Study of the convergence of the finite-element method for parabolic equations with a nonlinear nonlocal spatial operator

© 2015, Pleiades Publishing, Ltd. We consider a parabolic equation whose spatial operator depends nonlinearly not only on the unknown function and its gradient but also on a nonlocal (integral) characteristic of the solution. By using the semidiscretization method with respect to the variable t and the finite element method in the space variables, we construct an approximate solution method in which the nonlocality is pulled down to the lower layer. We prove a theorem on the convergence of the constructed algorithm under minimal assumptions on the smoothness of the original data

The finite element method explicit scheme for a solution of one problem of surface and ground water combined movement

© Published under licence by IOP Publishing Ltd.We investigate the initial-boundary value problem for the system of two nonlinear degenerate parabolic combined equations, when the one of equations is set in the domain we consider, and the second is set on the conducted section of this domain. With help of the semidiscretization methods with respect to time variable and finite element method (FEM) with respect to space variable we construct an explicit difference scheme. We obtained conditions which provide us convergence of constructed method. The result of convergence was obtained with the minimum conditions for smoothness of the initial data

On the convergence of an explicit difference scheme for evolution variational inequalities with nonlocal space operator

© 2017, Pleiades Publishing, Ltd.A nonlinear parabolic variational inequality with nonlocal space operator monotone with respect to gradient is considered. An explicit difference scheme with respect to the space operator and an implicit difference scheme with respect to the penalty operator are constructed by using the penalty method and the method of integral identities. Stability conditions for the constructed difference scheme are obtained. A convergence theorem with minimal assumptions on the smoothness of the initial data is proved

On the solvability of an evolution variational inequality with a nonlocal space operator

By using semidiscretization and penalty methods, we prove the existence of a generalized solution of a variational inequality of parabolic type with a space operator monotone in the gradient and depending on an integral characteristic of the solution with respect to the space variables. © 2014 Pleiades Publishing, Ltd

Electrochemical Properties of PrBaCo2O6electrode in the Oxidation of Glucose and Methyle Orange

In this work, we investigate the possibility of using double cobaltite with the composition PrBaCo2O6 as an electrocatalyst in the oxidation of organic compounds. A screen-printed carbon electrode modified with the PrBaCo2O6 drop method was investigated as a sensor for glucose. The amperometric signal of this sensor is logarithmically dependent on the analyte concentration according to the equation: I (μA) = 9.485⋅ln(C (mM)) + 17.864 (R = 0.9951). The limit of detection is 0.52 μM (at S/N = 3). The linearity range is 0.0-17.5 mM, which corresponds to the physiological values of blood glucose concentration (3.3-5.5 mM). In addition, the possibility of electrooxidation of a refractory organic compound (methylene orange) using a modified electrode was shown. © Published under licence by IOP Publishing Ltd.The authors appreciate the support of this work within the government assignment No AAAA-A19-119110190048-7

A comparative study of Epipactis atrorubens in two different forest communities of the Middle Urals, Russia

The objective of this study was to compare eco-physiological and morphological parameters of a regionally endangered orchid species, Epipactis atrorubens (Hoffm. ex Bernh.) Bess., growing in two forest communities (on serpentine and granite outcrops) of the Middle Urals, Russia. Biodiversity, dominance, and phytocoenosis studies showed the colonization of a wide range of plant species on both sites. The physicochemical properties of the soil, chemical composition and morphological features of E. atrorubens, growing under technogenic conditions (asbestos deposits), on serpentine outcrops and in the natural environment of the granite massif were studied for the first time. The serpentine substrate differed from the granite one by its greater stoniness, circumneutral pH and lower contents of available nitrogen and phosphorus. Extremely high concentrations of magnesium were found in the serpentine soil, some 79 times higher than in the granite substrate. High concentrations of nickel (94 times), chromium (59 times), cobalt (17 times), and iron (4 times) were found in the serpentine substrate, higher than in the granite substrate. The differences between the sites for available metal contents and for root and shoot metal contents were significantly less. Concentrations of most of the metals in the roots were higher than in the shoots. Despite higher metal concentrations and lower nitrogen and phosphorus levels in serpentine soils, E. atrorubens had a larger population and greater viability compared to those growing on granite. Plants on serpentine outcrops were characterized by the formation of a larger number of fruits, greater root lengths and thicker leaf blades, compared to plants on granites. The well-developed orchid mycorrhizae contributed to the survival of this species under unfavorable serpentine conditions. Hence, serpentine outcrops formed due to the mining of asbestos could be a suitable substrate for the light-demanding E. atrorubens due to its capacity to adapt to dry, rocky, nutrient-depleted soils and limited competition from other plants. © 2019, The Author(s).The work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the State Task of UrFU No. 6.7696.2017

