Pengantar tenta n g sist em, sin y al d an sist em linier...
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1 l a y n i s , m e t s i s g n a t n e t r a t n a g n e P r e i n i l m e t s i s n a d g n a y r u s n u / n e m e l e n a l u p m u k e s g n a t n e t a r a c i b r e b i t r a r e b m e t s i s g n a t n e t a r a c i b r e B n e m e l e a r a t n a n a g n u b u h r e b a r a c g n a t n e t a r a c i b r e b n a d , m e t s i s n u s u y n e m - n e m e l e n a y n e m m e t s i s n a i t r e g n e p a y n m u m U . u t i n u s u y n e p n e m e l e i r a d n u s u s r e t g n a y u t a u s e s t u k g - h a u b e s , s i p o k s o r k i m a r a c e s i p a t ( m e t s i s t u b e s i d t a p a d k a d i t n e n o p m o k h a u b e s i d a J . n e m e l e n e m e l e i r a d n u s u s r e t a g u j n e m e l e - m e t s i s t u b e s i d t a p a d a g g n i h e s l i c e k h i b e l g n a y n e m e l e n e m e l E . ) a g u j - p m e m m e t s i s n u s u y n e p n e m e l e u a t a , m e t s i s m a l a d s a h k g n a y u k a l i r e p i a y n u h a u b e s a k i J . n i a l n e m e l e h e l o n a k i t n a g i d t a p a d k a d i t g n a y k i f i s e p s g n a y s a g u t i a y n u p m e m i t n a g r e b m e t s i s u a t a a d a k a d i t i d a j n e m m e t s i s a k a m , a d a k a d i t m e t s i s n u s u y n e p n e m e l e . n i a l m e t s i s i d a j n e m a t f a d n e m i n i l e b a T p a i t e s i s g n u f n a d n u s u y n e p n e m e l e t u k i r e b m e t s i s a p a r e b e b h o t n o c r . n e m e l e m e t s i S n e m e l E n e m e l e i s g n u F o i d u a m e t s i S k c a b y a l p k i n a k e M s i r t k e l e l a y n i s e k t e s a k i r a d s i t e n g a m l a y n i s h a b u g n e M t a u g n e P s i r t k e l e l a y n i s t a u k r e p m e M r e k a e p S k e l e l a y n i s h a b u g n e M o i d u a / a r a u s l a y n i s i d a j n e m s i r t e m u l o v l o b m o T t a u g n e p n a t a u g n e p h a b u g n e M a y r u s a t a T i r a h a t a M a y r u s a t a t t a s u P t e n a l P a y r u s a t a t t a s u p i r a t i g n e M t i l e t a S t e n a l p i r a t i g n e M d k a d i t a k a m , a d a k a d i t a y n u t a s h a l a s a k i j , n e m e l e t a p m e i a y n u p m e m o i d u a m e t s i S i g a l t a p a a p n a T . k a s u r n a k a t a k i d m e t s i s , k c a b y a l p k i n a k e m n a d t a u g n e p a p n a T . o i d u a m e t s i s t u b e s i d a u m e s , e m u l o v l o b m o t a p n a T . n a k t a a f n a m i d t a p a d k a d i t n a d p a k g n e l k a d i t m e t s i s , r e k a e p s . a w a t r e t n a k a g n a r o g n a r o e s e s a k i t e k i t a k a p e s i d k u t n u g n i t n e p g n a y l a H h a l a d a k i n k e t m e t s i s g n a t n e t a r a c i b r e b , m e t s i s n a r a u l e k n a r a s e b i t a k a p e y n e m i t r a r e b m e t s i s h a u b e s n a k l e d o m e M . m e t s i s l e d o m n a d n a r a u l e k a r a t n a n a g n u b u h n a k u t n e n e m a y n r i h k a n a d m e t s i s n a k u s a m n a k u t n e n e m u l a l . u t i n a k u s a m s i t a m e t a m n a a m a s r e P t u b e s i d t a p a d k i n o r t k e l e n e n o p m o k l e d o m u t i a y , m e t s i s l e d o m a g g n i h e s , r o t s i s e r s u r a h a l a d a i t a k a p e s i d g n a y n a r a u l e k n a r a s e b , i n i l e d o m m a l a D . r o t s i s e r h a l a d a n a k u s a m n a d n a r a u l e k n a r a t n a n a g n u b u h n a d n a g n a g e t h a l a d a a y n n a k u s a m . i r i d n e s u t i s i t a m e t a m n a a m a s r e p l b m a r g a i D : m e t s i s i r a d m u m u k u t n e b n a k a t a y n e m i n i t u k i r e b k o , k o l b m a r g a i d k u t n e b m a l a D . l e d o m t u b e s i d t a p a d h a d u s s a t a i d k o l b m a r g a i d k u t n e B n a a m a s r e p a l u p t a p a d n a d , i u h a t e k i d h a d u s n a r a u l e k n a d n a k u s a m n a r a s e b a y n a s a i b
Transcript of Pengantar tenta n g sist em, sin y al d an sist em linier...
