中国科学院数学与系统科学研究院期刊网

15 May 2014, Volume 57 Issue 3
    

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  • The Semisimplicity of Weak Doi-Hopf Modules
    Quan Guo CHEN, Ding Guo WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 417-426. https://doi.org/10.12386/A2014sxxb0041
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    In weak Hopf group coalgebra, we discuss the separability of a family of forgetful functors from the category of weak Doi-Hopf group modules to the category of modules over some algebra, and induce the conceptions of normalized integrals of weak Doi-Hopf group datums, and show that the existence of normalized integrals is the criterion for the forgetful functors to be separable. Then the applications of our results to the category of weak quantum Yetter-Drinfel'd group modules and the category of weak relative Hopf group modules are considered.
  • Global Existence and Blow up of Nonlinear Klein-Gordon Equation Based on Cross Variational Method
    Run Zhang XU, Ming You ZHANG, Xiao Li JIANG, Xue Mei WANG, Ji Hong SHEN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 427-444. https://doi.org/10.12386/A2014sxxb0042
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    This paper discusses the initial boundary value problem of the nonlinear Klein-Gordon equation. By the potential well method, we obtain the global existence and blow up of solutions when the initial energy is less than the mountain pass level value. Moreover, the global existence and nonexistence of solutions are derived under the critical initial energy case. In the end, by using the concavity method, we establish a blow up result for certain solutions with arbitrary positive initial energy.
  • Sharp Weighted Norm Inequality for the Commutator of Hardy-Littlewood Maximal Operators
    Yan Ping CHEN, Han HAN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 445-452. https://doi.org/10.12386/A2014sxxb0043
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    We proved a sharp weighted inequality for the m-the order commutator of the Hardy-Littlewood maximal operator M and b∈BMO Finally we construct an example showing our bound is sharp for the case of 1<p≤2.
  • Codimension 2 and 3 Bifurcations of Heterodimensional Cycles in Reversible Vector Field in R3
    Gui Feng DENG, Wei Peng ZHANG, Qiu Ying LU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 453-472. https://doi.org/10.12386/A2014sxxb0044
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    In this paper, the bifurcations of symmetric heterodimensional cycles with two saddle points are investigated in three-dimensional reversible system. Here, the reversibility means that there exists a linear involution R such that the system is invariant under time-reversal up to it. In case the fixed points space of R is one dimensional, i.e., dim Fix(R) = 1, we obtain the existence and coexistence of R-symmetric heteroclinic loop, R-symmetric periodic orbit, homoclinic loops, double periodic orbit and a singleparameter family of periodic orbits. The double homoclinic bifurcation of symmetric heterodimensional cycle is found. It is shown there are infinitely many periodic orbits accumulating onto a homoclinic loop. The bifurcation surfaces and their existence regions are also located. In case dim Fix(R)=2, the existence of R-symmetric periodic orbit and R-symmetric heteroclinic loop is also derived.
    • Articles
  • Bell Inequalities on Two Classes of Observables
    Ying YANG, Huai Xin CAO, Jing LI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 473-484. https://doi.org/10.12386/A2014sxxb0045
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    The expectations of two classes of observables â and â⊗ with respect to a density matrix ρ are defined as Eρ(â)=Tr(âρ) and Eρ(â,)=Tr((â⊗)(ρ),and some properties of them are obtained. Especially, corresponding Bell inequality is proved, which reads .
  • Monoidal Comonads and Monoidal Category
    Xiao Hui ZHANG, Sheng Xiang WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 485-492. https://doi.org/10.12386/A2014sxxb0046
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    In this paper, the monoidal structure on C(F,G)(ψ), i.e. the category of (F,G)-bicomodule where F and G is monoidal comonad on a category C and ψ is a comonad distributive is discussed. Finally some necessary and sufficient propositions of that C(F,G)(ψ) could admit a monoidal structure is given.
