基于优势关系下不协调目标信息系统的分布约简

在基于优势关系下的不协调目标信息系统中引入了分布约简和最大分布约简的概念,并讨论了二者之间的关系,而且得到了分布和最大分布约简的判定定理以及辨识矩阵,建立了不协调目标信息系统的分布和最大分布约简的具体方法,同时通过实例验证了该方法的有效性,从而进一步丰富了粗糙集理论。     

基于优势关系的不协调区间值目标信息系统的分布约简

区间值信息系统是单值信息系统的的一种推广,知识约简是粗糙集理论的核心问题之一.在基于优势关系下的不协调区间值信息系统中引入了分布约简和最大分布约简的概念,进一步建立了分布约简和最大分布约简的判定定理和辨识矩阵,从而利用辨识矩阵给出了在优势关系下不协调区间值目标信息系统分布约简的具体方法.     

基于优势-等价关系下不协调目标信息系统的分布约简

引入优势-等价关系下不协调目标信息系统的概念,讨论了该系统的分布约简和最大分布约简之间的关系,得到了辨识矩阵及分布约简和最大分布约简的判定定理,并通过实例验证了该方法的有效性.     

集值决策表基于邻域关系的属性约简

集值信息系统是完备信息系统的广义形式,它当中的一些对象在某些属性下的取值可能不止一个,反映的是信息的不确定性.本文在集值信息系统上引入对象的邻域关系,并以每个对象的邻域作为基本集,建立了集值信息系统的粗糙集方法.为了简化的知识表示,我们进一步讨论了邻域协调集值决策表的正域约简与邻域不协调集值决策表的近似分布约简,给出了正域约简与近似分布约简的等价刻画条件,并借助区分函数给出了计算正域约简与近似分布约简的方法.     

基于优势关系的不协调区间值目标信息系统的分配约简

区间值信息系统是单值信息系统的一种推广模型,知识约简是粗糙集理论的核心问题之一,在基于优势关系下的不协调区间值目标信息系统中引入了分配约简和近似约简的概念,分别讨论了它们二者之间的关系,进一步给出了知识约简的判断定理和辨识矩阵,从而提供了在优势关系下不协调区间值目标信息系统分配约简的具体方法。     

优势关系下不协调目标信息系统的部分一致约简

在基于优势关系下的不协调目标信息系统中引入了部分一致约简的概念, 并得到了部分一致约简的判定定理以及辨识矩阵, 建立了不协调目标信息系统的部分一致约简的具体方法, 同时通过实例验证了该方法的有效性, 从而为优势关系下信息系统的知识发现提供了理论基础.     

不完备模糊目标信息系统的α,β精度约简算法

本文首先定义了不完备模糊目标信息系统及其非对称相似关系,然后借鉴经典的可辨识矩阵精度约简算法,提出一种新的基于非对称相似关系的可辨识矩阵(α,β)精度约简算法,对不完备模糊目标信息系统进行属性约简.最后给出一个实例,检验算法的可行性.     

不一致不完备直觉模糊信息系统的属性约简

利用广义优势关系,可完成不完备直觉模糊信息系统属性约简工作.若不完备直觉模糊信息系统属性约简不一致时,则可进一步利用广义优势关系定义此类信息系统的分布函数和最大分布函数,然后介绍分布约简和最大分布约简的概念,最后给出求分布约简和最大分布约简的有效方法.由此可成功解决不一致不完备直觉模糊信息系统属性约简问题.     

基于依赖空间的不协调决策信息系统的分配约简

从属性集角度研究不协调决策信息系统的分配约简问题。定义了一种决策分配二元关系,并利用这种关系建立了属性集幂集上的等价关系,由此产生依赖空间。同时利用决策分配二元关系和依赖空间给出了不协调决策信息系统分配协调集的判定定理,进而得到了一种保持不协调决策信息系统分配不变的属性约简方法。同时通过实例验证方法的有效性。     

基于变精度粗糙集模型的属性约简的β值稳定区间讨论

引入了基于变精度粗糙集模型的上、下分布属性约简方法的关于β值的稳定区间的概念,通过β值的稳定区间讨论,将β的取值区间[0,0.5]划分成为有限个稳定区间,当β值落在某个稳定区间内时,使得基于变精度模型的上、下分布约简不发生改变.不仅从理论上证明了β值稳定区间的个数是有限的,而且通过实例说明求解方法的简便和易于实现.为决策者提供了一种如何选择β值而获得上、下分布约简的参考.     

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.     

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.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.