Human–robot interaction is becoming increasingly common to perform useful tasks in everyday life. From the human–machine communication perspective, achieving effective interaction in natural language is one challenge. To address it, natural language processing strategies have recently been used, commonly following a supervised machine learning framework. In this context, most approaches rely on the use of linguistic resources (e.g., taggers or embeddings), including training corpora. Unfortunately, such resources are scarce for some languages in specific domains, increasing the complexity of solution approaches. Motivated by these challenges, this paper explores deep learning methods for understanding natural language commands emitted to service robots that guide their movements in low-resource scenarios, defined by the use of Spanish and Nahuatl languages, for which linguistic resources are scarcely unavailable for this specific task. Particularly, we applied natural language understanding (NLU) techniques using deep neural networks and transformers-based models. As part of the research methodology, we introduced a labeled dataset of movement commands in the mentioned languages. The results show that models based on transformers work well to recognize commands (intent classification task) and their parameters (e.g., quantities and movement units) in Spanish, achieving a performance of 98.70% (accuracy) and 96.96% (F1) for the intent classification and slot-filling tasks, respectively). In Nahuatl, the best performance obtained was 93.5% (accuracy) and 88.57% (F1) in these tasks, respectively. In general, this study shows that robot movements can be guided in natural language through machine learning models using neural models and cross-lingual transfer strategies, even in low-resource scenarios.

This paper presents a comprehensive analysis of the plastic injection molding process through the integration of data acquisition technologies and classification models. In collaboration with a company specializing in plastic injection, data were extracted directly from the machine during a specific period at the beginning of a shift change. These data were subjected to exploratory analysis to identify correlations between important variables, such as injection time, cycle time, and mold pressures. Additionally, classification models, including Random Forest and Logistic Regression, were constructed to predict and classify the process state based on these variables. The model results demonstrated high predictive performance, with 99.5% accuracy for Random Forest and 97% for Logistic Regression. These results provide a strong foundation for the early identification of potential problems and informed decision making to improve the efficiency of the plastic injection molding process. This study contributes to the advancement of the integration of intelligent technologies in industrial process optimization, aligned with the principles of Industry 4.0.

This research communication aims to present three mathematical methods for analyzing inventory management in dynamic supply chains, starting from the basic definition in differential equations for inventory levels, which relates with production and demand rates. Initially, the study adopts a systemic perspective to examine the role of energy within a production–inventory system. Subsequently, the analysis focuses on inventory dynamics under parameters expressed in complex variables, with the aim of quantifying fluctuations in a generic production system and demonstrating the influence of inventory variation rates on system behavior. Finally, the investigation addresses the impact of variable capacity on production system inventories, drawing on analogies with corresponding physical systems to support the analysis.

Agri-food supply chains have experienced notable changes in recent decades, with tomatoes (Solanum lycopersicum) maintaining their status as a key global crop in terms of both production and consumption. These supply chains comprise a complex network of stakeholders—including producers, processors, distributors, and retailers—who collectively ensure the delivery of tomatoes from farms to consumers. This study develops mathematical models of agri-food tomato supply chains (AFTSCs) and examines their behavior through stability analysis and dynamic simulations based on a compartmental approach. Furthermore, the environmental impact is evaluated using a sustainability index, to which the waste diversion rate is introduced. This metric is defined as the proportion of diverted waste (i.e., materials recycled, reused, or composted) relative to the total waste generated, thereby enabling the quantification of sustainability performance within the system. Finally, a sensitivity analysis is conducted on the proposed dynamical models to validate and reinforce the findings.

An automatic temperature control system is an important application used in almost all modern gadgets, smart homes and industries; however, there are almost no available prototypes to practise with, and the ones that do exist cost more than an average student in Mexico can afford. This project is based on the implementation of a digital PID controller, realised through widely studied mathematical concepts, applied to a fan that blows air into an enclosed area housing an incandescent bulb, thereby controlling the internal temperature. A Kalman filter was used to reduce the thermocouple noise. The performance of the controller was tested by observing its ability to maintain the desired temperature setpoint steadily. This test highlighted the PID controller’s ability to reach and maintain the desired temperature, validating its effectiveness as both an educational tool and a method of control for industrial applications.

In this study, a numerical analysis of the mathematical model of a single-phase transformer is presented, incorporating a comprehensive expression for the mutual magnetic flux to assess its effect on energy transfer efficiency. Drawing on Faraday’s and Ampère’s laws, the fundamental relationships between magnetic flux, currents, and voltages in the windings are established. Through numerical simulations, the influence of mutual leakage flux is investigated, alongside structural parameters such as resistance, reactance, and the number of turns. The results obtained confirm the model’s effectiveness in predicting transformer behaviour under varying load and network conditions, offering an analytical tool for the design and enhancement of these electrical machines. This approach not only deepens the theoretical understanding of transformers but also supports the development of more efficient and reliable electrical systems.