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25 February 2007, Volume 27 Issue 1 Previous Issue    Next Issue

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Factorization of Analytic Function of Order Less Than Deng Guantie Acta mathematica scientia,Series A. 2007, 27 (1):  1-006.  Abstract ( 2407 )   RICH HTML PDF (220KB) ( 2211 )   Save In this paper, the author proves that an analytic function of order less than 2 in a half plane can be factored into the product of the three functions: weighted Blaschke product, weighted singular inner function and weighted outer function. This is a generalization of the classical factorization about analytic functions in the Hardy space. Related Articles | Metrics

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Explicit Construction of Wavelet Tight Frames with Dilation factor α Huang Yongdong; Cheng Zhengxing Acta mathematica scientia,Series A. 2007, 27 (1):  7-018.  Abstract ( 2457 )   RICH HTML PDF (337KB) ( 1938 )   Save This paper studies wavelet tight frames associated with given scaling functions with dilatin factor α. The wavelet tight frames consist of finite number of functions ψ1,ψ2,...,ψn. First, the authors present sufficient conditions for existence of wavelet tight frames generated by the n functions, then give explicit constructing formula of wavelet tight frames. In particular, if mask of the scaling function are rational functions, the mask of the corresponding wavelet tight frames are rational. Finally, the paper derive the decomposition and reconstruction formulas, and give five numercial examples of wavelet tight frames. Related Articles | Metrics

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Composition Operators from Spaces F(p,q,s) to Bloch Zhang Xuejun; Liu Jingcheng Acta mathematica scientia,Series A. 2007, 27 (1):  19-026.  Abstract ( 2339 )   RICH HTML PDF (291KB) ( 1554 )   Save In this paper, some sufficient and necessary conditions are given for the composition operator C_{varphi} to be a bounded or compact operator from the space F(p, q, s) to the space βα on B. At the same time, as corollaries, some corresponding results between Bloch type spaces are obtained. Related Articles | Metrics

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Stability of Compacton Solutions and Backlund Transformation for One Type of Nonlinear Equations Yin Jiuli; Tian Lixin Acta mathematica scientia,Series A. 2007, 27 (1):  27-036.  Abstract ( 3135 )   RICH HTML PDF (368KB) ( 2421 )   Save Introducing K(m,n,1) equation with linear fifth-order dispersion, the authors obtain sin-compacton solutions by Adomian decomposition method. Using the homogeneous balance(HB) method, the authors obtain a Backlund transformation of a special equation K(2,2,1) to determine some new solitary solutions of the equation. The authors finally show the linear stability of all obtained sin-typed multi-compacton solutions. Related Articles | Metrics

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On the Existence and Uniqueness of Periodic Solutions to a Type Liu Xiping; Jia Mei; Ren Rui Acta mathematica scientia,Series A. 2007, 27 (1):  37-044.  Abstract ( 2611 )   RICH HTML PDF (346KB) ( 1530 )   Save By means of the methods presented in the topological degree theory, the existence of periodic solutions to a type of the Duffing functional differential equation x''(t)+g(x(t - τ(t, x(t))))=f(t) with complex time lag is studied, sufficient and necessary condition of the equation with periodic solutions is obtained, and the existence and uniqueness of periodic solutions is given when the time lag is constant, the instance is given to the problem. Related Articles | Metrics

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An Upwind-mixed Finite Element Method for Compressible Miscible Displacement Wang Huan; Yuan Yirang Acta mathematica scientia,Series A. 2007, 27 (1):  45-056.  Abstract ( 2060 )   RICH HTML PDF (629KB) ( 1428 )   Save Consider an upwind-mixed finite element method for computing the two-phase compressible miscible displacement with dispersion in porous media. Optimal-order error estimates for concentration approximation in L2 and pressure approximation in H1 are derived. Numerical experiment proves the method is effective for avoiding numerical diffusion and nonphysical oscillations. Related Articles | Metrics

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Several Hardy Type Inequalities of Generalized Greiner Operator Han Junqiang; Niu Pengcheng Acta mathematica scientia,Series A. 2007, 27 (1):  57-066.  Abstract ( 2015 )   RICH HTML PDF (323KB) ( 1332 )   Save The vector fields $X_j = \frac{\partial}{\partial x_j } + 2ky_j \vert z\vert ^{2k - 2}\frac{\partial}{\partial t}$, $Y_j = \frac{\partial }{\partial y_j } - 2kx_j \vert z\vert ^{2k - 2}\frac{\partial }{\partial t}$, j = 1,...,n, x,y ∈ Rn, $z = x + \sqrt { - 1} y$, t ∈ R, k ≥ 1 are considered. Hardy type inequalities in the pseudo ball and outside the pseudo ball are obtained. The generalized Picone type identity and then Hardy type inequalities on the whole space containing the known results in [3] are established. When p = 2 the sharp constant in the Hardy type inequality is discussed. Related Articles | Metrics

