中国科学院数学与系统科学研究院期刊网

15 November 2015, Volume 58 Issue 6
    

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  • Hai Cheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 881-896. https://doi.org/10.12386/A2015sxxb0088
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    Let A be a hereditary abelian category and P the full subcategory consisting of projective objects of A . We mainly study the coalgebra structure on the Bridgeland–Hall algebra of the category Cm(P) of m-cyclic complexes for any positive integer m ≥ 2. Inspired by the work of Yanagida, we define a new exact structure on Cm(P) and then obtain a coalgebra structure on the Bridgeland–Hall algebra of Cm(P). Moreover, we prove that there exists a coalgebra embedding from the extended Ringel–Hall algebra of A to the Bridgeland–Hall algebra of Cm(P).
  • Chang Xiong NIE, Yan Mei YU, Li He ZHENG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 897-910. https://doi.org/10.12386/A2015sxxb0089
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    In [Classification of type I time-like Hyperspaces with parallel conformal second fundamental forms in the conformal space, Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 125–136], we have classified the Type I Lorentzian hypersurfaces with parallel conformal second fundamental forms in the conformal space. In this paper, we study the rest types of Lorentzian hypersurfaces and classify completely Lorentzian Hypersurfaces with parallel conformal second fundamental forms in the conformal space.
  • Jing LU, Kai Yun WANG, Bin ZHAO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 911-922. https://doi.org/10.12386/A2015sxxb0090
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    We introduce the notion of meet Z-quantales. We prove that the family of all Z-closed sets of a meet Z-quantale, when ordered by inclusion, is a Frame. Moreover, the relations between nuclei, quotients and congruences on meet Z-quantales are investigated. Finally, we show that the category of quantales is a reflective subcategory of the category of Z-quantales.
  • Jian Jun CHEN, Xiao Feng WANG, Jin XIA
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 923-934. https://doi.org/10.12386/A2015sxxb0091
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    We study the compactness of Toeplitz operators on bounded symmetric domains Ω. Then we will obtain the result that if S equals a finite sum of finite products of Toeplitz operators on Dirichlet space, then S is compact if and only if its Berezin transformation (z) → 0 as z → ∂Ω.
  • Yi Qiu DU, Yu WANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 935-940. https://doi.org/10.12386/A2015sxxb0092
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    Let A be an associative ring. Let GA. We say that G is an allderivable point of A if every derivable additive map φ : AA at G (i.e., φ(ST) = φ(S)T +Sφ(T) for all S, T ∈ A with ST = G) is a derivation. The aim of the paper is to show that every nonzero element in certain triangular rings is an all-derivable point. As a corollary we prove that every nonzero element in upper triangular matrix rings over a certain field is an all-derivable point.
  • Jie Sheng XIAO, Guang Fu CAO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 941-952. https://doi.org/10.12386/A2015sxxb0093
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    We prove that the multiplier Tznβ zn is similar to ⊕1nTzβ on the Hardy–Sobolev spaces. In addition, we also deal with the commutant of certain multipliers with the symbol which is the power of univalent and nonvanishing analytic function on these spaces.
  • Yong LIN, Shou Dong MAN
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 953-964. https://doi.org/10.12386/A2015sxxb0094
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    We obtain improved Li–Yau gradient estimates on graphs for the solutions u to the general heat equation (Δ - ∂/∂t - q)u = 0, where q is a potential satisfying Γ(q) ≤ η2 and η is a constant, and get Harnack inequalities, extending previous results.
  • Hong HUO, Ling Qi ZHAO, Wei FENG, Yuan Sheng YANG, Jirimutu
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 965-976. https://doi.org/10.12386/A2015sxxb0095
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    Based on the definition of a Hamiltonian cycle gived by Janfang Wang and Tony Lee, and the definition of a Hamiltonian chain gived by Katona–Kierstead in a uniform hypergraph, recently, many domestic and foreign researchers studied the hamiltonian cycle decomposition of the uniform hypergraphs Kn(3), and obtained a series of results. Especially, Bailey–Stevens and Meszka–Rosa studied the hamiltonian cycle decomposition of the complete 3-uniform hypergraphs Kn(3), showed the result of hamiltonian cycle decomposition of Kn(3) for n = 6k + 1, 6k + 2 (k= 1, 2, 3, 4, 5). In this paper, using the methods of edge-partition proposed by Jirimutu, we will continue study Hamiltonian decomposition of the complete 3-uniform hypergraphs Kn(3), design an algorithm of Hamiltonian decompositions of Kn(3), and use the algorithm, we show the result of hamiltonian cycle decomposition of Kn(3) for n = 6k + 2, 6k + 4 (k= 1, 2, 3, 4, 5, 6, 7), n = 6k+5 (k= 1, 2, 3, 4, 5, 6). These results improve results of Hamiltonian decompositions from all admissible n ≤ 32 (Meszka–Rosa's paper) to all admissible n ≤ 46 and n = 43.
