статті, матеріали конференцій https://ir.lib.vntu.edu.ua//handle/123456789/3064 2026-04-17T21:31:36Z 2026-04-17T21:31:36Z Сачанюк-Кавецька, Н. В. Гуда, О. В. Крадінова, Т. А. Sachaniuk-Kavetska, N. Huda, O. Kradinova, T. https://ir.lib.vntu.edu.ua//handle/123456789/51173 2026-04-17T11:52:11Z 2026-01-01T00:00:00Z

Диференціальні рівняння в техніці й природничих науках: чисельне та дано-орієнтоване моделювання логістичної динаміки Сачанюк-Кавецька, Н. В.; Гуда, О. В.; Крадінова, Т. А.; Sachaniuk-Kavetska, N.; Huda, O.; Kradinova, T. Recent studies on differential equations increasingly combine classical mathematical modeling with data-driven identification techniques. This trend is especially relevant in engineering and natural sciences, where real systems are often described by nonlinear dynamics, while the available data are limited or affected by noise. In such a context, a modern manuscript should not remain purely descriptive; it must demonstrate a reproducible computational result that quantitatively confirms the declared methodological approach. The purpose of this paper is twofold: first, to summarize the applied role of differential equations in engineering and natural sciences; second, to verify, on a reproducible control problem, the accuracy of two approaches to dynamic modeling: classical numerical integration and data-driven identification of the right-hand side from limited noisy observations. The study uses the logistic equation dN/dt = rN(1−N/K) with parameters r = 1, K = 100, N(0) = 10 on the interval t ∈ [0; 10]. The exact analytical solution is used as a benchmark. Numerical integration is performed by the explicit Euler method and the fourth-order Runge-Kutta method with a time step h = 0.5. In addition, a simplified data-driven model of the right-hand side is considered in the form f(N)=aN+bN². The coefficients are identified by least squares from synthetic derivative data corrupted by 2% relative noise. The identified model is then reintegrated and compared with the benchmark trajectory. The obtained results demonstrate a substantial difference in accuracy between the two numerical schemes. For the same step size, the Euler method yields RMSE = 2.664, while RK4 gives RMSE = 0.0039. The final value N(10) is reproduced much more accurately by RK4. At the same time, the identified data-driven model recovers coefficients a = 1.0053 and b = -0.01006, which are close to the theoretical values 1 and -0.01. The reconstructed trajectory has RMSE ≈ 0.15, showing that even a simple parametric representation can preserve the essential nonlinear behavior and saturation near the carrying capacity. The scientific contribution of the paper lies in methodological consistency. Instead of declaratively referring to neural differential equations without quantitative evidence, the manuscript provides a transparent comparative numerical experiment and a reproducible data-driven identification procedure. This removes the discrepancy between the stated goal, the applied methods, and the conclusions. The proposed framework may serve as a basis for further extensions to multidimensional systems, partial differential equations, and neural differential models with a complete training and validation pipeline.

2026-01-01T00:00:00Z Dalishchuk, А. Pavlov, S. Polishchuk, S. Polishchuk, V. Sachaniuk-Kavets`ka, N. Davydiuk, L. Kornilenko, O. Павлов, С. В. Сачанюк-Кавецька, Н. В. Давидюк, Л. П. Корніленко, О. С. https://ir.lib.vntu.edu.ua//handle/123456789/50959 2026-03-24T13:22:28Z 2025-01-01T00:00:00Z

