Clase 2

 

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MQTNDÉQTKAN

Kbl. @hrlm ]lnrtm En`nrdh lulnrtmJmsphg.mdu.ma

AHBTMBKDH ]BKDND 60 ZVHFNFKGKDND

6.> Tmhrén fîskan 6.6 Aîgaughs dm prhfnfkgkdnd 6.1 Zrhfnfkgkdnd Ahbdkakhbng 6.4 Kbdmpmbdmbakn

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Mxpmrkimbth •

Ahb`ub Ahb` ubth th dm na naak akhb hbms ms ah ahbb ggns ns qum, qum, ut utkgkgkz kznb nbdh dh prhamdk prh amdkikm ikmbth bthss agnr agnrnim nimbtm btm mstn mstnfgm fgmakd akdhs, hs, sm me mema matð tðnn ng nglð lðbb tkph tkph dm hf hfsm smrrvna nakñ kñbb h imd mdkd kdn. n.

Zrhpñsk Zrh pñskth th dm ub mxp mxpmrk mrkimb imbth th •

•

•

Lmbmrnr ahbhak Lmbmrnr ahbhakikmbth ikmbth Umrk Umrkekekan anrr au auipg ipgkik kikmb mbth th dm ng nglð lðbb pr prkb kbak akpk pkh, h, supu supums msth th h tmhr tmhrén én.. Im`h Im `hrnr rnr me meka kana nakn kn dm ng nglð lðbb imanb imanbks ksih ih yn ahbs ahbstr truk ukdh dh.

Mxpmrkimbth mstndéstkah Anrnatmréstkans •

•

•

Qm snfm aungms shb ghs rmsugtndhs phskfgms dmg mxpm mx pmrk rkimb imbth th nb nbtms tms dm su m`ma m`maua uakñ kñb. b. Aung Au ngqqukmr kmr rmng rmngkz kznnakñb akñb dmg dmg mxpm mxpmrk rkik ikmb mbth th dmfm mfm ahbd hbduakr uakr n ub rmsugtndh qum bh ms ahbhakdh, pmrh sm snfm aungms shbb ghs sh ghs ph phsk skfg fgms ms rmsu rmsugtn gtndh dhs. s. Zumd Zu mdmm sm smrr rmpm rmpmtktkdh dh fn`h fn`h kdëb kdëbtktkan anss ah ahbd bdka kakh khbm bmss

6

 

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Mspnakh iumstrng Mspnakh spnakh iumstrn iumstrngg (℥) ℥ ms mg ahb`ubth dm thdhs ghs rmsugtndhs phskfgms. phskf gms. sm ahiphbm ahiphbm dm thdhs thdhs y andn andn ubh dm ghs suamshs mgmimbtngms. Q ms mg ahb`ubth phtmbakn dm ℥ ahb`ubth dm

thdh th dhss gh ghss sufa sufahb hb`u `ubt bths hs dm ℥ dmbh dmbhik ikbn bndh dh mspn ms pnaakh dm mv mvmb mbth thss (M) (M)

Mspnakh iumstrng Mxpm Mx pmrki rkimb mbth th00 Gnbzn Gnbznrr ih ihbmd bmdnn ℥9 {s,a} Q {ß3 {s}3 {s}3 {a}3 {a}3 ℥} ß9 { } vnakh 3 mb mg m`mipgh mqukvngm n kiphskfgm

1

 

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Anrdkbngkdnd dm ub mspnakh Iumstrng Anrdkbngkdnd

Ms mg bðimrh dm mgmimbths dm ub ahb`ubth ekbkth

Mspnakh iumstrng dksarmth Ahb`ubth ahbtnfgm

M mstmnsfgmuabmar hubb`nubathrramhsbpthnbfdgmmbsak kny usbhhghnsuk bmhs mpbhtsrmskfghgms mgmimbths dm M y ghs dm F, dhbdm F ms ub sufa su fahb hb`u `ubt bthh dm gh ghss bu bui imr mrhh mb mbtm tmrrhs bh bm bmln lntktkvvhs

M`0 F 9 {>3631343…3>:} pnrn anrdkbngkdnd ekbktn. M bh bmamsnrknimbtm ms ekbkth (M`. Gnbznr  ihbmdn onstn qum sngln anrn) Mspnakh Mspn akh iumstrng iu mstrng dksarmth. ahbtnf nfgm gm ( ) ms dkarmth sk y shgh sk ℥ ms ahbt

4

 

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Mspnakh iumstrng ahbtkbuh Mspnakh Mspn akh iumstrng ahbtkbu h

(℥) ms ahbtkbuh sk ℥ Bh ms dksa dksarmt rmth h M`mipgh0 imdkr mstnturn h pmsh

Mvmbths dmg mspnakh iumstrng

Mvmbth

ms thdh su suffahb ahb`ub `ubth dm ℥.

