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Yakutsk, Russia

Kiselev A.I.,Russian Academy of Sciences | Yarmolyuk V.V.,Russian Academy of Sciences | Kolodeznikov I.I.,Yakutsk State University
Doklady Earth Sciences

Based on isotopic and geochemical data for Late Riphean dikes and sills and for Devonian dolerite dikes and basalt covers within the Sette-Daban rift in the western part of the Siberian platform, we proved conceptions about the participation of various deep sources in their formation. The inverse correlation in Devonian basites between concentrations of Nb, light rare earth elements, and a number of other highly incompatible elements on the one hand and Zr, Y, and other moderate incompatible elements, including heavy rare earth elements on the other hand allows us to assume that two sources participated in the formation of melts. The source of dolerites is close to the EMORB type, and the source of basalts is close to the OIB type. The compositions of Riphean rocks correspond to a trend for which magma formation occurred with the participation of a source with characteristics between NMORB and EMORB and also a component typical of subduction zones. The data obtained imply associate formation of basites with the influence of mantle plumes on the lithosphere of the southeastern part of the Siberian craton in the Late Riphean and Middle Paleozoic. In the Riphean the plume mantle was composed of a moderately depleted mantle of the EMODB type and a mantle with the composition close to the above-subduction mantle, which was metosomatically changed under the influence of fluid water, which caused the appearance of a Nb and Ta deficit in melting products. The isotopic characteristics Nd(147Sm/144Nd = 0.165 and εNd(T) ̃ 2.3-4.7) of rocks show the moderate depleted nature of these sources. © 2010 Pleiades Publishing, Ltd. Source

Borodin O.V.,RAS Sobolev Institute of Mathematics | Ivanova A.O.,Yakutsk State University
Journal of Applied and Industrial Mathematics

A graph G is (2, 1)-colorable if its vertices can be partitioned into subsets V1 and V2 such that each component in G[V1] contains at most two vertices while G[V2] is edgeless. We prove that every graph with maximum average degree mad(G) < 7/3 is (2, 1)-colorable. It follows that every planar graph with girth at least 14 is (2, 1)-colorable. We also construct a planar graph Gn with mad (Gn) = (18n - 2)/(7n - 1) that is not (2, 1)-colorable. © Pleiades Publishing, Ltd., 2010. Source

Romanov G.N.,Yakutsk State University
Russian Journal of Non-Ferrous Metals

The liquid-phase sintering of the Al-Si system is performed in two stages, namely, an increase in the volume (growth) of the powder body (first) and then shrinkage (second). The bulk variations are caused by the diffusion nature of the interaction between two metals, one of which is in a liquid state. The formation mechanisms of the polyhedral structure are the dissolution of aluminum particles and the crystallization of the melt on undissolved particles upon cooling and the process of dissolution-precipitation under the conditions of holding at a constant temperature. © 2011 Allerton Press, Inc. Source

Neustroeva N.V.,Yakutsk State University
Journal of Applied and Industrial Mathematics

A family of problems under consideration describes the contact of elastic plates situated at a given angle to each other and, in the natural condition, touching along a line. The plates are subjected only to bending. The limiting process from the elastic inclusion to the rigid one is studied. It is demonstrated that the limit problems precisely describe the contact of an elastic plate with a rigid beam and the problem of the equilibrium of an elastic plate with a rigid inclusion. The solvability of the problems is established; the boundary conditions holding on the possible contact set are found as well as their precise interpretation. © 2010 Pleiades Publishing, Ltd. Source

Ivanova A.O.,Yakutsk State University
Journal of Applied and Industrial Mathematics

The trivial lower bound for the 2-distance chromatic number χ2(G) of a graph G with maximum degree Δ is Δ + 1. There are available some examples of the graphs with girth g ≤ 6 that have arbitrarily large Δ and χ2(G) ≥ Δ + 2. In the paper we improve the known restrictions on Δ and g under which a planar graph G has χ2(G) = Δ + 1. © 2011 Pleiades Publishing, Ltd. Source

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