Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

Interpolation and extrapolation of gamma detection efficiency curve as a function of distance

Summary The paper deals with the common mistake of interpolating calculation of the efficiency of gamma-detectors by the inverse square law of the distance of the source from the detector cap and suggests the use of the distance from the virtual point detector instead.     

Asymptotic Directions for Best Approximations of n-Dimensional Linear Forms

Some results about asymptotic directions for best approximations of linear forms similar to known results on best simultaneous approximations are obtained.     

Preparative synthesis of the stable α-fluorosulfatotetrafluoro-ethylbis(perfluoroisopropyl)methyl radical

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2450–2451, October, 1990.     

Fluoroaliphatic esters of fluorosulfonic acid. 4. Reactions of α-fluorosulfatoperfluoro ketones with nucleophilic reagents

-Fluorosulfatoperfluoroethyl isopropyl ketone I and fluorosulfatopentafluoroacetone II react with alkali metal chlorides and bromides to form the corresponding -haloperfluoro ketones as a result of direct nucleophilic substitution.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2066–2069, September, 1990.     

Derivatives of bis (pentafluoroethyl) arsinous acid

Conclusions Replacement of the fluorine in bis (pentafluoroethyl)fluoroarsine gave a number of bis (pentafluoroethyl)arsinous acid derivatives and bis(pentafluoroethyl)phenylarsine.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 121–122, January, 1973.