中国科学院数学与系统科学研究院期刊网
AMS

15 September 2011, Volume 27 Issue 9
    

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  • Graphs Whose Critical Groups Have Larger Rank
    Yao Ping HOU, Wai Chee SHIU, Wai Hong CHAN
    Acta Mathematica Sinica. 2011, 27(9): 1663-1670. https://doi.org/10.1007/s10114-011-9358-6
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    The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n - 3 and all graphs with r(G) = β(G) = n - 3 are characterized.  
  • Stochastic Generalized Porous Media Equations with Lévy Jump
    Guo Li ZHOU, Zhen Ting HOU
    Acta Mathematica Sinica. 2011, 27(9): 1671-1696. https://doi.org/10.1007/s10114-011-9194-8
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    In this paper, we first prove the existence and uniqueness of a general stochastic differential equation in finite dimension, then extend the result to the infinite dimension by the classical Galerkin method. As an application, we prove the existence and uniqueness of the generalized stochastic porous medium equation perturbed by Lévy process.  
  • Von Neumann Algebras Associated with the Group SL2(R)
    Wen Ming WU
    Acta Mathematica Sinica. 2011, 27(9): 1697-1704. https://doi.org/10.1007/s10114-011-9028-8
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    Let M and N be the von Neumann algebras induced by the rational action of the group SL2(R) and its subgroup P on the upper half plane H. We have shown that N is spatial isomorphic to the group von Neumann algebra LP and characterized M and its commutant M′ and gotten a generalization of the Mautner's lemma. It is also shown that the Berezin operator commutates with the Laplacian operator.  
  • Behavior of Theta-series under Modular Substitutions
    Bing Yong XIE
    Acta Mathematica Sinica. 2011, 27(9): 1705-1716. https://doi.org/10.1007/s10114-011-8677-y
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    In this article we provide a transformation formula of certain theta series, and apply it to obtain non-holomorphic vector-valued modular forms.  
  • The Cayley-Bacharach Theorem for Continuous Piecewise Algebraic Curves over Cross-cut Triangulations
    Renhong WANG, Shaofan WANG
    Acta Mathematica Sinica. 2011, 27(9): 1717-1724. https://doi.org/10.1007/s10114-011-8595-z
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    A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, we propose the Cayley-Bacharach theorem for continuous piecewise algebraic curves over cross-cut triangulations. We show that, if two continuous piecewise algebraic curves of degrees m and n respectively meet at mnT distinct points over a cross-cut triangulation, where T denotes the number of cells of the triangulation, then any continuous piecewise algebraic curve of degree m + n - 2 containing all but one point of them also contains the last point.  
  • Commuting Dual Toeplitz Operators on Weighted Bergman Spaces of the Unit Ball
    Yu Feng LU, Jun YANG
    Acta Mathematica Sinica. 2011, 27(9): 1725-1742. https://doi.org/10.1007/s10114-011-8577-1
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    In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.  
  • Dirac-Lu Space with Pseudo-Riemannian Metric of Constant Curvature
    Xin An REN, Li CHEN, Gui Dong WANG
    Acta Mathematica Sinica. 2011, 27(9): 1743-1752. https://doi.org/10.1007/s10114-011-8563-7
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    In this paper, we will discuss the geometries of the Dirac-Lu space whose boundary is the third conformal space N defined by Dirac and Lu. We firstly give the SO(3, 3) invariant pseudo- Riemannian metric with constant curvature on this space, and then discuss the timelike geodesics. Finally we get a solution of the Yang-Mills equation on it by using the reduction theorem of connections.  
  • Numbers of Subnormal Solutions for Higher Order Periodic Differential Equations
    Zong Xuan CHEN, Kwang Ho SHON
    Acta Mathematica Sinica. 2011, 27(9): 1753-1768. https://doi.org/10.1007/s10114-011-8551-y
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    In this paper, we estimate the number of subnormal solutions for higher order linear periodic differential equations, and estimate the growth of subnormal solutions and all other solutions. We also give a representation of subnormal solutions of a class of higher order linear periodic differential equations.  
