Multidimensional periodic wavelet systems with matrix dilation in the framework of periodic multiresolution analyses are studied. In this work we use notion of a periodic multiresolution analysis, the most general definition of which was given by Maksimenko and M. Skopina in [25].
An algorithmic method of constructing multidimensional periodic dual wavelet frames from a suitable set of Fourier coefficients of one function is provided. This function is used as the first function in a scaling sequence that forms two periodic multiresolution analyses, which are used to construct wavelet systems. Conditions that the initial function has to satisfy are presented in terms of a certain rate of decay of its Fourier coefficients, and also mutual arrangement of zero and non-zero coefficients.

We study generalized almost quaternionic manifolds of vertical type. Examples of this type of manifolds are given. It is proved that on a generalized almost quaternionic manifold there always exists an almost 𝛼-quaternionic connection, which in the main bundle induces a metric connection. The criterion of the auto-duality of the projected vertical 2-form on an almost 𝛼-quaternion manifold is obtained. The components of the structural endomorphism on the space of the 𝐺-structure are obtained. The answer to the question is obtained: when
does the Riemann-Christoffel endomorphism preserve the K¨ahler module of a variety. It is proved that the Riemann-Christoffel Hermitian endomorphism of an almost 𝛼-quaternionic variety of vertical type preserves the K¨ahler module of a variety if and only if the structural sheaf of this variety is Einstein. Hence, as a consequence, we obtain that a four-dimensional manifold with a Riemannian or neutral pseudo-Riemannian metric is an Einstein manifold if and only if its module of auto-dual forms is invariant with respect to the Riemann-Christoffel
endomorphism. The resulting corollary shows that the previous result is a broad generalization of the Atiyah-Hitchin-Singer theorem, which gives the Einstein criterion for 4-dimensional Riemannian manifolds in terms of auto-dual forms, since the result generalizes this theorem to the case of a neutral pseudo-Riemannian metric. On the other hand, this result is closely related to the well-known result of Berger, who clarifies it in the special case of quaternionic-
K¨ahler manifolds: if a variety 𝑀 is quaternionic-Koehler, then its Riemann connectivity (and not just the Riemann-Christoffel operator) preserves the Koehler modulus of the variety. In this case, 𝑀 is an Einstein manifold.

In paper Minkowski’s theorem on linear forms [1] is applied to polynomials with integer coefficients
𝑃(𝑥) = 𝑎𝑛𝑥𝑛 + 𝑎𝑛−1𝑥𝑛−1 + . . . + 𝑎1𝑥 + 𝑎0 (3)
with degree 𝑑𝑒𝑔𝑃 = 𝑛 and height 𝐻(𝑃) = max06𝑖6𝑛 |𝑎𝑖|. Then, for any 𝑥 ∈ [0, 1) and a natural number 𝑄 > 1, we obtain the inequality
|𝑃(𝑥)| < 𝑐1(𝑛)𝑄−𝑛 (4)
for some 𝑃(𝑥),𝐻(𝑃) ≤ 𝑄. Inequality (4) means that the entire interval [0, 1) can be covered by intervals 𝐼𝑖, 𝑖 = 1, 2, . . . at all points of which inequality (4) is true. An answer is given to the question about the size of the 𝐼𝑖 intervals. The main result of this paper is proof of the following statement.
For any 𝑣, 0 ≤ 𝑣 < (𝑛+1)/3 , there is an interval 𝐽𝑘, 𝑘 = 1, . . . ,𝐾, such that for all 𝑥 ∈ 𝐽𝑘, the inequality (4) holds and, moreover,
𝑐2𝑄−𝑛−1+𝑣 < 𝜇𝐽𝑘 < 𝑐3𝑄−𝑛−1+𝑣.

In paper we study the topology of integrable billiard books, (i.e. systems on CW-complexes glued from flat domains of confocal billiards. Significant progress has been made in proving the local version of the billiard Fomenko conjecture. In particular, billiards were used to realize an important class of subgraphs of the Fomenko - Zieschang graph invariants (that classify Liouville foliations of integrable systems in topological sense). Then we classify in combinatorial sense
billiard books of low complexity (with a small number of one-dimensional cells), glued from flat domains that contain foci of the family of quadrics. Calculation of Fomenko–Zieschang invariants for these systems is in progress.

