Search

[EN] n this work, doubly stochastic combined matrices are studied. The combined matrix is known as Relative Gain Array in control the- ory. In particular, the characterization of all matrices such that their combined matrix is doubly stochastic is studied for real matrices of order 3. In addition, we give necessary and sufficient conditions so that three positive real numbers are the diagonal entries of a doubly stochastic matrix.

[ES] Actualmente existe una clara concienciación de la población por la sostenibilidad, el cuidado del medio ambiente y el bienestar animal. Pero, además los consumidores exigen alimentos seguros lo que implica a toda la cadena productiva empezando por la producción primaria. Un adecuado control de las enfermedades transmisibles a este nivel es uno de los pilares fundamentales de la seguridad alimentaria junto con el control en el momento del sacrificio, procesado y distribución. En esta tesis se plantea la utilización de herramientas matemáticas que permitan optimizar el uso de las medidas de bioseguridad, de implantación general en granjas de aves, como son la vacunación, la limpieza y desinfección, y la detección y eliminación de animales infectados. Esto con la fi nalidad de lograr una producción libre de infección y por lo tanto evitar el sacrificio temprano de los animales. De esta forma, se puede contribuir a la sostenibilidad de las granjas. Además, de garantizar la inocuidad de los alimentos a nivel de la producción primaria. Así se ha estudiado el comportamiento de un modelo matemático estructurado que incorpora la contaminación del medio ambiente como un modo indirecto de transmisión de la enfermedad, centrándose en el análisis de un brote de Salmonella en una granja de pollos. Las variables consideradas han sido: individuos susceptibles e infectados y la cantidad de bacterias acumuladas en el recinto (sistema (SIB), y se considera la reposición de los individuos muertos de forma que el tamaño de la población es el mismo en cualquier etapa. El sistema se considera dinámico y no lineal, en tiempo discreto y por ello su modelización se basa en ecuaciones en diferencias. Se ha analizado el comportamiento del sistema alrededor de los puntos de equilibrio a) libre de enfermedad y b) endémico. Tras el análisis del proceso se ha obtenido el número reproductivo básico R0. Este número indica el comportamiento de la enfermedad, ya que si R0 es menor que la unidad, [CA] Actualment existeix una clara conscienciacio de la poblacio per la sostenibilitat, la cura del medi ambient i el benestar animal. Pero, a mes els consumidors exigeixen aliments segurs el que implica a tota la cadena productiva comencant per la produccio primaria. Un adequat control de les malalties transmissibles a aquest nivell es un dels pilars fonamentals de la seguretat alimentaria juntament amb el control en el moment del sacri ci, processament i distribucio. En aquesta tesi es planteja la utilitzacio d'eines matematiques que permeten optimitzar l'us de les mesures de bioseguretat, d'implantacio general en granges d'ocells, com son la vacunacio, la neteja i desinfeccio, i la deteccio i eliminaci o d'animals infectats. Aixo amb la nalitat d'aconseguir una produccio lliure d'infeccio i per tant evitar el sacri ci primerenc dels animals. D'aquesta manera, es pot contribuir a la sostenibilitat de les granges. A mes, de garantir la innocu tat dels aliments a nivell de la produccio primaria. Aix, s'ha estudiat el comportament d'un model matematic estructurat que incorpora la contaminacio del medi ambient com una manera indirecta de transmissio de la malaltia, centrant-se en l'analisi d'un brot de Salmonella en una granja de pollastres. Les variables considerades han sigut: individus susceptibles i infectats i la quantitat de bacteris acumulats en el recinte (sistema SIB), i, a mes, es considera reposicio dels individus morts de manera que la grandaria de la poblacio es el mateix en qualsevol etapa. El sistema es considera dinamic i no lineal, en temps discret i per aixo la seua modelitzacio es basa en equacions en diferencies. S'ha analitzat el comportament del sistema al voltant dels punts d'equilibri a) lliure de malaltia i b) endemic. Despres de l'analisi del proces s'ha obtingut el numero reproductiu basic R0. Aquest numero indica el comportament de la malaltia, ja ix que si R0. es menor que la unitat, la malaltia tendeix a desapareixer pero en cas contrari, [EN] There is currently a clear awareness of the population for sustainability, care for the environment and animal welfare. But in addition, consumers demand safe food, which involves the entire production chain, starting with primary production. Adequate control of communicable diseases at this level is one of the fundamental pillars of food security along with control at the time of slaughter, processing and distribution. This thesis proposes the use of mathematical tools to optimize the use of biosafety measures, general implementation in bird farms, such as vaccination, cleaning and disinfection, and the detection and elimination of infected animals. This in order to achieve an infection free production and therefore avoid early slaughter of animals. In this way, it can contribute to the sustainability of farms. In addition, to ensure food safety at the level of primary production. Thus, the behavior of a structured mathematical model that incorporates environmental pollution as an indirect mode of disease transmission has been studied, focusing on the analysis of a Salmonella outbreak on a farm. chickens. The variables considered were susceptible and infected individuals and the amount of bacteria accumulated in the enclosure (SIB system), and, in addition, replacement of dead individuals is considered so that the size of the population is the same at any stage. The system is considered dynamic and nonlinear, in discrete time and therefore its modeling is based on equations in dierences. The behavior of the system around the equilibrium points a) free of disease and b) endemic has been analyzed. After the analysis of the process the basic reproductive number R0. was obtained. This number indicates the behavior of the disease, as if R0 is less than unity, the disease tends to disappear but otherwise the disease remains xiii endemic or may grow. The result obtained from the model indicates that R0 is less than one, if and only if, the population remains below a

