拟连续Domain及其子范畴间的伴随关系

基于Snyth幂Domain的构造,本文证明了连续半格范畴CSL(分别地,有界完备连续Domain范畴CBD)是拟连续Domain范畴QCONT(分别地,Coherent拟连续Domain范畴QCCOH)的反射子范畴反例表明,连续Domain范畴CONT作为范畴QCONT的真子范畴并非其反射子范畴.所有结果均被进一步推广到拟代数Domain范畴。     

FS-相容Domain的定向完备化及相关范畴性质

引入FS-相容Domain概念，研究FS-相容Domain的性质，主要结果有：（1）FS-相容Domain的收缩核与连续函数空间还是FS-相容Domain；（2）FS-相容Domain是有限生成上集，从而是Scott紧的；（3）FS-相容Domain的定向完备化是FS-Domaln；（4）有最大元的FS-Domain去掉最大元后是FS-相容Domain；（5）证明了以Scott连续映射为态射，FS-相容Domain为对象的范畴FS-CDOM是笛卡儿闭范畴并以FS-Domain范畴FS-DOM作为满的反射子范畴。     

超连续Domain与拟超连续Domian

讨论了超连续domain与拟超连续domain的相关性质,证明了超连续半格范畴为有性质M*的拟超连续domain范畴的反射子范畴。     

连续Domain的遗传性及其不变性

引入Domain子空间的概念,得到Scott开集和闭集都是Domain的子空间。证明连续Domain或代数Domain对开子空间和闭子空间都是可遗传的。证明连续Domain或代数Domain在保Waybelow序的Scott连续映射下保持不变。     

Rudin性质与拟Z-连续Domain

对一般子集系统Z,引入了Rudin性质,给出了它的映射式刻划.作为拟连续偏序集和Z-连续偏序集的公共推广,引入了拟Z-连续Domain的概念,讨论了拟Z-连续Domain的基本性质,特别地,给出了Rudin性质及其映射式刻划在拟Z-连续Domain方面的若干应用,将关于拟连续偏序集的主要结果推广至了拟Z-连续Domain情形.     

相容连续Domain的遗传性

定义相容Domain的子Domain与子空间等概念,得到Scott开集和Scott闭集都是相容Domain的子Domain与子空间的结论,证明了相容连续Domain或相容代数Domain对开子空间和闭子空间都是可遗传的。     

Rudin性质与拟Z-连续Domain

对一般子集系统 Z,引入了 Rudin性质,给出了它的映射式刻划,作为拟连续偏序集和Z-连续偏序集的公共推广,引入了拟Z-连续Domain的概念,讨论了拟Z-连续Domain的基本性质,特别地,给出了 Rudin性质及其映射式刻划在拟 Z-连续Domain方面的若干应用,将关于拟连续偏序集的主要结果推广至了拟 Z-连续 Domain情形。     

拟Z-极小集及其应用

定义了拟Z-极小集,并证明了拟Z-连续Domain的每个元都有拟Z-极小集,在拟Z-连续Domain中,给出了保拟Z-极小集映射的几个等价刻画,并且在此基础上,运用Rudin性质,得到了拟Z-连续Domain上的两个相应扩张定理.     

拟连续Domain的拟基及其权

在定向完备偏序集(即dcpo)上引入了拟基的概念,给出了拟基的若干刻画并在此基础上定义了拟连续Domain的权。探讨了拟连续Domain的权与该拟连续Domain上赋予内蕴拓扑时的拓扑空间的权之间的关系。     

相容半连续Domain

引入了相容半连续Domain、相容强连续Domain的概念,给出了一系列性质,讨论了相容半连续Domain、相容强连续Domain与相容连续Domain间的关系.引入了相容半Scott拓扑,并讨论了其相关性质.     

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.