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Irregular but Nonfractal Drums and n-Dimensional Weyl Conjecture

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Acta Mathematica Sinica,English Series 1995年第2期11卷 168-178页

作者： Chen Hua department of Mathematics wuhan university {2., 430072 china department of Mathematics Wuhan University Wuhan People's Republic of China

In this paper, we study the asymptotics of the spectrum of the Dirichlet （or Neumann） Laplacian in a bounded open set ΩRn（n≥1） with irregular but nonfractal boundary Ω. We give a partial resolution of the Weyl conjecture, i.e. for the counting function Ni（λ）（i=0: Dirichlet; i=i: Neumann）, we have got a precise estimate of the remainder term Ψi（λ）=φ（λ）-Ni（λ） for large λ, where φ（λ） is the Weyl term. This implies that for the irregular but nonfractal drum Ω, not only the volume |Ω|n is spectral invariant but also the area of boundary |Ω|n-1 might be spectral invariant as well.

关键词： Math Irregular but Nonfractal Drums and n-Dimensional Weyl Conjecture

On the value distribution of Julia points

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Chinese Science Bulletin 1997年第22期42卷 1856-1857页

作者： SUN Daochundepartment of Mathematics, wuhan university,{2., china department of Mathematics Wuhan University Wuhan China

CONSIDER the rational fractional mapping R: V→V on the complex sphere V. We use themethod of the value distribution to study the properties near Julia points to understand Juliapoints.

关键词： complex dynamics Julia point value distribution.

Removal　of heavy　metals（Cr^（6＋），Ni^（2.））　from　polluted　water　using　decaying　leaves　of　plane（Plantanus　orientalis）

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Journal of Environmental sciences 1996年第2期8卷 191-195页

作者： Tan Zhiqun (Tzitschung T. Tahn) Wang Yuanxiang Yan Guoan (department of Environmental sciences,{2. university,{2. 430072,china) department of Environmental sciences Wuhan University Wuhan 430072 China

plane decaying leaves have been found capable of removing chromium and nickel ions from aqueous solutions. The removal efficiency depends upon the pH conditions, ions components and concentrations, and concentrations of leaves in media. The maximum removal for unique Cr6+ is about 7.5-8.0g/kg leaves at pH 4. 0, for unique Ni2. about 2. 6g/kg at the region of PH5. 0-5.5. Under the described conditions nickel increases chromium uptake by plane decaying leaves from solution.

关键词： plane decaying leaves chromium nickel heavy metals.

The Ground and Excitation Levels of the Trimer

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wuhan university Journal of Natural {2. 1998年第2期3卷 163-164页

作者： You Pu(department of Physics, wuhan university,{2.,china) wuhan university Department of Physics Wuhan China (GRID:grid.49470.3e) (ISNI:***)

The ground and excited levels of the trimer (4He)3 are obtained theoretically by solving the 2.D Faddeev integral equation in the momentum space. In solving the equation, the direct matrix inversion method (I. M.) is used instead of the iteration and Pade approximate method. The new HFD-B Aziz potential ν is used in the calculation.

关键词： Trimer Faddeev equation matrix inversion method

Equivalence problem for Bishop surfaces

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Science china Mathematics 2010年第3期53卷 687-700页

作者： HUANG XiaoJun 1, & YIN WanKe 2.1 department of Mathematics, Rutgers university, New Brunswick, NJ 08902. USA 2.{2. of Mathematics and Statistics, wuhan university, wuhan 430072, china 1. department of Mathematics Rutgers University New Brunswick NJ 08902 USA2. School of Mathematics and Statistics Wuhan University Wuhan 430072 China

The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of the recent studies of Bishop surfaces, which, in particular, includes the work of the authors. In the second part of the paper, we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant. More precisely, we let M be a real submanifold of C 2.defined by an equation of the form w = zz + 2.e(z s + az s+1 ) with s≥ 3 and a a complex parameter. We will prove in the second part of the paper that for s≥ 4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation. When s = 3, we show that surfaces of this type with two different real parameters are not holomorphically equivalent.

关键词： equivalence problem Bishop surface Chern-Moser theory elliptic and hyperbolic complex tangents normal form and modular space

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science china Mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. department of Mathematics,wuhan {2.,wuhan 430072,china 2. Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088. china 1. department of Mathematics Wuhan University 430072 Wuhan China 2. Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

THE NON-DIFFERENTIABILITY OF A CLASS OFFRACTAL INTERPOLATION FUNCTIONS

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Acta Mathematica Scientia 1999年第4期19卷 425-430页

作者：陈世荣 wuhan Univ Dept Phys Wuhan 430072 Peoples R China

Hardin and Massopust([1]) introduced a class of fractal interpolation functions and calculated their Bouligand dimensions. This paper deals with the non-differentiability of these functions and shows some conditions under which they are nowhere differentiable. The basic technique here is based on the presentation the author obtains.

关键词： fractal interpolation iterated system nowhere differentiablity Hausdorff metric

SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 159-166页

作者： ZHANG YIPING department of Mathematics, wuhan university,{2., china.Project supported by the National Natural Science Foundation of china. wuhan UNIV DEPT MATH WUHAN 430072 PEOPLES R CHINA

The object of this paper is to study the non-tangential increasing properties of positiveharmonic function u in Lipschitz domain by means of Martin representation theory. A necessaryand sufficient condition of the control of growth of u near any fixed boundary point is obtained.It is shown that the non-tangential increasing degree of u near a boundary point is exactlythe local degree of its representation measure with respect to the harmonic measure. Someexamples are given.

关键词： Martin representation Harmonic function Harmonic measure

Effect of Substrate-Water Interaction on the Wetting Behavior in Water-Oil and Substrate-Water-Oil Systems

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wuhan university Journal of Natural {2. 2003年第4A期8卷 1097-1102页

作者： Yuan Yin-quan 1,2., Zou Xian-wu 1 , Jin Zhun-zhi 1 1. school of Physics and Technology, wuhan university,{2., Hubei, china 2. department of Physics, Xiaogan university, Xiaogan 432.00, Hubei, china wuhan university School of Physics and Technology Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Xiaogan university Department of Physics Xiaogan Hubei China (GRID:grid.49470.3e) wuhan university School of Physics and Technology Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

The effects of the substrate-water interaction on the wetting behavior in water-oil and surfactant-water-oil systems confined by one substrate which has the preferential interaction to one species of particles have been investigated by using the free energy analysis and discontinuous molecular dynamic simulations. As the preferential interaction between the substrate and water particles varies from small repulsion to large attraction, the partial drying, partial wetting and complete wetting state are observed in sequence. In addition, the wetting behavior of surfactant aqueous solution on the substrate is not only dependent on the interaction, but also limited by the maximum equilibrium concentration of surfactants at the interface.

关键词： wetting behavior wetting transition preferential interaction substrate