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Generalization of Furuta type Inequalities with Negative Powers YANG Chang-Sen, HU Qing-Wen, ZUO Gong-Liang Acta mathematica scientia,Series A    2005, 25 (1): 21-26.   Abstract （3192）      PDF（pc） （313KB）（1150）       Save First,the autuors show that Furta type inequalities tiwh negative powers are equivalent to Tanhshi's inequality.Neext,the authors point out these inequalities can be ganeralized to an order preserving inequality. Reference | Related Articles | Metrics

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Geometric Inequalities-From Integral Geometry Point of View ZHOU Jia-Zu, REN De-Lin Acta mathematica scientia,Series A    2010, 30 (5): 1322-1339.   Abstract （3147）      PDF（pc） （482KB）（1798）       Save This paper first surveys geometric inequalities achieved mainly by the Chinese mathematicians. By estimating the containment measure of a random convex body to be contained in, or to contain, another convex body via the fundamental kinematic formula of Blaschke and the formula of Poincarè in plane integral geometry, we obtain the classical isoperimetric inequality and some Bonnesen-style inequalities. Then some new geometric inequalities, such as the symmetric mixed isoperimetric inequality, Minkowski  and Bonnesen style symmetric mixed isohomothetic inequalities, are obtained. We also investigate the Gage type isoperimetric inequalities and the Ros type isoperimetric inequalities. Reference | 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    Abstract （3130）      PDF（pc） （368KB）（2403）       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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Some Properties on Currents in Metric Spaces Zhao Peibiao;Yang Xiaoping Acta mathematica scientia,Series A    Abstract （3013）      PDF（pc） （352KB）（2203）       Save The authors study the representation theorem of current by using the view of algebra. The similar Radon-Nikodym theorem for completely invariant current is obtained by virtue of the constructing minimal triple. 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    Abstract （2951）      PDF（pc） （270KB）（1714）       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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Discontinuous Finite Elements in Solving Initial Value Problem of Nonlinear ODE Li Tianran;Chen Chuanmiao Acta mathematica scientia,Series A    Abstract （2926）      PDF（pc） （315KB）（1873）       Save In this paper the initial value problem of nonlinear ODE is solved with discontinuous finite elements of order u'=f(x,u),u(0)=u0. For m≥1, the authors prove that the left limits of discontinuous finite elements of order m at their node have a superconvergence estimate (u-U(xj-0)=O(h2m+1) and at characteristic points xji of order m+1 of every elements. There is the superconvergence estimate (u-U)(xji)=O(hm+2). Related Articles | Metrics

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On the Strong Convergence of the Modified Reich-Takahashi Zeng Liuchuan Acta mathematica scientia,Series A    Abstract （2916）      PDF（pc） （283KB）（1557）       Save Let E be a real Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Let D be a nonempty bounded closed convex subset of $E$ and $T:D\rightarrow D be an asymptotically nonexpansive mapping. It is shown that under some suitable conditions,the modified Reich-Takahashi type iteration method converges strongly to a fixed point of T. Related Articles | Metrics

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Positive Periodic Solutions of a Delayed Predator-Prey System with Holling Type II Functional Response Chen Fengde;Chen Xiaoxing ;Zhang Huiying Acta mathematica scientia,Series A    Abstract （2881）      PDF（pc） （394KB）（1850）       Save By using a continuation theorem based on Gaines and Mawhin's coincidence degree, the authors study the global exisence of positive periodic solutions of a delayed predator-prey system with Holling II type response and stage structure for predator. A set of easily verifiable sufficient conditions is obtained, which improves some known results. Also, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the global attractivity of the positive periodic solution are obtained. 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    Abstract （2876）      PDF（pc） （344KB）（2179）       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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A Forward and Backward Diffusion Model for Gray Level Image Restoration KONG Ling-Hai, HUAN Zhong-Dan Acta mathematica scientia,Series A    2009, 29 (6): 1771-1784.   Abstract （2818）      PDF（pc） （541KB）（1470）       Save In this paper, a spacially adaptive smoothing and enhancing partial differential equation for image restoation,  is presented, which is  coupled with time-delay regularization. In order to reverse the process of image degradation, a newly defined shock filter for edge enhancement is incorporated with a level set motion based equation for noise removal. The balance between the two processes is achieved by an edge discrimination function, which is coupled with time-delay regularization, for distinguishing boundary areas and homogeneous regions in  given images. The proposed model is well-posed in terms of viscosity solutions: the existence and uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical examples of some kinds of images are presented for illuminaating the efficiency of the proposed model. Reference | Related Articles | Metrics

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Existence and Uniqueness of Global Solutions of a Free Boundary Problem Modeling Tumor Growth Wei Xuemei, Cui Shangbin Acta mathematica scientia,Series A    Abstract （2792）      PDF（pc） （338KB）（1573）       Save In this paper the authors study the general nonnecrotic tumor growth model proposed by Byrne and Chaplain in 1995. This is a free boundary problem for a system of nonlinear reaction diffusion equations. The authors apply the Lp theory of parabolic equations and the Banach fixed point theorem to prove the existence and uniqueness of a local solution, and apply the continuation method to get the existence and uniqueness of a global solution. Related Articles | Metrics

