Ta2 Tema 10
August 22, 2022 | Author: Anonymous | Category: N/A
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Pcok ;6. Vribjcoks gdtrktkbjcs Okducj Juquc Ekjjcei
Ïd`gac Jks ajkscs V y DV Sd pribjcok DV-aiopjcti Vribjcok `c jk sktgslkagbgjg`k` sktgslkagbgjg`k` rcstrgdeg`i Itris pribjcoks DV-aiopjctis
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
2
Gdtri`uaagñd
Kdkjgzkr ji quc sc puc`c aioputkr aid clgagcdagk Mky quc rcair`kr quc>
Jis pribjcoks rcsijubjcs cd tgcopi pijgdñogai cd ud aioputk`ir y cd udk OP sid jis ogsois @gvgsgñd lud`kocdtkj cdtrc jis pribjcoks rcsijubjcs cd tgcopi pijgdñogai y jis quc rcqugcrcd ud tgcopi cxpidcdagkj i okyir
Pcirïk `c jkk‚gdtrktkbgjg`k`‟> `cstgdk`ks oistrkr quc udAidnudti pribjcok`cditçadgaks puc`c rcsijvcrsc cd tgcopi pijgdñogai Vribjcok gdtrktkbjc ouy gopirtkdtc> Qktgslkagbgjg`k` `c udk cxprcsgñd biijckdk
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
1
Gdtri`uaagñd
Aidacpti `c rc`uaagñd `c ud pribjcok k itri cd tgcopi pijgdñogai Jis rcsujtk`is sibrc pribjcoks gdtrktkbjcs `cpcd`cd `c udk aidncturk di pribk`k> V ≦ DV Qupidcois quc mky pribjcoks rcsijubjcs cd tgcopi pijgdñogai udk OPcdditgcopi `ctcrogdgstk (OPD) quc di sid pir rcsijubjcs pijgdñogai pir udk OP `ctcrogdgstk (OP@)
I ti`is çstis tgcdcd sijuagidcs `ctcrogdgstks cdbgcd t. pijgdñogai i bgcd dgdeudi jk tgcdc
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
0
;6.; Jks ajkscs V y DV
Vribjcoks rcsijubjcs cd tgcopi pijgdñogai Cncopji> Kjeirgtoi `c Hrushkj Pgcopi pijgdñogai di `ctcrogdgstk Cncopji `c DV > cj pribjcok `cj vgknkdtc `c aiocragi Rc`uaagidcs cd tgcopi pijgdñogai Vribjcoks DV-aiopjctis
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
3
Vribjcoks rcsijubjcs cd tgcopi pijgdñogai
@cl.> Sdk OP tgcdc aiopjcng`k` tcopirkj P (d ) sg sc `ctgcdc kj akbi `c P (d )
oivgogcdtis aioi oëxgoid aukd`i rcagbc udk cdtrk`k w `c jidegtu` @cl.> Qc `gac quc ud jcdeuknc J cstë cd jk ajksc V sg cxgstc kjeþd pijgdiogi P (d ) tkj quc J?J(O ) pkrk kjeudk OP `ctcrogdgstk `ctcrogdgstk O auyk aiopjcng`k` tcopirkj cs P (d ) Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
<
Cncopji> Kjeirgtoi `c Hrushkj
Cncopji `c pribjcok quc cstë cd V > Cdaidtrkr cj ërbij `c pcsi oïdgoi quc kbkrak ud erkli (KVOKE)
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
5
Cncopji> Kjeirgtoi `c Hrushkj
Ak`k di`i tgcdc ud pcsi cdtcri Sd ërbij quc kbkrak cj erkli cs ud subaidnudti `c jis kraisoc`gkdtc tkj quc ti`is di`is quc`kd aidcatk`is cstisjiskrais pcri di sc lirok dgdeþd agaji
Cj ërbijsuok `c pcsi cs `c cj quc tgcdc jk ocdir titkjoïdgoi `c pcsis jis krais
Cncopji kdtcrgir> Cj ërbij `c pcsi oïdgoi kpkrcac `gbunk`i aid jïdcks erucsks
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
=
Cncopji> Kjeirgtoi `c Hrushkj
Kjeirgtoi `c Hrushkj pkrk cdaidtrkr ud KVOKE> Vkrk ak`k di`i, kditkr jk aiopidcdtc aidcxk cd jk quc ;. kpkrcac 2.
Qc cjgec cj krai `c ocdir pcsi quc kþd di sc mkyk cxkogdk`i k)
Qg aidcatk `is di`is `c aiopidcdtcs aidcxks `gstgdtks> •
Qc scjcaagidk pkrk gdajugrji cd cj ërbij
Qc udcd jks `is aiopidcdtcs aidcxks `c jis `is di`is Cd itri aksi cj krai sc `csakrtk
•
b)
1.
Qc cjgecd krais mkstk quc ti`is mkykd sg`i cxkogdk`is cxkogdk`is i mkstk quc tcdekois ud ërbij quc kbkrquc cj erkli
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
7
Cncopji> Kjeirgtoi `c Hrushkj
Gopjcocdtkagñd `cj kjeirgtoi cd ud aioputk`ir pkrk mkjjkr cj ërbij quc kbkrak ud erkli `c o di`is y c krais cd ud tgcopi I (o+c jie jiec ) Sdk gopjcocdtkagñd oës sgopjc tcd`rïk udk aiopjcng`k` tcopirkj I (o (o+c ))))
Pgcopi pijgdñogai rcspcati kj tkokûi `c jk cdtrk`k (o+c )
Aucstgidcs kpribjcok rcsijvcr (G)>jcdeukncs, y su þdgak skjg`k Cd OP jis pribjcoks s scaid vcdOP aioi cs kacptkr y rcamkzkr
Cncopji> @k`i cj erkli E y cj jïjïog ogtc tc U , ¹cxgstc cd E ud ërbij quc ji kbkrquc aid pcsi ocdir i geukj k U 9
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;6
Cncopji> Kjeirgtoi `c Hrushkj
Aucstgidcs k rcsijvcr aid OP (GG)>
Cd udk OP jks cdtrk`ks mkd `c ai`glgakrsc, pir ji qucCncopji> sucjcdCjscr oës`c jkreks qucsccjpuc`c tkokûi gdtugtgvi tkokûi ud erkli vcr aioi cj
dþocri `c di`is i krais quc tgcdc Vcri cjji di cs pribjcok>
Okducj Juquc Ekjjcei
Jk ai`glgakagñd sc sucjc mkacr cd tkokûi jiekrïtogai Qc okdtgcdc jk aiopjcng`k` tcopirkj pijgdñogak Jk jidegtu` `c jk ak`cdk `c cdtrk`k cs udk oc`g`k oës cxkatk cx katk `cj dþocri `c bgts dcacskrgis cd ud aioputk`ir
Pcok ;6. Vribjcoks gdtrktkbjcs
;;
Cncopji> Kjeirgtoi `c Hrushkj
Ai`glgakagñd aid OP `cj pribjcok `cj KVOKE> ‚@k`i cj erkli E y cj jjïïogtc U , ¹cxgstc cd E ud ërbij quc ji kbkrquc aid pcsi ocdir i geukj k U 9‟ 9‟ 3 sïobijis> 6, ;, (, ) y jk aiok
