Skew fields of noncommutative rational functions (preliminary version)
George W. Bergman (1969-1970)
Séminaire Schützenberger
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George W. Bergman (1969-1970)
Séminaire Schützenberger
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Heide Glüsing-Lüerssen, Paolo Vettori, Sandro Zampieri (2001)
Kybernetika
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This paper presents a survey on the recent contributions to linear time- invariant delay-differential systems in the behavioral approach. In this survey both systems with commensurate and with noncommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with noncommensurate...
de la Sen, M. (2008)
Mathematical Problems in Engineering
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Eva Zerz (2008)
International Journal of Applied Mathematics and Computer Science
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We survey the so-called behavioral approach to systems and control theory, which was founded by J. C. Willems and his school. The central idea of behavioral systems theory is to put the focus on the set of trajectories of a dynamical system rather than on a specific set of equations modelling the underlying phenomenon. Moreover, all signal components are treated on an equal footing at first, and their partition into inputs and outputs is derived from the system law, in a way that admits...
Caleb Emmons, Mike Krebs, Anthony Shaheen (2012)
Open Mathematics
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A K-quasiderivation is a map which satisfies both the Product Rule and the Chain Rule. In this paper, we discuss several interesting families of K-quasiderivations. We first classify all K-quasiderivations on the ring of polynomials in one variable over an arbitrary commutative ring R with unity, thereby extending a previous result. In particular, we show that any such K-quasiderivation must be linear over R. We then discuss two previously undiscovered collections of (mostly) nonlinear...
Devitt, J.S., Mollin, R.A. (1986)
International Journal of Mathematics and Mathematical Sciences
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Miroslav Kureš, Ladislav Skula (2008)
Annales UMCS, Mathematica
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It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.