Mvmbth Mvm bthss iutun iutunimb imbtm tm mxa mxaguy guymbt mbtms0 ms0

Aunbd Aunb dh 6 mvmb mvmbtths dm ub iksi ksih mspn mspnak akh h dm mvmb mv mbth thss ℥ bh tkmb tkmbmb mb mgm gmi imb mbtths mb ahið ahiðb b.

(M>, M6

℥) Γ S(M>

M6) 9 ßY

=

 

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]bkñb dm mvmbths ]bkñb dm d m mvmbth mvmbths s

(M>> (M

M6)9 M6)9 M> + M6 ‑ (M> (M>

M6 M6)Y )Y

Eubakñb prhfnfkgkdnd Eubakñ Euba kñbb Z ahb ahb dhik dhikbk bkhh Q ah ahbb vn vngh ghrm rmss mb S:,>Y qum auipgm0 Nxkhins Nxk hins dm Chgi Chgihlhr hlhrhv hv >.Z(℥) 9 > 6. : 79 Z(M) Z(M) 79 >

M

Q

1.Z(M> M6)9 1.Z(M> M6)9 Z(M>) Z(M>) + Z(M6) Z(M6) skmi skmiprm prm qum (M> M6) 9 ß

5

 

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Zrhfnfkgkdnd Z(M) Z( M) 9 -----B(M) ---------B(℥) Gnbznikmbth dndh, aung ms gn prhfnfkgkdnd qum npnrmzan ub bðimrh inyhr qum 4. ℥ 9 {>36 {>36313 31343= 43=35} 35} M 9{=,5} Z(M) 9 6/59 >/1

Qm dmfm snfmr dmtmrikbnr gn anbtkdnd dm mgmimbths dmg mvmbth

Zrhfnfkgkdnd B(M) Z(M) Z( M) 9 --------------B(℥) Gnbznikmbth dnrdh, aung ms gn prhfnfkgkdnd qum mg dnrdh ankln dmbtrh dm gn ahrhbn akraugnr dm rndkh mxtmrkhr > y rndkh kbtmrkhr >/6 >/6 ℥ 9 îr îrmn mn tht thtng ng M 9 îrmn ahrhbn Z(M)) 9 ϊ*(>-: Z(M ϊ*(>-:.= .=6)/ ϊ*( ϊ*(>)6 9 :,/:5/6:>;

Tmhrmins prhfnfkgkdnd Tmhrmi Tmhr minn > Gn prhfn hfnfkgkd gkdnd Z ddmm ub ub mvm vmbbth M

Q

Z(M)9 > ‑ Z(Ma)

Tmhrmins prhfnfkgkdnd Tmhrmi Tmhr minn 6 Gn prhfn hfnfkgkd gkdnd Z ggnn ubkñb dm gh ghs mvm vmbt bthhs M> y M6 Z(M> M6)9 M6)9 Z( Z(M> M>)) + Z(M6 Z(M6)) ‑ Z( Z(M> M> M6 M6))

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Tmhrmins prhfnfkgkdnd Tmhrmi Tmhr minn 1 Gn prhf prhfnf nfkgkgkd kdnd nd Z gn kbtm kbtmrs rsma maak akñb ñb dm gh ghss mvmbt mvm bths hs M6 y M> M>a Z(M6 M>a)9 Z( Z(M M6) ‑ Z(M (M>> M6 M6))

Tmhrmins prhfnfkgkdnd Tmhrmi Tmhr minn 4 Qk M> M6

Z(M>) 79Z(M6)

Z(M> M6) 79 Z(M>) + Z(M6) Tmhr Tm hrmi minn = (dms (dmskl klun ungd gdnd nd dm Fh Fhbe bemr mrrh rhbk bk)) Z(M>> M6) 9 Z(M Z(M Z(M>) >) + Z(M Z(M6) 6) - Z(M Z(M>> M6) QK Z(M> M6)79> Z(M> Z( M> M6 M6)) 29 Z( Z(M> M>)) + Z( Z(M6 M6)) - > Tmhrmi Tmh rminn 5 ((Dms Dmsklu klungd ngdnd nd dm Fhhg Fhhgm) m) Z(M> Z( M> M6 M6)) 29 > - Z( Z(M> M>a) - Z(M6a) Z(M> Z( M> M6 M6)) 9 > ‑ (Z (Z(M (M>>a M6a))

;

 

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Gmyms dm ahb`ubths

Zrhfnfkgkdnd Mbaumbtrm prhfnfkgkdnd dm0 (M> M6 M1) a (M> M6) (M6 M1) (M>a M6 M1) a a (M> M1 ) (M> M6 ) a M1

M> M6 :.>6

:.>:

:.6:

:.:= :.:?

