中国科学院数学与系统科学研究院期刊网

15 March 1998, Volume 41 Issue 2
    

  • Select all
    |
    论文
  • YaoChen Zhu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0079
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application algebraic independence of values of certain gap series at algebraic and transcendental points is given.
  • DaShan Fan(1),ShanZhen Lu(2),Y
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0061
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Suppose that {α k} ∞ k=-∞ is a Lacunary sequence of positive numbers satisfying inf k α k+1 /α k=α>1 and that Ω( y′) is a function in the Besov space B 0,1 1(S n-1 ) where S n-1 is the unit sphere on R n (n2) . We prove that if ∫ S n-1 Ω( y′) dσ(y′)=0 then the discrete singular integral operatorT Ω f(x)=∑∞k=-∞∫ S n-1 f(x-α ky′) Ω (y′)dσ(y′)and the associated maximal operatorT * Ω f(x)= sup N∑∞k=N∫ S n-1 f(x-α ky′) Ω (y′) dσ(y′)are both bounded in the space L 2 (R n ) . The theorems in ths paper improve a result by Duoandikoetxea and Rubio de Francia in the L 2 case.
  • GuangFu Cao(1),P. Ghatage(2),N
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0062
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study composition operators on a Banach space of analytic functions, denoted by X , which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman space L 1 a(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators. Our proof of the fact that Fredholm composition operators on X are invertible also works for some other spaces with a reproducing kernel, including Hardy and Bergman spaces. We also investigate when a composition operator has a closed range.
  • YuHua Li
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0063
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we prove the following result: Let f and g be two nonconstant entire functions, while c j(z) (∞)(j=1,2,3,4) be four distinct meromorphic functions which satisfy T(r,c j(z))=S(r,f),T(r,c j(z))=S(r,g)(j=1,2,3,4) . Assume {z:f(z)=c j(z)}={z:g(z)=c j(z)}(j=1,2,3,4) , then f≡g .
  • Ping Sun,TianMing Wang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0064
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we prove that the Stirling numbers of the first and second types both are moment of sum of common random variables, and make use of the probabilistic methods and skills to the computation of combinatorical sums, discovery and proof of combinatorial identities, and asymptotic estimation of combinatorial sums. As a result of the applications, many new results are obtained.
  • CuiBo Jiang(1),DaoJi Meng(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0073
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we discuss the problem of isomorphism of complete Lie algebras. We also discuss the properties of complete Lie algebras whose nilpotent radicals are direct sums of Heisenberg algebras and abelian Lie algebras.
  • ShuZhong Shi,BingWu Wang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0070
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The differentiability of a norm of a Banach space may be characterized by its unit sphere. This paper generalizes these geometric conditions of norm’s differentiability to the case of a regular locally Lipschitz function.
  • YinNian He,KaiTai Li
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0074
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The aim of this paper is to present a general algorithm for solving the nonlinear operator equations in a Hilbert space, namely the k -order Taylor expansion algorithm, k1 . The standard Galerkin method can be viewed as the 1-order Taylor expansion algorithm; while the optimum nonlinear Galerkin method can be viewed as the 2-order Taylor expansion algorithm. The general algorithm is then applied to the study of the numerical approximations for the steady Navier-Stokes equations. Finally, the theoretical analysis and numerical experiments show that, in some situations, the optimum nonlinear Galerkin method provides higher convergencerate than the standard Galerkin method and nonlinear Galerkin method.
  • ChunQin Zhou
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0075
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we consider the heat flows for weakly p -harmonic maps into spheres or Riemannian Homogeneous space respectively. By using the symmetric structure of spheres or Riemannian Homogeneous spaces, we prove that heat flows for weakly p -harmonic maps have compactness properties.
  • YouLong Yang,HongKe Du,JianHua
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0076
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we prove that the sufficient and necessary conditions for a width-two CSL algebra in a separable Hilbert space to be decomposed into the direct sum of the diagonal and its norm closed ideal (i.e. the set of operators set satisfying Ringrose condition): it is generated by a finite CSL and a complemented CSL.
  • CaiJun Zhou
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0077
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We give several sufficient conditions for a poset to be acyclic or contractible. The results of the paper extend some of the results in , and generalize some of the results in to infinite posets.
  • DongGui Chen
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0072
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we consider the Cauchy problem for a inhomogeneous Kirchhoff equation which the nonlocal term is merely locally Lipschitz continuous function. Under the assumption that the initial datas and right-hand side are “small” enough, we obtain the existence and uniqueness of global solution.
  • ZhenLu Jiang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0071
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper it′s prove that the Cauchy problem for the relativistic Boltzmann equation with hard relativistic interactions has a global mild solution of the initial distribution function satisfies finite mass, energy and entropy.
  • ZhiGuo Liu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0065
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, two identities of q -differential operator are proved by using the Leibniz rule for q -differential operator. With these two operator identities and some well-known summation formulas for q -series, a new proof of the Nassrallah-Rahman integral is given. Finally, an easy evaluation of Nassrallah and Rahman’s integral representation for q -series 8Φ 7 is give.
  • QiRong Deng(1),JianBao Chen(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0066
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Consider the multivariate linear model Y~N(XΘ,σ 2I mV) , and the estimation problem of SXΘ ,selecting the loss as (δ-SXΘ)′(δ-SXΘ) We have defined the so-called k -admissibility and Φ(k) -admissibility can be defined. The necessary and sufficient conditions, under some restriction, for the estimator LY+D of SXΘ to be k -admissible and Φ(k) -admissible are obtained,respectively. For general case the necessary conditions and sufficientconditions are also given.
  • YuMing Chu(1),YingQing Song(1)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0067
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we proved that the bounded convex domain in three space must be quasiball, and hence the Riemann mapping theorem of quasiconformal mappings is holds in bounded convex domains of three space.
  • LiQin Zhao
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0068
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we investigate the bifurcation diagrams of the general three-parameter deformations of three kinds of planar polycycles and ensembles containing two saddle-nodes of multiplicity two and one hyperbolic saddle with hyperbolicity ratio different from 1. We prove that at most three limit cycles will be generated from these kinds of polycycles and ensembles.
  • MingHua Chen(1),Zhe Ren(1),Shu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0069
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Consider the heteroscedastic regression model: y i=x iβ+g(t i)+σ ie i,1in , where σ 2 i=f(u i) . Here the design points (x i,t i,u i) are known and nonrandom, g and f are unknown functions, and e i is an unobserved disturbance. For the least squares estimator n and the weighted least squares estimator n of β given in based on the family of nonparametric estimates of g(·) and f(·) , we establish their strong consistency under suitable conditions.
  • DaPeng Zhan
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): . https://doi.org/10.12386/A1998sxxb0060
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper discusses the extension of isometries between the unit spheres of some subspaces of L 1( Ω, X) . And in some cases, the problems are solved positively.
  • MinLi Li,BingRen Li

