数学季刊

马红彩, 张娅莉, 邓爱平

2008, 23(2): 159-164.

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In this paper, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. We study the (2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions. The method used here can be also extended to other nonlinear partial differential equations.

一类三阶牛顿变形方法

赵玲玲, 王霞

2008, 23(2): 165-170.

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A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton’s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton’s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.

弱P-反演半群上的P-核正规系

陈倩华, 范兴奎

2008, 23(2): 171-177.

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In this paper, we first give the concept of weakly P-inversive semigroup S(P). Then we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S(P) are isomorphic.

分支依赖于人口总数的具有交互作用的超布朗运动

陈丽, 闫国军

2008, 23(2): 178-187.

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In this paper, we investigate the interacting super-Brownian motion depending on population size. This process can be viewed as the high density limit of a sequence of particle systems with branching mechanism depending on their population size. We will construct a limit function-valued dual process.

单调递增分形函数上、下界的估计

马冠忠, 袁瑰霞, 崔振文

2008, 23(2): 188-194.

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Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f(x)(it is a monotone increasing fractal function) and its some applications.

p-w-亚正规算子的一些性质

李海英, 杨长森

2008, 23(2): 195-201.

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In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop’s property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.

限位排序的若干结果

陈友军, 林诒勋

2008, 23(2): 202-206.

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In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj=1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.

图上的随机动力系统及其诱导的马尔可夫链

郑洁, 刘朝阳

2008, 23(2): 207-214.

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In this paper, we define a model of random dynamical systems(RDS) on graphs and prove that they are actually homogeneous discrete-time Markov chains. Moreover, a necessary and suffcient condition is obtained for that two state vectors can communicate with each other in a random dynamical system(RDS).

关于矩阵Γ_α-群逆和Γ_α序

章劲鸥, 岑建苗

2008, 23(2): 215-221.

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The Γ_α-group inverse and the Γ_α-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γ_α-sharp ordering are given. The relations between the Γ_α-sharp ordering and the Γ_α-minus ordering are discussed.

一类非线性反应-扩散方程有限差分格式的稳定性研究

徐琛梅

2008, 23(2): 222-227.

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In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

Marcinkiewicz积分在加权Herz空间上的有界性

谢如龙, 束立生

2008, 23(2): 228-234.

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In this paper, it is proved that the Marcinkiewicz integral operator μΩ is bounded on K_q^α,p(ω₁;ω₂).

具相互作用项的非线性Schrodinger方程的散射

苑佳

2008, 23(2): 235-239.

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In this paper, we give a simplified proof on the energy scattering for the nonlinear Schrodinger equations with interaction terems by use of the interaction Morawetz estimate, which is originally introduced in [4].

几类增算子方程解的存在唯一性及应用

郝建丽

2008, 23(2): 240-244.

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By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces. The results presented here improve and generalize some corresponding results for increasing operator.

知识规律与规律的属性扰动

张冠宇, 杜英玲, 邱育峰

2008, 23(2): 245-251.

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By employing the knowledge(R-element equivalence class) in one direction S- rough sets and dual of one direction S-rough sets, the concept of knowledge law is given; the generation theorem of knowledge law, the excursion theorem of knowledge law, and the attribute disturbance discernible theorem of knowledge law are proposed. Knowledge law is a new characteristic of S-rough sets.

关于q-Bernstein多项式的加速问题

云连英, 项雪艳, 王慧

2008, 23(2): 252-259.

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In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f,q;x) to B∞(f,q;x) but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.

广度kdv方程的精确解:改进的齐次平衡法

王秀梅, 朱跃峰

2008, 23(2): 260-269.

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In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact(new) solutions of the generalized KdV equation are obtained.

矩形校正公式的误差分析

肖泽昌, 杜跃鹏

2008, 23(2): 270-275.

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This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.

退化的半线性反应扩散方程组解的熄灭

李梅

2008, 23(2): 276-283.

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In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.

奇异杂交边界点方法求解泊松方程

司马玉洲, 朱宏平, 苗雨

2008, 23(2): 284-291.

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As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both boundary element method(BEM) and meshless method. In this paper, the dual reciprocity method(DRM) is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function(RBF). Only randomly distributed nodes on the bounding surface of the domain are required and it doesn’t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable. 还原

具时滞的Hopfield网络周期解的指数稳定性

向红军, 王金华

2008, 23(2): 292-300.

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The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying. By constructing Lyapunov functionals and using inequality techniques, some new suffcient criteria are obtained to guarantee the existence and global exponential stability of periodic attractor. Our results improve and extend some existing ones in [13～14]. One example is also worked out to demonstrate the advantages of our results.

一般非线性渗流方程广义解的存在唯一性与Blow-up

霍振宏, 李海峰

2008, 23(2): 301-308.

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In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations u_t-D_j(a^ij(x,t,u)D_i+(u))+bⁱ(t,u)D_iu+C(x,t,u)=0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.

一类由正四面体和正八面体组成的共轭套中心构型

刘学飞, 向以华

2008, 23(2): 309-316.

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A new case configuration in R³, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ(r = √3/3 ρ is the radius ratio of the sizes) and mass ratio τ = m~/m must be satisfied τ = ... and for any mass ratio τ, when mass ratio τ is in the open interval (0,0.03871633950 ···), there exist three central configuration solutions(the initial configuration conditions who im- ply hamagraphic solutions) corresponding radius ratios are r₁,r₂, and r₃, two of them in the interval (2.639300779··· ,+∞) and one is in the interval (0.7379549890···, 1.490942703···). when mass ratio τ is in the open interval (130.8164950··· ,+∞), in the same way there have three corresponding radius ratios, two of them in the interval (0,0.4211584789···) and one is in the interval (0.7379549890···, 1.490942703···). When mass ratio τ is in the open interval (0.03871633950···, 130.8164950···), there has only one solution r in the interval (0.7379549890···, 1.490942703···).

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