A study of how hydrostatic pressure of up to 13 kbar affects the superconducting transition and electrical resistivity of D-intercalated 2H-NbSe2 samples, in a temperature range of 4.2–50 K. It is shown that the growth of Tc in the intercalated samples cannot be associated solely with the suppression of the charge density wave (CDW). For a more complete explanation of the effect of increasing Tc, it is necessary to account for changes in the density of the electron states at the Fermi level, not associated with CDW, and also changes in the constants of the electron-phonon coupling, caused by the pressure.

Nano-structured polycrystalline СеО 2 is proposed to be used as a candidate electrolyte material for solid oxide fuel cells (SOFC) operating at temperatures ≤ 600 °С. Here we show that in this material the diffusion activation energy of oxygen ions is 0.35 eV. The diffusion mechanism corresponds to the "single-file" diffusion mechanism, associated with the presence of one-dimensional channels in the anion sublattice of СеО 2 . The small grain size of the material ≈ 10 nm, as well as its stoichiometric state (Се 2 О 3 ), minimize the contribution of the electronic and polaron components of the electrical conductivity of this material, which also contribute to the optimization of SOFC operation.

The electrical resistivity of niobium diselenide (NbSe2) with hydrogen was investigated in the temperature range Tc – 300 K. It was determined that hydrogen inhibits the formation of a charge density wave. It was shown that hydride phase with niobium is formed due to hydrogen in NbSe2 layers at low temperatures, which decomposes with increasing temperature to form a solid solution. The temperature dependence of the resistivity is approximated by the Bloch–Grüneisen function. The approximation parameters vary depending on the amount of dissolved hydrogen.

Combinatorial optimization problems and methods of their solution have been a subject of numerous studies, since a large number of practical problems are described by combinatorial optimization models. Many studies consider approaches to and describe methods of solution for combinatorial optimization problems with linear or fractionally linear target functions on combinatorial sets such as permutations and arrangements. Studies consider solving combinatorial problems by means of well-known methods, as well as developing new methods and algorithms of searching a solution. We describe a method of solving a problem of a linear target function localization on a permutation set. The task is to find those locally admissible permutations on the permutation set, for which the linear function possesses a given value. In a general case, this problem may have no solutions at all. In the article, we propose a newly developed method that allows us to obtain a solution of such a problem (in the case that such solution exists) by the goal-oriented seeking for locally admissible permutations with a minimal enumeration that is much less than the number of all possible variants. Searching for the solution comes down to generating various permutations and evaluating them. Evaluation of each permutation includes two steps. The first step consists of function decreasing by transposing the numbers in the first n – 3 positions, and the second step is evaluation of the permutations for the remaining three numbers. Then we analyze the correlation (which is called balance) to define whether the considered permutation is the solution or not. In our article, we illustrate the localization method by solving the problem for n = 5. Keywords: localization, linear function, permutation, transposition, balance, position.

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