Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

Coxeter Transformation and Quasiquivers

Mathematical Notes -     

Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Strictly majorizing tests in problems with nuisance parameters

An existence theorem is proved for a strictly majorizing test of composite hypotheses. Statistical corollaries of the theorem are explored.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 73–78, 1986.     

Solving the problem of contact equilibrium of a punch and an elastic body

The variational problem of contact equilibrium of a punch and an elastic body is considered. An equivalent formulation of the problem is given in variational inequality form. Existence and uniqueness of the solution is investigated in a particular case. A penalty method is proposed for approximate solution of the problem.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 97–103, 1985.     

Reaction of methyl bromopropiolate with diamines as a method of synthesis of imidazolidine derivatives

A convenient method of synthesis of 2-(methoxycarbonylmethylene)-substituted imidazolidines and imidazolidinium bromides, and also of bicyclic diazo compounds has been developed starting from methyl bromopropiolate and ethylenediamine and its derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1205–1208, September, 1991.     

Free and nonsteady-state oscillations of elastic fluid-filled systems situated on an elastic base

We develop a method of computing the nonsteady-state and free oscillations of a framed elastic structure situated on an elastic base and containing an ideal compressible fluid. The solution uses the method of integral transforms in conjunction with the method of orthogonal polynomials. In the transform space the problem reduces to systems of linear algebraic equations. The Fourier transform is applied to return to the original space. Examples of the computation are given.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 69–72.