American Journal of Numerical Analysis
ISSN (Print): 2372-2118 ISSN (Online): 2372-2126 Website: http://www.sciepub.com/journal/ajna Editor-in-chief: Emanuele Galligani
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American Journal of Numerical Analysis. 2014, 2(2), 29-34
DOI: 10.12691/ajna-2-2-1
Open AccessArticle

Wavelet Analysis of a Number of Prime Numbers

P.M. Mazurkin1,

1Doctor of Engineering Science, Professor, Academician of RANS, member of EANS, Volga Region State Technological University, Russia

Pub. Date: February 19, 2014

Cite this paper:
P.M. Mazurkin. Wavelet Analysis of a Number of Prime Numbers. American Journal of Numerical Analysis. 2014; 2(2):29-34. doi: 10.12691/ajna-2-2-1

Abstract

We adhere to the concepts of Descartes, the need to apply algebraic equations directly as a final decision. The concept of wavelet signal allows to abstract from an unknown number of primes of a physical quantity. Any number of primes can be decomposed into a finite set of asymmetric wavelets with variable amplitude and frequency. For example, taken a number of A000040. The first term of the total number of model А000040 according to the law of exponential growth is the contribution of the absolute error 97,53 %. The first member of the general model of a number of А000040 on the law of exponential growth is the contribution of the absolute error 97,53 %. The remaining 35 wavelets amount to a total of 2.47 %. But their influence on the number of primes very significant. It is proved that any type of fnite-dimensional number of primes can be decomposed into a fnite-dimensional set of asymmetric wavelets with variable amplitude and frequency of oscillatory perturbations.

Keywords:
prime numbers the family of wavelets fractal levels

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References:

[1]  Mazurkin P.M. The statistical model of the periodic system of chemical elements D.I. Mendeleev. Yoshkar-Ola: MarSTU, 2006, 152.
 
[2]  Astafieva N.M. Wavelet-analysis: fundamentals of theory and examples of the application // The successes of the physical sciences. 1996. Volume 166, № 11 (november), 1145-1170.
 
[3]  Don Zagier. The first 50 million prime numbers. URL:http://www.ega-math.narod.ru/Liv/Zagier.html.