INTEGRATING MULTIPERIODIC FUNCTIONS ALONG THE PERIODIC CHARACTERISTICS OF THE DIAGONAL DIFFERENTIATION OPERATOR
Sartabanov Zh. Omarova B. Aitenova G. Zhumagaziyev A.
31 December 2023al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2023#120Issue 452 - 68 pp.
In this paper, trajectory of time changing along a helical line is represented by parametric equations in Cartesian coordinates of Euclidean space. On the basis of a cycloidal sweep of a cylindrical surface onto a plane, analytical form of a helix is determined. On its basis, integral surface is determined, which is called the periodic characteristic of the diagonal differentiation operator and its connection with its linear characteristic is established. a) elements of new approach related to the periodic characteristic of diagonal differentiation operator are proposed, b) method for reducing integral along the periodic characteristic to an integral with linear characteristic, c) conditions establishing structure of the integral as sum of linear and multiperiodic functions. Some consequences of these results and recommendations of an algorithmic nature for further expansion of research in this direction are given.
autonomous systems , differentiation operator , infinite cylindrical surface , multiperiodicity , periodic characteristic , vector field
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K. Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
M. Utemisov West Kazakhstan University, Uralsk, Kazakhstan
K. Zhubanov Aktobe Regional University
M. Utemisov West Kazakhstan University
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