变时滞随机Cohen-Grossberg神经网络的指数稳定性的新判据

通过建立L算子不等式,利用随机分析技巧得到了变时滞随机Cohen-Grossberg神经网络的p-阶矩指数稳定的一个充分条件,并给出实例进行了说明.

On p-ω-hyponormal Operators

In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.

Strong Converse Inequalities for Szasz-Mirakjan Operators with Weights

In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.

Inequalities in Connection with Post-Widder Operators

The purpose of this paper is to derive the inequalities in connection with PostWidder operators， the result is corresponding to Wickeren in connection with Bernstein polynomials.

Exponential stabilization of distributed parameter switched systems under dwell time constraints

The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.

A Note of log A≥log B

In this paper, firstly we shall show some equivalent conditions of A 〉 B 〉 0; secondly by using the results of ours we shall show some characterizations of the chaotic order（i.e., logA≥log B） by norm inequalities.

Weighted Norm Inequalities for the Hardy Operator

In this paper.a characterizationis,obtained for those pairs of weight funetions on (0=∞) for which the Hardy operator Pf(x)=f(t)dt is bounded from (μ) to ,0<q<1<p <+∞.

Littlewood-Paley Operators on Weighted Lipschitz Spaces

Littlewood-Paley operators, the g-function, the area integral and the function g^＊λ, are considered as operators on weighted Lipschitz spaces. It is proved that the image of a weighted Lipschitz function under one of these operators is either equal to infinity almost everywhere or is in weighted Lipschitz spaces.

Hardy-type inequalities on strong and weak Orlicz-Lorentz spaces

In the present paper, the characterization of strong-type modular inequality ∫ 0 ∞φ(Sf (t))w(t)dt≤∫0∞ φ(Cf (t))w(t)dt, f↓ is given, where φ∈Δ' and S is a Hardy operator. Furthermore, the equivalent conditions of modular inequalities and norm inequalities related to weak Orlicz-Lorentz spaces are researched. We also explore the conditions for Orlicz-Lorentz spaces and weak Orlicz-Lorentz spaces to be normable. Finally, the weak boundedness of certain Hardy-type operators on Orlicz-Lorentz spaces is studied.

Operator-valued martingale transforms in rearrangement invariant spaces and applications

In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales,then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces.These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces.Finally we give an equivalent characterization of UMD Banach lattices,and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.

COMPARISON,SYMMETRY AND MONOTONICITY RESULTS FOR SOME DEGENERATE ELLIPTIC OPERATORS IN CARNOT-CARATHEODORY SPACES

This paper studies the properties of solutions of quasilinear equations involving the p-laplacian type operator in general Carnot-Caratheodory spaces. The authors show some comparison results for solutions of the relevant differential inequalities and use them to get some symmetry and monotonicity properties of solutions, in bounded or unbounded domains.

UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES: AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

This paper considers a class of variational inequalities that model the buckling of a von Karman plate clamped on a part of its boundary and lying on a fiat rigid support. The existence and bifurcation results of D. Goeleven, V. H. Nguyen and M. Thera[6] rely on the Leray- Schauder degree. Using the topological degree for pseudo-monotone operators of type (S+), the author establishes a more general existence result for such unilateral eigenvalue problems.

TWO-WEIGHT NORM INEQUALITY FOR IMAGINARY POWERS OF A LAPLACE OPERATOR

We study two-weight norm inequality for imaginary powers of a Laplace operator in R^n, n ≥ 1, especially from weighted Lebesgue space Lv^p（R^n） to weighted Lebesgue space Lμ^p（R^n）, where 1 〈 p 〈 ∞. We prove that the two-weighted norm inequality holds whenever for some t 〉 1, （μ^t, v^t） ∈ Ap, or if （μ, v） ∈Ap, where μ and v^-1/（p-1） satisfy the growth condition and reverse doubling property.

Existence and regularity of solutions to semi-linear Dirichlet problem of infinitely degenerate elliptic operators with singular potential term

In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the existence and regularity of multiple nontrivial solutions have been proved.

Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality

We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.

Strong Converse Inequality for Modified Szasz Operators

In this paper, we show the direct and converse theorems of strong type of approximation for modified Szasz operators. Rom these theorems, the characterization of approximation for these operators is derived. The obtained results are similar to the corresponding ones of the Szasz operators.

bmo _ρ(ω) Spaces and Riesz transforms associated to Schrdinger operators

We introduce the BMO-type space bmo ρ（w） and establish the duality between h^1ρ（ω） and bmo ρ（ω）,where ω∈A1^ρ∞（R^n） and ω＇s locally behave as Muckenhoupt＇s weights but actually include them. We also give the Fefferman-Stein type decomposition of bmop（ω） with respect to Riesz transforms associated to Schrodinger operator L,where L=-△＋V is a SchrSdinger operator on R^2 （n≥3） and V is a non-negative function satisfying the reverse HSlder inequality.

Equivalent Properties for CD Inequalities on Graphs with Unbounded Laplacians

The CD inequalities are introduced to imply the gradient estimate of Laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,∞) and CD(K,n).

Multiple weighted estimates for commutators of multilinear fractional integral operators

Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.

ＯＮＴＨＥＨＹＰＥＲＢＯＬＩＣＯＢＳＴＡＣＬＥ ＰＲＯＢＬＥＭＯＦＦＩＲＳＴＯＲＤＥＲ

This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.