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Introduction. At present, the issues of the Far East accelerated economic development remain in the focus of the state attention. Among the key mechanisms of state policy is the formation of advanced development territories (ADT). The article sets the task of studying the impact of the institutional measures taken on the welfare and the population's life quality in the Far Eastern territories. Particular attention is paid to studying migration processes and analyzing the economic activity of the Far East population. The purpose of the article is to study the effects of implementing mechanisms for accelerated economic growth, as well as assess their impact on the life quality in the Far East regions. Methods. The authors use the following methods: economic and mathematical modeling, computational and analytical methods, comparative and spatial analysis. Scientific novelty of the research. For a comprehensive assessment of the regional well-being, the authors propose to supplement the multiplicative model based on the A. Sen's extended welfare function with a composite ecological index. It takes into account the ecological conditions of human life, which are an important aspect of well-being. The authors obtain ecologically adjusted indicators of well-being for the eastern regions of the Russian Federation and study their dynamics, as well as the relations with the data on the population's migration activity during the formation of new institutions of advanced development in the East of the country. Results. The authors find out that most of the Far Eastern territories are still lagging behind the average Russian level in socio-economic development. The results of assessing the level of well-being of regions on the basis of a multiplicative model without taking into account the environmental factor show that the most prosperous areas are raw materials-based territories. It is shown that the role of environmental factors in the life quality in the Far Eastern territories of Russia is very significant - the ecologically adjusted level of well-being is noticeably lower than the indicator that does not take into account this aspect of well-being. The authors reveal that socio-economically disadvantaged regions with difficult natural and climatic living conditions have very high rates of migration outflow. Their coefficients of migration loss reflect the presence of a crisis in economic development, which has been increasing in recent years. An analysis of trends in economic activity shows a relationship between the dynamics of the number of employed and the implementation of ADT projects in the Far Eastern territories. Conclusions. The conclusion is that the measures taken by the state for the advanced economic development of the eastern territories of the country have not yet had a noticeable positive impact on the welfare and life quality in the Far East regions.

En este trabajo se analiza el fenómeno de la informalidad a partir de la década de 1950; se aplica el enfoque de Arthur Lewis, para quien el empleo informal es un resultado del funcionamiento de las economías en desarrollo, en las cuales existe una oferta laboral ilimitada a un determinado salario de equilibrio. En este trabajo la informalidad es el residuo, es la mano de obra sobrante una vez que el sector moderno ocupa la fuerza laboral necesaria a un salario real dado y conforme al capital disponible. En el documento se presenta primero una versión formal del modelo de Lewis, en el cual hay dos sectores: el moderno y el atrasado; a este último con salvedades, lo asimilamos al informal, para luego proceder a estimar una de sus principales conclusiones con datos de la economía mexicana. En este ejercicio se constata que el modelo de Lewis es una representación adecuada de los hechos estilizados que caracterizan a la economía mexicana, y que la importante intensificación de capital, es decir la relación entre el capital y el trabajo en el sector formal que se ha experimentado a partir de las reformas, ha elevado los costos de la creación de empleo formal. En estas condiciones, aunado a la escasa inversión en los últimos veinte años, se ha presentado un estancamiento de la proporción del empleo formal en el total y además unos muy precarios, casi nulos, avances en la productividad total promedio y en el ingreso por habitante. AbstractThis paper analyzes the trajectory of informality as it has evolved since 1950. For doing so, the analytic frame elaborated by Arthur Lewis was applied. For Lewis, the informal employment results from the incapacity of an economy, with unlimited labour supply, to absorb all the working force at a given equilibrium salary. Therefore, in this essay, informality represents the residual labour that remains stacked in the non-modern sector, once the modern sector has absorbed all the labour it can employ at a given equilibrium wage and available capital. The analysis starts with a mathematical formalization of the Lewis model and proceeds to evaluate one of its main conclusions using observed data of the Mexican economy. The model accurately represents the stylized facts of the economy and allows concluding that, after the introduction of the structural reforms, the modern sector of the Mexican economy experienced a large increase in capital intensity which enlarged its capital/labour ratio and inflated the costs of generating formal employment. In these conditions, and taking into consideration the meagre investments registered during the last two decades it is not surprising the immovability of the share of formal in total employment as well as the almost negligible increases in total labour productivity and total income per head.

