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26 October 2016, Volume 36 Issue 5 Previous Issue    Next Issue

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Compact Differences of Weighted Composition Operators on Bergman Spaces Aαp(Bn) Wang Maofa, Chen Fen, Yao Xingxing, Deng Fangwen Acta mathematica scientia,Series A. 2016, 36 (5):  809-820.  Abstract ( 116 )   RICH HTML PDF (353KB) ( 126 )   Save In this paper, we consider compact differences of weighted composition operators acting on the weighted Bergman spaces Aαp(Bn). Some necessary and sufficient conditions for the difference of two bounded weighted composition operators to be compact are given. Moreover, we also obtain some similar conditions for a sum of weighted composition operators. References | Related Articles | Metrics

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Spectral Analysis of a Transport Operators in Rotenberg Model Wang Shenghua, Wu Hongxing Acta mathematica scientia,Series A. 2016, 36 (5):  821-831.  Abstract ( 163 )   RICH HTML PDF (342KB) ( 94 )   Save The objective of this paper is to research Rotenberg model of a proliferating cell population with unsmooth boundary conditions in Lp(1 ≤p <+∞) space. It is to prove that the ninth-order remainder term R9(t) of the Dyson-Phillips expansion of corresponding transport operators generates semigroup for this model is compact on L1 and is weakly compact on (1 <p <+∞). It is to obtain that the spectrum of the transport operators only consisting of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane and the stability of the transport equation solution and so on. References | Related Articles | Metrics

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Lp Boundedness for Some Commutators Related to Schrödinger Operator Chen Dongxiang, Chen Xuemei Acta mathematica scientia,Series A. 2016, 36 (5):  832-847.  Abstract ( 102 )   RICH HTML PDF (335KB) ( 114 )   Save Let H2=(-△)2+V2 be the Schrödinger type operator, where V satisfies reverse Hölder inequality. In this paper, we establish the Lp boundedness for V▽2H2-1, V(3)/(2)▽H2-1, ▽2H2-1V, ▽H2-1V(3)/(2) and that of their commutators. We also prove that ▽2H2-1V, ▽H2-1V(3)/(2) are bounded on BMOL. References | Related Articles | Metrics

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Frame Properties of Wave Packet Systems in Sobolev Spaces Hs(Rd) Xu Meiyu, Lu Dayong Acta mathematica scientia,Series A. 2016, 36 (5):  848-860.  Abstract ( 216 )   RICH HTML PDF (393KB) ( 106 )   Save The traditional wave systems and Gabor systems are special cases of wave packet systems, which are obtained by applying a combination of dilations, translations and modulations to a finite family of functions. In this paper, first, a sufficient condition for a generalized shift-inveriant system to be a Bessel sequence or even a frame for the Sobolev spaces Hs(Rd) is established. Secondly, combining with the result that the wave packet system is a special case of the generalized shift-invariant system, the sufficient condition for the wave packet system to be a frame for the Sobolev spaces Hs(Rd) is obtained. Finally, using the eigenvalues of the matrix theory, this paper proves that if the Fourier transform of the function g on a certain open ball is greater than some positive number, then the wave packet system which is generated by it, cannot to be a frame for Hs(Rd). References | Related Articles | Metrics

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Orlicz Dual Mixed Quermassintegrls Sun Baolei, Yao Chunqing Acta mathematica scientia,Series A. 2016, 36 (5):  861-872.  Abstract ( 100 )   RICH HTML PDF (338KB) ( 108 )   Save In this paper, we shows the continuity and the uniqueness result of the Orlicz dual mixed quermassintegrls, prove a property of the Orlicz dual mixed quermassintegrls under linear transformation. Further, the circulate inequality for the Orlicz dual mixed quermassintegrls is obtained. The equivalence between the dual Orlicz-Minkowski inequality for dual Orlicz mixed quermassintegrals and the dual Orlicz-Brunn-Minkowski inequality for Orlicz radial combination are demonstrated. We generalize the dual Orlicz-Cauchy-Kubota formula. References | Related Articles | Metrics

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Packing Dimensional Results for Homogeneous Moran Sets Hu Xiaomei Acta mathematica scientia,Series A. 2016, 36 (5):  873-878.  Abstract ( 131 )   RICH HTML PDF (282KB) ( 122 )   Save In this paper, we construct a class of special homogeneous Moran set, called {mk}-quasi homogeneous Cantor set and discuss their packing dimensions. By adjusting the value of {mk}k≥1, we constructively prove the intermediate value theorem about packing dimensions of the homogeneous Moran sets. Moreover, we obtain a sufficient condition that the packing dimension of homogeneous Moran sets may get the minimum value. References | Related Articles | Metrics

