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THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

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Acta Mathematica Scientia 2010年第5期30卷 1501-1506页

作者：褚玉明孙天川 department of mathematics Huzhou Teachers College

In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2.……in=r（x1（i1x2.i2.…xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2. 3,...} As its applications, some analytic inequa... 详细信息

关键词： symmetric function Schur convex Schur harmonic convex

K-Spaces Property of Product Spaces

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Acta Mathematica Sinica,English Series 1997年第4期13卷 537-544页

作者： Liu Chuan Lin Shou department of mathematics, Guangxi University, Nanning 530004,{2. department of mathematics, Ningde teachers College, Fujian 352.00,{2. 广西大学数学系广西南宁宁德师范学院数学系福建宁德 352100

Let K be a class of spaces which are eigher a pseudo-open s-image of a metric space or a k-space having a compact-countable closed k-network. Let K′ be a class of spaces which are either a Fréchet space with a point-countable k-network or a point-G_δ k-space having a compact-countable k-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many spaces in the class K or K′ are a k-space. The main results are that Theorem A If X, Y ∈ K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka’s condition. Theorem B The following are equivalent: (a) BF(w2. is false. (b) For each X, Y ∈ K′, X x Y is a k-space if and only if (X, Y) has the Tanaka’s condition.

关键词： K--space K--network Weak base Product space BF(ω2. Tanaka’s condition

线性时滞系统的记忆与无记忆复合H^∞状态反馈控制

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系统工程理论与实践 2002年第6期22卷 21-25页

作者：姜偕富费树岷冯纯伯东南大学自动化研究所

对于存在状态时滞的线性时滞系统 ,研究了无记忆与带记忆的复合 H∞ 状态反馈控制器的设计问题 ,通过解相应的线性矩阵不等式求得满足设计要求的状态反馈控制器 ,得到了很好的控制效果 .最后给出一个数字仿真实例说明所得结论的有效性 .

关键词：线性时滞系统复合H^∞状态反馈控制线性矩阵不等式渐近稳定性

Injective Homogeneity and Homological Homogeneity of the Ore Extensions

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Acta Mathematica Sinica,English Series 1997年第4期13卷 433-442页

作者： Yi Zhong department of mathematics, Guangxi {2. University, Guilin 541004. china 广西师范大学数学系广西桂林

In this paper we prove that under some natural conditions, the Ore extensions and skew Laurent polynomial rings are injectively homogeneous or homologically homogeneous if so are their coefficient rings. Specifically, we prove that if R is a commutative Noetherian ring of positive characteristic, then An（R）, the nth Weyl algebra over R, is injectively homogeneous （resp. homologically homogeneous） if R has finite injective dimension （resp. global dimension）.

关键词： Injectively homogeneous ring Homologically homogeneous ring Ore extension Quotient ring

SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS

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Systems Science and Mathematical Sciences 1993年第3期6卷 239-244页

作者： WANG Zhijian department of mathematics, Suzhou Railway {2. College, Suzhou 2.5009, china

Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x（G）, x1（G） and x2.G）, respectively. Forany simple graph G of order p and its complement G, the foll... 详细信息

Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x（G）, x1（G） and x2./sub>（G）, respectively. Forany simple graph G of order p and its complement G, the following inequalities of theNordhaus-Gaddum class are obtained:（i）|2.1/2./sup>|-ε1≤x（G）+x1（G）≤2.-2.and 0≤x（G）·x1（G）≤（p-1）2./sup> for p≥2.（ii）|2.1/2./sup>|+ε1≤x（G）+x2./sub>（G）≤2.-1 and 0≤x（G）·x2./sub>（G）≤p（p-1） for p≥3,（iii）p≤x1（G）+x2./sub>（G）≤2.-1 and 0≤x1（G）·x2./sub>（G）≤p（p-1） for p≥3,where ε1=0, if p1/2./sup> is an odd integer, 1, otherwise,ε2./sub>=1, if p1/2./sup> is an even integer, 0, otherwise,and [x] denotes the ceiling of x. We also show that these bounds are sharp for everypositive integer p.

关键词： Complementary graph chromatic number edge chromatic number total chromatic number theorem of Nordhaus-Gaddum class

A CLASS OF NONLINEAR SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

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Applied mathematics(A Journal of Chinese Universities) 2007年第2期22卷 201-206页

作者： Mo Jiaqi department of mathematics, Anhui Normal University, Wuhu 2.1000,{2. department of mathematics, Huzhou teachers College, Huzhou 313000,{2. Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 2.02.0,{2.. department of mathematics Anhui Normal University Wuhu 241000 China

A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptoti... 详细信息

关键词： nonlinear reaction diffusion singular perturbation boundary perturbation

FOUR VALUES THEOREM OF DERIVATIVES OF MEROMORPHIC FUNCTIONS

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Systems Science and Mathematical Sciences 1998年第3期11卷 245-248页

作者： QIU Gandi(department of mathematics, Ningde {2. College, Fujian 352.00, china) 宁德师范高等专科学校数学系福建宁德 352100

In this paper, we mainly discuss the uniqueness problem of k (k ≥ 1) order derivatives of two meromorphic functions that share some values, and consider the case of Navanlinna’s Four Values Theorem when the derivati... 详细信息

关键词： Meromorphic function small function uniqueness

The Green formula and heredity of algebras

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Science china mathematics 2005年第5期48卷 610-617页

作者： ZHANG Guanglian & WANG Shuai department of Mathematical Sciences, Tsinghua University, Beijing 100084, china Yancheng {2. College, Yancheng 2.4002. china department of mathematics, Johns Hopkins University, Baltimore, MD2.2.8, U.S.A. 1. department of Mathematical Sciences Tsinghua University 100084 Beijing China 2. Yancheng teachers College 224002 Yancheng China 3. department of mathematics Johns Hopkins University 21218 Baltimore MD USA

Let A be a finite dimensional algebra over a field k with q elements. It is shown that the Green formula is true in mod-A if and only if A is a hereditary algebra.

关键词： Green formula idempotent ideal hereditary algebra.

The Interaction Programming Problem

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Journal of Systems Science and Systems Engineering 2001年第2期13卷 173-184页

作者： LI Rong-sheng 1, CHENG Ying 2..Institute of Operations Research, Qufu Normal University, Qufu 2.3165,china2.mathematics {2., Heze teachers College, Heze 2.4015, china Institute of Operations Research Qufu Normal UniversityQufu 273165 China mathematics department Heze Teachers CollegeHeze 274015 China

Based upon the research to the economic equilibrium problems,we present a kind of new mathematical programming problem——interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple parametric programming problems which is interrelated with each other. The IPP reflects the equality and mutual benefit relationship between two (or among multiple) economic planners in an economic system. In essence, the IPP is similar to the generalized Nash equilibria (GNE) game which has been given several names in the literature: social equilibria games, pseudo-Nash equilibria games, and equilibrium programming problems. In this paper, we establish the mathematical model and some basic concepts to the IPP. We investigate the structure and the properties of the *** also give a necessary and sufficient conditions for the existence of the equilibrium points to a kind of linear IPP.

关键词： Interaction programming problem equilibrium points partial solutions optimal solutions