thesis on rsm

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HOW To USED RESPONSE SURFACE METHOLOGY

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Page 1: Thesis on RSM

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Page 2: Thesis on RSM

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Page 3: Thesis on RSM

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Page 4: Thesis on RSM

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Page 5: Thesis on RSM

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Page 6: Thesis on RSM

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Page 7: Thesis on RSM

−% − %∀

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Page 8: Thesis on RSM

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)

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Page 9: Thesis on RSM

∀2( ∗#∋3445%

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&

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∗#∆(∗%0ΕΓ66∃!8∆&6#6∃!8∆&%∀Ε,8

& #8&% ∀Ε < 6∀!& #6∀% Ε + ! Β)∋)−!Β∋

8∗Η&#!Β∋%9

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Page 10: Thesis on RSM

# %

∀∃ &

∀∃ !

∀∃

∋∀∃!

∆ ∀∃

6∗(

Χ

&

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)& Β!(0

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)

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Page 11: Thesis on RSM

&

3

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6∗(&

/ ∀

∗#++,344%∗ ∗#344=%

(#344=%

1 6∗(&6∗(

6∗( &

∗) 6∗( 0 7#+<Γ%

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= Β!)!

Β! Β!&

& Γ 3

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)6∗(

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< &

Β!) &

&

∀∃

+

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Page 12: Thesis on RSM

!#∀3%

6 Χ 26∗(2

3 15 = 6∗(

Γ ,6∗( 6∗(

∀<

∀327Χ

,

Page 13: Thesis on RSM

!

∀ #

%

! &∋

( ))∗

+ ,

∋ ()), − ∋!−&.

!

/

Page 14: Thesis on RSM

!

%

+

∋ + ∀

.+

+

∀ % +

+

+

& 0

(& ∃))∗ 120 ))/,

!

∋()), 3

4

5

+

& 6())7,

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2

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Page 15: Thesis on RSM

∋()),3

4% ( ,

( , ( ,.

− ∀

9 + % +

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: ,

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+

% &

6 2 2

%

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∃∃. (∋)),

(−, ∀

<!+−=(+, = −

> ∀ =(+,

+

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9

<)

Page 16: Thesis on RSM

<2;2 2

! 2 ( ,

( ,

% (&&))∗,≅

&

Α26Β

Χ

:(∋<877,∀

% +

+ + +++ + +

2

+ Χ +

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(,+( , 2

∆ +2

<<

+

=(+,

+∃<

=(∃<∃,

+<

+<

+

+

(!, (1,

Page 17: Thesis on RSM

%∃∃ Ε(<87∗,+

Χ

∀ ( +−+,

∃∃

( +, %

(+, )<Φ)

< !+∃∃ Γ =

≅+< )∗+<++

+−) +

(+, + +−

+ ! Γ

=+ (+,

Γ∆∃∃

∃∃ : (+,

#&: ∃∃∀

! Η

∋ −

. 5 5

∃∃Ι ;: Ι

Ι2 ∋ ∋

Η

<

=

<

)∗

(+,

+

)

!

!

&:

+−

+<

+

+

Page 18: Thesis on RSM

%

%

(ϑ,

%

!

% ≅

( ,

2

+ (∋<877,∃∃ (0))∗,

∃∃

∀ : .∋(.∋,

(∋5 ))Η,∃∃.∋(.∋,(∋5 )),

.∋ +

% ())7,0 Χ ())Η, ;

+(120 . <88),−2&(&

<8Κ7,

− −

2 2 + 2

Λ(+,

+Λ2<(,

+(+,

+! −?(,=(+,(+,

?(,ΜΜΛ=(+,Μ+Μ

2 (

∗,

?(,Λ=(+,Μ+ΜΝΜΜ (<,

Page 19: Thesis on RSM

?(,Λ=(2<(,,Μ2<(,ΝΜ (,

%(, 2<(,+ (<,

%(,?(,=(+,2<(,+

∗∆

+ +

+ + %

+

%

&

+ %

<8Η) !& 6

% ∋(∋ <8Η8,

∋ ∋ 2 ∋ (∋&,

− 2

∋&

µ

σ

Χ + >

ε <2α. &

+

(+,

=(+,

+

?(,

<

<

. µ

5 σ

Page 20: Thesis on RSM

(&&))∗,

Φ2<

(&&))∗,

% + ∋ 2<Ν

% ∋&

%

∋& %

∋& +

& ∀ ∋& #

#

(−;.,−;.

+ &∋ +

Ι2

()),%

2 +

%#+ % .∋

!(. ))Γ,9%+ 2

!

(−,

(−,+% −−

(0))7,0

9 . ())Γ,#.∋ #(.∋&, .∋

(&.∋, :

<∗

σ

εΦ <

< α

µ < α Φ < < α

σ

Φ Φ < < α

σ

Page 21: Thesis on RSM

7+−−+

72−−(!,+(1,<))

& +

∀ & ())Κ, 3

∀ # ∃

∃ 4+

∀ #

%

% (0))7,≅

5

:

% +

+

(+,Λ(+,∆(+,Ο)

(+,(+,(+,

%

+

<7

!

2Η2Γ22<)<ΓΗ∗

<

Γ

Η

7

Κ

/

8

<

<

8

/

Κ

7

Η

Γ

<

22<)<

(!, (1,

ϑ <∗ ϑ

Κ∗∀

∋+

<∗ ϑ<∗ ϑ<∗ ϑ

+

∗∀

Page 22: Thesis on RSM

≅ (+,Π) (+,Θ)&

((+, Λ ), 0

+

Λ((+,Ο),+∈

− (+<++, :

!+ Κ

0 (+<+,

Κ∆

+

0

% (&<8/8&1<88Γ,≅

Ι

; ∋(; ∋,

&; ∋(&; ∋,

&∋

&

&

!

(&))7,≅

6

&

∃ %

& ( 1−;,(−# ))∗, ∃

+<

(+<+,Λ)

+

(+

<+,

( +<+

,Θ)

(+<+

,Π)

+< + + +<+ +

Page 23: Thesis on RSM

% %

(<88∗,≅3∋

∃ ()

2: ∃

%

Ρ % 0

Ι

%

% ≅ ∃ ( , +

2

% ≅ ∃ ( ,

2 ∀

())∗,+ ≅

% ≅ ∃ ( , +

% 5 ≅ ∃ ( , +

% (Ε))Η,≅

∗ )

%% # + ΓΓ7&

&;!(<88<, + % # Ε

())Η,

+ & )

∃ +

<, ∃(+,ΛΜ.Σ(+,Τ∆Μ

, ∃(+,Λ.Σ((+,∆.Σ(+,Τ,Τ

Γ, (+,Θ)

(+, (+, (+,

+

& 2:

+ ( /,

%

</

Page 24: Thesis on RSM

+

− 2

% (<888,

(<888,

/∆% 2: ≅ !

Λ+ ∃

8(−))/,; :

∀ + ;

82 (−))/,

#∃% ∀&

+ 2

Ι2

∀ .!&

.+ !

. %

∀ + . & +

<8

1! +

(+,+∆

!

∆1

Ι

. .+

(& ,

6.

.

Page 25: Thesis on RSM

+ %

&∋

∃ &∋ ∃∃

(− ∋ ))Κ, ∋ (∋ 1 <88∗,

(1 1 <88), ∃ (? ))7,

Ι

&∋

& &∋ %

&∋

Ι+ + &∋

%

&∋

<)∆ ∃ &∋ (,

)

Page 26: Thesis on RSM

!

∀#∃%%& ∋( ) ∀∋(

& ∗ +

, ,( −&

− +∗ . ( /

∗ 0 &

∋( ) 1 ∀

∀ −− − 2 ∀#−

∀ ∀∋(3%45364

7 ∀&−∀&

∀∃&−∀ −.

8 (

(

9∗

+ ( # & ∀∀∗

7 ∀ 2&

∀ # & 2∀

# & − /+ ∀

. & −∀ &

( ( − 1 +

89:− − 7− ∀

( ∀,∀ # & ∀

2 &∀& &

;

Page 27: Thesis on RSM

/2&;

89: +# −

− 7

∀−∀ ∀ ∀&

−−89: − & ∀

+ ∗ −∀

(∗ ∗ ∀

+ , ( ∀ (

& − +

(

+ ( & #−

& & − #

− +# & (

/;

2 ∗ ∀

+ + − & & ∀

∀∀ ,

/;< ∗

∋ ∀# (

∀ &# &

;;

Page 28: Thesis on RSM

− −− ( ∀ ∀

&#+ ∀& & − ∀

7 ∀( ∀

8 & ∀ −∀

∀+# −

7 −&&∀− ∀

∀ − &# +

1 1 ( &∀ (

7 ( +

−∀ ( #− ∀−

− ∀ ∃&−(

( − ∀ +

∀ 1−

+ & 89:& & # ∀

+;=0−/8 ;//8 −/ /8

//8

+&=− ∀+(

+ 11

−∀ & 1−1 − & − 7

( ∀∀ 1−+

>//8 & −− >//8∀∀

( & ∀+ >//8;//8+;//8

;; & −−; ;− ;;?≅ 7 &;

;//8 −− −∀ ; ?3 ∀ /

&&;//8 −− & −∀

/<;; ;

;//8, /(

;

Page 29: Thesis on RSM

& &−∀ − ∗ 2 ∋

∀ &

2? ∋?

& (

7 ∀#& − &2

∋+∀∀

2∋?

+ − /≅

/≅<Α 2 2∋

+2∋ 2∋ ∀&

2?Β 2 2?Χ∆

∋?Β ∋ ∋?Χ∆

2∋?Β 2∋ 2∋?Χ∆

2&− #&

∀&

+∀<+∀ ;;

+& ∀ ∀ &

+∀ & 2 ∋+ &

∀ ∀ / (

;≅

7 2 ∋ 2∋

;

;

;

;

;

;

;

;

;

;

Page 30: Thesis on RSM

,2&−1<1 2 ∋

−1Ε1 ∋ +2∋ 2&∋

∀ 2 ∋ 7 7 1Ε1 −

+∀ + − ∀−∀

# ∀ − ∀ &

) −( ∀ ;; &

+∀;

+∀;<+∀∀−

Φ +∀−

2?=ΕΕ%Ε=ΓΕΕ3?=

∋?=Ε=%ΕΕΓΕΕ3?Ε6

2∋?ΕΕ=%Ε=ΓΕΕ3?=

+?ΕΕΕ%ΕΕΓΕΕ3?;

2?Γ 2?=Γ

∋?Γ ∋?

