Investigacion Sobre Triangulos

August 21, 2022 | Author: Anonymous | Category: N/A

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OJV [BOJFM@LBV CB VBGBAJLQJ ] F@LE[RBLFMJ BL EB@GBS[ÇJ YOJLJ, RLJ Y[@YRBVSJ CMCÊFSMFJ YJ[J OJ BCRFJFMÖL KÊVMFJ.

CMJLJ YJS[MFMJ FJ[CBLJV FRBVSJ

RLMTB[VMCJC LJFM@LJO CB F@O@GKMJ DJFROSJC CB FMBLFMJV CBYJ[SJGBLS@ CB GJSBGÊSMFJV K@E@SÊ, C.F. ;9:6

OJV [BOJFM@LBV CB VBGBAJLQJ ] F@LE[RBLFMJ BL EB@GBS[ÇJ YOJLJ, RLJ Y[@YRBVSJ CMCÊFSMFJ YJ[J OJ BCRFJFMÖL KÊVMFJ CMJLJ YJS[MFMJ FJ[CBLJV FRBVSJ

Srjkja` Dmljo cb Gjbstrçj prbsbltjc` f`g` rbqumsmt` pjrfmjo pjrj `ptjr jo tçtuo` cb1 Gjemstbr bl blsbújlzj cb ojs fmblfmjs bxjftjs y ljturjobs

Cmrbft`r [`crme` Cuqub Kjrjfjoc`

Omlbj cb mlvbstmejfmöl1 Ybcjeèçj

Rlmvbrsmcjc Ljfm`ljo cb Fò`gkmj Djfuotjc cb Fmblfmjs Cbpjrtjgblt` cb Gjtbgêtmfjs Kè`tê C.F. ;9:6

Cbcmfjt`rmj

J Cm`s p`r hjfbr p`smkob o` mgp`smkob . . . J gm gjgê, p`r t`c` o` qub gb hj cjc` bl bstj vmcj, bspbfmjogbltb p`r sus sjkm`s f`lsba`s, p`r bstjr smbgprb j gm ojc` jp`yêlc`gb y fòjk`rêlc`gb bl o`s g`gblt`s gês cmdçfmobs . . . J Aujl Bstbkjl gm hma`, qumíl bs gm g`tmvjfmöl y joberçj fjcj cmj . . . J gm Sçj Fbfm, Cmbe` y gm Cjcm`s p`r su mlf`lcmfm`ljo jp`y`, y sjkm`s f`lsba`s. . . J Fbsjr... qumbl cçj j cçj bs gm jgme` y f`gpjúbr` cb kjtjooj.

m

Jerjcbfmgmblt`s

Bo jut`r bxprbsj sus jerjcbfmgmblt`s j t`c`s jquboo`s qub cb ulj u `trj d`rgj hjl fòjk`rjc`, f`ltrmkumc` ` jp`rtjc` bl bo cbsjrròo` cb bstb trjkja`> j oj pr`dbs`rj Gyrmjg Jfbvbc` qumbl joeulj vbz pr`pus` bo tbgj y jo pr`dbs`r [`crme` Cuqub Kjrjfjoc` p`r su f`lstjltb jp`y`, cbcmfjfmöl y rbvmsm`lbs `p`rtuljs.

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[bsugbl O`s Bstêlcjrbs Kêsmf`s cb F`gpbtblfmjs, F`gpbtblfmjs, ^:: ^::WW pojltbjl cbscb bo prmgbr erjc` cb kêsmfj prmgjrmj, tbgjs rbojfm`ljc`s f`l bo pblsjgmblt` bspjfmjo y o`s smstbgjs eb`gítrmf`s, pjrtmblc` cbo rbf`l`fmgmblt` y fojsm﬊fjfmöl cb ﬊eurjs kmcmgblsm`ljobs, hjstj oobejr j oj mltbrprbtjfmöl y jpomfjfmöl cb pr`pmbcjcbs y rbojfm`lbs eb`gítrmfjs. Bl t`c`s o`s erjc`s sb hjfb bldjsms bl bo bstucm` cb ojs rbojfm`lbs cb f`lerublfmj y sbgbajlzj bltrb ﬊eurjs qub bs bo tbgj fbltrjo cb bstb trjkja`. F`l kjsb j bst` sb pojltbj ulj pr`pubstj cmcêftmfj pjrj oj blsbújlzj cb oj eb`gbtrçj bl o`s lmvbobs cb bcufjfmöl kêsmfj, t`gjlc` f`g` cmrbftrçz o`s f`lfbpt`s cb f`lerublfmj y sbgbajlzj, qub f`lstj cb c`s pjrtbs, ul pojl cb jsmeljturj c`lcb sb `rejlmzjl o`s f`ltblmc`s tbgêtmf`s p`r fmfo`s pjrj oj blsbújlzj cb oj eb`gbtrçj y uljs euçjs cmcêftmfjs pjrj fjcj fmfo` c`lcb sb cbsjrròojl tbgjs pjrj oj blsbújlzj - jprblcmzjab cb oj eb`gbtrçj qub pubcbl sbrvmr f`g` gjtbrmjo gjtbrmjo cb jp`y` jp`y` pjrj bstj jsmeljturj jsmeljturj.. Oj pr`pubstj sb `rmemlj t`gjlc` f`g` rbdbrbl rbdbrbltb tb pbcjeöemf` oj tb`rçj cbo cbsjrròo` cb pblsjgmblt` eb`gítrmf` cb Y. Tjl Hmbob ^;4W, ^;4W, o`s Bstêlcjrbs Kêsmf`s cb F`gpbtblfmjs (;994) ^::W (;994) ^::W,, y o`s Omlbjgmblt`s furrmfuojrbs cb Gjtbgêtmfjs (:==:) ^:4W (:==:) ^:4W.. Vbrê jpomfjcj jpomfjcj bl bo fòbem` Vjl Jeustml MBC a`rljcj tjrcb y sb prbtblcb qub o`s bstucmjltbs oèrbl vmsujomzjr, f`gprblcbr y jpomfjr o`s f`ltblmc`s cb bstj jsmeljturj pjrj qub pubcjl f`gblzjr j trjkjajr gês bo pblsjgmblt` eb`gítrmf` bl bstj mlstmtufm`l bcufjtmvj. Jcbgês sb pr`p`lbl (vbr jlbx`) joeuljs euçjs cmcêftmfjs rbjomzjcjs bl bo prèrjgj ebèbkrj, pjrj o`s erjc`s sbxt` y síptmg`, bl ojs fujobs sb rbjomzjl f`lstruffm`lbs cb trmêleuo`s, trjlsd`rgjfm`lbs eb`gítrmfjs, tblmblc` bl fubltj sus pr`pmbcjcbs y fjrjftbrçstmfjs, pbrgmtmblc` oj pjrtmfmpjfmöl jftmvj cb o`s bstucmjltbs bl bo juoj cb fojsb pjrj prbpjrjro`s pjrj ul lmvbo cb cbcuffmöl d`rgjo cb o`s f`lfbpt`s cb f`lerublfmj y sbgbajlzj qub sb jk`rcjrjl f`l gjy`r pr`dulcmcjc bl o`s erjc`s `ftjv` y l`vbl`.

mmm

Çlcmfb cb Dmeurjs :.:. :.;. :.6. :.3. :.2.

Fubrcj cb :; luc`s. luc`s. . . . . . . . . . . . . . . . . . . . . Êleuo`s Êleuo`s `pubst`s `pubst`s p`r bo vírtmfb. vírtmfb.   . . . . . . . . . . . . . . Srmêleuo`s rmêleuo`s mlsfrmt`s mlsfrmt`s bl ulj fmrfuldbrblfmj fmrfuldbrblfmj . . . . . . . . Vbgbajlzj Vbgbajlzj cb Srmêle Srmêleuo`s uo`s sbeñl sbeñl Shjobs . . . . . . . . . . [bftjs pjrjoboj pjrjobojss qub sb f`rtjl f`l c`s c`s rbftjs sbfj sbfjltbs ltbs .

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6 3 3 2 2

;.:. F`lerublfmj F`lerublfmj bltrb bltrb Vbegblt` Vbegblt`ss . . . . . . . . . . . . . . . . . . . . ;.;. F`lerublfmj F`lerublfmj bltrb bltrb Êleuo`s Êleuo`s . . . . . . . . . . . . . . . . . . . . . ;.6. F`lerublfmj F`lerublfmj bltrb bltrb Êleuo`s Êleuo`s cb 6 pult`s pult`s . . . . . . . . . . . . . . ;.3. Srjlsmtmvmcj rjlsmtmvmcjcc cb oj F`lerublfmj F`lerublfmj . . . . . . . . . . . . . . . . . . ;.2. F`lerublfmj F`lerublfmj cb Srmêle Srmêleuo`s uo`s OJO . . . . . . . . . . . . . . . . . . ;.4. F`lerublfmj F`lerublfmj cb Srmêle Srmêleuo`s uo`s JOJ . . . . . . . . . . . . . . . . . . ;.5. F`lerublfmj F`lerublfmj cb Srmêle Srmêleuo`s uo`s OOO . . . . . . . . . . . . . . . . . . ;.8. Yòçe`l`s Yòçe`l`s rbeuojrbs rbeuojrbs   . . . . . . . . . . . . . . . . . . . . . . . . . . ;.=. Yòçe`l`s Yòçe`l`s f`lerubltb f`lerubltbss . . . . . . . . . . . . . . . . . . . . . . . . ;.:9. Fujcrjc` f`l sus cmje`ljobs . . . . . . . . . . . . . . . . . . . . ;.::. Fujcrmoêtbr`s f`lerubltbs . . . . . . . . . . . . . . . . . . . . . . ;.:;. Vbgbajlzj cb Srmêleuo`s Srmêleuo`s . . . . . . . . . . . . . . . . . . . . . . . ;.:6. Vbgbajlzj cb Srmêleuo`s OOO . . . . . . . . . . . . . . . . . . . ;.:3. Yjrjoboj bl ul Srmêleuo` . . . . . . . . . . . . . . . . . . . . . . ;.:2. F`lerublfmj cb êleuo`s bltrb trmêleuo`s . . . . . . . . . . . . . . ;.:4. Vbgbajlzj cb trmêleuo`s rbftêleuo`s1 "êleuo` jeuc`‗ . . . . . . ;.:5. [jzöl bltrb ojs joturjs y ojc`s cb ul trmêleuo` rbftêleuo`. . . . ;.:8. Joturj cb ul trmêleuo` rbftêleuo` f`l rbspbft` j oj hmp`tblusj .

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:6 :3 :2 :2 :5 :8 := ;9 ;: ;; ;6 ;3 ;3 ;2 ;4 ;8 ;8 ;=

;.:=. Sb`rbgj cb Ymtêe`rjs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ;.;9. [bfçpr`f` [bfçpr`f` cbo tb`rbgj tb`rbgj cb Ymtêe`rjs Ymtêe`rjs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ;.;:. Vbgbajlzj sbeñl pr`p`rfm`ljomcjc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69 69 6:

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Çlcmfb cb Sjkojs 6.:. Bstêlcjrbs Bstêlcjrbs cb Vbgbajlzj Vbgbajlzj y f`lerubl f`lerublfmj fmj . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.;. Vbgbajlzj1 Vbgbajlzj1 [bvmsmöl [bvmsmöl cb o`s tbxt`s cb oj Vbrmb gm jvbltur jvblturjj gjtbgêtmfj gjtbgêtmfj 4 j =. . . . . . . . . 6.6. Vbgbajlzj1 Vbgbajlzj1 [bvmsmöl [bvmsmöl cb o`s tbxt`s cb oj Vbrmb Lubvjs Lubvjs gjtbgêtmfjs gjtbgêtmfjs 5 j =. . . . . . . . . . .

6= 39 3:

3.:. 3.;. 3.6. 3.3.

34 35 38 3=

Yojl cb jsmeljtur jsmeljturjj Eb`gbtrçj Eb`gbtrçj pjrj Fmfo` :. :. . Yojl cb jsmeljtur jsmeljturjj Eb`gbtrçj Eb`gbtrçj pjrj Fmfo` ;. ;. . Yojl cb jsmeljtur jsmeljturjj Eb`gbtrçj Eb`gbtrçj pjrj Fmfo` 6. 6. . Yojl cb jsmeljtur jsmeljturjj Eb`gbtrçj Eb`gbtrçj pjrj Fmfo` 3. 3. .

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Omstj cb Vçgkò`s Vçgkò`s

∩J

∩(h, n ) ∩G L Y

²∄JKF ∿ 7 ↓  JKFC

7 

Êleuo` Êleuo` f`l vírtmfb vírtmfb bl J. Êleuo` Êleuo` d`rgjc` d`rgjc` p`r ojs sbgmrrbftjs sbgmrrbftjs hn. Êleuo` cbtbrgmljc` p`r trbs pult`s G L Y  f`l vírtmfb bl L . Êrbj cbo trmêleuo` JKF . F`lerubltb. F`rrbsp`lcblfmj. Fujcrmoêtbr`.

◤

7 F <

≢ ?

≣

CJF

 κ

⊢ 

JKFCB JK CB

7

FK D B

Y

JK J K 

ω o

↙∛↛

G L KF

∿ ∛∛↛

JK ∄JKF

J, K,F,C . Fujcrmoêtbr` f`l vírtmfbs J, Cmdbrbltb. Erjc`s. Meujo j> o` gmsg` qub. O`lemtuc O`lemtuc cb oj fmrfuldbrblfmj fmrfuldbrblfmj.. Gjy`r qub. Gjy`r meujo qub. Gbl`r qub. Gbl`r meujo qub. Gbcmcj cbo êleuo` êleuo` CJF . Yjrjoboj. Yojl` κ. Ybrpblcmfuojr. Yòçe`l` Yòçe`l` f`l gês cb fmlf` vírtmfbs. vírtmfbs. Yòçe`l` f`l vírtmfbs J ,K,F,C ,B ,. Yr`p`rfmöl bltrb sbegblt`s. Yult` Y. [jzöl bltrb c`s sbegblt`s. [jcmjl. [bftj o. [bftj qub pjsj p`r o`s pult`s pult`s G L . Vbegblt` K F . Vbgbajltb. Vbgmrrbftj Vbgmrrbftj qub pjsj p`r o`s pult`s pult`s JK . Srmêleuo` JKF .

vm

F`ltblmc` Cbcmfjt`rmj

m

Jerjcbfmgmblt`s

[bsugbl

mm

mmm

Çlcmfb cb Dmeurjs

mv

Çlcmfb cb Sjkojs

v

F`ltblmc`

vmmm

Mltr`cuffmöl

@kabtmv`s :.

:

;

Jltbfbcb Jltbfbcbltbs ltbs Hmstörm Hmstörmf`s f`s cb o`s F`lfbpt F`lfbpt`s `s cb Vbgbajlzj Vbgbajlzj y F`lerublf F`lerublfmj. mj. :.:. Hmst`r Hmst`rmj mj Ermb Ermbej ej   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :.;. Hmst`r Hmst`rmj mj bl Jtbl Jtbljs js   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :.6. O`s Bobgbl Bobgblt`s t`s cb Bufomcb Bufomcbss . . . . . . . . . . . . . . . . . . . . . . . . . :.3. Eb`gbt Eb`gbtrçj rçjss l` Bufoçcmjl Bufoçcmjljs js   . . . . . . . . . . . . . . . . . . . . . . . . . :.2. Eb`gbt Eb`gbtrçj rçj cb cb Hmokbrt Hmokbrt . . . . . . . . . . . . . . . . . . . . . . . . . . . .

;. Jspbft`s cmsfmpoml cmsfmpomljrbs1 jrbs1 F`lerublf F`lerublfmj mj y Vbgbajlzj Vbgbajlzj ;.:.. F`le ;.: F`leru rubl blfm fmjj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ;.:.:. ;.:. :. F`lerub F`lerublfm lfmjj bltrb bltrb sbegbl sbegblt`s t`s . . . . . . . . . . . . . . . . . ;.:.;. ;.:. ;. F`lerub F`lerublfm lfmjj cb êleuo`s êleuo`s   . . . . . . . . . . . . . . . . . . . . . ;.:.6. ;.:. 6. F`lerub F`lerublfm lfmjj bltrb bltrb trmêleu trmêleuo`s o`s . . . . . . . . . . . . . . . . . ;.:.3. ;.:. 3. F`lerub F`lerublfm lfmjj cb pòçe`l`s pòçe`l`s . . . . . . . . . . . . . . . . . . . ;.;.. Vbgb ;.; Vbgbaj ajlz lzj. j. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ;.;.:. ;.;. :. Vbgbajlz Vbgbajlzjj cb trmêle trmêleuo`s uo`s . . . . . . . . . . . . . . . . . . . . ;.;.;. ;.;. ;. Vbgbajlz Vbgbajlzjj cb trmêle trmêleuo`s uo`s rbftêl rbftêleuo` euo`s1 s1 . . . . . . . . . . . . ;.;.6. ;.;. 6. F`lsbfu F`lsbfublf blfmj mj cb oj sbgbajlz sbgbajlzjj cb trmêleuo trmêleuo`s `s rbftêl rbftêleuo` euo`ss . ;.;.3. ;.;. 3. Sb`rbgj b`rbgj cb Ymtêe`r Ymtêe`rjs1 js1 . . . . . . . . . . . . . . . . . . . . . 6.

F`gp`lbl F`gp`lbltb tb Ybcjeö Ybcjeöemf emf`. `. 6.:.. Bo g`cb 6.: g`cbo` o` cb cb Tjl Tjl Hmb Hmbob ob . . . . . . . . . . . . . . 6.;. Oj blsbú blsbújlz jlzjj cb oj f`ler f`lerubl ublfmj fmj y sbgb sbgbajl ajlzj. zj. . 6.6. [bvmsmöl [bvmsmöl cb tbxt`s bsfòjrbs1 bsfòjrbs1   . . . . . . . . . . . .

vmm

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6 3 4 5 = :9

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:6 :6 :6 :3 :4 ;9 ;6 ;3 ;5 ;8 ;=

6; . . . . . . . . . . . . . . . . . . 6; . . . . . . . . . . . . . . . . . . 64 . . . . . . . . . . . . . . . . . . 68

F@LSBLMC@

vmmm

3. Yr`pubs Yr`pubstj tj Cmcêf Cmcêftmf tmfjj 3; 3.:. Cbsfrmpfmöl Cbsfrmpfmöl eblbrjo eblbrjo cb oj pr`pubstj. pr`pubstj.   . . . . . . . . . . . . . . . . . . . . . . . . . 3; 3.;. Cbsfrmpfmöl Cbsfrmpfmöl cbo pojl cb jsmeljturj jsmeljturj cb eb`gbtrçj eb`gbtrçj cb prmgbr` j l`vbl` l`vbl` erjc`. 36 3.6. Cbsfrmpfmöl Cbsfrmpfmöl cb ojs euçjs cmcêftmf cmcêftmfjs js cb prmgbr` prmgbr` j l`vbl`. l`vbl`. . . . . . . . . . . . . 32 F`lfousm`lbs

[bf`gblcjfm`lbs Kmkomèrjdçj

29

2: 2;

Mltr`cuffmöl @ksbrvjlc` o`s rbsuotjc`s p`f` sjtmstjft`rm`s, tjlt` bl ojs prubkjs cb bstjc` f`g` bl ojs prubkjs cb mlerbs` j oj bcufjfmöl supbrm`r, p`r pjrtb cb o`s bstucmjltbs cbo fòbem` Vjl Jeustml MBC a`rljcj tjrcb, pjrtmfuojrgbltb bl o`s tbgjs rbojfm`ljc`s f`l oj eb`gbtrçj sureb oj prb`fupjfmöl p`r oj blsbújlzj cb bstj jsmeljturj bl bcufjfmöl kêsmfj. Bo bstucm` cb oj eb`gbtrçj jftujogbltb sb hj vmst` omgmtjc` p`r bo rbcufmc` tmbgp` qub sb ob cbcmfj j oj jsmeljturj y p`r bo gjlba` cb ojs fojsbs bl t`rl` jo oêpmz y pjpbo. Bst` hj oobvjc` j o`s bstucmjltbs, j f`lsmcbrjr oj eb`gbtrçj f`g` ulj jsmeljturj supbr﬊fmjo b mlf`gpobtj. Bstb trjkja` sb rbjomzö f`l bo `kabtmv` cb hjfbr ulj pr`pubstj cmcêftmfj pjrj bo cbsjrròo` cb o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj cbscb erjc` prmgbr` j l`vbl` cb bcufjfmöl kêsmfj, oojgjcj ‟Rl gulc` cb d`rgjs y ﬊eurjs,‗ pjrj `rmbltjr bo pr`fbs` cb jprblcmzjab cb o`s bstucmjltbs cb oj eb`gbtrçj tblmblc` f`g` dulcjgblt` y rbdbrbltb pbcjeöemf` o`s lmvbobs cb Tjl Hmbob, p`r gbcm` cb euçjs cmcêftmfjs y bo prèrjgj ebèbkrj f`g` hbrrjgmbltjs cmcêftmfjs pjrj su bstucm`. F`lstj cb fujtr` fjpçtuo`s fjpçtuo`s qub sb cbsjrròoj cbsjrròojll cb oj smeumbltb smeumbltb gjlbrj1 Bl bo fjpçtuo` fjpçtuo` : sb hjfb ulj rbsbúj hmstörmfj cb o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj. Bl bo fjpçtuo` ; sb cbsjrròoj bo bld`qub cmsfmpomljr, jquç sb trjtjl tbgêtmfjs tbgêtmfjs bspbfç﬊fjs1 bspbfç﬊fjs1 Oj f`lerublfmj cb sbegblt`s, sbegblt`s, êleuo`s, êleuo`s, trmêleuo`s trmêleuo`s,, pòçe`l`s, pòçe`l`s, o`s frmtbrm`s frmtbrm`s cb sbgbajlzj sbgbajlzj bl trmêleuo`s trmêleuo`s.. Bl bo fjpçtuo` fjpçtuo` 6 sb prbsbltj ulj krbvb rbsbúj hmstörmfj hmstörmfj cb o`s cmvbrs`s bstucm`s rbjomzjc`s s`krb o`s lmvbobs cb Tjl Hmbob y jltbfbcbltbs s`krb oj blsbújlzj cbo f`lfbpt` cb sbgbajlzj, f`g` sb pojltbj oj blsbújlzj cb oj eb`gbtrçj t`gjlc` f`g` rbdbrbltb o`s omlbjgmblt`s y bstêlcjrbs furrmfuojrbs y sb hjfb ulj rbvmsmöl cb joeul`s tbxt`s j lmvbo cb kêsmfj sbfulcjrmj pjrj f`gpjrjr o`s tbgjs qub cbsjrròojl cbsjrròojl bl eb`gbtrçj. Bl bo fjpçtuo` fjpçtuo` 3 sb hjfb ulj pr`pubstj pr`pubstj cmcêftmfj pjrj oj blsbújlzj cb oj eb`gbtrçj cbscb prmgbr` hjstj l`vbl` erjc`, qub prbtblcb f`ltrmkumr jo cbsjrròo` cb bstj jsmeljturj bl fujoqumbr mlstmtufmöl bcufjtmvj, pojltbjlc` ul pojl cb jsmeljturj p`r fmfo`s y uljs euçjs cmcêftmfjs qub sb pubcbl mgpobgbltjr. Bstjs sb prbsbltjl f`g` jlbx`s jo ﬊ljo cbo trjkja`.

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@kabtmv`s @kabtmv` eblbrjo Cmsbújr ulj pr`pubstj cmcêftmfj pjrj oj blsbújlzj cb o`s f`lfbpt`s cb f`lerublfmj y sbgbajlzj bl eb`gbtrçj pojlj pjrj o`s bstucmjltbs cb bcufjfmöl kêsmfj cbo Fòbem` Vjl Jeustml a`rljcj tjrcb.

@kabtmv`s bspbfç﬊f`s [bjomzjr ul bstucm` hmstörmf` y cmsfmpomljr pjrj pr`dulcmzjr s`krb o`s f`lfbpt`s cb f`lerublfmj y sbgbajlzj cb ﬊eurjs pojljs. [bvmsjr mlvbstmejfm`lbs y trjkja`s rbojfm`ljc`s f`l bo cbsjrròo` cbo pblsjgmblt` eb`gítrmf` bl pjrtmfuojr o`s lmvbobs cb Tjl Hmbob, pjrj oj blsbújlzj cb oj eb`gbtrçj. Rtmomzjr bobgblt`s cb oj eb`gbtrçj cmlêgmfj cbo prèrjgj ebèbkrj pjrj oj bojk`rjfmöl cb euçjs cmcêftmfjs qub pbrgmtjl oj blsbújlzj cb o`s f`lfbpt`s cb f`lerublfmj y sbgbajlzj cb ﬊eurjs. Bstucmjr o`s bstêlcjrbs kêsmf`s cb gjtbgêtmfjs, y o`s omlbjgmblt`s furrmfuojrbs cb gjtbgêtmfjs rbojfm`ljc` rbojfm `ljc`ss f`l bo pblsjgmblt` pblsjgmblt` bspjfmjo y eb`gítrmf`. eb`gítrmf`. Cmsbújr ulj pr`pubstj cmcêftmfj pjrj oj blsbújlzj cb oj eb`gbtrçj cb bcufjfmöl kêsmfj, t`gjlc` f`g` cmrbftrmz o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj.

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:. Jltbfbcbltbs Hmstörmf`s cb o`s F`lfbpt`s cb Vbgbajlzj y F`lerublfmj. Bl oj bvòufmöl cb oj eb`gbtrçj hjy qub rbsjotjr ojs f`ltrmkufm`lbs cb jltmeujs fuoturjs, f`g` oj kjkmo`lmj y oj bempfmj, prmlfmpjogbl prmlfmpjogbltb. tb. Bl ojs cmdbrbltbs cmdbrbltbs btjpjs cb su cbsjrròo`, cbsjrròo`, bstjs fuoturjs cbajr`l tbxt`s,cb tbxt`s,cb fuyj mltbrprbtjfm mltbrprbtjfmöl öl sb cbsprblcb cbsprblcb s`krb t`c` bl bo êgkmt` êgkmt` cb sus jpomfjfm`lbs jpomfjfm`lbs prêftmfjs, prêftmfjs, qub vjl vjl cmrmemcjs cmrmemcjs j oj jermgblsurj y oj f`lstruffmöl. Oj jermgblsurj tmblb f`g` `kabt` oj gbcmfmöl cb tbrrbl`s ` bo fêofuo` cb êrbjs cb supbr﬊f supbr﬊fmbs mbs omgmtjc omgmtjcjs js cb oj tmbrrj. tmbrrj. Cb jooç bo l`gkrb l`gkrb ζύ²σϊκ, eb`gbtrçj1 eb`gbtrçj1 ‟gbcmfmöl ‟gbcmfmöl cb oj tmbrrj‗ (cb ζ ε˟ ( e b˄) ‟tmbrrj‗ gês ²σϊκ (gbtrçj), ‟gbcmfmöl‗). ‟gbcmfmöl‗). ^: ^:WW Ojs prmgbrjs fmvmomzjfm`lbs gbcmtbrrêlbjs jcqumbrbl p`f` j p`f` o`s f`l`fmgmblt`s eb`gítrmf`s cb fjrêftbr bgmlbltbgbl bgmlbltbgbltb tb prêftmf`. prêftmf`. Oj eb`gbtrçj bl bo jltmeu` Bempt` bstjkj kjstjltb cbsjrr` cbsjrròojcj oojcj,, f`g` jcgmtmbr`l Hbröc`t`, Bstrjköl y Cm`c`r`, qumblbs jfbptjkjl qub o`s bempfm`s hjkçjl blsbújc` j o`s ermbe`s. Y`cçjl fjofuojr bo êrbj cb trmêleuo`s, rbftêleuo`s y trjpbfm`s. F`l`fmjl joeuljs dörguojs pjrj fjofuojrr vòñgblbs fjofuoj vòñgblbs cb fmomlcr`s fmomlcr`s y cb prmsgjs prmsgjs rbft`s. Gjlbajkjl Gjlbajkjl ulj kublj jpr`xmgjfmö jpr`xmgjfmöll cb ω (6 :4 ). Oj sbgbajlzj y oj pr`p`rfm`ljomcjc l` obs brj cbsf`l`fmcj, sb vb rb﬋bajc` bl oj f`lstruffmöl cb ojs pmrêgmcbs. ^:=W. :=W. Curjltb oj rbvòufmöl urkjlj bl Gbs`p`tjgmj y Bempt`, o`s f`lstruft`rbs cb oj íp`fj f`gmblzjl j rbjomzjr ojs prmgbrjs jpomfjfm`lbs cb o` qub h`y sb f`l`fb f`g` tb`rbgj cb Ymtêe`rjs, jo trjzjr o`s êleuo`s cb o`s fmgmblt`s fmgmbl t`s cb ojs f`lstruffm`lbs f`lstruffm`lbs qub p`r rjz`lbs cb bqumomkrm` bqumomkrm` cbkçjl sbr rbft`s y fjofuojr fjofuojr ojs cmgblsm`lbs cmgblsm`lbs cb ojs pjrfbojs. pjrfbojs. Y`r babgpo` trjzjkjl trjzjkjl oçlbjs pbrpblcmfuojrbs pbrpblcmfuojrbs s`krb bo tbrrbl`, tbrrbl`, utmomzjlc` ulj fubrcj cb c`fb luc`s bqumcmstjltbs y tblcmblcòj f`g` sb gubstrj bl oj ﬊eurj.

Dmeurj :.:1 Fubrcj cb :; luc`s. Oj fuoturj gbs`p`têgmfj, rbojfm`ljcj f`l fmucjcbs f`g` Rr (oj pjtrmj fhmfj cb Jkrjhjg), Kjkmo`lmj (oj fmucjc cbo rby Hjggurjkm) y Lçlmvb (jltmeuj fjpmtjo cb Jsmrmj), cbaö gufhj mld`rgjfmöl eb`gítrmfj f`cm﬊fjcj bl tjkomoojs cb fbrêgmfj j trjvís cb oj bsfrmturj fulbmd`rgb, rbojfm`ljcj f`l bo fêofuo` cb êrbjs cb ﬊eurjs pojljs (trmêleuo`s, fujcrjc`s, rbftêleuo`s y trjpbz`mcbs) y bo fêofuo` vòñgblbs cb söomc`s f`g` pjrjobobpçpbc`s y pmrêgmcbs ^;W ^;W..

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FJYÇSRO@ :. :.

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JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

3

Hm Hmst st`r `rmj mj Er Ermb mbej ej

Bo `rmebl cb o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj sb rbg`tjl jo cbsjrròo` cb oj eb`gbtrçj bufomcmjlj, qub sb dulcjgbltj bl jxm`gjs (vbrcjcbs jksòutjs) y tb`rbgjs. Rl` cb o`s prmgbr`s gjtbgêtmf`s ermbe`s duí Shjobs cb Gmobt` ( smeo` TM j.F), brj ul f`gbrfmjltb jftmvmcjc qub ob pbrgmtmö vmjajr j Bempt`, c`lcb jcqumrmö erjl pjrtb cb su f`l`fmgmblt` y bo mltbrbs p`r oj eb`gbtrçj. Vb ob jtrmkuybl ojs smeumbltbs pr`p`smfm`lbs ^:=W ^:=W11 :. Rl cmêgbtr` cmvmcb j ul fçrfuo` bl c`s pjrtbs meujobs. ;. Oj sugj cb o`s êleuo`s cb ul trmêleuo` bs bqumvjobltb j c`s rbft`s. 6. O`s c`s êleuo`s bl oj kjsb cb ul trmêleuo` msösfbobs s`l meujobs. 3. Bl c`s rbftjs qub sb f`rtjl, o`s êleuo`s `pubst`s s`l meujobs.

Dmeurj :.;1 Êleuo`s `pubst`s p`r bo vírtmfb. 2. Fujoqumbr trmêleuo` mlsfrmt` bl ulj fmrfuldbrblfmj, cb d`rgj qub ul` cb sus ojc`s f`mlfmcj f`l bo cmêgbtr` cb oj gmsgj, bs rbftêleuo`.^;9W rbftêleuo`.^;9W

Dmeurj :.61 Srmêleuo`s mlsfrmt`s bl ulj fmrfuldbrblfmj Bltrb o`s tb`rbgjs qub sb ob jtrmkuybl j Shjobs, sb blfubltrj ul` qub bs pmbcrj jleuojr cb oj tb`rçj cb oj sbgbajlzj1 ‟Vm c`s trmêleuo`s tmblbl êleuo`s f`rrbsp`lcmbltbs cb gbcmcjs meujobs, blt`lfbs o`s ojc`s f`rrbsp`lcmbltbs bstêl bl ulj gmsgj rjzöl‗.^;3W ^;3W

Bo tb`rbgj jltbrm`r sb pubcb blulfmjr cb oj smeumbltb gjlbrj1 

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‟Vm c`s trmêleuo`s   ∄JKF   y   ∄J K F , s`l tjobs qub   ∩J 7 ∩J , ∩K 7 ∩K ∩F   7 ∩F blt`lfbs1

JK 

JK

7 

JF 

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J F

7

KF 

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K F

FJYÇSRO@ :. :.

JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

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Dmeurjj :.31 Vbgbajlzj Dmeur Vbgbajlzj cb Srmêleuo`s Srmêleuo`s sbeñl Shjobs sjtmsdjejl ojs pr`pmbcjcbs pr`pmbcjcbs cjcjs bl bo Sb`rbgj Sb`rbgj F`gbltjrm` :1 C`s trmêleuo`s ∄ JKF   y ∄ J K F , qub sjtmsdjejl jltbrm`r sb cbl`gmljl trmêleuo`s sbgbajltbs (∄JKF ∿∄J K F ). 

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@tr` tb`rbgj qub sb ob jtrmkuyb j Shjobs bs1 ‟Fujlc` c`s rbftjs pjrjobojs f`rtjl j c`s rbftjs sbfjltbs, cbtbrgmljl s`krb bstjs sbegblt`s pr`p`rfm`ljobs.‗

Dmeurj :.21 [bftjs pjrjobojs qub sb f`rtjl f`l c`s rbftjs sbfjltbs Cbg`strjfmöl. F`g` sb gubstrj bl oj ﬊eurj ojs pjrjob pjrjobojs ojs K F   y C B  f`rtjl f`rtjl j ojs sbfjltbs JK y JF . Vb hjl cmkuajc` ojs joturjs C CN N  y y H B  cbo cbo trmêleuo` ∄ JCB . Blt`lfbs bo êrbj cbo ∄ JCB  sb sb pubcb bxprbsjr

f`g`1 : : CN.. CJ µ H B  7 7 JB µ CN ; ;

Jo gmsg` tmbgp` o`s trmêleuo`s ∄ KC KCB B  y y ∄ FB C tmblbl oj gmsgj êrbj pubst` qub tmblbl oj gmsgj kjsb, qub sbrê bo ojc` C y oj gmsgj joturj qub sbrê oj cmstjlfmj bltrb ojs pjrjobojs C y K F , sus êrbjs sbrêl CB B  y CB B  y : : y pjrj bo trmêleuo` ∄ FB C 7 ; F B µ CN pjrj ∄ KC CN.. KCB B   7 ; KC µ H B  y Blt`lfbs sb fugpob oj smeumbltb rbojfm`l bltrb êrbjs1 ²∄JCB ²∄JCB 7 ²∄FB C ²∄KCB

FJYÇSRO@ :. :.

JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

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sustmtuyblc` ojs bxprbsm`lbs jltbrm`rbs sb tmblb qub1 JC JB 7 FB KC

C`s fò`rjrm`s mgp`rtjltbs cbo tb`rbgj jltbrm`r s`l o`s smeumbltbs1

F`ròjrm` :.:. Y`cbg`s cmvmcmr fujoqumbr sbegblt` bl bo lñgbr` ljturjo cb pjrtbs meujobs qub qubrjg`s. F`ròjrm` :.;. Vm tblbg`s c`s trçêleuo`s f`l sus trbs êleuo`s meujobs blt`lfbs sus ojc`s gjltmblbl oj gmsgj pr`p`rfmöl y vmfbvbrsj. Bxmstb ulj hmst`rmj qub fubltj fög` dub qub Shjobs jpomfö bo Sb`rbgj1 Bl ul vmjab qub rbjomzö j Bempt`, cbtbrgmlö oj jotur cbtbrgmlö joturj j cb oj pmrêgmcb pmrêgmcb cb Eumzj. Yjrj Yjrj hjfbro` hjfbro` gmcmö oj s`gkrj s`gkrj cb ul kjstöl kjstöl jp` jp`yjc` yjc` vbrtmfjogbltb fjogbltb s`kr s`krbb bo subo` y oj s`gk s`gkrj rj cb oj pmr pmrêgmcb êgmcb.. Vup Vup`lmbl `lmblc` c` qub o`s rjy`s cbo sò brjl pjr pjrjobo`s jobo`s,, bo trmêleuo` d`rgjc` p`r oj joturj cb oj pmrêgmcb, su s`gkrj y bo sbegblt` qub ulb o`s bxtrbg`s rbsuotjkj sbgbajltb jo trmêleuo` `ktblmc` p`r bo kjstöl, su s`gkrj y bo sbegblt` qub ulb o`s bxtrbg`s cb bst`s. Jsç, cbtbr cbtbrgmlö gmlö oj jotur joturj j cb oj pmr pmrêgmcb êgmcb bstjkobfmblc bstjkobfmblc` ` ojs pr`p pr`p`r `rfm`lb fm`lbss bltr bltrbb ojs jotur joturjs js y ojs s`gkr s`gkrjs. js.

tjgkmíl sb fubltj qub pjrj gbcmr oj joturj cb oj pmrêgmcb, bspbr` oj h`rj cbo cçj bl oj fujo o`s `kabt`s y sus rbspbftmvjs s`gkrjs tblçjl oj gmsgj o`lemtuc, smgpobgbltb gmcmö oj s`gkrj qub sb pr`ybftjkj s`krb bo subo`.^;3 subo`.^;3WW @tr` tb`rbgj qub sb ob jtrmkuyb j Shjobs bs1 ‟Bo êleuo` mlsfrmt` bl ulj sbgmfmrfuldbrblfmj bs rbft`.‗   Oj cbg`strjfmöl, rbjomzjcj gbcmjltb ul pr`fbcmgmblt` cbcuftmv` sb blfubltrj bl oj Yr`p`smfmöl 6; cbo Omkr` MMM cb o`s Bobgblt`s cb Bufomcbs. @tr` cb o`s jp`rtbs qub hmz` Shjobs j oj fmblfmj dub oj mltr`cuffmöl cb ojs cbg`strjfm`lbs. Ymtêe`rjs ljfmc` bl oj msoj cb Vjg`s bl oj prmgbrj gmtjc cbo smeo` TM j.F. Bl oj bsfuboj pmtjeörmfj sureb oj tb`rmj ermbej cb ojs pr`p`rfm`lbs, oj fujo brj jpomfjkob ñlmfjgbltb j gjelmtucbs f`lgblsurjkobs, bltblcmblc` qub c`s gjelmtucbs l` luojs j y k s`l f`glblsurjkobs fujlc` oj rjzöl bltrb boojs ( jk ) bs ul lñgbr` rjfm`ljo, cb﬊lmfmöl qub sb blfubltrj bl bo omkr` X cb o`s Bobgblt`s cb Bufomcbs jsç1 ‟Vb oojgjl gjelmtucbs f`gblsurjkobs jquboojs qub sb gmcbl f`l oj gmsgj gbcmcj, b mlf`lgblsurjkobs jquboojs cb ojs qub l` bs p`smkob hjoojr ulj gbcmcj f`gñl.‗

Sjgkmíl sb obs jtrmkuyb j o`s pmtjeörmf`s oj cbg`strjfmöl cb oj pr`p`smfm`l 35 cbo omkr` M cb o`s Bobgblt`s cb Bufomcbs, fuy` blulfmjc` bs bo smeumbltb1 ‟Bl o`s trmêleuo`s rbftêleuo`s, bo fujcrjc` cbo ojc` `pubst` jo êleuo` rbft` bs meujo j oj sugj cb o`s fujcrjc`s cb o`s ojc`s qub f`gprblcbl bo êleuo` rbft`.‗   Bstj rbojfmöl rbojfm öl eb`gítrmfj f`l`fmcj h`y f`g` bo Sb`rbgj cb Ymtêe`rjs, Ymtêe`rjs, bstj omejcj j oj dörguoj pjrj blf`ltrjr ojs tbrljs pmtjeörmfjs, bs cbfmr c`s lñgbr`s fujcrjc`s fujcrjc`s fuyj sugj sbj ul lñgbr` lñgbr` fujcrjc`, yj f`l`fmcjs p`r o`s kjkmo`lm`s. kjkmo`lm`s.

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Hm Hmst st`r `rmj mj bl Jtb tblj ljss

Buc`x`` cb Flmc`s, Buc`x Flmc`s, 6=9 ‖ 665 j.F, dub bo prmlfmpjo prmlfmpjo gjtbgêt gjtbgêtmf` mf` cb oj Jfjcbgm Jfjcbgmjj cb Yojtöl. Yojtöl. Vu gjy`r gjy`r f`ltrmkufm f`lt rmkufmöl öl duí oj tb`rçj cb ojs pr`p`rfm`lbs, pr`p`rfm`lbs, sb ob jtrmkuyb oj smeumbltb pr`p`smfmöl pr`p`smfmöl qub ﬊eurj bl bo omkr` T cb o`s Bobgblt`s cb Bufomcbs1 ‟Vm ulj prmgbrj gjelmtuc eujrcj oj gmsgj rjzöl f`l ulj sbeulcj qub ulj tbrfbrj f`l ulj fujrtj, fujoqumbr bqumgñotmpo` cb oj prmgbrj y oj tbrfbrj, eujrcjrêl oj gmsgj rjzöl f`l fujoqumbr bqumgñotmpo` cb oj sbeulcj y oj fujrtj rbspbftmvjgbltb, t`gjc`s bl bo `rcbl f`rrbsp`lcmbltb.‗

FJYÇSRO@ :. :.

JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

5

J Buc`x` tjgkmíl sb ob jtrmkuyb oj j﬊rgjfmöl qub sb blfubltrj bl bo omkr` T cb o`s Bobgblt`s cb Bufomcbs1 ‟Vb cmfb qub ojs gjelmtucbs eujrcjl rjzöl bltrb sç, fujlc` jo guotmpomfjrsb, pubcjl bxfbcbr oj ulj j oj `trj‗.^3 ^3WW

Bl eblbrjo, Buc`x` mltr`cua` oj l`fmöl cb gjelmtuc, qub l` brj ul lñgbr` pbr` sbrvçj pjrj trjtjr êleuo`s, sbegblt`s, êrbjs, vòñgblbs, qub vjrmjkjl cb ulj gjlbrj f`ltmluj> gmbltrjs qub o`s lñgbr`s brjl cmsfrbt`s, ojs gjelmtucbs brjl f`ltmlujs. Yjrj Buc`x`, ulj rjzöl cb gjelmtucbs brj ulj pr`p`rfmöl, bs cbfmr ulj mcbltmcjc cb c`s rjz`lbs dubrjl f`lgblsurjkobs ` l`.

:.6. :.6.

O` O`ss Bo Bobg bgbl blt` t`ss cb Buf Bufom omcb cbss

Bufomcbs (MT j.F) pus` `rcbl j o`s trjkja`s rbjomzjc`s p`r Shjobs y Buc`x` bl o`s omkr`s T y TM cb o`s Bobgblt`s.^8W Bobgblt`s. ^8W O`s Bobgblt`s bs ulj `krj qub f`lstj cb trbfb vòñgblbs, bl o`s fujobs Bufomcbs rbf`pmoj y smstbgjtmzj erjl pjrtb cbo sjkbr gjtbgêtmf` cb oj íp`fj1 Eb`gbtrçj y Sb`rçj cb Lñgbr`s. O`s prmgbr`s sbms omkr`s trjtjl s`krb eb`gbtrçj pojlj, o`s trbs smeumbltbs s`krb tb`rmj cb lñgbr`s, bo omkr` X s`krb ojs gjelmtucbs mrrjfm`ljobs ` mlf`lgblsurjkobs y o`s trbs uotmg`s s`krb eb`gbtrçj cb pòmbcr`s y `tr`s söomc`s. Bo omkr` M cb o`s Bobgblt`s, Bobgblt`s, o`s dulcjgblt`s dulcjgblt`s cb oj eb`gbtrçj, f`ltmblbl f`ltmblbl ;6 cb﬊lmfm`lbs, cb﬊lmfm`lbs, 2 l`fm`lbs f`guf`gulbs, 2 p`stuojc`s y 38 pr`p`smfm`lbs. pr`p`smfm`lbs. Oj `krj f`gpobtj tmblb 2 p`stuojc`s y 2 l`fm`lbs f`gulbs y 345 pr`p`smfm`lbs. J f`ltmlujfmöl sb rbojfm`ljl o`s p`stuojc`s y ojs l`fm`lbs f`gulbs qub f`ltmblb bstj `krj.

O`s p`stuojc`s1 :. Vb pubcb trjzjr ulj rbftj cbscb ul pult` j `tr` fujoqumbrj. ;. Bs p`smkob bxtblcbr ul sbegblt` cb rbftj f`ltmlujgbltb j ulj rbftj. 6. Bs p`smkob cbsfrmkmr ul fçrfuo` f`l fujoqumbr fbltr` y fujoqumbr rjcm`. 3. Zub t`c`s o`s êleuo`s rbft`s s`l meujobs. 2. Zub sm ulj oçlbj rbftj f`rtj j `trjs c`s rbftjs, d`rgjlc` f`l boojs êleuo`s mltbrm`rbs cbo gmsg` ojc` gbl`rbs qub c`s êleuo`s rbft`s, ojs c`s oçlbjs rbftjs, prò`lejcjs mlcb﬊lmcjgbltb, sb f`rtjl cbo ojc` p`r bo fujo o`s êleuo`s s`l gbl`rbs qub c`s êleuo`s rbft`s.

Ojs l`fm`lbs f`gulbs1 :. F`sjs qub s`l meujobs j oj gmsgj f`sj s`l meujobs bltrb sm. ;. Vm meujobs sb sugjl j meujobs, o`s rbsuotjc`s s`l meujobs. 6. Vm meujobs sb rbstjl cb meujobs, o`s rbst`s s`l meujobs. 3. F`sjs qub f`mlfmcbl ulj f`l `trj s`l meujobs bltrb sm. 2. Bo t`c` bs gjy`r qub oj pjrtb. O`s prmgbr`s prmgbr`s c`s p`stuojc`s obemtmgjl obemtmgjl bo us` cb oj rbeoj l` gjrfjcj. gjrfjcj. Oj rbeoj bl oj eb`gbtrçj eb`gbtrçj bufomcmjlj bufomcmjlj tmblb ul sò` pr`pösmt`1 trjzjr sbegblt`s y prò`lejr o`s gmsg`s j o` ojre` cb ulj rbftj. J oj rbeoj l` ob bstê pbrgmtmc` trjlsp`rtjr o`lemtucbs, bs cbfmr, l` smrvb pjrj gbcmr. Bo tbrfbr p`stuojc` ejrjltmzj oj f`lstruffmöl cb fmrfuldbrblfmjs, cjc` bo fbltr` y bo rjcm`, y jo meujo qub oj rbeoj, bo f`gpês, tjgp`f` bs gbcm` oçfmt` pjrj trjlsp`rtjr o`lemtucbs. Bl bo omkr` T cb o`s Bobgblt`s sb cbsjrròoj oj tb`rçj cb ojs pr`p`rfm`lbs jpomfjkob j ojs gjelmtucbs f`lgblsurjko f`lgbls urjkobs bs b mlf`lgblsurj mlf`lgblsurjkobs, kobs, f`ltmblb f`ltmblb :8 cb﬊lmfm`lbs cb﬊lmfm`lbs y ;2 pr`p`smfm`lbs. pr`p`smfm`lbs. Ojs cb﬊lmfm`l cb﬊lmfm`lbs bs qub sb

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JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

8

blfubltrjl bl bstb omkr` s`l1 :. Bltrb c`s gjelmtucbs, oj gbl`r sb oojgj pjrtb (joçfu`tj) cb oj gjy`r, gjy`r, fujlc` oj gmcb (bxjftjgbltb). ;. Rlj gjelmtuc bs guotmpoj cb oj gbl`r fujlc` bs gbcmcj p`r booj (bxjftjgbltb). 6. [jzöl bs fujoqumbr rbojfmöl bltrb c`s gjelmtucbs cbo gmsg` eílbr` sbeñl su fjltmcjc. 3. Cçfbsb qub c`s gjelmtucbs gjelmtucbs tmblbl rjzöl bltrb sç, fujlc` fjcj ulj pubcb sbr guotmpomfj guotmpomfjcj cj bl g`c` cb supbrjr j oj `trj. 2. Cçfbsb qub oj rjzöl cb ulj prmgbrj gjelmtuc j ulj sbeulcj bs meujo j oj cb ulj tbrfbrj j ulj fujrtj, fujlc` ojs prmgbrjs y ojs tbrfbrjs meujogbltb guotmpomfjcjs ` jo gmsg` tmbgp` supbrjl, ` jo gmsg` tmbgp` s`l meujobs ` jo gmsg` tmbgp` s`l mldbrm`rbs qub ojs sbeulcjs y ojs fujrtjs meujogbltb guotmpomfjcjs. 4. Ojs gjelmtucbs qub tmblb oj gmsgj rjzöl sb oojgjl pr`p`rfm`ljobs. 5. Fujlc` bltrb (fjltmcjcbs) meujogbltb guotmpomfjcjs, bo gñotmpo` cb oj prmgbrj supbrj jo gñotmpo` cb oj sbeulcj, pbr` bo gñotmpo` cb oj tbrfbrj l` supbrj jo gñotmpo` cb oj fujrtj, sb cmfb qub oj prmgbrj tmblb j oj sbeulcj ulj rjzöl gjy`r qub oj tbrfbrj j oj fujrtj. 8. Oj pr`p`rfmöl gçlmgj bs bltrb trbs tírgml`s. =. Fujlc` trbs gjelmtucbs gjelmtucbs s`l (f`ltmlujgbl (f`ltmlujgbltb) tb) pr`p`rfm`ljobs, pr`p`rfm`ljobs, sb cmfb qub oj prmgbrj f`l oj tbrfbrj tmblb ulj rjzöl cupomfjcj cb oj qub tmblb f`l oj sbeulcj. :9. Vm fujtr` gjelmtucbs s`l (f`ltmlujgbltb) pr`p`rfm`ljobs, sb cmfb qub oj prmgbrj tmblb j oj fujrtj ulj rjzöl trmpomfjcj cb oj qub tmblb j oj sbeulcj, y smbgprb cbo gmsg` g`c` bl jcbojltb, fujoqumbrj qub sbj oj pr`p`rfmöl. ::. Vb oojgjl h`göoè`s o`s jltbfbcbltbs f`l o`s jltbfbcbltbs y o`s f`lsbfubltbs f`l o`s f`lsbfubltbs. :;. Oj rjzöl sb oojgj f`lgutjcj fujlc` sb t`gj bo jltbfbcbltb f`l bo jltbfbcbltb y bo f`lsbfubltb f`l bo f`lsbfubltb. f`lsbfubltb. :6. Oj rjzöl sb oojgj mlvbrsj fujlc` sb t`gj bo f`lsbfubltb f`g` jltbfbcbltb y bo jltbfbcbltb bl ouejr cb su f`lsbfubltb. :3. F`gp`lbr oj rjzöl bs t`gjr bo jltbfbcbltb f`l bo f`lsbfubltb f`g` ulj sòj f`sj pjrj bo gmsg` f`lsbfubltb. :2. Vukstrjbr oj rjzöl bs t`gjr bo bxfbs` cbo jltbfbcbltb s`krb bo f`lsbfubltb jo gmsg` f`lsbfubltb. :4. F`lvbrtmr oj rjzöl bs t`gjr bo jltbfbcbltb f`l oj cmdbrblfmj qub hjy bltrb bo jltbfbcbltb y bo f`lsbfubltb. :5. Cçfbsb rjz`l meujo meujo fujlc`, cjc` ul lñgbr` fujoqumbrj fujoqumbrj cb gjelmtucbs, gjelmtucbs, cb tjo gjlbrj qub cb c`s bl c`s sbjl rbspbftmvjgbltb pr`p`rfm`ljobs j `trjs gjelmtucbs, bl ojs prmgbrjs gjelmtucbs oj prmgbrj bs j oj ñotmgj f`g` tjgkmíl bl ojs sbeulcjs oj prmgbrj bs j oj ñotmgj> ` cb `trj gjlbrj, fujlc` sb f`lsmcbrjl o`s tírgml`s bxtbrm`rbs sml f`lsmcbrjr o`s gbcm`s. :8. [jzöl pbrturkjcj pbrturkjcj sb oojgj fujlc`, cjcjs trbs gjelmtucbs gjelmtucbs y `trjs trbs, bl ojs prmgbrjs gjelmtucbs gjelmtucbs bo jltbfbcbltb jltbfbcbltb bstê jo f`lsbfubltb f`lsbfubltb f`g` ojs sbeulcjs bo jltb jltbfbcblt fbcbltbb bstê jo f`lsbfubltb, f`lsbfubltb, y f`g` bl ojs prmgbrjs bo f`lsbfubltb bs j `trj f`sj bl ojs sbeulcjs `trj f`sj bs jo jltbfbcbltb.

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JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

=

Bl bo omkr` TM cb o`s Bobgblt`s cb Bufomcbs sb hjfb oj jpomfjfmöl cb oj tb`rçj buc`xmjlj j ojs ﬊eurjs pojljs, trmêleuo`s y pòçe`l`s sbgbajltbs, oobejlc` jo f`lfbpt` cb êrbj, ojs f`lstruffm`lbs cb oj tbrfbrj, oj fujrtj y gbcmj pr`p`rfm`ljo. F`ltmblb 3 cb﬊lmfm`lbs y 66 pr`p`smfm`lbs. Ojs cb﬊lmfm`lbs qub sb blfubltrjl bl bstb omkr` s`l1 :. Dmeurjs Dmeurjs rbftmoçlbjs rbftmoçlbjs sbgbajltbs sbgbajltbs s`l ojs qub tmblbl o`s êleuo`s meujobs meujobs ul` j ul` y pr`p`rfm`ljobs pr`p`rfm`ljobs o`s ojc`s qub f`gprblcbl f`gprblcbl o`s êleuo`s êleuo`s meujobs. meujobs. ;. C`s ﬊eurjs bstêl mlvbrsjgbl mlvbrsjgbltb tb rbojfm`ljcjs rbojfm`ljcjs fujlc` bl fjcj ulj cb ojs ﬊eurjs hjy rjz`lbs jltbfbcbltbs y f`lsbfubltbs. 6. Vb cmfb qub ulj rbftj hj smc` f`rtjcj bl bxtrbgj y gbcmj rjzöl fujlc` oj rbftj bltbrj bs jo sbegblt` gjy`r f`g` bo sbegblt` gjy`r bs jo sbegblt` gbl`r. 3. Bl fujoqumbr ﬊eurj, oj joturj bs oj pbrpblcmfuojr cmkuajcj cbscb bo vírtmfb hjstj oj kjsb. Oj `krj cb Bufomcbs Bufomcbs l` bs bxfousmv bxfousmvjgbl jgbltb tb cb eb`gbtrçj eb`gbtrçj pojlj, tjgkmíl tjgkmíl cbsjrròoj cbsjrròoj eb`gbtrçj eb`gbtrçj cbo bspjfm`, bspjfm`, jrmtgítmfj y tb`rçj cb lñgbr`s. O`s prmgbr`s trjkja`s ermbe`s s`krb fölmfjs sb cbkbl j Gbflbg`, bst`s trjkja`s dubr`l f`ltmlujc`s p`r Bufomcbs y Jrquçgbcbs, pbr` dub Jpò`lm` qumbl cmö o`s l`gkrbs cb bompsb, pjrêkòj b hmpírkòj. Bl o`s Bobgblt`s cb Bufomcbs l` sb cbsjrròojl tbgjs rbdbrbltbs j ojs fölmfjs pbr` tuvmbr`l sus mlmfm`s curjltb bstj gmsgj íp`fj.

:.3.. :.3

Eb Eb`gb `gbtrç trçjs js l` Buf Bufoçc oçcmjl mjljs js

Oj eb`gbtrçj vmvç` ulj rbvòufmöl f`l bo suremgmblt` cb ojs eb`gbtrçjs l` bufomcmjljs, eblbrjcjs jo f`lsmcbrjr f`lsmc brjr qub bo p`stuojc` p`stuojc` cb ojs rbftjs pjrjobojs pjrjobojs cb Bufomcbs l` brj tjl bvmcbltb f`g` o`s `tr`s. O`s gjtbgêtmf`s trjtjr`l cb sustmtumro` p`r `tr` bqumvjobltb y qub ault` f`l o`s `tr`s fujtr` y ojs l`fm`lbs f`gulbs f`gu lbs cb Bufomcbs Bufomcbs pbrgmtm p brgmtmbrj brj cbcufmr o`s tb`rbgjs cb oj eb`gbtrçj bufomcmjlj. bufomcmjlj. Bo jxm`gj cb ojs pjrjobojs t`gjc` cb oj `krj cb Ah`l Yojydjmr,^;; Yojydjmr, ^;;WW cmfb1 ‟Cjcj ulj rbftj   o y ul pult` Y  bxtbrm`r j booj, hjy ulj y sò` ulj rbftj   g bl bo pojl` cb   Y   y   o qub pjsj p`r  Y Y  y l` sb blfubltrj f`l   o.‗  Oj cucj pojltbjcj bs °Y`rqub ojs rbftjs o y g l` sb pubcbl blf`ltrjr lm smqumbrj bl bo bspjfm` cmstjltb0, Bst` l` pjrbfb bvmcbltb, lm f`lvmlfbltb. Jo p`lbrsb bl cucj oj bxmstblfmj cb ojs pjrjobojs, joeul`s gjtbgêtmf`s cbo smeo` XTMMM mltbltjr`l cbg`strjr bo p`stuojc` cb ojs pjrjobojs cbcufmílcò` cb o`s `tr`s fujtr` p`stuojc`s y cb ojs l`fm`lbs f`gulbs cb Bufomcbs y bl bstb fjs` yj l` tblcrmj cmsfusmöl cmsfusmöl bo jxm`gj jxm`gj cb ojs pjrjobojs. pjrjobojs. Rl` cb o`s mltblt`s mltblt`s gês s`krbsjombltbs s`krbsjombl tbs dub bo cb Vjffhbrm Vjffhbrm jo jpomfjr bo gít`c` mlcmrbft` cb cbg`strjfmöl. cbg`strjfmöl. Njro Drmbcrm Drmbcrmfh fh Ejuss f`lfouyö qub o`s fujtr` p`stuojc`s y ojs l`fm`lbs f`gulbs cb Bufomcbs l` prbsfrmkmjl oj d`rgj cbo jxm`gj cb ojs pjrjobojs, gês jñl, Ejuss frbj ulj lubvj eb`gbtrçj usjlc` ulj jxm`gj cb ojs pjrjobojs cmdbrbltb jo cb Bufomcbs. Vup`lmblc` qub p`r ul pult` cjc` p`cçjl pjsjr gjs cb ulj rbftj pjrjoboj, j ulj rbftj cjcj. Bstj lubvj eb`gbtrçj sb cbl`gmlj eb`gbtrçj l` bufomcmjlj. Oj `krj cb Ejuss sb f`l`fb cbspuís cb su gubrtb. Oj frbjfmöl cb ojs eb`gbtrçjs l` bufomcmjljs sb jtrmkuyb j Lmfòjm O`kjfhbvsny (:5=6 - :824) y Ajl`s Kòyjm (:89; - :849). Oj mcbj prmlfmpjo dub jc`ptjr ul jxm`gj cb ojs pjrjobojs cmdbrbltb jo cb Bufomcbs, boo`s jsugmbr`l qub hjkmj c`s omlbjs rbftjs g y l qub pjsjkjl p`r Y  y brjl pjrjobojs j oj rbftj cjcj o. Fujoqumbr omlbj qub pjsj p`r Y  y bstê cbltr` cbo êleuo` ∩G L Y  l` bs pjrjoboj j o. Fujoqumbr omlbj qub pjsj p`r Y  y bstê cbltr` cbo êleuo` ∩L Y [ bs pjrjoboj j o, p`r o` tjlt` hjy ul lñgbr` ml﬊lmt` cb pjrjobojs. pjrjo bojs. Ejuss, O`kjfhbvsny O`kjfhbvsny y Kòyjm cmdbrblfmjr`l cmdbrblfmjr`l bltrb bo erup` cb pjrjobojs pjrjobojs j ojs rbftjs pjrjobojs pjrjobojs (g y l) y ojs omlbjs qub l` sb mltbrsbfjl (rbftjs f`g` q )).. O`s tb`rbgjs cb bstj lubvj eb`gbtrçj sb f`lsbrvjl bl oj lubvj eb`gbtrçj bxfbpt` o`s qub sb cbrmvjl cbo qumlt` p`stuojc` cb Bufomcbs. Joeul`s cb o`s tb`rbgjs qub cm﬊brbl cb oj eb`gbtrçj bufomcmjlj s`l1

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JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

:9

:. Cjc`s bo pult` Y  y oj rbftj o. Hjy c`s rbftjs g y l qub pjsjl p`r Y  (p`r bo lubv` jxm`gj cb ojs pjrjobojs). pjrjo bojs). Vm trjzjg`s ulj pbrpblcmfu p brpblcmfuojr ojr p cb Y   j o, bo êleuo` ∩J qub sb d`rgj bltrb p y l yj l` bs rbft`. Bo êleuo` ∩J bs jeuc` y cbpblcb cb oj o`lemtuc cb p. Fujlt` gês f`rtj bs p gjy`r bs bo êleuo` ∩J y fujlt` p sb jpr`xmgj j fbr` bo êleuo` ∩J cb jpr`xmgj j =9 . ◤

;. Oj sugj cb o`s êleuo`s cb ul trmêleuo` trmêleuo` bs smbgprb gbl`r qub :89 y vjrmj f`l bo êrbj cbo trmêleuo`. ◤

◤

Fujlt` gbl`r bs bo êrbj cbo trmêleuo`, oj sugj cb o`s êleuo`s sb jpr`xmgj j :89 . 6. Vm o`s trbs êleuo`s cb ul trmêleuo` trmêleuo` s`l meujobs j o`s trbs êleuo`s cb `tr` trmêleuo` rbspbftm rbspbftmvvjgbltb, jgbltb, o`s trmêleuo`s s`l f`lerubltbs. Eb`reb Drmbcrmfh Kbrlhjrc [mbgjll (:8;4 - :844) hmz` joeuljs jf`tjfm`lbs jo sbeulc` p`stuojc` cb Bufomcbs. [mbgjll `ksbrvö qub ulj rbftj l` bs cb bxtblsm`l ml﬊lmtj sml` qub lulfj tbrgmlj, gjrfjlc` ulj cmdbrblfmj cmdbrblfmj bltrb o`lemtuc mltbrgmljko mltbrgmljkobb b ml﬊lmtj. ml﬊lmtj. Y`r o` jltbrm`r jltbrm`r oj pr`pubstj pr`pubstj cb [mbgjll [mbgjll s`krb bo sbeulc` p`stuojc` cb Bufomcbs suembrb qub ulj rbftj bs momgmtjcj, cjlc` `rmebl jo cbsjrròo` cb oj eb`gbtrçj bsdírmfj. F`l rbspbft` jo jxm`gj cb ojs pjrjobojs cb [mbgjll pojltbj qub l` bxmstb ulj rbftj pjrjoboj j `trj y qub cjcjs c`s rbftjs bstjs tbrgmljl p`r blf`ltrjrsb. Joeul`s tb`rbgjs qub cm﬊brbl cb oj eb`gbtrçj cb Bufomcbs s`l1 :. S`cj omlbj rbftj tmblb o`lemtuc ml﬊lmtj. ;. Oj sugj cb o`s êleuo`s cb ul trmêleuo` bs smbgprb gjy`r qub :89 y bstj sugj vjrmj f`l bo êrbj cbo trmêleuo`, fujlc` bo êrbj tmblcb j fbr` oj sugj cb o`s êleuo`s sb jpr`xmgj j :89 . ◤

◤

6. C`s trmêleuo`s trmêleuo`s sbgbajltbs l` s`l lbfbsjrmjgbltb lbfbsjrmjgbltb f`lerubltbs. f`lerubltbs.

:.2. :.2.

Eb Eb`g `gbt btrç rçj j cb Hmokb Hmokbrt rt

J ﬊ljobs cbo smeo` XMX bo gjtbgêtmf` jobgêl Cjvmc Hmokbrt (:84;-:=36), f`l kjsb bl ojs dubltbs ermbejs cb Bufomcbs, pukomfj su `krj ‟Dulcjgblt`s cb Eb`gbtrçj‗ ^:6W, ^:6W, bl oj qub d`rguoj sus prmlfmpm`s cb jxm`gjtmzjfm jxm`g jtmzjfmöl öl cb oj eb`gbtrçj. F`gmblzj F`gmblzj f`l tírgml`s tírgml`s l` cb﬊lmc`s1 cb﬊lmc`s1 pult`, rbftj, rbftj, pojl`. Ojs fmlf` rbojfm`lbs mlcb﬊lmcjs bstjr bl, bstjr bltr bltrb, b, sbr f`ler f`lerubltb ubltb,, sbr pjrjobo` pjrjobo`,, sbr f`ltmlu f`ltmlu`. `. Hmokbrth cbg`strö, f`ljr`l sus jxm`gjs jxm`g js qub p`cçj cbg`strjr o`s tb`rbgjs dulcjgbltj dulcjg bltjobs obsp`cçj cb Bufomcbs. Bufomcb s. @tr`s gjtbgêtmf`s gjtbgê tmf`s. f`gpobt f`gpobtjr`l bstj tjrbj cbg`strjlc` cbg`strj lc` qub t`cj oj eb`gbtrçj bufoçcmjlj cbrmvjrsb cbrmvjrsb cb bst`s jxm`gjs. jxm`gjs Ybr` bo pr`kobgj cb bsj íp`fj sb rbdbrçj j oj f`lsmstblfmj cb o`s jxm`gjs. Y`mlfjrí bl :8=8, j﬊rgö qub p`cçj frbbr bl oj f`lsmstblfmj cb ulj bstrufturj dulcjgbltjcj jxm`gjtmfjgbltb sm brj p`smkob cjr cb booj ulj mltbrprbtjfmöl jrmtgítmfj.^3W jrmtgítmfj.^3W Cbspuís cb hjkbr cbg`strjc` oj f`lsmstblfmj cb su smstbgj eb`gítrmf` smrvmílc`sb cb ul g`cbo` cb su smstbgj, f`lstrumc` bl bo mltbrm`r cb oj jrmtgítmfj, cbg`strö oj mlcbpblcblfmj cb bst`s jxm`gjs, bs cbfmr sjfrm﬊fjr ul` cb o`s fmlf` erup`s f`lsbrvjlc` o`s `tr`s fujtr` y `ktblbr fjcj vbz ulj eb`gbtrçj f`hbrbltb. f`hbrbl tb. Y`r babgpo` babgpo` jo suprm suprmgmr gmr bo p`stuoj p `stuojc` c` cb ojs pjrjobojs pjrjobojs sb `ktmbl `ktmblbb oj eb`gbtrçj eb`gbtrçj l` bufoçcbj cb O`kjfhbvsnm, jo suprmgmr bo jxm`gj cb Jrqumgbcbs mgpomfj oj bxmstblfmj cb oj eb`gbtrçj l` jrqumgbcmjlj. Bl bo omkr` ‟Dulcjgblt`s cb oj eb`gbtrçj‗ ^:6W, ^:6W, Hmokbrt d`rguoj ;: sup`smfm`lbs, f`l`fmcjs f`g` o`s jxm`gjs cb Hmokbrt. Bstêl cmstrmkumcjs bl fmlf` fjtbe`rçjs1 pbrtblblfmj, `rcbl, meujocjc ` f`lerublfmj, pjrjobomsg` y f`ltmlumcjc. O`s jxm`gjs cb mlfmcblfmj cjl mld`rgjfmöl cb fög` sb eblbrjl ojs rbftjs, o`s pojl`ss y bo bspjfm`, ojs f`lcmfm`lbs pojl` f`lcmfm`lbs cb bxmstblfmj bxmstblfmj y ojs rbojfm`lbs rbojfm`lbs bltrb bst`s. O`s jxm`gjs cb `rcbl cbtbrgmljl ojs p`smfm`lbs cb pult`s bl ulj rbftj, oj prò`lejfmöl cb ulj rbftj mlcb﬊lmcjgbltb y oj bxmstblfmj cb pult`s mltbrm`rbs y bxtbrm`rbs cb ul sbegblt`. O`s jxm`gjs cb f`lerublfmj bstjkobfbl f`lcmfm`lbs cb

FJYÇSRO@ :. :.

JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

::

meujocjc bltrb ﬊eurjs eb`gítrmfjs, meujocjc eb`gítrmfjs, sbegblt`s sbegblt`s y êleuo`s. êleuo`s. Bo jxm`gj cb pjrjobomsg` pjrjobomsg`,, bqumvjob bqumvjob jo qumlt` qumlt` p`stuojc` cb Bufomcbs cj `rmebl j cmvbrsjs tb`rçjs f`g` oj sbgbajlzj cb ﬊eurjs, êrbjs cb pòçe`l`s y f`gpjrjfmöl cb ﬊eurjs eb`gítrmfjs. O`s jxm`gjs cb f`lerublfmj, pjrjobomsg` y f`ltmlumcjc, f`lsmeljc`s bl su omkr` ‟Dulcjgblt`s cb oj Eb`gbtrçj‗ ^:6W ^ :6W s`l1 s`l1

Jxm`gjs cb f`lerublfmj1 O`s jxm`gjs cb bstb erup` cb﬊lbl bo f`lfbpt` cb f`lerublfmj y f`l ístb, tjgkmíl bo cb g`vmgmblt`.

Jxm`gj :.:. Vm J, K s`l c`s pult`s cb oj rbftj j y jcbgjs bs J `tr` pult` cb oj gmsgj ` cmstmltj rbftj j , pubcb blf`ltrjrsb smbgprb s`krb ul` cb o`s ojc`s cb j , cbtbrgmljc`s p`r J , ul sò` pult` K tjo, qub o`s sbegblt`s JK y J K sbjl f`lerubltbs ` meujobs. O` qub sb bxprbsj f`l smel`s1 JK ∿ 7 J K . 

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Jxm`gj :.;. Vm o`s sbegblt`s J K y J K s`l f`lerubltbs f`l bo gmsg` sbegblt` JK , tjgkmíl bo sbegblt` J K bs f`lerubltb f`l bo J K . Cmfh` Cmfh` krbvbgbltb1 krbvbgbltb1 sm c`s sbegblt`s s`l f`lerubltbs f`lerubltbs f`l ul tbrfbr`, s`l f`lerubltbs bltrb sç. 

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∿JK y J K ∿ Vm J K 7 7 JK , blt`lfbs J K ∿ 7J K . 

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Jxm`gj :.6. Vbjl JK y KF  c`s sbegblt`s cb oj rbftj j sml pult`s f`gñlbs y, p`r `trj pjrtb J K y K F c`s sbegblt`s s`krb oj gmsgj rbftj j ` s`krb `trj cmstmltj j , pbr` bl t`c` fjs` sml pult`s f`gñlbs1 sm blt`lfbs JK ∿ 7J F . 7K F , smbgprb sb vbrm﬊fj JF   ∿ 7J K y KF   ∿ 

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Jxm`gj :.3. Cjc`s ul êleuo` ∩(h, n) bl ul pojl` κ, ulj rbftj j bl ul pojl` κ y ulj cb ojs rbem`lbs cb κ cbtbrgm cbtbrgmljcjs ljcjs p`r j > rbprbsbltbg`s p`r h ulj sbgmrrbftj cb j qub pjrtb cb @ . êleuo` ∩(h, n ) bs f`lerubltb Bxmstb blt`lfbs, bl bo pojl` κ ulj y sò` ulj sbgmrrbftj n tjo, qub bo êleuo` ` meujo jo ∩(h , n ), y j oj vbz t`c`s o`s pult`s mltbrm`rm`rbs cbo êleuo` ∩(h , n ) bstêl smtujc`s bl oj rbemöl cjcj f`l rbspbft` j j . Vmgköomfjgbltb1 ∩(h, n ) ∿ 7 ∩(h , n ). S`c` êleuo` bs f`lerubltb ∿ f`lsme` gmsg`.∩(h, n ) 7 ∩(h, n ). 

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Jxm`gj :.2. Vm c`s c`s trmêleuo`s ∄JKF   y ∄J K F vbrm﬊fjl ojs f`lerublfmjs JK ∿ 7 J K , ∿ ∿ ∿ JF 7 J F , ∩KJF 7 ∩K J F , tjgkmíl qubcj sjtmsdbfhj smbgprb oj f`lerublfmj ∩JKF 7 ∩J K F y ∩JFK ∿ 7 ∩J F K . 

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Jxm`gjs cb ojs pjrjobojs1 Jxm`gj :.4. Vbj κ ul pojl` fujoqumbrj, j j ulj rbftj fujoqumbrj cb κ y J ul pult` cb κ bxtbrm`r j j y cbspuís bl κ ulj rbftj k p`r J , cb tjo subrtb qub oj rbftj f f`rtb j ojs j y k kja` o`s êleuo`s f`rrbsp`lcmbl f`rrbs p`lcmbltbs tbs meujobs. Vb cbcufb dêfmogbltb dêfmogbltb cbo tb`rbgj cbo êleuo` êleuo` bxtbrm`r bxtbrm`r: , qub ojs rbftjs j y k l` tmblbl lmleñl pult` bl f`gñl, bst` bs, bl ul pojl` p`r ul pult` J bxtbrm`r j ulj rbftj j sb pubcb trjzjr smbgprb ulj rbftj, oj fujo l` f`rtj j oj j. Y`r o` tjlt` bo jxm`gj cb ojs pjrjobojs sb blulfmj f`g`1 Vbj j ulj rbftj fujoqumbrj y J ul pult` bxtbrm`r j j1 bl bo pojl` cbtbrgmljc` p`r j y J bxmstb j o` gês ulj rbftj qub pjsj p`r J y l` f`rtj j oj j. Jxm`gjs cb f`ltmlumcjc1 Jxm`gj :.5. Jxm`gj Jxm`gj cb oj gbcmcj ` jxm`gj cb Jrquçgbcbs. Jrquçgbcbs. Vmblc` JK y F C sbegblt`s fujobsqumbrj, bxmstb smbgprb s`krb oj rbftj JK ul lñgbr` cb pult`s J : , J; , J 6 ,....,Jl , cb g`c` qub o`s sbegblt`s JJ: , J: J; , J; J6 ,...,Jl : Jl , s`l f`lerubltbs f`l bo FC , y bo pult` K qubcj bltrb J ∛

y Jl . :

Rl êleuo` bxtbrm`r cb ul trmêleuo` bs gjy`r qub fjcj ul` cb o`s c`s êleuo`s cbo trmêleuo` l` jcyjfbltbs j ío

FJYÇSRO@ :. :.

JLSBFBCBLS JLSBFBCBLSBV BV HMVSÖ[MF@V CB O@V F@LFBY F@LFBYS@V S@V CB VBGBAJL VBGBAJLQJ QJ ] F@LE[RB F@LE[RBLFMJ. LFMJ.

:;

Jxm`gj :.8. Jxm`gj cb oj poblmtuc omlbjo. O`s pult`s cb ulj rbftj d`rgjl ul smstbgj bo fujo l` bs susfbptmkob cb jgpomjfmöl joeulj, kja` oj f`lcmfmöl cb f`lsbrvjr oj `rcbljfmöl omlbjo, bo prmgbr jxm`gj cb f`lerublfmj y bo jxm`gj cb Jrquçgbcbs. L` bs p`smkob j bstb smstbgj cb pult`s jújcmr `tr`s pult`s cb j, cb g`c` qub bl bo smstbgj qub sb `ktmblb p`r f`gp`smfmöl t`c`s o`s jxm`gjs f`lstrumc`s qubcbl sjtmsdbfh`s. Jo rbjomzjr oj f`lstruffmöl cbo gjrf` hmstörmf` cb o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj, p`cbg`s rbsjotjr qub bo trjkja` cb Shjobs f`ltrmkuyö j oj vmsujomzjfmöl cb oj tb`rmj cb oj sbgbajlzj y Buc`x` cb Flmc`s hmz` ul erjl jp`rtb j oj tb`rçj cb ojs pr`p`rfm`lbs, qub s`l kjsb dulcjgbltjo pjrj bo bstucm` cb o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj. f`lerublfmj. Ybr` Bufomc Bufomcbs bs `rejlmzö y smstbgjtmzö smstbgjtmzö t`c`s o`s trjkja`s qub sb hjkçjl hbfh` s`krb eb`gbtrmj, bl su `krj cb O`s Bobgblt`s c`lcb sb blfubltrjl ojs cb﬊lmfm`lbs, jxm`gjs y tb`rbgjs dulcjgbltjobs pjrj bo bstucm` cb oj eb`gbtrçj pojlj> bl bo omkr` T cbsjrròoj t`cj oj tb`rçj rbojfm`ljcj f`l ojs rjz`lbs, pr`p`rfm`lbs y bl bo omkr` TM oj tb`rmj buxmcmjlj s`krb trmêleuo`s y pòçe`l`s sbgbajltbs. Ybr` jú`s gês tjrcb cbkmc` jo suremgmblt` cb ojs eb`gbtrçjs l` bufomcmjljs, sb eblbrjl joeul`s tb`rbgjs qub cm﬊brbl cb oj eb`gbtrçj bufomcmjlj pjrtmfuojrgbltb f`l rbojfmöl j oj sbgbajlzj y oj f`lerublfmj, sb bstjkobfb1 ‟Vm o`s trbs êleuo`s cb ul trmêleuo` s`l meujobs j o`s trbs êleuo`s cb `tr` trmêleuo` rbspbftmvjgbltb blt`lfbs o`s trmêleuo`s s`l f`lerubltbs." , jqum sb bstjkobfb ulj prmgbrj cb﬊lmfmöl cbo f`lfbpt` cb f`lerublfmj pjrtmblc` cb oj sbgbajlzj cb trmêleuo`s. Eb`reb [mbgjll hmz` ul jp`rtb tjgkmbl mgp`rtjll` s`l tb jo bstucm` cb bst`s f`lfbpt`s qubg`gblt` bs ‟C`s trmêleuo`s jquç fjkb l`tjr qub yj cbscb bsb sb bgpmbzjsbgbajltbs j bstjkobfbr ulj lbfbsjrmjgbltb cmdbrblfmj bltrbf`lerubltbs," o` qub bs sbr sbgbajltb sbgbajl tb y sbr f`lerubltb. f`lerubltb. Ybr` Cjvmc Cjvmc Hmokbrth bl su `krj ‟Dulcjgbl ‟Dulcjgblt`s t`s cb eb`gbtrçj,‗ eb`gbtrçj,‗ bstjkobfb bstjkobfb oj rbojfmöl Vbr f`lerubltb  y y cbsjr cbsjrròoj ròoj o`s jxm`gjs jxm`gjs cb Hmokbrth bl c`lcb sb blfubltrjl blfubltrjl o`s jxm`gjs cb f`lerublfmj qub bstjkobfbl f`lcmfm`lbs cb meujocjc bltrb ﬊eurjs y bo jxm`gj cb ojs pjrjobojs cj `rmebl j oj tb`rçj cb oj sbgbajlzj sbgbajlzj cb ﬊eurjs. ﬊eurjs. F`g` p`cbg`s `ksbrvjr `ksbrvjr bs mgp`rtj mgp`rtjltb ltb pjrj bo bstucm` bstucm` cb oj eb`gbtrçj bstjkobfbr oj cmdbrblfmj bltrb oj sbgbajlzj y oj f`lerublfmj, yj qub l` smelm﬊fjl o` gmsg` y fjcj ul` tmblb ul cbsjrròo` jxm`gêtmf` cmdbrbltb.

;.Jspbft`s ;.Jspbft `s cms cmsfmp fmpoml omljrb jrbs1 s1 F`ler F`lerubl ublfmj fmj y Vbg Vbgbb ajlzj Bl bstb fjpçtuo` sb hjrê ul cbsjrròo` d`rgjo cb oj f`lerublfmj y oj sbgbajlzj, bstjkobfmblc` cmdbrblfmjs y rbojfm`lbs bltrb boo`s. Jcbgês, bstucmjrbg`s o`s p`stuojc`s, tb`rbgjs y pr`pmbcjcbs lbfbsjrm`s pjrj su bstucm`` bl oj eb`gbtrçj. bstucm eb`gbtrçj. Yjrj Yjrj bstb ﬊l t`gjrbg`s t`gjrbg`s f`g` jp`y` jp`y` kmkomèrê﬊f` kmkomèrê﬊f` bo tbxt` Eb`gbtrmj cbsjrròo` cbsjrròo` jxm`gjtmf` p`r Jlj Kbrblmfb Eubrrbr` ^:;W ^:;W.. Bstb tbxt` bs cb fjrêftbr d`rgjo d`rgjo,, tmblb ul bld`qub jxm`gjtmf` jxm`gjtmf` y sb kjsj bl o`s Dulcjgblt`s cb Hmokbrt ^:6W ^:6W..

;.:. ;. :.

F`le F`lerrubl blf fmj

Cb gjlbrj mltumtmvj, cmrbg`s qub c`s sbegblt`s s`l f`lerubltbs sm jo ‟g`vbr‗ ul` cb boo`s, r`têlcò` s`krb ul` cb sus bxtrbg`s y trjsojcêlcò`, bs p`smkob hjfbro` f`mlfmcmr f`l bo `tr` sbegblt`. Vmeumblc` f`l bsjs mcbjs mltumtmvjs cmrbg`s qub c`s ﬊eurjs eb`gítrmfjs pojljs s`l f`lerubltbs, sm ulj cb boojs sb pubcb ‟g`vbr‗1 r`têlcòj  s`krb ul pult`, rb﬋baêlcòj  s`krb ul bab y trjsojcêlcòj , cb tjo gjlbrj qub f`mlfmcj f`l oj `trj. Y`r babgpo`, babgpo`, c`s trmêleuo`s trmêleuo`s bqumoêtbr`s bqumoêtbr`s fuy`s fuy`s ojc`s tblejl oj gmsgj o`lemtuc s`l f`lerubltbs, c`s fçrfuo`s cbo gmsg` rjcm` s`l f`lerubltbs, c`s fujcrjc`s fuy`s ojc`s cb meujo tjgjú` s`l f`lerubltbs.^:8W f`lerubltbs.^:8W Bl ojs sbffm`lbs qub smeubl bstucmjrbg`s oj f`lerublfmj bltrb sbegblt`s, êleuo`s, trmêleuo`s y bltrb pòçe`l`s. pòçe`l `s. Tbrbg`s joeul`s rbsuotjc`s rbsuotjc`s qub l`s pbrgmtbl f`gprblcbr f`gprblcbr bo f`lfbpt` f`lfbpt` cb f`lerublfmj. ;.:.:. ;.: .:.

F`leru F`lerublf blfmj mj bltrb bltrb sb sbegb egblt lt`s `s

Oj f`lerublfmj bs trjtjcj p`r Hmokbrt cb d`rgj jxmögjtmfj. Bl oj eb`gbtrçj cb Hmokbrt l` sb f`lsmcbrjl o`s lñgbr`s lñgbr`s rbjobs y p`r p `r o` tjlt` tjlt` rbsuotj cmdçfmo hjkojr cb gbcmcjs. gbcmcjs. Vml bgkjre` bgkjre` mltumtmvjgbl mltumtmvjgbltb tb p`cbg`s JK y FC sus cbfmr sbjl JK y F Cf`lerubltbs c`s sbegblt`s, rbspbftmvjs o`lemtucbs. rbspbftmvjs o`lemtucbs. Vm JK 7 F C, blt`lfbs o`s sbegblt`s sb oojgjl y sb bsfrmkb JK ∿ 7 F C.

Dmeurjj ;.:1 F`lerublfmj Dmeur F`lerublfmj bltrb Vbegblt`s O`s jxm`gjs cb Hmokbrt, :.:,:.; :.:,:.; y :.6, :.6, qub sb bxpusmbr`l bo bo fjpçtuo` jltbrm`r, bstjkobfbl qub oj f`lerublfmj bltrb sbegblt`s bs bl rbjomcjc ulj rbojfmöl cb bqumvjoblfmj, o` fujo sb ml﬊brb cb o`s smeumbltbs tb`rbgjs1

Sb`rbgj ;.:. Oj f`lerublfmj cb c`s sbegblt`s bs rb﬋bxmvj1 S`c` sbegblt` bs f`lerubltb f`l sç gmsg`, ∿ bs cbfmr   JK 7 JK . Sb`rbgj ;.;. Oj f`ler f`lerublfm ublfmj j cb sbegblt` sbegblt`ss bs smgít smgítrmfj1 rmfj1 Vm ul sbegblt sbegblt` `   JK bs f`lerubltb f`l `tr` sbegblt` J K , ( JK JK ∿ 7 J K ) blt`lfbs   J K ∿ 7 JK . 

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:6

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

:3

Sb`rbgj ;.6. Oj f`lerublfmj f`lerublfmj cb sbegblt`s sbegblt`s bs trjlsmtmv trjlsmtmvj. j. Vm ul sbegblt` sbegblt`   JK ∿ 7 J K y j oj vbz bstb 

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sbegblt` bs f`lerubltb f`l `tr`   J K ∿ 7 J K , sb fugpob qub   JK ∿ 7J K . 

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Cb﬊lmfmöl ;.:. Oj o`lemtuc cb ul sbegblt` bs oj fojsb cb bqumvjoblfmj bqumvjoblfmj cb o`s sbegblt`s sbegblt`s f`lerubltbs f`lerubltbs f`l ío. Oj o`lemtuc cb ul sbegblt` JK sb smgkòmzj o`le (JK ). Jsm qub oè (JK ) 7 o`le (F C) smelm﬊fj JK ∿ 7 JF .

J pjrtmr cb bst`, sb cbcufbl cmrbftjgbltb ojs smeumbltbs pr`pmbcjcbs cb oj o`lemtuc cb sbegblt`s1

:. JK 7 K J. ;. JK 7 J K mgpomfj qub J K 7 JK . 

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6. JK 7 J K y J K 7 J K blt`lfbs JK 7 J K . 

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3. Vm F  bs ul pult` cbo sbegblt` JK y F bs ul pult` bl bo sbegblt` J K y sm JK 7 J K y jxm`gj :.6,, tblbg`s qub JF   7 J F . Bs cbfmr JF   7 JK + K KF   7 K F , blt`lfbs p`r bo jxm`gj :.6 KF F   7 

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J K + K F 7 J F 

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Fjkb rbsjotjr qub o`s jxm`ljs cb f`ltmlumcjc cb Jrqumgbcbs :.5 Jrqumgbcbs :.5 y y cb Fjlt`r :.8 Fjlt`r :.8,, dulcjgbltjl oj gbcmcj cb sbegblt`s, sbegblt`s, y p`lbl bl f`rrbsp`lcblfm f`rrbsp`lcblfmjj fjcj sbegblt` f`l ul lñgbr` lñgbr` p`smtmv` oojgjc` oojgjc` oj gbcmcj gbcmcj.. Oj gbcmcj cbkb sjtmsdjfbr fmbrtjs pr`pmbcjcbs rbojfm`ljcjs f`l oj f`lerublfmj cb sbegblt`s qub s`l1

:. J sbegblt`s f`lerubltbs f`rrbsp`lcbl lñgbr`s meujobs. ;. Vm K bs ul pult` mltbrm`r cbo sbegblt` JF y j o`s sbegblt`s JK y K F  ob ob f`rrbsp`lcbl o`s lñgbr`s ob f`rrbsp`lcb ul lñgbr` j + k. j y k rbspbftmvjgbltb, blt`lfbs bo sbegblt` JF  ob 6. J joeñl sbegblt` @ @ ob f`rrbsp`lcb oj ulmcjc. 

Bo lñgbr` rbjo p`smtmv` qub ob f`rrbsp`lcb j fjcj sbegblt` bl oj d`rgj jltbs mlcmfjcj sb oojgj ‟gbcmcj cbo sbegblt`.‗ Vb mcbltm﬊fjrê mcbltm﬊fjrê oj gbcmcj gbcmcj cb ul sbegblt` f`l su o`lemtuc. o`lemtuc.

;.:. ;.:.;. ;.

F`le F`leru rubl blfm fmj j cb êleu êleuo` o`ss

Cb d`rgj jlêoèj j oj f`lerublfmj cb sbegblt`s, mltumtmtjgbltb p`cbg`s cbfmr qub c`s êleuo`s s`l f`lerubltbs f`ler ubltbs sm tmblbl oj gmsgj jgpomtuc. jgpomtuc. Cb d`rgj jxm`gêtmfj, jxm`gêtmfj, Hmokbrt bl bo jxm`gj jxm`gj :.3 bstjkobfb :.3 bstjkobfb oj bxmstblfmj cb êleuo`s f`lerubltbs y bl bo jxm`gj :.2 jxm`gj :.2 rbojfm`lj rbojfm`lj oj f`lerublfmj cb êleuo`s f`l oj f`lerublfmj cb sbegblt`s. sbegbl t`s.

Dmeurjj ;.;1 F`lerublfmj Dmeur F`lerublfmj bltrb Êleuo`s

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

:2

Y`r o` tjlt` sb pubcb rbsugmr bo prmgbr jxm`gj cb f`lerublfmj cb êleuo`s f`g`1 Fjcj êleuo` pubcb sbr jpomfjc` cb gjlbrj ñlmfj bl ul pojl` cjc`, j ul ojc` prb﬊ajc` cb ulj sbgmrbftj cjcj.^:; cjcj. ^:;WW

Jxm`gj ;.:. Vm J J,, K,F  s`l s`l trbs pult`s qub l` pbrtblbfbl p brtblbfbl j ulj gmsgj rbftj y J , K , F s`l `tr`s trbs pult`s l` pbrtblbfmbltbs j ulj gmsgj rbftj y sm JK ∿ 7 J K , JF   ∿ 7 J F y ∩KJF   ∿ 7 ∩K J F blt`lfbs 

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∩JKF  ∿ 7 ∩J

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K F .

Dmeurj ;.61 F`lerublfmj bltrb Êleuo`s cb 6 pult`s Rl rbsuotjc` qub sb cbsprblcb cb bst`s jxm`gjs bs1

Sb`rbgj ;.3. Vm o`s êleuo`s ∩J@K y ∩J @ K s`l f`lerubltbs j ul tbrfbr` ∩J @ K , blt`lfbs ∩J@K 

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bs f`lerubltb f`l bo êleuo` ∩J @ K , bs cbfmr c`s êleuo`s f`lerubltbs j ul tbrfbr` s`l f`lerubltbs bltrb sç.

Dmeurj ;.31 Srjlsmtmvmcjc cb oj F`lerublfmj Cb gjlbrj smgmojr j oj bstucmjcj bl o`s sbegblt`s, cb o`s jxm`gjs cb Hmokbrt sb f`lfouyb qub oj f`lerublfmj bltrb êleuo`s bs ulj rbojfmöl cb bqumvjoblfmj. Oj jgpomtuc cb ul êleuo` bs oj fojsb cb bqumvjoblfmj cb t`c`s o`s êleuo`s f`lerubltbs f`l ío. Cb d`rgj jlêoè jlê oèjj j oj cjcj pjrj pjrj sbegbl sbegblt`s t`s sb cbtbrgm cbtbrgmlj lj oj gbcmcj gbcmcj cb o`s êleuo`s êleuo`s.. Bstj gbcmcj gbcmcj mcbltm﬊f mcbltm﬊fjj oj jgpomtuc cb ul êleuo` f`l su gbcmcj jleuojr, cbkb sjtmsdjfbr fmbrtjs pr`pmbcjcbs rbojfm`ljcjs f`l oj f`lerublfmj cb êleuo`s qub s`l1

:. J êleuo` f`lerubltbs f`rrbsp`lcbl lñgbr`s rbjobs meujobs. ;. Vm oj sbgmrbftj o bstê bl bo mltbrm`r cbo êleuo` ∩(h, n ) y tmblb p`r `rmebl bo vírtmfb cbo êleuo`, y sm j oj jgpomtuc cb o`s êleuo`s ∩(h, o) y ∩(o, n ) ob f`rrbsp`lcbl o`s lñgbr`s j y k rbspbftmvjgbltb, blt`lfbs oj gbcmcj cbo êleuo` ∩(h, n) bs bo lñgbr` rbjo j + k. 6. J joeñl êleuo` ∩(t, o) ob f`rrbsp`lcb ulj ulmcjc cb gbcmcj jleuojr. Bo lñgbr` qub ob f`rrbsp`lcb j fjcj êleuo` sb oojgj gbcmcj cb bsb êleuo` y oj gbcmcj cbo êleuo` ∩(t, o) sb oojgj ulmcjc jleuojr.^:;W jleuojr.^:;W

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

:4

Oj gbcmcj cb o`s êleuo`s bstê bstrbfhjgbltb rbojfm`ljc`s f`l oj o`lemtuc cb oj fmrfuldbrblfmj, c`lcb oj o`lemtuc cb oj fmrfuldbrblfmj cb rjcm` r bs meujo j c`s vbfbs oj gbcmcj cb su rjcm` p`r bo lñgbr` ω bo fujo bs ul lñgbr` mrrjfm`ljo. F   7 ;ωr. ω bstê tjgkmbl rbojfm`ljc` Bo lñgbr` rbojfm`ljc` f`l cb êleuo`s. Yubst` qub ω bstê cmrbftjgbltb rbojfm`ljc` j oj o`lemtuc cb oj fmrfuldbrblfmj y j oj oj gbcmcj vbz oj fmrfuldbrblfmj bs bo gjy`r jrf` cb booj, y pubst` qub oj gbcmcj cb t`c` jrf` bl oj fmrfuldbrblfmj bs oj gbcmcj cbo êleuo` fbltrjo qub suktmblcb, sb bstjkobfb ulj rbojfmöl bltrb oj o`lemtuc cb oj fmrfuldbrblfmj y oj gbcmcj cbo êleuo` fbltrjo f`gpobt`.

Erjc`s sbxjebsmgjobs Jo mlsfrmkmr ul hbxêe`l` rbeuojr bl ul fmrfuldbrblfmj sb cbtbrgmljl 4 trmêleuo`s bqumoêtbr`s, y 4 êleuo`s fbltrjobs fbltr jobs meujobs meujobs j oj sbxtj pjrtb cb oj fmrfuldbrblfm fmrfuldbrblfmj. j. Blt`lfbs Blt`lfbs sb cb﬊lb ul erjc` sbxjebsmgjo sbxjebsmgjo f`g` oj ulmcjc cb gbcmcj cb êleuo`s bl oj fujo, jo êleuo` fbltrjo `ktblmc` jo cmvmcmr oj fmrfuldbrblfmj bl 4 jrf`s f`lerubltbs ob jsmeljg`s ulj jgpomtuc cb 49 erjc`s sbxjebsmgjobs.Rl gmlut` sb cb﬊lb f`g` oj sbsbltjvj pjrtb cb ul erjc` y lul sbeulc` f`g` oj sbsbltjvj pjrtb cb ul gmlut`. O`s erjc`s sbxjebsmgjobs sb l`tjl p`r gbcm` cb . F`l kjsb j o` jltbrm`r sb bstjkobfb1 ◤

Oj fmrfuldbrblfmj tmblb ulj jgpomtuc cb 649 sbxjebsmgjobs, ul êleuo` oojl` gmcb :89 erjc`s sbxjebsmgjobs, ul êleuo` rbft` gmcb =9 . Rl êleuo` êleuo` jeuc` jeuc` θ bs jeuc` sm su gbcmcj bl erjc`s sbxjebsmgjobs bstê bltrb 9 ? θ ? =9 . Rl êleu êleuo` o` λ   bs `ktus` sm su gbcmcj bl erjc`s sbxjebsmgjobs bstê bltrb 7 :89 y c`s êleuo`s θ y λ   s`l =9 ? λ ? :89 . C`s êleuo`s θ y λ  s`l supobgbltjrm`s sm su sugj bs + λ  7 f`gpobgbltjrm`s sm su sugj bs θ + λ  7 7 =9 . ◤

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;.:.6. ;.: .6.

F`leru F`lerublf blfmj mj bltrb bltrb trmêle trmêleuo` uo`ss

J pjrtmr cb oj f`lerublfmj cb sbegblt`s y êleuo`s bs p`smkob bstjkobfbr fojsm﬊fjfm`lbs cb o`s trmêleuo`s. Sblmblc` bl fubltj oj f`lerublfmj bltrb o`s ojc`s, o`s trmêleuo`s sb fojsm﬊fjl f`g`1 Srmêleuo` bqumoêtbr`, sm t`c`s sus ojc`s s`l f`lerubltbs. Srmêleuo` msösfbobs , sm c`s cb sus ojc`s s`l f`lerubltbs y Srmêleuo` bsfjobl`, sm t`c`s sus ojc`s tmblbl cmdbrbltb gbcmcj. Vbeñl oj gbcmcj cb sus êleuo`s, o`s trmêleuo`s sb fojsm﬊fjl f`g`1 Srmêleuo` jfutêleuo`, sm sus trbs êleuo`s s`l jeuc`s, bs cbfmr, fjcj ul` cb o`s êleuo`s gmcb gbl`s cb =9 . Srmêleuo` `ktusêleuo`, sm ul` cb sus êleuo`s bs `ktus` (gmcb gês cb =9 y gbl`s cb :89 ). Srmêleuo` rbftêleuo`, sm tmblb ul êleuo` rbft`> bl bstb fjs` o`s ojc`s qub d`rgjl bo êleuo` rbft` rbfmkbl bo l`gkrb cb fjtbt`s y bo ojc` `pubst` jo êleuo` rbft` rbfmkb bo l`gkrb cb hmp`tblusj. ◤

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Bs ljturjo pblsjr qub c`s trmêleuo`s s`l f`lerubltbs sm ul` sb pubcb supbrp`lbr bl bo `tr`. Jh`rj kmbl oj f`lerublfmj bltrb trmêleuo`s sb bstjkobfb j pjrtmr cb oj f`lerublfmj cb sbegblt`s y cb êleuo`s, cb oj smeumbltb smeum bltb gjlbrj1 C`s trmêleuo`s trmêleuo`s ∄JKF   y ∄J K F s`l f`lerubltbs sm sus rbspbftmv`s ojc`s y êleuo`s s`l f`lerubltbs. 

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Bs cbfmr, ∄ JKF   ∿ 7 ∄ J K F sm bxmstb ulj f`rrbsp`lcblfmj bltrb o`s vírtmfbs J y J , K y K , F   y F tjo qub 

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JK ∿ 7 J K , 

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KF   ∿ 7 K F , 

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JF   ∿ 7 J F 

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y ∩FJK ∿ 7 ∩F J 

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K,

∩JKF   ∿ 7 ∩J

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K F ,

y

∩FK J

∿ 7 ∩F K J . 

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O`s smeumbltbs tb`rbgjs bstjkobfbl frmtbrm`s pjrj cbtbrgmljr oj f`lerublfmj cb trmêleuo`s.

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FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

Sb`rbgj ;.2.

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OJO1

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:5

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Vm c`s trmêleuo`s   ∄JKF   y   ∄J K F tmblbl c`s ojc`s f`lerubltbs, y bo êleuo` qub sb d`rgj bltrb boo`s tjgkmíl bs f`lerubltb, blt`lfbs o`s c`s trmêleuo`s s`l f`lerubltbs. Bstb tb`rbgj tb`rbgj sb pubcb bsfrmkmr bsfrmkmr smgkòmfjgbl smgkòmfjgbltb tb jsç1 Vm o`s trmêleuo`s trmêleuo`s   ∄ ∄ JKF   y   ∄ ∄ J K F sjtmsdjfbl 

JK ∿ 7 J K , 

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JF   ∿ 7 J F y   ∩KJF   ∿ 7 ∩K J F

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(;.:)

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blt`lfbs ∄JKF   ∿ 7 ∄ J K F 

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(;.:), ), blt`lfbs o`s trmêleuo`s ∄JKF   y ∄J K F qub sjtmsdjfbl ojs f`lerublfmjs (;.: sjtmsdjfbl ojs f`lcmfm`lbs cbo jxm`gj ;.:. jxm`gj ;.:. Y`r Y`r o` tjlt` ∩JKF   ∿ 7 ∩J K F y tjgkmíl ∩JFK ∿ 7 ∩J F K .

Cbg`strjfmöl. F`g`

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Yjrj cbg`strjr qub o`s ojc`s KF   y K F tjgk tjgkmíl míl s`l f`lerubltbs f`lerubltbs sb rjz`lj p`r oj f`ltrjcmffm f`ltrjcmffmöl1 öl1 Jsugmblc` qub o`s ojc`s K F   y K F l` s`l f`lerubltbs. f`lerubltbs. Blt`lfbs Blt`lfbs sb cbkb fugpomr ulj cb ojs smeumbltbs smeumbltbs cbsmeujocjcbs1 K F < KF   ` KF < K F . 

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Vm K F < KF  bxmstb ul pult` C bl bo mltbrm`r cbo sbegblt` K F tjo qub KF   ∿ 7 C F . Blt`lfbs bl o`s jxm`gj ;.:.. trmêleuo`s ∄ JKF   y ∄ J K F sb sjtmsdjfbl ojs f`lcmfm`lbs cbo jxm`gj ;.: 

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Dmeurj ;.21 F`lerublfmj cb Srmêleuo`s OJO JK ∿ 7 J K , 

FK ∿ 7 F C ,

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∩FJK ∿ 7 ∩F J 

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C

Oube` ∩FJK ∿ ∩F J C , pbr` p`r hmpötbsms (;.: ( ;.:), ), ∩FJK ∿ ∩F J K . F`g` F`g` bo pult` pult` C bstê bl bo 7 7 mltbrm`r cbo sbegblt` K F , tblbg`s qub cbscb bo gmsg` vírtmfb J y s`krb bo gmsg` ojc` cb oj sbgmrrbf sbgmrrbftj tj ∛∛↛ ∛∛∛↛ ∛∛↛ J F bxmstbl c`s sbgmrrbftjs sbgmrrbftjs J K y J C, qub d`rgjl f`l J F êleuo` êleuo`ss f`lerubltbs f`lerubltbs f`l bo ∩F JK . 

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Bstj j﬊rgjfmöl f`ltrjcmfb bo jxm`gj :.3 jxm`gj :.3 cb cb f`lerublfmj cb êleuo`s y p`r o` tjlt` bstj sup`smfmöl l` sb sjtmsdjfb, bs cbfmr K F l` bs gjy`r qub KF . 

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F`l jreugblt`s smgmojrbs sb cbgubstrj qub oj cbsmeujocjc KF < K F tjgp`f` sb tmblb. Y`r o` tjlt` ∿K F . KF   7 

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Sb`rbgj ;.4. Vm ul trmêleuo` tmblb c`s êleuo`s f`lerubltbs blt`lfbs o`s ojc`s `pubst`s j bs`s êleuo`s s`l f`lerubltbs. Cbg`strjfmöl. Vbjo

bo ∄ JKF   f`l ∩JKF   ∿ 7 ∩KF J.

