Chinese Quarterly Journal of Mathematics

Constructing Measure by Repeated Infinite Subdivision

YAN Zhi-bin

2005, 20(3): 221-225.

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This paper generalizes the method of constructing measure by repeated finite subdivision in fractal geometry to that by infinite subdivision. Two conditions for the existing method are removed. A measure on the interval [0,1] is constructed using this generalized method.

Some Unicity Results for Meromorphic Functions Whose n-th Derivatives Share the Same 1-Points

YUAN Wen-jun, Seiki MORI

2005, 20(3): 226-231.

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In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors.

The Rigid Body Type Poisson Structure for the Constrained NLS System

DU Dian-lou, MA Yuri-ling

2005, 20(3): 232-237.

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A constrained system associated with a 3×3 matrix spectral problem of the nonlinear Schrodinger(NLS) hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body type Poisson structure on the Poisson manifold R3N. Further, the reduction of the constrained system extended to the common level set of the complex cones is proved to be the constrained AKNS system on C2N.

The Extended Problems of Solution for Cauchy-Riemann Equation

MA Zhong-tai, ZHAO Hong-ling

2005, 20(3): 238-241.

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This paper, we discuss the solutions’ characterize of Cauchy-Riemann equation and the extension phenomenon of Hartogs in Cn and, a series of new extended results of the solutions for Cauchy-Riemann equations is obtained by using the latest developments of the solutions’ extension. Furthermore, the case of the extension’s limitation for the solutions is also given.

Heron Triangle and Diophantine Equation

YANG Shi-chun, MA Chang-wei

2005, 20(3): 242-246.

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In this paper,we study the quantic Diophantine equation(1)with elementary geometry method,therefore all positive integer solutions of the equation(1)are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.

The Existence of Solutions of Three-point Boundary Value Problems for Second Order Impulsive Differential Equation

CAI Guo-lan, ZHANG Jian-ping, GE Wei-gao

2005, 20(3): 247-257.

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We study the existence of solutions to the second order three-point boundary value problem: where 0 <η< 1, α∈R, and f : [0, 1]×R×R→R, I_i: R×R→R, J_i: R×R→R(i=1,2,…k) are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.

Properties for Solutions of Nonlinear Functional Difference Equations

DUANMU Lian-xi

2005, 20(3): 258-264.

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In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.

A Note on Weak Open cs-images of Metric Spaces

LI Ke-dian, LIANG Hong-liang

2005, 20(3): 265-268.

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In this paper, we prove that a space with a compact countable weak base if and only if it is a weak open cs-image of a metric space.

Global Smooth Solution for the Quasi-linear Wave Equation

SONG Chang-ming, JIANG Shi-jing

2005, 20(3): 269-279.

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In this paper, we study the Cauchy problem for the following quasi-linear wave equation u_tt-2ku_xxtt=β(u_xⁿ)x, where k>0 and βare real numbers, and n≥2 is an integer. We prove that for any T>0, the Cauchy problem admits a unique global smooth solution u ∈C^∞((0, T); H^∞(R))∩C ([0, T]; H²(R))∩C¹([0, T]; L²(R)) under suitable assumptions on the initial data.

Singular Stabilization and H∞ Control of Nonlinear Systems with Ordinary Homogeneous Properties

FANG Jian-yin, MU Xiao-wu

2005, 20(3): 280-288.

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In this paper, the nonlinear singular stabilization, H∞control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogeneous. Secondly, by vitue of Hamilton-Jacobi-Isaacs equations or inequalities, we solve regular H∞, of nonlinear systems with homogeneous properties. To overcome the H∞, problem of singular nonlinear system, we try to transform inputs of the singular nonlinear system into two parts: regular part input and singular part input. Following the previous results, we solve the singular nonlinear system H∞control, we give the Lyapunov function and the state feedback controller of the singular nonlinear systems with homogeneous properties.

A Class Curves with Some Geometric and Physical Properties in a Higher Dimensional Space

JIA Xing-qin, LI Xian

2005, 20(3): 289-295.

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In this paper, we have considered a class curves with some geometric properties in a higher dimensional space and obtained the differential equation of such a class curves, which are called the hyperbolas. We have considered also hyperbola-preserving conformal transformation and the relevant physical sense. And therefore obtained other invariant properties under the illustrious concircular transformation.

Exponential Stability for the Compressible Navier-Stokes Equations

QIN Yu-ming, WANG Xiu-qin

2005, 20(3): 296-300.

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We establish the exponential stability of global solutions and Co-semigroup for the compressible Navier-Stokes equations of a viscous polytropic ideal gas in both bounded domain in R¹ and bounded annular domains in Rⁿ(n=2,3).

Closure Operators of Lattice-valued Propositional Logic LP(X)

WANG Xue-fang, ZHENG Feng-bin, XU Yang

2005, 20(3): 301-308.

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In this paper, closure operators of lattice-valued propositional logic LP(X) are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP(X) is investigated. At the same time, a tool for checking compactness of LP(X) is given.

High Accuracy Analysis for Nonconforming Mortar Finite Element with a Class of Irregular Meshes

WU Jing-zhu, SHI Dong-yang

2005, 20(3): 309-318.

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In this paper,the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile,the superclose result coincides with conventional methods is obtained by means of integral identities techniques.

Asymptotic of the Solutions of the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors (Ⅱ)

YAN Shu-xia, WANG Zhi-juna

2005, 20(3): 319-325.

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The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.

The Feature Value of Sturm-Liouville

CHENG Chuan-rui, LIU Yan

2005, 20(3): 326-330.

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This article discuss on the existence condition and of Sturm-Liouville feature value by analyzing its existence, asymptotic distribution and locus formula in special instance.

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