A mathematical formulation of the line-of-sight control problem is proposed for the case when this line is directed at a target. An operator situated on a moving platform controls the line of sight...

The description of the inhomogeneity of the cosmic ray spectrum in the region of 10 TV, which is observed in experimental data, in terms of isotropic diffusion from a single close source is considered. It is shown that such a description is possible, and the area of possible localization of the source in space and time and its energy are found. The method of penalty functions is used to account for the data on the spectrum of all particles.

In the presented work, the object of research is the "Notes of the Decembrist I.I. Gorbachevsky", which are one of the most valuable sources on the history of the Decembrist movement, created by its participants themselves. They highlight the formation and development of such a Decembrist organization as the Society of United Slavs, which later joined the Southern Society of Decembrists. Written in exile in Siberia, these notes represent not only a source of factual material, but also an original concept of the secret society's development, and a retrospective "inside look" at the mistakes made by the conspirators. However, Gorbachevsky's "Notes" are notable for another circumstance. Contrary to their well-established name in literature, we cannot unequivocally assert that their author was I.I. Gorbachevsky himself from among the Decembrists. The fact is that the first publication of the "Notes" – in the journal "Russian Archive" in 1882 – was presented under the heading "Notes of an Unknown Person from the Society of the United Slavs." The subject of the research in the presented work is the question of the authorship of the "Notes", which has no clear answer among historians today. In this paper, we propose a solution to the problem of determining the authorship of the "Notes of the Decembrist I.I. Gorbachevsky" using machine learning methods. I.I. Gorbachevsky himself, as well as the Decembrist P.I. Borisov, are considered as possible authors. The novelty of the research lies in the fact that machine learning methods were used to determine the authorship of the "Notes". The authors trained four types of models to predict the authorship of each of the sentences in the Notes. As a result, most of the proposals of the "Notes" were assessed as written by Gorbachev. The largest percentage of offers, 69.2%, was attributed to Gorbachev by the Count Vectorizer + SVC model. The accuracy of all models exceeded 80% on average, while those based on BERT coding averaged close to 90%. The main conclusion of the work, therefore, can be considered that the "Notes" were more likely to have been written by I.I. Gorbachevsky than by P.I. Borisov. The methods used in the framework of the presented study provide another argument in favor of this version. The code and dataset are available at the link: https://github.com/WLatonov/Gorbachevskiy_notes .

The subject of the research in this paper is the liberal agenda in the Russian press of the pre-Decabrist period. The object of the study is the newspapers published during this period. The novelty of the work lies in the fact that the proposed study searches for pink noise in the data that were obtained from the press of the first quarter of the XIX century. The paper shows that the public consciousness of this period was in a state of self-organized criticality. Previously, the state of self-organized criticality could be found only in systems that arose at the end of the XIX century or later. The difficulty of the problem considered in this paper is that there are almost no mass sources for such an early historical period, and very few of the available ones lend themselves to formalization. The novelty of the conducted research lies in the application of the scientific tool of the theory of self-organized criticality to data having origins in the first quarter of the XIX century. The main conclusion made by the authors of the article is that the public consciousness in the pre-Decabrist period was in a state of self-organized criticality. For the analysis, statistics of publications in newspapers and magazines were collected, which served as a reflection of the liberal agenda relevant to the period of the genesis of the Decembrists. The paper shows that the sequence of publications on liberal information issues in the Russian press in the period 1815-1825 contains pink noise. Fourier analysis was used to determine it in the dynamic series.

The minimax problem of stabilization is solved for a line of sight near a programmed trajectory. The motion of this line is described by a system of fourth-order linear differential equations. In...