Matrices y sistemas de ecuaciones lineales

En este libro, en su primera parte, es estudia e identifica la estructura de una ecuación lineal, y su gráfica en dos y tres variables. En la segunda parte del contenido se expone la teoría del álgebra matricial, que posteriormente será utilizada en la tercera parte para resolver sistemas de ecuaciones lineales; en este sentido, el lector podrá darse cuenta de las bondades de los métodos que se desarrollarán y las aplicaciones que se pueden plantear y resolver con los métodos gaussianos desarrollados en el álgebra lineal. Igualmente, se presentará el uso del MATLAB para la solución de sistemas de ecuaciones lineales y operaciones con matrices, empleando el computador.

Vapor–liquid equilibrium of binary mixtures containing isopropyl acetate and alkanols at 101.32 kPa

Isobaric vapor-liquid equilibria of binary mixtures of isopropyl acetate plus an alkanol (1-propanol, 2-propanol, 1-butanol, or 2-butanol) were measured at 101.32 kPa, using a dynamic recirculating still. An azeotropic behavior was observed only in the mixtures of isopropyl acetate + 2-propanol and isopropyl acetate + 1-propanol. The application of four thermodynamic consistency tests (the Herington test, the Van Ness test, the infinite dilution test, and the pure component test) showed the high quality of the experimental data. Finally, both NRTL and UNIQUAC activity coefficient models were successfully applied in the correlation of the measured data, with the average absolute deviations in vapor phase composition and temperature of 0.01 and 0.16 K, respectively.

Grupos de lie de matrices reales o complejos

Como la historia lo viene diciendo, en general los resultados importantes y trascendentales en Matemática son los capaces de vincular dos estructuras, en su esencia, totalmente distintas. En el año 1973, el matemático Noruego Marius Sophus Lie (1849-1925) estudiando propiedades de soluciones de sistemas de ecuaciones diferenciales, dio origen a las ideas que conformaron la hoy denominada Teoría de Lie, la cual plantea la relación entre geometría, álgebra y la topología, este matemático creó en gran parte la teoría de la simetría continua, y la aplicó al estudio de la geometría y las ecuaciones diferenciales. Con aportes posteriores de los matemáticos Weyl, Cartan, Chevalley, Killing, Harish Chandra y otros estructuran la teoría de Lie, se presentan en este trabajo de investigación las nociones básicas que subyacen en dicha teoría. En los primeros trabajos de Sophus Lie, la idea subyacente era construir una teoría de grupos continuos, que complementara la ya existente teoría de grupos.

Matrices y sistemas de ecuaciones lineales

En este libro, en su primera parte, es estudia e identifica la estructura de una ecuación lineal, y su gráfica en dos y tres variables. En la segunda parte del contenido se expone la teoría del álgebra matricial, que posteriormente será utilizada en la tercera parte para resolver sistemas de ecuaciones lineales; en este sentido, el lector podrá darse cuenta de las bondades de los métodos que se desarrollarán y las aplicaciones que se pueden plantear y resolver con los métodos gaussianos desarrollados en el álgebra lineal. Igualmente, se presentará el uso del MATLAB para la solución de sistemas de ecuaciones lineales y operaciones con matrices, empleando el computador. En la segunda parte del contenido se expone la teoría del álgebra matricial, que posteriormente será utilizada en la tercera parte para resolver sistemas de ecuaciones lineales; en este sentido, el lector podrá darse cuenta de las bondades de los métodos que se desarrollarán y las aplicaciones que se pueden plantear y resolver con los métodos gaussianos desarrollados en el álgebra lineal. Igualmente, se presentará el uso del MATLAB para la solución de sistemas de ecuaciones lineales y operaciones con matrices, empleando el computador.

Testing the link specification in binary choice models. A semiparametric approach.

Doutoramento em Matemática.

