An elementary proof of the irrationality of Tschakaloff series

We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment: 5 pages, AMSTe

Dynamics of Vocatives in American, Russian and British Political Communication

The paper analyses dynamic aspects of the vocative system in American, Russian and British political communication. The research considers inaugural addresses of the presidents of the USA (1789-2017), those of the presidents of the Russian Federation (1991-2012), Coronation speeches of British monarchs (1937 and 1953) as a special genre of political discourse. Vocatives used in these addresses and speeches are a source of linguistic analysis which reveals typological differences and similarities in American, Russian and British communication. The author characterizes linguistic-cultural peculiarities of political discourse of the USA, Russia and the United Kingdom. The author proves that status terms of address predominate in comparison to emotive ones in American and Russian presidents' political discourse; British monarchs usually omit forms of address in the epideictic genre discussed in the paper. The American presidents use various vocatives (special status vocatives and general status terms of address) in comparison to those used in inaugural addresses of the presidents of the Russian Federation (special status vocatives); the British monarchs use zero vocatives in the Coronation speeches. Functions of vocatives used in the addresses and speeches in question (appellative, contact-establishing and attitude-characterizing) contribute to shortening a social status distance between the leaders of the countries and addressees

Research technique and test experiments for the analysis of petrophysical properties of weak-consolidated and friable rocks

With the use of created measuring system for the study of petrophysical properties of incompetent, friable and loose rocks and sludge samples test experiments were performed on pit sand samples of known grain-size distribution, consolidated and disintegrated rock samples of Subbotin oil field of the Maykop formation. It was experimentally established that the shrinkage rate of soft rocks decreases sharply and attenuates at the effective pressure of 30 to 35MPa, which leads to stabilization of their filtration-capacitive and deformation behavior. The research of rocks, which are returned during drilling in the form of sand and cuttings, opens opportunities for using the obtained data for interpretation of production well logging and calculation of hydrocarbon reserves