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@CAMI\OT@

3DHYNH@B‟T NCQ

ZHOM\T \H RI@I@BIR 

3  @cami|ot` qct eort| hbtiruil om |fi `omircn dcnnil `cami|o|i &Ei4H</ O| ot dcnnil

nhcl &tfhqoma |fi lorid|ohmt/ t|hmi 

2  Zrhzir|oit he c `cami|;

c/ Qfim c `cami| ot eriin tytzimlil hr zouh|il. o| dh`it |h rit| tfhqoma mhr|f cmlthy|f lorid|ohmt

b/ Nogi zhnit rizin cml ymnogi zhnit c||rcd| icdf h|fir &Lyec‟t ncq/

d/ C `cami| c||rcd|t tybt|cmdit nogi orhm. modgin. dhbcn|. t|iin i|d

4 Zhni t|rima|f &`/ ;

c Zhni t|rima|f ot c tdcncr

b TO ymo| ot c`ziri-`i|ri

d Lo`imtohmcn ehr`ync he ` 0 WONP

l O| &c/ lizimlt hm mc|yri he |fi `c|irocn he |fi `cami| &b/ lizimlt hm niuin he 

`cami|o{c|ohm &d/ ot lorid|n zrhzhr|ohmcn |h cric he drhtt-tid|ohm

i Othnc|il `cami|od zhnit lh mh| ivot| \fi cri o`caomcr

<  @cami|od `h`im| ;

c O| ot |fi zrhlyd| he `cami|od nima|f cml zhni t|rima|f @ 0 2n Ñ `

b O|t TO ymo| ot c`ziri-`i|ri2

hr Khyni ( \itnc hr M—`4 (qibir

d Lo`imtohmcn ehr`ync ot WO3N

2P

l O| ot c uid|hr qo|f o|t lorid|ohm erh` Thy|f Zhni |h Mhr|f Zhni cnhma o|t cvocn nomi

&TM/

9  Dhynh`b‟t omuirti tsycri ncq ;

&o/ \fi ehrdi he c||rcd|ohm bi|qiim |qh zhom| `cami|od zhnit ot lorid|n zrhzhr|ohmcn|h |fi zrhlyd| he |fior zhni t|rima|ft cml omuirtin zrhzhr|ohmcn |h |fi tsycri he 

|fi lot|cmdi |fi` E ∐2

23

l

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Qfiri `3. `2 cri zhni t|rima|f‖l‟ ot |fi lot|cmdi bi|qiim |fi `cami|od zhnit

&oo/ E02

23

l

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<ϊ

¹ 

Firi : r  ¹ ¹ ¹ 0

 qfiri

r  ¹  0 rinc|oui zir`icbono| cml ¹: 0 cbthny|i

zir`icbono|

¹: 0 <ϊ  Ñ3:—1

F`—3

&Fimr ( `i|ir/ cml ehr cor hr ucdyy`

¹ r 0 3

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uo/  Oe E ot |fi ehrdi bi|qiim |qh `cami|od zhnit om |fi `iloy` cml E: ot |fi ehrdi

bi|qiim |fi tc`i zhnit qfim |fi cri om cor hr ucdyy`. |fim |fi rinc|oui

zir`icbono| ot aouim b:

rE

E0¹  

uoo/  Ehrdi ivziroimdil b c `cami|od zhni ‖`‟ qfim zncdil om c ymoehr` eoinl B ot

E 0 `B Miq|hm

5  Ymo| Zhni; Ymo| zhni ot hmi qfodf qfim zncdil c| c lot|cmdi he hmi `i|ir czcr| erh`c to`oncr zhni om cor hr ucdyy` rizint o| qo|f c ehrdi he 3:

—1Miq|hm

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1  @cami|od nomit he ehrdi; C nomi he ehrdi om c `cami|od eoinl ot |fi zc|f hr |fi dyrui

cnhma qfodf c erii ymo| mhr|f zhni |rcuint \fi |cmaim| |h |fi `cami|od eoinl nomi c| c

zhom| aouit |fi lorid|ohm he |fi eoinl omlyd|ohm B c| |fc| zhom|

Uir Tfhr| Cmtqir Syit|ohmt;

3  Lieomi |fi `cami|od `h`im| he c bcr `cami| Qfc| ot o|t lorid|ohm8

Cmt ; @cami|od `h`im| &@/ ; O| ot lieomil ct |fi |hrsyi cd|oma hm c bcr `cami| qfodf

qfim zncdil zirzimlodyncr |h |fi lorid|ohm he ymoehr` `cami|od eoinl he ymo|omlyd|ohm 

O| ot cnth lieomil ct |fi zrhlyd| nima|f he c `cami| cml o|t zhni t|rima|f @ 0

2n`

O| ot c uid|hr sycm|o| O|t lorid|ohm ot ehr Thy|f Zhni |h Mhr|f Zhni cnhma |fi cvot

he |fi `cami|

2  Lot|omayotf bi|qiim ymoehr` cml mhm-ymoehr` `cami|od eoinlt Aoui ivc`znit 

& Kymi2:3: /

 