MULTI-WAVELENGTH SPECKLE REDUCTION FOR LASER PICO-PROJECTORS USING DIFFRACTIVE OPTICS

Personal electronic devices, such as cell phones and tablets, continue to decrease in size while the number of features and add-ons keep increasing. One particular feature of great interest is an integrated projector system. Laser pico-projectors have been considered, but the technology has not been developed enough to warrant integration. With new advancements in diode technology and MEMS devices, laser-based projection is currently being advanced for pico-projectors. A primary problem encountered when using a pico-projector is coherent interference known as speckle. Laser speckle can lead to eye irritation and headaches after prolonged viewing. Diffractive optical elements known as diffusers have been examined as a means to lower speckle contrast. Diffusers are often rotated to achieve temporal averaging of the spatial phase pattern provided by diffuser surface. While diffusers are unable to completely eliminate speckle, they can be utilized to decrease the resultant contrast to provide a more visually acceptable image. This dissertation measures the reduction in speckle contrast achievable through the use of diffractive diffusers. A theoretical Fourier optics model is used to provide the diffuser’s stationary and in-motion performance in terms of the resultant contrast level. Contrast measurements of two diffractive diffusers are calculated theoretically and compared with experimental results. In addition, a novel binary diffuser design based on Hadamard matrices will be presented. Using two static in-line Hadamard diffusers eliminates the need for rotation or vibration of the diffuser for temporal averaging. Two Hadamard diffusers were fabricated and contrast values were subsequently measured, showing good agreement with theory and simulated values. Monochromatic speckle contrast values of 0.40 were achieved using the Hadamard diffusers. Finally, color laser projection devices require the use of red, green, and blue laser sources; therefore, using a monochromatic diffractive diffuser may not optimal for color speckle contrast reduction. A simulation of the Hadamard diffusers is conducted to determine the optimum spacing between the two diffusers for polychromatic speckle reduction. Experimental measured results are presented using the optimal spacing of Hadamard diffusers for RGB color speckle reduction, showing 60% reduction in contrast.

Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.

IMPROVED SAMPLE INTRODUCTION SYSTEMS FOR INDUCTIVELY COUPLED PLASMA OPTICAL EMISSION SPECTROMETRY AND THEIR APPLICATION TO THE ANALYSIS OF SIMPLE AND COMPLEX MATRICES

The objective of this thesis is to explore new and improved methods for greater sample introduction efficiency and enhanced analytical performance with inductively coupled plasma optical emission spectrometry (ICP-OES). Three projects are discussed in which the capabilities and applications of ICP-OES are expanded: 1. In the first project, a conventional ultrasonic nebuliser was modified to replace the heater/condenser with an infrared heated pre-evaporation tube. In continuation from previous works with pre-evaporation, the current work investigated the effects of heating with infrared block and rope heaters on two different ICP-OES instruments. Comparisons were made between several methods and setups in which temperatures were varied. By monitoring changes to sensitivity, detection limit, precision, and robustness, and analyzing two certified reference materials, a method with improved sample introduction efficiency and comparable analytical performance to a previous method was established. 2. The second project involved improvements to a previous work in which a multimode sample introduction system (MSIS) was modified by inserting a pre-evaporation tube between the MSIS and torch. The new work focused on applying an infrared heated ceramic rope for pre-evaporation. This research was conducted in all three MSIS modes (nebulisation mode, hydride generation mode, and dual mode) and on two different ICP-OES instruments, and comparisons were made between conventional setups in terms of sensitivity, detection limit, precision, and robustness. By tracking both hydride-forming and non-hydride forming elements, the effects of heating in combination with hydride generation were probed. Finally, optimal methods were validated by analysis of two certified reference materials. 3. A final project was completed in collaboration with ZincNyx Energy Solutions. This project sought to develop a method for the overall analysis of a 12 M KOH zincate fuel, which is used in green energy backup systems. By employing various techniques including flow injection analysis and standard additions, a final procedure was formulated for the verification of K concentration, as well as the measurement of additives (Al, Fe, Mg, In, Si), corrosion products (such C from CO₃²¯), and Zn particles both in and filtered from solution. Furthermore, the effects of exposing the potassium zincate electrolyte fuel to air were assessed.

