Сибирский федеральный университет (СФУ) входит в топ-15 вузов России. Ведущие научные школы Красноярска. Лучший в России кампус. Мировые индустриальные партнёры

This paper presents a parallel corpus of raw texts between the Uzbek and Kazakh languages as a dataset for machine translation applications, focusing on the data collection process, dataset description, and its potential for reuse. The dataset-building process includes three separate stages, starting with a tiny portion of already available parallel data, then some more compiled from openly available resources like literature books, and web news texts, which were aligned using the sentence alignment method, encompassing a wide range of topics and genres. Finally, the majority of the dataset was taken from a raw text corpus in Uzbek and manually translated into Kazakh by a group of experts who are fluent in both languages. The resulting parallel corpus serves as a valuable resource for researchers and practitioners interested in Kazakh and Uzbek language processing tasks, particularly in the context of neural machine translation, where the presented data can be used for testing the rule-based machine translation models, or it can be used for both training statistical and neural machine translation models as well. The dataset has been made accessible through the widely recognized Hugging Face platform, a repository known for facilitating collaborative efforts and advancing Natural Language Processing (NLP) applications. This combination of methods to obtain a parallel corpus plays as a pivot for other languages among other low-resource Turkic languages.

Microseismic phenomena are studied by a Sel’kov generalized nonlinear dynamic system. This system is mainly applied in biology to describe substrate and product glycolytic oscillations. Thus, Sel’kov dynamic system can also describe interaction of two types of fractures in an elastic-friable medium. The first type includes seed fractures with lower energy and the second type are large fractures which generate microseisms. The first type of fractures are triggers for the second type of fractures. However opposite transition is possible. For example, when large fractures lose their energy and partially become seed ones. After their concentration increase, the process repeats providing auto oscillation character of microseism sources. Generalization of Sel’kov dynamic system is its analogue which is based on hereditarity. Hereditarity is studied within hereditary mechanics and it shows that a dynamic system can “remember” for some time the impact which was made upon it. It is typical for viscoelastic and yielding mediums. The Sel’kov generalized dynamic system will be called Sel’kov fractional dynamic system as long as from the point of view of mathematical description, it can be represented in the form of a system of differential equations with fractional derivatives. Fractional derivative orders are associated with system hereditarity and are responsible for energy dissipation intensity emitted by first- and second-type fractures. In the paper, the Sel’kov fractional dynamic model was numerically solved by Adams-Bashforth-Moulton method. Oscillo-grams and phase trajectories were plotted. It was shown that fractional dynamic model may have relaxation and damped oscillations.

The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of a fractional variable order of the Riemann–Liouville type. The issues of stability and convergence of an implicit finite-difference scheme are considered. Test examples are given to substantiate the theoretical results. Using the Runge rule, the results of the implicit scheme are compared with the results of the explicit scheme. Phase trajectories and oscillograms for a Duffing oscillator with a fractional derivative of variable order of the Riemann–Liouville type are constructed, chaotic modes are detected using the spectrum of maximum Lyapunov exponents and Poincare sections. Q-factor surfaces, amplitude-frequency and phase-frequency characteristics are constructed for the study of forced oscillations. The results of the study showed that the implicit finite-difference scheme shows more accurate results than the explicit one.