有限交换环上极限线性群的Sylowp—子集

本文给出了有限交换局部环Ｒ上无限线性群ＧＬ（Ｒ）＝∪ｎＧＬｎＲ的Ｓｙｌｏｗｐ－了群的形式。令Ｍ是有限交换局部环Ｒ的唯一极大理想，ｋ＝Ｒ／Ｍ为Ｒ的剩余类域。用ｘ（ｋ）表示ｋ的特征，并假定ｐ与ｘ（ｋ）互素。     

有限交换环上典型群的Sylow子群

令Ｒ为有限交换局部环，Ｍ表其唯一的极大理想，ｋ表其剩余类域．本文定出了Ｒ上的一般线性群ＧＬｎＲ，辛群Ｓｐ２ｎＲ及双曲正交群Ｏ２ｎＲ的Ｓｙｌｏｗ子群．一般讲，若ｃｈａｒｘ＝ｐ，上述三类典型群的Ｓｙｌｏｗ ｐ－子群分别同构于由某些特殊形式的矩阵生成的子群；若ｃｈａｒｋ≠ｐ，上述三类典型群的Ｓｙｌｏｗｐ－子群分别同构于一循环群或半二面体群与若干Ｚｐ型循环群的圈积。     

Schur—Zassenhaus定理的推广

本文证明了如下结论：（１）若有限群Ｇ的一个Ｈａｌｌπ－子群Ｈ在ＧＦ内是Ｓ－半正规的，则Ｈ在Ｇ内有补且所有这样的补在Ｇ中互相共轭，（２）令Ｐ／Ｇ／，若有限群Ｇ的Ｓｙｌｏｗｐ－子群在Ｇ内是Ｓ－半正规的，则Ｇ是ｐ－可解的；（３）如果Ｇ与ＰＳＬ（２，７）是无关的，则Ｇ是π－可分的；（４）令Ｐ是一个奇素数，则其每个极小Ｐ－子群一Ｓ－半正规的有限群Ｇ－一定是Ｐ＝超可解的。     

2-(υ,7,1)设计的可解区传递自同构群

设Ｇ是一个２－（υ,７,１）设计的可解区传递自同构群,则Ｇ是点－本原,且下列之一成立： （１）υ＝７ｎ,Ｇ是旗一传递的; （２）υ＝５６,Ｇ＝Ｚ５６：Ｈ,这里Ｈ是ＧＬ（６,５）的可解且不可约的子群; （３）υ＝ｐｎ,Ｇ≤ＡＬ（１,ｐｎ）．特别地,ｐ≠２且ｐｎ≡ｌ（ｍｏｄ ４２）．     

关于n—可解群与n—幂零群的两个结果

本文证明了下面主要结果：设Ｇ是ｎ－可解群，π是一些素数之集，若对任意ｐ∈∩π（Ｇ），（ｐ，ｎ（１－ｎ））＝１，则Ｇ的π－Ｈａｌｌ子群的个数ｒ＝ｋ１ｋ２．．．ｋｔ，每ｋｉ≡１（ｍｏｄｐ），某Ｐ∈π，且每ｋｉ整除Ｇ的一个主因子。     

GL(n,Z)中的局部有限子群的一点注记

证明了：若Ｇ是一般线性群ＧＬ（ｎ,Ｚ）中的局部有限子群,则Ｇ含有一个２~ｍ阶的初等阿贝尔２－子群,且 Ｇ同构于 ＧＬ（ｎ,Ｚ_ｐ）的一个子群,其中户为任意奇素数．当 ｎ＝１,２,３,４时,Ｇ的阶分别是 ２,３· ２~ｋ（ｋ＝ｍｉｎ（４,ｍ＋１）,０≤ｍ≤４）,３·２~ｋ（ｋ＝ｍｉｎ｛５,ｍ＋１｝,０≤ｍ≤５）,３~２·５·２~ｋ（ｋ＝ｍｉｎ｛９,ｍ＋６｝,０≤ｍ≤９）的一个因子,而当ｎ≥５时,Ｇ的阶是（ｐ~ｉ－１）的一个因子,其中ｐ为任意素数．     

具有独立贡献的相依回归模型

考虑相依回归（ＳＵＲ）模型ｙｉ＝Ｘｉβｉ＿ｅｉ，ｉ＝１，２，…，ｍ，Ｅｅｉ＝０，ｉ，ｊ＝１；２，…ｍ，其中ｙｉ和ｅｉ是ｎ×１维随机向量，Ｘｉ是ｎ×ｐｉ已知矩阵，βｉ是ｐｉ×１维参数向量，∑＝（σｉｊ）ｍ×ｍ＞０．文中给出了两个概念：独立贡献和简洁估计．主要结果是如下五种叙述等价：（１）ＳＵＲ模型具有独立贡献；（２）βｉ的ＢＬＵＥ是简洁估计；（３）协方差改进估计是ＢＬＵＥＺ（４）βｉ的ＢＬＵＥ具有形式其中，ｊ＝１，２，…，ｍ；（５）ＰｋＮｉＮｊ＝０，ｉ≠ｊ，ｋ，Ｉ，ｊ＝１，２，…，ｍ     

关于l－群的半单结构

令Ｇ是一个ｌ－群，Ｇ的一个凸ｌ－子群Ａ叫做多余的，如果对Ｇ的任－凸ｌ－子群Ｗ，只要Ａ∨Ｗ＝Ｇ，就有Ｗ＝Ｇ．复令Ｒ（Ｇ）为Ｇ的所有多余凸ｌ－子群的集合并生成的凸ｌ－子群．我们证明了Ｒ（Ｇ）是ｌ－群Ｇ的一种报并且是在Ａｍｉｔｓｕｒ－Ｋｕｒｏｓｈ意义下的根．进一步我们得到了有限值ｌ－群的半单结构定理即Ｒ（Ｇ）＝０当且仅当Ｇｌ－同构于具有半单性的单ｌ－群的亚直积，同时我们还得到了一系列有意义的推论．     

关于l－群的半单结构

令Ｇ是一个ｌ－群，Ｇ的一个凸ｌ－子群Ａ叫做多余的，如果对Ｇ的任－凸ｌ－子群Ｗ，只要Ａ∨Ｗ＝Ｇ，就有Ｗ＝Ｇ．复令Ｒ（Ｇ）为Ｇ的所有多余凸ｌ－子群的集合并生成的凸ｌ－子群．我们证明了Ｒ（Ｇ）是ｌ－群Ｇ的一种报并且是在Ａｍｉｔｓｕｒ－Ｋｕｒｏｓｈ意义下的根．进一步我们得到了有限值ｌ－群的半单结构定理即Ｒ（Ｇ）＝０当且仅当Ｇｌ－同构于具有半单性的单ｌ－群的亚直积，同时我们还得到了一系列有意义的推论．     

PSL（2，F）的一个嵌入定理及其应用

设Ｆ是任意域，Ｇ代表ＳＬ（２，Ｆ）或ＰＳＬ（２，Ｆ）．本文的主要结果是：设Ｋ是Ｆ的子域，则Ｇ中同构于ＳＬ（２，Ｋ）或ＰＳＬ（２，Ｋ）的子群在Ｇ的自同构的作用下彼此共轭，利用这一结果，本文明确确定了A₁^[1]型的仿射Ｋａｃ－Ｍｏｏｄｙ群的一类极大正规子群．     

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.