S.A. Horkov
IS ABOUT THE EXPONENT, THE EXPONENTIAL FUNCTION AND THE HYPERBOLA IN CENOLOGY
Annotation. It is shown that in the cenosis model the exponential function describing the distribution of the number of elements by its types (ranks) is transformed, in it the argument (exponent) is replaced by the logarithm of the argument and a power function is obtained. It is shown that in the cenosis model in the form of a hierarchical tree the exponential function (exponent) characterizes the distribution of the number of elements or the distribution of their size by species (ranks), and the power function (hyperbola) characterizes the distribution of distance (and time) between the levels of tree branching. It is established that the coefficient of the argument of the exponent of the exponential function and the exponent of the exponential function expressed using the logarithm of the number of elements in the fork node of the hierarchical tree. It is shown that in the power function the value of this index and its sign characterize the speed and direction of branching of the hierarchical tree, respectively.
Key words: cenosis model, self-similar structure, hierarchical tree.
For citation: Horkov S.A. [Is about the exponent, the exponential function and the hyperbola in zenology]. Upravlenie texnosferoj, 2019, vol. 2, issue 1. (In Russ) Available at: f-ing.udsu.ru/technosphere
REFERENCES
- Kudrin B. I. Matematika tsenozov: vidovoye, rangovidovoye, rangovoye po parametru giperbolicheskiye N-raspredeleniya i zakony Lotki, TSipfa, Pareto, Mandel’brota [The Mathematics of cenoses: species, rangewide, ranked according to the parameter of the hyperbolic N-distribution and the laws of the Trays, texts, Pareto, Mandelbrot]. Filosofskiye osnovaniya tekhnetiki. TSenologicheskiye issledovaniya. issue 19, Moscow: The center for system studies, 2002, pp. 357 – 412. (In Russ)
- ZHilin B.V. Entropiynyy kriteriy na ispol’zovaniye konechnogo resursa v granitsakh tsenoza [The entropy criterion for the use of finite resource within the limits of cenosis] Filosofskiye osnovaniya tekhnetiki. TSenologicheskiye issledovaniya, issue 19, Moscow: The center for system studies, 2002, pp. 286 – 290. (In Russ)
- ZHilin B.V. Tekhnotsenologicheskiy podkhod B.I. Kudrina i ego razvitiye [The technocenological approach of B. I. Kudrin and its development] TSenologicheskoye videniye soobshchestv material’nykh i ideal’nykh real’nostey: fundamental’nost’ teorii i vseobshchnost’ praktiki. TSenologicheskiye issledovaniya, issue 53, Moscow: Tekhnetika, 2014, pp. 389 – 404. (In Russ)
- SHreder M. Fraktaly, khaos, stepennyye zakony. Miniatyury iz beskonechnogo raya. [Fractals, chaos, power laws. Miniatures from the infinite Paradise]. Izhevsk: NITS «Regular and chaotic dynamics», 528 p. (In Russ)
- KHor’kov S.A. CHislovaya model’ elektropotrebleniya mnogonomenklaturnogo tsekha promyshlennogo predpriyatiya [Numerical model of power consumption of diversified shop of the industrial enterprise]. Promyshlennaya energetika. 2018, no. 5, pp.44 – 51. (In Russ)
- KHor’kov S.A. The problem of element-by-element calculation of power consumption of diversified plant of industrial enterprise, models and methods for its solution, (In Russ., unpublished).
About the Authors
Horkov Sergey Alekseevich
Department of Heat Power Engineering,
Udmurt State University,
Oil and Gas Institute of. M.S. Gutseriev.
426034, Russia, Izhevsk, University str. 1/7,
E-mail: Адрес электронной почты защищен от спам-ботов. Для просмотра адреса в вашем браузере должен быть включен Javascript.
