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In the basis of a special area of genre PRology as a branch of the science of public relations the authors put the criterion of the diversity of PR-information in multi-channel public communication via new media. As a subject of genre PRology, the authors consider convergence of information formats of a PR text in a multi-channel PR. In the genre revision of PR communication in social media, the genre transformations of PR texts are influenced by the following factors: 1) technological, 2) intentional, 3) structural. Technologically, PR texts functioning in the space of social networks are characterized by 1) a polycode structure, which implies the equivalence of verbal and non-verbal levels of meaning; 2) the transgressive nature of the publication, which determines the animation of the message and its transgression (movement) in the digital space. PR texts are multi-intentional in nature. Structurally, PR texts in social networks undergo three types of convergence: 1) structural or presentational, 2) discursive, and 3) genre. Structural, or presentational, convergence of PR texts in social media is associated with the allocation in the post structure of the presentation (the actual text and iconic materials) and the reaction (readers’ comments). Discourse convergence of PR-text is associated with 1) diffusion of institutional and intentional types of discourse, 2) inter-institutional discursive interaction (PR and advertising). Genre convergence of PR-texts is a genre symbiosis of three types – convergence of primary and secondary speech genres, convergence of primary simple genres of PR-text, and intermedial convergence.

In the article the author examines the features of training convergent journalists within student’s media. For this purpose, the main typological characteristics of student’s media were studied, the influence of student’s media on the formation of professional competencies among students was revealed, the principles and methods of organizing the work of student media editorial offices were considered, and finally, the process of their unification into the convergent editorial office of FST-media was studied. During this research an expert interview was conducted with the expert community about the features of training convergent journalists, and also a content-analysis of the content of student’s media in terms of their correlation with the information demand thanks to the basic principle of training future journalists, from narrow specialization to universalism.

The article analyzes the international experience of convergence of regional development. The features of the European development of regional policy are defined. The main stages of formation of regional policy of some European countries have been allocated. It is substantiated that the change of the conception of the Europe of nations into the conception of the Europe of regions has led to the formation of a single market, in which the regions are considered as independent players due to increasing their competitiveness. The main tasks of regional development support funds in European countries have been formed. It is determined that on the basis of support and implementation of socioeconomic reforms, introduction of innovative technologies, an increase in the competitiveness of regions and an increase in the level of employment of the population has been achieved. In developed countries, programs are being developed to improve energy infrastructure, which include the development of alternative energy, the introduction of energy-saving technologies, and the creation of new energy communications. It is determined that in regional development an important role is played by stimulation of medium and small businesses, which is implemented on the basis of support of such initiatives by providing them with simplified access to capital, activation of enterprises engaged in tourism activities. It is determined that, despite the different levels of regional development, the main vector is the creation of prerequisites for the balanced development of all territories through minimizing the impact of negative environmental factors. The main instruments for ensuring the convergence of regional development have been allocated. The policy of France in the direction of stimulating the convergence of regions, which consists in the State-controlled system of contracts for planning regional development, is substantiated. The regional development policy of the Netherlands and Austria is more focused on the development of instruments of influence. The peculiarity of the Danish system of regional development is the refusal to stimulate and support certain problem regions and the application of a market approach, which is aimed at creating the necessary conditions for their independent development. The features of the policy of regional convergence of the USA, China, Canada and Australia have been studied, which allowed to allocate the features of their policy of stimulating the development of territories. The main aspects of the formation of regional development policy in Ukraine are also examined and the priority tasks in this aspect are allocated.

It is determined that one of the priorities in any national economy is the problem of forecasting and assessing the level of transparency of development, quality and reliability of functioning of industrial enterprises, their technological and economic subsystems. This has a direct impact on the level of investment, the nature of financing, the distribution of costs for the production of finished products with the achievement of a given quality and reliability, as well as on the financial condition and image. In addition, it has a direct proportional effect on the well-being of society and the quality of life of the population. On the other hand, investing in the real sector of the economy requires banks and other investors not only to optimize investment programs, but also to take into account the specifics of financial, production, economic and socioeconomic activities of industrial enterprises as market participants, and, accordingly, application of models that appropriately link investments with sales policies, production, management, staff, location of production facilities, taxation, etc. It is concluded that the positive level of management of transparency of development of industrial enterprises in the context of convergence of investment processes is inseparable from the processes of planning, regulation, control and forecasting of production and technological processes, as well as the allocation of resources in the process of performing certain complex tasks. Determining the optimal options for current and future development is often associated with solving large-dimensional optimization problems with a large number of different conditions and constraints (for example, requirements for the completeness of variables combined with requirements for the absence of time losses), which, due to their extreme nature, complicate the solution of such problems. Effective methods for optimizing multi-purpose investment decisions in managing the transparency of the development of industrial enterprises in the context of convergence of investment processes include methods for analyzing the usefulness of goals, criteria and alternatives, including those with several vectors; methods of hierarchy of goals, taking into account a number of advantages; information about the chosen strategy, alternatives, their parameterization, stochasticity, substitution ratios, and other characteristics. All these factors can be taken into account for the classification of models of multi-purpose and program-target solutions and the use of the most effective of them when choosing the optimal investment solution in managing the transparency of the development of industrial enterprises in the context of convergence of investment processes.

A cutting method for solving the problem of convex programming was proposed. The method calculates iteration points based on approximation by polyhedral sets of the constraint region and the epigraph of the objective function. Its distinguishing feature is that the main sequence of approximations is constructed within the admissible region. At each step, it is also possible to assess how close the current value of the function is to the optimal value. The convergence of the method was proved. A few of its implementations were outlined.

It is determined that under the current conditions of intensification of competition struggle between domestic industrial enterprises and increasing market pressure from foreign competing firms, there is an urgent issue of highlighting the process of managing development transparency as one of the most important criteria for efficiency of the activities. The mechanism for managing the transparency of enterprise development on a synectic-compensatory basis, which is implemented in the context of convergence of investment processes, is formed due to the complex reflection of the dynamism and variability of economic interests and parametrization of the effective process of their balancing in a dynamic model of formation and use of the development potential of enterprises and in the presence of high quality of managerial decisions in comparison with competitors, which provides industrial enterprises with a competitive position in the market and forms a sustainable level of their development. That is, the effectiveness of managing the transparency of the development of industrial enterprises in the context of convergence of investment processes will be determined by the ability of the management system to achieve the set goals, outlining the need for their systematic and analytical research. It is appropriate to assess the quality and efficiency of the management system at industrial enterprises through the construction of a balanced system of signifiers and indicators, which is the basis for assessing the effectiveness of enterprises’ operation and is aimed at achieving their strategic goals. The unity of the backbone basis of the developed management mechanism in accordance with the managerial efficiency is confirmed by the consolidation of the elements of its construction, which is actualized in the format of accumulation of changes as a reflexive reaction to the processes of transformation. This allows to comprehensively manage all components of transparency in the development of enterprises in order to increase their efficiency, optimal organization of investment, supply, production and sales activities of the enterprise, reduce logistics costs, provide production with the necessary material resources and their effective use, optimize material, financial and information flows.