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laynis ,metsis gnatnet ratnagneP reinil metsis nad gnay rusnu/nemele nalupmukes gnatnet aracibreb itrareb metsis gnatnet aracibreB
nemele aratna nagnubuhreb arac gnatnet aracibreb nad ,metsis nusuynem - nemelenaynem metsis naitregnep aynmumU .uti nusuynep nemele irad nususret gnay utauses tukg -
haubes ,sipoksorkim araces ipat( metsis tubesid tapad kadit nenopmok haubes idaJ .nemelenemele irad nususret aguj nemele - metsis tubesid tapad aggnihes licek hibel gnay nemele
nemelE .)aguj - pmem metsis nusuynep nemele uata ,metsis malad sahk gnay ukalirep iaynu haubes akiJ .nial nemele helo nakitnagid tapad kadit gnay kifiseps gnay sagut iaynupmem itnagreb metsis uata ada kadit idajnem metsis akam ,ada kadit metsis nusuynep nemele
.nial metsis idajnem
atfadnem ini lebaT paites isgnuf nad nusuynep nemele tukireb metsis aparebeb hotnoc r.nemele
metsiS nemelE nemele isgnuF
oidua metsiS
kcabyalp kinakeM sirtkele laynis ek tesak irad sitengam laynis habugneM taugneP sirtkele laynis taukrepmeM rekaepS kele laynis habugneM oidua/araus laynis idajnem sirt
emulov lobmoT taugnep nataugnep habugneM
ayrus ataT irahataM ayrus atat tasuP
tenalP ayrus atat tasup iratigneM tiletaS tenalp iratigneM
d kadit akam ,ada kadit aynutas halas akij ,nemele tapme iaynupmem oidua metsiS igal tapa apnaT .kasur nakatakid metsis ,kcabyalp kinakem nad taugnep apnaT .oidua metsis tubesid aumes ,emulov lobmot apnaT .naktaafnamid tapad kadit nad pakgnel kadit metsis ,rekaeps
.awatret naka gnaro
gnaroeses akitek itakapesid kutnu gnitnep gnay laH halada kinket metsis gnatnet aracibreb ,metsis naraulek naraseb itakapeynem itrareb metsis haubes nakledomeM .metsis ledom nad naraulek aratna nagnubuh nakutnenem aynrihka nad metsis nakusam nakutnenem ulal
.uti nakusam
sitametam naamasreP tubesid tapad kinortkele nenopmok ledom utiay ,metsis ledom aggnihes ,rotsiser sura halada itakapesid gnay naraulek naraseb ,ini ledom malaD .rotsiser halada nakusam nad naraulek naratna nagnubuh nad nagnaget halada aynnakusam
.iridnes uti sitametam naamasrep
lb margaiD :metsis irad mumu kutneb nakataynem ini tukireb ko
,kolb margaid kutneb malaD .ledom tubesid tapad hadus sata id kolb margaid kutneB naamasrep alup tapad nad ,iuhatekid hadus naraulek nad nakusam naraseb aynasaib
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mutnacid nad iuhatekid hadus aynsitametam haubes kolb margaiD .kolb lebal adap nak:tukireb itrepes halada sura naraulek nagned rotsiser
gnudnagnem halsurah nakusam nautnenep akam ,itakapesid halet metsis naraulek akiJakij awhab metsis kisif atkaf irad helorepid uti nasalA .)isatnemugra( nasala nakusam
habuid - ,rotsiser metsis naraulek iagabes itakapesid sura akiJ .habureb naraulek akam habuhabuid rotsiser nagnaget akij halada aynnasalA .nakusam halada nagnaget akam - habu
.habureb rotsiser sura akam
k naktapadnem kutnu nakduskamid kadit naledomeP gnay metsis gnatnet kaltum naranebe nad ledom irad taafnam helorepmem kutnu nakduskamid naledomeP .nakledomid
satab malad lanoisidnok halada aynnaranebek - .naktaraysrepid gnay satab
sitametam naamasrep ukalreb rotsiser padahreT tsiser haubes akij aynitrA . ro1 .A 1 rasebes sura apureb tuptuo helorepid naka akam V 1 nagnaget apureb tupni irebid
satab malad ukalreb sata id naamasreP - 1 rotsiseR .utnetret satab irebid tapad ttaw 5d tapad kadit uti rotsiser ipat ,A 1 sura naklisahgnem nad kutnu V 1 nagnaget nagnaget irebi
rasebes surA .naknijiid gnay satab raul id adareb rotsiser nakbabeynem naka anerak V 01 nad rotsiser ek kusam ttaw 001 rasebes ayad nakbabeynem naka naklisahid gnay A 01
