Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of an arbitrary TV real matrix is considered and addressed using the singular value decomposition (SVD) and the zeroing neural network (ZNN) approaches. Since SVD is frequently used to compute the inverse or pseudoinverse of a matrix, this research proposes a new ZNN model based on the SVD method as well as the technique of Tikhonov regularization, for solving the problem in continuous time. Numerical experiments, involving the pseudoinversion of square, rectangular, singular, and nonsingular input matrices, indicate that the proposed models are effective for solving the problem of the inversion or pseudoinversion of time varying matrices.

Wind power engineering is one of the environmentally safe areas of energy and certainly makes a significant contribution to the fight against CO2 emissions. The study of the air masses movement in the zone of wind turbines and their influence on the boundary layer of the atmosphere is a fundamental basis for the efficient use of wind energy. The paper considers the theory of the movement of air masses in the rotation zone of a wind turbine, and presents an analytical review of applied methods for modeling the atmospheric boundary layer and its interaction with a wind turbine. The results of modeling the boundary layer in the wind turbine zone using the STAR CCM+ software product are presented. The wind speed and intensity of turbulence in the near and far wake of the wind turbine at nominal load parameters are investigated. There is a significant decrease in the average wind speed in the near wake of the wind generator by 3 m/s and an increase in turbulent intensity by 18.3%. When considering the long-distance track behind the wind turbine, there is a decrease in the average speed by 0.6 m/s, while the percentage taken from the average value of the turbulent intensity is 7.2% higher than in the section in front of the wind generator. The influence of a wind turbine on the change in the temperature stratification of the boundary layer is considered. The experiments revealed a temperature change (up to 0.5 K), which is insignificant, but at night the stratification reaches large values due to an increase in the temperature difference in the surface boundary layer. In the long term, the research will contribute to the sustainable and efficient development of regional wind energy.

In this paper, we consider the integration of the special second‐order initial value problem (IVP) ζ′′=ψfalse(x,ζfalse)$$ {\zeta}^{\prime \prime }=\psi \left(x,\zeta \right) $$ by Runge‐Kutta‐Nyström (RKN) pairs of algebraic orders 6 and 4. For achieving this, we have to solve a certain set of order conditions. The main contribution of the present work is that we introduce a new methodology of solving them that possesses nine free parameters instead of four used by similar pairs until now. This family uses the FSAL (first stage as last) devise. Selecting these extra coefficients properly we may construct methods with better properties. Here, we exploit the free parameters in order to derive a pair with coefficients trained to furnish better results on problems with periodic solutions. Extensive numerical tests justify our approach.

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Runge-Kutta-Nyström pair of orders 7(5) using six stages per step have been discovered very recently. Here we modify four of its weights. The resulting method integrates exactly the harmonic oscillator 𝜓 ′′ = −𝜇 2 𝜓, 𝜇 ∈ R, which serves as model problem. The new weights are O(𝜇 2 ) perturbations of the original ones. Order reduction which is usually present in such modifications is avoided.Numerical results over standard six stages pairs justify our efforts.