North Ossetian State University

In line with the modern trend of searching for inexpensive alternatives to noble-metal based catalysts, in the present work a comparative study of the process of carbon monoxide oxidation on the surface of the ternary system Mo-B-O, on the one hand, and the Au/TiO2(110) system, on the other hand, is carried out. Model systems of both types as substrates were created in a controlled way under ultrahigh vacuum (UHV) conditions and studied in situ by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, low-energy electron diffraction, scanning tunneling microscopy, temperature-programmed reaction, and work function measurements. To form the Mo-B-O system, a 4-monolayer-thick film of boron atoms was first formed on the surface of the Mo(110) crystal, after which the formed film system was annealed to form a binary Mo-B compound. Then, this compound was oxidized in situ by oxygen admitted to the UHV chamber to form a ternary compound Mo-B-O with an atomically ordered surface structure of c(1 & times; 3)R30 degrees symmetry relative to bare Mo(110). The peculiarity of this system is its rather high efficiency of CO oxidation, comparable to that of the Au/TiO2 system, a prototype widely used in practical applications for low-temperature CO oxidation. The basis for such high efficiency of Mo-B-O is a significant transformation of the electronic state of both CO and O2 molecules during their co-adsorption. In addition to high catalytic activity, the Mo-B-O system exhibits high stability during the reaction, which, along with its low cost, can be a more acceptable alternative to the currently widely used Au/TiO2 catalyst.

We consider a boundary value problem for a network beam equation with a forcing term. The main aim of the paper is to obtain upper and lower bounds for the restoring force, ensuring the property of inverse positivity of the corresponding differential operator. These bounds are based on spectral theory, in fact the bounds of the obtained interval are given by suitable eigenvalues of the differential operator with different boundary conditions. The proof of this result is based on abstract methods of functional analysis of operators in ordered spaces. Thus, the proposed method allows to avoid the explicit calculation of the related Green's function.

Introduction. The Taganrog Bay of the Azov Sea is one of the most eutrophic and ecologically vulnerable water areas in Russia, where massive blooms of toxic cyanobacteria (Microcystis, Aphanizomenon, Anabaena, Nodularia) regularly occur during summer. Their proliferation is accompanied by the accumulation of cyanotoxins (microcystin, anatoxin, cylindrospermopsin, saxitoxin), posing a serious threat to public health. This paper considers an approach to the biological rehabilitation of the bay based on the controlled introduction of the freshwater green microalgae Chlorella vulgaris, which competes with cyanobacteria for nutrients. The aim of the study is to develop and apply a comprehensive mathematical model describing phytoplankton kinetics and substance transport processes under conditions of increasing bay salinity, as well as to assess the ecological-hygienic and medical consequences of the proposed method. Materials and Methods. The research object is the Taganrog Bay of the Azov Sea. The modelling is based on the threedimensional hydrodynamic model “Azov3D”, previously used to calculate currents and vertical mixing under conditions of changing salinity. Water environment parameters (salinity, temperature, current velocities) were used as input data for solving the linearized hydrobiological problem. The source of bathymetric data was digitized nautical charts processed using automated depth recognition algorithms. The model grid was generated considering the actual coastline configuration and bottom topography. Calculations were performed on the computing cluster of the Southern Federal University. The numerical method is based on finite-difference schemes previously applied for hydrobiological calculations in the Azov Sea. Results. It is shown that a 30% increase in salinity leads to a shift in the cyanobacteria habitat from the Azov Sea water area to the eastern part of the Taganrog Bay, which is consistent with hydrological observations. Model calculations demonstrate an increase in the proportion of green algae with the controlled introduction of Chlorella vulgaris cultures, reflecting the potential for biomelioration. The forecast of the spatial distribution of populations shows stable dominance of green and blue-green algae, constituting 60−70% of the bay’s phytoplankton biomass, under various impact scenarios. Discussion. The results indicate that mathematical modelling is an effective tool for predicting the dynamics of phytoplankton populations under changing hydrological conditions. The model allows for assessing the influence of biological regulation and salinization scenarios, providing a basis for management decisions in the field of ecological rehabilitation of water bodies. Conclusion. The application of Chlorella vulgaris may be a promising biomelioration method but requires further verification based on field observations and controlled field experiments. The modelling results indicate the possibility of adaptive ecological management of the Taganrog Bay and minimizing the risk of toxic blooms.

В статье исследуется обобщение классических теорем Штурма о перемежаемости нулей и о сравнении для решений дифференциальных уравнений четвертого порядка, заданных на метрических графах. Подобные уравнения возникают в задачах математического моделирования плоских стержневых систем. Анализ проводится с учетом условий согласования в узлах графа, которые отражают различные механические способы соединения стержней (упруго-шарнирные, жесткие или условия $\delta$-типа) и имеют вариационную природу. Установлено, что ключевые положения теорем Штурма, известные для уравнений второго порядка на графах, допускают обобщение на случай уравнений четвертого порядка. Сформулированы аналоги теорем сравнения и перемежаемости нулей, а также проведен анализ свойств решений соответствующих дифференциальных неравенств. Дано явное описание условий, обеспечивающих выполнение принципов Штурма на графах. Библиография: 24 названия.

The introduction of the professional income tax has provided citizens with a simple and legitimate tool for carrying out individual labor activities without the risk of administrative prosecution and with minimal fiscal burden. This tax was introduced in 2019 as a pilot project, and in 2020, it became effective throughout the Russian Federation. The professional income tax has numerous advantages, but it is worth noting that the distribution of the tax regime across the country is highly uneven. In some regions, the share of self-employed individuals in the total economically active population is significantly higher than in other regions of the Russian Federation. The same difference is observed in the amount of tax revenue per taxpayer. This unevenness makes a detailed regional comparison relevant. The percentage of registered self-employed people in relation to the number of employed people in a region is an indicator of how effectively the mechanism for legalizing income works in a particular region.