Authors:Linda Eroh; Cong X. Kang; Eunjeong Yi Pages: 731 - 747 Abstract: The metric dimension dim(G) of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z(G) of a graph G is the minimum cardinality of a set S of black vertices (whereas vertices in V(G)S are colored white) such that V(G) is turned black after finitely many applications of “the color-change rule”: a white vertex is converted black if it is the only white neighbor of a black vertex. We show that dim(T) ≤ Z(T) for a tree T, and that dim(G) ≤ Z(G)+1 if G is a unicyclic graph; along the way, we characterize trees T attaining dim(T) = Z(T). For a general graph G, we introduce the “cycle rank conjecture”. We conclude with a proof of dim(T) − 2 ≤ dim(T + e) ≤ dim(T) + 1 for \(e \in E\left( {\bar T} \right)\) . PubDate: 2017-06-01 DOI: 10.1007/s10114-017-4699-4 Issue No:Vol. 33, No. 6 (2017)

Authors:Han Jun Yu; Jun Shan Shen; Zhao Nan Li; Xiang Zhong Fang Pages: 748 - 760 Abstract: In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study. PubDate: 2017-06-01 DOI: 10.1007/s10114-016-6357-7 Issue No:Vol. 33, No. 6 (2017)

Authors:Dragos Patru Covei Pages: 761 - 774 Abstract: In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system $$\left\{ {\begin{array}{*{20}c} {S_{k_1 } \left( {\lambda \left( {D^2 u_1 } \right)} \right) + a_1 \left( {\left x \right } \right)\left {\nabla u_1 } \right ^{k_1 } = p_1 \left( {\left x \right } \right)f_1 \left( {u_2 } \right)} & {for x \in \mathbb{R}^N ,} \\ {S_{k_2 } \left( {\lambda \left( {D^2 u_2 } \right)} \right) + a_2 \left( {\left x \right } \right)\left {\nabla u_2 } \right ^{k_2 } = p_2 \left( {\left x \right } \right)f_2 \left( {u_1 } \right)} & {for x \in \mathbb{R}^N .} \\ \end{array} } \right.$$ Here \({S_{{k_i}}}\left( {\lambda \left( {{D^2}{u_i}} \right)} \right)\) is the k i -Hessian operator, a 1, p 1, f 1, a 2, p 2 and f 2 are continuous functions. PubDate: 2017-06-01 DOI: 10.1007/s10114-017-6291-3 Issue No:Vol. 33, No. 6 (2017)

Authors:Jing Hui Qiu Pages: 775 - 792 Abstract: In my former paper “A pre-order principle and set-valued Ekeland variational principle” (see [J. Math. Anal. Appl., 419, 904–937 (2014)]), we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles (denoted by EVPs) in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy’s EVP in [On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381–396 (2011)], where the perturbation contains a weak τ-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy’s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances. PubDate: 2017-06-01 DOI: 10.1007/s10114-017-5062-5 Issue No:Vol. 33, No. 6 (2017)

Authors:Wen Jing Chen; Zhong Kui Liu; Xiao Yan Yang Pages: 793 - 806 Abstract: We introduce the singularity category with respect to Ding projective modules, D dpsg b (R), as the Verdier quotient of Ding derived category D DP b (R) by triangulated subcategory K b (DP), and give some triangle equivalences. Assume DP is precovering. We show that D DP b (R) ≈ K −,dpb (DP) and D dpsg b (R) ≈ D defect b (R). We prove that each R-module is of finite Ding projective dimension if and only if D dpsg b (R) = 0. PubDate: 2017-06-01 DOI: 10.1007/s10114-017-6209-0 Issue No:Vol. 33, No. 6 (2017)

Authors:Sheng Jun Fan Pages: 807 - 838 Abstract: We prove several existence and uniqueness results for L p (p > 1) solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works. PubDate: 2017-06-01 DOI: 10.1007/s10114-016-6281-x Issue No:Vol. 33, No. 6 (2017)

Authors:Na Na Luan Pages: 839 - 850 Abstract: Let X H = {X H(t), t ∈ ℝ+} be a subfractional Brownian motion in ℝ d . We provide a sufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that X H has the property of strong local nondeterminism. Applying this property and a stochastic integral representation of X H, we establish Chung’s law of the iterated logarithm for X H. PubDate: 2017-06-01 DOI: 10.1007/s10114-016-6090-2 Issue No:Vol. 33, No. 6 (2017)

Authors:Jian Xin Wei Pages: 851 - 860 Abstract: Generalized Fibonacci cube Q d (f), introduced by Ilić, Klavžar and Rho, is the graph obtained from the hypercube Q d by removing all vertices that contain f as factor. A word f is good if Q d (f) is an isometric subgraph of Q d for all d ≥ 1, and bad otherwise. A non-extendable sequence of contiguous equal digits in a word μ is called a block of μ. Ilić, Klavžar and Rho shown that all the words consisting of one block are good, and all the words consisting of three blocks are bad. So a natural problem is to study the words consisting of other odd number of blocks. In the present paper, a necessary condition for a word consisting of odd number of blocks being good is given, and all the good (bad) words consisting of 5 blocks is determined. PubDate: 2017-06-01 DOI: 10.1007/s10114-017-6134-2 Issue No:Vol. 33, No. 6 (2017)

Authors:Wen Peng Zhang; Xiao Xue Li Pages: 861 - 867 Abstract: The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it. PubDate: 2017-06-01 DOI: 10.1007/s10114-016-6347-9 Issue No:Vol. 33, No. 6 (2017)

