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25 October 2015, Volume 35 Issue 5 Previous Issue    Next Issue

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Global Existence for Some Quasi-Linear Parabolic Equations with Locally Arbitrary Growth and Memory Ma Wenya, Zhang Qiaofu, Cui Junzhi Acta mathematica scientia,Series A. 2015, 35 (5):  833-844.  Abstract ( 135 )   RICH HTML PDF (418KB) ( 124 )   Save Existence theory for a kind of quasi-linear parabolic equations is established by the Schauder fixed point method. Actually a linearized map is defined by fixing the function variables in the coefficients and the right-hand term. Its domain is chosen to be bounded but a locally arbitrary growth condition is considered. Therefore its range is contained in a closed convex set through the maximum principle. This map is continuous since the solution smoothly depends on the data. Compactness is deduced from the embedding theorem, so there exists a fixed point. The coefficients are just required to be continuous with respect to the function variables, but can be only measurable with respect to the space and time variables. Moreover, memory terms are also considered. References | Related Articles | Metrics

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Multiple Solutions for Quasilinear Elliptic Exterior Problem with Neumann Boundary Conditions Song Hongxue, Yan Qinglun Acta mathematica scientia,Series A. 2015, 35 (5):  845-854.  Abstract ( 136 )   RICH HTML PDF (375KB) ( 117 )   Save In this paper, we consider the following quasi-linear elliptic exterior problem with Neumann boundary value conditions  where Ω is a smooth exterior domain of the Euclidean space(RN,|·|)(N ≥ 3), and n is the unit vector of the outward normal on the boundary ∂Ω. λ is a positive parameter, 1< p< N, 1< q< p< r< p*, p*=Np/(N-p). By the mountain-pass theorem and Ekeland's variational principle, we establish the existence of two solutions for this problem when functions a(x), b(x), h1(x), h2(x) and g(x) satisfy certain conditions. References | Related Articles | Metrics

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Global Regularity of the 3D Axially Symmetric Incompressible MHD Equations with Anisotropic Data Wu Jihui, Wang Shu, Lu Lei Acta mathematica scientia,Series A. 2015, 35 (5):  855-866.  Abstract ( 99 )   RICH HTML PDF (322KB) ( 98 )   Save In this paper, we show that the global regularity of two kinds of particular solutions to the three-dimensional incompressible axially symmetric MHD equations:(1) uθ=0,Br=Bz=0,(2) Br=Bz=0 for a family of large anisotropic initial data. References | Related Articles | Metrics

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Monotonicity Method for Hyperbolic Type Nonlinear Differential Equation with Generalized p-Laplacian Wei Li, Agarwal Ravi P Acta mathematica scientia,Series A. 2015, 35 (5):  867-877.  Abstract ( 124 )   RICH HTML PDF (365KB) ( 101 )   Save By using the results on the perturbations of the ranges for pseudo-monotone operators and maximal monotone operators, we present the abstract result for the existence of the unique solution of hyperbolic type nonlinear differential equation involving the generalized p-Laplacian with mixed boundaries. It is an extension of the corresponding studies on nonlinear elliptic equation and nonlinear parabolic equation with generalized p-Laplacian. Some new techniques are employed in the discussion. Moreover, the connections between the unique solution studied in this paper and the zero point of a maximal monotone operator is exemplified. References | Related Articles | Metrics

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The Asymptotic Stability of the Zero Solution for A Nonlinear Volterra Equation Zhong Yue, Yuan Qian Acta mathematica scientia,Series A. 2015, 35 (5):  878-883.  Abstract ( 122 )   RICH HTML PDF (270KB) ( 71 )   Save The aim of this paper is to deal with the stability of the zero solution for a nonlinear Volterra integro-differential equation x'(t)=-a(t)x(t)+b(t)x'(g(t))+∫0tk(t,s)f(x(s),x(v(s)))ds+h(t),, The asymptotic stability of the zero solution for the equation is established by using fixed-point theory and constructing contraction mapping. References | Related Articles | Metrics

