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Journal of Mathematical Physics
Article . 2021 . Peer-reviewed
License: CC BY
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Journal of Mathematical Physics
Article
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Article . 2021
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https://dx.doi.org/10.48550/ar...
Article . 2019
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Effective impedance over ordered fields

Authors: Anna Muranova;

Effective impedance over ordered fields

Abstract

In this paper, we study the properties of effective impedances of finite electrical networks, considering them as weighted graphs over an ordered field. We prove that a star-mesh transform of finite network does not change its effective impedance. Moreover, we consider two particular examples of infinite ladder networks (Feynman’s network or LC-network and CL-network, both with zero at infinity) as networks over the ordered Levi–Cività field R. We show that the sequence of effective impedances of finite LC-networks converges to the limit in the order topology of R, but the sequence of effective impedances of finite CL-networks does not converge in the same topology. We calculate an effective impedance of a finite ladder network as an auxiliary result.

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Keywords

FOS: Physical sciences, Mathematical Physics (math-ph), Technical applications of optics and electromagnetic theory, Mathematics - Spectral Theory, finite electrical networks, impedance, FOS: Mathematics, Mathematics - Combinatorics, 05C22, 34B45, 05C25, 39A12, 12J15, Non-Archimedean analysis, Combinatorics (math.CO), Spectral Theory (math.SP), Mathematical Physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Average
Green
hybrid