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BROYDEN'S METHOD FOR SOLVING VARIATIONAL INEQUALITIES WITH GLOBAL AND SUPERLINEAR CONVERGENCE

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Journal of Computational mathematics 2000年第3期18卷 289-304页

作者： yu-fei Yang Dong-hui Li (Department of applied mathematics, Hnnan university, changsha 410082. china) 湖南大学湖南长沙 410082

In this paper, we establish a quasi-Newton method for solving the KKT system arising from variational inequalities. The subproblems of the proposed method are lower-dimensional mixed linear complementarity problems. A suitable line search is introduced. We show that under suitable conditions, the proposed method converges globally and superlinearly.

关键词： Variational inequality quasi-Newton method global convergence,superlinear convergence

Stability Caused by Impulses for Delay Difierential Equations

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Acta Mathematica Sinica,English Series 1997年第2期13卷 193-198页

作者： yu Jianshe (Department of applied mathematics,hunan university,changsha 410082.china)

In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential equation caused by impulses.

关键词： Delay differential equation Stability Impulse

Formation and evolution mechanisms of large-clusters during rapid solidification process of liquid metal Al

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Science china(Physics,Mechanics & Astronomy) 2005年第1期48卷 101-112页

作者： LIU Rangsu, DONG Kejun, LIU Fengxiang, ZHENG Caixing, LIU Hairong & LI Jiyong Department of applied Physics, hunan university, changsha 410082. china College of Materials Science and Engineering, hunan university, changsha 410082. china College of Chemistry and Chemical Engineering, hunan university, changsha 410082. china Department of applied Physics Hunan University Changsha 410082 China College of Materials Science and Engineering Hunan University Changsha 410082 China College of Chemistry and Chemical Engineering Hunan University Changsha 410082 China

A molecular dynamics simulation study has been performed for the formation and evolution characteristics of nano-clusters in a large-scale system consisting of 400000 atoms of liquid metal Al. The center-atom method combined with pair-bond analysis technique and cluster-type index method (CTIM) has been applied here to describe the structural configurations of various basic clusters. It is demonstrated that both the 1551 bond-type and the icosahedral cluster (12 0 12 0) constructed by 1551 bond-types are dominant among all the bond-types and cluster-types, respectively, in the system and play a critical role in the microstructure transitions of liquid metal Al. The nano-clusters (containing up to 150 atoms) are formed by the combination of some middle and small clusters with distinctly different sizes, through mutual competition by unceasing annex and evolution in a seesaw manner (in turn of obtaining and losing),which do not occur as the multi-shell structures accumulated with an atom as the center and the surrounding atoms are arranged according to a certain rule. This is the essential distinction of nano-cluster in liquid metal from those obtained by gaseous deposition, ionic spray methods, and so on. Though the nano-clusters differ from each other in shape and size, all of them possess protruding corners that could become the starting points of various dendrite structures in the solidification processes of liquid metals.

关键词： liquid metal, solidification process, large-cluster configuration, evolution mechanism, computer simulation.

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 Convergence Rate of a Space Decomposition Method

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 455-460页

作者： Shu-zi Zhou, Jinping Zeng, Gui-hua ShanDepartment of applied mathematics, hunan university, changsha 410082. china Department of applied mathematics Hunan University Changsha China

Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which... 详细信息

关键词： Nonlinear problem space decomposition method Schwarz algorithm geometrical convergence

Asymptotic Behavior of Solutions for a Class of Retarded Difference Equations

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Acta Mathematica Sinica,English Series 1998年第3期14卷 419-422页

作者： Huang Lihong yu Jianshe Dai Binxiang Department of applied mathematics, hunan university, changsha 410082. china Department of applied mathematics Hunan University 410082 Changsha China

Consider the retarded difference equation xn-xn-1=F（-f（xn）+g（xn-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）>0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.

关键词： Retarded difference equation Asymptotic behavior

Molecular dynamics simulation of thermal stability of nanocrystalline vanadium

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Science china(Technological Sciences) 2006年第4期49卷 400-407页

作者： WEI Mingzhi1, XIAO Shifang1, yuAN Xiaojian2 & HU Wangyu1,2 1. Material Science and Engineering College, hunan university, changsha 410082. china 2. Department of applied Physics, hunan university, changsha 410082. china Material Science and Engineering College Hunan University Department of applied Physics Hunan University

The microstructure and thermal stability of nanocrystalline vanadium with an average grain size ranging from 2.86 to 7.50 nm are calculated by means of the analytic embedded-atom method and molecular dynamics. The grain boundary and nanocrystal- line grain atoms are differentiated by the common neighbor analysis method. The results indicate that the fraction of grain boundary increases with the grain size decreasing, and the mean energy of atoms is higher than that of coarse crystals. The thermal-stable tem- peratures of nanocrystalline vanadium are determined from the evolution of atomic energy, fraction of grain boundary and radial distribution function. It is shown that the stable tem- perature decreases obviously with the grain size decreasing. In addition the reasons which cause the grain growth of nanocrystalline vanadium are discussed.

关键词： nanocrystalline, embedded-atom method, molecular dynamics, thermal stability.

PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2004年第3期24卷 337-348页

作者：马世旺王志成许强 Department of mathematics Shanghai Jiaotong University Shanghai 200030 China Department of applied mathematics Hunan University Changsha 410082 China x(t + s) + f(t)where x and / are ra-dimensional vectors A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.

Consider the linear neutral FDEd/dt[x(t) + Ax(t - r)] = R [dL(s)]x(t + s) + f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.

关键词： Linear neutral FDE bounded total variation periodic solution

A TRUST REGION ALGORITHM WITH NULL SPACE TECHNIQUE FOR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2004年第1期17卷 54-63页

作者： TONGXiaojiao LIDonghui Instituteofmathematics ChangshaUniversityofScienceandTechnologyChangsha410077China Instituteofappliedmathematics HunanUniversityChangsha410082China

This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.

关键词： trust region method null space technique equality constrained optimization global convergence