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25 December 2006, Volume 26 Issue 6 Previous Issue    Next Issue

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On the Existence of Almost Periodic Solutions for Some Feng Chunhua Acta mathematica scientia,Series A. 2006, 26 (6):  987.  Abstract ( 2719 )   RICH HTML PDF (238KB) ( 1770 )   Save A set of sufficient conditions is derived for the existence of almostperiodic solutions for some nonhomogeneous delay differentialequations by using exponential dichotomy and fixed point theorem.This criterion provides a method for the existence analysis ofalmost periodic solution of some nonhomogeneous time delaysystems. Related Articles | Metrics

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On the Weighted Moore-Penrose Inverse of the Matrices Liu Xiaoji Acta mathematica scientia,Series A. 2006, 26 (6):  993.  Abstract ( 2196 )   RICH HTML PDF (215KB) ( 1538 )   Save A sufficient and necessary condition for the existence of the weighted Moore-Penrose inverse of a matrix and its expression are given by using the generalized singular value decomposition. Related Articles | Metrics

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Darboux Transformation of Broer-Kaup System Liu Ping Acta mathematica scientia,Series A. 2006, 26 (6):  999.  Abstract ( 2190 )   RICH HTML PDF (382KB) ( 1475 )   Save Based on the resulting Lax pairs of Broer-Kaup system, a new Darboux Transformation with multi-parameters is derived with the help of a gaugetransformation of Broer-Kaup system spectral problem. From a trivial seed,using Darboux Transformation, the generalized soliton solutions of Broer-Kaup system are given, and we discuss N=1 and N=2 two cases. It is a new type for soliton figures associated with 2X2 matrix spectral problem. Related Articles | Metrics

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Vertex Algebra Associated to Nondegenerate Solvable Lie Algebras Wang Shuqin Acta mathematica scientia,Series A. 2006, 26 (6):  1008.  Abstract ( 2393 )   RICH HTML PDF (390KB) ( 1355 )   Save The main purpose of this article is to construct the vertex algebra of associated to finite-nondegenerate solvable Lie algebra. Avoid the notion of module of vertex algebra and tire some the Jacobi identity. Apply the equivalent condition with the Jacobi identity:the weak commutativity and the D-derivatve-bracket formula. On the theorems of the representation of finite-nondegenerate solvable Lie algebra g and the level l restricted module of the affine algebra $\hat{g}$ of g. Construct and prove a kind the vertex algebras , which equipped the structure of different with that the vertex algebra of associated to Heisenberg algebra and non-twist Kac-moody algebra. Related Articles | Metrics

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Periodic Solutions for a Class of Degenerate Neutral Zhou Zongfu; Li Lei; Wang Jinfong; Hu Xiulin Acta mathematica scientia,Series A. 2006, 26 (6):  1025.  Abstract ( 2560 )   RICH HTML PDF (256KB) ( 1486 )   Save This article discusses a class of degenerate neutral differential system. Some sufficient conditions of the existence of periodic solution for the system are obtained by using the fixed point theorem. Related Articles | Metrics

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Least-Squares Solutions of Inverse Problems for Anti-Symmetric Ortho-Symmetric Matrices on the Linear Manifold Yu Lei; Zhang Kaiyuan; Shi Zhongke Acta mathematica scientia,Series A. 2006, 26 (6):  1031.  Abstract ( 2213 )   RICH HTML PDF (288KB) ( 1228 )   Save This paper discusses the least-squares solutions of matrix equation AX=Bfor anti-symmetric ortho-symmetric matrices on the linear manifold and its optimal approximation problems. The general expression of the least-squares solution set is given.In addition,the expression of the optimal approximation solution to the given matrix is obtained.Numerical methods of the optimal approximation to a given matrix and numerical experiments are described. Related Articles | Metrics

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Pseudo-Compact Conservative Finite Difference Approximate Solution for the Symmetric Regularized-Long-Wave Equation Wang Tingchun; Zhang Luming Acta mathematica scientia,Series A. 2006, 26 (6):  1039.  Abstract ( 2126 )   RICH HTML PDF (308KB) ( 1299 )   Save In this paper, a pseudo-compact finite difference scheme is proposed for symmetric Regularized-Long-wave(SRLW) equation. Existence and uniquence of numerical solutions are shown. A priori estimate and second order convergence as well as conservation of energy of the finite difference approxmate solution are discussed. Related Articles | Metrics

