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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, shanghai 200240, c.ina 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.

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

Almost periodic solutions of difference systems

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chinese Science Bulletin 1998年第24期43卷 2041-2046页

作者： ZHANG Shunian department of Applied mathematics, shanghai jiaotong university, shanghai 200240, c.ina department of Applied mathematics Shanghai Jiaotong University Shanghai China

For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.

关键词： difference systems mean values of almost periodic sequences almost periodic solutions existence uniqueness uniform asymptotic stability

Quantitative result on stability for delay difference systems

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chinese Science Bulletin 1997年第22期42卷 1858-1861页

作者： ZHANG Shuniandepartment of Applied mathematics, shanghai jiaotong university, shanghai 200240, c.ina department of Applied mathematics Shanghai Jiaotong University Shanghai China

IN ref. [1] we have established the stability criteria for the finite delay difference systems ofthe general form in terms of the discrete Liapunov functionals as well as Liapunov *** then, some other results have app... 详细信息

关键词： quadratic delay difference systems uniform stability uniform asymptotic stability stability region asymptotic stability region.

ON THE DOMAIN DEcOMPOSITION METHOD FOR MORLEYELEMENT-FROM WEAK OVERLAP TO NONOVERLAP

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Journal of computational mathematics 1999年第6期17卷 615-628页

作者： Jian-guo Huang(department of Applied mathematics, shanghai Jiao Tong university, shanghai 200240,c.ina) shanghai Jiao Tong Univ Dept Math Appl Shanghai 200240 Peoples R China

In this paper, following our original ideas[9], we first consider a weakly overlapping additive Schwarz preconditioner according to the framework of [2] for Morley element and show that its condition number is quasi-optimal; we then analyze in detail the structure of this preconditioner, and after proper choices of the inexact solvers, we obtain a quasi-optimal nonoverlapping domain decomposition preconditioner in the last. compared with [12], [13], it seems that according to this paper's procedure we can make out more thoroughly the relationship between overlapping and nonoverlapping domain decomposition methods for nonconforming plate elements, and certainly, we have also proposed another formal and simple strategy to construct nonoverlapping domain decomposition preconditioners for nonconforming plate elements.

关键词： Morley element domain decomposition weak overlap

THE ScHWARZ cHAOTIc RELAXATION METHOD WITH INEXAcT SOLVERS ON THE SUBDOMAINS

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Journal of computational mathematics 1999年第2期17卷 125-132页

作者： Jian-guo Huang(department of Applied mathematics, shanghai Jiao Tong university,shanghai 200240, c.ina) 上海交通大学应用数学系上海

In this paper, a S-cR method with inexact solvers on the subdomains is presented, and then its convergence property is proved under very general conditions. This result is important because it guarantees the effective... 详细信息

关键词： S-cR method chaotic algorithm inexact solvers

A note on the 2-connectivity in one-dimensional ad hoc networks

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Science c.ina(Information Sciences) 2011年第1期54卷 123-128页

作者： SHANG YiLun department of mathematics,shanghai Jiao Tong university, shanghai 200240,c.ina 1. department of mathematics Shanghai Jiao Tong University Shanghai 200240 China

2-connectivity is the basic graph theoretical metric for fault tolerance to node failures,and it is an extremely desirable property in network *** a one-dimensional finite ad hoc network formed by n nodes uniformly and independently distributed in a closed interval[0,z](z∈R+),we give a closed form expression for the probability that a connected one-dimensional finite ad hoc network becomes disconnected after removing a *** also sketch a procedure of finding the exact formula for 2-connectivity in a one-dimensional ad hoc network.

关键词： ad hoc network one-dimensional network 2-connectivity

Some variational principles in electroelastic media under finite deformation

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Science c.ina(Physics,Mechanics & Astronomy) 2008年第9期51卷 1390-1402页

作者： KUANG ZhenBang department of Engineering Mechanics,shanghai jiaotong university,shanghai 200240,c.ina department of Engineering Mechanics Shanghai Jiaotong University Shanghai 200240 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

Bi-Lipschitz Maps in Q-regular Loewner Spaces

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1555-1568页

作者： Ke Ying cHEN Ai Nong FANG department of mathematics,shanghai jiaotong university,shanghai 200240,P.R.c.ina department of mathematics Shanghai Jiaotong University Shanghai 200240 P. R. China

By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz maps are also obtained. These results generalize Rohde’s theorem in ? n and improve Balogh’s corresponding results in carnot groups.

关键词： Quasiconformal maps bi Lipschitz maps Loewner spaces modulus