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An equilibrium problem of a two-dimensional body with a thin defect whose properties are characterized by a fracture parameter is considered. The problem is discretized, and an approximation accuracy theorem is proved. To solve the problem, a dual method based on a modified Lagrange functional is used. In computational experiments, when solving the direct problem, a generalized Newton's method is used with a step satisfying Armijo's condition.

An effect of molting anseriform birds on structure and elemental composition of phytoplankton (seston) was evaluated in 20 Arctic lakes of the Taimyr Peninsula. In lakes (lake area) inhabited with ~50-700 birds of 6 species, an average stoichiometric ratio N : P (mol: mol) was statistically significantly lower, than in lakes without anseriforms: 15.8 ± 1.4 и 22.4 ± 2.7, respectively. Besides, there was a tendency of higher average specific electrical conductivity in lakes with the birds, 113 ± 32 µS/cm, compared with those without anseriforms, 60 ± 18 µS/cm. The differences observed could be likely explained by an effect of guanotrophication, namely by a flow in water of metabolites of molting anseriforms. Total biomass of phytoplankton and proportions of algal taxa and cyanobacteria in the total biomass did not differ statistically significantly in lakes with and without molting anseriforms. Thereby, under the guanotrophication, the main threat of eutrophication was absent: an increase of biomass of cyanobacteria causing nuisance “bloom” of water. Moreover, an opposite tendency occurred: in lakes with molting anseriforms, the proportion of cyanobacteria in total biomass of phytoplankton was on average lower, than that in lakes without the birds, 16.2 ± 5.3 and 30.8 ± 9.3 %, respectively. Thus, a hypothesis was confirmed, that an artificial guanotrophication should be regarded as a suitable ecotechnology for an increase of productivity of oligotrophic Arctic lakes.

Within the ecological direction of studying humus using traditional methods and terms, the peculiarities of the transformation of organic matter of peat eutrophic soils (Hypereutric Sapric Histosols) and peaty gleezems (Eutric Histic Gleysols) 20 years after a forest-peat fire are discussed. The object of the study was the green moss-hypnum spruce forests (Picea obovata Ledeb.) of eastern slope of the Kuznetsk Alatau (absolute height 622 m). The composition of organic matter of pyrogenic soils (0-30 cm) is characterized by high variability (coefficient of variation 12-92 %). According to the factor analysis, 76 % of the total variance is due to a combination of humic substances, 24 % - polysaccharides. Using the cluster analysis procedure, we identified two groups of objects whose statistical reliability was confirmed by discriminant analysis. Soil clusters reflect the peculiarities of pyrogenic processes - underground focal smoldering, below the point of ignition, and open intense and medium strength fire. Relative to the background carbon content of 41 % (peats not covered by fire), its amount decreases to 26.5 and 13.4 %, respectively. At the same time, there is an almost equal formation of humification products (∑GC + ∑FC) - 55.4 and 53.7 % due mainly to fulvic acids (Cgc/Cfc 0.2-0.6). The peculiarities of the thermal effect are occurred mainly at the fractional level. The specificity of underground smoldering is an increased yield of fulvic acids of the first fraction, free and loosely bound to R₂O₃. An open fire is accompanied by the predominant formation of humic and fulvic acids associated with calcium. According to standardized coefficients of canonical analysis, the first and second fractions of humic and fulvic acids make the greatest cumulative contribution to cluster discrimination, the maximum personal weight is HC-2, FC-1 and FC-2. Based on previously obtained information about the group composition of buried peats and the important role of anaerobiosis in the formation of humic acids, which are more correspond with the restored nature of the substance compared to fulvic acids, it can be assumed that peat genesis continuing in the area of the fire can cause the transformation of fulvate humus into fulvate-humate and/or humate. In the case of burial of a pyrogenic peat layer of 0-30 cm, this can happen in about 270 years, based on the rate of linear growth of peat in the spruce forests of the Kuznetsk Alatau - 1.12 mm/ year. The research results confirm the validity of the traditional division of humic acids into fractions.

Introduction. The most important challenge for modern humanity is the information technology era, in which knowledge is both a factor of positive transformation of reality and a source that disrupts the balance of human life and society. Parallel to these processes, transformations are also observed in art, in the form of the emergence and formation of generalized expressive images and symbols, easily recognizable, with deep meaning and cognitive potential. The purpose of the article is philosophical understanding of the genesis and integration of knowledge and art as a factor of value-positive transformation of reality. The research methodology includes a review of literary sources and a dialectical approach to the historical and art criticism analysis of the unity of the epistemological and logical in the value-containing discourse. The focus of the research is aimed at analyzing the integrative processes of knowledge through the prism of art. Discussion. A generalization is made that human civilization is developing due to the genesis of epistemological science, which sets guidelines for processes occurring at various levels of human existence. Prediction of the results of the integration of knowledge is possible provided that philosophical knowledge is addressed and its correlates are found in ideal and material value orientations. Conclusion. Integrative processes in the main forms of human knowledge (art, philosophy, science) have become the most important value bases in the formation of gnosiology, epistemology and axiology. It is reasonable that at all stages of the genesis of human knowledge, art has contributed to the integration of knowledge, contributing to the building of a certain educational system and praxiological methods for solving various life contradictions (concentration and storage of information, art therapy, emotional reflection of reality, patriotic education, preservation of museum values, the use of digital technologies and future possibilities of artificial intelligence), which, in general, contributes to the positive transformation of the social and educational space.

