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Lie groups theory in robotics
Horník, Petr ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
In this thesis we focus on the mathematical description of the forward kinematics in three-dimensional space using orthogonal transformations and matrix theory. Applying the acquired knowledge we solve an example using the method of moving frame. Between bases we pass using the passage matrix and we implement the example in the MATLAB environment. Consequently, we focus on deeper relation with exponential functions and extend the theory by the theory of Lie groups and algebras. Especially, we take notice of the special orthogonal group SO(3). Finally, we enrich the theory with homogeneous transformation and special Euclidean group.
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Implementation of Statistical Functions Using HLS
Šinaľ, Peter ; Martínek, Tomáš (referee) ; Dvořák, Milan (advisor)
The aim of this thesis was to design and implement selected statistical functions used in technical analysis. I focused on moving averages, Black-Schles model for calculating option prices and Indicator Delta. These functions are through HLS transformed into an appropriate description for programmable FPGA. During the transformation process, emphasis is on low latency and resource consumption. Created solutions demonstrate the potential of HLS. They show complexity of the technical analysis and hardware requirements. Achieved results show high accuracy in the simulations. Deviation from the reference value is approximately 6,615*10e-3. The results also indicate thet that reducing latency does not necessarily cause an increase in the consumption of resources on the chip.
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Aplikace matematických znalostí při výuce biologie
STUDENÁ, Lucie
The Theses deals with applications of mathematical knowledge in teaching biology and it is divided into four chapters. Each chapter is dedicated to another application: 1. Application of conditional probability in medical diagnostics, 2. Application of exponential function in population ecology, 3. Application of logic functions in mathematical modelation of neuron and 4. Aplication of binomial theorem and binomial distribution in genetics. Each application contains solved problems, a worksheet for students and a solution for each worksheet. Two application (1. and 2.) have been tested in teaching and as an assessment of my lessons students filled questionnaires. Results of these questionnaires are processed in the end of these chapters. This Thesis can be used in teaching or self-studying.
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Implementation of Statistical Functions Using HLS
Šinaľ, Peter ; Martínek, Tomáš (referee) ; Dvořák, Milan (advisor)
The aim of this thesis was to design and implement selected statistical functions used in technical analysis. I focused on moving averages, Black-Schles model for calculating option prices and Indicator Delta. These functions are through HLS transformed into an appropriate description for programmable FPGA. During the transformation process, emphasis is on low latency and resource consumption. Created solutions demonstrate the potential of HLS. They show complexity of the technical analysis and hardware requirements. Achieved results show high accuracy in the simulations. Deviation from the reference value is approximately 6,615*10e-3. The results also indicate thet that reducing latency does not necessarily cause an increase in the consumption of resources on the chip.
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Lie groups theory in robotics
Horník, Petr ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
In this thesis we focus on the mathematical description of the forward kinematics in three-dimensional space using orthogonal transformations and matrix theory. Applying the acquired knowledge we solve an example using the method of moving frame. Between bases we pass using the passage matrix and we implement the example in the MATLAB environment. Consequently, we focus on deeper relation with exponential functions and extend the theory by the theory of Lie groups and algebras. Especially, we take notice of the special orthogonal group SO(3). Finally, we enrich the theory with homogeneous transformation and special Euclidean group.
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The use of logarithmic and exponential functions in various disciplines
KRULEC, Radek
This bachelor thesis discusses practical use of logarithmic and exponential function in different fields. The aim of this thesis is read up real situations in which we deals with logarithmic and exponential dependences and create a file of application examples. This thesis should show how important is task of mathematics in various branches of science and in which branches mathematics is needed.
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The development and demographic consequences of suburbanization in the base of Prague
Postlerová, Marika ; Pechholdová, Markéta (advisor) ; Nývlt, Ondřej (referee)
This bachelor work shows the characteristic progress of suburbanization in the base capital city of the Czech Republic, after the Velvet Revolution. The Second World War interrupted the very successful dynamic era of Czechoslovakia and the following socialistic era had been holding the natural pressure on suburbanization, till the fall of the communist regime at 1989. After the transformation of 1989, it appeared that all those years of struggling; still the Czechs desire to live in a family house in the countryside also known as the suburb. Finally, it was possible to have a restful life in the countryside with job opportunities a short distance nearby capital city. The analyst is using the suburbanization calculations in Central Bohemia Region, depending upon the capital city, using exponential function for the period 2001-2011, which shows the general estimation of suburbanization process in the certain area and also refers to the possible reasons for the differences which are diverged from the general trends. The analyst results may also help to explain future impacts for certain areas. At the end of this work, the main goals have been set up for the regional politics, which is trying to help every region to stay independent and also increase their cooperation and solidarity.
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