15 November 2015, Volume 31 Issue 11

    

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  The Classification of 2 and 3 Torsion Free Polyhedra

  Jian Zhong PAN, Zhong Jian ZHU

  Acta Mathematica Sinica. 2015, 31(11): 1659-1682. https://doi.org/10.1007/s10114-015-5119-2

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  We classify the stable homotopy types of (n-1)-connected, (n+k)-dimensional polyhedra with 2 and 3-torsion free homologies for k ≤ 6. The technique used is matrix problem (bimodule categories) which is given by Drozd.
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  Nonsolvable D₂-groups

  Yang LIU, Zi Qun LU

  Acta Mathematica Sinica. 2015, 31(11): 1683-1702. https://doi.org/10.1007/s10114-015-4669-7

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  Let G be a finite group. Let 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. The main purpose of this paper is to classify nonsolvable D₂-groups.
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  Hausdorff Operators on the Heisenberg Group

  Jiu Hua GUO, Li Jing SUN, Fa You ZHAO

  Acta Mathematica Sinica. 2015, 31(11): 1703-1714. https://doi.org/10.1007/s10114-015-5109-4

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  This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hⁿ. The sharp bounds for the strong type (p, p) (1 ≤ p ≤ ∞) estimates of n-dimensional Hausdorff operators on Hⁿ are obtained. The sharp bounds for strong (p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hⁿ. The weak type (p, p) (1 ≤ p ≤ ∞) estimates are also obtained.
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  Common Properties of the Operator Products in Local Spectral Theory

  Kai YAN, Xiao Chun FANG

  Acta Mathematica Sinica. 2015, 31(11): 1715-1724. https://doi.org/10.1007/s10114-015-5116-5

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  Let X, Y be Banach spaces, A,D : X → Y and B,C : Y → X be the bounded linear operators satisfying operator equation set
  
  In this paper, we show that AC and BD share some basic operator properties such as the injectivity and the invertibility. Moreover, we show that AC and BD share many common local spectral properties including SVEP, Bishop property (β) and Dunford property (C).
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  Homoclinic Orbits for First Order Hamiltonian Systems with Some Twist Conditions

  Yuan SHAN

  Acta Mathematica Sinica. 2015, 31(11): 1725-1738. https://doi.org/10.1007/s10114-015-4444-9

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  In this paper, we study the nonperiodic first-order Hamiltonian system ?= JL(t)u + JH' (t, u), where H ∈ C¹(R × R²ⁿ). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation, we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin.
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  A Characterization of Almost Simple K₃-groups

  Yan Xiong YAN, Hai Jing XU, Gui Yun CHEN

  Acta Mathematica Sinica. 2015, 31(11): 1739-1750. https://doi.org/10.1007/s10114-015-4438-7

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  It is a well-known fact that characters of a finite group can give important information about the group's structure. Also it was proved by the third author of this article that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost simple group by using less information of its character table, and successfully characterize the almost simple K₃-groups by their orders and at most three irreducible character degrees of their character tables.
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  Blaschke Isoparametric Hypersurfaces in the Conformal Space Q₁ⁿ⁺¹, I

  Chang Xiong NIE

  Acta Mathematica Sinica. 2015, 31(11): 1751-1758. https://doi.org/10.1007/s10114-015-4077-z

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  Let x : M → Q₁ⁿ⁺¹ be a regular hypersurface in the conformal space Q₁ⁿ⁺¹. We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the conformal equivalence.
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  Fractional Square Functions and Potential Spaces, II

  Jorge J. BETANCOR, Juan C. FARIÑA, Lourdes RODRÍGUEZ-MESA, Ricardo TESTONI, José L. TORREA

  Acta Mathematica Sinica. 2015, 31(11): 1759-1774. https://doi.org/10.1007/s10114-015-4046-6

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  In this paper, we study fractional square functions associated with the Poisson semigroup for Schrödinger operators. We characterize the potential spaces in the Schrödinger setting by using vertical, area and g_λ^* fractional square functions.
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  The Generalized L^p-Mixed Affine Surface Area

  Tong Yi MA

  Acta Mathematica Sinica. 2015, 31(11): 1775-1788. https://doi.org/10.1007/s10114-015-3140-0

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  In this article, we put forward the concept of the (i, j)-type L^p-mixed affine surface area, such that the notion of L^p-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the (i,-p)-type L^p-mixed affine surface area and the extensions of the well-known L^p-Petty affine projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized L^p-Winterniz monotonicity problem.
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  A Class of Normal Weighted Composition Operators on the Fock Space of Cⁿ

  Lian Kuo ZHAO

  Acta Mathematica Sinica. 2015, 31(11): 1789-1797. https://doi.org/10.1007/s10114-015-4758-7

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  This paper characterizes a class of normal weighted composition operators and their spectrum on the Fock space of Cⁿ.
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  On Gradient Solitons of the Ricci–Harmonic Flow

  Hong Xin GUO, Robert PHILIPOWSKI, Anton THALMAIER

  Acta Mathematica Sinica. 2015, 31(11): 1798-1804. https://doi.org/10.1007/s10114-015-4446-7

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  In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.
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  On the Number of Limit Cycles of a Z₄-equivariant Quintic Near-Hamiltonian System

  Xian Bo SUN, Mao An HAN

  Acta Mathematica Sinica. 2015, 31(11): 1805-1824. https://doi.org/10.1007/s10114-015-2117-3

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  In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z₄- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.