city vologiannidis
TRANSCRIPT
-
7/31/2019 City Vologiannidis
1/76
,
http://find/ -
7/31/2019 City Vologiannidis
2/76
( ) = + + ...+ , C
( ) = , C
( ) = ( )
( )
( )
( )
( ), ( )
( ) ( )#( ) =
http://find/ -
7/31/2019 City Vologiannidis
3/76
( ) = + + ...+ , C
( ) = , C
( ) = ( )
( )
( )
( )
( ), ( )
( ) ( )#( ) =
http://find/ -
7/31/2019 City Vologiannidis
4/76
( )( ) ( )
( ) =
,
( ) =
( ) ( )( )
http://find/ -
7/31/2019 City Vologiannidis
5/76
( )( ) ( )
( ) =
,
( ) =
( ) ( )( )
http://find/ -
7/31/2019 City Vologiannidis
6/76
( )( ) ( )
( ) =
,
( ) =
( ) ( )( )
http://find/ -
7/31/2019 City Vologiannidis
7/76
+ + + +...+ = + + + + ...+
R , = , , , , . . .
R
, = , , , , . . . R , = , , . . . , R , = , , . . . , .
() = ()
() = = , () = = = + .
()
http://find/ -
7/31/2019 City Vologiannidis
8/76
+ + + +...+ = + + + + ...+
R , = , , , , . . .
R , = , , , , . . .
R , = , , . . . , R , = , , . . . , .
() = ()
() = = , () = = = + .
()
http://find/ -
7/31/2019 City Vologiannidis
9/76
+ + + +...+ = + + + + ...+
R , = , , , , . . .
R , = , , , , . . .
R , = , , . . . , R , = , , . . . , .
() = ()
() = = , () = = = + .
()
http://find/ -
7/31/2019 City Vologiannidis
10/76
+
=
().
().
http://find/ -
7/31/2019 City Vologiannidis
11/76
+
=
().
().
http://find/ -
7/31/2019 City Vologiannidis
12/76
() = + + ...+ C C
C( ) = .
()
() = (),
( ) =
(),
.
http://find/ -
7/31/2019 City Vologiannidis
13/76
() = + + ...+ C C
C( ) = .
()
() = (),
( ) =
(),
.
http://find/ -
7/31/2019 City Vologiannidis
14/76
-
7/31/2019 City Vologiannidis
15/76
() = + + .
= ==
http://find/ -
7/31/2019 City Vologiannidis
16/76
() = + + .
= ==
http://find/ -
7/31/2019 City Vologiannidis
17/76
() = + + .
= ==
http://find/ -
7/31/2019 City Vologiannidis
18/76
http://find/ -
7/31/2019 City Vologiannidis
19/76
http://find/ -
7/31/2019 City Vologiannidis
20/76
http://find/ -
7/31/2019 City Vologiannidis
21/76
( )
http://find/ -
7/31/2019 City Vologiannidis
22/76
( )
http://find/ -
7/31/2019 City Vologiannidis
23/76
( )
http://find/ -
7/31/2019 City Vologiannidis
24/76
( )
http://find/ -
7/31/2019 City Vologiannidis
25/76
( )
http://find/ -
7/31/2019 City Vologiannidis
26/76
( )
http://find/ -
7/31/2019 City Vologiannidis
27/76
http://find/ -
7/31/2019 City Vologiannidis
28/76
( )( )
=
( )
( )
, = , , . . . , ,
=
= { , ( )}.
http://find/ -
7/31/2019 City Vologiannidis
29/76
I = ( , , . . . , ){ , , , . . . , } I :=
, { , , , . . . , } =| | = .
I I I I
I I I = I
http://find/ -
7/31/2019 City Vologiannidis
30/76
I = ( , , . . . , ){ , , , . . . , } I :=
, { , , , . . . , } =| | = .
I I I I
I I I = I
http://find/ -
7/31/2019 City Vologiannidis
31/76
I = ( , , . . . , ){ , , , . . . , } I :=
, { , , , . . . , } =| | = .
