Vibrations in engineering and technology


Issue №: 4(91)

Published: 2018.09.26

The journal deals with the problems of vibration technologies and machines, mathematical methods of vibration process studies, information on design and technological development, presents teaching and methodological aspects of teaching in the Higher School of Applied Sciences, where vibration machines and technologies are studied.

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Establishing the conditions for effective coverage with the area of the square of the square and some cases of generalization

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Dubchak Viktor – PhD, Associate Professor of the department Mathematics, physics and computer technologies of the Vinnytsia National Agrarian University (Sonyachna St. 3, Vinnytsia, 21008, Ukraine e-mail: dubchak@vsau.vin.ua).


In this paper, the problem of optimal, extreme (minimal) coverage of the area of one flat figure, namely, a square (rectangle) of the area of another flat geometric figure, as circle (ellipse), is investigated. The value of some function that determines the difference between the areas of non-conformities of the intersection of geometric figures is given in the first case, this function depends on one variable argument, in the second case-two arguments, in both cases a study was conducted on the extremality of a given function, it was shown that at the found point The extremum function, which determines the discrepancy of the areas of figures, acquires a minimal value. The conditions of such an extremally-minimal covering of one area correspondingly to another area are established, the figures are given for a better understanding of the statement and the solution of the problem, the conclusions are drawn, in which quality the values of the required arguments are given, when the corresponding function acquires the minimum values.

Keywords: Circle (ellipse) and its parts, square (rectangle) and its parts, extremity (minimum) of functions of one and several variables.

List of references

1. Akhtershev, S.P.(2005) Tasks for maximum and minimum,  BHV-Petersburg, - 85-98. [in Rassian].

2. Belyaeva, E.S.( 1977) Extreme tasks, Moscow: Enlightenment, - 45-53. [in Rassian].

3. Gabasov, R.F.( 1997) Extreme problems in modern science and applications, Soorov educational journal.  - №6. -  115-120. [in Rassian].

4. Pontrjagin, L.S.( 1985) Mathematical theory of optimal processes -M .: Fizmatgiz, 119-158, [in Rassian].

5. Galeev, E.M., Tikhomirov V.M.( 1989) Brief course of the theory of extreme problems Study. allowance -M .: Izvst. Of Moscow State University,. -131-142, [in Rassian].

6. Bronstein, I.M.( 2007) Mathematical Reference for engineers and students of the Institute - M .: Nauka. – 563-585, [in Rassian].

7. Vasiliev, F.P. (2002) Numerical methods for solving extreme problems. - M .: Nauka. -327-339. [in Rassian].


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About journal

Topics of the journal:

The journal "Vibrations   in engineering  and technology" presents materials on the following issues

• Theory of processes and machines
• Mechanical Engineering and materialprocessing
• Processing and food production

Key information:
ISSN (print): 2306-8744
DOI: 10.37128/2306-8744

The certificateof massmediaState registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University

Kind of publication: journal
Type of publication : Scientific
Publication status: Domestic
Year of founding:
Periodicity: 4 times a year
Extent: 18.75 nominal printed pages
ISSN: 2306-8744 (printed version), (online)
Language of edition  : (mixed languages) Ukrainian, English
The scope of the distribution and the category of readers: national, foreign, teaching staff, scientists, businessmen.
Periodical is included in the list of scientific professional editions of Ukraine approved by the Order of Ministry of Education and Sciences of Ukraine from 21.12.2015 No. 1328.
The journal "Vibrations in engineering and technology" is included in the "Catalogue of periodicals of Ukraine".
Journal subscription can be executed in each post office department.
 Subscription Index is  99720.


Old version of site: http://vibrojournal.vsau.edu.ua/

History of journal:

In June 1994 the 2nd International Scientific and Technical Conference "Application of vibrations for technological purposes" was organized on the basis of Vinnytsia State Agricultural Institute. Leading experts in this field, noting the significant contribution to the school of Vibration Engineering under the leadership of P. S. Bernyk, proposed to create a professional all-Ukrainian scientific and technical journal "Vibration in engineering and technology..The journal was foundedat Vinnytsia State Agricultural Institute and P.S. Bernyk was elected to be the chief editor .
For all these years (since 1994) theJournal "vibration in engineering and technology" published  94 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Kaletnik H.M  PhD , professor, academician NAAS is the chief editor of the "Vibrations in engineering  and Technology"
The journal "Vibration in Engineering and technology", which has no analogues on the territory of Ukraine, is well known abroad.