二阶奇异边值问题两个非负解的存在性

利用拓扑度理论,给出了边值问题ｕ″（ｔ）＋λａ（ｔ）ｆ（ｕ（ｔ））＝０,０〈ｔ〈１,ａｕ（０）－βｕ’（０）＝０,γｕ（１）＋δｕ’（１）＝０两个非负解的存在性结果,这里允许ａ在ｔ＝０和ｔ＝１处有奇性。     

Volterra型积分微分方程非线性边值问题解的存在性和唯一性

本文利用上下解方法得到了带Ｖｏｌｔｅｒｒａ型积分算子的非线性边值问题，ｕ＾ｎ＝ｆ（ｔ，ｕ，ｕ′，Ｔｕ），ａ１ｕ（０）－ａ２ｕ′（０）＝Ａ，ｂ１ｕ（１）＋ｂ２ｕ′（１）＝Ｂ解的存在性和唯一性。     

非线性四阶常微分方程三点边值问题解的存在性

本文利用文献〔１〕、〔２〕的方法，讨论了非线性四阶常微分方程ｙ（４）＝ｆ（ｔ，ｙ，ｙ′，ｙ″，ｙ′″）满足如下条件ｇ（ｇ（ａ），ｙ′（ａ），ｙ″（ａ），ｙ′″（ａ）＝０，ｈ（ｙ）ｎ），ｙ″（ｂ．））＝０，ｙ′（ｂ）＝ｂ１，ｋ（ｙ（ｃ），ｙ′（ｃ），ｙ″（ｃ），ｙ′″（ｃ）＝０的三点边值问题解的存在性。对于非线性四阶常微子方程ｙ（４）＝ｆ（ｔ，ｙ，ｙ′，ｙ″，ｙ′″）的边值问题，到目前已经有了一系列     

一阶急式微分方程周期边值问题(英文)

本文我们描述了一个构造性方法．在存在一个上解β及下解α且α≤β情形下,得到两个单调序列一致收敛于如下周期边值问题．ｘ′（ｔ）＝ｆ（ｔ,ｘ（ｔ）,ｘ′（ｔ））,ｔ∈［０,Ｔ］ｘ（０）＝ｘ（Ｔ）,｛的极值解     

某些三阶三点边值问题的可解性

本文考虑如下三阶三点边值问题：ｘ＝ｆ（ｔ，ｘ，ｘ′，ｘ″）（０≤ｘ≤１），ｘ∈Ｂ，其中Ｂ表以下边值条件之一：ｘ′（０）＝ｘ′（１）＝ｘ（ξ）＝０，ｘ′（０）＝ｘ″（１）＝ｘ（ξ）＝０，ｘ″（０）＝ｘ′（１）＝ｘ（ξ）＝０，ξ∈［０，１］是给定的．对以上边值问题，给出不限制ｆ增长的可解条件．     

四阶奇异边值问题正解的存在性

本文考虑奇异边值问题ｕ（４）（ｔ）＝λα（ｔ）ｆ（ｔ,ｕ（ｔ））,０＜ｔ＜１,ｕ（０）＝ｕ（１）＝０,ｕ＇＇（０）＝ｕ＇＇（１）＝０当λ在某一区间内变化时,得到了上述边值问题存在正解的一些充分条件。     

半线性三阶差分方程边值问题的非负解

该文研究了一类半线性三阶差分方程边值问题Δ３ｕ（ｔ）＋ａ（ｔ）ｆ（ｕ（ｔ））＝０,２≤Ｔ≤Ｔ＋２,ｕ（０）＝ｕ（１）＝ｕ（Ｔ＋３）＝０的非负解,得到了该方程在锥与环形域相交部分非负解的存在性,包含、改近和推广了文［３,４,５,６］的主要结果．     

多项式翻转公式的一个新结果(英文)

设ｆ（ｘ）是一个实函数，ｆ（ｘ＋ｉｙ）在某个包含区间［ａ，ｂ］的某区域内解析，则∑ａ＜ｎ≤ｂｅ（ｆ（ｎ））＝ｅ（－１８）∑α＜ｎ≤β｜ｆ″（ｘｎ）｜－１２ｅ（ｆ（ｘｎ）－ｎｘｎ）＋△（ｆ，ａ，ｂ）其中α，β，ｘｎ的定义是（１），余项△是（９），它改进了文［１］，［２］的结果．     

一类n阶拟线性奇异摄动边值问题的一致有效渐近展开

本文研究一类ｎ阶拟线性奇异摄动边值问题：εｙ（ｎ）＝ｆ（ｔ，ε，ｙ，…，ｙ（ｎ－２）ｙ（ｎ－１）＋ｇ（ｔ，ε，ｙ，…，ｙ（ｎ－２），ｐｊ（ε）ｙ（ｊ）（０，ε）－ｑｊ（ε）ｙ（ｊ＋１）（０，ε）＝αｊ（ε）（０≤ｊ≤ｎ－２），ｂ１（ε）ｙ（ｎ－２）（１，ε）＋ｂ２（ε）ｙ（ｎ－１）（１，ε）＝β（ε），其中ε＞０为小参数．在较一般的条件之下，应用Ｂａｎａｃｈ／Ｐｉｃａｒｄ不动点定理证明了摄动解的存在性及局部唯一性，并给出了摄动解直到ｎ阶导函数的一致有效渐近展开式，推广和改进了已有的结果［１－５］．     

关于非线性两点边界值问题u″＋g（t,u）=f（t）,u（0）=u（2π）=0？…

本给出了ｍａｘ－ｍｉｎ原理的一个非变分形式，证明了非线性两点边界值问题ｕ″＋ｇ（ｔ，ｕ）＝ｆ（ｔ），ｕ（０）＝ｕ（２π）＝０的解的一个存在性和唯一性定理。     

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.     

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.     

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).     

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.