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A problem of internal waves in a two-layer stratified fluid with a density that depends exponentially on the depth inside the layers and has a jump at the interface is considered. An equation for the second long-wavelength approximation is derived, which describes solitary waves. The spectral properties of the equations of small perturbations of a horizontal piecewise constant flow are studied and the possible mechanisms for the occurrence of shear instability of a stratified flow are characterized.

A technique for manufacturing a metal composite material from Ti64 titanium alloy reinforced with SiC ceramic fibers using surface laser cladding technology is proposed. The influence of the parameters of laser action on the shape of a single track is studied. The stability of the formed composite material under high-speed impact has been studied. It is shown that for a sample reinforced with ceramic fibers, the depth of the crater in the substrate is 37% less than for a sample made of Ti64 alloy.

A technique has been developed and a program has been created for numerical calculation by the smoothed particle hydrodynamics method of the process of deformation of an elastoplastic material in the axisymmetric case in the presence of contact boundaries and thermal conductivity of materials. With the help of this program, the problem of the collision of an aluminum particle with a titanium plate under conditions of cold gas-dynamic spraying is solved. It is shown that during a collision in the vicinity of the contact boundary between a particle obstacle, an aluminum particle is intensely heated up to temperatures of the order of 400oC. The calculated temperature is much lower than the melting temperature of aluminum. An explanation is proposed for the mechanism of the formation of a chemical bond between an aluminum particle and a titanium plate under conditions of cold gas-dynamic spraying due to the formation of an intermetallic compound in a hot layer near the contact boundary due to self-propagating high-temperature synthesis.

An engineering method is proposed for determining the oscillation amplitudes during vortex excitation, taking into account the dependence of the excitation force coefficient, the Strouhal number and the logarithmic decrement of oscillations on the oscillation amplitude of the structure, the distribution of the correlation of aerodynamic force pulsations along the length of the structure, and including the Eurocode method as a special case. It is shown that the developed technique, in contrast to the known ones, makes it possible to more reliably calculate the amplitudes of oscillations of span structures during vortex excitation.

Integral Fourier and Laplace transforms are used to numerically obtain an analytical solution to a quasistatic problem of thermoelasticity for a band with constant properties. Results of numerical calculations are presented.

Three-dimensional periodic contact problems on infinite straight chains of punches acting on the face of a transversally isotropic elastic layer, the other face of which is under conditions of a sliding embedment, are studied. The isotropy planes are parallel or perpendicular to the layer faces. To solve contact problems, the method of nonlinear boundary integral equations is used, which makes it possible to simultaneously determine the contact area and contact pressures. Calculations are performed for known transversally isotropic materials.

The structure of foam materials is analyzed. It is noted that foam materials under uniaxial tension and compression have different strain diagrams. A simplified physical model for a heteromodular foam material in the form of a steel ring is proposed. The model was tested on a Walter + Bai AG LFM-L-1 test machine. The deformation of the model was analyzed using the ANSYS Workbench software package taking into account the contact interaction between its elements. The calculation results were compared with experimental data.

Introduction. The theory of modernization, the neo-institutional concept of world culture and the world-system approach explain the current world situation in different ways and offer different ways to change it. The article discusses the theoretical and methodological advantages of the world-system approach, as well as how these advantages are reflected in the field of comparative education and critical pedagogy. Methodology. The idea of the paradigm development of science by T. Kuhn and the idea of I. Lakatos about the commensurability of the empirical bases of research programs formed on the basis of paradigms were used as a methodological basis. Discussion. The world-systems approach has a larger empirical base than competing paradigms. The ontology and methodological base available in the world-system approach allow in the field of comparative education to raise and resolve issues related to social conflicts, inequality, and anti-systemic processes. In contrast to the theory of modernization and the neo-institutional concept of world culture, the world-system approach breaks with Eurocentrism, opening up new perspectives for studying the development of education systems, taking into account their diversity. The appeal of the supporters of the world-system approach in comparative education to critical pedagogy is a consistent transition from solving theoretical problems to the practice of the educational process. Conclusion. The comparison of the three paradigms is incomplete and in the future can be continued on the basis of the methodology of the research programs of I. Lakatos. However, already at this stage, the advantages of the world-system paradigm and the prospects for its use in the field of comparative education are clearly visible. The authors express the hope that the pedagogical projects of critical world-system education will find wide support and humanity will have the opportunity to choose the path to a less repressive form of social organization.

