一类三阶非线性时滞系统的全局渐近稳定性

运用"类比法"对一类三阶非线性时滞系统构造了较好的Lyapunov函数,得到该系统零解全局渐近稳定的充分条件.     

基于一类时滞不等式的时滞微分方程的渐近稳定性

利用Lyapunov的方法讨论了时滞微分方程x.(t)=f(t,x(t),x(t-τ(t)))的全局指数渐近稳定性和全局渐近稳定性.     

一类三阶时滞微分方程解的渐进稳定性

本文研究了三阶非线性时滞微分方程解的渐近稳定性.利用Lyapunov泛函,得到了微分方程的零解是渐进稳定的,这一结果推广了文献[2]的结果.     

一类三阶时滞微分方程解的渐进稳定性

本文研究了三阶非线性时滞微分方程解的渐近稳定性. 利用Lyapunov 泛函, 得到了微分方程的零解是渐进稳定的, 这一结果推广了文献[2] 的结果.     

一类非线性脉冲泛函微分方程解的渐近性

利用构造Lyapunov泛函方法讨论了一类具有正负系数的非线性脉冲泛函微分方程解的渐近性,给出方程的解趋于一个正常数的充分条件,并举例说明定理条件和结论的可实现性.     

一类具有时滞和移民项的传染病模型的稳定性分析（英文）

本文研究一类具有移民项和潜伏期时滞的传染病模型,讨论了模型平衡点的存在性和解的一致持续性,利用Lyapunov泛函和Lyapounov-LaSalle不变性原理,建立了唯一的平衡点的全局渐近稳定性.     

具有时滞和基于比率的三种群捕食系统的持久性与全局渐近稳定性

研究一类具有时滞和基于比率的三种群食物链捕食-被捕食动力学模型.证明了该系统在适当条件下的一致持久性;通过构造Lyapunov泛函,得到了该系统正平衡点全局渐近稳定的充分条件.     

一类比率型功能性反应捕食模型的稳定性分析

研究了一类具有比率型功能性反应的捕食模型,对模型进行了定性和稳定性分析,讨论了模型唯一正平衡点的存在条件,以及模型各个平衡点的性态.得到了各个平衡点全局渐近稳定的充分条件.通过绘制模型的相轨线,分析轨线的走向得到了原点全局渐近稳定的条件,并证明了模型不存在非平凡正周期解的条件,通过构造Lyapunov函数得到了模型的唯一正平衡点是全局渐近稳定的结论.     

时滞Hopfield神经网络模型渐进稳定性的新准则

在不考虑激励函数有界,可微和单调的情况下,利用Lyapunov泛函方法,得到了时滞Hopfield神经网络模型的平衡点存在性和全局渐近稳定性的新准则.研究结果改进和推广了以前相关文献的结果.     

一类时滞多组传染病模型的全局稳定性分析

本文研究具有变量分离发生率的具时滞的多组传染病模型.首先,分别针对强连通和非强连通情形,得到基本再生数$R_0$. 然后运用Lyapunov泛函方法和LaSalle不变集原理分别分析了当$R_0<1$时无病平衡点$P_0$ 的全局渐近稳定性以及$R_0>1$时地方病平衡点$P^*$的全局渐近稳定性.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.