Finite Lattices as Lattices of Relative Congruences of Finite Unars and Abelian Groups

It is proved that every finite lattice is isomorphic to an R-congruence lattice of a finite unar (finite Abelian group), as well as to a lattice of R-varieties for some locally finite finitely axiomatizable quasivariety of unars (Abelian groups) R.     

Covariant quantization of null supermembranes in four-dimensional spacetime

Kharkov State University; Kharkov Physicotechnical Institute, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 3, pp. 358–375, September, 1991.     

Low-frequency asymptotics of the Green's functions of magnets with spontaneously broken symmetry

Physicotechnical Institute, Ukrainian SSR Academy of Sciences, Kharkov; Kharkov State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 2, pp. 293–303, November, 1991.     

Flat unars: the primal, the semi-primal and the dualisable

A flat unar is a semilattice of height one with an additional unary operation. We characterise the primal, semi-primal and dualisable finite flat unars. Along the way, we give a useful characterisation of primality in general and use an array of techniques from the theory of natural dualities.     

The unity of physical theory and its mathematical formalism

The relation between the physical theory and its mathematical formalism is shown. Kharkov Physicotechnical Institute, Kharkov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1594–1600, December, 1997.     

On characteristic operator-functions of Lie-algebras

An algebra Lie of linear operators in a Hilbert space with given characteristic function and given structure constants is defined up to a unitary transformation of the Hilbert space.This paper was originally published in Russian in "Proc. of Kharkov University", U.S.S.R. Kharkov 1972, No. 83, pp.41–45.The editor is grateful to S. Levin (Ben-Gurion University of the Negev) for the translation.     

Holographic interferometry study of deformation of cement and concrete under mechanical and thermal loads

Compressive strain of concrete is accompanied by rotation of the rigid aggregate and by local shifts of the cement matrix, which by analogy with local deformation of metals is the cause of a decrease of the real strength of the material. It is shown that deformation of concrete with haydite and granite aggregates in the presence of a heat supply (within limits of positive operating temperatures) is distinguished by damping of deformations in the first case and by local deformation of the aggregate in the second.Presented at the Ninth International Conference on Mechanics of Composite Materials, Riga. October, 1995.Kharkov State Technical Academy of Railroad Transport, Ukraine. Kharkov State Technical Construction and Architecture University, Ukraine. Kharkov Fire Safety Institute Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 202–208, March–April, 1996.     

A sufficient condition for strong almost-periodicity of scalarly almost periodic representations of the group of real numbers

We prove the following theorem: If every separable subspace Y of a Banach space X has a separable weak sequential closure in Y ^**, then every scalarly almost periodic group acting in X is strongly almost periodic. Kharkov State Academy of Municipal Economy, Kharkov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 523–526, April, 1997.     

Simple and pseudosimple algebras with operators

In this work, algebras with operators, i.e., algebras with an additional system of unary operations acting as endomorphisms with respect to the basic operations, are considered. We find necessary conditions for the simplicity and pseudosimplicity of an arbitrary universal algebra with a fixed operator and explore how several properties of congruences of this algebra depend on the structure of the unary reduct of a given algebra. For algebras with one ternary operation, defined in the standard way and satisfying the Mal’cev identities, and one operator (i.e., unars with Mal’cev operation), necessary and sufficient conditions for their simplicity and pseudosimplicity are obtained.     

Extremal properties of nondifferentiable convex functions on euclidean sets of combinations with repetitions

A general approach is suggested for studying extremal properties of nondifferentiable convex functions on Euclidean combinatorial sets. On the basis of this approach, by solving the linear optimization problem on a set of combinations with repetitions, we obtain estimates of minimum values of convex and strongly convex objective functions in optimization problems on sets of combinations with repetitions and establish sufficient conditions for the existence of the corresponding minima. Kharkov Institute of Radioelectronics, Kharkov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 680–691, June, 1994.     

Invariant analytic curves for entire functions

Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 3, pp. 3–8, May–June, 1989.     

Total property of bounded approximation

Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 3, pp. 180–181, May–June, 1989.     

Resolving and strictly resolving regularizers

Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 3, pp. 59–63, May–June, 1988.     

Aharonov-Bohm oscillations in relativistic Fermi and Bose systems

Kharkov State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 1, pp. 115–128, April, 1990.     

Min-problem for Markov moments and the speed of response

Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 1, pp. 60–71, January–February, 1991.     

On Fenchel's problem

Kharkov State University. Translated from Matematicheskie Zametki, Vol. 56, No. 5, pp. 87–97, November, 1994.     

An integral representation of subharmonic functions of finite order in a cone

Kharkov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 3, pp. 109–123, May–June, 1989.