Biomedical Engineering Reference
In-Depth Information
Lemma4.12
−
1
<
C
′
+
C
′
<
1.
.
row
col
Lemma4.13
i
i
Considering.a.distribution.matrix.
B
( )
=
b
( )
.with.size.
M
.×.
M
,.one.has
{
}
mn
∑
∑
M
( )
i
Q
=
b
=
4
(1
+
C
′
+
C
′
);
1
mn
row
col
.
ξ
∈
Z
ξ
∈
Z
m
n
∑
∑
M
( )
i
Q
=
b
=
4
(1
−
C
′
−
C
′
);
2
mn
row
col
.
ξ
∈
Z
′
ξ
∈
Z
′
m
n
∑
∑
M
( )
i
Q
=
b
=
4
(1
−
C
′
+
C
′
);
3
mn
row
col
.
ξ
∈
Z
ξ
∈
Z
′
m
n
∑
∑
M
( )
i
Q
=
b
=
4
(1
+
C
′
−
C
′
)
4
mn
row
col
.
ξ
∈
Z
′
ξ
∈
Z
m
n
where.
Z
.is.
Z
odd
.or.
Z
even
.
4.3.4 Proof of Theorem 4.1
First,.by.mathematical.induction,.the.case.when.
M
=.2.is.considered..Recalling.
(
)
i
P
(
ξ
,
t
+
1)
=
Y t A Y t
′
( )
( )
.
i
.
(4.63)
where
P
(
ξ
ξ
, )
t
1
( )
=
Y t
P
(
, )
t
2
.
and
a
( )
i
a
( )
i
( )
11
12
i
A
=
.
a
( )
i
a
( )
i
21
22
.
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