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.

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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.

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.