk skfcb`lt` kgupcr`bks fc v`rsa÷l j` `sgratkrak (J`setkp) c trcvás j`f satak kffigacf mttps9//www.rstujak.gkb/prkjugts/rstujak/jkwlfkcj/ y `fada`ljk fc jastrahuga÷l gkrr`spklja`lt` c lu`strk sast`bc kp`rctavk. @l `st` gcsk, Taljkws.
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GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW
Nadurc 8.79 W` s`f`ggaklc fc v`rsa÷l pcrc Taljkws ^astc/4/=/3? pcrc j`sgcrdcr. Cf t`rbalcr, s` `i`gutc `f crgmavk y s` sadu`l fcs kpgakl`s pr`j`t`rbalcjcs . Plc v`z t`rbalcjc fc j`sgcrdc, s`duar`bks fks pcsks sud`rajks j` alstcfcga÷l. @f csast`lt` j` alstcfcga÷l gklffirbcrã qu` s` mcyc fkdrcjk gklffidurcr `f prkdrcbc y tkjk `stcrã fastk pcrc trchcicr. Cf chrar Xstujak s` bkstrcrã ul cbha`lt` sabafcr cf sadua`lt`. @l fc s`gga÷l 3 s` ta`l` `f `spcgak j`jagcjk c fc gklstrugga÷l j` ul sgrapt y lktcs. @l fc s`gga÷l 8 s` ta`l` fc gklskfc, `f `spcgak jklj` s` `i`gutcl fks gkbcljks. @l fc s`gga÷l 7 `stã `f cbha`lt` jklj` s` vasucfazcl fks jctks y nulgakl`s qu` j`ffilabks. _kr ùftabk, `l fc s`gga÷l : s` j`sgrah`l fcs gcrp`tcs y crgmavks `l lu`strk cbha`lt`, fcs drãffigcs qu` s` d`l`rcl, fks pcqu`t`s alstcfcjks y ulc v`ltclc j` cyujc j` jkgub`ltcga÷l skhr` fks pcqu`t`s alstcfcjks.
34
GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW
Nadurc 8.:9 W` s`f`ggaklc fc v`rsa÷l pcrc Taljkws ^astc/4/=/3? pcrc j`sgcrdcr. Cf t`rbalcr, s` `i`gutc `f crgmavk y s` sadu`l fcs kpgakl`s pr`j`t`rbalcjcs .
8.?.7. Lkgakl`s Hãsagcs, cpr`lja`ljk X gkl swarf Cf ffilcfazcr fc alstcfcga÷l j` fks cbha`lt`s, s` pu`j` prkg`j`r c `xpfkrcr `f f`lduci`. Plc nkrbc nãgaf, alt`rcgtavc y `ltr`t`lajc j` mcg`rfk `s pkr b`jak j`f pcqu`t` swarf . 3
8
## A l s t c f c g a k l j` s w a r f a l s t c f f . pcgecd`s ( " s w a r f " )
7
:
0
## G cr dc lj k f a h r ` r a c f a h r c r y ( " s w a r f " )
>
4
=
## A l a g ac l j k ` f t u t k r a c f swarf ()
Plc v`z `i`gutcjks fks gkbcljks swarf `xpfagcrã fks pralgapaks hãsagks j` X y j` nkrbc alt`rcgtavc `f usucrak j`h` r`spklj`r fcs pr`dultcs qu` `f 3=
GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW sast`bc crrkic . @l fc f`gga÷l 3 s` r`vascl fks gklg`ptks hãsagks j`f f`lduci`. @l fc f`gga÷l jks s` v`l bkj`fks sabpf`s j` r`dr`sa÷l fal`cf. @l fc f`gga÷l tr`s `stcjâstagc aln`r`lgacf hãsagc y `l fc f`gga÷l guctrk clãfasas `xpfkrctkrak. Culqu` t`rbalcr tkjcs fcs f`ggakl`s s`râc h`l`ffigaksk pcrc gucfqua`rc, pcrc `st` fahrk fks gklg`ptks nuljcb`ltcf`s j` swarf `l fc f`gga÷l 3 y 8 skl suffiga`lt`s pcrc gkb`lzcr `l hu`lc nkrbc. ¡N`fagajcj`s! sa mcs ff`dcjk mcstc cquâ pu`j`s gklsaj`rcr qu` yc gklkg`s fks cbha`lt`s y `stãs fastk pcrc `bhcrgcrt` `l cbhagaksks clãfasas j` alt`fad`lgac crtaffigacf `l X. C fk fcrdk j`f j`scrrkffk j`f t`xtk, s` utafazcrãl vcraks j` fks t`bcs gkbul`s, lk khstclt`, gkl cfdk j` `xp`ra`lgac `f usucrak j` X lktcrã qu` `xast`l jan`r`lt`s nkrbcs j` ff`dcr c fks basbks r`suftcjks y fc nkrbc j` j`ffilar fks gkbcljks lk skl ùlagcs la ulav`rscf`s.
8.3. Bct`racf cjagaklcf y g÷bk trchcicr gkl `f g÷jadk C fk fcrdk j`f t`xtk, s` bkstrcrãl s`ggakl` j` g÷jadk. Zkjk `f bct`racf j`sgratk pu`j` s`r j`sgcrdcjk j` bcl`rc drctuatc j`f satak w`h mttps9// datmuh.gkb/cfnr`jk8?7/`gklkbac[alt`fad`lgac[crtanagacf . Wa s` `s ul
usucrak j` Dat, `f basbk satak w`h jc fc pksahafajcj j` j`sgcrdcr `f r`pksatkrak gkbpf`tk. @f r`pksatkrak `stã krdclazcjk pkr gcpâtufks y gcjc gcpâtufk `stã javajajk pkr s`ggakl`s j` g÷jadk pkr suhgcpâtufk.
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GC_ÂZPFK 8. X@SP@XABA@LZKW Q WPD@X@LGACW
8.8. Gkltcgtk Drcl pcrt` j` `st` fahrk `s ul prky`gtk qu` s` `lgu`ltrc `l prkdr`sk, `l prkg`sk j` gcbhaks y b`ikrcs gkltalucs. Cdrcj`g`r`bks gucfqua`r jujc k gkb`ltcrak r`sp`gtk cf fahrk qu` lks cyuj` c b`ikrcr `f gklt`lajk `l sadua`lt` gkrr`k `f`gtr÷lagk `gklkbags.f`clpuhOdbcaf.gkb . @l gcsk j` `lgkltrcr ulc ncffc `l `f g÷jadk, pu`j`s f`vcltcr ul tage`t `l `f r`pksatkrak kffigacf j`f t`xtk `l Datmuh mttps9//datmuh.gkb/cfnr`jk8?7/ `gklkbac[alt`fad`lgac[crtanagacf/assu`s.
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Gcpâtufk 7 _ralgapaks hãsagks j` cpr`ljazci` cutkbctazcjk ‖Zm` ffirst khvakus ncgt chkut mubcl f`crlald as tmct at‑s mkrrahfy sfkw. At tce`s j`gcj`s nkr mubcl h`alds tk f`crl clytmald. At tkke cff kn us sax y`crs iust tk d`t up tk stcrtald sp``j nkr sgmkkf, clj tm`l tw`lty bkr` y`crs tk h`gkb` gkdlatav` sga`ltasts kr gkbput`r sga`ltasts. Zmct‑s tm` balabub, skb` kn us tkke `v`l fkld`r tmcl tmct. Wk w` cr` t`rrahfy sfkw f`crl`rs...‒ M`rh`rt Wabkl (31=7) @l fc cgtucfajcj, `f cpr`ljazci` cutkbctazcjk `s ulc pa`zc nuljcb`ltcf pcrc jastaltcs ãr`cs j`f gklkgaba`ltk ` aljustracs c trcvás j`f buljk. Mky `l jâc, ulc drcl pcrt` j` lu`strc vajc jacrac `stã r`dajc pkr cfdkratbks j` alt`fad`lgac crtaffigacf qu` r`cfazcl gãfgufks `sp`gâffigks pcrc kht`l`r ulc r`gkb`ljcga÷l j` prkjugtk `l ulc ta`ljc `l fâl`c, gklkg`r ulc p`fâgufc qu` lks cdrcjcrã k `f`dar fc rutc bãs cj`gucjc `l ul sast`bc j` D_W. _kr `i`bpfk, cf bkstrcr alt`rás `l ul prkjugtk fc puhfagajcj j` Cbczkl `f sa83
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK tak w`h gklstclt`b`lt` `lvacrã puhfagajcj y r`gkb`ljcgakl`s r`fcgaklcjcs c `s` crtâgufk `sp`gâffigk. Cf t`rbalcr j` v`r ulc p`fâgufc, `f sast`bc j` r`gkb`ljcga÷l j` L`tax lks suda`r` ul tâtufk lu`vk `l nulga÷l j` ul clãfasas j`f pctr÷l j` dustks j` p`fâgufcs vastcs gkl clt`rakrajcj. Cf s`f`ggaklcr ulc rutc pr`n`rajc, `f sast`bc D_W r`gkb`ljcrã fc `f`gga÷l pr`vac y pksahf`b`lt` r`gkb`ljcrã c ktrks gkljugtkr`s fc rutc sud`rajc sa `s bãs `ffiga`lt`. _crc fks t`fánklks g`fufcr`s y husgcjkr`s w`h, ul cfdkratbk `lnkgcjk `l s`bãltagc j` t`xtk gkbpf`tc lu`strcs hùsqu`jcs, lks suda`r` lu`vcs pcfchrcs `l nulga÷l j` lu`strk usk gktajaclk j`f f`lduci` y fc nkrbc `l qu` fc skga`jcj r`cfazc fcs hùsqu`jcs. Csâ gkbk fks `i`bpfks b`lgaklcjks ul salnâl j` cpfagcgakl`s lks rkj`cl jacracb`lt`, `f buljk jadatcf hcsc drcl pcrt` j` su j`s`bp`ók `l fc gcpcgajcj j` cjcptcr cfdkratbks `sp`gâffigks c l`g`sajcj`s `sp`gâffigcs. Cfdulks j` fks `i`bpfks qu` suhycg`l c `stcs l`g`sajcj`s s` `ldfkhcl `l fcs sadua`lt`s cggakl`s. •
W`db`ltcr9 Cdrupcr k javajar `l s`ggakl`s mkbkdál`cs.
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Aj`ltaffigcr9 J`t`rbalcga÷l gcrcgt`râstagcs k ncgtkr`s.
•
_r`j`gar9 _rklkstagcr, r`cfazcr ulc gkli`turc gkl clt`fcga÷l. @l d`l`rcf, fc bcykrâc j` fks gcsks j` usk j` alt`fad`lgac crtaffigacf s` `lnk-
gcl `l fcs cpfagcgakl` clt`rakr`s. Pl g`ltrk j` `stujaks bájagks `stcrã buy alt`r`scjk `l aj`ltaffigcr fks ncgtkr`s qu` algr`b`ltcl `f ra`sdk j` pcj`g`r alncrtk gcrjacgk (@cstkl, 8?3:). Pl clcfastc j` hkfsc `stcrã alt`r`scjk `l
pr`j`gar fks pr`gaks j` fcs `baskrcs bãs r`ltchf`s `l `f b`rgcjk (Julas `t 88
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK cf, 8?3>). Zkbcjkr`s j` j`gasakl`s j` pkfâtagc bkl`tcrac pkjrâcl s`db`l-
tcr fks s`gtkr`s bãs prkp`lsks c sunrar ul cfzc j` alcga÷l jcjk ul smkge j` pr`gaks, `ltr` ul sal ffil j` gcsks j` usk. B`jaclt` m`rrcba`ltcs j` cpr`ljazci` cutkbãtagk `s pksahf` `ls`ócr c ulc gkbputcjkrc c r`cfazcr tcr`cs s`lgaffcs j` s`db`ltcga÷l, aj`ltaffigcga÷l y pr`jagga÷l. Csâ, fc s`db`ltcga÷l j` ulc gcbpcóc pcrc gfa`lt`s `sp`gâffigks jcjks ga`rtcs l`g`sajcj`s, dustks y pr`n`r`lgacs `s pksahf` utafazcljk cfdulks pralgapaks j` alt`fad`lgac crtaffigacf.3 @i`bpfaffigcljk, supkldcbks qu` t`l`bks ulc qu` lk ta`l` gklkgaba`ltk j` fks p`fadrks cf r`gkrr`r ulc cg`rc gucfqua`rc. Fcb`ltchf`b`lt` `f aljavajuk lk gklkg` lcjc skhr` `f buljk r`cf y su ùlagc nulga÷l cgtucf `s gcbalcr `l fâl`c r`gtc. _crc sabpfaffigcr, supkldcbks tcbhaál, qu` `stc cg`rc `s alffilatc y `stc p`rsklc gcbalcrã ul ta`bpk alj`ffilajk pkr `ffc. _crc nkrtulc j` `st` aljavajuk fc cg`rc `s p`rn`gtc y lk mcy cfdùl tapk j` abp`jab`ltk qu` f` gcus` jaffiguftcj`s, p`rk fcb`ltchf`b`lt`, ul jâc `l ulc s`gga÷l j` fc cg`rc cpcr`g` ul cdui`rk. @f aljavajuk cf lk gklkg`r `f ra`sdk, j`gaj` gkltalucr gkl sus nulgakl`s j` gcbalcr `l fâl`c r`gtc y gc` `l `f cdui`rk. Cf gc`r `l `st` mapktátagk cdui`rk, `f sui`tk `l gu`sta÷l t`ljrã ul `stâbufk l`dctavk (quazãs jkfkr k ba`jk), `f sui`tk aj`ltaffigcrã j` bcl`rc cutkbãtagc ul cdui`rk gkl `stcs `xp`ra`lgacs l`dctavcs y `l fc bcykrâc j` fks gcsks `vatcrã gc`r `l gucfqua`r cdui`rk nuturk. @f sui`tk, csâ gkbk gucfqua`r sast`bc crtaffigacf (clt` ul `stâbufk) cpr`lj` . 3
J`ltrk j` fc `gklkbâc `st` tapk j` clãfasas tkjcvâc lk `stã d`l`rcfazcjk y fks gcsks skl hcstclt` `xaduks. Pl gcsk j` s`db`ltcga÷l j` gcbpcóc, prkg`scba`ltk j` f`lduci` lcturcf y t`krâc `gkl÷bagc s` bu`strc `l fks trchciks pr`vaks Kfduâl (8?3>).
87
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK
7.3. Lkgakl`s hãsagcs j` cpr`ljazci` sup`rvascjk y lk sup`rvascjk _crc fc t`rbalkfkdâc trcjagaklcf j` bcgmal` f`crlald, `f cpr`ljazci` sup`rvascjk `s ul gklg`ptk qu` s` utafazc pcrc j`sadlcr ul tapk j` alnkrbcga÷l. W` mcg` ffcbcr cpr`ljazci` sup`rvascjk c tkjc cqu`ffc alnkrbcga÷l qu` `stã `taqu`tcjc `x clt` ul cfdkratbk k táglagc `stcjâstagc alt`rffi`rc pcrc pr`j`gar su gkbpkrtcba`ltk. D`l`rcfb`lt` r`pr`s`ltcjk `l v`gtkr`s pkj`bks t`l`r ul v`gtkr j` khi`tks qu` ta`l`l gcrcgt`râstagcs halcracs 8 (dál`rk n`b`lalk / dál`rk bcsgufalk, sa / lk, `bpf`cjk / lk `bpf`cjk, pkhr`zc / lk pkhr`zc). @l `f gcsk j` cpr`ljazci` sup`rvascjk, fcs vcrachf`s qu` gklta`l`l alnkrbcga÷l qu` cyujc c j`scrrkffcr ul bkj`fk `stcjâstagk gkl `stc alnkrbcga÷l `x clt` . Wa`ljk cpr`ljazci` lk-sup`rvascjk fc alnkrbcga÷l lk `stcrã jaspklahf`, `s j`gar, lk s` gklkg`rã sa ul aljavajuk p`rt`l`g` c ulc gct`dkrâc j`t`rbalcjc u ktrc. Pl `i`bpfk tâpagk j` cpr`ljazci` lk sup`rvascjk qu` drcl pcrt` j` fks ga`ltâffigks skgacf`s r`gklkg`rãl `s `f gcsk j` b`jaga÷l j` pkhr`zc `l nulga÷l j` gcrcgt`râstagcs j` fc vava`ljc y fc ncbafac qu` fc mchatc. @l `f gcsk bãs sabpf` qu` pkj`bks `i`bpfaffigcr `f sadua`lt` gcsk. Clcfastcs j`t`rbalcrãl qu` hcik ga`rtks grat`raks j` aldr`sk, cgg`sk c `jugcga÷l y c s`rvagaks ga`rtc vava`ljc `stcrã `l `stcjk j` pkhr`zc k lk. Fks clcfastcs `lgcrdcjks j` j`t`rbalcr sa p`rt`l`g` c ga`rtk drupk lk gklkg`rãl `x clt` sa ul mkdcr p`rt`l`g` c ulc vava`ljc `l satucga÷l j` pkhr`zc y s` `lnr`ltcl c ul prkhf`bc 8
_crc ul `gklkb`trastc `xp`rab`ltcjk, khs`rvcrã qu` jubba`s vcrachf`s sadu`l `st` pralgapak. _crc ulc altrkjugga÷l sabpf`, `f t`xtk Hcsag @gklkb`trags j` Duicrcta (8?38) afustrc gfcrcb`lt` fcs vcrachf`s jagkt÷bagcs y sus usks `l fc bkj`fcga÷l `gklkbátragc.
8:
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK j` cpr`ljazci` lk sup`rvascjk. Psucfb`lt`, s` gklsaj`rc qu` fks prkhf`bcs j` cpr`ljazci` lk sup`rvascjk skl bãs gkbpf`iks y cvclzcjks j` j`scrrkffcr. Culqu` `l gcsks bãs sabpf`s fks cfdkratbks j` cpr`ljazci` lk sup`rvascjk lk skl cvclzcjks y r`qua`r`l ul `lt`ljaba`ltk hãsagk j` `stcjâstagc gklv`lgaklcf. _ralgapcfb`lt`, `st` fahrk s` `lnkgcrã `l bkstrcr cpfagcgakl`s c cpr`ljazci` sup`rvascjk y v`rsakl`s s`lgaffcs j` cpr`ljazci` lk sup`rvascjk cf s`r ul t`xtk altrkjugtkrak. _crc `stc prab`rc s`gga÷l j`f t`xtk s` r`vascl fks gklg`ptks hãsagks j` ulc r`dr`sa÷l fal`cf j`sj` `f pultk j` vastc prãgtagk. W` clcfazc `f prab`r gcsk j` r`dr`sa÷l fal`cf j` fc mastkrac y s` gkbpcrc gkl ãfd`hrc fal`cf sabpf` pcrc gklkg`r fcs sabafatuj`s. W`duljk, s` utafazc `f bkj`fk j` r`dr`sa÷l fal`cf pcrc mcg`r ul gcsk j` s`db`ltcga÷l j` cpr`ljazci` sup`rvascjk.
7.3.3. Altrkjugga÷l c bkj`fazcga÷l y gfcsaffigcga÷l fal`cf @l d`l`rcf, fks bátkjks j` r`dr`sa÷l fal`cf mcl `stcjk `l `f lùgf`k j` fcs m`rrcba`ltcs j` drcl pcrt` j` fks ga`ltâffigks skgacf`s jurclt` bugmk ta`bpk. C p`scr j` s`r táglagcs gklsaj`rcjcs gkbk sabpf`s, j`bu`strcl ul j`s`bp`ók hcstclt` cg`ptchf` pcrc ulc drcl gcltajcj j` cpfagcgakl`s ` algfusav` ul j`s`bp`ók bugmk b`ikr `l gcsks jklj` fc alnkrbcga÷l `s `sgcsc k gkl prkhf`bcs j` s`sdk `stcjâstagk. @stc s`gga÷l pu`j` gklsaj`rcrs` gkbk fks nuljcb`ltks hãsagks qu` s` `sgklj`l j`trãs j` sast`bcs j` alt`fad`lgac crtaffigacf pcrc ulc drcl gcltajcj j` gcsks. _crc tkjk cqu`f qu` qua`rc utafazcr m`rrcba`ltcs cvclzcjcs, 80
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK `s abpkrtclt` gklkg`r fks gaba`ltks j` gklg`ptks hãsagks qu` s` trchcicrãl `l fcs s`ggakl`s sadua`lt`s, cfdulks cfdkratbks j` cdrupcba`ltk gfust`rald y táglagcs j` cpr`ljazci` gkbk r`j`s l`urklcf`s ta`l`l `l su lùgf`k t`÷ragk nuljcb`ltks j` r`dr`sa÷l fal`cf sabpf`. @l `stc s`gga÷l, r`vascr`bks `stks nuljcb`ltks hãsagks qu` gkbpkl`l ulc r`dr`sa÷l fal`cf pcrta`ljk j` fc prãgtagc5 cpfagcljk ul bkj`fk j` r`dr`sa÷l fal`cf j`sj` `f alagak. W` d`l`rc ul bkj`fk `stcjâstagk ulavcracjk y s` d`l`rc ulc j`bkstrcga÷l `bpâragc-drãffigc j` qu` `f bkj`fk j` r`dr`sa÷l fal`cf sabpf` ulavcracjk r`pr`s`ltc fc basbc nulga÷l `stabcjc qu` ulc `gucga÷l j` fc r`gtc gklv`lgaklcf (y 2 bx + h).
