Annotation: Digital technologies have long and firmly entered our lives, but recently the emphasis of their application has been shifting. The object of research in this article is digital education, and the subject is the scenarios of using digital technologies within it. The article describes the results of the study of the learning process using digital and information technologies. The main directions of their effective use in the educational sphere are outlined, negative aspects of quick access to digital information for students are noted. The process is considered from the point of view of educational environment and application of digital and information technologies. The scenarios of using digital technologies in the educational process are presented: face-to-face training with the use of digital tools and technologies, distance learning, blended learning. The analysis of practical application of the scenarios is given, the assessment of positive and negative experience of using digital technologies in professional activity is given, including on the basis of questionnaire survey of teachers of the Republic of Bashkortostan.

Annotation: The article presents an overview of the methods for the development of eastern systems of psychophysical train- ing, described in the research of N.V. Abayev. The subject of the study is the forming of competence in health prevention issues based on Eastern systems of psychophysical training. The work highlights the importance of Chan/Zen Buddhism, which is embedded in this system, calling for mental well-being, flexibility of thinking, improvement of memory, attention, forming physical intelligence. The author comes to the conclusion that the system of psychophysical training, that is, the development of mental and physical abilities of a person with the help of special exercises, can be used in the field of education as a mechanism that promotes the development of intellectual, personal, creative potential of students. The article uses the historical and philosophical method of scientific literature analyzis on the proposed research topic and the method of synthesis as a combination of the considered material in a new quality. Hermeneutical and dialectical research methods were also used in the work.

Annotation: The features of solving inverse problems within the framework of the educational technology of parallel interdis- ciplinary integration of chemistry and computer science are presented: discussion of the meaningful formulation and transition to a mathematical problem at chemistry seminars, implementation of the solution in a software environment in computer classes and subsequent analysis of the obtained results at chemistry seminars. The emphasis on solving chemical problems familiar to students using various software tools is justified. Special at- tention is paid to software tools for solving equations and systems of equations. The main thematic blocks related to solving inverse problems are described: problems for mixing solutions (fractional linear equations), problems for the interaction of a mixture of metals with oxidizing acids (systems of linear equations), problems for chemical equilibrium (nonlinear equations-polynomials). The sequence of blocks is determined by the complexity of both chemical tasks and software tools for their solution. The results of the application of the developed educational technology are presented at the Institute of Fine Chemical Technologies of the Russian Technological University, which indicates its effectiveness.

Annotation: The article reveals the conceptual, methodological and methodical foundations of foresight as an educational technology. The purpose, objectives and principles of implementing humanitarian foresight in the educational process of a technical university are determined; an algorithm is developed, including pre-foresight, foresight session and reflection. The results of approbation of this technology on the basis of the Bauman Moscow State Technical University as part of teaching cultural studies to future engineers are presented. The scenario method was chosen as a method for conducting a foresight session, which involves the development, representation and assessment of polar – optimistic and pessimistic – options for the future of technogenic culture. The importance of foresight as an educational technology that promotes the formation of future-oriented thinking, a culture of participation, creative orientation and the ethos of future engineers is substantiated. In addition, the risks arising in the process of testing humanitarian foresight in the educational process of a technical university are identified.

Annotation: The article is devoted to the development of leadership qualities of students in the psychological and pedagogical field of training in the process of studying at a university. In the process of solving professional tasks, a teacher- psychologist uses his personal resources, including the ability to motivate participants in educational relations, organize joint work, give an expert assessment and actively assist in solving pedagogical issues. The leadership potential of students can be revealed in the learning process, therefore, it is of particular importance to search in the educational space of the university for opportunities for students to form leadership competencies. The article analyzes leadership qualities as professionally significant in the activities of a teacher-psychologist. The conditions are presented in which the leadership qualities of future teachers-psychologists will be actualized and revealed, allowing students to realize their own leadership potential. Pedagogical technologies for the de- velopment of students’ leadership qualities are presented: activation of students’ problem-finding and research activities, inclusion of students in curatorial, mentoring, volunteer activities and student government activities, as well as solving practical cases with involved specialists in the field of team management. The results of the study can be used to improve the process of professional training of future educational psychologists.

Annotation: The article describes the development of digital information culture as a pedagogical process at the level of principles is considered as an object of the study. The purpose of the study is to review the relevant principles with a meaningful justification of their applicability, taking into account the specifics of information activities. The main objectives of the study are the differentiation of didactic and educational principles, as well as general and particular principles, with the identification of their interrelation on this basis. The relevance of the work is due to an increase in the share of information activity in the context of digitalization, and the novelty is the filling of the gap in the study of digital issues at a purely theoretical level using an analytical approach as opposed to the traditionally accepted ostensive one, which is specific for the practical works of a methodological nature. As a result of the research, the author concludes about the merging of the didactic and educational planes in the prism of information culture at the level of principles as pedagogical units of a high order, as well as about the validity of particular principles originating from the general provisions of theoretical pedagogy with a meaning- ful clarification towards the specifics of digital information activity.

Annotation: The article considers the application of telegram channel as a didactic means of digitalizing learning, which is dictated by the increasing role of mobile applications in society and the opportunities they can provide – interactivity, accessibility, speed of information ex-change, and receiving feedback. The meth- odology of this study is based on the concept of person-alized learning and some elements of the digital transformation strategy of education. The differ-entiation method as a tool for identifying the didactic and educational essence in the digital ser-vices used, a survey, and a pedagogical experiment were used as investigation methods. During the study the possibilities of using online services for educational purposes were analyzed. A ho-listic didactic solution for using the telegram channel for teaching biology at school has been de-veloped. Possible prospects of its use are shown, including at an in-depth level, and a set of func-tional tools is justified. An example of a learning channel for studying biology in the 9th grade is demonstrated, the author’s experience of using the service is summarized, confirming the im-provement of the accessibility and personalization of learning. The prospects for further develop-ment of educational technology using the telegram channel are proposed. The practical applica-bility of the research results is ensured by the possibility of replicating positive experience: for example, the creation of personal teacher channels based on the proposed approaches.

