中国科学院数学与系统科学研究院期刊网

15 January 2017, Volume 33 Issue 1
    

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  • Valentin BURCEA
    Acta Mathematica Sinica. 2017, 33(1): 1-20. https://doi.org/10.1007/s10114-016-5190-3
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    Let (z11,..., z1N,..., zm1,..., zmN, w11,..., wmm) be the coordinates in CmN+m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=ZZt+O(3), where W={wij}1≤i,jm and Z={zij}1≤i≤m,1≤jN. We prove that M is biholomorphically equivalent to the model W=ZZt if and only if is formally equivalent to it.

  • Li Chien SHEN
    Acta Mathematica Sinica. 2017, 33(1): 21-36. https://doi.org/10.1007/s10114-016-6180-1
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    We shall study the differential equation y'2=Tn(y)-(1-2μ2); where μ2 is a constant, Tn(x) are the Chebyshev polynomials with n=3, 4, 6. The solutions of the differential equations will be expressed explicitly in terms of the Weierstrass elliptic function which can be used to construct theories of elliptic functions based on 2F1(1/4, 3/4; 1; z), 2F1(1/3, 2/3; 1; z), 2F1(1/6, 5/6; 1; z) and provide a unified approach to a set of identities of Ramanujan involving these hypergeometric functions.

  • Liu Quan WANG
    Acta Mathematica Sinica. 2017, 33(1): 37-50. https://doi.org/10.1007/s10114-016-5673-2
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    Let p3(n) be the number of overpartition triples of n. By elementary series manipulations, we establish some congruences for p3(n) modulo small powers of 2, such as p3(16n+14)≡0 (mod 32), p3(8n+7)≡0 (mod 64). We also find many arithmetic properties for p3(n) modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences:for any integers α≥1 and n≥0, we have p3(32α+1(3n+2))≡0 (mod 9·24), p3(4α-1(56n+49))≡0 (mod 7), p3(72α+1(7n+3))≡p3(72α+1(7n+5))≡p3(72α+1(7n+6))≡0 (mod 7), and for r∈{1, 2, 3, 4, 5, 6}, p3(11·74α-1(7n+r))≡0 (mod 11).

  • Youngsoo SEOL
    Acta Mathematica Sinica. 2017, 33(1): 51-60. https://doi.org/10.1007/s10114-016-5470-y
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    We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between Nt and Tn.

  • Hyunjin LEE, Eunmi PAK, Young Jin SUH
    Acta Mathematica Sinica. 2017, 33(1): 61-70. https://doi.org/10.1007/s10114-016-4738-6
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    In this paper, we consider a new notion of generalized Tanaka-Webster D-parallel shape operator for a real hypersurface in a complex two-plane Grassmannian and prove a non-existence theorem of a real hypersurface.

  • Yan REN, Shao Bo GAN, Peng Fei ZHANG
    Acta Mathematica Sinica. 2017, 33(1): 71-76. https://doi.org/10.1007/s10114-016-5134-y
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    We give three equivalent conditions for non-accessibility of an Anosov diffeomorphism on the 3-torus with a partially hyperbolic splitting. Since accessibility is an open property, this gives a negative answer to Hammerlindl's question about homology boundedness of strong unstable foliation.

  • Yang LIU, Zi Qun LU
    Acta Mathematica Sinica. 2017, 33(1): 77-95. https://doi.org/10.1007/s10114-016-5353-2
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    Let G be a finite group, Irr1(G) be the set of nonlinear irreducible characters of G and cd1(G) the set of degrees of the characters in Irr1(G). A group G is said to be a D2-group if|cd1(G)|=|Irr1(G)|-2. In this paper, we give a complete classification of solvable D2-groups.

  • La Mei YUAN, Sheng CHEN, Cai Xia HE
    Acta Mathematica Sinica. 2017, 33(1): 96-116. https://doi.org/10.1007/s10114-016-6074-2
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    The aim of this paper is to introduce and study Hom-Gel'fand-Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing HomGel'fand-Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel'fand-Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel'fand-Dorfman super-bialgebras.

  • Joel FOTSO TACHAGO, Hubert NNANG
    Acta Mathematica Sinica. 2017, 33(1): 117-152. https://doi.org/10.1007/s10114-016-5597-x
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    Stochastic-periodic homogenization is studied for the Maxwell equations with the linear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions to a class of highly oscillatory problems converges to the solution of a homogenized Maxwell equation.

  • Ce SHI
    Acta Mathematica Sinica. 2017, 33(1): 153-164. https://doi.org/10.1007/s10114-017-5684-7
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    A mixed covering array (MCA) of type (v1, v2,..., vk), denoted by MCAλ(N; t, k, (v1, v2,..., vk)), is an N×k array with entries in the i-th column from a set Vi of vi symbols and has the property that each N×t sub-array covers all the t-tuples at least λ times, where 1≤i≤k. An MCAλ(N; t, k, (v1, v2,..., vk)) is said to be super-simple, if each of its N×(t+1) sub-arrays contains each (t+1)-tuple at most once. Recently, it was proved by Tang, Yin and the author that an optimum super-simple MCA of type (a, b, b,..., b) is equivalent to a mixed detecting array (DTA) of type (a, b, b,..., b) with optimum size. Such DTAs can be used to generate test suites to identify and determine the interaction faults between the factors in a component-based system. In this paper, some combinatorial constructions of optimum super-simple MCAs of type (a, b, b,..., b) are provided. By employing these constructions, some optimum super-simple MCAs are then obtained. In particular, the spectrum across which optimum super-simple MCA2(2b2; 2, 4, (a, b, b, b))'s exist, is completely determined, where 2≤ab.