In this work, we study geometrical and physical properties of exact spacetimes that belong to non-expanding Pleba'nski-Demia'nski class. It is a family of solutions of type D that also belong to the Kundt class, and contain seven arbitrary parameters including a cosmological constant. We present here the results of three extensive articles, each focusing on a different aspect of the problem. In the first article, we investigate the meaning of individual parame- ters in the non-expanding Pleba'nski-Demia'nski metric. First, we set almost all parameters to zero and obtain Minkowski and (anti-)de Sitter backgrounds. Af- terwards, we allow other parameters to be non-zero and we study the B-metrics, non-singular "anti-NUT" solutions and conclude with the full electrovacuum Pleba'nski-Demia'nski metric. In the second article, we focus on the de Sitter and anti-de Sitter backgrounds where we present and analyse 11 new diagonal metric forms of (anti-)de Sitter spacetime. We find five-dimensional parametriza- tions, draw coordinate surfaces and conformal diagrams. In the third article, we show that the AII-metric together with the BI-metric describes gravitational field around a tachyon on both Minkowski and (anti-)de Sitter backgrounds. Fi- nally, in order to better understand the global structure and...

This Master's thesis discusses the Problem - based learning as one of the constructive teaching concept methods, it's position in the system of teaching methods and the possible uses in primary school regard to the key competencies of solving the problems. This theme is very actual because of the influence in the real life. The objectives of the Master's thesis is to define the basic concept of the Problem-based learning (problem, problematic situations, types of the problematic tasks and the way of their solving), key competencies and appropriate organizational forms of the teaching. The objective of the practical level is to define the principles of the effective use of this method in teaching, to verify the possibilities of uses of the Problem-based learning and focus on the way of fulfilling of the key competencies of solving the problems using various organizational forms of teaching. The thesis contains the empirical and theoretical part. The empirical part comes from the analysis and the comparation of the study of the vocational literature. This part focuses on the research as the method of achieving the goals. The research uses two basic methods; the method of the observation of the pupils during their work and method of the collection and analysis of the outcome of the pupils work. The...

Stochastic partial differential equations have proven useful in many applied areas of mathematics, such as physics or mathematical finance. A major part of such equations consists of linear equations with additive noise. In certain cases, however, the drift part of the differential equation additionally contains a possibly problematic non-linear term, which makes it unsolvable by the standard methods and even a solution in the mild sense may be out of reach. In such situations, we may still find a solution in the weak sense by employing a suitable transformation of the probability space. This thesis deals with semilinear stochastic evolution equations in a separable Hilbert space, where the driving process is an element of a large class of processes - so called Volterra processes, which can be understood as a generalisation of the Wiener process and may be of use to model a wide range of phenomena. The weak solutions, however, have been studied so far only for equations with the cylindrical fractional Brownian motion as the driving process. In this thesis, we introduce a generalisation of the Girsanov theorem for cylindrical Gaussian Volterra processes and give, in full generality, sufficient conditions for the existence of a weak solution and the uniqueness of the equation in law. Further, we introduce...

Internal gravity waves (GWs) are an important component of the atmospheric dynamics, significantly affecting the middle atmosphere by momentum and energy transport and deposition. In order to be able to improve global circulation models, in which the majority of the GW spectrum is not resolved, it is necessary to quantify their effects as precise as possible. We study GWs in a high-resolution simulation of the WRF model around Southern Andes, Antarctic Peninsula and South Georgia Island. We analyse a Gaussian high-pass filter method for separation of GWs from the basic flow. To overcome an observed problem of dependence of the method on a cutoff parameter, we propose an improved method that determines the parameter at each time step from the horizontal kinetic energy spectrum. The differences between the methods are further examined using the horizontal kinetic energy spectrum, vertical potential energy spectrum and forcing to the divergence equation evaluated by the active wind method, which is a recent theory-based method that divides the flow into a balanced flow and a perturbation field. The results suggest that the high-pass filter method does not produce correct results for time periods with strong wave activity.

