Everywhere Differentiable Functions without Monotonicity Intervals and Transcendental Numbers
- Authors: Agadzhanov A.N.1
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Affiliations:
- Trapeznikov Institute of Control Sciences
- Issue: Vol 97, No 3 (2018)
- Pages: 219-222
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225498
- DOI: https://doi.org/10.1134/S1064562418030067
- ID: 225498
Cite item
Abstract
The class of everywhere differentiable functions without monotonicity intervals is considered in terms of number theory. A number-theoretic representation of the set of points of the unit interval is constructed using the classification of transcendental numbers proposed by K. Mahler, and a theorem on sufficient conditions for differentiable functions to belong to this class is stated. Results concerning the behavior of derivatives of functions from this class are presented. A mixed problem for the heat equation modeling heat transfer in a distributed system is considered. It is shown that the control function for this system can be everywhere differentiable but having no monotonicity intervals.
About the authors
A. N. Agadzhanov
Trapeznikov Institute of Control Sciences
Author for correspondence.
Email: ashot_ran@mail.ru
Russian Federation, Moscow, 117997