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The vector potential of the magnetic field is determined in the region between the inductor, the upper part of the floating zone, the liquid film, the feed rod, and the protective screen in an axisymmetric problem of crucible-free zone melting of a silicon sample with a radius of 5÷10 cm. The boundary condition at infinity is transferred to a semicircular arc connecting the feed rod to the protective screen and located at a sufficiently large distance from the inductor, which allows the problem to be considered in a finite domain. This domain is conformally mapped onto a rectangle, within which the problem of determining the magnetic field vector potential is solved. The problem is reduced to solving Laplace’s equation for the only non-zero component of the vector potential, A_φ , where φ is the polar angle, with first- or second-type boundary conditions on the edges of the rectangle. The method can be applied to calculate the variable thickness and shape of the liquid film adjacent to the lower part of the feed rod, as well as the hydrodynamic flow within it.

The article evaluates the potential for expanding the analysis of the territorial organization of production and settlement using an institutional approach. A counter movement by economists and sociologists toward geography as a science exploring the diversity of the environment external to institutions has been noted. In geographical studies, the institution itself rarely becomes the subject of spatial analysis; it primarily serves as an attribute of the object of study. It is demonstrated that the geographical view on institutions suggests two directions of research: the reflection of territorial characteristics in the nature and forms of certain institutions; and the spatial variability of institutions themselves, determined by the properties of the territory. The economic-geographical analysis primarily uses formal institutions, i.e., legalized norms and organizations. Informal behavioral stereotypes appear in socio-geographical works without corresponding generalizations as institutions, most often when studying rural areas. A comparison is made with the views of foreign scholars on the institutionalization of economic geography, identifying three directions for the development of the institutional analysis. The first one is the study of the evolution of the economic landscape, since institutions are characterized by inertia and maintain dependence on the previous path. Within the framework of this direction, the predisposition of local economies to innovation is considered. The second direction is the study of the embeddedness of economic action in local social structures, i.e., dependence on networks of communication with the local community. The third direction is increasing the importance of the local level in economic and geographical research, differentiating the locations where certain norms, rules, and interaction networks operate. Using the principles of evolution, embeddedness, and differentiation within the institutional approach, it is possible to develop a theoretical and methodological basis for studying the causes of various spatial processes, including population outflow from strategically important regions and the incomplete implementation of major investment projects, as well as for formulating an ideology of the territorial economic development based on endogenous resources under the conditions of an expected reduction in federal support funds.

The relevance of the issue of socioeconomic development of regions has been determined from the standpoint of Russia’s national security. It is shown that systematic monitoring of the dynamics of socioeconomic processes is necessary to implement a balanced state policy aimed at reducing interregional disparities. An analysis of the country’s socioeconomic development was carried out using key indicators of the standard of living and quality of the population for 2000-2021 at the federal and regional levels. At the first stage, district types were identified based on the combination of poverty level and life expectancy. At the second stage, integral indices of the standard of living and quality of the population were calculated at two hierarchical levels as an additional characteristic. An indicative analysis method with risk zone gradation was used to analyze the socioeconomic development of federal districts and subjects of the Russian Federation. The analysis revealed a decrease in the poverty level of the population and an increase in life expectancy for the Russian Federation as a whole. However, despite positive trends, the threshold values оf these indicators were not reached, and the combination of “poverty level and life expectancy” in terms of security remained static over the period under review. A similar trend is observed in the federal districts, with the exception of the Central and Northwestern ones. The North Caucasus, Siberian (SFD) and Far Eastern (FEFD) federal districts remain in the worst situation. The following contradictions related to the standard of living in the SFD are identified: insufficient consideration of natural and climatic conditions in the leveling of regions with a low level of economic development and diverging trajectories between GRP per capita and the standard of living of the population in “strong” industrial subjects. The low quality of the population in the SFD and FEFD has persisted over a long period. Based on the analysis of indicators of the standard of living and quality of the population, it is concluded that the current situation, particularly in the SFD and FEFD, contradicts the principle of social justice and requires fundamental changes in the state’s regional policy.

The article presents the results of the spatial analysis of travel freedom and countries’ openness to international tourism. The relevance of the study is determined by the transformation of the international tourism space in the context of the global multi-crisis. An institutional approach has been applied, the essence of which consists in identifying and studying the institutionally determined factors of the spatial development of tourism, which are formed at the international level. The article examines the geographical space within which general principles of partnership and cooperation between countries in the field of travel organization operate. A significant factor in the spatial development of tourism is tourist formalities, which are considered in a core-periphery context. They represent the most significant institutional barriers to tourist mobility, standing in the way of international tourist flows. It has been revealed that most countries of the global economic core are characterized by a high level of freedom of movement and, at the same time, increased requirements for incoming travelers. In the periphery, many island states with tourism playing a high role in their economies stand out for their openness. The share of the population traveling around the world without a visa has remained relatively stable over a long period of time. In the countries that largely shape global politics and economy of the modern world (the USA, Great Britain, China, Russia, Germany, and France), changes in visa-free travel opportunities occur synchronously. The general trend of increasing travel freedom observed for citizens of most countries indicates an expansion of the tourism space, despite growing economic and political instability, as well as the consequences of the global tourism crisis resulting from the coronavirus pandemic.

