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This article presents the early results of synchronous multiwavelength observations of one of the brightest gamma-ray bursts (GRBs) GRB 160625B with the detailed continuous fast optical photometry of its optical counterpart obtained by MASTER and with hard X-ray and gamma-ray emission, obtained by the Lomonosov and Konus-Wind spacecraft. The detailed photometry led us to detect the quasi-periodical emission components in the intrinsic optical emission. As a result of our analysis of synchronous multiwavelength observations, we propose a three-stage collapse scenario for this long and bright GRB. We suggest that quasiperiodic fluctuations may be associated with forced precession of a self-gravitating rapidly rotating superdense body (spinar), whose evolution is determined by a powerful magnetic field. The spinar's mass allows it to collapse into a black hole at the end of evolution., Comment: 22 pages, 12 figures, 4 tables, accepted for publication in ApJ

We demonstrate the laser-induced control over spin-wave (SW) transport in the magnonic crystal (MC) waveguide formed from the semiconductor slab placed on the ferrite film. We considered bilayer MC with periodical grooves performed on the top of the n-type gallium arsenide slab side that oriented to the yttrium iron garnet film. To observe the appearance of magnonic gap induced by laser radiation, the fabricated structure was studied by the use of microwave spectroscopy and Brillouin light-scattering. We perform detailed numerical studies of this structure. We showed that the optical control of the magnonic gaps (frequency width and position) is related to the variation of the charge carriers' concentration in GaAs. We attribute these to nonreciprocity of SW transport in the layered structure. Nonreciprocity was induced by the laser exposure of the GaAs slab due to SWs' induced electromagnetic field screening by the optically-generated charge carriers. We showed that SW dispersion, nonreciprocity, and magnonic band gap position and width in the ferrite-semiconductor magnonic crystal can be modified in a controlled manner by laser radiation. Our results show the possibility of the integration of magnonics and semiconductor electronics on the base of YIG/GaAs structures.

We consider the isomorphism problem for formal matrix rings over a given ring. Principal factor matrices of such rings play an important role in this case. The work is supported by Russian Scientific Foundation, project 23-21-00375 (P.A. Krylov) and project 22-11-00052 (A.A. Tuganbaev)., Comment: arXiv admin note: substantial text overlap with arXiv:2211.02957

Let $\mathfrak{g}$ be a complex simple finite dimensional Lie algebra and $G$ be the adjoint Lie group with the Lie algebra $\mathfrak{g}$. To every $C \in G$ one can associate a commutative subalgebra $B(C)$ in the Yangian $Y(\mathfrak{g})$, which is responsible for the integrals of the (generalized) $XXX$ Heisenberg magnet chain. Using the approach of arXiv:1708.05105, we construct a natural structure of affine crystals on spectra of $B(C)$ in Kirillov-Reshetikhin $Y(\mathfrak{g})$-modules in type $A$. We conjecture that such a construction exists for arbitrary $\mathfrak{g}$ and gives Kirillov-Reshetikhin crystals. Our main technical tool is the degeneration of Bethe subalgebras in the Yangian to commutative subalgebras $\mathcal{A}_\chi^{\mathrm{u}}$ in the universal enveloping of the current Lie algebra, $U(\mathfrak{g}[t])$, which depend on the parameter $\chi$ from the Lie algebra $\mathfrak{g}$ (and are of independent interest). We show that these subalgebras come from the Feigin-Frenkel center on the critical level as described by Feigin, Frenkel and Toledano Laredo in arXiv:math/0612798. This allows to prove that our affine crystals in type $A$ are indeed Kirillov-Reshetikhin by reducing to the crystal structure on the spectra of inhomogeneous Gaudin model which is already known (arXiv:1708.05105)., Comment: 66 pages

We prove the existence of strong solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Strong uniqueness is also discussed., Comment: 32 pages, previous article is completely reworked. arXiv admin note: text overlap with arXiv:2206.07871, much stronger result is obtained, somewhat better organized, one reference added

We consider realization and isomorphism problems for formal matrix rings over a given ring. Principal multiplier matrices of such rings play an important role in this case.\\ The work of A.A.Tuganbaev is supported by Russian Scientific Foundation, project 22-11-00052.

Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a simple highest weight $\widehat{\mathfrak{g}}$-module are either bounded or are given by a linear function of the weight. We explain and generalize this observation using Kazhdan-Lusztig theory, by computing values at $q=1$ of certain (parabolic) affine inverse Kazhdan-Lusztig polynomials. In particular, we obtain explicit character formulas for some $\widehat{\mathfrak{g}}$-modules of negative integer level $k$ when $\mathfrak g$ is of type $D_n$, $E_6$, $E_7$, $E_8$ and $k \geqslant -2, -3, -4, -6$ respectively, as conjectured by Kac and Wakimoto. The calculation relies on the explicit description of the canonical basis in the cell quotient of the anti-spherical module over the affine Hecke algebra corresponding to the subregular cell. We also present an explicit description of the corresponding objects in the derived category of equivariant coherent sheaves on the Springer resolution, they correspond to irreducible objects in the heart of a certain $t$-structure related to the so called non-commutative Springer resolution., Comment: 42 pages, v2: few typos corrected, v3: extended the proof of lemma 4.7

De Concini-Procesi introduced varieties known as wonderful compactifications, which are smooth projective compactifications of semisimple adjoint groups $G$. We study the Frobenius pushforwards of invertible sheaves on the wonderful compactifications, and in particular its decomposition into locally free subsheaves. We give necessary and sufficient conditions for a specific line bundle to be a direct summand of the Frobenius pushforward of another line bundle, formulated in terms of the weight lattice of $\widetilde{G}$, the universal cover of $G$ (identified with the Picard group of the wonderful compactification). In the case of $G=\mathsf{PSL}_n$, we offer lower bounds on the multiplicities (as direct summands) for those line bundles satisfying the sufficient conditions. We also decompose Frobenius pushforwards of line bundles into a direct sum of vector subbundles, whose ranks are determined by invariants on the weight lattice of $G$. We study a particular block which decomposes as a direct sum of line bundles, and identify the line bundles which appear in this block. Finally, we present two approaches to compute the class of the Frobenius pushforward of line bundles on wonderful compactifications in the rational Grothendieck group and in the rational Chow group., Comment: 54 pages

The Nuclotron-base Ion Collider fAcility (NICA) is under construction at the Joint Institute for Nuclear Research (JINR), with commissioning of the facility expected in late 2022. The Multi-Purpose Detector (MPD) has been designed to operate at NICA and its components are currently in production. The detector is expected to be ready for data taking with the first beams from NICA. This document provides an overview of the landscape of the investigation of the QCD phase diagram in the region of maximum baryonic density, where NICA and MPD will be able to provide significant and unique input. It also provides a detailed description of the MPD set-up, including its various subsystems as well as its support and computing infrastructures. Selected performance studies for particular physics measurements at MPD are presented and discussed in the context of existing data and theoretical expectations., Comment: 53 pages, 68 figures, submitted as a Review article to EPJA

Recent advances in increasing the spectroscopic energy resolution in scanning tunneling microscopy (STM) have been achieved by integrating electron spin resonance (ESR) with STM. Here, we demonstrate the design and performance of a home-built STM capable of ESR at temperatures ranging from 1 K to 10 K. The STM is incorporated with a home-built Joule-Thomson refrigerator and a 2-axis vector magnet. Our STM design allows for the deposition of atoms and molecules directly into the cold STM, eliminating the need to extract the sample for deposition. In addition, we adopt two methods to apply radio-frequency (RF) voltages to the tunnel junction, the early design of wiring to the STM tip directly, and a more recent idea to use an RF antenna. Direct comparisons of ESR results measured using the two methods and simulations of electric field distribution around the tunnel junction show that, despite their different designs and capacitive couplings to the tunnel junction, there is no discernible difference in the driving and detection of ESR. Furthermore, at a magnetic field of 1.6 T, we observe ESR signals (near 40 GHz) sustained up to 10 K, which is the highest temperature for ESR-STM measurement reported to date, to the best of our knowledge. Although the ESR intensity exponentially decreases with increasing temperature, our ESR-STM system with low noise at the tunnel junction allows us to measure weak ESR signals with intensities in the sub-fA range. Our new design of ESR-STM, which is operational in a large frequency and temperature range, can broaden the use of ESR spectroscopy in STM and enable the simple modification of existing STM systems, which will hopefully accelerate a generalized use of ESR-STM.

We discuss various relations between part of the results in arXiv:2103.05803v4 and recent author's results., Comment: 5 pages, better organized, new development taken into account

We prove strong existence and uniqueness of solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class type. In a sense we are treating a "supercritical" case., Comment: I found an error

We prove strong existense of solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class type., Comment: I found an error