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26 June 2018, Volume 38 Issue 3 Previous Issue    Next Issue

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Several Integrals of Quaternionic Field on Hyperbolic Matrix Space Shu Fuwen, Shen Yougen Acta mathematica scientia,Series A. 2018, 38 (3):  417-432.  Abstract ( 118 )   RICH HTML PDF (423KB) ( 97 )   Save Some integrals of matrix spaces over a quaternionic field have been calculated in this work. The associated volume of hyperbolic matrix spaces over a quaternionic field has also been calculated by making use of these integrals, and it is of great significance in calculating related kernel functions of these spaces. References | Related Articles | Metrics

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The Schwarz-Pick Lemma for Bounded Pluriharmonic Mappings in the Unit Ball of Cn Huang Ziyan, Zhao Di, Li Hongyi Acta mathematica scientia,Series A. 2018, 38 (3):  433-445.  Abstract ( 126 )   RICH HTML PDF (342KB) ( 160 )   Save In this paper, we extend the classical Schwarz-Pick lemma to the n-dimension complex space Cn, and obtain the Schwarz-Pick lemma for bounded pluriharmonic mappings from the unit ball in Cn to the unit disk in the complex plane. References | Related Articles | Metrics

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On the Invariance of Maximal Distributional Chaos of Weighted Shift Operators on ∑(X) Wang Jianjun Acta mathematica scientia,Series A. 2018, 38 (3):  446-453.  Abstract ( 133 )   RICH HTML PDF (327KB) ( 102 )   Save This paper proves that the weighted shift operator Bw on an normed linear space ∑(X) admits an invariant distributionally ε-scrambled set for any 0 < ε < 2, improving the main results of[27, 32]. References | Related Articles | Metrics

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Boundary Optimal Control for the Timoshenko Beam Zhang Chunguo, Liu Yubiao, Liu Weiwei Acta mathematica scientia,Series A. 2018, 38 (3):  454-466.  Abstract ( 123 )   RICH HTML PDF (348KB) ( 88 )   Save This paper studies the boundary optimal control problem governed by a Timoshenko beam equation. Firstly, the well posedness of the system is token by using the theory of the linear operator semigroup. Based on the objective function, the optimality principle (the maximum principle) and the corresponding optimal control are obtained by using the adjoint system. Finally, by the eigenfunction asymptotic expansion of the homogeneous system, the exhaustive calculation steps of optimal control and optimal trajectory are given. References | Related Articles | Metrics

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Estimates for Eigenvalues of the Operator in Divergence Form on H-Type Group Tan Shenyang, Huang Tiren, Liu Dajin Acta mathematica scientia,Series A. 2018, 38 (3):  467-475.  Abstract ( 85 )   RICH HTML PDF (300KB) ( 89 )   Save In this paper, we investigate the eigenvalue problem of the operator in divergence form -divG+〈▽G,▽Gψ〉+V on Heisenberg-type group. we obtain a first Yang-type inequality for eigenvalues of this problem. We also get second Yang type inequality. References | Related Articles | Metrics

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The Essential Spectra of Infinite Dimensional Hamilton Operator Li Yudan, Wu Deyu, Alatancang Acta mathematica scientia,Series A. 2018, 38 (3):  476-483.  Abstract ( 109 )   RICH HTML PDF (310KB) ( 105 )   Save In this paper, the essential spectra of infinite dimensional Hamilton operator on Hilbert spaces is studied. Under perturbations belonging to any closed two-sided ideal of the algebra of bounded linear operators contained in the set of Fredholm perturbations, the relationship between the essential spectra of infinite dimensional Hamilton operator and the essential spectra of its Schur complement is given. References | Related Articles | Metrics

