Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics 2022-11-14T17:17:35+02:00 Irina Rozora // Ірина Розора Open Journal Systems <p>The journal contains results of new research in various fields of mathematics, computer science, mechanics, and physics. For researchers, teachers, postgraduates, engineers and students. </p> Rheological models of biological cells 2022-11-14T14:30:44+02:00 Liliya V. Batyuk Natalya M. Kizilova <p><em>The most important experimental methods of studying the mechanical properties of cells, as well as the most common rheological models, among which the discrete models of the micro/nanostructure of the cell and continuous models that allow calculating the modulus of elasticity and viscosity of the cell in normal and pathological conditions are discussed. A review of continuous models is given with an indication of their features and differences. A new continuum model of the cell as a multi-layer shell filled with a viscoelastic fluid is proposed. Equations of the model and their solutions for cases of isotonic, isometric and dynamic experiments are obtained. Peculiarities of the mechanical behavior of the models depending on the identified parameters are investigated. A comparison with the data of experimental measurements is given. It is shown that the proposed multi-layer model allows evaluation of separate contribution of the mechanical properties of the cytoskeleton, membrane, adsorbed substances and the hydrated shell, which is important for clinical diagnosis of diseases by measuring the mechanical parameters of cells.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 37 - 41</p> <p><em><strong>Language of the article</strong>: Ukrainian</em></p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Mathematical modeling of the stressed state of a viscoelastic half-plane with inclusions 2022-07-19T18:23:23+03:00 D. V. Zatula N. I. Zatula <p><em>The application of the method of boundary integral equations is considered for studying the stress state of flat viscoelastic bodies with inclusions. The method is based on the use of complex potentials and the apparatus of generalized functions. An analytical solution of the problem is obtained for a half-plane with inclusions of arbitrary shape. For a numerical study of the change in the stress state depending on the time and geometry of the inclusions, a discrete analogue of the system of boundary-time integral equations has been developed.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 42 - 45</p> <p><em><strong>Language of the article</strong>: English</em></p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 D. V. Zatula, N. I. Zatula Improving the quality of optoacoustic imaging: a comparison of physical and numerical experiment 2022-11-14T14:56:40+02:00 A. G. Rudnitskii M. A. Rudnytska L. V. Tkachenko <p><em>Optoacoustic imaging is based on the generation of thermoelastic waves by heating an object in an optically inhomogeneous medium with a short laser pulse. The generated ultrasonic waves contain information about the distribution of structures with predominant optical absorption. Detection of acoustic perturbations on the surface of the object and the application of the backprojection algorithm are used to create a picture of the absorbed energy inside the environment. Conventional reconstruction methods lead to artifacts due to the peculiarities of the recovery algorithm. This study proposes an iterative procedure to reduce these artifacts. The algorithm minimizes the error between the measured signals and the signals calculated from the recovered image. The paper compares the results of processing optoacoustic signals implemented in numerical experiments with the results of physical experiments. It is shown that the quality of the recovered images improves even with a small number of iterations.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 46 - 56</p> <p><em><strong>Language of the article</strong>: Ukrainian</em></p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Bounded solutions of a second order difference equation with jumps of operator coefficient 2022-11-14T15:10:47+02:00 Andrii Chaikovs’kyi Oksana Lagoda <p><em>We study the problem of existence of a unique bounded solution of a difference equation of the second order with a variable operator coefficient in a Banach space. In the case of a finite number of jumps of an operator coefficient necessary and sufficient conditions are obtained.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 57 - 61</p> <p><strong><em>Language of the article</em></strong>: English</p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Properties of solutions to linear KdV equations with φ-sub-Gaussian initial conditions 2022-11-02T20:35:28+02:00 O. M. Hopkalo L. M. Sakhno O. I. Vasylyk <p>In this paper, there are studied sample paths properties of stochastic processes representing solutions (in L_2(Ω) sense) to the linear Korteweg–de Vries equation (called also the Airy equation) with random initial conditions given by φ-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded domains. Also, there are presented some examples to illustrate the results of the study.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 11 - 19</p> <p><strong><em>Language of the article</em></strong>: English</p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Estimation of ruin probability for binomially distributed number of $\varphi$-sub-Gaussian claims 2022-09-12T16:30:42+03:00 Rostyslav Yamnenko Aounallah Lamin <p>In this paper, we study the properties of a risk process, formed by binomial sum of $\varphi$-sub-Gaussian risks. Estimates for probability of exceeding a monotone increasing continuous curve by such a sum are obtained. In particular, the ruin probability estimate is derived for the risk process in case of linearly incoming premiums.</p> <p><strong><em>Pages of the article in the issue</em></strong>: 20 - 27</p> <p><em><strong>Language of the article</strong></em>: Ukrainian</p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Some applications of generalized fractional derivatives 2022-11-14T14:19:16+02:00 L.M. Sakhno <p>The paper presents a concise summary of main properties of generalized fractional derivatives, so-called convolution type derivatives with respect to Bernstein functions. Applications are considered to modeling time dependent random fields on the sphere as solutions to partial differential equations with the generalized fractional derivative in time and random initial condition.