Jis di`is sc duocrkd `cs`c ; k o
o y U Ai`glgakois cd bgdkrgi cj vkjir `c Ak`k krai cdtrc jis di`is g y n aid pcsi w sc ai`glgak aioi (g,n,w )
Cncopji> Vkrk cj erkli kdtcrgir, aid U ?06>
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;2
Cncopji> Kjeirgtoi `c Hrushkj
Cj t. `c cncauagñd `cj kjeirgtoi `c Hrushkj gopjcocdtk`i cd ud jcdeuknc `c prierkokagñd cs )) Qustgtuycd`i o y c pir d (jidegtu` `c jk I (o (o+c )) cdtrk`k) cj t. `c cncauagñd cs I (d (d+d ))? ))?I (d 2) Qc puc`c `coistrkr quc tkobgçd sc puc`c gopjcocdtkr cd I (d 2) pksis cd udk OP aid vkrgks agdtks 2 2
0
Sdk udk agdtk cn cncaut cautkrë krë cj kjeirgtoi kjeirgtoi cd cd I ((d ) )?I (d ) pksisOP aid udk Aidajusgñd> Cj pribjcok `cj KVOKE liroujk`i cd tçrogdis `c kacptkagñ kacp tkagñdd `c ud jcdeuknc jcdeuknc pir pir udk OP cstë cd V
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;1
Pgcopi pijgdñogai di `ctcrogdgstk
@cl.> Qc `gac quc ud jcdeuknc J cs cstë të cd jk ajk ajksc DV sg cxgstc udk OP di `ctcrogdgstk O y ud pijgdiogi P (d ) tkj quc J?J(O ) y aukd`i O rcagbc d , di cxgstcd udk cdtrk`k `c jidegtu` scaucdagks `c oës `c P (d ) oivgogcdtis `c O Aioi ti`k OP@ cs ud aksi pkrtgaujkr `c OPD V ⊌DV
Sdk aucstgñd kbgcrtk cs sg V ?DV
Qc puc`c pcdskr quc di sid geukjcs pucs udk OPD cdskyk ud d¾ cxpidcdagkj cxpidcdagkj `c `c sijuagidcs sijuagidcs ‚cd ppkrkjcji‟ krkjcji‟
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;0
Cncopji `c DV > cj pribjcok `cj vgknkdtc `c aiocragi
Vribjcok quc pkrcac cstkr cd DV pcri di cd V > cj pribjcok `cj vgknkdtc `c aiocragi (V\A)
Jk cs jk ogsok quc jkaidtgcdc `cj KVOKE Discdtrk`k prceudtkois sg cj erkli ud ‚agraugti mkogjti mko gjtidgkd dgkdi‟ i‟ `c pcs pcsii aioi aioi ouami ouami geukj k U Sd agraugti mkogjtidgkdi cs ud aidnudti `c krais quc aidcatkd jis di`is pkrk lirokr ud agaji quc pksk pir ak`k di`i cxkatkocdtc udk vcz Cncopji> cj erkli `cj cncopji tgcdc ud siji agaji mkogjtidgkdi> cj agaji (;, 2, 0, 1, ;), `c pcsi cj pribjcok `cj vgknkdtc `c aiocragi
Di mky lirok `c rcsijvcr cj pribjcok sgd pribkr ti`is jis agajis y akjaujkr cj pcsi Aid ud aioputk`ir di `ctcrogdgstk pi`rïkois cjcegr udk pcroutkagñd krbgtrkrgk `c di`is y akjaujkr su pcsi cd di oës `c I (d ) pksis Sdk OPD aid udk agdtk busakrïk y pribkrïk ak`k pcroutkagñd cd I (d 2) pksis Sdk OPD aid udk agdtk rcsijvcrïk cj pribjcok cd I (d 0) pksis Aida Ai dajus jusgñd gñd>> Cj V\A V\A cst cstëë cd DV
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;<
Rc`uaagidcs cd tgcopi pijgdñogai
Cj ibnctgvi cs `coistrkr `coistrkr quc ud pribjcok V 2 di cstë cd V uskd`i cj mcami `c quc ud pribjcok V ;, quc skbcois quc di cstë cd V , sc puc`c rc`uagr k V 2
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;5
Rc`uaagidcs cd tgcopi pijgdñogai
Cj kjeirgtoi kjeirgtoi ‚Aidstruyc‟ ‚Aidstruyc‟ `cj csqucok csqucok kdtcrgi kdtcrgirr `cbc auopjgr quc>
Copjck ud tgcopi pijgdñogai rcspcati k jk jidegtu` `c jk V 2 tcd`r cdtrk`k jidegtu` `cjjidegtu tcd`rë ud jidegtu` tu` pijgdñoga pijg dñogakk Jk rcspcati rcsp cati k jk jiaksi degtu```c`cj aksi `c `ëcudk V k jideg ;
Qg jk rc`uaagñd vcrglgak csk aid`gagñd, sg V 2 cstë cd V , tkobgçd V cstë cd V ; jk gdtrktkbgjg`k` sñji usk rc`uaagidcs cd Jk tcirïk `c tgcopi pijgdñogai > kqucjjks quc tkr`kd ud t. pijgdñogai rcspcati k jk jidegtu` `cj aksi `c V ;
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;=
Vribjcoks DV-aiopjctis
@cl.> Qck J ud jcdeuknc (pribjcok) cd DV . Qc `gac quc J cs DV-aiopjcti sg sc auopjc quc>
Vkrk ti`i jcdeuknc J‗ cd DV , cxgstc udk rc`uaagñd cd t. pijgdñogai `c J‗ k J
Cj V\A cs ud pribjcok DV-aiopjcti
J cstë cd DV
V≦DV
cdtidacs Aioi pkrcac di cstkrïk quc cd V , sg ud pribjcok cs DV-aiopjcti
Vribjcok DV-aiopjcti k uskr> QKP
@coistrkr quc cj jcdeuknc `c aukjqugcr OPD cd t. pijgdñogai puc`c rc`uagrsc cd t. pijgdñogai k QKP
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;7
Vribjcoks DV-aiopjctis
Pcircok> Qg V ; cs DV-aiopjcti, y cxgstc udk rc`uaagñd cd t. pijgdñogai `c V ; k V 2 cdtidacs 2 cs DV-aiopjcti V Qck J ud jcdeuknc `c DV V ; cs DV-aiopjcti J sc rc`uac k V ; cd p (d ) pksis
V ; k V 2 cd q (d ) pksis Rc`uaagñd `c J sc rc`uac k V 2 cd p (d )+ )+q (p (d )) )) pksis
Pcircok> Qg ud pribjcok DV-aiopjcti V cstë cd V cdtidacs V ? DV
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
26
;6.2 Sd pribjcok DV-aiopjcti Cj pribjcok `c jk sktgslkagbgjg`k` sktgslkagbgjg`k` Rcprcscdtk Rcprcscdtkagñd agñd `c jis pribjcoks QKP Cj pribjcok QKP cs DV-aiopjct DV-aiopjctii
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
2;
Cj pribjcok `c jk sktgslkagbgjg`k`
Jks cxprcsgidcs biijckdks sc aidstruycd k pkrtgr `c> ;. 2. 1. 0.
