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We carried out a detailed geological, geochronological, geochemical, and isotope study of diorites from a dike located in the central part of the Baikal uplift of the Siberian craton. The geochemical and isotope data obtained for diorites of the studied intrusion were compared with coeval mafic and intermediate igneous rocks of the southern part of the Siberian craton. The U-Pb (ID-TIMS) baddeleyite age of 1862 ± 7 Ma has been estimated for diorite from a dike located in the area of the Onguren Village. The obtained data are the first reliable age determination for the Paleoproterozoic mafic and intermediate igneous rocks of the Baikal uplift, which are part of the South Siberian postcollisional magmatic belt. The dike is of NE strike. The dike rocks correspond in chemical composition to diorites and are highly differentiated varieties (mg# = 36.5-37.4). There are no significant variations in the composition of diorites in the marginal and central parts of the dike. The rocks are characterized by low contents of TiO₂, P₂O₅, and Nb, high contents of Th, Zr, Ba, and LREE, and low negative values of ε_Nd( T ) (-5.9 to -6.2). We assume that the diorites formed from the enriched subcontinental lithospheric mantle. The obtained geochemical and isotope data show similar negative values of ε_Nd( T ) from -4.3 to -11.6 for most of Paleoproterozoic mafic and intermediate igneous rocks of the South Siberian postcollisional magmatic belt within the Aldan Shield, the Baikal uplift, and the Irkut block of the Sharyzhalgai uplift. These rocks correspond in geochemical features to rocks resulted from the melting of subduction-modified lithospheric mantle sources in the postcollisional extension setting at the final Paleoproterozoic stage of formation of the Siberian craton.

Au-Ag mineralization occurrences in sphalerite ores of hydrothermal genesis are paradoxical in view of the incompatibility of these elements in sphalerite. The formation of sphalerite with Au and Ag impurities under hydrothermal crystallization of ZnS at 450 ^oC and 1kbar pressure was studied experimentally. Sn impurity was taken as a source of point defects in crystals modelling the interaction of Au and Ag with vacancies. The Ag solubility in low-Fe sphalerite is estimated as 3.8 ± 0.7 µg/g, Au ̶ ≤ 0.6 µg/g. The main forms of Ag and Au occurrence in sphalerite are the inclusions of (Ag, Au) _x S phases with x varies mainly from 1.8 to 2.0, and Au varies from 0.01 to 0.75 a.p.f.u. The primary forms of the elements in ores might be microinclusions (Ag, Au) _1.8-2.1S or close to (Ag, Au)S at higher f _S2. In presence of Sn, solubilities of Au and Ag become higher. The behavior of Au corresponds to the substitution reaction Sn⁴⁺ + Au⁺ + v^- ↔ 2Zn²⁺ in the presence of two types of vacancy defects (v^-) - the “inherent” vacancies dependent on the crystallization conditions and the vacancies accompanying Sn⁴⁺ incorporation. Ag entrance is seemingly more dependent on f _S2 conditions and does not correlate with Sn. The extra vacancies arise because of metastable crystallization under the conditions of oversaturation of growth medium. This is supported by the spherulite morphology of growth products and the admixture of wurtzite ZnS form. The distribution and cocrystallization coefficients show an increasing trend for both precious metals (PM), due to which Au changes from incompatible to the category of highly compatible elements in sphalerite. The geochemical environments favorable for the formation of imperfect mineral crystals are considered. Such crystals are capable to uptake PMs and other incompatible in “ideal” crystal elements because of their interaction with vacancies, both constitutional (inherent to the substance) and non-equilibrium defects, and surficial nano-sized formations (nonautonomous phases). The evolution of these initially “invisible” forms of PM under metamorphic processes and remobilization of ore substance may result in Au and Ag escape and aggregation into microparticles.

This paper describes a detailed mineralogical and geochemical study (using electron probe microanalysis and secondary ion mass spectrometry) of zircon from rare metal pegmatites of the Polmostundra and Kolmozero lithium deposits (Kola Peninsula, Arctic zone, Russia). The zircons studied here have several distinguishing features. Firstly, anomalously high lithium content (up to 327 ppm Li according to secondary ion mass spectrometry data). Secondly, high hafnium content (up to 39.21 wt.% of HfO₂ according to electron probe microanalysis data). Thirdly, low Zr/Hf ratios (from 0.74 to 4.70). Fourthly, high content of volatile components (up to 5.98 wt.% of H₂O, up to 0.65 wt.% of F, and up to 0.12 wt.% of Cl according to secondary ion mass spectrometry data). Finally, higher content of impurity elements, the main of which are Th, Ta, U, Nb, Ca, and P. It is revealed by the results obtained that the rare metal specificity of the composition of highly fractionated pegmatite melts of the Polmostundra and Kolmozero deposits, from which zircons crystallized, are the key indicator of the high degree of its fluid saturation. The extremely low values of the Zr/Hf ratio for zircons can be explained by the combined influence of fractionation of the initial granitic melt with the accumulation of Li in the residual melt at the final stage of the evolution of pegmatites and the role of fluids saturated with volatile elements. Zircon crystallization occurred at the magmatic stage of pegmatite formation, and zircon alterations occurred at the hydrothermal stage. The nature of the rare earth element distribution in zircons from the Polmostundra and Kolmozero deposits indicates that the formation of the central zones and margins of grains took place during the magmatic and the hydrothermal stage, respectively.

