Udmurt State University

Abstract: A local nonequilibrium approach to rapid solidification of undercooled alloys is presented. Taking into account the finite speed of mass signals, a steady-state solution to the nonisothermal rapid solidification problem has been obtained. We have found that, if the solidification front moves at a velocity V equal to or higher than the diffusive speed ${\mathrm{V}}_{\mathrm{D}}^{\mathrm{L}g}$ in the liquid, a partitionless thermal-controlled situation takes place. The solidification mechanism changes at V=${\mathrm{V}}_{\mathrm{D}}^{\mathrm{L}g}$ and the constitutional undercooling is lacking ahead of the solidification front. Some comparisons with the known experimental and theoretical results are discussed.

Abstract: This paper can be regarded as a continuation of our previous work [1, 2] on the hierarchy of the dynamical behavior of nonholonomic systems. We consider different mechanical systems with nonholonomic constraints; in particular, we examine the existence of tensor invariants (laws of conservation) and their connection with the behavior of a system. Considerable attention is given to the possibility of conformally Hamiltonian representation of the equations of motion, which is mainly used for the integration of the considered systems.

Abstract: Digital technology in the modern world is not only a tool, but also a living environment that opens up new opportunities: learning at any convenient time, continuing education, etc. This article aims to describe the specificity of digital education, the current state of its implementation, the expected results and concerns in this respect. Having shown the core of the digital education and the state of its implementation in modern society, this type of education must be critically analyzed in terms of advantages and risks with reference to contemporary students and the effectiveness of the teaching – learning process, in which they participate. In the study pros and cons of digital learning are revealed.