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  • Explicit Multi-symplectic Method for a High Order Wave Equation of KdV Type

    WANG JUN-JIE;WANG XIU-YING;

    In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.

    2018年03期 v.34 193-204页 [查看摘要][在线阅读][下载 447K]
  • A Kind of Boundary Value Problems for Stochastic Differential Equations

    HU LING;WU ZHENG;WEI ZHANG-ZHE;WANG LIANG-LONG;

    In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions(in sense of mean value). Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.

    2018年03期 v.34 205-211页 [查看摘要][在线阅读][下载 144K]
  • Existence and Uniqueness of Fixed Points for Mixed Monotone Operators with Application

    WU YUE-XING;HUO YAN-MEI;

    In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.

    2018年03期 v.34 212-220页 [查看摘要][在线阅读][下载 152K]
  • Discrete Arzelà-Ascoli Theorem on the Half Line and Its Application

    LU YAN-QING;MA RU-YUN;

    The compactness criterion in l_◇={x(·)∈l~∞(0,∞))|lim t→∞ x(t)=x(∞)} is given and as an application,we study the existence of positive solutions of second order boundary value problems of difference equation on the half line by the fixedpoint theorem in cones.

    2018年03期 v.34 221-229页 [查看摘要][在线阅读][下载 163K]
  • A Note on Homogenization of Parabolic Equation in Perforated Domains

    YANG ZHAN-YING;SHU WAN;PAN ZHANG-PING;PENG CHAN-QUAN;

    We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh(Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci.(Math. Sci.), 2002, 112(1): 195–207). Moreover,these results generalize those obtained by Donato and Nabil(Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50: 115–144).

    2018年03期 v.34 230-240页 [查看摘要][在线阅读][下载 171K]
  • J-clean and Strongly J-clean Rings

    XIANG YUE-MING;OUYANG LUN-QUN;

    Let R be a ring and J(R) the Jacobson radical. An element a of R is called(strongly) J-clean if there is an idempotent e ∈ R and w ∈ J(R) such that a = e + w(and ew = we). The ring R is called a(strongly) J-clean ring provided that every one of its elements is(strongly) J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.

    2018年03期 v.34 241-252页 [查看摘要][在线阅读][下载 162K]
  • Embedding Cartesian Product of Some Graphs in Books

    YANG JIAO;SHAO ZE-LING;LI ZHI-GUO;

    The book embedding of a graph G consists of placing the vertices of G in a line called spine and assigning edges of the graph to pages so that the edges assigned to the same page do not intersect. The number of pages is the minimum number in which the graph can be embedded. In this paper, we study the book embedding of the Cartesian product Pm × Sn, Pm × Wn, Cn × Sm, Cn × Wm, and get an upper bound of their pagenumber.

    2018年03期 v.34 253-260页 [查看摘要][在线阅读][下载 485K]
  • O-convexity of Orlicz-Bochner Spaces with Orlicz Norm

    ZHOU CHENG-HUA;GONG WAN-ZHONG;ZHANG DAO-XIANG;

    In this paper we give some characterizations of O-convexity of Banach spaces, and show the criteria for O-convexity in Orlicz-Bochner function space L_M(μ, X) and Orlicz-Bochner sequence space l_M(X_s) endowed with Orlicz norm.Moreover, we give a sufficient condition for the dual of such a space to have the fixed point property.

    2018年03期 v.34 261-277页 [查看摘要][在线阅读][下载 203K]
  • Exponential Convergence of Finite-dimensional Approximations to Linear Bond-based Peridynamic Boundary Value Problems

    WU HAO;

    In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

    2018年03期 v.34 278-288页 [查看摘要][在线阅读][下载 166K]
  • Communications in Mathematical Research

    <正>Aims and Scope Communications in Mathematical Research(CMR)is a comprehensive mathematical journal carrying original papers on pure and applied mathematics.It was launched in September,1985.The journal is formerly Northeastern Mathematical Journal(NMJ),and publishes quarterly.The primary purpose is to present the latest achievements in mathematical research and to promote of the journal international academic exchange.The Editorial

    2018年03期 v.34 289页 [查看摘要][在线阅读][下载 432K]
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