  • Hai bo LIU, Qun Ying LIAO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 977-984. https://doi.org/10.12386/A2015sxxb0096
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    One can define different error-correcting codes, according to different ways of describing the distance between two vectors in vector spaces. The deletion errorcorrecting code is defined by Levenshtein distance. In this paper, with a positive integer v fixed, some necessary conditions for the existence of the perfect deletion error-correcting code T{2, {4, 5, 6}, v} are obtained, by the method and technique of the elementary number theory and directed pairwise balanced designs. In particular, for v ≥ 4 and v ∉ {8, 9, 14}, there exists a perfect deletion error-correcting code with parameters T{2, {4, 5, 6}, v}.
  • Jian Li LIU, Xiao Dan ZHANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 985-992. https://doi.org/10.12386/A2015sxxb0097
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    We consider classical solutions to Cauchy problem for the model of twolayer flows, which appears in shallow water theory. Under the appropriate assumptions on initial data, we can obtain the necessary and sufficient conditions of the global existence of C1 solutions. Furthermore, similar conclusion can be obtained for the system of one-layer flow.
  • Jian Ping WANG, Shao Hua WU
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 993-1000. https://doi.org/10.12386/A2015sxxb0098
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    We study a hyperbolic model for chemotaxis in one space dimension. Comparing with the generalized Goldstein–Kac model which describes the movement of total population, the model we present here explains the movement of each particle. We assume the speed and turning rates are constant, and the reproduction and degradation of s is linear. Local existence and uniqueness for weak solutions are shown.
  • Xu Jian HUANG, Dong Ni TAN
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 1001-1008. https://doi.org/10.12386/A2015sxxb0099
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    We study the geometric unitaries in vector-valued function spaces. By using numerical index theory, we characterize the geometric unitaries in the spaces C(Ω, X) on a compact Hausdorff space Ω, L(μ, X) for every σ-finite measure μ and L(l1(Γ),X)for every nonempty index set Γ. We also describe the geometric unitaries in the injective and projective tensor product of Banach spaces.
  • Chun Mei DING, Fei Long CAO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 1009-1020. https://doi.org/10.12386/A2015sxxb0100
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    This paper studies the approximation of convolution operators defined on the unit sphere in d-dimensional Euclidean space Rd. By using the multiplier theory and the equivalence relation between K-functional and modulus of smoothness, the direct and converse theorems of the approximation by a class of spherical convolution operators are investigated. In particular, the inverse inequalities of the approximation of strong type are established, and thus the essential order of approximation for the convolution operators is reflected. As applications of the obtained main results, the estimates of the same orders of approximation bounds for the spherical Jackson–Matsuoka operators and spherical Abel–Poisson operators are given, respectively.
  • Xiao Fei QI, Lin GONG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 1021-1034. https://doi.org/10.12386/A2015sxxb0101
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    Let A and B be unitial rings, and M be an (A, B)-bimodule. Assume that U = Tri(A, M, B) is a triangular ring. Under some mild conditions, the structure of additive left derivations on U is given from different points of view. Also, two different characterizations of additive left derivations on rings with some conditions are obtained.
  • Zhi Xia HUANG, Jian Hua HUANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 1035-1044. https://doi.org/10.12386/A2015sxxb0102
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    We introduce a new split variational inequality problem and construct two algorithms for solving the problems. The weak and strong convergence of the sequences defined by two general algorithms is respectively obtained.
  • Zheng Hua LUO, Long Fa SUN, Li Zhen CHEN
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 1045-1052. https://doi.org/10.12386/A2015sxxb0103
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    Let Y be a subspace of a Banach space X, BX,BY be the closed unit ball of X and Y respectively. We investigate the approximative compactness of BY. We prove that BY is approximative compact in X if and only if for every translation YT of Y with YTBX ≠ ∅, YTBX is approximative compact in YT . We also obtain the stability result of the approximative compactness of BY.
  • Hao WANG, Huan Xia FA
    Acta Mathematica Sinica, Chinese Series. 2015, 58(6): 1053-1056. https://doi.org/10.12386/A2015sxxb0104
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    We obtain that every irreducible weight module over a class of super W-algebra with a nontrivial finite dimensional weight space is a Harish–Chandra module.