中国科学院数学与系统科学研究院期刊网

15 September 2014, Volume 57 Issue 5
    

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  • A Hilbert-Type Integral Inequality with Quasi-Homogeneous Kernel and Several Functions
    Yong HONG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 833-840. https://doi.org/10.12386/A2014sxxb0077
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    A new concept of quasi-homogeneous function of several variables is defined, the Hilbert-type integral inequality with quasi-homogeneous integral kernel and several functions are studies, it's the best constant factor is discussed.
  • Reducing Subspaces of Certain Analytic Toeplitz Operators
    Chun Mei WANG, Tian Qiu YU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 841-850. https://doi.org/10.12386/A2014sxxb0078
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    We consider the reducing subspaces of analytic Toeplitz operators on the Hilbert spaces of analytic function with symmetric measures. In particular, given any positive integer n, the reducing subspaces of analytic Toeplitz operator Tzn are completely described.
  • The Hypersurfaces with Parallel Laguerre Form in Rn
    Ding Xing ZHONG, Zu Jin ZHANG, Ling Yang TAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 851-862. https://doi.org/10.12386/A2014sxxb0079
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    Let x: M → Rn be an umbilical free oriented hypersurface with non-zero principal curvatures, four basic Laguerre invariants under the Laguerre transformation group are the Laguerre metric g, the Laguerre second fundamental form B, the Laguerre form C and the Laguerre tensor L. In this paper, we study the relationships between parallel Laguerre form and vanishing metric Laguerre form.
  • The Explicit Formula for the Complexity of a Class of Gauss Period Normal Bases over Finite Fields
    Qun Ying LIAO, Xiao Lan HU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 863-874. https://doi.org/10.12386/A2014sxxb0080
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    In this paper, by characterizing some properties of cyclotomic numbers, we obtain the explicit formula for the complexity of a class of Gauss period normal bases over finite fields. Furthermore, we show that the type 7 Gauss period normal basis of Fqn over Fq is just the desired basis except for n= 4.
  • Harmonic Quasiconformal Mappings from Unit Disk onto an Infinite Horizontal Strip Domain
    Xin Zhong HUANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 875-880. https://doi.org/10.12386/A2014sxxb0081
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    We study the analytic characteristic property for sense preserving univalent harmonic mappings on the unit disk onto an infinite horizontal strip domain with a normalization at the origin. By deriving an analytic representing formula for these univalent harmonic mappings, we obtain one necessary and sufficient condition for sense preserving univalent harmonic mappings on the unit disk onto an infinite horizontal strip domain with a normalization at the origin to be harmonic quasiconformal mappings, we also obtain sharp coefficient estimates for these harmonic quasiconformal mappings. As an application, distortion theorems on length and area for image in Euclidean metric between the one for preimage in noneuclidean metric are also obtained. Our results improve and generalize the one made by Hengartner and Schober.
  • Some New Properties of g-Frames
    Xun Xiang GUO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 881-892. https://doi.org/10.12386/A2014sxxb0082
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    In this paper, some properties of g-frames are considered. Firstly, we generalize the projection methods for frames to g-frames and a similar if and only if condition for such method works is established. Then we study the g-frames which contain g-Riesz bases. We obtain that under some constraint g-Riesz frame contains a g-Riesz basis. We also introduce the conception of g-frames with sub-g-frame property and show that under some restriction g-frame with sub-g-frame property contains a g-Riesz basis. Finally, we get several equivalent properties between g-frames and frames induced by the g-frames under some assumptions.
  • Banach Space Valued Bochner-Musielak-Orlicz Spaces
    Bao Hua DONG, Jing Shi XU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 893-906. https://doi.org/10.12386/A2014sxxb0083
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    In this paper, let E be a Banach space and (A,A,u) be a σ-finite complete measure space, E valued Bochner-Musielak-Orlicz spaces Lφ(A,E) are introduced. Firstly, these spaces are Banach spaces. Then if E*, the dual space of E, has Radon- Nikodym property, the dual space of Lφ(A,E) is given. Finally, we discuss the uniform convexity and uniform smoothness of Lφ(A,E) and give their applications.
  • A Mean Value Formula of Parabolic Equations on the Heisenberg Group
    Hai Rong LIU, Xiao Ping YANG, Ni XIANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 907-922. https://doi.org/10.12386/A2014sxxb0084
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    We derive two equivalent definitions of the viscosity solutions to the homogeneous sub-p-Laplace parabolic equations on the Heisenberg group, and characterize the viscosity solutions in terms of an asymptotic mean value formula when 1 < p ≤∞.
  • The Limit Theory of Galton-Watson Branching Process in Random Environment
    Wei Gang WANG, Rui Xing MING, Jian Jun GAN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 923-930. https://doi.org/10.12386/A2014sxxb0085
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    We studied the Galton-Watson process in varying environment. We gave the first hitting time of the process and the large deviation of log Zn at the almost sure environments when the mathematical expectation and variance of the environments are finite.
  • Fixed Points of Some Dyadic Operators in Ordered Banach Spaces and Its Applications
    Zeng Qin ZHAO, Jin Xiu MAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 931-938. https://doi.org/10.12386/A2014sxxb0086
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    For condensing mixed monotone operators which have upper and lower solutions, only the coupled fixed points were studied in known literature. This paper investigates some dyadic operators, which are generalizations of mixed monotone operators. We obtain the existence of fixed points for the operators. By given iterative sequences, we also obtain the uniqueness of fixed points or an interval containing the fixed points. The corollary is also an improvement of known results. Lastly, we apply the results to a boundary value problem of nonlinear second order elliptic equations.
  • Dimensions of Non-differentiability Points of Generalized Cantor Functions
    In Soo BAEK, Wen Xia LI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 939-946. https://doi.org/10.12386/A2014sxxb0087
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    For a probability vector p = (p1, . . ., pN), there is a corresponding selfsimilar measure γp supported on the generalized Cantor set K in R generated by the family {hk(x)=akx+bkx,k=1,...,N} (N ≥ 2) of contractive similitudes satisfying the strong separation condition. We consider the generalized Cantor function f(x) = γp([0, x] ∩ K) satisfying min1≤k≤ N(log pk/log ak)< 1 < max1≤k≤ N(log pk/log ak) on the unit interval. The numbers q+β(q) and ξ, where β'(q) = -1 with ∑k=1N pkq akβ(q)=1, and ∑k=1N akξ=1 give full information for the dimensions of the non-differentiability points and the null differentiability points and the infinity differentiability points of K.
  • The Dual Isotropic Constant and the LYZ Ellipsoid of Convex Bodie
    Ge XIONG, Jia Qi HU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 947-960. https://doi.org/10.12386/A2014sxxb0088
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    We mainly study the analytical characterizations of convex bodies when they are positioned in the dual isotropic position. Several new lower bounds are established for the dual isotropic constant. Also we find the necessary and sufficient conditions such that the LYZ ellipsoid and the John ellipsoid are the same. To further distinguish the two important ellipsoids, we calculate and depict the LYZ ellipsoids and John ellipsoids of several specific convex polygons.
  • Global Canonical Family of Deformations on Compact H-Twisted Generalized Calabi-Yau Manifolds
    Kang WEI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 961-972. https://doi.org/10.12386/A2014sxxb0089
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    We get the formula to determine whether the canonical sections on compact H-twisted generalized Calabi-Yau manifolds are holomorphic:e∈ dHe-∈ρ = ∂Hρ +∂H(-∈ρ).
  • Sufficient Conditions for the Existence of a Positive Definite Solution of Matrix Equation X-A*X-1A+B*X-2B=I
    Xiao Mei CUI, Li Hui TAN, Shi Jia ZHAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 973-980. https://doi.org/10.12386/A2014sxxb0090
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    In this paper, hermitian positive definite solution of matrix equation X-A*X-1A+B*X-2B=I is investigated by constructing monotonous bounded iterative sequences. Sufficient conditions for existence and the range of a positive solution of the equation are derived.
  • The Lowey Series of Regular Nilpotent Representations for sl(3, k)
    Yi Yang LI, Bin SHU, Yu Feng YAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 981-992. https://doi.org/10.12386/A2014sxxb0091
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    Let k be an algebraically closed field of prime characteristic p = 5, Lie algebra g = sl(3, k). In this paper, when p-character χ is regular nilpotent and has standard Levi form, the Lowey series of principle indecomposable g-modules and the dimensions for the self-extension of irreducible g-modules were given.
  • Positive Solutions for p-Laplacian Sturm-Liouville Boundary Value Problems on Time Scales
    Ke Yu ZHANG, Jian Guo WANG, Jia Fa XU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 993-1000. https://doi.org/10.12386/A2014sxxb0092
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    We investigate the existence of two positive solutions for the following fourth order p-Laplacian Sturm-Liouville boundary value problems on time scales
     
