Asymptotics for the number of n-quasigroups of order 4

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.Comment: 15 p., 3 fi

Algorithms for solving inverse geophysical problems on parallel computing systems

For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled "Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers." Some problems with "quasi-model" and real data are solved. © 2013 Pleiades Publishing, Ltd

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Accounting procedures in the system of searching and generating the balance sheet of accounting information by various stakeholder groups

This article emphasizes the importance of analyzing critically and using the multi-option models of running the accounting records that make it possible to considerably improve the harmonization of interests of various stakeholder groups and the quality of the accounting data as well. The authors have resorted to various conceptual principles as their study subject to carry out the research that is used by modern science and that is intended to tackle the challenges of realizing a quantum leap in business processes. The authors have demonstrated the peculiarities of generating and using multi-option models of running the accounting records, the specific features of their demonstration in the GAAP, IFRS systems, the continental accounting model and in the Russian practices. They consider the aggregate scenarios in financial and economic development of business entities as obtained by means of accounting sampling to be the most promising trend in optimizing the accounting information in the system of possible stakeholder inquiries. By reference to the results of the research the authors conclude that the interests of the property owners, executive management and mass public that are aimed at the neutrality criterion as obtained by means of the accounting information should be harmonized.peer-reviewe

IMPROVING INFORMATION SUPPORT OF CRISIS MANAGEMENT BY ENTERPRISES ON THE BASIS OF USING COMMUNICATION TOOLS OF THE TECHNOLOGICAL PLATFORM

Information support of crisis management requires the creation of a communication infrastructure, based on the program-target method, within which technological standards and profiles are formed – technological platforms. The information support of the crisis management of enterprises, based on the use of communication tools of the technological platform, as an interface of the innovative infrastructure, allowing increase the efficiency of the information component of the enterprise management system, has been improved in the paper. Based on the technological platform, new research and production cooperations, innovation clusters will be formed, which will allow overcome the crisis state of enterprises

Открытые проблемы, сформулированные на XIII школе-конференции по теории групп, посвященной 85-летию В.А. Белоногова

A review of the main events of the 13th School–Conference on Group Theory, which was held online on August 3–7, 2020, is presented, and a list of open questions with comments is given. Open questions were formulated by the participants at the Open Problems Session held at the end of the school–conference. Among the posed problems there are a series of questions on the characterization of a finite group by its arithmetic invariants such as the spectrum, the Gruenberg–Kegel graph, the solvabile graph, and the degrees of irreducible complex characters (L. S. Kazarin, A. S. Kondrat’ev, and N. V. Maslova); the question of the conjugacy of the Sylow 2-subgroups in locally finite groups with additional conditions on these subgroups (V. D. Mazurov); a series of problems on the characterization of distance-regular graphs by their intersection arrays (A. A. Makhnev); the question of the nilpotent length of a finite solvable group whose Carter subgroup coincides with the Gaschütz subgroup (V. S. Monakhov); a series of problems about the structure of conjugately biprimitively finite groups or Shunkov groups (A. I. Sozutov); a question on the structure of some matrix groups over a residue ring Zn for a positive integer n (V. A. Roman’kov); a question on the characterization of Mazurov triples in finite groups (A. V. Timofeenko); and other open questions of the modern group theory and its applications. V. A. Belonogov’s brief biography and the list of his main publications are also presented. © Krasovskii Institute of Mathematics and Mechanics

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on $n_0$. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in $n_0$ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum Path-Integral Monte Carlo calculations.Comment: 12 pages, 8 Postscript figure

Chemical analysis of bioactive substances in seven siberian Saussurea species

Main groups of biologically active substances of seven siberian Saussurea species (S. controversa DC., S. latifolia Ledeb., S. parviflora (Poir.) DC., S. frolowii Ledeb, S. amara (L.) DC., S. salicifolia (L.) DC. and S. daurica Adams) have been studied using paper, thin-layer, performance liquid chromatography, IR spectroscopy, spectrophotometry and mass spectrometry with inductively coupled plasma. Siberian Saussurea species have a rich elemental composition and contain a variety of phenolic compounds, amino acids, polysaccharides. The majority of polysaccharides are accumulated by S. controversa, S. salicifolia and S. frolowii. These plants contain a significant amount of calcium that may be a species characteristic. All plants contain quercetin and its glycosides, in some species luteolin, kaempferol, glycosides of apigenin and myricetin were revealed. Phenolic acids with predominant content of caffeic, chlorogenic and cinnamic acids were found in all the species. The maximum amount of phenolic acids and flavonoids was determined in the grass of S. latifolia, S. controversa and S. daurica. Characteristic absorption bands of lactone carbonyl of sesquiterpenoids in IR spectrum found in S. latifolia, S. controversa, S. daurica, S. amara and S. salicifolia. HPLC / UV analysis showed that peaks with absorption maxima of 242-246 nm due to the presence of α,β-unsaturated ketone group in the structure of ecdysteroids were found in S. salicifolia, S. controversa, S. daurica and S. latifolia