[EN] Let A be an irreducible totally nonnegative matrix with rank r and principal rank p, that is, all minors of A are nonnegative, r is the size of the largest invertible square submatrix of A and p is the size of its largest invertible principal submatrix. A triple (n,r,p) is called realizable if there exists an n*n irreducible totally nonnegative matrix A with rank r and principal rank p. In this work we present a method to construct irreducible totally nonnegative matrices associated with a realizable triple (n,r,p) and with a prescribed Jordan canonical form corresponding to its zero eigenvalue.

[EN] Let A is an element of R-nxn be a totally nonpositive matrix (t.n.p.) with rank r and principal rank p, that is, every minor of A is nonpositive and p is the size of the largest invertible principal submatrix of A. We introduce that a triple (n, r, p) will be called negatively realizable if there exists a t.n.p. matrix A of order n and such that its rank is r and its principal rank is p. In this work we extend the results obtained for irreducible totally nonnegative matrices given in Canto and Urbano (Linear Algebra Appl 551:125-146. https://doi.org/10.1016/j.laa.2018.03.045, 2018) to t.n.p. matrices. For that, we consider the sequence of the first p-indices of A and study the linear dependence relations between their rows and columns. These relations allow us to construct t.n.p. matrices associated with a triple (n, r, p) negatively realizable and a specific sequence of the first p-indices.

[EN] Let A¿Rn×n be an irreducible totally nonnegative matrix (ITN), that is, A is irreducible with all its minors nonnegative. A triple (n,r,p) is called realizable if there exists an ITN matrix A¿Rn×n with rank(A)=r and p-rank(A)=p (recall that p-rank(A) is the size of the largest invertible principal submatrix of A). Each ITN matrix associated with a realizable triple (n,r,p) has positive and distinct eigenvalues, and for the zero eigenvalue it is verified that n¿r and n¿p are the geometric and the algebraic multiplicity, respectively. Moreover, since rank(A)=r, has n¿r zero Jordan blocks whose sizes are given by the Segre characteristic, S= (s1, s2,.. . , s_n-r ), with s_i¿ p, i = 1, 2, . . . , n¿r. We know the number of zero Jordan canonical forms of ITN matrices associated with a realizable triple (n,r,p) and all these zero Jordan canonical forms. The following important question that we present in this talk deals with how to construct an ITN matrix associated with (n,r,p) and exactly with one of these Segre characteristic S corresponding to the zero eigenvalue.