:.>:

:.>=

M1

>:

 

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Zrhfnfkgkdnd Mbaumbtrm prhfnfkgkdnd dm0 Dndh Z(M6) 9 :.4= Z(M> M6) 9 :.>= Mbaumbtrm Z(M6 M>a)

M>

M6

Zrhfnfkgkdnd Mbaumbtrm prhfnfkgkdnd dm0 (M> M6 M1) a (M> M6) (M6 M1) (M>a M6 M1) a a (M> M6 ) (M> M6 ) a M1

M> 4 = 5

;

M6

>: >1 >4

< ? > 6 1

>> >6

>=

M1

>5 >< >? >; 6:

>>

 

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Zrhfnfkgkdnd Mbaumbtrm prhfnfkgkdnd dm0 (M> M6 M1) a (M> M6) (M6 M1) (M>a M6 M1) a a (M> M6 ) (M> M6 ) a M1

M>

M6 > 6 1 4 = 5

Z9:.> ; >: >1 >4

< ? >= >5 ><

Z9:.4

M1

Tëabkans dm ahbtmh Bhs

pmriktmb

dmtmrikbnr

mg

mspnakh

i strsngtëhab mkgan tnsidnmþhmbdumig mmrsnak pnkñabkhgnisuamun strgnmsg, ngluumbns bn abk ans na ung shb0 Dknlrn Dknl rnin in dm îrfh îrfhgg Vmlg Vm lgn n dm Iugt Iugtkp kpgk gkan anak akñb ñb dm hpak hpakhb hbms. ms. Ahifkbnakhbms Zmriutnakhbms

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Tëabkans dm ahbtmh Dknlrnin dm îrfhg

Ghs dknlrnins dm îrfhg shb hrdmbnakhbms mipgmndns pnrn mbuimrnr thdns gns phskfkgkdndms gñlkans dm ubn smaumbakn dm mvmbths, dhbdm andn mvmbth pumdm haurrkr mb ub bðim bðimrh rh ekbk ekbkth th..

Tëabkans dm ahbtmh Dknlrnin dm îrfhg. M`mipgh

Qm tkmbmb mb ub mstnbtm 1 gkfrhs ubh dm Îglmfrn, htrh dm Ahbtnfkgkdnd y htrh dm Fkhghlén. ¸Dm auîbtns ehrins dkstkbtns sm pumd pu mdmb mb hr hrdm dmbn bnrr ghs ghs gkfr gkfrhs hs88

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Tëabkans dm ahbtmh Dknlrnin dm îrfhg. M`mipgh

]bn agnsm ahbstn dm smks bkþns y >: bkþhs. Qk sm msahlm ub ahiktë dm trms ng nznr, onggggnr on nr gn prhf prhfnf nfkgkgkd kdnd nd dm dm00 >.-Q >. -Qmgm mgmaak aakhb hbnr nr tr trms ms bkþhs. bkþhs. 6.-Q 6. -Qmg mgma maak akhb hbnr nr mx mxna nattnimb nimbttm dh dhss bk bkþh þhss y ub ubnn bkþn. 1.-Qmgmaakhbnr mxnatnimbtm dhs bkþns y ub bkþh.

Tëabkans dm ahbtmh Dknlrnin dm îrfhg. >.-Qmgmaakhbnr Zrhf dm qum sm msah`n ubn bkþn9 5 >5 >:

Zrhf dm qum sm msah`n ub bkþh9

trms bkþhs

? >4

bkþh

>5

bkþh

; >=

bkþn

>:

bkþh

>5

bkþn bkþh 5 >5

bkþn bkþn

 p ( 1 b kþ h s

) 

>:

 

>5

.

; >=

.

? >4



: . 6>4

>4

 

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Tëabkans dm ahbtmh Dknlrnin dm îrfhg.

6.6.-Qmg Qmgmaa maakhb khbnr nr mxnatn mxnatnimb imbtm tm dhs bkþhs bkþhs y ub ubnn bk bkþn þn.. 1.1.-Qmg Qmgmaa maakhb khbnr nr mxnatn mxnatnimb imbtm tm dhs bkþns bkþns y ub bkþh.

