Вісники НТУ "ХПІ"
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/2494
З 1961 р. у ХПІ видається збірник наукових праць "Вісник Харківського політехнічного інституту".
Згідно до наказу ректора № 158-1 від 07.05.2001 року "Про упорядкування видання вісника НТУ "ХПІ", збірник був перейменований у Вісник Національного Технічного Університету "ХПІ".
Вісник Національного технічного університету "Харківський політехнічний інститут" включено до переліку спеціалізованих видань ВАК України і виходить по серіях, що відображають наукові напрямки діяльності вчених університету та потенційних здобувачів вчених ступенів та звань.
Зараз налічується 30 діючих тематичних редколегій. Вісник друкує статті як співробітників НТУ "ХПІ", так і статті авторів інших наукових закладів України та зарубіжжя, які представлені у даному розділі.
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Документ Examples of information technologies for reconstruction from the data of the spectrum of some classes of random functions(Національний технічний університет "Харківський політехнічний інститут", 2022) Prishchenko, Olga Petrivna; Cheremskaya, Nadezhda Valentinovna; Bukhkalo, Svetlana IvanovnaIt is known that a stationary random process is represented as a superposition of harmonic oscillations with real frequencies and uncorrelated amplitudes. In the study of nonstationary processes, it is natural to have increasing or declining oscillationсs. This raises the problem of constructing algorithms that would allow constructing broad classes of nonstationary processes from elementary nonstationary random processes. A natural generalization of the concept of the spectrum of a nonstationary random process is the transition from the real spectrum in the case of stationary to a complex or infinite multiple spectrum in the nonstationary case. There is also the problem of describing within the correlation theory of random processes in which the spectrum has no analogues in the case of stationary random processes, namely, the spectrum point is real, but it has infinite multiplicity for the operator image of the corresponding operator, and when the spectrum itself is complex. Reconstruction of the complex spectrum of a nonstationary random function is a very important problem in both theoretical and applied aspects. In the paper the procedure of reconstruction of random process, sequence, field from a spectrum for Gaussian random functions is developed. Compared to the stationary case, there are wider possibilities, for example, the construction of a nonstationary random process with a real spectrum, which has infinite multiplicity and which can be distributed over the entire finite segment of the real axis. The presence of such a spectrum leads, in contrast to the case of a stationary random process, to the appearance of new components in the spectral decomposition of random functions that correspond to the internal states of "strings", i. e. generated by solutions of systems of equations in partial derivatives of hyperbolic type. The paper deals with various cases of the spectrum of a non-self-adjoint operator A, namely, the case of a discrete spectrum and the case of a continuous spectrum, which is located on a finite segment of the real axis, which is the range of values of the real non-decreasing function a(x). The cases a(x) = 0, a(x) = const, a(x) = x and a(x) is a piecewise constant function are studied. The authors consider the recovery of nonstationary sequences for different cases of the spectrum of a non-self-adjoint operator A promising since spectral decompositions are a superposition of discrete or continuous internal states of oscillators with complex frequencies and uncorrelated amplitudes and therefore have deep physical meaning.Документ Innovative methods of teaching the discipline Higher mathematics to students studying chemical technology and engineering(Національний технічний університет "Харківський політехнічний інститут", 2022) Prishchenko, Olga Petrivna; Cheremskaya, Nadezhda Valentinovna; Chernogor, Tetyana Timofiyivna; Bukhkalo, Svetlana IvanovnaThe article discusses some innovative methods that can be used in practical classes in higher mathematics, teaching students of chemical specialties. The possibilities for the development of competencies in complex interuniversity projects are closely related to the issues of classifying all types of interrelationships of disciplines within the framework of courses according to curricula, as well as the choice of additional universal competencies. Mathematics for chemical process engineers is, first of all, a useful tool for solving many chemical and technological problems and tasks. The typical curriculum takes into account the modern needs of related and special disciplines in the mathematical education of students, and consists of four main sections: the foundations of algebra and analytical geometry, mathematical analysis, differential equations, probability theory and mathematical statistics. When writing the article, many years of experience in teaching students of chemical specialties by the department "Higher Mathematics" of the National Technical University "KhPI" were used. The purpose of the scientific research of teachers and students presented in the article is to increase the competitiveness of Ukrainian technical education in the world market by developing and implementing innovative models and methods. When writing this article, the authors pursued three goals. First, to give the general course of mathematics for students of chemical and related specialties an appropriate professional orientation; secondly, to form in students of the first years of study ideas about the mathematical apparatus, information technologies and the mathematical modeling of modern chemistry and, thirdly, to instill in students the primary skills of building mathematical models of the simplest physical and mathematical processes when studying a mathematics course.