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Boundary Behavior of μ(z)-homeomorphisms Chen Zhiguo Acta mathematica scientia,Series A. 2007, 27 (1):  67-76.  Abstract ( 2158 )   RICH HTML PDF (287KB) ( 1403 )   Save In this paper the author studies the boundary behavior of μ(z)-homeomorphisms. A sufficient condition is given such that the μ(z)-homeomorphism of the upper half plane onto itself can be topologically extended to the boundary. The auther also estimates the ρ-function by the dilatation function of μ(z)-homeo morphism. Related Articles | Metrics

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The Transforms Related to Laplace-Stieltjes Transforms in the Right Half Plane Luo Xi; Sun Daochun Acta mathematica scientia,Series A. 2007, 27 (1):  74-078.  Abstract ( 1608 )   RICH HTML PDF (227KB) ( 1473 )   Save In the paper, the authors study Laplace-Stieltjes transforms convergent in the right half plane, and its relative transforms. Related Articles | Metrics

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On the Dynamics of a Food Chain with Monod-Haldane Functional Response Wang Yuquan; Liu Laifu Acta mathematica scientia,Series A. 2007, 27 (1):  79-089.  Abstract ( 2588 )   RICH HTML PDF (507KB) ( 1897 )   Save A dynamics model of food chain for three species including prey, predator and toppredator is studied. The Monod-Haldance functional response is used in the food chain system. By applying qualitative analysis and Hopf bifurcation theory, criteria are derived for global stability of the boundary equilibria, existence of periodic orbits and persistence of the system. To summarize and classify the global dynamics of the system, the parameters regions with different dynamics behavior are derived. According to the regions, the authors show that the system can lead to a very complicated dynamics behavior and present an example to illustrate the conclusions by using MATLAB software. Related Articles | Metrics

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Forced Oscillations for First Order Delay Differential Equations of the Neutral Type Wang Hongzhou; Yu Yuanhong Acta mathematica scientia,Series A. 2007, 27 (1):  90-096.  Abstract ( 1923 )   RICH HTML PDF (233KB) ( 1355 )   Save In this paper, some new sufficient conditions have been obtained for the oscillation of bounded solutions or solutions tending to zero as t→∞ for the forced first order neutral delay differential equations with positive and negative coefficients. Related Articles | Metrics

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On Relations of Classical Convex Geometric Inequalities Zhao Changjian; Leng Gangsong Acta mathematica scientia,Series A. 2007, 27 (1):  97-101.  Abstract ( 2284 )   RICH HTML PDF (233KB) ( 2025 )   Save The purpose of the present paper is to point out the relations of several famous classical inequalities which are some inequalities of singular importance in convex geometry. Related Articles | Metrics

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Tietze Extension Theorem on Additive Generalized Algebraic Lattice Chen Xueyou; Li Qingguo; Long Fei; Deng Zike Acta mathematica scientia,Series A. 2007, 27 (1):  102-108.  Abstract ( 2057 )   RICH HTML PDF (319KB) ( 1301 )   Save The category of additive generalized algebraic lattices with lower homomorphisms is equivalent to the category of T0-topological spaces with continuous mappings ([11]). Follow the view, in this paper, using the generalized way below relation, the greatest system of subsets ([11]) and the lower homomorphisms ([12]) as tools, the notion of normal is defined, and Urysohn Lemma, Tietze extension theorem are constructed. Related Articles | Metrics

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Exponential Stability in Mean Square for Stochastic Hopfield Delay Neural Networks: an LMI Approach Chen Wuhua; Lu Xiaomei; Li Qunhong; Guan Zhihong Acta mathematica scientia,Series A. 2007, 27 (1):  109-117.  Abstract ( 2881 )   RICH HTML PDF (344KB) ( 2187 )   Save By using a technique of model transformation of the system, a new type of Lyapunov functional is introduced. By applying this new Lyapunov functional, a novel delay-dependent sufficient condition of exponential stability in mean square for stochastic Hopfield delay neural networks is derived in terms of linear matrix inequalities (LMIs). A delay-independent sufficient condition is also presented. Numerical examples show that the proposed method is less conservative than the previous ones. Related Articles | Metrics

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Local Influence Assessment in the General Linear Model with Correlated Errors Shi Lei; Chen Fei Acta mathematica scientia,Series A. 2007, 27 (1):  118-130.  Abstract ( 2022 )   RICH HTML PDF (472KB) ( 1225 )   Save Assessment local influence analysis in linear model with correlated errors is studied in this paper. The method is based on generalized Cook statistic (Shi, 1997) with a suitable choice of M/c such that the local influence measure is invariant under parameterization. A perturbation scheme is introduced through covariance matrix. The local influence measures for the estimators of regression coefficients, variance coefficient and the best unbiased linear prediction are derived. The results are compared with those of case-deletion, and a concrete example is used to illustration. Related Articles | Metrics

