Akbergenov A.A.

Periodical Solutions of Nonlinear Difference Equations and Their Properties

P. 5–9.

Refs.: 7 titles.

This paper establishes sufficient conditions for existence and uniqueness of continuous N-periodic solution (N is a positive integer) of a large class of nonlinear difference equations, as well as studies its properties at Ε→0.

Amirgalieva S.N., Ostapenko V.V., Ostapenko O.V.

Differential Games with a Casual Markov Hindrance

P. 10–15.

Refs.: 11 titles.

The paper considers new challenges to the theory of differential games in which the second player (opponent) is a random hindrance, and the first player (ally) uses Pshenichniy’s e-strategies, or counterstrategies in specific cases. At certain moments the first player is informed about implementing the hindrance. Therefore, the first player aims to minimize mathematical expectation of the objective functional. By employing statement constructions, we describe the structure of the game and outline a general approach to the construction of the first player’s optimal e-strategies. Crucially, we estimate the cost of the simple-motion game and describe some optimal counterstrategies.

Buldygin V.V., Blazhievska I.P.

On Asymptotic Properties of the Cross-Correlogram Estimators of Impulse Response Functions in Linear Systems

P. 16–26.

Refs.: 17 titles.

In this paper, we consider the cross-correlogram estimators of impulse response functions in linear systems. We hypothesize that the system is disturbed by a family of Gaussian processes close to white noise. We study the asymptotic normality of finite-dimensional distributions of estimators and their asymptotic normality in the space of continuous functions given that the impulse response function belongs to L2R.

Virchenko N.O., Boltovska M.O.

On Application of Some Generalized Integral Transforms

P. 27–34.

Refs.: 13 titles.

This study presents new generalizations of some classic integral transforms (sin-, cos- Fourier transforms, Glasser transforms, Pv,2-transforms). Moreover, we address the issues related to the theory of these new integral transforms. We prove the inversion formulas and propose the ways of application for integrals evaluation, as well as for solving the differential equations. 

Haiday V.O.

Recurrence Formulas for the Generalized Fox–Wright Function

P. 35–39.

Refs.: 8 titles.

In this paper, we obtain new recurrence formulas with the generalized Fox–Wright function, whose individual cases are the Fox–Wright function, generalized hypergeometric functions, the Mittag-Leffler functions, and generalization of the Bessel function.

Gorbatenko Ya.V.

Solvability and Strong Correctness of the Cauchy Problem for Abstract Linear Differential Equations in the Banach Spaces

P. 40–43.

Refs.: 6 titles.

We consider linear differential equations with operator coefficients in the Banach space. In addition, we provide sufficient conditions of solvability and strong correctness of the Cauchy problem for such equations of arbitrary order.

Grechko A.L.

On Smoothness of Invariant Sets of the Monotone Linear Extensions

P. 44–48.

Refs.: 11 titles.

This paper considers the monotone linear extensions of dynamic systems. Moreover, we use the projection dynamics to prove the smoothness of invariant sets (manifolds) of linear extensions.

Denysiuk V.P., Rybachuk L.V. 

A Class of Approximate Fractional Integro-Differentiation

P. 49–54.

Refs.: 6 titles.

The study examines a class of methods of approximate calculation of fractional derivatives and Liouville–Weyl integrals. It is based on interpolation of functions by trigonometric polynomials and trigonometric splines.

Yendovitskij P.О.

Exact Asymptotic Approximation of the Group Size in Generalization of Birthday Paradox

P. 55–59.

Refs.: 7 titles.

This paper aims to prove the theorem on asymptotic behavior of a group size in the birthday paradox. In fact, the theorem presents asymptotically imperfect estimates for the group size in case of non-uniform and independent particle’s cell occupancy.

Zhurakovskyi B.M., Ivanov O.V.

The Estimator consistency of Least Squares parameters of a sum of harmonic oscillations in the models with strongly dependent noise

P. 60–66.

Refs.: 9 titles.

In this paper, we obtain sufficient conditions the estimator weak consistency of least squares amplitudes and angular frequencies of a sum of harmonic oscillations observed on the random noise background. We expect that the noise is a local functional of the Gaussian stationary strongly dependent process.

Ilienko A.B., Podkalyuk I.V.

On Continuous Modifications of Poisson and Binomial Distributions

P. 67–71.

Fig. 1. Refs.: 6 titles.

We introduce continuous analogues of Poisson and binomial distributions. We also consider a connection between continuous Poisson distribution and Г-process characteristic.

Kapustyan O.V., Kapustyan O.A., Sukretna A.V.

The Approximate Synthesis in the Optimal Control Problem for the Nonlinear Wave Equation

P. 72–77.

Refs.: 12 titles.

The study explores the optimal control problem with a semi-definite quality criterion for the wave equation disturbed by weak nonlinearity. Based on the exact formula for a corresponding linear-quadratic problem, we construct and prove approximate feedback control that provides close to optimal behavior for a controlled system.

Кubaychuk О.О.

The Estimator Asymptotic Behavior of the Empirical Risk Minimization Method for Bayesian Border

P. 78–85.

Refs.: 10 titles.

This paper highlights the estimator asymptotic behavior for the Bayesian border. Specifically, it is constructed for a sample from the mixture with varying concentrations by the Empirical Risk Minimization method.

Kudin A.M.

Comparative Analyses of Mathematical Models of Security Cryptosystems

P. 86–90.

Fig. 1. Refs.: 11 titles.

