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In-Depth Information
(
)
2
m
+
m
+
2
m
m
+
3
k
=
,
,
j
=
1
m
,
i
=
1
n
,
2
2
~
~
j
and the wei
ghe
d segment of product of numbers
and
, where
,
2
k
=
1
m
X
k
j
=
1
m
,
i
=
1
n
, with
(
)
(
)
⎥
⎦
⎤
⎡
θ
1
b
k
,
b
k
L
,
b
k
R
,
θ
2
b
k
,
b
k
L
,
b
k
R
⎢
⎣
~
~
~
2
~
2
i
j
i
j
a
X
a
X
,
k
k
~
~
~
X
i
p
X
,
i
j
and the weighed segment of product of numbers
and
with
[
]
(
)
(
)
θ
1
b
k
,
b
k
L
,
b
k
R
,
θ
2
b
k
,
b
k
L
,
b
k
R
~
~
~
~
~
~
i
p
i
i
p
i
j
a
X
X
a
X
X
k
j
k
where
(
)
m
m
+
1
k
=
m
+
1
,
p
=
1
m
−
1
j
=
2
m
,
p
≠
j
,
p
<
j
,
i
=
2
n
.
2
According to the proposition 6.4,
1
1
1
(
)
⎡
⎤
⎡
⎤
()
()
q
q
1
k
k
L
k
R
k
ji
q
ji
M
k
L
ji
q
ji
M
θ
b
,
b
,
b
=
b
x
+
−
1
x
−
b
x
+
−
1
x
;
~
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
~
i
j
a
X
6
6
12
q
q
k
(
)
⎡
1
⎤
⎡
1
1
⎤
()
()
r
r
2
b
k
,
b
k
L
,
b
k
R
=
b
k
x
ji
+
−
1
x
ji
M
+
b
k
R
x
ji
+
−
1
x
ji
M
,
θ
~
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
~
r
r
j
a
X
6
6
12
r
r
k
where
(
)
⎧
k
k
L
2
1
b
−
b
≥
0
m
+
m
+
2
m
m
+
3
k
=
,
;
j
=
1
m
;
i
=
2
n
;
q
=
0
⎩
⎨
k
k
R
2
2
2
b
+
b
<
L
,
q
=
1
⎧
k
k
L
L
,
r
=
1
⎩
⎨
⎧
2
b
−
b
≥
0
⎩
⎨
⎧
M
=
;
r
=
0
M
=
.
⎩
⎨
q
r
R
,
q
=
2
1
b
k
+
b
k
R
<
R
,
r
=
2
According to the proposition 6.5
()
⎡
q
⎤
−
1
1
(
)
2
2
1
k
k
L
k
R
k
ji
q
ji
q
ji
M
ji
M
θ
b
,
b
,
b
=
b
x
+
x
x
+
x
−
⎢
⎣
⎥
⎦
~
2
~
3
12
i
j
a
X
q
q
k
()
⎡
q
⎤
1
−
1
1
2
2
b
k
L
x
ji
q
x
ji
q
x
ji
M
x
ji
M
;
−
+
+
⎢
⎣
⎥
⎦
6
6
6
q
q