Introduction. New existential schemes imposed to the world and the human being in the struggle for survival in the conditions of the pandemic era exacerbate the need to rethink the modern human ontology. The purpose of this article is the author’s attempt to build understanding of the essence of such ontology as the aim of modern education. Methodology. The article is based on the following methodological understanding: being fixed in variants, ontology is “objectified” in an individual worldview and “inculcated” into a person on the basis of ways of thinking and activity, as well as the meanings of this activity. Such methodological complex is transmitted through the education system. An attempt is being made to analyze it. Discussion. Based on the analysis of the methodological complex characteristic of the modern education system, the thesis is put forward about a variant of the ontology of a modern person as a competent “user” of a demiurge system opposing his/her creative potential, focused on survival and potentially unable to surpass this system. It becomes necessary to rethink the human dimension of such ontology in the context of education. The problem of modern education lies in the absence of the supposed goal of a broad existential framework for understanding educational processes and mechanisms for creating conditions for the formation of the human in the human being. Ontologically oriented education is aimed at creating and building a natural environment for the manifestation and development of natural human subjectivity. This requires a number of conditions: the content integrity of education, the development of appropriate types of thinking (unsupported, critical, systemic, methodological), the development of reflection, the development of imagination and the ability to dream, the aesthetic nature of education, the formation of existential human meanings, the development of the theme of soul and spirituality in education. Conclusion. The mission of modern education is to turn the signs of the instability of the epoch into the possibility of building a humane (human-sized) ontology of the human. In this context, innovations become significant, but understood as a variant of traditional experience. In the case of ontologically oriented education, this is the experience of cultivating the human in the human being.

Introduction. The intensification of post-industrial social development in the technical sphere of production significantly affects the well-being/disadvantage of people and the environment. The problem of developing deontological foundations for the formation of readiness of graduates of the higher education institution of the engineering profile for moral responsibility for the safety and reliability of the result of professional activity is actualized. Methodology. Epistemological analysis involves the identification of the “object-knowledgeˮ relationship. As an object, moral duty is considered as an integral part of the professional duty of an engineering and technical employee; and as knowledge, an appeal to the provisions of deontology, which represents the ethics of duty in modern philosophy. This approach involves the differentiation of socio-philosophical positions of duty and the search for information and semantic forms of objectification of the moral duty of an engineering and technical worker. Discussion. The function of deontological elements in the structure of the educational process is realized by the competencies of a university graduate of a moral and ethical nature, administratively approved as educational goals. The presentation of educational goals in the aspect of deontology, reflecting the readiness of a graduate of an engineering higher education institution to bear professional responsibility, is achieved by taking its provisions in the field of ethical theory for granted, through appropriate imperatives in a specific form of manifestation of social necessity. The use of the provisions of deontology as a theoretical basis for the development of the structural composition and content of moral and ethical educational goals supports the accuracy of the orientation of pedagogical influence on the formation of the readiness of an engineering graduate to bear professional responsibility. The categorical status of duty described in deontology connects it with the regulatory principles of morality, reflecting the unconditional fulfillment of the requirements of moral duty in the course of professional activity of the engineering profile. Its boundaries are determined by the specific imperative of moral duty. Conclusion. Based on the concept of modern epistemology, emphasizing the social prerequisites for the functioning of knowledge, the involvement of the analytical and philosophical foundation of deontology provides a scientifically based objectification of the structural composition of the moral and ethical educational goals of the engineering profile.

Introduction. The relevance of the implementation of the Federal (Presidential) program for the training of managerial personnel for the organizations of the national economy of the Russian Federation requires a formed educational and methodological complex for the digitalization of management based on domestic experience and the best international practices of digitalization for their comprehension and dissemination. In modern management, there are many new concepts, methods and tools. The fact is stated that the “And - Andˮ principle operates in modern management, the manifestation of which is the co-existence of old and new methods and tools. Researchers note that now business processes based on Internet resources of the XXI century, managerial postulates of the mid-XX century and management principles developed in the XIX century coexist in any company. The methodology of the research is based on the analysis of the evolution of views on the training of managers and the interpretation of international experience in the implementation of the Program for the training of managerial personnel. Discussion. The article shows the development of approaches to professional retraining of Russian managers based on the analysis of 25 years of experience in the implementation of the Federal (Presidential) program of training managerial personnel for organizations of the national economy of the Russian Federation. It is noted that the Program has become an instrument of “softˮ infrastructure of support for the development of companies and management culture in the country and regions. The stages of the Program development are highlighted, reflecting the change of emphasis in the training of practical managers. The best practices of each stage of the Program implementation are described. The main challenges of the external environment are systematized and the main components and problems of the formation of digital competencies of managers are considered. Conclusion. Along with traditional skills in management, it is necessary to talk about digital competencies of managers in a broader context: modern trends in global economic and technological development; a new understanding of the principles of working with data and managing an organization based on digital technologies.

