Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

Paper is devoted to the effective stationary heat conductivity for the fibre composite materials. We are aimed on getting on analytical expression for effective thermal conductivity coefficient. Asymptotic homogenization approach, based on the multiple scale perturbation method, is used. This allows to reduce the original boundary value problem in multiply connected domain to the sequence of boundary value problems in simply connected domains. These problems include: the local problem for the periodically repeated cell and homogenized problem with effective coefficient. It is shown that for densely packed and high contrast fibre composites, the cell problem can be solved analytically. For this aim, lubrication approach (asymptotics of thin layer) has been employed. We also generalise obtained solution to the case of medium-sized inclusions in the framework of the Padé approximants

Development of Ukrainian and Global Online Education

The article enlightens the activities of the main public online educational platforms in Ukraine, their role in the modernization of education and their socio-political influence on changes in the state. Interdependence is observed between the specificity, inherent in different stages of distance education progress. Problematic issues in the field of innovative educational technologies are highlighted: socialization of students, difficulties in control of their knowledge, metacognitive monitoring of mastering the material by them etc. The degree of organization in operation of electronic cabinets is examined and other measures supposed to introduce the telecommunicative teaching means in Ukrainian higher education