Socioeconomic and foreign policy turbulence poses a challenge for the scientific community of developing scientifically based approaches to assessing the sustainability of regional tourism systems, their adaptive management, and creating mechanisms to increase their sustainability. Of particular interest in this context are the regions of the Siberian Federal District (SFD), which have significant, but unevenly realized, tourism potential. This study focuses on the features of response of the tourism sector of the SFD subjects to the crisis shocks of 2000-2024, identified through the analysis of the dynamics of overnight stays. The work aims not only to diagnose the levels of regional sustainability, but also to identify key factors in their ability to adapt and recover from the crisis. The study is based on the combined application of two complementary methods: a multicriteria analysis of long-term trends in the indicator of tourist overnight stays; and the identification and analysis of specific response models (V-, U-, L-, W-types) to economic crises. Using the results of the analysis, areas of consistency in the findings obtained applying both methods, as well as illusory contradictions explained when proceeding to a qualitative analysis of the dynamics were identified and interpreted. Based on the synthesis of methods, an integrated classification of the SFD regions was developed. In addition to describing the current state, the resulting typology reflects the dynamics of the regions’ adaptive potential. The research results can be used by regional government bodies to develop differentiated anti-crisis policies in the tourism sector, thereby facilitating the implementation of the national project “Tourism and Hospitality” and the state program “Tourism Development”.

The problem of atmospheric pollution in a large industrial city is considered. The relevance of using spatial modeling for identifying urban areas most susceptible to atmospheric air pollution and developing measures to improve the atmo-ecological situation is shown. The article substantiates the proposition that the degree of pollution of the ground layers of the atmosphere in an industrial city, as well as the resistance of the urban environment to air pollution, are determined by the effect of opposing processes: atmospheric pollution by emissions from transport and industrial enterprises, on the one hand, and self-purification of the atmosphere due to natural conditions and built-up area patterns, on the other. The degree of resistance of the urban environment to atmospheric pollution depends on the character of interaction between natural and anthropogenic factors, the most significant of which are topographic features, wind regime, climatic characteristics, the actual amount of pollutant emissions, and built-up area patterns. These factors are described in the created analytical models, reflecting three blocks of data: the natural ventilation potential of the territory, stable zones of actual pollution, and the aeration potential of the built-up area. Based on analytical models, a polystructural atmo-ecological model of the urban environment of Saratov was constructed, reflecting the territory’s resistance to atmospheric pollution, taking into account the natural ventilation potential of the city’s territory, the aeration potential of the existing urban development, and the formed permanent halos of atmospheric pollution. The model identifies four categories of urban areas according to the degree of resistance to atmospheric pollution (highly resistant, resistant, non-resistant, extremely non-resistant), for each of which measures are proposed to improve the atmo-ecological situation.

The article presents the results of a comprehensive assessment of the ecological state of waters of the Yenisei River along the entire length, obtained using chemical and biological methods. Materials from Roshydromet, regional State reports on the state and protection of the environment, and the results of our own field research were used as the initial data. It was revealed that persistent pollutants in the Yenisei River include metals (ions of total iron, copper, aluminum, manganese, and zinc), petroleum products, phenols, and organic substances. The upper section of the Yenisei River is rich in biogenic elements; after the confluence with the Angara River, their concentrations significantly decrease due to both dilution and biological processes. However, while the content of organic and biogenic substances decreases, the concentrations of copper, zinc, and petroleum products increase from the middle reaches to the mouth of the river. According to the specific combinatorial water pollution index, the Yenisei water corresponds to categories ranging from “slightly polluted” (class 2) to “dirty” (class 4a). A steady trend of increasing pollution from the headwaters to the mouth of the river is observed. Communities of benthic animals, whose development in the Yenisei is not limited by high-velocity conditions, as compared to planktonic organisms, were used as bioindicators. All bioindicative parameters (13 indices and metrics) consistently demonstrated a trend of water quality deterioration from the headwaters to the lower reaches of the Yenisei, supporting the hydrochemical methods. After the confluence with the Angara River, due to a decrease in the concentrations of organic and biogenic substances, an improvement in water quality was noted according to a number of indices taking into account organisms sensitive to pollution. The reason for the water quality deterioration relative to natural conditions is the reduced self-purification capacity of the watercourse after the cascades of hydroelectric power plants and the high level of pollution from waste water of large cities. Biogenic elements and organic substance accumulate in the reservoir beds. The ecological water quality of the Yenisei River is influenced by both anthropogenic and natural factors, particularly by heterogeneous hydrological conditions and a network of large right tributaries.

