Articles publicats (Matemàtica)

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Open Access
Empirical significance test of the goodness-of-fit for some pyramidal clustering procedures
(Institut d'Estadística de Catalunya, 1995) Capdevila Marqués, Carles; Arcas Pons, Antoni
Through a series of simulation tests by Monte Carlo methods, some aspects relating to the inference concerning pyramidal trees built by the maximum and minimum methods are considered. In this sense, the quantiles of the γ-Goodman-Kruskal statistic allow us to tabulate a significance test of the goodness-of-fit of a pyramidal clustering procedure. On the other side, the pyramidal method of maximum is observed to be clearly better (more efficient) than that of the minimum in terms of the expected value for the gamma statistic. Both for the maximum and minimum methods, a relation between the number of objets to classify and the gamma distribution id observed.
Open Access
Pirámides indexadas y disimilaridades piramidales
(Institut d'Estadística de Catalunya, 1995) Capdevila Marqués, Carles; Arcas Pons, Antoni
En este trabajo se pretende una formalización de las bases matemáticas sobre las que se amparan los modelos de clasificación y representación piramidal, estableciéndose para ello una relación entre los conceptos de pirámide indexada y disimilaridad piramidal. Asimismo se precisa el concepto de información redundante, contenida en una estructura piramidal, y se dan criterios objetivos para poder prescindir de ella sin que ello suponga una modificación de la estructura piramidal.
Open Access
Algunas propiedades de un algoritmo de clasificación piramidal
(Instituto Nacional de Estadística, 1995) Capdevila Marqués, Carles; Gil Estallo, Àngel J.; Arcas Pons, Antoni
En este trabajo se enuncia un Algoritmo de Clasificacián Ascendente Piramidal y se establecen algunas de sus propiedades, que ponen de manifiesto la mejora que éste supone respecto a otros algoritmos establecidos con anterioridad, en el sentido de producir pirámides indexadas en sentido estricto y sin problemas de inversión, lo cual facilita su aplicación en problemas reales. Asimismo se establecen algunas propiedades características de los algoritmos piramidales del mínimo y del máximo.
Open Access
Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
(Universitat Autònoma de Barcelona. Departament de Matemàtiques, 1996) Chavarriga Soriano, Javier; Giné, Jaume
In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.
Open Access
Behaviour of the current in a membrane-covered disc microelectrode under steady-state conditions
(The Royal Society of Chemistry, 1996) Galceran i Nogués, Josep; Salvador, José; Puy Llorens, Jaume; Cecilia Averós, Joan; Gavaghan, David J.
The inlaid disc electrode covered with a membrane can be modelled as a system with axial symmetry containing several parallel layers with different permeabilities. A recent solution of the steady state under diffusion limited conditions of an electroactive species in such a system is implemented with Mathematica. Computation of the theoretical current becomes an easy and fast procedure, capable of being implemented on any personal computer or workstation. The effects of the membrane permeability, the thickness of the membrane, the electrode radius and the electrolyte layer thickness on the current are analysed. We define an index of edge-effect contribution of each layer to the overall flux, providing their formulae together with the physical interpretation. For many sets of parameters, the edge-effect is responsible for an important contribution of the radial diffusion within the electrolyte and membrane. More accurate determination of the permeabilities of the different media is now possible experimentally, as the functional dependence of the current on the physical parameters is readily available for fitting procedures.
Restricted
Analytical solution for the steady-state diffusion towards an inlaid disc microelectrode in a multi-layered medium
(Elsevier Science, 1997) Galceran i Nogués, Josep; Salvador, José; Puy Llorens, Jaume; Cecilia Averós, Joan; Gavaghan, David J.
The rigorous analytical expression for the steady-state diffusion-limited current produced by an electroactive species diffusing towards an inlaid disc electrode through a multi-layered medium (such as the membrane covered sensor) is presented. This theoretical approach reformulates the problem in terms of a dual integral equation and takes full account of the edge effect that one-dimensional formulations cannot include. The solution is found by solving a linear system of equations where the entries of the matrix are integrals involving Bessel functions, and can be easily and quickly computed with standard software such as Mathematica. Comparison of this analytical solution (corresponding to the axisymmetric geometry) with previous models (linear, spherical and mixed) for the membrane-covered gas sensor allows us to demonstrate the restricted ranges of applicability of these previous models. Through a variety of approximations, we show that it is possible to obtain accurate estimates of the current (also valid for liquid samples) using very simple expressions, which in turn allows procedures such as the fast estimation of a medium permeability. The model can be easily extended to any number of parallel layers with a variety of boundary conditions in the interface or layer furthest away from the insulator plane; thus some interesting limiting cases are analysed (such as the validity of ignoring a very thin layer next to the electrode or the unattainability of steady-state just by horizontal radial diffusion).