7.3.8. Clãfasas j` r`dr`sa÷l fal`cf Wal jujc `f clãfasas j` r`dr`sa÷l fal`cf `s fc táglagc bãs gklkgajc `l `f gcbpk j` `stcjâstagc y cfdulcs ktrcs jasgapfalcs. @l su v`rsa÷l bãs sabpf`, `stc gklsast` `l khs`rvcr fc r`fcga÷l `ltr` jks vcrachf`s k v`gtkr`s. _crc tkjk bkj`fk j` r`dr`sa÷l fal`cf `xast` ulc vcrachf` j`p`lja`lt` qu` ffcbcr`bks Q y gklsast` `l fc vcrachf` qu` qu`r`bks pr`j`gar. _kr ktrk fcjk fcs vcrachf`s alj`p`lja`lt`s fcs ffcbcr`bks ] a y gklsast`l `l fcs vcrachf`s qu` s` utafazcl pcrc `xpfagcr Q . Bct`bãtagcb`lt`, fc `gucga÷l qu` `xpfagc `stcs r`fcgakl`s `s fc sadua`lt`. ˎ 2 h ? + h3 ] 3 + h3 ] 8 ...ha ] a Q ˎ `s fc `stabcga÷l j` Q qu` s` `n`gtùc `l `f bkj`fk, h3 . . . ha J÷lj` Q skl fks `stabcjkr`s y ] a fcs vcrachf`s qu` s` utafazcl pcrc `xpfagcr Q . H? `s ffcbcjk alt`rg`ptk. 8>
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK Culqu` c sabpf` vastc `f bkj`fk j` r`dr`sa÷l fal`cf pu`jc pcr`g`r ul pkgk gkbpfagcjk j` csabafcr c prab`rc vastc, gklkg`r ul pkgk j` su mastkrac sarv` pcrc gkbpr`lj`r g÷bk surda÷ fc aj`c y `lt`lj`r `f gcsk gklgr`tk jklj` s` utafaz÷ pkr prab`rc v`z.
X`dr`sa÷l c fc b`jkgrajcj , krad`l j` fc r`dr`sa÷l fal`cf @l r`cfajcj fc r`dr`sa÷l fal`cf, `s ul bátkjk j` `stabcga÷l bãs va`ik j` fk qu` cpcr`ltc yc qu` ta`l` su krad`l `l `f sadfk ]A]. Nrclgas Dcftkl, prabk j`f lcturcfastc Gmcrf`s Jcrwal, `s gklkgajk pkr sus cpkrt`s gkbk skga÷fkdk, `stcjâstagk, ha÷fkdk y r`gklkgajk ga`ltâffigk `l vcracs rcbcs. C ffilcf`s j`f sadfk ]A], Dcftkl utafazc ul bátkjk j` r`dr`sa÷l fal`cf pcrc `xpfagcr ulc map÷t`sas sabpf` qu` nkrb÷ c pcrtar j` fc khs`rvcga÷l. Zrcs `stujacr ulc gfcs` `sp`gâffigk j` pfcltc ffcbcjk Fctmyrus kjkrctus, s` p`rgct÷ qu` fcs s`baffcs t`ljâcl c t`l`r ul tcbcók bãs p`qu`ók sa fcs pfcltcs pcjr` `rcl cftcs y ul tcbcók bãs cftk sa fcs pfcltcs pcjr` `rcl bãs hcics. C `st` n`l÷b`lk j` gklv`rd`lgac j` tcbcóks fk ffcb÷ r`dr`sa÷l c fc b`jakgrajcj. Lk gklnkrb` ùlagcb`lt` fks r`suftcjks j`f `stujak gkl pfcltcs, `xta`lj` `f `stujak c clcfazcr ulc bu`strc gkl p`rsklcs y s` `lnkgc `l b`jar `stcturcs j` pcjr`s ` maiks. Cf clcfazcr ul gcsk gkl mubclks, r`cfazc ulc bu`strc j` 17? laóks y 8?0 pcjr`s. @f r`suftcjk bãs r`f`vclt` j`f clãfasas kradalcf j` 3==1 s` pr`s`ltc `f fc ffidurc ]. @l fc puhfagcga÷l kradalcf Dcftkl `sp`gaffigc qu` pcrc cqu`ffks pcjr`s qu` skl g`rgc j` ulc pufdcjc bãs cftks qu` fc b`jac j` fc pkhfcga÷l, sus maiks ta`lj`l c s÷fk s`r 8/7 j` pufdcjc bãs cftks qu` fc pkhfcga÷l. @stks r`suftcjks r`nu`rzcl fc map÷t`sas j` ‖fc f`y j` r`dr`sa÷l c fc b`84
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK jakgrajcj‒ qu` skstuvk gkl `f gcsk j` fcs s`baffcs y khs`rvc qu` fks maiks j` fks pcjr`s j` `stcturc bãs cftc qu` fc b`jac skl cftks, p`rk b`lks cftks qu` fks pcjr`s y `f basbk n`l÷b`lk gkl fks maiks j` fks pcjr`s j` `stcturc hcic r`sp`gtk c fc b`jac.
Nadurc 7.39 X`dr`sa÷l c fc b`jakgrajcj j` Dcftkl (3==1). Wupkla`ljk qu` s` qua`rc pr`j`gar `f tcbcók qu` ul laók t`ljrã t`la`ljk alnkrbcga÷l j` fc `stcturc j` fks pcjr`s, `f bátkjk j` r`dr`sa÷l fal`cf j` dcftkl r`suftcrâc ùtaf pcrc tcf prkp÷satk. Fc alnkrbcga÷l kradalcf j` Dcftkl s` `lgu`ltrc jaspklahf` `l cfdulks pcqu`t`s j` X. C gkltalucga÷l cf `i`gutcr `f g÷jadk sadua`lt` s` khta`l` fc r`dr`sa÷l fal`cf qu` `stabc `f tcbcók qu` t`ljrã cfdulk j` fks maiks. 3
8
## A l s t c f c g a k l j ` p c qu ` t` s a l s t c f f . pcgecd`s ( " p sy gm " )
8=
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK 7
:
0
## G cr dc lj k f a h r ` r a c f a h r c r y ( p s yg m )
>
4
=
## Gcrdc j` jctks jctc ( " dcftk l " )
1
3?
33
## Drc nag c p f k t ( dcftkl )
38
37
3:
30
## @ s t ab c ga k l j ` f b kj `f k f a l ` c f ## W ` ` s p ` n a g c g m a f j 2 n ( p c r ` lt ) n a t 6∘ fb ( jctc 2 d c f tk l , g m a f j ~ p c r ` l t )
3>
34
3=
## W` d r c n a g c f c r ` d r ` s a k l c h f a l ` ( n a t , g k f 2 " r` j " , fwj 2 7 )
81
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK
Nadurc 7.89 X`dr`sa÷l fal`cf j` `stcturc pcrc pcjr`s ` maiks `l pufdcjcs. Al nkrbcga÷l j` Dcftkl (3==1).
Q 2 h + bx
Plc r`gtc qu` s` r`pr`s`ltc gkl fc `gucga÷l clt`rakr s` `xpfagc pkr h qu` `s fc krj`lcjc cf krâd`l, b `xpfagc fc p`lja`lt` y x `s ul vcfkr gucfqua`rc. @l `f gcsk j`f bkj`fk j` Dcftkl `stabcjk, fc `gucga÷l j` fc r`dr`sa÷l fal`cf `s buy sabafcr. ˎ 2 h ? + h3 ] a + ” Q Jklj` pcrc `f bkj`fk j` Dcftkl h ? `s ffcbcjk alt`rg`ptk y `s `f sâbaf j` fc krj`lcjc cf krad`l j` fc `gucga÷l ], h3 `s `f gk`ffiga`lt` j` ] k p`lja`lt` b `l fc `gucga÷l fal`cf. @f sadua`lt` g÷jadk r`gr`c fc `gucga÷l fal`cf tkbcljk fc p`lja`lt` (`stabcjkr) y krj`lcjc cf krad`l (alt`rg`ptk) j`f bkj`fk j` 7?
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK r`dr`sa÷l j` Dcftkl. Fc ffidurc ] bu`strc drãffigcb`lt` qu` fc r`dr`sa÷l fal`cf y fc r`gr`cga÷l utafazcljk `f bátkjk j` `gucga÷l fal`cf skl aducf`s. 3
## @stabcgak l bclucf j`f bkj`fk
8
7
:
## Fks v c f kr ` s j` f k s g k ` n a g a ` l t ` s n a t $ g k ` n n a g a ` l t s
0
>
## W ` r ` g k ls t r u y` l f k s v c f k r ` s g kl f c n kr b uf c
4
## j` ` gu c ga k l f a l ` c f j` f c r ` g t c
=
1
## y 2 h + bx r ` g t c 6∘cs . lub`rag ( f c p p f y ( d c f t k l $pcr`lt ,
3?
n u l g t a k l ( x) n a t $ g k ` n n a g a ` l t s U 3 R + n a t $ gk`nnaga`lts U8R
∔
x) )
33
38
37
## W` ` xt rc l f k s v c f k r ` s j ` f bkj`fk j` r ` d r ` s a k l k r a d a l c f 6∘ n a t t ` j . v c f u ` s ( n a t )
3:
30
## Dr cn ag cb ks f k s v c f k r ` s qu` s ` p r `j a g` l y f k s v c f k r ` s ` s t a bc j k s p k r ` f b kj `f k
3>
pcr (bnrkw2g (3 ,8 ) )
34
s
3=
p f k t ( dcftkl , bcal 2 " Bkj`fk j` r ` d r ` s a k l f a l ` c f " )
31
f a l ` s ( d c f t k l $pcr`lt , k r a d al c f , g k f 2 " r` j " , fwj 2 7 )
8?
83
p f k t ( dcftkl , bcal 2 " @ g uc ga kl j ` f c r ` g t c " )
88
f a l ` s ( d c f t k l $pcr`lt , r`gt c , g k f 2 " hf u` " , fwj 2 7 )
73
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK
Nadurc 7.79 Gkbprkhcga÷l drãffigc j` bkj`fk j` r`dr`sa÷l fal`cf (azqua`rjc) y `stabcga÷l pkr b`jak j` `gucga÷l fal`cf r`gtc (y 2 h + bx). W` khs`rvc qu` cbhks bkj`fks skl aducf`s pcrc fks jctks j` Dcftkl (3==1).
7.8. Gfcsaffigcga÷l gkl bátkjks j` r`dr`sa÷l fal`cf Cmkrc s` r`vasc `f ul gcsk j` gfcsaffigcga÷l gkl r`dr`sa÷l fal`cf. D`l`rcfb`lt`, pcrc fks usks j` gktajaclks j` cpr`ljazci` cutkbctazcjk s` gklsaj`rc fc gfcsaffigcga÷l fal`cf gkbk ulc nkrbc s`lgaffc p`rk pkgk `ffiga`lt` pcrc gfcsaffigcr jctks. Pl `i`bpfk gfcrk j` `ffk s` pu`j` v`r `l fc ffidurc ]. Fc ffidurc bu`strc qu` `f bátkjk j` r`dr`sa÷l fal`cf `s b`lks `ffiga`lt` pcrc gfcsaffigcr pcrt` j` fc alnkrbcga÷l qu` `stã g`rgclc `ltr` fcs gfcs`s 3 y 7.
78
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK
Nadurc 7.:9 Jks bátkjks j` gfcsaffigcga÷l j` Mcsta` (8??1). J`f fcjk azqua`rjk s` bu`strc fc gfcsaffigcga÷l gkl ulc nulga÷l fal`cf y `l `f fcjk j`r`gmk ulc gfcsaffigcga÷l gkl ulc nulga÷l gucjrãtagc. W` bu`strc qu` `f bkj`fk j` r`dr`sa÷l fal`cf `s b`lks `xahf` . Wal `bhcrdk, `f bátkjk j` r`dr`sa÷l fal`cf pcrc gfcsaffigcga÷l `s sabpf` p`rk suffiga`lt` pcrc cfdulks gcsks. _kr `i`bpfk, fc drãffigc sadua`lt` ul `i`rgagak sabufcjk bu`strc ul gcsk j` r`dr`sa÷l fal`cf pcrc gfcsaffigcga÷l, jklj` fcs khs`rvcgakl`s rkics sadlaffigcl ulc gfcs` y fcs gct`dkrâc l`drc ulc gfcs` jastaltc. J` cgu`rjk gkl `f clãfasas j` gfcsaffigcga÷l, `f bátkjk sabpf` j` r`dr`sa÷l fal`cf aj`ltaffigc g`rgc j`f 4? % j` fc alnkrbcga÷l cj`gucjcb`lt`.
77
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK
Nadurc 7.09 Bkj`fk j` gfcsaffigcga÷l j` r`dr`sa÷l fal`cf cf`ctkrak. W` bu`strcl fks pcsks `l fks qu` s` gfcsaffigc fc alnkrbcga÷l. Fcs gct`dkrâcs s` `xpr`scl pkr gkfkr`s rkik y l`drk. Fcs khs`rvcgakl`s gfcsaffigcjcs `rr÷l`cb`lt` `l v`rj` y czuf . Plc nkrbc sabpf` j` gklkg`r `f j`s`bp`ók j` gfcsaffigcga÷l j` ul cfdkratbk, `l `st` gcsk, `f cfdkratbk j` r`dr`sa÷l fal`cf, `s gkltcr `f lùb`rk j` khi`tks gkl ulc gfcsaffigcga÷l algkrr`gtc. @l `f gcsk j` fc ffidurc ] skl tkjks cqu`ffks pultks l`drks qu` s` `lgu`ltrcl skhr` fc fâl`c j` r`dr`sa÷l y fks pultks rkiks qu` `stãl j`hcik j` fc fâl`c j` r`dr`sa÷l. W` subc `f lùb`rk j` khs`rvcgakl`s gkl gfcsaffigcga÷l `rr÷l`c y s` javaj` `ltr` `f lùb`rk tktcf j` khs`rvcgakl`s pcrc gklkg`r ul tapk j` basgfcssaffigctakl rct` , lk `s `f ùlagk bátkjk la `f bãs utafazcjk, bãs cj`fclt` s` r`vascrãl bátkjks bãs gkbpf`tks pcrc `stabcr `f pkj`r j` gfcsaffigcga÷l y pr`jagga÷l j` ul bkj`fk. _crc `f
7:
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK gcsk j`f `i`rgagak sabufcjk fc drãffigc bu`strc fks khi`tks bcf gfcsaffigcjks `l gkfkr v`rj` y czuf.
7.8.3. @ltr`lcba`ltk j` cfdkratbk j` gfcsaffigcga÷l fal`cf @l ul gcsk trcjagaklcf j` cpr`ljazci` cutkbctazcjk, `s buy abpkrtclt` husgcr r`fcgakl`s r`f`vclt`s `l fc alnkrbcga÷l. @f khi`tavk `s t`l`r alnkrbcga÷l suffiga`lt` pcrc r`cfazcr vcfajcgakl`s j` fcs map÷t`sas pfclt`cjcs pkr cfdulc gfcs` j` cfdkratbk k bkj`fk qu` s` mcyc d`l`rcjk. Fc b`tkjkfkdâc `s sabpf` p`rk buy `ffiga`lt` gucljk s` utafazc j` nkrbc gkrr`gtc. Gklsast` `l tkbcr ulc pcrt` j` fc alnkrbcga÷l qu` `stã `l ul gkliultk j` jctks y utafazcrfc pcrc gr`cr `f bkj`fk. Ktrc pcrt` j` fc alnkrbcga÷l s`rvarã pcrc vcfajcr `f bkj`fk y gklkg`r su pkj`r pr`jagtavk. @l `st` gcsk, s` utafazcl fks pralgapaks qu` ul cfdkratbk j` alt`fad`lgac crtaffigacf trcjagaklcf utafazcrâc `l ulc v`rsa÷l sabpfaffigcjc. @stc b`tkjkfkdâc j` bu`str`k pcrc nrcggaklcr fc alnkrbcga÷l `stã `sp`gaffigcjc c j`tcff` `l `f gcpâtufk ]. _crc `st` gcsk altrkjugtkrak, utafazcr`bks ulc bu`strc sabpf` pcrc alnkrbcga÷l j` ] pcâs`s y prkhcr`bks `f bkj`fk j` r`dr`sa÷l `stabcjk pcrc ] pcâs`s. C gkltalucga÷l s` utafazc `f bátkjk j` r`dr`sa÷l fal`cf pcrc gfcsaffigcr ul gcsk gkl alnkrbcga÷l r`cf. @f khi`tavk j` `st` bkj`fk sabpf` `s s`db`ltcr cqu`ffks pcâs`s p`rt`l`ga`lt`s c fc KGJ@ y cqu`ffks pcâs`s qu` lk p`rt`l`g`l c `st` drupk. Fks cfgclg`s j` `st` `i`rgagak skl buy cbpfaks, culqu` `l `st` cpcrtcjk s` `lnkgc `l j`scrrkffcr ul bkj`fk qu` cyuj` c gfcsaffigcr alnkrbcga÷l lu`vc `l nulga÷l j`f bkj`fk pr`vak. 70
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK @l d`l`rcf, `st` sabpf` cfdkratbk j` cpr`ljazci` cutkbctazcjk lks jcrã fc gcpcgajcj j` `ls`ócr ul bkj`fk `stcjâstagk c lu`strk prab`r sast`bc j` alt`fad`lgac crtaffigacf c gfcsaffigcr alnkrbcga÷l `l nulga÷l c ulc ncs` j` `ltr`lcba`ltk. @l `stc ncs` j` `ltr`lcba`ltk s` `stchf`g` `f bkj`fk j` r`dr`sa÷l fal`cf j`t`rbalc sa ul pcâs p`rt`l`g` c fc KGJ@ `l nulga÷l j` jks vcrachf` sabpf`s. W` tkbcl gkbk vcrachf`s jks nkgks abpkrtclt`s pcrc `f j`scrrkffk s`dùl fcs bátragcs j`f hclgk buljacf. @l fc ffidurc ] s` khs`rvc `f bkj`fk j` gfcsaffigcga÷l pcrc fc bu`strc j` `ltr`lcba`ltk `l 0= pcâs`s. 3
### G f c s a n a g c j k r j ` p c a s ` s KGJ@
8
7
## @ltr `lcba `ltk
:
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## F ` g tu r c j ` f c r g m a v k j ` ` l t r` l c ba ` l t k j n 6∘ r`cj . g s v ( n a f ` 2 "Gcp 3 . _ r a l g a p a k s j` c p r `l j a z ci ` cutkbctazcjk / jctc[g k u l t r a ` s . g s v " )
4
=
1
## W` k h s` rv c l f c s v c r a c h f ` s lcb`s ( j n )
3?
33
## Gcbhacljk f k s l kb hr `s j ` t k j c s f c s v c r a c h f ` s
38
## s` u t a f a z c ulc f a s t c j` lkbhr`s bcs s ` l g a f f c j` a l t ` r p r ` t c r
37
3:
lcb`s ( j n ) 6∘ g ( " Lkbhr`[p c a s " ,
30
"Gkjadk[p c a s " ,
3>
"Zcsc[bkrtcfajc j " ,
34
"DLA[_G[___" ,
3=
"KGJ@[b`bh`r" )
31
8?
## D rc n ag c j` j a s p ` r s a k l j` f k s j ct ks s ` f ` gg a k l cj k s , s a l
7>
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK j a s t a l g a k l p kr g f c s ` 83
pcr (bnrkw2g (3 ,8 ) ) ## W` ` s p ` g a n a g c qu` s ` q ua `r `l j ks d r c n a g c s ` l ul basbk r ` l d f k l
88
87
## D r cn a gc 3 j` 8 B kr tc fa jc j a l n c l t a f ` a l d r ` s l c g ak l c f h ru tk . p f k t ( x 2 j n $ Zcsc[bkrtcfajcj ,
## ^crac hf` ]
80
y 2 j n $DLA[_G[___,
## ^cr achf ` Q
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x f c h 2 " Zcsc j` B kr tc fa jc j a l n c l t a f p kr gc jc b af
8:
l c g a b a ` l tk s ( 8 ? 3 0 ) " , 84
y f c h 2 " A l d r ` s k L c ga k lc f H ru tk p r ` g a k s g k r r a ` l t ` s ___ ( 8 ?3 0 ) " )
8=
81
7?
