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Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence
Caggio, Matteo; Bodnár, Tomáš
2017 - anglický
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.
Klíčová slova:
Camassa-Holm equations; turbulent boundary layer
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence
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 ...
Error patterns in computation in concept cartoons
Samková, L.; Tichá, Marie; Hošpesová, A.
2015 - anglický
The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to prepare Concept Cartoons displaying various mental computation strategies and error patterns.
Klíčová slova:
concept Cartoons; error patterns; mental computation strategies
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
Error patterns in computation in concept cartoons
The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to ...
Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task
Roubíček, Filip
2015 - anglický
The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster describes communicative situations in solving of inquiry based problems and presents examples of pupils’ solutions and discussion in the classroom.
Klíčová slova:
inquiry based education; teaching of geometry; problem solving; mathematical discourse
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task
The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster ...
Separable reductions and rich families in theory of Fréchet subdifferentials
Fabian, Marián
2015 - anglický
We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; all statements being considered in Fréchet sense. Given a nonseparable Banach space X, we show how the validity of these statements is implied by the validity of them in every separable subspace of X. Such a reasoning is called “separable reduction”. We show that, behind this approach, there is a modern and powerful concept of rich subfamily of the family of all separable subspaces of X.
Klíčová slova:
Fréchet subdifferentials
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
Separable reductions and rich families in theory of Fréchet subdifferentials
We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; ...
Talk about patterns in the mathematics classroom
Roubíček, Filip
2015 - anglický
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical patterns in a triangle grid and their transformation into arithmetic patterns or algebraic functions. It shows how pupils/students reason about relationships in these patterns and among these patterns, how they describe and express their generalizations in words or symbols.
Klíčová slova:
discourse; mathematics classroom; patterns
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
Talk about patterns in the mathematics classroom
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical ...
How primary school teachers posed problems for inquiry based mathematics education
Hošpesová, A.; Samková, L.; Tichá, Marie; Roubíček, Filip
2015 - anglický
The paper reports on a survey whose aim is to contribute to the research in the area of inquiry based mathematics education (IBME), primary school teacher training, and problem posing. The core of the study is an empirical survey with a qualitative design. We let pre-service and in-service primary school teachers pose problems which they believe enable IBME, perform the problems with pupils, and write self-reflections on this activity. We investigated the nature of the posed problems in relation to the self-reflections.
Klíčová slova:
inquiry based mathematics education; posing problems; primary school teacher training; pre-service and in-service teachers
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
How primary school teachers posed problems for inquiry based mathematics education
The paper reports on a survey whose aim is to contribute to the research in the area of inquiry based mathematics education (IBME), primary school teacher training, and problem posing. The core of the ...
Preliminary results on Type I and II Kaluza–Klein reductions of vacuum spacetimes
Tintěra, Tomáš
2014 - anglický
We review the formalism used for the algebraic classification of higher- dimensional spacetimes, together with a few basic results in this field. Then we use this formalism to discuss some problems involving type I and II Kaluza–Klein reductions of vacuum spacetimes and to present a few results.
Klíčová slova:
algebraic classification; high-dimensional spacetime; vacuum
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
Preliminary results on Type I and II Kaluza–Klein reductions of vacuum spacetimes
We review the formalism used for the algebraic classification of higher- dimensional spacetimes, together with a few basic results in this field. Then we use this formalism to discuss some problems ...
Posing problems with a given structure by pre-service teachers
Hošpesová, A.; Tichá, Marie
2013 - anglický
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.
Klíčová slova:
teachers' knowledge; scheme; structure of problem
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
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) ...
Spectral methods for reaction-diffusion systems
Rybář, Vojtěch
2013 - anglický
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.
Klíčová slova:
reaction-diffusion system
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
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 ...
The search for ways of enhancement of knowledge base for teaching
Tichá, Marie
2011 - anglický
Poster shows a problem posing as a significant way to improving teachers' knowledge. The presentation focused on the division of fractions. The presentation displayed examples of common misconceptions and their probable cause.
Klíčová slova:
teachers' competence; teachers' knowledge; problem posing
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
The search for ways of enhancement of knowledge base for teaching
Poster shows a problem posing as a significant way to improving teachers' knowledge. The presentation focused on the division of fractions. The presentation displayed examples of common misconceptions ...
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