https://bphm.knu.ua/index.php/bphm/issue/feedBulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences2024-01-17T10:56:38+02:00Irina Rozora // Ірина Розораirozora@knu.uaOpen 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>https://bphm.knu.ua/index.php/bphm/article/view/383Mykhailo Moklyachuk – to the 75th anniversary of his birth2023-12-04T14:04:30+02:00Oleksandr BorysenkoVolodymyr ZubchenkoYuliya MishuraMykola PerestyukRostyslav YamnenkoTetyana Yanevych<p>On September 28, 2023, Mykhailo Moklyachuk, Doctor of Physical and Mathematical Sciences, Professor, Laureate of the State Prize of Ukraine in Education, Honored Worker of Science and Technology of Ukraine, and Academician of the Academy of Sciences of the Higher School of Ukraine, celebrated his 75th birthday.</p> <p>His scientific research is devoted to the study of stationary random processes, functionalities of stationary processes, and random fields.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 13 - 15</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Oleksandr Borysenko, Volodymyr Zubchenko, Yuliya Mishura, Mykola Perestyuk, Rostyslav Yamnenko, Tetyana Yanevychhttps://bphm.knu.ua/index.php/bphm/article/view/384Automorphisms of Mackey groups2023-12-26T16:48:37+02:00Oksana Bezushchak<p>We consider total subspaces of linear functionals on an infinite-dimensional vector space and the related Mackey algebras and groups. We outline the description of automorphisms of Mackey groups SL<sub>∞</sub>(V|W), O<sub>∞</sub>(f), and SU<sub>∞</sub>(f) over fields of characteristics not equal to 2, 3. Moreover, the paper explores the relationship between field automorphisms and automorphisms of the aforementioned groups.</p> <p>J.Hall proved that infinite simple finitary torsion groups are the alternating groups on infinite sets or Mackey groups over a field, which is an algebraic extension of a finite field. J.Schreier and S.Ulam described automorphisms of infinite alternating groups. With the description of automorphisms of finitary Mackey groups and special finitary unitary Mackey groups we finish classification of automorphisms of all infinite simple finitary torsion groups over fields of characteristics not equal to 2, 3. The proof is based of description of automorphisms of elementary linear groups over associative rings that due to I.Golubchik, A.Mikhalev and E.Zelmanov.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 16 - 19</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Oksana Bezushchakhttps://bphm.knu.ua/index.php/bphm/article/view/382Comparison of 2D convolutions and dense neural networks for natural language processing models with multi-sentence input2023-11-28T12:17:40+02:00Tetyana YanevychVitaliy GolomoziyYuliya MishuraIryna Izarova<p>This paper is devoted to the analysis of court cases based on multiple sentences that represent plaintiff's claim, claim motivation and defendant's response. Based on these parameters we classify a given case into one of seven categories designed for our task and then predict its decision in the first court's instance. We use fine-tuned XLM\RoBERTa for this task. There were compared two approaches for building fine-tuned model's head. One is based on stacking the numerical representation of multiple sentences so that they form a matrix and applying 2D convolutions. Second approach is based on concatenated sentences and application of dense neural networks. The latter demonstrates a slightly better performance in our experiments, while the former exhibits the simpler training process.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 20 - 29</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Tetyana Yanevych, Vitaliy Golomoziy, Yuliya Mishura, Iryna Izarovahttps://bphm.knu.ua/index.php/bphm/article/view/385Filtering problem for periodically correlated stochastic sequences with missing observations2023-12-27T16:39:44+02:00I. I. GolichenkoM. P. Moklyachuk<p>The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence from observations of the sequence with missings is considered. Formulas for calculation the mean-square error and the spectral characteristic of the optimal estimate of the functionals are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, when spectral densities of sequences are not exactly known but the class of admissible spectral densities is given.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 30 - 43</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 I. I. Golichenko, M. P. Moklyachukhttps://bphm.knu.ua/index.php/bphm/article/view/386Investigation of the scoring model for bank borrowers2023-12-28T11:29:24+02:00Volodymyr ZubchenkoA. V. Avramenko<p>In the paper we investigate scoring models as a tool for credit risk management, their importance, types, features and applications. We consider the history of scoring models and the development of the modern concepts of creditworthiness and scoring, examine scoring types and their features, methods (logistic regression, decision trees, linear programming, decision trees, and others), strengths and weaknesses of each considered method and stages of building scoring models; we stress the importance of scoring cards for building scoring models, indicate the main quantitative and qualitative features, their classification used for and describe the procedure of creating scoring cards. In the paper we consider the factors needed to be considered for more effective scoring model building process; we indicate the main formulas used to assess the creditworthiness of borrowers and improve the accuracy of scoring models, including Population Stability Index (PSI), R-Square Coefficient, Kolmogorov-Smirnov Coefficient, GINI Coefficient, and others; the practical application of scoring models in banks of Ukraine and their steps after applying scoring models are described on the example of a typical borrower.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 44 - 53</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Volodymyr Zubchenko, A. V. Avramenkohttps://bphm.knu.ua/index.php/bphm/article/view/387Asymptotically normal estimation of parameters of mixed fractional Brownian motion2023-12-28T12:39:27+02:00Kostiantyn RalchenkoMykyta Yakovliev<p>We investigate the mixed fractional Brownian motion of the form X<sub>t</sub> = σ W<sub>t</sub> + κ B<sub>t</sub><sup>H</sup>, driven by a standard Brownian motion W and a fractional Brownian motion B<sup>H</sup> with Hurst parameter H. We consider strongly consistent estimators of unknown model parameters (H, κ, σ) based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for H ∈ (0, 1/2) ∪ (1/2, 3/4).</p> <p><em><strong>Pages of the article in the issue</strong></em>: 54 - 62</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Kostiantyn Ralchenko, Mykyta Yakovlievhttps://bphm.knu.ua/index.php/bphm/article/view/379Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche2023-08-18T16:15:37+03:00Andrius Grigutis<p>This article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions and derivation of the inequality where the probability of default is involved under the influence of systematic factor. The author anticipates adding more clarity, especially for early career analysts or scholars, regarding the assumption of borrowers' independence, conditional independence, and interaction between the probability distributions such as binomial, beta, normal, and others. There is also shown the relation between the probability of default and the joint distribution of \sqrt{ϱ}X - \sqrt{1-ϱ}Y, where X, including but not limiting, is the standard normal, Y admits, including but not limiting, the beta-normal distribution and X, Y are independent.