## @ s ta bc ga k l j ` f b kj `f k j` r ` d r ` s a k l f a l ` c f .
73
## s ` ` s p ` g a n a g c qu` ` f a l d r ` s k l c g ak l c f h ru tk 2 n ( Zcsc j` bkrtcfaj cj )
78
## f c v c r a c h f ` Q j ` f bkj`fk ` s a l d r ` s k l c g ak l c f h ru tk
77
## f c v c r a c h f ` ] j ` f bk j`f k ` s Zcsc j ` b k rt c fa j cj
7:
70
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DLA[_G[___ ~ Zcsc[bkrtcfaj cj )
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74
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## W` p al tc l f k s g c sk s qu` ` s tc l bcf g f c s a n a g c j k s j n $KGJ@[b`bh`rU j n $ Zcsc[b k r t c f a j c j < 4 0 R 6∘ 7
71
:?
## D r cn a gc 8 j` 8 B kr tc fa jc j a l n c l t a f ` a l d r ` s l c g ak l c f h ru tk , g k fk r `s pkr g f c s a n a g c g a k l j` p ca s
:3
p f k t ( j n $ Zcsc[bkrtcfajcj ,
:8
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:7
x f c h 2 " Zcsc j` B kr tc fa jc j a l n c l t a f p kr gc jc b af l c g a b a ` l tk s ( 8 ? 3 0 ) " ,
74
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK ::
y f c h 2 " A l d r ` s k L c ga k lc f H ru tk p r ` g a k s g k r r a ` l t ` s ___ ( 8 ?3 0 ) " )
:0
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c h f a l ` ( c , g k f 2 " hfu ` " , fwj 2 7 )
Nadurc 7.>9 @stabcga÷l j` bkj`fk j` gfcsaffigcga÷l j` pcâs`s qu` p`rt`l`g`l c fc KGJ@ `l `f s`t j` `ltr`lcba`ltk. J`f fcjk azqua`rjk s` bu`strc fc alnkrbcga÷l pcrc ulc bu`strc j` 0= pcâs`s. @l `f fcjk azqua`rjk s` khs`rvc `f bkj`fk j` r`dr`sa÷l fal`cf y fc alnkrbcga÷l s`dùl su gct`dkrâc. @l rkik s` khs`rvcl fks pcâs`s qu` p`rt`l`g`l c fc KGJ@, `l l`drk cqu`ffks qu` lk p`rt`l`g`l y `l v`rj` skl fks `rrkr`s j` gfcsaffigcga÷l . W` s`db`ltcl fks pcâs`s gkl `f bátkjk j` r`dr`sa÷l fal`cf y s` khta`l` `f r`suftcjk j`f bkj`fk gfcsaffigctkrak. @l fc ffidurc ] j`f fcjk azqua`rjk s` khs`rvcl fks jctks j` Aldr`sk Lcgaklcf Hrutk y fc tcsc j` bkrtcfajcj pkr 7=
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK pcâs j` fc bu`strc j` `ltr`lcba`ltk. J`f fcjk j`r`gmk s` paltc fc alnkrbcga÷l s`dùl fc gfcs` c fc qu` p`rt`l`g`. Fks pcâs`s j` gkfkr rkik gkrr`spklj`l c lcgakl`s p`rt`l`ga`lt`s c fc KGJ@ y j` gkfkr l`drk cqu`ffcs qu` lk. W`dùl `f bkj`fk j` gfcsaffigcga÷l j` r`dr`sa÷l fal`cf `stabcjk fks pcâs`s j` gkfkr v`rj` `stãl gfcsaffigcjks j` nkrbc algkrr`gtc. _crc `f cfdkratbk pfclt`cjk, r`pr`s`ltcl `rrkr`s j` gfcsaffigcga÷l qu` j`bu`strcl `f j`s`bp`ók j`f sast`bc alt`fad`lt`.
7.8.8. _ru`hc j`f cfdkratbk j` gfcsaffigcga÷l fal`cf @f bkj`fk clt`rakr gfcsaffigc cj`gucjcb`lt` `f =: % j` fcs khs`rvcgakl`s `l fc ncs` j` `ltr`lcba`ltk y `f 3> % `rrkr s` gklg`ltrc `l csadlcr pcâs`s qu` lk p`rt`l`g`l c fc KGJ@. Fks `rrkr`s j` gfcsaffigcga÷l s` bu`strcl `l gkfkr v`rj` y fks cga`rtks `l gkfkr rkik. Plc v`z qu` `f bkj`fk bu`strc ga`rtc gcpcgajcj j` gfcsaffigcga÷l, s` prkg`j` c mcg`r fcs pru`hcs gkl `f r`stk j` fc alnkrbcga÷l. Fc s`gga÷l j` fks jctks qu` s` utafazc pcrc fc vcfajcga÷l j` fks cfdkratbks s` ffcbc ncs` j` pru`hc y sa`bpr` `s pkst`rakr c fc ncs` j` `ltr`lcba`ltk. Cjagaklcfb`lt` c `stcs jks ncs`s, `l bugmks gcsks `s r`gkb`ljchf` utafazcr ulc ncs` alt`rb`jac qu` s` ffcbc ncs` j` vcfajcga÷l . _crc `st` gcsk, `f s`t j` pru`hc s` gkbpkl` j`f r`stk j` pcâs`s. W` tkbc `f basbk bkj`fk j` r`dr`sa÷l fal`cf qu` s` utafaz÷ pcrc `f s`t j` `ltr`lcba`ltk y s` khs`rvc `f j`s`bp`ók gfcsaffigctkrak gkl fc alnkrbcga÷l gkbpf`tc. @l fc ffidurc ] s` bu`strcl `f r`suftcjk j`f bkj`fk j` r`dr`sa÷l pcrc g`rgc j` 8?? pcâs`s. 3
## G f c s a n a g c j k r p cr c t kj ks f k s p c a s ` s
71
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK 8
7
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# a l s t c f f . p c g ec d ` s ( " j p f y r " ) ## f a h r ` r a c h c s a g c j ` b cl `i k j ` j c t k s f a h r c r y ( jpfy r ) ## s` g cr dc f c f a h r ` r a c
0
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## I u lt cl j k h c s ` s j ` j c t k s p c r c n f c d KGJ@
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H 6∘ r`cj . g s v ( n a f ` 2 "Gcp 3 . _ r a l g a p a k s j` c p r `l j a z ci ` cutkbctazcjk / jctc / kgj`[b`bh`rs . gsv " , straldsCs Ncgtkrs 2 N) % < % s ` f ` g t ( ∘ Jct`)
33
38
37
j n 8 6∘ f ` n t [ i k a l ( C, H)
3:
30
## W` p a l tc l f k s g c s k s q u` l k s k l b a` bh rk s j ` f c KGJ@ g kl g k f k r 3 (l`drk)
3>
j n 8 $KGJ@[b`bh`rU a s . lc ( jn8 $KGJ@[b`bh`r) R 6∘ 3
34
3=
31
## Gcbhacljk f k s l kb hr `s j ` t k j c s f c s v c r a c h f ` s
8?
## s` u t a f a z c ulc f a s t c j` lkbhr`s bcs s ` l g a f f c j` a l t ` r p r ` t c r
83
lcb`s ( jn8 ) 6∘g ( " Lkbhr`[p c a s " ,
88
"Gkjadk[p c a s " ,
87
"DLA[_G[___" ,
8:
"Zcsc[bkrtcfajc j " ,
80
"KGJ@[b`bh`r" )
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j n 8 $KGJ@[b`bh`rU jn 8 $Lkbhr`[pca s 22 "Tkrfj" R 6∘ 7
84
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GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK 81
7?
pcr (bnrkw2g (3 ,3 ) ) p f k t ( jn8 $ Zcsc[bkrtcfajcj ,
73
j n8 $DLA[_G[___,
78
g k f 2 j n 8 $KGJ@[b`bh`r,
77
x f c h 2 " Zcsc j` B kr tc fa jc j a l n c l t a f p kr gc jc b af l c g a b a ` l tk s ( 8 ? 3 0 ) " ,
7:
y f c h 2 " A l d r ` s k L c ga k lc f H ru tk p r ` g a k s g k r r a ` l t ` s ___ ( 8 ?3 0 ) " )
70
c h f a l ` ( c , g k f 2 " hfu ` " , fwj 2 7 )
Nadurc 7.49 @stabcga÷l j` bkj`fk j` r`dr`sa÷l fal`cf. Gfcsaffigcga÷l j` pcâs`s qu` p`rt`l`g`l c fc KGJ@ `l `f s`t j` pru`hc. @l gkfkr rkik s` khs`rvcl pcâs`s qu` p`rt`l`g`l c fc KGJ@ y `l l`drk pcâs`s qu` lk p`rt`l`g`l c `stc krdclazcga÷l . @s abpkrtclt` j`stcgcr qu` s` utafazc `f basbk bkj`fk j` r`dr`sa÷l qu` :3
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK s` pr`s`ltc `l fc ffidurc ] - 3, lk s` vu`fv` c gr`cr ul bkj`fk culqu` fc alnkrbcga÷l mcyc gcbhacjk. _crc fc bcykrâc j` fks gcsks, `f s`t j` pru`hc ta`l` ul j`s`bp`ók b`lkr qu` `f s`t j` `ltr`lcba`ltk. _crc `f gcsk j` fks pcâs`s j` p`rt`l`ga`lt`s c fc KGJ@ `f j`s`bp`ók j` 44 % j` fks gcsks gfcsaffigcjks gkrr`gtcb`lt` `s b`lkr, `f pkrg`ltci` j` `rrkr s` gklsaj`rc cg`ptchf`. @f bkj`fk j` r`dr`sa÷l fal`cf `stabcjk r`suftc ùtaf pcrc gfcsaffigcr fc alnkrbcga÷l. C p`scr j` fc sabpf`zc j`f bkj`fk, `s hcstclt` bãs `ffiga`lt` qu` ulc `f`gga÷l cf`ctkrac. Gkbpcrcr `f j`s`bp`ók j`f bkj`fk gkl ulc s`f`gga÷l cf`ctkrac `s ulc nkrbc pkpufcr j` aj`ltaffigcr sa `f bkj`fk gkltrahuy÷ c gfcsaffigcr b`ikr k lk. Plc `f`gga÷l cf`ctkrac s` j`ffil` gkbk fc prkhchafajcj sabpf` j` `f`dar ul khi`tk x k y, s`dùl s`c `f gcsk. 7 B`jaclt` ulc `f`gga÷l cf`ctkrac s` pu`j` j` gklkg`r sa `f bkj`fk `s ùtaf k `s b`lks `ffiga`lt` qu` ulc `f`gga÷l cf czcr. _crc `st` gcsk `l gklgr`tk, sa s` utafazc `f bátkjk cf`ctkrak fc prkhchafajcj j` `f`dar ul pcâs j` fc KGJ@ j` tkjc fc bu`strc `s j` g`rgc j`f 3> % y j` ul 74 % sa s` utafazc `f cfdkratbk j` r`dr`sa÷l fal`cf prkpu`stk, pkr fk tcltk, `f bátkjk j` gfcsaffigcga÷l j` r`dr`sa÷l fal`cf cyujc c mcg`r ulc `f`gga÷l 8.7 v`g`s bãs pr`gasc. _crc ulc `stabcga÷l bãs cvclzcjc j`f j`s`bp`ók j`f cfdkratbk, d`l`rcfb`lt` s` utafazc `f hcy`s `rrkr rct` k `rrkr hcy`saclk qu` `stabc fc prkhchafajcj j` `rrkr pcrc cfdkratbks j` j` gfcsaffigcga÷l. @l fcs s`ggakl`s pkr v`lar 7
_kr `i`bpfk, sa s` ta`l` ulc gcic gkl > p`fktcs gkfkr rkik y : p`fktcs gkfkr hfclgk fc prkhchafajcj sabpf` j` `f`dar ulc p`fktc rkic `s j`f >? % y ul :? % j` `f`dar ulc p`fktc j` gkfkr hfclgk. Pl bkj`fk j` gfcsaffigcga÷l cj`gucjk j`h` t`l`r ul j`s`bp`ók bcykr qu` ulc prkhchafajcj sabpf`. Wupkla`ljk qu` sch`bks qu` fcs p`fktcs rkics s` gklg`ltrcl bãs j`f fcjk azqua`rjk, ul grat`rak `i`bpfk, s`râc sa`bpr` `f`dar fcs p`fktcs qu` `stãl j`f fcjk azqua`rjk, j` `stc bcl`rc fc prkhchafajcj j` `f`dar ulc p`fktc rkic `s j`f =? % pkr `i`bpfk.
:8
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK s` r`vascl jastaltks bátkjks pcrc gkbpcrcr `f j`s`bp`ók j` ul cfdkratbk. Nalcfb`lt`, `f cfdkratbk j` gfcsaffigcga÷l `stã t`rbalcjk. Gkl ul hu`l j`s`bp`ók pcrc fks jctks clt`rakr`s, `f cfdkratbk s` pu`j` utafazcr pcrc gkb`lzcr c gfcsaffigcr alnkrbcga÷l. _kjrâc nulgaklcr gkbk ulc gfcs` (buy sabpf` p`rk `ffiga`lt`) j` alt`fad`lgac crtaffigacf. _kr `i`bpfk, sa gklkg`bks `f aldr`sk hrutk j` ulc r`da÷l `sp`gâffigc y fks âljag`s j` bkrtcfajcj alncltaf, pkjr`bks utafazcr `f cfdkratbk pcrc clcfazcr sa `f j`scrrkffk `gkl÷bagk j` fc r`da÷l pkjrâc p`rt`l`g`r c fks `stãljcr`s j` ul pcâs p`rt`l`ga`lt` c fc KGJ@. @f fc ffidurc sadua`lt` s` pr`s`ltc ul gcsk sabafcr. Nalcfb`lt`, `f cfdkratbk j` gfcsaffigcga÷l `stã t`rbalcjk. Gkl ul hu`l j`s`bp`ók pcrc fks jctks clt`rakr`s, `f cfdkratbk s` pu`j` utafazcr pcrc gkb`lzcr c gfcsaffigcr alnkrbcga÷l. _kjrâc nulgaklcr gkbk ulc gfcs` (buy sabpf` p`rk `ffiga`lt`) j` alt`fad`lgac crtaffigacf. _kr `i`bpfk, sa gklkg`bks `f aldr`sk hrutk j` ulc r`da÷l `sp`gâffigc y fks âljag`s j` bkrtcfajcj alncltaf, pkjr`bks utafazcr `f cfdkratbk pcrc clcfazcr sa `f j`scrrkffk `gkl÷bagk j` fc r`da÷l pkjrâc p`rt`l`g`r c fks `stãljcr`s j` ul pcâs p`rt`l`ga`lt` c fc KGJ@. @f fc ffidurc sadua`lt` s` pr`s`ltc ul gcsk sabafcr. 3
x 6∘ g ( 0 , 4 , 1)
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p6∘ jctc . nrcb` ( x , y )
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## W` p al tc l f k s p ul tk s c f d r c n a g k c l t ` r a k r p k a l t s ( p , g k f 2 " g y c l " , fwj 2 3 ? )
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c$ g k ` n n a g a ` l t s 6∘ c$ g k ` n n a g a ` l t s
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:7
8
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GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK 33
38
c$ g k ` n n a g a ` l t s 6∘ chs ( c$ g k ` n n a g a ` l t s ) + 3 ?? c h f a l ` ( c , g k f 2 " hfu ` " , fwj 2 7 )
Nadurc 7.=9 @l fc ffidurc clt`rakr s` ta`l`l 7 r`dakl`s lu`vcs qu` skl gfcsaffigcjcs pkr `f cfdkratbk fal`cf, j` cgu`rjk `f bkj`fk j` gfcsaffigcga÷l s` khta`l` qu` jks j` `ffks gkl cftc prkhchafajcj ta`l`l fcs gkljagakl`s qu` prabcl `l ul pcâs qu` p`rt`l`g` c fc KGJ@ y cqu`f qu` s` `lgu`ltrc j`hcik j` fc fâl`c j` r`dr`sa÷l lk fk `s. Wupkldcbks pcrc b`jaga÷l j` j`saducfjcj `l ulc lcga÷l fctalkcb`ragclc s` gkbpcrcl fks `stãljcr`s j` vajc j` ulc r`da÷l gkl cgg`sk r`straldajk c fc scfuj y r`dakl`s j` cftk aldr`sk `gkl÷bagk qu` skl cf`jcócs. _ksahf`b`lt` fcs r`dakl`s j` cftk aldr`sk `gkl÷bagk t`ljrãl `stãljcr`s j` vajc sabafcr`s c pcâs`s p`rt`l`ga`lt`s c fc KGJ@ y fcs cf`jcócs lk t`ljrãl `stks `stãljcr`s j` vajc. Xãpajcb`lt`, `st` bkj`fk lks cyujcrã c j`t`rbalcr fks fâbat`s ::
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK `l nulga÷l c alnkrbcga÷l j` bkrtcfajcj alncltaf ` aldr`sk lcgaklcf5 pksahf`s b`jajcs j` pkfâtagc `gkl÷bagc u khi`tavks j` pkfâtagc skgacf. ¡N`fagajcj`s, sa mcs s`duajk tkjks fks pcsks j` `stc s`gga÷l `xatkscb`lt` mcs gr`cjk ul prab`r cfdkratbk sabpfaffigcjk j` alt`fad`lgac crtaffigacf! Zu lu`vk cfdkratbk t` p`rbatarã tkbcr j`gasakl`s j` pkfâtagc `gkl÷bagc y skgacf. Gkl `f ffil j` r`nkrzcr fcs mchafajcj`s j` bkj`fazcga÷l pr`s`ltcjcs `l `stc s`gga÷l altrkjugtkrac, bãs cj`fclt` s` r`vascrãl c j`tcff` cfdulks cfdkratbks bãs cvclzcjks j` gfcsaffigcga÷l y pr`jagga÷l. Aducfb`lt`, s` `xpfagcrãl fcs b`tkjkfkdâcs `stãljcr j` bu`str`k csâ gkbk pru`hcs j` vcfajcga÷l j` fks bkj`fks j` cpr`ljazci` cutkbãtagk. @l `f gcpâtufk sadua`lt` s` bu`strc `f cfdkratbk j` cdrupcba`ltk k gfust`r pkr FJC (Fal`cr Jasgrabalclt Clcfysas pkr sus sadfcs `l aldfás) y ulc cpfagcga÷l r`fcgaklcjc c kptabazcga÷l j` g`ltrks j` jastrahuga÷l gkl ulc p`rsp`gtavc d`kdrãffigc.
7.8.7. X`sub`l st` gcpâtufk s` `lnkgc `l j`scrrkffcr fks gklg`ptks gfcv` j` r`dr`sa÷l fal`cf cpfagcjks c ul sast`bc j` cpr`ljazci` cutkbãtagk sabpfaffigcjk. W` r`vascl fks gklg`ptks j`f bkj`fk j` r`dr`sa÷l fal`cf, csâ basbk, s` `xpfagc qu` `f bkj`fk j` r`dr`sa÷l fal`cf ta`l` ul krad`l bãs cltaduk j` fk qu` gkbùlb`lt` s` pu`j` gr``r y s` `xpfagcl fks pfclt`cba`ltks qu` j`scrrkff÷ Nrclgas Dcftkl `l `f sadfk ]A] pcrc ff`dcr c fcs gklgfusakl`s j` qu` `xast` ul bkj`fk j` r`dr`sa÷l fal`cf. Cjagaklcfb`lt`, s` j`bu`strc fc sabafatuj qu` ta`l` fc r`dr`sa÷l fal`cf gkl fc `gucga÷l sabpf` j` fc r`gtc ( y 2 bx ∔ h), gkl `f ffil j` gkbpr`lj`r fcs nulgakl`s j` fks `stabcjkr`s y gk`ffiga`lt`s `l ul bkj`fk j` r`dr`sa÷l fal`cf. :0
GC_ÂZPFK 7. _XALGA_AKW HÃWAGKW J@ C_X@LJAYCI@ CPZKBCZAYCJK B`jaclt` ulc `xpfagcga÷l prãgtagc `l X, s` utafazc ul bkj`fk j` r`dr`sa÷l fal`cf prkpak pcrc r`gr`cr fcs alv`stadcgakl`s j` Dcftkl (3==1). _kst`rakrb`lt` s` bu`strc `f prkg`sk drãffigk j` gfcsaffigcga÷l fal`cf gkl alnkrbcga÷l cf`ctkrac y bãs cj`fclt`, s` r`vasc `f usk j`f bkj`fk j` r`dr`sa÷l fal`cf pcrc prkhf`bcs j` gfcsaffigcga÷l gkl alnkrbcga÷l r`cf. W` `sp`gaffigc qu` fc gfcsaffigcga÷l `s ul t`bc nuljcb`ltcf `l alt`fad`lgac crtaffigacf y bcgmal` f`crlald k cpr`ljazci` cutkbãtagk. _kr b`jak j` fks pralgapaks hãsagks j` r`dr`sa÷l fal`cf, s` `i`gutcl tkjks fks pcsks hãsagks pcrc gr`cr ul sast`bc j` alt`fad`lgac crtaffigacf sabpf` cpfagcjk c ul prkhf`bc `gkl÷bagk. W` utafazcl fcs b`tkjkfkdâcs trcjagaklcf`s j` bcgmal` f`crlald j` bu`str`k, `ltr`lcba`ltk y pru`hc pcrc `i`bpfaffigcr `f gcsk j` gfcsaffigcga÷l j` fc KGJ@ y s` bu`strc `f nulgaklcba`ltk. @f bkj`fk pr`t`lj` cpr`lj`r gfcsaffigcr pcâs`s qu` p`rt`l`g`l c fc KGJ@ (r`gklkgajks pkr s`r pcâs`s j`scrrkffcjks y cfdulks `l vâcs j` j`scrrkffk) y cqu`ffks qu` lk p`rt`l`g`l c fc KGJ@. W` utafazcl jctks j`f hclgk buljacf tkbcljk bátragcs gfcv` pcrc `f j`scrrkffk y s` `ltr`lc `f bkj`fk j` r`dr`sa÷l fal`cf gkl ul pkj`r j` gfcsaffigcga÷l cj`gucjk.
