Exponential and hyperbolic types of distribution in macrosystems: their combined symmetry and finite properties
Journal Title: Восточно-Европейский журнал передовых технологий - Year 2018, Vol 3, Issue 4
Abstract
<p>This paper proposes the extended entropy method that identifies certain new relations in the organization of macro systems and which sheds light on several existing theoretical issues. It is shown that the type of distribution within the macrosystem is determined by the ratio of the kinetic properties of its agents ‒ "carriers" and "resources". If the relaxation time is shorter for the "carriers", there forms the exponential type of distribution; if it is shorter for the "resources" ‒ there forms the extreme hyperbolic distribution with a heavy tail. Analytical expressions were derived for them and their spectra. A convenient technique to parametrically record them via modal characteristics was devised.</p><p>Author discovered the existence of the combined symmetry of these two types of distributions. They can be regarded as alternative statistical interpretations of a single state of the macrosystem.</p><p>Distributions of real macro systems possess finite properties; given the natural constraints, they form the right bounds. The proposed method makes it possible to determine their coordinates based on the extreme principle, considering the right bounds of finite distributions as a product of self-organization of macro systems. Strict ratios were constructed, taking into consideration the finite features of distributions. Parametrically, they depend on the specific volume of "resources", and the magnitude of a form-parameter ‒ ratio between modal and boundary coordinates.</p><p>The value of the obtained results is in that they shed light on a number of problematic issues in the statistical theory of macro systems, as well as include a set of convenient tools in order to analyze two types of distributions with finite properties.</p>
Authors and Affiliations
Nikolaj Delas
Keywords
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- EP ID EP527976
- DOI 10.15587/1729-4061.2018.134062
- Views 81
- Downloads 0
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