Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

A subgroup H of a group G is said to be pronormal in G if H and H g are conjugate in 〈 H, H g〉 for every g ∈ G. In this paper, we determine the finite simple groups of type E 6 (q) and E 6 2 (q) in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.This work was supported by the Russian Science Foundation (project 19-71-10067)

Ellipsoidal configurations in the de Sitter spacetime

The cosmological constant $\Lambda$ modifies certain properties of large astrophysical rotating configurations with ellipsoidal geometries, provided the objects are not too compact. Assuming an equilibrium configuration and so using the tensor virial equation with $\Lambda$ we explore several equilibrium properties of homogeneous rotating ellipsoids. One shows that the bifurcation point, which in the oblate case distinguishes the Maclaurin ellipsoid from the Jacobi ellipsoid, is sensitive to the cosmological constant. Adding to that, the cosmological constant allows triaxial configurations of equilibrium rotating the minor axis as solutions of the virial equations. The significance of the result lies in the fact that minor axis rotation is indeed found in nature. Being impossible for the oblate case, it is permissible for prolate geometries, with $\Lambda$ zero and positive. For the triaxial case, however, an equilibrium solution is found only for non-zero positive $\Lambda$. Finally, we solve the tensor virial equation for the angular velocity and display special effects of the cosmological constant there.Comment: 15 pages, 11 figures, published in Class. Quant. Grav. References adde

Landscape science: a Russian geographical tradition

The Russian geographical tradition of landscape science (landshaftovedenie) is analyzed with particular reference to its initiator, Lev Semenovich Berg (1876-1950). The differences between prevailing Russian and Western concepts of landscape in geography are discussed, and their common origins in German geographical thought in the late nineteenth and early twentieth centuries are delineated. It is argued that the principal differences are accounted for by a number of factors, of which Russia's own distinctive tradition in environmental science deriving from the work of V. V. Dokuchaev (1846-1903), the activities of certain key individuals (such as Berg and C. O. Sauer), and the very different social and political circumstances in different parts of the world appear to be the most significant. At the same time it is noted that neither in Russia nor in the West have geographers succeeded in specifying an agreed and unproblematic understanding of landscape, or more broadly in promoting a common geographical conception of human-environment relationships. In light of such uncertainties, the latter part of the article argues for closer international links between the variant landscape traditions in geography as an important contribution to the quest for sustainability

Features of the preservation of vitamins in chocolate

Bitter, milk and white chocolate differ in terms of identification, including the content of the total dry residue of cocoa and the mass fraction of fat. The mass fraction of fat is regulated by state standards and is an important indicator of the quality of chocolate. Different receipts of chocolate cause different vitamins content. Chocolate contains a significant amount of tocopherols with high antioxidant activity, this allows preserving unsaturated fatty acids and biologically active components for a long shelf life. Losses of vitamins occur due to their oxidation and transition to more stable forms during storing of chocolate and chocolate products. Unstable and increased storage temperature leads not only to deterioration of organoleptic parameters, but also to a significant decrease in the content of vitamins. Objects of research have been samples of bitter, milk and white chocolate. The change in the content of vitamins during addition and storage at the temperature of 20 °C and under conditions of "accelerated aging" at the temperature of 50 °C in bitter, milk and white chocolate has been studied. Model samples of milk chocolate have been made using cocoa butter as a fat component to determine the loss of vitamins when introduced. The greatest losses have been found for nicotinamide and folic acid with the introduction of vitamins into chocolate. Significantly smaller losses have been established for thiamine and riboflavin. The loss of various vitamins when introduced is 10–15 %. The loss of vitamins after one month of storage at the temperature of 20 °C is from 5 to 15 %. The results are used to develop a methodology for assessing the safety of vitamins in confectionery

Frequency dependence of the scattering pulse broadening for the crab pulsar

We measured the frequency dependence of the pulsar pulse broadening by scattering over a wide frequency range, from 40 to 2228 MHz, based on direct measurements of this parameter using giant pulses from the pulsar PSR B0531+21 in the Crab Nebula. Our measurements were carried out at the following seven frequencies: 40, 60, and 111 MHz at the Pushchino Radio Astronomy Observatory (Astrospace Center, Lebedev Physical Institute, Russian Academy of Sciences), 406 MHz at the Medicina Observatory (Instituto di Radioasfronomia, Italy), and 594, 1430, and 2228 MHz at the Kalyazin Radio Astronomy Observatory (Astrospace Center, Lebedev Physical Institute, Russian Academy of Sciences). The measured frequency dependence of the pulse broadening by scattering T-SC(v) alpha nu(gamma), where gamma = -3.8 +/- 0.2, agrees with a model Gaussian distribution of interstellar inhomogeneities (gamma = -4) but falls outside the error limits of correspondence to a Kolmogorov model spectrum of inhomogeneities (gamma = -4.4). (C) 2002 MAIK ''Nauka/Interperiodica''