... 90727, 16 pages
doi:10.1155/2007/90727
Research Article
Sparse Approximation of Images Inspired from the Functional
Architecture of the Primary Visual Areas
Sylvain Fischer,
1, 2
Rafael Redondo,
1
Laurent ... computational hypothesis about how the primary visual
areas could achieve a noise robust sparse approximation of
the visual information unde...
... inequality of L
p
approximation by the Baskakov-Durrmeyer operator
given in 1.10. By means of K -functional and modulus of smoothness defined in 5, we will
extend 1.4 to the case of higher ... proof of Theorem 2.2 is
finished.
Acknowledgment
The research was supported by the National Natural Science Foundation of China no.
90818020.
References
1 V. A. Baskakov...
... pages
doi:10.1155/2010/476913
Research Article
Viscosity Approximation to Common Fixed
Points of Families of Nonexpansive Mappings with
Weakly Contractive Mappings
A. Razani
1, 2
and S. Homaeipour
1
1
Department of Mathematics, ... p
≤ 0, ∀y ∈ F. 3.3
Proof.
Step 1. We prove the uniqueness of the solution to the variational inequality 3.3.Suppose
that p, q ∈ F are di...
... ≥ 0 for t ∈ 0, 1
, then the solution of 2.16 is nonnegative.
Corollary 2.5. Let Φ : M → C0, 1 ∩ C
1
0, 1 be the operator such that Φf is the solution of
2.16. Then we have
i if f
1
t ... u
1
0.
2.18
Then there exist m mf > 0, M Mf > 0 such that
ml
t
≤ u
t
≤ Ml
t
for t ∈
0, 1
. 2.19
2.2. The Proof of Theorem 1.1
Claim 1 see...
... is,
∞
i=1
α
i
=∞. (3.61)
The necessity of condition (b) is proved.
Summing up the about argument, the conclusion (1) of Theorem 3.3 is proved.
The conclusion (2) of Theorem 3.3 can be obtained from Theorem 3.2 ... ∈
N
i
=1
(F(T
i
)
C), then this p is the unique solution of the following vari-
ational inequality:
(I − f )(p),J(p − u)
≤
0, ∀u ∈
N
i=1
F
T
i...
... ω
0
M, A, p, ·, ,·, and this completes the proof.
Acknowledgments
The author wishes to thank the referees for their careful reading of the paper and for their
helpful suggestions.
References
1 ... l
M, q, ·, ,·. This completes the proof.
The following result is a consequence of the above theorem.
Corollary 2.5. i If 0 <p
k,l
< 1 for each k and l,then...
... it can be seen from Figure 12 that the
rate of increase of the mean of the presence probabilities
of the void cells also increases. These observations validate
the effectiveness of the proposed ... left or to the
bottom of the static cell, and if they are moved a distance of
r
− (r/
√
2) (at the worst case) beyond the cell center towards
the static cell,...
... Yz is the Z transform of the output sequence ykT, Fz is the Z transform of the
input sequence fkT,andPSE{u} denotes the expression, which results from the power
series expansion of the function ... that is, the use
of the generating function 2.13 for β 1,γ 1/2 and then the PSE, which is convergent of
order 2. Other forms of generation functions f...
... that
the features of the UML language do not bias the definition of
the domain-modeling problem. This is because the semantics
of the model become separated from the notation of the
model.
After ... between
IP blocks in the active mode of the system. In addition, the
requirement is further refined by the functional specification
of the system represented...
... 12 Journal of Inequalities and Applications
Proof. From the proof of Theorem 1.2, when the conditions H
1
∗
and H
2
are satisfied, the
iterative sequences {v
n
} and ... satisfied. From iii, it is easy to see that assumption H
2
is
satisfied. Therefore, the following result is deduced from Theorem 1.2.
Theorem 3.1. If the assumptions i–iii are satisfied, then t...