I I I I
I I I = I
( + )
http://find/ -
7/31/2019 City Vologiannidis
32/76
, Z ( : ) :=
( , + ,..., ),
, >
= .
I = ( , , . . . , ) I =( , , . . . , )
I
I ,
=
( )
=
( )
( + )
http://find/ -
7/31/2019 City Vologiannidis
33/76
, Z ( : ) :=
( , + ,..., ),
, >
= .
I = ( , , . . . , ) I =( , , . . . , )
I
I ,
=
( )
=
( )
( )
( + )
http://find/ -
7/31/2019 City Vologiannidis
34/76
, Z ( : ) :=
( , + ,..., ),
, >
= .
I = ( , , . . . , ) I =( , , . . . , )
I
I ,
=
( )
=
( )
Z ( )
( , + ,..., ),
http://find/ -
7/31/2019 City Vologiannidis
35/76
, Z ( : ) :=
( , + ,..., ),
, >
= .
I = ( , , . . . , ) I =( , , . . . , )
I
I ,
=
( )
=
( )
http://find/ -
7/31/2019 City Vologiannidis
36/76
I = ( , , . . . , ) I, I,
< , = ,= + < < .
I = ( , , , , , , , ) I = ( , , , , , , , )
I I
I ( , , , , , , , ) ( , , , , , , , ) ...
http://find/ -
7/31/2019 City Vologiannidis
37/76
I = ( , , . . . , ) I, I,
< , = ,= + < < .
I = ( , , , , , , , ) I = ( , , , , , , , )
I I
I ( , , , , , , , ) ( , , , , , , , ) ...
http://find/ -
7/31/2019 City Vologiannidis
38/76
I = ( , , . . . , ) I, I,
< , = ,= + < < .
I = ( , , , , , , , ) I = ( , , , , , , , )
I I
I ( , , , , , , , ) ( , , , , , , , ) ...
http://find/ -
7/31/2019 City Vologiannidis
39/76
I = ( , , . . . , ) I, I,
< , = ,= + < < .
I = ( , , , , , , , ) I = ( , , , , , , , )
I I
I ( , , , , , , , ) ( , , , , , , , ) ...
http://find/ -
7/31/2019 City Vologiannidis
40/76
I = ( , , . . . , ) I, I,
< , = ,
= + < < .
I = ( , , , , , , , ) I = ( , , , , , , , )
I I
I ( , , , , , , , ) ( , , , , , , , ) ...
http://find/ -
7/31/2019 City Vologiannidis
41/76
( : )
( : ) =
( + )
+
, <
, = ,
http://find/ -
7/31/2019 City Vologiannidis
42/76
I = =
( : ) ( : ) {}.
I =
=
( : ) ( : ) {}
= I = ( , , , , , , , , , ). A
I = ( )( )( )( ) =
I = ( )( )( )( ).
http://find/ -
7/31/2019 City Vologiannidis
43/76
I = =
( : ) ( : ) {}.
I =
=
( : ) ( : ) {}
= I = ( , , , , , , , , , ). A
I = ( )( )( )( ) =
I = ( )( )( )( ).
http://find/ -
7/31/2019 City Vologiannidis
44/76
I
I
I
I
http://find/ -
7/31/2019 City Vologiannidis
45/76
I
I
I
I
http://find/ -
7/31/2019 City Vologiannidis
46/76
:= =
( )
( )
, = , . . . ,
:= =
= { ( ), }.
( )( )( )( ) =
http://find/ -
7/31/2019 City Vologiannidis
47/76
:= =
( )
( )
, = , . . . ,
:= =
= { ( ), }.
( )( )( )( ) =
http://find/ -
7/31/2019 City Vologiannidis
48/76
:= =
( )
( )
, = , . . . ,
:= =
= { ( ), }.
( )( )( )( ) =
http://find/ -
7/31/2019 City Vologiannidis
49/76
:= =
( )
( )
, = , . . . ,
:= =
= { ( ), }.
( )( )( )( ) =
http://find/ -
7/31/2019 City Vologiannidis
50/76
( ) ,
{ , , . . . , }.
