中国科学院数学与系统科学研究院期刊网

15 November 2013, Volume 56 Issue 6
    

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  • Empirical Likelihood Estimator of Medical Costs with Censored Data
    Yong ZHOU, Jun TIAN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 817-828. https://doi.org/10.12386/A2013sxxb0080
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The statistical analysis and inference of medical cost is often challenged by the fact that the survival times are censored. In this paper, we consider the case that medical cost history is available. An empirical likelihood procedure is proposed for making statistical inference on the mean cost when censoring is present, then we can easily get the confidence intervals for the parameters of interest at a given confidence level. In the simulation sdudies, we use different sample sizes to compare the finite sample performances of our procedure with some popular procedures in the literatures. We show that our procedure gives better confidential intervals for the mean of medical cost. The proposed procedure is also applied to a real dataset collected in a cardiology trial.
  • Bochner-Martinelli Type Formulae for Spinor-Valued Functions
    Fu Li HE, Jin Yuan DU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 829-840. https://doi.org/10.12386/A2013sxxb0081
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    In this paper, in comparison with the Bochner-Martinelli fomulae in several complex analysis, we show the Bochner-Martinelli type formulae for spinor-valued functions in Hermite Clifford analysis and get some reproducing Pompeiu formulae of Bochner-Martinelli type and Bochner-Martinelli formulae in some special cases.
  • Strong Convergence Rate of the Location Parameter Change-Point Estimator
    Chang Chun, TAN Jun HUI, Bai Qi MIAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 841-850. https://doi.org/10.12386/A2013sxxb0082
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    In this paper, we consider the problem of the location parameter change point model allowing at most one change. With the help of slip window and U-statistics method, the strong consistency and strong convergence rate of the change point estimator are studied.
  • The Asymptotic Properties of CVaR Estimator under ρ Mixing Sequences
    Zhong De LUO, Shan Chao YANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 851-870. https://doi.org/10.12386/A2013sxxb0083
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    We discuss the strong consistency and asymptotic normality of CVaR estimator in cases where the samples are ρ mixing sequences, and their respective convergence rate are given.
  • Metric Equivalence of Hartogs Domains Whose Base Space Is a Product of Symmetric Domain
    An WANG, Zhi Qiang LI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 871-888. https://doi.org/10.12386/A2013sxxb0084
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the equivalent problem of the classical metric on a class of nonhomogeneous Hartogs domain. Firstly, it is proved that the equivalence between the Bergman and the Einstein-Kähler metrics on these domains; Secondly, it is shown that the Bergman metric, the Carathéodary metric, the Kobayashi metric and the Einstein- Kähler metric are equivalent, when parameters of the domain satisfy mσ + nτ < 1.
  • Some Estimates for Commutators of Fractional Integral Operators on Weighted Morrey Spaces
    Hua WANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 889-906. https://doi.org/10.12386/A2013sxxb0085
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    Let 0 < α < n and Iα be the fractional integral operator. In this paper, we will use a unified approach to show the boundedness properties of commutators [b, Iα] on the weighted Morrey spaces Lp,κ(w) under appropriate conditions on the weight w, where the symbol b belongs to weighted BMO or Lipschitz space or weighted Lipschitz space.
  • On the Collision and Avalanche Effect in a Family of Pseudorandom Binary Sequences
    Hua Ning LIU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 907-914. https://doi.org/10.12386/A2013sxxb0086
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    Assume that p is an odd prime, and f(x) ∈ Fp[x]. For (a, p) = 1, denote the multiplicative inverse of a by a with aa ≡ 1 mod p and 1 ≤ a ≤ p - 1. Let Ep-1 = {e1,...,ep-1} be defined by 