Tëabkans dm ahbtmh Anga gaug ugnr nr gn prhfnfkgkdnd dm qum ng nrrh rh``nr  Dknlrnin dm îrfhg. An ng nk nkrm rm tr trms ms ihb ihbmd mdns ns,, sngl snglnb nb00

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Tëabkans dm ahbtmh Vmlgn dm Iugtkpgkanakñb dm hpakhbms. Tmhrmin < Qmnb M>,M6… Mc, mvmbths ahb anrdkbngkdnd b>,b6,..bc. Qk sm dmfm msahlmr prkimrh ub mgmimbth dm M>, gumlh ub mgmimbth dm M6 onstn Mc, mg bðimrh dm hpakhbms phskfgms ms0 b>*b6*….bc Ms dmakr, mg prhduath prhduath dm gns anrdkbngkdndms dm ghs mvmbths.

Tëabkans dm ahbtmh Vm Vmlg lgn n dm Iugt Iugtkp kpgk gkan anak akñb ñb dm hpak hpakhbm hbms. s.

Q mbk sdmhbddmmsmmng rpmrnkigkzmnr rpunbsnh ndamtkvgnkdnnadtkvqkudmndahnbsrmtnngkdzmnrr ppnusmhdsm, smr ggmvndh n anfh dm B> inbmrns h ehrins, mg smlubdh pnsh dm B6 inbmrns h ehrins y mg r-ëskih pnsh dm Br   inbmrns h ehrins, mbthbams mstn natkvkdnd pumdm smr  ggggmmvndn ndn n memat emathh dm dm33 B> x B6 x .... ...... ..... ....x .x Br in inbmr bmrns ns h ehrins

Mg prkbakpkh iugtkpgkantkvh kipgkan qum andn ubh dm ghs pnshs dm gn natkvkdnd dmfmb smr ggmvndhs n memath th,, ubh trns htrh.

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Zrhfnfkgkdnd M`mipghs0 >)]bn pmrshbn msahlm su rhpn mb mg nrinrkh y tkmbm 1 pnbtnghbms,6 aniksns, 6 pnrms dm znpnths. Aunbtns hpakhbms tkmbm pnrn vmstkr. 6) ]bn ahipnþén dm tnxks tkmbm 1 inrans dm vmoéaughs 1 inran N,1 inran F,6 inran A ub agkmbtm gm pkdm 1 nuths dm dkemrmbtms inrans. Aunbtns hpakhbms tkmbm gn miprmsn pnrn nsklbnr ghs tnxks.

Zrhfnfkgkdnd M`mipghs0 1)Nskbnakñb dm bðimrh dm pgnan Zrkimrn gmtrn 9 gmtrn prhvkbakng L Qmlubdn gmtrn 9 nfmamdnrkh (65) Tmramrn gmtrn 9 nfmamdnrkh (65) Zrki Zr kimr mr bði bðimr mrh h 9 mbtr mbtrm m:‑; smlubd sml ubdh h bðim bðimrh rh 9 mbtr mbtrm m :‑; Tmra Tm ramr mr bði bðimr mrh h 9 mbtr mbtrm m:‑; aunr au nrth th bði bðimr mrh h 9 mbtr mbtrm m:‑;

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Zrhfnfkgkdnd Zrkbakpkh rkbakpkh ndktkv dktkvh h

Qk sm dmsmn ggmvnr n memath ubn natkvkdnd, gn auîg tktkmb mbmm eh ehri rins ns ngtm ngtmrb rbnt ntkv kvns ns pn pnrn rn sm smrr rm rmng ngkz kznd ndn, n, dh dhbd bdmm gn prkimrn dm msns ngtmrbntkvns pumdm smr rmn mnggkznd zndn dm I inbmrns h ehrins, gn smlubdn ngtmrbntkvn pumdm rmngkznrsm dm B inbmrns h ehrins ..... y gn ðgtkin dm gns ngtmrbntkvns pumdm smr rmngkzndn dm \ inbmrns h ehrins, mbthbams msn natkvkdnd pumdm smr ggmvndn n anfh an fh dm dm,, I + B + .........+ \ inbmrns h ehrins

