This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30

In this paper, we explored the application of the fractional calculus to digital watermarking. In order to reach this goal, we chose a set of watermarking systems and then we altered the watermark detection step of each system. The novelty of our proposal is that we deviated from the trend of proposing new embedding domains computed by using fractional calculus principles. Instead, we proposed to reformulate the detection equation set. Then, this paper contributes with a new equation set for detecting watermarks based on fractional calculus principles. In addition, we provided the proper order for the derivative; this equation set replaces the previous one, given as a result that the detection rate increased up to 88% for the best case compared to the original equation set. The main modification was to replace the system’s equations to another set that we derived by using the Riemann-Liouville fractional operator. To verify if this approach is effective, we performed tests on grayscale images of size 512×512; the test covered several attacks including noise addition, JPEG compression, scaling, among other attacks. The results showed that the modified systems detected more watermarks than their counterparts. The proposed scheme presented better results for 15 of 21 different tests and the other 6 ended in a draw. It is important to remark that the behavior holds for other embedding domains, for example, the Discrete Cosine Transform (DCT) coefficients, the singular Values Decomposition (SVD) values, etc. which suggests the regularity of the approach.

This review presents a synthesis of fuzzy logic-based (FL) controllers applied to photovoltaic (PV) systems over the last decade, with a specific focus on maximum power point tracking (MPPT) and power management. These subsystems are critical for improving the efficiency of PV energy conversion, as they directly address the nonlinear, time-varying, and uncertain behavior of solar generation under dynamic environmental conditions. FL-based control has proven to be a powerful and versatile tool for enhancing MPPT accuracy, inverter performance, and hybrid energy management strategies. The analysis concentrates on three main categories, namely, Mamdani, Takagi–Sugeno (T-S), and Type-2, highlighting their architectures, operational characteristics, and application domains. Mamdani controllers remain the most widely adopted due to their simplicity, interpretability, and effectiveness in scenarios with moderate response time requirements. T-S controllers excel in real-time high-frequency operations by eliminating the defuzzification stage and approximating system nonlinearities through local linear models, achieving rapid convergence to the maximum power point (MPP) and improved power quality in grid-connected PV systems. Type-2 fuzzy controllers represent the most advanced evolution, incorporating footprints of uncertainty (FOU) to handle high variability, sensor noise, and environmental disturbances, thereby strengthening MPPT accuracy under challenging conditions. This review also examines the integration of metaheuristic algorithms for automated tuning of membership functions and hybrid architectures that combine fuzzy control with artificial intelligence (AI) techniques. A bibliometric perspective reveals a growing research interest in T-S and Type-2 approaches. Quantitatively, Mamdani controllers account for 54.20% of publications, T-S controllers for 26.72%, and Type-2 fuzzy controllers for 19.08%, reflecting the balance between interpretability, computational performance, and robustness to uncertainty in PV-based MPPT and power management applications.

According to the World Health Organization (WHO), 5% of people around the world have hearing disabilities, which limits their capacity to communicate with others. Recently, scientists have proposed systems based on deep learning techniques to create a sign language-to-text translator, expecting this to help deaf people communicate; however, the performance of such systems is still low for practical scenarios. Furthermore, the proposed systems are language-oriented, which leads to particular problems related to the signs for each language. For this reason, to address this problem, in this paper, we propose a system based on a Recursive Neural Network (RNN) focused on Mexican Sign Language (MSL) that uses the spatial tracking of hands and facial expressions to predict the word that a person intends to communicate. To achieve this, we trained four RNN-based models using a dataset of 600 clips that were 30 s long; each word included 30 clips. We conducted two experiments; we tailored the first experiment to determine the most well-suited model for the target application and measure the accuracy of the resulting system in offline mode; in the second experiment, we measured the accuracy of the system in online mode. We assessed the system’s performance using the following metrics: the precision, recall, F1-score, and the number of errors during online scenarios, and the results computed indicate an accuracy of 0.93 in the offline mode and a higher performance for the online operating mode compared to previously proposed approaches. These results underscore the potential of the proposed scheme in scenarios such as teaching, learning, commercial transactions, and daily communications among deaf and non-deaf people.

In this paper, we explore the advantages of a fractional calculus based watermarking system for detecting Gaussian watermarks. To reach this goal, we selected a typical watermarking scheme and replaced the detection equation set by another set of equations derived from fractional calculus principles; then, we carried out a statistical assessment of the performance of both schemes by analyzing the Receiver Operating Characteristic (ROC) curve and the False Positive Percentage (FPP) when they are used to detect Gaussian watermarks. The results show that the ROC of a fractional equation based scheme has 48.3% more Area Under the Curve (AUC) and a False Positives Percentage median of 0.2% whilst the selected typical watermarking scheme has 3%. In addition, the experimental results suggest that the target applications of fractional schemes for detecting Gaussian watermarks are as a semi-fragile image watermarking systems robust to Gaussian noise.

This paper discusses the energy consumption of three parabolic, trapezoidal, and S-curve profiles when implemented using an embedded system. In addition, it presents an alternative methodology for implementing motion controllers using an Advanced RISC Machine (ARM) microcontroller, which computes the trajectory and performs the control action in hard real-time. We experimented using a linear plant composed of a direct current (DC) motor coupled to an endless screw where a carriage was mounted. It can move mechanically along a rail at a distance of 1.16 m. A 4096 pulses per revolution (PPR) encoder was connected to the motor to calculate position and angular velocity. A Hall-effect-based current sensor was used to assess energy consumption. We conducted 40 tests for each profile to compare the energy consumption for the three motion profiles, considering cases with and without load on the carriage. We determined that the parabolic profile provides $22.19\%$ lower energy consumption than the other profiles considered in this study, whereas the S-curve profile exhibited the highest energy consumption.