Number of found documents: 369
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Geometrické konstrukce a pravidelné mozaiky
Roubíček, Filip
2014 - Czech
Pravidelné mozaiky představují ve vyučování geometrii vhodné prostředí pro rozvíjení geometrické představivosti a konstrukčních postupů založených na užití shodných zobrazení v rovině. Mozaiky jsou rovinné teselace, tj. pokrytí roviny (většinou shodnými) útvary bez mezer a překrytí. Konstrukce geometrické mozaiky vychází z tvaru dlaždic a jejich uspořádání. Rozbor mozaiky je založen na identifikaci její sítě a konstrukce dlaždic. In the teaching of geometry regular mosaics represent a suitable environment for developing of geometrical imagination and constructing procedures based on the use of isometries in plane. Mosaics are plane tesselations, i.e. coverages of plane by (in most case identical) shapes without gaps and overlaps. The construction of a geometrical mosaic follows from a shape of tiles and their assembling. Analyse of a mosaics is based on identification of its grid and a construction of tiles. Keywords: teaching of geometry; tesselation; modelling Available at various institutes of the ASCR
Geometrické konstrukce a pravidelné mozaiky

Pravidelné mozaiky představují ve vyučování geometrii vhodné prostředí pro rozvíjení geometrické představivosti a konstrukčních postupů založených na užití shodných zobrazení v rovině. Mozaiky jsou ...

Roubíček, Filip
Matematický ústav, 2014

Sedm podob badatelsky orietovaného vyučování matematice III
Tichá, Marie; Hošpesová, A.
2014 - Czech
Cílem článku je pomocí konkrétních příkladů vyjasnit představu, jak chápeme badatelsky orientované vyučování matematice. Navazujeme v něm také na příspěvek Pravidelnosti a závislosti jako prostředí pro badatelsky orientované vyučování, který byl prosloven na Setkání v roce 2012, a rozvíjíme a prohlubujeme myšlenky prezentované ve zmíněném příspěvku. This article aims at using particular examples to clarify an idea of how we understand inquiry based mathematics teaching. It follows up on the contribution Regularities and dependences as an environment for inquiry-based education, which was published in the proceedings of the Setkání in 2012, and to develop and deepen the ideas presented in that contribution. Keywords: inquiry based teaching; substantial learning environments; problem posing Available at various institutes of the ASCR
Sedm podob badatelsky orietovaného vyučování matematice III

Cílem článku je pomocí konkrétních příkladů vyjasnit představu, jak chápeme badatelsky orientované vyučování matematice. Navazujeme v něm také na příspěvek Pravidelnosti a závislosti jako prostředí ...

Tichá, Marie; Hošpesová, A.
Matematický ústav, 2014

Variability of Turing patterns in reaction-diffusion systems
Rybář, Vojtěch; Vejchodský, Tomáš
2014 - English
The paper presents a result about the number of distinct stationary solutions of a reaction-diffusion system exhibing the Turing instability. Relative frequency of observed solutions as they evolve from random initial conditions is analysed as well. Keywords: diffusion driven instability; uniqueness; number of solutions Fulltext is available at external website.
Variability of Turing patterns in reaction-diffusion systems

The paper presents a result about the number of distinct stationary solutions of a reaction-diffusion system exhibing the Turing instability. Relative frequency of observed solutions as they evolve ...

Rybář, Vojtěch; Vejchodský, Tomáš
Matematický ústav, 2014

Posing problems with a given structure by pre-service teachers
Hošpesová, A.; Tichá, Marie
2013 - English
Posing problems of given structure is considered as a way of fostering teachers’ competence. We work with schemas from two perspectives: (a) schema as visualization of process of problem solving, (b) schema as representation of the structure of problem. We focused on the question: What problems do students pose if they are given a branched chain which represents the structure problem or solving procedure? Findings of ongoing research from work with teacher students are given. Keywords: teachers' knowledge; scheme; structure of problem Available at various institutes of the ASCR
Posing problems with a given structure by pre-service teachers

Posing problems of given structure is considered as a way of fostering teachers’ competence. We work with schemas from two perspectives: (a) schema as visualization of process of problem solving, (b) ...

