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A short review of the plethysm technique aiming to its application in finding branching rules for the reduction of an irreducible representation of a group under the restriction to one of its subgroups is given. The algebraic structure of the interacting boson model and some of its extensions is given together with the branching rules needed to classify their basis states, obtained by the use of plethysms.

This paper presents the results of natural radionuclide concentration and activity index study in materials used for construction in Latvia. Special attention is given to clay and clay ceramics. Concentrations of K-40 and Th- 232, U-238 radioactivity were determined using gamma-spectrometry method. In some building ware, maximal concentration of K-40 was 1440 Bq/kg, and of U-238 - 175 Bq/kg. In granite, the determined maximum concentration of Th-232 was 210 Bq/kg. It was found that radionuclide content in different period clay deposits can differ by more than two times, and up to five times in different clay ceramics. The results obtained are compared with analogous data from the other Baltic and North European countries.

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Systematic calculations of the neutron-nucleus scattering parameters at several neutron energies Ei < 2 keV have been performed for 37 isotopes (6Li,... 59Co) in the mass region of 6 ≤ A ≤ 60, using the large compilation of experimental neutron-nucleus scattering data obtained in Garching. In the first stage of these calculations, the s-wave potential scattering radius R’, the scattering lengths bcoh, b±, and the bound state parameters (Eb, Γγ , gΓ0n) have been calculated for each isotope, employing the general least squares fit (GLSQF) for the experimental and the corresponding theoretical values of the total neutron-nucleus cross sections σexptot(Ei) at several energies Ei, absorption cross sections σabs(Eo) and of the coherent scattering lengths bcoh. The theoretical expressions for these parameters were deduced on the basis of the usual S-matrix formalism with no assumption about the particular shape of the optical model potential. In the second stage of our calculations, the spherical Fiedeldey- Frahn optical potential was employed for the pure theoretical description or the above mentioned neutron-nucleus scattering characteristics. The results obtained have been analyzed and compared with the values deduced from measurements.