Báo cáo sinh học: " Research Article Global Optimal Regularity for the Parabolic Polyharmonic Equations" pptx
Báo cáo sinh học: " Research Article Global Optimal Regularity for the Parabolic Polyharmonic Equations" pptx
... Problems
Volume 2010, Article ID 879821, 12 pages
doi:10.1155/2010/879821
Research Article
Global Optimal Regularity for
the Parabolic Polyharmonic Equations
Fengping Yao
Department of Mathematics, Shanghai ... in
the theory of partial differential equations, are two fundamental estimates for elliptic and
parabolic equations and the basis for the existence, uniq...
Báo cáo sinh học: " Research Article Stabilities of Cubic Mappings in Fuzzy Normed Spaces" pptx
...
∗ was the historic transition from the following famous
Advances in Difference Equations 7
The first two terms on the right hand side of the above inequality tend to 1 as n →∞.
Therefore we have
N
C
x
− ... fxy−fx−fy≤ for all x, y ∈ X and some
>0. Then, there exists a unique additive mapping T : X → Y such that fx − Tx≤
for all x ∈ X. Hyers
,
theorem...
Báo cáo sinh học: " Research Article Boundary Value Problems for Delay Differential Systems" ppt
... 3.11, 3.12,
and the Cauchy matrix Kt, s has the form of 3.6. Therefore, the following theorem holds
see 10.
Theorem 3.1. Let Q be defined by 3.15 and rank Q n
1
. Then the homogeneous ... the method of their deriving is a crucial part of the proof of Theorem 4.1 where we
give their form as well.
Proof. Substitute 4.18 into 4.3 and equate the terms t hat are mu...
Báo cáo sinh học: "Research Article Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales" ppt
... 2.6
and for h 0, let C
0
C.
Definition 2.7. For h>0, let Z
h
be the strip
Z
h
z ∈ C : −
π
h
<Im
z
≤
π
h
, 2.7
and for h 0, let Z
0
C.
Definition 2.8. For h>0, we define the ... and ρtt, then t is called
left dense. We also need below the set T
k
which is derived from the time scale T as follows. If
T has a left-scattered maximum m, then T
k
T −...
Báo cáo sinh học: " Research Article Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions" docx
... physical optics approximation, the
ratio of the surface currents is the same as for the impedance strip. For the comparison
of the physical characteristics of the fractional and impedance strips ... used the assumption A
2
.AsΛ < 1, therefore is a contraction. Thus, the
conclusion of the theorem follows by the contraction mapping principle.
Now, we state Krasn...
Báo cáo sinh học: " Research Article Determining Consecutive Periods of the Lorenz Maps" pot
... some are the shift maps for other ones. Give the order to the arrays; see
Algorithm 5.
Program 2(b)
Check against the ordering rule of 2.1 and the condition of 2.2 and find out all of the true
periodic ... in which some are the shift maps for other ones. Give the order to the arrays. Let us
call the program Program 2.
By the steps we have a computer program in M...
Báo cáo sinh học: " Research Article Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem" docx
... ∞
sup
f
u
u
<r
−1
. 3.6
The aim of the following section is to establish some simple criteria for the existence of
multiple positive solutions of the BVP 1.1, which gives a positive answer to the questions
stated ... questions
stated above. The key tool in our approach is the following fixed point theorem, which is
a useful method to prove the existence of positiv...
Báo cáo sinh học: " Research Article New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions" pdf
... 7–23 and the references therein. However, the theory
of boundary value problems for nonlinear fractional differential equations is still in the initial
stages and many aspects of this theory need ... solutions for problem P, for example, see Pang et al. 26,YangandWei
27, Feng and Ge 28, and references therein. All of these results are based upon the fixed-
point index th...
Báo cáo sinh học: " Research Article Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks" ppt
... that have the form of (31)or(32)isexcluded
from the viewpoint of a necessary condition for the identity
to exist in y(T). Thus we obtain the following theorem.
Theorem 1. For a given T, the following ... 1.
Next, consider the adjacency matrix Φ
∈
{
0, 1}
(n+m+p)×(n+m+p)
for the directed graph induced by
the Boolean network of the system (21). For example, the
adjac...
Báo cáo sinh học: " Research Article Optimized Projection Matrix for Compressive Sensing" ppt
... to address the
problem of optimization the projection matrix, there is still
great work to do. Here are some advices for future research.
(1) How to perform the proposed method when the signals
are ... norm space which simplifies the
problem. An advantage of using l
2
in the given problem is
that it considers the errors of all elements. Therefore it forms
the following form...