Кафедра "Вища математика"

Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/7491

Офіційний сайт кафедри http://web.kpi.kharkov.ua/vm

Напевно відомо, що в 1923 році в ХТІ вже була кафедра математики, а її першим керівником був Бржечка Володимир Фомич. Кафедра вищої математики є одним із найстаріших підрозділів нашого університету. Дисципліни вища математика та нарисна геометрія викладалися починаючи з 1885 року.

У джерел розробки методики викладання математики стояли найвидатніші вчені, академіки Олександр Михайлович Ляпунов, Володимир Андрійович Стеклов й інші. Колектив кафедри намагається на всіх етапах її становлення й розвитку зберігати традиції, закладені засновниками кафедри, продовжує наукову працю, розвиває закладені напрямки в сучасній математичній підготовці студентів університету. Щорічно навчаються математиці майже чотири тисячі студентів денного відділення.

Кафедра входить до складу Навчально-наукового інституту механічної інженерії і транспорту Національного технічного університету "Харківський політехнічний інститут .

У складі науково-педагогічного колективу кафедри працюють: доктор фізико-математичних наук, доктор педагогічних наук, 2 доктора технічних наук, 8 кандидатів наук; 4 співробітника мають звання професора, 8 – доцента.

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90-летие профессора А. А. Грунауэра
(НТУ "ХПИ", 2011) Марченко, Андрей Петрович; Григорьев, Александр Львович; Зарубина, Алла Александровна; Ткачук, Николай Анатольевич
Статья посвящена 90-летию выдающегося ученого профессора А. А. Грунауэра. Описаны некоторые вехи его биографии и направления деятельности.
About one class of linear transformations of non-stationary random sequences
(Національний технічний університет "Харківський політехнічний інститут", 2019) Cheremskaya, Nadezhda Valentinovna
About the possibility of the cluster analysis application for the comparison of time series
(ТОВ "Планета – Принт", 2019) Antonova, I. V.; Chikina, N. A.
Almost automorphic derivative of an almost automorphic function
(Харківський національний університет ім. В. Н. Каразіна, 2017) Dimitrova-Burlayenko, S. D.
In this article are obtained conditions when the derivative of a continuous almost automorphic (an asymptotically almost automorphic, an almost periodic, an asymptotically almost periodic) function remains a continuous almost automorphic (an asymptotically almost automorphic, an almost periodic, an asymptotically almost periodic) function, respectively.
Almost automorphic derivative of an almost automorphic function
(University of Messina, 2015) Dimitrova-Burlayenko, S. D.
Analysis of Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells of a Complex Shape
(Marcílio Alves, 2017) Awrejcewicz, Jan; Kurpa, Lidiya; Shmatko, T.
Geometrically nonlinear vibrations of functionally graded shallow shells of complex planform are studied. The paper deals with a power-law distribution of the volume fraction of ceramics and metal through the thickness. The analysis is performed with the use of the R-functions theory and variational Ritz method. Moreover, the Bubnov-Galerkin and the Runge-Kutta methods are employed. A novel approach of discretization of the equation of motion with respect to time is proposed. According to the developed approach, the eigenfunctions of the linear vibration problem and some auxiliary functions are appropriately matched to fit unknown functions of the input nonlinear problem. Application of the R-functions theory on every step has allowed the extension of the proposed approach to study shallow shells with an arbitrary shape and different kinds of boundary conditions. Numerical realization of the proposed method is performed only for one-mode approximation with respect to time. Simultaneously, the developed method is validated by investigating test problems for shallow shells with rectangular and elliptical planforms, and then applied to new kinds of dynamic problems for shallow shells having complex planforms.
Analysis of opportunities of analytical method of optimization in chemical technology
(Національний технічний університет "Харківський політехнічний інститут", 2020) Prishchenko, Olga Petrivna; Chernogor, Tetyana Timofiyivna
The article analyzes the possibilities of optimization methods in chemical technology. The optimization of the technological process of production of any product contains an important stage - the determination (finding) of a mathematical model or the equation of the relationship of the output quality indicator of the product (target function, optimization parameter) with the parameters of this product or technological process (input factors). The search for optimal conditions is one of the most common scientific and technical problems. The process of solving these problems is called the optimization process or simply optimization. An example of optimization is the search for the optimal composition of multicomponent mixtures or alloys, increasing the productivity or operating efficiency of existing plants, improving product quality, reducing production costs. To solve optimization problems, you need to choose the right method. Of the main optimization methods that are most widely used in chemical technology, this article considers the analytical method.
