Institute of Mathematics AS CR, v. v. i.
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On the proper inclusion property of (discrete) Morrey spaces
No full textsummary:We construct a function which confirms the proper inclusion property of Morrey spaces, by using a relation between a class of functions, in Morrey spaces and discrete Morrey spaces. Our particular function is simpler than those constructed by H. Gunawan, D. I. Hakim, M. Idris (2018) and H. Gunawan, D. I. Hakim, M. Idris (2022)
On the rings generated by the inner automorphisms of finite groups
No full textsummary:For a finite group , let denote the set of all finite sums of inner automorphisms of . When forms a ring, is referred to as an I-group. It is known that if is an I-group, then it is nilpotent of class at most 3, and that is a commutative ring if and only if is nilpotent of class at most 2. We characterize the ring for an I-group . Additionally, for cases where is a commutative ring and is of order (with being a prime and or 4), as well as for orders and , we determine the ring structure of
A topological study in the set of zero-dimensional subrings of a commutative ring
Full text linksummary:We investigate the relationship between the space , defined as the largest closed subset of a ring with respect to a countable topology, and the classical prime spectrum of a subring . We explore the topological properties of and establish connections with under certain conditions
On a certain subclass of analytic functions defined by -Sălăgean operator associated with operator on Hilbert space
Full text linksummary:Using a Hilbert space operator, we define a new subclass of analytic functions defined by -valent -Sălăgean operator and determine coefficient estimates, distortion bounds, radii of close-to-convexity, starlikeness, and convexity for the functions in this class. We also investigate extreme points and the modified Hadamard product
Using a spreadsheet to solve the problems of the Mathematical
No full textsummary:První část článku se zaměřuje na digitální kompetence jako nové klíčové dovednosti v rámci základního vzdělávání. Podrobně popisuje, jak konkrétní škola rozvíjí tuto kompetenci ve vzdělávací oblasti Matematika a její aplikace. V praktické části je představeno řešení úloh z Matematické olympiády kategorie Z5 pro pátý ročník základní školy. Souhrnný průzkum obsahuje analýzu způsobu řešení úloh žáky, jejich aktivity a metodiky s využitím tabulkového kalkulátoru, což umožňuje posoudit schopnosti žáků aplikovat svou digitální kompetenci při řešení matematických úloh.summary:The first part of the article focuses on digital competence as a new key skill in basic education. It describes in detail how a particular school develops these competences in the educational area "Mathematics and its applications". In the practical part, the solution of tasks from the Mathematical category Z5 for the fifth year of primary school is presented. The summary survey includes an analysis of the way pupils solve the problems, their activity and methodology using a spreadsheet calculator, which allows to assess pupils' ability to apply their digital competences in solving mathematical problems
Finite solvable groups whose Gruenberg-Kegel graph has a cut-set
No full textsummary:Let be the Gruenberg-Kegel graph of a finite group . We prove that if is solvable and is a cut-set for , then has a -series of length 5 whose factors are controlled. As a consequence, we prove that if is a solvable group and has a cut-vertex , then the Fitting length of is bounded and the bound obtained is the best possible. A cut-set is said minimal if it does not contain any other proper subset that is a cut-set for the graph. For a finite solvable group , we give a geometrical description of when it has minimal cut-set of size 2
The anti-Ramsey problem for independent triangles in tripartite graphs
No full textsummary:An edge colored graph is a rainbow if all colors on its edges are distinct. For two graphs and , where contains as a subgraph, the anti-Ramsey number of in , denoted by , is the largest integer such that there exists a -edge-coloring of containing no rainbow . Let denote the union of independent triangles. The anti-Ramsey problem for cycles (including independent cycles) in a complete graph has been studied well. We consider the problem for independent cycles in a tripartite graph and obtain the value of for
Exponential Functions in Czech and Swedish Textbooks and Their Use in Application Problems
No full textsummary:Cílem článku je analyzovat způsoby zavedení a využití exponenciální funkce v českých a švédských středoškolských učebnicích matematiky. Pozornost je věnována rozdílům v definici exponenciální funkce i způsobu práce s aplikačními úlohami, které tuto funkci propojují s reálnými situacemi. Studie ukazuje, že využití rozšířeného zápisu exponenciální funkce, běžného například ve švédských učebnicích, přináší větší flexibilitu při modelování reálných jevů, jako je růst populace, změna cen nebo biologické procesy. Součástí článku je výběr příkladů aplikačních úloh přeložených ze švédských materiálů, které mohou sloužit jako inspirace pro výuku matematiky na českých středních školách.summary:The aim of this article is to analyse the ways in which exponential functions are introduced and used in applied problems in Czech and Swedish upper secondary mathematics textbooks. The focus is placed on differences in definitions of the exponential function as well as on the nature of related applied tasks, which connect the mathematical concept with real-life phenomena. The study shows that the use of a generalized form of the exponential function, as typically found in Swedish textbooks, allows greater flexibility in modelling real-world situations such as population growth, price changes or biological processes. The article includes a selection of applied problems translated from Swedish sources, which may serve as inspiration for mathematics education in the Czech context