Cmt ; Ymoehr` `cami|od eoinl ; Oe |fi `cami|od omlyd|ohm c| iuir zhom| om c eoinl ot

tc`i bh|f om `camo|yli cml om lorid|ohm. |fi eoinl ot tcol |h bi ymoehr` `cami|od

eoinl

Iv ;- 3/ \fi `cami|od eoinl bi|qiim |qh zhni zoidit he cm inid|rh`cami|od ot

ymoehr`

2/ Fhro{hm|cn dh`zhmim| he icr|f‟t `cami|od eoinl c| c aouim zncdi ot ymoehr`

Mhm —Ymoehr` @cami|od eoinl ; Oe |fi `cami|od omlyd|ohm ucroit erh` zhom| |h

zhom| om c eoinl bh|f om `camo|yli cml om lorid|ohm. |fim |fi eoinl ot tcol |h bi mhm

— ymoehr`

Iv ;- \fi `cami|od eoinl lyi |h bcr `cami| ot c mhm-ymoehr` eoinl

4 Qfc| cri |fi ymo|t he |fi ehnnhqoma `cami|od zftodcn sycm|o|oit8&o/ @cami|od

`h`im| &oo/ @cami|od zir`icbono|8 

Cmt; @cami|od `h`im|;2

 C` cml @cami|od zir`icbono|;3 2& / F` hr MC

− −

< 

Lh hy eoml |qh `cami|od eoinl nomit om|irtid|oma8 Qf8 

Cmt; \qh `cami|od eoinl nomit qonn mh| om|irtid| icdf h|fir Oe |fi om|irtid| c| |fi zhom| he 

om|irtid|ohm. |fi `cami|od eoinl tfhynl fcui |qh loeeirim| lorid|ohmt qfodf ot mh|

zhttobni

9  \fi ehrdi bi|qiim |qh `cami|od zhnit tizcrc|il b c lot|cmdi‖l‟ om cor ot E C| qfc|

lot|cmdi bi|qiim |fi` |fi ehrdi bidh`it lhybnil8

Cmt; Qi fcui2

3E 

l γ  By| . 2 32E E 0  

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2 223 2 322

2 3 2

E l l l 

E l ∼ 0 ⇒ 0  

2

32

2 2

l l l ⇒ 0 0  

5 Qfc| ot |fi ̀ cami|od `h`im| he c ti`o dordyncr `cami| he rcloyt ‖r‟ cml zhni

t|rima|f ‖`‟8

Cmt; Zhni t|rima|f 0 `

Nima|f he |fi `cami| &TM/ 0 2r

∼ @cami|od `h`im| &@/ 0 Zhni t|rima|f v nima|f he |fi `cami| 0 ` v 2r 0 2`r

1 \fi `cami|od ̀ h`im| he c bcr ̀ cami| ot @ Oe o| ot dy| om|h |qh zoidit om |fi rc|oh

3;2 zirzimlodyncr |h o|t nima|f. qfc| ot |fi rc|oh he |fior `cami|od `h`im|t8 

Cmt; Om |fot dcti. zhni t|rima|f ri`comt tc`i ehr bh|f |fi zoidit Fimdi 3 2; 3; 2 @ @  0  

THNUIL ZRHBNI@T

3 \fi lot|cmdi bi|qiim c mhr|f zhni he t|rima|f45 3: C`

−Ñ cml c thy|f zhni he 

t|rima|f46 3: C`

−Ñ ot 3: d` \fi zhnit cri tizcrc|il om cor Eoml |fi ehrdi

bi|qiim |fi`

Thn; \fi ehrdi bi|qiim |qh `cami|od zhnit ot. : 3 2

2<

` `E 

l 

 ¹ 

ϊ 0  

4 41 33

2

5 3: 6 3:3: <6 3:

&:3/E M 

− −− −Ñ Ñ Ñ

∼ 0 Ñ 0 Ñ  

2 C M-zhni he c uir nhma `cami|od miilni ot zncdil c| c lot|cmdi he 2:d` erh`c zhom| ‖Z‟ Oe |fi zhni t|rima|f he |fi `cami|od miilni ot <: C`. qfc| ot |fi

`cami|od omlyd|ohm c| |fi zhom| Z8

Thn; ∼ \fi `cami|od omlyd|ohm lyi |h |fi M-zhni c| Z ot.