Vers une compréhension mécanistique de la biocatalyse des composés pharmaceutiques dans des matrices complexes par traitement fongique (Trametes hirsuta)

La présence des contaminants organiques dans l’environnement est une problématique aux enjeux aussi bien scientifiques que politiques. Le caractère diffus et continu (différentes et multiples sources) de cette contamination ne permet pas à ces molécules biologiquement actives d’être soumises à une législation. Ces molécules, pouvant être très récalcitrantes, ne sont pas systématiquement éliminées par les systèmes de traitement des eaux conventionnels. Actuellement, de nouveaux procédés biotechnologiques basés sur des enzymes extracellulaires (e.g. Laccase) ou des champignons lignivores permettent l’élimination des composés les plus récalcitrants. Notre compréhension des mécanismes impliqués dans cette élimination reste incomplète. En effet, la biosorption et l’activité des enzymes extracellulaire sont les mécanismes les plus souvent mis en avant pour expliquer l’efficacité des procédés d’élimination fongique, mais ne sont pas capables d’expliquer les performances obtenues pour certains composés pharmaceutiques. Ces lacunes dans nos connaissances sur les mécanismes responsables de l’élimination fongique des contaminants organiques sont un frein à la pleine exploitation de ces procédés de traitement. De plus, il est forcé d’admettre qu’un grand nombre de travaux portant sur l’élimination fongique de contaminants organiques ont été réalisés dans des conditions de hautes concentrations, qui peuvent être peu représentatives des matrices environnementales. Ainsi, les effets observés à plus forte concentration peuvent etre le résultat dû au stress de l’organisme au contact des contaminants (toxicités). Cette thèse adresse deux questions ; ainsi quelle est l’influence des concentrations traces sur de tels procédés ? Et comment expliquer l’élimination de certains contaminants organiques lors des traitements fongiques ? Afin d’apporter des éléments de réponse sur les mécanismes mis en jeux lors de l’élimination fongique, les travaux présentés ici ont été réalisés sur un modèle de champignon lignivore connu pour ses propriétés en bioremediation. Dans un premier temps, un développement analytique permettant la quantification d’une sélection de contaminants organiques à l’état de traces a été réalisé. Cette méthode a permis d’effectuer des analyses de ces molécules à partir d’un seul échantillon environnemental de faible biomasse et à partir d’une seule injection instrumentale. Les résultats de cette thèse démontrent que l’élimination fongique de contaminants organiques résulte de mécanismes plus complexes que précédemment décrits. Notamment, la dégradation est fortement dépendante d’une étape initiale d’internalisation du contaminant par l’organisme ciblé et de la dégradation intracellulaire. Les mécanismes impliqués peuvent ainsi donnés lieux à des réactions de conjugaison intracellulaire des molecules (glucuronide, glutathione). Les résultats démontrent également que ces procédés d’élimination fongique sont efficaces sur une large gamme de concentration en contaminants organiques. Cependant, les faibles concentrations modifient les propriétés physico-chimiques et biologiques de l’organisme testé (i.e. un changement de la morphologie et du profil de la production enzymatique). La réponse biologique n’étant pas directement proportionnelle a l’exposition en contaminant. Cette étude a permis d’accroitre notre compréhension des mécanismes impliqués dans la dégradation fongique de contaminants organiques. Ceci ouvre la voie à de nouvelles études portant sur les interactions entre processus intra — et extracellulaires. Cette thèse contribue également à l’amélioration des connaissances en offrant des outils de compréhension nécessaire à l’optimisation et au développement du potentiel de ces procédés biotechnologiques (ciblage et role des enzymes réeellement impliquées dans les réactions de biocatalyse).

