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Adtevebab ng dfasn. Egvnstemadeôg bn pnradegnsAdtevebab ng dfasn. Egvnstemadeôg bn pnradegns
1.1. NgNg ugugaa cácáhrhrededaa bnbn dadakekesasass snsn ddgcgcndnddedeggagag bbss teteppss bnbn dadakekesasas:s: dadakekesasa egcrkegcrkaf y dakesa crkaf9 fa utefebaf y dakesa crkaf9 fa utefebab pr dabaab pr daba dakesa crkaf ns bndakesa crkaf ns bn ^T$ 8?^T$ 8? y pry pr daba dakedaba dakesasa egcegcrkarkaff ns bnns bn ^T$ 1?.^T$ 1?. _ar_araa ffnffnvar avar a dahdahfa cahrefa cahredadedadeôg bnôg bn ugauga dadakekesasa rnrnquequenrnnrn ququnn åsåstata papasnsn p`p`rr duduatatr`r` bnbnpapartrtakakngtngt`s:`s: bebesnñsnñ`,`, tataffffajajn,n, nsnstatakpkpabab yy tntnrkrkegegabab.. TnTn tetengngngng bebespspgegehfhfnn 2??2?? llrarass bnbn tetenknkpp ngng nfnf bnpartakngtbn besnñ, 4?? lras ng taffajn, >?? lras ng nstakpaby 8??bnpartakngt bn besnñ, 4?? lras ng taffajn, >?? lras ng nstakpab y 8?? lras ng tnrkegab.lras ng tnrkegab.
Ng fa semuengtn tahfa sn kunstrag fs rnqunrekengts bn kagbnhra pr ugebabNg fa semuengtn tahfa sn kunstrag fs rnqunrekengts bn kag bn hra pr ugebab ng daba ugbn fs bnpartakngts.ng daba ug bn fs bnpartakngts.
Te fa nkprnsa bnsna kaxekezar fa utefebab rnspgba:Te fa nkprnsa bnsna kaxekezar fa utefebab rnspgba:
a.a. °Duáf°Duáf ns nf kns nf kbnf bbnf bn prmran prmrakadeôgkadeôg fegnafegnaf para nf para nstn prstn prhfnka0hfnka h.h. °Duágt°Duágtas dakeas dakesas bn daba dsas bn daba dfasn bnhfasn bnhn cahredn cahredar para htar parahtngnr fa utngnr fa utefebaefebab káxekb káxeka ya y duaf ns nsta utefebab0duaf ns nsta utefebab
BnsarrffBnsarrff
Agáfeses bnf prhfnkaAgáfeses bnf prhfnka
Nf prhfnka pfagtnab prntngbn bar hasns duagtetatevas qun pnrketag tkarNf prhfnka pfagtnabprntngbn bar hasns duagtetatevas qun pnrketag tkar fa bndeseôg kás adnrtaba psehfn, tngengb ng dungta fas rnstreddegns qun snfa bndeseôg kás adnrtaba psehfn, tngengbng dungta fas rnstreddegns qun sn tengn y nf hjntev bn fa nkprnsa.tengn y nf hjntev bn fa nkprnsa.
Nspndëcedakngtn para nstn das, husda ngdgtrar fa dagtebab bn ugebabnsNspndëcedakngtn para nstn das, husda ngdgtrar fa dagtebab bn ugebabns kás adnrtaba para cahredar bn daba uga bn fas dakesas qun kagnja fakás adnrtaba para cahredar bn daba uga bn fas dakesas qun kagnja fa cáhreda, dg nf ceg bnhtngnr fa knjr utefebab psehfn. Dk ng tbas fascáhreda, dg nf ceg bn htngnr fa knjr utefebab psehfn. Dkng tbas fas cáhredas, fs rndurss G@ sg efeketabs, ns bnder, nxestng turgs qun feketagcáhredas, fs rndurss G@ sg efeketabs, ns bnder, nxestng turgs qun feketag fas lras bn kag bn hra bespgehfns, ug usnstahfndeb bn kaquegarea qunfas lras bn kag bn hra bespgehfns, ug usnstahfndeb bn kaquegarea qun feketa fas lras bn prbuddeôg bespgehfns, katnreafns bespgehfns qun feketafeketa fas lras bn prbuddeôg bespgehfns, katnreafns bespgehfns qun feketa fas ugebabns qun sn punbng cahredar, ngtrn trs cadtrns.fas ugebabns qun sn punbng cahredar, ngtrntrs cadtrns.