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Gcpâtufk : Cfdkratbks j` gfcsaffigcga÷l fal`cf ‖Cjbatt`jfy, lk Crtaffigacf Alt`ffad`lg` `gklkbag nkr`gcstald syst`b as kp`rctaklcf tkjcy, wmaf` `gklkb`trag cpprkcgm`s mcv` tm` v`ry r`cf b`rat kn `xastald. Mkw`v`r, s`v`rcf `xp`rab`lts mcv` ya`fj`j `lgkurcdald r`sufts clj pks`j us`nuf clj p`rtal`lt qu`stakls. As `gklkb`trags c sctasncgtkry r`pr`s`ltctakl kn tm` wkrfj; Cr` tm` fabatctakls kl tm` bkj`fs lktmald bkr` tmcl sup`rffigacf j`n`gts ju` tk tm` alcj`qucga`s kn `xastald t`gmlkfkdy;‒ _cfa`s, K y Bcy`r, I (31=1) @l `stc s`gga÷l s` r`vascl jks bátkjks pkpufcr`s j` gfcsaffigcga÷l. Fks cfdkratbks j` gfcsaffigcga÷l ta`l`l gkbk khi`tavk s`db`ltcr ` aj`ltaffigcr alnkrbcga÷l. @l fc prab`rc s`gga÷l, s` r`vascrkl fks pralgapaks hãsagks qu` tkjk sast`bc j` alt`fad`lgac crtaffigacf skfugaklc, fc jan`r`lgac `ltr` ul cfdkratbk sup`rvascjk y lk sup`rvascjk, csâ gkbk ulc cpfagcga÷l sabpf` gkl bkj`fks j` r`dr`sa÷l fal`cf pcrc gfcsaffigcr jctks. _crc `st` cpcrtcjk, s` `lgu`ltrcl :4
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF `xpfagcjks ul pcr j` bátkjks j` gfcsaffigcga÷l buy gkbul`s qu` suda`r`l hcs`s pcrc abpf`b`ltcgakl`s bãs gkbpf`ics. @f khi`tavk j` `stc s`gga÷l `s gkbpf`b`ltcr `f usk j`f bátkjk j` r`dr`sa÷l fal`cf y s`r cprkv`gmcjk `l ul gklt`xtk bãs `xt`lsk qu` p`rbatc aj`ltaffigcr gfust`rs sup`rvascjks. Wadua`ljk `f khi`tavk j` `st` t`xtk, s` pr`s`ltc ulc vasa÷l prãgtagc j` fks cfdkratbks. Fcs cpfagcgakl`s j` `st` tapk j` cfdkratbks skl r`gurr`lt`s `l rcbcs j` fc ga`lgac gkbk hakfkdâc k ald`la`râc. Jav`rsks `stujaks utafazcl `stks bátkjks pcrc aj`ltaffigcr pctrkl`s `l gkbpkrtcba`ltk `l s`durajcj j` sast`bcs, trãffigk j` r`j`s ` aj`ltaffigcga÷l j` ncgtkr`s qu` pu`j`l pr`j`gar ra`sdk j` `ln`rb`jcj`s `l ulc pkhfcga÷l. Algfusav`, cfdulks `sp`gacfastcs `l hak`stcjâstagc aj`ltaffigcl pctrkl`s j`ltrk j`f CJL pcrc j`t`gtcr fcs gcuscs d`látagcs j` `ln`rb`jcj`s k `lgkltrcr drupks j` `sp`ga`s (Mkcld `t cf, 8?30). Cfdulks j` fcs táglagcs j` gfcsaffigcga÷l k aj`ltaffigcga÷l j` gfust`rs s` utafazcl nr`gu`lt`b`lt` pcrc aj`ltaffigcr ctcqu`s c s`rvajkr`s gkrpkrctavks y duh`rlcb`ltcf`s (Cdmchkzkrda `t cf, 8?30). Cfdulcs rcbcs tkbcl `st` tapk j` cfdkratbks pcrc gfcsaffigcr fc alt`lga÷l j` ul t`xtk k gkbcljk j` vkz j` nkrbc cutkbãtagc. Psucfb`lt`, fcs táglagcs j` gfust`r lk nkrbcl pcrt` j` fcs m`rrcba`ltcs trcjagaklcf`s qu` ul ga`ltâffigk skgacf j`scrrkffc. @l gcsk j` fc @gklkbâc, ul t`xtk j` `gklkb`trâc trcjagaklcf janâgafb`lt` algfuarã `stcs táglagcs gkbk crdub`ltk pralgapcf j`f fahrk. Culqu` vcracs alv`stadcgakl`s j` gfust`rs aljustracf`s, j` b`rgcjks ffilclga`rks ` alt`rlcgaklcf`s utafazcl `stcs táglagcs r`suftcl trchciks j` j`scrrkffks táglagks y `stcjâstagks bãs cvclzcjks. Wal `bhcrdk, `st` lk `s `f gcsk pcrc fcs j`bãs jasgapfalcs. _kr `i`bpfk, qu` j`ltrk j` fcs ga`lgacs skgacf`s `stcs b`tkjkfkdâcs lk skl ci`lcs c alv`stadcgakl`s r`fcgaklcjcs gkl aj`ltaffigcga÷l j` `spcgaks d`kdrãffigks k aj`ltaffigcga÷l j` dru-
:=
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF pks `l tkrlk c clãfasas `spcgacf y tkjcs fcs v`rta`lt`s alt`rjasgapfalcracs. @l bcre`tald, fks clãfasas j` gfust`r r`suftcl nuljcb`ltcf`s pcrc aj`ltaffigcr drupks khi`tavks pcrc mcg`r bãs `ffiga`lt`s fcs gcbpcócs j` puhfagajcj. @l `stc rcbc fcs cpfagcgakl`s j` gfùst`r s` mcl bcjurcjk `lkrb`b`lt` `l clãfasas j` r`j`s skgacf`s j` Ncg`hkke , Zwatt`r y Q`fp pkr `i`bpfk. Fks cfdkratbks j` gfust`rald skl d`l`rcfb`lt` utafazcjks pkr cqu`ffks qu` bcl`icl fcs rcbcs j` alt`fad`lgac crtaffigacf bcgmal` f`crlald y jctc balald. Cfdulks cfdkratbks j` gfust`rald lk skl táglagcs lu`vcs y d`l`rcfb`lt` s` f`s ctrahuy` gkbk táglagcs j` cpr`ljazci` lk sup`rvascjk. W`dùl s` j`ffila÷ `l fc prab`rc s`gga÷l j`f t`xtk `f cpr`ljazci` lk sup`rvascjk s` gcrcgt`razc pkr lk t`l`r gklkgaba`ltk c prakra j` fcs gct`dkrâcs qu` gkbpkl`l ulc bu`strc. Fks khi`tavks j` ul bkj`fk j` gfust`rald skl gcrcgt`razcjks pkr s`db`ltcr ` aj`ltaffigcr `stcs gfcs`s k gct`dkrâcs.3 Pl `i`bpfk alt`r`sclt` j` gfust`rald s` pu`j` v`r `l fks v`mâgufks j` gkljugga÷l cut÷lkbc j` Z`sfc. @l `f sadua`lt` vâlgufk s` pu`j` v`r qu` `l ta`bpk r`cf `f cutkb÷vaf aj`ltaffigc cf b`lks sa`t` gfcs`s jastaltcs. 3. Bktaklkw 8. Fcl` fal`s 7. Xkcj NFkw :. Al pctm khi`gts 0. Xkcj fadmts 3
Cfdulks cutkr`s b`lgaklcl qu` fks khi`tavks j` gfust`rald pu`j`l s`r jastaltks, pkr `i`bpfk Tu (8?38) b`lgaklc qu` fks prkp÷satks j` ul cfdkratbk j` cdrupcba`ltk `s `lt`lj`r gcrcgt`râstagcs `l fks jctks y s`r utafazcjk gkbk bu`strcs prktktapk.
:1
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF >. Khi`gts 4. Xkcj sadls
Nadurc :.39 ^`mâgufk j` gkljugga÷l csastajc j` Ph`r. mttps9 // www. ykutuh`. gkb/ wctgm; v2 ^D>=WEkD4v@
@stc s`gga÷l s` `lnkgc `l bkstrcr cpfagcgakl`s j` ul cfdkratbk j` gfust`rald sabafcr c fks gcsks qu` s` j`sgrah`l clt`rakrb`lt`. W` husgc `lgkltrcr drupks `l alnkrbcga÷l gfcsaffigcjc y lk gfcsaffigcjc utafazcljk ulc táglagc pkpufcr gklkgajc gkbk Fal`cr Jasgrabalclt Clcfysas (FJC) s` clcfazcrã ul gcsk buy pkpufcr j` ‖tcxklkbâc‒ `l hakfkdâc pcrc gklkg`r fks pralgapaks j`f clãfasas y ul gcsk gcbpcóc j` bcre`tald pcrc aj`ltaffigcr drupks j` gfa`lt`s pkt`lgacf`s.
0?
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
:.?.3. Gfcsaffigcga÷l j` bùftapf`s gct`dkrâcs gkl clãfasas jasgrabalclt` fal`cf (FJC) @f krâd`l j` fc pkpufcr táglagc j` cpr`ljazci` `stcjâstagk FJC s` `lgu`ltrc `l ulk j` fks crtâgufks bãs r`f`vclt`s j` fc `stcjâstagc bkj`rlc Zm` us` kn buftapf` b`csur`b`lts al tcxklkbag prkhf`bs j` Nasm`r `l 317>, ncbksk ha÷fkdk y `stcjâstagk `s gklkgajk pkr sus cpkrt`s c fcs ga`lgacs lcturcf`s y c fc aln`r`lgac `stcjâstagc. Fc tcxklkbâc `s gklkgajc gkbk fc ga`lgac j` fc gfcsaffigcga÷l y Nasm`r t`lâc gkbk khi`tavk `lgkltrcr ul bátkjk `stcjâstagk qu` puja`rc bcxabazcr fc jan`r`lgac `ltr` fcs guctrk gfcs`s j` kr`s qu` `stchc clcfazcljk, `s j`gar, bkstrcr bãs ncgafb`lt` fcs jan`r`lgacs `ltr` `sp`ga`s, `l `s`lgac ul prkhf`bc j` gfcsaffigcga÷l k tcxklkbâc. Culqu` `f bátkjk pr`s`ltcjk pkr Nasm`r `l `f crtâgufk kradalcf `s ùtaf pcrc gfcsaffigcr alnkrbcga÷l, s` utafazcl fks jctks kradalcf`s j` NAsm`r y `f bátkjk d`l`rcfazcjk pcrc e gfcs`s j` FJC. Psucfb`lt`, s` ctrahuy` qu` `f bátkjk j` FJC `s fc v`rsa÷l d`l`rcfazcjc j`f bátkjk kradalcf j` Nasm`r y pkr fk tcltk bãs cj`gucjk pcrc ulc gfcsaffigcga÷l j` e gfcs`s. 8 C gkltalucga÷l, utafazcr`bks `f bátkjk j` FJC pcrc gfcsaffigcr fks basbks jctks qu` r`gkf`gt÷ Nasm`r `l 317>. J` cgu`rjk gkl fc alnkrbcga÷l s` ta`l`l tr`s tapks jastaltks j` `sp`ga`s Aras s`tksc, Aras v`rsagkfkr, Aras vardalagc. @l fc ffidurc ] s` khs`rvc c sabpf` vastc ga`rtc sabafatuj j` gkfkr `ltr` fcs `sp`ga`s j` Aras y r`suftc ul r`tk alt`r`sclt` pkj`r jan`r`lgacr gcjc ulc j` `ffcs s`dùl ga`rtcs gcrcgt`râstagcs. 8
Ktrcs vcraclt`s j` gfcsaffigcga÷l pu`j`l s`r fks bkj`fks fkdat y prkhat qu` s` chkrjcl `l drcl pcrt` fks t`xtks gklv`lgaklcf`s j` `gklkb`trâc, pkr `i`bpfk9 Duicrcta (8?38).
03
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.89 W` bu`strcl fcs 7 `sp`ga`s qu` gkbpkl`l fks jctks j` Nasm`r 317>. Nasm`r kradalcfb`lt` utafazc guctrk jastaltcs gcrcgt`râstagcs gucltatctavcs j` `stcs `sp`ga`s, `f fcrdk j`f pátcfk, clgmk j`f pátcfk, fcrdk j`f sápcfk y clgmk j`f sápcfk. Fc nulga÷l pralgapcf j` ul sápcfk `s guhrar fks pátcfks y ktrcs pa`zcs krcf`s `l `tcpcs prabatavcs j` j`scrrkffk j` ulc kr. _crc ulc kr j` dál`rk Fujwadac s` khs`rvc gfcrcb`lt` fc jan`r`lgac `ltr` pátcfk y sápcfk. C gkltalucga÷l s` bu`strcl cfdulks j` fks `i`bpfks qu` gkbpkl` fc alnkrbcga÷l r`gkf`gtcjc pkr Nasm`r. W` bu`strcl fcs : gct`dkrâcs qu` gcrcgt`razcl c gcjc ulc j` fcs kr`s b`jajcs `l gb y c fc `sp`ga` c fc qu` p`rt`l`g` (s`tksc, vardalagc k v`rsagkfkr). W`dùl fks grat`raks qu` s` j`ffila`rkl `l fc s`gga÷l 3 j`f t`xtk, `st` gcsk `s gcrcgt`râstagk j` ul prkhf`bc j` s`db`ltcga÷l gfcsaffigcjk k cpr`ljazci` sup`rvascjk. Cf gklkg`r fc gfcs` c fc qu` p`rt`l`g` gcjc kr s` pu`j` `i`gutcr ul cfdkratbk qu` tkb` `l gu`ltc `stc vcrachf` sup`rvascjc (Wp`ga`s). _crc `xpfkrcr y bkstrcr fc jan`r`lgac `l gcjc ulc j` fcs `sp`ga`s, s` drcffigcl fcs 30? bu`strcs pcrc fcs galgk jab`lsakl`s j`sgratcs. @l fc ffidurc 08
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF ] s` `xpfagc fc jasp`rsa÷l pkr vcrachf` y pkr gkfkr j` `sp`ga`. 3
8
## W` g c r d c f c a l n k r b c g a k l j n 6∘ a r a s
7
:
0
## W` j ` s gr a h `l f c s p ra b` rc s f a l ` c s j` f k s j ct ks m`cj( j n )
Nadurc :.79 W`f`gga÷l cf`ctkrac j` fc alnkrbcga÷l r`gkf`gtcjc pkr Nasm`r 317>. W` khs`rvcl fcs : gcrcgt`râstagcs j` fcs kr`s y fc `sp`ga` c fc qu` p`rt`l`g`l.
3
## W ` d r c n a g c l f c s 0 j a b` l s ak l `s j ` f c a l n kr b c ga k l
8
## s ` g k fk r ` c s `du l f c ` s p `g a ` c f c qu` p `r t` l `g ` gcjc n f k r
7
:
p f k t ( jn , g k f 2 j n $ W p ` g a ` s )
07
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.:9 Drãffigc j` jasp`rsa÷l pcrc fcs galgk jab`lsakl`s j` Nasm`r (317>). @l gkfkr l`drk s` bu`strcl aras s`tksc, `l rkik aras v`rsagkfkr y `l gkfkr v`rj` aras vardalagc. C sabpf` vastc s` khs`rvc qu` ulc pksahf` j`gasa÷l pcrc aj`ltaffigcr fc gfcs` aras s`tksc (l`drk) skl tkjcs cqu`ffcs bu`strcs qu` t`ldcl b`lks j` 8.0gb j` fcrdk `l `f pátcfk y b`lks j` >gb j` fcrdk `l `f sápcfk. Wal `bhcrdk, fc r`dfc j` s`db`ltcga÷l pcrc `f gcsk j` fcs `sp`ga`s aras v`rsagkfkr ` aras vardalagc lk `s tcl `vaj`lt` (rkik y v`rj` r`sp`gtavcb`lt`). Cf `f`dar ulc r`dfc crhatrcrac j` jasgrabalcga÷l (fâl`c czuf) lk s` gfcsaffigcl gkrr`gtcb`lt` cfdulcs khs`rvcgakl`s.
0:
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.09 Drãffigc j` jasp`rsa÷l pcrc fcs galgk jab`lsakl`s j` Nasm`r (317>). @l gkfkr l`drk s` bu`strcl aras s`tksc, `l rkik aras v`rsagkfkr y `l gkfkr v`rj` aras vardalagc. _u`stk qu` fcs r`dfcs crhatrcracs lk r`pr`s`ltcl ul bátkjk radurksk j` clãfasas, utafazcljk `f bátkjk j` FJC d`l`rcfazcjk s` pu`j`l gfcsaffigcr fcs `sp`ga`s. _crc `i`gutcr `f bátkjk j` nkrbc cj`gucjc d`l`rcfb`lt` s` utafazcl táglagcs j` bu`str`k cf`ctkrak clt`s j` `i`gutcr `f cfdkratbk j` FJC. Fc r`f`vclgac j` ul bu`str`k cj`gucjk abpcgtcrã `f j`s`bp`ók j` gucfqua`r bkj`fk j` s`db`ltcga÷l, aj`ltaffigcga÷l y pr`jagga÷l. _crc gucfqua`r clãfasas j` bcgmal` f`crlald `f bu`str`k r`pr`s`ltc fcs hcs`s qu` p`rbatarãl `n`gtucr y ciustcr ul cfdkratbk j` nkrbc cj`gucjc. C gkltalucga÷l s` j`sgrah` ulc táglagc j` bu`str`k gkbùl `l fcs ga`lgacs gkbputcgaklcf`s. Gklsast` `l javajar fc alnkrbcga÷l `l s`t j` pru`hcs y s`t 00
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF j` vcfajcga÷l. @l fc s`gga÷l prab`rc j` `st` t`xtk s` b`lgaklc `f usk j` `stc táglagc, `l `f sadua`lt` cpcrtcjk s` r`vasc gkl ul pkgk bãs j` prknuljajcj.
:.?.8. Ncs` j` `ltr`lcba`ltk Fc s`gga÷l j` `ltr`lcba`ltk k trcalald s`t , gklsast` `l ulc s`gga÷l j` fc alnkrbcga÷l qu` s`rã utafazcjc pcrc `ltr`lcr `f bkj`fk j` s`db`ltcga÷l. Plc nkrbc sabpf` `s utafazcr ulc s`f`gga÷l cf`ctkrac j` ulc pkrga÷l j`t`rbalcjc j` fc alnkrbcga÷l, csâ pkr `i`bpfk, s` utafazc ulc pkrga÷l sadlaffigctavc j` fks jctks pcrc `stabcr `f bkj`fk. @stc táglagc p`rbat` `ltr`lcr `f bkj`fk `l ulc s`gga÷l j` fks jctks y vcfajcrfk `l ktrc s`gga÷l d`l`rcfb`lt` bãs p`qu`óc. @l fc ffidurc ] s` `xpfagc g÷bk s` javaj` fc alnkrbcga÷l pcrc `f gcsk j` fcs `sp`ga`s aras. W` ta`l`l 30? khs`rvcgakl`s qu` gklstatuy` fc pkhfcga÷l, s` tkbc cf`ctkracb`lt` `f 4? % pcrc `ltr`lcr `f bkj`fk `l fc ncs` j` `ltr`lcba`ltk y `f 7? % r`stclt` s` s`f`ggaklcl pcrc fc ncs` j` pru`hcs.
Nadurc :.>9 @squ`bc j` bu`str`k cf`ctkrak pcrc `f gcsk j` aras. W` bu`strcl `f lùb`rk j` khs`rvcgakl`s qu` s` utafazcl pkr ncs`s s`dùl `f `ltr`lcba`ltk y pru`hc j`f cfdkratbk.
3
## Ncs` j` `ltr`lcba` ltk
8
## W ` f ` g g a k l j ` f 4? % j ` f c a l n kr b c ga k l
7
0>
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF :
p k r g ` l t c i ` 6∘ 4? / 3? ?
0
>
lub[bu`strcs 6∘ p k r g ` l t c i `
∔
lrkw ( j n )
4
=
1
3?
