[en] The authors consider one-parameter problems of calculating the stability of centrally compressed rods of step stiffness with linearly elastically compliant support constraints. The problem of calculating the stability is set as bifurcation. Euler’s exact solutions are obtained for different variants of the design scheme of a rod of two-stage rigidity. An iterative algorithm for calculating the stability beyond the limit of proportionality is proposed, based on the concept of the conditional flexibility of rod sections, using the experimentally obtained diagram σ - ε and the table of coefficients ϕ. Numerical examples illustrating the proposed methods and algorithms are considered. (paper)

[en] Spinel Mn²⁺ Fe_2−x³⁺Ce_x³⁺O₄ (where x = 0.01–0.05) polycrystalline nanoparticles were fabricated by solution combustion method using glucose and urea as fuels. X-ray diffractogram (XRD) proved the witness of the cubic crystal consort of products which have the crystallite sizes in between 12 and 8 nm. The size of the sample was accomplished via transmission electron microscopy. The elemental composition of iron and manganese ions valences of MnCe_xFe_2−xO₄ samples were analyzed by X-ray photoelectron spectroscopy. XPS data reveals iron in all samples was trivalent; manganese was divalent, although tetravalent manganese ions were present on the surface of particles. Magnetic characterization of samples was done via Mössbauer spectroscopy at room temperature and at low temperatures (15 K). The Mössbauer analysis determines the consequence of Ce³⁺ substitution on isomer shift and quadrupole splitting of all samples. The low temperature Mössbauer spectroscopy results indicate that the presence of Ce³⁺ ions in the octahedron sites causes the decrease in the concentration of Fe³⁺ ions.