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26 August 2017, Volume 37 Issue 4 Previous Issue    Next Issue

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A Remark on the Weak Specification Property Wu Xinxing Acta mathematica scientia,Series A. 2017, 37 (4):  601-606.  Abstract ( 311 )   RICH HTML   PDF (310KB) ( 133 )   Save This note proves that if a dynamical system has the weak specification property, then so does the dynamical system restricted on its measure center, and the converse does not hold. As a corollary, it is obtained that the weak specification property implies asymptotic average shadowing (no assumption that the map is onto). Finally, it is proved that every surjective system having the weak specification property exhibits uniformly distributional chaos. References | Related Articles | Metrics

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Two Representations of a Super Operator Wang Wenhua, Chen Zhengli, Li Wei Acta mathematica scientia,Series A. 2017, 37 (4):  607-614.  Abstract ( 489 )   RICH HTML   PDF (282KB) ( 301 )   Save Super operator is the linear mapping which performs the operator to operator, any super operator has the natural representation and Choi-Jamiolkowski representation, both of them are only dependent on the super-operator itself. In this paper, the natural representation Nφ and Choi-Jamiolkowski representation Jφ of a given super operator φ∈B(B(X)) is discussed, and then the transform relationship between them is established as Nφ=T (Jφ), then some important examples are presented. References | Related Articles | Metrics

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Conformal Vector Fields and Some Rigidity Theorems Huang Qin, Ruan Qihua, Chen Fan Acta mathematica scientia,Series A. 2017, 37 (4):  615-623.  Abstract ( 233 )   RICH HTML   PDF (316KB) ( 150 )   Save In this paper, we discuss a question about what condition can enforce a compact Riemannian manifold carrying a nontrivial conformal vector field and with a constant scalar curvature to be isometric to an Euclidean sphere. We also study a Riemannian manifold with nonconstant scalar curvature and obtain some corresponding rigidity theorems. References | Related Articles | Metrics

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The Normal Family of Meromorphic Functions Concerning Zero Numbers Yang Qi, Chen Wei, Yuan Wenjun Acta mathematica scientia,Series A. 2017, 37 (4):  624-636.  Abstract ( 220 )   RICH HTML   PDF (301KB) ( 144 )   Save This paper considers the normal families of meromorphic functions concerning zero numbers, and get three normal criteria. Our results improve some earlier related results. References | Related Articles | Metrics

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A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces Xia Hongchuan, Liu Hao, Zhong Chunping Acta mathematica scientia,Series A. 2017, 37 (4):  637-646.  Abstract ( 213 )   RICH HTML   PDF (305KB) ( 144 )   Save In this paper, we construct a new Roper-Suffridge extension operator on the unit ball B in complex Hilbert space X, where dim X ≥ n, f is a normalized locally biholomorphic function on the unit disc D, {ej∈X,j=1,2,…n} is a series of orthogonal unit vectors in X. Under some special conditions of βj, we prove the operator can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of order α on the unit ball B, respectively. References | Related Articles | Metrics

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Liouville Type Theorem for an Integral System on a Half Space Tang Sufang Acta mathematica scientia,Series A. 2017, 37 (4):  647-662.  Abstract ( 228 )   RICH HTML   PDF (370KB) ( 132 )   Save This paper considers Liouville type theorem for a system of integral equations on the upper half Euclidean space. Under the natural structure conditions, we prove the nonexistence of positive solutions to the system basing on the method of moving sphere in integral form and the Hardy-Littlewood-Sobolev (HLS) inequality. References | Related Articles | Metrics

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Existence of Infinitely Many Solutions to a Class of Klein-Gordon-Maxwell System with Superlinear and Sublinear Terms Chen Lizhen, Li Anran, Li Gang Acta mathematica scientia,Series A. 2017, 37 (4):  663-670.  Abstract ( 216 )   RICH HTML   PDF (319KB) ( 143 )   Save In this paper, we establish the multiplicity of solutions for the Klein-GordonMaxwell system where 4 < p < 6, 1 < q < 2, λ > 0. Under some assumptions on the a(x),b(x),λ, the multiplicity result of solutions for the system was obtained by variational methods. Our result is a complement to some recent works concerning the existence of solutions of the above equation. References | Related Articles | Metrics

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Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type Chen Lin Acta mathematica scientia,Series A. 2017, 37 (4):  671-683.  Abstract ( 255 )   RICH HTML   PDF (352KB) ( 167 )   Save In this paper, using Nehari manifold and fibering maps we study the existence of multiple nontrivial nonnegative solutions for the nonlocal quasilinear elliptic system where Ω is a bounded smooth domain of RN, △pu=div (|▽u|p-2▽u) is the p-Laplacian with 1 < p < N,α >1,β>1,α+β < p < p (k+1) < r < p*(p*=pN/N-p if N>p,p*=∞ if N ≤ p),λ,μ >0,h (x),g1(x),g2(x)∈C (Ω) are functions which change sign in Ω and M (s)=a+bsk,a,b,k>0. References | Related Articles | Metrics

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Existence of Strong Global Attractors for Damped Suspension Bridge Equations with History Memory Liu Shifang, Ma Qiaozhen Acta mathematica scientia,Series A. 2017, 37 (4):  684-697.  Abstract ( 207 )   RICH HTML   PDF (354KB) ( 131 )   Save In this paper, we study the long-time dynamical behavior of the solution for damped suspension bridge equations with history memory. We prove the existence of the global attractors in a strong space by using the contraction function method. References | Related Articles | Metrics

