弱鞅的极大值不等式及其应用

本文建立了弱鞅的一些极大值不等式,这些不等式推广和改进了Christofides在Maximal inequalities for demimartingale and a strong law of large numbers. Statist Probab Left,50：357-363（2000）中的结果．利用得到的极大值不等式,可以得到其它一些结果,例如弱鞅的Doob型极大值不等式、弱鞅和PA序列的强大数定律和强收敛速度．最后,还给出了弱半鞅一致可积性的一个等价条件．     

广义f-投影算子的稳定性及其应用

在Banach空间中,本文研究广义f-投影算子关于集合扰动的稳定性.作为应用,本文在Banach空间中运用广义f-投影算子解决了一类广义变分不等式问题.     

条件PA序列的条件Hájek-Rényi型不等式及其应用

本文利用条件弱鞅的一个极大值不等式,即引理1,得到了条件PA序列的条件H-R型不等式,所得结论推广了已有文献中的相关结果,同时给出了条件弱鞅上确界的条件期望有限的一个判定条件.     

B值拟鞅不等式及其应用

本文给出B值拟鞅的概率不等式与集合不等式,并用它们刻划了B空间的p可光滑性及q可凸性,作为应用,还证明了B值拟鞅的强大数律,收敛速度及极大值函数的可积性。     

集值混合变分不等式的一类自适应惯性投影次梯度算法

本文在实Hilbert空间上引入了一类求解集值混合变分不等式新的自适应惯性投影次梯度算法.在集值映射T为f-强伪单调或单调的条件下,我们证明了由该自适应惯性投影次梯度算法所产生的序列强收敛于集值混合变分不等式问题的的唯一解.     

MV-代数的f-微分

利用MV-代数的自同态在MV-代数上引入并研究了广义微分—f-微分.随之给出MV-代数上保序的f-微分及f-微分的不动点集F_d(M)等概念,得到保序的f-微分的几个等价条件以及每一个f-微分的不动点集F_d(M)和集d~(-1)(0)为M的格理想等重要结论.最后,利用保序f-微分及其不动点集F_d(M)给出了MV-代数成为Boolean-代数的一个等价刻画.     

图G中f-因子的一个结论

在简单图的顶点度和f-因子的关系方面,本文在Tutte定理的基础上给出了图G不存在f-因子时的一个结论.     

由Lvy过程驱动的BSDE定义的一般非线性期望

本文研究了平凡可积随机变量的一类非线性期望f-期望.利用陈增敬推广g-期望的方法,扩张了f-期望的定义空间.     

由Lévy过程驱动的BSDE定义的一般非线性期望

本文研究了平凡可积随机变量的一类非线性期望f-期望.利用陈增敬推广g-期望的方法,扩张了f-期望的定义空间.     

Banach空间中一类广义变分不等式的强收敛定理

应用广义f-投影算子引入了一类新的迭代方法,并用此方法在Banach空间的非紧子集上证明了一个关于一类广义变分不等式的强收敛定理;该定理中所涉及到的映射既不具备紧性也不具备单调性。所得结果推广了最近一些相关定理。     

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.