Renewable energy is a global interest area in achieving sustainable development. Renewable energy sustainability has been assessed using the most commonly used dimensions of this concept: economic, environmental, social, and institutional dimensions. In this paper, we designed a composite index named the Renewable Energy Sustainability Index. The proposed index may represent a national monitoring mechanism that points out the strengths and weaknesses of a state in terms of renewable energy. The data were normalized by calculating the z-score. We tested the proposed index on a selection of 15 European countries ranked by final energy consumption and with different levels of development. The Kayser-Mayer-Olkin values were above the 0.700 limit, which indicates the robustness of each dimension. The proposed index reveals the development stages of renewable energy sustainability and can provide solutions to increase the sustainability of a country by improving positive impact indicators and mitigating negative impact indicators.

The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero–Bogoyavlenskii–Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures.

Fixed point theory is a branch of mathematics that studies solutions that remain unchanged under a given transformation or operator, and it has numerous applications in fields such as mathematics, economics, computer science, engineering, and physics. In the present article, we offer a quicker iteration technique, the $D^{**}$ iteration technique, for approximating fixed points in generalized $\alpha$-nonexpansive mappings and nearly contracted mappings. In uniformly convex Banach spaces, we develop weak and strong convergence results for the $D^{**}$ iteration approach to the fixed points of generalized $\alpha$-nonexpansive mappings. In order to demonstrate the effectiveness of our recommended iteration strategy, we provide comprehensive analytical, numerical, and graphical explanations. Here, we also demonstrate the stability consequences of the new iteration technique. We approximately solve a fractional Volterra–Fredholm integro-differential problem as an application of our major findings. Our findings amend and expand upon some previously published results.

Short-term electricity load forecasting has attracted considerable attention as a result of the crucial role that it plays in power systems and electricity markets. This paper presents a novel hybrid forecasting method that combines an autoregressive model with Gaussian process regression. Mixed-user, hourly, historical data are used to train, validate, and evaluate the model. The empirical wavelet transform was used to preprocess the data. Among the perturbing factors, the most influential predictors that were recorded were the weather factors and day type. The developed methodology is upgraded using a novel closed-loop algorithm that uses the forecasting values and influential factors to predict the residuals. Most performance indicators that are computed indicate that forecasting the residuals actually improves the method’s precision, decreasing the mean absolute percentage error from 5.04% to 4.28%. Measured data are used to validate the effectiveness of the presented approach, making it a suitable tool for use in load forecasting by utility companies.

The aim of this paper is to develop an Artificial Neural Network (ANN) model for springback prediction in the free cylindrical bending of metallic sheets. The proposed ANN model was developed and tested using the Matlab software. The input parameters of the proposed ANN model were the sheet thickness, punch radius, and coefficient of friction. The resulting data is represented by the springback coefficient. Preparation, assessing and confirmation of the model were achieved using 126 data series obtained by Finite element analysis (FEA). ANN was trained by Levenberg - Marquardt back - propagation algorithm. The performance of the ANN model was evaluated using statistic measurements. The predictions of the ANN model, regarding FEA, had quite low root mean squared error (RMSE) values and the model performed well with the coefficient of determination values. This shows that the developed ANN model leads to the idea of being used as an instrument for springback prediction.

This work presents a robust control approach for Maximum Power Point Tracking (MPPT) of a standalone solar Photo Voltaic (PV) system, in order to boost its efficiency. For testing the algorithm, it was considered an 80W stand-alone solar PV cell. In order to improve the efficiency of the charge controller, the proposed control strategy follows the maximum power point output.