The article provides explicit formulas for the parameters of an effective stock portfolio obtained based on Markowitz’s theory, including for the Tobin’s Model. An empirical test was performed and confirmed the correctness of the obtained formulas. They can be useful in theoretical studies related to effective securities portfolios, as well as in the development of computer programs for analysing investments and the stock market.

Reproductive behavior is the primary basis of negative trends associated with a decrease in fertility in the world. The study of this phenomenon will allow us to find ways to regulate the current situation. However, the main problem lies in the complexity of statistical research of this phenomenon due to its specificity. In this article, an attempt was made to solve this problem by determining the location of Russian regions in the boundaries of reproductive behavior using the McKinsey matrix portfolio analysis method.

This article proposes an algorithm for calculating the vector of the stationary probability distribution for the Markov chain. Markov chains are effective for modeling complex systems in dynamics, including socio-economic processes, since instead of deterministic equations and dependencies, various scenarios are taken into account. At the same time, with an increase in the number of options, the complexity of solving the problem of finding a stationary probability distribution increases sharply. The idea of the algorithm is to replace the problem of solving the characteristic equation of the n-th degree for the matrix of probability transitions with the problem of linear programming. The mathematical formulation of the problem is formulated, including the definition of independent variables, finding the type of objective function, restrictions in the form of equalities. To perform calculations, a program was created in the algorithmic language Python. In order to verify and prove its effectiveness, calculations were carried out both for typical tasks of a general nature and for specific socio-economic cases. The obtained results completely coincided with the test ones and showed that the complexity of the algorithm is O(n). The developed technique allows wider application of Markov in the study of socio-economic processes and obtain more reliable results due to an increase in the number of probabilistic states of the system.

In modern conditions, the concept of sustainable economic development is effectively implemented through the processes of introducing ESG principles into the activities of enterprises in various industries. The hospitality industry is currently poorly engaged in the ESG transformation process. This is evidenced by the absence of companies from the hotel and restaurant business in ESG ratings. Modern realities require hospitality industry enterprises to reorient their activities in accordance with the principles of ESG transformation. ESG principles can be actively introduced into the cycle of use of fixed assets: from capital investment objects to liquidation objects. Fixed assets play a key role in the operations of hospitality businesses. Consumer demand for the company’s services depends on their volume, technical condition, as well as appearance. Corporate culture and the ESG agenda in modern conditions have a huge impact both on the entire resort and recreational industry of the country, and on the use of fixed assets within the industry. The purpose of this work is to assess the impact of corporate culture and the ESG agenda on the business activity of hospitality enterprises and the use of fixed assets. The ESG transformation of resort and recreational enterprises can be aimed at protecting the hospitality industry as a whole, as well as in the state economy, from risks that may arise due to conditions of uncertainty. The implementation of ESG transformation will contribute to the formation of a positive image, increasing the operating efficiency and competitiveness of entities in the hospitality sector.

This paper considers approaches to accounting for tax losses. It is determined that the accounting methodology depends on the way they are utilised. Tax losses claimed as a refund (Loss Carry-Back) represent a financial claim to the state, therefore they are qualified as an asset (receivable) within the current tax component. Losses claimed as a deduction (Loss Carry-Forward) qualify as a deferred tax asset in the deferred component. Three approaches to accounting for tax losses attributable to deferred taxes are characterised: conservative, mixed and positive. It is established that in the concept of temporary differences the economic benefit from the resulting tax loss is identified in relation to its tax base; in turn, in the concept of temporary (term) differences the tax effect is part of the «difference» between the accounting and tax result. It is concluded that the Russian Accounting Standard (PBU) 18/02 «Accounting for corporate income tax calculations» has the following shortcomings: tax losses are incorrectly classified, and the methodology of their accounting is not defined due to the distorted base of tax effects distribution. The results of this work may serve as a basis for improving national accounting standards.

The article examines the volatility of one of the key indices on the Russian stock market. Through the prism of statistical data analysis have been identified four key risk groups. The use of this method is justified by the obtained results. The proposed methodology can be used as a basis for forming an investment portfolio of shares with better diversification characteristics.

In the article author presents two approaches to libraries: functional and user defined. From the point of view of functional significance, the library performs the function of personality formation, educational, memorial, and communicative functions. From the point of view of the quality of services received by visitors, the library appears as an architectural, construction and professional library synthesis. The user can evaluate the quality of the services provided in real and virtual space. The library can provide leisure services - clubs, clubs, evenings, lectures, concerts. The functional importance of the library, combined with the high quality of the services provided, should be an attractive place for visitors. To research the real state of affairs, the results of sociological research conducted by All-Russian Center for the Study of Public Opinion in Russia in 2011, 2015, 2022, as well as in libraries in Novosibirsk in 2020 and 2024 are presented. All-Russian Center’s for the Study of Public Opinion results reflect attendance and solutions to the problem of low attendance. The results of the Novosibirsk study reflect an assessment of social attitudes towards libraries. Such an assessment was carried out through a content analysis of the system for collecting customer feedback on products, services, and organizations of Flame. The results of the study of Novosibirsk libraries were compared with some of the results of All-Russian Center for the Study of Public Opinion. The author concluded that the problems of non-attendance are somewhat “far-fetched”, which hide personal lack of activity, low motivation to work with book publications. The results of the research can be used in planning the library’s activities for the development of a user service system.