The present work aimed to examine the nature and degree of the cross-correlations among three different ionospheric indices: these are Optimum Working Frequency (OWF), Highest Probable Frequency (HPF), and Best Usable Frequency (BUF). VOCAP and ASASPS models were adopted to determine the datasets of the selected ionospheric indices. The determination was made for different transceiver stations that provide certain HF connection links during the minimum and maximum years of solar cycle 24, 2009 and 2014, respectively. Matlab program was implemented to produce the geodesic parameters for the selected transceiver stations. The determination was made for different path lengths (500, 1000, 1500, and 2000) Km and bearings (0o, 45o, 90o ........ 315o). Different correlation methods were used to examine the best determination coefficient values between the tested parameters. A third-order polynomial equation was set as the best correlation method that gave a better description for the correlation among the tested parameters. The proposed mathematical correlation equations were used to predict the seasonal values of the (HPF, OWF and BUF) parameters. The proposed equations were verified by comparing their values with the observed datasets during the study years. Also, the predicted values were tested using different statistical methods, which gave good results for all tested cases.

يهدف العمل الحالي إلى دراسة طبيعة ودرجة الترابط بين ثلاثة مؤشرات آيونوسفيرية مختلفة وهي (HPF,OWF and BUF), تم استخدام نماذج VOCAP و ASASPS لحساب قيم البيانات للمؤشرات الآيونوسفيرية المختارة. اجريت الحسابات لمحطات الإرسال / الاستقبال المختلفة التي توفر روابط اتصال عالية التردد خلال سنوات الصغرى والعظمى للدورة الشمسية 24 (2009 و 2014) على التوالي. تم تنفيذ برنامج Matlab لايجاد قيم المعلمات الجيوديسية لمحطات الإرسال / الاستلام لأطوال مسافات مختلفة (500، 1000، 1500 و 2000) كم واتجاهات مختلفة(0o, 45o, 90o ........ 315o). تم تطبيق طرق ارتباطية مختلفة لاختبار افضلها بين المعاملات المختبرة . تم اقتراح معادلات رياضية متعددة الحدود (الدرجة الثالثة) كأفضل طريقة تصف القيم الارتباطية بين المعاملات المحددة لغرض الدراسة. تمكنت المعادلات المقترحة من التنبؤ بالقيم الموسمية للمؤشرات ((HPF و(OWF) و (BUF).و تم التحقق منها من خلال مقارنتها مع قيم المعلمات المرصودة خلال سنوات الدراسة . كما تم اختبار القيم المتوقعة باستخدام طرق إحصائية مختلفة والتي قدمت نتائج جيدة لجميع الحالات المختبرة

Introduction. There are currently many different methods in the field of artificial intelligence research. Methods of mathematical, cognitive and philosophical sciences are dominant among them. All research approaches are united by the hypothesis that natural and artificial intelligence are fundamentally comparable. The sociality formed as a result of these changes attracts increasing attention from both foreign and Russian researchers. The purpose of this article is to clarify the theoretical and methodological approaches in the study of artificial intelligence in the social sciences, especially in sociology.Methodology and sources. The article is based on an interdisciplinary approach, which allows outlining the scale of the research problem, coordinating the methodological approach to the organization of research, smoothing the contradictions of ideas and categories, which are operated by different sciences in the study of artificial intelligence.Results and discussion. According to the authors, the widely used concept of Artificial Intelligence is more a scientific metaphor than a proven empirical fact. Currently there is no such thing as artificial intelligence. There are neural networks, machine learning, which can solve certain problems in the real world. Artificial intelligence is a metaphor that captures a certain level of human knowledge about the introduction of information technology, based on computer hardware and specialized software. To treat artificial intelligence as an empirical fact is a fallacy that is not appropriate in science.Conclusion. Sociology is only taking its first steps in the field of artificial intelligence research. It does not have its own methodological tools for analyzing artificial intelligence and the social reality that arises from its introduction into the everyday life of society. Artificial Intelligence changes people's daily lives, embedding itself in everyday social practices, and forming a hybrid social world for the social sciences to study. Today there is a debate about the place of artificial intelligence in sociology. According to the authors, sociological fantasies and speculations are not appropriate here. In order to correctly and accurately define the problem of artificial intelligence in the social sciences, it is necessary to carefully analyze the opinions of the experts in the exact sciences, in which artificial intelligence is understood as algorithms or models created by human, and which perform certain tasks and help them manage specific processes in various spheres of society.