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Some Remarks on P-Minimal Dynamical Systems Wu Xinxing, Wang Jianjun Acta mathematica scientia,Series A. 2016, 36 (5):  879-885.  Abstract ( 146 )   RICH HTML PDF (345KB) ( 93 )   Save This paper is devoted to the study of entropy-minimality and chaos-minimality of iteration systems and product systems. Firstly, we prove that an entropy-minimal system is either syndetically sensitive or minimal and equicontinuous. Then, we obtain that for each positive integer n≥2, there is an entropy-minimal and chaos-minimal system such that its n-th iteration system is neither entropy-minimal nor chaos-minimal. Besides, we show that each factor system is entropy-minimal provided that the product system is entropy-minimal, and its converse is not true. References | Related Articles | Metrics

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An Effective Iterative Updating Method for Undamped Structural Systems Yuan Yongxin, Zhao Wenhua, Liu Hao Acta mathematica scientia,Series A. 2016, 36 (5):  886-900.  Abstract ( 121 )   RICH HTML PDF (414KB) ( 84 )   Save Structural dynamics model updating is a procedure to minimize the differences between analytical and experimental results. In this paper, an iterative method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By the method, the optimal approximation mass and stiffness matrices which satisfy the required eigenvalue equation can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrix pair. The large number of unmeasured and unknown eigeninformation of the original model is preserved. Two numerical examples show that the introduced iterative algorithm is quite efficient. References | Related Articles | Metrics

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On the Behavior of Systems of Complex Difference Equations with Admissible Solutions Wang Yue, Gao Lingyun Acta mathematica scientia,Series A. 2016, 36 (5):  901-910.  Abstract ( 96 )   RICH HTML PDF (279KB) ( 105 )   Save Using Nevanlinna theory of the value distribution of meromorphic functions, we will mainly investigate the behavior of systems of complex difference equations when we add some conditions to the quality of the solutions, and obtain an interesting result. It extends some results concerning complex differential (difference) equations to the systems of difference equations. Examples show that our results are precise. References | Related Articles | Metrics

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Further Results on Periodicity and Unicity of Entire Functions Chen Shengjiang Acta mathematica scientia,Series A. 2016, 36 (5):  911-918.  Abstract ( 153 )   RICH HTML PDF (290KB) ( 119 )   Save In this paper, we mainly study the periodic entire functions sharing some values, and obtain some results on uniqueness for periodic entire functions. Furthermore, some results for elliptic entire functions are obtained too. Examples show that some conditions are necessary. References | Related Articles | Metrics

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Limit Cycles for Perturbing Quadratic Isochronous Center Inside Discontinuous Quadratic Polynomial Differential System Li Shimin, Cen Xiuli Acta mathematica scientia,Series A. 2016, 36 (5):  919-927.  Abstract ( 101 )   RICH HTML PDF (326KB) ( 86 )   Save In this paper, we bound the number of limit cycles which bifurcate from the period annulus of a class of quadratic isochronous center ?=-y-(4)/(3)x2,?=x-(16)/(3)xy, when perturbed inside the class of all discontinuous quadratic polynomial differential systems. Our results show that there are at most 4 limit cycles bifurcating from this system. Moreover, this bound is sharp. References | Related Articles | Metrics

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Method for Solving a Class of Fourth Order Nonlinear Differential Equations with Integral Boundary Conditions by Combining Collocation Method and Reproducing Kernel Method Liu Hongying, Lv Xueqin Acta mathematica scientia,Series A. 2016, 36 (5):  928-936.  Abstract ( 95 )   RICH HTML PDF (336KB) ( 156 )   Save In this paper, we study to solve a class of fourth order nonlinear differential equations with integral boundary conditions by combining collocation method and reproducing kernel method and especially illustrates the uniform convergence of the solution obtained by this method. Some numerical examples are displayed to demonstrate the validity and applicability of the present method. References | Related Articles | Metrics

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The Number of Zeros of Abelian Integrals for a Kind of Quartic Hamiltonians with a Nilpotent Center Yang Jihua, Liu Mei, He Zhicheng Acta mathematica scientia,Series A. 2016, 36 (5):  937-945.  Abstract ( 129 )   RICH HTML PDF (285KB) ( 76 )   Save In this paper, we prove that the number of zeros of Abelian integral for the Hamiltonians H(x,y)=-x2+ax2y2+bx4+cy4 on the interval (0,(c)/(a2-4bc)) is not more than 3n+3[(n-1)/(4)]+14 (taking into account the multiplicity), where a>0,b<-2,c<0,a2>4bc. References | Related Articles | Metrics