The paper presents the results of numerical modeling of the geomechanical behavior of the system “lava — operational excavation — enclosing potash rock mass” during mining operations. Numerical modeling includes a forecast of the mechanical behavior of the system at all stages of the system existence: from the natural stress-strain state (SSS) of the rock mass to excavation and safety measures installation, as well as the longwall mining operations. The results of numerical experiments are verified using the data from field studies of convergence of the roof and floor of the operational excavation and the side walls of this excavation. As a result of the studies, it is established that longwall mining has a significant impact on the operational excavation at a distance of about 40 m or less. In addition, the paper describes an algorithm for numerical simulation of the geomechanical behavior of the considered geotechnical system.

The article summarizes scientific ideas about essence of Russian regions and regional markets as actively transforming systems of economic relations in complex geopolitical and socio-economic conditions. The authors propose a process-role model of Russian regional markets functioning, consider relationship and dependence of median number and age structure of the country’s population, highlight the dominant problem of aging and decline in the number of able-bodied population. The researchers propose to consider combinatorics of the generations theory factors within the framework of Russian regional markets development. The research achievement consists in theoretical and methodological provisions development justifying amplification of market development factors considering different archetypes of consumer generations, consumer triggers presented, as well as regulatory aspects of regional policy aimed at strengthening the all-Russian civil identity and social stability in society. Methods of scientific research: system analysis, synthesis, economic and statistical method, methods of abstraction and inductive logic. The purpose of the study is to determine the content of regional markets meaning on the basis of the analysis of Russian regional markets regularities of transformations and corresponding regional specifics, to develop a process-role model considering existing paradigms of regional economy, realizing the dilemma of contradictions of consumers generations, business and state in the demands, values, and space of the market, entailing causal relationship of amplification of Russian markets transformation factors. The scope of application of the results obtained is multifaceted – from market infrastructure organizations to state structures. The latter will find the results useful in implementing state programs.

This study is devoted to the analysis of convergence in the economic development of regions, and these aspects are considered in the article in conjunction with the general trend of departure from economic globalization and transition to a new regionalism. The general trend of the new regionalism in the modern world, the manifestation of intraregional imbalances not only at the level of the integration association of countries, but at the intra-country level are considered. It is established that a significant motive in favor of regionalization is the strengthening of relations and strategic partnership between “friendly” countries, which changes the previously established models of international economic cooperation, and focuses on regional priorities of socio-economic development. The analysis of regional convergence has shown that such convergence has a historical trend towards a slowdown, which is generally manifested at the international and domestic levels, which is partly due to heterogeneous models of regional growth. In the future, countries and regions will need new mechanisms to adapt to crises and turbulence of the global economy.

A recent paper found that during 1995–2012 the dispersion of income inequality between Russian regions was decreasing, i.e. convergence of regional inequalities took place. This result is of no use for analyzing the impact of socio-economic policy, as it may aim at reducing income inequality of the entire country’s population and regional populations, but in no way at equalizing inequalities between regions. Moreover, the found phenomenon itself can be either positive, if regional inequalities converge to low values, or negative, when they converge to high values. In order to clarify this issue, a more detailed study of the convergence process is needed. The aim of this study is to reveal the ‘anatomy’ of regional inequality convergence in 1995–2012, and the divergence that followed it in 2013–2022, i.e. the internal pattern of these processes. To this end, the paper explores the evolution of the regional Gini indices distribution, namely, that of main distribution statistics and the distribution itself (represented by a histogram). The results obtained suggest that convergence of regional income inequalities in Russia in 1995–2012 is almost exclusively due to ‘catching-up’ of low-inequality regions with high-inequality regions. Therefore, this process cannot be considered positive. Divergence of regional inequalities in 2013–2022, on the contrary, was accompanied by a decrease in income inequalities in the regions, improving the situation with spatial inequality in Russia

The features of the formation of transversal competencies among students of physical and technical specialties are considered. The necessary elements for the formation of transversal competencies, such as self-awareness, value orientations, interpersonal and social relationships, relative independence in relation to the outside world and responsibility for one's actions have been identified. It has been established that transversal competencies are interdisciplinary in nature. It is shown that systemic-synergetic and convergent approaches can be used in the formation of transversal competencies. It has been established that independent educational and methodological activity is a fundamental element in the formation of transversal competencies. Using the example of practical classes in the discipline "Diffusion instability in multicomponent gaseous media", studied by undergraduates of the educational program "Technical Physics", the development of transversal competencies in students through the use of problem-solving methodology is shown. In the example under consideration, the problem-solving methodology used to develop transversal competencies involves the implementation of eight stages of work. The implementation of each stage of work involves the development of certain transversal competencies. It has been established that transversal competencies developed in this way during the implementation of practice-oriented training will contribute to the adaptation of master's graduates to rapidly changing situations. The latter assumes that the transversal competencies formed during the learning process will allow graduates of the master's program to transfer the acquired knowledge to a specific situation. [ABSTRACT FROM AUTHOR]

A cutting method was proposed for solving the convex programming problem. The method assumes that the constraint region of the problem is embedded into some polyhedral sets for constructing iteration points. It involves the construction of a sequence of approximations that belongs to the admissible set and is relaxed, as well as implies that the ε-solution of the initial problem is fixed after a finite number of steps. The method also allows to obtain mixed convergent algorithms by using, if desired, any known or new relaxation algorithms for constructing the main iteration points.

One of the leading factors contributing to emerging cardinal structural shifts in recent years has been increasing importance of innovation in economic systems development. The innovation process has transformed from a “rare” economic phenomenon into a driver of economic development. Innovations change the structure of reproduction, institutional structure, and technological structure of the economy, increase the rate of technological modes change, and achieve convergence of macro-technologies. Its introduction into the production sector is the cause of changes in industrial structure and its diversifiation. In this regard, the task of forecasting the rate of innovation development in the context of convergence of the Russian industrial enterprises becomes relevant. To solve this problem, a methodology ofinformation support for monitoring convergence ofindustrial sectors, as well as a structural and content model for managing convergence ofindustrial sectors within the framework ofmodern concepts, has been proposed. Thus, the system of industrial policy instruments has been formed. Its composition is determined by application of the developed model of information monitoring of convergence development level in industries. It allows to develop a set of control actions for each level of convergence, depending on the pace and scale of technological development, types of production activities included in the industry, with a focus on the most relevant modern concepts and development strategies.

In the article, the author explores the history of creation and development of the media franchise which revolves around the life of a fictional extravagant and in his own way genius serial killer and cannibal, Hannibal Lecter. The author of the study attempts to systematize the movies and series of the Hannibal universe, with a particular focus on the Hannibal TV series (2013–2015). The focus specifically on a TV series is due to the fact that such works have become a significant form of popular culture. The popular images that are formed within the context of a TV series are based on topical and meaningful categories of culture. This makes contemporary TV series, such as Hannibal, an influential tool for forcing the viewer to reflect on important issues. In this way, TV series today are able to influence cultural dynamics. On the other hand, as the author of the article shows on the example of Hannibal, the material of such media products is also a promising source for researching the processes and transformations taking place in society and identifying topical problems and challenges. The present study aims to identify various aspects of the complex and controversial personality of Hannibal in the context of contemporary culture. To achieve this purpose, the author, on the one hand, compares the image of the main character with the real and fictional characters of popular culture, and on the other hand, analyses several key categories of culture, including power, art and others, which all together allows defining the features of Hannibal’s personality within the coordinate system of culture.

