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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 On eigenvalues of banded matrices(Інститут математики НАН України, 2019) Akhiiezer, O. B.; Dunaievska, О. I.In the paper, asymptotics for eigenvalues of Hermitian, compact operators, generated by infinite, banded matrices is obtained in terms of the asymptotics of their matrix entries. Analogues for banded matrices of Gershgorin’s disks theory are discussed.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.Документ Machine learning methods application for solving the problem of biological data analysis(Національний технічний університет "Харківський політехнічний інститут", 2018) Akhiiezer, O. B.; Dunaievska, О. I.; Serdiuk, I. V.; Spivak, S. V.According to statistics, every fifth married couple is faced with the inability to conceive a child. Male germ cells are very vulnerable, and the growing number of cases of male infertility confirms that in today's world there are many factors that affect the activity of spermatozoa and their number. But the important thing is not so much their quantity, but quality. The spermogram is an objective method of laboratory diagnosis, which allows to accurately assess the man’s ability to fertilize by analyzing ejaculate for a number of key parameters. Only a spermogram can answer the question of a possible male infertility and the presence of urological diseases. When constructing spermograms, it is important to determine not only the number of good spermatozoa, but also their morphology and mobility. Therefore, research and improvement of some stages of spermogramm is the purpose of the study. This article addresses the problem of classification of spermatozoa in good and bad ones, taking into account their mobility and morphology, using methods of machine learning. In order to implement the first stage of machine learning (with a teacher) in the graphic editor, educational specimens (training sample) were created. The training was implemented by three methods: the method of support vector machine, the logistic regression and the method of K - the nearest neighbors. As a result of testing, the method K - the nearest neighbors is chosen. At the testing stage, a sample of 15 different spermatozoa was used in different variations of rotation around their axis. The test sample did not contain specimens from the training sample and was formed taking into account the morphological characteristics of the spermatozoa, but did not copy them from the training sample. At the final stage of study, the program's functioningwas tested on real data.