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Документ Methodology of project-based learning for training junior students in applied mathematics: general scheme of the educational process(IOP Publishing Ltd, 2023) Akhiiezer, O. B.; Haluza, O. A.; Savchenko, A. O.; Lyubchyk, Leonid Mykhailovych; Protsay, N. T.; Aslandukov, M. O.An original methodology of the project-based learning for junior students of the specialty applied mathematics is proposed in the paper. A complete step-by-step diagram (as a BPMN diagram) of the process of the project-based learning as a business process with a description of the specifi actions of all its participants is given. The paper specifid and clearly describes all the main aspects of the work on the project, starting from the criteria that the project problem must satisfy, and ending with the form of project defense. The roles of both students within the project team and all teachers are described in detail. Special attention is paid to all documents accompanying the work on the project, which should be submitted by the project team. The results of the article may be useful to those teams of teachers who are just starting to work on the implementation of project-based learning into the educational process for the specialty of applied mathematics or related ones.Документ Use of triangular models of non-stationary processes in modeling variability of heart rhythm(Харківський національний університет радіоелектроніки, 2019) Akhiiezer, O. B.; Dunaievska, О. I.; Shyshkin, Mykhailo; Butova, Olha; Rohovyi, AntonThe subject matter is a mathematical model describing the process of heart rhythm variability, which is based on the use of triangular models of non-stationary random processes in the Hilbert space. The goal of the research is to develop a mathematical model of nonstationary processes of cardiac activity based on a triangular model. This research was the basis for the development of a Matlab model that implements the proposed method for analyzing heart rate variability. Tasks are: to give a description of the variability heart rate as a non-stationary process in Hilbert space in terms of correlation functions; to research the possibility of constructing a correlation and spectral theory of a non-stationary process using triangular models; to synthesize the mathematical model of nonstationary process on the basis of correlation theory for solving mathematical processing and forecasting tasks on the basis of ECG data. Using the proposed mathematical method, we implemented the Matlab model of a heart signal generator, which allowed us to synthesize an ECG with different variability parameters in noisy conditions. Methods of mathematical statistics, simulation modeling, theory of random processes and control theory are used in this work. Results of this research are as follows: 1) It has been shown that the new approach to the description of the HRV as a random process in the application of the triangular model in the Hilbert space made it possible to obtain expressions for the correlation function. 2) The imitation simulation showed the sensitivity of the method within the 5% error rate under the conditions of different types of influence on HRV. The qualitative assessment of the possibilities of the proposed models to generate artificial ECG provided the possibility of visual analysis by the cardiologist of the identity of the interpretation of real ECG records. The identities of modeling results were checked on time samples of electrocardiographs of 7 patients from open PhysioNet cardiographic libraries on samples with the duration T = 10 s. 3) The standard low-frequency oscillations and "white noise" barrier are clearly differentiated on the applied correlation function by the distribution of spectral density power within the frequency range of 0,15-0,3 Hz. Conclusion. The simulation results confirmed the correctness of the theoretical conclusions about the possibility of using models based on the representation of non-stationary processes in a triangular Hilbert space.