... schemes 13
2 .1 Consistency 14
2.2 Stability 15
2.2 .1 Invariantdomains 15
2.2 .2 Entropyinequalities 16
2. 3 ApproximateRiemannsolverofHarten,Lax,VanLeer 19
2. 3 .1 Simplesolvers 22
2. 3 .2 Roesolver 24
2. 3.3 ... equation in (2 .16 4) to (2 .16 2) , we deduce that
e
n +1
i
≥ e(ρ
n +1
i
,s
n +1
i
), (2 .16 5)
where s
n +1
i
is computed by (2 .16 1). Therefore, e
n +1
i
≥ 0, and since by (1. 12)
(
∂s
∂e
)
ρ
=1/ T > 0, ... ρ
i
u
i
+
∆t
∆x
i
F
ρu
i +1/ 2
− F
ρu
i 1/ 2
=0,
ρ
n +1
i
s
n +1
i
− ρ
i
s
i
+
∆t
∆x
i
F
ρs
i +1/ 2
− F
ρs
i 1/ 2
=0,
(2 .16 1)
satisfying an entropy inequality
ρ
n +1
i
((u
n +1
i
)
2
/2+ e(ρ
n +1
i
,s
n +1
i
))−ρ
i
(u
2
i
/2+ e(ρ
i
,s
i
))+
∆t
∆x
i
F
e
i +1/ 2
−F
e
i 1/ 2
≤...
...
10 .
References
Kenneth W. Church and Patrick Hanks.
(19 90)Word
Association Norms, Mutual Information, And
Lexicography.
Computational Linguistics, 16 /1,
pp. 22 29 .
Barbara J. Grosz and ... Morris and Graeme Hirst. (19 91)
Lexical
Cohesion Computed by Thesaural Relations as an
Indicator of the Structure of Text.
Computational
Linguistics, 17 /1, pp. 21 48.
Tadashi Nomoto and Yoshihiko ...
Barbara J. Grosz and Candace L. Sidner. (19 86)
Attention, Intentions and the Structure of
Discourse.
Computational Linguistics, 12 , pp.
17 5 20 4.
Marti A. Hearst. (19 97)
TextTiling: Segmenting...
... 1
n
j =1
2
2
+
1 +
1
n
σ
2
−
2
n
E
x
2
j
−
2
n
j=k
E
[x
j
x
k
]
=
=
1
n − 1
n
j =1
2
2
+
1 +
1
n
σ
2
−
2
n
µ
2
+ σ
2
− 2
n − 1
n
µ
2
=
=
1
n − 1
n
j =1
n − 1
n
σ
2
−
2
n
µ
2
+
2
n
µ
2
= ... to
1
n − 1
n
j =1
E
(x
j
− ¯x)
2
=
=
1
n − 1
n
j =1
E
x
2
j
− 2
E
[x
j
¯x] +
E
¯x
2
=
=
1
n − 1
n
j =1
µ
2
+ σ
2
−
2
n
E
x
j
n
k =1
x
k
+ µ
2
+
σ
2
n
=
=
1
n − 1
n
j =1
2
2
+
1 ... 1
n
j =1
n − 1
n
σ
2
−
2
n
µ
2
+
2
n
µ
2
= σ
2
.
(10 0)
Hence, we get that
E
[s
2
] = σ
2
and that s
2
is an unbiased estimate for
σ
2
.
47
(a) (b)
(c) (d)
Figure 12 : Robust incremental vs....