  • Finite Modular Frames
    Bin MENG, Xi Xi CHEN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 493-504. https://doi.org/10.12386/A2014sxxb0047
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    This paper is devoted to studying modular frames for finitely generated Hilbert C*-modules. This research is motivated by the packets encoding technique in the information theory. We study the frame potential for modular frames, describe the robustness under the erasures of frame vectors, and investigate the optimal modular frames under 1-erasure. At last, we describe the Parseval modular frame vectors for a unitary system generated by one or two unitary operators on a Hilbert C*-module.
  • Positive Periodic Solutions of Second-Order Neutral Functional Differential Equations with Delayed Derivative Terms
    Yong Xiang LI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 505-516. https://doi.org/10.12386/A2014sxxb0048
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    This paper deals with the existence of positive ω-periodic solutions for the second-order neutral functional differential equation with a delayed derivative term in nonlinearity (u(t)-cu(t-δ))"+a(t)u(t)=f(t,u(t),u(t-τ(t)),u'(t-γa(t))) The essential conditions on the existence and nonexistence of positive periodic solutions of the equation are obtained. The conditions concern with the relation of the coefficient function a(t) and nonlinearity f(t, x, y, z).Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.
    • Articles
  • Tripled Coincidence Point Theorems under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces
    Jian Hui LIU, Chuan Xi ZHU, Zhao Qi WU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 517-526. https://doi.org/10.12386/A2014sxxb0049
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    We establish tripled coincidence point and tripled fixed point theorems for a pair of self-mappings G:X×X×X→X与 g:X→X, satisfying a nonlinear contractive condition in partially ordered complete probabilistic metric spaces. The obtained results generalize some coupled coincidence and coupled common fixed point theorems in the corresponding literatures. Finally, an example is given to illustrate our main results.
  • Positive Solutions for a High-Order Integral Boundary Value Problem with Impulsive Effects
    You Zheng DING, Jia Fa XU, Zhong Li WEI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 527-536. https://doi.org/10.12386/A2014sxxb0050
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    In this paper, the positive solutions are considered for a high-order integral boundary value problem with impulsive effects. Under some conditions involving the first eigenvalue of the corresponding linear operator, the existence results of single and multiple positive solutions are established by applying Krasnoselskii-Zabreiko fixed point theorem.
  • The Initial Trace and the Harnack Inequality of Doubly Nonlinear Parabolic Equations
    Hua Shui ZHAN
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 537-558. https://doi.org/10.12386/A2014sxxb0051
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    In the paper, the Cauchy problem for the quasi-linear parabolic equation ut-div a(x, t,u, Du)=b(x,t, u, Du),(x,t), Suppose that ai(x,t,u,Du) and b(x,t,u,Du)are Caratheodory functions, and they satisfy some other restrictions such as the monotone property of Du the increasing order condition of u,|Du| etc., the comparison theorem of the equation is established, the existence of the solution is obtained, and the Harnack inequality is proved.
  • On a Cauchy-Cubic Functional Equation and Its Hyers-Ulam Stability
    Pei Sheng JI, Ran Hong WEI, Rong Rong LIU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 559-568. https://doi.org/10.12386/A2014sxxb0052
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    We obtain the general solution and the generalized Hyers-Ulam stability of the Cauchy-cubic functional equation f(x1+x2,2y1+y2)+{f(x1+x2,2y1-y2)}={2f(x1,y1+y2)}+{2f(x1,y1-y2)}+{12f(x1,y1)}+{2f(x2,y1+y2)}+{2f(x2,y1-y2)}+{12f(x2,y1)} in Banach space and fuzzy Banach space using the direct method and the fixed point method, respectively.
