Vol 486, No 4 (2019)

In the present paper, we study the complexity of an infinite family of graphs H_n = H_n(G₁, G₂, ..., G_m) that are discrete Seifert foliations over a graph H on m vertices with fibers G₁, G₂, ..., G_m. Each fiber G_i = C_n(s_i,1, s_i,2, ..., s_i,ki) of this foliation is the circulant graph on n vertices with jumps s_i,1, s_i,2, ..., s_i,ki. The family of discrete Seifert foliations is sufficiently large. It includes the generalized Petersen graphs, I-graphs, Y-graphs, H-graphs, sandwiches of circulant graphs, discrete torus graph and others. We obtain a closed formula for the number t(n) of spanning trees in H_n in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as n → ∞.

The problem of variational data assimilation for a nonlinear evolutionary model is formulated as an optimal control problem to find simultaneously unknown parameters and the initial state of the model. The response function is considered as a functional of the optimal solution found as a result of assimilation. The sensitivity of the functional to observational data is studied. The gradient of the functional with respect to observations is associated with the solution of a nonstandard problem involving a system of direct and adjoint equations. On the basis of the Hessian of the original cost function, the solvability of the nonstandard problem is studied. An algorithm for calculating the gradient of the response function with respect to observational data is formulated and justified.

The methodics of characterization of 2D-nanofiller tactoids structure in polymer matrix of nanocomposite was proposed, which shown that the indicated tactoids are fractal objects with dimension of 1.75-2.16. This variation of tactoids structural state is due to interfacial interactions. It has been shown within the framework of reinforcement percolation theory, that structure of tactoids is single factor, defining reinforcement efficiency is characterized by its ability to create interfacial regions.

In n-dimensional space (multidimensional continuum) the compatibility equations are derived for the components of the generalized deformators of rank m which are connected with the generalized displacements of rank m - 1 by analogues of the Cauchy kinematic relations (m≥1, n≥2). They may be written in form of equal to zero for all the components of the incompatibility tensor of rank m(n - 2) or for dual to it the generalized Riemann-Christoffel tensor of rank 2m. The number of independent components of these tensors coinciding with the number of compatibility equations in terms of the generalized deformations, is obtained.

New techniques have been developed for the preparation of spongy materials and hydrogels based on triblock copolymers of lactide and ethylene glycol with various molecular structures. The influence of the composition of the initial copolymers and supramolecular structure on their mechanical characteristics and biocompatibility was studied. Cytological studies have shown that all materials have a high level of cell viability (GSP). The possibility of obtaining hydrogels with elastic moduli up to 4460 kPa, a record for such systems, was shown.

Polydiimidazopyridine was synthesized from 2,3,5,6-tetraaminopyridine and 2,5-dihydroxyterephtalatic acid in polyphosphoric acid and characterized. Polydiimidazopyridine possesses high viscosity, high thermal oxidation resistance and excellent film-forming properties. The polymer was processed from reaction mixture in polyphosphoric acid into proton conducting membranes. The membranes possess higher proton conductivity than for many known membranes at 20-200 °C.

This paper presents the results of U–Pb (LA–ICP–MS) and Lu–Hf ­isotope studies of detrital zircons from metasedimentary rocks of the Tokur Terrane. It has been shown that metasedimentary rocks of the Tokur and Ekimchan formations are characterized by similar age peaks of detrital zircons, which indicates a close (or same) age of these formations. The lower age of the sedimentation is determined by the age of the youngest zircons of 326–323 Ma. The upper age boundary is determined of 254–251 Ma, based on the intruded of the Late Permian granitoids. The main sources of zircons in the metasedimentary rocks of the Tokur Terrane are the igneous and metamorphic complexes of the southeast framing of the North Asia Craton. The Tokur Terrane can be considered as a fragment of the Paleozoic accretionary complex, the formation in front of the southeastern margin of the North Asia Craton.

The results of investigation of organic matter chemical structure of the coal-similar wood of Devonian and Jurassic geological periods by the methods of IR-, EPR-, chromate-masses-spectrometry and element analysis are presented. It is shown that the investigated samples are the products of the metamorphism of natural lignins, which confirms hypothesis about the important role of lignins in the processes of coal formation.

