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Registration Number

0219U003434, 0116U001537 , R & D reports

Title

Topology and its applications in fractal geometry and mathematical economics.

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Head

Banakh Taras, Доктор фізико-математичних наук

Registration Date

14-02-2019

Organization

Ivan Franko National University of Lviv

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In the direction of generalized metric spaces, new classes of Maslyuchenko and Piotrovski spaces were introduced, the hereditary properties were investigated and on the base of this it was proved that every A0-space is the Maslyuchenko space and every strongly fragmented space is a Piotrovski space. It is proved that every Baire Piotrovski space contains a dense metrizable Baire subspace, which is the best result of this type in the world (earlier, similar results existed only for the classes of fragmented spaces or Stigall spaces that are contained in the class of Piotrovski spaces). Also, there are investigated properties of one more class of generalized metric spaces, which are called P0-spaces, and posess a countable having a Pytkeev net as well as their local analogs, namely the spaces with strong Pytkeev property. In the direction of topological algebra, (absolute) H-closedness of complete topologizable semilattices is proved, sufficient conditions of H- closedness of topological inverse A-polycyclic monoids PA are found. For arbitrary infinite cardinal A, we construct the weakest semigroup inverse topology on PA and construct an example of a topological inverse monoid S that contains the monoid PA as dense discrete subsemigroup. All pseudocompact semigroup topologies on the monoid PA are described. New cardinal invariants of groups that allowed to distinguish the symmetric groups of cardinals are defined, this is a solution to a problem of a German mathematician G.Mildenberger. A general construction of finite degree is provided, even for the simplest functors of (hyper) symmetric power this construction gives new interesting metrics that can find applications in mathematical economics (specifically, in transport problems). It is shown that this monads in the category of compacta generate certain structures of abstract convexity, on which some topological properties of functorial parts of monads depend. It is proved that the binarity property of any convexity implies that the functorial part of the corresponding monad transforms the class of openly-generated compacta into the class of absolute extensors for the class of zero-dimensional compacta, and the class of open maps to the class of 0-soft maps. A new concept of a fractal structure was introduced and criteria (topological, isometric, or equiholder) embedding of fractal structures in Euclidean, Hilbert or Banach spaces were obtained. It is proved that an arbitrary finite-dimensional metrizable compact set containing an uncountable open null-dimensional subset ishomeomorphic to a fractal in a Euclidean space. The existence of the points of the Nash equilibrium for Max-Plus convex compacta of arbitrary dimension is proved. The existence of Nash equilibrium points for games in idempotent measures with mixed strategies is proved. The existence of points of strategic equilibrium for games in pure strategies is proved, where the beliefs of players on the choice of strategies by players are represented by idempotent measures. An example of a game that shows the difference between these approaches is given. The existence of points of strategic equilibrium for games in pure strategies has been proved, where the beliefs of players on the choice of strategies by players are presented by the capacities, and the payoff functions are calculated with the help of the Sugeno integral. The asymmetry and nonlinearity in the structure of behavior of a number of macroeconomic indicators that characterize the processes of the socio-economic sphere are investigated. The analysis and econometric modeling of the dynamic connections between real gross domestic product and unemployment rate in Ukraine are carried out. An empirical study of regional unevenness and the impact of economic integration on regional labor markets is presented. Dynamic relations between productivity, employment, unemployment rate and real wages in the domestic labor market are investigated, and the reaction of labor market indicators to macroeconomic disturbances is analyzed. The study of the dynamics of unemployment in the countries of Eastern Europe in different phases of the economic cycle was carried out.

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Базилевич Лідія Євгенівна
Банах Тарас Онуфрійович
Бардила Сергій Олегович
Бокало Богдан Михайлович
Бридун Вікторія Любомирівна
Гринів Олена Степанівна
Гуран Ігор Йосипович
Гутік Олег Володимирович
Зарічний Михайло Михайлович
Оліскевич Маріанна Олександрівна
Радул Тарас Миколайович
Холявка Ярослав Михайлович

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2020-04-02