Hardy-Hilbert积分不等式的一个新推广及其应用

通过引入一个形如x1 x(x∈[0, ∞))的幂指函数建立了带权的Hardy-Hilbert积分不等式的新推广.并证明了系数(2)(sinπp)是最佳值.作为应用,给出了Hardy-Littlewood积分不等式的一个推广.     

Approximation with wave packets generated by a refinable function

We consider best -term approximation in with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best -term approximation in for a large class of wave packets are completely characterized in terms of Besov spaces.

As an application of the main result, we show that for -term approximation in with elements from an oversampled version of a framelet system with compactly supported generators, the associated approximation classes turn out to be (essentially) Besov spaces.

     

Gamma算子在Orlicz空间L*_Φ(0,∞)中加Jacobi权同时逼近的强逆不等式

讨论由Young函数生成的Orlicz空间L*_Φ(0,∞)的性质,并给出Orlicz空间L*_Φ(0,∞)具有Hardy-Littlewood性质的充要条件,然后借助加Jacobi权修正的K-泛函和加Jacobi权连续模及其等价性建立Gamma算子在Orlicz空间L*_Φ(0,∞)中加权同时逼近的两种强逆不等式.     

Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

On the solution existence of implicit quasivariational inequalities with discontinuous multifunctions

In this article, we established some solution existence theorems for implicit quasivariational inequalities. We first established some results in finite-dimensional spaces and then a solution existence result in infinite-dimensional spaces was derived. Our theorems are proved for discontinuous mappings and sets which may be unbounded. The results presented in this article are improvements of results in Cubiotti, and Yao (Cubiotti, P. and Yao, J.C., 1997, Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings. Mathematical Methods of Operations Research, 46, 213–328; Cubiotti, P. and Yao, J.C., 2007, Discontinuous implicit generalized quasi-variational inequalities in Banach spaces. Journal of Global Optimization (To appear))     

单形内任一点的一个含参不等式

本文证明了与ｎ维单形内部任意一点有关的一个含参数不等式,并应用它得到了几个与ｎ维单形体积有关的不等式。     

A smoothing method for mathematical programs with equilibrium constraints

Received May 3, 1996 / Revised version received November 19, 1997 Published online January 20, 1999     

Analytical Linear Inequality Systems and Optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.     

Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper considers the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.     

Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach

Recent simulation results imply the lowering of the ground-state correlation energy per counterion at a charged planar wall, compared with that of the 2D and 3D one-component plasma systems. Our aim is to correctly evaluate the ground-state energy of strongly-coupled counterion systems by considering a quasi-2D bound state where bound counterions are confined to a layer of molecular thickness. We use a variational approach based on the Gibbs-Bogoliubov inequality for the lower-bound free energy so that the liquid-state theory can be incorporated into the formulations. The soft mean spherical approximation demonstrates that the lowered ground-state energy can be reproduced by the obtained analytical form of a quasi-2D bound state.