The paper studies the relationship between the problem of determining the number of points of a two-dimensional lattice of Dirichlet approximations in a hyperbolic cross and the integral representation of the hyperbolic zeta function of a two-dimensional lattice of Dirichlet approximations. The concept of components of hyperbolic zeta-functions of a twodimensional lattice of Dirichlet approximations is introduced. A representation is found for the first component of the hyperbolic zeta function of a two-dimensional lattice of Dirichlet
approximations via the Riemann zeta function. With respect to the first component, the paradoxical fact is established that it is continuous for any irrational 𝛽 and discontinuous at all rational points of 𝛽. This refers to the dependency only on the 𝛽 parameter.
For the second component of the hyperbolic zeta-function of the two-dimensional lattice of Dirichlet approximations in the case of a rational value 𝛽 = 𝑎
𝑏 , an asymptotic formula is obtained for the number of points of the second component of the two-dimensional lattice of Dirichlet approximations in the hyperbolic cross. The resulting formula gives an integral representation
in the half-plane 𝜎 > 1/2 .

The main research tool was the Euler summation formula. For the purposes of the work, it was necessary to obtain explicit expressions of the residual terms in asymptotic formulas for the number of points of residue classes of a two-dimensional lattice of Dirichlet approximations over a stretched fundamental lattice 𝑏Z×Z. Both Theorem 1 and Theorem 2, proved in the paper, show the dependence of the second term of the asymptotic formula and the deduction of
the hyperbolic zeta function of the lattice Λ(︀𝑎/𝑏)︀ depends on the magnitude of the denominator 𝑏 and independence from the numerator 𝑎. Earlier, similar effects were discovered by A. L. Roscheney for other generalizations of the Dirichlet problem.
The paper sets the task of clarifying the order of the residual term in asymptotic formulas by studying the quantities

$$𝑅*1(𝑇, 𝑏, 𝛿) =(√𝑇)/bΣ︁𝑞=1{︂𝑇/𝑏𝑞− 𝛿}︂−(√𝑇)/2𝑏, 𝑅*2(𝑇, 𝑏, 𝛿) =√𝑇−𝛿Σ︁𝑝=1{︂𝑇/(𝑏𝑝 + 𝑏𝛿)}︂−(√𝑇)/2.$$

It is proposed to first study the possibilities of the elementary method of I. M. Vinogradov,
and then to obtain the most accurate estimates using the method of trigonometric sums. The
paper outlines the directions of further research on this topic.

In this paper, various classes of almost contact metric structures are considered under the assumption that their contact distribution is completely integrable. An analytical criterion for the completely integrability of the contact distribution of an almost contact metric manifold is obtained. It is found which almost Hermitian structures are induced on the integral manifolds of the contact distribution of some almost contact metric manifolds. In particular, it is proved that an almost Hermitian structure induced on integral submanifolds of maximum dimension
of the first fundamental distribution of a Kenmotsu manifold is a K¨ahler structure. An almost Hermitian structure induced on integral manifolds of maximum dimension of a completely integrable first fundamental distribution of a normal manifold is a Hermitian structure. We show that a nearly cosymplectic structure with an involutive first fundamental distribution is the most closely cosymplectic one and approximately K¨ahler structure is induced on its integral submanifolds of the maximum dimension of a completely integrable contact distribution. It is
also proved that the contact distribution of an inquasi-Sasakian manifold is integrable only in case of this manifold is cosymplectic. K¨ahler structure is induced on the maximal integral manifolds of the contact distribution of a cosymplectic manifold. If 𝑀 is a 𝑙𝑐𝑄𝑆-manifold with an involutive first fundamental distribution, then the structure of the class 𝑊4 of almost Hermitian
structures in the Gray-Hervella classification is induced on integral manifolds of the maximum dimension of its contact distribution. It is K¨ahler if and only if 𝑔𝑟𝑎𝑑 𝜎 ⊂ 𝑀, where 𝜎 is an arbitrary smooth function on 𝑀 of corresponding conformal transformation.

We study the dependence of the functions of capital (resource) and consumption in the Ramsey-Kass-Koopmans economic model in the case when saving is an identical constant.
The system of differential equations describing the evolution of the economic model under consideration is solved in quadratures under the assumptions made. Upper estimates of the consumption function are found based on the obtained solution.

