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A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

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Journal of Computational Mathematics 2003年第5期21卷 625-636页

作者： Jin-yan Fan (department of Mathematics, shanghai jiaotong university, {2. 2.02.0, china) department of Mathematics Shanghai Jiaotong University 上海 200240

Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2.provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.

关键词： Singular nonlinear equations Levenberg-Marquardt method Trust region al- gorithm Quadratic convergence.

Some variational principles in electroelastic media under finite deformation

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Science china(physics,Mechanics & Astronomy) 2008年第9期51卷 1390-1402页

作者： KUANG ZhenBang department of Engineering Mechanics,shanghai {2. university,shanghai 2.02.0,china department of Engineering Mechanics Shanghai Jiaotong University Shanghai China

It is proposed that the universal thermodynamic energy variational principle is in-cluded in the first law of thermodynamics. Some variational principles in the elec-troelastic media under finite deformation are derived from this universal thermo-dynamic variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together with the discussed elec-troelastic medium. For the variational principle of nonlinear electroelastic media the variation of the electric potential is coupled with the virtual displacement,and the variation of the initial volume should be considered. The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the second order precision.

关键词： first law of thermodynamics variational principle the electroelastic media the governing equation

Superconductivity of small metal grains

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Science china(physics,Mechanics & Astronomy) 2005年第4期48卷 431-441页

作者： ZHENG Renrong1 CHEN Zhiqian2.& ZHU Shunquan1,3 1. department of physics, {2. Normal university, {2. 2.02.4, china 2. department of physics, Southwest Normal university, Chongqing 400715, china 3. department of Computer and Electric Technology, {2. Business School, {2. 2.1400, china department of physics Shanghai Normal University Shanghai China department of physics Southwest Normal University Chongqing China department of Computer and Electric Technology Shanghai Business School Shanghai China

The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关键词： size effect, superconductivity enhancements, small metallic grains.

Boundary element-free method for elastodynamics

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Science china(physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2.1. shanghai Institute of Applied Mathematics and Mechanics, shanghai {2., shanghai 2.0072. china 2. department of Civil Engineering, shanghai {2., shanghai 2.0072. china shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China department of Civil Engineering Shanghai University Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

One of the origins for curved edges of polyethylene singlecrystals

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Chinese Science Bulletin 1998年第7期43卷 564-568页

作者： YAN Deyue department of Applied Chemistry, shanghai jiaotong university,{2., china department of Applied Chemistry Shanghai Jiaotong University Shanghai China

A new concept of lattice strain was developed to explain the origin of the curved edges of polyethylene (PE) single crystals. In the crystallization of PE from poor solvents, the length of critical nucleus generated is rather short. The thin lamellae are thermodynamically unstable especially at high temperature. Thereby, during the growth of PE single crystals an annealing process is going on simultaneously, which results in a reduction of thickness from the center to growing faces of lamellae. It is known that the thinner the single crystals, the bigger the unit-cell dimensions. Consequently, unit-cells in the central part of single crystals formed are somewhat smaller than those in the outer part of the same crystals. In order to fit in with the gradual enlargement of unit-cell dimensions from the center to the edges of single crystals, the lattice planes of a faster growing dominant {110} deform to be a set of parallel arcs of concentric circles. Accordingly, the edge of a slower growing subordinate {200} becomes a part of an ellipse with obvious curvature while the edge of a {110} sector remains almost straight for it is a small part of a large circumference.

关键词： PE single crystals curved lateral habit lattice strain.

An improvement in stability of delay difference systems

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Chinese Science Bulletin 1998年第7期43卷 544-547页

作者： ZHANG Shunian department of Applied Mathematics, shanghai jiaotong university, {2. 2.02.0, china department of Applied Mathematics Shanghai Jiaotong University Shanghai China

A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.

关键词： delay difference systems uniform asymptotic stability in terms of two measures Liapunov functionals.

Different-Periodic Travelling Wave Solutions for Nonlinear Equations

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Communications in Theoretical physics 2004年第4期41卷 481-486页

作者： YE Li-Jun~1 LIN Ji~(1,2.1 department of physics,Zhejiang Normal {2.,Jinhua 32.004,china2.physics department,shanghai Jiao Tong {2.,shanghai 20003.,china department of physics Zhejiang Normal University Jinhua 321004 China physics department Shanghai Jiao Tong University Shanghai 200030 China

Using Jacobi elliptic function linear superposition approach for the(1+1)-dimensional Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation and the(2.1)-dimensional Nizhnik-Novikov-Veselov(NNV)equation,many new periodic travelling wave solutions with different periods and velocities are obtained based on the knownperiodic *** procedure is crucially dependent on a sequence of cyclic identities involving Jacobi ellipticfunctions sn(ξ,m),cn(ξ,m),and dn(ξ,m).

关键词： linear superposition nonlinear equation travelling wave solution

MORPHOLOGY OF MELT SPINNING SUPERSATURATED B2.NiAl

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Acta Metallurgica Sinica(English Letters) 1996年第2期9卷 89-93页

作者： SUN Baode CHE Xiaozhou LIN Dongliang ZHOU Yaohe(department of Materials Engineering,shanghai {2. university,shanghai 2.030,china)(department of Materials Science,shanghai {2. university,shanghai 20003.,china) shanghai jiaotong Univ Shanghai China

The morphology and structure of melt spinning Ni-33.6at% Al doped with B and RE were *** results show that the alloy consists of L10 martensitic grains and L12.Ni3Al at the grain boundaries when it contains no B and *** addition of 0.11-0.31wt% B can suppress the martensitic transformation and Ni3Al separation at the boundaries,and a supersaturated B2.single phase NiAl is *** addition of 0.05wt% RE can eliminate Ni3Al precipitated at the boundaries and get complete martensite,but 0.2.0.8wt% RE addition can suppress the martensitic transformation, and supersaturated B2.single phase NiAl is *** formation mechanism of supersaturated B2.single phase NiAl has been analyzed.

关键词： NiAl supersaturate morphologl melt spinning

REGULARITY RESULTS FOR SOME QUASI-LINEAR ELLIPTIC SYSTEMS INVOLVING CRITICAL EXPONENTS

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Chinese Annals of Mathematics,Series B 2005年第1期26卷 119-126页

作者： HUYEXIN LIJUAN departmentofMathematics ShanghaiJiaotongUniversityShanghai200240China departmentofMathematics ShanghaiJiaotongUniversityShanghai200240China.

The authors show the regularity of weak solutions for some typical quasi-linear elliptic systems governed by two p-Laplacian operators. The weak solutions of the following problem with lack of compactness are proved t... 详细信息

关键词： Elliptic equation system p-Laplacian operator Critical Sobolev exponent Regularity