中立双曲型时滞偏微分方程解振动的充要条件

本文讨论一类线性中立双曲型时滞微分方程解的振动性质，获得了其一切解振动的充要条件．     

中立型向量双曲偏微分方程的H-振动性

本文研究了一类中立型向量双曲偏微分方程边值问题的振动性.利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维泛函微分不等式正解的不存在性问题,获得了该类边值问题在Dirichlet边界条件下所有解H-振动的若干新的充分条件,其中H是Rm中的单位向量.     

脉冲向量中立型抛物方程解的H-振动性

研究一类脉冲向量中立型抛物偏微分方程边值问题解的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲中立型微分不等式正解的不存在性问题,并借助于一阶脉冲中立型微分不等式,给出了该类边值问题所有解H-振动的若干充分性判据,这里H是R~M中的单位向量.     

脉冲中立型时滞抛物偏微分方程组的振动准则

考虑一类脉冲中立型时滞抛物偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在Robin,Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

非线性中立抛物型偏微分方程系统的振动性定理

研究一类非线性中立抛物型时滞偏微分方程系统解的振动性质,利用积分不等式和泛函微分方程的某些结果,获得了该类系统在第一类边值条件下所有解振动的若干充分条件.结论充分表明振动是由时滞量引起的.     

一类脉冲中立型时滞抛物方程组的振动性

研究一类脉冲中立型时滞抛物方程组解的振动性,得到了该类方程组在两类不同边界条件下所有解振动的若干充分条件.     

时滞抛物型与双曲型微分方程解的振动性的讨论

对一类线性以及非线性抛物型时滞微分方程的解在第一或第二边值条件下解振动的充分必要条件进行了讨论,给出了解振动的一些结论.并且对一类线性以及带强迫项的非线性双曲型时滞微分方程的解在第一或第二边值条件下解振动的充分必要条件进行了讨论,也给出了一些结论.     

中立抛物型时滞偏微分方程解振动的充要条件

本丈讨论一类多滞量中立抛物型时滞偏微分方程解的振动性质。获得了其一切解振动的充要条件；所得充要条件将时滞偏微分方程解的振动判别问题转化为时滞微分方程解的振动判别问题；指出了其与普通抛物型偏微分方程解的质的差异．     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

二阶非线性中立型微分方程的振动准则

研究了一类二阶非线性中立型微分方程的振动性,得到了一些新的振动准则,推广、改进和统一了文献中的一些结果.     

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.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

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...     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

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.     

Invariant properties of systems of equations of the mechanics of inhomogeneous fluids

The invariant properties of the fundamental system of equations of the mechanics of inhomogeneous fluids and its widely used approximations are analysed by the methods of continuous group theory. Simplifying assumptions significantly alter the invariant properties of the systems of equations. Both extending and contracting the admissible symmetry group can occur and provide evidence of the violation of the conditions of equivalence between the original and derived systems. For example, the use of the incompressibility and Boussinesq approximations leads to extension of the concept of an inertial reference frame to all frames moving relative to one another with arbitrary linear acceleration.     

Stability estimates of solutions of systems of functional-differential equations of neutral type

A system of linear functional-differential equations of neutral type is considered. Investigation of stability is carried out by the method of Lyapunov functions of quadratic form. Sufficient conditions for the asymptotic stability and estimates of the exponential decay of solutions for an arbitrary and a small deviation of the argument are obtained.Candidate of the Physicomathematical Sciences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43. No. 9, pp. 1123–1135, September, 1991.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.