中国科学院数学与系统科学研究院期刊网

15 November 2014, Volume 30 Issue 11
    

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  • Zong Liang-SUN
    Acta Mathematica Sinica. 2014, 30(11): 1827-1982. https://doi.org/10.1007/s10114-014-3745-8
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    By explicit constructions, we give direct proofs of the following results: for any distinct homotopy classes of simple closed curves α and β in a closed surface of genus g > 1, there exist a hyperbolic structure X and a holomorphic quadratic differential q on X such that lX(α)≠ lX(β),extX(α) ≠ extX(β) and lq(α) ≠ lq(β), where lX(·), extX(·) and lq(·) are the hyperbolic length, the extremal length and the quadratic differential length respectively. These imply that there are no equivalent simple closed curves in hyperbolic surfaces or in flat surfaces.
  • Albert KUBZDELA, Cristina PEREZ-GARCIA
    Acta Mathematica Sinica. 2014, 30(11): 1833-1845. https://doi.org/10.1007/s10114-014-3522-8
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    A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property (OFDDP) if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces.This property has an influence in the non-Archimedean Grothendieck's approximation theory, where an open problem is the following: Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E. Does D have the OFDDP? In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP. Next we prove that, however, for certain classes of Banach spaces of countable type, the OFDDP is preserved by taking finite-codimensional subspaces.
  • Han Chun-YANG, Hong Jun-CHENG
    Acta Mathematica Sinica. 2014, 30(11): 1846-1860. https://doi.org/10.1007/s10114-014-3561-1
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    The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics, in which the flux contains the nonconvex function possessing an infinite number of inflection points. Firstly, the generalized Rankine-Hugoniot relations and entropy condition of delta shock waves and left(right)-contact delta shock waves are proposed and clarified. Secondly, with the help of the convex hull, seven kinds of structures of Riemann solutions are obtained. The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities, vacuums and delta shock waves. Finally, numerical experiments confirm the theoretical analysis.
  • Bo Qing-XUE
    Acta Mathematica Sinica. 2014, 30(11): 1861-1866. https://doi.org/10.1007/s10114-014-4038-y
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    Let Fp be the finite field of p elements with p prime. If A is a subset of Fp and g is an element of Fp* with order v, then
    max{|A + g · A|,|A · A|}>>(v/(v+|A|2))1/12|A|13/12.
  • Július CZAP, Dávid HUDÁK, Tomaš MADARAS
    Acta Mathematica Sinica. 2014, 30(11): 1867-1876. https://doi.org/10.1007/s10114-014-4017-3
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    A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar graph joins. We prove that the join G + H is 1-planar if and only if the pair [G,H] is subgraph-majorized by one of pairs [C3C3C3], [C4, C4], [C4,C3],[K2,1,1, P3] in the case when both elements of the graph join have at least three vertices. If one element has at most two vertices, then we give several necessary/sufficient conditions for the bigger element.
  • Mircea CRASMAREANU, Laurian-Ioan PISCORAN
    Acta Mathematica Sinica. 2014, 30(11): 1877-1884. https://doi.org/10.1007/s10114-014-3559-8
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    We determine a 2-codimensional para-CR structure on the slit tangent bundle T0M of a Finsler manifold (M,F) by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f-structure. This condition is satisfied when (M,F) is of scalar flag curvature (particularly constant) or if the Riemannian manifold (M,g) is of constant curvature.
  • Wei ZHONG
    Acta Mathematica Sinica. 2014, 30(11): 1885-1896. https://doi.org/10.1007/s10114-014-3694-2
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    Sure independence screening (SIS) has been proposed to reduce the ultrahigh dimensionality down to a moderate scale and proved to enjoy the sure screening property under Gaussian linear models. However, the observed response is often skewed or heavy-tailed with extreme values in practice,which may dramatically deteriorate the performance of SIS. To this end, we propose a new robust sure independence screening (RoSIS) via considering the correlation between each predictor and the distribution function of the response. The proposed approach contributes to the literature in the following three folds: First, it is able to reduce ultrahigh dimensionality effectively. Second, it is robust to heavy tails or extreme values in the response. Third, it possesses both sure screening property and ranking consistency property under milder conditions. Furthermore, we demonstrate its excellent finite sample performance through numerical simulations and a real data example.
  • Li Lu-ZHAO
    Acta Mathematica Sinica. 2014, 30(11): 1897-1904. https://doi.org/10.1007/s10114-014-3661-y
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    It is established that all even positive integers up to N but at most O(N15/16+ε) exceptions can be expressed in the form p12+p23+p34+p45, where p1,p2,p3 and p4 are prime numbers.
  • Hai Lin-JIN, Gang Song-LENG, Qi GUO
    Acta Mathematica Sinica. 2014, 30(11): 1905-1916. https://doi.org/10.1007/s10114-014-3502-z
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    The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry. In this paper, we first reveal a close connection between the Lp-mixed volumes proposed by E. Lutwak and the p-measures of asymmetry, which have the Minkowski measure as a special case, introduced by Q. Guo. Then, a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R. J. Gardner, D. Hug and W. Weil recently, which is an extension of the p-measures.
  • Shao Xiong-HOU, Da Chun-YANG, Si Bei-YANG
    Acta Mathematica Sinica. 2014, 30(11): 1917-1962. https://doi.org/10.1007/s10114-014-3181-9
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    Let X be a space of homogenous type and φ; : X ×[0,∞) → [0,∞) be a growth function such that φ;(·,t) is a Muckenhoupt weight uniformly in t and φ;(x,·) an Orlicz function of uniformly upper type 1 and lower type p ∈ (0,1]. In this article, the authors introduce a new Musielak-Orlicz BMO-type space BMOAφ(X) associated with the generalized approximation to the identity, give out its basic properties and establish its two equivalent characterizations, respectively, in terms of the spaces BMOA, maxφ(X) and (X). Moreover, two variants of the John-Nirenberg inequality on BMOAφ(X) are obtained. As an application, the authors further prove that the space BMO√Δφ(Rn),associated with the Poisson semigroup of the Laplace operator Δ on Rn, coincides with the space BMOφ(Rn) introduced by Ky.
  • Pei Xin-ZHAO, An Min-TANG, Nian Sheng-TANG
    Acta Mathematica Sinica. 2014, 30(11): 1963-1976. https://doi.org/10.1007/s10114-014-2185-9
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    Based on the double penalized estimation method, a new variable selection procedure is proposed for partially linear models with longitudinal data. The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components. Under some regularity conditions, the rate of convergence and asymptotic normality of the resulting estimators are established. In addition, to improve efficiency for regression coefficients, the estimation of the working covariance matrix is involved in the proposed iterative algorithm. Some simulation studies are carried out to demonstrate that the proposed method performs well.
  • Zhen Gang-ZHAO
    Acta Mathematica Sinica. 2014, 30(11): 1977-1988. https://doi.org/10.1007/s10114-014-1623-z
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    We obtain the explicit formulae for the harmonic Bergman kernels of Bn\{0} and Rn\Bn and study the connection between harmonic Bergman kernel and weighted harmonic Bergman kernel. We also get the explicit formula for the weighted harmonic Bergman kernel of Bn\{0} with the weight 1/(|x|4).
  • Marko KOSTIĆ
    Acta Mathematica Sinica. 2014, 30(11): 1989-1998. https://doi.org/10.1007/s10114-014-1279-8
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    In the paper under review, we consider the generation of fractional resolvent families by abstract differential operators. Our results can be simply incorporated in the study of corresponding abstract time-fractional equations with Caputo fractional derivatives.