This study deals with the effect of Cu on hydroxyapatite (HAp) thin films on silicon substrates prepared by pulsed laser deposition (PLD) technique for Cu concentrations ranging from 0 to 0.8 wt.%. Fourier transform infrared spectroscopy and Raman spectroscopy provide additional evidence of HAp in the films, which exhibit characteristic HAp bands such as the 960 cm-1 phosphate ion band. The X-ray diffraction patterns confirm the presence of HAp, without copper-related peaks, suggesting that it is not incorporated into the HAp lattice, which is present as an amorphous phase. X-ray photoelectron spectroscopy confirms the presence of Cu on the HAp thin films, possibly related to the adsorption of Cu2+ on HAp surfaces through electrostatic or interactions with (PO4)3- groups. Atomic force microscopy shows that the roughness of the films varies depending on the presence or absence of copper ions. Finally, density functional theory and kinetic Monte Carlo simulations explain the effects of atomic diffusion on roughness and HAp clustering. These changes correlate with the contact angle values, indicating the formation of hydrophobic films due to copper inclusions. Fabrication and characterization of hydroxyapatite thin films by pulsed laser deposition on silicon. image

In this study, we enter the field of nonlinear partial differential equations (PDEs) and propose a novel approach to their solution. We employ the iterative Adomian decomposition method (ADM) to address a distinct subclass of nonlinear PDEs. The main objective of this paper is to evaluate the efficiency and reliability of the ADM in handling complex mathematical models. To this end, we explore the convergence characteristics of the method when applied to the aforementioned class of equations. Our analysis sheds light on the intricate interplay between the iterative steps of the method and the underlying nonlinear dynamics, providing valuable insights into the behavior of the solution process. Through this investigation, we find noise terms in the context of inhomogeneous equations. We reveal that the presence of noise is intrinsically linked to the inherent heterogeneity of the equations, and its impact on convergence behavior is systematically elucidated. To validate the robustness and accuracy of the proposed method, we present a series of numerical results. These results not only underscore the reliability of the method in producing accurate solutions but also highlight its potential to overcome computational challenges associated with nonlinear PDEs. In summary, our study contributes to the broader picture of nonlinear PDE solvers by showing the potential of the Adomian decomposition method, especially in models involving noise terms and inhomogeneous equations. The efficiency of this method is illustrated by investigating the convergence results for this equation. We show that the noise terms are conditional for nonhomogeneous equations, and the numerical results demonstrate the reliability and accuracy of the ADM. Keywords: the Adomian method, noise terms, iterative method. https://doi.org/10.55463/issn.1674-2974.50.7.22

This study aims to present the design and implementation of a low-cost prosthesis prototype that covers the basic movement needs, built using 3D printing. The development of this prototype, in particular, focuses on low-income people, especially children with some amputation or malformation in their upper extremities. First, an electromyograph was developed to capture the electrical signals produced by the muscles of the body as they move and to amplify them for further processing by an Arduino development board that works as the central system of the prosthesis. With the electromyograph designed and built, we proceeded to design the mechanical part of the prosthesis in SolidWorks software and prototype it in a 3D printer. The first tests conducted with the finished prototype yielded various data regarding the treatment of the signals used to make modifications and reach the necessary performance. With this work, it is possible to develop a basic prosthesis prototype that helps low-income children who are victims of amputations or malformations to meet their basic motor needs and demonstrate once again that the implementation of engineering provides solutions to local and global problems. Keywords: Electromyograph, Signals, 3D Printer, Hand Prosthesis, Electrodes DOI： https://doi.org/10.35741/issn.0258-2724.58.3.20