    , where Rp(n) denotes the least non-negative residue of n modulo p. In this paper we study the collision and avalanche effect of Ep-1 by using the methods in analytic number theory.
  • The Additivity of Pointwise Preimage Entropy for Selfmaps on Torus
    Bao Jun HUANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 915-922. https://doi.org/10.12386/A2013sxxb0087
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    Pointwise preimage entropy is similar to topological entropy but, in general, their properties are not completely coincident such as additivity under Cartesian product. In this paper, we firstly give the conditions to the pointwise preimage entropy of the maps on tori satisfing additivity under Cartesian product. Then we will compute the pointwise preimage entropies of a kind of maps on tori.
  • The Cauchy Problem for a Generalized Two-Component Camassa-Holm System
    Ying ZHANG, Jiang Hong ZHANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 923-934. https://doi.org/10.12386/A2013sxxb0088
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    We investigate a generalized two-component Camassa-Holm system which can be derived from the theory of shallow water waves moving over a linear shear flow. We study the blow-up phenomena and establish a sufficient condition on the initial data to guarantee wave-breaking for the system. Moreover, the persistence properties of the strong solutions are also analyzed.
  • Discreteness Criteria for Subgroups of Isometry Groups of Pinched Hadamard Manifolds by Use of a Test Map
    Bin Lin DAI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 935-940. https://doi.org/10.12386/A2013sxxb0089
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    We study the discreteness of subgroups of isometry groups of pinched Hadamard manifolds by use of a loxodromic or parabolic test map and obtain several theorems about discreteness criteria of subgroups of Isom(X).
  • Normal Families and Shared Functions
    Xiao Yi LIU, Chun Nuan CHENG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 941-950. https://doi.org/10.12386/A2013sxxb0090
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let a and b be holomorphic functions on a plane domain D such that a has no zero, b is not zero identically, and a does not take the value 0 at the zeros of b. Let F = {f} be a family of meromorphic functions on D, all of whose zeros are multiple, such that f = a ⇔ f = b. Then the family F is normal on D. Examples are given to show the necessity of the conditions.
  • The Bergman-Type Toeplitz Operators on Dirichlet Space
    Sui HUANG, Yan HE
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 951-956. https://doi.org/10.12386/A2013sxxb0091
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    We prove that a Bergman-type Toeplitz operator on Dirichlet space arising from a bounded and harmornic function is compact if and only if its symbol is zero. Moreover, if symbol is continue on D, then the Toeplitz operator is compact if and only if its symbol is vanished on boundary of D.
  • Vector-Valued Ekeland’s Variational Principle in Locally Complete Locally Convex Space
    Yan Mei TENG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 957-960. https://doi.org/10.12386/A2013sxxb0092
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We show Ekeland's variational principle of vector-valued function and use subadditive, strictly increasing continuous functions as perturbations, where X is a locally complete locally convex space.
  • On Generalized Derivations of Lie Supertriple Systems
    Yao MA, Liang Yun CHEN, Dong LIU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 961-970. https://doi.org/10.12386/A2013sxxb0093
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the concepts of (generalized) (θ,φ)-derivations and (generalized) Jordan (θ,φ)-derivations on a Lie supertriple system are introduced. It is proved that Jordan (θ,φ)-derivations (resp. generalized Jordan (θ,φ)-derivations) are (θ,φ)-derivations (resp. generalized (θ,φ)-derivations) on a Lie supertriple system under some conditions. In particular, Jordan θ-derivations are θ-derivations on a Lie supertriple system.
  • Asymptotic Behaviors for Certain Harmonic Functions in a Cone
    Lei QIAO, Guan Tie DENG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 971-980. https://doi.org/10.12386/A2013sxxb0094
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    We give the asymptotic behaviors for certain harmonic functions at infinity in a cone, which generalize the results of Siegel-Talvila for a half space. Meanwhile, a solution of the Dirichlet problem in a cone is also obtained.
  • The Number of Zeros of Abelian Integral for Some Perturbed Hamiltonian System of Degree 5
    Xian Bo SUN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 981-992. https://doi.org/10.12386/A2013sxxb0095
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the number of zeros of the Abelian integral for some perturbed Hamiltonian system of degree 5. We prove the generating elements of the Abelian integral form a Chebeyshev system of accuracy of 1, therefore the number of zeros of the Abelian integral is 4. Last, we show a wrong result given in some previous work about the number of zeros for this Abelian integral, therefore the result we give is very new.
  • On the Structures of Finite Groups of Order 2744
    Song Liang CHEN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(6): 993-1008. https://doi.org/10.12386/A2013sxxb0096
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let G be finite groups of order 2744 (i.e. 23·73). We have showed that G has 153 nonisomorphic types, i.e. (1) If every Sylow subgroup is normal, G has 25 nonisomorphic types; (2) If every Sylow 2-subgroup is normal and every Sylow 7- subgroup is non-normal, G has 8 nonisomorphic types; (3) If every Sylow 7-subgroup is normal and every Sylow 2-subgroup is non-normal, G has 120 nonisomorphic types; (4) If every Sylow subgroup is non-normal, G has 0 nonisomorphic types.
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