In this paper influence of external force, assumed to be random stationary process, on the
behavior of large Hamiltonian particle systems is studied. The Hamiltonian system is assumed
to have quadratic interaction, and the external influence is assumed to be local. More exactly,
the external force acts on only one fixed particle. Such systems were studed earlier, it is given
short review of the previous papers. In our case, when the external force is a stationary random
process in the wider sense, large time asymptotics of the mean energy of the system is studied.
Main result is the characterization of 4 different cases for the spectrum of the matrix of quadratic
interaction and the spectral density of the correlation function of the stationary random process,
which give different asymptotic behaviour of the trajectories and of the mean energy. Typical
behaviour appears to be either uniform boundedness or quadratic growth of the mean energies.

In paper we consider aspects of the Hermitian geometry of 𝑙𝑐𝐴𝐶𝑆structures. The effect of the vanishing of the Neyenhuis tensor and the associated tensors 𝑁(1), 𝑁(2), 𝑁(3), 𝑁(4) on the class of almost Hermitian structure induced on the first fundamental distribution of 𝑙𝑐𝐴𝐶𝑆structures is investigated. It is proved that the almost Hermitian structure induced on integral manifolds of the first fundamental distribution: 𝑙𝑐𝐴𝐶𝑆-manifolds is a structure of the class 𝑊2 ⊕ 𝑊4,
and it will be almost K¨ahler if and only if 𝑔𝑟𝑎𝑑 𝜎 ⊂ 𝐿(𝜉); an integrable 𝑙𝑐𝐴𝐶𝑆-manifold is a structure of the class 𝑊4; a normal 𝑙𝑐𝐴𝐶𝑆-manifold is a K¨ahler structure; a 𝑙𝑐𝐴𝐶𝑆-manifold for which 𝑁(2)(𝑋, 𝑌 ) = 0, or 𝑁(3)(𝑋) = 0, or 𝑁(4)(𝑋) = 0, is an almost K¨ahler structure in the Gray-Herwell classification of almost Hermitian structures.

A ring of polyadic integers is a direct product of rings of integer 𝑝-adic numbers over all primes 𝑝. The elements 𝜃 of this ring can thus be considered as infinite-dimensional vectors whose coordinates in the corresponding ring of integer 𝑝-adic numbers are denoted by 𝜃^(𝑝). The infinite linear independence of polyadic numbers 𝜃_1, . . . , 𝜃_𝑚 means that for any nonzero linear form ℎ_1𝑥_1 + . . . + ℎ_𝑚*𝑥_𝑚 with integer coefficients ℎ_1, . . . , ℎ_𝑚 there is an infinite set of primes 𝑝 such that in the field Q_𝑝 the inequality

$$ℎ_1𝜃_1^(𝑝) + . . . + ℎ_𝑚𝜃_m^(𝑝) ̸= 0.$$

holds. At the same time, problems in which primes are considered only from some proper subsets of the set of primes are of interest. In this case, we will talk about infinite linear independence with restrictions on the specified set. Canonical representation of the element 𝜃 of the ring of polyadic integers has the form of a series

$$𝜃 =∞Σ︁𝑛=0𝑎_𝑛*𝑛!, 𝑎_𝑛 ∈ Z, 0 ≤ 𝑎_𝑛 ≤ 𝑛.$$

Of course, a series whose members are integers converging in all fields of 𝑝-adic numbers is a polyadic integer. We will call a polyadic number 𝜃 a polyadic Liouville number (or a Liouville polyadic number) if for any numbers 𝑛 and 𝑃 there exists a natural number 𝐴 such that for all primes 𝑝 satisfying the inequality 𝑝 ≤ 𝑃 the inequality

$$|𝜃 − 𝐴|_𝑝 < 𝐴^(−𝑛).$$

This work continues the development of the basic idea embedded in [15]. Here the infinite linear independence with restrictions on the set of prime numbers in the aggregate of arithmetic progressions. of polyadic numbers

$$𝑓_0(1) =∞Σ︁𝑛=0(𝜆)_𝑛, 𝑓_1(1) =∞Σ︁𝑛=0(𝜆 + 1)_𝑛.$$

will be proved. An important apparatus for obtaining this result are Hermite–Pade approximations of generalized hypergeometric functions constructed in the work of Yu.V. Nesterenko [4].
The approach from the work of Ernvall-Hytonen, Matala-Aho, Seppela [5] was used.