Документ Application of the correlation theory of inhomogeneous random fields to the study of the statistically inhomogeneous screen model(Національний технічний університет "Харківський політехнічний інститут", 2021) Cheremskaya, Nadezhda ValentinovnaThe article considers the problem of finding a field created by a system of fluctuating sources on the screen, which is characterized by a correlation function, where 1 2, AA K r r the correlation function is separable. This image corresponds to a random field on the screen, which is the sum of a separable field and a heterogeneous random field of the first rank, which significantly changes the correlation radius at a distance l. The model studied in this paper does not assume uncorrelated sources and coincidence of laws of intensity change and therefore corresponds to a system of sources with significantly different intensities and laws of their change in the direction of wave propagation in the transverse plane. The correlation function of the sources be not assumed to be separable and the field distribution on the screen is an inhomogeneous random field of the first rank or is the sum of a separable field and a statistically inhomogeneous field of the first rank. To find a solution in the approximation of a parabolic equation, a method of immersion in the corresponding Hilbert space is proposed, which allows one to quickly and efficiently find the statistical characteristics of the solution. As an example, the influence of statistical inhomogeneity on the intensity function of a luminous screen, which has the shape of a round disk, is considered. An off-screen correlation function is obtained, which contains information on the size and nature of inhomogeneities of emitting sources on a luminous screen. A numerical analysis of the representation for the correlation function is carried out in the case when the statistical heterogeneous of the environmen is generated by the presence of a continuous spectrum or a spectrum at zero. The article obtains approximate calculation formulas for the average temperature field and its dispersion, which take into account fluctuation processes in the calculation of thermal regimes of solar panels, which allow to make appropriate corrections in theoretical calculations.Документ Studying the behavior of rank (quasirank) and infinitesimal correlation functions or correlation differences in linear transformations of random functions(Національний технічний університет "Харківський політехнічний інститут", 2020) Cheremskaya, Nadezhda ValentinovnaThe first-order linear stochastic equation x (n +1) = ax (n) + bx (n), (х )nn=0=x0 determines the simplest kind of regression signal that is widely used in applications. The case where the right part is a non-stationary sequence has not actually been investigated. In the paper the properties of the solution of this equation are studied within the framework of the correlation theory in the case when x (n) belongs to a particular class of random nonstationary signals, in addition, the classification is carried out using the concepts of rank or quasirank of non-stationarity. The Hilbert approach to the correlation theory of random sequences utilized in the paper allows us to study the question of the asymptotic behavior of the correlation function and makes it possible to obtain a simple inhomogeneous representation of the correlation function in terms of the correlation difference.Документ Dependence of prognosis and filtration failure on different values of parameters for some classes of non-stationary random sequences(НТУ "ХПІ", 2019) Cheremskaya, Nadezhda ValentinovnaThe article continues the study of estimates of random functions at a future moment of time, linear with respect to the values of pre-histories of processes. The article considers the dependence of the mean square of the forecast error of a random sequence on the last value at different values of the parameters. For non-stationary random sequences, even with correlation functions of the simplest form, such studies haven’t been conducted. To obtain representations of correlation functions, a Hilbert approach is used to calculate correlation functions as scalar products in the corresponding Hilbert space. Investigations of the dependence of the mean square of the prediction error of a random sequence on the last value at various values of the parameters discussed in the article can be used to simulate filtration and prognosis processes in real systems in the case of non-stationary random signals.Документ Developing algorithms of optimal forecasting and filtering for some classes of nonstationary random sequences(НТУ "ХПІ", 2018) Cheremskaya, Nadezhda ValentinovnaThe problem of forecasting and filtering non-stationary random sequences is solved in the article. Optimal forecasting and filtering are performed using linear estimates and minimizing the mean squared error. For non-stationary random sequences, even with the correlation functions of the simplest form, such studies were not conducted. In this work, on the examples of non-stationary sequences, the problem of forecasting and filtering is solved explicitly. The correlation function image is obtained using the Hilbert approach, which allows one to calculate correlation functions as scalar products in a corresponding Hilbert space. The solution of the extrapolation problem with particular correlation function considered in the article can be used to simulate filtration and forecasting processes in real systems in the case of non-stationary random signals.