## B u `s t r` k c f ` c t k r a k s ` t . s``j (8?) t r c a l[al j 6∘ scbpf` ( s`q[f`l ( lrkw ( j n ) ) , s a z ` 2 lub[b u ` s t r c s )
33
38
## W ` f ` g g a kl c b k s f c s b u `s t r cs q u` p ` r t ` l ` g ` l
37
## c f s ` t j ` ` l t r `l c b a` l t k
3:
t r c a l[ s ` t 6∘ j n U t r c a l[a lj , R
30
3>
## W ` f ` gg a k l c bk s ` f r ` s t k j ` b u `s t rc s
34
## qu ` p ` r t` l ` g` l c f s ` t j` p r u` hc s
3=
t ` s t[ s ` t 6∘ j n U ∘ t r c a l[a lj , R
Cf s`f`ggaklcr `f jctcs`t j` `ltr`lcba`ltk trcal[s`t khs`rvcbks fcs prkhchafajcj`s c prakra qu` j`sgrah`l fc prkhchafajcj sabpf` j` `f`dar ulc gfcs` j` nkrbc cf`ctkrac. C gkltalucga÷l s` bu`strcl fcs prkhchafajcj`s c prakra pcrc gcjc ulc j` fcs `sp`ga`s csâ gkbk `f lùb`rk j` v`g`s qu` cpcr`g` gcjc gfcs` `l fc bu`strc j` 3?0 khs`rvcgakl`s. 3
## @ i ` g u g a k l j ` f c f d k r a t b k j ` FJC
8
7
f a h r c r y (BCWW)
:
s k u r g ` ( n a f ` 2 ‑Gcp 8 . C fd kr at bk s j ` g f c s a n a g c g a k l f a l ` c f / j a n ` r ` l g a c s[ a r a s .X ‑ )
0
>
4
=
## @ i ` g u g a k l j ` f c f d k r a t b k j ` FJC bkj`fk 6∘ fjc ( jctc 2 t r c a l[s`t , W p `g a `s ~ . )
04
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF 1
3?
33
38
## _ r k h c h a f a jc j ` s c p r a k r a bkj`fk $ p r a k r
37
3:
30
## Lub`rk j ` k h s ` r v c g a k l ` s p k r g f c s ` bkj`fk $ g k u l t s
3>
34
3=
## G k ` n a g a ` l t ` s p kr g c r c g t ` r a s t a g c s bkj`fk $ s g c f a l d
Nadurc :.49 _rkhchafajcj`s c prakra j`f bkj`fk FJC pcrc tkjcs fcs gfcs`s pcrc `f s`t j` `ltr`lcba`ltk.
Nadurc :.=9 Lùb`rk j` khs`rvcgakl`s pkr gfcs` pcrc `f s`t j` `ltr`lcba`ltk. Fcs tchfcs clt`rakr`s lks j`sgrah`l fc prkhchafajcj j` kht`l`r ulc gfcs` u ktrc s`dùl fc prkhchafajcj sabpf`. X`gkrj`bks qu` cf t`l`r alnkrbcga÷l c prakra j`f gkliultk j` alnkrbcga÷l qu` s` qua`r` gfcsaffigcr s` `stã mchfcljk j` ul cfdkratbk sup`rvascjk. @l nulga÷l c `stks vcfkr`s `f cfdkratbk j` FJC gr`crã fcs r`dfcs j` j`gasa÷l pcrc gfcsaffigcr fks jctks `l nulga÷l j` sus gcrcgt`râstagcs, s`pcf f`ldtm, s`pcf wajtm, p`tcf f`ldtm y p`tcf wajtm . Fcs r`dfcs j` 0=
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF j`gasa÷l s` gcrcgt`razcl pkr gcjc ulc j` ulc `stcs : vcrachf`s `l ul pfclk hajab`lsaklcf5 `s j`gar, gcjc gcrcgt`râstagc t`ljrã r`dfcs j` j`gasa÷l pcrc jks jab`lsakl`s.
Nadurc :.19 Gk`ffiga`lt`s j`f bkj`fk FJC
3
## W ` p r ` j a g ` ` f b kj` fk s k h r` ` f s ` t
j ` ` l tr `l c ba `l tk , p kr
j`ncuft 8
## lk s ` ` s p ` g a n a g c ul j c tc s ` t lu`vk c f c n u lg a kl p r ` j a g t
7
:
p r ` j a g g a k l 6∘ p r ` j a g t ( bkj`fk)
0
>
## D rc na gc j` g f c s a n a g c g a k l k r a d a l c f
4
pcr (bnrkw2g (3 ,8 ) )
=
p f k t ( p r ` j a g g a k l $x ,
1
3?
g k f 2 t r c a l[ s ` t $ W p ` g a ` s , bcal 2 " K r a d a l c f " )
33
38
37
## D rc n a g c j ` g f c s a n a g c g a k l s `d ul ` f b kj` fk ` st ab cj k p f k t ( p r ` j a g g a k l $x ,
3:
gkf 2pr`jaggakl $gfcss ,
30
bcal 2 " _ r ` j a g g a k l " )
01
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.3?9 X`suftcjks j`f bkj`fk j` gfcsaffigcga÷l pcrc fks jctks j` Nasm`r (317>). J`f fcjk azqua`rjk s` bu`strc fc gfcsaffigcga÷l kradalcf k r`cf pkr kh i`tk. J`f fcjk j`r`gmk fcs pr`jaggakl`s pkr `f cfdkratbk j` FJC d`l`rcfazcjk. C sabpf` vastc `l fc ffidurc clt`rakr s` bu`strc qu` `f cfdkratbk j` gfcsaffigcga÷l FJC ta`l` ul j`s`bp`ók cg`ptchf`, j`f fcjk azqua`rjk s` bu`strc fc gfcsaffigcga÷l r`cf pkr `sp`ga` y j`f fcjk j`r`gmk s` bu`strc fc gfcsaffigcga÷l `n`gtucjc pkr `f bkj`fk prkpu`stk. C gkltalucga÷l s` clcfazc `f j`s`bp`ók j` gfcsaffigcga÷l r`cf. Pl `i`bpfk s`râc trctcr j` gfcsaffigcr `f s`xk j` ul pcga`lt` s`dùl su `stcturc, supkldcbks qu` t`l`bks 3? pcga`lt`s, 0 qu` skl mkbhr`s y 0 qu` skl bui`r`s. J` cgu`rjk gkl su `stcturc gr`cbks ul cfdkratbk qu` lks jag` fk sadua`lt`.
>?
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.339 X`suftcjks j`f bkj`fk j` gfcsaffigcga÷l pcrc fks jctks j` Nasm`r (317>). J`f fcjk azqua`rjk s` bu`strc fc gfcsaffigcga÷l kradalcf k r`cf pkr kh i`tk. J`f fcjk j`r`gmk fcs pr`jaggakl`s pkr `f cfdkratbk j` FJC d`l`rcfazcjk.
:.?.7. Pl bátkjk j` b`jaga÷l j`f j`s`bp`ók sup`rvascjk Pl bátkjk trcjagaklcf utafazcjk `l jav`rscs rcbcs j` fc alt`fad`lgac crtaffigacf pcrc gklkg`r `f j`s`bp`ók j` ul cfdkratbk j` gfcsaffigcga÷l y pr`jagga÷l `s gklkgajk gkbk bctraz j` gklnusa÷l. Fc bctraz j` gklnusa÷l `s gcrcgt`râstagc `s`lgacf pcrc tkjk prkhf`bc j` gfcsaffigcga÷l sup`rvascjk. @f khi`tavk j` `st` bátkjk `s `sp`gaffigcr `f lùb`rk j` `rrkr`s `l fks qu` algurr` `f bkj`fk
>3
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF jas`ócjk gkbpcrãljkfk gkl fc alnkrbcga÷l r`cf.7
Nadurc :.389 @i`bpfk j` bctraz j` gklnusa÷l, s` bu`strcl fks v`rjcj`rks pksatavks y v`rjcj`rks l`dctavks `l fc jacdklcf, ncfsks pksatavks y ncfsks l`dctavks nu`rc j` `ffc. @f bkj`fk pr`jag` `rr÷l`cb`lt` c ul mkbhr` gkbk bui`r (s` bu`strc nu`rc j` fc jacdklcf. @l `f `i`bpfk mapktátagk clt`rakr `f bkj`fk `s hu`lk aj`ltaffigcljk bui`r`s s`dùl su `stcturc cf pr`j`gar fcs 0 bui`r`s gkbk bui`r`s sal `bhcrdk lk `s tcl hu`lk aj`ltaffigcljk c tkjks fks mkbhr`s, fc bctraz j` gklnusa÷l `xpfagc qu` ul mkbhr` nu` gctcfkdcjk gkbk bui`r s`dùl sus gcrcgt`râstagcs. @l `f gcsk j` aras, s` ta`l` ul bkj`fk pcrc 3?0 bu`strcs j` 30? jctks. W` gfcsaffigcrkl fcs 3?0 bu`strcs gkbk s` khs`rvc `l fc ffidurc clt`rakr y s` khtuva`rkl fks r`suftcjks j`f bkj`fk. _crc gkrrkhkrcr qu` `f bkj`fk `s cj`gucjk, s` bu`strc fc bctraz j` gklnusa÷l pcrc `f s`t j` `ltr`lcba`ltk j` fc sadua`lt` nkrbc. 3
## B c t r a z j ` g k l n u s a k l
8
## W` bu `s tr cl f c s g f c s a n a g c g a k l ` s g k r r ` g t c s
7
## ` l f c j a c d k l c f
:
0
t c h f ` ( p r ` j a g g a k l $ g f c s s , t rc a l[ s ` t $ W p ` g a ` s ) 7
Plc `xpfagcga÷l bãs gkbpf`tc j` `stc m`rrcba`ltc j` bcgmal` f`crlald pu`j` `lgkltrcrs` `l Mcsta` (8??1), y Burpmy (8?38). @l `st` cpcrtcjk altrkjugtkrak fcs gu`stakl`s j` j`s`bp`ók pkr `sp`gaffigajcj y s`lsahafajcj lk skl `xpfagcjcs c j`tcff`.
>8
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.379 Bctraz j` gklnusa÷l pcrc `f s`t j` `ltr`lcba`ltk. J` cgu`rjk gkl fc bctraz j` gklnusa÷l, s` khs`rvcl 8 gcsks `rr÷l`ks (nu`rc j` fc jacdklcf). _crc `st` gcsk s` bu`strc qu` `f bkj`fk fkdrc gfcsaffigcr 1= % j` fks gcsks gkrr`gtcb`lt` y `f 8 % `rr÷l`k gkrr`spklj` c fcs gfcs`s v`rsagkfkr y vardalagc. W` pu`j` khs`rvcr qu` `f cfdkratbk ta`l` ul j`s`bp`ók cftk pcrc `st` gcsk, pu`j` aj`ltaffigcr fcs 7 gfcs`s pcrc 1= % j` fks gcsks. Culqu` fc r`dfc j` j`gasa÷l fal`cf `s ul pkgk gkbpfagcjc pcrc fks gcsks v`rsagkfkr(rkik) y vardalagc (v`rj`) j` cgu`rjk c fc jasgusa÷l j` fcs drãffigcs ] `f cfdkratbk r`su`fv` fc j`gasa÷l y gfcsaffigc cj`gucjcb`lt`. Culqu` `f r`suftcjk j` fc bctraz j` gklnusa÷l `s pr`gask pcrc gfcsaffigcr fc alnkrbcga÷l, `f bkj`fk j`h` pkl`rs` c pru`hc `l ul `sg`lcrak bãs r`cfastc. Wupkldcbks qu` gklkg`bks `stcs 3?0 bu`strcs y sch`bks gfcsaffigcrfcs `l sus jan`r`lt`s 7 gfcs`s, ulc pr`dultc alt`r`sclt` s`râc »@s gcpcz qu` `f bkj`fk j` bcgmal` f`crlald s` ciust` c lu`vcs b`jagakl`s j` aras;, »Suá sug`j`râc sa s` skhr``stabc `st` gkliultk j` 3?0 bu`strcs;, »@l r`cfajcj `f bu`str`k r`suftc sadlaffigctavk pcrc tkjks fks gcsks j` aras qu` s` ta`l`l jaspklahf`s;. Zkjcs `stcs alt`rrkdclt`s s` r`su`fv`l cf utafazcr `f gkliultk j` pru`hcs pcrc vcfajcr `f bkj`fk
>7
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
:.?.:. J`s`bp`ók j` fc ncs` j` pru`hcs @f khi`tavk j` fc ncs` j` pru`hcs `s gklkg`r `f j`s`bp`ók j` ul bkj`fk u cfdkratbk, `s ulc s`gga÷l j`f gkliultk j` jctks kradalcf qu` s` utafazc pcrc vcfajcr `f bkj`fk. @f bátkjk hãsagk gklsast` `l utafazcr ulc pkrga÷l j` fc alnkrbcga÷l pcrc sabufcr ul `sg`lcrak r`cf jklj` ff`dc alnkrbcga÷l lu`vc qu` cùl lk s` khs`rvc, s` gfcsaffigc fc alnkrbcga÷l `l nulga÷l j` pr`jaggakl`s y s` baj` `f j`s`bp`ók j`f bkj`fk. _crc `f gcsk j` fks jctks j` Nasm`r (317>) s` s`f`ggaklc `f 7? % j` fc bu`strc pcrc `f gkliultk j` pru`hcs. W`dùl fk `sp`gaffigcjk `l fc ffidurc ] `f gkliultk j` pru`hcs pcrc `st` gcsk gkrr`spklj` c :0 bu`strcs. Fc cf`ctkra`jcj j`f prkg`sk j` s`f`gga÷l p`rbat` kht`l`r khs`rvcgakl`s j` fcs 7 gfcs`s aras s`tksc, aras s`tksc, aras v`rsagkfkr ` aras vardalagc (1, 88 y 3: gcsks r`sp`gtavcb`lt`). 3
## D r c n a g c j ` h c r r c s p kr lub`rk j ` k h s ` r v c g a k l ` s
8
7
h c r p f k t ( subbcry ( t r c a l[ s ` t $ W p ` g a ` s ) , bc al 2 " G k li ul t k j ` p r u ` h cs " )
:
h c r p f k t ( subbcry ( t ` s t[ s ` t $ W p ` g a ` s ) , bc al 2 " G k l i ul t k j ` `ltr`lcba` ltk " )
>:
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.3:9 Lùb`rk j` khs`rvcgakl`s pkr gfcs` j` aras. J`f fcjk azqua`rjk s` bu`strc `f lùb`rk j` khs`rvcgakl`s pcrc `f gkliultk j` pru`hcs y j`f fcjk j`r`gmk `f lùb`rk j` khs`rvcgakl`s `f gkliultk j` `ltr`lcba`ltk. W` prkg`j` c `i`gutcr fc vcfajcga÷l j`f bkj`fk, fc cprkxabcga÷l qu` s` bu`strc gklsast` `l tkbcr `f bkj`fk qu` s` `i`gut÷ pcrc fc ncs` j` `ltr`lcba`ltk (3?0 jctks) y `n`gtucr gfcsaffigcgakl`s gkl fc alnkrbcga÷l lu`vc j`f gkliultk j` pru`hcs(:0 jctks). @st` bátkjk p`rbat` gklkg`r sa `f prab`r bkj`fk pcrc fc ncs` j` `ltr`lcba`ltk `s suffiga`lt` k r`qua`r` ciust`s. _crc `f gcsk j` aras ul bkj`fk `xatksk `s cqu`f gcpcz j` gfcsaffigcr fcs tr`s gfcs`s j` kr`s gkl ul j`s`bp`ók sabafcr k b`ikr c fc ncs` j` `ltr`lcba`ltk. J` cgu`rjk gkl fc bctraz j` gklnusa÷l s` pu`j`l aj`ltaffigcr pksahf`s ncffks `l fks qu` `f bkj`fk lk `stã sa`ljk fk suffiga`lt`b`lt` s`lsahf` cf r`gklkg`r ulc gfcs`. Fc nkrbc j` b`jar `f j`s`bp`ók j` `st` bkj`fk s` baj` j` cgu`rjk >0
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF cf lùb`rk j` gfcsaffigcgakl`s `rr÷l`cs r`sp`gtk cf tktcf j` fc bu`strc5 pcrc `f gcsk j` fc ncs` j` `ltr`lcba`ltk ul 8 % j` `rrkr. C gkltalucga÷l s` bu`strc `f r`suftcjk j` fc gfcsaffigcga÷l j`f bkj`fk gkl fc alnkrbcga÷l `l fc ncs` j` pru`hcs t`st[s`t. W`dùl fc bctraz j` gklnusa÷l, ùlagcb`lt` ul vcfkr `s gfcsaffigcjk `rr÷l`cb`lt` y g`rgc j`f 1= % j` fks gcsks `s aj`ltaffigcjk s`dùl fc gfcs` c fc qu` r`cfb`lt` p`rt`l`g`. @f bkj`fk bu`strc ul j`s`bp`ók cj`gucjk y sabafcr cf s`t j` `ltr`lcba`ltk pkr fk gucf s` tkbcrã gkbk ul bkj`fk cptk pcrc fc gfcsaffigcga÷l cutkbctazcjc. 3
## ^cfa jcga kl j`f bkj`fk FJC
8
## W` ` i `g u t cl f c s p r ` j a g g a k l `s s k hr `
7
## ` f s ` t j` p ru `h cs gkl ` f bkj`fk k r a d a l c f
:
p r ` j a g g a k l 6∘ p r ` j a g t ( b k j` fk , l `w jc tc 2 t ` s t [ s ` t )
0
>
## B c t r a z j ` g k l n u s a k l
4
## W` bu `s tr cl f c s g f c s a n a g c g a k l ` s g k r r ` g t c s
=
## `l f c j a cd k lc f p cr c ` f s ` t j` p ru `h cs
1
t c h f ` ( p r ` j a g g a k l $ g f c s s , t `s t[ s ` t $ W p ` g a ` s )
Nadurc :.309 Bctraz j` gklnusa÷l pcrc `f s`t j` pru`hcs. Plc v`z gkrrkhkrcjc fc `ffiga`lgac j`f cfdkratbk j` FJC pcrc fc ncs` j` pru`hcs s` pu`j` gklsaj`rcr fastk pcrc gfcsaffigcr bãs alnkrbcga÷l skhr` fcs tr`s `sp`ga`s j` aras. Zkbcljk `l gu`ltc qu` `f cfdkratbk j` cpr`ljazci` >>
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF cutkbãtagk `s ùtaf pcrc jastalduar fcs tr`s `sp`ga`s j` pfcltcs `l ul gcsk j` bcykr `sgcfc. _crc `st` s`lgaffk `i`bpfk s` clcfazcrkl 30? pfcltcs, j` fcs gucf`s 3?0 s` utafazcrkl pcrc `ltr`lcr `f cfdkratbk y :0 pcrc pkl`rfk c pru`hc. _rkhchf`b`lt` `l ul cbha`lt` bugmk bãs g`rgclk c fc r`cfajcj fks vkfùb`l`s j` alnkrbcga÷l s`cl ga`ltks k baf`s j` v`g`s bãs drclj`s, sal `bhcrdk fks basbks pralgapaks j` bu`str`k, `ltr`lcba`ltk y pru`hc s` bclta`l`l. C gkltalucga÷l s` bu`strc ul gcsk gkl ul vkfùb`l j` alnkrbcga÷l bãs cbpfak y gkl ul `lnkqu` j` clãfasas j` b`rgcjks.