[EN] Let be an irreducible totally non-negative matrix with rank r and principal rank p, that is, every minor of A is non-negative and p is the size of the largest invertible principal submatrix of A. Using Number Theory, we calculate the number of Jordan canonical forms of irreducible totally non-negative matrices associated with a realizable triple . Moreover, by using full rank factorizations of A and applying the Flanders theorem we obtain all these Jordan canonical forms. Finally, some algorithms associated with these results are given

[EN] In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered.A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm.

[ES] En este trabajo presentamos las competencias matemáticas reflejadas en el Programa Internacional de Evaluación de Estudiantes (PISA) de la Organización para la Cooperación y Desarrollo Económico (OCDE). El objetivo principal de este programa es evaluar los sistemas de educación de todo el mundo con el fin de proporcionar información a los países, que les permita tomar decisiones para mejorar los niveles educativos y para preparar a los jóvenes para vivir en la sociedad actual. Por otra parte, la Universitat Politècnica de València (UPV) ha puesto en marcha un programa para que sus estudiantes adquieran unas competencias transversales mientras desarrollan sus estudios en la Universidad y su objetivo es preparar a los estudiantes para el mundo laboral. Los estudiantes que empiezan sus estudios de grado en la UPV tienen asignaturas de formación básica que incluyen la materia Matemáticas. Por ello, pretendemos relacionar las competencias matemáticas adquiridas en los sistemas educativos anteriores, con las competencias transversales de la UPV aplicadas a la materia Matemáticas, con el fin de conocer la similitud entre ambas y su acercamiento para facilitar la adquisición por parte de los alumnos a lo largo de su formación académica, [EN] In this paper we present the mathematical competences reflected in the Programme for International Student Assessment (PISA) of the Organization for Economic Cooperation and Development (OECD). The main objective of this program is to evaluate education systems worldwide in order to give information to the countries that allows them to make decisions to improve educational levels and to prepare young people to live in today's society. On the other hand, the Universitat Politècnica de València (UPV) has introduced a program for students to develop transversal competences while they are studying at the University, and its objective is to prepare students for the world work. Students who start their degree studies at the UPV have basic subjects that include Mathematics. For this reason we want to relate the mathematical competences acquired in the previous educational systems to the transversal competences of the UPV applied to Mathematics, in order to know the similarity between both and their approach to facilitate the acquisition by the students through their academic formation

[EN] We analyze the evolution of an infectious disease by combining different groups of a population when the route of transmission is via encounters with free-living virulent organisms that can survive for a long time outside the individual. This study involves matrix analysis of lower triangular block matrices and some of their spectral properties. We propose an N-periodic control strategy in order to stabilize the disease around the disease-free equilibrium point.

[EN] In this paper, an age-structured epidemiological process is considered. The disease model is based on a SIR model with unknown parameters. We addressed two important issues to analyzing the model and its parameters. One issue is concerned with the theoretical existence of unique solution, the identifiability problem. The second issue is how to estimate the parameters in the model. We propose an iterative algorithm to study the identifiability of the system and a method to estimate the parameters which are identifiable. A least squares approach based on a finite set of observations helps us to estimate the initial values of the parameters. Finally, we test the proposed algorithms.