Modern geo-economic and geopolitical processes create a need to rethink the integration interaction between the republics of the former USSR, now — sovereign countries. This is due not only to the rapidly increasing instability of the global financial system, the growth of trade and economic contradictions between countries, but also to the possibility of using the previous experience of inter-republican industrial-technological and intellectual cooperation to achieve the goals of economic development.Aim and tasks. The article’s main aim is to frame the technological and economic interaction between the former republics of the USSR in the new geo-economic and geopolitical conditions.Methods. The methods applied includes empirical and statistical analysis, the use of consistency, the principles of scientific discussion, dialectical methods of cognition, such as the unity of the historical and logical, the principles of induction and deduction, the principle of the linkage between qualitative and quantitative characteristics, the unity of analysis and synthesis.Results. The article highlights the features of the trajectory of the economic development of the former Soviet republics. The main problems associated with the transition to a “free market economy”, such as declining economies, population decrease, significant external debt, “Dutch disease” and deindustrialization of the economy, are identified.Conclusion. In conclusion the need to develop a new economic policy in the countries of the former USSR is argued from the standpoint of increased instability in the external economic environment and the need to strengthen their national economies, but also by the loss of economic independence and the accumulation of problems during the period of building a “market economy”. Significant efforts are required to restore the economy of the former republics of the USSR. The strategic direction is the reindustrialization of the economy, that is, the restoration of the lost economic potential on a new industrial and technological basis. For the successful implementation of the goal of strengthening economic sovereignty, it is of great importance to unite the scientific, intellectual and educational potential of the former republics of the USSR and create a common technological space. This will inevita bly lead to the formation o f a new system of international division of labor in the post-Soviet space, which is the main feature of a market economy.

The beginning of the 21st century can be characterized as a qualitatively new stage in the development of human civilization, for which the central concept is convergence, unification, rapprochement and interpenetration of sciences and technologies.Particular attention is paid to the convergence of four leading scientific areas: Nanotechnologies, Biotechnologies, Information technologies and Cognitive technologies (NBIC-convergences). It has been emphasized that joining this block of social and humanitarian technologies enhances their mutual synergistic effect.The study of the convergence of sciences and technologies as a new stage in the integration of scientific knowledge is the purpose of this research.The methodological basis of the research is general methods of scientific knowledge, such as analysis, synthesis, generalization; a systematic approach associated with the idea of an object as an integral system, with the identification of diverse types of connections of a complex object and their reduction into a single theoretical picture.The relevance of the topic and its practical significance is associated with the recent strengthening of the positions of fundamental research, for which convergence is becoming the main method and source of future knowledge.Substantiation of the tight entry of the concept of «convergence» into the general structure of modern scientific knowledge in the process of transition to the stage of directed conscious human evolution can be considered as the key conclusion.

We study a infinite system of algebraic equations with monotone nonlinearities and with an infinite Toeplitz type matrix. This system has applications in discrete problems of the dynamical theory of $p$-adic open-closed strings, the kinetic theory of gases, and mathematical biology. Under certain restrictions on the nonlinearities and on the corresponding Toeplitz matrix, it is possible to prove existence and uniqueness theorems for a nontrivial solution in the class of bounded sequences. The main tool for proving the uniqueness theorem for a nontrivial solution is an auxiliary independent theorem on the asymptotic behavior of a nonnegative nontrivial and bounded solution on $\pm\infty.$ At the end of the paper, specific applied examples of nonlinearities and the corresponding matrix are given to illustrate the importance of the results obtained.

The relevance of the study of the convergence of digital industrialization and industrial digitalization is due to the significant impact of digital technologies on modern economic systems, where they act as a catalyst for innovation, modernization of the industrial structure and sustainable development within the framework of the concepts of Industry 4.0 and 5.0. The purpose of the study is to develop an author's methodology for assessing the convergence of the digital industrialization and industrial digitalization in the conditions of Industry 4.0 and 5.0. This will fill the existing gap in the scientific literature and provide a tool for analyzing and comparing the effectiveness of digital applications in various economic systems. Particular attention is paid to the adaptation of this methodology for the conditions of Industry 4.0 and 5.0, which enriched the theoretical basis and practical recommendations in this area. The study applied methods of descriptive, criteria, quantitative, comparative and trend analysis; methods of systematization, aggregation and normalization. The source of initial data in dynamics from 2010 to 2022 was Rosstat in terms of information society indicators as of September 2023. The results of the study consist in the development and successful testing of the author's methodology for assessing the convergence of the digital industrialization and industrial digitalization in general in the Russian Federation, as well as in a comparative analysis of the dynamics of this process between Russia and China. The method includes 6 main stages. The novelty of the work lies in creation of a unique tool for convergence analysis in Industry 4.0 and 5.0, which includes a system of indicators for assessing the convergence of digital industrialization and industrial digitalization from 2 primary, 7 secondary and 19 tertiary indicators, which fills the existing gap in the academic literature. The practical value of the study is expressed in recommendations formulated on the basis of empirical data to stimulate the sustainable development of the digital economy in Russia. Further research may focus on detailing the convergence assessment methodology across industries and geographies, integration with other indicators of sustainability and resiliency, and effectiveness analysis for different stages and mechanisms of digital adoption.

Relevance of the research topic. The article is devoted to the problem of state regulation of the processes of convergence of air transport of Ukraine to the European Union (EU), the relevance of which is confirmed in the National Transport Strategy of Ukraine for the period until 2030 and the draft Plan for the Recovery of Ukraine. Analysis of recent research and publications. An overview of foreign and domestic scientific research on the problems of state regulation of air transport is presented. Setting the task, the goal of the research. The purpose of the article is to determine the problems and methods of state regulation of the processes of convergence of aviation transport of Ukraine to the EU and outline the means of their implementation. Highlighting unexplored parts of the general problem. Despite the large number of studies on the problems of state regulation of air transport, it is necessary to note the insufficiency of scientific works on this issue. Presentation of the main material. The author identified the systemic risks of the economic stability of the functioning of the aviation transport of Ukraine in the conditions of war and post-war recovery and the key actions to reduce them. The methods of state regulation of the processes of convergence of air transport of Ukraine to the EU (increasing the level of security; progressive liberal policy; deregulation of economic activity; promotion of foreign economic and international legal activity; technical improvement; introduction of information technologies) and the means of their implementation are given. Conclusions according to the article. Ukraine's signing of the Common Aviation Space Agreement with the EU countries contributes to the development of the domestic aviation industry and provides for the unification of the air transport markets of our country and the EU, the removal of barriers, which will contribute to the development of Ukraine's transit potential and integration into European aviation structures, strengthening the country's authority on the international the arena. During the post-war recovery of Ukraine, it is necessary to introduce new methods of state regulation of the processes of convergence of air transport to the EU: introduction of airspace free routes; development of the institute of the authorized economic operator; transformation of traditional airports into ecosystems; use of digitization, modern technologies of air traffic management, biometrics, artificial intelligence, electronic document management.

The «cross-cutting» institutions of criminal, civil, arbitration and administrative procedures are not always universal and identical. Despite terminological coincidences and generally similar notions of petitions in different types of proceedings, the places they occupy in criminal and civil proceedings are different. Purpose: to determine the balance of petitions and applications in criminal procedures, on the one hand and in civil, arbitration and administrative procedures, on the other hand. The determining method of the study is the method of comparative law. In addition, general and special methods (analysis and synthesis, logical, special-legal) are applied. Results: the criminal procedure concept of petitions includes heterogeneous appeals of law enforcement agencies to the court and requests addressed to these bodies by the participants in the pre-trial stages of proceedings, which have no analogues in civil procedure and «classic» petitions of the parties before the court. In criminal procedure, in contrast to arbitration, administrative and civil procedures, petitions many times prevail over applications.

