Papers by Victor Martinez Luaces
The Michaelis-Menten kinetics is a well-known model in biochemistry, widely used in enzyme-substr... more The Michaelis-Menten kinetics is a well-known model in biochemistry, widely used in enzyme-substrate interaction (Nelson and Cox, 2008). The same mathematical formula is called Langmuir equation (Masel, 1996) when is used to model generic adsorption of chemical species, and finally, an empirical equation of this form is applied to microbial growth and it is called J. Monod kinetics (Martinez-Luaces, 2008). A typical problem in chemistry and/or biochemistry consists in determining the parameters of these equations from experimental data. In order to solve this problem, several methods were proposed, Lineweaver-Burk, Hanes-Woolf, Hofstee, Scatchard and Cornish-Bowden-Eisenthal are the most important ones (Nelson and Cox, 2008). In this paper, all these methods are analysed and compared in terms of exactitude and precision. For this purpose, simulated data were generated and perturbed using Gaussian noise with different amplitudes. The same methodology was used in a previous work (Mart...
In this paper, applications and modelling problems for chemistry and or biochemistry courses are ... more In this paper, applications and modelling problems for chemistry and or biochemistry courses are analysed. They obtain better results than others, in order to motivate students of chemical careers towards mathematical problem solving, since these problems are specially tailored for their needs. A teaching experience, carried out during two decades is analysed and a particular example is exposed with further details. The results of this experience led us to several conclusions that are included in the last section of the article.
In the process of teaching and learning – as Ausubel (1968) mentioned – in order to achieve signi... more In the process of teaching and learning – as Ausubel (1968) mentioned – in order to achieve significant knowledge, the new knowledge must be related with the previous one and at the same time it should differ from it. Mathematical modelling gives the student an opportunity to acquire significant understanding. As Astolfi noted, in order to understand it is necessary to give up the previous knowledge. Finally, as Bachelard points out, this path to scientific learning is painful because it involves the loss of what is already known. On the other hand, these modelling activities help raise questions concerning the validity of the models, since they effectively interpret reality within certain limits and then, it is important to define the portion of reality where these models are applicable. According to Collins, Brown and Newman (1987), the teacher should show the students many problem-solving processes developed by experts and thus generate a path that can be withdrawn when the stude...
Problem solving and problem posing are both important topics in mathematics education. Since in m... more Problem solving and problem posing are both important topics in mathematics education. Since in many branches of science and technology, typical problems are posed in an inverse form, we will focus on inverse problems that require modeling skills in order to be solved, i.e., the so-called inverse modeling problems. In this article, we will analyze them from the view point of their potential for task enrichment. For this purpose, a research project was carried out, by using inverse modeling problems to develop prospective teacher`s task enrichment skills. The results of this experience, that took place in 2017, showed that only few participants were very creative, whereas many others posed trivial problems or simply imitated examples previously analyzed. After that, a new research essay was implemented during the first months of 2019, with the aim of avoiding – or at least attenuating – those difficulties observed in the previous field work. The new results showed some few similariti...
First order chemical reaction mechanisms are modelled through Ordinary Di erential Equations (O.D... more First order chemical reaction mechanisms are modelled through Ordinary Di erential Equations (O.D.E.) systems of the form: :X = AX , be- ing X the chemical species concentrations vector, :X its time derivative and A the associated system matrix. In previous papers, First Order Chemical Ki- netics Mechanisms (F.O.C.K.M.) involving two or three chemical species were considered and in all these cases, solutions show a weak stability (i.e., they are stable but not asymptotically). This fact implies that small errors due to mea- surements in the initial concentrations will remain bounded, but they do not tend to vanish as the reaction proceeds. In order to know if these results can be extended or not to other chemical mechanisms, a general result is obtained through an inverse modelling approach. For this purpose, theoretical mecha- nisms with and without nal products are proposed, and the corresponding F.O.C.K.M. matrices are studied. As a consequence of the particular structure of the ...
Differential equations and Laplace transform are widely used to solve problems concerned with mat... more Differential equations and Laplace transform are widely used to solve problems concerned with mathematical modelling and applications. These analytical tools appear regularly in chemical engineering courses, due to the usefulness in modelling chemical kinetics, mixing problems and reactors design, among other problems. The discussion in this paper will deal with non typical inverse problems and how they can be used in engineering courses. Recommendations will be drawn for undergraduate courses in differential equations for chemical engineering and other related careers.
