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,

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( ) = + + ...+ , C

( ) = , C

( ) = ( )

( )

( )

( )

( ), ( )

( ) ( )#( ) =

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( ) = + + ...+ , C

( ) = , C

( ) = ( )

( )

( )

( )

( ), ( )

( ) ( )#( ) =

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( )( ) ( )

( ) =

,

( ) =

( ) ( )( )

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( )( ) ( )

( ) =

,

( ) =

( ) ( )( )

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( )( ) ( )

( ) =

,

( ) =

( ) ( )( )

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+ + + +...+ = + + + + ...+

R , = , , , , . . .

R

, = , , , , . . . R , = , , . . . , R , = , , . . . , .

() = ()

() = = , () = = = + .

()

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7/31/2019 City Vologiannidis

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+ + + +...+ = + + + + ...+

R , = , , , , . . .

R , = , , , , . . .

R , = , , . . . , R , = , , . . . , .

() = ()

() = = , () = = = + .

()

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+ + + +...+ = + + + + ...+

R , = , , , , . . .

R , = , , , , . . .

R , = , , . . . , R , = , , . . . , .

() = ()

() = = , () = = = + .

()

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+

=

().

().

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+

=

().

().

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() = + + ...+ C C

C( ) = .

()

() = (),

( ) =

(),

.

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() = + + ...+ C C

C( ) = .

()

() = (),

( ) =

(),

.

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() = + + .

= ==

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() = + + .

= ==

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() = + + .

= ==

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( )

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( )

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( )

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( )

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( )

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( )

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( )( )

=

( )

( )

, = , , . . . , ,

=

= { , ( )}.

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I = ( , , . . . , ){ , , , . . . , } I :=

, { , , , . . . , } =| | = .

I I I I

I I I = I

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I = ( , , . . . , ){ , , , . . . , } I :=

, { , , , . . . , } =| | = .

I I I I

I I I = I

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I = ( , , . . . , ){ , , , . . . , } I :=

, { , , , . . . , } =| | = .

I I I I

I I I = I

( + )

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, Z ( : ) :=

( , + ,..., ),

, >

= .

I = ( , , . . . , ) I =( , , . . . , )

I

I ,

=

( )

=

( )

( + )

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, Z ( : ) :=

( , + ,..., ),

, >

= .

I = ( , , . . . , ) I =( , , . . . , )

I

I ,

=

( )

=

( )

( )

( + )

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, Z ( : ) :=

( , + ,..., ),

, >

= .

I = ( , , . . . , ) I =( , , . . . , )

I

I ,

=

( )

=

( )

Z ( )

( , + ,..., ),

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7/31/2019 City Vologiannidis

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, Z ( : ) :=

( , + ,..., ),

, >

= .

I = ( , , . . . , ) I =( , , . . . , )

I

I ,

=

( )

=

( )

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I = ( , , . . . , ) I, I,

< , = ,= + < < .

I = ( , , , , , , , ) I = ( , , , , , , , )

I I

I ( , , , , , , , ) ( , , , , , , , ) ...

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I = ( , , . . . , ) I, I,

< , = ,= + < < .

I = ( , , , , , , , ) I = ( , , , , , , , )

I I

I ( , , , , , , , ) ( , , , , , , , ) ...

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I = ( , , . . . , ) I, I,

< , = ,= + < < .

I = ( , , , , , , , ) I = ( , , , , , , , )

I I

I ( , , , , , , , ) ( , , , , , , , ) ...

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7/31/2019 City Vologiannidis

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I = ( , , . . . , ) I, I,

< , = ,= + < < .

I = ( , , , , , , , ) I = ( , , , , , , , )

I I

I ( , , , , , , , ) ( , , , , , , , ) ...

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I = ( , , . . . , ) I, I,

< , = ,

= + < < .

I = ( , , , , , , , ) I = ( , , , , , , , )

I I

I ( , , , , , , , ) ( , , , , , , , ) ...

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( : )

( : ) =

( + )

+

, <

, = ,

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I = =

( : ) ( : ) {}.

I =

=

( : ) ( : ) {}

= I = ( , , , , , , , , , ). A

I = ( )( )( )( ) =

I = ( )( )( )( ).

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I = =

( : ) ( : ) {}.

I =

=

( : ) ( : ) {}

= I = ( , , , , , , , , , ). A

I = ( )( )( )( ) =

I = ( )( )( )( ).

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I

I

I

I

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I

I

I

I

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:= =

( )

( )

, = , . . . ,

:= =

= { ( ), }.

( )( )( )( ) =

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:= =

( )

( )

, = , . . . ,

:= =

= { ( ), }.

( )( )( )( ) =

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:= =

( )

( )

, = , . . . ,

:= =

= { ( ), }.

( )( )( )( ) =

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7/31/2019 City Vologiannidis

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:= =

( )

( )

, = , . . . ,

:= =

= { ( ), }.

( )( )( )( ) =

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( ) ,

{ , , . . . , }.