:.?.0. Gfcsaffigcga÷l j` gfa`lt`s, gcsk j` r`tcaf bcre`tald _r`vacb`lt` s` r`vascl fks gklg`ptks hãsagks j`f cfdkratbk j` gfcsaffigcga÷l FJC. W` j`bu`strc ul gcsk prãgtagk gkl g`rgc j` 30? bu`strcs pcrc `f ncbksk gkliultk j` jctks j`f `stcjâstagk y ha÷fkdk Nasm`r (317>). W` `xpfagc ul gcsk jklj` s` gfcsaffigcl : `sp`ga`s jastaltcs j` kr`s y s` r`pfagc `f `xp`rab`ltk kradalcf qu` Nasm`r j`scrrkff÷ `l su bkb`ltk. Culqu` fks pralgapaks qu` s` ctrahuy`l pcrc `f `i`bpfk prãgtagk clt`rakr, fc gkbpf`iajcj j`f buljk cgtucf `xad` clãfasas gkl alnkrbcga÷l bãs `fchkrcjc y j` bkj`fazcga÷l ul pkgk bãs `sp`gâffigc. @l `stc s`gga÷l s` clcfazc ul gcsk j` alnkrbcga÷l j` trclscggakl`s alt`rlcgaklcf`s `l ul `squ`bc j` prkv``jurâc j` b`rgclgâcs c drcl `sgcfc. @st` s`gtkr j` `bpr`scs `s gklkgajk gkbk v`ltc j` r`tcaf y s` gcrcgt`razc pkr bcl`icr vkfùb`l`s c drclj`s `sgcfcs. Fks jctks p`rt`l`g`l c ulc `bpr`sc j` r`tcaf qu` kp`rc `l `f X`alk ulajk j` nkrbc Klfal` j` 8?33 cf 8?33. Fc >4
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF alnkrbcga÷l c clcfazcr gklsast` `l g`rgc j` 00,??? trclscggakl`s c lav`f dfkhcf pcrc 7= pcâs`s `l = jastaltcs vcrachf`s, bãs j` : baffkl`s j` jctks `l ul p`rakjk j` ul cók. Plk j` fks khi`tavks bãs `s`lgacf`s j`f bcre`tald `s s`db`ltcr fks b`rgcjks. Plc s`db`ltcga÷l gklsast` `l `lgkltrcr drupks j` gfa`lt`s cgtucf`s k pkt`lgacf`s qu` bu`str`l gcrcgt`râstagcs sabafcr`s pcrc `lnkgcr cfdulc gfcs` j` prkjugtk `sp`gâffigk s`dùl sus l`g`sajcj`s dustks y pr`n`r`lgacs, `ltr` ktrks gkbk uhagcga÷l d`kdrãffigc, gu`stakl`s gkljugtucf`s, `tlkdrãffigcs y gufturcf`s pkr `i`bpfk. Wa ha`l, `st` `i`rgagak lk pr`t`lj` `xpfagcr cbpfacb`lt` fcs jan`r`lt`s gcrcgt`râstagcs qu` `xast`l `l fc s`db`ltcga÷l j` b`rgcjks knr`g` ulc cpfagcga÷l r`cfastc j`f bátkjk j` s`db`ltcga÷l FJC `l nulga÷l j`f gkbpkrtcba`ltk trclscggaklcf `l gucltk c pr`gak y gcltajcj j` fc trclscggaklcfajcj j` fc `bpr`sc. @f khi`tavk j` `st` `i`bpfk `s r`skfv`r ul prkhf`bc gkbùl `l fc cgtucfajcj. Fc alnkrbcga÷l cfbcg`lcjc `l `quapks j` g÷bputk lk sa`bpr` skl ff`vcjks c gchk gkl fcs b`ikr`s prãgtagcs. Cfdulcs `bpr`scs ` alstatugakl`s j` tcbcók p`qu`ók y b`jaclk gklnâcl fc alnkrbcga÷l ducrjcjc `l `quapks fkgcf`s, `l hcs`s j` jctks `l mkics j` gãfgufk. @f bcl`ik alcj`gucjk j` fc alnkrbcga÷l gklff`vc ra`sdks qu` pu`j`l ff`dcr c s`r buy gkstksks. Pl gcsk `xtr`bk `s fc `bpr`sc L`wdd , ulc `bpr`sc j` r`tcaf qu` kp`rc `l Gcfankrlac @@.PP. qu` `l 8?30 sunra÷ ul ctcqu` j` mcge`rs prkn`saklcf`s qu` j`bcljchcl ul r`sgct` `l hatgkals, `f s`rvagak `stuvk alcgtavk pkr 0 mkrcs y cfdulcs trclscggakl`s r`suftcrkl `l párjajcs pcrc fc `bpr`sc. @l `st` `i`rgagak, s` sabufc fc párjajc j` alnkrbcga÷l j` trclscggakl`s c gfa`lt`s qu` prkva`l`l j` _kfklac y Icp÷l j`hajk c ul ctcqu` j` mcge`rs qu`
>=
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF qua`r`l j`struar fc `bpr`sc. Hcik `f supu`stk j` qu` lk s` ta`l`l fks r`gursks pcrc `f r`sgct` `l hatgkals, fks jar`gtavks j`gaj`l tkbcr `f ra`sdk y utafazcr cfdkratbks pcrc r`gup`rcr pcrt` j` fc alnkrbcga÷l p`rjajc. @f cpcrtcjk p`rbat` hraljcr ulc kpga÷l pcrc r`skfv`r fc kp`rcga÷l t`bpkrcf j` fc `bpr`sc `ltr`lcljk ul cfdkratbk j` alt`fad`lgac crtaffigacf gcpcz j` gfcsaffigcr fks p`jajks qu` prkva`l`l j` Icp÷l k _kfklac. @f `i`bpfk qu` s` j`scrrkffc `l `stc s`gga÷l gklsast` `l gklstruar `f cfdkratbk l`g`scrak pcrc gfcsaffigcr guãf`s trclscggakl`s k v`ltcs s` kradalcrkl `l gcjc ulk j` fks pcâs`s, csâ `vatcr gkstks all`g`scraks cf `lvacr drclj`s gcltajcj`s j` prkjugtks cf pcâs `quavkgcjk qu` pkjrâcl abpfagcr párjajcs baffklcracs pcrc fc `bpr`sc. @f cfdkratbk j` gfcsaffigcga÷l FJC p`rbat` gklkg`r `f pcâs j` krad`l j` fcs trclscggakl`s y `stchf`g`r ul pfcl j` `b`rd`lgac pcrc sctasncg`r fks p`jajks j` fks gfa`lt`s r`juga`ljk `f ra`sdk y pkr fk tcltk drclj`s gkstks j` mcg`r `lvâks algkrr`gtks. C gkltalucga÷l s` gcrdc fc alnkrbcga÷l `l `f cbha`lt` pcrc su pkst`rakr gfcsaffigcga÷l. J` cgu`rjk gkl `f g÷jadk sadua`lt` s` trclsnkrbc fc alnkrbcga÷l pcrc `vatcr algklsast`lgacs `l fks jctks. _rab`rk, s` `fabalcl lktcs j` grájatk: cf gcrdcr `f gkliultk j` jctks. W`duljk s` s`f`ggaklc ulc bu`strc pcrc jks pcâs`s _kfklac y Icp÷l pcrc sabpfaffigcr fc `xpfagcga÷l j`f bkj`fk. Z`rg`rk, s` drcffigc j` nkrbc `xpfkrctkrac cbhks pcâs`s. :
Plc lktc j` grájatk gklsast` `l ulc j`vkfuga÷l j`f prkjugtk pkst`rakr cf bkb`ltk j` fc gkbprc. D`l`rcfb`lt`, gucljk ulc `bpr`sc ktkrdc ul prkjugtk s` `n`gtùc ul pfczk pcrc qu` `f gfa`lt` v`raffiqu` qu` `stã `l fcs gkljagakl`s y gcltajcj`s cj`gucjcs. _kr bktavks gkltchf`s, fcs gcltajcj`s s` `sgrah`l l`dctavcs cf bkb`ltk j` mch`r ul p`jajk j`vu`ftk tktcf k pcrgacfb`lt`. @stc satucga÷l `s buy gkbùl `l fks l`dkgaks j` r`tcaf yc qu` `l vkfùb`l`s sadlaffigctavks fks gfa`lt`s skfagatcl grájatk `l ta`bpks j` jâcs j` pcdk (7?, 1? k 3=? jâcs pcrc pcdcr).
>1
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF 3
## Bc re `t al d r ` t c a f g f a ` l t s s ` db ` lt c ta k l
8
## N u ` l t` j ` a l n k r b c g a k l 9 m t t p s 9 // crg mav ` . ags . uga . `ju /bf / j c t c s ` t s / Klfal`+X`tcaf#
7
:
## A l s t c f c g g a k l j ` p c qu ` t` s
0
a l s t c f f . pcgecd`s ( " jpfyr " )
>
a l s t c f f . pcgecd`s ( "BCWW" )
4
a l s t c f f . pcgecd`s ( " gcr` t " )
=
1
f a h r c r y ( jpfy r )
3?
33
38
## W` g c r d c f c a l n k r b c g a k l j n 6∘ r`cj . g s v ( " K l f a l` X ` t c a f . g s v " , s t r a l d s C s N c g t k r s 2 N ) % <% n a f t ` r ( Sucltaty , Plat _rag` < ?) ## W` ` f a b a l c l j ` v k f u g a k l ` s
37
j ` p r k j u g tk ( l k t c s j ` g kb pr c ) 3:
30
3>
34
## W` ` f a d ` l j ks p c a s ` s bu`strc 6∘ j n % < % n a f t ` r ( Gk ul tr y 22 " _ k f c l j " | Gkultry 22 "Icpcl " )
3=
bu`strc $ Gkultry 6∘ cs . n c g t k r ( bu`strc $ Gkultry)
31
8?
83
88
87
## D r c n a g c ` x p f k r c t k r a c p f k t ( bu`strc $ Sucltaty ,
bu`strc $ Plat_rag` , g k f 2 c s . n c g t k r ( bu`strc $ Gkultry))
4?
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.3>9 Gcltajcj j` prkjugtk v`ljajk gkltrc `f pr`gak j`f prkjugtk. W` bu`strcl fcs gkbprcs prkv`la`lt`s j` _kfklac `l gkfkr rkik y Icp÷l `l gkfkr l`drk. J` cgu`rjk gkl fc ffidurc clt`rakr s` khs`rvc ulc gklg`ltrcga÷l j` fc alnkrbcga÷l g`rgclk cf krad`l pcrc cbhks `i`s. Fc alnkrbcga÷l guyc jastrahuga÷l lk `s ulankrb` `s ul gcsk tâpagk j` alnkrbcga÷l r`cf. @st` tapk j` jaffiguftcj`s r`suftc buy gkbùl `l `f clãfasas jacrak y `s l`g`scrak ff`vcr c gchk ul pr` prkg`scba`ltk j` fc alnkrbcga÷l pcrc gr`cr `f cfdkratbk j` FJC.
:.?.>. _r`prkg`scba`ltk j` jctks9 `sgcfcba`ltk y lkrbcfazcga÷l. @f `sgcfcba`ltk j` fc alnkrbcga÷l ta`l` gkbk ffil gklv`rtar fks v`gtkr`s j` alnkrbcga÷l qu` gkbpkl`l lu`strk gkliultk j` alnkrbcga÷l `l ulc nkrbc
43
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF bãs susg`ptahf` j` s`r clcfazcjc. _crc `st` gcsk `sp`gâffigk, s` khs`rvc ulc gklg`ltrcga÷l pkgk ncvkrchf` pcrc `f clãfasas `l fc ffidurc ]. J`ltrk j` fks bátkjks j` `sgcfcba`ltk y lkrbcfazcga÷l s` `lgu`ltrcl fcs trclsnkrbcgakl`s fkdcrâtbagcs, fks `sgcfcba`ltks `l nulga÷l j` bãxabks y bâlabks, `stcljcrazcga÷l `l nulga÷l j` fc j`svacga÷l `stãljcr, `ltr` ktrks. _crc fc bcykrâc j` fks gcsks `l fks qu` s` cpfagc ul cfdkratbk j` alt`fad`lgac crtaffigacf `st` prkg`sk `s nuljcb`ltcf y `l ulc drcl gcltajcj j` gcsks `stragtcb`lt` l`g`scrak pcrc kht`l`r ul bkj`fk j` gfcsaffigcga÷l cg`ptchf`. Wal `bhcrdk pu`j` mch`r satucgakl`s `l fc qu` lk `s l`g`scrak, `l fc s`gga÷l clt`rakr cf gfcsaffigcr `f prkhf`bc j` Nasm`r 317> lk r`suftchc l`g`scrak `f prkg`sk j` `sgcfcba`ltk pkr `i`bpfk. J` cgu`rjk ulc nulga÷l fkdcrâtbagc.
y 2 fkd (x)
Jklj` x `s ul vcfkr qu` s` `lgu`ltrc `l `f jkbalak j` fks r`cf`s pksatavks.
x”X 9 x < ?
W` gubpf`l fks sadua`lt`s fâbat`s. Fâbat` j` fc nulga÷l
Alt`rpr`tcga÷l
fab x
fkd (x) 2 ?
Zkjk vcfkr j` x qu` ta`ljc c 3 s`rã ? `l `f vcfkr y.
fab x
fkd (x) 2 ?
Zkjk vcfkr j` x qu` ta`ljc c alffilatk s`rã alffilatk `l vcfkr y.
fab x
fkd (x) 2 ?
Zkjk vcfkr j` x qu` ta`ljc c ? s`rã b`lks alffilatk `l `f vcfkr y.
↘3
↘3
↘3
@l fc nkrbc drãffigc, s` pu`j` r`gr`cr fc nulga÷l fkdcrâtbagc j` fc sadua`lt` nkrbc. 48
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
3
## D r c na g c j ` f c n u l g ak l f k d c r a t b a g c
8
## @ f j kb al ak v c j ` ? c 0
7
p f k t ( fk d , ? , 0 ,
:
bcal 2 " N u lg a kl 9 y 2 f k d ( x ) " ,
0
x f c h 2 " x " ,
>
y f c h 2 " y " )
4
=
1
## @ s p ` g a n a g c ` f p ul tk j kl j` x 2 3 c h f a l ` ( v 2 3 , m 2 ? , f t y 2 7 , g k f 2 " hfu ` " )
Cf sustatuar fks vcfkr`s x aducf`s c 3 s` `vatc gklstruar ul lu`vk v`gtkr y gkl vcfkr`s aducf`s c ? cf cpfagcr fc nulga÷l fkdcrâtbagc fk gucf pkjrâc gcuscr algklv`la`lt`s cf `n`gtucr `f cfdkratbk j` FJC ` algklsast`lgacs `l fc alt`rpr`tchafajcj j`f bkj`fk. @l `st` gcsk fc nulga÷l fkdcrâtbagc s` cpfagc c 47
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF fc gcltajcj j` prkjugtk skfagatcjk pkr `f gfa`lt` y s` `vatcl gcltajcj`s aducf`s c g`rk. @l `st` gcsk, s` utafazc fc trclsnkrbcga÷l fkdcrâtbagc pcrc kht`l`r ulc b`ikr jastrahuga÷l j` fc gcltajcj v`ljajc y fks pr`gaks j` fks prkjugtks. @f khi`tavk `s qu` fc alnkrbcga÷l s`c cgg`sahf` pcrc clãfasas y `ltr`lcba`ltk j`f cfdkratbk j` FJC. @f prkg`sk gklsast` `l cpfagcr fc nulga÷l fkdcrâtbagc hcs` 3? k fkdcratbk lcturcf cf v`gtkr j` pr`gaks y cf v`gtkr j` gcltajcj`s gkbk s` j`sgrah` c gkltalucga÷l. 3
8
## W ` r ` ` s g c f c f c a l n kr b c ga k l `l f k d c r a tb k s bu`strc $ Sucltaty U bu`strc $ Sucltaty 22 3R 6∘ 8
7
:
## G k ls t ru g ga k l j ` f k s v ` g t k r ` s j ` f k d c r a tb k s
0
bu`strc $ f k d [Sucltaty
6∘ f k d ( bu`strc $ Sucltaty)
>
bu`strc $ f k d [P l a t _ r a g `
6∘ f k d ( bu`strc $ P l a t _ r a g ` )
4
=
1
## G k f k r ` s p k r p c a s p f k t ( bu`strc $ f k d [Sucltaty , bu`strc $ f k d [P l a t _ r a g ` , g k f 2 bu`strc $ Gkultry)
4:
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.349 Fkdcratbks j` prkjugtk v`ljajk gkltrc `f pr`gak j`f prkjugtk. W` bu`strcl fcs gkbprcs prkv`la`lt`s j` _kfklac `l gkfkr rkik y Icp÷l `l gkfkr l`drk. Gkbk s` khs`rvc `l fc ffidurc ], fc alnkrbcga÷l hcik fc trclsnkrbcga÷l fkdcrâtbagc `s rczklchf`b`lt` bãs `lt`ljahf` qu` `f gcsk j` fc ffidurc ]3. J` cgu`rjk gkl fc drãffigc clt`rakr s` altuy` qu` Icp÷l `s ul gfa`lt` guyc j`bcljc j` prkjugtks `s bãs cftc qu` _kfklac cf `stcr bãs cf`icjk j`f krad`l `l tárbalks j` gcltajcj y j` pr`gak. Cf r`cfazcr fc trclsnkrbcga÷l fkdcrâtbagc `f cfdkratbk j` FJW s`rã bãs pr`gask cf `n`gtucr fc gfcsaffigcga÷l sup`rvascjc.
40
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
:.?.4. Ncs` j` `ltr`lcba`ltk @f s`t j` `ltr`lcba`ltk k trcalald s`t gklsast` `l ulc s`gga÷l j` fc alnkrbcga÷l qu` s`rã utafazcjc pcrc `ltr`lcr `f bkj`fk j` s`db`ltcga÷l. Gkbk s` b`lgaklc `l cfdkratbk clt`rakr ulc nkrbc sabpf` `s utafazcr ulc s`f`gga÷l cf`ctkrac j` ulc pkrga÷l j`t`rbalcjc j` fc alnkrbcga÷l, j` `stc nkrbc s` pu`j` utafazcr ulc pcrt` suffiga`lt` pcrc `ltr`lcr `f bkj`fk. 3
## Ncs` j` `ltr`lcba` ltk
8
## W ` f ` g g a k l j ` f 4? % j ` f c a l n kr b c ga k l
7
:
p k r g ` l t c i ` 6∘ 4? / 3? ?
0
>
lub[bu`strcs 6∘ p k r g ` l t c i `
∔
lrkw ( b u ` s t r c )
4
=
1
s ` t . s``j (:) t r c a l[al j 6∘ scbpf` ( s`q[f`l ( lrkw ( b u ` st rc ) ) , s a z ` 2 lub[b u ` s t r c s )
3?
33
## W ` f ` g g a kl c b k s f c s b u `s t r cs q u` p ` r t ` l ` g ` l
38
## c f s ` t j ` ` l t r `l c b a` l t k
37
t r c a l[ s ` t 6∘ bu`strc U tr ca l [al j , R
3:
30
## W ` f ` gg a k l c bk s ` f r ` s t k j ` b u `s t rc s
3>
## qu ` p ` r t` l ` g` l c f s ` t j` p r u` hc s
34
t ` s t[ s ` t 6∘ bu`strcU ∘ t r c a l[al j , R
Ktrc v`ltcic j` `st` bu`str`k sabpf` `s qu` p`rbat` `ltr`lcr `f bkj`fk j` FJC `l ulc pkrga÷l j` fc alnkrbcga÷l y vcfajcr `f bkj`fk `l `f r`stk j` fks jctks (usucfb`lt` j` b`lkr tcbcók). @l fc ffidurc ] s` `xpfagc g÷bk s` javaj` fc alnkrbcga÷l pcrc `f gcsk j` fcs `sp`ga`s aras. _crc `f gcsk j`f r`tcaf 4>
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF smkp, mcy ::0 jctks pcrc `f s`t j` `ltr`lcba`ltk (4? % j` fc alnkrbcga÷l) y 31> gcsks pcrc vcfajcr `f bkj`fk. C gkltalucga÷l s` `n`gtùc `f `ltr`lcba`ltk y fcs pr`jaggakl`s j`f bkj`fk j` FJC. @f g÷jadk `n`gtùc fcs pr`jaggakl`s pcrc `f s`t j` `ltr`lcba`ltk y j` nkrbc drãffigc s` v`raffigc qu` fc gfcsaffigcga÷l r`pr`s`lt` ulc gfcsaffigcga÷l cj`gucjc. @l fc ffidurc sadua`lt` s` bu`strc j`f fcjk azqua`rjk fks r`suftcjks j` gfcsaffigcga÷l j`f cfdkratbk prkpu`stk. _kr ktrk fcjk, j`f fcjk j`r`gmk s` khs`rvcl fcs gct`dkrâcs kradalcf`s c fcs qu` p`rt`l`g` gcjc ulk j` fks pultks. 3
## @ i ` g u g a k l j ` f c f d k r a t b k j ` FJC
8
7
f a h r c r y (BCWW)
:
f a h r c r y ( gcr` t )
0
pcr (bnrkw2g (3 ,8 ) ) ## W` ` s p ` g a n a g c qu` s ` q ua `r `l j ks d r c n a g c s ` l ul basbk r ` l d f k l
>
4
=
bkj`fk 6∘ fjc ( jctc 2 t r c a l[s`t , Gkultry ~ . )
1
p r ` j a g g a k l 6∘ p r ` j a g t ( b k j` fk , t y p ` 2 " Gfc ss " )
3?
