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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 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

Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science China mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2 1 department of mathematics, Zhejiang normal university, Jinhua 321004, China 2 department of mathematics, Kunming university of Science and Technology, Kunming 6.0093, China department of mathematics Zhejiang Normal University Jinhua 321004 China department of mathematics Kunming University of Science and Technology Kunming 650093 China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 34C37 34C23 74J30 58Z05

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

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Chinese Annals of mathematics,Series B 2003年第4期24卷 501-508页

作者： CHEN ZONGXUAN department of mathematics, jiangxi Normai university, nanchang 330027, China. Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China. jiangxi normal Univ Dept Math Nanchang 330027 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Inst Math Beijing 100080 Peoples R China

The author investigates the hyper order of solutions of the higher order linear equation, andimproves the results of M. Ozawa[15], G. Gundersen[6. and J. K. Langley[12].

关键词： Differential equation Entire function Hyper order

CYCLIC　VOLTAMMETRIC　INVESTIGATION　OF　THE　MICELLAR　PHASE　OF　SODIUM　DODECYL　SULFATE　IN　AQUEOUS　SOLUTIONS

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Chinese Chemical Letters 1995年第5期6卷 415-418页

作者： Chun Sheng MO Zhen Zhong HUANG Ming Hua ZHONG (department of Chemistry, jiangxi normal university, nanchang, 330027) jiangxi normal Univ Dept Chem Nanchang 330027 Peoples R China

Cyclic voltammetric measurements were made on sodium dodecyl sulfate(SDS) in aqueous solutions using K4Fe(CN)5 as the electroactive probe and H2SO4 as the supporting electrolyte. Using extrapolation, we estimated the diffusion coefficient Dm, hydrodynamic radius Rm, aggregation number n, and the molecular weight of SDS micelles in aqueous solutions at various surfactant *** partition coefficients,KD, of the electroactive probe between micelle and water continuous phase were also estimated.

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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.

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 200234, 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 20006., 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

SINGLE BIRTH PROCESSES

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Chinese Annals of mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of mathematics,Beijing normal university,Beijing 100875,China) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

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Chinese Annals of mathematics,Series B 2010年第2期31卷 201-210页

作者： Qingyan WU department of mathematics,Linyi normal university,Linyi 276.05,Shandong,China department of mathematics,Zhejiang university,Hangzhou 310027,China department of mathematics Linyi Normal University Linyi 276005 Shandong China department of mathematics Zhejiang University Hangzhou 310027 China

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al... 详细信息

关键词： Real-analytic infinitesimal CR automorphisms Rigid hypersurfaces Holomorphic automorphisms