Experience of distance learning in modern Russia (philosophical and educational experiments)

This article is devoted to the issue of distance learning for students. This form of education has become common in Russia in conditions of high risk of the coronavirus infection COVID-19. However, there are concerns that distance learning will become a regular norm. Meanwhile, the consequences of this may be negative, since education and promotion of students’ moral growth will become essentially impossible. The entire education system will be reduced to informing students about certain disciplines. Thus, distance learning should not take the form of a daily norm in the education system. English version of the article is available at URL: https://panor.ru/articles/experience-of-distance-learning-in-modern-russia-philosophical-and-educational-experiments/70447.html

Spatial numerical ranges of elements of Banach algebras

In this paper, the notion of spatial numerical range of elements of Banach algebras without identity is studied. Specifically, the relationship between spatial numerical ranges, numerical ranges and spectra is investigated. Among other results, it is shown that the closure of the spatial numerical range of an element of a Banach algebra without Identity but wlth regular norm is exactly its numerical range as an element of the unitized algebra. Futhermore, the closure of the spatial numerical range of a hermitian element coincides with the convex hull of its spectrum. In particular, spatial numerical ranges of the elements of the Banach algebraC0(X)are described.