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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.


Akulenko L.D.,Russian Academy of Sciences | Leshchenko D.D.,Odessa State Academy of Civil Engineering and Architecture | Rachinskaya A.L.,Odessa I I Mechnikov National University
Journal of Computer and Systems Sciences International | Year: 2012

A minimum-time problem on deceleration of rotations of a free rigid body is studied. It is assumed that the body contains a spherical cavity filled with highly viscous fluid. The body is subjected to a retarding torque of viscous friction. It is assumed that the body is dynamically asymmetric. An optimal control law for the deceleration of rotations of the body is synthesized, and the corresponding time and phase trajectories are determined. © 2012 Pleiades Publishing, Ltd.


Bekker M.B.,University of Missouri - Kansas City | Bohner M.J.,Missouri University of Science and Technology | Herega A.N.,Odessa State Academy of Civil Engineering and Architecture | Voulov H.,University of Missouri - Kansas City
Journal of Physics A: Mathematical and Theoretical | Year: 2010

For a number q bigger than 1, we consider a q-difference version of a second-order singular differential operator which depends on a real parameter. We give three exact parameter intervals in which the operator is semibounded from above, not semibounded, and semibounded from below, respectively. We also provide two exact parameter sets in which the operator is symmetric and self-adjoint, respectively. Our model exhibits a more complex behavior than in the classical continuous case but reduces to it when q approaches 1. © 2010 IOP Publishing Ltd.


Akulenko L.D.,Russian Academy of Sciences | Zinkevich Y.S.,Odessa State Academy of Civil Engineering and Architecture | Leshchenko D.D.,Odessa State Academy of Civil Engineering and Architecture
Journal of Computer and Systems Sciences International | Year: 2011

A minimum-time problem on deceleration of rotation of a free body is studied. The body is subject to a retarding torque of viscous friction. The body is assumed to be dynamically asymmetric. An optimal control law for deceleration of rotation of the body is synthesized, and the corresponding time and phase trajectories are determined. © 2011 Pleiades Publishing, Ltd.


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.


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.


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.


Paruta V.A.,Odessa State Academy of Civil Engineering and Architecture
Magazine of Civil Engineering | Year: 2014

Properties of plaster mortar must be appointed taking into account fracture mechanics of system "aerated concrete masonry - plaster covering", understanding the processes at his hardening and exploitation. Consideration of internal stress in plaster covering and area of its contact with masonry, processes of origin, accumulation and development of cracks at the cyclic and power loadings, is a condition precedent in the construction of theory of fracture mechanics of such system. In the article processes occurring at hardening of plaster mortar, fracture mechanics of system "aerated concrete masonry - plaster covering" are considered. Based on the information about the processes occurring during application and hardening of the plaster covering and fracture mechanics data, compositions of plaster for aerated concrete masonry were projected. The solutions obtained have the required physico-mechanical properties and fracture toughness. Application of these solutions ensures a high durability of the plaster covering and the wall structure.


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.


Plotnikov A.V.,Odessa State Academy of Civil Engineering and Architecture | Komleva T.A.,Odessa State Academy of Civil Engineering and Architecture
Journal of Uncertain Systems | Year: 2012

In this article we prove the substantiation of the method of full averaging for the fuzzy differential equations with small parameter on the metric space (En;D). Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging. © 2012 World Academic Press, UK.

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