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Main publications

  1. Zelenskaya, Т.S. and Siasiev, А.V., The dynamic problem of the longitudinal wave propagation in the steel ropes for elastic medium with variable borders. Вісник Дніпропетровського університету. – 2014. – Т. 22, вип. 18(1). – С. 58-62.

Considered initial-boundary value problem of mathematical physics that describes the longitudinal fluctuations of the rope variable length with a weight at the lower end. Provides a comparison of solutions using a modified method of continuation and numerical integration.

  1. Makarenkov, E.A. and Siasiev, А.V., Temperature field of cylinder with heat-insulated butt ends during heat exchange convection on the generatrix. Вісник Дніпропетровського університету. – 2015. – Т. 23, вип. 19(1). – С. 58-62.

To consider different elements of constructions, which are used in mechanical engineering, the attention can be paid to the fact that components, in the form of a thick-walled hollow cylinder, which cross-section is a doubly connected area, are used in these elements. The high-temperature speed gas or liquid flow, passing through the inner cavity, creates uneven heating, defined both by conditions of the flow and feature of design. The research arising through this complex thermostressed state is important in the design of mechanical engineering things. Taking into account the fact that we often have to deal with short-term impact of high temperatures, it is important to study unsteady temperature fields to determine their greatest unevenness. The latter thing can give rise to the thermostressed state, leading to disturbance of the operating mode. The proposed paper deals with the task of spreading the heat in the circular cylinder with defined radius and height with the specified starting temperature. The bases of the cylinder are heat-insulated, and along the generatrix is forced heat exchange with the environment. A mathematical statement of the internal problem that satisfies the heterogeneous equation of thermal conduction and homogeneous mixed condition on the generatrix of the cylinder is given. The solution of the problem is carried out by factorization using finite integral transforms of the mixed problem of mathematical physics to the cylinder.

  1. Zelenskaya, Т.S. and Siasiev, А.V., Investigation of the accuracy of the approximate solution of the mixed problem for hyperbolic equations on metabolic processes in vertical vessels. Машинобудування: Збірник наукових праць. 2015. № 15. С. 71-75.

The aim of this work is to compare the dynamic performance of wave processes in longitudinal movement of the rope through the production and numerical calculations, and obtain the equation of state of the rope on the pulley winding and outside of the pulley. The problem of elastic displacements in vertical vessels, was reduced to a boundary value problem with variable structure for hyperbolic equations, and the boundary between the different structures is movable. Analytical solution and its numerical realization is obtained in quadratures in the form of longitudinal waves propagating in the rope. Analysis of the solution of the problem shows that the distribution of the contact stresses on the surface of the rope (at a constant distance from the region of localization of the external load) practically does not depend on the distribution of the normal load in the area of localization only if its width is less than the thickness of the rope wound on the pulley. A significant influence on the dynamic tension in the vertical ropes have longitudinal movement, reflected from the moving region.

  1. Zelenskaya, Т.S. and Siasiev, А.V., DYNAMICS OF ELASTIC DYSPLACEMENTS OF LONGITUDINAL OSCILLATIONS IN ROPES AND CORES WITH MOBILE BORDERS. Машинобудування: Збірник наукових праць. 2012. № 10. С. 74-84.

Initial boundary value problems are considered for ropes and cores that change length throughout some interval of operation of the mechanism. Character of reflections of longitudinal waves from the mobile end are investigated.

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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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