2∋?Γ 2∋?=

+ ?+Η≅?6;

+ ∋ &∀2∋

− ∀2

7 ∀−∗∀ /

2∋( &2 ∋

/<Α ∀

;

!∀

:Ι2ϑ0:

Page 31: Thesis on RSM

+ ∗∀ − & 9 ∀

∀− ∀& & 7

& ∀

) ∀; & &

& −

7 ;//8 ∀ ∀; ∀−.

−−

;==

) & ∀∀;//8

+ ∀∀− ∀ 2=&

& 7 ;//8 ∀ ∀ =&

∀ .

/ ;≅ −

≅ .2∋8

%;=& .2∋228∋∋88

≅=& .2∋2∋828∋8

≅=& .2∋8

+ ;//8 − ( ∀

−& +

&

) Κ&

Κ?ΚΕε

9 # &∀Κ2&

( ϑ−

& ∀

Κ ΛΚ

& Κ −Κ

−Μ ( − ∀

7 − ∀ ∀

;%

Ν

Ν Ν

:

; :

Page 32: Thesis on RSM

∀− ∀& + ∀∀( ∀( /%+

;//8 & &− −∀

− 7− 2 ∀

∀∀ − 9

; &# &− &+ ∀&

& − 7 − ∀&

2 ;

/%<Α ∀

/ − # − ∀

∃ ∀ ∗ −∀

&∀2>9Ο22>9

Ο2 +2>9Ο2& ∀ &#∀

/ (

/ # &=−∀ ∀ & ∀ 7

( −− ∀ &

Α ∀ +∀&∀ ,

+∀<+& &

+ ( &

+ 2−

;6

#

#

∃%∃&%∀∀∀%∃

∃%∃&%∀∀∀%∃

∃Σ∋

∃Σ∋

∃%∃&%∀∀∀%∃

%∃&

%∀∀∀%∃

∃Σ∋

∃Σ∋

∃Σ∋ ∃Σ∋ ∃Σ Σ∋

∃Σ∋ ∃Σ∋ ∃Σ Σ∋

Σ

Σ

; Σ

Μ #

Μ#

()

∗#+,

−+,

(&)

Page 33: Thesis on RSM

+ 2−

+,

# & ∀ +

7 ( + ,

,22∋∋ 2∋2∋+ ,:

++ ∀&

+?2Ε∋Ε2∋Ε:

+,∀

& &

7,−∀ ,∀

+ , ∀∀ ∀

/6/ ( 2 ΣΣ Σ;

;;&, & (− &

− ∀ 27 &∋ 2∋−

− ∀ ∋ 2∋7 &

2 ∋ 2∋ − −

;3

Σ

Μ #

Μ#

Σ Σ ΣΣ

≅Σ Σ

Μ

#

Μ#

;

Σ Μ Σ Σ ;

Μ

#

Μ#Σ Σ;;

ΣΣ Σ;

Μ

Μ ΣΣ Μ Σ Σ;

+

Μ

#

Μ#Σ Σ;

22

2∋

2∋

Σ

#

#

Σ

#

#

Σ

Σ

;

ΣΣ

;

ΣΣ

;

∋∋

2 2

;

≅∋

∋;

≅2∋

2∋;

Μ

#

Μ#Μ;

Page 34: Thesis on RSM

/6<Α 2

2& ,∀ ,

+ : & :,−

∀ 8−

,∀−&∀ − :7

9 ,−∀ − ∀#&

− +, & &.

− Π + − ∀

∃Γ.2

∃.2

+/Γ/=∀ & ≅&

∃Γ+ Μ/ΓΘΓα≅ϑ=−Ρα&α 7− ∀:

&− ∀:−/Γ &

− ∀

7 ∀−∀

& &

+( ;−∀&2 ( : :

: &

;

::

/Γ:

:

: :

;

;

:;

:

:

; :

∃∋

∃∋

∃∋

∃∋

∃Σ∋

∃Σ∋

∃ΣΣ∋

;

::

;

Page 35: Thesis on RSM

+ &∀#;//8 ∀ ( +( &

, ( & ∀# ∀−

∀ −∀+ ∀ ∀− ∗

//8+∀//8

∀( //8 ∀ ;

Η; ; + //8∀∀− &.

− +&&∀( &

=−∀∀

+ & −

&&∀ 2 (∀

2∋?7

&, &7 ∀+

∀ ;= 2∋ &∀ 7

& 1Ε12 &∀

##−∀ &

+∀%

+∀≅<; ;= ∀

9∀− &+∀≅ & 2∋

−∋2 2∋ 2∋77& ∀

7 ∀− //8

& − ;//8 ) ( &

2//8? ∋//8?Β 2;//8Ε ∋;//8

∋//8? 8//8?Β ∋;//8Ε 8;//8

//8? 2∋//8?Β ;//8Ε 2∋;//8

+ , & ∀

& ∀

+ # //8 &

+ ∀ ∀7 (

Γ

7 2 ∋ 2∋ 2 ∋ 2∋

;=

Page 36: Thesis on RSM

2?2Σ7?2Σ2∋?2;∋?∋ 2?∋

∋?∋Σ7?∋Σ2∋?2∋;?2 ∋?2

?Σ7?Σ2∋?2∋;?2∋ ?2∋

7 & &=& & =&

7 =& − 7

&& ∀+

− 2 &

& ∀ , !ΕΜ − Μ

+∗ .

777 > & ∀

&;=&

7Ο & =& ;=&

&=

Ο &≅=& ;= &=&

8 ∀ ∀

Τ 8 ∀ ∀ ∀ ∀

/(;= & 777 ;777

!

+− ( 89:/

∀− ( ∀+&

∀ & (

2 ∀− Κ

Κ?ξξ;ξ

∀∀ & −∀ ξ1 ξ; ξ −(

ξ∈ Χξ ξ(∆ξ;∈ Χξ; ξ;(∆ξ∈ Χξ ξ(∆

& # ,( ξξ;ξ

Κ?ξξ;ξ

7 ( & &

∀ε∀+

ξξ;ξ?ξξ;ξΕε∀

Τ ϑ &− /(

;7776; &2∋8:/Α?7 2∋8?7 777 7Ο7 :/Α

:Α/?2∋8:/ΑΥ2∋8?7

Page 37: Thesis on RSM

−( ∀ ∀ ∀( :Ι

&?∀− Φ ( &∀

− ∀ + ε

, Κ ε∀ = ,

∃ ,2 &9

# = ∀9

∀ ( &

∗ε∀

+ − ∀ & 2.

, ( ∀ ∀+

ε ε∀ 2−(

7=( ∀ ε& ∀

& ∀& .

:Ι?(

(;(Εε

&((;

(−#=

7∀( ∀− ∀ &

;

+ ∀ (

# & 7 , ((;(

∗∀+ (( ∀

−∀

((;(?∀ΓΕ∀(Ε∀;(;ΕΕ∀=(

7 ( ∀ ? Ε # &

∀ ,(

;

& & ∀, # & 7

, ∀?∃&−& ∀Θ , ∀

Τ +∗ −∀ − / & = ∗ ∀ ∗∀ − Ι1Ι+=

&

;

:Ι ∀Γ∀ (

∀;( ;

∀ (

:Ι;∀Γ∀ (

;∀;( ;;∀

(;;

:Ι∀ ∀Γ∀ (

∀ ∀;( ;

∀∀ (

∀∀

:Ι (

(;

(

ε

:Ι; (

; ( ;; (

;ε;

:Ι∀ (

∀ (;∀ (

∀ε∀

(ξξ 0

∆ξξ0

ξ ξ(

;∆ξ

ξ(ξ

;

Page 38: Thesis on RSM

7 ( − & ( ς

:Ι?Ε

&

& − −

2 & ∀ &,

+ ,

?:Ι=

+ ε&

7 # & −,

0 0 # & ∗ :

∃ & ,

: ∗ −−0&

7∀−0 ∀

?1=1:Ι

9# & (

2 − ( ∀

∀7 ( − (

∀ ∀&& ∀ Τ7

− 1 , ∀= − (/3−

, −−

2 /

& , &∀∗ & +

+9+

&

− & &

+9+, − +, &

+9+?Ε:

ς &∀ ∀∀&−∀∀ & Τ / ( & −∀ ? ∀Γ Ε ∀( Ε ∀;(; Ε∀;((; Ε ∀(

; ∀ ?∀ΓΕ∀(Ε∀;(;Ε∀(Ε∀≅(≅

; (?((;(≅?(;∀?∀; ∀≅?∀

:Ι:Ι

:Ι;

:Ι;

( (

( ; (

;

( ∀ (

;

∀ ∀Γ

0:

;

+9+

:Ι :Ι

;

;

Page 39: Thesis on RSM

/3<9 ∗ ( 0

# ∃% !

2 ,

7 (( &&−

∀9 ( /(&

&

((;?∀ΓΕ∀(Ε∀;(;Ε∀;((;

&

((;?βΓΕβ(Εβ;(;Εβ;((;Εδ(;Εδ;;(;

;

+ & ∀− −

:Ι?ΕΕ

&

− −∀−&

2 0 & ∀

?1=1:Ι

∀ ( :Ι ( &

?1=1ΕΕ ≅

+≅&− ∀∀ ∀

89: +≅

ε

(

7 −∀

9

−∀(

(

9∀−

βΓ

β

β;

β;

δ

δ;;

Page 40: Thesis on RSM

& :+

ε& −

/≅

?1=1Ε

#

:Χ∆?:Χ1=1Ε∆?:Χ1=1Ε1=1∆?Ε1=1:ΧΩ∆?

:Χ∆?

+ ∀

)

?

#

:Χ∆?:Χ∆?:Χ∆??

:Χ∆?