Open Access
The null divergence factor
(Universitat Autònoma de Barcelona. Departament de Matemàtiques, 1997) Chavarriga Soriano, Javier; Giacomini, Héctor; Giné, Jaume
Let (P, Q) be a C 1 vector field defined in a open subset U ⊂ R2 . We call a null divergence factor a C 1 solution V (x, y) of the equation P ∂V + Q ∂V = ∂P + ∂Q V . In previous works ∂x ∂y ∂x ∂y it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux method to generate integrable systems.
Open Access
Concepciones de los profesores sobre la enseñanza de las ecuaciones diferenciales a estudiantes de química y biología: estudio de casos
(Universitat Autònoma de Barcelona. Institut de Ciències de l'Educació, 1997) Moreno Moreno, Ma. del Mar; Azcárate, Carmen
Intending to quest about the conceptions math teachers hold about how to teach Differential Equations to chemistry and biology students, we have devised a research tool which allows us to derive relevant information. We use different means to collect the adequate data related to the qualitative research, targeting the exploration of what teachers «say they do» and what athey do and would like to do». The use of concept maps and a questionnaire, along with a recorded interview, has revealed itself as an accurate means for the appropriate analysis of data, as shown in the case study we hereby include.
Open Access
Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
(Universitat Autònoma de Barcelona. Departament de Matemàtiques, 1997) Chavarriga Soriano, Javier; Giné, Jaume
In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.
Open Access
A survey of isochronous centers
(Edicions de la Universitat de Lleida, 1999) Chavarriga Soriano, Javier; Sabatini, Marco
Open Access
Voltammetric currents for any ligand-to-metal concentration ratio in fully labile metal-macromolecular complexation. Easy computations, analytical properties of the currents and graphical method to estimate the stability constant
(Elsevier, 1999) Galceran i Nogués, Josep; Cecilia Averós, Joan; Salvador, José; Monné Esquerda, Josep; Torrent, Marià; Companys Ferran, Encarnació; Puy Llorens, Jaume; Garcés, Josep Lluís; Mas i Pujadas, Francesc
In order to enable a wider use of voltammetric methods in speciation analysis, it is convenient not to be restricted by ligand excess conditions. This work assumes labile ideal complexation of a metal ion by a ligand, planar electrode, no electrodic adsorption and equal diffusion coefficients for the complex and the ligand, but very different from the metal ion. It is shown that the system of non-linear equations describing the diffusion of the species in a potentiostatic experiment for any ligand to metal ratio can be reduced to only one ordinary differential equation by means of a change of variable. Standard numerical methods can then be used in the computation of the solution with a great saving of computational time and resources in comparison with other existing methods. Some properties of the currents are also proved: (i) Cottrellian behaviour for any current in normal pulse polarography (NPP) and for limiting currents in reverse pulse polarography (RPP), (ii) the dependence of the normalised limiting current (φ) on just three parameters, and (iii) the equality of limiting NPP and RPP currents. The normalised current for high stability constant values depends on just two parameters, one of which is the ratio of total metal/total ligand concentrations, and can be found from an implicit algebraic equation. A new representation for the normalised limiting currents is suggested: the iso-φ diagram, which for each ratio of diffusion coefficients, ε, describes the currents for any stability constant in a unique drawing. A new graphical procedure arising from this diagram is suggested and then applied to data corresponding to Zn/poly(methacrylic) acid at pH 6 and fixed ionic strength.
