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25 June 2015, Volume 35 Issue 3 Previous Issue    Next Issue

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Obtaining Upper Bounds of Heat Kernels from Lower Bounds with Doubling Measure Dou Xiaoman Acta mathematica scientia,Series A. 2015, 35 (3):  449-463.  Abstract ( 298 )   RICH HTML   PDF (380KB) ( 222 )   Save This paper shows the relationship between lower bounds and upper bounds of the heat kernel on metric spaces with doubling measure. If in addition the Dirichlet form is local, then a near-diagonal lower bound implies an on-diagonal upper bound. This paper gives the upper estimate in balls and then extends it to full spaces. Compared with previous work, the conclusion of this paper not only contains former result but reveals a more general relationship between the lower and upper bounds. References | Related Articles | Metrics

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Dynamical Behavior of Gradient System with Small Time Delay Yin Xunwu, Li Desheng Acta mathematica scientia,Series A. 2015, 35 (3):  464-477.  Abstract ( 213 )   RICH HTML   PDF (383KB) ( 155 )   Save In this article, we investigate the dynamical behavior of the following general nonlinear gradient-like evolutionary equation with small time delay ∂tu+Au=f(u(t),u(t-τ)). We prove that each bounded solution of the delayed equation will converge to some equilibrium as t→∞ provided the delay is sufficiently small. This indicates that gradient system with small time delay behaves very much like the nondelayed one. The approach here is mainly based on the Morse structure of invariant sets of gradient system and some geometric analysis of evolutionary equations. The proof of this result is completed in two steps. First, with the hypothesis of gradient system, finite and isolated equilibria, we prove that there exists a sufficiently small delay such that any bounded solution of the delayed equation will ultimately enter and stay in the neighborhood of one equilibrium. Second, with the hypothesis of hyperbolic equilibrium, we utilize exponential dichotomies and a series estimates to prove that there exists ε > 0 and τ > 0 sufficiently small such that any solution of the delayed equation lying in the ε-neighborhood of one equilibrium will converge to this equilibrium as t → ∞. References | Related Articles | Metrics

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Darboux Transformation for A Generalized Self-Dual Yang-Mills Equation in 2n Dimensions Shen Shoufeng, Yu Shuimeng, Li Chunxia, Jin Yongyang Acta mathematica scientia,Series A. 2015, 35 (3):  478-486.  Abstract ( 270 )   RICH HTML   PDF (297KB) ( 204 )   Save A generalized self-dual Yang-Mills equation with negative powers of the spectral parameter is proposed by a set of spectral problems. It contains some well-known Lax integrable equations such the Takasaki case, the Belavin-Zakharov case, the Ablowitz-Chakravarty-Takhtajan case and the Ma case. The explicit formulation of Darboux transformation is established for this equation. References | Related Articles | Metrics

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Strong Convergence Theorems by A Viscosity Iterative Method for Fixed Point Problems of Nonexpansive Mappings in Banach Spaces Cai Gang Acta mathematica scientia,Series A. 2015, 35 (3):  487-502.  Abstract ( 226 )   RICH HTML   PDF (343KB) ( 153 )   Save In this paper, we first study some properties of attracting nonexpansive mappings. Furthermore, we use these properties to investigate some viscosity iterative methods for fixed point problems of two nonexpansive mappings in uniformly smooth Banach space. As an application, we obtain some strong convergence theorems for variational inequality problems, fixed point problems and equilibrium problems in Banach spaces or Hilbert spaces. The results obtained in this paper improve and extend many recent ones announced by many others in this literature. References | Related Articles | Metrics

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On Boundedness of Sublinear Operators on Generalized Weighted Grand Morrey Spaces Zheng Qingyu, Zhang Lei, Shi Shaoguang Acta mathematica scientia,Series A. 2015, 35 (3):  503-514.  Abstract ( 285 )   RICH HTML   PDF (347KB) ( 144 )   Save A version of generalized weighted grand Morrey spaces defined on Rn is adopted. Some results for the boundedness of some sublinear operators, including fractional integral operators, on certain spaces are given. Moreover, the corresponding results of the commutators are discussed. References | Related Articles | Metrics

