关于伽马函数的不等式与渐近展开式

给出伽马函数的一个渐近展开式.基于获得的结果,我们建立了伽马函数的不等式.     

关于伽马函数的不等式与渐近展开式（英文）

给出伽马函数的一个渐近展开式.基于获得的结果,我们建立了伽马函数的不等式.     

一类非线性奇摄动方程的匹配解法和解的精度估计

利用匹配渐近展开法,研究了一类非线性奇异摄动方程.在适当的条件下,得出了该类问题解的渐近展开式.并将结果应用于例子,对渐近解与精确解和用两变量方法求得的解进行比较,可知所得到的渐近解达到了较高精度.     

第二类两端奇异Fredholm积分方程的分数阶线性插值方法

考虑第二类两端奇异的Fredholm积分方程,假设核函数在区间的两个端点非光滑,存在分数阶的Taylor展开式.对于这种类型的核函数,在包含端点的小区间上采用分数阶插值,在剩余区间上采用分段线性插值逼近,由此得到一种分数阶线性插值退化核方法.本文讨论该方法收敛的条件,给出收敛阶估计.数值算例表明这种分数阶混合线性插值方法对于两端奇异核函数有着较好的计算效果.     

关于Landau常数和Euler-Mascheroni常数的渐近展开式以及Stirling级数的系数

文章给出一个递推关系式来确定Landau常数的渐近展开式的系数.考虑了Euler-Mascheroni常数和n!的渐近展开式,并给出了递推关系式来确定每个展开式的系数,没有利用Bernoulli数.     

化学动力学中一类奇摄动抛物型方程的周期解

本文研究来源于分层介质中化学动力学的奇摄动抛物型方程周期解问题,构造了一致有效的渐近展开式,并获得了渐近估计.     

渐近级数与收敛级数的比较

函数的渐近级数展开式与收敛级数展开式是解决非线性问题的有力工具.本文剖析了这两类展开式的特性、分析了它们的区别等,在此基础上对如何准确有效地使用这两类展开式进行了探讨.     

二阶线性差分方程解的渐近线性

本文给出充分或必要的条件使二阶线性差分方程的解在不同程度上渐近于线性函数,并对收敛速度作出估计.所用的主要工具是第一和第二 Riccati 差分方程.     

广义Kac方程的解的渐近稳定性

讨论了碰撞核具有一定奇异性的广义Kac方程的解的唯一性和渐近稳定性,证明了广义Kac方程的解在概率距离下以指数形式快速收敛到函数δ(v).     

关于Euler-Mascheroni常数的不等式与渐近展开式（英文）

给出一个递推关系式来确定调和数的渐近展开式的系数.我们建立了Euler-Mascheroni常数的不等式.     

A remark on the asymptotic expansion of density function of Wiener functionals

We consider the asymptotic expansion of density function of Wiener functionals as time tends to zero as in [S. Kusuoka, D.W. Stroock, Precise asymptotics of certain Wiener functionals, J. Funct. Anal. 99 (1991) 1-74], and give an explicit formula for the first coefficient.     

Two new asymptotic expansions of the ratio of two gamma functions

Formal expansions, giving as particular cases semiasymptotic expansions, of the ratio of two gamma functions are obtained.     

Singularly perturbed integral equations

We study singularly perturbed Fredholm equations of the second kind. We give sufficient conditions for existence and uniqueness of solutions and describe the asymptotic behavior of the solutions. We examine the relationship between the solutions of the perturbed and unperturbed equations, exhibiting the degeneration of the boundary layer to delta functions. The results are applied to several examples including the Volterra equations.     

Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expectations at each space–time node. Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants.     

On the eigenvalues of certain canonical higher-order ordinary differential operators

We consider the operator of taking the 2pth derivative of a function with zero boundary conditions for the function and its first p−1 derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for p=1 and p=3.     

Asymptotic expansion of solutions to nonlinear elliptic eigenvalue problems

We consider the nonlinear eigenvalue problem

where is an appropriately smooth bounded domain and 0$"> is a parameter. It is known that if , then the corresponding solution is almost flat and almost equal to inside . We establish an asymptotic expansion of when , which is explicitly represented by .

     

An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order

Han's ‘multinode higher-order expansion’ in [H] is shown to be a special case of an asymptotic error expansion available for any bounded linear map on C([a..b]) that reproduces polynomials of a certain order. The key is the formula for the divided difference at a sequence containing just two distinct points.     

Minimal compact global attractor for a damped semilinear wave equation

Abstract

The asymptotic behavior of eigenvalues of an elliptic operator with a divergence form is discussed. The coefficients of the operator are discontinuous through a boundary of a subdomain and degenerate to zero on the subdomain when a parameter tends to zero. We will prove that the eigenvalues approach eigenvalues of the Laplacian on the subdomain or on the complement. We will obtain precise asymptotic behavior of their convergence.     

Perturbation Theory for Critically Damped Nonlinear Systems

A simple analytical method is developed to obtain the time response of the second order critically damped nonlinear systems based on the method of variation of parameters. Solutions obtained for different initial conditions for a second order system whose linear equation has equal roots (negative) shows good agreement with those obtained by numerical method.AMS: 34E05