Fuzzy neural network method for assessing the effectiveness of odontogenic phlegmons treatment of the maxillofacial region Dalishchuk, А.; Pavlov, S.; Polishchuk, S.; Polishchuk, V.; Sachaniuk-Kavets`ka, N.; Davydiuk, L.; Kornilenko, O.; Павлов, С. В.; Сачанюк-Кавецька, Н. В.; Давидюк, Л. П.; Корніленко, О. С. The paper analyzes the main areas of application of mathematical methods in medical diagnostics, formulates the principles of diagnostics based on fuzzy logic. The basic structure of the MIS medical information system for assessing the degree of engraftment of effectiveness of odontogenic phlegmons treatment of the maxillofacial region was developed and the main recommendations for its design were put forward, namely: the selection and purpose of the system; selection of the structural scheme of the system; formation and analysis of the list of nosological forms, collection of statistically reliable information about the severity of symptoms; choosing a method of processing biomedical information; construction of an algorithm for solving the problems of evaluating biomedical information and forming diagnostic and prognostic conclusions. The practical value of the work lies in the possibility of using an automated medical expert system to solve the problems of medical diagnosis based on fuzzy logic when assessing the degree of engraftment of effectiveness of odontogenic phlegmons treatment of the maxillofacial region.

2025-01-01T00:00:00Z Polishchuk, V. Pavlov, S. Polishchuk, S. Shuvalov, S. Dalishchuk, A. Sachaniuk-Kavets`ka, N. Mukhsina, K. Nazerke, А. Павлов, С. В. Сачанюк-Кавецька, Н. В. https://ir.lib.vntu.edu.ua//handle/123456789/50956 2026-03-24T09:43:12Z 2024-01-01T00:00:00Z

Medical fuzzy-expert system for prediction of engraftment degree of dental implants in patients with chronic liver disease Polishchuk, V.; Pavlov, S.; Polishchuk, S.; Shuvalov, S.; Dalishchuk, A.; Sachaniuk-Kavets`ka, N.; Mukhsina, K.; Nazerke, А.; Павлов, С. В.; Сачанюк-Кавецька, Н. В. W artykule przedstawiono technologię informacyjną do oceny stopnia wszczepienia implantów stomatologicznych u pacjentów z przewlekłą chorobą wątroby za pomocą zbiorów rozmytych, co pozwala na zastosowanie tej metody do medycznych zadań diagnostycznych. Główne wyniki naukowe: opracowano algorytmy i modele matematyczne formalizujące proces wspomagania podejmowania decyzji diagnostycznych w oparciu o logikę rozmytą; opracowano matematyczne modele funkcji przynależności formalizujące reprezentację ilościowych i jakościowych cech informacyjnych opartych na regułach logiki rozmytej, które mogą być wykorzystane w informatycznych systemach ekspertowych do oceny stopnia wszczepienia implantów stomatologicznych u pacjentów z przewlekłą chorobą wątroby.; The paper presents an information technology for assessing the degree of engraftment of dental implants in the event of a pathology violation through the use of fuzzy sets, which allows using this method for medical diagnostic tasks. Main scientific results: developed algorithms and mathematical models that formalize the process supporting diagnostic decisions based on fuzzy logic; developed mathematical models of membership functions that formalize the presentation of qualitative and qualitative informational features based on the rules of fuzzy logic, which can be used in information expert systems when assessing the degree of engraftment of dental implants in case of disease with pathological diseases.

2024-01-01T00:00:00Z Вітюк, В. А. Бондаренко, З. В. Vitiuk, V. Bondarenko, Z. https://ir.lib.vntu.edu.ua//handle/123456789/50879 2026-03-18T10:15:08Z 2026-01-01T00:00:00Z

Реалізація та криптоаналіз блокового шифру Гілла засобами лінійної алгебри Вітюк, В. А.; Бондаренко, З. В.; Vitiuk, V.; Bondarenko, Z. The paper investigates the mathematical foundations of block encryption using the Hill cipher. Algebraic conditions for the existence of an inverse key matrix in the residue ring are determined. An algorithm for generating keys suitable for encryption is developed and described. Computer simulation of the process and evaluation of the method's resistance to breaking are performed.; В роботі досліджено математичні основи блокового шифрування на прикладі шифру Гілла. Визначено алгебраїчні умови існування оберненої матриці ключа в кільці лишків. Розроблено та описано алгоритм генерації придатних для шифрування ключів. Проведено комп`ютерне моделювання процесу та оцінку стійкості методу до злому.

2026-01-01T00:00:00Z