具有两个亏值的亚纯函数（Ⅱ）

本文讨论了具有两个亏值的亚纯函数的唯一性问题,改进了F.Gross和本文作者的几个结果。本文主要证明了:设f与g是两个非常数亚纯函数,a,a_1,a_2是三个判别的有穷复数,再设δ(∞,f)=δ(∞,g)=1,E_f({a_1,a_2})=E_g({a_1,a_2})。(1)如果2a≠a_1+a_2,且δ(a,f)+δ(a,g)>5/3,则f≡gr或(f-a)(g-a)≡(a_1-a)(a_2-a);(2)如果2a=a_1+a_2,且δ(a,f)+δ(a,g)>1,则f≡g或f+g≡2a或(f-a)(g-a)≡(a_1-a)·(a_2-a)。     

一类包含Bernoulli多项式的恒等式的计算公式

本文给出了sum from (a_1+a_2+…a_k)=n to ((B_(a_1)(x)B_(a_2)(x)…B_(a_k)(x))/(a_1!a_2!…a_k!))的求和计算公式,其中B_i(x)为i次Bernoulli多项式,nZ≥k为正整数,。l+a2+…+ak‘n表示对所有满足该式的^维正整数组(a_1+a_2+…a_k)求和。     

三类组合公式——兼谈等差数列的有关性质

本文将这三个公式推广,得到三类有用的组合公式,也是给出了等差数列的有关性质。 (一) 对公式(1)推广如下: 公式一:如果a_1,a_2,a_3,…,a_(n=1)是公差为d的等差数列,那么     

分担值与正规族

本文主要证明了如下的结论:设■为定义在区域D内的一族亚纯函数,a_1, a_2和a_3分别为三个互异的有限复数,如果对于任意的f∈■,有f和f′分担集合S={a_1,a_2,a_3},那么■在D内正．     

一类三次系统极限环的存在唯一性

本文研究三次系统 (?)=-y δx a_1y~2 a~2xy a~5xy~2,(?)=x的极限环的存在唯一性。证明了:当δ<0,|δ|《1时至少有一个极限环;当-(a_1a_2 a_5)a_1~(-2)<δ<0时至多有一个极限环;当δ≥0或δ≤-(a_1a_2 a_5)a_1~(-2)时没有极限环。当a_1=0,δ<0时存在唯一的极限环。此外还证明了,当-(a_1a_2 a_5)a_1~(-2)≤δ<0时存在鞍点分界线环。     

用矩阵的初等行变换求欧氏环中元素的最大公因子

本文给出了欧氏环中多个元素的最大公因子的矩阵求法,解决了求欧氏环上的n元一次不定方程的所有解问题。设R为欧氏环,a_i∈R(i=1,2,…,),则a_1,a_2,…,a_n的最大公因子d=(a_1,a_2,…,a_n)—     

实系数高次方程无实根的判定

在科学技术的许多问题中,常常需要解实系数高次方程,即求出这些高次方程的实根或判定它无实数根。本文介绍实系数高次方程a_0x~n+a_1x~(n-1)+…0+a_n=0 (a_i∈R,i=0,1,…,n,a_0≠0)无实根的几种判定方法. 定理1 若a_0>0,a_n>0,a_1,a_2,…,a_(n-1)≥0或a_0<0,a_n<0,a_1,a_2,…,a_(n-1)≤0,则方程     

关于证明不等式的一种图表法

古典不等式的讲述,在足够的范围内,对中学生之所以引起严重困难的主要原因,是因为每个不同的不等式的证明,需要自己特有的巧妙的变换法则。本文给出一个很一般的不等式,第一,它能够简单地证明基本的古典不等式及编篡一些新的不等式,第二,具有直观易记的形式。本文的材料适于选课或九至十年级学生小组活动采用。下列符号便于后面使用:A(a_1,a_2,…,a_n)与Γ(a_1,a_2,…,a_n)分别表示非负数a_1,a_2,…,a_n的算术平均数与几何平均数。     

m阶等差数列的一个充要条件

文[1]给出并证明了等差数列的一个有益的性质:如果数列a_1,a_2,…,a_(n+1)成等差数列,则当自然数n≥2时,下式总成立a_1-C_n~1a_2+C_n~2a_3-…十(-1)~nC_n~na_(n+1)=0。文[2]证明了等差数列这个性质的逆命题也成立。本文拟将     

关于在求极值时引进参数的问题

大家知道,在不等式的教学中,有一个很著名的公式其中a_1,a_2,…,a_n都是正数,利用这个公式可求某个函数的极值,也就是说,如果a_1+a_2+…+a_n是一个定常数,那么,当a_1=a_2=…=a_n时,a_1a_2…a_n有极大值;如果a_1a_2…a_n是一个定常数,那么,当a_1=a_2=…a_n时,a_1+a_2+…+a_n有极小值.这个公式在求函数的极值时,理论上是解决了,     

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 REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

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.