期刊：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,2016年2016 ISSN：1072-6691
通讯作者：
Gong, Zhaogang
作者机构：
[Yang, Zhifeng; Gong, Zhaogang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.
通讯机构：
[Gong, Zhaogang] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.
关键词：
Viscoelastic equation;blow-up;arbitrary positive initial energy
摘要：
We consider the viscoelastic equation u(tt)(x, t) - M(vertical bar vertical bar del u vertical bar vertical bar(2)(2))Delta u(x,t) +integral(t)(0)g(t-s)Delta u(x,s)ds + u(t) = vertical bar u vertical bar(p-1)u with suitable initial data and boundary conditions. Under certain assumptions on the kernel g and the initial data, we establish a new blow-up result for arbitrary positive initial energy, by using simple analysis techniques.
摘要：
In this paper, which is sequel to [10], we give a generalisation of the second Klein-Maskit combination theorem, the one dealing with HNN extensions, to higher dimension. We give some examples constructed as an application of the main theorem.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Chennai Ctr SETS, Indian Stat Inst, MGR Knowledge City, Madras 600113, Tamil Nadu, India.;[Rasila, Antti] Aalto Univ, Dept Math & Syst Anal, Aalto 00076, Finland.
关键词：
Majorant;Bloch space;Hardy space;Lipschitz space
摘要：
In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some applications to non-homogeneous Yukawa PDEs. We also consider some properties of the Lipschitz-type spaces on certain classes of complex-valued functions. Finally, we will study a class of composition operators on these spaces.
关键词：
NOD sequence;Stout's type weighted sum;complete convergence
摘要：
In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup. The more optimal moment condition is given. The main results also hold for END sequence.
关键词：
rho*-mixing sequences of random variables;Marcinkiewicz strong laws;Weighted sums
摘要：
Some strong laws are established for linear statistics that are weighted sums of, where {Xn; n 1} is a sequence of ρ∗-mixing random variables, and {ani; 1 i n, n 1} is an array of real numbers. The results obtained extend and generalize the corresponding results of Guanghui Cai (Anais da Academia Brasileira de Cincias, 78(4):615-621, 2006) for identically distributed ρ∗-mixing sequences of random variables.
摘要：
We prove Schwarz-Pick type estimates and coefficient estimates for a class of functions induced by the elliptic partial differential operators. Then we apply these results to obtain a Landau type theorem. (C) 2015 Elsevier Inc. All rights reserved.
摘要：
In this article, we consider the Euler-Bernoulli viscoelastic equation u(tt)(x,t) + Delta(2)u(x,t) - integral(t)(0) g(t-s)Delta(2)u(x,s)ds = vertical bar u vertical bar(p-1)u together with some suitable initial data and boundary conditions in Omega x (0, +infinity). Some sufficient conditions on blow-up of solutions are obtained under different initial energy states. And from these results we can clearly understand the competitive relationship between the viscoelastic damping and source.
摘要：
In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray-Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results. In this paper, the global stability has been investigated for a novel class of competitive neural networks with mixed time delays and discontinuous activations. Without presuming the boundedness of activation functions, we draw two set of sufficient conditions ensuring the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure, by linear matrix inequality, M-matrix, Leray-Schauder alternative theorem in multivalued analysis, general Lyapunov method, topological degree theory of set-valued map. Meanwhile, we present a result on the global convergence in finite time of given neural networks. The results in the literature are generalized and significantly improved. Finally, one example and simulations are presented to demonstrate the effectiveness of the theoretical results.
摘要：
In the article, the variational iteration algorithm LFVIA-II is implemented to solve the diffusion equation occurring in non-differentiable heat transfer. The operators take in sense of the local fractional operators. The obtained results show the fractal behaviors of heat transfer with non-differentiability.
作者机构：
[Zhang, Hanjun; Huang, Haiwu] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China.;[Huang, Haiwu] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Zhang, Qingxia] Southwest Petr Univ, Sch Sci, Chengdu 610500, Peoples R China.;[Peng, Jiangyan] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610054, Peoples R China.
通讯机构：
[Huang, Haiwu] X;Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China.
关键词：
Arrays of rowwise AANA random variables;Complete convergence;Marcinkiewicz-Zygmund type strong law of large numbers;Weighted sums
摘要：
In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. [19], but also partially improve the corresponding ones of Huang et al. [8].
