Exact solution of a quasipotential equation that describes a bound state of spinor particles

Theoretical and Mathematical Physics -     

Certain problems of the approximation of functions in two variables by Fourier-Hermite sums in the space L 2(Γ², e -x ² -y ²)

Summary We give an exact estimate of the deviation of the "triangular" partial sums of the double Fourier-Hermite series of functions of the class L^r₂(D) in the space L₂(Γ2, e^-x2-y2).     

Estimation of electron concentrations from oblique sounding data for a piecewise-one-dimensional model of the ionosphere

Translated from Aktual'nye Voprosy Prikladnoi Matematiki, pp. 28–31, 1989.     

Normal connection in the geometry of normalized submanifolds of affine space

A survey is given of results concerning the study of the structure of a normalized subraanifold of affine space with the help of a normal connection.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.93–107, 1989.     

Low-temperature reaction of magnesium with fluorobenzene

The low-temperature reaction of magnesium with fluorobenzene has been investigated. Joint condensation of magnesium and fluorobenzene vapours at low temperatures quantitatively gave phenylmagnesium fluoride in one stage.     

Isotopic effects in H-atom abstraction from matrix molecules by methyl radicals in poly(methyl methacrylate). Determination of the scale of relative reagent motions

The H-abstraction by ?H₃ and ?D₃ radicals from PMMA molecules is investigated at 77 and 120 K. The film samples are prepared from the mixture of normal and deuterated PMMA. The reaction is of the first order with respect to radical concentration. Its rate is retarded in time as compared to the exponential law. An analysis of the molecular product ratio for the reaction allows the primary isotopic effect to be estimated. The initial reaction rate depends nonmonotonously on the proportion of the deuterated polymer in the matrix. Namely, there exists a range of isotopic compositions, with the reaction rate increasing with the portion of a deuteropolymer in the mixture. At 77 K the reaction rate of ?D₃ is lower than that of ?H₃ in PMMA of a mixed isotopic composition. This results from the proximity of ?D₃ with unreactive parental macromolecules, which reduces the local H concentrations around ?D₃ as compared to the mean concentration. At 120 K the radical decay rates do not differ. This fact cannot be explained by unfrozen mobilities of radicals at high temperatures or by their migration from parental macromolecules. The phenomenon is interpreted in terms of thermal fluctuations involving a great area around a radical and ensuring its migration within this area. The electron spin echo method is used to estimate the distance between a radical and its parental macromolecule, a ≥ 9.6 Å. This is the lower limit of the reaction accessibility.