Optimisation de l’extraction de lumière de scintillation dans les matrices de détecteurs pixellisés pour des applications en tomographie d’émission par positrons (TEP) et en tomodensitométrie (TDM)

Résumé : Les performances de détecteurs à scintillation, composés d’un cristal scintillateur couplé à un photodétecteur, dépendent de façon critique de l’efficacité de la collecte et de l’extraction des photons de scintillation du cristal vers le capteur. Dans les systèmes d’imagerie hautement pixellisés (e.g. TEP, TDM), les scintillateurs doivent être arrangés en matrices compactes avec des facteurs de forme défavorables pour le transport des photons, au détriment des performances du détecteur. Le but du projet est d’optimiser les performances de ces détecteurs pixels par l'identification des sources de pertes de lumière liées aux caractéristiques spectrales, spatiales et angulaires des photons de scintillation incidents sur les faces des scintillateurs. De telles informations acquises par simulation Monte Carlo permettent une pondération adéquate pour l'évaluation de gains atteignables par des méthodes de structuration du scintillateur visant à une extraction de lumière améliorée vers le photodétecteur. Un plan factoriel a permis d'évaluer la magnitude de paramètres affectant la collecte de lumière, notamment l'absorption des matériaux adhésifs assurant l'intégrité matricielle des cristaux ainsi que la performance optique de réflecteurs, tous deux ayant un impact considérable sur le rendement lumineux. D'ailleurs, un réflecteur abondamment utilisé en raison de ses performances optiques exceptionnelles a été caractérisé dans des conditions davantage réalistes par rapport à une immersion dans l'air, où sa réflectivité est toujours rapportée. Une importante perte de réflectivité lorsqu'il est inséré au sein de matrices de scintillateurs a été mise en évidence par simulations puis confirmée expérimentalement. Ceci explique donc les hauts taux de diaphonie observés en plus d'ouvrir la voie à des méthodes d'assemblage en matrices limitant ou tirant profit, selon les applications, de cette transparence insoupçonnée.

Demography of a deep-sea lantern shark (Etmopterus spinax) caught in trawl fisheries of the northeastern Atlantic: Application of Leslie matrices with incorporated uncertainties

The deep-sea lantern shark Etmopterus spinax occurs in the northeast Atlantic on or near the bottoms of the outer continental shelves and slopes, and is regularly captured as bycatch in deep-water commercial fisheries. Given the lack of knowledge on the impacts of fisheries on this species, a demographic analysis using age-based Leslie matrices was carried out. Given the uncertainties in the mortality estimates and in the available life history parameters, several different scenarios, some incorporating stochasticity in the life history parameters (using Monte Carlo simulation), were analyzed. If only natural mortality were considered, even after introducing uncertainties in all parameters, the estimated population growth rate (A) suggested an increasing population. However, if fishing mortality from trawl fisheries is considered, the estimates of A either indicated increasing or declining populations. In these latter cases, the uncertainties in the species reproductive cycle seemed to be particularly relevant, as a 2-year reproductive cycle indicated a stable population, while a longer (3-year cycle) indicated a declining population. The estimated matrix elasticities were in general higher for the survivorship parameters of the younger age classes and tended to decrease for the older ages. This highlights the susceptibility of this deep-sea squaloid to increasing fishing mortality, emphasizing that even though this is a small-sized species, it shows population dynamics patterns more typical of the larger-sized and in general more vulnerable species. (C) 2014 Elsevier Ltd. All rights reserved.

Transition matrices characterizing a certain totally discontinuous map of the interval

We study a totally discontinuous interval map defined in [0,1] which is associated to a deformation of the shift map on two symbols 0−1. We define a sequence of transition matrices which characterizes the effect of the interval map on a family of partitions of the interval [0,1]. Recursive algorithms that build the sequence of matrices and their left and right eigenvectors are deduced. Moreover, we compute the Artin zeta function for the interval map.