Open Access
Voltammetric lability of metal complexes at spherical micorelectrodes with various radii
(Elsevier, 2001) Galceran i Nogués, Josep; Puy Llorens, Jaume; Salvador, José; Cecilia Averós, Joan; Leeuwen, Herman P. van
The size of a microelectrode can have a dramatic impact on the relative importance of the diffusional and kinetic contributions to the voltammetric current of an electroactive metal ion in a complexing medium. Decreasing the radius enhances the diffusional contribution and, as a consequence, the complex system tends to move away from labile behaviour (where an equilibrium relationship holds). Therefore, sufficiently small microelectrodes (either or not combined with short measuring times) should be able to sense free metal concentrations directly for not too fast association/dissociation kinetics. The particular case of steady-state spherical (or hemispherical) diffusion under ligand excess (pseudo-first-order kinetics) is solved analytically. The ensuing lability criterion is shown to be in accordance with a geometrical derivation based on an analysis of the random walk of the free metal ions produced by the dissociation of the complex. It is shown that, for a generated metal ion, the probability of reaching the microelectrode surface can be quite different from the planar case. Alternatively, the classical reaction layer concept can be used in the derivation of the lability criterion for spherical geometry as is shown in this work. All treatments show quantitatively how the lability of metal complexes is reduced with decreasing dimension of microelectrode.
Open Access
La enseñanza de estrategias de resolución de problemas matemáticos en la ESO: un ejemplo concreto
(Universitat Autònoma de Barcelona. Institut de Ciències de l'Educació, 2001) Pifarré Turmo, Manoli; Sanuy Burgués, Jaume
Within this article is included a description and justification of a didactical sequence to improve the learning of problem solving strategies of Secondary Education students. The design of the didactical sequence is guided by four principles: a) to context the activities and problems to solve in students’ every day practices; b) to use teaching methods that show the problem solving processes; c) to design didactical materials in order to guide strategies such as selection, organisation and control; d) to facilitate the co-operative learning of problem solving strategies.
Open Access
Evaluation of the Koutecký-Koryta approximation for voltammetric currents generated by metal complex systems with various labilities
(Elsevier, 2002) Leeuwen, Herman P. van; Puy Llorens, Jaume; Galceran i Nogués, Josep; Cecilia Averós, Joan
The voltammetric response of metal complex systems with various labilities is analyzed by rigorous numerical simulation with the Finite Element Method of the time-dependent concentration profiles of the different species. The ensuing exact fluxes and the corresponding currents are compared to those derived from the Koutecký
Koryta (KK) approximation which assumes a discontinuous transition in the concentration profiles from non-labile to labile behavior. The results indicate a relatively far-reaching correctness of the KK approximation in the complete kinetic range from non-labile to labile complexes, as long as the kinetic flux is computed from the effective concentration of the complex in the reaction layer. Some approximate analytical expressions for this concentration are provided. The KK approximation is shown to be applicable for any metal-to-ligand ratio, provided that the thickness of the reaction layer is expressed in terms of the ligand concentration at the electrode surface.
Open Access
Análisis de las actitudes y conocimientos estadísticos elementales en la formación del profesorado
(Sociedad Andaluza de Educación Matemática "Thales", 2002) Estrada Roca, M. Asunción
Open Access
Concepciones y creencias de los profesores universitarios de matemáticas acerca de la enseñanza de las ecuaciones diferenciales
(Universitat Autònoma de Barcelona. Institut de Ciències de l'Educació, 2003) Moreno Moreno, Ma. del Mar; Azcárate, Carmen
La investigación que aquí presentamos es una aproximación a las concepciones y creencias de los profesores universitarios de matemáticas acerca de la enseñanza de las ecuaciones diferenciales en estudios científico-experimentales. A parte de los intentos por caracterizar a cada profesor en términos de sus concepciones y creencias, y de establecer el nivel de coherencia y consistencia de éstas, a partir de los resultados del análisis se explica la persistencia de la utilización de métodos tradicionales de enseñanza. Las diferencias y similitudes entre las concepciones y creencias de cada profesor, y el nivel de coherencia demostrado nos han permitido establecer tres grupos de profesores, a los que hemos denominado I, II y III.
