Establishing the conditions for effective coverage with the area of the square of the square and some cases of generalization
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: email@example.com).
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.
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The journal "Vibrations in engineering and technology" presents materials on the following issues
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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.