中国科学院数学与系统科学研究院期刊网

15 May 2017, Volume 33 Issue 5
    

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  • Jerod MICHEL
    Acta Mathematica Sinica. 2017, 33(5): 591-606. https://doi.org/10.1007/s10114-016-6151-6
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    Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets (and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns (which were recently coined by Cunsheng Ding in "Codes from Difference Sets" (2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.
  • Yan Yun SU, Heng Jian CUI, Kai Can LI
    Acta Mathematica Sinica. 2017, 33(5): 607-619. https://doi.org/10.1007/s10114-016-3187-6
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    In this paper, the parameters of a p-dimensional linear structural EV (error-in-variable) model are estimated when the coefficients vary with a real variable and the model error is time series. The adjust weighted least squares (AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.
  • Wen WANG
    Acta Mathematica Sinica. 2017, 33(5): 620-634. https://doi.org/10.1007/s10114-016-6260-2
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    In this paper, let (Mn, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry-Émery Ricci curvature bounded below. By using the maximum principle, we first prove a Li-Yau type Harnack differential inequality for positive solutions to the parabolic equation #br#ut = LF(u) = ΔF(u)-∇f·∇F(u), #br#on compact Riemannian manifolds Mn, where FC2(0,∞), F' > 0 and f is a C2-smooth function defined on Mn. As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results.
  • Jing CHEN, Xian Wen ZHANG, Ran GAO
    Acta Mathematica Sinica. 2017, 33(5): 635-656. https://doi.org/10.1007/s10114-016-6310-9
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    We investigate the Cauchy problem for the Vlasov-Poisson system with radiation damping. By virtue of energy estimate and a refined velocity average lemma, we establish the global existence of nonnegative weak solution and asymptotic behavior under the condition that initial data have finite mass and energy. Furthermore, by building a Gronwall inequality about the distance between the Lagrangian flows associated to the weak solutions, we can prove the uniqueness of weak solution when the initial data have a higher order velocity moment.
  • Qing Lin LU
    Acta Mathematica Sinica. 2017, 33(5): 657-667. https://doi.org/10.1007/s10114-016-5292-y
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    In this paper, we study the class S of skew Motzkin paths, i.e., of those lattice paths that are in the first quadrat, which begin at the origin, end on the x-axis, consist of up steps U = (1, 1), down steps D = (1,-1), horizontal steps H = (1, 0), and left steps L = (-1,-1), and such that up steps never overlap with left steps. Let Sn be the set of all skew Motzkin paths of length n and let sn = |Sn|. Firstly we derive a counting formula, a recurrence and a convolution formula for sequence {sn}n≥0. Then we present several involutions on Sn and consider the number of their fixed points. Finally we consider the enumeration of some statistics on Sn.
  • Qing Hou ZENG, Jian Feng HOU, Jin DENG, Xia LEI
    Acta Mathematica Sinica. 2017, 33(5): 668-680. https://doi.org/10.1007/s10114-016-6043-9
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    Let G = (V,E) be a graph with m edges. For reals p ∈ [0, 1] and q = 1- p, let mp(G) be the minimum of qe(V1) +pe(V2) over partitions V = V1V2, where e(Vi) denotes the number of edges spanned by Vi. We show that if mp(G) = pqm-δ, then there exists a bipartition V1, V2 of G such that e(V1) ≤ p2m - δ + pm/2 + o(√m) and e(V2) ≤ q2m - δ + qm/2 + o(√m) for δ = o(m2/3). This is sharp for complete graphs up to the error term o(√m). For an integer k ≥ 2, let fk(G) denote the maximum number of edges in a k-partite subgraph of G. We prove that if fk(G) = (1 - 1/k)m + α, then G admits a k-partition such that each vertex class spans at most m/k2 - Ω(m/k7.5) edges for α = Ω(m/k6). Both of the above improve the results of Bollobás and Scott.
  • Qing Jin CHENG, Yun Bai DONG
    Acta Mathematica Sinica. 2017, 33(5): 681-690. https://doi.org/10.1007/s10114-016-6245-1
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    Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic. Then we prove that all unit spheres of the Lebesgue-Bochner function spaces Lp(μ,X) and Lq(μ,Y) are mutually uniformly homeomorphic where 1 ≤ p, q < ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space Lp(μ,X), 1 ≤ p < ∞, also has Property H.
  • Xiang Rong ZHU
    Acta Mathematica Sinica. 2017, 33(5): 691-704. https://doi.org/10.1007/s10114-016-5749-z
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    Let Ω be a bounded domain in Rn with smooth boundary. Here we consider the following Jacobian-determinant equation

    where f is a function on Ω with minΩf = δ > 0 and Ω f(x)dx = |Ω|. We prove that if fBn/pp1(Ω) for some p ∈ (n,∞), then there exists a solution uBn/p+1p1 (Ω) ⊂ C1(Ω) to this equation. On the other hand, we give a simple example such that uC10 (R2,R2) while det∇u does not lie in B2/pp1(R2) for anyp < ∞.
  • Jian Min CHEN, Jin Jing CHEN, Ya Nan LIN
    Acta Mathematica Sinica. 2017, 33(5): 705-724. https://doi.org/10.1007/s10114-016-5063-9
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    In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.
  • He Guo LIU, Yu Lei WANG
    Acta Mathematica Sinica. 2017, 33(5): 725-730. https://doi.org/10.1007/s10114-016-4016-7
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    A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group, the normalizer NG(P) controls p-fusion in G. Let P be a central extension as
    1 → ZpmP → Zp ×···×Zp → 1,
    and |P'| ≤ p, m ≥ 2. The purpose of this paper is to prove that P is resistant.