Bstb trmêleuo` sb pubcb f`lsmcbrjr cb c`s d`rgjs ∄ JKF y bo ∄ FK J.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

:8

Y`r hmpötbsms, p`r bo jxm`gj :.3 jxm`gj :.3 y y p`r bo tb`rbgj ;.: tb`rbgj ;.: bs`s bs`s trmêleuo`s sjtmsdjfbl ojs smeumbltbs f`lerublfmjs, ∩JKF   ∿ 7 ∩JFK



,

∩JFK ∿ 7 ∩JK F,

K F   ∿ 7 F K.

Oube` o`s trmêleuo`s trmêleuo`s sjtmsdjfbl sjtmsdjfbl bo tb`rbg tb`rbgjj ;.2 p`r ;.2 p`r o` tjlt`, ∄ JKF   ∿ 7∄JFK . ∿ JK JF , oube` ∄JKF bs Y`r ojc`sSjgkmíl h`göoè`s cb trmêleuo`s f`lerubltbs, bstbsm tmp` msösfbobs. sb pubcb j﬊rgjr qub ul trmêleuo` bs 7 msösfbobs sm y söo` tmblbcb c`strmêleuo` êleuo`s f`lerubltbs.

Sb`rbgj ;.5.

JOJ1 Vm

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J F ,

o`s trmêleuo`s  ∄ ∄ JKF y ∄J K F sjtmsdjfbl ojs f`lerublfmjs,

JK ∿ 7 J K , 

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∩KJF   ∿ 7 ∩K

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∩JKF   ∿ 7 ∩J

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K F ,

blt`lfbs o`s trmêleuo`s s`l f`lerubltbs.

Bo sbeulc` fjs` cb f`lerublfmj cb trmêleuo`s sb tmblb fujlc` c`s êleuo`s cb o`s trmêleuo`s y bo ojc` f`gñl j boo`s s`l f`lerubltbs. Cbg`strjfmöl. Cjc`s

o`s trmêleuo`s ∄JKF   y ∄J K F qub sjtmsdjfbl ojs f`lerublfmjs 

JK 7 J K , 

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∩KJF   7 ∩K

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J F ,

∩JKF   7 ∩J 

Y`r ∿ bo F tb`rbgj sb pubcb g`strjr qub o`sboo`s. trmêleuo`s `ktblbr oj f`lerublfmj bltrb FJ J pjrj ;.2 7 

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K F .

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∄JKF y ∄J K F sjtmsdjfb oj f`lerublfmj

Vup`lbg`s qub bo sbegblt` FJ l` bs f`lerubltb f`l bo sbegblt` F J blt`lfbs sb cbkb sjtmsdjfbr ulj cb ojs f`lcmfm`lbs smeumbltbs FJ < F J ` FJ ? F J . 

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Vm FJ < F J , blt`lfbs bxmstb ul pult` C bl bo sbegblt` F J tjo qub JC ∿ 7 J F . 

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Dmeurj ;.41 F`lerublfmj cb Srmêleuo`s JOJ Y`r bo fjs` cb oj f`lerublfmj (OJO), ∄ JKF   ∿ 7 ∄ J K F 

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h`göoè`s cb trmêleuo`s trmêleuo`s f`lerubltbs f`lerubltbs.. Jcbgês Jcbgês p`r hmpötbsms hmpötbsms Blt`lfbs ∩JKC ∿ 7 ∩J K F p`r êleuo`s h`göoè`s ∛∛↛ ∿ sb tmblb qub ∩JKF 7 ∩J K F , oube` f`l vírtmfb K y cbo gmsg` ojc` cb oj sbgmrrbftj KJ bxmstbl c`s ∛∛↛ ∛∛↛ ∛∛↛ sbgmrrbftjs, KC y KF  qub f`l oj sbgmrrbftj KJ d`rgjl êleuo`s f`lerubltbs f`l bo êleuo` ∩J K F . Bst` f`ltrjcmfb bo prmgbr jxm`gj cb f`lerublfmj cb êleuo`s. 

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Bstj f`ltrjcmffmöl l`s jsbeurj qub oj sup`smfmöl FJ < F J l` sb fugpob. Cb oj gmsgj d`rgj p`cbg`s vbr qub FJ ? F J l` bs p`smkob y p`r o` tjlt` sb cbkb fugpomr qub F J ∿ 7 F J . 

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Y`r o` tjlt` F J ∿ 7 F J , sb pubcb cbfmr qub o`s trmêleuo`s sjtmsdjfbl bo prmgbr fjs` cb f`lerublfmj (OJO), p`r o` tjlt` sb pubcb f`lfoumr qub ∄ JKF  ∿ 7 ∄ J K F. 

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Sb`rbgj ;.8. Vm c`s êleuo`s s`l f`lerubltbs, o`s êleuo`s jcyjfbltbs j bs`s êleuo`s s`l f`lerubltbs. Vb cb﬊lb f`g` jcyjfbltb qub c`s jleño`s bl bo gmsg` pojl` qub tmblbl bo gmsg` vírtmfb y ul ojc` bl f`gñl, y o`s ojc`s l` f`gñlbs d`rgjl ulj rbftj, bs cbfmr ul êleuo` oojl`.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

Sb`rbgj ;.=.

OOO1

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:=

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Vm bl o`s trmêleuo`s  ∄ ∄ JKF   y   ∄ ∄ J K F sb tmblbl ojs f`lerublfmjs JK ∿ 7 J K , 

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JF   ∿ 7 J F , 

KF   ∿ 7 K F

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blt`lfbs o`s trmêleuo`s s`l f`lerubltbs.

Dmeurj ;.51 F`lerublfmj cb Srmêleuo`s OOO Cbg`strjfmöl. Cjc`s

o`s trmêleuo`s ∄JKF   y ∄J K F bl o`s qub sb sjtmsdjfbl ojs f`lerublfmjs, 

JK ∿ 7 J K , 

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JF   ∿ 7 J F , 

KF   ∿ 7 K F

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Y`r bo tb`rbgj ;.5 tb`rbgj ;.5 oj oj f`lerublfmj cb o`s trmêleuo`s sb `ktmblb sm ul pjr cb êleuo`s f`rrbsp`lcmbltbs s`l f`lerubltbs. Vup`lmblc` qub o`s êleuo`s h`göoè`s cb o`s trmêleuo`s l` s`l f`lerubltbs, p`r bo jxm`gj :.3 f`l :.3 f`l `rmebl ∛∛↛ ↙↛ bl K bxmstb ulj sbgmrrbftj KB  bl bo sbgmpojl` cbtbrgmljc` p`r oj rbftj KF  `pubstj jo êleuo` J, tjo qub ∩FK B  ∿ 7 ∩F K J . 





∛∛↛

Bl oj sbgmrrbftj sbgmrrbftj KB  bxmstb ul pult` C tjo qub K C ∿ 7 K J blt`lfbs ∩F KB  sb mcbltm﬊fj f`l bo ∩FKC. 



∿ K F , p`r bo fjs` OJO, ∄KF C ∿ Yubst` qub KF   7 tb`rbgj ;.6, ;.6, tblbg`s 7 ∄ K F J , blt`lfbs y p`r bo tb`rbgj ∿ ∿ qub JF 7 C CF F   y JK 7 K KC. C. 

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Y`r o` tjlt` o`s trmêleuo`s ∄JKC y ∄JFC s`l msösfbobs, oube` ∄CJF   ∿ y ∄KJC ∿ 7 ∄ JCF  y 7 ∄ KCF. Bo êleuo` ∩KJF  ∿ jxm`gj :.3 cb cb f`lerublfmj cb Hmokbrt cjc` qub K J ∿ 7 ∩JCF. Y`r bo jxm`gj :.3 7 K C y JF   ∿ 7 CF , 7 ∩KFC. cb oj meujocjc cb o`s êleuo`s ∩KJF   y ∩KCF  sb `ktmblb ∩JFK ∿ ∛∛↛

Cb oj gmsgj d`rgj sm j pjrtmr cb oj sbgmrrbftj KF  f`l vírtmfb K y cbo gmsg` ojc` cbo pult` J trjzjg`s bo êleuo` ∩EKF  f`l f `l ∩EKF   ∿ EFC C 7 ∩J K F y tjo qub K E ∿ 7 K J , blt`lfbs o`s trmêleuo`s ∄ EKC y ∄ EF s`l msösfbobs. 

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Bo êleuo` ∩KEF   ∿ jxm`gj ;.: cb cb f`lerublfmj cb êleuo`s cjc` qub K KE E∿ KC C y EF   ∿ 7 ∩KCF. Y`r bo jxm`gj ;.: 7 K 7 F C ∿ sb tmblb oj f`lerublfmj ∩EFK 7 ∩KFC. ∛∛↛

∛∛↛

∛↛

J pjrtmr cb oj sbgmrrbftj KF  y s`krb bo gmsg` sbgmpojl` sbgmpojl` tblbg`s c`s sbgmrrbftjs FE y FJ qub d`rgjl f`l KF  êleuo`s f`lerubltbs f`l ío ∩KF C. Bstb hbfh` f`ltrjcmfb bo prmgbr jxm`gj cb f`lerublfmj cb êleuo`s, êleuo `s, oube` ojs sbgmrrbftjs cbkbl f`mlfmcmr. f`mlfmcmr. Vm FE f`mlfmcb f`l FJ , bo êleuo` ∩JKF   ∿ 7 ∩J K F y p`r o` tjlt`, ∄ JKF   y ∄ J K F . 

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F`g` oj f`lerublfmj cb trmêleuo`s bstê cbtbrgmljcj p`r oj f`lerublfmj cb o`s ojc`s y o`s êleuo`s cb o`s trmêleuo`s, sb pubcb cbfmr qub oj rbojfmöl sbr f`lerubltb , bs ulj rbojfmöl cb bqumvjoblfmj. Jsç cjc`s o`s trmêleuo`s ∄ JKF , ∄ CBD   y ∄EH EHN N  sb sb fugpob qub1

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;9

∿ ∄ JKF . :. ∄JKF   7 ∿ ∄ CB ;. ∄JKF   7 CBD D  blt`lfbs ∄ CB CBD D   ∿ 7∄JKF . ∿ ∄ CB 6. ∄JKF   7 CBD D   y ∄ CBD   ∿ EHN N , sb fugpob qub ∄ JKF   ∿ EHN N . 7 ∄ EH 7 ∄ EH

Jcbgês, sm c`s trmêleuo`s s`l f`lerubltbs tmblbl oj gmsgj êrbj. ;.:. ;.:.3. 3.

F`le F`leru rubl blfm fmj j cb pòçe pòçe`l `l`s `s

Rl pòçe`l` bs ulj omlbj pòme`ljo fbrrjcj fbrrjcj (ulmöl f`lsbfutmvj f`lsbfutmvj cb vjrm`s vjrm`s sbegblt`s). sbegblt`s). O`s bxtrbg`s cb o`s sbegblt`s cb oj oçlbj pòme`ljo sb oojgjl vírtmfbs cbo pòçe`l` y o`s sbegblt`s sb oojgjl ojc`s cbo pòçe`l`. Vb cmfb qub ul pòçe`l` bs bquçjleuo`, sm t`c`s sus êleuo` êleuo`ss f`leru f`lerubl bltbs tbs bltrb bltrb sç. Rl pòçe`l` pòçe`l` smgpob smgpob (f`lvbx`) sb cbl`gmlj pòçe`l` rbeuojr , sm t`c`s sus ojc`s s`l f`lerubltbs bltrb sç y t`c`s sus êleuo`s mltbrm`rbs s`l f`lerubltbs bltrb sç. Bltrb o`s pòçe`l`s rbeuojrbs sb blfubltrjl1 Bo fujcrjc`, bl bo fujo sus fujtr` êleuo`s s`l rbft`s. Bo hbxêe`l` rbeuojr, f`l sbms ojc`s s`l f`lerubltbs y c`lcb fjcj ul` cb sus sbms êleuo`s gmcb :;9 . ◤

Dmeurj ;.81 Yòçe`l`s rbeuojrbs @tr`s pòçe`l`s, pòçe`l`s, julqub l` sbjl rbeuojrbs rbeuojrbs pubcbl sbr bqumoêtbr`s bqumoêtbr`s ` bqumêleuo`s bqumêleuo`s,, p`r babgpo`1 Bo r`gk`, qub bs ul fujcrmoêtbr` f`l sus fujtr` ojc`s f`lerubltbs bltrb sç. Bo rbftêleuo`, tjgkmíl bs ul fujcrmoêtbr` qub tmblb sus fujtr` êleuo`s rbft`s. Bl eblbrjo, c`s pòçe`l`s f`l bo gmsg` lñgbr` cb ojc`s s`l f`lerubltbs sm tmblbl ojc`s y êleuo`s rbspbftmv tmvjgbl jgbltb tb f`lerubltbs f`leru bltbs.. Yjrj Yjrj pòçe`l`s pòçe`l`s f`lvbx`s f`lvbx`s p`cbg`s p` cbg`s bstjkobfbr joeul`s tb`rbgjs cb f`lerublfmj. f`lerublfmj. Jltbs ulj cb﬊lmfmöl1

Cb﬊lmfmöl ;.;. Rlj cmje`ljo cmje`ljo cb ul pòçe` p òçe`l` l` bs bo sbegblt` sbegblt` qub ulb c`s vírtmfbs l` f`lsbfutmv`s f`lsbfutmv`s cbo pòçe`l`. Sb`rbgj ;.:9. C`s pòçe`l`s s`l f`lerubltbs sm o`s trmêleuo`s cbtbrgmljc`s p`r ojs cmje`ljobs cbscb ul gmsg` vírtmfb bl ul` cb o`s pòçe`l`s s`l f`lerubltbs f`l o`s trmêleuo`s cbtbrgmljc`s p`r ojs cmje`ljobs cbscb ul vírtmfb f`rrbsp`lcmbltb bl bo `tr` pòçe`l`. Cbg`strjfmöl. Vbjl JKFCB   y J K F C B c`s pòçe`l`s f`lvbx`s, JF , JC c`s cmje`ljobs cbo prmgbr pòçe`l` pòçe`l` y J F , J C c`s cmje`ljobs cmje`ljobs cbo sbeulc` sbeulc` pòçe` p òçe`l` l` ojs fujobs cmvmcbl o`s pòçe`l`s bl o`s 

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trmêleuo`s f`lerubltbs, ∄JKF   ∿ 7 ∄ J K F , ∄FJC ∿ 7 ∄ F J C , ∄CJB  ∿ 7 ∄ C K B , 

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Cbkbg`s pr`kjr qub o`s ojc`s y o`s êleuo`s cb o`s pòçe`l`s s`l rbspbftmvjgbltb f`lerubltbs. Cb oj f`lerublfmj cb o`s trmêleuo`s sb smeub oj f`lerublfmj cb o`s ojc`s cb o`s pòçe`l`s, JK ∿ 7 J K , 



KF  ∿ 7 K F , 



FC ∿ 7 F C , 



CB  ∿ 7 C B , 



BJ ∿ 7 B J 



FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;:

Dmeurj ;.=1 Yòçe`l`s f`lerubltbs

Sjgkmíl p`r oj f`lerublfmj cb o`s trmêleuo`s sb tmblb oj f`lerublfmj cb o`s smeumbltbs êleuo`s, ∩JKF   ∿ 7 ∩J







K F ,

∩KF J

∿ 7 ∩K F J ,

∩FC J

∿ 7 ∩F C J ,

∩JCB  ∿ 7 ∩J

∩BJC

∿ 7 ∩B J C ,

∩CJF   ∿ 7 ∩C

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∩JFC

∿ 7 ∩J F C.

C B ,



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∩CBJ

∿ 7 ∩C B J .

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∩FJK ∿ 7 ∩F J

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J F ,

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K.

Yubst` qub o`s êleuo`s cbo pòçe`l` s`l meujobs j, ∩KJB  7 ∩KJF  + + ∩FJC + ∩CJB. ∩K

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J B 7 ∩K J F + ∩F J C + ∩C J B . ∩KF C 7 ∩KF J ∩K

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+ ∩JFC.

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F C 7 ∩K F J + ∩J F C .

∩FC B  7 7 ∩F CJ 

∩F C

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+ ∩JCB.

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B 7 ∩F C J + ∩J C B .

Y`r oj sugj cb êleuo`s f`lerubltbs sb `ktmblb, ∩BJK ∿ 7 ∩B J 

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K,

∩KF C

∿ 7 ∩K F C , 

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∩FC B  ∿ 7 ∩F C 

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B .

Oube` o`s pòçe`l`s tmblbl o`s ojc`s y o`s êleuo`s rbspbftmvbgbltb f`lerubltbs, p`r o` tjlt` JKFCB  ∿ 7 J

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K F C B .

F`ròjrm` ;.:. Vm ulj cmje`ljo cb ul fujcrmoêtbr` cmvmcb jo fujcrmoêtbr` bl c`s trmêleuo`s f`lerubltbs, bo fujcrmoêtbr` tmblb o`s êleuo`s `pubst`s f`lerubltbs y o`s ojc`s `pubst`s f`lerubltbs, ` o`s ojc`s f`lsbfutmv` f`lsbfu tmv`ss f`lerubltb f`lerubltbss ` t`c`s o`s ojc`s f`lerubltbs f`lerubltbs bltrb sç. Sb`rbgj ;.::. Ojs cmje`ljobs cb ul fujcrjc` cbtbrgmljl fujtr` trmêleuo`s f`lerubltbs. Cbg`strjfmöl. Vbj JKFC ul fujcrmoêtbr` bs cbfmr, JKFC bs ul fujcrjc`.

f`l êleuo`s mltbrm`rbs rbft`s y ojc`s f`lerubltbs bltrb sm,

Cjc` qub t`c`s o`s êleuo`s rbft`s s`l f`lerubltbs bltrb sç, o`s êleuo`s mltbrm`rbs cbo JKFC s`l f`lerubltbs. ∩JCF  ∿ CFK K ∿ 7 ∩CF 7 ∩FK J

∿ 7 ∩KJC.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;;

Dmeurj ;.:91 Fujcrjc` f`l sus cmje`ljobs Y`r cb﬊lmfmöl bo JKFC tmblb sus ojc`s f`lerubltbs bltrb sm, JC ∿ 7 CF  ∿ 7 F K ∿ 7 JK

Y`r sbr êleuo`s `pubst`s j o`s ojc`s meujobs bl trmêleuo`s msösfbobs, ∩KCF   ∿ 7 ∩FKC,

∩CJF  ∿ 7 ∩CFJ.

∩KJF   ∿ 7 ∩KFJ,

∩JCK ∿ 7 ∩JKC.

Y`r bo tb`rbgj ;.5, tb`rbgj ;.5, s`l s`l f`lerubltbs o`s smeumbltbs trmêleuo`s ∄CF CFK K ∿ CFK K ∿ 7 ∄ CJK, ∄CF 7 ∄ F KJ ∄CJK ∿ CFK K 7 ∄ JKF, ∄JCF  ∿ 7 ∄ CF

Y`r bobgblt`s f`rrbsp`lcmbltbs cb trmêleuo`s f`lerubltbs sb tmblb, ∩JKC

∿ 7 ∩KCF,

∩KCF   ∿ 7 ∩KJF.

∩KF J

∿ 7 ∩JKC,

∩KC KCF F   ∿ 7 ∩CJF.

Bs cbfmr o`s êleuo`s d`rgjc`s p`r ojs cmje`ljobs cbo fujcrjc` s`l bltrb sm f`lebubltbs. Blt`lfbs p`r bo tb`rbgj ;.5 tb`rbgj ;.5 ∄JBK ∿ 7 ∄ FBC, ∄JBC ∿ 7 ∄ FBK, ∄JBK ∿ 7 ∄ KBF, ∄JKB  ∿ 7 ∄ JBC.

F`ròjrm` ;.;. Ojs cmje`ljobs cb ul fujcrjc` cmvmcb o`s êleuo`s rbft`s cbo fujcrjc` bl c`s êleuo`s f`lerubltbs. Bs cbfmr, ojs cmje`ljobs cbo fujcrjc` s`l kmsbftrmfbs cb o`s êleuo`s cbo fujcrjc`. F`ròjrm` ;.6. Ojs cmje`ljobs cmje`ljobs cb ul fujcrjc` s`l f`lerubltbs. f`lerubltbs. F`ròjrm` ;.3. Ojs cmje`ljobs cmje`ljobs cb ul fujcrjc` sb f`rtjl d`rgjlc` d`rgjlc` sbegblt`s sbegblt`s f`lerubltbs f`lerubltbs bltrb sm. Sb`rbgj ;.:;. C`s fujcrmoêtbr`s s`l f`lerubltbs sm tmblbl sus ojc`s rbspbftmvjgbltb f`lerubltbs y ul êleuo` f`lerubltb. Cbg`strjfmöl. Vbjl JKFC y J K F C 

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c`s fujcrmoêtbr` fujcrmoêtbr`ss fuy`s fuy`s bobgbl bobgblt`s t`s sjtmsdjfbl sjtmsdjfbl ojs smeumbltbs smeumbltbs

f`lerublfmjs, JC ∿ J C , 

7

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CF   ∿ C F , 

7

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F K ∿ F K , 

KJ ∿ K J





7

7

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y

∩JCF   ∿ J

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

7

Y`r hmpötbsms y p`r bo tb`rbgj (OJO) ;.2, (OJO) ;.2, ∄ JCF   ∿ 7 J F . 7 ∄ J C F y p`r o` tjlt`, JF   ∿ 



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

C F

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

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;6

Dmeurj ;.::1 Fujcrmoêtbr`s f`lerubltbs Blt`lfbs p`r bo tb`rbgj (OOO) ;.=, (OOO) ;.=, sb sb tmblb qub ∄ JFK ∿ 7 ∩J K F . 7 ∄ J F K y p`r o` tjlt`, ∩JKF   ∿ 

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Y`r bobgblt`s cb trmêleuo`s f`lerubltbs, ∩CJF  ∿ 7 ∩C ∩CF CFJ J

J F ,

∩KJF   ∿ 7 ∩K

∿ 7 ∩C F J ,

∩JFK ∿ 7 ∩J

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





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J F

F K

Y`r sugj cb êleuo`s f`lerubltbs, 



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

J F + F J K CF CFJ J + JFK 7 C F J + J F K CJF  + + F JK 7 C

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Blt`lfbs o`s êleuo`s cbo fujcrmoêtbr` rbsuotjl f`lerubltbs, ∩CJK ∿ 7 ∩C







JK,

y

∩CF CFK K ∿ 7 ∩C





F K



tjgkmíl sb tmblb ojs f`lerublfmjs cb o`s trmêleuo`s, ∄CJK ∿ CFK K ∿ 7 ∄C J K y ∄CF 7 ∄C F K p`r bo frmtbrm` (OJO) oube` p`r oj sugj cb êleuo`s f`lerubltbs, 

∩JKF  ∿ 7 ∩J





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







K F .

Bl rbsugbl, o`s fujcrmoêtbr`s JKFC y J K F C tmblbl ojc`s y êleuo`s rbspbftmvjgbltb f`lerubltbs, p`r o` tjlt` 



JKFC

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

∿ 7 J K F C 

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

F`ròjrm` ;.2. C`s fujcrjc`s fujcrjc`s s`l f`lerubltbs f`lerubltbs sm tmblbl ul ojc` f`lerubltb. f`lerubltb. F`ròjrm` ;.4. C`s r`gk`s s`l f`lerubltbs f`lerubltbs sm tmblbl ul ojc` f`lerubltb f`lerubltb y ul êleuo` f`lerubltb. f`lerubltb. F`ròjrm` ;.5. Vm ul fujcrmoêtbr` tmblb o`s ojc`s `pubst`s f`lerubltbs, sus êleuo`s `pubst`s tjgkmíl s`l f`lerubltbs.

;.;. ;. ;.

Vbgb Vbgbaj ajlz lzj. j.

Oj rbojfmöl sbgbajlzj bltrb pòçe`l`s, sb bstjkobfb rbojfm`ljlc` ojc`s y êleuo`s h`göoè`s cb ojs ﬊eurjs. C`s pòçe`l`s s`l sbgbajltbs fujlc` oj gbcmcj cb o`s ojc`s h`göoè`s eujrcjl oj gmsgj pr`p`rfmöl y sus êleuo`s êleuo`s rbspbftmv`s rbspbftmv`s s`l f`lerubltb f`lerubltbs. s. Mltumtmv Mltumtmvjgbl jgbltb tb c`s ﬊eurjs s`l sbgbajltbs fujlc` tmblbl oj gmsgj d`rgj julqub su tjgjú` sbj cmdrbltb.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;3

Dmeurj ;.:;1 Vbgbajlzj cb Srmêleuo`s ;.;. ;.;.:. :.

Vbgb Vbgbaj ajlz lzj j cb tr trmê mêle leuo uo`s `s

C`s trmêleuo`s ∄ JKF  y ∄ CB sbgbajltbs sm y söo` sm sb fugpobl ojs smeumbltbs smeumbltbs rbojfm`lbs bltrb bltrb sus CBD D   s`l sbgbajltbs ojc`s y sus êleuo`s1 JF KF JK 7 7 CB BD CD

y

∩FJK ∿ 7 ∩DCB,

∩JKF   ∿ 7 ∩CBD,

∩JFK ∿ 7 ∩CD B

Vm m o`s trmêleuo`s ∄JKF   y ∄CB CBD D  s`l sbgbajltbs, sb bsfrmkb ∄JKF  ∿ ∄CB CBD D .

Sb`rbgj ;.:6. Vm c`s trmêleuo`s tmblbl sus êleuo`s rbspbftmv`s f`lerubltbs, sus ojc`s h`göoè`s s`l pr`p`rfm`ljobs.

Dmeurj ;.:61 Vbgbajlzj cb Srmêleuo`s OOO Cbg`strjfmöl. Vbjl

o`s trmêleuo`s ∄ JKF   y ∄ CBD  f`l sus rbspbftmv`s êleuo`s f`lerubltbs1 ∩JFK ∿ 7 ∩CDB,

∩F JK ∿ 7 ∩DCB,

∩JKF   ∿ 7 ∩CBD.

Vm sus ojc`s h`göoè`s s`l f`lerubltbs, o`s trmêleuo`s s`l f`lerubltbs y p`r tjlt` sbgbajltbs. Vup`lejg`s qub sus ojc`s h`göoè`s l` s`l f`lerubltbs, p`cbg`s sup`lbr qub FJ < DC , blt`lfbs bl bo sbegblt` F J bxmstb ul pult` E tjo qub F E ∿ 7 D C. Y`r bo pult` E trjzjg`s oj rbftj pjrjoboj j JK , bstj rbftj f`rtj jo ojc` FK bl ul pult` H , blt`lfbs EH    JK.

Y`r sbr êleuo`s f`rrbsp`lcmbltbs bltrb pjrjobojs, ∩F EH   ∿ oube` 7 ∩F JK . Y`r hmpötbsms ∩F JK ∿ 7 ∩D CB  oube` p`r trjlsmtmvmcjc cb oj f`lerublfmj cb êleuo`s sb tmblb qub ∩F EH   ∿ EFH H  f`ml f`ml7 ∩D CB . Yubst` qub ∩EF ∩

∩

∿

∿

∩

JFK y JFK 7 CD B  p`r fmcb `trj f`l ío fjs` cb f`lerublfmj JOJ, Y`r pjrtb cjc` qub o`s sbegblt`s p`r s`l bo pr`p`rfm`ljobs, sb fugpob qubtblbg`s qub ∄ F EH 7 ∄ D CB . FJ FK 7 FH FE

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;2

Y`r sbr o`s ojc`s cb trmêleuo`s f`lerubltbs FE ∿ Oube` oj pr`p`rfmöl pr`p`rfmöl jltbrm jltbrm`r `r bs 7 D C y F H   ∿ 7 D B . Oube` tjgkmíl meujo j FJ FK 7 D B DC

Jo trjzjr ulj rbftj pjrjoboj jo ojc` F J p`r bo pult` H . Vm [ bs bo pult` cb cmfhj pjrjoboj jo ojc` JK , blt`lfbs1 FK JK 7 FH H[

Yubst` qub bo fujcrmoêtbr` fujcrmoêtbr` J[EH  tmblb tmblb sus ojc`s `pubst`s pjrjobo`s pjrjobo`s meujobs bs ul pjrjoboèrj pjrjoboèrjg` g` y p`r ∿ ∿ ∿ boo` J[ 7 HE . Y`r oj f`lerublfm f`lerublfmjj cb trmêleuo`s trmêleuo`s ∄EH EHF F 7 ∄CBD , EH 7 CB  blt`lfbs J[ ∿ 7 CB . [bbgpojzjlc` [bbgpo jzjlc` bl oj pr`p`rfmöl pr`p`rfmöl jltbrm`r o`s sbegblt`s sbegblt`s f`lerubltbs f`lerubltbs sb `ktmblb1 `ktmblb1 JK FK 7 D B CB

oube`

JF F K JK 7 7 CB D B CD

Bs cbfmr o`s trmêleuo`s trmêleuo`s tmblbl sus ojc`s h`göoè`s h`göoè`s pr`p`rfm`ljobs. pr`p`rfm`ljobs.

Sb`rbgj ;.:3. Rlj pjrjoboj j ul ojc` cb ul trmêleuo` cbtbrgmlj `tr` trmêleuo` sbgbajltb jo prmgbr`.

Dmeurj ;.:31 Yjrjoboj bl ul Srmêleuo` Cbg`strjfmöl. Vbj ∄ JKF   y c ulj rbftj pjrjoboj jo ojc` JK oj fujo f`rtj bl o`s pult`s C y B  o`s FJ y FK rbspbftmvjgbltb.

ojc`s

Y`r êleuo`s f`rrbsp`lcmbl f`rrbsp`lcmbltbs tbs bltrb bltrb pjrjobojs, pjrjobojs, tblbg`s qub ∩F CB   ∿ 7 ∩FJK y ∩F BC ∿ 7 ∩FK J. Jcb ∿ ∿ gês ∩FC B 7 ∩JFK , blt`lfbs o`s trmêleuo`s ∄JKF 7 ∄CB CBF F  tmblbl sus êleuo`s rbspbftmvjgbltb f`lerubltbs. Y`r bo tb`rbgj ;.:6 tb`rbgj ;.:6 o`s o`s trmêleuo`s tmblbl sus ojc`s h`göoè`s pr`p`rfm`ljobs. Y`r cb﬊lmfmöl o`s trmêleuo`s s`l sbgbajltbs, tblbg`s ∄ JKF   ∿ ∄CBF . Yjrj trmêleuo`s, oj f`lcmfmöl cb sbgbajlzj sb pubcb rbcufmr j oj pr`p`rfm`ljomcjc bltrb o`s ojc`s h`göoè`s cb o`s trmêleuo`s. trmêleuo`s. tmblbl sus ojc`s h`göoè`s pr`p`rfm`ljobs, o`s trmêleuo`s tmblbl sus Sb`rbgj ;.:2. Vm c`s trmêleuo`s êleuo`s rbspbftmvjgbltb f`lerubltbs.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;4

Dmeurjj ;.:21 F`lerublfmj Dmeur F`lerublfmj cb êleuo`s êleuo`s bltrb trmêleuo`s trmêleuo`s Cbg`strjfmöl. Vbjl ∄ JKF   y ∄ CB CBD D f`l

sus ojc`s rbspbftmvjgbltb pr`p`rfm`ljobs, JK F J FK 7 7 D B DC CB

F`g` o`s trmêleuo`s l` s`l f`lerubltbs, sup`lbg`s qub FJ < DC . Y`r ojs pr`pmbcjcbs cb ojs pr`p`rfm`lbs sb cbkb fugpomr qub FK < DB . FJ FK . Vbjl G  y L  pult`s pult`s bl F J y F K rbspbftmvjgbltb tjobs qub F G   ∿ 7 FL 7 D C y F L   ∿ 7 D B , blt`lfbs FG ↙∛↛ Oj rbftj G L  bs pjrjoboj j JK .

JK FJ FK Y`r bo tb`rbgj jltbrm`r, ∄ JKF   ∿ ∄G L F , blt`lfbs blt`lfbs GL 7 FG 7 FL .

[bbgpojzjlc` F G   ∿ sb `ktmblb, 7 D C y F L   ∿ 7 D B  sb FJ F K JK JK . 7 7 7 CB D B DC G L

Oj meujocjc cb oj prmgbrj y ñotmgj rjz`lbs mgpomfj oj f`lerublfmj cb o`s sbegblt`s G L   ∿ 7 CB , oube` G L F   ∿

CBD CB D

p`r OOO. Yubst` qub o`s trmêleuo`s ∄JKF   y ∄G L F   tmblbl sus êleuo`s rbspbftmvjgbltb f`lerubltbs p`r sbr sbgbajltbs, o`s êleuo`s cb o`s trmêleuo`s ∄JKF  y y ∄CB CBD D  tmblbl tmb lbl sus êleuo`s rbspbftmvjgbltb f`lerubltbs. f`lerubltbs. ∄

7 ∄

Y`r o` tjlt` sb pubcbl bstjkobfbr o`s fjs`s cb sbgbajlzj cb trmêleuo`s qub s`l1

Frmtbrm` JJJ1 C`s trmêleuo`s s`l sbgbajltbs, sm y söo` sm tmblbl sus trbs êleuo`s f`rrbsp`lcmbltbs f`lerubltbs. Frmtbrm` JJ1 C`s trmêleuo`s s`l sbgbajltbs sm y söo` sm tmblbl c`s êleuo`s f`rrbsp`lcmbltbs f`lerubltbs. Frmtbrm` OOO1 C`s trmêleuo`s s`l sbgbajltbs, sm y söo` sm tmblbl sus ojc`s h`göoè`s rbspbftmvjgbltb Frmtbrm` pr`p`rfm`ljobs. Sb`rbgj ;.:4. C`s trmêleuo`s s`l sbgbajltbs sm y söo` sm tmblbl c`s ojc`s h`göoè`s pr`p`rfm`ljobs y o`s êleuo`s f`gprblcmc`s bltrb boo`s s`l f`lerubltbs. Cbg`strjfmöl. Vbjl ∄ JKF   y ∄ CB CBD D   trmêle trmêleuo`s uo`s bl

o`s fujobs sb sjtmsdjfbl sjtmsdjfbl ojs smeumbltbs smeumbltbs rbojfm`lbs. rbojfm`lbs.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

(:)

FJ F K 7 D B DC

;5

y (;)∩JFK ∿ 7 ∩CD B

Bo tb`rbgj tmblb c`kob mgpomfjfmöl1 mgpomfjfmöl1 Vm o`s trmêleuo`s trmêleuo`s ∄ JKF  y ∄ CD B  s`l s`l sbgbajltbs, blt`lfbs fugpobl ( ;). ojs c`s f`lcmfm`lbs f`lcmfm`lbs (:) y (;)

Vm ∄JKF   ∿ ∄CD B  sus sus êleuo`s rbspbftmv`s s`l f`lerubltbs y sus ojc`s h`göoè`s s`l pr`p`rfm`ljobs, bs cbfmr o`s trmêleuo`s trmêleuo`s sjtmsdjfbl sjtmsdjfbl ojs f`lcmfm`lbs (:) ( :) y (;) . Y`r `tr` ojc` p`cbg`s p` cbg`s pr`kjr oj mgpomfjfmöl mgpomfjfmöl bl oj qub o`s trmêleuo`s trmêleuo`s ∄ JKF   y ∄ CBD  qub sjtmsdjfbl ojs f`lcmfm`lbs (:) y (;) ( ;) l` s`l f`lerubltbs, blt`lfbs sus ojc`s h`göoè`s l`s s`l f`lerubltbs. Vm jcbgês sb tmblb bl fubltj qub FJ < DC p`r pr`pmbcjcbs cb ojs pr`p`rfm`lbs sb tmblb qub FK < DB Vbjl G   y L  pult`s cb F J y F K rbspbftmvjgbltb tjobs qub FG   ∿ 7 D C

FL ∿ D B 7

y

[bbgpojzjlc` [bbgpo jzjlc` bstjs bxprbsm`lbs bl oj bxprbsmöl bxprbsmöl (:) , tblbg`s1 FJ

7

F G

FK FL

↙∛↛

Cjc` qub oj rbftj G L  bs pjrjoboj j JK p`cbg`s j﬊rgjr qub ∄JKF   ∿ ∄G L F p`r o` tjlt` tjlt`

∩JKF   ∿ 7 ∩CBD   ∿ 7 ∩G L F

∿ ∄CBD p`r bo tb`rbgj (OJO);.2, Oube` ∄G L F   7 (OJO);.2, cb c`lcb sb pubcb f`lfoumr oj sbgbajlzj cb o`s trmêleuo`s ∄ JKF   ∿ ∄CBD.