Recycling of Gold Tailings of Silicate-Carbonate Ores

The implementation of the method for extracting gold, including melting of silicate-carbonate technogenic material, showed that gold passes into a free state, and the size of its particles increases significantly. However, when the material melts, a significant amount of slag is formed, which must be disposed. The chemical composition of the slag was compared with the norms of approximate and maximum permissible concentration. The content of Cu, As, Sb, S, and Mn exceeds the established standards. When the melt is blown with air and natural gas, sulfur, arsenic, and antimony will pass into the gas phase. In this regard, the installation must be equipped with a dust and gas cleaning system. If 12 wt.% CaO is added to the initial mixture before melting, the slag will meet the requirements when it is used as a correcting additive in cement. © Published under licence by IOP Publishing Ltd.The research was supported by the Ministry of Science and Higher Education in accordance with the state assignment for Ural State Mining University No. 0833-2020-0008 “Development and environmental and economic substantiation of the technology for reclamation of land disturbed by the mining and metallurgical complex based on reclamation materials and fertilizers of a new type”. We obtain the scientific results using the equipment of the Centre for the collective use of scientific equipment of the Federal Scientific Centre of biological systems and agricultural technologies of RAS as well (No Ross RU.0001.21 PF59, the Unified Russian Register of Centres for Collective Use - http://www.ckp-rf.ru/ckp/77384)

RESEARCH OF AN ENZYME-FREE FUEL CELL BASED ON DOUBLE PEROVSKITES FOR THE DETECTION OF HYDROGEN PEROXIDE

The electrochemical characteristics of glassy carbon electrodes modified with perovskites by voltammetric methods and in the power generation mode are studied. A fuel cell was as-sembled, generating direct current and potential at the electrodes, and its characteristics as a sensor were studied

Adaptive morphophysiological features of neottia ovata (Orchidaceae) contributing to its natural colonization on fly ash deposits

In previous decades, some species of the Orchidaceae family have been found growing in man-made habitats. Neottia ovata is one of the most widespread orchids in Europe, however it is quite rare in Russia and is included in several regional Red Data Books. The purpose of this study was to compare the chemical composition and morphophysiological parameters of N. ovata from two forest communities of the Middle Urals, Russia: natural and transformed (fly ash dump of Verkhnetagil’skaya Thermal Power Station) for determining orchid adaptive features. The content of most of the studied metals in the underground parts (rhizome + roots) of N. ovata was considerably higher than in the leaves, which diminished the harmful effect of toxic metals on the aboveground organs. The adaptive changes in the leaf mesostructure of N. ovata such as an increase in epidermis thickness, the number of chloroplasts in the cell, and the internal assimilating surface were found for the first time. The orchids from the fly ash deposits were characterized by a higher content of chlorophyll b and carotenoids than plants from the natural forest community that evidenced the compensatory response on the decrease in chlorophyll a. The ability of N. ovata from the transformed habitat to maintain a relatively favorable water balance and stable assimilation indexes further contribute to its high viability. The study of orchid adaptive responses to unfavorable factors is necessary for their successful naturalization and introduction into a new environment. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.The reported study was partly funded by RFBR and the Government of Sverdlovsk region, project number 20-44-660011 and the Ministry of Science and Higher Education of the Russian Federation as part of state task of the Ural Federal University, FEUZ-2020-0057

Natural Forest Colonisation and Soil Formation on Ash Dump in Southern Taiga

Ash dumps occupy significant areas around the world and make a negative influence on the environment. This effect is decreased by their natural colonisation determined by the bioclimatic conditions of the area. The purpose of the current study was to identify the structure of the forest communities and the initial stages of soil formation on the ash dump in southern taiga. This study was carried out on three sites in the forest phytocoenosis formed in the process of revegetation of the Verkhniy Tagil Power Station ash dump over 50 years, as well as on two background forest sites in the Middle Urals. Complex geobotanical and soil studies were carried out. The results of the study show that forest phytocoenoses with a predominance of hardwood species (Betula pendula Roth and Populus tremula L.) and a small admixture of coniferous species can form on the non-recultivated ash dump within 50 years in a boreal zone. In total, the studied mixed forest phytocoenoses are similar in composition to zonal secondary forests, but differ by having lower height and diameter of the stand, as well as herb–shrub layer coverage. Their species density and floristic richness are also lesser. The study proved that the process of soil formation is also proceeding according to the zonal type in the ash substrate under forest communities. The results of the study can be applied to justifying the forecasts of ecosystem restoration on the technogenic substrate, as well as for the species selecting for their recultivation in the studied area and similar to it. © 2020 by the Committee on Forestry Sciences and Wood Technology of the Polish Academy of Sciences and the Forest Research Institute in S´kocin Stary