关于多项式映射自同构恒等集的一个注记

本文给出了判定一个仿射代数集是否是一个自同构恒等集的充分条件.作为一个推论,我们给出了Mckay-Wang的一个问题的一个新证明.我们也给出了一些具体的例子来说明主要的定理.     

Dedekind 群的一个刻画

本文给出了Dedekind群的一个刻画.即如果一个群G有一个无不动点的弱幂同构,则G是一个Dedekind群.     

一个不可定向曲面的极小禁用子图的构造

曲面S的一个极小禁用子图是这样的一个图,它的任何一个顶点的度都不小于3,它不能嵌入在S上,但是删去任何一条边后得到的图能嵌入在S上.本文给出了四种构造一个不可定向曲面的极小禁用子图的方式,即粘合一个顶点,一个图的边被其它的图替换,粘合两个顶点,将一个图放在另一个图的一个曲面嵌入的面内.     

基于身份的门限密码体制

描述一个公钥密码体制,其中参与者的公钥是一个公开值,例如他的身份,这个体制由很多可信中心联合产生一个大合数N=pq,p,q为素数且p≡q≡3(mod 4),任意其中一个可信中心都不知道N的分解.另外,每一个可信中心拥有一个秘密指数的一个分享,这样产生一个门限解密.本文将讨论所提出的方案的安全性,并证明它与解决二次剩余问题的困难性有关.     

一个带约束的拟线性椭圆特征问题

通过构造伪梯度向量场和下降流的方法, 证明了一个带约束的拟线性椭圆特征值问题至少有一个正解、一个负解和一个变号解.     

浅谈中学代数中代数运算概念的教学

代数运算是近代算学中一个很重要的概念。下面是它的一个定义(不是函数观点的定义): 令M是一个集合,这个集合至少含有一个元素。若是有一个确定的法则,通过它对于集合M中一对有次序的元素a与b,能够得到集合M的一个确定的元素c与之对应,那么这个法则叫做集合M的一个代数运算。     

关于k－复盖图的几个条件

设Ｇ是一个图，ｋ为正整数．图Ｇ的一个ｋ－正则支撑子图Ｆ称做图Ｇ的一个ｋ－因子．若图Ｇ的每一条边ｅ都属于Ｇ的一个ｋ－因子，则称Ｇ是一个ｋ－复盖图．本文给出了一个图Ｇ是ｋ－复盖图的几个充分条件．     

关于Goldie环的一些注记

本文给出了一个判别准则来判定一个(半)素右Goldie环是否是一个左Goldie环,同时也考虑了一个拟生成元与其自同态环之间的关系。     

关于k—复盖图的几个条件

设Ｇ是一个图，ｋ为正整数，图Ｇ的一个ｋ－正则支撑子图Ｆ称做图Ｇ的一个ｋ－因子，若图Ｇ的每一条边ｅ都属于Ｇ的一个ｋ－因子，则称Ｇ是一个ｋ－复盖图，本文给出了一个图Ｇ是ｋ的复盖图的几个充分条件。     

Artin半单环的特征

本文证明了如下结果：环Ｒ是Ａｒｔｉｎ半单的当且仅当存在一个基数ｃ，使得任意左Ｒ－模是一个连续模和一个ｃ－限制的ＥＳ－模的直和，也当且仅当存在一个基数ｃ，使得任意左界Ｒ－模是一个拟投射模和一个ｃ－限制的ＥＳ－模的直和。     

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.