Cjc`s o`s fjs`s cb sbgbajlzj sb pubcbl cbcufmr `tr`s fjs`s cb sbgbajlzj qub s`l1

F`ròjrm` ;.8. C`s trmêleuo`s trmêleuo`s msösfbobs s`l sbgbajltbs sbgbajltbs sm tmblbl c`s êleuo`s êleuo`s f`lerubltbs. f`lerubltbs. trmêleuo`s msösfbobs s`l sbgbajltbs sbgbajltbs sm c`s pjrbs cb ojc`s s`l pr`p`rfm`ljobs. pr`p`rfm`ljobs. F`ròjrm` ;.=. C`s trmêleuo`s F`ròjrm` F`ròjr m` ;.:9. O`s trmêleuo`s bqumoêtbr`s s`l sbgbajltbs bltrb sç. ;.;.;. ;.; .;.

Vbgbaj Vbgbajlzj lzj cb trmêle trmêleuo` uo`ss rbft rbftêle êleuo` uo`s1 s1

O`s trmêleuo`s rbftêleuo`s sjtmsdjfbl ojs pr`pmbcjcbs pjrtmfuojrbs qub pbrgmtbl fjofuojr ojs êrbjs, o`s ojc`s, joturjs y jp`tbgjs cb o`s pòçe`l`s.

Sb`rbgj ;.:5. C`s trmêleuo`s rbftêleuo`s s`l sbgbajltbs sm tmblbl ul êleuo` jeuc` f`lerubltb. Cbg`strjfmöl. Cjc`s o`s trmêleuo`s rbftêleuo`s, ∄JKF   f`l ∩JFK rbft` sm ∩JKF  ∿ 7 ∩BD C o`s trmêleuo`s s`l sbgbajltbs.

y ∄BD C f`l ∩BD C rbft`,

Cjc` qub o`s êleuo`s jeuc`s cb ul trmêleuo` rbftêleuo` s`l f`gpobgbltjrm`s sb pubcb j﬊rgjr qub ∩JKF  + + ∩FJK 7 ∩BC BCD D   + ∩D BC

Yubst` qub p`r hmpötbsms ∩JFK ∿ BCD D , tjgkmíl sb tmblb oj f`lerublfmj, ∩FJK ∿ 7 ∩BC 7 ∩D BC . Y`r o` ∿ tjlt` ∄ JKF 7 ∄ BCD  p`r bo fjs` cb sbgbajlzj (JJJ) ;.;.:.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;8

Dmeurj ;.:41 Vbgbajlzj cb trmêleuo`s rbftêleuo`s1 "êleuo` jeuc`‗

F`ròjrm` F`ròjr m` ;.::. O`s trmêleuo`s rbftêleuo`s msösfbobs s`l sbgbajltbs bltrb sm. Sb`rbgj ;.:8. C`s trmêleuo`s rbftêleuo`s s`l sbgbajltbs sm tmblbl sus fjtbt`s pr`p`rfm`ljobs. ;.;.6. ;.; .6.

F`lsb F`lsbfub fublfm lfmj j cb oj sbgbaj sbgbajlzj lzj cb trmêl trmêleuo euo`s `s rbftêl rbftêleuo euo`s `s

Sb`rbgj ;.:=. Oj rjzöl bltrb c`s joturjs f`rrbsp`lcmbltbs cb c`s trmêleuo`s sbgbajltbs bs meujo j oj rjzöl bltrb c`s ojc`s f`rrbsp`lcmbltbs cb o`s trmêleuo`s.

Dmeurj ;.:51 [jzöl bltrb ojs joturjs y ojc`s cb ul trmêleuo` rbftêleuo`. Cbg`strjfmöl. Vbjl ∄JKF   ∿ ∄BD E, JC y BH  ojs

joturjs f`rrbsp`lcmbltbs j o`s ojc`s FK y ED rbspbftmvjgbl rbspbftmv jgbltb. tb. Y`r o`s frmtbrm`s cb sbgbajlzj sbgbajlzj o`s trmêleuo`s trmêleuo`s s`l f`lerubltbs f`lerubltbs y o`s ojc`s s`l pr`p`rfm`pr`p`rfm`ljobs, ∩FJK ∿ 7 ∩EBD , ∩JFK ∿ 7 ∩BED , ∩JKF   ∿ 7 ∩BD E, FJ JK FK EB   7 BD   7 ED

Ojs joturjs cbtbrgmljl o`s trmêleuo`s rbftêleuo`s ∄ JFC y ∄ BEH Yubst` qub ∩JFC ∿ 7 ∩BEH  blt`lfbs ∄ JFC ∿ 7 ∄ BEH , FJ JC FC 7 7 ED BH EB

Bst` qumbrb cbfmr qub oj rjzöl cb ojs joturjs JC y BH  cb o`s trmêleuo`s sbgbajltbs bs meujo j oj rjzöl cb o`s ojc`s h`göoè`s cb o`s trmêleuo`s.

Sb`rbgj ;.;9. Oj joturj s`krb oj hmp`tblusj cb ul trmêleuo` rbftêleuo` cmvmcb jo trmêleuo` bl c`s trmêleuo`s, fjcj ul` cb o`s fujobs bs sbgbajltb jo trmêleuo` rbftêleuo` cjc`.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

;=

Dmeurj ;.:81 Joturj cb ul trmêleuo` rbftêleuo` f`l rbspbft` j oj hmp`tblusj Cbg`strjfmöl. Vbj ∄JFK rbftêleuo` y JC joturj s`krb

oj hmp`tblusj KF .

O`s trmêleuo`s rbftêleuo`s ∄KC KCJ J y ∄ KJF  f`gpjrtbl bo ∩F KJ , oube` tmblb sus êleuo`s f`lerubltbs. O`s trmêleuo`s ∄JCF   y ∄ KJF  f`gpjrtbl bo ∩JFK , oube` tmblbl sus êleuo`s êleuo`s f`lerubltbs. f`lerubltbs. Y`r tblbr sus êleuo`s rbspbftmvjgbltb f`lerubltbs o`s trmêleuo`s s`l sbgbajltbs, ∄KC KCJ J ∿ ∄KJF   ∿ ∄JCF

F`ròjrm` ;.:;. Oj joturj s`krb oj hmp`tblusj cb ul trmêleuo` rbftêleuo` bs oj gbcmj pr`p`rfm`ljo bltrb o`s sbegblt`s qub cbtbrgmlj cbtbrgmlj oj hmp`tblusj. hmp`tblusj. Cbg`strjfmöl. Y`r

bo tb`rbgj jltbrm`r oj joturj JC s`krb oj hmp`tblusj hmp`tblusj cb ul trmêleuo` ∄ JKF  rbftêleuo`, cbtbrgmlj oj sbgbajlzj sbgbajlzj bltrb bltrb trbs trmêleuo`s trmêleuo`s ∄KC KCJ J ∿ ∄KJF   ∿ ∄JCF

Cb oj sbgbajlzj cb o`s trmêleuo`s ∄ KC KCJ J ∿ ∄KJF  sb tmblb oj pr`p`rfmöl, JC KC 7 FJ KJ

KC KJ 7 JC JF

Cb oj sbgbajlzj cb o`s trmêleuo`s ∄JCF  ∿ ∿ ∄KJF  sb tmblb oj pr`p`rfmöl, JC CF 7 KJ JF

JC KJ 7 CF JF

Oube` p`r trjlsmtmvmcjc cb oj meujocjc, KC JC . 7 CF JC

Bst` mgpomfj qub bo sbegblt` JF   bs gbcmj pr`p`rfm`ljo pr`p`rfm`ljo bltrb o`s sbegblt`s sbegblt`s K C y CF. CF . ;.;.3. ;.; .3.

Sb`rbg b`rbgj j cb Ymtêe` Ymtêe`rjs rjs11

Sb`rbgj ;.;:. Bl ul trmêleuo` rbftêleuo` oj gbcmcj cb oj hmp`tblusj jo fujcrjc` bs meujo j oj sugj cb o`s fujcrjc`s cb sus fjtbt`s.

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

69

Dmeurj ;.:=1 Sb`rbgj cb Ymtêe`rjs Ymtêe`rjs Cbg`strjfmöl. Y`r bo

tb`rbgj tb`rbgj jltbrm`r, cjc` bo trmêleuo` trmêleuo` ∄ JKF  rbftêleuo` f`l hmp`tblusj JF , sm KC bs oj joturj s`krb oj hmp`tblusj sb tmblb ∄JCK ∿ ∄JKF y ∄F CK ∿ ∄FK J

Y`r ojc`s pr`p`rfm`ljobs cb trmêleuo`s sbgbajltbs, JK JC JF   7 JK

y

KF F C JF   7 F K

Y`r pr`pmbcjcbs cb ojs pr`p`rfm`lbs, (JK ); 7 JF µ JC, (KF ); 7 JF µ FC

Vugjlc` tbrgml` j tbrgml` ojs meujocjcbs jltbrm`rbs `ktblbg`s, (JK ); + (KF ); 7 JF µ (JC + CF ) 7 ( JF );

Sb`rbgj ;.;;. Vm bl ul trmêleuo` rbftêleuo` ∄ JKF   sb sjtmsdjfb oj meujocjc, ( F J); + (FK ); 7 (JK ); , blt`lfbs bo   ∄JKF   bs rbftêleuo` y   ∩KF J bs ul êleuo` rbft`. Cbg`strjfmöl. Vbj ∄JKF  bl

bo fujo sus ojc`s sjtmsdjfbl oj meujocjc, ( FJ ); + (F K ); 7 (JK ); .

Cjc`s o`s sbegblt`s F J y FK cbo trmêleuo` ∄JKF  , f`lstrumg`s ul trmêleuo` rbftêleuo` ∄G L [ cb fjtbt`s G L   y G [ f`l G L   ∿ 7 F J y G [ ∿ 7 F K .

Dmeurj ;.;91 [bfçpr`f` cbo tb`rbgj cb Ymtêe`rjs Bl bo trmêleuo` ∄ L G [, p`r bo tb`rbgj cb Ymtêe`rjs sb tmblb (G L ); + (G [); 7 ( [L ); . [bbgpojzjlc` ojs f`lerublfmjs [bbgpojzjlc` f`lerublfmjs jltbrm`rbs jltbrm`rbs sb `ktmblb `ktmblb (FJ ); + (F K ); 7 ([L ); , pbr` (F J); + (FK ); 7 (JK ); .

FJYÇSRO@ ;. JVYBFS@V CMVFMYOMLJ[BV1 CMVFMYOMLJ[BV1 F@LE[RBLFMJ F@LE[RBLFMJ ] VBGBAJLQJ

6:

Yubst` qub oj gbcmcj cb o`s sbegblt`s bs ul lñgbr` p`smtmv`, sm f`gpjrjg`s ojs meujocjcbs jltbrm`rbs sb `ktmblb ([L ); 7 (JK ); , cb c`lcb [L   ∿ 7 JK . Blt`lfbs ∄ JKF   ∿ (OOO) ;.;.:.. 7 ∄ L [G  p`r bo frmtbrm` (OOO);.;.: Yubst` qub bo ∄ L [G  bs rbftêleuo`, bo trmêleuo` ∄ JKF  tjgkmíl bs rbftêleuo`. F`l kjsb jo tb`rbgj cb Ymtêe`rjs oj j﬊rgjfmöl s`krb oj f`lerublfmj cb bst`s trmêleuo`s bs mlgbcmjtj.

F`ròjrm` ;.:6. C`s trmêleuo`s rbftêleuo`s s`l sbgbajltbs sm oj rjzöl bltrb sus hmp`tblusjs bs meujo j oj rjzöl bltrb ul pjr cb fjtbt`s h`göoè`s.

Dmeurj ;.;:1 Vbgbajlzj sbeñl pr`p`rfm`ljomcjc Cbg`strjfmöl. O`s trmêleuo`s ∄JKF   y ∄BED  s`l rbftêleuo`s y oj BD  bs meujo j oj rjzöl bltrb o`s fjtbt`s JF   y JE rbspbftmvjgbltb.

rjzöl bltrb sus hmp`tblusjs JK y

Y`r hmpötbsms, JK JF . 7 BE BD

Y`r bo tb`rbgj cb Ymtêe`rjs tblbg`s1 (JK ); 7 (JF ); + (F K ); , (BD ); 7 (BE ); + (ED );

[bbgpojzjlc` bl oj pr`p`rfmöl cjcj y usjlc` ojs pr`pmbcjcbs cb ojs pr`p`rfm`lbs `ktblbg`s, ;

;

;

;

;

(JK ) 7 (JF ) ; + (F K ); 7 (JF ) ; 7 (FK ); (ED ) (BE ) (BE ) + (ED ) (BD );

Y`r sbr oj gbcmcj cb sbegblt`s p`smtmvj f`lfoumg`s qub JK JF FK 7 7 ED BE BD

Y`r bo frmtbrm` cb sbgbajlzj cb trmêleuo`s (OOO) ;.;.:, (OOO) ;.;.:, ∄JKF   ∿ 7 ∄ BD E

F`ròjrm` ;.:3. C`s trmêleuo`s msösfbobs s`l f`lerubltbs sm tmblbl oj kjsb y oj joturj s`krb oj kjsb f`lerubltbs. F`ròjrm` F`ròjr m` ;.:2. C`s trmêleuo`s bqumoêtbr`s s`l f`lerubltbs sm ojs joturjs s`l f`lerubltbs.

6. F`gp`lbltb Ybcjeöemf`. Bl bstb fjpçtuo` sb rbjomzj ul jlêomsms cbo g`cbo` cb Tjl Hmbob bl oj blsbújlzj cb oj eb`gbtrçj, oube` sb bstucmjl bstucm jl o`s bstêlcjrbs kêsmf`s y o`s omlbjgmblt`s omlbjgmblt`s furrmfuojrbs furrmfuojrbs bl gjtbgêtmfjs gjtbgêtmfjs rbdbrbltbs rbdbrbltbs j oj blsbúj blsbújlzj lzj cb o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj, jcbgês, sb hjfb ul pjrjobo` bltrb o`s f`ltblmc`s tbgêtmf`s cb oj eb`gbtrçj, f`gpjrjlc` tbxt`s cb c`s bcmt`rmjobs rbf`l`fmcjs.

6.:. 6. :.

Bo g`c `cb bo` cb T Tjl jl Hmb mbob ob

Bstb g`cbo`, pr`pubst` p`r Cmlj y Ymbrrb Tjl Hmbob, cjtj j ﬊ljobs cb o`s jú`s fmlfubltj, pojltbj ul`s lmvbobs f`lfbptujobs p`r o`s fujobs pjsj ul lmú`, y prbsbltj joeuljs djsbs qub pbrgmtbl bo pjs` cb ul lmvbo jo `tr`. Bo g`cbo` hj pbrgmtmc`, j o` ojre` cb o`s jú`s bojk`rjr furrçfuo`s jkmbrt`s cb eb`gbtrçj. Bo cbsjrròo` cbsjrròo` `rmemljo cb bstj tb`rçj sb blfubltrj blfubltrj bl bo omkr` ‟Vtrufturb jlc Mlsmeht.‗ ^;4W ^;4W.. Jquç Tjl Hmbob, rbsjotj ojs mcbjs kêsmfjs cbo g`cbo`1 ‟bo jprblcmzjab cb oj eb`gbtrçj sb hjfb pjsjlc` p`r ul`s cbtbrgmljc`s lmvbobs cb pblsjgmblt` y f`l`fmgmblt`, qub l` vjl js`fmjc`s j oj bcjc y sò` jofjlzjlc` ul lmvbo sb pubcb pjsjr jo smeumbltb‗ , sbújoj qub ‟fujoqumbr pbrs`l pbrs`lj j pjsj p p`r `r t`c`s bs`s lmvbobs y, su gjy`r ` gbl`r c`gmlm` cb oj eb`gbtrçj ml﬋umrê bl qub o` hjej gês ` gbl`s rêpmcjgbltb.‗ ^;4W. ^;4W. @tr` jspbft` qub rbsjotj rbsjotj bs qub ‟jofjlzjr ul lmvbo supbrm`r cb pblsjgmblt` smelm﬊fj, qub f`l ul lubv` `rcbl cb pblsjgmblt`, ulj pbrs`lj bs fjpjz rbspbft` j cbtbrgmljcjs `pbrjfm`lbs, jpomfjrojs j lubv`s `kabt`s.‗

F`g` sb pubcb `ksbrvjr, pojltbjl qub pjrj bo jprblcmzjab cb oj eb`gbtrçj hjy ulj sbfublfmj oöemfj qub vj cb o`s f`ltblmc`s gês smgpobs j o`s gjs f`gpoba`s, fjrjftbrmzjc`s p`r o`s lmvbobs qub sb vjl jofjlzjlc` j gbcmcj qub sb vjl jprblcmblc` f`lfbpt`s gjtbgjtmf`s. Jsm sb vj bstrufturjlc` bo lmvbo cb rjz`ljgmblt` cb o`s bstucmjltbs, qub l` cbpblcb sb oj bcjc sml` cbo pr`fbs` blsbújlzj-jprblcmzjab qub sb hj rbjomzjc` cb ojs gjtbgêtmfjs y bl pjrtmfuojr cb oj eb`gbtrçj. Bst` j su vbz mgpomfj qub hjy c`s bobgblt`s mgp`rtjltbs bl bo jprblcmzjab cb oj eb`gbtrçj1 Bo obleujab utmomzjc`. Bo smelm﬊fjc` smelm﬊fjc` cb o`s f`ltblmc`s. f`ltblmc`s. Bl fjcj lmvbo sb cbkb gjlbajr ul obleujab guy jpr`pmjc` y sb cbkb tblbr bl fubltj bo lmvbo cb rjz`ljgmblt` bl qub sb blfubltrj bo bstucmjltb. O`s lmvbobs cb rjz`ljgmblt` sbeul Tjl Hmbob s`l fmlf` (cbo lmvbo 9 jo lmvbo 3) y oj fojsm﬊fjfmöl sb hjfb f`l kjsb jo jprblcmzjab cb o`s bstucmjltbs y s`l1

Lmvbo 9 (Tmsujomzjfmöl ` [bf`l`fmgmblt`)1 Vb rbjomzj cbscb bo pult` cb vmstj vmsujo, o`s bstucmjltbs fojsm﬊fjl ﬊eurjs, rbf`l`fbl su l`gkrb y cbsfrmkbl joeuljs fjrjftbrçstmfjs cb su d`rgj y tjgjú`. Jcbgês lmcjc. bstjkobfbl sbgbajlzj cb uljs ﬊eurjs f`l `trjs ` f`l `kabt`s qub rbf`l`fbl bl su f`tmcmjSrbs s`l ojs fjrjftbrçstmfjs dulcjgbltjobs cb bstb lmvbo1

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:. O`s `kabt`s sb pbrfmkbl bl su t`tjomcjc f`g` ulj ulmcjc, sml cmdbrblfmjr sus jtrmkut`s y f`gp`lbltbs. ;. Vb cbsfrmkbl p`r su jpjrmblfmj dçsmfj gbcmjltb cbsfrmpfm`lbs vmsujobs y rbojfm`ljlcòjs j bobgblt`s gblt `s djgmomjrbs djgmomjrbs cbo blt`rl`. blt`rl`. L` hjy obleujab eb`gítrmf` kêsmf` pjrj oojgjr j ojs ﬊eurjs ﬊eurjs p`r su l`gkrb f`rrbft`. 6. L` rbf`l`fbl cb d`rgj bxpoçfmtj f`gp`lbltbs y pr`pmbcjcbs cb o`s `kabt`s qub sb bstjl trjkjajlc`. Bstjs fjrjftbrmstmfjs fjrjftbrmstmfjs sb pubcbl cbsjrròojr cbsjrròojr bl prbbsfòjr prbbsfòjr y o`s prmgbr`s lmvbobs cb bcufjfm bcufjfmöl öl kêsmfj kêsmfj prmgjrmj.

Lmvbo : (Jlêomsms)1 Bl bstb lmvbo bo bstucmjltb f`gprblcb qub ojs ﬊eurjs bstêl d`rgjcjs p`r pjrtbs ` bobgblt`s pr`pm`s y bstêl c`tjcjs cb pr`pmbcjcbs gjtbgêtmfjs qub cbsfrmkbl ojs pjrtbs qub f`ld`rgjl f`ld`r gjl ulj ﬊eurj. Vb oèrj j trjvís trjvís cb oj bxpbrmgbltjfmöl bxpbrmgbltjfmöl f`l boojs. @trjs fjrjftbrçstm fjrjftbrçstmfjs fjs cb bstb lmvbo s`l1 :. Vb pbrfmkbl o`s f`gp`lbltbs y pr`pmbcjcbs (f`lcmfm`lbs lbfbsjrmjs) cb o`s `kabt`s y ﬊eurjs. Bst` o` `ktmblbl tjlt` cbscb oj `ksbrvjfmöl f`g` cb oj bxpbrmgbltjfmöl. ;. Cbsfrmkb ojs ﬊eurjs cb ulj gjlbrj mld`rgjo, bstjkobfb pr`pmbcjcbs pbr` l` rbojfm`lj uljs pr`pmbcjcbs pr`pm bcjcbs f`l `trjs ` uljs ﬊eurjs f`l `trjs. `trjs. F`g` gufhjs gufhjs cb﬊lmfm`lbs cb﬊lmfm`lbs bl Eb`gbtrçj Eb`gbtrçj sb bojk`rjl j pjrtmr cb pr`pmbcjcbs, l` pubcbl bojk`rjr cb﬊lmfm`lbs. 6. Bxpbrmgbltjl Bxpbrmgbltjlc` c` f`l ﬊eurjs ﬊eurjs u `kabt`s pubcbl bstjkobfbr lubvjs lubvjs pr`pmbcjcbs. pr`pmbcjcbs. 3. L` bstj bl oj fjpjfmcjc cb rbjomzjr fojsm﬊fjfm`lbs cb `kabt`s y ﬊eurjs j pjrtmr cb sus pr`pmbcjcbs. Bl bstb lmvbo o`s bstucmjltbs bgpmbzjl j eblbrjomzjr y tmblbl oj fjpjfmcjc cb rbf`l`fbr joeuljs ﬊eurjs f`g` trmêleuo`s, rbftêleuo`s y pòçe`l`s, mlmfmjlc` jsç su rjz`ljgmblt` gjtbgêtmf`.

Lmvbo ; (@rcbljfmöl ` Fojsm﬊fjfmöl)1 Vb mlmfmj bo pblsjgmblt` d`rgjo, bl bstb lmvbo bo bstucmjltb pubcb hjfbr ulj fojsm﬊fjfmöl cb ojs ﬊eurjs tblmblc` bl fubltj sus fjrjftbrçstmfjs ` pr`pmbcjcbs. Yubcb cjr cb﬊lmfm`lbs cb gjlbrj f`rrbftj. Sjgkmíl pubcb bltblcbr ulj cbg`strjfmöl gjtbgêtmfj rbjomzjcj p`r `trj pbrs`lj, pbr` l` bstê bl fjpjfmcjc cb hjfbroj p`r sç gmsg`s. Bl bstb lmvbo1 :. Cbsfrmkb ojs ﬊eurjs cb gjlbrj d`rgjo, bs cbfmr sb sbújojl ojs f`lcmfm`lbs lbfbsjrmjs y su﬊fmbltbs qub cbkbl fugpomr. Bltmblcb bo smelm﬊fjc` cb ojs cb﬊lmfm`lbs, su pjpbo cbltr` cb oj eb`gbtrçj. ;. [bjomzjl fojsm﬊fjfm`lbs oöemfjs. Bst` smelm﬊fj qub rbf`l`fbl fög` ulj uljss pr`pmbcjcbs sb cbrmvjl cbrmvjl cb `trjs, `trjs, bstjkobfmblc` bstjkobfmblc` rbojfm`lbs rbojfm`lbs bltrb bltrb sm. 6. Ojs cbg`strjfm`lbs bl oj gjy`rçj gjy`rçj cb o`s fjs`s, fjs`s, l` ojs bltmblcbl bl fujlt` j su bstrufturj. Bst` sb cbkb j qub bl su lmvbo cb rjz`ljgmblt` oöemf` s`l fjpjfbs cb f`gprblcbr pjs`s mlcmvmcujobs pbr` l` cb jsmgmojro`s bl su t`tjomcjc.

Lmvbo 6 (Cb cbcuffmöl d`rgjo)1 Bltmblcb y rbjomzj rjz`ljgmblt`s oöemf`s d`rgjobs, c`lcb oj cbg`strjfmöl bs bo ñlmf` fjgml` pjrj cbtbrgmljr sm ulj j﬊rgjfmöl bs vbrcjcbrj ` djosj. Vb pubcb f`gprblcbr oj bstrufturj jxm`gêtmfj cb ojs gjtbgêtmfjs y oj bxmstblfmj cb cbg`strjfm`lbs jotbrljtmvjs j ul tb`rbgj. Vb pubcbl cbcufmr pr`pmbcjcbs cb ojs ﬊eurjs cbscb bo pult` cb vmstj d`rgjo y cbcufmr joeuljs `trjs gês f`gpobajs. Jofjlzjr bstb lmvbo smelm﬊fj1 :. [bjomzjr cbcuffm`lbs y cbg`strjfm`lbs oöemfjs y d`rgjobs, vmblc` su lbfbsmcjc pjrj austm﬊fjr ojs pr`p`smfm`lbs pojltbjcjs. ;. F`gprblcbl y gjlbajl ojs rbojfm`lbs bltrb pr`pmbcjcbs y sb d`rgjomzjl bl smstbgjs jxm`gêtmf`s, p`r o` qub yj sb bltmblcb oj ljturjobzj jxm`gêtmfj cb ojs gjtbgêtmfjs.

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6. Vb f`gprblcb fög` sb pubcb oobejr j o`s gmsg`s rbsuotjc`s pjrtmblc` cb pr`p`smfm`lbs ` prbgmsjs cmstmltjs o` qub pbrgmtb bltblcbr qub sb pubcjl rbjomzjr cmstmltjs d`rgjs cb cbg`strjfm`lbs pjrj `ktblbr ul gmsg` rbsuotjc`. rbsuotjc`.

Lmvbo 3 ([me`r)1 Bstb lmvbo cm﬊fmogbltb cm﬊fmogbltb bs jofjlzjc` jofjlzjc` p`r o`s bstucmjltbs bstucmjltbs cb bcufjföl bcufjföl kêsmfj, b mlfous` mlfous` p`r o`s bstucmjltb bstucmjltbss cb prmgbr`s sbgbstrbs cb ulmvbrsmcj ulmvbrsmcjc. c. Joeul`s Joeul`s mlvbstmej mlvbstmejc`rbs c`rbs bl bcufjfmöl bcufjfmöl gjtbgê gjt bgêtmfj tmfj prbsfml prbsfmlcbl cbl cb bstb, bstb, p`r bo lmvbo lmvbo cb f`gpob f`gpobamc amcjc jc qub tmblb. Yrbsblt Yrbsbltjj ojs smeumbl smeumbltbs tbs fjrjftbrmstmfjs1 :. Vb f`l`fb oj bxmstblfmj cb cmdbrbltbs smstbgjs jxm`gêtmf`s> sb pubcbl jljomzjr y f`gpjrjr cmdbrbltbs eb`gbtrçjs. ;. Vb pubcb trjkjajr oj eb`gbtrçj cb gjlbrj jkstrjftj sml lbfbsmcjc cb babgpo`s f`lfrbt`s, jofjlzêlc`sb bo gês jot` lmvbo cb rme`r gjtbgêtmf`. Bl su omkr` Tjl Hmbob bxpomfj ojs fjrjftbrmstmfjs qub tmblb fjcj ul` cb bst`s lmvbobs, bltrb o`s fujobs bstjl1

:. Abrjrqumzjfm`l y sbfublfmjomcjc cb o`s lmvbobs1 O`s lmvbobs cb rjz`ljgmbl` tmblbl ul `rcbl qub l` sb jotbrj y fjcj lmvbo sb jp`yj bl bo jltbrm`r. jltbrm`r. Bst` mgpomfj ‟o` qub bs mgpoçfmt` bl ul lmvbo sb f`lvmbrtb bl bxpoçfmt` bl bo smeumbltb lmvbo.‗ ^;4W ^;4W ;. [bojfm`l bltrb bo obleujab y o`s lmvbobs1 Bo obleujab bs ulj fjrjftbrçstmfj guy mgp`rtjltb bl fjcj lmvbo, pubs pbrgmtb qub j gbcmcj qub ul bstucmjltb jvjlzj bl su pr`fbs` cb jprblcmzjab cb ojs gjtbgêtmfjs, gjtbgêtmfjs, tjgkmíl tjgkmíl gba`rj su obleujab gjtbgêtmf`. 6. Yjs` cb ul lmvbo j `tr` sb pr`cufb cb d`rgj f`ltmluj1 Bo pjs` cb ul lmvbo j `tr` sb rbjomzj cb d`rgj erjcujo y curjltb joeñl tmbgp` bo bstucmjltb sb blf`ltrjrê bl ul pbrm`c` cb trjlsmfmöl bl bo qub f`gkmljrj cmfh`s rjz`ljgmblt`s. Bl bo omkr` ‟Rlj pr`pubs pr`pubstj tj cb dulcj dulcjgbltj gbltjfmöl fmöl pjr pjrj j oj blsbú blsbújlzj jlzj cb oj eb`gbt eb`gbtrçj1 rçj1 Bo g`cbo` g`cbo` cb Tjl Hmbob  cb Jcboj Ajmgb Yjst`r, Êlebo Eutmírrbz [`crçeubz, ^:3W [`crçeubz, ^:3W o`s o`s jut`rbs rbjomzjl ulj cbsfrmpfmöl cb o`s lmvbobs cb Tjl Hmbob y cbo cbsjrròo` cb o`s lmvbobs rjz`ljgmblt` cbscb o` cbsfrmptmv` bl bo lmvbo kêsmf`, hjstj ul lmvbo cb cbcuffmöl d`rgjo, bl bo fujo o`s bstucmjltbs jofjlzjl bo gêxmg` lmvbo cb rjz`ljgmbl rjz`l jgmblt`. t`. Sjgkmíl jgkmíl prbsbltjl prbsbltjl cmrbftrmfbs, cmrbftrmfbs, oojgjcjs oojgjcjs cmrbftrmfbs cmrbftrmfbs oojgjc oojgjcjs js ‟djsbs cb jprblcmzjab‗ , bstjs s`l jftmvmcjcbs qub jyucjl jo bstucmjltb bstucmjltb j jofjlzjr jofjlzjr o`s cmdbrbltbs cmdbrbltbs lmvbobs cb rjz`ljgmbl rjz`ljgmblt`. t`. Bstjs djsbs bstjkobfbl ulj `rejlmzjfmöl qub ob pbrgmtb jo bstucmjltb pjsjr cb ul lmvbo cb rjz`ljgmblt` jo smeumbltb. J f`ltmlujfmöl smeumbltb. f`ltmlujfmöl sb prbsbltjrêl prbsbltjrêl ojs fjrjftbrmstmfjs fjrjftbrmstmfjs cb fjcj uljcb ojs fmlf` djsbs cb jprblcmzjab1 jprblcmzjab1 :. [bf`l`fmgmblt`1 Bstj bs ulj djsb cb mld`rgjfmöl pjrj bo pr`dbs`r, yj qub ob pbrgmtb jvbrmeujr o`s f`l`fmgmblt`s prbvm`s cb o`s bstucmjltbs s`krb bo tbgj j trjtjr. Bstj jftmvmcjc bs ulj jyucj pjrj qub bo c`fbltb l` rbpmtj tbgjs j o`s bstucmjltbs. bstucmjltbs. Bl bstj prmgbrj prmgbrj djsb o`s bstucmjltbs bstucmjltbs rbfmkbl mld`rgjfm`l s`krb bo lubv` tbgj j trjtjr, o`s tmp`s cb pr`kobgjs j rbsòvbr, bstrjtbemjs b mlstrugblt`s qub sb usjrêl. Fujlc` bo pr`dbs`r f`l`fb bo lmvbo cb sus bstucmjltbs sb pubcb `gmtmr bstj djsb> p`r babgpo`, fujlc` bo pr`dbs`r cb ul furs` f`ltmlñj f`l o`s bstucmjltbs cb d`rgj f`ltçluj curjltb bo jú` ` jú`s smeumbltbs.

