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Multipoint identification of position and orientation of object
Řičánek, Dominik ; Ligocki, Adam (referee) ; Burian, František (advisor)
The goal of this paper is to find a good method to determine the pose of two, mutually rotated, objects and to try and implement it first in C++ without the usage of any external libraries and then in Kuka Robot Language (KRL). First we are going to look at two different approaches to solving this problem: The Iterative Closest Point algorithm (ICP) and the Kabsch Algorithm. From them one is going to be chosen and a program will be build around it. Following its implementation, the algorithm’s precision is going to be tested. Finally KRL will be briefly introduced and the various problems involving transition of the algorithm from C++ to KRL will be talked about.
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Sturm-Liouville problem in vibration of continuous systems
Varmusová, Alanis ; Nechvátal, Luděk (referee) ; Šremr, Jiří (advisor)
The goal of this thesis is to compile the theory concerning the Sturm-Liouville problem and partial diferential equations of the second order. Based on the findings the necessary eigenvalues, eigenfunctions and Green's functions, which are connected with the Sturm-Liouville problem, are derived in the thesis. Results of derivation are used in the solution of the initial-boundary value problem for wave equation, which results are then interpreted graphically.
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Mathematical methods in some ranking models
Pažourek, Lubomír ; Kureš, Miroslav (referee) ; Čermák, Jan (advisor)
The bachelor thesis deals with the mathematical essence of some ranking methods. Their unifying element is the so-called Perron-Frobenius theorem for non-negative and irreducible matrices, which formulates the conditions for the existence of a positive eigenvalue and a positive eigenvector of the given matrix. The goal of the thesis consists in providing an overview of the necessary theoretical results, explaining their application within some ranking methods and performing simulations during the evaluation of some competitions.
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Sturm-Liouville problem in vibration of continuous systems
Varmusová, Alanis ; Nechvátal, Luděk (referee) ; Šremr, Jiří (advisor)
The goal of this thesis is to compile the theory concerning the Sturm-Liouville problem and partial diferential equations of the second order. Based on the findings the necessary eigenvalues, eigenfunctions and Green's functions, which are connected with the Sturm-Liouville problem, are derived in the thesis. Results of derivation are used in the solution of the initial-boundary value problem for wave equation, which results are then interpreted graphically.
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Multipoint identification of position and orientation of object
Řičánek, Dominik ; Ligocki, Adam (referee) ; Burian, František (advisor)
The goal of this paper is to find a good method to determine the pose of two, mutually rotated, objects and to try and implement it first in C++ without the usage of any external libraries and then in Kuka Robot Language (KRL). First we are going to look at two different approaches to solving this problem: The Iterative Closest Point algorithm (ICP) and the Kabsch Algorithm. From them one is going to be chosen and a program will be build around it. Following its implementation, the algorithm’s precision is going to be tested. Finally KRL will be briefly introduced and the various problems involving transition of the algorithm from C++ to KRL will be talked about.
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Eigenvalues of Matrices and Their Localization
Borzíková, Žofia ; Škorpilová, Martina (advisor) ; Halas, Zdeněk (referee)
The diploma thesis is concerned with the topic of eigenvalues of matrices and their lo- calization in the complex plane. First introducing general theorems concerning eigenvalues, eigenvalues for special classes of matrices are then discussed. After presenting the theory of Jordan and Weyr canonical forms, the connection and relation of these two forms is also explained. The estimates of the localizations of the eigenvalues follows from Gershgo- rin's theorem. This text might be used as a didactic material for college-level students of mathematics, thanks to its form having theoretical parts accompanied by examples with commented solutions. It may also be used as a source of information for anyone interested in extending their knowledge of linear algebra. 1
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Affine mappings and transformations in the plane with solved examples
Barborka, Lukáš ; Zamboj, Michal (advisor) ; Jančařík, Antonín (referee)
Analytical geometry widely uses the apparatus of linear algebra, it is, of course, its natural application. The aim of this thesis is the theoretical interconnection, for many students still abstract, bases of the linear algebra with their practical application in the analyti- cal geometry, especially in affine transformations and their use in the solved examples in the plane. This thesis is intended to put concepts known from the course of Linear algebra (homomorphism, eigenvalues/eigenvectors, orthogonal matrices, transition matri- ces...) into context with practical using in the analytical geometry, whether in the form of proofs of important theorems using the linear algebra and arithmetic apparatus, or the following solved examples. The aim of the examples is to provide some insight or guidance on the solution of the same or analogous tasks. The theory and examples are in some cases supplemented with illustrations for better clarity. The work is divided into several parts for greater clarity. The introduction is repeated important concepts of linear algebra such as group, field, vector space, Euclidean space, linear mapping (homomorphism), change of coordinates matrix, eigenvalue/eigenvector of the matrix. It also switches to affine point space, affine coordinate system, transformation equation for...
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Okrajové úlohy pro rovnice 2. řádu se skákajícími nelinearitami
ZAHRADNÍKOVÁ, Michaela
The subject of this Thesis is to examine nontrivial solutions of boundary value problems for second order ODEs with unilateral jumping nonlinearities. Considered problems can be interpreted as models of a simple beam supported by three types of elastic obstacles. Couples of eigenvalues and eigenfunctions are found and discussed with respect to parameter which represents the strength of the obstacle.
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Affine mappings and transformations in the plane with solved examples
Barborka, Lukáš ; Tůmová, Veronika (advisor) ; Zamboj, Michal (referee)
Analytical geometry widely uses the apparatus of linear algebra, it is, of course, its natural application. The aim of this thesis is the theoretical interconnection, for many students still abstract, bases of the linear algebra with their practical application in the analyti- cal geometry, especially in affine transformations and their use in the solved examples in the plane. This thesis is intended to put concepts known from the course of Linear algebra (homomorphism, eigenvalues/eigenvectors, orthogonal matrices, transition matri- ces...) into context with practical using in the analytical geometry, whether in the form of proofs of important theorems using the linear algebra and arithmetic apparatus, or the following solved examples. The aim of the examples is to provide some insight or guidance on the solution of the same or analogous tasks. The theory and examples are in some cases supplemented with illustrations for better clarity. The work is divided into several parts for greater clarity. The introduction is repeated important concepts of linear algebra such as group, field, vector space, Euclidean space, linear mapping (homomorphism), change of coordinates matrix, eigenvalue/eigenvector of the matrix. It also switches to affine point space, affine coordinate system, transformation equation for...
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