Hierarchically organized chitin-based matrices

Chitin is the second most abundant biopolymer on Earth and the most diffused across the known species, being present in more than 70 % of them. It is present in a huge variety of different structures and morphologies being a massive pool of information for new material science approach. This thesis aims to study chitin at different level of organization using diverse approaches. Three main topics are discussed in this manuscript. The first is the use of a bottom-up approach to study chitin nanofibrils self-assembly in water triggering the assembly by pH increment. Successively, the assembly was studied in presence of another pH responsive biomacromolecule, the collagen, to get new composite materials and study how the assembly and the chitin/collagen ratio influence fibroblast’s viability. The second topic focuses on biogenic organized chitin-based matrices, in both Ariolimax californicus and Loligo vulgaris. This study aims to understand the features that give raise to the properties of those matrices. Finally, in the last section a top-up approach was used to exploit natural hierarchically organized chitinous matrices to obtain organized functional materials introducing a catechol on the free amino group of deacetylated chitin (DA 77 %). In conclusion, this study of chitin at different level of organization emphasized different novelties depending on the organization level studied. Moreover, this thesis gives many possibilities for future bioinspired routes to get highly organized materials, or for highly organized functional materials based on natural chitin-based matrices.

Extraction of antioxidants from corn by-products for applications in bio-based polymer matrices

The objective of this dissertation is the evaluation of the exploitability of corn cobs as natural additives for bio-based polymer matrices, in order to hone their properties while keeping the fundamental quality of being fully bio-derived. The first part of the project has the purpose of finding the best solvent and conditions to extract antioxidants and anti-degrading molecules from corn cobs, exploiting room and high-temperature processes, traditional and advanced extraction methods, as well as polar and nonpolar solvents. The extracts in their entirety are then analysed to evaluate their antioxidant content, in order to select the conditions able to maximise their anti-degrading properties. The second part of the project, instead, focuses on assessing chemical and physical properties of the best-behaving extract when inserted in a polymeric matrix. To achieve this, low-density polyethylene (LDPE) and poly (butylene succinate – co – adipate) (PBSA) are employed. These samples are obtained through extrusion and are subsequently characterised exploiting the DSC equipment and a sinusoidally oscillating rheometer. In addition, extruded polymeric matrices are subjected to thermal and photo ageing, in order to identify their behaviour after different forms of degradation and to assess their performances with respect to synthetically produced anti-degrading additives.

Assessing the fit of unidimensional IRT models for binary data under model misspecification

Model misspecification affects the classical test statistics used to assess the fit of the Item Response Theory (IRT) models. Robust tests have been derived under model misspecification, as the Generalized Lagrange Multiplier and Hausman tests, but their use has not been largely explored in the IRT framework. In the first part of the thesis, we introduce the Generalized Lagrange Multiplier test to detect differential item response functioning in IRT models for binary data under model misspecification. By means of a simulation study and a real data analysis, we compare its performance with the classical Lagrange Multiplier test, computed using the Hessian and the cross-product matrix, and the Generalized Jackknife Score test. The power of these tests is computed empirically and asymptotically. The misspecifications considered are local dependence among items and non-normal distribution of the latent variable. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the performance of the tests deteriorates. None of the tests considered show an overall superior performance than the others. In the second part of the thesis, we extend the Generalized Hausman test to detect non-normality of the latent variable distribution. To build the test, we consider a seminonparametric-IRT model, that assumes a more flexible latent variable distribution. By means of a simulation study and two real applications, we compare the performance of the Generalized Hausman test with the M2 limited information goodness-of-fit test and the Likelihood-Ratio test. Additionally, the information criteria are computed. The Generalized Hausman test has a better performance than the Likelihood-Ratio test in terms of Type I error rates and the M2 test in terms of power. The performance of the Generalized Hausman test and the information criteria deteriorates when the sample size is small and with a few items.