Number of found documents: 64
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The role of Sommerville tetrahedra in numerical mathematics
Hošek, Radim
2017 - English
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by its direct generalization to any dimension. Keywords: simplicial tessellations; simplicial mesh; Sommerville tetrahedron Available in digital repository of the ASCR
The role of Sommerville tetrahedra in numerical mathematics

In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine ...

Hošek, Radim
Matematický ústav, 2017

A particular smooth interpolation that generates splines
Segeth, Karel
2017 - English
There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $it smooth interpolation$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline. Keywords: data interpolation; smooth interpolation; spline interpolation Available in digital repository of the ASCR
A particular smooth interpolation that generates splines

There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one ...

Segeth, Karel
Matematický ústav, 2017

Cosmology on Small Scales 2016: Local Hubble Expansion and Selected Controversies in Cosmology
Křížek, Michal; Dumin, Y. V.
2016 - English
The problem of cosmological expansion on small scales (e.g., inside planetary systems) has a long history, dating back to the papers (McVittie, 1932, 1933), and quite many researchers dealt with this topic in the subsequent few decades. Although most of them concluded that the Hubble expansion should be strongly suppressed at small distances, there is no commonly-established criterion for such suppression at present. Moreover, some of the widely-used theoretical arguments against the local Hubble expansion contradict each other. Keywords: cosmology Fulltext is available at external website.
Cosmology on Small Scales 2016: Local Hubble Expansion and Selected Controversies in Cosmology

The problem of cosmological expansion on small scales (e.g., inside planetary systems) has a long history, dating back to the papers (McVittie, 1932, 1933), and quite many researchers dealt with this ...

Křížek, Michal; Dumin, Y. V.
Matematický ústav, 2016

Word problems of a given structure in the perspective of teacher training
Tichá, Marie; Hošpesová, A.
2016 - English
The paper reports on the results of a research study focusing on how to train prospective teachers for guiding their pupils through the process of solving word problems. The teaching experiment involved prospective teachers’ work with graphical representations called branched chains to solve and pose word problems. The paper shows the difficulties the students were facing, presents ideas from discussions during joint reflection, tries to describe the changes in the students’ skills and attitudes. It also points at the differences between prospective primary and secondary mathematics teachers. Keywords: inquiry based mathematics education; prospective teaching training; subject matter knowledge; knowledge base for teaching Fulltext is available at external website.
Word problems of a given structure in the perspective of teacher training

The paper reports on the results of a research study focusing on how to train prospective teachers for guiding their pupils through the process of solving word problems. The teaching experiment ...

Tichá, Marie; Hošpesová, A.
Matematický ústav, 2016

On the Friedmann equation for the three-dimensional hypersphere
Křížek, Michal; Mészáros, A.
2016 - English
The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an expanding threedimensional sphere which enabled him to avoid boundary conditions. However, his description was very brief. Therefore, the main objective of this article is to detailed a derivation of the Friedmann equation for an unknown expansion function a = a(t) representing the radius of the universe. Furthermore, we present serious arguments showing why the validity of Einstein’s equations should not be extrapolated to the entire universe. Keywords: Einstein's equations; standard cosmological model; dark matter; dark energy Available in digital repository of the ASCR
On the Friedmann equation for the three-dimensional hypersphere

The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an ...

Křížek, Michal; Mészáros, A.
Matematický ústav, 2016

Developing open approach to mathematics in future primary school teachers
Samková, L.; Tichá, Marie
2016 - English
In our contribution we focus on the possibility to develop open approach to mathematics in future primary school teachers during a university course on mathematics conducted in inquiry-based manner. We analyse data obtained in the beginning and in the end of the course with respect to two main aspects related to open approach to mathematics: searching for all solutions of a task, and acceptance of different forms of notation of a given solution. Data analysis revealed in the participants three different shifts towards open approach to mathematics, and showed that after the active participation in the course each of the participants improved at least in one of the monitored aspects, and that none of the participants got worse in any of the aspects. Keywords: argumentaion; concept Cartoons; future primary school teachers; inquiry-based Fulltext is available at external website.
Developing open approach to mathematics in future primary school teachers

In our contribution we focus on the possibility to develop open approach to mathematics in future primary school teachers during a university course on mathematics conducted in inquiry-based manner. ...