:

2<

` B

r 

 ¹ 

ϊ 0

1<

2 2

< 3: <:3:

< &2: 3: /\ 

ϊ 

ϊ 

−−

−

Ñ0 Ñ 0

Ñ  

Ymthnuil Zrhbni`

3  \qh `cami|od zhnit he t|rima|ft <: C` cml 3:C` cri tizcrc|il b c lot|cmdi he 2:

d` om cor Eoml |fi ehrdi bi|qiim |fi` Oe |fi lot|cmdi ot rilydil |h 3: d`. eoml |fi

ehrdi bi|qiim |fi`& @crdf2:33 /

Thn; Dcti &3/; ` 0 <: C`. `2 0 3:C`. l02: d` 

: 3 2

2

<

` `E 

l 

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ϊ 0 1

2 2

<: 3:3:

&2: 3: /E 

−

−

Ñ⇒ 0 Ñ

Ñ

43: M −0  

Dcti &2/ ;4

3 3:E M −0 . 3 2:l d`0 . 2 3:l d`0 . 2 8E  0  

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 M 

 M 

T T

 @ 

 @ 

:?:

2 4 2 2

3 2

2 2 2

2 3 2

3: &3: 3: /

&2: 3: /

E l 

E l E 

− −

−

Ñ0 ⇒ 0

Ñ 

4

2 < 3:E M −∼ 0 Ñ  

2 \qh `cami|od zhnit hmi he qfodf ot |frii |o`it t|rhmair |fcm |fi h|fir. ivir| hm

icdf h|fir c ehrdi isycn |h44 3: M 

−Ñ qfim tizcrc|il b c lot|cmdi he 3: d` Eoml

|fi t|rima|f he icdf zhni 

Cmt; Oe  3̀ `0 . |fim 2 4` `0 ` l 0 3: d`.44 3:E M 

−0 Ñ  

: 3 2

2<

` `E 

l 

 ¹ 

ϊ 0 Ñ

24 1

2

44 3: 3:

3:

`− −

−⇒ Ñ 0 Ñ 3:` C`⇒ 0  

3 3:` ` C` cml  ∼ 0 0 2 4 4 3: 4:` ` C`0 0 Ñ 0  

4 C bcr `cami| he `cami|od `h`im| @ ot bim| om|h c ti`odordni Qfc| ot o|t miq

`cami|od `h`im|8 

Cmt; Qfim c `cami| ot bim| om|h c ti`o dordyncr crd o|t lot|cmdi bi|qiim |fi zhnit ot

rilydil

∼ Miq `cami|od `h`im| 3 2 @ r`0  

By|2n

r ϊ 

0  

3

2 22

n` @  @ 

ϊ ϊ 

∼ 0 Ñ 0  

< \qh olim|odcn `cami|t cri zncdil zirzimlodyncr |h icdf h|fir qo|f |fior

ymnogi zhnit om dhm|cd| Oe icdf `cami| fct c `cami|od `h`im| @. qfc| ot |fi

`cami|od `h`im| |fi dh`bomc|ohm8

Cmt; 3 @ @ 0 cml 2 @ @ 0  

Cmani bi|qiim |fior cvit:?:ζ  0  

2 2

3 2 3 22 @ @ @ @ @ Dhtζ ′∼ 0 ' −  

2 2 @ @ @ ′⇒ 0 '  

2 @ @ ′∼ 0  

CTTITT _HYRTINE;

3  Dcm |fi ehrdi hm ymo| M-zhni bi|qiim |qh othnc|il nogi zhni bi {irh c| cm zhom|8

Cmt; _it. c| |fi `olzhom| he |fi nomi khomoma |fi |qh zhnit |fi ehrdi hm ymo| M-zhni

bidh`it {irh

2  Dcm |fi ehrdi hm ymo| M-zhni bi|qiim |qh othnc|il ymnogi zhnit bi {irh c| cm zhom|8

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g f l

Cmt; Mh C| iuir zhom| hm |fi nomi khomoma |fi` bi|qiim |fi zhnit |fi ehrdit lyi |h

bh|f |fi zhnit qonn bi om |fi tc`i lorid|ohm

2  Qfc| lh hy omeir erh` |fi `cami|od eoinl nomit crhyml c bcr `cami| qfodf cri

dnhtil nhhzt8 

Cmt; Othnc|il zhnit lh mh| ivot|

4  Qfc| fczzimt oe c bcr `cami| ot dy| om|h |qh isycn zoidit c/ cnhma o|t nima|f b/

zirzimlodyncr |h o|t nima|f 8 

Cmt; c/ \fi zhni t|rima|f ai|t fcnuil cml fimdi |fi `cami|od `h`im| he icdf zoidi bidh`it

fcne he |fi hroaomcn `h`im|

b/ \fi `cami|od nima|f ai|t fcnuil cml fimdi |fi `cami|od `h`im| he icdf zoidi

bidh`it fcne he |fi hroaomcn `h`im|

9 Qfc| ot |fi ̀ cami|od omlyd|ohm c| |fi `ol-zhom| he |fi t|rcoaf| nomi khomoma |fi |qh

zhnit he c fhrti tfhi `cami| tizcrc|il b c lot|cmdi ‖l‟8 &\fi zhni t|rima|f he icdf

zhni ot ‖`‟/

Cmt; @cami|od omlyd|ohm :

2

6

<

` B

l 

 ¹ 

ϊ 0 . |hqcrlt |fi T-zhni cml cqc erh` M-zhni