The article considers extremal problems of mean-square approximation of functions of a complex variable, regular in the domain D ⊂ C, by Fourier series orthogonal in the system of functions {𝜙_𝑘(𝑧)}∞𝑘=0 in D belonging to the weighted Bergman space 𝐵2,𝛾 with finite norm

$$‖𝑓‖2,𝛾 := ‖𝑓‖𝐵2,𝛾 =(1/2𝜋∫︁∫︁(D) 𝛾(|𝑧|)|𝑓(𝑧)|^2 𝑑𝜎)^(1/2),$$

where 𝛾 := 𝛾(|𝑧|) ≥ 0 is a real integrable function in the domain D, and the integral is understood in the Lebesgue sense, 𝑑𝜎 := 𝑑𝑥𝑑𝑦 is an element of area.
The formulated problem is investigated in more detail in the case when D is the unit disc in the space 𝐵_2,𝛾𝛼,𝛽 , 𝛾_𝛼,𝛽 = |𝑧|^𝛼(1 − |𝑧|)^𝛽, 𝛼, 𝛽 > −1 – Jacobi weight. Sharp Jackson-Stechkintype inequalities that relate the value of the best mean-squared polynomial approximation of 𝑓 ∈ ℬ^(𝑟)_2,𝛾𝛼,𝛽 and the Peetre K -functional were proved. In case when 𝛾𝛼,𝛽 ≡ 1 we will obtain the earlier known results.

One of the main problems of using tungsten-containing hard alloys at present is the high cost of tungsten. Due to the high melting point, there is a problem of their recycling for secondary use. One of the promising methods of their processing into spherical powders is electroerosive dispersion (EED). To date, there is no complete information in the modern scientific and technical literature on the use of T5K10 alloy particles dispersed by electroerosion as a charge for the production of tungsten-titanium-cobalt alloys and cutting tools from them. For these purposes, comprehensive theoretical and experimental studies are required.
In order to predict the high physical and mechanical properties of products from the resulting charge, it was necessary to optimize the modes of electroerosive dispersion of T5K10 alloy waste by the experimental planning method. For the charge, one of the main technological parameters is the optimal dispersion, therefore, the optimization of the process of obtaining the charge for the production of sintered hard alloys was carried out according to the average
particle size. Electroerosive dispersion of T5K10 alloy waste was carried out on an experimental installation (RF Patent No. 2449859). As a result of exposure to short-term electrical discharges, carbide particles of various shapes and sizes were formed. Optimization of the process of electrodispersion of particles obtained by the EED of solid alloy waste of the T5K10 brand was carried out by experimental determination of a combination of levels of factors at which the required value of the average diameter of the particles of the electroerosion charge was achieved. To do this, the method of steep ascent of Box and Wilson was used. Optimization
of the process of electrodispersing the T5K10 alloy in distilled water and lighting kerosene was carried out taking into account factors such as the voltage at the electrodes, the capacity of the discharge capacitors and the pulse repetition rate.
According to the conducted series of experiments, the limiting values of the optimization parameter for the average size of electroerosive particles were determined, which were: for distilled water – 57.1 microns with a capacity of discharge capacitors of 65.5 UF, a voltage at the electrodes of 200 V, a pulse repetition frequency of 200 Hz; for lighting kerosene - 64.1 microns with a capacity of discharge capacitors of 65.5 UF, a voltage at the electrodes of 200 V, a pulse repetition frequency of 200 Hz.
Carrying out the planned measures will solve the problem of recycling waste of tungstentitanium-cobalt alloys and their reuse in the manufacture of cutting tools.