This research aims to present the characterization of a fuel cell that generates HHO hydroxy gas; for this we will use the following methodology that conforms to the scientific method. Initially, we propose to determine the HHO gas generation based on the change in temperature and current of the cell through the following scheme: first, a fuel cell will be designed to generate the hydroxy gas; later, a PWM controller will be designed to control the current to measure the temperature. A thermal camera will be used to extract the temperature curve. The experimentation will allow us to demonstrate the direct relationship between the production of HHO gas and the current, and affectation that occurs according to the amount of electrolyte gas (NaOH). We will also show how a controller that regulates the production of HHO gas was designed and built at a very low cost in an innovative way, verifying with this work that it is possible to develop a basic control system to characterize a fuel cell by varying the current and temperature and demonstrate once again that the implementation of engineering can solve local and global problems. Keywords: HHO, Fuel Cells, Hydroxy Gas, Hydrogen, Characterization DOI： https://doi.org/10.35741/issn.0258-2724.58.3.23

Las aplicaciones de procesamiento de datos tradicionales son inadecuadas para el manejo de una cantidad elevada de datos. Para lograr una eficiente manipulación y extracción de características o muestras que representa la información, es necesario conocer aspectos como la captación y tratamiento de datos. En este documento se depuró una base de datos correspondiente al comportamiento del consumo de energía eléctrica en una carga residencial. La depuración y análisis estadístico de las muestras se realizó por medio del análisis de componentes principales. El entrenamiento del conjunto de datos de menor dimensión a la base de datos original se hizo por medio de las técnicas de máquina de soporte vectorial y redes neuronales artificiales. Finalmente, se presenta una propuesta de análisis de muestras que se encuentren o no dentro de los límites de operación por medio de la actualización de patrones dinámicos para la validación no supervisada de nuevas muestras.

Traditional data processing applications are unsuitable for handling large amounts of data. To achieve an efficient manipulation and extraction of characteristics or samples that the information represents, it is necessary to know aspects such as data collection and treatment. In this document, a database corresponding to the behavior of electrical energy consumption in a residential load was refined. The debugging and statistical analysis of the samples were carried out using the principal component analysis. The training of the smallest data set to the original database was made using vector support machine techniques and artificial neural networks. Finally, a proposal is presented for the analysis of samples that are within the operating limits or not using updating dynamic patterns for the unsupervised validation of new samples.

In the next manuscript we will show an interesting physical application of the technique of optimal control over a direct current, more exactly on a direct current motor. For this, the mathematical support or scaffolding that allows to establish the model of the problem will be presented in the development of the document, which contains a basic structure supported in a general dynamic system (linear or non-linear) and an objective function that will depend on the system. Although in essence the optimal control problems correspond to infinite spaces, the finite-dimensional case will be analyzed initially and then made an extension to the case of a quadratic linear regulator for an interval of infinite duration. The results of the implementation of this optimal control technique on a direct current motor will be analyzed by means of Bole diagrams that will represent the frequency response of the system and a follow-up diagram of set points and rejection of disturbances.

This document analyses the distribution of the electric potential due to two electrodes that excite a membrane. The solution obtained numerically was approximated by means of the finite element method. The qualitative analysis of the results allows to know the intensity of the electric potential along the membrane in such a way that said electrodes that excite the membrane can be strategically located for academic and clinical purposes. Additionally, in a two- dimensional domain that represents the geometry of a membrane, the finite element method was executed, which allowed the behavior of the potential to be analyzed for an electric pulse at any point in the membrane. The above was generated by two electrodes.

Este documento contiene una comparación detallada entre los métodos iniciales de solución numérica de ecuaciones diferenciales ordinarias, que parten del enfoque del método de Euler, que se basa en la solución de ecuaciones diferenciales por el método de Taylor, los otros dos métodos a comparar son mejoras de este. método, el de Euler, y son el método de Heun, y el método del punto medio. Se observará a partir de la solución de ecuaciones diferenciales de prueba su respectivo error con respecto a la solución analítica, obteniendo un índice de error dictado por el error cuadrático medio EMC. A través de este documento conoceremos la mejor aproximación numérica a la solución analítica de los diferentes PVI (problemas de valor inicial) planteados, fijando también un patrón de solución para determinados problemas, es decir, se estipulará el método adecuado para cada tipo de problema.

