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Systems of Polynomial Equations in Economics
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
Bachelor thesis is based on application of mathematical apparatus for the analysis of economic models, in particular models that lead to a system of polynomial equations. One of the parts is a summary of basic knowledge of algebra focused on Gröbner basis. Hereinafter are discussed economic models in which solution Gröbner basis are applied using the program Wolfram Mathematica. Own software package is implemented into this program as a concept of solution to simplify the calculation and work with models.
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The Frölicher-Nijenhuis bracket and its applications in geometry and calculus of variations
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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Gröbner basis, Zhuang-Zi algorithm and attacks of multivariable cryptosystems
Doktorová, Alice ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This diploma thesis is devoted to the multivariate cryptosystems. It includes an overview of commutative algebra with emphasis on Gröbner bases. Of all algorithms, especially the ones using Gröbner bases are studied, i.e. Buchberger's algorithm, which is already implemented in Wolfram Mathematica, and F4 algorithm, for which a program package has been created in the Wolfram Mathematica environment. Also Zhuang-Zi algorithm is described. To simplify its steps a program to compute the Lagrange interpolation polynomial has been created in Python.
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Development And Verification Of A New Method For Measuring The Stiffness And Damping Properties Of Joints In Parallel Kinematic Structures
Kolouch, Martin ; Tomáš, Jiří (referee) ; Knoflíček, Radek (advisor)
In this dissertation is presented the development of a new measurement method for the stiffness and damping characteristics of a joint in a parallel kinematic machine tool. The main contribution of this method is specially for applications, that demand accurate information about stiffness and damping parameters from assembled parts of machines tool. Methods for compensation of deformations in machines tool, that are carried out by control, belong to these applications. Another contribution of this work is the technical implementation of the proposed principle of the new method. At this point the focus of the work was devoted to signal processing, that differs in a certain degree from other types of signal processing methods, that are used in other dynamic measurements, e.g. modal analysis. One of the main requirements was the possibility to consider the nonlinear behavior of the measured structure. In another chapter the modified signal processing method was used for measuring a joint in a test rig. The results were compared with results from other measurement methods. On account of this comparison the statement was made that the new method can be used for measuring the stiffness and damping parameters of machine parts. Finally the new method was applied to measure the properties of a joint, which was built in a machine tool. Moreover, the problems, that appeared during the measurement, were also described.
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Proposal of Process Order Management in a Selected Organization
Hluštíková, Terezie ; Tomáš, Jiří (referee) ; Jurová, Marie (advisor)
The bachelor’s thesis is focused on the process management of an order in a selected company Pemax Print, s r. o., whose activity is printing production. Technical terms of production, quality and process are explained in the theoretical part. The analysis of the current state is devoted to an introduction of the company. The final part contains proposals which will contribute to the optimalization of order process.
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Tensors and their applications in mechanics
Adejumobi, Mudathir ; Doupovec, Miroslav (referee) ; Tomáš, Jiří (advisor)
The tensor theory is a branch of Multilinear Algebra that describes the relationship between sets of algebraic objects related to a vector space. Tensor theory together with tensor analysis is usually known to be tensor calculus. This thesis presents a formal category treatment on tensor notation, tensor calculus, and differential manifold. The focus lies mainly on acquiring and understanding the basic concepts of tensors and the operations over them. It looks at how tensor is adapted to differential geometry and continuum mechanics. In particular, it focuses more attention on the application parts of mechanics such as; configuration and deformation, tensor deformation, continuum kinematics, Gauss, and Stokes' theorem with their applications. Finally, it discusses the concept of surface forces and stress vector.
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Lie groups from the point of view of kinematics and applications in robotics
Kalenský, Jan ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
This diploma thesis deals with the kinematic and robotic implications of Lie theory. In the introductory section, a manifold is defined as a basic element of configuration space. The main body of the thesis deals with the definition of a structure in the configuration space - Lie group. Tangent space with vector field including a structure of Lie algebra is defined to represent velocity. These two structures are connected using exponential mapping. The conclusion of the thesis focuses on fibre space, especially considering principal bundle and principal connection. Throughout the thesis, numerous examples are presented to illustrate the terms used.
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Hyperbolic geometries
Brdečková, Johanka ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The present thesis deals with hyperbolic geometry. We derive parametric equations of the curve tractrix and the surface pseudosphere. Then we discuss two models of hyperbolic geometry, which are derived from the parametrization of pseudosphere.
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Geodesics
Čambalová, Kateřina ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The goal of the thesis is to create an overivew of geodesics. At the beginning of their study, they were considered shortest paths connecting two points on surfaces. In the thesis we will show more of the complexity of the term and introduced the properties, some uses of the geodesics and methods of their computation. Later, the Clairaut patches and their geodesics will be analysed. Clairaut patches are characterized by a specific property which makes computation of geodesics simpler. 3D plots of some Clairaut patches and their geodesics are also included.
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