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Publisher: Springer-Verlag   (Total: 2329 journals)

 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  [2329 journals]
• A comparison between the metric dimension and zero forcing number of trees
and unicyclic graphs
• 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)

• Semiparametric Bayesian inference for mean-covariance regression models
• 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)

• A remark on the existence of entire large and bounded solutions to a ( k 1
, k 2 )-Hessian system with gradient term
• 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)

• A revised pre-order principle and set-valued Ekeland variational
principles with generalized distances
• 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)

• Singularity categories with respect to Ding projective modules
• 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)

• Existence, uniqueness and approximation for L p solutions of reflected
BSDEs with generators of one-sided Osgood type
• 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)

• Chung’s law of the iterated logarithm for subfractional Brownian
motion
• 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)

• All good (bad) words consisting of 5 blocks
• 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)

• The fourth power mean of the general 2-dimensional Kloostermann sums mod p
• 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)

• A splitting primal-dual proximity algorithm for solving composite
optimization problems
• 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)

• Parameter estimation of varying coefficients structural EV model with time
series
• 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)

• Existence, uniqueness and asymptotic behavior for the Vlasov–Poisson
• 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)

• Skew Motzkin paths
• 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)

• Uniform homeomorphisms of unit spheres and Property H of
Lebesgue–Bochner function spaces
• 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)

• A class of finite resistant p -groups
• 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)

• Picard type theorems concerning certain small functions
• 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

• Distortion theorems for normalized biholomorphic quasi-convex mappings
• 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

• Normality concerning the sequence of functions
• 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

• An extension of a simply inequality between von Neumann–Jordan and James
constants in Banach spaces
• 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

• Energy scattering of a generalized Davey–Stewartson system in three
dimension
• 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

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