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Investigation of solutions of weakly perturbed boundary value problems for systems with impulse action 具有脉冲作用系统的弱摄动边值问题解的研究
Mathematics in Modern Technical University Pub Date : 2020-12-13 DOI: 10.20535/mmtu-2020.1-013
Z. P. Ordynska, R. Ovchar
{"title":"Investigation of solutions of weakly perturbed boundary value problems for systems with impulse action","authors":"Z. P. Ordynska, R. Ovchar","doi":"10.20535/mmtu-2020.1-013","DOIUrl":"https://doi.org/10.20535/mmtu-2020.1-013","url":null,"abstract":"The paper is devoted to the investigation of the existence and construction of solutions of weakly perturbed linear boundary value problems for systems with impulse action in the case when the generating boundary value problem with impulse action has no solutions for arbitrary right-hand sides.\u0000The relevance of this topic is due primarily to the importance of practical application of the theory of boundary value problems in various fields of science and technology - the theory of nonlinear oscillations, the theory of motion stability, control theory, a variety of geophysical problems. On the other hand, the question of the existence and construction of solutions of boundary value problems occupies one of the central and fundamentally important places in the qualitative theory of ordinary differential equations.","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128660313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The obvious — the incredible. Moebius tape 显而易见的——不可思议的。莫比乌斯带
Mathematics in Modern Technical University Pub Date : 2020-12-13 DOI: 10.20535/mmtu-2020.1-047
N. R. Konovalova
{"title":"The obvious — the incredible. Moebius tape","authors":"N. R. Konovalova","doi":"10.20535/mmtu-2020.1-047","DOIUrl":"https://doi.org/10.20535/mmtu-2020.1-047","url":null,"abstract":"The attraction to mathematics and mathematical abilities are manifested at a fairly early age.But these abilities must be developed systematically and skillfully. The path to mathematical sciencelies not through memorizing mathematical rules, but through conscious comprehension of mathemat-ical facts.If you ask any mathematician why he loves this science, he will most likely answer: “Because itis beautiful.” A little imagination and skills – and you can turn an ordinary tape into fascinatingworks of art, incredible inventions, even try to make unusual trips on it.The purpose of the article is to interest young lovers of mathematics. The article is based on aspeech to students of the Junior Academy of Sciences of Kyiv region.","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114054579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The story of one formula 一个公式的故事
Mathematics in Modern Technical University Pub Date : 2020-12-13 DOI: 10.20535/mmtu-2020.1-033
A. Kovtun, O. Demianenko
{"title":"The story of one formula","authors":"A. Kovtun, O. Demianenko","doi":"10.20535/mmtu-2020.1-033","DOIUrl":"https://doi.org/10.20535/mmtu-2020.1-033","url":null,"abstract":"This article aims to represent the diversity of approaches applicable to a certain mathematical problem – Stirling’s approximation was chosen here to achieve the mentioned goal. The first section of the work gives a sight of how the formula appeared, from the derivation of an idea to a publication of the strict results. Further, we provide readers with six different proofs of the approximation. Two of them use methods from calculus and mathematical analysis such that properties of logarithmic function and definite integral as well as representing functions as power series. The other two apply the Gamma function due to its connection with the notion of the factorial, namely Γ(n) = n!, n ∈ N. The last two have a probabilistic idea in their core: both of them combine Poisson distributed random variables with Central Limit Theorem to yield the desired formula. Some of the given proofs are not mathematically rigorous but rather give a sketch of a strict proof. Having all the results we assert that this story can be a good example of the variety of methods that can be used to solve one mathematical problem, even though all the listed proofs use only basic knowledge from several mathematical courses.\u0000Keywords: Stirling’s formula; factorial; Taylor series","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122769858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical models of the evolution of classical and solitary cylindrical waves 经典和孤立圆柱波演化的数学模型
Mathematics in Modern Technical University Pub Date : 2020-12-13 DOI: 10.20535/mmtu-2020.1-019
V. M. Yurchuk, Y. V. Simchuk