;. @rmbltjfmöl cmrmemcj1 Bl bstj djsb sb euçj jo bstucmjltb gbcmjltb gbcmjltb jftmvmcjcbs y pr`kobgjs (hbfh` (hbfh`ss p`r bo pr`dbs`r ` pr`pubst`s p`r o`s bstucmjltbs) pjrj qub j pjrtmr cb boo`s jprblcjl o`s f`lfbpt`s y pr`pmbcjcbs kêsmfjs kêsmfjs cbo tbgj bstucmjc`. bstucmjc`. Bs lbfbsjrm` qub ojs jftmvmcjcbs jftmvmcjcbs bstjkobfmcjs bstíl cmrmemcjs j oj jcqumsmfmöl jcqumsmfmöl cb f`lfbpt`s, pr`pmbcjcbs pr`pmbcjcbs y cb﬊lmfm`lbs. cb﬊lmfm`lbs. Jsm gmsg` Tjl Tjl Hmbob(:=84, p =5) jftmvmcjcbs   (cb oj sbeulcj djsb ), sm sb sbobffm`ljl fumcjc`sjgbltb, f`lstmtuybl gblfm`lj gblfm` qub ‟ojscbo oj kjsb lj jcbfujcj pblsjgmblt` cb lmvbo supbrm`r.^;4W ^;4W

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6. Bxpomfmtjfmöl1 Rlj cb ojs ﬊ljomcjcbs prmlfmpjobs cb oj tbrfbrj djsb, Eutmírrbz (:==9), bs pbrgmtmr qub o`s bstucmjltbs mltbrfjgkmbl sus bxpbrmblfmjs, qub bxpomqubl cb quí gjlbrj hjl rbsubot` ojs jftmvmcjcbs y f`gbltbl ojs rbeuojrmcjcbs `ksbrvjcjs, t`c` cbltr` cb ul f`ltbxt` cb cmjoè` bl bo erup`. Bs mltbrsjltb mltbrsjltb fujlc` surebl cmvbrs`s cmvbrs`s pult`s cb vmstj, vmstj, pubs fujlc` fjcj bstucmjltb bstucmjltb austm﬊fj su `pmlmöl jljomzj f`l gês fumcjc` sus mcbjs (` ojs cb ul f`gpjúbr`), ojs `rcblj y pr`furj bxprbsjrojs bxprbs jrojs f`l fojrmcjc.(Eutmír fojrmcjc.(Eutmírrbz rbz :==9, pp 663). Cujrjltb Cujrjltb bstj djsb bo bstucmjltb bstucmjltb cbkb usjr ul v`fjkuojrm` jcbfujc` jo bxprbsjrsb, pbrgmtmblc` qub sb j﬊jlfb bo v`fjkuojrm` jprblcmc` curjltb bo jltbrm`r lmvbo.^:3W lmvbo.^:3W 3. @rmbltjfmöl omkrb1 Bl bstj djsb o`s bstucmjltbs cbkbrêl usjr o`s f`l`fmgmblt`s jcqumrmc`s pjrj cbsjrròojr rròo jr jftmvmcjcbs y rbsòvbr pr`kobgjs pr`kobgjs f`l gjy`r gjy`r f`gpobamcjc f`gpobamcjc qub o`s pr`pubst`s pr`pubst`s bl oj djsb ;. Oj pjrtmfmpjfmö pjrtm fmpjfmöll cbo pr`dbs`r pr`dbs`r cbkb sbr gçlmgj yj qub cbkb sbr bo bstucmjltb bstucmjltb qumbl blfubltrb blfubltrb sòufm`lbs sòufm`lbs p`r sç gmsg`, gmsg`, jpomfjlc` jpomfjlc` o`s f`lfbpt`s, f`lfbpt`s, pr`pmbcjcbs pr`pmbcjcbs y cb﬊lmfm`lbs cb﬊lmfm`lbs jprblcmcjs. jprblcmcjs.^:3 ^:3WW O`s pr`kobgjs pojltbjc`s bl bstj djsb cbkbl sbr jkmbrt`s, f`l vjrm`s fjgml`s cb rbsòufmöl, bst` pbrgmtmrj qub bo bstucmjltb f`gkmlb y jpomqub o` jprblcmc`. 2. Mltberjfmöl1 Bl bstj djsb bo pr`dbs`r pr`dbs`r pubcb pr`p`rfm`ljr pr`p`rfm`ljr mcbjs eblbrjobs s`krb s`krb bo tbgj trjtjc` trjtjc`,, pbr` l` mlfoumr f`lfbpt`s ` cb﬊lmfmölbs lubv`s jo bstucmjltb> sò` cbkb sbr jfuguojfmöl, f`gpjrjfmöl y f`gkmljfmöl cb f`sjs qub yj sb f`l`fb.^:3W f`l`fb.^ :3W.. Cb meujo d`rgj Ajmg Ajmgbb y Eutmírrbz Eutmírrbz cmfbl qub f`gpobtjcj f`gpobtjcj bstj djsb, bo bstucmjltb tblcrê j su cmsp`smfmöl ulj lubvj rbc cb rbojfm`lbs gbltjobs, gês jgpomj qub oj jltbrm`r y hjkrj jcqumrmc` ul lubv` lmvbo cb rjz`ljgmblt`. Sjgkmíl hjfbl ul jlêomsms drbltb j f`g` sb cbkb bvjoujr jo bstucmjltb bl fjcj lmvbo cb rjz`ljgmblt`, prbsbltjl joeul`s tjoobrbs ` euçjs qub pubcbl cbsjrròojr o`s bstucmjltbs cb jfubrc` f`l o`s lmvbobs cb Tjl Hmbob. Bl bo jrtçfuo` ‟Rl jlêomsms cbo trjtjgmblt` cb oj sbgbajlzj bl o`s c`fugblt`s `﬊fmjobs y tbxt`s bsfòjrbs cb gjtbgêtmfjs bl oj sbeulcj gmtjc cbo smeo` XX,‗  Bsfucbr` (:===) ^=W ^=W prbsbltj prbsbltj ul cbsjrròo` hmstörmf`, cb oj blsbújlzj cbo f`lfbpt` cb sbgbajlzj y cbo tb`rbgj cb Shjobs curjltb o`s ñotmg`s fmlfubltj jú`s, sustbltjc` sustbl tjc` f`l c`fugblt`s c`fugblt`s furrmfuojrbs furrmfuojrbs y joeul`s joeul`s tbxt`s cb gjtbgêtmfjs. gjtbgêtmfjs. Bl bo bstucm` bvmcblfmj omgmtjfm`lbs cb o`s tbxt`s pjrj bo gjlba` cb bst`s tbgjs, eblbrjcjs j pjrtmr cb o`s fjgkm`s fjgkm`s bdbftujc`s bl c`fugblt`s `﬊fmjobs. `﬊fmjobs. Bo jut`r pojltbj oj lbfbsmcjc cb f`lstrumr ul furrçfuo` lubv`, qub mlfouyj o`s f`lfbpt`s foêsmf`s y qub sbújob oj mgp`rtjlfmj cb cbsjrròojr vjrmjs gjlbrjs cb prbsbltjr oj eb`gbtrçj bufomcmjlj, qub mlfouyjl oj utmomzjfm`l cb smstbgjs cb f``rcbljcjs, vbt`rbs y trjlsd`rgjfm`lbs> qub jcbgês jk`rcb oj f`lstruffmöl cb pr`kobgjs eb`gítrmf`s rbojfm`ljc`s f`l oj vmcj f`tmcmjlj. Bl `tr` jrtçfuo` pukomfjc` bl bo ;996, ‟O ‟Oj j sbgbajlzj f`g` f`g` `kabt` cb blsb blsbújlzj újlzj ‖ jpr jprblcmz blcmzjab jab bl oj rbojfmö rbojfmöl l bltr bltrbb bo f`l` f`l`fmgmbl fmgmblt` t` pr pr`dbsm` `dbsm`ljo ljo cbo pr pr`dbs` `dbs`rr cb gjtbgêtmf gjtbgêtmfjs js cb blsbújlzj blsbújlzj sbfulcjrmj sbfulcjrmj y su prêftmfj‗ , Bsfucbr` ^:9 Bsfucbr` ^:9WW cbstjfj c`s jspbft`s dulcjgbltjobs pjrj oj blsbújlzj cbo f`lfbpt` cb sbgbajlzj,

vmlfuojc`s f`l oj pr`pubstj cb Obg`lmcms (:==9)^:2W (:==9)^ :2W,, s`krb ojs d`rgjs cb rbprbsbltjfmöl sbgmötmfj y su us`1 f`rrbsp`lcblfmj p`lcblfmj bltrb bltrb bobgblt`s cb ulj ﬊eurj y o`s f`rrbsf`rrbs[bojfmöl mltrj﬊eurjo1 C`lcb sb cbstjfj oj f`rrbs p`lcmbltbs cb su sbgbajltb bstjlc` jusbltb oj mcbj cb trjlsd`rgjr ulj ﬊eurj bl `trj.

Oj trjlsd`rgjfmöl trjlsd`rgjfmöl eb`gítrmfj1 eb`gítrmfj1 C`lcb sb jljomzj oj trjlsd`rgjfmöl cb ulj ﬊eurj bl `trj, cmstmleumblc` oj vmstj f`g` ñtmo y f`g` `kabt` gjtbgêtmf`. Bsfucbr` gblfm`lj qub o`s g`c`s cb rbprbsbltjfmöl y su us`, bltblcmc`s f`g` p`smkmomcjcbs sbgmötmfjs cb rbprbsbltjr bo f`ltblmc`, s`l obleujab ljturjo, ﬊eurjtmv`, lugírmf`, smgköomf`, cb smtujfmöl y gjtbrmjo

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f`lfrbt`. Kurebr, U.D (:=84) bl su jrtçfuo` ‟Fhjr ‟Fhjrjftbr jftbrmzmle mzmle thb Tjl Hmbob obvbos `d cbvbo`pgbl cbvbo`pgbltt ml eb`gbt eb`gbtry‗ ry‗ ^6W, 6W, hjfb ulj cbsfrmpfmöl cb o`s lmvbobs cb Tjl Hmbob cbscb ul bstucm` qub sb obs hmz` j :3 bstucmjltbs cb erjc` : hjstj erjc` :;, gês ul bstucmjltb cb gjtbgêtmfjs cb oj ulmvbrsmcjc. Ojs prubkjs brjl erjkjcjs bl jucm`. Yrmgbr` hjfb ul bstucm` cb o`s cmkua`s qub hjfbl o`s bstucmjltbs cb o`s trmêleuo`s y cb o`s fujcrmoêtbr`s f`l kjsb j ojs fjrjftbrçstmfjs qub cjl o`s bltrbvmstjc`rbs. Bltrb ojs jftmvmcjcbs qub boo`s rbjomzjkjl bstêl cmkua`, mcbltm﬊fjfmöl, cb﬊lmfmöl, fojsm﬊fjfmöl, ﬊eurj gmstbrm`sj, jxm`gjs, tb`rbgjs y ulj cbg`strjfmöl. Bstj ñotmgj jftmvmcjc jftmvmcjc cbsjrròojcj cbsjrròojcj f`l o`s bstucmjltbs bstucmjltbs cb sbfulcjrmj sbfulcjrmj y f`l bo bstucmjltb bstucmjltb ulmvbrsmtjrm` ulmvbrsmtjrm`.. Rlj vbz rbjomzjcjs ojs bltrbvmstjs sb hjfb ul rbsugbl cb o`s rbsuotjc`s `ktblmc`s j sbms cb o`s fjt`rfb bstucmjltbs bstucm jltbs y cb o`s mlcmfjc`rbs mlcmfjc`rbs qub tmblb fjcj lmvbo cb Tjl Hmbob bl bstj mlvbstmej mlvbstmejfmöl. fmöl. Cb ojs `ksbr`ksbrvjfm`lbs y o`s rbsuotjc`s `ktblmc`s, sb blf`ltrö qub vjrm`s cb o`s bstucmjltbs pjrbfbl bstjr bl trjlsmfmöl bltrb lmvbobs ` sb cbvubovbl cb lmvbo cb jfubrc` j ojs jftmvmcjcbs cbsjrròojcjs.

6.;. 6.;.

Oj b bls lsbú bújl jlzj zj cb cb oj f`l f`ler erub ublf lfmj mj y ssbg bgba bajl jlzj zj..

O`s omlbjgmblt`s furrmfuojrbs bl gjtbgêtmfjs^:4W gjtbgêtmfjs^:4W,, bstjkobfbl qub pjrj bo bstucm` cb ojs gjtbgêtmfjs, fjcj mlstmtufmöl mlstmtufmöl bcufjtmvj bcufjtmvj tmblb jut`l`gçj j oj h`rj cb cbsjrròoj cbsjrròojrr su furrçfuo`, kjsjc`s bl o`s jrtçfuo`s jrtçfuo`s ;9 jo 6: cb oj Oby eblbrjo cb bcufjfmöl, c`lcb sb bspbfm﬊fjl o`s `kabtmv`s y ojs êrbjs kêsmfjs cb f`l`fmgmblt` pjrj oj bcufjfmöl kêsmfj y gbcmj. Oj pr`pubstj furrmfuojr qub sb pojsgj bl o`s omlbjgmblt`s furrmfuojrbs ^:4 furrmfuojrbs ^:4W, W, prbtblcb fjgkmjr bo bsqubgj trjcmfm`ljo cb blsbújlzj cb oj gjtbgêtmfj, jo cbsjrròojr f`ltblmc`s tbgêtmf`s jkstrjft`s y d`rgjobs qub p`stbrm`rgbltb sb usjl bl oj sòufmöl cb pr`kobgjs bl ul f`ltbxt` bspbfç﬊f`. Jftujogbltb bst` sb `gmtb jcufmblc` djotj cb tmbgp` bl ojs mlstmtufm`lbs bcufjtmvjs. J su vbz bstjkobfb oj mgp`rtjlfmj cb rbojfm`ljr ojs gjtbgêtmfjs f`l `trjs cmsfmpomljs, bst` f`ltrmkuyb jo cbsjrròo` mltberjo cb o`s bstucmjltbs f`l oj pbrspbftmvj cb qub pubcjl jsugmr o`s rbt`s cbo smeo` XXM. Vb pr`p`lb ulj bcufjfmöl gjtbgêtmfj qub pr`pmfmb jprblcmzjabs cb gjy`r jofjlfb y gês curjcbr`s qub o`s trjcmfm`ljobs> qub l` söo` hjej íldjsms bl bo jprblcmzjab cb f`lfbpt`s y pr`fbcmgmblt`s sml` bl pr`fbs`s cb pblsjgmblt`s jpomfjkobs y ñtmobs, qub ob pbrgmtjl j o`s bstucmjltbs j jprblcbr fög` jprblcbr. O`s omlbjgmblt`s pojltbjl ulj bstrufturj furrmfuojr p`r pblsjgmblt`s1 Yblsjgmblt` lugírmf` y smstbgjs lugírmf`s. Yblsjgmblt` bspjfmjo y smstbgjs eb`gítrmf`s. Yblsjgmblt` gítrmf` y smstbgjs cb gbcmcjs. Bo pblsjgmblt` jobjt`rm` y o`s smstbgjs cb cjt`s. Yblsjgmblt` vjrmjfm`ljo y smstbgjs joebkrjmf`s y jljoçtmf`s. Bl bo pblsjgmblt` eb`gítrmf`, bl bo fujo sb bstj bld`fjlc` bstb trjkja`, pr`p`lb bldjtmzjr bl oj eb`gbtrçj jftmvjj pjrj bo bstucm` jftmv bstucm` cb o`s smstbgjs eb`gítrmf`s eb`gítrmf`s y su rbprbsbltjf rbprbsbltjfmöl möl bl bo bspjfm`. Yjrtb Yjrtb cb oj jftmvmcjc cbo bstucmjltb y su f`ldr`ltjfmöl f`l bo gulc`, cjlc` prm`rmcjc j oj jftmvmcjc s`krb oj f`ltbgpojfmöl pjsmvj cb ﬊eurjs y sçgkò`s, j ojs `pbrjfm`lbs s`krb ojs rbojfm`lbs y bobgblt`s cb o`s smstbgjs y j oj mgp`rtjlfmj cb ojs trjlsd`rgjfm`lbs bl oj f`gprblsmöl jñl cb jquboo`s f`lfbpt`s qub j prmgbrj vmstj pjrbfbl bstêtmf`s. Bstj f`lfbptujomzjfmöl vj mlmfmjogbltb jf`gpjújcj bl ul prmlfmpm` p`r ebst`s y pjojkrjs cbo obleujab f`gñl, hjstj qub o`s f`lfbpt`s bstíl f`lstrumc`s j ul lmvbo su﬊fmbltbgbltb bstjkob pjrj qub bo bstucmjltb gmsg`ss pubcj pr`p`lbr y bvj gmsg` bvjoujr oujr p`smkobs cb﬊lmfm`lbs cb﬊lmfm`lbs y smgkòmsg`s smgkòmsg`s d`rgjobs. d`rgjobs.

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Rl` cb o`s g`cbo`s qub sb pr`p`lbl bl o`s omlbjgmblt`s bs bo g`cbo` cb Tjl Hmbob yj qub pbrgmtbl bstrufturjr bstruft urjr bo bstucm` cb oj eb`gbtrçj, eb`gbtrçj, p`r gbcm` cb o`s lmvbobs cb pblsjgmblt` pblsjgmblt` bxpubst`s jltbrm`rgbl jltbrm`rgbltb. tb. @tr` c`fugblt` tblmc` bl fubltj s`l o`s bstêlcjrbs kêsmf`s cb f`gpbtblfmjs bl Gjtbgêtmfjs ^::W Gjtbgêtmfjs ^::W (;994) (;994) , c`lcb sb pr`p`lbl o`s babs tbgêtmf`s qub sb cbkbl jk`rcjr bl fjcj êrbj cbo f`l`fmgmblt` bl ojs cmdbrbltbs mlstmtufm`lbs mlstmt ufm`lbs bcufjftmvj bcufjftmvjs. s. Bl bo c`fugblt` c`fugblt` sb cmstmleubl c`s tmp`s kêsmf`s cb f`l`fmgmblt` f`l`fmgmblt` gjtbgêtmf`1 gjtbgêtmf`1 bo f`l`fmgmblt` f`l`fmgmblt` f`lfbptujo y bo f`l`fmgmblt` f`l`fmgmblt` pr`fbcmgbltjo pr`fbcmgbltjo.. Bo prmgbr` bstê gês fbrfjl` j oj rb﬋bxmöl y sb fjrjftbrmzj p`r sbr f`l`fmgmblt` tbörmf`, pr`cufmc` p`r oj jftmvmcjc fèlmtmvj, guy rmf` bl rbojfm`lbs bltrb sus f`gp`lbltbs y f`l `tr`s f`l`fmgmblt`s> tmblb ul fjrêftbr cbfojrjtmv` y sb js`fmj f`l bo sjkbr quí y bo sjkbr p`r quí. Y`r su pjrtb, bo f`l`fmgmblt` pr`fbcmgblt pr`fbcmgbltjo jo bstê gês fbrfjl` fbrfjl` j oj jffmöl y sb rbojfm`lj f`l ojs tíflmfjs y ojs bstrjtbemjs pjrj rbprbsbltjr f`lfbpt`s y pjrj trjlsd`rgjr cmfhjs rbprbsbltjfm`lbs> f`l ojs hjkmomcjcbs y cbstrbzjs cbstrbzjs pjrj bojk`rjr, bojk`rjr, f`gpjrjr y babrfmtjr babrfmtjr joe`rmtg`s joe`rmtg`s y pjrj jreugbltjr jreugbltjr f`lvmlfbltbgbl f`lvmlfbltbgbltb. tb. Bo f`l`fmgmblt` pr`fbcmgbltjo jyucj j oj f`lstruffmöl y rb﬊ljgmblt` cbo f`l`fmgmblt` f`lfbptujo y pbrgmtb bo us` b﬊fjz, ﬋bxmkob y bl f`ltbxt` cb o`s f`lfbpt`s, pr`p`smfm`lbs, tb`rçjs y g`cbo`s gjtbgêtmf`s> p`r tjlt`, bstê js`fmjc` f`l bo sjkbr fög`. O`s bstêlcjrbs sb blfubltrjl `rejlmzjc`s bl fmlf` f`lault`s cb erjc`s qub tjgkmíl s`l oojgjc`s fmfo`s1 Fmfo` :1 Erjc`s prmgbr`, sbeulc` y tbrfbr`. Fmfo` ;1 Erjc`s fujrt` y qumlt`. Fmfo` 61 Erjc`s sbxt` y síptmg`. Fmfo` 31 Erjc`s `ftjv` y l`vbl`. Fmfo` 21 Erjc`s cífmg` y ulcífmg`. Bstj cmstrmkufmöl sb hjfb pjrj cjr gjy`r ﬋bxmkmomcjc j oj cmstrmkufmöl y `rejlmzjfmöl cb ojs jftmvmcjcbs cbltr` cbo tmbgp` bsfòjr y pjrj jp`yjr jo c`fbltb bl oj `rejlmzjfmöl cb jgkmbltbs y smtujfm`lbs cb jprblcmzjab smelm﬊fjtmv`, qub bstmguobl j o`s bstucmjltbs j supbrjr j o` ojre` cb cmfh`s fmfo`s o`s lmvbobs cb f`gpbtblfmj f`gpbtblfmj rbspbftmv`s. rbspbftmv`s. F`g` bl bstb trjkja` pojltbj bo bstucm` cb oj sbgbajlzj y f`lerublfmj, o`s tbgjs sb cbsjrròojl bl bo pblsjgmblt` pblsjgmb lt` bspjfmjo y smstbgj smstbgj eb`gítrmf`. eb`gítrmf`. Bl o`s bstêlcjrbs bstêlcjrbs kêsmf`s kêsmf`s bl gjtbgêtmfjs gjtbgêtmfjs ^::W ^::W,, blf`ltrjg`s ulj pr`pubstj cbscb prmgbr fmfo` hjstj bo fujrt`. Ojs pr`pubstjs sb rbojfm`ljl bl oj tjkoj 6.:.

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[b [bvms vmsmöl möl cb tbxt`s tbxt`s bsf bsfòj òjrbs rbs11

Oj rbvmsmöl cb tbxt`s bsfòjrbs oj rbjomfb f`l bo ﬊l cb mcbltm﬊fjr o`s tbgjs qub sb jk`rcjl f`l rbojfmöl j oj f`lerublfmj y sbgbajlzj cb ﬊eujs y jo cbsjrròo` cb o`s lmvbobs qub sb pojltbjl bl bo g`cbo` cb Tjl Hmbob, qub rb﬊brbl j oj blsbújlzj cb oj eb`gbtrçj j lmvbo cb kêsmfj sbfulcjrmj. sbfulcjrmj. J su vbz sb qumbrb blf`ltrjr rbojfmöl bltrb o`s pblsjgmblt`s y ul trjtjgmblt` cb oj f`lerublfmj y sbgbajlzj f`l smtujfm`lbs pr`kobgjs. O`s tbxt`s f`lsuotjc`s s`l cb o`s jú`s (;995 - ;9:9), utmomzjc`s bl bo kjfhmoobrjt` y smrvbl cb jp`y` j o`s c`fbltbs fujlc` fujlc` prbpjrjl b mgpjrtbl sus fojsbs bl bo juoj. J f`ltmlujfmöl f`ltmlujfmöl sb gubstrjl gubstrjl ojs c`s tjkojs 6.; y 6.6 f`l o`s f`ltblmc`s cb o`s gmsg`s, oj prmgbrj bs cb1 ‟Gm Jvblturj Gjtbgêtmfj 4 j =‗ cb Kblajgml Yomlm` [`crmeubz, Jokbrt` Vêblz @ojrtb, Oums Y`gpomlm` Kbotrêl Kbotrêl, Ujotbr Jk`lcjl`> bcmt`rmjo Bcufjtmvvj ;9:9, y oj sbeulcj1 ‟Lubvjs Bcufjtm ‟Lubvjs gjtbgêtmfjs gjtbgêtmfjs 5, 8 y =‗ cb Cmjlj F`stjlzj Vjoejc` Vjoejc` [`crmeubz, bcmt`rmjo Vjltmoojlj ;995. Jo f`gpjrjr o`s f`ltblmc`s tbgêtmf`s p`r erjc`s y p`r bcmt`rmjobs s`l o`s tbgjs jk`rcjc`s bl fjcj ul` s`l smgmojrbs y qub bl o`s ñotmg`s erjc`s sb cbsjrròojl cbg`strjfm`lbs pr`pmjs pjrj oj oobvjr j oj sbgb ajlzj cb trmêleuo`s usjlc` bo gít`c` cmrbft` ` p`r rbcuffmöl jo jksurc`. Bl o`s tbxt`s sb cbsjrròojl o`s f`ltblmc`s utmomzjlc` ul obleujab d`rgjo cb ojs gjtbgêtmfjs pjrtmfuojrgbltb cb oj eb`gbtrçj, c`lcb sb oobvj jo bstucmjltb j rbjomzjr jpomfjfmöl cb ojs pr`pmbcjcbs y f`lstruffmöl cb ﬊eurjs, sbegblt`s y sòufm`ljr pr`kobgjs c`lcb bo tblej oj fjpjfmcjc cb cbg`strjr qub ulj j﬊rgjfmöl ulj bs vbrcjcbrj ` l`. Y`r o` tjlt` sb pubcb `ksbrvjr qub oj pr`pubstj qub sb cbsjrròoj bl o`s tbxt`s trjtjl cb oobvjr jo bstucmjltb qub jofjlfb j cbsjrròojr bl su t`tjomcjc o`s lmvbobs cb pblsjgmblt` cb Tjl Hmbob, pjrtmfuojrgbltb f`l o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj, pbr` jo trjtjr cb jpomfjroj jo juoj cb fojsb j o`s bstucmjltbs cb gbcmj l` sb jofjlzj j cbsjrròoj cbsjrròojrr bstj pr`pubstj pr`pubstj furrmfuojr furrmfuojr qub sb cbsjrròoj cbsjrròoj bl o`s tbxt`s cb kêsmfj bl su t`tjomcjc p`r djotj cb tmbgp` y bl joeuljs `fjsm`lbs lm smqumbrj sb cbsjrròoj bstb tmp` cb pblsjgmblt` bl bo juoj cb fojsb.

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Sjkoj 6.:1 6.:1 Bstêlcjrbs Bstêlcjrbs cb Vbgbajlzj Vbgbajlzj y f`lerub f`lerublfmj lfmj

E[JC@V BVSJLCJ[ [bf`l`zf` f`lerublfmj y sbgb:` ∛ 6` ajlzj bltrb ﬊eurjs (jgpomjr, rbcufmr). [bf`l`zf` y jpomf` trjsojfm`lbs y emr`s s`krb ulj ﬊eurj.

3` ∛ 2`

4` ∛ 5`

8` ∛ =`

Mcbltm﬊f` y austm﬊f` rbojfm`lbs cb f`lerublfmj y sbgbajlzj bltrb ﬊eurjs.

Yrbcme` y f`gpjr` o`s rbsuotjc`s cb jpomfjr jpomfjr trjlsd`rgjf trjlsd`rgjfm`lbs m`lbs rçemcjs (trjsojfm`lbs, r`tjfm`lbs, rb﬋bxm`lbs) y h`g`tbfmjs (jgpomjfm`lbs y rbcuffm`lbs) s`krb ﬊eurjs kmcmgblsm`ljobs bl smtujfm`lbs gjtbgêtmfjs y bl bo jrtb. [bsubo [bs ubov` v` y d`r d`rgu guo` o` pr`kob pr`kobgjs gjs qub mlvòufrbl rbojfm`lbs y pr`pm pmbc bcjc jcbs bs cb sbgba sbgbajl jlzj zj y f`lf`lerublfmj erublf mj usjlc` usjlc` rbprbsbltj rbprbsbltjfm`fm`lbs vmsujobs. F`labtur` y vbrm﬊f` pr`pmbcjcbs cb f`lerublfmjs y sbgbajlzjs bltrb ﬊eurjs kmcmgblsm`ljobs y bltrb `kabt`s trmcmgblsm`ljobs bl oj sòufmöl cb pr`kobgjs. [bf`l`zf` y f`ltrjst` pr`pmbcjcbs y rbojfm`lbs eb`gítrmfjs utmomzjcjs bl cbg`strjfmöl cb tb`rbgjs kêsmf`s (Ymtêe`rjs y Shjobs). Jpom Jp omf` f` y au aust stm﬊ m﬊f` f` fr frmtb mtbrm rm`s `s cb f`lerublfmjs y sbgbajlzj bltrb trmêleuo`s bl oj rbsòufmöl y d`rguojfmöl cb pr`kobgjs.

LMTBO CB F@GYOBAMCJC Bs ul lmvbo mlmfmjo cb rjz`ljgmblt`, bo f`lfbpt` cb sbgbajlzj y f`lerublfmj bs bstrmftjgbltb vmsujo y p`smkobgbltb l` sbrê prbfms`, f`l kjsb j oj cb﬊lmfmöl d`rgjo. Rlj prmgbrj cb﬊lmfmöl cb ﬊eurjs sbgbajltbs qub sb pubcb cjr j o`s jougl`s bs qub s`l ﬊eurjs qub tmblbl bo gmsg` jspbft` pbr` tjgjú`s cmdbrbltbs, pjrj ﬊eurjs f`lerubltbs sb bstjkobfb oj rbojfmöl s`l meujobs. ]j bstjkobfb oj cmdbrblfmj bltrb sbr sbgbajltb y sbr f`lerubltb, fojsm﬊fj ojs ﬊eurjs pojljs y o`s söomc`s, rbf`l`fb sus fjrjftbrçstmfjs y ojs blulfmj. O`s jougl`s pubcbl f`gblzjr j hjfbr gbcmcjs cb êleuo`s, o`lemtucbs cb ojc`s, fjofuojr êrbjs y vòñgblbs (cb o`s söomc`s) qub sbjl sbgbajltbs. Bo bstucm` cb oj sbgbajlzj ﬊eurjs bstê bstrbfhjgbltb rbojfm`ljc` f`lcb bo bstucm` cbo rjz`ljgmblt` pr`p`rfm`ljo. Bo bstucmjltb bstucmjltb f`lstruyb f`lstruyb sbegblt`s, sbegblt`s, êleuo`s y vbrm﬊fj vbrm ﬊fj sus f`lerublfmjs f`lerublfmjs.. Sjgk jgkmíl míl smeub mlstruffm`lbs pjrj oj f`lstruffmöl cb ﬊eurjs f`l rbeoj y f`gpjs. Bstjkobfb f`gpjrjfm`lbs bltrb ﬊eurjs, ojs fojsm﬊fj, rbf`l`fb sus pr`pmbcjcbs y bstjkobfb cmdbrblfmjs y sbgbajlzjs bltrb o`s pòçe`l`s pòçe`l`s rbeuojrbs b mrrbeuojrbs. mrrbeuojrbs. Srjlsd`rgj ﬊eurjs gbcmjltb o`s g`vmgmblt`s bl bo pojl` bl o`s fujobs l`vjrçj bo êrbj.

Jo prmlfmpm` oj l`fmöl cb sbgbajlzj sb cbsjrròojrê cb gjlbrj mltumtmvj> cbspuís sb p`crê p` crê cjr ulj cb﬊lmfmöl gês prbfmsj1 C`s ﬊eurjs s`l sbgbajltbs sm t`c`s o`s êleuo`s s`l f`lerubltbs y ojs o`lemtucbs cb o`s ojc`s f`rrbsp`lcmbltbs s`l pr`p`rfm pr`p`rfm`lj `ljobs. obs. Cbtbrgm Cbtbrgmlj lj sm bs p`sm p`smkob kob ` l` f`lstrumr trmêleuo`s f`l joeuljs fjrjftbrçstmfjs tbrçstm fjs y cb jfubrc` j sus pr`pmbcjcbs. pr`pmbcjcbs. Vm ul ojc` cb ulj ﬊eurj sbgbajltb j `trj bs cb trmpob tjgjú` qub bo f`rrbsp`lcmbltb bl oj ﬊eurj pbqubúj, bsj gmsgj rbojfmöl hjkrê bltrb t`cjss ojs rbstjl t`cj rbstjltbs tbs cmgblsm` cmgblsm`lbs lbs.. Vm oj rjzöl rjzöl bltrb ojs o`lemtucbs f`rrbsp`lcmbltbs bs cb oj l, oj rjzöl bltrb ojs êrbjs sbrê cb : j l ; , y oj 6

rjzöl bltrbpubcb o`s vòñgblbs sbrê cb : j l . cbo Bo bstucmjltb rbjomzjr cbg`strjfm`lbs tb`rbgj cb Shjobs ` cb Ymtêe`rjs y o`s jpomfj bl oj sòufmöl cb pr`kobgjs.

FJYÇSRO@ FJYÇ SRO@ 6.

F@GY F@GY@LBL @LBLSB SB YBC YBCJEÖ JEÖEMF@ EMF@..

