Institute of Mathematics AS CR, v. v. i.
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Jorunal Rozhledy matematicko-fyzikálnías witnesses of happy coincidences and systematic research
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Theoretical solutions of flat roofs in the GeoGebra programme
No full textsummary:Článek představuje applet pro řešení plochých střech vytvořený v GeoGebře. Applet je založen na myšlence Voroneho diagramu. V článku je připomenuta potřebná teorie, vysvětlen princip fungování appletu a popsáno jeho užití včetně doporučení do výuky. Přílohou příspěvku je pracovní list obsahující 32 zadání a řešení plochých střech.summary:The paper presents an applet for solving flat roofs created with Geo\-Gebra. This applet is based on the idea of the Voronoi diagram. The paper provides the necessary theory, explains the principle of the applet's working and describes its use, including recommendations for teaching. A worksheet containing 32 tasks and solutions for flat roofs is attached
Conforming simplicial partitions of product-decomposed polytopes
No full textsummary:We propose some approaches for the generation of conforming simplicial partitions with various regularity properties for polytopic domains that are products or a union of products, thus generalizing our earlier results. The techniques presented can be used for finite element simulations of higher-dimensional problems
Theoretical analysis for - minimization with partial support information
No full textsummary:We investigate the recovery of -sparse signals using the - minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume -sparse signals with the prior support which is composed of true indices and wrong indices, i.e., . First, we derive a new condition based on RIP of order to guarantee signal recovery via - minimization with partial support information. Second, we also derive the high order RIP with for some to guarantee signal recovery via - minimization with partial support information
Integration and decompositions of weak-integrable multifunctions
No full textsummary:Conditions guaranteeing Pettis integrability of a Gelfand integrable multifunction and a decomposition theorem for the Henstock-Kurzweil-Gelfand integrable multifunctions are presented
Bifurcation of periodic solutions to nonlinear measure differential equations
No full textsummary:The paper is devoted to the periodic bifurcation problems for generalizations of ordinary differential systems. The bifurcation is understood in the static sense of Krasnoselski\u ı and Zabre\u ıko. First, the conditions necessary for the given point to be bifurcation point for non autonomous generalized ordinary differential equations (based on the Kurzweil gauge type generalized integral) are proved. Then, as the main contribution, analogous results are obtained also for the nonlinear non autonomous measure differential equations considered in the sense of distributions. To this aim their relationship to Kurzweil's generalized differential equations is disclosed. Although the measure differential equations turned out to be special cases of those Kurzweil's equations, the proofs of the main results of the paper are by no means the straightforward consequences of the analogous results for generalized differential equations. Essentially they rely on the theory of the Kurzweil-Stieltjes integration. It is worth noting that as the systems studied in the paper encompass many types of equations such as impulsive differential equations, ordinary differential equations, dynamic equations on time scales etc., the results of the paper offer applications to rather wide scale of practical problems. Two illustrating examples are included, as well
A Glimpse into the Story of Danish Mathematics
No full textsummary:Článek se zaměřuje na osudy a vědecký přínos významných představitelů dánské matematiky z druhé poloviny 19. století a první poloviny 20. století. Popisuje vznik, vývoj a klíčové aktivity Dánské matematické společnosti, která podstatně ovlivnila matematickou scénu v Dánsku i vývoj matematiky v širším mezinárodním kontextu
The Seven Liberal Arts: Mathematical and Artistic Journeys across Bohemia
No full textsummary:V článku představíme několik zajímavých uměleckých ztvárnění sedmi svobodných umění (gramatiky, dialektiky, rétoriky, geometrie, aritmetiky, astronomie a hudby), která byla od středověku základem vzdělávání a vzdělanosti na univerzitách a později na latinských gymnáziích. Nabídneme čtenářům náměty na několik pěkných výletů po Čechách, které návštěvník bez matematicko-historického vzdělání příliš neocení