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Some Integral Inequalities of Hermite-Hadamard Type for s-Logarithmically Convex Functions Xi Boyan, Qi Feng Acta mathematica scientia,Series A. 2015, 35 (3):  515-524.  Abstract ( 284 )   RICH HTML   PDF (245KB) ( 348 )   Save In the paper, we introduce the notion "s-logarithmically convex function", establish some new integral inequalities of Hermite-Hadamard type for functions the power of the absolute of whose first derivative is s-logarithmically convex, and apply these newly obtained inequalities to means. References | Related Articles | Metrics

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Convergence in W01,p Space for the Elliptic Reiterated Homogenization Problems Zhao Jie Acta mathematica scientia,Series A. 2015, 35 (3):  525-533.  Abstract ( 268 )   RICH HTML   PDF (309KB) ( 116 )   Save In this paper, we study the convergence of solutions for the elliptic reiterated homogenization problem of the form -div(A(x/ε,x/ε)▽uε)=f(x). We obtain the convergence rates in W01,p for solutions with Dirichlet boundary conditions. Our techniques are based on obtaining estimates for Green functions of the operators. References | Related Articles | Metrics

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Algebro-Geometric Solutions of A -Dimensional Integrable Equation Chen Xiaohong, Zhang Daqing, Zhang Hongqing, You Fucai Acta mathematica scientia,Series A. 2015, 35 (3):  534-544.  Abstract ( 208 )   RICH HTML   PDF (325KB) ( 163 )   Save In this paper, a (2+1)-dimensional integrable equation is presented with the help of (1+1)-dimensional soliton equations. The (2+1)-dimensional integrable equation is decomposed into solvable ordinary differential equations. A hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to strainghten the associated flow, from which the algebro-geometric solutions of the (2+1)-dimensional integrable equation are constructed by means of the Riemann theta functions. References | Related Articles | Metrics

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Exponential Synchronization for Impulsive Cohen-Grossberg Neural Networks with Mixed Time-Varying Delays Abdujelil Abdurahman, Jiang Haijun, Teng Zhidong Acta mathematica scientia,Series A. 2015, 35 (3):  545-557.  Abstract ( 279 )   RICH HTML   PDF (914KB) ( 174 )   Save In this paper, the exponential synchronization of Cohen-Grossberg neural networks with mixed time-varying delays and impulsive effects is investigated. Based on the contradiction method and constructing suitable Lyapunov function, some simple and useful criteria for the synchronization of considered network are obtained. Finally, a numerical example is given to show the effectiveness and feasibility of the proposed synchronization scheme. References | Related Articles | Metrics

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Distributional Chaos in Nonautonomous Discrete Systems Lu Tianxiu, Zhu Peiyong, Wu Xinxing Acta mathematica scientia,Series A. 2015, 35 (3):  558-566.  Abstract ( 319 )   RICH HTML   PDF (347KB) ( 158 )   Save New definition of distributional chaos in nonautonomous discrete systems is given. This paper studies the chaotic behaviour of sequences fn,∞=(fn, n+1, …), ∀n∈N (N is the set of natural numbers), and discusses that whether the distributional chaoticity of fn,∞ implies the distributional chaoticity of fn,∞[m] (m is a positive integer), or vice versa. References | Related Articles | Metrics

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Berezin Transform and Commutativity of Toeplitz Operators on the Hardy Space over the Polydisk Yu Tao, Zhuang Chunming Acta mathematica scientia,Series A. 2015, 35 (3):  567-577.  Abstract ( 237 )   RICH HTML   PDF (283KB) ( 206 )   Save In this paper we discuss the commutativity of Toeplitz operators on the Hardy space over the polydisk. Using the Berezin transform and the harmonic extension, we obtain a necessary and sufficient condition for two Toeplitz operators to commute with each other. References | Related Articles | Metrics

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Existence of A Ground State Solution for A Class of Superlinear p-Laplace Equations with Negative Potential Functions Deng Yihua, Luo Liping, Zhou Lijun Acta mathematica scientia,Series A. 2015, 35 (3):  578-586.  Abstract ( 231 )   RICH HTML   PDF (333KB) ( 182 )   Save Using (C)c sequences and variational methods, we discuss the existence of a ground state solution to p-Laplace equations without the Ambrosetti-Rabinowitz condition. By chosing suitable Banach space, we prove that there exists a ground state solution to a class of superlinear p-Laplace equations with negative potential functions in RN. References | Related Articles | Metrics

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Upper Local Entropy of Measures and Like-Bowen Entropy of Sets Dai Yuxia Acta mathematica scientia,Series A. 2015, 35 (3):  587-591.  Abstract ( 191 )   RICH HTML   PDF (230KB) ( 132 )   Save Let f be a continuous map on a metric space (X,d). In this paper, we show that the like-Bowen entropy of subsets X with respect to f can be determined via the upper local entropy of measures. References | Related Articles | Metrics

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A Stochastic Predator-Prey System with Time Delays and Prey Dispersal Zhang Shuwen Acta mathematica scientia,Series A. 2015, 35 (3):  592-603.  Abstract ( 278 )   RICH HTML   PDF (718KB) ( 146 )   Save In this paper, a stochastic predator-prey system with time delays and prey dispersal in two-patch environments is investigated. Firstly, a unique positive solution for the system with positive initial value is obtained. Secondly, the conditions for the extinction of species and persistent in the mean of the solution for system(1.1). Finally, computer simulations are carried out to verify our results. References | Related Articles | Metrics

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An SEI Epidemic Diffusive Model and Its Moving Front Liu Jiang, Zhu Lintao, Lin Zhigui Acta mathematica scientia,Series A. 2015, 35 (3):  604-617.  Abstract ( 288 )   RICH HTML   PDF (477KB) ( 138 )   Save This paper is concerned about an SEI model, in which the disease is infectious in the latent period and the infected period. We first consider the PDE system in a fixed domain, the local and global stabilities of equilibriums are given. More attention has been given to the free boundary problem, which describes the moving front. Global existence and uniqueness of the solution are first given and then the properties of the free boundary are discussed. We prove that either the disease spreads or vanishes. Sufficient conditions for spreading or extinction are given. Our results show that when the contact rate is very small or average incubation period is short, and the initial infected domain is small enough, then the disease vanishes; and when the contact rate is big or the average incubation period is long, and the initial infected domain is sufficiently large, then the disease spreads. References | Related Articles | Metrics

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Global Existence and Nonexistence of Solutions for A Class of Fourth Order Wave Equation with Nonlinear Damping and Source Terms Di Huafei, Shang Yadong Acta mathematica scientia,Series A. 2015, 35 (3):  618-633.  Abstract ( 248 )   RICH HTML   PDF (408KB) ( 252 )   Save In this paper, we consider the initial boundary value problem of the fourth order wave equation with nonlinear damping and source terms. By the combination of Galerkin approximations, Potential well and Monotonicity-Compactness methods, the global existence of solutions is obtained with the least amount of a priori estimates. Moreover, we prove that there are solutions with negative initial energy that blow up in finite time. References | Related Articles | Metrics

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Globally Asymptotic Stability of A New Class of Neutral Neural Networks with Time-Varying Delays Luo Ricai, Xu Honglei, Wang Wusheng Acta mathematica scientia,Series A. 2015, 35 (3):  634-640.  Abstract ( 200 )   RICH HTML   PDF (331KB) ( 145 )   Save In this paper, we study the stability problem of a class of neural neutral network systems whose involve an activation function with differential time-delay state variables. By constructing Lyapunov functions and using LMI techniques, we obtain a sufficient condition for the global asymptotic stability of these neural networks. Finally, we demonstrate the validity of our results by use of a numerical example. References | Related Articles | Metrics