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26 February 2017, Volume 37 Issue 1 Previous Issue    Next Issue

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A Note on Geodesic Loops in Complete Non-Compact Ricci Solitons Chen Chih-Wei Acta mathematica scientia,Series A. 2017, 37 (1):  1-6.  Abstract ( 272 )   RICH HTML PDF (513KB) ( 238 )   Save We give a visual description on the κ-noncollapsity of Ricci solitons with quadratic decaying curvature by studying closed loops in them. References | Related Articles | Metrics

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Normality Criteria of Meromorphic Functions with Zero Numbers Wang Qiong, Chen Wei, Yuan Wenjun, Tian Honggen Acta mathematica scientia,Series A. 2017, 37 (1):  7-17.  Abstract ( 200 )   RICH HTML PDF (351KB) ( 169 )   Save This paper considers normality criteria for a family of meromorphic functions concerning zero numbers. Let F be a family of meromorphic functions defined in a domain D, all of whose zeros and poles have multiplicity at least k and k+1 respectively, let m, n and k be three positive integers satisfying n≥m+2, and a(≠0), b be two finite constants. If for each function f∈F, f(k)-afn-b has at most m distinct zeros in D, then F is normal in D. Our results improve theorem 1 by Deng et al.[18] and generalize the related theorems of Ye et al.[16], Zhang et al.[22] and Chen et al.[19]. Meanwhile, some examples are given to show the sharpness of our results. References | Related Articles | Metrics

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Refinement of Schwarz Lemma for the Modulus of Holomorphic Mappings on the Unit Disk Zhang Yufang, Xu Qinghua Acta mathematica scientia,Series A. 2017, 37 (1):  18-25.  Abstract ( 161 )   RICH HTML PDF (273KB) ( 152 )   Save Let D be the unit disk in C, Bp={z∈Cn:|zi|p<1}, 1 < < +∞. In this note, it is proved that if f∈Hm(D, Bp), then |▽||f||(z)|≤(m|z|m-1)/(1-|z|2m)(1-||f(z)||2),z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on schwarz lemma. References | Related Articles | Metrics

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Weighted Estimates for Parametric Marcinkiewicz Integrals and Its Commutators Wu Ruimin, Jiang Yinsheng, Wang Lihong, Gao Jinling Acta mathematica scientia,Series A. 2017, 37 (1):  26-37.  Abstract ( 148 )   RICH HTML PDF (321KB) ( 120 )   Save In this paper, we obtain weighted Lp inequalities for Parametric Marcinkiewicz integrals by a class of new weight functions which conclude Muckenhoupt weight functions. References | Related Articles | Metrics

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Rough Marcinkiewicz Integrals Associated with Surfaces of Van der Corput Type Liu Feng, Xu Xiurong, Zhang Jing Acta mathematica scientia,Series A. 2017, 37 (1):  38-53.  Abstract ( 124 )   RICH HTML PDF (388KB) ( 119 )   Save This paper is concerned with the parametric Marcinkiewicz integrals with rough kernels associated with surfaces of Van der Corput type. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp bounds of such operators are given in an extrapolation argument. Some previous results are greatly extended and improved. References | Related Articles | Metrics

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New Results for Neumann Boundary Value Problem with Impulses via Variational Methods Chen Huiwen, Li Jianli, Shen Jianhua Acta mathematica scientia,Series A. 2017, 37 (1):  54-61.  Abstract ( 134 )   RICH HTML PDF (310KB) ( 152 )   Save In this paper, we study the existence of three solutions for Neumann boundary value problem with impulses. By using a very recent three critical points theorem, we obtain a new criterion for guaranteeing that Neumann boundary value problem with impulses has three solutions. Some recent results are generalized and significantly improved. Some examples are also presented to illustrate our main results. References | Related Articles | Metrics

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Fourier Truncation Regularization for a Class of Nonlinear Backward Heat Equation Yang Fan, Fu Chuli, Li Xiaoxiao, Ren Yupeng Acta mathematica scientia,Series A. 2017, 37 (1):  62-71.  Abstract ( 201 )   RICH HTML PDF (308KB) ( 135 )   Save In this paper, we consider the nonlinear backward heat equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A Fourier regularization method is proposed to solve this problem. For the regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is given. References | Related Articles | Metrics