Modern society faces large-scale challenges associated with the digitalization of economic and social processes, especially at its new stage – the development and implementation of artificial intelligence (AI) technologies. The point is that the use of AI entails great ethical risks, since creates an opportunity for non-observance of human rights to privacy. In Finland, a country that has been pursuing an innovation policy closely linked to socio-economic policies that responds to social challenges for several decades, this problem is widely discussed and strives to minimize and even eliminate the above risks in decisions on research and development (R&D) policy. Therefore, R&D in the field of AI technologies is carried out in Finland at the intersection of computer, mathematical and humanitarian sciences, since one of the most important issues of its application is the question of how moral and ethical its results will be. In this regard, the analysis and understanding of Finland's experience in this area is important and necessary. Finland has traditionally in recent decades prioritized the humanitarian component in the formation of innovation policy. The technological component was viewed through the prism of social problems that should be resolved in the course of economic development, the main driver of which is innovation processes. This approach is determined by the country's social development model. The openness of public administration, the high role of the country's citizens in making the most important strategic decisions, the social responsibility of business, taking into account the opinion of the expert community leads to a balanced promotion of technologies in the economy. Of course, opportunities for innovative development "with a human face" from time to time run into economic constraints – which was clearly manifested, for example, during a pandemic. Nevertheless, when it comes to digitalization and the use of AI, the Finnish state and society continue to strive to ensure the presumption of morality and ethics in the implementation of these technologies. The country is conducting humanitarian and sociological research in this area, as well as developing mechanisms for managing the ethics and morality of AI. The country strives to become a leader not only in AI technologies, but also in developing the principles of preserving the humanitarian and moral values that Finland shares with Europe.

Importance. The goal of the strategy for sustainable development of the Russian Federation is to ensure stable indicators of economic growth, as well as to solve socio-economic, industrial, technological and environmental problems on the basis of optimal use of innovative and scientific and technical potential, updating equipment and technologies, and expanding sales markets. At the same time, the effectiveness of the innovation process itself will largely depend on the readiness of economic entities to introduce and use modern knowledge-intensive technologies, which may manifest themselves in tax policy.Objectives. Justification and clarification of the facts that tax management is an integral part of the entire tax policy and is a system of principles and methods in the development and implementation of management decisions, the choice of the tax system, the calculation of tax payments, as well as constant monitoring of their implementation.Methods. The instrumental and methodological apparatus of the research is based on the use of General scientific and special methods, including abstract-logical, monographic, computational and constructive, methods of risk analysis, economic and mathematical modeling, graphic, methods of multidimensional statistical analysis, content analysis.Results. At all times, taxes have been the most important tool of state regulation, implementing the main tasks of the state. Taxation creates tax relations that need to be properly regulated through the application of tax legislation. This interaction encourages economic entities to manage their tax payments. Therefore, they begin to apply in their activities a wide variety of methods of making managerial decisions, called tax management in the market. Tax management is a management model of tax management implemented by taxpayers in a macro-economic environment that exploits their production capacity. Tax administration, as part of the market economy management system, is a relatively new area of knowledge in Russia, which was formed in the late XX-early XXI centuries. In particular, tax management appeared in the economic environment, i.e. in practice. Attempts to generalize and develop this category took place much later.Conclusions and Relevance. The article presents the author's concept of accounting and tax management analysis in a trade organization, which reflects a number of aspects of the concept: system representation of information resources, means and sources of information, forms and methods of transmitting various data. This will be the basis for integrating the information base that meets the needs and requests of tax administration.