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 63 - 74</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Andrius Grigutishttps://bphm.knu.ua/index.php/bphm/article/view/380Asymptotics of the mild solution of a parabolic equation with a general stochastic measure2023-08-18T16:50:43+03:00Irina Bodnarchuk<p>We study the Cauchy problem for a parabolic equation on the line driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 75 - 81</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Irina Bodnarchukhttps://bphm.knu.ua/index.php/bphm/article/view/388Semiempirical assessment of acoustic loads on the rocket head with a non-standard configuration of launch facilities2024-01-05T18:30:19+02:00T. Ya. BatutinaV. N. Oliynik<p>The paper deals with assessing the acoustic loads on the surface of a launching rocket obtained using the semiempirical technique NASA SP-8072 adapted for a launch pad located above the water area. The features of the launch facilities include the reduced length of the gas duct and the presence of a wedge-shaped gas-dynamic deflector divided into two symmetrical oppositely directed slopes. The calculations are made with the allowance for the limited length of the rocket jet's laminar core during take-off due to interaction with the gas-dynamic deflector. A corrected dependence is used for the overall acoustic energy distribution along the supersonic jet for the first time in domestic practice. The contributions of the sound sources associated with different jet sections and acoustic reflection from the water surface are assessed, depending on the current height of the rocket lift. A significant dependence of the resulting acoustic field around the rocket head on the length of the horizontal section of the gas duct is noted.</p> <p><em><strong>Pages of the article in the issue</strong></em>: 84 - 87</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 T. Ya. Batutina, V. N. Oliynikhttps://bphm.knu.ua/index.php/bphm/article/view/389Using combinations of two options of wave fields conjugation in the method of partial domains2024-01-05T18:46:06+02:00O. V. BoryseikoV. O. HusakV. T. Matsypura<p><em>The paper investigates the possibility of using combinations of two options of wave fields conjugation (the conjugation by points and the root mean square approximation) in the method of partial domains using the example of solving the problem of piston radiation in a finite wedge-shaped waveguide. It is shown that the option of using the root mean square approximation is the best, while the use of the conjugation by points of fields generally simplifies the calculation of the problem. The choice of the required calculation combination depends on the problem under consideration, and it is possible that the combined calculation option may lead to a better solution to the problem in terms of fulfilling the law of energy conservation or field conjugation conditions.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 88 - 91</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 O. V. Boryseiko, V. O. Husak, V. T. Matsypurahttps://bphm.knu.ua/index.php/bphm/article/view/390Investigation of porous stress state of semi-infinite hollow cylinder under axisymmetric loading2024-01-06T16:42:11+02:00N. D. VaysfeldZ. Yu. Zhuravlova<p><em>The exact solution of the poroelasticity problem for a semi-infinite hollow cylinder under the axisymmetric load is derived in the paper. The original problem was reduced to a one-dimensional problem by applying the integral Fourier transform. The one-dimensional boundary value problem in the transform domain is formulated in a vector form, its solution is found using the matrix differential calculation apparatus. The derived analytical formulas allow to investigate the change of displacements, stresses and pore pressure depending on the type of porous material, the applied load, the size of outer and inner radii of the cylinder.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 92 - 95</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 N. D. Vaysfeld, Z. Yu. Zhuravlovahttps://bphm.knu.ua/index.php/bphm/article/view/391Plane problem on beam plate’s oscillations on on rectangular base2024-01-08T12:26:08+02:00N. VaysfeldYu. ProtserovA. Tolkachov<p><em>The plane contact problem of a beam’s oscillations on a rectangular elastic base is considered. The vertical edges of the rectangular base are in conditions of the nonfriction contact, the lower edge is fixed, and a beam (beam plate) with free ends is attached to the upper edge. The normal loading is applied to the beam and harmonically changes in time. To solve the boundary valued problem for the elastic base the integral transform method is applied. The apparatus of the Green’s function is used to construct the solution for the boundary valued problem for a beam. The displacements of the rectangular base and the deflection of the beam were found. The interface condition between the base and the plate is used to derive the integral singular equation relatively the dynamical contact stress. The orthogonal polynomial method was used to solve the integral equation. The investigation of the oscillations’ frequency influence on the deflection of beam and elastic rectangular base’s displacements and stress was conducted.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 96 - 99</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 N. Vaysfeld, Yu. Protserov, A. Tolkachovhttps://bphm.knu.ua/index.php/bphm/article/view/392On brittle fracture of a body with partial healed star-shaped crack2024-01-08T14:56:04+02:00T. M. DalyakI. P. Shatsky<p><em>In this article, the express methodology for assessing the strength of a brittle material with a partially healed crack is used to model the renovation of a body with a star-shaped defect of a cyclically symmetrical structure. The rheology of the joint layer is not taken into account, but the specific surface energy in the healed area is generally different than in the solid body. Therefore, we have the problem of crack mechanics in a body that is homogeneous in terms of elastic properties and heterogeneous in terms of crack resistance. The degree of crack healing was described by two parameters: the ratio of the crack resistance of the joint and body materials and the ratio of the length of the healed area to the length of the initial crack. The subject of the analytical study was the efficiency of healing - the ratio of ultimate loads of brittle failure for a healed and primary crack. Two treatment options are considered in detail: near the peaks and near the center of the star defect.