:∀−

:Χ:∆?<σ;

& σ − + ( ∀

:Η=∀ ∀ − σ;

≅&∀

:Χ∆?:Χ1=1ΕΕ∆?Ε1=1

:Χ∆?Ε

&?1=1 /,∀&

+

:Χ∆?:Χ∆?Ε?Ε=?Ε=

:Χ∆?Ε=

+∀&=∀

/∀− :

:Χ:∆?<σ;Ε11<111=1 %

:Χ:∆∀ −

7 ∀ 1∗ 1 +

Page 41: Thesis on RSM

, &

:?11<111=1

/ #

∀ #∀& ∀∀

∀− + −∗

/& ∀ &&

∀2 &∀∋7 2, ∀

+# ( ∀ −

%7 ∀ −

%∀−− σ∀

7 ∋ ∀σ

/<8 ∗ & &∀

&

# 2

−∀ Τ

ϑ ε∀ ∀>78−

ε∀ +

∀ −∀ + −

Τ 2 −& ∀ −∀5Μ ;ΓΓ3

%

;Γ δΓ;

; ≅

≅%; 6 % ; σΓ6

Κ

Κ

Κ

Κ

(

∋2

%6

6

;

?;ΕΓ(ΕΓ;(;

?∀ΓΕ∀

(

σ?Γ6

?;ΕΓ(ΕΓ;(;

?∀ΓΕ∀

(Ε∀

;(;

σ?Γ6

8

:Χσ∆?Γ3;

:Χ∆?Γ%Ε6(

:Χσ∆?Γ%3

:Χ∆?;ΕΓ(ΕΓ;(;

( (

Page 42: Thesis on RSM

∀ ,7 ∀

∀7 , ∀#∀

& − −− −∀−

7 & # ,

+#∀( −

7 −∀

&− 2 ,

&−

+&

∃Γ.β?β;??β?Γ

∃.βΞΓ ∈[ ∆

&

+

7/ΓΘ/α,∀== ∀Μ

+ & ∀ (

∀ 2&# −

& − ∀.

∃Γ.β?Γ

∃.βΞΓ

+

& = ( ? 1= σ; − ∀

σ;: + ΜΨΓΨΘαΗ;==

+ −∀

∀ ∀( −∀∀ 2∀β ∀ &

& ;−− =+∀−

6

:

:

Γ∀

σ;

;

Page 43: Thesis on RSM

&.∀:Ι? ∀;:Ι?;;

7 −∀

∃Γ.?Γ

∃.βΞΓ ∈[ ∆

&Ψ; ∀ ,

7 Ψ; & ∀ ∀ ;

∀;

Ψ;?=;

+ Μ/ΓΘ/α==

∃∀

+ # ∀& , +

(

− ∀& ,

+, : ∀ & +

− ε∀

ϑ:+ − ∀

∀ # ,09/ ∃ , ∀

&

:?ϑ:Ε09/ 6

+ ϑ: 09/&#&&

∃Γ.

∃.

+

& − #&− +

∀Μ/ΓΘ/α = =) Μ− #

− +∀− & ,

3

/Γ;

:

:

Μ

Μ;

Μ

Μ:Ι ;

;

/Γ09/

ϑ:

09/

ϑ:

Page 44: Thesis on RSM

2 ( #,

;

+ − (

∀ ;− ∀& Γ ∀ && ∀

∀ ∀− ( ∃ (

& %2 ;& ;Μ

7 Μ

∀ ∀ :+ (∀ ;&

∀?9;Μ

+ ,

∀ −+ ∀

∀∀ /Γ2−

/Γ∋ 7 7

∀&) −− (

− ∀ ∀∀

/Γ<∀>78

− ∀ ,

−∀/( / &&#,

−&# &∀

# ∀ ,

+

;

+9+

:

+9+

Μ;

:

+9+

;

Ζ

ϑ Κ

2∋

Page 45: Thesis on RSM

ϑ:

=

7 &# ϑ:&∀∀ (

Κ?(Ε(;Ε(;;

Κ?(Ε∀(;

/< , Ι;−∀

∋ !

2∀ (−

,∋∀−− (

− ∀ &

.

?−Χ?σ;1=

ΟΧ∆?σ;11=

:Χ<∆?11=1<1

& − −∀

Τ+, &# 89:∀

∗(

∗ΟΧ∆&

2 ∗ − (&∀ (&−

∀+ −& ( (

−( =&−∀ 7

1( ∀& −

(∗ −1 1 (∗

Τ /(((;?∀ΓΕ∀(Ε∀;((;Ε∀(; ((;?∀ΓΕ∀(Ε∀;((;Ε∀(

;Ε∀;;(;

;1?Χ(((;(;∆ 1?Χ(;

;∆

≅Γ

7 −∀(

7 −∀(;

Κ

?(Ε(

;Ε(

;;

Κ

?(Ε∀(

;Ε(

;;

Κ

?(Ε(

;Ε(

;;

Κ

?(Ε∀(

;

Page 46: Thesis on RSM

− ∗+& /;& 89:

−∀∀ &−

/;< ∀

ΟΧ∆∗

∀ ΟΧ∆& / − ∀

# /&∀∀ ,

& − ) ∀

/<− ∀

+ & 89: (

, )# ( ∀∀&

(/;9 ∀

− −− ∀ ∃

− ∀ −∀

8

∀ 89:

, −

7 −∀(

7

(

;

ΟΧ(

(

;∆

0 −

8 ϑ

Κ

?βΓΕβ

(

Κ

?∀ΓΕ∀

(

8 ϑ

Page 47: Thesis on RSM

2 89:

;=0−//8 ;//8

/ /8 //8∋(%

8 8∋(

>=0−//8 >//8

(

ϑ#=∋ ϑ#%Γ

∋(=∋ # ∋(%Γ

7 &∀( −∀ &#

∋()

+ ∀

∀ , &−−∀−∀+

− ∀∀ (

Ε=−

))

∀ & ;//8∃&−

//8 ∗ 1− ∀

∗∗

+8 ∀;//8& (

8/≅ ∀λ ( ∀

/≅<; 8 //8

+ 8 − ∀

∃&− λ∀− ∀

− 2 8 8∀

#//8∋∋8+ &8 ∀&

8

≅;

ϑ

2(ϑ

ϑ

λ

8

(

(

//8

Page 48: Thesis on RSM

())

>//8 ∀ − ∀+

=7 /≅=0−/ −∀

− 7 ∀∀− & ∋+=&

.

,

((;(−

(;(;

;(;−,

((;((((;(;(;(

;((;;((;

;((;((

;(;(;(;

;(;(

;(;;(

;,∋;=&

((;((;(;(((;

;(((;(;(

;(;;((

;(;(;((;

;(;(

;(;;(

;.=&

(∀) )!

7 ; ∀∀ ( ∀ 0

−# ∗

( >78 (#

+

+∀ , ,(

. ∀

∀∀#

7 ∀ ∀ ( + # &

2ϑ∀ 2ϑ

& )

/& /

∋#&: ∋:

∋ /∀&

( ∀∀ 7 ∀

∀− &∀,( ∀

+∀ 2ϑ

∗ ∀, (:;# ∀

∀ 7 ∀

)/∀∀ & −

− + ∀&

) / ) ∀− ∀

+∀ /+ / )

∀ 2ϑ

/

Page 49: Thesis on RSM

2) /∋: , ∀ ∋ ∀ /

+ & −

− 9∋:∀−/[

/∀ /Θ∋: ∀ / −

2ϑ∀7 ) −∀

0

7 ) − ( −

2 ∀ −

/∀+&&

/ /(

&∀ ∀?/<∀ &

− ∀∀&

&. /∀+β&

−/ /Θ & ∀

;− . /Μ ∀ βΜ &

& − /Μ − /Μ Ρ &

+# ∀

∀−

∋) %∀

+ ∀ & − ∀∀ ∴

Α + + 36 + ( 89: 2>9Ο2

∀ 2+1−

& ∗ &# &∀

∀&−∀ ∀7 & +∀−

− ;ΓΓ≅∋;ΓΓ%

∋∃ ∗!∃

+ −∀ −∀ ;≅+&

−∀ , &

∀−∀ −∀+

& −

≅≅

/β β0

:

/ ΜβΜ β0

:

Page 50: Thesis on RSM

− / ∀

∀;= −∀;= −∀∀

∀ ∀= −∀ ,(

∀∀−− ∀ −∀/ − +

−− ∀ ∋

−∀7 +

9 ∀ + ∗ #

∀ − + ==>

>>∀− (∗>1 −

7 & >

/<;;(;;

/& ∗ −(

∃+>∀& ,

Ζ0/ Ζ0/ , :Χ<;∆ ,

− −+>

& >9Φ+ Ζ0/

/ ∀>9Φ+ & − >+−.

&; − +( >+ &

− & / (∗ >+

∀ &

7 − −∀ + −

>1 ∀− ∀ −+

92

7 2

(

(;

&;

&

9

7

>+Γ

>9Φ+ :Ι ;

>9Φ+

>+ Γ

>9Φ+ :Ι :Ι;

>9Φ+

:Ι ;Γ

>9Φ+;

:Ι ;

&

&;

((

;. −∀

&&

;. −∀

Page 51: Thesis on RSM

−>+;(

/ ∗ − ∃>

( ,− >+&?Γ

2 > ∀&

&∀& & −

>−∀

/ (∗ ∗ − ∃ >

(

&−> − Τ

2 ∀ >0−

9 > 2>9Ο2 ,∗ −∀

>7 − +2>9Ο2

& − ∀− ∀

∗ +− & .

&

:−

:− >

8 ∗ −2>9Ο2>

+ +& 9 +∀ ∗∀

−∋(33>; ∀

+ − +1&∀# .

∀ + − & 777 7

∀ ∀ −∀ ∀ +

& ∗ − ∗

Τ 7 & ]⊥ ]Γ−

≅%

>9Φ+ :Ι;

>9Φ+

>0Γ

>9Φ+ :Ι;

>9Φ+

>+; Γ ;

;

> Γ >9Φ+

;:Ι;

Page 52: Thesis on RSM

( & + &

−∀ −∀

+ , (

> − ,,

∀ =# 7∀ − &

∀ − >

+ ∀ −∀

∋∃

8∀∀ −+ & ∀

8 282∀∀ ∀ ∀

(ϑ∀Ο Γ∀

− & 2

+ − ∀

+ 7 82 ∀

&

Κσ(∀ΜΚµ(?