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Upper Semicontinuity of Pullback Attractors for Nonclassical Diffusion Equations in H01(Ω) Wang Yonghai, Qin Yuming Acta mathematica scientia,Series A. 2016, 36 (5):  946-957.  Abstract ( 85 )   RICH HTML PDF (358KB) ( 88 )   Save This paper is concerned with upper semicontinuity of pullback attractors, for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, under some proper assumptions, we prove that, the pullback attractor {Aε(t)}t∈R of equation (1.1) with ε∈[0,1] satisfies that for any [a,b]⊂R and ε0∈[0,1], distH01(Aε(t),Aε0(t))=0 and ∪t∈[a,b]∪ε∈[0,1]Aε(t) is precompact in H01(Ω). References | Related Articles | Metrics

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Blow-Up Questions of Solutions to a Class of p-Laplace Equation with Dissipative Gradient Term Ling Zhengqiu, Wang Zejia Acta mathematica scientia,Series A. 2016, 36 (5):  958-964.  Abstract ( 95 )   RICH HTML PDF (293KB) ( 105 )   Save This paper considers a type of p-Laplace equation with dissipative gradient term. By means of suitable defined auxiliary functions and resulting the first-order differential inequalities, the conditions which ensure that blow-up occurs or does not occur are given. In addition, the lower bound for blow-up time is also determined if blow-up occurs. References | Related Articles | Metrics

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Existence of Nontrivial Solution of a Periodic Thomas-Fermi-Dirac-von Weizsäcker Equation with a Large Parameter Chen Shaowei, Xiao Liqin Acta mathematica scientia,Series A. 2016, 36 (5):  965-977.  Abstract ( 100 )   RICH HTML PDF (321KB) ( 76 )   Save This paper studies a periodic Thomas-Fermi-Dirac-von Weizsäcker equation with a large parameter. Using a new infinite-dimensional linking theorem, we prove that, for sufficiently large parameter, this equation has a nontrivial solution. References | Related Articles | Metrics

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Stability of Non-Constant Equilibrium Solutions for Bipolar Non-Isentropic Euler-Poisson Equations Li Xin, Wang Shu, Feng Yuehong Acta mathematica scientia,Series A. 2016, 36 (5):  978-996.  Abstract ( 157 )   RICH HTML PDF (463KB) ( 95 )   Save This article is concerned with the bipolar non-isentropic Euler-Poisson equations in semiconductors. We investigated, by means of an induction argument on the order of the mixed time-space derivatives of solutions in energy estimates and the techniques of symmetrizer, the periodic problem in a three-dimensional torus. Under the assumption that initial data are close to a non constant equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state with exponential decay rates as the time goes to the infinity. This phenomenon on the charge transport shows the essential difference among the bipolar non-isentropic, the unipolar non-isentropic and the bipolar isentropic Euler-Poisson equations. References | Related Articles | Metrics

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Estimating Parameters of Stationary Distribution Using Forward Equation Hou Zhenting, Ma Yi, Liu Lu Acta mathematica scientia,Series A. 2016, 36 (5):  997-1009.  Abstract ( 128 )   RICH HTML PDF (387KB) ( 121 )   Save In this paper we give an estimation of the parameters of the stationary distribution of some mean field diffusion process using the differential equations of that distribution. The mean field stochastic process involved is dX(t)=b(μN,θ)dt+σ(X(t))dB(t), where θ is parameters to be estimated. μN is the empirical distribution of the N subjects consisting the mean field stochastic process. b(μ,θ) is continuous wrt μ at μ=p(τ-topology). Where p is the unique stationary distribution of the process. We restrict ourself to the study of the parameter estimation problem of the following model dX(t)=(aθ(X(t))+b<F,μ(t)>)dt+σ(X(t))dB(t), where a,b are parameters to be estimated. The data is the empirical distribution of large amount of subjects consisting the process on several time points. References | Related Articles | Metrics

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The E-Bayesian Estimation of the Parameter for Poisson Distribution and Its Properties Han Ming Acta mathematica scientia,Series A. 2016, 36 (5):  1010-1016.  Abstract ( 128 )   RICH HTML PDF (327KB) ( 203 )   Save In this paper, the definition of E-Bayesian estimation of the parameter is provided. Moreover, for Poisson distribution, based on the square error loss function, formulas of E-Bayesian estimation and hierarchical Bayesian estimation for the parameter are provided, and the properties of E-Bayesian estimation are also discussed. Finally, combined with the practical problem are calculated, the results show that the proposed method is feasible and convenient for application. References | Related Articles | Metrics