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 100 - 103</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 T. M. Dalyak, I. P. Shatskyhttps://bphm.knu.ua/index.php/bphm/article/view/393Interaction of foreign bodies in liquid caused by the acoustic radiation field2024-01-08T16:55:53+02:00O. P. ZhukY. A. ZhukT. V. Klimchuk<p><em>The problem of interaction of two foreign bodies placed in a liquid in an acoustic field propagating along the line connecting the bodies is under investigation. An approach is elaborated to characterize the interaction between the bodies caused by the acoustic radiation forces that are the time-constant components of hydrodynamic forces acting upon the bodies located in the outer liquidmedium. For example of the method application, propagation of the plane acoustic wave along the center line of two liquid spherical drops placed into a space filled with another liquid is under investigation. Study of the acoustic radiation forces is performed in the frame of two-step procedure. The first step comprises solution of the linear problem of incident wave diffraction on the bodies.The problem is solved by the variable separation method. To satisfy the boundary conditions on spherical surfaces, the expansion of the incident and reflected wave potentials over the spherical wave functions are used. The second step is calculation of the hydrodynamic forces acting upon each body followed by time averaging of forces determined. The analytical formula for the acoustic radiation force calculation is derived for the case under consideration.It is established that value of the acoustic radiation force affecting each liquid drop depends significantly on the incident wave frequency, densities, speed of sound in the outer and internal liquid as well as on the radius and distance between drops.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 104 - 107</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 O. P. Zhuk, Y. A. Zhuk, T. V. Klimchukhttps://bphm.knu.ua/index.php/bphm/article/view/394Experimental study of destruction of materials after shock-wave loading2024-01-09T12:43:19+02:00Y. O. ZhukM. M. MelnichenkoV. A. AndruschenkoA. M. KirievN. P. PuchkoM. A. Vodotovka<p><em>In work, systematic studies of the dynamics of destruction processes and the evolution of defects are carried out on the example of artificial stone samples. During the experimental study of samples made of artificial stone after shock wave loading, destruction of the samples was not observed. At the same time, only the formation of radial cracks is observed. In contrast to ceramics, under the same load conditions, the rate of crack growth in artificial stone samples is, on average, 75 km/s. Software tools for 3D surface reconstruction, with high spatial resolution, were used to study the initiation and movement of cracks after shock-wave loading. 3D reconstruction of the surface makes it possible to observe and study the entire pattern of crack growth from the center to the periphery of the sample. The study and analysis of individual parts of the crack were carried out, particularly in the areas where their bifurcation and further growth occur. The nucleation and movement of local cracks in different places of the samples were also observed. The latter makes it possible to assert the existence of complex multi-level destruction of samples under the influence of shock-wave loading.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 108 - 111</p> <p><em><strong>Language of the article</strong>: </em>Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Я. О. Жук, М. М. Мельниченко, В. О. Андрущенко, А. М. Кір'єв, Н. П. Пучко, М. А. Водотовкаhttps://bphm.knu.ua/index.php/bphm/article/view/395Application of BPOE and CVaR in the determination of optimal controls of round plate oscillations2024-01-09T16:03:37+02:00G. M. ZrazhevskyV. F. Zrazhevska<p><em>The work is devoted to the modeling of forced mono harmonic oscillations of a circular plate on active supports in order to determine the optimal location of the minimum number and optimal controls of supports, which ensure the deviation from the given shape of the wave motion of the plate surface with the required accuracy. It was assumed that the plate contains an ensemble of small inhomogeneities (defects) with unknown geometric and physical characteristics. Defects were modeled by high-order singularities, which ensure the equivalence of the boundary value problem solution with specified accuracy to a given power of a small parameter, which is the characteristic area of the regions of individual defects. Stochastic optimization is chosen as the main method of problem research. The probability of exceeding the rms deviation of the oscillation form of the controlled plate from the given wave profile (probability of failure) is considered as a criterion of optimality. The formation of a quantitative characteristic of the probability of failure was carried out by constructing scenarios with generated defects with random characteristics. It is proposed to use the risk measures bPOE and CVaR, which are quasi-convex with respect to random variables.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 112 - 115</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 G. M. Zrazhevsky, V. F. Zrazhevskahttps://bphm.knu.ua/index.php/bphm/article/view/396Two-parameter model of the prefracture zone in a quasi-elastic material near the tip of an interface crack2024-01-09T17:15:16+02:00A. O. KaminskyM. V. DudykYu. V. Reshitnyk<p><em>A model of the pre-fracture zone, which under plane strain conditions extends from the tip of the interface crack at an angle to the plane interface of two different homogeneous isotropic materials, has been developed. The pre-fracture zone is represented by the displacement discontinuity line, on which the strength condition of the Mises-Hill type is satisfied. The parameters of the model are the tensile resistance and shear resistance of the material in which the zone develops. The model takes into account brittle and ductile fracture mechanisms and can be used to describe the quasi-brittle fracture of a piece-homogeneous body with an interface crack. The possibility of a transition between brittle and ductile fracture mechanisms is shown when the ratio of tensile and shear resistance of the material changes.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 116 - 119</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 A. O. Kaminsky, M. V. Dudyk, Yu. V. Reshitnykhttps://bphm.knu.ua/index.php/bphm/article/view/397Wedging of the subinterface crack by plastic cladding2024-01-09T17:42:43+02:00O. G. KutsenkoO. M. KharytonovA. H. Kutsenko<p><em>The model problem of tension of a two-layer cylinder with an annular subcladding crack located at the base material of the cylinder is considered. It is assume that the base material of the cylinder is linear elastic. The cladding of the cylinder is considered as elastic-plastic with bilinear strengthening. The base material of the cylinder is considered to be linear-elastic, the cladding is considered to be elastic-plastic with bilinear strengthening. The dependence of the stress intensity factor on the internal crack front on the value of the tension stresses and the magnitude of the residual strains in the cladding is investigated. The problem was solved numerically using the finite element method. It was established that the plastic zone in cladding does not develop in the direction of crack extension, but at some angle to it. A preliminary analysis of the stress state in the absence of a crack made it possible to explain this phenomenon, as well as some other regularities obtained in the numerical results. The conclusions presented in the work can be useful in evaluating of the crack resistance of equipment and pipes with anti-corrosion cladding.