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Characteristics of partially pseudo-ordered (K-ordered) rings are considered. Properties of ideals in pseudo-ordered rings are described. A variation of the concept of the prime radical for a ring in the subclass of directed pseudo-ordered rings (AO-ordered rings) is investigated. The description of elements of AO-prime radicals for AO-ordered rings is obtained.

In this review, we consider applications of nonassociative algebraic structures for the construction of linearly optimal codes and cryptosystems.

This paper is devoted to the application aspects of homomorphic cryptography. It provides a description of a fully homomorphic matrix polynomial-based encryption scheme. It also gives the results of practical comparison of fully homomorphic encryption schemes. We consider some special cases of homomorphic encryption allowing computations of a limited number of functions.

A variety of linear algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free. A system of elements of a free algebra is primitive if there is a complement of this system with respect to a free generating set of the free algebra. An element of a free algebra of a Schreier variety is said to be almost primitive if it is not primitive in the free algebra, but it is a primitive element of any subalgebra that contains it. This survey article is devoted to the study of primitive and almost primitive elements of Schreier varieties.

Fluidization of two types of a bidisperse bed with marked bimodality of particle size distribution has been investigated experimentally. The possibility of using the mixture equivalent diameter is shown provided the latter is calculated by the weighted-mean diameter of the particles composing this mixture.

In this paper, we prove a criterion for elementary equivalence of stable linear groups over commutative local rings with invertible two.

New polyfunctional aromatic, nitroaromatic, and heterocyclic compounds linked to the 2,6-di-tert-butylphenol moiety via –NH–, –C(O)NH–, –S–, or–C=N– spacers were synthesized. These structures provide intramolecular charge transfer (ICT) and exhibit antioxidant activity. The structures of the new compounds were established by X-ray diffraction. The novel compounds were evaluated for antioxidant activity using the DPPH assay. The presence of the 2,4,6-trinitrophenyl moiety in combination with the –NH– spacer leads to a considerable increase in the antioxidant activity of 2,6-di-tert-butylphenols. These compounds are also weak lipoxygenase inhibitors. The results of this study provide an opportunity to search for new types of antioxidants with ICT.

We analyze algorithms for open construction of a key on some noncommutative group. Algorithms of factorization and decomposition for associative algebras (of small dimension) are considered. A survey of applications (in particular, in cryptography) of so-called “hidden matrices” is given.

The process of heating a granular bed under conditions of thermal fluidization with heat supplied through the upper boundary of the bed and through its gas distributor is investigated.

A design has been developed for three-layer composite substrate tapes based on a nickel-tungsten alloy and corrosion-resistant steel. Materials have been picked and experimental samples of three-layer composite tapes obtained. It has been shown that the substitution of corrosion-resistant steel for ferromagnetic nickel–tungsten alloy in 60% of the tape volume decreases the saturation magnetization of the substrate tape by a factor of 2. The mechanical properties of the composite three-layer tape have been investigated. It has been shown that composite tapes are close in terms of the mechanical properties to tapes made from a homogeneous nickel–tungsten alloy. The conditions for the formation of a sharp cubic texture have been determined.

New ruthenium and osmium carbonyl clusters with 1,3,5-triaza-7-phosphatricyclo-[3.3.1.13.7]decane and 3,7-diacetyl-1,3,7-triaza-5-phosphabicyclo[3.3.1]nonane ligands were synthesized using Me3NO as an initiator. The data on antiproliferative activity of new compounds against ovarian carcinoma cell cultures A2780 (cisplatin-sensitive) and A2780cisR (cisplatin-resistant) are reported. The dependence of cytotoxicity on the number of phosphine ligands was demonstrated.

In this paper, main properties of a commutator of two normal subloops of a loop are considered. The notion of a prime radical of loops is introduced and its characterization as a set of strongly Engel elements is given. Also an Ω-prime radical of Ω-loops is defined and its elementwise characterization is given.

