Кафедра вищої математики

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Відповідальний за розділ: доцент кафедри Вищої математики Глухов Олександр Дмитрович. E-mail: glukhov@nau.edu.ua

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Now showing 1 - 20 of 196
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    An alternative solution to the first boundary value problem for a differential equation of hyperbolic type
    (National Aviation University, 2023-04) Klyus, Iryna; Oliynyk, Оleg; Клюс, Ірина Степанівна; Олійник, Олег Петрович
    The construction of an approximate solution of the first boundary value problem for a hyperbolic type of differential equation using trigonometric splines is described. The expression of the approximate solution in trigonometric splines is proposed as an alternative solution, the minimization of the discrepancy is carried out by the method of collocations.
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    Analysis of mathematical methods of implementation the comparative approach in real estate avaluation
    (National Transport University, 2022) Liashenko, Yana Grygorivna; Bondarenko, Liudmyla Petrivna; Petrenko, Nataliia Valeriivna; Ляшенко, Яна Григорівна; Бондаренко, Людмила Петрівна; Петренко, Наталія Валеріївна
    The effectiveness of modern mathematical methods of implementation the comparative approach in real estate evaluation is analyzed in the work. Within this approach the following mathematical methods of determining corrective amendments to the value of the valuation object were analyzed: expert method, method based on solving a system of linear equations, calculation method based on normalized distances in the space of price-forming factors, and correlation-regression method. The main computing formulas and the sequence of calculations for each of the researched methods are outlined. The main criteria for choosing one or another method are defined on the basis of their advantages and disadvantages and application restrictions. The results of a computational experiment investigating the degree of sensitivity of mathematical methods regarding ways of formalization (digitization) of the initial qualitative information in determining the value of real estate objects within a comparative approach are presented. It is represented that the method of determining corrective amendments based on the solution of a system of linear equations is the most sensitive to the choice of the method of digitization of the initial data, the method of calculation based on normalized distances in the space of price-forming factors is less sensitive, and the correlation-regression method is not sensitive at all.
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    Analytical links in the tasks of digital content compression
    (National Aviation University, 2020) Kravchenko, Viktoriia; Kolganova, Olena; Tereshchenko, Lidiiia; Shutko, Volodymyr; Shutko, Mykola; Yevhen, Vasiliu
    The article is devoted to the development of a digital image compression algorithm. The new algorithm is based on multiscale decomposition with a spline as a basis function. In the process of multiscale analysis, when constructing a spline, we should take into account analytical links. The application of this approach give an increase in the compression ratio with the same quality of compressed images.
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    Assessment of the Impact of the Air Transport Processes on Soil Contamination with Petroleum Products
    (National Aviation University, 2023-04-20) Cherniak, Larysa; Mikhyeyev, Oleksandr; Maniecki, Tomasz; Shtyka, Oleksandr; Petrusenko, Valentyna; Черняк, Лариса Миколаївна; Міхєєв, Олександр Миколайович; Манецький, Томаш; Штика, Олександр; Петрусенко, Валентина Павлівна
    The authors analyze the problem of soil pollution in the territory adjacent to airport Control of the level of soil pollution in the airport area was carried out taking into account meteorological conditions, the topography of the area, as well as the characteristics of the area, where located airline. Obtained results of experimental studies of the soil level pollution of the territory adjacent to the airport indicates the need to develop a system for monitoring the ecological condition of the soils of these territories using modern methods environmental monitoring. One of these methods can be the phytoremediation method of quality restoration soil characteristics.
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    Aviation safety management system: problem of balanced allocation of resources
    (Київ, 2016-09) Антонова, А.О.; Кравченко, В.
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    Comparative Analysis of Goodwin's Business Cycle Models
    (AIP Publishing, 2016) Antonova, A.O.; Todorov, M.D.