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The Deficiency Index of a Class of Sturm-Liouville Operators with an Infinite Number of Interior Discontinuous Points Zhao Yingchun, Sun Jiong Acta mathematica scientia,Series A. 2018, 38 (3):  484-495.  Abstract ( 109 )   RICH HTML PDF (342KB) ( 82 )   Save In this paper, we study a class of Sturm-Liouville problems with an infinite number of interior discontinuous points, i.e., Sturm-Liouville problems with an infinite number of discontinuous conditions at interior points. Firstly, we construct a new Hilbert space associated with the discontinuous conditions and define the maximal and minimal operators associated with the discontinuous conditions in the new Hilbert space. And then we discuss the deficiency index of the minimal operator associated with the discontinuous conditions in the new Hilbert space. References | Related Articles | Metrics

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Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence Zou Xia, Wu Shiliang Acta mathematica scientia,Series A. 2018, 38 (3):  496-513.  Abstract ( 134 )   RICH HTML PDF (415KB) ( 270 )   Save This paper is concerned with the traveling waves of a nonlocal dispersal SIR epidemic model with delay and nonlinear incidence. The threshold dynamics are determined by the basic reproduction number R0 and the minimal wave speed c*. First, when c > c*, R0 > 1, the existence of the traveling waves is proved by applying Schauder's fixed point theorem and a limiting argument. Then, when 0 < c < c*, R0 > 1 or R0 ≤ 1, the non-existence of traveling wave solutions is established by two-side Laplace transform. References | Related Articles | Metrics

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Infinitely Many Solutions for a Bi-Nonlocal Problem Involving p(x)-Laplacian-Like Operator Zhang Shengui Acta mathematica scientia,Series A. 2018, 38 (3):  514-526.  Abstract ( 89 )   RICH HTML PDF (363KB) ( 89 )   Save In this article, we study a class of bi-nonlocal Dirichlet problem involving p(x)-Laplacian-like operator via variational methods. Using the fountain theorem and the symmetric mountain pass theorem, the existence of a sequence of high and low energy solutions for this problem are obtained, respectively. References | Related Articles | Metrics

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On Convexity for Energy Decay Rates of the Second-Order Evolution Equation with Memory and Time-Varying Delay Liu Gongwei, Diao Lin Acta mathematica scientia,Series A. 2018, 38 (3):  527-542.  Abstract ( 125 )   RICH HTML PDF (373KB) ( 120 )   Save In this paper, we consider the following abstract evolution equation with memory and time-varying delay of the form#br#utt(t) + Au(t)-∫0t g(t-s)Au(s)ds + μ1h1(ut(t)) + μ2h2(ut(x, t-τ(t)))=▽F(u(t)).#br#By introducing suitable energy and Lyapunov functionals, and making use of some properties of the convex functions, we establish decay estimate for the energy, which depends on the behavior of h1 and the relaxation g. The decay estimate can be applied to various concrete models. We shall also give some applications to illustrate our result. References | Related Articles | Metrics

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Positive Periodic Solution for Damped Duffing Equation with Singularity Yao Shaowen, Cheng Zhibo Acta mathematica scientia,Series A. 2018, 38 (3):  543-548.  Abstract ( 142 )   RICH HTML PDF (234KB) ( 103 )   Save By using Manasevich-Mawhin continuation theorem and some analysis skill, we establish some sufficient condition for existence of positive T -periodic solutions for a kind of damped Duffing equation with singularity. The results of this paper are new and they complement previous known results. References | Related Articles | Metrics

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Logarithmical Regularity Criteria in Terms of Pressure for the Three Dimensional Dissipative System Modeling Electro-Hydrodynamics Zhao Jihong Acta mathematica scientia,Series A. 2018, 38 (3):  549-564.  Abstract ( 131 )   RICH HTML PDF (422KB) ( 91 )   Save In this paper, logarithmically improved regularity criteria for the Navier-Stokes/Poisson-Nernst-Planck system are established in terms of both the pressure and the gradient of pressure in the homogeneous Besov spaces. References | Related Articles | Metrics

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Uniform Estimates in Time for the Solution to a Fluid-Particle Model Lin Jiaoyan Acta mathematica scientia,Series A. 2018, 38 (3):  565-570.  Abstract ( 141 )   RICH HTML PDF (222KB) ( 63 )   Save In the paper, we consider a fluid-particle model and study the uniform estimates in time for the solution. The main tools are energy method and uniform Gronwall inequality. References | Related Articles | Metrics

