数学物理学报

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一类非齐次时滞微分方程概周期解的存在性

冯春华

数学物理学报. 2006 (6): 987.

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该文研究一类非齐次时滞微分方程的概周期解, 结合运用指数二分法, 给出了系统存在概周期解的一组充分条件.

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矩阵的加权Moore-Penrose逆

刘晓冀

数学物理学报. 2006 (6): 993.

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利用矩阵的广义奇异值分解, 给出了复数域上矩阵的Moore-Penrose逆存在的充要条件及其表达式.

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Broer-Kaup系统的达布变换及其孤子解

刘萍

数学物理学报. 2006 (6): 999.

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根据Broer-Kaup系统的Lax对, 借助Broer-Kaup系统的谱问题的规范变换, 一个包含多参数的达布变换被构造出. 以一个平凡解作为种子解, 利用达布变换, 可以求得Broer-Kaup系统的非平凡解的一般表达式. 并且讨论了N=1和N=2两种孤子解的情形. 这是一种与2X2谱问题有关的孤子碰撞图像的新类型.

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构造相应于有限维非退化可解李代数的顶点代数

王书琴

数学物理学报. 2006 (6): 1008.

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设g是带有非退化不变对称双线性型的有限维可解李代数, 该文首先应用g的仿射李代数{\heiti $\hat{g}$}的表示理论,构造出一类水平为l的限制$\hat{g}$ -模$V_{\hat{g}}(l,0)$.然后应用顶点算子的局部理论在hom$(V_{\hat{g}}(l,0),V_{\hat{g}}(l,0)((x)))$中找到一类顶点代数$L_{V_{\hat{g}}(l,0)}$.建立了$L_{V_{\hat{g}}(l,0)}$到 $V_{\hat{g}}(l,0)$的映射,最后证明了这类映射是顶点代数同构.

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一类退化中立型微分系统的周期解

周宗福; 李蕾; 王敬丰; 胡秀林

数学物理学报. 2006 (6): 1025.

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该文考虑一类退化中立型微分系统, 利用不动点定理, 得到了这类系统周期解存在的充分条件.

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线性流形上反对称正交对称矩阵反问题的最小二乘解

于蕾; 张凯院; 史忠科

数学物理学报. 2006 (6): 1031.

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该文讨论了线性流形上矩阵方程AX=B反对称正交对称反问题的最小二乘解及其最佳逼近问题. 给出了最小二乘问题解集合的表达式, 得到了给定矩阵的最佳逼近问题的解, 最后给出计算任意矩阵的最佳逼近解的数值方法及算例.

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对称正则长波方程的拟紧致守恒差分逼近

王廷春; 张鲁明

数学物理学报. 2006 (6): 1039.

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该文对称正则长波方程的初边值问题进行了数值研究, 提出了一个两层隐式拟紧差分格式,格式很好地模拟了初值问题的守恒性质. 得到了差分解的存在唯一性, 并在先验估计基础上运用能量方法分析了格式的稳定性及二阶收敛性.

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关于(α,β) -度量的S -曲率

崔宁伟

数学物理学报. 2006 (6): 1047.

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给出(α,β) -度量F=α\phi(β/α)的S -曲率的计算公式. 证得对一般的(α,β) -度量,当β为关于α长度恒定的Killing1 -形式时,S=0.研究了Matsumoto -度量F=α²/(α-β)和(α,α) -度量F=α+εβ+kβ²/α)的S -曲率, 证得S=0当且仅当β为关于α长度恒定的Killing1 -形式.同时还得到这两类度量成为弱Berwald度量的充要条件.其中\phi(s)为光滑函数,α(y)=\sqrt{a_ij(x)yⁱy^j}为黎曼度量,β(y)=b_i(x)yⁱ为非零1 -形式且ε,k≠ 0为常数.

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THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORSCO SYSTEM

杨丕文

数学物理学报. 2006 (6): 1057.

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This article studies the inhomogeneous Moisil-Theodorsco system in the space R³, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R³, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved.

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RIGHT FOCAL BOUNDARY VALUE PROBLEM WITH SINGULARITY

田玉; 葛渭高

数学物理学报. 2006 (6): 1064.

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This article proves existence results for singular problem (-1)^n-px⁽ⁿ⁾(t)=f(t, x(t), ..., x^(n-1)(t)), for 0<t<1, x⁽ⁱ⁾(0)=0, i=1, 2, ..., p-1, x⁽ⁱ⁾(1)=0, i=p, p+1, ... , n-1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f(t, x₀, x₁, ..., x_n-1) are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali's convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.

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POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

蔡果兰; 葛渭高

数学物理学报. 2006 (6): 1077.

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In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phi_p(u''(t)))''- f(t,u(t))=0, t≠ t_i,△ u(t_i)=-I_i(u(t_i)), i=1, 2, ..., k,△u'(t_i)=-L_i(u(t_i)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u''(0)=0=u''(1)-\phi_q(α)u''(η),the authors translate the fourth-order impulsive differential equations with p-Laplacian (\star) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (\star) are obtained.

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CLASSIFICATION OF A CLASS OF HYPERBOLIC REINHARDT DOMAINS

严荣沐

数学物理学报. 2006 (6): 1083.

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In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reinhardt domains, and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n²-2 (where n is the dimension of domain).

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BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS

徐玉梅

数学物理学报. 2006 (6): 1089.

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In this article, the author considers the Cauchy problem for quasilinear non-strictly hyperbolic systems and obtain a blow-up result for the C¹ solution to the Cauchy problem with weaker decaying initial data.

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MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

林晓宁

数学物理学报. 2006 (6): 1105.

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In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It isproved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray--Schauder type and Krasnoselskii fixed point theorem in cones.

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ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K_1,8,n

黄元秋; 赵霆雷

数学物理学报. 2006 (6): 1115.

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The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph K_m,n (m≤ n) is Z(m,n), where Z(m,n)=\lfloor\frac{m}{2}\rfloor\lfloor\frac{m-1}{2}\rfloor\lfloor\frac{n}{2}\rfloor$$\lfloor\frac{n-1}{2}\rfloor$ (for any real number x, $\lfloor x\rfloor$ denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤ 6. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤9, then the crossing number of the complete tripartite graph K_1,8,n is $Z(9, n)+ 12\lfloor\frac{n}{2}\rfloor$.

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M-BAYESIAN CREDIBLE LIMIT METHOD OF PARAMETER AND ITS APPLICATION

韩明

数学物理学报. 2006 (6): 1123.

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This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method isapplied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.

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CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

谷峰

数学物理学报. 2006 (6): 1131.

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The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve thecorresponding results of [1, 2, 4-9, 11-15].

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WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS

李文明

数学物理学报. 2006 (6): 1144.

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The author derives a kind of weighted norm inequalities which relate the multilinear potential type integral operators to the corresponding maximal operators.

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A NOTE ON 2_IV^m-p DESIGNS WITH THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS

杨贵军; 刘民千; 张润楚

数学物理学报. 2006 (6): 1153.

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In this article, the authors obtain some theoretical results for 2_IV^m-p designsto have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2_IV^m-pdesigns with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration.

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A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS
AND THE APPLICATION TO THE FIXED POINT

文开庭

数学物理学报. 2006 (6): 1159.

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In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.

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UNIQUENESS OF MEROMORPHIC OR ENTIRE FUNCTIONS AND THEIR DIFFERENTIAL POLYNOMIALS

李江涛; 李纯红

数学物理学报. 2006 (6): 1166.

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This article studies the problem of uniqueness of two entire or meromorphic functions whose differential polynomials share a finite set. The results extendand improve on some theorems given in [3].

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