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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 2.02.4, 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 2.02.4, 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.

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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science china mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of mathematics, East china normal university, shanghai 200062, china college of mathematics & Information science, Northwest normal university, Lanzhou 730070, china 1. Department of mathematics East China Normal University Shanghai 200062 China 2. college of mathematics & Information science Northwest Normal University Lanzhou 730070 China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA

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Chinese Annals of mathematics,Series B 1996年第2期17卷 199-212页

作者： CHEN CAOYU Department of mathematics, shanghai normal university, shanghai 2.02.4, china. shanghai normal UNIV DEPT MATHSHANGHAI 200034PEOPLES R CHINA

Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.

关键词： Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra

Numerical Solution of Heat Tranfer Problemwith Flow and Solidification in Round BilletContinuous Casting of Steel

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Communications in Nonlinear science and Numerical Simulation 1999年第3期4卷 236-239页

作者： Jiahong GUO(shanghai Institute of Applied mathematics and Mechanics, shanghai university,shanghai 200072, china)Xin HONG(college of Material science, shanghai university, shanghai 200072, china) shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China college of Material science Shanghai University Shanghai 200072 China

IntroductionThetechnologyofc***g,***,itisimportallttostudythep... 详细信息

IntroductionThetechnologyofc***g,***,itisimportallttostudythep...

关键词： heat transfer flow and solidification round billet continuous casting

A LINE SEARCH FILTER SECANT METHOD FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems science & Complexity 2010年第2期23卷 343-361页

作者： Zhujun WANG Detong ZHU Department of mathematics Shanghai Normal University Shanghai 200234 China. Business college Shanghai Normal University Shanghai 200234 China.

This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for *** feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos *** convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the ***,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is ***,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.

关键词： Filter method nonlinear programming secant algorithm second order correction.

JACOBI SPECTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of Computational mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(Department of mathematics, shanghai normal university, shanghai 2.02.4, china)(COM2MAC, Pohang university of science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (Department of mathematics, East china normal university, shanghai 200062, china) E china normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

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Acta Mathematica Scientia 2008年第3期28卷 479-488页

作者：黎野平 Department of mathematics Xianning College

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.

关键词： Steady-state nonisentropic hydrodynamic model semiconductor subsonic