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- ДокументGalois coverings of one-sided bimodule problems(2021) Vyacheslav Babych, Nataliya GolovashchukApplying geometric methods of 2-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite representation type. Each admitted bimodule problem A is endowed with a quasi multiplicative basis. The main result shows that for a problem from the considered class having some finiteness restrictions and the schurian universal covering A', either A is schurian, or its basic bigraph contains a dotted loop, or it has a standard minimal non-schurian bimodule subproblem.
- ДокументSome applications of transversality for infinite dimensional manifolds(2021) Kaveh EftekharinasabWe present some transversality results for a category of Frechet manifolds, the so-called MCk - Frechet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings by virtue of which we prove a rank theorem, an invariance of domain theorem and a Bursuk-Ulam type theorem.
- ДокументDeformations of circle-valued Morse functions on 2-torus(2021) Bohdan FeshchenkoIn this paper we give an algebraic description of fundamental groups of orbits of circle-valued Morse functions on T2 with respect to the action of the group of diffeomorphisms of T2
- ДокументOn conformally reducible pseudo-Riemannian spaces(2021) Тетяна Iванiвна Шевченко, Тетяна Сергіївна Спічак, Дмитро Миколайович ДойковThe present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.