Some categorical properties of the functors O τ and O R of weakly additive functionals

In the paper, the spaces of weakly additive τ-smooth and Radon functionals are investigated. It is proved that the functors of weakly additive τ-smooth and Radon functionals weakly preserve the density of Tychonoff spaces, and the functor of weakly additive τ-smooth functionals forms a monad in the category of Tychonoff spaces and their continuous mappings. Examples and remarks are given showing that these functors fail to satisfy certain Shchepin normality conditions. Problems having positive solutions for normal functors are presented.     

REPRESENTATION OF SYMMETRIC SUPER－MARTINGALE MULTIPLICATIVE FUNCTIONALS

The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically. A representation for symmetric super-martingale multiplicative functionals are also given.     

集值映射的函数单调性和余强制性

本文介绍几个新的集值映射的函数单调性和余强制性概念，并讨论它们与已有概念间各种可能的蕴含关系．     

Solution of Parabolic Equations by Means of Lyapunov Functionals

We propose a new approach to defining the notion of a solution to linear and nonlinear parabolic equations. The main idea consists in studying connections between solutions to dynamic problems in the variational shape and the properties of the corresponding Lyapunov functionals which are strictly decreasing along the trajectories of the above-mentioned dynamic equations except for the equilibrium points. It turns out that the families of Lyapunov functionals constructed by T. I. Zelenyak enable us to propose a new approach to defining solutions to both linear and nonlinear parabolic problems. All results are given in the case of smooth solutions. Note that the Lyapunov functionals can be used for studying solutions with unbounded gradients.     

一类神经网络全局渐近稳定性分析

在这篇文章里,我们研究了一类时滞神经网络的平衡点的存在,唯一性,及其全局渐近稳定性(GA S).我们的主要思想方法是同胚映射,李雅谱诺夫泛函方法,我们在很弱的条件下解决一类时滞神经网络的GA S.     

Analysis of a predator-prey model with Crowley-Martin and modified Leslie-Gower schemes with stochastic perturbation

In this paper, we study a nonautonomous predator-prey model with Crowley-Martin and modified Leslie-Gower schemes with stochastic perturbation. The existence of a global positive solution and stochastically ultimate boundedness are obtained. Sufficient conditions are established for extinction, persistence in the mean, and stochastic permanence of the system. Finally, simulations are carried out to verify our results.     

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

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BOUNDEDNESS IN p-NFDES

1 IntroductionRecently, the papers (cf [1], [2]) have established stabi1ity of p-NFDEsusing Liapunov-Razumikhin functionaJs. However, in order to study the limtset and the existence of periodic solutions of p-NFDEs, we need to know notonly the stability but ajso the boundedness of solutions. In this paper, weshal1 discuss the boundedness properties of P-NFDEs by Liapunov functionals,which improve some boundedness conditions for FDEs in the literature. Someexamples are also worked out t…     

响应变量删失时函数型部分线性分位数回归模型的估计

最近几年,函数型数据分析的理论和应用飞速发展.在许多实际应用里,响应变量往往存在随机右删失的情况.考虑利用函数型部分线性分位数回归模型来刻画函数型和标量预测量与右删失响应变量之间的关系.基于函数型主成分基函数来逼近未知的斜率函数,通过极小化逆概率加权分位数损失函数得到未知系数的估计量.文章的估计方法容易通过加权分位数回归程序实现.在一定的假设条件下,给出了有限维参数估计量的渐近正态性与斜率函数估计量的收敛速度.最后,通过模拟计算与应用实例证明了所提方法的有效性.     

The \(C^1\) solution of the high dimensional Feigenbaum-like functional equation

By constructing a structure operator quite different from before, and using the Schauder's fixed point theory, the existence and uniqueness of the \(C^1\) solutions of the high dimensional Feigenbaum-like functional equations are discussed.     

Translation Continuous Functionals on CB(ℝ) and Their Supports

Two constructions of translation continuous functionals on the space of bounded continuous functions on a locally compact group are introduced and the properties of these functionals related to the notion of support of a functional are considered.     

