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.

In the present work, the design and implementation of a device capable of monitor the cardiac pulse by means of photoelectric sensors was carried out, using the oximetry technique and in turn the photometry. Heart rate monitoring has great relevance in the field of health and technology, due to the large number of cardiovascular diseases and millions of deaths worldwide annually. There are currently several heart rate counters with limitations that cannot send your information via internet or GPRS, and cannot be filed on a computer. This prototype was made, based on a microcontroller that receives an infrared sensor signal, once properly conditioned It can be transmitted to a computer. The information obtained can be analyzed and stored by medical specialists, as well as transmitted by Wi-Fi to an application of a remote device providing a service with the use of technologies.

The optimal placement of robotic manipulators within industrial workstations is a critical problem that directly affects task feasibility, accessibility, and operational efficiency. Improper base positioning can lead to joint saturation, reduced manipulability, and limited workspace utilization. This work presents an optimization framework for determining the optimal base placement of robotic manipulators by maximizing a joint-centering performance index based on the κ-index, which quantifies the proximity of joint variables to their allowable limits. The proposed methodology integrates geometric accessibility constraints with a constrained optimization formulation to ensure feasible robot configurations within the workspace. Three optimization strategies—constrained nonlinear programming, gradient projection methods, and genetic algorithms—are evaluated and compared in terms of solution quality and computational performance. Numerical simulations are conducted using a planar 2-DOF manipulator to illustrate the proposed framework and to analyze the influence of workspace geometry on optimal base placement. Additionally, an industrial case study involving the ABB IRB 120 robotic manipulator is presented to assess the practical applicability of the proposed approach. The results demonstrate that the optimization framework improves joint distribution within the allowable limits and enhances robot accessibility across the task workspace. The proposed method provides a practical tool for intelligent workstation design and robotic cell layout optimization in modern industrial environments.

Speed of convergence and robustness against disturbances affecting a dynamical system are of great importance in real-life applications. To satisfy these requirements, another approach called predefined time control has been developed in the last decade, which ensures the convergence of the states of a class of dynamical systems to the desired reference value in a time set by the control designer at will. However, previously proposed predefined time control algorithms have drawbacks that need to be tackled. For this reason, the authors present another form of predefined time control algorithm that can be coupled with any observer (in the case where not all the states of the system can be measured) or any other robust controller to robustify the system against matched disturbances. The development shows that the necessary form of the control law can be obtained using basic integration and backstepping. The performance of the control law is demonstrated through a series of numerical simulations utilizing the mathematical model of a permanent magnet synchronous motor (PMSM). The results show that the proposed control algorithm is, indeed, robust against any matched disturbance, and the convergence of the system states is ensured independently of any initial condition in the time set by the control designer at will.

This paper presents the design, mathematical modeling, control, and virtual validation of a fifteen-degree-of-freedom anthropomorphic robotic hand within a Digital Twin-oriented framework. The mechanical structure was designed in SolidWorks and integrated into MATLAB/Simscape Multibody to create a high-fidelity virtual prototype. Forward and inverse kinematic models were derived using the Denavit–Hartenberg methodology, while the dynamic behavior was obtained through the Euler–Lagrange formulation. A proportional-derivative controller with gravity compensation was implemented to evaluate trajectory tracking and motion performance. Stability of the closed-loop system was demonstrated using Lyapunov theory and LaSalle’s Invariance Principle. Simulation results confirmed accurate position tracking, low torque requirements, and stable convergence for both individual and simultaneous joint movements. The proposed Digital Twin framework enables efficient design validation, performance assessment, and future integration with real-time sensing and intelligent robotic manipulation systems. Keywords: Robotic hand; Digital Twin; Simscape Multibody; PD control with gravity compensation; Virtual prototyping. Spanish-language metadata / Metadatos en españolTítulo en español:Marco orientado a Gemelo Digital para el modelado, control y validación virtual de una mano robótica antropomórfica Resumen:Este artículo presenta el diseño, el modelado matemático, el control y la validación virtual de una mano robótica antropomórfica de quince grados de libertad dentro de un marco orientado a Gemelo Digital. La estructura mecánica se diseñó en SolidWorks y se integró en MATLAB/Simscape Multibody para crear un prototipo virtual de alta fidelidad. Los modelos cinemáticos directo e inverso se derivaron mediante la metodología de Denavit–Hartenberg, mientras que el comportamiento dinámico se obtuvo mediante la formulación de Euler–Lagrange. Se implementó un controlador proporcional-derivativo con compensación de gravedad para evaluar el seguimiento de trayectorias y el desempeño del movimiento. La estabilidad del sistema en lazo cerrado se demostró mediante la teoría de Lyapunov y el Principio de Invariancia de LaSalle. Los resultados de la simulación confirmaron un seguimiento preciso de la posición, bajos requerimientos de par y una convergencia estable tanto para movimientos articulares individuales como simultáneos. El marco de Gemelo Digital propuesto permite una validación eficiente del diseño, la evaluación del desempeño y la futura integración con sistemas de sensado en tiempo real y de manipulación robótica inteligente. Palabras Claves:Mano robótica, Gemelo Digital, Simscape Multibody, prototipado virtual Smart citations: SciteAI. Dimensions.Open Alex.