_ara fa cáhreda ng dunsteôg, sn tengn ugas lras káxekas bn trahaj ng daba_ara fa cáhreda ng dunsteôg, sn tengn ugas lras káxekas bn trahaj ng daba uga bn fas árnas pr bgbn bnhn druzar fa dakesa para qun sn dgvenrta nguga bn fas árnas pr bgbn bnhn druzar fa dakesa para qun sn dgvenrta ng ug prbudt tnrkegab: besnñ, taffajn, nstakpaby tnrkegab, bnheba fsug prbudt tnrkegab: besnñ, taffajn, nstakpaby tnrkegab, bnheba fs turgs bn fa kag bn hra ng daba uga bn bedlas árnas, sengb nstn nfturgs bn fa kag bn hra ng daba uga bn bedlas árnas, sengb nstn nf rndursfeketab. Rakheåg sn hregba fa utefebab qun mngnra daba dakesa,rndursfeketab. Rakheåg sn hregba fa utefebab qun mngnra daba dakesa, sengbnstn nfhjntevqun fa cáhreda bnsna kaxekezar.sengb nstn nf hjntev qun fa cáhreda bnsna kaxekezar.
DDakakesesaa ccrkrkafaf DDakakeesasa eegcgc``rkrkafaf Bnpt. besnñBnpt. besnñ 11 8 8..>>?? Bnpt. taffajnBnpt. taffajn 44 1 1..88>> Bnpt. nstakpabBnpt. nstakpab 22 4 4..88>> Bnpt. tnrkegabBnpt. tnrkegab 4 4..>> 8 8..>>
Ngtgdns, bn adunrb af rndursfeketab y nf hjntev qun sn bnsna afdagzar,Ngtgdns, bn adunrb af rndursfeketab y nf hjntev qun sn bnsna afdagzar, sn hregba fa egcrkadeôg bn fas lras qun rnquenrn daba tepbn dakesa ngsn hregba fa egcrkadeôg bn fas lras qun rnquenrn daba tep bn dakesa ng daba árna para qun cegafedn nf prdns (dg nf ceg bn qun sn asnmurn qun fasdaba árna para qun cegafedn nf prdns(dg nf ceg bn qun sn asnmurn qun fas ugebabns cahredabas gvayag a rnqunrer kás lras bn cahredadeôg bn fasugebabns cahredabas gvayag a rnqunrer kás lras bn cahredadeôg bn fas bespgehfns) y fa utefebab qun mngnra daba dakesa (dg nf ceg bn rnafezar fabespgehfns) y fa utefebab qun mngnra daba dakesa (dg nf ceg bn rnafezar fa dkhegadeôg bn ugebabns qun kás utefebab mngnrn).dkhegadeôg bn ugebabns qun kás utefebab mngnrn).
(^) _fagtnakengtkatnkáted bnf prhfnka_fagtnakengt katnkátedbnf prhfnka
Sareahfns bn bndeseôgSareahfns bn bndeseôg
\1; dagtebab bn dakesas crkafns a cahredar\1; dagtebab bn dakesas crkafns a cahredar \8; dagtebab bn dakesas egcrkafns a cahredar\8; dagtebab bn dakesas egcrkafns a cahredar
Cugdeôg hjntev: Kax Z, bgbn Z rnprnsngta fa utefebab bn fa nkprnsaCugdeôghjntev: Kax Z, bgbn Z rnprnsngta fa utefebab bn fa nkprnsa
Z; 8?x1 + 1?x8Z; 8?x1 + 1?x
Tujnta:Tujnt a:
X1: Lras rnqunrebas bn daba dakesa ng nf árna bn besnñ, fa duaf tengnX1: Lras rnqunrebas bn daba dakesa ng nf árna bn besnñ, fa duaf tengn káxek2?? lras para trahajar:káxek2?? lras para trahajar:
x1 + 8.> x86;2??x1 + 8.> x86;2??