utup idajnem rotsiser uata trohs idajnem rotsiseR .uti rotsiser kasurem taases aggnihes s.rilagnem gnay ilakes amas sura ada kadit uata kasur idajnem ayad utac naidumek
hotnoC - .lebat adap ijasret aynnasala atreseb metsis nakusam nautnenep gnatnet hotnoc
metsiS narauleK nakusaM nasalA
nemaliFakirtes sanap sura
a irebid akiJ .sanap nakraulegnem nemalif sur gnay sanap raseb nikames ,sura raseb nikameS
.nemalif nakraulekid
nagnudneB ek ria narilanahawasrep ria utnip isisop ria kaynab nikames ,ria utnip isisop iggnit nikameS
rilagnem
rotom adepeS natapecek lednah isisopsag
eS tapec nikames ,sag lednah tudus raseb nikamiralreb rotom adepes
.1 saguT ,aynnakusam nakutneT .aynnaraulek hilip/nakutneT .nial metsis aud haliraCnakatres elbuod satrek adap nakajreK .aynnasala - uata urib atnit nakanuG .siragreb oilof
greb satrek nakanug )2002 teraM 3 detadpu( .urib sira
layniS
irahes naanuggnep ipaT .taraysi halada laynis nial ataK - "taraysi" atak nad "laynis" atak irah tubesid ribib ek kujnulet nakkatelem nagned maid huruynem gnaroeseS .adebreb tikides
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em takgnareb atereK .taraysi irebmem napuit apureb AKPP sagutep irad laynis uggnun.tiulep
halada layniS .amas halada sata id atak audek ,kinket metsis gnatnet naaracibmep malaD ,duskamid gnay utkaw gnales malaD .utnetret utkaw gnales malad itamaid gnay naraseb
araces habureb naraseb aynasaib uata araus laynis lanekid nairahesek malaD .simanid gnay naraseb numaN .utkaw padahret habureb asaitnanes aynnaraseb gnay rabmag laynis nakapurem naklasa aguj laynis tubesid sinket araces utkaw padahret habureb kadit
utnetret utkaw gnales malad natamagnep upmal haubes irad raulek gnay ayahac aggniheS . iaynupmem rotom adepes haubeS .ayahac laynis tubesid )patet aynsatisnetni nupiksem(
nial nad ,gnillensrep halmuj ,natapecek ,naruku ,anraw ,tareb :kisif naraseb - aynaumeS .nialo nakraulekid gnay laynis halada .utnetret utkaw gnales malad itamaid akij rotom adepes hel
naraseb aratna id numaN - aynah nikgnum ,rotom adepes helo ikilimid gnay naraseb natapecek uti anerak helO .sitats tafisreb nial naraseb ,simanid ayntafis gnay natapecek
gnilap gnay naraseb nakapurem .rotom adepes kutnu nakitahrepid/itamaid kaynab
metsiS .laynis gnatnet naaracibmep naktabilem ilakgnires metsis gnatnet naaracibmeP laynis akimanid ada anerak itamaid metsis nad ,aynnakraulekid gnay laynis irad ilanekid
etsis naraulek nad nakusaM .aynadap halada oidua metsis irad nakusaM .laynis dujuwreb m metsis malaD .araus laynis halada aynnaraulek nad tesak atip irad sitengam laynis najuh ,laynis halada uluh irad ria narila ,laynis halada nahawasrep ek ria narila ,nagnudneb
sop nahabugnep ,laynis halada ttaw nakhab ,laynis halada isagiri sagutep helo ria utnip isiATLP ada akij( naklisahid gnay kirtsil - .laynis halada )ayn
tukireb rabmaG .aynnaraseb ialin nad naadarebek turunem nakadebid laynis sinket araceSnis :utiay laynis macam tapme naktahilrepmem ini uynitnok laynis ,)golana( uynitnok lay
.)latigid( isasitnaukret terksid laynis nad ,terksid laynis ,isasitnaukret
ria narila tibeD .mala id ada gnay laynis nakaynabek kutneb nakapurem uynitnok layniSaggnalep hamur haubes ek kusam gnay kirtsil sura ,iagnus nagnaur utaus uhus nad NLP n
apareb asib aynialin nad utkaw aumes id ialin iaynupmem uynitnok layniS .aynhotnoc halada aynah aynialin ipat utkaw aumes id ialin iaynupmem isasitnaukret uynitnok layniS .ajas
haipur rakut ialin halada aynhotnoC .ajas utnetret gnarab utaus agrah uata ,rallod padahretutkaw adap ialin iaynupmem terksid layniS .okot id - asib aynialin nad ajas utnetret utkaw
