Vol 485, No 5 (2019)

Mathematics
On the Hooley’s problem on the representation of a number as the sum of a square and a product
Bykovskii V.A., Ustinov A.V.
Abstract

The article is devoted to the Hooley’s problem on the representation of a number as the sum of a square and a product. For the first time we show that number of solutions satisfy an asymptotic formula with power saving in error term.

Доклады Академии наук. 2019;485(5):539-544
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On the uniqueness of a solution to an inverse problem of scattering by an inhomogeneous solid with a piecewise Hölder refractive index in a special function class
Smirnov Y.G., Tsupak A.A.
Abstract

The problem of reconstructing a piecewise Hölder continuous function describing the refractive index of an inhomogeneous obstacle scattering a monochromatic wave is considered. The boundary value scattering problem is reduced to a system of integral equations. The equivalence of the integral and differential formulations of the problem is proved. A two-step method for solving the inverse problem is proposed. A linear integral equation of the first kind is solved at the first step. Sufficient conditions for the uniqueness of its solution in the class of piecewise constant functions are obtained. At the second step, the unknown refractive index is explicitly expressed in terms of the solution obtained at the first step.

Доклады Академии наук. 2019;485(5):545-547
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On Lindeberg-Feller Limit Theorem
Presman E.L., Formanov S.K.
Abstract

In the Lindeberg-Feller theorem, the Lindeberg condition is present. The fulfillment of this condition must be checked for any ε > 0. We formulae a new condition in terms of some generalization of moments of order 2 + α, which does not depend on ε, and show that this condition is equivalent to the Lindeberg condition, and if this condition is valid for some α > 0 then it is valid for any α > 0. In the non-classical setting (in the absence of conditions of a uniform infinitely smallness) V.I. Rotar formulated an analogue of the Lindeberg condition in terms of the second pseudo-moments. The paper presents the same modification of Rotar`s condition, which does not depend on ε. In addition, we discuss variants of the simple proofs of theorems of Lindeberg-Feller and Rotar and some related inequalities.

Доклады Академии наук. 2019;485(5):548-552
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Informatics
Explicit methods for integrating stiff Cauchy problems
Belov A.A., Kalitkin N.N., Bulatov P.E., Zholkovskii E.K.
Abstract

An explicit method for solving stiff Cauchy problems is proposed. The method relies on explicit schemes and a step size selection algorithm based on the curvature of an integral curve. Closed-form formulas are derived for finding the curvature. For Runge-Kutta schemes with up to four stages, the corresponding sets of coefficients are given. The method is validated on a test problem with a given exact solution. It is shown that the method is as accurate and robust as implicit methods, but is substantially superior to them in efficiency. A numerical example involving chemical kinetics computations with 9 components and 50 reactions is given.

Доклады Академии наук. 2019;485(5):553-557
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Classification of lung nodules using CT images based on texture features and fractal dimension transformation
Kravchenko V.F., Ponomaryov V.I., Pustovoit V.I., Rendon-Gonzalez E.
Abstract

A new computer-aided detection (CAD) system for lung nodule detection and selection in computed tomography scans is substantiated and implemented. The method consists of the following stages: preprocessing based on threshold and morphological filtration, the formation of suspicious regions of interest using a priori information, the detection of lung nodules by applying the fractal dimension transformation, the computation of informative texture features for identified lung nodules, and their classification by applying the SVM and AdaBoost algorithms. A physical interpretation of the proposed CAD system is given, and its block diagram is constructed. The simulation results based on the proposed CAD method demonstrate advantages of the new approach in terms of standard criteria, such as sensitivity and the false-positive rate.

Доклады Академии наук. 2019;485(5):558-563
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Mechanics
On a model of indentation for a functionally graded strip
Vatulyan A.O., Plotnikov D.K.
Abstract

When different elements of engineering structures are manufactured, functionally graded coatings are applied to provide them with desired properties. The determination of the properties of the coatings after the coating process is an important stage in their development. Note that one of the most widely used techniques to identify the properties of new materials, including coatings, is the indentation method.