\krgkbjcs `c vkjircs biijckdis, quc tiokd jis vkjircs ; (\CR@K@CRI) y 6 (LKJQI) Jis ipcrk`ircs bgdkrgis ∥ y ∭, quc rcprcscdtkd jks ipcrkagidcs jñegaks W y I Cj ipcrk`ir udkrgi ¬, quc rcprcscdtk jk dcekagñd jñegak Jis pkrçdtcsgs pkrk kerupkr ipcrk`ircs •
Jk prcac`cdagk cdtrc ipcrk`ircs cs> ¬, ∥ y ∭.
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
22
Cj pribjcok `c jk sktgslkagbgjg`k`
Cncopji> Cxprcsgñd biijckdk x ∥¬ ∥¬(y ∭ z ). ).
y ∭ z tiok cj vkjir \CR@K@CRI sg y i z tgcdcd cj vkjir \CR@K@CRI,
y lkjsi cd itri aksi ) cs \CR@K@CRI sg (y ∭ z ) cs LKJQI sg y y z vkjcd LKJQI ¬(y ∭ z x ∥¬ ∥¬ y ∭ ∭ z ) cs \CR@K@CRI sg aukd`i x cs \CR@K@CRI c y y z vkjcd( LKJQI
@cl.> Ksgedkagñd `c vcr`k` k udk cxprcsgñd biijckdk C ksgedk cj vkjir \CR@K@CRI i LKJQI k ak`k vkrgkbjc `c C . \kjir C C aid @cl.> `c cxprcsgñd ksgedkagñd `c vcr`k` (`cditk`i (P jk )) cs )) cj rcsujtk`i `cjkcvkjukr C aukd`i ak`kP vkrgkbjc x sustgtuyc pir cj vkjir P (x ) @cl.> Sdk ksgedkagñd `c vcr`k` P sktg sktgsl slka kac c jk cxprcsgñd biijckdk C, sg C (P ) ? ;
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
21
Cj pribjcok `c jk sktgslkagbgjg`k`
@cl.> Sdk cxprcsgñd biijckdk C cs sktgslkagbjc sg mky kj ocdis udk ksgedkagñd `c vcr`k` P quc sktgslkac C Cncopji> Jk cxprcsgñd x ∥¬ ∥¬(y ∭ z ) cs sktgslkagbjc
Jk ksgedkagñd `c vcr`k` P `clgdg`k pir P (x )?;, )?;, P (y )?6 )?6 y P (z )?6 )?6 cs jk þdgak quc sktgslkac jk cxprcsgñd
y di cs sktgslkagbjc Cncopji> Jk cxprcsgñd C ? x ∥(¬x ∭ y ) ∥¬ ∥¬y Mky cxprcsgidcs aid oës `c udk ksgedkagñd quc jk sktgslkac Cj pribjcok `c jk sktgslkagbgjg`k` (`cdiogdk`i QKP ) sc cdudagk aioi> @k`k udk cxprcsgñd biijckdk, ¹cs sktgslkagbjc9 QKP aioi jcdeuknc cs cj aidnudti `c cxprcsgidcs biijckdk biijckdkss (ai`glgak`ks) sktgslkagbjcs
Jks ak`cdks quc`c dicxprcsgidcs sid añ`geisdi vëjg`is `c cxprcsgidcs b iijckdks quc sid añ`geis sktgslkagbjcs, di cstëdbiijckdks cd QKP i
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
20
Rcprcscdtkagñd `c jis pribjcoks QKP
Qupidcois quc jks vkrgkbjcs sc jjkokd x ;, x 2,…, kudquc cd jis cncopjis uscois diobrcs aioi y , z , … Mky quc g`ckr ud añ`gei aid ud kjlkbcti lgdgti lgni pkrk rcprcscdtkr rcprc scdtkr xprcsgidcs idcs aid ud QKP> d¾ krbgtrkrgi krbgtrkrgi `c vkrgkbjc vkrgkbjcss Kjlkbcti `cj ccxprcsg pribjcok-jcdeuknc
Jis sïobijis ∥, ∭, ¬, (, y ), sc rrcp cprc rcsc scdt dtkd kd ttkj kj aio aioii cstë cstëdd Jk vkrgkbjc x g sc rcprcscdtk aid x sceug`i pir jk rcprcscdtkagñd bgdkrgk `c g
Pi`is jis pribjcoks QKP sid ak`cdks `c sïobijis `cj kjlkbcti kdtcrgir Cncopji> x ∥¬ ∥¬(y ∭ z ), ), mkagcd`i x ? x , y ? x y z ? x , sc 2 1 ;;) ; rcprcscdtk aioi x ;∥¬(x ;6 ;6 ∭ x ;;)
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
23
Cj pribjcok QKP cs DV-aiopjcti
Pcircok `c Aiih> QKP cs DV-aiopjcti Csqucok `c jk `coistrkagñd>
@coistrk @coi strkrr quc quc QKP cstë cd DV
Pi`i jcdeuknc `c DV sc rc`uac k QKP cd t. pijgdñogai
@coist @co istrka rkagñd gñd `c `c quc QKP QKP cstë cstë cd DV
Sdk OPD prucbk sgoujtëdckocdtc ti`ks jks ksgedkagidcs pisgbjcs pkrk P `k`k C Cvkjukr C pkrk jk ksgedkagñd `c vcr`k` P
Bkstk quc sc cdaucdtrc udk rkok `c jk OPD pkrk jjcvkr k kacptkagñd
Aid udk OPD `c vkrgks agdtks cj rcaidiagogcdti `c QKP sc 0
2
mkac cd I (d ) pksis Aid udk agdtk tcdcois I (d ) pksis Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
2<
Cj pribjcok QKP cs DV-aiopjcti
@coistrkagñd `c quc ti`i jcdeuknc `c DV sc rc`uac k QKP cd t. pijgdñogai Qupidcois quc cxgstc udk OPD `c udk agdtk O , y ud pijgdiogi p (d ) tkj quc O di tkr`k oës `c p (d ) pksis aid udk cdtrk`k `c jidegtu` d Qg O kacptk jk cdtrk`k w `c jidegtu` d tcdcois jk
λ6 cs jk aidlgeurkagñd gdgagkj `c O aid w scaucdagk `c oivgogcdtis>
`id`c h ≠ p (d ) λ cs udk aidlgeurkagñd aid cstk`i `c kacptkagñd h
λ6⊢λ;⊢…⊢ λh , λ
oucvc g ktgcdc jk gzqugcr`k þdgakocdtc `c susïobijis sïobiji pisgagñd s di gdgagkj bjkdais y dudak sc Ak`k
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
25
Cj pribjcok QKP cs DV-aiopjcti
Jk cstrktcegk k sceugr cs>
Ak`k λg puc`c csargbgrsc aioi udk scaucdagk `c sïobijis ] g 6 ] g ;… ] g ,p (d ), `id`c udi cs ud cstk`i y jis `coës sid sïobijis `c agdtk Jk suacsgñd `c aidlgeurkagidcs sc `csargbc aid vkrgkbjcs biijckdks> jk gnK pkrk rcprcscdtkr jk pripisgagñd ] ggn n ? K sc arck jk vkrgkbjc y gnK Cxprcskois jk aid`gagñd `c quc jk suacsgñd `c aidlgeurkagidcs rcprcscdtk jk kacptkagñd `c w csargbgcd`i udk cxprcsgñd biijckdk quc cs sktgslkagbjc sg y sñji sg O kacptk w cd k ji suoi p (d ) pksis Jk rc`uaag rc`uaagñd ñd cd t. pijgdño pijgdñogak gak `c J(O ) k QKP cs airrcatk sg>
Copgczk bgcd Cj oivgogcdti sgeugcdtc cs airrcati Kakbk bgcd
Qupidcois quc ti`ks jks aidlgeurkagidcs tgcdcd jk ogsok jidegtu` (p (d )+;) y jis aëjaujis `urkd cxkatkocdtc p (d ) oivgogcdtis
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
2=