The present study investigates the existing models of security cryptographic systems. Crucially, we propose a novel mathematical model for estimating the security asymmetric cryptosystems. This model generalizes existing approaches to estimation of security asymmetric cryptosystems.

Ovcharenko O.V.

The Study of Integral Operators Properties with Generalized Hypergeometric Function in the Kernel

P. 91–94.

Refs.: 12 titles.

We consider the integral operators with generalized functions of hypergeometric type in the kernel, notably (τ,β) andі τ-generalized hypergeometric Gaussian functions and (τ,β)-generalized Kummer function. We also obtain compositional relations for these operators with Liouville fractional integral and fractional derivative.

Runovska М.К.

Convergence of Elements Sums of Autoregressive Sequences with Random Coefficients

P. 95–99.

Refs.: 11 titles.

This paper deals with autoregressive sequences with random coefficients. More precisely, we study necessary and sufficient conditions for convergence of almost surely the sums of elements of such sequences.

Savchuk M.M.

Vectorial  Random Processes and Statistical Tests for Binary Sequences

P. 100–104.

Refs.: 5 titles.

We construct the multidimensional statistical criteria of quality check of casual sequences. By using the weak convergence of vector casual processes, we discover asymptotic distributions of statistics.

Shvets О.Yu., Sirenko V.О.

Regular and Chaotic Attractors of the Liquid Resonant Oscillations in a Tank at Limited Excitation

P. 105–113.

Fig. 6. Refs.: 10 titles.

In this paper, we investigate a non-ideal dynamic system – the electric motor-tank with liquid. To that end, we construct the maps of the system’s dynamic modes. Crucially, we discover quasi-periodic attractors for this system for the first time ever, and verify the transition to deterministic chaos by a novel scenario of generalized intermittency.

Yuzhakova G.O.

Composition Formulas for the τ-Generalized Associated Legendre Functions of the τPkm,n(z) First Kind

P. 114–120.

Refs.: 11 titles.

The paper considers τ-generalized (by Wright) τPkm,n(z) Legendre functions. By employing the known properties of τ-generalized (by Wright) τ2F1(a,b,c,ξ) Gaussian hypergeometric function and the relation between τPkm,n(z) and τ2F1 functions, we formulate and prove the theorem of composition relations and the theorem of differentiation formulas for these functions.

Germasch L.P., Drozdenko O.V.

Quantum-Chemical Reserch of Interaction of Surface Structures of Silicon and Carbide Silicon with Transition Metals

P. 121–129.

Fig. 3. Tabl. 4. Refs.: 20 titles.

We study the interaction of silicon surface structures and silicon carbide with transition metals. On the experimental side, we explore the electronic structure of V, Cr, Ni, Mo and W metals oxides.

Gorobets Yu.I.

Statistical Characteristics of Trajectories of Diamagnetic Unicellular Organisms in a Magnetic Field

P. 130–133.

Fig. 1. Refs.: 6 titles.

Relying on the Boltzmann statistics and hypothesis on the anisotropy of diamagnetic susceptibility in diamagnetic microorganisms, we propose the statistical model for describing alignments of their trajectories in a strong magnetic field. Moreover, we calculate statistical parameters of these trajectories.

Dzhezherya Yu.I., Gryshchuk A.M., Klymuk O.S.

The Active Thermal Stabilization Process in the System of Combined Resistance-Magnetic First Order Phase Transition

P. 134–138.

Fig. 2. Refs.: 8 titles.

This paper analyzes the process of active thermal stabilization in a longitudinal magnetic field. Specifically, we calculate a part of ferromagnetic phase and temperature of the system (opening, ferromagnetic and paramagnetic layers). We demonstrate that the device’s chart enables efficient thermoregulation implementation. Furthermore, we obtain an inequality which determines the system performance, whose range is wide enough to ensure the mode of active thermal stabilization and not to cause fundamental difficulties.

Linchevskiy I.V., Petrischev O.M., Trohimets O.P.

Magnetomechanical Resonances in a Polarized Ferromagnetic Ring

P. 139–144.

Fig. 2. Refs.: 11 titles.

In this paper, we aim to construct and investigate the mathematical model of radial oscillations of a flat polycrystalline (magnetostrictive) ring. On the experimental side, we show that the coil inductance can undergo a number of resonant changes by the example of the toroidal coil inductance with an oscillating ring core. Finally, we propose the algorithm for recalculating these resonance frequencies to values of material constants of the material ring core.

Lukianov P.V.  

One-Dimensional Models of Compact Vortices

P. 145–150.

Fig. 4. Tabl. 1. Refs.: 9 titles.

The paper presents a non-viscous model of the compact vortex which consists of two domains that have different signs of vorticity. This vortex is compensated: the overall vorticity equals zero in it. The vortex compensation causes compactness of the velocity field. The study further analyzes self-similar solutions of the vortex turbulent diffusion problem that corresponds to high vorticity moments.

Chursanova M.V.

The Study of the Biomorphic Silicon Carbide Structure by Raman Spectroscopy

P. 151–155.

Fig. 4. Refs.: 9 titles.

Our paper studies biomorphic silicon carbide (bio-SiC) prepared by forced infiltration with liquid silicon of carbon matrixes derived from hardwood precursors. The Raman spectroscopy shows that 3C-polytype is formed at synthesis temperatures of about ~1550 °C, but both 3C and 6H SiC are formed at the increase of temperatures. By employing the film of silver nanoparticles deposited by immersion plating, we propose to use the surface enhancement effect for analysis of bio-SiC composition. This method allows detecting residual carbon clusters in bio-SiC.