Institute of Mathematics AS CR, v. v. i.
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The Grothendieck ring of quantum double of quaternion group
No full textsummary:Let be an algebraically closed field of characteristic , and let be the quaternion group. We describe the structures of all simple modules over the quantum double of group algebra . Moreover, we investigate the tensor product decomposition rules of all simple -modules. Finally, we describe the Grothendieck ring by generators with relations
Regularizing effect of the interplay between coefficients in some noncoercive integral functionals
No full textsummary:We are interested in regularizing effect of the interplay between the coefficient of zero order term and the datum in some noncoercive integral functionals of the type where , is a Carathéodory function such that is convex, and there exist constants such that for almost all , all and all . We show that, even if and only belong to , the interplay implies the existence of a minimizer which belongs to
Statistical convergence of order in topology and its applications to selection principles
No full textsummary:The statistical convergence in a topological space is constrained in this study up to order , where . A fresh group of open covers (namely - covers) and an entirely novel category of denseness (namely -denseness) are proposed using this notion of -convergence, which has been used to study various topological aspects of -density. It has been revealed that the class of - coverings falls somewhere between the class of covers and the class of - covers. The influence of - covers in topological games and selection principles are also investigated
Recording the Czech premiere of the “Fantasia Apocalyptica” multimedia work
No full textsummary:Dne 11. října 2019 se při příležitosti oslav 25. výročí založení Fakulty informatiky Masarykovy univerzity uskutečnila česká premiéra multimediálního díla „Fantasia Apocalyptica“ za osobní účasti autora, Donalda Knutha. Z představení byl pořízen záznam, který je dostupný na kanálu YouTube Fakulty informatiky. V tomto článku popisuji přípravu záznamu od akvizice a zpracování surových audiovizuálních dat přes přípravu replik panelů doprovázejících představení po spojení jednotlivých částí do výsledného záznamu. S výjimkou střihu úvodního slova a závěru, navýšení rozlišení videa a zúžení dynamického rozsahu zvuku proběhlo zpracování pomocí svobodných nástrojů jako TeX, Audacity, Aegisub, FFmpeg, MLT, PDFtk a ImageMagick. V článku ukazuji užití těchto nástrojů.summary:On October 11, 2019, the Czech premiere of the “Fantasia Apocalyptica” multimedia work was held for the 25th anniversary of Masaryk University's Faculty of Informatics, featuring its author, Donald Knuth. A video recording of the performance was taken and published at the YouTube channel of the Faculty of Informatics. In this article, I describe how the recording was prepared from processing the raw footage through replicating the panels that accompanied the performance to the final composition. Apart from super-resolution imaging, the editing of the intro and the wrap-up, and the compression of sound, only free open-source tools like TeX, Audacity, Aegisub, FFmpeg, MLT, PDFtk, and ImageMagick were used. In the article, I describe how readers can use these tools for their own recordings
Existence, uniqueness and continuity results of weak solutions for nonlocal nonlinear parabolic problems
Get PDFsummary:This paper is concerned with the study of a nonlocal nonlinear parabolic problem associated with the equation in , where is a bounded domain of , is a positive number, is an matrix of variable coefficients depending on and , , are given functions. We consider two different assumptions on . The existence of a weak solution for this problem is proved using the Schauder fixed point theorem for each of these assumptions. Moreover, if depends only on the variable , we investigate two uniqueness theorems and give a continuity result depending on the initial data
Relative co-annihilators in lattice equality algebras
Get PDFsummary:We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra and a filter of , we define the set of all -involutive filters of and show that by defining some operations on it, it makes a BL-algebra
Průměrná vzdálenost dvou bodů na kružnici
Get PDFsummary:Ukážeme, jak spočítat průměrnou vzdálenost dvou náhodně zvolených bodů na kružnici. Ale zejména si ukážeme nástroje a metody, jak lze podobné úlohy řešit