Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
50
9
2018
The Emergence and Formation of the Theory of Optimal Set Partitioning for Sets of the n Dimensional Euclidean Space. Theory and Application
1-24
Elena M.
Kiseleva
Oles Honchar Dnipro National University, Dnepr
The history of emergence and formation, the structure and main results of the theory of optimal set partitioning which was developed during the previous fifty years by the author and her students are presented. The examples of OSP application to the variety of essentially different theoretical optimization problems that can be interpreted mathematically as continuous optimal set partitioning problems are described. The real-world applications of the theory are illustrated by the example of solving the generalized locationâ€“allocation problem. The future directions of the optimal set partitioning theory are discussed.
Investigation of Uniform by Delay Stability of Nontrivial Equilibrium Point of One Population Model
25-37
Bedrik
Puzha
Brno University of Technology, Brno
Denis Ya.
Khusainov
Kiev National Taras Shevchenko University, Kiev
Veronika
Novotna
Brno University of Technology, Brno
Andrey V.
Shatyrko
Kiev National Taras Shevchenko University, Ukraine
Consideration was given to a mathematical model of population dynamics in the form of a system of two differential equations with a time delay argument and a quadratic right-hand side. The corresponding system without delay was preliminary studied and its phase portrait was constructed. The effect of delay on the qualitative behavior of solutions was considered. Using the Lyapunov direct method there was studied the stability of nonzero stationary equilibrium state. The results are formulated in the form of matrix algebraic inequalities.
On Some Classes of Spatial Configurations of Geometric Objects and their Formalization
38-50
Sergey V.
Yakovlev
N.E. Zhukovskiy National Aerospace University "Kharkov Aviation Institute", Kharkov
The problem of synthesis of spatial configurations of geometric objects is considered. There is introduced a configuration space whose generalized variables are metric and placement parameters of objects. Classification of spatial configuration taking into account relations on the set of geometric objects and their generalized variables is performed. Methods for formalizing constraints in packing, layout and covering problems are proposed.
Problem of Mathematical Safe of Two State Locks
51-59
Georgiy A.
Donets
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
Artem L.
Gurin
National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", Kiev
The problem of mathematical safe, given by a matrix composed by zeroes and units, is under consideration. Four potential cases are studied and the existing solutions are found for every of them.
Sequential Composition and Decomposition of Descriptor Control Systems
60-75
Larisa A.
Vlasenko
V. N. Karazin Kharkov National University, Ukraine
Anatoliy G.
Rutkas
Kharkov National University of Radio and Electronics, Kharkov
Valeriy V.
Semenets
Kharkov National University of Radio and Electronics, Kharkov
To analyze complex linear descriptor control systems described by relations unsolved with respect to the state derivative there is performed their decompositions into chains of simpler systems. In terms of invariant pairs of subspaces of characteristic and perturbed operator pencils of the system we establish the conditions to represent the system as a series connection of systems of smaller dimensions. The results are illustrated by examples of descriptor systems that describe transient modes in radiotechnical filters.
Investigation of Statistical and Dynamic Features of Currency Fluctuations of the Ukrainian Hryvnia to the US Dollar
76-86
Galina A.
Dolenko
Kiev National Taras Shevchenko University, Kiev
Darya A.
Manovytska
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Ekaterina A.
Viniarska
Kiev National Taras Shevchenko University, Kiev
Statistical and dynamical features of currency fluctuations of Ukrainian (UAH) to American dollar (USD) within 21 years (from 1996 to the end of 2017) are investigated. For this, the statistical characteristics of the exchange rate data sets were calculated. The distribution law also has been determined to which the statistical sampling of currency is subject to. Also, the statistical goodness of fit methods was used to identify the best distribution among candidates. The dynamical features of currency fluctuations have been assessed using modern methods of time series analysis.