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Main publications

  1. Kogut, P.I., Manzo, R. and Nechay, I.V., Topological Aspects of Scalarization in Vector Optimization Problems. Australian Journal of Mathematical Analysis and Applications, 2010, Vol.7, Issue 2., pp. 25–49.

In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vector-valued mappings with a weakened property of lower semicontinuity. We also prove the existence of the so-called generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.

  1. Сясев, А.В., Приближенный аналитический метод расчета растущих тел с учетом фазового перехода. Д.: ДДУ, Вісник Дніпропетр. ун-ту. Механика. 2001. Т.1, вип. 5. С. 125-137.

Представлена постановка связанной задачи термовязкоупругости для растущего цилиндрического двухфазного тела и метод ее решения. Предложена классификация различных постановок задач механики растущих вязкоупругих тел, которая необходима для реализации предлагаемого метода решения связанной задачи. Дан анализ результатов, полученных при их решении. В качестве тестового примера рассмотрена связана задача для стержня.

  1. Сясев, А.В., Вязкоупругое деформирование кругового цилиндра при внутреннем наращивании. Л.: Львівський національний університет ім. Івана Франка: Вісник Львівського ун-ту. Серія фізико-математична. 2001. Вип. 59. С. 204-211.

Рассмотрена задача о НДС вязкоупругого полого цилиндра, который наращивается под действием внутреннего давления. Процесс непрерывного наращивания происходит по внутреннему радиусу так, что радиус и давление изменяются по заданному закону. Рассмотрен частный случай линейного закона ползучести, а также представлены многочисленные результаты в виде графиков зависимости напряжений и перемещений от времени для различных точек цилиндра.

  1. Vesselovskiy, V.B., Kochubey, A.A., Syasev, A.V., Mamuzych, I., Klim, V.Y. and Syasev, V.A., Approximate methods of the solution of non-linear problems thermomecanics with driving border. Acta Metallurgica Slovaca, 8, 2002, 3 (321 – 335 ).

The mathematical models are adduced and the methods of the solution one and multiphase problems of Stefan are offered. For construction of selfcontained problem solvings of Stefan the solutions of not characteristic Cauchy problem is used. The algorithm of the solution is shown to integrating a system of dace differential equations. The approximated analytical computational method of diphasic bodies is adduced, when the motion of a demarcation descends owing to thermoexchange by enviroment. The method allows with the help of a variational principle of Gibbs to determine tight – strained state in a body, temperature field and law of motion of a demarcation of phases. The model of calculation of thermoexchange agglamareted of iron-ore stuffs by the way of preforms of the spherical shape up to temperatures of optimum development of deoxidation processes by multicomponent gas is submitted. The model is constructed on the basis of multiphase problem of Stefan. The solution of a problem is obtained by a method of final differences.

  1. Kochubey, A., Syasev, A.V., Vesselovskiy, V.B., Mamuzych, I., Makarenkov, E.A. and Scherbina, I.V., Mathematical modelling of metallurgical processes with usage of the theory of increasing bodies. Acta Metallurgica Slovaca, 8, 2002, 3 (308 – 320).

The mathematical model of increasing visco-elastic hollow of the barrel with a fluid phase inside is offered. The material of the barrel in a fluid modular state represents perfect fluid, and in solid state visco-elastic body. The analysis of temperature effect and geometrical sizes the component on tight – strained state is conducted. The mathematical model is designed and the calculation of a thermal state of rolls of hot-rolled steel is conducted.

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Journal of Optimization, Differential Equations and their Applications

The "Journal of Optimization, Differential Equations and their Applications” (shortly JODEA) publishes original research articles related with the recent developments both in theory and applications of ordinary differential equations, partial differential equations, integral equations, functional differential equations, stochastic differential equations, optimal control theory, scalar and vector optimization, and other related topics. The journal will also accept papers from some related fields such as functional analysis, probability theory, stochastic analysis, inverse problems, numerical computation, mathematical finance, game theory, system theory, etc., provided that they have some intrinsic connections with control theory and differential equations. Papers employing differential equations as tools serving the cause of interdisciplinary areas such as physical, biological, environmental and health sciences, mechanics and engineering are encouraged. The goal is to provide a complete and reliable source of mathematical methods and results in these fields.

The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. To be published in this journal, an original paper must be correct, new, nontrivial and of interesting to readers.

JODEA is issued two times per year. It is edited by a group of international leading experts in mathematical control theory, differential equations and related fields. The journal is essential reading for scientists and researchers who wish to keep abreast of the latest developments in the field of differential equations and their applications. The journal is founded in 2018 by Oles Honchar Dnipro National Universuty for researchers and PhD-students who are working in the field of mathematics and applied mathematics. JODEA is printed according to the decision of the Academic council of the Oles Honchar Dnipro National University and is continuation of the journal "Bulletin of the Dnipropetrovsk University. Series: Modeling" (2009 – 2017, ISSN (Print): 2312-4547, ISSN (Online): 2415-7325) and a series of releases of the collection of scientific works "Differential equations and their applications" which were annually printed during the period from 1968 to 2008.

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