X8: Lras rnqunrebas bn daba dakesa ng nf árna bn taffajn, fa duaf tengnX8: Lras rnqunrebas bn daba dakesa ng nf árna bn taffajn, fa duaf tengn káxek4?? lras para trahajar:káxek4?? lras para trahajar:
4 x1 + 1.8> x86;4??4 x1 + 1.8> x86;4??
X4: Lras rnqunrebas bn daba dakesa ng nf árna bn nstakpab, fa duaf tengnX4: Lras rnqunrebas bn daba dakesa ng nf árna bn nstakpab, fa duaf tengn káxek>?? lras para trahajar:káxek>?? lras para trahajar:
2 x1 + 4.8> x86;>??2 x1 + 4.8> x86;>??
X2: Lras rnqunrebas bn daba dakesa ng nf árna bn tnrkegab, fa duaf tengnX2: Lras rnqunrebas bn daba dakesa ng nf árna bn tnrkegab, fa duaf tengn káxek8?? lras para trahajar:káxek8?? lras para trahajar:
4.> x1 + 8.> x86;8??4.> x1 + 8.> x86;8??
X>: rnstreddegns bn g gnmatevebabX>: rnstreddegns bn g gnmatevebab
x17;?x17;? x87;?x87;?
?? >>?? 11 ???? 11 >>?? 88 ???? 88 >>?? 44 ???? 44 >>?? 22 ???? 22 >>??
??
1>4.<41>4.<
??
82?82?
??
34.1334.
13?13?
??
122122 X1X X8X X4X X2X
(Ng azuf y vnrbn nf árna ôpteka)(Ng azuf y vnrbn nf árna ôpteka)
SaSafefebabakkss ffss pupugtgtss 1.1. (?(?,<,<?),?), 8.8. (>=(>=.1.12,2, ?)?) yy 4.4. (8?(8?,>,>8)8),, hhtntngegengngbb ffss semuengtns rnsuftabs para Z:semuengtns rnsuftabs para Z:
Dg nf pugt 1 Z; <??Dg nf pugt 1 Z; <??
Dg nf pugt 8 Z; 1128.<3Dg nf pugt 8 Z; 1128.<3Dg nf pugt 4 Z; 2>8Dg nf pugt 4 Z; 2>
X1X
X8X
X4X
X2X
C@C@
Fa sfudeôg ôpteka ns Z ; 1128.<3Fa sfudeôg ôpteka ns Z ; 1128.< x1 ; >=.12x1 ; >=. x8 ; ?x8 ;?
Agáfeses bn sngsehefebab bnf kåtb mrácedAgáfeses bn sngsehefebab bnf kåtbmráced
tt 11 ≢≢
∘∘
dd 11 dd 88 ≢ t≢ t^88
Bn adunrbaf mráced, fa cugdeôg hjntev sn ngdungtra ngtrn fa rnstreddeôg 2Bn adunrbaf mráced, fa cugdeôg hjntev sn ngdungtra ngtrn fa rnstreddeôg 2 qun ns fa kás haja y fa rnstreddeôg 8, qun ns kayr qun fa rnstreddeôg 4 qunqun ns fa kás haja y fa rnstreddeôg 8, qun ns kayr qun fa rnstreddeôg 4 qun takheåg supnrpgn a fa cugdeôghjntev. Dg fagtnrer tngnks:takheåg supnrpgn a fa cugdeôg hjntev. Dg f agtnrer tngnks:
X2: 4.> x1 + 8.> x86;8??X2: 4.> x1 + 8.> x86;8??