Рассматриваются особенности перевода общественно-политической лексики в контексте анализа стратегий, использованных переводчиками Дж. Курносом, Л. Виардо, А. Файзи при переводе повести Н. В. Гоголя «Тарас Бульба», особое значение которой в настоящее время побуждает к поиску критериев оценки степени соответствия предметного содержания оригинала и транслятов на английском, французском и татарском языках. Экспонентом реализации данных стратегий признаны военно-административные и военно-исторические реалионимы предметно-тематической области «Общественно-политические отношения» группы «Военно-административное устройство общества». Указанные реалионимы и их трехъязычные эквиваленты сопоставляются с точки зрения использования стратегий доместикации и форенизации. Определяются конвергентные и дивергентные стратегии в переводах военно-административных и военно-исторических реалионимов текста-оригинала для оценки качества переводов. Эмпирической базой исследования послужил корпус из 28 военно-административных реалионимов повести Н. В. Гоголя «Тарас Бульба» (1842), отобранных с точки зрения принадлежности к предметно-тематической области «Общественно-политические отношения» с учетом симптоматической статистики, то есть частотности появления в тексте оригинала. Объект исследования образуют 84 эквивалента указанных реалионимов, зафиксированных в текстах переводов, которые выполнены на английском языке Дж. Курносом (1952), французском языке Л. Виардо (1853) и татарском языке А. Файзи (1953). Предметом изучения являются стратегии конвергенции и дивергенции предметного содержания повести Н. В. Гоголя «Тарас Бульба». Использованы обще- и частнонаучные методы. К общенаучным принадлежат методы логики (анализ, индукция, сравнение, группировка) и статистики (метод выборки, анализ соответствий), к частнонаучным – сопоставительный метод. Форенизация возрастает от английского перевода Дж. Курноса с 43 % общественно-политической лексики к 93 % в татарском переводе А. Файзи. Л. Виардо форенизировал 53 % реалионимов во французском тексте перевода. Только 12 из 84 переводческих решений являются дивергентными тексту оригинала, из них 6 содержится в английском переводе. А 54 из 84 единиц переводчики заимствовали, используя приемы транслитерации и транскрипции, а также необоснованной капитализации реалионимов. Можно констатировать, что на качество перевода повлияли следующие переводческие ошибки: опущение реалионима, его замена, неуместная модернизация (использование анахронизма), неверная капитализация, наличие «ложных друзей переводчика», фактологические ошибки. Анализ стратегий перевода реалионимов с точки зрения реализации стратегий конвергенции и дивергенции может выступать одним из критериев качества работы переводчика. Выбор конвергентной стратегии является базовым условием для осуществления более качественного перевода и тем самым репродукции замысла автора оригинала средствами языка перевода, а выбор противоположной, дивергентной, стратегии с высокой вероятностью будет искажать реалии исходного текста, вводя реципиента в заблуждение относительно предметного содержания оригинала. Выражением стратегий конвергенции и дивергенции на элементарном (микростилистическом) уровне при переводе реалионимной лексики выступают доместикация и форенизация.

Relevance. Regional differentiation refers to differences or diversity among different regions within a single country or territory. This may include differences in economic development, infrastructure, living standards, and other factors. The relevance of the research into regional differentiation is connected with the need for the state to build a single economic, social and cultural space within the country. The assessment of interregional differentiation is an important aspect for understanding the socio-economic development of a country or region, developing regional strategies and implementing state regulation measures. The purpose of the research is to study the dynamics of economic indicators (GDP per capita, investment, income, standard of living, etc.) in various subjects of the Russian Federation and the People's Republic of China in terms of their initial homogeneity, convergence or divergence. The object of this study is economic indicators characterizing economic and social processes in the Russian Federation and the People's Republic of China in the context of regions (provinces). The subject of the study is an approach to the study of regional inequality in the dynamics of the main economic indicators and the level of their convergence. The hypothesis of the study is the assumption that the successful development of the state as an economic system ensures a gradual convergence of the main indicators of socio-economic development of the regions. Research methods. General scientific methods of analysis and synthesis, as well as special methods of economic and statistical research (summary, grouping, correlation and regression analysis) were used. Results. The article considers the uneven distribution of benefits in the territorial, regional context. It is shown that striking economic inequality poses a threat to the territorial integrity of the country. Using the example of the provinces of the People's Republic of China, we analyzed the main economic indicators (the level of GDP per capita, indicators of investment, income, standard of living, etc.) in various territories of the country in terms of their initial homogeneity and convergence (or divergence) and compared them with the Russian Federation. A set of coefficients was used as methodological tools: the Gini coefficient; the Theil index; β-convergence and coefficient of variation. Conclusions. We proved that the successful development of the state as an economic system provides a gradual convergence of the main indicators of socio-economic development of the regions. Directions for further research: the formation of measures of state influence aimed at reducing regional differentiation, not from the point of view of reducing regional inequality in the development of productive forces, the material base of production, but from the point of view of the inadmissibility of sharp regional differences in the social living conditions of the population.

This article deals with the current theoretical and practical aspects of science and philosophy of education. The development of multi-level integrative processes suggests a new type of integration in the system of modern science. The newest areas of science development associated with the nano-, bio-, info-, cognitive (NBICS) science and technology give an example of convergent processes.

Computer networks are based on technology that provides the technical infrastructure where routing protocols are used to transmit packets over the Internet. Routing protocols define how routers communicate with each other by distributing information. They are used to describe how routers communicate with each other, learn available routes, build routing tables, make routing decisions, and share information between neighbors. The main purpose of routing protocols is to determine the best route from source to destination. A particular case of a routing protocol operating within an autonomous system is called an internal routing protocol (IGP – Interior Gateway Protocol). The article analyzes the problem of correctly choosing a routing protocol. Open Shortest Path First (OSPF) and Enhanced Interior Gateway Routing Protocol (EIGRP) are considered leading routing protocols for real-time applications. For this they are chosen to be studied. The main objective of the study is to compare the proposed routing protocols and to evaluate them based on different performance indicators. This assessment is carried out theoretically – by analyzing their characteristics and action, and practically – through simulation experiments. After the study of the literature, the simulation scenarios and quantitative indicators by which the performance of the protocols is compared are defined. First, a network model with OSPF is designed and simulated using the OPNET Modeler simulator. Second, EIGRP is implemented in the same network scenario and a new simulation is done. The implementation of the scenarios shall collect the necessary results and analyze the operation of the two protocols. The data shall be derived and an assessment and conclusion shall be made against the defined quantitative indicators.

We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations occur in the theoryp-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in.At the end, specific applied examples of the kernel and non-linearity are given that satisfy to all restrictions of the proven statements.

