时延细胞神经网络的概周期解的存在性和指数稳定性

研究时延细胞神经网络的概周期解存在性和全局指数稳定性问题 ,巧妙地引入可调实参数di>0 (i =1,2 ,… ,n) ,获得了该神经网络存在唯一的概周期解的充分条件和所有其它解均指数地收敛于此概周期解的充分条件 .     

具有混合时滞的中立型Hopfield神经网络的概周期解

研究一类具有混合时滞的中立型Hopfield神经网络概周期解.通过运用指数二分性及不动点定理,获得了其概周期解的存在性与全局指数稳定性的充分条件,所得结果是新的,并且推广和改进了已有文献的相关结果.     

具S-型分布时滞的模糊细胞神经网络的周期解及指数稳定性

研究了一类具S-型分布时滞的模糊细胞神经网络(FCNN)的周期解及全局指数稳定性问题.在不要求激励函数全局L ipsch itz条件下,通过使用指数型二分性和Schauder不动点定理以及构造Lyapunov函数,得到了模糊细胞神经网络模型周期解和指数稳定性的一些充分条件.此外,给出一个实例说明结果是可行的.     

时间尺度上漏项中具有变时滞的中立型模糊BAM神经网络的概周期解

本文研究了一类时间尺度上漏项中具有变时滞的中立型模糊BAM神经网络.利用时间尺度上线性动力学方程的指数二分法,Banach不动点定理和时间尺度上的微积分理论,得到了这类模糊BAM神经网络在时间尺度上概周期解的存在性和指数稳定性的充分条件.     

时滞细胞神经网络概周期解的存在性与全局指数稳定性

通过利用Banach 空间中的不动点定理和Lyapunov泛函的方法,获得了时滞细胞神经网络概周期解的存在性与全局指数稳定性的新结论. 所获结果在较大程度上改进和推广了已有文献中的相应结果.     

时间尺度上带有连结项的模糊神经网络的概周期解

首先根据压缩映射原理,得出了时间尺度上带有连结项的模糊神经网络的概周期解存在性的充分条件:当(H1)~(H4)成立时,该系统有唯一的概周期解。然后利用分析学的方法得出该概周期解是全局指数稳定性的充分条件:当(H1)~(H5)成立时,此概周期解是全局指数稳定的。     

具有时变时滞惯性四元Hopfield神经网络反周期解的动力学研究

周期性、反周期性和概周期性是时变神经网络的重要动态行为特性.本文在不将所研究的神经网络分解为实值系统的情况下,根据重合度理论中的延拓定理和不等式技巧,通过构造不同于现有平衡点稳定性研究的李雅普诺夫函数,研究了一类具有变时滞的惯性四元Hopfield神经网络的反周期解的动力学问题,给出了上述神经网络反周期解存在的一个新的判别条件.并通过构造李雅普诺夫函数论证了上述神经网络反周期解的指数稳定性.     

基于时间尺度的中立型时滞细胞神经网络概周期解的动态特征研究

在时间尺度上,通过使用线性动力方程的指数二分法、不动点理论和微积分理论,研究带有泄漏项的中立型时滞细胞神经网络模型,获得了一些使其概周期解存在和全局指数稳定的充分条件,并将以前的结论在时间尺度上做了扩展.     

具有时滞的细胞神经网络周期解与稳定性

本文研究了具有时滞的细胞神经网络周期解存在性和平凡解的稳定性问题 .利用 Lyapunov函数法并结合不等式分析技巧 ,我们首先证明了时滞细胞神经网络的解是有界的 ,然后建立了时滞细胞神经网络的周期解的存在准则 ,最后在时滞细胞神经网络有平衡点时 ,给出了神经网络系统的平衡点指数稳定的充分条件 .其结果推广了文 [7,8]的相应结果 .     

一类具分布时滞的Hopfield网络模型的概周期解存在性与稳定性

利用Banach空间压缩不动点定理和微分不等式的分析技巧,研究一类具分布时滞的Hopfield神经网络模型的概周期解的存在性和稳定性。得到了系统存在概周期和全局指数稳定的新的充分条件。所得结果改进和推广了相关文献的结论。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].