Browsing by Subject "półgrupy"

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Access status: Open Access ,
Dynamical model of propagation of pollutants in a river
(Wydawnictwa AGH, 2008) Żołopa, Elżbieta; Grabowski, Piotr
In this paper a dynamical model of propagation of pollutants in a river with $M$ point controls in the form of aerators and $K$ point measurements is being transformed to an abstract model on a suitably chosen Hilbert space. Our model belongs to the class of abstract models of the factor-type. It is shown that the semigroup generated by the state operator $A$ has a property of decaying in a finite-time, the observation operator is admissible, and the system transfer function is in the space $H^{\infty}$ ($\mathbb{C}^{+}$, $L(\mathbb{C}^{M}, \mathbb{C}^{K})$). In the final part we also formulate the LQ problem with infinite-time horizon.
Access status: Open Access ,
Semigroups, groups and grammar inference problem
(Wydawnictwa AGH, 2002) Sokolicki, Zbigniew
In the paper we analyse a problem of inferring a grammar from a given sample of a language. We try to present an algebraic formalism capable of describing the issue. We consider two cases: a case of inferring canonical finite-state grammars, and a case of inferring general grammars. In both cases we define a semigroup structure. Finally we look at the possibility of getting a structure of a group.