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p-Moment Boundedness of Functional Differential Equations with Random Impulses WU Shu-Jin, SONG Qiong, GUO Xiao-Lin Acta mathematica scientia,Series A    2010, 30 (1): 126-141.   Abstract （2787）      PDF（pc） （396KB）（1317）       Save Random impulsive functional differential equation is a mathematical model with extensive applications. By means of Liapunov's direct method coupled with Razumikhin technique and comparison principle, some sufficient conditions for uniformly (uniformly and ultimately, uniformly and uniformly ultimately) p-moment boundedness of such systems are presented, where dV(t, x(t))/dt is imposed only on a little restriction even to obtain uniform boundedness and uniformly ultimate boundedness. Thus the obtained results are very convenient to apply. Reference | Related Articles | Metrics

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Paired-domination Number in Cubic Graphs Chen Xuegang; Sun Liang; Xing Huaming Acta mathematica scientia,Series A    Abstract （2781）      PDF（pc） （222KB）（1849）       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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Nonautonomous Single Population |Models with Periodoc Coeffici ents and Their Optimal Harvesting Policies LU Hong-Ying, WANG Ke Acta mathematica scientia,Series A    2005, 25 (6): 926-932.   Abstract （2780）      PDF（pc） （370KB）（1656）       Save In this paper, using a new method, the authors  discuss the opti mal harvesting problems of nonautonomous single population biological resource.   The authors  choose the maximum annual sustainable yield  as the management obj ective and  investigate the optimal harvesting policies for a class of nonautonomous single  population models. The results include almost all nonautonomous single popul atiom models researched in literature. Reference | Related Articles | Metrics

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Positive Solutions of Multiple-point Boundary Value Problems for Systems of Nonlinear Second Order Differential Equations XIE Sheng-Li Acta mathematica scientia,Series A    2010, 30 (1): 258-266.   Abstract （2740）      PDF（pc） （301KB）（1177）       Save In this paper, by means of fixed point index theory, the existence of positive solutions and multiple positive solutions of m-point boundary value problems for the system of nonlinear second order singular differential equations are studied. Some limit type conditions for ensuring the existence of the solutions are given, which are applicable for more general functions. Reference | Related Articles | Metrics

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A Modified Lagrangian Algorithm for Solving Nonlinear Constrained Optimization Problems He Suxiang;Zhang Liwei Acta mathematica scientia,Series A    Abstract （2724）      PDF（pc） （345KB）（1668）       Save A modified Lagrangian algorithm for solving nonlinear constrained optimization problems is established, which is based on a modified Lagrange function with a controlling parameter.Under suitable conditions, the local convergence of the modified Lagrangian algorithm is proved and the error bounds of solutions are established, which shows that there exists a threshold of the parameter such that, when the parameter is less than this threshold, the sequence of points generated by the algorithm converges to a Kuhn-Tucker point locally. Numerical results by using the modified Lagrangian algorithm for solvingsome simple constrained optimization problems are illustrated. Related Articles | Metrics

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On the Existence of Almost Periodic Solutions for Some Feng Chunhua Acta mathematica scientia,Series A    Abstract （2717）      PDF（pc） （238KB）（1764）       Save A set of sufficient conditions is derived for the existence of almostperiodic solutions for some nonhomogeneous delay differentialequations by using exponential dichotomy and fixed point theorem.This criterion provides a method for the existence analysis ofalmost periodic solution of some nonhomogeneous time delaysystems. Related Articles | Metrics

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An Optimal Filtering Method for Solving a |Sideways Parabolic Equation LI Hong-Fang, FU Chu-Li, XIONG Xiang-Qiu, NA Nan Acta mathematica scientia,Series A    2009, 29 (2): 245-252.   Abstract （2682）      PDF（pc） （388KB）（1211）       Save The authors  consider a sideways parabolic equation in the quarter plane, i.e., a non-standard inverse heat conduction  equation with convection term. People want determine the solution u(x, t) for 0 < x <1 from the data along the line x=1. This is an  ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. Some special regularization method is needed for solving this problem.  This paper considers an optimal filtering method and  gives the H\"{o}lder optimal error estimate between the exact solution and its regularized approximation solution. Furthermore, the convergence of  the regularized approximation solution at x=0 is also obtained. Reference | Related Articles | Metrics

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Sampling Method by Allocating Random Order to Percentiles Guo Kui, Yu Dan Acta mathematica scientia,Series A    Abstract （2655）      PDF（pc） （334KB）（1384）       Save This paper presents a new sampling method, which is called sampling method by allocating random order to percentiles based on some random simulation problems of statistical computation. The sampling is attained by making use of percentiles of distribution function and pseudo-random order, also is applicable to multi-dimensional interval integrals and sampling random variables. Some examples are included to illustrate the method. Related Articles | Metrics

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Stability and Traveling Fronts in Lotka-Volterra Cooperation Model with Stage Structure Wu Shiliang ;Li Wantong Acta mathematica scientia,Series A    Abstract （2614）      PDF（pc） （385KB）（1439）       Save In this paper, the authors derive and study a delayed diffusion system, which models the interaction between the two species, the adult members of which are in cooperation. By using the method of sub- and super-solutions due to Redlinger, we show that the diffusive delay model generates simple global dynamics, i.e., the zero steady state and the boundary equilibria are linear unstable and the unique positive steady state is globally asymptotically stable. We also establish the existence of traveling wave fronts connecting the zero solution of this equation with the unique positive steady state. The approach used in this paper is the upper-lower solutions technique and the monotone iteration recently developed by Wang, Li and Ruan for reaction-diffusion systems with spatio-temporal delays. Related Articles | Metrics