Sums of exponential functions and their new fundamental properties

Details Sums of exponential functions and their new fundamental properties Sums of exponential functions and their new fundamental properties

2008-11-07

arxiv.org/abs/0811.1213v2

Shestopaloff Yu. K. "Sums of Exponential Functions and their New Fundamental Properties, with Applications to Natural Phenomen

Mathematics

Classical Analysis and ODEs

61 pages with 11 figures included into PDF file, added contact info as the readers advised

Scientific paper

This paper discovers and proves the fundamental properties of sums of exponential functions in the form of a theorem that is stated as follows: "A sum of exponential functions can have a maximum of two points of abscissa intersection, two extremums and two inflection points. Each subsequent derivative of this sum can be equal to zero no more than two times". The paper also introduces some new mathematical concepts. We developed them in order to prove the Theorem, however, these concepts have more general meaning. Given the fact that many natural phenomena are described adequately by exponential functions and their sums, this Theorem can provide many insights into the nature of studied phenomena and processes.

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