This article studies the peculiar properties of the emotional sphere of adolescents, reveals aggression, fears, anxiety, family education types that have an impact on the formation of emotional imbalance and disadaptation among the respondents, it also presents the results of the integrated program for the individual development, taking into consideration the health-saving factor that implements modern and innovative trends required in the work of the psychological service of an educational institution, and provides the justification of the importance and necessity of using associative metaphorical maps in work with adolescents and parents, as an innovative tool for more efficient work with a specific case. We have analyzed family relationships, behavior motives, parental position, parenting styles in order to draw up a special correctional program. The correctional work has been conducted with the parallel work of the adolescent group, parent seminar and parent group classes, as well as applying the method of cooperative interaction between the children and parents. The author's projective methodology "The Way to the Sun" proposed in the study, and aimed at diagnosing the adolescent's emotional sphere (anxiety, aggression fears), family relationships, have demonstrated their suitability and efficiency of work not only with adolescents but also with their parents, allowing us to work with emotions and feelings squeezed into the subconscious.Moreover, during the research, a model of psychological and pedagogical impact on students was developed with the purpose of regulation of their emotional sphere, the structural components of which included the following: organizational, research, cognitive and practical components. A comparative analysis of the availability of psychological problems among students, an integrated approach to the mental health of children and adolescents formed the basis of the pilot project "School of the Future" developed by us, which involves the implementation of a focal point in the education system in order to provide the social and psychological support to the school, combining four services: psychological, valeological, social educator service and school mediation service. Thus, the experimental research presented in this article has demonstrated the effectiveness of correctional and preventive programs, the efficiency of which has been tested applying methods of mathematical statistics and improving all of the above indicators.

AbstractIntroductionObservational studies suggest HIV and human papillomavirus (HPV) infections may have multiple interactions. We reviewed the strength of the evidence for the influence of HIV on HPV acquisition and clearance, and the influence of HPV on HIV acquisition.MethodsWe performed meta‐analytic systematic reviews of longitudinal studies of HPV incidence and clearance rate by HIV status (review 1) and of HIV incidence by HPV status (review 2). We pooled relative risk (RR) estimates across studies using random‐effect models. I2 statistics and subgroup analyses were used to quantify heterogeneity across estimates and explore the influence of participant and study characteristics including study quality. Publication bias was examined quantitatively with funnel plots and subgroup analysis, as well as qualitatively.Results and DiscussionIn review 1, 37 publications (25 independent studies) were included in the meta‐analysis. HPV incidence (pooled RR = 1.55, 95% CI: 1.29 to 1.88; heterosexual males: pooled RR = 1.95, 95% CI: 1.62, 2.34; females: pooled RR = 1.63, 95% CI: 1.26 to 2.11; men who have sex with men: pooled RR = 1.36, 95% CI: 1.01 to 1.82) and high‐risk HPV incidence (pooled RR = 2.20, 95% CI: 1.90 to 2.54) was approximately doubled among people living with HIV (PLHIV) whereas HPV clearance rate (pooled RR = 0.53, 95% CI: 0.42 to 0.67) was approximately halved. In review 2, 14 publications (11 independent studies) were included in the meta‐analysis. HIV incidence was almost doubled (pooled RR = 1.91, 95% CI 1.38 to 2.65) in the presence of prevalent HPV infection. There was more evidence of publication bias in review 2, and somewhat greater risk of confounding in studies included in review 1. There was some evidence that adjustment for key confounders strengthened the associations for review 2. Misclassification bias by HIV/HPV exposure status could also have biased estimates toward the null.ConclusionsThese results provide evidence for synergistic HIV and HPV interactions of clinical and public health relevance. HPV vaccination may directly benefit PLHIV, and help control both HPV and HIV at the population level in high prevalence settings. Our estimates of association are useful for mathematical modelling. Although observational studies can never perfectly control for residual confounding, the evidence presented here lends further support for the presence of biological interactions between HIV and HPV that have a strong plausibility.

