Institute of Mathematics AS CR, v. v. i.
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The narrow recurrence of random dynamical systems
No full textsummary:Let be a probability space, where is countably generated, and be a Polish space. Let be a random dynamical system with time on . The skew product flow induced by is a family of continuous operators acting on , the set of all probability measures on with marginal , which is a Polish space equipped with the narrow topology. In this work, we introduce and study the notion of narrow recurrence of the flow on and we give some results, which can be considered as an initiation of applications of properties of topological dynamics on stochastic process theory and random dynamical systems
Stabilizability of multi-agent systems over finite fields via fully actuated system approaches
No full textsummary:The problem of stabilizability of high-order fully actuated (HOFA) multi-agent systems over finite fields is considered in this paper. The necessary and sufficient conditions for the stabilizability of HOFA multi-agent systems are presented, which indicates the stabilizability is closely related to the interaction topology among agents. Using the full-actuation property of HOFA models, a stabilization control protocol with neighbor interaction is given for HOFA multi-agent systems. Additionally, when the multi-agent system is stabilizable, the time for the system to reach a stable state can be determined through the control protocol. Finally, the results are employed to solve the formation control problem, and some sufficient and/or necessary conditions are proposed. Numerical examples are presented to demonstrate the effectiveness of the proposed results
Finite interpolation on sequences in the disc
No full textsummary:This note deals with interpolation of values of analytic functions belonging to a given space, on finite sets of consecutive points of sequences in the disc, performed by rational functions and polynomials. Our goal is to identify sequences and spaces whose functions provide a bound of the error at the first uninterpolated point that is as small as desired. For certain sequences, we prove that this happens for bounded functions, Lipschitz functions and those that have derivatives in the disc algebra
Report from the TUG 2025 Conference
No full textsummary:Od pátku 18. do neděle 20. července se v indické Kérale po 14 letech konala konference TUG 2025. Autor přítomného textu se konference aktivně zúčastnil a ve zbytku článku referuje o průběhu konference.summary:From Thursday, July 17, to Sunday, July 20, the TUG 2025 conference was held in Kerala, India, for the first time in 14 years. The author of this article took an active part in the conference and reports on its proceedings
Selected TeX Packages from the Games Collection
No full textsummary:Pre mnohých ľudí je TeX nástroj na písanie dokumentov, prípadne prípravu čistého odborného textu. Široká ponuka balíčkov, ktoré boli k TeXu počas jeho existencie vytvorené, umožňuje ale vysádzanie mnohých iných vecí než len čistého textu. V tomto referáte sa pozrieme na zopár takýchto „nevšedných“ balíčkov zameraných na vysádzanie diagramov a stavov rôznych hier.summary:For many people, TeX is mainly a tool for writing scientific documents or creating complex texts. However, over the years of TeX's existence, various packages have been created that extend its functionality beyond typesetting text. In this article, we will take a look at a couple of these packages that focus on typesetting various diagrams and board states for different games
Sequential games with turn selection process and fuzzy utility functions
No full textsummary:A particular group of models of sequential games is studied where the order of the turns is not known beforehand by the players, and where the utility functions for each player are fuzzy numbers. For these models, a series of results are proven to show the existence of equilibria under two criteria, and a brief application is described where it usually is not possible to give utilities a precise value, hence, where fuzzy numbers are adequate
Constructions of uninorms with ordinal sum underlying t-norms (t-conorms) on bounded lattices
No full textsummary:Uninorms are a special type of aggregation operators proposed by Yager and Rybalov in 1996, and since then, there have been numerous research achievements on uninorms on the unit real interval. In 2015, the concept of uninorms was extended to a more general algebraic structure - bounded lattices. This article aims to study the construction of uninorms on bounded lattices. We first provide the construction methods of uninorms on bounded lattices by using ordinal sum t-norms or ordinal sum t-conorms. Then, we clarify that the new methods are the extensions of some construction methods in literature. Finally, some illustrative examples for the new constructions of uninorms on bounded lattices are provided. This study is the first attempt to construct using the ordinal sum underlying operators and it will open up new ideas for in-depth analysis of the structure of uninorms on bounded lattices
New representations of -inverses
No full textsummary:We investigate how to give new representations of -inverses in terms of core inverses and Drazin inverses. Various new criteria and representations of -inverses in terms of core inverses and Drazin inverses are established from a new perspective. Since Moore-Penrose inverses, pseudo-inverses, core inverses, dual core inverses, and Bott-Duffin -inverses are the special cases of -inverses, new characterizations involving these generalized inverses are also established as corollaries of our results
Jordan triple ()-derivations of prime rings
No full textsummary:Let be a 2-torsion free prime ring and let be endomorphisms of . We prove that if is commutative, then every Jordan triple -derivation of is a \hbox {-derivation} and if is noncommutative, then every Jordan triple -derivation of with either or an epimorphism, is a -derivation. As an application, we characterize Jordan triple semiderivations of prime rings. Our theorems naturally generalize the result for Jordan -derivations obtained by M. Brešar, J. Vukman (1991) and the result for Jordan semiderivations obtained by V. De Filippis, A. Mamouni, L. Oukhtite (2015)