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Main publications

  1. Menshikov, Yu., Identification of Rotor Unbalance as Inverse Problem of Measurement. Advances in Pure Mathematics, 2013, 3, 20-25. DOI: 10.4236/apm.2013.39A1004
Abstract

In this paper, the problem of identification of the characteristics of the rotor unbalance on two supports is investigated as the inverse problem of measurement. The vibration of rotor supports in two mutually perpendicular directions used as the initial information. The inverse problem is considered, taking into account the error of the mathematical description of rotor-bearings system. To obtain estimates of real unbalance characteristics, the hypothesis as to the exact solutions is applied. The method of Tikhonov regularization is used to obtain stable results. Test calculations are given to illustrate the proposed approach.


  1. Menshikov, Yu., Inverse problems for dynamic systems: classification and solution methods. Journal Advances in Pure Mathematics, 2013, v.3, n.4, p.390-393.
Abstract

The inverse problems for dynamic systems the motions of which are described by system of the ordinary differential equations are examined. The classification of such type of inverse problems is given. It was shown that inverse problems can be divided into two types: synthesis inverse problems and inverse problems of measurement (recognition). Each type of inverse problems requires separate approach to statements and solution methods. The regularization method for obtaining of stable solution of inverse problems was suggested. In some cases, instead of recognition inverse problems solution can be used the estimation of solution. Within the framework of this approach two practical inverse problems of measurement are considered.


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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.

JODEA is not a peer-reviewed journal without any donations and payment for publications.