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 120 - 123</p> <p><em><strong>Language of the article</strong>: Ukrainian</em></p>2023-12-23T00:00:00+02:00Copyright (c) 2023 O. G. Kutsenko, O. M. Kharytonov, A. H. Kutsenkohttps://bphm.knu.ua/index.php/bphm/article/view/398Regularities of flat cracks growth in plates2024-01-09T18:28:17+02:00O. G. KutsenkoL. V. KharytonovaR. M. Krush<p><em>The general regularities of the influence of the geometric parameters of a fatigue crack on the direction of its growth in elastic plates under uniaxial tension were studied. Straight cracks, cracks in the form of a full cosine period, cracks in the form of a circle arc and kinked cracks were considered in a broad range of their geometric parameters variations. The direction of crack growth was determined in accordance with the criteria of maximum tangential (circumferential) stresses. The stress intensity factor of mode I and mode II of fracture were determined numerically using the finite element method. The obtained results made it possible to conclude that in the case of smooth crack faces, the direction of its growth primarily depends on the angle between the tangent at the crack tip and the direction of tension. It was established that the presence of a corner point of the faces near crack tip significantly affects the direction of crack growth in the case of small angles, between the tangent and the direction of tension. For such cases, numerically, it was not possible to achieve a continuous limiting transition in the results when the corner point approaches the tip. This circumstance complicates the issue of choosing the size of the initial crack growth step.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 124 - 127</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 O. G. Kutsenko, L. V. Kharytonova, R. M. Krushhttps://bphm.knu.ua/index.php/bphm/article/view/399Modelling of the salt structures deforming due to gravitational buoyancy2024-01-09T21:03:27+02:00M. V. Lubkov<p><em>We consider modeling and geophysical interpretation of the obtained results in the deforming process of the salt structures due to gravitational buoyancy (halokinesis). For solving this geophysical problem, we use variation finite element method of elastic problem resolving with calculation of heterogeneous rocks distribution into considering salt structures. We have defined that salt structures deforming amplitudes mainly depend on linear sizes (length and thickness) of the bottom parts of these structures. Decreasing of these parameters lead to noticeable drop of the press-strain state near the whole region of the salt structure (diapirs). Another hand forms and linear sizes of the top parts of the salt stocks influence only on the deforming of the local regions near these structure elements and don’t essentially influence on the whole region deforming around the stock. Quantity characteristics of linear sizes of the salt diapirs structural elements define the whole picture of the stress-strain state around these objects.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 128 - 131</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 M. V. Lubkovhttps://bphm.knu.ua/index.php/bphm/article/view/400Analysis of the limit equilibrium of a bent spherical shell with collinear cracks according to local and integral failure criteria2024-01-10T12:28:20+02:00M. V. MakoviichukІ. P. Shatskyi<p><em>The stressed-strain state and limit equilibrium of shallow spherical shell weakened by two cross-cutting meridional collinear cracks is studied in the two-dimensional formulation. The crack closure caused by bending deformation was taken into account based on the model of the crack edges contact along a line in one of the face surfaces of the shell. The boundary problem for equations of classical shell theory with interrelated conditions along the line of the cracks is formulated within the framework of such model. Singular integral equation for the unknown jump of normal rotation angle on the cracks edges has been elaborated.</em></p> <p><em>Based on numerical solutions of singular integral equation the stressed-strain state and limit equilibrium of the spherical shell depending on the parameters of shell curvature and distance between cracks are investigated. Using the local and integral through-the-thickness energy failure criteria of linear mechanics of fracture, the upper and lower values of limit load were established. It was found that the upper estimate of the limit load according to the integral criterion is approximately twice the magnitude of the lower estimate according to the local criterion.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 132 - 135</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 M. V. Makoviichuk, І. P. Shatskyihttps://bphm.knu.ua/index.php/bphm/article/view/401Construction of long-term fatigue failure criteria for thin-walled laminated shells2024-01-10T15:15:12+02:00B. P. Maslov<p><em>A model and criterion of long-term fatigue failure for thin-walled layered shells is built, taking into account the influence of the type of stress state. The problem of calculating the number of cycles to failure under combined loading is considered. Solutions are built on the basis of the concept of equivalent stresses. The problem of determining local stresses in composites of random structure is formulated within the framework of the second-order nonlinear theory. The solution of the stochastic boundary value problem on determining the stress concentration in a unidirectional composite with a metal matrix (MMC) was obtained. To build a complete system of equations of the second order, the method of successive approximations is used. The parameters of the stress concentration at the boundary of the components are determined. The given examples show the importance of the influence of nonlinear properties on the redistribution of stresses near the fibers. The possibility of predicting the long-term strength of the material is shown. The necessary information about the material for the formulation of failure criteria is the S-N curves for individual components of the combined stresses.