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Realization of educational problem based on preloaded bolted joint apparatus
Žaba, Tomáš ; Náhlík, Luboš (referee) ; Vaverka, Michal (advisor)
In the master’s thesis an educational task concerning an experimental apparatus for quantity measurement in preloaded bolted joint is realised. In terms of its preparation an innovation of the apparatus leading to an easier and faster pretension realisation was implemented. The educational task for students and also teaching material were produced. The educational task itself consists in experimental confirmation of the relation between the tightening torque and the caused pretension. An FEM model simulating an apparatus flange deformation by given pretension was designed to verify the experiment. The thesis also contains information about the preloaded bolts, pretension elicitation methods and pretension control methods.
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Protection of highspeed communication systems
Smékal, David ; Martinásek, Zdeněk (referee) ; Hajný, Jan (advisor)
The diploma thesis deals with 128–bit AES data encryption and its implementation in FPGA network card using VHDL programming language. The theoretical part explains AES encryption and decryption, its individual steps and operating modes. Further was described the VHDL programming language, development environment Vivado, FPGA network card Combo–80G and configurable framework NetCOPE. The practical part is the implementation of AES–128 in VHDL. A simulation was used to eliminate errors, then the synthesis was performed. These steps were made using Vivado software. Last step of practical part was testing of synthesized firmware on COMBO–80G card. Total of 4 projects were implemented in FPGA card. Two of them were AES encryption and decryption with ECB mode and another two describe the encryption and decryption with CBC mode.
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Optical fibres and their polarization effect
Klesnil, Ondřej ; Dostál, Otto (referee) ; Filka, Miloslav (advisor)
This project describes the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. There are described basic the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation. After the introduction the first conception with bases of polarization mode dispersion (PMD) in optical fibers, they have become an important body of knowledge basic for the design of high-capacity optical communication systems. PMD effects are linear electromagnetic propagation phenomena occurring in so-called “single-mode“fibers. Despite their name, these fibers support two modes of propagation distinguished by their polarization. Because of optical birefringence in the fiber, the two modes travel with different group velocities, and the random change of this birefringence along the fiber length results in random coupling between the modes. With current practical transmission technology the resulting PMD phenomena lead to pulse distortion and system impairments that limit the transmission capacity of the fiber. I describe different ways of measuring PMD in optical fibre, PMD compensation techniques and analyse PMD results in optical fibres.
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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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Mapping project dependencies
Šárová, Irena ; Chocholatý, Drahomír (advisor) ; Roháčová, Barbora (referee)
This thesis describes the issue of project dependencies. In managing projects we meet almost every time some kind of dependency. Currently, the project is almost never an isolated group of activity that is able to independently bring same value or result. Therefore, this issue occurs in many areas of managing project. The first theoretical part is focused on some of these areas. It describes disciplines such as Project, Program and Portfolio management. These areas are characterized and then described how they can solve project dependencies. The second part is focused on matrices DSM and DMM, which can serve as one of the methods to effectively manage all connections and dependencies in projects. Area DSM and DMM matrix is first explained and then are expressed its possibilities. In the last part are the information gained in the previous phase applied to a practical example in the banking environment. The method is applied to 25 projects that are guided in an unnamed banking institution. For these projects are set dimensions and are subsequently compiled specific DSM (Dependency Structure Matrix) and DMM (Domain Mapping Matrix) matrices. To certain dimensions is then used clustering method and on the resulting matrix is used simple matrix notation, such as transposition and matrix multiplication. It will create basically a tool, which is a network of all the dependencies between dimensions and projects that can simulate pre-defined scenarios.
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Extremes of two-variable functions --- a digest of solved examples
SEKAL, Tomáš
The topic of this bachelor work is to create a collection of exercises on the extremes of functions of two variables. It focuses mainly on local extremes. Exercises are ordered from easiest to more difficult. For each example there is solution procedure presented and illustrated with 3D graphs of functions, created using the mathematical program Maple. In the very beginning is provided "first aid" in the form of instructions for solving this kind of examples. At the end are included in "nontraditional" examples from mathematics and physics.
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Using the method of least squares in economic applications
JANEČKOVÁ, Zuzana
The aim of bachelor thesis is the description and the theoretical deduction of the method of least squares. In my work I attend to the deduction of least-squares with an exclusive focus on polynomial functions. This method is applied to the indicators of foreign trade, specifically turnover, exports, imports and balance. I gradually attend to polynomial of the first, the second to the m-th power. The objective of least-squares method assumes that the best-fit curve of a given type is the curve that has the minimal sum of the deviations squared.
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High mathematics teaching text creation with using of the e-learning
NOVÁKOVÁ, Alena
Teaching text containing the following chapters of higher mathematics: complex numbers, matrices, determinants, numerical solution of equations, differential calculus of functions of several variables, vector analysis, differential equations. The text is supported by illustrated examples with the main aim of using the given mathematical concepts and theorems in physics. Part of this teaching text is its electronic form {\clqq}Electronic textbook of mathematics for physics``.
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