Наукові статті кафедри вищої математики

Permanent URI for this collection

http://er.nau.edu.ua/handle/NAU/48922

Browse

Now showing 1 - 20 of 78

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.
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.
Aviation safety management system: problem of balanced allocation of resources
(Київ, 2016-09) Антонова, А.О.; Кравченко, В.
Comparative Analysis of Goodwin's Business Cycle Models
(AIP Publishing, 2016) Antonova, A.O.; Todorov, M.D.
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.
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.
Lusternik-Schnirelmann Type Theorem for C1-Frechet Manifolds
(Informatics Publishing Limited, The Indian Mathematical Society, 2021) Еftekharinasab, Kaveh; Lastivka, Ivan
We prove a Lusternik-Schnirelmann type theorem for a C1-function φ : M → R, where M is a connected in nite dimensional Frechet manifold of class C1. To this end, in this context we prove the so-called Deformation Lemma and by using it we derive the result generalizing the Minimax Principle
Method for Improving the efficiency of online communication systems based on adaptive multi- scale transformation
(National Aviation University, 2020) Kravchenko, Viktoriia; Kolganova, Olena; Tereshchenko, Lidiia; Sitko, Alla
The article considers the issues of the development of multi-scale analysis taking into account a spline as the basic function. The algorithm of image data compression with the adaptive calculation of the detailing coefficients is proposed. The estimation of its advantages and prospects of use was conducted.
Mode-matching method applied to the sound reception problem using Helmholtz resonator
(Sumy State University, 2022) Naida, Serhiy Anatoliyovych; Найда, Сергій Анатолійович; Korzhyk, Oleksiy Volodymyrovych; Коржик, Олексій Володимирович; Lastivka, Ivan Oleksiyovych; Ластівка, Іван Олексійович; Pavlenko, Olga Vyacheslavivna; Павленко, Ольга Вячеславівна; Zheliaskova, Tetyana Mykolayivna; Желяскова, Тетяна Миколаївна
The study explores the problem of forming an acoustic field in the Helmholtz resonator cavity using the mode-matching method. Acoustic boundary value problems for the description of acoustic fields in resonator cavities under traditional boundary conditions and boundary conditions at the edge (and in its absence), which is characterized by the known acoustic properties, are set and solved. For certain dimensions of an air-filled resonator, the basic field characteristics in the resonator are calculated, analyzed and compared with experimental data. The influence on the results of field formation of the involved condition at the edge with acoustically rigid boundaries-surfaces is estimated. In view of the foregoing, the research aims to formulate and solve the wave problem of acoustic field formation in the cubic Helmholtz resonator taking into account classical boundary conditions, conjugation conditions, and conditions at angular points of structural elements formed by the mode-matching and applying the eponymous method.
Necessary condition for excitation the oscillations in Goodwin’s model of business cycle
(National Aviation University, 2014-09) Antonova, A. O.
We investigate the necessary condition for excitation of long-periodic Goodwin’s oscillations and short-periodic sawtooth oscillations in the Goodwin model of the business cycle with fixed delay in the induced investment and in the consumption.
Numerical study of flow in the stage of an axial compressor with different topology of computational grid
(National Technical University "Kharkiv Polytechnic Institute", 2017) Tereshchenko, Yuriy; Терещенко, Юрій Юрійович; Doroshenko, Ekaterina; Дорошенко, Екатерина Вікторівна; Lastivka, Ivan; Ластівка, Іван Олексійович; Tereshchenko, Yuriy; Терещенко, Юрій Матвійович
We conducted a series of calculations with the models of turbulent viscosity k–e, SST and three variants of three-dimensional unstructured computational grids. For each variant of the computational grid we calculated each of the two models of turbulent viscosity at axial velocity at input from 110 to 150 m/s. Comparison of results of numerical experiments with data of the physical experimental studies revealed that an error of the computational research is 0.3...8.6 %. Results of the study showed that at the first phase of calculation of the stage of an axial compressor one can recommend using the model of turbulent viscosity k–e and the coarse computational grid. To solve the problems on internal aerodynamics of compressors taking into account the flow in the near-border layer and aerodynamic trail, it is expedient to employ the model of turbulent viscosity SST and the fine adaptive grid.
On applcations of measure of noncompactness in Frechet spaces
(National Aviation University, 2019) Klyus, Iryna; Eftekharinasab, Kaveh; Клюс, Ірина Степанівна; Ефтехарінасаб, Кавех
