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In the evolution of proboscideans, the emergence of dwarf and semi-dwarf forms occurred repeatedly, on various territories and at various times, due to a lack of resources caused by geographic isolation on the islands and landscape isolation on the mainland. Despite a significant amount of information on the island forms of mammoths and elephants, the question of the association between a decrease in the body size and morphological changes in the dental system remains controversial. According to some data, the formation of dwarf forms was accompanied by a unidirectional decrease in the number of dental plates (NDP) of the tooth and thickening of the enamel. According to other data, changes in the dental system on the islands were mosaic in nature; that is, the NDP could decrease, remain unchanged, or even increase. Taking into account the importance of the NDP as a diagnostic tool for species identification of proboscidean taxa and the absence of a consensus on the stability of a trend towards a decrease in the NDP from tall continental ancestors to island dwarf descendants, we (1) summarize data on the finds of small teeth of mammoths from the Mammuthus genus with a reduced NDP in the localities in northern Eurasia, (2) present new radiocarbon dates, and (3) consider the NDP as a characteristic of developing dwarfism in continental mammoths. The study of small teeth of the last generation of M. primigenius from the coastal part of northeastern Siberia and a comparison with data from other regions demonstrated that the posterior sections of cheek teeth in mammoths are the most variable and represent a reduction complex. For woolly mammoth, the reduction primarily affects that part of the crown that became more complex by the gradual addition of the plates during phyletic evolution in the Middle–Late Pleistocene. A rapid loss of evolutionary achievements of the ancestral forms due to reduction is not a unique peculiarity of the woolly mammoth teeth, and was also traced in other mammals. The similarity of the reduction complexes of cheek teeth in proboscideans and rodents of the Arvicolinae subfamily was demonstrated; it can be traced by a decrease in the number of serially homologous elements of the crown: plates in proboscideans and pairs of prisms in arvicolines. A comparison of the NDP with the size of the M. primigenius teeth allowed us to make the assumption that a decrease in the NDP while maintaining other species-specific peculiarities of the tooth can be used as a criterion for separating semi-dwarf and small individuals of the woolly mammoth. The size of continental mammoths decreased most intensively during warmer intervals, when significant transformation of landscapes and a reduction in resource space occurred. [ABSTRACT FROM AUTHOR]

This article summarizes the authors' work on mathematical modeling of the non-stationary stress-strain state (SSS) of shells under impact actions on their front surfaces and ends. Mathematical modeling is based on the use of an asymptotic method for constructing approximate theories for the components in different areas of the phase plane of the solution, where its fundamentally different properties take place and different values of the variability and dynamism indicators are observed. The areas where the two-dimensional bending component of the Kirchhoff-Love theory, the quasi-plane problem of the theory of elasticity, the hyperbolic boundary layer in the vicinity of the shear wave, and the elliptical boundary layer in the vicinity of the conditional front of Rayleigh surface waves are identified. The derivation of asymptotically optimal equations for an elliptic boundary layer, which takes place both in the case of tangential surface impact actions and in the case of normal type end impacts, is given. In this case, in the case of end action, the problem for a semi-infinite shell is reduced by extracting a particular solution to an equivalent problem for an infinite shell. As an example, solutions are constructed for an elliptical boundary layer in cylindrical shells for both loading cases. The integral Laplace transforms in time and Fourier transforms in the longitudinal coordinate are used. The inversion of integral transformations made it possible to present solutions using the elementary function arctg of complex arguments. An analysis of these solutions in a small neighborhood of the quasifront (conditional front of Rayleigh surface waves) made it possible to determine their properties as they move away from the quasifront along the longitudinal coordinate. [ABSTRACT FROM AUTHOR]

The remains of the extinct Merck's rhinoceros (Stephanorhinus kirchbergensis (Jäger 1839)), well studied in Western Europe, are rare in Russia. However, thanks to the work of a number of researchers, the geography of the finds and the reconstructed range of the species have been significantly expanded. The time of the optimal existence of Merck's rhinoceros in Yakutia is now recognized as the Middle Pleistocene; the latest finds, dating from the beginning of the late Pleistocene, are known from the southeast of Western Siberia. We provide new radiocarbon dates for the root of a tooth and bone tissue from a previously unstudied lower jaw of the Merck's rhinoceros from Altai (AltR), whose taxonomic identity we confirm using genomic analysis. Both dates provide an age estimate of around 40 thousand years, which corresponds to the Karginsky time (MIS 3), and are the youngest for the species on the territory of Russia. The pollen spectrum from the soil filling the bone canal characterizes plant communities of open landscapes with forest areas on the upland or in the floodplain, and reflects either local features of the environment or communities of the cold stage within the Karginsky interstadial. A second Merck's rhinoceros from the Chondon River (ChR), in extreme northeast Yakutia, was determined by previous researchers to have lived either 45–70 thousand years ago or during the beginning of the Middle Pleistocene. Considering what habitats were available in the region, we propose that the ChR could have lived during the last—Kazantsevo—interglacial (MIS 5e) or later. Both finds, AltR and ChR, extend the temporal range of the species existence. [ABSTRACT FROM AUTHOR]