Authors:Yu Chao Tang; Chuan Xi Zhu; Meng Wen; Ji Gen Peng Pages: 868 - 886 Abstract: Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encountered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Furthermore, we propose a preconditioned method, of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography (CT) image reconstruction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality. PubDate: 2017-06-01 DOI: 10.1007/s10114-016-5625-x Issue No:Vol. 33, No. 6 (2017)

Authors:Yan Yun Su; Heng Jian Cui; Kai Can Li Pages: 607 - 619 Abstract: In this paper, the parameters of a p-dimensional linear structural EV (error-in-variable) model are estimated when the coefficients vary with a real variable and the model error is time series. The adjust weighted least squares (AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-3187-6 Issue No:Vol. 33, No. 5 (2017)

Authors:Jing Chen; Xian Wen Zhang; Ran Gao Pages: 635 - 656 Abstract: We investigate the Cauchy problem for the Vlasov–Poisson system with radiation damping. By virtue of energy estimate and a refined velocity average lemma, we establish the global existence of nonnegative weak solution and asymptotic behavior under the condition that initial data have finite mass and energy. Furthermore, by building a Gronwall inequality about the distance between the Lagrangian flows associated to the weak solutions, we can prove the uniqueness of weak solution when the initial data have a higher order velocity moment. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6310-9 Issue No:Vol. 33, No. 5 (2017)

Authors:Qing Lin Lu Pages: 657 - 667 Abstract: In this paper, we study the class S of skew Motzkin paths, i.e., of those lattice paths that are in the first quadrat, which begin at the origin, end on the x-axis, consist of up steps U = (1, 1), down steps D = (1,−1), horizontal steps H = (1, 0), and left steps L = (−1,−1), and such that up steps never overlap with left steps. Let S n be the set of all skew Motzkin paths of length n and let s n = S n . Firstly we derive a counting formula, a recurrence and a convolution formula for sequence {s n } n ≥0. Then we present several involutions on S n and consider the number of their fixed points. Finally we consider the enumeration of some statistics on S n . PubDate: 2017-05-01 DOI: 10.1007/s10114-016-5292-y Issue No:Vol. 33, No. 5 (2017)

Authors:Qing Jin Cheng; Yun Bai Dong Pages: 681 - 690 Abstract: Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic. Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L p (μ,X) and L q (μ, Y) are mutually uniformly homeomorphic where 1 ≤ p, q < ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L p (μ,X), 1 ≤ p < ∞, also has Property H. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6245-1 Issue No:Vol. 33, No. 5 (2017)

Authors:He Guo Liu; Yu Lei Wang Pages: 725 - 730 Abstract: A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group, the normalizer N G (P) controls p-fusion in G. Let P be a central extension as $$1 \to {\mathbb{Z}_{{p^m}}} \to P \to {\mathbb{Z}_p} \times \cdots {\mathbb{Z}_p} \to 1,$$ and P′ ≤ p, m ≥ 2. The purpose of this paper is to prove that P is resistant. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-4016-7 Issue No:Vol. 33, No. 5 (2017)

Authors:Pai Yang; Lei Qiao Abstract: Let f(z) be a meromorphic function in the complex plane, whose zeros have multiplicity at least k + 1 (k ≥ 2). If sin z is a small function with respect to f(z), then f(k)(z) − P(z) sinz has infinitely many zeros in the complex plane, where P(z) is a nonzero polynomial of deg(P(z)) ≠ 1. PubDate: 2017-05-13 DOI: 10.1007/s10114-017-6137-z

Authors:Xiao Fei Zhang; Tai Shun Liu; Yong Hong Xie Abstract: In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B n respectively. PubDate: 2017-05-13 DOI: 10.1007/s10114-017-6220-5

Authors:Bing Mao Deng; De Gui Yang; Ming Liang Fang Abstract: Let {f n } be a sequence of functions meromorphic in a domain D, let {h n } be a sequence of holomorphic functions in D, such that \({h_n}\left( z \right)\mathop \Rightarrow \limits^\chi h\left( z \right)\) , where h(z) ≢ 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ ℕ+, f n (z) ≠ 0 and f n (k) − h n (z) has at most k distinct zeros (ignoring multiplicity) in D, then {f n } is normal in D. PubDate: 2017-05-10 DOI: 10.1007/s10114-017-6234-z

Authors:Chang Sen Yang; Feng Hui Wang Abstract: For a non-trivial Banach space X, let J(X), C NJ(X), C NJ (p) (X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C NJ (p) (X) ≤ J(X) with p ≥ 2, which covers the well-known inequality C NJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al. PubDate: 2017-05-10 DOI: 10.1007/s10114-017-6211-6

Authors:Jing Lu; Xing Dong Tang Abstract: In this paper, we study the global scattering result of the solution for the generalized Davey–Stewartson system $$\left\{ {\begin{array}{*{20}{c}} {i{\partial _t}u + \Delta u = {{\left u \right }^2}u + u{v_{{x_1}}},\left( {t,x} \right) \in \mathbb{R} \times {\mathbb{R}^3},} \\ { - \Delta u = {{\left( {{{\left u \right }^2}} \right)}_{{x_1}}}.} \end{array}} \right.$$ The main difficulties are the failure of the interaction Morawetz estimate and the asymmetrical structure of nonlinearity (in particular, the nonlinearity is non-local). To compensate, we utilize the strategy derived from concentration-compactness idea, which was first introduced by Kenig and Merle [Invent. Math., 166, 645–675 (2006)]. PubDate: 2017-05-10 DOI: 10.1007/s10114-017-6301-5