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Matrices, Determinant and Body Volume
Šomplák, Radovan ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
In his thesis describes the basic properties of matrices, determinants and their use in display issues between vector spaces. In the final chapters devoted to determinants and its applications, which indicates the relation between determinants and calculation of volume. Subsequently determinanti describes how to use in calculating the elements using multiple integrals. Another possible application is the so-called Cramerovo rule which allows us to solving systems of linear equations.
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Image corrections by CGA
Machálek, Lukáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with conformal geometric algebra (CGA) in image processing. We focus on correct definitions of notions in geometric algebra, which we use for correcting image defects. First, the concepts of vector space are mentioned, then, the properties of geometric algebra are observed. Consequently, the 3D point is conformaly embedded into CGA, thereafter, another geometric objects are described with their representations in null spaces. In the end, the thesis deals with object transformation and with image defects correction.
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Distance measurement between nodes in IP networks
Šimák, Jan ; Novotný, Vít (referee) ; Komosný, Dan (advisor)
This thesis deals with delay prediction issue between nodes on the Internet. Accurate delay prediction helps with choosing of the nearest internet neighbor and contributes to effective usage of network sources. Unnecessary network load is decreased due to algorithms of delay prediction (no need for many latency measuring). The thesis focuses theoretically on the three main algorithms using coordinate systems - GNP, Vivaldi, Lighthouses. Last one is at the same time the main subject of the thesis too. Algorithm Lighthouses is explored in detail theoretically and in practise too. In order to verify the accurate of delay prediction of Lighthouses algorithm the simulation application was developed. The application is able to compute node coordinates of synthetic network using Lighthouses algorithm. Description of simulation application and evaluation of simalution results are part of practice part of this thesis.
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Geometric algebra computations
Tomešová, Tereza ; Vechetová, Jana (referee) ; Vašík, Petr (advisor)
This thesis deals with computing in geometric algebra and its illustration in software CLUCalc. Firstly, it introduces fundamental terms and properties of vector space, scalar product and Clifford algebra. Consequently, the term geometric algebra, its products and operations are defined. These terms are illustrated on a specific exampel, i.e. translation and rotation of a sphere along fixed curve in software CLUCalc.
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Transformer models for educational purposes
Beran, Vojtěch ; Ctibor, Jiří (referee) ; Pazdera, Ivo (advisor)
The aim of the bachelor's thesis is to project and realize models of transformers in Matlab and Simulink program. Projected models explain the theoretical precondition of the models. The aim is also to create manuals for models usage. The theoretical part bachelor's thesis is focused on transformer theory, which defines the properties, physical quantities, parameters and relations between them. In this part is defined transition from the basic model to models of current and voltage transformer, which forms the basis for the realization of simulations in Simulink. The next part describes vector transformation needed for modeling three phase system, defining the power, voltage and current of the transformer and for change of winding connection. Last part describes non-linear magnetic field. The practical part of the bachelor's thesis is the practical implementation of transformer models in Simulink. Realized models are models of current and voltage transformers. Each model has a form of linear and non-linear model and can work in single-phase or three-phase system. The output of simulation are values and voltage, current and power waveforms for a given load. There is a brief manual for usage for each model.
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Geometric algebra computations
Tomešová, Tereza ; Vechetová, Jana (referee) ; Vašík, Petr (advisor)
This thesis deals with computing in geometric algebra and its illustration in software CLUCalc. Firstly, it introduces fundamental terms and properties of vector space, scalar product and Clifford algebra. Consequently, the term geometric algebra, its products and operations are defined. These terms are illustrated on a specific exampel, i.e. translation and rotation of a sphere along fixed curve in software CLUCalc.
|
|
|
Image corrections by CGA
Machálek, Lukáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with conformal geometric algebra (CGA) in image processing. We focus on correct definitions of notions in geometric algebra, which we use for correcting image defects. First, the concepts of vector space are mentioned, then, the properties of geometric algebra are observed. Consequently, the 3D point is conformaly embedded into CGA, thereafter, another geometric objects are described with their representations in null spaces. In the end, the thesis deals with object transformation and with image defects correction.
|
|
|
Transformer models for educational purposes
Beran, Vojtěch ; Ctibor, Jiří (referee) ; Pazdera, Ivo (advisor)
The aim of the bachelor's thesis is to project and realize models of transformers in Matlab and Simulink program. Projected models explain the theoretical precondition of the models. The aim is also to create manuals for models usage. The theoretical part bachelor's thesis is focused on transformer theory, which defines the properties, physical quantities, parameters and relations between them. In this part is defined transition from the basic model to models of current and voltage transformer, which forms the basis for the realization of simulations in Simulink. The next part describes vector transformation needed for modeling three phase system, defining the power, voltage and current of the transformer and for change of winding connection. Last part describes non-linear magnetic field. The practical part of the bachelor's thesis is the practical implementation of transformer models in Simulink. Realized models are models of current and voltage transformers. Each model has a form of linear and non-linear model and can work in single-phase or three-phase system. The output of simulation are values and voltage, current and power waveforms for a given load. There is a brief manual for usage for each model.
|
|
|
Distance measurement between nodes in IP networks
Šimák, Jan ; Novotný, Vít (referee) ; Komosný, Dan (advisor)
This thesis deals with delay prediction issue between nodes on the Internet. Accurate delay prediction helps with choosing of the nearest internet neighbor and contributes to effective usage of network sources. Unnecessary network load is decreased due to algorithms of delay prediction (no need for many latency measuring). The thesis focuses theoretically on the three main algorithms using coordinate systems - GNP, Vivaldi, Lighthouses. Last one is at the same time the main subject of the thesis too. Algorithm Lighthouses is explored in detail theoretically and in practise too. In order to verify the accurate of delay prediction of Lighthouses algorithm the simulation application was developed. The application is able to compute node coordinates of synthetic network using Lighthouses algorithm. Description of simulation application and evaluation of simalution results are part of practice part of this thesis.
|
|
|
Matrices, Determinant and Body Volume
Šomplák, Radovan ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
In his thesis describes the basic properties of matrices, determinants and their use in display issues between vector spaces. In the final chapters devoted to determinants and its applications, which indicates the relation between determinants and calculation of volume. Subsequently determinanti describes how to use in calculating the elements using multiple integrals. Another possible application is the so-called Cramerovo rule which allows us to solving systems of linear equations.
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