  • Interpolation and Convergence of Bernstein-Bézier Coefficients
    Feng Jun LI
    Acta Mathematica Sinica. 2011, 27(9): 1769-1782. https://doi.org/10.1007/s10114-011-8462-y
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    In this paper, two ways of the proof are given for the fact that the Bernstein-Bézier coefficients (BB-coefficients) of a multivariate polynomial converge uniformly to the polynomial under repeated degree elevation over the simplex. We show that the partial derivatives of the inverse Bernstein polynomial An(g) converge uniformly to the corresponding partial derivatives of g at the rate 1/n. We also consider multivariate interpolation for the BB-coefficients, and provide effective interpolation formulas by using Bernstein polynomials with ridge form which essentially possess the nature of univariate polynomials in computation, and show that Bernstein polynomials with ridge form with least degree can be constructed for interpolation purpose, and thus a computational algorithm is provided correspondingly.  
  • Boundedness for Parabolic Singular Integral with Rough Kernels and Its Commutators on Triebel-Lizorkin Spaces
    Shuang Ping TAO, Yao Ming NIU
    Acta Mathematica Sinica. 2011, 27(9): 1783-1802. https://doi.org/10.1007/s10114-011-8372-z
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    In this paper, the authors give the boundedness on Triebel-Lizorkin spaces for the parabolic singular integral with rough kernel and its commutator.  
  • Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems
    Yong XIA
    Acta Mathematica Sinica. 2011, 27(9): 1803-1812. https://doi.org/10.1007/s10114-011-8351-4
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    In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.  
  • Rate Function of Large Deviation for a Class of Nonhomogeneous Markov Chains on Supercritical Percolation Network
    Zhong Hao XU, Dong HAN
    Acta Mathematica Sinica. 2011, 27(9): 1813-1830. https://doi.org/10.1007/s10114-011-8349-y
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    We model an epidemic with a class of nonhomogeneous Markov chains on the supercritical percolation network on Zd. The large deviations law for the Markov chain is given. Explicit expression of the rate function for large deviation is obtained.  
  • Semiparametric Additive Intensity Model with Frailty for Recurrent Events
    Yan Yan LIU, Yuan Shan WU
    Acta Mathematica Sinica. 2011, 27(9): 1831-1842. https://doi.org/10.1007/s10114-011-8232-x
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    The seminal Cox's proportional intensity model with multiplicative frailty is a popular approach to analyzing the frequently encountered recurrent event data in scientific studies. In the case of violating the proportional intensity assumption, the additive intensity model is a useful alternative. Both the additive and proportional intensity models provide two principal frameworks for studying the association between the risk factors and the disease recurrences. However, methodology development on the additive intensity model with frailty is lacking, although would be valuable. In this paper, we propose an additive intensity model with additive frailty to formulate the effects of possibly time-dependent covariates on recurrent events as well as to evaluate the intra-class dependence within recurrent events which is captured by the frailty variable. The asymptotic properties for both the regression parameters and the association parameters in frailty distribution are established. Furthermore, we also investigate the large-sample properties of the estimator for the cumulative baseline intensity function.  
  • Local Asymptotics of a Markov Modulated Random Walk with Heavy-tailed Increments
    Bing Chang WANG, Yuan Yuan LIU
    Acta Mathematica Sinica. 2011, 27(9): 1843-1854. https://doi.org/10.1007/s10114-011-8191-2
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    In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P(· ∈ (x, x + z]) for each z > 0, as x→∞. Our results extend and improve the existing ones in the literature.  
  • Smooth Solutions for a Stochastic Hydrodynamical Equation in Heisenberg Paramagnet
    Xue Ke PU, Bo Ling GUO, Yong Qian HAN
    Acta Mathematica Sinica. 2011, 27(9): 1855-1868. https://doi.org/10.1007/s10114-011-8159-2
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    In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.  
  • The Maximum Surplus Distribution before Ruin in an Erlang(n) Risk Process Perturbed by Diffusion
    Zhen Zhong ZHANG, Jie Zhong ZOU, Yuan Yuan LIU
    Acta Mathematica Sinica. 2011, 27(9): 1869-1880. https://doi.org/10.1007/s10114-011-8072-8
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    In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.  
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