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 136 - 139</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 B. P. Maslovhttps://bphm.knu.ua/index.php/bphm/article/view/402Frictional heating of system punch-elastic half plane when sliding along creative line2024-01-10T15:43:51+02:00V. M. OnyshkevychG. M. Barabash<p><em>Friction heating of system punch-elastic half plane when sliding along creative line is considered. Model of so-called “third body”, i.e., thin near-surface and intermediate layers, the physical and mechanical properties of which differ from those of the interacting bodies, and by the microgeometry of their surfaces in the contact zone, used for mathematical description of contact. The method of determination of thermal contact conductance in mathematical modelling of contact interaction with considering friction and hear generation by “third body” is presented. Using of modified conditions of heat contact in mathematical model of contact thermoelasticity, taking into account of friction and heat generation is proposed. The solution of the problem of thermoelasticity for a half-plane is obtained by means of the Fourier integral transformation. Heat conductivity problem for the punch is solved by method of straight lines. The system obtained of dual integral equations is reduced to the system of linear algebraic equations by means of points collocation method. Formulas for thermal fields, heat fluxes and contact stresses are proposed. In order to obtain the unknown contact area, the iterative scheme based on a control of a sign of normal stresses in the immediate contact interaction zones is used. Method of moving line of separation of boundary conditions is proposed.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 140 - 143</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. M. Onyshkevych, G. M. Barabashhttps://bphm.knu.ua/index.php/bphm/article/view/403To the computation of the fatigue life of prismatic bars under uniaxial asymmetric bending2024-01-10T17:11:48+02:00Alla V. PlashchynskaOlexander V. Romanov<p><em>An alternative approach to solving the fatigue life computing problems for material samples and structural elements under uniaxial asymmetric cyclic loading has been considered. This approach is based on the concept of equivalent stresses, which allows the asymmetric load cycle to be reduced to the equivalent symmetric cycle for the number of fracture cycles. The structure of equivalent stresses is obtained based on the hypothesis of the existence of single isochronous ultimate stress diagrams, which are invariant with respect to the number of cycles to fracture. As basic experiments, to determine the material constants in the original equations, easily reproducible standard tests of smooth samples of the material for short-term strength and fatigue under symmetric and asymmetric bending load cycles are used. Problems of multicycle fatigue analysis of prismatic rods under uniaxial asymmetric bending, considering the influence of mean stress, stress range, and amplitude coefficient, have been solved. Satisfactory agreement of calculation results with experimental data was obtained.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 144 - 147</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Alla V. Plashchynska, Olexander V. Romanovhttps://bphm.knu.ua/index.php/bphm/article/view/404Influence of longitudinal and transverse thermal conductivity of the interface crack on the effective parameters of the bi-material2024-01-10T18:06:02+02:00Kh. I. Serednytska<p><em>The effective parameters of the bi-material with a periodic system of interfacial cracks are studied, taking into account their longitudinal and transverse thermal conductivity. The bi-material is subjected to tensile forces and uniform heat flow. The transverse and longitudinal thermal conductivity of the cracks is taken into account by the thermal resistance of the filler and the thermal conductivity of the surface films, respectively. The thermal resistance of the filler is directly proportional to the opening of the cracks and inversely proportional to the thermal conductivity of the filler. Thermal conductivity of surface films does not change under the influence of load. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for an opening cracks and a temperature jump between the cracks faces. An analytical-numerical iterative procedure for solving this system is proposed. Based on the obtained solution, the effective temperature jump and the effective thermal resistance of the bi-material are determined. The dependences of the effective parameters of the bi-material on the applied load and thermal conductivity coefficients of the filler and the surface films of the cracks are analyzed.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 148 - 151</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 Kh. I. Serednytskahttps://bphm.knu.ua/index.php/bphm/article/view/405Stability of non-thin anisotropic cylindrical shells in spatial position under distributed lateral pressure2024-01-10T18:40:21+02:00V. M. TrachA. V. PodvornyiN. B. Zhukova<p><em>A three-dimensional approach to solving the problem of stability of non-thin cylindrical anisotropic layered shells under distributed lateral pressure is proposed. Based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous differential stability equations is obtained for the calculation of shells, the anisotropy of which is characterized by a material with one plane of elastic symmetry. The solution of the three-dimensional system was carried out using the Bubnov-Galerkin methods and numerical discrete orthogonalization.</em></p> <p><em>The influence of an increase in the number of cross-laid layers of the same thickness on the stability of an anisotropic cylindrical shell is studied. The results of the solution are presented by graphs and their analysis is given.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 152 - 155</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. M. Trach, A. V. Podvornyi, N. B. Zhukovahttps://bphm.knu.ua/index.php/bphm/article/view/406The use of cubic splines in the modeling of creep processes of linear viscoelastic materials under complex stress state2024-01-11T15:04:07+02:00V. S. UshakovaO. V. UshakovO. Y. Gorun<p><em>The processes of creep of thin-walled tubular elements made of linear viscoelastic materials under complex stress conditions are considered. The discrete values of basic experimental data on uniaxial tension and pure torsion are considered. These discrete values are used for identification of hereditary kernels normally used in creep modeling processes under complex stress conditions. As an example material, plexiglass ST1 is used for calculations. The area of linearity of the model is substantiated by the value of the quantile of statistics and the hypothesis of the existence of a unified creep function in a certain, predetermined confidence interval. The creep function is invariant with respect to stresses and is built with making use of the yield curves. Constitutive equations of the model contain a set of functions and coefficients determined from basic experiments. For further calculations, the experimental data are approximated by a power function followed by the smoothing with cubic splines. Approximation analysis is carried out by evaluation of the least squared deviation of experimental data from the calculated data. The approximating function is analyzed with making use of minimum of the quadratic deviation.