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26 October 2018, Volume 38 Issue 5 Previous Issue    Next Issue

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Covering Surface Inequality on the Ring and Its Applications Xiaojing Guo,Daochun Sun Acta mathematica scientia,Series A. 2018, 38 (5):  833-841.  Abstract ( 146 )   RICH HTML PDF (315KB) ( 385 )   Save The main purpose of this paper is to give the covering surface inequality for the meromorphic function on the ring, which studies the problem on ring sequence and promotes the classic Picard theorem. Furtherly, we use Valiron type function to obtain the Borel theorem for the finite positive meromorphic function on the infinite ring sequence. References | Related Articles | Metrics

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The Farkas Lemmas for Fractional Optimization Problem with Composite Functions Donghui Fang,Weilin Liu Acta mathematica scientia,Series A. 2018, 38 (5):  842-854.  Abstract ( 133 )   RICH HTML PDF (332KB) ( 119 )   Save In this paper, the fractional optimization problem with composite functions is turned into a constraint optimization problem by using the previous method. By introducing some news constraint qualifications, some duality results for the constraint optimization problem are established and some Farkas type lemmas for the fractional optimization problem with composite functions are then given. References | Related Articles | Metrics

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Improvements of Fixed Point Theorems for Mappings with ${\cal A}$-Contractions on Metric Spaces Yongjie Piao Acta mathematica scientia,Series A. 2018, 38 (5):  855-863.  Abstract ( 131 )   RICH HTML PDF (291KB) ( 234 )   Save In this paper, we introduce a new class ${\cal A}$* of 3-dimensional functions, which is a generalization of a known class ${\cal A}$, obtain a fixed point theorem for a mapping and a common fixed point theorem for a infinite family of mappings, and discuss the existence problems of fixed points for a mapping on a nonempty set with two metrics under the non-continuity and non-completeness. The obtained results generalize and improve many known conclusions. References | Related Articles | Metrics

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Lie Derivable Maps on von Neumann Algebras Lichun Yang,Runling An Acta mathematica scientia,Series A. 2018, 38 (5):  864-872.  Abstract ( 92 )   RICH HTML PDF (268KB) ( 129 )   Save Let ${\cal A}$ be a von Neumann algebra with no central abelian projections, $P\in{\cal A}$ be a projection with $\underline{P}=0$ and $\overline{P}=I$. An additive map $\delta:{\cal A}\rightarrow{\cal A}$ is said to be Lie derivable at $\Omega\in{\cal A}$, if $\delta([A, B])=[\delta(A), B]+[A, \delta(B)]$ for any $A, B\in{\cal A}$ with $AB=\Omega.$ We show that, if $\Omega\in{\cal A}$ such that $P\Omega=\Omega$, then $\delta$ is Lie derivable at $\Omega$ if and only if there exist a derivation $\tau:{\cal A} \rightarrow {\cal A}$ and and additive map $f: {\cal A}\rightarrow {\cal Z}({\cal A})$ vanishing at commutators $[A, B]$ with $AB=\Omega$ such that $\delta(A)=d(A)+f(A), \forall A\in {\cal A}.$ In particular, if ${\cal A}$ is a factor von Neuamnn algebra and $\Omega\in {\cal A}$ such that $\mbox{ker}(\Omega)\neq {0}$ or $\overline{\mbox{ran}(\Omega)}\neq H,$ then $\delta$ is Lie derivable at $\Omega$ if and only if it has the above form. References | Related Articles | Metrics

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Multigrid Uzawa-Type Mixed Finite Element Methods for Nearly Incompressible Linear Elasticity Problem Zhihao Ge,Yuanyuan Ge Acta mathematica scientia,Series A. 2018, 38 (5):  873-882.  Abstract ( 78 )   RICH HTML PDF (393KB) ( 106 )   Save In this paper, we propose two new multigrid Uzawa-type mixed finite element methods for the nearly incompressible elasticity problem, which could overcome the 'locking' phenomenon. By introducing an extra pressure variable, we reformulate the elasticity problem into a saddle-point system, and by coupling the Uzawa-type method with multigrid methods, we develop two effective iteration methods:multigrid Uzawa-type mixed finite element method and nested iteration multigrid Uzawa-type mixed finite element method. Also, we present the convergent results of the algorithms. The methods are locking-free and stable for any finite element pairs spaces. Finally, we give some numerical examples to verify the theoretical results of the paper. Figures and Tables | References | Related Articles | Metrics

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Derivation of a Higher Order Nonlinear Schrödinger Equation with Complete Coriolis Force Danni Wang,Hongli Yang,Liangui Yang Acta mathematica scientia,Series A. 2018, 38 (5):  883-892.  Abstract ( 97 )   RICH HTML PDF (392KB) ( 122 )   Save In this paper, based on the barotropic potential vorticity equation with complete Coriolis force, a new higher order nonlinear Schrödinger equation is derived by using perturbation expansion method to describe nonlinear modulated Rossby waves in the geophysical fluid. From this equation, the modulational wave trains are discussed. It is found that the horizontal component term of Coriolis force and the topography term has an effect on the uniform Rossby wave trains and the instability region have changed. In addition, the uniform background basic flow does affect the modulational instability of solitary Rossby wave train. Figures and Tables | References | Related Articles | Metrics

