一类四阶半线性方程的渐近解

在Sobolev空间给出了一类四阶半线性方程初值问题解的一个渐近方法，证明了渐近理论及形式近似解的合理性在时间变量无穷大时(即0≤t≤0(|ε|^-1))成立．作为渐近理论的应用，对一个带初值问题的特殊四阶半线性方程进行了探讨．     

Asymptotic results for over-dispersed operational risk by using the asymptotic expansion method

In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptotic expansion for the quantile of compound negative binomial process is explored for computing the capital charge of a bank for operational risk. Moreover, when the dependence structure between different risk cells is modeled by the Frank copula, this approach is extended to the multi-dimensional setting. A practical example is given to demonstrate the effectiveness of approximation results.     

特征值问题有限元解的高阶展开及外推

本文考虑模型问题:■,得到了下面的渐近展式: ■对于特征函数,本文也证明了相应的渐近展开.     

Razumikhin-type theorems for asymptotic stability of impulsive stochastic functional differential systems

<正>In this paper,we investigate the pth moment uniformly asymptotic stability of impulsive stochastic functional differential systems by extending some Razumikhin-type theorems.Based on the Lyapunov functions and Razumikhin techniques,some criteria are established and their applications to impulsive stochastic delay systems are proposed.An illustrative example shows the effectiveness of our results.     

二阶非线性泛函微分方程解的振动性与渐近性

讨论了两类二阶非线性泛函微分方程(a(t).(y'(t))σ)' q(t)f(y(τ(t)))g(y'(t))=0,(a(t).(y'(t))σ)' q(t)F(y(t),y(τ(t))g(y'(t))=0,其中t≥to,σ为正常数,当t≥to时a(t)>0,q(t)≥0,且q(t)不最终恒为0,τ'(t)>0,且limt→ ∞τ(t)= ∞.利用一些分析的技巧,得到了这两类方程的解振动与渐近性的充分性判据,所获结果可分别应用于σ=奇/奇与σ=偶/奇的情形.改进并推广了已有文献中的相应结论.     

关于Smarandache Ceil函数的一个混合均值

对任意正整数n,k≥2为给定整数,Smarandache Ceil函数sk(n)定义为最小的正整数x,使得n|xk,即Sk(n)=min{x∶x∈N,n|xk}.利用Smarandache Ceil函数的定义及解析的方法,研究Smarandache Cei函数sk(n)与欧拉函数的均值分布性质,并给出一个有趣的渐近公式.     

Lehmer DH数的分布性质的推广

设素数p≥3，利用广义Kloostermann和估计与三角和估计研究了模p剩余系中Lehmer DH数的分布性质，并得出分布的渐近公式。     

Large-sample results for optimization-based clustering methods

Many common (nonhierarchical) clustering and classification methods are optimization-based methods, in the sense described by Windham (1987) in this Journal. This paper gives some large sample properties for estimates derived by such methods. Under appropriate conditions, such estimates converge with probability one to a limit, and are asymptotically normally distributed around that limiting value. The conditions are satisfied by most of the common examples of optimization-based methods. Prepared for the 2nd International Conference, International Federation of Classification Societies, Charlottesville, VA, 1989. Supported in part by summer research funds, Graduate School of Business Administration, University of Colorado at Denver.     

一类中立型时滞微分大系统的渐近稳定性

ＷａｎｇＷ．Ｊ．（１９９１）利用Ｌｙａｐｕｎｏｖ函数的方法。研究了一类大型滞后系统的渐近稳定性。本文利用Ｍ－矩阵及不等式技巧首先讨论一类泛函积分方程的零解的渐近稳定性，得到了其零解渐近稳定的判定定理，并利用它来判定一类中立型大系统的渐近稳定性。     

关于回归函数的核估计的渐近正态性

研究了回归函数的核估计的渐近性质。证明了在一定条件下、回归函数的核估计序列是渐近正态的。