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:Mohamed Akel; Fatimah Alabbad Abstract: In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann–Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann–Hilbert problem for inhomogeneous Cauchy–Riemann equations. PubDate: 2017-06-25 DOI: 10.1007/s10114-016-6127-6

Authors:Sheng Yang; Sheng Gao; Chong Bin Xu Abstract: Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs’ approach to block structure. We consider the block B of a group G as a union of two sets, namely a set of irreducible ordinary characters of G having cardinality k(B) and a set of irreducible Brauer characters of G having cardinality l(B). We calculate k(B) and l(B) provided that D is normal in G and \(D \cong \left\langle {x,y,z {x^{{3^n}}} = {y^{{3^m}}} = {z^3} = \left[ {x,z} \right] = \left[ {y,z} \right] = 1,\left[ {x,y} \right] = z} \right\rangle \left( {n > m \geqslant 2} \right)\) . PubDate: 2017-06-15 DOI: 10.1007/s10114-017-5792-4

Authors:Xiang Mao Ding; Yu Ping Li; Ling Xian Meng Abstract: Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra. PubDate: 2017-06-15 DOI: 10.1007/s10114-017-6268-2

Authors:Jun-Muk Hwang Abstract: In a joint work with Mok in 1997, we proved that for an irreducible representation G ⊂ GL(V), if a holomorphic G-structure exists on a uniruled projective manifold, then the Lie algebra of G has nonzero prolongation. Using a different approach, we generalize this to an arbitrary connected algebraic subgroup G ⊂ GL(V) and a complex manifold containing an immersed rational curve. We also prove a partial converse: a construction of a holomorphic G-structure on a homogeneous complex manifold containing smooth rational curves, under the condition that G has no nonzero fixed vector in V and the prolongation of the Lie algebra of G is finite-dimensional and nonzero. PubDate: 2017-06-15 DOI: 10.1007/s10114-017-7014-5

Authors:Paul Norbury Abstract: We represent stationary descendant Gromov–Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of stationary descendant Gromov–Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov–Witten invariants are “virtual” stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants. PubDate: 2017-06-15 DOI: 10.1007/s10114-017-5314-4

Authors:Bo Ju Jiang; Xue Zhi Zhao Abstract: We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on manifolds and polyhedra. Special attention is paid to connections with geometric group theory and dynamics, as well as some formal approaches. PubDate: 2017-06-07 DOI: 10.1007/s10114-017-6503-x

Authors:Jiao Chen Abstract: The main purpose of this paper is to establish the Hörmander–Mihlin type theorem for Fourier multipliers with optimal smoothness on k-parameter Hardy spaces for k ≥ 3 using the multi-parameter Littlewood–Paley theory. For the sake of convenience and simplicity, we only consider the case k = 3, and the method works for all the cases k ≥ 3: $${T_m}f\left( {{x_1},{x_2},{x_3}} \right) = \frac{1}{{{{\left( {2\pi } \right)}^{{n_1} + {n_2} + {n_3}}}}}\int_{{\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}} {m\left( \xi \right)\widehat f} {e^{2\pi ix \cdot \xi }}d\xi $$ where \(x = \left( {{x_1},{x_2},{x_3}} \right) \in {\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}\) and \(\xi = \left( {{\xi _1},{\xi _2},{\xi _3}} \right) \in {\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}\) . One of our main results is the following: Assume that m(ξ) is a function on \({\mathbb{R}^{{n_1} + {n_2} + {n_3}}}\) satisfying \(\mathop {\sup }\limits_{j,k,l \in \mathbb{Z}} {\left\ {{m_{j,k,l}}} \right\ _{{W^{\left( {{s_1},{s_2},{s_3}} \right)}}}} < \infty \) with s i > n i (1/p−1/2) for 1 ≤ i ≤ 3. Then T m is bounded from \({H^p}\left( {{\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}} \right)\) to \({H^p}\left( {{\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}} \right)\) for all 0 < p ≤ 1 and \(\left\ {{T_m}} \right\ {}_{{H^P} \to {H^P}} \lesssim \mathop {\sup }\limits_{j,k,l \in \mathbb{Z}} {\left\ {{m_{j,k,l}}} \right\ _{{W^{\left( {{s_1},{s_{2,}}{s_3}} \right)}}}}\) . Moreover, the smoothness assumption on s i for 1 ≤ i ≤ 3 is optimal. Here we have used the notations m j,k,l (ξ) = m(2 j ξ 1, 2 k ξ 2, 2 l ξ 3)Ψ(ξ 1)Ψ(ξ 2)Ψ(ξ 3) and Ψ(ξ i ) is a suitable cut-off function on \({\mathbb{R}^{{n_i}}}\) for 1 ≤ i ≤ 3, and \({W^{\left( {{s_1},{s_2},{s_3}} \right)}}\) is a three-parameter Sobolev space on \({\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times {\mathbb{R}^{{n_3}}}\) . Because the Fefferman criterion breaks down in three parameters or more, we consider the L p boundedness of the Littlewood–Paley square function of T m f PubDate: 2017-06-07 DOI: 10.1007/s10114-017-6526-3

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