Vol 214 (2022)
Статьи
Lie algebras of projective motions of five-dimensional pseudo-riemannian spaces. III. Curvature forms of five-dimensional rigid h-spaces in a skew-normal frame
Abstract
This work is devoted to the problem of studying multidimensional pseudo-Riemannian manifolds that admit Lie algebras of infinitesimal projective (in particular, affine) transformations, wider than Lie algebras of infinitesimal homotheties. Such manifolds have numerous geometric and physical applications. This paper is the third part of the work. The first part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — 212. — P. 10-29. The second part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — 213. — P. 10-37. Continuation will be published in future issues.
3-20
21-29
On a set of Е-closed classes of multifunctions on a two-element set
Abstract
In this paper, we consider closed classes of multifunctions defined on a two-element set and their closure operator based on the composition operator by union and the equality predicate branching operator. We show that the set of multifunctions that does not take the value of zero at any set of variables contains 76 E-closed classes.
30-36
On the class of polynomially stable boolean functions
Abstract
The basic properties of polynomially stable Boolean functions are examined. We prove that any polynomially stable function can be represented as the sum of terms that are nonrepetitive in an elementary basis. Relationships between polynomially stable and symmetric Boolean functions are discussed and a criterion for polynomial stability is proved.
37-43
Combinatorial scheme of random placement of particles into cells of several types
Abstract
Based on the A-scheme of sequential trials, we examine two variants of random placement of particles in cells of r types. In one of these variants, there exist marked cells of each type. We find an explicit distribution of the number of nonempty cells in one of the variants and a distribution of the number of nonempty marked cells in the other, obtain numerical characteristics of these distributions, and prove limit theorems.
44-52
Combinatorial properties of flat sections of the generalized Pascal’s pyramid and construction of navigation routes
Abstract
The article describes the methods of the mathematical apparatus of hierarchical structures. The definition of the generalized Pascal pyramid is given and the sums of the elements of its flat sections are considered. Recurrence relations that these sums satisfy, as well as enumerative interpretations of the combinatorial objects under study are shown. Combinatorial paths on integer lattices and the use of recurrence relations to estimate the number of deviations of the trajectory of an unmanned aerial vehicle from a given motion vector are described.
53-59
The scenario of using a social network as a source of key material for the one-time pad
Abstract
The scenario of use of social media as a mean for delivery of key material for the one-time pad is described. Technical capabilities of social media to deliver plain text, capabilities of automatic intercept of data from social media, and matters of cryptographic strength are considered.
60-68
Fractal properties of binary matrices constructed using the generalized Pascal’s triangle and applications
Abstract
In this paper, we describe a method for composing binary matrices based on the generalization of Pascal’s triangle. The method of parameterization of these binary matrices by choosing certain generatrices is discussed and the properties of this construction are examined. We also present a well-known method for constructing a binary matrix by reducing the Pascal triangle by a simple or composite modulus and compare it with the method proposed in this paper. The fractal properties of these binary matrices are considered, and possible applications of fractal properties are presented.
69-75
Hypersurfaces with constant principal curvatures in euclidean space Vn+1
Abstract
Hypersurfaces in En+1 for which a thin fan is found are considered. It is shown that it exists only for hypersurfaces in En+1 with constant or proportional principal curvatures that differ from each other. The conditions for the existence of hypersurfaces in the Euclidean space Vn+1, whose main curvatures are constant (assuming that all the main curvatures are different from each other), are clarified.
76-81
Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. I. Equations of geodesics on the tangent bundle of a smooth п-dimensional manifold
Abstract
In many problems of dynamics, systems arise whose position spaces are four-dimensional manifolds. Naturally, the phase spaces of such systems are the tangent bundles of the corresponding manifolds. Dynamical systems considered have variable dissipation, and the complete list of first integrals consists of transcendental functions expressed in terms of finite combinations of elementary functions. In this paper, we prove the integrability of more general classes of homogeneous dynamical systems with variable dissipation on tangent bundles of four-dimensional manifolds.
82-106
Polynomial automorphisms, quantization, and Jacobian conjecture related problems. II. Quantization proof of Bergman’s centralizer theorem
Abstract
The purpose of this review is the collection and systematization of results concerning the quantization approach to the some classical aspects of non-commutative algebras, especially to the Jacobian conjecture. We start with quantization proof of Bergman centralizing theorem, then discourse authomorphisms of INd-schemes authomorphisms, then go to aproximation issues. Last chapter dedicated to relations between PI -theory Burnside type theorems and Jacobian Conjecture (Jagzev approach). This issue contains the second part of the work. The first part is: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 213 (2022), pp. 110-144. Continuation will be published in future issues.
107-126