arXiv subjects
Publications and source records attributed to I. V. Bayak.
It is described the group of arrowy permutations (that is extension of symmetric group) and the consequent process of generation of GL(n) and some its subgroups by this combinatoric group and its subgroups.
It is shown that the groups of automorphisms of Euclidean spaces are isomorphic to the groups of topologic automorphisms of respectively factored arithmetic spaces. In particular, the geometry of Euclidean n-space with positive signature is associated with factorization of n-dimensional arithmetic space into n-dimensional sphere.
It is shown that classical Clifford algebras are group algebras of cyclic subgroups of arrowy rermutations. It is established that Euclidean 3-space, Pauli and Dirac algebras and groups of global guage transformations are corollary from the geometry of 8-dimensional vacuum and 9-dimensional cosmos.
It is constructed the functor from category of product linear space to category of skew-symmetric tensor space. It is defined and described the bound bundle as analog of a symplex and as basis element of new constructive homology theory.
It is presented the concept of controled nuclear synthesis in top of cone formed by rotational dynamic flow of low-temperature plasma.
It is investigated a possibility of physical interpretation of vector fields (dynamic flows) in Euclidean spaces of higher dimension. There are analyzed the methods of measurements of dynamic flows, the characteristics of dynamic flow and the connection between its differential and integral characteristics. It is obtained the criterion of local minimality of (n-1)-surfaces that is not connected with interior geometry of surface. It is analyzed some analogy between harmonicity of dynamic flows and dynamic principle of nature.
It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that 1-dimensional (cylindrical) factorization of 4-dimensional Euclidean space provides a quantization of ths model.
Stated lemma contains the assertions about isomorphism of exact m-forms and exterior differentials of regular m-maps, of linearly harmonic m-forms and exterior differentials of regular harmonic m-maps, of global minimal (n-m)-surfaces and level (n-m)-surfaces of regular minimal m-maps. It hold in n-dimensional Euclidean space.