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 Acta Mathematica Sinica, English Series   [SJR: 0.406]   [H-I: 30]   [5 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1439-8516 - ISSN (Online) 1439-7617    Published by Springer-Verlag  [2352 journals]
• Multilinear singular integral operators with generalized kernels and their
multilinear commutators
• Authors: Yan Lin; Ya Yuan Xiao
Pages: 1443 - 1462
Abstract: Abstract 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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-7051-0
Issue No: Vol. 33, No. 11 (2017)

• Relative singularity categories with respect to gorenstein flat modules
• Authors: Zhen Xing Di; Zhong Kui Liu; Xiao Xiang Zhang
Pages: 1463 - 1476
Abstract: Abstract Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-modules. Denote by $${D^b}{\left( {R - Mod} \right)_{\widehat {\left[ {GF,C} \right]}}}$$ 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 $${D^b}{\left( {R - Mod} \right)_{\widehat {\left[ {GF,C} \right]}}}$$ /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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-6566-8
Issue No: Vol. 33, No. 11 (2017)

• On a classical theorem on the diameter and minimum degree of a graph
• Authors: Verónica Hernández; Domingo Pestana; José M. Rodríguez
Pages: 1477 - 1503
Abstract: Abstract 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, δ 0) be the set of graphs G with n vertices and minimum degree δ 0, 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, δ 0) = min{δ(G) G ∈ H(n, δ 0)}, b(n, δ 0) = max{δ(G) G ∈ H(n, δ 0)}, 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, δ 0) and we compute the precise value of a(n, δ 0), α(n, Δ) and β(n, Δ) for all values of n, δ 0 and Δ, respectively.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-6324-y
Issue No: Vol. 33, No. 11 (2017)

• Arithmetic properties for cubic partition pairs modulo powers of 3
• Authors: Shane Chern
Pages: 1504 - 1512
Abstract: Abstract 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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-7052-z
Issue No: Vol. 33, No. 11 (2017)

• Resolving subcategories of triangulated categories and relative
homological dimension
• Authors: Xin Ma; Ti Wei Zhao; Zhao Yong Huang
Pages: 1513 - 1535
Abstract: Abstract 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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-6416-8
Issue No: Vol. 33, No. 11 (2017)

• Analytic properties for holomorphic matrix-valued maps in ℂ 2×2
• Authors: Chao Fu; Ye Zhou Li; Xiao Yao
Pages: 1536 - 1548
Abstract: Abstract 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 ℂ2×2 and Julia set of one dimensional complex dynamic system.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-6397-7
Issue No: Vol. 33, No. 11 (2017)

• On the existence, uniqueness and stability of solutions for semi-linear
generalized elasticity equation with general damping term
• Authors: Abita Rahmoune
Pages: 1549 - 1564
Abstract: Abstract 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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-6466-y
Issue No: Vol. 33, No. 11 (2017)

• Every sub-Riemannian manifold is the Gromov–Hausdorff limit of a
sequence Riemannian manifolds
• Authors: Yong Hong Huang
Pages: 1565 - 1568
Abstract: Abstract In this paper, we will show that every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-4543-x
Issue No: Vol. 33, No. 11 (2017)

• Avramov–Martsinkovsky type exact sequences with tor functors
• Authors: Chun Xia Zhang; Li Liang
Pages: 1569 - 1577
Abstract: Abstract 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 $${\widehat {Tor}^{X.W}}$$ , 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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-7089-z
Issue No: Vol. 33, No. 11 (2017)

• Recursion relations for the constrained multi-component KP hierarchy
• Authors: Xu Gao; Chuan Zhong Li; Jing Song He
Pages: 1578 - 1586
Abstract: Abstract 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.
PubDate: 2017-11-01
DOI: 10.1007/s10114-017-6352-7
Issue No: Vol. 33, No. 11 (2017)

• Moderate deviations for marked Hawkes processes
• Authors: Youngsoo Seol
Pages: 1297 - 1304
Abstract: Abstract We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31, 433–451 (2015)]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-6433-7
Issue No: Vol. 33, No. 10 (2017)

• Two acyclicizations of a complex and an explicit recollement
• Authors: Huan Huan Li
Pages: 1305 - 1320
Abstract: Abstract By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the recollement preserve acyclic complexes.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-6565-9
Issue No: Vol. 33, No. 10 (2017)

• Sewing homeomorphism and conformal invariants
• Authors: Tao Cheng; Hui Qiang Shi; Shanshuang Yang
Pages: 1321 - 1338
Abstract: Abstract This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-6481-z
Issue No: Vol. 33, No. 10 (2017)

• On a class of weak nonhomogeneous affine bi-frames for reducing subspaces
of L 2 (ℝ d )
• Authors: Jian Ping Zhang; Yun Zhang Li
Pages: 1339 - 1351
Abstract: Abstract For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L 2(R d ), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-6445-3
Issue No: Vol. 33, No. 10 (2017)

• Weak solutions on Lorentzian 2-tori
• Authors: Liang Jin; Xiaojun Cui
Pages: 1352 - 1360
Abstract: Abstract In this paper, we classify the set of Lorentzian metrics on T2, analyse the topological structure of some subclasses and study whether a subclass could admit certain weak solutions to the eikonal equations.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-6348-3
Issue No: Vol. 33, No. 10 (2017)

• On the asymptotically PT −1 spaces
• Authors: Xin Luo; Ying Qing Xiao; Yue Ping Jiang
Pages: 1421 - 1430
Abstract: Abstract In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT−1 space are still an asymptotically PT−1 space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT−1 spaces under particular conditions, which provide some concrete examples of asymptotically PT−1 spaces.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-5257-9
Issue No: Vol. 33, No. 10 (2017)

• Isometries and additive mapping on the unit spheres of normed spaces
• Authors: Rui Dong Wang; Xu Jian Huang
Pages: 1431 - 1442
Abstract: Abstract In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.
PubDate: 2017-10-01
DOI: 10.1007/s10114-017-6589-1
Issue No: Vol. 33, No. 10 (2017)

• Multiple forced rotational solutions for the planar N -pendulum equation
• Authors: Hui Qiao
Abstract: Abstract This paper presents a theorem of existence of (N − N 0 + 1)2 N0 noncontractible periodic orbits of any given rotational vector with zero components for the planar forced N-pendulum equation, where N 0 denotes the number of zero components of given rotational vector. We make special arrangements for masses and length instead of the nondegenerate assumption. Moreover, for rotational vectors with identical components, similar results is also obtained.
PubDate: 2017-10-18
DOI: 10.1007/s10114-017-7037-y

• On the periodic logistic map
• Authors: Cui Ping Li; Ming Zhao
Abstract: Abstract In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic map $${x_{n + 1}} = {r_n}{x_n}\left( {1 - {x_n}} \right),n = 0,1, \ldots ,$$ where {r n } is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.
PubDate: 2017-10-18
DOI: 10.1007/s10114-017-6011-z

• On p -convergent operators on Banach lattices
• Authors: Elroy D. Zeekoei; Jan H. Fourie
Abstract: Abstract The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and Sánchez in the paper entitled “Dunford–Pettis-like properties of continuous vector function spaces”. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications (together with the notion of a weak p-convergent operator, which we introduce in the present paper) to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.
PubDate: 2017-10-18
DOI: 10.1007/s10114-017-7172-5

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