RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Program Systems: Theory and Applications:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Program Systems: Theory and Applications, 2018, Volume 9, Issue 4, Pages 253–264 (Mi ps330)  

Optimization Methods and Control Theory

Two-side bound of a root of an equation containing complete elliptic integrals

A. Yu. Popov, Yu. L. Sachkov

Ailamazyan Program Systems Institute of Russian Academy of Sciences

Abstract: We prove uniqueness of root of an equation arising in a problem of geometric control theory. The problem consists of description of singularity of the sub-Riemannian sphere on the Engel group near abnormal length minimizer.
During the proof, several new inequalities for complete elliptic integrals were obtained. For example, we proved that the function $K(k) E(k)$ is increasing at the segment $[0, 1)$; this fact was not noticed before in literature.
The method of investigation developed and the results obtained can be useful both for the study of elliptic integrals and for solving problems were such integrals arise (e.g. in problems of sub-Riemannian geometry). (In Russian).

Key words and phrases: asymptotics, complete elliptic integral, sub-Riemannian geometry.

Funding Agency Grant Number
Russian Science Foundation 17-11-01387


DOI: https://doi.org/10.25209/2079-3316-2018-9-4-253-264

Full text: PDF file (1475 kB)
References: PDF file   HTML file

UDC: 517.977
Received: 26.10.2018
02.12.2018
Accepted: 05.12.2018

Citation: A. Yu. Popov, Yu. L. Sachkov, “Two-side bound of a root of an equation containing complete elliptic integrals”, Program Systems: Theory and Applications, 9:4 (2018), 253–264

Citation in format AMSBIB
\Bibitem{PopSac18}
\by A.~Yu.~Popov, Yu.~L.~Sachkov
\paper Two-side bound of a root of an equation containing complete elliptic integrals
\jour Program Systems: Theory and Applications
\yr 2018
\vol 9
\issue 4
\pages 253--264
\mathnet{http://mi.mathnet.ru/ps330}
\crossref{https://doi.org/10.25209/2079-3316-2018-9-4-253-264}


Linking options:
  • http://mi.mathnet.ru/eng/ps330
  • http://mi.mathnet.ru/eng/ps/v9/i4/p253

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Program Systems: Theory and Applications
    Number of views:
    This page:59
    Full text:16
    References:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020