Samková, L.; Tichá, Marie
Matematický ústav, 2016

O některých miskoncepcích souvisejících se schopností argumentovat
Samková, L.; Tichá, Marie
2016 - Czech
Příspěvek se zaměřuje na různé způsoby prokazování pravdivosti obecných tvrzení (odkazy na autoritu, různé typy empirických argumentů, deduktivní argumenty). Podrobně sleduje argumentační schopnosti budoucích učitelů 1. Stupně ZŠ, zmiňuje často se vyskytující miskoncepce. Jako možnou cestu ke zlepšení argumentačních schopností nabízí badatelsky orientované vyučování. The contribution focuses on various ways of proving general statements (external convictions, various types of empirical arguments, deductive arguments). We observe in details argumentation skills of future primary school teachers, and mention often occurring misconceptions. We offer inquiry-based education as a possible way to development of argumentation skills. Keywords: general statements; argumentation skills; inqiry-based education Fulltext is available at external website.
O některých miskoncepcích souvisejících se schopností argumentovat

Příspěvek se zaměřuje na různé způsoby prokazování pravdivosti obecných tvrzení (odkazy na autoritu, různé typy empirických argumentů, deduktivní argumenty). Podrobně sleduje argumentační schopnosti ...

Samková, L.; Tichá, Marie
Matematický ústav, 2016

Numerical modeling of magnetostrictive materials
Kholmetska, I.; Chleboun, J.; Krejčí, Pavel
2016 - English
An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density function. The uncertainty is modeled through a fuzzy set approach. In galfenol, an alloy of gallium and iron, however, the hysteresis phenomenon is present only weakly. This allows to propose a simpler, but computationally faster model without hysteresis. The new, simpler model has been identified from the measured magnetic and magnetostrictive cycles. The amount of harvested energy is of the same order in both models. Again, an uncertainty in the identified model can be considered and its impact on the amount of the harvested energy calculated. Keywords: magnetostrictive materials; hysteresis; energy harvesting Available in digital repository of the ASCR
Numerical modeling of magnetostrictive materials

An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density ...

Kholmetska, I.; Chleboun, J.; Krejčí, Pavel
Matematický ústav, 2016

Anthropic principle and the local Hubble expansion
Křížek, Michal; Somer, L.
2016 - English
We claim that a local expansion of the universe, whose rate is comparable with the Hubble constant H0, had an essential influence on the development of intelligent life on the Earth. We present more than 10 examples showing that some antigravitational effects of the cosmological constant are observable locally in the Solar system. It is known that the luminosity of the Sun increased approximately linearly within the last 4.5Gyr starting at 70% of its present value. We give several independent arguments showing that the average Earth-Sun distance increases about 5m/yr due to antigravitational forces and such a large recession speed cannot be explained by solar wind, tidal forces, plasma outbursts from the Sun, or by the decrease of the Solar mass due to nuclear reactions. Models based on Newtonian mechanics can explain only a few cm per year. Keywords: antigravity; habitable zone; law of conservation of energy Available in digital repository of the ASCR
Anthropic principle and the local Hubble expansion

We claim that a local expansion of the universe, whose rate is comparable with the Hubble constant H0, had an essential influence on the development of intelligent life on the Earth. We present more ...

Křížek, Michal; Somer, L.
Matematický ústav, 2016

Programs and Algorithms of Numerical Mathematics 17 : Dolní Maxov, June 8-13, 2014 : Proceedings of Seminar
Chleboun, J.; Přikryl, Petr; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
2015 - English
This volume comprises peer-reviewed papers that are based on invited lectures, survey lectures, short communications, and posters presented at the 17th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Dolní Maxov, Czech Republic, June 8–13, 2014. The seminar was organized by the Institute of Mathematics of the Academy of Sciences of the Czech Republic. It continued the previous seminars on mathematical software and numerical methods held (with only one exception) biannually in\nAlšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, and Prague in the period 1983–2012. The objective of this series of seminars is to provide a forum for presenting and discussing advanced topics in numerical analysis, singleor multi-processor applications of computational methods, and new approaches to mathematical modeling. Keywords: numerical mathematics Available in digital repository of the ASCR
Programs and Algorithms of Numerical Mathematics 17 : Dolní Maxov, June 8-13, 2014 : Proceedings of Seminar

This volume comprises peer-reviewed papers that are based on invited lectures, survey lectures, short communications, and posters presented at the 17th seminar Programs and Algorithms of Numerical ...

Chleboun, J.; Přikryl, Petr; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš
Matematický ústav, 2015

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