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.

Triangular mesh parameterization with trimmed surfaces

Given a 2manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots, L_m\}\) -- \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1manifold having no intersection with the other \(L_j\) LOOPs -- The parametric surface \(S\) is a statistical fit of the mesh \(M\) -- \(L_0\) is the outermost LOOP bounding \(F\) and \(L_i\) is the LOOP of the ith hole in \(F\) (if any) -- The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc -- Stateofart mesh procedures parameterize a rectangular mesh \(M\) -- To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes \(M\) presenting holes and concavities -- We synthesize a parametric surface \(S \subset {\mathbb {R}}^3\) which approximates a superset of the mesh \(M\) -- Then, we compute a set of LOOPs trimming \(S\), and therefore completing the FACE \(F=\ {S,L_0,\ldots ,L_m\}\) -- Our algorithm gives satisfactory results for \(M\) having low Gaussian curvature (i.e., \(M\) being quasi-developable or developable) -- This assumption is a reasonable one, since \(M\) is the product of manifold segmentation preprocessing -- Our algorithm computes: (1) a manifold learning mapping \(\phi : M \rightarrow U \subset {\mathbb {R}}^2\), (2) an inverse mapping \(S: W \subset {\mathbb {R}}^2 \rightarrow {\mathbb {R}}^3\), with \ (W\) being a rectangular grid containing and surpassing \(U\) -- To compute \(\phi\) we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE) -- For the back mapping (NURBS) \(S\) the crucial step is to find a control polyhedron \(P\), which is an extrapolation of \(M\) -- We calculate \(P\) by extrapolating radial basis functions that interpolate points inside \(\phi (M)\) -- We successfully test our implementation with several datasets presenting concavities, holes, and are extremely nondevelopable -- Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization

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.

La metodología triangular como factor clave para diagnosticar la comunicación organizacional interna.

La Comunicación Interna es una herramienta decisiva para mejorar la dirección y la adaptación a los cambios en el marco de los objetivos estratégicos de las organizaciones. En este sentido, diversos estudios han demostrado la influencia positiva de la comunicación interna sobre la satisfacción laboral y el rendimiento de los empleados (v.g., Chiang, Salazar y Nuñez, 2007; Herencia-Leva, 2003). El Observatorio de Comunicación Interna e Identidad Corporativa (2010) indica que este tipo de comunicación crece en importancia y profesionalidad, especialmente en organizaciones de servicios, tales como, instituciones hospitalarias. En estas organizaciones sus empleados son responsables de toma de decisiones continuas ante la presión de tiempo. Ello implica que, deben tener un amplio conocimiento de su entidad y del entorno que le rodea. En este contexto, la comunicación interna es pieza fundamental para integrar y alienar a las personas con los objetivos de su empresa (Welch, 2003). Sin embargo, son pocos los centros hospitalarios que cuentan con un plan de comunicación adecuado. En este sentido, la Agencia Sanitaria Costa del Sol (ASCS), ante un escenario de crecimiento, considera necesario la elaboración e implantación de un Plan de Comunicación Interna. En base a ello, los objetivos fundamentales de este trabajo han sido (a) realizar un diagnóstico de la situación de comunicación interna de la empresa, y; (b) diseñar un plan de comunicación interna en función de la información obtenida. En concreto, siguiendo a Paul (1996), se ha realizado un proceso de auditoría basado en dos tipos de técnicas metodológicas: la administración del Cuestionario de Auditoría de la Comunicación (Varona, 1991) a 603 empleados/as, como técnica cuantitativa, y la realización de dos grupos focales multidisciplinares, de 15 personas cada uno, como técnica cualitativa. Por un lado, los resultados del cuestionario indican las dimensiones que son principales fortalezas o debilidades de la comunicación interna. Por el otro, del uso de la Técnica de Grupo Nominal se desprenden las principales actuaciones que son necesarias poner en marcha para la mejora de la comunicación interna en ASCS.