The remarkable class of measurable functions was introduced by classics of function theory. It has found different applications in various branches of mathematics. However this class turned out too restrictive for solving some natural mathematical problems because it is essentially connected with the property of countability. Therefore, along with it another remarkable class, essentially connected with the property of finiteness, was introduced. It is the class of uniform functions. Measurable functions are described both in the classical Lebesgue–Borel language of preimages and in the quite new language of covers. Uniform functions are described in the language of covers exclusively. Both the families of measurable functions and the families of uniform functions are determined by the rigid structure of their supports (descriptive spaces). For this reason, mathematicians weakened more that once the rigidity of the structure of descriptive spaces at the expense of using the additional property of negligence. The present paper is devoted to a contemporary formalization of the indicated ideas. Some applications of the introduced classes of functions to solving a number of known mathematical problems is traced in the paper.

Oxidation catalysts, e.g., those for biomass combustion in a fluidized bed (olivine sand and catalyst ShchKZ-1), were compared. Samples consisting of straw powder, straw powder and uncalcined olivine sand, straw powder and calcined olivine sand, and straw powder and crushed catalyst ShchKZ-1 were prepared. The calcined olivine sand and catalyst ShchKZ-1 had practically the same influence on the sample mass loss and heat generation from the straw by heating.

The possibility of determining the regime of fluidization of a bicomponent bed by the dependences of the statistical characteristics of the pulsations of the different pressure in this bed on the velocity of the gas blown through it is demonstrated. An algorithm of estimating the characteristic gas velocities corresponding to the transformation of the bed into the regimes of fluidization and turbulent fluidization at room temperature and at much higher temperatures has been developed. This algorithm allows one to determine the indicated velocities more exactly, as compared to the traditional methods, by the dependence of the differential pressure in the bed on the velocity of the gas blown through it.

Torrefaction is considered as a kind of mild pyrolysis that is carried out under inert atmosphere (usually nitrogen) conditions. During this process, the moisture of the initial fuel and a portion of its volatiles are removed from the biomass particles towards the inert atmosphere. The resulted torrefied solid biomass has high energy density, durability and less hydrophilic character. The most beneficial result of torrefaction process is that biomass feedstock logistics cost can be reduced, as less tones of biomass are required for a given amount of energy input. The development of a process model examining basic parameters as reaction temperature and residence time can provide useful information, which can be used for the more efficient design of a torrefaction reactor. This study presents such a process model for a straw torrefaction pilot plant. This model is based on the thermodynamic calculation of a single and/or a two batch reactor, built on the commercial software ASPEN Plus. The calculation of required flow rates of inert gas, cooling medium for a specific biomass feedstock value, is based on relevant results found in literature.

A relationship is established between statistical characteristics of the random process of press-gradient pulsation in a fluidized bed and changes in the bed’s fractional composition. This relationship can be used to monitor the process of defluidization (transition of the bed from the fluidized to the non-fluidized state) based on the results of a comparative analysis of the above-mentioned statistical characteristics. The feasibility of performing such monitoring was confirmed experimentally from the combustion of lowmelting biogranules (straw granules) in a fluidized bed. It was found that the bed remains in the fluidized state as long as the dimensionless amplitude of the pressure-gradient pulsations does not exceed 0.1. The utility of the proposed monitoring method was also substantiated by comparative studies of changes in the fractional composition of a fluidized bed and the temperature and chemical composition of the flue gases.

This paper contains a review of results on graded quotient rings and new results proved by the authors.

The problem of characterization of integrals as linear functionals is considered in the paper. It starts from the familiar results of F. Riesz (1909) and J. Radon (1913) on integral representation of bounded linear functionals by Riemann–Stieltjes integrals on a segment and by Lebesgue integrals on a compact in \( {\mathbb{R}^n} \), respectively. After works of J. Radon, M. Frechet, and F. Hausdorff the problem of characterization of integrals as linear functionals took the particular form of the problem of extension of Radon’s theorem from \( {\mathbb{R}^n} \) to more general topological spaces with Radon measures. This problem has turned out difficult and its solution has a long and rich history. Therefore, it may be naturally called the Riesz–Radon–Frechet problem of characterization of integrals. The important stages of its solution are connected with such mathematicians as S. Banach, S. Saks, S. Kakutani, P. Halmos, E. Hewitt, R. E. Edwards, N. Bourbaki, V. K. Zakharov, A. V. Mikhalev, et al. In this paper, the Riesz–Radon–Fr´echet problem is solved for the general case of arbitrary Radon measures on Hausdorff spaces. The solution is given in the form of a general parametric theorem in terms of a new notion of the boundedness index of a functional. The theorem implies as particular cases well-known results of the indicated authors characterizing Radon integrals for various classes of Radon measures and topological spaces.