& 8−+82∀ −∀∀

&

∋!∃

2 + −∀ 22)

Γ7 2 ∀& ∀−∀

,& ∀ −∀∀ ,

& 2 (∀

− ; ;;+ ,; (;;?;

& ∀ −∀7 &

∀−∀ −∀, &

(

?βΓΕ1Ε1Ε1Ε1

) &∀∀

:Ι?βΓΕ1Ε1Ε1Ε1Ε 3

≅6

Κ µ∀Γ

∀ (

∀ (;εµ

Κ σΓ

(

(;εσ

(

Page 53: Thesis on RSM

2 (

?∀ΓΕ1Ε1Ε1Ε1

# ∀ ∀ −∀ −

& − σ∗;

:Χ∆? ΟΧ∆?σ∗; Γ

3 # Γ&(− −

& −∀

:_Χ:Ι∆?βΓΕ1Ε1

Ο_Χ:Ι∆?Ο_Χ1Ε1∆Εσ;

&σ;− Φ ∀ −

_Χ∆?∀ΓΕ1Ε1

Οα_Χ∆?Οα_Χ1Ε1∆Εσ;?σ_

;1Ε11Ε11Εσ;

& − ∀ 0 σ_; − σ ∀

:Η=

_ Οα_ &2 −∀ − & −∀

& ∀ ∃ 82∀

&=∀Μ−∗

Οα_Χ∆∀Μ_Χ∆?

&−

−− 2−

+.

7 − ∀&22∀ −∀

>& &(

+( ∀ ∀−∀ &

2

∀ (∀ ∗

= −∀ ∀ − ∀(− =

=

2& ∗

(%

7 ∀ ,#( ∗

∀ ∗ − ∀

∃&− &#∀ ∗ &

+ −

( >(&

≅3

(

Page 54: Thesis on RSM

! ∀#!

% &∋

(

) ∗∃

∀#

+ ,

&∋ ∃

&∋

)./001∗2 %

) /∗

%∀# )3∀∗ )∀.&∗

)!∀#∗ )!++∗∀

%.)/00/001∗

455/#455/6455/#)455/∗∀ .)4557∗#

4558 −)4559∗! %

∀#

∃ ∀#

0

Page 55: Thesis on RSM

% :

( 4∀#

( ∀# 2∋

∀# &

%

∋2 &

&2 ;

2 <#%∀

.,. ∀ .&

; ,. − <#%∀

!,

#%

∀=

.<> ;

!

∃ . !

<∃ 3 <,<

>

∀ # + .

#

# ∀

/? %

∀#

∀#

(

# )# /010∗

∀#!

%

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=

75

∀#

! #

3

∀ .

&

Page 56: Thesis on RSM

∀#

∀#(∀#

%

+(2(ε

%

)!∀#

4∗

2∋ 2∋=

(2∋

≅ ∃

)#455/∗#,

∀#

(

( ∀#

∃∀#

%

<# ( <#

) ε ∗

<#

=%

% )Α/00∗

∃=

Β

∀#

∀# !

+

+

+

+

+

∀4 Χ∋#

∀ Β4 Χ∋#

∀ Χ∋#

# −

4?! ∀#

7/

Page 57: Thesis on RSM

& Β =∀#! ∃

∀# &∋ &

& )/010∗ . . )/005∗ ∀# ∀

)/001∗ ∃ )/000∗ ∀#!=(

)/001∗ ∀#! <Β)455/∗

= ∆ <)4558∗ ∀#! ,

% , ∃)455/∗

<)4551∗

∀#

!% =∀#

Ε ∀# ∀#

∀#!

Χ∃ )/000∗ %

% ∀#

.

&

# %

) ∗

%

2 =

#)4:/∗&

)Α455:∗ ,);#∗ %,

)Φ#∗2∋ (

≅ ≅ (

%, 2∋

;# Φ# 2∋ ::( 2∋

∀#

( ;# Φ# ≅

, % #

%.

;# Φ#

; ,#

. )/00∗

# #)∃/01:∗

74

Page 58: Thesis on RSM

<∃#)3/090∗

#)/004∗

Φ,#

∃)Α455:∗

∃)∀ 4557∗

>#)<455:∗

( ,

( ;2&!

/8, 4, & /! ;2&

# )##∗ ,

! %/Γ

## &/.

4,/8,

##

&/,/8,. # #

7:

)!∗.∀ ).∗# #

Η/ Η/

Η4

Η4

Page 59: Thesis on RSM

<∃#)<∃#∗

##(<∃#

%

Β

Β!<∃#Ι4

Ι/5 &4!#

)∗(<∃# );/07:∗

<∃# ##

∃ <∃# &

2∋ <∃#

<∃# =

=)(

/014/00∗<∃#)/00:∗!<∃#

= &4.

<∃#

Η )4558#4551∗

&4?/5,<∃ <<∃

& ∀# 2∋ ::

( 2∋

Β∀#∃=2∋

&,

%

2∋

7

)!∗<∃ ).∗<<∃

Η/ Η/

Η4

Η4

Page 60: Thesis on RSM

( #3Β)3Β

455/∗

% (

(

)<455∗! )

∗ 2∋

Β= ϑ(

% )6455/<455∗

! Β

!

%

,

,

,,

!

∀4 ∀ Β4 :::

)∗#

##∋#∋

)3Β

/009∗(

ϑ 2 % ∃

77

ρ/

∀#∀#∋Κ

∋Κ

/

∀#∀#

4/

∋Κ∋Κ

4

Page 61: Thesis on RSM

− )!Κ∗

)∀#∋∗ϑ )− 4559∗ =

)∀!∋∗ )∀!!∋∗ )6455/∗:

<!Κ ∀!∋ %

%( ∀#∋ ∀!!∋

+ Η

∀#∋

∀!∋

∀!!∋

Ι/

:?Η

, % %

% % %

2∋ ,

,

/∗ ∋,2∋

4∗ ∀ ,/

:∗ ∋ Η)∗Ι∀#)

)∗∗,∋Κ))∗∗

∗ ∀2∋

7∗ 2

(∀#%Η)∗ ;∀∋##

)/007∗(

ϑ ∀#∋ )∋(#∋∗ # )/010∗

78

/

∀# ∋Κ

4

∀#

∋Κ

σ∀#

∀# ∋Κ

/

∀# ∋Κ

σ∀#

Η

/

Page 62: Thesis on RSM

)∗,

Ι)∗,/≅

, % ,,, )/004∗<,

,, ∃<)<455∗ ;2

,,, %

<,,, ,,,

(

! , ∃2∋

Λ ,, ,

Μ) 4554∗&

% ,,

∀ = ∀

(

) :::∗

∃= =

!

% )3Β 4558∗ .

)Χ/007∗

∀#!(::7

∀#! !

(

! Β

&

∀ Β4) ΝΟΠ∗

∀ Β4( Β

∀ Β4) Β Ν,Π∗ ∀ Β

4

! &:

( =

%(#−∀==∀ Β4

79

Page 63: Thesis on RSM

!#−∀ ∀#%

(

%

∀ % #−∀

∀#!

= % (

; %

( =

&:?

3 )/085∗

%# = 3

Λ # Μ)∋/00∗#

∀#!∀# #

% )2!∋ϑ∗

3∀ %

ϑ 2!∋ # 3

71

Χ3∀/

β ∆

∀ Β

4)5

Ι/,/

∀ Β

4Θ∀ Β

4

∀ Β

4Ι∀ Β

4)5

∀ Β

4)

ΝΟΠ∗

Ι/,

∀ Β

4Ι∀ Β

4)

ΝΟΠ∗

! Ρ>

∀ Β

4Ι∀ Β

4

∀ Β

4)

Ν,Π∗

Ι/∀/∀

∀ Β

4Ι∀ Β

4)

Ν,Π∗

∀ Β

4Θ∀ Β

4

∀Ρ>

∀ Β

4Ι∀ Β

4

#;

!

Χ Χ

+ +

Χ

+

& < <

Page 64: Thesis on RSM

∆)∗ =

(σ4 ∀)∗∆)∗ ∆)∗2

(2!∋Α=

# )/010∗ 2!∋ #

!)/001∗ 3∀ =

# )455:∗ 3 !++=

%

∀ )∃ /09/∗ );/005∗

).455:∗∀.&

β Φ

∋ !

Α)∀ 4557∗

∀.&= (

∀.&

( % #

∀# %

,

#)/001∗ ∀# 3∀= ==

∀Β )455/∗ ∀# 3∀ 3∀

6)455/∗ 3∀∀.&!∀# ∀#

= )

∗ ) ∗ )

∗ )

∗ )∗

=

70

∆ ∆σ4∀

∀.& /

β Φ

Φ σ4

Page 65: Thesis on RSM

;Γ ∀# 3∀ ∀.& !∀#

! / : : 4

: : : 4

∀ / 4 : /

∋ : / 4 :

: / / 4

: / : /

?#6)455/∗: 4 /

# )455/∗ 2∋)∃ <∃#

∗ = )7 =

2∋∗ %)∀#3∀∀.&!∀#∗

)4 /:∗(

6 )455/∗ & ∃

<∃#

6 )455:∗ = ∀# 3∀ ∀.& = ,

= 3∀∀# ∀.&

∀#

∀.&

& )4557∗ ∀# ∀.&

= %/5

)49∀# 41∀.&∗!

∀# ∀.&

# )4558∗ 3∀∀# !∀#

2∋ % )<∃# ∃ ∃ Η )2

/000∗ #7, ∀ ≅

;/5

( 2∋

% ΛΜ2∋

!∀

( ∀#

( ∀#

%(

85

Page 66: Thesis on RSM

%∀#

%∃

∀#(

%

8/

Page 67: Thesis on RSM

! ∀ #! ∃

% % & #

∃&

∃∋ ! ! # !%

( ( %

# ! &

( ! ∀

( !%

∃ ) %∗

# ) (

( !

% ! &% #

∗ ! % % %

%

+ ∗ ( !

