Invariants of the Hilbert Transform for 23-Hilbert Problem
Advances in Sciences and Humanities
Volume 1, Issue 1, August 2015, Pages: 1-12
Received: Jul. 20, 2015; Accepted: Jul. 31, 2015; Published: Aug. 1, 2015
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Author
Mazurkin Peter Matveevich, Department of environmental engineering, Volga State University of Technology, Yoshkar-Ola, Republic of Mari El, Russian Federation
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Abstract
Process of identification of steady laws in the form of asymmetric wavelet signals is stated. Thus the wave equations with variables amplitude and the period of fluctuation are designed from the generalized invariant and its fragments. This invariant according to Hilbert is reasonable as the biotechnical law generalizing almost all known laws of distribution. The essence, structure and parameters of the biotechnical law and its fragments is in detail shown. For identification statistical data of measurements in the form of tabular model are required. Then Hilbert's 23rd problem is solved as a problem of statistical (probabilistic) modeling. At the first stage the variation of functions is reduced to conscious selection of steady laws and designing on their basis of steady wave regularities adequate to studied natural processes. At the second stage there is a consecutive structural and parametrical identification of regularities on statistical selections by the sum asymmetric wavelets. The decision 23-oh Hilbert's problems by the one and only universal algebraic wave equation, in the general form on Descartes's hypothesis where half of amplitude and the period are displayed by the biotechnical law is given. Everyone wavelet this algebraic equation contains two fundamental physical constants – the number of time or Napier and the number of space or Archimedes
Keywords
23-oh Hilbert's Problems, Algebraic Wave, Identification, Asymmetric Wavelet Signals
To cite this article
Mazurkin Peter Matveevich, Invariants of the Hilbert Transform for 23-Hilbert Problem, Advances in Sciences and Humanities. Vol. 1, No. 1, 2015, pp. 1-12. doi: 10.11648/j.ash.20150101.11
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