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We prove an analogue of Chebyshev's alternation theorem for linearly independent discrete functions $\Phi_n=\{\varphi_k\}_{k=1}^n$ on the interval $[0,q]_{\mathbb{Z}}=[0,q]\cap \mathbb{Z}$. In particular, we establish that the polynomial of best uniform approximation of a discrete function $f$ admits a Chebyshev alternance set of length $n+1$ if and only if $\Phi_n$ is a Chebyshev $T_{\mathbb{Z}}$-system. Also, we obtain a discrete version of Sturm's oscillation theorem, according to which the number of discrete zeros of the polynomial $\sum_{k=m}^{n}a_k\varphi_k$ is no less than $m-1$ and no more than $n-1$. This implies that $\Phi_n$ is a $T_{\mathbb{Z}}$-system and a discrete Sturm-Hurwitz spectral gap theorem is valid. As applications, we study the orthogonal polynomials with removed largest zeros. We establish the monotonicity property of coefficients in the Fourier expansions of such polynomials, thereby strengthening the results of H. Cohn and A. Kumar. We apply this to solve a Yudin-type extremal problem for polynomials with spectral gap., Comment: 31 pages

The study of cosmic rays in the energy range from 1 to 1000 PeV is crucial for understanding their origins and propagation paths. As part of this research, a new SPHERE-3 installation is being developed, featuring enhanced light sensitivity and optical resolution, based on the experience gained with the balloon-borne SPHERE-2 installation. This report describes a computational complex designed for simulating the formation of Cherenkov light on the detector grid of the SPHERE-3 telescope., Comment: Published as a conference paper at X International Conference on Mathematial Modeling. 4 pages, 1 figure

A new Cherenkov telescope of the SPHERE type is under development. Its main goal is to promote the solution of the problem of the primary cosmic ray mass composition at ultra high energies (1--100 PeV) using a newly developed technique of the primary mass assignment to EAS event on event-by-event basis. The telescope will carry out measurements of both the Cherenkov light reflected from the snow surface as well as the direct one. Sensitivity of the direct Cherenkov images' shapes to the primary mass is demonstrated., Comment: Published as a conference paper at 21st Lomonosov Conference on Elementary Particle Physics. 7 pages, 5 figures

A new SPHERE-3 telescope is being developed for cosmic rays spectrum and mass composition studies in the 5--1000 PeV energy range. Registration of extensive air showers using reflected Cherenkov light method applied in the SPHERE detector series requires a good trigger system for accurate separation of events from the background produced by starlight and airglow photons reflected from the snow. Here we present the results of convolutional networks application for the classification of images obtained from Monte Carlo simulation of the detector. Detector response simulations include photons tracing through the optical system, silicon photomultiplier operation and electronics response and digitization process. The results are compared to the SPHERE-2 trigger system performance., Comment: 7 pages, 5 figures Published as a conference paper at DLCP2024, June 19-21, 2024, Moscow, Russia. https://dlcp2024.sinp.msu.ru Submitted to Moscow University Physics Bulletin

Magnetic field-induced electric polarization has been observed in trigonal non-centrosymmetric paramagnetic Pr3Ga5SiO14 langasite. We detected quadratic electric polarization along the a-axis in the basal ab plane for various magnetic-field orientations. Electric polarization along the c-axis is only evident starting from the fourth power of magnetic field, in accordance with the trigonal symmetry. The magnetic properties of Pr3Ga5SiO14 primarily stem from the local anisotropic magnetic moment of the two lowest Pr3+ singlets (quasi-doublet) in the crystal electric field. The random distribution of Ga/Si in the 2d positions leads to a local distortion of C2 symmetry and to a splitting distribution of the quasi-doublet. By considering the interactions of local moments among different Pr3+ positions within a phenomenological approach for the allowed magnetoelectric coupling, we derive the electric polarization in terms of symmetry-allowed combinations of local magnetic susceptibilities and field components. The magnetic field dependence of electric polarization in the basal plane, P_{a,b*}, is mainly determined by the accumulation of effective local susceptibilities, exhibiting similar behavior in low fields, while polarization along the c-axis, P_c, arises from the non-equivalence of local effective magnetic susceptibilities in different Pr3+ positions. Our findings suggest that the temperature dependencies of magnetic and magnetoelectric susceptibilities are highly sensitive to the distribution of the quasi-doublet splitting, which reflects the local symmetry breaking.

