Кафедра математики та інформатики
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Item About heteroclinic travelling waves in discrete sine-Gordon type equation(2017) Bak, S. M.We study the discrete sine-Gordon equation (DSG) that describes the dynamics of an in nite system of nonlinearly coupled nonlinear oscillators on two-dimensional lattice. It is obtained a result on the existence of heteroclinic travelling waves for DSG with nonlinear interaction on 2D- lattice,Item About travelling waves in Fermi–Pasta–Ulam system on 2D–lattice(2020) Bak, Sergiy MykolaiovychWe study the Fermi-Pasta-Ulam system that describes the dynamics of an in nite system of nonlinearly coupled particles on two dimensional lattice. We obtain, by means of the critical points method, a results on the existence of nonconstant periodic and solitary travelling waves.Item Cайт «Математичний аналіз і диференціальні рівняння вивчаю сам» в освітньому просторі студента вищого навчального закладу(Вінниця : ФОП Рогальська І. О., 2017) Ковтонюк, М. М.; Kovtoniuk, M. M.В даній роботі проведено аналіз роботи сайту викладача www.kovtonyuk.inf.ua «Математичний аналіз і диференціальні рівняння вивчаю сам» за останні 5 років; визначено основні шляхи його розвитку.Item Existence of heteroclinic traveling waves in a system of oscillators on a two-dimensional lattice(2016) Bak, S. M.; Бак, С. М.; Бак, С. Н.By using the critical points method and the concentration-compactness principle, the problem of existence of heteroclinic travelling waves for a system of linearly coupled nonlinear oscillators in a two-dimensional lattice is studied.Item Existence of solitary traveling waves in a system of nonlinearly coupled oscillators on the 2D lattice(2017) Bak, S. M.; Бак, С. М.; Бак, С. Н.We consider a system of differential equations that describes the dynamics of an infinite system of nonlinearly coupled nonlinear oscillators on the 2D lattice. By the method of critical points, we obtain a result on the existence of solitary traveling waves.Item Existence of solitary traveling waves in Fermi-Pasta-Ulam system on 2D–lattice(matematychni Studii, 2018) Бак, С. М.; Bak, S. M.; Ковтонюк, Г. М.; Kovtonyuk, G. M.The article deals with the Fermi–Pasta–Ulam system that describes an infinite system of particles on 2D–lattice. The main result concerns the existence of solitary traveling wave solutions. By means of critical point theory, we obtain sufficient conditions for the existence of such solutions.Item III International Scientific and Practical Internet Conference "Mathematics and Informatics in Higher Education: Challenges of Modernity", dedicated to the memory of Professors Pankov O. A. and Trokhymenko V. S. (Vinnytsia, May 20-21, 2021) [Electronic network scientific publication]: book of abstracts(2021) Ковтонюк, Мар'яна Михайлівна; Kovtonyuk, Mariana; Бак, Сергій Миколайович; Bak, SergiyThe book contains abstracts of III International Scientific and Practical Internet Conference "Mathematics and Informatics in Higher Education: Challenges of Modernity" (dedicated to the memory of Professors Pankov O. A. and Trokhymenko V. S.), which took place on May 20-21, 2021 on the basis of the Faculty of Mathematics, Physics and Computer Science of Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University. The abstracts in the book are grouped by sections, in accordance with the main directions of the conference: Section 1. Modern problems of mathematics; Section 2. Modern problems of computer science. Mathematical and computer modeling; Section 3. Creation of educational environment in mathematics and computer science in higher education. Monitoring of the quality of education: tools and technologies; Section 4. Modern computer technologies in teaching mathematics and computer science. Methods of teaching mathematics and computer science in secondary education. The publication is addressed to researchers, lecturers, teachers, graduate students, undergraduates, as well as everyone who is interested in modern problems of science and education.Item Implementation of Cycle-Gan model for image transformation into image with Anime style(2021) Tkachenko, Svitlana; Bak, SergiyWe review the principle of CycleGAN modeling and describe the application of CycleGAN for the problem of images transformation into images with anime style.Item Innovative aspects of using digital technologies for the modelling activities of the university(2020) Klochko, Oksana; Fedorets, Vasyl; Obukh, IrynaIn the article, on the basis of innovative directions and ideas of technologization, features of use of digital technologies for the modelling activities of the University. The leading aspect of the research is modelling and studying the World University Rankings. Using machine learning algorithms Linear Regression and Decision Forest Regression, regression models were built, a comparative analysis of the results of their implementation. The model built on the machine learning algorithm Linear Regression is the best by all the described criteria, the forecast built on this model will be more accurate. The results of the study can be used to predict the ranking of the university and identify ways to improve it.Item Iснування відокремлених біжучих хвиль для системи нелінійно зв’язаних осциляторiв на двовимiрнiй ґратцi(2017) Бак, С. М.; Бак, С. Н.; Bak, S. M.