泰勒中值定理中值点的分析性质

讨论泰勒中值定理中中值点的连续性及可导性问题,给出泰勒中值定理中中值点连续及可导的充分条件,同时给出计算其导数的公式.     

二元函数微分中值定理中值点的分析性质

讨论二元函数微分中值定理中值点的连续性及可导性问题,给出二元函数微分中值定理中值点连续及偏导数存在的充分务停,同时给出计算其偏导数的公式。     

利用微分中值定理判断级数的敛散性

利用Lagrange中值定理和Taylor公式,给出判断几类特殊任意项级数的敛散性的方法.     

多元函数微分中值定理中介值点的分析性质

讨论了n元函数微分中值定理中介值点的唯一性、连续性、可微性问题.给出了介值点具有唯一性、连续性、可微性的充分条件,并且给出了介值点的导数公式.     

广义Taylor公式的几个简单证明方法

<正> 微分中值定理在高等数学中具有重要的理论意义。其中Taylor中值定理更具有一般性。文[1]给出了两个广义Taylor公式,文[2]对其中一个公式给出一个简单证明方法。本文对文[1]的两个公式再给出三个简单的证明方法。     

微分中值定理与Newton-Leibniz公式可互相证明

首先用微分中值定理推出了Newton-Leibniz公式,同时也用Newton-Leibniz公式推出了三个微分中值定理,从而证明了微分中值定理与Newton-Leibniz公式可互相证明.     

积分中值定理的推广及其应用

给出了积分中值定理的一个推广,讨论了推广的积分中值定理中间值的渐近性.     

一个广义的Cauchy型的Taylor公式

给出了一个高阶导数形式的、广义的C auchy型的T ay lor公式,它将数学分析中一阶微分形式的C auchy中值定理推广到高阶导数形式,同时它也是T ay lor中值定理的推广.     

广义Taylor中值函数若干分析性质

文[2-8]对微分中值定理及Taylor定理"中间点"的渐近性质进行了研究,本文在此基础上,给出了"广义Taylor中值函数"的定义,对"广义Taylor中值函数"的分析性质进行了系统的讨论,证明了"广义Taylor中值函数"的单调性、可积性、连续性、可微性等分析性质.     

广义柯西中值定理的“中间点”的渐近性

广义柯西中值定理的“中间点”的渐近性殷子和，马龙友（武汉工业大学北京研究生部）（北京建筑工程学院）文［１］、［２］对柯西中值定理的“中间点ξ”的渐近性问题进行了研究．本文给出广义柯西中值定理的“中间点ξ”的渐近性定理，并予以证明．柯西中值定理的一种推...     

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.     

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...     

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.     

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.     

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.     

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。