Vol 489, No 1 (2019)

In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the L₂-class is proved, that is, if f ∈ L_{2 (}Т^N) and f = 0 on an open set Ω ⊂ Т^N then it is shown that the spherical partial sums of this function converge to zero almost - ​everywhere on Ω. It has been previously known that the generalized localization is not valid in L_p (T^N) when 1 ≤ p < 2. Thus the problem of generalized localization for the spherical partial sums is completely solved in L_p (T^N), p ≥ 1: if p ≥ 2 then we have the generalized localization and if p < 2, then the generalized localization fails.

The paper proposes an original concept of building a factor model based on frames. A method has been developed for calculating the values of factors by searching for the eigenvalues of matrices of pairwise comparisons of the degree of influence of slots. Possible applications of the factor model in the study of complex processes and systems are discussed.

Optical properties of plasma are determined by presence of fluctuating micro-scopic electric field. In the present work, we construct a simple ab initio model of plasma microfield accounting for its heterogeneity up to octupole term for the first time. Comparison with experiments shows that only this model describes the observed number of spectral lines.

The task of creating a stable orbit of the Apophis asteroid satellite as a homogeneous triaxial ellipsoid is investigated. The simulation of the motion of the spacecraft around the asteroid was performed taking into account the main perturbations: from the attraction of celestial bodies, asteroid’s non-sphericity and solar radiation pressure, and taking into account the asteroid’s own rotation. It is shown that it is possible to create a stable orbit of an asteroid satellite. This orbit can be used for a detailed study of the characteristics of the asteroid and the refinement of its orbit using ground radio measurements of the motion of a satellite equipped with a radio beacon.

Proceeding from the electronic structure of the S‑alkyl esters of P(IV) acids the key rout - attack of the thiol sulfur (P-SMe) on the methyne carbon, of the new reaction of the dichloromethylarenes with S‑methyldiethylthiophosphinate was predicted and experimentally confirmed. The processes of the mono- and di(dechloromethylthioylation) on dichloromethyl group are realized. New approach to the synthesis of the arenecarbaldehyde dimethyl dithioacetals was developed without using of gaseous high toxic methyl mercaptan.

A composite based on aluminum oxide nanofibers (AONF) and modified nanodiamonds (MND) synthesized by explosion technique was made by mixing aqueous suspensions of components at a 5:1 weight ratio and incubating the mixture for 15 minutes at 32 °C. It is assumed that the formation of a composite is provided by the difference in the zeta-potentials of the components - negative for MND and positive for AONF. Vacuum filtration of the mixture through a fluoroplastic filter (pore diameter of 0.6 µm) formed discs with a diameter of 40 mm with subsequent heat treatment at 300 °C to impart structural stability to the composite. Using scanning electron microscopy (SEM), it was revealed that the resulting composite has a network structure in which the MND particles are distributed over the AONF surface. It was established that MND incorporated into the composite catalyze the azo coupling reaction (phenol - 4-aminoantipyrine - H2O2) with the formation of a colored product (quinoneimine). The applicability of the composite for the multiple detection of phenol in aqueous samples is demonstrated.

The article for the first time presents data on the material composition and structure of the Sezym Formation of the Lower Permian of the Western slope of the Polar Urals, which lies with stratigraphic disagreement on shallow medium-Carboniferous limestone and according to the overlapping deep-sea Artinian terrigenous deposits. New data are important for paleogeography and geodynamic reconstruction of the North-East of the European platform in the late Paleozoic.

Temperature relations of b-factors for 18O/16O substitutions in TiO2 polymorphs have been determined using the density functional theory (DFT):

1000lnbrt(18O/16O) = 6,93039x - 0,08158x2 + 0,00116x3 + 0,08305*P,

1000lnbant(18O/16O) = 7,34275x - 0,09906x2 + 0,00153x3 + 0,08027*P,

1000lnbbrk(18O/16O) = 7,19088x - 009157x2 + 0,00139x3 + 0,07601*P,

x = 106/T(K)2, P - pressure (GPa).

The relations can be applied for isotope thermometry if combined with β-factors of coexisting phases.

The phase and chemical composition of drop-shaped inclusions in directionally crystallized intermediate solid solution was studied. The initial melt contained (in mol.%): Fe 31,79; Cu 15,94; Ni 1,70; S 50,20; Sn 0,05; As 0,04; Pt, Pd, Rh, Ru, Ag, Au, Se, Te, Bi, Sb 0,03. Experimental data indicate the simultaneous crystallization of two types of liquids upon cooling of the initial sulfide melt. One of them is formed in the subsystem (Pd, Au, Ag)-(Bi, Sb, Te), and the second - in the subsystem Cu-(S, Bi, Sb, Te). When these liquids solidified, inclusions formed, which we divided into four classes. Class I has a eutectic-like structure with a matrix of Pd(Bi,Sb)xTe1_-x solid solution and Au crystallites with Ag, Cu, and Pd impurities. Class II is formed from sulfosalts with inclusions of Bi and Au. Class III includes inclusions of sperrylite Pt(As,S)₂. Class IV forms compound inclusions from fragments of classes I-III. The experiment described in the work showed a more complex behavior of noble metals and metalloid impurities during the crystallization of complex sulfide-metalloid melts compared with the previously described data of isothermal experiments.

