Fox H-Functions in Self-Consistent Description of a Free-Electron Laser

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which is employed for the self-consistent description of the high-gain free-electron laser (FEL). It is shown that the Fox H-function is the Laplace image of the kernel of the integro-differential equation, which is also known as a fractional FEL equation with Caputo–Fabrizio type fractional derivative. Asymptotic solutions of the equation are analyzed as well.

Light Propagation on a Moving Closed Contour and the Role of Simultaneity in Special Relativity

We consider an example of a moving closed contour and the role played by simultaneity in the description of light propagation on the contour's moving sections. We show that, when constrained to propagate along the contour, the local speed of light on a moving section is no longer arbitrary and a consistent description requires conservation of simultaneity.

Review to the “Kryz-Azerbaijani-English Dictionary”

In February 2020, a unique publication came out under the title “Kryz-Azerbaijani-English dictionary”, prepared by I. A. Gummetov and M. Rind-Pavlovsky. The publication was presented on February 8, 2020 in the Khachmas ethnographic Museum in Azerbaijan with the invitation of the Kryz intelligence and representatives of the Khachmas city hall. Employees of the Tsadasa Institute of language, literature and art of the Russian Academy of Sciences were also invited to the presentation of the dictionary in Azerbaijan. The present dictionary is exceptional in its originality and completeness as far as the various lexical units are concerned from the point of their description and specification. The Kryz language is one of the non-written Lezgian languages of the Nakh-Dagestan language family. The Kryz language is used in the household sphere. The reviewed book with a description of the Kryz language lexemes consists of an introduction, two chapters, a list of abbreviations, and an Appendix. The description of the Kryz language lexemes is confirmed by thematic indexes from the Azerbaijani and English languages. The dictionary entry includes grammatical and stylistic characteristics of the three languages. In general, the dictionary is characterized by a consistent description of both the vocabulary and toponymy of the non-written language. Keywords: the Kryz language, I. A. Gummetov, M. Rind-Pavlovsky, dictionary, description of lexemes

Mathematical Model of Decomposition of Methane Hydrate during the Injection of Liquid Carbon Dioxide into a Reservoir Saturated with Methane and Its Hydrate

The article describes a mathematical model of pumping of heated liquid carbon dioxide into a reservoir of finite extent, the pores of which in the initial state contain methane and methane gas hydrate. This model takes into account the existence in the reservoir of three characteristic regions. We call the first region “near”, the second “intermediate”, and the third “far”. According to the problem statement, the first region contains liquid CO2 and hydrate, the second region is saturated with methane and water, the third contains methane and hydrate. The main features of mathematical models that provide a consistent description of the considered processes are investigated. It was found that at sufficiently high injection pressures and low pressures at the right reservoir boundary, the boundary of carbon dioxide hydrate formation can come up with the boundary of methane gas hydrate decomposition. It is also shown that at sufficiently low values of pressure of injection of carbon dioxide and pressure at the right boundary of the reservoir, the pressure at the boundary of hydrate formation of carbon dioxide drops below the boiling pressure of carbon dioxide. In this case, for a consistent description of the considered processes, it is necessary to correct the mathematical model in order to take into account the boiling of carbon dioxide. Maps of possible solutions have been built, which show in what ranges of parameters one or another mathematical model is consistent.