Matematický ústav

Nejnovější přírůstky:
2017-10-30
13:46
Observing how future primary school teachers reason about fractions
Samková, L. ; Tichá, Marie
The contribution focuses on the possibility to use an educational tool called Concept Cartoons in future primary school teachers' education, especially as an instrument for observing how future primary school teachers reason about fractions. The task which we adapted to the Concept Cartoons form belongs to primary school mathematics, i.e. it focuses on the concept of a fraction per se, in particular on the parts-and-whole decision and on comparison of two pre-partitioned models with diverse wholes. Using Concept Cartoons, we observe which statements about the issue our respondents consider as correct, and which kinds of reasoning they use in their justifications. We also mention other related concepts (percentages), and related tasks from entrance exams to lower-secondary selective schools.

Úplný záznam
2017-08-31
14:50
Some practical aspects of parallel adaptive BDDC method
Šístek, Jakub ; Mandel, J. ; Sousedík, B.
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may represent one class of such challenging problems. The adaptive selection of constraints is shown to significantly increase the robustness of the method for this class of problems. However, since the cost of the set-up of the preconditioner with adaptive constraints is considerably larger than for the standard choices, computational feasibility of the presented implementation is obtained only for large contrasts of material coefficients.

Úplný záznam
2017-07-03
17:28
A particular smooth interpolation that generates splines
Segeth, Karel
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.

Úplný záznam
2017-07-03
17:28
The role of Sommerville tetrahedra in numerical mathematics
Hošek, Radim
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.

Úplný záznam
2017-02-23
15:49
On the boundary conditions in the numerical simulation of stably stratified fluids flows
Bodnár, Tomáš ; Fraunié, P.
This paper presents the results of a numerical study of the stably stratified flow over a low smooth hill. The emphasize is on certain problems related to artificial boundary conditions used in the numerical simulations. The numerical results of three-dimensional simulations are shown for a range of Froude and Reynolds numbers in order to demonstrate the varying importance of these boundary issues in different flow regimes. The simulations were performed using the Boussinesq approximation model solved by a high-resolution numerical code. The in-house developed code is based on compact finite-difference discretization in space and Strong Stability Preserving Runge–Kutta time integration.

Úplný záznam
2017-02-23
15:49
Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence
Caggio, Matteo ; Bodnár, Tomáš
The aim of this short communication is to briefly introduce the Camassa-Holm equations as a working model for simulation of incompressible fluid turbulence. In particular we discuss its application for turbulent boundary layer flows. This model (and related models) is studied for several years in mathematical community, starting from Leray [23]. It can be understood as a generalization of some classical fluid models (Navier-Stokes equations, Prandtl boundary layer equations), showing some interesting mathematical properties in the analysis of the behavior of it's solution (e.g. Layton and Lewandowski [22]). It has been found however, that the model predictions can lead to surprising extensions of the use of the model in technical applications, namely in simulating the turbulent fluid flows. This brief paper should be understood as an introductory note to this novel class of models for applied scientists.

Úplný záznam
2017-02-23
15:49
Note on the problem of dissipative measure-valued solutions to the compressible non-Newtonian system
Al Baba, Hind ; Caggio, Matteo ; Ducomet, B. ; Nečasová, Šárka
We introduce a dissipative measure-valued solution to the compressible non-Newtonian system. We generalized a result given by Novotný, Nečasová [14]. We derive a relative entropy inequality for measure-valued solution as an extension of the "classical" entropy inequality introduced by Dafermos [2], Mellet-Vasseur [11], Feireisl-Jin-Novotný [5].

Úplný záznam
2017-01-11
17:39
O některých miskoncepcích souvisejících se schopností argumentovat
Samková, L. ; Tichá, Marie
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.

Úplný záznam
2017-01-11
17:39
Znovuobjevování geometrických konstrukcí
Roubíček, Filip
Článek je věnován uplatnění principů badatelsky orientovaného vyučování matematice v didaktickém semináři určeném studentům učitelství prvního stupně základní školy, konkrétně aktivitě zaměřené na konstruování známých geometrických útvarů v prostředí překládaného papíru. V článku je popsáno sedm studentských postupů konstrukce čtverce.

Úplný záznam
2017-01-04
16:16
Developing open approach to mathematics in future primary school teachers
Samková, L. ; Tichá, Marie
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.

Úplný záznam