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Convergence analysis for general linear methods applied to stiff delay differential equations

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Progress in Natural science:Materials International 2002年第6期12卷 16-22页

作者： ZHANG Chengjian(Department of mathematics, huazhong university of science and technology, wuhan 43.074, China) huazhong Univ Sci & Technol Dept Math Wuhan 430074 Peoples R China

For Runge-Kutta methods applied to stiff delay differential equations (DDEs), the concept of D-convergence was proposed, which is an extension to that of B-convergence in ordinary differential equations (ODEs) . In this paper, D-convergence of general linear methods is discussed and the previous related results are improved. Some order results to determine D-convergence of the methods are obtained.

关键词： D-convergence general linear methods stiff delay differential equations.

The characteristics of arc beam shaping in hybrid plasma and laser deposition manufacturing

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science China(Technological sciences) 2006年第2期49卷 238-247页

作者： ZHANG Hai’ou1, QIAN Yingping1,3. WANG Guilan1 & zheng Qiguang2 1. School of Material science and technology,{3., wuhan 43.074, China 2. Institute of Laser technology and Engineering,{3., wuhan 43.074, China 3. Mechanical Engineering College, Hubei university of technology, wuhan 43.068, China 1. School of Material science and technology Huazhong University of Science and Technology Wuhan 430074 China 3. Mechanical Engineering College Hubei University of Technology Wuhan 430068 China 2. Institute of Laser technology and Engineering Huazhong University of Science and Technology Wuhan 430074 China

As a new direct metal prototyping technology,the hybrid plasma and laser deposition manufacturing (PLDM) is proposed in this paper. In order to figure out the characteristics of plasma arc beam and mould in the PLDM process of high temperature alloy, the high speed CCD camera is used to obtain the picture around the plasma arc. Afterwards the sketch of picture is clearly obtained. And the effect of laser parameter, such as average power, pulse width, pulse repetition frequency and the angle between laser beam and plasma arc beam on the plasma arc appearance, is studied experimentally. The results show that the modality of plasma arc beam is markedly influenced by laser beam. And the improvements of shape precision and surface state of the layer deposited by PLDM are confirmed.

关键词： plasma hybrid laser, direct deposition, plasma arc beam, molding character, high-temperature alloy.

D-CONVERGENCE AND STABILITY OF A CLASS OF LINEAR MULTISTEP METHODS FOR NONLINEAR DDES

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Journal of Computational mathematics 2000年第2期18卷 199-206页

作者： Cheng-jian Zhang Xiao-xin Liao (Department of mathematics, huazhong university of science and technology, wuhan 43.074, China) 华中科技大学湖北武汉 430074

Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential eq... 详细信息

关键词： D-convergence stability multistep methods nonlinear DDEs

A delay differential equation solver based on the parallel Adams algorithms

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Communications in Nonlinear science and Numerical Simulation 2001年第1期6卷 28-34页

作者： Chengjian ZHANG and Hongbing YU(Department of mathematics, huazhong university of science and technology, wuhan 43.074,China) Department of mathematics Huazhong University of Science and Technology Wuhan 430074 China

This paper constructs a class of parallel Adams algorithms for the systems of delay differential equations. The results on convergence and stability are given. The theoretical analysis and numerical test shows that th... 详细信息

关键词： parallel algorithms Adams algorithms delay differential equations

AN IMPLICIT SCHEME FOR INCOMPRESSIBLE LBGK MODEL

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Journal of Hydrodynamics 2005年第3期17卷 330-337页

作者： DURui SHIBao-chang WANGGuang-chao LIUHong-juan Departmentofmathematics HuazhongUniversityofScienceandTechnologyWuhan430074China Departmentofmathematics HuazhongUniversityofScienceandStateKeyLaboratoryofCoalCombustionHuazhongUniversity430074China／／TechnologyWuhan430074ChinaofScienceandTechnologyWuhan

In this paper, an implicit scheme (also called the θ method) was proposed for the Lattice Bhatager-Gross-Krook (LBGK) model simulating incompressible flows. The new parameter θ made the model more flexible. Through the Chapman-Enskog procedure the impressible Navie-Stokes equations could be recovered with the coupled kinetic viscosity. Boundary conditions were treated briefly and it kept the numerical accuracy of the Lattice Boltzmann Method (LBM). The two-dimensional Poiseuille flow was simulated with different values of the parameters. It is found that the numerical accuracy and stability of the implicit scheme can be improved if some adaptable parameters are chosen.

关键词： Lattice Boltzmann Method (LBM) implicit scheme θ-Lattice Bhatager-Gross-Krook (LBGK) model Poiseuille flow

Positive Periodic Solution for a Nonautonomous Delay Differential Equation

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Acta Mathematicae Applicatae Sinica 2003年第2期19卷 307-316页

作者： Bing LiuDepartment of mathematics, huazhong university of science and technology, wuhan 43.074, China Department of mathematics Huazhong University of Science and Technology Wuhan 430074 China

Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples ... 详细信息

关键词： Positive periodic solution delay differential equation Krsnoselskii fix point theorem

NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

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Journal of Computational mathematics 2002年第6期20卷 583-590页

作者： Cheng-jian Zhang(Department of mathematics, huazhong university of science and technology, wuhan 43.074, Hubei, P. R. China) Department of mathematics Huazhong University of Science and Technology Wuhan 430074

Presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDE). Discussion on the numerical analogous results of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDE; Review of the related concepts and results on RK methods; Information on the asymptotic stability and global stability of the induced NRK method.

关键词： nonlinear stability neutral delay differential equations natural Runge-Kutta methods

Effect of Powder Particle Size on the Properties and Microstructure of Ti(C,N)-Based Cermet

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Rare Metals 2001年第1期20卷 47-51页

作者： Yong zheng, Weihao Xiong (Key State Laboratory of Die technology, huazhong university of science and technology,{3., China) huazhong Univ Sci & Technol Key State Lab Die Technol Wuhan 430074 Peoples R China

The influence of raw powder particle size on the properties and microstructures of Ti (C, N)-based cermets has been studied. The conclusions are as follows: The microstructures of cermets were composed of two kinds of grains, the one with black cores surrounded by obvious rim structures, and the other whose cores were white with unconspicuous rim structures and adhesive phase. In the cermet made from fine powders, the amount of grains with white cores was much more than that in cermet made from coarse powders. In addition, their properties were also much better.

关键词： Ti(C, N)-based cermet powder particle size property microstructure

A New Clustering Algorithm for Categorical Attributes

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International Journal of Minerals,Metallurgy and Materials 2000年第4期14卷 318-322页

作者： Songfeng Lu, zhengding Lu (College of Computer science and technology,{3., wuhan 43.074, China) College of Computer science and technology Huazhong University of Science and Technology Wuhan 430074 China

In traditional data clustering, similarity of a cluster of objects is measured by distance between objects. Such measures are not appropriate for categorical data. A new clustering criterion to determine the similarity between points with categorical attributes is pre- sented. Furthermore, a new clustering algorithm for categorical attributes is addressed. A single scan of the dataset yields a good clus- tering, and more additional passes can be used to improve the quality further.

关键词： data mining clustering similarity Information