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Scale invariance in the ionosphere
Šauli, Petra ; Abry, P. ; Cosson, X. ; Roux, S.
Scaling invariance domains represent domains where no preferential period of oscillation exists. Scaling laws always reveal an important property of the analysed system: self-similarity or multifractality. The observed ground-based and satellite ionospheric time series contain a mix of fluctuations of different physical origin (solar, geomagnetic, neutral atmosphere variability etc.). Description based on scaling features can be applied in the solar wind-magnetosphere-ionosphere interaction studies for further comparison of basic characteristics of intermittent fluctuations in solar wind, magnetosphere and ionosphere systems. Finding the similar scaling features of the solar and geomagnetic data in the ionospheric response might be a signature of common nature of the observed fluctuations. A comprehensive understanding of the scaling properties of the ionospheric indices has relevance for the predictability of the behaviour of the ionosphere within specified time range.
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Modules over non-commutative rings for an analysis of control systems
Xia, X. ; Márquez-Martínez, L. ; Zagalak, Petr ; Moog, C.
The paper introduces some concepts of the theory of non-commutative rings into the theory of nonlinear systems with time delays. The left Ore ring of non-commutative polynomials defined over the field of meromorphic functions is studied and some properties of modules over such rings are presented. This approach is then generalized to a special class of nonlinear systems with delays that are called Generalized Roesser Systems. Finally, the theory is used to define and characterize.
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