Young planetary systems represent an opportunity to investigate the early stages of (exo)planetary formation because the gravitational interactions have not yet significantly changed the initial configuration of the system. TOI-4562 b is a highly eccentric temperate Jupiter analogue orbiting a young F7V-type star of $<700$ Myr in age with an orbital period of $P_{orb} \sim 225$ days and an eccentricity of $e=0.76$, and is one of the largest known exoplanets to have formed in situ. We observed a new transit of TOI-4562 b using the 0.6-m Zeiss telescope at the Pico dos Dias Observatory (OPD/LNA) in Minas Gerais, Brazil, and combine our data with Transiting Exoplanet Survey Satellite (TESS) and archive data, with the aim being to improve the ephemerides of this interesting system. The $O-C$ diagram for the new ephemeris is consistent with the presence of a giant planet in an outer orbit around TOI-4562. TOI-4562 c is a planet with a mass of $M=5.77 M_{Jup}$, an orbital period of $P_{orb}= 3990$ days, and a semi-major axis of $a = 5.219$ AU. We report the discovery of TOI-4562 c, the exoplanet with the longest orbital period discovered to date via the transit timing variation (TTV) method. The TOI-4562 system is in the process of violent evolution with intense dynamical changes - judging by its young age and high eccentricity - and is therefore a prime target for studies of formation and evolution of planetary systems., Comment: 5 pages and 3 figures (+ appendix). Accepted for publication in Astronomy & Astrophysics, Letters to the Editor

LiCu$_3$O$_3$ is a novel 2D S=1/2 antiferromagnet with randomly depleted square lattice. The crystal structure contains two types of square planes with different Cu$^{2+}\rightarrow$ Li$^{+}$ substitution rates (20% and 40%). $^7$Li NMR and magnetization measurements performed on single crystals of LiCu$_3$O$_3$ revealed the occurrence of magnetic order at $T_{c1}=123$ K and the change of the magnetic state at $T_{c2}\approx30$ K. The high temperature transition can be attributed to establishment of magnetic order in planes with higher concentration of magnetic ions and the low temperature transition -- to the magnetic ordering in planes with lower concentration of magnetic ions. Broad continuous NMR spectra below $T_{c1}$ reflect a continuous distribution of values or directions of magnetic moments in LiCu$_3$O$_3$ typical for spiral, spin-modulated magnetic structures or structures with frozen disorder. Magnetization measurements revealed a spin-flop transition which indicates weak uniaxial anisotropy of the spin structure. Relatively small value of magnetic susceptibility at all orientations of applied magnetic field shows that magnetic structure is rigid, since the estimated value of saturation field derived from differential susceptibility measured at $\mu_0 H=5$ T is $\mu_0H_{sat} \approx$200 T., Comment: 11 pages, 12 figures

We calculate analytically the charge density $\rho_{\text{ind}}(\boldsymbol{r})$ at small distances induced by a Coulomb impurity in two-dimensional transition metal dichalcogenides. The calculations were performed exactly in the coupling constant. We found the first three leading terms of the charge density asymptotics at small distances. Using this result, we demonstrate that the impurity with charge number $Z=1$ remains subcritical at any value of the coupling constant, whereas impurities with higher charge number could become supercritical at certain coupling constant values. Such a behavior is similar to that in graphene., Comment: 5 pages, 1 figure

We consider cosmological models with an arbitrary number of scalar fields nonminimally coupled to gravity and construct new integrable cosmological models. In the constructed models, the Ricci scalar is an integral of motion irrespectively of the type of metric. The general solutions of evolution equations in the spatially flat FLRW metric have been found for models with the quartic potentials., Comment: 10 pages; to be published in Physics of Particles and Nuclei