Este artigo apresenta uma pesquisa realizada na formação inicial de professores de Matemática na disciplina de Geometria Plana e Espacial, na qual buscamos explicitar os resultados da aplicação de uma Unidade de Ensino Potencialmente Significativa (UEPS) para o ensino de Geometria Plana e Espacial. A UEPS foi elaborada considerando os pressupostos da Teoria de Aprendizagem Significativa e aplicada na disciplina de Geometria Plana e Espacial, durante vinte e um encontros presenciais. A UEPS é composta de atividades associadas à construção de maquetes de casas para o desenvolvimento de conceitos de geometria plana e espacial. A coleta de dados aconteceu com alunos do segundo ano de um curso de Licenciatura em Matemática, de uma Universidade Pública do norte do Paraná. Registros escritos dos alunos, no desenvolvimento das atividades, bem como mapas conceituais por eles elaborados formam o corpus para análise qualitativa das atividades à luz da Teoria da Aprendizagem Significativa, incluindo a elaboração de maquetes de casa que podem ser utilizadas para a promoção da aprendizagem significativa dos conteúdos de Geometria Plana e Espacial. Os dados foram coletados e analisados qualitativamente de modo a permitir a interpretação dos resultados a partir da implementação da UEPS. Resultados indicam que, a partir dos mapas conceituais produzidos pelos alunos, é possível identificar indícios de Aprendizagem Significativa, por exemplo a ocorrência de diferenciação progressiva e de reconciliação integrativa, demonstrando que a UEPS elaborada promoveu evidências de AS dos alunos em relação aos conceitos matemáticos que foram abordados nas atividades.
Palavras-chave: Aprendizagem Significativa. Formação de Professores. Matemática.
AbstractThis paper presentes a research carried out in the initial training of Mathematics teachers in the discipline of Plane and Spatial Geometry, in which we seek to explain the results of the application of a Potentially Significant Teaching Unit (UEPS) for the teaching of Plane and Spatial Geometry. The UEPS was developed considering the assumptions of the Meaningful Learning Theory and applied to the Flat and Spatial Geometry discipline, during twenty-one face-to-face meetings. The UEPS is made up of activities associated with the construction of house models for the development of flat and spatial geometry concepts. Data collection took place with second-year students of a Mathematics Degree course at a Public University in northern Paraná. Written records from students during the development of activities, as well as conceptual maps created by them, form the corpus for qualitative analysis of activities in light of the Meaningful Learning Theory, including the creation of house models that can be used to promote meaningful learning of Flat and Spatial Geometry content. Data were collected and analyzed qualitatively in order to allow the interpretation of the UEPS implementation results. Results indicated that, it was possible to identify, from the conceptual maps, that the students showed signs of Meaningful Learning, highlighting that there was progressive differentiation and integrative reconciliation, demonstrating that the UEPS developed promoted evidence of students' SA in relation to the mathematical concepts that were covered in the activities.
Keywords: Meaningful Learning. Teacher training. Mathematics.