[ES] Diseño de una página web interactiva con contenidos matemáticos en las que el profesor dado de alta puede crear nuevos contenidos teóricos y nuevas preguntas con sus respuestas correctas, con el fin de reforzar el aprendizaje matemático del alumno. Por otra parte el alumno tendrá acceso a una web en la que dispondrá de un resumen del tema propuesto, dispuesto de manera afable, podrá contestar los distintos ejercicios interactivos y dispondrá de un examen de preguntas aleatorias que le ayudará a saber su nivel de conocimiento respecto al tema propuesto. Se trata de una página web que ayuda al alumno a recordar conocimientos y a afianzarlos mediante práctica y que facilita la labor del profesor ya que refuerza los contenidos dados por este., [EN] Design of an interactive website with mathematical content. In this webpage the teacher creates theoretical content and a lot of questions with their answers. Students will have access to website. In this page they will can read theoretical concepts in a nice environment, they will can answer different interactive exercises and they will can do a test with random questions. With this, the student will know their level of knowledge on the proposed topic. This is a website that helps students to remember different mathematic topics and helps the teacher's work because it reinforces the contents given by him.

[EN] In this paper we study the stability property of positive linear continuous-time systems. This property is useful to study the asymptotic behavior of a dynamical system and specifically, in positive systems. Stabilization of linear systems using feedbacks has been deeply studied during the last decades. Motivated by some results, in this paper we find conditions on the system such that the eigenvalues of the closed loop system are in the open left half plane of the complex plane C. We do this by applying a Brauer s theorem.

This paper studies some problems related to the stability and the spectral radius of a finite set of matrices. A seasonal epidemic model is given to illustrate the use of the obtained results. In this example, the relationship between the obtained results and the stability of a discrete time periodic linear system is obtained.

[EN] We propose a mathematical model for the indirect transmission via a contaminated environment by a disease agent and we analyze the possibility that the initial infection can spread in the population. We have used the significance of the basic reproduction number, since the disease free state is either stable or unstable depending on its value, to obtain an explicit expression for $ R_0$. This expression is found to give threshold conditions for the stability of the disease- free equilibrium or the existence of an endemic equilibrium in a population.

[EN] In this paper, we address our study to analyze diseases whose transmission occurs through a contaminated environment. Moreover, the individuals are organized in compartments by age range. This epidemiological process with indirect transmission of the disease has a mathematical representation by means of a nonlinear discrete-time invariant system. A strategy to act when the system is unstable is proposed. As a consequence of it, the new system is N-periodic and its stability is given by the monodromy matrix of the system. The above matrix analysis is applied to establish some conditions over the number of steps that we can be without action and being the epidemiological process asymptotically stable.

L'objecte d'aquesta publicació és servir d'ajuda en matèria de matemàtiques als estudiants de primer curs d'escoles tècniques, especialment: en enginyeria informàtica, en administració i direcció d'empreses, en enginyeria elèctrica, en enginyeria química i en enginyeria mecànica. En aquest treball estudiarem l'àlgebra amb l'ajuda del paquet matemàtic MATLAB, concretament en aquest treball s'utilitzarà la versió Matlab 2013b per a Windows. En cada un dels capítols s'inclourà un breu comentari teòric (en cursiva) sobre la matèria que s'està tractant, així com les ordres i les funcions del programa necessàries per a plantejar els problemes i per a fer els càlculs que es proposen en cada moment. També apareixen exemples que serveixen per a familiaritzar l'usuari tant en l'ús de les ordres i funcions del programa, com dels mètodes i tècniques que s'estudien. A més a més, al final de cada capítol es proposen una sèrie de problemes amb la finalitat que l'usuari consolide els conceptes que s'han estudiat

L'objecte d'aquesta publicació és servir d'ajuda en matèria de matemàtiques als estudiants de primer curs d'escoles tècniques, especialment: en enginyeria informàtica, en administració i direcció d'empreses, en enginyeria elèctrica, en enginyeria química i en enginyeria mecànica. En aquest treball estudiarem l'àlgebra amb l'ajuda del paquet matemàtic MATLAB, concretament en aquest treball s'utilitzarà la versió Matlab 2013b per a Windows. En cada un dels capítols s'inclourà un breu comentari teòric (en cursiva) sobre la matèria que s'està tractant, així com les ordres i les funcions del programa necessàries per a plantejar els problemes i per a fer els càlculs que es proposen en cada moment. També apareixen exemples que serveixen per a familiaritzar l'usuari tant en l'ús de les ordres i funcions del programa, com dels mètodes i tècniques que s'estudien. A més a més, al final de cada capítol es proposen una sèrie de problemes amb la finalitat que l'usuari consolide els conceptes que s'han estudiat

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton-Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number Script capital R-0 and the stability of the model in the equilibrium is studied using Script capital R-0 in terms of the model parameters.

