Institute of Mathematics AS CR, v. v. i.
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How Frank Wilcoxon helped statisticians discover non-parametric tests II
No full textsummary:Mezi často používané neparametrické testy statistické významnosti patří Wicoxonovy testy. Autorem matematického modelu, na kterém jsou tyto testy založeny, je americký statistik Frank Wilcoxon (1892–1965). Článek popisuje podstatu a vznik těchto testů, zejména Wilcoxonova dvouvýběrového testu, v matematickém a historickém kontextu.summary:One of the frequently used nonparametric tests of statistical significance are Wilcoxon tests. The author of the mathematical model on which these tests are based is the American statistician Frank Wilcoxon (1892–1965). The article describes the essence and origin of these tests, especially Wilcoxon rank sum test, in mathematical and historical context
Overview of mathematical competitions for upper secondary school pupils
No full textsummary:Matematické soutěže mohou být zajímavým a účinným nástrojem, jak zvýšit zájem studentů o matematiku. Celkem představíme 35 matematických soutěží, které jsou v tuto chvíli dostupné pro žáky a studenty základních a středních škol. V tomto článku je uvedeno 12 matematických soutěží určených studentům SŠ. Toto je čtvrtá (a poslední) část ze série článků pojednávajících o matematických soutěžích.summary:Mathematical competitions can be a very useful tool for increasing interest in mathematics among pupils and students. In a series of papers we present a list and a description of 35 mathematical competitions that are currently available for primary and secondary school students. In this article, we present 12 of them, that are intended for secondary school students
The Bogomolov multiplier of groups of order and exponent
No full textsummary:We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order and exponent . We present a comprehensive classification of these groups, identifying those with nontrivial Bogomolov multipliers and distinguishing them from groups with trivial multipliers. Our analysis not only clarifies the conditions under which the Bogomolov multiplier is nontrivial but also refines existing computational methods, enhancing the process of determining these multipliers for the specified class of -groups
Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on a class of unbounded complete Reinhardt domains
No full textsummary:We consider a class of unbounded nonhyperbolic complete Reinhardt domains where , , are positive real numbers and , are positive integers. We show that if a Hankel operator with anti-holomorphic symbol is Hilbert-Schmidt on the Bergman space , then it must be zero. This gives an example of high dimensional unbounded complete Reinhardt domain that does not admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols
Mean values related to the Dedekind zeta-function
No full textsummary:Let be a nonnormal cubic extension which is given by an irreducible polynomial . Denote by the Dedekind zeta-function of the field and the number of integral ideals in with norm . In this note, by the higher integral mean values and subconvexity bound of automorphic -functions, the second and third moment of is considered, i.e., where , are polynomials of degree 1, 4, respectively, is an arbitrarily small number
