arXiv subjects
Publications and source records attributed to Urszula Ostaszewska.
In this paper an emergence of leader-following model based on graph theory on the arbitrary time scales is investigated. It means that the step size is not necessarily constant but it is a function of time. We propose and prove conditions ensuring a leader-following consensus for any time scales using Grönwall inequality. The presented results are illustrated by examples.
t-entropy is the convex conjugate of the logarithm of the spectral radius of a weighted composition operator (WCO). Let $X$ be a nonnegative random variable. We show how the Cramér transform with respect to the spectral radius of WCO is expressed by the t-entropy and the Cramér transform of the given random variable X.
In this paper we present some general solution of the system of linear equations formed by Guibas and Odlyzko in Th.3.3 \cite{Gui}. We derive probabilities for given patterns to be first to appear in random text and the expected waiting time till one of them is observed and also till one of them occurs given it is known which pattern appears first.