Доклады Академии наук. 2019;485(5):564-567
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The spectrum of decaying 2D self-similar turbulence
Vigdorovich I.I.
Abstract

A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero. In this case, the enstrophy-dissipation rate has a nonzero finite limit. The correlation function of the vorticity field and the enstrophy spectral density in the inertial range of distances and wave numbers, where these functions are free from the effect of viscosity and large-scale flow parameters, is investigated. It turns out that the inertial range exists in the decaying 2D self-similar turbulence in physical space but is absent in the space of wavenumbers. This means that the turbulent vortices of the appropriate size do not contribute to the spectral density, and the well-known law of the first degree is not satisfied. At large wave numbers, the spectral density of enstrophy behaves nonmonotonically - it first decreases faster than the law of the minus first degree and, then, in the dissipation region, it has a growth segment and a second peak. In this case, the enstrophy flow along the spectrum on the left boundary of the dissipation region is only a fraction of the enstrophy-dissipation rate.

Доклады Академии наук. 2019;485(5):568-573
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Analysis of the generalized heat equation applied to the solution of the dynamic problem of thermoelasticity
Zimin B.A., Sudenkov Y.V.
Abstract

Based on the approximate solution of the dispersion equation, the paper presents an analysis of the system of dynamic thermoelasticity equations taking into account the generalized heat equation. It is noted that during the wave process of heat transfer, a sufficiently intensive process of energy exchange between thermal and elastic fields is realized, while depending on the relations of the characteristic relaxation times, the direction of energy exchange can change.

Доклады Академии наук. 2019;485(5):574-578
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Bernoulli-Euler beam under action of a moving thermal source: characteristics of the dynamic behavior
Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Privalova O.V., Semenov B.N., Shtukin L.V.
Abstract

The problem of a heating source acting on a certain part of a beam surface and moving along it with given speed is solved. It is shown that the most significant role in formation of the beam deflection under loading by a compression force is played by concentrated moments occurring at the moving boundary of the heating source. It is noted that for a source speed less than some critical value, the beam deflection is essentially nonmonotonic. In this case, the largest beam bending deflection occurs when the source speed reaches a value corresponding to the Euler critical force.

Доклады Академии наук. 2019;485(5):579-582
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New cases of integrable fifth-order systems with dissipation
Shamolin M.V.
Abstract

Integrability is shown for some classes of fifth-order dynamic systems homogeneous in variables, in which a system on the tangent bundle of two-dimensional manifolds is separated. Here, the force fields possess the dissipation of alternating signs and generalize the fields considered earlier.

Доклады Академии наук. 2019;485(5):583-587
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Physical chemistry
The method of cleaning and modification of the material for bone xenografts in bi-phase media containing high pressure CO2
Bulat M.V., Pigaleva M.A., Novikov I.V., Levin E.E., Gallyamov M.O.
Abstract

In the present work, a promising method was proposed for purification of fragments of animal bone tissue from high-molecular weight compounds in bi-phase media containing high-pressure CO2 for the first time, namely, in solutions of carbonic and peroxycarbonic acids. The effectiveness of this purification was confirmed by SEM and IR spectroscopy. It turned out that during the exposure of bone fragments in solutions of carbonic and peroxycarbonic acids under high pressure of CO2, the components of the mineral phase of bone tissue are also extracted, which allows to obtain highly dispersed particles of hydroxyapatite during the deposition of the extract. The structure and composition of the extracts were investigated by XRD analysis and SEM.

Доклады Академии наук. 2019;485(5):588-593
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Geology
New isotope constraints on the time of formation of the Nersinskii dolerite complex from the Biryusa-Sayan area
Vasyukova E.A., Metelkin D.V., Letnikov F.A., Letnikova E.F.
Abstract

New data on the Sm-Nd isotopic composition of the dolerites of the Nersinskii complex that are consistent with the petrographic study and the U-Pb dating of detrital zircon from the overlying sedimentary sequences of the Biryusa-Sayan area are presented. The data obtained indicate the absence of the supposed magmatic event 1.6 billion years ago and clearly indicate the Neoproterozoic age of the intrusions. Their source could have been the metasomatized mantle; after formation, dolerites went through several stages of metasomatism, which was reflected in the evolution of its isotopic systems.

Доклады Академии наук. 2019;485(5):594-598
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Geochemistry
The multi-isotope composition of sulfur in sulfides and microfossils of the Mesoarchean Leksa pyrite ore occurrence of the Karelian Craton: new data on abiogenic and biogenic effects on the formation of ancient ores
Vysotskii S.V., Khanchuk A.I., Kuleshevich L.V., Ignat’iev A.V., Slabunov A.I., Velivetskaya T.A.
Abstract

The first data on the multi-isotopic composition of sulfur of sulphides and fossilized microorganisms, first discovered in Mesoarchean (about 2.9 billion years) SCM of the Karelian Craton, are given. As a result of detailed electron-microscopic and microprobe studies, the presence of several varieties of suspected microfossils - silicate cocoids, pyrite-marcasitic spheroids, and hollow tubes - was found in sedimentary rocks of the Lex’s ore occurrence. It is shown that the isotopic composition of sulfur correlates with the typomorphic features of sulfides, their composition and indicates a significant participation of sedimentary sulfur in pyrite ore formation. The process of deposition of iron sulfide occurred with active biological participation.