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The Generalied Approximation and Growth Problem of Dirichlet Series in the Whole Plane Wen Qiong, Ning Juhong Acta mathematica scientia,Series A. 2017, 37 (1):  72-81.  Abstract ( 151 )   RICH HTML PDF (292KB) ( 76 )   Save In this paper, we study the growth of Dirichlet series in the whole plane by defining the generalized order and type. We also investigate the concept of error En-1(f,δ) and remainder Rn(f,δ) and get some interesting relationships on maximum modulus, the maximum term. References | Related Articles | Metrics

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Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives Dong Xiaoyu, Bai Zhanbing, Sun Sujing Acta mathematica scientia,Series A. 2017, 37 (1):  82-91.  Abstract ( 223 )   RICH HTML PDF (352KB) ( 86 )   Save In this paper, we establish the solvability of a class nonlinear fractional differential equation boundary value problem Dαu(t)+f(t, u(t))=0, 0 < t < 1, u(0)=u(1)=0, where 1 < α ≤ 2 is a real number, Dα is the conformable fractional derivative, and f:[0, 1]×[0, ∞)→[0, ∞) is a continuous function. One of the difficulty here is the corresponding Green's function G(t, s) is singular at s=0. By the use of approach method and fixed-point theorems on cone, some existence and multiplicity results of positive solutions are acquired. References | Related Articles | Metrics

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Nontrivial Solutions for a Class of Superlinear (p, 2)-Laplacian Dirichlet Problems Pei Ruichang, Zhang Jihui, Ma Caochuan Acta mathematica scientia,Series A. 2017, 37 (1):  92-101.  Abstract ( 148 )   RICH HTML PDF (343KB) ( 82 )   Save In this paper, we consider a class of particular (p,2)-Laplacian Dirichlet problem with nonlinearity which is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition at infinity. Some existence results for nontrivial solution are established by Morse theory in the general case 2 < p < N and similar results are also established by combining Morse theory with Moser-Trudinger inequality when p=N. References | Related Articles | Metrics

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The Global Existence Result of a Leray-α-Oldroyd Model to the Incompressible Viscoelastic Flow Qiu Hua, Zhang Yingshu, Fang Shaomei Acta mathematica scientia,Series A. 2017, 37 (1):  102-112.  Abstract ( 210 )   RICH HTML PDF (326KB) ( 64 )   Save In this paper, we introduce and study a new model for two-dimensional regularized viscoelastic fluid model, the Leray-α-Oldroyd model. This model is inspired by the Leray-α model describing turbulence, introduced by Cheskidov et al[16]. We study the Cauchy problem of the Leray-α-Oldroyd model and obtain the global existence for the strong solution of this model. References | Related Articles | Metrics

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Global Boundedness and Asymptotic Behavior in an Attraction-Repulsion Chemotaxis System with Logistic Source Gao Xinchun, Zhou Jian, Tian Miaoqing Acta mathematica scientia,Series A. 2017, 37 (1):  113-121.  Abstract ( 150 )   RICH HTML PDF (331KB) ( 69 )   Save This paper studies the attraction-repulsion chemotaxis system with logistic source ut=Δu-▽·(u▽v)+μ1u(1-u), 0=Δv+w-v, wt=Δw+▽·(w▽z)+μ2w(1-w), 0=Δz-z+u, in bounded domain Ω⊂RN, N≥1, subject to the homogeneous Neumann boundary conditions, and μ1,μ2>0. It is proved that for any nonegative initial data u0(x),w0(x)∈C(Ω), the solution (u(·,t),v(·,t),w(·,t),z(·,t)) is globally bounded. Furthermore, if μ1,μ2>(1)/(16), then (u(·,t),v(·,t),w(·,t),z(·,t)) converges asymptotically to the constant equilibrium (1,1,1,1) in the L∞-norm as t→∞. References | Related Articles | Metrics

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Higher Integrability for Very Weak Solutions of Obstacle Problems to Nonlinear Subelliptic Equations Du Guangwei, Niu Pengcheng Acta mathematica scientia,Series A. 2017, 37 (1):  122-145.  Abstract ( 185 )   RICH HTML PDF (458KB) ( 111 )   Save In this paper we first establish the local higher integrability for very weak solutions of the Kψ, u0r-obstacle problems to the nonlinear subelliptic equations constructed by Hörmander vector fields which implies the very weak solutions are classical weak solutions. As an application, the compactness results are obtained. We also derive the global higher integrability for very weak solutions of the Kψ, u0r-obstacle problems with a capacitary condition on Ω. References | Related Articles | Metrics

