On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.     

一个具最佳常数的复合核积分不等式

引入Γ-函数等特殊函数,利用权函数方法和实分析技巧,建立一个具最佳常数的复合核积分不等式.考虑了它的等价式,证明了它们的常数因子是最佳的,并通过取特殊的参数值,得到一些有意义的结果.     

非球面检测中最佳入射球面波和最佳参考球面波的确定

为了能够对非球面光学元件面型进行高精度的干涉检测,提出了一种确定最佳入射球面波和最佳参考球面波的新方法。该方法通过计算分析入射球面波与非球面反射波干涉条纹密度,确定最佳入射球面波的波源位置;通过计算分析在干涉图记录平面CCD上干涉条纹的密度,确定非球面检测时参考球面波波源的最佳位置。应用该理论与方法,不仅可明确非球面检测时CCD等光路元件选型的具体策略,而且可用于指导非球面检测调试过程,并能够通过对干涉图的深入分析,获得更多被测非球面的信息。     

The Order of Best Approximation in Some Classes of Functions

Starting from the equivalence between the Ditzian–Totik modulus and , where , in this article large classes of functions are introduced for which the modulus can be easily calculated. As a consequence, very good estimates for the bestapproximation are obtained. The attempts to estimate or calculate themodulus can be a very intricateproblem.     

Statistical mechanics and the Gauss principle

In an essentially statistical approach to statistical mechanics, it is seen that the Gauss principle of the arithmetic mean may be taken as the starting point. The equations from which the subject can be built up are deduced from the Gauss principle of the arithmetic mean.     

赋$\beta$-范空间中的最佳逼近问题

本文讨论赋$\beta$-范空间中的最佳逼近问题.以[1]引进的共轭锥为工具,借助[2]中关于$\beta$-次半范的Hahn-Banach延拓定理,第二节给出赋$\beta$-范空间的闭子空间中最佳逼近元的特征,第三节得到赋$\beta$-范空间中任何凸子集或子空间均为半Chebyshev集的充要条件是空间本身严格凸,文章最后证明了严格凸的赋$\beta$-范空间中任何有限维子空间都是Chebyshev集.     

On the sensitivity matrix of the Nash bargaining solution

In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson (J Econ Theory, 42: 50–58, 1987), this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strongly d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic.     

Classes of general H-matrices

Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. H-matrices such that their comparison matrices are nonsingular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or nonsingular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance property are used in the characterizations. Finally, a classification of the set of general H-matrices is obtained.     

An application of Furuta inequality and its best possibility

This paper shows the best possibility for outer exponents of some inequalities under some conditions, and a counter example is obtained.     

一个推广的具最佳常数的多参数Hardy-Hilbert不等式

引入λ1,λ2,α等多个参数,利用权系数方法,给出了一个推广的具最佳常数的多参数Hardy-Hilbert重级数不等式,并给出其等价形式.