... Networking
Volume 2010, Article ID 482975, 13 pages
doi:10.1155/2010/482975
Research Article
The Waterfilling Game-Theoretical Framework for Distributed
Wireless Network Information Flow
Gaoning ... according to the single-
player waterfilling that depends on the current state of the
game. The following theorem shows the convergence and
optimality of the algo...
... b
1.5
holds for all a, b > 0witha
/
b.
For more results, see 9–23.
The purpose of the present paper is to find the greatest values α
1
,α
2
and the least
values β
1
,β
2
such that the double ... result and the continuity of gt we clearly see that there exists δ δα
1
> 0
such that gt < 0fort ∈ 1, 1 δ. Then the last equality in 2.4 implies that f...
... Equations
Proof. The approach of the proof is very similar to those in 17, 19, 20. Here, we omit it.
Theorem 3.2. Provided that conditions (H
1
)–(H
4
) hold, then the system 2.2 with the conditions
2.3 ... ψ
a
exp
t
a
χ
s
ds
t
a
exp
t
s
χ
r
dr
ψ
s
ds, 2.9
for all t ∈ a, b.
In order to obtain our main results, we need the following hypot...
... A.6. Therefore the lemma is true and A.1 holds.
Acknowledgments
This work is supported by the Specialized Research Fund for the Doctoral Program of Higher
Education for New Teachers and the ... apply the twist condition between the zero and at infinity
for f to establish the existence of periodic solutions of 1.2. Under the superlinear conditions
1.5, there is no...
... 0,u
1
n
i1
β
i
u
θ
i
.
1.5
They established a corresponding iterative scheme for the problem by using the monotone
iterative technique.
All the above works were done under the assumption that the nonlinear ... Ax for x ∈ ∂D
K
. Then the following results hold.
1 If Ax≤x, x ∈ ∂D
K
,theni
K
A, D
K
1.
2 If there exists x
0
∈ K \{0} such that x
/
...
... D. 3.27
Therefore, the well-known jump relationships see 13, 14 imply that
−→
ψ
a, b, c, d
T
0, 0, 0, 0
T
. 3.28
So we complete the proof of the theorem.
Combining Theorems ... of it by the assumption that Im k>0, then Theorem 2.1 in Section 2
and Theorem 3.3 in Section 3 are also true.
Boundary Value Problems 7
Then zero extend b, c,andd to the whole ∂Ω in t...
... be
Caratheodory, by this we mean the following:
i for almost every t ∈ I, the function ft, ·, · is continuous;
ii for each x, y ∈ R × R, the function f·,x,y is measurable on I;
iii for ... that ut ≤ βt for any t ∈ T
1
,T
2
. The argument of the case of
αt ≤ ut for any t ∈ T
1
,T
2
is similar.
Assume that ut >βt for some t ∈ T
1
,T
2
, th...
... likewise the
power plots of their wavelet t ransformation are also simi-
lar (Figure 7(b)). As expected they also clustered together in
Figure 5.
To illustr a te the effect of the wavelet transformation,
we ... delay, the wavelet transform addresses it by
using dB2 (Figure 1) mother function that can be scaled. If
the signal and wavelet are in a good match, then the corre-
lation b...
... transitions. The M-GC filter benefits from the
optimization of the scale and tail parameters and therefore
perform at least as good as the myriad and meridian filters.
Similarly, the M-GC filter performs ... that the search space is the interval I
= (0, 2], the
function g (27) can be evaluated for a finite set of points P
∈
I, keeping the value that maximizes g, setting it as...
... mobile wireless networks, when a node
stores its data on other nodes [1, 2], it is desirable that the
chosen nodes are in the neighborhood in the future, so that
when there come the requests for the ... these F seconds. Then the size of
the transmission packets needed for collecting trajectory
information is
X/42Y(N/Z) of the data sent to the
identified near likely...