中国科学院数学与系统科学研究院期刊网
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15 November 2011, Volume 27 Issue 11
    

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  • Topological Minors in Bipartite Graphs
    Camino BALBUENA ,Martín CERA, Pedro GARCÍA-VÁZQUEZ, Juan Carlos VALENZUELA
    Acta Mathematica Sinica. 2011, 27(11): 2085-2100. https://doi.org/10.1007/s10114-011-0149-x
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    For a bipartite graph G on m and n vertices, respectively, in its vertices classes, and for integers s and t such that 2 ≤ s ≤ t, 0 ≤ m - s ≤ n - t, and m + n ≤ 2s + t - 1, we prove that if G has at least mn - (2(m - s) + n - t) edges then it contains a subdivision of the complete bipartite K(s,t) with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn - (2(m - s) + n - t + 1) edges for this topological Turan type problem.  
  • Order Topology and Bi-Scott Topology on a Poset
    Bin ZHAO, Kai Yun WANG
    Acta Mathematica Sinica. 2011, 27(11): 2101-2106. https://doi.org/10.1007/s10114-011-0273-7
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    In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posets.  
  • The Blow up Analysis of the General Curve Shortening Flow
    Rong Li HUANG, Ji Guang BAO
    Acta Mathematica Sinica. 2011, 27(11): 2107-2128. https://doi.org/10.1007/s10114-011-0126-4
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    It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.  
  • Toeplitz Operators with BMO Symbols on the Weighted Bergman Space of the Unit Ball
    Kan ZHANG, Chao Mei LIU, Yu Feng LU
    Acta Mathematica Sinica. 2011, 27(11): 2129-2142. https://doi.org/10.1007/s10114-011-0038-3
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    In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2(Bn) of the unit ball is completely determined by the behavior of its Berezin transform, where α > -1 and n ≥ 1.  
  • Stochastic Stability of FitzHugh-Nagumo Systems in Infinite Lattice Perturbed by Gaussian White Noise
    Yan ZHENG, Jian Hua HUANG
    Acta Mathematica Sinica. 2011, 27(11): 2143-2152. https://doi.org/10.1007/s10114-011-9549-1
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    The current paper is devoted to the study of stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. We first study the dynamics of stochastic FitzHugh-Nagumo systems, then prove the existence and uniqueness of their equilibriums, which mix exponentially. Finally, we investigate asymptotic behavior of equilibriums when the size of noise gets to zero.  
  • General Decay Pathwise Stability of Neutral Stochastic Differential Equations with Unbounded Delay
    Yang Zi HU, Fu Ke WU, Cheng Ming HUANG
    Acta Mathematica Sinica. 2011, 27(11): 2153-2168. https://doi.org/10.1007/s10114-011-9456-5
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    Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a class of neutral stochastic differential equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.  
  • The Ridge Function Representation of Polynomials and an Application to Neural Networks
    Ting Fan XIE, Fei Long CAO
    Acta Mathematica Sinica. 2011, 27(11): 2169-2176. https://doi.org/10.1007/s10114-011-9407-1
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    The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.  
  • Transition-layer Solutions of Quasilinear Elliptic Boundary Blow-up Problems and Dirichlet Problems
    Zong Ming GUO, Yao Yong YAN
    Acta Mathematica Sinica. 2011, 27(11): 2177-2190. https://doi.org/10.1007/s10114-011-9327-0
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    We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:
    -εΔpu = f(x, u) in Ω,
    where 1 < p < ∞, ε > 0 is a small parameter,
     
    where ω > 0, a(x) is a continuous function satisfying 0 < a(x) < 1 for x ∈ Ω, Ω is a bounded smooth domain in RN. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.  
  • Fuzzy Stability of Quadratic-cubic Functional Equations
    Zhi Hua WANG, Wan Xiong ZHANG
    Acta Mathematica Sinica. 2011, 27(11): 2191-2204. https://doi.org/10.1007/s10114-011-9250-4
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    In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation
    6f(x + y) - 6f(x - y) + 4f(3y) = 3f(x+ 2y) - 3f(x - 2y) + 9f(2y)
    in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.  
  • Variable Selection for Semiparametric Varying-Coefficient Partially Linear Models with Missing Response at Random
    Pei Xin ZHAO, Liu Gen XUE
    Acta Mathematica Sinica. 2011, 27(11): 2205-2216. https://doi.org/10.1007/s10114-011-9200-1
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    In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.  
