交换半环上的半Leibniz代数

在交换半环上定义半Leibniz代数,给出了半Leibniz代数的理想和商代数,研究了半Leibniz代数的同态和相关结论;利用半Leibniz代数的同余关系,得到半Leibniz代数的商代数的一个同构定理。     

微分算子Lie代数上的Leibniz 2-上循环

中心扩张问题在Leibniz代数的研究中起着非常重要的作用,因此有许多文章研究各种各样Leibniz代数的中心扩张问题.在这篇文章里,我们确定了微分算子Lie代数上的所有一维Leibniz中心扩张.     

完备Leibniz代数的性质及其低维分类

本文研究了完备Leibniz代数的性质及低维分类.利用Leibniz代数中平方元生成的双边理想,获得了小于五维的完备Leibniz代数完整的分类,以及五维时一类特殊情况下完备Leibniz代数的分类,从而推广了Leibniz代数的结构理论.     

从Leibniz超代数到Lie-Yamaguti超代数（英文）

本文研究了Lie-Yamaguti超代数的构造.利用左Leibniz超代数,先给出左Leibniz超代数的构造方法,再给出用左Leibniz超代数构造Lie-Yamaguti超代数的方法,获得了Lie-Yamaguti超代数的构造方法.将Leibniz代数和Lie-Yamaguti代数的构造推广到超代数的情形.     

三维Leibniz代数的分类

Leibniz代数是比Lie代数更广泛的一类代数,它通常不满足反交换性.在这篇文章里我们确定了维数等于3的Leibniz代数的同构类.     

Witt代数和Virasoro代数上的Poisson代数结构

Poisson代数是指同时具有结合代数结构和李代数结构的一类代数,其结合代数结构和李代数结构满足Leibniz法则.确定了特征为0和特征为p>0的基域上的Witt代数和Virasoro代数上的Poisson代数结构.     

模糊推理与粗糙集

本文从逻辑推理的角度建立起了模糊逻辑L*与粗糙集之间的密切联系,接着从另一不同角度出发定义了R0代数中元素的粗糙近似,并与已有文献进行了分析对比,最后,细致研究了粗糙逻辑度量空间的内部结构。     

一类伽利略共形李代数的Poisson结构

Poisson代数是其兼有的结合代数结构和李代数结构满足Leibniz法则.利用根系阶化的方法确定一类伽利略共形李代数gca代数上的Poisson代数结构.     

一类超W-代数上的Poisson超结构

源于Poisson几何的Poisson代数同时具有代数结构和李代数结构,其乘法与李代数乘法满足Leibniz法则.超W-代数是复数域C上的无限维李超代数.主要研究一类超W-代数上的Poisson超结构.     

区间值模糊数与区间值粗糙模糊数

把经典Z.Pawlak粗糙集与区间值模糊集相结合,研究区间值模糊数的基本理论.讨论区间值模糊数的基本性质和四则运算法则及其与其它各种区间数的关系,并给出区间值模糊数的刻画定理.同时,在经典Z.Pawlak粗糙集的框架下定义实直线上的粗闭区间套,提出区间值粗糙模糊数的定义.利用模糊数的表现定理给出区间值粗糙模糊数的一个刻画.     

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.     

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.     

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.     

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     

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     

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).     

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.     

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.