集值优化问题的Benson真有效解的广义最优性条件

引进了关于集值映射的(1,α)-阶Clarke导数,(1,α)-阶邻接导数,(1,α)-阶伴随导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型Kuhn-Tucker最优性条件。     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

α-阶近似锥-弧连通集值优化弱有效元的最优性条件

引进了α-阶近似锥-弧连通集值映射,举例说明了它是锥-弧连通集值映射的真推广.借助Y-切锥引进了广义Y-切上图导数,讨论了它与广义切上图导数的关系.当目标函数为α-阶近似锥-弧连通集值映射时,得到集值优化取得弱有效元的充分和必要条件.     

次预不变凸集值优化导数型最优性条件

引入了集值映射的α-阶锥次预不变凸概念,借助于α-阶相依上导数,建立了锥次预不变凸集值映射的导数型择—性定理,并利用择—性定理获得了集值优化导数型的最优性必要条件.     

α-阶次预不变凸集值优化（英文）

给出α-阶次预不变凸性概念,举例说明它是预不变凸性的真推广.利用广义切上图导数的性质,得到集值优化取得Henig真有效元的必要条件.当目标函数为α-阶次预不变凸时,建立了集值优化取得Henig有效元的充分条件,因而得到统一形式的充分和必要条件.并给出两个例子解释本文的主要结果.     

拟不变凸集值优化的Kuhn-Tucker条件与Wolfe对偶

研究了拟不变凸集值优化最优性的Kuhn-Tucker条件及Wolfe型对偶问题．首先引进了alpha-阶G-拟不变凸集和alpha-阶S-拟不变凸集值函数的概念,由此研究了alpha-阶G-拟不变凸集所对应的伴随切锥及alpha-阶伴随导数的性质;最后,借助alpha-阶伴随切导数刻画了alpha-阶S-拟不变凸集值优化最优性的Kuhn-Tucker条件和Wolfe型对偶．     

变序结构局部弱非控点的二阶刻画

引进了一种二阶切导数,借助该切导数给出了变序结构集值优化问题取得局部弱非控点的二阶最优性必要条件.在某种特殊情况下,给出了一阶最优性条件.通过修正的Dubovitskij-Miljutin切锥导出的约束规格,给出了两个集值映射之和的二阶相依切导数的关系式,进一步得到目标函数与变锥函数的二阶相依切导数分开形式的最优性必要条件.     

空间-时间分数阶对流扩散方程的数值解法

本文考虑一个空间-时间分数阶对流扩散方程.这个方程是将一般的对流扩散方程中的时间一阶导数用α(0＜α＜1)阶导数代替,空间二阶导数用β(1＜β＜2)阶导数代替.本文提出了一个隐式差分格式,验证了这个格式是无条件稳定的,并证明了它的收敛性,其收敛阶为O(ι h).最后给出了数值例子.     

集值优化问题的Benson真有效解的广义导数型最优性条件

引进了集值映射关于锥的Clarke切导数, Adjacent切导数与Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义导数型最优性条件．     

集值向量优化的二阶最优性必要条件

在赋范空间中给出了集值映射的二阶切集的概念,利用二阶切集,定义了集值映射的二阶切导数。然后,获得了集值向量优化问题弱极小元的两个二阶最优性必要条件。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.