In this paper, topologically primitive rings and rings possessing a faithful topologically irreducible module and bounded by this module are considered for the investigation of properties of their topological Jacobson radical. We investigate the topological Jacobson radical in some classes of topological rings such as left topologically Artinian rings, topological rings possessing a basis of neighborhoods of zero consisting of ideals, compact rings, and bounded strictly linearly compact rings.

In this paper, we give a simpler proof of the Golubchik–Mikhalev–Zelmanov theorem on the structure of isomorphisms between general linear groups over associative rings, and also prove an extension of this theorem for linear groups over rings graded by an Abelian group.

This article presents test results for a reactor model designed for low-temperature pyrolysis of biomass. The efficiency of the pyrolysis attains maximum values at 240–250°C and a process duration of 50 min. The test results are used in the development of an industrial reactor with a capacity of 1 ton/h with respect to initial biomass.

We obtain criteria that answer the question of when an anti-isomorphism of graded endomorphism rings of the strict gr-generators is induced by a graded Morita anti-equivalence or a graded anti-semilinear isomorphism.

This review paper is devoted to the Jacobi bound for systems of partial differential polynomials. We prove the conjecture for the system of n partial differential equations in n differential variables which are independent over a prime differential ideal \(\mathfrak{p}\). On the one hand, this generalizes our result about the Jacobi bound for ordinary differential polynomials independent over a prime differential ideal \(\mathfrak{p}\) and, on the other hand, the result by Tomasovic, who proved the Jacobi bound for linear partial differential polynomials.

Improved algorithms to construct complements of primitive systems of elements of free nonassociative algebras with respect to free generating sets and algorithms to realize the rank of a system of elements are constructed and implemented.

The notion of the prime radical for a directed group is considered. A series of results on commutants of AO-groups is obtained. Prime radicals of AO-groups are described.

The aim of this article is to consider the theoretical basis of an automated-system-vulnerability scanning (assessment) process and to prove the possibility of determining the internal-state distribution based on conducting the scanning process. According to international information security standards, the scanning process is called the vulnerability assessment process. Conducting this process and the existence of the required technical resources is a necessary condition for creating effective information-security systems.

The authors investigate semirings of cyclic types from the algebraic point of view. To simplify and facilitate the analysis, the local Fourier transform of these semirings is introduced. The authors describe zero divisors, nilpotent elements, invertible elements, idempotents, and the Jacobson radical.

In this paper, we prove that the semigroups of invertible matrices with nonnegative elements over linearly ordered associative rings are elementarily equivalent if and only if the matrices have the same dimension and the rings are elementarily equivalent as ordered rings.

The concept of prime radicals is important in the study of rings and groups. The purpose of this paper is to investigate a generalization of this concept to directed groups. Some results are obtained concerning convex directed subgroups of AO-groups. Prime radicals of pl-groups are described.

In this paper, we introduce the class of graded Ω-groups, which includes: groups; associative, conformal and vertex algebras; Lie algebras and graded algebras. The graded prime radical of a graded Ω-group is defined, and its elementwise characterization is given. It is shown that the graded prime radical of a graded Ω-groups with a finiteness condition coincides with the lower weakly solvable (in the Parfyonov sense) radical.

The paper is aimed at the problem of lifting automorphisms and derivations of a perfect conformal Lie superalgebra to its central extension. Such lifting is possible with the help of a universal central extension whose tensor model is constructed here for this purpose.

In this paper, we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly ordered associative ring on some specially defined subgroup coincides with the composition of an inner automorphism of the semigroup, an order-preserving automorphism of the ring, and a central homothety.