The article shows the determining role of the service sector in the economic and social development of Moscow. The dynamics of changes in the share of services in the structure of employment, the general building fund development, the production of gross regional product, the income and expenditure of the city budget are examined. The levels of the service sector development in Moscow and abroad in terms of the share of the service economy in the structure of employment and the production of gross regional product are compared. It is concluded that the service sector development in Moscow corresponds to that in the economically developed foreign countries. The service sector affects the social development of society, the growth of human potential, determines the lifestyle of the population, the model of consumer behavior. A developed service sector creates a comfortable urban environment, provides a high quality of life. The role of the service sector in the socioeconomic development of Moscow is studied. The growth of the share of the services economy in the structure of the socioeconomic complex is revealed; it is typical for the stage of transition to post-industrial development. The relationship between the dynamics and structure of the service sector, the formation of a new model of employment, life quality improvement, and human capital development is determined. The main components of the quality of life that determine the needs for the development and placement of service facilities in the city are considered. The role of the service sector in the socioeconomic development of Moscow for accounting in forecasting, design and management decisions in the development of social, administrative and business facilities in the city, the creation of jobs in the service economy in the transition to the knowledge economy and information technology is assessed. The research is carried out on the basis of official statistics (Rosstat, Mosgorstat), branch departments and directorates of Moscow. Statistical, analytical, sociological methods of research, expert assessments, analogies, field survey, mathematical modeling are used. The tendency is noted of the increasing role of the service sector in the socioeconomic development of Moscow, characteristic of the transition to the post-industrial type of economy: the growth of the share of the service economy in the structure of the economic complex, the growing impact on the level and quality of life, the reproduction of human capital, the formation of a comfortable environment. The tasks and main directions of the development of social infrastructure, an important component of the service sector, are formulated. The role of the service sector in the socioeconomic development of Moscow consists in (1) influencing the economic growth, the structure of the city's economic complex, the increase in the share of the service economy, and qualitative changes in the industries that are characteristic of the transition to post-industrial development, and (2) in influencing the social development of the city: maintaining the reproduction of human potential, improving the life quality of the population. In recent years, the service sector, including its most important component – social infrastructure, is becoming a priority sector of the economy, which corresponds to global trends in the transition to a knowledge economy.

The subject of the research. The level of the economy of any country depends on its scientific, technical, innovative potential. It determines the country's place in the global economy, the competitiveness of industries and enterprises. One of the important factors of innovative growth of the country's economy is the development of the field of intellectual property. The subject of the research is the analysis of the main indicators of the national intellectual property system of Ukraine and the study of the main trends of its development. The purpose of the article is to study the economic, market, legal aspects of the functioning of the field of intellectual property that form its potential, development and scientific substantiation of the directions of development of the national intellectual property system of Ukraine. The methodologyof the work. A systematic approach and methodologies of economic, statistical, economic and mathematical analysis are used to study the trends of the main factors influencing the potential and development of the intellectual property system of Ukraine. The results of the work. The article describes the dynamics of the main indicators of the functioning of the intellectual property sphere, the country's ratings in the international system for the protection of intellectual property rights. It has been determined that the effectiveness of such a system depends on many factors, the main of which are: compliance of the regulatory framework; development of the infrastructure of national and international systems of intellectual property legal protection; effectiveness of training and advanced training of specialists; level of financial support for its activities. The field of application of the results of the study of the main trends in the global, national innovation market and the national intellectual property system will allow for a more accurate adjustment of the direction and strategy of the development of the sphere and also identify the most problematic issues to bring the domestic legislation closer to the provisions of the association agreement with the European Union. Conclusiins. An effective structure for the protection of intellectual property rights is a solid foundation for the innovative development model of Ukraine, its modernization and global competitiveness. The study revealed, on the one hand, a significant growth potential in the field of intellectual property, on the other hand, an insufficient level of growth compared with the leading countries of the world. The key constraints for the development of innovation in Ukraine are the political and business environment, as well as the weak infrastructure of the market for innovation and creative work. The following are the next areas of development strategy for the field of intellectual property of Ukraine: the scientific and technological development of society; the implementation of European standards in the field of intellectual property with national legislation; elimination and systematization of existing contradictions. The results of the study indicate that the problem of using the potential of intellectual capital in the formation of an innovative development model has considerable scientific interest and requires further research.