The third part of the paper “On the way to the health of society” discusses the problem of developing the foundations for the healthy existence of society as a complex sociosystem with a full-fledged public consciousness, where the subjects of society are people capable of value-oriented systematic, purposeful, independent cognitive activity. In order to formulate ideas about the axiological social basis, the forms of social consciousness that correlate with value-based instrumental and educational practice are studied, allowing substantiating the principles of healthy existence of society in theoretical and applied aspects. Methodology. The socio-philosophical analysis uses: system-philosophical and dialectical methodology; the principle of integrity (holism); socio-cultural approach to the disclosure of the axiological social basis. The problem of ontological and epistemological foundations of social existence in relation to the fundamental role of education is revealed. Discussion. The general structure of an active social system includes three main parts or substructures: perceiving (external), transforming-conducting (middle) and concentrating (central, or the core of the system). The concentrating substructures (the core of the sociosystem) are: territorial-metropolitan cities, in structural and functional terms - the governing bodies of the sociosystem, in content terms - the value-significant spiritual and material foundations of the sociosystem. From the standpoint of the element-system organization of society, the basis of a healthy sociosystem should be spiritual and material, holistic (integral), axiological (value), and not partial (one-sided, for example, only material). The axiological basis of society should correspond to a healthy holistic, spiritual and bodily essence of a person. In such a basis, the sphere of education acquires a fundamental, attributive role, since it is in it that the elements of this society are formed - people of an ennobled image, and the latter form a creatively creative public consciousness. The axiological dialectic of society and education is associated with a new trajectory of activity-instrumental improvement of both the subject and the object of the educational ecosystem. Conclusion. The essence of a healthy society is predetermined by its axiological basis in relation to the fundamental role of a new educational axiosystem that forms a whole person.

Introduction. The image of modern society is largely determined by information technology. The global Internet network has an ambiguous impact on society. On the one hand, it contributes to the spread of mass culture, which creates risks of intellectual degradation and spiritual impoverishment of users, and on the other hand, by erasing physical and geographical boundaries, it provides ample opportunities for communication, knowledge, education and self-development. In such conditions, the problem of identifying the role and nature of education in the information society, as well as studying its transformations in connection with its differentiation into offline and online, is actualized. Methodology. Within the framework of postmodern concepts of social reality, the sociocultural conditions for the existence and development of modern education are revealed. The socio-phenomenological approach serves to interpret the relationship and mutual influence of society and the individual at the level of social and individual consciousness. The sociocultural approach makes it possible to single out informal education as a special social phenomenon. Discussion. The contradictory nature of the impact of digitalization on modern society is revealed. It is indicated that the blurring of both public consciousness and the simplification of its content leads to similar changes in the consciousness of the individual. The role of education as the most important institution for the transmission of socio-cultural experience and socialization is highlighted. The transformations of education under the influence of digitalization are highlighted: individualization, the development of online learning, the division of education into formal, non-formal and informal. The essence of informal education is revealed. The importance of both strengthening formal education and the formation and development of the cultural and educational environment where informal education is carried out is discussed. Conclusion. The conclusion is made about the change in the nature of the social distribution of knowledge under the influence of the Internet in the direction of increasing their availability with a simultaneous decrease in their quality. It is indicated that in the context of digitalization, education is undergoing dramatic changes: a significant part of the educational process is being transferred to the online spaces of the Internet, and the understanding of education is expanding to the level of distinguishing formal, informal and informal types within it.