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26 April 2017, Volume 37 Issue 2 Previous Issue    Next Issue

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On an Integral-Type Operator from Dirichlet Spaces to Zygmund Type Spaces on the Unit Ball Zhao Yanhui, Zhang Xuejun Acta mathematica scientia,Series A. 2017, 37 (2):  217-227.  Abstract ( 154 )   RICH HTML PDF (324KB) ( 110 )   Save Some questions of integral-type Operator from Dirichlet space to Zygmund type spaces in the unit ball were studied in this paper. By the methods of functional analysis and several complex variables, the necessary and sufficient conditions are given for integral-type operator to be bounded and compact from Dirichlet space to Zygmund type spaces in the unit ball. References | Related Articles | Metrics

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Stability of Fusion Frame Systems under Perturbation of the Local Frame Vectors Wang Wei, Zhu Yucan Acta mathematica scientia,Series A. 2017, 37 (2):  228-238.  Abstract ( 141 )   RICH HTML PDF (348KB) ( 122 )   Save This paper studies the relation between the two subspaces spanned by a frame sequence and its general perturbed version in Hilbert spaces by using the properties of orthogonal projection and the properties of dual frames. This paper also studies the stability of fusion frame systems under general perturbation of the local frame vectors. Our results generalize and improve the remarkable results which had been obtained by Casazza, Kutyniok and Li. References | Related Articles | Metrics

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The Distortion Estimation for Strongly Spirallike Mappings of Type α Along Unit Direction Liu Aichao, Cui Yanyan, Liu Hao Acta mathematica scientia,Series A. 2017, 37 (2):  239-247.  Abstract ( 152 )   RICH HTML PDF (319KB) ( 97 )   Save Various biholomorphic mappings'distortion estimation have been one of the hot issues studied for the theory of several complex variables. Since the definition of strongly spirallike mappings of type α was presented, the researchers only got growth and covering results, but its distortion estimation have been poorly understood. In response to this situation, we use growth and covering theorem of strongly spirallike mappings of type α, for the first time we obtained the distortion estimation of strongly spirallike mappings of type α in the open unit ball B of a complex Banach spaces and unit polydisc Dn of the European space along unit direction. The results made us have a new understanding for strongly spirallike mappings of type α. References | Related Articles | Metrics

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Convergence and Stability of Ishikawa Type Iterative Sequences for the φ-Hemi Pseudocontractive Operator Pair Wang Xuewu Acta mathematica scientia,Series A. 2017, 37 (2):  248-256.  Abstract ( 159 )   RICH HTML PDF (280KB) ( 87 )   Save In this paper, the stability conceptions for operator pair is introduced. Under the condition that φ(x)/x is nondecreasing, using the different method, we study the convergence and stability of Ishikawa type iterative sequences for the φ-hemi pseudocontrative operator pair. This results presented in this paper extend, improve and perfect the well-known corresponding results in iterative approximation theory. References | Related Articles | Metrics

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Characterizations of Robust Solution for Convex Optimization Problems with Data Uncertainty Sun Xiangkai Acta mathematica scientia,Series A. 2017, 37 (2):  257-264.  Abstract ( 126 )   RICH HTML PDF (311KB) ( 95 )   Save In this paper,we consider robust efficient solutions for a convex optimization problem in the face of data uncertainty. By using the properties of the subdifferential,we first introduce a robust-type subdifferential constraint qualification, and then obtain some completely characterizations of the robust efficient solution of this uncertain convex optimization problem. By using the robust-type subdifferential constraint qualification, we also characterize Wolfe type robust duality for the uncertain convex optimization problem and its uncertain dual problem. References | Related Articles | Metrics

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Complete Moment Convergence for Weighted Sums of ρ-Mixing Random Variable Sequences Qiu Dehua, Duan Zhenghua Acta mathematica scientia,Series A. 2017, 37 (2):  265-277.  Abstract ( 128 )   RICH HTML PDF (342KB) ( 124 )   Save In this paper, we discuss complete moment convergence for weighted sums of -mixing random variables. Complete moment convergence theorems for weighted sums of -mixing random variable sequences are obtained by utilizing the Rosenthal maximal type inequality, which generalize and extend the well-known results in the literature. References | Related Articles | Metrics