Hošpesová, A.; Tichá, Marie
Matematický ústav, 2013

On simplicial red refinement in three and higher dimensions
Korotov, S.; Křížek, Michal
2013 - English
We show that in dimensions higher than two, the popular “red refinement” tech- nique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original one. Keywords: red refinement; finite element analysis Fulltext is available at external website.
On simplicial red refinement in three and higher dimensions

We show that in dimensions higher than two, the popular “red refinement” tech- nique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never ...

Korotov, S.; Křížek, Michal
Matematický ústav, 2013

Analytical solution of rotationally symmetric Stokes flow near corners
Burda, P.; Novotný, Jaroslav; Šístek, Jakub
2013 - English
We present analytical solution of the Stokes problem in rotationally symmetric domains. This is then used to find the asymptotic behaviour of the solution in the vicinity of corners, also for Navier-Stokes equations. We apply this to construct very precise numerical finite element solution. Keywords: Stokes problem; rotationally symmetric domains Fulltext is available at external website.
Analytical solution of rotationally symmetric Stokes flow near corners

We present analytical solution of the Stokes problem in rotationally symmetric domains. This is then used to find the asymptotic behaviour of the solution in the vicinity of corners, also for ...

Burda, P.; Novotný, Jaroslav; Šístek, Jakub
Matematický ústav, 2013

Spectral methods for reaction-diffusion systems
Rybář, Vojtěch
2013 - English
Although spectral methods proved to be numerical methods that can significantly speed up the computation of solutions of systems of reaction-diffusion equations, finite difference and finite element methods still prevail as the most widespread methods. This contribution offers comparison of the performance of the Fourier spectral method with finite element method for reaction-diffusion system modeling the generation of pigment patterns on the coat of the leopard. Keywords: reaction-diffusion system Available at various institutes of the ASCR
Spectral methods for reaction-diffusion systems

Although spectral methods proved to be numerical methods that can significantly speed up the computation of solutions of systems of reaction-diffusion equations, finite difference and finite element ...

Rybář, Vojtěch
Matematický ústav, 2013

On selection of interface weights in domain decomposition methods
Čertíková, M.; Šístek, Jakub; Burda, P.
2013 - English
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem. Keywords: BDDC method Fulltext is available at external website.
On selection of interface weights in domain decomposition methods

Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included ...

Čertíková, M.; Šístek, Jakub; Burda, P.
Matematický ústav, 2013

A direct solver for finite element matrices requiring O(N log N) memory places
Vejchodský, Tomáš
2013 - English
We present a method that in certain sense stores the inverse of the stiffness matrix in O(N log N) memory places, where N is the number of degrees of freedom and hence the matrix size. The setup of this storage format requires O(N^(3/2)) arithmetic operations. However, once the setup is done, the multiplication of the inverse matrix and a vector can be performed with O(N log N) operations. This approach applies to the first order finite element discretization of linear elliptic and parabolic problems in triangular domains, but it can be generalized to higher-order elements, variety of problems, and general domains. The method is based on a special hierarchical enumeration of vertices and on a hierarchical elimination of suitable degrees of freedom. Therefore, we call it hierarchical condensation of degrees of freedom. Keywords: stiffness matrix; efficient Fulltext is available at external website.
A direct solver for finite element matrices requiring O(N log N) memory places

We present a method that in certain sense stores the inverse of the stiffness matrix in O(N log N) memory places, where N is the number of degrees of freedom and hence the matrix size. The setup of ...

Vejchodský, Tomáš
Matematický ústav, 2013

O diferenciálních rovnicích a prostorech funkcí
Kufner, Alois
2013 - Czech
Řešení každé diferenciální rovnice se hledá v nějaké třídě (prostoru) funkcí. Tento prostor je určen jednak požadavky, kladenými na řešení, jednak základními daty rovnice. Příspěvek by měl ukázat vzájemnou souvislost obou objektů - rovnice a prostoru. The paper explains (mainly on examples)the mutual connection between differential equations and the corresponding function spaces, depending on the type and data of the equation. Keywords: diferential equations; classical solutions; weak solutions; diferenciální rovnice; funkční prostory Available at various institutes of the ASCR
O diferenciálních rovnicích a prostorech funkcí

Řešení každé diferenciální rovnice se hledá v nějaké třídě (prostoru) funkcí. Tento prostor je určen jednak požadavky, kladenými na řešení, jednak základními daty rovnice. Příspěvek by měl ukázat ...

Kufner, Alois
Matematický ústav, 2013

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