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On Nonhomogeneous Elliptic Equations Involving Caffarelli-Kohn-Nirenberg Critical Exponent Fan Zi-an Acta mathematica scientia,Series A. 2015, 35 (5):  884-894.  Abstract ( 98 )   RICH HTML PDF (271KB) ( 76 )   Save This paper discusses one nonhomogeneous elliptic equations involving Caffarelli-Kohn-Nirenberg critical exponent. By Nehari manifold and Variational methods, we prove that the equation has at least two nontrivial solutions. References | Related Articles | Metrics

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Estimation of Unknown Function on A Class of Nonlinear Difference Inequality and Application Huang Chunmiao, Wang Wusheng Acta mathematica scientia,Series A. 2015, 35 (5):  895-909.  Abstract ( 110 )   RICH HTML PDF (332KB) ( 63 )   Save In this paper, we establish a class of nonlinear difference inequalities, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function. Firstly, the upper bounds of the unknown functions are given by technique of monotonization, amplification method, the mean-value theorem for integrals, technique of change of variable, difference and summation. Finally, we apply our derived results to the study of the estimation of solutions of difference equations. References | Related Articles | Metrics

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Spectral Properties for Sturm-Liouville Equations with Transmission Conditions Li Kun, Zheng Zhaowen Acta mathematica scientia,Series A. 2015, 35 (5):  910-926.  Abstract ( 162 )   RICH HTML PDF (386KB) ( 92 )   Save In this paper, a discontinuous Sturm-Liouville equation with eigenparameter-dependent boundary conditions and transmission conditions is considered. A new operator associated with the problem is constructed, the self-adjointness of the operator in an appropriate Hilbert space is proved, the fundamental solutions are constructed, some properties of the eigenvalues and corresponding eigenfunctions are investigated, the asymptotic formulas for the eigenvalues and eigenfunctions are given, the completeness of eigenfunctions, Green function and the resolvent operator are also involved. References | Related Articles | Metrics

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A New Notion of Generalized Subgradients and Its Properties Huang Zhenggang Acta mathematica scientia,Series A. 2015, 35 (5):  927-935.  Abstract ( 108 )   RICH HTML PDF (301KB) ( 87 )   Save This paper proposes a new notion of generalized subgradients and discusses some properties of it in terms of Tangent cone. Using some of those properties, necessary and sufficient optimality conditions for a nonconvex and nondifferentiable scalar optimization problem with inequalities constraints and an arbitrary set constraint are derived, also a necessary condition for a nonconvex and nondifferentiable unconstrained scalar optimization problem is derived. References | Related Articles | Metrics

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Generation Theorems of Semigroups for Hamiltonian Operator Matrices Liu Jie, Huang Junjie, Alatancang Acta mathematica scientia,Series A. 2015, 35 (5):  936-946.  Abstract ( 105 )   RICH HTML PDF (414KB) ( 69 )   Save This paper deals with the generation problem of semigroups for Hamiltonian operator matrices. Some necessary and sufficient conditions are obtained for Hamiltonian operator matrices to generate C0 semigroups. Then the spectral location of such operator matrices are further obtained. As applications, the solutions of mixed problems for a class of fourth-order partial differential equations are given, based on the semigroup method of Hamiltonian system. References | Related Articles | Metrics

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On Rank Invariance of Generalized Loewner Matrices Generated by Stieltjes Function Song Yanping, Tang Jinbo, Hu Yongjian Acta mathematica scientia,Series A. 2015, 35 (5):  947-955.  Abstract ( 94 )   RICH HTML PDF (323KB) ( 58 )   Save In this paper we study the statements on rank invariance of generalized Loewner matrices of two types generated by the values of a given Stieltjes function. We show that the ranks of such matrices of the first type of the same size are equal, while the ranks of such matrices of the second type with the same size are either equal or differ with difference one. References | Related Articles | Metrics

