MATHEMATICAL BASIS OF EXTREMAL THEORY OF DIMENSIONS
Keywords:
differential equations, extremal theory of dimensions.DOI:
https://doi.org/10.17654/0974324322014Abstract
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.
Received: January 9, 2022
Accepted: February 16, 2022
References
E. R. Smol’yakov, Singular extremals in the analysis of dimension, Doklady Math. 78 (2008), 585-589.
E. R. Smol’yakov, Singular extremals in analytical mechanics, Doklady Math. 82 (2010), 991-994.
E. R. Smol’yakov, Theory searching exact equations and movement lows, Russian Encyclopedia, Moscow, 2012 (in Russian).
E. R. Smol’yakov, Differential equations defining travels into past and future, Advances in Differential Equations and Control Processes 25(1) (2021), 27-36.
L. A. Sena, Units of the Physical Values and their Dimensions, Nauka, Moscow, 1977 (in Russian).
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