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    Consideration the rheological properties when investigating the heterogeneous behavior of a rock mass in time
    (National Transport University, 2023) Liashenko, Yana; Bondarenko, Liudmyla; Balashova, Yuliia; Ляшенко, Яна Григорівна; Бондаренко, Людмила Петрівна; Балашова, Юлія Борисівна
    The paper is devoted to the solution of nowadays relevant issue regarding the scientific substantiation of the most effective methods of mining rocks for various needs of the national economy, including for the construction of highways. The research was carried out on the basis of mathematical modeling methods, taking into account the rheological properties of rocks, heterogeneity of their structure, microdamage and behavior of the rock massif over time. As part of the work, geological material consisting of an isotropic viscoelastic matrix with stochastically placed inclusions in different directions was considered. The change in the stress-strain state of rocks with viscoelastic properties and containing randomly placed inclusions is determined. Provided that the size of the body is much greater than the size of the microinhomogeneities, the area containing the environment is considered infinite. The mathematical model is constructed on the basis of the fact that when homogeneous loads interact on a statistically homogeneous body, the random fields of stresses and strains that arise are also statistically homogeneous, and therefore, volume averaging can be performed as statistical averaging. The derivation of the calculation formulas is connected with the setting of an explicit form of density distribution of inclusions by direction. Based on the constructed mathematical model, microstructural stresses were investigated, effective parameters were calculated, and their dependence on the shape, orientation, and volume concentration of inclusions was determined. In addition, as a particular case, a fractured environment is considered. Taking into account such a significant heterogeneity of the geological rock and the presence of microdamages, the dependence of viscoelastic deformations on time and degree of damage was obtained. The obtained results make it possible to further evaluate the geomechanical situation, as well as to obtain the parameters of development systems for underground or open mining operations, which in turn will allow efficient mining of useful material.
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    Educational and methodical complex on Higher and Applied Mathematics (specialty 073 "Management")
    (National Avation University, 2021) Klyus, Iryna; Клюс, Ірина Степанівна
    The educational and methodological complex is a set of normative and educational and methodological materials in paper and electronic forms, necessary and sufficient for the effective implementation by students of the course training program of the educational discipline provided for in the curriculum of the training of students of the corresponding educational degree "Bachelor" in the specialty 073 "Management".This subject is considered as a theoretical and practical basis of knowledge and skills that form the expert’s profile in the field of management and administration.
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    Educational and methodical complex on Higher Mathematics
    (National Aviation University, 2021) Klyus, Iryna; Клюс, Ірина Степанівна
    Training course is the theoretical basis of knowledge and skills required to master the vast majority of disciplines of professional and practical training in the field of economics. The educational and methodological complex is a set of normative and educational and methodological materials in paper and electronic forms, necessary and sufficient for the effective implementation by students of the course training program of the educational discipline provided for in the curriculum of the training of students of the corresponding educational degree "Bachelor" in the specialty 275 " «Air Transport Technologies».
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    Educational and methodical complex on Higher Mathematics
    (National avation university, 2021) Klyus, Iryna; Клюс, Ірина Степанівна
    This training course is the theoretical basis of knowledge and skills required to master the vast majority of disciplines of professional and practical training in the field of economics.
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    Educational and methodical complex on Higher Mathematics
    (National Аvation University, 2021) Kravchenko, Viktoriia; Кравченко, Вікторія Валеріївна
    This subject is considered as a theoretical and practical basis of knowledge and skills that form the expert’s profile in the field of aviation technologies. The subject target is to teach students to master the mathematical apparatus that is sufficient to develop mathematical models related to the further practical activities of specialists.
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    Educational and methodical complex on Higher Mathematics
    (2021) Kravchenko, Viktoriia; Кравченко, Вікторія
    Сourse Training Program on «Higher Mathematics» is developed on the basis of the Educational Program on “Airplanes and Helicopters”, “Aircraft Equipment” Bachelor Curriculum and Extended Curriculum №CB-1-134-2/21, №ECB-1-134-2/21 for Speciality 134 «Aviation and Space Rocket Technology» and corresponding normative documents. The Course Training Program on «Higher Mathematics» is developed based on the "Methodical guidance for the subject course training program", approved by the order № 249/роз. of 29.04.2021 р., and correspondent normative documents.
