中国科学院数学与系统科学研究院期刊网

15 April 2019, Volume 35 Issue 4
    

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  • Shizuo KAJI, Stephen THERIAULT
    Acta Mathematica Sinica. 2019, 35(4): 445-462. https://doi.org/10.1007/s10114-019-8051-z
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    If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.
  • Tao ZHANG, Chun Qin ZHOU
    Acta Mathematica Sinica. 2019, 35(4): 463-480. https://doi.org/10.1007/s10114-019-7423-8
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    In this paper, we will analyze the blow-up behaviors for solutions to the Laplacian equation with exponential Neumann boundary condition. In particular, the boundary value is with a kind of singular data. We show a Brezis–Merle type concentration-compactness theorem, calculate the blow up value at the blow-up point, and give a point-wise estimate for the profile of the solution sequence at the blow-up point.
  • Javad BAGHERIAN
    Acta Mathematica Sinica. 2019, 35(4): 481-493. https://doi.org/10.1007/s10114-018-7072-3
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    An irreducible character χ of an association scheme is called nonlinear if the multiplicity of χ is greater than 1. The main result of this paper gives a characterization of commutative association schemes with at most two nonlinear irreducible characters. This yields a characterization of finite groups with at most two nonlinear irreducible characters. A class of noncommutative association schemes with at most two nonlinear irreducible character is also given.
  • Jian Min CHEN, Ya Nan LIN, Shi Quan RUAN
    Acta Mathematica Sinica. 2019, 35(4): 494-512. https://doi.org/10.1007/s10114-018-8187-2
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    The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular endomorphism algebras for the case of genus one via cluster tilting theory.
  • Guang Gui DING, Jian Ze LI
    Acta Mathematica Sinica. 2019, 35(4): 513-518. https://doi.org/10.1007/s10114-019-7509-3
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    In this paper, based on the smooth point of the unit ball and its support linear functional, we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case.
  • Yan Bin LIN, Ying LÜ, Chang Ping WANG
    Acta Mathematica Sinica. 2019, 35(4): 519-536. https://doi.org/10.1007/s10114-019-8042-0
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    In this paper, we first set up an alternative fundamental theory of Möbius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined completely by a system consisting of a function W and a tangent frame {Ei}. Then we give a complete classification for spacelike Möbius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either Möbius equivalent to spacelike Dupin hypersurfaces or to some cylinders constructed from logarithmic curves and hyperbolic logarithmic spirals. Some of them have parallel para-Blaschke tensors with non-vanishing Möbius form.
  • Dou Dou LI, Mei ZHANG
    Acta Mathematica Sinica. 2019, 35(4): 537-549. https://doi.org/10.1007/s10114-019-7441-6
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    In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration {Zn, n ≥ 0}. First we get some estimation for the probability generating function of Zn. Based on it, we get a large deviation for Zn+1/Zn. Lower and upper deviations for Zn are also studied. As a by-product, an upper deviation for max1≤in Zi is obtained.
  • Kai Hua BAO, Ai Hui SUN, Chao DENG
    Acta Mathematica Sinica. 2019, 35(4): 550-568. https://doi.org/10.1007/s10114-018-8069-7
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    In this paper, we compute lower dimensional volumes Vol4(1,1) and Vol6(2,2) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler– Kalau–Walze type theorems. We also give theoritic explaination of the gravitational action for 4, 6 dimensional manifolds with boundary by these noncommutative residues.
  • Wei Juan ZHANG, Jian Guo QIAN, Fu Ji ZHANG
    Acta Mathematica Sinica. 2019, 35(4): 569-576. https://doi.org/10.1007/s10114-019-7403-z
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    Cycle reversal had been shown as a powerful method to deal with the relation among orientations of a graph since it preserves the out-degree of each vertex and the connectivity of the orientations. A facial cycle reversal on an orientation of a plane graph is an operation that reverses all the directions of the edges of a directed facial cycle. An orientation of a graph is called an α-orientation if each vertex admits a prescribed out-degree. In this paper, we give an explicit formula for the minimum number of the facial cycle reversals needed to transform one α-orientation into another for plane graphs.
  • Wei DONG, Rui LI, Bao Gang XU
    Acta Mathematica Sinica. 2019, 35(4): 577-582. https://doi.org/10.1007/s10114-018-7186-7
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    A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most 2 receive distinct colors. The strong chromatic index χ's(G) of a graph G is the minimum number of colors used in a strong edge coloring of G. In an ordering Q of the vertices of G, the back degree of a vertex x of G in Q is the number of vertices adjacent to x, each of which has smaller index than x in Q. Let G be a graph of maximum degree Δ and maximum average degree at most 2k. Yang and Zhu [J. Graph Theory, 83, 334–339 (2016)] presented an algorithm that produces an ordering of the edges of G in which each edge has back degree at most 4kΔ -2k in the square of the line graph of G, implying that x's(G) ≤ 4kΔ -2k + 1. In this note, we improve the algorithm of Yang and Zhu by introducing a new procedure dealing with local structures. Our algorithm generates an ordering of the edges of G in which each edge has back degree at most (4k -1)Δ - 2k in the square of the line graph of G, implying that x's(G) ≤ (4k -1)Δ - 2k + 1.