Authors:Yan Lin; Ya Yuan Xiao Pages: 1443 - 1462 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)

Authors:Zhen Xing Di; Zhong Kui Liu; Xiao Xiang Zhang Pages: 1463 - 1476 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)

Authors:Verónica Hernández; Domingo Pestana; José M. Rodríguez Pages: 1477 - 1503 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)

Authors:Shane Chern Pages: 1504 - 1512 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)

Authors:Xin Ma; Ti Wei Zhao; Zhao Yong Huang Pages: 1513 - 1535 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)

Authors:Chao Fu; Ye Zhou Li; Xiao Yao Pages: 1536 - 1548 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)

Authors:Abita Rahmoune Pages: 1549 - 1564 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)

Authors:Yong Hong Huang Pages: 1565 - 1568 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)

Authors:Chun Xia Zhang; Li Liang Pages: 1569 - 1577 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)

Authors:Xu Gao; Chuan Zhong Li; Jing Song He Pages: 1578 - 1586 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)

Authors:Tao Cheng; Hui Qiang Shi; Shanshuang Yang Pages: 1321 - 1338 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)

Authors:Xin Luo; Ying Qing Xiao; Yue Ping Jiang Pages: 1421 - 1430 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)

Authors:Rui Dong Wang; Xu Jian Huang Pages: 1431 - 1442 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)

Authors:Ya Ming Lu Abstract: In this paper, we will prove for 0.9993 < γ < 1 that there are infinitely primes p of the form [n 1/γ ] with p + 2 having at most four prime factors. PubDate: 2017-11-04 DOI: 10.1007/s10114-017-7030-5

Authors:Jin Jiang Li; Pan Wang Wang; Min Zhang Abstract: Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A(x) = Ʃ n ≤ x a(n). In this paper, we establish an asymptotic formula of the fourth power moment of A(x) and prove that \(\int_1^T {{A^4}\left( x \right)dx = \frac{3}{{64\kappa {\pi ^4}}}{s_{4;2}}\left( {\tilde a} \right){T^{2\kappa }} + O\left( {{T^{2\kappa - {\delta _4} + \varepsilon }}} \right)} \) with δ4 = 1/8, which improves the previous result. PubDate: 2017-11-04 DOI: 10.1007/s10114-017-6508-5

Authors:Xiao Ming Pi Abstract: Let G = (V,E) be a simple graph. A function f: E → {+1,−1} is called a signed cycle domination function (SCDF) of G if Ʃ e∈E(C) f(e) ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc(G) = min{Ʃ e∈E f(e) f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γ′sc(G) = n. PubDate: 2017-11-04 DOI: 10.1007/s10114-017-6283-3

Authors:Jing Cheng Dong; Liang Yun Zhang; Li Dai Abstract: Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K(C) of C; that is, we prove that K(C) ≅= Fib⊗Z[Z2], where Fib is the Fibonacci fusion ring and Z[Z2] is the group ring on Z2. In particular, if C is braided, then it is equivalent to Fib⊠ \(Vec_{{\mathbb{Z}_2}}^\omega \) as fusion categories, where Fib is a Fibonacci category and \(Vec_{{\mathbb{Z}_2}}^\omega \) is a rank 2 pointed fusion category. PubDate: 2017-11-04 DOI: 10.1007/s10114-017-6375-0

Authors:Hui Qiao 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

Authors:Cui Ping Li; Ming Zhao 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

Authors:Elroy D. Zeekoei; Jan H. Fourie 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