We studied 63 woolly rhinoceros skulls from the northeast of Russia (northwestern Chukotka, northeastern Yakutia) housed in the collection of the "Ice Age" Museum-Theatre, Moscow. Both sexual dimorphism and size/shape variability of woolly rhinoceros skulls are explored using univariate and multivariate statistics for the first time. Peculiarities of the variability, which are probably related to gender, are expressed in (1) different sets of skull variables the variability of which does not depend on "general size" variations and (2) differences in skull allometry in males and females. The structure of morphological variability is discussed. Statistically significant morphological heterogeneity is detected within the male and female samples. This is shown to be the consequence of the presence of two size groups that are not related to individual age. Based on published radiocarbon dates, it is hypothesized that there was a decrease in skull size in the woolly rhinoceros is at the end of megainterstadial (MIS) 3 to the early Last Glacial Maximum MIS 2 in northeastern Asia. To test this hypothesis, new radiocarbon dates of the studied specimens are needed. [ABSTRACT FROM AUTHOR]

In this paper, asymmetric equations for an elliptical boundary layer in the vicinity of the conditional front of Rayleigh surface waves, which occurs in shells of revolution under shock end impacts of normal type are constructed. The technique of asymptotic derivation of these equations, based on the use of the symbolic Lurie method and the introduction of special coordinates that distinguish a small frontal zone required to reduce the original problem to an equivalent problem for an infinite shell by isolating a particular solution. The considered boundary layer complements the full description of the considered type of stress-strain state (SSS) in all sections of the phase plane. It also uses a quasi-static boundary layer of the Saint-Venant type in a small vicinity of the butt end, a parabolic boundary layer according to the two-dimensional Kirchhoff–Love theory, a quasi-plane short-wave component, and a hyperbolic boundary layer in a small neighborhood of the shear wave front. In conclusion, an example of constructing an elliptical boundary layer under shock action on the butt end of a cylindrical shell is considered. [ABSTRACT FROM AUTHOR]

The purpose of this study is to analyze the taxonomic composition of the branchiopod crustaceans (Crustacea: Branchiopoda) from the assemblage of animal and plant remains recovered from fossil mammoth hair found in the Allaikha River basin, Sakha Republic, Russian Federation. We studied the hair structure. AMS radiocarbon dating of both the hair itself and the remains demonstrated their different ages. We found different animal and plant remains in the hair taphocoenosis. The most diverse and numerous remains belong to branchiopod crustaceans: resting eggs and distal portions of the mandibles of Anostraca, distal portions of the mandibles of Notostraca, filtering limbs of some Anostraca or Daphniidae, ephippia of Daphnia (Daphnia) curvirostris, Daphnia (Ctenodaphnia) atkinsoni, and D. (C.) magna. No representatives of D. (Ctenodaphnia) now occur in northeastern Eurasia, but our findings of numerous ephippia in the fossil hair of two mammoths, one from the Allaikha River and the other, studied previously, from the Bol'shaya Chukochya River basin (see Kirillova et al., 2016), show that Daphnia (Ctenodaphnia) taxa occurred in the region at least in the past and were probably common and widely distributed there. The reasons for the extinction of Daphnia (Ctenodaphnia) in northeastern Eurasia require additional special study. We also emphasize the need for further studies of the morphology of ephippia, resting eggs, and mandibles of recent Branchiopoda, which would be essential for adequate identification of Pleistocene remains. [ABSTRACT FROM AUTHOR]

A plane acoustic layer bounded by elastic membranes is considered. Dispersion relations for symmetric and antisymmetric waves are derived. The limit behavior of dispersion curves is investigated for wave numbers tending to zero and to infinity. With the use of the resulting asymptotic expansions, the two-point Pade approximations are constructed. The orthogonality relations for eigenmodes are presented. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]