Calculation of current fields in a shallow lake

Translated from Issledovaniya po Prikladnoi Matematike, No. 16, pp. 69–74, 1989.     

Biradical with a polyfluorinated terphenylene backbone

Russian Chemical Bulletin - A method was developed for the synthesis of perfluoro-1,1′:4′,1″-terphenyl by the reaction of chloroperfluorobenzene with zinc dust followed by the...     

Regularization of linear difference equations with analytic coefficients and their applications

We propose a regularization method for four-element linear difference equations with analytic coefficients. We study these equations in the class of functions which are holomorphic in the complex plane with a cruciform cut and vanish at infinity. We give several examples illustrating the dependence of the solvability properties of equations on the choice of periodic coefficients. We describe various applications.     

Estimate for the Entropy Numbers of the Weighted Hardy Operators that Act from Banach Space to q-Banach Space

Siberian Mathematical Journal - We study weighted Hardy operators from the Banach space Lp to the q-Banach space Lq and obtain estimates for the entropy numbers of one- and two-weighted Hardy...     

ESR study of the nitric oxide production in tissues of animals under an external influence on the functioning of the cardiovascular and nervous systems

Electron spin resonance (ESR) of the ternary (DETC)₂-Fe²⁺-NO complex has been applied to determine the nitric oxide production in tissues of rats and snails. A preliminary ESR study of the NO content in tissues of rats before and after artificially induced acute myocardial infarct was performed. The analysis of the obtained results shows that the nitric oxide production during the first hour after the moment of inducing myocardial infarct decreases. It is also demonstrated that ESR may be useful in the study of the influence of the long-term sensitization of snails on the nitric oxide production in their body. The changes in the NO production after the external influences in both cases are discussed.     

Studying the properties of learning elements from their program implementation

Translated from Issledovaniya po Prikladnoi Matematike, No. 12, pp. 10–17, 1984.     

Asymptotic formulas for n-diameters of certain compacta in L2[0, 1]

In the current article the order of the Kolmogorov n-diameters of compacta, determined by the operatorsLy =p (x)dy/dx +q (x)y, Ly = [–d²/dx² +q (x) d/dx]^r y in L₂[0, 1] with a bound on the order of the error is studied and asymptotic formulas for d_n as a function of p(x), q(x), and r are derived.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 331–340, September, 1976.     

Hydrodynamic and Thermal Fields in a Porous Medium with Injection of Superheated Steam

The plane one-dimensional and radially symmetric problems of injection of superheated steam into a porous medium saturated with gas are considered. Self-similar solutions are constructed on the assumption that in this case four zones are formed in the porous medium, namely, a gas flow zone, superheated and wet steam zones, and a water slug zone formed due to steam condensation. On the basis of the solution obtained, both the effects of the boundary pressure, mass flow rate, and temperature of the injected superheated steam and the effect of the initial state of the porous medium on the propagation of the hydrodynamic and thermal fields in the porous medium are studied.     

Hardy—Steklov operators and Sobolev-type embedding inequalities

We characterize weighted inequalities corresponding to the embedding of a class of absolutely continuous functions into a fractional-order Sobolev space. As auxiliary results of the paper, which are also of independent interest, we obtain several new types of necessary and sufficient conditions for the boundedness of the Hardy–Steklov operator (integral operator with two variable limits) in weighted Lebesgue spaces.