Application of elements of studying the function of one variable when solving chemical problems
(Національний технічний університет "Харківський політехнічний інститут", 2021) Prishchenko, Olga Petrivna; Chernogor, Tetyana Timofiyivna
In the article some problems are examined with chemical maintenance, for the decision of that the elements of research of function one variable are used. A course of higher mathematics is basis of physical and mathematical training of specialists-chemists of university profile. The primary purpose of teaching of educational discipline "Higher mathematics" is preparation of students to using of modern mathematical vehicle as an effective instrument for the decision of scientific and practical problems in area of chemical and contiguous disciplines. Mathematics for chemical engineers is primarily a useful tool for solving many chemical engineering problems and tasks. It is difficult to find a branch of mathematics that is not at all used to solve these problems at all stages of their analysis. As a result of study of higher mathematics a student must know the methods of mathematical analysis in application to one function and a few real variables. Many chemical phenomena are described through functional dependence. At the study of chemical processes, it is necessary to use research elements functions of one variable, the exposure of properties of function, characterizing her different internals, behaves to that. In practical classes in higher mathematics, when considering the topic 'Derivative and its applications', it is often necessary to solve problems of a general nature. But for students of chemical specialties, tasks that are directly related to their profession are of greater interest. Thus, considering tasks similar to those given in this article, we will increase the interest and motivation of future specialists to study this material.
Application of interval statistics methods for power station equipment diagnostics in conditions of initial data uncertainty
(Polska Akademia Nauk Oddzial w Lublinie, 2012) Efimov, Aleksander; Potanina, Tatiana
In article principles of automated diagnostics system construction of the power units equipment and planning of repairs are investigated. The model constructed on the basis of interval data statistics of diagnostic functions is presented.
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 Valentinovna
The 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.
Clustering of multivariate heterogeneous time series
(ТОВ "Планета – Прінт", 2020) Antonova, I. V.; Chikina, N. A.
Complex numbers and their application to representing curves and domains on the complex plane
(National Technical University "Kharkiv Polytechnic Institute", 2024) Dimitrova, S. D.; Girya, N. P.; Burlayenko, V. M.; Naboka, O. O.
The educational-methodological textbook focuses on an important topic in mathematical analysis – the calculus of complex functions with a single variable. This textbook extensively explores the fundamental theoretical concepts and offers solutions to standard problems. It incorporates exercises for study and a series of tasks for individual student work. Tailored for students and lecturers in higher technical educational institutions.
Conductivity of the coronary arterial trees for steady and wave blood flows
(Харьковский национальный университет имени В. Н. Каразина, 2016) Solovyova (Philippova), H. N.
Constructing Steklov-type cubature formulas for a finite element in the shape of a bipyramid
(PC Tесhnology сеntеr, 2021) Motailo, Anzhelika; Tuluchenko, Galina
This paper reports the construction of cubature formulas for a finite element in the form of a bipyramid, which have a second algebraic order of accuracy. The proposed formulas explicitly take into consideration the parameter of bipyramid deformation, which is important when using irregular grids. The cubature formulas were constructed by applying two schemes for the location of interpolation nodes along the polyhedron axes: symmetrical and asymmetrical. The intervals of change in the elongation (compression) parameter of a bipyramid semi-axis have been determined, within which interpolation nodes of the constructed formulas belong to the integration region, while the weight coefficients are positive, which warrants the stability of calculations based on these cubature formulas. If the deformation parameter of the bipyramid is equal to unity, then both cubature formulas hold for the