Currently, one of the main problems of using the ZhS6U alloy is associated with the presence of expensive components in its composition, such as Ni, Ti, Mo, Co, etc. and the need to reuse it by grinding. One of the effective, but insufficiently studied metallurgical methods of grinding metal waste is electrodispersion. To date, in the modern scientific and technical literature there is no complete information about the composition, structure and properties of the particles of
the ZhS6U alloy obtained in the conditions of electroerosive metallurgy.
The purpose of this work was to conduct a dimensional analysis of powder particles obtained by electroerosive dispersion of heat-resistant nickel alloy ZhS6U in water.
Electrodispersion of the waste of the heat-resistant nickel alloy ZHS6U in the form of substandard "working"turbine blades of the jet engine of the aircraft was carried out in distilled water at the original installation. As a result of exposure to short-term electrical discharges, particles of heat-resistant nickel alloy ZHS6U powder of various sizes were formed in the water.
The dimensional characteristics of the powder particles obtained by electroerosive dispersion of the heat-resistant nickel alloy ZHS6U in water were studied using a laser particle size analyzer "Analysette 22 NanoTec".
Based on the conducted experimental studies, it was found that the powder particles obtained by electroerosive dispersion of heat-resistant nickel alloy ZHS6U in water have sizes from 0.1 to 285 microns with an average volumetric diameter of 67.1 microns. The features of the formation of the fractional composition of powder particles in the process of electroerosive metallurgy of metal waste of the ZhS6U brand are noted, namely, the presence of two extremes of particle sizes of 10 microns and 100 microns: a small fraction (0.1 . . . 25.0 microns) is formed
due to condensation of the vapor phase and a large fraction (25.0 . . . 300 microns) is formed due to condensation of the liquid phase. It is noted that the displacement of the extremes of the particle sizes formed during the crystallization of the vapor and liquid phases is determined by the electrical parameters of the installation: the voltage on the electrodes, the capacity of the discharge capacitors and the pulse repetition frequency. It is shown that the powder obtained
by electroerosive dispersion of heat-resistant nickel alloy ZHS6U in water contains: 5% particles with a size up to 1.69 microns; 10% particles with a size up to 3.36 microns; 25% particles with a size up to 11.71 microns; 50% particles with a size up to 50.07 microns; 75% particles with a size up to 99.02 microns; 90% of particles with a size up to 165.74 microns; 95% of particles with a size up to 210.72 microns; 99% of particles with a size up to 281.09 microns inclusive. In this case, the specific surface area of the powder is 7994 cm^2/cm^3.

The aim of this work is to study the history of the Poincar´e-Birkhoff theorem, which is not only one of the results underlying the theory of dynamical systems, but is important for applications. Until now, the Poincar´e-Birkhoff theorem has been considered historically only fragmentarily and has not been the subject of consistent historical research. The research is based on the analysis of original works, historical and scientific literature, involving the recollections of participants in the described events. Poincar´e’s idea was to establish the periodic motions of dynamical systems using the geometric theorem he proposed. Periodic movements, in turn, were supposed to serve as a basis for studying other, complex movements. The search for a proof was a powerful impetus for Birkhoff in the construction of the theory of dynamical systems, who, together with Poincar´e, is the founder of this area of mathematics. Poincar´e- Birkhoff theorem is of key importance in understanding the mechanism of the onset of chaotic motion in Hamiltonian systems. The history of the Poincar´e-Birkhoff theorem is not complete;
it plays a significant role in the modern theory of dynamical systems and its applications.
The search continues for a proof of a multidimensional analogue of the theorem, its various generalizations, and further applications.

The article presents an analysis of the possibility of using the NACE Standard TM0177- 2005 standard during accelerated laboratory tests for hydrogen embrittlement and corrosion cracking of rebar rolled products. It is shown that the use of the NACE standard in accelerated laboratory tests of reinforcing steels is impractical, due to the specific size and geometry of the test samples, which do not allow to bring the test conditions closer to real and a significant test time.

The article contains the scientific biography of J. A. Euler (1734-1800), the history and publication of the manuscript “History of Geometry” found by us with our comments. Johann Albrecht, the eldest son of Leonard Euler, was born in St. Petersburg, spent his youth with his father in Berlin, where he served as an inspector at the Berlin Observatory; at the age of 32, he with his family returned to St. Petersburg, where until the end of his life he was the conference secretary of the Imperial St. Petersburg Academy of Sciences. Huge administrative work and assistance to his blind father left him little time for independent scientific research. He retained meteorological and astronomical observations, as well as participation in his father’s home seminars on the theory of the moon and some questions of number theory. But his manuscript on the history of geometry shows the breadth of his mathematical culture, the rigor of his criteria, and the depth of knowledge of his contemporary geometry literature. Analysis of the text of the manuscript reveals the views of Euler-father and son on the history of geometry up to the 18th century, as well as the importance they attached to the applied directions of the development of geometry (astronomy, underground geometry, fortification, geodesy, cartography, auxiliary mathematical tools). The comments provide an overview of the sources used by I.A. Euler, both on the basis of direct links, and on the basis of the list of Euler’s collection and his personal contacts. For the first time, the names of many authors are introduced into the Russian historical and mathematical circulation. Despite the strong opinion that I.A. Euler, being the conference secretary of the St. Petersburg Academy of Sciences, did not have enough time for scientific work, we noted some of his important results, and also showed the range of his knowledge and
scientific criteria. For us, his work is interesting because it shows the level of development of practical geometry in the 18th century.

