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## An Exo-Jupiter Candidate in the Eclipsing Binary FL Lyr Astronomy Reports, 2015, Vol. 59, No. 11, pp. 1035-1051

Light curves of the eclipsing binary FL Lyr acquired by the Kepler space telescope are analyzed.

Eclipse timing measurements for FL Lyr testify to the presence of a third body in the system. Preliminary

estimates of its mass and orbital period are 2MJ and 7 yrs. The times of primary minimum in the light

curve of FL Lyr during the operation of the Kepler mission are presented.

According to recent observations, relative number of flare stars does not change very much from cool dwarfs to hot A stars. Flare energies are strongly correlated with stellar luminosity and radius. Whence it follows that the typical magnetic field associated with a flare is several tens of gauss and the typical flare loop length-scales are parts of the stellar radius. Flares on O-B stars were not observed, but they are possible, since strong magnetic fields are detected on O-B stars. Therefore, stars of O-M spectral classes are potential sources of cosmic rays. Energy estimates of a magnetic field strength in a tube in photospheres of O-M stars are performed. Basing on their values possible flare energies and numbers of accelerated protons are estimated. The values obtained for the Sun correspond to observations by order of magnitude that justify estimates for other stars. Values of magnetic field strength in a tube differ less than five times for O and M flares (700 and 3500 G), but corresponding flare energies and numbers of accelerated protons for O stars are greater by five orders. Contrary fluencies of stellar protons appear to be five orders less.

The article analyzes the near-Earth space as a future habitat for humankind. This article investigates the factors affecting the location in this environment. We estimate the boundaries of space and related space. The article highlights the main features of the near-Earth space as a human-friendly environment.

Optical and near-infrared photometry, optical spectroscopy, and soft X-ray and UV monitoring of the changing-look active galactic nucleus NGC 2617 show that it continues to have the appearance of a type-1 Seyfert galaxy. An optical light curve for 2010-2016 indicates that the change of type probably occurred between 2010 October and 2012 February and was not related to the brightening in 2013. In 2016, NGC 2617 brightened again to a level of activity close to that in 2013 April. We find variations in all passbands and in both the intensities and profiles of the broad Balmer lines. A new displaced emission peak has appeared in Hβ. X-ray variations are well correlated with UV-optical variability and possibly lead by ˜2-3 d. The K band lags the J band by about 21.5 ± 2.5 d and lags the combined B + J filters by ˜25 d. J lags B by about 3 d. This could be because J-band variability arises from the outer part of the accretion disc, while K-band variability comes from thermal re-emission by dust. We propose that spectral-type changes are a result of increasing central luminosity causing sublimation of the innermost dust in the hollow bi-conical outflow. We briefly discuss various other possible reasons that might explain the dramatic changes in NGC 2617.

The discovery of a terrestrial planet orbiting Proxima Centauri has led to a lot of papers discussing the possible conditions on this planet. Since the main factors determining space weather in the Solar System are the solar wind and cosmic rays (CRs), it seems important to understand what the parameters of the stellar wind, Galactic and stellar CRs near exoplanets are. Based on the available data, we present our estimates of the stellar wind velocity and density, the possible CR fluxes and fluences near Proxima b. We have found that there are virtually no Galactic CRs near the orbit of Proxima b up to particle energies ∼ 1 TeV due to their modulation by the stellar wind. Nevertheless, more powerful and frequent flares on Proxima Centauri than those on the Sun can accelerate particles to maximum energies ∼ 3150αβ GeV (α, β < 1). Therefore, the intensity of stellar CRs in the astrosphere may turn out to be comparable to the intensity of low-energy CRs in the heliosphere.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.