Cj pribjcok QKP cs DV-aiopjcti Cj kspcati `c ud aëjauji cd t. pijgdñogai `c O Lgjks> Quacsgñd `c
aidlgeurkagidcs Aijuodks> Acj`ks `c jk agdtk quc sc puc`cd utgjgzkr
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
27
Cj pribjcok QKP cs DV-aiopjcti
Cxprcsgñd biijckdk Q ∥D ∥L aidstrug`k k pkrtgr `c O y w Copgczk bgcd (Q )
Qck w?k ;…k d Q ? y
∥y
6,6,q6
Kakbk bgcd (L )
∥y
6,;,k;
∥…∥y ∥…∥ y
6,2,k2
∥y
6,d,kd
6,d +;,B
∥ ∥y
∥…∥y ∥…∥ y 6,p (d ),B
6,d +2,B
Jk kacptkagñd pir O cqugvkjc k cdaidtrkr ud cstk`i `c kacptkagñd cd λp (d )
Qckd k ;,…,k h jis cstk`is `c kacptkagñd `c O p (d ), ), n n ,k ;∭y p p (d ), ) n ,n ,k ;∭… ∭y p (d ), ) n ,n ,kh , quc rcprcscdtk quc ] p p ( d ), ), n n cs ud L n ? y p ∭y p Qck cstk`i `c kacptkagñd Cdtidacs L ? L 6∭ L ;∭… ∭ L p (d )
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
16
Cj pribjcok QKP cs DV-aiopjcti
Cj oivgogcdti sgeugcdtc cs airrcati
D cs ud ∥ `c cxprcsgidcs D g , g? 6,…, 6,…,p (d )-; )-; 6,…,p (d )-; 6,…, )-; Ak`k D cs ud ∥ `c cxprcsgidcs K ∭B , n? gn gn g Kgn `gac quc> Cj cstk`i `c λ cstëd cd ] g gn O puc`c cjcegr su oivgogcdti, `id`c ] cs cj cstk`i y ] gn g,n +; +;
cs cj sïobiji quc> jcï`i B gn `gac të ouy ouy jcni jcniss `c ] gn , aid ji quc di jc gdljuyc Cj cstk`i `c λ cs g cstë Jk aksgjjk di akobgk su vkjir> ] +;,n ? ] gn g +;
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
1;
Cj pribjcok QKP cs DV-aiopjcti
Sdk ksgedkagñd `c sïobijis cs vëjg`k sg>
] gn cs ud cstk`i cstk`i,, pcr pcrii ] g,n --;; y ] g,n +; +; sid sïobijis `c agdtk cs ud cstk`i Sdi sñji `c jis sïobijis ] , ] y ] g+;,n g+;,n +; g+;,n -; Cxgstc ud oivgogcdti `c O quc cxpjgak jk trkdsliro trkdslirokagñd kagñd `c ] g+;,n --;;] g+;,n ] g+;,n ++;; cd ] g,n --;;] g,n ] g,n +; +;
Kgn cs udk `gsyudagñd `c ti`is jis tçrogdis vëjg`is
Lgdkjocdtc>
D g ? (Kg 6∭B g 6)∥(Kg ;∭B g ;)∥…∥(Kg,p (d )∭B g,p (d )) D ? D 6 ∥ D ; ∥…∥ D p (d )
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
12
Cj pribjcok QKP cs DV-aiopjcti
Lgd `c jk `coistrkagñd `cj tcircok `c Aiih
Mcois aidstrug`i C O ,w ? Q ∥D ∥L O quc Vkrk aukjqugcr ludagidk cd tgcopi pijgdñogai p (d), (d),OPD mcois g`ck`i ud kjeirgtoi quc k pkrtgr `c w (|w |?d), |?d), pri`uac C O ,w
Aid udk OP@ aid vkrgks agdtks cd tgcopi I (p (d 2)) Aid udk agdtk cd tgcopi I (p (d 0))
Aidajusgñd>
Cs udk rc`uaagñd pijgdñogak> C O ,w cs sktgslkagbjc sg y sñji sg kacptk cd k ji suoi ( ) oivg oivgog ogcd cdti tiss O
Okducj Juquc Ekjjcei
w
p d
Pcok ;6. Vribjcoks gdtrktkbjcs
11
Cj pribjcok QKP cs DV-aiopjcti
Gopirtkdagkk `cj tcircok `c Aiih> Gopirtkdag
Qg QKP cstë cstë cd V cdtidacs ti`i jcdeuknc `c DV cstë cd V
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
10
;6.1 Vribjcok `c jk sktgslkagbgjg`k` rcstrgdeg`i Liroks dirokjcs `c cxprcsgidcs biijckdks Aidvcrsgñd `c cxprcsgidcs cd LDA AQKP cs DV-aiopjcti 1QKP cs DV-aiopjcti
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
13
Vribjcok `c jk sktgslkagbgjg`k` rcstrgdeg`i
Cxgstcd oës pribjcoks DV-aiopjctis
Rc`uaagñd `c QKP k ak`k udi `c cjjis
Cxgstc ud pribjcok gdtcroc`gi oës lëagj `c rc`uagr k itris> 1QKP Rc`uaagñd `c jk sktgslkagbgjg`k` `c udk cxprcsgñd biijckdk krbgtrkrgk k udk
cxprcsgñd cd jk lirok dirokj `c 1QKP Pcok ;6. Vribjcoks gdtrktkbjcs
1<
Okducj Juquc Ekjjcei
Liroks dirokjcs `c cxprcsgidcs biijckdks
@cl.> Sd jgtcrkj cs udk vkrgkbjc i udk vkrgkbjc dcek`k
@cl.> Sdk ajëusujk cs cj I jñegai `c udi i oës jgtcrkjcs
Cncopji> x , ¬y
Cncopji> x , x ∭y , x ∭¬y ∭¬y ∭z
@cl.> Qc `gac `gac quc udk cxprc cxprcsgñd sgñd biijck biijckdk dk cstë cd lirok dirokj aidnudtgvk (LDA), sg cs ud W jñegai `c ajëusujks Ditkagñd> ∭ sc rcprcscdtk aid + ∥ sc rcprcscdtk aid yuxtkpisgagñd rcprcscdtk aid aid ‗ (subrkyk`i (subrkyk`i supcrgir supcrgir cd cj cj jgbri) ¬ sc rcprcscdtk
Cncopji `c ditkagñd>
Jk cxprcsgñd cd lirok dirokj aidnudtgvk (x ∭¬y ∭¬y )∥(¬ x ∭z ) sc csargbc aioi (x+y‗ )∥(x‗+z )
Pcok ;6. Vribjcoks gdtrktkbjcs
15
Okducj Juquc Ekjjcei
Liroks dirokjcs `c cxprcsgidcs biijckdks
@cl.>Sdk @cl.>S dk cxpr cxprcsgñ csgñdd cstë cstë cd lirok dirokj aidnudtgvk-h (LDA-h ) sg cs ud pri`uati `c ajëusujks, ak`k udk jk suok `c h jgtcrkjcs `gstgdtis Pcdcois jis sgeugcdtcs pribjcoks>
Jjkokois AQKP kj pribjcok> `k`k udk cxprcsgñd biijckdk cd LDA, ¹cs sktgslkagbjc9
Jjkokois QKP kj pribjcok> pribjcok> `k`k udk udk cxprcsgñd cxprcsgñd bii biijckdk jckdk cd LDAh , ¹csh sktgslkagbjc9 \crcois quc AQKP, 1QKP y h QKP (h4 1) 1) sid DV
aiopjctis ;QKP y 2QKP tgcdcd aiopjcng`k` jgdckj Pcok ;6. Vribjcoks gdtrktkbjcs
1=
Okducj Juquc Ekjjcei
Aidvcrsgñd `c cxprcsgidcs cd LDA
Qc puc`c aidvcrtgr aukjqugcr cxprcsgñd k LDA, pcri jk aidvcrsgñd puc`c jjcvkr ud tgcopi okyir quc cj pijgdñogai Sdk rc`uaagñd `c QKP k AQKP di `coistrkrïk quc AQKP cs DV-aiopjcti Qc tiok ud aksi y sc aidvgcrtc cd ud aksi L C `c QKP `c AQKP tkj quc L sck sktgslkagbjc sg y sñji sg C ji cs Jk rc`uaagñd `c QKP k AQKP sc mkac cd `is pkrtcs> ;.
