中国科学院数学与系统科学研究院期刊网

15 September 2019, Volume 35 Issue 9
    

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  • Sheng Qing HU
    Acta Mathematica Sinica. 2019, 35(9): 1419-1452. https://doi.org/10.1007/s10114-019-8111-4
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    In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently close to the integrable ones preserve a large set of n-dimensional invariant tori.
  • Chia Fu YU
    Acta Mathematica Sinica. 2019, 35(9): 1453-1463. https://doi.org/10.1007/s10114-019-8269-9
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    A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper, we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori.
  • Kai ZHOU, Lu JIN
    Acta Mathematica Sinica. 2019, 35(9): 1464-1480. https://doi.org/10.1007/s10114-019-8261-4
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    This paper gives a generalization of the classical Borel's Lemma. Then as an application of this generalized Borel's Lemma, a uniqueness theorem for two linearly non-degenerate meromorphic maps of Cm into Pn(C) (n ≥ 2) sharing 2n + 2 hyperplanes in general position is proved.
  • Meng Fai LIM
    Acta Mathematica Sinica. 2019, 35(9): 1481-1490. https://doi.org/10.1007/s10114-019-8410-9
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    Let p be an odd prime and F a p-adic Lie extension of a number field F with Galois group G. Suppose that G is a compact pro-p p-adic Lie group with no torsion and that it contains a closed normal subgroup H such that G/H ≅Zp. Under various assumptions, we establish asymptotic upper bounds for the growth of p-exponents of the class groups in the said p-adic Lie extension. Our results generalize a previous result of Lei, where he established such an estimate under the assumption that H ≅Zp.
  • Jun Feng LIU
    Acta Mathematica Sinica. 2019, 35(9): 1491-1510. https://doi.org/10.1007/s10114-019-8149-3
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    In this paper, we establish a moderate deviation principle for the stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (1/4, 1/2) in the space variable. The weak convergence approach plays an important role.
  • Chang Hui WU, Zhi Jie WANG, Tao YU
    Acta Mathematica Sinica. 2019, 35(9): 1511-1519. https://doi.org/10.1007/s10114-019-7444-3
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    Let H2(γ) be the Hilbert space over the bidisk D2 generated by a positive sequence γ={γnm}n,m ≥ 0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H2(γ) with γ={γnm}n,m ≥ 0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D2.
  • San Guo ZHU
    Acta Mathematica Sinica. 2019, 35(9): 1520-1540. https://doi.org/10.1007/s10114-019-8117-y
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    Let E be a Moran set on R1 associated with a bounded closed interval J and two sequences (nk)k=1 and (Ck=(ck,j)j=1nk)k ≥ 1. Let μ be the Moran measure on E associated with a sequence (Pk)k ≥ 1 of positive probability vectors with Pk=(pk,j)j=1nk, k ≥ 1. We assume that

    For every n ≥ 1, let αn be an n optimal set in the quantization for μ of order r ∈ (0, ∞) and {Pa(αn)}aαn an arbitrary Voronoi partition with respect to αn. We write

    We show that J(αn, μ), J(αn, μ) and en,rr (μ) -en+1,rr(μ) are of the same order as 1/n en,rr (μ), where en,rr (μ):=∫ d(x, αn)r(x) is the nth quantization error for μ of order r. In particular, for the class of Moran measures on R1, our result shows that a weaker version of Gersho's conjecture holds.

  • Qing Yang LIU
    Acta Mathematica Sinica. 2019, 35(9): 1541-1548. https://doi.org/10.1007/s10114-019-8536-9
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    Sarnak's Disjointness Conjecture states that the Möbius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg's irregular flows on the infinite-dimensional torus.
  • Yuan HE
    Acta Mathematica Sinica. 2019, 35(9): 1549-1562. https://doi.org/10.1007/s10114-019-8283-y
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    In this paper, by making use of Abel's theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet L-function at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.
  • Li Xia FENG, Lian Kuo ZHAO
    Acta Mathematica Sinica. 2019, 35(9): 1563-1572. https://doi.org/10.1007/s10114-019-8549-4
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    By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.