    Here p > 1 and f: [ρ(a), b] × R+ → R+(R+:= [0,∞)) is continuous. Under sufficient growth conditions on the nonlinearity f and by virtue of fixed point theorems on cones, we obtain at least two positive solutions for the above problem.
  • Chromatic Properties of 6-Regular Graphs Embedded on the Klein Bottle
    Fu Gang CHAO, Han REN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 1001-1010. https://doi.org/10.12386/A2014sxxb0093
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    Brooks proved that if G is a connected simple graph and is neither an odd cycle nor a complete graph, then its chromatic number is at most Δ(G), where Δ(G) is the maximum degree of the graph G. It follows that the chromatic number of any 6-regular graphs embedded on the Klein bottle is at most 6. By analying the structure of graphs embedded on the Klein bottle, we prove that the chromatic number of any 6-regular graphs embedded on the Klein bottle is 5.
  • Asymptotic Patterns for a Nonlinear Periodic Reaction-Diffusion Equation with Nonlocal Effect
    Ye Hui HUANG, Pei Xuan WENG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 1011-1030. https://doi.org/10.12386/A2014sxxb0094
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    A periodic reaction-diffusion system with nonlinear-nonlocal functional response is considered in this paper. We use the asymptotic theory for periodic semiflow to discuss the existence of spreading speed c* and periodic traveling wave solutions. The threshold property for the spreading spread of solutions is described clearly according to the threshold parameter c* which is exactly the minimal wave speed as well. Finally, we give an estimate of the spreading speed and minimal wave speed c*.
  • Characterizations of K-g-Frames in Hilbert Spaces
    Yan ZHOU, Yu Can ZHU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(5): 1031-1040. https://doi.org/10.12386/A2014sxxb0095
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    We introduce the concepts of K-g-frames and K-g-Riesz bases in complex Hilbert spaces and study the essential distinctions between a K-g-frame and a g-frame. We give a characterization of a K-g-frames and an equivalent characterization of a K-g-Riesz basis in complex Hilbert spaces. Lastly, by using the analytical methods and techniques in frame theory, we obtain some sufficient conditions for the stability of perturbation of K-g-frames and K-g-Riesz bases.
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