In the paper, we investigate three-dimensional solvable Lie groups from the point of view of the generalized Hermitian geometry. The corresponding three-dimensional solvable Lie algebras were firstly classified by G. M. Mubarakzyanov in 1963. Using the classification in somewhat different notations, we construct basic left-invariant metric f-structures of rank 2 on all three-dimensional solvable Lie groups equipped with the standard left-invariant Riemannian metric. It was proved that all the considered f-structures belong to one or several classes of generalized almost Hermitian structures. As a result, it gives the opportunity to present new examples of left-invariant Killling, nearly Kähler, generalized nearly Kähler and Hermitian f-structures on solvable Lie groups.

The explicit form of the third-order electromagnetic corrections in the fine structure constant α³ to the anomalous magnetic moment of lepton a_L (L = e,μ,τ) from the contribution of the sixth – order vertex graph with insertion of fourth – order vacuum polarization. The approach is based on the consistent application of dispersion relations for the polarization operator and the Mellin – Barnes transform for massive particle propagators. Explicit analytical expressions for the corrections to a_L are obtained at r = m_ℓ/m_L > 1. Asymptotic expansions are found in the limit of both small and large values of the lepton mass ratio (r = m_ℓ/m_L), r ^ 1 and r → ∞. The expansions obtained are compared with the corresponding expressions given in the literature.

An analytical solution of the inverse ellipsometry problem on determining the complex permittivity of a substrate in the presence of a nanosized surface layer with previously unknown characteristics is formulated. The layer is taken into account only by one integral parameter, which is restored simultaneously with the substrate permittivity. The solution uses ellipsometric parameters Δ and Ψ, measured at two angles of light incidence on the structure. The optimal values of the incident angles are established from the condition of the minimum of the error coefficient of the substrate permittivity reconstruction. The efficiency of the solution is checked in numerical simulations and real experiments on the ellipsometry of silicon substrates with various surface layers. In particular, the band gap of a silicon substrate doped with boron and subjected to a rapid heat treatment to stabilize the surface layer is determined.

One of the possible designs of a double-gate quantum-barrier field-effect transistor based on a metallic single-wall carbon nanotube of the zigzag type is considered. The current-voltage characteristics of the transistor with the optimal geometry are calculated in the framework of the developed combined physical and mathematical model describing the charge carrier transport in the conducting channel of the transistor taking into account both quantum-dimensional effects and phonon scattering of particles. Optimum values of the nanotube length and diameter are determined at which the maximum values of the channel conductivity and the subthreshold swing are achieved for such a transistor.

The article presents the results of substantiation and approbation of the model of electromagnetic radiation interaction with rough surfaces. This model differs from analogues in the following: 1) surface roughness profiles are described using fractal geometry; 2) it is taken into account that the distribution of the electric field over the surfaces is characterized by the presence of strong discontinuities. The second of the indicated differences led to the use of Maxwell’s equations reduced to wave equations in the framework of the developed model. The developed model is recommended for use in the design of thin-film electromagnetic shields for microelectronics products protection from external and internal interference impact, as well as in the design of such products, in the design of radiophotonics products and theoretical evaluation of the optical and thermal properties of materials.

A deep feed-forward neural network model is developed and analyzed in this article to solve the financial loan classification problem. Using this model, based on historical data on previously issued loans, the values of the following traditional machine learning metrics that determine the quality of forecasting are calculated: cost function, truth, accuracy, completeness and F₁ measure. In order to obtain greater forecasting accuracy, optimization methods of mini-batch gradient descent, gradient descent with momentum, adaptive momentum estimation, and zero-level elimination method were used. An improved structure of the proposed neural network was determined, the impact of the so-called He initialization on the final result was analyzed, as well as the efficiency of using specific optimization algorithms. The study showed that the use of deep feed-forward neural network is reasonable in developing loan classifiers.