中国科学院数学与系统科学研究院期刊网

15 December 2012, Volume 28 Issue 12
    

  • Select all
    |
    Articles
  • Johannes H. HATTINGH, Ossama A. SALEH, Lucas C. VAN DER MERWE, Terry J. WALTERS
    Acta Mathematica Sinica. 2012, 28(12): 2365-2372. https://doi.org/10.1007/s10114-012-0727-6
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The induced path number ρ(G) of a graph G is defined as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a path. Broere et al. proved that if G is a graph of order n, then √nρ(G) + ρ(G) ≤ [3n/2]. In this paper, we characterize the graphs ρ(G) + ρ(G)=[3n/2], improve the lower bound on ρ(G) + ρ(G) by one when n is the square of an odd integer, and determine a best possible upper bound for ρ(G) + ρ(G) when neither G nor G has isolated vertices.
  • Zhong Qi YIN
    Acta Mathematica Sinica. 2012, 28(12): 2373-2394. https://doi.org/10.1007/s10114-012-1309-3
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions, in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions.
  • Yu Rong WU, Huo Xiong WU
    Acta Mathematica Sinica. 2012, 28(12): 2395-2406. https://doi.org/10.1007/s10114-012-1153-5
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn × Rm. Under the condition that Ω is a function in certain block spaces, which is optimal in some senses, the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.
  • Jie XU, Yun Min ZHU, Ji Cheng LIU
    Acta Mathematica Sinica. 2012, 28(12): 2407-2416. https://doi.org/10.1007/s10114-012-1003-5
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.
  • Fu Qing GAO, Ming Zhou XU
    Acta Mathematica Sinica. 2012, 28(12): 2417-2430. https://doi.org/10.1007/s10114-012-0726-7
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by G-Brownian motion.
  • Chun Hui ZHOU
    Acta Mathematica Sinica. 2012, 28(12): 2431-2442. https://doi.org/10.1007/s10114-012-0696-9
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ > 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author’s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ > 1.
  • Yong LIU, Feng Xia YANG
    Acta Mathematica Sinica. 2012, 28(12): 2443-2462. https://doi.org/10.1007/s10114-012-0672-4
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study some ergodic theorems of a class of linear systems of interacting diffusions, which is a parabolic Anderson model. First, under the assumption that the transition kernel a=(a(i, j))i,jS is doubly stochastic, we obtain the long-time convergence to an invariant probability measure νh starting from a bounded a-harmonic function h based on self-duality property, and then we show the convergence to the invariant probability measure νh holds for a broad class of initial distributions. Second, if (a(i, j))i,jS is transient and symmetric, and the diffusion parameter c remains below a threshold, we are able to determine the set of extremal invariant probability measures with finite second moment. Finally, in the case that the transition kernel (a(i, j))i,jS is doubly stochastic and satisfies Case I (see Case I in [Shiga, T.: An interacting system in population genetics. J. Math. Kyoto Univ., 20, 213-242 (1980)]), we show that this parabolic Anderson model locally dies out independent of the diffusion parameter c.
  • Yu Feng YAO, Bin SHU, Yi Yang LI
    Acta Mathematica Sinica. 2012, 28(12): 2463-2474. https://doi.org/10.1007/s10114-012-0665-3
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let (g, [p]) be a restricted Lie algebra over an algebraically closed field of characteristic p > 0. Then the inverse limits of “higher” reduced enveloping algebras {uχs (g)|s∈N} with χ running over g* make representations of g split into different “blocks”. In this paper, we study such an infinitedimensional algebra Aχ(g):=Uχs (g) for a given χ ∈ g*. A module category equivalence is built between subcategories of U(g)-mod and Aχ(g)-mod. In the case of reductive Lie algebras, (quasi) generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized χ-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity.
  • Zhi Bin ZHU, Jin Bao JIAN
    Acta Mathematica Sinica. 2012, 28(12): 2475-2488. https://doi.org/10.1007/s10114-012-0561-x
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.
  • Zhong Kui LIU
    Acta Mathematica Sinica. 2012, 28(12): 2489-2500. https://doi.org/10.1007/s10114-012-0550-0
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext≥1(X, Y)=0 for each object XX and each object YY. We show that if A,BC(R) are X-complexes and U, VC (R) are Y-complexes, then UVHom(A,U)Hom(A, V); AB Hom(B,U)Hom(A,U). As an application, we give a sufficient condition for the Hom evaluation morphism being invertible.
  • Fang DUAN, Guo Ping WANG
    Acta Mathematica Sinica. 2012, 28(12): 2501-2506. https://doi.org/10.1007/s10114-012-0459-7
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    A graph G is {K1,4,K1,4 + e}-free if G contains no induced subgraph isomorphic to K1,4 or K1,4 + e. In this paper, we show that G has a path which is either hamiltonian or of length at least 2δ(G) + 2 if G is a connected {K1,4,K1,4 + e}-free graph on at least 7 vertices.
  • Zheng Yan, LIN Hui ZHOU
    Acta Mathematica Sinica. 2012, 28(12): 2507-2526. https://doi.org/10.1007/s10114-012-0355-1
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let {ξi,-∞ < i < ∞} be a doubly infinite sequence of identically distributed φ-mixing random variables with zero means and finite variances, {ai,-∞ < i < ∞} be an absolutely summable sequence of real numbers and Xki=-∞+∞ aiξi+k be a moving average process. Under some proper moment conditions, the precise asymptotics are established for 
    1/-logε 1/n2ESn2i{|Sn|≥}=2EZ2.
    where Z~N(0,τ2),τ22i-∞ai)2, and
     ε2δ (log n)δ-1/n2ESn2i{|Sn|≥√nlog }=τ2δ+2/δE|N|2δ+2.
  • Ai Jun LI, Gang Song LENG
    Acta Mathematica Sinica. 2012, 28(12): 2527-2534. https://doi.org/10.1007/s10114-012-9735-9
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we consider the extremal problem of the lp-norm: min{lp(TK), oTKL, T ∈ GL(n)}, where K,L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Furthermore, the weaker optimization problem, min{(lp(TK))p:TKB2n,TKSn-1, T ∈ GL(n)}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetri convex body K is obtained.
  • Dian Xuan GONG, Ren Hong WANG
    Acta Mathematica Sinica. 2012, 28(12): 2535-2544. https://doi.org/10.1007/s10114-012-9679-0
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves, a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found. Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.
  • Chun Yan JI, Da Qing JIANG, Ning Zhong SHI
    Acta Mathematica Sinica. 2012, 28(12): 2545-2560. https://doi.org/10.1007/s10114-012-9668-3
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Furthermore, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 ≤ 1, which means the disease will die out. While if R0 > 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.
  • Jia Zu ZHOU, Yan Hua DU, Fei CHENG
    Acta Mathematica Sinica. 2012, 28(12): 2561-2568. https://doi.org/10.1007/s10114-012-9657-6
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We discuss the higher dimensional Bonnesen-style inequalities. Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in Rn (n≥3) are known. The results obtained in this paper are for general domains, convex or non-convex, in Rn.