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Lower Bounds of Blow-up Time for a Reaction-Diffusion Equation with Weighted Nonlocal Sources and Robin Type Boundary Conditions Ma Lingwei, Fang Zhongbo Acta mathematica scientia,Series A. 2017, 37 (1):  146-157.  Abstract ( 131 )   RICH HTML PDF (350KB) ( 143 )   Save We investigate a reaction-diffusion equation with weighted nonlocal inner sources and Robin type boundary conditions. By virtue of a differential inequality technique to determine lower bounds of blow-up time in the higher dimensional spaces under different measure sense when blow-up occurs. References | Related Articles | Metrics

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Random Attractors for the Stochastic Nonclassical Diffusion Equation on Unbounded Domains Li Dingshi, Fan Yingfei Acta mathematica scientia,Series A. 2017, 37 (1):  158-172.  Abstract ( 180 )   RICH HTML PDF (348KB) ( 120 )   Save In this paper, we prove the existence and uniqueness of a random attractor for a stochastic nonclassical diffusion equation on unbounded domains with additive noise. To overcome the difficulty caused by the non-compactness of Sobolev embeddings on unbounded domains, a cut-off method and a decomposition trick are combined to prove the asymptotic compactness of the solutions. References | Related Articles | Metrics

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Existence and Stability of Coexistence States for a Lotka-Volterra Competition Model Yuan Hailong, Li Yanling Acta mathematica scientia,Series A. 2017, 37 (1):  173-184.  Abstract ( 239 )   RICH HTML PDF (368KB) ( 126 )   Save In this paper, we consider the existence and stability of coexistence states in a Lotka-Volterra competition model with spatial heterogeneity of the environment. In particular, the two competing species are assumed that they have the different strengths of resources, the different intraspecific competition rates and the different interspecific competition rates. It turns out that the dynamics of system are determined by some scalar functions for small parameter τ. Our mathematical approach is based on Lyapunov-Schmidt reduction technique, spectral theory and monotone dynamical system theory. References | Related Articles | Metrics

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Exponential Stabilization of a Timoshenko Beam System with Internal Disturbances Zhang Liping, Liu Dongyi, Zhang Guoshan Acta mathematica scientia,Series A. 2017, 37 (1):  185-198.  Abstract ( 142 )   RICH HTML PDF (391KB) ( 125 )   Save In this paper, we consider the stabilization of a Timoshenko beam with interior disturbances. On the basis of the idea of sliding-mode control, we design nonlinear distributed feedback controllers to reduce the effects of the external disturbances. Due to the resulting controlled system is a nonlinear system, the theories of nonlinear maximal monotone operators and variation principle are employed for the solvability analysis of the nonlinear closed-loop system. Moreover we show that exponential stability of the closed-loop system by the Lyapunov method. References | Related Articles | Metrics

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The Dynamical Behaviors and the Numerical Simulation of a Five-Mode Lorenz-Like System of the MHD Equations for a Two-Dimensional Incompressible Fluid on a Torus Wang Heyuan Acta mathematica scientia,Series A. 2017, 37 (1):  199-216.  Abstract ( 159 )   RICH HTML PDF (4269KB) ( 125 )   Save In this paper, we investigate a ten-dimensional model of plane flow, obtained by a five-mode truncation of the magnetic hydrodynamic (MHD) equations for a two-dimensional incompressible fluid on a torus. First, we derive a model system by taking five modes in the Fouriers expansion, and then discuss the stability of stationary solutions of the five-mode system. Second, we find phenomena of Hopf bifurcation and chaos, and prove the existence of its attractor and global stability of the five-mode system. Finally, we present a detailed numerical result of the whole process from bifurcation to chaos, and analyze the influence of magnetism on the dynamical behavior of the system. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behavior of this low-dimensional model are revealed, the new chaos system exhibits a route to chaos via a period doubling cascade (Feigenbaum's Scenario). References | Related Articles | Metrics