Abstract
This work is devoted to the development and substantiation of a new tensor-geometric theory of large-dimensional electric circuits. Also, a new method is proposed for solving the complete problem on their eigenvalues. Electric circuits exemplify oscillatory systems with concentrated parameters. The problem on their eigenvalues and eigenvectors is, on the one hand, one of the most important problems of mathematical physics and oscillation theory, and, on the other hand, is universal since it has many different applications.
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A. A. Mylnikov and A. I. Prangishvili, “Homological and cohomological invariants of electric circuits,” Avtom. Telemekh., No. 4, 67–75 (2002).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 74, Proceedings of the International Conference “Modern Algebra and Its Applications” (Batumi, 2010), Part 1, 2011.
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Mylnikov, A.A., Prangishvili, A.I. Method of solving the generalized problem on eigenvalues of multi-dimensional circuits, II. J Math Sci 186, 795–797 (2012). https://doi.org/10.1007/s10958-012-1035-5
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DOI: https://doi.org/10.1007/s10958-012-1035-5