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Existence and Concentration of Nontrivial Solutions for the Fractional Schrödinger Equations with Sign-Changing Steep Well Potential Wenbo Wang,Quanqing Li Acta mathematica scientia,Series A. 2018, 38 (5):  893-902.  Abstract ( 122 )   RICH HTML PDF (373KB) ( 105 )   Save Consider the following fractional Schrödinger equation $\begin{equation}\renewcommand{\theequation}{$P_{\lambda}$} (-\Delta)^{s}u+\lambda V(x)u+V_{0}(x)u=P(x)|u|^{p-2}u+Q(x)|u|^{q-2}u, ~~~~~x\in {\Bbb R}^{N}, \end{equation}$ where $\lambda>0$, $s\in(0, 1)$, $N>2s$, $2<q<p<2_{s}^{\ast}$ ($2_{s}^{\ast}=\frac{2N}{N-2s}$), $P\in L^{\infty}$ is positive, $Q\in L^{\infty}$ may be positive, sign-changing or negative, $V$ is steep well potential, and $V_{0}\in L^{\infty}$. When $\lambda$ is large, the existence of nontrivial solutions is obtained via variational methods. Furthermore, if $V(x)\geq0$, concentration results are also obtained. In particular, the potential $V$ is allowed to be sign-changing for the existence. References | Related Articles | Metrics

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Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay Jun Wang,Tianlu Wang,Yanhua Wen,Xianfeng Zhou Acta mathematica scientia,Series A. 2018, 38 (5):  903-910.  Abstract ( 82 )   RICH HTML PDF (313KB) ( 115 )   Save The existence of global solutions of initial value problems (IVP) for differential equations is a precondition to study their stability in Lyapunov sense. This paper aims to investigate the existence of the global solutions of the IVP (1.10)-(1.11). The existence of a local solution of the IVP (1.10)-(1.11) is obtained first, which is an extension of the paper[14]. Then based on our extension theorem, we prove that the existence and uniqueness of the global solution of the IVP (1.10)-(1.11). References | Related Articles | Metrics

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Lower Bound of Blow-Up Time for a p-Laplacian Equation with Nonlocal Source Baoyan Sun Acta mathematica scientia,Series A. 2018, 38 (5):  911-923.  Abstract ( 114 )   RICH HTML PDF (364KB) ( 115 )   Save In this paper, we consider an initial boundary value problem for a p-Laplacian equation under Dirichlet boundary condition or Robin boundary condition in three dimensional space. We use a differential inequality technique to determine a lower bound of blow-up time for the blow-up solution. In addition, we also give a sufficient condition which implies that blow-up does not occur. References | Related Articles | Metrics

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Random Attractor for Non-Autonomous Stochastic Boussinesq Lattice Equations with Additive White Noises Min Zhao,Shengfan Zhou Acta mathematica scientia,Series A. 2018, 38 (5):  924-940.  Abstract ( 87 )   RICH HTML PDF (427KB) ( 47 )   Save In this paper, we study the asymptomatic behavior of non-autonomous stochastic Boussinesq lattice equations with time-dependent coupled coefficients, time-dependent deterministic forces and additive white noises. Firstly, we prove the existence of a random attractor for the continuous cocycle generated by the solutions of the non-autonomous stochastic Boussinesq lattice equations. Lastly we establish the upper semi-continuity of random attractors for the random systems as the intensity of the noises tends to zero. References | Related Articles | Metrics

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Exponential Attractors of 3D Benjamin-Bona-Mahony Equations Xudong Luo,Qiaozhen Ma Acta mathematica scientia,Series A. 2018, 38 (5):  941-953.  Abstract ( 74 )   RICH HTML PDF (344KB) ( 253 )   Save In this paper, we investigate the existence of exponential attractors of the three dimensional Benjamin-Bona-Mahony equation in the case that both the autonomous and nonautonomous systems, which extend and improve some previous results. References | Related Articles | Metrics

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A Class of Modified Non-Monotonic Spectral Conjugate Gradient Method and Applications to Non-Negative Matrix Factorization Xiangli Li,Juanjuan Shi,Xiaoliang Dong Acta mathematica scientia,Series A. 2018, 38 (5):  954-962.  Abstract ( 99 )   RICH HTML PDF (404KB) ( 111 )   Save Spectral conjugate gradient algorithm is an effective method to solve unconstrained optimization problems. It is based on the conjugate gradient method and combines the spectral method to maintain the advantages of the two methods. In this paper, we propose a class of modified non-monotonic spectral conjugate gradient algorithm, under certain assumptions, the convergence of the algorithm is proved. In addition, we applied the algorithm to the nonnegative matrix factorization, and the numerical results show that the algorithm is effective. Figures and Tables | References | Related Articles | Metrics