In metric and topological vector spaces the notion of measure of noncompactness is used to associate numerical values to sets so that compact sets get zero measures and other ones obtain positive values that indicate how far they are different from compact sets. This concept was initiated by Kuratowski in the early 30s and has been defined and developed in many different ways. The indices of noncompactness can give us sufficient conditions for formulating various fixed point theorems in metric spaces. Another important application of these measurements is in the characterization of Fredholm operators in infinite-dimensional topological vector spaces. The object of this paper is to provide an appropriate criterion that establishes a connection between Lipschitz-Fredholm operators in the more general context of Fréchet spaces, the Hausdorff, and lower measures of noncompactness. Furthermore, by using an arbitrary measure of noncompactness in the sense of Banas and Goebel we obtain a fixed point theorem for Fréchet spaces.
Problems of transport logistics development in Ukraine under martial law
(National Aviation University, 2023-10) Shevchenko, Irуna; Klyus, Irynа; Шевченко, Ірина Вікторівна; Клюс, Ірина Степанівна
The study considered the problems of modern logistics business in Ukraine, drew parallels with the main trends that were formed in the world during the coronavirus period, and considered the main directions of logistics flows and ways of their transformation due to the general international situation. In the study, it was determined that the so-called strategy of localization of logistics business began to take shape in the world, focused on the clustering of factories, transport companies, and especially consumers mainly in one region in order to avoid the risks of disruption of produc tion and the impossibility of meeting the needs of consumers. The world is actively moving from the concept of "delivery on time" to "delivery on demand". This is another step towards system-wide resilience and flexibility. Perhaps in the future, a more radical shift from goods to services will ease the burden on supply chains
Raising gas-dynamic stability margin of axial and centrifugalcompressor stages by meaans of vaned diffuser boundary layer control
(Technika. Vilnius, 2011) Ластівка, Іван Олексійович
Generalised research results that consider the upgradability of axial and centrifugal gas turbine engine compressors by means of gas-dynamic boundary layer control on bladed disks are demonstrated. Active and passive methods are used. Comparative analysis of the results has been carried out. The analysis is purposed to determine the influence of the flow circulation around the aerofoils on the performance of compressor single-row bladed disks with smooth blades and rough blades and under the condition that vortex generators are installed. An increase in the efficiency of aviation gas-turbine engines and in their gas-dynamic stability margin support leads to the enhancement of the parameters and performance of compressors: increase in loading of aerodynamic bladed disks, improvement of their economical efficiency, improvement of margin of the continuous flow around the compressor grids, etc. Airflow in the compressor grid is characterised by the flow region in the flow core and also by the flow regions in the wall boundary layers on the grid blades where shock waves, vortices, air swirls, and flow separation phenomena take place. The principle objective of the work is to research the possibilities of influence on the parameters of the elements of compressors and overall performance of gas-turbine engines via the methods of active and passive flow regulation. Active flow regulation is realised either by rendering the auxiliary gas mass to the blades boundary layer, or by suction (withdrawal) of the boundary layer (its part) from the surfaces of blades. Passive flow around regulation is characterised by influence on the boundary layer by means of energy redistribution in the flow itself.
Research into aero acoustic characteristics of two-row impellers of the axial compressor
(Національний технічний університет «Харківський політехнічний інститут», 2018) Doroshenko, Ekaterina; Дорошенко, Катерина Вікторівна; Tereshchenko, Yuriy; Терещенко, Юрій Юрійович; Lastivka, Ivan; Ластівка, Іван Олексійович; Kudzinovs'ka, Inna; Кудзіновська, Інна Павлівна
