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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 {2., Hnnan University,{2.) 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 {2.,Hunan University,{2. 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

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,{2. 2. Department of applied Physics, Hunan University,{2. 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.

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 2.0030, {2.Presend 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,{2. 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

The proof of FFD(L)≤11/9OPT(L) +7/9

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Chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： LI Rongheng, yuE Minyi1. Department of mathematics, Hunan Normal University, {2. 410081, {2. 2. Institute of applied mathematics, Chinese Academy of Sciences, Beijing 100080, {2. Department of mathematics Hunan Normal University Changsha 410081 China Institute of applied mathematics Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2.…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capaci... 详细信息

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2./sub>,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and yu yuanhong 3 1. Department of {2. mathematics, Beijing Institute of Technology, Beijing 100081, {2. 2. Department of mathematics, yunnan University, Kunming 650091, {2. 3. Institute of {2. mathematics, C Department of applied mathematics Beijing Institute of Technology Beijing China Department of mathematics Yunnan University Kunming China Institute of applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

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.

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 {2., Hunan University,{2. 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