Annotation: The article explores the topic of formal description and normalization of the generally accepted concept of “address” in the database. The relevance of the work is due to the high degree of variability of addresses and the need to create a significant number of grammatical rules for their formal description and normalization. The article proposes an approach to summarize the rules of this description. The criterion of sets equivalence of generated address strings is formulated. A system of formal grammar rules has been developed that converts a set of address details values into a string form. The address bar is considered as a linguistic variable, the source of which is the required address, transformed according to the rules of the generative grammar. In turn, each request address is considered as the result of converting the corresponding address bar using the rules of the recognizing grammar. Using the method of logical categorization of the conversion process of a specific address, an address tree has been built, the paths of which determine the structure of each address bar. A theoretical model is proposed for the automatic conversion of a mandatory normalized address into a string form. The results obtained can be useful for designers of information systems containing address description data or interacting with them.

Annotation: The article explores the category of “correspondence” in the field of information field and information modeling. The category of “correspondence” has a multifaceted nature of existence in terms of form, content, and relation- ships between objects. Correspondence can be a function, an image, a computational or logical operation, a way of transmitting information units, etc. Correspondence can be considered as a relationship, as a property between two entities, as a result of comparing information objects, as an assessment of the results of an infor- mation search. Correspondence can be procedural, semantic, morphological, structural, etc. Different types of correspondence determine the relevance of its research. The article presents a systematics of correspondences according to formal and applied features. The content of the correspondences of formal and applied meaning is revealed. Generalized properties of the category “correspondence” and its complement “nonconformity” are presented in terms of set theory and mathematical logic. The difference between full and partial correspondence is shown. It is shown that an important category of correspondence is ontological correspondence, which al- lows the formation of knowledge, and information correspondence, which is a composite correspondence in the information field. The developed foundations of the theory of correspondence between information objects are aimed at expanding and clarifying the formalized procedures of information retrieval and information modeling, and identifying implicit knowledge.

Annotation: Traditional models of the recurrent neural network (RNN), such as LSTM (Long Short-Term Memory) and GRU (Gated Recurrent Unit), have long been used for time series analysis, but have limitations in learning on long sequences and high computational requirements. Recent advances in time series forecasting have shown a de- crease in their importance. In this article, a new RNN architecture with linear temporal complexity and lower memory consumption is proposed. During the study, the proposed RNN model was tested and its performance was evaluated for various temporal series analysis tasks. The presented results of the experiment show that the proposed model is superior to modern alternatives. The competitiveness of the model was confirmed by comparison with advanced models such as PatchTST and TimesNet. In addition, the proposed model surpassed the perfor- mance of models based on multilayer perceptrons (MLP) and proved to be more effective than models based on transformers. The proposed RNN architecture may become a promising direction for future research in this field.

Annotation: Universities play a crucial role in training young professionals, ensuring their understanding of the goals of sustainable development, such as developing strategic partnerships, respecting and supporting human rights, efficient use of resources, and environmental protection. This list of qualities is formed through the educational process, which shapes the worldview of students. The article provides a brief review of initiatives and best practices in the field of training highly qualified specialists who can make a significant contribution to achieving the Sustainable Development Goals. The key directions for the development of education, scientific and upbring- ing activities of universities in the interests of sustainable development are identified. The concept of a holistic system for training specialists capable of promoting sustainable development goals is proposed. The empirical basis of the study is the reports and materials of the international conference “The Role of Universities in the Implementation of the Sustainable Development Goals”, held in May 2024 at the Belgorod University of Coop- eration, Economics and Law.

Annotation: The relevance of the topic is determined by the fact that the content of the university academic discipline “Phi- losophy” provides rich opportunities for the realization of not only educational and developmental, but also educational goals of teaching and shaping the worldview of young people, focused not so much on a positivist understanding of knowledge of the world, man, society and history, as on the formulation and search for answers to metaphysical questions. The object of the study is the didactic features of the investigation of problems of con- frontation and polemics of two ideological systems of human life navigation, which represent opposite solutions to the “main issue of philosophy”. The subject of the study is the didactic specifics of students’ acquaintance with the famous Pascal’s wager in the context of ideological searches for personality. The purpose of the work is to substantiate the presentation of Pascal’s wager not as one of the many elements of the history of philosophy covered with the “dust of centuries”, interesting to the present person only as a “monument of antiquity” and therefore completely uninteresting to modern students, but, on the contrary, as always, the actual basis of ideo- logical personal choice. The research methods are abstraction, idealization, thought experiment, comparative analysis, deductively and inductively organized conclusions, conclusions by analogy and empirical generalization. The result of the work and one of its conclusions is the position according to which the content of Pascal’s wager provides in fact a unique didactic opportunity to demonstrate and substantiate the metaphysical asymmetry of the worldview choice between the materialistic, atheistic, evolutionist, scientific and anthropovolutaristic ideological pole of life navigation, on the one hand, and the idealistic, theistic, creationist, anti-scientific and providentialist pole, on the other one. The field of application of the research results is the ideological search for personal- ity, multifaceted educational interactions and didactic strategies in both secondary and higher education. The first part of the article describes the didactic and ideological aspects of students studying the confrontation of materialism and atheism in the general course of philosophy, on the one hand, and philosophical idealism and theism, on the other hand, as two worldview teachings and systems of human life navigation, conditioned by various solutions to the “basic issue of philosophy”.