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Evaluation of interval polynomials
Firment, Roman ; Hladík, Milan (advisor) ; Hartman, David (referee)
In this thesis, we deal with the finding of an enclosure of the range of the real and interval polynomials in one variable. There are presented functional forms of the real polynomials which we implemented in the Matlab environment that is using interval arithmetic of the toolbox INTLAB. These forms can be used to effectively evaluate an enclosure of a polynomial. In the theoretical part there is introduced a reduction that makes possible to use an arbitrary functional form computing an enclosure of a real polynomial to evaluate an enclosure of interval polynomial. A numerical comparison is also the part of this thesis. Based on its results we designed two global functions solving our problem that apply one of the forms. A user has a possibility to indirectly influence the choice of the form by non-mandatory parameter that is specifying the strategy of computation. This parameter defines speed of evaluation and the amount of overestimation of the computed interval.
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Solving interval systems by the least squares method
Tomandl, David ; Hladík, Milan (advisor) ; Hartman, David (referee)
This thesis is describing, comparing and implementing enclosure methods for solving overdetermined system of interval linear equations by the least squares method. Input data of the methods are within given intervals. We describe the structure of the solution set, which is the basis of algorithms for computing interval hull of the solution set. Although computation of the interval hull is NP-hard problem, there exist algorithms which encloses the solution set with less than exponential steps. We are heavily focusing on these algorithms. The solution set can be alternatively characterized as a solution to the symmetric interval system. Therefore the work includes solvers of the symmetric interval system. This thesis contains numerical experiments for comparing the methods. All methods are implemented in Matlab with utilisation of the interval toolbox Intlab. Powered by TCPDF (www.tcpdf.org)
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Legal issues of commercial and investment banking
Hartman, David ; Kotáb, Petr (advisor) ; Kohajda, Michael (referee)
This thesis is dedicated to the Financial Law, namely to a special part of this branch of law - Banking Law, with a special focus on legal aspects of commercial and investment banking. Its concentrates on the specifics of the universal banking system in related to system of the Czech Republic. Chapter 1 deals with the general terms and concepts of the bank regulation, namely on model of universal banking model, segmented banking model and hybrid banking model, presentation of different types of banks and/or other financial institutions, variety types of bank systems a shows difference concept of banking systems, and description of basic parts of commercial and investment banking and its models of regulations. Chapter 2 describes the banking system of the Czech Republic, its history, situation on the market, types of banking institutions on the markets and detail description of bank regulations on European and national level. Chapter 3 is connected with commercial banking systems. Describes main categories of services or products provided by the commercial banks in the Czech Republic and its legal regulation. This services or products consist in a form of Banking transactions. Chapter 4 looks in detail on a model of investment banking in the market of the Czech Republic, its history and regulations...
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Extension property of structures
Hartman, David ; Nešetřil, Jaroslav (advisor) ; Pultr, Aleš (referee) ; Woodrow, Robert (referee)
This work analyses properties of relational structures that imply a high degree of symmetry. A structure is called homogeneous if every mapping from any finite substructure can be extended to a mapping over the whole structure. The various types of these mappings determine corresponding types of homogeneity. A prominent position belongs to ultrahomogeneity, for which every local isomorphism can be extended to an automorphism. In contrast to graphs, the classification of ultrahomogeneous relational struc- tures is still an open problem. The task of this work is to characterize "the distance" to homogeneity using two approaches. Firstly, the classification of homogeneous structures is studied when the "complexity" of a structure is increased by introducing more relations. This leads to various classifications of homomorphism-homogeneous L-colored graphs for different L, where L- colored graphs are graphs having sets of colors from a partially ordered set L assigned to vertices and edges. Moreover a hierarchy of classes of ho- mogeneous structures defined via types of homogeneity is studied from the viewpoint of classes coincidence. The second approach analyses for fixed classes of structures the least way to extend their language so as to achieve homogeneity. We obtain results about relational complexity for finite...
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Legal issues of commercial and investment banking
Hartman, David ; Kotáb, Petr (advisor) ; Kohajda, Michael (referee)
This thesis is dedicated to the Financial Law, namely to a special part of this branch of law - Banking Law, with a special focus on legal aspects of commercial and investment banking. Its concentrates on the specifics of the universal banking system in related to system of the Czech republic. Chapter 1 deals with the general terms and concepts of the bank regulation, namely on model of universal banking model, segmented banking model and hybrid banking model, presentation of different types of banks and/or other financial institutions, variety types of bank systems a shows difference concept of banking systems, and description of basic parts of commercial and investment banking and its models of regulations. Chapter 2 describes the banking system of the Czech Republic, its history, situation on the market, types of banking institutions on the markets and detail description of bank regulations on European and national level. Chapter 3 looks in detail on a model of investment banking in the market of the Czech Republic, its history and regulations on European level, namely MiFID I. and MiFID II. Regulations and description of legal framework of providing investing services in the Czech Republic. Chapter 4 describes the actually legal problems of bank regulations after Financial crisis which brings a...
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Eigenvalues of symmetric interval matrices
Kaleyski, Nikolay Stoyanov ; Hladík, Milan (advisor) ; Hartman, David (referee)
The goal of the thesis is to describe and possibly improve some algorithms for finding inner and outer approximations of the borders of eigenvalue intervals of real symmetric interval matrices, to modify them so that they perform verified computations and to implement them in the Matlab programming language. The main principles of verification and interval arithmetic are described, as well as the used theoretical foundations and the problems which occur when attempting to verify the individual algorithms, including possibilities of overcoming them. Experiments illustrating some empirical properties of the algorithms are described. The practical result of the thesis is a software package for computing approximations of the sets of eigenvalues of symmetric interval matrices. Powered by TCPDF (www.tcpdf.org)
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Opponent Modelling in Games with Imperfect Information
Kovačič, Milan ; Schmid, Martin (advisor) ; Hartman, David (referee)
The main concern of this paper is the problem of opponent modeling. The goal of this work is to introduce reasonable selection of techniques, which model the opponent's behavior and use it in effective way. In this work I focused on explanation of fundamental terms, introduction of relevant techniques and safety of opponent modeling considering the game of poker. The research showed that effective opponent modeling is indeed possible with reasonable safety and surprising effectivity in comparison with pessimistic equilibrium techniques.
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Vliv reálného kurzu koruny na český zahraniční obchod
Hartman, David Bc. ; Dvořák, Pavel (advisor) ; Fantová - Šumpíková, Markéta (referee)
Práce se pokouší zjistit případný vliv reálného efektivního kurzu koruny na český zahraniční obchod, resp. na vývoz a dovoz zboží a čistého exportu. Úvodní kapitola, je věnována teoretické části se zaměřením na vymezení důležitých pojmů, jako platební bilance, nominální a reálný měnový kurz, Marshall-Lernerova a zahraniční obchod. Druhá kapitola obsahuje datovou a analytickou část. V ní jsou analyzována výchozí makroekonomická data ? vývoj reálného efektivního kurzu koruny a vývoj zahraničního obchodu ČR od roku 1996 do roku 2006. Závěrečná kapitola se věnuje popisu vlivu změn reálného efektivního kurzu koruny na automobilový průmysl. Pomocí grafické analýzy se zde objasňuje případná závislost vývoje reálného efektivního kurzu a vývozu osobních automobilů z ČR do zahraničí. V závěru jsou shrnuty celkové výsledky práce.
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