Open Access
Lability and mobility effects on mixtures of ligands under steady-state conditions
(Royal Society of Chemistry, 2003) Galceran i Nogués, Josep; Puy Llorens, Jaume; Salvador, José; Cecilia Averós, Joan; Mas i Pujadas, Francesc; Garcés, Josep Lluís
Analytical solutions for the steady-state flux arriving at an active surface from a mixture (in which one active species reacts with non-active ligands in the medium) can be helpful in a variety of problems: voltammetric techniques, heterogeneous processes in reactors, toxic or nutrient uptake, techniques of diffusive gradients in thin films (DGT), etc. Under any geometry that sustains steady-state, a convenient combination of the reaction
diffusion equations leads to a simpler formulation of the problem for arbitrary diffusivities of the species and arbitrary rate constants of the first-order conversion between the active species and the non-active species. The resulting problem can be characterised in terms of a list of dimensionless parameters involving the kinetic and mobility properties of each species. A lability degree for each 1∶1 complex in terms of the surface concentrations leads to: (i) a lability criterion specific for each complex in the mixture and (ii) the assessment of the relative contribution of each complex to the resulting flux. Semi-infinite spherical diffusion (as in the Gel Integrated MicroElectrode, GIME, biouptake modelling of micro-organisms, etc.) is specifically considered and some consequences of its full analytical solutions are discussed.
Open Access
Rendimiento matemático en contextos bilingües: análisis de la incidencia de algunas variables del contexto socio-educativo
(Universidad de Murcia. Servicio de Publicaciones, 2003) Pifarré Turmo, Manoli; Sanuy Burgués, Jaume; Huguet, Àngel; Vendrell Serés, Mª Concepció
El trabajo que se presenta en este artículo se sitúa en el contexto bilingüe de la provincia de Lleida en la que coexisten dos lenguas en contacto, el catalán y el castellano, si bien existe un predominio de uso familiar y escolar de la primera de ellas. En este contexto, nuestro estudio analiza cómo influyen en el rendimiento en matemáticas las variables del contexto educativo de condición lingüística familiar y situación socio-profesional de la familia, así como las variables individuales de conciente intelectual y autoconcepto matemático. Los resultados globales muestran, en primer lugar, la importancia del lenguaje como instrumento mediador de la enseñanza-aprendizaje de contenidos matemáticos, ya que el rendimiento de los alumnos en esta área curricular está en función del dominio y el uso de la lengua vehicular de la enseñanza —el catalán—. En segundo lugar, se constata una correlación significativa entre el rendimiento matemático y las variables individuales de cociente intelectual y el autoconcepto sobre el propio rendimiento matemático.
Open Access
Actitudes hacia la estadística y su evaluación
(2003) Estrada Roca, M. Asunción
En este trabajo analizamos la problemática de la evaluación de las actitudes de los profesores hacía la Estadística. Es ésta una materia de reciente incorporación al curriculum de Educación Primaría y los profesores que deben impartirla necesitan conocer las actitudes de sus alumnos antes de iniciar cualquier proceso educativo. Analizamos la naturaleza de las actitudes, sus componentes y su importancia en los procesos de enseñanza/aprendizaje de la Estadística, vinculándola con la formación de profesores. Finalizaremos el estudio con una breve revisión de las diferentes escalas de evaluación existentes en la literatura internacional
Open Access
AGNES: a new electroanalytical technique for measuring free metal ion concentration
(Elsevier, 2004) Galceran i Nogués, Josep; Companys Ferran, Encarnació; Puy Llorens, Jaume; Cecilia Averós, Joan; Garcés, Josep Lluís
AGNES (absence of gradients and Nernstian equilibrium stripping) is a stripping technique consisting of two conceptual steps: (i) application of a potential program (e.g. a step at a fixed potential) generating a known concentration gain between the outer and inner concentrations of the metal at the mercury electrode surface together with null gradients of the concentration profiles (inside and outside the mercury electrode) and (ii) determination of the concentration of reduced metal inside the amalgam in a stripping step. In the present implementation, the stripping step under diffusion limited conditions leads to a measured current just proportional to the free metal ion concentration. In this paper we present the basic principles of the technique, analytical expressions for a simplified model of its voltammetric implementation and a numerical study for a more refined model together with preliminary experimental results in the Cd(II)/nitrilotriacetic acid system showing how this technique can be used as an alternative to other techniques (such as ion selective electrodes) in order to determine free metal activities or concentrations in the presence of complex mixtures avoiding complications such as electrodic adsorption or complexation kinetics.