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr, SETS, MGR Knowledge City, Chennai 600113, Tamil Nadu, India.;[Rasila, Antti] Aalto Univ, Dept Math & Syst Anal, FI-00076 Aalto, Finland.;[Rasila, Antti] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
通讯机构：
[Rasila, Antti] A;Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
关键词：
Harmonic and Bloch mappings;Quasiconformal mappings;Hardy and Lipschitz spaces;Length;Area function
摘要：
In this paper, we give bounds for length and area distortion for harmonic K-quasiconformal mappings, and investigate certain Lipschitz-type spaces on harmonic mappings.
摘要：
In this article, we are concerned with a class of fourth-order elliptic equations with sublinear perturbation and steep potential well. By using variational methods, we obtain that such equations admit at least two nontrivial solutions. We also explore the phenomenon of concentration of solutions.
摘要：
In this note, we get a necessary and sufficient condition such that the scalar curvature of generalized m-quasi-Einstein manifold with m = 1 is constant. In particular, we discuss a class of generalized quasi-Einstein manifolds which are more general than (m, rho)-quasi-Einstein manifolds and prove that these manifolds with dimension four are either Einstein or locally conformally flat under some suitable conditions. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
作者机构：
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] MGR Knowledge City, SETS, Chennai Ctr, ISI, Madras 600113, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] M;MGR Knowledge City, SETS, Chennai Ctr, ISI, Madras 600113, Tamil Nadu, India.
关键词：
Convex;Harmonic convolution;Partial sum;Stable harmonic convex and close-to-convex mappings;Starlike and close-to-convex harmonic mappings;Univalent
摘要：
In this article, we consider the class SHC of normalized stable harmonic convex mappings f = h + (g) over bar in the unit disk and determine r such that every section of f is close-to-convex or convex in the disk vertical bar z vertical bar < r. Also, we show that the convolution f * f is an element of SHC whenever f is an element of SHC. In addition, we prove that the harmonic convolution f(1) * f(2) is stable harmonic close-to-convex whenever f(1) is an element of SHC and f(2) is either a slanted half-plane mapping or an asymmetric vertical strip mapping or a mapping in the family P-H(0) (alpha) which is contained in the family of harmonic close-to-convex functions in vertical bar z vertical bar < 1. (C) 2014 Elsevier Ltd. All rights reserved.
期刊：
Journal of Mathematical Analysis and Applications,2015年432(1):356-366 ISSN：0022-247X
通讯作者：
Liu, Gang
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Gao, Junyang] China Univ Min & Technol Beijing, Sch Sci, Beijing 100083, Peoples R China.
通讯机构：
[Liu, Gang] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.
关键词：
Julia set;Konig's methods;Group of symmetries
摘要：
Let Sigma(R) be the group of symmetries of the Julia set of a rational map R and K-f,K-n be the Konig's method for polynomial f of order n (>= 2). For any given integer n >= 2, we prove that if f is in normal form, then Sigma(f) is a subgroup of Sigma(K-f,K-n). We also obtain a necessary and sufficient condition for the Julia set of K-f,K-n to be a line. (C) 2015 Elsevier Inc. All rights reserved.
期刊：
Applied Mathematics and Computation,2015年266(C):539-559 ISSN：0096-3003
通讯作者：
Li, Xiaoyue
作者机构：
[Ouyang, Mengqian] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Peoples R China.;[Li, Xiaoyue; Ouyang, Mengqian] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China.
通讯机构：
[Li, Xiaoyue] N;NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr SETS Soc Elect Transact & Secur, MGR Knowledge City, Chennai 600113, Tamil Nadu, India.;[Wang, Xiantao] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China.
摘要：
In this paper, we investigate some properties of pluriharmonic mappings defined in the unit ball. First, we discuss some geometric univalence criteria on pluriharmonic mappings, and then establish a Landau-Bloch theorem for a class of pluriharmonic mappings.
摘要：
This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations x(n+1) = A + x(n)/y(n-1)y(n-2), y(n+1) = A + y(n)/x(n-1)x(n-2), n = 0, 1,..., where A is an element of(0, infinity), x(-i) is an element of (0, infinity); y(-i) is an element of (0, infinity), i = 0, 1, 2. Some examples are given to demonstrate the effectiveness of the results obtained.