Sovereignty in the digital space is a relatively new phenomenon, which is discussed in this paper. It is complex in nature and depends both on the technological base which is used (primarily network equipment, including 5G, etc.), software products and platforms, and on the promoted content. The countries are faced with the difficult task of regulating the activities of global media holdings in order to maintain value-based sovereignty. The author gives a political and economic analysis of value sovereignty, showing the importance of the state as a regulator that allows to eliminate negative informational externalities. Particular attention is paid to the analysis of the international media landscape and the formation of multipolarity in the network space, including the growing phenomenon of technological convergence in the media industry, as well as the positions of individual countries and regions in the global media industry. The corporate structures of the world’s largest media holdings are studied and the increasing degree of diversification of their assets is revealed. The generational differentiation of socialization mechanisms in the post-pandemic era, including the proportion of time devoted to social platforms, traditional media (the case of television), as well as the main ways of accessing the Internet and the penetration of new technologies. The most promising for socialization and fast-growing segments are shown, including Internet TV, virtual reality technologies, video games and cyber-sports. In the final part of the paper the author discusses the main problems and challenges of regulating the national media space in order to ensure value sovereignty in the era of global convergent media.

This paper investigates a model of fluid flow in a fractured porous medium under the assumption of a uniform distribution of fractures throughout the volume. This model is based on the use of a fractional differential analogue of Darcy's law, as well as on the assumption that the properties of rock and fluid depend on pressure and its fractional derivative. Unlike previous studies, this study uses a fractional derivative in the Caputo-Fabrizio sense with a non-singular kernel. In this paper, we propose a numerical method for solving this initial boundary value problem and theoretically investigate the order of its convergence. The formulation of a fully discrete scheme is based on application of the finite difference approximation for integer and fractional timederivatives, and the Galerkin method in the spatial variable. A second-order formula is used to approximate both integer derivative and the fractional derivative in the sense of Caputo-Fabrizio. A priori estimates are obtained for both semi-discrete and fully discrete schemes, which imply their second-order convergence in time and space variables. A number of computational experiments were carried out on the example of a model problem to validate the accuracy of the scheme. The results of the numerical tests fully confirm the outcome of the theoretical analysis.

The paper proposes a hybrid numerical method for solving a model problem of two-phase nonequilibrium flow of an incompressible fluid in a porous medium. This problem is relevant in the modern theory of the motion of multiphase fluids in porous media and has many applications. The studied model is based on the assumption that the relative phase permeabilities and capillary pressure depend not only on saturation, but also on its time derivative. The saturation equation in this problem refers to the type of convection-diffusion with a predominance of convection, which also includes a third-order term to account for the nonequilibrium effects. Due to the hyperbolic nature of the equation, its solution is accompanied by a number of difficulties that lead to the need for an appropriate choice of the solution method. In contrast to previous works, this paper uses a finite volume element method for solving the problem, the construction of which is based on integral balance equations, and an approximate solution is chosen from the finite element space. To discretize the problem, two different dual grids are used based on the main triangulation. In this paper, a number of a priori estimates are obtained which yields the unconditional stability of the scheme as well as its convergence with the second order. The advantages of the approach used include the local conservatism of the scheme, as well as the comparative simplicity of the software implementation of the method. These results are confirmed by a numerical test carried out on the example of a model problem.

The paper develops a method for solving nonlinear equations of heat conduction. Two-layer container complexes have been created, the side faces of which are thermally insulated so that the 1D heat equation can be used. In order not to solve the boundary value problem with a contact discontinuity and lose the accuracy of the solution method, a temperature sensor was placed at the junction of two media, and a mixed boundary value problem is solved in each area (container). To provide initial data for the initial boundary value problem, three temperature sensors were used: two sensors measure air temperatures at the left and right boundaries of the container complex; the third sensor measures the temperature of the soil at the junction of two media. The paper numerically investigates the initial-boundary problem of heat conduction with nonlinear coefficients of heat conduction, heat capacity, heat transfer and density of the material. To solve a nonlinear initial-boundary value problem, the grid method is used. Two types of difference schemes are constructed: linearized and nonlinear. The linearized difference scheme is implemented numerically by the scalar sweep method, and the nonlinear difference problem is solved by the Newton method. On the basis of an a priori estimate of the solution of a nonlinear difference problem, we prove the convergence of the second degree of Newton’s method. The numerical calculations carried out show that, for small time intervals, the solutions of the linearized difference problem differ little from the solution of the nonlinear difference problem (1 - 3%). And for long periods of time, tens of days or months, the solutions of the two methods differ significantly, sometimes exceeding 20%

The present paper is aimed at studying the artistic mind of the modern English writer John Fowles as the creator of the original worldview in its postmodern style. It has been specified that British artistic culture does not demonstrate neither the extremes, peculiar to the art of “transition” or “frontier” nor sharp denial of everything that seemed inviolable. Inclining towards realistic forms of the English classics, a lot of postmodern authors, including Fowles, prefer a synthesis of the old with the new. This applies both to postmodernism and all avant-garde and neo-avant-garde movements, aimed at fundamental changing of the general ideas about the beauty and ugliness. “The French Lieutenant’s Woman”, written by John Fowles, proposes such a postmodern synthesis in the context of the “playing with the past” thesis. In his novel, the author presents a special type of “new reality”, corresponding to the period of the profound changes inside the movement during the period starting from the end of the 19th century till the end of the 20th century. Instead of the typical for English literature “hero in search”, the novel under consideration demonstrates an existential type of a man. The above-mentioned hero, who is embodied in the images of Charles and Sarah, seeks his individual freedom and “corrects” his own destiny. It should be emphasized that gaining true freedom is possible only through overcoming various life and social obstacles associated with breaking class and social ties, as well as with great internal suffering. Fowles’s peculiar style of narration helps to reveal the main theme of the novel. The author uses postmodern irony, which is meta-irony, and pastiche. The method of “overlapping epochs” forms an original intertext whereby the semantic field of the novel increases. The literary significance of the outlined method is multifaceted: an elitist reader perceives text-subtext-intertext; a “mass” reader gets acquainted with the work at the level of an entertaining storyline. The author of the article also analyses a mythological component of the novel “The French Lieutenant’s Woman”. A mention should also be made that Fowles in the analysed work acts both as a creator and a destroyer of the socio-ethical and literary myth of the Victorian era. Of primary interest to the writer was the literary myth of the time of Queen Victoria, which in the minds of readers has long been romanticized and become a legend. Therefore, the article shows the connection of everything that happens according to the tradition of English romantic narration and the principles of reformation of characters and situations that no longer correspond to the romantic worldview. The ironic understanding of the gentleman’s code of honor and the object of his passion, the reduction of love conflicts and places of romantic meetings are illustrated by specific examples from the text of the novel. The present paper has also devoted considerable attention to the psychology of the protagonists as well as the problem of the plot and compositional unity of the novel “The French Lieutenant’s Woman”. It is proved that the development of the storyline of the novel is a polystructural and polysemantic phenomenon. If Sarah’s character combines the traditional features of both “woman with a secret” and “infernal woman”, then respect for Charles’s traditional aristocracy is being called into question: it is repeatedly mentioned that he did not receive a Cambridge diploma, that he is an amateur paleontologist, that he considers the possibility of getting married for money, and that there is a very strong element of carnal passion in his romantic relationship with Sarah. The article offers the author’s commentary on the compositional completion of the novel. It is argued that the trinity of the epilogue, first of all, explains the “world-chaos” antithesis. The formula of the dissipating world, according to the author of the article, was supposed to become the basis of the postmodernist text in the original version of the novel “The French Lieutenant’s Woman”.