Sjkoj 6.;1 Vbgbajlzj1 [bvmsmöl cb o`s tbxt`s cb oj Vbrmb gm jvblturj gjtbgêtmfj 4 j =. E[JC@ E[JC @

4

5

8

F@GY@LB F@GY@LBLSB LSB SBGJ SBGJSMF@ CB CBVJ[[@OO@ CBO F@LFBYS@ CB VBGBVBGBAJLQJ ] F@LE[RBLFMJ AJLQJ ] F@LE[RBLFMJ F@LE[RBLFMJ Cb﬊lmfmöl cb f`lfbpt`s kêsmf`s cb L` sb hjfb ulj cb﬊lmfmöl d`rgjo cb o`s f`lfbpt`s eb`gbtrçj pojlj. cb sbgbajlzj y f`lerublfmj. Vb hjfb ulj jpr`xmÊleuo`s, fojsm﬊fjfmöl. gjfmöl cbo f`lfbpt` cb f`lerublfmj f`lerublfmj jo t`gjr ulj Srmêleuo`s, pr`pmbcjcbs y fojsm﬊fj- ﬊eurj eb`gítrmfj, trjsojcjroj, r`tjroj ` rb﬋bajroj, fmöl. l` fjgkmj fjgkmj su tjgj tjgjú` ú` lm su d`rgj. J sm gmsg` gmsg` Yòçe`l`s y su fojsm﬊fjfmöl. sb hjfb ulj jpr`xmgjfmöl jo f`lfbpt` cb sbgbG`vmgmblt`s bl bo pojl`. ajlzj fujlc` sb bxpomfj bo f`lfbpt` cb h`g`tbfmj fujlc` sb hjkoj cb ul djft`r cb f`lvbrsmöl. Êleuo`ss y su fojsm﬊fjfmöl Êleuo` fojsm﬊fjfmöl.. Vb hjfb ulj cb﬊lmfmöl cbo f`lfbpt` cb f`lerublYr`pmbcjcbs cb o`s trmêleuo`s. fmj f`g`1 C`s ﬊eurjs s`l f`lerubltbs sm hjy ulj F`lst F`l stru ruff ffmöl möl y f`le f`leru rubl blfmj fmj cb f`rrbsp`lcblfmj bltrb o`s vírtmfbs, ojc`s y êleutrmêleuo`s. o`s qub f`gp`lbl f`gp`lbl ojs ﬊eurjs ﬊eurjs.. Sjgkmí jgkmíl l sb hjfb Yul Yult` t`ss y oç oçlb lbjs js l`tj l`tjko kobs bs cb ul ulj bxpomfjfmöl cb oj f`lstruffmöl cb trmêleuo`s trmêleuo`. f`l kjsb j o`s frmtbrm`s OJO, JOJ, OOO. Vb hjSb`rbgj cb Shjobs. fb ulj bxpomfjfmöl s`krb sbegblt`s pr`p`rfm`ljSrmêleuo`s sbgbajltbs. obs y jpomfjl bo tb`rbgj cb Shjobs pjrj blf`ltrjr Sb`rbgj cb Ymtêe`rjs. oj gbcmcj cb ul sbegblt`, f`l`fmblc` o`s `tr`s trbs. Vb cj ulj cb﬊lmfmöl cb﬊lmfmöl cb trmêleuo`s sbgbajlsbgbajltbs f`g`1 C`s ﬊eurjs pòme`ljobs s`l sbgbajltbs fujlc` sus êleuo`s rbspbftmv`s s`l f`lerubltbs y o`s ojc`s rbspbftmv`s cb o`s pòçe`l`s s`l pr`p`rfm`ljo fm`ljobs. bs. J su vb vbzz hjfb ulj bxpomfjf bxpomfjfmöl möl cb o`s frmtbrm`s frmtbrm `s cb sbgbajlzj sbgbajlzj cb trmêleu trmêleuo`s. o`s. Dmeurjs eb`gítrmfjs f`lerubltbs. Vb cb﬊lb oj f`lerublfmj cb c`s ﬊eurjs eb`gítrmfjs Yr`pmbcjcbs cb oj rbojfmöl cb f`l- fujlc` tmblbl oj gmsgj d`rgj y bo gmsg` tjgjerublfmj. ú`. Sjgkm jgkmíl íl sb hjfb ulj bxpomfjfmöl bxpomfjfmöl cb ojs pr`Srmêleuo`s. rmêleuo`s. Oçlbjs y pult`s pult`s l`tjkobs. F`lerublfmj cb trmêleuo`s.

=

Yr`pmbcjcbs cb o`s trmêleuo`s. Sb`rbgj cb Shjobs. Vbgbajlzj cb trmêleuo`s. Sb`rbgj cb Ymtêe`rjs.

pmbcjcbs f`lerublfmjbspjrj ulj rbojfmöl cbojf`lerublfmj ulj bstjkobfbr rbojfmöl cbqub bqumvjoblfmj.. Vb rbjomzjl cbg`st oblfmj cbg`strjfm`l rjfm`lbs bs cb ojs pr`pmbpr`pmbcjcbs cb o`s trmêleuo`s y sb bxpomfjl fjcj ul` cb o`s trbs frmtbrm`s frmtbrm`s cb f`lerublfmj f`lerublfmj pjrj trmêleuo`s. Vb cb﬊lb bo tb`rbgj cb Shjobs, f`g`1 Vm vjrmjs pjrjobojs cbtbrgmljl sbegblt`s f`lerubltbs s`krb ulj trjlsvbrs trjlsvbrsjo, jo, tjgk tjgkmíl míl cbtbrgmljl cbtbrgmljl sbegblt`s sbegblt`s f`lerubltbs s`krb fujoqumbr `trj trjlsvbrsjo qub ojs f`rtb. Vm vjrmjs pjrjobojs s`l f`rtjcjs p`r c`s sbfjltbs blt`lfbs o`s sbegblt`s cbtbrgmljc`s s`krb ojs sbfjl sbfjltbs tbs s`l pr`p`rfm`ljobs pr`p`rfm`ljobs.. Vb cbsjrròoj oj cbg`strjfmöl y oube` sb cbsjrròoj o`s frmtbrm`s cb sbgbajlzj cb trmêleuo`s f`l sus rbspbftmvjs cbg`strjfm`lbs.

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FJYÇSRO@ FJYÇ SRO@ 6.

F@GY F@GY@LBL @LBLSB SB YBC YBCJEÖ JEÖEMF@ EMF@..

Sjkoj 6.61 Vbgbajlzj1 [bvmsmöl cb o`s tbxt`s cb oj Vbrmb Lubvjs gjtbgêtmfjs 5 j =.

E[JC@ E[JC @

5

8

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F@GY@LB F@GY@LBLSB LSB SBGJ SBGJSMF@ CB VBGBAJLQJ ] F@LE[RBLFMJ F`lerublfmj y sbgbajlzj. Yòçe`l`s f`lerubltbs. Yòçe`l`s Vbgbajltbs. H`g`tbfmjs.

CBVJ[[@OO@ CBO F@LFBYS@ CB VBGBAJLQJ ] F@LE[RBLFMJ F@LE[RBLFMJ Blulfmj Blu lfmj oj cb﬊lmf cb﬊lmfmöl möl cb pòçe`l`s pòçe`l`s f`leru f`lerubltb bltbss fujlc` o`s ojc`s y êleuo`s qub sb f`rrbsp`lcbl tmblbl oj gmsgj gbcmcj. Y`stbrm`rgbltb cbsjrròojl o`s frmtbrm`s cb f`lerublfmj bltrb trmêleuo`s y oube` sb cbsjrròoj oj pjrtb cb pòçe`l`s sbgb ajltbs cb oj smeumbltb gjlbrj1 C`s pòçe`l`s s`l sbgbajltbs sm hjy ulj f`rrbsp`lcblfmj bltrb sus vírtmfbs cb tjo gjlbrj qub o`s êleuo`s f`rrbsp`lcmbltbs s`l meujobs y o`s ojc`s f`rrbsp`lcmbltbs s`l pr`p`rfm`ljobs. Êleuo`ss y su fojsm﬊fjfmöl Êleuo` fojsm﬊fjfmöl.. Vb hjfb oj cb﬊lmfmöl eblbrjo cb ﬊eurjs f`lerublYr`pmbcjcbs cb o`s trmêleuo`s. tbs f`g`1 C`s ﬊eurjs eb`gítrm eb`gítrmfjs fjs s`l f`lerublF`lst F`l stru ruff ffmöl möl y f`le f`leru rubl blfmj fmj cb tbs sm tmblbl bxjftjgbltb oj gmsgj d`rgj y bo gmstrmêleuo`s. g` tjgjú`. tjgjú`. Cbs Cbspuí puíss hjfbl ulj cb﬊lmfmö cb﬊lmfmöl l gês Yul Yult` t`ss y oç oçlb lbjs js l`tj l`tjko kobs bs cb ul d`rgjo oobvêlcòj j oj f`lerublfmj cb trmêleuo`s trmêleuo`. cb oj smeumbltb gjlbrj1 gjlbrj1 C`s trmêleuo`s trmêleuo`s s`l f`lSb`rbgj cb Ymtêe`rjs. erubltbs sm bxmstb ulj f`rrbsp`lcblfmj bltrb sus Frmtbrm`s cb f`lerublfmj cb trmêleu- vírtmfbs cb gjlbrj qub o`s ojc`s y êleuo`s f`rrbso`s. p`lcmbltbs s`l f`lerubltbs.‗ Vbgbajlzjs Bl bo f`gmblz` cb oj ulmcjc sb hjfb ulj bxpomfj[jzöl cb c`s sbegblt`s. fmöl s`krb qub bs cbg`strjfmöl y o`s gít`c`s cb Vbegblt`s pr`p`rfm`ljobs. cbg`strjfmöl pjrj p`stbrm`rgbltb jk`rcjr oj ulmSb`rbgj cb Shjobs. cjc cb sbgbajlzj. Vb hjfb ul rbfublt` cb qub bs Vbgbajlzj cb Srmêleuo`s. ulj rjzöl, qub bs ulj pr`p`rfmöl, rjzöl bltrb sbeFrmtbrm`s cb sbgbajlzj cb trmêleu- gblt`s, Sb`rbgj cb Shjobs qub sb blulfmj f`g`1 o`s. Vbgbajlzj cb trmêleuo`s rbftêleuo`s.

Vm vjrmjs o`s pjrjobojs s`l f`rtjcjs p`r c`s sbfjltbs, blt`lfbs sbegblt`s cbtbrgmljc`s s`krb ojs sbfjltbs s`l pr`p`rfm`ljobs. Oube` sb hjfb ulj cbg`strjfmöl cb bstb tb`rbgj, y ojs f`lsbfublfmjs cbo gmsg`, pjrj cbspuís oobvjro` j oj cb﬊lmfmöl eblbrjo cb pòçe`l`s sbgbajltbs bl c`lcb sb bstjkobfb qub c`s pòçe`l`s s`l sbgbajltbs sm hjy ulj f`rrbsp`lcblfmj bltrb o`s vírtmfbs cb tjo gjlbrj qub o`s êleuo`s f`rrbsp`lcmbltbs s`l f`lerubltbs y o`s ojc`s f`rrbsp`lcmbltbs s`l pr`p`rfm`ljobs. Oube`, sb hjfb ulj bxpomfjfmöl cb o`s frmtbrm`s cb sbgbajlzj cb trmêleuo`s y p`stbrm`rgbltb sb cbtbrgmlj oj sbgbajlzj cb trmêleuo`s rbftêleuo`s f`l sus f`lcmfm`lbs.

3:

3.Yr`pubstj Cmcêftmfj O`s omlbjgmblt`s furrmfuojrbs bl gjtbgêtmfjs ^:4W ^:4W,, pojltbjl f`g` pr`pösmt` dulcjgbltjo cb oj bcufjfmöl gjtbgêtmfj cb o`s lmvbobs cb kêsmfj y gbcmj ‟f`ltrm ‟f`ltrmkumr kumr jo cbsjrr` cbsjrròo` oo` cbo pblsjgmblt` blsjgmblt` gjtbgêt gjtbgêtmf mf` ` j pjrtmr cbo trjkja` f`l smtujfm`lbs pr`kobgêtmfjs pr`vblmbltbs cbo f`ltbxt` s`fm`fuoturjo, cb `trjs fmblfmjs ` cb ojs gmsgjs gjtbgêtmfjs.‗   J su vbz pojltbj pojltbj oj mgp`rtjlfmj mgp`rtjlfmj cbo pblsjgmblt` pblsjgmblt` bspjfmjo bspjfmjo y smtbgjs smtbgjs eb`gítrmf`s cbsfrmkmblcò`s f`g`, ‟bo f`lault` cb oo`s `s pr` pr`fbs`s fbs`s fèlmtmv`s fèlmtmv`s gbcmjltb o`s fujobs sb f`lstruybl y sb gjlmpuojl ojs rbprbsbltjfm`lbs gbltjobs cb o`s `kabt`s cbo bspjfm`, ojs rbojfm`lbs bltrb boo`s, sus trjlsd`rgjfm`lbs y sus cmvbrsjs trjcuffm`lbs j rbprbsbltjfm`lbs gjtbrmjobs.‗

Y`r boo` bs mgp`rtjltb rbt`gjr bl ojs mlstmtufm`lbs bcufjftmvjs oj blsbújlzj cb oj eb`gbtrçj qub tmblb f`g` ﬊l oj bxpo`rjfmöl cbo bspjfm`, bo cbsjrròo` cb oj mgjemljfmöl trmcmgblsm`ljo, oj d`rguojfmöl y cmsfusmöl cb pr`kobgjs, auejr f`l ojs f`lstruffm`lbs eb`gbtrmfjs, cmsbú`s y rbjomzjr trjlsd`rgjfm`lbs ` g`vmgblt`s bl bo pojl` qub jyucbl j o`s lmú`s j d`rtjobfbr bo pblsjgmblt` bspjfmjo y smstbgjs eb`gítrmf`s. Bl bo Fòbem` Vjl Jeustml MBC a`rljcj tjrcb j o` ojre` cb o`s jú`s, sb hj vmst` oj lbfbsmcjc cb `rejlmzjr ul pojl cb jsmeljturj pjrj eb`gbtrçj bl t`c`s o`s lmvbobs cb bcufjfmöl kêsmfj, qub sbj ulm﬊fjc` pjrj t`cj oj mlstmtufmöl pubst` qub l` bxmstb ul pojl cb jsmeljturj y fjcj c`fbltb cbo êrbj cb gjtbgêtmfjs, cmftj bstj jsmeljturj t`gjlc` joeul`s tbgjs cbo pblsjgmblt` eb`gítrmf` y gítrmf`, qub rbsuotj smblc` rbpbtmtmv` jo pjsjr cb o`s jú`s ` bl `fjsm`lbs l` o` cmftjl y sb f`lfbltrjl bl jk`rcjr gês tbgjs gjtbgêtmf`s cbajlc` cb ojc` o`s tbgjs pr`pm`s cb oj eb`gbtrçj. Yjrj qub o`s bstucmjltbs oèrbl tblbr ul gba`r f`l`fmgmblt` cb oj eb`gbtrçj y pubcjl pr`dulcmzjr gês bl bst`s f`ltblmc`s, bo fòbem` jsmelö ulj h`rj cb eb`gbtrçj bl fjcj furs` ulj vbz j oj sbgjlj, qub dub mlf`rp`rjcj jo h`rjrm` cb fojsb cbscb erjc` sbxt` j erjc` l`vbl`, f`l bo ﬊l cb jk`rcjr t`c`s o`s tbgjs f`lfbrlmbltbs j bstb tmp` cb pblsjgmblt` y bl ul dutur` sb pubcj gba`rjr o`s rbsuotjc`s cb o`s bstucmjltbs bl prubkjs cb bstjc`, ` mlerbs` j oj bcufjfmöl supbrm`r.

3.:.. 3.:

Cb Cbsfr sfrmpfm mpfmöl öl e eblb blbrjo rjo c cb b oj p pr`p r`pubs ubstj. tj.

F`l bo êlmg` cb d`rtjobfbr bo pblsjgmblt` pblsjgmblt` bspjfmjo y eb`gítrmf`, eb`gítrmf`, sb pojltbj pojltbj oj smeumbltb smeumbltb pr`pubstj pr`pubstj cmcêftmfj qub bstê cmrmemcj j o`s bstucmjltbs y c`fbltbs cb gjtbgêtmfjs cb bcufjfmöl kêsmfj cbo fòbem` Vjl Jeustml a`rljcj tjrcb. F`lstj cb c`s pjrtbs1 Oj prmgbrj ul pojl cb jsmeljturj bl eb`gbtrçj pjrj o`s c`fbltbs cb gjtbgêtmfjs, c`lcb sb pojsgjl t`c`s o`s f`ltblmc`s tbgêtmf`s p`r pbrm`c`s, pjrj fjcj erjc` f`l o`s oèr`s qub o`s bstucmjltbs cbkbl jofjlzjr pjrj cbsjrròojr fjcj ul` cb o`s pbrtmlbltbs lmvbobs cb Tjl Hmbob, f`g` sb pojltbj bl o`s bstêlcjrbs kêsmf`s bl gjtbgêtmfjs y f`l jp`y` cb oj rbvmsmöl cb tbxt`s bsfòjrbs qub sb hmz` bl bo fjpçtuo` jltbrm`r (vbr tjkojs 6.; y 6.6 ), qub smrvj f`g` rbdbrbltb j oj h`rj cb jk`rcjr o`s tbgjs bl oj fojsb cb eb`gbtrçj y tblejl ulj sbfublfmj bl o`s f`ltblmc`s tbgêtmf`s cb bstj jsmeljturj. Oj sbeulcj oojgjcj ‟Rl gulc` cb d`rgjs y ﬊eurjs‗ qub f`lstj cb lubvb ulmcjcbs cb euçjs cmcêftmfjs, ulj pjrj fjcj furs` cmrmemcj j o`s bstucmjltbs, c`lcb sb cbsjrròojl jquboo`s prbf`lfbpt`s y tbgjs rboj-

3;

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

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fm`ljc`s f`l o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj pjrj fjcj fmfo` qub bs bo bab tbgêtmf` pr`pubst` bl bst bstbb trjkja`. trjkja`. Bstjs Bstjs euçjs cmcêftmfj cmcêftmfjss hjl smc` bojk`rjcj bojk`rjcjss f`l kjsb j ojs fmlf` djsbs cb jpr jprblc blcmzjab mzjab y fjrjftbrmstmfjs cbo g`cbo` cb blsbújlzj pjrj oj eb`gbtrçj cb Tjl Hmbob y pr`p`lbl jftmvmcjcbs qub oobvjl j o`s bstucmjltbs j oj f`gprblsmöl y f`l`fmgmblt` cb o`s f`lfbpt`s kêsmf`s y pubcjl jpomfjro` j oj rbsòufmöl cb pr`kobgjs, f`ltruffmöl y g`vmgblt`s cb ﬊eurjs bl bo pojl`, l` sò` bl t`rl` j ojs euçjs sml` qub tjgkmíl pubcjl utmomzjr hbrrjgmbltjs tbflòöemfjs f`g` `drbfb bo prèrjgj ebèbkrj pjrj rbjomzjr f`lstruffm`lbs y trjlsd`rgjfm`lbs eb`gítrmfjs cb gjlbrj mltbrjftmvj y cmlêgmfj bl bo juoj cb fojsb. J f`ltmlujfmöl sb hjfb ulj cbsfrmpfmöl cbo pojl cb jsmeljturj y cb ojs euçjs qub sb cbsjrròojr`l bl bstj pr`pubstj cmcêftmfj.

3.;.. 3.;

Cb Cbsfr sfrmpfm mpfmöl öl cbo poj pojl l cb jsme jsmeljt ljturj urj cb eb eb`gb `gbtrç trçj j cb prmgbr prmgbr` ` j l`vbl` erjc`.

Bl ojs smeumbltbs tjkojs sb hjfb ulj pr`pubstj s`krb bo pojl cb jsmeljturj cb eb`gbtrçj qub prbtblcb mgpobgbltjr mgpobg bltjr bl bo fòbem` fòbem` Vjl Jeustçl t`gjlc` f`g` kjsb o`s omlbjgmblt` omlbjgmblt`ss furrmfuojrb furrmfuojrbss ^:4W y ^:4W y o`s bstêlcjrbs kêsmf`s bl Gjtbgêtmfjs ^::W ^::W.. J f`ltmlujfmöl sb hjfb ul krbvb rbsugbl cb o`s f`ltblmc`s pr`pubst`s bl fjcj ulj cb boojs1 Yjrj cbsjrròojr oj pr`pubstj cb pojl cb jsmeljturj bl eb`gbtrçj cb oj Sjkoj 3.: Sjkoj 3.: ‟Yojl ‟Yojl cb jsmeljturj pjrj Fmfo` :‗, sb pojltbjl pojltbjl trbs ulmcjcbs ulj pjrj fjcj erjc` (vbr jlbx`s :,; y 6). Fjcj ulj f`lstj cb ul pjqubtb cb euçjs, qub kusfj d`rtjobfbr bo prmgbr lmvbo ` cb rbf`l`fmgmblt` cb Tjl Hmbob, c`lcb o`s bstucmjltbs jprblcjl f`lfbpt`s kêsmf`s cb eb`gbtrçj, rbojfm`lbs bspjfmjobs kêsmfjs pjrj su bstucm`, ﬊eurjs ﬊eurjs eb`gítrmfjs eb`gítrmfjs kêsmfjs y ojs rbf`l`zfjl p`r su l`gkrb. l`gkrb. Bl ojs euçjs pjrj erjc` prmgbr`, sb pojltbjl jftmvmcjcbs c`lcb rbf`l`zfjl joeuljs rbojfm`lbs bspjfmjobs y f`lfbpt`s kêsmf`s cb eb`gbtrçj, ojs omlbjs y su rbprbsbltjfmöl, fojsm﬊fjfmöl y ojs fujtr` ﬊eurjs eb`gítrmfjs kêsmfjs b mltr`cufmr j o`s lmú`s j oj fojsm﬊fjfmöl cb pòçe`l`s p`r su lñgbr` cb ojc`s. Bl ojs euçjs pjrj erjc` sbeulc`, sb pojltbj oj fojsm﬊fjfmöl cb ojs rbftjs sbeñl su p`smfmöl, rbftjs pjrjobojs, pbrpblcmfuojrbs, fojsm﬊fjfmöl cb ojs ﬊eurjs kêsmfjs p`r su lñgbr` cb ojc`s, o`s prmlfmpjobs fubrp`s eb`gítrmf`s y su fojsm﬊fjfmöl. Bl ojs euçjs pjrj erjc` tbrfbr`, sb pojltbjl jftmvmcjcbs pjrj jprblcbr o`s f`lfbpt`s cb sbegblt`s, rbftjs y sbgmrrbftjs, su l`tjfmöl eb`gítrmfj, êleuo`s y su fojsm﬊fjfmöl sbeñl su jgpomtuc, trçjleuo`s y fojsm﬊fjfmöl sbeñl oj gbcmcj cb sus ojc`s y sb mlmfmj f`l bo f`lfbpt` kêsmf` cb f`lerublfmj. Yjrj cbsjrròojr oj pr`pubstj cb pojl cb jsmeljturj bl eb`gbtrçj cb oj Sjkoj 3.; Sjkoj 3.; ‟Yojl ‟Yojl cb jsmeljturj pjrj Fmfo` ;‗, sb pojltbjl c`s ulmcjcbs ulmcjcbs ulj pjrj fjcj erjc` (vbr jlbx`s 3 y 2). Fjcj ulj f`ltmblb f`ltmblb ul pjqubtb cb euçjs c`lcb sb trjkjajl tbgjs kêsmf`s cb pojl` fjrtbsmjl`, rbprbsbltjfmöl cb pult`s bl bo pojl`, trjsojfmöl, r`tjfmöl, smgbtrçj, rb﬋bxmöl, f`lfbpt`s kêsmf`s cb f`lerublfmj y sbgbajlzj, rbjomzjlc` jftmvmcjcbs cb rbf`l`fmgmblt` cb ﬊eurjs sbgbajltbs p`r gbcm` cb oj jgpomjfm`l y rbcuffm`l utmomzjlc` utmomzjlc` f`g` hbrrjgmbltj hbrrjgmbltj oj fujcrçfuoj. fujcrçfuoj. F`l ojs jftmvmcjcbs pr`pubstjs pr`pubstjs bl bstjs euçjs sb kusfj jofjlzjr bo sbeulc` lmvbo ` cb jlêomsms sbeñl Tjl Hmbob. Yjrj cbsjrròojr oj pr`pubstj cb pojl cb jsmeljturj bl eb`gbtrçj cb oj Sjkoj 3.6 Sjkoj 3.6 ‟Yojl ‟Yojl cb jsmeljturj pjrj Fmfo` 6‗, sb pojltbjl c`s ulmcjcbs ulmcjcbs ulj pjrj fjcj erjc` (vbr jlbx jlbx`s `s 4 y 5). Vb qumbrb d`rtjobfbr bo tbrfbr lmvbo cb fojsm﬊fjfmöl sbeñl Tjl Hmbob, c`lcb bo bstucmjltb rbjomfb trjlsd`rgjfm`lbs eb`gítrmfjs gês f`gpobajs rbjomzjlc` r`tjfm`lbs, rbobxm`lbs y h`g`tbfmjs cb ﬊eurjs eb`gbtrmfjs pojljs. pojlj s. tjgkmíl tjgkmíl qub fojsm﬊qub fojsm﬊qub êleuo`s sbeñl su sugj y su p`smfmöl, o`s trmêleuo`s trmêleuo`s sus pr`pmbcjcbs pr`pmbcjcbs y o`s jpomqubl bl oj f`lstruffmöl cb bstjs ﬊eurjs bl bo prèrjgj ebèbkrj. Bl bo prmgbr jlbx` sb cbsjrròoj pjs` j pjs` oj f`lstruffmöl cb êleuo`s, trmêleuo`s, y g`vmgblt`s bl bo pojl` bld`fjc`

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

33

j erjc` sbxt`. Bl bo sbeulc` sbeulc` jlbx` sb pojltbj pojltbj oj bojk`rjfmöl cb trmêleuo`s trmêleuo`s f`l sus pr`pmbcjcbs pr`pmbcjcbs,, oçlbjs y pult`s l`tjkobs y pòçe`l`s f`lerubltbs pjrj erjc` síptmg` y pubcjl j su vbz rbjomzjro`s bl bo prèrjgj prèrjgj ebèbkrj. Yjrj cbsjrròojr oj pr`pubstj cb pojl cb jsmeljturj bl eb`gbtrçj cb oj Sjkoj 3.3 Sjkoj 3.3 ‟Yojl ‟Yojl cb jsmeljturj pjrj Fmfo` 3‗, sb pojltbjl c`s ulmcjcbs ulj pjrj fjcj erjc` (vbr jlbx`s 8 y =). Vb pojltbjl euçjs qub kusfjl p`tblfmjr bo tbrfbr lmvbo cb cbcuffmöl d`rgjo d`rgjo sbeñl Tjl Tjl Hmbob. Bl boojs sb kusfj qub o`s bstucmjltbs, jpomqubl bo tb`rbgj cb Shjobs, o`s frmtírm`s cb f`lerublfmj y sbgbajlzj cb trmêleuo`s bl oj sòufmöl cb pr`kobgjs. tjgkmíl sb pr`p`lbl uljs cbg`strjfm`lbs kêsmfjs pjrj jofjlzjr bstb lmvbo cb pblsjgmblt` eb`gítrmf` y pubcjl sòufm`ljr pr`kobgjs jpomfjlc` o`s f`lfbpt`s y tb`rbgjs cb oj f`lerublfmj y sbgbajlzj.

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

3.6.. 3.6

32

Cb Cbsfr sfrmpfm mpfmöl öl cb ojs euç euçjs js cmc cmcêft êftmfj mfjss cb prmg prmgbr` br` j l` l`v vbl bl`. `.

Bs mgp`rtjltb qub bl bo pr`fbs` blsbújlzj jprblcmzjab, bo c`fbltb djfmomtb jo bstucmjltb hbrrjgmbltjs lbfbsjrmjs qub f`ltrmkuyjl sjtmsdjft`rmjgbltb j qub ío sb cbsblvubovj drbltb j smtujfm`lbs rbjobs qub sb ob pubcjl prbsbltjr, prbsbltjr, jcbgês cb oj f`lstruffmöl cb su pr`pm` f`l`fmgmblt`, f`l`fmgmblt`, hjfmblc` hjfmblc` us` cb ojs hjkmomcjcbs hjkmomcjcbs prbvmj prbvmjgblt gbltbjb o`s jcqumrmcjs. jcqumrmcj s. Yjrjyojprbsjkbrbs f`lstruffmöl f`lstruffmöl cboj jprblcmzjab cb yj o`s qub bstucmj bstucmjltbs, tjgk míl ul sb pult` cbkb cjr rbobvjlfmj prbf`lfbpt`s drbltb cmfh` pr`fbs`, s`l ltbs, kjsb tjgkmíl ` gba`r cb pjrtmcj bl oj jcqumsmfmöl cb f`l`fmgmblt`, bl `trjs pjojkrjs hjfbr us` cb o`s jp`rtbs cbo jprblcmzjab smelm﬊fjtmv smelm ﬊fjtmv`` f`g` s`p`rtb fojvb fojvb bl bo cbsjrròo` cbsjrròo` fèlmtmv` fèlmtmv` cb o`s bstucmjltbs. bstucmjltbs. Ojs euçjs cmcêftmfjs cmcêftmfjs bl bo pr`fbs` bcufjtmv` sb fjrjftbrmzjl p`r sbr ulj hbrrjgmbltj pjrj bo bstucmjltb, c`lcb sb mlfouyb oj mld`rgjfmöl lbfbsjrmj lbfbsjrmj s`krb oj tbgêtmfj tbgêtmfj qub sb bstj jk`rcjlc` jk`rcjlc` y djfmomtjr djfmomtjr jo gmsg` tmbgp` oj f`lstruffmöl f`lstruffmöl cbo f`l`fmgmblt` cb gjlbrj smelm﬊fjtmvj. Oj `rejlmzjfmöl cbo furrçfuo` bl ojs euçjs cmcêftmfjs sup`lb oj jc`pfmöl cb `tr`s frmtbrm`s pjrj oj sbobffmöl cb ul `kabt` cb bstucm` f`g` s`l su lmvbo cb smelm﬊fjtmvmcjc, su fjpjfmcjc pjrj mltbrrbojfm`ljr f`l`fmgmblt`s l` lbfbsjrmjgbltb cmsfmpomljrbs ` su fjpjfmcjc cb mltberjr jftmvjgbltb j o`s jougl`s pbrgmtmblcòb gmtmblc òb trjkjajr j su pr`pm` rmtg` y `rejlmzjr jcufujcjgbl jcufujcjgbltb tb su tmbgp`. Bl gufhjs `fjsm`lbs `fjsm`lbs oj bstrufturj cb oj euçj cmcêftmfj qub pr`p`lbl f`mlfmcb f`l o`s gmsg`s bobgblt`s furrmfuojrbs (`kabtmv`s, f`ltblmc`s f`lt blmc`s,, jftmvmcjcbs, jftmvmcjcbs, frmtbrm`s gbt`còöemf`s gbt`còöemf`s y cb bvjoujfm bvjoujfmöl, öl, btf.) jújcmblc` jújcmblc` tjl söo` gjy`r gjy`r bspbfm﬊fmcjc, f`l ulj f`hbrblfmj gbt`còöemfj mltbrlj y p`r ul pbrç`c` cb tmbgp` cbtbrgmljc`. Yjrj qub ulj euçj cmcêftmfj cmcêftmfj fugpoj f`l su dulfmöl cbkb tblbr1 Vbr jerjcjkob jerjcjkob j oj vmstj, bo f`ltblmc` f`ltblmc` cbkb bstjr kmbl cmstrmkumc`, tblbr erê﬊f`s y bsqubgjs qub ob jyucbl j rbf`rcjr, l` cbkb f`ltblbr d`t`f`pmjs cb tbxt`s, cbkb rbgmtmr jo bstucmjltb j f`lsuotjr, mlvbstmejr, f`lstrumr, frbjr y oube` `rejlmzjrojs bl ul p`rtjdòm` p`rtjd` om` pjrj qub pbrgmtj p brgmtjll oj jut`bvjoujfm jut`bvjoujfmöl öl y oj f`bvj f`bvjoujfmö oujfmöl^ l^:5W :5W.. Ojs euçjs cmcêftmfjs cmcêftmfjs sb cmsbúr`l cmsbúr`l tblmblc` tblmblc` bl fubltj fubltj o`s smeumbltbs f`gp`lbltbs f`gp`lbltbs gbt`còöemf`s1 gbt`còöemf`s1 :. Blfjkbzjc`1 F`ltmblb o`s cjt`s kêsmf`s cbo fòbem`, l`gkrb cb oj jsmeljturj, l`gkrb cbo pr`dbs`r, bspjfm` pjrj bo l`gkrb cbo bstucmjltb, furs`, tmbgp` prbvmst` pjrj bo cbsjrròo` cbo tbgj, dbfhj. ;. F`ltblmc`1 Sbgêtmfjs qub sb bstj jk`rcjlc` bl oj euçj. 6. @kabtmv`1 Dmljomcjc ` gbtj j jofjlzjr f`l bo cbsjrròo` cb oj euçj cmcêftmfj. 3. Cbsjrròo` cb oj jftmvmcjc1 Rkmfj jo bstucmjltb bl bo tbgj j trjtjr, su mgp`rtjlfmj y f`ltmblb ulj smtujfmöl cb bltrjcj ` pr`kobgj cb mlmfm`, pjrj mltr`cufmr jo bstucmjltb jo tbgj j trjtjr, bo fujo cbkb sbr rbt`gjc` y sòufm`ljc` sòufm`ljc` jo ﬊ljomzjr oj fojsb f`l t`c` bo erup`. Rl krbvb gjrf` tbörmf` tbörmf` qub ob pbrgmtb f`lfbptujomzjr y rbf`rcjr o`s f`gp`lbltbs tbgêtmf`s kêsmf`s qub sb cbsjrròojrjl j o` ojre` cb oj euçj. Vb cjl ojs mlstruffm`lbs fojrjs pjrj su cbsjrròo`, o`s gjtbrmjobs qub sb lbfbsmtjrjl, pr`fbcmgmblt` j sbeumr, babgpo`s y babrfmfm`s ` jftmvmcjcbs cb jpomfjfmöl cbo tbgj trjtjc`. 2. Bv Bvjoujfm joujfm`l1 `l1 Jftmvmcjc Jftmvmcjcbs bs f`l bo ﬊l cb cbtbrgmljr sm sb fugpomö f`l bo `kabtmv` pr`pubst` pr`pubst` mlmfmjomlmfmjogbltb. Ojs euçjs cmcêftmfjs cbsjrròojcjs bl bstb trjkja` sb blfubltrjl f`lsmeljcjs bl o`s jlbx`s.

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

Sjkoj 3.:1 Yojl cb jsmeljturj Eb`gbtrçj pjrj Fmfo` :.

@KABSMT@1 Cbsjrròojr hjkmomcjcbs

kêsmfjs cbo pblsjgmblt` eb`gítrmf` y bspjfmjo p`r gbcm` cbo rbf`-

l`fmgmblt` ojsbstucmjltbs d`rgjs dçsmfjs cb o`s `kabt`s cbjoojqub bxpo`rjfmöl b mltbrjffmöl f`l su blt`rl`, qub ob pbrgmtjl cb j o`s cbsblvòvbrsb bl jbotrjvís bspjfm` pbrtblbfb. F@GYBSBLFMJV GJ GJSBGÊ SBGÊSMFJV SMFJV1 :. [JQ@LJGMBLS@. ;. YOJLSBJGMBLS@ ] [BV@ORFMÖL CB Y[@KOBGJV 6. F@GRLMFJSMTJ. E[JC@

YB[M@C@

:

Y[MGB[@

[boj [bojfm fm`l `lbs bs bspj bspjfm fmjo jobs bs (Sjg (Sjgjjú`,b ú`,blf lfmg mgjj - cbkja cbkja`, `, mzqu mzqumb mbrc rcj, j, cbrbfhj, cbltr` y dubrj).

VBERLC@

Oçlbjs rbftjs y omlbjs furvjs. Omlbjs furvjs (jkmbrtjs - fbrrjcjs).

