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26 June 2017, Volume 37 Issue 3 Previous Issue    Next Issue

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Common Fixed Point Results for Generalized Weak Contractions with a Rational Expression in Ordered Partial Metric Spaces Song Jiping, Wang Maofa Acta mathematica scientia,Series A. 2017, 37 (3):  401-415.  Abstract ( 173 )   RICH HTML   PDF (350KB) ( 117 )   Save In this paper, some common fixed point results for four mappings satisfying generalized weakly contractive conditions with a rational type expression are obtained in partially ordered complete partial metric spaces. A sufficient condition for the uniqueness of common fixed point is proved, an examples are given to support our results, and also, a homotopy result, as an application, is discussed. References | Related Articles | Metrics

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Decomposition Theorems for F(p,q,s) Spaces on the Unit Ball of Cn Zhao Yang, Peng Ru Acta mathematica scientia,Series A. 2017, 37 (3):  416-426.  Abstract ( 112 )   RICH HTML   PDF (333KB) ( 118 )   Save This paper is devoted to studying the decomposition of functions of F(p,q,s) spaces in the unit ball of Cn, which contain many classical function spaces, such as Bloch space, BMOA space and Qs spaces. By means of s-Carleson measure and Schur's Theorem, we characterize the decomposition theorems for F(p,q,s) spaces in the unit ball of Cn for the case of 1 < p < ∞. References | Related Articles | Metrics

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Spectral Theory of Linear Weighted Sturm-Liouville Eigenvalue Problems Luo Hua Acta mathematica scientia,Series A. 2017, 37 (3):  427-449.  Abstract ( 146 )   RICH HTML   PDF (456KB) ( 120 )   Save This paper discusses some global results on eigenvalue and zero distribution for eigenfunction of the linear weighted Sturm-Liouville eigenvalue problem on time scales. We obtain Sturm comparison theorem and Sturm separation theorem and prove the existence of the smallest positive eigenvalue and the corresponding positive eigenfunction. References | Related Articles | Metrics

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Hölder Inequality of Unitarily Invariant Norms for Matrices and Its Applications Zou Limin, Wu Yanqiu Acta mathematica scientia,Series A. 2017, 37 (3):  450-456.  Abstract ( 178 )   RICH HTML   PDF (237KB) ( 124 )   Save The relationship between two existing Hölder inequalities of unitary invariant norms for matrices is discussed. Meanwhile, we present some inequalities of unitarily invariant norms for matrices by using Hölder inequality of unitary invariant norms for matrices and some existing inequalities of unitary invariant norms. Our results are generalizations or refinements of ones shown Alakhrass and Lee. References | Related Articles | Metrics

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A Truncation Method Based on Hermite Functions Expansion for a Cauchy Problem of the Laplace Equation Xie Ou, Meng Zehong, Zhao Zhenyu, You Lei Acta mathematica scientia,Series A. 2017, 37 (3):  457-468.  Abstract ( 155 )   RICH HTML   PDF (387KB) ( 118 )   Save We investigate a Cauchy problem for the Laplace equation in this paper. To obtain a stable numerical solution for this ill posed problem, we present a truncation method based on Hermite functions expansion. Error estimate are obtained together with a discrepancy principle for the regularization parameter. Some numerical tests show that the method works effectively. References | Related Articles | Metrics

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Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs Xiong Jun, Li Junmin, He Chao Acta mathematica scientia,Series A. 2017, 37 (3):  469-477.  Abstract ( 160 )   RICH HTML   PDF (662KB) ( 131 )   Save This paper deals with the problem of fuzzy boundary control design for a class of semi-linear hyperbolic PDEs. A Takagi-Sugeno (T-S) fuzzy PDE model is applied to accurately represent the semilinear hyperbolic PDEs system via fuzzy control approach. Based on the T-S fuzzy PDE model, the fuzzy boundary controllers, which is easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and presented in term of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of the examples. References | Related Articles | Metrics