Vkskr mkagk `cdtri jks dcekagidcs, mkstk quc sñji sc dgceucd vkrgkbjcs 2. Csargbgr jk cxprcsgñd ibtcdg`k aioi pri`uati `c ajëusujks (cd LDA), gdtri`uagcd`i vkrgkbjcs ducvks pkrk rckjgzkr jk trkdslirokagñd cd tgcopi pijgdñogai Pcok ;6. Vribjcoks gdtrktkbjcs
17
Okducj Juquc Ekjjcei
Aidvcrsgñd `c cxprcsgidcs cd LDA
Vrgocr pksi> ¬(C ∥L ) ¬(C )∭¬(L ) ¬(C ∭L ) ¬(C )∥¬(L ) )) C ¬(¬(C ))
Cncopji>
Pcok ;6. Vribjcoks gdtrktkbjcs
06
Okducj Juquc Ekjjcei
Aidvcrsgñd `c cxprcsgidcs cd LDA
Pcircok> Pi`k cxprcsgñd biijckdk C cs cqugvkjcdtc k udk cxprcsgñd L cd jk quc ti`ks jks dcekagidcs kpkrcacd cd jis jgtcrkjcs, cs `cagr, sc kpjgakd `grcatkocdtc k vkrgkbjcs. K`coës, jk jidegtu` `c L cs jgdckj jgdc kj rcspcat rcspcatii kj d¾ `c sïobi sïobijis jis ``cc C , y L sc puc`c aidstrugr k pkrtgr `c C cd t. pijgdñogai @coistrkagñd> gd`uaagñd sibrc sibrc cj d¾ `c ipcrk`i ipcrk`ircs rcs cd C sc vc quc> Vir gd`uaagñd
Cxgstc udk cxprcsgñd cqugvkjcdtc L quc sñji tgcdc ¬ cd jis jgtcrkjcs Qg C tgcdc d ≣ ; ipcrk`ircs, L di tcd tcd`r `rëë oë oëss `c 2d- ;
Jk `coistrkagñd oucstrk jk trkdslirokagñd `c C k L Pcok ;6. Vribjcoks gdtrktkbjcs
0;
Okducj Juquc Ekjjcei
AQKP cs DV-aiopjcti
Pcircok> AQKP cs DV-aiopjcti @coistrkagñd (G)>
Oistrkois pijgdñogai añoi sc rc`uac QKP k AQKP cd t.
Qc aidvgcrtc ud aksi `c QKP k udk cxprcsgñd C auyis ¬ sñji cstçd cd jis jgtcrkjcs Qc aidvgcrtc C k udk cxprcsgñd L cd LDA cd t. pijgdñogai (ocdir i geukj quc a|C |2), tkj quc L cs sktgslkagbjc sg y sñji sg C ji cs
Sdk ksgedkagñd `c vcr`k` P k C mkac C \CR@K@CRI sg y sñji sg cxgstc udk cxtcdsgñd Q `c P quc mkac L \CR@K@CRI
Pcok ;6. Vribjcoks gdtrktkbjcs
02
Okducj Juquc Ekjjcei
AQKP cs DV-aiopjcti
@coistrkagñd (GG)> Vir gd`uaagñd sibrc cj @coistrkagñd d¾ `c sïob sïobij ijis is `c C
Vksi bksc>
C cs ud jgtcrkj C cstë cd LDA
Vksi gd`uatgvi> Qupidcois quc ti`k cxprcsgñd oës airtk quc C
puc`c aidvcrtgrsc cd pri`uati `c ajëusujks cd tgcopi ocdir i geukj quc ad 2 Pcok ;6. Vribjcoks gdtrktkbjcs
01
Okducj Juquc Ekjjcei
AQKP cs DV-aiopjcti
Aksi ;> C ? C ;∥C 2
Vir mgpñtcsgs `c gd`uaagñd cxgstcd cxprcsgidcs L ; y 2 ibtcdg`ks k pkrtgr `c C ; y C 2 tkjcs quc> L ;. Sdk ksgedkagñd `c vcr`k` sktgslkac C ; sg y sñji sg puc`c cxtcd`crsc k udk quc sktgslkac L ; (Ji ogsoi pkrk C 2 y L 2) 2. Qupidcois quc jks vkrgkbjcs `c L ; y L 2 sid `gsnudtks, 1.
cxacpti pir jks vkrgkbjcs quc kpkrcacd cd L ; y L 2 cstëd cd LDA
C
Qg mkacois L ? L ;∥L 2, tcdcois quc udk ksgedkagñd `c vcr`k` P pkrk C puc`c cxtcd`crsc k udk ksgedkagñd quc sktgslkek L sg y sñji sg P sktgslkac C Pcok ;6. Vribjcoks gdtrktkbjcs
00
Okducj Juquc Ekjjcei
AQKP cs DV-aiopjcti
Aksi ;> C ? C ;∭C 2
Vir mgpñtcsgs `c gd`uaagñd cxgstcd cxprcsgidcs L ; y L 2 ibtcdg`ks k pkrtgr `c C ; y C 2 tkjcs quc> ;. 2. 1.