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/ -
7/31/2019 City Vologiannidis
51/76
( ) ,
{ , , . . . , }.
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/ -
7/31/2019 City Vologiannidis
52/76
( ) ,
{ , , . . . , }.
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/ -
7/31/2019 City Vologiannidis
53/76
( ) ,
{ , , . . . , }.
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/ -
7/31/2019 City Vologiannidis
54/76
( ) ,
{ , , . . . , }.
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/ -
7/31/2019 City Vologiannidis
55/76
( ) ,
{ , , . . . , }.
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/ -
7/31/2019 City Vologiannidis
56/76
= P = ( , , ) N = ( , , ) RP = ( )LP = RN = LN = ( )
( ) =
.
(LP ,P,RP) = ( , , , ) satisfies the SIP(LN,N,RN) = ( , , , ) satisfies the SIP
http://find/ -
7/31/2019 City Vologiannidis
57/76
-
7/31/2019 City Vologiannidis
58/76
I I I
http://find/ -
7/31/2019 City Vologiannidis
59/76
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
http://find/ -
7/31/2019 City Vologiannidis
60/76
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
http://find/ -
7/31/2019 City Vologiannidis
61/76
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
http://find/ -
7/31/2019 City Vologiannidis
62/76
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
http://find/ -
7/31/2019 City Vologiannidis
63/76
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)
( )
http://find/ -
7/31/2019 City Vologiannidis
64/76
= P = ( ) P = ( , ) N = ( , )N = ( ) RP =P LN =N LP = RN =
( ) =
.
( ) = (LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)
http://find/ -
7/31/2019 City Vologiannidis
65/76
( ) C [ ]
=
C ( )
=
( : )
(P
,RP)
= = >
+ ( )
= C ( )
=
( : )
(LP ,P) = = > +( )
( ) = (LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)( ) [ ]
http://find/ -
7/31/2019 City Vologiannidis
66/76
( ) C [ ]
=
C ( )
=
( : )
(P
,RP)
= = >
+ ( )
= C ( )
=
( : )
(LP ,P) = = > +( )
( ) = (LN ,LP ,N,RP ,RN) (LN ,LP ,P,RP ,RN)( ) C [ ]
http://find/ -
7/31/2019 City Vologiannidis
67/76
( ) C [ ]
=
C ( )
=
( : )
(P
,RP)
= = >
+ ( )
= C ( )
=
( : )
(LP ,P) = = > +( )
http://find/ -
7/31/2019 City Vologiannidis
68/76
= P = ( , , ) N = ( , , ) RP = ( )LP = RN = LN = ( )
( ) =
.
(P,RP) = (( , , ),( )) (( , ),( , )) , is( )
( ) C [ ] ( )/ (L R )
http://find/ -
7/31/2019 City Vologiannidis
69/76
/ (LN,RN)
=
C ( )
=
( : )
(N,RN) = = >
( )
= C ( )
=
( : )
(LN ,N) = = >
( )
( ) C [ ] ( )/ (L R )
http://find/ -
7/31/2019 City Vologiannidis
70/76
/ (LN,RN)
=
C ( )
=
( : )
(N,RN) = = >
( )
= C ( )
=
( : )
(LN ,N) = = >
( )
( ) C [ ] ( )/ (L R )
http://find/ -
7/31/2019 City Vologiannidis
71/76
/ (LN,RN)
=
C ( )
=
( : )
(N,RN) = = >
( )
= C ( )
=
( : )
(LN ,N) = = >
( )
http://find/ -
7/31/2019 City Vologiannidis
72/76
= P = ( , , ) N = ( , , ) RP = ( )LP = RN = LN = ( )
( ) =
.
(N,RN) = ( , , ) (( ),( , )) is( )
http://find/ -
7/31/2019 City Vologiannidis
73/76
http://find/ -
7/31/2019 City Vologiannidis
74/76
http://find/ -
7/31/2019 City Vologiannidis
75/76
http://find/ -
7/31/2019 City Vologiannidis
76/76
http://find/