arXiv subjects

Dmitry Kudryavtsev

Publications and source records attributed to Dmitry Kudryavtsev.

8 recordsLinked to original sources

arXiv2025

Effects of semigroup properties on local embeddability

We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and Clifford semigroups (similarly to group and inverse semigroup cases studied previously) and a negative answer for $\J$-trivial semigroups (similarly to cancellative semigroups). Additionally, we resolve the standing question on the differences between local embeddability in and local wrappability by finite structures, providing a novel construction of $\J$-trivial semigroups which satisfy the latter, but not the former.

math.GR↗

arXiv2023

Restrictions on local embeddability into finite semigroups

In this paper the concept of local embeddability into finite structures (being LEF) for the class of semigroups is expanded with investigations of non-LEF structures, a closely related generalising property of local wrapping of finite structures (being LWF) and inverse semigroups. The established results include a description of a family of non-LEF semigroups unifying the bicyclic monoid and Baumslag--Solitar groups and establishing that inverse LWF semigroups with finite number of idempotents are LEF.

math.GR↗

arXiv2022

Spectropolarimetry of Magnetic Chemically Peculiar Stars in the Orion OB1 Association

We summarise the results of a spectropolarimetric survey of 56 chemically peculiar (CP) stars in the association of Orion OB1. We uniformly collected the observational material with the 6-m telescope BTA of the Special Astrophysical Observatory in 2013-2021. We identify 14 new magnetic CP stars with a longitudinal magnetic field exceeding approximately 500 G. The studied sample contains 31 magnetic stars or 55% of the whole CP population in Orion OB1. We show that the percentage of the magnetic CP stars and the field strength drops sharply with age. The mean longitudinal magnetic field in the young subgroup OB1b ($\log t=6.23$) is confidently almost three times stronger than in the older subgroups OB1a ($\log t=7.05$) and OB1c ($\log t=6.66$). In the Orion Nebula, a place with the youngest stellar population ($\log t < 6.0$), we detect the magnetic field only in 20% of CP stars. Such occurrence drastically differs from 83% of magnetic CP stars in the nearby subgroup OB1c. We consider this effect an observational bias caused by a significant portion of a very young population with the signatures of Herbig Ae/Be stars. The technique we used for magnetic measurements, and the quality of available data do not allow us to detect weak fields in the case of stars with a limited number of lines and emissions in spectra.

astro-ph.SR↗

arXiv2022

Values of the length function for nonassociative algebras

We study realizable values of the length function for unital possibly nonassociative algebras of a given dimension. To do this we apply the method of characteristic sequences and establish sufficient conditions of realisability for a given value of length. The proposed conditions are based on binary decompositions of the value and algebraic constructions that allow to modify length function of an algebra. Additionally we provide a classification of unital algebras of maximal possible length in terms of their basis.

math.RA↗

arXiv2022

Steady growth of length function and Malcev algebras

We introduce and investigate the algebras of steadily growing length, that is the class of algebras, where the length is bounded by a linear function of the dimension. In particular we show that Malcev algebras belong to this class and establish the exact upper bound for its length.

math.RA↗

arXiv2022

Algebras of slowly growing length

We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or equal to its dimension. We show that this class is considerably big, in particular, finite dimensional Lie algebras as well as many other important classical finite dimensional algebras belong to this class, for example, Leibniz algebras, Novikov algebras, and Zinbiel algebras. An exact upper bounds for the length of these algebras is proved. To do this we transfer the method of characteristic sequences to non-unital algebras and find certain polynomial conditions on the algebra elements that guarantee the slow growth of the length function.

math.RA↗

arXiv2011

Towards OWL-based Knowledge Representation in Petrology

This paper presents our work on development of OWL-driven systems for formal representation and reasoning about terminological knowledge and facts in petrology. The long-term aim of our project is to provide solid foundations for a large-scale integration of various kinds of knowledge, including basic terms, rock classification algorithms, findings and reports. We describe three steps we have taken towards that goal here. First, we develop a semi-automated procedure for transforming a database of igneous rock samples to texts in a controlled natural language (CNL), and then a collection of OWL ontologies. Second, we create an OWL ontology of important petrology terms currently described in natural language thesauri. We describe a prototype of a tool for collecting definitions from domain experts. Third, we present an approach to formalization of current industrial standards for classification of rock samples, which requires linear equations in OWL 2. In conclusion, we discuss a range of opportunities arising from the use of semantic technologies in petrology and outline the future work in this area.

cs.AI↗

arXiv2010

The extraordinary complex magnetic field of the helium-strong star HD 37776

The early-type chemically peculiar stars often show strong magnetic fields on their surfaces. These magnetic topologies are organized on large scales and are believed to be close to an oblique dipole for most of the stars. In a striking exception to this general trend, the helium-strong star HD 37776 shows an extraordinary double-wave rotational modulation of the longitudinal magnetic field measurements, indicating a topologically complex and, possibly, record strong magnetic field. Here we present a new investigation of the magnetic field structure of HD 37776, using both simple geometrical interpretation of the longitudinal field curve and detailed modeling of the time-resolved circular polarization line profiles with the help of magnetic Doppler imaging technique. We derive a model of the magnetic field structure of HD 37776, which reconciles for the first time all magnetic observations available for this star. We find that the local surface field strength does not exceed ~30 kG, while the overall field topology of HD 37776 is dominated by a non-axisymmetric component and represents by far the most complex magnetic field configuration found among early-type stars.

astro-ph.SR↗