The article studies dialogization of media monologue messages aimed at intensifying the interiorization of new information into the addressee’s picture of the world by stimulating a dialogue with the audience. There have been singled out two levels of dialogization–discourse and genre. The analysis of the media content in the advertising and political types of communication, as well as discussions and talk shows on any topic, suggested that the most effective factor stimulating the recipient’s response is the provocativeness of the discourse, found in the topic under discussion, categorical statements, controversial points of view and defiant behavior of the participants. The author analyses communicative ways of dialogization of three genre types–informative, evaluative and incentive genres (according to L. Duskaeva’s classification). The study has found that important factors determining the dialogization of discourse and genre are the interactivity of the information and communication system and the convergence of genres, the product of which is, for example, such social network genres as a blog and a forum which in their modern form depend only on the creative potential of their authors. Particular attention is paid to the dialogization of the social advertising genre which does not imply interactivity, but the real objective indicator of its effectiveness is the audience’s awareness of the problem and their subsequent actions. The author presents two directions of dialogization: firstly, the strengthening of dialogueness and interactivity with the help of rhetorical means and techniques that appeal to the addressee; secondly, the verbal expression of the interaction of two or more semantic positions, a form of representation of media facts, which presupposes the reaction of the audience.

An initial-boundary value problem is studied for a multidimensional loaded parabolic equation of general form with boundary conditions of the third kind. For a numerical solution, a locally one-dimensional difference scheme by A.A.Samarskii with order of approximationO(h2+) is constructed. Using the method of energy inequalities, we obtain a priori estimates in the differential and difference interpretations, which imply uniqueness, stability, and convergence of the solution of the locally one-dimensional difference scheme to the solution of the original differential problem in theL2 norm at a rate equal to the order of approximation of the difference scheme. An algorithm for the computational solution is constructed and numerical calculations of test cases are carried out, illustrating the theoretical calculations obtained in this work.

The urgency of developing unified approaches to the reform of procedural legislation is justified by its aggravated lack of system and chaotic nature of the changes introduced. Purpose: to analyze the current legislative work on the reform of criminal procedure and other legislation and its impact on the quality of criminal proceedings and the prospects for its convergence with other types of judicial process. Methods: the method of comparative law is the determining method of the research. In addition, general and special methods are applied (analysis and synthesis, logical, special-legal). Results: the study reveals the lack of consistency between the changes made and those planned in the sectoral procedural legislation. The development of digital technologies contributed to the spread of the use of web conferences in court and capabilities of Portal of Government Services in arbitration, civil and administrative proceedings, but not in criminal ones. The bills under consideration in the State Duma of the Russian Federation to modify the procedure for appealing challenges in criminal proceedings and to exclude decisions on administrative offences from the list of acts of prejudicial significance in criminal proceedings, do not take into account the state of the relevant universal institutions in other forms of justice.

The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gausstype quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation method.

The growth of financial and cyber fraud leads to the destabilization of the country's financial sector and negatively affects the development of their economy, which requires the development and implementation of effective tools and measures at the level of public administration. The convergence of the cybersecurity system and counteraction of money laundering and terrorist financing is a promising area in the fight against financial fraud. The subject of research in the article is a scientific and methodological approach to forming integrated indicators for assessing the state of various systems, which is based on the Harrington - Mencher function. The aim is to determine the level of potential convergence of the cybersecurity system and counteraction of money laundering and terrorist financing based on the definition of their integrated indicators and the application of the Harrington-Mencher function. Objectives: to form a base of factors for evaluation; to carry out their normalization by applying nonlinear normalization; to transform the normalized values of the selected indicators of the research base to the dimensionless scale of Harrington's desirability; identify the function type of the dependence of the intermediate indicator value to assess the level of convergence of the cybersecurity system and combating financial fraud, from their actual values; calculate indicators to formalize the Harrington-Mencher transformation; to determine weight indicators using canonical analysis; to calculate integrated indicators that characterize the level of development of the cybersecurity system and counteraction to money laundering, as well as to determine the level of systems convergence. The article uses general scientific methods: system analysis - to determine the factors that characterize cybersecurity systems and combat financial fraud; Harrington-Mencher method of preference and function during integrated evaluation. The following results were obtained: in terms of cybersecurity, the highest scores are given to economically developed countries - European countries, the United States, Canada, Australia, New Zealand, Japan. Other countries have many problems in this area, as evidenced by their assessments of "very poor", "poor" and "satisfactory". The level of opposition to money laundering has shown that this area is critical for countries with high levels of crime, terrorism, military conflicts and high levels of financial secrecy, making them potential actors in money laundering. It is also established that due to the convergence of the two systems, the country's level of development will increase. Conclusions: the results of the study should be taken into account in the process of developing a strategy for the convergence of the cybersecurity system and combating financial fraud at the macro level.

For the world economy, the integration process is one of the most widespread and global. The Eurasian Economic Union is a typical example of bringing countries together to achieve shared goals and to face diverse challenges successfully by implementing coordinated policies and harmonizing the regulatory framework. The formation of a monetary union will be the next stage of integration. The EAEU member States need to achieve a certain level of economic convergence for that purpose. Thus, the main aim of this research article is to analyze some of the economic indicators of the EAEU in order to identify common problems, the solution of which will be necessary for the successful formation and functioning of the monetary union. The authors have studied such indicators as GDP volumes and inflation levels, as well as the dynamics of changes in exchange rates and the level of mutual direct investment in terms of sigma convergence. The authors have also used methods of graphical representation of the scientific results. The reports of the Eurasian Economic Commission and the Central Banks of the EAEU Member States were used as the main sources of statistical data.

The theory of mediatization focuses on discussions on the intertwining of the media with social institutions such as politics, family and religion, influencing and being affected by these structures. In general, mediatization refers to the social and cultural process in which a field or institution becomes to some extent dependent on the logic of the media (Hjarvard, 2011). Hjarvard draws attention to the processes of mediatization as a concept by cultural and social phenomena through the media, and their symbolic content is more or less under the influence of the media. The media is determinative on the fictional world with it produces and, on its audience (consumers). It influences, directs and shapes them through the discourse it produces. Mediatization is an important issue in the context of media literacy and especially transmedia methods. Because transmedia content practices and methods increase the mediatization effect and affect the orientations of the individual and society, especially when it comes to inadequacy in the context of media literacy. Therefore, this study focused on the awareness of the audience (consumers) about transmedia applications. It is seen that the studies conducted in the field of transmedia have developed in terms of content production methods, strategies and audience engagement. It is understood that there are not enough studies on subjects such as audience impacts or audience awareness. In this context and in this study, the competence of multimedia viewers who use social media and follow a traditional media tool to understand and be aware of the content transitions between different media tools has been examined. The television channel was chosen as the traditional media medium for the research study due to its widespread viewing.

