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  • On the Reducibility of a Class of Linear Almost Periodic Differential Equations

    Afzal Muhammad;Guo Shu-zheng;

    In this paper, we use KAM methods to prove that there are positive measure Cantor sets such that for small perturbation parameters in these Cantor sets a class of almost periodic linear differential equations are reducible.

    2019年01期 v.35 1-9页 [查看摘要][在线阅读][下载 168K]
  • The Direct Sum Decomposition of Type G_2 Lie Algebra

    Zhu Xiao-yuan;Hao Hong-hua;Xin Bin;

    This article mainly discusses the direct sum decomposition of type G_2 Lie algebra, which, under such decomposition, is decomposed into a type A_1 simple Lie algebra and one of its modules. Four theorems are given to describe this module,which could be the direct sum of two or three irreducible modules, or the direct sum of weight modules and trivial modules, or the highest weight module.

    2019年01期 v.35 10-20页 [查看摘要][在线阅读][下载 177K]
  • Fundamental Solution of Dirichlet Boundary Value Problem of Axisymmetric Helmholtz Equation

    Zhang Kang-qun;

    Fundamental solution of Dirichlet boundary value problem of axisymmetric Helmholtz equation is constructed via modi?ed Bessel function of the second kind, which uni?ed the formulas of fundamental solution of Helmholtz equation, elliptic type Euler-Poisson-Darboux equation and Laplace equation in any dimensional space.

    2019年01期 v.35 21-26页 [查看摘要][在线阅读][下载 146K]
  • The Shephard Type Problems for General L_p-Centroid Bodies

    Zhang Juan;Wang Wei-Dong;

    In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.

    2019年01期 v.35 27-34页 [查看摘要][在线阅读][下载 163K]
  • On the Existence of Time-periodic Solution to the Compressible Heat-conducting Navier-Stokes Equations

    Cheng Ming;

    We study in this article the compressible heat-conducting Navier-Stokes equations in periodic domain driven by a time-periodic external force. The existence of the strong time-periodic solution is established by a new approach. First, we reformulate the system and consider some decay estimates of the linearized system.Under some smallness and symmetry assumptions on the external force, the existence of the time-periodic solution of the linearized system is then identi?ed as the ?xed point of a Poincare′ map which is obtained by the Tychonoff ?xed point theorem.Although the Tychonoff ?xed point theorem cannot directly ensure the uniqueness,but we could construct a set-valued function, the ?xed point of which is the timeperiodic solution of the original system. At last, the existence of the ?xed point is obtained by the Kakutani ?xed point theorem. In addition, the uniqueness of timeperiodic solution is also studied.

    2019年01期 v.35 35-56页 [查看摘要][在线阅读][下载 221K]
  • Coefficient Estimates for a Class of m-fold Symmetric Bi-univalent Function Defined by Subordination

    Guo Dong;Tang Huo;Ao En;Xiong Liang-peng;

    In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.

    2019年01期 v.35 57-64页 [查看摘要][在线阅读][下载 162K]
  • On a Generalized Matrix Algebra over Frobenius Algebra

    Xu Qing-bing;Zhang Kong-sheng;

    Let A be a Frobenius k-algebra. The matrix algebra R =(■) is called a generalized matrix algebra over a Frobenius algebra A. In this paper we show that R is also a Frobenius algebra.

    2019年01期 v.35 65-74页 [查看摘要][在线阅读][下载 171K]
  • Singly Covered Minimal Elements of Linked Partitions and Cycles of Permutations

    Guo Wen-kui;Niu Fei-fei;

    Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free probability theory.Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen et al.(Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. European J. Combin., 2008, 29(6): 1408–1426) de?ned the concept of singly covered minimal elements. Let L(n, k) denote the set of linked partitions of [n] with k singly covered minimal elements and let P(n, k) denote the set of permutations of [n] with k cycles. In this paper, we mainly establish two bijections between L(n, k) and P(n, k). The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in L(n, k) and the cycles in P(n, k).

    2019年01期 v.35 75-80页 [查看摘要][在线阅读][下载 188K]
  • Rota-Baxter Operators on 3-dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

    Cheng Yong-sheng;Wu Lin-li;Wang Pan-yin;

    In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.

    2019年01期 v.35 81-96页 [查看摘要][在线阅读][下载 184K]
  • Communications in Mathematical Research Aims and Scope

    <正>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 Ma.thematical Journal (NMJ), a.nd publishes quarterly. The primary purpose is to present the latest achievements in mathemat-

    2019年01期 v.35 97页 [查看摘要][在线阅读][下载 464K]
  • Instructions to Contributors

    <正>1. Papers to be published in CMR are required to be written in English.2. Manuscripts submitted to CMR are expected to be clear in exposition, valid in argument, concise in wording, and reliable in data. They should be submitted electronically along with the LaTex format and pdf files.3. A manuscript should begin with the title of the article, the authors name, and the

    2019年01期 v.35 97页 [查看摘要][在线阅读][下载 464K]
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