Newton binomial in the generalized Cauchy problem as exemplified by electrical systems

Yurii G. Vedmitskyi; Vasyl V. Kukharchuk; Valerii F. Hraniak; Inna V. Vishtak; Piotr Kacejko; Arman Abenov

doi:10.1117/12.2501600

1 October 2018 Newton binomial in the generalized Cauchy problem as exemplified by electrical systems

Yurii G. Vedmitskyi, Vasyl V. Kukharchuk, Valerii F. Hraniak, Inna V. Vishtak, Piotr Kacejko, Arman Abenov

Proceedings Volume 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018; 108082M (2018) https://doi.org/10.1117/12.2501600
Event: Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 2018, Wilga, Poland

Abstract

Presented in the paper are direct and indirect correspondence rules between the set of real and complex coefficients of two interrelated linear differential equations of random order, each of them being able in an individual and independent way to describe uninterrupted movement of generalized, in terms of the number of freedom degrees, dynamic system with lumped parameters in the fundamental Cauchy problem, which is formulated in the first case in terms of real time functions, and in another case – in terms of their complex images, which allows directly to set one of the said forms of Cauchy problem based on the other one both in the generalized form as to the order of differential equation and in particular form under given conditions, regardless of the physical nature of the system under examination.

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Yurii G. Vedmitskyi, Vasyl V. Kukharchuk, Valerii F. Hraniak, Inna V. Vishtak, Piotr Kacejko, and Arman Abenov "Newton binomial in the generalized Cauchy problem as exemplified by electrical systems", Proc. SPIE 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 108082M (1 October 2018); https://doi.org/10.1117/12.2501600

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