CONSTRUCTION AND RESEARCH INTO THE OPERATORS OF INTERLINEATION OF THE FUNCTIONS OF THREE VARIABLES ON A SYSTEM OF DISJOINT CURVES IN A CYLINDRICAL COORDINATE SYSTEM WITH THE PRESERVATION OF THE CLASS OF DIFFERENTIABILITY

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J. of Mech. Eng., 2016, vol. 19, no. 4, pp. 57-61

DOI:   https://doi.org/10.15407/pmach2016.04.057

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 4, 2016 (December)
Pages 57–61

 

Authors

I. V. Serhiienko, V. M. Glushkov Institute of Cybernetics of the NASU (40, Academician Glushkov Ave., Kyiv, 03187, Ukraine)

O. M. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine),
e-mail: academ_mail@ukr.net

O. O. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine)

O. V. Tkachenko, Zaporozhye Machine-Building Design Bureau Progress State Enterprise named after
Academician A. G. Ivchenko (2, Ivanova Str., 69068, Zaporozhye, Ukraine), e-mail: avt2007@outlook.com

O. L. Hrytsai, Zaporozhye Machine-Building Design Bureau Progress State Enterprise named after
Academician A. G. Ivchenko (2, Ivanova Str., 69068, Zaporozhye, Ukraine), e-mail: avt2007@outlook.com

 

Abstract

This article proposes a method for constructing the interlineational operators of Hermitian functions of three variables using their traces and traces of their derivatives on the indicated lines in a cylindrical coordinate system. The method allows you to restore these functions at points between a given system of closed disjoint curves in a cylindrical coordinate system, while automatically maintaining the class of differentiability to which the approximate function belongs.

 

Keywords: interlineation of functions, cylindrical coordinate system, preservation of a class of differentiability, traces of a function, traces of derivatives, Hermitian interlineation operator

 

References

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  2. Sergienko, I. V., Lytvyn, O. M., Lytvyn, O. O., Tkachenko, O. V., & Gritsay, O. L. (2014). Vidnovlennya funktsiy dvoh zminnyh iz zberezhennyam klasu Cr(R2) za dopomogoyu ih slidiv ta slidiv ih pohidnyh do fiksovanogo poryadku na zadaniy linii. Dopovidi NAN Ukrainy, no. 2, pp. 50–55 (in Ukrainian). https://doi.org/10.15407/dopovidi2014.02.050
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Received 05 October 2016