The magnetic properties of Ho-doped langasites (La:Ho)$_3$Ga$_5$SiO$_{14}$ are dominated by the Ising-like magnetic moments of the Ho$^{3+}$ ions. In their saturated regime, the induced magnetic state breaks both time and space inversion symmetries, leading to a novel linear magnetoelectric effect. However, due to distortions induced by a shared Ga/Si occupancy of the 2d sites, resolving the microscopic nature of the magnetic configuration remains a difficult task. Here we combine polarized neutron diffraction and angular dependent magnetization experiments to determine the local distortions of the Ho$^{3+}$ magnetic moments in doped langasites (La$_{1-x}$Ho$_x$)$_3$Ga$_5$SiO$_{14}$ with $x \approx 0.015$ and $x \approx 0.045$. We propose a model for a field-induced magnetic configuration with arbitrary orientations of the local Ising axis of Ho$^{3+}$ in distorted positions. The operations of broken local $C_2$ symmetry and rotations around the trigonal $C_3$ axis connect different sites, restoring the global P321 symmetry of the crystal and simplifying the description of the magnetic properties. The superposition of two distorted Ho$^{3+}$ positions connected by $C_2$ symmetry determines the local magnetic susceptibility tensor, which no longer appears Ising-like at low fields.

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in $JHK_{\rm s}$ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took $\sim 2000$ hours, covering about 4% of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_{\rm s}$ catalogue of $\gtrsim 1.5\times10^9$ point sources, as well as a $K_{\rm s}$ band catalogue of $\sim 10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST., Comment: 17 pages, 11 figures (+ appendix). Accepted for publication in Astronomy and Astrophysics in section 14: Catalogs and data

We have selected candidate massive stars in the galaxy IC 342 based on archival images from the Hubble Space Telescope and images from the 2 m telescope at the Natioal Astronomical Observatory Rozhen, Bulgaria. Spectral observations of 24 out of 27 selected stars are carried out with the 6 m BTA telescope at the SAO RAS and with the 3.5 m Apache Point Observatory telescope (USA) as part of the program for searching bright massive stars in galaxies outside the Local Group. Our analysis reveals that 12 objects have spectra lacking prominent features, except for the emission lines of the surrounding nebulae and are identified as single supergiants of classes O9 to F5 or spatially unresolved young compact clusters. One source with an absorption spectrum probably belongs to our Galaxy. The spectra of seven other objects show features typical of Wolf-Rayet stars or compact clusters containing Wolf-Rayet stars. Another source is a compact supernova remnant. Two other objects are tentatively classified as cold LBV candidates, and one object is classified as a B[e]-supergiant candidate.

The finite basis set method is commonly used to calculate atomic spectra, including QED contributions such as bound-electron self-energy. Still, it remains problematic and underexplored for vacuum-polarization calculations. We fill this gap by trying this approach in its application to the calculation of the vacuum-polarization charge density and the Wichmann-Kroll correction to the electron binding energy in a hydrogen-like ion. We study the convergence of the method with different types and sizes of basis sets. We cross-check our results for the Wichmann-Kroll correction by direct integration of the Green's function. As a relevant example, we consider several heavy hydrogen-like ions and evaluate the vacuum polarization correction for $S$ and $P$ electron orbitals., Comment: 10 pages, 7 figures

Planetary systems in mean motion resonances hold a special place among the planetary population. They allow us to study planet formation in great detail as dissipative processes are thought to have played an important role in their existence. Additionally, planetary masses in bright resonant systems may be independently measured both by radial velocities (RVs) and transit timing variations (TTVs). In principle, they also allow us to quickly determine the inclination of all planets in the system, as for the system to be stable, they are likely all in coplanar orbits. To describe the full dynamical state of the system, we also need the stellar obliquity that provides the orbital alignment of a planet with respect to the spin of their host star and can be measured thanks to the Rossiter-McLaughlin effect. It was recently discovered that HD 110067 harbours a system of six sub-Neptunes in resonant chain orbits. We here analyze an ESPRESSO high-resolution spectroscopic time series of HD 110067 during the transit of planet c. We find the orbit of HD 110067 c to be well aligned with sky projected obliquity $\lambda =6^{+24}_{-26}$ deg. This result is indicative that the current architecture of the system has been reached through convergent migration without any major disruptive events. Finally, we report transit-timing variation in this system as we find a significant offset of 19 $\pm$ 4 minutes in the center of the transit compared to the published ephemeris., Comment: Accepted to A&A

