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Abstract. Nowadays e-learning tools and delivery methods have been constantly expanding.Employs use e-learning to train their employees more often and often. New and experienced employees have the opportunity to improve upon their knowledge base and expand their skill sets. At home, individuals are granted the access to the programs that provided them with the ability to earn online degrees and enrich their lives through the expanded knowledge. The paper focuses on the analysis of the advantages and disadvantages of e-learning. The ways of applying on-line training used by employers are demonstrated. The experience of implementing active methods of e-learning is described as well as the conclusion about the possibility of their application is made. The paper also presents the results of the survey conducted among TPU teacher and students concerning the advisability of e-learning usage.

The study of

In Minkowski space, there has been developed the mathematic quantum model of the real particle located on the sphere evolving owing to the negative pressure inside the sphere. The developed model is analogous to the geometrodynamic model of the Lemaitre–Friedmann primordial atom in superspace-time, whose spatial coordinate is the scale factor functioning as a radial coordinate. There is a formulation of quantum geometrodynamics in which the spatial coordinate is an offset of the scale factor and wave function at the same time. With the help of the Dirac procedure for extracting the root from the Hamiltonian operator we have constructed a Dirac quantum dynamics of the sphere with fractional spin.