octahedron and have a third algebraic order of accuracy. The resulting formulas make it possible to find elements of the local stiffness matrix on a finite element in the form of a bipyramid. When calculating with a finite number of digits, a rounding error occurs, which has the same order for each of the two cubature formulas. The intervals of change in the elongation (compression) parameter of the bipyramid semi-axis have been determined, which meet the requirements, which are employed in the ANSYS software package, for deviations in the volume of the bipyramid from the volume of the octahedron. Among the constructed cubature formulas for a bipyramid, the optimal formula in terms of the accuracy of calculations has been chosen, derived from applying a symmetrical scheme of the arrangement of nodes relative to the center of the bipyramid. This formula is invariant in relation to any affinity transformations of the local bipyramid coordinate system. The constructed cubature formulas could be included in libraries of methods for approximate integration used by those software suites that implement the finite element method.
Dependence of prognosis and filtration failure on different values of parameters for some classes of non-stationary random sequences
(НТУ "ХПІ", 2019) Cheremskaya, Nadezhda Valentinovna
The 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.
Developing algorithms of optimal forecasting and filtering for some classes of nonstationary random sequences
(НТУ "ХПІ", 2018) Cheremskaya, Nadezhda Valentinovna
The 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.
Development of the creative potential of the personality as a basis for the creative competence formation in the learning process at technical university
(Technická univerzita v Košiciach, 2018) Dimitrova-Burlayenko, S. D.
The concept of "person creative potential" has been analyzed in this article. Its main characteristics have been formulated. The peculiarities of creating the creative potential of a person as a factor in the formation of readiness of students of technical universities to reveal creative competence in professional activity have been investigated. It is summed up that the development of the creative potential of the individual is decisive for the formation of cognitive and personality-reflective components of the creative competence of students of technical universities.
Discrete mathematical model of hypersingular integral equation on a system of intervals
(НТУ "ХПІ", 2018) Polyanskaya, Tatyana Semenovna; Naboka, Olena Oleksiyivna
We consider a hypersingular integral equation on a system of intervals, which is reduced to a system of hypersingular integral equations on the standard interval (−1,1). The discretization of this system is carried out on the basis of the method of discrete singularities. The unique solvability of the discrete problem is proved and an estimate of the rate of convergence of the solution of this problem to the exact solution of the system of hypersingular integral equations is given.
Distance learning as a prerequisite for the development of students' creative competencies
(Technická univerzita v Košiciach, 2021) Dimitrova, Svitlana; Girya, Nataliya
Research and experience show that distance learning can be as effective for developing students' creative competencies as traditional face-to-face learning. The development of creative competencies of students requires the creation of a creative environment in the academic space of universities. The use of the electronic course significantly increases the interest of students, provides the teacher with more tools and opportunities to form a creative component, stimulates the student to cognitive and independent work. The variety of forms of work, innovative technologies that can be used in distance learning, provides more opportunities to expand and deepen knowledge, form the necessary skills and qualities like a creativity, that is, creates a concept for the development of new pedagogical technology in the organization of learning.
Finite-step method for determining equilibrium state of gyrotheodolite
(Національний технічний університет "Харківський політехнічний інститут", 2020) Tokmakova, Iryna Anatoliyivna
The problem of orientation of a solid by using a torsion suspended gyrotheodolite is considered. Such gyrotheodolites are widely used in modern technology. During their operation, the problem arises of identifying the equilibrium position. It can be solved in many ways. A method is proposed for identifying the equilibrium position of a gyrotheodolite, which has several advantages over other well-known classical methods (least squares method, Kalman filter, and others). A mathematical description of the gyrotheodolite rotor motion is provided, a mathematical model of the method is given, and further development of the research is indicated.