We have conducted numerical simulation of current in the axial impellers with a single-row and a two-row geometrically equivalent blade crowns with a density of blade crowns over average radius of 1...2.5. The pressure characteristics of impellers obtained at q(λ)=0.45…0.8 show that using the two-row impellers can improve the pressure of a stage over the entire range of operation. Under the flow-around modes that correspond to the maximum pressure, the degree of pressure rise increases by 10.5 %. The research results showed that the two-row impellers demonstrate the higher level of losses compared with the level of losses in the equivalent single-row impellers. We have obtained results of research into aero acoustic characteristics of subsonic two-row impellers of the axial compressor. The research results showed that the use of two-row blade crowns in the impeller makes it possible to reduce the level of acoustic pressure in the range of operation q(λ)=0.45…0.8 by 0.5 dB to 3.2 dB at a density of blade crowns over average radius of 1...2.5. The replacement of a single-row blade crown in the impeller of a stage of the axial compressor with the equivalent two-row blade crown could ensure the enhancement of aerodynamic loading on the stage and reduce acoustic emission of the compressor.
The Dynamics of Two Linearly Coupled Goodwin Oscillators.
(Book of Abstract, 2017-06) Антонова, А.О.
The economic and mathematical analysis of migration of employable population as a factor of national modernization in crisis
(Alexandru Ioan Cuza University of Iasi, 2016-06) Андрощук, Л.
Аеродинамічний опір авіаційної силової установки з турбовентиляторною приставкою
(Національний університет "Запорізька політехніка", 2019) Терещенко, Юрій Юрійович; Tereshchenko, Yuriy; Терещенко, Юрій Матвійович; Tereshchenko, Yuriy; Ластівка, Іван Олексійович; Lastivka, Ivan
Ефективність пілотованих і безпілотних літальних апаратів істотно залежить від параметрів і характеристик силових установок. Ефективна тяга силової установки відрізняється від внутрішньої тяги ізольованого двигуна на величину втрат, зумовлених зовнішнім опором силової установки в польоті. Газотурбінний двигун (ГТД) з турбовентиляторною приставкою має ряд переваг у порівнянні з двоконтурними двигунами. По-перше, створення двигуна на основі універсального базового газогенератора дозволяє з найменшими економічними витратами реалізувати на практиці принцип модульності при створенні сімейства ГТД. По-друге, за рахунок усунення негативного впливу модуля вентилятора на потік перед компресором газогенераторного модуля поліпшуються тягово-економічні характеристики авіаційної силової установки з ГТД. Турбовентиляторна приставка виконується у вигляді двоярусного робочого колеса, внутрішня частина якого працює в турбінному режимі, зовнішня частина виконує функції вентилятора. Потужність, яку розвиває внутрішній турбінний контур турбовентиляторної приставки, передається в зовнішній вентиляторний контур турбовентиляторної приставки. Ефективна сила тяги авіаційної силової установки з турбовентиляторною приставкою повинна враховувати особливості аеродинамічних характеристик ступінчастої мотогондоли газогенераторного модуля і модуля турбовентиляторної приставки. Визначення ефективної тяги розглядається при наступних припущеннях: силова установка обтікається зовнішнім потоком повітря при нульовому куті атаки; зовнішній потік усталений, рівномірний; мотогондола газогенератора складається з головної частини (обичайки повітрозабірника), центральної циліндричної і кормової частин; мотогондола турбовентиляторної приставки складається з головної частини (обичайки), центральної циліндричної і кормової частин. В роботі запропоновано методику розрахунку ефективної сили тяги авіаційної силової установки з турбовентиляторною приставкою з урахуванням особливостей аеродинамічних характеристик ступінчастої мотогондоли авіаційної силової установки для одноконтурного і двоконтурного газогенераторів
Аппроксимация экспериментальных зависимостей усовершенствованным нетрадиционным методом повышенной точности с использованием программно-компьютерных средств моделирования
(ХАИ, 2005) Давидов, Олександр Сергійович; Ходак, Микола Олексійович; Вишневський, Олег Анатолійович
Рассматриваются вопросы процесса обработки экспериментальных данных по зависимостям абразивного износа поверхностей конструкционных материалов вертолётных авиационных газотурбинных двигателей (ГТД) и их покрытии при нежестко закрепленных абразивных частичках и предлагается усовершенствованный нетрадиционный метод их аппроксимации повышенной точности с использованием современных программно-компьютерных средств его моделирования
Варiацiйне виведення диференцiальних рiвнянь коливань п’єзокерамiчної оболонки при меридiональнiй поляризацiї
(Прикарпатський національний університет імені Василя Стефаника, 2014) Ластівка, Іван Олексійович; Lastivka, Ivan
Запропоновано побудову одного з варiантiв уточненої теорiї п’єзокерамiчної оболонки при її меридiональнiй поляризацiї, отримано систему диференцiальних рiвнянь коливань оболон- ки та граничнi умови з використанням варiацiйного принципу Рейсснера.

Browse

Browsing Наукові статті кафедри вищої математики by Title

Results Per Page

Sort Options