∘∘4.>4.> 8.>8.>
xx 11 ++ <?<?;;^ ==
xx 11 ++ <?<?
X1: 4 x1 + 1.8> x86;4??X1: 4 x1 + 1.8> x86;4??
∘∘ 44 1.8>1.8>
xx 11 ++82?82?;;^1818
xx 11 ++ 82?82?
C.@.: 8?x1 + 1?x8C.@.: 8?x1 + 1?x8 ^ d1; 8? d8;1?d1; 8? d8;1? r f agtnrer, tngnks nf semuengtn bnspnjn para d1:r f agtnrer, tngnks nf semuengtn bnspnjn para d1:
∘∘==
66 ∘∘^ dd^11 dd 88
66 ∘∘^1818
==
66 dd^11 1?1?
661818
== ??
66 dd 1166 18?18?
121266 dd 11668282
U nf keskprdnspara d8:U nf kesk prdns para d8:
∘∘==
66 ∘∘8?8? dd 88
66 ∘∘^1818
== 1??1??
77 dd 8877 1818 1??1??
12.8<12.8<^77 dd 8877 <.4<.
Nsts egtnrvafs gs pnrketng varear fs dncedengtns bn fa cugdeôghjntev,Nsts egtnrvafs gs pnrketng varear fs dncedengtns bn fa cugdeôg hjntev,htngengb fs kesks vafrns para x1 y x8 y ug gunv vafr para fa utefebab.htngengbfs kesks vafrns para x1 y x8 y ug gunvvafr para fa utefebab.
Tfudeôg pr knbebnf kåtbTfvnrTfudeôg pr knbebnf kåtbTfvnr
^sagbnf Tfvnr bn Nxdnf, pbnks rnsfvnr nstn pfagtnakengt bn fa semuengtn^sagbnf Tfvnr bn Nxdnf, pbnks rnsfvnr nstn pfagtnakengt bn fa semuengtn kagnra:kagnra:
Ng bgbnhtngnks fa keska sfudeôg ôpteka:Ng bgbnhtngnks fa keska sfudeôg ôpteka:
Z ; 1128.<3Z ; 1128.<
\1 ; >=.12\1 ; >=.
\8 ; ?\8 ;?
Tfudegns hásedasTfudegns hásedas
TT``ffuuddeeôôgg \1 1 \8 8 LL1 1 LL8 8 LL4 4 LL2 2 11 ?? ?? 2 2???? 4 4???? >>???? 8 8???? 88 ?? 118 8?? 1 1???? 1 1>>?? 111 1?? - -11???? 44 4 4???? ?? 1 1???? - -33???? - -==???? - -<<>>??
Agáfeses bn sngsehefebab bnf kåtb sekpfnxAgáfeses bn sngsehefebab bnf kåtb sekpfnx
_fagtnaks fa katrez egvnrsa bn fa tahfa cegaf sekpfnx:_fagtnaks fa katrez egvnrsa bn fa tahfa cegaf sekpfnx:
11 ?? ?? ∘∘ 11 ?? ?? ??
11 ?? ??
?? 11 ??
∘∘?.>?.> ∘∘1.41. ?.2?.
U nsdreheks nf vndtr bn fs rndurss bespgehfns:U nsdreheks nf vndtr bn fs rndurss bespgehfns:
2??2?? 4??4??
??>?? 8??8??
U bnsarrffaks nf prbudt:U bnsarrffaks nf prbudt:
11 ∝∝ 2 2???? ??∝∝ 4 4???? ??∝∝>??>?? ∘∘ 11 ∝∝8??8?? ??∝∝2??2?? ??∝∝2??2?? ??∝∝2??2??
11 ∝∝4??4?? ??∝∝4??4?? ??∝∝4??4??
??∝∝>??>?? 11 ∝∝>??>?? ??∝∝>??>??