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Study on the Convergence of Nonhomogeneous Markov Chains with Probability Distance Zhifeng Zhu,Shaoyi Zhang Acta mathematica scientia,Series A. 2018, 38 (5):  963-969.  Abstract ( 105 )   RICH HTML PDF (280KB) ( 91 )   Save In this paper, we study the convergence of nonhomogeneous Markov chains in general state space by using the probability distance and the coupling property, a condition for convergence of nonhomogeneous Markov chains in general state space is obtained. References | Related Articles | Metrics

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Razumikhin-Type Theorems on P-th Moment and Almost Sure Stability of Neutral Stochastic Switched Nonlinear Systems Haibo Gu,Caixia Gao Acta mathematica scientia,Series A. 2018, 38 (5):  970-983.  Abstract ( 86 )   RICH HTML PDF (436KB) ( 126 )   Save In this paper, P-th moment and almost sure stability for a class of neutral stochastic switched nonlinear systems have been investigated. By utilizing Lyapunov-Razumikhin approach, we employ the stochastic analysis techniques to establish novel stability criteria for neutral stochastic switched nonlinear systems. Some sufficient conditions have been derived to check the stability of the neutral stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the results. Figures and Tables | References | Related Articles | Metrics

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Stationary Distribution and Periodic Solution for Stochastic Predator-Prey Systems with Holling-Type Ⅲ Functional Response Guijie Lan,Yingjie Fu,Chunjin Wei,Shuwen Zhang Acta mathematica scientia,Series A. 2018, 38 (5):  984-1000.  Abstract ( 133 )   RICH HTML PDF (1105KB) ( 130 )   Save In this paper, we investigate the dynamics of stochastic predator-prey systems with Holling-type Ⅲ functional response. For the autonomous system, we firstly obtain that the system admits unique positive global solution starting from the positive initial value. Then, by comparison theorem for stochastic differential equation, sufficient conditions for extinction and persistence in mean are obtained. Thirdly, by constructing some suitable Lyapunov function, we prove that there are unique stationary distribution and they are ergodic. On the other hand, for the non-autonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Has'minskii. Finally, some numerical simulations are introduced to illustrate our theoretical result. Figures and Tables | References | Related Articles | Metrics

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The Research on a Class of the Predator-Prey-Mutualist System with Delays Lifei Zheng,Jie Guo,Meihua Wu,Xiaorui Wang,Aying Wan Acta mathematica scientia,Series A. 2018, 38 (5):  1001-1013.  Abstract ( 124 )   RICH HTML PDF (594KB) ( 312 )   Save In this paper, we establish a predator-prey-mutualist system with time delay, and the positive, persistence and local stability of the system are analyzed. The conclusion shows that it is possible that the system is stable, and the positive equilibrium point is asymptotically stable. Finally, numerical simulation with the relevant data in the ecosystem of ladybirds, cotton aphids and ants.The results show that development duration (time delay) of the prey and predator has an important influence on the whole system, and if growth duration is too long, the whole system will have periodic fluctuations. Figures and Tables | References | Related Articles | Metrics

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Analysis of M/G/1 Repairable Queueing System and Optimal Control Policy with a Replaceable Repair Facility Under Delay Min(N, D)-Policy Quyu Pan,Yinghui Tang Acta mathematica scientia,Series A. 2018, 38 (5):  1014-1031.  Abstract ( 134 )   RICH HTML PDF (762KB) ( 92 )   Save This paper considers the M/G/1 repairable queueing system with delay Min(N, D)-policy, in which the repair facility subject to breakdowns and then replaced during the repair facility busy period. By using the total probability decomposition technique and employing the Laplace transform tool, some reliability indices of the service station and the repair facility, such as the transient-state and steady-state unavailability, the expected failure number during (0, t] are discussed. Finally, it is determined the optimal control policy (N*, D*) such that the long-run expected cost rate is minimum under a given cost structure. Figures and Tables | References | Related Articles | Metrics

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Mathematical Modeling and Computer Simulation on Hand, Foot and Mouth Disease in Children Hua Li,Sanhong Liu,Yile Fang,Xingan Zhang Acta mathematica scientia,Series A. 2018, 38 (5):  1032-1040.  Abstract ( 124 )   RICH HTML PDF (538KB) ( 209 )   Save Hand, foot, and mouth disease (HFMD) is a contagious disease mainly caused by the enterovirus 71 (EV71) and coxsackievirus A 16 (CoxA16). The infectious of HFMD is mainly children. In this paper, we construct an SEIHRS model, simulate the HFMD data of infectious from 2012 to 2016, estimate the basic reproductive number each year from 2012 to 2016, predict the infectious number of HFMD in year 2017, compute the domain of vaccination rate on children and put forward the preventive measures and control strategy. The results of this paper can provide a theory basis for disease control and prevention of HFMD. Figures and Tables | References | Related Articles | Metrics