{"title":"Mathematical models of the evolution of classical and solitary cylindrical waves","authors":"V. M. Yurchuk, Y. V. Simchuk","doi":"10.20535/mmtu-2020.1-019","DOIUrl":"https://doi.org/10.20535/mmtu-2020.1-019","url":null,"abstract":"The evolution of nonlinear elastic cylindrical displacement waves for initial profiles in the form of a Hankel and Macdonald functions is analyzed theoretically and numerically. The difference between the two waves is that the MacDonald function has no hump, decreases monotonically and has a concave downward profile, and the Hankel function is a harmonic attenuating wave. \u0000The main novelty is that the evolution of cylindrical waves is studied for two different approaches to the solution of a nonlinear equation. Some significant differences of these waves are shown. First, the features of the Hankel wave, a harmonic wave (symmetrical profile), are briefly described. Then, theoretically and numerically, a single wave with an initial profile in the form of a MacDonald function is analyzed in more detail. Distortion of the initial profile due to the nonlinear interaction of the wave itself and the increase in the maximum amplitude during wave propagation is common to these profiles. Significant features of the McDonald wave are shown - an uncharacteristic initial profile (a profile without a classical hump) evolves in an uncharacteristic way - the profile becomes much steeper and remains convex downwards. \u0000Keywords: classical and solitary cylindrical waves; five-constant Murnaghan potential; approximate methods; Hankel and Macdonald initial wave profiles; evolution.","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123515832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some properties of the solutions of the linear differential-algebraic systems 线性微分代数系统解的若干性质
Mathematics in Modern Technical University Pub Date : 2020-12-13 DOI: 10.20535/mmtu-2020.1-005
M. Vira, P. Samusenko
{"title":"On some properties of the solutions of the linear differential-algebraic systems","authors":"M. Vira, P. Samusenko","doi":"10.20535/mmtu-2020.1-005","DOIUrl":"https://doi.org/10.20535/mmtu-2020.1-005","url":null,"abstract":"It has been compared the properties of the solutions of differential-algebraic systems and the solutions of systems of differential equations. The differences between the corresponding properties of these solutions are analyzed.","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129932782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Про тейлорівські коефіцієнти функцій із класу Гарді
Mathematics in Modern Technical University Pub Date : 2019-12-28 DOI: 10.20535/mmtu-2019.2-005
V. V. Bovsunovska, Mykola V. Haevskyi, P. V. Zaderei
{"title":"Про тейлорівські коефіцієнти функцій із класу Гарді","authors":"V. V. Bovsunovska, Mykola V. Haevskyi, P. V. Zaderei","doi":"10.20535/mmtu-2019.2-005","DOIUrl":"https://doi.org/10.20535/mmtu-2019.2-005","url":null,"abstract":"","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126031284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Знаходження скінченних сум, добутків та границь деяких числових послідовностей. Ч. 1. Застосування методів елементарної математики та основних понять теорії границь числових послідовностей
Mathematics in Modern Technical University Pub Date : 2019-12-28 DOI: 10.20535/mmtu-2019.2-061
Valerii O. Bilyi, Oleksandr G. Bilyi
{"title":"Знаходження скінченних сум, добутків та границь деяких числових послідовностей. Ч. 1. Застосування методів елементарної математики та основних понять теорії границь числових послідовностей","authors":"Valerii O. Bilyi, Oleksandr G. Bilyi","doi":"10.20535/mmtu-2019.2-061","DOIUrl":"https://doi.org/10.20535/mmtu-2019.2-061","url":null,"abstract":"","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114250232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Всеукраїнська олімпіада з математики для вступників до КПІ ім. Ігоря Сікорського: аналіз результатів і майбутні перспективи
Mathematics in Modern Technical University Pub Date : 2019-12-28 DOI: 10.20535/mmtu-2019.2-075
Olga O. Demianenko, Lesia A. Repeta, Igor V. Orlovskyi
{"title":"Всеукраїнська олімпіада з математики для вступників до КПІ ім. Ігоря Сікорського: аналіз результатів і майбутні перспективи","authors":"Olga O. Demianenko, Lesia A. Repeta, Igor V. Orlovskyi","doi":"10.20535/mmtu-2019.2-075","DOIUrl":"https://doi.org/10.20535/mmtu-2019.2-075","url":null,"abstract":"","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128521897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Асимптотичні властивості процесів, які виникають у задачах оптимального інвестування
Mathematics in Modern Technical University Pub Date : 2019-12-28 DOI: 10.20535/mmtu-2019.2-025
O. I. Klesov, O. Tymoshenko, Volodymyr V. Pavlenkov
{"title":"Асимптотичні властивості процесів, які виникають у задачах оптимального інвестування","authors":"O. I. Klesov, O. Tymoshenko, Volodymyr V. Pavlenkov","doi":"10.20535/mmtu-2019.2-025","DOIUrl":"https://doi.org/10.20535/mmtu-2019.2-025","url":null,"abstract":"","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121822369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Методика застосування чисельних методiв нульового порядку в задачах параметричної оптимiзацiї цифрових ПIД-регуляторiв дронiв
Mathematics in Modern Technical University Pub Date : 2019-12-28 DOI: 10.20535/mmtu-2019.2-051
Iryna V. Alekseeva, Oleksandr I. Lysenko
{"title":"Методика застосування чисельних методiв нульового порядку в задачах параметричної оптимiзацiї цифрових ПIД-регуляторiв дронiв","authors":"Iryna V. Alekseeva, Oleksandr I. Lysenko","doi":"10.20535/mmtu-2019.2-051","DOIUrl":"https://doi.org/10.20535/mmtu-2019.2-051","url":null,"abstract":"","PeriodicalId":134977,"journal":{"name":"Mathematics in Modern Technical University","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115278538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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