The paper traces the historical development process of one of the most important concepts of the mechanical oscillations theory – resonance, starting from the XVII century to the present day. It is noted that resonance is of great theoretical and practical importance, but there is no sufficiently strict and comprehensive definition for this term. The prehistory of resonance is mentioned and the initial studies associated with the works of Galileo Galilei, who first described
resonance using the example of an ordinary pendulum, and Christiaan Huygens, who studied the phenomenon of sympathetic resonance using the example of two pendulums on a common beam support, are discussed. The leading role of orbital resonances in the XVIII-XIX centuries, that indicate the evolutionary maturity of the Solar system, is noted, and the internal resonances in terrestrial mechanics are analyzed using the example of double and spherical pendulums. The classical harmonic resonance is analyzed in detail, and it played a significant role in technology.
The harmful role of resonance is demonstrated by the example of catastrophes with bridge structures. In addition, a classification of various types of resonance, which was formed in the XIX-XX centuries, is given. The term "autoresonance"associated with the name of A. A.
Andronov was the last step in this chain. Autoresonance made it possible to effectively swing the system using feedbacks, thereby adapting the driving forces to the properties of the system itself.
Several illustrative examples of autoresonance in pendulum systems are given. In conclusion, it is noted that autoresonances gradually began to take a serious place in robotics and biomechanics, and their use turned out to be the most important step into the world of optimal motion modes.

The article deals with the mathematical modeling of an inhomogeneous anisotropic coating of the elastic cylinder, providing the least reflection upon diffraction of a harmonic cylindrical sound wave. It is assumed that the elastic cylinder is homogeneous and isotropic, the coating material is radially inhomogeneous and transversely isotropic, the laws inhomogeneities of the
coating material are described by continuous functions, the body is placed in a boundless ideal fluid.
An analytical solution of the direct diffraction problem is obtained. The scattered acoustic field and wave fields in the cylinder and its coating are defined.
Wave fields in a containing medium and a homogeneous isotropic cylinder are described by expansions in cylindrical wave functions. A boundary value problem is constructed for a system of ordinary differential equations of the second order for finding displacement fields in an inhomogeneous anisotropic layer.
An analytical solution of the inverse problem of the diffraction about the determination of the inhomogeneity laws of the coating material, ensuring the minimum sound scattering in the specified frequency range at a fixed angle of observation and also at a given observation sector at a fixed frequency is obtained. The functionals expressing the average intensity of sound scattering in given frequency range and angular sector of observation are built. Minimization
of the functionals are implemented with the help of the burnout simulation algorithm.
The results of numerical calculations of frequency and angular dependencies of the intensity of the scatter acoustic field in the far zone at the optimal parabolic inhomogeneity laws are presented.

In paper the problem of harmonic cylindrical sound waves reflection and transmission through a homogeneous isotropic elastic plate with a continuously inhomogeneous in thickness elastic coating is considered. It is believed that the plate is placed in an infinite ideal fluid, the laws of heterogeneity of the coating material are described by continuous functions.
An analytical solution of the posed problem is obtained on the basis of the known solution of the problem about the passage of plane sound waves through plate with a continuously inhomogeneous coating and using integral representation of a cylindrical wave in the form of an expansion on flat waves.
Finding the displacement field in an inhomogeneous layer is reduced to solving boundary value problem for a system of ordinary differential equations of the second order.
The results of numerical calculations of frequency characteristics are presented for reflected and transmitted acoustic fields. Shown strong difference of frequency dependencies for different laws of inhomogeneity coating material.

This paper commemorates the seventy-fifth anniversary of Doctor of Physical and Mathematical Sciences, Professor Vasily Ivanovich Bernik. His curriculum vitae is presented, together with a brief analysis of his work in scientific research, education and management. 13 major scientific papers of V.I. Bernik are referenced.