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.

Drug of abuse analysis: new methods in herbal and biological matrices for medicinal chemistry and forensic investigation

In this Ph.D. project, original and innovative approaches for the quali-quantitative analysis of abuse substances, as well as therapeutic agents with abuse potential and related compounds were designed, developed and validated for application to different fields such as forensics, clinical and pharmaceutical. All the parameters involved in the developed analytical workflows were properly and accurately optimised, from sample collection to sample pretreatment up to the instrumental analysis. Advanced dried blood microsampling technologies have been developed, able of bringing several advantages to the method as a whole, such as significant reduction of solvent use, feasible storage and transportation conditions and enhancement of analyte stability. At the same time, the use of capillary blood allows to increase subject compliance and overall method applicability by exploiting such innovative technologies. Both biological and non-biological samples involved in this project were subjected to optimised pretreatment techniques developed ad-hoc for each target analyte, making also use of advanced microextraction techniques. Finally, original and advanced instrumental analytical methods have been developed based on high and ultra-high performance liquid chromatography (HPLC,UHPLC) coupled to different detection means (mainly mass spectrometry, but also electrochemical, and spectrophotometric detection for screening purpose), and on attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) for solid-state analysis. Each method has been designed to obtain highly selective, sensitive yet sustainable systems and has been validated according to international guidelines. All the methods developed herein proved to be suitable for the analysis of the compounds under investigation and may be useful tools in medicinal chemistry, pharmaceutical analysis, within clinical studies and forensic investigations.

[the Sociology Of Health In Brazil - The Creation Of An Identity].

This article analyzes the historical, social and cognitive dimensions of the sociology of medicine in the construction of its identity, from Wolf Lepenies' perspective. It is understood that the construction of an identity does not end with the first historical manifestations, but is consolidated when it is institutionalized and structured as a field of knowledge by creating its own forms of cognitive expression. The text is divided into three parts: in the first the precursors are presented, highlighting the role played by some travelers, naturalists and folklore scholars, followed by social physicians-scientists and the first social scientists (1940-1969). In the second part, aspects of the consolidation of the social sciences in health are presented at two significant moments, namely the 1970s and 1980s. In the third part, the issues raised by the field are addressed in general terms. It is considered that once the main structural stages are in place there is still a need for the formation of new generations of social scientists in health. It is also essential to disseminate scientific production and to ensure that the relations are studied in depth and institutionalized with the sociological matrices on the one hand and with the field of health on the other.

Bile And Liver Metallothionein Behavior In Copper-exposed Fish.

The present study analyzed metallothionein (MT) excretion from liver to bile in Nile Tilapia (Oreochromis niloticus) exposed to sub-lethal copper concentrations (2mgL(-1)) in a laboratory setting. MTs in liver and bile were quantified by spectrophotometry after thermal incubation and MT metal-binding profiles were characterized by size exclusion high performance liquid chromatography coupled to ICP-MS (SEC-HPLC-ICP-MS). Results show that liver MT is present in approximately 250-fold higher concentrations than bile MT in non-exposed fish. Differences between the MT profiles from the control and exposed group were observed for both matrices, indicating differential metal-binding behavior when comparing liver and bile MT. This is novel data regarding intra-organ MT comparisons, since differences between organs are usually present only with regard to quantification, not metal-binding behavior. Bile MT showed statistically significant differences between the control and exposed group, while the same did not occur with liver MT. This indicates that MTs synthesized in the liver accumulate more slowly than MTs excreted from liver to bile, since the same fish presented significantly higher MT levels in liver when compared to bile. We postulate that bile, although excreted in the intestine and partially reabsorbed by the same returning to the liver, may also release MT-bound metals more rapidly and efficiently, which may indicate an efficient detoxification route. Thus, we propose that the analysis of bile MTs to observe recent metal exposure may be more adequate than the analysis of liver MTs, since organism responses to metals are more quickly observed in bile, although further studies are necessary.