The study focuses on the compatriot community in Ukraine, particularly on the Crimea peninsula. In the introduction, attention is paid to the history of settlement of southern Ukraine by the Czech ethnic group in the 1860s. The reasons which made several hundreds of people leave their home region, their mother country, the initial problems they had to deal with in the new land, adaptation to the new living conditions, etc. are further discussed. Apart from the past, this essay also covers the present situation. This is the period when the former Czech villages have become multinational, while the Czechs do not form the majority population in any of them as they used to in the past. In spite of the gradual irrepressible process of assimilation, the Czech Republic tries to help its compatriots. This concerns above all the funding of reconstruction of associational buildings, purchase of their equipment, assistance with organizing compatriot meetings and so on. the main emphasis is, however, on the field of education, especially on Czech language retention.
An analysis is performed in the article of an output and propagation of a coherent light beam outgoing from a single frequency optical fibre supposing an inclined termination of the fibre, and also an analysis of a transformation of such a Gaussian beam of an ideal lens. Direct transformation performed analogously to the input beam gives the same result as a calculation of the diffraction on the lens if the beam is not apertured. For characterization of the beam transformed by the lens the concept of the Fresnel number of the Gaussian beam is used. and V článku je proveden rozbor výstupu a šíření koherentního světelného svazku vystupujícího z jednovidového optického vlákna za předpokladu šikmého zakončení čela vlákna a rozbor transformace takového gaussovského svazku ideální čočkou. Přímá transformace provedená analogicky k dopadajícímu svazku dává stejný výsledek jako výpočet difrakce na čočce, pokud svazek není cloněn. K charakterizaci transformovaného svazku čočkou je využito konceptu Fresnelova čísla gaussovského svazku.