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An Application of the Method of Moving Sphere in the Heisenberg Group——Liouville Type Theorem of a Class of Semilinear Equations Zhang Shutao, Han Yazhou Acta mathematica scientia,Series A. 2017, 37 (2):  278-286.  Abstract ( 129 )   RICH HTML PDF (340KB) ( 108 )   Save Firstly, a class of CR inversion in the Heisenberg group was introduced. This is the foundation of the method of moving sphere. As an application, we discussed a class of subcritical equations in the Heisenberg group and obtained the nonexistence of positive solutions with cylindrical symmetry. References | Related Articles | Metrics

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Positive Solutions for Nonlocal Boundary Value Problems of Fourth Order Differential Equation with Parameters Hao Xinan, Liu Lishan Acta mathematica scientia,Series A. 2017, 37 (2):  287-298.  Abstract ( 131 )   RICH HTML PDF (317KB) ( 88 )   Save This paper deals with the existence of positive solutions to fourth order nonlocal boundary value problems with two parameters. The proofs are based on a specially constructed cone and a fixed point theorem in a cone for a completely continuous operator, due to Krasnosel'skii and Zabreiko. The results extend and improve some known results. References | Related Articles | Metrics

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New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations Huang Decheng, Chen Shouxin Acta mathematica scientia,Series A. 2017, 37 (2):  299-306.  Abstract ( 125 )   RICH HTML PDF (357KB) ( 84 )   Save In this paper we use a direct variational method, with the help of Hardy type inequality, to give a new proof for the existence of minimizing energy solutions for the Ginzburg-Landau equations in R2 coupled with an external magnetic field or a source current. Moreover, the solution satisfies the Coulomb gauge. References | Related Articles | Metrics

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Partial Schauder Estimates for the Heat Equation Ba Na, Zheng Lie Acta mathematica scientia,Series A. 2017, 37 (2):  307-312.  Abstract ( 144 )   RICH HTML PDF (252KB) ( 109 )   Save In this paper, we study the partial regularity of solutions to the heat equation. The resulting partial Schauder estimates have a unified integral-typed expression, from which the known interior Schauder estimates can be derived when the nonhomogeneous term f(x,t) is Lipschitz continuous, Hölder continuous or Dini continuous respectively in a certain direction. In particular, when f(x,t) is Hölder continuous in the direction xn, so are the mixed derivatives uxxn with the same Hölder index. References | Related Articles | Metrics

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On the Ingegrable Coupled Generalization of Dispersionless BKP Hierarchy and Its Solutions Liu Jingxin, Wu Hongxia, Zeng Yunbo Acta mathematica scientia,Series A. 2017, 37 (2):  313-325.  Abstract ( 111 )   RICH HTML PDF (372KB) ( 89 )   Save The symmetry constraint for dispersionless BKP (dBKP) hierarchy is firstly derived by taking dispersionless limit of that for BKP hierarchy. Then, based on the symmetry constraint for dBKP hierarchy, a new extended dBKP hierarchy is constructed. In addition, the integrability of this new extended dBKP hierarchy is proved by presenting its zero-curvature equation and the related conservation equation. From its zero-curvature equation, two types of dBKP equations with self-consistent sources (dBKPESCS) together with their associated conservation equations are obtained. Hodograph solutions for the first type of dBKPESCS are finally obtained. References | Related Articles | Metrics

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Blow up of Periodic Solutions for a Class of Keller-Segel Equations Arising in Biology Duan Shuangshuang, Huang Shoujun Acta mathematica scientia,Series A. 2017, 37 (2):  326-341.  Abstract ( 150 )   RICH HTML PDF (396KB) ( 103 )   Save In this paper, we consider the blow up phenomenon of periodic solutions to the Cauchy problem for a class of Keller-Segel equations arising in biology. The initial data is assumed to be periodic and has a bounded total variations on a periodic interval. Then we are able to prove that the smooth periodic solutions of the Keller-Segel equations will blow up in finite time. Moreover, the lifespan for the solutions is also given. References | Related Articles | Metrics

