二次紧支撑样条小波插值及其应用

以二次紧支撑样条小波为基函数,构造了一类二次紧支撑样条小波插值函数,仔细讨论了其计算过程和误差.再将其应用于数值积分,给出了一类求数值积分的新公式,分析了其误差,最后给出一个数值例子.     

盖尔范德在整值整函数理论上的工作

本文基于原始文献,利用历史分析和比较的方法,首次研究了盖尔范德在整值整函数理论方面的工作及影响.他的工作奠定了该理论发展的重要方向.文章分析了其工作背景;研究了他的有关工作,揭示了其思想的演变过程;探讨了其工作的重要影响.     

具有广义FGM相依结构的复合泊松过程的Esscher定价泛函

本文考虑索赔额与等待时间具有广义FGM相依结构的复合泊松过程,仿照文献[5]的方法,求出了其矩母函数的显式表达式,给出了其矩母函数的n阶导数的计算方法,并最终求出了其Esscher定价泛函．     

一道数学竞赛题的证明、应用与推广

介绍了一道高等数学竞赛题的五种证明方法并举例说明其应用,另外介绍了其推广.     

浅谈求解二次函数的最值

近几年的中考数学试题突出了这么一个特点:其最后一道试题是与函数有关的综合题,也是整张试卷的压轴题和区分题.作为区分题的它,突出了其最精华的地方和其所在的重要位置.该题不但涉及到函数内容最基础的知识点,还容纳了大量的的综合知识.数形结合的知识考查是重中之重,不但综合考查了学生对基础知识的掌握,其综合能力的应用和解题方法的运用才是真正     

给一组高考题“卸妆”

审视很多高考试题,往往是对某些简单的问题的有意“妆饰”,一旦对其卸了“妆”,便还原了问题的本来面目,使其水落而石出,不难求解．本文对一组高考题卸妆还原,重现其原貌．     

奇异值的极值性质

考虑了矩阵奇异值的相关问题,研究了其极值性质,并得出了一些特殊情形下的结果.最后,考察了其在多元统计分析中的应用.     

具有热储备的并行可修系统稳态解的最优控制

研究了具有热储备的并行可修复系统中,其稳定解的最优控制问题,并给出了其最优解的存在唯一性.     

期望效用函数理论及其应用

分析了期望效用函数理论,并将其运用于图书馆的管理工作,从中发现其规律性.为图书馆的科学管理提供了一条有效的途径.     

基于截形式背景的属性约简分析

在模糊概念格中讨论了基于截形式背景的属性约简,其中着重分析了在精度的偏序关系下属性约简的包含关系,并证明了此说法的正确性,进而还举例说明了其正确性;在此基础之上,本文还给出了在用不同精度把模糊概念格转换了经典概念格时造成的误差,并给出其算法,最后举例说明其有效性.     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

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.     

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