Розглядається система звичайних диференціальних рівнянь, що описує динаміку нескінченної системи нелінійно зв'язаних нелінійних осциляторів на двовимірній ґратцi. За допомогою методу критичних точок отриманий результат про існування відокремлених біжучих хвиль.Item Iснування гетероклінічних біжучих хвиль у системі осциляторiв на двовимiрнiй ґратцi(2014) Бак, С. М.; Бак, С. Н.; Bak, S. M.За допомогою методу критичних точок і принципу концентрованої компактності досліджено питання про існування гетероклінічних біжучих хвиль для системи лінійно зв'язаних нелінійних осциляторів на двовимірної ґратцi.Item Iснування перiодичних за часом розв’язкiв системи осциляторiв на двовимiрнiй ґратці(2012) Бак, С. М.; Бак, С. Н.; Bak, S. M.Розглядається система диференціальних рівнянь, що описує динаміку нескінченної системи лінійно зв'язаних нелінійних осциляторів на двовимірній ґратці. Отримано результат про існування періодичних за часом розв'язків. За допомогою теореми про гірський перевал отримані достатні умови існування таких розв'язків.Item ON EXISTENCE OF SOLITARY TRAVELING WAVES IN FERMI-PASTA-ULAM TYPE SYSTEMS ON 2D-LATTICE(2023) Bak, Sergiy; Kovtonyuk, GalynaWe consider the Fermi-Pasta-Ulam type systems with saturable nonlinearities that describes an infinite systems of particles on a two dimensional lattice. The main result concerns the existence of solitary traveling waves solutions with vanishing relative displacement profiles. By means of critical point theory, we obtain sufficient conditions for the existence of such solutions.Item On the dynamical equations of a system of linearly coupled nonlinear oscillators(Ukrainian Mathematical Journal, 2006) Бак, С. М.; Bak, S. N.; Панков, О. А.; Pankov, A. A.; Панков, А. А.; Розглядається система диференціальних рівнянь, яка описує динаміку нескінченного ланцюга лінійно зв’язаних нелінійних осциляторів. Одержано результат про існування і єдність глобального розв’язку задачі Коші; We consider a system of differential equations that describes the dynamics of an infinite chain of linearly coupled nonlinear oscillators. Some results concerning the existence and uniqueness of global solutions of the Cauchy problem are obtained; Рассматривается система дифференциальных уравнений, которая описывает динамику бесконечной цепочки линейно связанных нелинейных осцилляторов. Получен результат о существовании и единство глобального решении задачи КошиWe consider a system of differential equations that describes the dynamics of an infinite chain of linearly coupled nonlinear oscillators. Some results concerning the existence and uniqueness of global solutions of the Cauchy problem are obtainedItem On well-posedness of the Cauchy problem for system of oscillators in weighted sequence spaces(2021) Bak, Sergiy; Kovtonyuk, GalynaWe consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two dimensional integer-valued lattice. We obtain the results on existence of a unique global solutions of the Cauchy problem in a wide class of weighted sequence spaces.Item On well-posedness of the Cauchy problem for system of oscillators in weighted spaces(2021) Bak, Sergiy; Kovtonyuk, GalynaWe consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two dimensional integer-valued lattice. We prove results on well-posedness of the Cauchy problem in a wide class of weighted $l^2$-spaces.Item Peridoc traveling waves in chains of oscillators(Communications in Mathematical Analysis, 2007) Бак, С. М.; Бак, С. Н.; Bak, S. M.It is considered the system of differential equations that describes the dynamics of an infinite chain of linearly coupled nonlinear oscillators. Results on existence of the periodic travelling waves are obtained.Item The existence of heteroclinic traveling waves in the discrete sine-Gordon equation with nonlinear interaction on a 2D-lattice(2018) Bak, S. M.; Бак, С. М.; Бак, С. Н.The article deals with the discrete sine-Gordon equation that describes an infinite system of nonlinearly coupled nonlinear oscillators on a 2D-lattice with the external potential V (r) = K(1-cos r). The main result concerns the existence of heteroclinic travelling waves solutions. Sufficient conditions for the existence of these solutions are obtained by using the critical points method and concentration-compactness principle.Item Traveling waves in systems of oscillators on 2D-lattices(2011) Bak, S. N.; Бак, С. М.; Бак, С. Н.; Pankov, А. А.; Панков, О. А.; Панков, А. А.A system of differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a 2D-lattice is considered. The exponential estimate of the solution and some results on the existence of periodic and solitary traveling waves are obtained.Item Well-posedness of initial value problem for discrete nonlinear wave equations(2010) Бак, C.; Bak, S.; N’Guerekata, G.; Pankov, A.We consider the initial value problem for discrete nonlinear wave equations. Under natural assumptions, we prove results on global well-posedness in a wide class of weighted l2 spaces. Admissible spaces include spaces power and exponential decaying sequences.