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A note on tension spline
Segeth, Karel
2015 - English
Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the results of a 1D numerical example that show the advantages and drawbacks of the tension spline.
Keywords:
smooth interpolation; tension spline; Fourier transform
Available in digital repository of the ASCR
A note on tension spline
Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization ...
Discovering the structure of word problems in teacher education
Tichá, Marie
2014 - Czech
In this paper we endeavor to show how we develop ways of improving the quality of teacher students and teachers professionalism. We continue to study the benefits and possibilities of utilization of activities connected with the problem posing. We aim at conscious respecting and implementation of the requirements that are imposed on the formulation of word problems, and especially at the awareness of the need to pay attention to the posed problems structure. V předloženém příspěvku se snažíme v návaznosti na předchozí práce ukázat, jak rozvíjíme cesty ke zkvalitňování profesionality studentů učitelství i učitelů. Pokračujeme ve studiu přínosu a možností využití činností spojených s tvořením (slovních) úloh. Jde nám o vědomé respektování a uplatňování požadavků, které jsou kladeny na formulaci slovních úloh a o uvědomení si potřeby věnovat pozornost struktuře vytvářených úloh.
Keywords:
professionalism; inquiry based education; problem posing; structure of problem
Available on request at various institutes of the ASCR
Discovering the structure of word problems in teacher education
In this paper we endeavor to show how we develop ways of improving the quality of teacher students and teachers professionalism. We continue to study the benefits and possibilities of utilization of ...
Preliminary results on Type I and II Kaluza–Klein reductions of vacuum spacetimes
Tintěra, Tomáš
2014 - English
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.
Keywords:
algebraic classification; high-dimensional spacetime; vacuum
Available on request at various institutes of the ASCR
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 ...
Seven forms of inquiry-based mathematics teaching
Roubíček, Filip
2014 - Czech
The paper is the second part of triple series that deals with the clarification of substance of inquiry-based mathematics teaching. This part is focused on geometrical environments that are based on modelling and enable to generate tasks with different difficulty. It describes three forms of inquiry-based mathematics teaching - three types of tasks which are classified according to the character of inputs: compact, visualized and given by environment. Článek je druhou částí třídílné série, která se zabývá vyjasněním podstaty badatelsky orientovaného vyučování. Tato část je zaměřena na geometrická prostředí, která jsou založena na modelování a která umožňují generovat úlohy různé obtížnosti. Popisuje tři podoby badatelsky orientovaného vyučování matematice - tři typy úloh klasifikovaných podle charakteru vstupních informací: kompaktní, vizualizovaná a daná prostředím.
Keywords:
inquiry-based mathematics teaching; geometrical environment; modelling
Available at various institutes of the ASCR
Seven forms of inquiry-based mathematics teaching
The paper is the second part of triple series that deals with the clarification of substance of inquiry-based mathematics teaching. This part is focused on geometrical environments that are based on ...
Problem solving and problem posing (not only in teacher training)
Hošpesová, A.; Tichá, Marie
2014 - Czech
Problem solving we can support by problem posing. The paper shows the different possibilities of problem posing (to a given calculation, to the given data or results, to given structure) and their illustrations through problems posed by students and teachers. It is outlined that problem posing can be understood as a goal of education, training and diagnostic tool and as a source of motivation. Řešení úloh můžeme podpořit tak, že řešitelé úlohy také tvoří. V příspěvku jsou ukázány různé možnosti tvoření úloh (k danému výpočtu, se zadanými údaji nebo výsledkem, určené struktury) a jejich ilustrace pomocí úloh vytvořených studenty učitelství. Je naznačeno, že tvoření úloh lze chápat jako cíl vzdělávání, vzdělávací a diagnostický prostředek a také jako zdroj motivace.
Keywords:
problem solving; problem posing; structure of problem
Available at various institutes of the ASCR
Problem solving and problem posing (not only in teacher training)
Problem solving we can support by problem posing. The paper shows the different possibilities of problem posing (to a given calculation, to the given data or results, to given structure) and their ...
Seven forms of inquiry-based mathematics teaching III
Tichá, Marie; Hošpesová, A.
2014 - Czech
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. 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.
Keywords:
inquiry based teaching; substantial learning environments; problem posing
Available at various institutes of the ASCR
Seven forms of inquiry-based mathematics teaching III
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 ...
Posing problems with a given structure
Tichá, Marie; Hošpesová, A.
2014 - Czech
In the contribution we present ongoing research findings concerning benefits of the activities connected with problem posing in education of teachers and student teachers as a way improving their professional skills. We remind (recall, commemorate) diagnostic, educational and motivational benefits of these activities. We justify (substantiate) the need to consciously pay attention to the structure of posed problems. V článku ukazujeme výsledky probíhajícího výzkumu přínosu činností spojených s tvořením úloh do vzdělávání jak učitelů, tak studentů učitelství jako jedné z cest zkvalitňování jejich profesních kompetencí. Připomínáme diagnostický, vzdělávací a motivační přínos těchto činností. Zdůvodňujeme potřebu vědomě věnovat pozornost struktuře vytvářených úloh.
Keywords:
education of teachers; improving professional skills; problem posing
Available at various institutes of the ASCR
Posing problems with a given structure
In the contribution we present ongoing research findings concerning benefits of the activities connected with problem posing in education of teachers and student teachers as a way improving their ...
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 ...
Geometrical constructions and regular mosaics
Roubíček, Filip
2014 - Czech
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. 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.
Keywords:
teaching of geometry; tesselation; modelling
Available on request at various institutes of the ASCR
Geometrical constructions and regular mosaics
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 ...
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 ...
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