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The Existence Theorem for a Qusi-Linear Elliptic Equations Involving Critical Sobolev Exponent on the Heisenberg Group Liu Lijing, Liu Xiaochun Acta mathematica scientia,Series A. 2017, 37 (3):  478-490.  Abstract ( 135 )   RICH HTML   PDF (350KB) ( 113 )   Save In this paper, we study the partial differential equations on the Heisenberg group with a singular potential and critical Sobolev exponent. With the help of Nehari manifold, we prove that our problem has at least one or two positive solutions under different conditions. The result generalized the corresponding result in Euclidean space. References | Related Articles | Metrics

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The Existence of Two Non-Negative Solutions for the Generalized Choquard-Pekar Equation Li Jinju, Zhang Zhengjie Acta mathematica scientia,Series A. 2017, 37 (3):  491-498.  Abstract ( 121 )   RICH HTML   PDF (293KB) ( 222 )   Save In the paper, we used variational method to study the generalized Choquard-Pekar equation on RN. We get that there exists two non-negative solutions for our problem, one solution is a local minimum and the other is of the mountain pass type. References | Related Articles | Metrics

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C2+α Local Solvability of the k-Hessian Equations Ba Na, Tian Fanji, Zheng Lie Acta mathematica scientia,Series A. 2017, 37 (3):  499-509.  Abstract ( 119 )   RICH HTML   PDF (369KB) ( 151 )   Save Overcoming the difficulty arising from the fact that the linearized operators of the elliptic k-Hessian ones do not satisfy the Maximum principle and employing Nash-Moser iteration, we prove the existence of C2+α local solutions of k-Hessian equation when the nonhomogeneous term f ∈ Cα changes sign or is nonnegative. Of course there exists C∞ local solution if f ∈ C∞. The technique is that, for the solution to the linearized equation, we prefer at first to prove its uniqueness from which the existence of solution, together with the higher regularity and a priori estimates of solutions, follows. References | Related Articles | Metrics

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The Existence of Minimizers for a Class of Constrained Variational Problem with Its Concentration Behavior Gu Longjiang, Sun Zhiyu, Zeng Xiaoyu Acta mathematica scientia,Series A. 2017, 37 (3):  510-518.  Abstract ( 150 )   RICH HTML   PDF (301KB) ( 159 )   Save In this paper, we mainly discuss the existence and non-existence of minimizers for the variational functional of a p-Laplacian eigenvalue problem involving harmonic potential. Moreover, the concentration behavior of the minimizers is also investigated by using the energy method when the related parameter closes to a critical value. References | Related Articles | Metrics

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The Topological Hausdorff Dimension of a Class of Fractal Squares Dai Yuxia, Ke Feng, Li Qing Acta mathematica scientia,Series A. 2017, 37 (3):  519-527.  Abstract ( 155 )   RICH HTML   PDF (907KB) ( 134 )   Save Balka, Buczolich, Elekes introduced a new concept of dimension for metric space, the so called topological Hausdorff dimension in[1]. The value of the topological Hausdorff dimension is always between the topological dimension and Husdorff dimension. Let n ≥ 2, D=d1,d2,…dm⊆0,1,…,n-12 be a digit set. The set F satisfying the set equation F=1/n(F+D) is called a fractal square. In this paper, we mainly discuss the Topological Hausdorff Dimension of F in the case n=3, m ≤ 5. References | Related Articles | Metrics

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A Note on Distortion Theorem for Biholomorphic Convex Mappings on the Unit Ball Lu Jin Acta mathematica scientia,Series A. 2017, 37 (3):  528-533.  Abstract ( 105 )   RICH HTML   PDF (262KB) ( 119 )   Save In this paper, applied the Schwarz lemma at the boundary of the unit ball in Cn, we give a new and simple proof of the distortion theorem for biholomorphic convex mappings on the unit ball. References | Related Articles | Metrics

