15 November 2017, Volume 33 Issue 11

    

• Select all
  |

Articles
• Select
  Multilinear Singular Integral Operators with Generalized Kernels and Their Multilinear Commutators

  Yan LIN, Ya Yuan XIAO

  Acta Mathematica Sinica. 2017, 33(11): 1443-1462. https://doi.org/10.1007/s10114-017-7051-0

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calderón–Zygmund operators and multilinear Calderón–Zygmund operators with Dini type kernels.

• Select
  Relative Singularity Categories with Respect to Gorenstein Flat Modules

  Zhen Xing, DI Zhong Kui LIU, Xiao Xiang ZHANG

  Acta Mathematica Sinica. 2017, 33(11): 1463-1476. https://doi.org/10.1007/s10114-017-6566-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let R be a right coherent ring and D^b(R-Mod) the bounded derived category of left R-modules. Denote by D^b(R-Mod)_[GF,C] the subcategory of D^b(R-Mod) consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b(F ∩ C) the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b(R-Mod)_[GF,C] /K^b(F ∩ C) is triangle-equivalent to the stable category GF ∩ C of the Frobenius category of all Gorenstein flat and cotorsion left R-modules.
• Select
  On a Classical Theorem on the Diameter and Minimum Degree of a Graph

  Verónica HERNÁNDEZ, Domingo PESTANA, José M. RODRÍGUEZ

  Acta Mathematica Sinica. 2017, 33(11): 1477-1503. https://doi.org/10.1007/s10114-017-6324-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this work, we obtain good upper bounds for the diameter of any graph in terms of its minimum degree and its order, improving a classical theorem due to Erdös, Pach, Pollack and Tuza. We use these bounds in order to study hyperbolic graphs (in the Gromov sense). To compute the hyperbolicity constant is an almost intractable problem, thus it is natural to try to bound it in terms of some parameters of the graph. Let H(n, δ₀) be the set of graphs G with n vertices and minimum degree δ₀, and J (n, Δ) be the set of graphs G with n vertices and maximum degree Δ. We study the four following extremal problems on graphs: a(n, δ₀) = min{δ(G) | G ∈ H(n, δ₀)}, b(n, δ₀) = max{δ(G) | G ∈ H(n, δ₀)}, α(n, Δ) = min{δ(G) | G ∈ J(n, Δ)} and β(n, Δ) = max{δ(G) | G ∈ J(n, Δ)}. In particular, we obtain bounds for b(n, δ₀) and we compute the precise value of a(n, δ0), α(n, Δ) and β(n, Δ) for all values of n, δ₀ and Δ, respectively.
• Select
  Arithmetic Properties for Cubic Partition Pairs Modulo Powers of 3

  Shane CHERN

  Acta Mathematica Sinica. 2017, 33(11): 1504-1512. https://doi.org/10.1007/s10114-017-7052-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let b(n) denote the number of cubic partition pairs of n. In this paper, we aim to provide a strategy to obtain arithmetic properties of b(n). This gives affirmative answers to two of Lin’s conjectures.
• Select
  Resolving Subcategories of Triangulated Categories and Relative Homological Dimension

  Xin MA, Ti Wei, ZHAO, Zhao Yong HUANG

  Acta Mathematica Sinica. 2017, 33(11): 1513-1535. https://doi.org/10.1007/s10114-017-6416-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We introduce and study (pre)resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.
• Select
  Analytic Properties for Holomorphic Matrix-valued Maps in C^2×2

  Chao FU, Ye Zhou LI, Xiao YAO

  Acta Mathematica Sinica. 2017, 33(11): 1536-1548. https://doi.org/10.1007/s10114-017-6397-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we investigate some analytic properties for a class of holomorphic matrixvalued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on C^2×2 and Julia set of one dimensional complex dynamic system.
• Select
  On the Existence, Uniqueness and Stability of Solutions for Semi-linear Generalized Elasticity Equation with General Damping Term

  Abita RAHMOUNE

  Acta Mathematica Sinica. 2017, 33(11): 1549-1564. https://doi.org/10.1007/s10114-017-6466-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we consider a semi-linear generalized hyperbolic boundary value problem associated to the linear elastic equations with general damping term and nonlinearities of variable exponent type. Under suitable conditions, local and global existence theorems are proved. The uniqueness of the solution have been gotten by eliminating some hypotheses that have been imposed by other authors for different particular problems. We show that any solution with nontrivial initial datum becomes stable.
• Select
  Every Sub-Riemannian Manifold Is the Gromov–Hausdorff Limit of a Sequence Riemannian Manifolds

  Yong Hong HUANG

  Acta Mathematica Sinica. 2017, 33(11): 1565-1568. https://doi.org/10.1007/s10114-017-4543-x

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we will show that every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds.
• Select
  Avramov–Martsinkovsky Type Exact Sequences with Tor Functors

  Chun Xia ZHANG, Li LIANG

  Acta Mathematica Sinica. 2017, 33(11): 1569-1577. https://doi.org/10.1007/s10114-017-7089-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  For two classes of right R-modules W, X such that P ⊂ W ⊂ X, where P is the class of projective right R-modules, we show that there is an Avramov–Martsinkovsky type exact sequence with generalized Tate homology functor Tor^X,W, relative homology functors Tor^W and Tor^X . Many results in Iacob [Comm. Algebra, 35, 1589–1606 (2007)] and Liang [Algebr. Represent. Theory, 16, 1541–1560 (2013)] are generalized and improved.
• Select
  Recursion Relations for the Constrained Multi-component KP Hierarchy

  Xu GAO, Chuan Zhong LI, Jing Song HE

  Acta Mathematica Sinica. 2017, 33(11): 1578-1586. https://doi.org/10.1007/s10114-017-6352-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we define a new constrained multi-component KP(cMKP) hierarchy which contains the constrained KP(cKP) hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.