一类非线性非自治系统周期解的存在性

本文给出了系统ｄｘ／ｄｔ＝Ａ（ｔ）ｘ＋ｇ（ｔ，ｘ），ｇ∈Ｒ‘，ｘ∈Ｒ＾Ｎ，ω周期解存在的充分条件，推广了文「１」中的Ｋｒａｓｎｏｓｅｌｓｋｉｉ的结果。     

模糊值函数与模糊数积分区间[A,B]上的N—L公式

文「１」给出模糊值函数在普通区间「ａ,ｂ」上的Ｎ－Ｌ公式。本文在文「１」的基础上进一步给出模糊值函数区间「Ａ,Ｂ」上的积分。这个积分是Ⅱ型糊集。文「３」已经指出（Ｆ２「１,１」,∪,∩,ｃ）不是软代数,但这个积分是一个特殊Ⅱ型模糊集具有许多良好的代数性质,并存在着Ｎ－Ｌ公式。     

格上Ising模型的临界失真估计

本文是我们先前工作「１」，「２」的继续，对格上Ｉｓｉｎｇ模型的临界失真ｄｃ的估计，Ｎｅｗｍａｎ和Ｂａｋｅｒ「６」证明了ｄｃ和Ｉｓｉｎｇ模型的Ｍａｙｅｒ级数之收敛半径Ｒ有以下关系：ｄｃ＝Ｒ／（１＋Ｒ），在「１」中匀提出了估计Ｒ及ｄｃ的新方法，并它计算了二维矩形格Ｚ＾２上Ｉｓｉｎｇ模型的临界失真ｄｃ，此文中我们继续应用此方法首次计算了定义在其它二维和三维格上Ｉｓｉｎｇ模型的临界失真ｄｃ，数值计算的结果     

希尔伯特空间中半线性随机发展方程适度解的存在性

本文讨论如下形式的希尔伯特空间中半线性随机发展方程Ｃａｕｃｈｙ问题｛ｄｙ（ｔ）「Ａｙ（ｔ）＝ｆ（ｔ，ｙ（ｔ））」ｄｔ＋Ｇ（ｔ，ｙ（ｔ））ｄｗ（ｔ）ｙ（０）＝ｙ０适度解的存在性。在一组条件下得到了解的整体存在性，推广了文「１」的存在性定理。     

关于图的（g,f）—因子分解的一些新结果

本文讨论图的（ｇ，ｆ）－因子分解问题，推广了文「１」关于图的因子分解的理论，改进了文「２」的一些结果，给出了一个图Ｇ是（ｇ，ｆ）－可因子化的若干充分条件。     

广义Lienard方程非平凡周期解的存在性

本文给出了广义Ｌｉｅｎａｒｄ方程ｘ＋ｆ（ｘ）（ｘ）ｘ＋ｇ（ｘ）＝０存在非平凡周期解的两个充分条件,推广了文「４,５」中的结果,并且指出文「１」中的一个疏漏。     

GAOR迭代法和Jacobi迭代法的敛散关系

本文将文［１］中ＡＯＲ法和Ｊａｃｏｂｉ法同时敛散的结论推广到ＧＡＯＲ法．证明了当Ｊａｃｏｂｉ矩阵Ｂ非负时，解线性方程组Ａｘ＝ｂ（Ａ为不可约矩阵）的ＧＡＯＲ法（０≤γ_ｉ＜ω_ｉ≤１，ｉ＝１，２，…，ｎ）和Ｊａｃｏｂｉ法同时敛散，给出了其谱半径ρ（Ｌ_Ｒ，Ω）和ρ（Ｂ）之间的关系．     

平面定常系统的奇点指标问题

本文引进Ｓ－交点的概念，用新的方法研究了平面定常系统一支上两相邻初等奇点的指标问题，把文「１」的有关结果推广到一般的平面定常系统，作为作用，证明了文「２」猜测（Ⅱ）对ｎ次系统是正确的。     

两类求解y“=f（x,y）具有极小相位延迟的显式方法

本文提出了两类数值积分二阶周期性初值问题ｙ〃＝ｆ（ｘ，ｙ），ｙ（ｘ０）＝ｙ０，ｙ（ｘ０）＝ｙ０具有检小相位延迟的显式两步法。这些方法推广和改进了文献「１」１－「７」中的某些方法。数值试验表明本文中的某些方法优于「１」－「７」中的某些方法。     

SINGULARITY AND QUADRATURE REGULARITY OF（0，1，．．．，m－2，m）─INTERPOLATION ON THE ZEROS OF（1－x）P_（n－1）~（αβ）（x）

ＳＩＮＧＵＬＡＲＩＴＹＡＮＤＱＵＡＤＲＡＴＵＲＥＲＥＧＵＬＡＲＩＴＹＯＦ（０，１，．．．，ｍ－２，ｍ）─ＩＮＴＥＲＰＯＬＡＴＩＯＮＯＮＴＨＥＺＥＲＯＳＯＦ（１－ｘ）Ｐ_（ｎ－１）~（αβ）（ｘ）ＳｈｉＹｉｎｇｇｕａｎｇ（史应光）（ＣｏｍｐｕｔｉｎｇＣｅ...     

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.