Classification of subsets of B n and additive channels

The paper deals with the classification problem for subsets of vertices of a unit n-dimensional cube on the basis of “symmetry.” Applications to the study of additive channels are presented.     

Optical transition radiation of relativistic electrons in amorphous quartz

Induced optical transition radiation of electrons with the energy of 7.5 MeV on inhomogeneities caused by energy losses of electrons has been investigated experimentally.     

On a theorem of Schauffler

Translated from Matematicheskie Zametki, Vol. 53, No. 2, pp. 84–93, February, 1993.     

Boole–De Morgan Algebras and Quasi-De Morgan Functions

In this paper we establish a Stone-type and a Birkhoff-type representation theorems for Boole–De Morgan algebras and prove that the free Boole–De Morgan algebra on n free generators is isomorphic to the Boole–De Morgan algebra of quasi-De Morgan functions of n variables. Also we introduce the concept of Zhegalkin polynomials for quasi-De Morgan functions and consider the representation problem of those functions by polynomials.     

A Characterization of (2, n)-Semigroup of n-Place Functions and De Morgan (2, n)-Semigroup of n-Place Functions

In this article, by defining n Mann's compositions and one unary operation on the set of n-place functions over some set, we construct a De Morgan (2, n)-semigroup of n-place functions and so find an abstract characterization of this algebras.     

Characterization of binary polynomials of idempotent algebras

In this paper, we characterize the set of all binary algebraic (or polynomial) operations of an idempotent algebra that has at least one r-ary algebraic operation, (r ≥ 2), depending on every variable such that there is no an (r+2)-ary algebraic operation depending on at least (r+1) variables. We prove that this set forms a finite Boolean algebra, and then we characterize this Boolean algebra.