The thesis deals with the question of Egypt's role of a biased mediator towards the Palestinian side in the Israeli-Palestinian conflict, and its stabilising effects on the region in the form of a case study applying the theory of a biased mediator in conflict resolution on the Egyptian example. In addition to this, the goal of this thesis is to demonstrate the beneficial effects of different forms of mediation activities and their combination, including biased and neutral mediation, in the transformation of intractable and protracted conflicts into their tractable form, using the example of the Israeli-Palestinian conflict. The identification of Egypt's positive role in contributing to the resolving of the Israeli-Palestinian conflict, of which it was once a warrying party, portrays the transformational capacity of conflicts. The thesis also highlights Egypt's potential in moderating extremist trends in the region, also through the successful mediation efforts in the inter-palestinian conflict involving the Fatah and Hamas movements, contributed to by Egypt's changing position in the region, her historical role in the Israeli-Palestinian conflict and her strategic and security concerns in the region.

In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyper- bolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochas- tic forcing and study their approximations in the sense of Bhatnagar-Gross- Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkohod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition. 1

This master thesis deals with past mediation attempts of Turkey to solve the Israeli- Palestinian conflict and with the potential of future Turkish mediation in the Israeli-Palestinian conflict. The Israeli-Palestinian conflict have been for several decades one of the biggest problems for the international security, therefore, analysing possible solutions is very important. Turkey is an actor with a special position, because it is a regional power with ties both to Islamic culture and to the West. That is why it has in theory a potential to play successful mediation role in this conflict. In this thesis, we will evaluate Turkey's existing role and after that, we will analyse the future potential with the help of the mediation conceptual framework that is described in the scholarly literature on conflict resolution and conflict management. Our research questions are: Can Turkey play a successful mediator role in the future? If yes, what conditions have to take place? Turkey tries to play a role in this conflict since the early 1990s and despite the fact that there has been a disruption of the diplomatic relations between Israel and Turkey, it is very likely that in the future a normalization will occur. If that happes, can Turkey broker peace?

Master thesis "Strategy of Armenia-Azerbaijan conflict resolution by participating states and key external actors"deals with the conflict between Armenia and Azerbaijan, in the center of which lies the dispute about the Nagorno Karabakh. Using qualitative analysis of grand strategy of Armenia and Azerbaijan and grand strategies of key regional and external stakeholders it uncovers interests, objectives and postures of the players in their strategic environment. On the basis of comprehensive analysis of the grand strategies I assess their effectiveness in relation to fulfillment of the state's goals and also the role, which conflict between Armenia and Azerbaijan plays in their strategy. In theoretical part I present short overview of the evolution of the concept of grand strategy and also operationalization of assessment of the strategies. In the second chapter I describe the historical background of south Caucasus, which is crucial for understanding of the conflictive nature of some interstate states in the region. In the third chapter I analyze grand strategies of Armenia, Azerbaijan, Iran, Turkey, Russia, USA and EU. In the last chapter I summarize the effectiveness and relevance of chosen strategies.

Title: Interpretation of calculations in word problems - looking for a question Author: Tereza Legová Department: Department of Mathematics and Mathematical Education Supervisor: prof. RNDr. Naďa Vondrová, Ph.D., Department of Mathematics and Mathematical Education Abstract: This thesis deals with an exploratory study of the introduction of modified word problems into the teaching of mathematics. The modification of the classical word problem consists in setting the context of the word problem and calculation. The task of pupils is to find out what we get by the given calculation, what question the calculation answers and substantiate their claims. The aim of the thesis was to describe how pupils think in solving this type of problem. Specifically, it investigated what strategies pupils elect and what difficulties arise in solving. The theoretical part of the thesis is a search of literature on the topic of solving word problems and their possible implementation in teaching. The practical part is divided into two phases. A test consisting of three problem contexts was given to pupils. The aim was to determine the meaning of the three given calculations for the each context. Before solving the test, a sample problem was discussed with the pupils. In the first phase, interviews were conducted with six pupils...

The thesis focuses on problems from the mathematical didactic test, which represents an exam in mathematics in the common part of the school leaving examination. The aim of the work is to identify problems that were solved with low success, explain possible difficulties and propose recommendations, the implementation of which in teaching or training pupils could contribute to their better readiness for similar types of problems in the leaving exam. An analysis of the success in solving the problems of didactic tests is performed based on available anonymized data and the problems with the lowest success rates in solving the spring terms of the leaving exam in 2017-2020 are identified. Several problems are selected for research in this work. First, based on didactic analysis the possible reasons for low success in solving the selected problems are presented. Furthermore, research is carried out. A test is compiled from selected problems and it is presented for solution and optional commenting to respondents from high school. Their solutions are then evaluated and analyzed in detail and discussed with respect to previously formulated expectations. There were errors of a milder nature in the pupils' solutions, as well as errors indicating serious shortcomings in the understanding. Some of the errors...