Institute of Mathematics AS CR, v. v. i.
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Conditional distributivity of overlap functions over uninorms with continuous underlying operators
Get PDFsummary:The investigations of conditional distributivity are encouraged by distributive logical connectives and their generalizations used in fuzzy set theory and were brought into focus by Klement in the closing session of Linzs 2000. This paper is mainly devoted to characterizing all pairs of aggregation functions that are satisfying conditional distributivity laws, where is an overlap function, and is a continuous t-conorm or a uninorm with continuous underlying operators
Equilibrium analysis of distributed aggregative game with misinformation
Get PDFsummary:This paper considers a distributed aggregative game problem for a group of players with misinformation, where each player has a different perception of the game. Player's deception behavior is inevitable in this situation for reducing its own cost. We utilize hypergame to model the above problems and adopt -Nash equilibrium for hypergame to investigate whether players believe in their own cognition. Additionally, we propose a distributed deceptive algorithm for a player implementing deception and demonstrate the algorithm converges to -Nash equilibrium for hypergame. Further, we provide conditions for the deceptive player to enhance its profit and offer the optimal deceptive strategy at a given tolerance . Finally, we present the effectiveness of the algorithm through numerical experiments
The unit group of some fields of the form
No full textsummary:Let and be two different prime integers such that with , and a positive odd square-free integer relatively prime to and . In this paper we investigate the unit groups of number fields
On generalized bihyperbolic Mersenne numbers
Get PDFsummary:In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented
Identification of source term in a nonlinear degenerate parabolic equation with memory
No full textsummary:In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach
The 2023 Nobel Prize in Physics - A Journey into the World of Attoseconds
No full textsummary:V roce 2023 byla Nobelova cena za fyziku udělena třem významným osobnostem v oblasti attosekundové fyziky. Článek shrnuje základy tohoto vědního oboru, jehož cílem je zachytit nejrychlejší jevy související s dynamikou elektronů v atomech, molekulách a pevných látkách
Grand Prize for Small Dots
No full textsummary:Článek se věnuje tématu kvantových teček, za které byla udělena loňská Nobelova cena za chemii. V úvodu jsou zařazeny krátké medailonky laureátů, po nichž následují části zabývající se fyzikální podstatou objevu a jeho komerčním využitím. Článek uzavírá část věnující se tématu kvantových teček v českém prostředí
Fibonacci, Mersenne, Mendel
Get PDFsummary:Článek krátce přibližuje Mendelovy základní objevy týkající se jeho experimentů s hrachem a také s experimenty spojenou kontroverzi