Institute of Mathematics AS CR, v. v. i.
Not a member yet
44818 research outputs found
Sort by
Weighted Calderón-Hardy spaces
No full textsummary:We present the weighted Calderón-Hardy spaces on Euclidean spaces and investigate their properties. As an application we show, for certain power weights, that the iterated Laplace operator is a bijection from these spaces onto classical weighted Hardy spaces. The main tools to achieve our result are an atomic decomposition of weighted Hardy spaces furnished by the author, fundamental solutions of iterated Laplacian and pointwise inequalities for certain maximal functions
How about a fractal? – Part 1
No full textsummary:V úvodu článku je stručně zodpovězena otázka, co je to fraktál, a jsou předloženy důvody, proč má smysl se ve výuce fraktály zabývat. Dále jsou představeny různé metody konstrukce fraktálů využitelné ve školní praxi. Fraktály lze snadno zařadit do výuky již na druhém stupni základních škol, ať už jako součást uceleného kurzu nebo jako jednotlivé tematické bloky. Konstrukce jsou vytvářeny především v programu GeoGebra, ale i tradičními metodami (tužka, papír) nebo pomocí dalších nástrojů (PowerPoint, webové aplikace). V závěru je ukázáno, že i pojem fraktální dimenze je přístupný pro středoškolské studenty.summary:The article begins by briefly answering the question of what a fractal is and provides reasons why fractals are worth exploring in education. Various methods of constructing fractals suitable for classroom use are then presented. Fractals can be easily integrated into the curriculum as early as upper primary school, either as part of a comprehensive course or as individual thematic units. Constructions are primarily created using GeoGebra, but also through traditional methods (pencil, paper) or other digital tools (PowerPoint, web applications). The conclusion demonstrates that the concept of fractal dimension can be accessible to high school students
Invitation to the seminar: Mathematics and Physics at School
No full textsummary:Oznámení o konání akce
How to Teach Mathematics to Pupils Aged 10–16
No full textsummary:Pozvánka na celostátní konferenci učitelů matematiky, která se zaměřuje na výuku na 2. stupni ZŠ, na období přechodu žáka z 1. na 2. stupeň a přechodu žáka ze ZŠ na SŠ
On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
No full textsummary:We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations. Furthermore, we show that if both lower and upper equilibria are stable, then the pendulum considered may possess a periodic motion that corresponds to the ``quasistatic solution'' of Bogolyubov as well as to the ``quasistatic balance'' of Kapitza
The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations
No full textsummary:We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions
Non-differentiability of Feynman paths
No full textsummary:A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof of Feynman's assertion