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A Note to Monotonicity Formula for Stable Solutions of the Weighted Elliptic System Lu Pingping, Hu Lianggen Acta mathematica scientia,Series A. 2017, 37 (4):  698-705.  Abstract ( 210 )   RICH HTML   PDF (268KB) ( 162 )   Save In this paper, we reconstruct a monotonicity formula for stable solution of the weighted elliptic system by the use of analysis technique. In contrast with[12, Theorem 2.1], the construction of method is more convenient and direct to compute. References | Related Articles | Metrics

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Local Regularity and Local Boundedness for Solutions to Obstacle Problems Gao Hongya, Jia Miaomiao Acta mathematica scientia,Series A. 2017, 37 (4):  706-713.  Abstract ( 199 )   RICH HTML   PDF (266KB) ( 139 )   Save This paper deals with solutions to Kψ,θ-obstacle problems of the A-harmonic equation divA (x,▽u (x))=0 under some coercivity and growth conditions on A(x,ξ):Ω×Rn → Rn whose prototype is A (x,ξ)=(μ2+|ξ|2)p-2/2ξ,μ ≥ 0. Local regularity and local boundedness results are obtained. References | Related Articles | Metrics

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Interactions of Delta Shock Waves for the Nonsymmetric Keyfitz-Kranzer System with Split Delta Functions Li Huahui, Shao Zhiqiang Acta mathematica scientia,Series A. 2017, 37 (4):  714-729.  Abstract ( 247 )   RICH HTML   PDF (427KB) ( 136 )   Save In this paper, we study the interactions of delta shock waves with contact discontinuities for the nonsymmetric Keyfitz-Kranzer system with split delta functions. The solutions are obtained constructively when the initial data are three piecewise constant states. The global structure and large time-asymptotic behaviors of the solutions are analyzed case by case. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with initial data by studying the limits of the solutions when the perturbed parameter ε→0. References | Related Articles | Metrics

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Almost Periodic Solution for a Non-Autonomous Two Species Competitive System with Feedback Controls on Time Scales Li Zhouhong, Zhang Fengshuo, Cao Jinde, Alsaedi Ahmed, Alsaadi Fuad E Acta mathematica scientia,Series A. 2017, 37 (4):  730-750.  Abstract ( 199 )   RICH HTML   PDF (538KB) ( 123 )   Save In this paper, applying the time scales calculus theory, we first study the permanence for a non-autonomous two species competitive system with feedback controls on time scales. Based on the permanence result, by the comparison theorems of the differential equation and constructing a suitable Lyapunov functional, we establish sufficient conditions on the existence of almost periodic solution of the considered system. Moreover, an example along with its numerical simulation is employed to illustrate effectiveness of our main results. References | Related Articles | Metrics

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Optimal Dividend Strategy in Compound Binomial Dual Model with Bounded Dividend Rates and Periodic Dividend Payments You Lingyun, Tan Jiyang, Li Ziqiang, Zhang Hanjun Acta mathematica scientia,Series A. 2017, 37 (4):  751-766.  Abstract ( 200 )   RICH HTML   PDF (784KB) ( 133 )   Save In this paper, we discusses the problem of optimal dividend payment in compound binomial dual model with bounded dividend rates and periodic dividend payments. Through transforming the value function, we obtain some properties of the optimal dividend payment strategy, and show that the optimal value function is the unique solution of a discrete HamiltonJacobi-Bellman equation. Meanwhile, a simple algorithm is obtained for the optimal strategy and the optimal value function. According to the properties of the optimal dividend strategy, an upper bound and a lower bound of the optimal value function are derived. Numerical examples are presented to illustrate the transformation method. References | Related Articles | Metrics

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Dynamic Analysis and Chaos Control of a Finance System with Delayed Feedbacks Yang Jihua, Zhang Erli, Liu Mei Acta mathematica scientia,Series A. 2017, 37 (4):  767-782.  Abstract ( 206 )   RICH HTML   PDF (1046KB) ( 263 )   Save We investigate the effect of delayed feedbacks on a finance system. Choosing the delays as the bifurcation parameters, the local stability of the equilibrium is studied and the Hopf bifurcation and Hopf-zero bifurcation happen while the delay passes through a sequence of critical values. For determining the properties of bifurcating periodic solutions, we derive explicit formulae by using the normal form method and the center manifold theory. By designing appropriate feedback strength and delay, chaotic oscillation can be controlled to be a stable equilibrium or stable periodic orbits. Finally, a numerical example is taken to confirm the theoretical results. References | Related Articles | Metrics

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The Analysis of Global Stability and Numerical Simulation of Chaos Behaviors of Rotating Flow Wang Heyuan, Cui Jin Acta mathematica scientia,Series A. 2017, 37 (4):  783-792.  Abstract ( 285 )   RICH HTML   PDF (10435KB) ( 162 )   Save There has been a very large number of experimental and theoretical studies of flow between concentric rotating cylinders in the century, since these pioneering works, the instability of Couette flow and Taylor vortex flow, now known as the "Couette-Taylor Problem" is a paradigm of nonlinear problem. this paper will investigate the problem of some dynamical behaviors and numerical simulation of Couette-Taylor flow between two concentric rotating cylinders. Dynamical behaviors of a three-model Lorenz-like system of Couette-Taylor flow have been discussed, such as evolutionary history of bifurcation and chaos of this low-dimensional model, as well as the analysis of global stability etc. References | Related Articles | Metrics