Abstract : Let and be without two semi-groups. We characterize outside direct result of two free semi-groups as an arranged pair of words with the end goal that and. We explore the introductions of the outer direct result of free semi-groups, state and demonstrate under certain conditions that the outer direct result of two limited created free semi-groups is limited produced, likewise the outside direct result of two limited exhibited free semi-groups is limitedly introduced
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Abstract : Investigation of the mathematical physics equations, which describe material media such as thermodynamic, gas-dynamic and cosmic and other media, shows that they possess hidden invariant properties. Such properties correspond to that of field theory equations, which describe physical fields. This discloses a mechanism of physical fields generation by material media. Such specific properties of mathematical physics equations are connected with conservation laws. They are described by skew-symmetric differential forms which properties correspond to conservation laws.
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Abstract : In this paper, basing on the principle of least action, we calculate the forces which act on the momentum of a particle in a tensor interaction field. These forces were obtained by Kadić-Edelen within the framework of the continuum dislocation theory in analogy with electrodynamics. It is shown that: 1) the centrally symmetric force of the tensor interaction field is similar to the Coulomb force. It contains a potential term of the Euler hydrodynamics equations and is responsible for the homogeneous motions of the continuous medium; 2) the vortex force of the tensor field is similar to the Lorentz force. It coincides with the force of Peach-Koehler, in a solid state, and is responsible for the vortex motion of the continuous medium. It is concluded that the forces obtained act in any medium, and not only in a solid state, as was previously stated in the theory of Kadić-Edelen.
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