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 28 - 34</p> <p><strong><em>Language of the article</em></strong>: English</p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Calculation of boundaries of the working zone of the round magnetic applicator 2022-11-14T17:17:35+02:00 V. M. Kupriianchuk M. M. Budnyk <p><em>We considered the problem of modeling a magnetic applicator of round shape, designed to act on an object (target) with a constant or variable magnetic field. Due to the fact that the magnetic field monotonically decreases with increasing distance to the applicator, the model includes 3 applicators with different radii, and the problem is solved based on their comparison At the same time, the larger and smaller applicators have radii that are larger or smaller than the radius of the average applicator by the same number of times (scale factor k). Analytical dependences on k of the near, far boundary, and middle of the intermediate zone, i.e., the working zone, in which the target should be located, were found in the approximation of the current loop. Asymptotics were found in extreme cases of minimal (k=1) and large (k&gt;&gt;1) scale factors. It is shown that the middle of the working zone at k=1 is equal to R/√2, (R is the radius of the applicator), and at k&gt;&gt;1 it grows as (R/2) k^(1/3). These results provide a solution to the "direct" problem of choosing target parameters for an applicator of a certain radius - size and distance to it. Such a selection is critical when the targets have a sufficiently large size and the distance to which cannot exceed a certain critical value (depth of occurrence), which takes place in particular for the action by magnetic field on certain organs or the area of localization of magnetic (nano)materials inside biological objects, including humans or animals.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 86 - 91</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) On probability estimation of buffer overflow for communication networks 2022-11-14T16:23:34+02:00 Y. S. Herasymiuk I. V. Rozora A. O. Pashko <p><em>In recent years, a large number of research of telecommunications traffic have been conducted. It was found that traffic has a number of specific properties that distinguish it from ordinary traffic. Namely: it has the properties of self-similarity, multifractality, long-term dependence and distribution of the amount of load coming from one source.</em></p> <p><em>At present, many other models of traffic with self-similarity properties and so on have been built in other researched works on this topic. Such models are investigated in this paper, which considers traffic in telecommunications networks, the probability of overflow traffic buffer. Statistical models are built to analyze traffic in telecommunications networks, in particular to research the probability of buffer overflow for communication networks. </em></p> <p><em>The article presents the results of the analysis of processes in telecommunication networks, in particular traffic; research of possibilities of representation of real processes in the form of random processes on the basis of use of statistical simulation model; the necessary mathematical and statistical models are selected and analyzed; software-implemented models using the Matlab environment; visual graphs for comparison of the received data are given; the analysis of the received models is carried out.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 64 - 69</p> <p><em><strong>Language of the article</strong>: Ukrainian</em></p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) ECG signal classification using machine learning techniques 2022-06-30T11:34:58+03:00 M. Kovalchuk V. Kharchenko A. Yavorskyi I. Bieda Taras V. Panchenko <p><em>The importance of electrocardiogram (ECG) analysis is difficult to overestimate. Rhythm of life, stress and other factors affect the frequency of diseases and their early appearance. At the same time, the technologization (digitalization) of life and hardware-software complexes, such as mobile electronic cardiographs and wearable devices in general, which are rapidly developing, open new opportunities for rapid analysis of human state by certain indicators, as well as allow to diagnose on the new higher level in almost real time.</em></p> <p><em>There are many methods for analyzing cardiograms. In this paper, the authors propose a new approach based on an ensemble of individual classifiers, which effectively solves the problem of ECG analysis. The study is based on the PhysioNet Computing in Cardiology Challenge 2017 and the MIT-BIH Arrhythmia Database. The algorithm consists of the following stages: data filtering</em> <em>using moving average and Butterworth filters, R-peak localization via threshold and grouping method, ECG resampling for the better comparability, “Noisy” vs “NotNoisy” classification as the most hard-to-identify class, final classification as “Normal”, “Atrial Fibrillation”, “Other” using an ensemble of 1D CNN classifiers and a final classifier of selection using logistic regression, random forest or support vector machine (SVM).</em></p> <p><em>The proposed method shows high accuracy by the metric F<sub>1</sub>, so it gives the background for further research, optimization and implementation. This way this algorithm could help to save human’s life by in-time detection of problems with cardiovascular system (CVS) at early stage.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 70 - 77</p> <p><em><strong>Language of the article</strong>: Ukrainian</em></p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s) Modeling of health and mortality functions based on data for the population of Ukraine 2022-11-14T17:05:36+02:00 I. O. Pashchuk H. V. Livinska <p><em>In the work the approach to modeling of data sets of the life table is given. Life expectancy limits based on stochastic mortality modeling and the application of the critically low first achievement theory are also investigated. Particular attention is paid to the representation of the function of health, together with a well-established theory of the Force of Mortality, as well as life tables. The parameters of the model are estimated and analyzed according to the data of demographic tables for the population of Ukraine.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 78 - 83</p> <p><em><strong>Language of the article</strong>: Ukrainian</em></p> 2022-10-12T00:00:00+03:00 Copyright (c) 2022 The Author(-s)