中国科学院数学与系统科学研究院期刊网

15 July 2017, Volume 33 Issue 7
    

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  • Robert LATERVEER
    Acta Mathematica Sinica. 2017, 33(7): 887-898. https://doi.org/10.1007/s10114-017-6477-8
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    This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family.
  • Xia ZHANG, Ming LIU
    Acta Mathematica Sinica. 2017, 33(7): 899-910. https://doi.org/10.1007/s10114-017-6444-4
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    In this paper, we first study the mean ergodicity of random linear operators using some techniques of measure theory and L0-convex analysis. Then, based on this, we give a characterization for a complete random normed module to be mean ergodic.
  • Teng Fei ZHAO
    Acta Mathematica Sinica. 2017, 33(7): 911-925. https://doi.org/10.1007/s10114-017-6499-2
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    We consider the defocusing nonlinear Schrödinger equations iutu = |u|pu with p being an even integer in dimensions d ≥ 5. We prove that an a priori bound of critical norm implies global well-posedness and scattering for the solution.
  • Xiao Shang JIN
    Acta Mathematica Sinica. 2017, 33(7): 926-932. https://doi.org/10.1007/s10114-017-6479-6
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    In this article, we extend the Weyl Schouten Theorem for a C0,1W2,2 manifold only under the assumptions on scalar curvature. Also we obtain a regularity of a C0,1W2,2 manifold by conformal transformation under some assumptions on Weyl curvature and scalar curvature.
  • Yun Feng JIANG
    Acta Mathematica Sinica. 2017, 33(7): 933-950. https://doi.org/10.1007/s10114-017-6163-x
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    We define the motivic Milnor fiber of cyclic L-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.
  • Xiao Ming WANG, Ben Ling LI
    Acta Mathematica Sinica. 2017, 33(7): 951-968. https://doi.org/10.1007/s10114-017-6333-x
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    Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general (α, β)-metrics, which are defined by a Riemannian metric α = √aij(x)yiyj and a 1-form β = bi(x)yi. We obtain the differential equations that characterizes these metrics with vanishing Douglas curvature. By solving the equivalent PDEs, the metrics in this class are totally determined. Then many new Douglas metrics are constructed.
  • Wen Dong WANG
    Acta Mathematica Sinica. 2017, 33(7): 969-980. https://doi.org/10.1007/s10114-017-6276-2
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    In this paper, we prove that suitable weak solution (u, b) of the 3-D MHD equations can be extended beyond T if uL(0, T;L3(R3)) and the horizontal components bh of the magnetic field satisfies the well-known Ladyzhenskaya-Prodi-Serrin condition, which improves the corresponding regularity criterion by Mahalov-Nicolaenko-Shilkin.
  • Ali BEN AMOR, Tarek KENZIZI
    Acta Mathematica Sinica. 2017, 33(7): 981-995. https://doi.org/10.1007/s10114-017-6246-8
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    We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied by some examples.
  • Xue Yi HUANG, Qiong Xiang HUANG, Lu LU
    Acta Mathematica Sinica. 2017, 33(7): 996-1010. https://doi.org/10.1007/s10114-017-6241-0
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    Let p be an odd prime, and D2p =<a, b|ap = b2 = 1, bab = a-1 the dihedral group of order 2p. In this paper, we completely classify the cubic Cayley graphs on D2p up to isomorphism by means of spectral method. By the way, we show that two cubic Cayley graphs on D2p are isomorphic if and only if they are cospectral. Moreover, we obtain the number of isomorphic classes of cubic Cayley graphs on D2p by using Gauss' celebrated law of quadratic reciprocity.
  • Hong Hai LIU
    Acta Mathematica Sinica. 2017, 33(7): 1011-1020. https://doi.org/10.1007/s10114-017-5788-0
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    In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation and λ-jump operators related to smooth truncations are bounded from H1 to L1.