The research found three different adsorbates E 1 , E 2 , and E 3 and measured the surface concen... more The research found three different adsorbates E 1 , E 2 , and E 3 and measured the surface concentrations by conventional electrochemical techniques. The initial objective of the group was to propose a mechanism with the closest fit to the experimental curves (Zinola et al., 1997). Nevertheless, as the research progressed, the focus shifted to explain, or try to explain the double inflexion that consistently appeared in the experimental curves of surface concentration versus time for one of the adsorbates (
Esta comunicacion expone el marco de un estudio sobre enriquecimiento de tareas escolares realiza... more Esta comunicacion expone el marco de un estudio sobre enriquecimiento de tareas escolares realizadas por futuros profesores y algunos de sus resultados. La experiencia que se presenta proviene del trabajo realizado con 74 profesores en formacion, matriculados en el Master en Profesorado de Ensenanza Secundaria, impartido por la Universidad de Granada en el curso 2016-2017. El estudio se centra en la reformulacion en modo inverso de unos problemas enunciados en modo directo por el grupo de docentes participantes. Las respuestas proporcionadas fueron estudiadas e interpretadas utilizando el Analisis Didactico, una metodologia de analisis basada en categorias didacticas. Se observa que los futuros profesores elaboran una amplia diversidad de formulaciones, pero muestran un dominio pobre de la reflexion didactica en lo que respecta al analisis de significados.
Matrix Theory - Applications and Theorems, Aug 29, 2018
In this chapter, mixing problems are considered since they always lead to linear ordinary differe... more In this chapter, mixing problems are considered since they always lead to linear ordinary differential equation (ODE) systems, and the corresponding associated matrices have different structures that deserve to be studied deeply. This structure depends on whether or not there is recirculation of fluids and if the system is open or closed, among other characteristics such as the number of tanks and their internal connections. Several statements about the matrix eigenvalues are analyzed for different structures, and also some questions and conjectures are posed. Finally, qualitative remarks about the differential equation system solutions and their stability or asymptotical stability are included.
Recent Trends in Computational Science and Engineering, May 30, 2018
A well-known technique, electrochemical noise analysis (ENA), measures the potential fluctuations... more A well-known technique, electrochemical noise analysis (ENA), measures the potential fluctuations produced by kinetic variations along the electrochemical corrosion process. This practice requires the application of diverse signal processing methods. Therefore, in order to propose and evaluate new methodologies, it is absolutely necessary to simulate signals by computer data generation using different algorithms. In the first approach, data were simulated by superimposing Gaussian noise to nontrivial trend lines. Then, several methods were assessed by using this set of computer-simulated data. These results indicate that a new methodology based on medians of moving intervals and cubic splines interpolation show the best performance. Nevertheless, relative errors are acceptable for the trend but not for noise. In the second approach, we used artificial intelligence for trend removal, combining an interval signal processing with backpropagation neural networks. Finally, a non-Gaussian noise function that simulates non-stationary pits was proposed and all detrending methods were re-evaluated, resulting that when increasing difference between trend and noise, the accuracy of the artificial neural networks (ANNs) was reduced. In addition, when polynomial fitting, moving average removal (MAR) and moving median removal (MMR) were evaluated, MMR yielded best results, though it is not a definitive solution.
ICME-13 Monographs, 2017
This paper describes author's experiences in both teaching with and research on counterexamples, ... more This paper describes author's experiences in both teaching with and research on counterexamples, puzzles and provocations in calculus as a pedagogical strategy. The results of several experimental studies with students and teachers/lecturers of calculus are presented and discussed. Examples of incorrect statements (to be disproved by counterexamples), selected puzzles and provocations offered to the participants of the studies are provided. The overwhelming statistics from those studies showed that both groups-students and lecturers-were very positive about using counterexamples, puzzles and provocations in teaching and learning of calculus. They found the strategy to be effective in the sense that it could help to: deepen conceptual understanding; reduce or eliminate common misconceptions; advance one's mathematical thinking beyond the merely procedural or algorithmic; enhance critical thinking skills; expand a student's 'example space' of functions with interesting properties; make teaching/learning more active and creative.
Mathematical Sciences and Applications E-Notes, 2015
The most simple unimolecular first order chemical reaction mechanism that involves two species, c... more The most simple unimolecular first order chemical reaction mechanism that involves two species, can be exemplified by the Mutarotation of Glucose [1]. The corresponding mathematical model is an O.D.E. linear system which solutions are stable, but not asymptotically [2]. When three chemical compounds are considered, the mechanism can vary from a simple two reactions sequence to a complicated one as the adsorption of Carbon Dioxide (CO 2) over Platinum (P t) surfaces [2]. Although in these examples the mechanisms are very different, in both cases the O.D.E. system has two negative eigenvalues and the other one is zero. Once again, solutions show a weak stability which implies that small errors due to measurements in the initial concentrations will remain bounded, but they do not tend to vanish as the reaction proceeds. In this paper, a general result for reversible reactions is stated through an inverse modelling approach [3] [4], proposing theoretical mechanisms and showing algebraically that all the eigenvalues are negative, except one, which is zero. From this fact, the conclusions about the stability of the solutions are obtained and their consequences on the propagation of measurements errors are analysed.