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 156 - 159</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. S. Ushakova, O. V. Ushakov, O. Y. Gorunhttps://bphm.knu.ua/index.php/bphm/article/view/407The vector algebra approach to the kinematic analysis of the structural groups of the 2nd class by Artobolevsky2024-01-11T16:27:57+02:00K. G. KhoroshevK. O. DuchenkoS. V. Kykot<p><em>The methodology for analyzing velocities and accelerations of characteristic points, as well as angular velocities and angular accelerations of links, of the structural groups of the 2nd class according to Artobolevsky is developed using exclusively the tools of vector algebra. There are exist five forms of the structural groups of the 2nd class by Artobolevsky, each form has been considered. The position analyses of the structural groups, which are described by the links’ direction vectors and the radius-vectors of points of external kinematic pairs, and in addition, if necessary, the position analysis of external links are assumed to have been carried out by the vector algebra or some other approach. Provided for all forms of the structural groups formulas for calculations are prepared for creating a software product that automatizes the kinematic analysis of planar linkages of the 2nd class according to Artobolevsky. Also, they can be used for the kinetostatic and dynamic analyses of the mentioned linkages. The specified limits of application of the presented approach are pointed out.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 160 - 163</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 K. G. Khoroshev, K. O. Duchenko, S. V. Kykothttps://bphm.knu.ua/index.php/bphm/article/view/408A set of collinear electrically and magnetically permeable cracks between two piezoelectromagnetic materials2024-01-12T10:38:25+02:00N. V. ShevelovaT. V. Khodanen<p><em>The plane strain problem for the bimaterial space consisting of two piezoelectromagnetic half-spaces with a finite set of cracks along the material interface is considered. It is assumed that the edges of the crack are electrically and magnetically permeable, and a mixed mechanical load and electric and magnetic fields can be set at infinity.</em></p> <p><em>The presentations of electro-magneto-mechanical quantities through a piecewise analytical vector function are constructed with the use of constitutive equations for piezoelectromagnetic materials. By means of these presentations the problem of linear relationship is formulated and solved analytically. Using the obtained solution, all the necessary mechanical, electrical, and magnetic components along the material interface as well as the energy release rate for all crack tips are found analytically. The asymptotic presentations of all fields around the crack tips and the crack closure integral method were used.</em></p> <p><em>Numerical results are obtained for different loads, location of the cracks, their number and lengths. A significant increase in energy release rates was demonstrated because of cracks converge, especially for the tips located closest to each other.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 164 - 167</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 N. V. Shevelova, T. V. Khodanenhttps://bphm.knu.ua/index.php/bphm/article/view/409Model of nonlinear deformation of granular composites2024-01-12T11:31:30+02:00E. N. ShikulaN. B. Zhukova<p><em>The model of nonlinear deformation of a granular composite material of a stochastic structure with physically nonlinear components was constructed. The basis is the stochastic differential equations of the physically nonlinear theory of elasticity by L.P. Khoroshun. The solution to the problem of the stress-strain state and effective deformable properties of the composite material is built using the averaging method. An algorithm for determining the effective properties of granular material with physically nonlinear components has been developed. The solution of nonlinear equations, taking into account their physical nonlinearity, is constructed by the iterative method. The law of the relationship between macrostresses and macrostrains in granular material and the dependence of average strains and stresses in its components on macrostrains has been established. Curves of deformation of the material were constructed for different values of the volume content of its components. The dependence of the effective deformable properties of the granular material on the volume content of the components was studied. The effect of component nonlinearity on the deformation of granular composite material was studied. It was established that the nonlinearity of the components significantly affects the effective deformable properties and the stress-strain state of granular materials.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 168 - 171</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 E. N. Shikula, N. B. Zhukovahttps://bphm.knu.ua/index.php/bphm/article/view/410Torsional elastic waves. Some aspects of nonlinear analysis2024-01-12T16:41:14+02:00V. M. YurchukS. V. Sinchilo<p><em>The features of the use of boundary conditions in the nonlinear problem of torsional wave propagation for an elastically deformable medium with an external boundary are analyzed. The formulation and wave analysis in the linear (classical) approach are briefly described, since the linear solution is used in the work as a first approximation in the nonlinear approach. The first feature for a torsional wave is a significant complication in the nonlinear approach of the boundary conditions due to the difference between the shape of the boundary before and after the deformation (in the linear approach, the shape of the boundary does not change). The second feature is the significant complication of the mathematical representation of the boundary conditions due to the appearance of additional nonlinear terms. For a torsional wave, it was found that the use of the condition of absence of stresses on the boundary surface (assumption of a free boundary) may not be completely correct.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 172 - 175</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. M. Yurchuk, S. V. Sinchilohttps://bphm.knu.ua/index.php/bphm/article/view/412Investigation of the stress-strain state of a cylinder with microstructural transformations under pulse loading2024-01-15T10:16:20+02:00N. D. YakovenkoS. M. Yakymenko<p><em>Axisymmetric dynamic problem of thermomechanical loading of a steel cylinder is considered. Volume strain caused by the microstructural transformations of the martensitic type under cooling solids as well as into consideration and dependence inelastic characteristics of material for multiphase state are taken. The thermomechanical nonlinear behavior of an isotropic material is described by unified flow model generalized for the case of multiphase material state. The problem is solved numerically by the implicit step-by-step time integration method, by the iterative method and by the finite element method. The investigation of the stress-strain state of an inelastic material with regard for the dependence of parameters of the flow model on the phase composition of a material is carried out by using of numerical simulation. We established that microstructural transformations significantly reduce residual inelastic strain and promote the appearance of compressive stresses. The results obtained in the work can be used in calculations of parameters of surface hardening technologies.