p f k t ( p r ` j a g g a k l $x , g k f 2 p r ` j a g g a k l $ g f c s s , bcal 2 " _ r ` j a g g a k l " )
33
p f k t ( p r ` j a g g a k l $x , g k f 2 t r c a l[ s ` t $ Gkultry , bcal 2 " K r a d a l c f " )
44
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF
Nadurc :.3=9 Gfcsaffigcga÷l j` gfa`lt`s s`dùl bkj`fk gfcsaffigctkrak FJC. J`f fcjk azqua`rjk s` bu`strc fc gfcsaffigcga÷l `n`gtucjc pkr `f cfdkratbk y j`f fcjk j`r`gmk s` bu`strcl fks gcsks r`cf`s. @f bátkjk j` vcfajcga÷l drãffigk clt`rakr `s vãfajk pcrc `xpfkrcr fc alnkrbcga÷l, `lgkltrcr t`lj`lgacs u khs`rvcr `rrkr`s `vaj`lt`s. Wal `bhcrdk, culqu` ul bkj`fk gfcsaffigctkrak fuzgc cpcr`lt`b`lt` cj`gucjk `s l`g`scrak r`cfazcr ulc pru`hc j`f j`s`bp`ók j`f cfdkratbk gklkgajk gkbk vcfajcga÷l. Fc vcfajcga÷l s` r`cfazc `l fc s`gga÷l r`stclt` j` alnkrbcga÷l qu` s` s`f`ggakl÷ cf`ctkracb`lt` cf gr`cr `f s`t j` `ltr`lcba`ltk y `f s`t j` pru`hcs. @l `f s`t j` pru`hcs s` utafazc `f bkj`fk pr`vacb`lt` `ltr`lcjk pcrc alt`ltcr pr`j`gar fcs gct`dkrâcs c fcs qu` p`rt`l`g` gcjc ulk j` fks gfa`lt`s. @l `st` gcsk `f bkj`fk `ltr`lcjk trctcrã j` pr`j`gar sa `f p`jajk p`rt`l`g`
4=
GC_ÂZPFK :. CFDKXAZBKW J@ GFCWANAGCGA×L FAL@CF c Icp÷l k c _kfklac j` cgu`rjk c fcs vcrachf`s pr`vacb`lt` j`ffilajcs gkbk vkfub`l j` b`rgclgâcs y pr`gak. Culqu` ul bkj`fk r`suft` cg`ptchf` j`ltrk j`f s`t j` `ltr`lcba`ltk, fc vcfajcga÷l `bpâragc `s sa`bpr` j`s`chf`. _crc `ffk, s` utafazc `f s`t j` pru`hcs y s` baj` `f j`s`bp`ók j`f bkj`fk `l ulc nrcgga÷l j` fc alnkrbcga÷l qu` sabufc ul gcsk r`cf j` alnkrbcga÷l lu`vc. C gkltalucga÷l s` baj` `f j`s`bp`ók j`f cfdkratbk `l nulga÷l j` guãltks gcsks skl gkrr`gtcb`lt` gfcsaffigcjks. 3
## B c t r a z j ` g k l n u s a k l
8
7
p r ` j a g g a k l 6∘ p r ` j a g t ( b k j` fk , l `w jc tc 2 t ` s t [ s ` t )
:
0
b c t r a z[g k l n u s a k l 6∘ t c h f ` ( p r ` j a g g a k l $ g f c s s , t `s t[ s ` t $ Gkultry)
>
4
gkln usak lBctr ax ( bctraz [g k l n u s a k l )
41
GC_ÂZPFK GC_ÂZPFK :. CFDKXAZBKW CFDKXAZBKW J@ GFCWANAGCGA GFCWANAGCGA×L ×L FAL@CF
Nadurc Nadurc :.319 Bctraz :.319 Bctraz j` gklnusa÷l @f `stcjâstagk utafazcjk `s gklkgajk gkbk bctraz j` gklnusa÷l. Pl `i`bpfk y j`scrrkffk j` sus usks s` `lgu`ltrcl `l fc s`gga÷l clt`rakr pcrc `f gcsk j` gfcsaffigcga÷l j` `sp`ga`s hakf÷dagcs. @l r`sub`l, fc bctraz j` gklnusa÷l aljagc `f lùb`rk j` pr`jaggakl`s qu` nu`rkl cg`rtcjcs csâ gkbk `f lùb`rk j` cqu`ffcs qu` nu`rkl gfcsaffigcjcs `rr÷l`cb`lt`. _crc `st` gcsk s` utafazc `f vcfkr j` pr`gasa÷l pr`gasa÷l j`f bkj`fk, `f `stcjâstag `stcjâstagkk cggurcgy cggurcgy vc j` ? c 3?? % sa`ljk 3?? % gfcsaffigcga÷l gfcsaffigcga÷l sal `rrkr`s `rrkr`s y ? % gfcsaffigcga÷l gfcsaffigcga÷l tktcfb`lt` tktcfb`lt` `rrcjc. `rrcjc. @f `i`rgagak `i`rgagak j` gfcsaffigcga gfcsaffigcga÷l ÷l clt`rakr clt`rakr bu`strc ul 4> % j` fks gcsks gkrr`ggkrr`gtcb`lt` tcb`lt` gfcsaffigcjks. gfcsaffigcjks. ^cfkr` ^cfkr`ss j` s`lsahafajcj s`lsahafajcj j`f 4> % y `sp`gaffigajcj `sp`gaffigajcj j` fc basbc bcdlatuj. J` cgu`rjk gkl CPZKX@W FKGKW `f j`s`bp`ók j` ul cfdkratbk cfdkratbk j` gfcsaffigcga gfcsaffigcga÷l ÷l r`suftc r`suftc hu`lk gucljk `stks vcfkr`s cfkr`s skl g`rgclks cf =?
GC_ÂZPFK GC_ÂZPFK :. CFDKXAZBKW CFDKXAZBKW J@ GFCWANAGCGA GFCWANAGCGA×L ×L FAL@CF =?%. @l `st` `i`bpfk, s` fkdrc gfcsaffigcr cj`gucjcb`lt` g`rgc j` 8?? trclscggakl`s. J` cgu`rjk cf pfclt`cba`ltk alagacf j` `st` cpcrtcjk s` pkjrã knr`g`r ulc p`rsp`gtavc j` alt`fad`lgac crtaffigacf pcrc pkj`r aj`ltaffigcr cfdulcs j` fcs ÷rj`l`s j` gkbprc qu` prkv`ldcl j` fks pcâs`s clcfazcjks. @f cfdkratbk j` FJC p`rbat` r`jugar `f ra`sdk y pkr fk tcltk gkstks j` `lvacr gcrdcb`ltks j` b`rgclgâcs cf ktrk fcjk j`f buljk j` nkrbc algkrr`gtc. Fc gfcsaffigcga÷l qu` s` `n`gtùc gkl ulc s`gga÷l j` fc alnkrbcga÷l gkbk ncs` j` `ltr`lcba`ltk `s suffiga`lt` pcrc pkj`r j`scrrkffcr ul bkj`fk qu` ta`l` fc gcpcgajcj j` s`db`ltcr sa ul p`jajk s` kradal÷ `l Icp÷l k _kfklac.
=3
Gcpâtufk 0 Cfdkratbks pr`jagtavks @l `stc s`gga÷l s` j`scrrkffcl cfdulcs j` fcs pkpufcr`s táglagcs j` pr`jagga÷l `l `f gcbpk j` fc alt`fad`lgac crtaffigacf j` tapk cpr`ljazci` cutkbãtagk k bcgmal` f`crlald. @l `f cpcrtcjk clt`rakr s` j`scrrkffcl cfdkratbks j` gfcsaffigcga÷l fal`cf gkl fc ffilcfajcj j` gct`dkrazcr alnkrbcga÷l jcjcs ga`rtcs gcrcgt`râstagcs (pralgapcfb`lt`, p`rk lk `xgfusavcb`lt`) gucltatctavcs. @l fc prab`rc s`gga÷l s` j`scrrkffcl fks pralgapaks hãsagks pcrc aj`ltaffigcr fks tr`s gcsks `l fks qu` s` utafazcl fcs táglagcs j` alt`fad`lgac crtaffigacf qu` gkbpkl`l `st` cpcrtcjk. J` cgu`rjk gkl `f gcpâtufk ulk s` pu`j`l aj`ltaffigcr tr`s gfcs`s `s`lgacf`s j` cfdkratbks j` bcgmal` f`crlald, s`db`ltcga÷l, aj`ltaffigcga÷l y pr`jagga÷l. Fks cfdkratbks j` pr`jagga÷l r`suftcl s`r `sp`gacfb`lt` ctrcgtavks j`hajk c qu` pu`j`l s`r utafazcjks `l ul sal ffil j` satucgakl`s. @ltr` cfdulcs j` `stcs utafajcj`s s` `lgu`ltrc gklkg`r fks pr`gaks j` ga`rtcs `baskrcs j` hkfsc gkl ul hcik drcjk j` alg`rtajubhr`, gklkg`r fks lav`f`s `sp`rcjks j` cuja`lgac `l ulc pfctcnkrbc j` Bcre`tald jadatcf, bkj`fcr `xp`gtctavcs y j`ffilar rcldk j` =8
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW ‖lkrbcfajcj‒ pcrc j`t`gtcr clkbcfâcs `l ul sast`bc. Cfdulks ktrks usks j` fks bátkjks j` pr`jagga÷l9 gklkg`r `f gkbpkrtcba`ltk j` gfa`lt`s pkt`lgacf`s `l ul `squ`bc j` alt`rcggakl`s `l fâl`c k algfusav` j`jugar gkbpkrtcba`ltk j` ulc bu`strc pkhfcgaklcf pcrc tkbcr j`gasakl`s y `n`gtucr ga`rtc b`jajc. Plc drcl pcrt` j` fks `sgratks gklsaj`rcl fcs táglagcs j` pr`jagga÷l ul t`bc alt`rb`jak j`ltrk j` fcs rcbcs j` ga`lgacs gkbputcgaklcf`s y fc ga`lgac `gkl÷bagc. Wa ha`l, j`scrrkffcr ul sast`bc qu` r`cfag` fcs nulgakl`s j` pr`jagga÷l jcjk ul cfdkratbk j` bcgmal` f`crlald lk `s ulc tcr`c s`lgaffc 3 c jan`r`lgac j` ktrks t`xtks `sp`gacfazcjks, `f khi`tavk j` `st` fahrk lk `s prknuljazcr `l fks pralgapaks `stcjâstagk-bct`bãtagks y gkbputcgaklcf`s qu` nuljcb`ltcl `stc gfcs` j` alt`fad`lgac crtaffigacf. Cnkrtulcjcb`lt`, pcrc ul lav`f altrkjugtkrak gklkg`r c j`tcff` fks bátkjks gklff`vc ulc drcl j`jagcga÷l cf s`r t`bcs ci`lks c gucfqua`r ga`lgac skgacf. Wal `bhcrdk, cpr`lj`r c utafazcr fcs m`rrcba`ltcs y r`nkrzcr fc t`krâc bãs cj`fclt` p`rbat` gkb`lzcr c j`scrrkffcr mchafajcj`s `l `f t`bc. @st` sast`bc j` `xpksaga÷l, pkpufcr `ltr` fks bclucf`s táglagks y ktrks t`xtks, cyujcl c hraljcr ul gklt`xtk prãgtagk. _kr ktrk fcjk, `st` t`xtk y fc suhs`gu`lt` s`gga÷l pr`t`lj` bkstrcr `f usk j` fcs m`rrcba`ltcs yc j`scrrkffcjcs gkl ul `lnkqu` nulgaklcf pcrc `f usk gktajaclk `l fcs ga`lgacs skgacf`s. 3
crc tkjk cqu`f `ltusacstc j` fks r`tks alt`f`gtucf`s, `f jar`gtkr j`f fchkrctkrak j` alt`fad`lgac crtaffigacf j` Wtclnkrj Cljr`w Ld knr`g` fc gfcs` j` bc`strâc j` j` Bcgmal` F`crlald, `f gursk s` `lgu`ltrc jaspklahf` j` nkrbc drctuatc `l fc pfctcnkrbc j` Gkurs`rc. X`suftc ul hu`l pultk j` pcrtajc pcrc gklkg`r fcs jaffiguftcj`s qu` gklff`vc gklstruar fks cfdkratbks j` alt`fad`lgac crtaffigacf y cpr`lj`r bãs cffã j`f usk prãgtagk qu` s` knr`g` `l `st` t`xtk.
=7
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
0.3. Gklt`xtk mast÷ragk J`scrrkffcr cf bãxabk `f gcbpk j` fc pr`jagga÷l mc sajk ulc j` fks bãxabks khi`tavks j`f s`r mubclk j`sj` ta`bpks clg`strcf`s. Fks prab`rks s`r`s mubclks qu` pkhfcrkl fc ta`rrc gr`crkl altralgcjks sast`bcs cstrcf`s gkl `f ffil j` pr`j`gar fcs b`ikr`s ta`bpks j` sa`bhrc, gks`gmc y r`gkf`gtc jurclt` fks pralgapaks j` fc jalãbagc s`j`ltcrac. @l ápkgcs t`bprclcs j`f j`scrrkffk táglagk, s` gr`crkl fks prab`rks sast`bcs j` b`jaga÷l-j`t`rbalcga÷l j`f ta`bpk8 gkl `f ffil j` kht`l`r alnkrbcga÷l gkl clt`fcga÷l skhr` `v`ltks pkr sug`j`r. @f trclsgursk j`f ta`bpk p`rbata÷ `f j`scrrkffk j` fcs nu`rzcs prkjugtavcs y gkl `f gr`gaba`ltk j` fc raqu`zc c lav`f buljacf fks b`rgcjks j` trclscgga÷l y prkjugga÷l j` b`rgclgâcs kr`ga`rkl, `f mkbhr` j`s`chc gklkg`r j` clt`bclk fks pr`gaks j` fks prkjugtks pcrc kht`l`r ul h`l`ffigak cf r`cfazcr ul gagfk j` prkjugga÷l ` alt`rgcbhak. X`suftc `vaj`lt` qu` cqu`ffks pks``jkr`s j` alnkrbcga÷l pr`gasc skhr` fks pr`gaks t`lâcl ulc gkb`rgacf v`ltcic sadlaffigctavc `l `f gkb`rgak skhr` cqu`ffks qu` nkrbufchcl pr`jaggakl`s algkrr`gtcs. Mky `l jâc fks usks j` ul sast`bc (k bkj`fk) pr`jagtavk `s vcfaksk pcrc prãgtagcb`lt` tkjcs fcs aljustracs, sal `bhcrdk fc skffistagcga÷l j` fc táglagc `stcjâstagk-bct`bãtagc y gkbputcgaklcf pkl` `f crt` j` pr`j`gar `l gklt`xtk rcjagcfb`lt` jastaltk. Hcik `f gklt`xtk `gkl÷bagk cgtucf fc alnkrbcga÷l iu`dc ul pcp`f grugacf bãs cg`f`rcjk qu` `l ápkgcs clt`rakr`s. Z`l`r fc gcpcgajcj j` pr`j`gar `f gkbpkrtcba`ltk j` ga`rtk n`l÷b`lk algurr` `l dclclgacs k `l t`rrahf`s pár8
_kr `i`bpfk, `f r`fki cstrkl÷bagk j` _rcdc nu` gklstruâjk c pralgapaks j`f sadfk ]^ gkl `f ffil j` pr`j`gar `qualkggaks, jâcs n`stavks, ápkgcs aj`cf`s j` sa`bhrc y gks`gmc.
=:
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW jajcs `l gcsk j` bcl`icrs` j` nkrbc algkrr`gtc. _crc `f gcsk j` fcs ga`lgacs bájagcs, aj`ltaffigcr ga`rtk tapk j` pctkfkdâc gkl ul bkj`fk j` pr`jagga÷l `rr÷l`k pu`j` sadlaffigcr skb`t`r c ul pcga`lt` c ul trctcba`ltk qu` lk l`g`satc k `l gcbhak, lk j`t`gtcr fc pctkfkdâc y lk knr`g`r laldùl tapk j` trctcba`ltk c ul pcga`lt` `ln`rbk. Fc l`g`sajcj j` hu`lcs pr`jaggakl`s lcg`l j` jastaltcs p`rsp`gtavcs, sal `bhcrdk fcs abpfagcgakl`s j` `n`gtucr ul prkl÷stagk `quavkgcjk skl r`f`vclt`s pcrc fc bcykrâc j` fks gcsks. @l `stc s`gga÷l, s` r`vascl jastaltks bkj`fks pr`jagtavks sabpf`s qu` sadu`l fks pralgapaks j` alt`fad`lgac crtaffigacf pr`vacb`lt` j`sgratks. @l d`l`rcf, gucfqua`r tapk j` cfdkratbk pr`jagtavk j` alt`fad`lgac crtaffigacf cgtucf s` gklsaj`rc ul t`bc cvclzcjk j` bkj`fazcga÷l. Psucfb`lt` saqua`rc `l gursks j` pksdrcjk j` Ga`lgacs Wkgacf`s skl gklt`bpfcjks gkbk pcrt` `s`lgacf y ul cj`gucjk gklkgaba`ltk skhr` fks nuljcb`ltks j`f basbk lk sa`bpr` `s cjquarajk. Wa ha`l, fcs m`rrcba`ltcs t`glkf÷dagcs qu` lks p`rbat`l `i`gutcr bkj`fks cvclzcjks, gklkg`r fks pralgapaks `s sa`bpr` r`gkb`ljcjk. @st` t`xtk pr`t`lj` knr`g`r ulc vasa÷l hãsagc ` altrkjugtkrac c pr`jagga÷l pkr b`jak j` cfdkratbks j` alt`fad`lgac crtaffigacf, ulc p`rsp`gtavc bãs cbpfac pu`j` `lgkltrcrs` `l t`xtks `sp`gacfazcjks ` algfusav` tâtufks `sp`gâffigks j`f cfdkratbk qu` s` j`s`c `bpf`cr. @l `stc s`gga÷l s` utafazcrãl jks v`rsakl`s j` cfdkratbk pr`jagtavk r`j`s l`urklcf`s crtaffigacf`s y ul bkj`fk `gklkbátragk trcjagaklcf j` v`gtkr`s j` cutkrr`dr`savks gkl ÷rj`l`s j` alt`drcga÷l (CXABC). Fks bátkjks pr`vacb`lt` b`lgaklcjks r`suftcl s`r m`rrcba`ltcs ùtaf`s pcrc pr`j`gar. @sp`gacfb`lt`, fcs r`j`s l`urklcf`s crtaffigacf`s skl gklkgajcs pkr bkstrcr ul hu`l j`s`bp`ók j` pr`jagga÷l pcrc gcsks jklj` fc alnkrbc-
=0
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW ga÷l s` pr`s`ltc j` nkrbc gkltaluc (s`ra`s j` ta`bpk k alnkrbcga÷l `strugturcjc). Jkbalcr cbhcs p`rsp`gtavcs, gklkg`r bkj`fks `gklkbátragks trcjagaklcf`s gkbk CXABC y cf basbk ta`bpk gklkg`r skhr` r`j`s l`urklcf`s crtaffigacf`s, p`rbat` gklkg`r ul `sp`gtrk hãsagk p`rk suffiga`lt` pcrc gkb`lzcr c `n`gtucr cfdulcs cpfagcgakl`s sabpf`s j` alt`fad`lgac crtaffigacf.
0.8. X`j`s l`urklcf`s crtaffigacf`s Fcs r`j`s l`urklcf`s crtaffigacf`s lcg`l j` fc chstrcgga÷l skhr` fcs l`urklcs qu` `xast`l `l fks sast`bcs hakf÷dagks jcjc su nulgaklcfajcj j` cpr`ljazci`. _crc `f gcsk j` r`j`s l`urklcf`s crtaffigacf`s, s` cs`b`icl c sabufcr `f nulgaklcba`ltk j` ul gkliultk j` l`urklcs hakf÷dagcs. Cfdulcs cpfagcgakl`s j` `stc táglagc j` bkj`fazcga÷l pu`j`l khs`rvcrs` `l sast`bcs ffilclga`rks, j`t`gga÷l j` clkbcfâcs `l s`durajcj j` sast`bcs ` algfusk v`mâgufks j` gkljugga÷l csastajc k gkljugga÷l cut÷lkbc (Jcsduptc `t cf, 8?335 Wm`l `t cf 8??=5 Z`xtkr, 8?38). Fcs v`ltcics pralgapcf`s j` `stc táglagc r`saj`l `l `n`gtucr r`fcgakl`s gkbpf`ics, yc s`cl fal`cf`s k lk fal`cf`s hcik fc `stabcga÷l j` pcrãb`trks j` cpr`ljazci` (Mcsta`, 8??1). @stk qua`r` j`gar, `f bkj`fk husgc r`fcgakl`s `l fc alnkrbcga÷l y trctc j` cpr`lj`r j` fks `rrkr`s j` nkrbc at`rctavc. Plc l`urklc hakf÷dagc, s` gkbpkl` j` jan`r`lt`s pcrt`s. @l fc ffidurc sadua`lt` s` bu`strcl fcs s`ggakl`s j` fc l`urklc. @f nulgaklcba`ltk rcjagc `l fc trclsbasa÷l j` alnkrbcga÷l j` fc j`ljratc cf lùgf`k. C su v`z, `stc alnkrbcga÷l vacic cf cx÷l. @f khi`tavk j`f lùgf`k `s prkg`scr `stc alnkrbcga÷l y s` trclsffi`r` c fc prkfkldcga÷l j`f skbc l`urklcf (_clacduc `t cf, 8??8).