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Bounded, Compact and Fredholm Toeplitz Operators on Harmonic Dirichlet Space Dh1 Xia Jin, Wang Xiaofeng, Cao Guangfu Acta mathematica scientia,Series A. 2015, 35 (5):  956-969.  Abstract ( 116 )   RICH HTML PDF (344KB) ( 72 )   Save We discuss the boundedness, compactness and spectra properties of the Toeplitz operators and Hankel operators on the Harmonic Dirichlet space Dh1; compute the Fredholm index of Fredholm Toeplitz operator. References | Related Articles | Metrics

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A New Subclass of Analytic Functions Associated with the Strip Domains Li Shuhai, Tang Huo, Ma Lina, Ao En Acta mathematica scientia,Series A. 2015, 35 (5):  970-986.  Abstract ( 158 )   RICH HTML PDF (279KB) ( 62 )   Save The S?l?gean operator is used here to introduce a new subclass of analytic functions associated with the strip domains. We obtain the bounds of coefficients and Fekete-szegö inequality for functions in this class. The results presented here extend some of the earlier results. References | Related Articles | Metrics

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Exponential Convergence of An Epidemic Model with Delays and Oscillating Recovery Rates Xu Yanli Acta mathematica scientia,Series A. 2015, 35 (5):  987-994.  Abstract ( 104 )   RICH HTML PDF (487KB) ( 65 )   Save This paper is concerned with an epidemic model with delays and oscillating recovery rates. Some new sufficient conditions are established to ensure that all solutions of this model converge exponentially to zero vector. Some numerical simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies. References | Related Articles | Metrics

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A Conditional Variance for g-Expectation Hao Tao Acta mathematica scientia,Series A. 2015, 35 (5):  995-1003.  Abstract ( 97 )   RICH HTML PDF (345KB) ( 182 )   Save A conditional variance for g-expectation, named conditional g-variance, is introduced in this paper. The uniqueness theorem for conditional g-variance is proved and the comparison theorem does not hold any more. The sufficient and necessary condition of the property of continuity of conditional g-variance depending on parameters is obtained. At last, we extend conditional g-variance from L4(Ω,FT,P) to L2(Ω,FT,μ) as a continuous mapping in HF1(0,T; R). References | Related Articles | Metrics

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The Risk Process with Dependence Based on FGM Copula under A Multi-Layer Dividend Strategy Yang Long Acta mathematica scientia,Series A. 2015, 35 (5):  1004-1017.  Abstract ( 127 )   RICH HTML PDF (395KB) ( 52 )   Save In this paper, we consider an extension to the classical compound Poisson risk model under a multi-layer dividend strategy, in which the claim size and inter-claim time are dependent. We assume that the dependence structure between the claim size and the inter-claim time is based on a Farlie-Gumbel-Morgenstern copula. Some piecewise integro-differential equations with certain boundary conditions for the Gerber-Shiu function are derived. Then, applying these results, some defective renewal equations for the Gerber-Shiu function are obtained and explicit expressions are solved. Finally, to illustrate the solution procedure, explicit expressions for the ruin probability are given for exponential claim size. References | Related Articles | Metrics

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Link Prediction for the Gene Regulatory Network Li Yan, Zhang Xiaofei, Yi Ming, Liu Yanyan Acta mathematica scientia,Series A. 2015, 35 (5):  1018-1024.  Abstract ( 137 )   RICH HTML PDF (475KB) ( 69 )   Save In order to build gene regulatory network, we proposed an algorithm based on gene expression levels and network anti-delivery. The algorithm used the network anti-delivery idea to analyze indirect effect produced from the traditional correlated calculation methods, and added an norm penalty term for controlling network sparsity after considering the sparsity of regulatory networks. We use the algorithm on the E. coli experimental data. This method improves the edge predictive ability of the correlation analysis on the regulatory network, Pearson correlation coefficient increased by 6.42%, Spearman correlation coefficient increased by 5.92%, mutual information improves 9.35%. Overall, this model provides a new idea on modifying a large number of system-related data, and can be applied to network edge prediction and the control dynamics of biological network inference. References | Related Articles | Metrics