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 239Pu sample at the maximum of the solar eclipse; amplitude of gravitational waves from the orbital period of 10 pulsars in the model splashing Universe.
| Published in | American Journal of Data Mining and Knowledge Discovery (Volume 1, Issue 1) |
| DOI | 10.11648/j.ajdmkd.20160101.14 |
| Page(s) | 29-46 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
23-th Hilbert Problem, Algebraic Wave, Identification, Asymmetric Wavelet Signals, Generalized Model, Examples, Patterns
| [1] | Brummelen, G. V., Kinyon, M. Mathematics and the Historian’s Craft. The Kenneth O. May Lectures. 2005. Springer Science, Business Media, Inc. Library of Congress Control Number: 2005923503. bok%3A978-0-387-28272-5.pdf. |
| [2] | Corry, L. Archive for History of Exact Sciences. Chapter: David Hilbert and the Axiomatization of Physics (1894-1905). Springer-Verlag, 1997. Р. 83-198. DOI 10.1007/BF00375141. |
| [3] | Corry, L. Modern Algebra and the Rise of the Mathematical Structures. Chapter 3. David Hilbert: Algebra and Axiomatics. Birkhäuser Basel, 2004. Р. 137-182. DOI 10.1007/978-3-0348-7917-0_4. |
| [4] | Invariant theory. Algebraic number fields. Axiomatic. Integral equations. Physics. URL: http://www.ega-math.narod.ru/Reid/Weyl.htm # ch1. |
| [5] | Progress in Mathematics. Volume 280. Series Editors H. Bass, J. Oesterle, A. Weinstein // Liaison, Schottky problem and Invariant Theory. Remembering Federico Gaeta. Maria Emilia Alonso, Enrique Arrondo, Raquel Mallavibarrena, Ignacio Sols, Editors. Birkhauser. 2010. Springer Basel AG. bok%3A978-3-0346-0201-3.pdf. |
| [6] | Rowe, D. E. Hilberrs Early Career: Encounters with Allies and Rivals. THE MATHEMATICAL INTELLIGENCER_9, 2005. Spnnger Science+Business Media. Inc. art%3A10.1007%2FBF02984817.pdfHilberrs. |
| [7] | Mazurkin, P. M. Invariants of the Hilbert Transform for 23-Hilbert Problem, Advances in Sciences and Humanities. Vol. 1, No. 1, 2015. P. 1-12. doi: 10.11648/j.ash.20150101.11. |
| [8] | Mazurkin P. M. Riemann’s Hypothesis and Critical Line of Prime Numbers, Advances in Sciences and Humanities. Vol. 1, No. 1, 2015, P. 13-29. doi: 10.11648/j.ash.20150101.12. |
| [9] | Mazurkin P. M. Wavelet Analysis Statistical Data. Advances in Sciences and Humanities. Vol. 1, No. 2, 2015, pp. 30-44. doi: 10.11648/j.ash.20150102.11. |
| [10] | Mazurkin P. M. Method of Identification of Wave Regularities According to Statistical Data (Of Dynamics of a Rate of Inflation of US Dollar). Advances in Sciences and Humanitie. Vol. 1, No. 2, 2015, P. 45-51. doi: 10.11648/j.ash.20150102.12. |
| [11] | Mazurkin, P. M. Wavelet analysis of hour increments of alpha activity 239Pu at a maximum of a solar eclipse // Science and the world: international scientific magazine. 2014. No. 2 (6). Volume 1. P. 46-55. |
| [12] | Mazurkin, P. M. Wavelet analysis of hour increments of alpha activity 239Pu after a solar eclipse // Science and the world: international scientific magazine. 2014. No. 3 (7). Volume 1. Page 31-40. |
| [13] | Mazurkin, P. M. Wavelet analysis of crisis dynamics of ruble exchange rate // Interdisciplinary researches in the field of mathematical modeling and informatics. Materials of the 3rd scientific and practical Internet conference. Ulyanovsk: SIMJET, 2014. Page 260-268. |
| [14] | Mazurkin, P. M. Asymmetric Wavelet Signal of Gravitational Waves, Applied Mathematics and Physics, vol. 2, No. 4 (2014). P. 128-134. doi: 10.12691/amp-2-4-2. |
| [15] | Mazurkin, P. M. Wavelet Analysis of a Number of Prime Numbers, American Journal of Numerical Analysis, vol. 2, No. 2 (2014). P. 29-34. doi: 10.12691/ajna-2-2-1. |
| [16] | Маzurkin P. М., Тishin D. V. Wave dynamics of tree-ring width jf Oak, Integrated Journal of British. Volume 2. 2015. Issue 1. JAN-FEB. Р. 55-67. IJBRITISH-223-PA.pdf. |
APA Style
P. M. Mazurkin. (2017). The Invariants of the Hilbert Transformation for Wavelet Analysis of Tabular Data. American Journal of Data Mining and Knowledge Discovery, 1(1), 29-46. https://doi.org/10.11648/j.ajdmkd.20160101.14
ACS Style
P. M. Mazurkin. The Invariants of the Hilbert Transformation for Wavelet Analysis of Tabular Data. Am. J. Data Min. Knowl. Discov. 2017, 1(1), 29-46. doi: 10.11648/j.ajdmkd.20160101.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajdmkd.20160101.14,
author = {P. M. Mazurkin},
title = {The Invariants of the Hilbert Transformation for Wavelet Analysis of Tabular Data},
journal = {American Journal of Data Mining and Knowledge Discovery},
volume = {1},
number = {1},
pages = {29-46},
doi = {10.11648/j.ajdmkd.20160101.14},
url = {https://doi.org/10.11648/j.ajdmkd.20160101.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajdmkd.20160101.14},
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 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 239Pu sample at the maximum of the solar eclipse; amplitude of gravitational waves from the orbital period of 10 pulsars in the model splashing Universe.},
year = {2017}
}
TY - JOUR T1 - The Invariants of the Hilbert Transformation for Wavelet Analysis of Tabular Data AU - P. M. Mazurkin Y1 - 2017/01/13 PY - 2017 N1 - https://doi.org/10.11648/j.ajdmkd.20160101.14 DO - 10.11648/j.ajdmkd.20160101.14 T2 - American Journal of Data Mining and Knowledge Discovery JF - American Journal of Data Mining and Knowledge Discovery JO - American Journal of Data Mining and Knowledge Discovery SP - 29 EP - 46 PB - Science Publishing Group SN - 2578-7837 UR - https://doi.org/10.11648/j.ajdmkd.20160101.14 AB - 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 239Pu sample at the maximum of the solar eclipse; amplitude of gravitational waves from the orbital period of 10 pulsars in the model splashing Universe. VL - 1 IS - 1 ER -
Information
Email: