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.     

Isolation of singularities in the density and the kernel of a two-dimensional integral equation for complex boundary surfaces

We consider the solution of integral equations in problems of three-dimensional electromagnetic fields in piecewise-homogeneous media. An algorithm is proposed for analytical isolation of singularities in the kernel and the density of the integral equation of potential theory for the case of complex boundary surfaces.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 14–17, 1985     

Numerical analysis of near electromagnetic fields of a parabolic cylinder and a paraboloid of revolution

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 119–127.     

Asymptotic description of solutions of the fourth Painlevé equations on the stokes rays analogs

The proof of the existence of classical solutions is given for the Painlevé type nonlinear ordinary differential equations. The solutions have asymptotic formulas, which can be obtained by the isomonodromic deformation method.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 101–109, 1989.     

Fluorescence spectra of different configurations of the diphenyl molecule in solid paraffin solutions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 2, pp. 212–217, August, 1989.     

Positive definite functions on the Heisenberg group

Work supported in part by the NSF