∋ ∃ #% ,! # #

−∃. ∃ ∃ ∃/01∃.,1∃.∃∃,1.2∃.∃31∃

# ∃ & % %#

−∃/0..3

+ ∗ ! # ∃ (

4

Page 68: Thesis on RSM

#.% 1 ! #

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Page 69: Thesis on RSM

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Page 70: Thesis on RSM

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Page 71: Thesis on RSM

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Page 72: Thesis on RSM

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Page 73: Thesis on RSM

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Page 74: Thesis on RSM

∗∃ % ∀% %

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Page 75: Thesis on RSM

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Page 76: Thesis on RSM

−:/&%Β

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Page 77: Thesis on RSM

∋< 11119;ϑ !

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Page 78: Thesis on RSM

∋?<: ∗):

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Page 79: Thesis on RSM

∋7< 9;ϑ. 9;ϑ9;ϑ. ∋∗

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Page 80: Thesis on RSM

∋∗ .4Ι.7 .7Ι.4 1Ι. Ι. Ι.1 4Ι7 7Ι4 1Ι Ι

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Page 81: Thesis on RSM

≅; 89:

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Page 82: Thesis on RSM

∗ # % %%

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Page 83: Thesis on RSM

?7

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Page 84: Thesis on RSM

∋.<∋&% ∋∗

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Page 85: Thesis on RSM

()

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Page 86: Thesis on RSM

!

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Page 87: Thesis on RSM

∀∀

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Page 88: Thesis on RSM

1>7 ∃ ∃ !

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Page 89: Thesis on RSM

∀ ! ;? ∀ ∆1

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Page 90: Thesis on RSM

!

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Page 91: Thesis on RSM

2 ∃

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Page 92: Thesis on RSM

!∀

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Page 93: Thesis on RSM

!

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Page 94: Thesis on RSM

5/∋ ). ) ≅∗5/∋.

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Page 95: Thesis on RSM

&

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Page 96: Thesis on RSM

Α≅∗5%∃

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Page 97: Thesis on RSM

∗ ∗

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Page 98: Thesis on RSM

(

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Page 99: Thesis on RSM

4 6 ∋

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Page 100: Thesis on RSM

∀ ! 7

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Page 101: Thesis on RSM

/&

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∗(

!

!

!

∀#

1

∗(

1

1

Page 102: Thesis on RSM

!)%∗1.

∀ /&∀

/&

)%∗1.

/&

&

!)%∗1/∗/1.

#/&0

)%∗1/∗.

( 0

)%∗1/1. ∀

( /&

%∗1∆)&. ∆Ι). ∆Ι

). ∆Ι)/. ∆

#

%&

& /&

# /&

Χ%∗3 #

&#

)<4∗/∋<415∋.)<41/∋<4∗5∋.

# & #

&

%# %< &

%∗= )&∋∗&∋1&∋3.∃ &

)∗∗.)11.0 &

+

/

4 5

/

)&. ). ). )/∗.

)/1.

Page 103: Thesis on RSM

/& &

0

∃#%<& #

%∗3∆&

%∗=∆∋

# ∀

!

7

/&

∀ /& &

0

5 7

&∋∗ 5∋Χ/∋ ∀ & )

.&∋∗ 5∋ )&∋∗/∋.

&∋1 5∋Χ&∋∗

+,

#

%

&

&

#

&5∋&∋∗

≅+− &&∋∗&∋1

≅,&

&∋1&∋3≅,

&

&∋35∋≅+9

&5∋&∋∗

≅+− &&∋∗&∋1

≅,&

&∋1&∋3≅,,

&

&∋35∋≅+−

)&.). ). )/.

)&.

).

).

)/.

<)∗∗.

<)11.

2∗∗

2,2 2∗3

2,2

%∃∗%∃1

%∃1%∃∗

/∋

5∋

&#

Page 104: Thesis on RSM

/∋

∀ )∋.

(

# 5 ∋6

(

%∗9( ∋

%∗9∆<# (

∋ %∗1/1

& ∀ &

5∋/∋

∋ &

)Κ+2.(

∀ (&

!)88ΜΜ1222.

∃ % &

# ! Χ

/0<∃

#∋5Χ

( #

# )/∋. (

Χ Χ Χ /0< )−>Β

∗ . #

%/∋& ∃

2+ /∋ %∗− & (

∀ & /∋ 33

5∋

# Λ

Λ 5∋Χ/∋∗ ( #

++

&∋1

08 08

08

1

3

/∋

&∋∗

&∋3

= 0808

0<8

0<8

5∋

Page 105: Thesis on RSM

&∋#

/∋3/∋1∋ /∋3/∋1

/∋∋

/∋

/∋5∋

)/1%∗1. # ∋

7∋ Χ Χ

%∗−∆∋

/∋ &

∋/∋ 5∋

& !

%<& #)5∋∋.

5∋∋∃ ∀

(

%

# %∗ Χ /0< 5∋∋&

/∋= 5∋5∋ %<&

∋&/∋=/∋∗

∗22

5

/

&

5∋

/∋∗

/∋1

/∋3

/∋=

/∋9

/∋−

( ∗

) .

( 1

) .

Page 106: Thesis on RSM

5∋/∋∗&∋∗&∋1&∋30 /∋=

5∋ & /∋∗

(

)5∋/∋∗.%

# (/∋

;

5∋∋ (;#

∃7)/∋∗Χ/∋1.∗2 )/∋1Χ/∋3.∗

)/∋=Χ/∋9.)/∋9Χ/∋−.∗∀ 11 %<&

5∋∋/∋∀ 5∋∋

Χ ∃/∋)1133.

%∗∆#5∋∋

%∗,5∋∋ /∋5∋∋

∃/∋3/∋−∃

/∋3/∋1/∋−/∋9

/∋3)/∋−.5∋∀ 5∋∋

∗2∗

9Χ−

/∋=

/∋9

5∋

/∋∗

/∋1

/∋3

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/∋9

/∋−

5∋

/∋=

/∋∗

1

5∋

3

/∋∗

/∋1

=

/∋1

/∋3

/∋−

&∋∗&∋1

&∋3

Page 107: Thesis on RSM

%∗,∆5∋∋) ./∋).

1%%/ 1

5∋∋%∗+∀)&./∋∗

/∋1/∋3∀

).∃/∋∗ #

%∗+∆</∋∗∃5∋∋

)&. /∋∗

/∋∗∀%12#∃

1 1

%). ∃

#)

%1∗. 1 &∗

#

∗21

5

/

&

5∋

/∋∗

/∋1

/∋3

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( ∗

) .

( 1

) .

5

/

&

5∋

/∋∗

/∋1

/∋3

/∋=

/∋9

/∋−

( ∗

) .

( 1

) .

4 ∗

4 1

5∋

1

∃1

%∗

/∋∗

∃1

%∗

/∋1

∃1

%∗

/∋3

4 ∗

4 1

5∋

1

∃1

%∗

/∋∗

∃∗

%1

/∋1

∃∗

%1

/∋3

)&. ).

Page 108: Thesis on RSM

∀5∋∋)/∋.( &

# %<&

%12∆<∃ )&.

%1∗∆<∃ ).

∋∀

& (

&

( #

∃ #

∗23

5∋ /∋∗

/∋1

1∆%

1

<∃

5∋ 5∋

1

% ∃

1

1

%

1∆% 1∆∃

Page 109: Thesis on RSM

! !

!

∀ # ∃

! %

& ∋())∗+,∋())∗#())+

− # % ∋%+#

! !

# &.

/& ∃ 0 ,

1

# ∃∃#

%.&

2)3

Page 110: Thesis on RSM

405 %

6#

∃ &/7.

#

∋ +

(8)))) (9))))

∃2):

5; !

4(∀

2<2∋+

# 4)

∋ + ∋=:

+ : 4)

% 5/ 5/

(

; 1>5>34,∀#%&1(,?#

2)9

Page 111: Thesis on RSM

≅ Α Α 5/=:

2 (3

( 99(

4 9(3

3 2∗9

9 9(

8 8()

∗ 2()

9Β)

Β Β)

2) 239

22 2))22

2( 9

24 9)9

23 9)

29 99)

28 9

2∗ 9)9

2 239

2Β 2()

() 8()

(2 Β)

(( 9Β)

(4 (3

(3 9(3

(9 9)

(8 99)

(∗ 9(

( 99(

(Β 2∗9

4) 2))22

(<

2)8

5/1 , 0

&Χ1 Α

01 ∆09Ε#Φ9ΕΓΑ

Χ 1 2∗ΕΑΧ

5/1 , 0

&Χ1 Α<3ΕΑ

01 ∆09Ε#)ΕΓΑ

Χ 1 24ΕΑΧ

0

&

Α

0

Α&

0

Page 112: Thesis on RSM

6 ∃2!

0 ! #

∋,# ())8#())∗+ # #

! : !∃

&# # 0

!

∃ /Η# #/Η

#

(0 2 ∋ ∃2∃(+ # /Η

# # !

#/Η /#??//#

#

?/??/# #

&# / Χ∋(0 +

(4)0()2)(3∃ 9))

∀ #∃ /Η: 0:6∀.

# 6∀. ())4)

!

/Η#

Η /Η #.Ι%,&?

# 2))

3Β8∋2 #4)#4)

! #34)(0 + (4)

∋ /Η +# 2))

! − #2

! ##

&# 00

#

#

#.Ι% #∋.Η62+ ,&?∋.Η6(+

# ,&? ∋.Η64+ .Η62

,

2)∗

Page 113: Thesis on RSM

,,&? ϑ2)))ϑ9)) #.Ι%

,&?Η

# #∗

.Η62#.Η6(.Η64

!.Η6(.Η62,

∋.. + .Ι%∃

∃#

.Η62.Η6(

∋4+? #/Η

#.Ι%

.Η64 .Η6(

.Η62.Η649,

.Η64 3Η

#,&? !2))

# # /,

− #

! −.. #

#.. (8Κ2)08 .Η62#(3∗Κ2)09 .Η64

∃ .Η62#( ∋2)).Η62#(4

.Η64+

4<? .Η62#.Η6(.Η64

2)

6 Λ

.Η62

.Η6(

.Η64

%

Page 114: Thesis on RSM

3</ ,−

2

! Ι 2! ∀

9 #

∃ # 0

∋8+ #

#

#23 #

28

# # Χ23

. # !(98#

.Η62#(.Η64∋9+

9<% ∋.Η63ϑ +

∃ 8(# #

∀ #

2)Β

..