SB[FB[@

Dmeurjs Dmeurjs eb`gítrmfjs eb`gítrmfjs (fojsm﬊fjfmö (fojsm﬊fjfmöl) l)

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SBGJV

Vöomc`s eb`gítrmf`s eb`gítrmf`s fjrjftb fjrjftbrçstmfj rçstmfjss kêsmfj kês mfjs. s. Bsdbrj Bsdbrj,, Fuk`, F`l`, Fmomlcr`. Y[MGB[@ [bo [bojf jfmöl möl bltrb bltrb d` d`rgj rgj y tjgj tjgjú` ú` FRJ[S@

;

`

VBERLC@

Cmdbrblf Cmdbrblfmjs mjs bltr bltrbb ﬊eurjs eb`gítrmeb`gítrmfjs sòmcjs y pojljs.

SB[FB[@

Yult` Yult` y oçlbjs f`g` trjybft`rmj trjybft`rmjs, s, sbegblt`s.

Fojsm﬊fjfmöl Fojsm﬊fjfmöl cb rbftjs, rbftjs, ml mltbrsbf tbrsbfjljltbs y pjrjobojs. Y[MGB[@ Êleuo`s Êleuo`s,, pjrtbs pjrtbs cb ul ul êleuo`. êleuo`. Fojsm﬊fjfmöl cb o`s êleuo`s sbeñl su jgpomtuc jgpomtuc VBERLC@ Yòçe`l`s fjrjftbrçstmfjs eblbrjobs. Srmêleuo`s y su fojsm﬊fjfmöl. FRJ[S@

6

`

SB[FB[@

L`fm`lbs cb h`rmz`lt h`rmz`ltjomcjc jomcjc,, vbrtmfjomcjc, pjrjobomsg` pjrjobo msg` y pbrpblcmfuojrmcj pbrpblcmfuojrmcjc c bl cmstmlt`s f`ltbxt`s.

FRJ[S@

F`lerublfmj, F`lerublfmj, emr`s, emr`s, cbspojzjgmb cbspojzjgmbllt`s, vòtbjr ﬊eurjs.

O@E[@V

F`gpjrj fjrjftbrçstmfjs bltrb `kabt`s f`g` erjlcb - gbcmjl` - pbqubú`, erubs` - cboejc`, jot` - kja`, jcbojltb - jtrês , jrrmkj - jkja`. [bf`l`fb y cmkuaj oçlbjs rbftjs, omlbjs furvjs, omlbjs jkmbrtjs y fbrrjcjs. Fojsmdçfj Fojsmdçfj ojs ﬊eurjs pojljs sbeñl su d`rgj, y sbeñl su lñgbr` cb ojc`s. [b [bf` f`l`f l`fbb o`s o`s cmdb cmdbrbl rbltb tbss fu fubrp brp`s `s eb`gítrmf`s bl su f`ltbxt`. Foj Fojsm sm﬊f ﬊fjj ``kabt kabt`s `s cb su bl blt` t`rl rl`` cb cb jfubrc` j su d`rgj y tjgjú`. Bojk`rj cmkua`s cb ﬊eurjs cb cmdbrbltbs d`rgjs y tjgjú`s. Cmkuaj y cbsfrmkb fubrp`s ` ﬊eurjs trmcmgblsm`ljobs bl cmstmltjs p`smfm`lbs y tjgjú`s. [bf`l`fb o`s bobgblt`s kêsmf`s cb oj eb`gbtrçj f`g` pult`, ulj oçlbj y ulj rbftj. Cmkuaj o`s bobgblt`s kêsmf`s cb oj eb`gbtrçj f`g` pult`, ulj oçlbj y ulj rbftj. Cmkuaj y fojsm﬊fj rbftjs mltbrsbfjltbs y pjrjobojs. Fojsm﬊fj y cmkuaj êleuo`s sbeñl su jgpomtuc. Fojsm﬊fj o`s pòçe`l`s cb jfubrc` f`l su lñgbr` cb ojc`s y o`s rbojfm`lj f`l `kabt`s cb su blt`rl`. F`lstr F`l struy uybb b mcblt mcbltm﬊f m﬊fjj êleuo` êleuo`ss y trmêleuo`s cb jfubrc` f`l sus fjrjftbrçstmfjs. [bf`l`f [bf `l`fbb l`fm l`fm`lb `lbss cb h`r h`rmz`l mz`ltjtjomc omcjc, jc, vb vbrtmf rtmfjomc jomcjc, jc, pjr pjrjob joboms omsg` g` y pbrpblcmfuojrmcjc bl cmstmlt`s f`ltbxt`s y su f`lcmfmöl rbojtmvj f`l rbspbft` j cmdbrbltbs smstbgjs cb rbdbrblfmj. [bf`l`fb f`lerublfmj bltrb ﬊eurjs.

34

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

Sjkoj 3.;1 Yojl cb jsmeljturj Eb`gbtrçj pjrj Fmfo` ;.

@KABSMT@1 Mcbl Mcbltm﬊fjr tm﬊fjr fjrjftbrçs fjrjftbrçstmfjs tmfjs tjlemkobs cb

`kabt`s cbo blt` blt`rl` rl` bstjkobfmblc bstjkobfmblc`` rbojfm` rbojfm`lbs lbs f`l o`s bobgblt`s y fjrjftbrçstmfjs cb o`s fubrp`s eb`gítrmf`s qub pubcjl rbojfm`ljro`s y jpomfjro`s j oj sòufmöl cb pr`kobgjs. F@GYBSBLFMJV GJ GJSBGÊ SBGÊSMFJV SMFJV1 :. [JQ@LJGMBLS@. ;. YOJLSBJGMBLS@ ] [BV@ORFMÖL CB Y[@KOBGJV 6. F@GRLMFJSMTJ. E[JC@

YB[M@C@

3

Y[MGB[@

F`gp`lbl F`gp`lbltbs tbs cb o`s `kabt`s `kabt`s trmcmgblsm`ljobs (fjrjs, ojc`s). F`gp`lbl F`gp` lbltbs tbs cb ojs ﬊eurjs ﬊eurjs kmc kmcmmgblsm`ljobs (êleuo`s, vírtmfbs).

VBERLC@

Yr`pmb Yr`pmbcjcbs cjcbs cb cb o`s `kabt`s eb`gíeb`gítrmf`s. Yòçe`l`s rbeuojrbs b mrrbeuojrbs.

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2

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SBGJV

SB[FB[@

Srjlsd`rgjfm` rjlsd`rgjfm`lbs1 lbs1 smgbtrçj, smgbtrçj, r`tjfmöl y rb﬋bxmöl. F`lfbptujomzjfmöl cbo f`lfbpt` cb f`lerublfmj y sbgbajlzj.

FRJ[S@

Bo fçrfuo` fçrfuo` y oj oj fmrfuldb fmrfuldbrblfmj rblfmj11 Yjrtbs cbo fçrfuo` y bobgblt`s cb oj fmrfuldbrblfmj.

Y[MGB[@

@kabt`s pojl pojl`s `s y sus sus f`gp`lb f`gp`lbltbs ltbs (êleuo`s, vírtmfbs). Yr`pmbcjcbs cb o`s Yòçe`l`s (fujcrmoêtbr`s y trmêleuo`s) VBERLC@ Srjlsd` rjlsd`rgjfm` rgjfm`lbs lbs bl bo pojl pojl`1 `1 [`tjfmöl, Srjsojfmöl, Vmgbtrçj, H`g`tbfmj. SB[FB[@ [bojfm`lbs cb f`lerublfmj y sbgbajlzj.

FRJ[S@

Yojl` fjrtbsmjl`

O@E[@V

[bf`l`fb o`s ojs fjrjs y o`s ojc`s qub f`gp`lbl o`s `kabt`s trmcmgblsm`ljobs. Bxpomfj ojs rbojfm`lbs qub blfubltrj jo f`gpjrjr o`s `kabt`s trmcmgblsm`ljobs f`l `kabt`s cb su blt`rl`. Bstjkobfb cmdbrblfmjs bltrb pòçe`l`s rbeuojrbs b mrrbeuojrbs. mrrbeuojrbs. L`gkrj o`s bobgblt`s cb ul pòçe`l`. [bjomzj y bxpomfj ojs trjlsd`rgjfm`lbs jo g`gblt` cb gjlmpuojr o`s `kabt`s kmcmgblsm`ljobs. Cmdbrbl Cmdb rblfmj fmj o`s f`l f`lfbp fbpt`s t`s cb f`l f`l-erublfmj y sbgbajlzj Jpomfj bo f`lfbpt` cb f`lerublfmj jo f`gpjr f`gpjrjr jr `kabt`s trmcmgblsm`l trmcmgblsm`ljjobs. Jpomfj bo f`lfbpt` cb sbgbajlzj jo f`gpjrjr `kabt`s trmcmgblsm`ljobs. Mcbltm﬊fj o`s bobgblt`s qub f`gp`lbl ul fçrfuo`. [bf`l`f [bf `l`fbb ojs cmdbrbl cmdbrblfmj fmjss qub hjy hjy bltrb fçrfuo` y fmrfuldbrblfmj. Bstjkobfb cmdbrblfmjs bltrb bo fçrfuo` y o`s pòçe`l`s. Mcblt Mcb ltm﬊f m﬊fjfm jfmöl öl y rbojfmöl rbojfmöl bl bltrb trb o`s f`gp`lb f`g p`lblt ltbs bs cb ulj ﬊eurj ﬊eurj kmc kmcmmgblsm`ljo (êleuo`s y vírtmfbs) [bjomzjfmöl cb g`vmgmblt`s cb ﬊eurjs pojljs bl bo pojl` fjrtbsmjl`. fjrtbsmjl`. Cmdbrbl Cmdb rblfmj fmj o`s f`l f`lfbp fbpt`s t`s cb f`l f`l-erublfmj y sbgbajlzj jo g`gblt` cb trjkjajr f`l `kabt`s eb`gítrmf`s. Jpomfj bo f`lfbpt` cb f`lerublfmj utmomzjlc` oj smgbtrçj bltrb ﬊eurjs kmcmgblsm`ljobs. Rkmfjfmöl cb pjrbajs `rcbljcjs bl bo pojl` fjrtbsmjl`. [bprbs [bp rbsbl bltjf tjfm`l m`l bl bo pojl pojl`` fjrtbfjrtbsmjl` cb ﬊eurjs ﬊eurjs pojljs. pojljs.

35

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

Sjkoj 3.61 Yojl cb jsmeljturj Eb`gbtrçj pjrj Fmfo` 6.

@KABSMT@1 Y`tblfmjr

bl o`s bstucmjltbs bo cbsjrròo` cbo pblsjgmblt` eb`gítrmf`, pjrj qub pubcj rbf`l`fbr smgmomtucbs y cmdbrblfmjs cb ﬊eurjs pojljs y cb o`s pòmbcr`s cjlc` fubltj cb sus pr`pmbcjcbs, fjrjftbrçstmfjs y bobgblt`s qub o`s f`gp`lbl. F@GYBSBLFMJV GJ GJSBGÊ SBGÊSMFJV SMFJV1 :. [JQ@LJGMBLS@. ;. YOJLSBJGMBLS@ ] [BV@ORFMÖL CB Y[@KOBGJV 6. F@GRLMFJSMTJ. E[JC@

YB[M@C@

4

Y[MGB[@

Cb﬊lmfm Cb﬊lmfmöl öl cb f`lfbpt`s f`lfbpt`s kêsmf`s kêsmf`s cb eb`gbtrçj pojlj. [bftjs pjrjobojs y pbrpblcmfuojrbs pbrpblcmfuojrbs

VBERLC@

Srmêleuo`s, pr`pmbcjcbs y fojsm﬊fjfmöl.

`

SBGJV

Oçlbjs euo`. y pult`s l`tjkobs cbo trmêlSB[FB[@ Yòçe`l`s y su fojsm﬊fjfmöl. Fujcrmoêtbr`s, fojsm﬊fjfmöl

FRJ[S@

5

`

Yòmbcr`s rbeuojrbs. G`vmgmblt`s bl bo pojl`.

Y[MGB[@

Êleuo`s, fojsm﬊fjfmöl, [bftjs pjrjobojs y pbrpblcmfuojrbs. pbrpblcmfuojrbs.

VBERLC@

Sr Srmêl mêleu euo` o`s, s,f`lstruffmöl pr`p pr`pmb mbcj cjcb cbs s trmêleucb o`s o`s trmêleuo`s, cb o`s f`lerubltbs..

SB[FB[@

Sb`rbgj cb Ymtêe`rjs Yòmbcr`s rbeuojrbs b mrrbeuojrbs

FRJ[S@

F`gp`smfmöl F`gp`smfmöl cb g`vmg g`vmgmblt` mblt`ss rçemc`s.

O@E[@V

[bf`l`fb o`s f`lfbpt`s kêsmf`s cb oj eb`gbtrçj bufomcmjlj. F`lstr F`l struy uybb rbftjs rbftjs pjrjob pjrjobojs ojs y pbrpblcmfuojrbs f`l kjsb j ulj cjcj. F`lstruyb trmêleuo`s, o`s fojsm﬊fj b mcbltm﬊fj sus oçlbjs y pult`s l`tjkobs. Bstjkobfb cmdbrblfmjs bltrb pòçe`l`s rbeuojrbs b mrrbeuojrbs. mrrbeuojrbs. Mcblt Mcb ltm﬊f m﬊fjj ojs cmdbrbl cmdbrbltbs tbs fojsbs fojsbs cb fujcrmoêtbr`s y rbf`l`fb sus fjrjftbrçstmfjs. Mcblt Mcb ltm﬊f m﬊fjj ojs pjrtbs pjrtbs cb o`s pòmbcr`s. [bjomzj g`vmgmblt`s bl bo pojl` f`g` r`tjfmöl, trjsojfmöl rb﬋bxmöl y h`g`tbfmjs. Fojsm﬊fj o`s êleuo`s sbeñl su jgpomtuc, p`smfmöl y su sugj. F`lstruyb f`l rbeoj y f`gpjs rbftjs pjrjobojs y pbrpblcmfuojrbs. pbrpblcmfuojrbs. Fojsm﬊fj o`sojc`s trmêleuo`s sbeñl gbcmcj cb sus y êleuo`s êleuo` s y oj jpomfj sus pr`pmbcjcbs. F`lstruyb F`lstr uyb trmêleuo`s trmêleuo`s f`lerubltb f`lerubltbss f`l kjsb j o`s frmtbrm`s cb f`lerublfmj y sbeñl ojs gbcmcjs cjcjs utmomzjlc` oj rbeoj, f`gpjs y trjlsp`rtjc`r. F`l`fb F`l `fb y jpomfj jpomfj f`rrbft f`rrbftjgb jgblt ltbb bo tb`rbgj cb Ymtêe`rjs. Mcbltm﬊fj o`s pòmbcr`s y o`s fojsm﬊fj bl rbeuojrbs b mrrbeuojrbs. [bjomzj y f`gp`lb g`vmgmblt`s cb ﬊eurjs bl bo pojl`, f`lsbrvjlc` oj d`rgj y bl `fjsm`lbs bo tjgjú` f`l jyucj cb oj rbeoj, f`gpjs y trjlsp`rtjc`r.

38

FJYÇSRO@ 3. Y[@YRBVSJ CMCÊFSMFJ CMCÊFSMFJ

Sjkoj 3.31 Yojl cb jsmeljturj Eb`gbtrçj pjrj Fmfo` 3.

@KABSMT@1

Bstjk Bstjkobfbr obfbr oj cmdbrblfmj bltrb bltrb o`s f`lfbpt`s f`lfbpt`s cb f`lerublfmj y sbgbajlzj sbgbajlzj cb ﬊eurjs y rbojfm`lj o`s frmtbrm`s cb oj sbgbajlzj y f`lerublfmj bl oj sòufmöl cb trmêleuo`s ` bl oj cbg`strjfmöl cb tb`rbgjs cb Shjobs ` cb Ymtêe`rjs. F@GYBSBLFMJV GJ GJSBGÊ SBGÊSMFJV SMFJV1 :. [JQ@LJGMBLS@. ;. YOJLSBJGMBLS@ ] [BV@ORFMÖL CB Y[@KOBGJV 6. F@GRLMFJSMTJ. E[JC@

YB[M@C@

8

Y[MGB[@

Êleuo`s, fojsm﬊fjfmöl. Êleuo`s d`rgjc`s bltrb c`s rbftjs pjrjobojs pjrjobo js y ulj sbfjltb.

VBERLC@

Srmêleuo`s, pr`pmbcjcbs y fojsm﬊fjfmöl.

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SBGJV

Oçlbjs euo`. y pult`s l`tjkobs cbo trmêlSB[FB[@ Srmêleuo`s f`lerubltbs Sb`rbgj cb Shjobs.

FRJ[S@

=

`

Y[MGB[@

Fujcrmoêtbr`s y su fojsm﬊fjfmöl. Yr`pmbcjcbs cb o`s fujcrmoêtbr`s

Mltr`cu Mltr`cuffmöl ffmöl j o`s o`s gít`c`s cb cb cbg`strjfmöl. Gít`c` cmrbft`, Gít`-

c` mlcmrbft`, Gít`c` p`r rbdutjfmöl ` f`ltrjbabgpo`. VBERLC@ [jz`lbs y pr`p`rfm`l pr`p`rfm`lbs bs Sb`rbgj cb Shjobs Yòçe`l`s sbgbajltbs

SB[FB[@

FRJ[S@

Vbgbajlzj cb trmêleuo`s Sb`rbgj cb Ymtêe`rjs [jz`lbs trme`l`gítrmfjs

fçrfuo` y fmrfuldbrblfmj Bobgblt`s cbo fçrfuo` Êleuo`s cb oj fmrfuldbrblfmj y sus gbcmcjs Yòçe`l`s mlsfrmt`s y fmrfulsfrmt`s

O@E[@V

[bf`l`fb o`s f`lfbpt`s kêsmf`s cb oj eb`gbtrçj bufomcmjlj. F`lstruyb f`l rbeoj y f`gpjs oj kmsbftrmz cb ul êleuo` y oj gbcmjtrmz cb ul sbegblt`. F`lstr F`l struy uybb rbftjs rbftjs pjrjob pjrjobojs ojs y pbrpblcmfuojrbs f`l kjsb j ulj cjcj. F`lstruyb trmêleuo`s, o`s fojsm﬊fj b mcbltm﬊fj sus oçlbjs y pult`s l`tjkobs. F`l`fb y jpomfj o`s p`stuojc`s cb f`lerublfmj cb trmêleuo`s. Jpomfj o`s frmtbrm`s cb f`lerublfmj cb trmêleuo`s bl oj rbsòufmöl y d`rguojfmöl cb pr`kobgjs. Rtmomzj ojs cb﬊lmfm`lbs y pr`pmbcjcbs bspbfç﬊f bspbfç﬊fjs js cb o`s pjr pjrjob joboè oèrjrjg`s (rbftêleuo`, fujcrjc`, r`gk`, trjpbfm`), bl oj sòufmöl cb pr`kobgjs. Jpomfj Jpo mfj o`s tb`rbg tb`rbgjs js cb sbegbl sbegblt` t` gbcm` pjrj trjpbfm`s. trjpbfm`s. [bf`l`fb y jpomfj o`s cmdbrbltbs gít`c`s cb cbg`strjfmöl bl eb`gbtrçj. Jpomfj ojs pr`pmbcjcbs cb oj pr`p`rfm`ljomcjc bl oj sòufmöl cb pr`kobgjs. Jpomfj bo tb`rbgj cb Shjobs bl oj sòufmöl cb pr`kobgjs. [bf`l`fb ojs f`lcmfm`lbs pjrj qub c`s pòçe`l`s sbjl sbgbajltbs Mcbltm﬊fj o`s frmtbrm`s cb sbgbajlzj cb trmêleuo`s. Jpomfj ojs rjz`lbs trme`l`gítrmfjs pjrj êleuo`s jeuc`s cb ul trmêleuo` rbftêleuo` bl oj sòufmöl cb pr`kobgjs cb su blt`rl`. Fjrjftbrmzj ojs oçlbjs y êleuo`s bspbfmjobs rbojfm`ljc`s f`l oj fmrfuldbrblfmj. F`lstruyb pòçe`l`s mlsfrmt`s y fmrfulsfrmt`s.

3=

F`lfousm`lbs Bo bstucm` qub sb hmz` s`krb oj hmst`rmj cb oj f`lerublfmj y sbgbajlzj, pbrgmtmö rb﬋bxm`ljr s`krb o`s f`ltblmc`s tbgêtmf`s qub hjkmtujogbltb sb blsbújl cb eb`gbtrçj, yj qub jo rbvmsjr o`s Bobgblt`s cb Bufomcbs y o`s jxm`gjs cb Hmokbrt, sb pubcb jprbfmjr qub l` s`l tblmc`s bl fubltj jftujogbltb bl oj bcufjfmöl kêsmfj y s`l cb sugj mgp`rtjlfmj pjrj oj blsbújlzj cb oj eb`gbtrçj. Bo cbsf`l`fmgmblt` cb oj hmst`rmj hj smc` ul djft`r cbtbrgmljltb bl oj ojk`r cbo pr`dbs`r cb gjtbgêtmfjs, qub blfubltrj gês dêfmo jp`yjrsb bl o`s omkr`s cb tbxt` trjcmfm`ljobs, qub bl ojs pr`pmjs dubltbs, c`lcb tuvmbr`l ouejr bo cbsjrròo` cb ojs mcbjs gjtbgêtmfjs, gjtbgêtmfjs, pbrcmílc pbrcmílc`sb `sb oj p`smkmomcjc p`smkmomcjc bl bstb pr`fbs` hmstörmf`, hmstörmf`, jcqumrmr bobgblt`s bobgblt`s qub jyucbl jyucbl j gba`rjrr su prêftmfj gba`rj prêftmfj c`fbltb. c`fbltb. Bo f`gp`lbltb pbcjeöemf` cb bstb trjkja` pbrgmtmö f`l`fbr joeul`s bstucm`s qub sb hjl rbjomzjc` s`krb oj blsbújlzj y jprblcmzjab cb oj eb`gbtrçj, pjrj p`cbr tblbr bl fubltj oj bstrufturj qub sb rbqumbrb bl bo pblsjgmblt` eb`gítrmf` y jsç p`cbr blfjcbljr o`s tbgjs qub sb cbkbl cbsjrròojr bl ul pojl cb jsmeljturj bl eb`gbtrçj, tblmblc` bl fubltj o`s bstêlcjrbs kêsmf`s bl gjtbgêtmfjs y o`s omlbjgmblt`s furrmfuojrbs, qub s`l oj l`rgjtmvmcjc jftujo vmebltb qub rmeb j ojs mltmftufm`lbs bcufjtmvjs j lmvbo ljfm`ljo. Bstj f`lsuotj dub guy mgp`rtjltb mgp`rtjltb rbjomzjroj p`rqub pbrgmtmö pojlbjr y `rejlmzjr `rejlmzjr o`s tbgjs cb eb`gbtrçj bl bo pojl cb jsmeljturj, qub sb cbkbl trjkjajr bl fjcj fmfo` y f`g` sb pubcbl jk`rcjr f`l cmdbrbltb lmvbo cb pr`dulcmcjc cb o`s fmfo`s : jo fmfo` 3 f`l kjsb j o`s lmvbobs cb Tjl Hmbob. Jo f`lstrumr f`lstrumr oj pr`pubstj pr`pubstj cmcêftmfj, bstucmjlc` bstucmjlc` joeul joeuljs js hbrrjgmbl hbrrjgmbltjs tjs gbt`còöemfjs sb `pt` p`r utmomzjr utmomzjr ojs euçjs cmcêftmfjs f`g` mlstrugblt` cb gbcmjfmöl pbcjeöemfj pjrj blsbújlzj y jprblcmzjab cb oj eb`gbtrçj.. Yjrj gbtrçj Yjrj oj bojk`rjfmöl cb euçjs bs mgp`rtjltb mgp`rtjltb tblbr fojrj oj bstrufturj y oj mltblfmöl f`l oj fujo sb bojk`rj, pjrj qub jo sbr mgpobgbltjcj bl bo juoj sbj jpr`pmjcj pjrj jofjlzjr o`s `kabtmv`s prbvmst`s bl oj gmsgj y sbj jerjcjkob j o`s bstucmjltbs j oj h`rj cb cbsjrròojrojs. Ojs euçjs rbjomzjcjs, c`lcb sb jk`rcjl o`s f`lfbpt`s cb sbgbajlzj y f`lerublfmj, sbrjl bo mlmfm` cb ul kjlf` cb euçjs pjrj bo êrbj cb gjtbgêtmfjs bl bo Fòbem` Vjl Jeustml yj qub jftujogbltb bl oj mlstmtufmöl l` f`ltjg`s f`l tbxt`s ` gjtbrmjo cb jp`y` pjrj rbjomzjr oj fojsb cb eb`gbtrçj. Bo utmomzjr f`g` gjtbrmjo cb jp`y` bo prèrjgj ebèbkrj pjrj oj blsbújlzj cb oj eb`gbtrçj, pubcb sbr ulj hbrrjgmbltj cmcêftmfj pjrj cbsjrròojr jftmvmcjcbs y prêftmfjs c`lcb o`s bstucmjltbs jpomqubl o`s tbgjs vmst`s bl fojsb cb d`rgj mltbrjftmvj y gês rêpmcj, smeumblc` pjs` j pjs` ojs mlstruffm`lbs cjcjs y oube` p`r gbcm` cb oj kjrrj cb ljvbejfmöl, pubcjl vmsujomzjr ojs f`lstruffm`lbs y trjlsd`rgjfm`lbs eb`gítrmfjs rbjomzjcjs. Oj utmomzjfmöl bstb prèrjgj rbcufb bo tmbgp` bl joeul`s tbgjs qub p`r su lmvbo cb f`lstruffmöl s`l gês f`gpoba`s, cbgjlcjl gufh` tmbgp` bl bo juoj cb fojsb y sb pubcb pr`dulcmzjr gês bl oj sòufmöl cb pr`kobgjs qub mlvòufrbl bo pblsjgmblt` eb`gítrmf` ` jk`rcjr t`c`s o`s tbgjs pojltbjc`s bl bo pojl cb jsmeljturj cb bstb trjkja`. Bs mgp`rtjltb rbsjotjr qub bstj pr`pubstj cmcêftmfj sb hmz` tblmblc` bl fubltj o`s lmvbobs y ojs djsbs cb jprblcmzjab cb Tjl Hmbob, y sb jpomfjr`l bl oj bojk`rjfmöl cb ojs euçjs cmcêftmfjs pjrj oj fojsb cb eb`gbtrçj cb o`s bstucmjltbs cbo Fòbem` Vjl Jeustml a`rljcj tjrcb.

29

[bf`gblcjfm`lbs Ojs euçjs pr`pubstjs pjrj o`s cmdbrbltbs lmvbobs dubr`l cmsbújc`s f`g` ulj pr`pubstj, bs cbfmr l` hjl smc` jpomfjc`s jpomfjc`s j ulj p`kojfmöl cbtbrgmljcj> cbtbrgmljcj> qubcj j aumfm` cb oj f`gulmcjc bcufjtmvj, bcufjtmvj, mgpobgbltjr mgpobgbltjr o`s tjoobrbs y rbjomzjr oj bvjoujfmöl f`rrbsp`lcmbltb, qub pubcb f`lvbrtmrsb bl ul trjkja` d`rgjo cb ulj duturj mlvbstmejfmöl bl oj blsbújlzj cb oj eb`gbtrçj.

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Kmkomèrjdçj ^:W Jeumojr, J. & Tjojpjm, D., (;998),Gjtbgêtmf Gjtbgêtmfjs js Vmgpom﬊fjc Vmgpom﬊fjcjs js , Gíxmf`, Gíxmf`, Ybjrs`l, Ybjrs`l, pp. 439-4=:. 439-4=:. ^;W Kboo, B. S., (:=82), Hmst`rmj cb ojs gjtbgêtmfjs , RVJ, D`lc` cb fuoturj bf`lögmfj. ^6W Kurebr, U.D. & Vhjuehlbssy, A.G., (:=84), Fhjrjftbrmzmle thb Tjl Hmbob obvbos `d cbvbo`pgblt ml eb`gbtry , Aùrljo d`r [bsbjrfh ml Gjthbgjtmfs Bcufjtm`l Tò :5 L`. :, pp. 6: - 38. ^3W Fòobttb, A. Y., (:=82), Hmst`rmj cb ojs gjtbgêtmfjs M y MM , Gíxmf`, Vmeo` vbmltmul`. ^2W Fjgp`s, J., (:==3), Jxm`gêtmfj y Eb`gbtrçj cbscb Bufomcbs hjstj Hmokbrt y Kùrkjnm ,Kè`tj, ,Kè`tj, Yr`ybft` cb mlvbstmejfmöl RL. ^4W F`rkbrêl, F`rkbrêl, [ & Eutmírrbz, J., (:==3), (:==3), Cmsbú` y bvjoujfmöl cb ulj pr`pubstj furrmfuojr cb jprblcmzjab cb oj Eb`gb Eb`gbtrç trçj j bl Bls Blsbúj bújlzj lzj Vbful Vbfulcjr cjrmj mj kjsjcj jsjcj bl bo G` G`cbo cbo` ` cb [jz` jz`ljg ljgmbl mblt` t` cb Tjl Hmbob Hmbob , Gjcrmc, Fòbffmöl ‟mlvbstmejfmöl‗ L`. =2, F.M.C.B. ^5W C`ljo, @., (;998), Oj f`labturj cb Y`mlfjrí. Bl kusfj cb oj d`rgj cbo ulmvbrs` , Kjrfbo`lj, Bspjúj, Susqubts Bcmt`rbs, pp. 45-:99. ^8W Bufomcbs, G., (:488), O`s sbms prmgbr`s omkr`s, `lfb y c`fb cb o`s Bobgblt`s cb Bufomcbs , Krusbojs. ^=W Bsfucbr`, Bsfucbr`, M., (:===), (:===), Rl jlêomsms cbo trjtjgmblt` cb oj sbgbajlzj bl o`s c`fugblt`s `﬊fmjobs y tbxt`s bsfòjrbs cb gjtbgêtmfjs bl oj sbeulcj gmtjc cbo smeo` XX , Bspjúj, Rlmvbrsmcjc cb Vbvmooj. ^:9W Bsfucbr`, M., (;996), Oj sbgbajlzj f`g` `kabt` cb blsbújlzj ‖ jprblcmzjab bl oj rbojfmöl bltrb bo f`l`fmgmblt` pr`dbsm`ljo cbo pr`dbs`r cb gjtbgêtmfjs cb blsbújlzj sbfulcjrmj y su prêftmfj , Bspjúj, Rlmvbrsmcjc cb Vbvmooj. ^::W GBL1 Bstêlcjrbs kêsmf`s bl gjtbgêtmfjs . F``pbrjtmvj bcmt`rmjo gjemstbrm`, (;994). http1//www.gmlbcufjfm`l.e`v.f`/fvl/:442/jrtmfobs-::493;Pjrfhmv`Ppcd;.pcd. ^:;W Eubrrbr`, J. K., (;994), Cbsjrròo` jxm`gêtmf` cb oj eb`gbtrçj , Kè`tê, Bf`b bcmfm`lbs, pp.6=-;59. ^:6W Hmokbrt, C., (:==4) Dulcjgblt`s cb oj Eb`gbtrçj , Gjcrmc, Bspjúj, FVMF. ^:3W Ajmgb, Y. Y. & Eutmírrbz, Eutmírrbz, J., (:==9),Rlj pr`pubstj cb dulcjgbltjfmöl pjrj oj blsbújlzj cb oj eb`gbtrçj1 bo g`cbo` cb Tjl Hmbob , Vbvmooj, Fòbffmöl ‟Fmblfmjs cb oj Bcufjfmöl‗ L`. 3, pp. ;=2-683. ^:2W Obg`lmcms, F., (:==9), F`lfbptm`l, ríjomsjtm`l bt rísuttjos c”ulb bxpírmblfb c”blsbmegblt cb M” h`g`thbtmb , Sbsms C`ft`rjo, Rlmvbrsmtí Oùms Yjstbur, Vtrjskùre. ^:4W GBL1 Omlbjgmblt`s furrmfuojrbs cb gjtbgêtmfjs , F``pbrjtmvj bcmt`rmjo gjemstbrm`, (:==8). ^:5W O`sjcj, J., G`ltjúj, D. & G`rbl`, H., (;998), Gít`c`s, Gít`c`s, Sí Síflmf flmfjs js y Bstr Bstrjtb jtbemjs emjs cb blsb blsbújlzj újlzj jprblcmzjab , Kè`tê, Fò`gkmj, Bcmfm`lbs V.B.G, pp. ::4 - ::5. ^:8W G`msb, B. & C`wls, D., (:=84), Eb`gbtrçj G`cbrlj , Gíxmf`, Jccms`l Ubsoby, pp.::5-;92. ^:=W Yêbz Eutmírrbz, S., (;99=), Ojs Ojs gjtbgêtm gjtbgêtmfj fjss j o` ojre` cb oj hmst`rmj1 hmst`rmj1 cb oj pr prbhmst` bhmst`rmj rmj j oj jltmeuj erbfmj , Bspjúj, Bspjúj, Tmsm`l Tmsm`l Omkr`s. Omkr`s.

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^;9W Ybríz, G. J., (;9:9), Rlj hmst`rmj cb ojs gjtbgêtmfjs1 rbt`s y f`lqumstjs j trjvís cb sus pbrs`ljabs , Bspjúj, Tmsm`l Omkr`s. ^;:W [`crmeubz, [`crmeubz, K., @ojrtb, J. & Jk`lcjl`, U., (;9:9), (;9:9), Vbrmb Gm Jvblturj Gjtbgêtmfj cb 4 j = , Kè`tê, Bcmt`rmjo Bcufjtmvj. ^;;W [umz, Ê., (;996), Hmst`rmj y ﬊o`s`dçj cb ojs gjtbgêtmfjs , F`stj [mfj, BRLBC. ^;6W Vjoejc`, C. F., (;995), Vbrmb Lubvjs gjtbgêtmfjs 5, 8 y =  , Kè`tê, Bcmt`rmjo Vjltmoojlj. ^;3W Vbstmbr, J., (:=8=), Hmst`rmj cb ojs gjtbgêtmfjs , Gíxmf`.C.D, Omgusj. ^;2W Vtjloby, [. F. & Yhjrbs, E. @., (:==8), Eb`gbtrçj , Gíxmf`, Ybjrs`l, pp. 86-66=. ^;4W Tjl Hmbob, Y., (:=84), Vtrufturb jlc Mlsmeht , Lbw ]`rn, Jfjcbgmf Yrbss. 6 6

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