中国科学院数学与系统科学研究院期刊网

15 February 2001, Volume 44 Issue 2
    

  • Select all
    |
    论文
  • Classification of Wavelet Bases by Translation Subgroups and Nonharmonic Wavelet Bases
    Qiao WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 193-196. https://doi.org/10.12386/A2001sxxb0025
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The structure of the set S of shiftable points of wavelet subspaces is researched in this paper. We prove that S = R or S =1\q Z where q ∈ N. The spectral and functional characterizations for the shiftability are given. Furthermore, the nonharmonic wavelet bases is discussed.
  • The Influence of Minimal Subgroups on the Structure of Finite Groups
    Yan Ming WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 197-206. https://doi.org/10.12386/A2001sxxb0026
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let G be a finite group. The question of how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars. In this paper we try to use c-normal condition on minimal subgroups to to characterize the structure of G. Some previously known results are generalized.
  • Quantitative Studies on Nonlinear Lipschitz Operator (V)-Numerical Ranges
    Li Sheng WANG(1),Shui Gen LI(1
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 201-208. https://doi.org/10.12386/A2001sxxb0027
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the numerical range of nonlinear Lipschitz continuous operator is presented. Using it, many insteresting properties of operator, including the invertibility) contractivity and stability are quantitatively studied. The relation of numerical range with spectrum of operator is discussed also.
  • Composition Operators Between Hardy Spaces on the Unit Ball
    Luo LUO,Ji Huai SHI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 209-216. https://doi.org/10.12386/A2001sxxb0028
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study composition operators between Hardy spaces on the unit ball in CN. We introduce the η-Carleson measure and use it to give the characterization of the bounded or compact composition operator C■: HP(B) → Hq(B).
  • Convergence of Filters without Points
    He WEI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 217-220. https://doi.org/10.12386/A2001sxxb0029
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We introduce a new definition of convergence of filters on a locale, which is equivalent to topological convergence on spatial lovales and can be applied to any locale. As applications, some characteriztions of compactness and description of Cauchy completeness are obtained.
  • The Core-Nilpotent Decomposition of Morphisms
    Tao Sheng LI,Ping ZHU,Yong Zhi
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 221-226. https://doi.org/10.12386/A2001sxxb0030
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we research the Drazin inverse of morphisms in the exact ad- ditive category.The existence and the uniqueness for the core-nilpotent decomposition of morphisms are proved.
  • Positive Solutions of Second Order Singular Initial Value Problem
    Hong Zhou WANG,Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 227-232. https://doi.org/10.12386/A2001sxxb0031
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By using fixed-point theorem in cones and analysis method, we study existence of positive solutions for a class of singular initial value problem. THe results are better than our main literature [1].
  • Compact Toeplitz Operators on the Weighted Bergman Spaces
    Tao YU,Shan Li SUN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 233-240. https://doi.org/10.12386/A2001sxxb0032
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we investigate the Toeplitz operators on the weighted Bergman spaces. It is shown that if S is the finite sum of finite product of Toeplitz operators, then S is compact iff the Berezin transform of S vanishes at the boundary of the unit disk.
  • The Compactness of Toeplitz Operators on Dirichlet Spaces
    Guang Fu CAO(1),Lu Tao ZHU(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 241-248. https://doi.org/10.12386/A2001sxxb0033
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In the present paper, an iff condition on the compactness of Toeplitz operators on Dirichlet spaces is obtained, in addition, it is proved that a Toeplitz operator with C1- symbol is compact if and only if it equals zero if and only if the boundary value of its symbol equals zero.
  • Radon-Nikodym Theorems for Set-Valued Measures and Pettis-Aumann Integral Representation for Set-Valued Operators
    Jian Rong WU(1),Cong Xin WU(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 249-258. https://doi.org/10.12386/A2001sxxb0034
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper establishes the Radon-Nikodym theorems for set-valued measures on Banach spaces, and gives Petits-Aumann integral representations for two kinds of set-valued operators.
  • Random Dirichlet Series of Infinite Order
    Dao Chun SUN,Te Wei CHEN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 259-268. https://doi.org/10.12386/A2001sxxb0035
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, We study Dirichlet series and random Dirichlet series on the right half-plane. We give a very good coefficient condition; count precision order; study random series with non-uniformly distribution random variables and know that every points it (t ∈ R) is Borel point with no finite exceptional value for random Dirichlet series of infinite order.
  • On the General Dedekind Sums and One Kind Identities of Dirichlet L-Functions
    Wen Peng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 269-272. https://doi.org/10.12386/A2001sxxb0036
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The main purpose of this paper is to introduce a general Dedekind sums, and deduce one kind identities for Dirichlet L-functions.
  • A Note on Almost Isometric Embedding
    Guang Gui DING
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 273-276. https://doi.org/10.12386/A2001sxxb0037
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, it is shown that there is no ε-isometric operator of any infinitely dimensional abstract LP space (0 < p < ∞) into (c) for ε > 0 small enough.
  • On Meromorphic Solutions of Algebraic Differentical Equation (f')~n = R(z, f)
    Wen Jun YUAN(1),Ye Zhou LI(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 277-286. https://doi.org/10.12386/A2001sxxb0038
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we first investigate the number of meromorphic solutions of algebraic differential equation (f')" = R(z,f) with rational coefficients and give examples to show its precise. Secondly, applying Nevanlinna distribution theories, we consider solutions of a typical algebraic differential equation (f')3 = a0(f - τ1)2(f- τ2)2(f-τ3)2. Results in this paper improve others, such as by Gao shi'an [1], Gundersen G. and Laine I[2], He Yuzan and Laine I.[3-5].