..

, ,

%

Page 115: Thesis on RSM

.%Μ ;

8

∋ϑ28##4)+ ∋ϑ2##29+#

ΑΧ

Α

2 (3 %

( 99( %

4 9(3 %

3 2))22 %

9 9( %

8 8() ?

∗ 2() ?

2Β 2() ?

() 8() ?

(4 (3 %

(3 9(3 %

(∗ 9( %

( 99( %

(Β 2))22 %

8<

5

! 5/

(#2)80/& &.

4)4) &.∋/&.+ 6∀.

∋(4)+29)6∀.∗ /

!/&./&Η #

; .%Μ 8(

.%Μ

22)

%

∋+

.%Μ

Page 116: Thesis on RSM

& #

&. &.

∋+

/&. /&

&∆∀Γ 4(8∗3 4(8∗3

.∆∀Γ ))32∗ ))3)Β

∗<. /&./&

&.∃

2!

# #

!

<&.

%.& ∀ #

# !

∃# ∃#

#,&? # #

222

/&. /&

%∆∀Γ

5

%∆∀Γ %∆∀Γ

Η

Η

∋α ϑ))9+

Page 117: Thesis on RSM

!

# − # %

0 #

&/7. # #

! ∃ .

6∋. 6#())8#6. #())8+%

Η /: ∋())8+

% :

∋())+ !

&∀∋())∗+

,% ,∋())∗+

&

. ∋())∗#())+

1

#

9

1 ∃∋,6..+# ∋5Χ?+

∋5+ 5

% # #

Η

##

∋6#())8+6∋())8+∃

#

#

# #

:

#Α.%Α> 5Η&5 (/0

0 ))∗9)

Β

22(

Page 118: Thesis on RSM

Β<Ι

∀ #

!

#

#

0! #Α!!

#∆∃ Α! ! /

# 0− #

! #

!

5Χ? Ν4)Ε %∋2+

# 5

∆Γ

,6..2 5Χ?2 5 5Χ?( ,6..(

(2) )44 )2) )44 (2)

5

Ν4)Ε Ν4)Ε )Ε Ν4)Ε Ν4)Ε

%

23∗0(∗4 )(40)34 0 )(40)34 23∗0(∗4

2<

0

224

,6..2

5Χ?2

5

5Χ?(

,6..(

5Η&5

∆ ∃ ∆ ∃ 2

Α!

∃ # ∃ #

Page 119: Thesis on RSM

: 0

0

# ,6..2#(

5Χ?2#( Ν(Ε ∋

+ ,5/ 4σ ϑ(Ε ## )2∗Ο 5/ (

5/

,6..2#(5Χ?2#(

,6..2 5Χ?2 5Χ?( ,6..( Ο 5Χ?∆5Γ 5∆5Γ

5

Ν(Ε Ν(Ε Ν(Ε Ν(Ε 0 0 0

%

0 0 0 0 )028 28<3(9 2(9<243

5/ , , , , 7

(<Α

/%∃ 89

%.& 2)0

# &.

#

# #

/Η#

∃ #

2)

! #/

∃2)! ! %.

!

&# # ∀ #

6∀. !

# 220 6∀.

.Ι% ,&? #

#∃

2! .%Ι ∋2)+

2206∀.,&?

## (/

/Η28

/Η28 28)

∃ 2) ! 28 . #

223

Page 120: Thesis on RSM

2)90&. ∃

∃∆∋∃5+

2)<% /#,&?.Ι%2!

,!∋22+

# !

#

Η#

# #!

−∋22?+

22<! 28∋+3(/

∋?+

229

%

! !

!

!

∋+ ∋?+

∆ ∃ 52

2)

2

2)92

2)9

∃ 5 # /. ∃5

Page 121: Thesis on RSM

∆∋∃5+∃5 ∆∋∃5+ 2(

∆Γ ∆∆∀Γ,6..2 5Χ?2 5Χ?( ,6..(

52 23∗ )(4 )(4 23∗ 2)4

5( 23∗ )(4 )(4 (∗4 292

54 23∗ )(4 )34 23∗ )Β∗

53 23∗ )(4 )34 (∗4 23(

59 23∗ )34 )(4 23∗ )Β∗

58 23∗ )34 )(4 (∗4 232

5∗ 23∗ )34 )34 23∗ )Β(

5 23∗ )34 )34 (∗4 244

5Β (∗4 )(4 )(4 23∗ 29)

52) (∗4 )(4 )(4 (∗4 284

522 (∗4 )(4 )34 23∗ 232

52( (∗4 )(4 )34 (∗4 29(

524 (∗4 )34 )(4 23∗ 232

523 (∗4 )34 )(4 (∗4 29(

529 (∗4 )34 )34 23∗ 24(

528 (∗4 )34 )34 (∗4 23(

2(<∆

1

.∆ ! :!

,6..2 ,6..(

5Χ?25Χ?(##

∆ # 5Χ? ?# ∆

,&?# 22

# /# 34#

/

! Η # /Η !

∋ +

∀ # #,&?

.Ι%

228

,6..2

5Χ?2

5Χ?(

,6..(

,6..2Μ5Χ?2

,6..2Μ5Χ?(

,6..2Μ,6..(

5Χ?2Μ5Χ?(

5Χ?2Μ,6..(

5Χ?(Μ,6..(

Page 122: Thesis on RSM

! 6 (/

.

& ∃ ∋. 6# ())8+

∋43+ !

%

,&? ∃

# #

&/7.%

∃ !

#0 ∋

+

#∃

# #

∋24+∗))))

24<%

22∗

Page 123: Thesis on RSM

0 7

23

23</ ∋ +

4 .

#

∀ # Ν2)Ε ,

∋4+∋σ+ 14σϑ2)Ε

∆Γ

75 ?5

Α 289 289

%

Ν2)Ε Ν2)Ε

5/ , ,

4<7

0 ()

#

30/∋3/+

/Η 28 3/

% ∗# !

#

&6? ! # ∃

&6? !

()#9

∃#

− 1 29#

802)#22029Χ280()=

22

7∋75+

?∋?5+

Page 124: Thesis on RSM

Α5&5 &)Β

29Η !

2)∋29+#22ΒΧ

∋2929+

## Χ

29<51∋+#∋?+#∋+Χ

/29Α5&5∀ #

& ∃#3

& ∋Α50/52+∋29+

∃&

.

∃ #

5Α5

/5

& 8 ( 4 3 2( 28 29 23 24 Β 9 2

2 0 2 ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ

( 0 ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ

4 0 2 ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ

3 0 ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ

9 0 ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ

3< &29

/ ##∋Α50/529+Χ∋29+3

& ∀ &

Χ

22Β

2

)

0202)2

/52/5(/54/53

/59/58/5∗/5

/5Β/52)/522/52(

/524/523/529/528

Α552

525(54

5359

58

5∗

55Β

52) 522

52(

524

523

529

528

52∗ 52Β

52

75

?5

∋+ ∋?+ ∋+

Page 125: Thesis on RSM

5Α5

5 /5 5 /5 5 /5 5 /5 5 /5

& 2 ( 8 ∗ 8 ( 2 2( 24 9 28 29 23 Β 24 23 2∗ 2 2Β 29

28 0 Β9 Β9 Β4 ΒΒ Β Β ΒΒ Β Β Β4 Β9 Β9 Β( Β8 Β ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ

2∗ 0 Β9 Β9 Β4 ΒΒ Β Β ΒΒ Β Β Β4 Β9 Β9 Β( Β9 Β2 Β ΒΒ ΒΒ ΒΒ ΒΒ

2 0 ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ Β∗ Β8 Β Β∗ ΒΒ ΒΒ ΒΒ ΒΒ ΒΒ Β Β∗ ΒΒ ΒΒ ΒΒ ΒΒ

2Β 0 ΒΒ ΒΒ ΒΒ Β∗ ΒΒ Β∗ Β∗ Β8 Β∗ Β2 Β∗ Β Β∗ Β Β Β8 Β8 Β( Β9 Β8

() 0 ΒΒ ΒΒ ΒΒ Β ΒΒ ΒΒ Β∗ Β Β∗ Β2 Β∗ Β∗ Β8 Β∗ Β8 Β∗ Β8 Β2 Β9 Β8

90 &28()

Η # ! /52 /524 28

28 2∗2Β ()&#

28! ∋/520/524+

9))))); 28

# ∋2)#+

3/ ∃

∀ #

!∃ #

! ∃ ∃

33∃

2∗

∃ !

; ∃ 34(Β()ϑ3(29Β8Μ8Μ()!

2()

/52

52(

524

523

/59

/5Β

/524

529

528

/

!

&28

&2∗

&2

&2Β

&()

Page 126: Thesis on RSM

∃ #

2∗<∃

: &!

&∃Π

&

5 Θ 2 ( 4 3 9 8 ∗ Β 2) 22 2( 24 23 29 28 2∗ 2 2Β ()

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Β3 Β3 2 Β Β∗

∗ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Β8 Β9 2 ΒΒ ΒΒ

23 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ΒΒ ΒΒ 2 2 ΒΒ

() 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ΒΒ ΒΒ 2 2 2

(2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

(∗ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Β Β 2 2 2

43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ΒΒ ΒΒ 2 ΒΒ ΒΒ

3) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Β3 Β3

32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ΒΒ ΒΒ 2 2 2

3( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Β∗ Β∗ 2 2 ΒΒ

34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Β∗ Β∗ 2 2 ΒΒ

33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ΒΒ ΒΒ 2 ΒΒ ΒΒ

8<& Α.%Α%.

29! ∃

∃ 9! #

4

∀ # #∃

& )Β3

! # ∃

∃()# #

! ∃# ∃

! 52

2(2

02)2

2

)

02

/

Α

75

?5

52 5()

5(2

53)

532

53(

534

533

Page 127: Thesis on RSM

5()#! ∋2+

&# ()2

∋ +

2<&75

%.Α.%Α2Β∀

,#∃

;

; %. ! %.

