集值Pramart的一类鞅逼近

在X^＊可分的条件下,首先讨论了集值Pramart有关支撑函数和距离函数的性质,利用支撑函数和距离函数研究了集值Pramart鞅逼近,在此基础上,给出了集值Pramart的一类鞅分解.     

离散参数集值序下鞅的Riesz分解及收敛性

本文研究了离散参数集值序下鞅的Riesz分解及收敛性.利用集值序关系及集值鞅方法,给出了离散参数集值序下鞅的Riesz分解的存在性及唯一性定理.并获得离散参数集值序下鞅的收敛性定理.     

集值上鞅的收敛定理及 Riesz 分解

本文给出了集值鞅的进一步性质;建立了集值上鞅外穿不等式;证明了一个集值上鞅收敛定理;研究了集值上鞅的 Riesz 分解.     

关于集值Pramart的某些结果

本文引进了Boohner可积函数空间L~1[Ω;X]中子集的可分解包的概念,给出了集值随机变量族本性上确界的定义及基本性质。以此为基础,研究了集值Pramart的性质;用类似于实值Snell包的方法给出了集值superpramart的上鞅逼近,证明了集值superpramart在Kuratowski-Mosco意义下的收敛定理。     

数值序上鞅的若干有关问题

本文研究了连续时间的集值序上鞅．在一定的假设下我们证明了集值序上鞅有ｈ－Ｒｉｅｓｚ分解,然后证明了集值序上鞅的Ｄｏｏｂ－Ｍｅｙｅｒ分解定理．     

集值序上鞅的若干有关问题

本文研究了连续时间的集值序上鞅,在一定的假设下我们证明了集值序上鞅有ｈ－Ｒｉｅｓｚ分解,然后证明了集值序上鞅的Ｄｏｏｂ－Ｍｅｙｅｒ分解定理。     

集值逆上鞅的Doob分解

假定(X,‖·‖)为可分的Banach空间,X*为其对偶空间,X*可分。本文首先给出了集值逆上鞅Doob分解的概念,其次,证明了实值逆上鞅Doob分解定理,在此基础上,利用支撑函数给出了集值逆上鞅可Doob分解的一个充分必要条件。同时证明了一维实空间R1中集值逆上鞅具有Doob分解,最后,用例子说明在二维实空间R2并非所有的集值逆上鞅都具有Doob分解。     

关于集值下鞅Riesz分解的注记

在X*可分的条件下给出了集值序列及集值下鞅的一些结果,在此基础上,利用支撑函数,给出了Banach空间集值下鞅的Riesz分解定理。     

集值序上鞅

本文研究了连续时间的集值序上鞅．在一定的条件下首先证明了集值序上鞅有（Ｋ－Ｍ）Ｒｉｅｓｚ分解;然后证明了集值序上鞅的Ｄｏｏｂ－停时定理．     

集值逆下鞅的Doob分解

假定(X,‖·‖)为实Banach空间,X*为其对偶空间,X*可分.本文证明了实值逆(下)鞅Doob分解定理,在此基础上,利用支撑函数给出了集值逆下鞅可Doob分解的一个充分条件.     

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.