Este artigo objetiva discutir a pesquisa empreendida em um processo de formação continuada de professores de matemática com foco no uso de tecnologia em tarefas investigativas para ensino de Geometria Espacial de Posição. A fundamentação teórica, quanto ao processo formativo, veio das ideias de Imbernón sobre formar o professor na e para a mudança, de Zeichner sobre reflexão coletiva e de Mishra e Koehler sobreo modelo TPACK. A pesquisa, de cunho qualitativo, na acepção de Bogdan e Biklen, se desenvolveu em uma formação continuada com seis encontros de quatro horas de duração com a participação de nove professores. A intenção foi propiciar aos professores a vivência de situações didáticas com tecnologias, especificamente o software Cabri 3D, de modo que refletissem sobre os processos de ensino e aprendizagem de geometria. A coleta de dados foi feita por observação direta, gravação em áudio e vídeo dos encontros e pelos registros produzidos pelosparticipantes. A análise interpretativa dos dados neste artigo foca no episódio relativo à tarefa "Quadrilátero Reverso", que permitiu observar indícios de reflexão e de reconstrução de conhecimentos sobre o conteúdo matemático. Tais constatações evidenciaram que os professores pesquisados tiveram oportunidade de construir o conhecimento tecnológico do conteúdo, de acordo com os níveis do modelo TPACK. Concluíse que atingir este nível de conhecimento é um processo complexo, pois depende da habilidade de integrar diversos conhecimentos. Finalmente,indica-se que isso não ocorre de imediato, requerendo um contínuo aprendizado do professor inclusive sobre a própria prática docente.Palavras-chave: Educação Continuada. TPACK. Reconstrução da Prática. Geometria Espacial. Cabri 3D.AbstractThis article aims to discuss the research carried out in a continuing Mathematics Teachers' education process focusing on the use of technology in investigative tasks for the teaching of Spatial Position Geometry. The theoretical basis for the formative process originated from Imbernón's ideas on Teachers' education in and for change, from Zeichner's ideas on collective reflection and from Mishra and Koehler's on the TPACK model. The qualitative research, in the Bogdan and Biklen's sense, was developed in a Continuing Teachers' education process with sixmeetings lasting four hours each with nine teachers participants. The intention was to provide teachers with the didactic situations experience within technologies, specifically Cabri 3D software, so that they couldreflect on geometry teaching and learning processes. The data collection was performed by direct observation, meetings' audio and video recording and through the participants' notes. The interpretative data analysisfocuses on the episode related to the "Skew Quadrilateral" task that allowed to observe the evidence of reflection and reconstruction of mathematical content knowledge. These findings revealed that the researched teachers had the opportunity to build the technological content knowledge, according to the TPACK model levels. It is concluded thus why it is a complex process to reach such levels, once it depends on theability to mix and converge different kinds of knowledge. Finally, it is pointed out that such processes do not occur immediately, requiring acontinuous learning effort about the teaching practice itself.Keywords: Continuing Education. TPACK, Practice Reconstruction. Spatial Geometry. Cabri 3D.

The subject of the research is conceptual provisions about the structure, components and threats of economic security in the conditions of martial law and war; possibilities of its preservation and maintenance. The purpose of the article is to substantiate the conceptual provisions regarding the structure and components of economic security in military conditions, as well as the possibilities of its preservation and support. The methodological basis of the article is the methods of dialectical unity and contradiction, historical, monographic, system-structural analysis and synthesis; statistical and economic methods (absolute and relative values, index, grouping and ranking), mathematical programming and modeling. Results of the article. It was revealed that the structure of economic security is formed by the following structural blocks: international politics, world economy, globalization processes; economic, state and public institutions; resources and productivity; ideology, strategies and models of the country's development; monitoring, methods of evaluation and diagnosis and forecasting. Factors affecting it are sources of formation and threats and risks of destruction. It was determined that the main threat to the economic security of Ukraine was the long-term Russian aggression and war, especially starting in 2022. It was not brutal, it led to the capture of approximately 20% of the territory; large-scale destruction of public infrastructure, energy, housing stock, industry and agriculture; displacement of millions of people; murders of hundreds of thousands of people; inflation and devaluation and threats of default; curtailment of social programs. Direct losses are accompanied by no less devastating indirect ones. Further measures to support economic security should be based on constant monitoring of not only the economic, but primarily the military situation, quantitative assessments and forecasts. Field of application of results. The conclusions of the article can be used in enterprises, institutions of higher education, research institutions, consulting organizations. Conclusions. Under these conditions, the state authorities, with the help of the international community, implemented the following measures for its preservation: the institutions of the executive power were optimized; millions of people and enterprises, institutions of higher education, etc., were relocated. to relatively safe places; budget expenditures were optimized and defense funding was increased; applied digital and online tools of activity and management. Law and order and personal safety of citizens in controlled territories are ensured; the integrity of the economy through the work of the banking, tax, customs systems, markets, trade and export-import operations. Further measures to support economic security should be based on constant monitoring of not only the economic, but primarily the military situation, quantitative assessments and forecasts.

