We discuss some well-known facts about Clifford algebras: matrix representations, Cartan’s periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in <span data-mathml="nn dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the method of averaging in Clifford algebras, the notion of quaternion type of Clifford algebra elements, the classification of Lie subalgebras of specific type in Clifford algebra, etc.
In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (x1, x2) with the constant magnetic field normal to this plane and with the potential V having the form of a harmonic oscillator in the direction x1 and periodic with respect to variable x2. Such a potential can be used for modeling a long molecule. We assume that the magnetic field is quite large, this allows us to make the averaging and to reduce the original problem to a spectral problem for a 1-D Schrödinger operator with effective periodic potential. Then we use semiclassical analysis to construct the band spectrum of this reduced operator, as well as that of the original 2-D magnetic Schrödinger operator.
The distractive effects on attentional task performance in different paradigms are analyzed in this paper. I demonstrate how distractors may negatively affect (interference effect), positively (redundancy effect) or neutrally (null effect). Distractor effects described in literature are classified in accordance with their hypothetical source. The general rule of the theory is also introduced. It contains the formal prediction of the particular distractor effect, based on entropy and redundancy measures from the mathematical theory of communication (Shannon, 1948). Single- vs dual-process frameworks are considered for hypothetical mechanisms which underpin the distractor effects. Distractor profiles (DPs) are also introduced for the formalization and simple visualization of experimental data concerning the distractor effects. Typical shapes of DPs and their interpretations are discussed with examples from three frequently cited experiments. Finally, the paper introduces hierarchical hypothesis that states the level-fashion modulating interrelations between distractor effects of different classes.
This article describes the expierence of studying factors influencing the social well-being of educational migrants as mesured by means of a psychological well-being scale (A. Perrudet-Badoux, G.A. Mendelsohn, J.Chiche, 1988) previously adapted for Russian by M.V. Sokolova. A statistical analysis of the scale's reliability is performed. Trends in dynamics of subjective well-being are indentified on the basis the correlations analysis between the condbtbions of adaptation and its success rate, and potential mechanisms for developing subjective well-being among student migrants living in student hostels are described. Particular attention is paid to commuting as a factor of adaptation.