**391**

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**Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings**

Recke, L.; Väth, Martin; Kučera, Milan; Navrátil, J.

2017 - English
We consider abstract equations of the type ..., where lambda is a bifurcation parameter and tau is a perturbation parameter. We suppose that ... for all lambda and tau, F is smooth and the unperturbed equation ... describes a Crandall-Rabinowitz bifurcation in lambda=0, that is, two half-branches of nontrivial solutions bifurcate from the trivial solution in lambda=0. Concerning G, we suppose only a certain Lipschitz condition; in particular, G is allowed to be non-differentiable. We show that for fixed small ... there exist also two half-branches of nontrivial solutions to the perturbed equation, but they bifurcate from the trivial solution in two bifurcation points, which are different, in general. Moreover, we determine the bifurcation directions of those two half-branches, and we describe, asymptotically as ..., how the bifurcation points depend on tau. Finally, we present applications to boundary value problems for quasilinear elliptic equations and...
Keywords:
*nonsmooth equation; Lipschitz bifurcation branch; formula for the bifurcation direction*
Available on request at various institutes of the ASCR
Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings

We consider abstract equations of the type ..., where lambda is a bifurcation parameter and tau is a perturbation parameter. We suppose that ... for all lambda and tau, F is smooth and the unperturbed ...

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**Clusterization of correlation functions**

Zuevsky, Alexander

2017 - English
Using the Zhu recursion formulas for correlation functions for vertex operator algebras, we introduce a cluster algebra structure over a non-commutative set of variables.
Keywords:
*vertex algebras; correlation functions; cluster algebras*
Available on request at various institutes of the ASCR
Clusterization of correlation functions

Using the Zhu recursion formulas for correlation functions for vertex operator algebras, we introduce a cluster algebra structure over a non-commutative set of variables.

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**Problem posing in prospective primary school teachers´ education: Case of Concept Cartoons**

Hošpesová, A.; Tichá, Marie

2017 - English
The presentation will discuss creation of Concept Cartoons as a possible way to support the development and refinement of prospective primary teachers' pedagogical concept knowledge.
Keywords:
*problem posing; Concept Cartoons; PCK of prospective teachers*
Available on request at various institutes of the ASCR
Problem posing in prospective primary school teachers´ education: Case of Concept Cartoons

The presentation will discuss creation of Concept Cartoons as a possible way to support the development and refinement of prospective primary teachers' pedagogical concept knowledge.

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**On the boundary conditions in the numerical simulation of stably stratified fluids flows**

Bodnár, Tomáš; Fraunié, P.

2017 - English
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.
Keywords:
*Boussinesq approximation; stable stratification; compact finite-difference*
Available on request at various institutes of the ASCR
On the boundary conditions in the numerical simulation of stably stratified fluids flows

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 ...

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**Higher dimensional Robinson-Trautman spacetimes sourced by p-forms: static and radiating black holes**

Ortaggio, Marcello; Podolský, J.; Žofka, M.

2017 - English
We summarize results about Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n >= 4 dimensions. While in odd dimensions the solutions reduce to static black holes dressed with an electric and a magnetic field (with an Einstein space horizon), in even dimensions 2p = n they may also describe black holes gaining (or losing) mass by receiving (or emitting) electromagnetic radiation. The Weyl type of the spacetimes is also briefly discussed in all the possible cases.
Keywords:
*Robinson-Trautman spacetimes; p-form fields; black holes*
Available on request at various institutes of the ASCR
Higher dimensional Robinson-Trautman spacetimes sourced by p-forms: static and radiating black holes

We summarize results about Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n >= 4 dimensions. While in odd dimensions the ...

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**On type N and III universal spacetimes**

Hervik, S.; Pravda, Vojtěch; Pravdová, Alena

2017 - English
We briefly summarize our recent results on type N and III universal spacetimes.
Keywords:
*generalized theories of gravity; universal spacetimes*
Available on request at various institutes of the ASCR
On type N and III universal spacetimes

We briefly summarize our recent results on type N and III universal spacetimes.

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**On type II universal spacetimes**

Hervik, S.; Málek, Tomáš; Pravda, Vojtěch; Pravdová, Alena

2017 - English
We briefly summarize our recent results on type II universal metrics of the Lorentzian signature. These metrics simultaneously solve all vacuum field equations of theories of gravity with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order. It turns out that the results critically depend on the dimensionality of the spacetime. While we discuss examples of type II universal metrics for all composite number dimensions, we have no examples for prime number dimensions. Furthermore, we have proven the non-existence of type II universal spacetimes in five dimensions.
Keywords:
*generalized theories of gravity; universal spacetimes*
Available on request at various institutes of the ASCR
On type II universal spacetimes

We briefly summarize our recent results on type II universal metrics of the Lorentzian signature. These metrics simultaneously solve all vacuum field equations of theories of gravity with the ...

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**The effect of irregular interfaces on the BDDC method for the Navier-Stokes equations**

Hanek, M.; Šístek, Jakub; Burda, P.

2017 - English
We investigate the effect of interface irregularity on the convergence of the BDDC method for Navier-Stokes equations. A benchmark problem of a sequence of contracting channels is proposed to evaluate the robustness of the iterative solver with respect to element aspect ratios at the interface. Partitioners based on graph of the mesh and the geometry of the domain are compared. It is shown, that the convergence is significantly improved by avoiding irregular interfaces for the benchmark problem as well as for an industrial problem of oil flow in hydrostatic bearing.
Keywords:
*Navier Stokes equations; domain decomposition methods; hydrostatic bearings*
Available at various institutes of the ASCR
The effect of irregular interfaces on the BDDC method for the Navier-Stokes equations

We investigate the effect of interface irregularity on the convergence of the BDDC method for Navier-Stokes equations. A benchmark problem of a sequence of contracting channels is proposed to evaluate ...

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**Observing how future primary school teachers reason about fractions**

Samková, L.; Tichá, Marie

2017 - English
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.
Keywords:
*concept Cartoons; fractions; future primary school teachers*
Available at various institutes of the ASCR
Observing how future primary school teachers reason about fractions

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 ...

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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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