The autonomous power supply system (APSS) from synchronous magnetoelectric generator and active voltage rectifier (AVR) maximally meets the requirements of the minimum specific mass and the complete coordination of the primary electric power source with the load. With multiphase (m > 3) execution of the electric machine, it is possible to obtain a trapezoidal electromotive force (EMF) and increase the specific power conversion provided that the EMF and the current at the output of the m-phase generator are fully matched. Therefore, the aim of the work is to synthesize the space-vector modulation (SVM) algorithm of the active voltage rectifier to fully match the primary source of electrical energy with the load under the condition of a trapezoidal EMF of the generator. Synthesis of the PVM algorithm for the m-phase AVR is based on the use of a vector-matrix mathematical apparatus. Using the example of a nine-phase system, a SVM algorithm has been developed, the feature of which is the transformation of the generalized voltage vector m-phase coordinate system into (m – 1)/2 voltage vectors with different angular velocities in two-phase orthogonal stationary αβ coordinate systems. At the same time, based on the developed PVM algorithm, it is possible to independently control the (m – 1)/2 voltage vectors in the corresponding αβ planes, providing a signal similar to the EMF of the generator at the input terminals of the AVR. In order to confirm the theoretical propositions, an imitation model of the space-vector modulation unit for the realization of trapezoidal signals at the terminals of a nine-phase AVR has been developed. The efficiency of the developed algorithm is confirmed by the results of simulation modelling. As a result of the evaluation of the energy parameters (operating power) of the phase of power supply system direct current, it is established that the application of the developed space-vector modulation algorithm for the active voltage rectifier in order to fully match the trapezoidal shape of the EMF and the current at the output of the m-phase generator will increase the power of the APSS by 14 % compared to a power supply system of direct current with a sinusoidal form of the EMF and the current of the generator phase. It is established that the developed measuring device can be used to establish the presence of defects like "delamination". The influence of the depth of the defect placement on the measured parameters is shown.

Since the financial crisis of 2008, risk based performance management has been one of the important indicator to determine the financial health of banks and financial institutions. This study relates to the problem within the Russian Banking sector for regulators to determine and reduce risks at the marco-level and assessing performance of banks at the micro-level. The objectives are: to analyse a range of performance indicators and to structure the Russian banking sector. To explore the structure of Russian Banking sector in terms of performance over the period 2000-2010, we took a sample of 1279 banks and the financial data which was in the HTML format was extracted through PHP programming. With the help of trend analysis, the period 2000-2010 was divided into four sub periods: the period of stabilization (2002-2004), substantial development (2004-2007), financial crisis (2007-2009) and moderate development (2009-2010). Multivariate analysis were applied to classify the sample banks in these sub periods which provides evidence that despite the changes in the stage of development of the economy, the Russian Banking sector can be described with quantitative modeling. Naturally, the structural changes are affected by the described economic cycles, but these changes do not affect the determination capabilities of the model. In the period 2002-2004, nine types of banks are found. There are some prosperous as well as weak banks. During the period 2004-2007, banks had a chance to increase their profits; the banking sector became more differentiated – 12 clusters are singled out. There is no doubt that the financial crisis also affected the banking industry; there were still 12 clusters in 2007-2009, but the majority were concentrated into a single cluster with low performance indicators. Finally, the Russian banking sector started its development in the period 2009-2010, uniting some bank clusters, 10 groups are found. The results indicated that through mathematical modelling, Russian banks could be rated as "rating groups" based on their performance which might be of particular interest to bank's managers, investors, credit analysts and bank regulators. Moreover, it could be emphasized that the changes in structure are not significant, as certain groups of banks can be found at any period of time. These groups or clusters can be referred to certain "rating groups" (from the banks with the best results to those with low results) and compared to international ratings.