=>
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
Nadurc 0.39 @squ`bc j` l`urklc hakf÷dagc. _crc `f gcsk j` ulc r`j l`urklcf crtaffigacf, `s ul gkliultk j` jav`rscs l`urklcs qu` sadu`l `st` pralgapak j` trclsbasa÷l j` alnkrbcga÷l. @l ul bkj`fk j` r`j`s l`urklcf`s crtaffigacf`s s` j`t`rbalcl jastaltcs gcpcs (gkl iultk j` l`urklcs) c fcs gucf`s s` f` trclsbat` fc alnkrbcga÷l. Drãffigcb`lt`, fc r`pr`s`ltcga÷l j` ulc r`j l`urklcf crtaffigacf s` `sp`gaffigc j` fc sadua`lt` bcl`rc.
=4
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
Nadurc 0.89 @strugturc j` X`j L`urklcf buftagcpc pcrc n vcrachf`s khi`tavk (Q). Nu`lt` Kfduâl (8?34). C gkltalucga÷l `l `st` cpcrtcjk s` utafazcrã ulc r`j l`urklcf crtaffigacf pcrc pr`j`gar `f pr`gak j` fcs cggakl`s j` ulc `baskrc gkl ul p`rakjk jacrak. W` gkbpcrcrã fc pr`gasa÷l j`f bkj`fk j` r`j`s l`urklcf`s r`sp`gtk c ul bátkjk trcjagaklcf j` nkr`gcstald pkpufcrb`lt` gklkgajk gkbk CXABC (Cutkr`dr`ssav` alt`drct`j bkvald cv`rcd`) j` nkrbc `stcjâstagc y drãffigc. @f j`s`bp`ók j` fks bkj`fks s` b`jarãl pkr `f lav`f j` `rrkr qu` gcjc ulk prkv``, b`lkr `rrkr j` pr`jagga÷l gkrr`spklj`rã cf bkj`fk bãs pr`gask.
==
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
0.8.3. _r`jagga÷l j` pr`gak j` cggakl`s gkl r`j`s l`urklcf`s crtaffigacf`s Csâ gkbk `l fcs s`ggakl`s clt`rakr`s j`f t`xtk, `f prab`r pcsk qu` s` j`scrrkffc `s fc kht`lga÷l j` fc alnkrbcga÷l c clcfazcr. _crc `ffk s` utafazc `f pcqu`t` qucltbkj (Xycl `t cf, 8?34) qu` lks p`rbat` `xtrc`r alnkrbcga÷l skhr` fcs gktazcgakl`s jacracs 7 j` fcs `baskrcs bãs pkpufcr`s. _crc `st` gcsk, s` khta`l`l fks pr`gaks j` ga`rr` y s` drcffigc fc ffidurc j` v`fcs k gcljf`stage gmcrt. 3
## J ` s g cr d c lj k f c a l n k r b c g a k l
8
f a h r c r y ( qucltbkj)
7
d`tWybhkfs( "DKKD" , srg2" dkkdf` " )
:
## Drc nag c qucltbkj
0
hcrGm crt (DKKD) 7
Cjagaklcfb`lt`, `st` pcqu`t` gklta`l` ul C_A pcrc kht`l`r alnkrbcga÷l j`f ncbksk r`pksatkrak j` jctks N`j`rcf X`s`rv` @gklkbag Jctc (NX@J).
=1
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
Nadurc 0.79 _r`gak jacrak j` fc Cfpmch`t Alg (Dkkdf`) 8?3:-8?3=. Plc v`z vasucfazcjc fc alnkrbcga÷l, s` pu`j` s`f`ggaklcr fc vcrachf` khi`tavk c `ltr`lcr `f bkj`fk j` r`j`s l`urklcf`s. Wadua`ljk fks pralgapaks j` fc ncs` j` pru`hcs `xpfagcjks `l `f gcpâtufk jks, `f s`t j` `ltr`lcba`ltk k trcalald s`t gklsast` `l ulc s`gga÷l j` fc alnkrbcga÷l (`l `st` gcsk ulc pkrga÷l j` fc s`ra` j` ta`bpk) qu` s`rã utafazcjc pcrc `ltr`lcr k ciustcr `f bkj`fk pr`jagtavk j` s`ra`s j` ta`bpk. _crc `f gcsk j` s`ra`s j` ta`bpk, `s abpkrtclt` `f`dar j` nkrbc krj`lcjc fc alnkrbcga÷l:, fc s`db`ltcga÷l krj`lcjc r`suftc s`r `f bátkjk bãs sabpf` pcrc `st` gcsk. @l `f g÷jadk qu` s` bu`strc c gkltalucga÷l s` khs`rvc `f prkg`sk j` trcls:
C jan`r`lgac j` fks cfdkratbks j` gfcsaffigcga÷l `i`bpfaffigcjks pr`vacb`lt` qu` s` gcrcgt`razcl pkr su ct`bpkrcfajcj, ul cfdkratbk k bkj`fk j` s`ra`s j` ta`bpk r`qua`r` ulc s`db`ltcga÷l krj`lcjc y lk ulc s`f`gga÷l cf`ctkrac j` fc alnkrbcga÷l.
1?
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW nkrbcga÷l j` fc alnkrbcga÷l l`g`scrac pcrc `ltr`lcr `f bkj`fk. _kst`rakrb`lt`, s` tkbcl khs`rvcgakl`s pcrc `ltr`lcr `f bkj`fk qu` gkrr`spklj`l c fc prab`rc s`gga÷l j` fc alnkrbcga÷l. Cj`bãs, s` `fad`l 33 khs`rvcgakl`s pcrc prkhcr `f j`s`bp`ók j`f bkj`fk. 3
j n U ( lrkw (DKKD)∘lub[t ` s t[jcys) 9 lrkw (DKKD) , R
8
j n . t ` s t . v c f u ` s 6∘ j n . t ` s t $DKKD. Gf ks ` U 3 9 lub[t ` s t[jcys R
7
j n . t ` s t $j## @ xt rc y` lj k f c a l n k r b c g a k l c ul j c tc n rc b`
:
j n 6∘ cs . jctc . nrcb` (DKKD)
0
>
## W` s ` f ` g g a k l c ` f lub`rk j` j a c s c p r ` j ` g ar
4
lub[t ` s t[jcys 6∘ 3?
=
1
3?
## W` j a v a j ` ` f s ` t j ` ` l tr ` lc b a` l tk ## W ` ` f a d ` l 3 13 k h s ` r v c g a k l `s p cr c ` l t r ` lc r ` f bk j` fk
33
j n . t r c a l 6∘ j n U ( lrkw (DKKD) ∘ 8??) 9 ( lrkw (DKKD)∘lub[t ` s t [j cy s ) , R
38
j n . t r c a l $ jcys 6∘ cs . Jct` ( rkw . lcb`s ( j n . t r c a l ) )
37
3:
## W` s ` f ` g g a k l c f c s ` g g a kl qu` g k rr ` sp k lj ` c f s ` t j` p ru `h cs
30
## W` ` f a d ` l 3 3 k h s ` r v c g a k l `s ( f c s bcs r ` g a ` l t ` s ) p cr c p rk hc r
3>
## ` f j`s`bp`lk j`f bkj`fk
34
j n . t ` s t 6∘cys 6∘ cs . Jct` ( rkw . lcb`s ( j n . t ` s t ) )
3=
31
8?
## W` d r c na g c l f k s p r ` g ak s j` g a ` r r ` p f k t ( j n . t r c a l $ jcys ,
83
j n . t r c a l $DKKD. Gfks` ,
88
t y p` 2 " f " ,
87
bcal 2 " _ r ` g ak j a c r a k j` f c ` b as k rc C fp mc h` t A l g ( D k kd f` ) " )
13
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
Nadurc 0.:9 _r`gak jacrak cf ga`rr` j` fc Cfpmch`t Alg (Dkkdf`) gkrr`spklja`lt` cf s`t j` `ltr`lcba`ltk. C gkltalucga÷l s` `i`gutc `f bkj`fk j` r`j`s l`urklcf`s crtaffigacf`s. @l pralgapak, s` j`ffil`l `f lùb`rk j` gcpcs kguftcs ` at`rcgakl`s gkbk jks gcpcs kguftcs y galgk baf at`rcgakl`s. W` s`f`ggaklc fc kpga÷l j` `sgcfcba`ltk cutkbãtagk (sgcf`.alputs) j`hajk c qu` gucfqua`r bkj`fk j` r`j`s l`urklcf`s r`qua`r` r`sgcfcba`ltk j` fc alnkrbcga÷l pcrc ciustcr cj`gucjcb`lt` `f bkj`fk.
0
@l gcsk j` s`f`ggaklcr fc kpga÷l sgcf`.alputs 2 NCFW@ `f j`s`bp`ók
j`f bkj`fk `s buy hcik pcrc `st` gcsk. 3
f a h r c r y ( n k r ` g c s t )
8
0
@l fc s`duljc s`gga÷l j`f t`xtk s` prknuljazc `l ul gcsk j` `sgcfcba`ltk bclucf gkl fkdcratbks. _crc `st` gcsk s` utafazc fc trclsnkrbcga÷l Hkx-Gkx (Fa, 8??0).
18
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW 7
## C i u s t ` j ` f b kj `f k
:
pcr (bnrkw2g (8 ,3 ) )
0
n a t . l l 6∘ ll`tcr ( j n . t r c a l $DKKD. G f ks ` , s a z ` 2 8 , r ` p ` c t s 2 0 ? ? ? , s g c f ` . al pu ts 2 ZXP@)
>
4
=
## C i u st ` j ` f b kj `f k j ` r ` j ` s l ` u r k l c f ` s n g c s t . l l 6∘ n k r ` g c s t ( n a t . l l , m 2 lub[t ` s t[j c y s )
1
3?
## D r c na g c j ` f c s p r ` j a g g a k l ` s
33
p f k t ( n g c s t . l l )
38
f a l ` s ( n a t t ` j ( n g c s t . l l ) ,
37
g k f 2 " r` j " ) ## s ` d r c n a g c ` f c i u s t ` j` ` lt r` lc ba `l tk `l rkik
3:
30
3>
## Zchfc r`sub`l j` j`s`bp`lk j`f bkj`fk cggurcgy . ll 6∘ cs . jctc . nrcb` ( cggurcg y ( ngc st . ll$b`cl , x 2 j n . t ` s t . v cf u` s ) )
34
3=
## C i u s t ` j ` f b kj `f k c r ab c
31
n a t . crabc 6∘cutk . crabc ( j n . t r c a l $DKKD. Gfks` )
8?
ng cs t . crabc 6∘ n k r ` g c s t ( n a t . c ra bc , m 2 lub[t ` s t[j c y s )
83
p f k t ( n g c s t . c ra bc )
88
f a l ` s ( n a t t ` j ( na t . crabc) , g k f 2 " dr` `l " )
87
8:
cggu rcgy . crabc 6∘ cs . jctc . nrcb` ( cggurcg y ( ng cs t . crabc $b`cl , x 2 j n . t ` s t . v c f u ` s ) )
80
8>
cggurcgy . t c h f `6∘ r h a l j ( c g g u r c g y . l l , c g g u r c g y . c r ab c )
84
rkw . lcb`s ( cggu rcg y . t c h f ` ) 6∘ g ( " X`j L ` u rk l c f " , "CXABC" )
8=
cggurcgy . t c h f `
17
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
Nadurc 0.09 Bkj`fk j` r`j`s l`urklcf`s crtaffigacf`s (crrahc) y bkj`fk CXABC (chcik) pcrc `f pr`gak jacrak cf ga`rr` j` fc Cfpmch`t Alg (Dkkdf`) gkrr`spklja`lt` cf s`t j` `ltr`lcba`ltk (l`drk). W` khs`rvc `f ciust` j`f bkj`fk `l rkik pcrc cbhks gcsks y `l czuf fks vcfkr`s j` fc pr`jagga÷l. _crc ff`vcr c gchk ulc gkbpcrcga÷l pr`gasc j`f j`s`bp`ók j` fks bkj`fks s` bu`strcl fcs tchfcs r`sub`l j` `rrkr j` gcjc bkj`fk r`sp`gtk c fc s`gga÷l j` fc alnkrbcga÷l j` pru`hcs. Plc alt`rpr`tcga÷l rãpajc bu`strc qu` `f BC_@ (@rrkr _krg`ltucf Chskfutk B`jak) `s sadlaffigctavcb`lt` bãs hcik `l `f bkj`fk j` r`j`s l`urklcf`s r`sp`gtk cf bkj`fk CXABC.
1:
GC_ÂZPFK 0. CFDKXAZBKW _X@JAGZA^KW
D`l`rcfb`lt`, ul bkj`fk guyk `rrkr bãs hcik `s ul b`ikr bkj`fk pcrc pr`j`gar. Cf b`jar `f j`s`bp`ók j`f bkj`fk r`sp`gtk c fc s`gga÷l j` alnkrbcga÷l j` pru`hcs p`rbat` sabufcr ul `sg`lcrak r`cfastc jklj` `f bkj`fk s` gklnrkltc gkl fc r`cfajcj. @l fc tchfc clt`rakr, s` bu`strcl `rrkr`s bãs hciks pcrc fc r`j l`urklcf `l tkjcs fcs bátragcs j` j`s`bp`ók pr`s`ltcjcs.
10
Gcpâtufk > Hahfakdrcnâc
1>
GC_ÂZPFK >. HAHFAKDXCNÂC 3. H`jacek-Cscr`, M., Hu `tt, W. clj Nf`bald, B. T. (8?3>) Cjvclg`s al Crtaffigacf Alt`ffad`lg`, 34tm Gkln`r`lg` kn tm` Wpclasm Csskgactakl nkr Crtaffigacf Alt`ffad`lg`, GC@_AC 8?3>. jka9 3?.3??4/14=-7-731-::>7>-7. 8. H`jacek-Cscr`, M., Hu `tt, W. clj Nf`bald, B. T. (8?3>) Cjvclg`s al Crtaffigacf Alt`ffad`lg`, Gclcjacl Gkln`r`lg` kl CA. jka9 3?.3??4/14=-7>:8-83?:7-7. 7. H`ffctr`gm`, F., Cb`ur, Q. C. clj _cpcjkpkufks, D. C. (8?3>) ”Bkj`fs clj jctc `ldal``rald‑, Nutur` D`l`rctakl Gkbput`r Wyst`bs. @fs`va`r H.^., 4?, pp. 3‗7. jka9 3?.3?3>/i.nutur`.8?3>.33.?31. :. Gm`l, W. (8?3>) ”J`gasakl @gklkbags, Al Gkbb`bkrctakl kn tm` Hartm G`lt`llacf kn M`rh`rt C. Wabkl 313>-8?3> (Lkh`f _raz` al @gklkbags 314=)‑, :40(Iclucry), pp. 3‗4. jka9 3?.3??4/14=-7-731-:?333-1. 0. Gachurrk, D. clj ^`lect`swcrcl, H. (8?34). L`urcf l`twkres watm X. >. Jcvas, I. H. (8?37) ”Zm` `b`rd`lg` kn cd`lt-hcs`j bkj`fald al `gklkbags9 Aljavajucfs gkb` tk hats‑, Nafkskffic j` fc @gklkbac, 3(8), pp. 881‗8:>. 4. J`sgcrt`s, X, & Sualtcs, D 8??8, Fks _ralgapaks J` Fc Nafksknâc, l.p.9 Hcrg`fklc =. Julas F., G., Bajjf`tkl T., _., Zm`kffifctks, E. clj Ecrctmclcskpkufks, C. (8?3>) Crtaffigacf alt`ffad`lg` al ffilclgacf bcre`ts. Guttald-@jd` Cppfagctakls nkr Xase Bclcd`b`lt, _krtnkfak Kptabazctakl clj @gklkbags. _cfdrcv` Bcgbaffcl. Cvcafchf` ct9 mttp9//crxav.krd/chs/3>3?.?4=>8. 14
GC_ÂZPFK >. HAHFAKDXCNÂC 1. Nasm`r, X. C. (317>) ”Zm` us` kn buftapf` b`csur`b`lts al tcxklkbag prkhf`bs‑, Cllcfs kn @ud`lags, 4(8), pp. 341‗3==. jka9 3?.3333/i.3:>13=?1.317>.th?8374.x.Tu, I. (8?38) Cjvclg`s al E-b`cls Gfust`rald. Cvcafchf` ct9 mttp9//fale.sprald`r.gkb/3?.3??4/14=-7->:8-81=?4-7. 3?. NfcsaŊsea, B. (8?3>) Altrkjugtakl tk Crtaffigacf Alt`ffad`lg`. jka9 3?.3??4/14=7-731-:??88-=. 33. Dcftkl, N. (3==>) ”X`dr`ssakl tkwcrj b`jakgraty al m`r`jatcry stctur`‑, Zm` Ikurlcf kn tm` Cltmrkpkfkdagcf Alstatut` kn Dr`ct Hratcal clj Ar`fclj, pp. 8:>‗>7. jka9 3?.87?4/8=:30=7. 38. Daf, J. clj Wkld, A.-Q. (8?3>) ”Bkj`fald clj Bclcd`b`lt kn Had Jctc9 Gmcff`ld`s clj kppkrtulata`s‑, Nutur` D`l`rctakl Gkbput`r Wyst`bs. @fs`va`r H.^., >7, pp. 1>‗11. jka9 3?.3?3>/i.nutur`.8?30.?4.?31. 37. Dkkjn`ffkw, A. I., Wmf`ls, I. clj Wz`d`jy, G. (8?3:) ”@xpfcalald clj Mcrl`ssald Cjv`rscracf @xcbpf`s‑, pp. 3‗33. Cvcafchf` ct9 mttp9//crxav.krd/chs/3:38.>048. 3:. M`rlcljk, X 8?38, ‑Duicrcta, Jcbkjcr y _krt`r. Hcsag @gklkb`trags‑, @lscyks J` @gklkbâc, X`_@g, @HWGKmkst, va`w`j 7? Iclucry 8?3=. 30. Msu, G.-M. (8?3:) ”Alt`ffad`lt had jctc prkg`ssald‑, Nutur` D`l`rctakl Gkbput`r Wyst`bs. @fs`va`r H.^., 7>, pp. 3>‗3=. jka9 3?.3?3>/i.nutur`.8?3:.?8.??7. 3>. Ek`le`r, X. (8??>) ”@gklkbags :43 F`gtur` 3 X`dr`ssakl tk B`jakgraty9 Dcftkl ‑ s Wtujy kn tm` Alm`ratclg` kn M`admt‑, pp. 3‗0. 34. Bcrwcfc, Z. (8?37). @gklkbag Bkj`fald Psald Crtaffigacf Alt`ffad`lg` B`tmkjs. Wprald`r Alt`rlctaklcf _uhfasmald. 1=
GC_ÂZPFK >. HAHFAKDXCNÂC 3=. Burpmy, E_ 8?38, Bcgmal` F`crlald 9 C _rkhchafastag _`rsp`gtav`, l.p.9 Gcbhrajd`, Bcsscgmus`tts 9 BAZ _r`ss, g8?38, FAHXPLCB, @HWGKmkst, va`w`j 30 N`hrucry 8?3=. 31. Fcltz, H 8?30, Bcgmal` F`crlald Tatm X 9 Jasgkv`r Mkw Zk Huafj Bcgmal` F`crlald Cfdkratmbs, _r`pcr` Jctc, Clj Jad J``p Altk Jctc _r`jagtakl Z`gmlaqu`s Tatm X, l.p.9 Harbaldmcb 9 _cget, 8?30, FAHXPLCB, @HWGKmkst, va`w`j 8 N`hrucry 8?3=. 8?. L`w`ff, C. clj Wabkl, M. (310>) ”Zm` Fkdag Zm`kry Bcgmal`9 C Gkbpf`x Alnkrbctakl _rkg`ssald Wyst`b‑, AX@ Zrclscgtakls kl Alnkrbctakl Zm`kry, pp. >3‗41. 83. K‑X`dcl, D. (8?3>) Altrkjugtakl tk tm` Mastkry kn Gkbputald. jka9 3?.3??4/14=-7-731-7737=->. 88. _cfa`s, K. clj Bcy`r, I. (31=1) ”@gklkbags r`csklald hy `gklkb`trags kr crtaffigacf alt`ffad`lg`‑, Zm`kry clj J`gasakl, 84, pp. 370‗3:>. 87. _cre`s, J. G. clj T`ffbcl, B. _. (8?30) ”@gklkbag r`csklald clj crtaffigacf alt`ffad`lg`‑, Wga`lg`, 7:1(>8:0), pp. 8>4‗848. jka9 3?.338>/sga`lg`.ccc=:?7.Fkwra`, A. (8?34) ”Cfdkratmbag rctaklcfaty9 @past`bkfkdy clj `ga`lgy al tm` jctc sga`lg`s‑, Had Jctc & Wkga`ty, :(3), p. 8?071034344??18. jka9 3?.3344/8?071034344??180. 8:. Wmu-M`ld Gm`l, _cuf _. Tcld Zzu-T`l, Euk (8??4) Gkbputctaklcf Alt`ffad`lg` al @gklkbags clj Nalclg` vkf.8.NfcsaŊsea, B. (8?3>) Altrkjugtakl tk Crtaffigacf Alt`ffad`lg`. jka9 3?.3??4/14=-7-731-:??88-=.
11