    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 225-022. https://doi.org/10.12386/A1998sxxb0080
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we point out th
  • ZuChi Chen,XiaoDong Yan
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 241-024. https://doi.org/10.12386/A1998sxxb0081
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we consider a qu
  • Shu Wang(1),ChunHong Xie(2)
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 261-026. https://doi.org/10.12386/A1998sxxb0082
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We prove the existence of the
  • YanZe Peng
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 291-029. https://doi.org/10.12386/A1998sxxb0083
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the defect of [
  • HeGuo Liu
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 299-030. https://doi.org/10.12386/A1998sxxb0084
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we have given s
  • BaoJun Huang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 313-031. https://doi.org/10.12386/A1998sxxb0085
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we prove that co
  • Yao Wang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 347-035. https://doi.org/10.12386/A1998sxxb0086
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we introduce th
  • ShiQing Zhang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 365-037. https://doi.org/10.12386/A1998sxxb0087
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Ljusternik-Schnirelmann理论 In
  • ShaoYi Zhang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 393-039. https://doi.org/10.12386/A1998sxxb0088
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the existence o
  • XueJin Wang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 399-040. https://doi.org/10.12386/A1998sxxb0089
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper is intended to prov
  • JiHua Liang
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 411-041. https://doi.org/10.12386/A1998sxxb0090
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the product of
  • XingHua Wang,DanFu Han
    Acta Mathematica Sinica, Chinese Series. 1998, 41(2): 423-042. https://doi.org/10.12386/A1998sxxb0091
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In the hypthesis that $f$ is a