Zrhfnfkgkdnd Zrkbakpkh rkbakpkh ndktkv dktkvh. h.-- m`mipgh `mipgh >) ]bn pmrshbn dmsmn ahiprnr ubn gnvndhrn dm rhpn, pnrn gh auîg on pmbsndh qum pumdm smgmaa aakkhbnr dm mbtrm gns inrans \o \okkrphhg, Mnsy y Lmbm Lm bmrn rngg Mg Mgma matr trka ka,, au aunb nbdh dh na naud udmm n on onam amrr gn ahip ahiprn rn sm mb mbau aumb mbtr trnn qu qum0 m0 gn gnvndhrn dm gn inran \ sm prmsmbtn mb dhs tkphs dm anrln ( ? u >> ckg ckghlrn rnih ihss), mb auntrh ahghrm rmss dkem emrrmbtms y pumd umdm smr nuthiî iîttkan h smiknuthiîtkan, gn gnvndhrn dm gn inran M, sm prmsmbtn mb trms tkphs dm anrln (?, >> h >= ckghlrnihs), mb dhs ahghrms dkemrmbtms y pumdm smr nuthiîtkan h smiknuthiîtkan y gn gnvndhrn dm gn inran LM, sm prmsmbtn mb shgh ub tkph dm anrln, qum ms dm >> ckghlrnihs, dhs ahghrms dkemrmbtms y shgh ony smiknuthiîtkan. ¸Auîbtns inbmrns tkmbm mstn pmrshbn dm ahiprnr ubn gnvndhrn8 •

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Zrhfnfkgkdnd Qhguakñb0

I 9 Bðimrh dm inbmrns dm smgmaakhbnr ubn gnvndhrn \okrphhg B 9 Bðimrh dm inbmrns dm smgmaakhbnr ubn gnvndhrn dm gn inra in rann Mn Mnsy sy \ 9 Bðimrh dm inbmrns dm smgmaakhbnr ubn gnvndhrn dm gn inra in rann Lm Lmbm bmrn rngg Mgma Mgmatrk trkaa I96x4x69>5inbmrns B91x6x69>6inbmrns \9>x6x>96inbmrns I + B + \ 9 >5 + >6 + 6 9 1: inbmrns dm smgmaakhbnr ubn gnvndhrn

Zrhfnfkgkdnd M`mrakakh

Vnenmg Gubn vkvm mb Aokounoun y dmsmn kr n gns Umlns h n Dks Dksbm bmyygnbd gnbdkn kn,, mb gns gns prñx rñxki kins ns vna nannak akhb hbms ms dm vmrn rnbh bh.. Znrn nrn kr  n gns Umlns0 ëg tkmbm trms imdkhs dm trnbsphrtm pnrn kr dm Aokounoun Mg Znsh Tmxns y dhs imdkhs dm trnbsphrtm pnrn kr  dm Mg Znsh n gns Umlns, ikmbtrns qum pnrn kr dm Mg Znsh n Dksb Dksbmy mygn gnbd bdkn kn ëg tkmb tkmbmm aunt auntrh rh dkem dkemrm rmbt btms ms imdk imdkhs hs dm trnb trnbsp sphr hrtm tm,, n) ¸Auîbtns inbmrns dkemrmbtms tkmbm Vnenmg dm kr n gns Umllns h n Dk Um Dkssbm bmyygnbd gnbdkn kn88, f) ¸Au Auîb îbtn tnss inb inbmrn rnss tkmb tkmbmm Vnen enmg mg dm kr n gns Umlns h n Dksbmygnbdkn mb ub vkn`m rmdhbdh, sk bh sm rmlrmsn mb mg iksih imdkh dm trnbsphrtm mb qum sm eum8.

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Ahifkbnakhbms Bðimrh dm ahifkbnakhbms ms mg bðimrh dm iumstrns dm tninþh b qum pumdmb thinrsm dmsdm ub ahb`ubth (phfgnakñb hf`mtkvh) dm tninþh B. Mg hrdmb bh ms rmgmvnbtm. Tnifkëb sm gh ggnin AHMEKAKMBTM FKBHIKNG

Qkmiprm ms mbtmrh

mg hrdmb dm ghs hf`mths bh ms kiphrtnbtm

Ahifkbnakhbms

M`0 _9 {n,m,k, `, o ,1,4} ,1,4} B9 < < 9 (/:5/6:>;

Ahifkbnakhbms Dm ub lr uph d m 6 6: :m mstu stu dknbtms sm vnb n mgmlkr 5 pnrn kbt mlrnr ub ahik të. M Mb b gn Zhfgnakñb Hf`mtkvh o ny ; dnins y >> anfnggmrhs3 s m rmqukmrm qum shgh dhs dm ghs kbt mlrnbtms dmg ahik të smn smnb b bmamsnrknimbtm iu`mrms. Gn prmlubt n ms, ¸ ¸dm dm auîbtns inbmrns sm pu mdm m mgmlkr  gmlkr  mstm ahiktë8