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The Optimality Conditions of Set-valued Vector Optimization on Super Efficiency Hou Zhenmei; Liu Sanyang; Zhou Yong Acta mathematica scientia,Series A. 2007, 27 (1):  131-137.  Abstract ( 2079 )   RICH HTML PDF (292KB) ( 1526 )   Save This paper deals with Fritz-John and Kuhn-Tucker conditions of the set-valued optimization in the sense of super efficiency in Hausdorff locally convex vector space. First the authors introduce the concept of lower semidifferentiability and then give the Fritz-John condition and Kuhn-Tucker condition. Finally the authors obtain the sufficient conditions of set-valued optimization problems on super efficiency. Related Articles | Metrics

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Initial Value Problems for Second Order Nonlinear Impulsive Integro-differential Equations in Banach Spaces Xie Shengli Acta mathematica scientia,Series A. 2007, 27 (1):  138-145.  Abstract ( 2955 )   RICH HTML PDF (270KB) ( 1717 )   Save In this paper, by using fixed point theory, the existence of solutions of initial value problems for second order nonlinear impulsive integro-differential equations in Banach spaces is investigated under some relaxed conditions. The compactness and growth restrictions on the impulsive terms have been dropped and thus the results substantially improve and generalize the specific ones. Related Articles | Metrics

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Asymptotic Properties in Nonlinear Reproductive Dispersion Models with Random Effects Xia Tian; Tang Niansheng; Wang Xueren; Zhang Wenzhuan Acta mathematica scientia,Series A. 2007, 27 (1):  146-154.  Abstract ( 2408 )   RICH HTML PDF (316KB) ( 1820 )   Save This paper proposes some regularity conditions analogous to those given by Barndorff-Nielsen and Cox(1989), Severini and Wong(1992). On the basis of the proposed regularity conditions and Laplaces's approximation, the existence, the strong consistency and the asymptotic normality of maximum likelihood estimator (MLE) are proved in nonlinear reproductive dispersion models with random effects. Related Articles | Metrics

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On (f,τ)-Compatible Hopf Algebra Pair (B,H) Zhao Wenzheng Acta mathematica scientia,Series A. 2007, 27 (1):  155-165.  Abstract ( 1729 )   RICH HTML PDF (267KB) ( 1384 )   Save In this paper, the author defines (f,τ)-compatible Hopf algebra pair (B, H). Using such a pair (B,H), the author obtains a new braided monoidal category, which is a submonoidal category of left H-comodules category HM, and obtains a kind of new quantum Yang-Baxt operators. The author also constructs a Hopf algebra in the Yetter-Drinfeld category HHYD$ by twisting the multiplication of B. Related Articles | Metrics

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Paired-domination Number in Cubic Graphs Chen Xuegang; Sun Liang; Xing Huaming Acta mathematica scientia,Series A. 2007, 27 (1):  166-170.  Abstract ( 2781 )   RICH HTML PDF (222KB) ( 1851 )   Save Let G=(V,E) be a simple graph. For a subset $S\subseteq V$, let G[S] denote the subgraph of G induced by S. S is a paired-dominating set of G if S is a dominating set of G and G[S] contains at least one perfect matching. The paired domination number, denoted by γp(G), is the minimum cardinality of a paired dominating set of G. In this paper, the authors show that for any cubic graph G of order n, γp(G)≤3n/ 5. Related Articles | Metrics

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A Note on Closed s-images of Locally Separable Metric Spaces Lin Shou; Yan Pengfei Acta mathematica scientia,Series A. 2007, 27 (1):  171-175.  Abstract ( 1640 )   RICH HTML PDF (288KB) ( 1133 )   Save In this note a decomposition theorem about closed s-images of locally separable metric spaces is discussed. It is showed that a regular Fréchet space is a closed s-image of a locally separable metric space if and only if it has a point-countable cs*-network, each first countable closed subset is locally separable, and each Lindelof closed subset is separable. Related Articles | Metrics

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On Applications of Wu's Method in Bilevel-Programming Problems Wu Tianjiao Acta mathematica scientia,Series A. 2007, 27 (1):  176-183.  Abstract ( 1721 )   RICH HTML PDF (313KB) ( 1157 )   Save The bilevel-programming problems are important in mathematical applications. They are usually solved by various kinds of numerical methods. This will give solutions in the form of local extremal values but not necessarily global optimal ones. Consider the case for which all functions occurred in the bilevel-programming problems are polynomial ones. The present paper shows how to solve the problems by the MM-method (Mathematics-Mechanization method) or Wu's method. Wu's method is different from the numerical methods in that the computations are symbolic instead of numerical ones. Theoretically it is based on computer algebra and algebraic geometry. The author uses the computer to get complete blobal solutions of some practical test problems in the bilevel-programming. The computations show that Wu's method furnishes the true optimal values of the bilevel-programming problems, and is also quite efficient. Related Articles | Metrics

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Linear Hyperbolic Systems with Discontinuous Coefficients Liu Fagui; Ge Yunfei; Li Caizhong Acta mathematica scientia,Series A. 2007, 27 (1):  184-192.  Abstract ( 1625 )   RICH HTML PDF (266KB) ( 1083 )   Save In this article the authors consider Riemann problem for linear hyperbolic systems with discontinuous coefficients, and show that it maybe admit measure solution contained δ wave. Related Articles | Metrics