L ; ? e ;∥e 2∥… ∥ e p y L 2 ? m ;∥m 2∥… ∥ m q , Qupidekois quc `id`c jks e y m sid ajëusujks Gdtri`uagoiss udk ducvk vkrgkbjc, y , y mkacois> Gdtri`uagoi
C ;ogsoi L ; (Ji C 2 y L 2) Sdk cxtcd`crsc ksgedkagñd k udk`cquc vcr`k` sktgslkac sktgslkac sg y sñji sg puc`c pkrk Qupidcois quc jks vkrgkbjcs `c L ; y L 2 sid `gsnudtks, cxacpti pir jks vkrgkbjcs quc kpkrcacd cd C L ; y L 2 cstëd cd LDA
‗+m ;)∥(y ‗+ ‗+m 2)∥…∥(y ‗+ ‗+m q ) L ? (y +e ;)∥(y +e 2)∥…∥(y +e p )∥(y ‗+
C puc`c Sdk ksgedkagñd `c vcr`k`L Psgpkrk cxtcd`crsc ksgedkagñd quc sktgslkek y sñji sg P sktgslkac C k udk
03
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
AQKP cs DV-aiopjcti
@coistrkr quc cj tgcopi pkrk aidstrugr L k pkrtgr `c C cs, aioi ouami, auk`rëtgai cd d (jidegtu` `c C )
Jk `gvgsgñd `c C cd C ; y C 2, y jk aidstruaagñd `c L cd C ; y C 2 jjcvk ud tgcopi jgdckj rcspcati kj tkokûi `c C > ad 2 Caukagñd rcaursgvk pkrk P (d ) quc `k cj tgcopi dcacskrgi pkrk aidstrugr L k pkrtgr `c aukjqugcr C `c jidegtu` d >
(;) ? P (2) (2) ≠ c pkrk kjeudk aidstkdtc c P (;) P (d ) ≠ `d + a okx6≠g:d -; )+P (d -;-;-g )) )) pkrk d ≣1 -;(P (g )+ @id`c a cs udk aidstkdtc pir `ctcrogdkr tkj quc sc auopjk quc P (d ) ≠ ad 2
Qc puc`c `coistrkr pir gd`uaagñd sibrc d quc P (d ) ≠ ad 2
03
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
AQKP cs DV-aiopjcti Cncopji `c rc`uaagñd `c QKP k AQKP> Qck jk cxprcsgñd C ?( ?(xy‗ )+ )+x ‗(‗(y +z ) Jk trkdslirokagñd k LDA cs> L? (u +x )( )(u +y‗ )( )(u‗ +x‗ )( )(u ‗+ ‗+v +y )( )(u ‗+ ‗+v ‗+ ‗+z )
0<
Okducj Juquc Ekjjcei
05
Pcok ;6. Vribjcoks gdtrktkbjcs
AQKP cs DV-aiopjcti
Aidstruaagñd `cj ërbij>
Jks minks airrcspid`cd k jis jgtcrkjcs Di`i W> Qc mkac cj pri`uati `c ti`ks jks ajëusujks `c jks `is subcxprcsgidcs Di`i I> Qc gdtri`uac udk ducvk vkrgkbjc, vkrgkbjc, quc sc kûk`c cd jks ajëusujks `cj jk`i gzqugcr`i y sc kûk`c dcek`k cd jks `cj `crcami
P C puc`c k udk ksgedkagñd Cjquc tcircok sktgslkac dis `gac quc cxtcd`crsc aukjqugcr ksgedkagñd `c vcr`k` `c vcr`k` Q quc sktgslkac L Cncopji> P (x )?6, )?6, P (y )?;, )?;, y P (x )?; )?; sktgslkac C
cxtcd`cr ksï> Q (x )?6, Q (y )?;, Q (z )?;, Q (u )?; y Q (v )?6, L yQcQ puc`c sktgslkac
Okducj Juquc Ekjjcei
0=
Pcok ;6. Vribjcoks gdtrktkbjcs
1QKP cs DV-aiopjcti
Cj pribjcok 1QKP cs>
@k`k udk cxprcsgñd biijckdk C geukj k ud pri`uati `c ajëusujks, ak`k udk `c jks aukjcs cs jk suok `c trcs jgtcrkjcs `gstgdtis, ¹cs C sktgslkagbjc9
Pcircok> 1QKP cs DV-aiopjcti
1QKP 1Q KP cstë cstë cd DV Vribkr cs DV-aiopjcti AQKP kpjkzko 1QKP @k`kquc udk1QKP cxprcsgñd cd LDA, C ? c rc`uagcd`i rccopjk zkois is ;∥c 2∥… ∥ c h , rcco
ak`k ajëusujk c g pkrk arckr udk cxprcsgñd ducvk L Cj tgcopi quc jjcvk aidstrugr L cs jgdckj rcspcati k jk jidegtu` `c C , y udk ksgedkagñd `c vcr`k` sktgslkac C sg y sñji sg sc puc`c cxtcd`cr k udk ksgedkagñd `c vcr`k` quc sktgslkek L
Okducj Juquc Ekjjcei
07
Pcok ;6. Vribjcoks gdtrktkbjcs
1QKP cs DV-aiopjcti
Rccopjkzi `c ak`k c g
Qg c g cs ud siji jgtcrkj, x , gdtri`uagois `is vkrgkbjcs ducvks, u y v . Qc rccopjkzk x pir jks 0 ajëusujks (x +u +v )(x +u +v ‗)(x +u ‗+v )(x +u ‗+v ‗) 2. Qg c g cs jk suok `c `is jgtcrkjcs, (x +y ), ), sc gdtri`uac udk vkrgkbjc ducvk z , y sc sustgtuyc c g pir (x +y +z )( )(x +y +z ‗)‗) 1. Qg c g cs jk suok `c trcs jgtcrkjcs di sc mkac dk`k 0. Qg c g ? (x ;+ x 2+…+x o ) pkrk kjeþd o ≣0. Gdtri`uagois jks vkrgkbjcs ducvks y ;+ y 2+…+y o -1-1, y sustgtugois c g pir> (x ;+x 2+y ;)(x 1+y ;‗+y 2)(x ;+ y 2‗+y 1)…(x o -2-2+y o -0-0‗+y o -1-1) (x o -;-;+x o +y o -1-1‗) ;.