В работе рассмотрены математические модели осесимметричных капиллярных менисков — лежащая и висящая капли, развернутый мениск, учитывающие размерную зависимость поверхностного натяжения. Доказаны теоремы существования и единственности решений задач, описывающих равновесные поверхности менисков. Разработаны и протестированы эффективные численные методы, предназначенные для приближенного расчета профилей менисков. На языке «Wolfram Language» написана компьютерная программа, с помощью которой проведены масштабные вычислительные эксперименты по выявлению степени и характера влияния параметров моделей на равновесную форму каждого из рассматриваемых менисков

Relevance. More than 75 % of underground mine workings are supported by anchorage nowadays. In the case of long-term mine workings maintenance the deformations of surrounding rock massif and anchoring elements occur. The surrounding rock massif typical forms deformations determination in order to develop the design solutions and substantiate anchorage parameters is currently urgent scientific and practical task. Especially it is important in case of mine workings support repair or recovery stages. The main aim is mine working anchorage design solutions and parameters substantiate during the repair and recovery stages. Methods: field measurements, statistical processing of results. Results. The paper introduces the description, causes of occurrence and manifestation forms of geomechanical processes in surrounding rock massif supported by anchorage. Based on the long-term field measurements six forms of rock massif typical deformations have been established.The roof bridging begins with decompaction of rocks, which causes rocks stratification under the influence of gravity. This results in cavities formation and lower layers separation from upper ones. Because of formation of the plastic deformation zone around mine workings the extraction and dumping coal from walls occur. Coal and rocks are in an unbound state and are kept in balance due to the forces of friction and resistance of the support in the zones of plastic deformations. Its width depends on many factors such as the working width and the internal friction angle. The coefficient of stress concentration in the walls rises up due to growth of mine working widht.

In series of numerical experiments involving the Shu-Osher problem of nonlinear acoustics and the Woodward-Colella problem of two interacted blast waves, the author studied the computational properties of a new algorithm for the hybrid large-particle method. The numerical method is a two-step predictor-corrector type in time. Spatial derivatives are split by physical processes. At the first stage of splitting, the gradient and deformation terms of the conservation laws are taken into account, and at the second stage, convective flows are taken into account. The proposed balanced algorithm of the method includes a more dissipative upwind reconstruction of fluxes at the “predictor” step and a centered (non-dissipative on smooth solutions) approximation at the correction step: CDP2-UC (Customizable Dissipative Properties — Upwind-Centered). For a more flexible control of the numerical viscosity, a nonlinear correction of the scheme based on a parametric combination of known limiters is implemented. The numerical scheme has a second-order approximation in space and time on smooth solutions. The balanced algorithm of the hybrid large-particle method demonstrated a monotonic solution with a qualitative resolution of the details of the gas flow in the entire domain of determining the test problems. No spurious oscillations occurred during the process of fining the mesh, and convergence to the reference density profile was observed. The influence of a limiter on the numerical dissipation of the CDP2-UC scheme is analyzed. The results present the comparison with the following variants of the schemes: MUSCL (Monotone Upstream Scheme for Conservation Laws), MUSCL-CABARET with a NOLD limiter (Non-Oscillatory Low-Dissipative), the discontinuous Galerkin method with various forms of nonlinear correction, the hybrid weighted nonlinear scheme of the fourth order of approximation (CCSSR-HW4) and the popular WENO5 scheme (Weighted Essentially Non-Oscillatory Scheme) with fifth order of accuracy. The proposed algorithm successfully competes with modern numerical methods that have a formally higher (fourth and fifth) order of approximation. The hybrid large-particle method has the simplicity, uniformity, and cost-effectiveness of the algorithm, as well as high resolution. The test calculations allowed the author to estimate the range of parametric control of the numerical dissipation of the method for correct numerical modeling of the applied problems with nonlinear wave fields and strong shock waves.

This article completes the series of publications, which explores the political and social phenomenon of the Russian dissent during his three-century history. It shows that the processes akin to convergence of the power and its opponents, primarily from intelligentsia, have first become apparent in the time of the Thaw and led to the mitigation of the confrontation between the power and dissenters. It has happened since this confrontation was caused not by ontological cruelty and psychopathology of people in law-enforcement bodies, but by century-long uncompromising class struggle in the Russian Empire and the USSR. The collapse of the Soviet Union and the rejection of socialism have happened in the end of 20th century overall dynamically and bloodlessly. The majority of the Russians saw in socialism with the domination of the State in the major fields of activity the main cause of the degradation of economy, underdevelopment of social sphere, dissociation with the rest of the world professing different forms of individualism. The rejection of a dominant ideology fixed in the Constitution of the New Russia, active inculcation of individual and corporative entrepreneurship has made the traditional dissent senseless, but have given rise to its new forms; dissent as business, in particular. Placidity in relation to disappearance “forever” of the “power-dissenters” confrontation has proved to be premature. In the future we have very likely to expect hot political discussions in the Internet and in power-controlled form in traditional media, but, in the main, young-people street protests. The goal of these coordinated and spontaneous actions – to take hold of information and power resources for the realization of no longer national but individual or corporative interests.

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In this paper, we study an initial boundary value problem for a differential equation with a fractional order derivative in time in the Caputo-Fabrizio sense. This equation is of great practical importance in modeling the processes of fluid motion in porous media and anomalous dispersion. The uniqueness and continuous dependence of the solution of the problem on the input data in differential form is proved. A computationally efficient implicit difference scheme with weights isproposed. A priori estimates are obtained for the solution of the problem under the assumption that the solution exists in the class of sufficiently smooth functions. The uniqueness of the solution and the stability of the difference scheme with respect to the initial data and the right-hand side of the equation follows from the obtained estimates. The convergence of the difference problem solution to the differential problem solution with the second order in time and space variablesis proved. The results of computational experiments confirming the reliability of the theoretical analysis are presented.

The article examines the benefits and risks of the euro adoption for the Czech Republic. In the last decade, in the light of structural problems of the economic and monetary union of the European Union and the Czech euroscepticism that has intensified against this background, the problem has become more of political nature and one of burning issues in relations between the Czech Republic and the EU. The paper analyzes the benefits and risks of such a decision. Special attention is paid to political factors – starting from the possible membership in the EMU institutions and ending with the potential overall improvement of relations with the leading countries of the EU. The authors conclude that from an economic point of view, the eurozone membership is beneficial for the Czech Republic if the level of labour productivity increases before the adoption. However, this issue presents the problem of the overall geopolitical orientation of the Czech Republic, which has to choose between striving to get into the «core» of the integration or the relentless defense of its national sovereignty within the European Union.

Let function P be a probability on a finite group G, i.e. $P(g)\geq0\ $ $(g\in G),\ \sum\limits_{g}P(g)=1$ (we write $\sum\limits_{g}$ instead of $\sum\limits_{g\in G})$. Convolution of two functions $P, \; Q$ on group $G$ is \linebreak $ (P*Q)(h)=\sum\limits_{g}P(g)Q(g^{-1}h)\ \ (h\in G)$. Let $E(g)=\frac{1}{|G|}\sum\limits_{g}g$ be the uniform (trivial) probability on the group $G$, $P^{(n)}=P*...*P$ ($n$ times) an $n$-fold convolution of $P$. Under well known mild condition probability $P^{(n)}$ converges to $E(g)$ at $n\rightarrow\infty$. A lot of papers are devoted to estimation the rate of this convergence for different norms. Any probability (and, in general, any function with values in the field $R$ of real numbers) on a group can be associated with an element of the group algebra of this group over the field $R$. It can be done as follows. Let $RG$ be a group algebra of a finite group $G$ over the field $R$. A probability $P(g)$ on the group $G$ corresponds to the element $ p = \sum\limits_{g} P(g)g $ of the algebra RG. We denote a function on the group $G$ with a capital letter and the corresponding element of $RG$ with the same (but small) letter, and call the latter a probability on $RG$. For instance, the uniform probability $E(g)$ corresponds to the element $e=\frac{1}{|G|}\sum\limits_{g}g\in RG. $ The convolution of two functions $P, Q$ on $G$ corresponds to product $pq$ of corresponding elements $p,q$ in the group algebra $RG$. For a natural number $n$, the $n$-fold convolution of the probability $P$ on $G$ corresponds to the element $p^n \in RG$. In the article we study the case when a linear combination of two probabilities in algebra $RG$ equals to the probability $e\in RG$. Such a linear combination must be convex. More exactly, we correspond to a probability $p \in RG$ another probability $p_1 \in RG$ in the following way. Two probabilities $p, p_1 \in RG$ are called complementary if their convex linear combination is $e$, i.e. $ \alpha p + (1- \alpha) p_1 = e$ for some number $\alpha$, $0

