辛群胚与泊松群胚作用的充要条件

研究了辛群胚与泊松群胚的作用.利用李群胚作用及相关性质,得到了李群胚作用成为辛群胚和泊松群胚作用的充要条件,推广了辛群胚和泊松群胚的性质,为辛群胚与泊松群胚理论的进一步研究起到了推动作用.     

关于辛群胚的拉格朗日双截面

本文研究了辛群胚上的拉格朗日双截面.利用李群胚和辛群胚的相关性质, 得到了李群胚和辛群胚的李代数胚的截面空间中向量场X的指数映射能成为拉格朗日双截面的充分必要条件,并给出了辛群胚之间的一种同构,推广了拉格朗日双截面在群胚理论中的应用.     

Proto双代数胚上的Dirac结构

proto双代数胚包含了李代数胚, 李双代数胚, 李拟双代数胚, 拟李双代数胚等多种代数胚结构. 本文的主要工作是将李双代数胚的Driac理论推广到proto双代数胚上. 利用特征对的概念给出了极大迷向子丛可积的充要条件. 同时发现在这些可积条件中蕴含了proto双代数胚的扭关系，这样就给出了可积条件的几何解释.最后文章讨论了一些 特殊情形.     

关于李群胚的几点讨论

文章讨论了李群胚作为丛的一些性质,得出李群胚的内子群胚是主丛的结论;研究了李群胚在其内子群胚上的作用,并证明了李群胚上的Maurer-cartan形式在其任意左不变向量场上作用的结果为常数.文末推广了关于李代数胚态射的一个结论.     

G匚W上的泊松群胚结构

从泊松作用的角度考察了群胚上的半直积结构,定义了泊松群胚对泊松群胚的泊松作用,讨论了其性质,并证明了两个泊松群胚的半直积仍是泊松群胚,从而对群胚的半直积结构有了更多的认识.     

李群的余切丛上的两种辛群胚结构

本文研究了李群的余切丛上的辛群胚结构.利用李代数胚的对偶丛上有自然诱导的泊松结构,.构造出了同一余切丛上的不同的辛群胚结构,推广了辛群胚的性质.     

强群胚及其性质

首先提出了强群胚,强子群胚,陪集和商强群胚的定义,接着讨论了k重强群胚,然后给出了它们的性质和同态定理并予以严格证明.此外提出的k重相容的强群胚将在流形变换,李群胚和系统结构的兼容性等方面有重要的应用.     

辛轨形群胚的辛邻域定理

本文给出一种几何的子轨形群胚的定义,还给出了判定子轨形群胚的依据,并证明了紧子轨形群胚的轨形管状邻域、紧辛子轨形群胚的辛邻域和紧Lagrangian子轨形群胚的Lagrangian邻域的存在性.     

广义近似空间的粗糙同胚与拓扑同胚

对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性,探讨了他们的性质及相互关系.证明了两个粗糙连续映射的复合还是粗糙连续的,每个粗糙连续的映射都是拓扑连续的.在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念,证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性.     

矩映射在泊松几何学中的应用

本文研究了矩映射在泊松G-空间及辛群胚中的应用. 利用基本群胚上的提升作用有等变的矩映射,得到了连通的辛群胚上矩映射的存在性及相关的性质,推广了长矩映射在辛群胚等研究中的作用.     

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.