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Oscillation Analysis of Numerical Solutions in the θ-Methods for a Kind of Nonlinear Delay Differential Equation Wang Yunzhu, Gao Jianfang Acta mathematica scientia,Series A. 2017, 37 (2):  342-351.  Abstract ( 117 )   RICH HTML PDF (444KB) ( 70 )   Save This paper is concerned with oscillations of numerical solutions for a kind of nonlinear delay differential equation. According to the oscillatory theory, the oscillation of the nonlinear delay differential equation is transformed to that of the linear delay differential equation. The form of the numerical solution is obtained by using the linear θ-method. Some conditions under which the numerical solution is oscillatory are obtained and the properties of non-oscillatory numerical solutions are investigated. To verify results, the article gives numerical experiments. References | Related Articles | Metrics

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M/G/1 Repairable Queueing System and Optimal Control Policy with Min(N,D)-Policy Gao Lijun, Tang Yinghui Acta mathematica scientia,Series A. 2017, 37 (2):  352-365.  Abstract ( 111 )   RICH HTML PDF (683KB) ( 89 )   Save This paper considers the M/G/1 repairable queueing system with Min(N,D)-policy, in which the service station may fail during the server busy period. By using the total probability decomposition technique and employing the Laplace transform tool, the queueing indices of the system are discussed. Meanwhile, the emphasis is upon obtained some reliability indices of the service station, such as the probability distribution of the first failure time, the unavailability and the expected failure number during a given time interval (0,t]. Finally, we numerically determined the optimal control policy (N*，D*) under a constructed cost model. References | Related Articles | Metrics

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Turing Instability and Hopf Bifurcation of a Bimolecular Model with Autocatalysis and Saturation Law Zhou Jun Acta mathematica scientia,Series A. 2017, 37 (2):  366-373.  Abstract ( 150 )   RICH HTML PDF (628KB) ( 89 )   Save This paper deals with a bimolecular model with autocatalysis and saturation law. By analyzing the eigenvalues of the linearized system and using the bifurcation theory, we derive the conditions to occurrence Turing instability and Hopf bifurcation from the unique constant solution. Numerical simulations are presented to verify and illustrate the theoretical results. References | Related Articles | Metrics

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New Unequal Delay Partitioning Methods to Stability Analysis for Neural Networks with Discrete and Distributed Delays Yin Chun, Zhou Shiwei, Wu Shanshan, Cheng Yuhua, Wei Xiuling, Wang Wei Acta mathematica scientia,Series A. 2017, 37 (2):  374-389.  Abstract ( 134 )   RICH HTML PDF (857KB) ( 90 )   Save This paper deal with the problems of stability analysis for neural networks with with discrete and distributed delays. It addresses the newly unequal delay-partitioning methods which is different from previous methods. By unequally separating the delay interval into multiple diminishing subintervals, a novel Lyapunov-Krasovskii functionals is established including triple integrals terms. And together with some effective mathematical techniques and newly unequal delay-partitioning methods, the new stability criterion has been proposed to reduce the conservatism. Some numerical simulations are given to demonstrate the effectiveness of the proposed techniques comparing with some existing results. References | Related Articles | Metrics

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Some Dynamics in Spatial Homogeneous and Inhomogeneous Activator-Inhibitor Model Yang Wenbin, Wu Jianhua Acta mathematica scientia,Series A. 2017, 37 (2):  390-400.  Abstract ( 179 )   RICH HTML PDF (1593KB) ( 77 )   Save The diffusive Gierer-Meinhardt activator-inhibitor model system with Neumann boundary condition is investigated. For the spatial homogeneous (ODE) system, we perform the asymptotic behavior of the interior equilibrium and the existence and stability of limit cycle surrounding the interior equilibrium. For the spatial inhomogeneous (PDE) system, we consider the Turing instability of the interior equilibrium and show the existence of Turing pattern and inhomogeneous periodic oscillatory pattern. To verify our theoretical results, some numerical simulations are also done as a complement. References | Related Articles | Metrics