∘∘?.>?.>∝∝8??8?? ∘∘1.41.4∝∝8??8?? ?.2?.2∝∝8??8??
;;
8??8?? 8??8?? 82?82?
Al
ra dakheaks nf vndt
r bn fs rndurs
s bespgehfns:Al
ra dakheaks nf vndt
r bn fs rndurs
s bespgehfns:
2??2??++tt 4??4??
??>?? 8??8??
U bnsarrffaks gunvakngtn nf prbudt:U bnsarrffaks gunvakngtn nf prbudt:
((
11 ∝∝2??2??++^ tt ??∝∝ 4 4???? ??∝∝>??>?? ∘∘ 11 ∝∝8??8?? ??∝∝2??2??++ tt ??∝∝2??2??++ tt ??∝∝2??2??++ tt
11 ∝∝4??4?? ??∝∝4??4?? ??∝∝4??4??
??∝∝>??>?? 11 ∝∝>??>?? ??∝∝>??>??
∘∘ ?.>?.>∝∝8??8?? ∘∘1.41.4∝∝8??8?? ?.2?.2∝∝8??8??
))
;; ((
8??8??++tt 8??8?? 82?82?
))
Alra bnspnjaks t:Alra bnspnjaks t:
8??8??++^ tt ≮≮^ ?? ↘↘ tt ≢≢∘∘8??8??
Dg nst, nstn rndurstngbrá dkegtnrvaf bn ptekafebab ns Y-8?? , ∗[. FDg nst, nstn rndurstngbrá dkegtnrvaf bn ptekafebab ns Y-8?? , ∗[. F qun gsqun gs pnrketpnrketn dgdfuer qunn dgdfuer qun pbnkpbnks beskeguer ng 8??s beskeguer ng 8?? ugebabugebabns nfns nf rndursrndurs aukngtarf egcegetakngtn y gtngbrnks dakhes ng fas rnspunstas: aukngtarfegcegetakngtn y g tngbrnks dakhes ng fas rnspunstas:
Dgdfusegns shrn fas sngsehefebabns dafdufabasDgdfusegns shrn fas sngsehefebabns dafdufabas
Dg fs agáfeses bn sngsehefebab rnafezabs ng nf kåtbmráced gs pnrketnDg fs agáfeses bn sngsehefebab rnafezabs ng nf kåtb mrácedgs pnrketn agafezar ng quå egtnrvafpbnks kvnrgs para dakhear nf dncedengtn ng faagafezar ng quå egtnrvafpbnks kvnrgs para dakhear nf dncedengtn ng fa cucugdegdeôgôg hhjnjntetevv,, ququnn ngng nstnstnn dasdas`` ggss rnrnprnprnsnsngtgtaa fafa ututefefebebabab.. DDgg nstnstaa egcrkadeôg, fa cáhreda punbn tkar bndesegns shrn dakheng prnde egcrkadeôg, fa cáhreda punbn tkar bndesegns shrn dakhe ng prndests, dg nf ceg bn aukngtar fa utefebab pnrdeheba seg tngnrnstratnmeas ng dsts, dg nf ceg bn aukngtar fa utefebab pnrdeheba seg tngnr qun aukngtar nf gúknrbn ugebabns prbudtevas.qun aukngtar nf gúknrbn ugebabns prbudtevas.
Xnspndtaf agáfeses bn sngsehefebab dg nf kåtb sekpfnx, gs pnrketnXnspndt af agáfeses bn sngsehefebab dg nf kåtbsekpfnx, gs pnrketn dgdnr ng qun egtnrvafpbnks kvnrgs para rnafezar dakhes ng fsdgdnr ng qun egtnrvaf pbnks kvnrgs para rnafezar dakhes ng fs rndurss feketabs dg fs qun sn dungta. Nsta egcrkadeôg punbn snr usabarndurss feketabs dg fs qun sn dungta. Nsta egcrkadeôg punbn snr usaba
