**90**

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**Artificial far-field pressure boundary conditions for wall-bounded stratified flows**

Bodnár, Tomáš; Fraunié, P.

2018 - English
This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions on the arti cial boundaries of the computational domain. The simple three dimensional test case deals with the steady flow of an incompressible, variable density fluid over a low smooth model hill. The Boussinesq approximation model is solved by an in-house developed high-resolution numerical code, based on compact finite-difference discretization in space and Strong Stability Preserving Runge-Kutta method for (pseudo-) time stepping.
Keywords:
*Boussinesq approximation; stable stratification; compact finite-difference; pressure boundary condition*
Available in digital repository of the ASCR
Artificial far-field pressure boundary conditions for wall-bounded stratified flows

This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions ...

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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 ...

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**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 ...

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**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 ...

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**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. ...

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**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 ...

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**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 ...

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**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 ...

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**Word problems of a given structure in the perspective of teacher training**

Tichá, Marie; Hošpesová, A.

2015 - 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 ...

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**Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability**

Kůs, Pavel

2015 - English
In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problém are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.
Keywords:
*convergence; finite element method; Turing instability; reaction-diffusion*
Available in digital repository of the ASCR
Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability

In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this ...

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