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An improvement in stability of delay difference systems

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Chinese Science Bulletin 1998年第7期43卷 544-547页

作者： ZHANG Shunian department of Applied mathematics, shanghai jiaotong university, shanghai 2.02.0, china department of Applied mathematics Shanghai Jiaotong University Shanghai China

A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.

关键词： delay difference systems uniform asymptotic stability in terms of two measures Liapunov functionals.

REGULARITY RESULTS FOR SOME QUASI-LINEAR ELLIPTIC SYSTEMS INVOLVING CRITICAL EXPONENTS

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Chinese Annals of mathematics,Series B 2005年第1期26卷 119-126页

作者： HUYEXIN LIJUAN departmentofmathematics ShanghaiJiaotongUniversityShanghai200240China departmentofmathematics ShanghaiJiaotongUniversityShanghai200240China.

The authors show the regularity of weak solutions for some typical quasi-linear elliptic systems governed by two p-Laplacian operators. The weak solutions of the following problem with lack of compactness are proved t... 详细信息

关键词： Elliptic equation system p-Laplacian operator Critical Sobolev exponent Regularity

Almost periodic solutions of difference systems

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Chinese Science Bulletin 1998年第24期43卷 2041-2046页

作者： ZHANG Shunian department of Applied mathematics, shanghai jiaotong university, shanghai 2.02.0, china department of Applied mathematics Shanghai Jiaotong University Shanghai China

For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.

关键词： difference systems mean values of almost periodic sequences almost periodic solutions existence uniqueness uniform asymptotic stability

REFINED CONNECTIVITY PROPERTIES OF ABELIAN CAYLEY GRAPHS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 409-414页

作者： LI QIAOLIANG (department of Applied mathematics, shanghai jiaotong university, shanghai 200030, chinaPresend in department of mathematics, Hunan Normal university, Changsha 410082, china.)LI QIAO (department of Applied mathematics, shanghai jiaotong Univ department of Applied mathematics Shanghai Jiaotong University Shanghai 200030 China department of mathematics Hunan Normal University Changsha 410082 China

Restricted edge connectivity of a graph G is defined to be the minimum size |U| of a set U of edges such that G-U is disconnected and G-U contains no trivial component K1. The high order edge connectivity Ni, i1, is the number of edge outsets of size i. TO determine all Ni, i 1, for a general graph is NP-hard. In this paper, the authors evaluated the restricted edge connectivity and the high order edge connectivity Ni, 1 i -1, for any connected Abelian Cayley graphs explicitly.

关键词： Abelian Cayley graph Restricted edge connectivity High order edge connectivity

On the Limit Cycles of Quadratic Differential Systems

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Acta Mathematica Sinica,English Series 2002年第4期18卷 803-816页

作者： Xiang ZHANG department of mathematics, shanghai jiaotong university, shanghai 200030, P. R. china department of mathematics Shanghai Jiaotong University Shanghai P. R. China

In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems to be weak foci, and solve an open problem proposed by Yanqian Ye.

关键词： Quadratic differential system Limit cycle Ergodicity.

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of mathematics, shanghai Normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, shanghai Normal university, shanghai 200234, china) department of mathematics Shanghai Normal University 上海 200234

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

Lie bialgebras of generalized Witt type

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Science china mathematics 2006年第4期49卷 533-544页

作者： SONG Guang’ai & SU Yucai College of mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, china department of mathematics, university of Science and Technology of china, Hefei 230026, china department of mathematics, shanghai jiaotong university, shanghai 2.02.0, china College of mathematics and Information Science Shandong Institute of Business and Technology Yantai China department of mathematics Shanghai Jiaotong University Shanghai China department of mathematics University of Science and Technology of China Hefei China

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.

关键词： Lie bialgebras, Yang-Baxter equation, Lie algebra of generalized Witt type.

SEMI-DEFINITE RELAXATION ALGORITHM FOR SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES

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Chinese Annals of mathematics,Series B 2005年第1期26卷 153-158页

作者： CHENFENG ZHANGLIANSHENG departmentofmathematics ShanghaiUniversityShanghai200436China／／DepartmentofIndustrialEngineeringandManagementShanghaiJiaotongUniversityShanghai200030China. departmentofmathematics ShanghaiUniversityShanghai200436China

The authors present a semi-definite relaxation algorithm for the scheduling problem with controllable times on a single machine. Their approach shows how to relate this problem with the maximum vertex-cover problem with kernel constraints (MKVC).The established relationship enables to transfer the approximate solutions of MKVCinto the approximate solutions for the scheduling problem. Then, they show how to obtain an integer approximate solution for MKVC based on the semi-definite relaxation and randomized rounding technique.

关键词： Scheduling with controllable times Semi-definite programming Approximation algorithm