Introduction. In the last decade, the introduction of inclusive practice in the preschool education system has actualized the problem of ensuring the readiness of teachers to work in innovative conditions. The analysis of scientific research and the study of the real situation indicate significant barriers and difficulties of teachers in working with children in special purpose groups. Therefore, the development of a model of professional support for teachers and a program for its implementation in an inclusive preschool educational organization is not only relevant, but also has theoretical and practical significance. Methodology. The theoretical and methodological basis was made up of domestic scientific developments in the field of inclusive education. Traditional psychological and pedagogical methods were used: theoretical (study, analysis, synthesis, generalization of theoretical sources) and empirical (survey methods, methods of qualitative and quantitative analysis of empirical material). Discussion. The development of the conceptual apparatus in the aspect of the chosen topic made it possible to interpret the professional support of teachers as a specially organized and systematic interaction aimed at assisting the teacher in choosing the most effective ways to solve problems and typical problems of professional activity. The results of diagnostics of a set of valid and reliable methods with the participation of 65 kindergarten teachers allowed us to obtain complete and reliable information about the difficulties and problems of teachers who are directly related to the implementation of inclusive education in a particular educational organization. Conclusion. In the course of the study, a model of professional support for teachers of an inclusive preschool educational organization was developed in the form of a matrix that includes content and organizational components. A program has been compiled to ensure the professional readiness of teachers of a preschool educational organization to implement inclusive practice. The program has a modular structure and contains a description of the activities for the implementation of each module.

Introduction. The article analyses the terms of “interdisciplinarityˮ and “integrationˮ as integral conditions in the field of engineering education. Reasonably, in order to increase the flexibility of engineering education and the introduction of new foreign language teaching methods, the article proposes a new technology of engineering students’ foreign language training based on “interdisciplinary assembling” with an emphasis on students’ cognitive activity and self-learning advancement along with an individual foreign language educational tracking. The methodology of this research is based on analytical methods of interpretation of authors’ theories. The scientific basis of the study is an interdisciplinary approach, from the standpoint of which foreign language teaching of future engineers by means of interdisciplinary assembling is the process and result of the introduction of integrative and developmental technology, due to the thematic unification/integration of modules of several disciplines in favor of foreign language practice. The practice-oriented research tactic is an integrative-advancing approach, from the standpoint of which an engineering student’ communicative competence is studied as an integrative, dynamic professional and personal quality. Discussion. A big difference of the innovative format of interdisciplinary interaction is that it can take place at the level of personal communication and by mutual introduction of achievements and results of various sciences. The article shares the idea of interdisciplinarity as a modern educational trend. Conclusion. From the analytical review, it has been revealed that integration as a pedagogical phenomenon allows us to intensify the educational process in line with the transformation and reconfiguration of educational programs and their content within the framework of strategic and tactical purposes. From the analysis of the experience of Russian universities, it is noted that it is the variability of approaches to interdisciplinary integration that becomes a collective asset of development and the basis for the transfer and export of the most striking and effective educational practices.

Introduction. The digitalization of education leads to changes in the implementation of educational activities of teachers and students and requires reflection in terms of the adoption of innovations. The rate of adoption of innovations depends on the resource state of organizations and their subjects and varies for different cases. This leads to the use of case analysis and interest in the assessments of different groups of subjects of educational activity. Methodology. The theoretical framework of the study is based on the principles of integration of the provisions established in the theories of the digital society, digital methods of cognition of social reality, Data-anthropo approach in the analytics of educational data, digital pedagogy and didactics, and monitoring studies. The object of the study was the digitalization of educational practices of teachers in higher education. The study was aimed at identifying attitudes to changes in the professional activities of university teachers when using the digital educational environment. The study was conducted in the form of a questionnaire survey based on a continuous sample. Discussion. There is a contradiction in the assessments of the possibilities of digital educational technologies in educational communications. The proportion of teachers who believe that digital technologies bring anthropological, psychological and educational risks to the educational process remains high. At the same time, positive dynamics was recorded in the assessments of the digital educational environment and changes in professional activities occurring in the process of digitalization. Conclusion. Competencies in demand when using the digital educational environment are the skills of creating educational content of various types and design and analytics of educational data. The study of the professional activities of subjects of education in the digital space demonstrates the continuing contradictions, despite the wide educational opportunities of digital services and platforms.