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Ergodic Theorems of Periodic Discrete Dynamical Systems Huang Qiuling, Shi Yuming, Zhang Lijuan Acta mathematica scientia,Series A. 2017, 37 (3):  534-543.  Abstract ( 117 )   RICH HTML   PDF (356KB) ( 141 )   Save This paper focuses on ergodic theorems for periodic discrete systems. The mean ergodic theorem in Hilbert spaces and ergodic theorems for autonomous dynamical systems are generalized to periodic discrete systems, including von Neumann mean ergodic theorem and Birkhoff pointwise ergodic theorem. References | Related Articles | Metrics

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A General Result of Precise Asymptotics in Complete Moment Convergence for ρ-mixing Sequence Fu Zongkui, Wu Qunying Acta mathematica scientia,Series A. 2017, 37 (3):  544-552.  Abstract ( 88 )   RICH HTML   PDF (298KB) ( 108 )   Save Let X,Xn;n ≥ 1 be a strictly stationary sequence of ρ-mixing random variables with mean zeros, if some conditions are satisfied, by the weak convergence theorem and moment inequalities of ρ-mixing random variables, a general result on precise asymptotics for ρ-mixing random variables, then the known results of this field are improved and extended. References | Related Articles | Metrics

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Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls Fu Jinbo, Chen Lansun Acta mathematica scientia,Series A. 2017, 37 (3):  553-561.  Abstract ( 135 )   RICH HTML   PDF (379KB) ( 122 )   Save In this paper, by using species dynamic theory, a delay nonautonomous LotkaVolterra multiple species competition system with ecological environment and feedback controls is established, and the high order nonlinear function is used in the construction of the feedback control variables. By using Continuation Theorem based on Gaines and Mawhin's coincidence degree theory, the sufficient conditions for existence of positive periodic solution of the system are obtained. Using Barbalat Lemma and constructing an appropriate Lyapunov function, the algebraic criterion for the uniqueness and global attractivity of positive periodic solutions of the system are obtained. References | Related Articles | Metrics

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Augmented Lagrangian Method for Matrix Equation Least-squares Problem Under a Matrix Inequality Constraint Li Jiaofen, Song Dandan, Zhou Xuelin, Xing Yumeng Acta mathematica scientia,Series A. 2017, 37 (3):  562-576.  Abstract ( 149 )   RICH HTML   PDF (452KB) ( 119 )   Save We say that a matrix X∈Rm×n is real (R, S) symmetric matrix if X=RXS, where R∈Rm×m and S∈Rn×n are real nontrivial involutions; thus R=R-1≠±Im, S=S-1≠±In. In this paper we apply the augmented Lagrangian method, for minimizing general smooth functions on convex sets in optimization theory, to solve the (R, S) symmetric matrix least squares problem under a linear inequality constraint. That is, given positive integers m, n, p, t, q, matrices Ai∈Rm×m, Bi∈Rn×n (i=1,2,…,q), C∈Rm×n, E∈Rp×m, F∈Rn×t and D∈Rp×t, find a (R, S) symmetric matrix X∈Rm×n that minimize||AiXBi-C||under matrix inequality constraint EXF ≥ D, where EXF-D means that matrix EXF -D nonnegative. We present matrix-form iterative format basing on the augmented Lagrangian method to solve the proposed problem and give some numerical examples to show that the iterative method is feasible and effective. References | Related Articles | Metrics

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Dynamics Analysis of an Ebola Epidemic Model Wei Aiju, Zhang Xinjian, Wang Junyi, Li Kezan Acta mathematica scientia,Series A. 2017, 37 (3):  577-592.  Abstract ( 191 )   RICH HTML   PDF (1249KB) ( 140 )   Save In this paper, we consider the human-animal coupling epidemic where an Ebola epidemic model with isolation compartment and animal compartment is proposed. Then, the basic reproductive number is obtained by using the method of the second generation matrix. Applying the stability theory and dynamical system theory, we prove both the existence and global stability of disease-free equilibrium, boundary equilibrium and coexistence equilibrium. Moreover, sensitivity analysis of model's parameters is also performed. Finally, the theoretical results are all verified by numerical simulations. This work has important significance for guiding us to prevent and control the Ebola spread. References | Related Articles | Metrics