agrah skedni ialin uata ,oloS id najuh haruc nairah atad halada aynhotnoC .ajas aparebunep taas adap asrub id nagnubag mahas isasitnaukret terksid layniS .iskasnart naput
utkaw adap ialin iaynupmem - aynhotnoC .utnetret aynah aynialin nad ajas utnetret utkaw.latigid isakinumok laynis halada
uynitnok laynis tukgnaynem halada mumu araces reinil metsis hailuk malad naaracibmePd nad .isasitnaukret kadit gnay terksi
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reiniL metsiS
nagnubuh aynitrA .satireinil apureb susuhk tafis nagned metsis halada reinil metsiS apureb uti nagnubuh kifarg adap rabmagid akiJ .reinil tafisreb aynnaraulek nad nakusam
b sifarg narabmag numaN .surul sirag metsis taas adap ukalreb aynah surul sirag apure akiJ .)neisnart( isisnart isidnok adap nakub nad )ydaets( patnam isidnok adap adareb
abit rotsiser - .mho mukuh iauses lucnum gnusgnal kadit rotsiser sura ,nagnaget irebid abitb isidnok irad isisnart asam adA patnam isidnok ujunem )lawa isidnok( nagnaget irebid mule
ukalreb aynah mho mukuH .)kitedonan uata kitedorkim nagnutih malad aynah nupiksem( kinortkele naiakgnar niased adap nakitahrepid kadit ini isisnart isidnoK .patnam isidnok adap
i isidnok ipat ,asaib habureb laynis anam id iggnit isneukerf metsis adap naitahrep idajnem in.tapec tagnas nagned
:ulrep idajnem reinil metsis iduts apagnem gnitnep nasala aud adA
.1 halet aynnasahabmep nad hadum hibel irajalepid tapad reinil metsis ledoMna utnab talA .maladnem .aidesret kaynab halet reinil metsis niased nad sisila
.2 .reinil metsis nagned nakledomid tapad kisif metsis nakaynabeK
mth.30nilsis/nilsis/smu_insuh/gro.seiticoo.www//:ptth
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metsiS hotnoC layniS nad
nakisinifednem aisunam haletes nakisinifedid urab ilakgnires metsis awhab nakitahreP uata nakukalid kadneh gnay apa natamagnep nakataynem aisunam aynitra ,ayntseretni
.metsis naisinifednep irad helorepid nigni gnay apa taafnam
h gnay natamagneP id gnutnaj kated nad nasafanrep amari itamagnem :nakukalid kadne kutnu nakukalid gnitnep ini natamagneP .)nasuibmep( aisehtseana huragnep hawab
tapet gnay suib tabo halmuj nakirebmem
metsis amaN isatropsnart nad isaripser metsiS :
:narauleK amarI .1 ,)tinem rep kated malad( gnutnaj
)tinem rep safan malad( nasafanrep isneukerF .2
)lm malad( suib tabo sisoD :nakusaM
gnay nakusam laynis kutneb aud ada akam ,iuhatekid hadus suib tabo sisod akiJ:metsis ek nakirebid tapad
.1 nusid suib tabO :eslupmi layniS gnay utkaw malad suib tabo halmujeS .nakkit.metsis ek nakkusamid "takgnis"
.2 suib tabo halmujeS .sufni narila iulalem nakkusamid suib tabO :pets layniS suib tabo halmujes amirenem natsnok araces naka hubuT .sufni lotob ek nakkusamid
fitaler gnay utkaw malad .amal
etsis naisinifedneP :isnerefer turunem laynis nad m
yarruM - ,"enicideM yrotaripseR ni ssecorP gnilledoM" ,.J.D ,htimS metsyS yrotaripseR ehT ,.8891 ,mleH moorC ,nodnoL ,613 .p ,5 .on ,2 .lov
layniS
m naraulek nad nakusam ,reinil metsis sisilana malaD tapad gnay laynis nakapure halognem metsiS .sifarg rabmag nupuata sitametam isgnuf ,lebat kutneb malad nakataynid isgnuf ,metsis nahalognep tabikA .naraulek laynis nakraulegnem nad nakusam laynis
sunis laynis haubes hotnoc iagabeS .habureb laynis sitametam nakkusamid akij t nis = )t(x+t(x A = )t(y naraulek laynis idajnem habureb naka lelarap rotisapak naiakgnar ek A = )
+t(nis aracibreb ini baB .habureb laynis esaf nad odutilpma awhab itrareb sisif araces gnay )
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anamiagab nad laynis kutneb padahret sitametam isarepo huragnep ajas apa gnatnetkutneb - .rasad laynis kutneb
laynis nemugra padahret sitametam isarepO .2
a .isageN .
