Global dynamics and stability limits for planetary systems around HD 12661, HD 38529, HD 37124 and HD 160691

In order to distinguish between regular and chaotic planetary orbits we apply a new technique called MEGNO in a wide neighbourhood of orbital parameters determined using standard two-body Keplerian fits for HD 12661, HD 38529, HD 37124 and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system.Comment: 12 pages, 3 figures, accepted ApJ, revised version following the referee's repor

On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes

The algebraic hyperstructure of elementary particles in physical theory

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.Comment: 13 page

Phoebe 2.0 – Triple and multiple systems

Some close binary formation theories require the presence of a third body so that the binary orbit can shrink over time. Tidal friction and Kozai cycles transfer energy from the binary to its companion, resulting in a close inner binary and a wide third body orbit. Spectroscopy and imaging studies have found 40% of binaries with periods less than 10 days, and 96% with periods less than 3 days, have a wide tertiary companion. With recent advancements in large photometric surveys, we are now beginning to detect many of these triple systems by observing tertiary eclipses or through the effect they have on the eclipse timing variations (ETVs) of the inner-binary. In the sample of 2600 Kepler EBs, we have detected the possible presence of a third body in ∼20%, including several circumbinary planets. Some multiple systems are quite dynamical and feature disappearing and reappearing eclipses, apsidal motion, and large disruptions to the inner-binary. phoebe is a freely available binary modeling code which can dynamically model all of these systems, allowing us to better test formation theories and probe the physics of eclipsing binaries

Lermontov’s Sketch “Russia Has no Past...” in Context of “Eastern Question”: to Problem of Poet’s Artistic Historiosophy

The subject of the study was the content of Lermontov’s autograph “Russia has no past...” from the “Notebook donated by V. F. Odoevsky” in the aspect of the poet’s historical views. The purpose of the article is connected with the establishment of the historical and cultural genesis of the text and the clarification of its meaning in the context of Lermontov’s work, Russian-Caucasian interaction, as well as the historiosophical concepts of the first third of the 19th century. The research methodology is connected with textological, historical-genetic, cultural-historical, comparative-historical approaches to text analysis. The specific tools are the description of the autograph, as well as the preparation of a textological passport that reflects the technical aspects of the handwritten text. Lermontov’s note is presented in the context of a dialogue with contemporaries and folklore tradition. The historical and literary context of Lermontov’s note, its allusions to the facts of sociohistorical thought and images of Russian literature emphasize Lermontov’s patriotism. As a result of the study, Lermontov’s protoPan-Slavic concept was reconstructed, which correlates with ideas about the ways of Russia’s development as a great power. The conclusion of the study was the understanding of Lermontov’s sketch “Russia has no past...” as an emanation of the poet’s reflections on relations between Russia and the Caucasus in the aspect of the “Eastern question”

From the experience of teaching russian as a foreign in a remote format at the preparatory department for foreign students

Статья посвящена основным проблемам, с которыми сталкиваются преподаватели, проводящие практические занятия в дистанционном формате, обзору программ для обучения, а также преимуществам и недостаткам данного формата работыThe article is devoted to the main problems faced by teachers who conduct practical classes in a distance format, an overview of learning programs, as well as the advantages and disadvantages of this format of work

From the Experience of Work with Egyptian Students

Статья посвящена описанию некоторых трудностей, с которыми сталкиваются преподаватели русского языка как иностранного, работающие в египетских группах, а также возможным путям их решения.The article describes some of the difficulties faced by teachers of Russian as a foreign language working in Egyptian groups, as well as possible ways to solve them