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On the S-curvature of Some (α,β)-metrics Cui Ningwei Acta mathematica scientia,Series A. 2006, 26 (6):  1047.  Abstract ( 2241 )   RICH HTML PDF (273KB) ( 1888 )   Save This paper gives an explicit formula of the S-curvature of (α,β)-metrics F=α\phi(β/α), and proves that if β is Killing 1-form of constant length with respect to α, then S=0. Next, the author studies the S-curvature of Matsumoto-metric F=α2/(α-β) and (α,β)-metrics F=α+εβ+kβ2/α), and obtains that S=0 if and only if β is Killing 1-form of constant length with respect to α. Actually, the author also obtains the condition of above two metrics to be weak Berwaldian. Here \phi(s) is a C∞ function, α(y)=\sqrt{aij(x)yiyj} is Riemannian metric, β(y)=bi(x)yi is non zero 1-form and ε,k≠ 0 are constants. Related Articles | Metrics

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THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORSCO SYSTEM Yang Piwen Acta mathematica scientia,Series A. 2006, 26 (6):  1057.  Abstract ( 1891 )   RICH HTML PDF (127KB) ( 1680 )   Save 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. Related Articles | Metrics

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RIGHT FOCAL BOUNDARY VALUE PROBLEM WITH SINGULARITY Tian Yu; Ge Weigao Acta mathematica scientia,Series A. 2006, 26 (6):  1064.  Abstract ( 2208 )   RICH HTML PDF (173KB) ( 1468 )   Save 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, ..., xn-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. Related Articles | Metrics

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POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN Cai Guolan; Ge Weigao Acta mathematica scientia,Series A. 2006, 26 (6):  1077.  Abstract ( 1801 )   RICH HTML PDF (119KB) ( 1310 )   Save In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phip(u''(t)))''- f(t,u(t))=0, t≠ ti,△ u(ti)=-Ii(u(ti)), i=1, 2, ..., k,△u'(ti)=-Li(u(ti)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u''(0)=0=u''(1)-\phiq(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. Related Articles | Metrics

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CLASSIFICATION OF A CLASS OF HYPERBOLIC REINHARDT DOMAINS Yan Rongmu Acta mathematica scientia,Series A. 2006, 26 (6):  1083.  Abstract ( 1585 )   RICH HTML PDF (119KB) ( 1221 )   Save 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). Related Articles | Metrics

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BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS Xu Yumei Acta mathematica scientia,Series A. 2006, 26 (6):  1089.  Abstract ( 1611 )   RICH HTML PDF (173KB) ( 1319 )   Save 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. Related Articles | Metrics

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MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS Lin Xiaoning Acta mathematica scientia,Series A. 2006, 26 (6):  1105.  Abstract ( 1890 )   RICH HTML PDF (141KB) ( 1662 )   Save 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. Related Articles | Metrics

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ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K1,8,n Huang Yuanqiu; Zhao Tinglei Acta mathematica scientia,Series A. 2006, 26 (6):  1115.  Abstract ( 1883 )   RICH HTML PDF (204KB) ( 2472 )   Save The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,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 K1,8,n is $Z(9, n)+ 12\lfloor\frac{n}{2}\rfloor$. Related Articles | Metrics

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M-BAYESIAN CREDIBLE LIMIT METHOD OF PARAMETER AND ITS APPLICATION Han Ming Acta mathematica scientia,Series A. 2006, 26 (6):  1123.  Abstract ( 1643 )   RICH HTML PDF (128KB) ( 1631 )   Save 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. Related Articles | Metrics

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CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS Gu Feng Acta mathematica scientia,Series A. 2006, 26 (6):  1131.  Abstract ( 1842 )   RICH HTML PDF (146KB) ( 1478 )   Save 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]. Related Articles | Metrics

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WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS Li Wenming Acta mathematica scientia,Series A. 2006, 26 (6):  1144.  Abstract ( 1603 )   RICH HTML PDF (142KB) ( 1428 )   Save The author derives a kind of weighted norm inequalities which relate themultilinear potential type integral operators to the corresponding maximal operators. Related Articles | Metrics

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A NOTE ON 2IVm-p DESIGNS WITH THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS Yang Guijun; Liu Minqian; Zhang Runchu Acta mathematica scientia,Series A. 2006, 26 (6):  1153.  Abstract ( 1656 )   RICH HTML PDF (121KB) ( 1146 )   Save In this article, the authors obtain some theoretical results for 2IVm-p designsto have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2IVm-p designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration. Related Articles | Metrics

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A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT Wen Kaiting Acta mathematica scientia,Series A. 2006, 26 (6):  1159.  Abstract ( 1679 )   RICH HTML PDF (124KB) ( 1647 )   Save 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. Related Articles | Metrics

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UNIQUENESS OF MEROMORPHIC OR ENTIRE FUNCTIONS AND THEIR DIFFERENTIAL POLYNOMIALS Li Jiangtao; Li Chunghong Acta mathematica scientia,Series A. 2006, 26 (6):  1166.  Abstract ( 1803 )   RICH HTML PDF (138KB) ( 1530 )   Save 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]. Related Articles | Metrics