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
;6.0 Itris pribjcoks DVaiopjctis
@csargpagñd `c jis pribjcoks DV-aiopjctis Cj pribjcok `c jis aidnudtis gd`cpcd`gcdtcs Cj pribjcok `cj rcaubrgogcdti `c di`is Vribjcok `cj agraugti mkogjtidgkdi irgcdtk`i Jis agraug agraugtis tis mkogjti mkogjtidgkd dgkdis is di irgcdtk` irgcdtk`is is y cj V\A Rcsuocd `c jis pribjcoks DV-aiopjctis
36
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
@csargpagñd `c jis pribjcoks DVaiopjctis
Vkrk gdtri`uagr gdtri`uagr pribjcoks pribjcoks ducvis DV-aiopjctis DV-aiopjctis sc uskrë jk `clgdgagñd> Diobrc `cj pribjcok, y usukjocdtc udk kbrcvgkturk Cdtrk`k `cj pribjcok Qkjg`k `csck`k> auëd`i jk skjg`k cs ‚QG‟ Cj pribjcok quc sc rc`uac k çstc pkrk `coistrkr quc cs DVaiopjcti
Cncopji> @csargpagñd `c 1QKP y `coistrkagñd `c quc cs DVaiopjcti Vribjcok> Qktgslkagbgjg`k` `c jks cxprcsgidcs cd LDA-1 (1QKP)
Cdtrk`k>
Sdk cxprcsgñd biijckdk cd LDA-1 ‚QG‟ sg y sñji sñji sg jk cxpr cxprcsg csgñd ñd cs cs sk sktgs tgslkag lkagbjc bjc Qkjg`k> ‚QG‟
Rc`uaagñd `cs`c
> AQKP
3;
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `c jis aidnudtis gd`cpcd`gcdtcs
@cl.> @k`i E ud erkli di `grgeg`i, ud subaidnudti G `c jis di`is `c E sc `gac quc cs ud aidnudti gd`cpcd`gcdtc sg di mky `is di`is `c G aidcatk`is pir ud krai `c E cs @cl.> Sd aidnudti gd`cpcd`gcdtc okxgokj sg di mky dgdeþd itri
aidnudti gd`cpcd`gcdtc aid oës di`is
Cncopji {;, 0} cs ud aidnudti gd`cpcd`gcdtc
okxgokj {;, 2, 0} di cs gd`cpcd`gcdtc {;} cs gd`cpcd`gcdtc, pcri di okxgokj
32
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `c jis aidnudtis gd`cpcd`gcdtcs
@clgdgagñd `cj pribjcok `cj aidnudti gd`cpcd`gcdtc okxgokj okxgokj>> > Aidnudti Aidnudti gd`cpcd`gcd gd`cpcd`gcdtc tc (Gd`cpcd`cd (Gd`cpcd`cdtt Qct), VAG Cdtrk`k> Sd erkli E y udk aitk gdlcrgir h Vribjcok
Qkjg`k
di`is > ‚QG‟ ‚QG‟ sg y sñji sñji sg E aidtgcdc ud aidnudti gd`cpcd`gcdtc `c h Rc`uaagñd `cs`c> 1QKP
Pcircok> Cj pribjcok `cj aidnudti gd`cpcd`gcdtc cs DV-aiopjcti @coistrkagñdd (G)> @coistrkagñ
Cj VAG VAG cstë cstë cd DV
Qc cjgecd kj kzkr h di`is y sc aioprucbk sg sid gd`cpcd`gcdt gd`cpcd`gcdtcs cs
Qc rc`uac 1QKP kj VAG
31
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `c jis aidnudtis gd`cpcd`gcdtcs
@coistrkagñd (GG)>
Qck C ? (c ;)(c 2)…(c o ) udk cxprcsgñd LDA-1 K pkrtgr `ccd C aidstrugois ud erkli E aid 1o di`is, aid diobrcs Xg , n _ `id`c ;≠g ≠o y n? ;,2,ñ 1
Cj di`i Xg , n _ rcprcscdtk kj jgtcrkj n- çsgoi çsgoi cd jk jk ajëus ajëusujk ujk c g Cncopji>
30
Okducj Juquc Ekjjcei
33
Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `c jis aidnudtis gd`cpcd`gcdtcs
@coistrkagñd (GGG)>
Jks aijuodks rcprcscdtkd jks ajëusujks Qc utgjgzkd jis krais pkrk lirzkr quc ud aidnudti gd`cpcd`gcdtc gd`cpcd`gcdtc okxgokj aid o di`is rcprcscdtc udk okdcrk `c sktgslkacr jk cxprcsgñd C , aid 2 rcejks>
Dis ksceurkois `c quc sñji sc puc`c di`i airrcspid`gcdtc k udk ajëusujk `k`k Mky krai krais s cdtrc jis 1 di`is dcsaiecr i`is `cud ak ak`k `k aijuod aijuodk k Gopc`gois quc sc cjgnkd `is di`is pkrk cj aidnudti gd`cpcd`gcdtc, sg rcprcscdtkd jgtcrkjcs aiopjcocdtkrgis Qc trkzkd krais cdtrc cjjis
Jk aitk h pkrk cj erkli aidstrug`i cs o Cj erkli y jk aitk puc`cd aidstrugrsc k pkrtgr `c C cd ud tgcopi pripiragidkj kj auk`rk`i `c jk jidegtu` `c C Jk aidvcrsgñd `c C cd E cs udk rc`uaagñd cd tgcopi pijgdñogai Qc puc`c `coistrkr quc>
C cs sktgslkagbjc sg y sñji sg E aidtgcdc ud aidnudti gd`cpcd`gcdtc `c tkokûi o
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `c jis aidnudtis gd`cpcd`gcdtcs
Cncopji> Qck C >
Jis di`is cd dcergtk lirokd ud aidnudti gd`cpcd`gcdtc gd`cpcd`gcdtc G Aid jis jgtcrkjcs `c jis di`is `c G aidstrugois udk ksgedkagñd `c vcr`k` P tkj quc P (x ;)?;, P (x 2)?;, P (x 1)?;, P (x 0)?6 K x 3 sc jc ksgedk aukjqugcr vkjir P sktgslkac k C
3<
Okducj Juquc Ekjjcei
35
Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `cj rcaubrgogcdti `c di`is
Sd rcaubrgogcdti `c di`is `c ud erkli cs ud aidnudti `c di`is tkj quc ak`k krai tgcdc kj ocdis ud cxtrcoi cd ud di`i `cj aidnudti Sd rcaubrgogcdti `c di`is cs ogdgokj sg tgcdc tgcdc ud d¾ d¾ `c ddi` i`is is ocdir i geukj quc aukjqugcr itri rcaubrgogcdti `c di`is `cj ogsoi erkli @clgdgagñd `cj pribjcok `cj rcaubrgogcdti `c di`is > Vribjcok Vribjcok `cj rcaubrgogcd rcaubrgogcdti ti `c di`is di`is (VRD) (VRD) Cdtrk`k> Sd erkli E y udk aitk supcrgir h , aioprcd`g`k cdtrc 6 y cj d¾ `c di`is ;ji sg E aidtgcdc ud rcaubrgogcdti aid h di`is i ‚Qocdis G‟ sg y sñji sñ Qkjg`k> ‚QG‟ ocdis Rc`uaagñd `cs`c> Aidnudti gd`cpcd`gcdtc Vribjcok
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Pcok ;6. Vribjcoks gdtrktkbjcs
Cj pribjcok `cj rcaubrgogcdti `c di`is
Pcircok> Cj pribjcok `cj rcaubrgogcdti `c di`is cs DV-aiopjcti @coistrkagñd>
Cj VRD VRD cstë cstë cd DV
Qc tiok ud aidnudti aukjqugcrk `c di`is y sc aioprucbk quc ak`k krai `c E tgcdc kj ocdis ud cxtrcoi cd cj aidnudti
Qc rc`uac cj VAG kj VRD uskd`i jk klgrokagñd>
E h sg y sñji sg E aidtgcdc aidnudti gd`cpcd`gcdtc tkokûi aidtgcdc udud rcaubrgogcdti `c di`is `c`c tkokûi d -h
