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Symbolické reprezentace kompaktních prostorů
Kazda, Alexandr
Title: Symbolic representations of compact spaces Author: Alexandr Kazda Department: Department of Algebra Supervisor: Prof. RNDr. Petr Kůrka, CSc. Supervisor's e-mail address: kurka@cts.cuni.cz Abstract: The thesis concerns itself with Möbius number systems. These systems represent points using sequences of Möbius transformations. We are mainly inter- ested in representing the unit circle (which is equivalent to representing R ∪ {∞}). The main aim of the thesis is to improve already known tools for proving that a given subshift-iterative system pair is in fact a Möbius number system. We also study the existence problem: How to describe iterative systems resp. subshifts for which there exists a subshift resp. iterative system such that the resulting pair forms a Möbius number system. While we were unable to provide a complete answer to this question, we present both positive and negative partial results. As Möbius number systems are also subshifts, we can ask when a given Möbius number system is sofic. We give this problem a short treatment at the end of our thesis. Keywords: Möbius transformation, numeral system, subshift
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Symbolické reprezentace kompaktních prostorů
Kazda, Alexandr
Title: Symbolic representations of compact spaces Author: Alexandr Kazda Department: Department of Algebra Supervisor: Prof. RNDr. Petr Kůrka, CSc. Supervisor's e-mail address: kurka@cts.cuni.cz Abstract: The thesis concerns itself with Möbius number systems. These systems represent points using sequences of Möbius transformations. We are mainly inter- ested in representing the unit circle (which is equivalent to representing R ∪ {∞}). The main aim of the thesis is to improve already known tools for proving that a given subshift-iterative system pair is in fact a Möbius number system. We also study the existence problem: How to describe iterative systems resp. subshifts for which there exists a subshift resp. iterative system such that the resulting pair forms a Möbius number system. While we were unable to provide a complete answer to this question, we present both positive and negative partial results. As Möbius number systems are also subshifts, we can ask when a given Möbius number system is sofic. We give this problem a short treatment at the end of our thesis. Keywords: Möbius transformation, numeral system, subshift
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Projektivní geometrie - náhled z vyšší dimenze
Gottvald, Aleš
Upon recognizing principal and ubiquitous role of projective geometry in theory and applications, we select some of its basic concepts and ideas (homogeneous coordinates, Möbius transformation, cross-ratio, Cayley's hyperbolic distance, ...), and show their first metamorphoses.
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