诺贝尔经济学奖与数学(续二)

19981998年的诺贝尔经济学奖授予印度经济学家AmartyaSen（1933－）,以奖励他对福利经济学的贡献．Sen可以说又是一位经济学家中的数学家．他对福利经济学中有多项关键贡献：社会选择的公理化理论,福利与贫穷指标的定义,饥荒的经验研究．其中社会选择的公理化理论研究几乎可以说是“纯数学”的．所谓社会选择理论就是研究如何由个体选择来导出集体选择．最为人们熟知的集体选择规则是“少数服从多数”．但是著名的“投票俘论”指出,“少数服从多数”规则在三个以上的候选人时选举可能出现不满足传递律的情况．例如,有A,B,C三个候…     

May简单多数规则的描述

本文将Asan就两个备选对象定义的弱路径独立性和Woeginger就两个备选对象定义的亚社会可约性概念推广到任意备选对象集,在给定的有限参与人集及任意备选对象集的条件下,讨论了一社会福利函数是简单多数规则的充要条件,从而推广了Asan和Woeginger的工作.     

PPDA中的几个结论

本文证明了文[1]中，对一切RP中的单位向量a，Eflogfa有限条件为充要条件，并给出了RP中的P个单位向量a1，a2，…，aP线性无关时，Eflogfai有限的充要条件以及给出由E*（f，gn）→0可推出E（f，gn）→0的条件．     

多维指数分布

本文讨论了服从多维指数分布的随机向量的各分量间的独立性与相关性，证明了诸分量相互独立的充分必要条件是它们两两无关；并证明了多维指数分布类在弱收敛下的封闭性．     

L-模糊SP-紧集

本文在L-模糊拓扑空间引入了一种新的紧性—SP-紧性，给出了SP-紧性的α-网，α-滤子，r-SP-覆盖，r^ -有限交性质等多种刻画．这种紧性是针对任意L-模糊子集来定义的，且保持了一般拓扑空间中紧性的许多好的性质．     

环的广义Noether性(英)

众所周知,环R是右Noether的当且仅当任意内射右R-模的直和是内射的．本文我们将用Ne-内射模和U-内射模来刻画Ne-Noether环和U-Noether环．     

只具有半正规和反正规子群的有限群

群Ｇ的子群Ｈ称为是Ｇ的半正规子群，若对任意Ｇ的子群Ｋ，只要Ｋ的阶数与Ｈ互质，则Ｈ与Ｋ可置换；称Ｈ在Ｇ中是反正规的，若对任意ｇ∈Ｇ，ｇ，∈＜Ｈ．Ｈｇ＞．本文刻画了每个子群是半正规的，或反正规的有限群，推广了［１］及［２］中的结果．     

广义次指数族的卷积根的封闭性

设F是支撑在（-∞，∞）上的分布函数．口是一个取有限个整数值的非负随机变量，F#v为F的U重卷积．在一定条件下，本文得到了如下结论：对任意0≤y〈∞，F#v∈S（y）茸F∈S（y）．特别地，若口三挖，”≥2，本文得到了支撑在（一。。，。。）上的S（y）族的卷积根的封闭性．上述所得结果推广了[2]对应结果．     

有限群为超可解群的充要条件

用置换条件刻画有限可解群的超可解性已有大量结果,本文的目的是给出另外一些有限可解群为超可解的充要条件。其主要结果是: 1.设G是满足置换条件的有限可解群,则G是超可解群当且仅当如下条件之一成立。 1)G的2-Sylow子群G_2的换位子群G_2′G. 2)G有正规2-补。 2.设G是有限可解群,则G超可解当且仅当G和G′均满足置换条件.     

Orlicz-Hardy空间与BMO空间之间的鞅变换

以鞅变换为工具,刻画了Orlicz-Hardy鞅空间与BMO空间之间的相互关系.证明了如下结论:对任意上指标有限(等价于满足△_2-条件)的Young函数Φ,鞅f∈H_Φ{P_Φ,Q_Φ}的充分必要条件是,f是BMO∈{BMO_1,BMO_2}中某个鞅g的鞅变换.     

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.