Institute of Mathematics AS CR, v. v. i.
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Modelování rozptylu světla v mlhovinách v rámci Talentové akademie ELI Beamlines a HiLASE
Get PDFsummary:Tento článek se zabývá modelováním rozptylu světla v reflexních mlhovinách. Cílem je popsat experiment provedený v laserových centrech ELI Beamlines a HiLASE v září 2023 během akce Talentová akademie. Účelem této akce bylo umožnit středoškolským studentům pracovat v profesionálním vědeckém prostředí a poskytnout jim nové dovednosti. Článek je rozdělen do dvou částí: v úvodní teoretické části jsou popsány jevy emise a rozptylu světla, princip laseru a objekt, jehož chování se snažíme modelovat – mlhovina. V druhé praktické části je popsán postup experimentu, který mlhovinu simuloval pomocí zlatých nanočástic a laseru
On stochastic properties of past varentropy with applications
No full textsummary:To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on past varentropy. Further, we illustrate some of its applications in reliability modeling and in the diversity measure of Boltzmann distribution
Certified methodology Diagnostics of pupil’s aptitudes for solving mathematics problems
No full textsummary:Příspěvek popisuje certifikovanou metodiku, která má pomoci učitelům matematiky odhalit možné příčiny selhání žáka v průběhu řešení matematické úlohy a ukázat možné způsoby práce s žáky na základě získaných výsledků diagnostiky
On manifolds homotopy equivalent to the total spaces of -bundles over
Get PDFsummary:We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles
Maxwell-Schrödinger equations in singular electromagnetic field
No full textsummary:We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness of the weak solutions to this system
The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated
Get PDFsummary:Let be a numerical semigroup. In this work we show that \mathcal {J}(\Delta ) =\{I\cup \nobreak \{0\}\colon I \mbox { is an ideal of } \Delta \} is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set for a given As a consequence, we obtain another algorithm that computes all the elements of with a fixed genus