Доклады Академии наук. 2019;485(5):599-603
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High-alumina pyroxenite xenoliths from Quaternary basalts of NW Spitsbergen - evidence of continental crust delamination
Koreshkova M.Y., Marin Y.B., Nikitina L.P., Downes H., A. Tokusheva A., Goncharov A.G.
Abstract

The origin of spinel-garnet pyroxenite from xenoliths in Quaternary basaltoids of Spitsbergen Island (Svalbard Archipelago) is discussed. The rocks have a high concentration of Al2O3 and MgO and low Cr. The primary magmatic association Spl-Opx-Cpx and the high Al content in pyroxenes provide evidence for the formation of these rocks as cumulates of hydrous basaltic melts in the lower crust at a pressure of ~1.2 GPa. Transformation of the texture from the magmatic hypidiomorphic to the metamorphic granoblastic and growth of garnet at the expense of spinel and high-alumina pyroxenes indicate transport of rocks to a depth below the spinel/garnet phase transition boundary in the Cr2O3-free CaO-MgO-Al2O3-SiO2 system. The parameters of the Grt-Opx equilibrium range within 1060-1120 °C and 2.2-2.6 GPa. Thus, magmatic pyroxenite was transported to a great depth into the mantle, which provides evidence for delamination in the region of the lower continental crust containing ultramafic cumulates.

Доклады Академии наук. 2019;485(5):604-608
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Identification of sp2 carbon in lunar soil from probe of AS “LUNA-24”
Mokhov A.V., Bukalov S.S., Gornostaeva Т.А., Leites L.A., Aisin R.R., Kartashov P.M., Bogatikov O.A.
Abstract

During studying samples of lunar regolith from samples of the AS “Luna-24” using the methods of Raman spectroscopy, the presence of three structural modifications of carbon was established: amorphous sp2 carbon, shungite-like carbon and turbostratic graphite. At the same time, no signs of hydrocarbons or other organic compounds were found, what excludes contamination of the sample at the preparation stage and the effect of the adhesive layer of the scotch on which the regolith fragments under study were mounted, and also contamination of the sample by the exhaust of hydrazine landing engines of the descent capsule of the AS “Luna-24”.

Доклады Академии наук. 2019;485(5):609-613
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Low-temperature acidic melts of Bazman volcano (Iran)
Prokofiev V.Y., Naumov V.B., Roman’ko A.E., Balashova A.L., Plechov P.Y., Imamverdiyev N.A.
Abstract

The inclusions of a silicate melt were investigated in quartz insets of the extrusive rhyolite collected at Bazman Cenozoic volcano (Iran) and associated with the process of recent subduction. Low temperatures of the silicate melt along with high concentrations of water in the melt are ascertained. The microelemental composition of the melt showed a similarity to acidic melts of island-arc formations.

Доклады Академии наук. 2019;485(5):614-618
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Phenomena of crystal splitting during growth as a result of the Sternberg-Punin and Rebinder effects
Spiridonov E.M.
Abstract

The causes of growth blocking, splitting, twisting of crystals are considered. These phenomena are the result of the combined effect of the Punin effect (total autodeformation due to intersectorial heterometry, appearing when impurities are unequally captured by different faces or their parts) and the Rehbinder effect (a sharp decrease in the strength of the surface layer of a growing crystal several times covered by a film of mother solution containing active substances).

Доклады Академии наук. 2019;485(5):619-620
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Geography
Quantitative approach to regionalization of arid territories of Russia taking into account climatic and soil-granulometric parameters
Rukhovich D.I., Pankova E.I., Kalinina N.V., Chernousenko G.I., Ivanov A.L.
Abstract

A new quantitative approach to the zoning of arid territories is proposed on the basis of a new climatic parameter for zoning (the sum of precipitation exceedances over evaporation) and a soil textural water recharge coefficient.

