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The degree of influence of corrections was studied by the method of high-temperature radiography of alloys of Cu-Ni, Fe-Ni, Au-Ag, KCl-KBr systems on the reverse imaging chamber on the diffuse temperature scattering of X-rays and scattering by defects of the crystal lattice. The research of the concentration and temperature dependences of the mean squares of the values of static and dynamic displacements of hypothetical atoms on their equilibrium positions in the crystal lattice was carried out. The method of separating the values of root-mean-square (RMS) dynamic and static displacements of atoms was described. The article is based on the choice of objects and research method. Mathematical relations for determining the temperature dependence of the X-ray characteristic temperature and complete RMS dynamic and static displacements of hypothetical atoms from the position of their equilibrium in the lattice are presented. The formulas for finding the values of the correction for temperature diffuse scattering of X-rays and the formula for calculating the values of static displacements are given through the parameter of the crystal lattice of the solid solution and the solvent, as well as through the values of the elastic constants of the investigated alloys. Some of the results of the investigation are illustrated graphically, and others -analytically. The advantage of the Chipman-Paskin method for determining the X-ray characteristic temperature and the advantage of evaluating the values of static displacements by temperature changes of the lattice parameter of the solid solution and the solvent are proved.

In this paper we proved that if R is right ω-Euclidean domain, then skew Laurent formal series ring is right ω-Euclidean domain. We also showed that if R is a right ω-Euclidean domain with multiplicative norm, then skew Laurent formal series ring is a right principal ideal domain. In addition, we proved that if R is a noncommutative ω-Euclidean domain with a multiplicative norm, then R and skew Laurent formal series ring is a ring with elementary reduction of matrices.

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