[EN] In this paper, the robust stability problem of structured linear systems is analyzed. In order to preserve the structure of the initial system, the structure of the admissible perturbations is characterized. Frobenius and infinity matrix norms are used to study the robust stability of the system affected by different admissible perturbations. Upper bounds for the perturbations are obtained, which guarantee that the perturbed system remains stable. Finally, some examples are shown to illustrate the results. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

This paper deals mainly with the structural properties of positive reachability and stability. We focus our attention on positive discrete-time systems and analyze the behavior of these systems subject to some perturbation. The effects of permutation and similar transformations are discussed in order to determine the structure of the perturbation such that the closed-loop system is positively reachable and stable. Finally, the results are applied to Leslie’s population model. The structure of the perturbation is shown such that the properties of the original system remain and an explicit expression of its set of positively reachable populations is given.

The stabilization problem of positive linear discrete-time systems (PLDS) by linear state feedback is considered. A method based on a Brauer s theorem is proposed for solving the problem. It allows us to modify some eigenvalues of the system without hanging the rest of them. The problem is studied for the single-input single-output (SISO) and for multi-input multioutput (MIMO) cases and sufficient conditions for stability and positivity of the closed-loop system are proved.The results are illustrated by numerical examples and the proposed method is used in stochastic systems.

In this paper seasonal epidemiological processes are considered and a strategy of periodic vaccination is proposed. The invariant formulations associated with an N-periodic system and the reproduction numbers associated with them are considered. A collection of measures to study the stability of the system is introduced. Moreover, the collection of s-basic reproduction number at time j help us to establish conditions on the periodic vaccination rates in the vaccination program. Finally, an SIR model is showed and a comparison between the results obtained using constant or periodic vaccination program is analyzed. (C) 2014 Elsevier Inc. All rights reserved.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10910-013-0149-4, The dynamics of the composition of chemical species in reacting systems can be characterized by a set of autonomous differential equations derived from mass conservation principles and some elementary hypothesis related to chemical reactivity. These sets of ordinary differential equations are basically non-linear, their complexity grows as much increases the number of substances present in the reacting media an can be characterized by a set of phenomenological constants which contains all the relevant information about the physical system. The determination of these kinetic constants is critical for the design or control of chemical systems from a technological point of view but the non-linear nature of the equations implies that there are hidden correlations between the parameters which maybe can be revealed with a identifiability analysis.

En este trabajo se presenta un modelo epidemiológico en el que los individuos están en las categorías de susceptibles, infectados y recuperados, con todos los parámetros no negativos. Por las características del modelo este es no lineal. Tras linealizar el modelo se obtiene un sistema lineal discreto. El comportamiento del modelo se analiza a partir del número reproductivo básico del sistema obtenido, determinando así cuando la epidemia constituye sólo un brote y cuando no. Con el fin de determinar una posible política de vacunación y estudiar cómo afectaría esta política al comportamiento de la epidemia, se ha modificado el modelo añadiendo la categoría de vacunados. Por esta vía, se ha obtenido el número reproductivo básico del sistema cuando la vacunación está presente y con los dos números reproductivos básicos se ha obtenido el número de vacunas necesarias para este caso de epidemiología.

