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Komleva T.A.,Odessa State Academy of Civil Engineering and Architecture
Journal of Advanced Research in Dynamical and Control Systems | Year: 2011

In this paper, we will prove a possibility of use of the scheme of a full average at research of the linear fuzzy differential equations with a small parameter, when the right-hand side is 2π-periodic. © 2011 Institute of Advanced Scientific Research. Source


Klymchuk S.,Auckland University of Technology | Plotnikov A.,Odessa I I Mechnikov National University | Plotnikov A.,Odessa State Academy of Civil Engineering and Architecture | Skripnik N.,Odessa I I Mechnikov National University
Physica D: Nonlinear Phenomena | Year: 2012

In this review, we will first look in detail at Plotnikov's results on the substantiation of full and partial schemes of averaging of differential inclusions of the standard form on finite and infinite intervals. Then we will consider the algorithms where it is not possible to find the average, but there is a possibility to find its estimation from below and from above. Such an approach is also used when the average can be found only approximately. This situation is common for differential inclusions with fast and slow variables. In the end, we will present the results on the substantiation of the full and partial averaging methods for impulsive differential inclusions on finite and infinite intervals. © 2011 Elsevier B.V. All rights reserved. Source


Zinkevich Y.S.,Odessa State Academy of Civil Engineering and Architecture
Mechanics of Solids | Year: 2016

We study the problem of quasi-optimal (with respect to the response time) deceleration of rotational motion of a free rigid body which experiences a small retarding torque generated by a linearly resisting medium. We assume that the undeformed body is dynamically symmetric and its mass is concentrated on the symmetry axis. A system of nonlinear differential equations describing the evolution of rotation of the rigid body is obtained and studied. © 2016, Allerton Press, Inc. Source


Herega A.N.,Odessa State Academy of Civil Engineering and Architecture
International Journal of Nanomechanics Science and Technology | Year: 2013

A model of the oscillatory component of interaction of inner boundaries is studied; and the features of generation of the composite structure in interim asymptotics are considered. A model of a multiscale net of inner boundaries was used to obtain analytical expressions for calculating the force fields of the Sierpinski pre-fractal and its modifications. © 2013 by Begell House, Inc. Source


Herega A.N.,Odessa State Academy of Civil Engineering and Architecture
International Journal of Nanomechanics Science and Technology | Year: 2013

A range of percolation models of cluster systems of composites is discussed. In the models the parameters of the clusters of a substance and inner boundaries were obtained by the Monte Carlo method, and the possibility of affecting the properties of composite materials at the early stages of structure formation was studied. The models of technological cracks and the features of evolution of the clusters of a substance with transforming elements were investigated. The continual percolation problem was solved analytically on the Sierpinski carpet with hybrid branching. A system of simulation of algorithms for construction and study of cluster structures in materials was proposed. © 2013 by Begell House, Inc. Source

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