In recent years a new physics known as complexity has emerged, whose fundamental structure is based on the general theory of systems or the so-called mathematical biology. There, problems arise with a large number of variables on which decisions must be made, and it is important to have selection techniques that are robust and efficient, In this research work, a couple of techniques are presented that will serve the aforementioned purpose; these are: the Lasso regularized linear regression technique and the Ridge regression technique, the latter with the slight difference in the penalty, since it makes use of a different rule than the Euclidean one, which implies very different consequences. One of these techniques was applied in a clinical problem and corresponds to the study of patients with diabetes. With this objective, the algorithm of descent of coordinates was implemented for the type of regularization loop and the analytical solution of regression of ridges. In addition, Kernels was used for the implementation of the regularized vector machine. The above algorithms were compared with the Ridge regularization and the Euclidean regularized vector machine. These types of techniques are common in physics, and it is vitally important to be able to implement other types of rules for a problem in which the choice of them can be simplified.

This paper proposes a desing of a boost-type DC-DC converter, based on a state space model and calculation of a controller with multiplicative unstructured uncertainty. Performance of the converter at low frequencies was analyzed; as well, weight of the weighting function was adjusted, to reduce noise at certain frequencies. Results of system simulation, in open loop and closed loop, demostrate that the designed controller allows modifying cutoff frequency, through the variation of weighting functions. It is concluded that this technique optimizes dynamics behavior of the system.

En este trabajo se presenta la formulación de un convertidor DC-DC tipo elevador (boost), a partir de un modelo de espacio de estados y el cálculo de un controlador con incertidumbre no estructurada multiplicativa. Se analizó el rendimiento del convertidor a bajas frecuencias, ajustando el peso de la función de ponderación, con el fin de reducir el ruido a determinadas frecuencias. Los resultados de la simulación del sistema, en lazo abierto y lazo cerrado, muestran que el controlador diseñado permite modificar la frecuencia de corte, a través de la variación de las funciones de ponderación y de esta manera, mejorar los comportamientos dinámicos del sistema.

In the following manuscript we will show as a starting point a theoretical analysis of the gradient method, known as one of the first descent methods, and from this we will identify the strength of the conjugate gradient methods. Taking an objective function, we will determine the values that optimize it by means of different methods, indicating the differences of geometric type that these have. Different systems will be used, in order to serve as a test, obtaining their solution in each case and finding the speed at which they converge in accordance with the conjugate gradient methods proposed by Hestenes-Stiefel and Fletcher-Reeves.

espanolEn la actualidad el analisis numerico nos brinda poderosas herramientas para determinar la solucion de diversos problemas cuyo modelo matematico puede ser representado por un sistema de ecuaciones lineales, estas herramientas corresponden a un sinnumero de metodos directos e iterativos entre los que se encuentran el metodo de Carl Gustav Jakob Jacobi y el metodo de Doolittle y Crout los cuales analizamos y comparamos en este documento .Para ello exploraremos inicialmente los conceptos de condicionamiento del problema para determinar que tan estable es el sistema de donde se obtuvo el modelo , hasta llegar a la descomposicion de matrices LU propuestas en el metodo de Doolittle y Crout. Como resultado del analisis y comparacion en este documento dependiendo de lo que se busque al resolver un sistema de ecuaciones ya sea de tamano muy grande o lo suficiente pequeno para nuestra computadora, podemos optar por una aproximacion que traera un resultado a corto plazo con un error debido al punto de partida tal y como como se propone en el metodo del Jacobi o es posible llegar a un resultado directo implementando menor cantidad de iteraciones como se propone en el metodo de Doolittle y Crout. EnglishAt present, numerical analysis provides us with powerful tools to determine the solution of various problems whose mathematical model can be represented by a system of linear equations, these tools correspond to a number of direct and iterative methods, among which are Carl's method. Gustav Jakob Jacobi and the Doolittle and Crout method, which we analyze and compare in this document. To do this we will initially explore the concepts of conditioning the problem to determine how stable is the system from which the model was obtained, until we reach the decomposition of LU arrays proposed in the Doolittle and Crout method. As a result of the analysis and comparison in this document, depending on what is sought when solving a system of equations, either very large or small enough for our computer, we can choose an approximation that will bring a short-term result with an error. Due to the starting point as proposed in the Jacobi method, or it is possible to reach a direct result by implementing fewer iterations as proposed in the Doolittle and Crout metho