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 176 - 179</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 N. D. Yakovenko, S. M. Yakymenkohttps://bphm.knu.ua/index.php/bphm/article/view/413Sensor Systems with Optical Reponse2024-01-15T10:46:43+02:00V. M. YashchukA. G. GrebinykI. V. LebedyevaO. V. VashchilinaM. Yu. LosytskyyO. M. Navozenko<p><em>This paper is a review of the scientific works of the co-authors. In the paper, the basic principles of action of sensor systems with optical response of two types are considered. In particular, two spectroscopic technologies for probing some objects or events in non-living (synthetic) or biological environments are considered. In the first part of the work, sensor technologies related to the use of probes with optical response specially introduced into the sensor system are analyzed. As a rule, these probes are specially developed systems, the spectral properties of which change significantly under interaction with the object of probing. In the first part of the work, sensors of the first type are considered. In particular, the main ideas used in this type of sensors are given and specific examples of the use of such sensors are analyzed: specially created molecules that have a low fluorescence quantum yield due to a significant number of mechanical intramolecular degrees of freedom. The intercalation of such probes to large biomolecules leads to a change in the spectral characteristics of these probes, in particular, to a significant increase in fluorescence (up to 1000 times). The case of two-photon absorption of molecular probes in the transparency window of biological tissues is examined. Semiconductor and metal nanoparticles whose absorption and fluorescence spectra depend on their sizes were also proposed as probes of the first type (as sensors of elastic vibrations of the environment).The second part of the paper is devoted to the mechanisms of autosensing (the case when the medium's own optical centers are used to detect processes occurring in biological or synthetic systems). The main ideas that underlie the operation of sensors with optical response of this type were analyzed, and examples of such use were also given. In particular, the use of the own spectral properties of biomacromolecules and some coenzymes for changes in the external environment is considered. The use of the optical response of synthetic macromolecules on the value of their molecular weight was also analyzed.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 180 - 183</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. M. Yashchuk, A. G. Grebinyk, I. V. Lebedyeva, O. V. Vashchilina, M. Yu. Losytskyy, O. M. Navozenkohttps://bphm.knu.ua/index.php/bphm/article/view/414Construction of asymptotics of the solution for a system of singularly perturbed equations by the method of essentially singular functions2024-01-15T15:00:07+02:00V. V. SobchukI. O. Zelenska<p><em>Singularly perturbed problems with turning points arise as mathematical models for various physical phenomena. The internal turning point problem is a one-dimensional version of the steady-state convection-diffusion problem with a dominant convective term and a velocity field that changes sign in the reservoir. Boundary turning point problems, on the other hand, arise in geophysics and in the modeling of thermal boundary layers in laminar flow. The paper analyzes the results from the asymptotic analysis of singularly perturbed problems with turning points. For a homogeneous system of singularly perturbed differential equations with a small parameter at the highest derivative and a turning point, the conditions for constructing a uniform asymptotic solution are obtained. We consider the case when the spectrum of the limit operator contains multiple and identically zero elements. The asymptotics are constructed by the method of essentially singular functions, which allows using the Airy model operator in the vicinity of the turning point. The construction of asymptotic solutions contains arbitrary constants, which are determined uniquely during the solution of the iterative equations. At the same time, the conditions for the existence of a solution of a system of differentials with a small parameter for the highest derivative and for the presence of a turning point are obtained, provided that the turning point is located on the interval [0; l]. An example of constructing the asymptotic of a homogeneous system of differential equations is given.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 184 - 192</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. V. Sobchuk, I. O. Zelenskahttps://bphm.knu.ua/index.php/bphm/article/view/415Dynamics analysis and forecast of number of individuals with stress syndrome under uncertainties2024-01-15T16:57:46+02:00S. BekesieneO. NakonechnyiO. KapustianI. ShevchukM. Loseva<p><em>In this work, we propose a population dynamics model of the spread of stressful processes in several groups with different characteristics. Such a model is described by a system of nonlinear differential equations. Also, this model provides for the possibility of studying external influences, that is, the effectiveness of actions aimed at increasing the psychological stability of the population. The main objective of the study was to propose algorithms for finding guaranteed predictive estimates of the dynamics of such models. Two scenarios of this challenge are considered: for the case when there are available accurate data on the number of persons under stressful influence in each of the groups during a specific time interval; and for a similar case, but when there is observational data on the dynamics of such individuals. In both cases, we apply the methodology of finding guaranteed predictive estimations of the dynamics within these models. As an example, we consider the special case of the equation of population dynamics without external influence for one group of persons.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 195 - 199</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 S. Bekesiene, O. Nakonechnyi, O. Kapustian, I. Shevchuk, M. Losevahttps://bphm.knu.ua/index.php/bphm/article/view/381Recognition of heart rhythm disorders in children by integral parameters of electrocardiograms2023-10-24T16:13:40+03:00S. M. IvanovS. O. Matviienko<p><em>The article deals with the organization of a database table for the accumulation of integral parameters of electrocardiograms of male and female children in the front-line region of residence (the city of Kharkiv and the Kharkiv region of Ukraine). The calculated main numerical characteristics of integral ECG parameters such as mathematical expectation, variance and standard deviation with heart rhythm disorders are presented. The application of logistic regression to determine the degree of heart rhythm disturbance, which is determined in the interval (0;1), is considered. Representation of logistic regression as multiple linear regression is described. The LSE method is used to estimate the parameters. A correlation matrix of linearly independent integral ECG parameters is given. The obtained results may be of interest to developers of software applications designed for personal health monitoring.