  • On the (α,β)-Essential Spectrum of Upper Triangular Operator Matrices
    Guo Jun HAI, Alatancang
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 569-580. https://doi.org/10.12386/A2014sxxb0053
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    Let H and K be separable infinite dimensional Hilbert spaces, and let A∈B(H) and B∈B(K), be given operators. A necessary and sufficient condition is obtained for (???569-01.jpg???) to be an (α,β)- semi-Fredholm operator for some (respectively, all) C∈B(K, H).Furthermore, some related results are obtained.
  • Correlated Two-Sided Jump-Diffusion Model Under the Barrier Dividend
    Ying Hui DONG, Ya Juan XU
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 581-592. https://doi.org/10.12386/A2014sxxb0054
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    In the perturbed classical risk model, the perturbed part is usually interpreted as the fluctuation of the total claim amount, the premium income and the surplus investment return. This paper uses a double exponential jump-diffusion model which depends on the aggregate claim process to describe the fluctuation. We consider the ruin problem under a correlated two-sided jump-diffusion model with a barrier dividend, and give the explicit expression for the Laplace transform of the ruin time.
  • The Surviving Descendent Distributions in General Birth-Death Branching Processes
    Yun Zhi YAN, Yun Bin FU, Han Xing WANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 593-600. https://doi.org/10.12386/A2014sxxb0055
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    We investigate a model of birth-death branching processes, of which some (conditional) independence is assumed and the birth and death rates for each surviving individual are both time dependent. Given a time that an individual is alive (or is dead), the conditional distribution of its surviving descendant number is obtained. Furthermore, assume that an individual's birth and death times are both given, the distribution of its surviving descendant number at any given time is deduced.
  • Some Properties of Additive Representation Functions
    Min TANG
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 601-606. https://doi.org/10.12386/A2014sxxb0056
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    Let A={a1, a2,…}(a1≤a2≤…) be an infinite sequence of nonnegative integers. Let k≥2 be a fixed integer and for n∈N,let Rk(A,n)be the number of solutions of ai1+…+aik=n.Let Rk(1)(A,n) and Rk(2)(A,n) denote the number of solutions with the additional restrictions i1 <…k and i1≤…≤ik respectively. Recently, Yong-Gao Chen and the author proved the following result: let dbe a positive integer. If Rk(A,n)≥d for all sufficiently large integers n, then Rk(A,n)≥ d+2[k/2]√d +([k/2]!)2 for infinitely many positive integers nIn this paper, we obtain the analogue results for Rk(1)(A,n) and Rk(2)(A,n).
  • Approximation by Diffuse Functional of Generalized Moving Least Squares on the Sphere
    Fei Long CAO, Yong Li ZHANG, Ming LI
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 607-614. https://doi.org/10.12386/A2014sxxb0057
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    This paper considers the approximation problem of generalized moving least squares on the unit sphere. The point-evaluation functional of the standard moving least squares is replaced by general functional, and the definition of generalized moving least squares on the unit sphere is given. Based on this, the definition of the diffuse functional of moving least square approximation is proposed according to diffuse derivatives. Also, the approximation order is estimated in terms of the spherical mesh norm. This method can be understood as a kind of simultaneous approximation.
  • Some Sufficient Conditions for the Identity of ANOVA Estimator and SD Estimator in Mixed-Effects Models
    Mi Xia WU, Yan ZHAO
    Acta Mathematica Sinica, Chinese Series. 2014, 57(3): 615-624. https://doi.org/10.12386/A2014sxxb0058
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    The mixed-effects models are an important class of statistical models that are used in many fields of applications. For these models, we compare two estimators of the variance components, the analysis of variance (ANOVA) estimator and the spectral decomposition (SD) estimator. Based on the spectral decomposition of covariance matrix [A new method of spectral decomposition of covariance matrix in mixed effects models and its applications, Sci. China, Ser. A, 2005, 48: 1451-1464], we establish two sufficient conditions for the identity of ANOVA estimator and SD estimator, and present some corresponding statistical properties of ANOVA estimator and SD estimator. Applications of the methods to circular models and mixed analysis of variance models are discussed.
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