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p-Adic numbers Dubiel, Richard ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee) Univerzita Karlova v Praze Matematicko-fyzikální fakulta BAKALÁŘSKÁ PRÁCE Richard Dubiel p-adická čísla Katedra algebry Vedoucí bakalářské práce: Mgr. Jan Šťovíček, Ph.D. Studijní program: Matematika Studijní obor: obecná matematika Abstract: This thesis deals with construction of the field of p-adic numbers as a completion of rational numbers field and introduces several important properties of this field. It will introduce concepts of an absolute value, metric, ultrametric and completion of field with respect to absolute value. Then we introduce a p-adic absolute value - one that measures "how much" is a number divsible by a prime number p. Then we construct the completion of the field of rational numbers with respect to this absolute value - field of p-adic numbers. We show, how can one represent these numbers. At last, we introduce two of the most important results of the theory of p-adic numbers - Hensel lemma and Hasse-Minkowski theorem. Detailed record

Source parameters of mining induced seismic events in Zabrze Mine (Poland): Preliminary results Dubiel, R. ; Idziak, F. ; Kaláb, Zdeněk ; Knejzlík, Jaromír Seismic network in Zabrze mine consist of 15 stations in distances up to 3,5 km from source area. The source parameters were estimated directly from the velocity spectra. Preliminary results of source parameters of mining induced seismic events in Zabrze mine are presented, obtained relations for selected data set document basic properties of foci. Detailed record

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1	Dubiel, Richard

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