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ON MULTIPLE POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM IN R^N

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Chinese Annals of mathematics,Series B 2000年第3期21卷 351-358页

作者： YANG HAITAO(department of mathematics, Zhejiang university, HangZhou 310027, China.) WU SHAOPING(department of mathematics, Zhejiang university, HangZhou 310027, China.) department of mathematics Zhejiang University Hangzhou 310027 China

By making use of Variational method, the authors obtain some results about existence of multiple positive solutions and their asymptotic behavior as the parameter →＋∞ for a semilinear elliptic problem in RN.

关键词： Critical point Asymptotic behavior Concentration

A NEW PERTURBATION SIMPLEX ALGORITHM FOR LINEARPROGRAMMING

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Journal of Computational mathematics 1999年第3期17卷 233-242页

作者： Ping-qi Pan(department of Applied mathematics, Southeast university, Naming 210096, China) 东南大学应用数学系江苏南京

In this paper, we first propose a perturbation procedure for achieving dual feasibility, which starts with any basis without introducing artificial variables. This procedure and the dual simplex method are then incorporated into a general purpose algorithm; then, a modification of it using a perturbation technique is made in order to handle highly degenerate problems efficiently. Some interesting theoretical results are presented. Nmerical results obtained are reported, which are very encouraging though still preliminary.

关键词： linear programming simplex method perturbation dual feasibility

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 Shanghai Jiao Tong Univ Dept Appl Phys Shanghai 200030 Peoples R China Hunan Normal Univ Dept Math Changsha 410082 Peoples R 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

GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS

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Journal of Computational mathematics 2001年第4期19卷 337-346页

作者： Qin Ni (department of mathematics, Nanjing university of Aeronautics and Astronautics, Nanjing 210016, China) 南京航空航天大学江苏南京 210016

An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.

关键词： Nonlinear programming Large-scale problem Sparse.

The extension of the first main theorem for π-blocks

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Science China mathematics 2006年第5期49卷 620-625页

作者： HAI Jinke department of mathematics, Qingdao university, Qingdao 266071, China College of mathematics ,Shandong university, Jinan 250100, China department of mathematics Qingdao University Qingdao 266071 China College of mathematics Shandong University Jian 250100 China

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

关键词： π-block, π-separable group, π-regular classes, defect group.

AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS

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Journal of Computational mathematics 2001年第5期19卷 459-466页

作者： Ying-guang Shi (department of mathematics, Hunan Normal university, Changsha 410081, China) 湖南师范大学湖南长沙 410081

Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.

关键词： an extremal approach Birkhoff quadrature formulas

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 Shanghai 200234 China

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.

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 103-114页

作者： FANG XIAOCHUN(department of mathematics, Tongji university, Shanghai 200029, China.) TONGJI UNIV DEPT MATHSHANGHAI 200029PEOPLES R CHINA

Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. *** introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.

关键词： C~*-groupoid dynamic system Induced representation Haar system

A new sieve for distinct coordinate counting

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Science China mathematics 2010年第9期53卷 2351-2362页

作者： LI JiYou1 & WAN DaQing2,1department of mathematics,Shanghai Jiao Tong university,Shanghai 200240,China 2department of mathematics,university of California,Irvine,CA 92697-3875,usa 1. department of mathematics Shanghai Jiao Tong University Shanghai 200240 China2. Department of Mathematics University of California Irvine CA 92697-3875 USA

We present a new sieve for the distinct coordinate counting *** significantly improves the classical inclusion-exclusion sieve for this problem,in the sense that the number of terms is reduced from 2(k 2) to k!,and reduced further to p(k) in the symmetric case,where p(k) denotes the number of partitions of *** an illustration of applications,we give an in-depth study of a basic example arising from coding theory and graph theory.

关键词： sieve distinct coordinate counting