International Journal of Mathematical Education in Science and Technology, 2019
Task enrichment is an important teacher competency that can be considered as a special case of pr... more Task enrichment is an important teacher competency that can be considered as a special case of problem posing. For that reason, the theoretical framework of this article includes an overview of this topic, complemented with the analysis of inverse problems. The field work of this research was carried out in master courses in the University of Granada, Spain, where a couple of modelling problems were proposed to prospective teachers, who were asked to reformulate them in an inverse way to produce a richer version. The results are described, and the prospective teachers' strategies for problem posing and task enrichment are analysed, and also conclusions about this experience in teacher training courses are presented.
Theorizing STEM Education in the 21st Century, 2019
Problem solving is considered as one of the most important topics in STEM (science, technology, e... more Problem solving is considered as one of the most important topics in STEM (science, technology, engineering, and mathematics) education, and this is especially relevant when problems require modeling skills in order to be solved. Also, it should be noted that in many branches of science and technology, typical problems are posed in an inverse form. Then, combining both characteristics, the so-called inverse modeling problems deserve to be studied deeply, particularly in their potential for task enrichment. For those reasons, since 2016, a research project was carried out, by using inverse modeling problems to develop prospective teacher'staskenrichmentskills. The results of this experience that took place in 2017 showed nine different groups of proposals where only few participants were very creative, whereas many others posed trivial problems or simply imitated examples analyzed previously. After that, a new research design was proposed during 2018 and implemented during the first months of 2019, with the aim of avoiding-or at least attenuating-those difficulties observed in the previous fieldwork. The new results showed interesting differences and few similarities when compared with the other experience. In this chapter, both experiences are analyzed, and lastly, findings and final conclusions are reported.
Success in Higher Education, 2016
I report on the development of a research group that evolved out of a curriculum initiative, whic... more I report on the development of a research group that evolved out of a curriculum initiative, which had the aim to increase the applied components in science and engineering courses. The curriculum development itself did not continue due to a change in economic circumstances in Uruguay; however, a successful research group emerged from the students who had been through the curriculum renewal, the Electrochemistry Interdisciplinary Research Group. Successful research outcomes are leading to more students taking courses through this research group.
La matemática es un idioma como varios autores han mencionado en diferentes trabajos científicos.... more La matemática es un idioma como varios autores han mencionado en diferentes trabajos científicos. En este artículo se analizan y comparan cuatro componentes del lenguaje y la matemática. Por otra parte, la matemática no es exactamente como otros idiomas. De hecho, la matemática parece ser más precisa y más limitada que los otros idiomas y esto tiene varias consecuencias en lo que se refiere a la enseñanza de dicha disciplina. En este artículo comentaremos nuestras experiencias, desarrolladas en Argentina, Alemania y Uruguay, teniendo en cuenta este enfoque de la enseñanza de la matemática como una extensión de la enseñanza de la lengua, y veremos cómo este enfoque ayudó a los estudiantes de los cursos de Cálculo, en diferentes formas. Palabras clave Matemática, idiomas, resolución de problemas, experiencias de aula, cursos de Cálculo.
Despite the many reports highlighting the importance of mathematics in modern societies, concerns... more Despite the many reports highlighting the importance of mathematics in modern societies, concerns have been raised repeatedly about the need to raise the profile of mathematics education at all levels to serve the needs of research and development, to support the industry and financial sectors, and to inform policy development. This paper presents the current status of undergraduate mathematics education in the countries represented consistently in the DELTA series of conferences, and sampling five continents. Using a survey methodology, this paper summarizes their undergraduate programmes and their outcomes. It discusses what a mathematics graduate looks like, the knowledge base and set of skills they are likely to have, the different pathways into mathematics programmes and their pathways into employment, as well as the initiatives taken in their countries to support mathematics.
International Journal of Corrosion, 2014
The potential distribution in tubes of a heat exchanger is simulated when applying cathodic polar... more The potential distribution in tubes of a heat exchanger is simulated when applying cathodic polarization to its extremes. The comparison of two methods to achieve this goal is presented: a numeric solution based on boundary elements carried out with the commercial software Beasy-GID and a semianalytical method developed by the authors. The mathematical model, the simplifications considered, and the problem solving are shown. Since both approaches use polarization curves as a boundary condition, experimental polarization curves (voltage versus current density) were determined in the laboratory under flow conditions and cylindrical cell geometry. The results obtained suggest the impossibility of extending the protection along the whole tube length; therefore, other protection methods are considered.
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Papers by Victor Martinez Luaces