进化泛函网络多维函数逼近理论及学习算法

提出了一种用于多维函数逼近的进化策略修正泛函网络基函数系数的新算法,并给出了其算法学习过程.利用进化策略的自适应性来确定基函数前的系数,改进了泛函网络的参数通过解方程组来得到这一传统方法.仿真结果表明,这种新的逼近算法简单可行,能够逼近给定的函数到预先给定的精度,具有较快的收敛速度和良好的逼近性能.     

Controllability of Neutral Functional Differential and Integrodifferential Inclusions with Infinite Delay

Sufficient conditions are derived for the controllability of neutral functional differential and integrodifferential inclusions with infinite delay in a Banach space. The results are obtained by using a fixed-point theorem for condensing maps due to Martelli. An example is given to illustrate the results.     

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This paper studies estimation in functional partial linear composite quantile regression model in which the dependent variable is related to both a function-valued random variable in linear form and a real-valued random variable in nonparametric form. The functional principal component analysis and regression splines are employed to estimate the slope function and the nonparametric function respectively, and the convergence rates of the estimators are obtained under some regularity conditions. Simulation studies and a real data example are presented for illustration of the performance of the proposed estimators.     

On Approximate Solutions in Vector Optimization Problems Via Scalarization

This work deals with approximate solutions in vector optimization problems. These solutions frequently appear when an iterative algorithm is used to solve a vector optimization problem. We consider a concept of approximate efficiency introduced by Kutateladze and widely used in the literature to study this kind of solutions. Necessary and sufficient conditions for Kutateladze’s approximate solutions are given through scalarization, in such a way that these points are approximate solutions for a scalar optimization problem. Necessary conditions are obtained by using gauge functionals while monotone functionals are considered to attain sufficient conditions. Two properties are then introduced to describe the idea of parametric representation of the approximate efficient set. Finally, through scalarization, characterizations and parametric representations for the set of approximate solutions in convex and nonconvex vector optimization problems are proved and the obtained results are applied to Pareto problems. AMS Classification:90C29, 49M37 This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.     

Stability for impulsive functional differential equations with infinite delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.     

非线性中立抛物型泛函微分方程解的振动判据

讨论一类多滞量中立抛物型泛函微分方程解的振动性质,获得了其一切解振动的充分条件及线性情况下的充要条件;指出了与普通抛物型偏微分方程质的差异。     

The exact boundaries of the stability domains of linear differential equations with distributed delay

For a differential equation with a distributed varying delay, sufficient criteria for the asymptotic and uniform stability of solutions are obtained. The constructed examples demonstrate exactness of the boundary of the obtained stability domain.     

W_2~1[a,b]中的最佳逼近泛函及应用

1 引言 线性泛函的逼近问题有着十分广泛的应用背景,本文在具有再生核的W_2~1[a,b]空间中讨论线性泛函L(f)的形如 L_n(f)=sum from i=1 to n(i/1)w_if(x_i) (1)的逼近问题,其中{w_i}_1~n是待定系数,如果存在一组常数{w_i~x}_1~n使 L_n~x=sum from i=1 to n(i/1)w_i~xf(x_i) (2)满足||L—L_n~x||=inf||L—L_n||,则称L_n~x是L的最佳逼近,记 w_i E_n=L—L_n, E_n~3=L—L_n~x,则称E_n~x是最佳逼近误差泛函。 本文在§1中给出L_n~x的表达式及L_(n+1)~x与L_n~x之间的递推公式。并证明L_n~x的收敛性。§3中讨论了上L_n~x(f)在数值积分及常微分方程数值解中的应用,并给出数值算例。     

Functional Inequalities for the Decay of Sub-Markov Semigroups

A general functional inequality is introduced to describe various decays of semigroups. Our main result generalizes the classical one on the equivalence of the L ²-exponential decay of a sub-Markov semigroup and the Poincaré inequality for the associated Dirichlet form. Conditions for the general inequality to hold are presented. The corresponding isoperimetric inequality is studied in the context of diffusion and jump processes. In particular, Cheeger's inequality for the principal eigenvalue is generalized. Moreover, our results are illustrated by examples of diffusion and jump processes.