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 200 - 205</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 S. M. Ivanov, S. O. Matviienkohttps://bphm.knu.ua/index.php/bphm/article/view/417An effective numerical method for solving the Richards-Klute equation with tracking of full saturated zone2024-01-16T12:30:22+02:00V. A. Kolesnykov<p><em>The article presents modifications for numerical methods for modeling of mass transfer process in porous medium with full saturated zone tracking. The goal of the article is to increase computational efficiency of finding an approximate solution process using division of the area into the two non-intersecting parts: unsaturated zone and zone with full saturation. Numerical methods for solving the one-dimensional Richards-Klute equation with tracking of the full saturated zone have been developed. The cases of monotonic solution and solution with general properties of Richards-Klute equation were considered. A modification of the full saturated zone tracking process using a doubly connected edge list structure have been developed for two-dimensional case. Efficiency increase estimation is proven for one- and two-dimensional cases using probability distibution for a measure of the full saturated zone. A comparative analysis of the proposed modifications was carried out. The results of numerical experiments coincide with the estimates predicted by theory.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 206 - 213</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. A. Kolesnykovhttps://bphm.knu.ua/index.php/bphm/article/view/418Updated DTW+K-Means approach with LSTM and ARIMA-type models for Core Inflation forecasting2024-01-16T20:40:43+02:00D. Krukovets<p><em>The paper is dedicated to evaluating performance in forecasting tasks of the novel routine that includes adapted DTW + K-Means for aggregating series with similar dynamics. The algorithm was developed throughout the series of papers. Novel parts are designed in a way to work with periodic series, like in the investigated monthly data case. It is used over hundreds of Consumer Price Index components to find similar dynamics and aggregate them by the similarity of their dynamics. Then aggregated series are given as input to the ARIMA, SARIMA, and LSTM models, to forecast the total Core Consumer Price Index. The choice is based on the necessity to capture possible non-linear relationships between series. The dataset is quite rich and contains hundreds of Consumer Price Index components, which is a level of prices for different goods. Data suffers from multiple issues, including seasonality, so controlling them either with satellite models such as X-12 or with the architecture of the forecasting model is sufficient. The research results are important for different groups of agents. Private businesses seek to plan their pricing while government structures want to employ their administrative measures in a proactive data-driven manner. The result shows that the SARIMA currently outperforms other models. An LSTM model combined with DTW + K-Means method shows worse results yet it was able to catch non-linearities, unlike more traditional models. Further investigation of LSTM + DTW/K-Means performance and fitting is necessary.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 214 - 225</p> <p><strong><em>Language of the article</em></strong>: English</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 D. Krukovetshttps://bphm.knu.ua/index.php/bphm/article/view/419Solution of the traveling salesman problem based on the annealing method with the fuzziness of the time perception2024-01-17T10:20:14+02:00V. O. Rets<p><em>This paper investigates the use of fuzzy numbers and the annealing method to improve the results of the traveling salesman problem (TSP) by more accurately representing real-world circumstances, where the value of the objective function represents the subjective perception of the length of the time interval required to travel between cities. TSP is a classic combinatorial optimization problem that involves finding the shortest route between a set of cities. Fuzzy numbers are used to model input inaccuracy and uncertainty, as they allow for a more detailed representation of real-world constraints and factors that may affect the problem. The annealing method is used to optimize the TSP solution by gradually decreasing the temperature of the system, which allows exploring different solutions and avoiding getting stuck in local minima. To demonstrate the effectiveness of this approach, a Python program was developed that was used to compare the results of the TSP problem using crisp and fuzzy numbers using the annealing method. The results show that the use of fuzzy numbers, particularly triangular and parabolic, with the annealing method leads to a significant improvement in the results of the TSP problem compared to the use of crisp numbers, assuming a model is called realistic if it has possible deviations from the expected fixed mean. Computational results of the program are presented and analyzed, demonstrating the potential of this approach for real-world optimization problems involving imprecise or uncertain data and which can be particularly applied to the optimization of processes with subjective time perception.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 226 - 231</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 V. O. Retshttps://bphm.knu.ua/index.php/bphm/article/view/420Neural approaches for writing assistant tasks2024-01-17T10:56:38+02:00O. H. SkurzhanskyiA. A. Marchenko<p><em>The article is devoted to the analysis of tasks for building a writing assistant, one of the most prominent fields of natural language processing and artificial intelligence in general. Specifically, we explore monolingual local sequence transduction tasks: grammatical and spelling errors correction, text simplification, paraphrase generation. To give a better understanding of the considered tasks, we show examples of expected rewrites. Then we take a deep look at such key aspects as existing publicly available datasets and their training splits, quality metrics for high quality evaluation, and modern solutions based primarily on neural networks. For each task, we analyze its main peculiarities and how they influence the state-of-the-art models. Eventually, we investigate the most eloquent shared features for the whole group of tasks in general and for approaches that provide solutions to them.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 232 - 238</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>2023-12-23T00:00:00+02:00Copyright (c) 2023 O. H. Skurzhanskyi, A. A. Marchenko