MATHEMATICAL BASIS OF EXTREMAL THEORY OF DIMENSIONS

  • Smol’yakov EduardRimovich Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia
Article ID: 2551
Keywords: differential equations; extremal theory of dimensions

Abstract

The paper offers the full theoretical basis of “extremal theory of dimensions”. This simple theory, using only the notion “singular extremum” on the set of dimensional physical parameters, permits to find unknown laws of nature and very complex differential equations including many arbitrary additive terms. Note that almost all known equations of physics and their some generalizations already were found in the framework of this theory.

References

[1]E. R. Smol’yakov, Singular extremals in the analysis of dimension, Doklady Math. 78 (2008), 585-589.

[2]E. R. Smol’yakov, Singular extremals in analytical mechanics, Doklady Math. 82 (2010), 991-994.

[3]E. R. Smol’yakov, Theory searching exact equations and movement lows, Russian Encyclopedia, Moscow, 2012 (in Russian).

[4]E. R. Smol’yakov, Differential equations defining travels into past and future, Advances in Differential Equations and Control Processes 25(1) (2021), 27-36.

[5]L. A. Sena, Units of the Physical Values and their Dimensions, Nauka, Moscow, 1977 (in Russian).

Published
2025-01-10
How to Cite
EduardRimovich, S. (2025). MATHEMATICAL BASIS OF EXTREMAL THEORY OF DIMENSIONS. Advances in Differential Equations and Control Processes, 27. Retrieved from https://ojs.acad-pub.com/index.php/ADECP/article/view/2551
Section
Articles