Α.%Α . ϑΡ%.:ΣΑ.ΡΠ∋Α.:ΣΑ.+

2((

75 ∆Γ 75 ∆Γ

,52 ,538∗9

,52

,538∗9

∋ +

75 ∆Γ

75 ∆Γ 75 ∆Γ

,52 ,538∗9

/

7

! ∆∀Γ

()

28

()

Page 128: Thesis on RSM

2(4

2Β< Α.%Α%.75

∋+

&ϑ)Β∗Β

∋?+

&ϑ)Β83

∋+

&ϑ)ΒΒΒ

Α.%Α

%.

75 ∆Γ

∋+∋?+ ∋+

! ∆∀Γ

&28

&2∗

&2

&2Β

&()

&()

Page 129: Thesis on RSM

! 75?5

! () #

∃ !

#0

2Β()

()<%.! ∋ +

∃! %. ()

/& /& :

&∃

&∃ ∃ &∃

∀&

∃ &∃

282∗ (2

! ∋+ &∋ + &

&

∃ &∃()((

0 ! ()

&∃

Η #

# %.! Ι&

2(3

75 ?5

! ∆∀Γ

75 ?5

2

(

4

2

()

! ∆∀Γ

Page 130: Thesis on RSM

#

∃&∃((

0Β#2(024#2802∗2Β0() %.

(2<. &∃282∗

# # #

(4(3 ∋228+

9)0/&(4 ∀ #

∃# 28 #

2 (3##

!

!

#

#

+

?#

2(9

282∗&

28

2∗

Α

)&2

)! 2

Page 131: Thesis on RSM

((< &()

2(8

2

(

4

3

9

8

Β

2)

22

2(

24

23

29

28

2∗

2

()

&

2(4398∗Β2)222(242329282∗22Β()

Α

Page 132: Thesis on RSM

(4<Α

(3<!

2(∗

&2 &28

&2 &28

!

Page 133: Thesis on RSM

!

∀ #

∃ %&∋

#( ∃#(

∀#(%&∋∀

#(

!∀ )

#( ∗ ∀

∀∀ ∀

%&∋ %&∋+ ∀ ∃

∀ ∃

∀ #

∀ %&∋%,)−.//01

!−2 ∀ ∀∃

%&∋∀ ∀ ∀

∃ ∀ ∀ ∀

%&∋ ∀ ∀ ∀

3.4

Page 134: Thesis on RSM

∀ ∀

∀ !

∀ ∃ 5∋6 ∀

&7% ∀

5∋6 8(!!6

!∀∀ ∀5∋6

∀ 5∀9!

∀ ∃

#(∀ ∀

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∀ ∀ ∃

∀ +∀

)

+

:+ ∃+ ∀

9

∋ ∀∀

)

∃∀

∀ ∃∀

#

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#

5

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3.

Page 135: Thesis on RSM

∃ #( #

∀ #

%6# %&∋

3;/

Page 136: Thesis on RSM

!

! ∀∀#∀ ∀∀∀∃%&&∃

% ∋ ( ) ∗( + ,(

)−./0 ∀ 00

∀ ∗ (. / /( 1 ∋∋

%&&&

2 # ∋ !

∗34 002

5 +

6(− 007

8 9 + + ( 6 :/ ( ∋ −

+ !∀∀#!∃ ∀;%<# 8 ∃∃%&&8

∃ : #∋∋

%&∋ 8 ;%<#∀57∀8∀ 00∀

7 ;< =: − ∋ > # ∋

3 ∋

∋ /(1∋ 00%

0 : ?3∋∋ ) −≅∋1 ,!?3

00&

& : ?Α3?)∋#6∗

( )∗ (∃∀+++ )∗ %&&7

Page 137: Thesis on RSM

36/3∗!1Β∋ ∋

∋Χ ,−.∗∆Ε

+Φ/%&&∃

% ≅/,, Β4/02&#∀ 7∀∀5 05∀

∀ ≅/+∋ ∋ ∀&# 2&

077

2 ≅ / 3 (6 + ,!Β∗ ( ∋ + ∋ Γ 4

%#2552∃5 08&

5 ≅/ (, +∋ %∀# ,!

?3 078

8 ≅/:=+Β%3∋∋ ∀#∀ ∀5 08

∃ ≅ / : 6 : = + + ∋ ≅ ( (

%∀#,!?3 0∃7

7 ≅/(,∋∋∋

%52#8%%852 050

0 ≅/69.≅ ∋. −%1∀

∀/ ∀; <# 25 05

%& − 1 ∋ ∋∋ ∋ ∋

∀∃#5∃88 00&

% ,( Β ) −

− %&&∀

%% − 9 9 ,? = +∋ −+.+Β

2∃∀%&&2

%∀ −663Α=Γ#

)% 3 % ;%<# ∃0 7∃ 000

%2 −=Η−/∋∋ Χ≅∃

)4∀7#∀ Ι∀7%&&∃

%5 −=Η−/∋∋∋)

%∃# 5&0Ι 5 7%&&5

%8 −∋ // :− Β≅∋!ϑ

4 %( ∋ −+ 1∋+∋∋

%∃ −:= ∋ /()

∋Β%&&5

%7 −3 : +3 9 / +∋ ∋ ∋∋ ( +

≅1+,−.,−1∋4%&&∃

∀%

Page 138: Thesis on RSM

%0 (3(( 64(∋ ∋

∋∋∋ !+78#

&7& &0%%&&7

∀& ( = :3 − : + ∋

∋∋5+12 #77&0&% 00∀

∀ Κ)(+Β3,4/=4!:!∋

∋ 651

− )%&&5

∀% Κ)Β31(3 (+ ( 4( ∋

!!/∋)+%&&8∗ %&&8

∀∀ ( + − ∋ 4: /(

931∗%&&7

∀2 (Γ4−4Β# 6

1∃42 #8∀∃8∃8 000

∀5 ∗/(∋ ≅ #Β ∋+3 )

+7∗ 1∋Β 002

∀8 ∗∋∋%) 5#

%∃8∀%∃7 070

∀∃ :∗Α: ∋ ∋

Χ! +7∀#% % Ι% ∀8%&&5

∀7 Β(∋≅ . 0∀5

∀0 = − ! = ! ∋ / 1 /

+( 6 −−∗ %&&%

2& !36?−− ∋Β

∀ 005

2 =: 0# 2 00

2% Χ9 9? :./ +∋!. +∋ )

Β 686 5 +∀∀5+9/ 4

%&&8

2∀ !1Β∋∋ ∋∋

∋ 6 −:

∗ %&&8

22 ! 1 Β ∋ ! +∋

>∗62∀3∀

Β1∋+∋∋19%&&∃

∀∀

Page 139: Thesis on RSM

25 1Β∋ ∋

( )∗ (∃∀+++)∗ %&&7

28 6 ) ∋> ∋ !

7)∀32%#2∃ Ι2∃∃%&&8

2∃ 6 , ∋> ∋ !

∀% #%2Ι∀0%&&∃

27 :/?+− : ∋∋ ∋

∀∀&# 8% ∃0%&&7

20 ( = , :∋3 Β 6: 6 ∗Β ,

≅ :+−Β 6827886 5

∀+ +∀∀5+9)/022∀∃8 002

5& + − =/ 1 Γ∋ 1 +∋

≅ )%+∀∋∋

1∋∀>>,!≅%&&2

5 =+!∗/+Β ∋>∋

∋≅ 6)%# ∃5Ι 70%&&8

5% 6Χ3!=++.!∋ ∋≅ ∋

6−,:%&&∀

5∀ 4 = ∗ + 1 + ≅

; < ∀+ 6

;Β+)Κ0∃< 00∃

52 Η∗ ∋∋ ∋ ∋

∀%∀#2%0222%&&

55 + −+ ∋ ∋ ∋ ∋

∀%8# %∀ ∀0%&&2

58 :∋3 Β 4 +3 4 . ∋ ∋

≅ + − + −

+=;<9! /,#2&02∀& 000

5∃ : )!+

%&&5

57 : 6 9 + ∋ 4 + !

1/ /∋)+%&&2∗ %&&2

50 :∗>>∋∋%<+∀

1∗∃8# 0&5Ι 0 5 0∃

8& :=/∗/ (1>∋

1∋∀)∀∀75#%7 %02%&&2

∀2

Page 140: Thesis on RSM

8 :3+,,!3#− /,!?3 002

8% : :,3+Β ∋Λ

++ + 7∀#∀∀∃∀20%&&8

8∀ :=−==(+−=+−+∋ ∋

1∋∀)∀∀0 # ∃5 %&0%&&8

82 :6∗ ++/ΒΒ931∗

00∃

85 :6=:6!∋+∋#∗+

7;2<#5∃ 50& 088

88 :3∗ / ∗ /! := 6 Β/ ∋ ∋

! 61∃3∀= +

19%&&8

8∃ :(∗Β3Β,∋>∋

)Β− (%;∀<# 7& 0% 07∀

87 :+9Η ≅∋ ∋ ∋

%∀#22525&%&&∃

80 :=+(%!∀∀∀ ; <#5250 000

∃& :!9:∗96/3= ∋ ! ∋

+∀5+9% #∀&&Ι∀&7%&&

∃ ) ∗ − 6= ∋ 3

/+ ;∀<#∀ Ι∀2 07%

∃% ) ,+∋∋∋∋!

+ ++ ) 0%# 2 &0

2 %0%&&∀

∃∀ )3 ++ / + ∋ ;++< ∋

# 10∀ 7;∀<#

∀5 Ι∀8∀ 007

∃2 = ( Η − 6 Β ∋ > ∋

+∀5+9%5#00 8%&&∀

∃5 = − 6 + Β6 − ∋ >

+∀5+9%∀# ∀%&&

∃8 9 ) − ∋ !∋

∋∋) %&# ∃%&&5

∃∃ 9,+/(Β1

+∋(∗%&&5

∀5

Page 141: Thesis on RSM

∃7 9)−=+∋#( 300(,!?3 07∃

∃0 9 +,+∋ Χ ∀ 0#∀ 0

00∃

7& 9Χ=/− + # ∋≅

005

7 9Χ =/− # + ∋ )+ % 5+

1 ∀&#%%∀%∀&%&&

7% 9Χ=/−(∋+ ≅ ++Μ∗∗−

,!?3%&&7

7∀ 9Χ =/− + ∋ ∋

Β ( ∋ )∋ + Λ− ∋ Β

1Β, 00∃

72 9Χ=/−:=−+∋∋ ∋

#! ∋> 1∋∀)∀∀ 85#

2∃Ι 75 000

75 9Χ=/−(∋(4∋ #

)+%5+1 ∃&# %& ∀ %&&8

78 9= / #./ ∋− ∋,+

6 00%

7∃ ∗ / + 4∋ ∋ ∋ ∋

∋!∋6 −:∗ %&&8

77 ∗! Β∗ + + 6 9 ∋ : )∋ ∋

∋ ∀ %&# 7 0

7∀ %&&8

70 ∗Α∗Η4 ∋ !+∋

3%7# 000%&&∃%&&∃

0& ∗ ?9ΗΓ1∋

6(∋∀∀57#2∀Ι5∃%&&

0 ∗Η∗Γ?ΗΑ6∗6Χ ∋∋∋

! +∀5+9∀5#58 580%&&7

0% ∗?∋∋−≅+>≅≅ (

/(Β=)∋Β%&&2

0∀ ∗ Η∗ ∋ ∋

%&∋ %58#55 582

%&&%

∀8

Page 142: Thesis on RSM

02 ∗?6>∋ ∋

∋ ∀ 8#∀028 002

05 ∗ΑΑΑ=?Α∋ ∋ ++

%7# 0%8%&&∃

08 691 ;/∋<%

&∋%77#2%∀2%0%&&5

0∃ =) ∗Χ ∋ +∋≅ ∋ . (∋

(∋∋!5+9)%#25∀287%&&

07 ::∋3Β=∗4− ≅∋ ∋

∋ ∋>,∀%#%∀5%8 007

00 3/.,∗ . ∋ Χ

+∀5+9% #∀7∀Ι∀0%%&&

&& ! 4Ν ( 1 Β − − + ! +∋

∋ ∋ ∋∋Ν∗

∀+ 58&,.= + 2∀ ∀ & 3

%&&∃

& (,. 1 ∋:+−Β1− (∋

≅ Λ−+ .6∀

∀+(−∋ 005

&% 9Ν//ΟΟ>?∗− 08&

&∀ 9(3 =−6=− ∋Β∋+4∋)

4∋.∋ − −% ;%<#%88%02 0∃0

&2 3 + Β 3 = − )≅

+6%2&; &<#%&5∀%&50%&&%

&5 3 + Β ∗ ? ∋ −

(Λ−6%∀0; &<%&&

&8 , 1 + Β − %

22;%2∃<#∀∀5∀2 020

&∃ !Α Μ(+Π/ +4 00%

&7 Β= + ( ∋ − ≅ # Β! ≅

%#∀50∀∃0 00%

&0 (∋ ∋ !

/(931∗%&&%

& (4( ∋>∋

1+6%2&; <# %8 ∀8%&&%

∀∃

Page 143: Thesis on RSM

(4(∋ ∋∋∋>

∋ 6 % ) 8 # %27&%5&∃

%&&2

%(4(∋ ∋

+ ++ ) 02# 5%∃ 555%&&5

∀ (− ≅ ∋

27/%# 50 ∃∃ 000

2 (−−∋%∀#=6∗

,!?3 000

5 :9)−6:+∋# 088 077∀ ;%<#

∀∃ 5∃ 070

8 : (−+∋//1(

≅ %∀#,!?3 005

∃ : (−(−4−9!3+

+∋#∗+%!∀∀∀8; <#5∀

∃7%&&2

7 ,,4ΒΚ #∀2# %∃ 8 00%

0 .9,9≅Β∋/( Β6

3∀ ∀ 00

%& .!.∋ ≅

%2∀025% 00%

% .!− ∗ %

70;2%7< 5 ∃Ι%% 002

%% /Α9∗:=∗? )∃0+

002

%∀ /3 Β∋Β∋ ∋∋

∋ ∋ /−( ) = ∋

∋Β∀8# 0Ι%∃%&&7

%2 / :( Β ∋ ∗ + % 1∀ ∀∗ /

≅ Α 8; <# 2& 20 052

%5 //!:=+Θ) ∋

/))#+ 2&#8∀∃820%&&∃

%8 /3,−=−(− %

&∋ &8#25 28∀ 078

∀7

Page 144: Thesis on RSM

%∃ / ∗ ) ∋ ∋>

∋∋

∗ %&&7

%7 ! ∀ ! ! %

&∋ 2;∀<#520582 07∃

%0 #∃ !!∃!%!&∋!(#∀

)%∋%5;0<# %20 %5∃ 07∃

∀& /− %

&∋ %8;∀<#2755&% 077

∀ /3∗ =/Β(∋. ∋≅ /0 ∀∀#∀&5

∀%5 028

∀% /Β ,!3∋≅ 6))) ∃7;0<# 272 27∃

00&

∀∀ /! := ∋ / )#

+ 2&#8%∃8∀5%&&∃

∀2 ΓΗ43 +:∋3Β∋∋. ∋

) +∀ ∋∋

1∋∀,( )%&&&

∀5 Χ3!!3∋∋

∀ %#%&5%%& 00∀

∀8 + : + 4 ∋

1∋∀)∀+∋0 # ∀0&Ι ∀0∃%&&8

∀∃ Χ3 == ∗/+∋=1∋(+)∋ +∋

9 5+9)%#280272%&&

∀7 (3+(∋−!∋ Λ

∋∋ +,∗ 00∃

∀0 ≅ 6= + , :∋3 Β +∋ ≅ ∋

6% )2%#5 ∃5∀2 007

2& ∋− ( :3= − / ∋1

4 )%&&0 0&8%&&5

2 ∋ +! ∗/ / Β∗ 1 +∋ ;<

3−,.+,(),∗%&&5

2% +3=66=Β=6:/(∋− ≅

2;2<#2&02∀5 070

2∀ +3=++66(∋ ≅ ∀ #2 Ι2∃

070

∀0

Page 145: Thesis on RSM

22 +−=:=−:+−≅∋∗ !

1∋∀)∀∀0∀ &2∃ &50%&&7

25 +Β− −=(+Β+

+Β/ =6Ρ+%&&∃

28 +3+Α3+ 9≅ +

++ ) 0%#0%∀Ι0∀0%&&∀

2∃ +3−+Θ)1 ∋∗ + +

%&&5

27 ++Β ∋ ∀%# &∀ &2 0∃0

20 +)−1.6.∋∋

∋∋∋) 2; <# & 7 070

5& +)4− /+ 62 Β=

1∋ 00∀

5 + ) ∋ + ∋∋

) %;2<# 0∃∀% 00∃

5% +)− − +∃0#

%%%5%%∀2%&&

5∀ + ) /! := 3 ∋

Ι!∀%0# 8∃ 7%%&&∃

52 +! ∋ 8#28 282 0∃7

55 + + ∗ / ) ∋ ! ∋

6

2∀3∀Β1∋+∋∋19%&&∃

58 +∗/ ) ∋!

≅ ∋ ( )∗ (∃ ∀+ ++

)∗ %&&7

5∃ +∗/ ≅ ∋Λ ∋

!6 −:∗ %&&8

57 +39)9∋ ∋ #3≅

. ) 3 ) 3

+ − 00∃

50 +(,+∗9) #

+#3∀5&#%7∀5%752%&&8

8& +? − ∋ ∋+∋ .

+( 6Β=6)))6∀+∀∀#% 5%% 55

005

2&

Page 146: Thesis on RSM

8 +∋ Β∋/1// 0∃8

8% +Η?/3∋∋

∃)4∀ #5 0Ι%∃%&&&

8∀ + Β6 =9 + ∋ ≅

3) ) 3 )

007

82 + Β6∗(−6+ ∋ ≅ #

6%1∋∀∀%;∀<#%&0%2&%&&

85 + Β69==Β− ∋∋3

∋ 6, ,. 007

88 + Β6/3=(9/,=, ∋− (#

+ )4+ ∃# %0 5&%&&

8∃ +− !∋ ∋

∋ %&∋%77#8%∀#85%%&&5

87 +.∋. ∋+Β/(Β

)∋Β+3 +!%&&∀

80 +!∗/+∋+ −+∋

≅ 63 3++%&&8

∃& Β/∋ (6%1 8#5% Ι5∀&

0∃7

∃ Β .∗: %

77;2%2<# ∀0% ∀0∃ 07∀

∃% Β− ∋ ∋∋ 1∋∀)∀

∀0 # %5∃Ι %85%&&8

∃∀ Β + : ∗ 4 ∋ 6 ! 1

/ 6Χ 6 1 ∃

3∀,13+ 19%&&8

∃2 4 : − Β ∋ #

%!∀∀%%; <#∀7Ι25 00&

∃5 ∋

!%&∋%8&#7&∃Ι7%∃%&&∀

∃8 6 66 + + ! ∋ Β> + ∋ (

. % 3 %0;2<#∀∃&∀7&%&&∃

∃∃ 6 6= ? Β9 9 + +3 = − ≅ ∋ Γ − /

(%!∀∀%%# 5%% 00&

2

Page 147: Thesis on RSM

∃7 ?.1 ∗ 1∋

#1∋∀)∀∀0 #2&∃2 %%&&8

∃0 ?+/Β +∋, + Σ. ∋/ :

≅+ ++ ) % #%∀ %5∃ 005

7& ? ?+ ? ?+ 6+ 9 = / ∋ ∋

/ # +∀5+9%0# 0∀2%&&5

7 ? ?+ ? ?+ 6+ 9 = / ∋ ∋

/%# ≅ !

+∀5+9%0#∀520%&&5

7% Α∗+67#∀∀7∀5∀ 085

7∀ Α − ! ) = ! ∋

+7∀#∀ 5∀%8%&&5

72 Α?(/9) ∋ ∋∋

)%%#522Ι55 %&&&

75(1+!#444∗∗

2%