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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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Design of linear structures on transistor level
Gajdoš, Adam ; Kubánek, David (referee) ; Koton, Jaroslav (advisor)
Bachelor thesis deals with the development of software for automated design frequency filters using active elements instead of inductors. The first part deals with the allocation of frequency filers by transmitted specrum and type of components used. It also deals with working mode in the circuit. Thesis also focuses on the description developmet environment in Wolfram Mathematica,and overall development and also advantages. The next chapter is devoted to the theoretical description of the program and all the necessary theoretical provisions, that are needed to manage the program, i.e. description modified nodal analysis, replacement of MOSFET transistor for Voltage Controlled Current Source and writing passive elements in programming language too. The last chapter is dedicated to the development of the program and detailed description.
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Invariants of jet groups and applications in continuum mechanics
Buriánek, Martin ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
This thesis is focused on jet groups and their matrix representations. The opening section deals with group representations, group actions on sets and invariants of actions. Another section explains terms such as smooth manifolds, Lie group and Lie algebra. The following part clarifies terms jet and jet group as a special example of Lie group. First of all, groups $G_1^r$ and $G_n^1$ are described, then description of group $G_n^2$ and its subgroups ensues. Representations of these jet groups are proposed. Finally, applications of jet groups in continuum mechanics are mentioned. The thesis is complemented with algorithm of chosen problems in program Wolfram Mathematica.
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Rings of order p^2 and p^3
Haluza, Vít ; Hrdina, Jaroslav (referee) ; Kureš, Miroslav (advisor)
This Bachelor thesis deals with classification and studying of properties of rings of order p^2 and p^3 (p is prime). Terms such as ring ideal or polynomial over finite field are introduced and used in this thesis. Apart from abstract unspecified rings, some special types of finite rings are also mentioned and classified. Program package, which is able to automatically classify given ring of order p^2 is also part of this thesis.
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Economic Curves
Hrubešová, Gabriela ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
The topic of this bachelor's thesis is to study some economic curves, a description of their attributes and a determining the mathematical expression. In the first part, it is explained the issues of general plane curves. Next part focuses on the characteristics of the most important economic curves and their use. The mathematical properties of the individual curves are described below. The last part is a software implementation in the program Wolfram Mathematica.
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Interactive Tools for Teaching Chemistry - Interactive Teaching Supported by Wolfram Mathematica
Helceletová, Zuzana ; Čapek Adamec, Martin (advisor) ; Duschinská, Karolina (referee)
Information and communication technologies (further referred to as "ICT") are increasingly influencing whole structure of the society. The integration of ICT into education together with the transition of the traditional teaching into a modern learning environment is therefore understood as one of the key factors of further development. This work examines some of the possibilities of applying electronical support for teaching chemistry at high schools. It focuses mainly on the visualisation of the subject matter, suitable positive motivation and incitement of the students. This paper describes in detail the presentation of subjects in chemistry using software applets of Wolfram Mathematica. One of the goals of this paper is to introduce the software and to present its potential application in teaching chemistry. Furthermore it shall encourage the use of particular demonstrations applets of the software Wolfram Mahematica. To achieve this goals, the author of this paper describes in detail the source codes of seven demonstrations applets called "Formulas and Structures for Some Simple Molecules", "Build Your Own Atoms", "Visualizing Atomic Orbitals", "Alkanes", "Oxidation States of Carbon", "Valence Shell Electron Pair Repulsion (VSEPR) Theory" and "Ideal Gas Law", which are available for free on...
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Invariants of jet groups and applications in continuum mechanics
Buriánek, Martin ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
This thesis is focused on jet groups and their matrix representations. The opening section deals with group representations, group actions on sets and invariants of actions. Another section explains terms such as smooth manifolds, Lie group and Lie algebra. The following part clarifies terms jet and jet group as a special example of Lie group. First of all, groups $G_1^r$ and $G_n^1$ are described, then description of group $G_n^2$ and its subgroups ensues. Representations of these jet groups are proposed. Finally, applications of jet groups in continuum mechanics are mentioned. The thesis is complemented with algorithm of chosen problems in program Wolfram Mathematica.
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Rapid research with computer algebra systems
Fischer, Cyril
Computer algebra systems (CAS) are gaining popularity not only among young students and scholars but also as a tool for serious work. These highly complicated software systems, which used to just be regarded as toys for computer enthusiasts, have reached maturity. Nowadays such systems are available on a variety of computer platforms, starting from freely-available on-line services up to complex and expensive software packages. The aim of this review paper is to show some selected capabilities of CAS and point out some problems with their usage from the point of view of 25 years of experience.
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Optimal portfolios
Vacek, Lukáš ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
In this diploma thesis, selected techniques for construction of optimal portfo- lios are presented. Risk measures and other criteria (Markowitz approach, Value at risk, Conditional value at risk, Mean absolute deviation, Spectral risk measure and Kelly criterion) are defined in the first part. We derived analytical solution for some cases of optimization problems, in some other cases there exists numeri- cal solution only however. Advantages and disadvantages, theoretical properties and practical aspects of software implementation in Wolfram Mathematica are also mentioned. Simulation methods suitable for portfolio optimization are brie- fly presented with their motivation in the second part. Multivariate distributions: normal, t-distribution and skewed t-distribution are presented in the third part with connection to optimization of portfolio with assumption of multivariate dis- tribution of financial losses. Optimization methods are illustrated on real data in the fourth part of this thesis. Analytical methods are compared with numerical ones. 1
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