\cr cd cj kdtcrgir cncopji quc cj aidnudti `c di`is di okrak`is lirokd ud rcaubrgogcdti `c di`is ogdgokj
Jk rc`uaagñd sc tgcdc cd tgcopi jgdckj Cs udk rc`uaagñd pijgdñogak
3=
Okducj Juquc Ekjjcei
37
Pcok ;6. Vribjcoks gdtrktkbjcs
Vribjcok `cj agraugti mkogjtidgkdi irgcdtk`i
@clgdgagñd `cj pribjcok `cj agraugti mkogjtidgkdi> > Vribjcok Vribjcok `cj agraugti agraugti mkogjtidgkdi mkogjtidgkdi Cdtrk`k> Sd erkli di irgcdtk`i, E Vribjcok
Qkjg`k
‚Q sg y sñji sñpkrtgaujkr ji sg E aidtgcdc ud agraugti Cj VAM cs> ‚QG‟ udG‟aksi `cj V\A, `id`cmkogjtidgkdi jis pcsis `c jis krais sid ; Jk rc`uaagñd `cj VAM kj V\A cs gdoc`gktk Vkrk `coistrkr `coistrkr quc cj VAM cs DV-aiopjcti DV-aiopjcti `cldgois `cldgois udk vcrsgñd vcrsgñd `cj VAM oës rcstrgdeg`k> > Vribjcok Vribjcok `cj agraugti agraugti mkogjtidgkdi mkogjtidgkdi irgcdtk irgcdtk`i `i (VAMI) Cdtrk`k> Sd erkli irgcdtk`i, E ‚QG‟ sg y sñji sñji sg cxgs cxgstc tc ud agaji agaji irgcd irgcdtk`i tk`i cd E quc pksk Qkjg`k> ‚QG‟ cxkatkocdtc udk vcz pir ak`k di`i Vribjcok
Rc`uaagñd
`cs`c>
1QKP
Okducj Juquc Ekjjcei
Pcok ;6. Vribjcoks gdtrktkbjcs
Vribjcok `cj agraugti mkogjtidgkdi irgcdtk`i
Pcircok> Cj pribjcok `cj agraugti mkogjtidgkdi irgcdtk`i cs DV-aiopjcti @coistrkagñd (G)>
VAMI VA MI cstë cstë cd DV
Qc tiok ud agaji y sc aioprucbk sg ti`is jis krais quc dcacsgtk pcrtcdcacd kj erkli
Rc`uaagñd `c 1QKP k VAMI
c h jgtcrkjcs c 2∥…`c∥c C ? c ;∥suok ∥1 , `id`c Qck cs udk ajëusujk, ak`kjkc g cxprcsgñd Qckd x ;, x 2,…, x d , jks vkrgkbjcs `c C Vkrk ak`k x g sc aidstruyc ud suberkli M g
Erkli aid k g (di`i akbczk), b gn , a gn y ` g (di`i pgc) o gg > oëxgoi cdtrc cdtrc cj d¾ `c kp kpkrgagi krgagidcs dcs `c x g g y x g g‗ cd C
Cj erkli cdtcri tgcdc ud mcxëeidi M g pkrk ak`k vkrgkbjc x g Krai `cj di`i pgc `c udk pgczk kj di`i akbczk `c jk pgczk sgeugcdtc Qñji mky 2 pisgbgjg`k`cs `c agraugti mkogjtidgkdi cd ak`k M g >
k g ,b g 6,a g 6,b g ;,a g ;,…,` ; Qc trktk aioi sg x g vkjc \CR@K@CRI k g ,a g 6,b g 6,a g ;,b g ;,…,` ; Qc trktk aioi sg x g vkjc LKJQI
Sd agaji aiopjcti pkrk cj erkli `c jk lgeurk l geurk sñji tcd`rïk 2 pisgbgjg`k`cs cd ak`k M g 2d agraugtis agraugt is mkogjtidgkd mkogjtidgkdis is irgcdtk`is irgcdtk`is (ksgedkagidcs `c vcr`k` k d vkrgkbjcs)
Vkrk ak`k ajëusujk c n sc arck ud suberkli G n Vripgc`k`cs `c ud agaji cd G n >
Qg cdtrk pir r g , `cbc skjgr pir u g
s gg `cbc skjgr pir v gg Qg Qg cdtrk cdtrk pir pir t g ,, `cbc skjgr pir w g
Aidcatkr jis G n k jis M g
Qg cj prgocr jgtcrkj `c jk ajëusujk cs c n cs x g sgd dcekr
Qc cjgec ud a gp di usk`i, y trkzkois krais `c a gp k r n , y `c u n k a g ,p +; +; dcek`kk sc mkac ji ogsoi pcri cjg cjgegcd`i egcd`i uudd b ggp p Qg x g g cstë dcek`
di usk`i Vkrk cj sceud`i y cj tcracr jgtcrkj `c c g sc mkac ji ogsoi pcri aid s n y v n , y t n y w n rcspcatgvkocdtc
Jucei ak`k G n tgcdc trcs aidcxgidcs k jks pgczks M g quc rcprcscdtkd sus vkrgkbjcs
Cj erkli aidstrug`i aidtgcdc ud agraugti mkogjtidgkdi irgcdtk`i sg y sñji sg jk cxprcsgñd C cs sktgslkagbjc
Cncopji>
C ?( ?(x ;+x 2+x 1)(x ;‗+ x 2‗+ x 1)
Jis krais erucsis gd`gakd ud agaji mkogjtidgkdi aiopjcti airrcspid`gcdtc k jk ksgedkagñd x ;?;, x ;?6, x ;?6 quc sktgslkac C
Vribjcok `cj agraugti mmkogjtidg kogjtidgkdi kdi di irgc irgcdtk`i dtk`i Sd erkli di irgcdtk`i, E Qkjg`k> ‚QG ‚QG‟‟ sg y sñji sñji sg E aidtgcdc ud agraugti mkogjtidgkdi
Vribjcok>
Cdtrk`k>
Rc`uaagñd `cs`c
> VAMI Pcircok> VAM cs DV-aiopjcti
Rc`uaagñd `cj VAMI kj VAM
Qck cj erkli di irgcdtk`i E 6 Aidstrugois cj erkli di irgcdtk`i E d Vkrk ak`k di`i v `c E 6 cxgstcd 1 di`is v 6, v ; y v 2, cd E d E d di`i Vkrk`c ak`k sid>v `c E 6 cxgstcd krais (v (6),v (;)) y (v (;),v (2)) cd E d Jis krais
Qg cxgstc ud krai `c v k w cd E 6 mky ud krai (v (2),v (6)) cd E d Jk aidstruaagñd `c E d k pkrtgr `c E 6 sc mkac cd tgcopi t gcopi pijgdñogai E d aidtgcdc ud agraugti mkogjtidgkdi sg y sñji sg E 6 aidtgcdc ud agraugti
mkogjtidgkdi irgcdtk`i
Vribjcok Vribjcok `cj vgknkdtc vgknkdtc `c `c aiocragi aiocragi (V\A) (V\A) Cdtrk`k> Sd erkli di irgcdtk`i E aid pcsis cdtcris cd jis krais, y jïogtc h Qkjg`k> ‚QG‟ ‚QG‟ sg y sñji sñji sg E aidtgcdc ud agraugti mkogjtidgkdi tkj quc jk suok `c jis pcsis cd jis krais `cj agaji cs ocdir i geukj quc h Rc`uaagñd `cs`c> VAM Vribjcok
Pcircok> Cj pribjcok `cj vgknkdtc `c aiocragi cs DV-aiopjcti @coistrkagñd>
Rc`uaagñd `cj VAM kj V\A>
@k`i E , sc aidstruyc ud erkli E ‗ aid ji jiss ogsoi ogsoiss di` di`is is y kkrais rais ``cc E , pcri aid pcsi ; cd ak`k krai, y ud jïogtc h geuk geukjj kj d¾ `c ddi`is i`is `c E E ‗ tgcd tgcdcc ud agraug agraugti ti `c pcsi d sg y sñji sg E aidtgcdc ud agraugti mkogjtidgkdi
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Pcok ;6. Vribjcoks gdtrktkbjcs
Rcsuocd `c jis pribjcoks DVaiopjctis
Pi`ks jks rc`uaagidcs vgstks cd cj akpïtuji
Cj `c aukjqugcr di jcdeuknc `ctcrogdgstk sc rc`uacOP k QKP
Pi`is jis pribjcoks DVaiopjctis sc puc`cd rc`uagr udis k itris cd tgcopi pijgdñogai
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