One can infer the orbital alignment of exoplanets with respect to the spin of their host stars using the Rossiter-McLaughlin effect, thereby giving us the chance to test planet formation and migration theories and improve our understanding of the currently observed population. We analyze archival HARPS and HARPS-N spectroscopic transit time series of six gas giant exoplanets on short orbits, namely WASP-77 Ab, WASP-101b, WASP-103b, WASP-105b, WASP-120b and WASP-131b. We find a moderately misaligned orbit for WASP-101b ($\lambda =34\degree\ \pm$ 3) and a highly misaligned orbit for WASP-131b ($\lambda =161\degree\ \pm$ 5), while the four remaining ones appear aligned: WASP-77 Ab ($\lambda =-8\degree\ ^{+19}_{-18}$), WASP-103b ($\lambda =2\degree\ ^{+35}_{-36}$), WASP-105b ($\lambda =-14\degree\ ^{+28}_{-24}$), and WASP-120b ($\lambda =-2\degree\ \pm$ 4). For WASP-77 Ab, we were able to infer its true orbital obliquity ($\Psi =48\degree\ ^{+22}_{-21}$). We additionally perform transmission spectroscopy of the targets in search of strong atomic absorbers in the exoatmospheres, but are unable to detect any features, most likely due to the presence of high-altitude clouds or Rayleigh scattering muting the strength of the features. Finally, we comment on future perspectives for studying these targets with the upcoming space missions to investigate the evolution and migration histories of these planets., Comment: Accepted to A&A

We have performed a comprehensive search of a VISTA Variables in the Via Lactea (VVV) database of 9.5 yr light curves for variable sources with $\Delta K_s \ge 4$ mag, aiming to provide a large sample of high amplitude eruptive young stellar objects (YSOs) and detect unusual or new types of infrared variable source. We find 222 variable or transient sources in the Galactic bulge and disc, most of which are new discoveries. The sample mainly comprises novae, YSOs, microlensing events, Long Period Variable stars (LPVs) and a few rare or unclassified sources. Additionally, we report the discovery of a significant population of aperiodic late-type giant stars suffering deep extinction events, strongly clustered in the Nuclear Disc of the Milky Way. We suggest that these are metal-rich stars in which radiatively driven mass loss has been enhanced by super-solar metallicity. Among the YSOs, 32/40 appear to be undergoing episodic accretion. Long-lasting YSO eruptions have a typical rise time of $\sim$2 yr, somewhat slower than the 6-12 month timescale seen in the few historical events observed on the rise. The outburst durations are usually at least 5 yr, somewhat longer than many lower amplitude VVV events detected previously. The light curves are diverse in nature, suggesting that multiple types of disc instability may occur. Eight long-duration extinction events are seen wherein the YSO dims for a year or more, attributable to inner disc structure. One binary YSO in NGC 6530 displays periodic extinction events (P=59 days) similar to KH 15D., Comment: Accepted by MNRAS. 38 pages. Full source lists and light curves are available in the Ancillary Files

The detection of radio emission from an exoplanet would constitute the best way to determine its magnetic field. Indeed, the presence of a planetary magnetic field is a necessary condition for radio emission via the Cyclotron Maser Instability. The presence of a magnetic field is, however, not sufficient. At the emission site, the local cyclotron frequency has to be sufficiently high compared to the local plasma frequency. As strong stellar insolation on a low-mass planet can lead to an extended planetary atmosphere, the magnetospheric plasma frequency depends on the planetary mass, its orbital distance, and its host star. We show that an extended planetary atmosphere can quench the radio emission. This seems to be true, in particular, for an important fraction of the planets less massive than approximately two Jupiter masses and with orbital distances below $\sim$0.2 AU. Most of the best candidates suggested by radio scaling laws lie in this parameter space. Taking this effect quenching into account will have important implications for the target selection of observation campaigns. At the same time, this effect will have consequences for the interpretation of observational data., Comment: 6 pages, 1 figure. Proceedings of Planetary, Solar and Heliospheric Radio Emissions IX (2023)