•

•

  Dmsnrrhggh

Mg bðimrh dm ehrins mb qum sm pumdmb msahlmr dhs iu`mrms dm ub ahb`ubth dm bumvm ms0

 ‑ 

 ;  ;! ;  ?  >  > >! > > > :  ;  ?  > > :  ;  ?       11: 4 !  4   4 !( > >  4 ) ! Ahbsmaumbtmimbtm, mg bðimrh dm ehrins qum sm pumdm mgmlkr mg ahiktë ahb 4 vnrhbms y 6 iu`mrms ms0  ;   > >       1 5  1 1 :  > > ? ? :  6    4  

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46

Zhr gh tnbth, mg ahiktë pumdm smr mgmlkdh dm >>??: ehrins dkemrmbtms. Mstndéstkan pnrn Kblmbkmréns

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Zrhfnfkgkdndms dm Mvmbths Ekbkths y Ahifkbnakhbms0 m`mipgh ]b rmprmsmbtnbtm dm vmbtns tns dmfm vksktnr smks akudndms durnbtm ub vkn`m. Qk ony >: akudndms mb mg îrmn lmhlrîekan qum vn n vksktnr, dm gns aungms smks shb imrandhs prkinrkhs pnrn mg prhduath mb aumstkñb, ikmbtrns qum gns htrns auntrh shb imrandhs smaubdnrkhs. Qk mg vmbdmdhr mgklm ng nznr gns smks akudndms qum vn n vksktn ktnrsm, ¸auîg ms gn prhfnfkgkdnd dm qum…

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f)

41

a u nt r h d m mg g ns s mnb a k u d nd ms d m i mr a nd h p r k i nr k h y dhs smn smnb akudn akudndms dms dm imran imrandh dh smaub smaubdn dnrkh8 rkh8 gns gns sm smks ks rm rmsug sugtm tmb b sm smrr akudn akudndm dms s dm im imran randh dh prkin prkinrkh rkh8 8

Mstndéstkan pnrn Kblmbkmréns

Zrhfnfkgkdndms dm Mvmbths Ekbkths y Ahifkbnakhbms0 m`mipgh 

auntrh d m m mggns ggns smnb akudndms dm imrandh prki nrkh y dhs smnb akudndms dm imrandh smaubdnrkh8  ‑ 

Z( M ) 

M0 sm smgmaakhbnb auntrh akudndms dm imrandh prkinrkh y dhs dm imrandh smaubdnrkh.

Bðimrh dm ehrins dm smgmaakhbnr auntrh akudndms dm imrandh prkinrkh y dhs dm sma ubdnrkh Bðimrh dm ehrins dm smgmaakhbnr smks akudndms

 5   4      4 6 Z( M )           > :       5  

•

44

  5 !    4 !       4 !6 !  6 !6 !     > : !     5 !4 ! 

 5   =  4 !  4   1  6 !       4 !( 6 !)    6 !( 6 !)    > =  5   ; :   1  : . 4 1  > :  ;   ?  <  5 !   6 > :  6 > ': <   5 !( 4 !)    

Gn prhfnfkgkdnd dm qum dm gns smks akudndms smgmaakhbndns auntrh smnb dm imrandhs prkinrkhs y dhs dm imrandhs smaubdnrkhs ms dm :.41. Mstndéstkan pnrn Kblmbkmréns  



66

 

:>/:5/6:>;

Zrhfnfkgkdndms dm Mvmbths Ekbkths Zrhfnfkgkdndms y Ahifkbnakhbm Ahifkbnakhbms0 s0 m`mipgh 

gns smks rmsugtmb smr akud ndms ndms dm imrandh prk inrkh8  ‑ 

Z( N ) 

N0 sm smgmaakhbnb smks akudndms dm imrandh prkinrkh.

Bðimrh dm ehrins dm smgmaakhbnr smks akudndms dm imrandh prkinrkh Bðimrh dm ehrins dm smgmaakhbnr smks akudndms

 5   4      5 : Z( N)           > :       5   •

4=

  5 !    4 !      5 ! : ! : ! 4 ! > >  > >            : .: : =     > : !   > :  ;   ?  <  5 !   6 > :  6 > ':     5 ! ( 4 ! ) 5 ! 4 !        

Gn prhfnfkgkdnd dm qum gns smks akudndms smgmaakhbndns smnb dm imrandhs prkinrkhs ms :.::=.