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    Educational-methodical complex on "Mathematics for economists"
    (Національний авіаційний університет, 2024) Liashenko, Yana; Shevchenko, Iryna; Ляшенко, Яна Григорівна; Шевченко, Ірина Вікторівна
    This subject is considered as a theoretical and practical basis of knowledge and skills that form the expert’s profile in the field of economics. The subject target is to teach students to master the mathematical apparatus that is sufficient to develop mathematical models related to the further practical activities of specialists.
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    Formation of foreign language communicative competence of future aviation specialists in teaching higher mathematics
    (National Aviation University, 2023) Trofymenko, Viktoriya Igorivna; Yaschuk, Olesya Petryvna; Трофименко, Вікторія Ігорівна; Ящук, Олеся Петрівна
    It should be noted that in order to form the foreign language communicative competence of future aviation specialists in teaching higher mathematics, it is advisable to combine such components as: information and communication support of the course, further integration of mathematics with the cycle of professional disciplines, and increasing the effectiveness of students' independent work.
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    Geometry via spray on Frechet manifolds
    (Igor Sikorsky Kyiv Polytechnic Institute, 2023-10) Eftekharinasab, Kaveh; Ефтехарінасаб, Кавех Ахмадалі
    For Frechet manifolds by employing sprays we will construct connection, linear symmetric connections on tangent and second-order tangent bundles.
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    Higher mathematics. Number and functional series: A guide to independent work of higher education applicants of technical specialties
    (Національний авіаційний університет, 2022) Ляшенко, Яна Григорівна; Ластівка, Іван Олексійович
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    HIGHER MATHEMATICS. PROBABILITY THEORY. RANDOM EVENTS. Method Guide to self-study for students of majors: 192 «Building and civil engineering», 272 «Aviation Transport», 101 «Ecology».
    (Національний авіаційний університет, 2018) Klyus, Iryna Stepanivna; Lastivka, Ivan Oleksiiovych; Trofymenko, Victoriia Ihorivna; Клюс, Ірина Степанівна; Ластівка, Іван Олексійович; Трофименко, Вікторія Ігорівна
    Method guide contains tasks for students’ self-study on the academic subject «Higher Mathematics. Probability theory. Random events» and recommended literature. For students of majors: 192 «Building and civil engineering», 272 «Aviation transport», 101 «Ecology».
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    Higher mathematics. Theory of functions of complex variable: A guide to independent work of higher education applicants of technical specialties
    (National Aviation University, 2023) Liashenko, Yana; Lastivka, Ivan; Repeta, Victor; Ляшенко, Яна Григорівна; Ластівка, Іван Олексійович; Репета, Віктор Кузьмич
    The guide is compiled according to the syllabus of the "Higher Mathematics" subject. The guide includes examples of solutions of typical problems of the topic "Theory of functions of complex variable", questions and tasks for self-test and problems for self-assignments. For higher education applicants of technical specialties.
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    Investigation of estimation of the mixed second-order moment in bilinear unbiased estimates class.
    (National Aviation University, 2016-09) Liashenko, Yana Grugorivna; Tupko, Natalia Petrivna; Ляшенко, Яна Григорівна; Тупко, Наталія Петрівна
    The best estimate (with minimum variance) of the mixed second-order moment in a class of bilinear unbiased estimates is proposed. The application of these techniques allows for the statistical analysis of accumulated data with the aim of generalization of the information in formulas. One of the main tasks that arise is the definition of distribution law of random variables and corresponding numerical characteristics on experimental data.
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    Investigation of the flow in compressor cascades with active flow control in supercirculation mode
    (National Aviation University, 2018-10) Tereshchenko, Yuriy; Терещенко, Юрій Юрійович; Doroshenko, Katerіna; Дорошенко, Катерина Вікторівна; Lastivka, Ivan; Ластівка, Іван Олексійович; Tereshchenko, Yuriy; Терещенко, Юрій Матвійович
    The paper presents the results of numerical simulation of flow in compressor cascades with active flow control at different angles of attack. It is shown that the active control of flow past the blades affects the value of deviation angle of flow behind the blades. The paper analyzes the influence of the effect of supercirculation on the aerodynamic characteristics of compressor cascades with active control of the flow past the blades.