Generalized equations of solutions motion are given both in porous media and in cavities taking into account the osmotic effect. The corresponding corrections which are usually small play a key role in some cases since they are the main reason for the solution movement. Based on the generalized equations, several problems of practical importance have been solved. Due to the limited scope of the paper, only one simplest example is given.

It is generally accepted that PKP‑waves “precursors”, which are observed on a real data ahead of PKP‑waves, are explained by scattering on small-scale inhomogeneities in the lower mantle. In this paper, a stable analytical solution (without interference) was obtained for the wave field of longitudinal waves in a layered (discrete) ball of planetary size. The calculations of the total wave field, rays and travel-time curves of longitudinal waves for the spherical model of the Earth AK135 with a carrier frequency of 1 hertz are presented. The analytical solution showed that at angles smaller than 145 degrees ahead of the PKP‑waves, low-amplitude waves appear, with a higher frequency of about 1,3 hertz. Indeed, these high-frequency oscillations have the form characteristic for waves scattered at a certain object. The ray pattern and the travel-time graph show that these high-frequency oscillations are due to exclusively to the spherical geometry of the Earth. This could be explained by the interference of refracted and reflected longitudinal waves in the bottom of a discrete outer core. This field propagates even further towards smaller angles due to the interference of diffraction waves.

Microinclusions of organic matter were dated using acceleration mass spectrometry in seven samples from the upper part of the thick Pleistocene syngenetic ice wedges uncovered in the outcrop of the Batagay yedoma located in northern Yakutia along the upper Yana River (67,58° N, 134,77° E). The dated fragment of ice wedge was formed within 22 760-20 010 radiocarbon years BP (or 27 100-33 800 cal BP). Using detailed isotope data, the January average air temperature in the Late Pleistocene (25-30 cal kyr BP) was calculated for the Batagay section along with a series of reference sections in northwestern Yakutia. It was shown that the minimum January average air temperature (-51 °C) was characteristic at that time for the area of the Batagaika crater, with values 4-5° higher in areas 500-600 km further north. This effect was caused by the occurrence of the Yakutian anticyclone in winter during the Late Pleistocene, which was just as pronounced as that at the present time.

Influence of XRCC1 protein oxidation on the modification of proteins catalyzed by poly(ADP‑ribose)polyme-rases (PARP1 and PARP2) has been studied for the first time. XRCC1, PARP1 and PARP2 are responsible for coordination of multistep repair of most abundant DNA lesions, functioning as scaffold proteins. We have shown that the XRCC1 oxidation reduces the efficiency of its ADP‑ribosylation and the protein affinity for poly(ADP‑ribose). The ADP‑ribose modification of various XRCC1 forms is enhanced in the presence of DNA polymerase b (Polb) capable to form a stable complex with XRCC1. The oxidation suppresses the inhibiting activity of XRCC1 and its complex with Polb towards the automodification of PARP1 and PARP2 that may enhance the efficiency of repair. The results of this study indicate that the oxidation of XRCC1 play a role in fine regulation of poly(ADP‑ribosyl)ation levels of proteins and their coordinating functions in the DNA repair.

Based on the analysis of information on the structure of the hard cover of different taxons of osteostracan jawless vertebrates (Osteostraci, Agnatha), the geometric regularities of the formation of possible variants of armor relief during the exoskeletal morphogenesis of vertebrates are revealed. A circular model of the сonstruction of superficial relief is proposed. It is shown that the early vertebrates have already possessed the mechanism providing realization of complete set of variants of the formation of exoskeletal sculpture of different types.

External morphological, X‑ray and tomographic study of the rodent frozen mummy from the Upper Pleistocene Yedoma deposits on the Tirekhtyakh River (tributary of the Semyulyakh River, Abyi District, Republic of Sakha (Yakutia)) showed its belonging to Lemmus sp. The radiocarbon age of the find is 41 305-41 885 cal BP. This is the first Pleistocene discovery of a frozen mummy of the representative of the genus Lemmus. In terms of body and skull size, coat color, length of the lower incisor and the structure of the molars, the specimen studied is closed to the Recent Lemmus sibiricus (Kerr, 1792). Comparison of the mitochondrial COI gene sequence with the DNA sequences presented in the GenBank database demonstrates maximum similarity with the Recent Siberian brown lemming too.