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Ondřej Kolouch and Lukáš Novotný

Abstract

This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos’ results on irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.

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Jaroslav Hančl, Ondřej Kolouch and Lukáš Novotný

Abstract

Using an idea of Erdős the paper establishes a criterion for the linear independence of infinite products which consist of rational numbers. A criterion for irrationality is obtained as a consequence.

Open access

Sandra Kreisslová and Lukáš Novotný

Abstract

Language preservation is considered to be one of the central missions of ethnic groups. For the German minority in the Czech Republic too, language plays an important role in group identity. Its current language situation is a result of the negative historic developments after World War II and under the communist regime. Due to the forced resettlement of most German-speaking inhabitants and the subsequent assimilation policies of the communist regime, the German community underwent strong cultural and language assimilation, which is also attested by the steady decline of its membership. The study focuses on issues of the language situation of the German minority and the revitalization efforts that have been undertaken by its elite in cooperation with other relevant institutions. A research survey of the main representatives of the minority and its regional associations demonstrates their evaluations of the ways in which German language is currently used and promoted in the Czech Republic, and it also points to the different strategies they have been striving to implement to reverse the language shift.