Conventional regulators or controllers are used regularly in control engineering, however, there are limitations to their use. In this document we develop the essential mathematical concepts and expressions in the study of adaptive control techniques. To do this, we will initially make a brief deduction of the equations that are identified in a linear regressor control system, and also for the case of the parameter identification algorithm. Next, we will apply this control technique in a non-linear state space system for a magnetic levitation system, allowing us to conclude, among other things, that this technique makes the control more robust.

Abstract The spatial distribution of an electrical potential in a cell membrane subjected to an electric field was numerically obtained using an equivalent electrical circuit where the spatial variables that depend on the geometry are combined and an electrical circuit that relates the dynamics in the time of said excitation in four branches that represent the middle. It was observed that the potential decreases linearly in the geometry of the membrane due to the characteristics of the medium (sodium, potassium). On the other hand, the finite element method was developed for a two-dimensional domain that represents the geometry of a membrane, in such a way that it is possible to qualitatively analyze the behavior of the potential at any point of the membrane for an electrical pulse (electrode).

One of the problems derived from the overcrowding of cities and industry is the location of optimal facilities, these types of problems suffer from the problem of dimensionality themselves. In the following article, the problem is formulated in a mathematical way and it is approached from a metaheuristic epistemology which is the only methodology for now to find local optimum, since these optimization problems are still open in the scientific literature because they are considered problems of nondeterministic polynomial time. The explored technique is that of genetic algorithms which uses the classical theory of evolution to formulate and solve optimization problems.

Abstract The surgical intervention called deep brain stimulation, is a stereotactic surgery that allows the control of some motor functions in the human body. For its execution it is necessary to make use of software engineering and an understanding of the operation and electrical activation in the brain. Based on the finite element method, this document will provide a solution to the Laplace differential equation that models the electrical potential generated during deep brain stimulation. To achieve this objective, we will initially present the theoretical foundations of the finite element method that include the approximation of Galerkin and the Max Milgram and Poincaré theorems; then assuming that the model of the human head is isotropic and uniform, the brain regions will be modeled with the characteristics of the environment (external skin of the skull, skull and brain) in such a way that the attenuation, direction and value of the potential a can be visualized as it changes material and moves along the surfaces that make up the human head model. The simulations obtained using the finite element method allowed determining which areas of the brain are involved by the interaction of potential sources, observing that bioelectric sources originate electrochemical activity in brain cells that are inactive in such a way that they generate controlled movements in the human body.

From the study of nonlinear dynamics, the study of chaotic dynamics in deterministic systems has been developed. If a system is deterministic, its behavior would be easy to predict. However, there are systems in which their behavior seems to be unpredictable due to the complexity of the dynamics of the system, which is reflected in an aperiodic behavior. This article presents the application of parameter exploration techniques for the study of aperiodic deterministic systems using time constraint estimation through the calculation of the Lyapunov exponent in order to estimate future system values. This technique is developed on a part of the energy matrix of the Colombian system, especially with hydroelectric production.

New technologies are constantly generated and advanced every day and, with them, the need to use them to maintain constant communication with different people located anywhere in the world is also increasing. But this exponential growth also generates a very important security problem, since any information that is found in a device connected to the communications network or that travels through it, can be susceptible to being detected or intercepted by an unauthorized person that can be used improperly, causing large economic losses to companies or personal problems. For this reason, it is essential to use some mechanism that helps to protect the information from a malicious attack, one of the most used is cryptography that is responsible for writing in secret, providing confidentiality to the information through an encryption method.