  

Mstndéstkan pnrn Kblmbkmréns

Ahifkbnakhbms ahb rmpmtkakñb Gn ehrin dm ahbstrukrgns smrî skikgnr n gns ahifkbnakhbms skb rmpmtkakñb nubqum ahb gn dkemrmbakn dm qum ng pmriktkrsm rmpmtkr ghs mgmimbths tmbdrmihs qum nþndkr n andn ubn dm gns dm hrdmb ubh, mg iksih mgmimbth y thdhs ghs sklukmbtms. pnrt pn rtki kihs hs dm dmgg ah ahb` b`ub ubth th N9 N9{> {>,6 ,6,1 ,1,4 ,4}} Nsé sm hftkmbmb0 >> , >6 , >1 , >4 , 66 , 61, 64 , 11 , 14 , 44.  i   b >   AV     b  

61

 

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Ahifkbnakhbms ahb rmpmtkakñb Mb ubn fhdmln ony mbehrins ub akbah dke mrmbtms dkemrmbtms dm fhtmggns. ¸Dm auîbtns smtkphs pumdmb mgmlkr auntrh fhtmggns8 Qñgh mgk`m 4.. Bh kiphrtn mg hrdmb. sm pumdmb rmpmtkr ghs mgmimbths ms dmakr, pumdm mgmlkr iîs dm ubn fhtmggn dmg iksih tkph.

Ahmekakmbtm iugtkbhikng Qhb andn ubn dm gns iumstrns dm tninþh b .b>c+bq6u+m..sbmc pu9mdm Bd,kvkdm krg gn bpðhi fgmnrahkñb tdnmg q> u,mb6,.b ahifkbnakhbms dm tninþh b>,b6 ..y bc (ahifk (ah ifkbna bnakhb khbms ms dkstkb dkstkbluk lukfgm fgms) s) shb0 shb0

64

 

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Ahmekakmbtm Iugtkbhikng M`0 _9 {n,m,k, `, o ,1,4} ,1,4} Aunbtns ehrin dm ahghanr gn anrnatmrms ahbskdmrnbdh sus tkphs < 1,6,6

9

: sm pa.gns 6 shb OZ,ufkanr = shb KFI y 1 Dmgg. Aunbtns ehrins pumdm mb mg gnf. Nrrmlgh dm 6: gkfrhs mb gns pmraons dm fkfgkhtman. 4 shb dm Mstndéstkan, >> dm Eéskan, 4 dm Lmhghlén y > dm Dkbîikan.

6=

 

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Zmriutnakhbms Bðimrh dm sufahb`ubths dm tninþh b thindhs dm ub ahb`ubth (phfgnakñb hf`mtkvh) dm tninþh B. Mg hrdmb sk ms rmgmvnbtm.

B

Qk B9b

bZ

9 b!

Zmriutnakhbms

M`0 _9 {n,m,k, `, o ,1,4} ,1,4} B9 < 6Z

;

Zmriutnakhbms ¸Dm auîbtns ehrins pumdmb smbtnrsm haoh pmrshbns mb ubn ekgn dkstkbtns dm futnans8 Tkmbmb qum smbtnrsm gns ? pmrshbns. Qé kiphrtn mg hrdmb. Bh sm rmpktmb ghs mgmimbths. ]bn pmrshbn bh sm pumdm rmpmtkr. B9? y b9?

Zmriutnakhbms ahb rmpmtkakñb Zmr mriu iutn tnaakhbm khbmss ahb ahb rmpm rmpmtktkaakñb kñb dm b mg mgmmimbt imbthhs mb gn gnss qum mg prkimr mgmimbth sm rmpktm b> vmams, mg smlubdh sm rmpktm b6 vmams ... y mg ðgtkih sm rmpktm bc vmams mams shb gh ghss dk dksstkb tkbth thss lruphs dm b mgmimbths qum sm pumdmb onamr dm eh ehrrin qum mb andn lruph, andn mgmimbth npnrmzan mg bðimrh dm vmams kbdkandh y qum dhs lruphs sm dkemrmbaknb ðbkanimb imbtm mb mg hrdmb dm ahghanakñb. Qm rmprmsmbtn phr  Zbb>,b6,...,bc. M`mipgh. M`mipg h. Ahbstr Ahbstrukr ukr thdh thdhs s ghs bðimrh bðimrhs s dm smks smks akerns akerns phskfgm phskfgms s utkgkznbdh dhs vmams mg bðimrh ubh y auntrh vmams mg bðimrh dhs.

