偏序集中网和滤子的Scott收敛及其Scott拓扑

本文的目的是在偏序集上直接定义和研究网和滤子的Scott收敛理论,指出其相互之间的协调性,及其它们的导出拓扑与Scott拓扑的一致性.     

抽象基上的伪e拓扑与伪ρ拓扑

在抽象基上引入了伪e拓扑和伪ρ拓扑,研究了这两种内蕴拓扑的性质以及与其它内蕴拓扑的关系。利用伪e拓扑与伪ρ拓扑得到具有辅助关系的偏序集的辅助基的若干等价刻画。证明了具有辅助关系的偏序集的辅助基恰是伪ρ拓扑的稠子集。     

关于Scott开滤子拓扑核紧性的注记

本文构造了两个例子:(1)利用康托三分集构造了一个非连续的DCPO,这个非连续DCPO关于所有Scott开滤子为子基生成的拓扑是核紧的,T0的,且以Scott开滤子为基,从而回答了[2]提出的一个问题;(2)利用Domain函数空间给出一个非连续的DCPO,其上的Scott拓扑有开滤子基,这个例子比[3]中给出的更直观.     

Domain函数空间上的Isbell拓扑和Scott拓扑的一致性

本文主要讨论了Domain函数空间上Isbell拓扑和Scott拓扑的一致性.利用Domain函数空间给出了一个例子: Scott拓扑有开滤子基的非连续的DCPO.     

分层偏序集上的广义Scott拓扑与不可约拓扑

分层偏序集指的是一个偏序集,且具有其交为已知偏序的按包含递减的偏序族[10]。本文仿照[1]的思路,在分层偏序集上定义了不可约拓扑,讨论了该拓扑的基本性质,特别是限制到偏序集上即得Scott拓扑。不同于一般偏序集上的Scott拓扑恰为Alexandroff拓扑的不可约拓扑,本文通过例子表明分层偏序集上的广义Scott拓扑并非广义Alexandroff拓扑的不可约拓扑。     

关于自然偏序集的自然连续性

在自然偏序集中引入自然way-below关系,定义自然偏序集的自然连续性.证明在自然连续的自然偏序集上,自然way-below关系具有插入性,自然Scott开集格是完全分配格.利用(&)*收敛刻画了自然偏序集上的自然way-below关系,自然Scott拓扑和自然连续性.     

关于Scott开滤子拓扑的core紧性

本文讨论了那样一些ＤＣＰＯ（即定向完备偏序集）的刻划问题,它们在赋以Ｓｃｏｔｔ开滤子拓扑后,其拓扑空间的开集格是连续格。该问题也是由ＬａｗｓｏｎＪＤ。与ＭｉｓｌｏｖｅＭ．提出的一系列公开问题中的一个［１］。     

Z-连通连续偏序集的特征和浓度

引入了Z-连通连续偏序集的局部基和稠密子集的概念,给出了局部基的一些刻画,在此基础上定义了Z-连通连续偏序集的特征和浓度。证明了Z-连通连续偏序集的特征和浓度与Z-连通连续偏序集带上Scott拓扑时的拓扑空间的特征和浓度相等,它们分别小于Z-连通连续偏序集带上Lawson拓扑时拓扑空间的特征、浓度。     

L-Fuzzy Domain上的广义Scott拓扑

本文研究了L-fuzzy domain上的广义Scott拓扑,利用[1]中引入的L-fuzzy domain.获得了其上的广义Scott拓扑,它是Domain上Scott拓扑的推广,证明了一个L-fuzzy单调映射是L-fuzzy Scott连续映射当且仅当它关于L-fuzzy domain上的广义Scott拓扑连续.     

偏序集的内蕴拓扑连通性北大核心

从序与拓扑的交叉考虑,进一步研究偏序集在多种内蕴拓扑下的连通性和局部连通性.主要结果有:(1)一个偏序集是序连通的当且仅当它赋予Alexandrov拓扑是连通的,也当且仅当它赋予Scott拓扑是连通的;(2)每一偏序集赋予Alexandrov拓扑是局部连通的,每一偏序集赋予Scott拓扑是局部连通的;(3)如果拓扑空间的特殊化偏序集序连通,则该拓扑空间是连通的;(4)构造反例说明了存在偏序集赋予下拓扑后是连通空间,但该偏序集本身不是序连通的.     

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.