  • The Credibility Premiums for Exponential Principle
    Li Min WEN, Wei WANG, Jing Long WANG
    Acta Mathematica Sinica. 2011, 27(11): 2217-2228. https://doi.org/10.1007/s10114-011-9198-4
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    In the classical credibility theory, the credibility premium is derived on the basis of pure premium. However, the insurance practice demands that the premium must be charged under some adaptable premium principle and serves the purpose for insurance business. In this paper, the balanced credibility models have been built under exponential principle, and the credibility estimator of individual exponential premium is derived. This result is also extended to the versions of multitude contracts, and the estimation of the structure parameters is investigated. Finally, the simulations have been introduced to show the consistency of the credibility estimator and its differences from the classical one.  
  • Some Sufficient Conditions for Tunnel Numbers of Connected Sum of Two Knots Not to Go Down
    Guo Qiu YANG, Feng Chun LEI
    Acta Mathematica Sinica. 2011, 27(11): 2229-2244. https://doi.org/10.1007/s10114-011-9021-2
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    In this paper, we show the following result: Let Ki be a knot in a closed orientable 3- manifold Mi such that (Mi,Ki) is not homeomorphic to (S2 ×S1, x0 ×S1), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(Ki) is less than the difference of one and twice of the tunnel number of Ki. Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.
    We further show that if the distance of a Heegaard splitting of each knot complement is strictly bigger than twice the tunnel number of the knot (twice the sum of the tunnel number of the knot and one, respectively), then the tunnel number of connected sum of two such knots is additive (super additive, respectively).  
  • Large Deviations for Parameter Estimators of Some Time Inhomogeneous Diffusion Process
    Shou Jiang ZHAO, Fu Qing GAO
    Acta Mathematica Sinica. 2011, 27(11): 2245-2258. https://doi.org/10.1007/s10114-011-8626-9
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    The goal of this paper is to study large deviations for estimator and score function of some time inhomogeneous diffusion process. Large deviation in the non-steepness case with explicit rate functions is obtained by using parameter-dependent change of measure.  
  • On the Distribution of Laplacian Eigenvalues of a Graph
    Ji Ming GUO, Xiao Li WU, Jiong Ming ZHANG, Kun Fu FANG
    Acta Mathematica Sinica. 2011, 27(11): 2259-2268. https://doi.org/10.1007/s10114-011-8624-y
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    This paper presents some bounds on the number of Laplacian eigenvalues contained in various subintervals of [0, n] by using the matching number and edge covering number for G, and asserts that for a connected graph the Laplacian eigenvalue 1 appears with certain multiplicity. Furthermore, as an application of our result (Theorem 13), Grone and Merris' conjecture [The Laplacian spectrum of graph II. SIAM J. Discrete Math., 7, 221-229 (1994)] is partially proved.  
  • Eigenvalues of the Manifold Sp(n)/U(n)
    Yi HONG, Wen Ge CHEN
    Acta Mathematica Sinica. 2011, 27(11): 2269-2274. https://doi.org/10.1007/s10114-011-8591-3
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    In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λs(f2, f2, . . . , fn) of the Lie group Sp(n), corresponding to the representation with label (f1, f2, . . . , fn), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f1, f2, . . . , fn are all even.  
  • A Spectrum Relation of Almost Periodic Solution of Second Order Scalar Functional Differential Equations with Piecewise Constant Argument
    Li WANG, Rong YUAN, Chuan Yi ZHANG
    Acta Mathematica Sinica. 2011, 27(11): 2275-2284. https://doi.org/10.1007/s10114-011-8392-8
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    In this paper, the spectrum relation of almost periodic solution for the equation (x(t) + px(t - 1))″ = qx([t]) + f(t) is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.  
  • An Inner Product Formula on Two-dimensional Complex Hyperbolic Space
    Lei YANG
    Acta Mathematica Sinica. 2011, 27(11): 2285-2300. https://doi.org/10.1007/s10114-011-8071-9
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    We study the Eisenstein series for a convex cocompact discrete subgroup on a two-dimensional complex hyperbolic space HC2. We find an inner product formula which gives the connection between Eisenstein series and automorphic Green functions on a two-dimensional complex hyperbolic space HC2. As an application of our inner product formula, we obtain the functional equations of Eisenstein series.  
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