中国科学院数学与系统科学研究院期刊网

15 January 2014, Volume 57 Issue 1
    

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    Articles
  • The Boundedness of Hausdorff Operators on Campanato Spaces
    Xiao Mei WU, Gui Lian GAO, Xiao YU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 1-8. https://doi.org/10.12386/A2014sxxb0001
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    We study several kinds of Hausdorff operators on Campanato spaces and obtain the sharp bounds for them. Furthermore, we also discuss the boundedness of multilinear Hausdorff operator on Morrey space.
  • Local Ruin Probability in a Risk Model with Variable Premium Rates
    Xiu Chun BI, Rong LI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 9-16. https://doi.org/10.12386/A2014sxxb0002
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    We introduce a catastrophe risk model with variable premium rates and obtain a local result of the ruin probability under heavy-tailed claims. In addition, we extend the risk model and propose a regression-type size-dependence one under the framework of web Markov skeleton process, which has some theoretic and practical value in the field of actuarial, and allows applications in various areas.
  • Relaxed Alternating Projection Method for Solving Linear Matrix Equation Problem under Closed Convex Constraint
    Jiao Fen LI, Xi Yan HU, Lei ZHANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 17-34. https://doi.org/10.12386/A2014sxxb0003
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    We discuss the existing relaxed alternating projection method for solving the linear matrix equation AXB=C under some closed convex constraints to X. The considered closed convex constrained set, denoted by R, is (1) the set of bounded matrices, (2) the set of Q-positive definite matrices, (3) the solution set of a linear matrix inequality. We prove the weak convergence of the matrix sequence generated by the proposed algorithm, and present some numerical examples for solving AXB=C under symmetric nonnegative and symmetric positive semidefinite matrices constraint to illustrate the feasibility and efficiency of the proposed algorithm, and to show its clear superiority comparing with alternating projection method and spectral projected gradient method.
  • Perturbation of the Generalized Drazin Inverse in Banach Algebra
    Xiao Ji LIU, Yong Hui QIN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 35-46. https://doi.org/10.12386/A2014sxxb0004
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    We present the necessary and sufficient conditions for the element after perturbing and investigate the perturbation bounds for the generalized Drazin inverse by using block technology in Banach algebra.
  • Totally Umbilical Property of Hyper-surfaces in a Positive Curvature Space Form and Higher Order Curvature
    Qi WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 47-50. https://doi.org/10.12386/A2014sxxb0005
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    We study the totally umbilical property of compact closed equal-distance immersed hyper-surfaces Mn in the positive curvature space form Sn+1(c) (c>0) and the higher order mean curvatures, and obtain a result which improves the relevant recent theorems in this research field.
  • Hausdorff Dimension of Sets Arising from Dvoretzky Random Covering
    Jun Min TANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 51-70. https://doi.org/10.12386/A2014sxxb0006
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    We consider the random intervals In(ω)=ωn+(-ln/2,ln/2) (mod 1), where {ln}n≥1 is a sequence of positive real numbers which is decreasing to zero and {ωn}n≥1 is an i.i.d. sequence with Gibbs distribution measure on the circle T= R/Z. Using the tools from multi-fractal analysis, we estimate the Hausdorff dimension of sets which are covered finitely or infinitely many times by {In(ω)}.
    • Articles
  • Automorphisms of Generalized Orthogonal Graphs of Odd Characteristic
    Li Jun HUO, Wen Bin GUO, Chang Li MA
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 71-88. https://doi.org/10.12386/A2014sxxb0007
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    In this paper, the automorphism group of the generalized orthogonal graph ΓGO2ν+δ(q,m,S) over Fq of odd characteristic is determined, where 1<m<ν.
  • On Approximation by Univariate Sigmoidal Neural Networks
    Guo Chun MA, Dan Sheng YU, Ping ZHOU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 89-100. https://doi.org/10.12386/A2014sxxb0008
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    We first introduce a new type of neural network operators with sigmoidal functions, and give the pointwise and global estimates of the approximation by the networks. The new neural network operators can approximate the functions with a very good rate which can not be obtained by polynomial approximation. To further improve the approximation rate for functions of smoothness, we also introduce a new type of combinations of neural network operators, and give pointwise and global estimates of the approximation by the combinations. A numerical example is given to demonstrate our new method.
  • Trace-Kernel Operator Semigroup of Free Monogenic Inverse Semigroup
    Wei LONG, Li Min WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 101-108. https://doi.org/10.12386/A2014sxxb0009
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    For congruence ρ on an inverse semigroup, there are maximal element ρT and minimal element ρt in a trace class; by the same token, there are maximal element ρK and minimal element ρk in a kernel class. So we can find four operators Γ= {K, k, T, t} on congruence lattice C(S) of an inverse semigroup S. Inthis paper,we gained extremum congruence which is not identity relation on free monogenic inverse semigroup Ix. Then establishing relations in Γ on congruence lattice C(S), we obtain trace-kernel operator semigroup Γ+/Σ* of Ix finally.
  • Quantization on Generalized Heisenberg-Virasoro Algebra
    Hai Bo CHEN, Ran SHEN, Jian Gang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 109-116. https://doi.org/10.12386/A2014sxxb0010
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    In a recent paper, Lie bialgebra structures on generalized Heisenberg- Virasoro algebra L are considered by the authors. In this paper, the explicit formula of the quantization on generalized Heisenberg-Virasoro algebra is presented.