P ( : ) LP ,RP( : ) (LP ,P,RP)

N ( : ) LN,RN

( : ) (LN,N,RN)

(LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

( )

/ (LP ,RP) / (LN,RN)

( )

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( ) ,

{ , , . . . , }.

P ( : ) LP ,RP( : ) (LP ,P,RP)

N ( : ) LN,RN

( : ) (LN,N,RN)

(LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

( )

/ (LP ,RP) / (LN,RN)

( )

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( ) ,

{ , , . . . , }.

P ( : ) LP ,RP( : ) (LP ,P,RP)

N ( : ) LN,RN

( : ) (LN,N,RN)

(LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

( )

/ (LP ,RP) / (LN,RN)

( )

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( ) ,

{ , , . . . , }.

P ( : ) LP ,RP( : ) (LP ,P,RP)

N ( : ) LN,RN

( : ) (LN,N,RN)

(LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

( )

/ (LP ,RP) / (LN,RN)

( )

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( ) ,

{ , , . . . , }.

P ( : ) LP ,RP( : ) (LP ,P,RP)

N ( : ) LN,RN

( : ) (LN,N,RN)

(LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

( )

/ (LP ,RP) / (LN,RN)

( )

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( ) ,

{ , , . . . , }.

P ( : ) LP ,RP( : ) (LP ,P,RP)

N ( : ) LN,RN

( : ) (LN,N,RN)

(LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

( )

/ (LP ,RP) / (LN,RN)

http://find/

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= P = ( , , ) N = ( , , ) RP = ( )LP = RN = LN = ( )

( ) =

.

(LP ,P,RP) = ( , , , ) satisfies the SIP(LN,N,RN) = ( , , , ) satisfies the SIP

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I I I

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I

P = P ,P ,N = N ,N

P = ( , , . . . , ), P = ( , , . . . , )

N = ( , , . . .), N =( , , . . .)

LP = RP =P LN =N RN =

LN,LP ,N,RP ,RN

(LN ,LP ,N

,RP ,RN) (

LN ,LP ,P

,RP ,RN)

( )

I I I

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I

P = P ,P ,N = N ,N

P = ( , , . . . , ), P = ( , , . . . , )

N = ( , , . . .), N =( , , . . .)

LP = RP =P LN =N RN =

LN,LP ,N,RP ,RN

(LN ,LP ,N

,RP ,RN) (

LN ,LP ,P

,RP ,RN)

( )

I I I

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P = P ,P ,N = N ,N

P = ( , , . . . , ), P = ( , , . . . , )

N = ( , , . . .), N =( , , . . .)

LP = RP =P LN =N RN =

LN,LP ,N,RP ,RN

(LN ,LP ,N

,RP ,RN) (

LN ,LP ,P

,RP ,RN)

( )

I I I

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P = P ,P ,N = N ,N

P = ( , , . . . , ), P = ( , , . . . , )

N = ( , , . . .), N =( , , . . .)

LP = RP =P LN =N RN =

LN,LP ,N,RP ,RN

(LN ,LP ,N

,RP ,RN)

(LN ,LP ,P

,RP ,RN)

( )

I I I

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P = P ,P ,N = N ,N

P = ( , , . . . , ), P = ( , , . . . , )

N = ( , , . . .), N =( , , . . .)

LP = RP =P LN =N RN =

LN,LP ,N,RP ,RN

(LN ,LP ,N

,RP ,RN)

(LN ,LP ,P

,RP ,RN)

( )

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= P = ( ) P = ( , ) N = ( , )N = ( ) RP =P LN =N LP = RN =

( ) =

.

( ) = (LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)

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( ) C [ ]

=

C ( )

=

( : )

(P

,RP)

= = >

+ ( )

= C ( )

=

( : )

(LP ,P) = = > +( )

( ) = (LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)( ) [ ]

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( ) C [ ]

=

C ( )

=

( : )

(P

,RP)

= = >

+ ( )

= C ( )

=

( : )

(LP ,P) = = > +( )

( ) = (LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)( ) C [ ]

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( ) C [ ]

=

C ( )

=

( : )

(P

,RP)

= = >

+ ( )

= C ( )

=

( : )

(LP ,P) = = > +( )

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= P = ( , , ) N = ( , , ) RP = ( )LP = RN = LN = ( )

( ) =

.

(P,RP) = (( , , ),( )) (( , ),( , )) , is( )

( ) C [ ] ( )/ (L R )

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/ (LN,RN)

=

C ( )

=

( : )

(N,RN) = = >

( )

= C ( )

=

( : )

(LN ,N) = = >

( )

( ) C [ ] ( )/ (L R )

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/ (LN,RN)

=

C ( )

=

( : )

(N,RN) = = >

( )

= C ( )

=

( : )

(LN ,N) = = >

( )

( ) C [ ] ( )/ (L R )

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/ (LN,RN)

=

C ( )

=

( : )

(N,RN) = = >

( )

= C ( )

=

( : )

(LN ,N) = = >

( )

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= P = ( , , ) N = ( , , ) RP = ( )LP = RN = LN = ( )

( ) =

.

(N,RN) = ( , , ) (( ),( , )) is( )

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