加速牛顿迭代收敛的新方法

提出了加速牛顿迭代收敛的新思想，构造出一类加权牛顿迭代格式，通过选取最优加权因子，使得该格式具有高阶收敛性和较小的渐近误差常数。     

一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。     

On Quasiclassical Field Theories Invariant with Respect to a Lie Group

Mathematical Notes -     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

Asymptotic Correction of More Sturm–Liouville Eigenvalue Estimates

The asymptotic correction technique of Paine, de Hoog and Anderssen can dramatically improve the accuracy of finite difference or finite element eigenvalues at negligible extra cost if closed form expressions are available for the errors in a simpler related problem. This paper gives closed form expressions for the errors in the eigenvalues of certain Sturm–Liouville problems obtained by various methods, thereby increasing the range of problems for which asymptotic correction can achieve maximum efficiency. It also investigates implementation of the method for more general problems.     

Asymptotic Methods Applied to Contact Problems

Asymptotic methods for contact problems are expounded. Some typical integral equations are considered     

Nonparametric estimation and adaptive control in a class of finite Markov decision chains

We consider a class of Markov decision processes withfinite state and action spaces which, essentially, is determined by the following condition: The state space isirreducible under the action of any stationary policy. However, except by this restriction, the transition law iscompletely unknown to the controller. In this context, we find a set of policies under which thefrequency estimators of the transition law are strongly consistent and then, this result is applied to constructadaptive asymptotically discount-optimal policies.Dedicated to Professor Truman O. Lewis, on the occasion of his sixtieth birthdayThis research was supported in part by the Third World Academy of Sciences (TWAS) under Grant TWAS RG MP 898-152, and in part by the Consejo Nacional de Ciencia y Tecnología (CONACYT) under Grant A128CCOEO550 (MT-2).     

A system-theoretic framework for a wide class of systems I: Applications to numerical analysis

A system-theoretic framework is proposed, which allows the study of hybrid uncertain systems, which do not satisfy the so-called “semigroup property.” Characterizations of the notion of robust global asymptotic output stability (RGAOS) are given. Based on the provided characterizations, the qualitative behavior of hybrid systems obtained by time-discretization of systems of ordinary differential equations with a globally asymptotically stable equilibrium point, is studied.     

Estimating means from a non-I.I.D. Mixture of Poisson samples

In this paper, a family of estimators for estimating means when mixing two independent Poisson samples is proposed. This family is based on the probability-generating function of the Poisson distribution and is offered as an alternative to the maximum likelihood estimators, which have some drawbacks. These estimators include the method of moments estimators as a special limiting case.