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HARMONIC LAW DISTRIBUTION RAYLEIGH-RICE
Aleksandr A. Smirnov, Victoria V. Bondar, Olga D. Rozhenko,
Anna D. Darjania, Marina V. Mirzoyan,
Federal Autonomous Educational Institution of Higher Education North-Caucasian Federal University, Stavropol, Russia,
shursun@mail.ru
Abstract
The mathematical models of the propagation of waves or signals arises a problem of determination of the distribution amplitude in the endpoint. If there are no amplitude fluctuations in the models, the distribution in most problems is considered to be harmonic with an indefinite phase distributed uniformly. However, in addition to phase fluctuations as a result of various physical processes, additional amplitude fluctuations occur during wave propagation. In most problems, the distribution of amplitudes in a single beam is considered to be subject to the rice distribution or the Rayleigh distribution in the limiting case without a regular component. A new distribution law is obtained on the basis of averaging the law of distribution of amplitudes of the harmonic distribution over the distribution of amplitudes with the regular component of rice. The proposed method of obtaining a happy harmony of the laws of distribution. The reliability of the obtained result is confirmed by the fact that in particular cases the distribution is reduced to the known.
Keywords:distribution law, rice distribution, Rayleigh distribution, one-way normal distribution.
References
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Information about authors:
Aleksandr A. Smirnov, associate Professor, doctor of technical Sciences, Professor of the Department: Higher mathematics,
Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia
Author’s page on the website http://www.ncfu.ru/spisok-sotrudnikov/2529-smirnov-aleksandr-aleksandrovich.html
Victoria V. Bondar, associate Professor, candidate of physical and mathematical Sciences, head of the Department of Higher mathematics, Institute of mathematics and natural Sciences of the North Caucasus Federal University, Stavropol, Russia
Author’s page on the website http://www.ncfu.ru/spisok-sotrudnikov/2462-bondar-viktoriya-vitalevna.html
Olga D. Rozhenko, candidate of pedagogical Sciences, associate Professor of Higher mathematics, Institute of mathematics and natural Sciences of the North Caucasus Federal University, Stavropol, Russia
Author’s page on the website http://www.ncfu.ru/spisok-sotrudnikov/2472-rozhenko-olga-dmitrievna.html
Anna D. Darjania, candidate of pedagogical Sciences, associate Professor of mathematics, Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia
Author’s page on the website http://www.ncfu.ru/spisok-sotrudnikov/9102-darzhaniya-anna-dmitrievna.html
Marina V. Mirzoyan, candidate of pedagogical Sciences, associate Professor of mathematics, Institute of mathematics and natural Sciences North-Caucasus Federal University, Stavropol, Russia
Author’s page on the website http://www.ncfu.ru/spisok-sotrudnikov/2471-mirzoyan-marine-vaganovna.html