The paper presents an approach to the parametric convergence performance improvement applied to the direct adaptive multi-sinusoidal disturbance compensation problem. The proposed method improves the performance of the existing solutions and ensures the transient monotonicity. The Dynamic Regressor Extension and Mixing (DREM) procedure followed by the discrete gradient estimator is applied for disturbance parameters estimation. The paper proves the applicability of Kreisselmeier’s scheme as an extension of the algorithm in procedure dynamic regressor extension. A numerical simulation is presented to illustrate the improvement of the transient processes of estimating the parameters of an unmeasured perturbation using the DREM procedure. The work can be used in solving practical problems in the fields of processing and evaluating harmonic and multi-harmonic signals, e.g., to suppress vibrations in electromechanical systems.

To effectively solve the problems of operational dispatch control of the operating modes of the unified power system, its individual power systems and power districts, in particular, oil production power districts, it is required to carry out calculations of the established modes of electrical networks. In addition, along with the calculations of steady-state regimes, it is important to study the stability of the power grid operation. The convergence and rate of convergence of widely used iterative methods for calculating steady-state modes depend on many operating and design factors determined by the network and mode parameters, the choice of initial approximations, and the method for specifying the initial data. Therefore, the development of new methods that make it possible to calculate all steady-state regimes are of significant practical interest.One of the promising techniques is the holomorphic imbedding method. In this method, the unknown parameters of the nodes are represented in the form of holomorphic functions, which can be written in the form of power series, the coefficients of which are calculated using recurrent expressions, and the problem is reduced to finding the coefficients of the power series. In a previously published article by the authors, the method is considered for a circuit with load nodes. For a complete correct analysis of the modes of real power systems, it is necessary to show how to calculate for generating units. The paper presents recurrent expressions for calculating the unknown coefficients of the holomorphic functions of the unknown parameters of the system of steady-state equations for the load and generator nodes. The expressions obtained, in contrast to those proposed in the works of other authors, are more general. The principle of forming a matrix equation for finding unknown coefficients with the division of complex parameters into real and imaginary parts is shown. A method for obtaining converging power-law in some cases is proposed. On the example of a test power system, the advantage over the Newton–Raphson method is shown. We consider the question of evaluating the existence of a solution to the system of equations of the steady state for a multinode network based on a sigma-graph. An approach is proposed to determine the indicator of the static stability margin of the power system, based on the Fabry criterion. The aim of the research isto apply the analytical method of holomorphic imbedding to calculate an electrical circuitcontaining load and generator units; to evaluate the influence of the number of calculated power series coefficients on the accuracy of the obtained solution, and also to consider ways to increase the numerical accuracy of the solution, consider the question of evaluating the existence of a solution to the system of equations of the steady state for a multi-node network based on the analysis of power series. Methods: Taylor expansion, analytic continuation, Padé approximation, solving algebraic equations by the recursive method. Results. Using the example of a scheme with a poorly conditioned Jacobi matrix, in which the Newton–Raphson method does not converge from a flat start, the advantage of the holomorphic immersion method is shown. The influence of the number of members of the power series on the calculation error is shown. For the considered scheme, a graphical estimate of the existence of a solution to the system of equations is performed. Conclusions. For load and generator nodes, the unknown parameters can be represented as holomorphic functions, which can be written down as a Taylor series, the coefficients of which are calculated using recurrent expressions. Partial consideration of shunts to the ground in the diagonal elements of the matrix of successive conductances makes it possible to obtain converging power series in some cases. The considered graphical method for assessing the possibility of the regime existence allows us to make a rough estimate. Unlike classical iterative methods, an initial approximation is not specified for the holomorphic immersion method.

Государственная политика в сфере образования определяет значимость дополнительного образования детей как элемента общей системы выявления и развития талантов и способностей у детей и молодежи. Дополнительное образование, являясь подсистемой общего образования, в региональном контексте рассматривается как открытая вариативная педагогическая система, работающая на достижение общенациональной цели по развитию талантов и самореализации подрастающего поколения. Отвечая вызовам современности, постепенно формируются новые региональные практики управления сферой дополнительного образования, включающие активные горизонтальные и межуровневые связи, интеграцию внеинституциональных поставщиков образовательных услуг в общий содержательный контур, децентрализацию управленческих механизмов. Рассматриваемое как основа «образования в течение жизни» понятие «дополнительное образование детей» приобретает новые смысловые характеристики, включающие требования к содержанию образовательных результатов, преемственность образовательных программ, ориентацию на различные категории обучающихся. Для разрешения противоречия между складывающейся региональной практикой и недостаточной научной обоснованностью используемых подходов требуется переосмысление традиционно применяемых исследователями методологических подходов к управлению сферой дополнительного образования на региональном уровне. Предпринята попытка применения экосистемного подхода к описанию сферы дополнительного образования в условиях конвергентной образовательной среды.

The article concerns the problem of the dominant language influence in the translingual language competence on the phonetic system of the second language. How intensive can this influence be in a translingual situation? As most researchers say, languages in the processes of transculturation and translinguism are to a certain extent intelligible. In our opinion, it concerns the content aspects of language and speech, which are capable of generating new discourses: lexis, grammar, syntax, word formation. The phonetic level as a building material for content units should not be affected in the process of translinguism, because in this case we can no longer talk about translinguism as a noncontradictory tendency in the contact coexistence of two languages and cultures.

The article is aimed at more profound elaborating the theoretical and methodological principles while improving the content of the concept of «cross-border region», singling out its characteristic features, and carrying out a systematization. Taking into account the review of the existing scientific works, the author’s own approach to the interpretation of definition of «cross-border region» is proposed. As a result of research, the principles of functioning of the cross-border region are substantiated, i. e.: subsidiarity, vertical and horizontal partnership, aggregate of the development programs and concepts, institutionalization of structures at local and regional levels, co-financing, systemacity, bi- and multipolarity, proportionality. The author brings in proposals for classification of cross-border regions by introducing a number of new criterion features, such as: scale, development and degree of cross-border cooperation; integration type; geographical location; homogeneity (uniformity); level of development and support in the EU’s structural policy; natural features; implementation mechanism; instruments and forms of implementation. This approach allowed to identify cross-border regions as follows: identical, homogenic and with no affinity; peripheral and underdeveloped; leaders; initiators of cross-border cooperation; functional. Prospects for further developments in this direction are the study of the latest organizational forms of cross-border cooperation and substantiation of the methodological approaches to evaluating the degree of integration and interpenetration in the cross-border region.