Este proyecto surge ante la necesidad de unos miembros del departamento de matemática aplicada a la hora de elaborar una página Web interactiva necesaria para promocionar y gestionar el congreso POSTA. ¿Positive Systems: Theory and Applications¿, es un congreso que trata sobre el estudio de los sistemas positivos desde el punto de vista matemático. El objetivo principal de este proyecto es la creación de una página Web que cumpla 3 requisitos: - El primero es informar a cualquier asistente del congreso del contenido de las charlas, la forma de llegar al lugar donde se celebra el congreso, las fechas, las personas invitadas y cuanta información de carácter general que sea necesaria. - El segundo es permitir que los interesados en asistir a las charlas puedan realizar una pre-registración de forma sencilla y rápida. - Y, por ultimo, crear una zona privada para que los autores que quieran mostrar sus resultados en las charlas puedan enviar los documentos y para que los correctores puedan corregir los mismos y aceptarlos o rechazarlos. Esta zona es la más complicada de elaborar, ya que, al ser una corrección anónima, esta zona debe ser privada.

Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells.

Este trabajo es un tutorial introductorio al preprocesamiento de imágenes en MATLAB, es decir, operaciones para preparar la imagen, y para ello utilizaremos técnicas como mejora (binarización, eliminación de ruido) y restauración (en la que se pretende obtener la imagen sin deformación alguna).

The final publication is available at Springer via http://dx.doi.org/10.1007/s10910-011-9941-1, A dynamic gas-liquid transfer model without chemical reaction based on unsteady film theory is considered. In this case, the mathematical model presented for gas-liquid mass-transfer processes is based on mass balances of the transferred substance in both phases. The identificability property of this model is studied in order to confirm the possible identifiable parameters of the model from a given set of experimental data. For that, a different modeled of the system is given. A procedure for the identification is proposed. On the other hand, the aim of this work is to solve the quadratic optimal control problem, using an explicit representation of the model. The problem includes some results on controllability, observability and stability criteria and the relation between these properties and the parameters of the model. Using the optimal control problem we study the stability of the system and show how the choice of the weighting matrices can improve the behavior of the system but with an increase of the energy control cost. © 2011 Springer Science+Business Media, LLC.

This paper presents the use of an iteration method to solve the identifiability problem for a class of discretized linear partial differential algebraic equations. This technique consists in replacing the partial derivatives in the PDAE by differences and analyzing the difference algebraic equations obtained. For that, the theory of discrete singular systems, which involves Drazin inverse matrix, is used. This technique can also be applied to other differential equations in mathematical physics. © 2011 Begoa Cant et al.

[EN] This paper presents T-wave alternans (TWA) detection, applying the Wavelet Transform (WT) to electrocardiographic (ECG) synthetic signals. The TWA is generated with or without the sinusoidal addition of the wave with the required electrical level from 0.01 to 1 mV. The TWA is measured using the difference between the amplitudes of the augmented T-waves and the normal ones. (C) 2009 Elsevier Ltd. All rights reserved

[EN] Structured singular systems depending on a parametric vector are considered. The identification of the parameters is analyzed in terms of the input-output behavior of the system. The role of the reachability and observability properties in this analysis is studied and a characterization of the structural identifiability property is given. Finally, the structural identifiability of a positive reachable system is studied.

Ejecución paso a paso, y mediante un ejemplo, del algoritmo de Dijkstra utilizando el paquete matemático Matlab.

Los sistemas con retardo aparecen frecuentemente en cualquier tipo de proceso que involucre transmisión de datos a largas distancias y en procesos químicos, biológicos, eléctricos, etc. El modelo matemático que permite analizar este tipo de procesos corresponde a un sistema dinámico de control. En este trabajo se estudia el caso en que los coeficientes del sistema varían de forma periódica y se analiza la influencia del retardo cuando este afecta al estado del sistema. Para ello, se obtiene la solución del sistema y se construyen las matrices de alcanzabilidad del mismo. Estas matrices se utilizan para caracterizar la propiedad de alcanzabilidad de un sistema generalizado N-periódico en tiempo discreto cuando se considera un retardo en el estado.