  • Quasi-Convex Mappings on Bounded Convex Circular Domains
    Tai Shun LIU(1),Hao LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 287-292. https://doi.org/10.12386/A2001sxxb0039
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this papers we study a subclass of starlike mappings-quasi-convex map- pings on bounded convex circular domains in Cn. The relations between quasi-convex mappings and starlike mappings or convex mappings are established. Moreover, the growth and covering theorems which are same as convex mappings are given.
  • On the Permanence and Extinction in Nonautonomous Lotka-Volterra Comptitive Systems with Delays
    Zhi Dong TENG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 293-306. https://doi.org/10.12386/A2001sxxb0040
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the permanence and extinction of general nonautonomous Nspecies Lotka-Volterra type competitive systems with pure-delays are studied. Some new criteria are established. The results obtained in [8-10] for nondelayed nonautonomous Lotka-Volterra type competitive systems are improved and extended.
  • Similarity Small Module Compact of Essentially Normal Operators
    Fa Hui ZHAI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 307-310. https://doi.org/10.12386/A2001sxxb0041
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we prove a class of essentially normal operators A'(Ω'; 1) (T ∈ A'(Ω'; 1), if T satisfies: (1) T, T|H(T) are essentially normal, respectively; (2) σ(T) = Ω', ρF(T) ∩σ(T)=Ω'; (3) ind(T-)(λ) = -1, nul(T) -λ) = 0, λ ∈Ω '; (4) σ(T|H(T)) is a perfet set, where Ω' is connected analtic Cauchy domain, Hl(T)=V{ker(T - λ)*: λ∈ρrs-F(T)} are similiar small module compact.
  • Oscillation and Nonoscillation for a Class of Quasilinear Differential Equations of Second Order
    Xiao Jing YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 311-318. https://doi.org/10.12386/A2001sxxb0042
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Some oscillation and nonoscillation criteria for quasilinear differential equation (p(x'))' + q(t)p(x) = 0, t ≥ to, q(t) ≥ 0, where p(u) = |u|p-1u, p > 0 is a constant, are given, which improves the results of [2].
  • Optimiality Condition for a Class of Semi-Linear Elliptic Equations
    Hang GAO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 319-332. https://doi.org/10.12386/A2001sxxb0043
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the optimal control problem for a class of elliptic equations that may possess multiple solutions. By constructing a sequence of parabolic control problems and using the results for the parabolic control problems, we obtain necessary conditions for optimal control of the elliptic equation.
  • The Average Variance Criterion for Nonstationary MDP with Borel State Space
    Xian Ping GUO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 333-342. https://doi.org/10.12386/A2001sxxb0044
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we consider the average variance criterion for nonstationary Markov decision processes (MDP) with Borel state space. First, from the optimality equations we prove the existence of optimal Markov policies under ergodic conditions. Secondly, by the theory on Markov processes and structuring a new model we also prove that there exists a Markov policy, which is optimal in an average expected criterion, minimizes the average variance in the class of optimal policies for average expected criterion. So we extend the main results obtained by Dynkin E. B. and Yushkevich A. A. and by Kurano M. etc.
  • The Operators T in Quaternionic Analysis and Two Classes of Boundary Value Problems
    Pei Wen YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 343-350. https://doi.org/10.12386/A2001sxxb0045
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study the inhomogeneous Dirac equation in quaternionic analysis. Introduce the distribution solution of the equation, or the operator T, and show some properties of the operator T, discuss the Dirichlet boundary value problem for the inhomogeneous Dirac equation. In addition, we study also the case of the inhomogeneous Dirac equation of higher order and a class of boundary value problem for the equation.
  • Cayley Graphs of Order pqr are Hamiltonian
    Deng Xin LI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 351-358. https://doi.org/10.12386/A2001sxxb0046
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let G be a group of order pqr, where p, q, r are distinct primes. In this paper, we prove that every connected Cayley graph on G is Hamiltonian.
  • Characterisation of the Symbolic Spaces OpS_(1,1)~m in Kernel-Distribution Spaces
    Qi Xiang YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 359-364. https://doi.org/10.12386/A2001sxxb0047
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In1950's, one has established the formal relation between the symbol and the kernel-distribution, then the symbol school and the Calderon-Zygmund school remain in two isolated class. As for OpS1,1m, one has established only a relation between OpS1,1m and a kernel-distribution space in some sense. Here one establishes a characterisation of OpS1,1m in kernel-distribution space OpKm.
  • Strong Stability of Attractors and the Properties of Ω-Limit Sets
    Tu Sen HUANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 365-370. https://doi.org/10.12386/A2001sxxb0048
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The persistence and strong stability of attractors of flows defined on a compact Hausdorff topological space are proved under small perturbation and some properties of Ω-limit sets are given in this paper.
  • Oscillation Criteria for Second Order Nonlinear Differential Equations
    Qi Ru WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 371-376. https://doi.org/10.12386/A2001sxxb0049
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper discusses the oscillation of second order nonlinear ordinary differential equations and delay differential equations. Some new oscillation criteria for the equations are obtained.
  • The Unfoldings of Equivariant Two-Parameter Bifurcation Problems
    Bing LI(1),Xiang Zheng QIAN(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(2): 377-384. https://doi.org/10.12386/A2001sxxb0050
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Under the action of equivariant U-equivalent group, the unfoldings of equivariant bifurcation problems with two-parameters (here the parameters are vector variables) are studied. The main results include the necessary and sufficient condition that a unfolding is a versal unfolding, and the necessary and sufficient condition that a unfolding is factor through another unfolding of the same equivariant two-parameters bifurcation problems.
Journal Online
News More