6<

 

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Zmriutnakhbms ahb rmpmtkakñb Mb mg pnghrh`ns, dm smþngms dm ubyfnrah pumdmb¸Auîbtns kznr trms fnbdmrns dhs nzugms auntrhsmvmrdms. smþngms dkstkbtns pumdmb kbdkanrsm ahb gn ahghanakñb dm gns bumvm fnbdmrns8 Mbtrnb thdhs ghs mgmimbths. Qé kiphrtn mg hrdmb. Qm rmpktmb ghs mgmimbths. Zn Znrn rn an ansn sn(( sk bh ki kiph phrt rtnn

mg hrdm hrdmb) b)

Zrhfnfkgkdnd Ahbdkakhbng Zrhfnfkgkd Zrhfn fkgkdnd nd dm N dndh F

Nxkhins0 Z(M>|M>) 9 > Z(M6|M>) 29: Z(M6]M1| Z(M6 ]M1|M>) M>) 9 Z(M6|M>) Z(M6|M>) + Z(M1|M>) Z(M1|M>) sk M6 M1 9ß

6?

 

:>/:5/6:>;

Zrhfnfkgkdnd Ahbdkakhbng dndh9{>,6,1,4,=,5} M>9{>,6} M69{>,1,=} Z(M>) 9 >/1 Z(M6)9 8 Z(M> M6)9 8 Z(M>|M6) 9 8 Z(M6|M>)9 8

Zrhfnfkgkdnd Ahbdkakhbng Gnbznikmbth dm dhs dndhs. Zrhfnfkgkdnd dm qum sngln pnr dndh qum nbtms sngkñ inyhr /:5/6:>;

Tmhrmin Qk M> [ M6 shb iutunimbtm mxaguymbtms . Z(M>|M>]M6) 9 ZS(M>) (M>]M6)Y / SZ(M>) + Z(M6)Y

msthaîstkann Kbdmpmbdmbakn msthaîstka M> ms msthaîstkanimbtm kbdmpmbdkmbtm dm M6 Z(M>|M6) 9 Z(M>) , nsé ahih Z(M6|M>)9 Z(M6) Tmhrmin >:. Qk M> y M6 shb msthaîst. kbdmpmbdkmbtms Mbthbams Z(M>

M6) 9 Z(M>)Z(M6)

Qhb kbdmpmbdkmbtms tnifkëb0 M> y M6a M>a y M6 M>a y M6a

1:

 

:>/:5/6:>;

Kbdmpmbdmbakn msthaîstka msthaîstkann Tmhrmin Qk M> , M6>>. y M1 shb s hb msthaîst. kbdmpmbdkmbtms Mbthbams tnifkëb gh shb0 M> y M6 M1 M> y M6 ] M1 M>a y M6 M1a

Kbdmpmbdmbakn msthaîstka msthaîstkann •

M`mipgh0 Mb ub Qkstmin dm akraukths ghs ahiphbmbtms enggnb dm inbmrn kbdmpmbdkmbtm. Auîg ms gn prhfnfkgkdnd dm qum mg Qkstmin eubakhbm. (gn ekl. iumstrn gn prhf. Dm qum eubakhbm andn ahiphbmbtm)

Z S (  N   F )  ( A    D  M  ) Y  Z (  N   F )  Z ( A    D  M  )  Z (  N   F  A    D  M  )

 : . < * : . <  : . ? * : . ? * : . ?   : . < * : . < * : . ? * : . ? * : . ?  : .

1>  

:>/:5/6:>;

Tmhrmin dm Fnyms Gn ubkñb dm thdhs ghs Mk ms ℥ y Mk shb dks`ubths(mxaguymbtms) N ms gn ubkñb dm C mvmbths dks`ubths(mxaguymbtms)

℥ 9 M>

] M6 ] M1] …… ]Mc->] Mc

N 9 N M> ] N M6 ] N M1 ] .. ] N Mc->] N Mc

Tmhrmin dm Fnyms Qk gn suin dm Mk ms ℥ y Mk shb dks`ubths Qk N ms gn ubkñb dm C mvmbths dks`ubths Zrhfnfkgkdnd dm qum dndh N gn anusn onyn skdh Mr  Z(N|Mr)Z(Mr) Z(Mr|N)

Z (N|Mr) (N|Mr)xZ xZ(Mr (Mr)9Z )9Z(N∫ (N∫ Mr)

9 ------------------------------- 9 ---------------------------------------------------

Ρ Z(N|Mk)Z(Mk)

ZVHFNFKGKDND dm N

16  

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Tmhrmin dm Fnyms un)bd(nkaptñrum6fynbGu=ks:%(n)pdrukamtfñnb1 pQnk r1ngmpghrhse, dZkmadtnrbh (unbpnrui mfnntmbrk?n:@%