一种故障树分析的新算法

本论文中，首先引入了ＢＤＤ（ＢｒｉｎａｒｙＤｅｃｉｓｉｏｎＤｉａｇｒａｍｓ－ＢＤＤ）的概念，介绍由故障树到ＢＤＤ转化算法一递归法，及ＢＤＤ进行故障树分析的方法。     

关于丢番图方程D1x^2＋2^mD2=y^n的解数

设Ｄ１、Ｄ２、ｍ、ｘ、ｙ是适合Ｄ１〉１，Ｄ２〉１，２├Ｄ１Ｄ２，ｇｃｄ（Ｄ１，Ｄ２）＝ｇｃｄ（ｘ，ｙ）＝１的正整数，ｎ是适合ｎ├ｈ的奇素数，其中ｈ是虚二次域Ｑ（√－２＾ｍＤ１Ｄ２）的类数。本文主要证明了：方程Ｄ１ｘ＾２＋２＾ｍＤ２＝ｙ＾ｎ至多有５．１０＾１６组例外解（Ｄ１，Ｄ２，ｘ，ｙ，ｍ，ｎ）而且这些解都满足了７≤ｎ〈８．５．１０＾６以及ｙ＾ｎ〈ｅｘｐ（ｅｘｐ（ｅｘｐ４６））。     

整环上二元多项或代数的自同构

设Ｄ是交换整环，本文讨沦了二元多项式代数Ｄ［Ｘ，ｙ］的自同构．证明了，如果Ｄ不是域则Ｄ［ｘ，ｙ］有非标准的自同构；如果Ｄ是唯一分解环，τ是Ｄ［ｘ，ｙ］的Ｄ－自同态，则τ是自同构，当且仅当，上其中条件１）可换为：τ将Ｄ［ｘ，ｙ］的任一本原多项式变为本原多项式．     

线性自治NDDE与CDDE解空间为有限维的充要条件

本文把文［２］中关于 Ｒ Ｄ Ｄ Ｅ 解空间为有限维的结果完整地推广到 Ｎ Ｄ Ｄ Ｅ 和 Ｃ Ｄ Ｄ Ｅ 上去，给出了相应的充要条件     

Brauer对的局部熔合

本文引入Ｓｙｌｏｗｂ－对图的概念研究Ｂｒａｕｅｒ对的局部熔合，证明了下面主要结果：简化的ｂ－对族是共轭族．若Ｆ是Ｓｙｌｏｗｂ－对（Ｄ，ｂＤ）内的基本ｂ－对族，Ｆ１＝｛（Ｐ，ｂＰ）｜存在ｇ∈Ｇ使（Ｐ，ｂＰ）是同时含在（Ｄ，ｂＤ）及（Ｄ，ｂＤ）ｇ内的极大ｂ－对且（Ｐ，ｂｐ）在（Ｄ，ｂＤ）与（Ｄ，ｂＤ）ｇ内极端｝则Ｆ１也是共轭族．这些结果统一了Ａｌｐｅｒｉｎ－Ｂｒｏｕｅ及Ｐｕｉｇ的熔合定理．     

矩阵DA的特征值及在系统稳定性分析中的应用

本文分析了矩阵ＤＡ的特征值，并提出了一种新的矩阵稳定性问题：Ｄ－－稳定性和块Ｄ－－稳定性．这里Ｄ是一个正对角阵，Ａ是给定的矩阵．应用劳斯判据及李雅普诺夫方法等，详细地分析了此类稳定性问题，提出了一些易于验证的结果，可用于分析多变量奇异摄动系统稳定问题．     

无限维李代数L(α,β)的导子李代数

本文讨论了无限维李代数Ｌ（α，β）的导子李代数的结构．分三种情况：（１）当α，β在Ｑ上线性无关时，ＤｅｒＬ（α，β）＝ＣＤｆ０ＣＤｇ０ａｄＬ（α，β），其中Ｄｆ０，Ｄｇ０是由ｆ０，ｇ０决定的导子，ｆ０，ｇ０是定义在Ｚ×Ｚ上的线性函数；（２）当α，β在Ｑ上线性相关且不同时为０时，ＤｅｒＬ（α，β）ｄｅｒＬ（α′，０）（α′≠０），ｄｅｒＬ（α，０）＝ＣＤ－α０ＣＤ－αｇ０ＣＤｆ０ａｄＬ（α，０），（α≠０），其中Ｄ－α０是某一个固定的导子，Ｄ－αｇ０，Ｄｆ０是由ｇ０，ｆ０决定的导子；（３）当α＝β＝０时，ＤｅｒＬ（０，０）＝ＣＤｆ０ＣＤｇ０ａｄＬ（０，０）．     

一类k步k＋1阶SDBDF型混杂法

本文在ＳＤＢＤＦ方法的基础上构造了一类ｋ步ｋ＋１阶的ＳＤＢＤＦ型混杂法，讨论了该方法的稳定性质，证明了ｋ＝１，２，３时，方法是Ａ稳定的，ｋ＝４～１０时方法是ｓｔｉｆ稳定的，同ＢＤＦ型和Ａｄａｍｓ型混杂法相比，该方法的ｓｔｉｆ稳定阶大有提高，这两类方法的ｓｔｉｆ稳定阶只能分别达到８阶和９阶〔２，３，５〕．在实现Ｎｅｗｔｏｎ迭代计算时，我们的方法要优于原ＳＤＢＤＦ方法，因此对于求解ｓｔｉｆ问题，我们的这类方法具有一定的优势，最后给出了数值实例     

（u,4,1）IGD[v,n）的存在性

（ｕ，４，１）ＩＧＤ［ｖ，ｎ］的存在性吴佃华（广西师范大学桂林５４１００４）关于ＰＢＤ，ＢＩＢＤ，ＧＤＤ的概念，我们假定读者已知（参看［１］，关于ＩＧＤＤ的定义请参看［２］，关于ＩＧＤＤ的存在性，我们绘出以下必要条件（参看［２］）定理１若存在（ｕ，ｋ...     

无限的可解SD2—群（II）—有限剩余情形

如果对多重循环群Ｇ的每个有限剩余Ｇ，Ｇ的真子群都具有可以由二元生成的，那么我们就把Ｇ叫做ＲＤ２－群，在本文里，我们确定了无限的ＲＤ２－群的结构，证明了ＲＤ２－群是可以由二元生成的，这些结构推广了作者已经得到了关于无限的可解ＳＤ２群的全部结果，见（４）。     

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.