nagned nailakreP .b .naalaksnep/atnatsnok
atnatsnok nagned nemugra nahalmujneP .naresegrep/atnatsnok nagned nahalmujneP .c nagnarugnep nakgnades atnatsnok ialin huajes irik ek resegret laynis nakbabeynem naka
m naka atnatsnok nagned nemugra k resegret laynis nakbabeyne e .nanak
nad isagen isarepo helo ihuragnepid atnatsnok nagned nahalmujnep tabika naresegreP laynis nakbabeynem isagen lisah laynis adap atnatsnok nagned nahalmujneP .naalaksnep
agned nagnarugnep nakgnades nanak ek resegret resegret laynis nakbabeynem atnatsnok n(x layniS .irik ek -t- (x laynis itrepes kutneb iaynupmem )2 - .irik ek 2 huajes resegret gnay )t
naresegrep ialin nakbabeynem alaksret gnay laynis adap atnatsnok nagned nahalmujnePgnihes alaksret )t2(x layniS .alaksret kutneb ilak 2/1 idajnem turekgnem laynis kutneb ag
t2(x layniS .)t(x laynis - ek resegret ipat )t2(x laynis nagned amas kutneb iaynupmem )2.alaksret tuki naresegrep ialiN .)2 huajes nakub( 2/2 huajes nanak
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gnay ini tukireb laynis audek aratna id hakanaM ???raneb
1.2 nahital laoS
.)t(h nad )t(x uynitnok laynis aud kapmat sata id rabmag adaP gnay gnirim sirag iaynupmem )t(x laynis awhab nakitahreP
,b( kitit id rihkareb nad )2,0( kitit irad lawareb - b nagned )1lrabmaG .araduas MIN rihkaret tigid halada kiab nagned ha
laynis - :ini tukireb laynis
(x .a - )t
)2+t(x .b )t2(x .c
.d - )t(x2 t3(x .e - )3
(x .f - t2 - )2 )t(h)t(x .g
t(x .h - )3/t2(h)1
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.2.2 nahital laoS
awhab nakitahreP .]n[h laynis naklipmanem sata id rabmaG nagned 1=n id slupmi gnudnagnem ]n[h laynis b rasebes ialin
kiab nagned halrabmaG .araduas MIN rihkaret tigid utiaylaynis - :ini tukireb laynis
]2+2/n3[h .a [h .b -n- 2/]1
tapad gnay laynis nakapurem naraulek nad nakusam ,reinil metsis sisilana malaDta sitametam isgnuf ,lebat kutneb malad nakataynid halognem metsiS .sifarg rabmag nupua
isgnuf ,metsis nahalognep tabikA .naraulek laynis nakraulegnem nad nakusam laynis nakkusamid akij t nis = )t(x sunis laynis haubes hotnoc iagabeS .habureb laynis sitametam
nem habureb naka lelarap rotisapak naiakgnar ek +t(x A = )t(y naraulek laynis idaj A = )+t(nis aracibreb ini baB .habureb laynis esaf nad odutilpma awhab itrareb sisif araces gnay )
anamiagab nad laynis kutneb padahret sitametam isarepo huragnep ajas apa gnatnetkutneb - .rasad laynis kutneb
is kutneB .3 rasad uynitnok layn .uynitnok laynis rasad kutneb agit adA
.1 eC = )t(x skelpmok ladiosunis laisnenopske layniS ta halada e ,ini nasumur malaD . retemarap halada a nad C ,utkaw nemugra halada t , ...817,2 larutan nagnalib
eC laynis kutneB .skelpmok ta isairavreb .a nad C ialin gnutnagret o laisnenopske utiay ,laisnenopske kutnebreb naka layniS .leir a nad C kutnU
laynis ialin ,0=t taas adaP .0 < a akij nurut laisnenopske nad 0 > a akij kian.C=)t(x halada
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o nem silutid tapad a renijami nagnaliB .renijami a kutnU j=a idaj aggniheseC = )t(x idajnem laynis nasumur j t j soc C = j nis j + t nad tahilret gnaY .t
soc C = })t(x{eR utiay aynleir naigab halada skelpmok laynis irad isketedretj isneukerf nad C odutilpma nagned ladiosunis kutnebreb naka layniS .t .