The article presents the results of the analysis of archive materials of the long-term (1936-2015) observations of floods on the Barguzin River. A digital elevation model was created for geomorphometric analysis of the river basin relief. Automated analysis of relief indices in the Saga GIS software environment and expert interpretation of Landsat images from different periods made it possible to differentiate the basin territory into homogeneous hydrological sites characterized by similar physical and geographical parameters of flood development. An assessment of flood formation was carried out, their genesis was determined, and metric characteristics and features of passage in different parts of the basin were identified. Maps of average water levels and flooded areas were compiled. The flood zone mapping was performed in the ArcGIS software environment based on the interpretation of Landsat satellite data from different periods and a topographic base at a scale of 1:100 000. As hydrological information for obtaining absolute flood zone boundary elevations, a sample of maximum water levels was collected from long-term observation series, and calculated water levels at the cross-sections obtained from the distribution curves of annual probabilities of exceeding maximum water levels of rain floods for hydrological posts were used. The combination of layers of hydrological sites and flood zones with the layer of agricultural lands made it possible to establish the average long-term values of flooding of the territory for hydrological sites, and to determine the areas of flooded agricultural lands and settlements. A probabilistic-areal approach was used for the cartographic assessment of risk from floods. The risk calculation procedure is based on hazard indicators through a vulnerability parameter, allowing us to determine the physical risk or damage to the territory, economic facilities, and the population (in specific indicators), which forms the basis for calculating economic risk. Specific maps and an integrated risk map were compiled.

The article examines the features of paleocryological development of the north of Western Siberia, identified by the authors during the study of the interaction of polygonal-wedge ice (PWI) and cryopedogenesis. The paleosols of this area have been discovered and studied in detail by the authors. The article also considers the traces of the PWI south of their modern boundary, which have been little covered in the literature. It has been established that the identified paleocryogenic complexes reliably mark paleocryological events, which is especially important when their superimposing on the freezing of rocks phenomena also generated by cold, but caused by elements of the cryogenic system with a specific organization of matter, in particular, those associated with cryopedogenesis. The area between the Arctic Circle and the latitudinal course of the Ob River was explored. Here, the traces of the former PWI clearly reflect the fact that their development differed significantly from that observed in the zone of the modern PWI, which disappear south of 68 ° N. The latter grew during all the cold epochs of the Late Quaternary under conditions of syncryogenesis, influenced by the transgressive-regressive dynamics of the Arctic seas. Further south, the traces of the PWI record their epigenetic development outside the zone of this influence and only in MIS-2. Moreover, the formation of the PWI and their successor structures was closely linked to cryohydromorphic soils, about which nothing was previously known. They developed on the former basis of the seasonally thawed layer (SRL), forming a single cryopedogenic complex with the PWI and their successor structures. They played a particularly important role during the terminal phase of MIS-2, when the PWI thawed due to the onset of warming, but the host rocks remained frozen, and cryohydromorphic soils slid along the walls of the PWI, filling the space vacated by ice. This process continued until the mid-Holocene. Later, all the sediments that contained the PWI were overlain by podzols - soils on a free-draining rock matrix - recording their thawing, and at present, permafrost islands persist only in areas with poor drainage, where peatlands form.

The article identifies modern features of long-term fluctuations in air temperature for a year as a whole, and for cold (October-April) and warm (May-September) seasons in the Lena River basin with a widespread occurrence of permafrost rocks. It is shown that the increase in temperature during the cold season, which began in the mid-1980s, has had virtually no effect on the river runoff. A more important factor is the increase in temperature during the warm season since the mid-1990s, which promotes a more active participation of suprapermafrost waters (perched water runoff) in the formation of the Lena River runoff. It has been found that the distribution of the average long-term annual runoff across the catchment area is largely determined by the distribution of annual precipitation (correlation coefficient R = 0,8). Long-term fluctuations in the annual river runoff are also largely caused by fluctuations in annual precipitation (R = 0,7-0,9). In recent years (2008-2022), an increase in the runoff has been observed in the middle and lower reaches of the Lena River. Near the villages of Tabaga and Kyusyur, it amounted to 17 and 5 %, respectively, compared to the average runoff for 1930-1980, according to the State Hydrological Institute. In the upper reaches, at the cross-section near the working settlement of Kachug, the runoff, on the contrary, decreased by 6 % compared to the early 1960s. An assessment of the main elements of the genetic vertical structure of the Lena River runoff is given. In recent years, the share of the surface component of the runoff in the total runoff has been 35-50 %. A significant role in the formation of the river runoff in the warm season is played by the runoff of seasonal perched water (suprapermafrost waters) and aufeis, which constitute 20-25 % of the annual total runoff. Sustained groundwater runoff, primarily interpermafrost and subpermafrost water, accounts for 20-40 %.