**364**

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**Classification of distances in cosmology**

Křížek, Michal; Mészáros, A.

2018 - English
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single natural distance, since the universe is expanding, curved, and we look back in time. In this survey paper we will concentrate on geometrical interpretations of the above-mentioned distances.
Keywords:
*standard cosmological model; cosmological principle; Friedmann equation; cosmological parameters; Einstein static universe*
Available in digital repository of the ASCR
Classification of distances in cosmology

In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single ...

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**Analysis of the turbulence parameterisations for the atmospheric surface layer**

Caggio, Matteo; Bodnár, Tomáš

2018 - English
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer in function of the stability of the atmosphere. The case of very stable conditions (strong strati cation), where theoretical approaches provide conflicting results (see Luhar et al. [11]), is analysed in detail to provide some insight into the limits of applicability for some of the most popular models of turbulence. The problem of the existence of the critical flux Richardson number is also taken into account.
Keywords:
*atmospheric boundary layer; Monin-Obukhov similarity theory; turbulence parameterisations; strong strati cation*
Available in digital repository of the ASCR
Analysis of the turbulence parameterisations for the atmospheric surface layer

The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer in function of the stability of the atmosphere. The case of ...

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**Neglected gravitational redshift in detections of gravitational waves**

Křížek, Michal; Somer, L.

2018 - English
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the authors have not taken into account a large gravitational redshift of this binary system, which is a direct consequence of time dilation in a strong gravitational field. Thus the proposed masses are overestimated. In our paper we also give other arguments for this statement.
Keywords:
*gravitational redshift; time dilatation; black holes; wavelets*
Available in digital repository of the ASCR
Neglected gravitational redshift in detections of gravitational waves

In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the ...

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**Parallel domain decomposition solver for flows in hydrostatic bearings**

Hanek, Martin; Šístek, Jakub; Burda, P.; Stach, E.

2018 - English
We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used for discretization. The arising nonlinear system of algebraic equations is linearized using the Picard’s iteration, and the Balancing Domain Decomposition based on Constraints (BDDC) method is used to solve the linear systems of equations. The solver is first validated with an experiment for the case of a bearing without motion, and it is then applied to simulation of flow in a sliding bearing.
Keywords:
*hydrostatic bearings; BDDC*
Available in digital repository of the ASCR
Parallel domain decomposition solver for flows in hydrostatic bearings

We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used ...

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**Artificial far-field pressure boundary conditions for wall-bounded stratified flows**

Bodnár, Tomáš; Fraunié, P.

2018 - English
This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions on the arti cial boundaries of the computational domain. The simple three dimensional test case deals with the steady flow of an incompressible, variable density fluid over a low smooth model hill. The Boussinesq approximation model is solved by an in-house developed high-resolution numerical code, based on compact finite-difference discretization in space and Strong Stability Preserving Runge-Kutta method for (pseudo-) time stepping.
Keywords:
*Boussinesq approximation; stable stratification; compact finite-difference; pressure boundary condition*
Available in digital repository of the ASCR
Artificial far-field pressure boundary conditions for wall-bounded stratified flows

This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions ...

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**Assessing a teacher’s competence for implementation of inquiry based mathematics education from a discussion of open geometrical situations**

Roubíček, Filip

2017 - English
The study is focused on the possibility to assess and develop primary teachers’ abilities to implement some principles of inquiry based mathematics education into their teaching practice. The requirements on a primary teacher and their competence are assessed through a joint discussion of open geometrical situations presented through Concept Cartoons. Teachers’ written comments and notes and verbal statements expressed in the discussion of four geometrical problems were analysed and presented.
Keywords:
*inguiry based mathematics education; primary teacher; elementary geometry*
Available at various institutes of the ASCR
Assessing a teacher’s competence for implementation of inquiry based mathematics education from a discussion of open geometrical situations

The study is focused on the possibility to assess and develop primary teachers’ abilities to implement some principles of inquiry based mathematics education into their teaching practice. The ...

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**Sine-Gordon model in the homogeneous higher grading**

Zuevsky, Alexander

2017 - English
A construction of equations and solutions for the sine-Gordon model in the homogeneous grading as an example of higher grading a ne Toda models are considered.
Keywords:
*soliton solutions; affine Toda modes; homogeneous sine-Gordon model*
Available on request at various institutes of the ASCR
Sine-Gordon model in the homogeneous higher grading

A construction of equations and solutions for the sine-Gordon model in the homogeneous grading as an example of higher grading a ne Toda models are considered.

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**Courant algebroid connections and string effective actions**

Jurčo, B.; Vysoký, Jan

2017 - English
Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiber-wise metric. Imposing further conditions resembling standard Levi-Civita connections, one obtains a class of connections whose curvature tensor in certain cases gives a new geometrical description of equations of motion of low energy effective action of string theory. Two examples are given. One is the so called symplectic gravity, the second one is an application to the the so called heterotic reduction. All necessary definitions, propositions and theorems are given in a detailed and self-contained way.
Keywords:
*Courant algebroid connections; low-energy effective actions; Levi-Civita connections*
Available on request at various institutes of the ASCR
Courant algebroid connections and string effective actions

Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant ...

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**Genus two prime form formula for vertex operator characters**

Zuevsky, Alexander

2017 - English
We find an expression for the self-sewn genus two Riemann surface counterpart of the torus formula for for an $n$-vertex operator character for the Heisenberg vertex operator algebra an $n$-point correlation function for a vertex operator algebra module with complex parameterization of corresponding states.
Keywords:
*prime forms; vertex operator algebras; correlation functions; prime form identities*
Available at various institutes of the ASCR
Genus two prime form formula for vertex operator characters

We find an expression for the self-sewn genus two Riemann surface counterpart of the torus formula for for an $n$-vertex operator character for the Heisenberg vertex operator algebra an $n$-point ...

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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 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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