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Smoothing quadratic and cubic splines
Oukropcová, Kateřina ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
Title: Smoothing quadratic and cubic splines Author: Kateřina Oukropcová Department: Department of Numerical Mathematics Supervisor: RNDr. Václav Kučera, Ph.D., Department of Numerical Mathematics Abstract: The aim of this bachelor thesis is to study the topic of smoothing quadratic and cubic splines on uniform partitions. First, we define the basic con- cepts in the field of splines, next we introduce interpolating splines with a focus on their minimizing properties for odd degree and quadratic splines and finally smoo- thing odd degree and quadratic splines. We derive algorithms for the construction of smoothing cubic and quadratic splines. In the last chapter, the presented al- gorithms are implemented in Matlab and applied to test data. Obtained results are presented in graphic form and discussed. Keywords: interpolation, approximation, cubic spline, quadratic spline, smoo- thing spline 1
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The Czech Republic as a party to the proceedings for the failure to fulfill an obligation resulting from EU Treaties
Kučera, Václav ; Zemánek, Jiří (advisor) ; Král, Richard (referee)
The aim of this diploma thesis is partly a reflection on the history and current form of the institute of infringement proceedings and in particular the analysis of the Czech Republic's participation in this type of procedure since its entry into the European Union. Proceedings for failure to fulfill an obligation is introduced as the main sanction- control mechanism under EU law, the purpose of which is to ensure that Member States comply with the obligations they adopted in connection with accession to the EU and that union norms have full effect. At the beginning is outlined the historical development of the infringement proceedings, i.e. on what purpose and in which way was this control mechanism initially incorporated into the primary law of the European Community, how its parameters gradually changed and whit what kind of proposals are currently mentioned in order to ensure the maximum efficiency of the procedure. Thesis emphasizes on a detailed introduction and evaluation of all aspects of procedure. Particular chapters are devoted to the question of object to the proceedings, legal entities and their rights during the proceedings, the system of sanctions and the effects of the European Court's decisions in the case. Control and discretion power is in infringement proceedings exercised by...
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Visualization of computed flows using particle tracing methods
Miloš, Vojtěch ; Hron, Jaroslav (advisor) ; Kučera, Václav (referee)
A mesh of tetrahedrons is build from a real data that were obtained by CT (computer tomography) or MRI (magnetic resonance imaging) scan of a blood vessel and then velocity vectors are computed in every vertex using the nite element method. The objective of the work is to design and implement a particle tracing algorithm in such a mesh with an emphasis on a maximum accuracy of the result. For this purpose, an analytic integration method is presented, which can be used thanks to piecewise linear vector eld. We propose our own modi cation of this method and compare its results with the conventional numerical integration. Furthermore, the work describes modi cations of common step methods that are used to determine the cell that contains a particular particle without the need to search the whole mesh in each step. Powered by TCPDF (www.tcpdf.org)
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Numerical solution of equations describing the dynamics of flocking
Živčáková, Andrea ; Kučera, Václav (advisor) ; Janovský, Vladimír (referee)
This work is devoted to the numerical solution of equations describing the dynamics of flocks of birds. Specifically, we pay attention to the Euler equations for compressible flow with a right-hand side correction. This model is based on the work Fornasier et al. (2010). Due to the complexity of the model, we focus only on the one-dimensional case. For the numerical solution we use a semi-implicit discontinuous Galerkin method. Discretization of the right-hand side is chosen so that we preserve the structure of the semi-implicit scheme for the Euler equations presented in the work Feistauer, Kučera (2007). The proposed numerical scheme was implemented and numerical experiments showing the robustness of the scheme were carried out. Powered by TCPDF (www.tcpdf.org)
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Exact and approximate Riemann solvers for the Euler equations
Živčáková, Andrea ; Kučera, Václav (advisor) ; Felcman, Jiří (referee)
In this work we deal with the solution and implementation of the problem of solving a partial differential equation with a piecewise constant initial condition, the so-called Riemann's problem. Specifically, we study the equations of conservation laws describing inviscid adiabatic flow of an ideal gas - the Euler equations. After some investigation, we show that these equations can be transformed to a quasilinear hyperbolic partial differential equation of first order. We are especially interested in the one-dimensional Euler equations for which we want to get an analytically exact Riemann's solver. The solution is found by investigation of properties of waves, namely rarefaction waves, shock waves and contact discontinuities were treated. The output of this work is a program in C for finding the exact Riemann's solver for one-dimensional Euler equations. The program is based on a theoretical analysis summarized in the first two chapters, and is tested on standard test data. The theory is based on the books [1] and [2].
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Interpolace hladkých funkcí pomocí kvadratických a kubických splinů
Eckstein, Jiří ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
In this thesis, we study properties of cubic and quadratic spline interpolation. First, we define the notions of spline and interpolation. We then merge them to study cubic and quadratic spline interpolations. We go through the individual spline interpolation types, show an algorithm for constructing selected types and sum up their basic properties. We then present a computer program based on the provided algorithms. We use it to construct spline interpolations of some sample functions and we calculate errors of these interpolation and compare them with theoretical estimates.
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Council of the EU after Lisbon treaty: changes in gualified majority decision-making and their influence on the positions of member states
Kučera, Václav ; Plechanovová, Běla (advisor) ; Karlas, Jan (referee)
The main aim of this thesis is to analyze the impact of a new system of qualified majority voting under the Lisbon Treaty on the position of member states in the Council. The paper mainly deals with potential transformation of member states weight in the Council. With the help of so-called power indexes, the absolute and relative voting power of member states in the Council will be determined. In the first part of the thesis, qualified majority is introduced also in the historical development, i.e., how its form ranged from the emergence of the European Communities to the present. Emphasis is of course placed on detailed description of the key articles of the Lisbon Treaty, relating to qualified majority voting in the Council. The answer to the question whether the new criteria of qualified majority will mean a different result of the vote in the Council, can be found in the fourth chapter of this thesis. An important element of analysis of qualified majority under the Lisbon Treaty is its comparison with the Nice system in terms of fairness and efficiency. At the conclusion of this thesis, the historical development of the expansion of qualified majority voting in the Council at the expense of unanimity is included. Identification of those states which were most often in the past, when voting by...
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