参系数零维分片代数簇的实零点

分片代数簇是一些多元样条函数的公共零点集. 文中表明: 解参系数分片代数簇问题可转化为解有限个包含严格不等式的参系数多项式系统. 利用半代数系统的正则分解和柱形代数分解方法, 提出了计算零维参系数分片代数簇无挠实零点数的上确界, 以及达到上确界时实零点在各个胞腔内的数目分布情形的算法. 该算法同时能产生达到上确界的充要条件, 以及达到上确界时实零点数在各个$n$维胞腔内 取得某种分布的充要条件. 也给出了另一算法, 用于产生零维分片代数簇在$n$维复形中的 各个$n$维胞腔内恰有指定数目的相异无挠实零点的充分必要条件.     

Tarski模型外的一类机器可判定问题

利用对称多项式的降维方法和证明代数不等式的胞腔分解方法,给出了一个实用的算法, 用于判定一类变元个数也是变量的多项式正性命题.这是一类在Tarski模型外的机器可判定问题.在Maple平台上,根据该算法设计的程序nprove,可以快速实现判定目标.     

刻画排列的连通分支

应用柱代数分解算法和简化的胞腔相邻算法,得到一个刻画R3中由n个紧半代数集所组成排列连通分支的算法.     

胞腔代数的箭图构造(英文)

本文研究了胞腔代数.利用箭图及关系,我们刻画民平凡扩张是胞腔代数的路代数,并得到了两种直接构造胞腔代数的方法.     

三维半群代数

首先给出代数闭域上三维半群代数的幂等元集和Jacobson根,并且刻画了三维半群代数的同构类.通过计算箭图,研究了三维代数的表示型.进一步,证明一个三维(或者二维)半群代数是胞腔的,当且仅当它是交换的.作为推论,得到一个左零带所对应的半群代数是胞腔的,当且仅当这个左零带是一个半格.     

胞腔代数和仿射胞腔代数简介

表示论中一个最基本的问题是确定不可约表示的参数集,这个问题至今没有完全解决.对于Graham和Lehrer引入的有限维胞腔代数,这个问题得到了完满解答,并被成功地应用于数学和物理中出现的许多代数.近来,人们引入仿射胞腔代数,将Graham和Lehrer有限维胞腔代数的表示理论框架推广到一类无限维代数上.仿射胞腔代数不仅包括有限维胞腔代数,也包括无限维的仿射Temperley-Lieb代数和Lusztig的A-型仿射Hecke代数.本文将对胞腔代数的发展历史和主要研究成果做一些综述,同时,对新引入的仿射胞腔代数及其最新成果做一点简介.     

具有特殊卡当矩阵的胞腔代数

本文研究了胞腔代数的直接构造问题.利用构造箭图并在其上添加关系的方法,获得了一种不可分解胞腔代数的构造方法.证明了总存在不可分解的胞腔代数A(对λ∈S(n))使得其卡当矩阵具有形如{n,1,…,1}的谱,从而拓广了胞腔代数的构造途径.     

仿射Weyl群上的Demazur乘积

Demazure乘积是定义在一般Coxeter群上的一类幺半群乘积.它自然地出现在李理论中的不同领域中.本文将研究仿射Weyl群上Demazur乘积.我们的主要结果是发现了它与有限Weyl群上的量子Bruhat图之间的一个紧密联系.作为应用,我们给出了仿射Weyl群最低双边胞腔元素之间Demazure乘积的显示表达式,并得到了最低双边胞腔元素的一般牛顿点以及Lusztig-Vogan映射的具体刻画.     

D_0型仿射Weyl群α值4的双边胞腔

本文描述了型仿射Ｗｅｙｌ群α值４的双边胞腔中所有左胞腔．     

胞腔代数中的Rota-Baxter代数结构（英文）

一个带有非平凡幂等元的结合代数带有自然的Rota-Baxter代数结构.本文研究胞腔代数的不同拟幂等元给出的Rota-Baxter结构间的同构关系.     

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.