layniS araces lucnum laynis kutneb aynitra ,kidoirep tafisreb ini ladiosunisgnalureb - gnalureb ialum laynis taas utkaw akgnaJ .)t(x=)T+t(x aggnihes gnalu tubesid p 2 = T ,ini ladiosunis laynis kutnU .T utiay edoire .
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o pmok atnatsnoK .skelpmok a nad C kutnU = C idajnem silutid tapad C skele|C| j j + r = a iagabes silutid tapad a skelpmok atnatsnok nad nasumuR .
idajnem naka laynis
e|C| = )t(x j e j + r( t) e|C| = )t(x tr e (j +t )
e|C| = })t(x{eR halada laynis leir naigaB tr ( soc +t) naka rabmagid akij gnay )b .ladiosunis laisnenopske kutnebre
o .2 ( nautas aggnat layniS pets tinu aggnat laynis kutneB .aggnat aynitra petS .)t(u )
idajret laynis nakianek ,nautas aggnat laynis kutnU .aggnat kana utas itrepes haladametam araceS .utas rasebes aynnakianek nad 0=t id 0 > t kutnu 1=)t(u laynis ,sita
sesorp nakledomem kutnu iakapid gnires aggnat layniS .0 < t kutnu 0=)t(u nadno naralkasnep - .ffo
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.3 ( nautas slupmi layniS eslupmi tinu ) halada slupmi layniS .tuyned aynitra eslupmI .)t( tuyned haubes amal aparebeS .ilabmek gnalih ulal taases lucnum gnay laynis gnutnaj sativitka ,aisunam igaB !fitaler tagnaS ?slupmi tubesid tapad raga lucnum
nutnaj laynis ,retupmok igab ipat ,tuyned halada kayal kadit nad amal tagnas g ayag irebmem naka gnidnid ,gnidnid ek rapmelid alob haubes akiteK .tuyned tubesid alob padahret gnidnid nakparetid gnay ayaG .takgnis gnay utkaw malad alob adapek
abid takgnis pukuc ayag naadarebek anerak slupmi/tuyned tubesid sativitka gnidn nagned 0=t id lucnum aynah gnay laynis halada slupmi tinu ,sitametam araceS .alob
,nial atak nagneD .1 rasebes igrene nad 0=t kutnu 1=)t( t kutnu 0=)t( .0
layniS - ynis padahret sitametam isarepo nagned aynkutneb habuid tapad rasad laynis .lalaynis irad nugnabid tapad mala id laynis raseb naigabes nakhaB - tukireB .rasad laynis
t(u layniS .sitametam isarepo irebid gnay rasad laynis kutneb hotnoc halada - laynis halada )1at naalaksnep imalagnem )t2(u layniS .nanak ek 1 huajes resegid gnay )t(u tahilret kadit ip
t2(u layniS .)t(u laynis irad adebreb - nanak ek 2/1 huajes resegid gnay )t2(u laynis halada )1 ,nakalaksid laynis naresegrep nakbabeynem naalaksnep kefe awhab nakitahreP(
t2(u laynis naresegrep - .)nanak ek 2/1 naknialem ,nanak ek 1 nakub )1 e layniS (- t)i4+1 )t(u nailakrep kefE .ladiosunis laisnenopske laynis nagned )t(u laynis nailakrep lisah nakapurem laynis 0 > t kutnu nad 0 idajnem laynis ialin 0 < t kutnu halada )t(u laynis nagned )t(x laynis
.alumes kutneb itrepes patet
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