Доклады Академии наук. 2019;485(5):621-624
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Biochemistry, biophysics, molecular biology
Neuroprotective action of amidic neurolipins in models of neurotoxicity on the culture of human neural-like cells SH-SY5Y
Akimov M.G., Ashba A.M., Fomina-Ageeva E.V., Gretskaya N.M., Myasoedov N.F., Bezuglov V.V.
Abstract

It was established that in neurodegeneration models in the human neuron-like cell line SH-SY5Y, amide derivatives of arachidonic and docosahexaenoic acids were inactive in experiments with MPP+ and CoCl2 but protected from H2O2. The protective activity of neurolipins decreased in the series DHA-DA > AA-SER >= AA-GLY > AA-GABA >= AA-EA and was manifested starting from a concentration of 0.5 nM.

Доклады Академии наук. 2019;485(5):625-628
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Study of humoral immunity indicators for evaluation of chronic pain state
Myagkova M.A., Levashova A.I., Panchenko L.F.
Abstract

189 patients with chronic low back pain (LBP) caused by vertebral pain syndrome were surveyed. Pain levels, measured by differential visual-analog scale, and variations of natural antibody levels to the pain bioregulators (nAbs) in blood serum at LBP were studied during 21 days. We revealed gender features of immuno-profiles: more elevated nAbs levels against opioids at women at 1st day and equal levels in both gender groups at 21 days. Generally nAbs levels remained above normal up to 21st day in most of patients despite a three-fold decrease of pain intensity. A significant decrease in nAb levels was found in 4-20% of patients, depending on the bioregulator. These observations support the hypothesis that antibodies can be a factor in the prolongation of pain, so the analysis of the dynamics of nAbs for patients with LBP can be recommended, which will be useful to predict the further course of the disease.

Доклады Академии наук. 2019;485(5):629-633
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Xenobiotic response elements (XRE) from human CYP1A1 gene enhance the hTERT promoter activity
Shepelev M.V., Kalinichenko S.V., Saakian E.K., Korobko I.V.
Abstract

A hybrid 6XRE-hTERT promoter consisting of the hTERT tumor-specific promoter and six copies of the XRE element from the CYP1A1 human gene promoter was created. Using a human lung cancer cells as a model, we showed that XRE elements in the hybrid promoter greatly increase the activity of the hTERT promoter and ensure the reporter gene transcriptional activation in response to the treatment of the cells with the AhR ligand benzo(a)pyrene. However, similar effects were also observed in normal human bronchial epithelial cells HBEpC, which indicates the loss of the tumor-specific activity by the 6XRE-hTERT hybrid promoter. XRE elements can be used for nonspecific transcription enhancement but are unsuitable for the creation of tumor-specific promoters with enhanced activity.

Доклады Академии наук. 2019;485(5):634-637
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General biology
Winter reproduction of cyclomorphic mammals: from a case to the phenomenon
Grigorkina E.B., Olenev G.V., Smirnov N.G.
Abstract

In 2010 (a year of drought), the true winter breeding (TWB) of the pygmy wood mouse (S. uralensis) was first recorded in the Southern Urals and confirmed by the morphological parameters and age markers. The young born in winter fulfilled successfully their reproductive potential under favorable climatic conditions. The true winter breeding and the age cross of animals during the year of drought promoted the maximum population growth and enhanced population genetic heterogeneity. In subsequent years, TWB of S. uralensis became common, which is regarded as a climatic pattern. Extreme drought rearranged the rodent community and caused TWB of S. uralensis, which resulted in a higher abundance of the species.

Доклады Академии наук. 2019;485(5):638-641
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Ultrastructure and nanomorphology of the American mink (mustela vison) kidney
Ezhkov V.O., Ezhkova M.S., Yapparov I.A., Yapparov A.K., Nizameev I.R., Nefediev E.S., Ezhkova A.M., Larina J.V.
Abstract

The ultrastructure of the nephron subcellular organelles was studied in healthy mink kidneys. The data obtained were compared with the results of transmission electron microscopy. The renal cell nanomorphology proved to be similar when electronograms and the atomic force microscopy images were analyzed. The methods used enabled us to visualize the glomerular capillary endotheliocytes with cytolemma pits in the area of fenestrae that provide blood filtration; in the proximal nephron part, on the apical pole of the epithelial cells, brush-border soft microvilli were observed. The microvilli were characterized by a well-organized structure along their entire length and the membrane integrity. The data obtained show morphological parameters of the healthy mink organ and can be helpful in diagnosing of nephropathology.

Доклады Академии наук. 2019;485(5):642-645
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