The invariants of the Hilbert transform data wavelet analysis
2016
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 e of time or Napier and the number π of space or Archimedes.Examples of modeling, identification of the amount of asymmetric wavelet signal behavior of natural objects: the pulse of the electrocardiogram of a healthy person; natural drying samples meadow grass; mutual influence of forest cover and tilled territory; Crisis dynamics of the ruble and default 1998 y.; volume of patenting and forecast innovations in Russia until 2020 y.; dynamics of forest fires in the national park for the 1982-2011 y.; hour increments pulses alpha decay 239 Pu sample at the maximum of the solar eclipse; amplitude of gravitational waves from the orbital period of 10 pulsars in the model splashing Universe.