  • The Existence for Self-Orthogonal Cyclic Codes over Finite Fields
    Qun Ying LIAO, Yan Bin LI, Huan LIAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 117-124. https://doi.org/10.12386/A2014sxxb0011
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    We obtain a necessary and sufficient condition for that there exists a nontrivial self-orthogonal or self-dual cyclic codes over finite fields and the explicit enumerating formula. As a corollary, a simple and easy criterion for several classes of non-trivial self-orthogonal cyclic codes is given.
  • Nonexistence of Solutions for a Singular Semilinear Elliptic Equation
    Wen Shu ZHOU, Xiao Dan WEI, Xu Long QIN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 125-130. https://doi.org/10.12386/A2014sxxb0012
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    We study the nonexistence of solutions for a singular semilinear elliptic equations. The results improve and implement a work by Arcoya et al. [Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246: 4006-4042], whose proofs are very simple and based on Poincaré inequality, Lusin theorem and Egoroff theorem.
  • Existence of Positive Solution for a Quasilinear System with Nonlinear Boundary Condition
    Guo Ying YANG, Jun Xiang CHENG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 131-138. https://doi.org/10.12386/A2014sxxb0013
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    In this paper, we consider the quasilinear elliptic systems with the nonlinear boundary condition and weight function. With the help of the Nehari manifold, we obtain the system has at least two nontrival positive solutions under the proper region of parameters.
    • Articles
  • Mean Curvature Flow with a Forcing Field in Direction of the Position Vector of Submanifolds
    Shun Zi GUO, Guang Han LI, Chuan Xi WU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 139-150. https://doi.org/10.12386/A2014sxxb0014
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    This paper considers the evolution by mean curvature vector plus a forcing field in the direction of its position vector of a closed submanifold of dimension n (≥ 2) in Rn+p. Suppose that mean curvature vector is nonzero everywhere and that the full norm of the second fundamental form is bounded by a fixed multiple (depending only on n) of the length of the mean curvature vector at every point. It is shown that such submanifolds may contract to a point in finite time if the forcing field is small, or exist for all time and expand to infinity if it is large enough. Moreover, if the evolving submanifolds undergo suitable homotheties and the time parameter is transformed appropriately into a parameter t, 0 ≤ t < ∞, it is also shown the normalized submanifolds in any case converge smoothly to a round sphere in some (n + 1)-dimensional subspace of Rn+p as t→∞.
  • Complete Convergence for Weighted Sums of Arrays ρ-Mixing Random Variables
    De Hua QIU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 151-162. https://doi.org/10.12386/A2014sxxb0015
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    The complete convergence for weighted sums of arrays ρ-mixing random variables is discussed under general conditions by utilizing the Rosenthal type inequality of ρ-mixing random variables. General complete convergence theorems and convergence for moving average processes generated by sequences of ρ-mixing random variables are obtained, which improve and extend the related known works in the literature.
  • Mean-square Convergence Rate of Stochastic-Theta Methods for a Class of Stochastic Differential Delay Equations
    Jun LIU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 163-170. https://doi.org/10.12386/A2014sxxb0016
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    We provide a mean-square convergence rate of stochastic theta methods for a class of stochastic differential delay equations whose coefficients are not Lipschitz but only Hölder continuous.
  • Real Vector Cone Metric Space and Fixed Point Theorems
    Fei HE, Jing Hui QIU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 171-180. https://doi.org/10.12386/A2014sxxb0017
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We introduce real vector cone metric spaces, where cone metric is the mapping on a real vector space without topological structures. We also prove some new fixed point theorems in real vector cone metric spaces. By using nonlinear scalarization functions, we establish the equivalence between these and some other fixed point results in metric and in real vector cone metric spaces. Our results improve and generalize some results from the literature.
  • Meromorphic Solutions of Painlevé Ⅲ Difference Equations
    Ji Long ZHANG, Lian Zhong YANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 181-188. https://doi.org/10.12386/A2014sxxb0018
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    We investigate the properties of meromorphic solutions of Painlevé Ⅲ difference equations. In particular, we study the existence of Borel exceptional value, the exponent of convergence of zeros, poles and fixed points of a transcendental meromorphic solution. Several sharp examples of meromorphic solutions of some Painlevé Ⅲ difference equations are given.
  • Nodal Solutions for p-Laplacian Problems with Jumping Nonlinearities
    Guo Wei DAI, Ru Yun MA
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 189-194. https://doi.org/10.12386/A2014sxxb0019
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    We study the existence of nodal solutions for the p-Laplacian problems with jumping nonlinearities at zero and infinity. More precisely, we show that there exists at least one nodal solution to the problems if nonlinearities crossing the Fučik spectrum.
  • On the Diophantine Equation x2+By2p=z3
    Zhong Feng ZHANG, Jia Gui LUO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 195-198. https://doi.org/10.12386/A2014sxxb0020
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    In this paper, for some choices of integers B, we give all the integer solutions of equation x2+By2p=z3 with xyz≠0 and x, y, z pairwise coprime for prime p ≥ 11.
  • Numerical Upper Bounds for the Mean Values of Smooth Weyl Sums of Fractional Moments
    Tian Qin WANG, Hua Ke LIU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(1): 200-208. https://doi.org/10.12386/A2014sxxb0021
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    We discuss some relationship of the numerical upper bounds for the mean values of smooth Weyl sums of fractional moments. Some new results on the numerical upper bounds of the mean values are given when the moments are in the interval [4, 5].
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