Factorization problem with intersection

We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a subalgebra in $\mathcal{G}$, $M, N$ are $\mathcal{G}_0$-modules, and $\mathcal{G}_0 +M$, $\mathcal{G}_0 +N$ are subalgebras in $\mathcal{G}$. In particular, we consider the case when $\mathcal{G}$ is a $\Z$-graded Lie algebra. Using this generalization, we construct some top-like systems related to the algebra $so(3,1)$. According to the general scheme, these systems can be reduced to linear systems with variable coefficients. For the top-like systems first integrals and infinitesimal symmetries are found

ANALYSIS OF THE CHEMICAL COMPOSITION OF CHAROITE ROCKS

The unique charoite mineralization, established on the Murun alkaline massif in the northwestern part of the Aldan shield on the border of the Irkutsk region and Yakutia, is still of great interest to some of researchers (geologists, crystallographers, geochemists, etc.). The outcrops of charoite-bearing rocks at the “Sirenevyi Kamen” deposit are noted both in the indigenous outcrops and in eluvial clatters [Bondarenko, 2009].The unique charoite mineralization, established on the Murun alkaline massif in the northwestern part of the Aldan shield on the border of the Irkutsk region and Yakutia, is still of great interest to some of researchers (geologists, crystallographers, geochemists, etc.). The outcrops of charoite-bearing rocks at the “Sirenevyi Kamen” deposit are noted both in the indigenous outcrops and in eluvial clatters [Bondarenko, 2009]

Search for glitches of gamma-ray pulsars with deep learning

The pulsar glitches are generally assumed to be an apparent manifestation of the superfluid interior of the neutron stars. Most of them were discovered and extensively studied by continuous monitoring in the radio wavelengths. The Fermi-LAT space telescope has made a revolution uncovering a large population of gamma-ray pulsars. In this paper we suggest to employ these observations for the searches of new glitches. We develop the method capable of detecting step-like frequency change associated with glitches in a sparse gamma-ray data. It is based on the calculations of the weighted H-test statistics and glitch identification by a convolutional neural network. The method demonstrates high accuracy on the Monte Carlo set and will be applied for searches of the pulsar glitches in the real gamma-ray data in the future works.Comment: 4 pages, 5 figure

The theory of traces for systems with nondeterminism and probability

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories

The earliest spectroscopy of the GRB 030329 afterglow with 6-m telescope

The earliest BTA (SAO RAS 6-m telescope) spectroscopic observations of the GRB 030329 optical transient (OT) are presented, which almost coincide in time with the "first break" ($t\sim 0.5$ day after the GRB) of the OT light curve. The beginning of spectral changes are seen as early as $\sim 10-12$ hours after the GRB. So, the onset of the spectral changes for $t<1$ day indicates that the contribution from Type Ic supernova (SN) into the OT optical flux can be detected earlier. The properties of early spectra of GRB 030329/SN 2003dh can be consistent with a shock moving into a stellar wind formed from the pre-SN. Such a behavior (similar to that near the UV shock breakout in SNe) can be explained by the existence of a dense matter in the immediate surroundings of massive stellar GRB/SN progenitor). The urgency is emphasized of observation of early GRB/SN spectra for solving a question that is essential for understanding GRB physical mechanism: {\it Do all} long-duration gamma-ray bursts are caused by (or physically connected to) {\it ordinary} core-collapse supernovae? If clear association of normal/ordinary core-collapse SNe (SN Ib/c, and others SN types) and GRBs would be revealed in numbers of cases, we may have strong observational limits for gamma-ray beaming and for real energetics of the GRB sources.Comment: 4 pages, 5 figures. Proceedings of the 4th Workshop "Gamma-Ray Bursts in the Afterglow Era", Roma, 2004 October 18-22, eds. L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

Methanol Formation Chemistry with Revised Reactions Scheme

The aim of the presented work is to analyze the impact of experimentally evaluated reactions of hydrogen abstraction on surfaces of interstellar grains on the chemical evolution of methanol and its precursors on grains and in the gas phase under conditions of a cold dark cloud and during the collapse of a translucent cloud into a dark cloud. Analysis of simulation results shows that those reactions are highly efficient destruction channels for HCO and H2CO on grain surfaces, and significantly impact the abundances of almost all molecules participating in the formation of CH3OH. Next, in models with those reactions, maximum abundances of methanol in gas and on grain surfaces decrease by more than 2-3 orders of magnitude in comparison to models without surface abstraction reactions of hydrogen. Finally, we study the impact of binding energies of CH2OH and CH3O radicals on methanol chemistry. © 2020 National Astronomical Observatories, CAS and IOP Publishing Ltd.Acknowledgements The reported study was funded by RFBR according to the research project 18-32-00645. The author thanks A. B. Ostrovskii and A. I. Vasyunin for valuable discussions during the course of this work. The author thanks the anonymous referee for his helpful review of this paper