Diamond crystals from the Istok (25 crystals) and Mayat (49 crystals) placers were studied using the EPR-, IR-, and luminescence methods. The total content of impurity nitrogen in forms of A-, B-, and C (P1)-centers ranges from 50 to 1200 ppm. According to the EPR-spectroscopy, the presence of nitrogen C(P1), N3V nitrogen-titanium OK1, N3, NU1 impurity centers was established in the investigated crystals. Crystals from the Istok placer contain the OK1, N3, NU1 centers, but luminescence attributed to the oxygen-containing centers is absent in the region of 610-670 nm. For the Mayat placer crystals, the reverse situation was observed. The luminescence ascribed to the oxygen-containing centers was detected for 17 crystals, but there were no OK1, N3 and NU1 centers according to the EPR- and luminescence. This result contradicts the arguments of a number of authors about the oxygen nature of these defects. For 5 crystals from the Mayat placer, the nickel impurity was registered. This indicates the presence of ultrabasic paragenesis diamond crystals in this placer.

Long term observations of sea waves with one second discreteness in the port harbor of Sea of Okhotsk (Sakhalin island) at a depth of about two meters under the ice were carried out using autonomous wave recorders in 2009-2017. Spectral analysis of the data showed the presence of several significant peaks on the periods from 2 to 15 seconds in the spectra for the moments of strong swell at sea. These peaks are caused by wave processes that are generated due to the nonlinear transformation of the swell coming in ice. The numerical simulation of the reaction of the dynamic system - the water area described by the Duffing equation, depending on the parameters included in the equation and determined from experimental observations, is carried out. It is shown, including using the Poincare mapping that the amplitude of external forcing has the greatest influence on the transition of the system to chaos.

In April 2017 and in October 2018, a Russian expedition on the R/V “Akademik Sergey Vavilov” in the South-West Atlantic carried out measurements of temperature, salinity, and velocity over a standard section across the deep Vema Channel at 31(градус) 12(минут) S. Extremely high and extremely low velocities and transports of Atlantic Bottom Water (AABW) in the entire history of our observations over this section were found. In 2017, the maximum speed over the section reached 55 cm/s, and in 2018, it did not exceed 30 cm/s. In 2018, a core of high velocities in the bottom layers of the channel characteristic of the AABW flow was not found.

Based on the archival data for the period from 1956 to 2010, space-time pH changes in the Black Sea upper layer are analyzed. In the surface layer, a statistically significant decreasing in the pH value (at a level of -0.06 pH units per 50 years) was found. It is mostly due to the growing concentrations of carbon dioxide in the atmosphere. Intermediate layers are characterized by a negative pH trend which absolute value more than fivefold exceeds the surface pH trend. Likely reason of the pH decreases here is a long-term upward moving of acidic waters with a typical velocity of ~1 m per year.

The functioning of Vibrio fischeri NAD(P)H: FMN-oxidoreductase (Red) under conditions of macromolecular crowding (MMC) modeled in vitro by adding biopolymers (starch and gelatin) was studied. The dissociation rate constants and the activation energies of dissociation of Red to the subunits were calculated; the process of denaturation of Red was analyzed. It was shown that the functioning of Red both under conditions of MMC and diluted solutions is the same. The result refutes the common belief that due to MMC the stabilization of enzymes’ native conformation occurs in vivo when compared to in vitro.

Cardiolipin (CL) plays a central role in lipid peroxidation (LPO) of the mitochondrial inner membrane due to higher content of unsaturated fatty acids in CL in comparison with the other phospholipids. CL oxidation plays an important role in the regulation of various intracellular signaling pathways and its excessive oxidation contributes to the development of various pathologies and, possibly, participates in the aging process. Mitochondria-targeted antioxidants containing triphenylphosphonium cation (TPP⁺) effectively protect CL from oxidation. It is assumed that fluorescent probes on the basis of the C11-BODIPY fluorophore sensitive to LPO and containing TPP⁺ can selectively register CL oxidation. To test this possibility, we carried out a molecular dynamic simulation of such probes in a model mitochondrial membrane. It is shown that the probes are located in the membrane at the same depth as the unsaturated bonds in CL molecules sensitive to oxidation. Increasing the length of the linker that binds the fluorophore and TPP⁺ residue has little effect on the position of the probe in the membrane. This indicates the possibility of modifying the linker to increase the selectivity of the probes to CL.