The effects of hydrogen absorption and manganese substitution on structural, electronic, optical, and thermoelectric properties of silicon-carbon nanotubes (SiCNT) are studied using the density functional theory and the GGA approximation. An examination of the PDOS curves and the electronic band structure showed that the Mn substitution leads to an increase in magnetic anisotropy and the occurrence of semi-metallic behavior and that the hydrogen absorption shifts the band gap toward the lower energies. A study of these nanostructures’ thermoelectric behavior reveals that the H absorption leads to a significant escalation in the figure of merit of the SiCNT to about 1.6 in the room temperature range. The effects of the H absorption on this nanotube’s optical properties, including the dielectric functions and its absorption spectra, are also investigated.

The paper discusses a method of quantitative comparison of cylindricity profiles measured with different strategies. The method is based on applying so-called Legendre-Fourier coefficients. The comparison is carried out by computing the correlation coefficient between the profiles. It is conducted by applying a normalized cross-correlation function and it requires approximation of cylindrical surfaces using the Legendre-Fourier method. As the example two sets of measurement data are employed: the first from the CMM and the second one from the traditional radial measuring instrument. The measuring data are compared by analyzing the values of selected cylindricity parameters and calculating the coefficient of correlation between profiles.

The standard approach to the wave propagation in an inhomogeneous elastic layer leads to the displacement in a form of a product of a function of space and a harmonic function of time. This product represents the standing, and not the running wave. The part depending on the space variable is governed by the linear ordinary second order differential equation. In order to calculate the propagation speed in the present paper the inhomogeneous material is separated by a plane into two parts. Between the two inhomogeneous parts the virtual homogeneous elastic extra layer is added. The elasticity modulus and the mass density of the extra layer have the same values as the inhomogeneous material on the separation plane. In further calculations the extra layer is assumed to be infinitesimally thin. The virtual layer allows to decompose the motion into two waves: a wave running to the right and a wave running to the left. Energy conservation equation is derived.