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A Type of New Lower Order Nonconforming Mixed Finite Elements Methods for the Extended Fisher-Kolmogorov Equation Zhang Houchao, Wang Junjun, Shi Dongyang Acta mathematica scientia,Series A. 2018, 38 (3):  571-587.  Abstract ( 109 )   RICH HTML PDF (522KB) ( 105 )   Save The purpose of this paper is to study the mixed finite element methods with a type of lower order nonconforming finite elements for the extended Fisher-Kolmogorov(EFK) equation. Firstly, a nonconforming mixed finite element scheme is established by splitting the EFK equation into two second order equations through a intermediate variable v=-△u. Some a priori bounds are derived by use of Lyapunov functional, existence and uniqueness for the approximation solutions are also proved. The optimal error estimates for both the primitive solution u and the intermediate variable v in H1-norm are deduced for semi-discrete scheme by use of the above priori bounds and properties of the elements. Furthermore, the superclose properties with order O(h2) are obtained through high accuracy results of the elements. Secondly, a new linearized backward Euler full-discrete scheme is established. The optimal error estimates and superclose results for u and v in H1-norm with orders O(h+τ) and O(h2 +τ) are obtained respectively through the new splitting techniques for consistency errors and nonlinear terms. Here, h, τ are parameter of the subdivision in space and time step. Finally, numerical results are provided to confirm the theoretical analysis. Our analysis provides a new understanding with nonconforming mixed finite element methods to analyze other fourth order initial boundary value problems. References | Related Articles | Metrics

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Iterative Learning Control for Second Order Hyperbolic Distributed Parameter Systems Based on Finite Differential Method Li Xiangdong, Fu Qin, Wu Jianrong Acta mathematica scientia,Series A. 2018, 38 (3):  588-598.  Abstract ( 101 )   RICH HTML PDF (490KB) ( 84 )   Save In this paper, the iterative learning control for distributed parameter systems based on finite differential method is considered. Here, the considered distributed parameter systems are composed of second order hyperbolic partial differential equations. According to the initialboundary conditions of the systems, iterative learning control laws are proposed based on finite differential method. Using the iterative converge principle, we show that the schemes can guarantee the state tracking errors can converge to a small region of the origin along the iteration axis. Finally, the simulation result verifies the effectiveness of the proposed algorithm. References | Related Articles | Metrics

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Convergence Analysis of Iterative Learning Control for Linear Continuous-Time Switched Systems with Arbitrary Time-Driven Switching Rules Yang Xuan, Ruan Xiaoe, Wang Peng Acta mathematica scientia,Series A. 2018, 38 (3):  599-612.  Abstract ( 137 )   RICH HTML PDF (445KB) ( 58 )   Save This paper addresses the convergence performance of first-order and higher-order PD-type iterative learning control strategies for a class of linear continuous-time switched systems. The manipulated systems are elaborated by arbitrary time-driven switching signals and can repetitively operate over a finite time interval. By employing the generalized Young inequality of convolution integral theoretical analysis is launched in the sense of Lebesgue-p norm. Simultaneously, sufficient convergence conditions of the algorithms are derived and the effect of the state matrices on the learning performance is quantized. To illustrate the validity and effectiveness of the theoretical results, numerical simulations are conducted. References | Related Articles | Metrics

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Emission SPECT Image Reconstruction Methods with Uniformly Attenuated Projection Data Ye Liying, Li Jing, Wang Jinping Acta mathematica scientia,Series A. 2018, 38 (3):  613-624.  Abstract ( 115 )   RICH HTML PDF (480KB) ( 94 )   Save In this work, we give some basic inversion formulae of the exponential Radon transform; then we study emission SPECT reconstruction methods with uniformly attenuated projection data. We construct an intermediate function by the dual operator and obtain the inversion formula by use of the intermediate function, and we extend it to the fan-beam projection case. Finally we develop the numerical implementation of the finite weighted Hilbert transform. References | Related Articles | Metrics